LMFDB - Embedded newform 512.2.i.a.161.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.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:	$4.08834058349$
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			161.4
Character	$\chi$	$=$	512.161
Dual form			512.2.i.a.353.4

$q$-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 $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$1$

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	$-0.419504\pi$
$3$	0.191980	+	0.0381873i	0.110840	+	0.0220474i	−0.139359	+	0.990242i	$0.544504\pi$
$4$		0			0
$5$	0.967135	−	1.44742i	0.432516	−	0.647306i	−0.549634	−	0.835406i	$-0.685233\pi$
$5$	0.967135	−	1.44742i	0.432516	−	0.647306i	0.982150	+	0.188100i	$0.0602328\pi$
$6$		0			0
$7$	−4.53283	+	1.87756i	−1.71325	+	0.709651i	−0.713288	+	0.700871i	$0.752795\pi$
$7$	−4.53283	+	1.87756i	−1.71325	+	0.709651i	−0.999961	+	0.00878062i	$0.997205\pi$
$8$		0			0
$9$	−2.73624	−	1.13339i	−0.912080	−	0.377796i
$10$		0			0
$11$	−0.540778	−	2.71867i	−0.163051	−	0.819711i	−0.972569	−	0.232616i	$-0.925271\pi$
$11$	−0.540778	−	2.71867i	−0.163051	−	0.819711i	0.809518	−	0.587095i	$-0.199729\pi$
$12$		0			0
$13$	−1.42546	−	2.13334i	−0.395350	−	0.591683i	0.579383	−	0.815055i	$-0.303294\pi$
$13$	−1.42546	−	2.13334i	−0.395350	−	0.591683i	−0.974733	+	0.223372i	$0.928294\pi$
$14$		0			0
$15$	0.240944	−	0.240944i	0.0622115	−	0.0622115i
$16$		0			0
$17$	−2.43954	−	2.43954i	−0.591675	−	0.591675i	0.346409	−	0.938084i	$-0.387401\pi$
$17$	−2.43954	−	2.43954i	−0.591675	−	0.591675i	−0.938084	+	0.346409i	$0.887401\pi$
$18$		0			0
$19$	−1.88371	+	1.25865i	−0.432152	+	0.288755i	−0.752559	−	0.658525i	$-0.771181\pi$
$19$	−1.88371	+	1.25865i	−0.432152	+	0.288755i	0.320406	+	0.947280i	$0.396181\pi$
$20$		0			0
$21$	−0.941914	+	0.187358i	−0.205543	+	0.0408850i
$22$		0			0
$23$	0.690956	−	1.66811i	0.144074	−	0.347826i	−0.835326	−	0.549755i	$-0.814721\pi$
$23$	0.690956	−	1.66811i	0.144074	−	0.347826i	0.979400	+	0.201929i	$0.0647211\pi$
$24$		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	−0.544560	−	0.838722i	$-0.683303\pi$
$29$	1.50522	−	7.56726i	0.279513	−	1.40521i	0.824073	−	0.566483i	$-0.191697\pi$
$30$		0			0
$31$			3.63299i			0.652505i	0.945283	+	0.326253i	$0.105786\pi$
$31$			3.63299i			0.652505i	−0.945283	+	0.326253i	$0.894214\pi$
$32$		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	$-0.127589\pi$
$37$	5.55115	+	3.70916i	0.912603	+	0.609782i	−0.00813317	+	0.999967i	$0.502589\pi$
$38$		0			0
$39$	−0.192193	−	0.463995i	−0.0307755	−	0.0742986i
$40$		0			0
$41$	−0.926510	+	2.23679i	−0.144697	+	0.349328i	−0.979567	−	0.201118i	$-0.935542\pi$
$41$	−0.926510	+	2.23679i	−0.144697	+	0.349328i	0.834870	+	0.550446i	$0.185542\pi$
$42$		0			0
$43$	−6.41133	+	1.27529i	−0.977718	+	0.194480i	−0.657988	−	0.753028i	$-0.728592\pi$
$43$	−6.41133	+	1.27529i	−0.977718	+	0.194480i	−0.319730	+	0.947509i	$0.603592\pi$
$44$		0			0
$45$	−4.28680	+	2.86435i	−0.639039	+	0.426992i
$46$		0			0
$47$	−3.58669	−	3.58669i	−0.523172	−	0.523172i	0.395356	−	0.918528i	$-0.370621\pi$
$47$	−3.58669	−	3.58669i	−0.523172	−	0.523172i	−0.918528	+	0.395356i	$0.870621\pi$
$48$		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	$-0.00458942\pi$
$53$	0.513941	+	2.58375i	0.0705952	+	0.354906i	−0.929301	+	0.369324i	$0.879589\pi$
$54$		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	−0.291854	−	0.956463i	$-0.594272\pi$
$59$	5.40361	−	8.08707i	0.703490	−	1.05285i	0.995344	−	0.0963843i	$-0.0307278\pi$
$60$		0			0
$61$	−13.1016	−	2.60608i	−1.67749	−	0.333674i	−0.737624	−	0.675211i	$-0.764052\pi$
$61$	−13.1016	−	2.60608i	−1.67749	−	0.333674i	−0.939868	+	0.341537i	$0.889052\pi$
$62$		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	$-0.491770\pi$
$67$	−2.72425	−	0.541887i	−0.332820	−	0.0662021i	−0.358672	+	0.933464i	$0.616770\pi$
$68$		0			0
$69$	0.196351	−	0.293860i	0.0236379	−	0.0353765i
$70$		0			0
$71$	−4.17620	+	1.72984i	−0.495623	+	0.205294i	−0.616472	−	0.787377i	$-0.711439\pi$
$71$	−4.17620	+	1.72984i	−0.495623	+	0.205294i	0.120848	+	0.992671i	$0.461439\pi$
$72$		0			0
$73$	−5.46867	−	2.26520i	−0.640059	−	0.265121i	0.0389610	−	0.999241i	$-0.487595\pi$
$73$	−5.46867	−	2.26520i	−0.640059	−	0.265121i	−0.679020	+	0.734119i	$0.737595\pi$
$74$		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	−0.308569	−	0.951202i	$-0.599850\pi$
$79$	5.71185	−	5.71185i	0.642633	−	0.642633i	0.951202	+	0.308569i	$0.0998500\pi$
$80$		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	$-0.447279\pi$
$83$	10.3786	−	6.93477i	1.13920	−	0.761189i	0.974330	+	0.225126i	$0.0722793\pi$
$84$		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	0.993694	+	0.112129i	$0.0357670\pi$
$89$	3.49372	+	8.43458i	0.370333	+	0.894064i	−0.623360	+	0.781935i	$0.714233\pi$
$90$		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	$0.161695\pi$
$97$			9.58124i			0.972828i	−0.873728	+	0.486414i	$0.838305\pi$
$98$		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	$-0.239725\pi$
$101$	3.78774	+	2.53089i	0.376894	+	0.251833i	−0.352666	+	0.935749i	$0.614725\pi$
$102$		0			0
$103$	0.503843	+	1.21638i	0.0496451	+	0.119854i	0.946756	−	0.321951i	$-0.104338\pi$
$103$	0.503843	+	1.21638i	0.0496451	+	0.119854i	−0.897111	+	0.441804i	$0.854338\pi$
$104$		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	$-0.618435\pi$
$107$	−3.54726	+	0.705594i	−0.342927	+	0.0682124i	0.0206225	+	0.999787i	$0.493435\pi$
$108$		0			0
$109$	7.61993	−	5.09147i	0.729857	−	0.487675i	−0.134272	−	0.990944i	$-0.542870\pi$
$109$	7.61993	−	5.09147i	0.729857	−	0.487675i	0.864129	+	0.503270i	$0.167870\pi$
$110$		0			0
$111$	0.924069	+	0.924069i	0.0877088	+	0.0877088i
$112$		0			0
$113$	−9.25522	+	9.25522i	−0.870658	+	0.870658i	−0.992544	−	0.121886i	$-0.961106\pi$
$113$	−9.25522	+	9.25522i	−0.870658	+	0.870658i	0.121886	+	0.992544i	$0.461106\pi$
$114$		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	$-0.243921\pi$
$131$	12.8274	+	2.55153i	1.12074	+	0.222928i	0.400256	+	0.916404i	$0.368921\pi$
$132$		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	0.231635	−	0.972803i	$-0.425593\pi$
$137$	−3.42304	−	1.41787i	−0.292450	−	0.121137i	−0.524085	+	0.851666i	$0.675593\pi$
$138$		0			0
$139$	−3.82451	−	19.2271i	−0.324391	−	1.63082i	−0.707213	−	0.707001i	$-0.750048\pi$
$139$	−3.82451	−	19.2271i	−0.324391	−	1.63082i	0.382822	−	0.923822i	$-0.374952\pi$
$140$		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	$-0.688137\pi$
$149$	−9.20724	+	1.83143i	−0.754287	+	0.150037i	−0.197053	+	0.980393i	$0.563137\pi$
$150$		0			0
$151$	6.60900	−	15.9555i	0.537833	−	1.29844i	−0.388400	−	0.921491i	$-0.626972\pi$
$151$	6.60900	−	15.9555i	0.537833	−	1.29844i	0.926233	−	0.376952i	$-0.123028\pi$
$152$		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	$-0.882661\pi$
$157$	0.838120	−	4.21351i	0.0668893	−	0.336275i	0.999710	+	0.0240647i	$0.00766076\pi$
$158$		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	−0.904854	−	0.425723i	$-0.860020\pi$
$163$	1.20061	−	6.03588i	0.0940391	−	0.472766i	0.998893	−	0.0470438i	$-0.0149800\pi$
$164$		0			0
$165$	−0.785346	−	0.524751i	−0.0611391	−	0.0408518i
$166$		0			0
$167$	2.59281	+	6.25960i	0.200638	+	0.484382i	0.991889	−	0.127109i	$-0.0405698\pi$
$167$	2.59281	+	6.25960i	0.200638	+	0.484382i	−0.791251	+	0.611492i	$0.790570\pi$
$168$		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	$-0.908179\pi$
$173$	−13.9780	+	9.33980i	−1.06273	+	0.710092i	−0.104046	+	0.994572i	$0.533179\pi$
$174$		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	−0.987644	−	0.156717i	$-0.949909\pi$
$179$	−10.0942	−	15.1070i	−0.754476	−	1.12915i	0.233167	−	0.972437i	$-0.425091\pi$
$180$		0			0
$181$	−1.33053	−	6.68904i	−0.0988977	−	0.497192i	−0.998206	−	0.0598766i	$-0.980929\pi$
$181$	−1.33053	−	6.68904i	−0.0988977	−	0.497192i	0.899308	−	0.437316i	$-0.144071\pi$
$182$		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	$-0.781290\pi$
$197$	1.52669	−	2.28486i	0.108772	−	0.162789i	0.881862	+	0.471507i	$0.156290\pi$
$198$		0			0
$199$	−0.831551	+	0.344440i	−0.0589471	+	0.0244167i	−0.411962	−	0.911201i	$-0.635156\pi$
$199$	−0.831551	+	0.344440i	−0.0589471	+	0.0244167i	0.353015	+	0.935618i	$0.385156\pi$
$200$		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	$-0.846072\pi$
$211$	−11.5419	+	7.71208i	−0.794581	+	0.530922i	0.0907556	+	0.995873i	$0.471072\pi$
$212$		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	$0.0676880\pi$
$223$			6.30327i			0.422098i	−0.977475	+	0.211049i	$0.932312\pi$
$224$		0			0
$225$		−	5.83341i		−	0.388894i
$226$		0			0
$227$	3.46768	−	17.4332i	0.230158	−	1.15708i	−0.676899	−	0.736076i	$-0.736677\pi$
$227$	3.46768	−	17.4332i	0.230158	−	1.15708i	0.907057	−	0.421007i	$-0.138323\pi$
$228$		0			0
$229$	−7.65290	−	5.11350i	−0.505718	−	0.337910i	0.276398	−	0.961043i	$-0.410859\pi$
$229$	−7.65290	−	5.11350i	−0.505718	−	0.337910i	−0.782115	+	0.623134i	$0.785859\pi$
$230$		0			0
$231$	1.01873	+	2.45944i	0.0670277	+	0.161819i
$232$		0			0
$233$	5.24399	−	12.6601i	0.343545	−	0.829391i	−0.653807	−	0.756662i	$-0.726829\pi$
$233$	5.24399	−	12.6601i	0.343545	−	0.829391i	0.997352	−	0.0727295i	$-0.0231710\pi$
$234$		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	0.381575	−	0.924338i	$-0.375382\pi$
$239$	−8.39091	−	8.39091i	−0.542763	−	0.542763i	−0.924338	+	0.381575i	$0.875382\pi$
$240$		0			0
$241$	3.97755	−	3.97755i	0.256217	−	0.256217i	−0.567297	−	0.823513i	$-0.692011\pi$
$241$	3.97755	−	3.97755i	0.256217	−	0.256217i	0.823513	+	0.567297i	$0.192011\pi$
$242$		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	0.362848	+	0.931848i	$0.381804\pi$
$251$	−10.0908	+	15.1019i	−0.636924	+	0.953224i	−0.999772	+	0.0213753i	$0.993196\pi$
$252$		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	0.297825	−	0.954620i	$-0.403739\pi$
$263$	19.1921	−	7.94964i	1.18344	−	0.490196i	0.885613	+	0.464425i	$0.153739\pi$
$264$		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	$-0.122224\pi$
$269$	3.71107	+	5.55401i	0.226268	+	0.338634i	−0.700914	+	0.713246i	$0.747224\pi$
$270$		0			0
$271$	−2.68097	+	2.68097i	−0.162858	+	0.162858i	−0.783831	−	0.620974i	$-0.786737\pi$
$271$	−2.68097	+	2.68097i	−0.162858	+	0.162858i	0.620974	+	0.783831i	$0.286737\pi$
$272$		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	$-0.490135\pi$
$277$	7.35826	−	1.46365i	0.442115	−	0.0879421i	0.411128	+	0.911578i	$0.365135\pi$
$278$		0			0
$279$	4.11759	−	9.94075i	0.246514	−	0.595137i
$280$		0			0
$281$	−8.64142	−	20.8622i	−0.515504	−	1.24454i	−0.940640	−	0.339407i	$-0.889774\pi$
$281$	−8.64142	−	20.8622i	−0.515504	−	1.24454i	0.425136	−	0.905130i	$-0.360226\pi$
$282$		0			0
$283$	−26.0256	−	17.3898i	−1.54706	−	1.03371i	−0.977288	−	0.211915i	$-0.932030\pi$
$283$	−26.0256	−	17.3898i	−1.54706	−	1.03371i	−0.569776	−	0.821800i	$-0.692970\pi$
$284$		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	$-0.508780\pi$
$293$	−16.4610	−	10.9989i	−0.961661	−	0.642561i	−0.934082	+	0.357058i	$0.883780\pi$
$294$		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	0.975633	+	0.219408i	$0.0704126\pi$
$307$	14.1044	+	21.1087i	0.804981	+	1.20474i	−0.170652	+	0.985331i	$0.554587\pi$
$308$		0			0
$309$	0.0502776	+	0.252762i	0.00286019	+	0.0143791i
$310$		0			0
$311$	−13.9327	−	5.77111i	−0.790051	−	0.327250i	−0.0490867	−	0.998795i	$-0.515631\pi$
$311$	−13.9327	−	5.77111i	−0.790051	−	0.327250i	−0.740964	+	0.671545i	$0.765631\pi$
$312$		0			0
$313$	5.08075	−	2.10452i	0.287181	−	0.118954i	−0.234443	−	0.972130i	$-0.575327\pi$
$313$	5.08075	−	2.10452i	0.287181	−	0.118954i	0.521624	+	0.853176i	$0.325327\pi$
$314$		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	$-0.392400\pi$
$317$	4.93180	+	0.980996i	0.276997	+	0.0550982i	−0.0546367	+	0.998506i	$0.517400\pi$
$318$		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	$-0.124228\pi$
$331$	−1.36801	−	6.87743i	−0.0751924	−	0.378018i	−0.999997	+	0.00242459i	$0.999228\pi$
$332$		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	0.316383	−	0.948631i	$-0.397531\pi$
$337$	−11.6065	−	11.6065i	−0.632248	−	0.632248i	−0.948631	+	0.316383i	$0.897531\pi$
$338$		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	$-0.160929\pi$
$347$	14.1994	+	9.48772i	0.762262	+	0.509327i	−0.112635	+	0.993636i	$0.535929\pi$
$348$		0			0
$349$	2.26631	−	11.3935i	0.121313	−	0.609881i	−0.871519	−	0.490362i	$-0.836865\pi$
$349$	2.26631	−	11.3935i	0.121313	−	0.609881i	0.992832	−	0.119519i	$-0.0381353\pi$
$350$		0			0
$351$			2.99410i			0.159813i
$352$		0			0
$353$		−	11.5221i		−	0.613261i	−0.951829	−	0.306631i	$-0.900798\pi$
$353$		−	11.5221i		−	0.613261i	0.951829	−	0.306631i	$-0.0992016\pi$
$354$		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	0.954752	−	0.297405i	$-0.0961210\pi$
$359$	1.31387	+	3.17197i	0.0693435	+	0.167410i	−0.885408	+	0.464815i	$0.846121\pi$
$360$		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	0.980152	+	0.198245i	$0.0635242\pi$
$367$	22.5749	+	22.5749i	1.17840	+	1.17840i	0.198245	+	0.980152i	$0.436476\pi$
$368$		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	0.641250	+	0.767332i	$0.278416\pi$
$373$	6.61395	+	33.2506i	0.342457	+	1.72165i	−0.298793	+	0.954318i	$0.596584\pi$
$374$		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	$-0.993505\pi$
$379$	−11.6484	+	17.4330i	−0.598337	+	0.895474i	0.401455	+	0.915879i	$0.368505\pi$
$380$		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	$-0.786442\pi$
$389$	1.79208	−	2.68204i	0.0908621	−	0.135985i	0.874116	+	0.485717i	$0.161442\pi$
$390$		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	$-0.234001\pi$
$397$	−3.22276	−	4.82320i	−0.161746	−	0.242069i	−0.903486	+	0.428618i	$0.859001\pi$
$398$		0			0
$399$	1.53847	−	1.53847i	0.0770200	−	0.0770200i
$400$		0			0
$401$	18.2413	+	18.2413i	0.910926	+	0.910926i	0.996345	−	0.0854187i	$-0.0272228\pi$
$401$	18.2413	+	18.2413i	0.910926	+	0.910926i	−0.0854187	+	0.996345i	$0.527223\pi$
$402$		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	0.990656	−	0.136381i	$-0.0435473\pi$
$409$	3.91775	+	9.45829i	0.193720	+	0.467682i	−0.796936	+	0.604064i	$0.793547\pi$
$410$		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	−0.462392	−	0.886676i	$-0.653009\pi$
$419$	6.22515	−	31.2959i	0.304119	−	1.52891i	0.766511	−	0.642232i	$-0.221991\pi$
$420$		0			0
$421$	−9.43550	−	6.30460i	−0.459858	−	0.307268i	0.303976	−	0.952680i	$-0.401686\pi$
$421$	−9.43550	−	6.30460i	−0.459858	−	0.307268i	−0.763835	+	0.645412i	$0.776686\pi$
$422$		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	0.998154	−	0.0607373i	$-0.0193452\pi$
$431$	19.4613	+	19.4613i	0.937417	+	0.937417i	−0.0607373	+	0.998154i	$0.519345\pi$
$432$		0			0
$433$	−25.2269	+	25.2269i	−1.21233	+	1.21233i	−0.242069	+	0.970259i	$0.577826\pi$
$433$	−25.2269	+	25.2269i	−1.21233	+	1.21233i	−0.970259	+	0.242069i	$0.922174\pi$
$434$		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	−0.354704	−	0.934979i	$-0.615418\pi$
$439$	−26.5392	−	10.9929i	−1.26665	−	0.524662i	−0.911943	+	0.410316i	$0.865418\pi$
$440$		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	$-0.812437\pi$
$443$	0.00461809	−	0.00691146i	0.000219412	−	0.000328373i	0.831579	+	0.555406i	$0.187437\pi$
$444$		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	0.0405569	−	0.999177i	$-0.487087\pi$
$457$	−13.6237	−	5.64312i	−0.637290	−	0.263974i	−0.677847	+	0.735203i	$0.737087\pi$
$458$		0			0
$459$	0.785435	+	3.94865i	0.0366610	+	0.184307i
$460$		0			0
$461$	−16.5649	−	24.7911i	−0.771504	−	1.15464i	−0.984120	−	0.177502i	$-0.943198\pi$
$461$	−16.5649	−	24.7911i	−0.771504	−	1.15464i	0.212616	−	0.977136i	$-0.431802\pi$
$462$		0			0
$463$	7.31500	−	7.31500i	0.339957	−	0.339957i	−0.516394	−	0.856351i	$-0.672726\pi$
$463$	7.31500	−	7.31500i	0.339957	−	0.339957i	0.856351	+	0.516394i	$0.172726\pi$
$464$		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	$-0.953176\pi$
$467$	−26.6310	+	17.7943i	−1.23233	+	0.823420i	−0.243135	+	0.969992i	$0.578176\pi$
$468$		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	$-0.813305\pi$
$479$		−	24.2263i		−	1.10693i	0.832873	−	0.553465i	$-0.186695\pi$
$480$		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	−0.912011	−	0.410167i	$-0.865470\pi$
$487$	−12.2953	−	29.6835i	−0.557153	−	1.34509i	0.354857	−	0.934921i	$-0.384530\pi$
$488$		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	$-0.696425\pi$
$491$	−17.7528	+	3.53125i	−0.801173	+	0.159363i	−0.222510	+	0.974930i	$0.571425\pi$
$492$		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	0.995143	+	0.0984427i	$0.0313861\pi$
$499$	15.7545	+	23.5782i	0.705267	+	1.05551i	−0.289875	+	0.957064i	$0.593614\pi$
$500$		0			0
$501$	0.258732	+	1.30073i	0.0115593	+	0.0581125i
$502$		0			0
$503$	29.1486	+	12.0738i	1.29967	+	0.538342i	0.921854	−	0.387538i	$-0.126674\pi$
$503$	29.1486	+	12.0738i	1.29967	+	0.538342i	0.377819	+	0.925880i	$0.376674\pi$
$504$		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	$-0.479837\pi$
$509$	−5.86884	−	1.16739i	−0.260132	−	0.0517435i	−0.323433	+	0.946251i	$0.604837\pi$
$510$		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	0.873451	−	0.486912i	$-0.161877\pi$
$521$	26.1756	+	10.8423i	1.14678	+	0.475010i	0.273325	+	0.961922i	$0.411877\pi$
$522$		0			0
$523$	−1.00914	−	5.07326i	−0.0441264	−	0.221838i	0.952430	−	0.304758i	$-0.0985756\pi$
$523$	−1.00914	−	5.07326i	−0.0441264	−	0.221838i	−0.996556	+	0.0829195i	$0.973576\pi$
$524$		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	$-0.945131\pi$
$541$	−0.217556	+	1.09373i	−0.00935346	+	0.0470230i	0.975827	+	0.218546i	$0.0701313\pi$
$542$		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	0.916058	+	0.401045i	$0.131353\pi$
$547$	−1.95857	+	9.84642i	−0.0837426	+	0.421002i	−0.999801	+	0.0199572i	$0.993647\pi$
$548$		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	$-0.510451\pi$
$557$	20.7214	−	13.8456i	0.877994	−	0.586657i	0.910820	+	0.412804i	$0.135451\pi$
$558$		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	0.908078	+	0.418800i	$0.137549\pi$
$563$	22.4818	+	33.6463i	0.947493	+	1.41802i	0.0394146	+	0.999223i	$0.487451\pi$
$564$		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	0.110347	−	0.993893i	$-0.464804\pi$
$569$	21.2575	−	8.80516i	0.891163	−	0.369132i	0.780816	+	0.624762i	$0.214804\pi$
$570$		0			0
$571$	21.4891	−	32.1606i	0.899289	−	1.34588i	−0.0387126	−	0.999250i	$-0.512326\pi$
$571$	21.4891	−	32.1606i	0.899289	−	1.34588i	0.938002	−	0.346631i	$-0.112674\pi$
$572$		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	$-0.0477354\pi$
$587$	0.438329	+	2.20363i	0.0180918	+	0.0909534i	−0.970685	+	0.240357i	$0.922735\pi$
$588$		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	−0.998633	−	0.0522765i	$-0.983352\pi$
$593$	−25.5913	−	25.5913i	−1.05091	−	1.05091i	−0.0522765	−	0.998633i	$-0.516648\pi$
$594$		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	−0.990437	−	0.137968i	$-0.955943\pi$
$599$	−4.71217	+	11.3762i	−0.192534	+	0.464819i	0.797903	+	0.602786i	$0.205943\pi$
$600$		0			0
$601$	−8.85882	−	21.3871i	−0.361359	−	0.872397i	−0.995102	−	0.0988537i	$-0.968482\pi$
$601$	−8.85882	−	21.3871i	−0.361359	−	0.872397i	0.633743	−	0.773543i	$-0.281518\pi$
$602$		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	$0.0740246\pi$
$607$			11.3561i			0.460929i	−0.973081	+	0.230465i	$0.925975\pi$
$608$		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	$-0.478869\pi$
$613$	−20.5529	−	13.7330i	−0.830122	−	0.554670i	−0.896459	+	0.443127i	$0.853869\pi$
$614$		0			0
$615$	0.315705	+	0.762179i	0.0127304	+	0.0307340i
$616$		0			0
$617$	−1.48976	+	3.59660i	−0.0599754	+	0.144793i	−0.951026	−	0.309110i	$-0.899969\pi$
$617$	−1.48976	+	3.59660i	−0.0599754	+	0.144793i	0.891051	+	0.453903i	$0.149969\pi$
$618$		0			0
$619$	−0.987852	+	0.196496i	−0.0397051	+	0.00789784i	−0.214903	−	0.976635i	$-0.568944\pi$
$619$	−0.987852	+	0.196496i	−0.0397051	+	0.00789784i	0.175198	+	0.984533i	$0.443944\pi$
$620$		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	0.807561	−	0.589783i	$-0.200787\pi$
$631$	24.1540	+	10.0049i	0.961554	+	0.398289i	0.153992	+	0.988072i	$0.450787\pi$
$632$		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	$-0.503637\pi$
$643$	−10.2606	−	2.04096i	−0.404638	−	0.0804875i	−0.393214	+	0.919447i	$0.628637\pi$
$644$		0			0
$645$	−1.23750	+	1.85205i	−0.0487264	+	0.0729242i
$646$		0			0
$647$	−2.38405	+	0.987505i	−0.0937266	+	0.0388228i	−0.429054	−	0.903279i	$-0.641153\pi$
$647$	−2.38405	+	0.987505i	−0.0937266	+	0.0388228i	0.335328	+	0.942102i	$0.391153\pi$
$648$		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	$-0.135001\pi$
$653$	4.66186	+	6.97696i	0.182433	+	0.273030i	−0.728970	+	0.684546i	$0.760001\pi$
$654$		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	$-0.700257\pi$
$659$	−1.71040	+	1.14285i	−0.0666278	+	0.0445192i	0.521810	+	0.853062i	$0.325257\pi$
$660$		0			0
$661$	2.70170	−	0.537402i	0.105084	−	0.0209025i	−0.142268	−	0.989828i	$-0.545440\pi$
$661$	2.70170	−	0.537402i	0.105084	−	0.0209025i	0.247352	+	0.968926i	$0.420440\pi$
$662$		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	$0.0421178\pi$
$673$			6.84519i			0.263863i	−0.991259	+	0.131931i	$0.957882\pi$
$674$		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	$-0.427650\pi$
$677$	−15.3133	−	10.2320i	−0.588539	−	0.393249i	−0.813882	+	0.581030i	$0.802650\pi$
$678$		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	$-0.458030\pi$
$683$	16.5246	−	3.28694i	0.632296	−	0.125771i	0.500825	+	0.865549i	$0.333030\pi$
$684$		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	$-0.256429\pi$
$691$	−6.27571	−	9.39227i	−0.238739	−	0.357299i	−0.931420	+	0.363945i	$0.881429\pi$
$692$		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	$-0.251675\pi$
$701$	28.6261	+	5.69409i	1.08119	+	0.215063i	0.377817	+	0.925880i	$0.376675\pi$
$702$		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	0.143524	−	0.989647i	$-0.454157\pi$
$709$	26.7046	−	39.9663i	1.00291	−	1.50097i	0.859390	−	0.511320i	$-0.170843\pi$
$710$		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	−0.955938	−	0.293570i	$-0.905157\pi$
$719$	−17.7608	+	17.7608i	−0.662368	+	0.662368i	0.293570	+	0.955938i	$0.405157\pi$
$720$		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	−0.0797551	+	0.996814i	$0.525414\pi$
$727$	−19.6348	+	47.4026i	−0.728214	+	1.75806i	−0.648459	+	0.761250i	$0.724586\pi$
$728$		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	$-0.917442\pi$
$733$	0.665236	−	3.34437i	0.0245710	−	0.123527i	0.991124	+	0.132940i	$0.0424416\pi$
$734$		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	−0.792599	−	0.609743i	$-0.791273\pi$
$739$	4.70308	−	23.6440i	0.173006	−	0.869758i	0.965605	−	0.260015i	$-0.0837274\pi$
$740$		0			0
$741$	0.946044	+	0.632126i	0.0347538	+	0.0232217i
$742$		0			0
$743$	16.2703	+	39.2800i	0.596899	+	1.44104i	0.876725	+	0.480992i	$0.159723\pi$
$743$	16.2703	+	39.2800i	0.596899	+	1.44104i	−0.279826	+	0.960051i	$0.590277\pi$
$744$		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	0.677782	−	0.735263i	$-0.262941\pi$
$751$	−1.57525	−	1.57525i	−0.0574817	−	0.0574817i	−0.735263	+	0.677782i	$0.762941\pi$
$752$		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	0.989203	+	0.146552i	$0.0468175\pi$
$757$	3.61478	+	18.1727i	0.131382	+	0.660500i	−0.857821	+	0.513948i	$0.828183\pi$
$758$		0			0
$759$	−0.905091	−	0.374901i	−0.0328527	−	0.0136080i
$760$		0			0
$761$	−25.7162	+	10.6520i	−0.932211	+	0.386135i	−0.796517	−	0.604616i	$-0.793327\pi$
$761$	−25.7162	+	10.6520i	−0.932211	+	0.386135i	−0.135694	+	0.990751i	$0.543327\pi$
$762$		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	−0.202331	−	0.979317i	$-0.564852\pi$
$773$	21.6826	−	32.4503i	0.779869	−	1.16716i	0.982200	−	0.187839i	$-0.0601482\pi$
$774$		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	$-0.727734\pi$
$787$	−5.88104	+	3.92959i	−0.209637	+	0.140075i	0.446320	+	0.894874i	$0.352734\pi$
$788$		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	−0.637979	−	0.770054i	$-0.720229\pi$
$797$	6.94836	−	34.9318i	0.246124	−	1.23735i	0.884103	−	0.467293i	$-0.154771\pi$
$798$		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	0.0349550	−	0.999389i	$-0.488871\pi$
$809$	20.3911	−	49.2285i	0.716913	−	1.73078i	0.681958	−	0.731392i	$-0.261129\pi$
$810$		0			0
$811$	20.2159	−	4.02118i	0.709875	−	0.141203i	0.173070	−	0.984910i	$-0.444631\pi$
$811$	20.2159	−	4.02118i	0.709875	−	0.141203i	0.536804	+	0.843707i	$0.319631\pi$
$812$		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	$-0.0113397\pi$
$821$	1.78916	+	8.99472i	0.0624421	+	0.313918i	−0.936923	+	0.349535i	$0.886340\pi$
$822$		0			0
$823$	27.9325	+	11.5700i	0.973664	+	0.403305i	0.812075	−	0.583553i	$-0.198338\pi$
$823$	27.9325	+	11.5700i	0.973664	+	0.403305i	0.161589	+	0.986858i	$0.448338\pi$
$824$		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	$-0.786039\pi$
$827$	2.65323	−	3.97084i	0.0922619	−	0.138080i	0.874729	+	0.484612i	$0.161039\pi$
$828$		0			0
$829$	−22.9462	−	4.56428i	−0.796953	−	0.158524i	−0.220213	−	0.975452i	$-0.570675\pi$
$829$	−22.9462	−	4.56428i	−0.796953	−	0.158524i	−0.576740	+	0.816928i	$0.695675\pi$
$830$		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	−0.634582	−	0.772855i	$-0.718828\pi$
$839$	−15.5489	+	6.44058i	−0.536809	+	0.222354i	0.0977736	+	0.995209i	$0.468828\pi$
$840$		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	$-0.830890\pi$
$853$	−42.7816	+	8.50979i	−1.46481	+	0.291370i	−0.602653	+	0.798003i	$0.705890\pi$
$854$		0			0
$855$	4.46986	−	10.7912i	0.152866	−	0.369051i
$856$		0			0
$857$	21.1682	+	51.1045i	0.723091	+	1.74570i	0.664350	+	0.747422i	$0.268709\pi$
$857$	21.1682	+	51.1045i	0.723091	+	1.74570i	0.0587410	+	0.998273i	$0.481291\pi$
$858$		0			0
$859$	30.3027	+	20.2476i	1.03392	+	0.690840i	0.952094	−	0.305807i	$-0.0989262\pi$
$859$	30.3027	+	20.2476i	1.03392	+	0.690840i	0.0818217	+	0.996647i	$0.473926\pi$
$860$		0			0
$861$	0.453611	−	2.28046i	0.0154590	−	0.0777177i
$862$		0			0
$863$		−	45.1415i		−	1.53663i	−0.640070	−	0.768317i	$-0.721095\pi$
$863$		−	45.1415i		−	1.53663i	0.640070	−	0.768317i	$-0.278905\pi$
$864$		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	$-0.630715\pi$
$877$	8.73879	−	5.83907i	0.295088	−	0.197171i	0.694297	+	0.719688i	$0.255715\pi$
$878$		0			0
$879$	−2.74017	−	2.74017i	−0.0924236	−	0.0924236i
$880$		0			0
$881$	−22.1067	+	22.1067i	−0.744795	+	0.744795i	−0.973496	−	0.228702i	$-0.926552\pi$
$881$	−22.1067	+	22.1067i	−0.744795	+	0.744795i	0.228702	+	0.973496i	$0.426552\pi$
$882$		0			0
$883$	0.0585565	+	0.0876360i	0.00197058	+	0.00294919i	0.832454	−	0.554095i	$-0.186935\pi$
$883$	0.0585565	+	0.0876360i	0.00197058	+	0.00294919i	−0.830483	+	0.557044i	$0.811935\pi$
$884$		0			0
$885$	−0.646564	−	3.25050i	−0.0217340	−	0.109264i
$886$		0			0
$887$	14.2474	+	5.90145i	0.478380	+	0.198151i	0.608826	−	0.793304i	$-0.291641\pi$
$887$	14.2474	+	5.90145i	0.478380	+	0.198151i	−0.130446	+	0.991455i	$0.541641\pi$
$888$		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	−0.985596	−	0.169114i	$-0.945909\pi$
$907$	−4.20851	−	21.1576i	−0.139741	−	0.702527i	0.845855	−	0.533413i	$-0.179091\pi$
$908$		0			0
$909$	−7.49569	−	11.2181i	−0.248616	−	0.372081i
$910$		0			0
$911$	−29.1379	+	29.1379i	−0.965382	+	0.965382i	−0.999421	−	0.0340388i	$-0.989163\pi$
$911$	−29.1379	+	29.1379i	−0.965382	+	0.965382i	0.0340388	+	0.999421i	$0.489163\pi$
$912$		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	−0.435889	−	0.900000i	$-0.643566\pi$
$919$	15.4221	−	37.2322i	0.508727	−	1.22818i	0.944617	−	0.328176i	$-0.106434\pi$
$920$		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	$0.0485152\pi$
$929$			9.25514i			0.303651i	−0.988407	+	0.151826i	$0.951485\pi$
$930$		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	−0.880764	−	0.473556i	$-0.842970\pi$
$937$	2.35348	−	5.68181i	0.0768850	−	0.185617i	0.957649	+	0.287939i	$0.0929701\pi$
$938$		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	$-0.926825\pi$
$941$	−34.8411	+	23.2801i	−1.13579	+	0.758908i	−0.162094	+	0.986775i	$0.551825\pi$
$942$		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	$-0.316155\pi$
$947$	−13.4472	−	20.1252i	−0.436975	−	0.653980i	−0.982961	+	0.183815i	$0.941155\pi$
$948$		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	−0.0203159	−	0.999794i	$-0.506467\pi$
$953$	20.7537	−	8.59648i	0.672279	−	0.278467i	0.692595	+	0.721326i	$0.256467\pi$
$954$		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	0.135392	−	0.990792i	$-0.456771\pi$
$967$	28.9735	−	12.0012i	0.931724	−	0.385933i	0.796332	+	0.604859i	$0.206771\pi$
$968$		0			0
$969$	1.41348	+	0.585481i	0.0454074	+	0.0188084i
$970$		0			0
$971$	5.69005	+	28.6058i	0.182602	+	0.918004i	0.958052	+	0.286595i	$0.0925233\pi$
$971$	5.69005	+	28.6058i	0.182602	+	0.918004i	−0.775450	+	0.631409i	$0.782477\pi$
$972$		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	0.982849	+	0.184412i	$0.0590380\pi$
$977$	36.4851	+	36.4851i	1.16726	+	1.16726i	0.184412	+	0.982849i	$0.440962\pi$
$978$		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	−0.948534	−	0.316676i	$-0.897433\pi$
$983$	−1.68976	+	4.07944i	−0.0538950	+	0.130114i	0.894639	+	0.446790i	$0.147433\pi$
$984$		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	$0.113023\pi$
$991$			21.8887i			0.695318i	−0.937621	+	0.347659i	$0.886977\pi$
$992$		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	$-0.157546\pi$
$997$	24.5633	+	16.4127i	0.777927	+	0.519794i	−0.102068	+	0.994777i	$0.532546\pi$
$998$		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	512.2.i.a.161.4		56
4.3	odd	2		512.2.i.b.161.4		56
8.3	odd	2		64.2.i.a.29.5	✓	56
8.5	even	2		256.2.i.a.209.4		56
24.11	even	2		576.2.bd.a.541.3		56
64.11	odd	16		512.2.i.b.353.4		56
64.21	even	16		256.2.i.a.49.4		56
64.43	odd	16		64.2.i.a.53.5	yes	56
64.53	even	16	inner	512.2.i.a.353.4		56
192.107	even	16		576.2.bd.a.181.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.5	✓	56	8.3	odd	2
64.2.i.a.53.5	yes	56	64.43	odd	16
256.2.i.a.49.4		56	64.21	even	16
256.2.i.a.209.4		56	8.5	even	2
512.2.i.a.161.4		56	1.1	even	1	trivial
512.2.i.a.353.4		56	64.53	even	16	inner
512.2.i.b.161.4		56	4.3	odd	2
512.2.i.b.353.4		56	64.11	odd	16
576.2.bd.a.181.3		56	192.107	even	16
576.2.bd.a.541.3		56	24.11	even	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.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

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Database

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