LMFDB - Embedded newform 1710.2.q.a.179.5

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			179.5
Root			$-1.40721 + 0.140577i$ of defining polynomial
Character	$\chi$	$=$	1710.179
Dual form			1710.2.q.a.449.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.358719 - 2.20711i) q^{5} -4.46512i q^{7} +1.00000i q^{8} +(0.792893 - 2.09077i) q^{10} +4.90538i q^{11} +(-2.12132 - 3.67423i) q^{13} +(2.23256 - 3.86690i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.15731 - 5.46863i) q^{17} +(-3.50000 + 2.59808i) q^{19} +(1.73205 - 1.41421i) q^{20} +(-2.45269 + 4.24818i) q^{22} +(2.29129 + 3.96863i) q^{23} +(-4.74264 + 1.58346i) q^{25} -4.24264i q^{26} +(3.86690 - 2.23256i) q^{28} +(-3.67423 - 6.36396i) q^{29} +(-0.866025 + 0.500000i) q^{32} +(5.46863 - 3.15731i) q^{34} +(-9.85499 + 1.60172i) q^{35} -7.73381 q^{37} +(-4.33013 + 0.500000i) q^{38} +(2.20711 - 0.358719i) q^{40} +(5.47293 - 9.47939i) q^{41} +(3.49117 + 2.01563i) q^{43} +(-4.24818 + 2.45269i) q^{44} +4.58258i q^{46} +(-6.31463 - 10.9373i) q^{47} -12.9373 q^{49} +(-4.89898 - 1.00000i) q^{50} +(2.12132 - 3.67423i) q^{52} +(-1.67771 + 0.968627i) q^{53} +(10.8267 - 1.75966i) q^{55} +4.46512 q^{56} -7.34847i q^{58} +(-1.22474 + 2.12132i) q^{59} +(0.468627 + 0.811686i) q^{61} -1.00000 q^{64} +(-7.34847 + 6.00000i) q^{65} +(2.12132 + 3.67423i) q^{67} +6.31463 q^{68} +(-9.33553 - 3.54036i) q^{70} +(3.67423 - 6.36396i) q^{71} +(-9.85513 - 5.68986i) q^{73} +(-6.69767 - 3.86690i) q^{74} +(-4.00000 - 1.73205i) q^{76} +21.9031 q^{77} +(-6.00000 - 3.46410i) q^{79} +(2.09077 + 0.792893i) q^{80} +(9.47939 - 5.47293i) q^{82} +10.3923 q^{83} +(-13.2024 - 5.00682i) q^{85} +(2.01563 + 3.49117i) q^{86} -4.90538 q^{88} +(3.02344 + 5.23675i) q^{89} +(-16.4059 + 9.47194i) q^{91} +(-2.29129 + 3.96863i) q^{92} -12.6293i q^{94} +(6.98975 + 6.79289i) q^{95} +(2.12132 - 3.67423i) q^{97} +(-11.2040 - 6.46863i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.358719	−	2.20711i	−0.160424	−	0.987048i
$5$	−0.358719	−	2.20711i	−0.160424	−	0.987048i
$6$		0			0
$7$		−	4.46512i		−	1.68765i	−0.536615	−	0.843827i	$-0.680297\pi$
$7$		−	4.46512i		−	1.68765i	0.536615	−	0.843827i	$-0.319703\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.792893	−	2.09077i	0.250735	−	0.661160i
$11$			4.90538i			1.47903i	0.673141	+	0.739514i	$0.264945\pi$
$11$			4.90538i			1.47903i	−0.673141	+	0.739514i	$0.735055\pi$
$12$		0			0
$13$	−2.12132	−	3.67423i	−0.588348	−	1.01905i	−0.994449	−	0.105221i	$-0.966445\pi$
$13$	−2.12132	−	3.67423i	−0.588348	−	1.01905i	0.406100	−	0.913828i	$-0.366888\pi$
$14$	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
$25$	−4.74264	+	1.58346i	−0.948528	+	0.316693i
$26$		−	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	$-0.927652\pi$
$29$	−3.67423	−	6.36396i	−0.682288	−	1.18176i	0.291993	−	0.956421i	$-0.405682\pi$
$30$		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
$35$	−9.85499	+	1.60172i	−1.66580	+	0.270741i
$36$		0			0
$37$	−7.73381			−1.27143			−0.635715	−	0.771924i	$-0.719295\pi$
$37$	−7.73381			−1.27143			−0.635715	+	0.771924i	$0.719295\pi$
$38$	−4.33013	+	0.500000i	−0.702439	+	0.0811107i
$39$		0			0
$40$	2.20711	−	0.358719i	0.348974	−	0.0567185i
$41$	5.47293	−	9.47939i	0.854728	−	1.48043i	−0.0221696	−	0.999754i	$-0.507057\pi$
$41$	5.47293	−	9.47939i	0.854728	−	1.48043i	0.876897	−	0.480678i	$-0.159609\pi$
$42$		0			0
$43$	3.49117	+	2.01563i	0.532398	+	0.307380i	0.741992	−	0.670408i	$-0.233881\pi$
$43$	3.49117	+	2.01563i	0.532398	+	0.307380i	−0.209595	+	0.977788i	$0.567214\pi$
$44$	−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
$55$	10.8267	−	1.75966i	1.45987	−	0.237272i
$56$	4.46512			0.596676
$57$		0			0
$58$		−	7.34847i		−	0.964901i
$59$	−1.22474	+	2.12132i	−0.159448	+	0.276172i	−0.934670	−	0.355517i	$-0.884305\pi$
$59$	−1.22474	+	2.12132i	−0.159448	+	0.276172i	0.775222	+	0.631689i	$0.217638\pi$
$60$		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	0.966017	−	0.258478i	$-0.0832208\pi$
$67$	2.12132	+	3.67423i	0.259161	+	0.448879i	−0.706857	+	0.707357i	$0.749887\pi$
$68$	6.31463			0.765761
$69$		0			0
$70$	−9.33553	−	3.54036i	−1.11581	−	0.423154i
$71$	3.67423	−	6.36396i	0.436051	−	0.755263i	−0.561329	−	0.827592i	$-0.689710\pi$
$71$	3.67423	−	6.36396i	0.436051	−	0.755263i	0.997381	+	0.0723293i	$0.0230432\pi$
$72$		0			0
$73$	−9.85513	−	5.68986i	−1.15346	−	0.665948i	−0.203728	−	0.979027i	$-0.565306\pi$
$73$	−9.85513	−	5.68986i	−1.15346	−	0.665948i	−0.949727	+	0.313080i	$0.898639\pi$
$74$	−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	$0.794102\pi$
$80$	2.09077	+	0.792893i	0.233755	+	0.0886482i
$81$		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
$85$	−13.2024	−	5.00682i	−1.43200	−	0.543066i
$86$	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	0.980588	−	0.196080i	$-0.0628212\pi$
$89$	3.02344	+	5.23675i	0.320484	+	0.555094i	−0.660104	+	0.751174i	$0.729488\pi$
$90$		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
$95$	6.98975	+	6.79289i	0.717133	+	0.696936i
$96$		0			0
$97$	2.12132	−	3.67423i	0.215387	−	0.373062i	−0.738005	−	0.674795i	$-0.764232\pi$
$97$	2.12132	−	3.67423i	0.215387	−	0.373062i	0.953392	+	0.301733i	$0.0975652\pi$
$98$	−11.2040	−	6.46863i	−1.13177	−	0.653430i
$99$		0			0
$100$	−3.74264	−	3.31552i	−0.374264	−	0.331552i
$101$	−2.44949	+	1.41421i	−0.243733	+	0.140720i	−0.616891	−	0.787048i	$-0.711608\pi$
$101$	−2.44949	+	1.41421i	−0.243733	+	0.140720i	0.373158	+	0.927768i	$0.378275\pi$
$102$		0			0
$103$	0.751475			0.0740450			0.0370225	−	0.999314i	$-0.488213\pi$
$103$	0.751475			0.0740450			0.0370225	+	0.999314i	$0.488213\pi$
$104$	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	$0.304846\pi$
$110$	10.2560	+	3.88944i	0.977873	+	0.370844i
$111$		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	0.882215	−	0.470848i	$-0.156052\pi$
$127$	0.375737	+	0.650796i	0.0333413	+	0.0577488i	−0.848873	+	0.528596i	$0.822718\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−9.36396	+	1.52192i	−0.821274	+	0.133481i
$131$	9.22401	+	5.32548i	0.805906	+	0.465290i	0.845532	−	0.533925i	$-0.179283\pi$
$131$	9.22401	+	5.32548i	0.805906	+	0.465290i	−0.0396264	+	0.999215i	$0.512617\pi$
$132$		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	0.907375	−	0.420321i	$-0.138083\pi$
$149$	12.1706	+	7.02670i	0.997054	+	0.575650i	0.0896790	+	0.995971i	$0.471416\pi$
$150$		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	0.997403	−	0.0720167i	$-0.0229435\pi$
$157$	17.9647	+	10.3719i	1.43374	+	0.827768i	0.436333	+	0.899785i	$0.356277\pi$
$158$	−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	$-0.830529\pi$
$163$		−	12.9615i		−	1.01522i	0.861586	−	0.507611i	$-0.169471\pi$
$164$	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
$175$	7.07035	+	21.1764i	0.534468	+	1.60079i
$176$	−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	$-0.427441\pi$
$179$	6.04688			0.451965			0.225982	+	0.974131i	$0.427441\pi$
$180$		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
$185$	2.77427	+	17.0693i	0.203968	+	1.25496i
$186$		0			0
$187$	26.8257	+	15.4878i	1.96169	+	1.13258i
$188$	6.31463	−	10.9373i	0.460541	−	0.797681i
$189$		0			0
$190$	2.65685	+	9.37769i	0.192748	+	0.680329i
$191$			9.81076i			0.709882i	0.934889	+	0.354941i	$0.115499\pi$
$191$			9.81076i			0.709882i	−0.934889	+	0.354941i	$0.884501\pi$
$192$		0			0
$193$	−6.36396	+	11.0227i	−0.458088	+	0.793432i	−0.998860	−	0.0477376i	$-0.984799\pi$
$193$	−6.36396	+	11.0227i	−0.458088	+	0.793432i	0.540772	+	0.841169i	$0.318132\pi$
$194$	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	$0.775903\pi$
$200$	−1.58346	−	4.74264i	−0.111968	−	0.335355i
$201$		0			0
$202$	−2.82843			−0.199007
$203$	−28.4158	+	16.4059i	−1.99440	+	1.15147i
$204$		0			0
$205$	−22.8853	−	8.67889i	−1.59838	−	0.606160i
$206$	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
$215$	3.19635	−	8.42842i	0.217989	−	0.574813i
$216$		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	−0.668933	−	0.743322i	$-0.733249\pi$
$223$	4.61838	−	7.99927i	0.309269	−	0.535670i	0.978203	+	0.207652i	$0.0665822\pi$
$224$	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	$0.789316\pi$
$230$	10.1142	−	1.64386i	0.666913	−	0.108393i
$231$		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	$0.333425\pi$
$239$			26.7813i			1.73234i	−0.499750	+	0.866170i	$0.666575\pi$
$240$		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
$245$	4.64084	+	28.5539i	0.296493	+	1.82424i
$246$		0			0
$247$	16.9706	+	7.34847i	1.07981	+	0.467572i
$248$		0			0
$249$		0			0
$250$	−0.449747	+	11.1713i	−0.0284445	+	0.706534i
$251$	6.12372	−	3.53553i	0.386526	−	0.223161i	−0.294128	−	0.955766i	$-0.595029\pi$
$251$	6.12372	−	3.53553i	0.386526	−	0.223161i	0.680654	+	0.732605i	$0.261696\pi$
$252$		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
$260$	−8.87039	−	3.36396i	−0.550118	−	0.208624i
$261$		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	−0.900944	−	0.433934i	$-0.857125\pi$
$269$	−1.22474	+	2.12132i	−0.0746740	+	0.129339i	0.826270	+	0.563274i	$0.190458\pi$
$270$		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
$275$	−7.76749	−	23.2645i	−0.468397	−	1.40290i
$276$		0			0
$277$		−	1.58176i		−	0.0950388i	−0.998870	−	0.0475194i	$-0.984868\pi$
$277$		−	1.58176i		−	0.0950388i	0.998870	−	0.0475194i	$-0.0151316\pi$
$278$		−	4.00000i		−	0.239904i
$279$		0			0
$280$	−1.60172	−	9.85499i	−0.0957213	−	0.588948i
$281$	10.3719	+	17.9647i	0.618736	+	1.07168i	0.989717	+	0.143042i	$0.0456883\pi$
$281$	10.3719	+	17.9647i	0.618736	+	1.07168i	−0.370981	+	0.928641i	$0.620978\pi$
$282$		0			0
$283$	−15.4676	−	8.93023i	−0.919454	−	0.530847i	−0.0359933	−	0.999352i	$-0.511459\pi$
$283$	−15.4676	−	8.93023i	−0.919454	−	0.530847i	−0.883461	+	0.468505i	$0.844793\pi$
$284$	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
$290$	−16.2189	+	2.63604i	−0.952404	+	0.154794i
$291$		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
$295$	5.12132	+	1.94218i	0.298175	+	0.113078i
$296$		−	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	−0.980554	−	0.196248i	$-0.937124\pi$
$307$	−5.61249	+	9.72111i	−0.320321	+	0.554813i	0.660233	+	0.751061i	$0.270458\pi$
$308$	10.9515	+	18.9686i	0.624022	+	1.08084i
$309$		0			0
$310$		0			0
$311$			14.1421i			0.801927i	0.916094	+	0.400963i	$0.131325\pi$
$311$			14.1421i			0.801927i	−0.916094	+	0.400963i	$0.868675\pi$
$312$		0			0
$313$	−0.751475	+	0.433864i	−0.0424759	+	0.0245235i	−0.521088	−	0.853503i	$-0.674474\pi$
$313$	−0.751475	+	0.433864i	−0.0424759	+	0.0245235i	0.478612	+	0.878027i	$0.341140\pi$
$314$	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
$320$	0.358719	+	2.20711i	0.0200530	+	0.123381i
$321$		0			0
$322$	20.4617			1.14029
$323$	3.15731	+	27.3431i	0.175678	+	1.52141i
$324$		0			0
$325$	15.8787	+	14.0665i	0.880791	+	0.780271i
$326$	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
$340$	−2.26518	−	13.9371i	−0.122847	−	0.755843i
$341$		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
$355$	−15.3640	−	5.82655i	−0.815434	−	0.309241i
$356$	−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	0.652817	−	0.757516i	$-0.273587\pi$
$359$	6.12372	+	3.53553i	0.323198	+	0.186598i	−0.329619	+	0.944114i	$0.606920\pi$
$360$		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
$365$	−9.02290	+	23.7924i	−0.472280	+	1.24535i
$366$		0			0
$367$	−4.86101	+	2.80651i	−0.253743	+	0.146498i	−0.621477	−	0.783433i	$-0.713467\pi$
$367$	−4.86101	+	2.80651i	−0.253743	+	0.146498i	0.367734	+	0.929931i	$0.380134\pi$
$368$	−4.58258			−0.238883
$369$		0			0
$370$	−6.13208	+	16.1696i	−0.318792	+	0.840618i
$371$	4.32503	+	7.49117i	0.224544	+	0.388922i
$372$		0			0
$373$	18.9588			0.981648			0.490824	−	0.871259i	$-0.336696\pi$
$373$	18.9588			0.981648			0.490824	+	0.871259i	$0.336696\pi$
$374$	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	$0.654764\pi$
$380$	−2.38794	+	9.44975i	−0.122499	+	0.484762i
$381$		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
$385$	−7.85706	−	48.3424i	−0.400433	−	2.46376i
$386$	−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	−0.117942	−	0.993020i	$-0.537630\pi$
$389$	13.4722	−	7.77817i	0.683067	−	0.394369i	0.801010	+	0.598651i	$0.204296\pi$
$390$		0			0
$391$	28.9373			1.46342
$392$		−	12.9373i		−	0.653430i
$393$		0			0
$394$	13.5000	+	7.79423i	0.680120	+	0.392668i
$395$	−5.49333	+	14.4853i	−0.276399	+	0.728834i
$396$		0			0
$397$	5.36985	+	3.10029i	0.269505	+	0.155599i	0.628663	−	0.777678i	$-0.283603\pi$
$397$	5.36985	+	3.10029i	0.269505	+	0.155599i	−0.359158	+	0.933277i	$0.616936\pi$
$398$			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	−0.720138	−	0.693831i	$-0.755922\pi$
$401$	4.82213	−	8.35218i	0.240806	−	0.417088i	0.960944	+	0.276743i	$0.0892550\pi$
$402$		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
$415$	−3.72792	−	22.9369i	−0.182996	−	1.12593i
$416$	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	$0.178630\pi$
$419$			21.7872i			1.06437i	−0.846627	+	0.532187i	$0.821370\pi$
$420$		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	0.582254	−	0.813007i	$-0.302171\pi$
$431$	−8.57321	−	14.8492i	−0.412957	−	0.715263i	−0.995212	+	0.0977438i	$0.968837\pi$
$432$		0			0
$433$	9.10365	+	15.7680i	0.437494	+	0.757761i	0.997495	−	0.0707302i	$-0.0225329\pi$
$433$	9.10365	+	15.7680i	0.437494	+	0.757761i	−0.560002	+	0.828491i	$0.689200\pi$
$434$		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	$0.626262\pi$
$440$	1.75966	+	10.8267i	0.0838883	+	0.516142i
$441$		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	$-0.509778\pi$
$449$	−1.30159			−0.0614260			−0.0307130	+	0.999528i	$0.509778\pi$
$450$		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	$0.00114426\pi$
$457$			0.153696i			0.00718959i	−0.999994	+	0.00359479i	$0.998856\pi$
$458$	−20.6759	−	11.9373i	−0.966123	−	0.557791i
$459$		0			0
$460$	9.58111	+	3.63349i	0.446722	+	0.169412i
$461$	10.9459	+	6.31959i	0.509799	+	0.294333i	0.732751	−	0.680497i	$-0.238236\pi$
$461$	10.9459	+	6.31959i	0.509799	+	0.294333i	−0.222952	+	0.974829i	$0.571569\pi$
$462$		0			0
$463$		−	9.21040i		−	0.428044i	−0.976829	−	0.214022i	$-0.931344\pi$
$463$		−	9.21040i		−	0.428044i	0.976829	−	0.214022i	$-0.0686563\pi$
$464$	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
$470$	−27.8741	+	4.53036i	−1.28574	+	0.208970i
$471$		0			0
$472$	−2.12132	−	1.22474i	−0.0976417	−	0.0563735i
$473$	−9.88741	+	17.1255i	−0.454623	+	0.787431i
$474$		0			0
$475$	12.4853	−	17.8639i	0.572864	−	0.819650i
$476$		−	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	0.404713	−	0.914444i	$-0.367372\pi$
$479$	30.6186	−	17.6777i	1.39900	−	0.807713i	0.994288	+	0.106731i	$0.0340382\pi$
$480$		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
$485$	−8.87039	−	3.36396i	−0.402784	−	0.152750i
$486$		0			0
$487$	27.4441			1.24361			0.621805	−	0.783172i	$-0.286400\pi$
$487$	27.4441			1.24361			0.621805	+	0.783172i	$0.286400\pi$
$488$	−0.811686	+	0.468627i	−0.0367433	+	0.0212137i
$489$		0			0
$490$	−10.2579	+	27.0488i	−0.463403	+	1.22194i
$491$	24.9920	+	14.4291i	1.12787	+	0.651178i	0.943399	−	0.331660i	$-0.107609\pi$
$491$	24.9920	+	14.4291i	1.12787	+	0.651178i	0.184474	+	0.982837i	$0.440942\pi$
$492$		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	$0.289953\pi$
$500$	−5.97514	+	9.44975i	−0.267216	+	0.422606i
$501$		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	$-0.795298\pi$
$509$	−20.7438	−	35.9293i	−0.919453	−	1.59254i	−0.119206	−	0.992869i	$-0.538035\pi$
$510$		0			0
$511$	−25.4059	+	44.0043i	−1.12389	+	1.94663i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−9.87451			−0.435546
$515$	−0.269569	−	1.65859i	−0.0118786	−	0.0730860i
$516$		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	$-0.603204\pi$
$521$	−14.5432			−0.637151			−0.318576	+	0.947897i	$0.603204\pi$
$522$		0			0
$523$	−14.0978	−	24.4180i	−0.616452	−	1.06773i	−0.990128	−	0.140167i	$-0.955236\pi$
$523$	−14.0978	−	24.4180i	−0.616452	−	1.06773i	0.373676	−	0.927559i	$-0.378097\pi$
$524$			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
$530$	0.694931	+	4.27573i	0.0301859	+	0.185726i
$531$		0			0
$532$	−7.73381	+	17.8605i	−0.335303	+	0.774349i
$533$	−46.4393			−2.01151
$534$		0			0
$535$	10.8970	−	1.77109i	0.471120	−	0.0765709i
$536$	−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
$545$	15.0205	−	39.6073i	0.643406	−	1.69659i
$546$		0			0
$547$	−0.751475	−	1.30159i	−0.0321307	−	0.0556521i	0.849513	−	0.527568i	$-0.176896\pi$
$547$	−0.751475	−	1.30159i	−0.0321307	−	0.0556521i	−0.881644	+	0.471916i	$0.843563\pi$
$548$	−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
$560$	3.54036	−	9.33553i	0.149607	−	0.394498i
$561$		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
$565$	−10.8970	+	1.77109i	−0.458442	+	0.0745103i
$566$	−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	$-0.626382\pi$
$569$	−18.4480			−0.773381			−0.386691	+	0.922209i	$0.626382\pi$
$570$		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
$575$	−17.1509	−	15.1936i	−0.715243	−	0.633617i
$576$		0			0
$577$			25.2089i			1.04946i	0.851268	+	0.524731i	$0.175834\pi$
$577$			25.2089i			1.04946i	−0.851268	+	0.524731i	$0.824166\pi$
$578$		−	22.8745i		−	0.951454i
$579$		0			0
$580$	−15.3640	−	5.82655i	−0.637954	−	0.241934i
$581$		−	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
$595$	−22.3560	+	58.9504i	−0.916509	+	2.41673i
$596$			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	$-0.981119\pi$
$599$	−13.4722	−	23.3345i	−0.550459	−	0.953423i	0.447782	−	0.894143i	$-0.352214\pi$
$600$		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
$605$	4.68586	+	28.8309i	0.190507	+	1.17214i
$606$		0			0
$607$	35.9293			1.45833			0.729163	−	0.684340i	$-0.239909\pi$
$607$	35.9293			1.45833			0.729163	+	0.684340i	$0.239909\pi$
$608$	1.73205	−	4.00000i	0.0702439	−	0.162221i
$609$		0			0
$610$	2.06862	−	0.336211i	0.0837560	−	0.0136128i
$611$	−26.7907	+	46.4028i	−1.08384	+	1.87726i
$612$		0			0
$613$	−34.1838	−	19.7360i	−1.38067	−	0.797130i	−0.388430	−	0.921478i	$-0.626983\pi$
$613$	−34.1838	−	19.7360i	−1.38067	−	0.797130i	−0.992239	+	0.124348i	$0.960316\pi$
$614$	−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
$625$	19.9853	−	15.0196i	0.799411	−	0.600784i
$626$	−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
$640$	−0.792893	+	2.09077i	−0.0313419	+	0.0826450i
$641$	−7.27162	+	12.5948i	−0.287212	+	0.497465i	−0.973143	−	0.230201i	$-0.926062\pi$
$641$	−7.27162	+	12.5948i	−0.287212	+	0.497465i	0.685931	+	0.727666i	$0.259395\pi$
$642$		0			0
$643$	2.87280	+	1.65861i	0.113292	+	0.0654092i	0.555575	−	0.831466i	$-0.312498\pi$
$643$	2.87280	+	1.65861i	0.113292	+	0.0654092i	−0.442283	+	0.896875i	$0.645831\pi$
$644$	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
$650$	6.71807	+	20.1213i	0.263504	+	0.789223i
$651$		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
$655$	8.44508	−	22.2687i	0.329977	−	0.870111i
$656$	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	$-0.924151\pi$
$659$	−17.7204	−	30.6926i	−0.690288	−	1.19561i	0.281456	−	0.959574i	$-0.409183\pi$
$660$		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
$665$	30.3311	−	31.2100i	1.17619	−	1.21027i
$666$		0			0
$667$	16.8375	−	29.1633i	0.651949	−	1.12921i
$668$	17.2662	+	9.96863i	0.668048	+	0.385698i
$669$		0			0
$670$	9.36396	−	1.52192i	0.361761	−	0.0587968i
$671$	−3.98163	+	2.29879i	−0.153709	+	0.0887439i
$672$		0			0
$673$	1.50295			0.0579345			0.0289672	−	0.999580i	$-0.490778\pi$
$673$	1.50295			0.0579345			0.0289672	+	0.999580i	$0.490778\pi$
$674$		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
$680$	5.00682	−	13.2024i	0.192003	−	0.506290i
$681$		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
$700$	−14.8042	+	16.7113i	−0.559545	+	0.631629i
$701$	20.5901	+	11.8877i	0.777678	+	0.448993i	0.835607	−	0.549328i	$-0.185116\pi$
$701$	20.5901	+	11.8877i	0.777678	+	0.448993i	−0.0579287	+	0.998321i	$0.518450\pi$
$702$		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	−0.188525	−	0.982068i	$-0.560371\pi$
$719$	−30.3881	−	17.5446i	−1.13328	−	0.654302i	−0.944759	+	0.327766i	$0.893704\pi$
$720$		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
$725$	27.5027	+	24.3640i	1.02142	+	0.904855i
$726$		0			0
$727$	−21.0801	−	12.1706i	−0.781818	−	0.451383i	0.0552565	−	0.998472i	$-0.482402\pi$
$727$	−21.0801	−	12.1706i	−0.781818	−	0.451383i	−0.837074	+	0.547090i	$0.815736\pi$
$728$	−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	$-0.915153\pi$
$733$		−	14.2631i		−	0.526819i	0.964684	−	0.263409i	$-0.0848470\pi$
$734$	−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
$745$	11.1428	−	29.3824i	0.408242	−	1.07649i
$746$	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
$755$	−41.8112	+	6.79554i	−1.52166	+	0.247315i
$756$		0			0
$757$	3.11543	+	1.79869i	0.113232	+	0.0653746i	0.555546	−	0.831485i	$-0.312509\pi$
$757$	3.11543	+	1.79869i	0.113232	+	0.0653746i	−0.442314	+	0.896860i	$0.645842\pi$
$758$	−17.2118	+	29.8118i	−0.625162	+	1.08281i
$759$		0			0
$760$	−6.79289	+	6.98975i	−0.246404	+	0.253545i
$761$			11.8877i			0.430929i	0.976512	+	0.215465i	$0.0691266\pi$
$761$			11.8877i			0.430929i	−0.976512	+	0.215465i	$0.930873\pi$
$762$		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	$0.834054\pi$
$770$	17.3668	−	45.7943i	0.625856	−	1.65031i
$771$		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
$785$	16.4476	−	43.3706i	0.587041	−	1.54796i
$786$		0			0
$787$	36.6808			1.30753			0.653765	−	0.756698i	$-0.273189\pi$
$787$	36.6808			1.30753			0.653765	+	0.756698i	$0.273189\pi$
$788$	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
$800$	3.31552	−	3.74264i	0.117221	−	0.132322i
$801$		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	$0.111568\pi$
$809$			19.5328i			0.686736i	−0.939201	+	0.343368i	$0.888432\pi$
$810$		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
$815$	−28.6074	+	4.64954i	−1.00207	+	0.162866i
$816$		0			0
$817$	−17.4558	+	2.01563i	−0.610702	+	0.0705178i
$818$	29.4449			1.02952
$819$		0			0
$820$	−3.92649	−	24.1587i	−0.137119	−	0.843657i
$821$	15.8448	−	9.14802i	0.552989	−	0.319268i	−0.197338	−	0.980336i	$-0.563230\pi$
$821$	15.8448	−	9.14802i	0.552989	−	0.319268i	0.750327	+	0.661067i	$0.229896\pi$
$822$		0			0
$823$	−3.11543	+	1.79869i	−0.108597	+	0.0626985i	−0.553315	−	0.832972i	$-0.686637\pi$
$823$	−3.11543	+	1.79869i	−0.108597	+	0.0626985i	0.444718	+	0.895671i	$0.353304\pi$
$824$			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	$0.644604\pi$
$830$	8.23999	−	21.7279i	0.286014	−	0.754187i
$831$		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	$-0.512542\pi$
$839$	24.4949	−	42.4264i	0.845658	−	1.46472i	0.885049	−	0.465498i	$-0.154125\pi$
$840$		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
$845$	10.4539	+	3.96447i	0.359623	+	0.136382i
$846$		0			0
$847$			58.3267i			2.00413i
$848$		−	1.93725i		−	0.0665256i
$849$		0			0
$850$	−20.9362	+	23.6334i	−0.718107	+	0.810618i
$851$	−17.7204	−	30.6926i	−0.607447	−	1.05213i
$852$		0			0
$853$	−4.86101	−	2.80651i	−0.166438	−	0.0960929i	0.414467	−	0.910064i	$-0.363968\pi$
$853$	−4.86101	−	2.80651i	−0.166438	−	0.0960929i	−0.580905	+	0.813971i	$0.697301\pi$
$854$	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	$0.789411\pi$
$860$	8.89740	−	1.44609i	0.303399	−	0.0493112i
$861$		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
$865$	−6.29339	+	16.5950i	−0.213982	+	0.564246i
$866$			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	−0.969842	−	0.243735i	$-0.921627\pi$
$877$	−8.10954	+	14.0461i	−0.273840	+	0.474305i	0.696002	+	0.718040i	$0.254960\pi$
$878$	2.65242	+	4.59412i	0.0895147	+	0.155044i
$879$		0			0
$880$	−3.88944	+	10.2560i	−0.131113	+	0.345730i
$881$		−	27.5328i		−	0.927603i	−0.885939	−	0.463802i	$-0.846485\pi$
$881$		−	27.5328i		−	0.927603i	0.885939	−	0.463802i	$-0.153515\pi$
$882$		0			0
$883$	14.0978	−	8.13935i	0.474428	−	0.273911i	−0.243664	−	0.969860i	$-0.578349\pi$
$883$	14.0978	−	8.13935i	0.474428	−	0.273911i	0.718091	+	0.695949i	$0.245016\pi$
$884$	−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
$890$	13.3461	−	2.16913i	0.447362	−	0.0727095i
$891$		0			0
$892$	9.23676			0.309269
$893$	50.5170	+	21.8745i	1.69049	+	0.732002i
$894$		0			0
$895$	−2.16913	−	13.3461i	−0.0725061	−	0.446111i
$896$	−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	$-0.422328\pi$
$907$	28.9470	−	50.1377i	0.961170	−	1.66479i	0.719572	−	0.694418i	$-0.244338\pi$
$908$	6.11652	−	3.53137i	0.202984	−	0.117193i
$909$		0			0
$910$	6.79554	+	41.8112i	0.225270	+	1.38603i
$911$	−43.7834			−1.45061			−0.725305	−	0.688428i	$-0.758301\pi$
$911$	−43.7834			−1.45061			−0.725305	+	0.688428i	$0.758301\pi$
$912$		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
$925$	36.6787	−	12.2462i	1.20599	−	0.402653i
$926$	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	0.00391689	−	0.999992i	$-0.498753\pi$
$929$	−26.2167	−	15.1362i	−0.860143	−	0.496604i	−0.864060	+	0.503388i	$0.832087\pi$
$930$		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
$935$	24.5604	−	64.7629i	0.803210	−	2.11797i
$936$		0			0
$937$	−36.0624	+	20.8207i	−1.17811	+	0.680181i	−0.955576	−	0.294744i	$-0.904766\pi$
$937$	−36.0624	+	20.8207i	−1.17811	+	0.680181i	−0.222532	+	0.974925i	$0.571432\pi$
$938$	18.9439			0.618540
$939$		0			0
$940$	−26.4049	−	10.0136i	−0.861232	−	0.326609i
$941$	−6.12372	−	10.6066i	−0.199628	−	0.345765i	0.748780	−	0.662819i	$-0.230640\pi$
$941$	−6.12372	−	10.6066i	−0.199628	−	0.345765i	−0.948408	+	0.317053i	$0.897307\pi$
$942$		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
$950$	19.7445	−	9.22792i	0.640596	−	0.299393i
$951$		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
$955$	21.6534	−	3.51931i	0.700687	−	0.113882i
$956$	−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
$965$	26.6112	+	10.0919i	0.856644	+	0.324869i
$966$		0			0
$967$	−30.3169	−	17.5034i	−0.974924	−	0.562873i	−0.0741904	−	0.997244i	$-0.523637\pi$
$967$	−30.3169	−	17.5034i	−0.974924	−	0.562873i	−0.900734	+	0.434371i	$0.856971\pi$
$968$		−	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	−0.997075	−	0.0764343i	$-0.975646\pi$
$971$	−13.4722	+	23.3345i	−0.432343	+	0.748841i	0.564731	+	0.825275i	$0.308980\pi$
$972$		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
$985$	−5.59188	−	34.4054i	−0.178172	−	1.09625i
$986$	−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	$-0.332937\pi$
$997$	47.3969	−	27.3646i	1.50108	−	0.866647i	0.999999	−	0.00124421i	$-0.000396044\pi$
$998$	−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.179.5	yes	16
3.2	odd	2	inner	1710.2.q.a.179.3	yes	16
5.4	even	2	inner	1710.2.q.a.179.2	✓	16
15.14	odd	2	inner	1710.2.q.a.179.8	yes	16
19.12	odd	6	inner	1710.2.q.a.449.7	yes	16
57.50	even	6	inner	1710.2.q.a.449.1	yes	16
95.69	odd	6	inner	1710.2.q.a.449.4	yes	16
285.164	even	6	inner	1710.2.q.a.449.6	yes	16

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.358719 - 2.20711i) q^{5} -4.46512i q^{7} +1.00000i q^{8} +(0.792893 - 2.09077i) q^{10} +4.90538i q^{11} +(-2.12132 - 3.67423i) q^{13} +(2.23256 - 3.86690i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.15731 - 5.46863i) q^{17} +(-3.50000 + 2.59808i) q^{19} +(1.73205 - 1.41421i) q^{20} +(-2.45269 + 4.24818i) q^{22} +(2.29129 + 3.96863i) q^{23} +(-4.74264 + 1.58346i) q^{25} -4.24264i q^{26} +(3.86690 - 2.23256i) q^{28} +(-3.67423 - 6.36396i) q^{29} +(-0.866025 + 0.500000i) q^{32} +(5.46863 - 3.15731i) q^{34} +(-9.85499 + 1.60172i) q^{35} -7.73381 q^{37} +(-4.33013 + 0.500000i) q^{38} +(2.20711 - 0.358719i) q^{40} +(5.47293 - 9.47939i) q^{41} +(3.49117 + 2.01563i) q^{43} +(-4.24818 + 2.45269i) q^{44} +4.58258i q^{46} +(-6.31463 - 10.9373i) q^{47} -12.9373 q^{49} +(-4.89898 - 1.00000i) q^{50} +(2.12132 - 3.67423i) q^{52} +(-1.67771 + 0.968627i) q^{53} +(10.8267 - 1.75966i) q^{55} +4.46512 q^{56} -7.34847i q^{58} +(-1.22474 + 2.12132i) q^{59} +(0.468627 + 0.811686i) q^{61} -1.00000 q^{64} +(-7.34847 + 6.00000i) q^{65} +(2.12132 + 3.67423i) q^{67} +6.31463 q^{68} +(-9.33553 - 3.54036i) q^{70} +(3.67423 - 6.36396i) q^{71} +(-9.85513 - 5.68986i) q^{73} +(-6.69767 - 3.86690i) q^{74} +(-4.00000 - 1.73205i) q^{76} +21.9031 q^{77} +(-6.00000 - 3.46410i) q^{79} +(2.09077 + 0.792893i) q^{80} +(9.47939 - 5.47293i) q^{82} +10.3923 q^{83} +(-13.2024 - 5.00682i) q^{85} +(2.01563 + 3.49117i) q^{86} -4.90538 q^{88} +(3.02344 + 5.23675i) q^{89} +(-16.4059 + 9.47194i) q^{91} +(-2.29129 + 3.96863i) q^{92} -12.6293i q^{94} +(6.98975 + 6.79289i) q^{95} +(2.12132 - 3.67423i) q^{97} +(-11.2040 - 6.46863i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 24 q^{10} - 8 q^{16} - 56 q^{19} - 8 q^{25} + 24 q^{34} + 24 q^{40} - 80 q^{49} - 8 q^{55} - 56 q^{61} - 16 q^{64} - 24 q^{70} - 64 q^{76} - 96 q^{79} - 24 q^{85} - 72 q^{91}+O(q^{100}) \) 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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