LMFDB - Embedded newform 256.2.i.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(17,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("256.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.i (of order $16$, degree $8$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	256.49
Dual form			256.2.i.a.209.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.191980 + 0.0381873i) q^{3} +(-0.967135 - 1.44742i) q^{5} +(-4.53283 - 1.87756i) q^{7} +(-2.73624 + 1.13339i) q^{9} +O(q^{10})$	\(q+(-0.191980 + 0.0381873i) q^{3} +(-0.967135 - 1.44742i) q^{5} +(-4.53283 - 1.87756i) q^{7} +(-2.73624 + 1.13339i) q^{9} +(0.540778 - 2.71867i) q^{11} +(1.42546 - 2.13334i) q^{13} +(0.240944 + 0.240944i) q^{15} +(-2.43954 + 2.43954i) q^{17} +(1.88371 + 1.25865i) q^{19} +(0.941914 + 0.187358i) q^{21} +(0.690956 + 1.66811i) q^{23} +(0.753743 - 1.81970i) q^{25} +(0.970283 - 0.648322i) q^{27} +(-1.50522 - 7.56726i) q^{29} -3.63299i q^{31} +0.542583i q^{33} +(1.66624 + 8.37677i) q^{35} +(-5.55115 + 3.70916i) q^{37} +(-0.192193 + 0.463995i) q^{39} +(-0.926510 - 2.23679i) q^{41} +(6.41133 + 1.27529i) q^{43} +(4.28680 + 2.86435i) q^{45} +(-3.58669 + 3.58669i) q^{47} +(12.0716 + 12.0716i) q^{49} +(0.375184 - 0.561503i) q^{51} +(-0.513941 + 2.58375i) q^{53} +(-4.45807 + 1.84659i) q^{55} +(-0.409700 - 0.169703i) q^{57} +(-5.40361 - 8.08707i) q^{59} +(13.1016 - 2.60608i) q^{61} +14.5309 q^{63} -4.46645 q^{65} +(2.72425 - 0.541887i) q^{67} +(-0.196351 - 0.293860i) q^{69} +(-4.17620 - 1.72984i) q^{71} +(-5.46867 + 2.26520i) q^{73} +(-0.0752147 + 0.378130i) q^{75} +(-7.55573 + 11.3080i) q^{77} +(5.71185 + 5.71185i) q^{79} +(6.12117 - 6.12117i) q^{81} +(-10.3786 - 6.93477i) q^{83} +(5.89040 + 1.17167i) q^{85} +(0.577946 + 1.39529i) q^{87} +(3.49372 - 8.43458i) q^{89} +(-10.4668 + 6.99371i) q^{91} +(0.138734 + 0.697464i) q^{93} -3.94381i q^{95} -9.58124i q^{97} +(1.60161 + 8.05186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{5}{16}\right)$	$1$

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
$3$	−0.191980	+	0.0381873i	−0.110840	+	0.0220474i	−0.250199	−	0.968195i	$-0.580496\pi$
$3$	−0.191980	+	0.0381873i	−0.110840	+	0.0220474i	0.139359	+	0.990242i	$0.455496\pi$
$4$		0			0
$5$	−0.967135	−	1.44742i	−0.432516	−	0.647306i	0.549634	−	0.835406i	$-0.314767\pi$
$5$	−0.967135	−	1.44742i	−0.432516	−	0.647306i	−0.982150	+	0.188100i	$0.939767\pi$
$6$		0			0
$7$	−4.53283	−	1.87756i	−1.71325	−	0.709651i	−0.999961	−	0.00878062i	$-0.997205\pi$
$7$	−4.53283	−	1.87756i	−1.71325	−	0.709651i	−0.713288	−	0.700871i	$-0.752795\pi$
$8$		0			0
$9$	−2.73624	+	1.13339i	−0.912080	+	0.377796i
$10$		0			0
$11$	0.540778	−	2.71867i	0.163051	−	0.819711i	−0.809518	−	0.587095i	$-0.800271\pi$
$11$	0.540778	−	2.71867i	0.163051	−	0.819711i	0.972569	−	0.232616i	$-0.0747286\pi$
$12$		0			0
$13$	1.42546	−	2.13334i	0.395350	−	0.591683i	−0.579383	−	0.815055i	$-0.696706\pi$
$13$	1.42546	−	2.13334i	0.395350	−	0.591683i	0.974733	+	0.223372i	$0.0717065\pi$
$14$		0			0
$15$	0.240944	+	0.240944i	0.0622115	+	0.0622115i
$16$		0			0
$17$	−2.43954	+	2.43954i	−0.591675	+	0.591675i	−0.938084	−	0.346409i	$-0.887401\pi$
$17$	−2.43954	+	2.43954i	−0.591675	+	0.591675i	0.346409	+	0.938084i	$0.387401\pi$
$18$		0			0
$19$	1.88371	+	1.25865i	0.432152	+	0.288755i	0.752559	−	0.658525i	$-0.228819\pi$
$19$	1.88371	+	1.25865i	0.432152	+	0.288755i	−0.320406	+	0.947280i	$0.603819\pi$
$20$		0			0
$21$	0.941914	+	0.187358i	0.205543	+	0.0408850i
$22$		0			0
$23$	0.690956	+	1.66811i	0.144074	+	0.347826i	0.979400	−	0.201929i	$-0.0647211\pi$
$23$	0.690956	+	1.66811i	0.144074	+	0.347826i	−0.835326	+	0.549755i	$0.814721\pi$
$24$		0			0
$25$	0.753743	−	1.81970i	0.150749	−	0.363939i
$26$		0			0
$27$	0.970283	−	0.648322i	0.186731	−	0.124770i
$28$		0			0
$29$	−1.50522	−	7.56726i	−0.279513	−	1.40521i	−0.824073	−	0.566483i	$-0.808303\pi$
$29$	−1.50522	−	7.56726i	−0.279513	−	1.40521i	0.544560	−	0.838722i	$-0.316697\pi$
$30$		0			0
$31$		−	3.63299i		−	0.652505i	−0.945283	−	0.326253i	$-0.894214\pi$
$31$		−	3.63299i		−	0.652505i	0.945283	−	0.326253i	$-0.105786\pi$
$32$		0			0
$33$			0.542583i			0.0944516i
$34$		0			0
$35$	1.66624	+	8.37677i	0.281646	+	1.41593i
$36$		0			0
$37$	−5.55115	+	3.70916i	−0.912603	+	0.609782i	−0.920737	−	0.390185i	$-0.872411\pi$
$37$	−5.55115	+	3.70916i	−0.912603	+	0.609782i	0.00813317	+	0.999967i	$0.497411\pi$
$38$		0			0
$39$	−0.192193	+	0.463995i	−0.0307755	+	0.0742986i
$40$		0			0
$41$	−0.926510	−	2.23679i	−0.144697	−	0.349328i	0.834870	−	0.550446i	$-0.185542\pi$
$41$	−0.926510	−	2.23679i	−0.144697	−	0.349328i	−0.979567	+	0.201118i	$0.935542\pi$
$42$		0			0
$43$	6.41133	+	1.27529i	0.977718	+	0.194480i	0.657988	−	0.753028i	$-0.271408\pi$
$43$	6.41133	+	1.27529i	0.977718	+	0.194480i	0.319730	+	0.947509i	$0.396408\pi$
$44$		0			0
$45$	4.28680	+	2.86435i	0.639039	+	0.426992i
$46$		0			0
$47$	−3.58669	+	3.58669i	−0.523172	+	0.523172i	−0.918528	−	0.395356i	$-0.870621\pi$
$47$	−3.58669	+	3.58669i	−0.523172	+	0.523172i	0.395356	+	0.918528i	$0.370621\pi$
$48$		0			0
$49$	12.0716	+	12.0716i	1.72451	+	1.72451i
$50$		0			0
$51$	0.375184	−	0.561503i	0.0525363	−	0.0786261i
$52$		0			0
$53$	−0.513941	+	2.58375i	−0.0705952	+	0.354906i	−0.999896	−	0.0144176i	$-0.995411\pi$
$53$	−0.513941	+	2.58375i	−0.0705952	+	0.354906i	0.929301	+	0.369324i	$0.120411\pi$
$54$		0			0
$55$	−4.45807	+	1.84659i	−0.601126	+	0.248994i
$56$		0			0
$57$	−0.409700	−	0.169703i	−0.0542661	−	0.0224777i
$58$		0			0
$59$	−5.40361	−	8.08707i	−0.703490	−	1.05285i	−0.995344	−	0.0963843i	$-0.969272\pi$
$59$	−5.40361	−	8.08707i	−0.703490	−	1.05285i	0.291854	−	0.956463i	$-0.405728\pi$
$60$		0			0
$61$	13.1016	−	2.60608i	1.67749	−	0.333674i	0.737624	−	0.675211i	$-0.235948\pi$
$61$	13.1016	−	2.60608i	1.67749	−	0.333674i	0.939868	+	0.341537i	$0.110948\pi$
$62$		0			0
$63$	14.5309			1.83072
$64$		0			0
$65$	−4.46645			−0.553995
$66$		0			0
$67$	2.72425	−	0.541887i	0.332820	−	0.0662021i	−0.0258515	−	0.999666i	$-0.508230\pi$
$67$	2.72425	−	0.541887i	0.332820	−	0.0662021i	0.358672	+	0.933464i	$0.383230\pi$
$68$		0			0
$69$	−0.196351	−	0.293860i	−0.0236379	−	0.0353765i
$70$		0			0
$71$	−4.17620	−	1.72984i	−0.495623	−	0.205294i	0.120848	−	0.992671i	$-0.461439\pi$
$71$	−4.17620	−	1.72984i	−0.495623	−	0.205294i	−0.616472	+	0.787377i	$0.711439\pi$
$72$		0			0
$73$	−5.46867	+	2.26520i	−0.640059	+	0.265121i	−0.679020	−	0.734119i	$-0.737595\pi$
$73$	−5.46867	+	2.26520i	−0.640059	+	0.265121i	0.0389610	+	0.999241i	$0.487595\pi$
$74$		0			0
$75$	−0.0752147	+	0.378130i	−0.00868504	+	0.0436627i
$76$		0			0
$77$	−7.55573	+	11.3080i	−0.861056	+	1.28866i
$78$		0			0
$79$	5.71185	+	5.71185i	0.642633	+	0.642633i	0.951202	−	0.308569i	$-0.0998500\pi$
$79$	5.71185	+	5.71185i	0.642633	+	0.642633i	−0.308569	+	0.951202i	$0.599850\pi$
$80$		0			0
$81$	6.12117	−	6.12117i	0.680129	−	0.680129i
$82$		0			0
$83$	−10.3786	−	6.93477i	−1.13920	−	0.761189i	−0.164871	−	0.986315i	$-0.552721\pi$
$83$	−10.3786	−	6.93477i	−1.13920	−	0.761189i	−0.974330	+	0.225126i	$0.927721\pi$
$84$		0			0
$85$	5.89040	+	1.17167i	0.638903	+	0.127086i
$86$		0			0
$87$	0.577946	+	1.39529i	0.0619623	+	0.149590i
$88$		0			0
$89$	3.49372	−	8.43458i	0.370333	−	0.894064i	−0.623360	−	0.781935i	$-0.714233\pi$
$89$	3.49372	−	8.43458i	0.370333	−	0.894064i	0.993694	−	0.112129i	$-0.0357670\pi$
$90$		0			0
$91$	−10.4668	+	6.99371i	−1.09722	+	0.733141i
$92$		0			0
$93$	0.138734	+	0.697464i	0.0143861	+	0.0723236i
$94$		0			0
$95$		−	3.94381i		−	0.404626i
$96$		0			0
$97$		−	9.58124i		−	0.972828i	−0.873728	−	0.486414i	$-0.838305\pi$
$97$		−	9.58124i		−	0.972828i	0.873728	−	0.486414i	$-0.161695\pi$
$98$		0			0
$99$	1.60161	+	8.05186i	0.160968	+	0.809242i
$100$		0			0
$101$	−3.78774	+	2.53089i	−0.376894	+	0.251833i	−0.729560	−	0.683917i	$-0.760275\pi$
$101$	−3.78774	+	2.53089i	−0.376894	+	0.251833i	0.352666	+	0.935749i	$0.385275\pi$
$102$		0			0
$103$	0.503843	−	1.21638i	0.0496451	−	0.119854i	−0.897111	−	0.441804i	$-0.854338\pi$
$103$	0.503843	−	1.21638i	0.0496451	−	0.119854i	0.946756	+	0.321951i	$0.104338\pi$
$104$		0			0
$105$	−0.639772	−	1.54455i	−0.0624353	−	0.150732i
$106$		0			0
$107$	3.54726	+	0.705594i	0.342927	+	0.0682124i	0.363549	−	0.931575i	$-0.381565\pi$
$107$	3.54726	+	0.705594i	0.342927	+	0.0682124i	−0.0206225	+	0.999787i	$0.506565\pi$
$108$		0			0
$109$	−7.61993	−	5.09147i	−0.729857	−	0.487675i	0.134272	−	0.990944i	$-0.457130\pi$
$109$	−7.61993	−	5.09147i	−0.729857	−	0.487675i	−0.864129	+	0.503270i	$0.832130\pi$
$110$		0			0
$111$	0.924069	−	0.924069i	0.0877088	−	0.0877088i
$112$		0			0
$113$	−9.25522	−	9.25522i	−0.870658	−	0.870658i	0.121886	−	0.992544i	$-0.461106\pi$
$113$	−9.25522	−	9.25522i	−0.870658	−	0.870658i	−0.992544	+	0.121886i	$0.961106\pi$
$114$		0			0
$115$	1.74621	−	2.61340i	0.162835	−	0.243700i
$116$		0			0
$117$	−1.48248	+	7.45294i	−0.137055	+	0.689024i
$118$		0			0
$119$	15.6384	−	6.47764i	1.43357	−	0.593804i
$120$		0			0
$121$	3.06392	+	1.26912i	0.278539	+	0.115374i
$122$		0			0
$123$	0.263289	+	0.394040i	0.0237400	+	0.0355293i
$124$		0			0
$125$	−11.8996	+	2.36697i	−1.06433	+	0.211709i
$126$		0			0
$127$	−8.28837			−0.735474			−0.367737	−	0.929930i	$-0.619867\pi$
$127$	−8.28837			−0.735474			−0.367737	+	0.929930i	$0.619867\pi$
$128$		0			0
$129$	−1.27955			−0.112658
$130$		0			0
$131$	−12.8274	+	2.55153i	−1.12074	+	0.222928i	−0.720480	−	0.693475i	$-0.756079\pi$
$131$	−12.8274	+	2.55153i	−1.12074	+	0.222928i	−0.400256	+	0.916404i	$0.631079\pi$
$132$		0			0
$133$	−6.17534	−	9.24205i	−0.535470	−	0.801387i
$134$		0			0
$135$	−1.87679	−	0.777392i	−0.161528	−	0.0669072i
$136$		0			0
$137$	−3.42304	+	1.41787i	−0.292450	+	0.121137i	−0.524085	−	0.851666i	$-0.675593\pi$
$137$	−3.42304	+	1.41787i	−0.292450	+	0.121137i	0.231635	+	0.972803i	$0.425593\pi$
$138$		0			0
$139$	3.82451	−	19.2271i	0.324391	−	1.63082i	−0.382822	−	0.923822i	$-0.625048\pi$
$139$	3.82451	−	19.2271i	0.324391	−	1.63082i	0.707213	−	0.707001i	$-0.249952\pi$
$140$		0			0
$141$	0.551608	−	0.825540i	0.0464538	−	0.0695230i
$142$		0			0
$143$	−5.02901	−	5.02901i	−0.420547	−	0.420547i
$144$		0			0
$145$	−9.49725	+	9.49725i	−0.788704	+	0.788704i
$146$		0			0
$147$	−2.77849	−	1.85653i	−0.229166	−	0.153124i
$148$		0			0
$149$	9.20724	+	1.83143i	0.754287	+	0.150037i	0.557234	−	0.830356i	$-0.311863\pi$
$149$	9.20724	+	1.83143i	0.754287	+	0.150037i	0.197053	+	0.980393i	$0.436863\pi$
$150$		0			0
$151$	6.60900	+	15.9555i	0.537833	+	1.29844i	0.926233	+	0.376952i	$0.123028\pi$
$151$	6.60900	+	15.9555i	0.537833	+	1.29844i	−0.388400	+	0.921491i	$0.626972\pi$
$152$		0			0
$153$	3.91022	−	9.44010i	0.316123	−	0.763187i
$154$		0			0
$155$	−5.25847	+	3.51360i	−0.422370	+	0.282219i
$156$		0			0
$157$	−0.838120	−	4.21351i	−0.0668893	−	0.336275i	0.932821	−	0.360340i	$-0.117339\pi$
$157$	−0.838120	−	4.21351i	−0.0668893	−	0.336275i	−0.999710	+	0.0240647i	$0.992339\pi$
$158$		0			0
$159$		−	0.515656i		−	0.0408942i
$160$		0			0
$161$		−	8.85860i		−	0.698155i
$162$		0			0
$163$	−1.20061	−	6.03588i	−0.0940391	−	0.472766i	−0.998893	−	0.0470438i	$-0.985020\pi$
$163$	−1.20061	−	6.03588i	−0.0940391	−	0.472766i	0.904854	−	0.425723i	$-0.139980\pi$
$164$		0			0
$165$	0.785346	−	0.524751i	0.0611391	−	0.0408518i
$166$		0			0
$167$	2.59281	−	6.25960i	0.200638	−	0.484382i	−0.791251	−	0.611492i	$-0.790570\pi$
$167$	2.59281	−	6.25960i	0.200638	−	0.484382i	0.991889	+	0.127109i	$0.0405698\pi$
$168$		0			0
$169$	2.45565	+	5.92846i	0.188896	+	0.456035i
$170$		0			0
$171$	−6.58082	−	1.30901i	−0.503248	−	0.100102i
$172$		0			0
$173$	13.9780	+	9.33980i	1.06273	+	0.710092i	0.958682	−	0.284480i	$-0.0918211\pi$
$173$	13.9780	+	9.33980i	1.06273	+	0.710092i	0.104046	+	0.994572i	$0.466821\pi$
$174$		0			0
$175$	−6.83318	+	6.83318i	−0.516540	+	0.516540i
$176$		0			0
$177$	1.34621	+	1.34621i	0.101187	+	0.101187i
$178$		0			0
$179$	10.0942	−	15.1070i	0.754476	−	1.12915i	−0.233167	−	0.972437i	$-0.574909\pi$
$179$	10.0942	−	15.1070i	0.754476	−	1.12915i	0.987644	−	0.156717i	$-0.0500911\pi$
$180$		0			0
$181$	1.33053	−	6.68904i	0.0988977	−	0.497192i	−0.899308	−	0.437316i	$-0.855929\pi$
$181$	1.33053	−	6.68904i	0.0988977	−	0.497192i	0.998206	−	0.0598766i	$-0.0190707\pi$
$182$		0			0
$183$	−2.41574	+	1.00063i	−0.178577	+	0.0739688i
$184$		0			0
$185$	10.7374	+	4.44759i	0.789431	+	0.326993i
$186$		0			0
$187$	5.31306	+	7.95156i	0.388530	+	0.581476i
$188$		0			0
$189$	−5.61540	+	1.11697i	−0.408460	+	0.0812477i
$190$		0			0
$191$	−4.13034			−0.298861			−0.149430	−	0.988772i	$-0.547744\pi$
$191$	−4.13034			−0.298861			−0.149430	+	0.988772i	$0.547744\pi$
$192$		0			0
$193$	2.74997			0.197947			0.0989737	−	0.995090i	$-0.468444\pi$
$193$	2.74997			0.197947			0.0989737	+	0.995090i	$0.468444\pi$
$194$		0			0
$195$	0.857471	−	0.170562i	0.0614048	−	0.0122142i
$196$		0			0
$197$	−1.52669	−	2.28486i	−0.108772	−	0.162789i	0.773090	−	0.634296i	$-0.218710\pi$
$197$	−1.52669	−	2.28486i	−0.108772	−	0.162789i	−0.881862	+	0.471507i	$0.843710\pi$
$198$		0			0
$199$	−0.831551	−	0.344440i	−0.0589471	−	0.0244167i	0.353015	−	0.935618i	$-0.385156\pi$
$199$	−0.831551	−	0.344440i	−0.0589471	−	0.0244167i	−0.411962	+	0.911201i	$0.635156\pi$
$200$		0			0
$201$	−0.502310	+	0.208064i	−0.0354302	+	0.0146757i
$202$		0			0
$203$	−7.38507	+	37.1273i	−0.518331	+	2.60582i
$204$		0			0
$205$	−2.34152	+	3.50433i	−0.163539	+	0.244753i
$206$		0			0
$207$	−3.78124	−	3.78124i	−0.262814	−	0.262814i
$208$		0			0
$209$	4.44054	−	4.44054i	0.307158	−	0.307158i
$210$		0			0
$211$	11.5419	+	7.71208i	0.794581	+	0.530922i	0.885336	−	0.464951i	$-0.153928\pi$
$211$	11.5419	+	7.71208i	0.794581	+	0.530922i	−0.0907556	+	0.995873i	$0.528928\pi$
$212$		0			0
$213$	0.867806	+	0.172617i	0.0594611	+	0.0118275i
$214$		0			0
$215$	−4.35474	−	10.5133i	−0.296991	−	0.716999i
$216$		0			0
$217$	−6.82117	+	16.4678i	−0.463051	+	1.11790i
$218$		0			0
$219$	0.963376	−	0.643707i	0.0650989	−	0.0434977i
$220$		0			0
$221$	1.72692	+	8.68183i	0.116165	+	0.584003i
$222$		0			0
$223$		−	6.30327i		−	0.422098i	−0.977475	−	0.211049i	$-0.932312\pi$
$223$		−	6.30327i		−	0.422098i	0.977475	−	0.211049i	$-0.0676880\pi$
$224$		0			0
$225$			5.83341i			0.388894i
$226$		0			0
$227$	−3.46768	−	17.4332i	−0.230158	−	1.15708i	−0.907057	−	0.421007i	$-0.861677\pi$
$227$	−3.46768	−	17.4332i	−0.230158	−	1.15708i	0.676899	−	0.736076i	$-0.263323\pi$
$228$		0			0
$229$	7.65290	−	5.11350i	0.505718	−	0.337910i	−0.276398	−	0.961043i	$-0.589141\pi$
$229$	7.65290	−	5.11350i	0.505718	−	0.337910i	0.782115	+	0.623134i	$0.214141\pi$
$230$		0			0
$231$	1.01873	−	2.45944i	0.0670277	−	0.161819i
$232$		0			0
$233$	5.24399	+	12.6601i	0.343545	+	0.829391i	0.997352	+	0.0727295i	$0.0231710\pi$
$233$	5.24399	+	12.6601i	0.343545	+	0.829391i	−0.653807	+	0.756662i	$0.726829\pi$
$234$		0			0
$235$	8.66026	+	1.72263i	0.564933	+	0.112372i
$236$		0			0
$237$	−1.31468	−	0.878443i	−0.0853978	−	0.0570610i
$238$		0			0
$239$	−8.39091	+	8.39091i	−0.542763	+	0.542763i	−0.924338	−	0.381575i	$-0.875382\pi$
$239$	−8.39091	+	8.39091i	−0.542763	+	0.542763i	0.381575	+	0.924338i	$0.375382\pi$
$240$		0			0
$241$	3.97755	+	3.97755i	0.256217	+	0.256217i	0.823513	−	0.567297i	$-0.192011\pi$
$241$	3.97755	+	3.97755i	0.256217	+	0.256217i	−0.567297	+	0.823513i	$0.692011\pi$
$242$		0			0
$243$	−2.88636	+	4.31974i	−0.185160	+	0.277112i
$244$		0			0
$245$	5.79780	−	29.1475i	0.370408	−	1.86217i
$246$		0			0
$247$	5.37028	−	2.22444i	0.341703	−	0.141538i
$248$		0			0
$249$	2.25731	+	0.935008i	0.143051	+	0.0592537i
$250$		0			0
$251$	10.0908	+	15.1019i	0.636924	+	0.953224i	0.999772	+	0.0213753i	$0.00680450\pi$
$251$	10.0908	+	15.1019i	0.636924	+	0.953224i	−0.362848	+	0.931848i	$0.618196\pi$
$252$		0			0
$253$	4.90871	−	0.976404i	0.308608	−	0.0613860i
$254$		0			0
$255$	−1.17558			−0.0736179
$256$		0			0
$257$	−15.1836			−0.947128			−0.473564	−	0.880760i	$-0.657033\pi$
$257$	−15.1836			−0.947128			−0.473564	+	0.880760i	$0.657033\pi$
$258$		0			0
$259$	32.1266	−	6.39038i	1.99625	−	0.397079i
$260$		0			0
$261$	12.6953	+	18.9998i	0.785819	+	1.17606i
$262$		0			0
$263$	19.1921	+	7.94964i	1.18344	+	0.490196i	0.885613	−	0.464425i	$-0.153739\pi$
$263$	19.1921	+	7.94964i	1.18344	+	0.490196i	0.297825	+	0.954620i	$0.403739\pi$
$264$		0			0
$265$	4.23683	−	1.75495i	0.260266	−	0.107806i
$266$		0			0
$267$	−0.348632	+	1.75269i	−0.0213359	+	0.107263i
$268$		0			0
$269$	−3.71107	+	5.55401i	−0.226268	+	0.338634i	−0.927182	−	0.374612i	$-0.877776\pi$
$269$	−3.71107	+	5.55401i	−0.226268	+	0.338634i	0.700914	+	0.713246i	$0.252776\pi$
$270$		0			0
$271$	−2.68097	−	2.68097i	−0.162858	−	0.162858i	0.620974	−	0.783831i	$-0.286737\pi$
$271$	−2.68097	−	2.68097i	−0.162858	−	0.162858i	−0.783831	+	0.620974i	$0.786737\pi$
$272$		0			0
$273$	1.74236	−	1.74236i	0.105452	−	0.105452i
$274$		0			0
$275$	−4.53956	−	3.03323i	−0.273746	−	0.182911i
$276$		0			0
$277$	−7.35826	−	1.46365i	−0.442115	−	0.0879421i	−0.0309870	−	0.999520i	$-0.509865\pi$
$277$	−7.35826	−	1.46365i	−0.442115	−	0.0879421i	−0.411128	+	0.911578i	$0.634865\pi$
$278$		0			0
$279$	4.11759	+	9.94075i	0.246514	+	0.595137i
$280$		0			0
$281$	−8.64142	+	20.8622i	−0.515504	+	1.24454i	0.425136	+	0.905130i	$0.360226\pi$
$281$	−8.64142	+	20.8622i	−0.515504	+	1.24454i	−0.940640	+	0.339407i	$0.889774\pi$
$282$		0			0
$283$	26.0256	−	17.3898i	1.54706	−	1.03371i	0.569776	−	0.821800i	$-0.307030\pi$
$283$	26.0256	−	17.3898i	1.54706	−	1.03371i	0.977288	−	0.211915i	$-0.0679699\pi$
$284$		0			0
$285$	0.150603	+	0.757133i	0.00892096	+	0.0448487i
$286$		0			0
$287$			11.8786i			0.701171i
$288$		0			0
$289$			5.09731i			0.299842i
$290$		0			0
$291$	0.365882	+	1.83941i	0.0214484	+	0.107828i
$292$		0			0
$293$	16.4610	−	10.9989i	0.961661	−	0.642561i	0.0275790	−	0.999620i	$-0.491220\pi$
$293$	16.4610	−	10.9989i	0.961661	−	0.642561i	0.934082	+	0.357058i	$0.116220\pi$
$294$		0			0
$295$	−6.47937	+	15.6426i	−0.377243	+	0.910746i
$296$		0			0
$297$	−1.23787	−	2.98848i	−0.0718285	−	0.173409i
$298$		0			0
$299$	4.54359	+	0.903776i	0.262763	+	0.0522667i
$300$		0			0
$301$	−26.6670	−	17.8183i	−1.53706	−	1.02703i
$302$		0			0
$303$	0.630524	−	0.630524i	0.0362227	−	0.0362227i
$304$		0			0
$305$	−16.4431	−	16.4431i	−0.941531	−	0.941531i
$306$		0			0
$307$	−14.1044	+	21.1087i	−0.804981	+	1.20474i	0.170652	+	0.985331i	$0.445413\pi$
$307$	−14.1044	+	21.1087i	−0.804981	+	1.20474i	−0.975633	+	0.219408i	$0.929587\pi$
$308$		0			0
$309$	−0.0502776	+	0.252762i	−0.00286019	+	0.0143791i
$310$		0			0
$311$	−13.9327	+	5.77111i	−0.790051	+	0.327250i	−0.740964	−	0.671545i	$-0.765631\pi$
$311$	−13.9327	+	5.77111i	−0.790051	+	0.327250i	−0.0490867	+	0.998795i	$0.515631\pi$
$312$		0			0
$313$	5.08075	+	2.10452i	0.287181	+	0.118954i	0.521624	−	0.853176i	$-0.325327\pi$
$313$	5.08075	+	2.10452i	0.287181	+	0.118954i	−0.234443	+	0.972130i	$0.575327\pi$
$314$		0			0
$315$	−14.0534	−	21.0323i	−0.791817	−	1.18504i
$316$		0			0
$317$	−4.93180	+	0.980996i	−0.276997	+	0.0550982i	−0.331634	−	0.943408i	$-0.607600\pi$
$317$	−4.93180	+	0.980996i	−0.276997	+	0.0550982i	0.0546367	+	0.998506i	$0.482600\pi$
$318$		0			0
$319$	−21.3869			−1.19744
$320$		0			0
$321$	−0.707950			−0.0395139
$322$		0			0
$323$	−7.66591	+	1.52484i	−0.426543	+	0.0848446i
$324$		0			0
$325$	−2.80761	−	4.20189i	−0.155738	−	0.233079i
$326$		0			0
$327$	1.65731	+	0.686479i	0.0916493	+	0.0379624i
$328$		0			0
$329$	22.9921	−	9.52364i	1.26760	−	0.525055i
$330$		0			0
$331$	1.36801	−	6.87743i	0.0751924	−	0.378018i	−0.924805	−	0.380442i	$-0.875772\pi$
$331$	1.36801	−	6.87743i	0.0751924	−	0.378018i	0.999997	+	0.00242459i	$0.000771771\pi$
$332$		0			0
$333$	10.9854	−	16.4408i	0.601994	−	0.900948i
$334$		0			0
$335$	−3.41906	−	3.41906i	−0.186803	−	0.186803i
$336$		0			0
$337$	−11.6065	+	11.6065i	−0.632248	+	0.632248i	−0.948631	−	0.316383i	$-0.897531\pi$
$337$	−11.6065	+	11.6065i	−0.632248	+	0.632248i	0.316383	+	0.948631i	$0.397531\pi$
$338$		0			0
$339$	2.13025	+	1.42339i	0.115699	+	0.0773079i
$340$		0			0
$341$	−9.87693	−	1.96464i	−0.534866	−	0.106391i
$342$		0			0
$343$	−18.9104	−	45.6538i	−1.02107	−	2.46507i
$344$		0			0
$345$	−0.235441	+	0.568404i	−0.0126757	+	0.0306018i
$346$		0			0
$347$	−14.1994	+	9.48772i	−0.762262	+	0.509327i	−0.874897	−	0.484309i	$-0.839071\pi$
$347$	−14.1994	+	9.48772i	−0.762262	+	0.509327i	0.112635	+	0.993636i	$0.464071\pi$
$348$		0			0
$349$	−2.26631	−	11.3935i	−0.121313	−	0.609881i	−0.992832	−	0.119519i	$-0.961865\pi$
$349$	−2.26631	−	11.3935i	−0.121313	−	0.609881i	0.871519	−	0.490362i	$-0.163135\pi$
$350$		0			0
$351$		−	2.99410i		−	0.159813i
$352$		0			0
$353$			11.5221i			0.613261i	0.951829	+	0.306631i	$0.0992016\pi$
$353$			11.5221i			0.613261i	−0.951829	+	0.306631i	$0.900798\pi$
$354$		0			0
$355$	1.53515	+	7.71770i	0.0814770	+	0.409613i
$356$		0			0
$357$	−2.75490	+	1.84077i	−0.145805	+	0.0974237i
$358$		0			0
$359$	1.31387	−	3.17197i	0.0693435	−	0.167410i	−0.885408	−	0.464815i	$-0.846121\pi$
$359$	1.31387	−	3.17197i	0.0693435	−	0.167410i	0.954752	+	0.297405i	$0.0961210\pi$
$360$		0			0
$361$	−5.30684	−	12.8118i	−0.279307	−	0.674307i
$362$		0			0
$363$	−0.636678	−	0.126643i	−0.0334169	−	0.00664704i
$364$		0			0
$365$	8.56763	+	5.72471i	0.448450	+	0.299645i
$366$		0			0
$367$	22.5749	−	22.5749i	1.17840	−	1.17840i	0.198245	−	0.980152i	$-0.436476\pi$
$367$	22.5749	−	22.5749i	1.17840	−	1.17840i	0.980152	−	0.198245i	$-0.0635242\pi$
$368$		0			0
$369$	5.07031	+	5.07031i	0.263950	+	0.263950i
$370$		0			0
$371$	7.18076	−	10.7468i	0.372807	−	0.557945i
$372$		0			0
$373$	−6.61395	+	33.2506i	−0.342457	+	1.72165i	0.298793	+	0.954318i	$0.403416\pi$
$373$	−6.61395	+	33.2506i	−0.342457	+	1.72165i	−0.641250	+	0.767332i	$0.721584\pi$
$374$		0			0
$375$	2.19410	−	0.908825i	0.113303	−	0.0469315i
$376$		0			0
$377$	−18.2892	−	7.57563i	−0.941942	−	0.390165i
$378$		0			0
$379$	11.6484	+	17.4330i	0.598337	+	0.895474i	0.999792	−	0.0204046i	$-0.00649543\pi$
$379$	11.6484	+	17.4330i	0.598337	+	0.895474i	−0.401455	+	0.915879i	$0.631495\pi$
$380$		0			0
$381$	1.59121	−	0.316510i	0.0815199	−	0.0162153i
$382$		0			0
$383$	−0.0590227			−0.00301592			−0.00150796	−	0.999999i	$-0.500480\pi$
$383$	−0.0590227			−0.00301592			−0.00150796	+	0.999999i	$0.500480\pi$
$384$		0			0
$385$	23.6748			1.20658
$386$		0			0
$387$	−18.9883	+	3.77701i	−0.965231	+	0.191996i
$388$		0			0
$389$	−1.79208	−	2.68204i	−0.0908621	−	0.135985i	0.783254	−	0.621702i	$-0.213558\pi$
$389$	−1.79208	−	2.68204i	−0.0908621	−	0.135985i	−0.874116	+	0.485717i	$0.838558\pi$
$390$		0			0
$391$	−5.75504	−	2.38382i	−0.291045	−	0.120555i
$392$		0			0
$393$	2.36518	−	0.979688i	0.119307	−	0.0494187i
$394$		0			0
$395$	2.74331	−	13.7916i	0.138031	−	0.693929i
$396$		0			0
$397$	3.22276	−	4.82320i	0.161746	−	0.242069i	−0.741740	−	0.670687i	$-0.765999\pi$
$397$	3.22276	−	4.82320i	0.161746	−	0.242069i	0.903486	+	0.428618i	$0.140999\pi$
$398$		0			0
$399$	1.53847	+	1.53847i	0.0770200	+	0.0770200i
$400$		0			0
$401$	18.2413	−	18.2413i	0.910926	−	0.910926i	−0.0854187	−	0.996345i	$-0.527223\pi$
$401$	18.2413	−	18.2413i	0.910926	−	0.910926i	0.996345	+	0.0854187i	$0.0272228\pi$
$402$		0			0
$403$	−7.75043	−	5.17867i	−0.386076	−	0.257968i
$404$		0			0
$405$	−14.7799	−	2.93990i	−0.734419	−	0.146085i
$406$		0			0
$407$	7.08206	+	17.0976i	0.351045	+	0.847497i
$408$		0			0
$409$	3.91775	−	9.45829i	0.193720	−	0.467682i	−0.796936	−	0.604064i	$-0.793547\pi$
$409$	3.91775	−	9.45829i	0.193720	−	0.467682i	0.990656	+	0.136381i	$0.0435473\pi$
$410$		0			0
$411$	0.603012	−	0.402920i	0.0297444	−	0.0198746i
$412$		0			0
$413$	9.30969	+	46.8030i	0.458100	+	2.30302i
$414$		0			0
$415$			21.7291i			1.06664i
$416$		0			0
$417$			3.83728i			0.187912i
$418$		0			0
$419$	−6.22515	−	31.2959i	−0.304119	−	1.52891i	−0.766511	−	0.642232i	$-0.778009\pi$
$419$	−6.22515	−	31.2959i	−0.304119	−	1.52891i	0.462392	−	0.886676i	$-0.346991\pi$
$420$		0			0
$421$	9.43550	−	6.30460i	0.459858	−	0.307268i	−0.303976	−	0.952680i	$-0.598314\pi$
$421$	9.43550	−	6.30460i	0.459858	−	0.307268i	0.763835	+	0.645412i	$0.223314\pi$
$422$		0			0
$423$	5.74893	−	13.8792i	0.279523	−	0.674828i
$424$		0			0
$425$	2.60044	+	6.27801i	0.126140	+	0.304528i
$426$		0			0
$427$	−64.2806	−	12.7862i	−3.11076	−	0.618768i
$428$		0			0
$429$	1.15752	+	0.773428i	0.0558854	+	0.0373415i
$430$		0			0
$431$	19.4613	−	19.4613i	0.937417	−	0.937417i	−0.0607373	−	0.998154i	$-0.519345\pi$
$431$	19.4613	−	19.4613i	0.937417	−	0.937417i	0.998154	+	0.0607373i	$0.0193452\pi$
$432$		0			0
$433$	−25.2269	−	25.2269i	−1.21233	−	1.21233i	−0.970259	−	0.242069i	$-0.922174\pi$
$433$	−25.2269	−	25.2269i	−1.21233	−	1.21233i	−0.242069	−	0.970259i	$-0.577826\pi$
$434$		0			0
$435$	1.46061	−	2.18596i	0.0700310	−	0.104809i
$436$		0			0
$437$	−0.798020	+	4.01192i	−0.0381745	+	0.191916i
$438$		0			0
$439$	−26.5392	+	10.9929i	−1.26665	+	0.524662i	−0.911943	−	0.410316i	$-0.865418\pi$
$439$	−26.5392	+	10.9929i	−1.26665	+	0.524662i	−0.354704	+	0.934979i	$0.615418\pi$
$440$		0			0
$441$	−46.7126	−	19.3490i	−2.22441	−	0.921380i
$442$		0			0
$443$	−0.00461809	−	0.00691146i	−0.000219412	−	0.000328373i	0.831360	−	0.555734i	$-0.187563\pi$
$443$	−0.00461809	−	0.00691146i	−0.000219412	−	0.000328373i	−0.831579	+	0.555406i	$0.812563\pi$
$444$		0			0
$445$	−15.5873	+	3.10050i	−0.738908	+	0.146978i
$446$		0			0
$447$	−1.83755			−0.0869130
$448$		0			0
$449$	13.9393			0.657838			0.328919	−	0.944358i	$-0.393316\pi$
$449$	13.9393			0.657838			0.328919	+	0.944358i	$0.393316\pi$
$450$		0			0
$451$	−6.58215	+	1.30927i	−0.309941	+	0.0616511i
$452$		0			0
$453$	−1.87810	−	2.81077i	−0.0882407	−	0.132061i
$454$		0			0
$455$	20.2457	+	8.38604i	0.949132	+	0.393143i
$456$		0			0
$457$	−13.6237	+	5.64312i	−0.637290	+	0.263974i	−0.677847	−	0.735203i	$-0.737087\pi$
$457$	−13.6237	+	5.64312i	−0.637290	+	0.263974i	0.0405569	+	0.999177i	$0.487087\pi$
$458$		0			0
$459$	−0.785435	+	3.94865i	−0.0366610	+	0.184307i
$460$		0			0
$461$	16.5649	−	24.7911i	0.771504	−	1.15464i	−0.212616	−	0.977136i	$-0.568198\pi$
$461$	16.5649	−	24.7911i	0.771504	−	1.15464i	0.984120	−	0.177502i	$-0.0568016\pi$
$462$		0			0
$463$	7.31500	+	7.31500i	0.339957	+	0.339957i	0.856351	−	0.516394i	$-0.172726\pi$
$463$	7.31500	+	7.31500i	0.339957	+	0.339957i	−0.516394	+	0.856351i	$0.672726\pi$
$464$		0			0
$465$	0.875348	−	0.875348i	0.0405933	−	0.0405933i
$466$		0			0
$467$	26.6310	+	17.7943i	1.23233	+	0.823420i	0.989200	−	0.146573i	$-0.0468242\pi$
$467$	26.6310	+	17.7943i	1.23233	+	0.823420i	0.243135	+	0.969992i	$0.421824\pi$
$468$		0			0
$469$	−13.3660	−	2.65866i	−0.617185	−	0.122766i
$470$		0			0
$471$	0.321805	+	0.776907i	0.0148280	+	0.0357980i
$472$		0			0
$473$	6.93421	−	16.7407i	0.318835	−	0.769737i
$474$		0			0
$475$	3.71020	−	2.47908i	0.170236	−	0.113748i
$476$		0			0
$477$	−1.52213	−	7.65227i	−0.0696936	−	0.350373i
$478$		0			0
$479$			24.2263i			1.10693i	0.832873	+	0.553465i	$0.186695\pi$
$479$			24.2263i			1.10693i	−0.832873	+	0.553465i	$0.813305\pi$
$480$		0			0
$481$			17.1298i			0.781050i
$482$		0			0
$483$	0.338286	+	1.70068i	0.0153925	+	0.0773835i
$484$		0			0
$485$	−13.8681	+	9.26636i	−0.629717	+	0.420764i
$486$		0			0
$487$	−12.2953	+	29.6835i	−0.557153	+	1.34509i	0.354857	+	0.934921i	$0.384530\pi$
$487$	−12.2953	+	29.6835i	−0.557153	+	1.34509i	−0.912011	+	0.410167i	$0.865470\pi$
$488$		0			0
$489$	0.460987	+	1.11292i	0.0208466	+	0.0503281i
$490$		0			0
$491$	17.7528	+	3.53125i	0.801173	+	0.159363i	0.578663	−	0.815567i	$-0.303575\pi$
$491$	17.7528	+	3.53125i	0.801173	+	0.159363i	0.222510	+	0.974930i	$0.428575\pi$
$492$		0			0
$493$	22.1327	+	14.7886i	0.996805	+	0.666044i
$494$		0			0
$495$	10.1054	−	10.1054i	0.454206	−	0.454206i
$496$		0			0
$497$	15.6821	+	15.6821i	0.703440	+	0.703440i
$498$		0			0
$499$	−15.7545	+	23.5782i	−0.705267	+	1.05551i	0.289875	+	0.957064i	$0.406386\pi$
$499$	−15.7545	+	23.5782i	−0.705267	+	1.05551i	−0.995143	+	0.0984427i	$0.968614\pi$
$500$		0			0
$501$	−0.258732	+	1.30073i	−0.0115593	+	0.0581125i
$502$		0			0
$503$	29.1486	−	12.0738i	1.29967	−	0.538342i	0.377819	−	0.925880i	$-0.376674\pi$
$503$	29.1486	−	12.0738i	1.29967	−	0.538342i	0.921854	+	0.387538i	$0.126674\pi$
$504$		0			0
$505$	7.32651	+	3.03474i	0.326025	+	0.135044i
$506$		0			0
$507$	−0.697828	−	1.04437i	−0.0309916	−	0.0463823i
$508$		0			0
$509$	5.86884	−	1.16739i	0.260132	−	0.0517435i	−0.0633013	−	0.997994i	$-0.520163\pi$
$509$	5.86884	−	1.16739i	0.260132	−	0.0517435i	0.323433	+	0.946251i	$0.395163\pi$
$510$		0			0
$511$	29.0416			1.28473
$512$		0			0
$513$	2.64374			0.116724
$514$		0			0
$515$	−2.24790	+	0.447136i	−0.0990544	+	0.0197031i
$516$		0			0
$517$	7.81144	+	11.6906i	0.343547	+	0.514154i
$518$		0			0
$519$	−3.04016	−	1.25928i	−0.133448	−	0.0552762i
$520$		0			0
$521$	26.1756	−	10.8423i	1.14678	−	0.475010i	0.273325	−	0.961922i	$-0.411877\pi$
$521$	26.1756	−	10.8423i	1.14678	−	0.475010i	0.873451	+	0.486912i	$0.161877\pi$
$522$		0			0
$523$	1.00914	−	5.07326i	0.0441264	−	0.221838i	−0.952430	−	0.304758i	$-0.901424\pi$
$523$	1.00914	−	5.07326i	0.0441264	−	0.221838i	0.996556	+	0.0829195i	$0.0264244\pi$
$524$		0			0
$525$	1.05090	−	1.57278i	0.0458649	−	0.0686417i
$526$		0			0
$527$	8.86283	+	8.86283i	0.386071	+	0.386071i
$528$		0			0
$529$	13.9583	−	13.9583i	0.606881	−	0.606881i
$530$		0			0
$531$	23.9514	+	16.0038i	1.03940	+	0.694505i
$532$		0			0
$533$	−6.09255	−	1.21188i	−0.263898	−	0.0524925i
$534$		0			0
$535$	−2.40939	−	5.81678i	−0.104167	−	0.251481i
$536$		0			0
$537$	−1.36099	+	3.28573i	−0.0587312	+	0.141790i
$538$		0			0
$539$	39.3468	−	26.2907i	1.69479	−	1.13242i
$540$		0			0
$541$	0.217556	+	1.09373i	0.00935346	+	0.0470230i	0.985180	−	0.171523i	$-0.0548687\pi$
$541$	0.217556	+	1.09373i	0.00935346	+	0.0470230i	−0.975827	+	0.218546i	$0.929869\pi$
$542$		0			0
$543$			1.33497i			0.0572892i
$544$		0			0
$545$			15.9534i			0.683368i
$546$		0			0
$547$	1.95857	+	9.84642i	0.0837426	+	0.421002i	0.999801	+	0.0199572i	$0.00635300\pi$
$547$	1.95857	+	9.84642i	0.0837426	+	0.421002i	−0.916058	+	0.401045i	$0.868647\pi$
$548$		0			0
$549$	−32.8955	+	21.9801i	−1.40395	+	0.938087i
$550$		0			0
$551$	6.68916	−	16.1491i	0.284968	−	0.687973i
$552$		0			0
$553$	−15.1665	−	36.6152i	−0.644946	−	1.55704i
$554$		0			0
$555$	−2.23122	−	0.443816i	−0.0947098	−	0.0188390i
$556$		0			0
$557$	−20.7214	−	13.8456i	−0.877994	−	0.586657i	0.0328255	−	0.999461i	$-0.489549\pi$
$557$	−20.7214	−	13.8456i	−0.877994	−	0.586657i	−0.910820	+	0.412804i	$0.864549\pi$
$558$		0			0
$559$	11.8597	−	11.8597i	0.501612	−	0.501612i
$560$		0			0
$561$	−1.32365	−	1.32365i	−0.0558846	−	0.0558846i
$562$		0			0
$563$	−22.4818	+	33.6463i	−0.947493	+	1.41802i	−0.0394146	+	0.999223i	$0.512549\pi$
$563$	−22.4818	+	33.6463i	−0.947493	+	1.41802i	−0.908078	+	0.418800i	$0.862451\pi$
$564$		0			0
$565$	−4.44514	+	22.3472i	−0.187008	+	0.940155i
$566$		0			0
$567$	−39.2391	+	16.2534i	−1.64789	+	0.682577i
$568$		0			0
$569$	21.2575	+	8.80516i	0.891163	+	0.369132i	0.780816	−	0.624762i	$-0.214804\pi$
$569$	21.2575	+	8.80516i	0.891163	+	0.369132i	0.110347	+	0.993893i	$0.464804\pi$
$570$		0			0
$571$	−21.4891	−	32.1606i	−0.899289	−	1.34588i	−0.938002	−	0.346631i	$-0.887326\pi$
$571$	−21.4891	−	32.1606i	−0.899289	−	1.34588i	0.0387126	−	0.999250i	$-0.487674\pi$
$572$		0			0
$573$	0.792944	−	0.157726i	0.0331257	−	0.00658911i
$574$		0			0
$575$	3.55627			0.148307
$576$		0			0
$577$	12.9731			0.540076			0.270038	−	0.962850i	$-0.412964\pi$
$577$	12.9731			0.540076			0.270038	+	0.962850i	$0.412964\pi$
$578$		0			0
$579$	−0.527941	+	0.105014i	−0.0219405	+	0.00436423i
$580$		0			0
$581$	34.0241	+	50.9206i	1.41156	+	2.11254i
$582$		0			0
$583$	6.74646	+	2.79448i	0.279410	+	0.115735i
$584$		0			0
$585$	12.2213	−	5.06222i	0.505288	−	0.209297i
$586$		0			0
$587$	−0.438329	+	2.20363i	−0.0180918	+	0.0909534i	−0.988776	−	0.149404i	$-0.952265\pi$
$587$	−0.438329	+	2.20363i	−0.0180918	+	0.0909534i	0.970685	+	0.240357i	$0.0772646\pi$
$588$		0			0
$589$	4.57268	−	6.84350i	0.188414	−	0.281982i
$590$		0			0
$591$	0.380347	+	0.380347i	0.0156454	+	0.0156454i
$592$		0			0
$593$	−25.5913	+	25.5913i	−1.05091	+	1.05091i	−0.0522765	+	0.998633i	$0.516648\pi$
$593$	−25.5913	+	25.5913i	−1.05091	+	1.05091i	−0.998633	+	0.0522765i	$0.983352\pi$
$594$		0			0
$595$	−24.5003	−	16.3706i	−1.00441	−	0.671128i
$596$		0			0
$597$	0.172795	+	0.0343710i	0.00707202	+	0.00140671i
$598$		0			0
$599$	−4.71217	−	11.3762i	−0.192534	−	0.464819i	0.797903	−	0.602786i	$-0.205943\pi$
$599$	−4.71217	−	11.3762i	−0.192534	−	0.464819i	−0.990437	+	0.137968i	$0.955943\pi$
$600$		0			0
$601$	−8.85882	+	21.3871i	−0.361359	+	0.872397i	0.633743	+	0.773543i	$0.281518\pi$
$601$	−8.85882	+	21.3871i	−0.361359	+	0.872397i	−0.995102	+	0.0988537i	$0.968482\pi$
$602$		0			0
$603$	−6.84004	+	4.57037i	−0.278548	+	0.186120i
$604$		0			0
$605$	−1.12628	−	5.66219i	−0.0457898	−	0.230201i
$606$		0			0
$607$		−	11.3561i		−	0.460929i	−0.973081	−	0.230465i	$-0.925975\pi$
$607$		−	11.3561i		−	0.460929i	0.973081	−	0.230465i	$-0.0740246\pi$
$608$		0			0
$609$		−	7.40973i		−	0.300257i
$610$		0			0
$611$	2.53898	+	12.7643i	0.102716	+	0.516389i
$612$		0			0
$613$	20.5529	−	13.7330i	0.830122	−	0.554670i	−0.0663364	−	0.997797i	$-0.521131\pi$
$613$	20.5529	−	13.7330i	0.830122	−	0.554670i	0.896459	+	0.443127i	$0.146131\pi$
$614$		0			0
$615$	0.315705	−	0.762179i	0.0127304	−	0.0307340i
$616$		0			0
$617$	−1.48976	−	3.59660i	−0.0599754	−	0.144793i	0.891051	−	0.453903i	$-0.149969\pi$
$617$	−1.48976	−	3.59660i	−0.0599754	−	0.144793i	−0.951026	+	0.309110i	$0.899969\pi$
$618$		0			0
$619$	0.987852	+	0.196496i	0.0397051	+	0.00789784i	0.214903	−	0.976635i	$-0.431056\pi$
$619$	0.987852	+	0.196496i	0.0397051	+	0.00789784i	−0.175198	+	0.984533i	$0.556056\pi$
$620$		0			0
$621$	1.75190	+	1.17058i	0.0703013	+	0.0469738i
$622$		0			0
$623$	−31.6729	+	31.6729i	−1.26895	+	1.26895i
$624$		0			0
$625$	7.97082	+	7.97082i	0.318833	+	0.318833i
$626$		0			0
$627$	−0.682924	+	1.02207i	−0.0272734	+	0.0408175i
$628$		0			0
$629$	4.49360	−	22.5909i	0.179172	−	0.900757i
$630$		0			0
$631$	24.1540	−	10.0049i	0.961554	−	0.398289i	0.153992	−	0.988072i	$-0.450787\pi$
$631$	24.1540	−	10.0049i	0.961554	−	0.398289i	0.807561	+	0.589783i	$0.200787\pi$
$632$		0			0
$633$	−2.51033	−	1.03981i	−0.0997767	−	0.0413289i
$634$		0			0
$635$	8.01597	+	11.9968i	0.318104	+	0.476077i
$636$		0			0
$637$	42.9604	−	8.54535i	1.70215	−	0.338579i
$638$		0			0
$639$	13.3877			0.529607
$640$		0			0
$641$	−6.97029			−0.275310			−0.137655	−	0.990480i	$-0.543956\pi$
$641$	−6.97029			−0.275310			−0.137655	+	0.990480i	$0.543956\pi$
$642$		0			0
$643$	10.2606	−	2.04096i	0.404638	−	0.0804875i	0.0114247	−	0.999935i	$-0.496363\pi$
$643$	10.2606	−	2.04096i	0.404638	−	0.0804875i	0.393214	+	0.919447i	$0.371363\pi$
$644$		0			0
$645$	1.23750	+	1.85205i	0.0487264	+	0.0729242i
$646$		0			0
$647$	−2.38405	−	0.987505i	−0.0937266	−	0.0388228i	0.335328	−	0.942102i	$-0.391153\pi$
$647$	−2.38405	−	0.987505i	−0.0937266	−	0.0388228i	−0.429054	+	0.903279i	$0.641153\pi$
$648$		0			0
$649$	−24.9083	+	10.3173i	−0.977735	+	0.404991i
$650$		0			0
$651$	0.680672	−	3.42197i	0.0266776	−	0.134118i
$652$		0			0
$653$	−4.66186	+	6.97696i	−0.182433	+	0.273030i	−0.911403	−	0.411516i	$-0.864999\pi$
$653$	−4.66186	+	6.97696i	−0.182433	+	0.273030i	0.728970	+	0.684546i	$0.239999\pi$
$654$		0			0
$655$	16.0990	+	16.0990i	0.629039	+	0.629039i
$656$		0			0
$657$	12.3962	−	12.3962i	0.483624	−	0.483624i
$658$		0			0
$659$	1.71040	+	1.14285i	0.0666278	+	0.0445192i	0.588438	−	0.808542i	$-0.299743\pi$
$659$	1.71040	+	1.14285i	0.0666278	+	0.0445192i	−0.521810	+	0.853062i	$0.674743\pi$
$660$		0			0
$661$	−2.70170	−	0.537402i	−0.105084	−	0.0209025i	0.142268	−	0.989828i	$-0.454560\pi$
$661$	−2.70170	−	0.537402i	−0.105084	−	0.0209025i	−0.247352	+	0.968926i	$0.579560\pi$
$662$		0			0
$663$	−0.663071	−	1.60079i	−0.0257515	−	0.0621697i
$664$		0			0
$665$	−7.40473	+	17.8766i	−0.287143	+	0.693225i
$666$		0			0
$667$	11.5830	−	7.73953i	0.448496	−	0.299676i
$668$		0			0
$669$	0.240705	+	1.21010i	0.00930618	+	0.0467853i
$670$		0			0
$671$		−	37.0284i		−	1.42947i
$672$		0			0
$673$		−	6.84519i		−	0.263863i	−0.991259	−	0.131931i	$-0.957882\pi$
$673$		−	6.84519i		−	0.263863i	0.991259	−	0.131931i	$-0.0421178\pi$
$674$		0			0
$675$	−0.448406	−	2.25429i	−0.0172592	−	0.0867677i
$676$		0			0
$677$	15.3133	−	10.2320i	0.588539	−	0.393249i	−0.225343	−	0.974280i	$-0.572350\pi$
$677$	15.3133	−	10.2320i	0.588539	−	0.393249i	0.813882	+	0.581030i	$0.197350\pi$
$678$		0			0
$679$	−17.9894	+	43.4302i	−0.690369	+	1.66670i
$680$		0			0
$681$	1.33145	+	3.21442i	0.0510214	+	0.123177i
$682$		0			0
$683$	−16.5246	−	3.28694i	−0.632296	−	0.125771i	−0.131471	−	0.991320i	$-0.541970\pi$
$683$	−16.5246	−	3.28694i	−0.632296	−	0.125771i	−0.500825	+	0.865549i	$0.666970\pi$
$684$		0			0
$685$	5.36279	+	3.58330i	0.204902	+	0.136911i
$686$		0			0
$687$	−1.27394	+	1.27394i	−0.0486037	+	0.0486037i
$688$		0			0
$689$	4.77944	+	4.77944i	0.182082	+	0.182082i
$690$		0			0
$691$	6.27571	−	9.39227i	0.238739	−	0.357299i	−0.692681	−	0.721244i	$-0.743571\pi$
$691$	6.27571	−	9.39227i	0.238739	−	0.357299i	0.931420	+	0.363945i	$0.118571\pi$
$692$		0			0
$693$	7.85800	−	39.5049i	0.298501	−	1.50067i
$694$		0			0
$695$	−31.5285	+	13.0595i	−1.19595	+	0.495377i
$696$		0			0
$697$	7.71700	+	3.19648i	0.292302	+	0.121075i
$698$		0			0
$699$	−1.49020	−	2.23024i	−0.0563645	−	0.0843554i
$700$		0			0
$701$	−28.6261	+	5.69409i	−1.08119	+	0.215063i	−0.703377	−	0.710817i	$-0.748325\pi$
$701$	−28.6261	+	5.69409i	−1.08119	+	0.215063i	−0.377817	+	0.925880i	$0.623325\pi$
$702$		0			0
$703$	−15.1253			−0.570461
$704$		0			0
$705$	−1.72838			−0.0650947
$706$		0			0
$707$	21.9211	−	4.36037i	0.824427	−	0.163989i
$708$		0			0
$709$	−26.7046	−	39.9663i	−1.00291	−	1.50097i	−0.859390	−	0.511320i	$-0.829157\pi$
$709$	−26.7046	−	39.9663i	−1.00291	−	1.50097i	−0.143524	−	0.989647i	$-0.545843\pi$
$710$		0			0
$711$	−22.1027	−	9.15525i	−0.828917	−	0.343349i
$712$		0			0
$713$	6.06025	−	2.51024i	0.226958	−	0.0940092i
$714$		0			0
$715$	−2.41536	+	12.1428i	−0.0903293	+	0.454116i
$716$		0			0
$717$	1.29046	−	1.93132i	0.0481933	−	0.0721264i
$718$		0			0
$719$	−17.7608	−	17.7608i	−0.662368	−	0.662368i	0.293570	−	0.955938i	$-0.405157\pi$
$719$	−17.7608	−	17.7608i	−0.662368	−	0.662368i	−0.955938	+	0.293570i	$0.905157\pi$
$720$		0			0
$721$	−4.56767	+	4.56767i	−0.170109	+	0.170109i
$722$		0			0
$723$	−0.915505	−	0.611721i	−0.0340480	−	0.0227501i
$724$		0			0
$725$	−14.9047	−	2.96472i	−0.553546	−	0.110107i
$726$		0			0
$727$	−19.6348	−	47.4026i	−0.728214	−	1.75806i	−0.648459	−	0.761250i	$-0.724586\pi$
$727$	−19.6348	−	47.4026i	−0.728214	−	1.75806i	−0.0797551	−	0.996814i	$-0.525414\pi$
$728$		0			0
$729$	−9.54909	+	23.0535i	−0.353670	+	0.853835i
$730$		0			0
$731$	−18.7518	+	12.5296i	−0.693560	+	0.463422i
$732$		0			0
$733$	−0.665236	−	3.34437i	−0.0245710	−	0.123527i	0.966553	−	0.256467i	$-0.0825584\pi$
$733$	−0.665236	−	3.34437i	−0.0245710	−	0.123527i	−0.991124	+	0.132940i	$0.957558\pi$
$734$		0			0
$735$			5.81716i			0.214569i
$736$		0			0
$737$		−	7.69939i		−	0.283611i
$738$		0			0
$739$	−4.70308	−	23.6440i	−0.173006	−	0.869758i	−0.965605	−	0.260015i	$-0.916273\pi$
$739$	−4.70308	−	23.6440i	−0.173006	−	0.869758i	0.792599	−	0.609743i	$-0.208727\pi$
$740$		0			0
$741$	−0.946044	+	0.632126i	−0.0347538	+	0.0232217i
$742$		0			0
$743$	16.2703	−	39.2800i	0.596899	−	1.44104i	−0.279826	−	0.960051i	$-0.590277\pi$
$743$	16.2703	−	39.2800i	0.596899	−	1.44104i	0.876725	−	0.480992i	$-0.159723\pi$
$744$		0			0
$745$	−6.25379	−	15.0980i	−0.229121	−	0.553148i
$746$		0			0
$747$	36.2581	+	7.21219i	1.32662	+	0.263880i
$748$		0			0
$749$	−14.7544	−	9.85854i	−0.539112	−	0.360223i
$750$		0			0
$751$	−1.57525	+	1.57525i	−0.0574817	+	0.0574817i	−0.735263	−	0.677782i	$-0.762941\pi$
$751$	−1.57525	+	1.57525i	−0.0574817	+	0.0574817i	0.677782	+	0.735263i	$0.262941\pi$
$752$		0			0
$753$	−2.51393	−	2.51393i	−0.0916127	−	0.0916127i
$754$		0			0
$755$	16.7026	−	24.9971i	0.607868	−	0.909739i
$756$		0			0
$757$	−3.61478	+	18.1727i	−0.131382	+	0.660500i	0.857821	+	0.513948i	$0.171817\pi$
$757$	−3.61478	+	18.1727i	−0.131382	+	0.660500i	−0.989203	+	0.146552i	$0.953183\pi$
$758$		0			0
$759$	−0.905091	+	0.374901i	−0.0328527	+	0.0136080i
$760$		0			0
$761$	−25.7162	−	10.6520i	−0.932211	−	0.386135i	−0.135694	−	0.990751i	$-0.543327\pi$
$761$	−25.7162	−	10.6520i	−0.932211	−	0.386135i	−0.796517	+	0.604616i	$0.793327\pi$
$762$		0			0
$763$	24.9803	+	37.3857i	0.904348	+	1.35345i
$764$		0			0
$765$	−17.4455	+	3.47013i	−0.630744	+	0.125463i
$766$		0			0
$767$	−24.9551			−0.901077
$768$		0			0
$769$	9.14052			0.329615			0.164808	−	0.986326i	$-0.447300\pi$
$769$	9.14052			0.329615			0.164808	+	0.986326i	$0.447300\pi$
$770$		0			0
$771$	2.91496	−	0.579821i	0.104980	−	0.0208817i
$772$		0			0
$773$	−21.6826	−	32.4503i	−0.779869	−	1.16716i	−0.982200	−	0.187839i	$-0.939852\pi$
$773$	−21.6826	−	32.4503i	−0.779869	−	1.16716i	0.202331	−	0.979317i	$-0.435148\pi$
$774$		0			0
$775$	−6.61095	−	2.73835i	−0.237472	−	0.0983643i
$776$		0			0
$777$	−5.92365	+	2.45366i	−0.212510	+	0.0880244i
$778$		0			0
$779$	1.07007	−	5.37962i	0.0383393	−	0.192745i
$780$		0			0
$781$	−6.96126	+	10.4183i	−0.249093	+	0.372795i
$782$		0			0
$783$	−6.36652	−	6.36652i	−0.227521	−	0.227521i
$784$		0			0
$785$	−5.28815	+	5.28815i	−0.188742	+	0.188742i
$786$		0			0
$787$	5.88104	+	3.92959i	0.209637	+	0.140075i	0.655956	−	0.754799i	$-0.272266\pi$
$787$	5.88104	+	3.92959i	0.209637	+	0.140075i	−0.446320	+	0.894874i	$0.647266\pi$
$788$		0			0
$789$	−3.98809	−	0.793280i	−0.141980	−	0.0282415i
$790$		0			0
$791$	24.5751	+	59.3296i	0.873791	+	2.10952i
$792$		0			0
$793$	13.1161	−	31.6651i	0.465768	−	1.12446i
$794$		0			0
$795$	−0.746371	+	0.498709i	−0.0264711	+	0.0176874i
$796$		0			0
$797$	−6.94836	−	34.9318i	−0.246124	−	1.23735i	−0.884103	−	0.467293i	$-0.845229\pi$
$797$	−6.94836	−	34.9318i	−0.246124	−	1.23735i	0.637979	−	0.770054i	$-0.279771\pi$
$798$		0			0
$799$		−	17.4997i		−	0.619096i
$800$		0			0
$801$			27.0388i			0.955368i
$802$		0			0
$803$	3.20100	+	16.0925i	0.112961	+	0.567892i
$804$		0			0
$805$	−12.8221	+	8.56746i	−0.451920	+	0.301963i
$806$		0			0
$807$	0.500360	−	1.20798i	0.0176135	−	0.0425228i
$808$		0			0
$809$	20.3911	+	49.2285i	0.716913	+	1.73078i	0.681958	+	0.731392i	$0.261129\pi$
$809$	20.3911	+	49.2285i	0.716913	+	1.73078i	0.0349550	+	0.999389i	$0.488871\pi$
$810$		0			0
$811$	−20.2159	−	4.02118i	−0.709875	−	0.141203i	−0.173070	−	0.984910i	$-0.555369\pi$
$811$	−20.2159	−	4.02118i	−0.709875	−	0.141203i	−0.536804	+	0.843707i	$0.680369\pi$
$812$		0			0
$813$	0.617074	+	0.412316i	0.0216417	+	0.0144605i
$814$		0			0
$815$	−7.57529	+	7.57529i	−0.265351	+	0.265351i
$816$		0			0
$817$	10.4719	+	10.4719i	0.366366	+	0.366366i
$818$		0			0
$819$	20.7132	−	30.9995i	0.723777	−	1.08321i
$820$		0			0
$821$	−1.78916	+	8.99472i	−0.0624421	+	0.313918i	−0.999366	−	0.0356170i	$-0.988660\pi$
$821$	−1.78916	+	8.99472i	−0.0624421	+	0.313918i	0.936923	+	0.349535i	$0.113660\pi$
$822$		0			0
$823$	27.9325	−	11.5700i	0.973664	−	0.403305i	0.161589	−	0.986858i	$-0.448338\pi$
$823$	27.9325	−	11.5700i	0.973664	−	0.403305i	0.812075	+	0.583553i	$0.198338\pi$
$824$		0			0
$825$	0.987337	+	0.408968i	0.0343747	+	0.0142385i
$826$		0			0
$827$	−2.65323	−	3.97084i	−0.0922619	−	0.138080i	0.782467	−	0.622692i	$-0.213961\pi$
$827$	−2.65323	−	3.97084i	−0.0922619	−	0.138080i	−0.874729	+	0.484612i	$0.838961\pi$
$828$		0			0
$829$	22.9462	−	4.56428i	0.796953	−	0.158524i	0.220213	−	0.975452i	$-0.429325\pi$
$829$	22.9462	−	4.56428i	0.796953	−	0.158524i	0.576740	+	0.816928i	$0.304325\pi$
$830$		0			0
$831$	1.46853			0.0509429
$832$		0			0
$833$	−58.8982			−2.04070
$834$		0			0
$835$	−11.5679	+	2.30099i	−0.400323	+	0.0796291i
$836$		0			0
$837$	−2.35535	−	3.52503i	−0.0814129	−	0.121843i
$838$		0			0
$839$	−15.5489	−	6.44058i	−0.536809	−	0.222354i	0.0977736	−	0.995209i	$-0.468828\pi$
$839$	−15.5489	−	6.44058i	−0.536809	−	0.222354i	−0.634582	+	0.772855i	$0.718828\pi$
$840$		0			0
$841$	−28.2052	+	11.6830i	−0.972595	+	0.402862i
$842$		0			0
$843$	0.862312	−	4.33513i	0.0296996	−	0.149310i
$844$		0			0
$845$	6.20603	−	9.28798i	0.213494	−	0.319516i
$846$		0			0
$847$	−11.5054	−	11.5054i	−0.395331	−	0.395331i
$848$		0			0
$849$	−4.33235	+	4.33235i	−0.148686	+	0.148686i
$850$		0			0
$851$	−10.0229	−	6.69709i	−0.343581	−	0.229573i
$852$		0			0
$853$	42.7816	+	8.50979i	1.46481	+	0.291370i	0.862161	−	0.506634i	$-0.169110\pi$
$853$	42.7816	+	8.50979i	1.46481	+	0.291370i	0.602653	+	0.798003i	$0.294110\pi$
$854$		0			0
$855$	4.46986	+	10.7912i	0.152866	+	0.369051i
$856$		0			0
$857$	21.1682	−	51.1045i	0.723091	−	1.74570i	0.0587410	−	0.998273i	$-0.481291\pi$
$857$	21.1682	−	51.1045i	0.723091	−	1.74570i	0.664350	−	0.747422i	$-0.268709\pi$
$858$		0			0
$859$	−30.3027	+	20.2476i	−1.03392	+	0.690840i	−0.952094	−	0.305807i	$-0.901074\pi$
$859$	−30.3027	+	20.2476i	−1.03392	+	0.690840i	−0.0818217	+	0.996647i	$0.526074\pi$
$860$		0			0
$861$	−0.453611	−	2.28046i	−0.0154590	−	0.0777177i
$862$		0			0
$863$			45.1415i			1.53663i	0.640070	+	0.768317i	$0.278905\pi$
$863$			45.1415i			1.53663i	−0.640070	+	0.768317i	$0.721095\pi$
$864$		0			0
$865$		−	29.2649i		−	0.995036i
$866$		0			0
$867$	−0.194652	−	0.978584i	−0.00661074	−	0.0332344i
$868$		0			0
$869$	18.6175	−	12.4398i	0.631555	−	0.421992i
$870$		0			0
$871$	2.72727	−	6.58420i	0.0924099	−	0.223097i
$872$		0			0
$873$	10.8593	+	26.2166i	0.367530	+	0.887297i
$874$		0			0
$875$	58.3829	+	11.6131i	1.97370	+	0.392594i
$876$		0			0
$877$	−8.73879	−	5.83907i	−0.295088	−	0.197171i	0.399209	−	0.916860i	$-0.369285\pi$
$877$	−8.73879	−	5.83907i	−0.295088	−	0.197171i	−0.694297	+	0.719688i	$0.744285\pi$
$878$		0			0
$879$	−2.74017	+	2.74017i	−0.0924236	+	0.0924236i
$880$		0			0
$881$	−22.1067	−	22.1067i	−0.744795	−	0.744795i	0.228702	−	0.973496i	$-0.426552\pi$
$881$	−22.1067	−	22.1067i	−0.744795	−	0.744795i	−0.973496	+	0.228702i	$0.926552\pi$
$882$		0			0
$883$	−0.0585565	+	0.0876360i	−0.00197058	+	0.00294919i	−0.832454	−	0.554095i	$-0.813065\pi$
$883$	−0.0585565	+	0.0876360i	−0.00197058	+	0.00294919i	0.830483	+	0.557044i	$0.188065\pi$
$884$		0			0
$885$	0.646564	−	3.25050i	0.0217340	−	0.109264i
$886$		0			0
$887$	14.2474	−	5.90145i	0.478380	−	0.198151i	−0.130446	−	0.991455i	$-0.541641\pi$
$887$	14.2474	−	5.90145i	0.478380	−	0.198151i	0.608826	+	0.793304i	$0.291641\pi$
$888$		0			0
$889$	37.5698	+	15.5619i	1.26005	+	0.521930i
$890$		0			0
$891$	−13.3313	−	19.9516i	−0.446614	−	0.668405i
$892$		0			0
$893$	−11.2707	+	2.24188i	−0.377159	+	0.0750216i
$894$		0			0
$895$	−31.6287			−1.05723
$896$		0			0
$897$	−0.906793			−0.0302769
$898$		0			0
$899$	−27.4918	+	5.46846i	−0.916904	+	0.182383i
$900$		0			0
$901$	−5.04939	−	7.55695i	−0.168220	−	0.251758i
$902$		0			0
$903$	5.79998	+	2.40243i	0.193011	+	0.0799479i
$904$		0			0
$905$	−10.9686	+	4.54336i	−0.364610	+	0.151026i
$906$		0			0
$907$	4.20851	−	21.1576i	0.139741	−	0.702527i	−0.845855	−	0.533413i	$-0.820909\pi$
$907$	4.20851	−	21.1576i	0.139741	−	0.702527i	0.985596	−	0.169114i	$-0.0540907\pi$
$908$		0			0
$909$	7.49569	−	11.2181i	0.248616	−	0.372081i
$910$		0			0
$911$	−29.1379	−	29.1379i	−0.965382	−	0.965382i	0.0340388	−	0.999421i	$-0.489163\pi$
$911$	−29.1379	−	29.1379i	−0.965382	−	0.965382i	−0.999421	+	0.0340388i	$0.989163\pi$
$912$		0			0
$913$	−24.4659	+	24.4659i	−0.809703	+	0.809703i
$914$		0			0
$915$	3.78468	+	2.52884i	0.125118	+	0.0836009i
$916$		0			0
$917$	62.9352	+	12.5186i	2.07830	+	0.413400i
$918$		0			0
$919$	15.4221	+	37.2322i	0.508727	+	1.22818i	0.944617	+	0.328176i	$0.106434\pi$
$919$	15.4221	+	37.2322i	0.508727	+	1.22818i	−0.435889	+	0.900000i	$0.643566\pi$
$920$		0			0
$921$	1.90168	−	4.59107i	0.0626626	−	0.151281i
$922$		0			0
$923$	−9.64332	+	6.44346i	−0.317414	+	0.212089i
$924$		0			0
$925$	2.56541	+	12.8972i	0.0843500	+	0.424056i
$926$		0			0
$927$			3.89937i			0.128072i
$928$		0			0
$929$		−	9.25514i		−	0.303651i	−0.988407	−	0.151826i	$-0.951485\pi$
$929$		−	9.25514i		−	0.303651i	0.988407	−	0.151826i	$-0.0485152\pi$
$930$		0			0
$931$	7.54541	+	37.9333i	0.247291	+	1.24321i
$932$		0			0
$933$	2.45442	−	1.63999i	0.0803541	−	0.0536909i
$934$		0			0
$935$	6.37080	−	15.3805i	0.208347	−	0.502995i
$936$		0			0
$937$	2.35348	+	5.68181i	0.0768850	+	0.185617i	0.957649	−	0.287939i	$-0.0929701\pi$
$937$	2.35348	+	5.68181i	0.0768850	+	0.185617i	−0.880764	+	0.473556i	$0.842970\pi$
$938$		0			0
$939$	−1.05577	−	0.210006i	−0.0344538	−	0.00685328i
$940$		0			0
$941$	34.8411	+	23.2801i	1.13579	+	0.758908i	0.973692	−	0.227867i	$-0.0731752\pi$
$941$	34.8411	+	23.2801i	1.13579	+	0.758908i	0.162094	+	0.986775i	$0.448175\pi$
$942$		0			0
$943$	3.09105	−	3.09105i	0.100658	−	0.100658i
$944$		0			0
$945$	7.04757	+	7.04757i	0.229258	+	0.229258i
$946$		0			0
$947$	13.4472	−	20.1252i	0.436975	−	0.653980i	−0.545986	−	0.837795i	$-0.683845\pi$
$947$	13.4472	−	20.1252i	0.436975	−	0.653980i	0.982961	+	0.183815i	$0.0588447\pi$
$948$		0			0
$949$	−2.96290	+	14.8955i	−0.0961797	+	0.483528i
$950$		0			0
$951$	0.909347	−	0.376664i	0.0294876	−	0.0122142i
$952$		0			0
$953$	20.7537	+	8.59648i	0.672279	+	0.278467i	0.692595	−	0.721326i	$-0.256467\pi$
$953$	20.7537	+	8.59648i	0.672279	+	0.278467i	−0.0203159	+	0.999794i	$0.506467\pi$
$954$		0			0
$955$	3.99459	+	5.97833i	0.129262	+	0.193454i
$956$		0			0
$957$	4.10587	−	0.816708i	0.132724	−	0.0264004i
$958$		0			0
$959$	18.1782			0.587005
$960$		0			0
$961$	17.8013			0.574237
$962$		0			0
$963$	−10.5059	+	2.08975i	−0.338547	+	0.0673412i
$964$		0			0
$965$	−2.65959	−	3.98036i	−0.0856154	−	0.128132i
$966$		0			0
$967$	28.9735	+	12.0012i	0.931724	+	0.385933i	0.796332	−	0.604859i	$-0.206771\pi$
$967$	28.9735	+	12.0012i	0.931724	+	0.385933i	0.135392	+	0.990792i	$0.456771\pi$
$968$		0			0
$969$	1.41348	−	0.585481i	0.0454074	−	0.0188084i
$970$		0			0
$971$	−5.69005	+	28.6058i	−0.182602	+	0.918004i	0.775450	+	0.631409i	$0.217523\pi$
$971$	−5.69005	+	28.6058i	−0.182602	+	0.918004i	−0.958052	+	0.286595i	$0.907477\pi$
$972$		0			0
$973$	−53.4360	+	79.9726i	−1.71308	+	2.56380i
$974$		0			0
$975$	0.699466	+	0.699466i	0.0224008	+	0.0224008i
$976$		0			0
$977$	36.4851	−	36.4851i	1.16726	−	1.16726i	0.184412	−	0.982849i	$-0.440962\pi$
$977$	36.4851	−	36.4851i	1.16726	−	1.16726i	0.982849	−	0.184412i	$-0.0590380\pi$
$978$		0			0
$979$	−21.0416	−	14.0595i	−0.672491	−	0.449344i
$980$		0			0
$981$	26.6206	+	5.29516i	0.849930	+	0.169062i
$982$		0			0
$983$	−1.68976	−	4.07944i	−0.0538950	−	0.130114i	0.894639	−	0.446790i	$-0.147433\pi$
$983$	−1.68976	−	4.07944i	−0.0538950	−	0.130114i	−0.948534	+	0.316676i	$0.897433\pi$
$984$		0			0
$985$	−1.83063	+	4.41953i	−0.0583287	+	0.140818i
$986$		0			0
$987$	−4.05035	+	2.70636i	−0.128924	+	0.0861443i
$988$		0			0
$989$	2.30261	+	11.5760i	0.0732187	+	0.368095i
$990$		0			0
$991$		−	21.8887i		−	0.695318i	−0.937621	−	0.347659i	$-0.886977\pi$
$991$		−	21.8887i		−	0.695318i	0.937621	−	0.347659i	$-0.113023\pi$
$992$		0			0
$993$			1.37257i			0.0435573i
$994$		0			0
$995$	0.305673	+	1.53672i	0.00969049	+	0.0487174i
$996$		0			0
$997$	−24.5633	+	16.4127i	−0.777927	+	0.519794i	−0.879995	−	0.474983i	$-0.842454\pi$
$997$	−24.5633	+	16.4127i	−0.777927	+	0.519794i	0.102068	+	0.994777i	$0.467454\pi$
$998$		0			0
$999$	−2.98146	+	7.19787i	−0.0943291	+	0.227731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.i.a.49.4		56
4.3	odd	2		64.2.i.a.53.5	yes	56
8.3	odd	2		512.2.i.b.353.4		56
8.5	even	2		512.2.i.a.353.4		56
12.11	even	2		576.2.bd.a.181.3		56
64.3	odd	16		512.2.i.b.161.4		56
64.29	even	16	inner	256.2.i.a.209.4		56
64.35	odd	16		64.2.i.a.29.5	✓	56
64.61	even	16		512.2.i.a.161.4		56
192.35	even	16		576.2.bd.a.541.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.5	✓	56	64.35	odd	16
64.2.i.a.53.5	yes	56	4.3	odd	2
256.2.i.a.49.4		56	1.1	even	1	trivial
256.2.i.a.209.4		56	64.29	even	16	inner
512.2.i.a.161.4		56	64.61	even	16
512.2.i.a.353.4		56	8.5	even	2
512.2.i.b.161.4		56	64.3	odd	16
512.2.i.b.353.4		56	8.3	odd	2
576.2.bd.a.181.3		56	12.11	even	2
576.2.bd.a.541.3		56	192.35	even	16

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.191980 + 0.0381873i) q^{3} +(-0.967135 - 1.44742i) q^{5} +(-4.53283 - 1.87756i) q^{7} +(-2.73624 + 1.13339i) q^{9} +O(q^{10})\)	\(q+(-0.191980 + 0.0381873i) q^{3} +(-0.967135 - 1.44742i) q^{5} +(-4.53283 - 1.87756i) q^{7} +(-2.73624 + 1.13339i) q^{9} +(0.540778 - 2.71867i) q^{11} +(1.42546 - 2.13334i) q^{13} +(0.240944 + 0.240944i) q^{15} +(-2.43954 + 2.43954i) q^{17} +(1.88371 + 1.25865i) q^{19} +(0.941914 + 0.187358i) q^{21} +(0.690956 + 1.66811i) q^{23} +(0.753743 - 1.81970i) q^{25} +(0.970283 - 0.648322i) q^{27} +(-1.50522 - 7.56726i) q^{29} -3.63299i q^{31} +0.542583i q^{33} +(1.66624 + 8.37677i) q^{35} +(-5.55115 + 3.70916i) q^{37} +(-0.192193 + 0.463995i) q^{39} +(-0.926510 - 2.23679i) q^{41} +(6.41133 + 1.27529i) q^{43} +(4.28680 + 2.86435i) q^{45} +(-3.58669 + 3.58669i) q^{47} +(12.0716 + 12.0716i) q^{49} +(0.375184 - 0.561503i) q^{51} +(-0.513941 + 2.58375i) q^{53} +(-4.45807 + 1.84659i) q^{55} +(-0.409700 - 0.169703i) q^{57} +(-5.40361 - 8.08707i) q^{59} +(13.1016 - 2.60608i) q^{61} +14.5309 q^{63} -4.46645 q^{65} +(2.72425 - 0.541887i) q^{67} +(-0.196351 - 0.293860i) q^{69} +(-4.17620 - 1.72984i) q^{71} +(-5.46867 + 2.26520i) q^{73} +(-0.0752147 + 0.378130i) q^{75} +(-7.55573 + 11.3080i) q^{77} +(5.71185 + 5.71185i) q^{79} +(6.12117 - 6.12117i) q^{81} +(-10.3786 - 6.93477i) q^{83} +(5.89040 + 1.17167i) q^{85} +(0.577946 + 1.39529i) q^{87} +(3.49372 - 8.43458i) q^{89} +(-10.4668 + 6.99371i) q^{91} +(0.138734 + 0.697464i) q^{93} -3.94381i q^{95} -9.58124i q^{97} +(1.60161 + 8.05186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Introduction

L-functions

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Database

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