LMFDB - Embedded newform 1008.2.t.j.193.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(193,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.193"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.5
Root			$-0.674693 + 1.59524i$ of defining polynomial
Character	$\chi$	$=$	1008.193
Dual form			1008.2.t.j.961.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.674693 + 1.59524i) q^{3} +4.14520 q^{5} +(-0.190437 - 2.63889i) q^{7} +(-2.08958 + 2.15260i) q^{9} -0.868858 q^{11} +(2.86231 - 4.95766i) q^{13} +(2.79674 + 6.61258i) q^{15} +(-1.44613 + 2.50478i) q^{17} +(2.00703 + 3.47627i) q^{19} +(4.08117 - 2.08423i) q^{21} +5.82977 q^{23} +12.1827 q^{25} +(-4.84373 - 1.88104i) q^{27} +(-0.900417 - 1.55957i) q^{29} +(-1.48046 - 2.56422i) q^{31} +(-0.586213 - 1.38604i) q^{33} +(-0.789399 - 10.9387i) q^{35} +(-2.64925 - 4.58864i) q^{37} +(9.83984 + 1.22116i) q^{39} +(-5.89325 + 10.2074i) q^{41} +(2.00703 + 3.47627i) q^{43} +(-8.66171 + 8.92293i) q^{45} +(1.17218 - 2.03028i) q^{47} +(-6.92747 + 1.00508i) q^{49} +(-4.97142 - 0.616973i) q^{51} +(-1.09116 + 1.88995i) q^{53} -3.60159 q^{55} +(-4.19136 + 5.54711i) q^{57} +(-1.52715 - 2.64510i) q^{59} +(-2.81659 + 4.87848i) q^{61} +(6.07839 + 5.10423i) q^{63} +(11.8648 - 20.5505i) q^{65} +(-1.25539 - 2.17440i) q^{67} +(3.93331 + 9.29988i) q^{69} +1.09143 q^{71} +(0.723285 - 1.25277i) q^{73} +(8.21956 + 19.4343i) q^{75} +(0.165463 + 2.29282i) q^{77} +(-1.06464 + 1.84401i) q^{79} +(-0.267330 - 8.99603i) q^{81} +(-2.18784 - 3.78946i) q^{83} +(-5.99451 + 10.3828i) q^{85} +(1.88038 - 2.48861i) q^{87} +(5.83373 + 10.1043i) q^{89} +(-13.6278 - 6.60919i) q^{91} +(3.09170 - 4.09174i) q^{93} +(8.31953 + 14.4098i) q^{95} +(-3.98779 - 6.90706i) q^{97} +(1.81555 - 1.87030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4 q^{5} + 3 q^{7} + 10 q^{9} + 4 q^{11} + 2 q^{13} - 7 q^{15} + 2 q^{17} - 7 q^{19} - 2 q^{21} + 22 q^{23} + 18 q^{25} - 9 q^{27} + q^{29} + q^{31} + 5 q^{33} + 19 q^{35} + 10 q^{37} + 20 q^{39}+ \cdots - 7 q^{99}+O(q^{100}) $ 14 * q + 4 * q^5 + 3 * q^7 + 10 * q^9 + 4 * q^11 + 2 * q^13 - 7 * q^15 + 2 * q^17 - 7 * q^19 - 2 * q^21 + 22 * q^23 + 18 * q^25 - 9 * q^27 + q^29 + q^31 + 5 * q^33 + 19 * q^35 + 10 * q^37 + 20 * q^39 - 33 * q^41 - 7 * q^43 + 5 * q^45 + 3 * q^47 - 13 * q^49 - 20 * q^51 - 15 * q^53 + 28 * q^55 - 18 * q^57 + 14 * q^59 - 10 * q^61 + 39 * q^63 + 15 * q^65 - 6 * q^67 - 43 * q^69 - 2 * q^71 + 21 * q^73 - q^75 + 19 * q^77 + 10 * q^79 + 22 * q^81 + 25 * q^83 + 8 * q^85 + 2 * q^87 - 6 * q^89 - 2 * q^91 + 16 * q^93 + 28 * q^95 - 18 * q^97 - 7 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.674693	+	1.59524i	0.389534	+	0.921012i
$3$	0.674693	+	1.59524i	0.389534	+	0.921012i
$4$		0			0
$5$	4.14520			1.85379			0.926894	−	0.375322i	$-0.122468\pi$
$5$	4.14520			1.85379			0.926894	+	0.375322i	$0.122468\pi$
$6$		0			0
$7$	−0.190437	−	2.63889i	−0.0719784	−	0.997406i
$7$	−0.190437	−	2.63889i	−0.0719784	−	0.997406i
$8$		0			0
$9$	−2.08958	+	2.15260i	−0.696526	+	0.717532i
$10$		0			0
$11$	−0.868858			−0.261971			−0.130985	−	0.991384i	$-0.541814\pi$
$11$	−0.868858			−0.261971			−0.130985	+	0.991384i	$0.541814\pi$
$12$		0			0
$13$	2.86231	−	4.95766i	0.793861	−	1.37501i	−0.129698	−	0.991554i	$-0.541401\pi$
$13$	2.86231	−	4.95766i	0.793861	−	1.37501i	0.923560	−	0.383455i	$-0.125266\pi$
$14$		0			0
$15$	2.79674	+	6.61258i	0.722115	+	1.70736i
$16$		0			0
$17$	−1.44613	+	2.50478i	−0.350739	+	0.607498i	−0.986379	−	0.164488i	$-0.947403\pi$
$17$	−1.44613	+	2.50478i	−0.350739	+	0.607498i	0.635640	+	0.771986i	$0.280736\pi$
$18$		0			0
$19$	2.00703	+	3.47627i	0.460444	+	0.797512i	0.998983	−	0.0450884i	$-0.0143570\pi$
$19$	2.00703	+	3.47627i	0.460444	+	0.797512i	−0.538539	+	0.842600i	$0.681024\pi$
$20$		0			0
$21$	4.08117	−	2.08423i	0.890585	−	0.454817i
$22$		0			0
$23$	5.82977			1.21559			0.607795	−	0.794094i	$-0.292054\pi$
$23$	5.82977			1.21559			0.607795	+	0.794094i	$0.292054\pi$
$24$		0			0
$25$	12.1827			2.43653
$26$		0			0
$27$	−4.84373	−	1.88104i	−0.932176	−	0.362005i
$28$		0			0
$29$	−0.900417	−	1.55957i	−0.167203	−	0.289604i	0.770232	−	0.637763i	$-0.220140\pi$
$29$	−0.900417	−	1.55957i	−0.167203	−	0.289604i	−0.937435	+	0.348159i	$0.886807\pi$
$30$		0			0
$31$	−1.48046	−	2.56422i	−0.265898	−	0.460548i	0.701901	−	0.712275i	$-0.252335\pi$
$31$	−1.48046	−	2.56422i	−0.265898	−	0.460548i	−0.967798	+	0.251727i	$0.919002\pi$
$32$		0			0
$33$	−0.586213	−	1.38604i	−0.102047	−	0.241278i
$34$		0			0
$35$	−0.789399	−	10.9387i	−0.133433	−	1.84898i
$36$		0			0
$37$	−2.64925	−	4.58864i	−0.435535	−	0.754368i	0.561804	−	0.827270i	$-0.310107\pi$
$37$	−2.64925	−	4.58864i	−0.435535	−	0.754368i	−0.997339	+	0.0729017i	$0.976774\pi$
$38$		0			0
$39$	9.83984	+	1.22116i	1.57564	+	0.195543i
$40$		0			0
$41$	−5.89325	+	10.2074i	−0.920371	+	1.59413i	−0.121528	+	0.992588i	$0.538780\pi$
$41$	−5.89325	+	10.2074i	−0.920371	+	1.59413i	−0.798842	+	0.601541i	$0.794554\pi$
$42$		0			0
$43$	2.00703	+	3.47627i	0.306069	+	0.530127i	0.977499	−	0.210941i	$-0.0676529\pi$
$43$	2.00703	+	3.47627i	0.306069	+	0.530127i	−0.671430	+	0.741068i	$0.734320\pi$
$44$		0			0
$45$	−8.66171	+	8.92293i	−1.29121	+	1.33015i
$46$		0			0
$47$	1.17218	−	2.03028i	0.170980	−	0.296147i	−0.767783	−	0.640711i	$-0.778640\pi$
$47$	1.17218	−	2.03028i	0.170980	−	0.296147i	0.938763	+	0.344564i	$0.111973\pi$
$48$		0			0
$49$	−6.92747	+	1.00508i	−0.989638	+	0.143583i
$50$		0			0
$51$	−4.97142	−	0.616973i	−0.696138	−	0.0863935i
$52$		0			0
$53$	−1.09116	+	1.88995i	−0.149883	+	0.259605i	−0.931184	−	0.364549i	$-0.881223\pi$
$53$	−1.09116	+	1.88995i	−0.149883	+	0.259605i	0.781301	+	0.624154i	$0.214556\pi$
$54$		0			0
$55$	−3.60159			−0.485638
$56$		0			0
$57$	−4.19136	+	5.54711i	−0.555159	+	0.734733i
$58$		0			0
$59$	−1.52715	−	2.64510i	−0.198818	−	0.344363i	0.749327	−	0.662200i	$-0.230377\pi$
$59$	−1.52715	−	2.64510i	−0.198818	−	0.344363i	−0.948146	+	0.317837i	$0.897044\pi$
$60$		0			0
$61$	−2.81659	+	4.87848i	−0.360628	+	0.624625i	−0.988064	−	0.154042i	$-0.950771\pi$
$61$	−2.81659	+	4.87848i	−0.360628	+	0.624625i	0.627437	+	0.778668i	$0.284104\pi$
$62$		0			0
$63$	6.07839	+	5.10423i	0.765805	+	0.643072i
$64$		0			0
$65$	11.8648	−	20.5505i	1.47165	−	2.54898i
$66$		0			0
$67$	−1.25539	−	2.17440i	−0.153370	−	0.265645i	0.779094	−	0.626907i	$-0.215679\pi$
$67$	−1.25539	−	2.17440i	−0.153370	−	0.265645i	−0.932464	+	0.361262i	$0.882346\pi$
$68$		0			0
$69$	3.93331	+	9.29988i	0.473514	+	1.11957i
$70$		0			0
$71$	1.09143			0.129529			0.0647647	−	0.997901i	$-0.479370\pi$
$71$	1.09143			0.129529			0.0647647	+	0.997901i	$0.479370\pi$
$72$		0			0
$73$	0.723285	−	1.25277i	0.0846541	−	0.146625i	−0.820590	−	0.571518i	$-0.806355\pi$
$73$	0.723285	−	1.25277i	0.0846541	−	0.146625i	0.905244	+	0.424893i	$0.139688\pi$
$74$		0			0
$75$	8.21956	+	19.4343i	0.949113	+	2.24408i
$76$		0			0
$77$	0.165463	+	2.29282i	0.0188562	+	0.261291i
$78$		0			0
$79$	−1.06464	+	1.84401i	−0.119781	+	0.207468i	−0.919681	−	0.392666i	$-0.871553\pi$
$79$	−1.06464	+	1.84401i	−0.119781	+	0.207468i	0.799900	+	0.600134i	$0.204886\pi$
$80$		0			0
$81$	−0.267330	−	8.99603i	−0.0297034	−	0.999559i
$82$		0			0
$83$	−2.18784	−	3.78946i	−0.240147	−	0.415947i	0.720609	−	0.693342i	$-0.243862\pi$
$83$	−2.18784	−	3.78946i	−0.240147	−	0.415947i	−0.960756	+	0.277395i	$0.910529\pi$
$84$		0			0
$85$	−5.99451	+	10.3828i	−0.650196	+	1.12617i
$86$		0			0
$87$	1.88038	−	2.48861i	0.201598	−	0.266807i
$88$		0			0
$89$	5.83373	+	10.1043i	0.618374	+	1.07105i	0.989783	+	0.142585i	$0.0455415\pi$
$89$	5.83373	+	10.1043i	0.618374	+	1.07105i	−0.371409	+	0.928469i	$0.621125\pi$
$90$		0			0
$91$	−13.6278	−	6.60919i	−1.42858	−	0.692831i
$92$		0			0
$93$	3.09170	−	4.09174i	0.320594	−	0.424294i
$94$		0			0
$95$	8.31953	+	14.4098i	0.853566	+	1.47842i
$96$		0			0
$97$	−3.98779	−	6.90706i	−0.404899	−	0.701306i	0.589411	−	0.807834i	$-0.299360\pi$
$97$	−3.98779	−	6.90706i	−0.404899	−	0.701306i	−0.994310	+	0.106528i	$0.966027\pi$
$98$		0			0
$99$	1.81555	−	1.87030i	0.182469	−	0.187972i
$100$		0			0
$101$	−3.76370			−0.374502			−0.187251	−	0.982312i	$-0.559958\pi$
$101$	−3.76370			−0.374502			−0.187251	+	0.982312i	$0.559958\pi$
$102$		0			0
$103$	−10.8556			−1.06963			−0.534815	−	0.844969i	$-0.679619\pi$
$103$	−10.8556			−1.06963			−0.534815	+	0.844969i	$0.679619\pi$
$104$		0			0
$105$	16.9173	−	8.63956i	1.65096	−	0.843135i
$106$		0			0
$107$	4.82343	+	8.35442i	0.466298	+	0.807653i	0.999259	−	0.0384875i	$-0.0122540\pi$
$107$	4.82343	+	8.35442i	0.466298	+	0.807653i	−0.532961	+	0.846140i	$0.678921\pi$
$108$		0			0
$109$	−5.86131	+	10.1521i	−0.561412	+	0.972394i	0.435962	+	0.899965i	$0.356408\pi$
$109$	−5.86131	+	10.1521i	−0.561412	+	0.972394i	−0.997374	+	0.0724288i	$0.976925\pi$
$110$		0			0
$111$	5.53255	−	7.32212i	0.525127	−	0.694985i
$112$		0			0
$113$	2.88981	−	5.00530i	0.271851	−	0.470859i	−0.697485	−	0.716599i	$-0.745698\pi$
$113$	2.88981	−	5.00530i	0.271851	−	0.470859i	0.969336	+	0.245740i	$0.0790310\pi$
$114$		0			0
$115$	24.1655			2.25345
$116$		0			0
$117$	4.69083	+	16.5208i	0.433667	+	1.52735i
$118$		0			0
$119$	6.88523	+	3.33918i	0.631168	+	0.306103i
$120$		0			0
$121$	−10.2451			−0.931371
$122$		0			0
$123$	−20.2594	−	2.51427i	−1.82673	−	0.226704i
$124$		0			0
$125$	29.7736			2.66303
$126$		0			0
$127$	−6.47468			−0.574535			−0.287268	−	0.957850i	$-0.592747\pi$
$127$	−6.47468			−0.574535			−0.287268	+	0.957850i	$0.592747\pi$
$128$		0			0
$129$	−4.19136	+	5.54711i	−0.369029	+	0.488396i
$130$		0			0
$131$	17.7303			1.54910			0.774551	−	0.632511i	$-0.217976\pi$
$131$	17.7303			1.54910			0.774551	+	0.632511i	$0.217976\pi$
$132$		0			0
$133$	8.79129	−	5.95833i	0.762301	−	0.516653i
$134$		0			0
$135$	−20.0782	−	7.79726i	−1.72806	−	0.671081i
$136$		0			0
$137$	2.72232			0.232583			0.116292	−	0.993215i	$-0.462899\pi$
$137$	2.72232			0.232583			0.116292	+	0.993215i	$0.462899\pi$
$138$		0			0
$139$	−8.65431	+	14.9897i	−0.734049	+	1.27141i	0.221090	+	0.975253i	$0.429038\pi$
$139$	−8.65431	+	14.9897i	−0.734049	+	1.27141i	−0.955139	+	0.296157i	$0.904295\pi$
$140$		0			0
$141$	4.02964	+	0.500095i	0.339357	+	0.0421156i
$142$		0			0
$143$	−2.48694	+	4.30751i	−0.207968	+	0.360212i
$144$		0			0
$145$	−3.73241	−	6.46472i	−0.309959	−	0.536865i
$146$		0			0
$147$	−6.27727	−	10.3728i	−0.517740	−	0.855538i
$148$		0			0
$149$	−6.84685			−0.560916			−0.280458	−	0.959866i	$-0.590486\pi$
$149$	−6.84685			−0.560916			−0.280458	+	0.959866i	$0.590486\pi$
$150$		0			0
$151$	−9.28166			−0.755331			−0.377666	−	0.925942i	$-0.623273\pi$
$151$	−9.28166			−0.755331			−0.377666	+	0.925942i	$0.623273\pi$
$152$		0			0
$153$	−2.36996	−	8.34687i	−0.191600	−	0.674804i
$154$		0			0
$155$	−6.13678	−	10.6292i	−0.492918	−	0.853759i
$156$		0			0
$157$	−6.83840	−	11.8445i	−0.545764	−	0.945291i	−0.998558	−	0.0536759i	$-0.982906\pi$
$157$	−6.83840	−	11.8445i	−0.545764	−	0.945291i	0.452795	−	0.891615i	$-0.350427\pi$
$158$		0			0
$159$	−3.75113	−	0.465530i	−0.297484	−	0.0369189i
$160$		0			0
$161$	−1.11020	−	15.3841i	−0.0874963	−	1.21244i
$162$		0			0
$163$	1.65003	+	2.85793i	0.129240	+	0.223850i	0.923382	−	0.383882i	$-0.125413\pi$
$163$	1.65003	+	2.85793i	0.129240	+	0.223850i	−0.794142	+	0.607732i	$0.792080\pi$
$164$		0			0
$165$	−2.42997	−	5.74540i	−0.189173	−	0.447279i
$166$		0			0
$167$	−5.96228	+	10.3270i	−0.461375	+	0.799125i	−0.999030	−	0.0440399i	$-0.985977\pi$
$167$	−5.96228	+	10.3270i	−0.461375	+	0.799125i	0.537655	+	0.843165i	$0.319310\pi$
$168$		0			0
$169$	−9.88562	−	17.1224i	−0.760432	−	1.31711i
$170$		0			0
$171$	−11.6769	−	2.94363i	−0.892951	−	0.225105i
$172$		0			0
$173$	4.81694	−	8.34319i	0.366225	−	0.634321i	−0.622747	−	0.782424i	$-0.713983\pi$
$173$	4.81694	−	8.34319i	0.366225	−	0.634321i	0.988972	+	0.148103i	$0.0473166\pi$
$174$		0			0
$175$	−2.32003	−	32.1487i	−0.175378	−	2.43021i
$176$		0			0
$177$	3.18922	−	4.22081i	0.239716	−	0.317255i
$178$		0			0
$179$	11.5285	−	19.9680i	0.861682	−	1.49248i	−0.00862183	−	0.999963i	$-0.502744\pi$
$179$	11.5285	−	19.9680i	0.861682	−	1.49248i	0.870304	−	0.492515i	$-0.163922\pi$
$180$		0			0
$181$	−11.8325			−0.879504			−0.439752	−	0.898119i	$-0.644934\pi$
$181$	−11.8325			−0.879504			−0.439752	+	0.898119i	$0.644934\pi$
$182$		0			0
$183$	−9.68268	−	1.20166i	−0.715764	−	0.0888292i
$184$		0			0
$185$	−10.9817	−	19.0208i	−0.807390	−	1.39844i
$186$		0			0
$187$	1.25649	−	2.17630i	0.0918833	−	0.159147i
$188$		0			0
$189$	−4.04142	+	13.1403i	−0.293970	+	0.955815i
$190$		0			0
$191$	−3.14254	+	5.44303i	−0.227386	+	0.393844i	−0.957033	−	0.289980i	$-0.906351\pi$
$191$	−3.14254	+	5.44303i	−0.227386	+	0.393844i	0.729647	+	0.683824i	$0.239685\pi$
$192$		0			0
$193$	−6.86559	−	11.8915i	−0.494196	−	0.855972i	0.505782	−	0.862661i	$-0.331204\pi$
$193$	−6.86559	−	11.8915i	−0.494196	−	0.855972i	−0.999978	+	0.00668919i	$0.997871\pi$
$194$		0			0
$195$	40.7881	+	5.06197i	2.92090	+	0.362495i
$196$		0			0
$197$	−0.161495			−0.0115061			−0.00575303	−	0.999983i	$-0.501831\pi$
$197$	−0.161495			−0.0115061			−0.00575303	+	0.999983i	$0.501831\pi$
$198$		0			0
$199$	12.4140	−	21.5016i	0.880003	−	1.52421i	0.0286672	−	0.999589i	$-0.490874\pi$
$199$	12.4140	−	21.5016i	0.880003	−	1.52421i	0.851336	−	0.524621i	$-0.175793\pi$
$200$		0			0
$201$	2.62168	−	3.46970i	0.184919	−	0.244733i
$202$		0			0
$203$	−3.94405	+	2.67310i	−0.276818	+	0.187615i
$204$		0			0
$205$	−24.4287	+	42.3117i	−1.70617	+	2.95518i
$206$		0			0
$207$	−12.1818	+	12.5491i	−0.846690	+	0.872225i
$208$		0			0
$209$	−1.74382	−	3.02039i	−0.120623	−	0.208925i
$210$		0			0
$211$	−9.44607	+	16.3611i	−0.650295	+	1.12634i	0.332757	+	0.943013i	$0.392021\pi$
$211$	−9.44607	+	16.3611i	−0.650295	+	1.12634i	−0.983051	+	0.183331i	$0.941312\pi$
$212$		0			0
$213$	0.736384	+	1.74110i	0.0504562	+	0.119298i
$214$		0			0
$215$	8.31953	+	14.4098i	0.567387	+	0.982743i
$216$		0			0
$217$	−6.48477	+	4.39508i	−0.440215	+	0.298357i
$218$		0			0
$219$	2.48646	+	0.308580i	0.168019	+	0.0208519i
$220$		0			0
$221$	8.27856	+	14.3389i	0.556876	+	0.964538i
$222$		0			0
$223$	−7.04717	−	12.2061i	−0.471914	−	0.817378i	0.527570	−	0.849512i	$-0.323103\pi$
$223$	−7.04717	−	12.2061i	−0.471914	−	0.817378i	−0.999484	+	0.0321333i	$0.989770\pi$
$224$		0			0
$225$	−25.4566	+	26.2243i	−1.69711	+	1.74829i
$226$		0			0
$227$	−25.9782			−1.72424			−0.862118	−	0.506708i	$-0.830862\pi$
$227$	−25.9782			−1.72424			−0.862118	+	0.506708i	$0.830862\pi$
$228$		0			0
$229$	24.9157			1.64648			0.823239	−	0.567695i	$-0.192165\pi$
$229$	24.9157			1.64648			0.823239	+	0.567695i	$0.192165\pi$
$230$		0			0
$231$	−3.54596	+	1.81090i	−0.233307	+	0.119149i
$232$		0			0
$233$	−3.05923	−	5.29874i	−0.200417	−	0.347132i	0.748246	−	0.663421i	$-0.230896\pi$
$233$	−3.05923	−	5.29874i	−0.200417	−	0.347132i	−0.948663	+	0.316289i	$0.897563\pi$
$234$		0			0
$235$	4.85893	−	8.41591i	0.316961	−	0.548993i
$236$		0			0
$237$	−3.65995	−	0.454214i	−0.237739	−	0.0295044i
$238$		0			0
$239$	7.71988	−	13.3712i	0.499357	−	0.864912i	−0.500643	−	0.865654i	$-0.666903\pi$
$239$	7.71988	−	13.3712i	0.499357	−	0.864912i	1.00000		0.000742080i	$0.000236211\pi$
$240$		0			0
$241$	9.84518			0.634183			0.317092	−	0.948395i	$-0.397294\pi$
$241$	9.84518			0.634183			0.317092	+	0.948395i	$0.397294\pi$
$242$		0			0
$243$	14.1705	−	6.49602i	0.909035	−	0.416720i
$244$		0			0
$245$	−28.7157	+	4.16627i	−1.83458	+	0.266173i
$246$		0			0
$247$	22.9789			1.46211
$248$		0			0
$249$	4.56897	−	6.04685i	0.289546	−	0.383204i
$250$		0			0
$251$	−26.8843			−1.69692			−0.848461	−	0.529258i	$-0.822470\pi$
$251$	−26.8843			−1.69692			−0.848461	+	0.529258i	$0.822470\pi$
$252$		0			0
$253$	−5.06524			−0.318449
$254$		0			0
$255$	−20.6075	−	2.55748i	−1.29049	−	0.160155i
$256$		0			0
$257$	11.0127			0.686954			0.343477	−	0.939161i	$-0.388395\pi$
$257$	11.0127			0.686954			0.343477	+	0.939161i	$0.388395\pi$
$258$		0			0
$259$	−11.6044	+	7.86494i	−0.721063	+	0.488703i
$260$		0			0
$261$	5.23861	+	1.32060i	0.324262	+	0.0817434i
$262$		0			0
$263$	7.31095			0.450812			0.225406	−	0.974265i	$-0.427629\pi$
$263$	7.31095			0.450812			0.225406	+	0.974265i	$0.427629\pi$
$264$		0			0
$265$	−4.52309	+	7.83423i	−0.277851	+	0.481253i
$266$		0			0
$267$	−12.1828	+	16.1235i	−0.745576	+	0.986742i
$268$		0			0
$269$	−2.08048	+	3.60349i	−0.126849	+	0.219709i	−0.922454	−	0.386107i	$-0.873820\pi$
$269$	−2.08048	+	3.60349i	−0.126849	+	0.219709i	0.795605	+	0.605815i	$0.207153\pi$
$270$		0			0
$271$	4.18300	+	7.24516i	0.254099	+	0.440112i	0.964650	−	0.263533i	$-0.0848878\pi$
$271$	4.18300	+	7.24516i	0.254099	+	0.440112i	−0.710551	+	0.703645i	$0.751554\pi$
$272$		0			0
$273$	1.34865	−	26.1988i	0.0816239	−	1.58562i
$274$		0			0
$275$	−10.5850			−0.638300
$276$		0			0
$277$	−2.79856			−0.168149			−0.0840745	−	0.996459i	$-0.526793\pi$
$277$	−2.79856			−0.168149			−0.0840745	+	0.996459i	$0.526793\pi$
$278$		0			0
$279$	8.61326	+	2.17132i	0.515662	+	0.129994i
$280$		0			0
$281$	−5.44314	−	9.42779i	−0.324710	−	0.562415i	0.656743	−	0.754114i	$-0.271933\pi$
$281$	−5.44314	−	9.42779i	−0.324710	−	0.562415i	−0.981454	+	0.191699i	$0.938600\pi$
$282$		0			0
$283$	−1.01212	−	1.75304i	−0.0601642	−	0.104207i	0.834374	−	0.551198i	$-0.185829\pi$
$283$	−1.01212	−	1.75304i	−0.0601642	−	0.104207i	−0.894539	+	0.446990i	$0.852496\pi$
$284$		0			0
$285$	−17.3740	+	22.9939i	−1.02915	+	1.36204i
$286$		0			0
$287$	28.0585	+	13.6078i	1.65624	+	0.803241i
$288$		0			0
$289$	4.31739	+	7.47794i	0.253964	+	0.439879i
$290$		0			0
$291$	8.32788	−	11.0216i	0.488189	−	0.646100i
$292$		0			0
$293$	−9.65448	+	16.7220i	−0.564021	+	0.976912i	0.433120	+	0.901336i	$0.357413\pi$
$293$	−9.65448	+	16.7220i	−0.564021	+	0.976912i	−0.997140	+	0.0755757i	$0.975921\pi$
$294$		0			0
$295$	−6.33035	−	10.9645i	−0.368567	−	0.638377i
$296$		0			0
$297$	4.20851	+	1.63435i	0.244203	+	0.0948348i
$298$		0			0
$299$	16.6866	−	28.9020i	0.965011	−	1.67145i
$300$		0			0
$301$	8.79129	−	5.95833i	0.506721	−	0.343433i
$302$		0			0
$303$	−2.53935	−	6.00401i	−0.145882	−	0.344921i
$304$		0			0
$305$	−11.6753	+	20.2223i	−0.668527	+	1.15792i
$306$		0			0
$307$	13.1378			0.749813			0.374907	−	0.927063i	$-0.377675\pi$
$307$	13.1378			0.749813			0.374907	+	0.927063i	$0.377675\pi$
$308$		0			0
$309$	−7.32417	−	17.3172i	−0.416658	−	0.985142i
$310$		0			0
$311$	−6.76606	−	11.7192i	−0.383668	−	0.664533i	0.607915	−	0.794002i	$-0.292006\pi$
$311$	−6.76606	−	11.7192i	−0.383668	−	0.664533i	−0.991583	+	0.129469i	$0.958673\pi$
$312$		0			0
$313$	12.6000	−	21.8238i	0.712194	−	1.23356i	−0.251838	−	0.967770i	$-0.581035\pi$
$313$	12.6000	−	21.8238i	0.712194	−	1.23356i	0.964032	−	0.265787i	$-0.0856318\pi$
$314$		0			0
$315$	25.1961	+	21.1580i	1.41964	+	1.19212i
$316$		0			0
$317$	6.14888	−	10.6502i	0.345356	−	0.598173i	−0.640063	−	0.768323i	$-0.721092\pi$
$317$	6.14888	−	10.6502i	0.345356	−	0.598173i	0.985418	+	0.170149i	$0.0544250\pi$
$318$		0			0
$319$	0.782335	+	1.35504i	0.0438023	+	0.0758679i
$320$		0			0
$321$	−10.0730	+	13.3312i	−0.562218	+	0.744075i
$322$		0			0
$323$	−11.6097			−0.645982
$324$		0			0
$325$	34.8705	−	60.3975i	1.93427	−	3.35025i
$326$		0			0
$327$	−20.1496	−	2.50065i	−1.11428	−	0.138286i
$328$		0			0
$329$	−5.58091	−	2.70662i	−0.307685	−	0.149221i
$330$		0			0
$331$	−9.96285	+	17.2562i	−0.547608	+	0.948484i	0.450830	+	0.892610i	$0.351128\pi$
$331$	−9.96285	+	17.2562i	−0.547608	+	0.948484i	−0.998438	+	0.0558745i	$0.982205\pi$
$332$		0			0
$333$	15.4133	+	3.88556i	0.844645	+	0.212927i
$334$		0			0
$335$	−5.20383	−	9.01330i	−0.284316	−	0.492449i
$336$		0			0
$337$	−0.966380	+	1.67382i	−0.0526421	+	0.0911788i	−0.891146	−	0.453717i	$-0.850098\pi$
$337$	−0.966380	+	1.67382i	−0.0526421	+	0.0911788i	0.838504	+	0.544896i	$0.183431\pi$
$338$		0			0
$339$	9.93439	+	1.23290i	0.539562	+	0.0669618i
$340$		0			0
$341$	1.28631	+	2.22795i	0.0696574	+	0.120650i
$342$		0			0
$343$	3.97155	+	18.0894i	0.214444	+	0.976736i
$344$		0			0
$345$	16.3043	+	38.5498i	0.877796	+	2.07545i
$346$		0			0
$347$	8.48241	+	14.6920i	0.455360	+	0.788706i	0.998709	−	0.0508006i	$-0.0161773\pi$
$347$	8.48241	+	14.6920i	0.455360	+	0.788706i	−0.543349	+	0.839507i	$0.682844\pi$
$348$		0			0
$349$	−6.25767	−	10.8386i	−0.334966	−	0.580177i	0.648513	−	0.761204i	$-0.275391\pi$
$349$	−6.25767	−	10.8386i	−0.334966	−	0.580177i	−0.983478	+	0.181027i	$0.942058\pi$
$350$		0			0
$351$	−23.1898	+	18.6295i	−1.23778	+	0.994368i
$352$		0			0
$353$	32.3857			1.72372			0.861859	−	0.507149i	$-0.169300\pi$
$353$	32.3857			1.72372			0.861859	+	0.507149i	$0.169300\pi$
$354$		0			0
$355$	4.52421			0.240120
$356$		0			0
$357$	−0.681382	+	13.2365i	−0.0360626	+	0.700550i
$358$		0			0
$359$	−8.98559	−	15.5635i	−0.474242	−	0.821410i	0.525323	−	0.850903i	$-0.323944\pi$
$359$	−8.98559	−	15.5635i	−0.474242	−	0.821410i	−0.999565	+	0.0294922i	$0.990611\pi$
$360$		0			0
$361$	1.44368	−	2.50052i	0.0759830	−	0.131606i
$362$		0			0
$363$	−6.91229	−	16.3434i	−0.362801	−	0.857804i
$364$		0			0
$365$	2.99816	−	5.19297i	0.156931	−	0.271812i
$366$		0			0
$367$	−8.16840			−0.426387			−0.213194	−	0.977010i	$-0.568386\pi$
$367$	−8.16840			−0.426387			−0.213194	+	0.977010i	$0.568386\pi$
$368$		0			0
$369$	−9.65801	−	34.0149i	−0.502776	−	1.77075i
$370$		0			0
$371$	5.19517	+	2.51954i	0.269720	+	0.130808i
$372$		0			0
$373$	−5.16161			−0.267258			−0.133629	−	0.991031i	$-0.542663\pi$
$373$	−5.16161			−0.267258			−0.133629	+	0.991031i	$0.542663\pi$
$374$		0			0
$375$	20.0880	+	47.4960i	1.03734	+	2.45268i
$376$		0			0
$377$	−10.3091			−0.530945
$378$		0			0
$379$	−21.0017			−1.07878			−0.539392	−	0.842055i	$-0.681346\pi$
$379$	−21.0017			−1.07878			−0.539392	+	0.842055i	$0.681346\pi$
$380$		0			0
$381$	−4.36843	−	10.3287i	−0.223801	−	0.529154i
$382$		0			0
$383$	−29.5589			−1.51039			−0.755194	−	0.655501i	$-0.772458\pi$
$383$	−29.5589			−1.51039			−0.755194	+	0.655501i	$0.772458\pi$
$384$		0			0
$385$	0.685876	+	9.50419i	0.0349555	+	0.484379i
$386$		0			0
$387$	−11.6769	−	2.94363i	−0.593568	−	0.149633i
$388$		0			0
$389$	−16.5379			−0.838505			−0.419252	−	0.907870i	$-0.637708\pi$
$389$	−16.5379			−0.838505			−0.419252	+	0.907870i	$0.637708\pi$
$390$		0			0
$391$	−8.43063	+	14.6023i	−0.426355	+	0.738469i
$392$		0			0
$393$	11.9625	+	28.2840i	0.603429	+	1.42674i
$394$		0			0
$395$	−4.41315	+	7.64379i	−0.222049	+	0.384601i
$396$		0			0
$397$	15.4394	+	26.7418i	0.774881	+	1.34213i	0.934861	+	0.355014i	$0.115524\pi$
$397$	15.4394	+	26.7418i	0.774881	+	1.34213i	−0.159980	+	0.987120i	$0.551143\pi$
$398$		0			0
$399$	15.4364	+	10.0042i	0.772786	+	0.500835i
$400$		0			0
$401$	10.6323			0.530951			0.265475	−	0.964118i	$-0.414471\pi$
$401$	10.6323			0.530951			0.265475	+	0.964118i	$0.414471\pi$
$402$		0			0
$403$	−16.9501			−0.844343
$404$		0			0
$405$	−1.10814	−	37.2903i	−0.0550638	−	1.85297i
$406$		0			0
$407$	2.30183	+	3.98688i	0.114097	+	0.197622i
$408$		0			0
$409$	7.39782	+	12.8134i	0.365799	+	0.633582i	0.988904	−	0.148556i	$-0.0474625\pi$
$409$	7.39782	+	12.8134i	0.365799	+	0.633582i	−0.623105	+	0.782138i	$0.714129\pi$
$410$		0			0
$411$	1.83673	+	4.34275i	0.0905993	+	0.214212i
$412$		0			0
$413$	−6.68931	+	4.53371i	−0.329159	+	0.223089i
$414$		0			0
$415$	−9.06904	−	15.7080i	−0.445182	−	0.771078i
$416$		0			0
$417$	−29.7512	−	3.69224i	−1.45692	−	0.180810i
$418$		0			0
$419$	1.56134	−	2.70432i	0.0762765	−	0.132115i	−0.825364	−	0.564601i	$-0.809030\pi$
$419$	1.56134	−	2.70432i	0.0762765	−	0.132115i	0.901641	+	0.432486i	$0.142363\pi$
$420$		0			0
$421$	−0.644580	−	1.11645i	−0.0314149	−	0.0544122i	0.849891	−	0.526959i	$-0.176668\pi$
$421$	−0.644580	−	1.11645i	−0.0314149	−	0.0544122i	−0.881305	+	0.472547i	$0.843335\pi$
$422$		0			0
$423$	1.92100	+	6.76566i	0.0934023	+	0.328958i
$424$		0			0
$425$	−17.6178	+	30.5149i	−0.854587	+	1.48019i
$426$		0			0
$427$	13.4101	+	6.50363i	0.648962	+	0.314733i
$428$		0			0
$429$	−8.54943	−	1.06102i	−0.412770	−	0.0512265i
$430$		0			0
$431$	11.5916	−	20.0773i	0.558350	−	0.967090i	−0.439285	−	0.898348i	$-0.644768\pi$
$431$	11.5916	−	20.0773i	0.558350	−	0.967090i	0.997634	−	0.0687421i	$-0.0218986\pi$
$432$		0			0
$433$	35.6437			1.71293			0.856464	−	0.516207i	$-0.172657\pi$
$433$	35.6437			1.71293			0.856464	+	0.516207i	$0.172657\pi$
$434$		0			0
$435$	7.79454	−	10.3158i	0.373720	−	0.494604i
$436$		0			0
$437$	11.7005	+	20.2659i	0.559711	+	0.969448i
$438$		0			0
$439$	8.00620	−	13.8671i	0.382115	−	0.661843i	−0.609249	−	0.792979i	$-0.708529\pi$
$439$	8.00620	−	13.8671i	0.382115	−	0.661843i	0.991364	+	0.131136i	$0.0418625\pi$
$440$		0			0
$441$	12.3119	−	17.0122i	0.586283	−	0.810106i
$442$		0			0
$443$	7.17778	−	12.4323i	0.341027	−	0.590676i	−0.643597	−	0.765365i	$-0.722559\pi$
$443$	7.17778	−	12.4323i	0.341027	−	0.590676i	0.984624	+	0.174689i	$0.0558920\pi$
$444$		0			0
$445$	24.1819	+	41.8844i	1.14633	+	1.98551i
$446$		0			0
$447$	−4.61953	−	10.9224i	−0.218496	−	0.516610i
$448$		0			0
$449$	5.72475			0.270168			0.135084	−	0.990834i	$-0.456870\pi$
$449$	5.72475			0.270168			0.135084	+	0.990834i	$0.456870\pi$
$450$		0			0
$451$	5.12040	−	8.86879i	0.241110	−	0.417615i
$452$		0			0
$453$	−6.26228	−	14.8065i	−0.294227	−	0.695669i
$454$		0			0
$455$	−56.4900	−	27.3964i	−2.64829	−	1.28436i
$456$		0			0
$457$	−7.33175	+	12.6990i	−0.342965	+	0.594033i	−0.984982	−	0.172658i	$-0.944765\pi$
$457$	−7.33175	+	12.6990i	−0.342965	+	0.594033i	0.642017	+	0.766690i	$0.278098\pi$
$458$		0			0
$459$	11.7163	−	9.41223i	0.546868	−	0.439325i
$460$		0			0
$461$	−12.9720	−	22.4681i	−0.604164	−	1.04644i	−0.992183	−	0.124792i	$-0.960174\pi$
$461$	−12.9720	−	22.4681i	−0.604164	−	1.04644i	0.388018	−	0.921652i	$-0.373160\pi$
$462$		0			0
$463$	6.46277	−	11.1939i	0.300351	−	0.520223i	−0.675865	−	0.737026i	$-0.736230\pi$
$463$	6.46277	−	11.1939i	0.300351	−	0.520223i	0.976215	+	0.216803i	$0.0695630\pi$
$464$		0			0
$465$	12.8157	−	16.9611i	0.594314	−	0.786552i
$466$		0			0
$467$	16.3104	+	28.2504i	0.754755	+	1.30727i	0.945496	+	0.325633i	$0.105577\pi$
$467$	16.3104	+	28.2504i	0.754755	+	1.30727i	−0.190741	+	0.981640i	$0.561089\pi$
$468$		0			0
$469$	−5.49892	+	3.72692i	−0.253916	+	0.172093i
$470$		0			0
$471$	14.2809	−	18.9003i	0.658030	−	0.870878i
$472$		0			0
$473$	−1.74382	−	3.02039i	−0.0801811	−	0.138878i
$474$		0			0
$475$	24.4509	+	42.3503i	1.12189	+	1.94316i
$476$		0			0
$477$	−1.78823	−	6.29804i	−0.0818774	−	0.288367i
$478$		0			0
$479$	25.3478			1.15817			0.579084	−	0.815268i	$-0.303410\pi$
$479$	25.3478			1.15817			0.579084	+	0.815268i	$0.303410\pi$
$480$		0			0
$481$	−30.3319			−1.38302
$482$		0			0
$483$	23.7923	−	12.1506i	1.08259	−	0.552871i
$484$		0			0
$485$	−16.5302	−	28.6311i	−0.750597	−	1.30007i
$486$		0			0
$487$	−17.7383	+	30.7236i	−0.803799	+	1.39222i	0.113299	+	0.993561i	$0.463858\pi$
$487$	−17.7383	+	30.7236i	−0.803799	+	1.39222i	−0.917099	+	0.398660i	$0.869475\pi$
$488$		0			0
$489$	−3.44582	+	4.56041i	−0.155825	+	0.206229i
$490$		0			0
$491$	−13.2554	+	22.9590i	−0.598208	+	1.03613i	0.394877	+	0.918734i	$0.370787\pi$
$491$	−13.2554	+	22.9590i	−0.598208	+	1.03613i	−0.993085	+	0.117393i	$0.962546\pi$
$492$		0			0
$493$	5.20849			0.234579
$494$		0			0
$495$	7.52580	−	7.75276i	0.338260	−	0.348461i
$496$		0			0
$497$	−0.207849	−	2.88017i	−0.00932332	−	0.129193i
$498$		0			0
$499$	6.00261			0.268714			0.134357	−	0.990933i	$-0.457103\pi$
$499$	6.00261			0.268714			0.134357	+	0.990933i	$0.457103\pi$
$500$		0			0
$501$	−20.4967	−	2.54373i	−0.915725	−	0.113645i
$502$		0			0
$503$	22.9460			1.02311			0.511556	−	0.859250i	$-0.329069\pi$
$503$	22.9460			1.02311			0.511556	+	0.859250i	$0.329069\pi$
$504$		0			0
$505$	−15.6013			−0.694248
$506$		0			0
$507$	20.6446	−	27.3223i	0.916857	−	1.21343i
$508$		0			0
$509$	29.8697			1.32395			0.661975	−	0.749526i	$-0.269719\pi$
$509$	29.8697			1.32395			0.661975	+	0.749526i	$0.269719\pi$
$510$		0			0
$511$	−3.44365	−	1.67010i	−0.152338	−	0.0738807i
$512$		0			0
$513$	−3.18250	−	20.6134i	−0.140511	−	0.910105i
$514$		0			0
$515$	−44.9984			−1.98287
$516$		0			0
$517$	−1.01846	+	1.76402i	−0.0447918	+	0.0775817i
$518$		0			0
$519$	16.5593	+	2.05508i	0.726875	+	0.0902081i
$520$		0			0
$521$	15.5980	−	27.0166i	0.683362	−	1.18362i	−0.290587	−	0.956849i	$-0.593851\pi$
$521$	15.5980	−	27.0166i	0.683362	−	1.18362i	0.973949	−	0.226769i	$-0.0728162\pi$
$522$		0			0
$523$	3.07911	+	5.33318i	0.134640	+	0.233203i	0.925460	−	0.378846i	$-0.123679\pi$
$523$	3.07911	+	5.33318i	0.134640	+	0.233203i	−0.790820	+	0.612049i	$0.790346\pi$
$524$		0			0
$525$	49.7196	−	25.3915i	2.16994	−	1.10818i
$526$		0			0
$527$	8.56375			0.373043
$528$		0			0
$529$	10.9862			0.477661
$530$		0			0
$531$	8.88494	+	2.23981i	0.385574	+	0.0971995i
$532$		0			0
$533$	33.7366	+	58.4335i	1.46129	+	2.53103i
$534$		0			0
$535$	19.9941	+	34.6307i	0.864419	+	1.49722i
$536$		0			0
$537$	39.6319	+	4.91849i	1.71024	+	0.212248i
$538$		0			0
$539$	6.01899	−	0.873275i	0.259256	−	0.0376146i
$540$		0			0
$541$	−13.5137	−	23.4064i	−0.580999	−	1.00632i	−0.995361	−	0.0962083i	$-0.969329\pi$
$541$	−13.5137	−	23.4064i	−0.580999	−	1.00632i	0.414362	−	0.910112i	$-0.364005\pi$
$542$		0			0
$543$	−7.98332	−	18.8757i	−0.342597	−	0.810033i
$544$		0			0
$545$	−24.2963	+	42.0824i	−1.04074	+	1.80261i
$546$		0			0
$547$	−14.9426	−	25.8814i	−0.638900	−	1.10661i	−0.985675	−	0.168658i	$-0.946057\pi$
$547$	−14.9426	−	25.8814i	−0.638900	−	1.10661i	0.346775	−	0.937948i	$-0.387277\pi$
$548$		0			0
$549$	−4.61590	−	16.2569i	−0.197002	−	0.693829i
$550$		0			0
$551$	3.61432	−	6.26019i	0.153975	−	0.266693i
$552$		0			0
$553$	5.06889	+	2.45830i	0.215551	+	0.104538i
$554$		0			0
$555$	22.9335	−	30.3517i	0.973474	−	1.28836i
$556$		0			0
$557$	10.6650	−	18.4722i	0.451889	−	0.782694i	−0.546615	−	0.837384i	$-0.684084\pi$
$557$	10.6650	−	18.4722i	0.451889	−	0.782694i	0.998503	+	0.0546900i	$0.0174171\pi$
$558$		0			0
$559$	22.9789			0.971905
$560$		0			0
$561$	4.31946	+	0.536062i	0.182368	+	0.0226326i
$562$		0			0
$563$	15.7317	+	27.2482i	0.663014	+	1.14837i	0.979820	+	0.199884i	$0.0640564\pi$
$563$	15.7317	+	27.2482i	0.663014	+	1.14837i	−0.316805	+	0.948491i	$0.602610\pi$
$564$		0			0
$565$	11.9788	−	20.7480i	0.503954	−	0.872873i
$566$		0			0
$567$	−23.6886	+	2.41863i	−0.994828	+	0.101573i
$568$		0			0
$569$	−14.6696	+	25.4084i	−0.614980	+	1.06518i	0.375408	+	0.926860i	$0.377503\pi$
$569$	−14.6696	+	25.4084i	−0.614980	+	1.06518i	−0.990388	+	0.138317i	$0.955831\pi$
$570$		0			0
$571$	−13.7473	−	23.8111i	−0.575308	−	0.996463i	−0.996008	−	0.0892631i	$-0.971549\pi$
$571$	−13.7473	−	23.8111i	−0.575308	−	0.996463i	0.420700	−	0.907200i	$-0.361785\pi$
$572$		0			0
$573$	−10.8032	−	1.34072i	−0.451310	−	0.0560094i
$574$		0			0
$575$	71.0221			2.96183
$576$		0			0
$577$	−20.2293	+	35.0381i	−0.842156	+	1.45866i	0.0459122	+	0.998945i	$0.485381\pi$
$577$	−20.2293	+	35.0381i	−0.842156	+	1.45866i	−0.888068	+	0.459712i	$0.847953\pi$
$578$		0			0
$579$	14.3377	−	18.9754i	0.595854	−	0.788591i
$580$		0			0
$581$	−9.58331	+	6.49513i	−0.397583	+	0.269463i
$582$		0			0
$583$	0.948067	−	1.64210i	0.0392649	−	0.0680089i
$584$		0			0
$585$	19.4444	+	68.4820i	0.803927	+	2.83138i
$586$		0			0
$587$	13.6559	+	23.6528i	0.563641	+	0.976255i	0.997175	+	0.0751177i	$0.0239333\pi$
$587$	13.6559	+	23.6528i	0.563641	+	0.976255i	−0.433533	+	0.901137i	$0.642733\pi$
$588$		0			0
$589$	5.94263	−	10.2929i	0.244862	−	0.424113i
$590$		0			0
$591$	−0.108960	−	0.257624i	−0.00448201	−	0.0105972i
$592$		0			0
$593$	14.2898	+	24.7507i	0.586813	+	1.01639i	0.994647	+	0.103334i	$0.0329512\pi$
$593$	14.2898	+	24.7507i	0.586813	+	1.01639i	−0.407833	+	0.913056i	$0.633716\pi$
$594$		0			0
$595$	28.5406	+	13.8416i	1.17005	+	0.567449i
$596$		0			0
$597$	42.6759	+	5.29625i	1.74661	+	0.216761i
$598$		0			0
$599$	19.9919	+	34.6270i	0.816848	+	1.41482i	0.907994	+	0.418984i	$0.137614\pi$
$599$	19.9919	+	34.6270i	0.816848	+	1.41482i	−0.0911461	+	0.995838i	$0.529053\pi$
$600$		0			0
$601$	−12.6948	−	21.9880i	−0.517831	−	0.896910i	−0.999785	−	0.0207133i	$-0.993406\pi$
$601$	−12.6948	−	21.9880i	−0.517831	−	0.896910i	0.481954	−	0.876196i	$-0.339927\pi$
$602$		0			0
$603$	7.30383	+	1.84123i	0.297435	+	0.0749806i
$604$		0			0
$605$	−42.4679			−1.72657
$606$		0			0
$607$	37.2939			1.51371			0.756856	−	0.653581i	$-0.226734\pi$
$607$	37.2939			1.51371			0.756856	+	0.653581i	$0.226734\pi$
$608$		0			0
$609$	−6.92526	−	4.48819i	−0.280626	−	0.181870i
$610$		0			0
$611$	−6.71029	−	11.6226i	−0.271469	−	0.470199i
$612$		0			0
$613$	−11.7319	+	20.3203i	−0.473848	+	0.820729i	−0.999552	−	0.0299390i	$-0.990469\pi$
$613$	−11.7319	+	20.3203i	−0.473848	+	0.820729i	0.525704	+	0.850668i	$0.323802\pi$
$614$		0			0
$615$	−83.9792	−	10.4222i	−3.38637	−	0.420262i
$616$		0			0
$617$	6.56888	−	11.3776i	0.264453	−	0.458047i	−0.702967	−	0.711223i	$-0.748142\pi$
$617$	6.56888	−	11.3776i	0.264453	−	0.458047i	0.967420	+	0.253176i	$0.0814752\pi$
$618$		0			0
$619$	−21.5553			−0.866380			−0.433190	−	0.901303i	$-0.642612\pi$
$619$	−21.5553			−0.866380			−0.433190	+	0.901303i	$0.642612\pi$
$620$		0			0
$621$	−28.2378	−	10.9660i	−1.13314	−	0.440050i
$622$		0			0
$623$	25.5532	−	17.3188i	1.02377	−	0.693862i
$624$		0			0
$625$	62.5040			2.50016
$626$		0			0
$627$	3.64170	−	4.81965i	0.145435	−	0.192478i
$628$		0			0
$629$	15.3247			0.611036
$630$		0			0
$631$	6.15223			0.244916			0.122458	−	0.992474i	$-0.460922\pi$
$631$	6.15223			0.244916			0.122458	+	0.992474i	$0.460922\pi$
$632$		0			0
$633$	−32.4730	−	4.03004i	−1.29069	−	0.160180i
$634$		0			0
$635$	−26.8388			−1.06507
$636$		0			0
$637$	−14.8457	+	37.2209i	−0.588207	+	1.47475i
$638$		0			0
$639$	−2.28064	+	2.34942i	−0.0902206	+	0.0929415i
$640$		0			0
$641$	−4.47364			−0.176698			−0.0883491	−	0.996090i	$-0.528159\pi$
$641$	−4.47364			−0.176698			−0.0883491	+	0.996090i	$0.528159\pi$
$642$		0			0
$643$	−8.98009	+	15.5540i	−0.354140	+	0.613389i	−0.986970	−	0.160902i	$-0.948560\pi$
$643$	−8.98009	+	15.5540i	−0.354140	+	0.613389i	0.632830	+	0.774291i	$0.281893\pi$
$644$		0			0
$645$	−17.3740	+	22.9939i	−0.684101	+	0.905383i
$646$		0			0
$647$	−6.02992	+	10.4441i	−0.237061	+	0.410601i	−0.959870	−	0.280447i	$-0.909517\pi$
$647$	−6.02992	+	10.4441i	−0.237061	+	0.410601i	0.722809	+	0.691048i	$0.242851\pi$
$648$		0			0
$649$	1.32688	+	2.29822i	0.0520845	+	0.0902131i
$650$		0			0
$651$	−11.3864	−	7.37943i	−0.446269	−	0.289222i
$652$		0			0
$653$	−48.2733			−1.88908			−0.944540	−	0.328397i	$-0.893492\pi$
$653$	−48.2733			−1.88908			−0.944540	+	0.328397i	$0.893492\pi$
$654$		0			0
$655$	73.4955			2.87171
$656$		0			0
$657$	1.18534	+	4.17469i	0.0462445	+	0.162870i
$658$		0			0
$659$	−14.5795	−	25.2525i	−0.567937	−	0.983696i	−0.996770	−	0.0803122i	$-0.974408\pi$
$659$	−14.5795	−	25.2525i	−0.567937	−	0.983696i	0.428832	−	0.903384i	$-0.358925\pi$
$660$		0			0
$661$	7.27428	+	12.5994i	0.282937	+	0.490061i	0.972107	−	0.234539i	$-0.0753581\pi$
$661$	7.27428	+	12.5994i	0.282937	+	0.490061i	−0.689170	+	0.724600i	$0.742025\pi$
$662$		0			0
$663$	−17.2885	+	22.8806i	−0.671429	+	0.888611i
$664$		0			0
$665$	36.4416	−	24.6985i	1.41315	−	0.957766i
$666$		0			0
$667$	−5.24922	−	9.09192i	−0.203251	−	0.352040i
$668$		0			0
$669$	14.7169	−	19.4773i	0.568989	−	0.753035i
$670$		0			0
$671$	2.44722	−	4.23871i	0.0944738	−	0.163633i
$672$		0			0
$673$	11.6825	+	20.2348i	0.450329	+	0.779993i	0.998406	−	0.0564349i	$-0.0179733\pi$
$673$	11.6825	+	20.2348i	0.450329	+	0.779993i	−0.548077	+	0.836428i	$0.684640\pi$
$674$		0			0
$675$	−59.0095	−	22.9160i	−2.27128	−	0.882038i
$676$		0			0
$677$	8.85875	−	15.3438i	0.340469	−	0.589710i	−0.644051	−	0.764983i	$-0.722747\pi$
$677$	8.85875	−	15.3438i	0.340469	−	0.589710i	0.984520	+	0.175273i	$0.0560807\pi$
$678$		0			0
$679$	−17.4675	+	11.8387i	−0.670343	+	0.454328i
$680$		0			0
$681$	−17.5273	−	41.4415i	−0.671649	−	1.58804i
$682$		0			0
$683$	−21.7769	+	37.7186i	−0.833269	+	1.44326i	0.0621637	+	0.998066i	$0.480200\pi$
$683$	−21.7769	+	37.7186i	−0.833269	+	1.44326i	−0.895432	+	0.445198i	$0.853133\pi$
$684$		0			0
$685$	11.2846			0.431161
$686$		0			0
$687$	16.8105	+	39.7466i	0.641360	+	1.51643i
$688$		0			0
$689$	6.24650	+	10.8193i	0.237973	+	0.412181i
$690$		0			0
$691$	11.7672	−	20.3814i	0.447645	−	0.775345i	−0.550587	−	0.834778i	$-0.685596\pi$
$691$	11.7672	−	20.3814i	0.447645	−	0.775345i	0.998232	+	0.0594333i	$0.0189294\pi$
$692$		0			0
$693$	−5.28126	−	4.43485i	−0.200619	−	0.168466i
$694$		0			0
$695$	−35.8738	+	62.1353i	−1.36077	+	2.35693i
$696$		0			0
$697$	−17.0449	−	29.5225i	−0.645620	−	1.11825i
$698$		0			0
$699$	6.38872	−	8.45523i	0.241644	−	0.319806i
$700$		0			0
$701$	45.1804			1.70644			0.853219	−	0.521552i	$-0.174647\pi$
$701$	45.1804			1.70644			0.853219	+	0.521552i	$0.174647\pi$
$702$		0			0
$703$	10.6343	−	18.4191i	0.401079	−	0.694689i
$704$		0			0
$705$	16.7037	+	2.07299i	0.629097	+	0.0780735i
$706$		0			0
$707$	0.716748	+	9.93199i	0.0269561	+	0.373531i
$708$		0			0
$709$	13.5064	−	23.3937i	0.507242	−	0.878568i	−0.492723	−	0.870186i	$-0.663998\pi$
$709$	13.5064	−	23.3937i	0.507242	−	0.878568i	0.999965	−	0.00838223i	$-0.00266818\pi$
$710$		0			0
$711$	−1.74476	−	6.14495i	−0.0654337	−	0.230453i
$712$		0			0
$713$	−8.63071	−	14.9488i	−0.323223	−	0.559838i
$714$		0			0
$715$	−10.3089	+	17.8555i	−0.385529	+	0.667757i
$716$		0			0
$717$	26.5388	+	3.29358i	0.991111	+	0.123001i
$718$		0			0
$719$	11.2096	+	19.4156i	0.418048	+	0.724080i	0.995743	−	0.0921724i	$-0.0293811\pi$
$719$	11.2096	+	19.4156i	0.418048	+	0.724080i	−0.577695	+	0.816253i	$0.696048\pi$
$720$		0			0
$721$	2.06730	+	28.6466i	0.0769902	+	1.06686i
$722$		0			0
$723$	6.64247	+	15.7054i	0.247036	+	0.584091i
$724$		0			0
$725$	−10.9695	−	18.9997i	−0.407396	−	0.705631i
$726$		0			0
$727$	−21.9820	−	38.0740i	−0.815268	−	1.41208i	−0.909136	−	0.416500i	$-0.863256\pi$
$727$	−21.9820	−	38.0740i	−0.815268	−	1.41208i	0.0938680	−	0.995585i	$-0.470077\pi$
$728$		0			0
$729$	19.9234	+	18.2224i	0.737904	+	0.674905i
$730$		0			0
$731$	−11.6097			−0.429401
$732$		0			0
$733$	0.866772			0.0320149			0.0160075	−	0.999872i	$-0.494904\pi$
$733$	0.866772			0.0320149			0.0160075	+	0.999872i	$0.494904\pi$
$734$		0			0
$735$	−26.0205	−	42.9975i	−0.959781	−	1.58599i
$736$		0			0
$737$	1.09075	+	1.88924i	0.0401785	+	0.0695911i
$738$		0			0
$739$	−13.0442	+	22.5932i	−0.479838	+	0.831103i	−0.999733	−	0.0231270i	$-0.992638\pi$
$739$	−13.0442	+	22.5932i	−0.479838	+	0.831103i	0.519895	+	0.854230i	$0.325971\pi$
$740$		0			0
$741$	15.5037	+	36.6569i	0.569544	+	1.34662i
$742$		0			0
$743$	−22.5842	+	39.1170i	−0.828533	+	1.43506i	0.0706551	+	0.997501i	$0.477491\pi$
$743$	−22.5842	+	39.1170i	−0.828533	+	1.43506i	−0.899189	+	0.437561i	$0.855842\pi$
$744$		0			0
$745$	−28.3816			−1.03982
$746$		0			0
$747$	12.7288	+	3.20882i	0.465724	+	0.117405i
$748$		0			0
$749$	21.1278	−	14.3195i	0.771994	−	0.523222i
$750$		0			0
$751$	20.5988			0.751662			0.375831	−	0.926688i	$-0.377357\pi$
$751$	20.5988			0.751662			0.375831	+	0.926688i	$0.377357\pi$
$752$		0			0
$753$	−18.1387	−	42.8869i	−0.661009	−	1.56288i
$754$		0			0
$755$	−38.4743			−1.40022
$756$		0			0
$757$	−39.0856			−1.42059			−0.710294	−	0.703905i	$-0.751438\pi$
$757$	−39.0856			−1.42059			−0.710294	+	0.703905i	$0.751438\pi$
$758$		0			0
$759$	−3.41749	−	8.08028i	−0.124047	−	0.293295i
$760$		0			0
$761$	−28.8872			−1.04716			−0.523581	−	0.851976i	$-0.675404\pi$
$761$	−28.8872			−1.04716			−0.523581	+	0.851976i	$0.675404\pi$
$762$		0			0
$763$	27.9065	+	13.5340i	1.01028	+	0.489964i
$764$		0			0
$765$	−9.82396	−	34.5994i	−0.355186	−	1.25094i
$766$		0			0
$767$	−17.4847			−0.631336
$768$		0			0
$769$	−11.1407	+	19.2962i	−0.401742	+	0.695838i	−0.993936	−	0.109957i	$-0.964929\pi$
$769$	−11.1407	+	19.2962i	−0.401742	+	0.695838i	0.592194	+	0.805796i	$0.298262\pi$
$770$		0			0
$771$	7.43021	+	17.5679i	0.267592	+	0.632693i
$772$		0			0
$773$	−21.3593	+	36.9955i	−0.768242	+	1.33063i	0.170273	+	0.985397i	$0.445535\pi$
$773$	−21.3593	+	36.9955i	−0.768242	+	1.33063i	−0.938515	+	0.345238i	$0.887798\pi$
$774$		0			0
$775$	−18.0359	−	31.2391i	−0.647868	−	1.12214i
$776$		0			0
$777$	−20.3759	−	13.2054i	−0.730980	−	0.473741i
$778$		0			0
$779$	−47.3116			−1.69512
$780$		0			0
$781$	−0.948302			−0.0339329
$782$		0			0
$783$	1.42777	+	9.24784i	0.0510245	+	0.330491i
$784$		0			0
$785$	−28.3465	−	49.0976i	−1.01173	−	1.75237i
$786$		0			0
$787$	−0.143384	−	0.248349i	−0.00511110	−	0.00885268i	0.863459	−	0.504420i	$-0.168294\pi$
$787$	−0.143384	−	0.248349i	−0.00511110	−	0.00885268i	−0.868570	+	0.495567i	$0.834960\pi$
$788$		0			0
$789$	4.93265	+	11.6627i	0.175607	+	0.415203i
$790$		0			0
$791$	−13.7588	−	6.67270i	−0.489205	−	0.237254i
$792$		0			0
$793$	16.1239	+	27.9274i	0.572577	+	0.991732i
$794$		0			0
$795$	−15.5492	−	1.92971i	−0.551472	−	0.0684399i
$796$		0			0
$797$	−0.457746	+	0.792840i	−0.0162142	+	0.0280838i	−0.874019	−	0.485892i	$-0.838495\pi$
$797$	−0.457746	+	0.792840i	−0.0162142	+	0.0280838i	0.857804	+	0.513976i	$0.171828\pi$
$798$		0			0
$799$	3.39026	+	5.87211i	0.119939	+	0.207740i
$800$		0			0
$801$	−33.9405	−	8.55609i	−1.19923	−	0.302315i
$802$		0			0
$803$	−0.628433	+	1.08848i	−0.0221769	+	0.0384115i
$804$		0			0
$805$	−4.60201	−	63.7702i	−0.162200	−	2.24760i
$806$		0			0
$807$	−7.15211	−	0.887606i	−0.251766	−	0.0312452i
$808$		0			0
$809$	−14.3721	+	24.8932i	−0.505297	+	0.875199i	0.494685	+	0.869073i	$0.335284\pi$
$809$	−14.3721	+	24.8932i	−0.505297	+	0.875199i	−0.999981	+	0.00612685i	$0.998050\pi$
$810$		0			0
$811$	−14.3005			−0.502157			−0.251079	−	0.967967i	$-0.580785\pi$
$811$	−14.3005			−0.502157			−0.251079	+	0.967967i	$0.580785\pi$
$812$		0			0
$813$	−8.73553	+	11.5611i	−0.306368	+	0.405467i
$814$		0			0
$815$	6.83969	+	11.8467i	0.239584	+	0.414971i
$816$		0			0
$817$	−8.05632	+	13.9540i	−0.281855	+	0.488187i
$818$		0			0
$819$	42.7033	−	15.5247i	1.49217	−	0.542478i
$820$		0			0
$821$	−17.8125	+	30.8521i	−0.621660	+	1.07675i	0.367516	+	0.930017i	$0.380208\pi$
$821$	−17.8125	+	30.8521i	−0.621660	+	1.07675i	−0.989177	+	0.146730i	$0.953125\pi$
$822$		0			0
$823$	−11.2157	−	19.4261i	−0.390953	−	0.677151i	0.601622	−	0.798781i	$-0.294521\pi$
$823$	−11.2157	−	19.4261i	−0.390953	−	0.677151i	−0.992576	+	0.121630i	$0.961188\pi$
$824$		0			0
$825$	−7.14164	−	16.8856i	−0.248640	−	0.587882i
$826$		0			0
$827$	26.6728			0.927505			0.463753	−	0.885965i	$-0.346503\pi$
$827$	26.6728			0.927505			0.463753	+	0.885965i	$0.346503\pi$
$828$		0			0
$829$	−16.0078	+	27.7263i	−0.555973	+	0.962973i	0.441854	+	0.897087i	$0.354321\pi$
$829$	−16.0078	+	27.7263i	−0.555973	+	0.962973i	−0.997827	+	0.0658866i	$0.979012\pi$
$830$		0			0
$831$	−1.88817	−	4.46437i	−0.0654998	−	0.154867i
$832$		0			0
$833$	7.50053	−	18.8053i	0.259878	−	0.651563i
$834$		0			0
$835$	−24.7148	+	42.8074i	−0.855292	+	1.48141i
$836$		0			0
$837$	2.34753	+	15.2052i	0.0811425	+	0.525568i
$838$		0			0
$839$	−9.10375	−	15.7682i	−0.314296	−	0.544377i	0.664991	−	0.746851i	$-0.268435\pi$
$839$	−9.10375	−	15.7682i	−0.314296	−	0.544377i	−0.979288	+	0.202474i	$0.935102\pi$
$840$		0			0
$841$	12.8785	−	22.3062i	0.444086	−	0.769180i
$842$		0			0
$843$	11.3671	−	15.0440i	0.391505	−	0.518142i
$844$		0			0
$845$	−40.9778	−	70.9757i	−1.40968	−	2.44164i
$846$		0			0
$847$	1.95104	+	27.0356i	0.0670386	+	0.928956i
$848$		0			0
$849$	2.11365	−	2.79734i	0.0725403	−	0.0960044i
$850$		0			0
$851$	−15.4445	−	26.7507i	−0.529432	−	0.917003i
$852$		0			0
$853$	20.9242	+	36.2419i	0.716432	+	1.24090i	0.962404	+	0.271621i	$0.0875596\pi$
$853$	20.9242	+	36.2419i	0.716432	+	1.24090i	−0.245972	+	0.969277i	$0.579107\pi$
$854$		0			0
$855$	−48.4029	−	12.2019i	−1.65534	−	0.417297i
$856$		0			0
$857$	15.7141			0.536783			0.268391	−	0.963310i	$-0.413508\pi$
$857$	15.7141			0.536783			0.268391	+	0.963310i	$0.413508\pi$
$858$		0			0
$859$	−24.2046			−0.825849			−0.412924	−	0.910765i	$-0.635493\pi$
$859$	−24.2046			−0.825849			−0.412924	+	0.910765i	$0.635493\pi$
$860$		0			0
$861$	−2.77675	+	53.9411i	−0.0946314	+	1.83831i
$862$		0			0
$863$	−26.0542	−	45.1272i	−0.886896	−	1.53615i	−0.843525	−	0.537090i	$-0.819523\pi$
$863$	−26.0542	−	45.1272i	−0.886896	−	1.53615i	−0.0433714	−	0.999059i	$-0.513810\pi$
$864$		0			0
$865$	19.9672	−	34.5842i	0.678904	−	1.17590i
$866$		0			0
$867$	−9.01619	+	11.9326i	−0.306206	+	0.405252i
$868$		0			0
$869$	0.925022	−	1.60219i	0.0313792	−	0.0543504i
$870$		0			0
$871$	−14.3732			−0.487018
$872$		0			0
$873$	23.2009	+	5.84874i	0.785232	+	0.197950i
$874$		0			0
$875$	−5.66999	−	78.5691i	−0.191680	−	2.65612i
$876$		0			0
$877$	−13.9768			−0.471964			−0.235982	−	0.971757i	$-0.575831\pi$
$877$	−13.9768			−0.471964			−0.235982	+	0.971757i	$0.575831\pi$
$878$		0			0
$879$	−33.1895	−	4.11895i	−1.11945	−	0.138929i
$880$		0			0
$881$	28.1210			0.947421			0.473710	−	0.880681i	$-0.342914\pi$
$881$	28.1210			0.947421			0.473710	+	0.880681i	$0.342914\pi$
$882$		0			0
$883$	35.1633			1.18334			0.591670	−	0.806180i	$-0.298469\pi$
$883$	35.1633			1.18334			0.591670	+	0.806180i	$0.298469\pi$
$884$		0			0
$885$	13.2199	−	17.4961i	0.444383	−	0.588124i
$886$		0			0
$887$	26.9219			0.903950			0.451975	−	0.892031i	$-0.350720\pi$
$887$	26.9219			0.903950			0.451975	+	0.892031i	$0.350720\pi$
$888$		0			0
$889$	1.23302	+	17.0860i	0.0413541	+	0.573045i
$890$		0			0
$891$	0.232272	+	7.81627i	0.00778142	+	0.261855i
$892$		0			0
$893$	9.41041			0.314907
$894$		0			0
$895$	47.7880	−	82.7713i	1.59738	−	2.76674i
$896$		0			0
$897$	57.3640	+	7.11911i	1.91533	+	0.237700i
$898$		0			0
$899$	−2.66605	+	4.61774i	−0.0889179	+	0.154010i
$900$		0			0
$901$	−3.15594	−	5.46625i	−0.105140	−	0.182107i
$902$		0			0
$903$	15.4364	+	10.0042i	0.513691	+	0.332918i
$904$		0			0
$905$	−49.0481			−1.63041
$906$		0			0
$907$	44.7142			1.48471			0.742355	−	0.670007i	$-0.233709\pi$
$907$	44.7142			1.48471			0.742355	+	0.670007i	$0.233709\pi$
$908$		0			0
$909$	7.86455	−	8.10173i	0.260851	−	0.268717i
$910$		0			0
$911$	13.7822	+	23.8715i	0.456626	+	0.790899i	0.998780	−	0.0493800i	$-0.0157246\pi$
$911$	13.7822	+	23.8715i	0.456626	+	0.790899i	−0.542154	+	0.840279i	$0.682391\pi$
$912$		0			0
$913$	1.90093	+	3.29250i	0.0629115	+	0.108966i
$914$		0			0
$915$	−40.1366	−	4.98112i	−1.32688	−	0.164671i
$916$		0			0
$917$	−3.37650	−	46.7882i	−0.111502	−	1.54508i
$918$		0			0
$919$	21.3836	+	37.0376i	0.705381	+	1.22176i	0.966554	+	0.256464i	$0.0825575\pi$
$919$	21.3836	+	37.0376i	0.705381	+	1.22176i	−0.261173	+	0.965292i	$0.584109\pi$
$920$		0			0
$921$	8.86398	+	20.9579i	0.292078	+	0.690587i
$922$		0			0
$923$	3.12402	−	5.41096i	0.102828	−	0.178104i
$924$		0			0
$925$	−32.2750	−	55.9019i	−1.06119	−	1.83804i
$926$		0			0
$927$	22.6835	−	23.3676i	0.745025	−	0.767493i
$928$		0			0
$929$	−23.9748	+	41.5256i	−0.786589	+	1.36241i	0.141456	+	0.989945i	$0.454822\pi$
$929$	−23.9748	+	41.5256i	−0.786589	+	1.36241i	−0.928045	+	0.372468i	$0.878512\pi$
$930$		0			0
$931$	−17.3976	−	22.0645i	−0.570182	−	0.723136i
$932$		0			0
$933$	14.1299	−	18.7003i	0.462591	−	0.612221i
$934$		0			0
$935$	5.20838	−	9.02118i	0.170332	−	0.295024i
$936$		0			0
$937$	33.9136			1.10791			0.553955	−	0.832547i	$-0.313118\pi$
$937$	33.9136			1.10791			0.553955	+	0.832547i	$0.313118\pi$
$938$		0			0
$939$	43.3154	+	5.37562i	1.41354	+	0.175427i
$940$		0			0
$941$	4.27395	+	7.40270i	0.139327	+	0.241321i	0.927242	−	0.374463i	$-0.122173\pi$
$941$	4.27395	+	7.40270i	0.139327	+	0.241321i	−0.787915	+	0.615784i	$0.788839\pi$
$942$		0			0
$943$	−34.3563	+	59.5068i	−1.11879	+	1.93781i
$944$		0			0
$945$	−16.7525	+	54.4691i	−0.544958	+	1.77188i
$946$		0			0
$947$	0.411563	−	0.712848i	0.0133740	−	0.0231645i	−0.859261	−	0.511538i	$-0.829076\pi$
$947$	0.411563	−	0.712848i	0.0133740	−	0.0231645i	0.872635	+	0.488373i	$0.162409\pi$
$948$		0			0
$949$	−4.14053	−	7.17161i	−0.134407	−	0.232800i
$950$		0			0
$951$	21.1382	+	2.62334i	0.685453	+	0.0850675i
$952$		0			0
$953$	−44.6726			−1.44709			−0.723544	−	0.690278i	$-0.757488\pi$
$953$	−44.6726			−1.44709			−0.723544	+	0.690278i	$0.757488\pi$
$954$		0			0
$955$	−13.0264	+	22.5625i	−0.421526	+	0.730104i
$956$		0			0
$957$	−1.63378	+	2.16225i	−0.0528127	+	0.0698956i
$958$		0			0
$959$	−0.518430	−	7.18390i	−0.0167410	−	0.231980i
$960$		0			0
$961$	11.1165	−	19.2544i	0.358597	−	0.621108i
$962$		0			0
$963$	−28.0626	−	7.07433i	−0.904305	−	0.227967i
$964$		0			0
$965$	−28.4592	−	49.2928i	−0.916135	−	1.58679i
$966$		0			0
$967$	18.2289	−	31.5735i	0.586203	−	1.01533i	−0.408521	−	0.912749i	$-0.633955\pi$
$967$	18.2289	−	31.5735i	0.586203	−	1.01533i	0.994724	−	0.102585i	$-0.0327114\pi$
$968$		0			0
$969$	−7.83301	−	18.5203i	−0.251632	−	0.594957i
$970$		0			0
$971$	−8.63674	−	14.9593i	−0.277166	−	0.480066i	0.693513	−	0.720444i	$-0.256062\pi$
$971$	−8.63674	−	14.9593i	−0.277166	−	0.480066i	−0.970679	+	0.240378i	$0.922729\pi$
$972$		0			0
$973$	41.2043	+	19.9832i	1.32095	+	0.640631i
$974$		0			0
$975$	119.875	+	14.8770i	3.83909	+	0.476446i
$976$		0			0
$977$	−4.51775	−	7.82497i	−0.144536	−	0.250343i	0.784664	−	0.619921i	$-0.212835\pi$
$977$	−4.51775	−	7.82497i	−0.144536	−	0.250343i	−0.929200	+	0.369578i	$0.879502\pi$
$978$		0			0
$979$	−5.06868	−	8.77921i	−0.161996	−	0.280585i
$980$		0			0
$981$	−9.60567	−	33.8306i	−0.306686	−	1.08013i
$982$		0			0
$983$	22.8573			0.729034			0.364517	−	0.931197i	$-0.381234\pi$
$983$	22.8573			0.729034			0.364517	+	0.931197i	$0.381234\pi$
$984$		0			0
$985$	−0.669430			−0.0213298
$986$		0			0
$987$	0.552303	−	10.7290i	0.0175800	−	0.341508i
$988$		0			0
$989$	11.7005	+	20.2659i	0.372055	+	0.644417i
$990$		0			0
$991$	4.37884	−	7.58437i	0.139098	−	0.240925i	−0.788057	−	0.615602i	$-0.788913\pi$
$991$	4.37884	−	7.58437i	0.139098	−	0.240925i	0.927156	+	0.374677i	$0.122246\pi$
$992$		0			0
$993$	−34.2496	−	4.25051i	−1.08688	−	0.134886i
$994$		0			0
$995$	51.4584	−	89.1285i	1.63134	−	2.82556i
$996$		0			0
$997$	6.93070			0.219498			0.109749	−	0.993959i	$-0.464995\pi$
$997$	6.93070			0.219498			0.109749	+	0.993959i	$0.464995\pi$
$998$		0			0
$999$	4.20087	+	27.2095i	0.132910	+	0.860870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.j.193.5		14
3.2	odd	2		3024.2.t.j.1873.1		14
4.3	odd	2		252.2.l.b.193.3	yes	14
7.2	even	3		1008.2.q.j.625.1		14
9.2	odd	6		3024.2.q.j.2881.7		14
9.7	even	3		1008.2.q.j.529.1		14
12.11	even	2		756.2.l.b.361.1		14
21.2	odd	6		3024.2.q.j.2305.7		14
28.3	even	6		1764.2.j.h.589.5		14
28.11	odd	6		1764.2.j.g.589.3		14
28.19	even	6		1764.2.i.i.373.1		14
28.23	odd	6		252.2.i.b.121.7	yes	14
28.27	even	2		1764.2.l.i.949.5		14
36.7	odd	6		252.2.i.b.25.7	✓	14
36.11	even	6		756.2.i.b.613.7		14
36.23	even	6		2268.2.k.f.1621.7		14
36.31	odd	6		2268.2.k.e.1621.1		14
63.2	odd	6		3024.2.t.j.289.1		14
63.16	even	3	inner	1008.2.t.j.961.5		14
84.11	even	6		5292.2.j.h.1765.7		14
84.23	even	6		756.2.i.b.37.7		14
84.47	odd	6		5292.2.i.i.1549.1		14
84.59	odd	6		5292.2.j.g.1765.1		14
84.83	odd	2		5292.2.l.i.361.7		14
252.11	even	6		5292.2.j.h.3529.7		14
252.23	even	6		2268.2.k.f.1297.7		14
252.47	odd	6		5292.2.l.i.3313.7		14
252.79	odd	6		252.2.l.b.205.3	yes	14
252.83	odd	6		5292.2.i.i.2125.1		14
252.115	even	6		1764.2.j.h.1177.5		14
252.151	odd	6		1764.2.j.g.1177.3		14
252.187	even	6		1764.2.l.i.961.5		14
252.191	even	6		756.2.l.b.289.1		14
252.223	even	6		1764.2.i.i.1537.1		14
252.227	odd	6		5292.2.j.g.3529.1		14
252.247	odd	6		2268.2.k.e.1297.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.7	✓	14	36.7	odd	6
252.2.i.b.121.7	yes	14	28.23	odd	6
252.2.l.b.193.3	yes	14	4.3	odd	2
252.2.l.b.205.3	yes	14	252.79	odd	6
756.2.i.b.37.7		14	84.23	even	6
756.2.i.b.613.7		14	36.11	even	6
756.2.l.b.289.1		14	252.191	even	6
756.2.l.b.361.1		14	12.11	even	2
1008.2.q.j.529.1		14	9.7	even	3
1008.2.q.j.625.1		14	7.2	even	3
1008.2.t.j.193.5		14	1.1	even	1	trivial
1008.2.t.j.961.5		14	63.16	even	3	inner
1764.2.i.i.373.1		14	28.19	even	6
1764.2.i.i.1537.1		14	252.223	even	6
1764.2.j.g.589.3		14	28.11	odd	6
1764.2.j.g.1177.3		14	252.151	odd	6
1764.2.j.h.589.5		14	28.3	even	6
1764.2.j.h.1177.5		14	252.115	even	6
1764.2.l.i.949.5		14	28.27	even	2
1764.2.l.i.961.5		14	252.187	even	6
2268.2.k.e.1297.1		14	252.247	odd	6
2268.2.k.e.1621.1		14	36.31	odd	6
2268.2.k.f.1297.7		14	252.23	even	6
2268.2.k.f.1621.7		14	36.23	even	6
3024.2.q.j.2305.7		14	21.2	odd	6
3024.2.q.j.2881.7		14	9.2	odd	6
3024.2.t.j.289.1		14	63.2	odd	6
3024.2.t.j.1873.1		14	3.2	odd	2
5292.2.i.i.1549.1		14	84.47	odd	6
5292.2.i.i.2125.1		14	252.83	odd	6
5292.2.j.g.1765.1		14	84.59	odd	6
5292.2.j.g.3529.1		14	252.227	odd	6
5292.2.j.h.1765.7		14	84.11	even	6
5292.2.j.h.3529.7		14	252.11	even	6
5292.2.l.i.361.7		14	84.83	odd	2
5292.2.l.i.3313.7		14	252.47	odd	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.674693 + 1.59524i) q^{3} +4.14520 q^{5} +(-0.190437 - 2.63889i) q^{7} +(-2.08958 + 2.15260i) q^{9} -0.868858 q^{11} +(2.86231 - 4.95766i) q^{13} +(2.79674 + 6.61258i) q^{15} +(-1.44613 + 2.50478i) q^{17} +(2.00703 + 3.47627i) q^{19} +(4.08117 - 2.08423i) q^{21} +5.82977 q^{23} +12.1827 q^{25} +(-4.84373 - 1.88104i) q^{27} +(-0.900417 - 1.55957i) q^{29} +(-1.48046 - 2.56422i) q^{31} +(-0.586213 - 1.38604i) q^{33} +(-0.789399 - 10.9387i) q^{35} +(-2.64925 - 4.58864i) q^{37} +(9.83984 + 1.22116i) q^{39} +(-5.89325 + 10.2074i) q^{41} +(2.00703 + 3.47627i) q^{43} +(-8.66171 + 8.92293i) q^{45} +(1.17218 - 2.03028i) q^{47} +(-6.92747 + 1.00508i) q^{49} +(-4.97142 - 0.616973i) q^{51} +(-1.09116 + 1.88995i) q^{53} -3.60159 q^{55} +(-4.19136 + 5.54711i) q^{57} +(-1.52715 - 2.64510i) q^{59} +(-2.81659 + 4.87848i) q^{61} +(6.07839 + 5.10423i) q^{63} +(11.8648 - 20.5505i) q^{65} +(-1.25539 - 2.17440i) q^{67} +(3.93331 + 9.29988i) q^{69} +1.09143 q^{71} +(0.723285 - 1.25277i) q^{73} +(8.21956 + 19.4343i) q^{75} +(0.165463 + 2.29282i) q^{77} +(-1.06464 + 1.84401i) q^{79} +(-0.267330 - 8.99603i) q^{81} +(-2.18784 - 3.78946i) q^{83} +(-5.99451 + 10.3828i) q^{85} +(1.88038 - 2.48861i) q^{87} +(5.83373 + 10.1043i) q^{89} +(-13.6278 - 6.60919i) q^{91} +(3.09170 - 4.09174i) q^{93} +(8.31953 + 14.4098i) q^{95} +(-3.98779 - 6.90706i) q^{97} +(1.81555 - 1.87030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4 q^{5} + 3 q^{7} + 10 q^{9} + 4 q^{11} + 2 q^{13} - 7 q^{15} + 2 q^{17} - 7 q^{19} - 2 q^{21} + 22 q^{23} + 18 q^{25} - 9 q^{27} + q^{29} + q^{31} + 5 q^{33} + 19 q^{35} + 10 q^{37} + 20 q^{39}+ \cdots - 7 q^{99}+O(q^{100}) \) 14 * q + 4 * q^5 + 3 * q^7 + 10 * q^9 + 4 * q^11 + 2 * q^13 - 7 * q^15 + 2 * q^17 - 7 * q^19 - 2 * q^21 + 22 * q^23 + 18 * q^25 - 9 * q^27 + q^29 + q^31 + 5 * q^33 + 19 * q^35 + 10 * q^37 + 20 * q^39 - 33 * q^41 - 7 * q^43 + 5 * q^45 + 3 * q^47 - 13 * q^49 - 20 * q^51 - 15 * q^53 + 28 * q^55 - 18 * q^57 + 14 * q^59 - 10 * q^61 + 39 * q^63 + 15 * q^65 - 6 * q^67 - 43 * q^69 - 2 * q^71 + 21 * q^73 - q^75 + 19 * q^77 + 10 * q^79 + 22 * q^81 + 25 * q^83 + 8 * q^85 + 2 * q^87 - 6 * q^89 - 2 * q^91 + 16 * q^93 + 28 * q^95 - 18 * q^97 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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