LMFDB - Embedded newform 1512.2.c.e.757.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
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			757.19
Root			$1.37874 - 0.314750i$ of defining polynomial
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.e.757.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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	$0.0773827\pi$
$13$			1.73584i			0.481435i	−0.970595	+	0.240717i	$0.922617\pi$
$14$	−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	$-0.401646\pi$
$17$	2.50762			0.608188			0.304094	+	0.952642i	$0.401646\pi$
$18$		0			0
$19$		−	6.85261i		−	1.57210i	−0.618166	−	0.786048i	$-0.712124\pi$
$19$		−	6.85261i		−	1.57210i	0.618166	−	0.786048i	$-0.287876\pi$
$20$	−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	$-0.347472\pi$
$23$	4.42226			0.922106			0.461053	+	0.887373i	$0.347472\pi$
$24$		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	$-0.882457\pi$
$37$		−	4.39099i		−	0.721875i	0.932590	−	0.360938i	$-0.117543\pi$
$38$	−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	$-0.559985\pi$
$41$	−2.39907			−0.374672			−0.187336	+	0.982296i	$0.559985\pi$
$42$		0			0
$43$		−	4.35614i		−	0.664306i	−0.943226	−	0.332153i	$-0.892225\pi$
$43$		−	4.35614i		−	0.664306i	0.943226	−	0.332153i	$-0.107775\pi$
$44$	−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	$-0.676815\pi$
$47$	−7.23070			−1.05471			−0.527353	+	0.849646i	$0.676815\pi$
$48$		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	$0.156155\pi$
$61$			7.35936i			0.942269i	−0.882061	+	0.471135i	$0.843845\pi$
$62$	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	$-0.875196\pi$
$67$		−	6.25549i		−	0.764230i	0.924115	−	0.382115i	$-0.124804\pi$
$68$	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	$-0.511492\pi$
$71$	−0.608276			−0.0721891			−0.0360946	+	0.999348i	$0.511492\pi$
$72$		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	$-0.686268\pi$
$89$	−10.4217			−1.10469			−0.552347	+	0.833614i	$0.686268\pi$
$90$		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	$0.0322749\pi$
$109$			2.11355i			0.202442i	−0.994864	+	0.101221i	$0.967725\pi$
$110$	−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	$-0.428589\pi$
$113$	4.72972			0.444935			0.222467	+	0.974940i	$0.428589\pi$
$114$		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	$-0.617240\pi$
$137$	−8.42852			−0.720097			−0.360048	+	0.932934i	$0.617240\pi$
$138$		0			0
$139$		−	13.8639i		−	1.17592i	−0.808890	−	0.587961i	$-0.799931\pi$
$139$		−	13.8639i		−	1.17592i	0.808890	−	0.587961i	$-0.200069\pi$
$140$	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	$0.175213\pi$
$157$			13.1081i			1.04614i	−0.852290	+	0.523070i	$0.824787\pi$
$158$	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	$-0.637806\pi$
$163$		−	23.1785i		−	1.81548i	0.419533	−	0.907740i	$-0.362194\pi$
$164$	−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	$-0.588950\pi$
$167$	−7.12880			−0.551643			−0.275821	+	0.961209i	$0.588950\pi$
$168$		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	$0.0533035\pi$
$181$			4.48480i			0.333353i	−0.986012	+	0.166676i	$0.946697\pi$
$182$	−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	$-0.851138\pi$
$191$	−24.6726			−1.78525			−0.892624	+	0.450802i	$0.851138\pi$
$192$		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	$0.0521039\pi$
$211$			4.73424i			0.325918i	−0.986633	+	0.162959i	$0.947896\pi$
$212$	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	$0.187244\pi$
$229$			16.7944i			1.10980i	−0.831916	+	0.554901i	$0.812756\pi$
$230$	−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	$-0.722932\pi$
$233$	−19.6756			−1.28899			−0.644494	+	0.764609i	$0.722932\pi$
$234$		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	$-0.218970\pi$
$239$	23.8874			1.54515			0.772573	+	0.634926i	$0.218970\pi$
$240$		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	$-0.466885\pi$
$257$	3.32955			0.207692			0.103846	+	0.994593i	$0.466885\pi$
$258$		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	$-0.666895\pi$
$263$	−16.2375			−1.00124			−0.500622	+	0.865666i	$0.666895\pi$
$264$		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	$0.194646\pi$
$277$			19.1097i			1.14819i	−0.818788	+	0.574096i	$0.805354\pi$
$278$	−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	$-0.296998\pi$
$281$	19.9611			1.19078			0.595389	+	0.803438i	$0.296998\pi$
$282$		0			0
$283$			16.1413i			0.959503i	0.877404	+	0.479752i	$0.159273\pi$
$283$			16.1413i			0.959503i	−0.877404	+	0.479752i	$0.840727\pi$
$284$	−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	$-0.855106\pi$
$307$		−	15.4062i		−	0.879278i	0.898175	−	0.439639i	$-0.144894\pi$
$308$	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	$-0.304299\pi$
$311$	20.3442			1.15361			0.576806	+	0.816881i	$0.304299\pi$
$312$		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	$-0.732548\pi$
$331$		−	27.1007i		−	1.48959i	0.667295	−	0.744793i	$-0.267452\pi$
$332$	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	$0.155738\pi$
$349$			17.5598i			0.939954i	−0.882679	+	0.469977i	$0.844262\pi$
$350$	−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	$-0.336753\pi$
$353$	18.4376			0.981335			0.490668	+	0.871347i	$0.336753\pi$
$354$		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	$-0.433933\pi$
$359$	7.80894			0.412140			0.206070	+	0.978537i	$0.433933\pi$
$360$		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	$0.275365\pi$
$373$			29.4005i			1.52230i	−0.648575	+	0.761150i	$0.724635\pi$
$374$	−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	$0.0201377\pi$
$379$			2.46161i			0.126444i	−0.997999	+	0.0632222i	$0.979862\pi$
$380$	−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	$-0.570493\pi$
$383$	−8.59739			−0.439306			−0.219653	+	0.975578i	$0.570493\pi$
$384$		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	$0.240833\pi$
$397$			27.3549i			1.37290i	−0.727175	+	0.686452i	$0.759167\pi$
$398$	−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	$-0.551883\pi$
$401$	−6.49913			−0.324551			−0.162276	+	0.986745i	$0.551883\pi$
$402$		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	$-0.911167\pi$
$421$		−	11.3043i		−	0.550938i	0.961310	−	0.275469i	$-0.0888332\pi$
$422$	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	$-0.329062\pi$
$431$	21.2412			1.02315			0.511575	+	0.859238i	$0.329062\pi$
$432$		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	$-0.638704\pi$
$449$	−17.8880			−0.844185			−0.422093	+	0.906553i	$0.638704\pi$
$450$		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	$-0.731357\pi$
$479$	−29.0868			−1.32901			−0.664504	+	0.747284i	$0.731357\pi$
$480$		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	$-0.808670\pi$
$499$		−	25.2662i		−	1.13107i	0.824724	−	0.565535i	$-0.191330\pi$
$500$	−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	$-0.264717\pi$
$503$	30.2176			1.34734			0.673669	+	0.739033i	$0.264717\pi$
$504$		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	$-0.459997\pi$
$521$	5.72198			0.250685			0.125342	+	0.992114i	$0.459997\pi$
$522$		0			0
$523$		−	0.348058i		−	0.0152195i	−0.999971	−	0.00760976i	$-0.997578\pi$
$523$		−	0.348058i		−	0.0152195i	0.999971	−	0.00760976i	$-0.00242229\pi$
$524$	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	$-0.941547\pi$
$541$		−	8.49464i		−	0.365213i	0.983186	−	0.182606i	$-0.0584534\pi$
$542$	−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	$0.235337\pi$
$547$			31.5175i			1.34759i	−0.738918	+	0.673796i	$0.764663\pi$
$548$	−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	$-0.172975\pi$
$569$	40.8350			1.71189			0.855946	+	0.517065i	$0.172975\pi$
$570$		0			0
$571$			20.7134i			0.866831i	0.901194	+	0.433415i	$0.142692\pi$
$571$			20.7134i			0.866831i	−0.901194	+	0.433415i	$0.857308\pi$
$572$	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	$-0.834273\pi$
$593$	−42.2499			−1.73500			−0.867498	+	0.497440i	$0.834273\pi$
$594$		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	$-0.720951\pi$
$599$	−31.3138			−1.27945			−0.639723	+	0.768605i	$0.720951\pi$
$600$		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	$-0.957341\pi$
$613$		−	6.61633i		−	0.267231i	0.991033	−	0.133616i	$-0.0426587\pi$
$614$	−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	$-0.358539\pi$
$617$	21.3584			0.859855			0.429928	+	0.902863i	$0.358539\pi$
$618$		0			0
$619$			0.0210409i			0.000845707i	1.00000		0.000422854i	$0.000134598\pi$
$619$			0.0210409i			0.000845707i	−1.00000		0.000422854i	$0.999865\pi$
$620$	−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	$-0.469484\pi$
$641$	4.84692			0.191442			0.0957210	+	0.995408i	$0.469484\pi$
$642$		0			0
$643$		−	3.72899i		−	0.147057i	−0.997293	−	0.0735285i	$-0.976574\pi$
$643$		−	3.72899i		−	0.147057i	0.997293	−	0.0735285i	$-0.0234260\pi$
$644$	−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	$-0.145949\pi$
$647$	45.6179			1.79342			0.896712	+	0.442615i	$0.145949\pi$
$648$		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	$0.0453672\pi$
$661$			7.30385i			0.284087i	−0.989860	+	0.142043i	$0.954633\pi$
$662$	−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	$-0.681682\pi$
$691$		−	44.2400i		−	1.68297i	0.540281	−	0.841485i	$-0.318318\pi$
$692$	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	$-0.823667\pi$
$709$		−	28.0152i		−	1.05213i	0.850444	−	0.526066i	$-0.176333\pi$
$710$	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	$-0.532363\pi$
$719$	−5.44311			−0.202994			−0.101497	+	0.994836i	$0.532363\pi$
$720$		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	$0.316747\pi$
$733$			45.4197i			1.67762i	−0.544428	+	0.838808i	$0.683253\pi$
$734$	−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	$-0.982234\pi$
$739$		−	3.03287i		−	0.111566i	0.998443	−	0.0557830i	$-0.0177655\pi$
$740$	−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	$-0.773875\pi$
$743$	−41.3290			−1.51621			−0.758106	+	0.652131i	$0.773875\pi$
$744$		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	$-0.653801\pi$
$757$		−	48.7279i		−	1.77104i	0.464597	−	0.885522i	$-0.346199\pi$
$758$	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	$-0.656913\pi$
$761$	−26.1095			−0.946468			−0.473234	+	0.880937i	$0.656913\pi$
$762$		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	$0.333848\pi$
$787$			48.6354i			1.73367i	−0.498599	+	0.866833i	$0.666152\pi$
$788$	−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	$-0.800915\pi$
$809$	−46.1176			−1.62141			−0.810704	+	0.585456i	$0.800915\pi$
$810$		0			0
$811$		−	13.2874i		−	0.466585i	−0.972407	−	0.233293i	$-0.925050\pi$
$811$		−	13.2874i		−	0.466585i	0.972407	−	0.233293i	$-0.0749500\pi$
$812$	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	$-0.661845\pi$
$829$		−	50.3002i		−	1.74700i	0.486826	−	0.873499i	$-0.338155\pi$
$830$	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	$-0.651256\pi$
$839$	−26.5035			−0.915004			−0.457502	+	0.889209i	$0.651256\pi$
$840$		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	$-0.949544\pi$
$853$		−	9.22041i		−	0.315701i	0.987463	−	0.157850i	$-0.0504564\pi$
$854$	−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	$-0.252207\pi$
$857$	41.1124			1.40437			0.702187	+	0.711993i	$0.252207\pi$
$858$		0			0
$859$		−	7.51805i		−	0.256513i	−0.991741	−	0.128256i	$-0.959062\pi$
$859$		−	7.51805i		−	0.256513i	0.991741	−	0.128256i	$-0.0409380\pi$
$860$	−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	$-0.613520\pi$
$863$	−20.5122			−0.698245			−0.349122	+	0.937077i	$0.613520\pi$
$864$		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	$-0.643856\pi$
$877$		−	53.2820i		−	1.79921i	0.436710	−	0.899603i	$-0.356144\pi$
$878$	−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	$-0.284707\pi$
$881$	37.1591			1.25192			0.625960	+	0.779855i	$0.284707\pi$
$882$		0			0
$883$			30.5599i			1.02842i	0.857664	+	0.514211i	$0.171915\pi$
$883$			30.5599i			1.02842i	−0.857664	+	0.514211i	$0.828085\pi$
$884$	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	$-0.205616\pi$
$887$	47.5640			1.59704			0.798521	+	0.601967i	$0.205616\pi$
$888$		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	$0.276448\pi$
$907$			45.9789i			1.52670i	−0.645982	+	0.763352i	$0.723552\pi$
$908$	−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	$-0.450082\pi$
$911$	9.42797			0.312363			0.156181	+	0.987728i	$0.450082\pi$
$912$		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	$-0.173685\pi$
$929$	52.1072			1.70958			0.854791	+	0.518973i	$0.173685\pi$
$930$		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	$-0.673454\pi$
$953$	−32.0038			−1.03670			−0.518352	+	0.855167i	$0.673454\pi$
$954$		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	$-0.607084\pi$
$977$	−20.6361			−0.660207			−0.330103	+	0.943945i	$0.607084\pi$
$978$		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	$-0.579144\pi$
$983$	−15.4308			−0.492167			−0.246083	+	0.969249i	$0.579144\pi$
$984$		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	$-0.907881\pi$
$997$		−	18.0217i		−	0.570753i	0.958416	−	0.285376i	$-0.0921186\pi$
$998$	−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.757.19	yes	20
3.2	odd	2	inner	1512.2.c.e.757.2	yes	20
4.3	odd	2		6048.2.c.e.3025.10		20
8.3	odd	2		6048.2.c.e.3025.11		20
8.5	even	2	inner	1512.2.c.e.757.20	yes	20
12.11	even	2		6048.2.c.e.3025.12		20
24.5	odd	2	inner	1512.2.c.e.757.1	✓	20
24.11	even	2		6048.2.c.e.3025.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.e.757.1	✓	20	24.5	odd	2	inner
1512.2.c.e.757.2	yes	20	3.2	odd	2	inner
1512.2.c.e.757.19	yes	20	1.1	even	1	trivial
1512.2.c.e.757.20	yes	20	8.5	even	2	inner
6048.2.c.e.3025.9		20	24.11	even	2
6048.2.c.e.3025.10		20	4.3	odd	2
6048.2.c.e.3025.11		20	8.3	odd	2
6048.2.c.e.3025.12		20	12.11	even	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 $\F_{q}$

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

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

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Database

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