LMFDB - Embedded newform 1710.2.q.a.179.8

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			179.8
Root			$1.40721 - 0.140577i$ of defining polynomial
Character	$\chi$	$=$	1710.179
Dual form			1710.2.q.a.449.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.09077 - 0.792893i) q^{5} +4.46512i q^{7} +1.00000i q^{8} +(2.20711 + 0.358719i) q^{10} -4.90538i q^{11} +(2.12132 + 3.67423i) q^{13} +(-2.23256 + 3.86690i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.15731 - 5.46863i) q^{17} +(-3.50000 + 2.59808i) q^{19} +(1.73205 + 1.41421i) q^{20} +(2.45269 - 4.24818i) q^{22} +(2.29129 + 3.96863i) q^{23} +(3.74264 - 3.31552i) q^{25} +4.24264i q^{26} +(-3.86690 + 2.23256i) q^{28} +(3.67423 + 6.36396i) q^{29} +(-0.866025 + 0.500000i) q^{32} +(5.46863 - 3.15731i) q^{34} +(3.54036 + 9.33553i) q^{35} +7.73381 q^{37} +(-4.33013 + 0.500000i) q^{38} +(0.792893 + 2.09077i) q^{40} +(-5.47293 + 9.47939i) q^{41} +(-3.49117 - 2.01563i) q^{43} +(4.24818 - 2.45269i) q^{44} +4.58258i q^{46} +(-6.31463 - 10.9373i) q^{47} -12.9373 q^{49} +(4.89898 - 1.00000i) q^{50} +(-2.12132 + 3.67423i) q^{52} +(-1.67771 + 0.968627i) q^{53} +(-3.88944 - 10.2560i) q^{55} -4.46512 q^{56} +7.34847i q^{58} +(1.22474 - 2.12132i) q^{59} +(0.468627 + 0.811686i) q^{61} -1.00000 q^{64} +(7.34847 + 6.00000i) q^{65} +(-2.12132 - 3.67423i) q^{67} +6.31463 q^{68} +(-1.60172 + 9.85499i) q^{70} +(-3.67423 + 6.36396i) q^{71} +(9.85513 + 5.68986i) q^{73} +(6.69767 + 3.86690i) q^{74} +(-4.00000 - 1.73205i) q^{76} +21.9031 q^{77} +(-6.00000 - 3.46410i) q^{79} +(-0.358719 + 2.20711i) q^{80} +(-9.47939 + 5.47293i) q^{82} +10.3923 q^{83} +(2.26518 - 13.9371i) q^{85} +(-2.01563 - 3.49117i) q^{86} +4.90538 q^{88} +(-3.02344 - 5.23675i) q^{89} +(-16.4059 + 9.47194i) q^{91} +(-2.29129 + 3.96863i) q^{92} -12.6293i q^{94} +(-5.25770 + 8.20711i) q^{95} +(-2.12132 + 3.67423i) q^{97} +(-11.2040 - 6.46863i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	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
$7$			4.46512i			1.68765i	0.536615	+	0.843827i	$0.319703\pi$
$7$			4.46512i			1.68765i	−0.536615	+	0.843827i	$0.680297\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.20711	+	0.358719i	0.697948	+	0.113437i
$11$		−	4.90538i		−	1.47903i	−0.673141	−	0.739514i	$-0.735055\pi$
$11$		−	4.90538i		−	1.47903i	0.673141	−	0.739514i	$-0.264945\pi$
$12$		0			0
$13$	2.12132	+	3.67423i	0.588348	+	1.01905i	0.994449	+	0.105221i	$0.0335550\pi$
$13$	2.12132	+	3.67423i	0.588348	+	1.01905i	−0.406100	+	0.913828i	$0.633112\pi$
$14$	−2.23256	+	3.86690i	−0.596676	+	1.03347i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.15731	−	5.46863i	0.765761	−	1.32634i	−0.174082	−	0.984731i	$-0.555696\pi$
$17$	3.15731	−	5.46863i	0.765761	−	1.32634i	0.939843	−	0.341606i	$-0.110971\pi$
$18$		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
$22$	2.45269	−	4.24818i	0.522915	−	0.905716i
$23$	2.29129	+	3.96863i	0.477767	+	0.827516i	0.999675	−	0.0254855i	$-0.00811315\pi$
$23$	2.29129	+	3.96863i	0.477767	+	0.827516i	−0.521909	+	0.853001i	$0.674780\pi$
$24$		0			0
$25$	3.74264	−	3.31552i	0.748528	−	0.663103i
$26$			4.24264i			0.832050i
$27$		0			0
$28$	−3.86690	+	2.23256i	−0.730776	+	0.421914i
$29$	3.67423	+	6.36396i	0.682288	+	1.18176i	0.974281	+	0.225337i	$0.0723484\pi$
$29$	3.67423	+	6.36396i	0.682288	+	1.18176i	−0.291993	+	0.956421i	$0.594318\pi$
$30$		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
$34$	5.46863	−	3.15731i	0.937862	−	0.541475i
$35$	3.54036	+	9.33553i	0.598430	+	1.57799i
$36$		0			0
$37$	7.73381			1.27143			0.635715	−	0.771924i	$-0.280705\pi$
$37$	7.73381			1.27143			0.635715	+	0.771924i	$0.280705\pi$
$38$	−4.33013	+	0.500000i	−0.702439	+	0.0811107i
$39$		0			0
$40$	0.792893	+	2.09077i	0.125367	+	0.330580i
$41$	−5.47293	+	9.47939i	−0.854728	+	1.48043i	0.0221696	+	0.999754i	$0.492943\pi$
$41$	−5.47293	+	9.47939i	−0.854728	+	1.48043i	−0.876897	+	0.480678i	$0.840391\pi$
$42$		0			0
$43$	−3.49117	−	2.01563i	−0.532398	−	0.307380i	0.209595	−	0.977788i	$-0.432786\pi$
$43$	−3.49117	−	2.01563i	−0.532398	−	0.307380i	−0.741992	+	0.670408i	$0.766119\pi$
$44$	4.24818	−	2.45269i	0.640438	−	0.369757i
$45$		0			0
$46$			4.58258i			0.675664i
$47$	−6.31463	−	10.9373i	−0.921083	−	1.59536i	−0.797743	−	0.602998i	$-0.793973\pi$
$47$	−6.31463	−	10.9373i	−0.921083	−	1.59536i	−0.123340	−	0.992364i	$-0.539361\pi$
$48$		0			0
$49$	−12.9373			−1.84818
$50$	4.89898	−	1.00000i	0.692820	−	0.141421i
$51$		0			0
$52$	−2.12132	+	3.67423i	−0.294174	+	0.509525i
$53$	−1.67771	+	0.968627i	−0.230451	+	0.133051i	−0.610780	−	0.791800i	$-0.709144\pi$
$53$	−1.67771	+	0.968627i	−0.230451	+	0.133051i	0.380329	+	0.924851i	$0.375811\pi$
$54$		0			0
$55$	−3.88944	−	10.2560i	−0.524452	−	1.38292i
$56$	−4.46512			−0.596676
$57$		0			0
$58$			7.34847i			0.964901i
$59$	1.22474	−	2.12132i	0.159448	−	0.276172i	−0.775222	−	0.631689i	$-0.782362\pi$
$59$	1.22474	−	2.12132i	0.159448	−	0.276172i	0.934670	+	0.355517i	$0.115695\pi$
$60$		0			0
$61$	0.468627	+	0.811686i	0.0600015	+	0.103926i	0.894466	−	0.447136i	$-0.147556\pi$
$61$	0.468627	+	0.811686i	0.0600015	+	0.103926i	−0.834464	+	0.551062i	$0.814223\pi$
$62$		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	0.706857	−	0.707357i	$-0.250113\pi$
$67$	−2.12132	−	3.67423i	−0.259161	−	0.448879i	−0.966017	+	0.258478i	$0.916779\pi$
$68$	6.31463			0.765761
$69$		0			0
$70$	−1.60172	+	9.85499i	−0.191443	+	1.17790i
$71$	−3.67423	+	6.36396i	−0.436051	+	0.755263i	−0.997381	−	0.0723293i	$-0.976957\pi$
$71$	−3.67423	+	6.36396i	−0.436051	+	0.755263i	0.561329	+	0.827592i	$0.310290\pi$
$72$		0			0
$73$	9.85513	+	5.68986i	1.15346	+	0.665948i	0.949727	−	0.313080i	$-0.101361\pi$
$73$	9.85513	+	5.68986i	1.15346	+	0.665948i	0.203728	+	0.979027i	$0.434694\pi$
$74$	6.69767	+	3.86690i	0.778589	+	0.449518i
$75$		0			0
$76$	−4.00000	−	1.73205i	−0.458831	−	0.198680i
$77$	21.9031			2.49609
$78$		0			0
$79$	−6.00000	−	3.46410i	−0.675053	−	0.389742i	0.122936	−	0.992415i	$-0.460769\pi$
$79$	−6.00000	−	3.46410i	−0.675053	−	0.389742i	−0.797988	+	0.602673i	$0.794102\pi$
$80$	−0.358719	+	2.20711i	−0.0401061	+	0.246762i
$81$		0			0
$82$	−9.47939	+	5.47293i	−1.04682	+	0.604384i
$83$	10.3923			1.14070			0.570352	−	0.821401i	$-0.306807\pi$
$83$	10.3923			1.14070			0.570352	+	0.821401i	$0.306807\pi$
$84$		0			0
$85$	2.26518	−	13.9371i	0.245693	−	1.51169i
$86$	−2.01563	−	3.49117i	−0.217350	−	0.376462i
$87$		0			0
$88$	4.90538			0.522915
$89$	−3.02344	−	5.23675i	−0.320484	−	0.555094i	0.660104	−	0.751174i	$-0.270512\pi$
$89$	−3.02344	−	5.23675i	−0.320484	−	0.555094i	−0.980588	+	0.196080i	$0.937179\pi$
$90$		0			0
$91$	−16.4059	+	9.47194i	−1.71980	+	0.992929i
$92$	−2.29129	+	3.96863i	−0.238883	+	0.413758i
$93$		0			0
$94$		−	12.6293i		−	1.30261i
$95$	−5.25770	+	8.20711i	−0.539429	+	0.842031i
$96$		0			0
$97$	−2.12132	+	3.67423i	−0.215387	+	0.373062i	−0.953392	−	0.301733i	$-0.902435\pi$
$97$	−2.12132	+	3.67423i	−0.215387	+	0.373062i	0.738005	+	0.674795i	$0.235768\pi$
$98$	−11.2040	−	6.46863i	−1.13177	−	0.653430i
$99$		0			0
$100$	4.74264	+	1.58346i	0.474264	+	0.158346i
$101$	2.44949	−	1.41421i	0.243733	−	0.140720i	−0.373158	−	0.927768i	$-0.621725\pi$
$101$	2.44949	−	1.41421i	0.243733	−	0.140720i	0.616891	+	0.787048i	$0.288392\pi$
$102$		0			0
$103$	−0.751475			−0.0740450			−0.0370225	−	0.999314i	$-0.511787\pi$
$103$	−0.751475			−0.0740450			−0.0370225	+	0.999314i	$0.511787\pi$
$104$	−3.67423	+	2.12132i	−0.360288	+	0.208013i
$105$		0			0
$106$	−1.93725			−0.188163
$107$			4.93725i			0.477302i	0.971105	+	0.238651i	$0.0767053\pi$
$107$			4.93725i			0.477302i	−0.971105	+	0.238651i	$0.923295\pi$
$108$		0			0
$109$	16.4059	+	9.47194i	1.57140	+	0.907247i	0.995998	+	0.0893754i	$0.0284871\pi$
$109$	16.4059	+	9.47194i	1.57140	+	0.907247i	0.575400	+	0.817872i	$0.304846\pi$
$110$	1.75966	−	10.8267i	0.167777	−	1.03228i
$111$		0			0
$112$	−3.86690	−	2.23256i	−0.365388	−	0.210957i
$113$		−	4.93725i		−	0.464458i	−0.972661	−	0.232229i	$-0.925398\pi$
$113$		−	4.93725i		−	0.464458i	0.972661	−	0.232229i	$-0.0746018\pi$
$114$		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
$119$	24.4180	+	14.0978i	2.23840	+	1.29234i
$120$		0			0
$121$	−13.0627			−1.18752
$122$			0.937254i			0.0848550i
$123$		0			0
$124$		0			0
$125$	5.19615	−	9.89949i	0.464758	−	0.885438i
$126$		0			0
$127$	−0.375737	−	0.650796i	−0.0333413	−	0.0577488i	0.848873	−	0.528596i	$-0.177282\pi$
$127$	−0.375737	−	0.650796i	−0.0333413	−	0.0577488i	−0.882215	+	0.470848i	$0.843948\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	3.36396	+	8.87039i	0.295039	+	0.777984i
$131$	−9.22401	−	5.32548i	−0.805906	−	0.465290i	0.0396264	−	0.999215i	$-0.487383\pi$
$131$	−9.22401	−	5.32548i	−0.805906	−	0.465290i	−0.845532	+	0.533925i	$0.820717\pi$
$132$		0			0
$133$	−11.6007	−	15.6279i	−1.00591	−	1.35511i
$134$		−	4.24264i		−	0.366508i
$135$		0			0
$136$	5.46863	+	3.15731i	0.468931	+	0.270737i
$137$	1.11847	+	1.93725i	0.0955577	+	0.165511i	0.909841	−	0.414957i	$-0.136203\pi$
$137$	1.11847	+	1.93725i	0.0955577	+	0.165511i	−0.814284	+	0.580467i	$0.802870\pi$
$138$		0			0
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	0.768655	−	0.639664i	$-0.220926\pi$
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	−0.938293	+	0.345843i	$0.887593\pi$
$140$	−6.31463	+	7.73381i	−0.533683	+	0.653626i
$141$		0			0
$142$	−6.36396	+	3.67423i	−0.534052	+	0.308335i
$143$	18.0235	−	10.4059i	1.50720	−	0.870183i
$144$		0			0
$145$	12.7279	+	10.3923i	1.05700	+	0.863034i
$146$	5.68986	+	9.85513i	0.470896	+	0.815616i
$147$		0			0
$148$	3.86690	+	6.69767i	0.317857	+	0.550545i
$149$	−12.1706	−	7.02670i	−0.997054	−	0.575650i	−0.0896790	−	0.995971i	$-0.528584\pi$
$149$	−12.1706	−	7.02670i	−0.997054	−	0.575650i	−0.907375	+	0.420321i	$0.861917\pi$
$150$		0			0
$151$		−	18.9439i		−	1.54163i	−0.637058	−	0.770816i	$-0.719849\pi$
$151$		−	18.9439i		−	1.54163i	0.637058	−	0.770816i	$-0.280151\pi$
$152$	−2.59808	−	3.50000i	−0.210732	−	0.283887i
$153$		0			0
$154$	18.9686	+	10.9515i	1.52854	+	0.882500i
$155$		0			0
$156$		0			0
$157$	−17.9647	−	10.3719i	−1.43374	−	0.827768i	−0.436333	−	0.899785i	$-0.643723\pi$
$157$	−17.9647	−	10.3719i	−1.43374	−	0.827768i	−0.997403	+	0.0720167i	$0.977056\pi$
$158$	−3.46410	−	6.00000i	−0.275589	−	0.477334i
$159$		0			0
$160$	−1.41421	+	1.73205i	−0.111803	+	0.136931i
$161$	−17.7204	+	10.2309i	−1.39656	+	0.806305i
$162$		0			0
$163$			12.9615i			1.01522i	0.861586	+	0.507611i	$0.169471\pi$
$163$			12.9615i			1.01522i	−0.861586	+	0.507611i	$0.830529\pi$
$164$	−10.9459			−0.854728
$165$		0			0
$166$	9.00000	+	5.19615i	0.698535	+	0.403300i
$167$	17.2662	−	9.96863i	1.33610	−	0.771396i	0.349870	−	0.936798i	$-0.386226\pi$
$167$	17.2662	−	9.96863i	1.33610	−	0.771396i	0.986226	+	0.165403i	$0.0528924\pi$
$168$		0			0
$169$	−2.50000	+	4.33013i	−0.192308	+	0.333087i
$170$	8.93023	−	10.9373i	0.684917	−	0.838849i
$171$		0			0
$172$		−	4.03125i		−	0.307380i
$173$	−6.87386	−	3.96863i	−0.522610	−	0.301729i	0.215392	−	0.976528i	$-0.430897\pi$
$173$	−6.87386	−	3.96863i	−0.522610	−	0.301729i	−0.738002	+	0.674799i	$0.764230\pi$
$174$		0			0
$175$	14.8042	+	16.7113i	1.11909	+	1.26326i
$176$	4.24818	+	2.45269i	0.320219	+	0.184878i
$177$		0			0
$178$		−	6.04688i		−	0.453233i
$179$	−6.04688			−0.451965			−0.225982	−	0.974131i	$-0.572559\pi$
$179$	−6.04688			−0.451965			−0.225982	+	0.974131i	$0.572559\pi$
$180$		0			0
$181$	13.4059	−	7.73989i	0.996451	−	0.575301i	0.0892549	−	0.996009i	$-0.471551\pi$
$181$	13.4059	−	7.73989i	0.996451	−	0.575301i	0.907196	+	0.420707i	$0.138218\pi$
$182$	−18.9439			−1.40421
$183$		0			0
$184$	−3.96863	+	2.29129i	−0.292571	+	0.168916i
$185$	16.1696	−	6.13208i	1.18881	−	0.450840i
$186$		0			0
$187$	−26.8257	−	15.4878i	−1.96169	−	1.13258i
$188$	6.31463	−	10.9373i	0.460541	−	0.797681i
$189$		0			0
$190$	−8.65685	+	4.47871i	−0.628034	+	0.324920i
$191$		−	9.81076i		−	0.709882i	−0.934889	−	0.354941i	$-0.884501\pi$
$191$		−	9.81076i		−	0.709882i	0.934889	−	0.354941i	$-0.115499\pi$
$192$		0			0
$193$	6.36396	−	11.0227i	0.458088	−	0.793432i	−0.540772	−	0.841169i	$-0.681868\pi$
$193$	6.36396	−	11.0227i	0.458088	−	0.793432i	0.998860	+	0.0477376i	$0.0152011\pi$
$194$	−3.67423	+	2.12132i	−0.263795	+	0.152302i
$195$		0			0
$196$	−6.46863	−	11.2040i	−0.462045	−	0.800285i
$197$	15.5885			1.11063			0.555316	−	0.831640i	$-0.312597\pi$
$197$	15.5885			1.11063			0.555316	+	0.831640i	$0.312597\pi$
$198$		0			0
$199$	2.53137	+	4.38447i	0.179444	+	0.310807i	0.941690	−	0.336481i	$-0.109237\pi$
$199$	2.53137	+	4.38447i	0.179444	+	0.310807i	−0.762246	+	0.647287i	$0.775903\pi$
$200$	3.31552	+	3.74264i	0.234442	+	0.264645i
$201$		0			0
$202$	2.82843			0.199007
$203$	−28.4158	+	16.4059i	−1.99440	+	1.15147i
$204$		0			0
$205$	−3.92649	+	24.1587i	−0.274238	+	1.68731i
$206$	−0.650796	−	0.375737i	−0.0453431	−	0.0261789i
$207$		0			0
$208$	−4.24264			−0.294174
$209$	12.7445	+	17.1688i	0.881559	+	1.18759i
$210$		0			0
$211$	−11.9059	−	6.87386i	−0.819635	−	0.473216i	0.0306558	−	0.999530i	$-0.490240\pi$
$211$	−11.9059	−	6.87386i	−0.819635	−	0.473216i	−0.850290	+	0.526314i	$0.823574\pi$
$212$	−1.67771	−	0.968627i	−0.115226	−	0.0665256i
$213$		0			0
$214$	−2.46863	+	4.27579i	−0.168752	+	0.292287i
$215$	−8.89740	−	1.44609i	−0.606798	−	0.0986224i
$216$		0			0
$217$		0			0
$218$	9.47194	+	16.4059i	0.641521	+	1.11115i
$219$		0			0
$220$	6.93725	−	8.49637i	0.467710	−	0.572825i
$221$	26.7907			1.80214
$222$		0			0
$223$	−4.61838	+	7.99927i	−0.309269	+	0.535670i	−0.978203	−	0.207652i	$-0.933418\pi$
$223$	−4.61838	+	7.99927i	−0.309269	+	0.535670i	0.668933	+	0.743322i	$0.266751\pi$
$224$	−2.23256	−	3.86690i	−0.149169	−	0.258368i
$225$		0			0
$226$	2.46863	−	4.27579i	0.164211	−	0.284421i
$227$		−	7.06275i		−	0.468771i	−0.972144	−	0.234385i	$-0.924692\pi$
$227$		−	7.06275i		−	0.468771i	0.972144	−	0.234385i	$-0.0753078\pi$
$228$		0			0
$229$	−23.8745			−1.57767			−0.788836	−	0.614604i	$-0.789316\pi$
$229$	−23.8745			−1.57767			−0.788836	+	0.614604i	$0.789316\pi$
$230$	3.63349	+	9.58111i	0.239585	+	0.631760i
$231$		0			0
$232$	−6.36396	+	3.67423i	−0.417815	+	0.241225i
$233$	−10.8972	+	18.8745i	−0.713899	+	1.23651i	0.249483	+	0.968379i	$0.419739\pi$
$233$	−10.8972	+	18.8745i	−0.713899	+	1.23651i	−0.963382	+	0.268131i	$0.913594\pi$
$234$		0			0
$235$	−21.8745	−	17.8605i	−1.42694	−	1.16509i
$236$	2.44949			0.159448
$237$		0			0
$238$	14.0978	+	24.4180i	0.913823	+	1.58279i
$239$		−	26.7813i		−	1.73234i	−0.499750	−	0.866170i	$-0.666575\pi$
$239$		−	26.7813i		−	1.73234i	0.499750	−	0.866170i	$-0.333425\pi$
$240$		0			0
$241$	6.00000	−	3.46410i	0.386494	−	0.223142i	−0.294146	−	0.955761i	$-0.595035\pi$
$241$	6.00000	−	3.46410i	0.386494	−	0.223142i	0.680640	+	0.732618i	$0.261702\pi$
$242$	−11.3127	−	6.53137i	−0.727206	−	0.419853i
$243$		0			0
$244$	−0.468627	+	0.811686i	−0.0300008	+	0.0519629i
$245$	−27.0488	+	10.2579i	−1.72809	+	0.655351i
$246$		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	$-0.738304\pi$
$251$	−6.12372	+	3.53553i	−0.386526	+	0.223161i	0.294128	+	0.955766i	$0.404971\pi$
$252$		0			0
$253$	19.4676	−	11.2396i	1.22392	−	0.706630i
$254$		−	0.751475i		−	0.0471517i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.55157	+	4.93725i	−0.533433	+	0.307977i	−0.742413	−	0.669942i	$-0.766319\pi$
$257$	−8.55157	+	4.93725i	−0.533433	+	0.307977i	0.208981	+	0.977920i	$0.432985\pi$
$258$		0			0
$259$			34.5323i			2.14574i
$260$	−1.52192	+	9.36396i	−0.0943853	+	0.580728i
$261$		0			0
$262$	−5.32548	−	9.22401i	−0.329010	−	0.569861i
$263$	3.40976	−	5.90588i	0.210255	−	0.364172i	−0.741539	−	0.670909i	$-0.765904\pi$
$263$	3.40976	−	5.90588i	0.210255	−	0.364172i	0.951794	+	0.306737i	$0.0992373\pi$
$264$		0			0
$265$	−2.73969	+	3.35542i	−0.168298	+	0.206122i
$266$	−2.23256	−	19.3345i	−0.136887	−	1.18548i
$267$		0			0
$268$	2.12132	−	3.67423i	0.129580	−	0.224440i
$269$	1.22474	−	2.12132i	0.0746740	−	0.129339i	−0.826270	−	0.563274i	$-0.809542\pi$
$269$	1.22474	−	2.12132i	0.0746740	−	0.129339i	0.900944	+	0.433934i	$0.142875\pi$
$270$		0			0
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	−0.834053	−	0.551684i	$-0.813985\pi$
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	0.894799	+	0.446469i	$0.147319\pi$
$272$	3.15731	+	5.46863i	0.191440	+	0.331584i
$273$		0			0
$274$			2.23695i			0.135139i
$275$	−16.2639	−	18.3591i	−0.980748	−	1.10709i
$276$		0			0
$277$			1.58176i			0.0950388i	0.998870	+	0.0475194i	$0.0151316\pi$
$277$			1.58176i			0.0950388i	−0.998870	+	0.0475194i	$0.984868\pi$
$278$		−	4.00000i		−	0.239904i
$279$		0			0
$280$	−9.33553	+	3.54036i	−0.557905	+	0.211577i
$281$	−10.3719	−	17.9647i	−0.618736	−	1.07168i	−0.989717	−	0.143042i	$-0.954312\pi$
$281$	−10.3719	−	17.9647i	−0.618736	−	1.07168i	0.370981	−	0.928641i	$-0.379022\pi$
$282$		0			0
$283$	15.4676	+	8.93023i	0.919454	+	0.530847i	0.883461	−	0.468505i	$-0.155207\pi$
$283$	15.4676	+	8.93023i	0.919454	+	0.530847i	0.0359933	+	0.999352i	$0.488541\pi$
$284$	−7.34847			−0.436051
$285$		0			0
$286$	20.8118			1.23063
$287$	−42.3266	−	24.4373i	−2.49846	−	1.44249i
$288$		0			0
$289$	−11.4373	−	19.8099i	−0.672780	−	1.16529i
$290$	5.82655	+	15.3640i	0.342147	+	0.902203i
$291$		0			0
$292$			11.3797i			0.665948i
$293$		−	12.8745i		−	0.752137i	−0.926592	−	0.376068i	$-0.877276\pi$
$293$		−	12.8745i		−	0.752137i	0.926592	−	0.376068i	$-0.122724\pi$
$294$		0			0
$295$	0.878680	−	5.40629i	0.0511587	−	0.314766i
$296$			7.73381i			0.449518i
$297$		0			0
$298$	−7.02670	−	12.1706i	−0.407046	−	0.705024i
$299$	−9.72111	+	16.8375i	−0.562186	+	0.973735i
$300$		0			0
$301$	9.00000	−	15.5885i	0.518751	−	0.898504i
$302$	9.47194	−	16.4059i	0.545049	−	0.944052i
$303$		0			0
$304$	−0.500000	−	4.33013i	−0.0286770	−	0.248350i
$305$	1.62337	+	1.32548i	0.0929540	+	0.0758966i
$306$		0			0
$307$	5.61249	−	9.72111i	0.320321	−	0.554813i	−0.660233	−	0.751061i	$-0.729542\pi$
$307$	5.61249	−	9.72111i	0.320321	−	0.554813i	0.980554	+	0.196248i	$0.0628757\pi$
$308$	10.9515	+	18.9686i	0.624022	+	1.08084i
$309$		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
$313$	0.751475	−	0.433864i	0.0424759	−	0.0245235i	−0.478612	−	0.878027i	$-0.658860\pi$
$313$	0.751475	−	0.433864i	0.0424759	−	0.0245235i	0.521088	+	0.853503i	$0.325526\pi$
$314$	−10.3719	−	17.9647i	−0.585321	−	1.01381i
$315$		0			0
$316$		−	6.92820i		−	0.389742i
$317$	30.0935	−	17.3745i	1.69022	−	0.975850i	0.735889	−	0.677102i	$-0.236765\pi$
$317$	30.0935	−	17.3745i	1.69022	−	0.975850i	0.954332	−	0.298747i	$-0.0965687\pi$
$318$		0			0
$319$	31.2176	−	18.0235i	1.74785	−	1.00912i
$320$	−2.09077	+	0.792893i	−0.116878	+	0.0443241i
$321$		0			0
$322$	−20.4617			−1.14029
$323$	3.15731	+	27.3431i	0.175678	+	1.52141i
$324$		0			0
$325$	20.1213	+	6.71807i	1.11613	+	0.372651i
$326$	−6.48074	+	11.2250i	−0.358935	+	0.621694i
$327$		0			0
$328$	−9.47939	−	5.47293i	−0.523412	−	0.302192i
$329$	48.8361	−	28.1955i	2.69242	−	1.55447i
$330$		0			0
$331$		−	22.5167i		−	1.23763i	−0.785538	−	0.618814i	$-0.787614\pi$
$331$		−	22.5167i		−	1.23763i	0.785538	−	0.618814i	$-0.212386\pi$
$332$	5.19615	+	9.00000i	0.285176	+	0.493939i
$333$		0			0
$334$	19.9373			1.09092
$335$	−7.34847	−	6.00000i	−0.401490	−	0.327815i
$336$		0			0
$337$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$337$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$338$	−4.33013	+	2.50000i	−0.235528	+	0.135982i
$339$		0			0
$340$	13.2024	−	5.00682i	0.716002	−	0.271533i
$341$		0			0
$342$		0			0
$343$		−	26.5105i		−	1.43143i
$344$	2.01563	−	3.49117i	0.108675	−	0.188231i
$345$		0			0
$346$	−3.96863	−	6.87386i	−0.213355	−	0.369541i
$347$	1.73205	−	3.00000i	0.0929814	−	0.161048i	−0.815783	−	0.578358i	$-0.803694\pi$
$347$	1.73205	−	3.00000i	0.0929814	−	0.161048i	0.908764	+	0.417310i	$0.137027\pi$
$348$		0			0
$349$	−17.0627			−0.913348			−0.456674	−	0.889634i	$-0.650959\pi$
$349$	−17.0627			−0.913348			−0.456674	+	0.889634i	$0.650959\pi$
$350$	4.46512	+	21.8745i	0.238670	+	1.16924i
$351$		0			0
$352$	2.45269	+	4.24818i	0.130729	+	0.226429i
$353$	−21.3982			−1.13891			−0.569455	−	0.822022i	$-0.692846\pi$
$353$	−21.3982			−1.13891			−0.569455	+	0.822022i	$0.692846\pi$
$354$		0			0
$355$	−2.63604	+	16.2189i	−0.139906	+	0.860808i
$356$	3.02344	−	5.23675i	0.160242	−	0.277547i
$357$		0			0
$358$	−5.23675	−	3.02344i	−0.276771	−	0.159794i
$359$	−6.12372	−	3.53553i	−0.323198	−	0.186598i	0.329619	−	0.944114i	$-0.393080\pi$
$359$	−6.12372	−	3.53553i	−0.323198	−	0.186598i	−0.652817	+	0.757516i	$0.726413\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$	15.4798			0.813599
$363$		0			0
$364$	−16.4059	−	9.47194i	−0.859902	−	0.496465i
$365$	25.1163	+	4.08213i	1.31465	+	0.213668i
$366$		0			0
$367$	4.86101	−	2.80651i	0.253743	−	0.146498i	−0.367734	−	0.929931i	$-0.619866\pi$
$367$	4.86101	−	2.80651i	0.253743	−	0.146498i	0.621477	+	0.783433i	$0.286533\pi$
$368$	−4.58258			−0.238883
$369$		0			0
$370$	17.0693	+	2.77427i	0.887393	+	0.144227i
$371$	−4.32503	−	7.49117i	−0.224544	−	0.388922i
$372$		0			0
$373$	−18.9588			−0.981648			−0.490824	−	0.871259i	$-0.663304\pi$
$373$	−18.9588			−0.981648			−0.490824	+	0.871259i	$0.663304\pi$
$374$	−15.4878	−	26.8257i	−0.800856	−	1.38712i
$375$		0			0
$376$	10.9373	−	6.31463i	0.564046	−	0.325652i
$377$	−15.5885	+	27.0000i	−0.802846	+	1.39057i
$378$		0			0
$379$			34.4237i			1.76822i	0.467275	+	0.884112i	$0.345236\pi$
$379$			34.4237i			1.76822i	−0.467275	+	0.884112i	$0.654764\pi$
$380$	−9.73641	−	0.449747i	−0.499467	−	0.0230716i
$381$		0			0
$382$	4.90538	−	8.49637i	0.250981	−	0.434712i
$383$	24.1400	+	13.9373i	1.23350	+	0.712160i	0.967757	−	0.251884i	$-0.0810502\pi$
$383$	24.1400	+	13.9373i	1.23350	+	0.712160i	0.265741	+	0.964045i	$0.414384\pi$
$384$		0			0
$385$	45.7943	−	17.3668i	2.33389	−	0.885094i
$386$	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	$-0.795704\pi$
$389$	−13.4722	+	7.77817i	−0.683067	+	0.394369i	0.117942	+	0.993020i	$0.462370\pi$
$390$		0			0
$391$	28.9373			1.46342
$392$		−	12.9373i		−	0.653430i
$393$		0			0
$394$	13.5000	+	7.79423i	0.680120	+	0.392668i
$395$	−15.2913	−	2.48528i	−0.769388	−	0.125048i
$396$		0			0
$397$	−5.36985	−	3.10029i	−0.269505	−	0.155599i	0.359158	−	0.933277i	$-0.383064\pi$
$397$	−5.36985	−	3.10029i	−0.269505	−	0.155599i	−0.628663	+	0.777678i	$0.716397\pi$
$398$			5.06275i			0.253773i
$399$		0			0
$400$	1.00000	+	4.89898i	0.0500000	+	0.244949i
$401$	−4.82213	+	8.35218i	−0.240806	+	0.417088i	−0.960944	−	0.276743i	$-0.910745\pi$
$401$	−4.82213	+	8.35218i	−0.240806	+	0.417088i	0.720138	+	0.693831i	$0.244078\pi$
$402$		0			0
$403$		0			0
$404$	2.44949	+	1.41421i	0.121867	+	0.0703598i
$405$		0			0
$406$	−32.8118			−1.62842
$407$		−	37.9373i		−	1.88048i
$408$		0			0
$409$	25.5000	−	14.7224i	1.26089	−	0.727977i	0.287646	−	0.957737i	$-0.407127\pi$
$409$	25.5000	−	14.7224i	1.26089	−	0.727977i	0.973247	+	0.229759i	$0.0737939\pi$
$410$	−15.4798	+	18.9588i	−0.764492	+	0.936307i
$411$		0			0
$412$	−0.375737	−	0.650796i	−0.0185113	−	0.0320624i
$413$	9.47194	+	5.46863i	0.466084	+	0.269094i
$414$		0			0
$415$	21.7279	−	8.23999i	1.06658	−	0.404485i
$416$	−3.67423	−	2.12132i	−0.180144	−	0.104006i
$417$		0			0
$418$	2.45269	+	21.2409i	0.119965	+	1.03893i
$419$		−	21.7872i		−	1.06437i	−0.846627	−	0.532187i	$-0.821370\pi$
$419$		−	21.7872i		−	1.06437i	0.846627	−	0.532187i	$-0.178630\pi$
$420$		0			0
$421$	−31.4059	−	18.1322i	−1.53063	−	0.883709i	−0.999333	−	0.0365229i	$-0.988372\pi$
$421$	−31.4059	−	18.1322i	−1.53063	−	0.883709i	−0.531296	−	0.847186i	$-0.678295\pi$
$422$	−6.87386	−	11.9059i	−0.334614	−	0.579569i
$423$		0			0
$424$	−0.968627	−	1.67771i	−0.0470407	−	0.0814769i
$425$	−6.31463	−	30.9352i	−0.306304	−	1.50058i
$426$		0			0
$427$	−3.62427	+	2.09247i	−0.175391	+	0.101262i
$428$	−4.27579	+	2.46863i	−0.206678	+	0.119326i
$429$		0			0
$430$	−6.98233	−	5.70105i	−0.336718	−	0.274929i
$431$	8.57321	+	14.8492i	0.412957	+	0.715263i	0.995212	−	0.0977438i	$-0.0311626\pi$
$431$	8.57321	+	14.8492i	0.412957	+	0.715263i	−0.582254	+	0.813007i	$0.697829\pi$
$432$		0			0
$433$	−9.10365	−	15.7680i	−0.437494	−	0.757761i	0.560002	−	0.828491i	$-0.310800\pi$
$433$	−9.10365	−	15.7680i	−0.437494	−	0.757761i	−0.997495	+	0.0707302i	$0.977467\pi$
$434$		0			0
$435$		0			0
$436$			18.9439i			0.907247i
$437$	−18.3303	−	7.93725i	−0.876857	−	0.379690i
$438$		0			0
$439$	4.59412	+	2.65242i	0.219265	+	0.126593i	0.605610	−	0.795762i	$-0.292929\pi$
$439$	4.59412	+	2.65242i	0.219265	+	0.126593i	−0.386345	+	0.922354i	$0.626262\pi$
$440$	10.2560	−	3.88944i	0.488937	−	0.185422i
$441$		0			0
$442$	23.2014	+	13.3953i	1.10358	+	0.637152i
$443$	0.811686	+	1.40588i	0.0385644	+	0.0667954i	0.884663	−	0.466230i	$-0.154388\pi$
$443$	0.811686	+	1.40588i	0.0385644	+	0.0667954i	−0.846099	+	0.533026i	$0.821055\pi$
$444$		0			0
$445$	−10.4735	−	8.55157i	−0.496491	−	0.405384i
$446$	−7.99927	+	4.61838i	−0.378776	+	0.218687i
$447$		0			0
$448$		−	4.46512i		−	0.210957i
$449$	1.30159			0.0614260			0.0307130	−	0.999528i	$-0.490222\pi$
$449$	1.30159			0.0614260			0.0307130	+	0.999528i	$0.490222\pi$
$450$		0			0
$451$	46.5000	+	26.8468i	2.18960	+	1.26417i
$452$	4.27579	−	2.46863i	0.201116	−	0.116114i
$453$		0			0
$454$	3.53137	−	6.11652i	0.165736	−	0.287062i
$455$	−26.7907	+	32.8118i	−1.25597	+	1.53824i
$456$		0			0
$457$		−	0.153696i		−	0.00718959i	−0.999994	−	0.00359479i	$-0.998856\pi$
$457$		−	0.153696i		−	0.00718959i	0.999994	−	0.00359479i	$-0.00114426\pi$
$458$	−20.6759	−	11.9373i	−0.966123	−	0.557791i
$459$		0			0
$460$	−1.64386	+	10.1142i	−0.0766453	+	0.471579i
$461$	−10.9459	−	6.31959i	−0.509799	−	0.294333i	0.222952	−	0.974829i	$-0.428431\pi$
$461$	−10.9459	−	6.31959i	−0.509799	−	0.294333i	−0.732751	+	0.680497i	$0.761764\pi$
$462$		0			0
$463$			9.21040i			0.428044i	0.976829	+	0.214022i	$0.0686563\pi$
$463$			9.21040i			0.428044i	−0.976829	+	0.214022i	$0.931344\pi$
$464$	−7.34847			−0.341144
$465$		0			0
$466$	−18.8745	+	10.8972i	−0.874345	+	0.504803i
$467$	−14.4700			−0.669591			−0.334795	−	0.942291i	$-0.608667\pi$
$467$	−14.4700			−0.669591			−0.334795	+	0.942291i	$0.608667\pi$
$468$		0			0
$469$	16.4059	−	9.47194i	0.757553	−	0.437374i
$470$	−10.0136	−	26.4049i	−0.461895	−	1.21797i
$471$		0			0
$472$	2.12132	+	1.22474i	0.0976417	+	0.0563735i
$473$	−9.88741	+	17.1255i	−0.454623	+	0.787431i
$474$		0			0
$475$	−4.48528	+	21.3280i	−0.205799	+	0.978594i
$476$			28.1955i			1.29234i
$477$		0			0
$478$	13.3907	−	23.1933i	0.612475	−	1.06084i
$479$	−30.6186	+	17.6777i	−1.39900	+	0.807713i	−0.994288	−	0.106731i	$-0.965962\pi$
$479$	−30.6186	+	17.6777i	−1.39900	+	0.807713i	−0.404713	+	0.914444i	$0.632628\pi$
$480$		0			0
$481$	16.4059	+	28.4158i	0.748044	+	1.29565i
$482$	6.92820			0.315571
$483$		0			0
$484$	−6.53137	−	11.3127i	−0.296881	−	0.514212i
$485$	−1.52192	+	9.36396i	−0.0691067	+	0.425196i
$486$		0			0
$487$	−27.4441			−1.24361			−0.621805	−	0.783172i	$-0.713600\pi$
$487$	−27.4441			−1.24361			−0.621805	+	0.783172i	$0.713600\pi$
$488$	−0.811686	+	0.468627i	−0.0367433	+	0.0212137i
$489$		0			0
$490$	−28.5539	−	4.64084i	−1.28993	−	0.209652i
$491$	−24.9920	−	14.4291i	−1.12787	−	0.651178i	−0.184474	−	0.982837i	$-0.559058\pi$
$491$	−24.9920	−	14.4291i	−1.12787	−	0.651178i	−0.943399	+	0.331660i	$0.892391\pi$
$492$		0			0
$493$	46.4028			2.08988
$494$	−11.0227	−	14.8492i	−0.495935	−	0.668099i
$495$		0			0
$496$		0			0
$497$	−28.4158	−	16.4059i	−1.27462	−	0.735904i
$498$		0			0
$499$	−8.43725	+	14.6138i	−0.377703	+	0.654201i	−0.990728	−	0.135863i	$-0.956619\pi$
$499$	−8.43725	+	14.6138i	−0.377703	+	0.654201i	0.613024	+	0.790064i	$0.289953\pi$
$500$	11.1713	−	0.449747i	0.499595	−	0.0201133i
$501$		0			0
$502$	−7.07107			−0.315597
$503$	11.7632	+	20.3745i	0.524496	+	0.908454i	0.999593	+	0.0285209i	$0.00907971\pi$
$503$	11.7632	+	20.3745i	0.524496	+	0.908454i	−0.475097	+	0.879934i	$0.657587\pi$
$504$		0			0
$505$	4.00000	−	4.89898i	0.177998	−	0.218002i
$506$	22.4793			0.999326
$507$		0			0
$508$	0.375737	−	0.650796i	0.0166707	−	0.0288744i
$509$	20.7438	+	35.9293i	0.919453	+	1.59254i	0.800247	+	0.599671i	$0.204702\pi$
$509$	20.7438	+	35.9293i	0.919453	+	1.59254i	0.119206	+	0.992869i	$0.461965\pi$
$510$		0			0
$511$	−25.4059	+	44.0043i	−1.12389	+	1.94663i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−9.87451			−0.435546
$515$	−1.57116	+	0.595839i	−0.0692336	+	0.0262558i
$516$		0			0
$517$	−53.6514	+	30.9756i	−2.35958	+	1.36231i
$518$	−17.2662	+	29.9059i	−0.758632	+	1.31399i
$519$		0			0
$520$	−6.00000	+	7.34847i	−0.263117	+	0.322252i
$521$	14.5432			0.637151			0.318576	−	0.947897i	$-0.396796\pi$
$521$	14.5432			0.637151			0.318576	+	0.947897i	$0.396796\pi$
$522$		0			0
$523$	14.0978	+	24.4180i	0.616452	+	1.06773i	0.990128	+	0.140167i	$0.0447640\pi$
$523$	14.0978	+	24.4180i	0.616452	+	1.06773i	−0.373676	+	0.927559i	$0.621903\pi$
$524$		−	10.6510i		−	0.465290i
$525$		0			0
$526$	5.90588	−	3.40976i	0.257509	−	0.148673i
$527$		0			0
$528$		0			0
$529$	1.00000	−	1.73205i	0.0434783	−	0.0753066i
$530$	−4.05035	+	1.53604i	−0.175936	+	0.0667211i
$531$		0			0
$532$	7.73381	−	17.8605i	0.335303	−	0.774349i
$533$	−46.4393			−2.01151
$534$		0			0
$535$	3.91472	+	10.3227i	0.169248	+	0.446288i
$536$	3.67423	−	2.12132i	0.158703	−	0.0916271i
$537$		0			0
$538$	2.12132	−	1.22474i	0.0914566	−	0.0528025i
$539$			63.4621i			2.73351i
$540$		0			0
$541$	1.00000	+	1.73205i	0.0429934	+	0.0744667i	0.886721	−	0.462304i	$-0.152977\pi$
$541$	1.00000	+	1.73205i	0.0429934	+	0.0744667i	−0.843728	+	0.536771i	$0.819644\pi$
$542$	1.73205	−	1.00000i	0.0743980	−	0.0429537i
$543$		0			0
$544$			6.31463i			0.270737i
$545$	41.8112	+	6.79554i	1.79099	+	0.291089i
$546$		0			0
$547$	0.751475	+	1.30159i	0.0321307	+	0.0556521i	0.881644	−	0.471916i	$-0.156437\pi$
$547$	0.751475	+	1.30159i	0.0321307	+	0.0556521i	−0.849513	+	0.527568i	$0.823104\pi$
$548$	−1.11847	+	1.93725i	−0.0477788	+	0.0827554i
$549$		0			0
$550$	−4.90538	−	24.0314i	−0.209166	−	1.02470i
$551$	−29.3939	−	12.7279i	−1.25222	−	0.542228i
$552$		0			0
$553$	15.4676	−	26.7907i	0.657750	−	1.13926i
$554$	−0.790881	+	1.36985i	−0.0336013	+	0.0581992i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	14.9205	+	25.8431i	0.632204	+	1.09501i	0.987100	+	0.160103i	$0.0511827\pi$
$557$	14.9205	+	25.8431i	0.632204	+	1.09501i	−0.354897	+	0.934906i	$0.615484\pi$
$558$		0			0
$559$		−	17.1031i		−	0.723386i
$560$	−9.85499	−	1.60172i	−0.416449	−	0.0676852i
$561$		0			0
$562$		−	20.7438i		−	0.875025i
$563$		−	27.8745i		−	1.17477i	−0.809307	−	0.587385i	$-0.800157\pi$
$563$		−	27.8745i		−	1.17477i	0.809307	−	0.587385i	$-0.199843\pi$
$564$		0			0
$565$	−3.91472	−	10.3227i	−0.164693	−	0.434278i
$566$	8.93023	+	15.4676i	0.375366	+	0.650152i
$567$		0			0
$568$	−6.36396	−	3.67423i	−0.267026	−	0.154167i
$569$	18.4480			0.773381			0.386691	−	0.922209i	$-0.373618\pi$
$569$	18.4480			0.773381			0.386691	+	0.922209i	$0.373618\pi$
$570$		0			0
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$	18.0235	+	10.4059i	0.753601	+	0.435092i
$573$		0			0
$574$	−24.4373	−	42.3266i	−1.01999	−	1.76668i
$575$	21.7335	+	7.25635i	0.906350	+	0.302611i
$576$		0			0
$577$		−	25.2089i		−	1.04946i	−0.851268	−	0.524731i	$-0.824166\pi$
$577$		−	25.2089i		−	1.04946i	0.851268	−	0.524731i	$-0.175834\pi$
$578$		−	22.8745i		−	0.951454i
$579$		0			0
$580$	−2.63604	+	16.2189i	−0.109456	+	0.673451i
$581$			46.4028i			1.92511i
$582$		0			0
$583$	4.75148	+	8.22981i	0.196786	+	0.340844i
$584$	−5.68986	+	9.85513i	−0.235448	+	0.407808i
$585$		0			0
$586$	6.43725	−	11.1497i	0.265921	−	0.460588i
$587$	−12.0157	+	20.8118i	−0.495940	+	0.858993i	−0.999989	−	0.00468172i	$-0.998510\pi$
$587$	−12.0157	+	20.8118i	−0.495940	+	0.858993i	0.504049	+	0.863675i	$0.331843\pi$
$588$		0			0
$589$		0			0
$590$	3.46410	−	4.24264i	0.142615	−	0.174667i
$591$		0			0
$592$	−3.86690	+	6.69767i	−0.158929	+	0.275273i
$593$	−13.4409	−	23.2804i	−0.551953	−	0.956011i	−0.998134	−	0.0610679i	$-0.980549\pi$
$593$	−13.4409	−	23.2804i	−0.551953	−	0.956011i	0.446180	−	0.894943i	$-0.352784\pi$
$594$		0			0
$595$	62.2306	+	10.1143i	2.55120	+	0.414645i
$596$		−	14.0534i		−	0.575650i
$597$		0			0
$598$	−16.8375	+	9.72111i	−0.688535	+	0.397526i
$599$	13.4722	+	23.3345i	0.550459	+	0.953423i	0.998241	+	0.0592803i	$0.0188806\pi$
$599$	13.4722	+	23.3345i	0.550459	+	0.953423i	−0.447782	+	0.894143i	$0.647786\pi$
$600$		0			0
$601$		−	34.5323i		−	1.40860i	−0.709901	−	0.704302i	$-0.751260\pi$
$601$		−	34.5323i		−	1.40860i	0.709901	−	0.704302i	$-0.248740\pi$
$602$	15.5885	−	9.00000i	0.635338	−	0.366813i
$603$		0			0
$604$	16.4059	−	9.47194i	0.667546	−	0.385408i
$605$	−27.3112	+	10.3574i	−1.11036	+	0.421087i
$606$		0			0
$607$	−35.9293			−1.45833			−0.729163	−	0.684340i	$-0.760091\pi$
$607$	−35.9293			−1.45833			−0.729163	+	0.684340i	$0.760091\pi$
$608$	1.73205	−	4.00000i	0.0702439	−	0.162221i
$609$		0			0
$610$	0.743142	+	1.95958i	0.0300890	+	0.0793412i
$611$	26.7907	−	46.4028i	1.08384	−	1.87726i
$612$		0			0
$613$	34.1838	+	19.7360i	1.38067	+	0.797130i	0.992239	−	0.124348i	$-0.0396841\pi$
$613$	34.1838	+	19.7360i	1.38067	+	0.797130i	0.388430	+	0.921478i	$0.373017\pi$
$614$	9.72111	−	5.61249i	0.392312	−	0.226502i
$615$		0			0
$616$			21.9031i			0.882500i
$617$	0.504897	+	0.874508i	0.0203264	+	0.0352064i	0.876010	−	0.482294i	$-0.160196\pi$
$617$	0.504897	+	0.874508i	0.0203264	+	0.0352064i	−0.855683	+	0.517500i	$0.826863\pi$
$618$		0			0
$619$	21.8118			0.876689			0.438344	−	0.898807i	$-0.355565\pi$
$619$	21.8118			0.876689			0.438344	+	0.898807i	$0.355565\pi$
$620$		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
$626$	0.867729			0.0346814
$627$		0			0
$628$		−	20.7438i		−	0.827768i
$629$	24.4180	−	42.2933i	0.973611	−	1.68634i
$630$		0			0
$631$	21.4686	+	37.1848i	0.854653	+	1.48030i	0.876967	+	0.480551i	$0.159563\pi$
$631$	21.4686	+	37.1848i	0.854653	+	1.48030i	−0.0223144	+	0.999751i	$0.507103\pi$
$632$	3.46410	−	6.00000i	0.137795	−	0.238667i
$633$		0			0
$634$	34.7490			1.38006
$635$	−1.30159	−	1.06275i	−0.0516521	−	0.0421738i
$636$		0			0
$637$	−27.4441	−	47.5345i	−1.08737	−	1.88339i
$638$	36.0470			1.42712
$639$		0			0
$640$	−2.20711	−	0.358719i	−0.0872436	−	0.0141796i
$641$	7.27162	−	12.5948i	0.287212	−	0.497465i	−0.685931	−	0.727666i	$-0.740605\pi$
$641$	7.27162	−	12.5948i	0.287212	−	0.497465i	0.973143	+	0.230201i	$0.0739383\pi$
$642$		0			0
$643$	−2.87280	−	1.65861i	−0.113292	−	0.0654092i	0.442283	−	0.896875i	$-0.354169\pi$
$643$	−2.87280	−	1.65861i	−0.113292	−	0.0654092i	−0.555575	+	0.831466i	$0.687502\pi$
$644$	−17.7204	−	10.2309i	−0.698281	−	0.403153i
$645$		0			0
$646$	−10.9373	+	25.2585i	−0.430321	+	0.993783i
$647$	−0.504897			−0.0198496			−0.00992478	−	0.999951i	$-0.503159\pi$
$647$	−0.504897			−0.0198496			−0.00992478	+	0.999951i	$0.503159\pi$
$648$		0			0
$649$	−10.4059	−	6.00784i	−0.408467	−	0.235828i
$650$	14.0665	+	15.8787i	0.551735	+	0.622813i
$651$		0			0
$652$	−11.2250	+	6.48074i	−0.439604	+	0.253805i
$653$	47.7752			1.86959			0.934793	−	0.355192i	$-0.115585\pi$
$653$	47.7752			1.86959			0.934793	+	0.355192i	$0.115585\pi$
$654$		0			0
$655$	−23.5078	−	3.82071i	−0.918527	−	0.149288i
$656$	−5.47293	−	9.47939i	−0.213682	−	0.370108i
$657$		0			0
$658$	56.3911			2.19835
$659$	17.7204	+	30.6926i	0.690288	+	1.19561i	0.971743	+	0.236039i	$0.0758494\pi$
$659$	17.7204	+	30.6926i	0.690288	+	1.19561i	−0.281456	+	0.959574i	$0.590817\pi$
$660$		0			0
$661$	−32.8118	+	18.9439i	−1.27623	+	0.736832i	−0.976153	−	0.217084i	$-0.930346\pi$
$661$	−32.8118	+	18.9439i	−1.27623	+	0.736832i	−0.300077	+	0.953915i	$0.597012\pi$
$662$	11.2583	−	19.5000i	0.437567	−	0.757889i
$663$		0			0
$664$			10.3923i			0.403300i
$665$	−36.6457	−	23.4762i	−1.42106	−	0.910369i
$666$		0			0
$667$	−16.8375	+	29.1633i	−0.651949	+	1.12921i
$668$	17.2662	+	9.96863i	0.668048	+	0.385698i
$669$		0			0
$670$	−3.36396	−	8.87039i	−0.129961	−	0.342693i
$671$	3.98163	−	2.29879i	0.153709	−	0.0887439i
$672$		0			0
$673$	−1.50295			−0.0579345			−0.0289672	−	0.999580i	$-0.509222\pi$
$673$	−1.50295			−0.0579345			−0.0289672	+	0.999580i	$0.509222\pi$
$674$		0			0
$675$		0			0
$676$	−5.00000			−0.192308
$677$			12.8745i			0.494808i	0.968912	+	0.247404i	$0.0795774\pi$
$677$			12.8745i			0.494808i	−0.968912	+	0.247404i	$0.920423\pi$
$678$		0			0
$679$	−16.4059	−	9.47194i	−0.629600	−	0.363500i
$680$	13.9371	+	2.26518i	0.534462	+	0.0868657i
$681$		0			0
$682$		0			0
$683$		−	30.6863i		−	1.17418i	−0.809523	−	0.587089i	$-0.800274\pi$
$683$		−	30.6863i		−	1.17418i	0.809523	−	0.587089i	$-0.199726\pi$
$684$		0			0
$685$	3.87451	+	3.16352i	0.148037	+	0.120872i
$686$	13.2553	−	22.9588i	0.506088	−	0.876571i
$687$		0			0
$688$	3.49117	−	2.01563i	0.133099	−	0.0768450i
$689$	−7.11793	−	4.10954i	−0.271171	−	0.156561i
$690$		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
$697$	34.5595	+	59.8588i	1.30903	+	2.26731i
$698$	−14.7768	−	8.53137i	−0.559309	−	0.322917i
$699$		0			0
$700$	−7.07035	+	21.1764i	−0.267234	+	0.800394i
$701$	−20.5901	−	11.8877i	−0.777678	−	0.448993i	0.0579287	−	0.998321i	$-0.481550\pi$
$701$	−20.5901	−	11.8877i	−0.777678	−	0.448993i	−0.835607	+	0.549328i	$0.814884\pi$
$702$		0			0
$703$	−27.0683	+	20.0930i	−1.02090	+	0.757823i
$704$			4.90538i			0.184878i
$705$		0			0
$706$	−18.5314	−	10.6991i	−0.697437	−	0.402666i
$707$	6.31463	+	10.9373i	0.237486	+	0.411338i
$708$		0			0
$709$	−20.4059	−	35.3440i	−0.766359	−	1.32737i	−0.939525	−	0.342480i	$-0.888733\pi$
$709$	−20.4059	−	35.3440i	−0.766359	−	1.32737i	0.173166	−	0.984893i	$-0.444600\pi$
$710$	−10.3923	+	12.7279i	−0.390016	+	0.477670i
$711$		0			0
$712$	5.23675	−	3.02344i	0.196255	−	0.113308i
$713$		0			0
$714$		0			0
$715$	29.4323	−	36.0470i	1.10070	−	1.34808i
$716$	−3.02344	−	5.23675i	−0.112991	−	0.195706i
$717$		0			0
$718$	−3.53553	−	6.12372i	−0.131945	−	0.228535i
$719$	30.3881	+	17.5446i	1.13328	+	0.654302i	0.944759	−	0.327766i	$-0.106296\pi$
$719$	30.3881	+	17.5446i	1.13328	+	0.654302i	0.188525	+	0.982068i	$0.439629\pi$
$720$		0			0
$721$		−	3.35542i		−	0.124962i
$722$	13.8564	−	13.0000i	0.515682	−	0.483810i
$723$		0			0
$724$	13.4059	+	7.73989i	0.498226	+	0.287651i
$725$	34.8511	+	11.6360i	1.29434	+	0.432152i
$726$		0			0
$727$	21.0801	+	12.1706i	0.781818	+	0.451383i	0.837074	−	0.547090i	$-0.184264\pi$
$727$	21.0801	+	12.1706i	0.781818	+	0.451383i	−0.0552565	+	0.998472i	$0.517598\pi$
$728$	−9.47194	−	16.4059i	−0.351053	−	0.608042i
$729$		0			0
$730$	19.7103	+	16.0934i	0.729509	+	0.595642i
$731$	−22.0454	+	12.7279i	−0.815379	+	0.470759i
$732$		0			0
$733$			14.2631i			0.526819i	0.964684	+	0.263409i	$0.0848470\pi$
$733$			14.2631i			0.526819i	−0.964684	+	0.263409i	$0.915153\pi$
$734$	5.61301			0.207180
$735$		0			0
$736$	−3.96863	−	2.29129i	−0.146286	−	0.0844580i
$737$	−18.0235	+	10.4059i	−0.663905	+	0.383306i
$738$		0			0
$739$	−26.3118	+	45.5733i	−0.967894	+	1.67644i	−0.266263	+	0.963900i	$0.585789\pi$
$739$	−26.3118	+	45.5733i	−0.967894	+	1.67644i	−0.701631	+	0.712541i	$0.747544\pi$
$740$	13.3953	+	10.9373i	0.492423	+	0.402061i
$741$		0			0
$742$		−	8.65006i		−	0.317554i
$743$	0.757346	+	0.437254i	0.0277843	+	0.0160413i	0.513828	−	0.857893i	$-0.328227\pi$
$743$	0.757346	+	0.437254i	0.0277843	+	0.0160413i	−0.486043	+	0.873935i	$0.661560\pi$
$744$		0			0
$745$	−31.0174	−	5.04123i	−1.13639	−	0.184696i
$746$	−16.4188	−	9.47939i	−0.601134	−	0.347065i
$747$		0			0
$748$		−	30.9756i		−	1.13258i
$749$	−22.0454			−0.805522
$750$		0			0
$751$	−21.0000	+	12.1244i	−0.766301	+	0.442424i	−0.831553	−	0.555445i	$-0.812548\pi$
$751$	−21.0000	+	12.1244i	−0.766301	+	0.442424i	0.0652526	+	0.997869i	$0.479215\pi$
$752$	12.6293			0.460541
$753$		0			0
$754$	−27.0000	+	15.5885i	−0.983282	+	0.567698i
$755$	−15.0205	−	39.6073i	−0.546651	−	1.44146i
$756$		0			0
$757$	−3.11543	−	1.79869i	−0.113232	−	0.0653746i	0.442314	−	0.896860i	$-0.354158\pi$
$757$	−3.11543	−	1.79869i	−0.113232	−	0.0653746i	−0.555546	+	0.831485i	$0.687491\pi$
$758$	−17.2118	+	29.8118i	−0.625162	+	1.08281i
$759$		0			0
$760$	−8.20711	−	5.25770i	−0.297703	−	0.190717i
$761$		−	11.8877i		−	0.430929i	−0.976512	−	0.215465i	$-0.930873\pi$
$761$		−	11.8877i		−	0.430929i	0.976512	−	0.215465i	$-0.0691266\pi$
$762$		0			0
$763$	−42.2933	+	73.2541i	−1.53112	+	2.65198i
$764$	8.49637	−	4.90538i	0.307388	−	0.177470i
$765$		0			0
$766$	13.9373	+	24.1400i	0.503573	+	0.872215i
$767$	10.3923			0.375244
$768$		0			0
$769$	−0.0627461	−	0.108679i	−0.00226268	−	0.00391908i	0.864892	−	0.501958i	$-0.167387\pi$
$769$	−0.0627461	−	0.108679i	−0.00226268	−	0.00391908i	−0.867155	+	0.498039i	$0.834054\pi$
$770$	48.3424	+	7.85706i	1.74214	+	0.283149i
$771$		0			0
$772$	12.7279			0.458088
$773$	4.43881	−	2.56275i	0.159653	−	0.0921756i	−0.418045	−	0.908426i	$-0.637285\pi$
$773$	4.43881	−	2.56275i	0.159653	−	0.0921756i	0.577698	+	0.816251i	$0.303951\pi$
$774$		0			0
$775$		0			0
$776$	−3.67423	−	2.12132i	−0.131897	−	0.0761510i
$777$		0			0
$778$	−15.5563			−0.557722
$779$	−5.47293	−	47.3969i	−0.196088	−	1.69817i
$780$		0			0
$781$	31.2176	+	18.0235i	1.11706	+	0.644932i
$782$	25.0604	+	14.4686i	0.896158	+	0.517397i
$783$		0			0
$784$	6.46863	−	11.2040i	0.231022	−	0.400143i
$785$	−45.7838	−	7.44121i	−1.63409	−	0.265588i
$786$		0			0
$787$	−36.6808			−1.30753			−0.653765	−	0.756698i	$-0.726811\pi$
$787$	−36.6808			−1.30753			−0.653765	+	0.756698i	$0.726811\pi$
$788$	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
$793$	−1.98822	+	3.44369i	−0.0706036	+	0.122289i
$794$	−3.10029	−	5.36985i	−0.110025	−	0.190569i
$795$		0			0
$796$	−2.53137	+	4.38447i	−0.0897221	+	0.155403i
$797$		−	10.0627i		−	0.356441i	−0.983991	−	0.178220i	$-0.942966\pi$
$797$		−	10.0627i		−	0.356441i	0.983991	−	0.178220i	$-0.0570340\pi$
$798$		0			0
$799$	−79.7490			−2.82132
$800$	−1.58346	+	4.74264i	−0.0559839	+	0.167678i
$801$		0			0
$802$	−8.35218	+	4.82213i	−0.294926	+	0.170275i
$803$	27.9109	−	48.3431i	0.984955	−	1.70599i
$804$		0			0
$805$	−28.9373	+	35.4408i	−1.01990	+	1.24912i
$806$		0			0
$807$		0			0
$808$	1.41421	+	2.44949i	0.0497519	+	0.0861727i
$809$		−	19.5328i		−	0.686736i	−0.939201	−	0.343368i	$-0.888432\pi$
$809$		−	19.5328i		−	0.686736i	0.939201	−	0.343368i	$-0.111568\pi$
$810$		0			0
$811$	−11.9059	+	6.87386i	−0.418072	+	0.241374i	−0.694252	−	0.719732i	$-0.744265\pi$
$811$	−11.9059	+	6.87386i	−0.418072	+	0.241374i	0.276180	+	0.961106i	$0.410931\pi$
$812$	−28.4158	−	16.4059i	−0.997200	−	0.575734i
$813$		0			0
$814$	18.9686	−	32.8546i	0.664850	−	1.15155i
$815$	10.2771	+	27.0995i	0.359990	+	0.949253i
$816$		0			0
$817$	17.4558	−	2.01563i	0.610702	−	0.0705178i
$818$	29.4449			1.02952
$819$		0			0
$820$	−22.8853	+	8.67889i	−0.799188	+	0.303080i
$821$	−15.8448	+	9.14802i	−0.552989	+	0.319268i	−0.750327	−	0.661067i	$-0.770104\pi$
$821$	−15.8448	+	9.14802i	−0.552989	+	0.319268i	0.197338	+	0.980336i	$0.436770\pi$
$822$		0			0
$823$	3.11543	−	1.79869i	0.108597	−	0.0626985i	−0.444718	−	0.895671i	$-0.646696\pi$
$823$	3.11543	−	1.79869i	0.108597	−	0.0626985i	0.553315	+	0.832972i	$0.313363\pi$
$824$		−	0.751475i		−	0.0261789i
$825$		0			0
$826$	5.46863	+	9.47194i	0.190278	+	0.329571i
$827$	30.2565	−	17.4686i	1.05212	−	0.607444i	0.128880	−	0.991660i	$-0.458862\pi$
$827$	30.2565	−	17.4686i	1.05212	−	0.607444i	0.923243	+	0.384216i	$0.125528\pi$
$828$		0			0
$829$			51.7442i			1.79715i	0.438821	+	0.898575i	$0.355396\pi$
$829$			51.7442i			1.79715i	−0.438821	+	0.898575i	$0.644604\pi$
$830$	22.9369	+	3.72792i	0.796152	+	0.129398i
$831$		0			0
$832$	−2.12132	−	3.67423i	−0.0735436	−	0.127381i
$833$	−40.8470	+	70.7490i	−1.41526	+	2.45131i
$834$		0			0
$835$	28.1955	−	34.5323i	0.975747	−	1.19504i
$836$	−8.49637	+	19.6215i	−0.293853	+	0.678624i
$837$		0			0
$838$	10.8936	−	18.8683i	0.376313	−	0.651794i
$839$	−24.4949	+	42.4264i	−0.845658	+	1.46472i	0.0393910	+	0.999224i	$0.487458\pi$
$839$	−24.4949	+	42.4264i	−0.845658	+	1.46472i	−0.885049	+	0.465498i	$0.845875\pi$
$840$		0			0
$841$	−12.5000	+	21.6506i	−0.431034	+	0.746574i
$842$	−18.1322	−	31.4059i	−0.624877	−	1.08232i
$843$		0			0
$844$		−	13.7477i		−	0.473216i
$845$	−1.79360	+	11.0355i	−0.0617016	+	0.379634i
$846$		0			0
$847$		−	58.3267i		−	2.00413i
$848$		−	1.93725i		−	0.0665256i
$849$		0			0
$850$	9.99899	−	29.9480i	0.342962	−	1.02721i
$851$	17.7204	+	30.6926i	0.607447	+	1.05213i
$852$		0			0
$853$	4.86101	+	2.80651i	0.166438	+	0.0960929i	0.580905	−	0.813971i	$-0.302699\pi$
$853$	4.86101	+	2.80651i	0.166438	+	0.0960929i	−0.414467	+	0.910064i	$0.636032\pi$
$854$	−4.18495			−0.143206
$855$		0			0
$856$	−4.93725			−0.168752
$857$	−7.03688	−	4.06275i	−0.240375	−	0.138781i	0.374974	−	0.927035i	$-0.377652\pi$
$857$	−7.03688	−	4.06275i	−0.240375	−	0.138781i	−0.615349	+	0.788255i	$0.710985\pi$
$858$		0			0
$859$	4.03137	+	6.98254i	0.137549	+	0.238241i	0.926568	−	0.376127i	$-0.122744\pi$
$859$	4.03137	+	6.98254i	0.137549	+	0.238241i	−0.789020	+	0.614368i	$0.789411\pi$
$860$	−3.19635	−	8.42842i	−0.108995	−	0.287407i
$861$		0			0
$862$			17.1464i			0.584010i
$863$			5.81176i			0.197835i	0.995096	+	0.0989173i	$0.0315379\pi$
$863$			5.81176i			0.197835i	−0.995096	+	0.0989173i	$0.968462\pi$
$864$		0			0
$865$	−17.5184	−	2.84725i	−0.595642	−	0.0968093i
$866$		−	18.2073i		−	0.618709i
$867$		0			0
$868$		0			0
$869$	−16.9927	+	29.4323i	−0.576439	+	0.998422i
$870$		0			0
$871$	9.00000	−	15.5885i	0.304953	−	0.528195i
$872$	−9.47194	+	16.4059i	−0.320760	+	0.555573i
$873$		0			0
$874$	−11.9059	−	16.0390i	−0.402722	−	0.542528i
$875$	44.2024	+	23.2014i	1.49431	+	0.784351i
$876$		0			0
$877$	8.10954	−	14.0461i	0.273840	−	0.474305i	−0.696002	−	0.718040i	$-0.745040\pi$
$877$	8.10954	−	14.0461i	0.273840	−	0.474305i	0.969842	+	0.243735i	$0.0783728\pi$
$878$	2.65242	+	4.59412i	0.0895147	+	0.155044i
$879$		0			0
$880$	10.8267	+	1.75966i	0.364968	+	0.0593180i
$881$			27.5328i			0.927603i	0.885939	+	0.463802i	$0.153515\pi$
$881$			27.5328i			0.927603i	−0.885939	+	0.463802i	$0.846485\pi$
$882$		0			0
$883$	−14.0978	+	8.13935i	−0.474428	+	0.273911i	−0.718091	−	0.695949i	$-0.754984\pi$
$883$	−14.0978	+	8.13935i	−0.474428	+	0.273911i	0.243664	+	0.969860i	$0.421651\pi$
$884$	13.3953	+	23.2014i	0.450534	+	0.780348i
$885$		0			0
$886$			1.62337i			0.0545382i
$887$	12.2330	−	7.06275i	0.410745	−	0.237144i	−0.280365	−	0.959894i	$-0.590455\pi$
$887$	12.2330	−	7.06275i	0.410745	−	0.237144i	0.691110	+	0.722750i	$0.257122\pi$
$888$		0			0
$889$	2.90588	−	1.67771i	0.0974601	−	0.0562686i
$890$	−4.79453	−	12.6426i	−0.160713	−	0.423782i
$891$		0			0
$892$	−9.23676			−0.309269
$893$	50.5170	+	21.8745i	1.69049	+	0.732002i
$894$		0			0
$895$	−12.6426	+	4.79453i	−0.422596	+	0.160263i
$896$	2.23256	−	3.86690i	0.0745845	−	0.129184i
$897$		0			0
$898$	1.12721	+	0.650796i	0.0376156	+	0.0217174i
$899$		0			0
$900$		0			0
$901$			12.2330i			0.407541i
$902$	26.8468	+	46.5000i	0.893900	+	1.54828i
$903$		0			0
$904$	4.93725			0.164211
$905$	21.8917	−	26.8118i	0.727705	−	0.891253i
$906$		0			0
$907$	−28.9470	+	50.1377i	−0.961170	+	1.66479i	−0.241598	+	0.970376i	$0.577672\pi$
$907$	−28.9470	+	50.1377i	−0.961170	+	1.66479i	−0.719572	+	0.694418i	$0.755662\pi$
$908$	6.11652	−	3.53137i	0.202984	−	0.117193i
$909$		0			0
$910$	−39.6073	+	15.0205i	−1.31297	+	0.497924i
$911$	43.7834			1.45061			0.725305	−	0.688428i	$-0.241699\pi$
$911$	43.7834			1.45061			0.725305	+	0.688428i	$0.241699\pi$
$912$		0			0
$913$		−	50.9782i		−	1.68713i
$914$	0.0768479	−	0.133105i	0.00254190	−	0.00440271i
$915$		0			0
$916$	−11.9373	−	20.6759i	−0.394418	−	0.683152i
$917$	23.7789	−	41.1863i	0.785249	−	1.36009i
$918$		0			0
$919$	34.8118			1.14833			0.574167	−	0.818738i	$-0.305326\pi$
$919$	34.8118			1.14833			0.574167	+	0.818738i	$0.305326\pi$
$920$	−6.48074	+	7.93725i	−0.213664	+	0.261684i
$921$		0			0
$922$	−6.31959	−	10.9459i	−0.208125	−	0.360483i
$923$	−31.1769			−1.02620
$924$		0			0
$925$	28.9449	−	25.6416i	0.951701	−	0.843089i
$926$	−4.60520	+	7.97644i	−0.151336	+	0.262122i
$927$		0			0
$928$	−6.36396	−	3.67423i	−0.208907	−	0.120613i
$929$	26.2167	+	15.1362i	0.860143	+	0.496604i	0.864060	−	0.503388i	$-0.167913\pi$
$929$	26.2167	+	15.1362i	0.860143	+	0.496604i	−0.00391689	+	0.999992i	$0.501247\pi$
$930$		0			0
$931$	45.2804	−	33.6120i	1.48400	−	1.10159i
$932$	−21.7944			−0.713899
$933$		0			0
$934$	−12.5314	−	7.23499i	−0.410039	−	0.236736i
$935$	−68.3665	−	11.1116i	−2.23582	−	0.363387i
$936$		0			0
$937$	36.0624	−	20.8207i	1.17811	−	0.680181i	0.222532	−	0.974925i	$-0.428568\pi$
$937$	36.0624	−	20.8207i	1.17811	−	0.680181i	0.955576	+	0.294744i	$0.0952343\pi$
$938$	18.9439			0.618540
$939$		0			0
$940$	4.53036	−	27.8741i	0.147764	−	0.909153i
$941$	6.12372	+	10.6066i	0.199628	+	0.345765i	0.948408	−	0.317053i	$-0.102693\pi$
$941$	6.12372	+	10.6066i	0.199628	+	0.345765i	−0.748780	+	0.662819i	$0.769360\pi$
$942$		0			0
$943$	−50.1602			−1.63344
$944$	1.22474	+	2.12132i	0.0398621	+	0.0690431i
$945$		0			0
$946$	−17.1255	+	9.88741i	−0.556798	+	0.321467i
$947$	−0.306788	+	0.531373i	−0.00996928	+	0.0172673i	−0.870967	−	0.491342i	$-0.836507\pi$
$947$	−0.306788	+	0.531373i	−0.00996928	+	0.0172673i	0.860998	+	0.508609i	$0.169840\pi$
$948$		0			0
$949$			48.2801i			1.56724i
$950$	−14.5484	+	16.2279i	−0.472011	+	0.526503i
$951$		0			0
$952$	−14.0978	+	24.4180i	−0.456911	+	0.791394i
$953$	1.84073	+	1.06275i	0.0596271	+	0.0344257i	0.529517	−	0.848299i	$-0.322373\pi$
$953$	1.84073	+	1.06275i	0.0596271	+	0.0344257i	−0.469890	+	0.882725i	$0.655706\pi$
$954$		0			0
$955$	−7.77888	−	20.5120i	−0.251719	−	0.663754i
$956$	23.1933	−	13.3907i	0.750125	−	0.433085i
$957$		0			0
$958$	−35.3553			−1.14228
$959$	−8.65006	+	4.99412i	−0.279325	+	0.161268i
$960$		0			0
$961$	31.0000			1.00000
$962$			32.8118i			1.05789i
$963$		0			0
$964$	6.00000	+	3.46410i	0.193247	+	0.111571i
$965$	4.56575	−	28.0919i	0.146977	−	0.904310i
$966$		0			0
$967$	30.3169	+	17.5034i	0.974924	+	0.562873i	0.900734	−	0.434371i	$-0.143029\pi$
$967$	30.3169	+	17.5034i	0.974924	+	0.562873i	0.0741904	+	0.997244i	$0.476363\pi$
$968$		−	13.0627i		−	0.419853i
$969$		0			0
$970$	−6.00000	+	7.34847i	−0.192648	+	0.235945i
$971$	13.4722	−	23.3345i	0.432343	−	0.748841i	−0.564731	−	0.825275i	$-0.691020\pi$
$971$	13.4722	−	23.3345i	0.432343	−	0.748841i	0.997075	+	0.0764343i	$0.0243535\pi$
$972$		0			0
$973$	15.4676	−	8.93023i	0.495869	−	0.286290i
$974$	−23.7673	−	13.7220i	−0.761552	−	0.439682i
$975$		0			0
$976$	−0.937254			−0.0300008
$977$			25.0627i			0.801828i	0.916116	+	0.400914i	$0.131307\pi$
$977$			25.0627i			0.801828i	−0.916116	+	0.400914i	$0.868693\pi$
$978$		0			0
$979$	−25.6882	+	14.8311i	−0.821000	+	0.474004i
$980$	−22.4080	−	18.2960i	−0.715797	−	0.584446i
$981$		0			0
$982$	−14.4291	−	24.9920i	−0.460452	−	0.797527i
$983$	−37.1304	−	21.4373i	−1.18428	−	0.683742i	−0.227276	−	0.973830i	$-0.572982\pi$
$983$	−37.1304	−	21.4373i	−1.18428	−	0.683742i	−0.957000	+	0.290088i	$0.906315\pi$
$984$		0			0
$985$	32.5919	−	12.3600i	1.03846	−	0.393822i
$986$	40.1860	+	23.2014i	1.27978	+	0.738884i
$987$		0			0
$988$	−2.12132	−	18.3712i	−0.0674882	−	0.584465i
$989$		−	18.4735i		−	0.587424i
$990$		0			0
$991$	40.4059	+	23.3283i	1.28354	+	0.741049i	0.977493	−	0.210969i	$-0.0676618\pi$
$991$	40.4059	+	23.3283i	1.28354	+	0.741049i	0.306042	+	0.952018i	$0.400995\pi$
$992$		0			0
$993$		0			0
$994$	−16.4059	−	28.4158i	−0.520363	−	0.901295i
$995$	8.76893	+	7.15980i	0.277994	+	0.226981i
$996$		0			0
$997$	−47.3969	+	27.3646i	−1.50108	+	0.866647i	−0.501077	+	0.865403i	$0.667063\pi$
$997$	−47.3969	+	27.3646i	−1.50108	+	0.866647i	−0.999999	+	0.00124421i	$0.999604\pi$
$998$	−14.6138	+	8.43725i	−0.462590	+	0.267077i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.q.a.179.8	yes	16
3.2	odd	2	inner	1710.2.q.a.179.2	✓	16
5.4	even	2	inner	1710.2.q.a.179.3	yes	16
15.14	odd	2	inner	1710.2.q.a.179.5	yes	16
19.12	odd	6	inner	1710.2.q.a.449.6	yes	16
57.50	even	6	inner	1710.2.q.a.449.4	yes	16
95.69	odd	6	inner	1710.2.q.a.449.1	yes	16
285.164	even	6	inner	1710.2.q.a.449.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.q.a.179.2	✓	16	3.2	odd	2	inner
1710.2.q.a.179.3	yes	16	5.4	even	2	inner
1710.2.q.a.179.5	yes	16	15.14	odd	2	inner
1710.2.q.a.179.8	yes	16	1.1	even	1	trivial
1710.2.q.a.449.1	yes	16	95.69	odd	6	inner
1710.2.q.a.449.4	yes	16	57.50	even	6	inner
1710.2.q.a.449.6	yes	16	19.12	odd	6	inner
1710.2.q.a.449.7	yes	16	285.164	even	6	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.09077 - 0.792893i) q^{5} +4.46512i q^{7} +1.00000i q^{8} +(2.20711 + 0.358719i) q^{10} -4.90538i q^{11} +(2.12132 + 3.67423i) q^{13} +(-2.23256 + 3.86690i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.15731 - 5.46863i) q^{17} +(-3.50000 + 2.59808i) q^{19} +(1.73205 + 1.41421i) q^{20} +(2.45269 - 4.24818i) q^{22} +(2.29129 + 3.96863i) q^{23} +(3.74264 - 3.31552i) q^{25} +4.24264i q^{26} +(-3.86690 + 2.23256i) q^{28} +(3.67423 + 6.36396i) q^{29} +(-0.866025 + 0.500000i) q^{32} +(5.46863 - 3.15731i) q^{34} +(3.54036 + 9.33553i) q^{35} +7.73381 q^{37} +(-4.33013 + 0.500000i) q^{38} +(0.792893 + 2.09077i) q^{40} +(-5.47293 + 9.47939i) q^{41} +(-3.49117 - 2.01563i) q^{43} +(4.24818 - 2.45269i) q^{44} +4.58258i q^{46} +(-6.31463 - 10.9373i) q^{47} -12.9373 q^{49} +(4.89898 - 1.00000i) q^{50} +(-2.12132 + 3.67423i) q^{52} +(-1.67771 + 0.968627i) q^{53} +(-3.88944 - 10.2560i) q^{55} -4.46512 q^{56} +7.34847i q^{58} +(1.22474 - 2.12132i) q^{59} +(0.468627 + 0.811686i) q^{61} -1.00000 q^{64} +(7.34847 + 6.00000i) q^{65} +(-2.12132 - 3.67423i) q^{67} +6.31463 q^{68} +(-1.60172 + 9.85499i) q^{70} +(-3.67423 + 6.36396i) q^{71} +(9.85513 + 5.68986i) q^{73} +(6.69767 + 3.86690i) q^{74} +(-4.00000 - 1.73205i) q^{76} +21.9031 q^{77} +(-6.00000 - 3.46410i) q^{79} +(-0.358719 + 2.20711i) q^{80} +(-9.47939 + 5.47293i) q^{82} +10.3923 q^{83} +(2.26518 - 13.9371i) q^{85} +(-2.01563 - 3.49117i) q^{86} +4.90538 q^{88} +(-3.02344 - 5.23675i) q^{89} +(-16.4059 + 9.47194i) q^{91} +(-2.29129 + 3.96863i) q^{92} -12.6293i q^{94} +(-5.25770 + 8.20711i) q^{95} +(-2.12132 + 3.67423i) q^{97} +(-11.2040 - 6.46863i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 24 q^{10} - 8 q^{16} - 56 q^{19} - 8 q^{25} + 24 q^{34} + 24 q^{40} - 80 q^{49} - 8 q^{55} - 56 q^{61} - 16 q^{64} - 24 q^{70} - 64 q^{76} - 96 q^{79} - 24 q^{85} - 72 q^{91}+O(q^{100}) \) 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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