LMFDB - Embedded newform 1134.2.g.k.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(163,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1134.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.g (of order $3$, degree $2$, minimal)

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:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1134.163
Dual form			1134.2.g.k.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.84981 + 3.20397i) q^{5} +(-1.23855 + 2.33795i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.84981 + 3.20397i) q^{5} +(-1.23855 + 2.33795i) q^{7} +1.00000 q^{8} +(-1.84981 - 3.20397i) q^{10} +(0.738550 + 1.27921i) q^{11} +2.69963 q^{13} +(-1.40545 - 2.24159i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.28799 + 5.69497i) q^{17} +(-0.444368 + 0.769668i) q^{19} +3.69963 q^{20} -1.47710 q^{22} +(-3.14400 + 5.44556i) q^{23} +(-4.34362 - 7.52338i) q^{25} +(-1.34981 + 2.33795i) q^{26} +(2.64400 - 0.0963576i) q^{28} -2.51052 q^{29} +(-3.40545 - 5.89841i) q^{31} +(-0.500000 - 0.866025i) q^{32} -6.57598 q^{34} +(-5.19963 - 8.29305i) q^{35} +(-1.38874 + 2.40536i) q^{37} +(-0.444368 - 0.769668i) q^{38} +(-1.84981 + 3.20397i) q^{40} +4.11126 q^{41} -0.0123797 q^{43} +(0.738550 - 1.27921i) q^{44} +(-3.14400 - 5.44556i) q^{46} +(3.49381 - 6.05146i) q^{47} +(-3.93199 - 5.79133i) q^{49} +8.68725 q^{50} +(-1.34981 - 2.33795i) q^{52} +(-1.60507 - 2.78007i) q^{53} -5.46472 q^{55} +(-1.23855 + 2.33795i) q^{56} +(1.25526 - 2.17417i) q^{58} +(-3.45489 - 5.98404i) q^{59} +(2.86652 - 4.96497i) q^{61} +6.81089 q^{62} +1.00000 q^{64} +(-4.99381 + 8.64953i) q^{65} +(4.73236 + 8.19669i) q^{67} +(3.28799 - 5.69497i) q^{68} +(9.78180 - 0.356487i) q^{70} -5.46472 q^{71} +(-6.03273 - 10.4490i) q^{73} +(-1.38874 - 2.40536i) q^{74} +0.888736 q^{76} +(-3.90545 + 0.142330i) q^{77} +(-5.72617 + 9.91802i) q^{79} +(-1.84981 - 3.20397i) q^{80} +(-2.05563 + 3.56046i) q^{82} -4.47710 q^{83} -24.3287 q^{85} +(0.00618986 - 0.0107211i) q^{86} +(0.738550 + 1.27921i) q^{88} +(-4.43818 + 7.68715i) q^{89} +(-3.34362 + 6.31159i) q^{91} +6.28799 q^{92} +(3.49381 + 6.05146i) q^{94} +(-1.64400 - 2.84748i) q^{95} +13.1767 q^{97} +(6.98143 - 0.509538i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8} - 5 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 3 q^{16} - 4 q^{17} - 3 q^{19} + 10 q^{20} + 2 q^{22} - 7 q^{23} - 2 q^{25} - 2 q^{26} + 4 q^{28} + 10 q^{29} - 14 q^{31} - 3 q^{32} + 8 q^{34} - 19 q^{35} - 9 q^{37} - 3 q^{38} - 5 q^{40} + 24 q^{41} - 36 q^{43} - q^{44} - 7 q^{46} + 3 q^{47} + 12 q^{49} + 4 q^{50} - 2 q^{52} + 9 q^{53} + 14 q^{55} - 2 q^{56} - 5 q^{58} + 4 q^{59} + 4 q^{61} + 28 q^{62} + 6 q^{64} - 12 q^{65} + 5 q^{67} - 4 q^{68} + 17 q^{70} + 14 q^{71} - 25 q^{73} - 9 q^{74} + 6 q^{76} - 17 q^{77} + 7 q^{79} - 5 q^{80} - 12 q^{82} - 16 q^{83} - 28 q^{85} + 18 q^{86} - q^{88} - 9 q^{89} + 4 q^{91} + 14 q^{92} + 3 q^{94} + 2 q^{95} + 56 q^{97} - 12 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8 - 5 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 3 * q^16 - 4 * q^17 - 3 * q^19 + 10 * q^20 + 2 * q^22 - 7 * q^23 - 2 * q^25 - 2 * q^26 + 4 * q^28 + 10 * q^29 - 14 * q^31 - 3 * q^32 + 8 * q^34 - 19 * q^35 - 9 * q^37 - 3 * q^38 - 5 * q^40 + 24 * q^41 - 36 * q^43 - q^44 - 7 * q^46 + 3 * q^47 + 12 * q^49 + 4 * q^50 - 2 * q^52 + 9 * q^53 + 14 * q^55 - 2 * q^56 - 5 * q^58 + 4 * q^59 + 4 * q^61 + 28 * q^62 + 6 * q^64 - 12 * q^65 + 5 * q^67 - 4 * q^68 + 17 * q^70 + 14 * q^71 - 25 * q^73 - 9 * q^74 + 6 * q^76 - 17 * q^77 + 7 * q^79 - 5 * q^80 - 12 * q^82 - 16 * q^83 - 28 * q^85 + 18 * q^86 - q^88 - 9 * q^89 + 4 * q^91 + 14 * q^92 + 3 * q^94 + 2 * q^95 + 56 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.84981	+	3.20397i	−0.827262	+	1.43286i	0.0729162	+	0.997338i	$0.476769\pi$
$5$	−1.84981	+	3.20397i	−0.827262	+	1.43286i	−0.900178	+	0.435522i	$0.856564\pi$
$6$		0			0
$7$	−1.23855	+	2.33795i	−0.468128	+	0.883661i
$7$	−1.23855	+	2.33795i	−0.468128	+	0.883661i
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.84981	−	3.20397i	−0.584963	−	1.01318i
$11$	0.738550	+	1.27921i	0.222681	+	0.385695i	0.955621	−	0.294598i	$-0.0951858\pi$
$11$	0.738550	+	1.27921i	0.222681	+	0.385695i	−0.732940	+	0.680293i	$0.761852\pi$
$12$		0			0
$13$	2.69963			0.748742			0.374371	−	0.927279i	$-0.377859\pi$
$13$	2.69963			0.748742			0.374371	+	0.927279i	$0.377859\pi$
$14$	−1.40545	−	2.24159i	−0.375621	−	0.599090i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.28799	+	5.69497i	0.797455	+	1.38123i	0.921268	+	0.388927i	$0.127154\pi$
$17$	3.28799	+	5.69497i	0.797455	+	1.38123i	−0.123813	+	0.992306i	$0.539512\pi$
$18$		0			0
$19$	−0.444368	+	0.769668i	−0.101945	+	0.176574i	−0.912486	−	0.409108i	$-0.865840\pi$
$19$	−0.444368	+	0.769668i	−0.101945	+	0.176574i	0.810541	+	0.585682i	$0.199173\pi$
$20$	3.69963			0.827262
$21$		0			0
$22$	−1.47710			−0.314919
$23$	−3.14400	+	5.44556i	−0.655568	+	1.13548i	0.326182	+	0.945307i	$0.394238\pi$
$23$	−3.14400	+	5.44556i	−0.655568	+	1.13548i	−0.981751	+	0.190171i	$0.939096\pi$
$24$		0			0
$25$	−4.34362	−	7.52338i	−0.868725	−	1.50468i
$26$	−1.34981	+	2.33795i	−0.264720	+	0.458509i
$27$		0			0
$28$	2.64400	−	0.0963576i	0.499668	−	0.0182099i
$29$	−2.51052			−0.466192			−0.233096	−	0.972454i	$-0.574886\pi$
$29$	−2.51052			−0.466192			−0.233096	+	0.972454i	$0.574886\pi$
$30$		0			0
$31$	−3.40545	−	5.89841i	−0.611636	−	1.05938i	−0.990965	−	0.134123i	$-0.957178\pi$
$31$	−3.40545	−	5.89841i	−0.611636	−	1.05938i	0.379329	−	0.925262i	$-0.376155\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−6.57598			−1.12777
$35$	−5.19963	−	8.29305i	−0.878898	−	1.40178i
$36$		0			0
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	−0.957306	−	0.289075i	$-0.906652\pi$
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	0.729000	+	0.684514i	$0.239986\pi$
$38$	−0.444368	−	0.769668i	−0.0720860	−	0.124857i
$39$		0			0
$40$	−1.84981	+	3.20397i	−0.292481	+	0.506592i
$41$	4.11126			0.642072			0.321036	−	0.947067i	$-0.395969\pi$
$41$	4.11126			0.642072			0.321036	+	0.947067i	$0.395969\pi$
$42$		0			0
$43$	−0.0123797			−0.00188789			−0.000943944	−	1.00000i	$-0.500300\pi$
$43$	−0.0123797			−0.00188789			−0.000943944		1.00000i	$0.500300\pi$
$44$	0.738550	−	1.27921i	0.111341	−	0.192848i
$45$		0			0
$46$	−3.14400	−	5.44556i	−0.463557	−	0.802904i
$47$	3.49381	−	6.05146i	0.509625	−	0.882696i	−0.490313	−	0.871546i	$-0.663118\pi$
$47$	3.49381	−	6.05146i	0.509625	−	0.882696i	0.999938	−	0.0111494i	$-0.00354904\pi$
$48$		0			0
$49$	−3.93199	−	5.79133i	−0.561713	−	0.827332i
$50$	8.68725			1.22856
$51$		0			0
$52$	−1.34981	−	2.33795i	−0.187186	−	0.324215i
$53$	−1.60507	−	2.78007i	−0.220474	−	0.381872i	0.734478	−	0.678632i	$-0.237427\pi$
$53$	−1.60507	−	2.78007i	−0.220474	−	0.381872i	−0.954952	+	0.296760i	$0.904094\pi$
$54$		0			0
$55$	−5.46472			−0.736863
$56$	−1.23855	+	2.33795i	−0.165508	+	0.312421i
$57$		0			0
$58$	1.25526	−	2.17417i	0.164824	−	0.285483i
$59$	−3.45489	−	5.98404i	−0.449788	−	0.779056i	0.548584	−	0.836096i	$-0.315167\pi$
$59$	−3.45489	−	5.98404i	−0.449788	−	0.779056i	−0.998372	+	0.0570397i	$0.981834\pi$
$60$		0			0
$61$	2.86652	−	4.96497i	0.367021	−	0.635699i	−0.622077	−	0.782956i	$-0.713711\pi$
$61$	2.86652	−	4.96497i	0.367021	−	0.635699i	0.989098	+	0.147257i	$0.0470444\pi$
$62$	6.81089			0.864984
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.99381	+	8.64953i	−0.619406	+	1.07284i
$66$		0			0
$67$	4.73236	+	8.19669i	0.578150	+	1.00138i	0.995692	+	0.0927271i	$0.0295584\pi$
$67$	4.73236	+	8.19669i	0.578150	+	1.00138i	−0.417542	+	0.908658i	$0.637108\pi$
$68$	3.28799	−	5.69497i	0.398728	−	0.690616i
$69$		0			0
$70$	9.78180	−	0.356487i	1.16915	−	0.0426084i
$71$	−5.46472			−0.648543			−0.324271	−	0.945964i	$-0.605119\pi$
$71$	−5.46472			−0.648543			−0.324271	+	0.945964i	$0.605119\pi$
$72$		0			0
$73$	−6.03273	−	10.4490i	−0.706078	−	1.22296i	−0.966301	−	0.257414i	$-0.917130\pi$
$73$	−6.03273	−	10.4490i	−0.706078	−	1.22296i	0.260223	−	0.965548i	$-0.416204\pi$
$74$	−1.38874	−	2.40536i	−0.161437	−	0.279618i
$75$		0			0
$76$	0.888736			0.101945
$77$	−3.90545	+	0.142330i	−0.445067	+	0.0162200i
$78$		0			0
$79$	−5.72617	+	9.91802i	−0.644244	+	1.11586i	0.340231	+	0.940342i	$0.389495\pi$
$79$	−5.72617	+	9.91802i	−0.644244	+	1.11586i	−0.984475	+	0.175522i	$0.943839\pi$
$80$	−1.84981	−	3.20397i	−0.206816	−	0.358215i
$81$		0			0
$82$	−2.05563	+	3.56046i	−0.227007	+	0.393187i
$83$	−4.47710			−0.491426			−0.245713	−	0.969343i	$-0.579022\pi$
$83$	−4.47710			−0.491426			−0.245713	+	0.969343i	$0.579022\pi$
$84$		0			0
$85$	−24.3287			−2.63882
$86$	0.00618986	−	0.0107211i	0.000667469	−	0.00115609i
$87$		0			0
$88$	0.738550	+	1.27921i	0.0787297	+	0.136364i
$89$	−4.43818	+	7.68715i	−0.470446	+	0.814836i	−0.999429	−	0.0337963i	$-0.989240\pi$
$89$	−4.43818	+	7.68715i	−0.470446	+	0.814836i	0.528983	+	0.848633i	$0.322574\pi$
$90$		0			0
$91$	−3.34362	+	6.31159i	−0.350507	+	0.661634i
$92$	6.28799			0.655568
$93$		0			0
$94$	3.49381	+	6.05146i	0.360359	+	0.624160i
$95$	−1.64400	−	2.84748i	−0.168670	−	0.292146i
$96$		0			0
$97$	13.1767			1.33789			0.668947	−	0.743310i	$-0.266745\pi$
$97$	13.1767			1.33789			0.668947	+	0.743310i	$0.266745\pi$
$98$	6.98143	−	0.509538i	0.705231	−	0.0514711i
$99$		0			0
$100$	−4.34362	+	7.52338i	−0.434362	+	0.752338i
$101$	−2.62729	−	4.55059i	−0.261425	−	0.452801i	0.705196	−	0.709012i	$-0.250859\pi$
$101$	−2.62729	−	4.55059i	−0.261425	−	0.452801i	−0.966621	+	0.256212i	$0.917526\pi$
$102$		0			0
$103$	−0.833104	+	1.44298i	−0.0820882	+	0.142181i	−0.904147	−	0.427222i	$-0.859492\pi$
$103$	−0.833104	+	1.44298i	−0.0820882	+	0.142181i	0.822059	+	0.569403i	$0.192826\pi$
$104$	2.69963			0.264720
$105$		0			0
$106$	3.21015			0.311797
$107$	−5.38255	+	9.32284i	−0.520350	+	0.901273i	0.479370	+	0.877613i	$0.340865\pi$
$107$	−5.38255	+	9.32284i	−0.520350	+	0.901273i	−0.999720	+	0.0236602i	$0.992468\pi$
$108$		0			0
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	0.861462	−	0.507823i	$-0.169550\pi$
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	−0.870518	+	0.492136i	$0.836216\pi$
$110$	2.73236	−	4.73259i	0.260520	−	0.451234i
$111$		0			0
$112$	−1.40545	−	2.24159i	−0.132802	−	0.211810i
$113$	13.5636			1.27596			0.637978	−	0.770054i	$-0.279771\pi$
$113$	13.5636			1.27596			0.637978	+	0.770054i	$0.279771\pi$
$114$		0			0
$115$	−11.6316	−	20.1466i	−1.08465	−	1.87868i
$116$	1.25526	+	2.17417i	0.116548	+	0.201867i
$117$		0			0
$118$	6.90978			0.636097
$119$	−17.3869	+	0.633646i	−1.59385	+	0.0580862i
$120$		0			0
$121$	4.40909	−	7.63676i	0.400826	−	0.694251i
$122$	2.86652	+	4.96497i	0.259523	+	0.449507i
$123$		0			0
$124$	−3.40545	+	5.89841i	−0.305818	+	0.529692i
$125$	13.6414			1.22013
$126$		0			0
$127$	−2.85669			−0.253490			−0.126745	−	0.991935i	$-0.540453\pi$
$127$	−2.85669			−0.253490			−0.126745	+	0.991935i	$0.540453\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−4.99381	−	8.64953i	−0.437986	−	0.758614i
$131$	−0.0778435	+	0.134829i	−0.00680122	+	0.0117801i	−0.869406	−	0.494098i	$-0.835498\pi$
$131$	−0.0778435	+	0.134829i	−0.00680122	+	0.0117801i	0.862605	+	0.505878i	$0.168832\pi$
$132$		0			0
$133$	−1.24907	−	1.99218i	−0.108308	−	0.172744i
$134$	−9.46472			−0.817627
$135$		0			0
$136$	3.28799	+	5.69497i	0.281943	+	0.488340i
$137$	1.70582	+	2.95456i	0.145738	+	0.252425i	0.929648	−	0.368449i	$-0.120111\pi$
$137$	1.70582	+	2.95456i	0.145738	+	0.252425i	−0.783910	+	0.620874i	$0.786778\pi$
$138$		0			0
$139$	13.5105			1.14595			0.572974	−	0.819574i	$-0.305790\pi$
$139$	13.5105			1.14595			0.572974	+	0.819574i	$0.305790\pi$
$140$	−4.58217	+	8.64953i	−0.387264	+	0.731019i
$141$		0			0
$142$	2.73236	−	4.73259i	0.229295	−	0.397150i
$143$	1.99381	+	3.45338i	0.166731	+	0.288786i
$144$		0			0
$145$	4.64400	−	8.04364i	0.385663	−	0.667988i
$146$	12.0655			0.998545
$147$		0			0
$148$	2.77747			0.228307
$149$	−0.166896	+	0.289073i	−0.0136727	+	0.0236818i	−0.872781	−	0.488112i	$-0.837686\pi$
$149$	−0.166896	+	0.289073i	−0.0136727	+	0.0236818i	0.859108	+	0.511794i	$0.171019\pi$
$150$		0			0
$151$	9.95489	+	17.2424i	0.810117	+	1.40316i	0.912781	+	0.408448i	$0.133930\pi$
$151$	9.95489	+	17.2424i	0.810117	+	1.40316i	−0.102664	+	0.994716i	$0.532737\pi$
$152$	−0.444368	+	0.769668i	−0.0360430	+	0.0624283i
$153$		0			0
$154$	1.82946	−	3.45338i	0.147422	−	0.278281i
$155$	25.1978			2.02393
$156$		0			0
$157$	3.48143	+	6.03001i	0.277848	+	0.481248i	0.970850	−	0.239689i	$-0.0770454\pi$
$157$	3.48143	+	6.03001i	0.277848	+	0.481248i	−0.693001	+	0.720936i	$0.743712\pi$
$158$	−5.72617	−	9.91802i	−0.455550	−	0.789035i
$159$		0			0
$160$	3.69963			0.292481
$161$	−8.83743	−	14.0951i	−0.696487	−	1.11085i
$162$		0			0
$163$	4.03706	−	6.99240i	0.316207	−	0.547687i	−0.663486	−	0.748189i	$-0.730924\pi$
$163$	4.03706	−	6.99240i	0.316207	−	0.547687i	0.979693	+	0.200502i	$0.0642572\pi$
$164$	−2.05563	−	3.56046i	−0.160518	−	0.278025i
$165$		0			0
$166$	2.23855	−	3.87728i	0.173745	−	0.300935i
$167$	−19.4858			−1.50785			−0.753927	−	0.656959i	$-0.771843\pi$
$167$	−19.4858			−1.50785			−0.753927	+	0.656959i	$0.771843\pi$
$168$		0			0
$169$	−5.71201			−0.439385
$170$	12.1643	−	21.0693i	0.932963	−	1.61594i
$171$		0			0
$172$	0.00618986	+	0.0107211i	0.000471972	+	0.000817480i
$173$	−11.2818	+	19.5407i	−0.857740	+	1.48565i	0.0163405	+	0.999866i	$0.494798\pi$
$173$	−11.2818	+	19.5407i	−0.857740	+	1.48565i	−0.874080	+	0.485782i	$0.838535\pi$
$174$		0			0
$175$	22.9691	−	0.837082i	1.73630	−	0.0632775i
$176$	−1.47710			−0.111341
$177$		0			0
$178$	−4.43818	−	7.68715i	−0.332656	−	0.576176i
$179$	0.166896	+	0.289073i	0.0124744	+	0.0216063i	0.872195	−	0.489158i	$-0.162696\pi$
$179$	0.166896	+	0.289073i	0.0124744	+	0.0216063i	−0.859721	+	0.510764i	$0.829363\pi$
$180$		0			0
$181$	23.2422			1.72758			0.863789	−	0.503853i	$-0.168085\pi$
$181$	23.2422			1.72758			0.863789	+	0.503853i	$0.168085\pi$
$182$	−3.79418	−	6.05146i	−0.281243	−	0.448564i
$183$		0			0
$184$	−3.14400	+	5.44556i	−0.231778	+	0.401452i
$185$	−5.13781	−	8.89894i	−0.377739	−	0.654263i
$186$		0			0
$187$	−4.85669	+	8.41204i	−0.355157	+	0.615149i
$188$	−6.98762			−0.509625
$189$		0			0
$190$	3.28799			0.238536
$191$	8.16071	−	14.1348i	0.590488	−	1.02276i	−0.403679	−	0.914901i	$-0.632269\pi$
$191$	8.16071	−	14.1348i	0.590488	−	1.02276i	0.994167	−	0.107854i	$-0.0343980\pi$
$192$		0			0
$193$	7.16071	+	12.4027i	0.515439	+	0.892766i	0.999839	+	0.0179200i	$0.00570443\pi$
$193$	7.16071	+	12.4027i	0.515439	+	0.892766i	−0.484400	+	0.874846i	$0.660962\pi$
$194$	−6.58836	+	11.4114i	−0.473017	+	0.819289i
$195$		0			0
$196$	−3.04944	+	6.30087i	−0.217817	+	0.450062i
$197$	2.42402			0.172704			0.0863520	−	0.996265i	$-0.472479\pi$
$197$	2.42402			0.172704			0.0863520	+	0.996265i	$0.472479\pi$
$198$		0			0
$199$	−3.05563	−	5.29251i	−0.216608	−	0.375176i	0.737161	−	0.675717i	$-0.236166\pi$
$199$	−3.05563	−	5.29251i	−0.216608	−	0.375176i	−0.953769	+	0.300541i	$0.902833\pi$
$200$	−4.34362	−	7.52338i	−0.307141	−	0.531983i
$201$		0			0
$202$	5.25457			0.369710
$203$	3.10940	−	5.86946i	0.218237	−	0.411956i
$204$		0			0
$205$	−7.60507	+	13.1724i	−0.531161	+	0.919999i
$206$	−0.833104	−	1.44298i	−0.0580451	−	0.100537i
$207$		0			0
$208$	−1.34981	+	2.33795i	−0.0935928	+	0.162107i
$209$	−1.31275			−0.0908049
$210$		0			0
$211$	−11.4451			−0.787910			−0.393955	−	0.919130i	$-0.628893\pi$
$211$	−11.4451			−0.787910			−0.393955	+	0.919130i	$0.628893\pi$
$212$	−1.60507	+	2.78007i	−0.110237	+	0.190936i
$213$		0			0
$214$	−5.38255	−	9.32284i	−0.367943	−	0.637296i
$215$	0.0229002	−	0.0396643i	0.00156178	−	0.00270508i
$216$		0			0
$217$	18.0080	−	0.656281i	1.22246	−	0.0445513i
$218$	0.189108			0.0128080
$219$		0			0
$220$	2.73236	+	4.73259i	0.184216	+	0.319071i
$221$	8.87636	+	15.3743i	0.597088	+	1.03419i
$222$		0			0
$223$	7.22253			0.483656			0.241828	−	0.970319i	$-0.422253\pi$
$223$	7.22253			0.483656			0.241828	+	0.970319i	$0.422253\pi$
$224$	2.64400	−	0.0963576i	0.176659	−	0.00643816i
$225$		0			0
$226$	−6.78180	+	11.7464i	−0.451119	+	0.781361i
$227$	−6.82760	−	11.8258i	−0.453164	−	0.784903i	0.545417	−	0.838165i	$-0.316371\pi$
$227$	−6.82760	−	11.8258i	−0.453164	−	0.784903i	−0.998581	+	0.0532622i	$0.983038\pi$
$228$		0			0
$229$	−8.68725	+	15.0468i	−0.574070	+	0.994318i	0.422073	+	0.906562i	$0.361303\pi$
$229$	−8.68725	+	15.0468i	−0.574070	+	0.994318i	−0.996142	+	0.0877555i	$0.972031\pi$
$230$	23.2632			1.53393
$231$		0			0
$232$	−2.51052			−0.164824
$233$	7.62110	−	13.2001i	0.499275	−	0.864769i	−0.500725	−	0.865606i	$-0.666933\pi$
$233$	7.62110	−	13.2001i	0.499275	−	0.864769i	1.00000		0.000837426i	$0.000266561\pi$
$234$		0			0
$235$	12.9258	+	22.3881i	0.843186	+	1.46044i
$236$	−3.45489	+	5.98404i	−0.224894	+	0.389528i
$237$		0			0
$238$	8.14468	−	15.3743i	0.527942	−	0.996568i
$239$	−18.9505			−1.22580			−0.612902	−	0.790159i	$-0.709998\pi$
$239$	−18.9505			−1.22580			−0.612902	+	0.790159i	$0.709998\pi$
$240$		0			0
$241$	12.2527	+	21.2223i	0.789267	+	1.36705i	0.926417	+	0.376500i	$0.122872\pi$
$241$	12.2527	+	21.2223i	0.789267	+	1.36705i	−0.137150	+	0.990550i	$0.543794\pi$
$242$	4.40909	+	7.63676i	0.283427	+	0.490910i
$243$		0			0
$244$	−5.73305			−0.367021
$245$	25.8287	−	1.88510i	1.65013	−	0.120435i
$246$		0			0
$247$	−1.19963	+	2.07782i	−0.0763305	+	0.132208i
$248$	−3.40545	−	5.89841i	−0.216246	−	0.374549i
$249$		0			0
$250$	−6.82072	+	11.8138i	−0.431380	+	0.747173i
$251$	−12.1236			−0.765238			−0.382619	−	0.923906i	$-0.624978\pi$
$251$	−12.1236			−0.765238			−0.382619	+	0.923906i	$0.624978\pi$
$252$		0			0
$253$	−9.28799			−0.583931
$254$	1.42835	−	2.47397i	0.0896224	−	0.155231i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.10439	−	7.10900i	0.256025	−	0.443448i	−0.709149	−	0.705059i	$-0.750921\pi$
$257$	4.10439	−	7.10900i	0.256025	−	0.443448i	0.965173	+	0.261611i	$0.0842539\pi$
$258$		0			0
$259$	−3.90359	−	6.22595i	−0.242557	−	0.386862i
$260$	9.98762			0.619406
$261$		0			0
$262$	−0.0778435	−	0.134829i	−0.00480919	−	0.00832976i
$263$	2.67309	+	4.62992i	0.164830	+	0.285493i	0.936595	−	0.350414i	$-0.113959\pi$
$263$	2.67309	+	4.62992i	0.164830	+	0.285493i	−0.771765	+	0.635908i	$0.780626\pi$
$264$		0			0
$265$	11.8764			0.729559
$266$	2.34981	−	0.0856364i	0.144076	−	0.00525071i
$267$		0			0
$268$	4.73236	−	8.19669i	0.289075	−	0.500692i
$269$	9.24219	+	16.0079i	0.563506	+	0.976022i	0.997187	+	0.0749550i	$0.0238813\pi$
$269$	9.24219	+	16.0079i	0.563506	+	0.976022i	−0.433681	+	0.901067i	$0.642785\pi$
$270$		0			0
$271$	−3.67742	+	6.36947i	−0.223387	+	0.386918i	−0.955834	−	0.293906i	$-0.905045\pi$
$271$	−3.67742	+	6.36947i	−0.223387	+	0.386918i	0.732447	+	0.680824i	$0.238378\pi$
$272$	−6.57598			−0.398728
$273$		0			0
$274$	−3.41164			−0.206104
$275$	6.41597	−	11.1128i	0.386897	−	0.670126i
$276$		0			0
$277$	4.54944	+	7.87987i	0.273349	+	0.473455i	0.969717	−	0.244230i	$-0.0785351\pi$
$277$	4.54944	+	7.87987i	0.273349	+	0.473455i	−0.696368	+	0.717685i	$0.745202\pi$
$278$	−6.75526	+	11.7005i	−0.405154	+	0.701747i
$279$		0			0
$280$	−5.19963	−	8.29305i	−0.310737	−	0.495604i
$281$	−12.0087			−0.716377			−0.358188	−	0.933649i	$-0.616605\pi$
$281$	−12.0087			−0.716377			−0.358188	+	0.933649i	$0.616605\pi$
$282$		0			0
$283$	−4.92147	−	8.52423i	−0.292551	−	0.506713i	0.681861	−	0.731481i	$-0.261171\pi$
$283$	−4.92147	−	8.52423i	−0.292551	−	0.506713i	−0.974412	+	0.224768i	$0.927837\pi$
$284$	2.73236	+	4.73259i	0.162136	+	0.280827i
$285$		0			0
$286$	−3.98762			−0.235793
$287$	−5.09201	+	9.61192i	−0.300572	+	0.567373i
$288$		0			0
$289$	−13.1218	+	22.7276i	−0.771870	+	1.33692i
$290$	4.64400	+	8.04364i	0.272705	+	0.472339i
$291$		0			0
$292$	−6.03273	+	10.4490i	−0.353039	+	0.611481i
$293$	−21.4203			−1.25139			−0.625694	−	0.780069i	$-0.715184\pi$
$293$	−21.4203			−1.25139			−0.625694	+	0.780069i	$0.715184\pi$
$294$		0			0
$295$	25.5636			1.48837
$296$	−1.38874	+	2.40536i	−0.0807186	+	0.139809i
$297$		0			0
$298$	−0.166896	−	0.289073i	−0.00966804	−	0.0167455i
$299$	−8.48762	+	14.7010i	−0.490852	+	0.850180i
$300$		0			0
$301$	0.0153329	−	0.0289431i	0.000883773	−	0.00166825i
$302$	−19.9098			−1.14568
$303$		0			0
$304$	−0.444368	−	0.769668i	−0.0254862	−	0.0441435i
$305$	10.6051	+	18.3685i	0.607245	+	1.05178i
$306$		0			0
$307$	−5.68725			−0.324588			−0.162294	−	0.986742i	$-0.551889\pi$
$307$	−5.68725			−0.324588			−0.162294	+	0.986742i	$0.551889\pi$
$308$	2.07598	+	3.31105i	0.118290	+	0.188665i
$309$		0			0
$310$	−12.5989	+	21.8219i	−0.715569	+	1.23940i
$311$	5.86033	+	10.1504i	0.332309	+	0.575576i	0.982964	−	0.183797i	$-0.0588390\pi$
$311$	5.86033	+	10.1504i	0.332309	+	0.575576i	−0.650655	+	0.759373i	$0.725506\pi$
$312$		0			0
$313$	13.3869	−	23.1868i	0.756671	−	1.31059i	−0.187868	−	0.982194i	$-0.560158\pi$
$313$	13.3869	−	23.1868i	0.756671	−	1.31059i	0.944539	−	0.328398i	$-0.106509\pi$
$314$	−6.96286			−0.392937
$315$		0			0
$316$	11.4523			0.644244
$317$	−0.951246	+	1.64761i	−0.0534273	+	0.0925388i	−0.891502	−	0.453016i	$-0.850348\pi$
$317$	−0.951246	+	1.64761i	−0.0534273	+	0.0925388i	0.838075	+	0.545555i	$0.183681\pi$
$318$		0			0
$319$	−1.85414	−	3.21147i	−0.103812	−	0.179808i
$320$	−1.84981	+	3.20397i	−0.103408	+	0.179107i
$321$		0			0
$322$	16.6254	−	0.605896i	0.926499	−	0.0337653i
$323$	−5.84431			−0.325186
$324$		0			0
$325$	−11.7262	−	20.3103i	−0.650451	−	1.12661i
$326$	4.03706	+	6.99240i	0.223592	+	0.387273i
$327$		0			0
$328$	4.11126			0.227007
$329$	9.82072	+	15.6634i	0.541434	+	0.863550i
$330$		0			0
$331$	−2.78366	+	4.82144i	−0.153004	+	0.265010i	−0.932330	−	0.361608i	$-0.882228\pi$
$331$	−2.78366	+	4.82144i	−0.153004	+	0.265010i	0.779327	+	0.626618i	$0.215561\pi$
$332$	2.23855	+	3.87728i	0.122856	+	0.212794i
$333$		0			0
$334$	9.74288	−	16.8752i	0.533107	−	0.923368i
$335$	−35.0159			−1.91313
$336$		0			0
$337$	33.7738			1.83977			0.919887	−	0.392184i	$-0.128280\pi$
$337$	33.7738			1.83977			0.919887	+	0.392184i	$0.128280\pi$
$338$	2.85600	−	4.94674i	0.155346	−	0.269067i
$339$		0			0
$340$	12.1643	+	21.0693i	0.659704	+	1.14264i
$341$	5.03018	−	8.71253i	0.272400	−	0.471810i
$342$		0			0
$343$	18.4098	−	2.01993i	0.994035	−	0.109066i
$344$	−0.0123797			−0.000667469
$345$		0			0
$346$	−11.2818	−	19.5407i	−0.606513	−	1.05051i
$347$	15.2033	+	26.3328i	0.816154	+	1.41362i	0.908496	+	0.417893i	$0.137231\pi$
$347$	15.2033	+	26.3328i	0.816154	+	1.41362i	−0.0923418	+	0.995727i	$0.529435\pi$
$348$		0			0
$349$	12.5956			0.674230			0.337115	−	0.941464i	$-0.390549\pi$
$349$	12.5956			0.674230			0.337115	+	0.941464i	$0.390549\pi$
$350$	−10.7596	+	20.3103i	−0.575124	+	1.08563i
$351$		0			0
$352$	0.738550	−	1.27921i	0.0393648	−	0.0681819i
$353$	3.76578	+	6.52252i	0.200432	+	0.347159i	0.948668	−	0.316274i	$-0.102432\pi$
$353$	3.76578	+	6.52252i	0.200432	+	0.347159i	−0.748235	+	0.663433i	$0.769099\pi$
$354$		0			0
$355$	10.1087	−	17.5088i	0.536515	−	0.929271i
$356$	8.87636			0.470446
$357$		0			0
$358$	−0.333792			−0.0176415
$359$	−3.44801	+	5.97213i	−0.181979	+	0.315197i	−0.942554	−	0.334053i	$-0.891584\pi$
$359$	−3.44801	+	5.97213i	−0.181979	+	0.315197i	0.760575	+	0.649250i	$0.224917\pi$
$360$		0			0
$361$	9.10507	+	15.7705i	0.479214	+	0.830024i
$362$	−11.6211	+	20.1283i	−0.610791	+	1.05792i
$363$		0			0
$364$	7.13781	−	0.260130i	0.374123	−	0.0136345i
$365$	44.6377			2.33645
$366$		0			0
$367$	−11.5618	−	20.0257i	−0.603522	−	1.04533i	−0.992283	−	0.123992i	$-0.960430\pi$
$367$	−11.5618	−	20.0257i	−0.603522	−	1.04533i	0.388761	−	0.921339i	$-0.372903\pi$
$368$	−3.14400	−	5.44556i	−0.163892	−	0.283869i
$369$		0			0
$370$	10.2756			0.534204
$371$	8.48762	−	0.309322i	0.440655	−	0.0160592i
$372$		0			0
$373$	−14.5822	+	25.2571i	−0.755036	+	1.30776i	0.190320	+	0.981722i	$0.439047\pi$
$373$	−14.5822	+	25.2571i	−0.755036	+	1.30776i	−0.945356	+	0.326039i	$0.894286\pi$
$374$	−4.85669	−	8.41204i	−0.251134	−	0.434976i
$375$		0			0
$376$	3.49381	−	6.05146i	0.180180	−	0.312080i
$377$	−6.77747			−0.349058
$378$		0			0
$379$	−13.5622			−0.696645			−0.348322	−	0.937375i	$-0.613249\pi$
$379$	−13.5622			−0.696645			−0.348322	+	0.937375i	$0.613249\pi$
$380$	−1.64400	+	2.84748i	−0.0843352	+	0.146073i
$381$		0			0
$382$	8.16071	+	14.1348i	0.417538	+	0.723197i
$383$	1.41783	−	2.45575i	0.0724475	−	0.125483i	−0.827526	−	0.561428i	$-0.810252\pi$
$383$	1.41783	−	2.45575i	0.0724475	−	0.125483i	0.899973	+	0.435945i	$0.143586\pi$
$384$		0			0
$385$	6.76833	−	12.7762i	0.344946	−	0.651137i
$386$	−14.3214			−0.728941
$387$		0			0
$388$	−6.58836	−	11.4114i	−0.334474	−	0.579325i
$389$	9.30401	+	16.1150i	0.471732	+	0.817064i	0.999477	−	0.0323388i	$-0.0102956\pi$
$389$	9.30401	+	16.1150i	0.471732	+	0.817064i	−0.527745	+	0.849403i	$0.676962\pi$
$390$		0			0
$391$	−41.3497			−2.09115
$392$	−3.93199	−	5.79133i	−0.198595	−	0.292506i
$393$		0			0
$394$	−1.21201	+	2.09926i	−0.0610601	+	0.105759i
$395$	−21.1847	−	36.6930i	−1.06592	−	1.84622i
$396$		0			0
$397$	−10.2880	+	17.8193i	−0.516340	+	0.894326i	0.483481	+	0.875355i	$0.339372\pi$
$397$	−10.2880	+	17.8193i	−0.516340	+	0.894326i	−0.999820	+	0.0189712i	$0.993961\pi$
$398$	6.11126			0.306330
$399$		0			0
$400$	8.68725			0.434362
$401$	3.37704	−	5.84921i	0.168642	−	0.292096i	−0.769301	−	0.638887i	$-0.779395\pi$
$401$	3.37704	−	5.84921i	0.168642	−	0.292096i	0.937942	+	0.346791i	$0.112729\pi$
$402$		0			0
$403$	−9.19344	−	15.9235i	−0.457958	−	0.793206i
$404$	−2.62729	+	4.55059i	−0.130712	+	0.226400i
$405$		0			0
$406$	3.52840	+	5.62755i	0.175112	+	0.279291i
$407$	−4.10260			−0.203358
$408$		0			0
$409$	−7.66071	−	13.2687i	−0.378798	−	0.656097i	0.612090	−	0.790788i	$-0.290329\pi$
$409$	−7.66071	−	13.2687i	−0.378798	−	0.656097i	−0.990888	+	0.134691i	$0.956996\pi$
$410$	−7.60507	−	13.1724i	−0.375588	−	0.650537i
$411$		0			0
$412$	1.66621			0.0820882
$413$	18.2694	−	0.665809i	0.898980	−	0.0327623i
$414$		0			0
$415$	8.28180	−	14.3445i	0.406538	−	0.704144i
$416$	−1.34981	−	2.33795i	−0.0661801	−	0.114627i
$417$		0			0
$418$	0.656376	−	1.13688i	0.0321044	−	0.0556064i
$419$	8.64283			0.422230			0.211115	−	0.977461i	$-0.432291\pi$
$419$	8.64283			0.422230			0.211115	+	0.977461i	$0.432291\pi$
$420$		0			0
$421$	−37.1272			−1.80947			−0.904735	−	0.425975i	$-0.859931\pi$
$421$	−37.1272			−1.80947			−0.904735	+	0.425975i	$0.859931\pi$
$422$	5.72253	−	9.91171i	0.278568	−	0.482494i
$423$		0			0
$424$	−1.60507	−	2.78007i	−0.0779493	−	0.135012i
$425$	28.5636	−	49.4736i	1.38554	−	2.39982i
$426$		0			0
$427$	8.05749	+	12.8511i	0.389929	+	0.621910i
$428$	10.7651			0.520350
$429$		0			0
$430$	0.0229002	+	0.0396643i	0.00110434	+	0.00191278i
$431$	−4.71015	−	8.15822i	−0.226880	−	0.392967i	0.730002	−	0.683445i	$-0.239519\pi$
$431$	−4.71015	−	8.15822i	−0.226880	−	0.392967i	−0.956882	+	0.290478i	$0.906186\pi$
$432$		0			0
$433$	−0.208771			−0.0100329			−0.00501645	−	0.999987i	$-0.501597\pi$
$433$	−0.208771			−0.0100329			−0.00501645	+	0.999987i	$0.501597\pi$
$434$	−8.43563	+	15.9235i	−0.404923	+	0.764353i
$435$		0			0
$436$	−0.0945538	+	0.163772i	−0.00452831	+	0.00784326i
$437$	−2.79418	−	4.83967i	−0.133664	−	0.231513i
$438$		0			0
$439$	4.98398	−	8.63250i	0.237872	−	0.412007i	−0.722231	−	0.691652i	$-0.756883\pi$
$439$	4.98398	−	8.63250i	0.237872	−	0.412007i	0.960104	+	0.279645i	$0.0902167\pi$
$440$	−5.46472			−0.260520
$441$		0			0
$442$	−17.7527			−0.844410
$443$	7.84981	−	13.5963i	0.372956	−	0.645979i	−0.617063	−	0.786914i	$-0.711678\pi$
$443$	7.84981	−	13.5963i	0.372956	−	0.645979i	0.990019	+	0.140935i	$0.0450109\pi$
$444$		0			0
$445$	−16.4196	−	28.4396i	−0.778364	−	1.34817i
$446$	−3.61126	+	6.25489i	−0.170998	+	0.296178i
$447$		0			0
$448$	−1.23855	+	2.33795i	−0.0585160	+	0.110458i
$449$	33.6253			1.58688			0.793439	−	0.608650i	$-0.208288\pi$
$449$	33.6253			1.58688			0.793439	+	0.608650i	$0.208288\pi$
$450$		0			0
$451$	3.03637	+	5.25915i	0.142977	+	0.247644i
$452$	−6.78180	−	11.7464i	−0.318989	−	0.552505i
$453$		0			0
$454$	13.6552			0.640871
$455$	−14.0371	−	22.3881i	−0.658068	−	1.04957i
$456$		0			0
$457$	−16.3541	+	28.3262i	−0.765015	+	1.32504i	0.175224	+	0.984529i	$0.443935\pi$
$457$	−16.3541	+	28.3262i	−0.765015	+	1.32504i	−0.940239	+	0.340516i	$0.889398\pi$
$458$	−8.68725	−	15.0468i	−0.405928	−	0.703089i
$459$		0			0
$460$	−11.6316	+	20.1466i	−0.542327	+	0.939338i
$461$	4.14331			0.192973			0.0964865	−	0.995334i	$-0.469240\pi$
$461$	4.14331			0.192973			0.0964865	+	0.995334i	$0.469240\pi$
$462$		0			0
$463$	16.6835			0.775349			0.387675	−	0.921796i	$-0.373278\pi$
$463$	16.6835			0.775349			0.387675	+	0.921796i	$0.373278\pi$
$464$	1.25526	−	2.17417i	0.0582740	−	0.100934i
$465$		0			0
$466$	7.62110	+	13.2001i	0.353040	+	0.611484i
$467$	14.9585	−	25.9089i	0.692198	−	1.19892i	−0.278918	−	0.960315i	$-0.589976\pi$
$467$	14.9585	−	25.9089i	0.692198	−	1.19892i	0.971116	−	0.238608i	$-0.0766909\pi$
$468$		0			0
$469$	−25.0247	+	0.911998i	−1.15553	+	0.0421121i
$470$	−25.8516			−1.19245
$471$		0			0
$472$	−3.45489	−	5.98404i	−0.159024	−	0.275438i
$473$	−0.00914304	−	0.0158362i	−0.000420397	−	0.000728149i
$474$		0			0
$475$	7.72067			0.354249
$476$	9.24219	+	14.7407i	0.423615	+	0.675637i
$477$		0			0
$478$	9.47524	−	16.4116i	0.433387	−	0.750649i
$479$	1.47965	+	2.56283i	0.0676068	+	0.117098i	0.897847	−	0.440307i	$-0.145130\pi$
$479$	1.47965	+	2.56283i	0.0676068	+	0.117098i	−0.830241	+	0.557405i	$0.811797\pi$
$480$		0			0
$481$	−3.74907	+	6.49358i	−0.170943	+	0.296082i
$482$	−24.5054			−1.11619
$483$		0			0
$484$	−8.81818			−0.400826
$485$	−24.3745	+	42.2179i	−1.10679	+	1.91701i
$486$		0			0
$487$	−14.0309	−	24.3022i	−0.635800	−	1.10124i	−0.986345	−	0.164691i	$-0.947337\pi$
$487$	−14.0309	−	24.3022i	−0.635800	−	1.10124i	0.350546	−	0.936546i	$-0.385996\pi$
$488$	2.86652	−	4.96497i	0.129761	−	0.224753i
$489$		0			0
$490$	−11.2818	+	23.3109i	−0.509660	+	1.05308i
$491$	−34.1469			−1.54103			−0.770513	−	0.637424i	$-0.780000\pi$
$491$	−34.1469			−1.54103			−0.770513	+	0.637424i	$0.780000\pi$
$492$		0			0
$493$	−8.25457	−	14.2973i	−0.371767	−	0.643920i
$494$	−1.19963	−	2.07782i	−0.0539738	−	0.0934854i
$495$		0			0
$496$	6.81089			0.305818
$497$	6.76833	−	12.7762i	0.303601	−	0.573092i
$498$		0			0
$499$	1.14035	−	1.97515i	0.0510493	−	0.0884199i	−0.839372	−	0.543558i	$-0.817077\pi$
$499$	1.14035	−	1.97515i	0.0510493	−	0.0884199i	0.890421	+	0.455138i	$0.150410\pi$
$500$	−6.82072	−	11.8138i	−0.305032	−	0.528331i
$501$		0			0
$502$	6.06182	−	10.4994i	0.270552	−	0.468610i
$503$	13.9890			0.623739			0.311869	−	0.950125i	$-0.399045\pi$
$503$	13.9890			0.623739			0.311869	+	0.950125i	$0.399045\pi$
$504$		0			0
$505$	19.4400			0.865067
$506$	4.64400	−	8.04364i	0.206451	−	0.357583i
$507$		0			0
$508$	1.42835	+	2.47397i	0.0633726	+	0.109765i
$509$	−12.8090	+	22.1859i	−0.567750	+	0.983373i	0.429038	+	0.903287i	$0.358853\pi$
$509$	−12.8090	+	22.1859i	−0.567750	+	0.983373i	−0.996788	+	0.0800859i	$0.974481\pi$
$510$		0			0
$511$	31.9010	−	1.16260i	1.41122	−	0.0514304i
$512$	1.00000			0.0441942
$513$		0			0
$514$	4.10439	+	7.10900i	0.181037	+	0.313565i
$515$	−3.08217	−	5.33848i	−0.135817	−	0.235242i
$516$		0			0
$517$	10.3214			0.453935
$518$	7.34362	−	0.267630i	0.322660	−	0.0117590i
$519$		0			0
$520$	−4.99381	+	8.64953i	−0.218993	+	0.379307i
$521$	−20.9127	−	36.2219i	−0.916203	−	1.58691i	−0.805130	−	0.593099i	$-0.797904\pi$
$521$	−20.9127	−	36.2219i	−0.916203	−	1.58691i	−0.111073	−	0.993812i	$-0.535429\pi$
$522$		0			0
$523$	7.88323	−	13.6542i	0.344710	−	0.597055i	−0.640591	−	0.767882i	$-0.721311\pi$
$523$	7.88323	−	13.6542i	0.344710	−	0.597055i	0.985301	+	0.170827i	$0.0546440\pi$
$524$	0.155687			0.00680122
$525$		0			0
$526$	−5.34617			−0.233104
$527$	22.3942	−	38.7878i	0.975505	−	1.68962i
$528$		0			0
$529$	−8.26942	−	14.3231i	−0.359540	−	0.622742i
$530$	−5.93818	+	10.2852i	−0.257938	+	0.446762i
$531$		0			0
$532$	−1.10074	+	2.07782i	−0.0477233	+	0.0900848i
$533$	11.0989			0.480746
$534$		0			0
$535$	−19.9134	−	34.4911i	−0.860932	−	1.49118i
$536$	4.73236	+	8.19669i	0.204407	+	0.354043i
$537$		0			0
$538$	−18.4844			−0.796918
$539$	4.50433	−	9.30701i	0.194015	−	0.400881i
$540$		0			0
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.0887957	+	0.996050i	$0.528302\pi$
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.818207	+	0.574924i	$0.805031\pi$
$542$	−3.67742	−	6.36947i	−0.157959	−	0.273592i
$543$		0			0
$544$	3.28799	−	5.69497i	0.140971	−	0.244170i
$545$	0.699628			0.0299688
$546$		0			0
$547$	−40.6712			−1.73897			−0.869486	−	0.493957i	$-0.835550\pi$
$547$	−40.6712			−1.73897			−0.869486	+	0.493957i	$0.835550\pi$
$548$	1.70582	−	2.95456i	0.0728689	−	0.126213i
$549$		0			0
$550$	6.41597	+	11.1128i	0.273578	+	0.473851i
$551$	1.11559	−	1.93227i	0.0475259	−	0.0823173i
$552$		0			0
$553$	−16.0956	−	25.6714i	−0.684457	−	1.09166i
$554$	−9.09888			−0.386575
$555$		0			0
$556$	−6.75526	−	11.7005i	−0.286487	−	0.496210i
$557$	6.68794	+	11.5838i	0.283377	+	0.490823i	0.972214	−	0.234093i	$-0.0752119\pi$
$557$	6.68794	+	11.5838i	0.283377	+	0.490823i	−0.688837	+	0.724916i	$0.741879\pi$
$558$		0			0
$559$	−0.0334206			−0.00141354
$560$	9.78180	−	0.356487i	0.413357	−	0.0150643i
$561$		0			0
$562$	6.00433	−	10.3998i	0.253277	−	0.438689i
$563$	16.3807	+	28.3722i	0.690364	+	1.19574i	0.971719	+	0.236141i	$0.0758828\pi$
$563$	16.3807	+	28.3722i	0.690364	+	1.19574i	−0.281355	+	0.959604i	$0.590784\pi$
$564$		0			0
$565$	−25.0901	+	43.4574i	−1.05555	+	1.82827i
$566$	9.84294			0.413729
$567$		0			0
$568$	−5.46472			−0.229295
$569$	8.36398	−	14.4868i	0.350636	−	0.607320i	−0.635725	−	0.771916i	$-0.719299\pi$
$569$	8.36398	−	14.4868i	0.350636	−	0.607320i	0.986361	+	0.164596i	$0.0526321\pi$
$570$		0			0
$571$	13.7367	+	23.7926i	0.574863	+	0.995691i	0.996057	+	0.0887207i	$0.0282778\pi$
$571$	13.7367	+	23.7926i	0.574863	+	0.995691i	−0.421194	+	0.906971i	$0.638389\pi$
$572$	1.99381	−	3.45338i	0.0833654	−	0.144393i
$573$		0			0
$574$	−5.77816	−	9.21576i	−0.241176	−	0.384659i
$575$	54.6253			2.27803
$576$		0			0
$577$	1.41714	+	2.45455i	0.0589962	+	0.102184i	0.894015	−	0.448037i	$-0.147877\pi$
$577$	1.41714	+	2.45455i	0.0589962	+	0.102184i	−0.835019	+	0.550221i	$0.814543\pi$
$578$	−13.1218	−	22.7276i	−0.545794	−	0.945343i
$579$		0			0
$580$	−9.28799			−0.385663
$581$	5.54511	−	10.4672i	0.230050	−	0.434253i
$582$		0			0
$583$	2.37085	−	4.10644i	0.0981908	−	0.170071i
$584$	−6.03273	−	10.4490i	−0.249636	−	0.432383i
$585$		0			0
$586$	10.7101	−	18.5505i	0.442432	−	0.766315i
$587$	4.69591			0.193821			0.0969105	−	0.995293i	$-0.469104\pi$
$587$	4.69591			0.193821			0.0969105	+	0.995293i	$0.469104\pi$
$588$		0			0
$589$	6.05308			0.249413
$590$	−12.7818	+	22.1387i	−0.526218	+	0.911437i
$591$		0			0
$592$	−1.38874	−	2.40536i	−0.0570767	−	0.0988597i
$593$	0.636024	−	1.10163i	0.0261184	−	0.0452383i	−0.852671	−	0.522449i	$-0.825019\pi$
$593$	0.636024	−	1.10163i	0.0261184	−	0.0452383i	0.878789	+	0.477210i	$0.158352\pi$
$594$		0			0
$595$	30.1323	−	56.8792i	1.23530	−	2.33182i
$596$	0.333792			0.0136727
$597$		0			0
$598$	−8.48762	−	14.7010i	−0.347085	−	0.601168i
$599$	−21.9258	−	37.9766i	−0.895864	−	1.55168i	−0.832732	−	0.553676i	$-0.813224\pi$
$599$	−21.9258	−	37.9766i	−0.895864	−	1.55168i	−0.0631320	−	0.998005i	$-0.520109\pi$
$600$		0			0
$601$	13.4327			0.547930			0.273965	−	0.961740i	$-0.411665\pi$
$601$	13.4327			0.547930			0.273965	+	0.961740i	$0.411665\pi$
$602$	0.0173990	+	0.0277502i	0.000709131	+	0.00113101i
$603$		0			0
$604$	9.95489	−	17.2424i	0.405059	−	0.701582i
$605$	16.3120	+	28.2532i	0.663177	+	1.14866i
$606$		0			0
$607$	2.29232	−	3.97042i	0.0930425	−	0.161154i	−0.815747	−	0.578408i	$-0.803674\pi$
$607$	2.29232	−	3.97042i	0.0930425	−	0.161154i	0.908790	+	0.417254i	$0.137007\pi$
$608$	0.888736			0.0360430
$609$		0			0
$610$	−21.2101			−0.858774
$611$	9.43199	−	16.3367i	0.381577	−	0.660911i
$612$		0			0
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	0.551695	−	0.834046i	$-0.313981\pi$
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	−0.998152	+	0.0607587i	$0.980648\pi$
$614$	2.84362	−	4.92530i	0.114759	−	0.198769i
$615$		0			0
$616$	−3.90545	+	0.142330i	−0.157355	+	0.00573463i
$617$	−12.0087			−0.483450			−0.241725	−	0.970345i	$-0.577713\pi$
$617$	−12.0087			−0.483450			−0.241725	+	0.970345i	$0.577713\pi$
$618$		0			0
$619$	8.78180	+	15.2105i	0.352970	+	0.611363i	0.986768	−	0.162136i	$-0.0518383\pi$
$619$	8.78180	+	15.2105i	0.352970	+	0.611363i	−0.633798	+	0.773499i	$0.718505\pi$
$620$	−12.5989	−	21.8219i	−0.505983	−	0.876389i
$621$		0			0
$622$	−11.7207			−0.469956
$623$	−12.4752	−	19.8971i	−0.499810	−	0.797162i
$624$		0			0
$625$	−3.51602	+	6.08993i	−0.140641	+	0.243597i
$626$	13.3869	+	23.1868i	0.535047	+	0.926729i
$627$		0			0
$628$	3.48143	−	6.03001i	0.138924	−	0.240624i
$629$	−18.2646			−0.728258
$630$		0			0
$631$	−44.9381			−1.78896			−0.894479	−	0.447110i	$-0.852453\pi$
$631$	−44.9381			−1.78896			−0.894479	+	0.447110i	$0.852453\pi$
$632$	−5.72617	+	9.91802i	−0.227775	+	0.394518i
$633$		0			0
$634$	−0.951246	−	1.64761i	−0.0377788	−	0.0654348i
$635$	5.28435	−	9.15276i	0.209703	−	0.363216i
$636$		0			0
$637$	−10.6149	−	15.6344i	−0.420578	−	0.619459i
$638$	3.70829			0.146813
$639$		0			0
$640$	−1.84981	−	3.20397i	−0.0731203	−	0.126648i
$641$	14.4920	+	25.1008i	0.572398	+	0.991422i	0.996319	+	0.0857228i	$0.0273199\pi$
$641$	14.4920	+	25.1008i	0.572398	+	0.991422i	−0.423921	+	0.905699i	$0.639347\pi$
$642$		0			0
$643$	−12.0617			−0.475669			−0.237834	−	0.971306i	$-0.576438\pi$
$643$	−12.0617			−0.475669			−0.237834	+	0.971306i	$0.576438\pi$
$644$	−7.78799	+	14.7010i	−0.306890	+	0.579300i
$645$		0			0
$646$	2.92216	−	5.06132i	0.114971	−	0.199135i
$647$	18.8825	+	32.7055i	0.742349	+	1.28579i	0.951423	+	0.307887i	$0.0996219\pi$
$647$	18.8825	+	32.7055i	0.742349	+	1.28579i	−0.209073	+	0.977900i	$0.567045\pi$
$648$		0			0
$649$	5.10322	−	8.83903i	0.200319	−	0.346962i
$650$	23.4523			0.919876
$651$		0			0
$652$	−8.07413			−0.316207
$653$	−18.7040	+	32.3962i	−0.731942	+	1.26776i	0.224109	+	0.974564i	$0.428053\pi$
$653$	−18.7040	+	32.3962i	−0.731942	+	1.26776i	−0.956052	+	0.293198i	$0.905281\pi$
$654$		0			0
$655$	−0.287992	−	0.498817i	−0.0112528	−	0.0194904i
$656$	−2.05563	+	3.56046i	−0.0802589	+	0.139013i
$657$		0			0
$658$	−18.4752	+	0.673310i	−0.720240	+	0.0262484i
$659$	−29.8713			−1.16362			−0.581810	−	0.813325i	$-0.697655\pi$
$659$	−29.8713			−1.16362			−0.581810	+	0.813325i	$0.697655\pi$
$660$		0			0
$661$	−2.80401	−	4.85669i	−0.109063	−	0.188904i	0.806328	−	0.591469i	$-0.201452\pi$
$661$	−2.80401	−	4.85669i	−0.109063	−	0.188904i	−0.915391	+	0.402566i	$0.868119\pi$
$662$	−2.78366	−	4.82144i	−0.108190	−	0.187391i
$663$		0			0
$664$	−4.47710			−0.173745
$665$	8.69344	−	0.316823i	0.337117	−	0.0122859i
$666$		0			0
$667$	7.89307	−	13.6712i	0.305621	−	0.529351i
$668$	9.74288	+	16.8752i	0.376963	+	0.652920i
$669$		0			0
$670$	17.5080	−	30.3247i	0.676392	−	1.17155i
$671$	8.46829			0.326915
$672$		0			0
$673$	9.44506			0.364080			0.182040	−	0.983291i	$-0.441730\pi$
$673$	9.44506			0.364080			0.182040	+	0.983291i	$0.441730\pi$
$674$	−16.8869	+	29.2489i	−0.650458	+	1.12663i
$675$		0			0
$676$	2.85600	+	4.94674i	0.109846	+	0.190259i
$677$	−5.53087	+	9.57975i	−0.212569	+	0.368180i	−0.952518	−	0.304483i	$-0.901516\pi$
$677$	−5.53087	+	9.57975i	−0.212569	+	0.368180i	0.739949	+	0.672663i	$0.234850\pi$
$678$		0			0
$679$	−16.3200	+	30.8065i	−0.626305	+	1.18224i
$680$	−24.3287			−0.932963
$681$		0			0
$682$	5.03018	+	8.71253i	0.192616	+	0.333620i
$683$	−4.41961	−	7.65499i	−0.169112	−	0.292910i	0.768996	−	0.639253i	$-0.220757\pi$
$683$	−4.41961	−	7.65499i	−0.169112	−	0.292910i	−0.938108	+	0.346343i	$0.887423\pi$
$684$		0			0
$685$	−12.6218			−0.482254
$686$	−7.45558	+	16.9533i	−0.284655	+	0.647280i
$687$		0			0
$688$	0.00618986	−	0.0107211i	0.000235986	−	0.000408740i
$689$	−4.33310	−	7.50516i	−0.165078	−	0.285924i
$690$		0			0
$691$	−12.5309	+	21.7041i	−0.476697	+	0.825663i	−0.999643	−	0.0267023i	$-0.991499\pi$
$691$	−12.5309	+	21.7041i	−0.476697	+	0.825663i	0.522947	+	0.852365i	$0.324833\pi$
$692$	22.5636			0.857740
$693$		0			0
$694$	−30.4065			−1.15422
$695$	−24.9920	+	43.2873i	−0.947999	+	1.64198i
$696$		0			0
$697$	13.5178	+	23.4135i	0.512023	+	0.886850i
$698$	−6.29782	+	10.9082i	−0.238376	+	0.412880i
$699$		0			0
$700$	−12.2095	−	19.4732i	−0.461474	−	0.736019i
$701$	−43.4858			−1.64243			−0.821217	−	0.570616i	$-0.806705\pi$
$701$	−43.4858			−1.64243			−0.821217	+	0.570616i	$0.806705\pi$
$702$		0			0
$703$	−1.23422	−	2.13773i	−0.0465495	−	0.0806260i
$704$	0.738550	+	1.27921i	0.0278351	+	0.0482119i
$705$		0			0
$706$	−7.53156			−0.283454
$707$	13.8931	−	0.506318i	0.522503	−	0.0190420i
$708$		0			0
$709$	11.3702	−	19.6937i	0.427016	−	0.739613i	−0.569591	−	0.821928i	$-0.692898\pi$
$709$	11.3702	−	19.6937i	0.427016	−	0.739613i	0.996606	+	0.0823158i	$0.0262316\pi$
$710$	10.1087	+	17.5088i	0.379373	+	0.657094i
$711$		0			0
$712$	−4.43818	+	7.68715i	−0.166328	+	0.288088i
$713$	42.8268			1.60388
$714$		0			0
$715$	−14.7527			−0.551720
$716$	0.166896	−	0.289073i	0.00623721	−	0.0108032i
$717$		0			0
$718$	−3.44801	−	5.97213i	−0.128679	−	0.222878i
$719$	6.06182	−	10.4994i	0.226068	−	0.391561i	−0.730571	−	0.682836i	$-0.760746\pi$
$719$	6.06182	−	10.4994i	0.226068	−	0.391561i	0.956639	+	0.291275i	$0.0940796\pi$
$720$		0			0
$721$	−2.34176	−	3.73495i	−0.0872119	−	0.139097i
$722$	−18.2101			−0.677712
$723$		0			0
$724$	−11.6211	−	20.1283i	−0.431895	−	0.748063i
$725$	10.9048	+	18.8876i	0.404993	+	0.701468i
$726$		0			0
$727$	−46.1817			−1.71278			−0.856392	−	0.516327i	$-0.827299\pi$
$727$	−46.1817			−1.71278			−0.856392	+	0.516327i	$0.827299\pi$
$728$	−3.34362	+	6.31159i	−0.123923	+	0.233923i
$729$		0			0
$730$	−22.3189	+	38.6574i	−0.826058	+	1.43077i
$731$	−0.0407044	−	0.0705021i	−0.00150551	−	0.00260761i
$732$		0			0
$733$	18.0149	−	31.2026i	0.665394	−	1.15250i	−0.313785	−	0.949494i	$-0.601597\pi$
$733$	18.0149	−	31.2026i	0.665394	−	1.15250i	0.979178	−	0.203002i	$-0.0650696\pi$
$734$	23.1236			0.853509
$735$		0			0
$736$	6.28799			0.231778
$737$	−6.99017	+	12.1073i	−0.257486	+	0.445979i
$738$		0			0
$739$	23.2119	+	40.2042i	0.853865	+	1.47894i	0.877694	+	0.479221i	$0.159081\pi$
$739$	23.2119	+	40.2042i	0.853865	+	1.47894i	−0.0238296	+	0.999716i	$0.507586\pi$
$740$	−5.13781	+	8.89894i	−0.188870	+	0.327132i
$741$		0			0
$742$	−3.97593	+	7.50516i	−0.145961	+	0.275523i
$743$	−1.19777			−0.0439419			−0.0219709	−	0.999759i	$-0.506994\pi$
$743$	−1.19777			−0.0439419			−0.0219709	+	0.999759i	$0.506994\pi$
$744$		0			0
$745$	−0.617454	−	1.06946i	−0.0226218	−	0.0391820i
$746$	−14.5822	−	25.2571i	−0.533891	−	0.924727i
$747$		0			0
$748$	9.71339			0.355157
$749$	−15.1298	−	24.1309i	−0.552829	−	0.881724i
$750$		0			0
$751$	−24.0600	+	41.6731i	−0.877961	+	1.52067i	−0.0243853	+	0.999703i	$0.507763\pi$
$751$	−24.0600	+	41.6731i	−0.877961	+	1.52067i	−0.853575	+	0.520970i	$0.825570\pi$
$752$	3.49381	+	6.05146i	0.127406	+	0.220674i
$753$		0			0
$754$	3.38874	−	5.86946i	0.123410	−	0.213753i
$755$	−73.6588			−2.68072
$756$		0			0
$757$	49.6006			1.80276			0.901382	−	0.433025i	$-0.142554\pi$
$757$	49.6006			1.80276			0.901382	+	0.433025i	$0.142554\pi$
$758$	6.78111	−	11.7452i	0.246301	−	0.426606i
$759$		0			0
$760$	−1.64400	−	2.84748i	−0.0596340	−	0.103289i
$761$	18.7701	−	32.5108i	0.680416	−	1.17852i	−0.294438	−	0.955671i	$-0.595132\pi$
$761$	18.7701	−	32.5108i	0.680416	−	1.17852i	0.974854	−	0.222845i	$-0.0715342\pi$
$762$		0			0
$763$	0.500000	−	0.0182220i	0.0181012	−	0.000659679i
$764$	−16.3214			−0.590488
$765$		0			0
$766$	1.41783	+	2.45575i	0.0512281	+	0.0887297i
$767$	−9.32691	−	16.1547i	−0.336775	−	0.583312i
$768$		0			0
$769$	26.9184			0.970704			0.485352	−	0.874319i	$-0.338692\pi$
$769$	26.9184			0.970704			0.485352	+	0.874319i	$0.338692\pi$
$770$	7.68037	+	12.2497i	0.276781	+	0.441447i
$771$		0			0
$772$	7.16071	−	12.4027i	0.257719	−	0.446383i
$773$	25.1130	+	43.4971i	0.903254	+	1.56448i	0.823245	+	0.567687i	$0.192162\pi$
$773$	25.1130	+	43.4971i	0.903254	+	1.56448i	0.0800089	+	0.996794i	$0.474505\pi$
$774$		0			0
$775$	−29.5840	+	51.2409i	−1.06269	+	1.84063i
$776$	13.1767			0.473017
$777$		0			0
$778$	−18.6080			−0.667130
$779$	−1.82691	+	3.16431i	−0.0654560	+	0.113373i
$780$		0			0
$781$	−4.03597	−	6.99050i	−0.144418	−	0.250140i
$782$	20.6749	−	35.8099i	0.739332	−	1.28056i
$783$		0			0
$784$	6.98143	−	0.509538i	0.249337	−	0.0181978i
$785$	−25.7600			−0.919414
$786$		0			0
$787$	0.829462	+	1.43667i	0.0295671	+	0.0512118i	0.880430	−	0.474176i	$-0.157254\pi$
$787$	0.829462	+	1.43667i	0.0295671	+	0.0512118i	−0.850863	+	0.525387i	$0.823920\pi$
$788$	−1.21201	−	2.09926i	−0.0431760	−	0.0747830i
$789$		0			0
$790$	42.3694			1.50744
$791$	−16.7992	+	31.7110i	−0.597311	+	1.12751i
$792$		0			0
$793$	7.73855	−	13.4036i	0.274804	−	0.475974i
$794$	−10.2880	−	17.8193i	−0.365107	−	0.632384i
$795$		0			0
$796$	−3.05563	+	5.29251i	−0.108304	+	0.187588i
$797$	30.7403			1.08888			0.544439	−	0.838800i	$-0.316742\pi$
$797$	30.7403			1.08888			0.544439	+	0.838800i	$0.316742\pi$
$798$		0			0
$799$	45.9505			1.62561
$800$	−4.34362	+	7.52338i	−0.153570	+	0.265992i
$801$		0			0
$802$	3.37704	+	5.84921i	0.119248	+	0.206543i
$803$	8.91095	−	15.4342i	0.314461	−	0.544662i
$804$		0			0
$805$	61.5079	−	2.24159i	2.16787	−	0.0790056i
$806$	18.3869			0.647650
$807$		0			0
$808$	−2.62729	−	4.55059i	−0.0924276	−	0.160089i
$809$	−1.44251	−	2.49850i	−0.0507159	−	0.0878425i	0.839553	−	0.543278i	$-0.182817\pi$
$809$	−1.44251	−	2.49850i	−0.0507159	−	0.0878425i	−0.890269	+	0.455435i	$0.849484\pi$
$810$		0			0
$811$	28.5461			1.00239			0.501195	−	0.865334i	$-0.332894\pi$
$811$	28.5461			1.00239			0.501195	+	0.865334i	$0.332894\pi$
$812$	−6.63781	+	0.241908i	−0.232941	+	0.00848930i
$813$		0			0
$814$	2.05130	−	3.55296i	0.0718981	−	0.124531i
$815$	14.9356	+	25.8693i	0.523172	+	0.906161i
$816$		0			0
$817$	0.00550115	−	0.00952827i	0.000192461	−	0.000333352i
$818$	15.3214			0.535701
$819$		0			0
$820$	15.2101			0.531161
$821$	−3.98329	+	6.89926i	−0.139018	+	0.240786i	−0.927125	−	0.374752i	$-0.877728\pi$
$821$	−3.98329	+	6.89926i	−0.139018	+	0.240786i	0.788107	+	0.615538i	$0.211061\pi$
$822$		0			0
$823$	−20.2731	−	35.1140i	−0.706675	−	1.22400i	−0.966084	−	0.258229i	$-0.916861\pi$
$823$	−20.2731	−	35.1140i	−0.706675	−	1.22400i	0.259409	−	0.965768i	$-0.416472\pi$
$824$	−0.833104	+	1.44298i	−0.0290225	+	0.0502685i
$825$		0			0
$826$	−8.55810	+	16.1547i	−0.297775	+	0.562094i
$827$	1.22115			0.0424636			0.0212318	−	0.999775i	$-0.493241\pi$
$827$	1.22115			0.0424636			0.0212318	+	0.999775i	$0.493241\pi$
$828$		0			0
$829$	−7.07530	−	12.2548i	−0.245735	−	0.425626i	0.716603	−	0.697481i	$-0.245696\pi$
$829$	−7.07530	−	12.2548i	−0.245735	−	0.425626i	−0.962338	+	0.271856i	$0.912363\pi$
$830$	8.28180	+	14.3445i	0.287466	+	0.497905i
$831$		0			0
$832$	2.69963			0.0935928
$833$	20.0531	−	41.4344i	0.694798	−	1.43562i
$834$		0			0
$835$	36.0450	−	62.4318i	1.24739	−	2.16054i
$836$	0.656376	+	1.13688i	0.0227012	+	0.0393197i
$837$		0			0
$838$	−4.32141	+	7.48491i	−0.149281	+	0.258562i
$839$	−2.39197			−0.0825801			−0.0412900	−	0.999147i	$-0.513147\pi$
$839$	−2.39197			−0.0825801			−0.0412900	+	0.999147i	$0.513147\pi$
$840$		0			0
$841$	−22.6973			−0.782665
$842$	18.5636	−	32.1531i	0.639744	−	1.10807i
$843$		0			0
$844$	5.72253	+	9.91171i	0.196978	+	0.341175i
$845$	10.5662	−	18.3011i	0.363487	−	0.629577i
$846$		0			0
$847$	12.3935	+	19.7667i	0.425845	+	0.679193i
$848$	3.21015			0.110237
$849$		0			0
$850$	28.5636	+	49.4736i	0.979724	+	1.69693i
$851$	−8.73236	−	15.1249i	−0.299341	−	0.518475i
$852$		0			0
$853$	16.6800			0.571111			0.285556	−	0.958362i	$-0.407822\pi$
$853$	16.6800			0.571111			0.285556	+	0.958362i	$0.407822\pi$
$854$	−15.1582	+	0.552423i	−0.518702	+	0.0189035i
$855$		0			0
$856$	−5.38255	+	9.32284i	−0.183972	+	0.318648i
$857$	6.92580	+	11.9958i	0.236581	+	0.409770i	0.959731	−	0.280921i	$-0.0906399\pi$
$857$	6.92580	+	11.9958i	0.236581	+	0.409770i	−0.723150	+	0.690691i	$0.757307\pi$
$858$		0			0
$859$	−24.2472	+	41.9974i	−0.827304	+	1.43293i	0.0728414	+	0.997344i	$0.476793\pi$
$859$	−24.2472	+	41.9974i	−0.827304	+	1.43293i	−0.900146	+	0.435589i	$0.856540\pi$
$860$	−0.0458003			−0.00156178
$861$		0			0
$862$	9.42030			0.320857
$863$	2.96541	−	5.13624i	0.100944	−	0.174840i	−0.811130	−	0.584866i	$-0.801147\pi$
$863$	2.96541	−	5.13624i	0.100944	−	0.174840i	0.912074	+	0.410026i	$0.134480\pi$
$864$		0			0
$865$	−41.7385	−	72.2932i	−1.41915	−	2.45804i
$866$	0.104386	−	0.180801i	0.00354717	−	0.00614387i
$867$		0			0
$868$	−9.57234	−	15.2672i	−0.324906	−	0.518203i
$869$	−16.9163			−0.573844
$870$		0			0
$871$	12.7756	+	22.1280i	0.432885	+	0.749779i
$872$	−0.0945538	−	0.163772i	−0.00320200	−	0.00554602i
$873$		0			0
$874$	5.58836			0.189029
$875$	−16.8956	+	31.8930i	−0.571176	+	1.07818i
$876$		0			0
$877$	−1.96472	+	3.40300i	−0.0663439	+	0.114911i	−0.897289	−	0.441443i	$-0.854467\pi$
$877$	−1.96472	+	3.40300i	−0.0663439	+	0.114911i	0.830945	+	0.556354i	$0.187800\pi$
$878$	4.98398	+	8.63250i	0.168201	+	0.291333i
$879$		0			0
$880$	2.73236	−	4.73259i	0.0921078	−	0.159535i
$881$	37.6552			1.26864			0.634318	−	0.773072i	$-0.281281\pi$
$881$	37.6552			1.26864			0.634318	+	0.773072i	$0.281281\pi$
$882$		0			0
$883$	−53.2334			−1.79145			−0.895723	−	0.444613i	$-0.853341\pi$
$883$	−53.2334			−1.79145			−0.895723	+	0.444613i	$0.853341\pi$
$884$	8.87636	−	15.3743i	0.298544	−	0.517094i
$885$		0			0
$886$	7.84981	+	13.5963i	0.263720	+	0.456776i
$887$	18.4938	−	32.0322i	0.620961	−	1.07554i	−0.368346	−	0.929689i	$-0.620076\pi$
$887$	18.4938	−	32.0322i	0.620961	−	1.07554i	0.989307	−	0.145848i	$-0.0465910\pi$
$888$		0			0
$889$	3.53816	−	6.67879i	0.118666	−	0.224000i
$890$	32.8392			1.10077
$891$		0			0
$892$	−3.61126	−	6.25489i	−0.120914	−	0.209429i
$893$	3.10507	+	5.37815i	0.103907	+	0.179973i
$894$		0			0
$895$	−1.23491			−0.0412784
$896$	−1.40545	−	2.24159i	−0.0469527	−	0.0748862i
$897$		0			0
$898$	−16.8127	+	29.1204i	−0.561046	+	0.971761i
$899$	8.54944	+	14.8081i	0.285140	+	0.493877i
$900$		0			0
$901$	10.5549	−	18.2817i	0.351636	−	0.609052i
$902$	−6.07275			−0.202200
$903$		0			0
$904$	13.5636			0.451119
$905$	−42.9937	+	74.4673i	−1.42916	+	2.47538i
$906$		0			0
$907$	19.5080	+	33.7888i	0.647752	+	1.12194i	0.983659	+	0.180044i	$0.0576239\pi$
$907$	19.5080	+	33.7888i	0.647752	+	1.12194i	−0.335907	+	0.941895i	$0.609043\pi$
$908$	−6.82760	+	11.8258i	−0.226582	+	0.392451i
$909$		0			0
$910$	26.4072	−	0.962383i	0.875391	−	0.0319027i
$911$	25.6181			0.848764			0.424382	−	0.905483i	$-0.360491\pi$
$911$	25.6181			0.848764			0.424382	+	0.905483i	$0.360491\pi$
$912$		0			0
$913$	−3.30656	−	5.72713i	−0.109431	−	0.189540i
$914$	−16.3541	−	28.3262i	−0.540947	−	0.936948i
$915$		0			0
$916$	17.3745			0.574070
$917$	−0.218810	−	0.348986i	−0.00722574	−	0.0115245i
$918$		0			0
$919$	10.3367	−	17.9038i	0.340978	−	0.590591i	−0.643637	−	0.765331i	$-0.722575\pi$
$919$	10.3367	−	17.9038i	0.340978	−	0.590591i	0.984615	+	0.174740i	$0.0559086\pi$
$920$	−11.6316	−	20.1466i	−0.383483	−	0.664212i
$921$		0			0
$922$	−2.07165	+	3.58821i	−0.0682263	+	0.118171i
$923$	−14.7527			−0.485591
$924$		0			0
$925$	24.1286			0.793343
$926$	−8.34176	+	14.4484i	−0.274127	+	0.474803i
$927$		0			0
$928$	1.25526	+	2.17417i	0.0412059	+	0.0713708i
$929$	1.87017	−	3.23922i	0.0613582	−	0.106275i	−0.833715	−	0.552196i	$-0.813790\pi$
$929$	1.87017	−	3.23922i	0.0613582	−	0.106275i	0.895073	+	0.445920i	$0.147123\pi$
$930$		0			0
$931$	6.20465	−	0.452845i	0.203349	−	0.0148414i
$932$	−15.2422			−0.499275
$933$		0			0
$934$	14.9585	+	25.9089i	0.489458	+	0.847766i
$935$	−17.9680	−	31.1214i	−0.587615	−	1.01778i
$936$		0			0
$937$	−27.1345			−0.886445			−0.443223	−	0.896412i	$-0.646165\pi$
$937$	−27.1345			−0.886445			−0.443223	+	0.896412i	$0.646165\pi$
$938$	11.7225	−	22.1280i	0.382754	−	0.722505i
$939$		0			0
$940$	12.9258	−	22.3881i	0.421593	−	0.730221i
$941$	−3.16435	−	5.48081i	−0.103155	−	0.178669i	0.809828	−	0.586667i	$-0.199560\pi$
$941$	−3.16435	−	5.48081i	−0.103155	−	0.178669i	−0.912983	+	0.407998i	$0.866227\pi$
$942$		0			0
$943$	−12.9258	+	22.3881i	−0.420922	+	0.729058i
$944$	6.90978			0.224894
$945$		0			0
$946$	0.0182861			0.000594531
$947$	−15.6396	+	27.0886i	−0.508218	+	0.880260i	0.491736	+	0.870744i	$0.336362\pi$
$947$	−15.6396	+	27.0886i	−0.508218	+	0.880260i	−0.999955	+	0.00951587i	$0.996971\pi$
$948$		0			0
$949$	−16.2861	−	28.2084i	−0.528670	−	0.915684i
$950$	−3.86033	+	6.68630i	−0.125246	+	0.216932i
$951$		0			0
$952$	−17.3869	+	0.633646i	−0.563512	+	0.0205366i
$953$	4.28937			0.138946			0.0694732	−	0.997584i	$-0.477868\pi$
$953$	4.28937			0.138946			0.0694732	+	0.997584i	$0.477868\pi$
$954$		0			0
$955$	30.1916	+	52.2933i	0.976977	+	1.69217i
$956$	9.47524	+	16.4116i	0.306451	+	0.530789i
$957$		0			0
$958$	−2.95930			−0.0956105
$959$	−9.02035	+	0.328737i	−0.291282	+	0.0106155i
$960$		0			0
$961$	−7.69413	+	13.3266i	−0.248198	+	0.429891i
$962$	−3.74907	−	6.49358i	−0.120875	−	0.209361i
$963$		0			0
$964$	12.2527	−	21.2223i	0.394633	−	0.683525i
$965$	−52.9839			−1.70561
$966$		0			0
$967$	15.1840			0.488285			0.244142	−	0.969739i	$-0.421494\pi$
$967$	15.1840			0.488285			0.244142	+	0.969739i	$0.421494\pi$
$968$	4.40909	−	7.63676i	0.141713	−	0.245455i
$969$		0			0
$970$	−24.3745	−	42.2179i	−0.782618	−	1.35553i
$971$	1.62364	−	2.81223i	0.0521052	−	0.0902489i	−0.838796	−	0.544445i	$-0.816740\pi$
$971$	1.62364	−	2.81223i	0.0521052	−	0.0902489i	0.890902	+	0.454196i	$0.150074\pi$
$972$		0			0
$973$	−16.7335	+	31.5869i	−0.536450	+	1.01263i
$974$	28.0617			0.899156
$975$		0			0
$976$	2.86652	+	4.96497i	0.0917552	+	0.158925i
$977$	−7.77197	−	13.4614i	−0.248647	−	0.430670i	0.714503	−	0.699632i	$-0.246653\pi$
$977$	−7.77197	−	13.4614i	−0.248647	−	0.430670i	−0.963151	+	0.268962i	$0.913319\pi$
$978$		0			0
$979$	−13.1113			−0.419038
$980$	−14.5469	−	21.4258i	−0.464683	−	0.684421i
$981$		0			0
$982$	17.0734	−	29.5721i	0.544835	−	0.943682i
$983$	−6.19158	−	10.7241i	−0.197481	−	0.342047i	0.750230	−	0.661177i	$-0.229943\pi$
$983$	−6.19158	−	10.7241i	−0.197481	−	0.342047i	−0.947711	+	0.319130i	$0.896609\pi$
$984$		0			0
$985$	−4.48398	+	7.76648i	−0.142871	+	0.247461i
$986$	16.5091			0.525758
$987$		0			0
$988$	2.39926			0.0763305
$989$	0.0389218	−	0.0674145i	0.00123764	−	0.00214366i
$990$		0			0
$991$	−3.32760	−	5.76358i	−0.105705	−	0.183086i	0.808321	−	0.588742i	$-0.200377\pi$
$991$	−3.32760	−	5.76358i	−0.105705	−	0.183086i	−0.914026	+	0.405656i	$0.867043\pi$
$992$	−3.40545	+	5.89841i	−0.108123	+	0.187275i
$993$		0			0
$994$	7.68037	+	12.2497i	0.243607	+	0.388536i
$995$	22.6094			0.716766
$996$		0			0
$997$	−2.40104	−	4.15872i	−0.0760417	−	0.131708i	0.825497	−	0.564406i	$-0.190895\pi$
$997$	−2.40104	−	4.15872i	−0.0760417	−	0.131708i	−0.901539	+	0.432698i	$0.857562\pi$
$998$	1.14035	+	1.97515i	0.0360973	+	0.0625223i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.g.k.163.1		6
3.2	odd	2		1134.2.g.n.163.3		6
7.2	even	3		7938.2.a.cb.1.3		3
7.4	even	3	inner	1134.2.g.k.487.1		6
7.5	odd	6		7938.2.a.by.1.1		3
9.2	odd	6		378.2.e.c.37.3		6
9.4	even	3		126.2.h.c.79.1	yes	6
9.5	odd	6		378.2.h.d.289.1		6
9.7	even	3		126.2.e.d.121.1	yes	6
21.2	odd	6		7938.2.a.bu.1.1		3
21.5	even	6		7938.2.a.bx.1.3		3
21.11	odd	6		1134.2.g.n.487.3		6
36.7	odd	6		1008.2.q.h.625.3		6
36.11	even	6		3024.2.q.h.2305.3		6
36.23	even	6		3024.2.t.g.289.1		6
36.31	odd	6		1008.2.t.g.961.3		6
63.2	odd	6		2646.2.f.o.1765.3		6
63.4	even	3		126.2.e.d.25.1	✓	6
63.5	even	6		2646.2.f.n.883.1		6
63.11	odd	6		378.2.h.d.361.1		6
63.13	odd	6		882.2.h.o.79.3		6
63.16	even	3		882.2.f.l.589.3		6
63.20	even	6		2646.2.e.o.1549.1		6
63.23	odd	6		2646.2.f.o.883.3		6
63.25	even	3		126.2.h.c.67.1	yes	6
63.31	odd	6		882.2.e.p.655.3		6
63.32	odd	6		378.2.e.c.235.3		6
63.34	odd	6		882.2.e.p.373.3		6
63.38	even	6		2646.2.h.p.361.3		6
63.40	odd	6		882.2.f.m.295.1		6
63.41	even	6		2646.2.h.p.667.3		6
63.47	even	6		2646.2.f.n.1765.1		6
63.52	odd	6		882.2.h.o.67.3		6
63.58	even	3		882.2.f.l.295.3		6
63.59	even	6		2646.2.e.o.2125.1		6
63.61	odd	6		882.2.f.m.589.1		6
252.11	even	6		3024.2.t.g.1873.1		6
252.67	odd	6		1008.2.q.h.529.3		6
252.95	even	6		3024.2.q.h.2881.3		6
252.151	odd	6		1008.2.t.g.193.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.1	✓	6	63.4	even	3
126.2.e.d.121.1	yes	6	9.7	even	3
126.2.h.c.67.1	yes	6	63.25	even	3
126.2.h.c.79.1	yes	6	9.4	even	3
378.2.e.c.37.3		6	9.2	odd	6
378.2.e.c.235.3		6	63.32	odd	6
378.2.h.d.289.1		6	9.5	odd	6
378.2.h.d.361.1		6	63.11	odd	6
882.2.e.p.373.3		6	63.34	odd	6
882.2.e.p.655.3		6	63.31	odd	6
882.2.f.l.295.3		6	63.58	even	3
882.2.f.l.589.3		6	63.16	even	3
882.2.f.m.295.1		6	63.40	odd	6
882.2.f.m.589.1		6	63.61	odd	6
882.2.h.o.67.3		6	63.52	odd	6
882.2.h.o.79.3		6	63.13	odd	6
1008.2.q.h.529.3		6	252.67	odd	6
1008.2.q.h.625.3		6	36.7	odd	6
1008.2.t.g.193.3		6	252.151	odd	6
1008.2.t.g.961.3		6	36.31	odd	6
1134.2.g.k.163.1		6	1.1	even	1	trivial
1134.2.g.k.487.1		6	7.4	even	3	inner
1134.2.g.n.163.3		6	3.2	odd	2
1134.2.g.n.487.3		6	21.11	odd	6
2646.2.e.o.1549.1		6	63.20	even	6
2646.2.e.o.2125.1		6	63.59	even	6
2646.2.f.n.883.1		6	63.5	even	6
2646.2.f.n.1765.1		6	63.47	even	6
2646.2.f.o.883.3		6	63.23	odd	6
2646.2.f.o.1765.3		6	63.2	odd	6
2646.2.h.p.361.3		6	63.38	even	6
2646.2.h.p.667.3		6	63.41	even	6
3024.2.q.h.2305.3		6	36.11	even	6
3024.2.q.h.2881.3		6	252.95	even	6
3024.2.t.g.289.1		6	36.23	even	6
3024.2.t.g.1873.1		6	252.11	even	6
7938.2.a.bu.1.1		3	21.2	odd	6
7938.2.a.bx.1.3		3	21.5	even	6
7938.2.a.by.1.1		3	7.5	odd	6
7938.2.a.cb.1.3		3	7.2	even	3

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.84981 + 3.20397i) q^{5} +(-1.23855 + 2.33795i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.84981 + 3.20397i) q^{5} +(-1.23855 + 2.33795i) q^{7} +1.00000 q^{8} +(-1.84981 - 3.20397i) q^{10} +(0.738550 + 1.27921i) q^{11} +2.69963 q^{13} +(-1.40545 - 2.24159i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.28799 + 5.69497i) q^{17} +(-0.444368 + 0.769668i) q^{19} +3.69963 q^{20} -1.47710 q^{22} +(-3.14400 + 5.44556i) q^{23} +(-4.34362 - 7.52338i) q^{25} +(-1.34981 + 2.33795i) q^{26} +(2.64400 - 0.0963576i) q^{28} -2.51052 q^{29} +(-3.40545 - 5.89841i) q^{31} +(-0.500000 - 0.866025i) q^{32} -6.57598 q^{34} +(-5.19963 - 8.29305i) q^{35} +(-1.38874 + 2.40536i) q^{37} +(-0.444368 - 0.769668i) q^{38} +(-1.84981 + 3.20397i) q^{40} +4.11126 q^{41} -0.0123797 q^{43} +(0.738550 - 1.27921i) q^{44} +(-3.14400 - 5.44556i) q^{46} +(3.49381 - 6.05146i) q^{47} +(-3.93199 - 5.79133i) q^{49} +8.68725 q^{50} +(-1.34981 - 2.33795i) q^{52} +(-1.60507 - 2.78007i) q^{53} -5.46472 q^{55} +(-1.23855 + 2.33795i) q^{56} +(1.25526 - 2.17417i) q^{58} +(-3.45489 - 5.98404i) q^{59} +(2.86652 - 4.96497i) q^{61} +6.81089 q^{62} +1.00000 q^{64} +(-4.99381 + 8.64953i) q^{65} +(4.73236 + 8.19669i) q^{67} +(3.28799 - 5.69497i) q^{68} +(9.78180 - 0.356487i) q^{70} -5.46472 q^{71} +(-6.03273 - 10.4490i) q^{73} +(-1.38874 - 2.40536i) q^{74} +0.888736 q^{76} +(-3.90545 + 0.142330i) q^{77} +(-5.72617 + 9.91802i) q^{79} +(-1.84981 - 3.20397i) q^{80} +(-2.05563 + 3.56046i) q^{82} -4.47710 q^{83} -24.3287 q^{85} +(0.00618986 - 0.0107211i) q^{86} +(0.738550 + 1.27921i) q^{88} +(-4.43818 + 7.68715i) q^{89} +(-3.34362 + 6.31159i) q^{91} +6.28799 q^{92} +(3.49381 + 6.05146i) q^{94} +(-1.64400 - 2.84748i) q^{95} +13.1767 q^{97} +(6.98143 - 0.509538i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} - 5 q^{5} - 2 q^{7} + 6 q^{8} - 5 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 3 q^{16} - 4 q^{17} - 3 q^{19} + 10 q^{20} + 2 q^{22} - 7 q^{23} - 2 q^{25} - 2 q^{26} + 4 q^{28} + 10 q^{29} - 14 q^{31} - 3 q^{32} + 8 q^{34} - 19 q^{35} - 9 q^{37} - 3 q^{38} - 5 q^{40} + 24 q^{41} - 36 q^{43} - q^{44} - 7 q^{46} + 3 q^{47} + 12 q^{49} + 4 q^{50} - 2 q^{52} + 9 q^{53} + 14 q^{55} - 2 q^{56} - 5 q^{58} + 4 q^{59} + 4 q^{61} + 28 q^{62} + 6 q^{64} - 12 q^{65} + 5 q^{67} - 4 q^{68} + 17 q^{70} + 14 q^{71} - 25 q^{73} - 9 q^{74} + 6 q^{76} - 17 q^{77} + 7 q^{79} - 5 q^{80} - 12 q^{82} - 16 q^{83} - 28 q^{85} + 18 q^{86} - q^{88} - 9 q^{89} + 4 q^{91} + 14 q^{92} + 3 q^{94} + 2 q^{95} + 56 q^{97} - 12 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 5 * q^5 - 2 * q^7 + 6 * q^8 - 5 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 3 * q^16 - 4 * q^17 - 3 * q^19 + 10 * q^20 + 2 * q^22 - 7 * q^23 - 2 * q^25 - 2 * q^26 + 4 * q^28 + 10 * q^29 - 14 * q^31 - 3 * q^32 + 8 * q^34 - 19 * q^35 - 9 * q^37 - 3 * q^38 - 5 * q^40 + 24 * q^41 - 36 * q^43 - q^44 - 7 * q^46 + 3 * q^47 + 12 * q^49 + 4 * q^50 - 2 * q^52 + 9 * q^53 + 14 * q^55 - 2 * q^56 - 5 * q^58 + 4 * q^59 + 4 * q^61 + 28 * q^62 + 6 * q^64 - 12 * q^65 + 5 * q^67 - 4 * q^68 + 17 * q^70 + 14 * q^71 - 25 * q^73 - 9 * q^74 + 6 * q^76 - 17 * q^77 + 7 * q^79 - 5 * q^80 - 12 * q^82 - 16 * q^83 - 28 * q^85 + 18 * q^86 - q^88 - 9 * q^89 + 4 * q^91 + 14 * q^92 + 3 * q^94 + 2 * q^95 + 56 * q^97 - 12 * q^98

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