LMFDB - Embedded newform 512.2.g.e.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(65,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(8))

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("512.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.g (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			449.2
Root			$0.500000 + 1.44392i$ of defining polynomial
Character	$\chi$	$=$	512.449
Dual form			512.2.g.e.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.943920 + 2.27882i) q^{3} +(-1.70711 - 0.707107i) q^{5} +(0.665096 + 0.665096i) q^{7} +(-2.18073 + 2.18073i) q^{9} +O(q^{10})$	\(q+(0.943920 + 2.27882i) q^{3} +(-1.70711 - 0.707107i) q^{5} +(0.665096 + 0.665096i) q^{7} +(-2.18073 + 2.18073i) q^{9} +(-1.52971 + 3.69304i) q^{11} +(-4.26475 + 1.76652i) q^{13} -4.55765i q^{15} +3.61706i q^{17} +(0.470294 - 0.194802i) q^{19} +(-0.887839 + 2.14343i) q^{21} +(1.33490 - 1.33490i) q^{23} +(-1.12132 - 1.12132i) q^{25} +(-0.191470 - 0.0793096i) q^{27} +(2.37691 + 5.73838i) q^{29} +1.17157 q^{31} -9.85970 q^{33} +(-0.665096 - 1.60568i) q^{35} +(1.23348 + 0.510925i) q^{37} +(-8.05117 - 8.05117i) q^{39} +(-1.66981 + 1.66981i) q^{41} +(1.05608 - 2.54960i) q^{43} +(5.26475 - 2.18073i) q^{45} -1.49824i q^{47} -6.11529i q^{49} +(-8.24264 + 3.41421i) q^{51} +(-1.90329 + 4.59495i) q^{53} +(5.22274 - 5.22274i) q^{55} +(0.887839 + 0.887839i) q^{57} +(4.94392 + 2.04784i) q^{59} +(-5.67897 - 13.7102i) q^{61} -2.90079 q^{63} +8.52951 q^{65} +(1.41088 + 3.40617i) q^{67} +(4.30205 + 1.78197i) q^{69} +(9.66157 + 9.66157i) q^{71} +(7.55765 - 7.55765i) q^{73} +(1.49685 - 3.61373i) q^{75} +(-3.47363 + 1.43882i) q^{77} +17.2176i q^{79} +8.74088i q^{81} +(11.6602 - 4.82981i) q^{83} +(2.55765 - 6.17471i) q^{85} +(-10.8331 + 10.8331i) q^{87} +(5.43882 + 5.43882i) q^{89} +(-4.01138 - 1.66157i) q^{91} +(1.10587 + 2.66981i) q^{93} -0.940588 q^{95} +6.15862 q^{97} +(-4.71765 - 11.3894i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 8 q^{5} + 8 q^{7}+O(q^{10}) $ 8 * q - 4 * q^3 - 8 * q^5 + 8 * q^7	$ 8 q - 4 q^{3} - 8 q^{5} + 8 q^{7} - 12 q^{11} + 4 q^{19} + 16 q^{21} + 8 q^{23} + 8 q^{25} - 16 q^{27} + 8 q^{29} + 32 q^{31} - 16 q^{33} - 8 q^{35} + 16 q^{37} - 16 q^{39} - 8 q^{41} + 20 q^{43} + 8 q^{45} - 32 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 28 q^{59} - 40 q^{63} + 12 q^{67} + 24 q^{71} + 32 q^{73} - 20 q^{75} - 16 q^{77} + 36 q^{83} - 8 q^{85} - 56 q^{87} + 16 q^{89} - 32 q^{93} - 8 q^{95} + 32 q^{97} + 4 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 8 * q^5 + 8 * q^7 - 12 * q^11 + 4 * q^19 + 16 * q^21 + 8 * q^23 + 8 * q^25 - 16 * q^27 + 8 * q^29 + 32 * q^31 - 16 * q^33 - 8 * q^35 + 16 * q^37 - 16 * q^39 - 8 * q^41 + 20 * q^43 + 8 * q^45 - 32 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 28 * q^59 - 40 * q^63 + 12 * q^67 + 24 * q^71 + 32 * q^73 - 20 * q^75 - 16 * q^77 + 36 * q^83 - 8 * q^85 - 56 * q^87 + 16 * q^89 - 32 * q^93 - 8 * q^95 + 32 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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
$3$	0.943920	+	2.27882i	0.544972	+	1.31568i	0.921177	+	0.389143i	$0.127229\pi$
$3$	0.943920	+	2.27882i	0.544972	+	1.31568i	−0.376205	+	0.926536i	$0.622771\pi$
$4$		0			0
$5$	−1.70711	−	0.707107i	−0.763441	−	0.316228i	−0.0332288	−	0.999448i	$-0.510579\pi$
$5$	−1.70711	−	0.707107i	−0.763441	−	0.316228i	−0.730213	+	0.683220i	$0.760579\pi$
$6$		0			0
$7$	0.665096	+	0.665096i	0.251383	+	0.251383i	0.821537	−	0.570155i	$-0.193117\pi$
$7$	0.665096	+	0.665096i	0.251383	+	0.251383i	−0.570155	+	0.821537i	$0.693117\pi$
$8$		0			0
$9$	−2.18073	+	2.18073i	−0.726911	+	0.726911i
$10$		0			0
$11$	−1.52971	+	3.69304i	−0.461224	+	1.11349i	0.506672	+	0.862139i	$0.330876\pi$
$11$	−1.52971	+	3.69304i	−0.461224	+	1.11349i	−0.967895	+	0.251353i	$0.919124\pi$
$12$		0			0
$13$	−4.26475	+	1.76652i	−1.18283	+	0.489944i	−0.885414	−	0.464804i	$-0.846125\pi$
$13$	−4.26475	+	1.76652i	−1.18283	+	0.489944i	−0.297416	+	0.954748i	$0.596125\pi$
$14$		0			0
$15$		−	4.55765i		−	1.17678i
$16$		0			0
$17$			3.61706i			0.877266i	0.898666	+	0.438633i	$0.144537\pi$
$17$			3.61706i			0.877266i	−0.898666	+	0.438633i	$0.855463\pi$
$18$		0			0
$19$	0.470294	−	0.194802i	0.107893	−	0.0446907i	−0.328084	−	0.944649i	$-0.606403\pi$
$19$	0.470294	−	0.194802i	0.107893	−	0.0446907i	0.435977	+	0.899958i	$0.356403\pi$
$20$		0			0
$21$	−0.887839	+	2.14343i	−0.193742	+	0.467736i
$22$		0			0
$23$	1.33490	−	1.33490i	0.278347	−	0.278347i	−0.554102	−	0.832449i	$-0.686938\pi$
$23$	1.33490	−	1.33490i	0.278347	−	0.278347i	0.832449	+	0.554102i	$0.186938\pi$
$24$		0			0
$25$	−1.12132	−	1.12132i	−0.224264	−	0.224264i
$26$		0			0
$27$	−0.191470	−	0.0793096i	−0.0368485	−	0.0152631i
$28$		0			0
$29$	2.37691	+	5.73838i	0.441382	+	1.06559i	0.975464	+	0.220158i	$0.0706573\pi$
$29$	2.37691	+	5.73838i	0.441382	+	1.06559i	−0.534082	+	0.845433i	$0.679343\pi$
$30$		0			0
$31$	1.17157			0.210421			0.105210	−	0.994450i	$-0.466448\pi$
$31$	1.17157			0.210421			0.105210	+	0.994450i	$0.466448\pi$
$32$		0			0
$33$	−9.85970			−1.71635
$34$		0			0
$35$	−0.665096	−	1.60568i	−0.112422	−	0.271410i
$36$		0			0
$37$	1.23348	+	0.510925i	0.202783	+	0.0839955i	0.481763	−	0.876301i	$-0.339996\pi$
$37$	1.23348	+	0.510925i	0.202783	+	0.0839955i	−0.278980	+	0.960297i	$0.589996\pi$
$38$		0			0
$39$	−8.05117	−	8.05117i	−1.28922	−	1.28922i
$40$		0			0
$41$	−1.66981	+	1.66981i	−0.260780	+	0.260780i	−0.825371	−	0.564591i	$-0.809034\pi$
$41$	−1.66981	+	1.66981i	−0.260780	+	0.260780i	0.564591	+	0.825371i	$0.309034\pi$
$42$		0			0
$43$	1.05608	−	2.54960i	0.161051	−	0.388811i	−0.822669	−	0.568521i	$-0.807516\pi$
$43$	1.05608	−	2.54960i	0.161051	−	0.388811i	0.983720	+	0.179710i	$0.0575159\pi$
$44$		0			0
$45$	5.26475	−	2.18073i	0.784823	−	0.325084i
$46$		0			0
$47$		−	1.49824i		−	0.218540i	−0.994012	−	0.109270i	$-0.965149\pi$
$47$		−	1.49824i		−	0.218540i	0.994012	−	0.109270i	$-0.0348513\pi$
$48$		0			0
$49$		−	6.11529i		−	0.873614i
$50$		0			0
$51$	−8.24264	+	3.41421i	−1.15420	+	0.478086i
$52$		0			0
$53$	−1.90329	+	4.59495i	−0.261437	+	0.631164i	−0.999028	−	0.0440833i	$-0.985963\pi$
$53$	−1.90329	+	4.59495i	−0.261437	+	0.631164i	0.737591	+	0.675248i	$0.235963\pi$
$54$		0			0
$55$	5.22274	−	5.22274i	0.704235	−	0.704235i
$56$		0			0
$57$	0.887839	+	0.887839i	0.117597	+	0.117597i
$58$		0			0
$59$	4.94392	+	2.04784i	0.643644	+	0.266606i	0.680537	−	0.732713i	$-0.261746\pi$
$59$	4.94392	+	2.04784i	0.643644	+	0.266606i	−0.0368939	+	0.999319i	$0.511746\pi$
$60$		0			0
$61$	−5.67897	−	13.7102i	−0.727117	−	1.75542i	−0.651971	−	0.758244i	$-0.726058\pi$
$61$	−5.67897	−	13.7102i	−0.727117	−	1.75542i	−0.0751463	−	0.997173i	$-0.523942\pi$
$62$		0			0
$63$	−2.90079			−0.365466
$64$		0			0
$65$	8.52951			1.05796
$66$		0			0
$67$	1.41088	+	3.40617i	0.172367	+	0.416130i	0.986329	−	0.164788i	$-0.0526939\pi$
$67$	1.41088	+	3.40617i	0.172367	+	0.416130i	−0.813962	+	0.580918i	$0.802694\pi$
$68$		0			0
$69$	4.30205	+	1.78197i	0.517906	+	0.214524i
$70$		0			0
$71$	9.66157	+	9.66157i	1.14662	+	1.14662i	0.987214	+	0.159403i	$0.0509571\pi$
$71$	9.66157	+	9.66157i	1.14662	+	1.14662i	0.159403	+	0.987214i	$0.449043\pi$
$72$		0			0
$73$	7.55765	−	7.55765i	0.884556	−	0.884556i	−0.109438	−	0.993994i	$-0.534905\pi$
$73$	7.55765	−	7.55765i	0.884556	−	0.884556i	0.993994	+	0.109438i	$0.0349051\pi$
$74$		0			0
$75$	1.49685	−	3.61373i	0.172842	−	0.417277i
$76$		0			0
$77$	−3.47363	+	1.43882i	−0.395856	+	0.163969i
$78$		0			0
$79$			17.2176i			1.93714i	0.248750	+	0.968568i	$0.419980\pi$
$79$			17.2176i			1.93714i	−0.248750	+	0.968568i	$0.580020\pi$
$80$		0			0
$81$			8.74088i			0.971208i
$82$		0			0
$83$	11.6602	−	4.82981i	1.27987	−	0.530140i	0.363921	−	0.931430i	$-0.381438\pi$
$83$	11.6602	−	4.82981i	1.27987	−	0.530140i	0.915951	+	0.401290i	$0.131438\pi$
$84$		0			0
$85$	2.55765	−	6.17471i	0.277416	−	0.669741i
$86$		0			0
$87$	−10.8331	+	10.8331i	−1.16143	+	1.16143i
$88$		0			0
$89$	5.43882	+	5.43882i	0.576514	+	0.576514i	0.933941	−	0.357427i	$-0.116346\pi$
$89$	5.43882	+	5.43882i	0.576514	+	0.576514i	−0.357427	+	0.933941i	$0.616346\pi$
$90$		0			0
$91$	−4.01138	−	1.66157i	−0.420506	−	0.174179i
$92$		0			0
$93$	1.10587	+	2.66981i	0.114673	+	0.276846i
$94$		0			0
$95$	−0.940588			−0.0965023
$96$		0			0
$97$	6.15862			0.625313			0.312657	−	0.949866i	$-0.398781\pi$
$97$	6.15862			0.625313			0.312657	+	0.949866i	$0.398781\pi$
$98$		0			0
$99$	−4.71765	−	11.3894i	−0.474141	−	1.14468i
$100$		0			0
$101$	−7.47612	−	3.09671i	−0.743902	−	0.308134i	−0.0216512	−	0.999766i	$-0.506892\pi$
$101$	−7.47612	−	3.09671i	−0.743902	−	0.308134i	−0.722251	+	0.691631i	$0.756892\pi$
$102$		0			0
$103$	4.72764	+	4.72764i	0.465828	+	0.465828i	0.900560	−	0.434732i	$-0.143157\pi$
$103$	4.72764	+	4.72764i	0.465828	+	0.465828i	−0.434732	+	0.900560i	$0.643157\pi$
$104$		0			0
$105$	3.03127	−	3.03127i	0.295822	−	0.295822i
$106$		0			0
$107$	−1.06774	+	2.57774i	−0.103222	+	0.249200i	−0.967050	−	0.254587i	$-0.918060\pi$
$107$	−1.06774	+	2.57774i	−0.103222	+	0.249200i	0.863828	+	0.503787i	$0.168060\pi$
$108$		0			0
$109$	8.35544	−	3.46094i	0.800306	−	0.331498i	0.0552270	−	0.998474i	$-0.482412\pi$
$109$	8.35544	−	3.46094i	0.800306	−	0.331498i	0.745079	+	0.666976i	$0.232412\pi$
$110$		0			0
$111$			3.29316i			0.312573i
$112$		0			0
$113$		−	11.7757i		−	1.10776i	−0.832596	−	0.553881i	$-0.813146\pi$
$113$		−	11.7757i		−	1.10776i	0.832596	−	0.553881i	$-0.186854\pi$
$114$		0			0
$115$	−3.22274	+	1.33490i	−0.300522	+	0.124480i
$116$		0			0
$117$	5.44798	−	13.1526i	0.503666	−	1.21596i
$118$		0			0
$119$	−2.40569	+	2.40569i	−0.220529	+	0.220529i
$120$		0			0
$121$	−3.52035	−	3.52035i	−0.320032	−	0.320032i
$122$		0			0
$123$	−5.38136	−	2.22903i	−0.485221	−	0.200985i
$124$		0			0
$125$	4.65685	+	11.2426i	0.416522	+	1.00557i
$126$		0			0
$127$	13.0590			1.15880			0.579400	−	0.815043i	$-0.303287\pi$
$127$	13.0590			1.15880			0.579400	+	0.815043i	$0.303287\pi$
$128$		0			0
$129$	6.80695			0.599319
$130$		0			0
$131$	2.70128	+	6.52146i	0.236012	+	0.569783i	0.996863	−	0.0791431i	$-0.0252184\pi$
$131$	2.70128	+	6.52146i	0.236012	+	0.569783i	−0.760851	+	0.648926i	$0.775218\pi$
$132$		0			0
$133$	0.442353	+	0.183228i	0.0383568	+	0.0158879i
$134$		0			0
$135$	0.270780	+	0.270780i	0.0233050	+	0.0233050i
$136$		0			0
$137$	−4.88118	+	4.88118i	−0.417027	+	0.417027i	−0.884178	−	0.467151i	$-0.845281\pi$
$137$	−4.88118	+	4.88118i	−0.417027	+	0.417027i	0.467151	+	0.884178i	$0.345281\pi$
$138$		0			0
$139$	4.88098	−	11.7837i	0.413999	−	0.999482i	−0.570054	−	0.821607i	$-0.693078\pi$
$139$	4.88098	−	11.7837i	0.413999	−	0.999482i	0.984053	−	0.177875i	$-0.0569223\pi$
$140$		0			0
$141$	3.41421	−	1.41421i	0.287529	−	0.119098i
$142$		0			0
$143$		−	18.4522i		−	1.54305i
$144$		0			0
$145$		−	11.4768i		−	0.953093i
$146$		0			0
$147$	13.9357	−	5.77235i	1.14940	−	0.476095i
$148$		0			0
$149$	2.37691	−	5.73838i	0.194724	−	0.470106i	−0.796116	−	0.605144i	$-0.793116\pi$
$149$	2.37691	−	5.73838i	0.194724	−	0.470106i	0.990840	+	0.135038i	$0.0431155\pi$
$150$		0			0
$151$	−11.1504	+	11.1504i	−0.907405	+	0.907405i	−0.996062	−	0.0886573i	$-0.971742\pi$
$151$	−11.1504	+	11.1504i	−0.907405	+	0.907405i	0.0886573	+	0.996062i	$0.471742\pi$
$152$		0			0
$153$	−7.88784	−	7.88784i	−0.637694	−	0.637694i
$154$		0			0
$155$	−2.00000	−	0.828427i	−0.160644	−	0.0665409i
$156$		0			0
$157$	−0.507395	−	1.22496i	−0.0404945	−	0.0977624i	0.902338	−	0.431029i	$-0.141849\pi$
$157$	−0.507395	−	1.22496i	−0.0404945	−	0.0977624i	−0.942833	+	0.333266i	$0.891849\pi$
$158$		0			0
$159$	−12.2676			−0.972886
$160$		0			0
$161$	1.77568			0.139943
$162$		0			0
$163$	−8.83176	−	21.3218i	−0.691757	−	1.67005i	−0.741211	−	0.671272i	$-0.765748\pi$
$163$	−8.83176	−	21.3218i	−0.691757	−	1.67005i	0.0494542	−	0.998776i	$-0.484252\pi$
$164$		0			0
$165$	16.8316	+	6.97186i	1.31034	+	0.542759i
$166$		0			0
$167$	−10.8863	−	10.8863i	−0.842404	−	0.842404i	0.146767	−	0.989171i	$-0.453113\pi$
$167$	−10.8863	−	10.8863i	−0.842404	−	0.842404i	−0.989171	+	0.146767i	$0.953113\pi$
$168$		0			0
$169$	5.87515	−	5.87515i	0.451935	−	0.451935i
$170$		0			0
$171$	−0.600774	+	1.45040i	−0.0459423	+	0.110915i
$172$		0			0
$173$	1.77504	−	0.735246i	0.134954	−	0.0558997i	−0.314184	−	0.949362i	$-0.601731\pi$
$173$	1.77504	−	0.735246i	0.134954	−	0.0558997i	0.449138	+	0.893462i	$0.351731\pi$
$174$		0			0
$175$		−	1.49157i		−	0.112752i
$176$		0			0
$177$			13.1993i			0.992121i
$178$		0			0
$179$	−4.53823	+	1.87980i	−0.339203	+	0.140503i	−0.545782	−	0.837928i	$-0.683767\pi$
$179$	−4.53823	+	1.87980i	−0.339203	+	0.140503i	0.206578	+	0.978430i	$0.433767\pi$
$180$		0			0
$181$	−0.778175	+	1.87868i	−0.0578413	+	0.139641i	−0.950158	−	0.311768i	$-0.899079\pi$
$181$	−0.778175	+	1.87868i	−0.0578413	+	0.139641i	0.892317	+	0.451410i	$0.149079\pi$
$182$		0			0
$183$	25.8827	−	25.8827i	1.91331	−	1.91331i
$184$		0			0
$185$	−1.74441	−	1.74441i	−0.128251	−	0.128251i
$186$		0			0
$187$	−13.3579	−	5.53304i	−0.976829	−	0.404616i
$188$		0			0
$189$	−0.0745976	−	0.180095i	−0.00542618	−	0.0131000i
$190$		0			0
$191$	−19.4022			−1.40389			−0.701946	−	0.712231i	$-0.747685\pi$
$191$	−19.4022			−1.40389			−0.701946	+	0.712231i	$0.747685\pi$
$192$		0			0
$193$	−18.0461			−1.29898			−0.649492	−	0.760368i	$-0.725018\pi$
$193$	−18.0461			−1.29898			−0.649492	+	0.760368i	$0.725018\pi$
$194$		0			0
$195$	8.05117	+	19.4372i	0.576556	+	1.39193i
$196$		0			0
$197$	−0.208872	−	0.0865175i	−0.0148815	−	0.00616412i	0.375230	−	0.926932i	$-0.377564\pi$
$197$	−0.208872	−	0.0865175i	−0.0148815	−	0.00616412i	−0.390112	+	0.920768i	$0.627564\pi$
$198$		0			0
$199$	11.8992	+	11.8992i	0.843513	+	0.843513i	0.989314	−	0.145801i	$-0.0465759\pi$
$199$	11.8992	+	11.8992i	0.843513	+	0.843513i	−0.145801	+	0.989314i	$0.546576\pi$
$200$		0			0
$201$	−6.43030	+	6.43030i	−0.453558	+	0.453558i
$202$		0			0
$203$	−2.23570	+	5.39745i	−0.156915	+	0.378827i
$204$		0			0
$205$	4.03127	−	1.66981i	0.281556	−	0.116624i
$206$		0			0
$207$			5.82214i			0.404667i
$208$		0			0
$209$			2.03480i			0.140750i
$210$		0			0
$211$	−9.00647	+	3.73060i	−0.620031	+	0.256825i	−0.670511	−	0.741900i	$-0.733925\pi$
$211$	−9.00647	+	3.73060i	−0.620031	+	0.256825i	0.0504799	+	0.998725i	$0.483925\pi$
$212$		0			0
$213$	−12.8973	+	31.1367i	−0.883706	+	2.13345i
$214$		0			0
$215$	−3.60568	+	3.60568i	−0.245906	+	0.245906i
$216$		0			0
$217$	0.779208	+	0.779208i	0.0528961	+	0.0528961i
$218$		0			0
$219$	24.3564	+	10.0887i	1.64585	+	0.681733i
$220$		0			0
$221$	−6.38960	−	15.4259i	−0.429811	−	1.03766i
$222$		0			0
$223$	22.6174			1.51458			0.757288	−	0.653081i	$-0.226524\pi$
$223$	22.6174			1.51458			0.757288	+	0.653081i	$0.226524\pi$
$224$		0			0
$225$	4.89060			0.326040
$226$		0			0
$227$	3.94039	+	9.51294i	0.261533	+	0.631396i	0.999034	−	0.0439500i	$-0.0139942\pi$
$227$	3.94039	+	9.51294i	0.261533	+	0.631396i	−0.737501	+	0.675346i	$0.763994\pi$
$228$		0			0
$229$	−15.7697	−	6.53200i	−1.04209	−	0.431647i	−0.205027	−	0.978756i	$-0.565728\pi$
$229$	−15.7697	−	6.53200i	−1.04209	−	0.431647i	−0.837061	+	0.547109i	$0.815728\pi$
$230$		0			0
$231$	−6.55765	−	6.55765i	−0.431462	−	0.431462i
$232$		0			0
$233$	−10.4486	+	10.4486i	−0.684512	+	0.684512i	−0.961013	−	0.276502i	$-0.910825\pi$
$233$	−10.4486	+	10.4486i	−0.684512	+	0.684512i	0.276502	+	0.961013i	$0.410825\pi$
$234$		0			0
$235$	−1.05941	+	2.55765i	−0.0691084	+	0.166843i
$236$		0			0
$237$	−39.2360	+	16.2521i	−2.54865	+	1.05569i
$238$		0			0
$239$			11.6733i			0.755085i	0.925992	+	0.377543i	$0.123231\pi$
$239$			11.6733i			0.755085i	−0.925992	+	0.377543i	$0.876769\pi$
$240$		0			0
$241$			13.8288i			0.890791i	0.895334	+	0.445396i	$0.146937\pi$
$241$			13.8288i			0.890791i	−0.895334	+	0.445396i	$0.853063\pi$
$242$		0			0
$243$	−20.4933	+	8.48861i	−1.31465	+	0.544545i
$244$		0			0
$245$	−4.32417	+	10.4395i	−0.276261	+	0.666953i
$246$		0			0
$247$	−1.66157	+	1.66157i	−0.105723	+	0.105723i
$248$		0			0
$249$	22.0126	+	22.0126i	1.39499	+	1.39499i
$250$		0			0
$251$	13.0065	+	5.38745i	0.820961	+	0.340053i	0.753318	−	0.657656i	$-0.228452\pi$
$251$	13.0065	+	5.38745i	0.820961	+	0.340053i	0.0676429	+	0.997710i	$0.478452\pi$
$252$		0			0
$253$	2.88784	+	6.97186i	0.181557	+	0.438317i
$254$		0			0
$255$	16.4853			1.03235
$256$		0			0
$257$	−18.9043			−1.17922			−0.589609	−	0.807689i	$-0.700718\pi$
$257$	−18.9043			−1.17922			−0.589609	+	0.807689i	$0.700718\pi$
$258$		0			0
$259$	0.480569	+	1.16020i	0.0298611	+	0.0720911i
$260$		0			0
$261$	−17.6973	−	7.33046i	−1.09543	−	0.453744i
$262$		0			0
$263$	−13.9086	−	13.9086i	−0.857643	−	0.857643i	0.133417	−	0.991060i	$-0.457405\pi$
$263$	−13.9086	−	13.9086i	−0.857643	−	0.857643i	−0.991060	+	0.133417i	$0.957405\pi$
$264$		0			0
$265$	6.49824	−	6.49824i	0.399183	−	0.399183i
$266$		0			0
$267$	−7.26031	+	17.5279i	−0.444324	+	1.07269i
$268$		0			0
$269$	12.1968	−	5.05209i	0.743653	−	0.308031i	0.0215042	−	0.999769i	$-0.493154\pi$
$269$	12.1968	−	5.05209i	0.743653	−	0.308031i	0.722149	+	0.691737i	$0.243154\pi$
$270$		0			0
$271$		−	4.41512i		−	0.268199i	−0.990968	−	0.134100i	$-0.957186\pi$
$271$		−	4.41512i		−	0.268199i	0.990968	−	0.134100i	$-0.0428142\pi$
$272$		0			0
$273$		−	10.7096i		−	0.648175i
$274$		0			0
$275$	5.85637	−	2.42579i	0.353152	−	0.146280i
$276$		0			0
$277$	9.54573	−	23.0454i	0.573547	−	1.38467i	−0.324969	−	0.945725i	$-0.605354\pi$
$277$	9.54573	−	23.0454i	0.573547	−	1.38467i	0.898516	−	0.438941i	$-0.144646\pi$
$278$		0			0
$279$	−2.55489	+	2.55489i	−0.152957	+	0.152957i
$280$		0			0
$281$	5.83509	+	5.83509i	0.348092	+	0.348092i	0.859399	−	0.511306i	$-0.170838\pi$
$281$	5.83509	+	5.83509i	0.348092	+	0.348092i	−0.511306	+	0.859399i	$0.670838\pi$
$282$		0			0
$283$	3.18656	+	1.31992i	0.189421	+	0.0784609i	0.475378	−	0.879782i	$-0.342311\pi$
$283$	3.18656	+	1.31992i	0.189421	+	0.0784609i	−0.285957	+	0.958243i	$0.592311\pi$
$284$		0			0
$285$	−0.887839	−	2.14343i	−0.0525911	−	0.126966i
$286$		0			0
$287$	−2.22117			−0.131111
$288$		0			0
$289$	3.91688			0.230405
$290$		0			0
$291$	5.81324	+	14.0344i	0.340778	+	0.822712i
$292$		0			0
$293$	6.99307	+	2.89663i	0.408540	+	0.169223i	0.577482	−	0.816403i	$-0.304035\pi$
$293$	6.99307	+	2.89663i	0.408540	+	0.169223i	−0.168943	+	0.985626i	$0.554035\pi$
$294$		0			0
$295$	−6.99176	−	6.99176i	−0.407076	−	0.407076i
$296$		0			0
$297$	0.585786	−	0.585786i	0.0339908	−	0.0339908i
$298$		0			0
$299$	−3.33490	+	8.05117i	−0.192862	+	0.465611i
$300$		0			0
$301$	2.39813	−	0.993336i	0.138226	−	0.0572550i
$302$		0			0
$303$		−	19.9598i		−	1.14666i
$304$		0			0
$305$			27.4205i			1.57009i
$306$		0			0
$307$	−7.59225	+	3.14481i	−0.433313	+	0.179484i	−0.588668	−	0.808375i	$-0.700348\pi$
$307$	−7.59225	+	3.14481i	−0.433313	+	0.179484i	0.155356	+	0.987859i	$0.450348\pi$
$308$		0			0
$309$	−6.31095	+	15.2360i	−0.359017	+	0.866744i
$310$		0			0
$311$	15.0543	−	15.0543i	0.853651	−	0.853651i	−0.136930	−	0.990581i	$-0.543723\pi$
$311$	15.0543	−	15.0543i	0.853651	−	0.853651i	0.990581	+	0.136930i	$0.0437234\pi$
$312$		0			0
$313$	−18.3365	−	18.3365i	−1.03644	−	1.03644i	−0.999311	−	0.0371274i	$-0.988179\pi$
$313$	−18.3365	−	18.3365i	−1.03644	−	1.03644i	−0.0371274	−	0.999311i	$-0.511821\pi$
$314$		0			0
$315$	4.95196	+	2.05117i	0.279012	+	0.115570i
$316$		0			0
$317$	3.94476	+	9.52348i	0.221560	+	0.534892i	0.995102	−	0.0988523i	$-0.0315171\pi$
$317$	3.94476	+	9.52348i	0.221560	+	0.534892i	−0.773543	+	0.633744i	$0.781517\pi$
$318$		0			0
$319$	−24.8280			−1.39010
$320$		0			0
$321$	−6.88208			−0.384120
$322$		0			0
$323$	0.704611	+	1.70108i	0.0392056	+	0.0946507i
$324$		0			0
$325$	6.76299	+	2.80132i	0.375143	+	0.155389i
$326$		0			0
$327$	15.7737	+	15.7737i	0.872289	+	0.872289i
$328$		0			0
$329$	0.996470	−	0.996470i	0.0549372	−	0.0549372i
$330$		0			0
$331$	−3.13734	+	7.57421i	−0.172444	+	0.416316i	−0.986346	−	0.164685i	$-0.947339\pi$
$331$	−3.13734	+	7.57421i	−0.172444	+	0.416316i	0.813902	+	0.581002i	$0.197339\pi$
$332$		0			0
$333$	−3.80408	+	1.57570i	−0.208462	+	0.0863480i
$334$		0			0
$335$		−	6.81234i		−	0.372198i
$336$		0			0
$337$		−	16.8910i		−	0.920110i	−0.887890	−	0.460055i	$-0.847830\pi$
$337$		−	16.8910i		−	0.920110i	0.887890	−	0.460055i	$-0.152170\pi$
$338$		0			0
$339$	26.8347	−	11.1153i	1.45746	−	0.603700i
$340$		0			0
$341$	−1.79216	+	4.32666i	−0.0970510	+	0.234302i
$342$		0			0
$343$	8.72293	−	8.72293i	0.470994	−	0.470994i
$344$		0			0
$345$	−6.08402	−	6.08402i	−0.327553	−	0.327553i
$346$		0			0
$347$	−28.1455	−	11.6582i	−1.51093	−	0.625847i	−0.535179	−	0.844739i	$-0.679756\pi$
$347$	−28.1455	−	11.6582i	−1.51093	−	0.625847i	−0.975749	+	0.218892i	$0.929756\pi$
$348$		0			0
$349$	−4.13818	−	9.99044i	−0.221512	−	0.534776i	0.773584	−	0.633694i	$-0.218462\pi$
$349$	−4.13818	−	9.99044i	−0.221512	−	0.534776i	−0.995096	+	0.0989174i	$0.968462\pi$
$350$		0			0
$351$	0.956675			0.0510636
$352$		0			0
$353$	0.673711			0.0358580			0.0179290	−	0.999839i	$-0.494293\pi$
$353$	0.673711			0.0358580			0.0179290	+	0.999839i	$0.494293\pi$
$354$		0			0
$355$	−9.66157	−	23.3251i	−0.512783	−	1.23797i
$356$		0			0
$357$	−7.75293	−	3.21137i	−0.410328	−	0.169964i
$358$		0			0
$359$	−3.92568	−	3.92568i	−0.207190	−	0.207190i	0.595882	−	0.803072i	$-0.296802\pi$
$359$	−3.92568	−	3.92568i	−0.207190	−	0.207190i	−0.803072	+	0.595882i	$0.796802\pi$
$360$		0			0
$361$	−13.2518	+	13.2518i	−0.697463	+	0.697463i
$362$		0			0
$363$	4.69933	−	11.3452i	0.246651	−	0.595467i
$364$		0			0
$365$	−18.2458	+	7.55765i	−0.955027	+	0.395585i
$366$		0			0
$367$		−	16.4759i		−	0.860033i	−0.902821	−	0.430016i	$-0.858508\pi$
$367$		−	16.4759i		−	0.860033i	0.902821	−	0.430016i	$-0.141492\pi$
$368$		0			0
$369$		−	7.28281i		−	0.379128i
$370$		0			0
$371$	−4.32195	+	1.79021i	−0.224384	+	0.0929431i
$372$		0			0
$373$	5.25180	−	12.6790i	0.271928	−	0.656492i	−0.727638	−	0.685962i	$-0.759382\pi$
$373$	5.25180	−	12.6790i	0.271928	−	0.656492i	0.999566	+	0.0294695i	$0.00938180\pi$
$374$		0			0
$375$	−21.2243	+	21.2243i	−1.09602	+	1.09602i
$376$		0			0
$377$	−20.2739	−	20.2739i	−1.04416	−	1.04416i
$378$		0			0
$379$	−12.2339	−	5.06746i	−0.628414	−	0.260298i	0.0456649	−	0.998957i	$-0.485459\pi$
$379$	−12.2339	−	5.06746i	−0.628414	−	0.260298i	−0.674079	+	0.738659i	$0.735459\pi$
$380$		0			0
$381$	12.3267	+	29.7592i	0.631514	+	1.52461i
$382$		0			0
$383$	14.5667			0.744322			0.372161	−	0.928168i	$-0.378617\pi$
$383$	14.5667			0.744322			0.372161	+	0.928168i	$0.378617\pi$
$384$		0			0
$385$	6.94725			0.354065
$386$		0			0
$387$	3.25697	+	7.86303i	0.165561	+	0.399700i
$388$		0			0
$389$	34.4739	+	14.2795i	1.74789	+	0.724002i	0.998052	+	0.0623850i	$0.0198707\pi$
$389$	34.4739	+	14.2795i	1.74789	+	0.724002i	0.749842	+	0.661617i	$0.230129\pi$
$390$		0			0
$391$	4.82843	+	4.82843i	0.244184	+	0.244184i
$392$		0			0
$393$	−12.3115	+	12.3115i	−0.621032	+	0.621032i
$394$		0			0
$395$	12.1747	−	29.3923i	0.612576	−	1.47889i
$396$		0			0
$397$	21.4480	−	8.88405i	1.07644	−	0.445877i	0.227183	−	0.973852i	$-0.427048\pi$
$397$	21.4480	−	8.88405i	1.07644	−	0.445877i	0.849260	+	0.527975i	$0.177048\pi$
$398$		0			0
$399$			1.18100i			0.0591238i
$400$		0			0
$401$		−	2.51509i		−	0.125598i	−0.998026	−	0.0627989i	$-0.979997\pi$
$401$		−	2.51509i		−	0.125598i	0.998026	−	0.0627989i	$-0.0200027\pi$
$402$		0			0
$403$	−4.99647	+	2.06961i	−0.248892	+	0.103094i
$404$		0			0
$405$	6.18073	−	14.9216i	0.307123	−	0.741461i
$406$		0			0
$407$	−3.77373	+	3.77373i	−0.187057	+	0.187057i
$408$		0			0
$409$	5.32666	+	5.32666i	0.263386	+	0.263386i	0.826428	−	0.563042i	$-0.190369\pi$
$409$	5.32666	+	5.32666i	0.263386	+	0.263386i	−0.563042	+	0.826428i	$0.690369\pi$
$410$		0			0
$411$	−15.7308	−	6.51590i	−0.775942	−	0.321406i
$412$		0			0
$413$	1.92617	+	4.65019i	0.0947807	+	0.228821i
$414$		0			0
$415$	−23.3204			−1.14475
$416$		0			0
$417$	31.4603			1.54062
$418$		0			0
$419$	−4.37032	−	10.5509i	−0.213504	−	0.515444i	0.780453	−	0.625214i	$-0.214988\pi$
$419$	−4.37032	−	10.5509i	−0.213504	−	0.515444i	−0.993957	+	0.109770i	$0.964988\pi$
$420$		0			0
$421$	4.16464	+	1.72505i	0.202972	+	0.0840739i	0.481854	−	0.876252i	$-0.339964\pi$
$421$	4.16464	+	1.72505i	0.202972	+	0.0840739i	−0.278881	+	0.960326i	$0.589964\pi$
$422$		0			0
$423$	3.26725	+	3.26725i	0.158859	+	0.158859i
$424$		0			0
$425$	4.05588	−	4.05588i	0.196739	−	0.196739i
$426$		0			0
$427$	5.34157	−	12.8957i	0.258497	−	0.624066i
$428$		0			0
$429$	42.0492	−	17.4173i	2.03015	−	0.840917i
$430$		0			0
$431$			16.9800i			0.817897i	0.912557	+	0.408949i	$0.134104\pi$
$431$			16.9800i			0.817897i	−0.912557	+	0.408949i	$0.865896\pi$
$432$		0			0
$433$		−	16.9567i		−	0.814886i	−0.913231	−	0.407443i	$-0.866421\pi$
$433$		−	16.9567i		−	0.814886i	0.913231	−	0.407443i	$-0.133579\pi$
$434$		0			0
$435$	26.1535	−	10.8331i	1.25396	−	0.519409i
$436$		0			0
$437$	0.367755	−	0.887839i	0.0175921	−	0.0424711i
$438$		0			0
$439$	−10.5596	+	10.5596i	−0.503982	+	0.503982i	−0.912673	−	0.408691i	$-0.865985\pi$
$439$	−10.5596	+	10.5596i	−0.503982	+	0.503982i	0.408691	+	0.912673i	$0.365985\pi$
$440$		0			0
$441$	13.3358	+	13.3358i	0.635039	+	0.635039i
$442$		0			0
$443$	15.2358	+	6.31087i	0.723874	+	0.299838i	0.714032	−	0.700113i	$-0.246867\pi$
$443$	15.2358	+	6.31087i	0.723874	+	0.299838i	0.00984190	+	0.999952i	$0.496867\pi$
$444$		0			0
$445$	−5.43882	−	13.1305i	−0.257825	−	0.622444i
$446$		0			0
$447$	15.3204			0.724629
$448$		0			0
$449$	8.07197			0.380940			0.190470	−	0.981693i	$-0.438999\pi$
$449$	8.07197			0.380940			0.190470	+	0.981693i	$0.438999\pi$
$450$		0			0
$451$	−3.61235	−	8.72098i	−0.170099	−	0.410655i
$452$		0			0
$453$	−35.9348	−	14.8847i	−1.68836	−	0.699343i
$454$		0			0
$455$	5.67294	+	5.67294i	0.265952	+	0.265952i
$456$		0			0
$457$	7.68314	−	7.68314i	0.359402	−	0.359402i	−0.504191	−	0.863592i	$-0.668209\pi$
$457$	7.68314	−	7.68314i	0.359402	−	0.359402i	0.863592	+	0.504191i	$0.168209\pi$
$458$		0			0
$459$	0.286867	−	0.692559i	0.0133898	−	0.0323259i
$460$		0			0
$461$	−14.2487	+	5.90199i	−0.663627	+	0.274883i	−0.688964	−	0.724796i	$-0.741934\pi$
$461$	−14.2487	+	5.90199i	−0.663627	+	0.274883i	0.0253371	+	0.999679i	$0.491934\pi$
$462$		0			0
$463$			27.3231i			1.26981i	0.772589	+	0.634907i	$0.218962\pi$
$463$			27.3231i			1.26981i	−0.772589	+	0.634907i	$0.781038\pi$
$464$		0			0
$465$		−	5.33962i		−	0.247619i
$466$		0			0
$467$	−22.7075	+	9.40577i	−1.05078	+	0.435247i	−0.840170	−	0.542323i	$-0.817545\pi$
$467$	−22.7075	+	9.40577i	−1.05078	+	0.435247i	−0.210610	+	0.977570i	$0.567545\pi$
$468$		0			0
$469$	−1.32706	+	3.20380i	−0.0612779	+	0.147938i
$470$		0			0
$471$	2.31253	−	2.31253i	0.106556	−	0.106556i
$472$		0			0
$473$	7.80029	+	7.80029i	0.358658	+	0.358658i
$474$		0			0
$475$	−0.745786	−	0.308915i	−0.0342190	−	0.0141740i
$476$		0			0
$477$	−5.86978	−	14.1709i	−0.268759	−	0.648842i
$478$		0			0
$479$	3.91155			0.178723			0.0893616	−	0.995999i	$-0.471517\pi$
$479$	3.91155			0.178723			0.0893616	+	0.995999i	$0.471517\pi$
$480$		0			0
$481$	−6.16305			−0.281011
$482$		0			0
$483$	1.67610	+	4.04646i	0.0762651	+	0.184120i
$484$		0			0
$485$	−10.5134	−	4.35480i	−0.477390	−	0.197741i
$486$		0			0
$487$	8.14685	+	8.14685i	0.369169	+	0.369169i	0.867174	−	0.498005i	$-0.165934\pi$
$487$	8.14685	+	8.14685i	0.369169	+	0.369169i	−0.498005	+	0.867174i	$0.665934\pi$
$488$		0			0
$489$	40.2520	−	40.2520i	1.82026	−	1.82026i
$490$		0			0
$491$	−4.67590	+	11.2886i	−0.211020	+	0.509448i	−0.993581	−	0.113127i	$-0.963913\pi$
$491$	−4.67590	+	11.2886i	−0.211020	+	0.509448i	0.782560	+	0.622575i	$0.213913\pi$
$492$		0			0
$493$	−20.7561	+	8.59744i	−0.934806	+	0.387209i
$494$		0			0
$495$			22.7788i			1.02383i
$496$		0			0
$497$			12.8517i			0.576479i
$498$		0			0
$499$	29.9533	−	12.4071i	1.34089	−	0.555417i	0.407152	−	0.913361i	$-0.366522\pi$
$499$	29.9533	−	12.4071i	1.34089	−	0.555417i	0.933743	+	0.357944i	$0.116522\pi$
$500$		0			0
$501$	14.5321	−	35.0836i	0.649247	−	1.56742i
$502$		0			0
$503$	−8.77059	+	8.77059i	−0.391061	+	0.391061i	−0.875066	−	0.484004i	$-0.839182\pi$
$503$	−8.77059	+	8.77059i	−0.391061	+	0.391061i	0.484004	+	0.875066i	$0.339182\pi$
$504$		0			0
$505$	10.5728	+	10.5728i	0.470485	+	0.470485i
$506$		0			0
$507$	18.9341	+	7.84276i	0.840893	+	0.348309i
$508$		0			0
$509$	−8.32546	−	20.0994i	−0.369020	−	0.890892i	−0.993912	−	0.110181i	$-0.964857\pi$
$509$	−8.32546	−	20.0994i	−0.369020	−	0.890892i	0.624892	−	0.780711i	$-0.285143\pi$
$510$		0			0
$511$	10.0531			0.444724
$512$		0			0
$513$	−0.105497			−0.00465780
$514$		0			0
$515$	−4.72764	−	11.4135i	−0.208325	−	0.502941i
$516$		0			0
$517$	5.53304	+	2.29186i	0.243343	+	0.100796i
$518$		0			0
$519$	3.35099	+	3.35099i	0.147092	+	0.147092i
$520$		0			0
$521$	29.8910	−	29.8910i	1.30955	−	1.30955i	0.387807	−	0.921741i	$-0.373233\pi$
$521$	29.8910	−	29.8910i	1.30955	−	1.30955i	0.921741	−	0.387807i	$-0.126767\pi$
$522$		0			0
$523$	−13.5719	+	32.7654i	−0.593456	+	1.43273i	0.286688	+	0.958024i	$0.407446\pi$
$523$	−13.5719	+	32.7654i	−0.593456	+	1.43273i	−0.880144	+	0.474706i	$0.842554\pi$
$524$		0			0
$525$	3.39903	−	1.40792i	0.148346	−	0.0614468i
$526$		0			0
$527$			4.23765i			0.184595i
$528$		0			0
$529$			19.4361i			0.845046i
$530$		0			0
$531$	−15.2472	+	6.31558i	−0.661670	+	0.274073i
$532$		0			0
$533$	4.17157	−	10.0711i	0.180691	−	0.436226i
$534$		0			0
$535$	3.64548	−	3.64548i	0.157608	−	0.157608i
$536$		0			0
$537$	−8.56744	−	8.56744i	−0.369713	−	0.369713i
$538$		0			0
$539$	22.5840	+	9.35460i	0.972762	+	0.402931i
$540$		0			0
$541$	4.67751	+	11.2925i	0.201102	+	0.485502i	0.991968	−	0.126486i	$-0.0403699\pi$
$541$	4.67751	+	11.2925i	0.201102	+	0.485502i	−0.790867	+	0.611988i	$0.790370\pi$
$542$		0			0
$543$	−5.01571			−0.215245
$544$		0			0
$545$	−16.7109			−0.715815
$546$		0			0
$547$	7.92207	+	19.1256i	0.338723	+	0.817750i	0.997839	+	0.0657087i	$0.0209308\pi$
$547$	7.92207	+	19.1256i	0.338723	+	0.817750i	−0.659116	+	0.752042i	$0.729069\pi$
$548$		0			0
$549$	42.2827	+	17.5141i	1.80458	+	0.747482i
$550$		0			0
$551$	2.23570	+	2.23570i	0.0952439	+	0.0952439i
$552$		0			0
$553$	−11.4514	+	11.4514i	−0.486962	+	0.486962i
$554$		0			0
$555$	2.32861	−	5.62177i	0.0988442	−	0.238631i
$556$		0			0
$557$	29.8439	−	12.3617i	1.26452	−	0.523783i	0.353229	−	0.935537i	$-0.385084\pi$
$557$	29.8439	−	12.3617i	1.26452	−	0.523783i	0.911295	+	0.411753i	$0.135084\pi$
$558$		0			0
$559$			12.7390i			0.538803i
$560$		0			0
$561$		−	35.6631i		−	1.50570i
$562$		0			0
$563$	−25.4797	+	10.5540i	−1.07384	+	0.444800i	−0.848345	−	0.529444i	$-0.822400\pi$
$563$	−25.4797	+	10.5540i	−1.07384	+	0.444800i	−0.225497	+	0.974244i	$0.572400\pi$
$564$		0			0
$565$	−8.32666	+	20.1023i	−0.350305	+	0.845712i
$566$		0			0
$567$	−5.81352	+	5.81352i	−0.244145	+	0.244145i
$568$		0			0
$569$	23.7855	+	23.7855i	0.997139	+	0.997139i	0.999996	−	0.00285688i	$-0.000909375\pi$
$569$	23.7855	+	23.7855i	0.997139	+	0.997139i	−0.00285688	+	0.999996i	$0.500909\pi$
$570$		0			0
$571$	−2.18343	−	0.904405i	−0.0913736	−	0.0378482i	0.336528	−	0.941673i	$-0.390747\pi$
$571$	−2.18343	−	0.904405i	−0.0913736	−	0.0378482i	−0.427902	+	0.903825i	$0.640747\pi$
$572$		0			0
$573$	−18.3141	−	44.2141i	−0.765082	−	1.84707i
$574$		0			0
$575$	−2.99371			−0.124846
$576$		0			0
$577$	24.8839			1.03593			0.517965	−	0.855402i	$-0.326690\pi$
$577$	24.8839			1.03593			0.517965	+	0.855402i	$0.326690\pi$
$578$		0			0
$579$	−17.0340	−	41.1238i	−0.707910	−	1.70905i
$580$		0			0
$581$	10.9674	+	4.54286i	0.455006	+	0.188469i
$582$		0			0
$583$	−14.0578	−	14.0578i	−0.582216	−	0.582216i
$584$		0			0
$585$	−18.6006	+	18.6006i	−0.769039	+	0.769039i
$586$		0			0
$587$	16.6383	−	40.1685i	0.686738	−	1.65793i	−0.0645151	−	0.997917i	$-0.520550\pi$
$587$	16.6383	−	40.1685i	0.686738	−	1.65793i	0.751253	−	0.660015i	$-0.229450\pi$
$588$		0			0
$589$	0.550984	−	0.228225i	0.0227029	−	0.00940384i
$590$		0			0
$591$		−	0.557647i		−	0.0229385i
$592$		0			0
$593$			9.10197i			0.373773i	0.982382	+	0.186886i	$0.0598397\pi$
$593$			9.10197i			0.373773i	−0.982382	+	0.186886i	$0.940160\pi$
$594$		0			0
$595$	5.80785	−	2.40569i	0.238099	−	0.0986238i
$596$		0			0
$597$	−15.8843	+	38.3481i	−0.650102	+	1.56948i
$598$		0			0
$599$	−3.04488	+	3.04488i	−0.124410	+	0.124410i	−0.766571	−	0.642160i	$-0.778038\pi$
$599$	−3.04488	+	3.04488i	−0.124410	+	0.124410i	0.642160	+	0.766571i	$0.278038\pi$
$600$		0			0
$601$	−9.53880	−	9.53880i	−0.389096	−	0.389096i	0.485269	−	0.874365i	$-0.338722\pi$
$601$	−9.53880	−	9.53880i	−0.389096	−	0.389096i	−0.874365	+	0.485269i	$0.838722\pi$
$602$		0			0
$603$	−10.5047	−	4.35119i	−0.427784	−	0.177194i
$604$		0			0
$605$	3.52035	+	8.49887i	0.143123	+	0.345528i
$606$		0			0
$607$	−3.66391			−0.148714			−0.0743568	−	0.997232i	$-0.523690\pi$
$607$	−3.66391			−0.148714			−0.0743568	+	0.997232i	$0.523690\pi$
$608$		0			0
$609$	−14.4102			−0.583929
$610$		0			0
$611$	2.64666	+	6.38960i	0.107072	+	0.258496i
$612$		0			0
$613$	−28.0079	−	11.6012i	−1.13123	−	0.468570i	−0.263029	−	0.964788i	$-0.584722\pi$
$613$	−28.0079	−	11.6012i	−1.13123	−	0.468570i	−0.868198	+	0.496218i	$0.834722\pi$
$614$		0			0
$615$	7.61040	+	7.61040i	0.306881	+	0.306881i
$616$		0			0
$617$	−5.86100	+	5.86100i	−0.235955	+	0.235955i	−0.815173	−	0.579218i	$-0.803358\pi$
$617$	−5.86100	+	5.86100i	−0.235955	+	0.235955i	0.579218	+	0.815173i	$0.303358\pi$
$618$		0			0
$619$	15.2917	−	36.9173i	0.614624	−	1.48383i	−0.243245	−	0.969965i	$-0.578212\pi$
$619$	15.2917	−	36.9173i	0.614624	−	1.48383i	0.857869	−	0.513868i	$-0.171788\pi$
$620$		0			0
$621$	−0.361465	+	0.149724i	−0.0145051	+	0.00600821i
$622$		0			0
$623$			7.23468i			0.289851i
$624$		0			0
$625$		−	14.5563i		−	0.582254i
$626$		0			0
$627$	−4.63696	+	1.92069i	−0.185182	+	0.0767050i
$628$		0			0
$629$	−1.84804	+	4.46157i	−0.0736864	+	0.177895i
$630$		0			0
$631$	21.0543	−	21.0543i	0.838159	−	0.838159i	−0.150458	−	0.988616i	$-0.548075\pi$
$631$	21.0543	−	21.0543i	0.838159	−	0.838159i	0.988616	+	0.150458i	$0.0480748\pi$
$632$		0			0
$633$	−17.0028	−	17.0028i	−0.675799	−	0.675799i
$634$		0			0
$635$	−22.2931	−	9.23412i	−0.884676	−	0.366445i
$636$		0			0
$637$	10.8028	+	26.0802i	0.428022	+	1.03334i
$638$		0			0
$639$	−42.1386			−1.66698
$640$		0			0
$641$	−6.57429			−0.259669			−0.129835	−	0.991536i	$-0.541445\pi$
$641$	−6.57429			−0.259669			−0.129835	+	0.991536i	$0.541445\pi$
$642$		0			0
$643$	9.98462	+	24.1050i	0.393755	+	0.950608i	0.989114	+	0.147149i	$0.0470096\pi$
$643$	9.98462	+	24.1050i	0.393755	+	0.950608i	−0.595360	+	0.803459i	$0.702990\pi$
$644$		0			0
$645$	−11.6202	−	4.81324i	−0.457545	−	0.189521i
$646$		0			0
$647$	−19.1598	−	19.1598i	−0.753250	−	0.753250i	0.221835	−	0.975084i	$-0.428795\pi$
$647$	−19.1598	−	19.1598i	−0.753250	−	0.753250i	−0.975084	+	0.221835i	$0.928795\pi$
$648$		0			0
$649$	−15.1255	+	15.1255i	−0.593727	+	0.593727i
$650$		0			0
$651$	−1.04017	+	2.51119i	−0.0407674	+	0.0984212i
$652$		0			0
$653$	−13.8416	+	5.73339i	−0.541665	+	0.224365i	−0.636703	−	0.771109i	$-0.719702\pi$
$653$	−13.8416	+	5.73339i	−0.541665	+	0.224365i	0.0950389	+	0.995474i	$0.469702\pi$
$654$		0			0
$655$		−	13.0429i		−	0.509629i
$656$		0			0
$657$			32.9624i			1.28599i
$658$		0			0
$659$	−0.489009	+	0.202554i	−0.0190491	+	0.00789039i	−0.392188	−	0.919885i	$-0.628282\pi$
$659$	−0.489009	+	0.202554i	−0.0190491	+	0.00789039i	0.373139	+	0.927776i	$0.378282\pi$
$660$		0			0
$661$	−2.67268	+	6.45241i	−0.103955	+	0.250970i	−0.967295	−	0.253652i	$-0.918368\pi$
$661$	−2.67268	+	6.45241i	−0.103955	+	0.250970i	0.863340	+	0.504622i	$0.168368\pi$
$662$		0			0
$663$	29.1216	−	29.1216i	1.13099	−	1.13099i
$664$		0			0
$665$	−0.625581	−	0.625581i	−0.0242590	−	0.0242590i
$666$		0			0
$667$	10.8331	+	4.48723i	0.419461	+	0.173746i
$668$		0			0
$669$	21.3490	+	51.5411i	0.825402	+	1.99270i
$670$		0			0
$671$	59.3196			2.29001
$672$		0			0
$673$	−24.3285			−0.937793			−0.468897	−	0.883253i	$-0.655348\pi$
$673$	−24.3285			−0.937793			−0.468897	+	0.883253i	$0.655348\pi$
$674$		0			0
$675$	0.125768	+	0.303631i	0.00484081	+	0.0116868i
$676$		0			0
$677$	3.88054	+	1.60737i	0.149141	+	0.0617763i	0.456005	−	0.889977i	$-0.349280\pi$
$677$	3.88054	+	1.60737i	0.149141	+	0.0617763i	−0.306864	+	0.951753i	$0.599280\pi$
$678$		0			0
$679$	4.09607	+	4.09607i	0.157193	+	0.157193i
$680$		0			0
$681$	−17.9589	+	17.9589i	−0.688187	+	0.688187i
$682$		0			0
$683$	−10.2780	+	24.8133i	−0.393277	+	0.949455i	0.595944	+	0.803026i	$0.296778\pi$
$683$	−10.2780	+	24.8133i	−0.393277	+	0.949455i	−0.989221	+	0.146429i	$0.953222\pi$
$684$		0			0
$685$	11.7842	−	4.88118i	0.450251	−	0.186500i
$686$		0			0
$687$		−	42.1019i		−	1.60629i
$688$		0			0
$689$		−	22.9585i		−	0.874650i
$690$		0			0
$691$	20.6870	−	8.56885i	0.786972	−	0.325974i	0.0472463	−	0.998883i	$-0.484955\pi$
$691$	20.6870	−	8.56885i	0.786972	−	0.325974i	0.739725	+	0.672909i	$0.234955\pi$
$692$		0			0
$693$	4.43736	−	10.7127i	0.168561	−	0.406943i
$694$		0			0
$695$	−16.6647	+	16.6647i	−0.632128	+	0.632128i
$696$		0			0
$697$	−6.03979	−	6.03979i	−0.228774	−	0.228774i
$698$		0			0
$699$	−33.6732	−	13.9479i	−1.27364	−	0.527558i
$700$		0			0
$701$	−11.6625	−	28.1557i	−0.440486	−	1.06343i	−0.975779	−	0.218760i	$-0.929799\pi$
$701$	−11.6625	−	28.1557i	−0.440486	−	1.06343i	0.535293	−	0.844667i	$-0.320201\pi$
$702$		0			0
$703$	0.679628			0.0256326
$704$		0			0
$705$	−6.82843			−0.257173
$706$		0			0
$707$	−2.91273	−	7.03195i	−0.109544	−	0.264464i
$708$		0			0
$709$	30.0346	+	12.4408i	1.12797	+	0.467223i	0.867092	−	0.498148i	$-0.165986\pi$
$709$	30.0346	+	12.4408i	1.12797	+	0.467223i	0.260883	+	0.965370i	$0.415986\pi$
$710$		0			0
$711$	−37.5471	−	37.5471i	−1.40812	−	1.40812i
$712$		0			0
$713$	1.56394	−	1.56394i	0.0585699	−	0.0585699i
$714$		0			0
$715$	−13.0476	+	31.4998i	−0.487954	+	1.17803i
$716$		0			0
$717$	−26.6015	+	11.0187i	−0.993450	+	0.411501i
$718$		0			0
$719$		−	33.6333i		−	1.25431i	−0.778894	−	0.627155i	$-0.784219\pi$
$719$		−	33.6333i		−	1.25431i	0.778894	−	0.627155i	$-0.215781\pi$
$720$		0			0
$721$			6.28867i			0.234202i
$722$		0			0
$723$	−31.5134	+	13.0533i	−1.17200	+	0.485457i
$724$		0			0
$725$	3.76928	−	9.09984i	0.139988	−	0.337960i
$726$		0			0
$727$	7.43334	−	7.43334i	0.275687	−	0.275687i	−0.555697	−	0.831385i	$-0.687549\pi$
$727$	7.43334	−	7.43334i	0.275687	−	0.275687i	0.831385	+	0.555697i	$0.187549\pi$
$728$		0			0
$729$	−20.1459	−	20.1459i	−0.746145	−	0.746145i
$730$		0			0
$731$	9.22207	+	3.81991i	0.341090	+	0.141284i
$732$		0			0
$733$	0.136110	+	0.328598i	0.00502733	+	0.0121371i	0.926373	−	0.376607i	$-0.122909\pi$
$733$	0.136110	+	0.328598i	0.00502733	+	0.0121371i	−0.921346	+	0.388744i	$0.872909\pi$
$734$		0			0
$735$	−27.8714			−1.02805
$736$		0			0
$737$	−14.7373			−0.542857
$738$		0			0
$739$	18.1780	+	43.8857i	0.668690	+	1.61436i	0.783804	+	0.621008i	$0.213277\pi$
$739$	18.1780	+	43.8857i	0.668690	+	1.61436i	−0.115114	+	0.993352i	$0.536723\pi$
$740$		0			0
$741$	−5.35480	−	2.21803i	−0.196714	−	0.0814814i
$742$		0			0
$743$	30.3220	+	30.3220i	1.11240	+	1.11240i	0.992825	+	0.119580i	$0.0381548\pi$
$743$	30.3220	+	30.3220i	1.11240	+	1.11240i	0.119580	+	0.992825i	$0.461845\pi$
$744$		0			0
$745$	−8.11529	+	8.11529i	−0.297321	+	0.297321i
$746$		0			0
$747$	−14.8952	+	35.9603i	−0.544988	+	1.31572i
$748$		0			0
$749$	−2.42459	+	1.00430i	−0.0885927	+	0.0366963i
$750$		0			0
$751$		−	51.3686i		−	1.87447i	−0.348701	−	0.937234i	$-0.613377\pi$
$751$		−	51.3686i		−	1.87447i	0.348701	−	0.937234i	$-0.386623\pi$
$752$		0			0
$753$			34.7248i			1.26544i
$754$		0			0
$755$	26.9194	−	11.1504i	0.979697	−	0.405804i
$756$		0			0
$757$	−6.32270	+	15.2644i	−0.229803	+	0.554793i	−0.996153	−	0.0876302i	$-0.972071\pi$
$757$	−6.32270	+	15.2644i	−0.229803	+	0.554793i	0.766350	+	0.642423i	$0.222071\pi$
$758$		0			0
$759$	−13.1618	+	13.1618i	−0.477741	+	0.477741i
$760$		0			0
$761$	−26.6859	−	26.6859i	−0.967362	−	0.967362i	0.0321218	−	0.999484i	$-0.489774\pi$
$761$	−26.6859	−	26.6859i	−0.967362	−	0.967362i	−0.999484	+	0.0321218i	$0.989774\pi$
$762$		0			0
$763$	7.85902	+	3.25531i	0.284516	+	0.117850i
$764$		0			0
$765$	7.88784	+	19.0429i	0.285185	+	0.688499i
$766$		0			0
$767$	−24.7021			−0.891943
$768$		0			0
$769$	44.0390			1.58809			0.794044	−	0.607861i	$-0.207972\pi$
$769$	44.0390			1.58809			0.794044	+	0.607861i	$0.207972\pi$
$770$		0			0
$771$	−17.8441	−	43.0796i	−0.642641	−	1.55147i
$772$		0			0
$773$	−37.1790	−	15.4001i	−1.33724	−	0.553902i	−0.404526	−	0.914526i	$-0.632564\pi$
$773$	−37.1790	−	15.4001i	−1.33724	−	0.553902i	−0.932711	+	0.360625i	$0.882564\pi$
$774$		0			0
$775$	−1.31371	−	1.31371i	−0.0471898	−	0.0471898i
$776$		0			0
$777$	−2.19027	+	2.19027i	−0.0785754	+	0.0785754i
$778$		0			0
$779$	−0.460018	+	1.11058i	−0.0164819	+	0.0397908i
$780$		0			0
$781$	−50.4599	+	20.9012i	−1.80560	+	0.747903i
$782$		0			0
$783$		−	1.28724i		−	0.0460022i
$784$		0			0
$785$			2.44992i			0.0874413i
$786$		0			0
$787$	2.29020	−	0.948632i	0.0816368	−	0.0338151i	−0.341491	−	0.939885i	$-0.610932\pi$
$787$	2.29020	−	0.948632i	0.0816368	−	0.0338151i	0.423128	+	0.906070i	$0.360932\pi$
$788$		0			0
$789$	18.5667	−	44.8240i	0.660992	−	1.59578i
$790$		0			0
$791$	7.83196	−	7.83196i	0.278472	−	0.278472i
$792$		0			0
$793$	48.4388	+	48.4388i	1.72011	+	1.72011i
$794$		0			0
$795$	20.9421	+	8.67452i	0.742741	+	0.307654i
$796$		0			0
$797$	1.14556	+	2.76562i	0.0405777	+	0.0979632i	0.942869	−	0.333164i	$-0.108116\pi$
$797$	1.14556	+	2.76562i	0.0405777	+	0.0979632i	−0.902291	+	0.431127i	$0.858116\pi$
$798$		0			0
$799$	5.41921			0.191718
$800$		0			0
$801$	−23.7212			−0.838149
$802$		0			0
$803$	16.3497	+	39.4717i	0.576968	+	1.39292i
$804$		0			0
$805$	−3.03127	−	1.25559i	−0.106838	−	0.0442539i
$806$		0			0
$807$	23.0256	+	23.0256i	0.810541	+	0.810541i
$808$		0			0
$809$	7.12825	−	7.12825i	0.250616	−	0.250616i	−0.570607	−	0.821223i	$-0.693292\pi$
$809$	7.12825	−	7.12825i	0.250616	−	0.250616i	0.821223	+	0.570607i	$0.193292\pi$
$810$		0			0
$811$	−11.3805	+	27.4750i	−0.399624	+	0.964777i	0.588131	+	0.808765i	$0.299864\pi$
$811$	−11.3805	+	27.4750i	−0.399624	+	0.964777i	−0.987755	+	0.156012i	$0.950136\pi$
$812$		0			0
$813$	10.0613	−	4.16751i	0.352864	−	0.146161i
$814$		0			0
$815$			42.6435i			1.49374i
$816$		0			0
$817$		−	1.40479i		−	0.0491474i
$818$		0			0
$819$	12.3712	−	5.12431i	0.432284	−	0.179058i
$820$		0			0
$821$	−14.1603	+	34.1861i	−0.494199	+	1.19310i	0.458364	+	0.888764i	$0.348435\pi$
$821$	−14.1603	+	34.1861i	−0.494199	+	1.19310i	−0.952564	+	0.304339i	$0.901565\pi$
$822$		0			0
$823$	−27.3810	+	27.3810i	−0.954440	+	0.954440i	−0.999006	−	0.0445659i	$-0.985810\pi$
$823$	−27.3810	+	27.3810i	−0.954440	+	0.954440i	0.0445659	+	0.999006i	$0.485810\pi$
$824$		0			0
$825$	11.0559	+	11.0559i	0.384916	+	0.384916i
$826$		0			0
$827$	19.2661	+	7.98030i	0.669950	+	0.277502i	0.691619	−	0.722263i	$-0.256898\pi$
$827$	19.2661	+	7.98030i	0.669950	+	0.277502i	−0.0216689	+	0.999765i	$0.506898\pi$
$828$		0			0
$829$	1.48945	+	3.59585i	0.0517307	+	0.124889i	0.947632	−	0.319364i	$-0.103469\pi$
$829$	1.48945	+	3.59585i	0.0517307	+	0.124889i	−0.895901	+	0.444253i	$0.853469\pi$
$830$		0			0
$831$	61.5269			2.13434
$832$		0			0
$833$	22.1194			0.766391
$834$		0			0
$835$	10.8863	+	26.2818i	0.376735	+	0.909518i
$836$		0			0
$837$	−0.224321	−	0.0929169i	−0.00775368	−	0.00321168i
$838$		0			0
$839$	−13.8461	−	13.8461i	−0.478020	−	0.478020i	0.426478	−	0.904498i	$-0.359754\pi$
$839$	−13.8461	−	13.8461i	−0.478020	−	0.478020i	−0.904498	+	0.426478i	$0.859754\pi$
$840$		0			0
$841$	−6.77318	+	6.77318i	−0.233558	+	0.233558i
$842$		0			0
$843$	−7.78929	+	18.8050i	−0.268277	+	0.647679i
$844$		0			0
$845$	−14.1839	+	5.87515i	−0.487940	+	0.202111i
$846$		0			0
$847$		−	4.68274i		−	0.160901i
$848$		0			0
$849$			8.50750i			0.291977i
$850$		0			0
$851$	2.32861	−	0.964543i	0.0798239	−	0.0330641i
$852$		0			0
$853$	−7.48055	+	18.0597i	−0.256129	+	0.618351i	−0.998676	−	0.0514436i	$-0.983618\pi$
$853$	−7.48055	+	18.0597i	−0.256129	+	0.618351i	0.742547	+	0.669794i	$0.233618\pi$
$854$		0			0
$855$	2.05117	−	2.05117i	0.0701485	−	0.0701485i
$856$		0			0
$857$	6.35294	+	6.35294i	0.217012	+	0.217012i	0.807238	−	0.590226i	$-0.200961\pi$
$857$	6.35294	+	6.35294i	0.217012	+	0.217012i	−0.590226	+	0.807238i	$0.700961\pi$
$858$		0			0
$859$	23.4855	+	9.72800i	0.801314	+	0.331915i	0.745483	−	0.666525i	$-0.232219\pi$
$859$	23.4855	+	9.72800i	0.801314	+	0.331915i	0.0558315	+	0.998440i	$0.482219\pi$
$860$		0			0
$861$	−2.09660	−	5.06164i	−0.0714520	−	0.172500i
$862$		0			0
$863$	−0.0884535			−0.00301099			−0.00150550	−	0.999999i	$-0.500479\pi$
$863$	−0.0884535			−0.00301099			−0.00150550	+	0.999999i	$0.500479\pi$
$864$		0			0
$865$	−3.55008			−0.120706
$866$		0			0
$867$	3.69722	+	8.92588i	0.125564	+	0.303139i
$868$		0			0
$869$	−63.5854	−	26.3379i	−2.15699	−	0.893453i
$870$		0			0
$871$	−12.0341	−	12.0341i	−0.407761	−	0.407761i
$872$		0			0
$873$	−13.4303	+	13.4303i	−0.454547	+	0.454547i
$874$		0			0
$875$	−4.38018	+	10.5747i	−0.148077	+	0.357490i
$876$		0			0
$877$	−10.2487	+	4.24514i	−0.346073	+	0.143348i	−0.548948	−	0.835857i	$-0.684971\pi$
$877$	−10.2487	+	4.24514i	−0.346073	+	0.143348i	0.202875	+	0.979205i	$0.434971\pi$
$878$		0			0
$879$			18.6702i			0.629729i
$880$		0			0
$881$		−	23.9859i		−	0.808105i	−0.914736	−	0.404052i	$-0.867601\pi$
$881$		−	23.9859i		−	0.808105i	0.914736	−	0.404052i	$-0.132399\pi$
$882$		0			0
$883$	−18.7075	+	7.74892i	−0.629559	+	0.260772i	−0.674566	−	0.738215i	$-0.735669\pi$
$883$	−18.7075	+	7.74892i	−0.629559	+	0.260772i	0.0450067	+	0.998987i	$0.485669\pi$
$884$		0			0
$885$	9.33333	−	22.5326i	0.313736	−	0.757426i
$886$		0			0
$887$	36.4494	−	36.4494i	1.22385	−	1.22385i	0.257600	−	0.966252i	$-0.417068\pi$
$887$	36.4494	−	36.4494i	1.22385	−	1.22385i	0.966252	−	0.257600i	$-0.0829315\pi$
$888$		0			0
$889$	8.68550	+	8.68550i	0.291302	+	0.291302i
$890$		0			0
$891$	−32.2804	−	13.3710i	−1.08143	−	0.447944i
$892$		0			0
$893$	−0.291859	−	0.704611i	−0.00976670	−	0.0235789i
$894$		0			0
$895$	9.07646			0.303392
$896$		0			0
$897$	−21.4951			−0.717700
$898$		0			0
$899$	2.78473	+	6.72293i	0.0928759	+	0.224222i
$900$		0			0
$901$	−16.6202	−	6.88431i	−0.553699	−	0.229350i
$902$		0			0
$903$	4.52728	+	4.52728i	0.150658	+	0.150658i
$904$		0			0
$905$	2.65685	−	2.65685i	0.0883168	−	0.0883168i
$906$		0			0
$907$	15.8541	−	38.2753i	0.526428	−	1.27091i	−0.407421	−	0.913241i	$-0.633572\pi$
$907$	15.8541	−	38.2753i	0.526428	−	1.27091i	0.933848	−	0.357669i	$-0.116428\pi$
$908$		0			0
$909$	23.0565	−	9.55032i	0.764737	−	0.316764i
$910$		0			0
$911$			12.5214i			0.414851i	0.978251	+	0.207426i	$0.0665085\pi$
$911$			12.5214i			0.414851i	−0.978251	+	0.207426i	$0.933492\pi$
$912$		0			0
$913$			50.4497i			1.66964i
$914$		0			0
$915$	−62.4864	+	25.8827i	−2.06574	+	0.855657i
$916$		0			0
$917$	−2.54079	+	6.13401i	−0.0839043	+	0.202563i
$918$		0			0
$919$	−1.19513	+	1.19513i	−0.0394238	+	0.0394238i	−0.726544	−	0.687120i	$-0.758875\pi$
$919$	−1.19513	+	1.19513i	−0.0394238	+	0.0394238i	0.687120	+	0.726544i	$0.258875\pi$
$920$		0			0
$921$	−14.3330	−	14.3330i	−0.472287	−	0.472287i
$922$		0			0
$923$	−58.2715	−	24.1369i	−1.91803	−	0.794475i
$924$		0			0
$925$	−0.810217	−	1.95604i	−0.0266398	−	0.0643141i
$926$		0			0
$927$	−20.6194			−0.677231
$928$		0			0
$929$	45.1410			1.48103			0.740514	−	0.672041i	$-0.234582\pi$
$929$	45.1410			1.48103			0.740514	+	0.672041i	$0.234582\pi$
$930$		0			0
$931$	−1.19127	−	2.87599i	−0.0390424	−	0.0942566i
$932$		0			0
$933$	48.5162	+	20.0961i	1.58835	+	0.657915i
$934$		0			0
$935$	18.8910	+	18.8910i	0.617801	+	0.617801i
$936$		0			0
$937$	−2.58002	+	2.58002i	−0.0842857	+	0.0842857i	−0.747993	−	0.663707i	$-0.768982\pi$
$937$	−2.58002	+	2.58002i	−0.0842857	+	0.0842857i	0.663707	+	0.747993i	$0.268982\pi$
$938$		0			0
$939$	24.4774	−	59.0937i	0.798790	−	1.92845i
$940$		0			0
$941$	5.42523	−	2.24720i	0.176857	−	0.0732568i	−0.292498	−	0.956266i	$-0.594486\pi$
$941$	5.42523	−	2.24720i	0.176857	−	0.0732568i	0.469355	+	0.883009i	$0.344486\pi$
$942$		0			0
$943$			4.45807i			0.145175i
$944$		0			0
$945$			0.360189i			0.0117170i
$946$		0			0
$947$	42.4032	−	17.5640i	1.37792	−	0.570753i	0.433996	−	0.900915i	$-0.357103\pi$
$947$	42.4032	−	17.5640i	1.37792	−	0.570753i	0.943924	+	0.330162i	$0.107103\pi$
$948$		0			0
$949$	−18.8808	+	45.5822i	−0.612896	+	1.47966i
$950$		0			0
$951$	−17.9788	+	17.9788i	−0.583003	+	0.583003i
$952$		0			0
$953$	−14.8079	−	14.8079i	−0.479673	−	0.479673i	0.425354	−	0.905027i	$-0.360150\pi$
$953$	−14.8079	−	14.8079i	−0.479673	−	0.479673i	−0.905027	+	0.425354i	$0.860150\pi$
$954$		0			0
$955$	33.1216	+	13.7194i	1.07179	+	0.443949i
$956$		0			0
$957$	−23.4357	−	56.5787i	−0.757568	−	1.82893i
$958$		0			0
$959$	−6.49290			−0.209667
$960$		0			0
$961$	−29.6274			−0.955723
$962$		0			0
$963$	−3.29292	−	7.94981i	−0.106113	−	0.256179i
$964$		0			0
$965$	30.8066	+	12.7605i	0.991698	+	0.410775i
$966$		0			0
$967$	−24.8604	−	24.8604i	−0.799455	−	0.799455i	0.183554	−	0.983010i	$-0.441240\pi$
$967$	−24.8604	−	24.8604i	−0.799455	−	0.799455i	−0.983010	+	0.183554i	$0.941240\pi$
$968$		0			0
$969$	−3.21137	+	3.21137i	−0.103164	+	0.103164i
$970$		0			0
$971$	9.66725	−	23.3388i	0.310237	−	0.748978i	−0.689459	−	0.724324i	$-0.742152\pi$
$971$	9.66725	−	23.3388i	0.310237	−	0.748978i	0.999696	−	0.0246533i	$-0.00784817\pi$
$972$		0			0
$973$	11.0836	−	4.59099i	0.355325	−	0.147180i
$974$		0			0
$975$			18.0559i			0.578251i
$976$		0			0
$977$		−	54.7057i		−	1.75019i	−0.483952	−	0.875094i	$-0.660799\pi$
$977$		−	54.7057i		−	1.75019i	0.483952	−	0.875094i	$-0.339201\pi$
$978$		0			0
$979$	−28.4056	+	11.7660i	−0.907846	+	0.376042i
$980$		0			0
$981$	−10.6736	+	25.7684i	−0.340782	+	0.822720i
$982$		0			0
$983$	7.85315	−	7.85315i	0.250477	−	0.250477i	−0.570689	−	0.821166i	$-0.693324\pi$
$983$	7.85315	−	7.85315i	0.250477	−	0.250477i	0.821166	+	0.570689i	$0.193324\pi$
$984$		0			0
$985$	0.295389	+	0.295389i	0.00941188	+	0.00941188i
$986$		0			0
$987$	3.21137	+	1.33019i	0.102219	+	0.0423405i
$988$		0			0
$989$	−1.99371	−	4.81324i	−0.0633963	−	0.153052i
$990$		0			0
$991$	−52.4878			−1.66733			−0.833665	−	0.552270i	$-0.813762\pi$
$991$	−52.4878			−1.66733			−0.833665	+	0.552270i	$0.813762\pi$
$992$		0			0
$993$	−20.2217			−0.641716
$994$		0			0
$995$	−11.8992	−	28.7272i	−0.377230	−	0.910715i
$996$		0			0
$997$	31.0060	+	12.8431i	0.981970	+	0.406745i	0.815155	−	0.579243i	$-0.196652\pi$
$997$	31.0060	+	12.8431i	0.981970	+	0.406745i	0.166815	+	0.985988i	$0.446652\pi$
$998$		0			0
$999$	−0.195654	−	0.195654i	−0.00619021	−	0.00619021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.g.e.449.2		8
4.3	odd	2		512.2.g.g.449.1		8
8.3	odd	2		512.2.g.f.449.2		8
8.5	even	2		512.2.g.h.449.1		8
16.3	odd	4		128.2.g.b.49.2		8
16.5	even	4		256.2.g.d.97.2		8
16.11	odd	4		256.2.g.c.97.1		8
16.13	even	4		32.2.g.b.21.2	✓	8
32.3	odd	8		512.2.g.f.65.2		8
32.5	even	8		32.2.g.b.29.2	yes	8
32.11	odd	8		256.2.g.c.161.1		8
32.13	even	8	inner	512.2.g.e.65.2		8
32.19	odd	8		512.2.g.g.65.1		8
32.21	even	8		256.2.g.d.161.2		8
32.27	odd	8		128.2.g.b.81.2		8
32.29	even	8		512.2.g.h.65.1		8
48.29	odd	4		288.2.v.b.181.1		8
48.35	even	4		1152.2.v.b.433.1		8
64.13	even	16		4096.2.a.k.1.7		8
64.19	odd	16		4096.2.a.q.1.7		8
64.45	even	16		4096.2.a.k.1.2		8
64.51	odd	16		4096.2.a.q.1.2		8
80.13	odd	4		800.2.ba.d.149.1		8
80.29	even	4		800.2.y.b.501.1		8
80.77	odd	4		800.2.ba.c.149.2		8
96.5	odd	8		288.2.v.b.253.1		8
96.59	even	8		1152.2.v.b.721.1		8
160.37	odd	8		800.2.ba.d.349.1		8
160.69	even	8		800.2.y.b.701.1		8
160.133	odd	8		800.2.ba.c.349.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.21.2	✓	8	16.13	even	4
32.2.g.b.29.2	yes	8	32.5	even	8
128.2.g.b.49.2		8	16.3	odd	4
128.2.g.b.81.2		8	32.27	odd	8
256.2.g.c.97.1		8	16.11	odd	4
256.2.g.c.161.1		8	32.11	odd	8
256.2.g.d.97.2		8	16.5	even	4
256.2.g.d.161.2		8	32.21	even	8
288.2.v.b.181.1		8	48.29	odd	4
288.2.v.b.253.1		8	96.5	odd	8
512.2.g.e.65.2		8	32.13	even	8	inner
512.2.g.e.449.2		8	1.1	even	1	trivial
512.2.g.f.65.2		8	32.3	odd	8
512.2.g.f.449.2		8	8.3	odd	2
512.2.g.g.65.1		8	32.19	odd	8
512.2.g.g.449.1		8	4.3	odd	2
512.2.g.h.65.1		8	32.29	even	8
512.2.g.h.449.1		8	8.5	even	2
800.2.y.b.501.1		8	80.29	even	4
800.2.y.b.701.1		8	160.69	even	8
800.2.ba.c.149.2		8	80.77	odd	4
800.2.ba.c.349.2		8	160.133	odd	8
800.2.ba.d.149.1		8	80.13	odd	4
800.2.ba.d.349.1		8	160.37	odd	8
1152.2.v.b.433.1		8	48.35	even	4
1152.2.v.b.721.1		8	96.59	even	8
4096.2.a.k.1.2		8	64.45	even	16
4096.2.a.k.1.7		8	64.13	even	16
4096.2.a.q.1.2		8	64.51	odd	16
4096.2.a.q.1.7		8	64.19	odd	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.943920 + 2.27882i) q^{3} +(-1.70711 - 0.707107i) q^{5} +(0.665096 + 0.665096i) q^{7} +(-2.18073 + 2.18073i) q^{9} +O(q^{10})\)	\(q+(0.943920 + 2.27882i) q^{3} +(-1.70711 - 0.707107i) q^{5} +(0.665096 + 0.665096i) q^{7} +(-2.18073 + 2.18073i) q^{9} +(-1.52971 + 3.69304i) q^{11} +(-4.26475 + 1.76652i) q^{13} -4.55765i q^{15} +3.61706i q^{17} +(0.470294 - 0.194802i) q^{19} +(-0.887839 + 2.14343i) q^{21} +(1.33490 - 1.33490i) q^{23} +(-1.12132 - 1.12132i) q^{25} +(-0.191470 - 0.0793096i) q^{27} +(2.37691 + 5.73838i) q^{29} +1.17157 q^{31} -9.85970 q^{33} +(-0.665096 - 1.60568i) q^{35} +(1.23348 + 0.510925i) q^{37} +(-8.05117 - 8.05117i) q^{39} +(-1.66981 + 1.66981i) q^{41} +(1.05608 - 2.54960i) q^{43} +(5.26475 - 2.18073i) q^{45} -1.49824i q^{47} -6.11529i q^{49} +(-8.24264 + 3.41421i) q^{51} +(-1.90329 + 4.59495i) q^{53} +(5.22274 - 5.22274i) q^{55} +(0.887839 + 0.887839i) q^{57} +(4.94392 + 2.04784i) q^{59} +(-5.67897 - 13.7102i) q^{61} -2.90079 q^{63} +8.52951 q^{65} +(1.41088 + 3.40617i) q^{67} +(4.30205 + 1.78197i) q^{69} +(9.66157 + 9.66157i) q^{71} +(7.55765 - 7.55765i) q^{73} +(1.49685 - 3.61373i) q^{75} +(-3.47363 + 1.43882i) q^{77} +17.2176i q^{79} +8.74088i q^{81} +(11.6602 - 4.82981i) q^{83} +(2.55765 - 6.17471i) q^{85} +(-10.8331 + 10.8331i) q^{87} +(5.43882 + 5.43882i) q^{89} +(-4.01138 - 1.66157i) q^{91} +(1.10587 + 2.66981i) q^{93} -0.940588 q^{95} +6.15862 q^{97} +(-4.71765 - 11.3894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 8 q^{5} + 8 q^{7}+O(q^{10}) \) 8 * q - 4 * q^3 - 8 * q^5 + 8 * q^7	\( 8 q - 4 q^{3} - 8 q^{5} + 8 q^{7} - 12 q^{11} + 4 q^{19} + 16 q^{21} + 8 q^{23} + 8 q^{25} - 16 q^{27} + 8 q^{29} + 32 q^{31} - 16 q^{33} - 8 q^{35} + 16 q^{37} - 16 q^{39} - 8 q^{41} + 20 q^{43} + 8 q^{45} - 32 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 28 q^{59} - 40 q^{63} + 12 q^{67} + 24 q^{71} + 32 q^{73} - 20 q^{75} - 16 q^{77} + 36 q^{83} - 8 q^{85} - 56 q^{87} + 16 q^{89} - 32 q^{93} - 8 q^{95} + 32 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 8 * q^5 + 8 * q^7 - 12 * q^11 + 4 * q^19 + 16 * q^21 + 8 * q^23 + 8 * q^25 - 16 * q^27 + 8 * q^29 + 32 * q^31 - 16 * q^33 - 8 * q^35 + 16 * q^37 - 16 * q^39 - 8 * q^41 + 20 * q^43 + 8 * q^45 - 32 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 28 * q^59 - 40 * q^63 + 12 * q^67 + 24 * q^71 + 32 * q^73 - 20 * q^75 - 16 * q^77 + 36 * q^83 - 8 * q^85 - 56 * q^87 + 16 * q^89 - 32 * q^93 - 8 * q^95 + 32 * q^97 + 4 * q^99

Introduction

L-functions

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