LMFDB - Embedded newform 525.2.bc.b.493.1

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			493.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	525.493
Dual form			525.2.bc.b.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67303 - 0.448288i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(2.38014 + 1.15539i) q^{7} +(1.22474 + 1.22474i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-1.67303 - 0.448288i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(2.38014 + 1.15539i) q^{7} +(1.22474 + 1.22474i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(3.00000 - 5.19615i) q^{11} +(-0.258819 + 0.965926i) q^{12} +(-3.53553 + 3.53553i) q^{13} +(-3.46410 - 3.00000i) q^{14} +(-2.50000 - 4.33013i) q^{16} +(1.67303 - 0.448288i) q^{18} +(2.59808 + 4.50000i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(-7.34847 + 7.34847i) q^{22} +(0.896575 - 3.34607i) q^{23} +(-0.866025 + 1.50000i) q^{24} +(7.50000 - 4.33013i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.48356 + 2.19067i) q^{28} +(3.00000 + 1.73205i) q^{31} +(1.34486 + 5.01910i) q^{32} +(5.79555 + 1.55291i) q^{33} -1.00000 q^{36} +(8.36516 + 2.24144i) q^{37} +(-2.32937 - 8.69333i) q^{38} +(-4.33013 - 2.50000i) q^{39} +10.3923i q^{41} +(2.00120 - 4.12252i) q^{42} +(2.44949 + 2.44949i) q^{43} +(5.19615 - 3.00000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(3.53553 - 3.53553i) q^{48} +(4.33013 + 5.50000i) q^{49} +(-4.82963 + 1.29410i) q^{52} +(0.866025 + 1.50000i) q^{54} +(1.50000 + 4.33013i) q^{56} +(-3.67423 + 3.67423i) q^{57} +(3.46410 - 6.00000i) q^{59} +(-1.50000 + 0.866025i) q^{61} +(-4.24264 - 4.24264i) q^{62} +(-2.63896 + 0.189469i) q^{63} +1.00000i q^{64} +(-9.00000 - 5.19615i) q^{66} +(2.24144 + 8.36516i) q^{67} +3.46410 q^{69} +12.0000 q^{71} +(-1.67303 - 0.448288i) q^{72} +(-1.81173 - 6.76148i) q^{73} +(-12.9904 - 7.50000i) q^{74} +5.19615i q^{76} +(13.1440 - 8.90138i) q^{77} +(6.12372 + 6.12372i) q^{78} +(9.52628 - 5.50000i) q^{79} +(0.500000 - 0.866025i) q^{81} +(4.65874 - 17.3867i) q^{82} +(-8.48528 + 8.48528i) q^{83} +(-1.73205 + 2.00000i) q^{84} +(-3.00000 - 5.19615i) q^{86} +(10.0382 - 2.68973i) q^{88} +(6.92820 + 12.0000i) q^{89} +(-12.5000 + 4.33013i) q^{91} +(2.44949 - 2.44949i) q^{92} +(-0.896575 + 3.34607i) q^{93} +(-4.50000 + 2.59808i) q^{96} +(-3.53553 - 3.53553i) q^{97} +(-4.77886 - 11.1428i) q^{98} +6.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.67303	−	0.448288i	−1.18301	−	0.316987i	−0.386892	−	0.922125i	$-0.626451\pi$
$2$	−1.67303	−	0.448288i	−1.18301	−	0.316987i	−0.796121	+	0.605138i	$0.793118\pi$
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.73205i		−	0.707107i
$7$	2.38014	+	1.15539i	0.899608	+	0.436698i
$7$	2.38014	+	1.15539i	0.899608	+	0.436698i
$8$	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	$-0.193114\pi$
$12$	−0.258819	+	0.965926i	−0.0747146	+	0.278839i
$13$	−3.53553	+	3.53553i	−0.980581	+	0.980581i	−0.999815	−	0.0192343i	$-0.993877\pi$
$13$	−3.53553	+	3.53553i	−0.980581	+	0.980581i	0.0192343	+	0.999815i	$0.493877\pi$
$14$	−3.46410	−	3.00000i	−0.925820	−	0.801784i
$15$		0			0
$16$	−2.50000	−	4.33013i	−0.625000	−	1.08253i
$17$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$17$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$18$	1.67303	−	0.448288i	0.394338	−	0.105662i
$19$	2.59808	+	4.50000i	0.596040	+	1.03237i	0.993399	+	0.114708i	$0.0365932\pi$
$19$	2.59808	+	4.50000i	0.596040	+	1.03237i	−0.397360	+	0.917663i	$0.630073\pi$
$20$		0			0
$21$	−0.500000	+	2.59808i	−0.109109	+	0.566947i
$22$	−7.34847	+	7.34847i	−1.56670	+	1.56670i
$23$	0.896575	−	3.34607i	0.186949	−	0.697703i	−0.807256	−	0.590201i	$-0.799048\pi$
$23$	0.896575	−	3.34607i	0.186949	−	0.697703i	0.994205	−	0.107501i	$-0.0342850\pi$
$24$	−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
$28$	1.48356	+	2.19067i	0.280367	+	0.413998i
$29$		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	$0.565974\pi$
$32$	1.34486	+	5.01910i	0.237740	+	0.887260i
$33$	5.79555	+	1.55291i	1.00888	+	0.270328i
$34$		0			0
$35$		0			0
$36$	−1.00000			−0.166667
$37$	8.36516	+	2.24144i	1.37522	+	0.368490i	0.869384	−	0.494137i	$-0.164516\pi$
$37$	8.36516	+	2.24144i	1.37522	+	0.368490i	0.505840	+	0.862627i	$0.331183\pi$
$38$	−2.32937	−	8.69333i	−0.377874	−	1.41024i
$39$	−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	$0.698650\pi$
$42$	2.00120	−	4.12252i	0.308792	−	0.636119i
$43$	2.44949	+	2.44949i	0.373544	+	0.373544i	0.868766	−	0.495222i	$-0.164913\pi$
$43$	2.44949	+	2.44949i	0.373544	+	0.373544i	−0.495222	+	0.868766i	$0.664913\pi$
$44$	5.19615	−	3.00000i	0.783349	−	0.452267i
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$47$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$48$	3.53553	−	3.53553i	0.510310	−	0.510310i
$49$	4.33013	+	5.50000i	0.618590	+	0.785714i
$50$		0			0
$51$		0			0
$52$	−4.82963	+	1.29410i	−0.669749	+	0.179459i
$53$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$53$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$54$	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	−0.547460	−	0.836832i	$-0.684405\pi$
$59$	3.46410	−	6.00000i	0.450988	−	0.781133i	0.998448	+	0.0556984i	$0.0177385\pi$
$60$		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
$63$	−2.63896	+	0.189469i	−0.332478	+	0.0238708i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−9.00000	−	5.19615i	−1.10782	−	0.639602i
$67$	2.24144	+	8.36516i	0.273835	+	1.02197i	0.956618	+	0.291346i	$0.0941030\pi$
$67$	2.24144	+	8.36516i	0.273835	+	1.02197i	−0.682783	+	0.730622i	$0.739230\pi$
$68$		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	$0.247758\pi$
$72$	−1.67303	−	0.448288i	−0.197169	−	0.0528312i
$73$	−1.81173	−	6.76148i	−0.212047	−	0.791371i	−0.987185	−	0.159579i	$-0.948986\pi$
$73$	−1.81173	−	6.76148i	−0.212047	−	0.791371i	0.775138	−	0.631792i	$-0.217680\pi$
$74$	−12.9904	−	7.50000i	−1.51010	−	0.871857i
$75$		0			0
$76$			5.19615i			0.596040i
$77$	13.1440	−	8.90138i	1.49790	−	1.01441i
$78$	6.12372	+	6.12372i	0.693375	+	0.693375i
$79$	9.52628	−	5.50000i	1.07179	−	0.618798i	0.143120	−	0.989705i	$-0.454286\pi$
$79$	9.52628	−	5.50000i	1.07179	−	0.618798i	0.928670	+	0.370907i	$0.120953\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	4.65874	−	17.3867i	0.514472	−	1.92004i
$83$	−8.48528	+	8.48528i	−0.931381	+	0.931381i	−0.997792	−	0.0664117i	$-0.978845\pi$
$83$	−8.48528	+	8.48528i	−0.931381	+	0.931381i	0.0664117	+	0.997792i	$0.478845\pi$
$84$	−1.73205	+	2.00000i	−0.188982	+	0.218218i
$85$		0			0
$86$	−3.00000	−	5.19615i	−0.323498	−	0.560316i
$87$		0			0
$88$	10.0382	−	2.68973i	1.07008	−	0.286726i
$89$	6.92820	+	12.0000i	0.734388	+	1.27200i	0.954991	+	0.296634i	$0.0958641\pi$
$89$	6.92820	+	12.0000i	0.734388	+	1.27200i	−0.220603	+	0.975364i	$0.570803\pi$
$90$		0			0
$91$	−12.5000	+	4.33013i	−1.31036	+	0.453921i
$92$	2.44949	−	2.44949i	0.255377	−	0.255377i
$93$	−0.896575	+	3.34607i	−0.0929705	+	0.346971i
$94$		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	$-0.331693\pi$
$97$	−3.53553	−	3.53553i	−0.358979	−	0.358979i	−0.863437	+	0.504457i	$0.831693\pi$
$98$	−4.77886	−	11.1428i	−0.482738	−	1.12560i
$99$			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
$103$	−6.76148	−	1.81173i	−0.666228	−	0.178515i	−0.0901732	−	0.995926i	$-0.528742\pi$
$103$	−6.76148	−	1.81173i	−0.666228	−	0.178515i	−0.576055	+	0.817411i	$0.695409\pi$
$104$	−8.66025			−0.849208
$105$		0			0
$106$		0			0
$107$	−6.69213	−	1.79315i	−0.646953	−	0.173350i	−0.0796020	−	0.996827i	$-0.525365\pi$
$107$	−6.69213	−	1.79315i	−0.646953	−	0.173350i	−0.567351	+	0.823476i	$0.692032\pi$
$108$	−0.258819	−	0.965926i	−0.0249049	−	0.0929463i
$109$	−6.06218	−	3.50000i	−0.580651	−	0.335239i	0.180741	−	0.983531i	$-0.442150\pi$
$109$	−6.06218	−	3.50000i	−0.580651	−	0.335239i	−0.761392	+	0.648292i	$0.775484\pi$
$110$		0			0
$111$			8.66025i			0.821995i
$112$	−0.947343	−	13.1948i	−0.0895155	−	1.24679i
$113$	−12.2474	−	12.2474i	−1.15214	−	1.15214i	−0.986122	−	0.166021i	$-0.946908\pi$
$113$	−12.2474	−	12.2474i	−1.15214	−	1.15214i	−0.166021	−	0.986122i	$-0.553092\pi$
$114$	7.79423	−	4.50000i	0.729996	−	0.421464i
$115$		0			0
$116$		0			0
$117$	1.29410	−	4.82963i	0.119639	−	0.446499i
$118$	−8.48528	+	8.48528i	−0.781133	+	0.781133i
$119$		0			0
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	2.89778	−	0.776457i	0.262352	−	0.0702971i
$123$	−10.0382	+	2.68973i	−0.905114	+	0.242524i
$124$	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	−0.851077	−	0.525041i	$-0.824050\pi$
$127$	−3.67423	+	3.67423i	−0.326036	+	0.326036i	0.525041	+	0.851077i	$0.324050\pi$
$128$	3.13801	−	11.7112i	0.277364	−	1.03514i
$129$	−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
$133$	0.984508	+	13.7124i	0.0853677	+	1.18902i
$134$		−	15.0000i		−	1.29580i
$135$		0			0
$136$		0			0
$137$	−0.896575	−	3.34607i	−0.0765996	−	0.285874i	0.916992	−	0.398906i	$-0.130610\pi$
$137$	−0.896575	−	3.34607i	−0.0765996	−	0.285874i	−0.993591	+	0.113033i	$0.963943\pi$
$138$	−5.79555	−	1.55291i	−0.493350	−	0.132193i
$139$	−22.5167			−1.90984			−0.954919	−	0.296866i	$-0.904058\pi$
$139$	−22.5167			−1.90984			−0.954919	+	0.296866i	$0.904058\pi$
$140$		0			0
$141$		0			0
$142$	−20.0764	−	5.37945i	−1.68477	−	0.451434i
$143$	7.76457	+	28.9778i	0.649306	+	2.42324i
$144$	4.33013	+	2.50000i	0.360844	+	0.208333i
$145$		0			0
$146$			12.1244i			1.00342i
$147$	−4.19187	+	5.60609i	−0.345740	+	0.462382i
$148$	6.12372	+	6.12372i	0.503367	+	0.503367i
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	−0.271821	−	0.962348i	$-0.587626\pi$
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	0.697507	+	0.716578i	$0.254293\pi$
$150$		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	$0.923520\pi$
$152$	−2.32937	+	8.69333i	−0.188937	+	0.705122i
$153$		0			0
$154$	−25.9808	+	9.00000i	−2.09359	+	0.725241i
$155$		0			0
$156$	−2.50000	−	4.33013i	−0.200160	−	0.346688i
$157$	22.2163	−	5.95284i	1.77305	−	0.475088i	0.783764	−	0.621058i	$-0.213297\pi$
$157$	22.2163	−	5.95284i	1.77305	−	0.475088i	0.989289	+	0.145970i	$0.0466304\pi$
$158$	−18.4034	+	4.93117i	−1.46409	+	0.392302i
$159$		0			0
$160$		0			0
$161$	6.00000	−	6.92820i	0.472866	−	0.546019i
$162$	−1.22474	+	1.22474i	−0.0962250	+	0.0962250i
$163$	0.448288	−	1.67303i	0.0351126	−	0.131042i	−0.946145	−	0.323744i	$-0.895058\pi$
$163$	0.448288	−	1.67303i	0.0351126	−	0.131042i	0.981257	+	0.192702i	$0.0617250\pi$
$164$	−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	$-0.403692\pi$
$167$	−8.48528	−	8.48528i	−0.656611	−	0.656611i	−0.954577	+	0.297966i	$0.903692\pi$
$168$	−3.79435	+	2.56961i	−0.292741	+	0.198250i
$169$		−	12.0000i		−	0.923077i
$170$		0			0
$171$	−4.50000	−	2.59808i	−0.344124	−	0.198680i
$172$	0.896575	+	3.34607i	0.0683632	+	0.255135i
$173$	−5.79555	−	1.55291i	−0.440628	−	0.118066i	0.0316829	−	0.999498i	$-0.489913\pi$
$173$	−5.79555	−	1.55291i	−0.440628	−	0.118066i	−0.472311	+	0.881432i	$0.656580\pi$
$174$		0			0
$175$		0			0
$176$	−30.0000			−2.26134
$177$	6.69213	+	1.79315i	0.503011	+	0.134781i
$178$	−6.21166	−	23.1822i	−0.465583	−	1.73758i
$179$		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	$-0.172197\pi$
$182$	22.8541	−	1.64085i	1.69405	−	0.121628i
$183$	−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	$0.902984\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	20.0764	−	5.37945i	1.44513	−	0.387221i	0.550803	−	0.834635i	$-0.314321\pi$
$193$	20.0764	−	5.37945i	1.44513	−	0.387221i	0.894327	+	0.447414i	$0.147655\pi$
$194$	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	−0.963995	−	0.265920i	$-0.914324\pi$
$197$	−9.79796	+	9.79796i	−0.698076	+	0.698076i	0.265920	+	0.963995i	$0.414324\pi$
$198$	2.68973	−	10.0382i	0.191151	−	0.713384i
$199$	7.79423	−	13.5000i	0.552518	−	0.956990i	−0.445574	−	0.895245i	$-0.647000\pi$
$199$	7.79423	−	13.5000i	0.552518	−	0.956990i	0.998092	−	0.0617444i	$-0.0196664\pi$
$200$		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
$207$	0.896575	+	3.34607i	0.0623163	+	0.232568i
$208$	24.1481	+	6.47048i	1.67437	+	0.448647i
$209$	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
$213$	3.10583	+	11.5911i	0.212808	+	0.794210i
$214$	10.3923	+	6.00000i	0.710403	+	0.410152i
$215$		0			0
$216$		−	1.73205i		−	0.117851i
$217$	5.13922	+	7.58871i	0.348873	+	0.515155i
$218$	8.57321	+	8.57321i	0.580651	+	0.580651i
$219$	6.06218	−	3.50000i	0.409644	−	0.236508i
$220$		0			0
$221$		0			0
$222$	3.88229	−	14.4889i	0.260562	−	0.972430i
$223$	16.2635	−	16.2635i	1.08908	−	1.08908i	0.0934584	−	0.995623i	$-0.470208\pi$
$223$	16.2635	−	16.2635i	1.08908	−	1.08908i	0.995623	−	0.0934584i	$-0.0297922\pi$
$224$	−2.59808	+	13.5000i	−0.173591	+	0.902007i
$225$		0			0
$226$	15.0000	+	25.9808i	0.997785	+	1.72821i
$227$	−23.1822	+	6.21166i	−1.53866	+	0.412282i	−0.925832	−	0.377936i	$-0.876634\pi$
$227$	−23.1822	+	6.21166i	−1.53866	+	0.412282i	−0.612826	+	0.790218i	$0.709967\pi$
$228$	−5.01910	+	1.34486i	−0.332398	+	0.0890657i
$229$	−7.79423	−	13.5000i	−0.515057	−	0.892105i	−0.999847	−	0.0174746i	$-0.994437\pi$
$229$	−7.79423	−	13.5000i	−0.515057	−	0.892105i	0.484790	−	0.874630i	$-0.338896\pi$
$230$		0			0
$231$	12.0000	+	10.3923i	0.789542	+	0.683763i
$232$		0			0
$233$	0.896575	−	3.34607i	0.0587366	−	0.219208i	−0.930319	−	0.366751i	$-0.880470\pi$
$233$	0.896575	−	3.34607i	0.0587366	−	0.219208i	0.989056	+	0.147543i	$0.0471366\pi$
$234$	−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	$0.648900\pi$
$242$	11.2072	+	41.8258i	0.720426	+	2.68867i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−1.73205			−0.110883
$245$		0			0
$246$	18.0000			1.14764
$247$	−25.0955	−	6.72432i	−1.59679	−	0.427858i
$248$	1.55291	+	5.79555i	0.0986102	+	0.368018i
$249$	−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	$0.815910\pi$
$252$	−2.38014	−	1.15539i	−0.149935	−	0.0727830i
$253$	−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
$257$	4.65874	−	17.3867i	0.290604	−	1.08455i	−0.654041	−	0.756459i	$-0.726928\pi$
$257$	4.65874	−	17.3867i	0.290604	−	1.08455i	0.944646	−	0.328092i	$-0.106405\pi$
$258$	4.24264	−	4.24264i	0.264135	−	0.264135i
$259$	17.3205	+	15.0000i	1.07624	+	0.932055i
$260$		0			0
$261$		0			0
$262$	−5.79555	+	1.55291i	−0.358051	+	0.0959394i
$263$	13.3843	−	3.58630i	0.825309	−	0.221141i	0.178643	−	0.983914i	$-0.442829\pi$
$263$	13.3843	−	3.58630i	0.825309	−	0.221141i	0.646666	+	0.762773i	$0.276163\pi$
$264$	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
$268$	−2.24144	+	8.36516i	−0.136918	+	0.510984i
$269$	−1.73205	+	3.00000i	−0.105605	+	0.182913i	−0.913985	−	0.405747i	$-0.867011\pi$
$269$	−1.73205	+	3.00000i	−0.105605	+	0.182913i	0.808380	+	0.588661i	$0.200345\pi$
$270$		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
$273$	−7.41782	−	10.9534i	−0.448947	−	0.662927i
$274$			6.00000i			0.362473i
$275$		0			0
$276$	3.00000	+	1.73205i	0.180579	+	0.104257i
$277$	1.34486	+	5.01910i	0.0808050	+	0.301568i	0.994487	−	0.104862i	$-0.0334401\pi$
$277$	1.34486	+	5.01910i	0.0808050	+	0.301568i	−0.913682	+	0.406430i	$0.866773\pi$
$278$	37.6711	+	10.0939i	2.25936	+	0.605394i
$279$	−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
$283$	0.258819	+	0.965926i	0.0153852	+	0.0574183i	0.973192	−	0.229996i	$-0.0738712\pi$
$283$	0.258819	+	0.965926i	0.0153852	+	0.0574183i	−0.957806	+	0.287414i	$0.907204\pi$
$284$	10.3923	+	6.00000i	0.616670	+	0.356034i
$285$		0			0
$286$		−	51.9615i		−	3.07255i
$287$	−12.0072	+	24.7351i	−0.708763	+	1.46007i
$288$	−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
$292$	1.81173	−	6.76148i	0.106024	−	0.395686i
$293$	16.9706	−	16.9706i	0.991431	−	0.991431i	−0.00853273	−	0.999964i	$-0.502716\pi$
$293$	16.9706	−	16.9706i	0.991431	−	0.991431i	0.999964	+	0.00853273i	$0.00271609\pi$
$294$	9.52628	−	7.50000i	0.555584	−	0.437409i
$295$		0			0
$296$	7.50000	+	12.9904i	0.435929	+	0.755051i
$297$	−5.79555	+	1.55291i	−0.336292	+	0.0901092i
$298$	−10.0382	+	2.68973i	−0.581497	+	0.155812i
$299$	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
$303$	0.896575	−	3.34607i	0.0515069	−	0.192226i
$304$	12.9904	−	22.5000i	0.745049	−	1.29046i
$305$		0			0
$306$		0			0
$307$	22.6274	+	22.6274i	1.29141	+	1.29141i	0.933912	+	0.357503i	$0.116372\pi$
$307$	22.6274	+	22.6274i	1.29141	+	1.29141i	0.357503	+	0.933912i	$0.383628\pi$
$308$	15.8338	−	1.13681i	0.902212	−	0.0647759i
$309$		−	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	$0.830064\pi$
$312$	−2.24144	−	8.36516i	−0.126896	−	0.473584i
$313$	−25.1141	−	6.72930i	−1.41953	−	0.380362i	−0.534214	−	0.845349i	$-0.679392\pi$
$313$	−25.1141	−	6.72930i	−1.41953	−	0.380362i	−0.885317	+	0.464987i	$0.846059\pi$
$314$	−39.8372			−2.24814
$315$		0			0
$316$	11.0000			0.618798
$317$	−10.0382	−	2.68973i	−0.563801	−	0.151070i	−0.0343491	−	0.999410i	$-0.510936\pi$
$317$	−10.0382	−	2.68973i	−0.563801	−	0.151070i	−0.529452	+	0.848340i	$0.677602\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		−	6.92820i		−	0.386695i
$322$	−13.1440	+	8.90138i	−0.732488	+	0.496055i
$323$		0			0
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$		0			0
$326$	−1.50000	+	2.59808i	−0.0830773	+	0.143894i
$327$	1.81173	−	6.76148i	0.100189	−	0.373911i
$328$	−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	$0.949627\pi$
$332$	−11.5911	+	3.10583i	−0.636145	+	0.170454i
$333$	−8.36516	+	2.24144i	−0.458408	+	0.122830i
$334$	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	−0.560971	−	0.827835i	$-0.689572\pi$
$337$	4.89898	−	4.89898i	0.266864	−	0.266864i	0.827835	+	0.560971i	$0.189572\pi$
$338$	−5.37945	+	20.0764i	−0.292604	+	1.09201i
$339$	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
$343$	3.95164	+	18.0938i	0.213368	+	0.976972i
$344$			6.00000i			0.323498i
$345$		0			0
$346$	9.00000	+	5.19615i	0.483843	+	0.279347i
$347$	−5.37945	−	20.0764i	−0.288784	−	1.07776i	−0.946030	−	0.324080i	$-0.894945\pi$
$347$	−5.37945	−	20.0764i	−0.288784	−	1.07776i	0.657245	−	0.753677i	$-0.271722\pi$
$348$		0			0
$349$	6.92820			0.370858			0.185429	−	0.982658i	$-0.440632\pi$
$349$	6.92820			0.370858			0.185429	+	0.982658i	$0.440632\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$	30.1146	+	8.06918i	1.60511	+	0.430089i
$353$	1.55291	+	5.79555i	0.0826533	+	0.308466i	0.994859	−	0.101265i	$-0.0322891\pi$
$353$	1.55291	+	5.79555i	0.0826533	+	0.308466i	−0.912206	+	0.409731i	$0.865622\pi$
$354$	−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	−0.935423	−	0.353529i	$-0.884981\pi$
$359$	−20.7846	+	12.0000i	−1.09697	+	0.633336i	−0.161546	+	0.986865i	$0.551648\pi$
$360$		0			0
$361$	−4.00000	+	6.92820i	−0.210526	+	0.364642i
$362$	−6.21166	+	23.1822i	−0.326477	+	1.21843i
$363$	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
$367$	−15.4548	+	4.14110i	−0.806735	+	0.216164i	−0.638539	−	0.769590i	$-0.720461\pi$
$367$	−15.4548	+	4.14110i	−0.806735	+	0.216164i	−0.168196	+	0.985754i	$0.553794\pi$
$368$	−16.7303	+	4.48288i	−0.872129	+	0.233686i
$369$	−5.19615	−	9.00000i	−0.270501	−	0.468521i
$370$		0			0
$371$		0			0
$372$	−2.44949	+	2.44949i	−0.127000	+	0.127000i
$373$	−1.34486	+	5.01910i	−0.0696344	+	0.259879i	−0.991963	−	0.126527i	$-0.959617\pi$
$373$	−1.34486	+	5.01910i	−0.0696344	+	0.259879i	0.922329	+	0.386406i	$0.126284\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	0.328169	+	4.57081i	0.0168792	+	0.235097i
$379$			5.00000i			0.256833i	0.991720	+	0.128416i	$0.0409894\pi$
$379$			5.00000i			0.256833i	−0.991720	+	0.128416i	$0.959011\pi$
$380$		0			0
$381$	−4.50000	−	2.59808i	−0.230542	−	0.133103i
$382$	2.68973	+	10.0382i	0.137618	+	0.513599i
$383$	17.3867	+	4.65874i	0.888417	+	0.238051i	0.674035	−	0.738699i	$-0.264560\pi$
$383$	17.3867	+	4.65874i	0.888417	+	0.238051i	0.214382	+	0.976750i	$0.431226\pi$
$384$	12.1244			0.618718
$385$		0			0
$386$	−36.0000			−1.83235
$387$	−3.34607	−	0.896575i	−0.170090	−	0.0455755i
$388$	−1.29410	−	4.82963i	−0.0656977	−	0.245187i
$389$	−25.9808	−	15.0000i	−1.31728	−	0.760530i	−0.333987	−	0.942578i	$-0.608394\pi$
$389$	−25.9808	−	15.0000i	−1.31728	−	0.760530i	−0.983290	+	0.182047i	$0.941728\pi$
$390$		0			0
$391$		0			0
$392$	−1.43280	+	12.0394i	−0.0723671	+	0.608081i
$393$	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
$397$	0.517638	−	1.93185i	0.0259795	−	0.0969569i	−0.951719	−	0.306971i	$-0.900684\pi$
$397$	0.517638	−	1.93185i	0.0259795	−	0.0969569i	0.977698	+	0.210014i	$0.0673511\pi$
$398$	−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	$0.881200\pi$
$402$	14.4889	−	3.88229i	0.722640	−	0.193631i
$403$	−16.7303	+	4.48288i	−0.833397	+	0.223308i
$404$	−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	−0.794616	−	0.607112i	$-0.792328\pi$
$409$	2.59808	−	4.50000i	0.128467	−	0.222511i	0.923083	+	0.384602i	$0.125661\pi$
$410$		0			0
$411$	3.00000	−	1.73205i	0.147979	−	0.0854358i
$412$	−4.94975	−	4.94975i	−0.243857	−	0.243857i
$413$	15.1774	−	10.2784i	0.746832	−	0.505769i
$414$		−	6.00000i		−	0.294884i
$415$		0			0
$416$	−22.5000	−	12.9904i	−1.10315	−	0.636906i
$417$	−5.82774	−	21.7494i	−0.285386	−	1.06507i
$418$	−52.1600	−	13.9762i	−2.55123	−	0.683600i
$419$	−3.46410			−0.169232			−0.0846162	−	0.996414i	$-0.526966\pi$
$419$	−3.46410			−0.169232			−0.0846162	+	0.996414i	$0.526966\pi$
$420$		0			0
$421$	−17.0000			−0.828529			−0.414265	−	0.910156i	$-0.635961\pi$
$421$	−17.0000			−0.828529			−0.414265	+	0.910156i	$0.635961\pi$
$422$	−31.7876	−	8.51747i	−1.54740	−	0.414624i
$423$		0			0
$424$		0			0
$425$		0			0
$426$		−	20.7846i		−	1.00702i
$427$	−4.57081	+	0.328169i	−0.221197	+	0.0158812i
$428$	−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	$-0.0903517\pi$
$432$	−1.29410	+	4.82963i	−0.0622622	+	0.232366i
$433$	1.41421	−	1.41421i	0.0679628	−	0.0679628i	−0.672308	−	0.740271i	$-0.734697\pi$
$433$	1.41421	−	1.41421i	0.0679628	−	0.0679628i	0.740271	+	0.672308i	$0.234697\pi$
$434$	−5.19615	−	15.0000i	−0.249423	−	0.720023i
$435$		0			0
$436$	−3.50000	−	6.06218i	−0.167620	−	0.290326i
$437$	17.3867	−	4.65874i	0.831717	−	0.222858i
$438$	−11.7112	+	3.13801i	−0.559584	+	0.149940i
$439$	−9.52628	−	16.5000i	−0.454665	−	0.787502i	0.544004	−	0.839082i	$-0.316908\pi$
$439$	−9.52628	−	16.5000i	−0.454665	−	0.787502i	−0.998669	+	0.0515804i	$0.983574\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$		0			0
$443$	−6.27603	+	23.4225i	−0.298183	+	1.11283i	0.640473	+	0.767980i	$0.278738\pi$
$443$	−6.27603	+	23.4225i	−0.298183	+	1.11283i	−0.938656	+	0.344854i	$0.887928\pi$
$444$	−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
$448$	−1.15539	+	2.38014i	−0.0545873	+	0.112451i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$		0			0
$451$	54.0000	+	31.1769i	2.54276	+	1.46806i
$452$	−4.48288	−	16.7303i	−0.210857	−	0.786928i
$453$	−16.4207	−	4.39992i	−0.771514	−	0.206726i
$454$	41.5692			1.95094
$455$		0			0
$456$	−9.00000			−0.421464
$457$	−18.4034	−	4.93117i	−0.860873	−	0.230670i	−0.198736	−	0.980053i	$-0.563684\pi$
$457$	−18.4034	−	4.93117i	−0.860873	−	0.230670i	−0.662137	+	0.749383i	$0.730350\pi$
$458$	6.98811	+	26.0800i	0.326533	+	1.21864i
$459$		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	$-0.0257059\pi$
$462$	−15.4176	−	22.7661i	−0.717294	−	1.05918i
$463$	−6.12372	−	6.12372i	−0.284594	−	0.284594i	0.550344	−	0.834938i	$-0.314496\pi$
$463$	−6.12372	−	6.12372i	−0.284594	−	0.284594i	−0.834938	+	0.550344i	$0.814496\pi$
$464$		0			0
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	−1.55291	+	5.79555i	−0.0718603	+	0.268186i	−0.992503	−	0.122220i	$-0.960999\pi$
$467$	−1.55291	+	5.79555i	−0.0718603	+	0.268186i	0.920643	+	0.390406i	$0.127665\pi$
$468$	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
$472$	11.5911	−	3.10583i	0.533524	−	0.142957i
$473$	20.0764	−	5.37945i	0.923113	−	0.247348i
$474$	−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	$0.384891\pi$
$479$	−13.8564	+	24.0000i	−0.633115	+	1.09659i	−0.986911	+	0.161265i	$0.948443\pi$
$480$		0			0
$481$	−37.5000	+	21.6506i	−1.70985	+	0.987184i
$482$	−2.12132	−	2.12132i	−0.0966235	−	0.0966235i
$483$	8.24504	+	4.00240i	0.375163	+	0.182116i
$484$		−	25.0000i		−	1.13636i
$485$		0			0
$486$	−1.50000	−	0.866025i	−0.0680414	−	0.0392837i
$487$	−6.27603	−	23.4225i	−0.284394	−	1.06137i	−0.949281	−	0.314429i	$-0.898187\pi$
$487$	−6.27603	−	23.4225i	−0.284394	−	1.06137i	0.664887	−	0.746944i	$-0.268480\pi$
$488$	−2.89778	−	0.776457i	−0.131176	−	0.0351486i
$489$	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	$0.633134\pi$
$492$	−10.0382	−	2.68973i	−0.452557	−	0.121262i
$493$		0			0
$494$	38.9711	+	22.5000i	1.75339	+	1.01232i
$495$		0			0
$496$		−	17.3205i		−	0.777714i
$497$	28.5617	+	13.8647i	1.28117	+	0.621918i
$498$	14.6969	+	14.6969i	0.658586	+	0.658586i
$499$	−19.9186	+	11.5000i	−0.891678	+	0.514811i	−0.874491	−	0.485042i	$-0.838804\pi$
$499$	−19.9186	+	11.5000i	−0.891678	+	0.514811i	−0.0171872	+	0.999852i	$0.505471\pi$
$500$		0			0
$501$	6.00000	−	10.3923i	0.268060	−	0.464294i
$502$	7.76457	−	28.9778i	0.346550	−	1.29334i
$503$	8.48528	−	8.48528i	0.378340	−	0.378340i	−0.492163	−	0.870503i	$-0.663794\pi$
$503$	8.48528	−	8.48528i	0.378340	−	0.378340i	0.870503	+	0.492163i	$0.163794\pi$
$504$	−3.46410	−	3.00000i	−0.154303	−	0.133631i
$505$		0			0
$506$	18.0000	+	31.1769i	0.800198	+	1.38598i
$507$	11.5911	−	3.10583i	0.514779	−	0.137935i
$508$	−5.01910	+	1.34486i	−0.222686	+	0.0596687i
$509$	3.46410	+	6.00000i	0.153544	+	0.265945i	0.932528	−	0.361098i	$-0.117598\pi$
$509$	3.46410	+	6.00000i	0.153544	+	0.265945i	−0.778984	+	0.627044i	$0.784265\pi$
$510$		0			0
$511$	3.50000	−	18.1865i	0.154831	−	0.804525i
$512$	6.12372	−	6.12372i	0.270633	−	0.270633i
$513$	1.34486	−	5.01910i	0.0593772	−	0.221599i
$514$	−15.5885	+	27.0000i	−0.687577	+	1.19092i
$515$		0			0
$516$	−3.00000	+	1.73205i	−0.132068	+	0.0762493i
$517$		0			0
$518$	−22.2535	−	32.8601i	−0.977761	−	1.44379i
$519$		−	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
$523$	−3.86370	−	1.03528i	−0.168948	−	0.0452695i	0.173353	−	0.984860i	$-0.444540\pi$
$523$	−3.86370	−	1.03528i	−0.168948	−	0.0452695i	−0.342301	+	0.939590i	$0.611206\pi$
$524$	3.46410			0.151330
$525$		0			0
$526$	−24.0000			−1.04645
$527$		0			0
$528$	−7.76457	−	28.9778i	−0.337910	−	1.26110i
$529$	9.52628	+	5.50000i	0.414186	+	0.239130i
$530$		0			0
$531$			6.92820i			0.300658i
$532$	−6.00361	+	12.3676i	−0.260289	+	0.536202i
$533$	−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	$0.785252\pi$
$542$	−17.3867	+	4.65874i	−0.746821	+	0.200110i
$543$	13.3843	−	3.58630i	0.574374	−	0.153903i
$544$		0			0
$545$		0			0
$546$	7.50000	+	21.6506i	0.320970	+	0.926562i
$547$	−7.34847	+	7.34847i	−0.314198	+	0.314198i	−0.846533	−	0.532336i	$-0.821314\pi$
$547$	−7.34847	+	7.34847i	−0.314198	+	0.314198i	0.532336	+	0.846533i	$0.321314\pi$
$548$	0.896575	−	3.34607i	0.0382998	−	0.142937i
$549$	0.866025	−	1.50000i	0.0369611	−	0.0640184i
$550$		0			0
$551$		0			0
$552$	4.24264	+	4.24264i	0.180579	+	0.180579i
$553$	29.0285	−	2.08416i	1.23442	−	0.0886273i
$554$		−	9.00000i		−	0.382373i
$555$		0			0
$556$	−19.5000	−	11.2583i	−0.826984	−	0.477460i
$557$	−8.96575	−	33.4607i	−0.379891	−	1.41777i	−0.846065	−	0.533080i	$-0.821034\pi$
$557$	−8.96575	−	33.4607i	−0.379891	−	1.41777i	0.466174	−	0.884693i	$-0.345632\pi$
$558$	5.79555	+	1.55291i	0.245345	+	0.0657401i
$559$	−17.3205			−0.732579
$560$		0			0
$561$		0			0
$562$	40.1528	+	10.7589i	1.69374	+	0.453837i
$563$	−7.76457	−	28.9778i	−0.327238	−	1.22127i	−0.912043	−	0.410094i	$-0.865496\pi$
$563$	−7.76457	−	28.9778i	−0.327238	−	1.22127i	0.584806	−	0.811174i	$-0.301171\pi$
$564$		0			0
$565$		0			0
$566$		−	1.73205i		−	0.0728035i
$567$	2.19067	−	1.48356i	0.0919995	−	0.0623038i
$568$	14.6969	+	14.6969i	0.616670	+	0.616670i
$569$	25.9808	−	15.0000i	1.08917	−	0.628833i	0.155815	−	0.987786i	$-0.450200\pi$
$569$	25.9808	−	15.0000i	1.08917	−	0.628833i	0.933355	+	0.358954i	$0.116866\pi$
$570$		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	$0.240594\pi$
$572$	−7.76457	+	28.9778i	−0.324653	+	1.21162i
$573$	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
$577$	32.8415	−	8.79985i	1.36721	−	0.366342i	0.500750	−	0.865592i	$-0.333058\pi$
$577$	32.8415	−	8.79985i	1.36721	−	0.366342i	0.866458	+	0.499249i	$0.166391\pi$
$578$	28.4416	−	7.62089i	1.18301	−	0.316987i
$579$	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	$-0.462509\pi$
$587$	−21.2132	−	21.2132i	−0.875563	−	0.875563i	−0.993072	+	0.117509i	$0.962509\pi$
$588$	−6.43331	+	2.75908i	−0.265305	+	0.113782i
$589$			18.0000i			0.741677i
$590$		0			0
$591$	−12.0000	−	6.92820i	−0.493614	−	0.284988i
$592$	−11.2072	−	41.8258i	−0.460613	−	1.71903i
$593$	17.3867	+	4.65874i	0.713985	+	0.191312i	0.597486	−	0.801879i	$-0.296166\pi$
$593$	17.3867	+	4.65874i	0.713985	+	0.191312i	0.116499	+	0.993191i	$0.462833\pi$
$594$	10.3923			0.426401
$595$		0			0
$596$	6.00000			0.245770
$597$	15.0573	+	4.03459i	0.616254	+	0.165125i
$598$	−7.76457	−	28.9778i	−0.317517	−	1.18499i
$599$	−31.1769	−	18.0000i	−1.27385	−	0.735460i	−0.298143	−	0.954521i	$-0.596367\pi$
$599$	−31.1769	−	18.0000i	−1.27385	−	0.735460i	−0.975711	+	0.219061i	$0.929701\pi$
$600$		0			0
$601$			29.4449i			1.20108i	0.799594	+	0.600541i	$0.205048\pi$
$601$			29.4449i			1.20108i	−0.799594	+	0.600541i	$0.794952\pi$
$602$	−1.13681	−	15.8338i	−0.0463330	−	0.645335i
$603$	−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
$607$	−3.36465	+	12.5570i	−0.136567	+	0.509674i	0.863420	+	0.504486i	$0.168318\pi$
$607$	−3.36465	+	12.5570i	−0.136567	+	0.509674i	−0.999987	+	0.00518808i	$0.998349\pi$
$608$	−19.0919	+	19.0919i	−0.774278	+	0.774278i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$613$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$614$	−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	−0.481820	−	0.876270i	$-0.660024\pi$
$617$	9.79796	−	9.79796i	0.394451	−	0.394451i	0.876270	+	0.481820i	$0.160024\pi$
$618$	−3.13801	+	11.7112i	−0.126229	+	0.471095i
$619$	−5.19615	+	9.00000i	−0.208851	+	0.361741i	−0.951353	−	0.308103i	$-0.900306\pi$
$619$	−5.19615	+	9.00000i	−0.208851	+	0.361741i	0.742502	+	0.669844i	$0.233639\pi$
$620$		0			0
$621$	−3.00000	+	1.73205i	−0.120386	+	0.0695048i
$622$	21.2132	+	21.2132i	0.850572	+	0.850572i
$623$	2.62536	+	36.5665i	0.105183	+	1.46501i
$624$			25.0000i			1.00080i
$625$		0			0
$626$	39.0000	+	22.5167i	1.55875	+	0.899947i
$627$	8.06918	+	30.1146i	0.322252	+	1.20266i
$628$	22.2163	+	5.95284i	0.886527	+	0.237544i
$629$		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	$0.114931\pi$
$632$	18.4034	+	4.93117i	0.732046	+	0.196151i
$633$	4.91756	+	18.3526i	0.195456	+	0.729450i
$634$	15.5885	+	9.00000i	0.619097	+	0.357436i
$635$		0			0
$636$		0			0
$637$	−34.7547	−	4.13613i	−1.37703	−	0.163879i
$638$		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	$0.0905072\pi$
$642$	−3.10583	+	11.5911i	−0.122577	+	0.457465i
$643$	3.53553	−	3.53553i	0.139428	−	0.139428i	−0.633948	−	0.773376i	$-0.718567\pi$
$643$	3.53553	−	3.53553i	0.139428	−	0.139428i	0.773376	+	0.633948i	$0.218567\pi$
$644$	8.66025	−	3.00000i	0.341262	−	0.118217i
$645$		0			0
$646$		0			0
$647$	−17.3867	+	4.65874i	−0.683540	+	0.183154i	−0.583846	−	0.811864i	$-0.698453\pi$
$647$	−17.3867	+	4.65874i	−0.683540	+	0.183154i	−0.0996938	+	0.995018i	$0.531786\pi$
$648$	1.67303	−	0.448288i	0.0657229	−	0.0176104i
$649$	−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
$653$	−0.896575	+	3.34607i	−0.0350857	+	0.130942i	−0.981247	−	0.192753i	$-0.938258\pi$
$653$	−0.896575	+	3.34607i	−0.0350857	+	0.130942i	0.946162	+	0.323695i	$0.104925\pi$
$654$	−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	$0.304941\pi$
$659$			42.0000i			1.63609i	−0.575156	+	0.818044i	$0.695059\pi$
$660$		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	$0.948788\pi$
$662$	5.82774	+	21.7494i	0.226502	+	0.845315i
$663$		0			0
$664$	−20.7846			−0.806599
$665$		0			0
$666$	15.0000			0.581238
$667$		0			0
$668$	−3.10583	−	11.5911i	−0.120168	−	0.448474i
$669$	19.9186	+	11.5000i	0.770097	+	0.444616i
$670$		0			0
$671$			10.3923i			0.401190i
$672$	−13.7124	+	0.984508i	−0.528968	+	0.0379782i
$673$	6.12372	+	6.12372i	0.236052	+	0.236052i	0.815213	−	0.579161i	$-0.196620\pi$
$673$	6.12372	+	6.12372i	0.236052	+	0.236052i	−0.579161	+	0.815213i	$0.696620\pi$
$674$	−10.3923	+	6.00000i	−0.400297	+	0.231111i
$675$		0			0
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−10.8704	+	40.5689i	−0.417783	+	1.55919i	0.361411	+	0.932407i	$0.382295\pi$
$677$	−10.8704	+	40.5689i	−0.417783	+	1.55919i	−0.779194	+	0.626782i	$0.784372\pi$
$678$	−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
$682$	−34.7733	+	9.31749i	−1.33154	+	0.356785i
$683$	−23.4225	+	6.27603i	−0.896235	+	0.240146i	−0.677399	−	0.735616i	$-0.736893\pi$
$683$	−23.4225	+	6.27603i	−0.896235	+	0.240146i	−0.218837	+	0.975762i	$0.570226\pi$
$684$	−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
$688$	4.48288	−	16.7303i	0.170908	−	0.637838i
$689$		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
$693$	−6.93237	+	14.2808i	−0.263339	+	0.542484i
$694$			36.0000i			1.36654i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−11.5911	−	3.10583i	−0.438730	−	0.117557i
$699$	3.46410			0.131024
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−8.36516	−	2.24144i	−0.315723	−	0.0845977i
$703$	11.6469	+	43.4667i	0.439270	+	1.63938i
$704$	5.19615	+	3.00000i	0.195837	+	0.113067i
$705$		0			0
$706$		−	10.3923i		−	0.391120i
$707$	−5.13922	−	7.58871i	−0.193280	−	0.285403i
$708$	4.89898	+	4.89898i	0.184115	+	0.184115i
$709$	14.7224	−	8.50000i	0.552913	−	0.319224i	−0.197383	−	0.980326i	$-0.563244\pi$
$709$	14.7224	−	8.50000i	0.552913	−	0.319224i	0.750296	+	0.661102i	$0.229911\pi$
$710$		0			0
$711$	−5.50000	+	9.52628i	−0.206266	+	0.357263i
$712$	−6.21166	+	23.1822i	−0.232792	+	0.868790i
$713$	8.48528	−	8.48528i	0.317776	−	0.317776i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	40.1528	−	10.7589i	1.49849	−	0.401519i
$719$	−5.19615	−	9.00000i	−0.193784	−	0.335643i	0.752717	−	0.658344i	$-0.228743\pi$
$719$	−5.19615	−	9.00000i	−0.193784	−	0.335643i	−0.946501	+	0.322700i	$0.895409\pi$
$720$		0			0
$721$	−14.0000	−	12.1244i	−0.521387	−	0.451535i
$722$	9.79796	−	9.79796i	0.364642	−	0.364642i
$723$	−0.448288	+	1.67303i	−0.0166720	+	0.0622208i
$724$	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	$-0.364612\pi$
$727$	−13.4350	−	13.4350i	−0.498278	−	0.498278i	−0.910902	+	0.412624i	$0.864612\pi$
$728$	−20.6126	−	10.0060i	−0.763954	−	0.370847i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		0			0
$732$	−0.448288	−	1.67303i	−0.0165692	−	0.0618371i
$733$	18.3526	+	4.91756i	0.677868	+	0.181634i	0.581297	−	0.813692i	$-0.302546\pi$
$733$	18.3526	+	4.91756i	0.677868	+	0.181634i	0.0965718	+	0.995326i	$0.469212\pi$
$734$	27.7128			1.02290
$735$		0			0
$736$	18.0000			0.663489
$737$	50.1910	+	13.4486i	1.84881	+	0.495387i
$738$	4.65874	+	17.3867i	0.171491	+	0.640012i
$739$	−37.2391	−	21.5000i	−1.36986	−	0.790890i	−0.378952	−	0.925416i	$-0.623715\pi$
$739$	−37.2391	−	21.5000i	−1.36986	−	0.790890i	−0.990910	+	0.134526i	$0.957049\pi$
$740$		0			0
$741$		−	25.9808i		−	0.954427i
$742$		0			0
$743$	7.34847	+	7.34847i	0.269589	+	0.269589i	0.828935	−	0.559345i	$-0.188947\pi$
$743$	7.34847	+	7.34847i	0.269589	+	0.269589i	−0.559345	+	0.828935i	$0.688947\pi$
$744$	−5.19615	+	3.00000i	−0.190500	+	0.109985i
$745$		0			0
$746$	4.50000	−	7.79423i	0.164757	−	0.285367i
$747$	3.10583	−	11.5911i	0.113636	−	0.424097i
$748$		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
$753$	−16.7303	+	4.48288i	−0.609687	+	0.163365i
$754$		0			0
$755$		0			0
$756$	0.500000	−	2.59808i	0.0181848	−	0.0944911i
$757$	−6.12372	+	6.12372i	−0.222571	+	0.222571i	−0.809580	−	0.587009i	$-0.800305\pi$
$757$	−6.12372	+	6.12372i	−0.222571	+	0.222571i	0.587009	+	0.809580i	$0.300305\pi$
$758$	2.24144	−	8.36516i	0.0814127	−	0.303836i
$759$	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
$763$	−10.3849	−	15.3347i	−0.375960	−	0.555153i
$764$		−	6.00000i		−	0.217072i
$765$		0			0
$766$	−27.0000	−	15.5885i	−0.975550	−	0.563234i
$767$	8.96575	+	33.4607i	0.323735	+	1.20819i
$768$	−18.3526	−	4.91756i	−0.662242	−	0.177447i
$769$	6.92820			0.249837			0.124919	−	0.992167i	$-0.460133\pi$
$769$	6.92820			0.249837			0.124919	+	0.992167i	$0.460133\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	20.0764	+	5.37945i	0.722565	+	0.193611i
$773$	−9.31749	−	34.7733i	−0.335127	−	1.25071i	−0.903732	−	0.428099i	$-0.859183\pi$
$773$	−9.31749	−	34.7733i	−0.335127	−	1.25071i	0.568605	−	0.822611i	$-0.307483\pi$
$774$	5.19615	+	3.00000i	0.186772	+	0.107833i
$775$		0			0
$776$		−	8.66025i		−	0.310885i
$777$	−10.0060	+	20.6126i	−0.358964	+	0.739473i
$778$	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
$787$	−4.82963	+	1.29410i	−0.172158	+	0.0461295i	−0.343868	−	0.939018i	$-0.611737\pi$
$787$	−4.82963	+	1.29410i	−0.172158	+	0.0461295i	0.171710	+	0.985147i	$0.445071\pi$
$788$	−13.3843	+	3.58630i	−0.476795	+	0.127757i
$789$	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
$793$	2.24144	−	8.36516i	0.0795958	−	0.297056i
$794$	−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	$-0.216111\pi$
$797$	4.24264	+	4.24264i	0.150282	+	0.150282i	−0.627962	+	0.778244i	$0.716111\pi$
$798$	23.7506	−	1.70522i	0.840763	−	0.0603641i
$799$		0			0
$800$		0			0
$801$	−12.0000	−	6.92820i	−0.423999	−	0.244796i
$802$	2.68973	+	10.0382i	0.0949775	+	0.354461i
$803$	−40.5689	−	10.8704i	−1.43164	−	0.383608i
$804$	−8.66025			−0.305424
$805$		0			0
$806$	30.0000			1.05670
$807$	−3.34607	−	0.896575i	−0.117787	−	0.0315610i
$808$	−1.55291	−	5.79555i	−0.0546313	−	0.203887i
$809$	25.9808	+	15.0000i	0.913435	+	0.527372i	0.881535	−	0.472119i	$-0.156511\pi$
$809$	25.9808	+	15.0000i	0.913435	+	0.527372i	0.0319002	+	0.999491i	$0.489844\pi$
$810$		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
$817$	−4.65874	+	17.3867i	−0.162989	+	0.608282i
$818$	−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	$0.731630\pi$
$822$	−5.79555	+	1.55291i	−0.202143	+	0.0541641i
$823$	15.0573	−	4.03459i	0.524864	−	0.140637i	0.0133486	−	0.999911i	$-0.495751\pi$
$823$	15.0573	−	4.03459i	0.524864	−	0.140637i	0.511516	+	0.859274i	$0.329084\pi$
$824$	−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	−0.0223756	+	0.999750i	$0.507123\pi$
$827$	−29.3939	+	29.3939i	−1.02213	+	1.02213i	−0.999750	+	0.0223756i	$0.992877\pi$
$828$	−0.896575	+	3.34607i	−0.0311582	+	0.116284i
$829$	−19.9186	+	34.5000i	−0.691801	+	1.19823i	0.279446	+	0.960161i	$0.409849\pi$
$829$	−19.9186	+	34.5000i	−0.691801	+	1.19823i	−0.971247	+	0.238073i	$0.923484\pi$
$830$		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
$837$	−0.896575	−	3.34607i	−0.0309902	−	0.115657i
$838$	5.79555	+	1.55291i	0.200204	+	0.0536445i
$839$	45.0333			1.55472			0.777361	−	0.629054i	$-0.216558\pi$
$839$	45.0333			1.55472			0.777361	+	0.629054i	$0.216558\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$	28.4416	+	7.62089i	0.980161	+	0.262633i
$843$	−6.21166	−	23.1822i	−0.213941	−	0.798438i
$844$	16.4545	+	9.50000i	0.566387	+	0.327003i
$845$		0			0
$846$		0			0
$847$	−4.73672	−	65.9740i	−0.162756	−	2.26689i
$848$		0			0
$849$	−0.866025	+	0.500000i	−0.0297219	+	0.0171600i
$850$		0			0
$851$	15.0000	−	25.9808i	0.514193	−	0.890609i
$852$	−3.10583	+	11.5911i	−0.106404	+	0.397105i
$853$	−1.41421	+	1.41421i	−0.0484218	+	0.0484218i	−0.730903	−	0.682481i	$-0.760901\pi$
$853$	−1.41421	+	1.41421i	−0.0484218	+	0.0484218i	0.682481	+	0.730903i	$0.260901\pi$
$854$	7.79423	+	1.50000i	0.266713	+	0.0513289i
$855$		0			0
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	−17.3867	+	4.65874i	−0.593917	+	0.159140i	−0.543243	−	0.839576i	$-0.682804\pi$
$857$	−17.3867	+	4.65874i	−0.593917	+	0.159140i	−0.0506743	+	0.998715i	$0.516137\pi$
$858$	50.1910	−	13.4486i	1.71349	−	0.459129i
$859$	22.5167	+	39.0000i	0.768259	+	1.33066i	0.938506	+	0.345262i	$0.112210\pi$
$859$	22.5167	+	39.0000i	0.768259	+	1.33066i	−0.170248	+	0.985401i	$0.554457\pi$
$860$		0			0
$861$	−27.0000	−	5.19615i	−0.920158	−	0.177084i
$862$	−36.7423	+	36.7423i	−1.25145	+	1.25145i
$863$	−7.17260	+	26.7685i	−0.244158	+	0.911211i	0.729646	+	0.683825i	$0.239685\pi$
$863$	−7.17260	+	26.7685i	−0.244158	+	0.911211i	−0.973805	+	0.227386i	$0.926982\pi$
$864$	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
$868$	0.656339	+	9.14162i	0.0222776	+	0.310287i
$869$		−	66.0000i		−	2.23890i
$870$		0			0
$871$	−37.5000	−	21.6506i	−1.27064	−	0.733604i
$872$	−3.13801	−	11.7112i	−0.106267	−	0.396592i
$873$	4.82963	+	1.29410i	0.163458	+	0.0437985i
$874$	−31.1769			−1.05457
$875$		0			0
$876$	7.00000			0.236508
$877$	−25.0955	−	6.72432i	−0.847414	−	0.227064i	−0.191118	−	0.981567i	$-0.561211\pi$
$877$	−25.0955	−	6.72432i	−0.847414	−	0.227064i	−0.656297	+	0.754503i	$0.727878\pi$
$878$	8.54103	+	31.8756i	0.288246	+	1.07575i
$879$	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	$0.695658\pi$
$882$	9.71003	+	7.26054i	0.326954	+	0.244475i
$883$	−3.67423	−	3.67423i	−0.123648	−	0.123648i	0.642575	−	0.766223i	$-0.277866\pi$
$883$	−3.67423	−	3.67423i	−0.123648	−	0.123648i	−0.766223	+	0.642575i	$0.777866\pi$
$884$		0			0
$885$		0			0
$886$	21.0000	−	36.3731i	0.705509	−	1.22198i
$887$	−4.65874	+	17.3867i	−0.156425	+	0.583787i	0.842554	+	0.538612i	$0.181051\pi$
$887$	−4.65874	+	17.3867i	−0.156425	+	0.583787i	−0.998979	+	0.0451749i	$0.985615\pi$
$888$	−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
$892$	22.2163	−	5.95284i	0.743857	−	0.199316i
$893$		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
$903$	−7.58871	+	5.13922i	−0.252536	+	0.171022i
$904$		−	30.0000i		−	0.997785i
$905$		0			0
$906$	25.5000	+	14.7224i	0.847181	+	0.489120i
$907$	1.34486	+	5.01910i	0.0446554	+	0.166656i	0.984653	−	0.174526i	$-0.0558393\pi$
$907$	1.34486	+	5.01910i	0.0446554	+	0.166656i	−0.939997	+	0.341182i	$0.889173\pi$
$908$	−23.1822	−	6.21166i	−0.769329	−	0.206141i
$909$	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	$0.147496\pi$
$912$	25.0955	+	6.72432i	0.830995	+	0.222664i
$913$	18.6350	+	69.5467i	0.616728	+	2.30166i
$914$	28.5788	+	16.5000i	0.945304	+	0.545771i
$915$		0			0
$916$		−	15.5885i		−	0.515057i
$917$	9.14162	−	0.656339i	0.301883	−	0.0216742i
$918$		0			0
$919$	27.7128	−	16.0000i	0.914161	−	0.527791i	0.0323936	−	0.999475i	$-0.489687\pi$
$919$	27.7128	−	16.0000i	0.914161	−	0.527791i	0.881768	+	0.471684i	$0.156354\pi$
$920$		0			0
$921$	−16.0000	+	27.7128i	−0.527218	+	0.913168i
$922$	−1.55291	+	5.79555i	−0.0511425	+	0.190866i
$923$	−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
$927$	6.76148	−	1.81173i	0.222076	−	0.0595051i
$928$		0			0
$929$	−12.1244	−	21.0000i	−0.397787	−	0.688988i	0.595665	−	0.803233i	$-0.296888\pi$
$929$	−12.1244	−	21.0000i	−0.397787	−	0.688988i	−0.993453	+	0.114245i	$0.963555\pi$
$930$		0			0
$931$	−13.5000	+	33.7750i	−0.442445	+	1.10693i
$932$	2.44949	−	2.44949i	0.0802357	−	0.0802357i
$933$	4.48288	−	16.7303i	0.146763	−	0.547726i
$934$	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	$-0.197772\pi$
$937$	7.07107	+	7.07107i	0.231002	+	0.231002i	−0.582109	+	0.813111i	$0.697772\pi$
$938$	17.3309	−	35.7021i	0.565875	−	1.16571i
$939$		−	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	$0.684649\pi$
$942$	−10.3106	−	38.4797i	−0.335938	−	1.25374i
$943$	34.7733	+	9.31749i	1.13238	+	0.303419i
$944$	−34.6410			−1.12747
$945$		0			0
$946$	−36.0000			−1.17046
$947$	50.1910	+	13.4486i	1.63099	+	0.437022i	0.954203	−	0.299159i	$-0.0967062\pi$
$947$	50.1910	+	13.4486i	1.63099	+	0.437022i	0.676784	+	0.736181i	$0.263373\pi$
$948$	2.84701	+	10.6252i	0.0924666	+	0.345090i
$949$	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	0.480346	−	0.877079i	$-0.340511\pi$
$953$	−12.2474	−	12.2474i	−0.396734	−	0.396734i	−0.877079	+	0.480346i	$0.840511\pi$
$954$		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
$962$	72.4444	−	19.4114i	2.33570	−	0.625850i
$963$	6.69213	−	1.79315i	0.215651	−	0.0577835i
$964$	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	−0.403134	−	0.915141i	$-0.632079\pi$
$967$	15.9217	−	15.9217i	0.512007	−	0.512007i	0.915141	+	0.403134i	$0.132079\pi$
$968$	11.2072	−	41.8258i	0.360213	−	1.34433i
$969$		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
$973$	−53.5928	−	26.0156i	−1.71811	−	0.834023i
$974$			42.0000i			1.34577i
$975$		0			0
$976$	7.50000	+	4.33013i	0.240069	+	0.138604i
$977$	−0.896575	−	3.34607i	−0.0286840	−	0.107050i	0.950100	−	0.311946i	$-0.100981\pi$
$977$	−0.896575	−	3.34607i	−0.0286840	−	0.107050i	−0.978784	+	0.204896i	$0.934314\pi$
$978$	−2.89778	−	0.776457i	−0.0926607	−	0.0248284i
$979$	83.1384			2.65712
$980$		0			0
$981$	7.00000			0.223493
$982$	30.1146	+	8.06918i	0.960995	+	0.257498i
$983$	−9.31749	−	34.7733i	−0.297182	−	1.10910i	−0.939469	−	0.342633i	$-0.888681\pi$
$983$	−9.31749	−	34.7733i	−0.297182	−	1.10910i	0.642288	−	0.766464i	$-0.277985\pi$
$984$	−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	$0.947534\pi$
$992$	−4.65874	+	17.3867i	−0.147915	+	0.552027i
$993$	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
$997$	33.8074	−	9.05867i	1.07069	−	0.286891i	0.319914	−	0.947447i	$-0.396346\pi$
$997$	33.8074	−	9.05867i	1.07069	−	0.286891i	0.750777	+	0.660556i	$0.229679\pi$
$998$	38.4797	−	10.3106i	1.21806	−	0.326377i
$999$	−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.493.1	yes	8
5.2	odd	4	inner	525.2.bc.b.157.2	yes	8
5.3	odd	4	inner	525.2.bc.b.157.1	yes	8
5.4	even	2	inner	525.2.bc.b.493.2	yes	8
7.5	odd	6	inner	525.2.bc.b.418.2	yes	8
35.12	even	12	inner	525.2.bc.b.82.1	✓	8
35.19	odd	6	inner	525.2.bc.b.418.1	yes	8
35.33	even	12	inner	525.2.bc.b.82.2	yes	8

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

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