LMFDB - Embedded newform 128.2.g.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, 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("128.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	128.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:	$1.02208514587$
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			81.2
Root			$0.500000 + 1.44392i$ of defining polynomial
Character	$\chi$	$=$	128.81
Dual form			128.2.g.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.27882 + 0.943920i) q^{3} +(-0.707107 - 1.70711i) q^{5} +(0.665096 - 0.665096i) q^{7} +(2.18073 + 2.18073i) q^{9} +O(q^{10})$	\(q+(2.27882 + 0.943920i) q^{3} +(-0.707107 - 1.70711i) q^{5} +(0.665096 - 0.665096i) q^{7} +(2.18073 + 2.18073i) q^{9} +(-3.69304 + 1.52971i) q^{11} +(-1.76652 + 4.26475i) q^{13} -4.55765i q^{15} -3.61706i q^{17} +(-0.194802 + 0.470294i) q^{19} +(2.14343 - 0.887839i) q^{21} +(1.33490 + 1.33490i) q^{23} +(1.12132 - 1.12132i) q^{25} +(0.0793096 + 0.191470i) q^{27} +(-5.73838 - 2.37691i) q^{29} -1.17157 q^{31} -9.85970 q^{33} +(-1.60568 - 0.665096i) q^{35} +(0.510925 + 1.23348i) q^{37} +(-8.05117 + 8.05117i) q^{39} +(1.66981 + 1.66981i) q^{41} +(2.54960 - 1.05608i) q^{43} +(2.18073 - 5.26475i) q^{45} -1.49824i q^{47} +6.11529i q^{49} +(3.41421 - 8.24264i) q^{51} +(4.59495 - 1.90329i) q^{53} +(5.22274 + 5.22274i) q^{55} +(-0.887839 + 0.887839i) q^{57} +(-2.04784 - 4.94392i) q^{59} +(13.7102 + 5.67897i) q^{61} +2.90079 q^{63} +8.52951 q^{65} +(3.40617 + 1.41088i) q^{67} +(1.78197 + 4.30205i) q^{69} +(9.66157 - 9.66157i) q^{71} +(-7.55765 - 7.55765i) q^{73} +(3.61373 - 1.49685i) q^{75} +(-1.43882 + 3.47363i) q^{77} +17.2176i q^{79} -8.74088i q^{81} +(-4.82981 + 11.6602i) q^{83} +(-6.17471 + 2.55765i) q^{85} +(-10.8331 - 10.8331i) q^{87} +(-5.43882 + 5.43882i) q^{89} +(1.66157 + 4.01138i) q^{91} +(-2.66981 - 1.10587i) q^{93} +0.940588 q^{95} +6.15862 q^{97} +(-11.3894 - 4.71765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

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	$-0.122771\pi$
$3$	2.27882	+	0.943920i	1.31568	+	0.544972i	0.389143	+	0.921177i	$0.372771\pi$
$4$		0			0
$5$	−0.707107	−	1.70711i	−0.316228	−	0.763441i	−0.999448	−	0.0332288i	$-0.989421\pi$
$5$	−0.707107	−	1.70711i	−0.316228	−	0.763441i	0.683220	−	0.730213i	$-0.260579\pi$
$6$		0			0
$7$	0.665096	−	0.665096i	0.251383	−	0.251383i	−0.570155	−	0.821537i	$-0.693117\pi$
$7$	0.665096	−	0.665096i	0.251383	−	0.251383i	0.821537	+	0.570155i	$0.193117\pi$
$8$		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	$-0.830876\pi$
$11$	−3.69304	+	1.52971i	−1.11349	+	0.461224i	−0.251353	+	0.967895i	$0.580876\pi$
$12$		0			0
$13$	−1.76652	+	4.26475i	−0.489944	+	1.18283i	0.464804	+	0.885414i	$0.346125\pi$
$13$	−1.76652	+	4.26475i	−0.489944	+	1.18283i	−0.954748	+	0.297416i	$0.903875\pi$
$14$		0			0
$15$		−	4.55765i		−	1.17678i
$16$		0			0
$17$		−	3.61706i		−	0.877266i	−0.898666	−	0.438633i	$-0.855463\pi$
$17$		−	3.61706i		−	0.877266i	0.898666	−	0.438633i	$-0.144537\pi$
$18$		0			0
$19$	−0.194802	+	0.470294i	−0.0446907	+	0.107893i	−0.944649	−	0.328084i	$-0.893597\pi$
$19$	−0.194802	+	0.470294i	−0.0446907	+	0.107893i	0.899958	+	0.435977i	$0.143597\pi$
$20$		0			0
$21$	2.14343	−	0.887839i	0.467736	−	0.193742i
$22$		0			0
$23$	1.33490	+	1.33490i	0.278347	+	0.278347i	0.832449	−	0.554102i	$-0.186938\pi$
$23$	1.33490	+	1.33490i	0.278347	+	0.278347i	−0.554102	+	0.832449i	$0.686938\pi$
$24$		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	$-0.570657\pi$
$29$	−5.73838	−	2.37691i	−1.06559	−	0.441382i	−0.845433	+	0.534082i	$0.820657\pi$
$30$		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	$-0.0899965\pi$
$37$	0.510925	+	1.23348i	0.0839955	+	0.202783i	−0.876301	+	0.481763i	$0.839996\pi$
$38$		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	$-0.190966\pi$
$41$	1.66981	+	1.66981i	0.260780	+	0.260780i	−0.564591	+	0.825371i	$0.690966\pi$
$42$		0			0
$43$	2.54960	−	1.05608i	0.388811	−	0.161051i	−0.179710	−	0.983720i	$-0.557516\pi$
$43$	2.54960	−	1.05608i	0.388811	−	0.161051i	0.568521	+	0.822669i	$0.307516\pi$
$44$		0			0
$45$	2.18073	−	5.26475i	0.325084	−	0.784823i
$46$		0			0
$47$		−	1.49824i		−	0.218540i	−0.994012	−	0.109270i	$-0.965149\pi$
$47$		−	1.49824i		−	0.218540i	0.994012	−	0.109270i	$-0.0348513\pi$
$48$		0			0
$49$			6.11529i			0.873614i
$50$		0			0
$51$	3.41421	−	8.24264i	0.478086	−	1.15420i
$52$		0			0
$53$	4.59495	−	1.90329i	0.631164	−	0.261437i	−0.0440833	−	0.999028i	$-0.514037\pi$
$53$	4.59495	−	1.90329i	0.631164	−	0.261437i	0.675248	+	0.737591i	$0.264037\pi$
$54$		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	$-0.238254\pi$
$59$	−2.04784	−	4.94392i	−0.266606	−	0.643644i	−0.999319	+	0.0368939i	$0.988254\pi$
$60$		0			0
$61$	13.7102	+	5.67897i	1.75542	+	0.727117i	0.997173	+	0.0751463i	$0.0239424\pi$
$61$	13.7102	+	5.67897i	1.75542	+	0.727117i	0.758244	+	0.651971i	$0.226058\pi$
$62$		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	$-0.302694\pi$
$67$	3.40617	+	1.41088i	0.416130	+	0.172367i	−0.164788	+	0.986329i	$0.552694\pi$
$68$		0			0
$69$	1.78197	+	4.30205i	0.214524	+	0.517906i
$70$		0			0
$71$	9.66157	−	9.66157i	1.14662	−	1.14662i	0.159403	−	0.987214i	$-0.449043\pi$
$71$	9.66157	−	9.66157i	1.14662	−	1.14662i	0.987214	−	0.159403i	$-0.0509571\pi$
$72$		0			0
$73$	−7.55765	−	7.55765i	−0.884556	−	0.884556i	0.109438	−	0.993994i	$-0.465095\pi$
$73$	−7.55765	−	7.55765i	−0.884556	−	0.884556i	−0.993994	+	0.109438i	$0.965095\pi$
$74$		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	$0.419980\pi$
$79$			17.2176i			1.93714i	−0.248750	+	0.968568i	$0.580020\pi$
$80$		0			0
$81$		−	8.74088i		−	0.971208i
$82$		0			0
$83$	−4.82981	+	11.6602i	−0.530140	+	1.27987i	0.401290	+	0.915951i	$0.368562\pi$
$83$	−4.82981	+	11.6602i	−0.530140	+	1.27987i	−0.931430	+	0.363921i	$0.881438\pi$
$84$		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	−0.933941	−	0.357427i	$-0.883654\pi$
$89$	−5.43882	+	5.43882i	−0.576514	+	0.576514i	0.357427	+	0.933941i	$0.383654\pi$
$90$		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	−0.999766	−	0.0216512i	$-0.993108\pi$
$101$	−3.09671	−	7.47612i	−0.308134	−	0.743902i	0.691631	−	0.722251i	$-0.256892\pi$
$102$		0			0
$103$	4.72764	−	4.72764i	0.465828	−	0.465828i	−0.434732	−	0.900560i	$-0.643157\pi$
$103$	4.72764	−	4.72764i	0.465828	−	0.465828i	0.900560	+	0.434732i	$0.143157\pi$
$104$		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	$-0.668060\pi$
$107$	−2.57774	+	1.06774i	−0.249200	+	0.103222i	0.254587	+	0.967050i	$0.418060\pi$
$108$		0			0
$109$	3.46094	−	8.35544i	0.331498	−	0.800306i	−0.666976	−	0.745079i	$-0.732412\pi$
$109$	3.46094	−	8.35544i	0.331498	−	0.800306i	0.998474	−	0.0552270i	$-0.0175882\pi$
$110$		0			0
$111$			3.29316i			0.312573i
$112$		0			0
$113$			11.7757i			1.10776i	0.832596	+	0.553881i	$0.186854\pi$
$113$			11.7757i			1.10776i	−0.832596	+	0.553881i	$0.813146\pi$
$114$		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	$-0.275218\pi$
$131$	6.52146	+	2.70128i	0.569783	+	0.236012i	−0.0791431	+	0.996863i	$0.525218\pi$
$132$		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	0.884178	−	0.467151i	$-0.154719\pi$
$137$	4.88118	+	4.88118i	0.417027	+	0.417027i	−0.467151	+	0.884178i	$0.654719\pi$
$138$		0			0
$139$	11.7837	−	4.88098i	0.999482	−	0.413999i	0.177875	−	0.984053i	$-0.443078\pi$
$139$	11.7837	−	4.88098i	0.999482	−	0.413999i	0.821607	+	0.570054i	$0.193078\pi$
$140$		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	$-0.706884\pi$
$149$	−5.73838	+	2.37691i	−0.470106	+	0.194724i	0.135038	+	0.990840i	$0.456884\pi$
$150$		0			0
$151$	−11.1504	−	11.1504i	−0.907405	−	0.907405i	0.0886573	−	0.996062i	$-0.471742\pi$
$151$	−11.1504	−	11.1504i	−0.907405	−	0.907405i	−0.996062	+	0.0886573i	$0.971742\pi$
$152$		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	$-0.358151\pi$
$157$	1.22496	+	0.507395i	0.0977624	+	0.0404945i	−0.333266	+	0.942833i	$0.608151\pi$
$158$		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	$-0.734252\pi$
$163$	−21.3218	−	8.83176i	−1.67005	−	0.691757i	−0.998776	+	0.0494542i	$0.984252\pi$
$164$		0			0
$165$	6.97186	+	16.8316i	0.542759	+	1.31034i
$166$		0			0
$167$	−10.8863	+	10.8863i	−0.842404	+	0.842404i	−0.989171	−	0.146767i	$-0.953113\pi$
$167$	−10.8863	+	10.8863i	−0.842404	+	0.842404i	0.146767	+	0.989171i	$0.453113\pi$
$168$		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	$-0.851731\pi$
$173$	0.735246	−	1.77504i	0.0558997	−	0.134954i	0.949362	+	0.314184i	$0.101731\pi$
$174$		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	$-0.816233\pi$
$179$	1.87980	−	4.53823i	0.140503	−	0.339203i	0.978430	+	0.206578i	$0.0662329\pi$
$180$		0			0
$181$	1.87868	−	0.778175i	0.139641	−	0.0578413i	−0.311768	−	0.950158i	$-0.600921\pi$
$181$	1.87868	−	0.778175i	0.139641	−	0.0578413i	0.451410	+	0.892317i	$0.350921\pi$
$182$		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	$-0.127564\pi$
$197$	−0.0865175	−	0.208872i	−0.00616412	−	0.0148815i	−0.926932	+	0.375230i	$0.877564\pi$
$198$		0			0
$199$	11.8992	−	11.8992i	0.843513	−	0.843513i	−0.145801	−	0.989314i	$-0.546576\pi$
$199$	11.8992	−	11.8992i	0.843513	−	0.843513i	0.989314	+	0.145801i	$0.0465759\pi$
$200$		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	$-0.766075\pi$
$211$	3.73060	−	9.00647i	0.256825	−	0.620031i	0.998725	+	0.0504799i	$0.0160751\pi$
$212$		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	$-0.263994\pi$
$227$	9.51294	+	3.94039i	0.631396	+	0.261533i	−0.0439500	+	0.999034i	$0.513994\pi$
$228$		0			0
$229$	−6.53200	−	15.7697i	−0.431647	−	1.04209i	−0.978756	−	0.205027i	$-0.934272\pi$
$229$	−6.53200	−	15.7697i	−0.431647	−	1.04209i	0.547109	−	0.837061i	$-0.315728\pi$
$230$		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	$-0.0891751\pi$
$233$	10.4486	+	10.4486i	0.684512	+	0.684512i	−0.276502	+	0.961013i	$0.589175\pi$
$234$		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	$0.123231\pi$
$239$			11.6733i			0.755085i	−0.925992	+	0.377543i	$0.876769\pi$
$240$		0			0
$241$		−	13.8288i		−	0.890791i	−0.895334	−	0.445396i	$-0.853063\pi$
$241$		−	13.8288i		−	0.890791i	0.895334	−	0.445396i	$-0.146937\pi$
$242$		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	−0.997710	−	0.0676429i	$-0.978452\pi$
$251$	−5.38745	−	13.0065i	−0.340053	−	0.820961i	0.657656	−	0.753318i	$-0.271548\pi$
$252$		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	−0.991060	−	0.133417i	$-0.957405\pi$
$263$	−13.9086	+	13.9086i	−0.857643	+	0.857643i	0.133417	+	0.991060i	$0.457405\pi$
$264$		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	−0.691737	−	0.722149i	$-0.743154\pi$
$269$	5.05209	−	12.1968i	0.308031	−	0.743653i	0.999769	−	0.0215042i	$-0.00684553\pi$
$270$		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
$275$	−2.42579	+	5.85637i	−0.146280	+	0.353152i
$276$		0			0
$277$	−23.0454	+	9.54573i	−1.38467	+	0.573547i	−0.945725	−	0.324969i	$-0.894646\pi$
$277$	−23.0454	+	9.54573i	−1.38467	+	0.573547i	−0.438941	+	0.898516i	$0.644646\pi$
$278$		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	$-0.829162\pi$
$281$	−5.83509	+	5.83509i	−0.348092	+	0.348092i	0.511306	+	0.859399i	$0.329162\pi$
$282$		0			0
$283$	−1.31992	−	3.18656i	−0.0784609	−	0.189421i	0.879782	−	0.475378i	$-0.157689\pi$
$283$	−1.31992	−	3.18656i	−0.0784609	−	0.189421i	−0.958243	+	0.285957i	$0.907689\pi$
$284$		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	$-0.0540353\pi$
$293$	2.89663	+	6.99307i	0.169223	+	0.408540i	−0.816403	+	0.577482i	$0.804035\pi$
$294$		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	$-0.799652\pi$
$307$	3.14481	−	7.59225i	0.179484	−	0.433313i	0.987859	+	0.155356i	$0.0496524\pi$
$308$		0			0
$309$	15.2360	−	6.31095i	0.866744	−	0.359017i
$310$		0			0
$311$	15.0543	+	15.0543i	0.853651	+	0.853651i	0.990581	−	0.136930i	$-0.0437234\pi$
$311$	15.0543	+	15.0543i	0.853651	+	0.853651i	−0.136930	+	0.990581i	$0.543723\pi$
$312$		0			0
$313$	18.3365	−	18.3365i	1.03644	−	1.03644i	0.0371274	−	0.999311i	$-0.488179\pi$
$313$	18.3365	−	18.3365i	1.03644	−	1.03644i	0.999311	−	0.0371274i	$-0.0118208\pi$
$314$		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	$-0.468483\pi$
$317$	−9.52348	−	3.94476i	−0.534892	−	0.221560i	−0.633744	+	0.773543i	$0.718483\pi$
$318$		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	$-0.697339\pi$
$331$	−7.57421	+	3.13734i	−0.416316	+	0.172444i	0.164685	+	0.986346i	$0.447339\pi$
$332$		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	$0.152170\pi$
$337$			16.8910i			0.920110i	−0.887890	+	0.460055i	$0.847830\pi$
$338$		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	0.844739	+	0.535179i	$0.179756\pi$
$347$	11.6582	+	28.1455i	0.625847	+	1.51093i	−0.218892	+	0.975749i	$0.570244\pi$
$348$		0			0
$349$	9.99044	+	4.13818i	0.534776	+	0.221512i	0.633694	−	0.773584i	$-0.281538\pi$
$349$	9.99044	+	4.13818i	0.534776	+	0.221512i	−0.0989174	+	0.995096i	$0.531538\pi$
$350$		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	−0.803072	−	0.595882i	$-0.796802\pi$
$359$	−3.92568	+	3.92568i	−0.207190	+	0.207190i	0.595882	+	0.803072i	$0.296802\pi$
$360$		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	$-0.858508\pi$
$367$		−	16.4759i		−	0.860033i	0.902821	−	0.430016i	$-0.141492\pi$
$368$		0			0
$369$			7.28281i			0.379128i
$370$		0			0
$371$	1.79021	−	4.32195i	0.0929431	−	0.224384i
$372$		0			0
$373$	−12.6790	+	5.25180i	−0.656492	+	0.271928i	−0.685962	−	0.727638i	$-0.740618\pi$
$373$	−12.6790	+	5.25180i	−0.656492	+	0.271928i	0.0294695	+	0.999566i	$0.490618\pi$
$374$		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	$-0.0145406\pi$
$379$	5.06746	+	12.2339i	0.260298	+	0.628414i	−0.738659	+	0.674079i	$0.764541\pi$
$380$		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	0.661617	+	0.749842i	$0.269871\pi$
$389$	14.2795	+	34.4739i	0.724002	+	1.74789i	0.0623850	+	0.998052i	$0.480129\pi$
$390$		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	−0.527975	−	0.849260i	$-0.677048\pi$
$397$	8.88405	−	21.4480i	0.445877	−	1.07644i	0.973852	−	0.227183i	$-0.0729516\pi$
$398$		0			0
$399$			1.18100i			0.0591238i
$400$		0			0
$401$			2.51509i			0.125598i	0.998026	+	0.0627989i	$0.0200027\pi$
$401$			2.51509i			0.125598i	−0.998026	+	0.0627989i	$0.979997\pi$
$402$		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	−0.826428	−	0.563042i	$-0.809631\pi$
$409$	−5.32666	+	5.32666i	−0.263386	+	0.263386i	0.563042	+	0.826428i	$0.309631\pi$
$410$		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	$-0.464988\pi$
$419$	−10.5509	−	4.37032i	−0.515444	−	0.213504i	−0.625214	+	0.780453i	$0.714988\pi$
$420$		0			0
$421$	1.72505	+	4.16464i	0.0840739	+	0.202972i	0.960326	−	0.278881i	$-0.0899636\pi$
$421$	1.72505	+	4.16464i	0.0840739	+	0.202972i	−0.876252	+	0.481854i	$0.839964\pi$
$422$		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	$0.134104\pi$
$431$			16.9800i			0.817897i	−0.912557	+	0.408949i	$0.865896\pi$
$432$		0			0
$433$			16.9567i			0.814886i	0.913231	+	0.407443i	$0.133579\pi$
$433$			16.9567i			0.814886i	−0.913231	+	0.407443i	$0.866421\pi$
$434$		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	0.408691	−	0.912673i	$-0.365985\pi$
$439$	−10.5596	−	10.5596i	−0.503982	−	0.503982i	−0.912673	+	0.408691i	$0.865985\pi$
$440$		0			0
$441$	−13.3358	+	13.3358i	−0.635039	+	0.635039i
$442$		0			0
$443$	−6.31087	−	15.2358i	−0.299838	−	0.723874i	−0.999952	−	0.00984190i	$-0.996867\pi$
$443$	−6.31087	−	15.2358i	−0.299838	−	0.723874i	0.700113	−	0.714032i	$-0.253133\pi$
$444$		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	0.504191	−	0.863592i	$-0.331791\pi$
$457$	−7.68314	−	7.68314i	−0.359402	−	0.359402i	−0.863592	+	0.504191i	$0.831791\pi$
$458$		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	$-0.991934\pi$
$461$	−5.90199	+	14.2487i	−0.274883	+	0.663627i	0.724796	+	0.688964i	$0.241934\pi$
$462$		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
$467$	9.40577	−	22.7075i	0.435247	−	1.05078i	−0.542323	−	0.840170i	$-0.682455\pi$
$467$	9.40577	−	22.7075i	0.435247	−	1.05078i	0.977570	−	0.210610i	$-0.0675449\pi$
$468$		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	−0.498005	−	0.867174i	$-0.665934\pi$
$487$	8.14685	−	8.14685i	0.369169	−	0.369169i	0.867174	+	0.498005i	$0.165934\pi$
$488$		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	$-0.713913\pi$
$491$	−11.2886	+	4.67590i	−0.509448	+	0.211020i	0.113127	+	0.993581i	$0.463913\pi$
$492$		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	0.357944	+	0.933743i	$0.383478\pi$
$499$	−12.4071	+	29.9533i	−0.555417	+	1.34089i	−0.913361	+	0.407152i	$0.866522\pi$
$500$		0			0
$501$	−35.0836	+	14.5321i	−1.56742	+	0.649247i
$502$		0			0
$503$	−8.77059	−	8.77059i	−0.391061	−	0.391061i	0.484004	−	0.875066i	$-0.339182\pi$
$503$	−8.77059	−	8.77059i	−0.391061	−	0.391061i	−0.875066	+	0.484004i	$0.839182\pi$
$504$		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	$-0.214857\pi$
$509$	20.0994	+	8.32546i	0.890892	+	0.369020i	0.110181	+	0.993912i	$0.464857\pi$
$510$		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	−0.921741	−	0.387807i	$-0.873233\pi$
$521$	−29.8910	−	29.8910i	−1.30955	−	1.30955i	−0.387807	−	0.921741i	$-0.626767\pi$
$522$		0			0
$523$	−32.7654	+	13.5719i	−1.43273	+	0.593456i	−0.958024	−	0.286688i	$-0.907446\pi$
$523$	−32.7654	+	13.5719i	−1.43273	+	0.593456i	−0.474706	+	0.880144i	$0.657446\pi$
$524$		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	$-0.459630\pi$
$541$	−11.2925	−	4.67751i	−0.485502	−	0.201102i	−0.611988	+	0.790867i	$0.709630\pi$
$542$		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	$-0.229069\pi$
$547$	19.1256	+	7.92207i	0.817750	+	0.338723i	0.0657087	+	0.997839i	$0.479069\pi$
$548$		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	−0.411753	−	0.911295i	$-0.635084\pi$
$557$	12.3617	−	29.8439i	0.523783	−	1.26452i	0.935537	−	0.353229i	$-0.114916\pi$
$558$		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	−0.529444	−	0.848345i	$-0.677600\pi$
$563$	10.5540	−	25.4797i	0.444800	−	1.07384i	0.974244	−	0.225497i	$-0.0724004\pi$
$564$		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	−0.999996	−	0.00285688i	$-0.999091\pi$
$569$	−23.7855	+	23.7855i	−0.997139	+	0.997139i	0.00285688	+	0.999996i	$0.499091\pi$
$570$		0			0
$571$	0.904405	+	2.18343i	0.0378482	+	0.0913736i	0.941673	−	0.336528i	$-0.109253\pi$
$571$	0.904405	+	2.18343i	0.0378482	+	0.0913736i	−0.903825	+	0.427902i	$0.859253\pi$
$572$		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	$-0.270550\pi$
$587$	40.1685	−	16.6383i	1.65793	−	0.686738i	0.997917	+	0.0645151i	$0.0205501\pi$
$588$		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	$-0.940160\pi$
$593$		−	9.10197i		−	0.373773i	0.982382	−	0.186886i	$-0.0598397\pi$
$594$		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	0.642160	−	0.766571i	$-0.278038\pi$
$599$	−3.04488	−	3.04488i	−0.124410	−	0.124410i	−0.766571	+	0.642160i	$0.778038\pi$
$600$		0			0
$601$	9.53880	−	9.53880i	0.389096	−	0.389096i	−0.485269	−	0.874365i	$-0.661278\pi$
$601$	9.53880	−	9.53880i	0.389096	−	0.389096i	0.874365	+	0.485269i	$0.161278\pi$
$602$		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	−0.964788	−	0.263029i	$-0.915278\pi$
$613$	−11.6012	−	28.0079i	−0.468570	−	1.13123i	0.496218	−	0.868198i	$-0.334722\pi$
$614$		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	$-0.196642\pi$
$617$	5.86100	+	5.86100i	0.235955	+	0.235955i	−0.579218	+	0.815173i	$0.696642\pi$
$618$		0			0
$619$	36.9173	−	15.2917i	1.48383	−	0.614624i	0.513868	−	0.857869i	$-0.328212\pi$
$619$	36.9173	−	15.2917i	1.48383	−	0.614624i	0.969965	+	0.243245i	$0.0782120\pi$
$620$		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	0.988616	−	0.150458i	$-0.0480748\pi$
$631$	21.0543	+	21.0543i	0.838159	+	0.838159i	−0.150458	+	0.988616i	$0.548075\pi$
$632$		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	$-0.202990\pi$
$643$	24.1050	+	9.98462i	0.950608	+	0.393755i	0.147149	+	0.989114i	$0.452990\pi$
$644$		0			0
$645$	−4.81324	−	11.6202i	−0.189521	−	0.457545i
$646$		0			0
$647$	−19.1598	+	19.1598i	−0.753250	+	0.753250i	−0.975084	−	0.221835i	$-0.928795\pi$
$647$	−19.1598	+	19.1598i	−0.753250	+	0.753250i	0.221835	+	0.975084i	$0.428795\pi$
$648$		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	$-0.969702\pi$
$653$	−5.73339	+	13.8416i	−0.224365	+	0.541665i	0.771109	+	0.636703i	$0.219702\pi$
$654$		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	$-0.871718\pi$
$659$	0.202554	−	0.489009i	0.00789039	−	0.0190491i	0.927776	+	0.373139i	$0.121718\pi$
$660$		0			0
$661$	6.45241	−	2.67268i	0.250970	−	0.103955i	−0.253652	−	0.967295i	$-0.581632\pi$
$661$	6.45241	−	2.67268i	0.250970	−	0.103955i	0.504622	+	0.863340i	$0.331632\pi$
$662$		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	$-0.0992798\pi$
$677$	1.60737	+	3.88054i	0.0617763	+	0.149141i	−0.889977	+	0.456005i	$0.849280\pi$
$678$		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	$-0.796778\pi$
$683$	−24.8133	+	10.2780i	−0.949455	+	0.393277i	−0.146429	+	0.989221i	$0.546778\pi$
$684$		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	0.672909	+	0.739725i	$0.265045\pi$
$691$	−8.56885	+	20.6870i	−0.325974	+	0.786972i	−0.998883	+	0.0472463i	$0.984955\pi$
$692$		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	$-0.179799\pi$
$701$	28.1557	+	11.6625i	1.06343	+	0.440486i	0.218760	+	0.975779i	$0.429799\pi$
$702$		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	0.965370	+	0.260883i	$0.0840136\pi$
$709$	12.4408	+	30.0346i	0.467223	+	1.12797i	−0.498148	+	0.867092i	$0.665986\pi$
$710$		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	$-0.784219\pi$
$719$		−	33.6333i		−	1.25431i	0.778894	−	0.627155i	$-0.215781\pi$
$720$		0			0
$721$		−	6.28867i		−	0.234202i
$722$		0			0
$723$	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	0.831385	−	0.555697i	$-0.187549\pi$
$727$	7.43334	+	7.43334i	0.275687	+	0.275687i	−0.555697	+	0.831385i	$0.687549\pi$
$728$		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	$-0.377091\pi$
$733$	−0.328598	−	0.136110i	−0.0121371	−	0.00502733i	−0.388744	+	0.921346i	$0.627091\pi$
$734$		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	$-0.0367234\pi$
$739$	43.8857	+	18.1780i	1.61436	+	0.668690i	0.621008	+	0.783804i	$0.286723\pi$
$740$		0			0
$741$	−2.21803	−	5.35480i	−0.0814814	−	0.196714i
$742$		0			0
$743$	30.3220	−	30.3220i	1.11240	−	1.11240i	0.119580	−	0.992825i	$-0.461845\pi$
$743$	30.3220	−	30.3220i	1.11240	−	1.11240i	0.992825	−	0.119580i	$-0.0381548\pi$
$744$		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	$-0.613377\pi$
$751$		−	51.3686i		−	1.87447i	0.348701	−	0.937234i	$-0.386623\pi$
$752$		0			0
$753$		−	34.7248i		−	1.26544i
$754$		0			0
$755$	−11.1504	+	26.9194i	−0.405804	+	0.979697i
$756$		0			0
$757$	15.2644	−	6.32270i	0.554793	−	0.229803i	−0.0876302	−	0.996153i	$-0.527929\pi$
$757$	15.2644	−	6.32270i	0.554793	−	0.229803i	0.642423	+	0.766350i	$0.277929\pi$
$758$		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	$-0.510226\pi$
$761$	26.6859	−	26.6859i	0.967362	−	0.967362i	0.999484	+	0.0321218i	$0.0102264\pi$
$762$		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	−0.914526	−	0.404526i	$-0.867436\pi$
$773$	−15.4001	−	37.1790i	−0.553902	−	1.33724i	0.360625	−	0.932711i	$-0.382564\pi$
$774$		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	$-0.889068\pi$
$787$	−0.948632	+	2.29020i	−0.0338151	+	0.0816368i	0.906070	+	0.423128i	$0.139068\pi$
$788$		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	$-0.391884\pi$
$797$	−2.76562	−	1.14556i	−0.0979632	−	0.0405777i	−0.431127	+	0.902291i	$0.641884\pi$
$798$		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	0.570607	−	0.821223i	$-0.306708\pi$
$809$	−7.12825	−	7.12825i	−0.250616	−	0.250616i	−0.821223	+	0.570607i	$0.806708\pi$
$810$		0			0
$811$	−27.4750	+	11.3805i	−0.964777	+	0.399624i	−0.808765	−	0.588131i	$-0.799864\pi$
$811$	−27.4750	+	11.3805i	−0.964777	+	0.399624i	−0.156012	+	0.987755i	$0.549864\pi$
$812$		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	$-0.401565\pi$
$821$	34.1861	−	14.1603i	1.19310	−	0.494199i	0.888764	+	0.458364i	$0.151565\pi$
$822$		0			0
$823$	−27.3810	−	27.3810i	−0.954440	−	0.954440i	0.0445659	−	0.999006i	$-0.485810\pi$
$823$	−27.3810	−	27.3810i	−0.954440	−	0.954440i	−0.999006	+	0.0445659i	$0.985810\pi$
$824$		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	$-0.243102\pi$
$827$	−7.98030	−	19.2661i	−0.277502	−	0.669950i	−0.999765	+	0.0216689i	$0.993102\pi$
$828$		0			0
$829$	−3.59585	−	1.48945i	−0.124889	−	0.0517307i	0.319364	−	0.947632i	$-0.396531\pi$
$829$	−3.59585	−	1.48945i	−0.124889	−	0.0517307i	−0.444253	+	0.895901i	$0.646531\pi$
$830$		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	−0.904498	−	0.426478i	$-0.859754\pi$
$839$	−13.8461	+	13.8461i	−0.478020	+	0.478020i	0.426478	+	0.904498i	$0.359754\pi$
$840$		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	$-0.516382\pi$
$853$	18.0597	−	7.48055i	0.618351	−	0.256129i	0.669794	+	0.742547i	$0.266382\pi$
$854$		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	$-0.799039\pi$
$857$	−6.35294	+	6.35294i	−0.217012	+	0.217012i	0.590226	+	0.807238i	$0.299039\pi$
$858$		0			0
$859$	−9.72800	−	23.4855i	−0.331915	−	0.801314i	−0.998440	−	0.0558315i	$-0.982219\pi$
$859$	−9.72800	−	23.4855i	−0.331915	−	0.801314i	0.666525	−	0.745483i	$-0.267781\pi$
$860$		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	$-0.934971\pi$
$877$	−4.24514	+	10.2487i	−0.143348	+	0.346073i	0.835857	+	0.548948i	$0.184971\pi$
$878$		0			0
$879$			18.6702i			0.629729i
$880$		0			0
$881$			23.9859i			0.808105i	0.914736	+	0.404052i	$0.132399\pi$
$881$			23.9859i			0.808105i	−0.914736	+	0.404052i	$0.867601\pi$
$882$		0			0
$883$	7.74892	−	18.7075i	0.260772	−	0.629559i	−0.738215	−	0.674566i	$-0.764331\pi$
$883$	7.74892	−	18.7075i	0.260772	−	0.629559i	0.998987	+	0.0450067i	$0.0143309\pi$
$884$		0			0
$885$	−22.5326	+	9.33333i	−0.757426	+	0.313736i
$886$		0			0
$887$	36.4494	+	36.4494i	1.22385	+	1.22385i	0.966252	+	0.257600i	$0.0829315\pi$
$887$	36.4494	+	36.4494i	1.22385	+	1.22385i	0.257600	+	0.966252i	$0.417068\pi$
$888$		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	$-0.383572\pi$
$907$	38.2753	−	15.8541i	1.27091	−	0.526428i	0.913241	+	0.407421i	$0.133572\pi$
$908$		0			0
$909$	9.55032	−	23.0565i	0.316764	−	0.764737i
$910$		0			0
$911$			12.5214i			0.414851i	0.978251	+	0.207426i	$0.0665085\pi$
$911$			12.5214i			0.414851i	−0.978251	+	0.207426i	$0.933492\pi$
$912$		0			0
$913$		−	50.4497i		−	1.66964i
$914$		0			0
$915$	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	0.687120	−	0.726544i	$-0.258875\pi$
$919$	−1.19513	−	1.19513i	−0.0394238	−	0.0394238i	−0.726544	+	0.687120i	$0.758875\pi$
$920$		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	0.747993	−	0.663707i	$-0.231018\pi$
$937$	2.58002	+	2.58002i	0.0842857	+	0.0842857i	−0.663707	+	0.747993i	$0.731018\pi$
$938$		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	$-0.844486\pi$
$941$	2.24720	−	5.42523i	0.0732568	−	0.176857i	0.956266	+	0.292498i	$0.0944864\pi$
$942$		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	0.330162	+	0.943924i	$0.392897\pi$
$947$	−17.5640	+	42.4032i	−0.570753	+	1.37792i	−0.900915	+	0.433996i	$0.857103\pi$
$948$		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	−0.425354	−	0.905027i	$-0.639850\pi$
$953$	14.8079	−	14.8079i	0.479673	−	0.479673i	0.905027	+	0.425354i	$0.139850\pi$
$954$		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	−0.983010	−	0.183554i	$-0.941240\pi$
$967$	−24.8604	+	24.8604i	−0.799455	+	0.799455i	0.183554	+	0.983010i	$0.441240\pi$
$968$		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	$-0.492152\pi$
$971$	23.3388	−	9.66725i	0.748978	−	0.310237i	0.724324	+	0.689459i	$0.242152\pi$
$972$		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	$0.339201\pi$
$977$			54.7057i			1.75019i	−0.483952	+	0.875094i	$0.660799\pi$
$978$		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	0.821166	−	0.570689i	$-0.193324\pi$
$983$	7.85315	+	7.85315i	0.250477	+	0.250477i	−0.570689	+	0.821166i	$0.693324\pi$
$984$		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	0.985988	+	0.166815i	$0.0533483\pi$
$997$	12.8431	+	31.0060i	0.406745	+	0.981970i	−0.579243	+	0.815155i	$0.696652\pi$
$998$		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	128.2.g.b.81.2		8
3.2	odd	2		1152.2.v.b.721.1		8
4.3	odd	2		32.2.g.b.29.2	yes	8
8.3	odd	2		256.2.g.d.161.2		8
8.5	even	2		256.2.g.c.161.1		8
12.11	even	2		288.2.v.b.253.1		8
16.3	odd	4		512.2.g.e.65.2		8
16.5	even	4		512.2.g.f.65.2		8
16.11	odd	4		512.2.g.h.65.1		8
16.13	even	4		512.2.g.g.65.1		8
20.3	even	4		800.2.ba.c.349.2		8
20.7	even	4		800.2.ba.d.349.1		8
20.19	odd	2		800.2.y.b.701.1		8
32.3	odd	8		512.2.g.h.449.1		8
32.5	even	8		256.2.g.c.97.1		8
32.11	odd	8		32.2.g.b.21.2	✓	8
32.13	even	8		512.2.g.g.449.1		8
32.19	odd	8		512.2.g.e.449.2		8
32.21	even	8	inner	128.2.g.b.49.2		8
32.27	odd	8		256.2.g.d.97.2		8
32.29	even	8		512.2.g.f.449.2		8
64.11	odd	16		4096.2.a.k.1.2		8
64.21	even	16		4096.2.a.q.1.2		8
64.43	odd	16		4096.2.a.k.1.7		8
64.53	even	16		4096.2.a.q.1.7		8
96.11	even	8		288.2.v.b.181.1		8
96.53	odd	8		1152.2.v.b.433.1		8
160.43	even	8		800.2.ba.d.149.1		8
160.107	even	8		800.2.ba.c.149.2		8
160.139	odd	8		800.2.y.b.501.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.21.2	✓	8	32.11	odd	8
32.2.g.b.29.2	yes	8	4.3	odd	2
128.2.g.b.49.2		8	32.21	even	8	inner
128.2.g.b.81.2		8	1.1	even	1	trivial
256.2.g.c.97.1		8	32.5	even	8
256.2.g.c.161.1		8	8.5	even	2
256.2.g.d.97.2		8	32.27	odd	8
256.2.g.d.161.2		8	8.3	odd	2
288.2.v.b.181.1		8	96.11	even	8
288.2.v.b.253.1		8	12.11	even	2
512.2.g.e.65.2		8	16.3	odd	4
512.2.g.e.449.2		8	32.19	odd	8
512.2.g.f.65.2		8	16.5	even	4
512.2.g.f.449.2		8	32.29	even	8
512.2.g.g.65.1		8	16.13	even	4
512.2.g.g.449.1		8	32.13	even	8
512.2.g.h.65.1		8	16.11	odd	4
512.2.g.h.449.1		8	32.3	odd	8
800.2.y.b.501.1		8	160.139	odd	8
800.2.y.b.701.1		8	20.19	odd	2
800.2.ba.c.149.2		8	160.107	even	8
800.2.ba.c.349.2		8	20.3	even	4
800.2.ba.d.149.1		8	160.43	even	8
800.2.ba.d.349.1		8	20.7	even	4
1152.2.v.b.433.1		8	96.53	odd	8
1152.2.v.b.721.1		8	3.2	odd	2
4096.2.a.k.1.2		8	64.11	odd	16
4096.2.a.k.1.7		8	64.43	odd	16
4096.2.a.q.1.2		8	64.21	even	16
4096.2.a.q.1.7		8	64.53	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.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

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