LMFDB - Embedded newform 1134.2.h.t.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(109,1134)]

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([2, 4]))

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

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

chi := DirichletCharacter("1134.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.h (of order $3$, degree $2$, not 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.2
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1134.109
Dual form			1134.2.h.t.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.64575 q^{5} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.64575 q^{5} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(1.82288 - 3.15731i) q^{10} -3.64575 q^{11} +(2.32288 - 4.02334i) q^{13} +2.64575 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.82288 - 3.15731i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(-1.82288 - 3.15731i) q^{20} +(-1.82288 + 3.15731i) q^{22} +1.29150 q^{23} +8.29150 q^{25} +(-2.32288 - 4.02334i) q^{26} +(1.32288 - 2.29129i) q^{28} +(1.17712 + 2.03884i) q^{29} +(2.32288 + 4.02334i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.82288 - 3.15731i) q^{34} +(4.82288 + 8.35347i) q^{35} +(5.96863 + 10.3380i) q^{37} -2.00000 q^{38} -3.64575 q^{40} +(5.46863 - 9.47194i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(1.82288 + 3.15731i) q^{44} +(0.645751 - 1.11847i) q^{46} +(2.46863 - 4.27579i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(4.14575 - 7.18065i) q^{50} -4.64575 q^{52} +(3.00000 - 5.19615i) q^{53} -13.2915 q^{55} +(-1.32288 - 2.29129i) q^{56} +2.35425 q^{58} +(4.17712 + 7.23499i) q^{59} +(-3.67712 + 6.36897i) q^{61} +4.64575 q^{62} +1.00000 q^{64} +(8.46863 - 14.6681i) q^{65} +(1.14575 + 1.98450i) q^{67} -3.64575 q^{68} +9.64575 q^{70} -15.6458 q^{71} +(-5.29150 + 9.16515i) q^{73} +11.9373 q^{74} +(-1.00000 + 1.73205i) q^{76} +(-4.82288 - 8.35347i) q^{77} +(-5.61438 + 9.72439i) q^{79} +(-1.82288 + 3.15731i) q^{80} +(-5.46863 - 9.47194i) q^{82} +(-6.64575 - 11.5108i) q^{83} +(6.64575 - 11.5108i) q^{85} -5.00000 q^{86} +3.64575 q^{88} +(2.46863 + 4.27579i) q^{89} +12.2915 q^{91} +(-0.645751 - 1.11847i) q^{92} +(-2.46863 - 4.27579i) q^{94} +(-3.64575 - 6.31463i) q^{95} +(-6.79150 - 11.7632i) q^{97} +(3.50000 + 6.06218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8} + 2 q^{10} - 4 q^{11} + 4 q^{13} - 2 q^{16} + 2 q^{17} - 4 q^{19} - 2 q^{20} - 2 q^{22} - 16 q^{23} + 12 q^{25} - 4 q^{26} + 10 q^{29} + 4 q^{31} + 2 q^{32} - 2 q^{34} + 14 q^{35} + 8 q^{37} - 8 q^{38} - 4 q^{40} + 6 q^{41} - 10 q^{43} + 2 q^{44} - 8 q^{46} - 6 q^{47} - 14 q^{49} + 6 q^{50} - 8 q^{52} + 12 q^{53} - 32 q^{55} + 20 q^{58} + 22 q^{59} - 20 q^{61} + 8 q^{62} + 4 q^{64} + 18 q^{65} - 6 q^{67} - 4 q^{68} + 28 q^{70} - 52 q^{71} + 16 q^{74} - 4 q^{76} - 14 q^{77} + 4 q^{79} - 2 q^{80} - 6 q^{82} - 16 q^{83} + 16 q^{85} - 20 q^{86} + 4 q^{88} - 6 q^{89} + 28 q^{91} + 8 q^{92} + 6 q^{94} - 4 q^{95} - 6 q^{97} + 14 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^8 + 2 * q^10 - 4 * q^11 + 4 * q^13 - 2 * q^16 + 2 * q^17 - 4 * q^19 - 2 * q^20 - 2 * q^22 - 16 * q^23 + 12 * q^25 - 4 * q^26 + 10 * q^29 + 4 * q^31 + 2 * q^32 - 2 * q^34 + 14 * q^35 + 8 * q^37 - 8 * q^38 - 4 * q^40 + 6 * q^41 - 10 * q^43 + 2 * q^44 - 8 * q^46 - 6 * q^47 - 14 * q^49 + 6 * q^50 - 8 * q^52 + 12 * q^53 - 32 * q^55 + 20 * q^58 + 22 * q^59 - 20 * q^61 + 8 * q^62 + 4 * q^64 + 18 * q^65 - 6 * q^67 - 4 * q^68 + 28 * q^70 - 52 * q^71 + 16 * q^74 - 4 * q^76 - 14 * q^77 + 4 * q^79 - 2 * q^80 - 6 * q^82 - 16 * q^83 + 16 * q^85 - 20 * q^86 + 4 * q^88 - 6 * q^89 + 28 * q^91 + 8 * q^92 + 6 * q^94 - 4 * q^95 - 6 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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
$5$	3.64575			1.63043			0.815215	−	0.579159i	$-0.196619\pi$
$5$	3.64575			1.63043			0.815215	+	0.579159i	$0.196619\pi$
$6$		0			0
$7$	1.32288	+	2.29129i	0.500000	+	0.866025i
$7$	1.32288	+	2.29129i	0.500000	+	0.866025i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.82288	−	3.15731i	0.576444	−	0.998430i
$11$	−3.64575			−1.09924			−0.549618	−	0.835416i	$-0.685227\pi$
$11$	−3.64575			−1.09924			−0.549618	+	0.835416i	$0.685227\pi$
$12$		0			0
$13$	2.32288	−	4.02334i	0.644250	−	1.11587i	−0.340224	−	0.940344i	$-0.610503\pi$
$13$	2.32288	−	4.02334i	0.644250	−	1.11587i	0.984474	−	0.175529i	$-0.0561636\pi$
$14$	2.64575			0.707107
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.82288	−	3.15731i	0.442112	−	0.765761i	−0.555734	−	0.831360i	$-0.687563\pi$
$17$	1.82288	−	3.15731i	0.442112	−	0.765761i	0.997846	+	0.0655994i	$0.0208959\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	−1.82288	−	3.15731i	−0.407607	−	0.705997i
$21$		0			0
$22$	−1.82288	+	3.15731i	−0.388638	+	0.673141i
$23$	1.29150			0.269297			0.134648	−	0.990893i	$-0.457009\pi$
$23$	1.29150			0.269297			0.134648	+	0.990893i	$0.457009\pi$
$24$		0			0
$25$	8.29150			1.65830
$26$	−2.32288	−	4.02334i	−0.455553	−	0.789042i
$27$		0			0
$28$	1.32288	−	2.29129i	0.250000	−	0.433013i
$29$	1.17712	+	2.03884i	0.218587	+	0.378603i	0.954376	−	0.298607i	$-0.0965221\pi$
$29$	1.17712	+	2.03884i	0.218587	+	0.378603i	−0.735790	+	0.677210i	$0.763189\pi$
$30$		0			0
$31$	2.32288	+	4.02334i	0.417201	+	0.722613i	0.995657	−	0.0931007i	$-0.0296779\pi$
$31$	2.32288	+	4.02334i	0.417201	+	0.722613i	−0.578456	+	0.815714i	$0.696345\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−1.82288	−	3.15731i	−0.312621	−	0.541475i
$35$	4.82288	+	8.35347i	0.815215	+	1.41199i
$36$		0			0
$37$	5.96863	+	10.3380i	0.981236	+	1.69955i	0.657596	+	0.753371i	$0.271573\pi$
$37$	5.96863	+	10.3380i	0.981236	+	1.69955i	0.323640	+	0.946180i	$0.395093\pi$
$38$	−2.00000			−0.324443
$39$		0			0
$40$	−3.64575			−0.576444
$41$	5.46863	−	9.47194i	0.854056	−	1.47927i	−0.0234619	−	0.999725i	$-0.507469\pi$
$41$	5.46863	−	9.47194i	0.854056	−	1.47927i	0.877518	−	0.479544i	$-0.159198\pi$
$42$		0			0
$43$	−2.50000	−	4.33013i	−0.381246	−	0.660338i	0.609994	−	0.792406i	$-0.291172\pi$
$43$	−2.50000	−	4.33013i	−0.381246	−	0.660338i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	1.82288	+	3.15731i	0.274809	+	0.475983i
$45$		0			0
$46$	0.645751	−	1.11847i	0.0952108	−	0.164910i
$47$	2.46863	−	4.27579i	0.360086	−	0.623688i	−0.627888	−	0.778303i	$-0.716081\pi$
$47$	2.46863	−	4.27579i	0.360086	−	0.623688i	0.987975	+	0.154616i	$0.0494139\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	4.14575	−	7.18065i	0.586298	−	1.01550i
$51$		0			0
$52$	−4.64575			−0.644250
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$		0			0
$55$	−13.2915			−1.79223
$56$	−1.32288	−	2.29129i	−0.176777	−	0.306186i
$57$		0			0
$58$	2.35425			0.309128
$59$	4.17712	+	7.23499i	0.543815	+	0.941916i	0.998680	+	0.0513554i	$0.0163541\pi$
$59$	4.17712	+	7.23499i	0.543815	+	0.941916i	−0.454865	+	0.890560i	$0.650313\pi$
$60$		0			0
$61$	−3.67712	+	6.36897i	−0.470808	+	0.815463i	−0.999443	−	0.0333867i	$-0.989371\pi$
$61$	−3.67712	+	6.36897i	−0.470808	+	0.815463i	0.528635	+	0.848849i	$0.322704\pi$
$62$	4.64575			0.590011
$63$		0			0
$64$	1.00000			0.125000
$65$	8.46863	−	14.6681i	1.05040	−	1.81935i
$66$		0			0
$67$	1.14575	+	1.98450i	0.139976	+	0.242445i	0.927487	−	0.373855i	$-0.121964\pi$
$67$	1.14575	+	1.98450i	0.139976	+	0.242445i	−0.787511	+	0.616300i	$0.788631\pi$
$68$	−3.64575			−0.442112
$69$		0			0
$70$	9.64575			1.15289
$71$	−15.6458			−1.85681			−0.928405	−	0.371571i	$-0.878819\pi$
$71$	−15.6458			−1.85681			−0.928405	+	0.371571i	$0.878819\pi$
$72$		0			0
$73$	−5.29150	+	9.16515i	−0.619324	+	1.07270i	0.370286	+	0.928918i	$0.379260\pi$
$73$	−5.29150	+	9.16515i	−0.619324	+	1.07270i	−0.989609	+	0.143782i	$0.954074\pi$
$74$	11.9373			1.38768
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−4.82288	−	8.35347i	−0.549618	−	0.951966i
$78$		0			0
$79$	−5.61438	+	9.72439i	−0.631667	+	1.09408i	0.355544	+	0.934660i	$0.384296\pi$
$79$	−5.61438	+	9.72439i	−0.631667	+	1.09408i	−0.987211	+	0.159420i	$0.949038\pi$
$80$	−1.82288	+	3.15731i	−0.203804	+	0.352998i
$81$		0			0
$82$	−5.46863	−	9.47194i	−0.603909	−	1.04600i
$83$	−6.64575	−	11.5108i	−0.729466	−	1.26347i	−0.957109	−	0.289728i	$-0.906435\pi$
$83$	−6.64575	−	11.5108i	−0.729466	−	1.26347i	0.227643	−	0.973745i	$-0.426898\pi$
$84$		0			0
$85$	6.64575	−	11.5108i	0.720833	−	1.24852i
$86$	−5.00000			−0.539164
$87$		0			0
$88$	3.64575			0.388638
$89$	2.46863	+	4.27579i	0.261674	+	0.453233i	0.966687	−	0.255962i	$-0.0823922\pi$
$89$	2.46863	+	4.27579i	0.261674	+	0.453233i	−0.705013	+	0.709194i	$0.749059\pi$
$90$		0			0
$91$	12.2915			1.28850
$92$	−0.645751	−	1.11847i	−0.0673242	−	0.116609i
$93$		0			0
$94$	−2.46863	−	4.27579i	−0.254619	−	0.441014i
$95$	−3.64575	−	6.31463i	−0.374046	−	0.647867i
$96$		0			0
$97$	−6.79150	−	11.7632i	−0.689573	−	1.19437i	−0.971976	−	0.235079i	$-0.924465\pi$
$97$	−6.79150	−	11.7632i	−0.689573	−	1.19437i	0.282404	−	0.959296i	$-0.408868\pi$
$98$	3.50000	+	6.06218i	0.353553	+	0.612372i
$99$		0			0
$100$	−4.14575	−	7.18065i	−0.414575	−	0.718065i
$101$	−8.35425			−0.831279			−0.415639	−	0.909529i	$-0.636442\pi$
$101$	−8.35425			−0.831279			−0.415639	+	0.909529i	$0.636442\pi$
$102$		0			0
$103$	3.93725			0.387949			0.193975	−	0.981007i	$-0.437862\pi$
$103$	3.93725			0.387949			0.193975	+	0.981007i	$0.437862\pi$
$104$	−2.32288	+	4.02334i	−0.227777	+	0.394521i
$105$		0			0
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$		0			0
$109$	1.67712	−	2.90486i	0.160639	−	0.278236i	−0.774459	−	0.632624i	$-0.781978\pi$
$109$	1.67712	−	2.90486i	0.160639	−	0.278236i	0.935098	+	0.354389i	$0.115311\pi$
$110$	−6.64575	+	11.5108i	−0.633648	+	1.09751i
$111$		0			0
$112$	−2.64575			−0.250000
$113$	1.17712	−	2.03884i	0.110735	−	0.191798i	−0.805332	−	0.592824i	$-0.798013\pi$
$113$	1.17712	−	2.03884i	0.110735	−	0.191798i	0.916067	+	0.401026i	$0.131346\pi$
$114$		0			0
$115$	4.70850			0.439070
$116$	1.17712	−	2.03884i	0.109293	−	0.189301i
$117$		0			0
$118$	8.35425			0.769071
$119$	9.64575			0.884225
$120$		0			0
$121$	2.29150			0.208318
$122$	3.67712	+	6.36897i	0.332911	+	0.576619i
$123$		0			0
$124$	2.32288	−	4.02334i	0.208600	−	0.361306i
$125$	12.0000			1.07331
$126$		0			0
$127$	1.35425			0.120170			0.0600851	−	0.998193i	$-0.480863\pi$
$127$	1.35425			0.120170			0.0600851	+	0.998193i	$0.480863\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−8.46863	−	14.6681i	−0.742748	−	1.28648i
$131$	14.5830			1.27412			0.637062	−	0.770813i	$-0.280150\pi$
$131$	14.5830			1.27412			0.637062	+	0.770813i	$0.280150\pi$
$132$		0			0
$133$	2.64575	−	4.58258i	0.229416	−	0.397360i
$134$	2.29150			0.197956
$135$		0			0
$136$	−1.82288	+	3.15731i	−0.156310	+	0.270737i
$137$	−1.29150			−0.110341			−0.0551703	−	0.998477i	$-0.517570\pi$
$137$	−1.29150			−0.110341			−0.0551703	+	0.998477i	$0.517570\pi$
$138$		0			0
$139$	−0.791503	+	1.37092i	−0.0671344	+	0.116280i	−0.897639	−	0.440732i	$-0.854719\pi$
$139$	−0.791503	+	1.37092i	−0.0671344	+	0.116280i	0.830504	+	0.557012i	$0.188052\pi$
$140$	4.82288	−	8.35347i	0.407607	−	0.705997i
$141$		0			0
$142$	−7.82288	+	13.5496i	−0.656481	+	1.13706i
$143$	−8.46863	+	14.6681i	−0.708182	+	1.22661i
$144$		0			0
$145$	4.29150	+	7.43310i	0.356390	+	0.617285i
$146$	5.29150	+	9.16515i	0.437928	+	0.758513i
$147$		0			0
$148$	5.96863	−	10.3380i	0.490618	−	0.849776i
$149$	−22.9373			−1.87909			−0.939547	−	0.342421i	$-0.888753\pi$
$149$	−22.9373			−1.87909			−0.939547	+	0.342421i	$0.888753\pi$
$150$		0			0
$151$	−19.2288			−1.56481			−0.782407	−	0.622767i	$-0.786008\pi$
$151$	−19.2288			−1.56481			−0.782407	+	0.622767i	$0.786008\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$		0			0
$154$	−9.64575			−0.777277
$155$	8.46863	+	14.6681i	0.680216	+	1.17817i
$156$		0			0
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	0.934731	−	0.355357i	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$	5.61438	+	9.72439i	0.446656	+	0.773631i
$159$		0			0
$160$	1.82288	+	3.15731i	0.144111	+	0.249608i
$161$	1.70850	+	2.95920i	0.134648	+	0.233218i
$162$		0			0
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	0.884943	−	0.465700i	$-0.154198\pi$
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	−0.845780	+	0.533533i	$0.820864\pi$
$164$	−10.9373			−0.854056
$165$		0			0
$166$	−13.2915			−1.03162
$167$	−4.29150	+	7.43310i	−0.332086	+	0.575191i	−0.982921	−	0.184029i	$-0.941086\pi$
$167$	−4.29150	+	7.43310i	−0.332086	+	0.575191i	0.650834	+	0.759220i	$0.274419\pi$
$168$		0			0
$169$	−4.29150	−	7.43310i	−0.330116	−	0.571777i
$170$	−6.64575	−	11.5108i	−0.509706	−	0.882836i
$171$		0			0
$172$	−2.50000	+	4.33013i	−0.190623	+	0.330169i
$173$	−7.29150	+	12.6293i	−0.554363	+	0.960184i	0.443590	+	0.896230i	$0.353705\pi$
$173$	−7.29150	+	12.6293i	−0.554363	+	0.960184i	−0.997953	+	0.0639546i	$0.979629\pi$
$174$		0			0
$175$	10.9686	+	18.9982i	0.829150	+	1.43613i
$176$	1.82288	−	3.15731i	0.137404	−	0.237991i
$177$		0			0
$178$	4.93725			0.370063
$179$	8.46863	−	14.6681i	0.632975	−	1.09634i	−0.353965	−	0.935259i	$-0.615167\pi$
$179$	8.46863	−	14.6681i	0.632975	−	1.09634i	0.986940	−	0.161086i	$-0.0514997\pi$
$180$		0			0
$181$	−2.70850			−0.201321			−0.100661	−	0.994921i	$-0.532096\pi$
$181$	−2.70850			−0.201321			−0.100661	+	0.994921i	$0.532096\pi$
$182$	6.14575	−	10.6448i	0.455553	−	0.789042i
$183$		0			0
$184$	−1.29150			−0.0952108
$185$	21.7601	+	37.6897i	1.59984	+	2.77100i
$186$		0			0
$187$	−6.64575	+	11.5108i	−0.485985	+	0.841752i
$188$	−4.93725			−0.360086
$189$		0			0
$190$	−7.29150			−0.528981
$191$	−10.4059	+	18.0235i	−0.752943	+	1.30414i	0.193447	+	0.981111i	$0.438033\pi$
$191$	−10.4059	+	18.0235i	−0.752943	+	1.30414i	−0.946390	+	0.323025i	$0.895300\pi$
$192$		0			0
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	0.964059	−	0.265689i	$-0.0855996\pi$
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	−0.712123	+	0.702055i	$0.752266\pi$
$194$	−13.5830			−0.975203
$195$		0			0
$196$	7.00000			0.500000
$197$	−4.70850			−0.335467			−0.167733	−	0.985832i	$-0.553645\pi$
$197$	−4.70850			−0.335467			−0.167733	+	0.985832i	$0.553645\pi$
$198$		0			0
$199$	−3.03137	+	5.25049i	−0.214888	+	0.372198i	−0.953238	−	0.302221i	$-0.902272\pi$
$199$	−3.03137	+	5.25049i	−0.214888	+	0.372198i	0.738350	+	0.674418i	$0.235605\pi$
$200$	−8.29150			−0.586298
$201$		0			0
$202$	−4.17712	+	7.23499i	−0.293901	+	0.509052i
$203$	−3.11438	+	5.39426i	−0.218587	+	0.378603i
$204$		0			0
$205$	19.9373	−	34.5323i	1.39248	−	2.41184i
$206$	1.96863	−	3.40976i	0.137161	−	0.237569i
$207$		0			0
$208$	2.32288	+	4.02334i	0.161062	+	0.278968i
$209$	3.64575	+	6.31463i	0.252182	+	0.436792i
$210$		0			0
$211$	−7.43725	+	12.8817i	−0.512002	+	0.886813i	0.487902	+	0.872899i	$0.337763\pi$
$211$	−7.43725	+	12.8817i	−0.512002	+	0.886813i	−0.999903	+	0.0139142i	$0.995571\pi$
$212$	−6.00000			−0.412082
$213$		0			0
$214$	−6.00000			−0.410152
$215$	−9.11438	−	15.7866i	−0.621595	−	1.07663i
$216$		0			0
$217$	−6.14575	+	10.6448i	−0.417201	+	0.722613i
$218$	−1.67712	−	2.90486i	−0.113589	−	0.196742i
$219$		0			0
$220$	6.64575	+	11.5108i	0.448056	+	0.776057i
$221$	−8.46863	−	14.6681i	−0.569661	−	0.986683i
$222$		0			0
$223$	6.93725	+	12.0157i	0.464553	+	0.804629i	0.999181	−	0.0404581i	$-0.0128817\pi$
$223$	6.93725	+	12.0157i	0.464553	+	0.804629i	−0.534628	+	0.845087i	$0.679548\pi$
$224$	−1.32288	+	2.29129i	−0.0883883	+	0.153093i
$225$		0			0
$226$	−1.17712	−	2.03884i	−0.0783011	−	0.135622i
$227$	−6.00000			−0.398234			−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000			−0.398234			−0.199117	+	0.979976i	$0.563807\pi$
$228$		0			0
$229$	−9.35425			−0.618146			−0.309073	−	0.951038i	$-0.600019\pi$
$229$	−9.35425			−0.618146			−0.309073	+	0.951038i	$0.600019\pi$
$230$	2.35425	−	4.07768i	0.155235	−	0.268874i
$231$		0			0
$232$	−1.17712	−	2.03884i	−0.0772820	−	0.133856i
$233$	−9.64575	−	16.7069i	−0.631914	−	1.09451i	−0.987160	−	0.159735i	$-0.948936\pi$
$233$	−9.64575	−	16.7069i	−0.631914	−	1.09451i	0.355246	−	0.934773i	$-0.384397\pi$
$234$		0			0
$235$	9.00000	−	15.5885i	0.587095	−	1.01688i
$236$	4.17712	−	7.23499i	0.271908	−	0.470958i
$237$		0			0
$238$	4.82288	−	8.35347i	0.312621	−	0.541475i
$239$	−5.46863	+	9.47194i	−0.353736	+	0.612689i	−0.986901	−	0.161328i	$-0.948422\pi$
$239$	−5.46863	+	9.47194i	−0.353736	+	0.612689i	0.633165	+	0.774017i	$0.281756\pi$
$240$		0			0
$241$	5.00000			0.322078			0.161039	−	0.986948i	$-0.448515\pi$
$241$	5.00000			0.322078			0.161039	+	0.986948i	$0.448515\pi$
$242$	1.14575	−	1.98450i	0.0736517	−	0.127568i
$243$		0			0
$244$	7.35425			0.470808
$245$	−12.7601	+	22.1012i	−0.815215	+	1.41199i
$246$		0			0
$247$	−9.29150			−0.591204
$248$	−2.32288	−	4.02334i	−0.147503	−	0.255482i
$249$		0			0
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$		0			0
$253$	−4.70850			−0.296021
$254$	0.677124	−	1.17281i	0.0424866	−	0.0735889i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.8745			−0.990225			−0.495112	−	0.868829i	$-0.664873\pi$
$257$	−15.8745			−0.990225			−0.495112	+	0.868829i	$0.664873\pi$
$258$		0			0
$259$	−15.7915	+	27.3517i	−0.981236	+	1.69955i
$260$	−16.9373			−1.05040
$261$		0			0
$262$	7.29150	−	12.6293i	0.450471	−	0.780238i
$263$	4.93725			0.304444			0.152222	−	0.988346i	$-0.451357\pi$
$263$	4.93725			0.304444			0.152222	+	0.988346i	$0.451357\pi$
$264$		0			0
$265$	10.9373	−	18.9439i	0.671870	−	1.16371i
$266$	−2.64575	−	4.58258i	−0.162221	−	0.280976i
$267$		0			0
$268$	1.14575	−	1.98450i	0.0699879	−	0.121223i
$269$	−8.35425	+	14.4700i	−0.509368	+	0.882250i	0.490574	+	0.871400i	$0.336787\pi$
$269$	−8.35425	+	14.4700i	−0.509368	+	0.882250i	−0.999941	+	0.0108507i	$0.996546\pi$
$270$		0			0
$271$	−2.61438	−	4.52824i	−0.158812	−	0.275071i	0.775628	−	0.631190i	$-0.217433\pi$
$271$	−2.61438	−	4.52824i	−0.158812	−	0.275071i	−0.934441	+	0.356119i	$0.884100\pi$
$272$	1.82288	+	3.15731i	0.110528	+	0.191440i
$273$		0			0
$274$	−0.645751	+	1.11847i	−0.0390113	+	0.0675695i
$275$	−30.2288			−1.82286
$276$		0			0
$277$	−2.06275			−0.123938			−0.0619692	−	0.998078i	$-0.519738\pi$
$277$	−2.06275			−0.123938			−0.0619692	+	0.998078i	$0.519738\pi$
$278$	0.791503	+	1.37092i	0.0474712	+	0.0822225i
$279$		0			0
$280$	−4.82288	−	8.35347i	−0.288222	−	0.499215i
$281$	9.76013	+	16.9050i	0.582241	+	1.00847i	0.995213	+	0.0977268i	$0.0311571\pi$
$281$	9.76013	+	16.9050i	0.582241	+	1.00847i	−0.412973	+	0.910743i	$0.635510\pi$
$282$		0			0
$283$	1.14575	+	1.98450i	0.0681078	+	0.117966i	0.898068	−	0.439856i	$-0.144970\pi$
$283$	1.14575	+	1.98450i	0.0681078	+	0.117966i	−0.829961	+	0.557822i	$0.811637\pi$
$284$	7.82288	+	13.5496i	0.464202	+	0.804022i
$285$		0			0
$286$	8.46863	+	14.6681i	0.500760	+	0.867342i
$287$	28.9373			1.70811
$288$		0			0
$289$	1.85425	+	3.21165i	0.109073	+	0.188921i
$290$	8.58301			0.504011
$291$		0			0
$292$	10.5830			0.619324
$293$	3.53137	−	6.11652i	0.206305	−	0.357331i	−0.744243	−	0.667909i	$-0.767189\pi$
$293$	3.53137	−	6.11652i	0.206305	−	0.357331i	0.950548	+	0.310578i	$0.100523\pi$
$294$		0			0
$295$	15.2288	+	26.3770i	0.886652	+	1.53573i
$296$	−5.96863	−	10.3380i	−0.346919	−	0.600882i
$297$		0			0
$298$	−11.4686	+	19.8642i	−0.664360	+	1.15070i
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$		0			0
$301$	6.61438	−	11.4564i	0.381246	−	0.660338i
$302$	−9.61438	+	16.6526i	−0.553245	+	0.958249i
$303$		0			0
$304$	2.00000			0.114708
$305$	−13.4059	+	23.2197i	−0.767619	+	1.32955i
$306$		0			0
$307$	7.58301			0.432785			0.216392	−	0.976306i	$-0.430571\pi$
$307$	7.58301			0.432785			0.216392	+	0.976306i	$0.430571\pi$
$308$	−4.82288	+	8.35347i	−0.274809	+	0.475983i
$309$		0			0
$310$	16.9373			0.961971
$311$	−6.76013	−	11.7089i	−0.383332	−	0.663950i	0.608204	−	0.793780i	$-0.291890\pi$
$311$	−6.76013	−	11.7089i	−0.383332	−	0.663950i	−0.991536	+	0.129830i	$0.958557\pi$
$312$		0			0
$313$	−6.35425	+	11.0059i	−0.359163	+	0.622089i	−0.987821	−	0.155593i	$-0.950271\pi$
$313$	−6.35425	+	11.0059i	−0.359163	+	0.622089i	0.628658	+	0.777682i	$0.283605\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	11.2288			0.631667
$317$	13.4059	−	23.2197i	0.752949	−	1.30415i	−0.193438	−	0.981112i	$-0.561964\pi$
$317$	13.4059	−	23.2197i	0.752949	−	1.30415i	0.946387	−	0.323034i	$-0.104703\pi$
$318$		0			0
$319$	−4.29150	−	7.43310i	−0.240278	−	0.416174i
$320$	3.64575			0.203804
$321$		0			0
$322$	3.41699			0.190422
$323$	−7.29150			−0.405710
$324$		0			0
$325$	19.2601	−	33.3595i	1.06836	−	1.85045i
$326$	1.00000			0.0553849
$327$		0			0
$328$	−5.46863	+	9.47194i	−0.301954	+	0.523000i
$329$	13.0627			0.720173
$330$		0			0
$331$	15.9373	−	27.6041i	0.875991	−	1.51726i	0.0202871	−	0.999794i	$-0.493542\pi$
$331$	15.9373	−	27.6041i	0.875991	−	1.51726i	0.855704	−	0.517466i	$-0.173125\pi$
$332$	−6.64575	+	11.5108i	−0.364733	+	0.631736i
$333$		0			0
$334$	4.29150	+	7.43310i	0.234821	+	0.406721i
$335$	4.17712	+	7.23499i	0.228221	+	0.395290i
$336$		0			0
$337$	15.2915	−	26.4857i	0.832981	−	1.44277i	−0.0626823	−	0.998034i	$-0.519965\pi$
$337$	15.2915	−	26.4857i	0.832981	−	1.44277i	0.895664	−	0.444732i	$-0.146701\pi$
$338$	−8.58301			−0.466854
$339$		0			0
$340$	−13.2915			−0.720833
$341$	−8.46863	−	14.6681i	−0.458602	−	0.794322i
$342$		0			0
$343$	−18.5203			−1.00000
$344$	2.50000	+	4.33013i	0.134791	+	0.233465i
$345$		0			0
$346$	7.29150	+	12.6293i	0.391994	+	0.678953i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	0.614378	+	1.06413i	0.0328869	+	0.0569618i	0.882000	−	0.471249i	$-0.156197\pi$
$349$	0.614378	+	1.06413i	0.0328869	+	0.0569618i	−0.849113	+	0.528210i	$0.822863\pi$
$350$	21.9373			1.17260
$351$		0			0
$352$	−1.82288	−	3.15731i	−0.0971596	−	0.168285i
$353$	12.0000			0.638696			0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000			0.638696			0.319348	+	0.947638i	$0.396536\pi$
$354$		0			0
$355$	−57.0405			−3.02740
$356$	2.46863	−	4.27579i	0.130837	−	0.226616i
$357$		0			0
$358$	−8.46863	−	14.6681i	−0.447581	−	0.775233i
$359$	5.58301	+	9.67005i	0.294660	+	0.510366i	0.974906	−	0.222618i	$-0.0714604\pi$
$359$	5.58301	+	9.67005i	0.294660	+	0.510366i	−0.680246	+	0.732984i	$0.738127\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−1.35425	+	2.34563i	−0.0711777	+	0.123283i
$363$		0			0
$364$	−6.14575	−	10.6448i	−0.322125	−	0.557937i
$365$	−19.2915	+	33.4139i	−1.00976	+	1.74896i
$366$		0			0
$367$	29.8745			1.55944			0.779718	−	0.626130i	$-0.215362\pi$
$367$	29.8745			1.55944			0.779718	+	0.626130i	$0.215362\pi$
$368$	−0.645751	+	1.11847i	−0.0336621	+	0.0583045i
$369$		0			0
$370$	43.5203			2.26251
$371$	15.8745			0.824163
$372$		0			0
$373$	4.58301			0.237299			0.118650	−	0.992936i	$-0.462144\pi$
$373$	4.58301			0.237299			0.118650	+	0.992936i	$0.462144\pi$
$374$	6.64575	+	11.5108i	0.343644	+	0.595208i
$375$		0			0
$376$	−2.46863	+	4.27579i	−0.127310	+	0.220507i
$377$	10.9373			0.563297
$378$		0			0
$379$	25.5830			1.31411			0.657055	−	0.753842i	$-0.271802\pi$
$379$	25.5830			1.31411			0.657055	+	0.753842i	$0.271802\pi$
$380$	−3.64575	+	6.31463i	−0.187023	+	0.323934i
$381$		0			0
$382$	10.4059	+	18.0235i	0.532411	+	0.922163i
$383$	−20.5830			−1.05174			−0.525871	−	0.850564i	$-0.676261\pi$
$383$	−20.5830			−1.05174			−0.525871	+	0.850564i	$0.676261\pi$
$384$		0			0
$385$	−17.5830	−	30.4547i	−0.896113	−	1.55211i
$386$	7.00000			0.356291
$387$		0			0
$388$	−6.79150	+	11.7632i	−0.344786	+	0.597187i
$389$	−19.2915			−0.978118			−0.489059	−	0.872251i	$-0.662660\pi$
$389$	−19.2915			−0.978118			−0.489059	+	0.872251i	$0.662660\pi$
$390$		0			0
$391$	2.35425	−	4.07768i	0.119059	−	0.206217i
$392$	3.50000	−	6.06218i	0.176777	−	0.306186i
$393$		0			0
$394$	−2.35425	+	4.07768i	−0.118605	+	0.205430i
$395$	−20.4686	+	35.4527i	−1.02989	+	1.78382i
$396$		0			0
$397$	8.32288	+	14.4156i	0.417713	+	0.723500i	0.995709	−	0.0925393i	$-0.0294984\pi$
$397$	8.32288	+	14.4156i	0.417713	+	0.723500i	−0.577996	+	0.816040i	$0.696165\pi$
$398$	3.03137	+	5.25049i	0.151949	+	0.263183i
$399$		0			0
$400$	−4.14575	+	7.18065i	−0.207288	+	0.359033i
$401$	20.8118			1.03929			0.519645	−	0.854382i	$-0.326064\pi$
$401$	20.8118			1.03929			0.519645	+	0.854382i	$0.326064\pi$
$402$		0			0
$403$	21.5830			1.07513
$404$	4.17712	+	7.23499i	0.207820	+	0.359954i
$405$		0			0
$406$	3.11438	+	5.39426i	0.154564	+	0.267713i
$407$	−21.7601	−	37.6897i	−1.07861	−	1.86821i
$408$		0			0
$409$	−7.43725	−	12.8817i	−0.367749	−	0.636959i	0.621465	−	0.783442i	$-0.286538\pi$
$409$	−7.43725	−	12.8817i	−0.367749	−	0.636959i	−0.989213	+	0.146483i	$0.953205\pi$
$410$	−19.9373	−	34.5323i	−0.984631	−	1.70543i
$411$		0			0
$412$	−1.96863	−	3.40976i	−0.0969873	−	0.167987i
$413$	−11.0516	+	19.1420i	−0.543815	+	0.941916i
$414$		0			0
$415$	−24.2288	−	41.9654i	−1.18934	−	2.06000i
$416$	4.64575			0.227777
$417$		0			0
$418$	7.29150			0.356639
$419$	14.4686	−	25.0604i	0.706839	−	1.22428i	−0.259185	−	0.965828i	$-0.583454\pi$
$419$	14.4686	−	25.0604i	0.706839	−	1.22428i	0.966024	−	0.258453i	$-0.0832127\pi$
$420$		0			0
$421$	7.35425	+	12.7379i	0.358424	+	0.620809i	0.987698	−	0.156375i	$-0.0499808\pi$
$421$	7.35425	+	12.7379i	0.358424	+	0.620809i	−0.629274	+	0.777184i	$0.716648\pi$
$422$	7.43725	+	12.8817i	0.362040	+	0.627071i
$423$		0			0
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	15.1144	−	26.1789i	0.733155	−	1.26986i
$426$		0			0
$427$	−19.4575			−0.941615
$428$	−3.00000	+	5.19615i	−0.145010	+	0.251166i
$429$		0			0
$430$	−18.2288			−0.879069
$431$	19.4059	−	33.6120i	0.934748	−	1.61903i	0.159666	−	0.987171i	$-0.448958\pi$
$431$	19.4059	−	33.6120i	0.934748	−	1.61903i	0.775082	−	0.631861i	$-0.217709\pi$
$432$		0			0
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	6.14575	+	10.6448i	0.295006	+	0.510965i
$435$		0			0
$436$	−3.35425			−0.160639
$437$	−1.29150	−	2.23695i	−0.0617809	−	0.107008i
$438$		0			0
$439$	−12.5830	+	21.7944i	−0.600554	+	1.04019i	0.392183	+	0.919887i	$0.371720\pi$
$439$	−12.5830	+	21.7944i	−0.600554	+	1.04019i	−0.992737	+	0.120303i	$0.961613\pi$
$440$	13.2915			0.633648
$441$		0			0
$442$	−16.9373			−0.805623
$443$	−9.64575	+	16.7069i	−0.458283	+	0.793770i	−0.998870	−	0.0475179i	$-0.984869\pi$
$443$	−9.64575	+	16.7069i	−0.458283	+	0.793770i	0.540587	+	0.841288i	$0.318202\pi$
$444$		0			0
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$	13.8745			0.656977
$447$		0			0
$448$	1.32288	+	2.29129i	0.0625000	+	0.108253i
$449$	−2.35425			−0.111104			−0.0555519	−	0.998456i	$-0.517692\pi$
$449$	−2.35425			−0.111104			−0.0555519	+	0.998456i	$0.517692\pi$
$450$		0			0
$451$	−19.9373	+	34.5323i	−0.938809	+	1.62606i
$452$	−2.35425			−0.110735
$453$		0			0
$454$	−3.00000	+	5.19615i	−0.140797	+	0.243868i
$455$	44.8118			2.10081
$456$		0			0
$457$	4.14575	−	7.18065i	0.193930	−	0.335897i	−0.752619	−	0.658456i	$-0.771210\pi$
$457$	4.14575	−	7.18065i	0.193930	−	0.335897i	0.946549	+	0.322559i	$0.104543\pi$
$458$	−4.67712	+	8.10102i	−0.218548	+	0.378536i
$459$		0			0
$460$	−2.35425	−	4.07768i	−0.109767	−	0.190123i
$461$	12.1144	+	20.9827i	0.564223	+	0.977263i	0.997122	+	0.0758200i	$0.0241575\pi$
$461$	12.1144	+	20.9827i	0.564223	+	0.977263i	−0.432899	+	0.901443i	$0.642509\pi$
$462$		0			0
$463$	−9.35425	+	16.2020i	−0.434729	+	0.752972i	−0.997273	−	0.0737945i	$-0.976489\pi$
$463$	−9.35425	+	16.2020i	−0.434729	+	0.752972i	0.562545	+	0.826767i	$0.309822\pi$
$464$	−2.35425			−0.109293
$465$		0			0
$466$	−19.2915			−0.893662
$467$	0.114378	+	0.198109i	0.00529280	+	0.00916739i	0.868660	−	0.495409i	$-0.164982\pi$
$467$	0.114378	+	0.198109i	0.00529280	+	0.00916739i	−0.863367	+	0.504577i	$0.831649\pi$
$468$		0			0
$469$	−3.03137	+	5.25049i	−0.139976	+	0.242445i
$470$	−9.00000	−	15.5885i	−0.415139	−	0.719042i
$471$		0			0
$472$	−4.17712	−	7.23499i	−0.192268	−	0.333017i
$473$	9.11438	+	15.7866i	0.419080	+	0.725867i
$474$		0			0
$475$	−8.29150	−	14.3613i	−0.380440	−	0.658942i
$476$	−4.82288	−	8.35347i	−0.221056	−	0.382880i
$477$		0			0
$478$	5.46863	+	9.47194i	0.250129	+	0.433236i
$479$	−3.64575			−0.166579			−0.0832893	−	0.996525i	$-0.526543\pi$
$479$	−3.64575			−0.166579			−0.0832893	+	0.996525i	$0.526543\pi$
$480$		0			0
$481$	55.4575			2.52864
$482$	2.50000	−	4.33013i	0.113872	−	0.197232i
$483$		0			0
$484$	−1.14575	−	1.98450i	−0.0520796	−	0.0902045i
$485$	−24.7601	−	42.8858i	−1.12430	−	1.94734i
$486$		0			0
$487$	−11.9373	+	20.6759i	−0.540929	+	0.936916i	0.457922	+	0.888992i	$0.348594\pi$
$487$	−11.9373	+	20.6759i	−0.540929	+	0.936916i	−0.998851	+	0.0479237i	$0.984740\pi$
$488$	3.67712	−	6.36897i	0.166456	−	0.288310i
$489$		0			0
$490$	12.7601	+	22.1012i	0.576444	+	0.998430i
$491$	12.8745	−	22.2993i	0.581018	−	1.00635i	−0.414341	−	0.910122i	$-0.635988\pi$
$491$	12.8745	−	22.2993i	0.581018	−	1.00635i	0.995359	−	0.0962315i	$-0.0306789\pi$
$492$		0			0
$493$	8.58301			0.386559
$494$	−4.64575	+	8.04668i	−0.209022	+	0.362037i
$495$		0			0
$496$	−4.64575			−0.208600
$497$	−20.6974	−	35.8489i	−0.928405	−	1.60804i
$498$		0			0
$499$	−6.16601			−0.276029			−0.138014	−	0.990430i	$-0.544072\pi$
$499$	−6.16601			−0.276029			−0.138014	+	0.990430i	$0.544072\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$		0			0
$502$	9.00000	−	15.5885i	0.401690	−	0.695747i
$503$	−3.87451			−0.172756			−0.0863779	−	0.996262i	$-0.527529\pi$
$503$	−3.87451			−0.172756			−0.0863779	+	0.996262i	$0.527529\pi$
$504$		0			0
$505$	−30.4575			−1.35534
$506$	−2.35425	+	4.07768i	−0.104659	+	0.181275i
$507$		0			0
$508$	−0.677124	−	1.17281i	−0.0300425	−	0.0520352i
$509$	−8.12549			−0.360156			−0.180078	−	0.983652i	$-0.557635\pi$
$509$	−8.12549			−0.360156			−0.180078	+	0.983652i	$0.557635\pi$
$510$		0			0
$511$	−28.0000			−1.23865
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−7.93725	+	13.7477i	−0.350097	+	0.606386i
$515$	14.3542			0.632524
$516$		0			0
$517$	−9.00000	+	15.5885i	−0.395820	+	0.685580i
$518$	15.7915	+	27.3517i	0.693839	+	1.20176i
$519$		0			0
$520$	−8.46863	+	14.6681i	−0.371374	+	0.643238i
$521$	−4.06275	+	7.03688i	−0.177992	+	0.308291i	−0.941193	−	0.337870i	$-0.890293\pi$
$521$	−4.06275	+	7.03688i	−0.177992	+	0.308291i	0.763201	+	0.646162i	$0.223627\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	0.876750	−	0.480946i	$-0.159707\pi$
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	−0.854887	+	0.518815i	$0.826373\pi$
$524$	−7.29150	−	12.6293i	−0.318531	−	0.551711i
$525$		0			0
$526$	2.46863	−	4.27579i	0.107637	−	0.186433i
$527$	16.9373			0.737798
$528$		0			0
$529$	−21.3320			−0.927479
$530$	−10.9373	−	18.9439i	−0.475084	−	0.822870i
$531$		0			0
$532$	−5.29150			−0.229416
$533$	−25.4059	−	44.0043i	−1.10045	−	1.90604i
$534$		0			0
$535$	−10.9373	−	18.9439i	−0.472859	−	0.819015i
$536$	−1.14575	−	1.98450i	−0.0494889	−	0.0857173i
$537$		0			0
$538$	8.35425	+	14.4700i	0.360177	+	0.623845i
$539$	12.7601	−	22.1012i	0.549618	−	0.951966i
$540$		0			0
$541$	−0.583005	−	1.00979i	−0.0250654	−	0.0434145i	0.853221	−	0.521550i	$-0.174646\pi$
$541$	−0.583005	−	1.00979i	−0.0250654	−	0.0434145i	−0.878286	+	0.478136i	$0.841313\pi$
$542$	−5.22876			−0.224594
$543$		0			0
$544$	3.64575			0.156310
$545$	6.11438	−	10.5904i	0.261911	−	0.453643i
$546$		0			0
$547$	−9.14575	−	15.8409i	−0.391044	−	0.677308i	0.601543	−	0.798840i	$-0.294553\pi$
$547$	−9.14575	−	15.8409i	−0.391044	−	0.677308i	−0.992588	+	0.121532i	$0.961219\pi$
$548$	0.645751	+	1.11847i	0.0275851	+	0.0477788i
$549$		0			0
$550$	−15.1144	+	26.1789i	−0.644479	+	1.11627i
$551$	2.35425	−	4.07768i	0.100294	−	0.173715i
$552$		0			0
$553$	−29.7085			−1.26333
$554$	−1.03137	+	1.78639i	−0.0438188	+	0.0758965i
$555$		0			0
$556$	1.58301			0.0671344
$557$	−2.88562	+	4.99804i	−0.122268	+	0.211774i	−0.920662	−	0.390362i	$-0.872350\pi$
$557$	−2.88562	+	4.99804i	−0.122268	+	0.211774i	0.798394	+	0.602136i	$0.205683\pi$
$558$		0			0
$559$	−23.2288			−0.982472
$560$	−9.64575			−0.407607
$561$		0			0
$562$	19.5203			0.823412
$563$	9.22876	+	15.9847i	0.388946	+	0.673674i	0.992308	−	0.123793i	$-0.0395060\pi$
$563$	9.22876	+	15.9847i	0.388946	+	0.673674i	−0.603362	+	0.797467i	$0.706173\pi$
$564$		0			0
$565$	4.29150	−	7.43310i	0.180545	−	0.312713i
$566$	2.29150			0.0963190
$567$		0			0
$568$	15.6458			0.656481
$569$	−8.46863	+	14.6681i	−0.355023	+	0.614918i	−0.987122	−	0.159970i	$-0.948860\pi$
$569$	−8.46863	+	14.6681i	−0.355023	+	0.614918i	0.632099	+	0.774888i	$0.282194\pi$
$570$		0			0
$571$	−4.64575	−	8.04668i	−0.194419	−	0.336743i	0.752291	−	0.658831i	$-0.228949\pi$
$571$	−4.64575	−	8.04668i	−0.194419	−	0.336743i	−0.946710	+	0.322088i	$0.895615\pi$
$572$	16.9373			0.708182
$573$		0			0
$574$	14.4686	−	25.0604i	0.603909	−	1.04600i
$575$	10.7085			0.446575
$576$		0			0
$577$	16.1458	−	27.9653i	0.672156	−	1.16421i	−0.305135	−	0.952309i	$-0.598702\pi$
$577$	16.1458	−	27.9653i	0.672156	−	1.16421i	0.977291	−	0.211900i	$-0.0679651\pi$
$578$	3.70850			0.154253
$579$		0			0
$580$	4.29150	−	7.43310i	0.178195	−	0.308643i
$581$	17.5830	−	30.4547i	0.729466	−	1.26347i
$582$		0			0
$583$	−10.9373	+	18.9439i	−0.452975	+	0.784575i
$584$	5.29150	−	9.16515i	0.218964	−	0.379257i
$585$		0			0
$586$	−3.53137	−	6.11652i	−0.145880	−	0.252671i
$587$	5.88562	+	10.1942i	0.242926	+	0.420759i	0.961546	−	0.274643i	$-0.0885596\pi$
$587$	5.88562	+	10.1942i	0.242926	+	0.420759i	−0.718621	+	0.695402i	$0.755226\pi$
$588$		0			0
$589$	4.64575	−	8.04668i	0.191425	−	0.331558i
$590$	30.4575			1.25392
$591$		0			0
$592$	−11.9373			−0.490618
$593$	20.4686	+	35.4527i	0.840546	+	1.45587i	0.889434	+	0.457064i	$0.151099\pi$
$593$	20.4686	+	35.4527i	0.840546	+	1.45587i	−0.0488882	+	0.998804i	$0.515568\pi$
$594$		0			0
$595$	35.1660			1.44167
$596$	11.4686	+	19.8642i	0.469773	+	0.813671i
$597$		0			0
$598$	−3.00000	−	5.19615i	−0.122679	−	0.212486i
$599$	4.93725	+	8.55157i	0.201731	+	0.349408i	0.949086	−	0.315017i	$-0.102010\pi$
$599$	4.93725	+	8.55157i	0.201731	+	0.349408i	−0.747355	+	0.664424i	$0.768677\pi$
$600$		0			0
$601$	−13.4373	−	23.2740i	−0.548117	−	0.949367i	−0.998404	−	0.0564824i	$-0.982012\pi$
$601$	−13.4373	−	23.2740i	−0.548117	−	0.949367i	0.450287	−	0.892884i	$-0.351322\pi$
$602$	−6.61438	−	11.4564i	−0.269582	−	0.466930i
$603$		0			0
$604$	9.61438	+	16.6526i	0.391204	+	0.677584i
$605$	8.35425			0.339649
$606$		0			0
$607$	5.41699			0.219869			0.109935	−	0.993939i	$-0.464936\pi$
$607$	5.41699			0.219869			0.109935	+	0.993939i	$0.464936\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$		0			0
$610$	13.4059	+	23.2197i	0.542788	+	0.940137i
$611$	−11.4686	−	19.8642i	−0.463971	−	0.803621i
$612$		0			0
$613$	21.1974	−	36.7149i	0.856154	−	1.48290i	−0.0194158	−	0.999811i	$-0.506181\pi$
$613$	21.1974	−	36.7149i	0.856154	−	1.48290i	0.875570	−	0.483091i	$-0.160486\pi$
$614$	3.79150	−	6.56708i	0.153013	−	0.265026i
$615$		0			0
$616$	4.82288	+	8.35347i	0.194319	+	0.336571i
$617$	0.760130	−	1.31658i	0.0306017	−	0.0530036i	−0.850319	−	0.526268i	$-0.823591\pi$
$617$	0.760130	−	1.31658i	0.0306017	−	0.0530036i	0.880921	+	0.473264i	$0.156924\pi$
$618$		0			0
$619$	−8.29150			−0.333264			−0.166632	−	0.986019i	$-0.553289\pi$
$619$	−8.29150			−0.333264			−0.166632	+	0.986019i	$0.553289\pi$
$620$	8.46863	−	14.6681i	0.340108	−	0.589085i
$621$		0			0
$622$	−13.5203			−0.542113
$623$	−6.53137	+	11.3127i	−0.261674	+	0.453233i
$624$		0			0
$625$	2.29150			0.0916601
$626$	6.35425	+	11.0059i	0.253967	+	0.439883i
$627$		0			0
$628$	2.00000	−	3.46410i	0.0798087	−	0.138233i
$629$	43.5203			1.73527
$630$		0			0
$631$	6.06275			0.241354			0.120677	−	0.992692i	$-0.461493\pi$
$631$	6.06275			0.241354			0.120677	+	0.992692i	$0.461493\pi$
$632$	5.61438	−	9.72439i	0.223328	−	0.386815i
$633$		0			0
$634$	−13.4059	−	23.2197i	−0.532416	−	0.922171i
$635$	4.93725			0.195929
$636$		0			0
$637$	16.2601	+	28.1634i	0.644250	+	1.11587i
$638$	−8.58301			−0.339804
$639$		0			0
$640$	1.82288	−	3.15731i	0.0720555	−	0.124804i
$641$	18.2288			0.719993			0.359996	−	0.932954i	$-0.382778\pi$
$641$	18.2288			0.719993			0.359996	+	0.932954i	$0.382778\pi$
$642$		0			0
$643$	1.56275	−	2.70676i	0.0616287	−	0.106744i	−0.833565	−	0.552422i	$-0.813704\pi$
$643$	1.56275	−	2.70676i	0.0616287	−	0.106744i	0.895194	+	0.445678i	$0.147037\pi$
$644$	1.70850	−	2.95920i	0.0673242	−	0.116609i
$645$		0			0
$646$	−3.64575	+	6.31463i	−0.143440	+	0.248446i
$647$	4.93725	−	8.55157i	0.194103	−	0.336197i	−0.752503	−	0.658589i	$-0.771154\pi$
$647$	4.93725	−	8.55157i	0.194103	−	0.336197i	0.946606	+	0.322392i	$0.104487\pi$
$648$		0			0
$649$	−15.2288	−	26.3770i	−0.597781	−	1.03539i
$650$	−19.2601	−	33.3595i	−0.755444	−	1.30847i
$651$		0			0
$652$	0.500000	−	0.866025i	0.0195815	−	0.0339162i
$653$	6.00000			0.234798			0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$		0			0
$655$	53.1660			2.07737
$656$	5.46863	+	9.47194i	0.213514	+	0.369817i
$657$		0			0
$658$	6.53137	−	11.3127i	0.254619	−	0.441014i
$659$	−12.1144	−	20.9827i	−0.471909	−	0.817371i	0.527574	−	0.849509i	$-0.323102\pi$
$659$	−12.1144	−	20.9827i	−0.471909	−	0.817371i	−0.999483	+	0.0321382i	$0.989768\pi$
$660$		0			0
$661$	1.58301	+	2.74185i	0.0615718	+	0.106645i	0.895168	−	0.445729i	$-0.147055\pi$
$661$	1.58301	+	2.74185i	0.0615718	+	0.106645i	−0.833596	+	0.552374i	$0.813722\pi$
$662$	−15.9373	−	27.6041i	−0.619419	−	1.07287i
$663$		0			0
$664$	6.64575	+	11.5108i	0.257905	+	0.446705i
$665$	9.64575	−	16.7069i	0.374046	−	0.647867i
$666$		0			0
$667$	1.52026	+	2.63317i	0.0588647	+	0.101957i
$668$	8.58301			0.332086
$669$		0			0
$670$	8.35425			0.322753
$671$	13.4059	−	23.2197i	0.517528	−	0.896385i
$672$		0			0
$673$	−7.87451	−	13.6390i	−0.303540	−	0.525747i	0.673395	−	0.739283i	$-0.264835\pi$
$673$	−7.87451	−	13.6390i	−0.303540	−	0.525747i	−0.976935	+	0.213536i	$0.931502\pi$
$674$	−15.2915	−	26.4857i	−0.589007	−	1.02019i
$675$		0			0
$676$	−4.29150	+	7.43310i	−0.165058	+	0.285888i
$677$	−22.9373	+	39.7285i	−0.881550	+	1.52689i	−0.0319331	+	0.999490i	$0.510166\pi$
$677$	−22.9373	+	39.7285i	−0.881550	+	1.52689i	−0.849617	+	0.527400i	$0.823167\pi$
$678$		0			0
$679$	17.9686	−	31.1226i	0.689573	−	1.19437i
$680$	−6.64575	+	11.5108i	−0.254853	+	0.441418i
$681$		0			0
$682$	−16.9373			−0.648561
$683$	−13.4059	+	23.2197i	−0.512962	+	0.888476i	0.486925	+	0.873444i	$0.338118\pi$
$683$	−13.4059	+	23.2197i	−0.512962	+	0.888476i	−0.999887	+	0.0150322i	$0.995215\pi$
$684$		0			0
$685$	−4.70850			−0.179902
$686$	−9.26013	+	16.0390i	−0.353553	+	0.612372i
$687$		0			0
$688$	5.00000			0.190623
$689$	−13.9373	−	24.1400i	−0.530967	−	0.919662i
$690$		0			0
$691$	19.3745	−	33.5576i	0.737041	−	1.27659i	−0.216781	−	0.976220i	$-0.569556\pi$
$691$	19.3745	−	33.5576i	0.737041	−	1.27659i	0.953822	−	0.300372i	$-0.0971109\pi$
$692$	14.5830			0.554363
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−2.88562	+	4.99804i	−0.109458	+	0.189587i
$696$		0			0
$697$	−19.9373	−	34.5323i	−0.755177	−	1.30801i
$698$	1.22876			0.0465091
$699$		0			0
$700$	10.9686	−	18.9982i	0.414575	−	0.718065i
$701$	26.5830			1.00403			0.502013	−	0.864860i	$-0.332593\pi$
$701$	26.5830			1.00403			0.502013	+	0.864860i	$0.332593\pi$
$702$		0			0
$703$	11.9373	−	20.6759i	0.450222	−	0.779807i
$704$	−3.64575			−0.137404
$705$		0			0
$706$	6.00000	−	10.3923i	0.225813	−	0.391120i
$707$	−11.0516	−	19.1420i	−0.415639	−	0.719909i
$708$		0			0
$709$	−18.9059	+	32.7459i	−0.710025	+	1.22980i	0.254822	+	0.966988i	$0.417983\pi$
$709$	−18.9059	+	32.7459i	−0.710025	+	1.22980i	−0.964847	+	0.262812i	$0.915350\pi$
$710$	−28.5203	+	49.3985i	−1.07035	+	1.85389i
$711$		0			0
$712$	−2.46863	−	4.27579i	−0.0925157	−	0.160242i
$713$	3.00000	+	5.19615i	0.112351	+	0.194597i
$714$		0			0
$715$	−30.8745	+	53.4762i	−1.15464	+	1.99990i
$716$	−16.9373			−0.632975
$717$		0			0
$718$	11.1660			0.416712
$719$	11.4686	+	19.8642i	0.427708	+	0.740811i	0.996669	−	0.0815529i	$-0.0259880\pi$
$719$	11.4686	+	19.8642i	0.427708	+	0.740811i	−0.568961	+	0.822364i	$0.692655\pi$
$720$		0			0
$721$	5.20850	+	9.02138i	0.193975	+	0.335974i
$722$	−7.50000	−	12.9904i	−0.279121	−	0.483452i
$723$		0			0
$724$	1.35425	+	2.34563i	0.0503303	+	0.0871746i
$725$	9.76013	+	16.9050i	0.362482	+	0.627837i
$726$		0			0
$727$	0.614378	+	1.06413i	0.0227860	+	0.0394666i	0.877194	−	0.480137i	$-0.159413\pi$
$727$	0.614378	+	1.06413i	0.0227860	+	0.0394666i	−0.854408	+	0.519603i	$0.826080\pi$
$728$	−12.2915			−0.455553
$729$		0			0
$730$	19.2915	+	33.4139i	0.714011	+	1.23670i
$731$	−18.2288			−0.674215
$732$		0			0
$733$	35.2288			1.30120			0.650602	−	0.759419i	$-0.274517\pi$
$733$	35.2288			1.30120			0.650602	+	0.759419i	$0.274517\pi$
$734$	14.9373	−	25.8721i	0.551344	−	0.954956i
$735$		0			0
$736$	0.645751	+	1.11847i	0.0238027	+	0.0412275i
$737$	−4.17712	−	7.23499i	−0.153866	−	0.266504i
$738$		0			0
$739$	15.7288	−	27.2430i	0.578592	−	1.00215i	−0.417050	−	0.908884i	$-0.636936\pi$
$739$	15.7288	−	27.2430i	0.578592	−	1.00215i	0.995641	−	0.0932664i	$-0.0297308\pi$
$740$	21.7601	−	37.6897i	0.799918	−	1.38550i
$741$		0			0
$742$	7.93725	−	13.7477i	0.291386	−	0.504695i
$743$	−14.4686	+	25.0604i	−0.530802	+	0.919377i	0.468551	+	0.883436i	$0.344776\pi$
$743$	−14.4686	+	25.0604i	−0.530802	+	0.919377i	−0.999354	+	0.0359406i	$0.988557\pi$
$744$		0			0
$745$	−83.6235			−3.06373
$746$	2.29150	−	3.96900i	0.0838979	−	0.145315i
$747$		0			0
$748$	13.2915			0.485985
$749$	7.93725	−	13.7477i	0.290021	−	0.502331i
$750$		0			0
$751$	−52.4575			−1.91420			−0.957101	−	0.289755i	$-0.906426\pi$
$751$	−52.4575			−1.91420			−0.957101	+	0.289755i	$0.906426\pi$
$752$	2.46863	+	4.27579i	0.0900216	+	0.155922i
$753$		0			0
$754$	5.46863	−	9.47194i	0.199156	−	0.344948i
$755$	−70.1033			−2.55132
$756$		0			0
$757$	48.9778			1.78013			0.890064	−	0.455836i	$-0.150660\pi$
$757$	48.9778			1.78013			0.890064	+	0.455836i	$0.150660\pi$
$758$	12.7915	−	22.1555i	0.464608	−	0.804725i
$759$		0			0
$760$	3.64575	+	6.31463i	0.132245	+	0.229056i
$761$	−2.58301			−0.0936339			−0.0468169	−	0.998903i	$-0.514908\pi$
$761$	−2.58301			−0.0936339			−0.0468169	+	0.998903i	$0.514908\pi$
$762$		0			0
$763$	8.87451			0.321279
$764$	20.8118			0.752943
$765$		0			0
$766$	−10.2915	+	17.8254i	−0.371847	+	0.644058i
$767$	38.8118			1.40141
$768$		0			0
$769$	−20.2915	+	35.1459i	−0.731730	+	1.26739i	0.224413	+	0.974494i	$0.427954\pi$
$769$	−20.2915	+	35.1459i	−0.731730	+	1.26739i	−0.956143	+	0.292900i	$0.905380\pi$
$770$	−35.1660			−1.26730
$771$		0			0
$772$	3.50000	−	6.06218i	0.125968	−	0.218183i
$773$	−23.1660	+	40.1247i	−0.833223	+	1.44319i	0.0622452	+	0.998061i	$0.480174\pi$
$773$	−23.1660	+	40.1247i	−0.833223	+	1.44319i	−0.895469	+	0.445125i	$0.853159\pi$
$774$		0			0
$775$	19.2601	+	33.3595i	0.691844	+	1.19831i
$776$	6.79150	+	11.7632i	0.243801	+	0.422275i
$777$		0			0
$778$	−9.64575	+	16.7069i	−0.345817	+	0.598973i
$779$	−21.8745			−0.783736
$780$		0			0
$781$	57.0405			2.04107
$782$	−2.35425	−	4.07768i	−0.0841878	−	0.145817i
$783$		0			0
$784$	−3.50000	−	6.06218i	−0.125000	−	0.216506i
$785$	7.29150	+	12.6293i	0.260245	+	0.450757i
$786$		0			0
$787$	5.85425	+	10.1399i	0.208681	+	0.361447i	0.951299	−	0.308268i	$-0.0997495\pi$
$787$	5.85425	+	10.1399i	0.208681	+	0.361447i	−0.742618	+	0.669715i	$0.766416\pi$
$788$	2.35425	+	4.07768i	0.0838666	+	0.145261i
$789$		0			0
$790$	20.4686	+	35.4527i	0.728241	+	1.26135i
$791$	6.22876			0.221469
$792$		0			0
$793$	17.0830	+	29.5886i	0.606635	+	1.05072i
$794$	16.6458			0.590736
$795$		0			0
$796$	6.06275			0.214888
$797$	−7.40588	+	12.8274i	−0.262330	+	0.454368i	−0.966861	−	0.255305i	$-0.917824\pi$
$797$	−7.40588	+	12.8274i	−0.262330	+	0.454368i	0.704531	+	0.709673i	$0.251157\pi$
$798$		0			0
$799$	−9.00000	−	15.5885i	−0.318397	−	0.551480i
$800$	4.14575	+	7.18065i	0.146574	+	0.253874i
$801$		0			0
$802$	10.4059	−	18.0235i	0.367444	−	0.636432i
$803$	19.2915	−	33.4139i	0.680782	−	1.17915i
$804$		0			0
$805$	6.22876	+	10.7885i	0.219535	+	0.380245i
$806$	10.7915	−	18.6914i	0.380114	−	0.658378i
$807$		0			0
$808$	8.35425			0.293901
$809$	7.70850	−	13.3515i	0.271016	−	0.469414i	−0.698106	−	0.715994i	$-0.745974\pi$
$809$	7.70850	−	13.3515i	0.271016	−	0.469414i	0.969122	+	0.246580i	$0.0793069\pi$
$810$		0			0
$811$	−29.2915			−1.02856			−0.514282	−	0.857621i	$-0.671941\pi$
$811$	−29.2915			−1.02856			−0.514282	+	0.857621i	$0.671941\pi$
$812$	6.22876			0.218587
$813$		0			0
$814$	−43.5203			−1.52538
$815$	1.82288	+	3.15731i	0.0638525	+	0.110596i
$816$		0			0
$817$	−5.00000	+	8.66025i	−0.174928	+	0.302984i
$818$	−14.8745			−0.520075
$819$		0			0
$820$	−39.8745			−1.39248
$821$	10.2915	−	17.8254i	0.359176	−	0.622111i	−0.628647	−	0.777690i	$-0.716391\pi$
$821$	10.2915	−	17.8254i	0.359176	−	0.622111i	0.987823	+	0.155579i	$0.0497245\pi$
$822$		0			0
$823$	17.5516	+	30.4003i	0.611811	+	1.05969i	0.990935	+	0.134342i	$0.0428922\pi$
$823$	17.5516	+	30.4003i	0.611811	+	1.05969i	−0.379124	+	0.925346i	$0.623774\pi$
$824$	−3.93725			−0.137161
$825$		0			0
$826$	11.0516	+	19.1420i	0.384535	+	0.666035i
$827$	43.7490			1.52130			0.760651	−	0.649161i	$-0.224880\pi$
$827$	43.7490			1.52130			0.760651	+	0.649161i	$0.224880\pi$
$828$		0			0
$829$	14.6458	−	25.3672i	0.508668	−	0.881039i	−0.491282	−	0.871001i	$-0.663471\pi$
$829$	14.6458	−	25.3672i	0.508668	−	0.881039i	0.999950	−	0.0100380i	$-0.00319525\pi$
$830$	−48.4575			−1.68198
$831$		0			0
$832$	2.32288	−	4.02334i	0.0805312	−	0.139484i
$833$	12.7601	+	22.1012i	0.442112	+	0.765761i
$834$		0			0
$835$	−15.6458	+	27.0992i	−0.541444	+	0.937808i
$836$	3.64575	−	6.31463i	0.126091	−	0.218396i
$837$		0			0
$838$	−14.4686	−	25.0604i	−0.499810	−	0.865697i
$839$	−24.6458	−	42.6877i	−0.850866	−	1.47374i	−0.880428	−	0.474180i	$-0.842745\pi$
$839$	−24.6458	−	42.6877i	−0.850866	−	1.47374i	0.0295622	−	0.999563i	$-0.490589\pi$
$840$		0			0
$841$	11.7288	−	20.3148i	0.404440	−	0.700510i
$842$	14.7085			0.506888
$843$		0			0
$844$	14.8745			0.512002
$845$	−15.6458	−	27.0992i	−0.538230	−	0.932242i
$846$		0			0
$847$	3.03137	+	5.25049i	0.104159	+	0.180409i
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$		0			0
$850$	−15.1144	−	26.1789i	−0.518419	−	0.897928i
$851$	7.70850	+	13.3515i	0.264244	+	0.457684i
$852$		0			0
$853$	−23.9373	−	41.4605i	−0.819596	−	1.41958i	−0.905980	−	0.423320i	$-0.860865\pi$
$853$	−23.9373	−	41.4605i	−0.819596	−	1.41958i	0.0863843	−	0.996262i	$-0.472469\pi$
$854$	−9.72876	+	16.8507i	−0.332911	+	0.576619i
$855$		0			0
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$	26.8118			0.915872			0.457936	−	0.888985i	$-0.348589\pi$
$857$	26.8118			0.915872			0.457936	+	0.888985i	$0.348589\pi$
$858$		0			0
$859$	−7.00000			−0.238837			−0.119418	−	0.992844i	$-0.538103\pi$
$859$	−7.00000			−0.238837			−0.119418	+	0.992844i	$0.538103\pi$
$860$	−9.11438	+	15.7866i	−0.310798	+	0.538317i
$861$		0			0
$862$	−19.4059	−	33.6120i	−0.660967	−	1.14483i
$863$	14.5830	+	25.2585i	0.496411	+	0.859810i	0.999991	−	0.00413896i	$-0.00131748\pi$
$863$	14.5830	+	25.2585i	0.496411	+	0.859810i	−0.503580	+	0.863949i	$0.667984\pi$
$864$		0			0
$865$	−26.5830	+	46.0431i	−0.903849	+	1.56551i
$866$	−9.50000	+	16.4545i	−0.322823	+	0.559146i
$867$		0			0
$868$	12.2915			0.417201
$869$	20.4686	−	35.4527i	0.694351	−	1.20265i
$870$		0			0
$871$	10.6458			0.360718
$872$	−1.67712	+	2.90486i	−0.0567946	+	0.0983711i
$873$		0			0
$874$	−2.58301			−0.0873715
$875$	15.8745	+	27.4955i	0.536656	+	0.929516i
$876$		0			0
$877$	26.6458			0.899763			0.449882	−	0.893088i	$-0.351466\pi$
$877$	26.6458			0.899763			0.449882	+	0.893088i	$0.351466\pi$
$878$	12.5830	+	21.7944i	0.424656	+	0.735526i
$879$		0			0
$880$	6.64575	−	11.5108i	0.224028	−	0.388028i
$881$	3.87451			0.130535			0.0652677	−	0.997868i	$-0.479210\pi$
$881$	3.87451			0.130535			0.0652677	+	0.997868i	$0.479210\pi$
$882$		0			0
$883$	−19.8745			−0.668830			−0.334415	−	0.942426i	$-0.608539\pi$
$883$	−19.8745			−0.668830			−0.334415	+	0.942426i	$0.608539\pi$
$884$	−8.46863	+	14.6681i	−0.284831	+	0.493341i
$885$		0			0
$886$	9.64575	+	16.7069i	0.324055	+	0.561280i
$887$	−15.8745			−0.533014			−0.266507	−	0.963833i	$-0.585870\pi$
$887$	−15.8745			−0.533014			−0.266507	+	0.963833i	$0.585870\pi$
$888$		0			0
$889$	1.79150	+	3.10297i	0.0600851	+	0.104070i
$890$	18.0000			0.603361
$891$		0			0
$892$	6.93725	−	12.0157i	0.232276	−	0.402315i
$893$	−9.87451			−0.330438
$894$		0			0
$895$	30.8745	−	53.4762i	1.03202	−	1.78751i
$896$	2.64575			0.0883883
$897$		0			0
$898$	−1.17712	+	2.03884i	−0.0392811	+	0.0680369i
$899$	−5.46863	+	9.47194i	−0.182389	+	0.315907i
$900$		0			0
$901$	−10.9373	−	18.9439i	−0.364373	−	0.631112i
$902$	19.9373	+	34.5323i	0.663838	+	1.14980i
$903$		0			0
$904$	−1.17712	+	2.03884i	−0.0391506	+	0.0678108i
$905$	−9.87451			−0.328240
$906$		0			0
$907$	36.2915			1.20504			0.602520	−	0.798104i	$-0.294163\pi$
$907$	36.2915			1.20504			0.602520	+	0.798104i	$0.294163\pi$
$908$	3.00000	+	5.19615i	0.0995585	+	0.172440i
$909$		0			0
$910$	22.4059	−	38.8081i	0.742748	−	1.28648i
$911$	14.4686	+	25.0604i	0.479367	+	0.830288i	0.999720	−	0.0236633i	$-0.00753296\pi$
$911$	14.4686	+	25.0604i	0.479367	+	0.830288i	−0.520353	+	0.853951i	$0.674200\pi$
$912$		0			0
$913$	24.2288	+	41.9654i	0.801855	+	1.38885i
$914$	−4.14575	−	7.18065i	−0.137129	−	0.237515i
$915$		0			0
$916$	4.67712	+	8.10102i	0.154537	+	0.267665i
$917$	19.2915	+	33.4139i	0.637062	+	1.10342i
$918$		0			0
$919$	−14.3856	−	24.9166i	−0.474538	−	0.821924i	0.525037	−	0.851079i	$-0.324051\pi$
$919$	−14.3856	−	24.9166i	−0.474538	−	0.821924i	−0.999575	+	0.0291557i	$0.990718\pi$
$920$	−4.70850			−0.155235
$921$		0			0
$922$	24.2288			0.797932
$923$	−36.3431	+	62.9482i	−1.19625	+	2.07196i
$924$		0			0
$925$	49.4889	+	85.7173i	1.62718	+	2.81837i
$926$	9.35425	+	16.2020i	0.307400	+	0.532432i
$927$		0			0
$928$	−1.17712	+	2.03884i	−0.0386410	+	0.0669282i
$929$	−8.46863	+	14.6681i	−0.277847	+	0.481244i	−0.970849	−	0.239690i	$-0.922954\pi$
$929$	−8.46863	+	14.6681i	−0.277847	+	0.481244i	0.693003	+	0.720935i	$0.256287\pi$
$930$		0			0
$931$	14.0000			0.458831
$932$	−9.64575	+	16.7069i	−0.315957	+	0.547254i
$933$		0			0
$934$	0.228757			0.00748514
$935$	−24.2288	+	41.9654i	−0.792365	+	1.37242i
$936$		0			0
$937$	−44.7490			−1.46189			−0.730943	−	0.682438i	$-0.760920\pi$
$937$	−44.7490			−1.46189			−0.730943	+	0.682438i	$0.760920\pi$
$938$	3.03137	+	5.25049i	0.0989778	+	0.171435i
$939$		0			0
$940$	−18.0000			−0.587095
$941$	−26.6974	−	46.2412i	−0.870310	−	1.50742i	−0.861676	−	0.507458i	$-0.830585\pi$
$941$	−26.6974	−	46.2412i	−0.870310	−	1.50742i	−0.00863340	−	0.999963i	$-0.502748\pi$
$942$		0			0
$943$	7.06275	−	12.2330i	0.229995	−	0.398362i
$944$	−8.35425			−0.271908
$945$		0			0
$946$	18.2288			0.592668
$947$	5.23987	−	9.07572i	0.170273	−	0.294921i	−0.768242	−	0.640159i	$-0.778868\pi$
$947$	5.23987	−	9.07572i	0.170273	−	0.294921i	0.938515	+	0.345238i	$0.112202\pi$
$948$		0			0
$949$	24.5830	+	42.5790i	0.797998	+	1.38217i
$950$	−16.5830			−0.538024
$951$		0			0
$952$	−9.64575			−0.312621
$953$	−52.3320			−1.69520			−0.847600	−	0.530635i	$-0.821953\pi$
$953$	−52.3320			−1.69520			−0.847600	+	0.530635i	$0.821953\pi$
$954$		0			0
$955$	−37.9373	+	65.7093i	−1.22762	+	2.12630i
$956$	10.9373			0.353736
$957$		0			0
$958$	−1.82288	+	3.15731i	−0.0588944	+	0.102008i
$959$	−1.70850	−	2.95920i	−0.0551703	−	0.0955577i
$960$		0			0
$961$	4.70850	−	8.15536i	0.151887	−	0.263076i
$962$	27.7288	−	48.0276i	0.894011	−	1.54847i
$963$		0			0
$964$	−2.50000	−	4.33013i	−0.0805196	−	0.139464i
$965$	12.7601	+	22.1012i	0.410763	+	0.711463i
$966$		0			0
$967$	−18.0314	+	31.2313i	−0.579850	+	1.00433i	0.415646	+	0.909526i	$0.363555\pi$
$967$	−18.0314	+	31.2313i	−0.579850	+	1.00433i	−0.995496	+	0.0948030i	$0.969778\pi$
$968$	−2.29150			−0.0736517
$969$		0			0
$970$	−49.5203			−1.59000
$971$	−4.93725	−	8.55157i	−0.158444	−	0.274433i	0.775864	−	0.630901i	$-0.217314\pi$
$971$	−4.93725	−	8.55157i	−0.158444	−	0.274433i	−0.934308	+	0.356467i	$0.883981\pi$
$972$		0			0
$973$	−4.18824			−0.134269
$974$	11.9373	+	20.6759i	0.382494	+	0.662500i
$975$		0			0
$976$	−3.67712	−	6.36897i	−0.117702	−	0.203866i
$977$	−25.9373	−	44.9246i	−0.829806	−	1.43727i	−0.898190	−	0.439608i	$-0.855118\pi$
$977$	−25.9373	−	44.9246i	−0.829806	−	1.43727i	0.0683837	−	0.997659i	$-0.478216\pi$
$978$		0			0
$979$	−9.00000	−	15.5885i	−0.287641	−	0.498209i
$980$	25.5203			0.815215
$981$		0			0
$982$	−12.8745	−	22.2993i	−0.410842	−	0.711599i
$983$	−20.8118			−0.663792			−0.331896	−	0.943316i	$-0.607688\pi$
$983$	−20.8118			−0.663792			−0.331896	+	0.943316i	$0.607688\pi$
$984$		0			0
$985$	−17.1660			−0.546955
$986$	4.29150	−	7.43310i	0.136669	−	0.236718i
$987$		0			0
$988$	4.64575	+	8.04668i	0.147801	+	0.255999i
$989$	−3.22876	−	5.59237i	−0.102668	−	0.177827i
$990$		0			0
$991$	13.0314	−	22.5710i	0.413955	−	0.716991i	−0.581363	−	0.813644i	$-0.697480\pi$
$991$	13.0314	−	22.5710i	0.413955	−	0.716991i	0.995318	+	0.0966529i	$0.0308137\pi$
$992$	−2.32288	+	4.02334i	−0.0737514	+	0.127741i
$993$		0			0
$994$	−41.3948			−1.31296
$995$	−11.0516	+	19.1420i	−0.350360	+	0.606842i
$996$		0			0
$997$	23.6863			0.750152			0.375076	−	0.926994i	$-0.377617\pi$
$997$	23.6863			0.750152			0.375076	+	0.926994i	$0.377617\pi$
$998$	−3.08301	+	5.33992i	−0.0975908	+	0.169032i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.h.t.109.2		4
3.2	odd	2		1134.2.h.q.109.1		4
7.2	even	3		1134.2.e.q.919.1		4
9.2	odd	6		1134.2.e.t.865.2		4
9.4	even	3		378.2.g.h.109.1	yes	4
9.5	odd	6		378.2.g.g.109.2	✓	4
9.7	even	3		1134.2.e.q.865.1		4
21.2	odd	6		1134.2.e.t.919.2		4
63.2	odd	6		1134.2.h.q.541.1		4
63.4	even	3		2646.2.a.bi.1.2		2
63.16	even	3	inner	1134.2.h.t.541.2		4
63.23	odd	6		378.2.g.g.163.2	yes	4
63.31	odd	6		2646.2.a.bf.1.1		2
63.32	odd	6		2646.2.a.bl.1.1		2
63.58	even	3		378.2.g.h.163.1	yes	4
63.59	even	6		2646.2.a.bo.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.g.g.109.2	✓	4	9.5	odd	6
378.2.g.g.163.2	yes	4	63.23	odd	6
378.2.g.h.109.1	yes	4	9.4	even	3
378.2.g.h.163.1	yes	4	63.58	even	3
1134.2.e.q.865.1		4	9.7	even	3
1134.2.e.q.919.1		4	7.2	even	3
1134.2.e.t.865.2		4	9.2	odd	6
1134.2.e.t.919.2		4	21.2	odd	6
1134.2.h.q.109.1		4	3.2	odd	2
1134.2.h.q.541.1		4	63.2	odd	6
1134.2.h.t.109.2		4	1.1	even	1	trivial
1134.2.h.t.541.2		4	63.16	even	3	inner
2646.2.a.bf.1.1		2	63.31	odd	6
2646.2.a.bi.1.2		2	63.4	even	3
2646.2.a.bl.1.1		2	63.32	odd	6
2646.2.a.bo.1.2		2	63.59	even	6

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.64575 q^{5} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.64575 q^{5} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(1.82288 - 3.15731i) q^{10} -3.64575 q^{11} +(2.32288 - 4.02334i) q^{13} +2.64575 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.82288 - 3.15731i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(-1.82288 - 3.15731i) q^{20} +(-1.82288 + 3.15731i) q^{22} +1.29150 q^{23} +8.29150 q^{25} +(-2.32288 - 4.02334i) q^{26} +(1.32288 - 2.29129i) q^{28} +(1.17712 + 2.03884i) q^{29} +(2.32288 + 4.02334i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.82288 - 3.15731i) q^{34} +(4.82288 + 8.35347i) q^{35} +(5.96863 + 10.3380i) q^{37} -2.00000 q^{38} -3.64575 q^{40} +(5.46863 - 9.47194i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(1.82288 + 3.15731i) q^{44} +(0.645751 - 1.11847i) q^{46} +(2.46863 - 4.27579i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(4.14575 - 7.18065i) q^{50} -4.64575 q^{52} +(3.00000 - 5.19615i) q^{53} -13.2915 q^{55} +(-1.32288 - 2.29129i) q^{56} +2.35425 q^{58} +(4.17712 + 7.23499i) q^{59} +(-3.67712 + 6.36897i) q^{61} +4.64575 q^{62} +1.00000 q^{64} +(8.46863 - 14.6681i) q^{65} +(1.14575 + 1.98450i) q^{67} -3.64575 q^{68} +9.64575 q^{70} -15.6458 q^{71} +(-5.29150 + 9.16515i) q^{73} +11.9373 q^{74} +(-1.00000 + 1.73205i) q^{76} +(-4.82288 - 8.35347i) q^{77} +(-5.61438 + 9.72439i) q^{79} +(-1.82288 + 3.15731i) q^{80} +(-5.46863 - 9.47194i) q^{82} +(-6.64575 - 11.5108i) q^{83} +(6.64575 - 11.5108i) q^{85} -5.00000 q^{86} +3.64575 q^{88} +(2.46863 + 4.27579i) q^{89} +12.2915 q^{91} +(-0.645751 - 1.11847i) q^{92} +(-2.46863 - 4.27579i) q^{94} +(-3.64575 - 6.31463i) q^{95} +(-6.79150 - 11.7632i) q^{97} +(3.50000 + 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8} + 2 q^{10} - 4 q^{11} + 4 q^{13} - 2 q^{16} + 2 q^{17} - 4 q^{19} - 2 q^{20} - 2 q^{22} - 16 q^{23} + 12 q^{25} - 4 q^{26} + 10 q^{29} + 4 q^{31} + 2 q^{32} - 2 q^{34} + 14 q^{35} + 8 q^{37} - 8 q^{38} - 4 q^{40} + 6 q^{41} - 10 q^{43} + 2 q^{44} - 8 q^{46} - 6 q^{47} - 14 q^{49} + 6 q^{50} - 8 q^{52} + 12 q^{53} - 32 q^{55} + 20 q^{58} + 22 q^{59} - 20 q^{61} + 8 q^{62} + 4 q^{64} + 18 q^{65} - 6 q^{67} - 4 q^{68} + 28 q^{70} - 52 q^{71} + 16 q^{74} - 4 q^{76} - 14 q^{77} + 4 q^{79} - 2 q^{80} - 6 q^{82} - 16 q^{83} + 16 q^{85} - 20 q^{86} + 4 q^{88} - 6 q^{89} + 28 q^{91} + 8 q^{92} + 6 q^{94} - 4 q^{95} - 6 q^{97} + 14 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^8 + 2 * q^10 - 4 * q^11 + 4 * q^13 - 2 * q^16 + 2 * q^17 - 4 * q^19 - 2 * q^20 - 2 * q^22 - 16 * q^23 + 12 * q^25 - 4 * q^26 + 10 * q^29 + 4 * q^31 + 2 * q^32 - 2 * q^34 + 14 * q^35 + 8 * q^37 - 8 * q^38 - 4 * q^40 + 6 * q^41 - 10 * q^43 + 2 * q^44 - 8 * q^46 - 6 * q^47 - 14 * q^49 + 6 * q^50 - 8 * q^52 + 12 * q^53 - 32 * q^55 + 20 * q^58 + 22 * q^59 - 20 * q^61 + 8 * q^62 + 4 * q^64 + 18 * q^65 - 6 * q^67 - 4 * q^68 + 28 * q^70 - 52 * q^71 + 16 * q^74 - 4 * q^76 - 14 * q^77 + 4 * q^79 - 2 * q^80 - 6 * q^82 - 16 * q^83 + 16 * q^85 - 20 * q^86 + 4 * q^88 - 6 * q^89 + 28 * q^91 + 8 * q^92 + 6 * q^94 - 4 * q^95 - 6 * q^97 + 14 * q^98

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