LMFDB - Embedded newform 8670.2.a.cc.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8670,2,Mod(1,8670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8670, 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("8670.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8670.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:	$69.2302985525$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.46609344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 15x^{4} + 72x^{2} - 111 $ x^6 - 15x^4 + 72x^2 - 111
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.86223$ of defining polynomial
Character	$\chi$	$=$	8670.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.49985 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.49985 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +2.98492 q^{11} -1.00000 q^{12} +0.0262790 q^{13} +3.49985 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} -2.12918 q^{19} +1.00000 q^{20} +3.49985 q^{21} -2.98492 q^{22} +7.10370 q^{23} +1.00000 q^{24} +1.00000 q^{25} -0.0262790 q^{26} -1.00000 q^{27} -3.49985 q^{28} +6.04755 q^{29} +1.00000 q^{30} -5.81284 q^{31} -1.00000 q^{32} -2.98492 q^{33} -3.49985 q^{35} +1.00000 q^{36} -10.3717 q^{37} +2.12918 q^{38} -0.0262790 q^{39} -1.00000 q^{40} -3.18796 q^{41} -3.49985 q^{42} -3.81646 q^{43} +2.98492 q^{44} +1.00000 q^{45} -7.10370 q^{46} +1.22351 q^{47} -1.00000 q^{48} +5.24897 q^{49} -1.00000 q^{50} +0.0262790 q^{52} -10.5633 q^{53} +1.00000 q^{54} +2.98492 q^{55} +3.49985 q^{56} +2.12918 q^{57} -6.04755 q^{58} +0.962526 q^{59} -1.00000 q^{60} -4.71454 q^{61} +5.81284 q^{62} -3.49985 q^{63} +1.00000 q^{64} +0.0262790 q^{65} +2.98492 q^{66} +9.85335 q^{67} -7.10370 q^{69} +3.49985 q^{70} -2.43703 q^{71} -1.00000 q^{72} +2.58271 q^{73} +10.3717 q^{74} -1.00000 q^{75} -2.12918 q^{76} -10.4468 q^{77} +0.0262790 q^{78} +3.86593 q^{79} +1.00000 q^{80} +1.00000 q^{81} +3.18796 q^{82} +14.3415 q^{83} +3.49985 q^{84} +3.81646 q^{86} -6.04755 q^{87} -2.98492 q^{88} +14.3190 q^{89} -1.00000 q^{90} -0.0919727 q^{91} +7.10370 q^{92} +5.81284 q^{93} -1.22351 q^{94} -2.12918 q^{95} +1.00000 q^{96} -10.3932 q^{97} -5.24897 q^{98} +2.98492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} + 6 q^{11} - 6 q^{12} + 6 q^{13} - 6 q^{15} + 6 q^{16} - 6 q^{18} + 6 q^{19} + 6 q^{20} - 6 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{25} - 6 q^{26} - 6 q^{27} - 6 q^{29} + 6 q^{30} - 12 q^{31} - 6 q^{32} - 6 q^{33} + 6 q^{36} - 12 q^{37} - 6 q^{38} - 6 q^{39} - 6 q^{40} - 12 q^{41} + 6 q^{44} + 6 q^{45} + 12 q^{46} - 6 q^{47} - 6 q^{48} + 6 q^{49} - 6 q^{50} + 6 q^{52} - 30 q^{53} + 6 q^{54} + 6 q^{55} - 6 q^{57} + 6 q^{58} + 6 q^{59} - 6 q^{60} - 6 q^{61} + 12 q^{62} + 6 q^{64} + 6 q^{65} + 6 q^{66} - 24 q^{67} + 12 q^{69} - 6 q^{71} - 6 q^{72} - 36 q^{73} + 12 q^{74} - 6 q^{75} + 6 q^{76} - 54 q^{77} + 6 q^{78} - 12 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} + 12 q^{83} + 6 q^{87} - 6 q^{88} - 18 q^{89} - 6 q^{90} + 24 q^{91} - 12 q^{92} + 12 q^{93} + 6 q^{94} + 6 q^{95} + 6 q^{96} - 30 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 + 6 * q^11 - 6 * q^12 + 6 * q^13 - 6 * q^15 + 6 * q^16 - 6 * q^18 + 6 * q^19 + 6 * q^20 - 6 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^25 - 6 * q^26 - 6 * q^27 - 6 * q^29 + 6 * q^30 - 12 * q^31 - 6 * q^32 - 6 * q^33 + 6 * q^36 - 12 * q^37 - 6 * q^38 - 6 * q^39 - 6 * q^40 - 12 * q^41 + 6 * q^44 + 6 * q^45 + 12 * q^46 - 6 * q^47 - 6 * q^48 + 6 * q^49 - 6 * q^50 + 6 * q^52 - 30 * q^53 + 6 * q^54 + 6 * q^55 - 6 * q^57 + 6 * q^58 + 6 * q^59 - 6 * q^60 - 6 * q^61 + 12 * q^62 + 6 * q^64 + 6 * q^65 + 6 * q^66 - 24 * q^67 + 12 * q^69 - 6 * q^71 - 6 * q^72 - 36 * q^73 + 12 * q^74 - 6 * q^75 + 6 * q^76 - 54 * q^77 + 6 * q^78 - 12 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 + 12 * q^83 + 6 * q^87 - 6 * q^88 - 18 * q^89 - 6 * q^90 + 24 * q^91 - 12 * q^92 + 12 * q^93 + 6 * q^94 + 6 * q^95 + 6 * q^96 - 30 * q^97 - 6 * q^98 + 6 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−3.49985	−1.32282	−0.661410	−	0.750025i	$-0.730042\pi$
$7$	−3.49985	−1.32282	−0.661410	+	0.750025i	$0.730042\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	2.98492	0.899986	0.449993	−	0.893032i	$-0.351426\pi$
$11$	2.98492	0.899986	0.449993	+	0.893032i	$0.351426\pi$
$12$	−1.00000	−0.288675
$13$	0.0262790	0.00728849	0.00364424	−	0.999993i	$-0.498840\pi$
$13$	0.0262790	0.00728849	0.00364424	+	0.999993i	$0.498840\pi$
$14$	3.49985	0.935375
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	−1.00000	−0.235702
$19$	−2.12918	−0.488467	−0.244233	−	0.969717i	$-0.578536\pi$
$19$	−2.12918	−0.488467	−0.244233	+	0.969717i	$0.578536\pi$
$20$	1.00000	0.223607
$21$	3.49985	0.763731
$22$	−2.98492	−0.636386
$23$	7.10370	1.48122	0.740612	−	0.671933i	$-0.234536\pi$
$23$	7.10370	1.48122	0.740612	+	0.671933i	$0.234536\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−0.0262790	−0.00515374
$27$	−1.00000	−0.192450
$28$	−3.49985	−0.661410
$29$	6.04755	1.12300	0.561501	−	0.827476i	$-0.310224\pi$
$29$	6.04755	1.12300	0.561501	+	0.827476i	$0.310224\pi$
$30$	1.00000	0.182574
$31$	−5.81284	−1.04402	−0.522009	−	0.852940i	$-0.674817\pi$
$31$	−5.81284	−1.04402	−0.522009	+	0.852940i	$0.674817\pi$
$32$	−1.00000	−0.176777
$33$	−2.98492	−0.519607
$34$	0	0
$35$	−3.49985	−0.591583
$36$	1.00000	0.166667
$37$	−10.3717	−1.70510	−0.852552	−	0.522643i	$-0.824946\pi$
$37$	−10.3717	−1.70510	−0.852552	+	0.522643i	$0.824946\pi$
$38$	2.12918	0.345398
$39$	−0.0262790	−0.00420801
$40$	−1.00000	−0.158114
$41$	−3.18796	−0.497876	−0.248938	−	0.968519i	$-0.580082\pi$
$41$	−3.18796	−0.497876	−0.248938	+	0.968519i	$0.580082\pi$
$42$	−3.49985	−0.540039
$43$	−3.81646	−0.582004	−0.291002	−	0.956722i	$-0.593989\pi$
$43$	−3.81646	−0.582004	−0.291002	+	0.956722i	$0.593989\pi$
$44$	2.98492	0.449993
$45$	1.00000	0.149071
$46$	−7.10370	−1.04738
$47$	1.22351	0.178468	0.0892338	−	0.996011i	$-0.471558\pi$
$47$	1.22351	0.178468	0.0892338	+	0.996011i	$0.471558\pi$
$48$	−1.00000	−0.144338
$49$	5.24897	0.749853
$50$	−1.00000	−0.141421
$51$	0	0
$52$	0.0262790	0.00364424
$53$	−10.5633	−1.45098	−0.725492	−	0.688231i	$-0.758388\pi$
$53$	−10.5633	−1.45098	−0.725492	+	0.688231i	$0.758388\pi$
$54$	1.00000	0.136083
$55$	2.98492	0.402486
$56$	3.49985	0.467688
$57$	2.12918	0.282016
$58$	−6.04755	−0.794082
$59$	0.962526	0.125310	0.0626551	−	0.998035i	$-0.480043\pi$
$59$	0.962526	0.125310	0.0626551	+	0.998035i	$0.480043\pi$
$60$	−1.00000	−0.129099
$61$	−4.71454	−0.603634	−0.301817	−	0.953366i	$-0.597593\pi$
$61$	−4.71454	−0.603634	−0.301817	+	0.953366i	$0.597593\pi$
$62$	5.81284	0.738232
$63$	−3.49985	−0.440940
$64$	1.00000	0.125000
$65$	0.0262790	0.00325951
$66$	2.98492	0.367418
$67$	9.85335	1.20378	0.601889	−	0.798580i	$-0.294415\pi$
$67$	9.85335	1.20378	0.601889	+	0.798580i	$0.294415\pi$
$68$	0	0
$69$	−7.10370	−0.855185
$70$	3.49985	0.418312
$71$	−2.43703	−0.289222	−0.144611	−	0.989489i	$-0.546193\pi$
$71$	−2.43703	−0.289222	−0.144611	+	0.989489i	$0.546193\pi$
$72$	−1.00000	−0.117851
$73$	2.58271	0.302283	0.151142	−	0.988512i	$-0.451705\pi$
$73$	2.58271	0.302283	0.151142	+	0.988512i	$0.451705\pi$
$74$	10.3717	1.20569
$75$	−1.00000	−0.115470
$76$	−2.12918	−0.244233
$77$	−10.4468	−1.19052
$78$	0.0262790	0.00297551
$79$	3.86593	0.434951	0.217475	−	0.976066i	$-0.430218\pi$
$79$	3.86593	0.434951	0.217475	+	0.976066i	$0.430218\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	3.18796	0.352052
$83$	14.3415	1.57418	0.787091	−	0.616837i	$-0.211586\pi$
$83$	14.3415	1.57418	0.787091	+	0.616837i	$0.211586\pi$
$84$	3.49985	0.381865
$85$	0	0
$86$	3.81646	0.411539
$87$	−6.04755	−0.648366
$88$	−2.98492	−0.318193
$89$	14.3190	1.51781	0.758906	−	0.651200i	$-0.225734\pi$
$89$	14.3190	1.51781	0.758906	+	0.651200i	$0.225734\pi$
$90$	−1.00000	−0.105409
$91$	−0.0919727	−0.00964136
$92$	7.10370	0.740612
$93$	5.81284	0.602764
$94$	−1.22351	−0.126196
$95$	−2.12918	−0.218449
$96$	1.00000	0.102062
$97$	−10.3932	−1.05527	−0.527636	−	0.849470i	$-0.676922\pi$
$97$	−10.3932	−1.05527	−0.527636	+	0.849470i	$0.676922\pi$
$98$	−5.24897	−0.530226
$99$	2.98492	0.299995
$100$	1.00000	0.100000
$101$	7.44701	0.741005	0.370503	−	0.928831i	$-0.379185\pi$
$101$	7.44701	0.741005	0.370503	+	0.928831i	$0.379185\pi$
$102$	0	0
$103$	−4.14190	−0.408113	−0.204057	−	0.978959i	$-0.565413\pi$
$103$	−4.14190	−0.408113	−0.204057	+	0.978959i	$0.565413\pi$
$104$	−0.0262790	−0.00257687
$105$	3.49985	0.341551
$106$	10.5633	1.02600
$107$	−10.5545	−1.02034	−0.510169	−	0.860074i	$-0.670417\pi$
$107$	−10.5545	−1.02034	−0.510169	+	0.860074i	$0.670417\pi$
$108$	−1.00000	−0.0962250
$109$	2.59698	0.248745	0.124373	−	0.992236i	$-0.460308\pi$
$109$	2.59698	0.248745	0.124373	+	0.992236i	$0.460308\pi$
$110$	−2.98492	−0.284601
$111$	10.3717	0.984442
$112$	−3.49985	−0.330705
$113$	−18.1039	−1.70307	−0.851534	−	0.524299i	$-0.824327\pi$
$113$	−18.1039	−1.70307	−0.851534	+	0.524299i	$0.824327\pi$
$114$	−2.12918	−0.199416
$115$	7.10370	0.662424
$116$	6.04755	0.561501
$117$	0.0262790	0.00242950
$118$	−0.962526	−0.0886077
$119$	0	0
$120$	1.00000	0.0912871
$121$	−2.09027	−0.190025
$122$	4.71454	0.426834
$123$	3.18796	0.287449
$124$	−5.81284	−0.522009
$125$	1.00000	0.0894427
$126$	3.49985	0.311792
$127$	0.227688	0.0202041	0.0101020	−	0.999949i	$-0.496784\pi$
$127$	0.227688	0.0202041	0.0101020	+	0.999949i	$0.496784\pi$
$128$	−1.00000	−0.0883883
$129$	3.81646	0.336020
$130$	−0.0262790	−0.00230482
$131$	−3.88226	−0.339194	−0.169597	−	0.985513i	$-0.554247\pi$
$131$	−3.88226	−0.339194	−0.169597	+	0.985513i	$0.554247\pi$
$132$	−2.98492	−0.259804
$133$	7.45180	0.646153
$134$	−9.85335	−0.851200
$135$	−1.00000	−0.0860663
$136$	0	0
$137$	20.2362	1.72889	0.864447	−	0.502724i	$-0.167669\pi$
$137$	20.2362	1.72889	0.864447	+	0.502724i	$0.167669\pi$
$138$	7.10370	0.604707
$139$	18.4296	1.56318	0.781588	−	0.623796i	$-0.214410\pi$
$139$	18.4296	1.56318	0.781588	+	0.623796i	$0.214410\pi$
$140$	−3.49985	−0.295792
$141$	−1.22351	−0.103038
$142$	2.43703	0.204511
$143$	0.0784407	0.00655954
$144$	1.00000	0.0833333
$145$	6.04755	0.502222
$146$	−2.58271	−0.213746
$147$	−5.24897	−0.432928
$148$	−10.3717	−0.852552
$149$	4.77106	0.390860	0.195430	−	0.980718i	$-0.437390\pi$
$149$	4.77106	0.390860	0.195430	+	0.980718i	$0.437390\pi$
$150$	1.00000	0.0816497
$151$	14.8624	1.20948	0.604742	−	0.796422i	$-0.293276\pi$
$151$	14.8624	1.20948	0.604742	+	0.796422i	$0.293276\pi$
$152$	2.12918	0.172699
$153$	0	0
$154$	10.4468	0.841825
$155$	−5.81284	−0.466899
$156$	−0.0262790	−0.00210401
$157$	11.7346	0.936520	0.468260	−	0.883591i	$-0.344881\pi$
$157$	11.7346	0.936520	0.468260	+	0.883591i	$0.344881\pi$
$158$	−3.86593	−0.307557
$159$	10.5633	0.837726
$160$	−1.00000	−0.0790569
$161$	−24.8619	−1.95939
$162$	−1.00000	−0.0785674
$163$	−14.1073	−1.10497	−0.552484	−	0.833523i	$-0.686320\pi$
$163$	−14.1073	−1.10497	−0.552484	+	0.833523i	$0.686320\pi$
$164$	−3.18796	−0.248938
$165$	−2.98492	−0.232375
$166$	−14.3415	−1.11311
$167$	6.62100	0.512349	0.256174	−	0.966631i	$-0.417538\pi$
$167$	6.62100	0.512349	0.256174	+	0.966631i	$0.417538\pi$
$168$	−3.49985	−0.270020
$169$	−12.9993	−0.999947
$170$	0	0
$171$	−2.12918	−0.162822
$172$	−3.81646	−0.291002
$173$	−12.2633	−0.932362	−0.466181	−	0.884689i	$-0.654370\pi$
$173$	−12.2633	−0.932362	−0.466181	+	0.884689i	$0.654370\pi$
$174$	6.04755	0.458464
$175$	−3.49985	−0.264564
$176$	2.98492	0.224997
$177$	−0.962526	−0.0723478
$178$	−14.3190	−1.07325
$179$	−14.8175	−1.10751	−0.553756	−	0.832679i	$-0.686806\pi$
$179$	−14.8175	−1.10751	−0.553756	+	0.832679i	$0.686806\pi$
$180$	1.00000	0.0745356
$181$	−0.805545	−0.0598757	−0.0299379	−	0.999552i	$-0.509531\pi$
$181$	−0.805545	−0.0598757	−0.0299379	+	0.999552i	$0.509531\pi$
$182$	0.0919727	0.00681747
$183$	4.71454	0.348509
$184$	−7.10370	−0.523692
$185$	−10.3717	−0.762545
$186$	−5.81284	−0.426218
$187$	0	0
$188$	1.22351	0.0892338
$189$	3.49985	0.254577
$190$	2.12918	0.154467
$191$	8.68313	0.628289	0.314144	−	0.949375i	$-0.398282\pi$
$191$	8.68313	0.628289	0.314144	+	0.949375i	$0.398282\pi$
$192$	−1.00000	−0.0721688
$193$	−23.8310	−1.71539	−0.857695	−	0.514159i	$-0.828104\pi$
$193$	−23.8310	−1.71539	−0.857695	+	0.514159i	$0.828104\pi$
$194$	10.3932	0.746190
$195$	−0.0262790	−0.00188188
$196$	5.24897	0.374926
$197$	−17.1647	−1.22294	−0.611468	−	0.791269i	$-0.709421\pi$
$197$	−17.1647	−1.22294	−0.611468	+	0.791269i	$0.709421\pi$
$198$	−2.98492	−0.212129
$199$	−3.55025	−0.251670	−0.125835	−	0.992051i	$-0.540161\pi$
$199$	−3.55025	−0.251670	−0.125835	+	0.992051i	$0.540161\pi$
$200$	−1.00000	−0.0707107
$201$	−9.85335	−0.695002
$202$	−7.44701	−0.523970
$203$	−21.1655	−1.48553
$204$	0	0
$205$	−3.18796	−0.222657
$206$	4.14190	0.288580
$207$	7.10370	0.493742
$208$	0.0262790	0.00182212
$209$	−6.35541	−0.439613
$210$	−3.49985	−0.241513
$211$	22.2956	1.53489	0.767447	−	0.641112i	$-0.221527\pi$
$211$	22.2956	1.53489	0.767447	+	0.641112i	$0.221527\pi$
$212$	−10.5633	−0.725492
$213$	2.43703	0.166983
$214$	10.5545	0.721488
$215$	−3.81646	−0.260280
$216$	1.00000	0.0680414
$217$	20.3441	1.38105
$218$	−2.59698	−0.175890
$219$	−2.58271	−0.174523
$220$	2.98492	0.201243
$221$	0	0
$222$	−10.3717	−0.696106
$223$	−16.1189	−1.07940	−0.539702	−	0.841856i	$-0.681463\pi$
$223$	−16.1189	−1.07940	−0.539702	+	0.841856i	$0.681463\pi$
$224$	3.49985	0.233844
$225$	1.00000	0.0666667
$226$	18.1039	1.20425
$227$	17.0694	1.13293	0.566467	−	0.824084i	$-0.308310\pi$
$227$	17.0694	1.13293	0.566467	+	0.824084i	$0.308310\pi$
$228$	2.12918	0.141008
$229$	16.1177	1.06509	0.532544	−	0.846403i	$-0.321236\pi$
$229$	16.1177	1.06509	0.532544	+	0.846403i	$0.321236\pi$
$230$	−7.10370	−0.468404
$231$	10.4468	0.687347
$232$	−6.04755	−0.397041
$233$	3.20217	0.209781	0.104891	−	0.994484i	$-0.466551\pi$
$233$	3.20217	0.209781	0.104891	+	0.994484i	$0.466551\pi$
$234$	−0.0262790	−0.00171791
$235$	1.22351	0.0798131
$236$	0.962526	0.0626551
$237$	−3.86593	−0.251119
$238$	0	0
$239$	21.3018	1.37790	0.688948	−	0.724811i	$-0.258073\pi$
$239$	21.3018	1.37790	0.688948	+	0.724811i	$0.258073\pi$
$240$	−1.00000	−0.0645497
$241$	−24.7808	−1.59627	−0.798135	−	0.602479i	$-0.794180\pi$
$241$	−24.7808	−1.59627	−0.798135	+	0.602479i	$0.794180\pi$
$242$	2.09027	0.134368
$243$	−1.00000	−0.0641500
$244$	−4.71454	−0.301817
$245$	5.24897	0.335344
$246$	−3.18796	−0.203257
$247$	−0.0559527	−0.00356018
$248$	5.81284	0.369116
$249$	−14.3415	−0.908854
$250$	−1.00000	−0.0632456
$251$	8.94755	0.564764	0.282382	−	0.959302i	$-0.408875\pi$
$251$	8.94755	0.564764	0.282382	+	0.959302i	$0.408875\pi$
$252$	−3.49985	−0.220470
$253$	21.2040	1.33308
$254$	−0.227688	−0.0142864
$255$	0	0
$256$	1.00000	0.0625000
$257$	−24.2371	−1.51187	−0.755935	−	0.654647i	$-0.772817\pi$
$257$	−24.2371	−1.51187	−0.755935	+	0.654647i	$0.772817\pi$
$258$	−3.81646	−0.237602
$259$	36.2996	2.25554
$260$	0.0262790	0.00162976
$261$	6.04755	0.374334
$262$	3.88226	0.239847
$263$	−28.9513	−1.78521	−0.892605	−	0.450839i	$-0.851125\pi$
$263$	−28.9513	−1.78521	−0.892605	+	0.450839i	$0.851125\pi$
$264$	2.98492	0.183709
$265$	−10.5633	−0.648899
$266$	−7.45180	−0.456899
$267$	−14.3190	−0.876309
$268$	9.85335	0.601889
$269$	−10.5960	−0.646049	−0.323025	−	0.946391i	$-0.604700\pi$
$269$	−10.5960	−0.646049	−0.323025	+	0.946391i	$0.604700\pi$
$270$	1.00000	0.0608581
$271$	7.90265	0.480052	0.240026	−	0.970766i	$-0.422844\pi$
$271$	7.90265	0.480052	0.240026	+	0.970766i	$0.422844\pi$
$272$	0	0
$273$	0.0919727	0.00556644
$274$	−20.2362	−1.22251
$275$	2.98492	0.179997
$276$	−7.10370	−0.427593
$277$	29.2597	1.75805	0.879023	−	0.476779i	$-0.158196\pi$
$277$	29.2597	1.75805	0.879023	+	0.476779i	$0.158196\pi$
$278$	−18.4296	−1.10533
$279$	−5.81284	−0.348006
$280$	3.49985	0.209156
$281$	−22.7679	−1.35822	−0.679110	−	0.734037i	$-0.737634\pi$
$281$	−22.7679	−1.35822	−0.679110	+	0.734037i	$0.737634\pi$
$282$	1.22351	0.0728591
$283$	−20.6884	−1.22979	−0.614897	−	0.788607i	$-0.710803\pi$
$283$	−20.6884	−1.22979	−0.614897	+	0.788607i	$0.710803\pi$
$284$	−2.43703	−0.144611
$285$	2.12918	0.126122
$286$	−0.0784407	−0.00463829
$287$	11.1574	0.658600
$288$	−1.00000	−0.0589256
$289$	0	0
$290$	−6.04755	−0.355124
$291$	10.3932	0.609262
$292$	2.58271	0.151142
$293$	−22.7680	−1.33012	−0.665061	−	0.746789i	$-0.731594\pi$
$293$	−22.7680	−1.33012	−0.665061	+	0.746789i	$0.731594\pi$
$294$	5.24897	0.306126
$295$	0.962526	0.0560404
$296$	10.3717	0.602845
$297$	−2.98492	−0.173202
$298$	−4.77106	−0.276380
$299$	0.186678	0.0107959
$300$	−1.00000	−0.0577350
$301$	13.3570	0.769887
$302$	−14.8624	−0.855234
$303$	−7.44701	−0.427820
$304$	−2.12918	−0.122117
$305$	−4.71454	−0.269954
$306$	0	0
$307$	−22.7883	−1.30060	−0.650299	−	0.759678i	$-0.725356\pi$
$307$	−22.7883	−1.30060	−0.650299	+	0.759678i	$0.725356\pi$
$308$	−10.4468	−0.595260
$309$	4.14190	0.235624
$310$	5.81284	0.330147
$311$	−10.5582	−0.598703	−0.299352	−	0.954143i	$-0.596770\pi$
$311$	−10.5582	−0.598703	−0.299352	+	0.954143i	$0.596770\pi$
$312$	0.0262790	0.00148776
$313$	29.9703	1.69402	0.847011	−	0.531575i	$-0.178400\pi$
$313$	29.9703	1.69402	0.847011	+	0.531575i	$0.178400\pi$
$314$	−11.7346	−0.662220
$315$	−3.49985	−0.197194
$316$	3.86593	0.217475
$317$	−6.36364	−0.357417	−0.178709	−	0.983902i	$-0.557192\pi$
$317$	−6.36364	−0.357417	−0.178709	+	0.983902i	$0.557192\pi$
$318$	−10.5633	−0.592361
$319$	18.0514	1.01069
$320$	1.00000	0.0559017
$321$	10.5545	0.589093
$322$	24.8619	1.38550
$323$	0	0
$324$	1.00000	0.0555556
$325$	0.0262790	0.00145770
$326$	14.1073	0.781331
$327$	−2.59698	−0.143613
$328$	3.18796	0.176026
$329$	−4.28211	−0.236080
$330$	2.98492	0.164314
$331$	−4.71648	−0.259241	−0.129620	−	0.991564i	$-0.541376\pi$
$331$	−4.71648	−0.259241	−0.129620	+	0.991564i	$0.541376\pi$
$332$	14.3415	0.787091
$333$	−10.3717	−0.568368
$334$	−6.62100	−0.362285
$335$	9.85335	0.538346
$336$	3.49985	0.190933
$337$	−29.7010	−1.61792	−0.808959	−	0.587864i	$-0.799969\pi$
$337$	−29.7010	−1.61792	−0.808959	+	0.587864i	$0.799969\pi$
$338$	12.9993	0.707069
$339$	18.1039	0.983267
$340$	0	0
$341$	−17.3509	−0.939601
$342$	2.12918	0.115133
$343$	6.12835	0.330900
$344$	3.81646	0.205769
$345$	−7.10370	−0.382451
$346$	12.2633	0.659280
$347$	−12.2852	−0.659502	−0.329751	−	0.944068i	$-0.606965\pi$
$347$	−12.2852	−0.659502	−0.329751	+	0.944068i	$0.606965\pi$
$348$	−6.04755	−0.324183
$349$	−22.9564	−1.22883	−0.614414	−	0.788984i	$-0.710607\pi$
$349$	−22.9564	−1.22883	−0.614414	+	0.788984i	$0.710607\pi$
$350$	3.49985	0.187075
$351$	−0.0262790	−0.00140267
$352$	−2.98492	−0.159097
$353$	4.72809	0.251651	0.125825	−	0.992052i	$-0.459842\pi$
$353$	4.72809	0.251651	0.125825	+	0.992052i	$0.459842\pi$
$354$	0.962526	0.0511577
$355$	−2.43703	−0.129344
$356$	14.3190	0.758906
$357$	0	0
$358$	14.8175	0.783130
$359$	21.3875	1.12879	0.564396	−	0.825504i	$-0.309109\pi$
$359$	21.3875	1.12879	0.564396	+	0.825504i	$0.309109\pi$
$360$	−1.00000	−0.0527046
$361$	−14.4666	−0.761400
$362$	0.805545	0.0423385
$363$	2.09027	0.109711
$364$	−0.0919727	−0.00482068
$365$	2.58271	0.135185
$366$	−4.71454	−0.246433
$367$	6.71121	0.350322	0.175161	−	0.984540i	$-0.443955\pi$
$367$	6.71121	0.350322	0.175161	+	0.984540i	$0.443955\pi$
$368$	7.10370	0.370306
$369$	−3.18796	−0.165959
$370$	10.3717	0.539201
$371$	36.9701	1.91939
$372$	5.81284	0.301382
$373$	−2.38081	−0.123274	−0.0616368	−	0.998099i	$-0.519632\pi$
$373$	−2.38081	−0.123274	−0.0616368	+	0.998099i	$0.519632\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−1.22351	−0.0630978
$377$	0.158924	0.00818499
$378$	−3.49985	−0.180013
$379$	−29.4511	−1.51280	−0.756400	−	0.654110i	$-0.773043\pi$
$379$	−29.4511	−1.51280	−0.756400	+	0.654110i	$0.773043\pi$
$380$	−2.12918	−0.109224
$381$	−0.227688	−0.0116648
$382$	−8.68313	−0.444267
$383$	30.0636	1.53618	0.768090	−	0.640342i	$-0.221207\pi$
$383$	30.0636	1.53618	0.768090	+	0.640342i	$0.221207\pi$
$384$	1.00000	0.0510310
$385$	−10.4468	−0.532417
$386$	23.8310	1.21296
$387$	−3.81646	−0.194001
$388$	−10.3932	−0.527636
$389$	−9.47529	−0.480416	−0.240208	−	0.970721i	$-0.577216\pi$
$389$	−9.47529	−0.480416	−0.240208	+	0.970721i	$0.577216\pi$
$390$	0.0262790	0.00133069
$391$	0	0
$392$	−5.24897	−0.265113
$393$	3.88226	0.195834
$394$	17.1647	0.864746
$395$	3.86593	0.194516
$396$	2.98492	0.149998
$397$	17.0124	0.853829	0.426915	−	0.904292i	$-0.359600\pi$
$397$	17.0124	0.853829	0.426915	+	0.904292i	$0.359600\pi$
$398$	3.55025	0.177958
$399$	−7.45180	−0.373057
$400$	1.00000	0.0500000
$401$	−32.4644	−1.62119	−0.810597	−	0.585604i	$-0.800857\pi$
$401$	−32.4644	−1.62119	−0.810597	+	0.585604i	$0.800857\pi$
$402$	9.85335	0.491440
$403$	−0.152756	−0.00760931
$404$	7.44701	0.370503
$405$	1.00000	0.0496904
$406$	21.1655	1.05043
$407$	−30.9588	−1.53457
$408$	0	0
$409$	−27.3298	−1.35137	−0.675685	−	0.737191i	$-0.736152\pi$
$409$	−27.3298	−1.35137	−0.675685	+	0.737191i	$0.736152\pi$
$410$	3.18796	0.157442
$411$	−20.2362	−0.998177
$412$	−4.14190	−0.204057
$413$	−3.36870	−0.165763
$414$	−7.10370	−0.349128
$415$	14.3415	0.703995
$416$	−0.0262790	−0.00128843
$417$	−18.4296	−0.902500
$418$	6.35541	0.310853
$419$	−3.19382	−0.156028	−0.0780141	−	0.996952i	$-0.524858\pi$
$419$	−3.19382	−0.156028	−0.0780141	+	0.996952i	$0.524858\pi$
$420$	3.49985	0.170775
$421$	12.8644	0.626974	0.313487	−	0.949592i	$-0.398503\pi$
$421$	12.8644	0.626974	0.313487	+	0.949592i	$0.398503\pi$
$422$	−22.2956	−1.08533
$423$	1.22351	0.0594892
$424$	10.5633	0.513000
$425$	0	0
$426$	−2.43703	−0.118075
$427$	16.5002	0.798500
$428$	−10.5545	−0.510169
$429$	−0.0784407	−0.00378715
$430$	3.81646	0.184046
$431$	0.943136	0.0454292	0.0227146	−	0.999742i	$-0.492769\pi$
$431$	0.943136	0.0454292	0.0227146	+	0.999742i	$0.492769\pi$
$432$	−1.00000	−0.0481125
$433$	31.3296	1.50560	0.752802	−	0.658247i	$-0.228702\pi$
$433$	31.3296	1.50560	0.752802	+	0.658247i	$0.228702\pi$
$434$	−20.3441	−0.976548
$435$	−6.04755	−0.289958
$436$	2.59698	0.124373
$437$	−15.1250	−0.723529
$438$	2.58271	0.123407
$439$	−10.4823	−0.500294	−0.250147	−	0.968208i	$-0.580479\pi$
$439$	−10.4823	−0.500294	−0.250147	+	0.968208i	$0.580479\pi$
$440$	−2.98492	−0.142300
$441$	5.24897	0.249951
$442$	0	0
$443$	3.08005	0.146337	0.0731687	−	0.997320i	$-0.476689\pi$
$443$	3.08005	0.146337	0.0731687	+	0.997320i	$0.476689\pi$
$444$	10.3717	0.492221
$445$	14.3190	0.678786
$446$	16.1189	0.763254
$447$	−4.77106	−0.225663
$448$	−3.49985	−0.165353
$449$	22.1974	1.04756	0.523780	−	0.851853i	$-0.324521\pi$
$449$	22.1974	1.04756	0.523780	+	0.851853i	$0.324521\pi$
$450$	−1.00000	−0.0471405
$451$	−9.51580	−0.448082
$452$	−18.1039	−0.851534
$453$	−14.8624	−0.698296
$454$	−17.0694	−0.801106
$455$	−0.0919727	−0.00431175
$456$	−2.12918	−0.0997078
$457$	−6.93302	−0.324313	−0.162156	−	0.986765i	$-0.551845\pi$
$457$	−6.93302	−0.324313	−0.162156	+	0.986765i	$0.551845\pi$
$458$	−16.1177	−0.753130
$459$	0	0
$460$	7.10370	0.331212
$461$	14.5574	0.678004	0.339002	−	0.940786i	$-0.389911\pi$
$461$	14.5574	0.678004	0.339002	+	0.940786i	$0.389911\pi$
$462$	−10.4468	−0.486028
$463$	3.98460	0.185180	0.0925901	−	0.995704i	$-0.470485\pi$
$463$	3.98460	0.185180	0.0925901	+	0.995704i	$0.470485\pi$
$464$	6.04755	0.280751
$465$	5.81284	0.269564
$466$	−3.20217	−0.148338
$467$	2.33193	0.107909	0.0539545	−	0.998543i	$-0.482817\pi$
$467$	2.33193	0.107909	0.0539545	+	0.998543i	$0.482817\pi$
$468$	0.0262790	0.00121475
$469$	−34.4853	−1.59238
$470$	−1.22351	−0.0564364
$471$	−11.7346	−0.540700
$472$	−0.962526	−0.0443038
$473$	−11.3918	−0.523796
$474$	3.86593	0.177568
$475$	−2.12918	−0.0976933
$476$	0	0
$477$	−10.5633	−0.483661
$478$	−21.3018	−0.974319
$479$	−17.0691	−0.779906	−0.389953	−	0.920835i	$-0.627509\pi$
$479$	−17.0691	−0.779906	−0.389953	+	0.920835i	$0.627509\pi$
$480$	1.00000	0.0456435
$481$	−0.272559	−0.0124276
$482$	24.7808	1.12873
$483$	24.8619	1.13126
$484$	−2.09027	−0.0950125
$485$	−10.3932	−0.471932
$486$	1.00000	0.0453609
$487$	−25.7596	−1.16728	−0.583640	−	0.812013i	$-0.698372\pi$
$487$	−25.7596	−1.16728	−0.583640	+	0.812013i	$0.698372\pi$
$488$	4.71454	0.213417
$489$	14.1073	0.637954
$490$	−5.24897	−0.237124
$491$	−5.36894	−0.242297	−0.121148	−	0.992634i	$-0.538658\pi$
$491$	−5.36894	−0.242297	−0.121148	+	0.992634i	$0.538658\pi$
$492$	3.18796	0.143724
$493$	0	0
$494$	0.0559527	0.00251743
$495$	2.98492	0.134162
$496$	−5.81284	−0.261004
$497$	8.52925	0.382589
$498$	14.3415	0.642657
$499$	3.68209	0.164833	0.0824166	−	0.996598i	$-0.473736\pi$
$499$	3.68209	0.164833	0.0824166	+	0.996598i	$0.473736\pi$
$500$	1.00000	0.0447214
$501$	−6.62100	−0.295805
$502$	−8.94755	−0.399348
$503$	−20.0575	−0.894320	−0.447160	−	0.894454i	$-0.647564\pi$
$503$	−20.0575	−0.894320	−0.447160	+	0.894454i	$0.647564\pi$
$504$	3.49985	0.155896
$505$	7.44701	0.331388
$506$	−21.2040	−0.942631
$507$	12.9993	0.577320
$508$	0.227688	0.0101020
$509$	−29.7942	−1.32061	−0.660303	−	0.750999i	$-0.729572\pi$
$509$	−29.7942	−1.32061	−0.660303	+	0.750999i	$0.729572\pi$
$510$	0	0
$511$	−9.03910	−0.399866
$512$	−1.00000	−0.0441942
$513$	2.12918	0.0940054
$514$	24.2371	1.06905
$515$	−4.14190	−0.182514
$516$	3.81646	0.168010
$517$	3.65208	0.160618
$518$	−36.2996	−1.59491
$519$	12.2633	0.538300
$520$	−0.0262790	−0.00115241
$521$	9.78878	0.428854	0.214427	−	0.976740i	$-0.431212\pi$
$521$	9.78878	0.428854	0.214427	+	0.976740i	$0.431212\pi$
$522$	−6.04755	−0.264694
$523$	−44.2906	−1.93669	−0.968347	−	0.249607i	$-0.919699\pi$
$523$	−44.2906	−1.93669	−0.968347	+	0.249607i	$0.919699\pi$
$524$	−3.88226	−0.169597
$525$	3.49985	0.152746
$526$	28.9513	1.26233
$527$	0	0
$528$	−2.98492	−0.129902
$529$	27.4626	1.19403
$530$	10.5633	0.458841
$531$	0.962526	0.0417701
$532$	7.45180	0.323077
$533$	−0.0837765	−0.00362876
$534$	14.3190	0.619644
$535$	−10.5545	−0.456309
$536$	−9.85335	−0.425600
$537$	14.8175	0.639423
$538$	10.5960	0.456826
$539$	15.6677	0.674857
$540$	−1.00000	−0.0430331
$541$	−6.62477	−0.284821	−0.142411	−	0.989808i	$-0.545485\pi$
$541$	−6.62477	−0.284821	−0.142411	+	0.989808i	$0.545485\pi$
$542$	−7.90265	−0.339448
$543$	0.805545	0.0345693
$544$	0	0
$545$	2.59698	0.111242
$546$	−0.0919727	−0.00393607
$547$	−38.3016	−1.63766	−0.818830	−	0.574036i	$-0.805377\pi$
$547$	−38.3016	−1.63766	−0.818830	+	0.574036i	$0.805377\pi$
$548$	20.2362	0.864447
$549$	−4.71454	−0.201211
$550$	−2.98492	−0.127277
$551$	−12.8763	−0.548549
$552$	7.10370	0.302354
$553$	−13.5302	−0.575362
$554$	−29.2597	−1.24313
$555$	10.3717	0.440256
$556$	18.4296	0.781588
$557$	−17.9277	−0.759619	−0.379810	−	0.925065i	$-0.624010\pi$
$557$	−17.9277	−0.759619	−0.379810	+	0.925065i	$0.624010\pi$
$558$	5.81284	0.246077
$559$	−0.100293	−0.00424193
$560$	−3.49985	−0.147896
$561$	0	0
$562$	22.7679	0.960407
$563$	−9.65201	−0.406784	−0.203392	−	0.979097i	$-0.565197\pi$
$563$	−9.65201	−0.406784	−0.203392	+	0.979097i	$0.565197\pi$
$564$	−1.22351	−0.0515191
$565$	−18.1039	−0.761635
$566$	20.6884	0.869596
$567$	−3.49985	−0.146980
$568$	2.43703	0.102256
$569$	4.67227	0.195872	0.0979359	−	0.995193i	$-0.468776\pi$
$569$	4.67227	0.195872	0.0979359	+	0.995193i	$0.468776\pi$
$570$	−2.12918	−0.0891814
$571$	−7.94290	−0.332400	−0.166200	−	0.986092i	$-0.553150\pi$
$571$	−7.94290	−0.332400	−0.166200	+	0.986092i	$0.553150\pi$
$572$	0.0784407	0.00327977
$573$	−8.68313	−0.362743
$574$	−11.1574	−0.465701
$575$	7.10370	0.296245
$576$	1.00000	0.0416667
$577$	4.80335	0.199966	0.0999830	−	0.994989i	$-0.468121\pi$
$577$	4.80335	0.199966	0.0999830	+	0.994989i	$0.468121\pi$
$578$	0	0
$579$	23.8310	0.990381
$580$	6.04755	0.251111
$581$	−50.1931	−2.08236
$582$	−10.3932	−0.430813
$583$	−31.5306	−1.30586
$584$	−2.58271	−0.106873
$585$	0.0262790	0.00108650
$586$	22.7680	0.940538
$587$	−14.9372	−0.616524	−0.308262	−	0.951301i	$-0.599747\pi$
$587$	−14.9372	−0.616524	−0.308262	+	0.951301i	$0.599747\pi$
$588$	−5.24897	−0.216464
$589$	12.3766	0.509968
$590$	−0.962526	−0.0396265
$591$	17.1647	0.706062
$592$	−10.3717	−0.426276
$593$	−4.24673	−0.174392	−0.0871961	−	0.996191i	$-0.527791\pi$
$593$	−4.24673	−0.174392	−0.0871961	+	0.996191i	$0.527791\pi$
$594$	2.98492	0.122473
$595$	0	0
$596$	4.77106	0.195430
$597$	3.55025	0.145302
$598$	−0.186678	−0.00763385
$599$	32.8537	1.34236	0.671182	−	0.741292i	$-0.265787\pi$
$599$	32.8537	1.34236	0.671182	+	0.741292i	$0.265787\pi$
$600$	1.00000	0.0408248
$601$	−1.10283	−0.0449852	−0.0224926	−	0.999747i	$-0.507160\pi$
$601$	−1.10283	−0.0449852	−0.0224926	+	0.999747i	$0.507160\pi$
$602$	−13.3570	−0.544392
$603$	9.85335	0.401259
$604$	14.8624	0.604742
$605$	−2.09027	−0.0849817
$606$	7.44701	0.302514
$607$	47.2862	1.91929	0.959643	−	0.281220i	$-0.0907392\pi$
$607$	47.2862	1.91929	0.959643	+	0.281220i	$0.0907392\pi$
$608$	2.12918	0.0863495
$609$	21.1655	0.857671
$610$	4.71454	0.190886
$611$	0.0321527	0.00130076
$612$	0	0
$613$	2.22857	0.0900110	0.0450055	−	0.998987i	$-0.485669\pi$
$613$	2.22857	0.0900110	0.0450055	+	0.998987i	$0.485669\pi$
$614$	22.7883	0.919662
$615$	3.18796	0.128551
$616$	10.4468	0.420912
$617$	−0.256532	−0.0103276	−0.00516379	−	0.999987i	$-0.501644\pi$
$617$	−0.256532	−0.0103276	−0.00516379	+	0.999987i	$0.501644\pi$
$618$	−4.14190	−0.166612
$619$	−12.2077	−0.490669	−0.245334	−	0.969439i	$-0.578898\pi$
$619$	−12.2077	−0.490669	−0.245334	+	0.969439i	$0.578898\pi$
$620$	−5.81284	−0.233449
$621$	−7.10370	−0.285062
$622$	10.5582	0.423347
$623$	−50.1144	−2.00779
$624$	−0.0262790	−0.00105200
$625$	1.00000	0.0400000
$626$	−29.9703	−1.19785
$627$	6.35541	0.253811
$628$	11.7346	0.468260
$629$	0	0
$630$	3.49985	0.139437
$631$	24.2993	0.967338	0.483669	−	0.875251i	$-0.339304\pi$
$631$	24.2993	0.967338	0.483669	+	0.875251i	$0.339304\pi$
$632$	−3.86593	−0.153778
$633$	−22.2956	−0.886172
$634$	6.36364	0.252732
$635$	0.227688	0.00903553
$636$	10.5633	0.418863
$637$	0.137938	0.00546529
$638$	−18.0514	−0.714663
$639$	−2.43703	−0.0964075
$640$	−1.00000	−0.0395285
$641$	−6.76408	−0.267165	−0.133582	−	0.991038i	$-0.542648\pi$
$641$	−6.76408	−0.267165	−0.133582	+	0.991038i	$0.542648\pi$
$642$	−10.5545	−0.416551
$643$	−44.1671	−1.74178	−0.870890	−	0.491478i	$-0.836457\pi$
$643$	−44.1671	−1.74178	−0.870890	+	0.491478i	$0.836457\pi$
$644$	−24.8619	−0.979697
$645$	3.81646	0.150273
$646$	0	0
$647$	−43.6709	−1.71688	−0.858441	−	0.512912i	$-0.828567\pi$
$647$	−43.6709	−1.71688	−0.858441	+	0.512912i	$0.828567\pi$
$648$	−1.00000	−0.0392837
$649$	2.87306	0.112777
$650$	−0.0262790	−0.00103075
$651$	−20.3441	−0.797348
$652$	−14.1073	−0.552484
$653$	−39.0720	−1.52901	−0.764503	−	0.644621i	$-0.777015\pi$
$653$	−39.0720	−1.52901	−0.764503	+	0.644621i	$0.777015\pi$
$654$	2.59698	0.101550
$655$	−3.88226	−0.151692
$656$	−3.18796	−0.124469
$657$	2.58271	0.100761
$658$	4.28211	0.166934
$659$	−12.1230	−0.472245	−0.236122	−	0.971723i	$-0.575877\pi$
$659$	−12.1230	−0.472245	−0.236122	+	0.971723i	$0.575877\pi$
$660$	−2.98492	−0.116188
$661$	26.7969	1.04228	0.521140	−	0.853471i	$-0.325507\pi$
$661$	26.7969	1.04228	0.521140	+	0.853471i	$0.325507\pi$
$662$	4.71648	0.183311
$663$	0	0
$664$	−14.3415	−0.556557
$665$	7.45180	0.288969
$666$	10.3717	0.401897
$667$	42.9600	1.66342
$668$	6.62100	0.256174
$669$	16.1189	0.623194
$670$	−9.85335	−0.380668
$671$	−14.0725	−0.543263
$672$	−3.49985	−0.135010
$673$	41.1989	1.58810	0.794051	−	0.607851i	$-0.207968\pi$
$673$	41.1989	1.58810	0.794051	+	0.607851i	$0.207968\pi$
$674$	29.7010	1.14404
$675$	−1.00000	−0.0384900
$676$	−12.9993	−0.499973
$677$	7.56056	0.290576	0.145288	−	0.989389i	$-0.453589\pi$
$677$	7.56056	0.290576	0.145288	+	0.989389i	$0.453589\pi$
$678$	−18.1039	−0.695275
$679$	36.3748	1.39594
$680$	0	0
$681$	−17.0694	−0.654100
$682$	17.3509	0.664399
$683$	41.2818	1.57960	0.789801	−	0.613363i	$-0.210184\pi$
$683$	41.2818	1.57960	0.789801	+	0.613363i	$0.210184\pi$
$684$	−2.12918	−0.0814111
$685$	20.2362	0.773185
$686$	−6.12835	−0.233981
$687$	−16.1177	−0.614928
$688$	−3.81646	−0.145501
$689$	−0.277594	−0.0105755
$690$	7.10370	0.270433
$691$	30.2751	1.15172	0.575859	−	0.817549i	$-0.304668\pi$
$691$	30.2751	1.15172	0.575859	+	0.817549i	$0.304668\pi$
$692$	−12.2633	−0.466181
$693$	−10.4468	−0.396840
$694$	12.2852	0.466339
$695$	18.4296	0.699073
$696$	6.04755	0.229232
$697$	0	0
$698$	22.9564	0.868912
$699$	−3.20217	−0.121117
$700$	−3.49985	−0.132282
$701$	20.7889	0.785184	0.392592	−	0.919713i	$-0.371578\pi$
$701$	20.7889	0.785184	0.392592	+	0.919713i	$0.371578\pi$
$702$	0.0262790	0.000991838 0
$703$	22.0833	0.832886
$704$	2.98492	0.112498
$705$	−1.22351	−0.0460801
$706$	−4.72809	−0.177944
$707$	−26.0634	−0.980217
$708$	−0.962526	−0.0361739
$709$	−19.3441	−0.726483	−0.363241	−	0.931695i	$-0.618330\pi$
$709$	−19.3441	−0.726483	−0.363241	+	0.931695i	$0.618330\pi$
$710$	2.43703	0.0914602
$711$	3.86593	0.144984
$712$	−14.3190	−0.536627
$713$	−41.2927	−1.54642
$714$	0	0
$715$	0.0784407	0.00293351
$716$	−14.8175	−0.553756
$717$	−21.3018	−0.795529
$718$	−21.3875	−0.798176
$719$	−37.6479	−1.40403	−0.702014	−	0.712163i	$-0.747716\pi$
$719$	−37.6479	−1.40403	−0.702014	+	0.712163i	$0.747716\pi$
$720$	1.00000	0.0372678
$721$	14.4960	0.539860
$722$	14.4666	0.538391
$723$	24.7808	0.921607
$724$	−0.805545	−0.0299379
$725$	6.04755	0.224600
$726$	−2.09027	−0.0775773
$727$	42.1739	1.56414	0.782072	−	0.623188i	$-0.214163\pi$
$727$	42.1739	1.56414	0.782072	+	0.623188i	$0.214163\pi$
$728$	0.0919727	0.00340874
$729$	1.00000	0.0370370
$730$	−2.58271	−0.0955903
$731$	0	0
$732$	4.71454	0.174254
$733$	−25.5635	−0.944210	−0.472105	−	0.881542i	$-0.656506\pi$
$733$	−25.5635	−0.944210	−0.472105	+	0.881542i	$0.656506\pi$
$734$	−6.71121	−0.247715
$735$	−5.24897	−0.193611
$736$	−7.10370	−0.261846
$737$	29.4114	1.08338
$738$	3.18796	0.117351
$739$	48.6010	1.78782	0.893909	−	0.448248i	$-0.147952\pi$
$739$	48.6010	1.78782	0.893909	+	0.448248i	$0.147952\pi$
$740$	−10.3717	−0.381273
$741$	0.0559527	0.00205547
$742$	−36.9701	−1.35721
$743$	14.4130	0.528760	0.264380	−	0.964419i	$-0.414833\pi$
$743$	14.4130	0.528760	0.264380	+	0.964419i	$0.414833\pi$
$744$	−5.81284	−0.213109
$745$	4.77106	0.174798
$746$	2.38081	0.0871676
$747$	14.3415	0.524727
$748$	0	0
$749$	36.9391	1.34972
$750$	1.00000	0.0365148
$751$	−38.8250	−1.41674	−0.708371	−	0.705840i	$-0.750570\pi$
$751$	−38.8250	−1.41674	−0.708371	+	0.705840i	$0.750570\pi$
$752$	1.22351	0.0446169
$753$	−8.94755	−0.326067
$754$	−0.158924	−0.00578766
$755$	14.8624	0.540897
$756$	3.49985	0.127288
$757$	−14.2064	−0.516342	−0.258171	−	0.966099i	$-0.583120\pi$
$757$	−14.2064	−0.516342	−0.258171	+	0.966099i	$0.583120\pi$
$758$	29.4511	1.06971
$759$	−21.2040	−0.769655
$760$	2.12918	0.0772333
$761$	−53.7782	−1.94946	−0.974729	−	0.223389i	$-0.928288\pi$
$761$	−53.7782	−1.94946	−0.974729	+	0.223389i	$0.928288\pi$
$762$	0.227688	0.00824828
$763$	−9.08905	−0.329046
$764$	8.68313	0.314144
$765$	0	0
$766$	−30.0636	−1.08624
$767$	0.0252942	0.000913322 0
$768$	−1.00000	−0.0360844
$769$	−1.56547	−0.0564522	−0.0282261	−	0.999602i	$-0.508986\pi$
$769$	−1.56547	−0.0564522	−0.0282261	+	0.999602i	$0.508986\pi$
$770$	10.4468	0.376475
$771$	24.2371	0.872878
$772$	−23.8310	−0.857695
$773$	−34.5727	−1.24349	−0.621747	−	0.783219i	$-0.713577\pi$
$773$	−34.5727	−1.24349	−0.621747	+	0.783219i	$0.713577\pi$
$774$	3.81646	0.137180
$775$	−5.81284	−0.208804
$776$	10.3932	0.373095
$777$	−36.2996	−1.30224
$778$	9.47529	0.339705
$779$	6.78773	0.243196
$780$	−0.0262790	−0.000940940 0
$781$	−7.27434	−0.260296
$782$	0	0
$783$	−6.04755	−0.216122
$784$	5.24897	0.187463
$785$	11.7346	0.418824
$786$	−3.88226	−0.138476
$787$	−8.96128	−0.319435	−0.159718	−	0.987163i	$-0.551058\pi$
$787$	−8.96128	−0.319435	−0.159718	+	0.987163i	$0.551058\pi$
$788$	−17.1647	−0.611468
$789$	28.9513	1.03069
$790$	−3.86593	−0.137544
$791$	63.3608	2.25285
$792$	−2.98492	−0.106064
$793$	−0.123893	−0.00439958
$794$	−17.0124	−0.603749
$795$	10.5633	0.374642
$796$	−3.55025	−0.125835
$797$	19.3484	0.685355	0.342678	−	0.939453i	$-0.388666\pi$
$797$	19.3484	0.685355	0.342678	+	0.939453i	$0.388666\pi$
$798$	7.45180	0.263791
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	14.3190	0.505937
$802$	32.4644	1.14636
$803$	7.70917	0.272051
$804$	−9.85335	−0.347501
$805$	−24.8619	−0.876267
$806$	0.152756	0.00538060
$807$	10.5960	0.372997
$808$	−7.44701	−0.261985
$809$	−37.2096	−1.30822	−0.654109	−	0.756400i	$-0.726956\pi$
$809$	−37.2096	−1.30822	−0.654109	+	0.756400i	$0.726956\pi$
$810$	−1.00000	−0.0351364
$811$	−17.1330	−0.601620	−0.300810	−	0.953684i	$-0.597257\pi$
$811$	−17.1330	−0.601620	−0.300810	+	0.953684i	$0.597257\pi$
$812$	−21.1655	−0.742765
$813$	−7.90265	−0.277158
$814$	30.9588	1.08510
$815$	−14.1073	−0.494157
$816$	0	0
$817$	8.12591	0.284289
$818$	27.3298	0.955562
$819$	−0.0919727	−0.00321379
$820$	−3.18796	−0.111328
$821$	−38.6227	−1.34794	−0.673971	−	0.738757i	$-0.735413\pi$
$821$	−38.6227	−1.34794	−0.673971	+	0.738757i	$0.735413\pi$
$822$	20.2362	0.705818
$823$	56.4809	1.96880	0.984401	−	0.175941i	$-0.0562968\pi$
$823$	56.4809	1.96880	0.984401	+	0.175941i	$0.0562968\pi$
$824$	4.14190	0.144290
$825$	−2.98492	−0.103921
$826$	3.36870	0.117212
$827$	40.6505	1.41356	0.706778	−	0.707436i	$-0.250148\pi$
$827$	40.6505	1.41356	0.706778	+	0.707436i	$0.250148\pi$
$828$	7.10370	0.246871
$829$	−47.0653	−1.63464	−0.817322	−	0.576181i	$-0.804542\pi$
$829$	−47.0653	−1.63464	−0.817322	+	0.576181i	$0.804542\pi$
$830$	−14.3415	−0.497800
$831$	−29.2597	−1.01501
$832$	0.0262790	0.000911061 0
$833$	0	0
$834$	18.4296	0.638164
$835$	6.62100	0.229129
$836$	−6.35541	−0.219807
$837$	5.81284	0.200921
$838$	3.19382	0.110329
$839$	−39.1788	−1.35260	−0.676302	−	0.736625i	$-0.736418\pi$
$839$	−39.1788	−1.35260	−0.676302	+	0.736625i	$0.736418\pi$
$840$	−3.49985	−0.120756
$841$	7.57288	0.261134
$842$	−12.8644	−0.443338
$843$	22.7679	0.784169
$844$	22.2956	0.767447
$845$	−12.9993	−0.447190
$846$	−1.22351	−0.0420652
$847$	7.31565	0.251369
$848$	−10.5633	−0.362746
$849$	20.6884	0.710022
$850$	0	0
$851$	−73.6778	−2.52564
$852$	2.43703	0.0834913
$853$	−9.46850	−0.324195	−0.162098	−	0.986775i	$-0.551826\pi$
$853$	−9.46850	−0.324195	−0.162098	+	0.986775i	$0.551826\pi$
$854$	−16.5002	−0.564625
$855$	−2.12918	−0.0728163
$856$	10.5545	0.360744
$857$	−37.4169	−1.27814	−0.639068	−	0.769150i	$-0.720680\pi$
$857$	−37.4169	−1.27814	−0.639068	+	0.769150i	$0.720680\pi$
$858$	0.0784407	0.00267792
$859$	−43.8820	−1.49723	−0.748617	−	0.663003i	$-0.769282\pi$
$859$	−43.8820	−1.49723	−0.748617	+	0.663003i	$0.769282\pi$
$860$	−3.81646	−0.130140
$861$	−11.1574	−0.380243
$862$	−0.943136	−0.0321233
$863$	−11.2011	−0.381290	−0.190645	−	0.981659i	$-0.561058\pi$
$863$	−11.2011	−0.381290	−0.190645	+	0.981659i	$0.561058\pi$
$864$	1.00000	0.0340207
$865$	−12.2633	−0.416965
$866$	−31.3296	−1.06462
$867$	0	0
$868$	20.3441	0.690524
$869$	11.5395	0.391450
$870$	6.04755	0.205031
$871$	0.258936	0.00877372
$872$	−2.59698	−0.0879448
$873$	−10.3932	−0.351758
$874$	15.1250	0.511612
$875$	−3.49985	−0.118317
$876$	−2.58271	−0.0872616
$877$	39.5418	1.33523	0.667616	−	0.744506i	$-0.267315\pi$
$877$	39.5418	1.33523	0.667616	+	0.744506i	$0.267315\pi$
$878$	10.4823	0.353761
$879$	22.7680	0.767946
$880$	2.98492	0.100622
$881$	−26.2548	−0.884545	−0.442273	−	0.896881i	$-0.645828\pi$
$881$	−26.2548	−0.884545	−0.442273	+	0.896881i	$0.645828\pi$
$882$	−5.24897	−0.176742
$883$	−10.0607	−0.338569	−0.169285	−	0.985567i	$-0.554146\pi$
$883$	−10.0607	−0.338569	−0.169285	+	0.985567i	$0.554146\pi$
$884$	0	0
$885$	−0.962526	−0.0323549
$886$	−3.08005	−0.103476
$887$	−11.3848	−0.382265	−0.191132	−	0.981564i	$-0.561216\pi$
$887$	−11.3848	−0.382265	−0.191132	+	0.981564i	$0.561216\pi$
$888$	−10.3717	−0.348053
$889$	−0.796876	−0.0267263
$890$	−14.3190	−0.479974
$891$	2.98492	0.0999985
$892$	−16.1189	−0.539702
$893$	−2.60507	−0.0871754
$894$	4.77106	0.159568
$895$	−14.8175	−0.495295
$896$	3.49985	0.116922
$897$	−0.186678	−0.00623301
$898$	−22.1974	−0.740737
$899$	−35.1535	−1.17243
$900$	1.00000	0.0333333
$901$	0	0
$902$	9.51580	0.316842
$903$	−13.3570	−0.444494
$904$	18.1039	0.602125
$905$	−0.805545	−0.0267772
$906$	14.8624	0.493770
$907$	−27.0779	−0.899106	−0.449553	−	0.893254i	$-0.648417\pi$
$907$	−27.0779	−0.899106	−0.449553	+	0.893254i	$0.648417\pi$
$908$	17.0694	0.566467
$909$	7.44701	0.247002
$910$	0.0919727	0.00304887
$911$	4.86381	0.161145	0.0805725	−	0.996749i	$-0.474325\pi$
$911$	4.86381	0.161145	0.0805725	+	0.996749i	$0.474325\pi$
$912$	2.12918	0.0705041
$913$	42.8081	1.41674
$914$	6.93302	0.229324
$915$	4.71454	0.155858
$916$	16.1177	0.532544
$917$	13.5873	0.448693
$918$	0	0
$919$	1.49248	0.0492324	0.0246162	−	0.999697i	$-0.492164\pi$
$919$	1.49248	0.0492324	0.0246162	+	0.999697i	$0.492164\pi$
$920$	−7.10370	−0.234202
$921$	22.7883	0.750901
$922$	−14.5574	−0.479421
$923$	−0.0640428	−0.00210799
$924$	10.4468	0.343673
$925$	−10.3717	−0.341021
$926$	−3.98460	−0.130942
$927$	−4.14190	−0.136038
$928$	−6.04755	−0.198521
$929$	−24.2758	−0.796463	−0.398231	−	0.917285i	$-0.630376\pi$
$929$	−24.2758	−0.796463	−0.398231	+	0.917285i	$0.630376\pi$
$930$	−5.81284	−0.190611
$931$	−11.1760	−0.366278
$932$	3.20217	0.104891
$933$	10.5582	0.345662
$934$	−2.33193	−0.0763032
$935$	0	0
$936$	−0.0262790	−0.000858957 0
$937$	−3.13215	−0.102323	−0.0511615	−	0.998690i	$-0.516292\pi$
$937$	−3.13215	−0.102323	−0.0511615	+	0.998690i	$0.516292\pi$
$938$	34.4853	1.12598
$939$	−29.9703	−0.978044
$940$	1.22351	0.0399066
$941$	−20.5038	−0.668405	−0.334203	−	0.942501i	$-0.608467\pi$
$941$	−20.5038	−0.668405	−0.334203	+	0.942501i	$0.608467\pi$
$942$	11.7346	0.382333
$943$	−22.6463	−0.737466
$944$	0.962526	0.0313275
$945$	3.49985	0.113850
$946$	11.3918	0.370379
$947$	38.2158	1.24185	0.620923	−	0.783872i	$-0.286758\pi$
$947$	38.2158	1.24185	0.620923	+	0.783872i	$0.286758\pi$
$948$	−3.86593	−0.125560
$949$	0.0678710	0.00220319
$950$	2.12918	0.0690796
$951$	6.36364	0.206355
$952$	0	0
$953$	−0.0731284	−0.00236886	−0.00118443	−	0.999999i	$-0.500377\pi$
$953$	−0.0731284	−0.00236886	−0.00118443	+	0.999999i	$0.500377\pi$
$954$	10.5633	0.342000
$955$	8.68313	0.280979
$956$	21.3018	0.688948
$957$	−18.0514	−0.583520
$958$	17.0691	0.551477
$959$	−70.8237	−2.28702
$960$	−1.00000	−0.0322749
$961$	2.78916	0.0899729
$962$	0.272559	0.00878766
$963$	−10.5545	−0.340113
$964$	−24.7808	−0.798135
$965$	−23.8310	−0.767146
$966$	−24.8619	−0.799919
$967$	16.5246	0.531396	0.265698	−	0.964056i	$-0.414398\pi$
$967$	16.5246	0.531396	0.265698	+	0.964056i	$0.414398\pi$
$968$	2.09027	0.0671839
$969$	0	0
$970$	10.3932	0.333707
$971$	13.0769	0.419657	0.209829	−	0.977738i	$-0.432709\pi$
$971$	13.0769	0.419657	0.209829	+	0.977738i	$0.432709\pi$
$972$	−1.00000	−0.0320750
$973$	−64.5008	−2.06780
$974$	25.7596	0.825391
$975$	−0.0262790	−0.000841602 0
$976$	−4.71454	−0.150909
$977$	22.0230	0.704579	0.352289	−	0.935891i	$-0.385403\pi$
$977$	22.0230	0.704579	0.352289	+	0.935891i	$0.385403\pi$
$978$	−14.1073	−0.451102
$979$	42.7410	1.36601
$980$	5.24897	0.167672
$981$	2.59698	0.0829152
$982$	5.36894	0.171330
$983$	−34.2139	−1.09125	−0.545626	−	0.838029i	$-0.683708\pi$
$983$	−34.2139	−1.09125	−0.545626	+	0.838029i	$0.683708\pi$
$984$	−3.18796	−0.101629
$985$	−17.1647	−0.546913
$986$	0	0
$987$	4.28211	0.136301
$988$	−0.0559527	−0.00178009
$989$	−27.1110	−0.862079
$990$	−2.98492	−0.0948669
$991$	−25.0798	−0.796687	−0.398343	−	0.917236i	$-0.630415\pi$
$991$	−25.0798	−0.796687	−0.398343	+	0.917236i	$0.630415\pi$
$992$	5.81284	0.184558
$993$	4.71648	0.149673
$994$	−8.52925	−0.270531
$995$	−3.55025	−0.112550
$996$	−14.3415	−0.454427
$997$	−38.8869	−1.23156	−0.615780	−	0.787918i	$-0.711159\pi$
$997$	−38.8869	−1.23156	−0.615780	+	0.787918i	$0.711159\pi$
$998$	−3.68209	−0.116555
$999$	10.3717	0.328147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8670.2.a.cc.1.1	✓	6
17.16	even	2		8670.2.a.cd.1.6	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8670.2.a.cc.1.1	✓	6	1.1	even	1	trivial
8670.2.a.cd.1.6	yes	6	17.16	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:	\( N \)	\(=\)	\( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8670.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.49985 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.49985 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +2.98492 q^{11} -1.00000 q^{12} +0.0262790 q^{13} +3.49985 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} -2.12918 q^{19} +1.00000 q^{20} +3.49985 q^{21} -2.98492 q^{22} +7.10370 q^{23} +1.00000 q^{24} +1.00000 q^{25} -0.0262790 q^{26} -1.00000 q^{27} -3.49985 q^{28} +6.04755 q^{29} +1.00000 q^{30} -5.81284 q^{31} -1.00000 q^{32} -2.98492 q^{33} -3.49985 q^{35} +1.00000 q^{36} -10.3717 q^{37} +2.12918 q^{38} -0.0262790 q^{39} -1.00000 q^{40} -3.18796 q^{41} -3.49985 q^{42} -3.81646 q^{43} +2.98492 q^{44} +1.00000 q^{45} -7.10370 q^{46} +1.22351 q^{47} -1.00000 q^{48} +5.24897 q^{49} -1.00000 q^{50} +0.0262790 q^{52} -10.5633 q^{53} +1.00000 q^{54} +2.98492 q^{55} +3.49985 q^{56} +2.12918 q^{57} -6.04755 q^{58} +0.962526 q^{59} -1.00000 q^{60} -4.71454 q^{61} +5.81284 q^{62} -3.49985 q^{63} +1.00000 q^{64} +0.0262790 q^{65} +2.98492 q^{66} +9.85335 q^{67} -7.10370 q^{69} +3.49985 q^{70} -2.43703 q^{71} -1.00000 q^{72} +2.58271 q^{73} +10.3717 q^{74} -1.00000 q^{75} -2.12918 q^{76} -10.4468 q^{77} +0.0262790 q^{78} +3.86593 q^{79} +1.00000 q^{80} +1.00000 q^{81} +3.18796 q^{82} +14.3415 q^{83} +3.49985 q^{84} +3.81646 q^{86} -6.04755 q^{87} -2.98492 q^{88} +14.3190 q^{89} -1.00000 q^{90} -0.0919727 q^{91} +7.10370 q^{92} +5.81284 q^{93} -1.22351 q^{94} -2.12918 q^{95} +1.00000 q^{96} -10.3932 q^{97} -5.24897 q^{98} +2.98492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} + 6 q^{11} - 6 q^{12} + 6 q^{13} - 6 q^{15} + 6 q^{16} - 6 q^{18} + 6 q^{19} + 6 q^{20} - 6 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{25} - 6 q^{26} - 6 q^{27} - 6 q^{29} + 6 q^{30} - 12 q^{31} - 6 q^{32} - 6 q^{33} + 6 q^{36} - 12 q^{37} - 6 q^{38} - 6 q^{39} - 6 q^{40} - 12 q^{41} + 6 q^{44} + 6 q^{45} + 12 q^{46} - 6 q^{47} - 6 q^{48} + 6 q^{49} - 6 q^{50} + 6 q^{52} - 30 q^{53} + 6 q^{54} + 6 q^{55} - 6 q^{57} + 6 q^{58} + 6 q^{59} - 6 q^{60} - 6 q^{61} + 12 q^{62} + 6 q^{64} + 6 q^{65} + 6 q^{66} - 24 q^{67} + 12 q^{69} - 6 q^{71} - 6 q^{72} - 36 q^{73} + 12 q^{74} - 6 q^{75} + 6 q^{76} - 54 q^{77} + 6 q^{78} - 12 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} + 12 q^{83} + 6 q^{87} - 6 q^{88} - 18 q^{89} - 6 q^{90} + 24 q^{91} - 12 q^{92} + 12 q^{93} + 6 q^{94} + 6 q^{95} + 6 q^{96} - 30 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 + 6 * q^11 - 6 * q^12 + 6 * q^13 - 6 * q^15 + 6 * q^16 - 6 * q^18 + 6 * q^19 + 6 * q^20 - 6 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^25 - 6 * q^26 - 6 * q^27 - 6 * q^29 + 6 * q^30 - 12 * q^31 - 6 * q^32 - 6 * q^33 + 6 * q^36 - 12 * q^37 - 6 * q^38 - 6 * q^39 - 6 * q^40 - 12 * q^41 + 6 * q^44 + 6 * q^45 + 12 * q^46 - 6 * q^47 - 6 * q^48 + 6 * q^49 - 6 * q^50 + 6 * q^52 - 30 * q^53 + 6 * q^54 + 6 * q^55 - 6 * q^57 + 6 * q^58 + 6 * q^59 - 6 * q^60 - 6 * q^61 + 12 * q^62 + 6 * q^64 + 6 * q^65 + 6 * q^66 - 24 * q^67 + 12 * q^69 - 6 * q^71 - 6 * q^72 - 36 * q^73 + 12 * q^74 - 6 * q^75 + 6 * q^76 - 54 * q^77 + 6 * q^78 - 12 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 + 12 * q^83 + 6 * q^87 - 6 * q^88 - 18 * q^89 - 6 * q^90 + 24 * q^91 - 12 * q^92 + 12 * q^93 + 6 * q^94 + 6 * q^95 + 6 * q^96 - 30 * q^97 - 6 * q^98 + 6 * q^99

Introduction

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Database

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