LMFDB - Embedded newform 1134.2.h.q.109.1

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			109.1
Root			$1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1134.109
Dual form			1134.2.h.q.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.64575 q^{5} +(1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.64575 q^{5} +(1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +(1.82288 - 3.15731i) q^{10} +3.64575 q^{11} +(2.32288 - 4.02334i) q^{13} -2.64575 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.82288 + 3.15731i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(1.82288 + 3.15731i) q^{20} +(-1.82288 + 3.15731i) q^{22} -1.29150 q^{23} +8.29150 q^{25} +(2.32288 + 4.02334i) q^{26} +(1.32288 - 2.29129i) q^{28} +(-1.17712 - 2.03884i) q^{29} +(2.32288 + 4.02334i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.82288 - 3.15731i) q^{34} +(-4.82288 - 8.35347i) q^{35} +(5.96863 + 10.3380i) q^{37} +2.00000 q^{38} -3.64575 q^{40} +(-5.46863 + 9.47194i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(-1.82288 - 3.15731i) q^{44} +(0.645751 - 1.11847i) q^{46} +(-2.46863 + 4.27579i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-4.14575 + 7.18065i) q^{50} -4.64575 q^{52} +(-3.00000 + 5.19615i) q^{53} -13.2915 q^{55} +(1.32288 + 2.29129i) q^{56} +2.35425 q^{58} +(-4.17712 - 7.23499i) q^{59} +(-3.67712 + 6.36897i) q^{61} -4.64575 q^{62} +1.00000 q^{64} +(-8.46863 + 14.6681i) q^{65} +(1.14575 + 1.98450i) q^{67} +3.64575 q^{68} +9.64575 q^{70} +15.6458 q^{71} +(-5.29150 + 9.16515i) q^{73} -11.9373 q^{74} +(-1.00000 + 1.73205i) q^{76} +(4.82288 + 8.35347i) q^{77} +(-5.61438 + 9.72439i) q^{79} +(1.82288 - 3.15731i) q^{80} +(-5.46863 - 9.47194i) q^{82} +(6.64575 + 11.5108i) q^{83} +(6.64575 - 11.5108i) q^{85} +5.00000 q^{86} +3.64575 q^{88} +(-2.46863 - 4.27579i) q^{89} +12.2915 q^{91} +(0.645751 + 1.11847i) q^{92} +(-2.46863 - 4.27579i) q^{94} +(3.64575 + 6.31463i) q^{95} +(-6.79150 - 11.7632i) q^{97} +(-3.50000 - 6.06218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.803381\pi$
$5$	−3.64575			−1.63043			−0.815215	+	0.579159i	$0.803381\pi$
$6$		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	$-0.314773\pi$
$11$	3.64575			1.09924			0.549618	+	0.835416i	$0.314773\pi$
$12$		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	−0.997846	−	0.0655994i	$-0.979104\pi$
$17$	−1.82288	+	3.15731i	−0.442112	+	0.765761i	0.555734	+	0.831360i	$0.312437\pi$
$18$		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	$-0.542991\pi$
$23$	−1.29150			−0.269297			−0.134648	+	0.990893i	$0.542991\pi$
$24$		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	0.735790	−	0.677210i	$-0.236811\pi$
$29$	−1.17712	−	2.03884i	−0.218587	−	0.378603i	−0.954376	+	0.298607i	$0.903478\pi$
$30$		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	$0.492531\pi$
$41$	−5.46863	+	9.47194i	−0.854056	+	1.47927i	−0.877518	+	0.479544i	$0.840802\pi$
$42$		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	−0.987975	−	0.154616i	$-0.950586\pi$
$47$	−2.46863	+	4.27579i	−0.360086	+	0.623688i	0.627888	+	0.778303i	$0.283919\pi$
$48$		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	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		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	$-0.983646\pi$
$59$	−4.17712	−	7.23499i	−0.543815	−	0.941916i	0.454865	−	0.890560i	$-0.349687\pi$
$60$		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	$-0.121181\pi$
$71$	15.6458			1.85681			0.928405	+	0.371571i	$0.121181\pi$
$72$		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	$0.0935647\pi$
$83$	6.64575	+	11.5108i	0.729466	+	1.26347i	−0.227643	+	0.973745i	$0.573102\pi$
$84$		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	0.705013	−	0.709194i	$-0.250941\pi$
$89$	−2.46863	−	4.27579i	−0.261674	−	0.453233i	−0.966687	+	0.255962i	$0.917608\pi$
$90$		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	$-0.363558\pi$
$101$	8.35425			0.831279			0.415639	+	0.909529i	$0.363558\pi$
$102$		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	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$		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	−0.916067	−	0.401026i	$-0.868654\pi$
$113$	−1.17712	+	2.03884i	−0.110735	+	0.191798i	0.805332	+	0.592824i	$0.201987\pi$
$114$		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	$-0.719850\pi$
$131$	−14.5830			−1.27412			−0.637062	+	0.770813i	$0.719850\pi$
$132$		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	$-0.482430\pi$
$137$	1.29150			0.110341			0.0551703	+	0.998477i	$0.482430\pi$
$138$		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	$-0.111247\pi$
$149$	22.9373			1.87909			0.939547	+	0.342421i	$0.111247\pi$
$150$		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	−0.650834	−	0.759220i	$-0.725581\pi$
$167$	4.29150	−	7.43310i	0.332086	−	0.575191i	0.982921	+	0.184029i	$0.0589141\pi$
$168$		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	$-0.646295\pi$
$173$	7.29150	−	12.6293i	0.554363	−	0.960184i	0.997953	−	0.0639546i	$-0.0203713\pi$
$174$		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	$0.384833\pi$
$179$	−8.46863	+	14.6681i	−0.632975	+	1.09634i	−0.986940	+	0.161086i	$0.948500\pi$
$180$		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	$-0.561967\pi$
$191$	10.4059	−	18.0235i	0.752943	−	1.30414i	0.946390	−	0.323025i	$-0.104700\pi$
$192$		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	$-0.446355\pi$
$197$	4.70850			0.335467			0.167733	+	0.985832i	$0.446355\pi$
$198$		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	$-0.436193\pi$
$227$	6.00000			0.398234			0.199117	+	0.979976i	$0.436193\pi$
$228$		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	$0.0510638\pi$
$233$	9.64575	+	16.7069i	0.631914	+	1.09451i	−0.355246	+	0.934773i	$0.615603\pi$
$234$		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	−0.633165	−	0.774017i	$-0.718244\pi$
$239$	5.46863	−	9.47194i	0.353736	−	0.612689i	0.986901	+	0.161328i	$0.0515778\pi$
$240$		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	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		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	$-0.335127\pi$
$257$	15.8745			0.990225			0.495112	+	0.868829i	$0.335127\pi$
$258$		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	$-0.548643\pi$
$263$	−4.93725			−0.304444			−0.152222	+	0.988346i	$0.548643\pi$
$264$		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	$-0.663213\pi$
$269$	8.35425	−	14.4700i	0.509368	−	0.882250i	0.999941	−	0.0108507i	$-0.00345395\pi$
$270$		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	$-0.968843\pi$
$281$	−9.76013	−	16.9050i	−0.582241	−	1.00847i	0.412973	−	0.910743i	$-0.364490\pi$
$282$		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	−0.950548	−	0.310578i	$-0.899477\pi$
$293$	−3.53137	+	6.11652i	−0.206305	+	0.357331i	0.744243	+	0.667909i	$0.232811\pi$
$294$		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	0.991536	−	0.129830i	$-0.0414433\pi$
$311$	6.76013	+	11.7089i	0.383332	+	0.663950i	−0.608204	+	0.793780i	$0.708110\pi$
$312$		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	$0.438036\pi$
$317$	−13.4059	+	23.2197i	−0.752949	+	1.30415i	−0.946387	+	0.323034i	$0.895297\pi$
$318$		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	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		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	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$		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	0.680246	−	0.732984i	$-0.261873\pi$
$359$	−5.58301	−	9.67005i	−0.294660	−	0.510366i	−0.974906	+	0.222618i	$0.928540\pi$
$360$		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	$-0.323739\pi$
$383$	20.5830			1.05174			0.525871	+	0.850564i	$0.323739\pi$
$384$		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	$-0.337340\pi$
$389$	19.2915			0.978118			0.489059	+	0.872251i	$0.337340\pi$
$390$		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	$-0.673936\pi$
$401$	−20.8118			−1.03929			−0.519645	+	0.854382i	$0.673936\pi$
$402$		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	$0.416546\pi$
$419$	−14.4686	+	25.0604i	−0.706839	+	1.22428i	−0.966024	+	0.258453i	$0.916787\pi$
$420$		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	$0.551042\pi$
$431$	−19.4059	+	33.6120i	−0.934748	+	1.61903i	−0.775082	+	0.631861i	$0.782291\pi$
$432$		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	−0.540587	−	0.841288i	$-0.681798\pi$
$443$	9.64575	−	16.7069i	0.458283	−	0.793770i	0.998870	+	0.0475179i	$0.0151311\pi$
$444$		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	$-0.482308\pi$
$449$	2.35425			0.111104			0.0555519	+	0.998456i	$0.482308\pi$
$450$		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	$-0.975843\pi$
$461$	−12.1144	−	20.9827i	−0.564223	−	0.977263i	0.432899	−	0.901443i	$-0.357491\pi$
$462$		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	0.863367	−	0.504577i	$-0.168351\pi$
$467$	−0.114378	−	0.198109i	−0.00529280	−	0.00916739i	−0.868660	+	0.495409i	$0.835018\pi$
$468$		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	$-0.473457\pi$
$479$	3.64575			0.166579			0.0832893	+	0.996525i	$0.473457\pi$
$480$		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	$0.364012\pi$
$491$	−12.8745	+	22.2993i	−0.581018	+	1.00635i	−0.995359	+	0.0962315i	$0.969321\pi$
$492$		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	$-0.472471\pi$
$503$	3.87451			0.172756			0.0863779	+	0.996262i	$0.472471\pi$
$504$		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	$-0.442365\pi$
$509$	8.12549			0.360156			0.180078	+	0.983652i	$0.442365\pi$
$510$		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	−0.763201	−	0.646162i	$-0.776373\pi$
$521$	4.06275	−	7.03688i	0.177992	−	0.308291i	0.941193	+	0.337870i	$0.109707\pi$
$522$		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	−0.798394	−	0.602136i	$-0.794317\pi$
$557$	2.88562	−	4.99804i	0.122268	−	0.211774i	0.920662	+	0.390362i	$0.127650\pi$
$558$		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	0.603362	−	0.797467i	$-0.293827\pi$
$563$	−9.22876	−	15.9847i	−0.388946	−	0.673674i	−0.992308	+	0.123793i	$0.960494\pi$
$564$		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	−0.632099	−	0.774888i	$-0.717806\pi$
$569$	8.46863	−	14.6681i	0.355023	−	0.614918i	0.987122	+	0.159970i	$0.0511396\pi$
$570$		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	0.718621	−	0.695402i	$-0.244774\pi$
$587$	−5.88562	−	10.1942i	−0.242926	−	0.420759i	−0.961546	+	0.274643i	$0.911440\pi$
$588$		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	$-0.848901\pi$
$593$	−20.4686	−	35.4527i	−0.840546	−	1.45587i	0.0488882	−	0.998804i	$-0.484432\pi$
$594$		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	0.747355	−	0.664424i	$-0.231323\pi$
$599$	−4.93725	−	8.55157i	−0.201731	−	0.349408i	−0.949086	+	0.315017i	$0.897990\pi$
$600$		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	−0.880921	−	0.473264i	$-0.843076\pi$
$617$	−0.760130	+	1.31658i	−0.0306017	+	0.0530036i	0.850319	+	0.526268i	$0.176409\pi$
$618$		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	$-0.617222\pi$
$641$	−18.2288			−0.719993			−0.359996	+	0.932954i	$0.617222\pi$
$642$		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	−0.946606	−	0.322392i	$-0.895513\pi$
$647$	−4.93725	+	8.55157i	−0.194103	+	0.336197i	0.752503	+	0.658589i	$0.228846\pi$
$648$		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	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$		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	0.999483	−	0.0321382i	$-0.0102317\pi$
$659$	12.1144	+	20.9827i	0.471909	+	0.817371i	−0.527574	+	0.849509i	$0.676898\pi$
$660$		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	$-0.489834\pi$
$677$	22.9373	−	39.7285i	0.881550	−	1.52689i	0.849617	−	0.527400i	$-0.176833\pi$
$678$		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	$-0.661882\pi$
$683$	13.4059	−	23.2197i	0.512962	−	0.888476i	0.999887	−	0.0150322i	$-0.00478508\pi$
$684$		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	$-0.667407\pi$
$701$	−26.5830			−1.00403			−0.502013	+	0.864860i	$0.667407\pi$
$702$		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	0.568961	−	0.822364i	$-0.307345\pi$
$719$	−11.4686	−	19.8642i	−0.427708	−	0.740811i	−0.996669	+	0.0815529i	$0.974012\pi$
$720$		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	$-0.655224\pi$
$743$	14.4686	−	25.0604i	0.530802	−	0.919377i	0.999354	−	0.0359406i	$-0.0114427\pi$
$744$		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	$-0.485092\pi$
$761$	2.58301			0.0936339			0.0468169	+	0.998903i	$0.485092\pi$
$762$		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	$-0.519826\pi$
$773$	23.1660	−	40.1247i	0.833223	−	1.44319i	0.895469	−	0.445125i	$-0.146841\pi$
$774$		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	−0.704531	−	0.709673i	$-0.748843\pi$
$797$	7.40588	−	12.8274i	0.262330	−	0.454368i	0.966861	+	0.255305i	$0.0821759\pi$
$798$		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	−0.969122	−	0.246580i	$-0.920693\pi$
$809$	−7.70850	+	13.3515i	−0.271016	+	0.469414i	0.698106	+	0.715994i	$0.254026\pi$
$810$		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	−0.987823	−	0.155579i	$-0.950276\pi$
$821$	−10.2915	+	17.8254i	−0.359176	+	0.622111i	0.628647	+	0.777690i	$0.283609\pi$
$822$		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	$-0.775120\pi$
$827$	−43.7490			−1.52130			−0.760651	+	0.649161i	$0.775120\pi$
$828$		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	$0.157255\pi$
$839$	24.6458	+	42.6877i	0.850866	+	1.47374i	−0.0295622	+	0.999563i	$0.509411\pi$
$840$		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	$-0.651411\pi$
$857$	−26.8118			−0.915872			−0.457936	+	0.888985i	$0.651411\pi$
$858$		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	0.503580	−	0.863949i	$-0.332016\pi$
$863$	−14.5830	−	25.2585i	−0.496411	−	0.859810i	−0.999991	+	0.00413896i	$0.998683\pi$
$864$		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	$-0.520790\pi$
$881$	−3.87451			−0.130535			−0.0652677	+	0.997868i	$0.520790\pi$
$882$		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	$-0.414130\pi$
$887$	15.8745			0.533014			0.266507	+	0.963833i	$0.414130\pi$
$888$		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	0.520353	−	0.853951i	$-0.325800\pi$
$911$	−14.4686	−	25.0604i	−0.479367	−	0.830288i	−0.999720	+	0.0236633i	$0.992467\pi$
$912$		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	−0.693003	−	0.720935i	$-0.743713\pi$
$929$	8.46863	−	14.6681i	0.277847	−	0.481244i	0.970849	+	0.239690i	$0.0770460\pi$
$930$		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	$0.169415\pi$
$941$	26.6974	+	46.2412i	0.870310	+	1.50742i	0.00863340	+	0.999963i	$0.497252\pi$
$942$		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	−0.938515	−	0.345238i	$-0.887798\pi$
$947$	−5.23987	+	9.07572i	−0.170273	+	0.294921i	0.768242	+	0.640159i	$0.221132\pi$
$948$		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	$-0.178047\pi$
$953$	52.3320			1.69520			0.847600	+	0.530635i	$0.178047\pi$
$954$		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	0.934308	−	0.356467i	$-0.116019\pi$
$971$	4.93725	+	8.55157i	0.158444	+	0.274433i	−0.775864	+	0.630901i	$0.782686\pi$
$972$		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	$0.144882\pi$
$977$	25.9373	+	44.9246i	0.829806	+	1.43727i	−0.0683837	+	0.997659i	$0.521784\pi$
$978$		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	$-0.392312\pi$
$983$	20.8118			0.663792			0.331896	+	0.943316i	$0.392312\pi$
$984$		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.q.109.1		4
3.2	odd	2		1134.2.h.t.109.2		4
7.2	even	3		1134.2.e.t.919.2		4
9.2	odd	6		1134.2.e.q.865.1		4
9.4	even	3		378.2.g.g.109.2	✓	4
9.5	odd	6		378.2.g.h.109.1	yes	4
9.7	even	3		1134.2.e.t.865.2		4
21.2	odd	6		1134.2.e.q.919.1		4
63.2	odd	6		1134.2.h.t.541.2		4
63.4	even	3		2646.2.a.bl.1.1		2
63.16	even	3	inner	1134.2.h.q.541.1		4
63.23	odd	6		378.2.g.h.163.1	yes	4
63.31	odd	6		2646.2.a.bo.1.2		2
63.32	odd	6		2646.2.a.bi.1.2		2
63.58	even	3		378.2.g.g.163.2	yes	4
63.59	even	6		2646.2.a.bf.1.1		2

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