LMFDB - Embedded newform 1512.2.c.e.757.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1512,2,Mod(757,1512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1512, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1512.757"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	20.0.1646001224014411784746814245175296.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + x^{18} + 4x^{16} + 8x^{12} + 4x^{10} + 32x^{8} + 256x^{4} + 256x^{2} + 1024 $ x^20 + x^18 + 4x^16 + 8x^12 + 4x^10 + 32x^8 + 256x^4 + 256x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.1
Root			$-1.37874 - 0.314750i$ of defining polynomial
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.e.757.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37874 - 0.314750i) q^{2} +(1.80186 + 0.867919i) q^{4} -0.114591i q^{5} -1.00000 q^{7} +(-2.21113 - 1.76377i) q^{8} +(-0.0360676 + 0.157992i) q^{10} -0.412956i q^{11} -1.73584i q^{13} +(1.37874 + 0.314750i) q^{14} +(2.49343 + 3.12774i) q^{16} -2.50762 q^{17} +6.85261i q^{19} +(0.0994559 - 0.206478i) q^{20} +(-0.129978 + 0.569360i) q^{22} -4.42226 q^{23} +4.98687 q^{25} +(-0.546355 + 2.39327i) q^{26} +(-1.80186 - 0.867919i) q^{28} -1.85559i q^{29} +5.60373 q^{31} +(-2.45335 - 5.09716i) q^{32} +(3.45737 + 0.789274i) q^{34} +0.114591i q^{35} +4.39099i q^{37} +(2.15686 - 9.44798i) q^{38} +(-0.202113 + 0.253376i) q^{40} +2.39907 q^{41} +4.35614i q^{43} +(0.358412 - 0.744091i) q^{44} +(6.09716 + 1.39191i) q^{46} +7.23070 q^{47} +1.00000 q^{49} +(-6.87561 - 1.56962i) q^{50} +(1.50657 - 3.12774i) q^{52} +11.2241i q^{53} -0.0473212 q^{55} +(2.21113 + 1.76377i) q^{56} +(-0.584047 + 2.55838i) q^{58} +4.25900i q^{59} -7.35936i q^{61} +(-7.72610 - 1.76377i) q^{62} +(1.77820 + 7.79987i) q^{64} -0.198912 q^{65} +6.25549i q^{67} +(-4.51840 - 2.17641i) q^{68} +(0.0360676 - 0.157992i) q^{70} +0.608276 q^{71} -14.1550 q^{73} +(1.38207 - 6.05405i) q^{74} +(-5.94750 + 12.3475i) q^{76} +0.412956i q^{77} +8.19950 q^{79} +(0.358412 - 0.285726i) q^{80} +(-3.30771 - 0.755108i) q^{82} +4.88023i q^{83} +0.287352i q^{85} +(1.37110 - 6.00600i) q^{86} +(-0.728361 + 0.913100i) q^{88} +10.4217 q^{89} +1.73584i q^{91} +(-7.96832 - 3.83816i) q^{92} +(-9.96928 - 2.27586i) q^{94} +0.785249 q^{95} -3.42009 q^{97} +(-1.37874 - 0.314750i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{4} - 20 q^{7} - 12 q^{10} - 14 q^{16} + 8 q^{22} - 28 q^{25} + 2 q^{28} + 36 q^{31} - 6 q^{34} - 16 q^{40} - 18 q^{46} + 20 q^{49} + 94 q^{52} + 48 q^{55} + 66 q^{58} + 22 q^{64} + 12 q^{70}+ \cdots + 56 q^{97}+O(q^{100}) $ 20 * q - 2 * q^4 - 20 * q^7 - 12 * q^10 - 14 * q^16 + 8 * q^22 - 28 * q^25 + 2 * q^28 + 36 * q^31 - 6 * q^34 - 16 * q^40 - 18 * q^46 + 20 * q^49 + 94 * q^52 + 48 * q^55 + 66 * q^58 + 22 * q^64 + 12 * q^70 + 12 * q^76 + 64 * q^79 - 92 * q^88 - 24 * q^94 + 56 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	−1.37874	−	0.314750i	−0.974919	−	0.222562i
$2$	−1.37874	−	0.314750i	−0.974919	−	0.222562i
$3$		0			0
$3$		0			0
$4$	1.80186	+	0.867919i	0.900932	+	0.433959i
$5$		−	0.114591i		−	0.0512468i	−0.999672	−	0.0256234i	$-0.991843\pi$
$5$		−	0.114591i		−	0.0512468i	0.999672	−	0.0256234i	$-0.00815707\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.21113	−	1.76377i	−0.781753	−	0.623588i
$9$		0			0
$10$	−0.0360676	+	0.157992i	−0.0114056	+	0.0499615i
$11$		−	0.412956i		−	0.124511i	−0.998060	−	0.0622555i	$-0.980171\pi$
$11$		−	0.412956i		−	0.124511i	0.998060	−	0.0622555i	$-0.0198294\pi$
$12$		0			0
$13$		−	1.73584i		−	0.481435i	−0.970595	−	0.240717i	$-0.922617\pi$
$13$		−	1.73584i		−	0.481435i	0.970595	−	0.240717i	$-0.0773827\pi$
$14$	1.37874	+	0.314750i	0.368485	+	0.0841205i
$15$		0			0
$16$	2.49343	+	3.12774i	0.623359	+	0.781936i
$17$	−2.50762			−0.608188			−0.304094	−	0.952642i	$-0.598354\pi$
$17$	−2.50762			−0.608188			−0.304094	+	0.952642i	$0.598354\pi$
$18$		0			0
$19$			6.85261i			1.57210i	0.618166	+	0.786048i	$0.287876\pi$
$19$			6.85261i			1.57210i	−0.618166	+	0.786048i	$0.712124\pi$
$20$	0.0994559	−	0.206478i	0.0222390	−	0.0461699i
$21$		0			0
$22$	−0.129978	+	0.569360i	−0.0277114	+	0.121388i
$23$	−4.42226			−0.922106			−0.461053	−	0.887373i	$-0.652528\pi$
$23$	−4.42226			−0.922106			−0.461053	+	0.887373i	$0.652528\pi$
$24$		0			0
$25$	4.98687			0.997374
$26$	−0.546355	+	2.39327i	−0.107149	+	0.469360i
$27$		0			0
$28$	−1.80186	−	0.867919i	−0.340520	−	0.164021i
$29$		−	1.85559i		−	0.344575i	−0.985047	−	0.172287i	$-0.944884\pi$
$29$		−	1.85559i		−	0.344575i	0.985047	−	0.172287i	$-0.0551158\pi$
$30$		0			0
$31$	5.60373			1.00646			0.503230	−	0.864153i	$-0.332145\pi$
$31$	5.60373			1.00646			0.503230	+	0.864153i	$0.332145\pi$
$32$	−2.45335	−	5.09716i	−0.433695	−	0.901060i
$33$		0			0
$34$	3.45737	+	0.789274i	0.592934	+	0.135359i
$35$			0.114591i			0.0193695i
$36$		0			0
$37$			4.39099i			0.721875i	0.932590	+	0.360938i	$0.117543\pi$
$37$			4.39099i			0.721875i	−0.932590	+	0.360938i	$0.882457\pi$
$38$	2.15686	−	9.44798i	0.349888	−	1.53267i
$39$		0			0
$40$	−0.202113	+	0.253376i	−0.0319569	+	0.0400623i
$41$	2.39907			0.374672			0.187336	−	0.982296i	$-0.440015\pi$
$41$	2.39907			0.374672			0.187336	+	0.982296i	$0.440015\pi$
$42$		0			0
$43$			4.35614i			0.664306i	0.943226	+	0.332153i	$0.107775\pi$
$43$			4.35614i			0.664306i	−0.943226	+	0.332153i	$0.892225\pi$
$44$	0.358412	−	0.744091i	0.0540327	−	0.112176i
$45$		0			0
$46$	6.09716	+	1.39191i	0.898978	+	0.205225i
$47$	7.23070			1.05471			0.527353	−	0.849646i	$-0.323185\pi$
$47$	7.23070			1.05471			0.527353	+	0.849646i	$0.323185\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−6.87561	−	1.56962i	−0.972358	−	0.221977i
$51$		0			0
$52$	1.50657	−	3.12774i	0.208923	−	0.433740i
$53$			11.2241i			1.54175i	0.636983	+	0.770877i	$0.280182\pi$
$53$			11.2241i			1.54175i	−0.636983	+	0.770877i	$0.719818\pi$
$54$		0			0
$55$	−0.0473212			−0.00638079
$56$	2.21113	+	1.76377i	0.295475	+	0.235694i
$57$		0			0
$58$	−0.584047	+	2.55838i	−0.0766892	+	0.335932i
$59$			4.25900i			0.554475i	0.960801	+	0.277237i	$0.0894188\pi$
$59$			4.25900i			0.554475i	−0.960801	+	0.277237i	$0.910581\pi$
$60$		0			0
$61$		−	7.35936i		−	0.942269i	−0.882061	−	0.471135i	$-0.843845\pi$
$61$		−	7.35936i		−	0.942269i	0.882061	−	0.471135i	$-0.156155\pi$
$62$	−7.72610	−	1.76377i	−0.981216	−	0.223999i
$63$		0			0
$64$	1.77820	+	7.79987i	0.222276	+	0.974984i
$65$	−0.198912			−0.0246720
$66$		0			0
$67$			6.25549i			0.764230i	0.924115	+	0.382115i	$0.124804\pi$
$67$			6.25549i			0.764230i	−0.924115	+	0.382115i	$0.875196\pi$
$68$	−4.51840	−	2.17641i	−0.547936	−	0.263929i
$69$		0			0
$70$	0.0360676	−	0.157992i	0.00431090	−	0.0188837i
$71$	0.608276			0.0721891			0.0360946	−	0.999348i	$-0.488508\pi$
$71$	0.608276			0.0721891			0.0360946	+	0.999348i	$0.488508\pi$
$72$		0			0
$73$	−14.1550			−1.65671			−0.828357	−	0.560201i	$-0.810724\pi$
$73$	−14.1550			−1.65671			−0.828357	+	0.560201i	$0.810724\pi$
$74$	1.38207	−	6.05405i	0.160662	−	0.703769i
$75$		0			0
$76$	−5.94750	+	12.3475i	−0.682225	+	1.41635i
$77$			0.412956i			0.0470607i
$78$		0			0
$79$	8.19950			0.922516			0.461258	−	0.887266i	$-0.347398\pi$
$79$	8.19950			0.922516			0.461258	+	0.887266i	$0.347398\pi$
$80$	0.358412	−	0.285726i	0.0400717	−	0.0319451i
$81$		0			0
$82$	−3.30771	−	0.755108i	−0.365275	−	0.0833878i
$83$			4.88023i			0.535675i	0.963464	+	0.267838i	$0.0863091\pi$
$83$			4.88023i			0.535675i	−0.963464	+	0.267838i	$0.913691\pi$
$84$		0			0
$85$			0.287352i			0.0311677i
$86$	1.37110	−	6.00600i	0.147849	−	0.647644i
$87$		0			0
$88$	−0.728361	+	0.913100i	−0.0776436	+	0.0973368i
$89$	10.4217			1.10469			0.552347	−	0.833614i	$-0.313732\pi$
$89$	10.4217			1.10469			0.552347	+	0.833614i	$0.313732\pi$
$90$		0			0
$91$			1.73584i			0.181965i
$92$	−7.96832	−	3.83816i	−0.830755	−	0.400156i
$93$		0			0
$94$	−9.96928	−	2.27586i	−1.02825	−	0.234737i
$95$	0.785249			0.0805649
$96$		0			0
$97$	−3.42009			−0.347258			−0.173629	−	0.984811i	$-0.555549\pi$
$97$	−3.42009			−0.347258			−0.173629	+	0.984811i	$0.555549\pi$
$98$	−1.37874	−	0.314750i	−0.139274	−	0.0317945i
$99$		0			0
$100$	8.98566	+	4.32820i	0.898566	+	0.432820i
$101$			0.203905i			0.0202893i	0.999949	+	0.0101446i	$0.00322920\pi$
$101$			0.203905i			0.0202893i	−0.999949	+	0.0101446i	$0.996771\pi$
$102$		0			0
$103$	7.16809			0.706293			0.353147	−	0.935568i	$-0.385112\pi$
$103$	7.16809			0.706293			0.353147	+	0.935568i	$0.385112\pi$
$104$	−3.06162	+	3.83816i	−0.300217	+	0.376363i
$105$		0			0
$106$	3.53280	−	15.4752i	0.343136	−	1.50309i
$107$			7.46742i			0.721902i	0.932585	+	0.360951i	$0.117548\pi$
$107$			7.46742i			0.721902i	−0.932585	+	0.360951i	$0.882452\pi$
$108$		0			0
$109$		−	2.11355i		−	0.202442i	−0.994864	−	0.101221i	$-0.967725\pi$
$109$		−	2.11355i		−	0.202442i	0.994864	−	0.101221i	$-0.0322749\pi$
$110$	0.0652438	+	0.0148943i	0.00622075	+	0.00142012i
$111$		0			0
$112$	−2.49343	−	3.12774i	−0.235607	−	0.295544i
$113$	−4.72972			−0.444935			−0.222467	−	0.974940i	$-0.571411\pi$
$113$	−4.72972			−0.444935			−0.222467	+	0.974940i	$0.571411\pi$
$114$		0			0
$115$			0.506753i			0.0472550i
$116$	1.61050	−	3.34353i	0.149531	−	0.310439i
$117$		0			0
$118$	1.34052	−	5.87207i	0.123405	−	0.540568i
$119$	2.50762			0.229873
$120$		0			0
$121$	10.8295			0.984497
$122$	−2.31636	+	10.1467i	−0.209713	+	0.918636i
$123$		0			0
$124$	10.0972	+	4.86358i	0.906752	+	0.436763i
$125$		−	1.14441i		−	0.102359i
$126$		0			0
$127$	−9.55123			−0.847535			−0.423767	−	0.905771i	$-0.639293\pi$
$127$	−9.55123			−0.847535			−0.423767	+	0.905771i	$0.639293\pi$
$128$	0.00332222	−	11.3137i	0.000293646	−	1.00000i
$129$		0			0
$130$	0.274248	+	0.0626075i	0.0240532	+	0.00549104i
$131$			18.5084i			1.61709i	0.588435	+	0.808544i	$0.299744\pi$
$131$			18.5084i			1.61709i	−0.588435	+	0.808544i	$0.700256\pi$
$132$		0			0
$133$		−	6.85261i		−	0.594196i
$134$	1.96891	−	8.62471i	0.170088	−	0.745062i
$135$		0			0
$136$	5.54468	+	4.42288i	0.475453	+	0.379259i
$137$	8.42852			0.720097			0.360048	−	0.932934i	$-0.382760\pi$
$137$	8.42852			0.720097			0.360048	+	0.932934i	$0.382760\pi$
$138$		0			0
$139$			13.8639i			1.17592i	0.808890	+	0.587961i	$0.200069\pi$
$139$			13.8639i			1.17592i	−0.808890	+	0.587961i	$0.799931\pi$
$140$	−0.0994559	+	0.206478i	−0.00840556	+	0.0174506i
$141$		0			0
$142$	−0.838657	−	0.191455i	−0.0703785	−	0.0160665i
$143$	−0.716825			−0.0599439
$144$		0			0
$145$	−0.212635			−0.0176583
$146$	19.5161	+	4.45527i	1.61516	+	0.368721i
$147$		0			0
$148$	−3.81103	+	7.91198i	−0.313264	+	0.650361i
$149$			22.0358i			1.80525i	0.430432	+	0.902623i	$0.358361\pi$
$149$			22.0358i			1.80525i	−0.430432	+	0.902623i	$0.641639\pi$
$150$		0			0
$151$	5.40696			0.440012			0.220006	−	0.975498i	$-0.429392\pi$
$151$	5.40696			0.440012			0.220006	+	0.975498i	$0.429392\pi$
$152$	12.0864	−	15.1520i	0.980340	−	1.22899i
$153$		0			0
$154$	0.129978	−	0.569360i	0.0104739	−	0.0458804i
$155$		−	0.642139i		−	0.0515778i
$156$		0			0
$157$		−	13.1081i		−	1.04614i	−0.852290	−	0.523070i	$-0.824787\pi$
$157$		−	13.1081i		−	1.04614i	0.852290	−	0.523070i	$-0.175213\pi$
$158$	−11.3050	−	2.58079i	−0.899378	−	0.205317i
$159$		0			0
$160$	−0.584091	+	0.281132i	−0.0461764	+	0.0222255i
$161$	4.42226			0.348523
$162$		0			0
$163$			23.1785i			1.81548i	0.419533	+	0.907740i	$0.362194\pi$
$163$			23.1785i			1.81548i	−0.419533	+	0.907740i	$0.637806\pi$
$164$	4.32281	+	2.08220i	0.337555	+	0.162593i
$165$		0			0
$166$	1.53605	−	6.72859i	0.119221	−	0.522240i
$167$	7.12880			0.551643			0.275821	−	0.961209i	$-0.411050\pi$
$167$	7.12880			0.551643			0.275821	+	0.961209i	$0.411050\pi$
$168$		0			0
$169$	9.98687			0.768221
$170$	0.0904440	−	0.396184i	0.00693673	−	0.0303859i
$171$		0			0
$172$	−3.78078	+	7.84918i	−0.288282	+	0.598494i
$173$			20.8217i			1.58305i	0.611138	+	0.791524i	$0.290712\pi$
$173$			20.8217i			1.58305i	−0.611138	+	0.791524i	$0.709288\pi$
$174$		0			0
$175$	−4.98687			−0.376972
$176$	1.29162	−	1.02968i	0.0973596	−	0.0776150i
$177$		0			0
$178$	−14.3688	−	3.28022i	−1.07699	−	0.245863i
$179$			7.51282i			0.561535i	0.959776	+	0.280767i	$0.0905890\pi$
$179$			7.51282i			0.561535i	−0.959776	+	0.280767i	$0.909411\pi$
$180$		0			0
$181$		−	4.48480i		−	0.333353i	−0.986012	−	0.166676i	$-0.946697\pi$
$181$		−	4.48480i		−	0.333353i	0.986012	−	0.166676i	$-0.0533035\pi$
$182$	0.546355	−	2.39327i	0.0404985	−	0.177401i
$183$		0			0
$184$	9.77820	+	7.79987i	0.720859	+	0.575014i
$185$	0.503170			0.0369938
$186$		0			0
$187$			1.03554i			0.0757260i
$188$	13.0287	+	6.27566i	0.950219	+	0.457700i
$189$		0			0
$190$	−1.08266	−	0.247157i	−0.0785442	−	0.0179307i
$191$	24.6726			1.78525			0.892624	−	0.450802i	$-0.148862\pi$
$191$	24.6726			1.78525			0.892624	+	0.450802i	$0.148862\pi$
$192$		0			0
$193$	−0.335818			−0.0241727			−0.0120863	−	0.999927i	$-0.503847\pi$
$193$	−0.335818			−0.0241727			−0.0120863	+	0.999927i	$0.503847\pi$
$194$	4.71543	+	1.07647i	0.338548	+	0.0772864i
$195$		0			0
$196$	1.80186	+	0.867919i	0.128705	+	0.0619942i
$197$		−	13.3089i		−	0.948221i	−0.880465	−	0.474111i	$-0.842770\pi$
$197$		−	13.3089i		−	0.948221i	0.880465	−	0.474111i	$-0.157230\pi$
$198$		0			0
$199$	−9.24682			−0.655490			−0.327745	−	0.944766i	$-0.606289\pi$
$199$	−9.24682			−0.655490			−0.327745	+	0.944766i	$0.606289\pi$
$200$	−11.0266	−	8.79571i	−0.779700	−	0.621951i
$201$		0			0
$202$	0.0641790	−	0.281132i	0.00451562	−	0.0197804i
$203$			1.85559i			0.130237i
$204$		0			0
$205$		−	0.274913i		−	0.0192008i
$206$	−9.88296	−	2.25616i	−0.688579	−	0.157194i
$207$		0			0
$208$	5.42926	−	4.32820i	0.376451	−	0.300106i
$209$	2.82983			0.195743
$210$		0			0
$211$		−	4.73424i		−	0.325918i	−0.986633	−	0.162959i	$-0.947896\pi$
$211$		−	4.73424i		−	0.325918i	0.986633	−	0.162959i	$-0.0521039\pi$
$212$	−9.74165	+	20.2244i	−0.669059	+	1.38902i
$213$		0			0
$214$	2.35037	−	10.2956i	0.160668	−	0.703796i
$215$	0.499176			0.0340435
$216$		0			0
$217$	−5.60373			−0.380406
$218$	−0.665241	+	2.91405i	−0.0450558	+	0.197364i
$219$		0			0
$220$	−0.0852664	−	0.0410709i	−0.00574866	−	0.00276900i
$221$			4.35282i			0.292803i
$222$		0			0
$223$	9.68005			0.648224			0.324112	−	0.946019i	$-0.394935\pi$
$223$	9.68005			0.648224			0.324112	+	0.946019i	$0.394935\pi$
$224$	2.45335	+	5.09716i	0.163921	+	0.340569i
$225$		0			0
$226$	6.52107	+	1.48868i	0.433775	+	0.0990255i
$227$		−	22.8566i		−	1.51705i	−0.651646	−	0.758523i	$-0.725921\pi$
$227$		−	22.8566i		−	1.51705i	0.651646	−	0.758523i	$-0.274079\pi$
$228$		0			0
$229$		−	16.7944i		−	1.10980i	−0.831916	−	0.554901i	$-0.812756\pi$
$229$		−	16.7944i		−	1.10980i	0.831916	−	0.554901i	$-0.187244\pi$
$230$	0.159500	−	0.698682i	0.0105171	−	0.0460697i
$231$		0			0
$232$	−3.27284	+	4.10296i	−0.214873	+	0.269372i
$233$	19.6756			1.28899			0.644494	−	0.764609i	$-0.277068\pi$
$233$	19.6756			1.28899			0.644494	+	0.764609i	$0.277068\pi$
$234$		0			0
$235$		−	0.828576i		−	0.0540503i
$236$	−3.69647	+	7.67414i	−0.240619	+	0.499544i
$237$		0			0
$238$	−3.45737	−	0.789274i	−0.224108	−	0.0511610i
$239$	−23.8874			−1.54515			−0.772573	−	0.634926i	$-0.781030\pi$
$239$	−23.8874			−1.54515			−0.772573	+	0.634926i	$0.781030\pi$
$240$		0			0
$241$	−4.03141			−0.259686			−0.129843	−	0.991535i	$-0.541447\pi$
$241$	−4.03141			−0.259686			−0.129843	+	0.991535i	$0.541447\pi$
$242$	−14.9311	−	3.40857i	−0.959804	−	0.219111i
$243$		0			0
$244$	6.38732	−	13.2606i	0.408907	−	0.848921i
$245$		−	0.114591i		−	0.00732097i
$246$		0			0
$247$	11.8950			0.756861
$248$	−12.3906	−	9.88371i	−0.786803	−	0.627616i
$249$		0			0
$250$	−0.360203	+	1.57785i	−0.0227812	+	0.0997917i
$251$			8.40404i			0.530459i	0.964185	+	0.265229i	$0.0854476\pi$
$251$			8.40404i			0.530459i	−0.964185	+	0.265229i	$0.914552\pi$
$252$		0			0
$253$			1.82620i			0.114812i
$254$	13.1687	+	3.00625i	0.826278	+	0.188629i
$255$		0			0
$256$	−3.56557	+	15.5977i	−0.222848	+	0.974853i
$257$	−3.32955			−0.207692			−0.103846	−	0.994593i	$-0.533115\pi$
$257$	−3.32955			−0.207692			−0.103846	+	0.994593i	$0.533115\pi$
$258$		0			0
$259$		−	4.39099i		−	0.272843i
$260$	−0.358412	−	0.172639i	−0.0222278	−	0.0107066i
$261$		0			0
$262$	5.82553	−	25.5184i	0.359902	−	1.57653i
$263$	16.2375			1.00124			0.500622	−	0.865666i	$-0.333105\pi$
$263$	16.2375			1.00124			0.500622	+	0.865666i	$0.333105\pi$
$264$		0			0
$265$	1.28619			0.0790100
$266$	−2.15686	+	9.44798i	−0.132245	+	0.579293i
$267$		0			0
$268$	−5.42926	+	11.2715i	−0.331645	+	0.688519i
$269$		−	5.74732i		−	0.350420i	−0.984531	−	0.175210i	$-0.943940\pi$
$269$		−	5.74732i		−	0.350420i	0.984531	−	0.175210i	$-0.0560605\pi$
$270$		0			0
$271$	−11.6089			−0.705189			−0.352595	−	0.935776i	$-0.614700\pi$
$271$	−11.6089			−0.705189			−0.352595	+	0.935776i	$0.614700\pi$
$272$	−6.25259	−	7.84320i	−0.379119	−	0.475564i
$273$		0			0
$274$	−11.6208	−	2.65288i	−0.702036	−	0.160266i
$275$		−	2.05936i		−	0.124184i
$276$		0			0
$277$		−	19.1097i		−	1.14819i	−0.818788	−	0.574096i	$-0.805354\pi$
$277$		−	19.1097i		−	1.14819i	0.818788	−	0.574096i	$-0.194646\pi$
$278$	4.36366	−	19.1148i	0.261715	−	1.14643i
$279$		0			0
$280$	0.202113	−	0.253376i	0.0120786	−	0.0151421i
$281$	−19.9611			−1.19078			−0.595389	−	0.803438i	$-0.703002\pi$
$281$	−19.9611			−1.19078			−0.595389	+	0.803438i	$0.703002\pi$
$282$		0			0
$283$		−	16.1413i		−	0.959503i	−0.877404	−	0.479752i	$-0.840727\pi$
$283$		−	16.1413i		−	0.959503i	0.877404	−	0.479752i	$-0.159273\pi$
$284$	1.09603	+	0.527934i	0.0650375	+	0.0313271i
$285$		0			0
$286$	0.988317	+	0.225621i	0.0584404	+	0.0133412i
$287$	−2.39907			−0.141613
$288$		0			0
$289$	−10.7118			−0.630108
$290$	0.293169	+	0.0669268i	0.0172155	+	0.00393007i
$291$		0			0
$292$	−25.5053	−	12.2854i	−1.49259	−	0.718946i
$293$			7.16969i			0.418858i	0.977824	+	0.209429i	$0.0671604\pi$
$293$			7.16969i			0.418858i	−0.977824	+	0.209429i	$0.932840\pi$
$294$		0			0
$295$	0.488044			0.0284150
$296$	7.74472	−	9.70907i	0.450153	−	0.564328i
$297$		0			0
$298$	6.93578	−	30.3818i	0.401779	−	1.75997i
$299$			7.67633i			0.443934i
$300$		0			0
$301$		−	4.35614i		−	0.251084i
$302$	−7.45481	−	1.70184i	−0.428976	−	0.0979300i
$303$		0			0
$304$	−21.4332	+	17.0865i	−1.22928	+	0.979979i
$305$	−0.843319			−0.0482883
$306$		0			0
$307$			15.4062i			0.879278i	0.898175	+	0.439639i	$0.144894\pi$
$307$			15.4062i			0.879278i	−0.898175	+	0.439639i	$0.855106\pi$
$308$	−0.358412	+	0.744091i	−0.0204224	+	0.0423985i
$309$		0			0
$310$	−0.202113	+	0.885344i	−0.0114793	+	0.0502842i
$311$	−20.3442			−1.15361			−0.576806	−	0.816881i	$-0.695701\pi$
$311$	−20.3442			−1.15361			−0.576806	+	0.816881i	$0.695701\pi$
$312$		0			0
$313$	−26.5540			−1.50092			−0.750460	−	0.660916i	$-0.770168\pi$
$313$	−26.5540			−1.50092			−0.750460	+	0.660916i	$0.770168\pi$
$314$	−4.12577	+	18.0727i	−0.232831	+	1.01990i
$315$		0			0
$316$	14.7744	+	7.11650i	0.831125	+	0.400335i
$317$		−	17.8006i		−	0.999782i	−0.866088	−	0.499891i	$-0.833373\pi$
$317$		−	17.8006i		−	0.999782i	0.866088	−	0.499891i	$-0.166627\pi$
$318$		0			0
$319$	−0.766278			−0.0429033
$320$	0.893798	−	0.203767i	0.0499648	−	0.0113909i
$321$		0			0
$322$	−6.09716	−	1.39191i	−0.339782	−	0.0775679i
$323$		−	17.1837i		−	0.956129i
$324$		0			0
$325$		−	8.65639i		−	0.480170i
$326$	7.29543	−	31.9572i	0.404057	−	1.76995i
$327$		0			0
$328$	−5.30467	−	4.23142i	−0.292901	−	0.233641i
$329$	−7.23070			−0.398641
$330$		0			0
$331$			27.1007i			1.48959i	0.667295	+	0.744793i	$0.267452\pi$
$331$			27.1007i			1.48959i	−0.667295	+	0.744793i	$0.732548\pi$
$332$	−4.23565	+	8.79352i	−0.232461	+	0.482607i
$333$		0			0
$334$	−9.82878	−	2.24379i	−0.537807	−	0.122775i
$335$	0.716825			0.0391643
$336$		0			0
$337$	−9.19674			−0.500978			−0.250489	−	0.968119i	$-0.580591\pi$
$337$	−9.19674			−0.500978			−0.250489	+	0.968119i	$0.580591\pi$
$338$	−13.7693	−	3.14337i	−0.748953	−	0.170977i
$339$		0			0
$340$	−0.249398	+	0.517769i	−0.0135255	+	0.0280800i
$341$		−	2.31409i		−	0.125315i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	7.68325	−	9.63200i	0.414253	−	0.519323i
$345$		0			0
$346$	6.55364	−	28.7078i	0.352326	−	1.54334i
$347$			33.4386i			1.79508i	0.440935	+	0.897539i	$0.354647\pi$
$347$			33.4386i			1.79508i	−0.440935	+	0.897539i	$0.645353\pi$
$348$		0			0
$349$		−	17.5598i		−	0.939954i	−0.882679	−	0.469977i	$-0.844262\pi$
$349$		−	17.5598i		−	0.939954i	0.882679	−	0.469977i	$-0.155738\pi$
$350$	6.87561	+	1.56962i	0.367517	+	0.0838995i
$351$		0			0
$352$	−2.10491	+	1.01313i	−0.112192	+	0.0539998i
$353$	−18.4376			−0.981335			−0.490668	−	0.871347i	$-0.663247\pi$
$353$	−18.4376			−0.981335			−0.490668	+	0.871347i	$0.663247\pi$
$354$		0			0
$355$		−	0.0697032i		−	0.00369946i
$356$	18.7784	+	9.04516i	0.995255	+	0.479393i
$357$		0			0
$358$	2.36466	−	10.3583i	0.124976	−	0.547451i
$359$	−7.80894			−0.412140			−0.206070	−	0.978537i	$-0.566067\pi$
$359$	−7.80894			−0.412140			−0.206070	+	0.978537i	$0.566067\pi$
$360$		0			0
$361$	−27.9582			−1.47148
$362$	−1.41159	+	6.18339i	−0.0741916	+	0.324992i
$363$		0			0
$364$	−1.50657	+	3.12774i	−0.0789655	+	0.163938i
$365$			1.62204i			0.0849012i
$366$		0			0
$367$	−18.2964			−0.955066			−0.477533	−	0.878614i	$-0.658469\pi$
$367$	−18.2964			−0.955066			−0.477533	+	0.878614i	$0.658469\pi$
$368$	−11.0266	−	13.8317i	−0.574802	−	0.721028i
$369$		0			0
$370$	−0.693742	−	0.158373i	−0.0360659	−	0.00823340i
$371$		−	11.2241i		−	0.582729i
$372$		0			0
$373$		−	29.4005i		−	1.52230i	−0.648575	−	0.761150i	$-0.724635\pi$
$373$		−	29.4005i		−	1.52230i	0.648575	−	0.761150i	$-0.275365\pi$
$374$	0.325936	−	1.42774i	0.0168537	−	0.0738267i
$375$		0			0
$376$	−15.9880	−	12.7533i	−0.824520	−	0.657702i
$377$	−3.22100			−0.165890
$378$		0			0
$379$		−	2.46161i		−	0.126444i	−0.997999	−	0.0632222i	$-0.979862\pi$
$379$		−	2.46161i		−	0.126444i	0.997999	−	0.0632222i	$-0.0201377\pi$
$380$	1.41491	+	0.681532i	0.0725835	+	0.0349619i
$381$		0			0
$382$	−34.0172	−	7.76571i	−1.74047	−	0.397328i
$383$	8.59739			0.439306			0.219653	−	0.975578i	$-0.429507\pi$
$383$	8.59739			0.439306			0.219653	+	0.975578i	$0.429507\pi$
$384$		0			0
$385$	0.0473212			0.00241171
$386$	0.463006	+	0.105699i	0.0235664	+	0.00537992i
$387$		0			0
$388$	−6.16255	−	2.96836i	−0.312856	−	0.150696i
$389$			3.93550i			0.199538i	0.995011	+	0.0997688i	$0.0318103\pi$
$389$			3.93550i			0.199538i	−0.995011	+	0.0997688i	$0.968190\pi$
$390$		0			0
$391$	11.0894			0.560813
$392$	−2.21113	−	1.76377i	−0.111679	−	0.0890840i
$393$		0			0
$394$	−4.18898	+	18.3496i	−0.211038	+	0.924439i
$395$		−	0.939592i		−	0.0472760i
$396$		0			0
$397$		−	27.3549i		−	1.37290i	−0.727175	−	0.686452i	$-0.759167\pi$
$397$		−	27.3549i		−	1.37290i	0.727175	−	0.686452i	$-0.240833\pi$
$398$	12.7490	+	2.91044i	0.639049	+	0.145887i
$399$		0			0
$400$	12.4344	+	15.5977i	0.621722	+	0.779883i
$401$	6.49913			0.324551			0.162276	−	0.986745i	$-0.448117\pi$
$401$	6.49913			0.324551			0.162276	+	0.986745i	$0.448117\pi$
$402$		0			0
$403$		−	9.72716i		−	0.484545i
$404$	−0.176973	+	0.367409i	−0.00880473	+	0.0182793i
$405$		0			0
$406$	0.584047	−	2.55838i	0.0289858	−	0.126970i
$407$	1.81329			0.0898814
$408$		0			0
$409$	17.9897			0.889531			0.444765	−	0.895647i	$-0.353287\pi$
$409$	17.9897			0.889531			0.444765	+	0.895647i	$0.353287\pi$
$410$	−0.0865289	+	0.379034i	−0.00427336	+	0.0187192i
$411$		0			0
$412$	12.9159	+	6.22132i	0.636323	+	0.306503i
$413$		−	4.25900i		−	0.209572i
$414$		0			0
$415$	0.559232			0.0274516
$416$	−8.84785	+	4.25861i	−0.433801	+	0.208796i
$417$		0			0
$418$	−3.90160	−	0.890687i	−0.190834	−	0.0435649i
$419$		−	40.4247i		−	1.97487i	−0.158014	−	0.987437i	$-0.550509\pi$
$419$		−	40.4247i		−	1.97487i	0.158014	−	0.987437i	$-0.449491\pi$
$420$		0			0
$421$			11.3043i			0.550938i	0.961310	+	0.275469i	$0.0888332\pi$
$421$			11.3043i			0.550938i	−0.961310	+	0.275469i	$0.911167\pi$
$422$	−1.49010	+	6.52730i	−0.0725370	+	0.317744i
$423$		0			0
$424$	19.7969	−	24.8181i	0.961420	−	1.20527i
$425$	−12.5052			−0.606590
$426$		0			0
$427$			7.35936i			0.356144i
$428$	−6.48111	+	13.4553i	−0.313276	+	0.650385i
$429$		0			0
$430$	−0.688236	−	0.157116i	−0.0331897	−	0.00757679i
$431$	−21.2412			−1.02315			−0.511575	−	0.859238i	$-0.670938\pi$
$431$	−21.2412			−1.02315			−0.511575	+	0.859238i	$0.670938\pi$
$432$		0			0
$433$	−5.34136			−0.256690			−0.128345	−	0.991730i	$-0.540966\pi$
$433$	−5.34136			−0.256690			−0.128345	+	0.991730i	$0.540966\pi$
$434$	7.72610	+	1.76377i	0.370865	+	0.0846638i
$435$		0			0
$436$	1.83439	−	3.80834i	0.0878514	−	0.182386i
$437$		−	30.3040i		−	1.44964i
$438$		0			0
$439$	−20.0290			−0.955933			−0.477966	−	0.878378i	$-0.658626\pi$
$439$	−20.0290			−0.955933			−0.477966	+	0.878378i	$0.658626\pi$
$440$	0.104633	+	0.0834639i	0.00498820	+	0.00397898i
$441$		0			0
$442$	1.37005	−	6.00143i	0.0651667	−	0.285459i
$443$			21.3027i			1.01212i	0.862497	+	0.506062i	$0.168899\pi$
$443$			21.3027i			1.01212i	−0.862497	+	0.506062i	$0.831101\pi$
$444$		0			0
$445$		−	1.19423i		−	0.0566121i
$446$	−13.3463	−	3.04680i	−0.631966	−	0.144270i
$447$		0			0
$448$	−1.77820	−	7.79987i	−0.0840123	−	0.368509i
$449$	17.8880			0.844185			0.422093	−	0.906553i	$-0.361296\pi$
$449$	17.8880			0.844185			0.422093	+	0.906553i	$0.361296\pi$
$450$		0			0
$451$		−	0.990712i		−	0.0466508i
$452$	−8.52232	−	4.10502i	−0.400856	−	0.193084i
$453$		0			0
$454$	−7.19411	+	31.5134i	−0.337636	+	1.47900i
$455$	0.198912			0.00932513
$456$		0			0
$457$	19.3625			0.905740			0.452870	−	0.891577i	$-0.350400\pi$
$457$	19.3625			0.905740			0.452870	+	0.891577i	$0.350400\pi$
$458$	−5.28602	+	23.1551i	−0.247000	+	1.08197i
$459$		0			0
$460$	−0.439820	+	0.913100i	−0.0205067	+	0.0425735i
$461$		−	21.8751i		−	1.01882i	−0.860523	−	0.509412i	$-0.829863\pi$
$461$		−	21.8751i		−	1.01882i	0.860523	−	0.509412i	$-0.170137\pi$
$462$		0			0
$463$	26.0449			1.21041			0.605204	−	0.796070i	$-0.293091\pi$
$463$	26.0449			1.21041			0.605204	+	0.796070i	$0.293091\pi$
$464$	5.80382	−	4.62680i	0.269435	−	0.214794i
$465$		0			0
$466$	−27.1275	−	6.19288i	−1.25666	−	0.286880i
$467$		−	11.8214i		−	0.547028i	−0.961868	−	0.273514i	$-0.911814\pi$
$467$		−	11.8214i		−	0.547028i	0.961868	−	0.273514i	$-0.0881860\pi$
$468$		0			0
$469$		−	6.25549i		−	0.288852i
$470$	−0.260794	+	1.14239i	−0.0120295	+	0.0526947i
$471$		0			0
$472$	7.51191	−	9.41721i	0.345764	−	0.433462i
$473$	1.79890			0.0827133
$474$		0			0
$475$			34.1730i			1.56797i
$476$	4.51840	+	2.17641i	0.207100	+	0.0997557i
$477$		0			0
$478$	32.9345	+	7.51855i	1.50639	+	0.343890i
$479$	29.0868			1.32901			0.664504	−	0.747284i	$-0.268643\pi$
$479$	29.0868			1.32901			0.664504	+	0.747284i	$0.268643\pi$
$480$		0			0
$481$	7.62205			0.347536
$482$	5.55828	+	1.26889i	0.253173	+	0.0577962i
$483$		0			0
$484$	19.5132	+	9.39910i	0.886965	+	0.427232i
$485$			0.391913i			0.0177959i
$486$		0			0
$487$	−21.3338			−0.966728			−0.483364	−	0.875419i	$-0.660585\pi$
$487$	−21.3338			−0.966728			−0.483364	+	0.875419i	$0.660585\pi$
$488$	−12.9802	+	16.2725i	−0.587588	+	0.736622i
$489$		0			0
$490$	−0.0360676	+	0.157992i	−0.00162937	+	0.00713735i
$491$		−	20.2052i		−	0.911846i	−0.890019	−	0.455923i	$-0.849309\pi$
$491$		−	20.2052i		−	0.911846i	0.890019	−	0.455923i	$-0.150691\pi$
$492$		0			0
$493$			4.65312i			0.209566i
$494$	−16.4002	−	3.74395i	−0.737878	−	0.168448i
$495$		0			0
$496$	13.9725	+	17.5270i	0.627385	+	0.786987i
$497$	−0.608276			−0.0272849
$498$		0			0
$499$			25.2662i			1.13107i	0.824724	+	0.565535i	$0.191330\pi$
$499$			25.2662i			1.13107i	−0.824724	+	0.565535i	$0.808670\pi$
$500$	0.993254	−	2.06207i	0.0444196	−	0.0922186i
$501$		0			0
$502$	2.64517	−	11.5870i	0.118060	−	0.517154i
$503$	−30.2176			−1.34734			−0.673669	−	0.739033i	$-0.735283\pi$
$503$	−30.2176			−1.34734			−0.673669	+	0.739033i	$0.735283\pi$
$504$		0			0
$505$	0.0233657			0.00103976
$506$	0.574797	−	2.51786i	0.0255528	−	0.111933i
$507$		0			0
$508$	−17.2100	−	8.28969i	−0.763572	−	0.367796i
$509$		−	1.78140i		−	0.0789592i	−0.999220	−	0.0394796i	$-0.987430\pi$
$509$		−	1.78140i		−	0.0789592i	0.999220	−	0.0394796i	$-0.0125700\pi$
$510$		0			0
$511$	14.1550			0.626179
$512$	9.82536	−	20.3829i	0.434224	−	0.900805i
$513$		0			0
$514$	4.59060	+	1.04798i	0.202483	+	0.0462243i
$515$		−	0.821401i		−	0.0361953i
$516$		0			0
$517$		−	2.98596i		−	0.131322i
$518$	−1.38207	+	6.05405i	−0.0607245	+	0.266000i
$519$		0			0
$520$	0.439820	+	0.350836i	0.0192874	+	0.0153852i
$521$	−5.72198			−0.250685			−0.125342	−	0.992114i	$-0.540003\pi$
$521$	−5.72198			−0.250685			−0.125342	+	0.992114i	$0.540003\pi$
$522$		0			0
$523$			0.348058i			0.0152195i	0.999971	+	0.00760976i	$0.00242229\pi$
$523$			0.348058i			0.0152195i	−0.999971	+	0.00760976i	$0.997578\pi$
$524$	−16.0638	+	33.3497i	−0.701751	+	1.45689i
$525$		0			0
$526$	−22.3873	−	5.11074i	−0.976132	−	0.222839i
$527$	−14.0520			−0.612116
$528$		0			0
$529$	−3.44359			−0.149721
$530$	−1.77333	−	0.404828i	−0.0770283	−	0.0175846i
$531$		0			0
$532$	5.94750	−	12.3475i	0.257857	−	0.535331i
$533$		−	4.16440i		−	0.180380i
$534$		0			0
$535$	0.855701			0.0369952
$536$	11.0333	−	13.8317i	0.476565	−	0.597439i
$537$		0			0
$538$	−1.80897	+	7.92408i	−0.0779902	+	0.341631i
$539$		−	0.412956i		−	0.0177873i
$540$		0			0
$541$			8.49464i			0.365213i	0.983186	+	0.182606i	$0.0584534\pi$
$541$			8.49464i			0.365213i	−0.983186	+	0.182606i	$0.941547\pi$
$542$	16.0057	+	3.65389i	0.687502	+	0.156948i
$543$		0			0
$544$	6.15207	+	12.7818i	0.263768	+	0.548014i
$545$	−0.242195			−0.0103745
$546$		0			0
$547$		−	31.5175i		−	1.34759i	−0.738918	−	0.673796i	$-0.764663\pi$
$547$		−	31.5175i		−	1.34759i	0.738918	−	0.673796i	$-0.235337\pi$
$548$	15.1870	+	7.31527i	0.648759	+	0.312493i
$549$		0			0
$550$	−0.648183	+	2.83933i	−0.0276386	+	0.121069i
$551$	12.7156			0.541704
$552$		0			0
$553$	−8.19950			−0.348678
$554$	−6.01478	+	26.3474i	−0.255544	+	1.11939i
$555$		0			0
$556$	−12.0327	+	24.9809i	−0.510302	+	1.05943i
$557$			25.5635i			1.08316i	0.840649	+	0.541581i	$0.182174\pi$
$557$			25.5635i			1.08316i	−0.840649	+	0.541581i	$0.817826\pi$
$558$		0			0
$559$	7.56156			0.319820
$560$	−0.358412	+	0.285726i	−0.0151457	+	0.0120741i
$561$		0			0
$562$	27.5212	+	6.28275i	1.16091	+	0.265022i
$563$		−	18.6212i		−	0.784791i	−0.919796	−	0.392396i	$-0.871646\pi$
$563$		−	18.6212i		−	0.784791i	0.919796	−	0.392396i	$-0.128354\pi$
$564$		0			0
$565$			0.541985i			0.0228015i
$566$	−5.08049	+	22.2548i	−0.213549	+	0.935438i
$567$		0			0
$568$	−1.34498	−	1.07286i	−0.0564341	−	0.0450163i
$569$	−40.8350			−1.71189			−0.855946	−	0.517065i	$-0.827025\pi$
$569$	−40.8350			−1.71189			−0.855946	+	0.517065i	$0.827025\pi$
$570$		0			0
$571$		−	20.7134i		−	0.866831i	−0.901194	−	0.433415i	$-0.857308\pi$
$571$		−	20.7134i		−	0.866831i	0.901194	−	0.433415i	$-0.142692\pi$
$572$	−1.29162	−	0.622146i	−0.0540054	−	0.0260132i
$573$		0			0
$574$	3.30771	+	0.755108i	0.138061	+	0.0315176i
$575$	−22.0532			−0.919684
$576$		0			0
$577$	8.58023			0.357200			0.178600	−	0.983922i	$-0.442843\pi$
$577$	8.58023			0.357200			0.178600	+	0.983922i	$0.442843\pi$
$578$	14.7689	+	3.37155i	0.614304	+	0.140238i
$579$		0			0
$580$	−0.383139	−	0.184550i	−0.0159090	−	0.00766301i
$581$		−	4.88023i		−	0.202466i
$582$		0			0
$583$	4.63508			0.191965
$584$	31.2985	+	24.9662i	1.29514	+	1.03311i
$585$		0			0
$586$	2.25666	−	9.88516i	0.0932217	−	0.408352i
$587$		−	28.7023i		−	1.18467i	−0.805692	−	0.592334i	$-0.798206\pi$
$587$		−	28.7023i		−	1.18467i	0.805692	−	0.592334i	$-0.201794\pi$
$588$		0			0
$589$			38.4001i			1.58225i
$590$	−0.672888	−	0.153612i	−0.0277024	−	0.00632410i
$591$		0			0
$592$	−13.7339	+	10.9487i	−0.564460	+	0.449987i
$593$	42.2499			1.73500			0.867498	−	0.497440i	$-0.165727\pi$
$593$	42.2499			1.73500			0.867498	+	0.497440i	$0.165727\pi$
$594$		0			0
$595$		−	0.287352i		−	0.0117803i
$596$	−19.1253	+	39.7056i	−0.783403	+	1.62640i
$597$		0			0
$598$	2.41612	−	10.5837i	0.0988027	−	0.432799i
$599$	31.3138			1.27945			0.639723	−	0.768605i	$-0.279049\pi$
$599$	31.3138			1.27945			0.639723	+	0.768605i	$0.279049\pi$
$600$		0			0
$601$	9.40650			0.383699			0.191850	−	0.981424i	$-0.438551\pi$
$601$	9.40650			0.383699			0.191850	+	0.981424i	$0.438551\pi$
$602$	−1.37110	+	6.00600i	−0.0558817	+	0.244786i
$603$		0			0
$604$	9.74262	+	4.69280i	0.396421	+	0.190947i
$605$		−	1.24096i		−	0.0504523i
$606$		0			0
$607$	4.95314			0.201042			0.100521	−	0.994935i	$-0.467949\pi$
$607$	4.95314			0.201042			0.100521	+	0.994935i	$0.467949\pi$
$608$	34.9289	−	16.8118i	1.41655	−	0.681810i
$609$		0			0
$610$	1.16272	+	0.265434i	0.0470771	+	0.0107471i
$611$		−	12.5513i		−	0.507772i
$612$		0			0
$613$			6.61633i			0.267231i	0.991033	+	0.133616i	$0.0426587\pi$
$613$			6.61633i			0.267231i	−0.991033	+	0.133616i	$0.957341\pi$
$614$	4.84910	−	21.2412i	0.195694	−	0.857225i
$615$		0			0
$616$	0.728361	−	0.913100i	0.0293465	−	0.0367899i
$617$	−21.3584			−0.859855			−0.429928	−	0.902863i	$-0.641461\pi$
$617$	−21.3584			−0.859855			−0.429928	+	0.902863i	$0.641461\pi$
$618$		0			0
$619$		−	0.0210409i		−	0.000845707i	−1.00000		0.000422854i	$-0.999865\pi$
$619$		−	0.0210409i		−	0.000845707i	1.00000		0.000422854i	$-0.000134598\pi$
$620$	0.557324	−	1.15705i	0.0223827	−	0.0464681i
$621$		0			0
$622$	28.0494	+	6.40332i	1.12468	+	0.256750i
$623$	−10.4217			−0.417535
$624$		0			0
$625$	24.8032			0.992128
$626$	36.6111	+	8.35786i	1.46327	+	0.334047i
$627$		0			0
$628$	11.3768	−	23.6190i	0.453982	−	0.942501i
$629$		−	11.0110i		−	0.439036i
$630$		0			0
$631$	19.6037			0.780411			0.390206	−	0.920728i	$-0.372404\pi$
$631$	19.6037			0.780411			0.390206	+	0.920728i	$0.372404\pi$
$632$	−18.1302	−	14.4621i	−0.721180	−	0.575270i
$633$		0			0
$634$	−5.60274	+	24.5425i	−0.222513	+	0.974706i
$635$			1.09449i			0.0434335i
$636$		0			0
$637$		−	1.73584i		−	0.0687764i
$638$	1.05650	+	0.241186i	0.0418273	+	0.00954864i
$639$		0			0
$640$	−1.29645		0.000380698i	−0.0512468		1.50484e-5i
$641$	−4.84692			−0.191442			−0.0957210	−	0.995408i	$-0.530516\pi$
$641$	−4.84692			−0.191442			−0.0957210	+	0.995408i	$0.530516\pi$
$642$		0			0
$643$			3.72899i			0.147057i	0.997293	+	0.0735285i	$0.0234260\pi$
$643$			3.72899i			0.147057i	−0.997293	+	0.0735285i	$0.976574\pi$
$644$	7.96832	+	3.83816i	0.313996	+	0.151245i
$645$		0			0
$646$	−5.40858	+	23.6920i	−0.212798	+	0.932148i
$647$	−45.6179			−1.79342			−0.896712	−	0.442615i	$-0.854051\pi$
$647$	−45.6179			−1.79342			−0.896712	+	0.442615i	$0.854051\pi$
$648$		0			0
$649$	1.75878			0.0690382
$650$	−2.72460	+	11.9349i	−0.106868	+	0.468127i
$651$		0			0
$652$	−20.1171	+	41.7645i	−0.787845	+	1.63563i
$653$		−	6.34542i		−	0.248315i	−0.992263	−	0.124158i	$-0.960377\pi$
$653$		−	6.34542i		−	0.248315i	0.992263	−	0.124158i	$-0.0396229\pi$
$654$		0			0
$655$	2.12090			0.0828706
$656$	5.98193	+	7.50369i	0.233555	+	0.292970i
$657$		0			0
$658$	9.96928	+	2.27586i	0.388643	+	0.0887224i
$659$		−	12.6820i		−	0.494022i	−0.969013	−	0.247011i	$-0.920552\pi$
$659$		−	12.6820i		−	0.494022i	0.969013	−	0.247011i	$-0.0794484\pi$
$660$		0			0
$661$		−	7.30385i		−	0.284087i	−0.989860	−	0.142043i	$-0.954633\pi$
$661$		−	7.30385i		−	0.284087i	0.989860	−	0.142043i	$-0.0453672\pi$
$662$	8.52993	−	37.3648i	0.331525	−	1.45223i
$663$		0			0
$664$	8.60763	−	10.7908i	0.334041	−	0.418766i
$665$	−0.785249			−0.0304507
$666$		0			0
$667$			8.20591i			0.317734i
$668$	12.8451	+	6.18722i	0.496993	+	0.239391i
$669$		0			0
$670$	−0.988317	−	0.225621i	−0.0381820	−	0.00871648i
$671$	−3.03909			−0.117323
$672$		0			0
$673$	−4.21222			−0.162369			−0.0811846	−	0.996699i	$-0.525870\pi$
$673$	−4.21222			−0.162369			−0.0811846	+	0.996699i	$0.525870\pi$
$674$	12.6799	+	2.89467i	0.488413	+	0.111499i
$675$		0			0
$676$	17.9950	+	8.66779i	0.692115	+	0.333377i
$677$			18.0658i			0.694326i	0.937805	+	0.347163i	$0.112855\pi$
$677$			18.0658i			0.694326i	−0.937805	+	0.347163i	$0.887145\pi$
$678$		0			0
$679$	3.42009			0.131251
$680$	0.506823	−	0.635372i	0.0194358	−	0.0243654i
$681$		0			0
$682$	−0.728361	+	3.19054i	−0.0278904	+	0.122172i
$683$			41.3196i			1.58105i	0.612429	+	0.790526i	$0.290192\pi$
$683$			41.3196i			1.58105i	−0.612429	+	0.790526i	$0.709808\pi$
$684$		0			0
$685$		−	0.965835i		−	0.0369027i
$686$	1.37874	+	0.314750i	0.0526407	+	0.0120172i
$687$		0			0
$688$	−13.6249	+	10.8618i	−0.519444	+	0.414101i
$689$	19.4833			0.742254
$690$		0			0
$691$			44.2400i			1.68297i	0.540281	+	0.841485i	$0.318318\pi$
$691$			44.2400i			1.68297i	−0.540281	+	0.841485i	$0.681682\pi$
$692$	−18.0716	+	37.5180i	−0.686978	+	1.42622i
$693$		0			0
$694$	10.5248	−	46.1032i	0.399516	−	1.75006i
$695$	1.58868			0.0602622
$696$		0			0
$697$	−6.01597			−0.227871
$698$	−5.52694	+	24.2104i	−0.209198	+	0.916379i
$699$		0			0
$700$	−8.98566	−	4.32820i	−0.339626	−	0.163590i
$701$		−	33.0921i		−	1.24987i	−0.780676	−	0.624936i	$-0.785125\pi$
$701$		−	33.0921i		−	1.24987i	0.780676	−	0.624936i	$-0.214875\pi$
$702$		0			0
$703$	−30.0898			−1.13486
$704$	3.22100	−	0.734320i	0.121396	−	0.0276757i
$705$		0			0
$706$	25.4207	+	5.80324i	0.956722	+	0.218408i
$707$		−	0.203905i		−	0.00766863i
$708$		0			0
$709$			28.0152i			1.05213i	0.850444	+	0.526066i	$0.176333\pi$
$709$			28.0152i			1.05213i	−0.850444	+	0.526066i	$0.823667\pi$
$710$	−0.0219391	+	0.0961028i	−0.000823359	+	0.00360667i
$711$		0			0
$712$	−23.0437	−	18.3815i	−0.863598	−	0.688875i
$713$	−24.7812			−0.928062
$714$		0			0
$715$			0.0821419i			0.00307193i
$716$	−6.52052	+	13.5371i	−0.243683	+	0.505905i
$717$		0			0
$718$	10.7665	+	2.45786i	0.401803	+	0.0917266i
$719$	5.44311			0.202994			0.101497	−	0.994836i	$-0.467637\pi$
$719$	5.44311			0.202994			0.101497	+	0.994836i	$0.467637\pi$
$720$		0			0
$721$	−7.16809			−0.266954
$722$	38.5472	+	8.79984i	1.43458	+	0.327496i
$723$		0			0
$724$	3.89244	−	8.08100i	0.144661	−	0.300328i
$725$		−	9.25359i		−	0.343670i
$726$		0			0
$727$	14.7480			0.546972			0.273486	−	0.961876i	$-0.411823\pi$
$727$	14.7480			0.546972			0.273486	+	0.961876i	$0.411823\pi$
$728$	3.06162	−	3.83816i	0.113471	−	0.142252i
$729$		0			0
$730$	0.510536	−	2.23637i	0.0188958	−	0.0827718i
$731$		−	10.9236i		−	0.404022i
$732$		0			0
$733$		−	45.4197i		−	1.67762i	−0.544428	−	0.838808i	$-0.683253\pi$
$733$		−	45.4197i		−	1.67762i	0.544428	−	0.838808i	$-0.316747\pi$
$734$	25.2261	+	5.75880i	0.931111	+	0.212561i
$735$		0			0
$736$	10.8493	+	22.5410i	0.399912	+	0.830872i
$737$	2.58324			0.0951550
$738$		0			0
$739$			3.03287i			0.111566i	0.998443	+	0.0557830i	$0.0177655\pi$
$739$			3.03287i			0.111566i	−0.998443	+	0.0557830i	$0.982234\pi$
$740$	0.906644	+	0.436711i	0.0333289	+	0.0160538i
$741$		0			0
$742$	−3.53280	+	15.4752i	−0.129693	+	0.568113i
$743$	41.3290			1.51621			0.758106	−	0.652131i	$-0.226125\pi$
$743$	41.3290			1.51621			0.758106	+	0.652131i	$0.226125\pi$
$744$		0			0
$745$	2.52512			0.0925131
$746$	−9.25381	+	40.5358i	−0.338806	+	1.48412i
$747$		0			0
$748$	−0.898763	+	1.86590i	−0.0328620	+	0.0682241i
$749$		−	7.46742i		−	0.272853i
$750$		0			0
$751$	18.6220			0.679527			0.339763	−	0.940511i	$-0.389653\pi$
$751$	18.6220			0.679527			0.339763	+	0.940511i	$0.389653\pi$
$752$	18.0293	+	22.6158i	0.657460	+	0.824713i
$753$		0			0
$754$	4.44094	+	1.01381i	0.161729	+	0.0369208i
$755$		−	0.619591i		−	0.0225492i
$756$		0			0
$757$			48.7279i			1.77104i	0.464597	+	0.885522i	$0.346199\pi$
$757$			48.7279i			1.77104i	−0.464597	+	0.885522i	$0.653801\pi$
$758$	−0.774792	+	3.39393i	−0.0281417	+	0.123273i
$759$		0			0
$760$	−1.73629	−	1.38500i	−0.0629818	−	0.0502393i
$761$	26.1095			0.946468			0.473234	−	0.880937i	$-0.343087\pi$
$761$	26.1095			0.946468			0.473234	+	0.880937i	$0.343087\pi$
$762$		0			0
$763$			2.11355i			0.0765157i
$764$	44.4567	+	21.4138i	1.60839	+	0.774725i
$765$		0			0
$766$	−11.8536	−	2.70603i	−0.428288	−	0.0977728i
$767$	7.39293			0.266943
$768$		0			0
$769$	24.6590			0.889225			0.444612	−	0.895723i	$-0.353341\pi$
$769$	24.6590			0.889225			0.444612	+	0.895723i	$0.353341\pi$
$770$	−0.0652438	−	0.0148943i	−0.00235122	−	0.000536755i
$771$		0			0
$772$	−0.605098	−	0.291463i	−0.0217780	−	0.0104900i
$773$		−	15.7370i		−	0.566019i	−0.959117	−	0.283010i	$-0.908667\pi$
$773$		−	15.7370i		−	0.566019i	0.959117	−	0.283010i	$-0.0913329\pi$
$774$		0			0
$775$	27.9451			1.00382
$776$	7.56228	+	6.03227i	0.271470	+	0.216546i
$777$		0			0
$778$	1.23870	−	5.42604i	0.0444094	−	0.194533i
$779$			16.4399i			0.589021i
$780$		0			0
$781$		−	0.251191i		−	0.00898834i
$782$	−15.2894	−	3.49038i	−0.546747	−	0.124816i
$783$		0			0
$784$	2.49343	+	3.12774i	0.0890512	+	0.111705i
$785$	−1.50207			−0.0536113
$786$		0			0
$787$		−	48.6354i		−	1.73367i	−0.498599	−	0.866833i	$-0.666152\pi$
$787$		−	48.6354i		−	1.73367i	0.498599	−	0.866833i	$-0.333848\pi$
$788$	11.5511	−	23.9809i	0.411489	−	0.854283i
$789$		0			0
$790$	−0.295737	+	1.29546i	−0.0105218	+	0.0460903i
$791$	4.72972			0.168170
$792$		0			0
$793$	−12.7746			−0.453641
$794$	−8.60996	+	37.7154i	−0.305556	+	1.33847i
$795$		0			0
$796$	−16.6615	−	8.02549i	−0.590552	−	0.284456i
$797$		−	53.4156i		−	1.89208i	−0.324054	−	0.946038i	$-0.605046\pi$
$797$		−	53.4156i		−	1.89208i	0.324054	−	0.946038i	$-0.394954\pi$
$798$		0			0
$799$	−18.1319			−0.641459
$800$	−12.2345	−	25.4189i	−0.432556	−	0.898693i
$801$		0			0
$802$	−8.96063	−	2.04560i	−0.316411	−	0.0722327i
$803$			5.84538i			0.206279i
$804$		0			0
$805$		−	0.506753i		−	0.0178607i
$806$	−3.06162	+	13.4113i	−0.107841	+	0.472391i
$807$		0			0
$808$	0.359642	−	0.450860i	0.0126522	−	0.0158612i
$809$	46.1176			1.62141			0.810704	−	0.585456i	$-0.199085\pi$
$809$	46.1176			1.62141			0.810704	+	0.585456i	$0.199085\pi$
$810$		0			0
$811$			13.2874i			0.466585i	0.972407	+	0.233293i	$0.0749500\pi$
$811$			13.2874i			0.466585i	−0.972407	+	0.233293i	$0.925050\pi$
$812$	−1.61050	+	3.34353i	−0.0565176	+	0.117335i
$813$		0			0
$814$	−2.50006	−	0.570732i	−0.0876270	−	0.0200042i
$815$	2.65606			0.0930376
$816$		0			0
$817$	−29.8509			−1.04435
$818$	−24.8031	−	5.66224i	−0.867220	−	0.197976i
$819$		0			0
$820$	0.238602	−	0.495356i	0.00833235	−	0.0172986i
$821$			30.5087i			1.06476i	0.846505	+	0.532380i	$0.178702\pi$
$821$			30.5087i			1.06476i	−0.846505	+	0.532380i	$0.821298\pi$
$822$		0			0
$823$	−19.6955			−0.686542			−0.343271	−	0.939236i	$-0.611535\pi$
$823$	−19.6955			−0.686542			−0.343271	+	0.939236i	$0.611535\pi$
$824$	−15.8496	−	12.6429i	−0.552147	−	0.440436i
$825$		0			0
$826$	−1.34052	+	5.87207i	−0.0466427	+	0.204315i
$827$			5.77145i			0.200693i	0.994953	+	0.100347i	$0.0319951\pi$
$827$			5.77145i			0.200693i	−0.994953	+	0.100347i	$0.968005\pi$
$828$		0			0
$829$			50.3002i			1.74700i	0.486826	+	0.873499i	$0.338155\pi$
$829$			50.3002i			1.74700i	−0.486826	+	0.873499i	$0.661845\pi$
$830$	−0.771038	−	0.176018i	−0.0267631	−	0.00610969i
$831$		0			0
$832$	13.5393	−	3.08667i	0.469391	−	0.107011i
$833$	−2.50762			−0.0868840
$834$		0			0
$835$		−	0.816898i		−	0.0282699i
$836$	5.09896	+	2.45606i	0.176351	+	0.0849446i
$837$		0			0
$838$	−12.7237	+	55.7352i	−0.439532	+	1.92534i
$839$	26.5035			0.915004			0.457502	−	0.889209i	$-0.348744\pi$
$839$	26.5035			0.915004			0.457502	+	0.889209i	$0.348744\pi$
$840$		0			0
$841$	25.5568			0.881268
$842$	3.55803	−	15.5857i	0.122618	−	0.537120i
$843$		0			0
$844$	4.10893	−	8.53046i	0.141435	−	0.293630i
$845$		−	1.14441i		−	0.0393688i
$846$		0			0
$847$	−10.8295			−0.372105
$848$	−35.1063	+	27.9867i	−1.20555	+	0.961066i
$849$		0			0
$850$	17.2414	+	3.93601i	0.591376	+	0.135004i
$851$		−	19.4181i		−	0.665645i
$852$		0			0
$853$			9.22041i			0.315701i	0.987463	+	0.157850i	$0.0504564\pi$
$853$			9.22041i			0.315701i	−0.987463	+	0.157850i	$0.949544\pi$
$854$	2.31636	−	10.1467i	0.0792641	−	0.347212i
$855$		0			0
$856$	13.1708	−	16.5114i	0.450170	−	0.564349i
$857$	−41.1124			−1.40437			−0.702187	−	0.711993i	$-0.747793\pi$
$857$	−41.1124			−1.40437			−0.702187	+	0.711993i	$0.747793\pi$
$858$		0			0
$859$			7.51805i			0.256513i	0.991741	+	0.128256i	$0.0409380\pi$
$859$			7.51805i			0.256513i	−0.991741	+	0.128256i	$0.959062\pi$
$860$	0.899448	+	0.433244i	0.0306709	+	0.0147735i
$861$		0			0
$862$	29.2861	+	6.68565i	0.997489	+	0.227714i
$863$	20.5122			0.698245			0.349122	−	0.937077i	$-0.386480\pi$
$863$	20.5122			0.698245			0.349122	+	0.937077i	$0.386480\pi$
$864$		0			0
$865$	2.38599			0.0811261
$866$	7.36437	+	1.68119i	0.250251	+	0.0571293i
$867$		0			0
$868$	−10.0972	−	4.86358i	−0.342720	−	0.165081i
$869$		−	3.38604i		−	0.114863i
$870$		0			0
$871$	10.8585			0.367927
$872$	−3.72783	+	4.67334i	−0.126240	+	0.158259i
$873$		0			0
$874$	−9.53819	+	41.7815i	−0.322634	+	1.41328i
$875$			1.14441i			0.0386881i
$876$		0			0
$877$			53.2820i			1.79921i	0.436710	+	0.899603i	$0.356144\pi$
$877$			53.2820i			1.79921i	−0.436710	+	0.899603i	$0.643856\pi$
$878$	27.6149	+	6.30413i	0.931957	+	0.212754i
$879$		0			0
$880$	−0.117992	−	0.148009i	−0.00397752	−	0.00498937i
$881$	−37.1591			−1.25192			−0.625960	−	0.779855i	$-0.715293\pi$
$881$	−37.1591			−1.25192			−0.625960	+	0.779855i	$0.715293\pi$
$882$		0			0
$883$		−	30.5599i		−	1.02842i	−0.857664	−	0.514211i	$-0.828085\pi$
$883$		−	30.5599i		−	1.02842i	0.857664	−	0.514211i	$-0.171915\pi$
$884$	−3.77790	+	7.84320i	−0.127064	+	0.263795i
$885$		0			0
$886$	6.70504	−	29.3710i	0.225260	−	0.986738i
$887$	−47.5640			−1.59704			−0.798521	−	0.601967i	$-0.794384\pi$
$887$	−47.5640			−1.59704			−0.798521	+	0.601967i	$0.794384\pi$
$888$		0			0
$889$	9.55123			0.320338
$890$	−0.375885	+	1.64654i	−0.0125997	+	0.0551922i
$891$		0			0
$892$	17.4421	+	8.40150i	0.584006	+	0.281303i
$893$			49.5491i			1.65810i
$894$		0			0
$895$	0.860905			0.0287769
$896$	−0.00332222	+	11.3137i	−0.000110988	+	0.377964i
$897$		0			0
$898$	−24.6629	−	5.63024i	−0.823012	−	0.187883i
$899$		−	10.3982i		−	0.346800i
$900$		0			0
$901$		−	28.1459i		−	0.937676i
$902$	−0.311827	+	1.36594i	−0.0103827	+	0.0454808i
$903$		0			0
$904$	10.4580	+	8.34216i	0.347829	+	0.277456i
$905$	−0.513919			−0.0170833
$906$		0			0
$907$		−	45.9789i		−	1.52670i	−0.645982	−	0.763352i	$-0.723552\pi$
$907$		−	45.9789i		−	1.52670i	0.645982	−	0.763352i	$-0.276448\pi$
$908$	19.8377	−	41.1845i	0.658336	−	1.36676i
$909$		0			0
$910$	−0.274248	−	0.0626075i	−0.00909125	−	0.00207542i
$911$	−9.42797			−0.312363			−0.156181	−	0.987728i	$-0.549918\pi$
$911$	−9.42797			−0.312363			−0.156181	+	0.987728i	$0.549918\pi$
$912$		0			0
$913$	2.01532			0.0666974
$914$	−26.6959	−	6.09435i	−0.883023	−	0.201583i
$915$		0			0
$916$	14.5761	−	30.2612i	0.481609	−	0.999857i
$917$		−	18.5084i		−	0.611202i
$918$		0			0
$919$	−1.64588			−0.0542924			−0.0271462	−	0.999631i	$-0.508642\pi$
$919$	−1.64588			−0.0542924			−0.0271462	+	0.999631i	$0.508642\pi$
$920$	0.893798	−	1.12050i	0.0294676	−	0.0369417i
$921$		0			0
$922$	−6.88517	+	30.1601i	−0.226751	+	0.993270i
$923$		−	1.05587i		−	0.0347543i
$924$		0			0
$925$			21.8973i			0.719979i
$926$	−35.9092	−	8.19763i	−1.18005	−	0.269391i
$927$		0			0
$928$	−9.45825	+	4.55241i	−0.310482	+	0.149440i
$929$	−52.1072			−1.70958			−0.854791	−	0.518973i	$-0.826315\pi$
$929$	−52.1072			−1.70958			−0.854791	+	0.518973i	$0.826315\pi$
$930$		0			0
$931$			6.85261i			0.224585i
$932$	35.4527	+	17.0768i	1.16129	+	0.559369i
$933$		0			0
$934$	−3.72078	+	16.2986i	−0.121748	+	0.533308i
$935$	0.118664			0.00388072
$936$		0			0
$937$	10.2023			0.333294			0.166647	−	0.986017i	$-0.446706\pi$
$937$	10.2023			0.333294			0.166647	+	0.986017i	$0.446706\pi$
$938$	−1.96891	+	8.62471i	−0.0642873	+	0.281607i
$939$		0			0
$940$	0.719136	−	1.49298i	0.0234556	−	0.0486957i
$941$		−	0.500685i		−	0.0163219i	−0.999967	−	0.00816093i	$-0.997402\pi$
$941$		−	0.500685i		−	0.0163219i	0.999967	−	0.00816093i	$-0.00259773\pi$
$942$		0			0
$943$	−10.6093			−0.345487
$944$	−13.3211	+	10.6195i	−0.433564	+	0.345636i
$945$		0			0
$946$	−2.48022	−	0.566202i	−0.0806388	−	0.0184088i
$947$		−	49.4247i		−	1.60609i	−0.595921	−	0.803043i	$-0.703213\pi$
$947$		−	49.4247i		−	1.60609i	0.595921	−	0.803043i	$-0.296787\pi$
$948$		0			0
$949$			24.5707i			0.797599i
$950$	10.7560	−	47.1158i	0.348970	−	1.52864i
$951$		0			0
$952$	−5.54468	−	4.42288i	−0.179704	−	0.143346i
$953$	32.0038			1.03670			0.518352	−	0.855167i	$-0.326546\pi$
$953$	32.0038			1.03670			0.518352	+	0.855167i	$0.326546\pi$
$954$		0			0
$955$		−	2.82727i		−	0.0914882i
$956$	−43.0418	−	20.7323i	−1.39207	−	0.670530i
$957$		0			0
$958$	−40.1032	−	9.15506i	−1.29568	−	0.295787i
$959$	−8.42852			−0.272171
$960$		0			0
$961$	0.401788			0.0129609
$962$	−10.5089	−	2.39904i	−0.338819	−	0.0773482i
$963$		0			0
$964$	−7.26405	−	3.49893i	−0.233959	−	0.112693i
$965$			0.0384818i			0.00123877i
$966$		0			0
$967$	−45.6934			−1.46940			−0.734700	−	0.678392i	$-0.762677\pi$
$967$	−45.6934			−1.46940			−0.734700	+	0.678392i	$0.762677\pi$
$968$	−23.9454	−	19.1007i	−0.769634	−	0.613921i
$969$		0			0
$970$	0.123355	−	0.540348i	0.00396068	−	0.0173495i
$971$			9.06582i			0.290936i	0.989363	+	0.145468i	$0.0464688\pi$
$971$			9.06582i			0.290936i	−0.989363	+	0.145468i	$0.953531\pi$
$972$		0			0
$973$		−	13.8639i		−	0.444456i
$974$	29.4139	+	6.71482i	0.942482	+	0.215157i
$975$		0			0
$976$	23.0182	−	18.3501i	0.736794	−	0.587372i
$977$	20.6361			0.660207			0.330103	−	0.943945i	$-0.392916\pi$
$977$	20.6361			0.660207			0.330103	+	0.943945i	$0.392916\pi$
$978$		0			0
$979$		−	4.30369i		−	0.137547i
$980$	0.0994559	−	0.206478i	0.00317700	−	0.00659570i
$981$		0			0
$982$	−6.35957	+	27.8577i	−0.202942	+	0.888976i
$983$	15.4308			0.492167			0.246083	−	0.969249i	$-0.420856\pi$
$983$	15.4308			0.492167			0.246083	+	0.969249i	$0.420856\pi$
$984$		0			0
$985$	−1.52509			−0.0485933
$986$	1.46457	−	6.41546i	0.0466414	−	0.204310i
$987$		0			0
$988$	21.4332	+	10.3239i	0.681881	+	0.328447i
$989$		−	19.2640i		−	0.612560i
$990$		0			0
$991$	−25.7039			−0.816510			−0.408255	−	0.912868i	$-0.633863\pi$
$991$	−25.7039			−0.816510			−0.408255	+	0.912868i	$0.633863\pi$
$992$	−13.7479	−	28.5631i	−0.436496	−	0.906880i
$993$		0			0
$994$	0.838657	+	0.191455i	0.0266006	+	0.00607258i
$995$			1.05961i			0.0335918i
$996$		0			0
$997$			18.0217i			0.570753i	0.958416	+	0.285376i	$0.0921186\pi$
$997$			18.0217i			0.570753i	−0.958416	+	0.285376i	$0.907881\pi$
$998$	7.95254	−	34.8356i	0.251733	−	1.10270i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.e.757.1	✓	20
3.2	odd	2	inner	1512.2.c.e.757.20	yes	20
4.3	odd	2		6048.2.c.e.3025.9		20
8.3	odd	2		6048.2.c.e.3025.12		20
8.5	even	2	inner	1512.2.c.e.757.2	yes	20
12.11	even	2		6048.2.c.e.3025.11		20
24.5	odd	2	inner	1512.2.c.e.757.19	yes	20
24.11	even	2		6048.2.c.e.3025.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.e.757.1	✓	20	1.1	even	1	trivial
1512.2.c.e.757.2	yes	20	8.5	even	2	inner
1512.2.c.e.757.19	yes	20	24.5	odd	2	inner
1512.2.c.e.757.20	yes	20	3.2	odd	2	inner
6048.2.c.e.3025.9		20	4.3	odd	2
6048.2.c.e.3025.10		20	24.11	even	2
6048.2.c.e.3025.11		20	12.11	even	2
6048.2.c.e.3025.12		20	8.3	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37874 - 0.314750i) q^{2} +(1.80186 + 0.867919i) q^{4} -0.114591i q^{5} -1.00000 q^{7} +(-2.21113 - 1.76377i) q^{8} +(-0.0360676 + 0.157992i) q^{10} -0.412956i q^{11} -1.73584i q^{13} +(1.37874 + 0.314750i) q^{14} +(2.49343 + 3.12774i) q^{16} -2.50762 q^{17} +6.85261i q^{19} +(0.0994559 - 0.206478i) q^{20} +(-0.129978 + 0.569360i) q^{22} -4.42226 q^{23} +4.98687 q^{25} +(-0.546355 + 2.39327i) q^{26} +(-1.80186 - 0.867919i) q^{28} -1.85559i q^{29} +5.60373 q^{31} +(-2.45335 - 5.09716i) q^{32} +(3.45737 + 0.789274i) q^{34} +0.114591i q^{35} +4.39099i q^{37} +(2.15686 - 9.44798i) q^{38} +(-0.202113 + 0.253376i) q^{40} +2.39907 q^{41} +4.35614i q^{43} +(0.358412 - 0.744091i) q^{44} +(6.09716 + 1.39191i) q^{46} +7.23070 q^{47} +1.00000 q^{49} +(-6.87561 - 1.56962i) q^{50} +(1.50657 - 3.12774i) q^{52} +11.2241i q^{53} -0.0473212 q^{55} +(2.21113 + 1.76377i) q^{56} +(-0.584047 + 2.55838i) q^{58} +4.25900i q^{59} -7.35936i q^{61} +(-7.72610 - 1.76377i) q^{62} +(1.77820 + 7.79987i) q^{64} -0.198912 q^{65} +6.25549i q^{67} +(-4.51840 - 2.17641i) q^{68} +(0.0360676 - 0.157992i) q^{70} +0.608276 q^{71} -14.1550 q^{73} +(1.38207 - 6.05405i) q^{74} +(-5.94750 + 12.3475i) q^{76} +0.412956i q^{77} +8.19950 q^{79} +(0.358412 - 0.285726i) q^{80} +(-3.30771 - 0.755108i) q^{82} +4.88023i q^{83} +0.287352i q^{85} +(1.37110 - 6.00600i) q^{86} +(-0.728361 + 0.913100i) q^{88} +10.4217 q^{89} +1.73584i q^{91} +(-7.96832 - 3.83816i) q^{92} +(-9.96928 - 2.27586i) q^{94} +0.785249 q^{95} -3.42009 q^{97} +(-1.37874 - 0.314750i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{4} - 20 q^{7} - 12 q^{10} - 14 q^{16} + 8 q^{22} - 28 q^{25} + 2 q^{28} + 36 q^{31} - 6 q^{34} - 16 q^{40} - 18 q^{46} + 20 q^{49} + 94 q^{52} + 48 q^{55} + 66 q^{58} + 22 q^{64} + 12 q^{70}+ \cdots + 56 q^{97}+O(q^{100}) \) 20 * q - 2 * q^4 - 20 * q^7 - 12 * q^10 - 14 * q^16 + 8 * q^22 - 28 * q^25 + 2 * q^28 + 36 * q^31 - 6 * q^34 - 16 * q^40 - 18 * q^46 + 20 * q^49 + 94 * q^52 + 48 * q^55 + 66 * q^58 + 22 * q^64 + 12 * q^70 + 12 * q^76 + 64 * q^79 - 92 * q^88 - 24 * q^94 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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