LMFDB - Embedded newform 1456.2.s.o.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(113,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1456.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.s (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			113.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1456.113
Dual form			1456.2.s.o.1121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 0.633975i) q^{3} -1.73205 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.23205 + 2.13397i) q^{9} +O(q^{10})$	\(q+(-0.366025 + 0.633975i) q^{3} -1.73205 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.23205 + 2.13397i) q^{9} +(2.36603 - 4.09808i) q^{11} +(-1.59808 - 3.23205i) q^{13} +(0.633975 - 1.09808i) q^{15} +(2.13397 + 3.69615i) q^{17} +(1.00000 + 1.73205i) q^{19} -0.732051 q^{21} +(0.633975 - 1.09808i) q^{23} -2.00000 q^{25} -4.00000 q^{27} +(1.50000 - 2.59808i) q^{29} +6.19615 q^{31} +(1.73205 + 3.00000i) q^{33} +(-0.866025 - 1.50000i) q^{35} +(3.50000 - 6.06218i) q^{37} +(2.63397 + 0.169873i) q^{39} +(-2.59808 + 4.50000i) q^{41} +(5.09808 + 8.83013i) q^{43} +(-2.13397 - 3.69615i) q^{45} +0.928203 q^{47} +(-0.500000 + 0.866025i) q^{49} -3.12436 q^{51} +3.92820 q^{53} +(-4.09808 + 7.09808i) q^{55} -1.46410 q^{57} +(5.36603 + 9.29423i) q^{59} +(7.59808 + 13.1603i) q^{61} +(-1.23205 + 2.13397i) q^{63} +(2.76795 + 5.59808i) q^{65} +(2.09808 - 3.63397i) q^{67} +(0.464102 + 0.803848i) q^{69} +(3.00000 + 5.19615i) q^{71} +7.19615 q^{73} +(0.732051 - 1.26795i) q^{75} +4.73205 q^{77} -5.80385 q^{79} +(-2.23205 + 3.86603i) q^{81} -8.19615 q^{83} +(-3.69615 - 6.40192i) q^{85} +(1.09808 + 1.90192i) q^{87} +(0.464102 - 0.803848i) q^{89} +(2.00000 - 3.00000i) q^{91} +(-2.26795 + 3.92820i) q^{93} +(-1.73205 - 3.00000i) q^{95} +(7.19615 + 12.4641i) q^{97} +11.6603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{13} + 6 q^{15} + 12 q^{17} + 4 q^{19} + 4 q^{21} + 6 q^{23} - 8 q^{25} - 16 q^{27} + 6 q^{29} + 4 q^{31} + 14 q^{37} + 14 q^{39} + 10 q^{43} - 12 q^{45} - 24 q^{47} - 2 q^{49} + 36 q^{51} - 12 q^{53} - 6 q^{55} + 8 q^{57} + 18 q^{59} + 20 q^{61} + 2 q^{63} + 18 q^{65} - 2 q^{67} - 12 q^{69} + 12 q^{71} + 8 q^{73} - 4 q^{75} + 12 q^{77} - 44 q^{79} - 2 q^{81} - 12 q^{83} + 6 q^{85} - 6 q^{87} - 12 q^{89} + 8 q^{91} - 16 q^{93} + 8 q^{97} + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^7 - 2 * q^9 + 6 * q^11 + 4 * q^13 + 6 * q^15 + 12 * q^17 + 4 * q^19 + 4 * q^21 + 6 * q^23 - 8 * q^25 - 16 * q^27 + 6 * q^29 + 4 * q^31 + 14 * q^37 + 14 * q^39 + 10 * q^43 - 12 * q^45 - 24 * q^47 - 2 * q^49 + 36 * q^51 - 12 * q^53 - 6 * q^55 + 8 * q^57 + 18 * q^59 + 20 * q^61 + 2 * q^63 + 18 * q^65 - 2 * q^67 - 12 * q^69 + 12 * q^71 + 8 * q^73 - 4 * q^75 + 12 * q^77 - 44 * q^79 - 2 * q^81 - 12 * q^83 + 6 * q^85 - 6 * q^87 - 12 * q^89 + 8 * q^91 - 16 * q^93 + 8 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.366025	+	0.633975i	−0.211325	+	0.366025i	−0.952129	−	0.305695i	$-0.901111\pi$
$3$	−0.366025	+	0.633975i	−0.211325	+	0.366025i	0.740805	+	0.671721i	$0.234444\pi$
$4$		0			0
$5$	−1.73205			−0.774597			−0.387298	−	0.921954i	$-0.626592\pi$
$5$	−1.73205			−0.774597			−0.387298	+	0.921954i	$0.626592\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$		0			0
$9$	1.23205	+	2.13397i	0.410684	+	0.711325i
$10$		0			0
$11$	2.36603	−	4.09808i	0.713384	−	1.23562i	−0.250196	−	0.968195i	$-0.580495\pi$
$11$	2.36603	−	4.09808i	0.713384	−	1.23562i	0.963580	−	0.267421i	$-0.0861715\pi$
$12$		0			0
$13$	−1.59808	−	3.23205i	−0.443227	−	0.896410i
$13$	−1.59808	−	3.23205i	−0.443227	−	0.896410i
$14$		0			0
$15$	0.633975	−	1.09808i	0.163692	−	0.283522i
$16$		0			0
$17$	2.13397	+	3.69615i	0.517565	+	0.896449i	0.999792	+	0.0204023i	$0.00649471\pi$
$17$	2.13397	+	3.69615i	0.517565	+	0.896449i	−0.482227	+	0.876046i	$0.660172\pi$
$18$		0			0
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$	−0.732051			−0.159747
$22$		0			0
$23$	0.633975	−	1.09808i	0.132193	−	0.228965i	−0.792329	−	0.610094i	$-0.791132\pi$
$23$	0.633975	−	1.09808i	0.132193	−	0.228965i	0.924522	+	0.381130i	$0.124465\pi$
$24$		0			0
$25$	−2.00000			−0.400000
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		0			0
$31$	6.19615			1.11286			0.556431	−	0.830894i	$-0.312170\pi$
$31$	6.19615			1.11286			0.556431	+	0.830894i	$0.312170\pi$
$32$		0			0
$33$	1.73205	+	3.00000i	0.301511	+	0.522233i
$34$		0			0
$35$	−0.866025	−	1.50000i	−0.146385	−	0.253546i
$36$		0			0
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$		0			0
$39$	2.63397	+	0.169873i	0.421773	+	0.0272014i
$40$		0			0
$41$	−2.59808	+	4.50000i	−0.405751	+	0.702782i	−0.994409	−	0.105601i	$-0.966323\pi$
$41$	−2.59808	+	4.50000i	−0.405751	+	0.702782i	0.588657	+	0.808383i	$0.299657\pi$
$42$		0			0
$43$	5.09808	+	8.83013i	0.777449	+	1.34658i	0.933408	+	0.358818i	$0.116820\pi$
$43$	5.09808	+	8.83013i	0.777449	+	1.34658i	−0.155958	+	0.987764i	$0.549847\pi$
$44$		0			0
$45$	−2.13397	−	3.69615i	−0.318114	−	0.550990i
$46$		0			0
$47$	0.928203			0.135392			0.0676962	−	0.997706i	$-0.478435\pi$
$47$	0.928203			0.135392			0.0676962	+	0.997706i	$0.478435\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−3.12436			−0.437497
$52$		0			0
$53$	3.92820			0.539580			0.269790	−	0.962919i	$-0.413046\pi$
$53$	3.92820			0.539580			0.269790	+	0.962919i	$0.413046\pi$
$54$		0			0
$55$	−4.09808	+	7.09808i	−0.552584	+	0.957104i
$56$		0			0
$57$	−1.46410			−0.193925
$58$		0			0
$59$	5.36603	+	9.29423i	0.698597	+	1.21001i	0.968953	+	0.247245i	$0.0795253\pi$
$59$	5.36603	+	9.29423i	0.698597	+	1.21001i	−0.270356	+	0.962760i	$0.587141\pi$
$60$		0			0
$61$	7.59808	+	13.1603i	0.972834	+	1.68500i	0.686905	+	0.726747i	$0.258969\pi$
$61$	7.59808	+	13.1603i	0.972834	+	1.68500i	0.285929	+	0.958251i	$0.407698\pi$
$62$		0			0
$63$	−1.23205	+	2.13397i	−0.155224	+	0.268856i
$64$		0			0
$65$	2.76795	+	5.59808i	0.343322	+	0.694356i
$66$		0			0
$67$	2.09808	−	3.63397i	0.256321	−	0.443961i	−0.708933	−	0.705276i	$-0.750823\pi$
$67$	2.09808	−	3.63397i	0.256321	−	0.443961i	0.965253	+	0.261316i	$0.0841563\pi$
$68$		0			0
$69$	0.464102	+	0.803848i	0.0558713	+	0.0967719i
$70$		0			0
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$	7.19615			0.842246			0.421123	−	0.907004i	$-0.361636\pi$
$73$	7.19615			0.842246			0.421123	+	0.907004i	$0.361636\pi$
$74$		0			0
$75$	0.732051	−	1.26795i	0.0845299	−	0.146410i
$76$		0			0
$77$	4.73205			0.539267
$78$		0			0
$79$	−5.80385			−0.652984			−0.326492	−	0.945200i	$-0.605867\pi$
$79$	−5.80385			−0.652984			−0.326492	+	0.945200i	$0.605867\pi$
$80$		0			0
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$		0			0
$83$	−8.19615			−0.899645			−0.449822	−	0.893118i	$-0.648513\pi$
$83$	−8.19615			−0.899645			−0.449822	+	0.893118i	$0.648513\pi$
$84$		0			0
$85$	−3.69615	−	6.40192i	−0.400904	−	0.694386i
$86$		0			0
$87$	1.09808	+	1.90192i	0.117726	+	0.203908i
$88$		0			0
$89$	0.464102	−	0.803848i	0.0491947	−	0.0852077i	−0.840379	−	0.541998i	$-0.817668\pi$
$89$	0.464102	−	0.803848i	0.0491947	−	0.0852077i	0.889574	+	0.456791i	$0.151001\pi$
$90$		0			0
$91$	2.00000	−	3.00000i	0.209657	−	0.314485i
$92$		0			0
$93$	−2.26795	+	3.92820i	−0.235175	+	0.407336i
$94$		0			0
$95$	−1.73205	−	3.00000i	−0.177705	−	0.307794i
$96$		0			0
$97$	7.19615	+	12.4641i	0.730659	+	1.26554i	0.956602	+	0.291397i	$0.0941202\pi$
$97$	7.19615	+	12.4641i	0.730659	+	1.26554i	−0.225944	+	0.974140i	$0.572546\pi$
$98$		0			0
$99$	11.6603			1.17190
$100$		0			0
$101$	2.13397	−	3.69615i	0.212338	−	0.367781i	−0.740108	−	0.672489i	$-0.765225\pi$
$101$	2.13397	−	3.69615i	0.212338	−	0.367781i	0.952446	+	0.304708i	$0.0985588\pi$
$102$		0			0
$103$	−6.39230			−0.629853			−0.314926	−	0.949116i	$-0.601980\pi$
$103$	−6.39230			−0.629853			−0.314926	+	0.949116i	$0.601980\pi$
$104$		0			0
$105$	1.26795			0.123739
$106$		0			0
$107$	9.92820	−	17.1962i	0.959796	−	1.66241i	0.236805	−	0.971557i	$-0.423900\pi$
$107$	9.92820	−	17.1962i	0.959796	−	1.66241i	0.722991	−	0.690858i	$-0.242767\pi$
$108$		0			0
$109$	12.3923			1.18697			0.593484	−	0.804846i	$-0.297752\pi$
$109$	12.3923			1.18697			0.593484	+	0.804846i	$0.297752\pi$
$110$		0			0
$111$	2.56218	+	4.43782i	0.243191	+	0.421219i
$112$		0			0
$113$	3.69615	+	6.40192i	0.347705	+	0.602242i	0.985841	−	0.167681i	$-0.0536278\pi$
$113$	3.69615	+	6.40192i	0.347705	+	0.602242i	−0.638137	+	0.769923i	$0.720294\pi$
$114$		0			0
$115$	−1.09808	+	1.90192i	−0.102396	+	0.177355i
$116$		0			0
$117$	4.92820	−	7.39230i	0.455613	−	0.683419i
$118$		0			0
$119$	−2.13397	+	3.69615i	−0.195621	+	0.338826i
$120$		0			0
$121$	−5.69615	−	9.86603i	−0.517832	−	0.896911i
$122$		0			0
$123$	−1.90192	−	3.29423i	−0.171491	−	0.297031i
$124$		0			0
$125$	12.1244			1.08444
$126$		0			0
$127$	−1.19615	+	2.07180i	−0.106141	+	0.183842i	−0.914204	−	0.405254i	$-0.867183\pi$
$127$	−1.19615	+	2.07180i	−0.106141	+	0.183842i	0.808063	+	0.589097i	$0.200516\pi$
$128$		0			0
$129$	−7.46410			−0.657178
$130$		0			0
$131$	−3.46410			−0.302660			−0.151330	−	0.988483i	$-0.548356\pi$
$131$	−3.46410			−0.302660			−0.151330	+	0.988483i	$0.548356\pi$
$132$		0			0
$133$	−1.00000	+	1.73205i	−0.0867110	+	0.150188i
$134$		0			0
$135$	6.92820			0.596285
$136$		0			0
$137$	−10.9641	−	18.9904i	−0.936726	−	1.62246i	−0.771526	−	0.636198i	$-0.780506\pi$
$137$	−10.9641	−	18.9904i	−0.936726	−	1.62246i	−0.165200	−	0.986260i	$-0.552827\pi$
$138$		0			0
$139$	10.2942	+	17.8301i	0.873145	+	1.51233i	0.858726	+	0.512436i	$0.171257\pi$
$139$	10.2942	+	17.8301i	0.873145	+	1.51233i	0.0144194	+	0.999896i	$0.495410\pi$
$140$		0			0
$141$	−0.339746	+	0.588457i	−0.0286118	+	0.0495570i
$142$		0			0
$143$	−17.0263	−	1.09808i	−1.42381	−	0.0918257i
$144$		0			0
$145$	−2.59808	+	4.50000i	−0.215758	+	0.373705i
$146$		0			0
$147$	−0.366025	−	0.633975i	−0.0301893	−	0.0522893i
$148$		0			0
$149$	−0.232051	−	0.401924i	−0.0190103	−	0.0329269i	0.856364	−	0.516373i	$-0.172718\pi$
$149$	−0.232051	−	0.401924i	−0.0190103	−	0.0329269i	−0.875374	+	0.483446i	$0.839385\pi$
$150$		0			0
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$		0			0
$153$	−5.25833	+	9.10770i	−0.425111	+	0.736314i
$154$		0			0
$155$	−10.7321			−0.862019
$156$		0			0
$157$	−9.19615			−0.733933			−0.366966	−	0.930234i	$-0.619604\pi$
$157$	−9.19615			−0.733933			−0.366966	+	0.930234i	$0.619604\pi$
$158$		0			0
$159$	−1.43782	+	2.49038i	−0.114027	+	0.197500i
$160$		0			0
$161$	1.26795			0.0999284
$162$		0			0
$163$	2.90192	+	5.02628i	0.227296	+	0.393689i	0.957006	−	0.290069i	$-0.0936781\pi$
$163$	2.90192	+	5.02628i	0.227296	+	0.393689i	−0.729710	+	0.683757i	$0.760345\pi$
$164$		0			0
$165$	−3.00000	−	5.19615i	−0.233550	−	0.404520i
$166$		0			0
$167$	12.2942	−	21.2942i	0.951356	−	1.64780i	0.208861	−	0.977945i	$-0.433024\pi$
$167$	12.2942	−	21.2942i	0.951356	−	1.64780i	0.742495	−	0.669852i	$-0.233642\pi$
$168$		0			0
$169$	−7.89230	+	10.3301i	−0.607100	+	0.794625i
$170$		0			0
$171$	−2.46410	+	4.26795i	−0.188435	+	0.326378i
$172$		0			0
$173$	−7.73205	−	13.3923i	−0.587857	−	1.01820i	−0.994513	−	0.104617i	$-0.966638\pi$
$173$	−7.73205	−	13.3923i	−0.587857	−	1.01820i	0.406656	−	0.913581i	$-0.366695\pi$
$174$		0			0
$175$	−1.00000	−	1.73205i	−0.0755929	−	0.130931i
$176$		0			0
$177$	−7.85641			−0.590524
$178$		0			0
$179$	3.46410	−	6.00000i	0.258919	−	0.448461i	−0.707034	−	0.707180i	$-0.749967\pi$
$179$	3.46410	−	6.00000i	0.258919	−	0.448461i	0.965953	+	0.258719i	$0.0833004\pi$
$180$		0			0
$181$	−25.5885			−1.90198			−0.950988	−	0.309229i	$-0.899929\pi$
$181$	−25.5885			−1.90198			−0.950988	+	0.309229i	$0.899929\pi$
$182$		0			0
$183$	−11.1244			−0.822336
$184$		0			0
$185$	−6.06218	+	10.5000i	−0.445700	+	0.771975i
$186$		0			0
$187$	20.1962			1.47689
$188$		0			0
$189$	−2.00000	−	3.46410i	−0.145479	−	0.251976i
$190$		0			0
$191$	0.633975	+	1.09808i	0.0458728	+	0.0794540i	0.888050	−	0.459747i	$-0.152060\pi$
$191$	0.633975	+	1.09808i	0.0458728	+	0.0794540i	−0.842177	+	0.539201i	$0.818726\pi$
$192$		0			0
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$		0			0
$195$	−4.56218	−	0.294229i	−0.326704	−	0.0210702i
$196$		0			0
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	−0.996649	−	0.0818013i	$-0.973933\pi$
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	0.569166	+	0.822222i	$0.307266\pi$
$198$		0			0
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	0.899291	−	0.437351i	$-0.144083\pi$
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	−0.828403	+	0.560133i	$0.810750\pi$
$200$		0			0
$201$	1.53590	+	2.66025i	0.108334	+	0.187640i
$202$		0			0
$203$	3.00000			0.210559
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$		0			0
$207$	3.12436			0.217158
$208$		0			0
$209$	9.46410			0.654646
$210$		0			0
$211$	−6.09808	+	10.5622i	−0.419809	+	0.727130i	−0.995920	−	0.0902411i	$-0.971236\pi$
$211$	−6.09808	+	10.5622i	−0.419809	+	0.727130i	0.576111	+	0.817371i	$0.304570\pi$
$212$		0			0
$213$	−4.39230			−0.300956
$214$		0			0
$215$	−8.83013	−	15.2942i	−0.602210	−	1.04306i
$216$		0			0
$217$	3.09808	+	5.36603i	0.210311	+	0.364270i
$218$		0			0
$219$	−2.63397	+	4.56218i	−0.177988	+	0.308283i
$220$		0			0
$221$	8.53590	−	12.8038i	0.574187	−	0.861280i
$222$		0			0
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	−0.983451	−	0.181173i	$-0.942010\pi$
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	0.648626	+	0.761107i	$0.275344\pi$
$224$		0			0
$225$	−2.46410	−	4.26795i	−0.164273	−	0.284530i
$226$		0			0
$227$	−5.83013	−	10.0981i	−0.386959	−	0.670233i	0.605080	−	0.796165i	$-0.293141\pi$
$227$	−5.83013	−	10.0981i	−0.386959	−	0.670233i	−0.992039	+	0.125932i	$0.959808\pi$
$228$		0			0
$229$	6.39230			0.422415			0.211208	−	0.977441i	$-0.432260\pi$
$229$	6.39230			0.422415			0.211208	+	0.977441i	$0.432260\pi$
$230$		0			0
$231$	−1.73205	+	3.00000i	−0.113961	+	0.197386i
$232$		0			0
$233$	25.8564			1.69391			0.846955	−	0.531665i	$-0.178433\pi$
$233$	25.8564			1.69391			0.846955	+	0.531665i	$0.178433\pi$
$234$		0			0
$235$	−1.60770			−0.104874
$236$		0			0
$237$	2.12436	−	3.67949i	0.137992	−	0.239009i
$238$		0			0
$239$	26.1962			1.69449			0.847244	−	0.531204i	$-0.178260\pi$
$239$	26.1962			1.69449			0.847244	+	0.531204i	$0.178260\pi$
$240$		0			0
$241$	5.40192	+	9.35641i	0.347969	+	0.602699i	0.985888	−	0.167404i	$-0.0535383\pi$
$241$	5.40192	+	9.35641i	0.347969	+	0.602699i	−0.637920	+	0.770103i	$0.720205\pi$
$242$		0			0
$243$	−7.63397	−	13.2224i	−0.489720	−	0.848219i
$244$		0			0
$245$	0.866025	−	1.50000i	0.0553283	−	0.0958315i
$246$		0			0
$247$	4.00000	−	6.00000i	0.254514	−	0.381771i
$248$		0			0
$249$	3.00000	−	5.19615i	0.190117	−	0.329293i
$250$		0			0
$251$	−11.1962	−	19.3923i	−0.706695	−	1.22403i	−0.966076	−	0.258256i	$-0.916852\pi$
$251$	−11.1962	−	19.3923i	−0.706695	−	1.22403i	0.259382	−	0.965775i	$-0.416481\pi$
$252$		0			0
$253$	−3.00000	−	5.19615i	−0.188608	−	0.326679i
$254$		0			0
$255$	5.41154			0.338884
$256$		0			0
$257$	9.06218	−	15.6962i	0.565283	−	0.979099i	−0.431740	−	0.901998i	$-0.642100\pi$
$257$	9.06218	−	15.6962i	0.565283	−	0.979099i	0.997023	−	0.0771011i	$-0.0245664\pi$
$258$		0			0
$259$	7.00000			0.434959
$260$		0			0
$261$	7.39230			0.457572
$262$		0			0
$263$	2.36603	−	4.09808i	0.145895	−	0.252698i	−0.783811	−	0.620999i	$-0.786727\pi$
$263$	2.36603	−	4.09808i	0.145895	−	0.252698i	0.929707	+	0.368301i	$0.120060\pi$
$264$		0			0
$265$	−6.80385			−0.417957
$266$		0			0
$267$	0.339746	+	0.588457i	0.0207921	+	0.0360130i
$268$		0			0
$269$	−9.46410	−	16.3923i	−0.577036	−	0.999456i	−0.995817	−	0.0913690i	$-0.970876\pi$
$269$	−9.46410	−	16.3923i	−0.577036	−	0.999456i	0.418781	−	0.908087i	$-0.362458\pi$
$270$		0			0
$271$	8.09808	−	14.0263i	0.491923	−	0.852036i	−0.508034	−	0.861337i	$-0.669627\pi$
$271$	8.09808	−	14.0263i	0.491923	−	0.852036i	0.999957	+	0.00930143i	$0.00296078\pi$
$272$		0			0
$273$	1.16987	+	2.36603i	0.0708039	+	0.143198i
$274$		0			0
$275$	−4.73205	+	8.19615i	−0.285353	+	0.494247i
$276$		0			0
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	−0.999923	−	0.0124177i	$-0.996047\pi$
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	0.489207	−	0.872167i	$-0.337286\pi$
$278$		0			0
$279$	7.63397	+	13.2224i	0.457034	+	0.791606i
$280$		0			0
$281$	−7.39230			−0.440988			−0.220494	−	0.975388i	$-0.570767\pi$
$281$	−7.39230			−0.440988			−0.220494	+	0.975388i	$0.570767\pi$
$282$		0			0
$283$	−0.0980762	+	0.169873i	−0.00583003	+	0.0100979i	−0.868926	−	0.494943i	$-0.835189\pi$
$283$	−0.0980762	+	0.169873i	−0.00583003	+	0.0100979i	0.863096	+	0.505040i	$0.168522\pi$
$284$		0			0
$285$	2.53590			0.150214
$286$		0			0
$287$	−5.19615			−0.306719
$288$		0			0
$289$	−0.607695	+	1.05256i	−0.0357468	+	0.0619152i
$290$		0			0
$291$	−10.5359			−0.617625
$292$		0			0
$293$	5.59808	+	9.69615i	0.327043	+	0.566455i	0.981924	−	0.189277i	$-0.0606144\pi$
$293$	5.59808	+	9.69615i	0.327043	+	0.566455i	−0.654881	+	0.755732i	$0.727281\pi$
$294$		0			0
$295$	−9.29423	−	16.0981i	−0.541131	−	0.937266i
$296$		0			0
$297$	−9.46410	+	16.3923i	−0.549163	+	0.951178i
$298$		0			0
$299$	−4.56218	−	0.294229i	−0.263838	−	0.0170157i
$300$		0			0
$301$	−5.09808	+	8.83013i	−0.293848	+	0.508960i
$302$		0			0
$303$	1.56218	+	2.70577i	0.0897448	+	0.155443i
$304$		0			0
$305$	−13.1603	−	22.7942i	−0.753554	−	1.30519i
$306$		0			0
$307$	−26.5885			−1.51748			−0.758742	−	0.651392i	$-0.774186\pi$
$307$	−26.5885			−1.51748			−0.758742	+	0.651392i	$0.774186\pi$
$308$		0			0
$309$	2.33975	−	4.05256i	0.133103	−	0.230542i
$310$		0			0
$311$	−4.73205			−0.268330			−0.134165	−	0.990959i	$-0.542835\pi$
$311$	−4.73205			−0.268330			−0.134165	+	0.990959i	$0.542835\pi$
$312$		0			0
$313$	−12.7846			−0.722629			−0.361314	−	0.932444i	$-0.617672\pi$
$313$	−12.7846			−0.722629			−0.361314	+	0.932444i	$0.617672\pi$
$314$		0			0
$315$	2.13397	−	3.69615i	0.120236	−	0.208255i
$316$		0			0
$317$	0.464102			0.0260665			0.0130333	−	0.999915i	$-0.495851\pi$
$317$	0.464102			0.0260665			0.0130333	+	0.999915i	$0.495851\pi$
$318$		0			0
$319$	−7.09808	−	12.2942i	−0.397416	−	0.688345i
$320$		0			0
$321$	7.26795	+	12.5885i	0.405657	+	0.702619i
$322$		0			0
$323$	−4.26795	+	7.39230i	−0.237475	+	0.411319i
$324$		0			0
$325$	3.19615	+	6.46410i	0.177291	+	0.358564i
$326$		0			0
$327$	−4.53590	+	7.85641i	−0.250836	+	0.434460i
$328$		0			0
$329$	0.464102	+	0.803848i	0.0255868	+	0.0443176i
$330$		0			0
$331$	−13.4904	−	23.3660i	−0.741498	−	1.28431i	−0.951813	−	0.306679i	$-0.900782\pi$
$331$	−13.4904	−	23.3660i	−0.741498	−	1.28431i	0.210315	−	0.977634i	$-0.432551\pi$
$332$		0			0
$333$	17.2487			0.945224
$334$		0			0
$335$	−3.63397	+	6.29423i	−0.198545	+	0.343890i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$		0			0
$339$	−5.41154			−0.293915
$340$		0			0
$341$	14.6603	−	25.3923i	0.793897	−	1.37507i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−0.803848	−	1.39230i	−0.0432777	−	0.0749592i
$346$		0			0
$347$	5.36603	+	9.29423i	0.288063	+	0.498940i	0.973347	−	0.229336i	$-0.0736553\pi$
$347$	5.36603	+	9.29423i	0.288063	+	0.498940i	−0.685284	+	0.728276i	$0.740322\pi$
$348$		0			0
$349$	−8.39230	+	14.5359i	−0.449230	+	0.778089i	−0.998336	−	0.0576637i	$-0.981635\pi$
$349$	−8.39230	+	14.5359i	−0.449230	+	0.778089i	0.549106	+	0.835753i	$0.314968\pi$
$350$		0			0
$351$	6.39230	+	12.9282i	0.341196	+	0.690056i
$352$		0			0
$353$	−1.66987	+	2.89230i	−0.0888784	+	0.153942i	−0.907037	−	0.421050i	$-0.861662\pi$
$353$	−1.66987	+	2.89230i	−0.0888784	+	0.153942i	0.818159	+	0.574992i	$0.194995\pi$
$354$		0			0
$355$	−5.19615	−	9.00000i	−0.275783	−	0.477670i
$356$		0			0
$357$	−1.56218	−	2.70577i	−0.0826792	−	0.143205i
$358$		0			0
$359$	−5.07180			−0.267679			−0.133840	−	0.991003i	$-0.542731\pi$
$359$	−5.07180			−0.267679			−0.133840	+	0.991003i	$0.542731\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$	8.33975			0.437723
$364$		0			0
$365$	−12.4641			−0.652401
$366$		0			0
$367$	−3.09808	+	5.36603i	−0.161718	+	0.280104i	−0.935485	−	0.353366i	$-0.885037\pi$
$367$	−3.09808	+	5.36603i	−0.161718	+	0.280104i	0.773767	+	0.633471i	$0.218370\pi$
$368$		0			0
$369$	−12.8038			−0.666542
$370$		0			0
$371$	1.96410	+	3.40192i	0.101971	+	0.176619i
$372$		0			0
$373$	−4.69615	−	8.13397i	−0.243158	−	0.421161i	0.718454	−	0.695574i	$-0.244850\pi$
$373$	−4.69615	−	8.13397i	−0.243158	−	0.421161i	−0.961612	+	0.274413i	$0.911517\pi$
$374$		0			0
$375$	−4.43782	+	7.68653i	−0.229168	+	0.396931i
$376$		0			0
$377$	−10.7942	−	0.696152i	−0.555931	−	0.0358537i
$378$		0			0
$379$	−2.29423	+	3.97372i	−0.117847	+	0.204116i	−0.918914	−	0.394458i	$-0.870932\pi$
$379$	−2.29423	+	3.97372i	−0.117847	+	0.204116i	0.801067	+	0.598574i	$0.204266\pi$
$380$		0			0
$381$	−0.875644	−	1.51666i	−0.0448606	−	0.0777009i
$382$		0			0
$383$	2.83013	+	4.90192i	0.144613	+	0.250477i	0.929228	−	0.369506i	$-0.120473\pi$
$383$	2.83013	+	4.90192i	0.144613	+	0.250477i	−0.784616	+	0.619982i	$0.787140\pi$
$384$		0			0
$385$	−8.19615			−0.417715
$386$		0			0
$387$	−12.5622	+	21.7583i	−0.638571	+	1.10604i
$388$		0			0
$389$	−30.4641			−1.54459			−0.772296	−	0.635263i	$-0.780892\pi$
$389$	−30.4641			−1.54459			−0.772296	+	0.635263i	$0.780892\pi$
$390$		0			0
$391$	5.41154			0.273673
$392$		0			0
$393$	1.26795	−	2.19615i	0.0639596	−	0.110781i
$394$		0			0
$395$	10.0526			0.505799
$396$		0			0
$397$	−11.3923	−	19.7321i	−0.571763	−	0.990323i	−0.996385	−	0.0849523i	$-0.972926\pi$
$397$	−11.3923	−	19.7321i	−0.571763	−	0.990323i	0.424622	−	0.905371i	$-0.360407\pi$
$398$		0			0
$399$	−0.732051	−	1.26795i	−0.0366484	−	0.0634769i
$400$		0			0
$401$	−8.42820	+	14.5981i	−0.420884	+	0.728993i	−0.996026	−	0.0890606i	$-0.971614\pi$
$401$	−8.42820	+	14.5981i	−0.420884	+	0.728993i	0.575142	+	0.818054i	$0.304947\pi$
$402$		0			0
$403$	−9.90192	−	20.0263i	−0.493250	−	0.997580i
$404$		0			0
$405$	3.86603	−	6.69615i	0.192104	−	0.332734i
$406$		0			0
$407$	−16.5622	−	28.6865i	−0.820957	−	1.42194i
$408$		0			0
$409$	13.5981	+	23.5526i	0.672382	+	1.16460i	0.977227	+	0.212197i	$0.0680619\pi$
$409$	13.5981	+	23.5526i	0.672382	+	1.16460i	−0.304845	+	0.952402i	$0.598605\pi$
$410$		0			0
$411$	16.0526			0.791814
$412$		0			0
$413$	−5.36603	+	9.29423i	−0.264045	+	0.457339i
$414$		0			0
$415$	14.1962			0.696862
$416$		0			0
$417$	−15.0718			−0.738069
$418$		0			0
$419$	−10.9019	+	18.8827i	−0.532594	+	0.922480i	0.466682	+	0.884425i	$0.345449\pi$
$419$	−10.9019	+	18.8827i	−0.532594	+	0.922480i	−0.999276	+	0.0380543i	$0.987884\pi$
$420$		0			0
$421$	30.1769			1.47073			0.735366	−	0.677670i	$-0.237010\pi$
$421$	30.1769			1.47073			0.735366	+	0.677670i	$0.237010\pi$
$422$		0			0
$423$	1.14359	+	1.98076i	0.0556034	+	0.0963079i
$424$		0			0
$425$	−4.26795	−	7.39230i	−0.207026	−	0.358579i
$426$		0			0
$427$	−7.59808	+	13.1603i	−0.367697	+	0.636869i
$428$		0			0
$429$	6.92820	−	10.3923i	0.334497	−	0.501745i
$430$		0			0
$431$	17.6603	−	30.5885i	0.850665	−	1.47339i	−0.0299451	−	0.999552i	$-0.509533\pi$
$431$	17.6603	−	30.5885i	0.850665	−	1.47339i	0.880610	−	0.473843i	$-0.157133\pi$
$432$		0			0
$433$	−8.79423	−	15.2321i	−0.422624	−	0.732006i	0.573572	−	0.819155i	$-0.305557\pi$
$433$	−8.79423	−	15.2321i	−0.422624	−	0.732006i	−0.996195	+	0.0871498i	$0.972224\pi$
$434$		0			0
$435$	−1.90192	−	3.29423i	−0.0911903	−	0.157946i
$436$		0			0
$437$	2.53590			0.121308
$438$		0			0
$439$	−8.29423	+	14.3660i	−0.395862	+	0.685653i	−0.993211	−	0.116329i	$-0.962887\pi$
$439$	−8.29423	+	14.3660i	−0.395862	+	0.685653i	0.597349	+	0.801982i	$0.296221\pi$
$440$		0			0
$441$	−2.46410			−0.117338
$442$		0			0
$443$	11.3205			0.537854			0.268927	−	0.963161i	$-0.413331\pi$
$443$	11.3205			0.537854			0.268927	+	0.963161i	$0.413331\pi$
$444$		0			0
$445$	−0.803848	+	1.39230i	−0.0381060	+	0.0660016i
$446$		0			0
$447$	0.339746			0.0160694
$448$		0			0
$449$	6.00000	+	10.3923i	0.283158	+	0.490443i	0.972161	−	0.234315i	$-0.0752847\pi$
$449$	6.00000	+	10.3923i	0.283158	+	0.490443i	−0.689003	+	0.724758i	$0.741951\pi$
$450$		0			0
$451$	12.2942	+	21.2942i	0.578913	+	1.00271i
$452$		0			0
$453$	0.732051	−	1.26795i	0.0343947	−	0.0595734i
$454$		0			0
$455$	−3.46410	+	5.19615i	−0.162400	+	0.243599i
$456$		0			0
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	−0.965512	−	0.260358i	$-0.916159\pi$
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	0.708233	+	0.705979i	$0.249493\pi$
$458$		0			0
$459$	−8.53590	−	14.7846i	−0.398422	−	0.690086i
$460$		0			0
$461$	−7.79423	−	13.5000i	−0.363013	−	0.628758i	0.625442	−	0.780271i	$-0.284919\pi$
$461$	−7.79423	−	13.5000i	−0.363013	−	0.628758i	−0.988455	+	0.151513i	$0.951585\pi$
$462$		0			0
$463$	−26.5885			−1.23567			−0.617835	−	0.786308i	$-0.711990\pi$
$463$	−26.5885			−1.23567			−0.617835	+	0.786308i	$0.711990\pi$
$464$		0			0
$465$	3.92820	−	6.80385i	0.182166	−	0.315521i
$466$		0			0
$467$	19.5167			0.903123			0.451562	−	0.892240i	$-0.350867\pi$
$467$	19.5167			0.903123			0.451562	+	0.892240i	$0.350867\pi$
$468$		0			0
$469$	4.19615			0.193760
$470$		0			0
$471$	3.36603	−	5.83013i	0.155098	−	0.268638i
$472$		0			0
$473$	48.2487			2.21848
$474$		0			0
$475$	−2.00000	−	3.46410i	−0.0917663	−	0.158944i
$476$		0			0
$477$	4.83975	+	8.38269i	0.221597	+	0.383817i
$478$		0			0
$479$	2.36603	−	4.09808i	0.108106	−	0.187246i	−0.806897	−	0.590693i	$-0.798855\pi$
$479$	2.36603	−	4.09808i	0.108106	−	0.187246i	0.915003	+	0.403447i	$0.132188\pi$
$480$		0			0
$481$	−25.1865	−	1.62436i	−1.14841	−	0.0740642i
$482$		0			0
$483$	−0.464102	+	0.803848i	−0.0211174	+	0.0365763i
$484$		0			0
$485$	−12.4641	−	21.5885i	−0.565966	−	0.980281i
$486$		0			0
$487$	−0.392305	−	0.679492i	−0.0177770	−	0.0307907i	0.857000	−	0.515316i	$-0.172326\pi$
$487$	−0.392305	−	0.679492i	−0.0177770	−	0.0307907i	−0.874777	+	0.484526i	$0.838992\pi$
$488$		0			0
$489$	−4.24871			−0.192133
$490$		0			0
$491$	14.1962	−	24.5885i	0.640663	−	1.10966i	−0.344622	−	0.938742i	$-0.611993\pi$
$491$	14.1962	−	24.5885i	0.640663	−	1.10966i	0.985285	−	0.170920i	$-0.0546739\pi$
$492$		0			0
$493$	12.8038			0.576656
$494$		0			0
$495$	−20.1962			−0.907750
$496$		0			0
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$		0			0
$499$	−12.9808			−0.581099			−0.290549	−	0.956860i	$-0.593838\pi$
$499$	−12.9808			−0.581099			−0.290549	+	0.956860i	$0.593838\pi$
$500$		0			0
$501$	9.00000	+	15.5885i	0.402090	+	0.696441i
$502$		0			0
$503$	6.29423	+	10.9019i	0.280646	+	0.486093i	0.971544	−	0.236859i	$-0.0761181\pi$
$503$	6.29423	+	10.9019i	0.280646	+	0.486093i	−0.690898	+	0.722952i	$0.742785\pi$
$504$		0			0
$505$	−3.69615	+	6.40192i	−0.164477	+	0.284882i
$506$		0			0
$507$	−3.66025	−	8.78461i	−0.162558	−	0.390138i
$508$		0			0
$509$	−5.13397	+	8.89230i	−0.227559	+	0.394144i	−0.957084	−	0.289810i	$-0.906408\pi$
$509$	−5.13397	+	8.89230i	−0.227559	+	0.394144i	0.729525	+	0.683954i	$0.239741\pi$
$510$		0			0
$511$	3.59808	+	6.23205i	0.159170	+	0.275690i
$512$		0			0
$513$	−4.00000	−	6.92820i	−0.176604	−	0.305888i
$514$		0			0
$515$	11.0718			0.487882
$516$		0			0
$517$	2.19615	−	3.80385i	0.0965867	−	0.167293i
$518$		0			0
$519$	11.3205			0.496915
$520$		0			0
$521$	0.124356			0.00544812			0.00272406	−	0.999996i	$-0.499133\pi$
$521$	0.124356			0.00544812			0.00272406	+	0.999996i	$0.499133\pi$
$522$		0			0
$523$	16.5885	−	28.7321i	0.725363	−	1.25636i	−0.233462	−	0.972366i	$-0.575005\pi$
$523$	16.5885	−	28.7321i	0.725363	−	1.25636i	0.958825	−	0.283999i	$-0.0916612\pi$
$524$		0			0
$525$	1.46410			0.0638986
$526$		0			0
$527$	13.2224	+	22.9019i	0.575978	+	0.997623i
$528$		0			0
$529$	10.6962	+	18.5263i	0.465050	+	0.805490i
$530$		0			0
$531$	−13.2224	+	22.9019i	−0.573805	+	0.993859i
$532$		0			0
$533$	18.6962	+	1.20577i	0.809820	+	0.0522278i
$534$		0			0
$535$	−17.1962	+	29.7846i	−0.743455	+	1.28770i
$536$		0			0
$537$	2.53590	+	4.39230i	0.109432	+	0.189542i
$538$		0			0
$539$	2.36603	+	4.09808i	0.101912	+	0.176517i
$540$		0			0
$541$	−35.3923			−1.52163			−0.760817	−	0.648966i	$-0.775202\pi$
$541$	−35.3923			−1.52163			−0.760817	+	0.648966i	$0.775202\pi$
$542$		0			0
$543$	9.36603	−	16.2224i	0.401935	−	0.696171i
$544$		0			0
$545$	−21.4641			−0.919421
$546$		0			0
$547$	−28.1962			−1.20558			−0.602790	−	0.797900i	$-0.705944\pi$
$547$	−28.1962			−1.20558			−0.602790	+	0.797900i	$0.705944\pi$
$548$		0			0
$549$	−18.7224	+	32.4282i	−0.799054	+	1.38400i
$550$		0			0
$551$	6.00000			0.255609
$552$		0			0
$553$	−2.90192	−	5.02628i	−0.123402	−	0.213739i
$554$		0			0
$555$	−4.43782	−	7.68653i	−0.188375	−	0.326275i
$556$		0			0
$557$	12.8205	−	22.2058i	0.543222	−	0.940889i	−0.455494	−	0.890239i	$-0.650537\pi$
$557$	12.8205	−	22.2058i	0.543222	−	0.940889i	0.998716	−	0.0506499i	$-0.0161293\pi$
$558$		0			0
$559$	20.3923	−	30.5885i	0.862503	−	1.29375i
$560$		0			0
$561$	−7.39230	+	12.8038i	−0.312103	+	0.540579i
$562$		0			0
$563$	−5.02628	−	8.70577i	−0.211832	−	0.366905i	0.740456	−	0.672105i	$-0.234610\pi$
$563$	−5.02628	−	8.70577i	−0.211832	−	0.366905i	−0.952288	+	0.305201i	$0.901276\pi$
$564$		0			0
$565$	−6.40192	−	11.0885i	−0.269331	−	0.466495i
$566$		0			0
$567$	−4.46410			−0.187475
$568$		0			0
$569$	−14.5359	+	25.1769i	−0.609377	+	1.05547i	0.381967	+	0.924176i	$0.375247\pi$
$569$	−14.5359	+	25.1769i	−0.609377	+	1.05547i	−0.991343	+	0.131295i	$0.958086\pi$
$570$		0			0
$571$	24.7846			1.03720			0.518602	−	0.855016i	$-0.326453\pi$
$571$	24.7846			1.03720			0.518602	+	0.855016i	$0.326453\pi$
$572$		0			0
$573$	−0.928203			−0.0387762
$574$		0			0
$575$	−1.26795	+	2.19615i	−0.0528771	+	0.0915859i
$576$		0			0
$577$	32.8038			1.36564			0.682821	−	0.730586i	$-0.260753\pi$
$577$	32.8038			1.36564			0.682821	+	0.730586i	$0.260753\pi$
$578$		0			0
$579$	−1.83013	−	3.16987i	−0.0760575	−	0.131735i
$580$		0			0
$581$	−4.09808	−	7.09808i	−0.170017	−	0.294478i
$582$		0			0
$583$	9.29423	−	16.0981i	0.384928	−	0.666714i
$584$		0			0
$585$	−8.53590	+	12.8038i	−0.352916	+	0.529374i
$586$		0			0
$587$	−2.19615	+	3.80385i	−0.0906449	+	0.157002i	−0.907783	−	0.419441i	$-0.862226\pi$
$587$	−2.19615	+	3.80385i	−0.0906449	+	0.157002i	0.817138	+	0.576442i	$0.195559\pi$
$588$		0			0
$589$	6.19615	+	10.7321i	0.255308	+	0.442206i
$590$		0			0
$591$	−4.39230	−	7.60770i	−0.180675	−	0.312939i
$592$		0			0
$593$	41.4449			1.70194			0.850968	−	0.525217i	$-0.176016\pi$
$593$	41.4449			1.70194			0.850968	+	0.525217i	$0.176016\pi$
$594$		0			0
$595$	3.69615	−	6.40192i	0.151527	−	0.262453i
$596$		0			0
$597$	−1.46410			−0.0599217
$598$		0			0
$599$	−16.1436			−0.659609			−0.329805	−	0.944049i	$-0.606983\pi$
$599$	−16.1436			−0.659609			−0.329805	+	0.944049i	$0.606983\pi$
$600$		0			0
$601$	−10.9904	+	19.0359i	−0.448307	+	0.776490i	−0.998276	−	0.0586946i	$-0.981306\pi$
$601$	−10.9904	+	19.0359i	−0.448307	+	0.776490i	0.549969	+	0.835185i	$0.314640\pi$
$602$		0			0
$603$	10.3397			0.421067
$604$		0			0
$605$	9.86603	+	17.0885i	0.401111	+	0.694745i
$606$		0			0
$607$	3.19615	+	5.53590i	0.129728	+	0.224695i	0.923571	−	0.383427i	$-0.125256\pi$
$607$	3.19615	+	5.53590i	0.129728	+	0.224695i	−0.793843	+	0.608122i	$0.791923\pi$
$608$		0			0
$609$	−1.09808	+	1.90192i	−0.0444963	+	0.0770698i
$610$		0			0
$611$	−1.48334	−	3.00000i	−0.0600095	−	0.121367i
$612$		0			0
$613$	8.69615	−	15.0622i	0.351234	−	0.608356i	−0.635232	−	0.772322i	$-0.719095\pi$
$613$	8.69615	−	15.0622i	0.351234	−	0.608356i	0.986466	+	0.163966i	$0.0524287\pi$
$614$		0			0
$615$	3.29423	+	5.70577i	0.132836	+	0.230079i
$616$		0			0
$617$	−14.3038	−	24.7750i	−0.575851	−	0.997404i	−0.995949	−	0.0899245i	$-0.971337\pi$
$617$	−14.3038	−	24.7750i	−0.575851	−	0.997404i	0.420097	−	0.907479i	$-0.361996\pi$
$618$		0			0
$619$	37.3731			1.50215			0.751075	−	0.660217i	$-0.229536\pi$
$619$	37.3731			1.50215			0.751075	+	0.660217i	$0.229536\pi$
$620$		0			0
$621$	−2.53590	+	4.39230i	−0.101762	+	0.176257i
$622$		0			0
$623$	0.928203			0.0371877
$624$		0			0
$625$	−11.0000			−0.440000
$626$		0			0
$627$	−3.46410	+	6.00000i	−0.138343	+	0.239617i
$628$		0			0
$629$	29.8756			1.19122
$630$		0			0
$631$	14.3923	+	24.9282i	0.572949	+	0.992376i	0.996261	+	0.0863924i	$0.0275339\pi$
$631$	14.3923	+	24.9282i	0.572949	+	0.992376i	−0.423313	+	0.905984i	$0.639133\pi$
$632$		0			0
$633$	−4.46410	−	7.73205i	−0.177432	−	0.307321i
$634$		0			0
$635$	2.07180	−	3.58846i	0.0822167	−	0.142404i
$636$		0			0
$637$	3.59808	+	0.232051i	0.142561	+	0.00919419i
$638$		0			0
$639$	−7.39230	+	12.8038i	−0.292435	+	0.506512i
$640$		0			0
$641$	−0.571797	−	0.990381i	−0.0225846	−	0.0391177i	0.854512	−	0.519431i	$-0.173856\pi$
$641$	−0.571797	−	0.990381i	−0.0225846	−	0.0391177i	−0.877097	+	0.480314i	$0.840523\pi$
$642$		0			0
$643$	20.3923	+	35.3205i	0.804194	+	1.39290i	0.916834	+	0.399269i	$0.130736\pi$
$643$	20.3923	+	35.3205i	0.804194	+	1.39290i	−0.112640	+	0.993636i	$0.535931\pi$
$644$		0			0
$645$	12.9282			0.509048
$646$		0			0
$647$	−22.5167	+	39.0000i	−0.885221	+	1.53325i	−0.0397614	+	0.999209i	$0.512660\pi$
$647$	−22.5167	+	39.0000i	−0.885221	+	1.53325i	−0.845460	+	0.534039i	$0.820674\pi$
$648$		0			0
$649$	50.7846			1.99347
$650$		0			0
$651$	−4.53590			−0.177776
$652$		0			0
$653$	5.07180	−	8.78461i	0.198475	−	0.343768i	−0.749559	−	0.661937i	$-0.769735\pi$
$653$	5.07180	−	8.78461i	0.198475	−	0.343768i	0.948034	+	0.318169i	$0.103068\pi$
$654$		0			0
$655$	6.00000			0.234439
$656$		0			0
$657$	8.86603	+	15.3564i	0.345897	+	0.599110i
$658$		0			0
$659$	3.80385	+	6.58846i	0.148177	+	0.256650i	0.930554	−	0.366156i	$-0.119326\pi$
$659$	3.80385	+	6.58846i	0.148177	+	0.256650i	−0.782377	+	0.622805i	$0.785993\pi$
$660$		0			0
$661$	11.4019	−	19.7487i	0.443483	−	0.768136i	−0.554462	−	0.832209i	$-0.687076\pi$
$661$	11.4019	−	19.7487i	0.443483	−	0.768136i	0.997945	+	0.0640734i	$0.0204092\pi$
$662$		0			0
$663$	4.99296	+	10.0981i	0.193910	+	0.392177i
$664$		0			0
$665$	1.73205	−	3.00000i	0.0671660	−	0.116335i
$666$		0			0
$667$	−1.90192	−	3.29423i	−0.0736428	−	0.127553i
$668$		0			0
$669$	−3.66025	−	6.33975i	−0.141514	−	0.245109i
$670$		0			0
$671$	71.9090			2.77601
$672$		0			0
$673$	−9.08846	+	15.7417i	−0.350334	+	0.606797i	−0.986308	−	0.164914i	$-0.947265\pi$
$673$	−9.08846	+	15.7417i	−0.350334	+	0.606797i	0.635974	+	0.771711i	$0.280599\pi$
$674$		0			0
$675$	8.00000			0.307920
$676$		0			0
$677$	−36.9282			−1.41927			−0.709633	−	0.704571i	$-0.751139\pi$
$677$	−36.9282			−1.41927			−0.709633	+	0.704571i	$0.751139\pi$
$678$		0			0
$679$	−7.19615	+	12.4641i	−0.276163	+	0.478328i
$680$		0			0
$681$	8.53590			0.327096
$682$		0			0
$683$	4.26795	+	7.39230i	0.163309	+	0.282859i	0.936053	−	0.351858i	$-0.114450\pi$
$683$	4.26795	+	7.39230i	0.163309	+	0.282859i	−0.772745	+	0.634717i	$0.781117\pi$
$684$		0			0
$685$	18.9904	+	32.8923i	0.725585	+	1.25675i
$686$		0			0
$687$	−2.33975	+	4.05256i	−0.0892669	+	0.154615i
$688$		0			0
$689$	−6.27757	−	12.6962i	−0.239156	−	0.483685i
$690$		0			0
$691$	−10.1962	+	17.6603i	−0.387880	+	0.671828i	−0.992164	−	0.124941i	$-0.960126\pi$
$691$	−10.1962	+	17.6603i	−0.387880	+	0.671828i	0.604284	+	0.796769i	$0.293459\pi$
$692$		0			0
$693$	5.83013	+	10.0981i	0.221468	+	0.383594i
$694$		0			0
$695$	−17.8301	−	30.8827i	−0.676335	−	1.17145i
$696$		0			0
$697$	−22.1769			−0.840011
$698$		0			0
$699$	−9.46410	+	16.3923i	−0.357965	+	0.620014i
$700$		0			0
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$		0			0
$703$	14.0000			0.528020
$704$		0			0
$705$	0.588457	−	1.01924i	0.0221626	−	0.0383867i
$706$		0			0
$707$	4.26795			0.160513
$708$		0			0
$709$	16.0885	+	27.8660i	0.604215	+	1.04653i	0.992175	+	0.124854i	$0.0398464\pi$
$709$	16.0885	+	27.8660i	0.604215	+	1.04653i	−0.387960	+	0.921676i	$0.626820\pi$
$710$		0			0
$711$	−7.15064	−	12.3853i	−0.268170	−	0.464484i
$712$		0			0
$713$	3.92820	−	6.80385i	0.147112	−	0.254806i
$714$		0			0
$715$	29.4904	+	1.90192i	1.10288	+	0.0711279i
$716$		0			0
$717$	−9.58846	+	16.6077i	−0.358087	+	0.620226i
$718$		0			0
$719$	−5.36603	−	9.29423i	−0.200119	−	0.346616i	0.748448	−	0.663194i	$-0.230800\pi$
$719$	−5.36603	−	9.29423i	−0.200119	−	0.346616i	−0.948567	+	0.316578i	$0.897466\pi$
$720$		0			0
$721$	−3.19615	−	5.53590i	−0.119031	−	0.206168i
$722$		0			0
$723$	−7.90897			−0.294138
$724$		0			0
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		0			0
$727$	−21.1769			−0.785408			−0.392704	−	0.919665i	$-0.628460\pi$
$727$	−21.1769			−0.785408			−0.392704	+	0.919665i	$0.628460\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$		0			0
$731$	−21.7583	+	37.6865i	−0.804761	+	1.39389i
$732$		0			0
$733$	−7.58846			−0.280286			−0.140143	−	0.990131i	$-0.544756\pi$
$733$	−7.58846			−0.280286			−0.140143	+	0.990131i	$0.544756\pi$
$734$		0			0
$735$	0.633975	+	1.09808i	0.0233845	+	0.0405032i
$736$		0			0
$737$	−9.92820	−	17.1962i	−0.365710	−	0.633428i
$738$		0			0
$739$	−0.392305	+	0.679492i	−0.0144312	+	0.0249955i	−0.873151	−	0.487450i	$-0.837927\pi$
$739$	−0.392305	+	0.679492i	−0.0144312	+	0.0249955i	0.858720	+	0.512446i	$0.171260\pi$
$740$		0			0
$741$	2.33975	+	4.73205i	0.0859527	+	0.173836i
$742$		0			0
$743$	−14.1962	+	24.5885i	−0.520806	+	0.902063i	0.478901	+	0.877869i	$0.341035\pi$
$743$	−14.1962	+	24.5885i	−0.520806	+	0.902063i	−0.999707	+	0.0241941i	$0.992298\pi$
$744$		0			0
$745$	0.401924	+	0.696152i	0.0147253	+	0.0255051i
$746$		0			0
$747$	−10.0981	−	17.4904i	−0.369469	−	0.639940i
$748$		0			0
$749$	19.8564			0.725537
$750$		0			0
$751$	23.0981	−	40.0070i	0.842861	−	1.45988i	−0.0446053	−	0.999005i	$-0.514203\pi$
$751$	23.0981	−	40.0070i	0.842861	−	1.45988i	0.887466	−	0.460873i	$-0.152464\pi$
$752$		0			0
$753$	16.3923			0.597369
$754$		0			0
$755$	3.46410			0.126072
$756$		0			0
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	−0.683226	−	0.730207i	$-0.739424\pi$
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	0.973991	+	0.226587i	$0.0727569\pi$
$758$		0			0
$759$	4.39230			0.159431
$760$		0			0
$761$	−3.33975	−	5.78461i	−0.121066	−	0.209692i	0.799123	−	0.601168i	$-0.205298\pi$
$761$	−3.33975	−	5.78461i	−0.121066	−	0.209692i	−0.920188	+	0.391476i	$0.871965\pi$
$762$		0			0
$763$	6.19615	+	10.7321i	0.224316	+	0.388526i
$764$		0			0
$765$	9.10770	−	15.7750i	0.329289	−	0.570346i
$766$		0			0
$767$	21.4641	−	32.1962i	0.775024	−	1.16254i
$768$		0			0
$769$	23.5885	−	40.8564i	0.850622	−	1.47332i	−0.0300268	−	0.999549i	$-0.509559\pi$
$769$	23.5885	−	40.8564i	0.850622	−	1.47332i	0.880648	−	0.473771i	$-0.157107\pi$
$770$		0			0
$771$	6.63397	+	11.4904i	0.238917	+	0.413816i
$772$		0			0
$773$	−0.464102	−	0.803848i	−0.0166926	−	0.0289124i	0.857558	−	0.514387i	$-0.171980\pi$
$773$	−0.464102	−	0.803848i	−0.0166926	−	0.0289124i	−0.874251	+	0.485474i	$0.838647\pi$
$774$		0			0
$775$	−12.3923			−0.445145
$776$		0			0
$777$	−2.56218	+	4.43782i	−0.0919176	+	0.159206i
$778$		0			0
$779$	−10.3923			−0.372343
$780$		0			0
$781$	28.3923			1.01596
$782$		0			0
$783$	−6.00000	+	10.3923i	−0.214423	+	0.371391i
$784$		0			0
$785$	15.9282			0.568502
$786$		0			0
$787$	−19.4904	−	33.7583i	−0.694757	−	1.20335i	−0.970263	−	0.242055i	$-0.922179\pi$
$787$	−19.4904	−	33.7583i	−0.694757	−	1.20335i	0.275505	−	0.961300i	$-0.411155\pi$
$788$		0			0
$789$	1.73205	+	3.00000i	0.0616626	+	0.106803i
$790$		0			0
$791$	−3.69615	+	6.40192i	−0.131420	+	0.227626i
$792$		0			0
$793$	30.3923	−	45.5885i	1.07926	−	1.61889i
$794$		0			0
$795$	2.49038	−	4.31347i	0.0883247	−	0.152983i
$796$		0			0
$797$	6.80385	+	11.7846i	0.241005	+	0.417432i	0.961001	−	0.276546i	$-0.0891898\pi$
$797$	6.80385	+	11.7846i	0.241005	+	0.417432i	−0.719996	+	0.693978i	$0.755856\pi$
$798$		0			0
$799$	1.98076	+	3.43078i	0.0700743	+	0.121372i
$800$		0			0
$801$	2.28719			0.0808138
$802$		0			0
$803$	17.0263	−	29.4904i	0.600844	−	1.04069i
$804$		0			0
$805$	−2.19615			−0.0774042
$806$		0			0
$807$	13.8564			0.487769
$808$		0			0
$809$	−7.96410	+	13.7942i	−0.280003	+	0.484979i	−0.971385	−	0.237510i	$-0.923669\pi$
$809$	−7.96410	+	13.7942i	−0.280003	+	0.484979i	0.691382	+	0.722489i	$0.257002\pi$
$810$		0			0
$811$	−14.5885			−0.512270			−0.256135	−	0.966641i	$-0.582449\pi$
$811$	−14.5885			−0.512270			−0.256135	+	0.966641i	$0.582449\pi$
$812$		0			0
$813$	5.92820	+	10.2679i	0.207911	+	0.360113i
$814$		0			0
$815$	−5.02628	−	8.70577i	−0.176063	−	0.304950i
$816$		0			0
$817$	−10.1962	+	17.6603i	−0.356718	+	0.617854i
$818$		0			0
$819$	8.86603	+	0.571797i	0.309804	+	0.0199802i
$820$		0			0
$821$	−15.9282	+	27.5885i	−0.555898	+	0.962844i	0.441935	+	0.897047i	$0.354292\pi$
$821$	−15.9282	+	27.5885i	−0.555898	+	0.962844i	−0.997833	+	0.0657967i	$0.979041\pi$
$822$		0			0
$823$	10.5885	+	18.3397i	0.369090	+	0.639283i	0.989424	−	0.145055i	$-0.0463359\pi$
$823$	10.5885	+	18.3397i	0.369090	+	0.639283i	−0.620333	+	0.784338i	$0.713003\pi$
$824$		0			0
$825$	−3.46410	−	6.00000i	−0.120605	−	0.208893i
$826$		0			0
$827$	−34.9808			−1.21640			−0.608200	−	0.793784i	$-0.708108\pi$
$827$	−34.9808			−1.21640			−0.608200	+	0.793784i	$0.708108\pi$
$828$		0			0
$829$	15.7942	−	27.3564i	0.548556	−	0.950127i	−0.449818	−	0.893120i	$-0.648511\pi$
$829$	15.7942	−	27.3564i	0.548556	−	0.950127i	0.998374	−	0.0570068i	$-0.0181557\pi$
$830$		0			0
$831$	12.4449			0.431708
$832$		0			0
$833$	−4.26795			−0.147876
$834$		0			0
$835$	−21.2942	+	36.8827i	−0.736917	+	1.27638i
$836$		0			0
$837$	−24.7846			−0.856681
$838$		0			0
$839$	−9.00000	−	15.5885i	−0.310715	−	0.538173i	0.667803	−	0.744338i	$-0.267235\pi$
$839$	−9.00000	−	15.5885i	−0.310715	−	0.538173i	−0.978517	+	0.206165i	$0.933902\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	2.70577	−	4.68653i	0.0931917	−	0.161413i
$844$		0			0
$845$	13.6699	−	17.8923i	0.470258	−	0.615514i
$846$		0			0
$847$	5.69615	−	9.86603i	0.195722	−	0.339001i
$848$		0			0
$849$	−0.0717968	−	0.124356i	−0.00246406	−	0.00426787i
$850$		0			0
$851$	−4.43782	−	7.68653i	−0.152127	−	0.263491i
$852$		0			0
$853$	−25.5885			−0.876132			−0.438066	−	0.898943i	$-0.644336\pi$
$853$	−25.5885			−0.876132			−0.438066	+	0.898943i	$0.644336\pi$
$854$		0			0
$855$	4.26795	−	7.39230i	0.145961	−	0.252811i
$856$		0			0
$857$	−5.87564			−0.200708			−0.100354	−	0.994952i	$-0.531998\pi$
$857$	−5.87564			−0.200708			−0.100354	+	0.994952i	$0.531998\pi$
$858$		0			0
$859$	18.1962			0.620845			0.310422	−	0.950599i	$-0.399530\pi$
$859$	18.1962			0.620845			0.310422	+	0.950599i	$0.399530\pi$
$860$		0			0
$861$	1.90192	−	3.29423i	0.0648174	−	0.112267i
$862$		0			0
$863$	37.5167			1.27708			0.638541	−	0.769588i	$-0.279538\pi$
$863$	37.5167			1.27708			0.638541	+	0.769588i	$0.279538\pi$
$864$		0			0
$865$	13.3923	+	23.1962i	0.455352	+	0.788693i
$866$		0			0
$867$	−0.444864	−	0.770527i	−0.0151084	−	0.0261685i
$868$		0			0
$869$	−13.7321	+	23.7846i	−0.465828	+	0.806838i
$870$		0			0
$871$	−15.0981	−	0.973721i	−0.511579	−	0.0329933i
$872$		0			0
$873$	−17.7321	+	30.7128i	−0.600139	+	1.03947i
$874$		0			0
$875$	6.06218	+	10.5000i	0.204939	+	0.354965i
$876$		0			0
$877$	10.8923	+	18.8660i	0.367807	+	0.637060i	0.989222	−	0.146421i	$-0.0467754\pi$
$877$	10.8923	+	18.8660i	0.367807	+	0.637060i	−0.621415	+	0.783481i	$0.713442\pi$
$878$		0			0
$879$	−8.19615			−0.276449
$880$		0			0
$881$	19.7942	−	34.2846i	0.666885	−	1.15508i	−0.311886	−	0.950119i	$-0.600961\pi$
$881$	19.7942	−	34.2846i	0.666885	−	1.15508i	0.978771	−	0.204958i	$-0.0657059\pi$
$882$		0			0
$883$	−45.7654			−1.54013			−0.770064	−	0.637967i	$-0.779776\pi$
$883$	−45.7654			−1.54013			−0.770064	+	0.637967i	$0.779776\pi$
$884$		0			0
$885$	13.6077			0.457418
$886$		0			0
$887$	−11.6603	+	20.1962i	−0.391513	+	0.678120i	−0.992649	−	0.121026i	$-0.961382\pi$
$887$	−11.6603	+	20.1962i	−0.391513	+	0.678120i	0.601136	+	0.799147i	$0.294715\pi$
$888$		0			0
$889$	−2.39230			−0.0802353
$890$		0			0
$891$	10.5622	+	18.2942i	0.353846	+	0.612880i
$892$		0			0
$893$	0.928203	+	1.60770i	0.0310611	+	0.0537995i
$894$		0			0
$895$	−6.00000	+	10.3923i	−0.200558	+	0.347376i
$896$		0			0
$897$	1.85641	−	2.78461i	0.0619836	−	0.0929754i
$898$		0			0
$899$	9.29423	−	16.0981i	0.309980	−	0.536901i
$900$		0			0
$901$	8.38269	+	14.5192i	0.279268	+	0.483706i
$902$		0			0
$903$	−3.73205	−	6.46410i	−0.124195	−	0.215112i
$904$		0			0
$905$	44.3205			1.47326
$906$		0			0
$907$	7.29423	−	12.6340i	0.242201	−	0.419504i	−0.719140	−	0.694865i	$-0.755464\pi$
$907$	7.29423	−	12.6340i	0.242201	−	0.419504i	0.961341	+	0.275361i	$0.0887974\pi$
$908$		0			0
$909$	10.5167			0.348816
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	−19.3923	+	33.5885i	−0.641792	+	1.11162i
$914$		0			0
$915$	19.2679			0.636979
$916$		0			0
$917$	−1.73205	−	3.00000i	−0.0571974	−	0.0990687i
$918$		0			0
$919$	21.7846	+	37.7321i	0.718608	+	1.24467i	0.961551	+	0.274625i	$0.0885537\pi$
$919$	21.7846	+	37.7321i	0.718608	+	1.24467i	−0.242943	+	0.970040i	$0.578113\pi$
$920$		0			0
$921$	9.73205	−	16.8564i	0.320682	−	0.555437i
$922$		0			0
$923$	12.0000	−	18.0000i	0.394985	−	0.592477i
$924$		0			0
$925$	−7.00000	+	12.1244i	−0.230159	+	0.398646i
$926$		0			0
$927$	−7.87564	−	13.6410i	−0.258670	−	0.448030i
$928$		0			0
$929$	−3.74167	−	6.48076i	−0.122760	−	0.212627i	0.798095	−	0.602532i	$-0.205841\pi$
$929$	−3.74167	−	6.48076i	−0.122760	−	0.212627i	−0.920855	+	0.389905i	$0.872508\pi$
$930$		0			0
$931$	−2.00000			−0.0655474
$932$		0			0
$933$	1.73205	−	3.00000i	0.0567048	−	0.0982156i
$934$		0			0
$935$	−34.9808			−1.14399
$936$		0			0
$937$	−40.8038			−1.33300			−0.666502	−	0.745503i	$-0.732209\pi$
$937$	−40.8038			−1.33300			−0.666502	+	0.745503i	$0.732209\pi$
$938$		0			0
$939$	4.67949	−	8.10512i	0.152709	−	0.264501i
$940$		0			0
$941$	−55.8564			−1.82087			−0.910433	−	0.413656i	$-0.864252\pi$
$941$	−55.8564			−1.82087			−0.910433	+	0.413656i	$0.864252\pi$
$942$		0			0
$943$	3.29423	+	5.70577i	0.107275	+	0.185805i
$944$		0			0
$945$	3.46410	+	6.00000i	0.112687	+	0.195180i
$946$		0			0
$947$	−5.36603	+	9.29423i	−0.174372	+	0.302022i	−0.939944	−	0.341329i	$-0.889123\pi$
$947$	−5.36603	+	9.29423i	−0.174372	+	0.302022i	0.765572	+	0.643351i	$0.222456\pi$
$948$		0			0
$949$	−11.5000	−	23.2583i	−0.373306	−	0.754997i
$950$		0			0
$951$	−0.169873	+	0.294229i	−0.00550851	+	0.00954102i
$952$		0			0
$953$	−18.5885	−	32.1962i	−0.602139	−	1.04294i	−0.992497	−	0.122272i	$-0.960982\pi$
$953$	−18.5885	−	32.1962i	−0.602139	−	1.04294i	0.390357	−	0.920663i	$-0.372351\pi$
$954$		0			0
$955$	−1.09808	−	1.90192i	−0.0355329	−	0.0615448i
$956$		0			0
$957$	10.3923			0.335936
$958$		0			0
$959$	10.9641	−	18.9904i	0.354049	−	0.613231i
$960$		0			0
$961$	7.39230			0.238461
$962$		0			0
$963$	48.9282			1.57669
$964$		0			0
$965$	4.33013	−	7.50000i	0.139392	−	0.241434i
$966$		0			0
$967$	−3.01924			−0.0970921			−0.0485461	−	0.998821i	$-0.515459\pi$
$967$	−3.01924			−0.0970921			−0.0485461	+	0.998821i	$0.515459\pi$
$968$		0			0
$969$	−3.12436	−	5.41154i	−0.100369	−	0.173844i
$970$		0			0
$971$	8.32051	+	14.4115i	0.267018	+	0.462488i	0.968090	−	0.250602i	$-0.0806284\pi$
$971$	8.32051	+	14.4115i	0.267018	+	0.462488i	−0.701072	+	0.713090i	$0.747295\pi$
$972$		0			0
$973$	−10.2942	+	17.8301i	−0.330018	+	0.571608i
$974$		0			0
$975$	−5.26795	−	0.339746i	−0.168709	−	0.0108806i
$976$		0			0
$977$	18.8205	−	32.5981i	0.602121	−	1.04290i	−0.390378	−	0.920655i	$-0.627656\pi$
$977$	18.8205	−	32.5981i	0.602121	−	1.04290i	0.992499	−	0.122250i	$-0.0390110\pi$
$978$		0			0
$979$	−2.19615	−	3.80385i	−0.0701893	−	0.121571i
$980$		0			0
$981$	15.2679	+	26.4449i	0.487468	+	0.844320i
$982$		0			0
$983$	−17.3205			−0.552438			−0.276219	−	0.961095i	$-0.589082\pi$
$983$	−17.3205			−0.552438			−0.276219	+	0.961095i	$0.589082\pi$
$984$		0			0
$985$	10.3923	−	18.0000i	0.331126	−	0.573528i
$986$		0			0
$987$	−0.679492			−0.0216285
$988$		0			0
$989$	12.9282			0.411093
$990$		0			0
$991$	−16.4904	+	28.5622i	−0.523834	+	0.907307i	0.475781	+	0.879564i	$0.342166\pi$
$991$	−16.4904	+	28.5622i	−0.523834	+	0.907307i	−0.999615	+	0.0277436i	$0.991168\pi$
$992$		0			0
$993$	19.7513			0.626788
$994$		0			0
$995$	−1.73205	−	3.00000i	−0.0549097	−	0.0951064i
$996$		0			0
$997$	7.59808	+	13.1603i	0.240633	+	0.416789i	0.960895	−	0.276913i	$-0.0893115\pi$
$997$	7.59808	+	13.1603i	0.240633	+	0.416789i	−0.720261	+	0.693703i	$0.755978\pi$
$998$		0			0
$999$	−14.0000	+	24.2487i	−0.442940	+	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.s.o.113.1		4
4.3	odd	2		91.2.f.b.22.2	✓	4
12.11	even	2		819.2.o.b.568.1		4
13.3	even	3	inner	1456.2.s.o.1121.1		4
28.3	even	6		637.2.g.d.373.2		4
28.11	odd	6		637.2.g.e.373.2		4
28.19	even	6		637.2.h.e.165.1		4
28.23	odd	6		637.2.h.d.165.1		4
28.27	even	2		637.2.f.d.295.2		4
52.3	odd	6		91.2.f.b.29.2	yes	4
52.7	even	12		1183.2.c.e.337.1		4
52.19	even	12		1183.2.c.e.337.3		4
52.35	odd	6		1183.2.a.f.1.1		2
52.43	odd	6		1183.2.a.e.1.2		2
156.107	even	6		819.2.o.b.757.1		4
364.3	even	6		637.2.h.e.471.1		4
364.55	even	6		637.2.f.d.393.2		4
364.107	odd	6		637.2.g.e.263.2		4
364.139	even	6		8281.2.a.r.1.1		2
364.159	even	6		637.2.g.d.263.2		4
364.251	even	6		8281.2.a.t.1.2		2
364.263	odd	6		637.2.h.d.471.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.b.22.2	✓	4	4.3	odd	2
91.2.f.b.29.2	yes	4	52.3	odd	6
637.2.f.d.295.2		4	28.27	even	2
637.2.f.d.393.2		4	364.55	even	6
637.2.g.d.263.2		4	364.159	even	6
637.2.g.d.373.2		4	28.3	even	6
637.2.g.e.263.2		4	364.107	odd	6
637.2.g.e.373.2		4	28.11	odd	6
637.2.h.d.165.1		4	28.23	odd	6
637.2.h.d.471.1		4	364.263	odd	6
637.2.h.e.165.1		4	28.19	even	6
637.2.h.e.471.1		4	364.3	even	6
819.2.o.b.568.1		4	12.11	even	2
819.2.o.b.757.1		4	156.107	even	6
1183.2.a.e.1.2		2	52.43	odd	6
1183.2.a.f.1.1		2	52.35	odd	6
1183.2.c.e.337.1		4	52.7	even	12
1183.2.c.e.337.3		4	52.19	even	12
1456.2.s.o.113.1		4	1.1	even	1	trivial
1456.2.s.o.1121.1		4	13.3	even	3	inner
8281.2.a.r.1.1		2	364.139	even	6
8281.2.a.t.1.2		2	364.251	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 0.633975i) q^{3} -1.73205 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.23205 + 2.13397i) q^{9} +O(q^{10})\)	\(q+(-0.366025 + 0.633975i) q^{3} -1.73205 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.23205 + 2.13397i) q^{9} +(2.36603 - 4.09808i) q^{11} +(-1.59808 - 3.23205i) q^{13} +(0.633975 - 1.09808i) q^{15} +(2.13397 + 3.69615i) q^{17} +(1.00000 + 1.73205i) q^{19} -0.732051 q^{21} +(0.633975 - 1.09808i) q^{23} -2.00000 q^{25} -4.00000 q^{27} +(1.50000 - 2.59808i) q^{29} +6.19615 q^{31} +(1.73205 + 3.00000i) q^{33} +(-0.866025 - 1.50000i) q^{35} +(3.50000 - 6.06218i) q^{37} +(2.63397 + 0.169873i) q^{39} +(-2.59808 + 4.50000i) q^{41} +(5.09808 + 8.83013i) q^{43} +(-2.13397 - 3.69615i) q^{45} +0.928203 q^{47} +(-0.500000 + 0.866025i) q^{49} -3.12436 q^{51} +3.92820 q^{53} +(-4.09808 + 7.09808i) q^{55} -1.46410 q^{57} +(5.36603 + 9.29423i) q^{59} +(7.59808 + 13.1603i) q^{61} +(-1.23205 + 2.13397i) q^{63} +(2.76795 + 5.59808i) q^{65} +(2.09808 - 3.63397i) q^{67} +(0.464102 + 0.803848i) q^{69} +(3.00000 + 5.19615i) q^{71} +7.19615 q^{73} +(0.732051 - 1.26795i) q^{75} +4.73205 q^{77} -5.80385 q^{79} +(-2.23205 + 3.86603i) q^{81} -8.19615 q^{83} +(-3.69615 - 6.40192i) q^{85} +(1.09808 + 1.90192i) q^{87} +(0.464102 - 0.803848i) q^{89} +(2.00000 - 3.00000i) q^{91} +(-2.26795 + 3.92820i) q^{93} +(-1.73205 - 3.00000i) q^{95} +(7.19615 + 12.4641i) q^{97} +11.6603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{13} + 6 q^{15} + 12 q^{17} + 4 q^{19} + 4 q^{21} + 6 q^{23} - 8 q^{25} - 16 q^{27} + 6 q^{29} + 4 q^{31} + 14 q^{37} + 14 q^{39} + 10 q^{43} - 12 q^{45} - 24 q^{47} - 2 q^{49} + 36 q^{51} - 12 q^{53} - 6 q^{55} + 8 q^{57} + 18 q^{59} + 20 q^{61} + 2 q^{63} + 18 q^{65} - 2 q^{67} - 12 q^{69} + 12 q^{71} + 8 q^{73} - 4 q^{75} + 12 q^{77} - 44 q^{79} - 2 q^{81} - 12 q^{83} + 6 q^{85} - 6 q^{87} - 12 q^{89} + 8 q^{91} - 16 q^{93} + 8 q^{97} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^7 - 2 * q^9 + 6 * q^11 + 4 * q^13 + 6 * q^15 + 12 * q^17 + 4 * q^19 + 4 * q^21 + 6 * q^23 - 8 * q^25 - 16 * q^27 + 6 * q^29 + 4 * q^31 + 14 * q^37 + 14 * q^39 + 10 * q^43 - 12 * q^45 - 24 * q^47 - 2 * q^49 + 36 * q^51 - 12 * q^53 - 6 * q^55 + 8 * q^57 + 18 * q^59 + 20 * q^61 + 2 * q^63 + 18 * q^65 - 2 * q^67 - 12 * q^69 + 12 * q^71 + 8 * q^73 - 4 * q^75 + 12 * q^77 - 44 * q^79 - 2 * q^81 - 12 * q^83 + 6 * q^85 - 6 * q^87 - 12 * q^89 + 8 * q^91 - 16 * q^93 + 8 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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