LMFDB - Embedded newform 1008.2.df.b.689.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(689,1008)] 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, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.689"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,0,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			689.1
Root			$1.07065 + 1.85442i$ of defining polynomial
Character	$\chi$	$=$	1008.689
Dual form			1008.2.df.b.929.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61958 - 0.613974i) q^{3} +1.25299 q^{5} +(0.648211 + 2.56512i) q^{7} +(2.24607 + 1.98876i) q^{9} -0.616756i q^{11} +(-1.06343 - 0.613974i) q^{13} +(-2.02931 - 0.769301i) q^{15} +(-2.21501 + 3.83652i) q^{17} +(1.64679 - 0.950775i) q^{19} +(0.525087 - 4.55239i) q^{21} +4.74890i q^{23} -3.43003 q^{25} +(-2.41664 - 4.59998i) q^{27} +(-5.07629 + 2.93080i) q^{29} +(2.14851 - 1.24044i) q^{31} +(-0.378672 + 0.998884i) q^{33} +(0.812198 + 3.21405i) q^{35} +(1.33217 + 2.30738i) q^{37} +(1.34535 + 1.64730i) q^{39} +(2.09966 - 3.63671i) q^{41} +(2.24637 + 3.89083i) q^{43} +(2.81429 + 2.49189i) q^{45} +(-3.80738 + 6.59458i) q^{47} +(-6.15965 + 3.32547i) q^{49} +(5.94291 - 4.85358i) q^{51} +(2.67782 + 1.54604i) q^{53} -0.772786i q^{55} +(-3.25086 + 0.528768i) q^{57} +(-1.78229 - 3.08702i) q^{59} +(12.5136 + 7.22473i) q^{61} +(-3.64547 + 7.05057i) q^{63} +(-1.33247 - 0.769301i) q^{65} +(6.80644 + 11.7891i) q^{67} +(2.91570 - 7.69121i) q^{69} +10.4095i q^{71} +(9.95016 + 5.74473i) q^{73} +(5.55520 + 2.10595i) q^{75} +(1.58205 - 0.399788i) q^{77} +(-2.01592 + 3.49168i) q^{79} +(1.08967 + 8.93379i) q^{81} +(-4.36775 - 7.56516i) q^{83} +(-2.77538 + 4.80710i) q^{85} +(10.0209 - 1.62995i) q^{87} +(-0.811226 - 1.40508i) q^{89} +(0.885586 - 3.12582i) q^{91} +(-4.24128 + 0.689866i) q^{93} +(2.06341 - 1.19131i) q^{95} +(-8.76527 + 5.06063i) q^{97} +(1.22658 - 1.38528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{7} + 6 q^{13} + 3 q^{15} - 12 q^{17} - 3 q^{19} + 18 q^{21} - 14 q^{25} - 27 q^{27} - 15 q^{29} + 9 q^{31} - 9 q^{33} + 15 q^{35} + 6 q^{37} - 12 q^{39} - 9 q^{41} - 3 q^{43} + 15 q^{45} - 15 q^{47}+ \cdots - 21 q^{99}+O(q^{100}) $ 10 * q - 3 * q^7 + 6 * q^13 + 3 * q^15 - 12 * q^17 - 3 * q^19 + 18 * q^21 - 14 * q^25 - 27 * q^27 - 15 * q^29 + 9 * q^31 - 9 * q^33 + 15 * q^35 + 6 * q^37 - 12 * q^39 - 9 * q^41 - 3 * q^43 + 15 * q^45 - 15 * q^47 - 23 * q^49 + 24 * q^51 - 9 * q^53 - 36 * q^57 + 18 * q^59 + 12 * q^61 - 9 * q^63 - 3 * q^65 + 10 * q^67 - 3 * q^69 + 3 * q^73 + 21 * q^75 + 45 * q^77 - 20 * q^79 - 48 * q^81 + 15 * q^83 + 18 * q^85 - 30 * q^87 + 24 * q^89 + 24 * q^91 + 6 * q^93 + 6 * q^97 - 21 * q^99

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.61958	−	0.613974i	−0.935064	−	0.354478i
$3$	−1.61958	−	0.613974i	−0.935064	−	0.354478i
$4$		0			0
$5$	1.25299			0.560352			0.280176	−	0.959949i	$-0.409607\pi$
$5$	1.25299			0.560352			0.280176	+	0.959949i	$0.409607\pi$
$6$		0			0
$7$	0.648211	+	2.56512i	0.245001	+	0.969523i
$7$	0.648211	+	2.56512i	0.245001	+	0.969523i
$8$		0			0
$9$	2.24607	+	1.98876i	0.748690	+	0.662920i
$10$		0			0
$11$		−	0.616756i		−	0.185959i	−0.995668	−	0.0929794i	$-0.970361\pi$
$11$		−	0.616756i		−	0.185959i	0.995668	−	0.0929794i	$-0.0296391\pi$
$12$		0			0
$13$	−1.06343	−	0.613974i	−0.294944	−	0.170286i	0.345226	−	0.938520i	$-0.387802\pi$
$13$	−1.06343	−	0.613974i	−0.294944	−	0.170286i	−0.640169	+	0.768234i	$0.721136\pi$
$14$		0			0
$15$	−2.02931	−	0.769301i	−0.523965	−	0.198633i
$16$		0			0
$17$	−2.21501	+	3.83652i	−0.537220	+	0.930492i	0.461833	+	0.886967i	$0.347192\pi$
$17$	−2.21501	+	3.83652i	−0.537220	+	0.930492i	−0.999052	+	0.0435249i	$0.986141\pi$
$18$		0			0
$19$	1.64679	−	0.950775i	0.377800	−	0.218123i	−0.299061	−	0.954234i	$-0.596673\pi$
$19$	1.64679	−	0.950775i	0.377800	−	0.218123i	0.676861	+	0.736111i	$0.263340\pi$
$20$		0			0
$21$	0.525087	−	4.55239i	0.114583	−	0.993414i
$22$		0			0
$23$			4.74890i			0.990213i	0.868832	+	0.495107i	$0.164871\pi$
$23$			4.74890i			0.990213i	−0.868832	+	0.495107i	$0.835129\pi$
$24$		0			0
$25$	−3.43003			−0.686006
$26$		0			0
$27$	−2.41664	−	4.59998i	−0.465083	−	0.885267i
$28$		0			0
$29$	−5.07629	+	2.93080i	−0.942643	+	0.544235i	−0.890788	−	0.454419i	$-0.849847\pi$
$29$	−5.07629	+	2.93080i	−0.942643	+	0.544235i	−0.0518553	+	0.998655i	$0.516513\pi$
$30$		0			0
$31$	2.14851	−	1.24044i	0.385884	−	0.222790i	−0.294491	−	0.955654i	$-0.595150\pi$
$31$	2.14851	−	1.24044i	0.385884	−	0.222790i	0.680375	+	0.732864i	$0.261817\pi$
$32$		0			0
$33$	−0.378672	+	0.998884i	−0.0659183	+	0.173883i
$34$		0			0
$35$	0.812198	+	3.21405i	0.137287	+	0.543274i
$36$		0			0
$37$	1.33217	+	2.30738i	0.219007	+	0.379331i	0.954505	−	0.298196i	$-0.0963849\pi$
$37$	1.33217	+	2.30738i	0.219007	+	0.379331i	−0.735498	+	0.677527i	$0.763052\pi$
$38$		0			0
$39$	1.34535	+	1.64730i	0.215429	+	0.263779i
$40$		0			0
$41$	2.09966	−	3.63671i	0.327911	−	0.567959i	−0.654186	−	0.756334i	$-0.726989\pi$
$41$	2.09966	−	3.63671i	0.327911	−	0.567959i	0.982097	+	0.188375i	$0.0603220\pi$
$42$		0			0
$43$	2.24637	+	3.89083i	0.342568	+	0.593346i	0.984909	−	0.173073i	$-0.0553698\pi$
$43$	2.24637	+	3.89083i	0.342568	+	0.593346i	−0.642340	+	0.766419i	$0.722036\pi$
$44$		0			0
$45$	2.81429	+	2.49189i	0.419530	+	0.371468i
$46$		0			0
$47$	−3.80738	+	6.59458i	−0.555364	+	0.961918i	0.442512	+	0.896763i	$0.354088\pi$
$47$	−3.80738	+	6.59458i	−0.555364	+	0.961918i	−0.997875	+	0.0651551i	$0.979246\pi$
$48$		0			0
$49$	−6.15965	+	3.32547i	−0.879949	+	0.475067i
$50$		0			0
$51$	5.94291	−	4.85358i	0.832174	−	0.679637i
$52$		0			0
$53$	2.67782	+	1.54604i	0.367827	+	0.212365i	0.672509	−	0.740089i	$-0.265217\pi$
$53$	2.67782	+	1.54604i	0.367827	+	0.212365i	−0.304682	+	0.952454i	$0.598550\pi$
$54$		0			0
$55$		−	0.772786i		−	0.104202i
$56$		0			0
$57$	−3.25086	+	0.528768i	−0.430587	+	0.0700371i
$58$		0			0
$59$	−1.78229	−	3.08702i	−0.232035	−	0.401896i	0.726372	−	0.687302i	$-0.241205\pi$
$59$	−1.78229	−	3.08702i	−0.232035	−	0.401896i	−0.958407	+	0.285406i	$0.907872\pi$
$60$		0			0
$61$	12.5136	+	7.22473i	1.60220	+	0.925032i	0.991046	+	0.133521i	$0.0426284\pi$
$61$	12.5136	+	7.22473i	1.60220	+	0.925032i	0.611156	+	0.791510i	$0.290705\pi$
$62$		0			0
$63$	−3.64547	+	7.05057i	−0.459286	+	0.888288i
$64$		0			0
$65$	−1.33247	−	0.769301i	−0.165272	−	0.0954200i
$66$		0			0
$67$	6.80644	+	11.7891i	0.831539	+	1.44027i	0.896818	+	0.442400i	$0.145873\pi$
$67$	6.80644	+	11.7891i	0.831539	+	1.44027i	−0.0652791	+	0.997867i	$0.520794\pi$
$68$		0			0
$69$	2.91570	−	7.69121i	0.351009	−	0.925913i
$70$		0			0
$71$			10.4095i			1.23538i	0.786420	+	0.617692i	$0.211932\pi$
$71$			10.4095i			1.23538i	−0.786420	+	0.617692i	$0.788068\pi$
$72$		0			0
$73$	9.95016	+	5.74473i	1.16458	+	0.672369i	0.952397	−	0.304861i	$-0.0986100\pi$
$73$	9.95016	+	5.74473i	1.16458	+	0.672369i	0.212181	+	0.977230i	$0.431943\pi$
$74$		0			0
$75$	5.55520	+	2.10595i	0.641459	+	0.243174i
$76$		0			0
$77$	1.58205	−	0.399788i	0.180291	−	0.0455600i
$78$		0			0
$79$	−2.01592	+	3.49168i	−0.226809	+	0.392845i	−0.956861	−	0.290547i	$-0.906163\pi$
$79$	−2.01592	+	3.49168i	−0.226809	+	0.392845i	0.730052	+	0.683392i	$0.239496\pi$
$80$		0			0
$81$	1.08967	+	8.93379i	0.121075	+	0.992643i
$82$		0			0
$83$	−4.36775	−	7.56516i	−0.479422	−	0.830384i	0.520299	−	0.853984i	$-0.325820\pi$
$83$	−4.36775	−	7.56516i	−0.479422	−	0.830384i	−0.999721	+	0.0236001i	$0.992487\pi$
$84$		0			0
$85$	−2.77538	+	4.80710i	−0.301032	+	0.521403i
$86$		0			0
$87$	10.0209	−	1.62995i	1.07435	−	0.174749i
$88$		0			0
$89$	−0.811226	−	1.40508i	−0.0859897	−	0.148939i	0.819823	−	0.572617i	$-0.194072\pi$
$89$	−0.811226	−	1.40508i	−0.0859897	−	0.148939i	−0.905813	+	0.423679i	$0.860739\pi$
$90$		0			0
$91$	0.885586	−	3.12582i	0.0928346	−	0.327675i
$92$		0			0
$93$	−4.24128	+	0.689866i	−0.439801	+	0.0715357i
$94$		0			0
$95$	2.06341	−	1.19131i	0.211701	−	0.122226i
$96$		0			0
$97$	−8.76527	+	5.06063i	−0.889979	+	0.513829i	−0.873936	−	0.486042i	$-0.838440\pi$
$97$	−8.76527	+	5.06063i	−0.889979	+	0.513829i	−0.0160431	+	0.999871i	$0.505107\pi$
$98$		0			0
$99$	1.22658	−	1.38528i	0.123276	−	0.139226i
$100$		0			0
$101$	−1.71322			−0.170472			−0.0852360	−	0.996361i	$-0.527164\pi$
$101$	−1.71322			−0.170472			−0.0852360	+	0.996361i	$0.527164\pi$
$102$		0			0
$103$		−	7.40526i		−	0.729662i	−0.931074	−	0.364831i	$-0.881127\pi$
$103$		−	7.40526i		−	0.729662i	0.931074	−	0.364831i	$-0.118873\pi$
$104$		0			0
$105$	0.657926	−	5.70408i	0.0642070	−	0.556661i
$106$		0			0
$107$	0.131657	−	0.0760123i	0.0127278	−	0.00734839i	−0.493623	−	0.869676i	$-0.664328\pi$
$107$	0.131657	−	0.0760123i	0.0127278	−	0.00734839i	0.506350	+	0.862328i	$0.330994\pi$
$108$		0			0
$109$	2.70051	−	4.67742i	0.258662	−	0.448016i	−0.707222	−	0.706992i	$-0.750052\pi$
$109$	2.70051	−	4.67742i	0.258662	−	0.448016i	0.965884	+	0.258976i	$0.0833851\pi$
$110$		0			0
$111$	−0.740877	−	4.55490i	−0.0703210	−	0.432332i
$112$		0			0
$113$	−5.60391	−	3.23542i	−0.527171	−	0.304362i	0.212693	−	0.977119i	$-0.431777\pi$
$113$	−5.60391	−	3.23542i	−0.527171	−	0.304362i	−0.739864	+	0.672757i	$0.765110\pi$
$114$		0			0
$115$			5.95030i			0.554868i
$116$		0			0
$117$	−1.16750	−	3.49394i	−0.107936	−	0.323015i
$118$		0			0
$119$	−11.2769	−	3.19490i	−1.03375	−	0.292876i
$120$		0			0
$121$	10.6196			0.965419
$122$		0			0
$123$	−5.63341	+	4.60081i	−0.507947	+	0.414841i
$124$		0			0
$125$	−10.5627			−0.944757
$126$		0			0
$127$	2.93175			0.260151			0.130075	−	0.991504i	$-0.458478\pi$
$127$	2.93175			0.260151			0.130075	+	0.991504i	$0.458478\pi$
$128$		0			0
$129$	−1.24931	−	7.68072i	−0.109995	−	0.676250i
$130$		0			0
$131$	−16.2276			−1.41782			−0.708908	−	0.705301i	$-0.750812\pi$
$131$	−16.2276			−1.41782			−0.708908	+	0.705301i	$0.750812\pi$
$132$		0			0
$133$	3.50632	+	3.60791i	0.304036	+	0.312845i
$134$		0			0
$135$	−3.02802	−	5.76371i	−0.260610	−	0.496061i
$136$		0			0
$137$			17.4026i			1.48680i	0.668845	+	0.743402i	$0.266789\pi$
$137$			17.4026i			1.48680i	−0.668845	+	0.743402i	$0.733211\pi$
$138$		0			0
$139$	−5.45273	−	3.14813i	−0.462494	−	0.267021i	0.250598	−	0.968091i	$-0.419373\pi$
$139$	−5.45273	−	3.14813i	−0.462494	−	0.267021i	−0.713092	+	0.701070i	$0.752706\pi$
$140$		0			0
$141$	10.2153	−	8.34280i	0.860279	−	0.702591i
$142$		0			0
$143$	−0.378672	+	0.655879i	−0.0316661	+	0.0548474i
$144$		0			0
$145$	−6.36052	+	3.67225i	−0.528212	+	0.304963i
$146$		0			0
$147$	12.0178	−	1.60400i	0.991210	−	0.132296i
$148$		0			0
$149$		−	10.6269i		−	0.870592i	−0.900287	−	0.435296i	$-0.856644\pi$
$149$		−	10.6269i		−	0.870592i	0.900287	−	0.435296i	$-0.143356\pi$
$150$		0			0
$151$	−9.48930			−0.772229			−0.386114	−	0.922451i	$-0.626183\pi$
$151$	−9.48930			−0.772229			−0.386114	+	0.922451i	$0.626183\pi$
$152$		0			0
$153$	−12.6050	+	4.21196i	−1.01905	+	0.340517i
$154$		0			0
$155$	2.69205	−	1.55426i	0.216231	−	0.124841i
$156$		0			0
$157$	20.6214	−	11.9058i	1.64577	−	0.950185i	0.667040	−	0.745022i	$-0.267561\pi$
$157$	20.6214	−	11.9058i	1.64577	−	0.950185i	0.978728	−	0.205163i	$-0.0657723\pi$
$158$		0			0
$159$	−3.38771	−	4.14805i	−0.268663	−	0.328961i
$160$		0			0
$161$	−12.1815	+	3.07829i	−0.960035	+	0.242603i
$162$		0			0
$163$	4.41101	+	7.64009i	0.345497	+	0.598418i	0.985444	−	0.170001i	$-0.0543771\pi$
$163$	4.41101	+	7.64009i	0.345497	+	0.598418i	−0.639947	+	0.768419i	$0.721044\pi$
$164$		0			0
$165$	−0.474470	+	1.25159i	−0.0369375	+	0.0974360i
$166$		0			0
$167$	11.0335	−	19.1106i	0.853800	−	1.47883i	−0.0239535	−	0.999713i	$-0.507625\pi$
$167$	11.0335	−	19.1106i	0.853800	−	1.47883i	0.877754	−	0.479112i	$-0.159041\pi$
$168$		0			0
$169$	−5.74607	−	9.95249i	−0.442005	−	0.765576i
$170$		0			0
$171$	5.58967	+	1.13956i	0.427453	+	0.0871445i
$172$		0			0
$173$	2.03375	−	3.52256i	0.154623	−	0.267815i	−0.778299	−	0.627894i	$-0.783917\pi$
$173$	2.03375	−	3.52256i	0.154623	−	0.267815i	0.932922	+	0.360079i	$0.117250\pi$
$174$		0			0
$175$	−2.22338	−	8.79842i	−0.168072	−	0.665098i
$176$		0			0
$177$	0.991213	+	6.09396i	0.0745041	+	0.458050i
$178$		0			0
$179$	−7.20787	−	4.16146i	−0.538741	−	0.311042i	0.205827	−	0.978588i	$-0.434011\pi$
$179$	−7.20787	−	4.16146i	−0.538741	−	0.311042i	−0.744569	+	0.667546i	$0.767345\pi$
$180$		0			0
$181$		−	12.6701i		−	0.941763i	−0.882196	−	0.470881i	$-0.843936\pi$
$181$		−	12.6701i		−	0.941763i	0.882196	−	0.470881i	$-0.156064\pi$
$182$		0			0
$183$	−15.8310	−	19.3840i	−1.17026	−	1.43291i
$184$		0			0
$185$	1.66919	+	2.89111i	0.122721	+	0.212559i
$186$		0			0
$187$	2.36619	+	1.36612i	0.173033	+	0.0999008i
$188$		0			0
$189$	10.2330	−	9.18073i	0.744341	−	0.667800i
$190$		0			0
$191$	3.29133	+	1.90025i	0.238152	+	0.137497i	0.614327	−	0.789051i	$-0.289427\pi$
$191$	3.29133	+	1.90025i	0.238152	+	0.137497i	−0.376175	+	0.926549i	$0.622761\pi$
$192$		0			0
$193$	−3.39448	−	5.87942i	−0.244340	−	0.423210i	0.717606	−	0.696450i	$-0.245238\pi$
$193$	−3.39448	−	5.87942i	−0.244340	−	0.423210i	−0.961946	+	0.273240i	$0.911905\pi$
$194$		0			0
$195$	1.68571	+	2.06404i	0.120716	+	0.147809i
$196$		0			0
$197$			6.41453i			0.457017i	0.973542	+	0.228508i	$0.0733848\pi$
$197$			6.41453i			0.457017i	−0.973542	+	0.228508i	$0.926615\pi$
$198$		0			0
$199$	13.8921	+	8.02063i	0.984788	+	0.568568i	0.903712	−	0.428140i	$-0.140831\pi$
$199$	13.8921	+	8.02063i	0.984788	+	0.568568i	0.0810756	+	0.996708i	$0.474164\pi$
$200$		0			0
$201$	−3.78536	−	23.2723i	−0.266999	−	1.64150i
$202$		0			0
$203$	−10.8083	−	11.1215i	−0.758597	−	0.780576i
$204$		0			0
$205$	2.63084	−	4.55675i	0.183746	−	0.318257i
$206$		0			0
$207$	−9.44441	+	10.6664i	−0.656432	+	0.741363i
$208$		0			0
$209$	−0.586396	−	1.01567i	−0.0405619	−	0.0702552i
$210$		0			0
$211$	4.06070	−	7.03333i	0.279550	−	0.484194i	−0.691723	−	0.722163i	$-0.743148\pi$
$211$	4.06070	−	7.03333i	0.279550	−	0.484194i	0.971273	+	0.237968i	$0.0764815\pi$
$212$		0			0
$213$	6.39118	−	16.8590i	0.437916	−	1.15516i
$214$		0			0
$215$	2.81467	+	4.87515i	0.191959	+	0.332483i
$216$		0			0
$217$	4.57457	+	4.70711i	0.310542	+	0.319540i
$218$		0			0
$219$	−12.5880	−	15.4132i	−0.850615	−	1.04153i
$220$		0			0
$221$	4.71104	−	2.71992i	0.316899	−	0.182962i
$222$		0			0
$223$	6.96205	−	4.01954i	0.466213	−	0.269168i	−0.248440	−	0.968647i	$-0.579918\pi$
$223$	6.96205	−	4.01954i	0.466213	−	0.269168i	0.714653	+	0.699479i	$0.246585\pi$
$224$		0			0
$225$	−7.70409	−	6.82150i	−0.513606	−	0.454767i
$226$		0			0
$227$	20.8234			1.38210			0.691048	−	0.722809i	$-0.257149\pi$
$227$	20.8234			1.38210			0.691048	+	0.722809i	$0.257149\pi$
$228$		0			0
$229$		−	6.01918i		−	0.397759i	−0.980024	−	0.198879i	$-0.936270\pi$
$229$		−	6.01918i		−	0.397759i	0.980024	−	0.198879i	$-0.0637302\pi$
$230$		0			0
$231$	−2.80771	−	0.323850i	−0.184734	−	0.0213078i
$232$		0			0
$233$	−18.2156	+	10.5168i	−1.19335	+	0.688978i	−0.959064	−	0.283191i	$-0.908607\pi$
$233$	−18.2156	+	10.5168i	−1.19335	+	0.688978i	−0.234282	+	0.972169i	$0.575274\pi$
$234$		0			0
$235$	−4.77059	+	8.26291i	−0.311199	+	0.539013i
$236$		0			0
$237$	5.40875	−	4.41733i	0.351336	−	0.286936i
$238$		0			0
$239$	7.51079	+	4.33636i	0.485832	+	0.280496i	0.722844	−	0.691011i	$-0.242835\pi$
$239$	7.51079	+	4.33636i	0.485832	+	0.280496i	−0.237011	+	0.971507i	$0.576168\pi$
$240$		0			0
$241$			8.47315i			0.545804i	0.962042	+	0.272902i	$0.0879834\pi$
$241$			8.47315i			0.545804i	−0.962042	+	0.272902i	$0.912017\pi$
$242$		0			0
$243$	3.72030	−	15.1380i	0.238658	−	0.971104i
$244$		0			0
$245$	−7.71795	+	4.16677i	−0.493081	+	0.266205i
$246$		0			0
$247$	−2.33501			−0.148573
$248$		0			0
$249$	2.42910	+	14.9341i	0.153938	+	0.946407i
$250$		0			0
$251$	−23.4435			−1.47974			−0.739871	−	0.672749i	$-0.765113\pi$
$251$	−23.4435			−1.47974			−0.739871	+	0.672749i	$0.765113\pi$
$252$		0			0
$253$	2.92891			0.184139
$254$		0			0
$255$	7.44638	−	6.08146i	0.466310	−	0.380836i
$256$		0			0
$257$	−24.5170			−1.52933			−0.764665	−	0.644428i	$-0.777096\pi$
$257$	−24.5170			−1.52933			−0.764665	+	0.644428i	$0.777096\pi$
$258$		0			0
$259$	−5.05518	+	4.91283i	−0.314113	+	0.305269i
$260$		0			0
$261$	−17.2304	−	3.51274i	−1.06653	−	0.217433i
$262$		0			0
$263$			10.5544i			0.650811i	0.945575	+	0.325406i	$0.105501\pi$
$263$			10.5544i			0.650811i	−0.945575	+	0.325406i	$0.894499\pi$
$264$		0			0
$265$	3.35527	+	1.93716i	0.206112	+	0.118999i
$266$		0			0
$267$	0.451159	+	2.77372i	0.0276105	+	0.169749i
$268$		0			0
$269$	1.14451	−	1.98235i	0.0697821	−	0.120866i	−0.829023	−	0.559214i	$-0.811103\pi$
$269$	1.14451	−	1.98235i	0.0697821	−	0.120866i	0.898805	+	0.438348i	$0.144436\pi$
$270$		0			0
$271$	20.9239	−	12.0804i	1.27103	−	0.733831i	0.295851	−	0.955234i	$-0.404397\pi$
$271$	20.9239	−	12.0804i	1.27103	−	0.733831i	0.975182	+	0.221403i	$0.0710635\pi$
$272$		0			0
$273$	−3.35345	+	4.51878i	−0.202960	+	0.273489i
$274$		0			0
$275$			2.11549i			0.127569i
$276$		0			0
$277$	−11.3710			−0.683219			−0.341609	−	0.939842i	$-0.610972\pi$
$277$	−11.3710			−0.683219			−0.341609	+	0.939842i	$0.610972\pi$
$278$		0			0
$279$	7.29265	+	1.48675i	0.436600	+	0.0890092i
$280$		0			0
$281$	17.6382	−	10.1834i	1.05221	−	0.607492i	0.128941	−	0.991652i	$-0.458842\pi$
$281$	17.6382	−	10.1834i	1.05221	−	0.607492i	0.923267	+	0.384160i	$0.125509\pi$
$282$		0			0
$283$	−10.5318	+	6.08055i	−0.626052	+	0.361451i	−0.779222	−	0.626749i	$-0.784385\pi$
$283$	−10.5318	+	6.08055i	−0.626052	+	0.361451i	0.153169	+	0.988200i	$0.451052\pi$
$284$		0			0
$285$	−4.07328	+	0.662539i	−0.241280	+	0.0392454i
$286$		0			0
$287$	10.6896	+	3.02851i	0.630988	+	0.178767i
$288$		0			0
$289$	−1.31257	−	2.27345i	−0.0772103	−	0.133732i
$290$		0			0
$291$	17.3031	−	2.81444i	1.01433	−	0.164986i
$292$		0			0
$293$	13.4674	−	23.3262i	0.786773	−	1.36273i	−0.141161	−	0.989987i	$-0.545083\pi$
$293$	13.4674	−	23.3262i	0.786773	−	1.36273i	0.927934	−	0.372745i	$-0.121583\pi$
$294$		0			0
$295$	−2.23319	−	3.86799i	−0.130021	−	0.225203i
$296$		0			0
$297$	−2.83707	+	1.49048i	−0.164623	+	0.0864863i
$298$		0			0
$299$	2.91570	−	5.05014i	0.168619	−	0.292057i
$300$		0			0
$301$	−8.52431	+	8.28428i	−0.491333	+	0.477498i
$302$		0			0
$303$	2.77470	+	1.05187i	0.159402	+	0.0604286i
$304$		0			0
$305$	15.6793	+	9.05248i	0.897797	+	0.518343i
$306$		0			0
$307$			21.3700i			1.21965i	0.792536	+	0.609825i	$0.208760\pi$
$307$			21.3700i			1.21965i	−0.792536	+	0.609825i	$0.791240\pi$
$308$		0			0
$309$	−4.54664	+	11.9934i	−0.258649	+	0.682281i
$310$		0			0
$311$	−8.11558	−	14.0566i	−0.460192	−	0.797076i	0.538778	−	0.842448i	$-0.318886\pi$
$311$	−8.11558	−	14.0566i	−0.460192	−	0.797076i	−0.998970	+	0.0453714i	$0.985553\pi$
$312$		0			0
$313$	12.1941	+	7.04027i	0.689252	+	0.397940i	0.803332	−	0.595532i	$-0.203059\pi$
$313$	12.1941	+	7.04027i	0.689252	+	0.397940i	−0.114080	+	0.993472i	$0.536392\pi$
$314$		0			0
$315$	−4.56772	+	8.83426i	−0.257362	+	0.497754i
$316$		0			0
$317$	17.5776	+	10.1484i	0.987254	+	0.569991i	0.904452	−	0.426575i	$-0.140280\pi$
$317$	17.5776	+	10.1484i	0.987254	+	0.569991i	0.0828017	+	0.996566i	$0.473613\pi$
$318$		0			0
$319$	1.80759	+	3.13083i	0.101205	+	0.175293i
$320$		0			0
$321$	−0.259899	+	0.0422738i	−0.0145061	+	0.00235950i
$322$		0			0
$323$			8.42392i			0.468720i
$324$		0			0
$325$	3.64761	+	2.10595i	0.202333	+	0.116817i
$326$		0			0
$327$	−7.24550	+	5.91741i	−0.400677	+	0.327233i
$328$		0			0
$329$	−19.3838	−	5.49170i	−1.06867	−	0.302767i
$330$		0			0
$331$	13.2341	−	22.9221i	0.727411	−	1.25991i	−0.230563	−	0.973057i	$-0.574057\pi$
$331$	13.2341	−	22.9221i	0.727411	−	1.25991i	0.957974	−	0.286856i	$-0.0926100\pi$
$332$		0			0
$333$	−1.59668	+	7.83190i	−0.0874977	+	0.429186i
$334$		0			0
$335$	8.52836	+	14.7716i	0.465954	+	0.807057i
$336$		0			0
$337$	−1.73659	+	3.00785i	−0.0945979	+	0.163848i	−0.909441	−	0.415834i	$-0.863490\pi$
$337$	−1.73659	+	3.00785i	−0.0945979	+	0.163848i	0.814843	+	0.579682i	$0.196823\pi$
$338$		0			0
$339$	7.08951	+	8.68067i	0.385049	+	0.471469i
$340$		0			0
$341$	−0.765051	−	1.32511i	−0.0414298	−	0.0717585i
$342$		0			0
$343$	−12.5230	−	13.6446i	−0.676177	−	0.736739i
$344$		0			0
$345$	3.65333	−	9.63698i	0.196689	−	0.518837i
$346$		0			0
$347$	−8.14765	+	4.70405i	−0.437389	+	0.252527i	−0.702489	−	0.711694i	$-0.747928\pi$
$347$	−8.14765	+	4.70405i	−0.437389	+	0.252527i	0.265101	+	0.964221i	$0.414595\pi$
$348$		0			0
$349$	−12.3253	+	7.11603i	−0.659759	+	0.380912i	−0.792185	−	0.610281i	$-0.791057\pi$
$349$	−12.3253	+	7.11603i	−0.659759	+	0.380912i	0.132426	+	0.991193i	$0.457723\pi$
$350$		0			0
$351$	−0.254329	+	6.37554i	−0.0135751	+	0.340301i
$352$		0			0
$353$	17.1652			0.913614			0.456807	−	0.889566i	$-0.348993\pi$
$353$	17.1652			0.913614			0.456807	+	0.889566i	$0.348993\pi$
$354$		0			0
$355$			13.0430i			0.692250i
$356$		0			0
$357$	16.3023	+	12.0981i	0.862807	+	0.640300i
$358$		0			0
$359$	−24.4705	+	14.1281i	−1.29150	+	0.745650i	−0.978921	−	0.204241i	$-0.934528\pi$
$359$	−24.4705	+	14.1281i	−1.29150	+	0.745650i	−0.312583	+	0.949890i	$0.601194\pi$
$360$		0			0
$361$	−7.69205	+	13.3230i	−0.404845	+	0.701212i
$362$		0			0
$363$	−17.1993	−	6.52017i	−0.902729	−	0.342220i
$364$		0			0
$365$	12.4674	+	7.19806i	0.652574	+	0.376764i
$366$		0			0
$367$		−	23.0704i		−	1.20427i	−0.798396	−	0.602133i	$-0.794318\pi$
$367$		−	23.0704i		−	1.20427i	0.798396	−	0.602133i	$-0.205682\pi$
$368$		0			0
$369$	11.9485	−	3.99260i	0.622015	−	0.207847i
$370$		0			0
$371$	−2.22998	+	7.87108i	−0.115775	+	0.408646i
$372$		0			0
$373$	−13.8727			−0.718301			−0.359150	−	0.933280i	$-0.616933\pi$
$373$	−13.8727			−0.718301			−0.359150	+	0.933280i	$0.616933\pi$
$374$		0			0
$375$	17.1071	+	6.48523i	0.883408	+	0.334896i
$376$		0			0
$377$	7.19773			0.370702
$378$		0			0
$379$	−22.7814			−1.17020			−0.585101	−	0.810961i	$-0.698945\pi$
$379$	−22.7814			−1.17020			−0.585101	+	0.810961i	$0.698945\pi$
$380$		0			0
$381$	−4.74820	−	1.80002i	−0.243257	−	0.0922177i
$382$		0			0
$383$	15.2320			0.778317			0.389158	−	0.921171i	$-0.372766\pi$
$383$	15.2320			0.778317			0.389158	+	0.921171i	$0.372766\pi$
$384$		0			0
$385$	1.98229	−	0.500928i	0.101027	−	0.0255297i
$386$		0			0
$387$	−2.69241	+	13.2066i	−0.136863	+	0.671328i
$388$		0			0
$389$		−	14.1479i		−	0.717328i	−0.933467	−	0.358664i	$-0.883232\pi$
$389$		−	14.1479i		−	0.717328i	0.933467	−	0.358664i	$-0.116768\pi$
$390$		0			0
$391$	−18.2192	−	10.5189i	−0.921386	−	0.531962i
$392$		0			0
$393$	26.2819	+	9.96335i	1.32575	+	0.502584i
$394$		0			0
$395$	−2.52592	+	4.37503i	−0.127093	+	0.220131i
$396$		0			0
$397$	8.40688	−	4.85371i	0.421929	−	0.243601i	−0.273973	−	0.961737i	$-0.588338\pi$
$397$	8.40688	−	4.85371i	0.421929	−	0.243601i	0.695902	+	0.718136i	$0.255005\pi$
$398$		0			0
$399$	−3.46359	−	7.99608i	−0.173397	−	0.400305i
$400$		0			0
$401$		−	8.73133i		−	0.436022i	−0.975946	−	0.218011i	$-0.930043\pi$
$401$		−	8.73133i		−	0.436022i	0.975946	−	0.218011i	$-0.0699569\pi$
$402$		0			0
$403$	−3.04640			−0.151752
$404$		0			0
$405$	1.36535	+	11.1939i	0.0678446	+	0.556230i
$406$		0			0
$407$	1.42309	−	0.821622i	0.0705400	−	0.0407263i
$408$		0			0
$409$	−12.8967	+	7.44591i	−0.637700	+	0.368176i	−0.783728	−	0.621104i	$-0.786684\pi$
$409$	−12.8967	+	7.44591i	−0.637700	+	0.368176i	0.146028	+	0.989280i	$0.453351\pi$
$410$		0			0
$411$	10.6847	−	28.1849i	0.527039	−	1.39026i
$412$		0			0
$413$	6.76327	−	6.57283i	0.332799	−	0.323428i
$414$		0			0
$415$	−5.47272	−	9.47903i	−0.268645	−	0.465307i
$416$		0			0
$417$	6.89825	+	8.44648i	0.337809	+	0.413626i
$418$		0			0
$419$	2.13859	−	3.70414i	0.104477	−	0.180959i	−0.809048	−	0.587743i	$-0.800017\pi$
$419$	2.13859	−	3.70414i	0.104477	−	0.180959i	0.913524	+	0.406784i	$0.133350\pi$
$420$		0			0
$421$	5.76681	+	9.98841i	0.281057	+	0.486805i	0.971645	−	0.236443i	$-0.0759816\pi$
$421$	5.76681	+	9.98841i	0.281057	+	0.486805i	−0.690588	+	0.723248i	$0.742648\pi$
$422$		0			0
$423$	−21.6667	+	7.23993i	−1.05347	+	0.352017i
$424$		0			0
$425$	7.59756	−	13.1594i	0.368536	−	0.638323i
$426$		0			0
$427$	−10.4208	+	36.7820i	−0.504299	+	1.78000i
$428$		0			0
$429$	1.01598	−	0.829753i	0.0490521	−	0.0400609i
$430$		0			0
$431$	14.4497	+	8.34254i	0.696018	+	0.401846i	0.805863	−	0.592103i	$-0.201702\pi$
$431$	14.4497	+	8.34254i	0.696018	+	0.401846i	−0.109845	+	0.993949i	$0.535035\pi$
$432$		0			0
$433$		−	12.3503i		−	0.593516i	−0.954953	−	0.296758i	$-0.904094\pi$
$433$		−	12.3503i		−	0.593516i	0.954953	−	0.296758i	$-0.0959055\pi$
$434$		0			0
$435$	12.5560	−	2.04230i	0.602015	−	0.0979207i
$436$		0			0
$437$	4.51513	+	7.82044i	0.215988	+	0.374102i
$438$		0			0
$439$	19.1691	+	11.0673i	0.914892	+	0.528213i	0.882002	−	0.471246i	$-0.156195\pi$
$439$	19.1691	+	11.0673i	0.914892	+	0.528213i	0.0328902	+	0.999459i	$0.489529\pi$
$440$		0			0
$441$	−20.4486	−	4.78081i	−0.973741	−	0.227657i
$442$		0			0
$443$	4.22906	+	2.44165i	0.200929	+	0.116006i	0.597089	−	0.802175i	$-0.296324\pi$
$443$	4.22906	+	2.44165i	0.200929	+	0.116006i	−0.396160	+	0.918182i	$0.629657\pi$
$444$		0			0
$445$	−1.01645	−	1.76055i	−0.0481845	−	0.0834580i
$446$		0			0
$447$	−6.52466	+	17.2111i	−0.308606	+	0.814059i
$448$		0			0
$449$		−	12.4409i		−	0.587121i	−0.955941	−	0.293560i	$-0.905160\pi$
$449$		−	12.4409i		−	0.587121i	0.955941	−	0.293560i	$-0.0948401\pi$
$450$		0			0
$451$	−2.24296	−	1.29498i	−0.105617	−	0.0609780i
$452$		0			0
$453$	15.3687	+	5.82619i	0.722083	+	0.273738i
$454$		0			0
$455$	1.10963	−	3.91660i	0.0520201	−	0.183613i
$456$		0			0
$457$	5.38774	−	9.33185i	0.252028	−	0.436525i	−0.712056	−	0.702123i	$-0.752236\pi$
$457$	5.38774	−	9.33185i	0.252028	−	0.436525i	0.964084	+	0.265597i	$0.0855691\pi$
$458$		0			0
$459$	23.0008	+	0.917533i	1.07359	+	0.0428268i
$460$		0			0
$461$	−0.333303	−	0.577297i	−0.0155235	−	0.0268874i	0.858159	−	0.513383i	$-0.171608\pi$
$461$	−0.333303	−	0.577297i	−0.0155235	−	0.0268874i	−0.873683	+	0.486496i	$0.838275\pi$
$462$		0			0
$463$	20.7892	−	36.0079i	0.966155	−	1.67343i	0.259677	−	0.965696i	$-0.416384\pi$
$463$	20.7892	−	36.0079i	0.966155	−	1.67343i	0.706479	−	0.707734i	$-0.250283\pi$
$464$		0			0
$465$	−5.31426	+	0.864391i	−0.246443	+	0.0400852i
$466$		0			0
$467$	−19.6568	−	34.0465i	−0.909606	−	1.57548i	−0.814612	−	0.580006i	$-0.803050\pi$
$467$	−19.6568	−	34.0465i	−0.909606	−	1.57548i	−0.0949943	−	0.995478i	$-0.530283\pi$
$468$		0			0
$469$	−25.8284	+	25.1011i	−1.19264	+	1.15906i
$470$		0			0
$471$	−40.7078	+	6.62133i	−1.87572	+	0.305095i
$472$		0			0
$473$	2.39969	−	1.38546i	0.110338	−	0.0637036i
$474$		0			0
$475$	−5.64854	+	3.26119i	−0.259173	+	0.149633i
$476$		0			0
$477$	2.93987	+	8.79805i	0.134608	+	0.402835i
$478$		0			0
$479$	38.1153			1.74153			0.870767	−	0.491696i	$-0.163623\pi$
$479$	38.1153			1.74153			0.870767	+	0.491696i	$0.163623\pi$
$480$		0			0
$481$		−	3.27167i		−	0.149175i
$482$		0			0
$483$	21.6188	+	2.49358i	0.983691	+	0.113462i
$484$		0			0
$485$	−10.9828	+	6.34090i	−0.498701	+	0.287925i
$486$		0			0
$487$	3.80277	−	6.58659i	0.172320	−	0.298467i	−0.766911	−	0.641754i	$-0.778207\pi$
$487$	3.80277	−	6.58659i	0.172320	−	0.298467i	0.939231	+	0.343287i	$0.111540\pi$
$488$		0			0
$489$	−2.45316	−	15.0820i	−0.110936	−	0.682030i
$490$		0			0
$491$	−3.33297	−	1.92429i	−0.150415	−	0.0868420i	0.422904	−	0.906175i	$-0.361011\pi$
$491$	−3.33297	−	1.92429i	−0.150415	−	0.0868420i	−0.573318	+	0.819333i	$0.694344\pi$
$492$		0			0
$493$		−	25.9670i		−	1.16950i
$494$		0			0
$495$	1.53688	−	1.73573i	0.0690778	−	0.0780154i
$496$		0			0
$497$	−26.7016	+	6.74757i	−1.19773	+	0.302670i
$498$		0			0
$499$	32.1588			1.43962			0.719812	−	0.694169i	$-0.244228\pi$
$499$	32.1588			1.43962			0.719812	+	0.694169i	$0.244228\pi$
$500$		0			0
$501$	−29.6031	+	24.1769i	−1.32257	+	1.08014i
$502$		0			0
$503$	0.425693			0.0189807			0.00949035	−	0.999955i	$-0.496979\pi$
$503$	0.425693			0.0189807			0.00949035	+	0.999955i	$0.496979\pi$
$504$		0			0
$505$	−2.14664			−0.0955243
$506$		0			0
$507$	3.19565	+	19.6468i	0.141924	+	0.872544i
$508$		0			0
$509$	−25.7926			−1.14323			−0.571617	−	0.820520i	$-0.693684\pi$
$509$	−25.7926			−1.14323			−0.571617	+	0.820520i	$0.693684\pi$
$510$		0			0
$511$	−8.28610	+	29.2471i	−0.366555	+	1.29382i
$512$		0			0
$513$	−8.35326	−	5.27753i	−0.368805	−	0.233008i
$514$		0			0
$515$		−	9.27868i		−	0.408868i
$516$		0			0
$517$	4.06724	+	2.34822i	0.178877	+	0.103275i
$518$		0			0
$519$	−5.45658	+	4.45639i	−0.239517	+	0.195614i
$520$		0			0
$521$	−9.07174	+	15.7127i	−0.397440	+	0.688386i	−0.993409	−	0.114621i	$-0.963435\pi$
$521$	−9.07174	+	15.7127i	−0.397440	+	0.688386i	0.595969	+	0.803007i	$0.296768\pi$
$522$		0			0
$523$	−12.0723	+	6.96997i	−0.527887	+	0.304776i	−0.740155	−	0.672436i	$-0.765248\pi$
$523$	−12.0723	+	6.96997i	−0.527887	+	0.304776i	0.212269	+	0.977211i	$0.431915\pi$
$524$		0			0
$525$	−1.80106	+	15.6148i	−0.0786048	+	0.681487i
$526$		0			0
$527$			10.9904i			0.478749i
$528$		0			0
$529$	0.447980			0.0194774
$530$		0			0
$531$	2.13619	−	10.4782i	0.0927026	−	0.454716i
$532$		0			0
$533$	−4.46569	+	2.57827i	−0.193431	+	0.111677i
$534$		0			0
$535$	0.164965	−	0.0952423i	0.00713204	−	0.00411769i
$536$		0			0
$537$	9.11868	+	11.1653i	0.393500	+	0.481817i
$538$		0			0
$539$	2.05100	+	3.79900i	0.0883430	+	0.163634i
$540$		0			0
$541$	−14.8576	−	25.7341i	−0.638779	−	1.10640i	−0.985701	−	0.168503i	$-0.946107\pi$
$541$	−14.8576	−	25.7341i	−0.638779	−	1.10640i	0.346922	−	0.937894i	$-0.387227\pi$
$542$		0			0
$543$	−7.77913	+	20.5203i	−0.333834	+	0.880609i
$544$		0			0
$545$	3.38370	−	5.86074i	0.144942	−	0.251046i
$546$		0			0
$547$	9.13516	+	15.8226i	0.390591	+	0.676524i	0.992528	−	0.122020i	$-0.0389373\pi$
$547$	9.13516	+	15.8226i	0.390591	+	0.676524i	−0.601937	+	0.798544i	$0.705604\pi$
$548$		0			0
$549$	13.7382	+	41.1138i	0.586331	+	1.75469i
$550$		0			0
$551$	−5.57306	+	9.65282i	−0.237420	+	0.411224i
$552$		0			0
$553$	−10.2633	−	2.90773i	−0.436440	−	0.123649i
$554$		0			0
$555$	−0.928308	−	5.70723i	−0.0394045	−	0.242258i
$556$		0			0
$557$	−0.359456	−	0.207532i	−0.0152307	−	0.00879343i	0.492365	−	0.870389i	$-0.336132\pi$
$557$	−0.359456	−	0.207532i	−0.0152307	−	0.00879343i	−0.507596	+	0.861595i	$0.669466\pi$
$558$		0			0
$559$		−	5.51686i		−	0.233338i
$560$		0			0
$561$	−2.99347	−	3.66532i	−0.126385	−	0.154750i
$562$		0			0
$563$	−1.82962	−	3.16900i	−0.0771095	−	0.133558i	0.824892	−	0.565290i	$-0.191236\pi$
$563$	−1.82962	−	3.16900i	−0.0771095	−	0.133558i	−0.902002	+	0.431733i	$0.857902\pi$
$564$		0			0
$565$	−7.02161	−	4.05393i	−0.295401	−	0.170550i
$566$		0			0
$567$	−22.2099	+	8.58612i	−0.932727	+	0.360583i
$568$		0			0
$569$	30.4692	+	17.5914i	1.27733	+	0.737470i	0.976358	−	0.216162i	$-0.0693538\pi$
$569$	30.4692	+	17.5914i	1.27733	+	0.737470i	0.300977	+	0.953631i	$0.402687\pi$
$570$		0			0
$571$	−5.02680	−	8.70667i	−0.210365	−	0.364363i	0.741464	−	0.670993i	$-0.234132\pi$
$571$	−5.02680	−	8.70667i	−0.210365	−	0.364363i	−0.951829	+	0.306630i	$0.900799\pi$
$572$		0			0
$573$	−4.16387	−	5.09840i	−0.173948	−	0.212989i
$574$		0			0
$575$		−	16.2888i		−	0.679292i
$576$		0			0
$577$	0.0597672	+	0.0345066i	0.00248814	+	0.00143653i	0.501244	−	0.865306i	$-0.332876\pi$
$577$	0.0597672	+	0.0345066i	0.00248814	+	0.00143653i	−0.498755	+	0.866743i	$0.666209\pi$
$578$		0			0
$579$	1.88782	+	11.6063i	0.0784552	+	0.482342i
$580$		0			0
$581$	16.5743	−	16.1076i	0.687618	−	0.668256i
$582$		0			0
$583$	0.953529	−	1.65156i	0.0394911	−	0.0684006i
$584$		0			0
$585$	−1.46286	−	4.37786i	−0.0604820	−	0.181002i
$586$		0			0
$587$	11.4799	+	19.8838i	0.473827	+	0.820693i	0.999551	−	0.0299626i	$-0.00953881\pi$
$587$	11.4799	+	19.8838i	0.473827	+	0.820693i	−0.525724	+	0.850655i	$0.676205\pi$
$588$		0			0
$589$	2.35877	−	4.08550i	0.0971913	−	0.168340i
$590$		0			0
$591$	3.93836	−	10.3888i	0.162002	−	0.427340i
$592$		0			0
$593$	14.3970	+	24.9363i	0.591213	+	1.02401i	0.994069	+	0.108748i	$0.0346843\pi$
$593$	14.3970	+	24.9363i	0.591213	+	1.02401i	−0.402856	+	0.915263i	$0.631982\pi$
$594$		0			0
$595$	−14.1298	−	4.00316i	−0.579265	−	0.164114i
$596$		0			0
$597$	−17.5750	−	21.5195i	−0.719295	−	0.880733i
$598$		0			0
$599$	33.1588	−	19.1442i	1.35483	−	0.782212i	0.365910	−	0.930650i	$-0.380758\pi$
$599$	33.1588	−	19.1442i	1.35483	−	0.782212i	0.988922	+	0.148438i	$0.0474246\pi$
$600$		0			0
$601$	26.7618	−	15.4509i	1.09164	−	0.630257i	0.157625	−	0.987499i	$-0.449616\pi$
$601$	26.7618	−	15.4509i	1.09164	−	0.630257i	0.934012	+	0.357242i	$0.116283\pi$
$602$		0			0
$603$	−8.15793	+	40.0155i	−0.332216	+	1.62956i
$604$		0			0
$605$	13.3062			0.540975
$606$		0			0
$607$			33.1791i			1.34670i	0.739325	+	0.673349i	$0.235145\pi$
$607$			33.1791i			1.34670i	−0.739325	+	0.673349i	$0.764855\pi$
$608$		0			0
$609$	10.6766	+	24.6482i	0.432640	+	0.998795i
$610$		0			0
$611$	8.09780	−	4.67527i	0.327602	−	0.189141i
$612$		0			0
$613$	−2.01164	+	3.48426i	−0.0812492	+	0.140728i	−0.903787	−	0.427983i	$-0.859224\pi$
$613$	−2.01164	+	3.48426i	−0.0812492	+	0.140728i	0.822538	+	0.568711i	$0.192558\pi$
$614$		0			0
$615$	−7.05857	+	5.76474i	−0.284629	+	0.232457i
$616$		0			0
$617$	27.1191	+	15.6572i	1.09177	+	0.630336i	0.934048	−	0.357147i	$-0.116251\pi$
$617$	27.1191	+	15.6572i	1.09177	+	0.630336i	0.157726	+	0.987483i	$0.449584\pi$
$618$		0			0
$619$		−	13.9310i		−	0.559934i	−0.960010	−	0.279967i	$-0.909676\pi$
$619$		−	13.9310i		−	0.559934i	0.960010	−	0.279967i	$-0.0903235\pi$
$620$		0			0
$621$	21.8448	−	11.4764i	0.876603	−	0.460532i
$622$		0			0
$623$	3.07836	−	2.99168i	0.123332	−	0.119859i
$624$		0			0
$625$	3.91523			0.156609
$626$		0			0
$627$	0.326121	+	2.00499i	0.0130240	+	0.0800714i
$628$		0			0
$629$	−11.8031			−0.470620
$630$		0			0
$631$	4.61815			0.183846			0.0919229	−	0.995766i	$-0.470699\pi$
$631$	4.61815			0.183846			0.0919229	+	0.995766i	$0.470699\pi$
$632$		0			0
$633$	−10.8949	+	8.89787i	−0.433033	+	0.353659i
$634$		0			0
$635$	3.67344			0.145776
$636$		0			0
$637$	8.59213	+	0.245442i	0.340433	+	0.00972478i
$638$		0			0
$639$	−20.7020	+	23.3805i	−0.818960	+	0.924920i
$640$		0			0
$641$		−	42.4724i		−	1.67756i	−0.544473	−	0.838779i	$-0.683270\pi$
$641$		−	42.4724i		−	1.67756i	0.544473	−	0.838779i	$-0.316730\pi$
$642$		0			0
$643$	3.13514	+	1.81008i	0.123638	+	0.0713825i	0.560544	−	0.828125i	$-0.310592\pi$
$643$	3.13514	+	1.81008i	0.123638	+	0.0713825i	−0.436905	+	0.899507i	$0.643926\pi$
$644$		0			0
$645$	−1.56536	−	9.62383i	−0.0616361	−	0.378938i
$646$		0			0
$647$	−6.00617	+	10.4030i	−0.236127	+	0.408984i	−0.959600	−	0.281369i	$-0.909211\pi$
$647$	−6.00617	+	10.4030i	−0.236127	+	0.408984i	0.723473	+	0.690353i	$0.242545\pi$
$648$		0			0
$649$	−1.90394	+	1.09924i	−0.0747361	+	0.0431489i
$650$		0			0
$651$	−4.51883	−	10.4322i	−0.177107	−	0.408870i
$652$		0			0
$653$			46.1822i			1.80725i	0.428324	+	0.903625i	$0.359104\pi$
$653$			46.1822i			1.80725i	−0.428324	+	0.903625i	$0.640896\pi$
$654$		0			0
$655$	−20.3330			−0.794476
$656$		0			0
$657$	10.9239	+	32.6915i	0.426182	+	1.27542i
$658$		0			0
$659$	16.3479	−	9.43847i	0.636824	−	0.367671i	−0.146566	−	0.989201i	$-0.546822\pi$
$659$	16.3479	−	9.43847i	0.636824	−	0.367671i	0.783390	+	0.621530i	$0.213489\pi$
$660$		0			0
$661$	2.88202	−	1.66393i	0.112097	−	0.0647195i	−0.442903	−	0.896570i	$-0.646051\pi$
$661$	2.88202	−	1.66393i	0.112097	−	0.0647195i	0.555000	+	0.831850i	$0.312718\pi$
$662$		0			0
$663$	−9.29987	+	1.51267i	−0.361177	+	0.0587472i
$664$		0			0
$665$	4.39336	+	4.52066i	0.170367	+	0.175304i
$666$		0			0
$667$	−13.9181	−	24.1068i	−0.538909	−	0.933418i
$668$		0			0
$669$	−13.7435	+	2.23544i	−0.531353	+	0.0864273i
$670$		0			0
$671$	4.45589	−	7.71783i	0.172018	−	0.297944i
$672$		0			0
$673$	−16.3678	−	28.3499i	−0.630934	−	1.09281i	−0.987361	−	0.158487i	$-0.949339\pi$
$673$	−16.3678	−	28.3499i	−0.630934	−	1.09281i	0.356427	−	0.934323i	$-0.383995\pi$
$674$		0			0
$675$	8.28915	+	15.7781i	0.319050	+	0.607298i
$676$		0			0
$677$	−16.9228	+	29.3111i	−0.650396	+	1.12652i	0.332631	+	0.943057i	$0.392063\pi$
$677$	−16.9228	+	29.3111i	−0.650396	+	1.12652i	−0.983027	+	0.183461i	$0.941270\pi$
$678$		0			0
$679$	−18.6629	−	19.2036i	−0.716215	−	0.736966i
$680$		0			0
$681$	−33.7251	−	12.7850i	−1.29235	−	0.489923i
$682$		0			0
$683$	−4.79617	−	2.76907i	−0.183520	−	0.105956i	0.405425	−	0.914128i	$-0.367123\pi$
$683$	−4.79617	−	2.76907i	−0.183520	−	0.105956i	−0.588946	+	0.808173i	$0.700457\pi$
$684$		0			0
$685$			21.8052i			0.833133i
$686$		0			0
$687$	−3.69562	+	9.74854i	−0.140997	+	0.371930i
$688$		0			0
$689$	−1.89846	−	3.28822i	−0.0723254	−	0.125271i
$690$		0			0
$691$	−12.3417	−	7.12550i	−0.469502	−	0.271067i	0.246530	−	0.969135i	$-0.420710\pi$
$691$	−12.3417	−	7.12550i	−0.469502	−	0.271067i	−0.716031	+	0.698068i	$0.754043\pi$
$692$		0			0
$693$	4.34848	+	2.24837i	0.165185	+	0.0854083i
$694$		0			0
$695$	−6.83219	−	3.94456i	−0.259160	−	0.149626i
$696$		0			0
$697$	9.30154	+	16.1107i	0.352321	+	0.610238i
$698$		0			0
$699$	35.9587	−	5.84886i	1.36008	−	0.221224i
$700$		0			0
$701$		−	18.6105i		−	0.702908i	−0.936205	−	0.351454i	$-0.885687\pi$
$701$		−	18.6105i		−	0.702908i	0.936205	−	0.351454i	$-0.114313\pi$
$702$		0			0
$703$	4.38760	+	2.53318i	0.165482	+	0.0955408i
$704$		0			0
$705$	12.7996	−	10.4534i	0.482059	−	0.393698i
$706$		0			0
$707$	−1.11053	−	4.39462i	−0.0417657	−	0.165277i
$708$		0			0
$709$	6.74733	−	11.6867i	0.253401	−	0.438904i	−0.711059	−	0.703133i	$-0.751784\pi$
$709$	6.74733	−	11.6867i	0.253401	−	0.438904i	0.964460	+	0.264229i	$0.0851174\pi$
$710$		0			0
$711$	−11.4720	+	3.83338i	−0.430234	+	0.143763i
$712$		0			0
$713$	5.89074	+	10.2031i	0.220610	+	0.382107i
$714$		0			0
$715$	−0.474470	+	0.821807i	−0.0177442	+	0.0307338i
$716$		0			0
$717$	−9.50190	−	11.6345i	−0.354855	−	0.434498i
$718$		0			0
$719$	18.8692	+	32.6824i	0.703702	+	1.21885i	0.967158	+	0.254176i	$0.0818042\pi$
$719$	18.8692	+	32.6824i	0.703702	+	1.21885i	−0.263456	+	0.964671i	$0.584863\pi$
$720$		0			0
$721$	18.9954	−	4.80017i	0.707424	−	0.178768i
$722$		0			0
$723$	5.20230	−	13.7229i	0.193476	−	0.510362i
$724$		0			0
$725$	17.4118	−	10.0527i	0.646659	−	0.373348i
$726$		0			0
$727$	−1.98480	+	1.14592i	−0.0736121	+	0.0424999i	−0.536354	−	0.843993i	$-0.680199\pi$
$727$	−1.98480	+	1.14592i	−0.0736121	+	0.0424999i	0.462742	+	0.886493i	$0.346866\pi$
$728$		0			0
$729$	−15.3197	+	22.2330i	−0.567395	+	0.823446i
$730$		0			0
$731$	−19.9030			−0.736138
$732$		0			0
$733$			24.7888i			0.915596i	0.889056	+	0.457798i	$0.151362\pi$
$733$			24.7888i			0.915596i	−0.889056	+	0.457798i	$0.848638\pi$
$734$		0			0
$735$	15.0581	−	2.00979i	0.555427	−	0.0741322i
$736$		0			0
$737$	7.27099	−	4.19791i	0.267830	−	0.154632i
$738$		0			0
$739$	−8.10081	+	14.0310i	−0.297993	+	0.516139i	−0.975677	−	0.219214i	$-0.929651\pi$
$739$	−8.10081	+	14.0310i	−0.297993	+	0.516139i	0.677684	+	0.735354i	$0.262984\pi$
$740$		0			0
$741$	3.78173	+	1.43363i	0.138925	+	0.0526658i
$742$		0			0
$743$	18.8312	+	10.8722i	0.690848	+	0.398862i	0.803930	−	0.594724i	$-0.202739\pi$
$743$	18.8312	+	10.8722i	0.690848	+	0.398862i	−0.113081	+	0.993586i	$0.536072\pi$
$744$		0			0
$745$		−	13.3154i		−	0.487838i
$746$		0			0
$747$	5.23501	−	25.6783i	0.191539	−	0.939519i
$748$		0			0
$749$	0.280322	+	0.288444i	0.0102427	+	0.0105395i
$750$		0			0
$751$	7.57995			0.276596			0.138298	−	0.990391i	$-0.455837\pi$
$751$	7.57995			0.276596			0.138298	+	0.990391i	$0.455837\pi$
$752$		0			0
$753$	37.9686	+	14.3937i	1.38365	+	0.524536i
$754$		0			0
$755$	−11.8900			−0.432720
$756$		0			0
$757$	10.3436			0.375944			0.187972	−	0.982174i	$-0.439809\pi$
$757$	10.3436			0.375944			0.187972	+	0.982174i	$0.439809\pi$
$758$		0			0
$759$	−4.74360	−	1.79827i	−0.172182	−	0.0652732i
$760$		0			0
$761$	−34.4339			−1.24823			−0.624114	−	0.781333i	$-0.714540\pi$
$761$	−34.4339			−1.24823			−0.624114	+	0.781333i	$0.714540\pi$
$762$		0			0
$763$	13.7486	+	3.89517i	0.497734	+	0.141015i
$764$		0			0
$765$	−15.7939	+	5.27753i	−0.571028	+	0.190809i
$766$		0			0
$767$			4.37713i			0.158049i
$768$		0			0
$769$	−12.9344	−	7.46765i	−0.466425	−	0.269290i	0.248317	−	0.968679i	$-0.420123\pi$
$769$	−12.9344	−	7.46765i	−0.466425	−	0.269290i	−0.714742	+	0.699388i	$0.753456\pi$
$770$		0			0
$771$	39.7073	+	15.0528i	1.43002	+	0.542114i
$772$		0			0
$773$	19.9924	−	34.6278i	0.719076	−	1.24548i	−0.242290	−	0.970204i	$-0.577899\pi$
$773$	19.9924	−	34.6278i	0.719076	−	1.24548i	0.961366	−	0.275272i	$-0.0887680\pi$
$774$		0			0
$775$	−7.36945	+	4.25476i	−0.264719	+	0.152835i
$776$		0			0
$777$	11.2036	−	4.85297i	0.401927	−	0.174099i
$778$		0			0
$779$		−	7.98521i		−	0.286100i
$780$		0			0
$781$	6.42013			0.229730
$782$		0			0
$783$	25.7492	+	16.2681i	0.920201	+	0.581376i
$784$		0			0
$785$	25.8383	−	14.9178i	0.922209	−	0.532438i
$786$		0			0
$787$	1.94091	−	1.12059i	0.0691860	−	0.0399446i	−0.465008	−	0.885307i	$-0.653949\pi$
$787$	1.94091	−	1.12059i	0.0691860	−	0.0399446i	0.534194	+	0.845362i	$0.320615\pi$
$788$		0			0
$789$	6.48012	−	17.0937i	0.230698	−	0.608550i
$790$		0			0
$791$	4.66671	−	16.4719i	0.165929	−	0.585674i
$792$		0			0
$793$	−8.87159	−	15.3660i	−0.315039	−	0.545664i
$794$		0			0
$795$	−4.24475	−	5.19744i	−0.150546	−	0.184334i
$796$		0			0
$797$	−22.1077	+	38.2916i	−0.783094	+	1.35636i	0.147037	+	0.989131i	$0.453026\pi$
$797$	−22.1077	+	38.2916i	−0.783094	+	1.35636i	−0.930131	+	0.367227i	$0.880307\pi$
$798$		0			0
$799$	−16.8668	−	29.2142i	−0.596705	−	1.03352i
$800$		0			0
$801$	0.972303	−	4.76925i	0.0343546	−	0.168513i
$802$		0			0
$803$	3.54309	−	6.13682i	0.125033	−	0.216564i
$804$		0			0
$805$	−15.2632	+	3.85705i	−0.537957	+	0.135943i
$806$		0			0
$807$	−3.07074	+	2.50788i	−0.108095	+	0.0882814i
$808$		0			0
$809$	4.31478	+	2.49114i	0.151699	+	0.0875837i	0.573928	−	0.818906i	$-0.305419\pi$
$809$	4.31478	+	2.49114i	0.151699	+	0.0875837i	−0.422229	+	0.906489i	$0.638752\pi$
$810$		0			0
$811$		−	36.5749i		−	1.28432i	−0.766571	−	0.642160i	$-0.778039\pi$
$811$		−	36.5749i		−	1.28432i	0.766571	−	0.642160i	$-0.221961\pi$
$812$		0			0
$813$	−41.3049	+	6.71844i	−1.44863	+	0.235626i
$814$		0			0
$815$	5.52693	+	9.57292i	0.193600	+	0.335325i
$816$		0			0
$817$	7.39861	+	4.27159i	0.258845	+	0.149444i
$818$		0			0
$819$	8.20559	−	5.25959i	0.286726	−	0.183785i
$820$		0			0
$821$	34.8397	+	20.1147i	1.21591	+	0.702008i	0.964041	−	0.265753i	$-0.0856205\pi$
$821$	34.8397	+	20.1147i	1.21591	+	0.702008i	0.251872	+	0.967761i	$0.418954\pi$
$822$		0			0
$823$	−17.9016	−	31.0065i	−0.624011	−	1.08082i	−0.988731	−	0.149701i	$-0.952169\pi$
$823$	−17.9016	−	31.0065i	−0.624011	−	1.08082i	0.364720	−	0.931117i	$-0.381165\pi$
$824$		0			0
$825$	1.29886	−	3.42620i	0.0452204	−	0.119285i
$826$		0			0
$827$		−	32.0733i		−	1.11530i	−0.830077	−	0.557648i	$-0.811704\pi$
$827$		−	32.0733i		−	1.11530i	0.830077	−	0.557648i	$-0.188296\pi$
$828$		0			0
$829$	−14.0640	−	8.11986i	−0.488463	−	0.282014i	0.235474	−	0.971881i	$-0.424336\pi$
$829$	−14.0640	−	8.11986i	−0.488463	−	0.282014i	−0.723937	+	0.689866i	$0.757669\pi$
$830$		0			0
$831$	18.4163	+	6.98152i	0.638854	+	0.242186i
$832$		0			0
$833$	0.885474	−	30.9976i	0.0306799	−	1.07400i
$834$		0			0
$835$	13.8248	−	23.9453i	0.478429	−	0.828663i
$836$		0			0
$837$	−10.8982	−	6.88540i	−0.376697	−	0.237994i
$838$		0			0
$839$	1.35145	+	2.34077i	0.0466571	+	0.0808125i	0.888411	−	0.459049i	$-0.151810\pi$
$839$	1.35145	+	2.34077i	0.0466571	+	0.0808125i	−0.841754	+	0.539862i	$0.818477\pi$
$840$		0			0
$841$	2.67914	−	4.64041i	0.0923842	−	0.160014i
$842$		0			0
$843$	−34.8188	+	5.66346i	−1.19922	+	0.195060i
$844$		0			0
$845$	−7.19974	−	12.4703i	−0.247679	−	0.428992i
$846$		0			0
$847$	6.88375	+	27.2405i	0.236528	+	0.935996i
$848$		0			0
$849$	20.7904	−	3.38167i	0.713526	−	0.116058i
$850$		0			0
$851$	−10.9575	+	6.32632i	−0.375619	+	0.216864i
$852$		0			0
$853$	−41.3187	+	23.8554i	−1.41473	+	0.816793i	−0.995829	−	0.0912411i	$-0.970917\pi$
$853$	−41.3187	+	23.8554i	−1.41473	+	0.816793i	−0.418897	+	0.908034i	$0.637583\pi$
$854$		0			0
$855$	7.00378	+	1.42785i	0.239524	+	0.0488316i
$856$		0			0
$857$	17.8795			0.610751			0.305375	−	0.952232i	$-0.401218\pi$
$857$	17.8795			0.610751			0.305375	+	0.952232i	$0.401218\pi$
$858$		0			0
$859$			33.7058i			1.15003i	0.818144	+	0.575014i	$0.195003\pi$
$859$			33.7058i			1.15003i	−0.818144	+	0.575014i	$0.804997\pi$
$860$		0			0
$861$	−15.4532	−	11.4681i	−0.526645	−	0.390830i
$862$		0			0
$863$	16.4318	−	9.48693i	0.559347	−	0.322939i	−0.193537	−	0.981093i	$-0.561996\pi$
$863$	16.4318	−	9.48693i	0.559347	−	0.322939i	0.752883	+	0.658154i	$0.228662\pi$
$864$		0			0
$865$	2.54826	−	4.41371i	0.0866434	−	0.150071i
$866$		0			0
$867$	0.729981	+	4.48791i	0.0247915	+	0.152417i
$868$		0			0
$869$	2.15351	+	1.24333i	0.0730530	+	0.0421772i
$870$		0			0
$871$		−	16.7159i		−	0.566397i
$872$		0			0
$873$	−29.7518	−	6.06547i	−1.00695	−	0.205285i
$874$		0			0
$875$	−6.84685	−	27.0946i	−0.231466	−	0.915963i
$876$		0			0
$877$	37.2376			1.25742			0.628712	−	0.777638i	$-0.283582\pi$
$877$	37.2376			1.25742			0.628712	+	0.777638i	$0.283582\pi$
$878$		0			0
$879$	−36.1332	+	29.5100i	−1.21874	+	0.995347i
$880$		0			0
$881$	−4.71527			−0.158862			−0.0794308	−	0.996840i	$-0.525310\pi$
$881$	−4.71527			−0.158862			−0.0794308	+	0.996840i	$0.525310\pi$
$882$		0			0
$883$	−30.1766			−1.01552			−0.507762	−	0.861497i	$-0.669527\pi$
$883$	−30.1766			−1.01552			−0.507762	+	0.861497i	$0.669527\pi$
$884$		0			0
$885$	1.24197	+	7.63564i	0.0417485	+	0.256669i
$886$		0			0
$887$	−38.4434			−1.29080			−0.645402	−	0.763843i	$-0.723310\pi$
$887$	−38.4434			−1.29080			−0.645402	+	0.763843i	$0.723310\pi$
$888$		0			0
$889$	1.90039	+	7.52027i	0.0637370	+	0.252222i
$890$		0			0
$891$	5.50997	−	0.672063i	0.184591	−	0.0225149i
$892$		0			0
$893$			14.4799i			0.484550i
$894$		0			0
$895$	−9.03135	−	5.21425i	−0.301885	−	0.174293i
$896$		0			0
$897$	−7.82286	+	6.38894i	−0.261198	+	0.213320i
$898$		0			0
$899$	−7.27098	+	12.5937i	−0.242501	+	0.420023i
$900$		0			0
$901$	−11.8628	+	6.84900i	−0.395208	+	0.228173i
$902$		0			0
$903$	18.8921	−	8.18334i	0.628691	−	0.272325i
$904$		0			0
$905$		−	15.8755i		−	0.527719i
$906$		0			0
$907$	−43.5902			−1.44739			−0.723695	−	0.690120i	$-0.757558\pi$
$907$	−43.5902			−1.44739			−0.723695	+	0.690120i	$0.757558\pi$
$908$		0			0
$909$	−3.84802	−	3.40719i	−0.127631	−	0.113009i
$910$		0			0
$911$	1.67736	−	0.968423i	0.0555734	−	0.0320853i	−0.471956	−	0.881622i	$-0.656452\pi$
$911$	1.67736	−	0.968423i	0.0555734	−	0.0320853i	0.527529	+	0.849537i	$0.323119\pi$
$912$		0			0
$913$	−4.66585	+	2.69383i	−0.154417	+	0.0891528i
$914$		0			0
$915$	−19.8360	−	24.2879i	−0.655756	−	0.802934i
$916$		0			0
$917$	−10.5189	−	41.6258i	−0.347366	−	1.37460i
$918$		0			0
$919$	−4.61421	−	7.99205i	−0.152209	−	0.263634i	0.779830	−	0.625991i	$-0.215305\pi$
$919$	−4.61421	−	7.99205i	−0.152209	−	0.263634i	−0.932039	+	0.362357i	$0.881972\pi$
$920$		0			0
$921$	13.1206	−	34.6104i	0.432339	−	1.14045i
$922$		0			0
$923$	6.39118	−	11.0698i	0.210368	−	0.364368i
$924$		0			0
$925$	−4.56937	−	7.91438i	−0.150240	−	0.260223i
$926$		0			0
$927$	14.7273	−	16.6327i	0.483707	−	0.546291i
$928$		0			0
$929$	26.6849	−	46.2197i	0.875504	−	1.51642i	0.0192794	−	0.999814i	$-0.493863\pi$
$929$	26.6849	−	46.2197i	0.875504	−	1.51642i	0.856225	−	0.516603i	$-0.172804\pi$
$930$		0			0
$931$	−6.98187	+	11.3328i	−0.228822	+	0.371417i
$932$		0			0
$933$	4.51343	+	27.7485i	0.147763	+	0.908446i
$934$		0			0
$935$	2.96481	+	1.71173i	0.0969595	+	0.0559796i
$936$		0			0
$937$		−	28.6378i		−	0.935555i	−0.883846	−	0.467778i	$-0.845055\pi$
$937$		−	28.6378i		−	0.935555i	0.883846	−	0.467778i	$-0.154945\pi$
$938$		0			0
$939$	−15.4268	−	18.8891i	−0.503434	−	0.616424i
$940$		0			0
$941$	−0.688308	−	1.19218i	−0.0224382	−	0.0388641i	0.854588	−	0.519306i	$-0.173810\pi$
$941$	−0.688308	−	1.19218i	−0.0224382	−	0.0388641i	−0.877026	+	0.480442i	$0.840476\pi$
$942$		0			0
$943$	17.2704	+	9.97105i	0.562401	+	0.324702i
$944$		0			0
$945$	12.8218	−	11.5033i	0.417093	−	0.374203i
$946$		0			0
$947$	47.0080	+	27.1401i	1.52755	+	0.881933i	0.999464	+	0.0327450i	$0.0104249\pi$
$947$	47.0080	+	27.1401i	1.52755	+	0.881933i	0.528090	+	0.849188i	$0.322908\pi$
$948$		0			0
$949$	−7.05423	−	12.2183i	−0.228990	−	0.396622i
$950$		0			0
$951$	−22.2374	−	27.2283i	−0.721097	−	0.882939i
$952$		0			0
$953$		−	11.2998i		−	0.366036i	−0.983110	−	0.183018i	$-0.941413\pi$
$953$		−	11.2998i		−	0.366036i	0.983110	−	0.183018i	$-0.0585867\pi$
$954$		0			0
$955$	4.12399	+	2.38099i	0.133449	+	0.0770469i
$956$		0			0
$957$	−1.00528	−	6.18044i	−0.0324960	−	0.199785i
$958$		0			0
$959$	−44.6397	+	11.2805i	−1.44149	+	0.364268i
$960$		0			0
$961$	−12.4226	+	21.5166i	−0.400729	+	0.694083i
$962$		0			0
$963$	0.446882	+	0.0911054i	0.0144006	+	0.00293583i
$964$		0			0
$965$	−4.25324	−	7.36682i	−0.136917	−	0.237146i
$966$		0			0
$967$	−5.93412	+	10.2782i	−0.190829	+	0.330525i	−0.945525	−	0.325549i	$-0.894451\pi$
$967$	−5.93412	+	10.2782i	−0.190829	+	0.330525i	0.754696	+	0.656074i	$0.227784\pi$
$968$		0			0
$969$	5.17207	−	13.6432i	0.166151	−	0.438283i
$970$		0			0
$971$	−28.0837	−	48.6424i	−0.901249	−	1.56101i	−0.825875	−	0.563853i	$-0.809318\pi$
$971$	−28.0837	−	48.6424i	−0.901249	−	1.56101i	−0.0753736	−	0.997155i	$-0.524015\pi$
$972$		0			0
$973$	4.54081	−	16.0275i	0.145572	−	0.513819i
$974$		0			0
$975$	−4.61459	−	5.65029i	−0.147785	−	0.180954i
$976$		0			0
$977$	18.7626	−	10.8326i	0.600268	−	0.346565i	−0.168879	−	0.985637i	$-0.554015\pi$
$977$	18.7626	−	10.8326i	0.600268	−	0.346565i	0.769147	+	0.639072i	$0.220681\pi$
$978$		0			0
$979$	−0.866594	+	0.500328i	−0.0276964	+	0.0159906i
$980$		0			0
$981$	15.3678	−	5.13516i	0.490656	−	0.163953i
$982$		0			0
$983$	19.4001			0.618768			0.309384	−	0.950937i	$-0.399877\pi$
$983$	19.4001			0.618768			0.309384	+	0.950937i	$0.399877\pi$
$984$		0			0
$985$			8.03731i			0.256090i
$986$		0			0
$987$	28.0219	+	20.7954i	0.891947	+	0.661926i
$988$		0			0
$989$	−18.4771	+	10.6678i	−0.587539	+	0.339216i
$990$		0			0
$991$	12.6630	−	21.9330i	0.402254	−	0.696725i	−0.591743	−	0.806126i	$-0.701560\pi$
$991$	12.6630	−	21.9330i	0.402254	−	0.696725i	0.993998	+	0.109402i	$0.0348934\pi$
$992$		0			0
$993$	−35.5072	+	28.9988i	−1.12679	+	0.920248i
$994$		0			0
$995$	17.4066	+	10.0497i	0.551828	+	0.318598i
$996$		0			0
$997$			5.56584i			0.176272i	0.996108	+	0.0881360i	$0.0280910\pi$
$997$			5.56584i			0.176272i	−0.996108	+	0.0881360i	$0.971909\pi$
$998$		0			0
$999$	7.39454	−	11.7041i	0.233953	−	0.370300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.b.689.1		10
3.2	odd	2		3024.2.df.b.17.2		10
4.3	odd	2		63.2.s.b.59.1	yes	10
7.5	odd	6		1008.2.ca.b.257.1		10
9.2	odd	6		1008.2.ca.b.353.1		10
9.7	even	3		3024.2.ca.b.2033.2		10
12.11	even	2		189.2.s.b.17.5		10
21.5	even	6		3024.2.ca.b.2609.2		10
28.3	even	6		441.2.o.d.293.5		10
28.11	odd	6		441.2.o.c.293.5		10
28.19	even	6		63.2.i.b.5.5	✓	10
28.23	odd	6		441.2.i.b.68.5		10
28.27	even	2		441.2.s.b.374.1		10
36.7	odd	6		189.2.i.b.143.5		10
36.11	even	6		63.2.i.b.38.1	yes	10
36.23	even	6		567.2.p.d.80.1		10
36.31	odd	6		567.2.p.c.80.5		10
63.47	even	6	inner	1008.2.df.b.929.1		10
63.61	odd	6		3024.2.df.b.1601.2		10
84.11	even	6		1323.2.o.d.881.1		10
84.23	even	6		1323.2.i.b.1097.1		10
84.47	odd	6		189.2.i.b.152.1		10
84.59	odd	6		1323.2.o.c.881.1		10
84.83	odd	2		1323.2.s.b.962.5		10
252.11	even	6		441.2.o.d.146.5		10
252.47	odd	6		63.2.s.b.47.1	yes	10
252.79	odd	6		1323.2.s.b.656.5		10
252.83	odd	6		441.2.i.b.227.1		10
252.103	even	6		567.2.p.d.404.1		10
252.115	even	6		1323.2.o.d.440.1		10
252.131	odd	6		567.2.p.c.404.5		10
252.151	odd	6		1323.2.o.c.440.1		10
252.187	even	6		189.2.s.b.89.5		10
252.191	even	6		441.2.s.b.362.1		10
252.223	even	6		1323.2.i.b.521.5		10
252.227	odd	6		441.2.o.c.146.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.5	✓	10	28.19	even	6
63.2.i.b.38.1	yes	10	36.11	even	6
63.2.s.b.47.1	yes	10	252.47	odd	6
63.2.s.b.59.1	yes	10	4.3	odd	2
189.2.i.b.143.5		10	36.7	odd	6
189.2.i.b.152.1		10	84.47	odd	6
189.2.s.b.17.5		10	12.11	even	2
189.2.s.b.89.5		10	252.187	even	6
441.2.i.b.68.5		10	28.23	odd	6
441.2.i.b.227.1		10	252.83	odd	6
441.2.o.c.146.5		10	252.227	odd	6
441.2.o.c.293.5		10	28.11	odd	6
441.2.o.d.146.5		10	252.11	even	6
441.2.o.d.293.5		10	28.3	even	6
441.2.s.b.362.1		10	252.191	even	6
441.2.s.b.374.1		10	28.27	even	2
567.2.p.c.80.5		10	36.31	odd	6
567.2.p.c.404.5		10	252.131	odd	6
567.2.p.d.80.1		10	36.23	even	6
567.2.p.d.404.1		10	252.103	even	6
1008.2.ca.b.257.1		10	7.5	odd	6
1008.2.ca.b.353.1		10	9.2	odd	6
1008.2.df.b.689.1		10	1.1	even	1	trivial
1008.2.df.b.929.1		10	63.47	even	6	inner
1323.2.i.b.521.5		10	252.223	even	6
1323.2.i.b.1097.1		10	84.23	even	6
1323.2.o.c.440.1		10	252.151	odd	6
1323.2.o.c.881.1		10	84.59	odd	6
1323.2.o.d.440.1		10	252.115	even	6
1323.2.o.d.881.1		10	84.11	even	6
1323.2.s.b.656.5		10	252.79	odd	6
1323.2.s.b.962.5		10	84.83	odd	2
3024.2.ca.b.2033.2		10	9.7	even	3
3024.2.ca.b.2609.2		10	21.5	even	6
3024.2.df.b.17.2		10	3.2	odd	2
3024.2.df.b.1601.2		10	63.61	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.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61958 - 0.613974i) q^{3} +1.25299 q^{5} +(0.648211 + 2.56512i) q^{7} +(2.24607 + 1.98876i) q^{9} -0.616756i q^{11} +(-1.06343 - 0.613974i) q^{13} +(-2.02931 - 0.769301i) q^{15} +(-2.21501 + 3.83652i) q^{17} +(1.64679 - 0.950775i) q^{19} +(0.525087 - 4.55239i) q^{21} +4.74890i q^{23} -3.43003 q^{25} +(-2.41664 - 4.59998i) q^{27} +(-5.07629 + 2.93080i) q^{29} +(2.14851 - 1.24044i) q^{31} +(-0.378672 + 0.998884i) q^{33} +(0.812198 + 3.21405i) q^{35} +(1.33217 + 2.30738i) q^{37} +(1.34535 + 1.64730i) q^{39} +(2.09966 - 3.63671i) q^{41} +(2.24637 + 3.89083i) q^{43} +(2.81429 + 2.49189i) q^{45} +(-3.80738 + 6.59458i) q^{47} +(-6.15965 + 3.32547i) q^{49} +(5.94291 - 4.85358i) q^{51} +(2.67782 + 1.54604i) q^{53} -0.772786i q^{55} +(-3.25086 + 0.528768i) q^{57} +(-1.78229 - 3.08702i) q^{59} +(12.5136 + 7.22473i) q^{61} +(-3.64547 + 7.05057i) q^{63} +(-1.33247 - 0.769301i) q^{65} +(6.80644 + 11.7891i) q^{67} +(2.91570 - 7.69121i) q^{69} +10.4095i q^{71} +(9.95016 + 5.74473i) q^{73} +(5.55520 + 2.10595i) q^{75} +(1.58205 - 0.399788i) q^{77} +(-2.01592 + 3.49168i) q^{79} +(1.08967 + 8.93379i) q^{81} +(-4.36775 - 7.56516i) q^{83} +(-2.77538 + 4.80710i) q^{85} +(10.0209 - 1.62995i) q^{87} +(-0.811226 - 1.40508i) q^{89} +(0.885586 - 3.12582i) q^{91} +(-4.24128 + 0.689866i) q^{93} +(2.06341 - 1.19131i) q^{95} +(-8.76527 + 5.06063i) q^{97} +(1.22658 - 1.38528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{7} + 6 q^{13} + 3 q^{15} - 12 q^{17} - 3 q^{19} + 18 q^{21} - 14 q^{25} - 27 q^{27} - 15 q^{29} + 9 q^{31} - 9 q^{33} + 15 q^{35} + 6 q^{37} - 12 q^{39} - 9 q^{41} - 3 q^{43} + 15 q^{45} - 15 q^{47}+ \cdots - 21 q^{99}+O(q^{100}) \) 10 * q - 3 * q^7 + 6 * q^13 + 3 * q^15 - 12 * q^17 - 3 * q^19 + 18 * q^21 - 14 * q^25 - 27 * q^27 - 15 * q^29 + 9 * q^31 - 9 * q^33 + 15 * q^35 + 6 * q^37 - 12 * q^39 - 9 * q^41 - 3 * q^43 + 15 * q^45 - 15 * q^47 - 23 * q^49 + 24 * q^51 - 9 * q^53 - 36 * q^57 + 18 * q^59 + 12 * q^61 - 9 * q^63 - 3 * q^65 + 10 * q^67 - 3 * q^69 + 3 * q^73 + 21 * q^75 + 45 * q^77 - 20 * q^79 - 48 * q^81 + 15 * q^83 + 18 * q^85 - 30 * q^87 + 24 * q^89 + 24 * q^91 + 6 * q^93 + 6 * q^97 - 21 * q^99

Introduction

L-functions

Modular forms

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Database

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