LMFDB - Embedded newform 256.2.g.c.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(33,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, 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("256.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.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:	$2.04417029174$
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			97.1
Root			$0.500000 + 1.44392i$ of defining polynomial
Character	$\chi$	$=$	256.97
Dual form			256.2.g.c.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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
$3$	−2.27882	+	0.943920i	−1.31568	+	0.544972i	−0.926536	−	0.376205i	$-0.877229\pi$
$3$	−2.27882	+	0.943920i	−1.31568	+	0.544972i	−0.389143	+	0.921177i	$0.627229\pi$
$4$		0			0
$5$	0.707107	−	1.70711i	0.316228	−	0.763441i	−0.683220	−	0.730213i	$-0.739421\pi$
$5$	0.707107	−	1.70711i	0.316228	−	0.763441i	0.999448	−	0.0332288i	$-0.0105790\pi$
$6$		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
$11$	3.69304	+	1.52971i	1.11349	+	0.461224i	0.862139	−	0.506672i	$-0.169124\pi$
$11$	3.69304	+	1.52971i	1.11349	+	0.461224i	0.251353	+	0.967895i	$0.419124\pi$
$12$		0			0
$13$	1.76652	+	4.26475i	0.489944	+	1.18283i	0.954748	+	0.297416i	$0.0961249\pi$
$13$	1.76652	+	4.26475i	0.489944	+	1.18283i	−0.464804	+	0.885414i	$0.653875\pi$
$14$		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
$19$	0.194802	+	0.470294i	0.0446907	+	0.107893i	0.944649	−	0.328084i	$-0.106403\pi$
$19$	0.194802	+	0.470294i	0.0446907	+	0.107893i	−0.899958	+	0.435977i	$0.856403\pi$
$20$		0			0
$21$	−2.14343	−	0.887839i	−0.467736	−	0.193742i
$22$		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
$27$	−0.0793096	+	0.191470i	−0.0152631	+	0.0368485i
$28$		0			0
$29$	5.73838	−	2.37691i	1.06559	−	0.441382i	0.220158	−	0.975464i	$-0.429343\pi$
$29$	5.73838	−	2.37691i	1.06559	−	0.441382i	0.845433	+	0.534082i	$0.179343\pi$
$30$		0			0
$31$	−1.17157			−0.210421			−0.105210	−	0.994450i	$-0.533552\pi$
$31$	−1.17157			−0.210421			−0.105210	+	0.994450i	$0.533552\pi$
$32$		0			0
$33$	−9.85970			−1.71635
$34$		0			0
$35$	1.60568	−	0.665096i	0.271410	−	0.112422i
$36$		0			0
$37$	−0.510925	+	1.23348i	−0.0839955	+	0.202783i	−0.960297	−	0.278980i	$-0.910004\pi$
$37$	−0.510925	+	1.23348i	−0.0839955	+	0.202783i	0.876301	+	0.481763i	$0.160004\pi$
$38$		0			0
$39$	−8.05117	−	8.05117i	−1.28922	−	1.28922i
$40$		0			0
$41$	1.66981	−	1.66981i	0.260780	−	0.260780i	−0.564591	−	0.825371i	$-0.690966\pi$
$41$	1.66981	−	1.66981i	0.260780	−	0.260780i	0.825371	+	0.564591i	$0.190966\pi$
$42$		0			0
$43$	−2.54960	−	1.05608i	−0.388811	−	0.161051i	0.179710	−	0.983720i	$-0.442484\pi$
$43$	−2.54960	−	1.05608i	−0.388811	−	0.161051i	−0.568521	+	0.822669i	$0.692484\pi$
$44$		0			0
$45$	−2.18073	−	5.26475i	−0.325084	−	0.784823i
$46$		0			0
$47$			1.49824i			0.218540i	0.994012	+	0.109270i	$0.0348513\pi$
$47$			1.49824i			0.218540i	−0.994012	+	0.109270i	$0.965149\pi$
$48$		0			0
$49$		−	6.11529i		−	0.873614i
$50$		0			0
$51$	−3.41421	−	8.24264i	−0.478086	−	1.15420i
$52$		0			0
$53$	−4.59495	−	1.90329i	−0.631164	−	0.261437i	0.0440833	−	0.999028i	$-0.485963\pi$
$53$	−4.59495	−	1.90329i	−0.631164	−	0.261437i	−0.675248	+	0.737591i	$0.735963\pi$
$54$		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
$59$	2.04784	−	4.94392i	0.266606	−	0.643644i	−0.732713	−	0.680537i	$-0.761746\pi$
$59$	2.04784	−	4.94392i	0.266606	−	0.643644i	0.999319	+	0.0368939i	$0.0117464\pi$
$60$		0			0
$61$	−13.7102	+	5.67897i	−1.75542	+	0.727117i	−0.758244	+	0.651971i	$0.773942\pi$
$61$	−13.7102	+	5.67897i	−1.75542	+	0.727117i	−0.997173	+	0.0751463i	$0.976058\pi$
$62$		0			0
$63$	2.90079			0.365466
$64$		0			0
$65$	8.52951			1.05796
$66$		0			0
$67$	−3.40617	+	1.41088i	−0.416130	+	0.172367i	−0.580918	−	0.813962i	$-0.697306\pi$
$67$	−3.40617	+	1.41088i	−0.416130	+	0.172367i	0.164788	+	0.986329i	$0.447306\pi$
$68$		0			0
$69$	−1.78197	+	4.30205i	−0.214524	+	0.517906i
$70$		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	−0.993994	−	0.109438i	$-0.965095\pi$
$73$	−7.55765	+	7.55765i	−0.884556	+	0.884556i	0.109438	+	0.993994i	$0.465095\pi$
$74$		0			0
$75$	−3.61373	−	1.49685i	−0.417277	−	0.172842i
$76$		0			0
$77$	1.43882	+	3.47363i	0.163969	+	0.395856i
$78$		0			0
$79$		−	17.2176i		−	1.93714i	−0.248750	−	0.968568i	$-0.580020\pi$
$79$		−	17.2176i		−	1.93714i	0.248750	−	0.968568i	$-0.419980\pi$
$80$		0			0
$81$			8.74088i			0.971208i
$82$		0			0
$83$	4.82981	+	11.6602i	0.530140	+	1.27987i	0.931430	+	0.363921i	$0.118562\pi$
$83$	4.82981	+	11.6602i	0.530140	+	1.27987i	−0.401290	+	0.915951i	$0.631438\pi$
$84$		0			0
$85$	6.17471	+	2.55765i	0.669741	+	0.277416i
$86$		0			0
$87$	−10.8331	+	10.8331i	−1.16143	+	1.16143i
$88$		0			0
$89$	−5.43882	−	5.43882i	−0.576514	−	0.576514i	0.357427	−	0.933941i	$-0.383654\pi$
$89$	−5.43882	−	5.43882i	−0.576514	−	0.576514i	−0.933941	+	0.357427i	$0.883654\pi$
$90$		0			0
$91$	−1.66157	+	4.01138i	−0.174179	+	0.420506i
$92$		0			0
$93$	2.66981	−	1.10587i	0.276846	−	0.114673i
$94$		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
$99$	11.3894	−	4.71765i	1.14468	−	0.474141i
$100$		0			0
$101$	3.09671	−	7.47612i	0.308134	−	0.743902i	−0.691631	−	0.722251i	$-0.743108\pi$
$101$	3.09671	−	7.47612i	0.308134	−	0.743902i	0.999766	−	0.0216512i	$-0.00689233\pi$
$102$		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
$107$	2.57774	+	1.06774i	0.249200	+	0.103222i	0.503787	−	0.863828i	$-0.331940\pi$
$107$	2.57774	+	1.06774i	0.249200	+	0.103222i	−0.254587	+	0.967050i	$0.581940\pi$
$108$		0			0
$109$	−3.46094	−	8.35544i	−0.331498	−	0.800306i	−0.998474	−	0.0552270i	$-0.982412\pi$
$109$	−3.46094	−	8.35544i	−0.331498	−	0.800306i	0.666976	−	0.745079i	$-0.267588\pi$
$110$		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
$115$	−1.33490	−	3.22274i	−0.124480	−	0.300522i
$116$		0			0
$117$	13.1526	+	5.44798i	1.21596	+	0.503666i
$118$		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
$123$	−2.22903	+	5.38136i	−0.200985	+	0.485221i
$124$		0			0
$125$	11.2426	−	4.65685i	1.00557	−	0.416522i
$126$		0			0
$127$	−13.0590			−1.15880			−0.579400	−	0.815043i	$-0.696713\pi$
$127$	−13.0590			−1.15880			−0.579400	+	0.815043i	$0.696713\pi$
$128$		0			0
$129$	6.80695			0.599319
$130$		0			0
$131$	−6.52146	+	2.70128i	−0.569783	+	0.236012i	−0.648926	−	0.760851i	$-0.724782\pi$
$131$	−6.52146	+	2.70128i	−0.569783	+	0.236012i	0.0791431	+	0.996863i	$0.474782\pi$
$132$		0			0
$133$	−0.183228	+	0.442353i	−0.0158879	+	0.0383568i
$134$		0			0
$135$	0.270780	+	0.270780i	0.0233050	+	0.0233050i
$136$		0			0
$137$	4.88118	−	4.88118i	0.417027	−	0.417027i	−0.467151	−	0.884178i	$-0.654719\pi$
$137$	4.88118	−	4.88118i	0.417027	−	0.417027i	0.884178	+	0.467151i	$0.154719\pi$
$138$		0			0
$139$	−11.7837	−	4.88098i	−0.999482	−	0.413999i	−0.177875	−	0.984053i	$-0.556922\pi$
$139$	−11.7837	−	4.88098i	−0.999482	−	0.413999i	−0.821607	+	0.570054i	$0.806922\pi$
$140$		0			0
$141$	−1.41421	−	3.41421i	−0.119098	−	0.287529i
$142$		0			0
$143$			18.4522i			1.54305i
$144$		0			0
$145$		−	11.4768i		−	0.953093i
$146$		0			0
$147$	5.77235	+	13.9357i	0.476095	+	1.14940i
$148$		0			0
$149$	5.73838	+	2.37691i	0.470106	+	0.194724i	0.605144	−	0.796116i	$-0.293116\pi$
$149$	5.73838	+	2.37691i	0.470106	+	0.194724i	−0.135038	+	0.990840i	$0.543116\pi$
$150$		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
$155$	−0.828427	+	2.00000i	−0.0665409	+	0.160644i
$156$		0			0
$157$	−1.22496	+	0.507395i	−0.0977624	+	0.0404945i	−0.431029	−	0.902338i	$-0.641849\pi$
$157$	−1.22496	+	0.507395i	−0.0977624	+	0.0404945i	0.333266	+	0.942833i	$0.391849\pi$
$158$		0			0
$159$	12.2676			0.972886
$160$		0			0
$161$	1.77568			0.139943
$162$		0			0
$163$	21.3218	−	8.83176i	1.67005	−	0.691757i	0.671272	−	0.741211i	$-0.265748\pi$
$163$	21.3218	−	8.83176i	1.67005	−	0.691757i	0.998776	+	0.0494542i	$0.0157482\pi$
$164$		0			0
$165$	−6.97186	+	16.8316i	−0.542759	+	1.31034i
$166$		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
$171$	1.45040	+	0.600774i	0.110915	+	0.0459423i
$172$		0			0
$173$	−0.735246	−	1.77504i	−0.0558997	−	0.134954i	0.893462	−	0.449138i	$-0.148269\pi$
$173$	−0.735246	−	1.77504i	−0.0558997	−	0.134954i	−0.949362	+	0.314184i	$0.898269\pi$
$174$		0			0
$175$			1.49157i			0.112752i
$176$		0			0
$177$			13.1993i			0.992121i
$178$		0			0
$179$	−1.87980	−	4.53823i	−0.140503	−	0.339203i	0.837928	−	0.545782i	$-0.183767\pi$
$179$	−1.87980	−	4.53823i	−0.140503	−	0.339203i	−0.978430	+	0.206578i	$0.933767\pi$
$180$		0			0
$181$	−1.87868	−	0.778175i	−0.139641	−	0.0578413i	0.311768	−	0.950158i	$-0.399079\pi$
$181$	−1.87868	−	0.778175i	−0.139641	−	0.0578413i	−0.451410	+	0.892317i	$0.649079\pi$
$182$		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
$187$	−5.53304	+	13.3579i	−0.404616	+	0.976829i
$188$		0			0
$189$	−0.180095	+	0.0745976i	−0.0131000	+	0.00542618i
$190$		0			0
$191$	19.4022			1.40389			0.701946	−	0.712231i	$-0.252315\pi$
$191$	19.4022			1.40389			0.701946	+	0.712231i	$0.252315\pi$
$192$		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
$195$	−19.4372	+	8.05117i	−1.39193	+	0.576556i
$196$		0			0
$197$	0.0865175	−	0.208872i	0.00616412	−	0.0148815i	−0.920768	−	0.390112i	$-0.872436\pi$
$197$	0.0865175	−	0.208872i	0.00616412	−	0.0148815i	0.926932	+	0.375230i	$0.122436\pi$
$198$		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
$203$	5.39745	+	2.23570i	0.378827	+	0.156915i
$204$		0			0
$205$	−1.66981	−	4.03127i	−0.116624	−	0.281556i
$206$		0			0
$207$		−	5.82214i		−	0.404667i
$208$		0			0
$209$			2.03480i			0.140750i
$210$		0			0
$211$	−3.73060	−	9.00647i	−0.256825	−	0.620031i	0.741900	−	0.670511i	$-0.233925\pi$
$211$	−3.73060	−	9.00647i	−0.256825	−	0.620031i	−0.998725	+	0.0504799i	$0.983925\pi$
$212$		0			0
$213$	−31.1367	−	12.8973i	−2.13345	−	0.883706i
$214$		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
$219$	10.0887	−	24.3564i	0.681733	−	1.64585i
$220$		0			0
$221$	−15.4259	+	6.38960i	−1.03766	+	0.429811i
$222$		0			0
$223$	−22.6174			−1.51458			−0.757288	−	0.653081i	$-0.773476\pi$
$223$	−22.6174			−1.51458			−0.757288	+	0.653081i	$0.773476\pi$
$224$		0			0
$225$	4.89060			0.326040
$226$		0			0
$227$	−9.51294	+	3.94039i	−0.631396	+	0.261533i	−0.675346	−	0.737501i	$-0.736006\pi$
$227$	−9.51294	+	3.94039i	−0.631396	+	0.261533i	0.0439500	+	0.999034i	$0.486006\pi$
$228$		0			0
$229$	6.53200	−	15.7697i	0.431647	−	1.04209i	−0.547109	−	0.837061i	$-0.684272\pi$
$229$	6.53200	−	15.7697i	0.431647	−	1.04209i	0.978756	−	0.205027i	$-0.0657282\pi$
$230$		0			0
$231$	−6.55765	−	6.55765i	−0.431462	−	0.431462i
$232$		0			0
$233$	10.4486	−	10.4486i	0.684512	−	0.684512i	−0.276502	−	0.961013i	$-0.589175\pi$
$233$	10.4486	−	10.4486i	0.684512	−	0.684512i	0.961013	+	0.276502i	$0.0891751\pi$
$234$		0			0
$235$	2.55765	+	1.05941i	0.166843	+	0.0691084i
$236$		0			0
$237$	16.2521	+	39.2360i	1.05569	+	2.54865i
$238$		0			0
$239$		−	11.6733i		−	0.755085i	−0.925992	−	0.377543i	$-0.876769\pi$
$239$		−	11.6733i		−	0.755085i	0.925992	−	0.377543i	$-0.123231\pi$
$240$		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
$243$	−8.48861	−	20.4933i	−0.544545	−	1.31465i
$244$		0			0
$245$	−10.4395	−	4.32417i	−0.666953	−	0.276261i
$246$		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
$251$	5.38745	−	13.0065i	0.340053	−	0.820961i	−0.657656	−	0.753318i	$-0.728452\pi$
$251$	5.38745	−	13.0065i	0.340053	−	0.820961i	0.997710	−	0.0676429i	$-0.0215479\pi$
$252$		0			0
$253$	6.97186	−	2.88784i	0.438317	−	0.181557i
$254$		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
$259$	−1.16020	+	0.480569i	−0.0720911	+	0.0298611i
$260$		0			0
$261$	7.33046	−	17.6973i	0.453744	−	1.09543i
$262$		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
$267$	17.5279	+	7.26031i	1.07269	+	0.444324i
$268$		0			0
$269$	−5.05209	−	12.1968i	−0.308031	−	0.743653i	−0.999769	−	0.0215042i	$-0.993154\pi$
$269$	−5.05209	−	12.1968i	−0.308031	−	0.743653i	0.691737	−	0.722149i	$-0.256846\pi$
$270$		0			0
$271$			4.41512i			0.268199i	0.990968	+	0.134100i	$0.0428142\pi$
$271$			4.41512i			0.268199i	−0.990968	+	0.134100i	$0.957186\pi$
$272$		0			0
$273$		−	10.7096i		−	0.648175i
$274$		0			0
$275$	2.42579	+	5.85637i	0.146280	+	0.353152i
$276$		0			0
$277$	23.0454	+	9.54573i	1.38467	+	0.573547i	0.945725	−	0.324969i	$-0.105354\pi$
$277$	23.0454	+	9.54573i	1.38467	+	0.573547i	0.438941	+	0.898516i	$0.355354\pi$
$278$		0			0
$279$	−2.55489	+	2.55489i	−0.152957	+	0.152957i
$280$		0			0
$281$	−5.83509	−	5.83509i	−0.348092	−	0.348092i	0.511306	−	0.859399i	$-0.329162\pi$
$281$	−5.83509	−	5.83509i	−0.348092	−	0.348092i	−0.859399	+	0.511306i	$0.829162\pi$
$282$		0			0
$283$	1.31992	−	3.18656i	0.0784609	−	0.189421i	−0.879782	−	0.475378i	$-0.842311\pi$
$283$	1.31992	−	3.18656i	0.0784609	−	0.189421i	0.958243	+	0.285957i	$0.0923113\pi$
$284$		0			0
$285$	−2.14343	+	0.887839i	−0.126966	+	0.0525911i
$286$		0			0
$287$	2.22117			0.131111
$288$		0			0
$289$	3.91688			0.230405
$290$		0			0
$291$	−14.0344	+	5.81324i	−0.822712	+	0.340778i
$292$		0			0
$293$	−2.89663	+	6.99307i	−0.169223	+	0.408540i	−0.985626	−	0.168943i	$-0.945965\pi$
$293$	−2.89663	+	6.99307i	−0.169223	+	0.408540i	0.816403	+	0.577482i	$0.195965\pi$
$294$		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
$299$	8.05117	+	3.33490i	0.465611	+	0.192862i
$300$		0			0
$301$	−0.993336	−	2.39813i	−0.0572550	−	0.138226i
$302$		0			0
$303$			19.9598i			1.14666i
$304$		0			0
$305$			27.4205i			1.57009i
$306$		0			0
$307$	−3.14481	−	7.59225i	−0.179484	−	0.433313i	0.808375	−	0.588668i	$-0.200348\pi$
$307$	−3.14481	−	7.59225i	−0.179484	−	0.433313i	−0.987859	+	0.155356i	$0.950348\pi$
$308$		0			0
$309$	−15.2360	−	6.31095i	−0.866744	−	0.359017i
$310$		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	$0.0118208\pi$
$313$	18.3365	+	18.3365i	1.03644	+	1.03644i	0.0371274	+	0.999311i	$0.488179\pi$
$314$		0			0
$315$	2.05117	−	4.95196i	0.115570	−	0.279012i
$316$		0			0
$317$	9.52348	−	3.94476i	0.534892	−	0.221560i	−0.0988523	−	0.995102i	$-0.531517\pi$
$317$	9.52348	−	3.94476i	0.534892	−	0.221560i	0.633744	+	0.773543i	$0.281517\pi$
$318$		0			0
$319$	24.8280			1.39010
$320$		0			0
$321$	−6.88208			−0.384120
$322$		0			0
$323$	−1.70108	+	0.704611i	−0.0946507	+	0.0392056i
$324$		0			0
$325$	−2.80132	+	6.76299i	−0.155389	+	0.375143i
$326$		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
$331$	7.57421	+	3.13734i	0.416316	+	0.172444i	0.581002	−	0.813902i	$-0.302661\pi$
$331$	7.57421	+	3.13734i	0.416316	+	0.172444i	−0.164685	+	0.986346i	$0.552661\pi$
$332$		0			0
$333$	1.57570	+	3.80408i	0.0863480	+	0.208462i
$334$		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
$339$	11.1153	+	26.8347i	0.603700	+	1.45746i
$340$		0			0
$341$	−4.32666	−	1.79216i	−0.234302	−	0.0970510i
$342$		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
$347$	−11.6582	+	28.1455i	−0.625847	+	1.51093i	0.218892	+	0.975749i	$0.429756\pi$
$347$	−11.6582	+	28.1455i	−0.625847	+	1.51093i	−0.844739	+	0.535179i	$0.820244\pi$
$348$		0			0
$349$	−9.99044	+	4.13818i	−0.534776	+	0.221512i	−0.633694	−	0.773584i	$-0.718462\pi$
$349$	−9.99044	+	4.13818i	−0.534776	+	0.221512i	0.0989174	+	0.995096i	$0.468462\pi$
$350$		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
$355$	23.3251	−	9.66157i	1.23797	−	0.512783i
$356$		0			0
$357$	3.21137	−	7.75293i	0.169964	−	0.410328i
$358$		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
$363$	−11.3452	−	4.69933i	−0.595467	−	0.246651i
$364$		0			0
$365$	7.55765	+	18.2458i	0.395585	+	0.955027i
$366$		0			0
$367$			16.4759i			0.860033i	0.902821	+	0.430016i	$0.141492\pi$
$367$			16.4759i			0.860033i	−0.902821	+	0.430016i	$0.858508\pi$
$368$		0			0
$369$		−	7.28281i		−	0.379128i
$370$		0			0
$371$	−1.79021	−	4.32195i	−0.0929431	−	0.224384i
$372$		0			0
$373$	12.6790	+	5.25180i	0.656492	+	0.271928i	0.685962	−	0.727638i	$-0.259382\pi$
$373$	12.6790	+	5.25180i	0.656492	+	0.271928i	−0.0294695	+	0.999566i	$0.509382\pi$
$374$		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
$379$	−5.06746	+	12.2339i	−0.260298	+	0.628414i	−0.998957	−	0.0456649i	$-0.985459\pi$
$379$	−5.06746	+	12.2339i	−0.260298	+	0.628414i	0.738659	+	0.674079i	$0.235459\pi$
$380$		0			0
$381$	29.7592	−	12.3267i	1.52461	−	0.631514i
$382$		0			0
$383$	−14.5667			−0.744322			−0.372161	−	0.928168i	$-0.621383\pi$
$383$	−14.5667			−0.744322			−0.372161	+	0.928168i	$0.621383\pi$
$384$		0			0
$385$	6.94725			0.354065
$386$		0			0
$387$	−7.86303	+	3.25697i	−0.399700	+	0.165561i
$388$		0			0
$389$	−14.2795	+	34.4739i	−0.724002	+	1.74789i	−0.0623850	+	0.998052i	$0.519871\pi$
$389$	−14.2795	+	34.4739i	−0.724002	+	1.74789i	−0.661617	+	0.749842i	$0.730129\pi$
$390$		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
$395$	−29.3923	−	12.1747i	−1.47889	−	0.612576i
$396$		0			0
$397$	−8.88405	−	21.4480i	−0.445877	−	1.07644i	−0.973852	−	0.227183i	$-0.927048\pi$
$397$	−8.88405	−	21.4480i	−0.445877	−	1.07644i	0.527975	−	0.849260i	$-0.322952\pi$
$398$		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
$403$	−2.06961	−	4.99647i	−0.103094	−	0.248892i
$404$		0			0
$405$	14.9216	+	6.18073i	0.741461	+	0.307123i
$406$		0			0
$407$	−3.77373	+	3.77373i	−0.187057	+	0.187057i
$408$		0			0
$409$	−5.32666	−	5.32666i	−0.263386	−	0.263386i	0.563042	−	0.826428i	$-0.309631\pi$
$409$	−5.32666	−	5.32666i	−0.263386	−	0.263386i	−0.826428	+	0.563042i	$0.809631\pi$
$410$		0			0
$411$	−6.51590	+	15.7308i	−0.321406	+	0.775942i
$412$		0			0
$413$	4.65019	−	1.92617i	0.228821	−	0.0947807i
$414$		0			0
$415$	23.3204			1.14475
$416$		0			0
$417$	31.4603			1.54062
$418$		0			0
$419$	10.5509	−	4.37032i	0.515444	−	0.213504i	−0.109770	−	0.993957i	$-0.535012\pi$
$419$	10.5509	−	4.37032i	0.515444	−	0.213504i	0.625214	+	0.780453i	$0.285012\pi$
$420$		0			0
$421$	−1.72505	+	4.16464i	−0.0840739	+	0.202972i	−0.960326	−	0.278881i	$-0.910036\pi$
$421$	−1.72505	+	4.16464i	−0.0840739	+	0.202972i	0.876252	+	0.481854i	$0.160036\pi$
$422$		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
$427$	−12.8957	−	5.34157i	−0.624066	−	0.258497i
$428$		0			0
$429$	−17.4173	−	42.0492i	−0.840917	−	2.03015i
$430$		0			0
$431$		−	16.9800i		−	0.817897i	−0.912557	−	0.408949i	$-0.865896\pi$
$431$		−	16.9800i		−	0.817897i	0.912557	−	0.408949i	$-0.134104\pi$
$432$		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
$435$	10.8331	+	26.1535i	0.519409	+	1.25396i
$436$		0			0
$437$	0.887839	+	0.367755i	0.0424711	+	0.0175921i
$438$		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
$443$	6.31087	−	15.2358i	0.299838	−	0.723874i	−0.700113	−	0.714032i	$-0.746867\pi$
$443$	6.31087	−	15.2358i	0.299838	−	0.723874i	0.999952	−	0.00984190i	$-0.00313282\pi$
$444$		0			0
$445$	−13.1305	+	5.43882i	−0.622444	+	0.257825i
$446$		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
$451$	8.72098	−	3.61235i	0.410655	−	0.170099i
$452$		0			0
$453$	14.8847	−	35.9348i	0.699343	−	1.68836i
$454$		0			0
$455$	5.67294	+	5.67294i	0.265952	+	0.265952i
$456$		0			0
$457$	−7.68314	+	7.68314i	−0.359402	+	0.359402i	−0.863592	−	0.504191i	$-0.831791\pi$
$457$	−7.68314	+	7.68314i	−0.359402	+	0.359402i	0.504191	+	0.863592i	$0.331791\pi$
$458$		0			0
$459$	−0.692559	−	0.286867i	−0.0323259	−	0.0133898i
$460$		0			0
$461$	5.90199	+	14.2487i	0.274883	+	0.663627i	0.999679	−	0.0253371i	$-0.00806593\pi$
$461$	5.90199	+	14.2487i	0.274883	+	0.663627i	−0.724796	+	0.688964i	$0.758066\pi$
$462$		0			0
$463$		−	27.3231i		−	1.26981i	−0.772589	−	0.634907i	$-0.781038\pi$
$463$		−	27.3231i		−	1.26981i	0.772589	−	0.634907i	$-0.218962\pi$
$464$		0			0
$465$		−	5.33962i		−	0.247619i
$466$		0			0
$467$	−9.40577	−	22.7075i	−0.435247	−	1.05078i	−0.977570	−	0.210610i	$-0.932455\pi$
$467$	−9.40577	−	22.7075i	−0.435247	−	1.05078i	0.542323	−	0.840170i	$-0.317545\pi$
$468$		0			0
$469$	−3.20380	−	1.32706i	−0.147938	−	0.0612779i
$470$		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
$475$	−0.308915	+	0.745786i	−0.0141740	+	0.0342190i
$476$		0			0
$477$	−14.1709	+	5.86978i	−0.648842	+	0.268759i
$478$		0			0
$479$	−3.91155			−0.178723			−0.0893616	−	0.995999i	$-0.528483\pi$
$479$	−3.91155			−0.178723			−0.0893616	+	0.995999i	$0.528483\pi$
$480$		0			0
$481$	−6.16305			−0.281011
$482$		0			0
$483$	−4.04646	+	1.67610i	−0.184120	+	0.0762651i
$484$		0			0
$485$	4.35480	−	10.5134i	0.197741	−	0.477390i
$486$		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
$491$	11.2886	+	4.67590i	0.509448	+	0.211020i	0.622575	−	0.782560i	$-0.286087\pi$
$491$	11.2886	+	4.67590i	0.509448	+	0.211020i	−0.113127	+	0.993581i	$0.536087\pi$
$492$		0			0
$493$	8.59744	+	20.7561i	0.387209	+	0.934806i
$494$		0			0
$495$		−	22.7788i		−	1.02383i
$496$		0			0
$497$			12.8517i			0.576479i
$498$		0			0
$499$	12.4071	+	29.9533i	0.555417	+	1.34089i	0.913361	+	0.407152i	$0.133478\pi$
$499$	12.4071	+	29.9533i	0.555417	+	1.34089i	−0.357944	+	0.933743i	$0.616522\pi$
$500$		0			0
$501$	35.0836	+	14.5321i	1.56742	+	0.649247i
$502$		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
$507$	7.84276	−	18.9341i	0.348309	−	0.840893i
$508$		0			0
$509$	−20.0994	+	8.32546i	−0.890892	+	0.369020i	−0.780711	−	0.624892i	$-0.785143\pi$
$509$	−20.0994	+	8.32546i	−0.890892	+	0.369020i	−0.110181	+	0.993912i	$0.535143\pi$
$510$		0			0
$511$	−10.0531			−0.444724
$512$		0			0
$513$	−0.105497			−0.00465780
$514$		0			0
$515$	11.4135	−	4.72764i	0.502941	−	0.208325i
$516$		0			0
$517$	−2.29186	+	5.53304i	−0.100796	+	0.243343i
$518$		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	$0.626767\pi$
$521$	−29.8910	+	29.8910i	−1.30955	+	1.30955i	−0.921741	+	0.387807i	$0.873233\pi$
$522$		0			0
$523$	32.7654	+	13.5719i	1.43273	+	0.593456i	0.958024	−	0.286688i	$-0.0925544\pi$
$523$	32.7654	+	13.5719i	1.43273	+	0.593456i	0.474706	+	0.880144i	$0.342554\pi$
$524$		0			0
$525$	−1.40792	−	3.39903i	−0.0614468	−	0.148346i
$526$		0			0
$527$		−	4.23765i		−	0.184595i
$528$		0			0
$529$			19.4361i			0.845046i
$530$		0			0
$531$	−6.31558	−	15.2472i	−0.274073	−	0.661670i
$532$		0			0
$533$	10.0711	+	4.17157i	0.436226	+	0.180691i
$534$		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
$539$	9.35460	−	22.5840i	0.402931	−	0.972762i
$540$		0			0
$541$	11.2925	−	4.67751i	0.485502	−	0.201102i	−0.126486	−	0.991968i	$-0.540370\pi$
$541$	11.2925	−	4.67751i	0.485502	−	0.201102i	0.611988	+	0.790867i	$0.290370\pi$
$542$		0			0
$543$	5.01571			0.215245
$544$		0			0
$545$	−16.7109			−0.715815
$546$		0			0
$547$	−19.1256	+	7.92207i	−0.817750	+	0.338723i	−0.752042	−	0.659116i	$-0.770931\pi$
$547$	−19.1256	+	7.92207i	−0.817750	+	0.338723i	−0.0657087	+	0.997839i	$0.520931\pi$
$548$		0			0
$549$	−17.5141	+	42.2827i	−0.747482	+	1.80458i
$550$		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
$555$	−5.62177	−	2.32861i	−0.238631	−	0.0988442i
$556$		0			0
$557$	−12.3617	−	29.8439i	−0.523783	−	1.26452i	−0.935537	−	0.353229i	$-0.885084\pi$
$557$	−12.3617	−	29.8439i	−0.523783	−	1.26452i	0.411753	−	0.911295i	$-0.364916\pi$
$558$		0			0
$559$		−	12.7390i		−	0.538803i
$560$		0			0
$561$		−	35.6631i		−	1.50570i
$562$		0			0
$563$	−10.5540	−	25.4797i	−0.444800	−	1.07384i	−0.974244	−	0.225497i	$-0.927600\pi$
$563$	−10.5540	−	25.4797i	−0.444800	−	1.07384i	0.529444	−	0.848345i	$-0.322400\pi$
$564$		0			0
$565$	−20.1023	−	8.32666i	−0.845712	−	0.350305i
$566$		0			0
$567$	−5.81352	+	5.81352i	−0.244145	+	0.244145i
$568$		0			0
$569$	−23.7855	−	23.7855i	−0.997139	−	0.997139i	0.00285688	−	0.999996i	$-0.499091\pi$
$569$	−23.7855	−	23.7855i	−0.997139	−	0.997139i	−0.999996	+	0.00285688i	$0.999091\pi$
$570$		0			0
$571$	−0.904405	+	2.18343i	−0.0378482	+	0.0913736i	−0.941673	−	0.336528i	$-0.890747\pi$
$571$	−0.904405	+	2.18343i	−0.0378482	+	0.0913736i	0.903825	+	0.427902i	$0.140747\pi$
$572$		0			0
$573$	−44.2141	+	18.3141i	−1.84707	+	0.765082i
$574$		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
$579$	41.1238	−	17.0340i	1.70905	−	0.707910i
$580$		0			0
$581$	−4.54286	+	10.9674i	−0.188469	+	0.455006i
$582$		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
$587$	−40.1685	−	16.6383i	−1.65793	−	0.686738i	−0.660015	−	0.751253i	$-0.729450\pi$
$587$	−40.1685	−	16.6383i	−1.65793	−	0.686738i	−0.997917	+	0.0645151i	$0.979450\pi$
$588$		0			0
$589$	−0.228225	−	0.550984i	−0.00940384	−	0.0227029i
$590$		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
$595$	2.40569	+	5.80785i	0.0986238	+	0.238099i
$596$		0			0
$597$	−38.3481	−	15.8843i	−1.56948	−	0.650102i
$598$		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	0.874365	−	0.485269i	$-0.161278\pi$
$601$	9.53880	+	9.53880i	0.389096	+	0.389096i	−0.485269	+	0.874365i	$0.661278\pi$
$602$		0			0
$603$	−4.35119	+	10.5047i	−0.177194	+	0.427784i
$604$		0			0
$605$	8.49887	−	3.52035i	0.345528	−	0.143123i
$606$		0			0
$607$	3.66391			0.148714			0.0743568	−	0.997232i	$-0.476310\pi$
$607$	3.66391			0.148714			0.0743568	+	0.997232i	$0.476310\pi$
$608$		0			0
$609$	−14.4102			−0.583929
$610$		0			0
$611$	−6.38960	+	2.64666i	−0.258496	+	0.107072i
$612$		0			0
$613$	11.6012	−	28.0079i	0.468570	−	1.13123i	−0.496218	−	0.868198i	$-0.665278\pi$
$613$	11.6012	−	28.0079i	0.468570	−	1.13123i	0.964788	−	0.263029i	$-0.0847215\pi$
$614$		0			0
$615$	7.61040	+	7.61040i	0.306881	+	0.306881i
$616$		0			0
$617$	5.86100	−	5.86100i	0.235955	−	0.235955i	−0.579218	−	0.815173i	$-0.696642\pi$
$617$	5.86100	−	5.86100i	0.235955	−	0.235955i	0.815173	+	0.579218i	$0.196642\pi$
$618$		0			0
$619$	−36.9173	−	15.2917i	−1.48383	−	0.614624i	−0.513868	−	0.857869i	$-0.671788\pi$
$619$	−36.9173	−	15.2917i	−1.48383	−	0.614624i	−0.969965	+	0.243245i	$0.921788\pi$
$620$		0			0
$621$	0.149724	+	0.361465i	0.00600821	+	0.0145051i
$622$		0			0
$623$		−	7.23468i		−	0.289851i
$624$		0			0
$625$		−	14.5563i		−	0.582254i
$626$		0			0
$627$	−1.92069	−	4.63696i	−0.0767050	−	0.185182i
$628$		0			0
$629$	−4.46157	−	1.84804i	−0.177895	−	0.0736864i
$630$		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
$635$	−9.23412	+	22.2931i	−0.366445	+	0.884676i
$636$		0			0
$637$	26.0802	−	10.8028i	1.03334	−	0.428022i
$638$		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
$643$	−24.1050	+	9.98462i	−0.950608	+	0.393755i	−0.803459	−	0.595360i	$-0.797010\pi$
$643$	−24.1050	+	9.98462i	−0.950608	+	0.393755i	−0.147149	+	0.989114i	$0.547010\pi$
$644$		0			0
$645$	4.81324	−	11.6202i	0.189521	−	0.457545i
$646$		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
$651$	2.51119	+	1.04017i	0.0984212	+	0.0407674i
$652$		0			0
$653$	5.73339	+	13.8416i	0.224365	+	0.541665i	0.995474	−	0.0950389i	$-0.0302975\pi$
$653$	5.73339	+	13.8416i	0.224365	+	0.541665i	−0.771109	+	0.636703i	$0.780298\pi$
$654$		0			0
$655$			13.0429i			0.509629i
$656$		0			0
$657$			32.9624i			1.28599i
$658$		0			0
$659$	−0.202554	−	0.489009i	−0.00789039	−	0.0190491i	0.919885	−	0.392188i	$-0.128282\pi$
$659$	−0.202554	−	0.489009i	−0.00789039	−	0.0190491i	−0.927776	+	0.373139i	$0.878282\pi$
$660$		0			0
$661$	−6.45241	−	2.67268i	−0.250970	−	0.103955i	0.253652	−	0.967295i	$-0.418368\pi$
$661$	−6.45241	−	2.67268i	−0.250970	−	0.103955i	−0.504622	+	0.863340i	$0.668368\pi$
$662$		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
$667$	4.48723	−	10.8331i	0.173746	−	0.419461i
$668$		0			0
$669$	51.5411	−	21.3490i	1.99270	−	0.825402i
$670$		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
$675$	−0.303631	+	0.125768i	−0.0116868	+	0.00484081i
$676$		0			0
$677$	−1.60737	+	3.88054i	−0.0617763	+	0.149141i	−0.951753	−	0.306864i	$-0.900720\pi$
$677$	−1.60737	+	3.88054i	−0.0617763	+	0.149141i	0.889977	+	0.456005i	$0.150720\pi$
$678$		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
$683$	24.8133	+	10.2780i	0.949455	+	0.393277i	0.803026	−	0.595944i	$-0.203222\pi$
$683$	24.8133	+	10.2780i	0.949455	+	0.393277i	0.146429	+	0.989221i	$0.453222\pi$
$684$		0			0
$685$	−4.88118	−	11.7842i	−0.186500	−	0.450251i
$686$		0			0
$687$			42.1019i			1.60629i
$688$		0			0
$689$		−	22.9585i		−	0.874650i
$690$		0			0
$691$	8.56885	+	20.6870i	0.325974	+	0.786972i	0.998883	+	0.0472463i	$0.0150446\pi$
$691$	8.56885	+	20.6870i	0.325974	+	0.786972i	−0.672909	+	0.739725i	$0.734955\pi$
$692$		0			0
$693$	10.7127	+	4.43736i	0.406943	+	0.168561i
$694$		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
$699$	−13.9479	+	33.6732i	−0.527558	+	1.27364i
$700$		0			0
$701$	−28.1557	+	11.6625i	−1.06343	+	0.440486i	−0.844667	−	0.535293i	$-0.820201\pi$
$701$	−28.1557	+	11.6625i	−1.06343	+	0.440486i	−0.218760	+	0.975779i	$0.570201\pi$
$702$		0			0
$703$	−0.679628			−0.0256326
$704$		0			0
$705$	−6.82843			−0.257173
$706$		0			0
$707$	7.03195	−	2.91273i	0.264464	−	0.109544i
$708$		0			0
$709$	−12.4408	+	30.0346i	−0.467223	+	1.12797i	0.498148	+	0.867092i	$0.334014\pi$
$709$	−12.4408	+	30.0346i	−0.467223	+	1.12797i	−0.965370	+	0.260883i	$0.915986\pi$
$710$		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
$715$	31.4998	+	13.0476i	1.17803	+	0.487954i
$716$		0			0
$717$	11.0187	+	26.6015i	0.411501	+	0.993450i
$718$		0			0
$719$			33.6333i			1.25431i	0.778894	+	0.627155i	$0.215781\pi$
$719$			33.6333i			1.25431i	−0.778894	+	0.627155i	$0.784219\pi$
$720$		0			0
$721$			6.28867i			0.234202i
$722$		0			0
$723$	−13.0533	−	31.5134i	−0.485457	−	1.17200i
$724$		0			0
$725$	9.09984	+	3.76928i	0.337960	+	0.139988i
$726$		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
$731$	3.81991	−	9.22207i	0.141284	−	0.341090i
$732$		0			0
$733$	0.328598	−	0.136110i	0.0121371	−	0.00502733i	−0.376607	−	0.926373i	$-0.622909\pi$
$733$	0.328598	−	0.136110i	0.0121371	−	0.00502733i	0.388744	+	0.921346i	$0.372909\pi$
$734$		0			0
$735$	27.8714			1.02805
$736$		0			0
$737$	−14.7373			−0.542857
$738$		0			0
$739$	−43.8857	+	18.1780i	−1.61436	+	0.668690i	−0.993352	−	0.115114i	$-0.963277\pi$
$739$	−43.8857	+	18.1780i	−1.61436	+	0.668690i	−0.621008	+	0.783804i	$0.713277\pi$
$740$		0			0
$741$	2.21803	−	5.35480i	0.0814814	−	0.196714i
$742$		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
$747$	35.9603	+	14.8952i	1.31572	+	0.544988i
$748$		0			0
$749$	1.00430	+	2.42459i	0.0366963	+	0.0885927i
$750$		0			0
$751$			51.3686i			1.87447i	0.348701	+	0.937234i	$0.386623\pi$
$751$			51.3686i			1.87447i	−0.348701	+	0.937234i	$0.613377\pi$
$752$		0			0
$753$			34.7248i			1.26544i
$754$		0			0
$755$	11.1504	+	26.9194i	0.405804	+	0.979697i
$756$		0			0
$757$	−15.2644	−	6.32270i	−0.554793	−	0.229803i	0.0876302	−	0.996153i	$-0.472071\pi$
$757$	−15.2644	−	6.32270i	−0.554793	−	0.229803i	−0.642423	+	0.766350i	$0.722071\pi$
$758$		0			0
$759$	−13.1618	+	13.1618i	−0.477741	+	0.477741i
$760$		0			0
$761$	26.6859	+	26.6859i	0.967362	+	0.967362i	0.999484	−	0.0321218i	$-0.0102264\pi$
$761$	26.6859	+	26.6859i	0.967362	+	0.967362i	−0.0321218	+	0.999484i	$0.510226\pi$
$762$		0			0
$763$	3.25531	−	7.85902i	0.117850	−	0.284516i
$764$		0			0
$765$	19.0429	−	7.88784i	0.688499	−	0.285185i
$766$		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
$771$	43.0796	−	17.8441i	1.55147	−	0.642641i
$772$		0			0
$773$	15.4001	−	37.1790i	0.553902	−	1.33724i	−0.360625	−	0.932711i	$-0.617436\pi$
$773$	15.4001	−	37.1790i	0.553902	−	1.33724i	0.914526	−	0.404526i	$-0.132564\pi$
$774$		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
$779$	1.11058	+	0.460018i	0.0397908	+	0.0164819i
$780$		0			0
$781$	20.9012	+	50.4599i	0.747903	+	1.80560i
$782$		0			0
$783$			1.28724i			0.0460022i
$784$		0			0
$785$			2.44992i			0.0874413i
$786$		0			0
$787$	0.948632	+	2.29020i	0.0338151	+	0.0816368i	0.939885	−	0.341491i	$-0.110932\pi$
$787$	0.948632	+	2.29020i	0.0338151	+	0.0816368i	−0.906070	+	0.423128i	$0.860932\pi$
$788$		0			0
$789$	44.8240	+	18.5667i	1.59578	+	0.660992i
$790$		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
$795$	8.67452	−	20.9421i	0.307654	−	0.742741i
$796$		0			0
$797$	2.76562	−	1.14556i	0.0979632	−	0.0405777i	−0.333164	−	0.942869i	$-0.608116\pi$
$797$	2.76562	−	1.14556i	0.0979632	−	0.0405777i	0.431127	+	0.902291i	$0.358116\pi$
$798$		0			0
$799$	−5.41921			−0.191718
$800$		0			0
$801$	−23.7212			−0.838149
$802$		0			0
$803$	−39.4717	+	16.3497i	−1.39292	+	0.576968i
$804$		0			0
$805$	1.25559	−	3.03127i	0.0442539	−	0.106838i
$806$		0			0
$807$	23.0256	+	23.0256i	0.810541	+	0.810541i
$808$		0			0
$809$	−7.12825	+	7.12825i	−0.250616	+	0.250616i	−0.821223	−	0.570607i	$-0.806708\pi$
$809$	−7.12825	+	7.12825i	−0.250616	+	0.250616i	0.570607	+	0.821223i	$0.306708\pi$
$810$		0			0
$811$	27.4750	+	11.3805i	0.964777	+	0.399624i	0.808765	−	0.588131i	$-0.200136\pi$
$811$	27.4750	+	11.3805i	0.964777	+	0.399624i	0.156012	+	0.987755i	$0.450136\pi$
$812$		0			0
$813$	−4.16751	−	10.0613i	−0.146161	−	0.352864i
$814$		0			0
$815$		−	42.6435i		−	1.49374i
$816$		0			0
$817$		−	1.40479i		−	0.0491474i
$818$		0			0
$819$	5.12431	+	12.3712i	0.179058	+	0.432284i
$820$		0			0
$821$	−34.1861	−	14.1603i	−1.19310	−	0.494199i	−0.304339	−	0.952564i	$-0.598435\pi$
$821$	−34.1861	−	14.1603i	−1.19310	−	0.494199i	−0.888764	+	0.458364i	$0.848435\pi$
$822$		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
$827$	7.98030	−	19.2661i	0.277502	−	0.669950i	−0.722263	−	0.691619i	$-0.756898\pi$
$827$	7.98030	−	19.2661i	0.277502	−	0.669950i	0.999765	+	0.0216689i	$0.00689796\pi$
$828$		0			0
$829$	3.59585	−	1.48945i	0.124889	−	0.0517307i	−0.319364	−	0.947632i	$-0.603469\pi$
$829$	3.59585	−	1.48945i	0.124889	−	0.0517307i	0.444253	+	0.895901i	$0.353469\pi$
$830$		0			0
$831$	−61.5269			−2.13434
$832$		0			0
$833$	22.1194			0.766391
$834$		0			0
$835$	−26.2818	+	10.8863i	−0.909518	+	0.376735i
$836$		0			0
$837$	0.0929169	−	0.224321i	0.00321168	−	0.00775368i
$838$		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
$843$	18.8050	+	7.78929i	0.647679	+	0.268277i
$844$		0			0
$845$	5.87515	+	14.1839i	0.202111	+	0.487940i
$846$		0			0
$847$			4.68274i			0.160901i
$848$		0			0
$849$			8.50750i			0.291977i
$850$		0			0
$851$	0.964543	+	2.32861i	0.0330641	+	0.0798239i
$852$		0			0
$853$	−18.0597	−	7.48055i	−0.618351	−	0.256129i	0.0514436	−	0.998676i	$-0.483618\pi$
$853$	−18.0597	−	7.48055i	−0.618351	−	0.256129i	−0.669794	+	0.742547i	$0.733618\pi$
$854$		0			0
$855$	2.05117	−	2.05117i	0.0701485	−	0.0701485i
$856$		0			0
$857$	−6.35294	−	6.35294i	−0.217012	−	0.217012i	0.590226	−	0.807238i	$-0.299039\pi$
$857$	−6.35294	−	6.35294i	−0.217012	−	0.217012i	−0.807238	+	0.590226i	$0.799039\pi$
$858$		0			0
$859$	9.72800	−	23.4855i	0.331915	−	0.801314i	−0.666525	−	0.745483i	$-0.732219\pi$
$859$	9.72800	−	23.4855i	0.331915	−	0.801314i	0.998440	−	0.0558315i	$-0.0177810\pi$
$860$		0			0
$861$	−5.06164	+	2.09660i	−0.172500	+	0.0714520i
$862$		0			0
$863$	0.0884535			0.00301099			0.00150550	−	0.999999i	$-0.499521\pi$
$863$	0.0884535			0.00301099			0.00150550	+	0.999999i	$0.499521\pi$
$864$		0			0
$865$	−3.55008			−0.120706
$866$		0			0
$867$	−8.92588	+	3.69722i	−0.303139	+	0.125564i
$868$		0			0
$869$	26.3379	−	63.5854i	0.893453	−	2.15699i
$870$		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
$875$	10.5747	+	4.38018i	0.357490	+	0.148077i
$876$		0			0
$877$	4.24514	+	10.2487i	0.143348	+	0.346073i	0.979205	−	0.202875i	$-0.0650285\pi$
$877$	4.24514	+	10.2487i	0.143348	+	0.346073i	−0.835857	+	0.548948i	$0.815029\pi$
$878$		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
$883$	−7.74892	−	18.7075i	−0.260772	−	0.629559i	0.738215	−	0.674566i	$-0.235669\pi$
$883$	−7.74892	−	18.7075i	−0.260772	−	0.629559i	−0.998987	+	0.0450067i	$0.985669\pi$
$884$		0			0
$885$	22.5326	+	9.33333i	0.757426	+	0.313736i
$886$		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
$891$	−13.3710	+	32.2804i	−0.447944	+	1.08143i
$892$		0			0
$893$	−0.704611	+	0.291859i	−0.0235789	+	0.00976670i
$894$		0			0
$895$	−9.07646			−0.303392
$896$		0			0
$897$	−21.4951			−0.717700
$898$		0			0
$899$	−6.72293	+	2.78473i	−0.224222	+	0.0928759i
$900$		0			0
$901$	6.88431	−	16.6202i	0.229350	−	0.553699i
$902$		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
$907$	−38.2753	−	15.8541i	−1.27091	−	0.526428i	−0.357669	−	0.933848i	$-0.616428\pi$
$907$	−38.2753	−	15.8541i	−1.27091	−	0.526428i	−0.913241	+	0.407421i	$0.866428\pi$
$908$		0			0
$909$	−9.55032	−	23.0565i	−0.316764	−	0.764737i
$910$		0			0
$911$		−	12.5214i		−	0.414851i	−0.978251	−	0.207426i	$-0.933492\pi$
$911$		−	12.5214i		−	0.414851i	0.978251	−	0.207426i	$-0.0665085\pi$
$912$		0			0
$913$			50.4497i			1.66964i
$914$		0			0
$915$	−25.8827	−	62.4864i	−0.855657	−	2.06574i
$916$		0			0
$917$	−6.13401	−	2.54079i	−0.202563	−	0.0839043i
$918$		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
$923$	−24.1369	+	58.2715i	−0.794475	+	1.91803i
$924$		0			0
$925$	−1.95604	+	0.810217i	−0.0643141	+	0.0266398i
$926$		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
$931$	2.87599	−	1.19127i	0.0942566	−	0.0390424i
$932$		0			0
$933$	−20.0961	+	48.5162i	−0.657915	+	1.58835i
$934$		0			0
$935$	18.8910	+	18.8910i	0.617801	+	0.617801i
$936$		0			0
$937$	2.58002	−	2.58002i	0.0842857	−	0.0842857i	−0.663707	−	0.747993i	$-0.731018\pi$
$937$	2.58002	−	2.58002i	0.0842857	−	0.0842857i	0.747993	+	0.663707i	$0.231018\pi$
$938$		0			0
$939$	−59.0937	−	24.4774i	−1.92845	−	0.798790i
$940$		0			0
$941$	−2.24720	−	5.42523i	−0.0732568	−	0.176857i	0.883009	−	0.469355i	$-0.155514\pi$
$941$	−2.24720	−	5.42523i	−0.0732568	−	0.176857i	−0.956266	+	0.292498i	$0.905514\pi$
$942$		0			0
$943$		−	4.45807i		−	0.145175i
$944$		0			0
$945$			0.360189i			0.0117170i
$946$		0			0
$947$	17.5640	+	42.4032i	0.570753	+	1.37792i	0.900915	+	0.433996i	$0.142897\pi$
$947$	17.5640	+	42.4032i	0.570753	+	1.37792i	−0.330162	+	0.943924i	$0.607103\pi$
$948$		0			0
$949$	−45.5822	−	18.8808i	−1.47966	−	0.612896i
$950$		0			0
$951$	−17.9788	+	17.9788i	−0.583003	+	0.583003i
$952$		0			0
$953$	14.8079	+	14.8079i	0.479673	+	0.479673i	0.905027	−	0.425354i	$-0.139850\pi$
$953$	14.8079	+	14.8079i	0.479673	+	0.479673i	−0.425354	+	0.905027i	$0.639850\pi$
$954$		0			0
$955$	13.7194	−	33.1216i	0.443949	−	1.07179i
$956$		0			0
$957$	−56.5787	+	23.4357i	−1.82893	+	0.757568i
$958$		0			0
$959$	6.49290			0.209667
$960$		0			0
$961$	−29.6274			−0.955723
$962$		0			0
$963$	7.94981	−	3.29292i	0.256179	−	0.106113i
$964$		0			0
$965$	−12.7605	+	30.8066i	−0.410775	+	0.991698i
$966$		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
$971$	−23.3388	−	9.66725i	−0.748978	−	0.310237i	−0.0246533	−	0.999696i	$-0.507848\pi$
$971$	−23.3388	−	9.66725i	−0.748978	−	0.310237i	−0.724324	+	0.689459i	$0.757848\pi$
$972$		0			0
$973$	−4.59099	−	11.0836i	−0.147180	−	0.355325i
$974$		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
$979$	−11.7660	−	28.4056i	−0.376042	−	0.907846i
$980$		0			0
$981$	−25.7684	−	10.6736i	−0.822720	−	0.340782i
$982$		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
$987$	1.33019	−	3.21137i	0.0423405	−	0.102219i
$988$		0			0
$989$	−4.81324	+	1.99371i	−0.153052	+	0.0633963i
$990$		0			0
$991$	52.4878			1.66733			0.833665	−	0.552270i	$-0.186238\pi$
$991$	52.4878			1.66733			0.833665	+	0.552270i	$0.186238\pi$
$992$		0			0
$993$	−20.2217			−0.641716
$994$		0			0
$995$	28.7272	−	11.8992i	0.910715	−	0.377230i
$996$		0			0
$997$	−12.8431	+	31.0060i	−0.406745	+	0.981970i	0.579243	+	0.815155i	$0.303348\pi$
$997$	−12.8431	+	31.0060i	−0.406745	+	0.981970i	−0.985988	+	0.166815i	$0.946652\pi$
$998$		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	256.2.g.c.97.1		8
4.3	odd	2		256.2.g.d.97.2		8
8.3	odd	2		32.2.g.b.21.2	✓	8
8.5	even	2		128.2.g.b.49.2		8
16.3	odd	4		512.2.g.e.449.2		8
16.5	even	4		512.2.g.f.449.2		8
16.11	odd	4		512.2.g.h.449.1		8
16.13	even	4		512.2.g.g.449.1		8
24.5	odd	2		1152.2.v.b.433.1		8
24.11	even	2		288.2.v.b.181.1		8
32.3	odd	8		256.2.g.d.161.2		8
32.5	even	8		512.2.g.f.65.2		8
32.11	odd	8		512.2.g.e.65.2		8
32.13	even	8		128.2.g.b.81.2		8
32.19	odd	8		32.2.g.b.29.2	yes	8
32.21	even	8		512.2.g.g.65.1		8
32.27	odd	8		512.2.g.h.65.1		8
32.29	even	8	inner	256.2.g.c.161.1		8
40.3	even	4		800.2.ba.d.149.1		8
40.19	odd	2		800.2.y.b.501.1		8
40.27	even	4		800.2.ba.c.149.2		8
64.3	odd	16		4096.2.a.k.1.2		8
64.29	even	16		4096.2.a.q.1.2		8
64.35	odd	16		4096.2.a.k.1.7		8
64.61	even	16		4096.2.a.q.1.7		8
96.77	odd	8		1152.2.v.b.721.1		8
96.83	even	8		288.2.v.b.253.1		8
160.19	odd	8		800.2.y.b.701.1		8
160.83	even	8		800.2.ba.c.349.2		8
160.147	even	8		800.2.ba.d.349.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.21.2	✓	8	8.3	odd	2
32.2.g.b.29.2	yes	8	32.19	odd	8
128.2.g.b.49.2		8	8.5	even	2
128.2.g.b.81.2		8	32.13	even	8
256.2.g.c.97.1		8	1.1	even	1	trivial
256.2.g.c.161.1		8	32.29	even	8	inner
256.2.g.d.97.2		8	4.3	odd	2
256.2.g.d.161.2		8	32.3	odd	8
288.2.v.b.181.1		8	24.11	even	2
288.2.v.b.253.1		8	96.83	even	8
512.2.g.e.65.2		8	32.11	odd	8
512.2.g.e.449.2		8	16.3	odd	4
512.2.g.f.65.2		8	32.5	even	8
512.2.g.f.449.2		8	16.5	even	4
512.2.g.g.65.1		8	32.21	even	8
512.2.g.g.449.1		8	16.13	even	4
512.2.g.h.65.1		8	32.27	odd	8
512.2.g.h.449.1		8	16.11	odd	4
800.2.y.b.501.1		8	40.19	odd	2
800.2.y.b.701.1		8	160.19	odd	8
800.2.ba.c.149.2		8	40.27	even	4
800.2.ba.c.349.2		8	160.83	even	8
800.2.ba.d.149.1		8	40.3	even	4
800.2.ba.d.349.1		8	160.147	even	8
1152.2.v.b.433.1		8	24.5	odd	2
1152.2.v.b.721.1		8	96.77	odd	8
4096.2.a.k.1.2		8	64.3	odd	16
4096.2.a.k.1.7		8	64.35	odd	16
4096.2.a.q.1.2		8	64.29	even	16
4096.2.a.q.1.7		8	64.61	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.g (of order \(8\), degree \(4\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more