LMFDB - Embedded newform 1710.2.q.a.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(179,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("1710.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.162447943996702457856.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} - 15x^{8} - 16x^{4} + 256 $ x^16 - x^12 - 15x^8 - 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.2
Root			$-0.140577 + 1.40721i$ of defining polynomial
Character	$\chi$	$=$	1710.449
Dual form			1710.2.q.a.179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.09077 - 0.792893i) q^{5} +2.01563i q^{7} +1.00000i q^{8} +(2.20711 - 0.358719i) q^{10} +6.31959i q^{11} +(2.12132 - 3.67423i) q^{13} +(-1.00781 - 1.74558i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.42526 + 2.46863i) q^{17} +(-3.50000 - 2.59808i) q^{19} +(-1.73205 + 1.41421i) q^{20} +(-3.15980 - 5.47293i) q^{22} +(2.29129 - 3.96863i) q^{23} +(3.74264 + 3.31552i) q^{25} +4.24264i q^{26} +(1.74558 + 1.00781i) q^{28} +(-3.67423 + 6.36396i) q^{29} +(0.866025 + 0.500000i) q^{32} +(-2.46863 - 1.42526i) q^{34} +(1.59818 - 4.21421i) q^{35} -3.49117 q^{37} +(4.33013 + 0.500000i) q^{38} +(0.792893 - 2.09077i) q^{40} +(-4.24818 - 7.35807i) q^{41} +(7.73381 - 4.46512i) q^{43} +(5.47293 + 3.15980i) q^{44} +4.58258i q^{46} +(-2.85052 + 4.93725i) q^{47} +2.93725 q^{49} +(-4.89898 - 1.00000i) q^{50} +(-2.12132 - 3.67423i) q^{52} +(-12.0700 - 6.96863i) q^{53} +(5.01076 - 13.2128i) q^{55} -2.01563 q^{56} -7.34847i q^{58} +(-1.22474 - 2.12132i) q^{59} +(-7.46863 + 12.9360i) q^{61} -1.00000 q^{64} +(-7.34847 + 6.00000i) q^{65} +(-2.12132 + 3.67423i) q^{67} +2.85052 q^{68} +(0.723044 + 4.44870i) q^{70} +(3.67423 + 6.36396i) q^{71} +(-1.36985 + 0.790881i) q^{73} +(3.02344 - 1.74558i) q^{74} +(-4.00000 + 1.73205i) q^{76} -12.7379 q^{77} +(-6.00000 + 3.46410i) q^{79} +(0.358719 + 2.20711i) q^{80} +(7.35807 + 4.24818i) q^{82} -10.3923 q^{83} +(-1.02254 - 6.29141i) q^{85} +(-4.46512 + 7.73381i) q^{86} -6.31959 q^{88} +(-6.69767 + 11.6007i) q^{89} +(7.40588 + 4.27579i) q^{91} +(-2.29129 - 3.96863i) q^{92} -5.70105i q^{94} +(5.25770 + 8.20711i) q^{95} +(-2.12132 - 3.67423i) q^{97} +(-2.54374 + 1.46863i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 24 q^{10} - 8 q^{16} - 56 q^{19} - 8 q^{25} + 24 q^{34} + 24 q^{40} - 80 q^{49} - 8 q^{55} - 56 q^{61} - 16 q^{64} - 24 q^{70} - 64 q^{76} - 96 q^{79} - 24 q^{85} - 72 q^{91}+O(q^{100}) $ 16 * q + 8 * q^4 + 24 * q^10 - 8 * q^16 - 56 * q^19 - 8 * q^25 + 24 * q^34 + 24 * q^40 - 80 * q^49 - 8 * q^55 - 56 * q^61 - 16 * q^64 - 24 * q^70 - 64 * q^76 - 96 * q^79 - 24 * q^85 - 72 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.09077	−	0.792893i	−0.935021	−	0.354593i
$5$	−2.09077	−	0.792893i	−0.935021	−	0.354593i
$6$		0			0
$7$			2.01563i			0.761835i	0.924609	+	0.380917i	$0.124392\pi$
$7$			2.01563i			0.761835i	−0.924609	+	0.380917i	$0.875608\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.20711	−	0.358719i	0.697948	−	0.113437i
$11$			6.31959i			1.90543i	0.303867	+	0.952714i	$0.401722\pi$
$11$			6.31959i			1.90543i	−0.303867	+	0.952714i	$0.598278\pi$
$12$		0			0
$13$	2.12132	−	3.67423i	0.588348	−	1.01905i	−0.406100	−	0.913828i	$-0.633112\pi$
$13$	2.12132	−	3.67423i	0.588348	−	1.01905i	0.994449	−	0.105221i	$-0.0335550\pi$
$14$	−1.00781	−	1.74558i	−0.269349	−	0.466527i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.42526	+	2.46863i	0.345677	+	0.598730i	0.985477	−	0.169812i	$-0.0543160\pi$
$17$	1.42526	+	2.46863i	0.345677	+	0.598730i	−0.639800	+	0.768542i	$0.720983\pi$
$18$		0			0
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$20$	−1.73205	+	1.41421i	−0.387298	+	0.316228i
$21$		0			0
$22$	−3.15980	−	5.47293i	−0.673671	−	1.16683i
$23$	2.29129	−	3.96863i	0.477767	−	0.827516i	−0.521909	−	0.853001i	$-0.674780\pi$
$23$	2.29129	−	3.96863i	0.477767	−	0.827516i	0.999675	+	0.0254855i	$0.00811315\pi$
$24$		0			0
$25$	3.74264	+	3.31552i	0.748528	+	0.663103i
$26$			4.24264i			0.832050i
$27$		0			0
$28$	1.74558	+	1.00781i	0.329884	+	0.190459i
$29$	−3.67423	+	6.36396i	−0.682288	+	1.18176i	0.291993	+	0.956421i	$0.405682\pi$
$29$	−3.67423	+	6.36396i	−0.682288	+	1.18176i	−0.974281	+	0.225337i	$0.927652\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	−2.46863	−	1.42526i	−0.423366	−	0.244430i
$35$	1.59818	−	4.21421i	0.270141	−	0.712331i
$36$		0			0
$37$	−3.49117			−0.573944			−0.286972	−	0.957939i	$-0.592649\pi$
$37$	−3.49117			−0.573944			−0.286972	+	0.957939i	$0.592649\pi$
$38$	4.33013	+	0.500000i	0.702439	+	0.0811107i
$39$		0			0
$40$	0.792893	−	2.09077i	0.125367	−	0.330580i
$41$	−4.24818	−	7.35807i	−0.663455	−	1.14914i	−0.979702	−	0.200460i	$-0.935756\pi$
$41$	−4.24818	−	7.35807i	−0.663455	−	1.14914i	0.316247	−	0.948677i	$-0.397577\pi$
$42$		0			0
$43$	7.73381	−	4.46512i	1.17939	−	0.680924i	0.223520	−	0.974699i	$-0.428245\pi$
$43$	7.73381	−	4.46512i	1.17939	−	0.680924i	0.955874	+	0.293776i	$0.0949119\pi$
$44$	5.47293	+	3.15980i	0.825075	+	0.476357i
$45$		0			0
$46$			4.58258i			0.675664i
$47$	−2.85052	+	4.93725i	−0.415792	+	0.720173i	−0.995511	−	0.0946437i	$-0.969829\pi$
$47$	−2.85052	+	4.93725i	−0.415792	+	0.720173i	0.579719	+	0.814816i	$0.303162\pi$
$48$		0			0
$49$	2.93725			0.419608
$50$	−4.89898	−	1.00000i	−0.692820	−	0.141421i
$51$		0			0
$52$	−2.12132	−	3.67423i	−0.294174	−	0.509525i
$53$	−12.0700	−	6.96863i	−1.65794	−	0.957215i	−0.973662	−	0.227997i	$-0.926782\pi$
$53$	−12.0700	−	6.96863i	−1.65794	−	0.957215i	−0.684282	−	0.729217i	$-0.739884\pi$
$54$		0			0
$55$	5.01076	−	13.2128i	0.675651	−	1.78162i
$56$	−2.01563			−0.269349
$57$		0			0
$58$		−	7.34847i		−	0.964901i
$59$	−1.22474	−	2.12132i	−0.159448	−	0.276172i	0.775222	−	0.631689i	$-0.217638\pi$
$59$	−1.22474	−	2.12132i	−0.159448	−	0.276172i	−0.934670	+	0.355517i	$0.884305\pi$
$60$		0			0
$61$	−7.46863	+	12.9360i	−0.956260	+	1.65629i	−0.224801	+	0.974405i	$0.572173\pi$
$61$	−7.46863	+	12.9360i	−0.956260	+	1.65629i	−0.731459	+	0.681886i	$0.761160\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−7.34847	+	6.00000i	−0.911465	+	0.744208i
$66$		0			0
$67$	−2.12132	+	3.67423i	−0.259161	+	0.448879i	−0.966017	−	0.258478i	$-0.916779\pi$
$67$	−2.12132	+	3.67423i	−0.259161	+	0.448879i	0.706857	+	0.707357i	$0.250113\pi$
$68$	2.85052			0.345677
$69$		0			0
$70$	0.723044	+	4.44870i	0.0864203	+	0.531721i
$71$	3.67423	+	6.36396i	0.436051	+	0.755263i	0.997381	−	0.0723293i	$-0.0230432\pi$
$71$	3.67423	+	6.36396i	0.436051	+	0.755263i	−0.561329	+	0.827592i	$0.689710\pi$
$72$		0			0
$73$	−1.36985	+	0.790881i	−0.160328	+	0.0925656i	−0.578017	−	0.816024i	$-0.696173\pi$
$73$	−1.36985	+	0.790881i	−0.160328	+	0.0925656i	0.417689	+	0.908590i	$0.362840\pi$
$74$	3.02344	−	1.74558i	0.351468	−	0.202920i
$75$		0			0
$76$	−4.00000	+	1.73205i	−0.458831	+	0.198680i
$77$	−12.7379			−1.45162
$78$		0			0
$79$	−6.00000	+	3.46410i	−0.675053	+	0.389742i	−0.797988	−	0.602673i	$-0.794102\pi$
$79$	−6.00000	+	3.46410i	−0.675053	+	0.389742i	0.122936	+	0.992415i	$0.460769\pi$
$80$	0.358719	+	2.20711i	0.0401061	+	0.246762i
$81$		0			0
$82$	7.35807	+	4.24818i	0.812563	+	0.469133i
$83$	−10.3923			−1.14070			−0.570352	−	0.821401i	$-0.693193\pi$
$83$	−10.3923			−1.14070			−0.570352	+	0.821401i	$0.693193\pi$
$84$		0			0
$85$	−1.02254	−	6.29141i	−0.110910	−	0.682400i
$86$	−4.46512	+	7.73381i	−0.481486	+	0.833958i
$87$		0			0
$88$	−6.31959			−0.673671
$89$	−6.69767	+	11.6007i	−0.709952	+	1.22967i	0.254923	+	0.966961i	$0.417950\pi$
$89$	−6.69767	+	11.6007i	−0.709952	+	1.22967i	−0.964874	+	0.262711i	$0.915383\pi$
$90$		0			0
$91$	7.40588	+	4.27579i	0.776347	+	0.448224i
$92$	−2.29129	−	3.96863i	−0.238883	−	0.413758i
$93$		0			0
$94$		−	5.70105i		−	0.588018i
$95$	5.25770	+	8.20711i	0.539429	+	0.842031i
$96$		0			0
$97$	−2.12132	−	3.67423i	−0.215387	−	0.373062i	0.738005	−	0.674795i	$-0.235768\pi$
$97$	−2.12132	−	3.67423i	−0.215387	−	0.373062i	−0.953392	+	0.301733i	$0.902435\pi$
$98$	−2.54374	+	1.46863i	−0.256956	+	0.148354i
$99$		0			0
$100$	4.74264	−	1.58346i	0.474264	−	0.158346i
$101$	−2.44949	−	1.41421i	−0.243733	−	0.140720i	0.373158	−	0.927768i	$-0.378275\pi$
$101$	−2.44949	−	1.41421i	−0.243733	−	0.140720i	−0.616891	+	0.787048i	$0.711608\pi$
$102$		0			0
$103$	−11.9764			−1.18007			−0.590037	−	0.807376i	$-0.700887\pi$
$103$	−11.9764			−1.18007			−0.590037	+	0.807376i	$0.700887\pi$
$104$	3.67423	+	2.12132i	0.360288	+	0.208013i
$105$		0			0
$106$	13.9373			1.35371
$107$		−	10.9373i		−	1.05734i	−0.848826	−	0.528672i	$-0.822690\pi$
$107$		−	10.9373i		−	1.05734i	0.848826	−	0.528672i	$-0.177310\pi$
$108$		0			0
$109$	−7.40588	+	4.27579i	−0.709355	+	0.409546i	−0.810822	−	0.585293i	$-0.800980\pi$
$109$	−7.40588	+	4.27579i	−0.709355	+	0.409546i	0.101467	+	0.994839i	$0.467646\pi$
$110$	2.26696	+	13.9480i	0.216146	+	1.32989i
$111$		0			0
$112$	1.74558	−	1.00781i	0.164942	−	0.0952294i
$113$			10.9373i			1.02889i	0.857523	+	0.514445i	$0.172002\pi$
$113$			10.9373i			1.02889i	−0.857523	+	0.514445i	$0.827998\pi$
$114$		0			0
$115$	−7.93725	+	6.48074i	−0.740153	+	0.604332i
$116$	3.67423	+	6.36396i	0.341144	+	0.590879i
$117$		0			0
$118$	2.12132	+	1.22474i	0.195283	+	0.112747i
$119$	−4.97583	+	2.87280i	−0.456133	+	0.263349i
$120$		0			0
$121$	−28.9373			−2.63066
$122$		−	14.9373i		−	1.35236i
$123$		0			0
$124$		0			0
$125$	−5.19615	−	9.89949i	−0.464758	−	0.885438i
$126$		0			0
$127$	−5.98822	+	10.3719i	−0.531369	+	0.920358i	0.467961	+	0.883749i	$0.344989\pi$
$127$	−5.98822	+	10.3719i	−0.531369	+	0.920358i	−0.999330	+	0.0366087i	$0.988344\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	3.36396	−	8.87039i	0.295039	−	0.777984i
$131$	18.9451	−	10.9380i	1.65524	−	0.955655i	0.680377	−	0.732862i	$-0.261816\pi$
$131$	18.9451	−	10.9380i	1.65524	−	0.955655i	0.974866	−	0.222793i	$-0.0715173\pi$
$132$		0			0
$133$	5.23675	−	7.05469i	0.454084	−	0.611719i
$134$		−	4.24264i		−	0.366508i
$135$		0			0
$136$	−2.46863	+	1.42526i	−0.211683	+	0.122215i
$137$	8.04668	−	13.9373i	0.687474	−	1.19074i	−0.285178	−	0.958474i	$-0.592053\pi$
$137$	8.04668	−	13.9373i	0.687474	−	1.19074i	0.972652	−	0.232266i	$-0.0746138\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$	−2.85052	−	3.49117i	−0.240913	−	0.295057i
$141$		0			0
$142$	−6.36396	−	3.67423i	−0.534052	−	0.308335i
$143$	23.2197	+	13.4059i	1.94173	+	1.12106i
$144$		0			0
$145$	12.7279	−	10.3923i	1.05700	−	0.863034i
$146$	0.790881	−	1.36985i	0.0654537	−	0.113369i
$147$		0			0
$148$	−1.74558	+	3.02344i	−0.143486	+	0.248525i
$149$	−7.27162	+	4.19827i	−0.595714	+	0.343936i	−0.767354	−	0.641224i	$-0.778427\pi$
$149$	−7.27162	+	4.19827i	−0.595714	+	0.343936i	0.171639	+	0.985160i	$0.445094\pi$
$150$		0			0
$151$		−	8.55157i		−	0.695917i	−0.937510	−	0.347959i	$-0.886875\pi$
$151$		−	8.55157i		−	0.695917i	0.937510	−	0.347959i	$-0.113125\pi$
$152$	2.59808	−	3.50000i	0.210732	−	0.283887i
$153$		0			0
$154$	11.0314	−	6.36897i	0.888933	−	0.513226i
$155$		0			0
$156$		0			0
$157$	−1.12721	+	0.650796i	−0.0899613	+	0.0519392i	−0.544306	−	0.838887i	$-0.683207\pi$
$157$	−1.12721	+	0.650796i	−0.0899613	+	0.0519392i	0.454344	+	0.890826i	$0.349874\pi$
$158$	3.46410	−	6.00000i	0.275589	−	0.477334i
$159$		0			0
$160$	−1.41421	−	1.73205i	−0.111803	−	0.136931i
$161$	7.99927	+	4.61838i	0.630430	+	0.363979i
$162$		0			0
$163$			12.9615i			1.01522i	0.861586	+	0.507611i	$0.169471\pi$
$163$			12.9615i			1.01522i	−0.861586	+	0.507611i	$0.830529\pi$
$164$	−8.49637			−0.663455
$165$		0			0
$166$	9.00000	−	5.19615i	0.698535	−	0.403300i
$167$	−3.51844	−	2.03137i	−0.272265	−	0.157192i	0.357651	−	0.933855i	$-0.383578\pi$
$167$	−3.51844	−	2.03137i	−0.272265	−	0.157192i	−0.629917	+	0.776663i	$0.716911\pi$
$168$		0			0
$169$	−2.50000	−	4.33013i	−0.192308	−	0.333087i
$170$	4.03125	+	4.93725i	0.309183	+	0.378670i
$171$		0			0
$172$		−	8.93023i		−	0.680924i
$173$	−6.87386	+	3.96863i	−0.522610	+	0.301729i	−0.738002	−	0.674799i	$-0.764230\pi$
$173$	−6.87386	+	3.96863i	−0.522610	+	0.301729i	0.215392	+	0.976528i	$0.430897\pi$
$174$		0			0
$175$	−6.68284	+	7.54376i	−0.505175	+	0.570255i
$176$	5.47293	−	3.15980i	0.412537	−	0.238179i
$177$		0			0
$178$		−	13.3953i		−	1.00402i
$179$	−13.3953			−1.00122			−0.500608	−	0.865674i	$-0.666890\pi$
$179$	−13.3953			−1.00122			−0.500608	+	0.865674i	$0.666890\pi$
$180$		0			0
$181$	−10.4059	−	6.00784i	−0.773463	−	0.446559i	0.0606456	−	0.998159i	$-0.480684\pi$
$181$	−10.4059	−	6.00784i	−0.773463	−	0.446559i	−0.834109	+	0.551600i	$0.814017\pi$
$182$	−8.55157			−0.633885
$183$		0			0
$184$	3.96863	+	2.29129i	0.292571	+	0.168916i
$185$	7.29923	+	2.76812i	0.536650	+	0.203516i
$186$		0			0
$187$	−15.6007	+	9.00708i	−1.14084	+	0.658663i
$188$	2.85052	+	4.93725i	0.207896	+	0.360086i
$189$		0			0
$190$	−8.65685	−	4.47871i	−0.628034	−	0.324920i
$191$			12.6392i			0.914539i	0.889328	+	0.457270i	$0.151173\pi$
$191$			12.6392i			0.914539i	−0.889328	+	0.457270i	$0.848827\pi$
$192$		0			0
$193$	6.36396	+	11.0227i	0.458088	+	0.793432i	0.998860	−	0.0477376i	$-0.0152011\pi$
$193$	6.36396	+	11.0227i	0.458088	+	0.793432i	−0.540772	+	0.841169i	$0.681868\pi$
$194$	3.67423	+	2.12132i	0.263795	+	0.152302i
$195$		0			0
$196$	1.46863	−	2.54374i	0.104902	−	0.181695i
$197$	−15.5885			−1.11063			−0.555316	−	0.831640i	$-0.687403\pi$
$197$	−15.5885			−1.11063			−0.555316	+	0.831640i	$0.687403\pi$
$198$		0			0
$199$	10.4686	−	18.1322i	0.742101	−	1.28536i	−0.209436	−	0.977822i	$-0.567163\pi$
$199$	10.4686	−	18.1322i	0.742101	−	1.28536i	0.951537	−	0.307535i	$-0.0995040\pi$
$200$	−3.31552	+	3.74264i	−0.234442	+	0.264645i
$201$		0			0
$202$	2.82843			0.199007
$203$	−12.8274	−	7.40588i	−0.900304	−	0.519791i
$204$		0			0
$205$	3.04781	+	18.7524i	0.212868	+	1.30972i
$206$	10.3719	−	5.98822i	0.722645	−	0.417219i
$207$		0			0
$208$	−4.24264			−0.294174
$209$	16.4188	−	22.1186i	1.13571	−	1.52997i
$210$		0			0
$211$	11.9059	−	6.87386i	0.819635	−	0.473216i	−0.0306558	−	0.999530i	$-0.509760\pi$
$211$	11.9059	−	6.87386i	0.819635	−	0.473216i	0.850290	+	0.526314i	$0.176426\pi$
$212$	−12.0700	+	6.96863i	−0.828972	+	0.478607i
$213$		0			0
$214$	5.46863	+	9.47194i	0.373828	+	0.647488i
$215$	−19.7100	+	3.20345i	−1.34421	+	0.218473i
$216$		0			0
$217$		0			0
$218$	4.27579	−	7.40588i	0.289593	−	0.501590i
$219$		0			0
$220$	−8.93725	−	10.9459i	−0.602550	−	0.737969i
$221$	12.0938			0.813514
$222$		0			0
$223$	−10.2309	−	17.7204i	−0.685109	−	1.18664i	−0.973402	−	0.229102i	$-0.926421\pi$
$223$	−10.2309	−	17.7204i	−0.685109	−	1.18664i	0.288293	−	0.957542i	$-0.406912\pi$
$224$	−1.00781	+	1.74558i	−0.0673373	+	0.116632i
$225$		0			0
$226$	−5.46863	−	9.47194i	−0.363768	−	0.630064i
$227$		−	22.9373i		−	1.52240i	−0.648518	−	0.761200i	$-0.724611\pi$
$227$		−	22.9373i		−	1.52240i	0.648518	−	0.761200i	$-0.275389\pi$
$228$		0			0
$229$	7.87451			0.520362			0.260181	−	0.965560i	$-0.416218\pi$
$229$	7.87451			0.520362			0.260181	+	0.965560i	$0.416218\pi$
$230$	3.63349	−	9.58111i	0.239585	−	0.631760i
$231$		0			0
$232$	−6.36396	−	3.67423i	−0.417815	−	0.241225i
$233$	−7.43310	−	12.8745i	−0.486959	−	0.843437i	0.512929	−	0.858431i	$-0.328560\pi$
$233$	−7.43310	−	12.8745i	−0.486959	−	0.843437i	−0.999888	+	0.0149940i	$0.995227\pi$
$234$		0			0
$235$	9.87451	−	8.06250i	0.644142	−	0.525940i
$236$	−2.44949			−0.159448
$237$		0			0
$238$	2.87280	−	4.97583i	0.186216	−	0.322535i
$239$		−	4.33138i		−	0.280173i	−0.990139	−	0.140087i	$-0.955262\pi$
$239$		−	4.33138i		−	0.280173i	0.990139	−	0.140087i	$-0.0447381\pi$
$240$		0			0
$241$	6.00000	+	3.46410i	0.386494	+	0.223142i	0.680640	−	0.732618i	$-0.261702\pi$
$241$	6.00000	+	3.46410i	0.386494	+	0.223142i	−0.294146	+	0.955761i	$0.595035\pi$
$242$	25.0604	−	14.4686i	1.61094	−	0.930079i
$243$		0			0
$244$	7.46863	+	12.9360i	0.478130	+	0.828145i
$245$	−6.14112	−	2.32893i	−0.392342	−	0.148790i
$246$		0			0
$247$	−16.9706	+	7.34847i	−1.07981	+	0.467572i
$248$		0			0
$249$		0			0
$250$	9.44975	+	5.97514i	0.597655	+	0.377901i
$251$	6.12372	+	3.53553i	0.386526	+	0.223161i	0.680654	−	0.732605i	$-0.261696\pi$
$251$	6.12372	+	3.53553i	0.386526	+	0.223161i	−0.294128	+	0.955766i	$0.595029\pi$
$252$		0			0
$253$	25.0801	+	14.4800i	1.57677	+	0.910350i
$254$		−	11.9764i		−	0.751469i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−18.9439	−	10.9373i	−1.18169	−	0.682247i	−0.225283	−	0.974293i	$-0.572331\pi$
$257$	−18.9439	−	10.9373i	−1.18169	−	0.682247i	−0.956404	+	0.292046i	$0.905664\pi$
$258$		0			0
$259$		−	7.03688i		−	0.437251i
$260$	1.52192	+	9.36396i	0.0943853	+	0.580728i
$261$		0			0
$262$	−10.9380	+	18.9451i	−0.675750	+	1.17043i
$263$	10.3380	+	17.9059i	0.637466	+	1.10412i	0.985987	+	0.166823i	$0.0533508\pi$
$263$	10.3380	+	17.9059i	0.637466	+	1.10412i	−0.348521	+	0.937301i	$0.613316\pi$
$264$		0			0
$265$	19.7103	+	24.1400i	1.21079	+	1.48291i
$266$	−1.00781	+	8.72791i	−0.0617930	+	0.535143i
$267$		0			0
$268$	2.12132	+	3.67423i	0.129580	+	0.224440i
$269$	−1.22474	−	2.12132i	−0.0746740	−	0.129339i	0.826270	−	0.563274i	$-0.190458\pi$
$269$	−1.22474	−	2.12132i	−0.0746740	−	0.129339i	−0.900944	+	0.433934i	$0.857125\pi$
$270$		0			0
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	0.894799	−	0.446469i	$-0.147319\pi$
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	−0.834053	+	0.551684i	$0.813985\pi$
$272$	1.42526	−	2.46863i	0.0864192	−	0.149682i
$273$		0			0
$274$			16.0934i			0.972235i
$275$	−20.9527	+	23.6520i	−1.26350	+	1.42627i
$276$		0			0
$277$			11.3797i			0.683741i	0.939747	+	0.341871i	$0.111060\pi$
$277$			11.3797i			0.683741i	−0.939747	+	0.341871i	$0.888940\pi$
$278$		−	4.00000i		−	0.239904i
$279$		0			0
$280$	4.21421	+	1.59818i	0.251847	+	0.0955093i
$281$	0.650796	−	1.12721i	0.0388233	−	0.0672439i	−0.845961	−	0.533245i	$-0.820972\pi$
$281$	0.650796	−	1.12721i	0.0388233	−	0.0672439i	0.884784	+	0.466001i	$0.154306\pi$
$282$		0			0
$283$	−6.98233	+	4.03125i	−0.415057	+	0.239633i	−0.692960	−	0.720976i	$-0.743694\pi$
$283$	−6.98233	+	4.03125i	−0.415057	+	0.239633i	0.277904	+	0.960609i	$0.410360\pi$
$284$	7.34847			0.436051
$285$		0			0
$286$	−26.8118			−1.58541
$287$	14.8311	−	8.56275i	0.875453	−	0.505443i
$288$		0			0
$289$	4.43725	−	7.68555i	0.261015	−	0.452091i
$290$	−5.82655	+	15.3640i	−0.342147	+	0.902203i
$291$		0			0
$292$			1.58176i			0.0925656i
$293$			18.8745i			1.10266i	0.834287	+	0.551330i	$0.185880\pi$
$293$			18.8745i			1.10266i	−0.834287	+	0.551330i	$0.814120\pi$
$294$		0			0
$295$	0.878680	+	5.40629i	0.0511587	+	0.314766i
$296$		−	3.49117i		−	0.202920i
$297$		0			0
$298$	4.19827	−	7.27162i	0.243199	−	0.421234i
$299$	−9.72111	−	16.8375i	−0.562186	−	0.973735i
$300$		0			0
$301$	9.00000	+	15.5885i	0.518751	+	0.898504i
$302$	4.27579	+	7.40588i	0.246044	+	0.426161i
$303$		0			0
$304$	−0.500000	+	4.33013i	−0.0286770	+	0.248350i
$305$	25.8721	−	21.1245i	1.48143	−	1.20958i
$306$		0			0
$307$	−5.61249	−	9.72111i	−0.320321	−	0.554813i	0.660233	−	0.751061i	$-0.270458\pi$
$307$	−5.61249	−	9.72111i	−0.320321	−	0.554813i	−0.980554	+	0.196248i	$0.937124\pi$
$308$	−6.36897	+	11.0314i	−0.362906	+	0.628571i
$309$		0			0
$310$		0			0
$311$		−	14.1421i		−	0.801927i	−0.916094	−	0.400963i	$-0.868675\pi$
$311$		−	14.1421i		−	0.801927i	0.916094	−	0.400963i	$-0.131325\pi$
$312$		0			0
$313$	11.9764	+	6.91460i	0.676949	+	0.390837i	0.798704	−	0.601724i	$-0.205519\pi$
$313$	11.9764	+	6.91460i	0.676949	+	0.390837i	−0.121756	+	0.992560i	$0.538852\pi$
$314$	0.650796	−	1.12721i	0.0367266	−	0.0636123i
$315$		0			0
$316$			6.92820i			0.389742i
$317$	24.8974	+	14.3745i	1.39838	+	0.807353i	0.994223	−	0.107338i	$-0.0342328\pi$
$317$	24.8974	+	14.3745i	1.39838	+	0.807353i	0.404154	+	0.914691i	$0.367566\pi$
$318$		0			0
$319$	−40.2176	−	23.2197i	−2.25176	−	1.30005i
$320$	2.09077	+	0.792893i	0.116878	+	0.0443241i
$321$		0			0
$322$	−9.23676			−0.514744
$323$	1.42526	−	12.3431i	0.0793037	−	0.686790i
$324$		0			0
$325$	20.1213	−	6.71807i	1.11613	−	0.372651i
$326$	−6.48074	−	11.2250i	−0.358935	−	0.621694i
$327$		0			0
$328$	7.35807	−	4.24818i	0.406281	−	0.234567i
$329$	−9.95165	−	5.74559i	−0.548652	−	0.316765i
$330$		0			0
$331$			22.5167i			1.23763i	0.785538	+	0.618814i	$0.212386\pi$
$331$			22.5167i			1.23763i	−0.785538	+	0.618814i	$0.787614\pi$
$332$	−5.19615	+	9.00000i	−0.285176	+	0.493939i
$333$		0			0
$334$	4.06275			0.222304
$335$	7.34847	−	6.00000i	0.401490	−	0.327815i
$336$		0			0
$337$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$337$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$338$	4.33013	+	2.50000i	0.235528	+	0.135982i
$339$		0			0
$340$	−5.95979	−	2.26016i	−0.323215	−	0.122574i
$341$		0			0
$342$		0			0
$343$			20.0298i			1.08151i
$344$	4.46512	+	7.73381i	0.240743	+	0.416979i
$345$		0			0
$346$	3.96863	−	6.87386i	0.213355	−	0.369541i
$347$	−1.73205	−	3.00000i	−0.0929814	−	0.161048i	0.815783	−	0.578358i	$-0.196306\pi$
$347$	−1.73205	−	3.00000i	−0.0929814	−	0.161048i	−0.908764	+	0.417310i	$0.862973\pi$
$348$		0			0
$349$	−32.9373			−1.76309			−0.881545	−	0.472099i	$-0.843496\pi$
$349$	−32.9373			−1.76309			−0.881545	+	0.472099i	$0.843496\pi$
$350$	2.01563	−	9.87451i	0.107740	−	0.527815i
$351$		0			0
$352$	−3.15980	+	5.47293i	−0.168418	+	0.291708i
$353$	30.5633			1.62672			0.813361	−	0.581759i	$-0.197635\pi$
$353$	30.5633			1.62672			0.813361	+	0.581759i	$0.197635\pi$
$354$		0			0
$355$	−2.63604	−	16.2189i	−0.139906	−	0.860808i
$356$	6.69767	+	11.6007i	0.354976	+	0.614836i
$357$		0			0
$358$	11.6007	−	6.69767i	0.613117	−	0.353983i
$359$	6.12372	−	3.53553i	0.323198	−	0.186598i	−0.329619	−	0.944114i	$-0.606920\pi$
$359$	6.12372	−	3.53553i	0.323198	−	0.186598i	0.652817	+	0.757516i	$0.273587\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$	12.0157			0.631530
$363$		0			0
$364$	7.40588	−	4.27579i	0.388174	−	0.224112i
$365$	3.49112	−	0.567409i	0.182733	−	0.0296995i
$366$		0			0
$367$	−17.5889	−	10.1550i	−0.918135	−	0.530085i	−0.0350953	−	0.999384i	$-0.511173\pi$
$367$	−17.5889	−	10.1550i	−0.918135	−	0.530085i	−0.883040	+	0.469299i	$0.844507\pi$
$368$	−4.58258			−0.238883
$369$		0			0
$370$	−7.70538	+	1.25235i	−0.400583	+	0.0651065i
$371$	14.0461	−	24.3286i	0.729239	−	1.26308i
$372$		0			0
$373$	14.7161			0.761973			0.380986	−	0.924581i	$-0.375584\pi$
$373$	14.7161			0.761973			0.380986	+	0.924581i	$0.375584\pi$
$374$	9.00708	−	15.6007i	0.465745	−	0.806694i
$375$		0			0
$376$	−4.93725	−	2.85052i	−0.254619	−	0.147005i
$377$	15.5885	+	27.0000i	0.802846	+	1.39057i
$378$		0			0
$379$			20.5673i			1.05647i	0.849099	+	0.528234i	$0.177146\pi$
$379$			20.5673i			1.05647i	−0.849099	+	0.528234i	$0.822854\pi$
$380$	9.73641	−	0.449747i	0.499467	−	0.0230716i
$381$		0			0
$382$	−6.31959	−	10.9459i	−0.323338	−	0.560039i
$383$	3.35542	−	1.93725i	0.171454	−	0.0989891i	−0.411817	−	0.911266i	$-0.635106\pi$
$383$	3.35542	−	1.93725i	0.171454	−	0.0989891i	0.583271	+	0.812277i	$0.301772\pi$
$384$		0			0
$385$	26.6321	+	10.0998i	1.35730	+	0.514735i
$386$	−11.0227	−	6.36396i	−0.561041	−	0.323917i
$387$		0			0
$388$	−4.24264			−0.215387
$389$	13.4722	+	7.77817i	0.683067	+	0.394369i	0.801010	−	0.598651i	$-0.204296\pi$
$389$	13.4722	+	7.77817i	0.683067	+	0.394369i	−0.117942	+	0.993020i	$0.537630\pi$
$390$		0			0
$391$	13.0627			0.660611
$392$			2.93725i			0.148354i
$393$		0			0
$394$	13.5000	−	7.79423i	0.680120	−	0.392668i
$395$	15.2913	−	2.48528i	0.769388	−	0.125048i
$396$		0			0
$397$	−22.2073	+	12.8214i	−1.11455	+	0.643487i	−0.940005	−	0.341161i	$-0.889180\pi$
$397$	−22.2073	+	12.8214i	−1.11455	+	0.643487i	−0.174548	+	0.984649i	$0.555846\pi$
$398$			20.9373i			1.04949i
$399$		0			0
$400$	1.00000	−	4.89898i	0.0500000	−	0.244949i
$401$	−14.6201	−	25.3227i	−0.730092	−	1.26456i	−0.956843	−	0.290604i	$-0.906144\pi$
$401$	−14.6201	−	25.3227i	−0.730092	−	1.26456i	0.226751	−	0.973953i	$-0.427190\pi$
$402$		0			0
$403$		0			0
$404$	−2.44949	+	1.41421i	−0.121867	+	0.0703598i
$405$		0			0
$406$	14.8118			0.735095
$407$		−	22.0627i		−	1.09361i
$408$		0			0
$409$	25.5000	+	14.7224i	1.26089	+	0.727977i	0.973247	−	0.229759i	$-0.0737939\pi$
$409$	25.5000	+	14.7224i	1.26089	+	0.727977i	0.287646	+	0.957737i	$0.407127\pi$
$410$	−12.0157	−	14.7161i	−0.593412	−	0.726778i
$411$		0			0
$412$	−5.98822	+	10.3719i	−0.295019	+	0.510987i
$413$	4.27579	−	2.46863i	0.210398	−	0.121473i
$414$		0			0
$415$	21.7279	+	8.23999i	1.06658	+	0.404485i
$416$	3.67423	−	2.12132i	0.180144	−	0.104006i
$417$		0			0
$418$	−3.15980	+	27.3646i	−0.154551	+	1.33845i
$419$			11.8877i			0.580753i	0.956913	+	0.290376i	$0.0937805\pi$
$419$			11.8877i			0.580753i	−0.956913	+	0.290376i	$0.906220\pi$
$420$		0			0
$421$	−7.59412	+	4.38447i	−0.370115	+	0.213686i	−0.673509	−	0.739179i	$-0.735214\pi$
$421$	−7.59412	+	4.38447i	−0.370115	+	0.213686i	0.303394	+	0.952865i	$0.401880\pi$
$422$	−6.87386	+	11.9059i	−0.334614	+	0.579569i
$423$		0			0
$424$	6.96863	−	12.0700i	0.338426	−	0.586172i
$425$	−2.85052	+	13.9647i	−0.138271	+	0.677386i
$426$		0			0
$427$	−26.0742	−	15.0540i	−1.26182	−	0.728512i
$428$	−9.47194	−	5.46863i	−0.457843	−	0.264336i
$429$		0			0
$430$	15.4676	−	12.6293i	0.745915	−	0.609037i
$431$	−8.57321	+	14.8492i	−0.412957	+	0.715263i	−0.995212	−	0.0977438i	$-0.968837\pi$
$431$	−8.57321	+	14.8492i	−0.412957	+	0.715263i	0.582254	+	0.813007i	$0.302171\pi$
$432$		0			0
$433$	13.3463	−	23.1165i	0.641382	−	1.11091i	−0.343743	−	0.939064i	$-0.611695\pi$
$433$	13.3463	−	23.1165i	0.641382	−	1.11091i	0.985125	−	0.171842i	$-0.0549719\pi$
$434$		0			0
$435$		0			0
$436$			8.55157i			0.409546i
$437$	−18.3303	+	7.93725i	−0.876857	+	0.379690i
$438$		0			0
$439$	28.4059	−	16.4001i	1.35574	−	0.782736i	0.366692	−	0.930342i	$-0.380490\pi$
$439$	28.4059	−	16.4001i	1.35574	−	0.782736i	0.989046	+	0.147606i	$0.0471568\pi$
$440$	13.2128	+	5.01076i	0.629896	+	0.238879i
$441$		0			0
$442$	−10.4735	+	6.04688i	−0.498173	+	0.287621i
$443$	12.9360	−	22.4059i	0.614610	−	1.06454i	−0.375843	−	0.926683i	$-0.622647\pi$
$443$	12.9360	−	22.4059i	0.614610	−	1.06454i	0.990453	−	0.137852i	$-0.0440199\pi$
$444$		0			0
$445$	23.2014	−	18.9439i	1.09985	−	0.898026i
$446$	17.7204	+	10.2309i	0.839084	+	0.484445i
$447$		0			0
$448$		−	2.01563i		−	0.0952294i
$449$	−20.7438			−0.978961			−0.489481	−	0.872014i	$-0.662814\pi$
$449$	−20.7438			−0.978961			−0.489481	+	0.872014i	$0.662814\pi$
$450$		0			0
$451$	46.5000	−	26.8468i	2.18960	−	1.26417i
$452$	9.47194	+	5.46863i	0.445523	+	0.257223i
$453$		0			0
$454$	11.4686	+	19.8642i	0.538249	+	0.932275i
$455$	−12.0938	−	14.8118i	−0.566964	−	0.694386i
$456$		0			0
$457$			39.0381i			1.82613i	0.407817	+	0.913064i	$0.366290\pi$
$457$			39.0381i			1.82613i	−0.407817	+	0.913064i	$0.633710\pi$
$458$	−6.81952	+	3.93725i	−0.318655	+	0.183976i
$459$		0			0
$460$	1.64386	+	10.1142i	0.0766453	+	0.471579i
$461$	−8.49637	+	4.90538i	−0.395715	+	0.228466i	−0.684634	−	0.728887i	$-0.740038\pi$
$461$	−8.49637	+	4.90538i	−0.395715	+	0.228466i	0.288918	+	0.957354i	$0.406704\pi$
$462$		0			0
$463$			36.1548i			1.68026i	0.542389	+	0.840128i	$0.317520\pi$
$463$			36.1548i			1.68026i	−0.542389	+	0.840128i	$0.682480\pi$
$464$	7.34847			0.341144
$465$		0			0
$466$	12.8745	+	7.43310i	0.596400	+	0.344332i
$467$	23.6351			1.09370			0.546852	−	0.837229i	$-0.315826\pi$
$467$	23.6351			1.09370			0.546852	+	0.837229i	$0.315826\pi$
$468$		0			0
$469$	−7.40588	−	4.27579i	−0.341972	−	0.197438i
$470$	−4.52032	+	11.9196i	−0.208507	+	0.549809i
$471$		0			0
$472$	2.12132	−	1.22474i	0.0976417	−	0.0563735i
$473$	28.2177	+	48.8745i	1.29745	+	2.24725i
$474$		0			0
$475$	−4.48528	−	21.3280i	−0.205799	−	0.978594i
$476$			5.74559i			0.263349i
$477$		0			0
$478$	2.16569	+	3.75108i	0.0990563	+	0.171571i
$479$	30.6186	+	17.6777i	1.39900	+	0.807713i	0.994288	−	0.106731i	$-0.0340382\pi$
$479$	30.6186	+	17.6777i	1.39900	+	0.807713i	0.404713	+	0.914444i	$0.367372\pi$
$480$		0			0
$481$	−7.40588	+	12.8274i	−0.337679	+	0.584877i
$482$	−6.92820			−0.315571
$483$		0			0
$484$	−14.4686	+	25.0604i	−0.657665	+	1.13911i
$485$	1.52192	+	9.36396i	0.0691067	+	0.425196i
$486$		0			0
$487$	6.23086			0.282347			0.141174	−	0.989985i	$-0.454912\pi$
$487$	6.23086			0.282347			0.141174	+	0.989985i	$0.454912\pi$
$488$	−12.9360	−	7.46863i	−0.585587	−	0.338089i
$489$		0			0
$490$	6.48283	−	1.05365i	0.292865	−	0.0475991i
$491$	−4.17134	+	2.40832i	−0.188250	+	0.108686i	−0.591163	−	0.806552i	$-0.701331\pi$
$491$	−4.17134	+	2.40832i	−0.188250	+	0.108686i	0.402913	+	0.915238i	$0.367998\pi$
$492$		0			0
$493$	−20.9470			−0.943405
$494$	11.0227	−	14.8492i	0.495935	−	0.668099i
$495$		0			0
$496$		0			0
$497$	−12.8274	+	7.40588i	−0.575386	+	0.332199i
$498$		0			0
$499$	7.43725	+	12.8817i	0.332937	+	0.576664i	0.983086	−	0.183142i	$-0.0586269\pi$
$499$	7.43725	+	12.8817i	0.332937	+	0.576664i	−0.650149	+	0.759807i	$0.725294\pi$
$500$	−11.1713	−	0.449747i	−0.499595	−	0.0201133i
$501$		0			0
$502$	−7.07107			−0.315597
$503$	6.56708	−	11.3745i	0.292811	−	0.507164i	−0.681662	−	0.731667i	$-0.738743\pi$
$503$	6.56708	−	11.3745i	0.292811	−	0.507164i	0.974473	+	0.224503i	$0.0720759\pi$
$504$		0			0
$505$	4.00000	+	4.89898i	0.177998	+	0.218002i
$506$	−28.9600			−1.28743
$507$		0			0
$508$	5.98822	+	10.3719i	0.265684	+	0.460179i
$509$	−1.30159	+	2.25442i	−0.0576921	+	0.0999256i	−0.893429	−	0.449204i	$-0.851707\pi$
$509$	−1.30159	+	2.25442i	−0.0576921	+	0.0999256i	0.835737	+	0.549130i	$0.185041\pi$
$510$		0			0
$511$	−1.59412	−	2.76110i	−0.0705197	−	0.122144i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	21.8745			0.964843
$515$	25.0400	+	9.49604i	1.10339	+	0.418446i
$516$		0			0
$517$	−31.2014	−	18.0142i	−1.37224	−	0.792262i
$518$	3.51844	+	6.09412i	0.154591	+	0.267760i
$519$		0			0
$520$	−6.00000	−	7.34847i	−0.263117	−	0.322252i
$521$	24.3412			1.06641			0.533204	−	0.845987i	$-0.320988\pi$
$521$	24.3412			1.06641			0.533204	+	0.845987i	$0.320988\pi$
$522$		0			0
$523$	2.87280	−	4.97583i	0.125619	−	0.217578i	−0.796356	−	0.604828i	$-0.793242\pi$
$523$	2.87280	−	4.97583i	0.125619	−	0.217578i	0.921975	+	0.387250i	$0.126575\pi$
$524$		−	21.8759i		−	0.955655i
$525$		0			0
$526$	−17.9059	−	10.3380i	−0.780734	−	0.450757i
$527$		0			0
$528$		0			0
$529$	1.00000	+	1.73205i	0.0434783	+	0.0753066i
$530$	−29.1396	−	11.0508i	−1.26574	−	0.480014i
$531$		0			0
$532$	−3.49117	−	8.06250i	−0.151361	−	0.349554i
$533$	−36.0470			−1.56137
$534$		0			0
$535$	−8.67207	+	22.8673i	−0.374926	+	0.988639i
$536$	−3.67423	−	2.12132i	−0.158703	−	0.0916271i
$537$		0			0
$538$	2.12132	+	1.22474i	0.0914566	+	0.0528025i
$539$			18.5622i			0.799533i
$540$		0			0
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	−0.843728	−	0.536771i	$-0.819644\pi$
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	0.886721	+	0.462304i	$0.152977\pi$
$542$	−1.73205	−	1.00000i	−0.0743980	−	0.0429537i
$543$		0			0
$544$			2.85052i			0.122215i
$545$	18.8742	−	3.06762i	0.808484	−	0.131402i
$546$		0			0
$547$	11.9764	−	20.7438i	0.512076	−	0.886941i	−0.487826	−	0.872941i	$-0.662210\pi$
$547$	11.9764	−	20.7438i	0.512076	−	0.886941i	0.999902	−	0.0140006i	$-0.00445669\pi$
$548$	−8.04668	−	13.9373i	−0.343737	−	0.595370i
$549$		0			0
$550$	6.31959	−	30.9596i	0.269468	−	1.32012i
$551$	29.3939	−	12.7279i	1.25222	−	0.542228i
$552$		0			0
$553$	−6.98233	−	12.0938i	−0.296919	−	0.514279i
$554$	−5.68986	−	9.85513i	−0.241739	−	0.418704i
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	7.99234	−	13.8431i	0.338646	−	0.586552i	−0.645532	−	0.763733i	$-0.723364\pi$
$557$	7.99234	−	13.8431i	0.338646	−	0.586552i	0.984178	+	0.177181i	$0.0566977\pi$
$558$		0			0
$559$		−	37.8878i		−	1.60248i
$560$	−4.44870	+	0.723044i	−0.187992	+	0.0305542i
$561$		0			0
$562$			1.30159i			0.0549044i
$563$			3.87451i			0.163291i	0.996661	+	0.0816455i	$0.0260175\pi$
$563$			3.87451i			0.163291i	−0.996661	+	0.0816455i	$0.973982\pi$
$564$		0			0
$565$	8.67207	−	22.8673i	0.364837	−	0.962034i
$566$	4.03125	−	6.98233i	0.169446	−	0.293489i
$567$		0			0
$568$	−6.36396	+	3.67423i	−0.267026	+	0.154167i
$569$	−37.8902			−1.58844			−0.794221	−	0.607629i	$-0.792121\pi$
$569$	−37.8902			−1.58844			−0.794221	+	0.607629i	$0.792121\pi$
$570$		0			0
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$	23.2197	−	13.4059i	0.970863	−	0.560528i
$573$		0			0
$574$	−8.56275	+	14.8311i	−0.357402	+	0.619039i
$575$	21.7335	−	7.25635i	0.906350	−	0.302611i
$576$		0			0
$577$		−	0.714033i		−	0.0297256i	−0.999890	−	0.0148628i	$-0.995269\pi$
$577$		−	0.714033i		−	0.0297256i	0.999890	−	0.0148628i	$-0.00473115\pi$
$578$			8.87451i			0.369131i
$579$		0			0
$580$	−2.63604	−	16.2189i	−0.109456	−	0.673451i
$581$		−	20.9470i		−	0.869028i
$582$		0			0
$583$	44.0389	−	76.2776i	1.82390	−	3.15909i
$584$	−0.790881	−	1.36985i	−0.0327269	−	0.0566846i
$585$		0			0
$586$	−9.43725	−	16.3458i	−0.389849	−	0.675239i
$587$	−15.4798	−	26.8118i	−0.638919	−	1.10664i	−0.985670	−	0.168683i	$-0.946049\pi$
$587$	−15.4798	−	26.8118i	−0.638919	−	1.10664i	0.346752	−	0.937957i	$-0.387285\pi$
$588$		0			0
$589$		0			0
$590$	−3.46410	−	4.24264i	−0.142615	−	0.174667i
$591$		0			0
$592$	1.74558	+	3.02344i	0.0717430	+	0.124263i
$593$	−18.6371	+	32.2804i	−0.765334	+	1.32560i	0.174736	+	0.984615i	$0.444093\pi$
$593$	−18.6371	+	32.2804i	−0.765334	+	1.32560i	−0.940070	+	0.340981i	$0.889241\pi$
$594$		0			0
$595$	12.6811	−	2.06106i	0.519876	−	0.0844950i
$596$			8.39655i			0.343936i
$597$		0			0
$598$	16.8375	+	9.72111i	0.688535	+	0.397526i
$599$	−13.4722	+	23.3345i	−0.550459	+	0.953423i	0.447782	+	0.894143i	$0.352214\pi$
$599$	−13.4722	+	23.3345i	−0.550459	+	0.953423i	−0.998241	+	0.0592803i	$0.981119\pi$
$600$		0			0
$601$			7.03688i			0.287040i	0.989647	+	0.143520i	$0.0458422\pi$
$601$			7.03688i			0.287040i	−0.989647	+	0.143520i	$0.954158\pi$
$602$	−15.5885	−	9.00000i	−0.635338	−	0.366813i
$603$		0			0
$604$	−7.40588	−	4.27579i	−0.301341	−	0.173979i
$605$	60.5012	+	22.9442i	2.45972	+	0.932812i
$606$		0			0
$607$	−2.25442			−0.0915043			−0.0457521	−	0.998953i	$-0.514568\pi$
$607$	−2.25442			−0.0915043			−0.0457521	+	0.998953i	$0.514568\pi$
$608$	−1.73205	−	4.00000i	−0.0702439	−	0.162221i
$609$		0			0
$610$	−11.8436	+	31.2304i	−0.479535	+	1.26448i
$611$	12.0938	+	20.9470i	0.489261	+	0.847425i
$612$		0			0
$613$	6.12133	−	3.53415i	0.247238	−	0.142743i	−0.371261	−	0.928529i	$-0.621074\pi$
$613$	6.12133	−	3.53415i	0.247238	−	0.142743i	0.618499	+	0.785786i	$0.287741\pi$
$614$	9.72111	+	5.61249i	0.392312	+	0.226502i
$615$		0			0
$616$		−	12.7379i		−	0.513226i
$617$	17.8254	−	30.8745i	0.717624	−	1.24296i	−0.244315	−	0.969696i	$-0.578563\pi$
$617$	17.8254	−	30.8745i	0.717624	−	1.24296i	0.961939	−	0.273265i	$-0.0881036\pi$
$618$		0			0
$619$	−25.8118			−1.03746			−0.518731	−	0.854937i	$-0.673595\pi$
$619$	−25.8118			−1.03746			−0.518731	+	0.854937i	$0.673595\pi$
$620$		0			0
$621$		0			0
$622$	7.07107	+	12.2474i	0.283524	+	0.491078i
$623$	−23.3827	−	13.5000i	−0.936808	−	0.540866i
$624$		0			0
$625$	3.01472	+	24.8176i	0.120589	+	0.992703i
$626$	−13.8292			−0.552726
$627$		0			0
$628$			1.30159i			0.0519392i
$629$	−4.97583	−	8.61839i	−0.198399	−	0.343638i
$630$		0			0
$631$	13.5314	−	23.4370i	0.538675	−	0.933013i	−0.460300	−	0.887763i	$-0.652258\pi$
$631$	13.5314	−	23.4370i	0.538675	−	0.933013i	0.998976	−	0.0452500i	$-0.0144084\pi$
$632$	−3.46410	−	6.00000i	−0.137795	−	0.238667i
$633$		0			0
$634$	−28.7490			−1.14177
$635$	20.7438	−	16.9373i	0.823193	−	0.672134i
$636$		0			0
$637$	6.23086	−	10.7922i	0.246876	−	0.427601i
$638$	46.4393			1.83855
$639$		0			0
$640$	−2.20711	+	0.358719i	−0.0872436	+	0.0141796i
$641$	12.1706	+	21.0801i	0.480710	+	0.832614i	0.999755	−	0.0221329i	$-0.00704571\pi$
$641$	12.1706	+	21.0801i	0.480710	+	0.832614i	−0.519045	+	0.854747i	$0.673712\pi$
$642$		0			0
$643$	−14.0978	+	8.13935i	−0.555962	+	0.320985i	−0.751523	−	0.659707i	$-0.770680\pi$
$643$	−14.0978	+	8.13935i	−0.555962	+	0.320985i	0.195561	+	0.980691i	$0.437347\pi$
$644$	7.99927	−	4.61838i	0.315215	−	0.181990i
$645$		0			0
$646$	4.93725	+	11.4021i	0.194254	+	0.448610i
$647$	−17.8254			−0.700789			−0.350394	−	0.936602i	$-0.613952\pi$
$647$	−17.8254			−0.700789			−0.350394	+	0.936602i	$0.613952\pi$
$648$		0			0
$649$	13.4059	−	7.73989i	0.526227	−	0.303817i
$650$	−14.0665	+	15.8787i	−0.551735	+	0.622813i
$651$		0			0
$652$	11.2250	+	6.48074i	0.439604	+	0.253805i
$653$	−11.1146			−0.434946			−0.217473	−	0.976066i	$-0.569781\pi$
$653$	−11.1146			−0.434946			−0.217473	+	0.976066i	$0.569781\pi$
$654$		0			0
$655$	−48.2825	+	7.84733i	−1.88655	+	0.306620i
$656$	−4.24818	+	7.35807i	−0.165864	+	0.287284i
$657$		0			0
$658$	11.4912			0.447973
$659$	−7.99927	+	13.8551i	−0.311607	+	0.539719i	−0.978710	−	0.205246i	$-0.934201\pi$
$659$	−7.99927	+	13.8551i	−0.311607	+	0.539719i	0.667103	+	0.744965i	$0.267534\pi$
$660$		0			0
$661$	14.8118	+	8.55157i	0.576111	+	0.332618i	0.759586	−	0.650407i	$-0.225401\pi$
$661$	14.8118	+	8.55157i	0.576111	+	0.332618i	−0.183475	+	0.983024i	$0.558735\pi$
$662$	−11.2583	−	19.5000i	−0.437567	−	0.757889i
$663$		0			0
$664$		−	10.3923i		−	0.403300i
$665$	−16.5425	+	10.5976i	−0.641489	+	0.410955i
$666$		0			0
$667$	16.8375	+	29.1633i	0.651949	+	1.12921i
$668$	−3.51844	+	2.03137i	−0.136133	+	0.0785962i
$669$		0			0
$670$	−3.36396	+	8.87039i	−0.129961	+	0.342693i
$671$	−81.7505	−	47.1987i	−3.15594	−	1.82208i
$672$		0			0
$673$	−23.9529			−0.923316			−0.461658	−	0.887058i	$-0.652745\pi$
$673$	−23.9529			−0.923316			−0.461658	+	0.887058i	$0.652745\pi$
$674$		0			0
$675$		0			0
$676$	−5.00000			−0.192308
$677$		−	18.8745i		−	0.725406i	−0.931905	−	0.362703i	$-0.881854\pi$
$677$		−	18.8745i		−	0.725406i	0.931905	−	0.362703i	$-0.118146\pi$
$678$		0			0
$679$	7.40588	−	4.27579i	0.284212	−	0.164090i
$680$	6.29141	−	1.02254i	0.241265	−	0.0392126i
$681$		0			0
$682$		0			0
$683$			48.6863i			1.86293i	0.363833	+	0.931464i	$0.381468\pi$
$683$			48.6863i			1.86293i	−0.363833	+	0.931464i	$0.618532\pi$
$684$		0			0
$685$	−27.8745	+	22.7594i	−1.06503	+	0.869594i
$686$	−10.0149	−	17.3463i	−0.382370	−	0.662285i
$687$		0			0
$688$	−7.73381	−	4.46512i	−0.294849	−	0.170231i
$689$	−51.2087	+	29.5654i	−1.95090	+	1.12635i
$690$		0			0
$691$	−17.0000			−0.646710			−0.323355	−	0.946278i	$-0.604811\pi$
$691$	−17.0000			−0.646710			−0.323355	+	0.946278i	$0.604811\pi$
$692$			7.93725i			0.301729i
$693$		0			0
$694$	3.00000	+	1.73205i	0.113878	+	0.0657477i
$695$	6.92820	−	5.65685i	0.262802	−	0.214577i
$696$		0			0
$697$	12.1096	−	20.9744i	0.458682	−	0.794460i
$698$	28.5245	−	16.4686i	1.07967	−	0.623347i
$699$		0			0
$700$	3.19167	+	9.55939i	0.120634	+	0.361311i
$701$	−37.7365	+	21.7872i	−1.42529	+	0.822891i	−0.996744	−	0.0806288i	$-0.974307\pi$
$701$	−37.7365	+	21.7872i	−1.42529	+	0.822891i	−0.428546	+	0.903520i	$0.640974\pi$
$702$		0			0
$703$	12.2191	+	9.07031i	0.460851	+	0.342093i
$704$		−	6.31959i		−	0.238179i
$705$		0			0
$706$	−26.4686	+	15.2817i	−0.996160	+	0.575133i
$707$	2.85052	−	4.93725i	0.107205	−	0.185685i
$708$		0			0
$709$	3.40588	−	5.89916i	0.127911	−	0.221548i	−0.794956	−	0.606667i	$-0.792506\pi$
$709$	3.40588	−	5.89916i	0.127911	−	0.221548i	0.922867	+	0.385119i	$0.125840\pi$
$710$	10.3923	+	12.7279i	0.390016	+	0.477670i
$711$		0			0
$712$	−11.6007	−	6.69767i	−0.434755	−	0.251006i
$713$		0			0
$714$		0			0
$715$	−37.9176	−	46.4393i	−1.41804	−	1.73673i
$716$	−6.69767	+	11.6007i	−0.250304	+	0.433539i
$717$		0			0
$718$	−3.53553	+	6.12372i	−0.131945	+	0.228535i
$719$	27.9386	−	16.1304i	1.04193	−	0.601561i	0.121553	−	0.992585i	$-0.461213\pi$
$719$	27.9386	−	16.1304i	1.04193	−	0.601561i	0.920380	+	0.391024i	$0.127879\pi$
$720$		0			0
$721$		−	24.1400i		−	0.899022i
$722$	−13.8564	−	13.0000i	−0.515682	−	0.483810i
$723$		0			0
$724$	−10.4059	+	6.00784i	−0.386732	+	0.223280i
$725$	−34.8511	+	11.6360i	−1.29434	+	0.432152i
$726$		0			0
$727$	−12.5948	+	7.27162i	−0.467116	+	0.269690i	−0.715032	−	0.699092i	$-0.753588\pi$
$727$	−12.5948	+	7.27162i	−0.467116	+	0.269690i	0.247916	+	0.968782i	$0.420254\pi$
$728$	−4.27579	+	7.40588i	−0.158471	+	0.274480i
$729$		0			0
$730$	−2.73969	+	2.23695i	−0.101401	+	0.0827932i
$731$	22.0454	+	12.7279i	0.815379	+	0.470759i
$732$		0			0
$733$		−	7.78233i		−	0.287447i	−0.989618	−	0.143724i	$-0.954092\pi$
$733$		−	7.78233i		−	0.287447i	0.989618	−	0.143724i	$-0.0459076\pi$
$734$	20.3100			0.749654
$735$		0			0
$736$	3.96863	−	2.29129i	0.146286	−	0.0844580i
$737$	−23.2197	−	13.4059i	−0.855307	−	0.493812i
$738$		0			0
$739$	21.3118	+	36.9131i	0.783966	+	1.35787i	0.929615	+	0.368532i	$0.120140\pi$
$739$	21.3118	+	36.9131i	0.783966	+	1.35787i	−0.145649	+	0.989336i	$0.546527\pi$
$740$	6.04688	−	4.93725i	0.222288	−	0.181497i
$741$		0			0
$742$			28.0923i			1.03130i
$743$	26.7381	−	15.4373i	0.980926	−	0.566338i	0.0783765	−	0.996924i	$-0.475026\pi$
$743$	26.7381	−	15.4373i	0.980926	−	0.566338i	0.902550	+	0.430586i	$0.141693\pi$
$744$		0			0
$745$	18.5321	−	3.01200i	0.678963	−	0.110351i
$746$	−12.7445	+	7.35807i	−0.466611	+	0.269398i
$747$		0			0
$748$			18.0142i			0.658663i
$749$	22.0454			0.805522
$750$		0			0
$751$	−21.0000	−	12.1244i	−0.766301	−	0.442424i	0.0652526	−	0.997869i	$-0.479215\pi$
$751$	−21.0000	−	12.1244i	−0.766301	−	0.442424i	−0.831553	+	0.555445i	$0.812548\pi$
$752$	5.70105			0.207896
$753$		0			0
$754$	−27.0000	−	15.5885i	−0.983282	−	0.567698i
$755$	−6.78049	+	17.8794i	−0.246767	+	0.650697i
$756$		0			0
$757$	13.7220	−	7.92242i	0.498736	−	0.287945i	−0.229456	−	0.973319i	$-0.573695\pi$
$757$	13.7220	−	7.92242i	0.498736	−	0.287945i	0.728191	+	0.685374i	$0.240361\pi$
$758$	−10.2836	−	17.8118i	−0.373518	−	0.646952i
$759$		0			0
$760$	−8.20711	+	5.25770i	−0.297703	+	0.190717i
$761$			21.7872i			0.789786i	0.918727	+	0.394893i	$0.129218\pi$
$761$			21.7872i			0.789786i	−0.918727	+	0.394893i	$0.870782\pi$
$762$		0			0
$763$	−8.61839	−	14.9275i	−0.312007	−	0.540411i
$764$	10.9459	+	6.31959i	0.396007	+	0.228635i
$765$		0			0
$766$	−1.93725	+	3.35542i	−0.0699958	+	0.121236i
$767$	−10.3923			−0.375244
$768$		0			0
$769$	−15.9373	+	27.6041i	−0.574712	+	0.995431i	0.421361	+	0.906893i	$0.361553\pi$
$769$	−15.9373	+	27.6041i	−0.574712	+	0.995431i	−0.996073	+	0.0885374i	$0.971781\pi$
$770$	−28.1140	+	4.56934i	−1.01316	+	0.164668i
$771$		0			0
$772$	12.7279			0.458088
$773$	−31.9343	−	18.4373i	−1.14860	−	0.663142i	−0.200051	−	0.979786i	$-0.564111\pi$
$773$	−31.9343	−	18.4373i	−1.14860	−	0.663142i	−0.948545	+	0.316644i	$0.897444\pi$
$774$		0			0
$775$		0			0
$776$	3.67423	−	2.12132i	0.131897	−	0.0761510i
$777$		0			0
$778$	−15.5563			−0.557722
$779$	−4.24818	+	36.7903i	−0.152207	+	1.31815i
$780$		0			0
$781$	−40.2176	+	23.2197i	−1.43910	+	0.830865i
$782$	−11.3127	+	6.53137i	−0.404540	+	0.233561i
$783$		0			0
$784$	−1.46863	−	2.54374i	−0.0524510	−	0.0908477i
$785$	2.87275	−	0.466907i	0.102533	−	0.0166646i
$786$		0			0
$787$	−14.2309			−0.507276			−0.253638	−	0.967299i	$-0.581627\pi$
$787$	−14.2309			−0.507276			−0.253638	+	0.967299i	$0.581627\pi$
$788$	−7.79423	+	13.5000i	−0.277658	+	0.480918i
$789$		0			0
$790$	−12.0000	+	9.79796i	−0.426941	+	0.348596i
$791$	−22.0454			−0.783844
$792$		0			0
$793$	31.6867	+	54.8830i	1.12523	+	1.94895i
$794$	12.8214	−	22.2073i	0.455014	−	0.788108i
$795$		0			0
$796$	−10.4686	−	18.1322i	−0.371051	−	0.642679i
$797$		−	25.9373i		−	0.918745i	−0.888244	−	0.459372i	$-0.848074\pi$
$797$		−	25.9373i		−	0.918745i	0.888244	−	0.459372i	$-0.151926\pi$
$798$		0			0
$799$	−16.2510			−0.574918
$800$	1.58346	+	4.74264i	0.0559839	+	0.167678i
$801$		0			0
$802$	25.3227	+	14.6201i	0.894177	+	0.516253i
$803$	−4.99804	−	8.65687i	−0.176377	−	0.305494i
$804$		0			0
$805$	−13.0627	−	15.9985i	−0.460401	−	0.563874i
$806$		0			0
$807$		0			0
$808$	1.41421	−	2.44949i	0.0497519	−	0.0861727i
$809$			47.8171i			1.68116i	0.541689	+	0.840579i	$0.317785\pi$
$809$			47.8171i			1.68116i	−0.541689	+	0.840579i	$0.682215\pi$
$810$		0			0
$811$	11.9059	+	6.87386i	0.418072	+	0.241374i	0.694252	−	0.719732i	$-0.255735\pi$
$811$	11.9059	+	6.87386i	0.418072	+	0.241374i	−0.276180	+	0.961106i	$0.589069\pi$
$812$	−12.8274	+	7.40588i	−0.450152	+	0.259895i
$813$		0			0
$814$	11.0314	+	19.1069i	0.386649	+	0.669696i
$815$	10.2771	−	27.0995i	0.359990	−	0.949253i
$816$		0			0
$817$	−38.6690	−	4.46512i	−1.35286	−	0.156215i
$818$	−29.4449			−1.02952
$819$		0			0
$820$	17.7639	+	6.73671i	0.620344	+	0.235256i
$821$	−3.59739	−	2.07695i	−0.125550	−	0.0724861i	0.435910	−	0.899990i	$-0.356427\pi$
$821$	−3.59739	−	2.07695i	−0.125550	−	0.0724861i	−0.561460	+	0.827504i	$0.689760\pi$
$822$		0			0
$823$	−13.7220	−	7.92242i	−0.478320	−	0.276158i	0.241396	−	0.970427i	$-0.422395\pi$
$823$	−13.7220	−	7.92242i	−0.478320	−	0.276158i	−0.719716	+	0.694269i	$0.755728\pi$
$824$		−	11.9764i		−	0.417219i
$825$		0			0
$826$	−2.46863	+	4.27579i	−0.0858945	+	0.148774i
$827$	−16.5088	−	9.53137i	−0.574068	−	0.331438i	0.184704	−	0.982794i	$-0.440867\pi$
$827$	−16.5088	−	9.53137i	−0.574068	−	0.331438i	−0.758772	+	0.651356i	$0.774201\pi$
$828$		0			0
$829$			3.24674i			0.112764i	0.998409	+	0.0563820i	$0.0179565\pi$
$829$			3.24674i			0.112764i	−0.998409	+	0.0563820i	$0.982044\pi$
$830$	−22.9369	+	3.72792i	−0.796152	+	0.129398i
$831$		0			0
$832$	−2.12132	+	3.67423i	−0.0735436	+	0.127381i
$833$	4.18636	+	7.25098i	0.145049	+	0.251232i
$834$		0			0
$835$	5.74559	+	7.03688i	0.198834	+	0.243521i
$836$	−10.9459	−	25.2784i	−0.378570	−	0.874271i
$837$		0			0
$838$	−5.94386	−	10.2951i	−0.205327	−	0.355637i
$839$	24.4949	+	42.4264i	0.845658	+	1.46472i	0.885049	+	0.465498i	$0.154125\pi$
$839$	24.4949	+	42.4264i	0.845658	+	1.46472i	−0.0393910	+	0.999224i	$0.512542\pi$
$840$		0			0
$841$	−12.5000	−	21.6506i	−0.431034	−	0.746574i
$842$	4.38447	−	7.59412i	0.151099	−	0.261711i
$843$		0			0
$844$		−	13.7477i		−	0.473216i
$845$	1.79360	+	11.0355i	0.0617016	+	0.379634i
$846$		0			0
$847$		−	58.3267i		−	2.00413i
$848$			13.9373i			0.478607i
$849$		0			0
$850$	−4.51370	−	13.5190i	−0.154819	−	0.463698i
$851$	−7.99927	+	13.8551i	−0.274211	+	0.474948i
$852$		0			0
$853$	−17.5889	+	10.1550i	−0.602234	+	0.347700i	−0.769920	−	0.638141i	$-0.779704\pi$
$853$	−17.5889	+	10.1550i	−0.602234	+	0.347700i	0.167686	+	0.985840i	$0.446370\pi$
$854$	30.1079			1.03027
$855$		0			0
$856$	10.9373			0.373828
$857$	34.5323	−	19.9373i	1.17960	−	0.681044i	0.223680	−	0.974663i	$-0.428193\pi$
$857$	34.5323	−	19.9373i	1.17960	−	0.681044i	0.955923	+	0.293619i	$0.0948597\pi$
$858$		0			0
$859$	11.9686	−	20.7303i	0.408364	−	0.707308i	−0.586342	−	0.810063i	$-0.699433\pi$
$859$	11.9686	−	20.7303i	0.408364	−	0.707308i	0.994707	+	0.102756i	$0.0327660\pi$
$860$	−7.08072	+	18.6711i	−0.241451	+	0.636678i
$861$		0			0
$862$		−	17.1464i		−	0.584010i
$863$		−	41.8118i		−	1.42329i	−0.702540	−	0.711644i	$-0.747951\pi$
$863$		−	41.8118i		−	1.42329i	0.702540	−	0.711644i	$-0.252049\pi$
$864$		0			0
$865$	17.5184	−	2.84725i	0.595642	−	0.0968093i
$866$			26.6926i			0.907051i
$867$		0			0
$868$		0			0
$869$	−21.8917	−	37.9176i	−0.742625	−	1.28627i
$870$		0			0
$871$	9.00000	+	15.5885i	0.304953	+	0.528195i
$872$	−4.27579	−	7.40588i	−0.144796	−	0.250795i
$873$		0			0
$874$	11.9059	−	16.0390i	0.402722	−	0.542528i
$875$	19.9537	−	10.4735i	0.674557	−	0.354069i
$876$		0			0
$877$	2.49706	+	4.32503i	0.0843197	+	0.146046i	0.905101	−	0.425196i	$-0.139795\pi$
$877$	2.49706	+	4.32503i	0.0843197	+	0.146046i	−0.820781	+	0.571242i	$0.806462\pi$
$878$	−16.4001	+	28.4059i	−0.553478	+	0.958652i
$879$		0			0
$880$	−13.9480	+	2.26696i	−0.470188	+	0.0764192i
$881$			16.3078i			0.549425i	0.961526	+	0.274712i	$0.0885826\pi$
$881$			16.3078i			0.549425i	−0.961526	+	0.274712i	$0.911417\pi$
$882$		0			0
$883$	−2.87280	−	1.65861i	−0.0966773	−	0.0558166i	0.450882	−	0.892584i	$-0.351110\pi$
$883$	−2.87280	−	1.65861i	−0.0966773	−	0.0558166i	−0.547559	+	0.836767i	$0.684443\pi$
$884$	6.04688	−	10.4735i	0.203378	−	0.352262i
$885$		0			0
$886$			25.8721i			0.869190i
$887$	−39.7285	−	22.9373i	−1.33395	−	0.770158i	−0.348049	−	0.937476i	$-0.613156\pi$
$887$	−39.7285	−	22.9373i	−1.33395	−	0.770158i	−0.985903	+	0.167319i	$0.946489\pi$
$888$		0			0
$889$	−20.9059	−	12.0700i	−0.701161	−	0.404815i
$890$	−10.6211	+	28.0066i	−0.356019	+	0.938783i
$891$		0			0
$892$	−20.4617			−0.685109
$893$	22.8042	−	9.87451i	0.763113	−	0.330438i
$894$		0			0
$895$	28.0066	+	10.6211i	0.936157	+	0.355024i
$896$	1.00781	+	1.74558i	0.0336687	+	0.0583158i
$897$		0			0
$898$	17.9647	−	10.3719i	0.599489	−	0.346115i
$899$		0			0
$900$		0			0
$901$		−	39.7285i		−	1.32355i
$902$	−26.8468	+	46.5000i	−0.893900	+	1.54828i
$903$		0			0
$904$	−10.9373			−0.363768
$905$	16.9927	+	20.8118i	0.564858	+	0.691806i
$906$		0			0
$907$	−17.7220	−	30.6955i	−0.588451	−	1.01923i	−0.994436	−	0.105347i	$-0.966405\pi$
$907$	−17.7220	−	30.6955i	−0.588451	−	1.01923i	0.405985	−	0.913880i	$-0.366929\pi$
$908$	−19.8642	−	11.4686i	−0.659218	−	0.380600i
$909$		0			0
$910$	17.8794	+	6.78049i	0.592696	+	0.224771i
$911$	33.9855			1.12599			0.562994	−	0.826461i	$-0.309649\pi$
$911$	33.9855			1.12599			0.562994	+	0.826461i	$0.309649\pi$
$912$		0			0
$913$		−	65.6751i		−	2.17353i
$914$	−19.5191	−	33.8080i	−0.645633	−	1.11827i
$915$		0			0
$916$	3.93725	−	6.81952i	0.130091	−	0.225323i
$917$	22.0469	+	38.1863i	0.728051	+	1.26102i
$918$		0			0
$919$	−12.8118			−0.422621			−0.211311	−	0.977419i	$-0.567773\pi$
$919$	−12.8118			−0.422621			−0.211311	+	0.977419i	$0.567773\pi$
$920$	−6.48074	−	7.93725i	−0.213664	−	0.261684i
$921$		0			0
$922$	4.90538	−	8.49637i	0.161550	−	0.279813i
$923$	31.1769			1.02620
$924$		0			0
$925$	−13.0662	−	11.5750i	−0.429613	−	0.380584i
$926$	−18.0774	−	31.3110i	−0.594060	−	1.02894i
$927$		0			0
$928$	−6.36396	+	3.67423i	−0.208907	+	0.120613i
$929$	2.94659	−	1.70121i	0.0966745	−	0.0558150i	−0.450883	−	0.892583i	$-0.648891\pi$
$929$	2.94659	−	1.70121i	0.0966745	−	0.0558150i	0.547558	+	0.836768i	$0.315558\pi$
$930$		0			0
$931$	−10.2804	−	7.63121i	−0.336926	−	0.250103i
$932$	−14.8662			−0.486959
$933$		0			0
$934$	−20.4686	+	11.8176i	−0.669754	+	0.386683i
$935$	39.7592	−	6.46203i	1.30026	−	0.211331i
$936$		0			0
$937$	36.0624	+	20.8207i	1.17811	+	0.680181i	0.955576	−	0.294744i	$-0.0952343\pi$
$937$	36.0624	+	20.8207i	1.17811	+	0.680181i	0.222532	+	0.974925i	$0.428568\pi$
$938$	8.55157			0.279219
$939$		0			0
$940$	−2.04508	−	12.5828i	−0.0667031	−	0.410407i
$941$	−6.12372	+	10.6066i	−0.199628	+	0.345765i	−0.948408	−	0.317053i	$-0.897307\pi$
$941$	−6.12372	+	10.6066i	−0.199628	+	0.345765i	0.748780	+	0.662819i	$0.230640\pi$
$942$		0			0
$943$	−38.9352			−1.26791
$944$	−1.22474	+	2.12132i	−0.0398621	+	0.0690431i
$945$		0			0
$946$	−48.8745	−	28.2177i	−1.58905	−	0.917437i
$947$	4.88936	+	8.46863i	0.158883	+	0.275193i	0.934466	−	0.356052i	$-0.115877\pi$
$947$	4.88936	+	8.46863i	0.158883	+	0.275193i	−0.775583	+	0.631245i	$0.782544\pi$
$948$		0			0
$949$			6.71084i			0.217843i
$950$	14.5484	+	16.2279i	0.472011	+	0.526503i
$951$		0			0
$952$	−2.87280	−	4.97583i	−0.0931078	−	0.161267i
$953$	−29.3362	+	16.9373i	−0.950292	+	0.548651i	−0.893172	−	0.449716i	$-0.851525\pi$
$953$	−29.3362	+	16.9373i	−0.950292	+	0.548651i	−0.0571205	+	0.998367i	$0.518192\pi$
$954$		0			0
$955$	10.0215	−	26.4256i	0.324289	−	0.855113i
$956$	−3.75108	−	2.16569i	−0.121319	−	0.0700434i
$957$		0			0
$958$	−35.3553			−1.14228
$959$	28.0923	+	16.2191i	0.907147	+	0.523742i
$960$		0			0
$961$	31.0000			1.00000
$962$		−	14.8118i		−	0.477550i
$963$		0			0
$964$	6.00000	−	3.46410i	0.193247	−	0.111571i
$965$	−4.56575	−	28.0919i	−0.146977	−	0.904310i
$966$		0			0
$967$	7.86691	−	4.54196i	0.252983	−	0.146060i	−0.368146	−	0.929768i	$-0.620008\pi$
$967$	7.86691	−	4.54196i	0.252983	−	0.146060i	0.621129	+	0.783708i	$0.286674\pi$
$968$		−	28.9373i		−	0.930079i
$969$		0			0
$970$	−6.00000	−	7.34847i	−0.192648	−	0.235945i
$971$	−13.4722	−	23.3345i	−0.432343	−	0.748841i	0.564731	−	0.825275i	$-0.308980\pi$
$971$	−13.4722	−	23.3345i	−0.432343	−	0.748841i	−0.997075	+	0.0764343i	$0.975646\pi$
$972$		0			0
$973$	−6.98233	−	4.03125i	−0.223843	−	0.129236i
$974$	−5.39608	+	3.11543i	−0.172902	+	0.0998248i
$975$		0			0
$976$	14.9373			0.478130
$977$			40.9373i			1.30970i	0.755759	+	0.654849i	$0.227268\pi$
$977$			40.9373i			1.30970i	−0.755759	+	0.654849i	$0.772732\pi$
$978$		0			0
$979$	−73.3118	−	42.3266i	−2.34305	−	1.35276i
$980$	−5.08747	+	4.15390i	−0.162513	+	0.132692i
$981$		0			0
$982$	2.40832	−	4.17134i	0.0768526	−	0.133113i
$983$	9.63496	−	5.56275i	0.307307	−	0.177424i	−0.338414	−	0.940997i	$-0.609890\pi$
$983$	9.63496	−	5.56275i	0.307307	−	0.177424i	0.645721	+	0.763573i	$0.276557\pi$
$984$		0			0
$985$	32.5919	+	12.3600i	1.03846	+	0.393822i
$986$	18.1406	−	10.4735i	0.577715	−	0.333544i
$987$		0			0
$988$	−2.12132	+	18.3712i	−0.0674882	+	0.584465i
$989$		−	40.9235i		−	1.30129i
$990$		0			0
$991$	16.5941	−	9.58062i	0.527130	−	0.304338i	−0.212717	−	0.977114i	$-0.568231\pi$
$991$	16.5941	−	9.58062i	0.527130	−	0.304338i	0.739847	+	0.672775i	$0.234898\pi$
$992$		0			0
$993$		0			0
$994$	7.40588	−	12.8274i	0.234900	−	0.406859i
$995$	−36.2644	+	29.6097i	−1.14966	+	0.938692i
$996$		0			0
$997$	36.7903	+	21.2409i	1.16516	+	0.672707i	0.952536	−	0.304427i	$-0.0984650\pi$
$997$	36.7903	+	21.2409i	1.16516	+	0.672707i	0.212626	+	0.977134i	$0.431798\pi$
$998$	−12.8817	−	7.43725i	−0.407763	−	0.235422i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.q.a.449.2	yes	16
3.2	odd	2	inner	1710.2.q.a.449.8	yes	16
5.4	even	2	inner	1710.2.q.a.449.5	yes	16
15.14	odd	2	inner	1710.2.q.a.449.3	yes	16
19.8	odd	6	inner	1710.2.q.a.179.4	yes	16
57.8	even	6	inner	1710.2.q.a.179.6	yes	16
95.84	odd	6	inner	1710.2.q.a.179.7	yes	16
285.179	even	6	inner	1710.2.q.a.179.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.q.a.179.1	✓	16	285.179	even	6	inner
1710.2.q.a.179.4	yes	16	19.8	odd	6	inner
1710.2.q.a.179.6	yes	16	57.8	even	6	inner
1710.2.q.a.179.7	yes	16	95.84	odd	6	inner
1710.2.q.a.449.2	yes	16	1.1	even	1	trivial
1710.2.q.a.449.3	yes	16	15.14	odd	2	inner
1710.2.q.a.449.5	yes	16	5.4	even	2	inner
1710.2.q.a.449.8	yes	16	3.2	odd	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.09077 - 0.792893i) q^{5} +2.01563i q^{7} +1.00000i q^{8} +(2.20711 - 0.358719i) q^{10} +6.31959i q^{11} +(2.12132 - 3.67423i) q^{13} +(-1.00781 - 1.74558i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.42526 + 2.46863i) q^{17} +(-3.50000 - 2.59808i) q^{19} +(-1.73205 + 1.41421i) q^{20} +(-3.15980 - 5.47293i) q^{22} +(2.29129 - 3.96863i) q^{23} +(3.74264 + 3.31552i) q^{25} +4.24264i q^{26} +(1.74558 + 1.00781i) q^{28} +(-3.67423 + 6.36396i) q^{29} +(0.866025 + 0.500000i) q^{32} +(-2.46863 - 1.42526i) q^{34} +(1.59818 - 4.21421i) q^{35} -3.49117 q^{37} +(4.33013 + 0.500000i) q^{38} +(0.792893 - 2.09077i) q^{40} +(-4.24818 - 7.35807i) q^{41} +(7.73381 - 4.46512i) q^{43} +(5.47293 + 3.15980i) q^{44} +4.58258i q^{46} +(-2.85052 + 4.93725i) q^{47} +2.93725 q^{49} +(-4.89898 - 1.00000i) q^{50} +(-2.12132 - 3.67423i) q^{52} +(-12.0700 - 6.96863i) q^{53} +(5.01076 - 13.2128i) q^{55} -2.01563 q^{56} -7.34847i q^{58} +(-1.22474 - 2.12132i) q^{59} +(-7.46863 + 12.9360i) q^{61} -1.00000 q^{64} +(-7.34847 + 6.00000i) q^{65} +(-2.12132 + 3.67423i) q^{67} +2.85052 q^{68} +(0.723044 + 4.44870i) q^{70} +(3.67423 + 6.36396i) q^{71} +(-1.36985 + 0.790881i) q^{73} +(3.02344 - 1.74558i) q^{74} +(-4.00000 + 1.73205i) q^{76} -12.7379 q^{77} +(-6.00000 + 3.46410i) q^{79} +(0.358719 + 2.20711i) q^{80} +(7.35807 + 4.24818i) q^{82} -10.3923 q^{83} +(-1.02254 - 6.29141i) q^{85} +(-4.46512 + 7.73381i) q^{86} -6.31959 q^{88} +(-6.69767 + 11.6007i) q^{89} +(7.40588 + 4.27579i) q^{91} +(-2.29129 - 3.96863i) q^{92} -5.70105i q^{94} +(5.25770 + 8.20711i) q^{95} +(-2.12132 - 3.67423i) q^{97} +(-2.54374 + 1.46863i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 24 q^{10} - 8 q^{16} - 56 q^{19} - 8 q^{25} + 24 q^{34} + 24 q^{40} - 80 q^{49} - 8 q^{55} - 56 q^{61} - 16 q^{64} - 24 q^{70} - 64 q^{76} - 96 q^{79} - 24 q^{85} - 72 q^{91}+O(q^{100}) \) 16 * q + 8 * q^4 + 24 * q^10 - 8 * q^16 - 56 * q^19 - 8 * q^25 + 24 * q^34 + 24 * q^40 - 80 * q^49 - 8 * q^55 - 56 * q^61 - 16 * q^64 - 24 * q^70 - 64 * q^76 - 96 * q^79 - 24 * q^85 - 72 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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