LMFDB - Embedded newform 448.2.z.a.47.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(47,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("448.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.z (of order $12$, degree $4$, 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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.5
Character	$\chi$	$=$	448.47
Dual form			448.2.z.a.143.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.350301 + 1.30734i) q^{3} +(1.09872 - 0.294400i) q^{5} +(1.56831 - 2.13082i) q^{7} +(1.01165 + 0.584076i) q^{9} +O(q^{10})$	\(q+(-0.350301 + 1.30734i) q^{3} +(1.09872 - 0.294400i) q^{5} +(1.56831 - 2.13082i) q^{7} +(1.01165 + 0.584076i) q^{9} +(-0.259891 + 0.969928i) q^{11} +(0.430308 - 0.430308i) q^{13} +1.53952i q^{15} +(3.08710 - 1.78234i) q^{17} +(-0.231866 + 0.0621282i) q^{19} +(2.23633 + 2.79674i) q^{21} +(3.02132 - 5.23308i) q^{23} +(-3.20962 + 1.85308i) q^{25} +(-3.98908 + 3.98908i) q^{27} +(4.74378 + 4.74378i) q^{29} +(3.96596 + 6.86925i) q^{31} +(-1.17698 - 0.679532i) q^{33} +(1.09581 - 2.80288i) q^{35} +(1.75224 + 6.53945i) q^{37} +(0.411821 + 0.713295i) q^{39} -6.90248 q^{41} +(4.70996 + 4.70996i) q^{43} +(1.28347 + 0.343904i) q^{45} +(4.33853 - 7.51455i) q^{47} +(-2.08082 - 6.68358i) q^{49} +(1.24871 + 4.66025i) q^{51} +(-7.76712 - 2.08119i) q^{53} +1.14219i q^{55} -0.324891i q^{57} +(-10.5029 - 2.81423i) q^{59} +(-3.00970 - 11.2323i) q^{61} +(2.83114 - 1.23964i) q^{63} +(0.346103 - 0.599468i) q^{65} +(6.97519 + 1.86900i) q^{67} +(5.78305 + 5.78305i) q^{69} -1.08385 q^{71} +(-6.49282 - 11.2459i) q^{73} +(-1.29827 - 4.84520i) q^{75} +(1.65916 + 2.07493i) q^{77} +(-6.29786 - 3.63607i) q^{79} +(-2.06548 - 3.57752i) q^{81} +(-6.72351 - 6.72351i) q^{83} +(2.86713 - 2.86713i) q^{85} +(-7.86348 + 4.53998i) q^{87} +(2.30426 - 3.99110i) q^{89} +(-0.242055 - 1.59176i) q^{91} +(-10.3697 + 2.77856i) q^{93} +(-0.236464 + 0.136523i) q^{95} +18.4267i q^{97} +(-0.829431 + 0.829431i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7}+O(q^{10}) $ 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7	$ 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} - 10 q^{21} + 12 q^{23} - 24 q^{29} - 12 q^{33} + 2 q^{35} + 6 q^{37} + 4 q^{39} + 12 q^{45} - 8 q^{49} + 34 q^{51} + 6 q^{53} - 42 q^{59} - 6 q^{61} - 4 q^{65} - 6 q^{67} + 80 q^{71} - 24 q^{75} + 10 q^{77} - 8 q^{81} - 28 q^{85} + 12 q^{87} - 16 q^{91} + 10 q^{93} + 16 q^{99}+O(q^{100}) $ 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 - 10 * q^21 + 12 * q^23 - 24 * q^29 - 12 * q^33 + 2 * q^35 + 6 * q^37 + 4 * q^39 + 12 * q^45 - 8 * q^49 + 34 * q^51 + 6 * q^53 - 42 * q^59 - 6 * q^61 - 4 * q^65 - 6 * q^67 + 80 * q^71 - 24 * q^75 + 10 * q^77 - 8 * q^81 - 28 * q^85 + 12 * q^87 - 16 * q^91 + 10 * q^93 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.350301	+	1.30734i	−0.202246	+	0.754793i	0.788025	+	0.615643i	$0.211104\pi$
$3$	−0.350301	+	1.30734i	−0.202246	+	0.754793i	−0.990271	+	0.139150i	$0.955563\pi$
$4$		0			0
$5$	1.09872	−	0.294400i	0.491361	−	0.131660i	−0.00462695	−	0.999989i	$-0.501473\pi$
$5$	1.09872	−	0.294400i	0.491361	−	0.131660i	0.495988	+	0.868330i	$0.334806\pi$
$6$		0			0
$7$	1.56831	−	2.13082i	0.592765	−	0.805376i
$7$	1.56831	−	2.13082i	0.592765	−	0.805376i
$8$		0			0
$9$	1.01165	+	0.584076i	0.337217	+	0.194692i
$10$		0			0
$11$	−0.259891	+	0.969928i	−0.0783602	+	0.292444i	−0.993974	−	0.109614i	$-0.965038\pi$
$11$	−0.259891	+	0.969928i	−0.0783602	+	0.292444i	0.915614	+	0.402058i	$0.131705\pi$
$12$		0			0
$13$	0.430308	−	0.430308i	0.119346	−	0.119346i	−0.644911	−	0.764257i	$-0.723106\pi$
$13$	0.430308	−	0.430308i	0.119346	−	0.119346i	0.764257	+	0.644911i	$0.223106\pi$
$14$		0			0
$15$			1.53952i			0.397503i
$16$		0			0
$17$	3.08710	−	1.78234i	0.748733	−	0.432281i	−0.0765030	−	0.997069i	$-0.524375\pi$
$17$	3.08710	−	1.78234i	0.748733	−	0.432281i	0.825236	+	0.564788i	$0.191042\pi$
$18$		0			0
$19$	−0.231866	+	0.0621282i	−0.0531936	+	0.0142532i	−0.285318	−	0.958433i	$-0.592099\pi$
$19$	−0.231866	+	0.0621282i	−0.0531936	+	0.0142532i	0.232124	+	0.972686i	$0.425432\pi$
$20$		0			0
$21$	2.23633	+	2.79674i	0.488007	+	0.610299i
$22$		0			0
$23$	3.02132	−	5.23308i	0.629989	−	1.09117i	−0.357564	−	0.933889i	$-0.616393\pi$
$23$	3.02132	−	5.23308i	0.629989	−	1.09117i	0.987553	−	0.157285i	$-0.0502740\pi$
$24$		0			0
$25$	−3.20962	+	1.85308i	−0.641924	+	0.370615i
$26$		0			0
$27$	−3.98908	+	3.98908i	−0.767700	+	0.767700i
$28$		0			0
$29$	4.74378	+	4.74378i	0.880898	+	0.880898i	0.993626	−	0.112728i	$-0.0359589\pi$
$29$	4.74378	+	4.74378i	0.880898	+	0.880898i	−0.112728	+	0.993626i	$0.535959\pi$
$30$		0			0
$31$	3.96596	+	6.86925i	0.712308	+	1.23375i	0.963989	+	0.265943i	$0.0856833\pi$
$31$	3.96596	+	6.86925i	0.712308	+	1.23375i	−0.251681	+	0.967810i	$0.580983\pi$
$32$		0			0
$33$	−1.17698	−	0.679532i	−0.204887	−	0.118291i
$34$		0			0
$35$	1.09581	−	2.80288i	0.185226	−	0.473773i
$36$		0			0
$37$	1.75224	+	6.53945i	0.288066	+	1.07508i	0.946569	+	0.322500i	$0.104523\pi$
$37$	1.75224	+	6.53945i	0.288066	+	1.07508i	−0.658503	+	0.752578i	$0.728810\pi$
$38$		0			0
$39$	0.411821	+	0.713295i	0.0659441	+	0.114219i
$40$		0			0
$41$	−6.90248			−1.07799			−0.538993	−	0.842310i	$-0.681195\pi$
$41$	−6.90248			−1.07799			−0.538993	+	0.842310i	$0.681195\pi$
$42$		0			0
$43$	4.70996	+	4.70996i	0.718263	+	0.718263i	0.968249	−	0.249987i	$-0.0804262\pi$
$43$	4.70996	+	4.70996i	0.718263	+	0.718263i	−0.249987	+	0.968249i	$0.580426\pi$
$44$		0			0
$45$	1.28347	+	0.343904i	0.191328	+	0.0512662i
$46$		0			0
$47$	4.33853	−	7.51455i	0.632839	−	1.09611i	−0.354129	−	0.935196i	$-0.615223\pi$
$47$	4.33853	−	7.51455i	0.632839	−	1.09611i	0.986969	−	0.160913i	$-0.0514439\pi$
$48$		0			0
$49$	−2.08082	−	6.68358i	−0.297260	−	0.954796i
$50$		0			0
$51$	1.24871	+	4.66025i	0.174854	+	0.652565i
$52$		0			0
$53$	−7.76712	−	2.08119i	−1.06690	−	0.285874i	−0.317679	−	0.948198i	$-0.602903\pi$
$53$	−7.76712	−	2.08119i	−1.06690	−	0.285874i	−0.749217	+	0.662324i	$0.769570\pi$
$54$		0			0
$55$			1.14219i			0.154012i
$56$		0			0
$57$		−	0.324891i		−	0.0430328i
$58$		0			0
$59$	−10.5029	−	2.81423i	−1.36735	−	0.366382i	−0.500843	−	0.865538i	$-0.666977\pi$
$59$	−10.5029	−	2.81423i	−1.36735	−	0.366382i	−0.866512	+	0.499157i	$0.833643\pi$
$60$		0			0
$61$	−3.00970	−	11.2323i	−0.385352	−	1.43815i	−0.837611	−	0.546267i	$-0.816049\pi$
$61$	−3.00970	−	11.2323i	−0.385352	−	1.43815i	0.452259	−	0.891886i	$-0.350618\pi$
$62$		0			0
$63$	2.83114	−	1.23964i	0.356690	−	0.156180i
$64$		0			0
$65$	0.346103	−	0.599468i	0.0429288	−	0.0743549i
$66$		0			0
$67$	6.97519	+	1.86900i	0.852156	+	0.228334i	0.658356	−	0.752707i	$-0.271252\pi$
$67$	6.97519	+	1.86900i	0.852156	+	0.228334i	0.193800	+	0.981041i	$0.437919\pi$
$68$		0			0
$69$	5.78305	+	5.78305i	0.696197	+	0.696197i
$70$		0			0
$71$	−1.08385			−0.128629			−0.0643145	−	0.997930i	$-0.520486\pi$
$71$	−1.08385			−0.128629			−0.0643145	+	0.997930i	$0.520486\pi$
$72$		0			0
$73$	−6.49282	−	11.2459i	−0.759927	−	1.31623i	−0.942887	−	0.333112i	$-0.891901\pi$
$73$	−6.49282	−	11.2459i	−0.759927	−	1.31623i	0.182960	−	0.983120i	$-0.441432\pi$
$74$		0			0
$75$	−1.29827	−	4.84520i	−0.149911	−	0.559475i
$76$		0			0
$77$	1.65916	+	2.07493i	0.189078	+	0.236460i
$78$		0			0
$79$	−6.29786	−	3.63607i	−0.708565	−	0.409090i	0.101965	−	0.994788i	$-0.467487\pi$
$79$	−6.29786	−	3.63607i	−0.708565	−	0.409090i	−0.810529	+	0.585698i	$0.800821\pi$
$80$		0			0
$81$	−2.06548	−	3.57752i	−0.229498	−	0.397502i
$82$		0			0
$83$	−6.72351	−	6.72351i	−0.738001	−	0.738001i	0.234190	−	0.972191i	$-0.424756\pi$
$83$	−6.72351	−	6.72351i	−0.738001	−	0.738001i	−0.972191	+	0.234190i	$0.924756\pi$
$84$		0			0
$85$	2.86713	−	2.86713i	0.310984	−	0.310984i
$86$		0			0
$87$	−7.86348	+	4.53998i	−0.843053	+	0.486737i
$88$		0			0
$89$	2.30426	−	3.99110i	0.244251	−	0.423056i	−0.717669	−	0.696384i	$-0.754791\pi$
$89$	2.30426	−	3.99110i	0.244251	−	0.423056i	0.961921	+	0.273328i	$0.0881245\pi$
$90$		0			0
$91$	−0.242055	−	1.59176i	−0.0253743	−	0.166862i
$92$		0			0
$93$	−10.3697	+	2.77856i	−1.07529	+	0.288123i
$94$		0			0
$95$	−0.236464	+	0.136523i	−0.0242607	+	0.0140069i
$96$		0			0
$97$			18.4267i			1.87095i	0.353390	+	0.935476i	$0.385029\pi$
$97$			18.4267i			1.87095i	−0.353390	+	0.935476i	$0.614971\pi$
$98$		0			0
$99$	−0.829431	+	0.829431i	−0.0833610	+	0.0833610i
$100$		0			0
$101$	0.259129	−	0.967082i	0.0257843	−	0.0962282i	−0.951835	−	0.306612i	$-0.900805\pi$
$101$	0.259129	−	0.967082i	0.0257843	−	0.0962282i	0.977619	+	0.210384i	$0.0674713\pi$
$102$		0			0
$103$	−4.73408	−	2.73322i	−0.466463	−	0.269312i	0.248295	−	0.968684i	$-0.420130\pi$
$103$	−4.73408	−	2.73322i	−0.466463	−	0.269312i	−0.714758	+	0.699372i	$0.753463\pi$
$104$		0			0
$105$	3.28045	+	2.41445i	0.320139	+	0.235626i
$106$		0			0
$107$	−1.04086	+	0.278899i	−0.100624	+	0.0269621i	−0.308780	−	0.951134i	$-0.599921\pi$
$107$	−1.04086	+	0.278899i	−0.100624	+	0.0269621i	0.208156	+	0.978096i	$0.433254\pi$
$108$		0			0
$109$	2.69627	−	10.0626i	0.258256	−	0.963824i	−0.707994	−	0.706218i	$-0.750400\pi$
$109$	2.69627	−	10.0626i	0.258256	−	0.963824i	0.966250	−	0.257606i	$-0.0829336\pi$
$110$		0			0
$111$	−9.16309			−0.869722
$112$		0			0
$113$	−1.87649			−0.176525			−0.0882625	−	0.996097i	$-0.528131\pi$
$113$	−1.87649			−0.176525			−0.0882625	+	0.996097i	$0.528131\pi$
$114$		0			0
$115$	1.77895	−	6.63915i	0.165888	−	0.619104i
$116$		0			0
$117$	0.686653	−	0.183988i	0.0634811	−	0.0170097i
$118$		0			0
$119$	1.04368	−	9.37334i	0.0956736	−	0.859252i
$120$		0			0
$121$	8.65306	+	4.99585i	0.786642	+	0.454168i
$122$		0			0
$123$	2.41794	−	9.02388i	0.218018	−	0.813656i
$124$		0			0
$125$	−7.00250	+	7.00250i	−0.626322	+	0.626322i
$126$		0			0
$127$			6.27400i			0.556728i	0.960476	+	0.278364i	$0.0897921\pi$
$127$			6.27400i			0.556728i	−0.960476	+	0.278364i	$0.910208\pi$
$128$		0			0
$129$	−7.80743	+	4.50762i	−0.687405	+	0.396874i
$130$		0			0
$131$	−18.6973	+	5.00993i	−1.63359	+	0.437719i	−0.954954	−	0.296755i	$-0.904096\pi$
$131$	−18.6973	+	5.00993i	−1.63359	+	0.437719i	−0.678637	+	0.734474i	$0.737429\pi$
$132$		0			0
$133$	−0.231252	+	0.591501i	−0.0200521	+	0.0512897i
$134$		0			0
$135$	−3.20848	+	5.55726i	−0.276142	+	0.478293i
$136$		0			0
$137$	5.20902	−	3.00743i	0.445036	−	0.256942i	−0.260695	−	0.965421i	$-0.583952\pi$
$137$	5.20902	−	3.00743i	0.445036	−	0.256942i	0.705732	+	0.708479i	$0.250618\pi$
$138$		0			0
$139$	0.598828	−	0.598828i	0.0507919	−	0.0507919i	−0.681255	−	0.732047i	$-0.738565\pi$
$139$	0.598828	−	0.598828i	0.0507919	−	0.0507919i	0.732047	+	0.681255i	$0.238565\pi$
$140$		0			0
$141$	8.30428	+	8.30428i	0.699346	+	0.699346i
$142$		0			0
$143$	0.305534	+	0.529200i	0.0255500	+	0.0442540i
$144$		0			0
$145$	6.60863	+	3.81550i	0.548817	+	0.316860i
$146$		0			0
$147$	9.46662	−	0.379080i	0.780793	−	0.0312660i
$148$		0			0
$149$	−4.37217	−	16.3172i	−0.358182	−	1.33675i	−0.876433	−	0.481525i	$-0.840083\pi$
$149$	−4.37217	−	16.3172i	−0.358182	−	1.33675i	0.518251	−	0.855229i	$-0.326583\pi$
$150$		0			0
$151$	1.85332	+	3.21005i	0.150821	+	0.261230i	0.931530	−	0.363666i	$-0.118475\pi$
$151$	1.85332	+	3.21005i	0.150821	+	0.261230i	−0.780708	+	0.624895i	$0.785142\pi$
$152$		0			0
$153$	4.16409			0.336647
$154$		0			0
$155$	6.37977	+	6.37977i	0.512436	+	0.512436i
$156$		0			0
$157$	−6.18954	−	1.65848i	−0.493979	−	0.132361i	0.00322541	−	0.999995i	$-0.498973\pi$
$157$	−6.18954	−	1.65848i	−0.493979	−	0.132361i	−0.497204	+	0.867634i	$0.665640\pi$
$158$		0			0
$159$	5.44166	−	9.42522i	0.431551	−	0.747469i
$160$		0			0
$161$	−6.41242	−	14.6450i	−0.505369	−	1.15419i
$162$		0			0
$163$	4.52983	+	16.9056i	0.354804	+	1.32415i	0.880731	+	0.473616i	$0.157052\pi$
$163$	4.52983	+	16.9056i	0.354804	+	1.32415i	−0.525928	+	0.850529i	$0.676282\pi$
$164$		0			0
$165$	−1.49323	−	0.400109i	−0.116247	−	0.0311484i
$166$		0			0
$167$			15.7966i			1.22237i	0.791486	+	0.611187i	$0.209308\pi$
$167$			15.7966i			1.22237i	−0.791486	+	0.611187i	$0.790692\pi$
$168$		0			0
$169$			12.6297i			0.971513i
$170$		0			0
$171$	−0.270855	−	0.0725753i	−0.0207128	−	0.00554997i
$172$		0			0
$173$	−2.94534	−	10.9922i	−0.223930	−	0.835720i	−0.982830	−	0.184512i	$-0.940929\pi$
$173$	−2.94534	−	10.9922i	−0.223930	−	0.835720i	0.758900	−	0.651207i	$-0.225737\pi$
$174$		0			0
$175$	−1.08510	+	9.74533i	−0.0820255	+	0.736678i
$176$		0			0
$177$	7.35831	−	12.7450i	0.553084	−	0.957970i
$178$		0			0
$179$	−3.74978	−	1.00475i	−0.280272	−	0.0750986i	0.115945	−	0.993256i	$-0.463010\pi$
$179$	−3.74978	−	1.00475i	−0.280272	−	0.0750986i	−0.396217	+	0.918157i	$0.629677\pi$
$180$		0			0
$181$	−12.1739	−	12.1739i	−0.904877	−	0.904877i	0.0909763	−	0.995853i	$-0.471001\pi$
$181$	−12.1739	−	12.1739i	−0.904877	−	0.904877i	−0.995853	+	0.0909763i	$0.971001\pi$
$182$		0			0
$183$	15.7388			1.16344
$184$		0			0
$185$	3.85043	+	6.66913i	0.283089	+	0.490324i
$186$		0			0
$187$	0.926430	+	3.45748i	0.0677473	+	0.252836i
$188$		0			0
$189$	2.24392	+	14.7561i	0.163222	+	1.07335i
$190$		0			0
$191$	−18.3380	−	10.5874i	−1.32689	−	0.766081i	−0.342073	−	0.939673i	$-0.611129\pi$
$191$	−18.3380	−	10.5874i	−1.32689	−	0.766081i	−0.984818	+	0.173593i	$0.944462\pi$
$192$		0			0
$193$	10.1337	+	17.5521i	0.729442	+	1.26343i	0.957119	+	0.289694i	$0.0935536\pi$
$193$	10.1337	+	17.5521i	0.729442	+	1.26343i	−0.227677	+	0.973737i	$0.573113\pi$
$194$		0			0
$195$	0.662468	+	0.662468i	0.0474403	+	0.0474403i
$196$		0			0
$197$	1.72167	−	1.72167i	0.122664	−	0.122664i	−0.643110	−	0.765774i	$-0.722356\pi$
$197$	1.72167	−	1.72167i	0.122664	−	0.122664i	0.765774	+	0.643110i	$0.222356\pi$
$198$		0			0
$199$	−2.21681	+	1.27987i	−0.157145	+	0.0907278i	−0.576510	−	0.817090i	$-0.695586\pi$
$199$	−2.21681	+	1.27987i	−0.157145	+	0.0907278i	0.419365	+	0.907818i	$0.362253\pi$
$200$		0			0
$201$	−4.88683	+	8.46424i	−0.344690	+	0.597021i
$202$		0			0
$203$	17.5479	−	2.66845i	1.23162	−	0.187289i
$204$		0			0
$205$	−7.58386	+	2.03209i	−0.529680	+	0.141927i
$206$		0			0
$207$	6.11304	−	3.52937i	0.424886	−	0.245308i
$208$		0			0
$209$		−	0.241040i		−	0.0166731i
$210$		0			0
$211$	8.70186	−	8.70186i	0.599061	−	0.599061i	−0.341002	−	0.940063i	$-0.610766\pi$
$211$	8.70186	−	8.70186i	0.599061	−	0.599061i	0.940063	+	0.341002i	$0.110766\pi$
$212$		0			0
$213$	0.379673	−	1.41696i	0.0260147	−	0.0970883i
$214$		0			0
$215$	6.56153	+	3.78830i	0.447492	+	0.258360i
$216$		0			0
$217$	20.8570	+	2.32233i	1.41587	+	0.157650i
$218$		0			0
$219$	16.9766	−	4.54888i	1.14718	−	0.307385i
$220$		0			0
$221$	0.561450	−	2.09536i	0.0377672	−	0.140949i
$222$		0			0
$223$	7.01129			0.469511			0.234755	−	0.972054i	$-0.424571\pi$
$223$	7.01129			0.469511			0.234755	+	0.972054i	$0.424571\pi$
$224$		0			0
$225$	−4.32935			−0.288624
$226$		0			0
$227$	6.17820	−	23.0574i	0.410062	−	1.53037i	−0.384463	−	0.923140i	$-0.625613\pi$
$227$	6.17820	−	23.0574i	0.410062	−	1.53037i	0.794525	−	0.607231i	$-0.207720\pi$
$228$		0			0
$229$	−8.66924	+	2.32291i	−0.572879	+	0.153503i	−0.533617	−	0.845726i	$-0.679168\pi$
$229$	−8.66924	+	2.32291i	−0.572879	+	0.153503i	−0.0392625	+	0.999229i	$0.512501\pi$
$230$		0			0
$231$	−3.29384	+	1.44223i	−0.216719	+	0.0948918i
$232$		0			0
$233$	−6.27425	−	3.62244i	−0.411040	−	0.237314i	0.280197	−	0.959943i	$-0.409600\pi$
$233$	−6.27425	−	3.62244i	−0.411040	−	0.237314i	−0.691236	+	0.722629i	$0.742934\pi$
$234$		0			0
$235$	2.55452	−	9.53362i	0.166639	−	0.621905i
$236$		0			0
$237$	6.95973	−	6.95973i	0.452083	−	0.452083i
$238$		0			0
$239$			2.43625i			0.157588i	0.996891	+	0.0787941i	$0.0251070\pi$
$239$			2.43625i			0.157588i	−0.996891	+	0.0787941i	$0.974893\pi$
$240$		0			0
$241$	−12.0616	+	6.96378i	−0.776958	+	0.448577i	−0.835351	−	0.549717i	$-0.814736\pi$
$241$	−12.0616	+	6.96378i	−0.776958	+	0.448577i	0.0583934	+	0.998294i	$0.481402\pi$
$242$		0			0
$243$	−10.9470	+	2.93324i	−0.702251	+	0.188168i
$244$		0			0
$245$	−4.25388	−	6.73076i	−0.271770	−	0.430012i
$246$		0			0
$247$	−0.0730393	+	0.126508i	−0.00464738	+	0.00804950i
$248$		0			0
$249$	11.1452	−	6.43466i	0.706296	−	0.407780i
$250$		0			0
$251$	−3.64643	+	3.64643i	−0.230161	+	0.230161i	−0.812760	−	0.582599i	$-0.802036\pi$
$251$	−3.64643	+	3.64643i	−0.230161	+	0.230161i	0.582599	+	0.812760i	$0.302036\pi$
$252$		0			0
$253$	4.29050	+	4.29050i	0.269741	+	0.269741i
$254$		0			0
$255$	2.74395	+	4.75267i	0.171833	+	0.297624i
$256$		0			0
$257$	12.7994	+	7.38974i	0.798405	+	0.460959i	0.842913	−	0.538050i	$-0.180839\pi$
$257$	12.7994	+	7.38974i	0.798405	+	0.460959i	−0.0445082	+	0.999009i	$0.514172\pi$
$258$		0			0
$259$	16.6825	+	6.52215i	1.03660	+	0.405267i
$260$		0			0
$261$	2.02832	+	7.56978i	0.125550	+	0.468557i
$262$		0			0
$263$	−0.304083	−	0.526688i	−0.0187506	−	0.0324769i	0.856498	−	0.516151i	$-0.172636\pi$
$263$	−0.304083	−	0.526688i	−0.0187506	−	0.0324769i	−0.875248	+	0.483674i	$0.839302\pi$
$264$		0			0
$265$	−9.14656			−0.561869
$266$		0			0
$267$	4.41054	+	4.41054i	0.269921	+	0.269921i
$268$		0			0
$269$	29.6167	+	7.93576i	1.80576	+	0.483852i	0.994854	−	0.101323i	$-0.0323077\pi$
$269$	29.6167	+	7.93576i	1.80576	+	0.483852i	0.810907	+	0.585175i	$0.198974\pi$
$270$		0			0
$271$	−2.52906	+	4.38046i	−0.153629	+	0.266094i	−0.932559	−	0.361017i	$-0.882430\pi$
$271$	−2.52906	+	4.38046i	−0.153629	+	0.266094i	0.778930	+	0.627111i	$0.215763\pi$
$272$		0			0
$273$	2.16577	+	0.241148i	0.131078	+	0.0145949i
$274$		0			0
$275$	−0.963197	−	3.59470i	−0.0580830	−	0.216769i
$276$		0			0
$277$	5.74404	+	1.53911i	0.345126	+	0.0924761i	0.427218	−	0.904149i	$-0.359494\pi$
$277$	5.74404	+	1.53911i	0.345126	+	0.0924761i	−0.0820925	+	0.996625i	$0.526160\pi$
$278$		0			0
$279$			9.26570i			0.554723i
$280$		0			0
$281$			0.464220i			0.0276931i	0.999904	+	0.0138465i	$0.00440763\pi$
$281$			0.464220i			0.0276931i	−0.999904	+	0.0138465i	$0.995592\pi$
$282$		0			0
$283$	12.6488	+	3.38924i	0.751895	+	0.201470i	0.614358	−	0.789027i	$-0.289415\pi$
$283$	12.6488	+	3.38924i	0.751895	+	0.201470i	0.137536	+	0.990497i	$0.456082\pi$
$284$		0			0
$285$	−0.0956478	−	0.356963i	−0.00566569	−	0.0211446i
$286$		0			0
$287$	−10.8252	+	14.7080i	−0.638992	+	0.868184i
$288$		0			0
$289$	−2.14652	+	3.71789i	−0.126266	+	0.218699i
$290$		0			0
$291$	−24.0900	−	6.45490i	−1.41218	−	0.378393i
$292$		0			0
$293$	−0.555113	−	0.555113i	−0.0324300	−	0.0324300i	0.690706	−	0.723136i	$-0.257300\pi$
$293$	−0.555113	−	0.555113i	−0.0324300	−	0.0324300i	−0.723136	+	0.690706i	$0.757300\pi$
$294$		0			0
$295$	−12.3682			−0.720102
$296$		0			0
$297$	−2.83239	−	4.90585i	−0.164352	−	0.284666i
$298$		0			0
$299$	−0.951737	−	3.55193i	−0.0550404	−	0.205414i
$300$		0			0
$301$	17.4228	−	2.64943i	1.00423	−	0.152711i
$302$		0			0
$303$	1.17353	+	0.677539i	0.0674176	+	0.0389236i
$304$		0			0
$305$	−6.61360	−	11.4551i	−0.378694	−	0.655917i
$306$		0			0
$307$	5.80791	+	5.80791i	0.331475	+	0.331475i	0.853146	−	0.521672i	$-0.174691\pi$
$307$	5.80791	+	5.80791i	0.331475	+	0.331475i	−0.521672	+	0.853146i	$0.674691\pi$
$308$		0			0
$309$	5.23160	−	5.23160i	0.297615	−	0.297615i
$310$		0			0
$311$	−6.01776	+	3.47436i	−0.341236	+	0.197013i	−0.660818	−	0.750546i	$-0.729791\pi$
$311$	−6.01776	+	3.47436i	−0.341236	+	0.197013i	0.319582	+	0.947558i	$0.396457\pi$
$312$		0			0
$313$	−5.59664	+	9.69366i	−0.316341	+	0.547918i	−0.979722	−	0.200364i	$-0.935788\pi$
$313$	−5.59664	+	9.69366i	−0.316341	+	0.547918i	0.663381	+	0.748282i	$0.269121\pi$
$314$		0			0
$315$	2.74567	−	2.19550i	0.154701	−	0.123702i
$316$		0			0
$317$	−22.4007	+	6.00226i	−1.25815	+	0.337121i	−0.825480	−	0.564431i	$-0.809095\pi$
$317$	−22.4007	+	6.00226i	−1.25815	+	0.337121i	−0.432671	+	0.901552i	$0.642429\pi$
$318$		0			0
$319$	−5.83399	+	3.36826i	−0.326641	+	0.188586i
$320$		0			0
$321$		−	1.45846i		−	0.0814033i
$322$		0			0
$323$	−0.605060	+	0.605060i	−0.0336664	+	0.0336664i
$324$		0			0
$325$	−0.583732	+	2.17852i	−0.0323796	+	0.120842i
$326$		0			0
$327$	12.2108	+	7.04988i	0.675256	+	0.389859i
$328$		0			0
$329$	−9.20804	−	21.0298i	−0.507655	−	1.15941i
$330$		0			0
$331$	−13.0928	+	3.50821i	−0.719647	+	0.192829i	−0.600014	−	0.799989i	$-0.704838\pi$
$331$	−13.0928	+	3.50821i	−0.719647	+	0.192829i	−0.119633	+	0.992818i	$0.538172\pi$
$332$		0			0
$333$	−2.04688	+	7.63907i	−0.112169	+	0.418619i
$334$		0			0
$335$	8.21399			0.448778
$336$		0			0
$337$	26.2240			1.42851			0.714257	−	0.699884i	$-0.246765\pi$
$337$	26.2240			1.42851			0.714257	+	0.699884i	$0.246765\pi$
$338$		0			0
$339$	0.657334	−	2.45320i	0.0357015	−	0.133240i
$340$		0			0
$341$	−7.69339	+	2.06144i	−0.416620	+	0.111633i
$342$		0			0
$343$	−17.5049	−	6.04804i	−0.945175	−	0.326563i
$344$		0			0
$345$	8.05645	+	4.65139i	0.433745	+	0.250423i
$346$		0			0
$347$	−4.38297	+	16.3575i	−0.235290	+	0.878115i	0.742728	+	0.669594i	$0.233532\pi$
$347$	−4.38297	+	16.3575i	−0.235290	+	0.878115i	−0.978018	+	0.208521i	$0.933135\pi$
$348$		0			0
$349$	−0.411582	+	0.411582i	−0.0220315	+	0.0220315i	−0.718037	−	0.696005i	$-0.754959\pi$
$349$	−0.411582	+	0.411582i	−0.0220315	+	0.0220315i	0.696005	+	0.718037i	$0.254959\pi$
$350$		0			0
$351$			3.43307i			0.183244i
$352$		0			0
$353$	−19.0364	+	10.9907i	−1.01321	+	0.584976i	−0.912129	−	0.409903i	$-0.865563\pi$
$353$	−19.0364	+	10.9907i	−1.01321	+	0.584976i	−0.101078	+	0.994878i	$0.532229\pi$
$354$		0			0
$355$	−1.19084	+	0.319085i	−0.0632033	+	0.0169353i
$356$		0			0
$357$	11.8885	+	4.64792i	0.629208	+	0.245994i
$358$		0			0
$359$	10.3507	−	17.9279i	0.546289	−	0.946200i	−0.452236	−	0.891899i	$-0.649373\pi$
$359$	10.3507	−	17.9279i	0.546289	−	0.946200i	0.998525	−	0.0543018i	$-0.0172933\pi$
$360$		0			0
$361$	−16.4046	+	9.47119i	−0.863399	+	0.498484i
$362$		0			0
$363$	−9.56244	+	9.56244i	−0.501898	+	0.501898i
$364$		0			0
$365$	−10.4446	−	10.4446i	−0.546693	−	0.546693i
$366$		0			0
$367$	−1.64489	−	2.84904i	−0.0858628	−	0.148719i	0.819896	−	0.572513i	$-0.194031\pi$
$367$	−1.64489	−	2.84904i	−0.0858628	−	0.148719i	−0.905759	+	0.423794i	$0.860698\pi$
$368$		0			0
$369$	−6.98289	−	4.03158i	−0.363515	−	0.209875i
$370$		0			0
$371$	−16.6159	+	13.2864i	−0.862654	+	0.689797i
$372$		0			0
$373$	3.57138	+	13.3286i	0.184919	+	0.690128i	0.994648	+	0.103323i	$0.0329476\pi$
$373$	3.57138	+	13.3286i	0.184919	+	0.690128i	−0.809729	+	0.586804i	$0.800386\pi$
$374$		0			0
$375$	−6.70166	−	11.6076i	−0.346072	−	0.599415i
$376$		0			0
$377$	4.08257			0.210263
$378$		0			0
$379$	−25.6709	−	25.6709i	−1.31863	−	1.31863i	−0.914864	−	0.403763i	$-0.867702\pi$
$379$	−25.6709	−	25.6709i	−1.31863	−	1.31863i	−0.403763	−	0.914864i	$-0.632298\pi$
$380$		0			0
$381$	−8.20225	−	2.19779i	−0.420214	−	0.112596i
$382$		0			0
$383$	17.0980	−	29.6146i	0.873666	−	1.51323i	0.0154891	−	0.999880i	$-0.495069\pi$
$383$	17.0980	−	29.6146i	0.873666	−	1.51323i	0.858177	−	0.513354i	$-0.171597\pi$
$384$		0			0
$385$	2.43380	+	1.79130i	0.124038	+	0.0912931i
$386$		0			0
$387$	2.01386	+	7.51582i	0.102370	+	0.382050i
$388$		0			0
$389$	33.9002	+	9.08354i	1.71881	+	0.460554i	0.977557	−	0.210671i	$-0.0675650\pi$
$389$	33.9002	+	9.08354i	1.71881	+	0.460554i	0.741254	+	0.671225i	$0.234232\pi$
$390$		0			0
$391$		−	21.5401i		−	1.08933i
$392$		0			0
$393$		−	26.1987i		−	1.32155i
$394$		0			0
$395$	−7.99002	−	2.14092i	−0.402022	−	0.107721i
$396$		0			0
$397$	−9.99766	−	37.3118i	−0.501768	−	1.87262i	−0.488229	−	0.872716i	$-0.662357\pi$
$397$	−9.99766	−	37.3118i	−0.501768	−	1.87262i	−0.0135393	−	0.999908i	$-0.504310\pi$
$398$		0			0
$399$	−0.692285	−	0.509529i	−0.0346576	−	0.0255083i
$400$		0			0
$401$	15.7630	−	27.3024i	0.787169	−	1.36342i	−0.140526	−	0.990077i	$-0.544879\pi$
$401$	15.7630	−	27.3024i	0.787169	−	1.36342i	0.927695	−	0.373339i	$-0.121787\pi$
$402$		0			0
$403$	4.66247	+	1.24931i	0.232254	+	0.0622323i
$404$		0			0
$405$	−3.32260	−	3.32260i	−0.165101	−	0.165101i
$406$		0			0
$407$	−6.79818			−0.336973
$408$		0			0
$409$	−1.54365	−	2.67368i	−0.0763286	−	0.132205i	0.825335	−	0.564644i	$-0.190986\pi$
$409$	−1.54365	−	2.67368i	−0.0763286	−	0.132205i	−0.901663	+	0.432439i	$0.857653\pi$
$410$		0			0
$411$	2.10701	+	7.86346i	0.103931	+	0.387876i
$412$		0			0
$413$	−22.4683	+	17.9661i	−1.10559	+	0.884056i
$414$		0			0
$415$	−9.36663	−	5.40783i	−0.459790	−	0.265460i
$416$		0			0
$417$	0.573102	+	0.992642i	0.0280649	+	0.0486099i
$418$		0			0
$419$	1.70209	+	1.70209i	0.0831526	+	0.0831526i	0.747460	−	0.664307i	$-0.231273\pi$
$419$	1.70209	+	1.70209i	0.0831526	+	0.0831526i	−0.664307	+	0.747460i	$0.731273\pi$
$420$		0			0
$421$	−17.4338	+	17.4338i	−0.849670	+	0.849670i	−0.990092	−	0.140421i	$-0.955154\pi$
$421$	−17.4338	+	17.4338i	−0.849670	+	0.849670i	0.140421	+	0.990092i	$0.455154\pi$
$422$		0			0
$423$	8.77814	−	5.06806i	0.426808	−	0.246418i
$424$		0			0
$425$	−6.60563	+	11.4413i	−0.320420	+	0.554984i
$426$		0			0
$427$	−28.6543	−	11.2026i	−1.38668	−	0.542133i
$428$		0			0
$429$	−0.798873	+	0.214057i	−0.0385700	+	0.0103348i
$430$		0			0
$431$	5.60309	−	3.23494i	0.269891	−	0.155822i	−0.358947	−	0.933358i	$-0.616864\pi$
$431$	5.60309	−	3.23494i	0.269891	−	0.155822i	0.628838	+	0.777536i	$0.283531\pi$
$432$		0			0
$433$		−	10.4458i		−	0.501991i	−0.967988	−	0.250996i	$-0.919242\pi$
$433$		−	10.4458i		−	0.501991i	0.967988	−	0.250996i	$-0.0807580\pi$
$434$		0			0
$435$	−7.30316	+	7.30316i	−0.350160	+	0.350160i
$436$		0			0
$437$	−0.375419	+	1.40108i	−0.0179587	+	0.0670228i
$438$		0			0
$439$	12.4100	+	7.16490i	0.592295	+	0.341962i	0.766005	−	0.642835i	$-0.222242\pi$
$439$	12.4100	+	7.16490i	0.592295	+	0.341962i	−0.173709	+	0.984797i	$0.555575\pi$
$440$		0			0
$441$	1.79866	−	7.97680i	0.0856503	−	0.379848i
$442$		0			0
$443$	−8.38857	+	2.24771i	−0.398553	+	0.106792i	−0.452528	−	0.891750i	$-0.649478\pi$
$443$	−8.38857	+	2.24771i	−0.398553	+	0.106792i	0.0539748	+	0.998542i	$0.482811\pi$
$444$		0			0
$445$	1.35675	−	5.06346i	0.0643161	−	0.240031i
$446$		0			0
$447$	22.8636			1.08141
$448$		0			0
$449$	−33.1429			−1.56411			−0.782055	−	0.623209i	$-0.785829\pi$
$449$	−33.1429			−1.56411			−0.782055	+	0.623209i	$0.785829\pi$
$450$		0			0
$451$	1.79389	−	6.69490i	0.0844712	−	0.315251i
$452$		0			0
$453$	−4.84584	+	1.29844i	−0.227677	+	0.0610060i
$454$		0			0
$455$	−0.734565	−	1.67764i	−0.0344369	−	0.0786488i
$456$		0			0
$457$	−0.252924	−	0.146026i	−0.0118313	−	0.00683079i	0.494073	−	0.869421i	$-0.335508\pi$
$457$	−0.252924	−	0.146026i	−0.0118313	−	0.00683079i	−0.505904	+	0.862590i	$0.668841\pi$
$458$		0			0
$459$	−5.20481	+	19.4246i	−0.242940	+	0.906664i
$460$		0			0
$461$	5.13365	−	5.13365i	0.239098	−	0.239098i	−0.577378	−	0.816477i	$-0.695924\pi$
$461$	5.13365	−	5.13365i	0.239098	−	0.239098i	0.816477	+	0.577378i	$0.195924\pi$
$462$		0			0
$463$		−	3.34181i		−	0.155307i	−0.996980	−	0.0776536i	$-0.975257\pi$
$463$		−	3.34181i		−	0.155307i	0.996980	−	0.0776536i	$-0.0247428\pi$
$464$		0			0
$465$	−10.5754	+	6.10569i	−0.490421	+	0.283145i
$466$		0			0
$467$	25.5619	−	6.84929i	1.18286	−	0.316947i	0.386802	−	0.922163i	$-0.373580\pi$
$467$	25.5619	−	6.84929i	1.18286	−	0.316947i	0.796062	+	0.605216i	$0.206913\pi$
$468$		0			0
$469$	14.9218	−	11.9317i	0.689023	−	0.550957i
$470$		0			0
$471$	4.33640	−	7.51086i	0.199811	−	0.346082i
$472$		0			0
$473$	−5.79240	+	3.34425i	−0.266335	+	0.153769i
$474$		0			0
$475$	0.629073	−	0.629073i	0.0288638	−	0.0288638i
$476$		0			0
$477$	−6.64203	−	6.64203i	−0.304118	−	0.304118i
$478$		0			0
$479$	1.27232	+	2.20372i	0.0581337	+	0.100691i	0.893628	−	0.448809i	$-0.148152\pi$
$479$	1.27232	+	2.20372i	0.0581337	+	0.100691i	−0.835494	+	0.549500i	$0.814818\pi$
$480$		0			0
$481$	3.56797	+	2.05997i	0.162686	+	0.0939266i
$482$		0			0
$483$	21.3922	−	3.25306i	0.973381	−	0.148019i
$484$		0			0
$485$	5.42483	+	20.2457i	0.246329	+	0.919312i
$486$		0			0
$487$	−3.28356	−	5.68729i	−0.148792	−	0.257716i	0.781989	−	0.623292i	$-0.214205\pi$
$487$	−3.28356	−	5.68729i	−0.148792	−	0.257716i	−0.930781	+	0.365576i	$0.880872\pi$
$488$		0			0
$489$	−23.6881			−1.07121
$490$		0			0
$491$	−5.34953	−	5.34953i	−0.241421	−	0.241421i	0.576017	−	0.817438i	$-0.304606\pi$
$491$	−5.34953	−	5.34953i	−0.241421	−	0.241421i	−0.817438	+	0.576017i	$0.804606\pi$
$492$		0			0
$493$	23.0996	+	6.18951i	1.04035	+	0.278762i
$494$		0			0
$495$	−0.667124	+	1.15549i	−0.0299850	+	0.0519356i
$496$		0			0
$497$	−1.69981	+	2.30949i	−0.0762468	+	0.103595i
$498$		0			0
$499$	6.64384	+	24.7952i	0.297419	+	1.10998i	0.939277	+	0.343160i	$0.111497\pi$
$499$	6.64384	+	24.7952i	0.297419	+	1.10998i	−0.641858	+	0.766824i	$0.721836\pi$
$500$		0			0
$501$	−20.6515	−	5.53354i	−0.922639	−	0.247220i
$502$		0			0
$503$			1.45685i			0.0649578i	0.999472	+	0.0324789i	$0.0103402\pi$
$503$			1.45685i			0.0649578i	−0.999472	+	0.0324789i	$0.989660\pi$
$504$		0			0
$505$		−	1.13884i		−	0.0506775i
$506$		0			0
$507$	−16.5113	−	4.42418i	−0.733291	−	0.196485i
$508$		0			0
$509$	2.75279	+	10.2736i	0.122015	+	0.455368i	0.999716	−	0.0238421i	$-0.00758990\pi$
$509$	2.75279	+	10.2736i	0.122015	+	0.455368i	−0.877700	+	0.479210i	$0.840923\pi$
$510$		0			0
$511$	−34.1458	−	3.80197i	−1.51052	−	0.168189i
$512$		0			0
$513$	0.677097	−	1.17277i	0.0298946	−	0.0517789i
$514$		0			0
$515$	−6.00607	−	1.60932i	−0.264659	−	0.0709152i
$516$		0			0
$517$	6.16102	+	6.16102i	0.270961	+	0.270961i
$518$		0			0
$519$	15.4023			0.676084
$520$		0			0
$521$	−2.75664	−	4.77465i	−0.120771	−	0.209181i	0.799301	−	0.600931i	$-0.205203\pi$
$521$	−2.75664	−	4.77465i	−0.120771	−	0.209181i	−0.920072	+	0.391750i	$0.871870\pi$
$522$		0			0
$523$	2.12757	+	7.94020i	0.0930321	+	0.347201i	0.996714	−	0.0810044i	$-0.0258128\pi$
$523$	2.12757	+	7.94020i	0.0930321	+	0.347201i	−0.903682	+	0.428205i	$0.859146\pi$
$524$		0			0
$525$	−12.3603	−	4.83238i	−0.539450	−	0.210903i
$526$		0			0
$527$	24.4867	+	14.1374i	1.06666	+	0.615834i
$528$		0			0
$529$	−6.75677	−	11.7031i	−0.293773	−	0.508829i
$530$		0			0
$531$	−8.98149	−	8.98149i	−0.389763	−	0.389763i
$532$		0			0
$533$	−2.97019	+	2.97019i	−0.128653	+	0.128653i
$534$		0			0
$535$	−1.06151	+	0.612860i	−0.0458929	+	0.0264963i
$536$		0			0
$537$	2.62710	−	4.55027i	0.113368	−	0.196359i
$538$		0			0
$539$	7.02337	−	0.281243i	0.302518	−	0.0121140i
$540$		0			0
$541$	6.57387	−	1.76146i	0.282633	−	0.0757312i	−0.114718	−	0.993398i	$-0.536596\pi$
$541$	6.57387	−	1.76146i	0.282633	−	0.0757312i	0.397351	+	0.917667i	$0.369930\pi$
$542$		0			0
$543$	20.1799	−	11.6509i	0.866002	−	0.499987i
$544$		0			0
$545$		−	11.8497i		−	0.507587i
$546$		0			0
$547$	23.8901	−	23.8901i	1.02147	−	1.02147i	0.0217033	−	0.999764i	$-0.493091\pi$
$547$	23.8901	−	23.8901i	1.02147	−	1.02147i	0.999764	−	0.0217033i	$-0.00690891\pi$
$548$		0			0
$549$	3.51578	−	13.1211i	0.150050	−	0.559994i
$550$		0			0
$551$	−1.39464	−	0.805197i	−0.0594138	−	0.0343026i
$552$		0			0
$553$	−17.6248	+	7.71716i	−0.749483	+	0.328167i
$554$		0			0
$555$	−10.0676	+	2.69761i	−0.427347	+	0.114507i
$556$		0			0
$557$	−3.62894	+	13.5434i	−0.153763	+	0.573852i	0.845445	+	0.534063i	$0.179335\pi$
$557$	−3.62894	+	13.5434i	−0.153763	+	0.573852i	−0.999208	+	0.0397894i	$0.987331\pi$
$558$		0			0
$559$	4.05347			0.171443
$560$		0			0
$561$	−4.84463			−0.204541
$562$		0			0
$563$	−10.2643	+	38.3071i	−0.432591	+	1.61445i	0.314176	+	0.949365i	$0.398272\pi$
$563$	−10.2643	+	38.3071i	−0.432591	+	1.61445i	−0.746767	+	0.665086i	$0.768395\pi$
$564$		0			0
$565$	−2.06172	+	0.552437i	−0.0867374	+	0.0232412i
$566$		0			0
$567$	−10.8624	−	1.20947i	−0.456176	−	0.0507931i
$568$		0			0
$569$	−1.41218	−	0.815324i	−0.0592018	−	0.0341802i	0.470107	−	0.882609i	$-0.344215\pi$
$569$	−1.41218	−	0.815324i	−0.0592018	−	0.0341802i	−0.529309	+	0.848429i	$0.677549\pi$
$570$		0			0
$571$	−3.09379	+	11.5462i	−0.129471	+	0.483193i	−0.999960	−	0.00899596i	$-0.997136\pi$
$571$	−3.09379	+	11.5462i	−0.129471	+	0.483193i	0.870488	+	0.492189i	$0.163803\pi$
$572$		0			0
$573$	20.2652	−	20.2652i	0.846591	−	0.846591i
$574$		0			0
$575$			22.3950i			0.933934i
$576$		0			0
$577$	32.3162	−	18.6578i	1.34534	−	0.776734i	0.357757	−	0.933815i	$-0.383542\pi$
$577$	32.3162	−	18.6578i	1.34534	−	0.776734i	0.987586	+	0.157081i	$0.0502084\pi$
$578$		0			0
$579$	−26.4965	+	7.09971i	−1.10116	+	0.295054i
$580$		0			0
$581$	−24.8712	+	3.78208i	−1.03183	+	0.156907i
$582$		0			0
$583$	4.03722	−	6.99266i	0.167204	−	0.289607i
$584$		0			0
$585$	0.700271	−	0.404301i	0.0289526	−	0.0167158i
$586$		0			0
$587$	18.8353	−	18.8353i	0.777414	−	0.777414i	−0.201976	−	0.979390i	$-0.564736\pi$
$587$	18.8353	−	18.8353i	0.777414	−	0.777414i	0.979390	+	0.201976i	$0.0647364\pi$
$588$		0			0
$589$	−1.34634	−	1.34634i	−0.0554752	−	0.0554752i
$590$		0			0
$591$	1.64770	+	2.85391i	0.0677775	+	0.117394i
$592$		0			0
$593$	26.9106	+	15.5368i	1.10508	+	0.638021i	0.937552	−	0.347846i	$-0.113087\pi$
$593$	26.9106	+	15.5368i	1.10508	+	0.638021i	0.167533	+	0.985867i	$0.446420\pi$
$594$		0			0
$595$	−1.61281	−	10.6059i	−0.0661186	−	0.434799i
$596$		0			0
$597$	−0.896681	−	3.34646i	−0.0366987	−	0.136961i
$598$		0			0
$599$	8.87729	+	15.3759i	0.362716	+	0.628243i	0.988407	−	0.151828i	$-0.0485160\pi$
$599$	8.87729	+	15.3759i	0.362716	+	0.628243i	−0.625690	+	0.780071i	$0.715183\pi$
$600$		0			0
$601$	0.186430			0.00760464			0.00380232	−	0.999993i	$-0.498790\pi$
$601$	0.186430			0.00760464			0.00380232	+	0.999993i	$0.498790\pi$
$602$		0			0
$603$	5.96482	+	5.96482i	0.242906	+	0.242906i
$604$		0			0
$605$	10.9780	+	2.94156i	0.446321	+	0.119591i
$606$		0			0
$607$	−15.7087	+	27.2083i	−0.637598	+	1.10435i	0.348361	+	0.937360i	$0.386738\pi$
$607$	−15.7087	+	27.2083i	−0.637598	+	1.10435i	−0.985958	+	0.166991i	$0.946595\pi$
$608$		0			0
$609$	−2.65845	+	23.8758i	−0.107726	+	0.967495i
$610$		0			0
$611$	−1.36667	−	5.10047i	−0.0552894	−	0.206343i
$612$		0			0
$613$	19.4764	+	5.21869i	0.786645	+	0.210781i	0.629712	−	0.776829i	$-0.283173\pi$
$613$	19.4764	+	5.21869i	0.786645	+	0.210781i	0.156932	+	0.987609i	$0.449840\pi$
$614$		0			0
$615$		−	10.6265i		−	0.428503i
$616$		0			0
$617$			8.07743i			0.325185i	0.986693	+	0.162593i	$0.0519856\pi$
$617$			8.07743i			0.325185i	−0.986693	+	0.162593i	$0.948014\pi$
$618$		0			0
$619$	34.2237	+	9.17020i	1.37557	+	0.368582i	0.869508	−	0.493918i	$-0.164436\pi$
$619$	34.2237	+	9.17020i	1.37557	+	0.368582i	0.506057	+	0.862500i	$0.331103\pi$
$620$		0			0
$621$	8.82290	+	32.9275i	0.354051	+	1.32134i
$622$		0			0
$623$	−4.89054	−	11.1693i	−0.195935	−	0.447487i
$624$		0			0
$625$	3.63316	−	6.29282i	0.145327	−	0.251713i
$626$		0			0
$627$	0.315121	+	0.0844363i	0.0125847	+	0.00337206i
$628$		0			0
$629$	17.0649	+	17.0649i	0.680421	+	0.680421i
$630$		0			0
$631$	−35.9453			−1.43096			−0.715481	−	0.698633i	$-0.753792\pi$
$631$	−35.9453			−1.43096			−0.715481	+	0.698633i	$0.753792\pi$
$632$		0			0
$633$	8.32802	+	14.4246i	0.331009	+	0.573325i
$634$		0			0
$635$	1.84707	+	6.89334i	0.0732986	+	0.273554i
$636$		0			0
$637$	−3.77139	−	1.98060i	−0.149428	−	0.0784742i
$638$		0			0
$639$	−1.09648	−	0.633050i	−0.0433759	−	0.0250431i
$640$		0			0
$641$	8.12685	+	14.0761i	0.320991	+	0.555973i	0.980693	−	0.195555i	$-0.0626507\pi$
$641$	8.12685	+	14.0761i	0.320991	+	0.555973i	−0.659702	+	0.751528i	$0.729317\pi$
$642$		0			0
$643$	−15.6304	−	15.6304i	−0.616401	−	0.616401i	0.328205	−	0.944606i	$-0.393556\pi$
$643$	−15.6304	−	15.6304i	−0.616401	−	0.616401i	−0.944606	+	0.328205i	$0.893556\pi$
$644$		0			0
$645$	−7.25110	+	7.25110i	−0.285512	+	0.285512i
$646$		0			0
$647$	8.55921	−	4.94166i	0.336497	−	0.194277i	−0.322225	−	0.946663i	$-0.604431\pi$
$647$	8.55921	−	4.94166i	0.336497	−	0.194277i	0.658722	+	0.752386i	$0.271097\pi$
$648$		0			0
$649$	5.45920	−	9.45561i	0.214292	−	0.371165i
$650$		0			0
$651$	−10.3423	+	26.4537i	−0.405346	+	1.03680i
$652$		0			0
$653$	16.9340	−	4.53745i	0.662679	−	0.177564i	0.0882241	−	0.996101i	$-0.471881\pi$
$653$	16.9340	−	4.53745i	0.662679	−	0.177564i	0.574455	+	0.818536i	$0.305214\pi$
$654$		0			0
$655$	−19.0681	+	11.0090i	−0.745052	+	0.430156i
$656$		0			0
$657$		−	15.1692i		−	0.591807i
$658$		0			0
$659$	−5.02925	+	5.02925i	−0.195912	+	0.195912i	−0.798245	−	0.602333i	$-0.794238\pi$
$659$	−5.02925	+	5.02925i	−0.195912	+	0.195912i	0.602333	+	0.798245i	$0.294238\pi$
$660$		0			0
$661$	−0.683581	+	2.55116i	−0.0265882	+	0.0992286i	−0.977945	−	0.208863i	$-0.933024\pi$
$661$	−0.683581	+	2.55116i	−0.0265882	+	0.0992286i	0.951357	+	0.308092i	$0.0996904\pi$
$662$		0			0
$663$	2.54267	+	1.46801i	0.0987491	+	0.0570128i
$664$		0			0
$665$	−0.0799428	+	0.717972i	−0.00310005	+	0.0278418i
$666$		0			0
$667$	39.1571	−	10.4921i	1.51617	−	0.406256i
$668$		0			0
$669$	−2.45606	+	9.16614i	−0.0949567	+	0.354383i
$670$		0			0
$671$	11.6767			0.450776
$672$		0			0
$673$	4.14811			0.159898			0.0799489	−	0.996799i	$-0.474524\pi$
$673$	4.14811			0.159898			0.0799489	+	0.996799i	$0.474524\pi$
$674$		0			0
$675$	5.41138	−	20.1955i	0.208284	−	0.777326i
$676$		0			0
$677$	34.8320	−	9.33320i	1.33870	−	0.358704i	0.482749	−	0.875759i	$-0.339638\pi$
$677$	34.8320	−	9.33320i	1.33870	−	0.358704i	0.855952	+	0.517055i	$0.172972\pi$
$678$		0			0
$679$	39.2641	+	28.8988i	1.50682	+	1.10903i
$680$		0			0
$681$	27.9796	+	16.1540i	1.07218	+	0.619023i
$682$		0			0
$683$	−0.489938	+	1.82847i	−0.0187469	+	0.0699645i	−0.974666	−	0.223667i	$-0.928197\pi$
$683$	−0.489938	+	1.82847i	−0.0187469	+	0.0699645i	0.955919	+	0.293632i	$0.0948639\pi$
$684$		0			0
$685$	4.83784	−	4.83784i	0.184844	−	0.184844i
$686$		0			0
$687$		−	12.1474i		−	0.463450i
$688$		0			0
$689$	−4.23781	+	2.44670i	−0.161448	+	0.0932118i
$690$		0			0
$691$	−9.68518	+	2.59514i	−0.368442	+	0.0987237i	−0.438289	−	0.898834i	$-0.644415\pi$
$691$	−9.68518	+	2.59514i	−0.368442	+	0.0987237i	0.0698475	+	0.997558i	$0.477749\pi$
$692$		0			0
$693$	0.466568	+	3.06817i	0.0177235	+	0.116550i
$694$		0			0
$695$	0.481647	−	0.834237i	0.0182699	−	0.0316444i
$696$		0			0
$697$	−21.3087	+	12.3026i	−0.807124	+	0.465993i
$698$		0			0
$699$	6.93363	−	6.93363i	0.262254	−	0.262254i
$700$		0			0
$701$	−0.307026	−	0.307026i	−0.0115962	−	0.0115962i	0.701285	−	0.712881i	$-0.252610\pi$
$701$	−0.307026	−	0.307026i	−0.0115962	−	0.0115962i	−0.712881	+	0.701285i	$0.752610\pi$
$702$		0			0
$703$	−0.812568	−	1.40741i	−0.0306466	−	0.0530815i
$704$		0			0
$705$	11.5688	+	6.67926i	0.435707	+	0.251556i
$706$		0			0
$707$	−1.65429	−	2.06884i	−0.0622159	−	0.0778067i
$708$		0			0
$709$	−3.08354	−	11.5079i	−0.115805	−	0.432189i	0.883541	−	0.468354i	$-0.155153\pi$
$709$	−3.08354	−	11.5079i	−0.115805	−	0.432189i	−0.999346	+	0.0361645i	$0.988486\pi$
$710$		0			0
$711$	−4.24749	−	7.35687i	−0.159293	−	0.275904i
$712$		0			0
$713$	47.9298			1.79498
$714$		0			0
$715$	0.491492	+	0.491492i	0.0183807	+	0.0183807i
$716$		0			0
$717$	−3.18501	−	0.853421i	−0.118946	−	0.0318716i
$718$		0			0
$719$	−2.72556	+	4.72080i	−0.101646	+	0.176056i	−0.912363	−	0.409382i	$-0.865744\pi$
$719$	−2.72556	+	4.72080i	−0.101646	+	0.176056i	0.810717	+	0.585438i	$0.199078\pi$
$720$		0			0
$721$	−13.2485	+	5.80096i	−0.493400	+	0.216039i
$722$		0			0
$723$	−4.87883	−	18.2081i	−0.181446	−	0.677165i
$724$		0			0
$725$	−24.0163	−	6.43515i	−0.891944	−	0.238996i
$726$		0			0
$727$		−	8.84759i		−	0.328139i	−0.986449	−	0.164069i	$-0.947538\pi$
$727$		−	8.84759i		−	0.328139i	0.986449	−	0.164069i	$-0.0524621\pi$
$728$		0			0
$729$		−	27.7318i		−	1.02711i
$730$		0			0
$731$	22.9349	+	6.14539i	0.848278	+	0.227296i
$732$		0			0
$733$	4.81667	+	17.9761i	0.177908	+	0.663961i	0.996038	+	0.0889281i	$0.0283441\pi$
$733$	4.81667	+	17.9761i	0.177908	+	0.663961i	−0.818130	+	0.575033i	$0.804989\pi$
$734$		0			0
$735$	10.2895	−	3.20347i	0.379535	−	0.118162i
$736$		0			0
$737$	−3.62558	+	6.27970i	−0.133550	+	0.231316i
$738$		0			0
$739$	11.2525	+	3.01509i	0.413929	+	0.110912i	0.459772	−	0.888037i	$-0.347931\pi$
$739$	11.2525	+	3.01509i	0.413929	+	0.110912i	−0.0458437	+	0.998949i	$0.514598\pi$
$740$		0			0
$741$	−0.139803	−	0.139803i	−0.00513579	−	0.00513579i
$742$		0			0
$743$	−3.37957			−0.123984			−0.0619922	−	0.998077i	$-0.519745\pi$
$743$	−3.37957			−0.123984			−0.0619922	+	0.998077i	$0.519745\pi$
$744$		0			0
$745$	−9.60754	−	16.6407i	−0.351993	−	0.609670i
$746$		0			0
$747$	−2.87480	−	10.7289i	−0.105183	−	0.392549i
$748$		0			0
$749$	−1.03811	+	2.65530i	−0.0379317	+	0.0970224i
$750$		0			0
$751$	14.8677	+	8.58389i	0.542531	+	0.313231i	0.746104	−	0.665829i	$-0.231922\pi$
$751$	14.8677	+	8.58389i	0.542531	+	0.313231i	−0.203573	+	0.979060i	$0.565255\pi$
$752$		0			0
$753$	−3.48978	−	6.04447i	−0.127175	−	0.220273i
$754$		0			0
$755$	2.98131	+	2.98131i	0.108501	+	0.108501i
$756$		0			0
$757$	16.8157	−	16.8157i	0.611177	−	0.611177i	−0.332076	−	0.943253i	$-0.607749\pi$
$757$	16.8157	−	16.8157i	0.611177	−	0.611177i	0.943253	+	0.332076i	$0.107749\pi$
$758$		0			0
$759$	−7.11210	+	4.10617i	−0.258153	+	0.149045i
$760$		0			0
$761$	2.82967	−	4.90113i	0.102575	−	0.177666i	−0.810170	−	0.586195i	$-0.800625\pi$
$761$	2.82967	−	4.90113i	0.102575	−	0.177666i	0.912745	+	0.408530i	$0.133958\pi$
$762$		0			0
$763$	−17.2131	−	21.5266i	−0.623156	−	0.779314i
$764$		0			0
$765$	4.57515	−	1.22591i	0.165415	−	0.0443228i
$766$		0			0
$767$	−5.73044	+	3.30847i	−0.206914	+	0.119462i
$768$		0			0
$769$			24.1880i			0.872241i	0.899888	+	0.436121i	$0.143648\pi$
$769$			24.1880i			0.872241i	−0.899888	+	0.436121i	$0.856352\pi$
$770$		0			0
$771$	−14.1445	+	14.1445i	−0.509403	+	0.509403i
$772$		0			0
$773$	2.22422	−	8.30089i	0.0799995	−	0.298562i	−0.914321	−	0.404991i	$-0.867275\pi$
$773$	2.22422	−	8.30089i	0.0799995	−	0.298562i	0.994320	+	0.106428i	$0.0339415\pi$
$774$		0			0
$775$	−25.4585	−	14.6985i	−0.914495	−	0.527984i
$776$		0			0
$777$	−14.3705	+	19.5249i	−0.515540	+	0.700453i
$778$		0			0
$779$	1.60045	−	0.428839i	0.0573420	−	0.0153647i
$780$		0			0
$781$	0.281683	−	1.05125i	0.0100794	−	0.0376168i
$782$		0			0
$783$	−37.8467			−1.35253
$784$		0			0
$785$	−7.28880			−0.260148
$786$		0			0
$787$	7.58704	−	28.3152i	0.270449	−	1.00933i	−0.688382	−	0.725349i	$-0.741679\pi$
$787$	7.58704	−	28.3152i	0.270449	−	1.00933i	0.958830	−	0.283979i	$-0.0916547\pi$
$788$		0			0
$789$	0.795080	−	0.213041i	0.0283056	−	0.00758446i
$790$		0			0
$791$	−2.94291	+	3.99846i	−0.104638	+	0.142169i
$792$		0			0
$793$	−6.12845	−	3.53826i	−0.217628	−	0.125647i
$794$		0			0
$795$	3.20405	−	11.9577i	0.113636	−	0.424095i
$796$		0			0
$797$	5.29908	−	5.29908i	0.187703	−	0.187703i	−0.606999	−	0.794702i	$-0.707627\pi$
$797$	5.29908	−	5.29908i	0.187703	−	0.187703i	0.794702	+	0.606999i	$0.207627\pi$
$798$		0			0
$799$		−	30.9309i		−	1.09426i
$800$		0			0
$801$	4.66222	−	2.69173i	0.164731	−	0.0951077i
$802$		0			0
$803$	12.5951	−	3.37486i	0.444473	−	0.119096i
$804$		0			0
$805$	−11.3569	−	14.2029i	−0.400278	−	0.500585i
$806$		0			0
$807$	−20.7495	+	35.9391i	−0.730416	+	1.26512i
$808$		0			0
$809$	32.7521	−	18.9094i	1.15150	−	0.664819i	0.202248	−	0.979334i	$-0.435175\pi$
$809$	32.7521	−	18.9094i	1.15150	−	0.664819i	0.949253	+	0.314515i	$0.101842\pi$
$810$		0			0
$811$	29.9995	−	29.9995i	1.05342	−	1.05342i	0.0549344	−	0.998490i	$-0.482505\pi$
$811$	29.9995	−	29.9995i	1.05342	−	1.05342i	0.998490	−	0.0549344i	$-0.0174950\pi$
$812$		0			0
$813$	−4.84082	−	4.84082i	−0.169775	−	0.169775i
$814$		0			0
$815$	9.95399	+	17.2408i	0.348673	+	0.603920i
$816$		0			0
$817$	−1.38470	−	0.799457i	−0.0484446	−	0.0279695i
$818$		0			0
$819$	0.684837	−	1.75169i	0.0239301	−	0.0612089i
$820$		0			0
$821$	−8.66045	−	32.3212i	−0.302252	−	1.12802i	−0.935285	−	0.353895i	$-0.884857\pi$
$821$	−8.66045	−	32.3212i	−0.302252	−	1.12802i	0.633034	−	0.774124i	$-0.281809\pi$
$822$		0			0
$823$	19.7859	+	34.2703i	0.689695	+	1.19459i	0.971937	+	0.235243i	$0.0755886\pi$
$823$	19.7859	+	34.2703i	0.689695	+	1.19459i	−0.282242	+	0.959343i	$0.591078\pi$
$824$		0			0
$825$	5.03690			0.175362
$826$		0			0
$827$	−22.9404	−	22.9404i	−0.797717	−	0.797717i	0.185018	−	0.982735i	$-0.440766\pi$
$827$	−22.9404	−	22.9404i	−0.797717	−	0.797717i	−0.982735	+	0.185018i	$0.940766\pi$
$828$		0			0
$829$	−16.6277	−	4.45537i	−0.577503	−	0.154742i	−0.0417677	−	0.999127i	$-0.513299\pi$
$829$	−16.6277	−	4.45537i	−0.577503	−	0.154742i	−0.535736	+	0.844386i	$0.679966\pi$
$830$		0			0
$831$	−4.02428	+	6.97025i	−0.139601	+	0.241795i
$832$		0			0
$833$	−18.3361	−	16.9242i	−0.635309	−	0.586388i
$834$		0			0
$835$	4.65051	+	17.3559i	0.160937	+	0.600627i
$836$		0			0
$837$	−43.2226	−	11.5815i	−1.49399	−	0.400313i
$838$		0			0
$839$			19.1043i			0.659555i	0.944059	+	0.329777i	$0.106974\pi$
$839$			19.1043i			0.659555i	−0.944059	+	0.329777i	$0.893026\pi$
$840$		0			0
$841$			16.0069i			0.551962i
$842$		0			0
$843$	−0.606893	−	0.162617i	−0.0209025	−	0.00560081i
$844$		0			0
$845$	3.71818	+	13.8764i	0.127909	+	0.477363i
$846$		0			0
$847$	24.2159	−	10.6031i	0.832070	−	0.364328i
$848$		0			0
$849$	−8.86178	+	15.3491i	−0.304136	+	0.526778i
$850$		0			0
$851$	39.5155	+	10.5882i	1.35458	+	0.362957i
$852$		0			0
$853$	−29.0051	−	29.0051i	−0.993116	−	0.993116i	0.00686001	−	0.999976i	$-0.497816\pi$
$853$	−29.0051	−	29.0051i	−0.993116	−	0.993116i	−0.999976	+	0.00686001i	$0.997816\pi$
$854$		0			0
$855$	−0.318958			−0.0109081
$856$		0			0
$857$	25.8112	+	44.7063i	0.881693	+	1.52714i	0.849457	+	0.527658i	$0.176930\pi$
$857$	25.8112	+	44.7063i	0.881693	+	1.52714i	0.0322362	+	0.999480i	$0.489737\pi$
$858$		0			0
$859$	13.7616	+	51.3588i	0.469538	+	1.75234i	0.641387	+	0.767218i	$0.278359\pi$
$859$	13.7616	+	51.3588i	0.469538	+	1.75234i	−0.171849	+	0.985123i	$0.554974\pi$
$860$		0			0
$861$	−15.4362	−	19.3044i	−0.526065	−	0.657893i
$862$		0			0
$863$	−39.7219	−	22.9335i	−1.35215	−	0.780664i	−0.363600	−	0.931555i	$-0.618452\pi$
$863$	−39.7219	−	22.9335i	−1.35215	−	0.780664i	−0.988550	+	0.150891i	$0.951786\pi$
$864$		0			0
$865$	−6.47219	−	11.2102i	−0.220061	−	0.381157i
$866$		0			0
$867$	−4.10861	−	4.10861i	−0.139536	−	0.139536i
$868$		0			0
$869$	5.16349	−	5.16349i	0.175159	−	0.175159i
$870$		0			0
$871$	3.80572	−	2.19723i	0.128952	−	0.0744505i
$872$		0			0
$873$	−10.7626	+	18.6414i	−0.364260	+	0.630916i
$874$		0			0
$875$	3.93902	+	25.9032i	0.133163	+	0.875686i
$876$		0			0
$877$	−30.9754	+	8.29983i	−1.04596	+	0.280265i	−0.740583	−	0.671965i	$-0.765450\pi$
$877$	−30.9754	+	8.29983i	−1.04596	+	0.280265i	−0.305381	+	0.952230i	$0.598784\pi$
$878$		0			0
$879$	0.920177	−	0.531265i	0.0310368	−	0.0179191i
$880$		0			0
$881$			12.4751i			0.420297i	0.977670	+	0.210148i	$0.0673947\pi$
$881$			12.4751i			0.420297i	−0.977670	+	0.210148i	$0.932605\pi$
$882$		0			0
$883$	−13.1980	+	13.1980i	−0.444148	+	0.444148i	−0.893403	−	0.449256i	$-0.851689\pi$
$883$	−13.1980	+	13.1980i	−0.444148	+	0.444148i	0.449256	+	0.893403i	$0.351689\pi$
$884$		0			0
$885$	4.33257	−	16.1694i	0.145638	−	0.543528i
$886$		0			0
$887$	32.7267	+	18.8948i	1.09886	+	0.634424i	0.935920	−	0.352212i	$-0.114571\pi$
$887$	32.7267	+	18.8948i	1.09886	+	0.634424i	0.162935	+	0.986637i	$0.447904\pi$
$888$		0			0
$889$	13.3688	+	9.83956i	0.448375	+	0.330008i
$890$		0			0
$891$	4.00673	−	1.07360i	0.134231	−	0.0359670i
$892$		0			0
$893$	−0.539090	+	2.01191i	−0.0180400	+	0.0673260i
$894$		0			0
$895$	−4.41574			−0.147602
$896$		0			0
$897$	4.97698			0.166176
$898$		0			0
$899$	−13.7725	+	51.3998i	−0.459340	+	1.71428i
$900$		0			0
$901$	−27.6873	+	7.41880i	−0.922398	+	0.247156i
$902$		0			0
$903$	−2.63950	+	23.7056i	−0.0878372	+	0.788872i
$904$		0			0
$905$	−16.9596	−	9.79164i	−0.563757	−	0.325485i
$906$		0			0
$907$	8.16939	−	30.4886i	0.271260	−	1.01236i	−0.687046	−	0.726614i	$-0.741093\pi$
$907$	8.16939	−	30.4886i	0.271260	−	1.01236i	0.958306	−	0.285743i	$-0.0922404\pi$
$908$		0			0
$909$	0.826997	−	0.826997i	0.0274298	−	0.0274298i
$910$		0			0
$911$		−	23.0133i		−	0.762465i	−0.924479	−	0.381232i	$-0.875500\pi$
$911$		−	23.0133i		−	0.762465i	0.924479	−	0.381232i	$-0.124500\pi$
$912$		0			0
$913$	8.26870	−	4.77394i	0.273654	−	0.157994i
$914$		0			0
$915$	17.2924	−	4.63349i	0.571670	−	0.153179i
$916$		0			0
$917$	−18.6478	+	47.6978i	−0.615806	+	1.57512i
$918$		0			0
$919$	13.9041	−	24.0826i	0.458653	−	0.794411i	−0.540237	−	0.841513i	$-0.681665\pi$
$919$	13.9041	−	24.0826i	0.458653	−	0.794411i	0.998890	+	0.0471022i	$0.0149986\pi$
$920$		0			0
$921$	−9.62742	+	5.55839i	−0.317234	+	0.183155i
$922$		0			0
$923$	−0.466388	+	0.466388i	−0.0153513	+	0.0153513i
$924$		0			0
$925$	−17.7421	−	17.7421i	−0.583357	−	0.583357i
$926$		0			0
$927$	−3.19282	−	5.53013i	−0.104866	−	0.181633i
$928$		0			0
$929$	−15.9529	−	9.21039i	−0.523397	−	0.302183i	0.214927	−	0.976630i	$-0.431049\pi$
$929$	−15.9529	−	9.21039i	−0.523397	−	0.302183i	−0.738323	+	0.674447i	$0.764382\pi$
$930$		0			0
$931$	0.897710	+	1.42041i	0.0294213	+	0.0465522i
$932$		0			0
$933$	−2.43414	−	9.08433i	−0.0796901	−	0.297408i
$934$		0			0
$935$	2.03577	+	3.52605i	0.0665767	+	0.115314i
$936$		0			0
$937$	41.3111			1.34957			0.674787	−	0.738012i	$-0.264235\pi$
$937$	41.3111			1.34957			0.674787	+	0.738012i	$0.264235\pi$
$938$		0			0
$939$	−10.7124	−	10.7124i	−0.349586	−	0.349586i
$940$		0			0
$941$	−32.7348	−	8.77125i	−1.06712	−	0.285935i	−0.317812	−	0.948154i	$-0.602948\pi$
$941$	−32.7348	−	8.77125i	−1.06712	−	0.285935i	−0.749310	+	0.662219i	$0.769615\pi$
$942$		0			0
$943$	−20.8546	+	36.1212i	−0.679120	+	1.17627i
$944$		0			0
$945$	6.80965	+	15.5522i	0.221518	+	0.505913i
$946$		0			0
$947$	−11.5687	−	43.1751i	−0.375933	−	1.40300i	−0.851977	−	0.523580i	$-0.824596\pi$
$947$	−11.5687	−	43.1751i	−0.375933	−	1.40300i	0.476043	−	0.879422i	$-0.342070\pi$
$948$		0			0
$949$	−7.63310	−	2.04528i	−0.247781	−	0.0663927i
$950$		0			0
$951$		−	31.3880i		−	1.01782i
$952$		0			0
$953$		−	15.5386i		−	0.503345i	−0.967812	−	0.251672i	$-0.919019\pi$
$953$		−	15.5386i		−	0.503345i	0.967812	−	0.251672i	$-0.0809805\pi$
$954$		0			0
$955$	−23.2652	−	6.23389i	−0.752844	−	0.201724i
$956$		0			0
$957$	−2.35980	−	8.80691i	−0.0762816	−	0.284687i
$958$		0			0
$959$	1.76104	−	15.8161i	0.0568671	−	0.510728i
$960$		0			0
$961$	−15.9577	+	27.6395i	−0.514764	+	0.891598i
$962$		0			0
$963$	−1.21589	−	0.325796i	−0.0391814	−	0.0104986i
$964$		0			0
$965$	16.3014	+	16.3014i	0.524762	+	0.524762i
$966$		0			0
$967$	−26.0733			−0.838460			−0.419230	−	0.907880i	$-0.637700\pi$
$967$	−26.0733			−0.838460			−0.419230	+	0.907880i	$0.637700\pi$
$968$		0			0
$969$	−0.579066	−	1.00297i	−0.0186023	−	0.0322201i
$970$		0			0
$971$	−9.54855	−	35.6357i	−0.306427	−	1.14360i	−0.931710	−	0.363204i	$-0.881683\pi$
$971$	−9.54855	−	35.6357i	−0.306427	−	1.14360i	0.625282	−	0.780399i	$-0.284984\pi$
$972$		0			0
$973$	−0.336851	−	2.21514i	−0.0107989	−	0.0710143i
$974$		0			0
$975$	−2.64358	−	1.52627i	−0.0846623	−	0.0488798i
$976$		0			0
$977$	10.9839	+	19.0246i	0.351405	+	0.608651i	0.986496	−	0.163786i	$-0.0523708\pi$
$977$	10.9839	+	19.0246i	0.351405	+	0.608651i	−0.635091	+	0.772437i	$0.719037\pi$
$978$		0			0
$979$	3.27222	+	3.27222i	0.104581	+	0.104581i
$980$		0			0
$981$	8.60502	−	8.60502i	0.274737	−	0.274737i
$982$		0			0
$983$	−18.5776	+	10.7258i	−0.592534	+	0.342100i	−0.766099	−	0.642723i	$-0.777805\pi$
$983$	−18.5776	+	10.7258i	−0.592534	+	0.342100i	0.173565	+	0.984822i	$0.444471\pi$
$984$		0			0
$985$	1.38477	−	2.39848i	0.0441223	−	0.0764220i
$986$		0			0
$987$	30.7186	−	4.67129i	0.977784	−	0.148689i
$988$		0			0
$989$	38.8780	−	10.4173i	1.23625	−	0.331251i
$990$		0			0
$991$	−7.26862	+	4.19654i	−0.230895	+	0.133307i	−0.610985	−	0.791642i	$-0.709226\pi$
$991$	−7.26862	+	4.19654i	−0.230895	+	0.133307i	0.380090	+	0.924950i	$0.375893\pi$
$992$		0			0
$993$		−	18.3457i		−	0.582184i
$994$		0			0
$995$	−2.05884	+	2.05884i	−0.0652698	+	0.0652698i
$996$		0			0
$997$	1.13442	−	4.23370i	0.0359274	−	0.134083i	−0.945633	−	0.325236i	$-0.894556\pi$
$997$	1.13442	−	4.23370i	0.0359274	−	0.134083i	0.981560	+	0.191154i	$0.0612228\pi$
$998$		0			0
$999$	−33.0762	−	19.0966i	−1.04649	−	0.604189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.z.a.47.5		56
4.3	odd	2		112.2.v.a.19.9	yes	56
7.3	odd	6	inner	448.2.z.a.367.5		56
8.3	odd	2		896.2.z.b.607.5		56
8.5	even	2		896.2.z.a.607.10		56
16.3	odd	4		896.2.z.a.159.10		56
16.5	even	4		112.2.v.a.75.11	yes	56
16.11	odd	4	inner	448.2.z.a.271.5		56
16.13	even	4		896.2.z.b.159.5		56
28.3	even	6		112.2.v.a.3.11	✓	56
28.11	odd	6		784.2.w.f.227.11		56
28.19	even	6		784.2.j.a.195.1		56
28.23	odd	6		784.2.j.a.195.2		56
28.27	even	2		784.2.w.f.19.9		56
56.3	even	6		896.2.z.b.479.5		56
56.45	odd	6		896.2.z.a.479.10		56
112.3	even	12		896.2.z.a.31.10		56
112.5	odd	12		784.2.j.a.587.2		56
112.37	even	12		784.2.j.a.587.1		56
112.45	odd	12		896.2.z.b.31.5		56
112.53	even	12		784.2.w.f.619.9		56
112.59	even	12	inner	448.2.z.a.143.5		56
112.69	odd	4		784.2.w.f.411.11		56
112.101	odd	12		112.2.v.a.59.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.11	✓	56	28.3	even	6
112.2.v.a.19.9	yes	56	4.3	odd	2
112.2.v.a.59.9	yes	56	112.101	odd	12
112.2.v.a.75.11	yes	56	16.5	even	4
448.2.z.a.47.5		56	1.1	even	1	trivial
448.2.z.a.143.5		56	112.59	even	12	inner
448.2.z.a.271.5		56	16.11	odd	4	inner
448.2.z.a.367.5		56	7.3	odd	6	inner
784.2.j.a.195.1		56	28.19	even	6
784.2.j.a.195.2		56	28.23	odd	6
784.2.j.a.587.1		56	112.37	even	12
784.2.j.a.587.2		56	112.5	odd	12
784.2.w.f.19.9		56	28.27	even	2
784.2.w.f.227.11		56	28.11	odd	6
784.2.w.f.411.11		56	112.69	odd	4
784.2.w.f.619.9		56	112.53	even	12
896.2.z.a.31.10		56	112.3	even	12
896.2.z.a.159.10		56	16.3	odd	4
896.2.z.a.479.10		56	56.45	odd	6
896.2.z.a.607.10		56	8.5	even	2
896.2.z.b.31.5		56	112.45	odd	12
896.2.z.b.159.5		56	16.13	even	4
896.2.z.b.479.5		56	56.3	even	6
896.2.z.b.607.5		56	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.350301 + 1.30734i) q^{3} +(1.09872 - 0.294400i) q^{5} +(1.56831 - 2.13082i) q^{7} +(1.01165 + 0.584076i) q^{9} +O(q^{10})\)	\(q+(-0.350301 + 1.30734i) q^{3} +(1.09872 - 0.294400i) q^{5} +(1.56831 - 2.13082i) q^{7} +(1.01165 + 0.584076i) q^{9} +(-0.259891 + 0.969928i) q^{11} +(0.430308 - 0.430308i) q^{13} +1.53952i q^{15} +(3.08710 - 1.78234i) q^{17} +(-0.231866 + 0.0621282i) q^{19} +(2.23633 + 2.79674i) q^{21} +(3.02132 - 5.23308i) q^{23} +(-3.20962 + 1.85308i) q^{25} +(-3.98908 + 3.98908i) q^{27} +(4.74378 + 4.74378i) q^{29} +(3.96596 + 6.86925i) q^{31} +(-1.17698 - 0.679532i) q^{33} +(1.09581 - 2.80288i) q^{35} +(1.75224 + 6.53945i) q^{37} +(0.411821 + 0.713295i) q^{39} -6.90248 q^{41} +(4.70996 + 4.70996i) q^{43} +(1.28347 + 0.343904i) q^{45} +(4.33853 - 7.51455i) q^{47} +(-2.08082 - 6.68358i) q^{49} +(1.24871 + 4.66025i) q^{51} +(-7.76712 - 2.08119i) q^{53} +1.14219i q^{55} -0.324891i q^{57} +(-10.5029 - 2.81423i) q^{59} +(-3.00970 - 11.2323i) q^{61} +(2.83114 - 1.23964i) q^{63} +(0.346103 - 0.599468i) q^{65} +(6.97519 + 1.86900i) q^{67} +(5.78305 + 5.78305i) q^{69} -1.08385 q^{71} +(-6.49282 - 11.2459i) q^{73} +(-1.29827 - 4.84520i) q^{75} +(1.65916 + 2.07493i) q^{77} +(-6.29786 - 3.63607i) q^{79} +(-2.06548 - 3.57752i) q^{81} +(-6.72351 - 6.72351i) q^{83} +(2.86713 - 2.86713i) q^{85} +(-7.86348 + 4.53998i) q^{87} +(2.30426 - 3.99110i) q^{89} +(-0.242055 - 1.59176i) q^{91} +(-10.3697 + 2.77856i) q^{93} +(-0.236464 + 0.136523i) q^{95} +18.4267i q^{97} +(-0.829431 + 0.829431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7}+O(q^{10}) \) 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7	\( 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} - 10 q^{21} + 12 q^{23} - 24 q^{29} - 12 q^{33} + 2 q^{35} + 6 q^{37} + 4 q^{39} + 12 q^{45} - 8 q^{49} + 34 q^{51} + 6 q^{53} - 42 q^{59} - 6 q^{61} - 4 q^{65} - 6 q^{67} + 80 q^{71} - 24 q^{75} + 10 q^{77} - 8 q^{81} - 28 q^{85} + 12 q^{87} - 16 q^{91} + 10 q^{93} + 16 q^{99}+O(q^{100}) \) 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 - 10 * q^21 + 12 * q^23 - 24 * q^29 - 12 * q^33 + 2 * q^35 + 6 * q^37 + 4 * q^39 + 12 * q^45 - 8 * q^49 + 34 * q^51 + 6 * q^53 - 42 * q^59 - 6 * q^61 - 4 * q^65 - 6 * q^67 + 80 * q^71 - 24 * q^75 + 10 * q^77 - 8 * q^81 - 28 * q^85 + 12 * q^87 - 16 * q^91 + 10 * q^93 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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