LMFDB - Embedded newform 525.2.bc.b.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	525.157
Dual form			525.2.bc.b.418.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.448288 - 1.67303i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.73205i q^{6} +(-1.15539 + 2.38014i) q^{7} +(1.22474 - 1.22474i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.448288 - 1.67303i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.73205i q^{6} +(-1.15539 + 2.38014i) q^{7} +(1.22474 - 1.22474i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.00000 - 5.19615i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(3.53553 + 3.53553i) q^{13} +(3.46410 + 3.00000i) q^{14} +(-2.50000 - 4.33013i) q^{16} +(-0.448288 - 1.67303i) q^{18} +(-2.59808 - 4.50000i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(-7.34847 - 7.34847i) q^{22} +(-3.34607 - 0.896575i) q^{23} +(0.866025 - 1.50000i) q^{24} +(7.50000 - 4.33013i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.19067 - 1.48356i) q^{28} +(3.00000 + 1.73205i) q^{31} +(-5.01910 + 1.34486i) q^{32} +(1.55291 - 5.79555i) q^{33} -1.00000 q^{36} +(-2.24144 + 8.36516i) q^{37} +(-8.69333 + 2.32937i) q^{38} +(4.33013 + 2.50000i) q^{39} +10.3923i q^{41} +(4.12252 + 2.00120i) q^{42} +(2.44949 - 2.44949i) q^{43} +(-5.19615 + 3.00000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-3.53553 - 3.53553i) q^{48} +(-4.33013 - 5.50000i) q^{49} +(-1.29410 - 4.82963i) q^{52} +(-0.866025 - 1.50000i) q^{54} +(1.50000 + 4.33013i) q^{56} +(-3.67423 - 3.67423i) q^{57} +(-3.46410 + 6.00000i) q^{59} +(-1.50000 + 0.866025i) q^{61} +(4.24264 - 4.24264i) q^{62} +(0.189469 + 2.63896i) q^{63} -1.00000i q^{64} +(-9.00000 - 5.19615i) q^{66} +(-8.36516 + 2.24144i) q^{67} -3.46410 q^{69} +12.0000 q^{71} +(0.448288 - 1.67303i) q^{72} +(-6.76148 + 1.81173i) q^{73} +(12.9904 + 7.50000i) q^{74} +5.19615i q^{76} +(8.90138 + 13.1440i) q^{77} +(6.12372 - 6.12372i) q^{78} +(-9.52628 + 5.50000i) q^{79} +(0.500000 - 0.866025i) q^{81} +(17.3867 + 4.65874i) q^{82} +(8.48528 + 8.48528i) q^{83} +(1.73205 - 2.00000i) q^{84} +(-3.00000 - 5.19615i) q^{86} +(-2.68973 - 10.0382i) q^{88} +(-6.92820 - 12.0000i) q^{89} +(-12.5000 + 4.33013i) q^{91} +(2.44949 + 2.44949i) q^{92} +(3.34607 + 0.896575i) q^{93} +(-4.50000 + 2.59808i) q^{96} +(3.53553 - 3.53553i) q^{97} +(-11.1428 + 4.77886i) q^{98} -6.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 24 q^{11} - 20 q^{16} - 4 q^{21} + 60 q^{26} + 24 q^{31} - 8 q^{36} - 24 q^{46} + 12 q^{56} - 12 q^{61} - 72 q^{66} + 96 q^{71} + 4 q^{81} - 24 q^{86} - 100 q^{91} - 36 q^{96}+O(q^{100}) $ 8 * q + 24 * q^11 - 20 * q^16 - 4 * q^21 + 60 * q^26 + 24 * q^31 - 8 * q^36 - 24 * q^46 + 12 * q^56 - 12 * q^61 - 72 * q^66 + 96 * q^71 + 4 * q^81 - 24 * q^86 - 100 * q^91 - 36 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.448288	−	1.67303i	0.316987	−	1.18301i	−0.605138	−	0.796121i	$-0.706882\pi$
$2$	0.448288	−	1.67303i	0.316987	−	1.18301i	0.922125	−	0.386892i	$-0.126451\pi$
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.73205i		−	0.707107i
$7$	−1.15539	+	2.38014i	−0.436698	+	0.899608i
$7$	−1.15539	+	2.38014i	−0.436698	+	0.899608i
$8$	1.22474	−	1.22474i	0.433013	−	0.433013i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	3.53553	+	3.53553i	0.980581	+	0.980581i	0.999815	−	0.0192343i	$-0.00612285\pi$
$13$	3.53553	+	3.53553i	0.980581	+	0.980581i	−0.0192343	+	0.999815i	$0.506123\pi$
$14$	3.46410	+	3.00000i	0.925820	+	0.801784i
$15$		0			0
$16$	−2.50000	−	4.33013i	−0.625000	−	1.08253i
$17$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$17$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$18$	−0.448288	−	1.67303i	−0.105662	−	0.394338i
$19$	−2.59808	−	4.50000i	−0.596040	−	1.03237i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$	−2.59808	−	4.50000i	−0.596040	−	1.03237i	0.397360	−	0.917663i	$-0.369927\pi$
$20$		0			0
$21$	−0.500000	+	2.59808i	−0.109109	+	0.566947i
$22$	−7.34847	−	7.34847i	−1.56670	−	1.56670i
$23$	−3.34607	−	0.896575i	−0.697703	−	0.186949i	−0.107501	−	0.994205i	$-0.534285\pi$
$23$	−3.34607	−	0.896575i	−0.697703	−	0.186949i	−0.590201	+	0.807256i	$0.700952\pi$
$24$	0.866025	−	1.50000i	0.176777	−	0.306186i
$25$		0			0
$26$	7.50000	−	4.33013i	1.47087	−	0.849208i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.19067	−	1.48356i	0.413998	−	0.280367i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	0.744599	−	0.667512i	$-0.232641\pi$
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	−0.205783	+	0.978598i	$0.565974\pi$
$32$	−5.01910	+	1.34486i	−0.887260	+	0.237740i
$33$	1.55291	−	5.79555i	0.270328	−	1.00888i
$34$		0			0
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−2.24144	+	8.36516i	−0.368490	+	1.37522i	0.494137	+	0.869384i	$0.335484\pi$
$37$	−2.24144	+	8.36516i	−0.368490	+	1.37522i	−0.862627	+	0.505840i	$0.831183\pi$
$38$	−8.69333	+	2.32937i	−1.41024	+	0.377874i
$39$	4.33013	+	2.50000i	0.693375	+	0.400320i
$40$		0			0
$41$			10.3923i			1.62301i	0.584349	+	0.811503i	$0.301350\pi$
$41$			10.3923i			1.62301i	−0.584349	+	0.811503i	$0.698650\pi$
$42$	4.12252	+	2.00120i	0.636119	+	0.308792i
$43$	2.44949	−	2.44949i	0.373544	−	0.373544i	−0.495222	−	0.868766i	$-0.664913\pi$
$43$	2.44949	−	2.44949i	0.373544	−	0.373544i	0.868766	+	0.495222i	$0.164913\pi$
$44$	−5.19615	+	3.00000i	−0.783349	+	0.452267i
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$47$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$48$	−3.53553	−	3.53553i	−0.510310	−	0.510310i
$49$	−4.33013	−	5.50000i	−0.618590	−	0.785714i
$50$		0			0
$51$		0			0
$52$	−1.29410	−	4.82963i	−0.179459	−	0.669749i
$53$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$53$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$54$	−0.866025	−	1.50000i	−0.117851	−	0.204124i
$55$		0			0
$56$	1.50000	+	4.33013i	0.200446	+	0.578638i
$57$	−3.67423	−	3.67423i	−0.486664	−	0.486664i
$58$		0			0
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	−0.998448	−	0.0556984i	$-0.982261\pi$
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	0.547460	+	0.836832i	$0.315595\pi$
$60$		0			0
$61$	−1.50000	+	0.866025i	−0.192055	+	0.110883i	−0.592944	−	0.805243i	$-0.702035\pi$
$61$	−1.50000	+	0.866025i	−0.192055	+	0.110883i	0.400889	+	0.916127i	$0.368701\pi$
$62$	4.24264	−	4.24264i	0.538816	−	0.538816i
$63$	0.189469	+	2.63896i	0.0238708	+	0.332478i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−9.00000	−	5.19615i	−1.10782	−	0.639602i
$67$	−8.36516	+	2.24144i	−1.02197	+	0.273835i	−0.730622	−	0.682783i	$-0.760770\pi$
$67$	−8.36516	+	2.24144i	−1.02197	+	0.273835i	−0.291346	+	0.956618i	$0.594103\pi$
$68$		0			0
$69$	−3.46410			−0.417029
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	0.448288	−	1.67303i	0.0528312	−	0.197169i
$73$	−6.76148	+	1.81173i	−0.791371	+	0.212047i	−0.631792	−	0.775138i	$-0.717680\pi$
$73$	−6.76148	+	1.81173i	−0.791371	+	0.212047i	−0.159579	+	0.987185i	$0.551014\pi$
$74$	12.9904	+	7.50000i	1.51010	+	0.871857i
$75$		0			0
$76$			5.19615i			0.596040i
$77$	8.90138	+	13.1440i	1.01441	+	1.49790i
$78$	6.12372	−	6.12372i	0.693375	−	0.693375i
$79$	−9.52628	+	5.50000i	−1.07179	+	0.618798i	−0.928670	−	0.370907i	$-0.879047\pi$
$79$	−9.52628	+	5.50000i	−1.07179	+	0.618798i	−0.143120	+	0.989705i	$0.545714\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	17.3867	+	4.65874i	1.92004	+	0.514472i
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	0.997792	−	0.0664117i	$-0.0211551\pi$
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	−0.0664117	+	0.997792i	$0.521155\pi$
$84$	1.73205	−	2.00000i	0.188982	−	0.218218i
$85$		0			0
$86$	−3.00000	−	5.19615i	−0.323498	−	0.560316i
$87$		0			0
$88$	−2.68973	−	10.0382i	−0.286726	−	1.07008i
$89$	−6.92820	−	12.0000i	−0.734388	−	1.27200i	−0.954991	−	0.296634i	$-0.904136\pi$
$89$	−6.92820	−	12.0000i	−0.734388	−	1.27200i	0.220603	−	0.975364i	$-0.429197\pi$
$90$		0			0
$91$	−12.5000	+	4.33013i	−1.31036	+	0.453921i
$92$	2.44949	+	2.44949i	0.255377	+	0.255377i
$93$	3.34607	+	0.896575i	0.346971	+	0.0929705i
$94$		0			0
$95$		0			0
$96$	−4.50000	+	2.59808i	−0.459279	+	0.265165i
$97$	3.53553	−	3.53553i	0.358979	−	0.358979i	−0.504457	−	0.863437i	$-0.668307\pi$
$97$	3.53553	−	3.53553i	0.358979	−	0.358979i	0.863437	+	0.504457i	$0.168307\pi$
$98$	−11.1428	+	4.77886i	−1.12560	+	0.482738i
$99$		−	6.00000i		−	0.603023i
$100$		0			0
$101$	−3.00000	−	1.73205i	−0.298511	−	0.172345i	0.343263	−	0.939239i	$-0.388468\pi$
$101$	−3.00000	−	1.73205i	−0.298511	−	0.172345i	−0.641774	+	0.766894i	$0.721801\pi$
$102$		0			0
$103$	−1.81173	+	6.76148i	−0.178515	+	0.666228i	0.817411	+	0.576055i	$0.195409\pi$
$103$	−1.81173	+	6.76148i	−0.178515	+	0.666228i	−0.995926	+	0.0901732i	$0.971258\pi$
$104$	8.66025			0.849208
$105$		0			0
$106$		0			0
$107$	1.79315	−	6.69213i	0.173350	−	0.646953i	−0.823476	−	0.567351i	$-0.807968\pi$
$107$	1.79315	−	6.69213i	0.173350	−	0.646953i	0.996827	−	0.0796020i	$-0.0253649\pi$
$108$	−0.965926	+	0.258819i	−0.0929463	+	0.0249049i
$109$	6.06218	+	3.50000i	0.580651	+	0.335239i	0.761392	−	0.648292i	$-0.224516\pi$
$109$	6.06218	+	3.50000i	0.580651	+	0.335239i	−0.180741	+	0.983531i	$0.557850\pi$
$110$		0			0
$111$			8.66025i			0.821995i
$112$	13.1948	−	0.947343i	1.24679	−	0.0895155i
$113$	−12.2474	+	12.2474i	−1.15214	+	1.15214i	−0.166021	+	0.986122i	$0.553092\pi$
$113$	−12.2474	+	12.2474i	−1.15214	+	1.15214i	−0.986122	+	0.166021i	$0.946908\pi$
$114$	−7.79423	+	4.50000i	−0.729996	+	0.421464i
$115$		0			0
$116$		0			0
$117$	4.82963	+	1.29410i	0.446499	+	0.119639i
$118$	8.48528	+	8.48528i	0.781133	+	0.781133i
$119$		0			0
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	0.776457	+	2.89778i	0.0702971	+	0.262352i
$123$	2.68973	+	10.0382i	0.242524	+	0.905114i
$124$	−1.73205	−	3.00000i	−0.155543	−	0.269408i
$125$		0			0
$126$	4.50000	+	0.866025i	0.400892	+	0.0771517i
$127$	−3.67423	−	3.67423i	−0.326036	−	0.326036i	0.525041	−	0.851077i	$-0.324050\pi$
$127$	−3.67423	−	3.67423i	−0.326036	−	0.326036i	−0.851077	+	0.525041i	$0.824050\pi$
$128$	−11.7112	−	3.13801i	−1.03514	−	0.277364i
$129$	1.73205	−	3.00000i	0.152499	−	0.264135i
$130$		0			0
$131$	3.00000	−	1.73205i	0.262111	−	0.151330i	−0.363186	−	0.931717i	$-0.618311\pi$
$131$	3.00000	−	1.73205i	0.262111	−	0.151330i	0.625297	+	0.780387i	$0.284978\pi$
$132$	−4.24264	+	4.24264i	−0.369274	+	0.369274i
$133$	13.7124	−	0.984508i	1.18902	−	0.0853677i
$134$			15.0000i			1.29580i
$135$		0			0
$136$		0			0
$137$	3.34607	−	0.896575i	0.285874	−	0.0765996i	−0.113033	−	0.993591i	$-0.536057\pi$
$137$	3.34607	−	0.896575i	0.285874	−	0.0765996i	0.398906	+	0.916992i	$0.369390\pi$
$138$	−1.55291	+	5.79555i	−0.132193	+	0.493350i
$139$	22.5167			1.90984			0.954919	−	0.296866i	$-0.0959415\pi$
$139$	22.5167			1.90984			0.954919	+	0.296866i	$0.0959415\pi$
$140$		0			0
$141$		0			0
$142$	5.37945	−	20.0764i	0.451434	−	1.68477i
$143$	28.9778	−	7.76457i	2.42324	−	0.649306i
$144$	−4.33013	−	2.50000i	−0.360844	−	0.208333i
$145$		0			0
$146$			12.1244i			1.00342i
$147$	−5.60609	−	4.19187i	−0.462382	−	0.345740i
$148$	6.12372	−	6.12372i	0.503367	−	0.503367i
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	−0.697507	−	0.716578i	$-0.745707\pi$
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	0.271821	+	0.962348i	$0.412374\pi$
$150$		0			0
$151$	−8.50000	+	14.7224i	−0.691720	+	1.19809i	0.279554	+	0.960130i	$0.409814\pi$
$151$	−8.50000	+	14.7224i	−0.691720	+	1.19809i	−0.971274	+	0.237964i	$0.923520\pi$
$152$	−8.69333	−	2.32937i	−0.705122	−	0.188937i
$153$		0			0
$154$	25.9808	−	9.00000i	2.09359	−	0.725241i
$155$		0			0
$156$	−2.50000	−	4.33013i	−0.200160	−	0.346688i
$157$	5.95284	+	22.2163i	0.475088	+	1.77305i	0.621058	+	0.783764i	$0.286703\pi$
$157$	5.95284	+	22.2163i	0.475088	+	1.77305i	−0.145970	+	0.989289i	$0.546630\pi$
$158$	4.93117	+	18.4034i	0.392302	+	1.46409i
$159$		0			0
$160$		0			0
$161$	6.00000	−	6.92820i	0.472866	−	0.546019i
$162$	−1.22474	−	1.22474i	−0.0962250	−	0.0962250i
$163$	−1.67303	−	0.448288i	−0.131042	−	0.0351126i	0.192702	−	0.981257i	$-0.438275\pi$
$163$	−1.67303	−	0.448288i	−0.131042	−	0.0351126i	−0.323744	+	0.946145i	$0.604942\pi$
$164$	5.19615	−	9.00000i	0.405751	−	0.702782i
$165$		0			0
$166$	18.0000	−	10.3923i	1.39707	−	0.806599i
$167$	8.48528	−	8.48528i	0.656611	−	0.656611i	−0.297966	−	0.954577i	$-0.596308\pi$
$167$	8.48528	−	8.48528i	0.656611	−	0.656611i	0.954577	+	0.297966i	$0.0963081\pi$
$168$	2.56961	+	3.79435i	0.198250	+	0.292741i
$169$			12.0000i			0.923077i
$170$		0			0
$171$	−4.50000	−	2.59808i	−0.344124	−	0.198680i
$172$	−3.34607	+	0.896575i	−0.255135	+	0.0683632i
$173$	−1.55291	+	5.79555i	−0.118066	+	0.440628i	−0.999498	−	0.0316829i	$-0.989913\pi$
$173$	−1.55291	+	5.79555i	−0.118066	+	0.440628i	0.881432	+	0.472311i	$0.156580\pi$
$174$		0			0
$175$		0			0
$176$	−30.0000			−2.26134
$177$	−1.79315	+	6.69213i	−0.134781	+	0.503011i
$178$	−23.1822	+	6.21166i	−1.73758	+	0.465583i
$179$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$179$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$180$		0			0
$181$		−	13.8564i		−	1.02994i	−0.857209	−	0.514969i	$-0.827803\pi$
$181$		−	13.8564i		−	1.02994i	0.857209	−	0.514969i	$-0.172197\pi$
$182$	1.64085	+	22.8541i	0.121628	+	1.69405i
$183$	−1.22474	+	1.22474i	−0.0905357	+	0.0905357i
$184$	−5.19615	+	3.00000i	−0.383065	+	0.221163i
$185$		0			0
$186$	3.00000	−	5.19615i	0.219971	−	0.381000i
$187$		0			0
$188$		0			0
$189$	0.866025	+	2.50000i	0.0629941	+	0.181848i
$190$		0			0
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	−5.37945	−	20.0764i	−0.387221	−	1.44513i	−0.834635	−	0.550803i	$-0.814321\pi$
$193$	−5.37945	−	20.0764i	−0.387221	−	1.44513i	0.447414	−	0.894327i	$-0.352345\pi$
$194$	−4.33013	−	7.50000i	−0.310885	−	0.538469i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−9.79796	−	9.79796i	−0.698076	−	0.698076i	0.265920	−	0.963995i	$-0.414324\pi$
$197$	−9.79796	−	9.79796i	−0.698076	−	0.698076i	−0.963995	+	0.265920i	$0.914324\pi$
$198$	−10.0382	−	2.68973i	−0.713384	−	0.191151i
$199$	−7.79423	+	13.5000i	−0.552518	+	0.956990i	0.445574	+	0.895245i	$0.353000\pi$
$199$	−7.79423	+	13.5000i	−0.552518	+	0.956990i	−0.998092	+	0.0617444i	$0.980334\pi$
$200$		0			0
$201$	−7.50000	+	4.33013i	−0.529009	+	0.305424i
$202$	−4.24264	+	4.24264i	−0.298511	+	0.298511i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	10.5000	+	6.06218i	0.731570	+	0.422372i
$207$	−3.34607	+	0.896575i	−0.232568	+	0.0623163i
$208$	6.47048	−	24.1481i	0.448647	−	1.67437i
$209$	−31.1769			−2.15655
$210$		0			0
$211$	19.0000			1.30801			0.654007	−	0.756489i	$-0.273087\pi$
$211$	19.0000			1.30801			0.654007	+	0.756489i	$0.273087\pi$
$212$		0			0
$213$	11.5911	−	3.10583i	0.794210	−	0.212808i
$214$	−10.3923	−	6.00000i	−0.710403	−	0.410152i
$215$		0			0
$216$		−	1.73205i		−	0.117851i
$217$	−7.58871	+	5.13922i	−0.515155	+	0.348873i
$218$	8.57321	−	8.57321i	0.580651	−	0.580651i
$219$	−6.06218	+	3.50000i	−0.409644	+	0.236508i
$220$		0			0
$221$		0			0
$222$	14.4889	+	3.88229i	0.972430	+	0.260562i
$223$	−16.2635	−	16.2635i	−1.08908	−	1.08908i	−0.995623	−	0.0934584i	$-0.970208\pi$
$223$	−16.2635	−	16.2635i	−1.08908	−	1.08908i	−0.0934584	−	0.995623i	$-0.529792\pi$
$224$	2.59808	−	13.5000i	0.173591	−	0.902007i
$225$		0			0
$226$	15.0000	+	25.9808i	0.997785	+	1.72821i
$227$	−6.21166	−	23.1822i	−0.412282	−	1.53866i	−0.790218	−	0.612826i	$-0.790033\pi$
$227$	−6.21166	−	23.1822i	−0.412282	−	1.53866i	0.377936	−	0.925832i	$-0.376634\pi$
$228$	1.34486	+	5.01910i	0.0890657	+	0.332398i
$229$	7.79423	+	13.5000i	0.515057	+	0.892105i	0.999847	+	0.0174746i	$0.00556263\pi$
$229$	7.79423	+	13.5000i	0.515057	+	0.892105i	−0.484790	+	0.874630i	$0.661104\pi$
$230$		0			0
$231$	12.0000	+	10.3923i	0.789542	+	0.683763i
$232$		0			0
$233$	−3.34607	−	0.896575i	−0.219208	−	0.0587366i	0.147543	−	0.989056i	$-0.452863\pi$
$233$	−3.34607	−	0.896575i	−0.219208	−	0.0587366i	−0.366751	+	0.930319i	$0.619530\pi$
$234$	4.33013	−	7.50000i	0.283069	−	0.490290i
$235$		0			0
$236$	6.00000	−	3.46410i	0.390567	−	0.225494i
$237$	−7.77817	+	7.77817i	−0.505247	+	0.505247i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−41.8258	+	11.2072i	−2.68867	+	0.720426i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	1.73205			0.110883
$245$		0			0
$246$	18.0000			1.14764
$247$	6.72432	−	25.0955i	0.427858	−	1.59679i
$248$	5.79555	−	1.55291i	0.368018	−	0.0986102i
$249$	10.3923	+	6.00000i	0.658586	+	0.380235i
$250$		0			0
$251$			17.3205i			1.09326i	0.837374	+	0.546630i	$0.184090\pi$
$251$			17.3205i			1.09326i	−0.837374	+	0.546630i	$0.815910\pi$
$252$	1.15539	−	2.38014i	0.0727830	−	0.149935i
$253$	−14.6969	+	14.6969i	−0.923989	+	0.923989i
$254$	−7.79423	+	4.50000i	−0.489053	+	0.282355i
$255$		0			0
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	17.3867	+	4.65874i	1.08455	+	0.290604i	0.756459	−	0.654041i	$-0.226928\pi$
$257$	17.3867	+	4.65874i	1.08455	+	0.290604i	0.328092	+	0.944646i	$0.393595\pi$
$258$	−4.24264	−	4.24264i	−0.264135	−	0.264135i
$259$	−17.3205	−	15.0000i	−1.07624	−	0.932055i
$260$		0			0
$261$		0			0
$262$	−1.55291	−	5.79555i	−0.0959394	−	0.358051i
$263$	−3.58630	−	13.3843i	−0.221141	−	0.825309i	−0.983914	−	0.178643i	$-0.942829\pi$
$263$	−3.58630	−	13.3843i	−0.221141	−	0.825309i	0.762773	−	0.646666i	$-0.223837\pi$
$264$	−5.19615	−	9.00000i	−0.319801	−	0.553912i
$265$		0			0
$266$	4.50000	−	23.3827i	0.275913	−	1.43368i
$267$	−9.79796	−	9.79796i	−0.599625	−	0.599625i
$268$	8.36516	+	2.24144i	0.510984	+	0.136918i
$269$	1.73205	−	3.00000i	0.105605	−	0.182913i	−0.808380	−	0.588661i	$-0.799655\pi$
$269$	1.73205	−	3.00000i	0.105605	−	0.182913i	0.913985	+	0.405747i	$0.132989\pi$
$270$		0			0
$271$	9.00000	−	5.19615i	0.546711	−	0.315644i	−0.201083	−	0.979574i	$-0.564446\pi$
$271$	9.00000	−	5.19615i	0.546711	−	0.315644i	0.747794	+	0.663930i	$0.231113\pi$
$272$		0			0
$273$	−10.9534	+	7.41782i	−0.662927	+	0.448947i
$274$		−	6.00000i		−	0.362473i
$275$		0			0
$276$	3.00000	+	1.73205i	0.180579	+	0.104257i
$277$	−5.01910	+	1.34486i	−0.301568	+	0.0808050i	−0.406430	−	0.913682i	$-0.633227\pi$
$277$	−5.01910	+	1.34486i	−0.301568	+	0.0808050i	0.104862	+	0.994487i	$0.466560\pi$
$278$	10.0939	−	37.6711i	0.605394	−	2.25936i
$279$	3.46410			0.207390
$280$		0			0
$281$	−24.0000			−1.43172			−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000			−1.43172			−0.715860	+	0.698244i	$0.753965\pi$
$282$		0			0
$283$	0.965926	−	0.258819i	0.0574183	−	0.0153852i	−0.229996	−	0.973192i	$-0.573871\pi$
$283$	0.965926	−	0.258819i	0.0574183	−	0.0153852i	0.287414	+	0.957806i	$0.407204\pi$
$284$	−10.3923	−	6.00000i	−0.616670	−	0.356034i
$285$		0			0
$286$		−	51.9615i		−	3.07255i
$287$	−24.7351	−	12.0072i	−1.46007	−	0.708763i
$288$	−3.67423	+	3.67423i	−0.216506	+	0.216506i
$289$	14.7224	−	8.50000i	0.866025	−	0.500000i
$290$		0			0
$291$	2.50000	−	4.33013i	0.146553	−	0.253837i
$292$	6.76148	+	1.81173i	0.395686	+	0.106024i
$293$	−16.9706	−	16.9706i	−0.991431	−	0.991431i	0.00853273	−	0.999964i	$-0.497284\pi$
$293$	−16.9706	−	16.9706i	−0.991431	−	0.991431i	−0.999964	+	0.00853273i	$0.997284\pi$
$294$	−9.52628	+	7.50000i	−0.555584	+	0.437409i
$295$		0			0
$296$	7.50000	+	12.9904i	0.435929	+	0.755051i
$297$	−1.55291	−	5.79555i	−0.0901092	−	0.336292i
$298$	2.68973	+	10.0382i	0.155812	+	0.581497i
$299$	−8.66025	−	15.0000i	−0.500835	−	0.867472i
$300$		0			0
$301$	3.00000	+	8.66025i	0.172917	+	0.499169i
$302$	20.8207	+	20.8207i	1.19809	+	1.19809i
$303$	−3.34607	−	0.896575i	−0.192226	−	0.0515069i
$304$	−12.9904	+	22.5000i	−0.745049	+	1.29046i
$305$		0			0
$306$		0			0
$307$	−22.6274	+	22.6274i	−1.29141	+	1.29141i	−0.357503	+	0.933912i	$0.616372\pi$
$307$	−22.6274	+	22.6274i	−1.29141	+	1.29141i	−0.933912	+	0.357503i	$0.883628\pi$
$308$	−1.13681	−	15.8338i	−0.0647759	−	0.902212i
$309$			7.00000i			0.398216i
$310$		0			0
$311$	−15.0000	−	8.66025i	−0.850572	−	0.491078i	0.0102718	−	0.999947i	$-0.496730\pi$
$311$	−15.0000	−	8.66025i	−0.850572	−	0.491078i	−0.860844	+	0.508869i	$0.830064\pi$
$312$	8.36516	−	2.24144i	0.473584	−	0.126896i
$313$	−6.72930	+	25.1141i	−0.380362	+	1.41953i	0.464987	+	0.885317i	$0.346059\pi$
$313$	−6.72930	+	25.1141i	−0.380362	+	1.41953i	−0.845349	+	0.534214i	$0.820608\pi$
$314$	39.8372			2.24814
$315$		0			0
$316$	11.0000			0.618798
$317$	2.68973	−	10.0382i	0.151070	−	0.563801i	−0.848340	−	0.529452i	$-0.822398\pi$
$317$	2.68973	−	10.0382i	0.151070	−	0.563801i	0.999410	−	0.0343491i	$-0.0109358\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		−	6.92820i		−	0.386695i
$322$	−8.90138	−	13.1440i	−0.496055	−	0.732488i
$323$		0			0
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$		0			0
$326$	−1.50000	+	2.59808i	−0.0830773	+	0.143894i
$327$	6.76148	+	1.81173i	0.373911	+	0.100189i
$328$	12.7279	+	12.7279i	0.702782	+	0.702782i
$329$		0			0
$330$		0			0
$331$	−6.50000	−	11.2583i	−0.357272	−	0.618814i	0.630232	−	0.776407i	$-0.282960\pi$
$331$	−6.50000	−	11.2583i	−0.357272	−	0.618814i	−0.987504	+	0.157593i	$0.949627\pi$
$332$	−3.10583	−	11.5911i	−0.170454	−	0.636145i
$333$	2.24144	+	8.36516i	0.122830	+	0.458408i
$334$	−10.3923	−	18.0000i	−0.568642	−	0.984916i
$335$		0			0
$336$	12.5000	−	4.33013i	0.681931	−	0.236228i
$337$	4.89898	+	4.89898i	0.266864	+	0.266864i	0.827835	−	0.560971i	$-0.189572\pi$
$337$	4.89898	+	4.89898i	0.266864	+	0.266864i	−0.560971	+	0.827835i	$0.689572\pi$
$338$	20.0764	+	5.37945i	1.09201	+	0.292604i
$339$	−8.66025	+	15.0000i	−0.470360	+	0.814688i
$340$		0			0
$341$	18.0000	−	10.3923i	0.974755	−	0.562775i
$342$	−6.36396	+	6.36396i	−0.344124	+	0.344124i
$343$	18.0938	−	3.95164i	0.976972	−	0.213368i
$344$		−	6.00000i		−	0.323498i
$345$		0			0
$346$	9.00000	+	5.19615i	0.483843	+	0.279347i
$347$	20.0764	−	5.37945i	1.07776	−	0.288784i	0.324080	−	0.946030i	$-0.394945\pi$
$347$	20.0764	−	5.37945i	1.07776	−	0.288784i	0.753677	+	0.657245i	$0.228278\pi$
$348$		0			0
$349$	−6.92820			−0.370858			−0.185429	−	0.982658i	$-0.559368\pi$
$349$	−6.92820			−0.370858			−0.185429	+	0.982658i	$0.559368\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$	−8.06918	+	30.1146i	−0.430089	+	1.60511i
$353$	5.79555	−	1.55291i	0.308466	−	0.0826533i	−0.101265	−	0.994859i	$-0.532289\pi$
$353$	5.79555	−	1.55291i	0.308466	−	0.0826533i	0.409731	+	0.912206i	$0.365622\pi$
$354$	10.3923	+	6.00000i	0.552345	+	0.318896i
$355$		0			0
$356$			13.8564i			0.734388i
$357$		0			0
$358$		0			0
$359$	20.7846	−	12.0000i	1.09697	−	0.633336i	0.161546	−	0.986865i	$-0.448352\pi$
$359$	20.7846	−	12.0000i	1.09697	−	0.633336i	0.935423	+	0.353529i	$0.115019\pi$
$360$		0			0
$361$	−4.00000	+	6.92820i	−0.210526	+	0.364642i
$362$	−23.1822	−	6.21166i	−1.21843	−	0.326477i
$363$	−17.6777	−	17.6777i	−0.927837	−	0.927837i
$364$	12.9904	+	2.50000i	0.680881	+	0.131036i
$365$		0			0
$366$	1.50000	+	2.59808i	0.0784063	+	0.135804i
$367$	−4.14110	−	15.4548i	−0.216164	−	0.806735i	−0.985754	−	0.168196i	$-0.946206\pi$
$367$	−4.14110	−	15.4548i	−0.216164	−	0.806735i	0.769590	−	0.638539i	$-0.220461\pi$
$368$	4.48288	+	16.7303i	0.233686	+	0.872129i
$369$	5.19615	+	9.00000i	0.270501	+	0.468521i
$370$		0			0
$371$		0			0
$372$	−2.44949	−	2.44949i	−0.127000	−	0.127000i
$373$	5.01910	+	1.34486i	0.259879	+	0.0696344i	0.386406	−	0.922329i	$-0.373716\pi$
$373$	5.01910	+	1.34486i	0.259879	+	0.0696344i	−0.126527	+	0.991963i	$0.540383\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	4.57081	−	0.328169i	0.235097	−	0.0168792i
$379$		−	5.00000i		−	0.256833i	−0.991720	−	0.128416i	$-0.959011\pi$
$379$		−	5.00000i		−	0.256833i	0.991720	−	0.128416i	$-0.0409894\pi$
$380$		0			0
$381$	−4.50000	−	2.59808i	−0.230542	−	0.133103i
$382$	−10.0382	+	2.68973i	−0.513599	+	0.137618i
$383$	4.65874	−	17.3867i	0.238051	−	0.888417i	−0.738699	−	0.674035i	$-0.764560\pi$
$383$	4.65874	−	17.3867i	0.238051	−	0.888417i	0.976750	−	0.214382i	$-0.0687737\pi$
$384$	−12.1244			−0.618718
$385$		0			0
$386$	−36.0000			−1.83235
$387$	0.896575	−	3.34607i	0.0455755	−	0.170090i
$388$	−4.82963	+	1.29410i	−0.245187	+	0.0656977i
$389$	25.9808	+	15.0000i	1.31728	+	0.760530i	0.983290	−	0.182047i	$-0.0582724\pi$
$389$	25.9808	+	15.0000i	1.31728	+	0.760530i	0.333987	+	0.942578i	$0.391606\pi$
$390$		0			0
$391$		0			0
$392$	−12.0394	−	1.43280i	−0.608081	−	0.0723671i
$393$	2.44949	−	2.44949i	0.123560	−	0.123560i
$394$	−20.7846	+	12.0000i	−1.04711	+	0.604551i
$395$		0			0
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	1.93185	+	0.517638i	0.0969569	+	0.0259795i	0.306971	−	0.951719i	$-0.400684\pi$
$397$	1.93185	+	0.517638i	0.0969569	+	0.0259795i	−0.210014	+	0.977698i	$0.567351\pi$
$398$	19.0919	+	19.0919i	0.956990	+	0.956990i
$399$	12.9904	−	4.50000i	0.650332	−	0.225282i
$400$		0			0
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	0.781345	−	0.624099i	$-0.214534\pi$
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	−0.931158	+	0.364615i	$0.881200\pi$
$402$	3.88229	+	14.4889i	0.193631	+	0.722640i
$403$	4.48288	+	16.7303i	0.223308	+	0.833397i
$404$	1.73205	+	3.00000i	0.0861727	+	0.149256i
$405$		0			0
$406$		0			0
$407$	36.7423	+	36.7423i	1.82125	+	1.82125i
$408$		0			0
$409$	−2.59808	+	4.50000i	−0.128467	+	0.222511i	−0.923083	−	0.384602i	$-0.874339\pi$
$409$	−2.59808	+	4.50000i	−0.128467	+	0.222511i	0.794616	+	0.607112i	$0.207672\pi$
$410$		0			0
$411$	3.00000	−	1.73205i	0.147979	−	0.0854358i
$412$	4.94975	−	4.94975i	0.243857	−	0.243857i
$413$	−10.2784	−	15.1774i	−0.505769	−	0.746832i
$414$			6.00000i			0.294884i
$415$		0			0
$416$	−22.5000	−	12.9904i	−1.10315	−	0.636906i
$417$	21.7494	−	5.82774i	1.06507	−	0.285386i
$418$	−13.9762	+	52.1600i	−0.683600	+	2.55123i
$419$	3.46410			0.169232			0.0846162	−	0.996414i	$-0.473034\pi$
$419$	3.46410			0.169232			0.0846162	+	0.996414i	$0.473034\pi$
$420$		0			0
$421$	−17.0000			−0.828529			−0.414265	−	0.910156i	$-0.635961\pi$
$421$	−17.0000			−0.828529			−0.414265	+	0.910156i	$0.635961\pi$
$422$	8.51747	−	31.7876i	0.414624	−	1.54740i
$423$		0			0
$424$		0			0
$425$		0			0
$426$		−	20.7846i		−	1.00702i
$427$	−0.328169	−	4.57081i	−0.0158812	−	0.221197i
$428$	−4.89898	+	4.89898i	−0.236801	+	0.236801i
$429$	25.9808	−	15.0000i	1.25436	−	0.724207i
$430$		0			0
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$	−4.82963	−	1.29410i	−0.232366	−	0.0622622i
$433$	−1.41421	−	1.41421i	−0.0679628	−	0.0679628i	0.672308	−	0.740271i	$-0.265303\pi$
$433$	−1.41421	−	1.41421i	−0.0679628	−	0.0679628i	−0.740271	+	0.672308i	$0.765303\pi$
$434$	5.19615	+	15.0000i	0.249423	+	0.720023i
$435$		0			0
$436$	−3.50000	−	6.06218i	−0.167620	−	0.290326i
$437$	4.65874	+	17.3867i	0.222858	+	0.831717i
$438$	3.13801	+	11.7112i	0.149940	+	0.559584i
$439$	9.52628	+	16.5000i	0.454665	+	0.787502i	0.998669	−	0.0515804i	$-0.0164258\pi$
$439$	9.52628	+	16.5000i	0.454665	+	0.787502i	−0.544004	+	0.839082i	$0.683092\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$		0			0
$443$	23.4225	+	6.27603i	1.11283	+	0.298183i	0.767980	−	0.640473i	$-0.221262\pi$
$443$	23.4225	+	6.27603i	1.11283	+	0.298183i	0.344854	+	0.938656i	$0.387928\pi$
$444$	4.33013	−	7.50000i	0.205499	−	0.355934i
$445$		0			0
$446$	−34.5000	+	19.9186i	−1.63362	+	0.943172i
$447$	−4.24264	+	4.24264i	−0.200670	+	0.200670i
$448$	2.38014	+	1.15539i	0.112451	+	0.0545873i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$		0			0
$451$	54.0000	+	31.1769i	2.54276	+	1.46806i
$452$	16.7303	−	4.48288i	0.786928	−	0.210857i
$453$	−4.39992	+	16.4207i	−0.206726	+	0.771514i
$454$	−41.5692			−1.95094
$455$		0			0
$456$	−9.00000			−0.421464
$457$	4.93117	−	18.4034i	0.230670	−	0.860873i	−0.749383	−	0.662137i	$-0.769650\pi$
$457$	4.93117	−	18.4034i	0.230670	−	0.860873i	0.980053	−	0.198736i	$-0.0636836\pi$
$458$	26.0800	−	6.98811i	1.21864	−	0.326533i
$459$		0			0
$460$		0			0
$461$		−	3.46410i		−	0.161339i	−0.996741	−	0.0806696i	$-0.974294\pi$
$461$		−	3.46410i		−	0.161339i	0.996741	−	0.0806696i	$-0.0257059\pi$
$462$	22.7661	−	15.4176i	1.05918	−	0.717294i
$463$	−6.12372	+	6.12372i	−0.284594	+	0.284594i	−0.834938	−	0.550344i	$-0.814496\pi$
$463$	−6.12372	+	6.12372i	−0.284594	+	0.284594i	0.550344	+	0.834938i	$0.314496\pi$
$464$		0			0
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	−5.79555	−	1.55291i	−0.268186	−	0.0718603i	0.122220	−	0.992503i	$-0.460999\pi$
$467$	−5.79555	−	1.55291i	−0.268186	−	0.0718603i	−0.390406	+	0.920643i	$0.627665\pi$
$468$	−3.53553	−	3.53553i	−0.163430	−	0.163430i
$469$	4.33013	−	22.5000i	0.199947	−	1.03895i
$470$		0			0
$471$	11.5000	+	19.9186i	0.529892	+	0.917800i
$472$	3.10583	+	11.5911i	0.142957	+	0.533524i
$473$	−5.37945	−	20.0764i	−0.247348	−	0.923113i
$474$	9.52628	+	16.5000i	0.437557	+	0.757870i
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.8564	−	24.0000i	0.633115	−	1.09659i	−0.353796	−	0.935323i	$-0.615109\pi$
$479$	13.8564	−	24.0000i	0.633115	−	1.09659i	0.986911	−	0.161265i	$-0.0515575\pi$
$480$		0			0
$481$	−37.5000	+	21.6506i	−1.70985	+	0.987184i
$482$	2.12132	−	2.12132i	0.0966235	−	0.0966235i
$483$	4.00240	−	8.24504i	0.182116	−	0.375163i
$484$			25.0000i			1.13636i
$485$		0			0
$486$	−1.50000	−	0.866025i	−0.0680414	−	0.0392837i
$487$	23.4225	−	6.27603i	1.06137	−	0.284394i	0.314429	−	0.949281i	$-0.398187\pi$
$487$	23.4225	−	6.27603i	1.06137	−	0.284394i	0.746944	+	0.664887i	$0.231520\pi$
$488$	−0.776457	+	2.89778i	−0.0351486	+	0.131176i
$489$	−1.73205			−0.0783260
$490$		0			0
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$	2.68973	−	10.0382i	0.121262	−	0.452557i
$493$		0			0
$494$	−38.9711	−	22.5000i	−1.75339	−	1.01232i
$495$		0			0
$496$		−	17.3205i		−	0.777714i
$497$	−13.8647	+	28.5617i	−0.621918	+	1.28117i
$498$	14.6969	−	14.6969i	0.658586	−	0.658586i
$499$	19.9186	−	11.5000i	0.891678	−	0.514811i	0.0171872	−	0.999852i	$-0.494529\pi$
$499$	19.9186	−	11.5000i	0.891678	−	0.514811i	0.874491	+	0.485042i	$0.161196\pi$
$500$		0			0
$501$	6.00000	−	10.3923i	0.268060	−	0.464294i
$502$	28.9778	+	7.76457i	1.29334	+	0.346550i
$503$	−8.48528	−	8.48528i	−0.378340	−	0.378340i	0.492163	−	0.870503i	$-0.336206\pi$
$503$	−8.48528	−	8.48528i	−0.378340	−	0.378340i	−0.870503	+	0.492163i	$0.836206\pi$
$504$	3.46410	+	3.00000i	0.154303	+	0.133631i
$505$		0			0
$506$	18.0000	+	31.1769i	0.800198	+	1.38598i
$507$	3.10583	+	11.5911i	0.137935	+	0.514779i
$508$	1.34486	+	5.01910i	0.0596687	+	0.222686i
$509$	−3.46410	−	6.00000i	−0.153544	−	0.265945i	0.778984	−	0.627044i	$-0.215735\pi$
$509$	−3.46410	−	6.00000i	−0.153544	−	0.265945i	−0.932528	+	0.361098i	$0.882402\pi$
$510$		0			0
$511$	3.50000	−	18.1865i	0.154831	−	0.804525i
$512$	6.12372	+	6.12372i	0.270633	+	0.270633i
$513$	−5.01910	−	1.34486i	−0.221599	−	0.0593772i
$514$	15.5885	−	27.0000i	0.687577	−	1.19092i
$515$		0			0
$516$	−3.00000	+	1.73205i	−0.132068	+	0.0762493i
$517$		0			0
$518$	−32.8601	+	22.2535i	−1.44379	+	0.977761i
$519$			6.00000i			0.263371i
$520$		0			0
$521$	21.0000	+	12.1244i	0.920027	+	0.531178i	0.883644	−	0.468160i	$-0.155083\pi$
$521$	21.0000	+	12.1244i	0.920027	+	0.531178i	0.0363831	+	0.999338i	$0.488416\pi$
$522$		0			0
$523$	−1.03528	+	3.86370i	−0.0452695	+	0.168948i	−0.984860	−	0.173353i	$-0.944540\pi$
$523$	−1.03528	+	3.86370i	−0.0452695	+	0.168948i	0.939590	+	0.342301i	$0.111206\pi$
$524$	−3.46410			−0.151330
$525$		0			0
$526$	−24.0000			−1.04645
$527$		0			0
$528$	−28.9778	+	7.76457i	−1.26110	+	0.337910i
$529$	−9.52628	−	5.50000i	−0.414186	−	0.239130i
$530$		0			0
$531$			6.92820i			0.300658i
$532$	−12.3676	−	6.00361i	−0.536202	−	0.260289i
$533$	−36.7423	+	36.7423i	−1.59149	+	1.59149i
$534$	−20.7846	+	12.0000i	−0.899438	+	0.519291i
$535$		0			0
$536$	−7.50000	+	12.9904i	−0.323951	+	0.561099i
$537$		0			0
$538$	−4.24264	−	4.24264i	−0.182913	−	0.182913i
$539$	−41.5692	+	6.00000i	−1.79051	+	0.258438i
$540$		0			0
$541$	3.50000	+	6.06218i	0.150477	+	0.260633i	0.931403	−	0.363990i	$-0.118586\pi$
$541$	3.50000	+	6.06218i	0.150477	+	0.260633i	−0.780926	+	0.624623i	$0.785252\pi$
$542$	−4.65874	−	17.3867i	−0.200110	−	0.746821i
$543$	−3.58630	−	13.3843i	−0.153903	−	0.574374i
$544$		0			0
$545$		0			0
$546$	7.50000	+	21.6506i	0.320970	+	0.926562i
$547$	−7.34847	−	7.34847i	−0.314198	−	0.314198i	0.532336	−	0.846533i	$-0.321314\pi$
$547$	−7.34847	−	7.34847i	−0.314198	−	0.314198i	−0.846533	+	0.532336i	$0.821314\pi$
$548$	−3.34607	−	0.896575i	−0.142937	−	0.0382998i
$549$	−0.866025	+	1.50000i	−0.0369611	+	0.0640184i
$550$		0			0
$551$		0			0
$552$	−4.24264	+	4.24264i	−0.180579	+	0.180579i
$553$	−2.08416	−	29.0285i	−0.0886273	−	1.23442i
$554$			9.00000i			0.382373i
$555$		0			0
$556$	−19.5000	−	11.2583i	−0.826984	−	0.477460i
$557$	33.4607	−	8.96575i	1.41777	−	0.379891i	0.533080	−	0.846065i	$-0.321034\pi$
$557$	33.4607	−	8.96575i	1.41777	−	0.379891i	0.884693	+	0.466174i	$0.154368\pi$
$558$	1.55291	−	5.79555i	0.0657401	−	0.245345i
$559$	17.3205			0.732579
$560$		0			0
$561$		0			0
$562$	−10.7589	+	40.1528i	−0.453837	+	1.69374i
$563$	−28.9778	+	7.76457i	−1.22127	+	0.327238i	−0.811174	−	0.584806i	$-0.801171\pi$
$563$	−28.9778	+	7.76457i	−1.22127	+	0.327238i	−0.410094	+	0.912043i	$0.634504\pi$
$564$		0			0
$565$		0			0
$566$		−	1.73205i		−	0.0728035i
$567$	1.48356	+	2.19067i	0.0623038	+	0.0919995i
$568$	14.6969	−	14.6969i	0.616670	−	0.616670i
$569$	−25.9808	+	15.0000i	−1.08917	+	0.628833i	−0.933355	−	0.358954i	$-0.883134\pi$
$569$	−25.9808	+	15.0000i	−1.08917	+	0.628833i	−0.155815	+	0.987786i	$0.549800\pi$
$570$		0			0
$571$	−5.50000	+	9.52628i	−0.230168	+	0.398662i	−0.957857	−	0.287244i	$-0.907261\pi$
$571$	−5.50000	+	9.52628i	−0.230168	+	0.398662i	0.727690	+	0.685907i	$0.240594\pi$
$572$	−28.9778	−	7.76457i	−1.21162	−	0.324653i
$573$	−4.24264	−	4.24264i	−0.177239	−	0.177239i
$574$	−31.1769	+	36.0000i	−1.30130	+	1.50261i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	8.79985	+	32.8415i	0.366342	+	1.36721i	0.865592	+	0.500750i	$0.166942\pi$
$577$	8.79985	+	32.8415i	0.366342	+	1.36721i	−0.499249	+	0.866458i	$0.666391\pi$
$578$	−7.62089	−	28.4416i	−0.316987	−	1.18301i
$579$	−10.3923	−	18.0000i	−0.431889	−	0.748054i
$580$		0			0
$581$	−30.0000	+	10.3923i	−1.24461	+	0.431145i
$582$	−6.12372	−	6.12372i	−0.253837	−	0.253837i
$583$		0			0
$584$	−6.06218	+	10.5000i	−0.250855	+	0.434493i
$585$		0			0
$586$	−36.0000	+	20.7846i	−1.48715	+	0.858604i
$587$	21.2132	−	21.2132i	0.875563	−	0.875563i	−0.117509	−	0.993072i	$-0.537491\pi$
$587$	21.2132	−	21.2132i	0.875563	−	0.875563i	0.993072	+	0.117509i	$0.0374910\pi$
$588$	2.75908	+	6.43331i	0.113782	+	0.265305i
$589$		−	18.0000i		−	0.741677i
$590$		0			0
$591$	−12.0000	−	6.92820i	−0.493614	−	0.284988i
$592$	41.8258	−	11.2072i	1.71903	−	0.460613i
$593$	4.65874	−	17.3867i	0.191312	−	0.713985i	−0.801879	−	0.597486i	$-0.796166\pi$
$593$	4.65874	−	17.3867i	0.191312	−	0.713985i	0.993191	−	0.116499i	$-0.0371670\pi$
$594$	−10.3923			−0.426401
$595$		0			0
$596$	6.00000			0.245770
$597$	−4.03459	+	15.0573i	−0.165125	+	0.616254i
$598$	−28.9778	+	7.76457i	−1.18499	+	0.317517i
$599$	31.1769	+	18.0000i	1.27385	+	0.735460i	0.975711	−	0.219061i	$-0.0702994\pi$
$599$	31.1769	+	18.0000i	1.27385	+	0.735460i	0.298143	+	0.954521i	$0.403633\pi$
$600$		0			0
$601$			29.4449i			1.20108i	0.799594	+	0.600541i	$0.205048\pi$
$601$			29.4449i			1.20108i	−0.799594	+	0.600541i	$0.794952\pi$
$602$	15.8338	−	1.13681i	0.645335	−	0.0463330i
$603$	−6.12372	+	6.12372i	−0.249377	+	0.249377i
$604$	14.7224	−	8.50000i	0.599047	−	0.345860i
$605$		0			0
$606$	−3.00000	+	5.19615i	−0.121867	+	0.211079i
$607$	−12.5570	−	3.36465i	−0.509674	−	0.136567i	−0.00518808	−	0.999987i	$-0.501651\pi$
$607$	−12.5570	−	3.36465i	−0.509674	−	0.136567i	−0.504486	+	0.863420i	$0.668318\pi$
$608$	19.0919	+	19.0919i	0.774278	+	0.774278i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$613$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$614$	27.7128	+	48.0000i	1.11840	+	1.93712i
$615$		0			0
$616$	27.0000	+	5.19615i	1.08786	+	0.209359i
$617$	9.79796	+	9.79796i	0.394451	+	0.394451i	0.876270	−	0.481820i	$-0.160024\pi$
$617$	9.79796	+	9.79796i	0.394451	+	0.394451i	−0.481820	+	0.876270i	$0.660024\pi$
$618$	11.7112	+	3.13801i	0.471095	+	0.126229i
$619$	5.19615	−	9.00000i	0.208851	−	0.361741i	−0.742502	−	0.669844i	$-0.766361\pi$
$619$	5.19615	−	9.00000i	0.208851	−	0.361741i	0.951353	+	0.308103i	$0.0996943\pi$
$620$		0			0
$621$	−3.00000	+	1.73205i	−0.120386	+	0.0695048i
$622$	−21.2132	+	21.2132i	−0.850572	+	0.850572i
$623$	36.5665	−	2.62536i	1.46501	−	0.105183i
$624$		−	25.0000i		−	1.00080i
$625$		0			0
$626$	39.0000	+	22.5167i	1.55875	+	0.899947i
$627$	−30.1146	+	8.06918i	−1.20266	+	0.322252i
$628$	5.95284	−	22.2163i	0.237544	−	0.886527i
$629$		0			0
$630$		0			0
$631$	47.0000			1.87104			0.935520	−	0.353273i	$-0.114931\pi$
$631$	47.0000			1.87104			0.935520	+	0.353273i	$0.114931\pi$
$632$	−4.93117	+	18.4034i	−0.196151	+	0.732046i
$633$	18.3526	−	4.91756i	0.729450	−	0.195456i
$634$	−15.5885	−	9.00000i	−0.619097	−	0.357436i
$635$		0			0
$636$		0			0
$637$	4.13613	−	34.7547i	0.163879	−	1.37703i
$638$		0			0
$639$	10.3923	−	6.00000i	0.411113	−	0.237356i
$640$		0			0
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	−0.722862	−	0.690992i	$-0.757174\pi$
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	0.959848	+	0.280521i	$0.0905072\pi$
$642$	−11.5911	−	3.10583i	−0.457465	−	0.122577i
$643$	−3.53553	−	3.53553i	−0.139428	−	0.139428i	0.633948	−	0.773376i	$-0.281433\pi$
$643$	−3.53553	−	3.53553i	−0.139428	−	0.139428i	−0.773376	+	0.633948i	$0.781433\pi$
$644$	−8.66025	+	3.00000i	−0.341262	+	0.118217i
$645$		0			0
$646$		0			0
$647$	−4.65874	−	17.3867i	−0.183154	−	0.683540i	−0.995018	−	0.0996938i	$-0.968214\pi$
$647$	−4.65874	−	17.3867i	−0.183154	−	0.683540i	0.811864	−	0.583846i	$-0.198453\pi$
$648$	−0.448288	−	1.67303i	−0.0176104	−	0.0657229i
$649$	20.7846	+	36.0000i	0.815867	+	1.41312i
$650$		0			0
$651$	−6.00000	+	6.92820i	−0.235159	+	0.271538i
$652$	1.22474	+	1.22474i	0.0479647	+	0.0479647i
$653$	3.34607	+	0.896575i	0.130942	+	0.0350857i	0.323695	−	0.946162i	$-0.395075\pi$
$653$	3.34607	+	0.896575i	0.130942	+	0.0350857i	−0.192753	+	0.981247i	$0.561742\pi$
$654$	6.06218	−	10.5000i	0.237050	−	0.410582i
$655$		0			0
$656$	45.0000	−	25.9808i	1.75695	−	1.01438i
$657$	−4.94975	+	4.94975i	−0.193108	+	0.193108i
$658$		0			0
$659$		−	42.0000i		−	1.63609i	−0.575156	−	0.818044i	$-0.695059\pi$
$659$		−	42.0000i		−	1.63609i	0.575156	−	0.818044i	$-0.304941\pi$
$660$		0			0
$661$	−34.5000	−	19.9186i	−1.34189	−	0.774743i	−0.354809	−	0.934939i	$-0.615454\pi$
$661$	−34.5000	−	19.9186i	−1.34189	−	0.774743i	−0.987085	+	0.160196i	$0.948788\pi$
$662$	−21.7494	+	5.82774i	−0.845315	+	0.226502i
$663$		0			0
$664$	20.7846			0.806599
$665$		0			0
$666$	15.0000			0.581238
$667$		0			0
$668$	−11.5911	+	3.10583i	−0.448474	+	0.120168i
$669$	−19.9186	−	11.5000i	−0.770097	−	0.444616i
$670$		0			0
$671$			10.3923i			0.401190i
$672$	−0.984508	−	13.7124i	−0.0379782	−	0.528968i
$673$	6.12372	−	6.12372i	0.236052	−	0.236052i	−0.579161	−	0.815213i	$-0.696620\pi$
$673$	6.12372	−	6.12372i	0.236052	−	0.236052i	0.815213	+	0.579161i	$0.196620\pi$
$674$	10.3923	−	6.00000i	0.400297	−	0.231111i
$675$		0			0
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−40.5689	−	10.8704i	−1.55919	−	0.417783i	−0.626782	−	0.779194i	$-0.715628\pi$
$677$	−40.5689	−	10.8704i	−1.55919	−	0.417783i	−0.932407	+	0.361411i	$0.882295\pi$
$678$	21.2132	+	21.2132i	0.814688	+	0.814688i
$679$	4.33013	+	12.5000i	0.166175	+	0.479706i
$680$		0			0
$681$	−12.0000	−	20.7846i	−0.459841	−	0.796468i
$682$	−9.31749	−	34.7733i	−0.356785	−	1.33154i
$683$	6.27603	+	23.4225i	0.240146	+	0.896235i	0.975762	+	0.218837i	$0.0702262\pi$
$683$	6.27603	+	23.4225i	0.240146	+	0.896235i	−0.735616	+	0.677399i	$0.763107\pi$
$684$	2.59808	+	4.50000i	0.0993399	+	0.172062i
$685$		0			0
$686$	1.50000	−	32.0429i	0.0572703	−	1.22341i
$687$	11.0227	+	11.0227i	0.420542	+	0.420542i
$688$	−16.7303	−	4.48288i	−0.637838	−	0.170908i
$689$		0			0
$690$		0			0
$691$	7.50000	−	4.33013i	0.285313	−	0.164726i	−0.350513	−	0.936558i	$-0.613993\pi$
$691$	7.50000	−	4.33013i	0.285313	−	0.164726i	0.635826	+	0.771832i	$0.280659\pi$
$692$	4.24264	−	4.24264i	0.161281	−	0.161281i
$693$	14.2808	+	6.93237i	0.542484	+	0.263339i
$694$		−	36.0000i		−	1.36654i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−3.10583	+	11.5911i	−0.117557	+	0.438730i
$699$	−3.46410			−0.131024
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	2.24144	−	8.36516i	0.0845977	−	0.315723i
$703$	43.4667	−	11.6469i	1.63938	−	0.439270i
$704$	−5.19615	−	3.00000i	−0.195837	−	0.113067i
$705$		0			0
$706$		−	10.3923i		−	0.391120i
$707$	7.58871	−	5.13922i	0.285403	−	0.193280i
$708$	4.89898	−	4.89898i	0.184115	−	0.184115i
$709$	−14.7224	+	8.50000i	−0.552913	+	0.319224i	−0.750296	−	0.661102i	$-0.770089\pi$
$709$	−14.7224	+	8.50000i	−0.552913	+	0.319224i	0.197383	+	0.980326i	$0.436756\pi$
$710$		0			0
$711$	−5.50000	+	9.52628i	−0.206266	+	0.357263i
$712$	−23.1822	−	6.21166i	−0.868790	−	0.232792i
$713$	−8.48528	−	8.48528i	−0.317776	−	0.317776i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−10.7589	−	40.1528i	−0.401519	−	1.49849i
$719$	5.19615	+	9.00000i	0.193784	+	0.335643i	0.946501	−	0.322700i	$-0.104591\pi$
$719$	5.19615	+	9.00000i	0.193784	+	0.335643i	−0.752717	+	0.658344i	$0.771257\pi$
$720$		0			0
$721$	−14.0000	−	12.1244i	−0.521387	−	0.451535i
$722$	9.79796	+	9.79796i	0.364642	+	0.364642i
$723$	1.67303	+	0.448288i	0.0622208	+	0.0166720i
$724$	−6.92820	+	12.0000i	−0.257485	+	0.445976i
$725$		0			0
$726$	−37.5000	+	21.6506i	−1.39176	+	0.803530i
$727$	13.4350	−	13.4350i	0.498278	−	0.498278i	−0.412624	−	0.910902i	$-0.635388\pi$
$727$	13.4350	−	13.4350i	0.498278	−	0.498278i	0.910902	+	0.412624i	$0.135388\pi$
$728$	−10.0060	+	20.6126i	−0.370847	+	0.763954i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		0			0
$732$	1.67303	−	0.448288i	0.0618371	−	0.0165692i
$733$	4.91756	−	18.3526i	0.181634	−	0.677868i	−0.813692	−	0.581297i	$-0.802546\pi$
$733$	4.91756	−	18.3526i	0.181634	−	0.677868i	0.995326	−	0.0965718i	$-0.0307877\pi$
$734$	−27.7128			−1.02290
$735$		0			0
$736$	18.0000			0.663489
$737$	−13.4486	+	50.1910i	−0.495387	+	1.84881i
$738$	17.3867	−	4.65874i	0.640012	−	0.171491i
$739$	37.2391	+	21.5000i	1.36986	+	0.790890i	0.990910	−	0.134526i	$-0.0429512\pi$
$739$	37.2391	+	21.5000i	1.36986	+	0.790890i	0.378952	+	0.925416i	$0.376285\pi$
$740$		0			0
$741$		−	25.9808i		−	0.954427i
$742$		0			0
$743$	7.34847	−	7.34847i	0.269589	−	0.269589i	−0.559345	−	0.828935i	$-0.688947\pi$
$743$	7.34847	−	7.34847i	0.269589	−	0.269589i	0.828935	+	0.559345i	$0.188947\pi$
$744$	5.19615	−	3.00000i	0.190500	−	0.109985i
$745$		0			0
$746$	4.50000	−	7.79423i	0.164757	−	0.285367i
$747$	11.5911	+	3.10583i	0.424097	+	0.113636i
$748$		0			0
$749$	13.8564	+	12.0000i	0.506302	+	0.438470i
$750$		0			0
$751$	9.50000	+	16.4545i	0.346660	+	0.600433i	0.985654	−	0.168779i	$-0.0539825\pi$
$751$	9.50000	+	16.4545i	0.346660	+	0.600433i	−0.638994	+	0.769212i	$0.720649\pi$
$752$		0			0
$753$	4.48288	+	16.7303i	0.163365	+	0.609687i
$754$		0			0
$755$		0			0
$756$	0.500000	−	2.59808i	0.0181848	−	0.0944911i
$757$	−6.12372	−	6.12372i	−0.222571	−	0.222571i	0.587009	−	0.809580i	$-0.300305\pi$
$757$	−6.12372	−	6.12372i	−0.222571	−	0.222571i	−0.809580	+	0.587009i	$0.800305\pi$
$758$	−8.36516	−	2.24144i	−0.303836	−	0.0814127i
$759$	−10.3923	+	18.0000i	−0.377217	+	0.653359i
$760$		0			0
$761$	36.0000	−	20.7846i	1.30500	−	0.753442i	0.323742	−	0.946145i	$-0.395059\pi$
$761$	36.0000	−	20.7846i	1.30500	−	0.753442i	0.981257	+	0.192704i	$0.0617257\pi$
$762$	−6.36396	+	6.36396i	−0.230542	+	0.230542i
$763$	−15.3347	+	10.3849i	−0.555153	+	0.375960i
$764$			6.00000i			0.217072i
$765$		0			0
$766$	−27.0000	−	15.5885i	−0.975550	−	0.563234i
$767$	−33.4607	+	8.96575i	−1.20819	+	0.323735i
$768$	−4.91756	+	18.3526i	−0.177447	+	0.662242i
$769$	−6.92820			−0.249837			−0.124919	−	0.992167i	$-0.539867\pi$
$769$	−6.92820			−0.249837			−0.124919	+	0.992167i	$0.539867\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	−5.37945	+	20.0764i	−0.193611	+	0.722565i
$773$	−34.7733	+	9.31749i	−1.25071	+	0.335127i	−0.822611	−	0.568605i	$-0.807483\pi$
$773$	−34.7733	+	9.31749i	−1.25071	+	0.335127i	−0.428099	+	0.903732i	$0.640817\pi$
$774$	−5.19615	−	3.00000i	−0.186772	−	0.107833i
$775$		0			0
$776$		−	8.66025i		−	0.310885i
$777$	−20.6126	−	10.0060i	−0.739473	−	0.358964i
$778$	36.7423	−	36.7423i	1.31728	−	1.31728i
$779$	46.7654	−	27.0000i	1.67554	−	0.967375i
$780$		0			0
$781$	36.0000	−	62.3538i	1.28818	−	2.23120i
$782$		0			0
$783$		0			0
$784$	−12.9904	+	32.5000i	−0.463942	+	1.16071i
$785$		0			0
$786$	−3.00000	−	5.19615i	−0.107006	−	0.185341i
$787$	−1.29410	−	4.82963i	−0.0461295	−	0.172158i	0.939018	−	0.343868i	$-0.111737\pi$
$787$	−1.29410	−	4.82963i	−0.0461295	−	0.172158i	−0.985147	+	0.171710i	$0.945071\pi$
$788$	3.58630	+	13.3843i	0.127757	+	0.476795i
$789$	−6.92820	−	12.0000i	−0.246651	−	0.427211i
$790$		0			0
$791$	−15.0000	−	43.3013i	−0.533339	−	1.53962i
$792$	−7.34847	−	7.34847i	−0.261116	−	0.261116i
$793$	−8.36516	−	2.24144i	−0.297056	−	0.0795958i
$794$	1.73205	−	3.00000i	0.0614682	−	0.106466i
$795$		0			0
$796$	13.5000	−	7.79423i	0.478495	−	0.276259i
$797$	−4.24264	+	4.24264i	−0.150282	+	0.150282i	−0.778244	−	0.627962i	$-0.783889\pi$
$797$	−4.24264	+	4.24264i	−0.150282	+	0.150282i	0.627962	+	0.778244i	$0.283889\pi$
$798$	−1.70522	−	23.7506i	−0.0603641	−	0.840763i
$799$		0			0
$800$		0			0
$801$	−12.0000	−	6.92820i	−0.423999	−	0.244796i
$802$	−10.0382	+	2.68973i	−0.354461	+	0.0949775i
$803$	−10.8704	+	40.5689i	−0.383608	+	1.43164i
$804$	8.66025			0.305424
$805$		0			0
$806$	30.0000			1.05670
$807$	0.896575	−	3.34607i	0.0315610	−	0.117787i
$808$	−5.79555	+	1.55291i	−0.203887	+	0.0546313i
$809$	−25.9808	−	15.0000i	−0.913435	−	0.527372i	−0.0319002	−	0.999491i	$-0.510156\pi$
$809$	−25.9808	−	15.0000i	−0.913435	−	0.527372i	−0.881535	+	0.472119i	$0.843489\pi$
$810$		0			0
$811$			22.5167i			0.790667i	0.918538	+	0.395333i	$0.129371\pi$
$811$			22.5167i			0.790667i	−0.918538	+	0.395333i	$0.870629\pi$
$812$		0			0
$813$	7.34847	−	7.34847i	0.257722	−	0.257722i
$814$	77.9423	−	45.0000i	2.73188	−	1.57725i
$815$		0			0
$816$		0			0
$817$	−17.3867	−	4.65874i	−0.608282	−	0.162989i
$818$	6.36396	+	6.36396i	0.222511	+	0.222511i
$819$	−8.66025	+	10.0000i	−0.302614	+	0.349428i
$820$		0			0
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$	−1.55291	−	5.79555i	−0.0541641	−	0.202143i
$823$	−4.03459	−	15.0573i	−0.140637	−	0.524864i	−0.999911	−	0.0133486i	$-0.995751\pi$
$823$	−4.03459	−	15.0573i	−0.140637	−	0.524864i	0.859274	−	0.511516i	$-0.170916\pi$
$824$	6.06218	+	10.5000i	0.211186	+	0.365785i
$825$		0			0
$826$	−30.0000	+	10.3923i	−1.04383	+	0.361595i
$827$	−29.3939	−	29.3939i	−1.02213	−	1.02213i	−0.999750	−	0.0223756i	$-0.992877\pi$
$827$	−29.3939	−	29.3939i	−1.02213	−	1.02213i	−0.0223756	−	0.999750i	$-0.507123\pi$
$828$	3.34607	+	0.896575i	0.116284	+	0.0311582i
$829$	19.9186	−	34.5000i	0.691801	−	1.19823i	−0.279446	−	0.960161i	$-0.590151\pi$
$829$	19.9186	−	34.5000i	0.691801	−	1.19823i	0.971247	−	0.238073i	$-0.0765158\pi$
$830$		0			0
$831$	−4.50000	+	2.59808i	−0.156103	+	0.0901263i
$832$	3.53553	−	3.53553i	0.122573	−	0.122573i
$833$		0			0
$834$		−	39.0000i		−	1.35046i
$835$		0			0
$836$	27.0000	+	15.5885i	0.933815	+	0.539138i
$837$	3.34607	−	0.896575i	0.115657	−	0.0309902i
$838$	1.55291	−	5.79555i	0.0536445	−	0.200204i
$839$	−45.0333			−1.55472			−0.777361	−	0.629054i	$-0.783442\pi$
$839$	−45.0333			−1.55472			−0.777361	+	0.629054i	$0.783442\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$	−7.62089	+	28.4416i	−0.262633	+	0.980161i
$843$	−23.1822	+	6.21166i	−0.798438	+	0.213941i
$844$	−16.4545	−	9.50000i	−0.566387	−	0.327003i
$845$		0			0
$846$		0			0
$847$	65.9740	−	4.73672i	2.26689	−	0.162756i
$848$		0			0
$849$	0.866025	−	0.500000i	0.0297219	−	0.0171600i
$850$		0			0
$851$	15.0000	−	25.9808i	0.514193	−	0.890609i
$852$	−11.5911	−	3.10583i	−0.397105	−	0.106404i
$853$	1.41421	+	1.41421i	0.0484218	+	0.0484218i	0.730903	−	0.682481i	$-0.239099\pi$
$853$	1.41421	+	1.41421i	0.0484218	+	0.0484218i	−0.682481	+	0.730903i	$0.739099\pi$
$854$	−7.79423	−	1.50000i	−0.266713	−	0.0513289i
$855$		0			0
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	−4.65874	−	17.3867i	−0.159140	−	0.593917i	−0.998715	−	0.0506743i	$-0.983863\pi$
$857$	−4.65874	−	17.3867i	−0.159140	−	0.593917i	0.839576	−	0.543243i	$-0.182804\pi$
$858$	−13.4486	−	50.1910i	−0.459129	−	1.71349i
$859$	−22.5167	−	39.0000i	−0.768259	−	1.33066i	−0.938506	−	0.345262i	$-0.887790\pi$
$859$	−22.5167	−	39.0000i	−0.768259	−	1.33066i	0.170248	−	0.985401i	$-0.445543\pi$
$860$		0			0
$861$	−27.0000	−	5.19615i	−0.920158	−	0.177084i
$862$	−36.7423	−	36.7423i	−1.25145	−	1.25145i
$863$	26.7685	+	7.17260i	0.911211	+	0.244158i	0.683825	−	0.729646i	$-0.260315\pi$
$863$	26.7685	+	7.17260i	0.911211	+	0.244158i	0.227386	+	0.973805i	$0.426982\pi$
$864$	−2.59808	+	4.50000i	−0.0883883	+	0.153093i
$865$		0			0
$866$	−3.00000	+	1.73205i	−0.101944	+	0.0588575i
$867$	12.0208	−	12.0208i	0.408248	−	0.408248i
$868$	9.14162	−	0.656339i	0.310287	−	0.0222776i
$869$			66.0000i			2.23890i
$870$		0			0
$871$	−37.5000	−	21.6506i	−1.27064	−	0.733604i
$872$	11.7112	−	3.13801i	0.396592	−	0.106267i
$873$	1.29410	−	4.82963i	0.0437985	−	0.163458i
$874$	31.1769			1.05457
$875$		0			0
$876$	7.00000			0.236508
$877$	6.72432	−	25.0955i	0.227064	−	0.847414i	−0.754503	−	0.656297i	$-0.772122\pi$
$877$	6.72432	−	25.0955i	0.227064	−	0.847414i	0.981567	−	0.191118i	$-0.0612113\pi$
$878$	31.8756	−	8.54103i	1.07575	−	0.288246i
$879$	−20.7846	−	12.0000i	−0.701047	−	0.404750i
$880$		0			0
$881$			48.4974i			1.63392i	0.576695	+	0.816960i	$0.304342\pi$
$881$			48.4974i			1.63392i	−0.576695	+	0.816960i	$0.695658\pi$
$882$	−7.26054	+	9.71003i	−0.244475	+	0.326954i
$883$	−3.67423	+	3.67423i	−0.123648	+	0.123648i	−0.766223	−	0.642575i	$-0.777866\pi$
$883$	−3.67423	+	3.67423i	−0.123648	+	0.123648i	0.642575	+	0.766223i	$0.277866\pi$
$884$		0			0
$885$		0			0
$886$	21.0000	−	36.3731i	0.705509	−	1.22198i
$887$	−17.3867	−	4.65874i	−0.583787	−	0.156425i	−0.0451749	−	0.998979i	$-0.514385\pi$
$887$	−17.3867	−	4.65874i	−0.583787	−	0.156425i	−0.538612	+	0.842554i	$0.681051\pi$
$888$	10.6066	+	10.6066i	0.355934	+	0.355934i
$889$	12.9904	−	4.50000i	0.435683	−	0.150925i
$890$		0			0
$891$	−3.00000	−	5.19615i	−0.100504	−	0.174078i
$892$	5.95284	+	22.2163i	0.199316	+	0.743857i
$893$		0			0
$894$	5.19615	+	9.00000i	0.173785	+	0.301005i
$895$		0			0
$896$	21.0000	−	24.2487i	0.701561	−	0.810093i
$897$	−12.2474	−	12.2474i	−0.408930	−	0.408930i
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$	76.3675	−	76.3675i	2.54276	−	2.54276i
$903$	5.13922	+	7.58871i	0.171022	+	0.252536i
$904$			30.0000i			0.997785i
$905$		0			0
$906$	25.5000	+	14.7224i	0.847181	+	0.489120i
$907$	−5.01910	+	1.34486i	−0.166656	+	0.0446554i	−0.341182	−	0.939997i	$-0.610827\pi$
$907$	−5.01910	+	1.34486i	−0.166656	+	0.0446554i	0.174526	+	0.984653i	$0.444161\pi$
$908$	−6.21166	+	23.1822i	−0.206141	+	0.769329i
$909$	−3.46410			−0.114897
$910$		0			0
$911$	54.0000			1.78910			0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000			1.78910			0.894550	+	0.446968i	$0.147496\pi$
$912$	−6.72432	+	25.0955i	−0.222664	+	0.830995i
$913$	69.5467	−	18.6350i	2.30166	−	0.616728i
$914$	−28.5788	−	16.5000i	−0.945304	−	0.545771i
$915$		0			0
$916$		−	15.5885i		−	0.515057i
$917$	0.656339	+	9.14162i	0.0216742	+	0.301883i
$918$		0			0
$919$	−27.7128	+	16.0000i	−0.914161	+	0.527791i	−0.881768	−	0.471684i	$-0.843646\pi$
$919$	−27.7128	+	16.0000i	−0.914161	+	0.527791i	−0.0323936	+	0.999475i	$0.510313\pi$
$920$		0			0
$921$	−16.0000	+	27.7128i	−0.527218	+	0.913168i
$922$	−5.79555	−	1.55291i	−0.190866	−	0.0511425i
$923$	42.4264	+	42.4264i	1.39648	+	1.39648i
$924$	−5.19615	−	15.0000i	−0.170941	−	0.493464i
$925$		0			0
$926$	7.50000	+	12.9904i	0.246465	+	0.426890i
$927$	1.81173	+	6.76148i	0.0595051	+	0.222076i
$928$		0			0
$929$	12.1244	+	21.0000i	0.397787	+	0.688988i	0.993453	−	0.114245i	$-0.0364449\pi$
$929$	12.1244	+	21.0000i	0.397787	+	0.688988i	−0.595665	+	0.803233i	$0.703112\pi$
$930$		0			0
$931$	−13.5000	+	33.7750i	−0.442445	+	1.10693i
$932$	2.44949	+	2.44949i	0.0802357	+	0.0802357i
$933$	−16.7303	−	4.48288i	−0.547726	−	0.146763i
$934$	−5.19615	+	9.00000i	−0.170023	+	0.294489i
$935$		0			0
$936$	7.50000	−	4.33013i	0.245145	−	0.141535i
$937$	−7.07107	+	7.07107i	−0.231002	+	0.231002i	−0.813111	−	0.582109i	$-0.802228\pi$
$937$	−7.07107	+	7.07107i	−0.231002	+	0.231002i	0.582109	+	0.813111i	$0.302228\pi$
$938$	−35.7021	−	17.3309i	−1.16571	−	0.565875i
$939$			26.0000i			0.848478i
$940$		0			0
$941$	−3.00000	−	1.73205i	−0.0977972	−	0.0564632i	0.450304	−	0.892875i	$-0.351316\pi$
$941$	−3.00000	−	1.73205i	−0.0977972	−	0.0564632i	−0.548101	+	0.836412i	$0.684649\pi$
$942$	38.4797	−	10.3106i	1.25374	−	0.335938i
$943$	9.31749	−	34.7733i	0.303419	−	1.13238i
$944$	34.6410			1.12747
$945$		0			0
$946$	−36.0000			−1.17046
$947$	−13.4486	+	50.1910i	−0.437022	+	1.63099i	0.299159	+	0.954203i	$0.403294\pi$
$947$	−13.4486	+	50.1910i	−0.437022	+	1.63099i	−0.736181	+	0.676784i	$0.763373\pi$
$948$	10.6252	−	2.84701i	0.345090	−	0.0924666i
$949$	−30.3109	−	17.5000i	−0.983933	−	0.568074i
$950$		0			0
$951$		−	10.3923i		−	0.336994i
$952$		0			0
$953$	−12.2474	+	12.2474i	−0.396734	+	0.396734i	−0.877079	−	0.480346i	$-0.840511\pi$
$953$	−12.2474	+	12.2474i	−0.396734	+	0.396734i	0.480346	+	0.877079i	$0.340511\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$	−33.9411	−	33.9411i	−1.09659	−	1.09659i
$959$	−1.73205	+	9.00000i	−0.0559308	+	0.290625i
$960$		0			0
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$	19.4114	+	72.4444i	0.625850	+	2.33570i
$963$	−1.79315	−	6.69213i	−0.0577835	−	0.215651i
$964$	−0.866025	−	1.50000i	−0.0278928	−	0.0483117i
$965$		0			0
$966$	−12.0000	−	10.3923i	−0.386094	−	0.334367i
$967$	15.9217	+	15.9217i	0.512007	+	0.512007i	0.915141	−	0.403134i	$-0.132079\pi$
$967$	15.9217	+	15.9217i	0.512007	+	0.512007i	−0.403134	+	0.915141i	$0.632079\pi$
$968$	−41.8258	−	11.2072i	−1.34433	−	0.360213i
$969$		0			0
$970$		0			0
$971$	−33.0000	+	19.0526i	−1.05902	+	0.611426i	−0.925161	−	0.379575i	$-0.876070\pi$
$971$	−33.0000	+	19.0526i	−1.05902	+	0.611426i	−0.133859	+	0.991000i	$0.542737\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−26.0156	+	53.5928i	−0.834023	+	1.71811i
$974$		−	42.0000i		−	1.34577i
$975$		0			0
$976$	7.50000	+	4.33013i	0.240069	+	0.138604i
$977$	3.34607	−	0.896575i	0.107050	−	0.0286840i	−0.204896	−	0.978784i	$-0.565686\pi$
$977$	3.34607	−	0.896575i	0.107050	−	0.0286840i	0.311946	+	0.950100i	$0.399019\pi$
$978$	−0.776457	+	2.89778i	−0.0248284	+	0.0926607i
$979$	−83.1384			−2.65712
$980$		0			0
$981$	7.00000			0.223493
$982$	−8.06918	+	30.1146i	−0.257498	+	0.960995i
$983$	−34.7733	+	9.31749i	−1.10910	+	0.297182i	−0.766464	−	0.642288i	$-0.777985\pi$
$983$	−34.7733	+	9.31749i	−1.10910	+	0.297182i	−0.342633	+	0.939469i	$0.611319\pi$
$984$	15.5885	+	9.00000i	0.496942	+	0.286910i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−18.3712	+	18.3712i	−0.584465	+	0.584465i
$989$	−10.3923	+	6.00000i	−0.330456	+	0.190789i
$990$		0			0
$991$	−20.0000	+	34.6410i	−0.635321	+	1.10041i	0.351126	+	0.936328i	$0.385799\pi$
$991$	−20.0000	+	34.6410i	−0.635321	+	1.10041i	−0.986447	+	0.164080i	$0.947534\pi$
$992$	−17.3867	−	4.65874i	−0.552027	−	0.147915i
$993$	−9.19239	−	9.19239i	−0.291712	−	0.291712i
$994$	41.5692	+	36.0000i	1.31850	+	1.14185i
$995$		0			0
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	9.05867	+	33.8074i	0.286891	+	1.07069i	0.947447	+	0.319914i	$0.103654\pi$
$997$	9.05867	+	33.8074i	0.286891	+	1.07069i	−0.660556	+	0.750777i	$0.729679\pi$
$998$	−10.3106	−	38.4797i	−0.326377	−	1.21806i
$999$	4.33013	+	7.50000i	0.136999	+	0.237289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.b.157.2	yes	8
5.2	odd	4	inner	525.2.bc.b.493.2	yes	8
5.3	odd	4	inner	525.2.bc.b.493.1	yes	8
5.4	even	2	inner	525.2.bc.b.157.1	yes	8
7.5	odd	6	inner	525.2.bc.b.82.1	✓	8
35.12	even	12	inner	525.2.bc.b.418.1	yes	8
35.19	odd	6	inner	525.2.bc.b.82.2	yes	8
35.33	even	12	inner	525.2.bc.b.418.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bc.b.82.1	✓	8	7.5	odd	6	inner
525.2.bc.b.82.2	yes	8	35.19	odd	6	inner
525.2.bc.b.157.1	yes	8	5.4	even	2	inner
525.2.bc.b.157.2	yes	8	1.1	even	1	trivial
525.2.bc.b.418.1	yes	8	35.12	even	12	inner
525.2.bc.b.418.2	yes	8	35.33	even	12	inner
525.2.bc.b.493.1	yes	8	5.3	odd	4	inner
525.2.bc.b.493.2	yes	8	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.448288 - 1.67303i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.73205i q^{6} +(-1.15539 + 2.38014i) q^{7} +(1.22474 - 1.22474i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.448288 - 1.67303i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.73205i q^{6} +(-1.15539 + 2.38014i) q^{7} +(1.22474 - 1.22474i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.00000 - 5.19615i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(3.53553 + 3.53553i) q^{13} +(3.46410 + 3.00000i) q^{14} +(-2.50000 - 4.33013i) q^{16} +(-0.448288 - 1.67303i) q^{18} +(-2.59808 - 4.50000i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(-7.34847 - 7.34847i) q^{22} +(-3.34607 - 0.896575i) q^{23} +(0.866025 - 1.50000i) q^{24} +(7.50000 - 4.33013i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.19067 - 1.48356i) q^{28} +(3.00000 + 1.73205i) q^{31} +(-5.01910 + 1.34486i) q^{32} +(1.55291 - 5.79555i) q^{33} -1.00000 q^{36} +(-2.24144 + 8.36516i) q^{37} +(-8.69333 + 2.32937i) q^{38} +(4.33013 + 2.50000i) q^{39} +10.3923i q^{41} +(4.12252 + 2.00120i) q^{42} +(2.44949 - 2.44949i) q^{43} +(-5.19615 + 3.00000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-3.53553 - 3.53553i) q^{48} +(-4.33013 - 5.50000i) q^{49} +(-1.29410 - 4.82963i) q^{52} +(-0.866025 - 1.50000i) q^{54} +(1.50000 + 4.33013i) q^{56} +(-3.67423 - 3.67423i) q^{57} +(-3.46410 + 6.00000i) q^{59} +(-1.50000 + 0.866025i) q^{61} +(4.24264 - 4.24264i) q^{62} +(0.189469 + 2.63896i) q^{63} -1.00000i q^{64} +(-9.00000 - 5.19615i) q^{66} +(-8.36516 + 2.24144i) q^{67} -3.46410 q^{69} +12.0000 q^{71} +(0.448288 - 1.67303i) q^{72} +(-6.76148 + 1.81173i) q^{73} +(12.9904 + 7.50000i) q^{74} +5.19615i q^{76} +(8.90138 + 13.1440i) q^{77} +(6.12372 - 6.12372i) q^{78} +(-9.52628 + 5.50000i) q^{79} +(0.500000 - 0.866025i) q^{81} +(17.3867 + 4.65874i) q^{82} +(8.48528 + 8.48528i) q^{83} +(1.73205 - 2.00000i) q^{84} +(-3.00000 - 5.19615i) q^{86} +(-2.68973 - 10.0382i) q^{88} +(-6.92820 - 12.0000i) q^{89} +(-12.5000 + 4.33013i) q^{91} +(2.44949 + 2.44949i) q^{92} +(3.34607 + 0.896575i) q^{93} +(-4.50000 + 2.59808i) q^{96} +(3.53553 - 3.53553i) q^{97} +(-11.1428 + 4.77886i) q^{98} -6.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 24 q^{11} - 20 q^{16} - 4 q^{21} + 60 q^{26} + 24 q^{31} - 8 q^{36} - 24 q^{46} + 12 q^{56} - 12 q^{61} - 72 q^{66} + 96 q^{71} + 4 q^{81} - 24 q^{86} - 100 q^{91} - 36 q^{96}+O(q^{100}) \) 8 * q + 24 * q^11 - 20 * q^16 - 4 * q^21 + 60 * q^26 + 24 * q^31 - 8 * q^36 - 24 * q^46 + 12 * q^56 - 12 * q^61 - 72 * q^66 + 96 * q^71 + 4 * q^81 - 24 * q^86 - 100 * q^91 - 36 * q^96

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