LMFDB - Embedded newform 1170.2.w.g.343.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(307,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,-14,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 2 x^{12} + 4 x^{11} + 112 x^{10} - 208 x^{9} + 200 x^{8} + 392 x^{7} + 1708 x^{6} + \cdots + 8 $ x^14 - 2x^13 + 2x^12 + 4x^11 + 112x^10 - 208x^9 + 200x^8 + 392x^7 + 1708x^6 - 1744x^5 + 872x^4 - 80x^3 + 4x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.3
Root			$0.372382 - 0.372382i$ of defining polynomial
Character	$\chi$	$=$	1170.343
Dual form			1170.2.w.g.307.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.372382 - 2.20484i) q^{5} +1.64209 q^{7} +1.00000i q^{8} +(-2.20484 + 0.372382i) q^{10} +(4.51787 + 4.51787i) q^{11} +(-0.732218 - 3.53042i) q^{13} -1.64209i q^{14} +1.00000 q^{16} +(5.07094 + 5.07094i) q^{17} +(-1.47753 - 1.47753i) q^{19} +(0.372382 + 2.20484i) q^{20} +(4.51787 - 4.51787i) q^{22} +(5.93054 - 5.93054i) q^{23} +(-4.72266 + 1.64209i) q^{25} +(-3.53042 + 0.732218i) q^{26} -1.64209 q^{28} +4.59341i q^{29} +(1.29856 - 1.29856i) q^{31} -1.00000i q^{32} +(5.07094 - 5.07094i) q^{34} +(-0.611485 - 3.62055i) q^{35} +2.57058 q^{37} +(-1.47753 + 1.47753i) q^{38} +(2.20484 - 0.372382i) q^{40} +(6.40807 - 6.40807i) q^{41} +(1.01618 - 1.01618i) q^{43} +(-4.51787 - 4.51787i) q^{44} +(-5.93054 - 5.93054i) q^{46} -7.69994 q^{47} -4.30354 q^{49} +(1.64209 + 4.72266i) q^{50} +(0.732218 + 3.53042i) q^{52} +(-2.67934 - 2.67934i) q^{53} +(8.27882 - 11.6436i) q^{55} +1.64209i q^{56} +4.59341 q^{58} +(-1.77537 + 1.77537i) q^{59} -6.19616 q^{61} +(-1.29856 - 1.29856i) q^{62} -1.00000 q^{64} +(-7.51135 + 2.92909i) q^{65} -8.73173i q^{67} +(-5.07094 - 5.07094i) q^{68} +(-3.62055 + 0.611485i) q^{70} +(1.40304 - 1.40304i) q^{71} +13.2123i q^{73} -2.57058i q^{74} +(1.47753 + 1.47753i) q^{76} +(7.41875 + 7.41875i) q^{77} -10.6201i q^{79} +(-0.372382 - 2.20484i) q^{80} +(-6.40807 - 6.40807i) q^{82} +9.18339 q^{83} +(9.29230 - 13.0690i) q^{85} +(-1.01618 - 1.01618i) q^{86} +(-4.51787 + 4.51787i) q^{88} +(1.46610 - 1.46610i) q^{89} +(-1.20237 - 5.79726i) q^{91} +(-5.93054 + 5.93054i) q^{92} +7.69994i q^{94} +(-2.70752 + 3.80794i) q^{95} -14.1647i q^{97} +4.30354i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{4} - 2 q^{5} + 4 q^{13} + 14 q^{16} + 14 q^{17} - 12 q^{19} + 2 q^{20} - 10 q^{25} + 6 q^{26} + 12 q^{31} + 14 q^{34} + 12 q^{35} + 20 q^{37} - 12 q^{38} - 2 q^{41} - 8 q^{47} + 14 q^{49} - 4 q^{52}+ \cdots + 24 q^{95}+O(q^{100}) $ 14 * q - 14 * q^4 - 2 * q^5 + 4 * q^13 + 14 * q^16 + 14 * q^17 - 12 * q^19 + 2 * q^20 - 10 * q^25 + 6 * q^26 + 12 * q^31 + 14 * q^34 + 12 * q^35 + 20 * q^37 - 12 * q^38 - 2 * q^41 - 8 * q^47 + 14 * q^49 - 4 * q^52 + 6 * q^53 + 32 * q^55 + 16 * q^58 - 16 * q^59 + 24 * q^61 - 12 * q^62 - 14 * q^64 - 4 * q^65 - 14 * q^68 - 4 * q^70 - 24 * q^71 + 12 * q^76 + 16 * q^77 - 2 * q^80 + 2 * q^82 + 8 * q^83 + 2 * q^85 + 42 * q^89 - 8 * q^91 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.372382	−	2.20484i	−0.166534	−	0.986036i
$5$	−0.372382	−	2.20484i	−0.166534	−	0.986036i
$6$		0			0
$7$	1.64209			0.620651			0.310326	−	0.950630i	$-0.399562\pi$
$7$	1.64209			0.620651			0.310326	+	0.950630i	$0.399562\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.20484	+	0.372382i	−0.697232	+	0.117758i
$11$	4.51787	+	4.51787i	1.36219	+	1.36219i	0.871121	+	0.491069i	$0.163394\pi$
$11$	4.51787	+	4.51787i	1.36219	+	1.36219i	0.491069	+	0.871121i	$0.336606\pi$
$12$		0			0
$13$	−0.732218	−	3.53042i	−0.203081	−	0.979162i
$13$	−0.732218	−	3.53042i	−0.203081	−	0.979162i
$14$		−	1.64209i		−	0.438867i
$15$		0			0
$16$	1.00000			0.250000
$17$	5.07094	+	5.07094i	1.22988	+	1.22988i	0.964007	+	0.265878i	$0.0856617\pi$
$17$	5.07094	+	5.07094i	1.22988	+	1.22988i	0.265878	+	0.964007i	$0.414338\pi$
$18$		0			0
$19$	−1.47753	−	1.47753i	−0.338969	−	0.338969i	0.517010	−	0.855979i	$-0.327045\pi$
$19$	−1.47753	−	1.47753i	−0.338969	−	0.338969i	−0.855979	+	0.517010i	$0.827045\pi$
$20$	0.372382	+	2.20484i	0.0832672	+	0.493018i
$21$		0			0
$22$	4.51787	−	4.51787i	0.963214	−	0.963214i
$23$	5.93054	−	5.93054i	1.23660	−	1.23660i	0.275223	−	0.961380i	$-0.411248\pi$
$23$	5.93054	−	5.93054i	1.23660	−	1.23660i	0.961380	−	0.275223i	$-0.0887517\pi$
$24$		0			0
$25$	−4.72266	+	1.64209i	−0.944533	+	0.328418i
$26$	−3.53042	+	0.732218i	−0.692372	+	0.143600i
$27$		0			0
$28$	−1.64209			−0.310326
$29$			4.59341i			0.852975i	0.904493	+	0.426487i	$0.140249\pi$
$29$			4.59341i			0.852975i	−0.904493	+	0.426487i	$0.859751\pi$
$30$		0			0
$31$	1.29856	−	1.29856i	0.233228	−	0.233228i	−0.580811	−	0.814039i	$-0.697264\pi$
$31$	1.29856	−	1.29856i	0.233228	−	0.233228i	0.814039	+	0.580811i	$0.197264\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	5.07094	−	5.07094i	0.869660	−	0.869660i
$35$	−0.611485	−	3.62055i	−0.103360	−	0.611984i
$36$		0			0
$37$	2.57058			0.422600			0.211300	−	0.977421i	$-0.432230\pi$
$37$	2.57058			0.422600			0.211300	+	0.977421i	$0.432230\pi$
$38$	−1.47753	+	1.47753i	−0.239688	+	0.239688i
$39$		0			0
$40$	2.20484	−	0.372382i	0.348616	−	0.0588788i
$41$	6.40807	−	6.40807i	1.00077	−	1.00077i	0.000773433	−	1.00000i	$-0.499754\pi$
$41$	6.40807	−	6.40807i	1.00077	−	1.00077i	1.00000		0.000773433i	$-0.000246191\pi$
$42$		0			0
$43$	1.01618	−	1.01618i	0.154967	−	0.154967i	−0.625365	−	0.780332i	$-0.715050\pi$
$43$	1.01618	−	1.01618i	0.154967	−	0.154967i	0.780332	+	0.625365i	$0.215050\pi$
$44$	−4.51787	−	4.51787i	−0.681095	−	0.681095i
$45$		0			0
$46$	−5.93054	−	5.93054i	−0.874411	−	0.874411i
$47$	−7.69994			−1.12315			−0.561576	−	0.827425i	$-0.689805\pi$
$47$	−7.69994			−1.12315			−0.561576	+	0.827425i	$0.689805\pi$
$48$		0			0
$49$	−4.30354			−0.614792
$50$	1.64209	+	4.72266i	0.232226	+	0.667885i
$51$		0			0
$52$	0.732218	+	3.53042i	0.101540	+	0.489581i
$53$	−2.67934	−	2.67934i	−0.368036	−	0.368036i	0.498725	−	0.866760i	$-0.333802\pi$
$53$	−2.67934	−	2.67934i	−0.368036	−	0.368036i	−0.866760	+	0.498725i	$0.833802\pi$
$54$		0			0
$55$	8.27882	−	11.6436i	1.11632	−	1.57002i
$56$			1.64209i			0.219433i
$57$		0			0
$58$	4.59341			0.603144
$59$	−1.77537	+	1.77537i	−0.231133	+	0.231133i	−0.813166	−	0.582032i	$-0.802258\pi$
$59$	−1.77537	+	1.77537i	−0.231133	+	0.231133i	0.582032	+	0.813166i	$0.302258\pi$
$60$		0			0
$61$	−6.19616			−0.793337			−0.396669	−	0.917962i	$-0.629834\pi$
$61$	−6.19616			−0.793337			−0.396669	+	0.917962i	$0.629834\pi$
$62$	−1.29856	−	1.29856i	−0.164917	−	0.164917i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−7.51135	+	2.92909i	−0.931669	+	0.363309i
$66$		0			0
$67$		−	8.73173i		−	1.06675i	−0.845879	−	0.533375i	$-0.820923\pi$
$67$		−	8.73173i		−	1.06675i	0.845879	−	0.533375i	$-0.179077\pi$
$68$	−5.07094	−	5.07094i	−0.614942	−	0.614942i
$69$		0			0
$70$	−3.62055	+	0.611485i	−0.432738	+	0.0730864i
$71$	1.40304	−	1.40304i	0.166510	−	0.166510i	−0.618933	−	0.785443i	$-0.712435\pi$
$71$	1.40304	−	1.40304i	0.166510	−	0.166510i	0.785443	+	0.618933i	$0.212435\pi$
$72$		0			0
$73$			13.2123i			1.54638i	0.634173	+	0.773191i	$0.281341\pi$
$73$			13.2123i			1.54638i	−0.634173	+	0.773191i	$0.718659\pi$
$74$		−	2.57058i		−	0.298824i
$75$		0			0
$76$	1.47753	+	1.47753i	0.169485	+	0.169485i
$77$	7.41875	+	7.41875i	0.845445	+	0.845445i
$78$		0			0
$79$		−	10.6201i		−	1.19485i	−0.801923	−	0.597427i	$-0.796190\pi$
$79$		−	10.6201i		−	1.19485i	0.801923	−	0.597427i	$-0.203810\pi$
$80$	−0.372382	−	2.20484i	−0.0416336	−	0.246509i
$81$		0			0
$82$	−6.40807	−	6.40807i	−0.707653	−	0.707653i
$83$	9.18339			1.00801			0.504004	−	0.863701i	$-0.331860\pi$
$83$	9.18339			1.00801			0.504004	+	0.863701i	$0.331860\pi$
$84$		0			0
$85$	9.29230	−	13.0690i	1.00789	−	1.41753i
$86$	−1.01618	−	1.01618i	−0.109578	−	0.109578i
$87$		0			0
$88$	−4.51787	+	4.51787i	−0.481607	+	0.481607i
$89$	1.46610	−	1.46610i	0.155406	−	0.155406i	−0.625121	−	0.780528i	$-0.714951\pi$
$89$	1.46610	−	1.46610i	0.155406	−	0.155406i	0.780528	+	0.625121i	$0.214951\pi$
$90$		0			0
$91$	−1.20237	−	5.79726i	−0.126042	−	0.607718i
$92$	−5.93054	+	5.93054i	−0.618302	+	0.618302i
$93$		0			0
$94$			7.69994i			0.794188i
$95$	−2.70752	+	3.80794i	−0.277786	+	0.390686i
$96$		0			0
$97$		−	14.1647i		−	1.43821i	−0.694902	−	0.719105i	$-0.744552\pi$
$97$		−	14.1647i		−	1.43821i	0.694902	−	0.719105i	$-0.255448\pi$
$98$			4.30354i			0.434724i
$99$		0			0
$100$	4.72266	−	1.64209i	0.472266	−	0.164209i
$101$		−	11.4416i		−	1.13848i	−0.822170	−	0.569242i	$-0.807237\pi$
$101$		−	11.4416i		−	1.13848i	0.822170	−	0.569242i	$-0.192763\pi$
$102$		0			0
$103$	10.0015	−	10.0015i	0.985476	−	0.985476i	−0.0144204	−	0.999896i	$-0.504590\pi$
$103$	10.0015	−	10.0015i	0.985476	−	0.985476i	0.999896	+	0.0144204i	$0.00459033\pi$
$104$	3.53042	−	0.732218i	0.346186	−	0.0717999i
$105$		0			0
$106$	−2.67934	+	2.67934i	−0.260240	+	0.260240i
$107$	−5.93186	+	5.93186i	−0.573455	+	0.573455i	−0.933092	−	0.359637i	$-0.882900\pi$
$107$	−5.93186	+	5.93186i	−0.573455	+	0.573455i	0.359637	+	0.933092i	$0.382900\pi$
$108$		0			0
$109$	3.40836	+	3.40836i	0.326462	+	0.326462i	0.851239	−	0.524777i	$-0.175851\pi$
$109$	3.40836	+	3.40836i	0.326462	+	0.326462i	−0.524777	+	0.851239i	$0.675851\pi$
$110$	−11.6436	−	8.27882i	−1.11017	−	0.789355i
$111$		0			0
$112$	1.64209			0.155163
$113$	6.74568	+	6.74568i	0.634580	+	0.634580i	0.949213	−	0.314633i	$-0.101881\pi$
$113$	6.74568	+	6.74568i	0.634580	+	0.634580i	−0.314633	+	0.949213i	$0.601881\pi$
$114$		0			0
$115$	−15.2843	−	10.8675i	−1.42527	−	1.01340i
$116$		−	4.59341i		−	0.426487i
$117$		0			0
$118$	1.77537	+	1.77537i	0.163436	+	0.163436i
$119$	8.32694	+	8.32694i	0.763329	+	0.763329i
$120$		0			0
$121$			29.8223i			2.71112i
$122$			6.19616i			0.560974i
$123$		0			0
$124$	−1.29856	+	1.29856i	−0.116614	+	0.116614i
$125$	5.37918	+	9.80124i	0.481129	+	0.876650i
$126$		0			0
$127$	−0.459975	−	0.459975i	−0.0408162	−	0.0408162i	0.686404	−	0.727220i	$-0.259188\pi$
$127$	−0.459975	−	0.459975i	−0.0408162	−	0.0408162i	−0.727220	+	0.686404i	$0.759188\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	2.92909	+	7.51135i	0.256898	+	0.658789i
$131$	−14.2201			−1.24242			−0.621208	−	0.783646i	$-0.713358\pi$
$131$	−14.2201			−1.24242			−0.621208	+	0.783646i	$0.713358\pi$
$132$		0			0
$133$	−2.42624	−	2.42624i	−0.210382	−	0.210382i
$134$	−8.73173			−0.754306
$135$		0			0
$136$	−5.07094	+	5.07094i	−0.434830	+	0.434830i
$137$	15.8813			1.35683			0.678416	−	0.734678i	$-0.262667\pi$
$137$	15.8813			1.35683			0.678416	+	0.734678i	$0.262667\pi$
$138$		0			0
$139$			18.1217i			1.53706i	0.639814	+	0.768530i	$0.279012\pi$
$139$			18.1217i			1.53706i	−0.639814	+	0.768530i	$0.720988\pi$
$140$	0.611485	+	3.62055i	0.0516799	+	0.305992i
$141$		0			0
$142$	−1.40304	−	1.40304i	−0.117740	−	0.117740i
$143$	12.6419	−	19.2580i	1.05717	−	1.61044i
$144$		0			0
$145$	10.1277	−	1.71050i	0.841064	−	0.142050i
$146$	13.2123			1.09346
$147$		0			0
$148$	−2.57058			−0.211300
$149$	−5.86140	−	5.86140i	−0.480185	−	0.480185i	0.425006	−	0.905191i	$-0.360272\pi$
$149$	−5.86140	−	5.86140i	−0.480185	−	0.480185i	−0.905191	+	0.425006i	$0.860272\pi$
$150$		0			0
$151$	5.54961	+	5.54961i	0.451621	+	0.451621i	0.895892	−	0.444271i	$-0.146537\pi$
$151$	5.54961	+	5.54961i	0.451621	+	0.451621i	−0.444271	+	0.895892i	$0.646537\pi$
$152$	1.47753	−	1.47753i	0.119844	−	0.119844i
$153$		0			0
$154$	7.41875	−	7.41875i	0.597820	−	0.597820i
$155$	−3.34668	−	2.37956i	−0.268812	−	0.191131i
$156$		0			0
$157$	3.23663	−	3.23663i	0.258312	−	0.258312i	−0.566056	−	0.824367i	$-0.691531\pi$
$157$	3.23663	−	3.23663i	0.258312	−	0.258312i	0.824367	+	0.566056i	$0.191531\pi$
$158$	−10.6201			−0.844889
$159$		0			0
$160$	−2.20484	+	0.372382i	−0.174308	+	0.0294394i
$161$	9.73848	−	9.73848i	0.767500	−	0.767500i
$162$		0			0
$163$			16.1076i			1.26164i	0.775927	+	0.630822i	$0.217282\pi$
$163$			16.1076i			1.26164i	−0.775927	+	0.630822i	$0.782718\pi$
$164$	−6.40807	+	6.40807i	−0.500387	+	0.500387i
$165$		0			0
$166$		−	9.18339i		−	0.712770i
$167$	−10.3428			−0.800348			−0.400174	−	0.916439i	$-0.631050\pi$
$167$	−10.3428			−0.800348			−0.400174	+	0.916439i	$0.631050\pi$
$168$		0			0
$169$	−11.9277	+	5.17007i	−0.917516	+	0.397698i
$170$	−13.0690	−	9.29230i	−1.00234	−	0.712687i
$171$		0			0
$172$	−1.01618	+	1.01618i	−0.0774834	+	0.0774834i
$173$	0.533953	−	0.533953i	0.0405957	−	0.0405957i	−0.686518	−	0.727113i	$-0.740862\pi$
$173$	0.533953	−	0.533953i	0.0405957	−	0.0405957i	0.727113	+	0.686518i	$0.240862\pi$
$174$		0			0
$175$	−7.75503	+	2.69646i	−0.586225	+	0.203833i
$176$	4.51787	+	4.51787i	0.340547	+	0.340547i
$177$		0			0
$178$	−1.46610	−	1.46610i	−0.109889	−	0.109889i
$179$	−10.8352			−0.809864			−0.404932	−	0.914347i	$-0.632705\pi$
$179$	−10.8352			−0.809864			−0.404932	+	0.914347i	$0.632705\pi$
$180$		0			0
$181$			4.52263i			0.336164i	0.985773	+	0.168082i	$0.0537574\pi$
$181$			4.52263i			0.336164i	−0.985773	+	0.168082i	$0.946243\pi$
$182$	−5.79726	+	1.20237i	−0.429722	+	0.0891254i
$183$		0			0
$184$	5.93054	+	5.93054i	0.437205	+	0.437205i
$185$	−0.957238	−	5.66772i	−0.0703775	−	0.416699i
$186$		0			0
$187$			45.8197i			3.35067i
$188$	7.69994			0.561576
$189$		0			0
$190$	3.80794	+	2.70752i	0.276257	+	0.196424i
$191$	−15.3851			−1.11323			−0.556613	−	0.830772i	$-0.687899\pi$
$191$	−15.3851			−1.11323			−0.556613	+	0.830772i	$0.687899\pi$
$192$		0			0
$193$		−	3.47402i		−	0.250066i	−0.992153	−	0.125033i	$-0.960096\pi$
$193$		−	3.47402i		−	0.250066i	0.992153	−	0.125033i	$-0.0399036\pi$
$194$	−14.1647			−1.01697
$195$		0			0
$196$	4.30354			0.307396
$197$			21.8842i			1.55918i	0.626289	+	0.779591i	$0.284573\pi$
$197$			21.8842i			1.55918i	−0.626289	+	0.779591i	$0.715427\pi$
$198$		0			0
$199$	4.82071			0.341731			0.170866	−	0.985294i	$-0.445344\pi$
$199$	4.82071			0.341731			0.170866	+	0.985294i	$0.445344\pi$
$200$	−1.64209	−	4.72266i	−0.116113	−	0.333943i
$201$		0			0
$202$	−11.4416			−0.805030
$203$			7.54279i			0.529400i
$204$		0			0
$205$	−16.5151	−	11.7425i	−1.15346	−	0.820135i
$206$	−10.0015	−	10.0015i	−0.696836	−	0.696836i
$207$		0			0
$208$	−0.732218	−	3.53042i	−0.0507702	−	0.244790i
$209$		−	13.3506i		−	0.923481i
$210$		0			0
$211$	−6.77515			−0.466421			−0.233210	−	0.972426i	$-0.574923\pi$
$211$	−6.77515			−0.466421			−0.233210	+	0.972426i	$0.574923\pi$
$212$	2.67934	+	2.67934i	0.184018	+	0.184018i
$213$		0			0
$214$	5.93186	+	5.93186i	0.405494	+	0.405494i
$215$	−2.61894	−	1.86212i	−0.178610	−	0.126995i
$216$		0			0
$217$	2.13235	−	2.13235i	0.144753	−	0.144753i
$218$	3.40836	−	3.40836i	0.230843	−	0.230843i
$219$		0			0
$220$	−8.27882	+	11.6436i	−0.558158	+	0.785010i
$221$	14.1895	−	21.6156i	0.954490	−	1.45402i
$222$		0			0
$223$	−13.7744			−0.922402			−0.461201	−	0.887296i	$-0.652581\pi$
$223$	−13.7744			−0.922402			−0.461201	+	0.887296i	$0.652581\pi$
$224$		−	1.64209i		−	0.109717i
$225$		0			0
$226$	6.74568	−	6.74568i	0.448716	−	0.448716i
$227$			25.3628i			1.68339i	0.539956	+	0.841693i	$0.318441\pi$
$227$			25.3628i			1.68339i	−0.539956	+	0.841693i	$0.681559\pi$
$228$		0			0
$229$	−2.22305	+	2.22305i	−0.146903	+	0.146903i	−0.776733	−	0.629830i	$-0.783125\pi$
$229$	−2.22305	+	2.22305i	−0.146903	+	0.146903i	0.629830	+	0.776733i	$0.283125\pi$
$230$	−10.8675	+	15.2843i	−0.716581	+	1.00782i
$231$		0			0
$232$	−4.59341			−0.301572
$233$	0.221543	−	0.221543i	0.0145138	−	0.0145138i	−0.699813	−	0.714326i	$-0.746733\pi$
$233$	0.221543	−	0.221543i	0.0145138	−	0.0145138i	0.714326	+	0.699813i	$0.246733\pi$
$234$		0			0
$235$	2.86732	+	16.9771i	0.187043	+	1.10747i
$236$	1.77537	−	1.77537i	0.115567	−	0.115567i
$237$		0			0
$238$	8.32694	−	8.32694i	0.539755	−	0.539755i
$239$	13.7444	+	13.7444i	0.889051	+	0.889051i	0.994432	−	0.105381i	$-0.0336062\pi$
$239$	13.7444	+	13.7444i	0.889051	+	0.889051i	−0.105381	+	0.994432i	$0.533606\pi$
$240$		0			0
$241$	−19.7069	−	19.7069i	−1.26943	−	1.26943i	−0.946382	−	0.323050i	$-0.895292\pi$
$241$	−19.7069	−	19.7069i	−1.26943	−	1.26943i	−0.323050	−	0.946382i	$-0.604708\pi$
$242$	29.8223			1.91705
$243$		0			0
$244$	6.19616			0.396669
$245$	1.60256	+	9.48864i	0.102384	+	0.606207i
$246$		0			0
$247$	−4.13443	+	6.29819i	−0.263068	+	0.400744i
$248$	1.29856	+	1.29856i	0.0824585	+	0.0824585i
$249$		0			0
$250$	9.80124	−	5.37918i	0.619885	−	0.340209i
$251$		−	8.85078i		−	0.558656i	−0.960196	−	0.279328i	$-0.909888\pi$
$251$		−	8.85078i		−	0.558656i	0.960196	−	0.279328i	$-0.0901117\pi$
$252$		0			0
$253$	53.5869			3.36898
$254$	−0.459975	+	0.459975i	−0.0288614	+	0.0288614i
$255$		0			0
$256$	1.00000			0.0625000
$257$	11.6574	+	11.6574i	0.727170	+	0.727170i	0.970055	−	0.242885i	$-0.0780937\pi$
$257$	11.6574	+	11.6574i	0.727170	+	0.727170i	−0.242885	+	0.970055i	$0.578094\pi$
$258$		0			0
$259$	4.22112			0.262288
$260$	7.51135	−	2.92909i	0.465834	−	0.181655i
$261$		0			0
$262$			14.2201i			0.878520i
$263$	6.91081	+	6.91081i	0.426139	+	0.426139i	0.887311	−	0.461172i	$-0.152571\pi$
$263$	6.91081	+	6.91081i	0.426139	+	0.426139i	−0.461172	+	0.887311i	$0.652571\pi$
$264$		0			0
$265$	−4.90978	+	6.90526i	−0.301606	+	0.424187i
$266$	−2.42624	+	2.42624i	−0.148762	+	0.148762i
$267$		0			0
$268$			8.73173i			0.533375i
$269$		−	24.5283i		−	1.49552i	−0.663970	−	0.747759i	$-0.731130\pi$
$269$		−	24.5283i		−	1.49552i	0.663970	−	0.747759i	$-0.268870\pi$
$270$		0			0
$271$	−12.8338	−	12.8338i	−0.779597	−	0.779597i	0.200165	−	0.979762i	$-0.435852\pi$
$271$	−12.8338	−	12.8338i	−0.779597	−	0.779597i	−0.979762	+	0.200165i	$0.935852\pi$
$272$	5.07094	+	5.07094i	0.307471	+	0.307471i
$273$		0			0
$274$		−	15.8813i		−	0.959425i
$275$	−28.7551	−	13.9176i	−1.73400	−	0.839265i
$276$		0			0
$277$	8.90530	+	8.90530i	0.535068	+	0.535068i	0.922076	−	0.387008i	$-0.126492\pi$
$277$	8.90530	+	8.90530i	0.535068	+	0.535068i	−0.387008	+	0.922076i	$0.626492\pi$
$278$	18.1217			1.08687
$279$		0			0
$280$	3.62055	−	0.611485i	0.216369	−	0.0365432i
$281$	17.4509	+	17.4509i	1.04104	+	1.04104i	0.999121	+	0.0419147i	$0.0133458\pi$
$281$	17.4509	+	17.4509i	1.04104	+	1.04104i	0.0419147	+	0.999121i	$0.486654\pi$
$282$		0			0
$283$	8.76312	−	8.76312i	0.520913	−	0.520913i	−0.396934	−	0.917847i	$-0.629926\pi$
$283$	8.76312	−	8.76312i	0.520913	−	0.520913i	0.917847	+	0.396934i	$0.129926\pi$
$284$	−1.40304	+	1.40304i	−0.0832550	+	0.0832550i
$285$		0			0
$286$	−19.2580	−	12.6419i	−1.13875	−	0.747532i
$287$	10.5226	−	10.5226i	0.621131	−	0.621131i
$288$		0			0
$289$			34.4289i			2.02523i
$290$	−1.71050	−	10.1277i	−0.100444	−	0.594722i
$291$		0			0
$292$		−	13.2123i		−	0.773191i
$293$			27.2016i			1.58914i	0.607175	+	0.794568i	$0.292303\pi$
$293$			27.2016i			1.58914i	−0.607175	+	0.794568i	$0.707697\pi$
$294$		0			0
$295$	4.57552	+	3.25329i	0.266397	+	0.189414i
$296$			2.57058i			0.149412i
$297$		0			0
$298$	−5.86140	+	5.86140i	−0.339542	+	0.339542i
$299$	−25.2797	−	16.5948i	−1.46197	−	0.959705i
$300$		0			0
$301$	1.66867	−	1.66867i	0.0961803	−	0.0961803i
$302$	5.54961	−	5.54961i	0.319344	−	0.319344i
$303$		0			0
$304$	−1.47753	−	1.47753i	−0.0847423	−	0.0847423i
$305$	2.30734	+	13.6616i	0.132118	+	0.782259i
$306$		0			0
$307$	19.5908			1.11811			0.559053	−	0.829132i	$-0.311165\pi$
$307$	19.5908			1.11811			0.559053	+	0.829132i	$0.311165\pi$
$308$	−7.41875	−	7.41875i	−0.422722	−	0.422722i
$309$		0			0
$310$	−2.37956	+	3.34668i	−0.135150	+	0.190078i
$311$		−	15.5581i		−	0.882217i	−0.897454	−	0.441108i	$-0.854585\pi$
$311$		−	15.5581i		−	0.882217i	0.897454	−	0.441108i	$-0.145415\pi$
$312$		0			0
$313$	−10.3697	−	10.3697i	−0.586128	−	0.586128i	0.350452	−	0.936581i	$-0.386028\pi$
$313$	−10.3697	−	10.3697i	−0.586128	−	0.586128i	−0.936581	+	0.350452i	$0.886028\pi$
$314$	−3.23663	−	3.23663i	−0.182654	−	0.182654i
$315$		0			0
$316$			10.6201i			0.597427i
$317$		−	7.90873i		−	0.444198i	−0.975024	−	0.222099i	$-0.928709\pi$
$317$		−	7.90873i		−	0.444198i	0.975024	−	0.222099i	$-0.0712909\pi$
$318$		0			0
$319$	−20.7524	+	20.7524i	−1.16191	+	1.16191i
$320$	0.372382	+	2.20484i	0.0208168	+	0.123254i
$321$		0			0
$322$	−9.73848	−	9.73848i	−0.542704	−	0.542704i
$323$		−	14.9850i		−	0.833786i
$324$		0			0
$325$	9.25528	+	15.4706i	0.513391	+	0.858155i
$326$	16.1076			0.892118
$327$		0			0
$328$	6.40807	+	6.40807i	0.353827	+	0.353827i
$329$	−12.6440			−0.697085
$330$		0			0
$331$	−23.7654	+	23.7654i	−1.30626	+	1.30626i	−0.382174	+	0.924090i	$0.624824\pi$
$331$	−23.7654	+	23.7654i	−1.30626	+	1.30626i	−0.924090	+	0.382174i	$0.875176\pi$
$332$	−9.18339			−0.504004
$333$		0			0
$334$			10.3428i			0.565932i
$335$	−19.2521	+	3.25154i	−1.05185	+	0.177651i
$336$		0			0
$337$	6.87634	+	6.87634i	0.374578	+	0.374578i	0.869142	−	0.494563i	$-0.164672\pi$
$337$	6.87634	+	6.87634i	0.374578	+	0.374578i	−0.494563	+	0.869142i	$0.664672\pi$
$338$	5.17007	+	11.9277i	0.281215	+	0.648782i
$339$		0			0
$340$	−9.29230	+	13.0690i	−0.503946	+	0.708764i
$341$	11.7334			0.635401
$342$		0			0
$343$	−18.5614			−1.00222
$344$	1.01618	+	1.01618i	0.0547890	+	0.0547890i
$345$		0			0
$346$	−0.533953	−	0.533953i	−0.0287055	−	0.0287055i
$347$	−12.9364	+	12.9364i	−0.694463	+	0.694463i	−0.963211	−	0.268748i	$-0.913390\pi$
$347$	−12.9364	+	12.9364i	−0.694463	+	0.694463i	0.268748	+	0.963211i	$0.413390\pi$
$348$		0			0
$349$	−0.121963	+	0.121963i	−0.00652851	+	0.00652851i	−0.710364	−	0.703835i	$-0.751469\pi$
$349$	−0.121963	+	0.121963i	−0.00652851	+	0.00652851i	0.703835	+	0.710364i	$0.251469\pi$
$350$	2.69646	+	7.75503i	0.144132	+	0.414524i
$351$		0			0
$352$	4.51787	−	4.51787i	0.240803	−	0.240803i
$353$	18.7416			0.997514			0.498757	−	0.866742i	$-0.333790\pi$
$353$	18.7416			0.997514			0.498757	+	0.866742i	$0.333790\pi$
$354$		0			0
$355$	−3.61595	−	2.57101i	−0.191915	−	0.136455i
$356$	−1.46610	+	1.46610i	−0.0777030	+	0.0777030i
$357$		0			0
$358$			10.8352i			0.572660i
$359$	6.51327	−	6.51327i	0.343757	−	0.343757i	−0.514021	−	0.857778i	$-0.671845\pi$
$359$	6.51327	−	6.51327i	0.343757	−	0.343757i	0.857778	+	0.514021i	$0.171845\pi$
$360$		0			0
$361$		−	14.6338i		−	0.770200i
$362$	4.52263			0.237704
$363$		0			0
$364$	1.20237	+	5.79726i	0.0630212	+	0.303859i
$365$	29.1310	−	4.92003i	1.52479	−	0.257526i
$366$		0			0
$367$	7.79589	−	7.79589i	0.406942	−	0.406942i	−0.473729	−	0.880671i	$-0.657092\pi$
$367$	7.79589	−	7.79589i	0.406942	−	0.406942i	0.880671	+	0.473729i	$0.157092\pi$
$368$	5.93054	−	5.93054i	0.309151	−	0.309151i
$369$		0			0
$370$	−5.66772	+	0.957238i	−0.294651	+	0.0497644i
$371$	−4.39971	−	4.39971i	−0.228422	−	0.228422i
$372$		0			0
$373$	−7.40248	−	7.40248i	−0.383286	−	0.383286i	0.488999	−	0.872284i	$-0.337362\pi$
$373$	−7.40248	−	7.40248i	−0.383286	−	0.383286i	−0.872284	+	0.488999i	$0.837362\pi$
$374$	45.8197			2.36928
$375$		0			0
$376$		−	7.69994i		−	0.397094i
$377$	16.2167	−	3.36338i	0.835201	−	0.173223i
$378$		0			0
$379$	−17.2417	−	17.2417i	−0.885646	−	0.885646i	0.108456	−	0.994101i	$-0.465409\pi$
$379$	−17.2417	−	17.2417i	−0.885646	−	0.885646i	−0.994101	+	0.108456i	$0.965409\pi$
$380$	2.70752	−	3.80794i	0.138893	−	0.195343i
$381$		0			0
$382$			15.3851i			0.787169i
$383$	−0.348683			−0.0178169			−0.00890844	−	0.999960i	$-0.502836\pi$
$383$	−0.348683			−0.0178169			−0.00890844	+	0.999960i	$0.502836\pi$
$384$		0			0
$385$	13.5946	−	19.1198i	0.692843	−	0.974434i
$386$	−3.47402			−0.176823
$387$		0			0
$388$			14.1647i			0.719105i
$389$	15.4386			0.782768			0.391384	−	0.920227i	$-0.371996\pi$
$389$	15.4386			0.782768			0.391384	+	0.920227i	$0.371996\pi$
$390$		0			0
$391$	60.1469			3.04176
$392$		−	4.30354i		−	0.217362i
$393$		0			0
$394$	21.8842			1.10251
$395$	−23.4156	+	3.95473i	−1.17817	+	0.198984i
$396$		0			0
$397$	0.259593			0.0130286			0.00651429	−	0.999979i	$-0.497926\pi$
$397$	0.259593			0.0130286			0.00651429	+	0.999979i	$0.497926\pi$
$398$		−	4.82071i		−	0.241640i
$399$		0			0
$400$	−4.72266	+	1.64209i	−0.236133	+	0.0821045i
$401$	15.5794	+	15.5794i	0.777999	+	0.777999i	0.979490	−	0.201491i	$-0.0645788\pi$
$401$	15.5794	+	15.5794i	0.777999	+	0.777999i	−0.201491	+	0.979490i	$0.564579\pi$
$402$		0			0
$403$	−5.53528	−	3.63363i	−0.275732	−	0.181004i
$404$			11.4416i			0.569242i
$405$		0			0
$406$	7.54279			0.374342
$407$	11.6135	+	11.6135i	0.575662	+	0.575662i
$408$		0			0
$409$	−5.60645	−	5.60645i	−0.277221	−	0.277221i	0.554778	−	0.831999i	$-0.312803\pi$
$409$	−5.60645	−	5.60645i	−0.277221	−	0.277221i	−0.831999	+	0.554778i	$0.812803\pi$
$410$	−11.7425	+	16.5151i	−0.579923	+	0.815620i
$411$		0			0
$412$	−10.0015	+	10.0015i	−0.492738	+	0.492738i
$413$	−2.91531	+	2.91531i	−0.143453	+	0.143453i
$414$		0			0
$415$	−3.41973	−	20.2479i	−0.167868	−	0.993932i
$416$	−3.53042	+	0.732218i	−0.173093	+	0.0359000i
$417$		0			0
$418$	−13.3506			−0.653000
$419$		−	0.132299i		−	0.00646324i	−0.999995	−	0.00323162i	$-0.998971\pi$
$419$		−	0.132299i		−	0.00646324i	0.999995	−	0.00323162i	$-0.00102866\pi$
$420$		0			0
$421$	−28.6488	+	28.6488i	−1.39626	+	1.39626i	−0.585804	+	0.810453i	$0.699221\pi$
$421$	−28.6488	+	28.6488i	−1.39626	+	1.39626i	−0.810453	+	0.585804i	$0.800779\pi$
$422$			6.77515i			0.329809i
$423$		0			0
$424$	2.67934	−	2.67934i	0.130120	−	0.130120i
$425$	−32.2753	−	15.6214i	−1.56558	−	0.757750i
$426$		0			0
$427$	−10.1747			−0.492386
$428$	5.93186	−	5.93186i	0.286727	−	0.286727i
$429$		0			0
$430$	−1.86212	+	2.61894i	−0.0897993	+	0.126296i
$431$	−13.6409	+	13.6409i	−0.657057	+	0.657057i	−0.954683	−	0.297626i	$-0.903805\pi$
$431$	−13.6409	+	13.6409i	−0.657057	+	0.657057i	0.297626	+	0.954683i	$0.403805\pi$
$432$		0			0
$433$	9.01360	−	9.01360i	0.433166	−	0.433166i	−0.456538	−	0.889704i	$-0.650911\pi$
$433$	9.01360	−	9.01360i	0.433166	−	0.433166i	0.889704	+	0.456538i	$0.150911\pi$
$434$	−2.13235	−	2.13235i	−0.102356	−	0.102356i
$435$		0			0
$436$	−3.40836	−	3.40836i	−0.163231	−	0.163231i
$437$	−17.5251			−0.838341
$438$		0			0
$439$	−5.55874			−0.265304			−0.132652	−	0.991163i	$-0.542349\pi$
$439$	−5.55874			−0.265304			−0.132652	+	0.991163i	$0.542349\pi$
$440$	11.6436	+	8.27882i	0.555086	+	0.394677i
$441$		0			0
$442$	−21.6156	−	14.1895i	−1.02815	−	0.674926i
$443$	5.91848	+	5.91848i	0.281195	+	0.281195i	0.833586	−	0.552390i	$-0.186284\pi$
$443$	5.91848	+	5.91848i	0.281195	+	0.281195i	−0.552390	+	0.833586i	$0.686284\pi$
$444$		0			0
$445$	−3.77846	−	2.68657i	−0.179116	−	0.127355i
$446$			13.7744i			0.652237i
$447$		0			0
$448$	−1.64209			−0.0775814
$449$	−7.11677	+	7.11677i	−0.335861	+	0.335861i	−0.854807	−	0.518946i	$-0.826325\pi$
$449$	−7.11677	+	7.11677i	−0.335861	+	0.335861i	0.518946	+	0.854807i	$0.326325\pi$
$450$		0			0
$451$	57.9017			2.72649
$452$	−6.74568	−	6.74568i	−0.317290	−	0.317290i
$453$		0			0
$454$	25.3628			1.19033
$455$	−12.3343	+	4.80983i	−0.578241	+	0.225488i
$456$		0			0
$457$			15.7988i			0.739036i	0.929224	+	0.369518i	$0.120477\pi$
$457$			15.7988i			0.739036i	−0.929224	+	0.369518i	$0.879523\pi$
$458$	2.22305	+	2.22305i	0.103876	+	0.103876i
$459$		0			0
$460$	15.2843	+	10.8675i	0.712636	+	0.506699i
$461$	−14.0129	+	14.0129i	−0.652644	+	0.652644i	−0.953629	−	0.300985i	$-0.902685\pi$
$461$	−14.0129	+	14.0129i	−0.652644	+	0.652644i	0.300985	+	0.953629i	$0.402685\pi$
$462$		0			0
$463$			5.90834i			0.274584i	0.990531	+	0.137292i	$0.0438398\pi$
$463$			5.90834i			0.274584i	−0.990531	+	0.137292i	$0.956160\pi$
$464$			4.59341i			0.213244i
$465$		0			0
$466$	−0.221543	−	0.221543i	−0.0102628	−	0.0102628i
$467$	−11.1464	−	11.1464i	−0.515795	−	0.515795i	0.400501	−	0.916296i	$-0.368836\pi$
$467$	−11.1464	−	11.1464i	−0.515795	−	0.515795i	−0.916296	+	0.400501i	$0.868836\pi$
$468$		0			0
$469$		−	14.3383i		−	0.662080i
$470$	16.9771	−	2.86732i	0.783097	−	0.132260i
$471$		0			0
$472$	−1.77537	−	1.77537i	−0.0817180	−	0.0817180i
$473$	9.18199			0.422188
$474$		0			0
$475$	9.40413	+	4.55165i	0.431491	+	0.208844i
$476$	−8.32694	−	8.32694i	−0.381665	−	0.381665i
$477$		0			0
$478$	13.7444	−	13.7444i	0.628654	−	0.628654i
$479$	−4.97107	+	4.97107i	−0.227134	+	0.227134i	−0.811494	−	0.584360i	$-0.801346\pi$
$479$	−4.97107	+	4.97107i	−0.227134	+	0.227134i	0.584360	+	0.811494i	$0.301346\pi$
$480$		0			0
$481$	−1.88222	−	9.07522i	−0.0858220	−	0.413794i
$482$	−19.7069	+	19.7069i	−0.897624	+	0.897624i
$483$		0			0
$484$		−	29.8223i		−	1.35556i
$485$	−31.2310	+	5.27469i	−1.41813	+	0.239511i
$486$		0			0
$487$		−	25.1117i		−	1.13792i	−0.822365	−	0.568961i	$-0.807346\pi$
$487$		−	25.1117i		−	1.13792i	0.822365	−	0.568961i	$-0.192654\pi$
$488$		−	6.19616i		−	0.280487i
$489$		0			0
$490$	9.48864	−	1.60256i	0.428653	−	0.0723964i
$491$		−	42.0378i		−	1.89714i	−0.316568	−	0.948570i	$-0.602530\pi$
$491$		−	42.0378i		−	1.89714i	0.316568	−	0.948570i	$-0.397470\pi$
$492$		0			0
$493$	−23.2929	+	23.2929i	−1.04906	+	1.04906i
$494$	6.29819	+	4.13443i	0.283369	+	0.186017i
$495$		0			0
$496$	1.29856	−	1.29856i	0.0583070	−	0.0583070i
$497$	2.30391	−	2.30391i	0.103345	−	0.103345i
$498$		0			0
$499$	−10.5783	−	10.5783i	−0.473548	−	0.473548i	0.429513	−	0.903061i	$-0.358685\pi$
$499$	−10.5783	−	10.5783i	−0.473548	−	0.473548i	−0.903061	+	0.429513i	$0.858685\pi$
$500$	−5.37918	−	9.80124i	−0.240564	−	0.438325i
$501$		0			0
$502$	−8.85078			−0.395030
$503$	−19.1823	−	19.1823i	−0.855296	−	0.855296i	0.135484	−	0.990780i	$-0.456741\pi$
$503$	−19.1823	−	19.1823i	−0.855296	−	0.855296i	−0.990780	+	0.135484i	$0.956741\pi$
$504$		0			0
$505$	−25.2270	+	4.26066i	−1.12259	+	0.189597i
$506$		−	53.5869i		−	2.38223i
$507$		0			0
$508$	0.459975	+	0.459975i	0.0204081	+	0.0204081i
$509$	−9.29714	−	9.29714i	−0.412089	−	0.412089i	0.470377	−	0.882466i	$-0.344118\pi$
$509$	−9.29714	−	9.29714i	−0.412089	−	0.412089i	−0.882466	+	0.470377i	$0.844118\pi$
$510$		0			0
$511$			21.6958i			0.959764i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	11.6574	−	11.6574i	0.514187	−	0.514187i
$515$	−25.7761	−	18.3273i	−1.13583	−	0.807598i
$516$		0			0
$517$	−34.7873	−	34.7873i	−1.52994	−	1.52994i
$518$		−	4.22112i		−	0.185465i
$519$		0			0
$520$	−2.92909	−	7.51135i	−0.128449	−	0.329395i
$521$	−13.7355			−0.601764			−0.300882	−	0.953661i	$-0.597281\pi$
$521$	−13.7355			−0.601764			−0.300882	+	0.953661i	$0.597281\pi$
$522$		0			0
$523$	−14.1158	−	14.1158i	−0.617243	−	0.617243i	0.327581	−	0.944823i	$-0.393767\pi$
$523$	−14.1158	−	14.1158i	−0.617243	−	0.617243i	−0.944823	+	0.327581i	$0.893767\pi$
$524$	14.2201			0.621208
$525$		0			0
$526$	6.91081	−	6.91081i	0.301325	−	0.301325i
$527$	13.1698			0.573687
$528$		0			0
$529$		−	47.3426i		−	2.05838i
$530$	6.90526	+	4.90978i	0.299945	+	0.213267i
$531$		0			0
$532$	2.42624	+	2.42624i	0.105191	+	0.105191i
$533$	−27.3153	−	17.9311i	−1.18316	−	0.776681i
$534$		0			0
$535$	15.2877	+	10.8699i	0.660947	+	0.469947i
$536$	8.73173			0.377153
$537$		0			0
$538$	−24.5283			−1.05749
$539$	−19.4429	−	19.4429i	−0.837463	−	0.837463i
$540$		0			0
$541$	30.0106	+	30.0106i	1.29026	+	1.29026i	0.934626	+	0.355633i	$0.115735\pi$
$541$	30.0106	+	30.0106i	1.29026	+	1.29026i	0.355633	+	0.934626i	$0.384265\pi$
$542$	−12.8338	+	12.8338i	−0.551258	+	0.551258i
$543$		0			0
$544$	5.07094	−	5.07094i	0.217415	−	0.217415i
$545$	6.24569	−	8.78412i	0.267536	−	0.376270i
$546$		0			0
$547$	14.6365	−	14.6365i	0.625810	−	0.625810i	−0.321201	−	0.947011i	$-0.604086\pi$
$547$	14.6365	−	14.6365i	0.625810	−	0.625810i	0.947011	+	0.321201i	$0.104086\pi$
$548$	−15.8813			−0.678416
$549$		0			0
$550$	−13.9176	+	28.7551i	−0.593450	+	1.22612i
$551$	6.78692	−	6.78692i	0.289132	−	0.289132i
$552$		0			0
$553$		−	17.4391i		−	0.741587i
$554$	8.90530	−	8.90530i	0.378350	−	0.378350i
$555$		0			0
$556$		−	18.1217i		−	0.768530i
$557$	−9.43515			−0.399780			−0.199890	−	0.979818i	$-0.564058\pi$
$557$	−9.43515			−0.399780			−0.199890	+	0.979818i	$0.564058\pi$
$558$		0			0
$559$	−4.33163	−	2.84349i	−0.183208	−	0.120267i
$560$	−0.611485	−	3.62055i	−0.0258400	−	0.152996i
$561$		0			0
$562$	17.4509	−	17.4509i	0.736124	−	0.736124i
$563$	−9.87788	+	9.87788i	−0.416303	+	0.416303i	−0.883927	−	0.467624i	$-0.845110\pi$
$563$	−9.87788	+	9.87788i	−0.416303	+	0.416303i	0.467624	+	0.883927i	$0.345110\pi$
$564$		0			0
$565$	12.3612	−	17.3851i	0.520039	−	0.731398i
$566$	−8.76312	−	8.76312i	−0.368341	−	0.368341i
$567$		0			0
$568$	1.40304	+	1.40304i	0.0588702	+	0.0588702i
$569$	−28.9627			−1.21418			−0.607090	−	0.794633i	$-0.707663\pi$
$569$	−28.9627			−1.21418			−0.607090	+	0.794633i	$0.707663\pi$
$570$		0			0
$571$		−	8.33577i		−	0.348841i	−0.984671	−	0.174421i	$-0.944195\pi$
$571$		−	8.33577i		−	0.348841i	0.984671	−	0.174421i	$-0.0558052\pi$
$572$	−12.6419	+	19.2580i	−0.528585	+	0.805220i
$573$		0			0
$574$	−10.5226	−	10.5226i	−0.439206	−	0.439206i
$575$	−18.2695	+	37.7464i	−0.761890	+	1.57413i
$576$		0			0
$577$			0.606180i			0.0252356i	0.999920	+	0.0126178i	$0.00401648\pi$
$577$			0.606180i			0.0252356i	−0.999920	+	0.0126178i	$0.995984\pi$
$578$	34.4289			1.43205
$579$		0			0
$580$	−10.1277	+	1.71050i	−0.420532	+	0.0710248i
$581$	15.0799			0.625622
$582$		0			0
$583$		−	24.2098i		−	1.00267i
$584$	−13.2123			−0.546729
$585$		0			0
$586$	27.2016			1.12369
$587$			34.4395i			1.42147i	0.703459	+	0.710736i	$0.251638\pi$
$587$			34.4395i			1.42147i	−0.703459	+	0.710736i	$0.748362\pi$
$588$		0			0
$589$	−3.83733			−0.158114
$590$	3.25329	−	4.57552i	0.133936	−	0.188371i
$591$		0			0
$592$	2.57058			0.105650
$593$			4.20670i			0.172748i	0.996263	+	0.0863741i	$0.0275280\pi$
$593$			4.20670i			0.172748i	−0.996263	+	0.0863741i	$0.972472\pi$
$594$		0			0
$595$	15.2588	−	21.4604i	0.625549	−	0.879791i
$596$	5.86140	+	5.86140i	0.240092	+	0.240092i
$597$		0			0
$598$	−16.5948	+	25.2797i	−0.678614	+	1.03377i
$599$			44.3351i			1.81148i	0.423830	+	0.905742i	$0.360685\pi$
$599$			44.3351i			1.81148i	−0.423830	+	0.905742i	$0.639315\pi$
$600$		0			0
$601$	−3.41676			−0.139372			−0.0696862	−	0.997569i	$-0.522200\pi$
$601$	−3.41676			−0.139372			−0.0696862	+	0.997569i	$0.522200\pi$
$602$	−1.66867	−	1.66867i	−0.0680098	−	0.0680098i
$603$		0			0
$604$	−5.54961	−	5.54961i	−0.225811	−	0.225811i
$605$	65.7536	−	11.1053i	2.67326	−	0.451495i
$606$		0			0
$607$	−14.0954	+	14.0954i	−0.572114	+	0.572114i	−0.932719	−	0.360605i	$-0.882570\pi$
$607$	−14.0954	+	14.0954i	−0.572114	+	0.572114i	0.360605	+	0.932719i	$0.382570\pi$
$608$	−1.47753	+	1.47753i	−0.0599219	+	0.0599219i
$609$		0			0
$610$	13.6616	−	2.30734i	0.553141	−	0.0934215i
$611$	5.63803	+	27.1840i	0.228090	+	1.09975i
$612$		0			0
$613$	0.220056			0.00888796			0.00444398	−	0.999990i	$-0.498585\pi$
$613$	0.220056			0.00888796			0.00444398	+	0.999990i	$0.498585\pi$
$614$		−	19.5908i		−	0.790620i
$615$		0			0
$616$	−7.41875	+	7.41875i	−0.298910	+	0.298910i
$617$		−	39.6937i		−	1.59801i	−0.601325	−	0.799004i	$-0.705360\pi$
$617$		−	39.6937i		−	1.59801i	0.601325	−	0.799004i	$-0.294640\pi$
$618$		0			0
$619$	14.5264	−	14.5264i	0.583866	−	0.583866i	−0.352097	−	0.935963i	$-0.614531\pi$
$619$	14.5264	−	14.5264i	0.583866	−	0.583866i	0.935963	+	0.352097i	$0.114531\pi$
$620$	3.34668	+	2.37956i	0.134406	+	0.0955653i
$621$		0			0
$622$	−15.5581			−0.623822
$623$	2.40746	−	2.40746i	0.0964530	−	0.0964530i
$624$		0			0
$625$	19.6071	−	15.5101i	0.784283	−	0.620403i
$626$	−10.3697	+	10.3697i	−0.414455	+	0.414455i
$627$		0			0
$628$	−3.23663	+	3.23663i	−0.129156	+	0.129156i
$629$	13.0353	+	13.0353i	0.519750	+	0.519750i
$630$		0			0
$631$	−5.41530	−	5.41530i	−0.215580	−	0.215580i	0.591053	−	0.806633i	$-0.298712\pi$
$631$	−5.41530	−	5.41530i	−0.215580	−	0.215580i	−0.806633	+	0.591053i	$0.798712\pi$
$632$	10.6201			0.422445
$633$		0			0
$634$	−7.90873			−0.314096
$635$	−0.842886	+	1.18546i	−0.0334489	+	0.0470435i
$636$		0			0
$637$	3.15113	+	15.1933i	0.124852	+	0.601981i
$638$	20.7524	+	20.7524i	0.821597	+	0.821597i
$639$		0			0
$640$	2.20484	−	0.372382i	0.0871541	−	0.0147197i
$641$			38.8895i			1.53604i	0.640424	+	0.768022i	$0.278759\pi$
$641$			38.8895i			1.53604i	−0.640424	+	0.768022i	$0.721241\pi$
$642$		0			0
$643$	−25.8618			−1.01989			−0.509946	−	0.860207i	$-0.670335\pi$
$643$	−25.8618			−1.01989			−0.509946	+	0.860207i	$0.670335\pi$
$644$	−9.73848	+	9.73848i	−0.383750	+	0.383750i
$645$		0			0
$646$	−14.9850			−0.589576
$647$	−6.25436	−	6.25436i	−0.245884	−	0.245884i	0.573395	−	0.819279i	$-0.305626\pi$
$647$	−6.25436	−	6.25436i	−0.245884	−	0.245884i	−0.819279	+	0.573395i	$0.805626\pi$
$648$		0			0
$649$	−16.0418			−0.629695
$650$	15.4706	−	9.25528i	0.606807	−	0.363022i
$651$		0			0
$652$		−	16.1076i		−	0.630822i
$653$	−9.13834	−	9.13834i	−0.357611	−	0.357611i	0.505321	−	0.862932i	$-0.331374\pi$
$653$	−9.13834	−	9.13834i	−0.357611	−	0.357611i	−0.862932	+	0.505321i	$0.831374\pi$
$654$		0			0
$655$	5.29531	+	31.3531i	0.206905	+	1.22507i
$656$	6.40807	−	6.40807i	0.250193	−	0.250193i
$657$		0			0
$658$			12.6440i			0.492914i
$659$		−	6.44506i		−	0.251064i	−0.992090	−	0.125532i	$-0.959936\pi$
$659$		−	6.44506i		−	0.251064i	0.992090	−	0.125532i	$-0.0400638\pi$
$660$		0			0
$661$	−7.50088	−	7.50088i	−0.291750	−	0.291750i	0.546021	−	0.837771i	$-0.316142\pi$
$661$	−7.50088	−	7.50088i	−0.291750	−	0.291750i	−0.837771	+	0.546021i	$0.816142\pi$
$662$	23.7654	+	23.7654i	0.923668	+	0.923668i
$663$		0			0
$664$			9.18339i			0.356385i
$665$	−4.44599	+	6.25297i	−0.172408	+	0.242480i
$666$		0			0
$667$	27.2414	+	27.2414i	1.05479	+	1.05479i
$668$	10.3428			0.400174
$669$		0			0
$670$	3.25154	+	19.2521i	0.125618	+	0.743773i
$671$	−27.9935	−	27.9935i	−1.08068	−	1.08068i
$672$		0			0
$673$	29.6887	−	29.6887i	1.14441	−	1.14441i	0.156780	−	0.987634i	$-0.449889\pi$
$673$	29.6887	−	29.6887i	1.14441	−	1.14441i	0.987634	−	0.156780i	$-0.0501113\pi$
$674$	6.87634	−	6.87634i	0.264867	−	0.264867i
$675$		0			0
$676$	11.9277	−	5.17007i	0.458758	−	0.198849i
$677$	−4.17961	+	4.17961i	−0.160636	+	0.160636i	−0.782848	−	0.622213i	$-0.786234\pi$
$677$	−4.17961	+	4.17961i	−0.160636	+	0.160636i	0.622213	+	0.782848i	$0.286234\pi$
$678$		0			0
$679$		−	23.2597i		−	0.892626i
$680$	13.0690	+	9.29230i	0.501172	+	0.356344i
$681$		0			0
$682$		−	11.7334i		−	0.449297i
$683$		−	16.7391i		−	0.640505i	−0.947332	−	0.320252i	$-0.896232\pi$
$683$		−	16.7391i		−	0.640505i	0.947332	−	0.320252i	$-0.103768\pi$
$684$		0			0
$685$	−5.91392	−	35.0158i	−0.225959	−	1.33788i
$686$			18.5614i			0.708678i
$687$		0			0
$688$	1.01618	−	1.01618i	0.0387417	−	0.0387417i
$689$	−7.49733	+	11.4211i	−0.285626	+	0.435107i
$690$		0			0
$691$	22.3775	−	22.3775i	0.851282	−	0.851282i	−0.139009	−	0.990291i	$-0.544392\pi$
$691$	22.3775	−	22.3775i	0.851282	−	0.851282i	0.990291	+	0.139009i	$0.0443917\pi$
$692$	−0.533953	+	0.533953i	−0.0202978	+	0.0202978i
$693$		0			0
$694$	12.9364	+	12.9364i	0.491059	+	0.491059i
$695$	39.9554	−	6.74819i	1.51560	−	0.255974i
$696$		0			0
$697$	64.9900			2.46167
$698$	0.121963	+	0.121963i	0.00461636	+	0.00461636i
$699$		0			0
$700$	7.75503	−	2.69646i	0.293113	−	0.101916i
$701$			11.8772i			0.448597i	0.974520	+	0.224298i	$0.0720091\pi$
$701$			11.8772i			0.448597i	−0.974520	+	0.224298i	$0.927991\pi$
$702$		0			0
$703$	−3.79811	−	3.79811i	−0.143249	−	0.143249i
$704$	−4.51787	−	4.51787i	−0.170274	−	0.170274i
$705$		0			0
$706$		−	18.7416i		−	0.705349i
$707$		−	18.7882i		−	0.706601i
$708$		0			0
$709$	−33.4113	+	33.4113i	−1.25479	+	1.25479i	−0.301241	+	0.953548i	$0.597401\pi$
$709$	−33.4113	+	33.4113i	−1.25479	+	1.25479i	−0.953548	+	0.301241i	$0.902599\pi$
$710$	−2.57101	+	3.61595i	−0.0964884	+	0.135704i
$711$		0			0
$712$	1.46610	+	1.46610i	0.0549443	+	0.0549443i
$713$		−	15.4023i		−	0.576821i
$714$		0			0
$715$	−47.1686	−	20.7021i	−1.76401	−	0.774214i
$716$	10.8352			0.404932
$717$		0			0
$718$	−6.51327	−	6.51327i	−0.243073	−	0.243073i
$719$	−8.08666			−0.301582			−0.150791	−	0.988566i	$-0.548182\pi$
$719$	−8.08666			−0.301582			−0.150791	+	0.988566i	$0.548182\pi$
$720$		0			0
$721$	16.4233	−	16.4233i	0.611637	−	0.611637i
$722$	−14.6338			−0.544613
$723$		0			0
$724$		−	4.52263i		−	0.168082i
$725$	−7.54279	−	21.6931i	−0.280132	−	0.805662i
$726$		0			0
$727$	−2.52063	−	2.52063i	−0.0934851	−	0.0934851i	0.658818	−	0.752303i	$-0.271057\pi$
$727$	−2.52063	−	2.52063i	−0.0934851	−	0.0934851i	−0.752303	+	0.658818i	$0.771057\pi$
$728$	5.79726	−	1.20237i	0.214861	−	0.0445627i
$729$		0			0
$730$	−4.92003	−	29.1310i	−0.182098	−	1.07819i
$731$	10.3060			0.381182
$732$		0			0
$733$	−2.66812			−0.0985493			−0.0492747	−	0.998785i	$-0.515691\pi$
$733$	−2.66812			−0.0985493			−0.0492747	+	0.998785i	$0.515691\pi$
$734$	−7.79589	−	7.79589i	−0.287752	−	0.287752i
$735$		0			0
$736$	−5.93054	−	5.93054i	−0.218603	−	0.218603i
$737$	39.4488	−	39.4488i	1.45312	−	1.45312i
$738$		0			0
$739$	−16.4289	+	16.4289i	−0.604346	+	0.604346i	−0.941463	−	0.337117i	$-0.890548\pi$
$739$	−16.4289	+	16.4289i	−0.604346	+	0.604346i	0.337117	+	0.941463i	$0.390548\pi$
$740$	0.957238	+	5.66772i	0.0351888	+	0.208350i
$741$		0			0
$742$	−4.39971	+	4.39971i	−0.161519	+	0.161519i
$743$	−32.1163			−1.17823			−0.589116	−	0.808049i	$-0.700524\pi$
$743$	−32.1163			−1.17823			−0.589116	+	0.808049i	$0.700524\pi$
$744$		0			0
$745$	−10.7408	+	15.1062i	−0.393512	+	0.553447i
$746$	−7.40248	+	7.40248i	−0.271024	+	0.271024i
$747$		0			0
$748$		−	45.8197i		−	1.67534i
$749$	−9.74065	+	9.74065i	−0.355916	+	0.355916i
$750$		0			0
$751$		−	2.39261i		−	0.0873074i	−0.999047	−	0.0436537i	$-0.986100\pi$
$751$		−	2.39261i		−	0.0873074i	0.999047	−	0.0436537i	$-0.0138998\pi$
$752$	−7.69994			−0.280788
$753$		0			0
$754$	−3.36338	−	16.2167i	−0.122487	−	0.590576i
$755$	10.1694	−	14.3026i	0.370104	−	0.520525i
$756$		0			0
$757$	15.9202	−	15.9202i	0.578631	−	0.578631i	−0.355895	−	0.934526i	$-0.615824\pi$
$757$	15.9202	−	15.9202i	0.578631	−	0.578631i	0.934526	+	0.355895i	$0.115824\pi$
$758$	−17.2417	+	17.2417i	−0.626246	+	0.626246i
$759$		0			0
$760$	−3.80794	−	2.70752i	−0.138128	−	0.0982121i
$761$	−0.132679	−	0.132679i	−0.00480963	−	0.00480963i	0.704698	−	0.709508i	$-0.251083\pi$
$761$	−0.132679	−	0.132679i	−0.00480963	−	0.00480963i	−0.709508	+	0.704698i	$0.751083\pi$
$762$		0			0
$763$	5.59684	+	5.59684i	0.202619	+	0.202619i
$764$	15.3851			0.556613
$765$		0			0
$766$			0.348683i			0.0125984i
$767$	7.56775	+	4.96784i	0.273256	+	0.179378i
$768$		0			0
$769$	30.0647	+	30.0647i	1.08416	+	1.08416i	0.996117	+	0.0880443i	$0.0280617\pi$
$769$	30.0647	+	30.0647i	1.08416	+	1.08416i	0.0880443	+	0.996117i	$0.471938\pi$
$770$	−19.1198	−	13.5946i	−0.689029	−	0.489914i
$771$		0			0
$772$			3.47402i			0.125033i
$773$	36.4700			1.31173			0.655867	−	0.754876i	$-0.272303\pi$
$773$	36.4700			1.31173			0.655867	+	0.754876i	$0.272303\pi$
$774$		0			0
$775$	−4.00030	+	8.26500i	−0.143695	+	0.296888i
$776$	14.1647			0.508484
$777$		0			0
$778$		−	15.4386i		−	0.553501i
$779$	−18.9363			−0.678463
$780$		0			0
$781$	12.6775			0.453637
$782$		−	60.1469i		−	2.15085i
$783$		0			0
$784$	−4.30354			−0.153698
$785$	−8.34154	−	5.93100i	−0.297722	−	0.211687i
$786$		0			0
$787$	11.9854			0.427232			0.213616	−	0.976918i	$-0.431476\pi$
$787$	11.9854			0.427232			0.213616	+	0.976918i	$0.431476\pi$
$788$		−	21.8842i		−	0.779591i
$789$		0			0
$790$	3.95473	+	23.4156i	0.140703	+	0.833091i
$791$	11.0770	+	11.0770i	0.393853	+	0.393853i
$792$		0			0
$793$	4.53694	+	21.8750i	0.161112	+	0.776806i
$794$		−	0.259593i		−	0.00921260i
$795$		0			0
$796$	−4.82071			−0.170866
$797$	5.03123	+	5.03123i	0.178215	+	0.178215i	0.790577	−	0.612362i	$-0.209780\pi$
$797$	5.03123	+	5.03123i	0.178215	+	0.178215i	−0.612362	+	0.790577i	$0.709780\pi$
$798$		0			0
$799$	−39.0459	−	39.0459i	−1.38135	−	1.38135i
$800$	1.64209	+	4.72266i	0.0580566	+	0.166971i
$801$		0			0
$802$	15.5794	−	15.5794i	0.550128	−	0.550128i
$803$	−59.6915	+	59.6915i	−2.10647	+	2.10647i
$804$		0			0
$805$	−25.0982	−	17.8454i	−0.884597	−	0.628967i
$806$	−3.63363	+	5.53528i	−0.127989	+	0.194972i
$807$		0			0
$808$	11.4416			0.402515
$809$			32.9783i			1.15945i	0.814811	+	0.579727i	$0.196841\pi$
$809$			32.9783i			1.15945i	−0.814811	+	0.579727i	$0.803159\pi$
$810$		0			0
$811$	−16.7487	+	16.7487i	−0.588126	+	0.588126i	−0.937123	−	0.348998i	$-0.886522\pi$
$811$	−16.7487	+	16.7487i	−0.588126	+	0.588126i	0.348998	+	0.937123i	$0.386522\pi$
$812$		−	7.54279i		−	0.264700i
$813$		0			0
$814$	11.6135	−	11.6135i	0.407055	−	0.407055i
$815$	35.5147	−	5.99819i	1.24403	−	0.210107i
$816$		0			0
$817$	−3.00289			−0.105058
$818$	−5.60645	+	5.60645i	−0.196025	+	0.196025i
$819$		0			0
$820$	16.5151	+	11.7425i	0.576731	+	0.410067i
$821$	−11.5961	+	11.5961i	−0.404708	+	0.404708i	−0.879888	−	0.475180i	$-0.842383\pi$
$821$	−11.5961	+	11.5961i	−0.404708	+	0.404708i	0.475180	+	0.879888i	$0.342383\pi$
$822$		0			0
$823$	−26.8196	+	26.8196i	−0.934873	+	0.934873i	−0.998005	−	0.0631321i	$-0.979891\pi$
$823$	−26.8196	+	26.8196i	−0.934873	+	0.934873i	0.0631321	+	0.998005i	$0.479891\pi$
$824$	10.0015	+	10.0015i	0.348418	+	0.348418i
$825$		0			0
$826$	2.91531	+	2.91531i	0.101437	+	0.101437i
$827$	−30.2380			−1.05148			−0.525738	−	0.850646i	$-0.676211\pi$
$827$	−30.2380			−1.05148			−0.525738	+	0.850646i	$0.676211\pi$
$828$		0			0
$829$	−49.1999			−1.70878			−0.854392	−	0.519630i	$-0.826070\pi$
$829$	−49.1999			−1.70878			−0.854392	+	0.519630i	$0.826070\pi$
$830$	−20.2479	+	3.41973i	−0.702816	+	0.118701i
$831$		0			0
$832$	0.732218	+	3.53042i	0.0253851	+	0.122395i
$833$	−21.8230	−	21.8230i	−0.756123	−	0.756123i
$834$		0			0
$835$	3.85147	+	22.8042i	0.133286	+	0.789172i
$836$			13.3506i			0.461741i
$837$		0			0
$838$	−0.132299			−0.00457020
$839$	21.4254	−	21.4254i	0.739686	−	0.739686i	−0.232831	−	0.972517i	$-0.574799\pi$
$839$	21.4254	−	21.4254i	0.739686	−	0.739686i	0.972517	+	0.232831i	$0.0747990\pi$
$840$		0			0
$841$	7.90058			0.272434
$842$	28.6488	+	28.6488i	0.987303	+	0.987303i
$843$		0			0
$844$	6.77515			0.233210
$845$	15.8409	+	24.3735i	0.544942	+	0.838473i
$846$		0			0
$847$			48.9709i			1.68266i
$848$	−2.67934	−	2.67934i	−0.0920089	−	0.0920089i
$849$		0			0
$850$	−15.6214	+	32.2753i	−0.535810	+	1.10703i
$851$	15.2449	−	15.2449i	0.522589	−	0.522589i
$852$		0			0
$853$		−	5.78152i		−	0.197955i	−0.995090	−	0.0989777i	$-0.968443\pi$
$853$		−	5.78152i		−	0.197955i	0.995090	−	0.0989777i	$-0.0315573\pi$
$854$			10.1747i			0.348169i
$855$		0			0
$856$	−5.93186	−	5.93186i	−0.202747	−	0.202747i
$857$	5.18577	+	5.18577i	0.177142	+	0.177142i	0.790109	−	0.612966i	$-0.210024\pi$
$857$	5.18577	+	5.18577i	0.177142	+	0.177142i	−0.612966	+	0.790109i	$0.710024\pi$
$858$		0			0
$859$			21.6315i			0.738057i	0.929418	+	0.369029i	$0.120310\pi$
$859$			21.6315i			0.738057i	−0.929418	+	0.369029i	$0.879690\pi$
$860$	2.61894	+	1.86212i	0.0893050	+	0.0634977i
$861$		0			0
$862$	13.6409	+	13.6409i	0.464610	+	0.464610i
$863$	34.7156			1.18173			0.590866	−	0.806770i	$-0.298786\pi$
$863$	34.7156			1.18173			0.590866	+	0.806770i	$0.298786\pi$
$864$		0			0
$865$	−1.37612	−	0.978447i	−0.0467894	−	0.0332682i
$866$	−9.01360	−	9.01360i	−0.306295	−	0.306295i
$867$		0			0
$868$	−2.13235	+	2.13235i	−0.0723766	+	0.0723766i
$869$	47.9802	−	47.9802i	1.62762	−	1.62762i
$870$		0			0
$871$	−30.8266	+	6.39353i	−1.04452	+	0.216636i
$872$	−3.40836	+	3.40836i	−0.115422	+	0.115422i
$873$		0			0
$874$			17.5251i			0.592797i
$875$	8.83310	+	16.0945i	0.298613	+	0.544094i
$876$		0			0
$877$			29.4836i			0.995590i	0.867295	+	0.497795i	$0.165857\pi$
$877$			29.4836i			0.995590i	−0.867295	+	0.497795i	$0.834143\pi$
$878$			5.55874i			0.187598i
$879$		0			0
$880$	8.27882	−	11.6436i	0.279079	−	0.392505i
$881$		−	9.72771i		−	0.327735i	−0.986482	−	0.163867i	$-0.947603\pi$
$881$		−	9.72771i		−	0.327735i	0.986482	−	0.163867i	$-0.0523969\pi$
$882$		0			0
$883$	2.79370	−	2.79370i	0.0940155	−	0.0940155i	−0.658535	−	0.752550i	$-0.728823\pi$
$883$	2.79370	−	2.79370i	0.0940155	−	0.0940155i	0.752550	+	0.658535i	$0.228823\pi$
$884$	−14.1895	+	21.6156i	−0.477245	+	0.727011i
$885$		0			0
$886$	5.91848	−	5.91848i	0.198835	−	0.198835i
$887$	−6.99439	+	6.99439i	−0.234849	+	0.234849i	−0.814713	−	0.579864i	$-0.803106\pi$
$887$	−6.99439	+	6.99439i	−0.234849	+	0.234849i	0.579864	+	0.814713i	$0.303106\pi$
$888$		0			0
$889$	−0.755320	−	0.755320i	−0.0253326	−	0.0253326i
$890$	−2.68657	+	3.77846i	−0.0900539	+	0.126654i
$891$		0			0
$892$	13.7744			0.461201
$893$	11.3769	+	11.3769i	0.380714	+	0.380714i
$894$		0			0
$895$	4.03485	+	23.8900i	0.134870	+	0.798554i
$896$			1.64209i			0.0548583i
$897$		0			0
$898$	7.11677	+	7.11677i	0.237490	+	0.237490i
$899$	5.96481	+	5.96481i	0.198938	+	0.198938i
$900$		0			0
$901$		−	27.1736i		−	0.905283i
$902$		−	57.9017i		−	1.92792i
$903$		0			0
$904$	−6.74568	+	6.74568i	−0.224358	+	0.224358i
$905$	9.97169	−	1.68415i	0.331470	−	0.0559829i
$906$		0			0
$907$	−31.9825	−	31.9825i	−1.06196	−	1.06196i	−0.997949	−	0.0640135i	$-0.979610\pi$
$907$	−31.9825	−	31.9825i	−1.06196	−	1.06196i	−0.0640135	−	0.997949i	$-0.520390\pi$
$908$		−	25.3628i		−	0.841693i
$909$		0			0
$910$	4.80983	+	12.3343i	0.159444	+	0.408878i
$911$	−20.6804			−0.685173			−0.342587	−	0.939486i	$-0.611303\pi$
$911$	−20.6804			−0.685173			−0.342587	+	0.939486i	$0.611303\pi$
$912$		0			0
$913$	41.4894	+	41.4894i	1.37310	+	1.37310i
$914$	15.7988			0.522577
$915$		0			0
$916$	2.22305	−	2.22305i	0.0734517	−	0.0734517i
$917$	−23.3507			−0.771107
$918$		0			0
$919$		−	2.17907i		−	0.0718809i	−0.999354	−	0.0359405i	$-0.988557\pi$
$919$		−	2.17907i		−	0.0718809i	0.999354	−	0.0359405i	$-0.0114427\pi$
$920$	10.8675	−	15.2843i	0.358290	−	0.503910i
$921$		0			0
$922$	14.0129	+	14.0129i	0.461489	+	0.461489i
$923$	−5.98064	−	3.92598i	−0.196855	−	0.129225i
$924$		0			0
$925$	−12.1400	+	4.22112i	−0.399160	+	0.138790i
$926$	5.90834			0.194160
$927$		0			0
$928$	4.59341			0.150786
$929$	27.3886	+	27.3886i	0.898591	+	0.898591i	0.995312	−	0.0967204i	$-0.0308353\pi$
$929$	27.3886	+	27.3886i	0.898591	+	0.898591i	−0.0967204	+	0.995312i	$0.530835\pi$
$930$		0			0
$931$	6.35863	+	6.35863i	0.208396	+	0.208396i
$932$	−0.221543	+	0.221543i	−0.00725690	+	0.00725690i
$933$		0			0
$934$	−11.1464	+	11.1464i	−0.364722	+	0.364722i
$935$	101.025	−	17.0625i	3.30388	−	0.558002i
$936$		0			0
$937$	13.3258	−	13.3258i	0.435334	−	0.435334i	−0.455104	−	0.890438i	$-0.650398\pi$
$937$	13.3258	−	13.3258i	0.435334	−	0.435334i	0.890438	+	0.455104i	$0.150398\pi$
$938$	−14.3383			−0.468161
$939$		0			0
$940$	−2.86732	−	16.9771i	−0.0935217	−	0.553733i
$941$	−34.6341	+	34.6341i	−1.12904	+	1.12904i	−0.138705	+	0.990334i	$0.544294\pi$
$941$	−34.6341	+	34.6341i	−1.12904	+	1.12904i	−0.990334	+	0.138705i	$0.955706\pi$
$942$		0			0
$943$		−	76.0067i		−	2.47512i
$944$	−1.77537	+	1.77537i	−0.0577833	+	0.0577833i
$945$		0			0
$946$		−	9.18199i		−	0.298532i
$947$	−45.2197			−1.46944			−0.734721	−	0.678369i	$-0.762687\pi$
$947$	−45.2197			−1.46944			−0.734721	+	0.678369i	$0.762687\pi$
$948$		0			0
$949$	46.6449	−	9.67428i	1.51416	−	0.314041i
$950$	4.55165	−	9.40413i	0.147675	−	0.305110i
$951$		0			0
$952$	−8.32694	+	8.32694i	−0.269878	+	0.269878i
$953$	11.7413	−	11.7413i	0.380337	−	0.380337i	−0.490887	−	0.871223i	$-0.663327\pi$
$953$	11.7413	−	11.7413i	0.380337	−	0.380337i	0.871223	+	0.490887i	$0.163327\pi$
$954$		0			0
$955$	5.72913	+	33.9217i	0.185390	+	1.09768i
$956$	−13.7444	−	13.7444i	−0.444525	−	0.444525i
$957$		0			0
$958$	4.97107	+	4.97107i	0.160608	+	0.160608i
$959$	26.0785			0.842119
$960$		0			0
$961$			27.6275i			0.891209i
$962$	−9.07522	+	1.88222i	−0.292597	+	0.0606853i
$963$		0			0
$964$	19.7069	+	19.7069i	0.634716	+	0.634716i
$965$	−7.65968	+	1.29367i	−0.246574	+	0.0416446i
$966$		0			0
$967$		−	6.32736i		−	0.203474i	−0.994811	−	0.101737i	$-0.967560\pi$
$967$		−	6.32736i		−	0.203474i	0.994811	−	0.101737i	$-0.0324401\pi$
$968$	−29.8223			−0.958526
$969$		0			0
$970$	5.27469	+	31.2310i	0.169360	+	1.00277i
$971$	9.00413			0.288956			0.144478	−	0.989508i	$-0.453850\pi$
$971$	9.00413			0.288956			0.144478	+	0.989508i	$0.453850\pi$
$972$		0			0
$973$			29.7574i			0.953979i
$974$	−25.1117			−0.804632
$975$		0			0
$976$	−6.19616			−0.198334
$977$			13.3948i			0.428538i	0.976775	+	0.214269i	$0.0687369\pi$
$977$			13.3948i			0.428538i	−0.976775	+	0.214269i	$0.931263\pi$
$978$		0			0
$979$	13.2473			0.423385
$980$	−1.60256	−	9.48864i	−0.0511920	−	0.303103i
$981$		0			0
$982$	−42.0378			−1.34148
$983$			39.9743i			1.27498i	0.770458	+	0.637491i	$0.220028\pi$
$983$			39.9743i			1.27498i	−0.770458	+	0.637491i	$0.779972\pi$
$984$		0			0
$985$	48.2511	−	8.14928i	1.53741	−	0.259658i
$986$	23.2929	+	23.2929i	0.741798	+	0.741798i
$987$		0			0
$988$	4.13443	−	6.29819i	0.131534	−	0.200372i
$989$		−	12.0531i		−	0.383265i
$990$		0			0
$991$	30.1024			0.956235			0.478118	−	0.878296i	$-0.341319\pi$
$991$	30.1024			0.956235			0.478118	+	0.878296i	$0.341319\pi$
$992$	−1.29856	−	1.29856i	−0.0412293	−	0.0412293i
$993$		0			0
$994$	−2.30391	−	2.30391i	−0.0730757	−	0.0730757i
$995$	−1.79515	−	10.6289i	−0.0569100	−	0.336959i
$996$		0			0
$997$	−35.4246	+	35.4246i	−1.12191	+	1.12191i	−0.130452	+	0.991455i	$0.541643\pi$
$997$	−35.4246	+	35.4246i	−1.12191	+	1.12191i	−0.991455	+	0.130452i	$0.958357\pi$
$998$	−10.5783	+	10.5783i	−0.334849	+	0.334849i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.w.g.343.3	yes	14
3.2	odd	2		1170.2.w.h.343.5	yes	14
5.2	odd	4		1170.2.m.h.577.6	yes	14
13.8	odd	4		1170.2.m.h.73.6	yes	14
15.2	even	4		1170.2.m.g.577.2	yes	14
39.8	even	4		1170.2.m.g.73.2	✓	14
65.47	even	4	inner	1170.2.w.g.307.3	yes	14
195.47	odd	4		1170.2.w.h.307.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.m.g.73.2	✓	14	39.8	even	4
1170.2.m.g.577.2	yes	14	15.2	even	4
1170.2.m.h.73.6	yes	14	13.8	odd	4
1170.2.m.h.577.6	yes	14	5.2	odd	4
1170.2.w.g.307.3	yes	14	65.47	even	4	inner
1170.2.w.g.343.3	yes	14	1.1	even	1	trivial
1170.2.w.h.307.5	yes	14	195.47	odd	4
1170.2.w.h.343.5	yes	14	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.372382 - 2.20484i) q^{5} +1.64209 q^{7} +1.00000i q^{8} +(-2.20484 + 0.372382i) q^{10} +(4.51787 + 4.51787i) q^{11} +(-0.732218 - 3.53042i) q^{13} -1.64209i q^{14} +1.00000 q^{16} +(5.07094 + 5.07094i) q^{17} +(-1.47753 - 1.47753i) q^{19} +(0.372382 + 2.20484i) q^{20} +(4.51787 - 4.51787i) q^{22} +(5.93054 - 5.93054i) q^{23} +(-4.72266 + 1.64209i) q^{25} +(-3.53042 + 0.732218i) q^{26} -1.64209 q^{28} +4.59341i q^{29} +(1.29856 - 1.29856i) q^{31} -1.00000i q^{32} +(5.07094 - 5.07094i) q^{34} +(-0.611485 - 3.62055i) q^{35} +2.57058 q^{37} +(-1.47753 + 1.47753i) q^{38} +(2.20484 - 0.372382i) q^{40} +(6.40807 - 6.40807i) q^{41} +(1.01618 - 1.01618i) q^{43} +(-4.51787 - 4.51787i) q^{44} +(-5.93054 - 5.93054i) q^{46} -7.69994 q^{47} -4.30354 q^{49} +(1.64209 + 4.72266i) q^{50} +(0.732218 + 3.53042i) q^{52} +(-2.67934 - 2.67934i) q^{53} +(8.27882 - 11.6436i) q^{55} +1.64209i q^{56} +4.59341 q^{58} +(-1.77537 + 1.77537i) q^{59} -6.19616 q^{61} +(-1.29856 - 1.29856i) q^{62} -1.00000 q^{64} +(-7.51135 + 2.92909i) q^{65} -8.73173i q^{67} +(-5.07094 - 5.07094i) q^{68} +(-3.62055 + 0.611485i) q^{70} +(1.40304 - 1.40304i) q^{71} +13.2123i q^{73} -2.57058i q^{74} +(1.47753 + 1.47753i) q^{76} +(7.41875 + 7.41875i) q^{77} -10.6201i q^{79} +(-0.372382 - 2.20484i) q^{80} +(-6.40807 - 6.40807i) q^{82} +9.18339 q^{83} +(9.29230 - 13.0690i) q^{85} +(-1.01618 - 1.01618i) q^{86} +(-4.51787 + 4.51787i) q^{88} +(1.46610 - 1.46610i) q^{89} +(-1.20237 - 5.79726i) q^{91} +(-5.93054 + 5.93054i) q^{92} +7.69994i q^{94} +(-2.70752 + 3.80794i) q^{95} -14.1647i q^{97} +4.30354i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{4} - 2 q^{5} + 4 q^{13} + 14 q^{16} + 14 q^{17} - 12 q^{19} + 2 q^{20} - 10 q^{25} + 6 q^{26} + 12 q^{31} + 14 q^{34} + 12 q^{35} + 20 q^{37} - 12 q^{38} - 2 q^{41} - 8 q^{47} + 14 q^{49} - 4 q^{52}+ \cdots + 24 q^{95}+O(q^{100}) \) 14 * q - 14 * q^4 - 2 * q^5 + 4 * q^13 + 14 * q^16 + 14 * q^17 - 12 * q^19 + 2 * q^20 - 10 * q^25 + 6 * q^26 + 12 * q^31 + 14 * q^34 + 12 * q^35 + 20 * q^37 - 12 * q^38 - 2 * q^41 - 8 * q^47 + 14 * q^49 - 4 * q^52 + 6 * q^53 + 32 * q^55 + 16 * q^58 - 16 * q^59 + 24 * q^61 - 12 * q^62 - 14 * q^64 - 4 * q^65 - 14 * q^68 - 4 * q^70 - 24 * q^71 + 12 * q^76 + 16 * q^77 - 2 * q^80 + 2 * q^82 + 8 * q^83 + 2 * q^85 + 42 * q^89 - 8 * q^91 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more