LMFDB - Embedded newform 460.2.s.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(9,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 10]))

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

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

chi := DirichletCharacter("460.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.s (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			9.2
Character	$\chi$	$=$	460.9
Dual form			460.2.s.a.409.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90027 + 1.64660i) q^{3} +(-2.22785 + 0.191526i) q^{5} +(-1.95670 - 0.893593i) q^{7} +(0.472816 - 3.28851i) q^{9} +O(q^{10})$	\(q+(-1.90027 + 1.64660i) q^{3} +(-2.22785 + 0.191526i) q^{5} +(-1.95670 - 0.893593i) q^{7} +(0.472816 - 3.28851i) q^{9} +(0.567111 + 0.166519i) q^{11} +(2.14319 - 0.978763i) q^{13} +(3.91816 - 4.03232i) q^{15} +(2.55726 - 3.97918i) q^{17} +(-2.84242 + 1.82671i) q^{19} +(5.18964 - 1.52382i) q^{21} +(4.78020 - 0.386862i) q^{23} +(4.92664 - 0.853381i) q^{25} +(0.438164 + 0.681796i) q^{27} +(-3.73961 - 2.40330i) q^{29} +(0.880493 - 1.01614i) q^{31} +(-1.35186 + 0.617372i) q^{33} +(4.53037 + 1.61603i) q^{35} +(9.77632 + 1.40562i) q^{37} +(-2.46102 + 5.38889i) q^{39} +(-1.46991 - 10.2234i) q^{41} +(-4.71465 + 4.08527i) q^{43} +(-0.423529 + 7.41685i) q^{45} -5.32725i q^{47} +(-1.55388 - 1.79327i) q^{49} +(1.69260 + 11.7723i) q^{51} +(-5.18487 - 2.36785i) q^{53} +(-1.29533 - 0.262363i) q^{55} +(2.39352 - 8.15158i) q^{57} +(-2.79321 - 6.11627i) q^{59} +(4.07329 - 4.70083i) q^{61} +(-3.86374 + 6.01210i) q^{63} +(-4.58725 + 2.59101i) q^{65} +(-1.22613 - 4.17582i) q^{67} +(-8.44669 + 8.60621i) q^{69} +(-6.69267 + 1.96514i) q^{71} +(-2.92446 - 4.55055i) q^{73} +(-7.95678 + 9.73384i) q^{75} +(-0.960864 - 0.832593i) q^{77} +(6.76581 + 14.8151i) q^{79} +(7.60796 + 2.23390i) q^{81} +(-7.46383 - 1.07314i) q^{83} +(-4.93509 + 9.35480i) q^{85} +(11.0636 - 1.59070i) q^{87} +(-6.22717 - 7.18654i) q^{89} -5.06819 q^{91} +3.38077i q^{93} +(5.98263 - 4.61404i) q^{95} +(-5.01954 + 0.721701i) q^{97} +(0.815737 - 1.78622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{9}+O(q^{10}) $ 120 * q + 20 * q^9	$ 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) $ 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{11}\right)$

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
$3$	−1.90027	+	1.64660i	−1.09712	+	0.950663i	−0.999009	−	0.0445121i	$-0.985827\pi$
$3$	−1.90027	+	1.64660i	−1.09712	+	0.950663i	−0.0981148	+	0.995175i	$0.531281\pi$
$4$		0			0
$5$	−2.22785	+	0.191526i	−0.996325	+	0.0856529i
$5$	−2.22785	+	0.191526i	−0.996325	+	0.0856529i
$6$		0			0
$7$	−1.95670	−	0.893593i	−0.739561	−	0.337746i	0.00976052	−	0.999952i	$-0.496893\pi$
$7$	−1.95670	−	0.893593i	−0.739561	−	0.337746i	−0.749322	+	0.662206i	$0.769620\pi$
$8$		0			0
$9$	0.472816	−	3.28851i	0.157605	−	1.09617i
$10$		0			0
$11$	0.567111	+	0.166519i	0.170990	+	0.0502073i	0.366107	−	0.930573i	$-0.380690\pi$
$11$	0.567111	+	0.166519i	0.170990	+	0.0502073i	−0.195117	+	0.980780i	$0.562509\pi$
$12$		0			0
$13$	2.14319	−	0.978763i	0.594415	−	0.271460i	−0.0954082	−	0.995438i	$-0.530416\pi$
$13$	2.14319	−	0.978763i	0.594415	−	0.271460i	0.689823	+	0.723978i	$0.257688\pi$
$14$		0			0
$15$	3.91816	−	4.03232i	1.01166	−	1.04114i
$16$		0			0
$17$	2.55726	−	3.97918i	0.620228	−	0.965093i	−0.378985	−	0.925403i	$-0.623727\pi$
$17$	2.55726	−	3.97918i	0.620228	−	0.965093i	0.999212	−	0.0396898i	$-0.0126370\pi$
$18$		0			0
$19$	−2.84242	+	1.82671i	−0.652096	+	0.419077i	−0.824432	−	0.565962i	$-0.808505\pi$
$19$	−2.84242	+	1.82671i	−0.652096	+	0.419077i	0.172335	+	0.985038i	$0.444869\pi$
$20$		0			0
$21$	5.18964	−	1.52382i	1.13247	−	0.332524i
$22$		0			0
$23$	4.78020	−	0.386862i	0.996741	−	0.0806664i
$23$	4.78020	−	0.386862i	0.996741	−	0.0806664i
$24$		0			0
$25$	4.92664	−	0.853381i	0.985327	−	0.170676i
$26$		0			0
$27$	0.438164	+	0.681796i	0.0843247	+	0.131212i
$28$		0			0
$29$	−3.73961	−	2.40330i	−0.694429	−	0.446282i	0.145229	−	0.989398i	$-0.453608\pi$
$29$	−3.73961	−	2.40330i	−0.694429	−	0.446282i	−0.839658	+	0.543116i	$0.817244\pi$
$30$		0			0
$31$	0.880493	−	1.01614i	0.158141	−	0.182505i	−0.671150	−	0.741322i	$-0.734199\pi$
$31$	0.880493	−	1.01614i	0.158141	−	0.182505i	0.829291	+	0.558817i	$0.188745\pi$
$32$		0			0
$33$	−1.35186	+	0.617372i	−0.235328	+	0.107471i
$34$		0			0
$35$	4.53037	+	1.61603i	0.765772	+	0.273160i
$36$		0			0
$37$	9.77632	+	1.40562i	1.60722	+	0.231083i	0.886697	−	0.462351i	$-0.152994\pi$
$37$	9.77632	+	1.40562i	1.60722	+	0.231083i	0.720520	+	0.693434i	$0.243903\pi$
$38$		0			0
$39$	−2.46102	+	5.38889i	−0.394079	+	0.862913i
$40$		0			0
$41$	−1.46991	−	10.2234i	−0.229561	−	1.59663i	−0.699964	−	0.714178i	$-0.746801\pi$
$41$	−1.46991	−	10.2234i	−0.229561	−	1.59663i	0.470403	−	0.882452i	$-0.344108\pi$
$42$		0			0
$43$	−4.71465	+	4.08527i	−0.718977	+	0.622997i	−0.935519	−	0.353276i	$-0.885068\pi$
$43$	−4.71465	+	4.08527i	−0.718977	+	0.622997i	0.216542	+	0.976273i	$0.430522\pi$
$44$		0			0
$45$	−0.423529	+	7.41685i	−0.0631360	+	1.10564i
$46$		0			0
$47$		−	5.32725i		−	0.777060i	−0.921436	−	0.388530i	$-0.872983\pi$
$47$		−	5.32725i		−	0.777060i	0.921436	−	0.388530i	$-0.127017\pi$
$48$		0			0
$49$	−1.55388	−	1.79327i	−0.221982	−	0.256181i
$50$		0			0
$51$	1.69260	+	11.7723i	0.237012	+	1.64845i
$52$		0			0
$53$	−5.18487	−	2.36785i	−0.712197	−	0.325250i	0.0261615	−	0.999658i	$-0.491672\pi$
$53$	−5.18487	−	2.36785i	−0.712197	−	0.325250i	−0.738359	+	0.674408i	$0.764399\pi$
$54$		0			0
$55$	−1.29533	−	0.262363i	−0.174662	−	0.0353770i
$56$		0			0
$57$	2.39352	−	8.15158i	0.317029	−	1.07970i
$58$		0			0
$59$	−2.79321	−	6.11627i	−0.363645	−	0.796271i	−0.999697	−	0.0246248i	$-0.992161\pi$
$59$	−2.79321	−	6.11627i	−0.363645	−	0.796271i	0.636052	−	0.771646i	$-0.280566\pi$
$60$		0			0
$61$	4.07329	−	4.70083i	0.521531	−	0.601879i	−0.432482	−	0.901642i	$-0.642362\pi$
$61$	4.07329	−	4.70083i	0.521531	−	0.601879i	0.954014	+	0.299763i	$0.0969076\pi$
$62$		0			0
$63$	−3.86374	+	6.01210i	−0.486786	+	0.757453i
$64$		0			0
$65$	−4.58725	+	2.59101i	−0.568979	+	0.321376i
$66$		0			0
$67$	−1.22613	−	4.17582i	−0.149796	−	0.510157i	0.850068	−	0.526673i	$-0.176561\pi$
$67$	−1.22613	−	4.17582i	−0.149796	−	0.510157i	−0.999864	+	0.0165158i	$0.994743\pi$
$68$		0			0
$69$	−8.44669	+	8.60621i	−1.01686	+	1.03607i
$70$		0			0
$71$	−6.69267	+	1.96514i	−0.794274	+	0.233220i	−0.653604	−	0.756837i	$-0.726744\pi$
$71$	−6.69267	+	1.96514i	−0.794274	+	0.233220i	−0.140670	+	0.990057i	$0.544926\pi$
$72$		0			0
$73$	−2.92446	−	4.55055i	−0.342282	−	0.532602i	0.626851	−	0.779139i	$-0.284344\pi$
$73$	−2.92446	−	4.55055i	−0.342282	−	0.532602i	−0.969133	+	0.246537i	$0.920707\pi$
$74$		0			0
$75$	−7.95678	+	9.73384i	−0.918770	+	1.12397i
$76$		0			0
$77$	−0.960864	−	0.832593i	−0.109501	−	0.0948828i
$78$		0			0
$79$	6.76581	+	14.8151i	0.761214	+	1.66683i	0.745098	+	0.666955i	$0.232403\pi$
$79$	6.76581	+	14.8151i	0.761214	+	1.66683i	0.0161156	+	0.999870i	$0.494870\pi$
$80$		0			0
$81$	7.60796	+	2.23390i	0.845329	+	0.248211i
$82$		0			0
$83$	−7.46383	−	1.07314i	−0.819262	−	0.117792i	−0.280075	−	0.959978i	$-0.590359\pi$
$83$	−7.46383	−	1.07314i	−0.819262	−	0.117792i	−0.539187	+	0.842186i	$0.681268\pi$
$84$		0			0
$85$	−4.93509	+	9.35480i	−0.535285	+	1.01467i
$86$		0			0
$87$	11.0636	−	1.59070i	1.18614	−	0.170541i
$88$		0			0
$89$	−6.22717	−	7.18654i	−0.660079	−	0.761772i	0.322711	−	0.946498i	$-0.395406\pi$
$89$	−6.22717	−	7.18654i	−0.660079	−	0.761772i	−0.982790	+	0.184726i	$0.940860\pi$
$90$		0			0
$91$	−5.06819			−0.531291
$92$		0			0
$93$			3.38077i			0.350569i
$94$		0			0
$95$	5.98263	−	4.61404i	0.613805	−	0.473391i
$96$		0			0
$97$	−5.01954	+	0.721701i	−0.509657	+	0.0732776i	−0.392346	−	0.919818i	$-0.628337\pi$
$97$	−5.01954	+	0.721701i	−0.509657	+	0.0732776i	−0.117311	+	0.993095i	$0.537427\pi$
$98$		0			0
$99$	0.815737	−	1.78622i	0.0819847	−	0.179521i
$100$		0			0
$101$	0.998535	−	6.94496i	0.0993580	−	0.691050i	−0.877876	−	0.478887i	$-0.841040\pi$
$101$	0.998535	−	6.94496i	0.0993580	−	0.691050i	0.977234	−	0.212163i	$-0.0680506\pi$
$102$		0			0
$103$	1.75942	−	5.99205i	0.173361	−	0.590414i	−0.826270	−	0.563274i	$-0.809542\pi$
$103$	1.75942	−	5.99205i	0.173361	−	0.590414i	0.999632	−	0.0271406i	$-0.00864018\pi$
$104$		0			0
$105$	−11.2699	+	4.38879i	−1.09983	+	0.428302i
$106$		0			0
$107$	1.26243	+	1.09390i	0.122043	+	0.105751i	0.713744	−	0.700406i	$-0.246998\pi$
$107$	1.26243	+	1.09390i	0.122043	+	0.105751i	−0.591701	+	0.806158i	$0.701543\pi$
$108$		0			0
$109$	10.7929	+	6.93619i	1.03377	+	0.664366i	0.943439	−	0.331545i	$-0.107570\pi$
$109$	10.7929	+	6.93619i	1.03377	+	0.664366i	0.0903350	+	0.995911i	$0.471206\pi$
$110$		0			0
$111$	−20.8922	+	13.4266i	−1.98300	+	1.27440i
$112$		0			0
$113$	3.36330	+	11.4544i	0.316393	+	1.07754i	0.952146	+	0.305643i	$0.0988714\pi$
$113$	3.36330	+	11.4544i	0.316393	+	1.07754i	−0.635753	+	0.771892i	$0.719310\pi$
$114$		0			0
$115$	−10.5755	+	1.77740i	−0.986169	+	0.165744i
$116$		0			0
$117$	−2.20533	−	7.51067i	−0.203883	−	0.694362i
$118$		0			0
$119$	−8.55955	+	5.50089i	−0.784653	+	0.504266i
$120$		0			0
$121$	−8.95990	−	5.75818i	−0.814537	−	0.523471i
$122$		0			0
$123$	19.6271	+	17.0070i	1.76971	+	1.53347i
$124$		0			0
$125$	−10.8124	+	2.84478i	−0.967087	+	0.254445i
$126$		0			0
$127$	4.98488	−	16.9769i	0.442337	−	1.50646i	−0.373198	−	0.927752i	$-0.621739\pi$
$127$	4.98488	−	16.9769i	0.442337	−	1.50646i	0.815534	−	0.578709i	$-0.196443\pi$
$128$		0			0
$129$	2.23234	−	15.5262i	0.196546	−	1.36701i
$130$		0			0
$131$	−4.65318	+	10.1890i	−0.406550	+	0.890220i	0.590014	+	0.807393i	$0.299122\pi$
$131$	−4.65318	+	10.1890i	−0.406550	+	0.890220i	−0.996564	+	0.0828271i	$0.973605\pi$
$132$		0			0
$133$	7.19409	−	1.03435i	0.623807	−	0.0896899i
$134$		0			0
$135$	−1.10674	−	1.43502i	−0.0952534	−	0.123507i
$136$		0			0
$137$		−	5.52772i		−	0.472265i	−0.971721	−	0.236133i	$-0.924120\pi$
$137$		−	5.52772i		−	0.472265i	0.971721	−	0.236133i	$-0.0758800\pi$
$138$		0			0
$139$	18.6860			1.58493			0.792464	−	0.609918i	$-0.208798\pi$
$139$	18.6860			1.58493			0.792464	+	0.609918i	$0.208798\pi$
$140$		0			0
$141$	8.77184	+	10.1232i	0.738722	+	0.852531i
$142$		0			0
$143$	1.37841	−	0.198186i	0.115269	−	0.0165731i
$144$		0			0
$145$	8.79159	+	4.63797i	0.730102	+	0.385162i
$146$		0			0
$147$	5.90558	+	0.849095i	0.487084	+	0.0700322i
$148$		0			0
$149$	9.91334	+	2.91082i	0.812132	+	0.238463i	0.661325	−	0.750100i	$-0.269995\pi$
$149$	9.91334	+	2.91082i	0.812132	+	0.238463i	0.150807	+	0.988563i	$0.451813\pi$
$150$		0			0
$151$	0.305390	+	0.668711i	0.0248523	+	0.0544189i	0.921651	−	0.388020i	$-0.126841\pi$
$151$	0.305390	+	0.668711i	0.0248523	+	0.0544189i	−0.896799	+	0.442439i	$0.854113\pi$
$152$		0			0
$153$	−11.8764	−	10.2910i	−0.960153	−	0.831977i
$154$		0			0
$155$	−1.76699	+	2.43245i	−0.141928	+	0.195379i
$156$		0			0
$157$	7.80335	+	12.1423i	0.622775	+	0.969057i	0.999094	+	0.0425669i	$0.0135536\pi$
$157$	7.80335	+	12.1423i	0.622775	+	0.969057i	−0.376318	+	0.926490i	$0.622810\pi$
$158$		0			0
$159$	13.7516	−	4.03783i	1.09057	−	0.320221i
$160$		0			0
$161$	−9.69910	−	3.51458i	−0.764396	−	0.276988i
$162$		0			0
$163$	−1.09456	−	3.72772i	−0.0857324	−	0.291978i	0.905455	−	0.424441i	$-0.139529\pi$
$163$	−1.09456	−	3.72772i	−0.0857324	−	0.291978i	−0.991188	+	0.132464i	$0.957711\pi$
$164$		0			0
$165$	2.89349	−	1.63433i	0.225258	−	0.127232i
$166$		0			0
$167$	10.5369	−	16.3957i	0.815370	−	1.26874i	−0.144838	−	0.989455i	$-0.546266\pi$
$167$	10.5369	−	16.3957i	0.815370	−	1.26874i	0.960208	−	0.279285i	$-0.0900975\pi$
$168$		0			0
$169$	−4.87789	+	5.62939i	−0.375223	+	0.433030i
$170$		0			0
$171$	4.66322	+	10.2110i	0.356605	+	0.780856i
$172$		0			0
$173$	0.569087	−	1.93813i	0.0432669	−	0.147353i	−0.935027	−	0.354577i	$-0.884625\pi$
$173$	0.569087	−	1.93813i	0.0432669	−	0.147353i	0.978294	+	0.207224i	$0.0664429\pi$
$174$		0			0
$175$	−10.4025	−	2.73260i	−0.786355	−	0.206565i
$176$		0			0
$177$	15.3789	+	7.02331i	1.15595	+	0.527904i
$178$		0			0
$179$	−2.81324	−	19.5665i	−0.210271	−	1.46247i	−0.772251	−	0.635318i	$-0.780869\pi$
$179$	−2.81324	−	19.5665i	−0.210271	−	1.46247i	0.561980	−	0.827151i	$-0.310040\pi$
$180$		0			0
$181$	−2.21088	−	2.55149i	−0.164333	−	0.189651i	0.667610	−	0.744511i	$-0.267317\pi$
$181$	−2.21088	−	2.55149i	−0.164333	−	0.189651i	−0.831944	+	0.554860i	$0.812772\pi$
$182$		0			0
$183$			15.6399i			1.15614i
$184$		0			0
$185$	−22.0494	−	1.25910i	−1.62110	−	0.0925709i
$186$		0			0
$187$	2.11286	−	1.83080i	0.154508	−	0.133882i
$188$		0			0
$189$	−0.248105	−	1.72561i	−0.0180470	−	0.125519i
$190$		0			0
$191$	11.2935	−	24.7293i	0.817169	−	1.78935i	0.244311	−	0.969697i	$-0.421438\pi$
$191$	11.2935	−	24.7293i	0.817169	−	1.78935i	0.572858	−	0.819654i	$-0.305835\pi$
$192$		0			0
$193$	−18.5650	−	2.66924i	−1.33634	−	0.192136i	−0.563172	−	0.826340i	$-0.690419\pi$
$193$	−18.5650	−	2.66924i	−1.33634	−	0.192136i	−0.773166	+	0.634204i	$0.781328\pi$
$194$		0			0
$195$	4.45068	−	12.4770i	0.318720	−	0.893496i
$196$		0			0
$197$	−17.0992	+	7.80893i	−1.21827	+	0.556363i	−0.917653	−	0.397383i	$-0.869919\pi$
$197$	−17.0992	+	7.80893i	−1.21827	+	0.556363i	−0.300613	+	0.953746i	$0.597191\pi$
$198$		0			0
$199$	2.41284	−	2.78457i	0.171042	−	0.197393i	−0.663756	−	0.747949i	$-0.731039\pi$
$199$	2.41284	−	2.78457i	0.171042	−	0.197393i	0.834798	+	0.550556i	$0.185584\pi$
$200$		0			0
$201$	9.20587	+	5.91625i	0.649332	+	0.417300i
$202$		0			0
$203$	5.16971	+	8.04422i	0.362842	+	0.564594i
$204$		0			0
$205$	5.23278	+	22.4947i	0.365473	+	1.57110i
$206$		0			0
$207$	0.987955	−	15.9026i	0.0686677	−	1.10531i
$208$		0			0
$209$	−1.91615	+	0.562633i	−0.132543	+	0.0389181i
$210$		0			0
$211$	−3.93001	+	2.52567i	−0.270553	+	0.173874i	−0.668882	−	0.743369i	$-0.733227\pi$
$211$	−3.93001	+	2.52567i	−0.270553	+	0.173874i	0.398328	+	0.917243i	$0.369590\pi$
$212$		0			0
$213$	9.48210	−	14.7544i	0.649703	−	1.01096i
$214$		0			0
$215$	9.72110	−	10.0043i	0.662973	−	0.682290i
$216$		0			0
$217$	−2.63088	+	1.20148i	−0.178595	+	0.0815618i
$218$		0			0
$219$	13.0502	+	3.83189i	0.881851	+	0.258935i
$220$		0			0
$221$	1.58603	−	11.0311i	0.106688	−	0.742032i
$222$		0			0
$223$	−18.3866	−	8.39686i	−1.23126	−	0.562296i	−0.309808	−	0.950799i	$-0.600265\pi$
$223$	−18.3866	−	8.39686i	−1.23126	−	0.562296i	−0.921447	+	0.388504i	$0.872992\pi$
$224$		0			0
$225$	−0.476958	−	16.6048i	−0.0317972	−	1.10698i
$226$		0			0
$227$	−12.4192	+	10.7613i	−0.824292	+	0.714253i	−0.961057	−	0.276351i	$-0.910875\pi$
$227$	−12.4192	+	10.7613i	−0.824292	+	0.714253i	0.136765	+	0.990604i	$0.456329\pi$
$228$		0			0
$229$	24.8233			1.64037			0.820186	−	0.572098i	$-0.193870\pi$
$229$	24.8233			1.64037			0.820186	+	0.572098i	$0.193870\pi$
$230$		0			0
$231$	3.19685			0.210337
$232$		0			0
$233$	1.46434	−	1.26886i	0.0959322	−	0.0831258i	−0.605574	−	0.795789i	$-0.707057\pi$
$233$	1.46434	−	1.26886i	0.0959322	−	0.0831258i	0.701507	+	0.712663i	$0.252511\pi$
$234$		0			0
$235$	1.02031	+	11.8683i	0.0665574	+	0.774204i
$236$		0			0
$237$	−37.2513	−	17.0121i	−2.41973	−	1.10506i
$238$		0			0
$239$	0.955971	−	6.64892i	0.0618366	−	0.430083i	−0.935262	−	0.353957i	$-0.884836\pi$
$239$	0.955971	−	6.64892i	0.0618366	−	0.430083i	0.997098	−	0.0761258i	$-0.0242551\pi$
$240$		0			0
$241$	14.7421	+	4.32868i	0.949624	+	0.278835i	0.719630	−	0.694357i	$-0.244311\pi$
$241$	14.7421	+	4.32868i	0.949624	+	0.278835i	0.229994	+	0.973192i	$0.426129\pi$
$242$		0			0
$243$	−20.3472	+	9.29224i	−1.30527	+	0.596098i
$244$		0			0
$245$	3.80526	+	3.69753i	0.243109	+	0.236226i
$246$		0			0
$247$	−4.30394	+	6.69706i	−0.273853	+	0.426123i
$248$		0			0
$249$	15.9503	−	10.2507i	1.01081	−	0.649609i
$250$		0			0
$251$	−3.06315	+	0.899421i	−0.193344	+	0.0567709i	−0.376971	−	0.926225i	$-0.623034\pi$
$251$	−3.06315	+	0.899421i	−0.193344	+	0.0567709i	0.183627	+	0.982996i	$0.441216\pi$
$252$		0			0
$253$	2.77533	+	0.576600i	0.174483	+	0.0362505i
$254$		0			0
$255$	−6.02557	−	25.9028i	−0.377336	−	1.62209i
$256$		0			0
$257$	15.4013	+	23.9649i	0.960706	+	1.49489i	0.866404	+	0.499344i	$0.166426\pi$
$257$	15.4013	+	23.9649i	0.960706	+	1.49489i	0.0943025	+	0.995544i	$0.469938\pi$
$258$		0			0
$259$	−17.8732	−	11.4864i	−1.11059	−	0.713731i
$260$		0			0
$261$	−9.67142	+	11.1614i	−0.598646	+	0.690874i
$262$		0			0
$263$	1.01648	−	0.464212i	0.0626790	−	0.0286245i	−0.383829	−	0.923404i	$-0.625395\pi$
$263$	1.01648	−	0.464212i	0.0626790	−	0.0286245i	0.446508	+	0.894780i	$0.352667\pi$
$264$		0			0
$265$	12.0046	+	4.28218i	0.737438	+	0.263053i
$266$		0			0
$267$	23.6667	+	3.40275i	1.44838	+	0.208245i
$268$		0			0
$269$	−6.75591	+	14.7934i	−0.411915	+	0.901968i	0.584007	+	0.811749i	$0.301484\pi$
$269$	−6.75591	+	14.7934i	−0.411915	+	0.901968i	−0.995922	+	0.0902195i	$0.971243\pi$
$270$		0			0
$271$	−0.475614	−	3.30797i	−0.0288915	−	0.200945i	0.970263	−	0.242052i	$-0.0778205\pi$
$271$	−0.475614	−	3.30797i	−0.0288915	−	0.200945i	−0.999155	+	0.0411075i	$0.986911\pi$
$272$		0			0
$273$	9.63095	−	8.34527i	0.582892	−	0.505078i
$274$		0			0
$275$	2.93605	+	0.336416i	0.177051	+	0.0202866i
$276$		0			0
$277$		−	11.5662i		−	0.694948i	−0.937690	−	0.347474i	$-0.887039\pi$
$277$		−	11.5662i		−	0.694948i	0.937690	−	0.347474i	$-0.112961\pi$
$278$		0			0
$279$	−2.92528	−	3.37596i	−0.175132	−	0.202113i
$280$		0			0
$281$	−4.28293	−	29.7885i	−0.255498	−	1.77703i	−0.563969	−	0.825796i	$-0.690726\pi$
$281$	−4.28293	−	29.7885i	−0.255498	−	1.77703i	0.308470	−	0.951234i	$-0.400183\pi$
$282$		0			0
$283$	−16.0327	−	7.32189i	−0.953045	−	0.435241i	−0.122671	−	0.992447i	$-0.539146\pi$
$283$	−16.0327	−	7.32189i	−0.953045	−	0.435241i	−0.830374	+	0.557206i	$0.811873\pi$
$284$		0			0
$285$	−3.77117	+	18.6189i	−0.223385	+	1.10289i
$286$		0			0
$287$	−6.25942	+	21.3176i	−0.369482	+	1.25834i
$288$		0			0
$289$	−2.23222	−	4.88788i	−0.131307	−	0.287522i
$290$		0			0
$291$	8.35015	−	9.63659i	0.489495	−	0.564907i
$292$		0			0
$293$	9.79860	−	15.2469i	0.572440	−	0.890734i	−0.427471	−	0.904029i	$-0.640596\pi$
$293$	9.79860	−	15.2469i	0.572440	−	0.890734i	0.999912	+	0.0132946i	$0.00423192\pi$
$294$		0			0
$295$	7.39427	+	13.0912i	0.430511	+	0.762197i
$296$		0			0
$297$	0.134956	+	0.459617i	0.00783092	+	0.0266697i
$298$		0			0
$299$	9.86625	−	5.50781i	0.570580	−	0.318525i
$300$		0			0
$301$	12.8757	−	3.78064i	0.742143	−	0.217913i
$302$		0			0
$303$	9.53807	+	14.8415i	0.547948	+	0.852623i
$304$		0			0
$305$	−8.17435	+	11.2529i	−0.468062	+	0.644338i
$306$		0			0
$307$	−5.17354	−	4.48290i	−0.295270	−	0.255853i	0.494609	−	0.869115i	$-0.335311\pi$
$307$	−5.17354	−	4.48290i	−0.295270	−	0.255853i	−0.789879	+	0.613263i	$0.789857\pi$
$308$		0			0
$309$	6.52310	+	14.2836i	0.371086	+	0.812566i
$310$		0			0
$311$	−10.3264	−	3.03209i	−0.585554	−	0.171934i	−0.0244810	−	0.999700i	$-0.507793\pi$
$311$	−10.3264	−	3.03209i	−0.585554	−	0.171934i	−0.561073	+	0.827766i	$0.689611\pi$
$312$		0			0
$313$	0.829640	+	0.119284i	0.0468940	+	0.00674235i	0.165722	−	0.986173i	$-0.447005\pi$
$313$	0.829640	+	0.119284i	0.0468940	+	0.00674235i	−0.118828	+	0.992915i	$0.537914\pi$
$314$		0			0
$315$	7.45636	−	14.1341i	0.420119	−	0.796364i
$316$		0			0
$317$	24.7923	−	3.56460i	1.39248	−	0.200208i	0.595082	−	0.803665i	$-0.297120\pi$
$317$	24.7923	−	3.56460i	1.39248	−	0.200208i	0.797395	+	0.603457i	$0.206211\pi$
$318$		0			0
$319$	−1.72058	−	1.98566i	−0.0963340	−	0.111175i
$320$		0			0
$321$	−4.20017			−0.234431
$322$		0			0
$323$			15.9819i			0.889256i
$324$		0			0
$325$	9.72347	−	6.65097i	0.539361	−	0.368929i
$326$		0			0
$327$	−31.9306	+	4.59093i	−1.76577	+	0.253879i
$328$		0			0
$329$	−4.76039	+	10.4238i	−0.262449	+	0.574683i
$330$		0			0
$331$	0.737519	−	5.12956i	0.0405377	−	0.281946i	−0.959462	−	0.281837i	$-0.909056\pi$
$331$	0.737519	−	5.12956i	0.0405377	−	0.281946i	1.00000		0.000108888i	$-3.46601e-5\pi$
$332$		0			0
$333$	9.24479	−	31.4849i	0.506611	−	1.72536i
$334$		0			0
$335$	3.53141	+	9.06826i	0.192942	+	0.495452i
$336$		0			0
$337$	18.9655	+	16.4337i	1.03312	+	0.895200i	0.994571	−	0.104057i	$-0.0331824\pi$
$337$	18.9655	+	16.4337i	1.03312	+	0.895200i	0.0385447	+	0.999257i	$0.487728\pi$
$338$		0			0
$339$	−25.2519	−	16.2284i	−1.37149	−	0.881406i
$340$		0			0
$341$	0.668545	−	0.429648i	0.0362037	−	0.0232667i
$342$		0			0
$343$	5.68022	+	19.3451i	0.306703	+	1.04454i
$344$		0			0
$345$	17.1696	−	20.7911i	0.924383	−	1.11936i
$346$		0			0
$347$	−6.73370	−	22.9329i	−0.361484	−	1.23110i	−0.916761	−	0.399436i	$-0.869206\pi$
$347$	−6.73370	−	22.9329i	−0.361484	−	1.23110i	0.555277	−	0.831665i	$-0.312612\pi$
$348$		0			0
$349$	−23.3168	+	14.9848i	−1.24812	+	0.802117i	−0.986612	−	0.163085i	$-0.947855\pi$
$349$	−23.3168	+	14.9848i	−1.24812	+	0.802117i	−0.261506	+	0.965202i	$0.584219\pi$
$350$		0			0
$351$	1.60639	+	1.03236i	0.0857426	+	0.0551034i
$352$		0			0
$353$	18.6781	+	16.1847i	0.994135	+	0.861423i	0.990353	−	0.138570i	$-0.0442507\pi$
$353$	18.6781	+	16.1847i	0.994135	+	0.861423i	0.00378211	+	0.999993i	$0.498796\pi$
$354$		0			0
$355$	14.5339	−	5.65987i	0.771379	−	0.300395i
$356$		0			0
$357$	7.20775	−	24.5473i	0.381474	−	1.29918i
$358$		0			0
$359$	−3.41899	+	23.7796i	−0.180448	+	1.25504i	0.675259	+	0.737580i	$0.264032\pi$
$359$	−3.41899	+	23.7796i	−0.180448	+	1.25504i	−0.855707	+	0.517460i	$0.826877\pi$
$360$		0			0
$361$	−3.15041	+	6.89843i	−0.165811	+	0.363075i
$362$		0			0
$363$	26.5077	−	3.81123i	1.39129	−	0.200038i
$364$		0			0
$365$	7.38681	+	9.57784i	0.386643	+	0.501327i
$366$		0			0
$367$			25.5000i			1.33109i	0.746358	+	0.665545i	$0.231801\pi$
$367$			25.5000i			1.33109i	−0.746358	+	0.665545i	$0.768199\pi$
$368$		0			0
$369$	−34.3148			−1.78636
$370$		0			0
$371$	8.02932	+	9.26633i	0.416862	+	0.481084i
$372$		0			0
$373$	9.05183	−	1.30146i	0.468686	−	0.0673869i	0.0960742	−	0.995374i	$-0.469371\pi$
$373$	9.05183	−	1.30146i	0.468686	−	0.0673869i	0.372612	+	0.927987i	$0.378462\pi$
$374$		0			0
$375$	15.8622	−	23.2095i	0.819123	−	1.19853i
$376$		0			0
$377$	−10.3670	−	1.49055i	−0.533926	−	0.0767670i
$378$		0			0
$379$	−1.45601	−	0.427522i	−0.0747901	−	0.0219603i	0.244123	−	0.969744i	$-0.421500\pi$
$379$	−1.45601	−	0.427522i	−0.0747901	−	0.0219603i	−0.318914	+	0.947784i	$0.603318\pi$
$380$		0			0
$381$	18.4815	+	40.4689i	0.946838	+	2.07329i
$382$		0			0
$383$	1.84452	+	1.59828i	0.0942504	+	0.0816685i	0.700712	−	0.713445i	$-0.252866\pi$
$383$	1.84452	+	1.59828i	0.0942504	+	0.0816685i	−0.606461	+	0.795113i	$0.707411\pi$
$384$		0			0
$385$	2.30012	+	1.67086i	0.117225	+	0.0851551i
$386$		0			0
$387$	11.2053	+	17.4357i	0.569595	+	0.886307i
$388$		0			0
$389$	−24.1556	+	7.09273i	−1.22474	+	0.359615i	−0.829262	−	0.558861i	$-0.811239\pi$
$389$	−24.1556	+	7.09273i	−1.22474	+	0.359615i	−0.395476	+	0.918476i	$0.629420\pi$
$390$		0			0
$391$	10.6848	−	20.0106i	0.540356	−	1.01198i
$392$		0			0
$393$	−7.93492	−	27.0239i	−0.400264	−	1.36317i
$394$		0			0
$395$	−17.9107	−	31.7099i	−0.901185	−	1.59550i
$396$		0			0
$397$	−0.0351432	+	0.0546838i	−0.00176378	+	0.00274450i	−0.842134	−	0.539268i	$-0.818701\pi$
$397$	−0.0351432	+	0.0546838i	−0.00176378	+	0.00274450i	0.840371	+	0.542012i	$0.182337\pi$
$398$		0			0
$399$	−11.9676	+	13.8113i	−0.599128	+	0.691431i
$400$		0			0
$401$	−13.0692	−	28.6175i	−0.652644	−	1.42909i	−0.889221	−	0.457479i	$-0.848753\pi$
$401$	−13.0692	−	28.6175i	−0.652644	−	1.42909i	0.236576	−	0.971613i	$-0.423975\pi$
$402$		0			0
$403$	0.892503	−	3.03959i	0.0444587	−	0.151413i
$404$		0			0
$405$	−17.3772	−	3.51967i	−0.863482	−	0.174894i
$406$		0			0
$407$	5.31020	+	2.42509i	0.263217	+	0.120207i
$408$		0			0
$409$	1.73107	+	12.0399i	0.0855960	+	0.595333i	0.986801	+	0.161940i	$0.0517750\pi$
$409$	1.73107	+	12.0399i	0.0855960	+	0.595333i	−0.901205	+	0.433394i	$0.857316\pi$
$410$		0			0
$411$	9.10193	+	10.5042i	0.448965	+	0.518134i
$412$		0			0
$413$			14.4637i			0.711711i
$414$		0			0
$415$	16.8338	+	0.961273i	0.826340	+	0.0471870i
$416$		0			0
$417$	−35.5086	+	30.7684i	−1.73886	+	1.50673i
$418$		0			0
$419$	−0.965216	−	6.71323i	−0.0471539	−	0.327963i	−0.999721	−	0.0236330i	$-0.992477\pi$
$419$	−0.965216	−	6.71323i	−0.0471539	−	0.327963i	0.952567	−	0.304330i	$-0.0984324\pi$
$420$		0			0
$421$	−13.4765	+	29.5094i	−0.656804	+	1.43820i	0.228667	+	0.973505i	$0.426563\pi$
$421$	−13.4765	+	29.5094i	−0.656804	+	1.43820i	−0.885471	+	0.464695i	$0.846164\pi$
$422$		0			0
$423$	−17.5187	−	2.51881i	−0.851788	−	0.122469i
$424$		0			0
$425$	9.20295	−	21.7863i	0.446409	−	1.05679i
$426$		0			0
$427$	−12.1708	+	5.55823i	−0.588987	+	0.268981i
$428$		0			0
$429$	−2.29303	+	2.64629i	−0.110708	+	0.127764i
$430$		0			0
$431$	18.5913	+	11.9479i	0.895513	+	0.575511i	0.905456	−	0.424439i	$-0.139529\pi$
$431$	18.5913	+	11.9479i	0.895513	+	0.575511i	−0.00994336	+	0.999951i	$0.503165\pi$
$432$		0			0
$433$	−12.5391	−	19.5113i	−0.602593	−	0.937653i	−0.999801	−	0.0199246i	$-0.993657\pi$
$433$	−12.5391	−	19.5113i	−0.602593	−	0.937653i	0.397208	−	0.917728i	$-0.369979\pi$
$434$		0			0
$435$	−24.3433	+	5.66280i	−1.16717	+	0.271510i
$436$		0			0
$437$	−12.8807	+	9.83169i	−0.616166	+	0.470313i
$438$		0			0
$439$	−35.4558	+	10.4108i	−1.69221	+	0.496878i	−0.978964	−	0.204033i	$-0.934595\pi$
$439$	−35.4558	+	10.4108i	−1.69221	+	0.496878i	−0.713249	+	0.700911i	$0.752777\pi$
$440$		0			0
$441$	−6.63187	+	4.26205i	−0.315804	+	0.202955i
$442$		0			0
$443$	−13.3035	+	20.7006i	−0.632067	+	0.983516i	0.366522	+	0.930410i	$0.380549\pi$
$443$	−13.3035	+	20.7006i	−0.632067	+	0.983516i	−0.998589	+	0.0531062i	$0.983088\pi$
$444$		0			0
$445$	15.2496	+	14.8179i	0.722901	+	0.702435i
$446$		0			0
$447$	−23.6310	+	10.7919i	−1.11771	+	0.510440i
$448$		0			0
$449$	−6.24263	−	1.83300i	−0.294608	−	0.0865047i	0.131089	−	0.991371i	$-0.458153\pi$
$449$	−6.24263	−	1.83300i	−0.294608	−	0.0865047i	−0.425697	+	0.904866i	$0.639971\pi$
$450$		0			0
$451$	0.868792	−	6.04258i	0.0409098	−	0.284534i
$452$		0			0
$453$	−1.68142	−	0.767880i	−0.0790001	−	0.0360781i
$454$		0			0
$455$	11.2912	−	0.970689i	0.529338	−	0.0455066i
$456$		0			0
$457$	−27.8051	+	24.0932i	−1.30067	+	1.12703i	−0.316730	+	0.948516i	$0.602585\pi$
$457$	−27.8051	+	24.0932i	−1.30067	+	1.12703i	−0.983937	+	0.178518i	$0.942870\pi$
$458$		0			0
$459$	3.83349			0.178932
$460$		0			0
$461$	−31.4139			−1.46309			−0.731545	−	0.681793i	$-0.761200\pi$
$461$	−31.4139			−1.46309			−0.731545	+	0.681793i	$0.761200\pi$
$462$		0			0
$463$	12.2024	−	10.5734i	0.567093	−	0.491389i	−0.323476	−	0.946236i	$-0.604852\pi$
$463$	12.2024	−	10.5734i	0.567093	−	0.491389i	0.890569	+	0.454847i	$0.150306\pi$
$464$		0			0
$465$	−0.647504	−	7.53185i	−0.0300273	−	0.349281i
$466$		0			0
$467$	−35.0982	−	16.0288i	−1.62415	−	0.741726i	−0.624913	−	0.780695i	$-0.714865\pi$
$467$	−35.0982	−	16.0288i	−1.62415	−	0.741726i	−0.999240	+	0.0389687i	$0.987593\pi$
$468$		0			0
$469$	−1.33232	+	9.26646i	−0.0615207	+	0.427886i
$470$		0			0
$471$	−34.8219	−	10.2246i	−1.60451	−	0.471126i
$472$		0			0
$473$	−3.35400	+	1.53172i	−0.154217	+	0.0704287i
$474$		0			0
$475$	−12.4447	+	11.4252i	−0.571002	+	0.524225i
$476$		0			0
$477$	−10.2382	+	15.9309i	−0.468774	+	0.729427i
$478$		0			0
$479$	−3.87324	+	2.48918i	−0.176973	+	0.113733i	−0.626128	−	0.779720i	$-0.715361\pi$
$479$	−3.87324	+	2.48918i	−0.176973	+	0.113733i	0.449155	+	0.893454i	$0.351725\pi$
$480$		0			0
$481$	22.3283	−	6.55618i	1.01808	−	0.298936i
$482$		0			0
$483$	24.2180	−	9.29183i	1.10196	−	0.422793i
$484$		0			0
$485$	11.0446	−	2.56921i	0.501508	−	0.116662i
$486$		0			0
$487$	12.2152	+	19.0072i	0.553523	+	0.861298i	0.999429	−	0.0337811i	$-0.0107549\pi$
$487$	12.2152	+	19.0072i	0.553523	+	0.861298i	−0.445906	+	0.895080i	$0.647119\pi$
$488$		0			0
$489$	8.21801	+	5.28140i	0.371631	+	0.238833i
$490$		0			0
$491$	12.0102	−	13.8605i	0.542014	−	0.625517i	−0.416990	−	0.908911i	$-0.636915\pi$
$491$	12.0102	−	13.8605i	0.542014	−	0.625517i	0.959004	+	0.283394i	$0.0914604\pi$
$492$		0			0
$493$	−19.1263	+	8.73471i	−0.861407	+	0.393392i
$494$		0			0
$495$	−1.47523	+	4.13566i	−0.0663069	+	0.185884i
$496$		0			0
$497$	14.8515	+	2.13533i	0.666183	+	0.0957827i
$498$		0			0
$499$	16.1002	−	35.2545i	0.720743	−	1.57821i	−0.0921171	−	0.995748i	$-0.529363\pi$
$499$	16.1002	−	35.2545i	0.720743	−	1.57821i	0.812860	−	0.582459i	$-0.197909\pi$
$500$		0			0
$501$	6.97417	+	48.5064i	0.311583	+	2.16711i
$502$		0			0
$503$	−0.807745	+	0.699915i	−0.0360156	+	0.0312077i	−0.672683	−	0.739931i	$-0.734858\pi$
$503$	−0.807745	+	0.699915i	−0.0360156	+	0.0312077i	0.636667	+	0.771139i	$0.280313\pi$
$504$		0			0
$505$	−0.894448	+	15.6636i	−0.0398024	+	0.697021i
$506$		0			0
$507$		−	18.7293i		−	0.831797i
$508$		0			0
$509$	−0.275769	−	0.318255i	−0.0122233	−	0.0141064i	0.749605	−	0.661885i	$-0.230243\pi$
$509$	−0.275769	−	0.318255i	−0.0122233	−	0.0141064i	−0.761828	+	0.647779i	$0.775698\pi$
$510$		0			0
$511$	1.65594	+	11.5173i	0.0732545	+	0.509496i
$512$		0			0
$513$	−2.49089	−	1.13755i	−0.109976	−	0.0502242i
$514$		0			0
$515$	−2.77210	+	13.6864i	−0.122153	+	0.603094i
$516$		0			0
$517$	0.887088	−	3.02114i	0.0390141	−	0.132870i
$518$		0			0
$519$	2.10990	+	4.62004i	0.0926143	+	0.202797i
$520$		0			0
$521$	−18.9641	+	21.8857i	−0.830831	+	0.958830i	−0.999640	−	0.0268187i	$-0.991462\pi$
$521$	−18.9641	+	21.8857i	−0.830831	+	0.958830i	0.168809	+	0.985649i	$0.446008\pi$
$522$		0			0
$523$	−0.546567	+	0.850474i	−0.0238997	+	0.0371886i	−0.852998	−	0.521914i	$-0.825218\pi$
$523$	−0.546567	+	0.850474i	−0.0238997	+	0.0371886i	0.829098	+	0.559103i	$0.188854\pi$
$524$		0			0
$525$	24.2671	−	11.9360i	1.05910	−	0.520931i
$526$		0			0
$527$	−1.79176	−	6.10219i	−0.0780505	−	0.265815i
$528$		0			0
$529$	22.7007	−	3.69856i	0.986986	−	0.160807i
$530$		0			0
$531$	−21.4341	+	6.29361i	−0.930159	+	0.273119i
$532$		0			0
$533$	−13.1566	−	20.4721i	−0.569876	−	0.886744i
$534$		0			0
$535$	−3.02201	−	2.19526i	−0.130653	−	0.0949093i
$536$		0			0
$537$	37.5640	+	32.5494i	1.62101	+	1.40461i
$538$		0			0
$539$	−0.582608	−	1.27573i	−0.0250947	−	0.0549497i
$540$		0			0
$541$	−18.2593	−	5.36140i	−0.785027	−	0.230505i	−0.135434	−	0.990786i	$-0.543243\pi$
$541$	−18.2593	−	5.36140i	−0.785027	−	0.230505i	−0.649594	+	0.760282i	$0.725061\pi$
$542$		0			0
$543$	8.40255	+	1.20810i	0.360588	+	0.0518447i
$544$		0			0
$545$	−25.3735	−	13.3857i	−1.08688	−	0.573379i
$546$		0			0
$547$	20.8062	−	2.99148i	0.889610	−	0.127907i	0.317669	−	0.948202i	$-0.397100\pi$
$547$	20.8062	−	2.99148i	0.889610	−	0.127907i	0.571941	+	0.820295i	$0.306191\pi$
$548$		0			0
$549$	−13.5328	−	15.6177i	−0.577565	−	0.666546i
$550$		0			0
$551$	15.0197			0.639861
$552$		0			0
$553$		−	35.0345i		−	1.48982i
$554$		0			0
$555$	43.9731	−	33.9138i	1.86655	−	1.43956i
$556$		0			0
$557$	−5.94797	+	0.855188i	−0.252023	+	0.0362355i	−0.267169	−	0.963650i	$-0.586088\pi$
$557$	−5.94797	+	0.855188i	−0.252023	+	0.0362355i	0.0151452	+	0.999885i	$0.495179\pi$
$558$		0			0
$559$	−6.10589	+	13.3700i	−0.258252	+	0.565492i
$560$		0			0
$561$	−1.00042	+	6.95806i	−0.0422377	+	0.293770i
$562$		0			0
$563$	12.6262	−	43.0008i	0.532130	−	1.81227i	−0.0494475	−	0.998777i	$-0.515746\pi$
$563$	12.6262	−	43.0008i	0.532130	−	1.81227i	0.581577	−	0.813491i	$-0.302436\pi$
$564$		0			0
$565$	−9.68674	−	24.8744i	−0.407524	−	1.04648i
$566$		0			0
$567$	−12.8903	−	11.1695i	−0.541340	−	0.469074i
$568$		0			0
$569$	14.7949	+	9.50811i	0.620235	+	0.398601i	0.812683	−	0.582706i	$-0.198006\pi$
$569$	14.7949	+	9.50811i	0.620235	+	0.398601i	−0.192448	+	0.981307i	$0.561643\pi$
$570$		0			0
$571$	10.8548	−	6.97596i	0.454260	−	0.291935i	−0.293433	−	0.955980i	$-0.594798\pi$
$571$	10.8548	−	6.97596i	0.454260	−	0.291935i	0.747693	+	0.664045i	$0.231162\pi$
$572$		0			0
$573$	19.2585	+	65.5883i	0.804534	+	2.73999i
$574$		0			0
$575$	23.2202	−	5.98527i	0.968348	−	0.249603i
$576$		0			0
$577$	6.93888	+	23.6316i	0.288869	+	0.983798i	0.968244	+	0.250007i	$0.0804329\pi$
$577$	6.93888	+	23.6316i	0.288869	+	0.983798i	−0.679375	+	0.733791i	$0.737749\pi$
$578$		0			0
$579$	39.6737	−	25.4968i	1.64878	−	1.05961i
$580$		0			0
$581$	13.6455	+	8.76943i	0.566110	+	0.363817i
$582$		0			0
$583$	−2.54611	−	2.20622i	−0.105449	−	0.0913721i
$584$		0			0
$585$	6.35164	+	16.3103i	0.262608	+	0.674347i
$586$		0			0
$587$	6.56564	−	22.3605i	0.270993	−	0.922917i	−0.705743	−	0.708468i	$-0.749386\pi$
$587$	6.56564	−	22.3605i	0.270993	−	0.922917i	0.976735	−	0.214448i	$-0.0687953\pi$
$588$		0			0
$589$	−0.646530	+	4.49672i	−0.0266398	+	0.185284i
$590$		0			0
$591$	19.6350	−	42.9946i	0.807674	−	1.76856i
$592$		0			0
$593$	18.1794	−	2.61380i	0.746538	−	0.107336i	0.241462	−	0.970410i	$-0.422373\pi$
$593$	18.1794	−	2.61380i	0.746538	−	0.107336i	0.505077	+	0.863074i	$0.331464\pi$
$594$		0			0
$595$	18.0158	−	13.8945i	0.738577	−	0.569620i
$596$		0			0
$597$			9.26443i			0.379168i
$598$		0			0
$599$	37.2351			1.52139			0.760693	−	0.649112i	$-0.224859\pi$
$599$	37.2351			1.52139			0.760693	+	0.649112i	$0.224859\pi$
$600$		0			0
$601$	−25.8583	−	29.8420i	−1.05478	−	1.21728i	−0.975401	−	0.220436i	$-0.929252\pi$
$601$	−25.8583	−	29.8420i	−1.05478	−	1.21728i	−0.0793787	−	0.996845i	$-0.525294\pi$
$602$		0			0
$603$	−14.3119	+	2.05775i	−0.582827	+	0.0837979i
$604$		0			0
$605$	21.0642	+	11.1123i	0.856380	+	0.451780i
$606$		0			0
$607$	44.2386	+	6.36055i	1.79559	+	0.258167i	0.957719	−	0.287704i	$-0.0928919\pi$
$607$	44.2386	+	6.36055i	1.79559	+	0.258167i	0.837869	+	0.545871i	$0.183801\pi$
$608$		0			0
$609$	−23.0694	−	6.77380i	−0.934821	−	0.274488i
$610$		0			0
$611$	−5.21412	−	11.4173i	−0.210941	−	0.461896i
$612$		0			0
$613$	−28.1796	−	24.4178i	−1.13817	−	0.986226i	−0.138174	−	0.990408i	$-0.544123\pi$
$613$	−28.1796	−	24.4178i	−1.13817	−	0.986226i	−0.999991	+	0.00418235i	$0.998669\pi$
$614$		0			0
$615$	−46.9835	−	34.1299i	−1.89456	−	1.37625i
$616$		0			0
$617$	−1.50074	−	2.33519i	−0.0604174	−	0.0940113i	0.809731	−	0.586802i	$-0.199613\pi$
$617$	−1.50074	−	2.33519i	−0.0604174	−	0.0940113i	−0.870148	+	0.492791i	$0.835977\pi$
$618$		0			0
$619$	−41.5933	+	12.2129i	−1.67177	+	0.490877i	−0.974210	−	0.225645i	$-0.927551\pi$
$619$	−41.5933	+	12.2129i	−1.67177	+	0.490877i	−0.697565	+	0.716522i	$0.745733\pi$
$620$		0			0
$621$	2.35827	+	3.08961i	0.0946342	+	0.123982i
$622$		0			0
$623$	5.76284	+	19.6264i	0.230883	+	0.786316i
$624$		0			0
$625$	23.5435	−	8.40860i	0.941739	−	0.336344i
$626$		0			0
$627$	2.71478	−	4.22429i	0.108418	−	0.168702i
$628$		0			0
$629$	30.5938	−	35.3072i	1.21986	−	1.40779i
$630$		0			0
$631$	−14.5063	−	31.7643i	−0.577485	−	1.26452i	−0.942715	−	0.333599i	$-0.891737\pi$
$631$	−14.5063	−	31.7643i	−0.577485	−	1.26452i	0.365230	−	0.930917i	$-0.380990\pi$
$632$		0			0
$633$	3.30935	−	11.2706i	0.131535	−	0.447966i
$634$		0			0
$635$	−7.85405	+	38.7768i	−0.311678	+	1.53881i
$636$		0			0
$637$	−5.08544	−	2.32244i	−0.201493	−	0.0920186i
$638$		0			0
$639$	3.29799	+	22.9380i	0.130466	+	0.907414i
$640$		0			0
$641$	26.2354	+	30.2773i	1.03624	+	1.19588i	0.980314	+	0.197446i	$0.0632647\pi$
$641$	26.2354	+	30.2773i	1.03624	+	1.19588i	0.0559230	+	0.998435i	$0.482190\pi$
$642$		0			0
$643$		−	14.7040i		−	0.579868i	−0.957047	−	0.289934i	$-0.906367\pi$
$643$		−	14.7040i		−	0.579868i	0.957047	−	0.289934i	$-0.0936334\pi$
$644$		0			0
$645$	−1.99964	+	35.0177i	−0.0787357	+	1.37882i
$646$		0			0
$647$	−11.8308	+	10.2515i	−0.465118	+	0.403027i	−0.855644	−	0.517565i	$-0.826839\pi$
$647$	−11.8308	+	10.2515i	−0.465118	+	0.403027i	0.390526	+	0.920592i	$0.372293\pi$
$648$		0			0
$649$	−0.565585	−	3.93373i	−0.0222011	−	0.154412i
$650$		0			0
$651$	3.02103	−	6.61513i	0.118403	−	0.259267i
$652$		0			0
$653$	−0.918336	−	0.132037i	−0.0359373	−	0.00516700i	0.124323	−	0.992242i	$-0.460324\pi$
$653$	−0.918336	−	0.132037i	−0.0359373	−	0.00516700i	−0.160260	+	0.987075i	$0.551233\pi$
$654$		0			0
$655$	8.41512	−	23.5908i	0.328806	−	0.921771i
$656$		0			0
$657$	−16.3472	+	7.46554i	−0.637767	+	0.291258i
$658$		0			0
$659$	5.18432	−	5.98303i	0.201953	−	0.233066i	−0.645735	−	0.763562i	$-0.723449\pi$
$659$	5.18432	−	5.98303i	0.201953	−	0.233066i	0.847687	+	0.530496i	$0.177994\pi$
$660$		0			0
$661$	6.15595	+	3.95619i	0.239439	+	0.153878i	0.654858	−	0.755752i	$-0.272729\pi$
$661$	6.15595	+	3.95619i	0.239439	+	0.153878i	−0.415419	+	0.909630i	$0.636365\pi$
$662$		0			0
$663$	15.1499	+	23.5737i	0.588373	+	0.915526i
$664$		0			0
$665$	−15.8293	+	3.68224i	−0.613832	+	0.142791i
$666$		0			0
$667$	−18.8059	−	10.0416i	−0.728166	−	0.388811i
$668$		0			0
$669$	48.7658	−	14.3189i	1.88539	−	0.553601i
$670$		0			0
$671$	3.09279	−	1.98761i	0.119396	−	0.0767309i
$672$		0			0
$673$	8.41063	−	13.0872i	0.324206	−	0.504474i	−0.640445	−	0.768004i	$-0.721250\pi$
$673$	8.41063	−	13.0872i	0.324206	−	0.504474i	0.964651	+	0.263529i	$0.0848866\pi$
$674$		0			0
$675$	2.74051	+	2.98504i	0.105482	+	0.114894i
$676$		0			0
$677$	−19.0702	+	8.70906i	−0.732927	+	0.334716i	−0.746675	−	0.665189i	$-0.768351\pi$
$677$	−19.0702	+	8.70906i	−0.732927	+	0.334716i	0.0137482	+	0.999905i	$0.495624\pi$
$678$		0			0
$679$	10.4666	+	3.07328i	0.401672	+	0.117942i
$680$		0			0
$681$	5.88037	−	40.8989i	0.225336	−	1.56725i
$682$		0			0
$683$	33.3444	+	15.2279i	1.27589	+	0.582679i	0.934071	−	0.357087i	$-0.116230\pi$
$683$	33.3444	+	15.2279i	1.27589	+	0.582679i	0.341818	+	0.939766i	$0.388957\pi$
$684$		0			0
$685$	1.05870	+	12.3149i	0.0404509	+	0.470530i
$686$		0			0
$687$	−47.1711	+	40.8740i	−1.79969	+	1.55944i
$688$		0			0
$689$	−13.4298			−0.511633
$690$		0			0
$691$	28.0683			1.06777			0.533884	−	0.845558i	$-0.320732\pi$
$691$	28.0683			1.06777			0.533884	+	0.845558i	$0.320732\pi$
$692$		0			0
$693$	−3.19230	+	2.76614i	−0.121265	+	0.105077i
$694$		0			0
$695$	−41.6297	+	3.57886i	−1.57910	+	0.135754i
$696$		0			0
$697$	−44.4398	−	20.2950i	−1.68328	−	0.768726i
$698$		0			0
$699$	−0.693351	+	4.82236i	−0.0262249	+	0.182398i
$700$		0			0
$701$	0.342207	+	0.100481i	0.0129250	+	0.00379512i	0.288189	−	0.957574i	$-0.406947\pi$
$701$	0.342207	+	0.100481i	0.0129250	+	0.00379512i	−0.275264	+	0.961369i	$0.588765\pi$
$702$		0			0
$703$	−30.3561	+	13.8632i	−1.14490	+	0.522859i
$704$		0			0
$705$	−21.4812	−	20.8730i	−0.809029	−	0.786124i
$706$		0			0
$707$	−8.15980	+	12.6969i	−0.306881	+	0.477516i
$708$		0			0
$709$	41.8564	−	26.8995i	1.57195	−	1.01023i	0.593230	−	0.805033i	$-0.297852\pi$
$709$	41.8564	−	26.8995i	1.57195	−	1.01023i	0.978720	−	0.205198i	$-0.0657839\pi$
$710$		0			0
$711$	51.9184	−	15.2446i	1.94709	−	0.571718i
$712$		0			0
$713$	3.81583	−	5.19800i	0.142904	−	0.194667i
$714$		0			0
$715$	−3.03294	+	0.705529i	−0.113425	+	0.0263853i
$716$		0			0
$717$	9.13149	+	14.2089i	0.341022	+	0.530640i
$718$		0			0
$719$	39.7291	+	25.5323i	1.48164	+	0.952195i	0.996993	+	0.0774881i	$0.0246900\pi$
$719$	39.7291	+	25.5323i	1.48164	+	0.952195i	0.484652	+	0.874707i	$0.338946\pi$
$720$		0			0
$721$	−8.79711	+	10.1524i	−0.327622	+	0.378095i
$722$		0			0
$723$	−35.1417	+	16.0487i	−1.30693	+	0.596856i
$724$		0			0
$725$	−20.4746	−	8.64888i	−0.760409	−	0.321211i
$726$		0			0
$727$	44.3275	+	6.37333i	1.64402	+	0.236374i	0.901288	−	0.433221i	$-0.142623\pi$
$727$	44.3275	+	6.37333i	1.64402	+	0.236374i	0.742727	+	0.669594i	$0.233532\pi$
$728$		0			0
$729$	13.4830	−	29.5236i	0.499369	−	1.09347i
$730$		0			0
$731$	4.19941	+	29.2075i	0.155321	+	1.08028i
$732$		0			0
$733$	11.0713	−	9.59330i	0.408926	−	0.354337i	−0.425976	−	0.904734i	$-0.640069\pi$
$733$	11.0713	−	9.59330i	0.408926	−	0.354337i	0.834903	+	0.550398i	$0.185524\pi$
$734$		0			0
$735$	−13.3194	−	0.760585i	−0.491293	−	0.0280546i
$736$		0			0
$737$		−	2.57233i		−	0.0947529i
$738$		0			0
$739$	−2.50884	−	2.89535i	−0.0922891	−	0.106507i	0.707726	−	0.706487i	$-0.249721\pi$
$739$	−2.50884	−	2.89535i	−0.0922891	−	0.106507i	−0.800016	+	0.599979i	$0.795175\pi$
$740$		0			0
$741$	−2.84869	−	19.8131i	−0.104649	−	0.727852i
$742$		0			0
$743$	27.6153	+	12.6115i	1.01311	+	0.462671i	0.851596	−	0.524199i	$-0.175635\pi$
$743$	27.6153	+	12.6115i	1.01311	+	0.462671i	0.161513	+	0.986871i	$0.448363\pi$
$744$		0			0
$745$	−22.6429	−	4.58621i	−0.829573	−	0.168026i
$746$		0			0
$747$	−7.05803	+	24.0374i	−0.258240	+	0.879484i
$748$		0			0
$749$	−1.49268	−	3.26852i	−0.0545415	−	0.119429i
$750$		0			0
$751$	−8.21262	+	9.47786i	−0.299683	+	0.345852i	−0.885541	−	0.464561i	$-0.846212\pi$
$751$	−8.21262	+	9.47786i	−0.299683	+	0.345852i	0.585858	+	0.810413i	$0.300757\pi$
$752$		0			0
$753$	4.33983	−	6.75291i	0.158152	−	0.246090i
$754$		0			0
$755$	−0.808439	−	1.43130i	−0.0294221	−	0.0520903i
$756$		0			0
$757$	−14.1270	−	48.1120i	−0.513453	−	1.74866i	−0.651913	−	0.758294i	$-0.726033\pi$
$757$	−14.1270	−	48.1120i	−0.513453	−	1.74866i	0.138460	−	0.990368i	$-0.455785\pi$
$758$		0			0
$759$	−6.22331	+	3.47415i	−0.225892	+	0.126103i
$760$		0			0
$761$	−19.4560	+	5.71280i	−0.705279	+	0.207089i	−0.614655	−	0.788796i	$-0.710705\pi$
$761$	−19.4560	+	5.71280i	−0.705279	+	0.207089i	−0.0906247	+	0.995885i	$0.528886\pi$
$762$		0			0
$763$	−14.9203	−	23.2165i	−0.540152	−	0.840493i
$764$		0			0
$765$	28.4299	+	20.6521i	1.02789	+	0.746680i
$766$		0			0
$767$	−11.9728	−	10.3745i	−0.432312	−	0.374600i
$768$		0			0
$769$	−11.3907	−	24.9421i	−0.410759	−	0.899437i	−0.996065	−	0.0886244i	$-0.971753\pi$
$769$	−11.3907	−	24.9421i	−0.410759	−	0.899437i	0.585306	−	0.810812i	$-0.300974\pi$
$770$		0			0
$771$	−68.7272	−	20.1801i	−2.47515	−	0.726769i
$772$		0			0
$773$	−1.95905	−	0.281668i	−0.0704620	−	0.0101309i	0.106994	−	0.994260i	$-0.465878\pi$
$773$	−1.95905	−	0.281668i	−0.0704620	−	0.0101309i	−0.177456	+	0.984129i	$0.556787\pi$
$774$		0			0
$775$	3.47071	−	5.75757i	0.124672	−	0.206818i
$776$		0			0
$777$	52.8775	−	7.60264i	1.89697	−	0.272743i
$778$		0			0
$779$	22.8533	+	26.3742i	0.818806	+	0.944953i
$780$		0			0
$781$	−4.12272			−0.147523
$782$		0			0
$783$		−	3.60269i		−	0.128750i
$784$		0			0
$785$	−19.7103	−	25.5566i	−0.703489	−	0.912154i
$786$		0			0
$787$	−19.9199	+	2.86405i	−0.710068	+	0.102092i	−0.487879	−	0.872911i	$-0.662229\pi$
$787$	−19.9199	+	2.86405i	−0.710068	+	0.102092i	−0.222189	+	0.975004i	$0.571320\pi$
$788$		0			0
$789$	−1.16722	+	2.55587i	−0.0415543	+	0.0909912i
$790$		0			0
$791$	3.65457	−	25.4181i	0.129942	−	0.903764i
$792$		0			0
$793$	4.12885	−	14.0616i	0.146620	−	0.499341i
$794$		0			0
$795$	−29.8631	+	11.6295i	−1.05914	+	0.412454i
$796$		0			0
$797$	3.62073	+	3.13738i	0.128253	+	0.111132i	0.716626	−	0.697458i	$-0.245686\pi$
$797$	3.62073	+	3.13738i	0.128253	+	0.111132i	−0.588373	+	0.808590i	$0.700231\pi$
$798$		0			0
$799$	−21.1981	−	13.6232i	−0.749935	−	0.481954i
$800$		0			0
$801$	−26.5773	+	17.0802i	−0.939062	+	0.603499i
$802$		0			0
$803$	−0.900743	−	3.06765i	−0.0317865	−	0.108255i
$804$		0			0
$805$	22.2813	+	5.97234i	0.785312	+	0.210497i
$806$		0			0
$807$	−11.5207	−	39.2357i	−0.405546	−	1.38116i
$808$		0			0
$809$	30.7873	−	19.7858i	1.08242	−	0.695632i	0.127308	−	0.991863i	$-0.459366\pi$
$809$	30.7873	−	19.7858i	1.08242	−	0.695632i	0.955116	+	0.296231i	$0.0957298\pi$
$810$		0			0
$811$	−5.45866	−	3.50807i	−0.191680	−	0.123185i	0.441281	−	0.897369i	$-0.354524\pi$
$811$	−5.45866	−	3.50807i	−0.191680	−	0.123185i	−0.632961	+	0.774184i	$0.718161\pi$
$812$		0			0
$813$	6.35068	+	5.50290i	0.222728	+	0.192995i
$814$		0			0
$815$	3.15247	+	8.09517i	0.110426	+	0.283561i
$816$		0			0
$817$	5.93841	−	20.2244i	0.207759	−	0.707561i
$818$		0			0
$819$	−2.39632	+	16.6668i	−0.0837342	+	0.582384i
$820$		0			0
$821$	−4.64243	+	10.1655i	−0.162022	+	0.354778i	−0.973179	−	0.230050i	$-0.926111\pi$
$821$	−4.64243	+	10.1655i	−0.162022	+	0.354778i	0.811157	+	0.584829i	$0.198838\pi$
$822$		0			0
$823$	−35.9249	+	5.16522i	−1.25226	+	0.180048i	−0.736355	−	0.676595i	$-0.763455\pi$
$823$	−35.9249	+	5.16522i	−1.25226	+	0.180048i	−0.515908	+	0.856644i	$0.672546\pi$
$824$		0			0
$825$	−6.13325	+	4.19522i	−0.213532	+	0.146059i
$826$		0			0
$827$			2.61554i			0.0909512i	0.998965	+	0.0454756i	$0.0144803\pi$
$827$			2.61554i			0.0909512i	−0.998965	+	0.0454756i	$0.985520\pi$
$828$		0			0
$829$	6.91066			0.240017			0.120009	−	0.992773i	$-0.461708\pi$
$829$	6.91066			0.240017			0.120009	+	0.992773i	$0.461708\pi$
$830$		0			0
$831$	19.0449	+	21.9790i	0.660661	+	0.762444i
$832$		0			0
$833$	−11.1094	+	1.59729i	−0.384918	+	0.0553429i
$834$		0			0
$835$	−20.3344	+	38.5454i	−0.703702	+	1.33392i
$836$		0			0
$837$	1.07860	+	0.155080i	0.0372820	+	0.00536034i
$838$		0			0
$839$	−10.4011	−	3.05403i	−0.359084	−	0.105437i	0.0972140	−	0.995264i	$-0.469007\pi$
$839$	−10.4011	−	3.05403i	−0.359084	−	0.105437i	−0.456298	+	0.889827i	$0.650825\pi$
$840$		0			0
$841$	−3.83820	−	8.40448i	−0.132352	−	0.289810i
$842$		0			0
$843$	57.1883	+	49.5540i	1.96967	+	1.70673i
$844$		0			0
$845$	9.78904	−	13.4757i	0.336753	−	0.463577i
$846$		0			0
$847$	12.3863	+	19.2735i	0.425599	+	0.662246i
$848$		0			0
$849$	42.5227	−	12.4858i	1.45938	−	0.428511i
$850$		0			0
$851$	47.2766	+	2.93707i	1.62062	+	0.100681i
$852$		0			0
$853$	−4.74463	−	16.1587i	−0.162453	−	0.553264i	−0.999976	−	0.00686250i	$-0.997816\pi$
$853$	−4.74463	−	16.1587i	−0.162453	−	0.553264i	0.837524	−	0.546401i	$-0.184003\pi$
$854$		0			0
$855$	−12.3446	−	21.8555i	−0.422177	−	0.747442i
$856$		0			0
$857$	29.3024	−	45.5955i	1.00095	−	1.55751i	0.182282	−	0.983246i	$-0.441652\pi$
$857$	29.3024	−	45.5955i	1.00095	−	1.55751i	0.818669	−	0.574265i	$-0.194712\pi$
$858$		0			0
$859$	19.6701	−	22.7005i	0.671135	−	0.774531i	−0.313419	−	0.949615i	$-0.601474\pi$
$859$	19.6701	−	22.7005i	0.671135	−	0.774531i	0.984553	+	0.175084i	$0.0560198\pi$
$860$		0			0
$861$	−23.2069	−	50.8160i	−0.790889	−	1.73181i
$862$		0			0
$863$	1.62106	−	5.52081i	0.0551814	−	0.187931i	−0.927290	−	0.374344i	$-0.877868\pi$
$863$	1.62106	−	5.52081i	0.0551814	−	0.187931i	0.982471	+	0.186413i	$0.0596862\pi$
$864$		0			0
$865$	−0.896638	+	4.42686i	−0.0304866	+	0.150518i
$866$		0			0
$867$	12.2902	+	5.61274i	0.417397	+	0.190619i
$868$		0			0
$869$	1.36998	+	9.52843i	0.0464734	+	0.323230i
$870$		0			0
$871$	−6.71497	−	7.74949i	−0.227528	−	0.262581i
$872$		0			0
$873$			16.8480i			0.570219i
$874$		0			0
$875$	23.6986	+	4.09548i	0.801158	+	0.138452i
$876$		0			0
$877$	−6.84644	+	5.93247i	−0.231188	+	0.200325i	−0.762749	−	0.646694i	$-0.776151\pi$
$877$	−6.84644	+	5.93247i	−0.231188	+	0.200325i	0.531561	+	0.847020i	$0.321605\pi$
$878$		0			0
$879$	6.48550	+	45.1077i	0.218751	+	1.52144i
$880$		0			0
$881$	−16.1237	+	35.3059i	−0.543220	+	1.18949i	0.416657	+	0.909064i	$0.363202\pi$
$881$	−16.1237	+	35.3059i	−0.543220	+	1.18949i	−0.959877	+	0.280422i	$0.909526\pi$
$882$		0			0
$883$	−12.6751	−	1.82240i	−0.426550	−	0.0613287i	−0.0743032	−	0.997236i	$-0.523673\pi$
$883$	−12.6751	−	1.82240i	−0.426550	−	0.0613287i	−0.352247	+	0.935907i	$0.614582\pi$
$884$		0			0
$885$	−35.6070	−	12.7014i	−1.19692	−	0.426954i
$886$		0			0
$887$	15.2805	−	6.97838i	0.513069	−	0.234311i	−0.142018	−	0.989864i	$-0.545359\pi$
$887$	15.2805	−	6.97838i	0.513069	−	0.234311i	0.655087	+	0.755553i	$0.272632\pi$
$888$		0			0
$889$	−24.9244	+	28.7643i	−0.835937	+	0.964722i
$890$		0			0
$891$	3.94257	+	2.53374i	0.132081	+	0.0848834i
$892$		0			0
$893$	9.73136	+	15.1423i	0.325648	+	0.506718i
$894$		0			0
$895$	10.0150	+	43.0524i	0.334763	+	1.43908i
$896$		0			0
$897$	−9.67944	+	26.7121i	−0.323187	+	0.891890i
$898$		0			0
$899$	−5.73480	+	1.68389i	−0.191266	+	0.0561609i
$900$		0			0
$901$	−22.6812	+	14.5763i	−0.755620	+	0.485608i
$902$		0			0
$903$	−18.2421	+	28.3853i	−0.607061	+	0.944605i
$904$		0			0
$905$	5.41418	+	5.26090i	0.179973	+	0.174878i
$906$		0			0
$907$	32.9532	−	15.0492i	1.09419	−	0.499701i	0.215216	−	0.976567i	$-0.430954\pi$
$907$	32.9532	−	15.0492i	1.09419	−	0.499701i	0.878976	+	0.476866i	$0.158227\pi$
$908$		0			0
$909$	−22.3664	−	6.56738i	−0.741848	−	0.217826i
$910$		0			0
$911$	−5.90410	+	41.0639i	−0.195611	+	1.36051i	0.621222	+	0.783634i	$0.286636\pi$
$911$	−5.90410	+	41.0639i	−0.195611	+	1.36051i	−0.816834	+	0.576873i	$0.804273\pi$
$912$		0			0
$913$	−4.05412	−	1.85146i	−0.134172	−	0.0612743i
$914$		0			0
$915$	−2.99545	−	34.8434i	−0.0990265	−	1.15189i
$916$		0			0
$917$	18.2097	−	15.7788i	0.601337	−	0.521062i
$918$		0			0
$919$	−52.7391			−1.73970			−0.869851	−	0.493314i	$-0.835785\pi$
$919$	−52.7391			−1.73970			−0.869851	+	0.493314i	$0.835785\pi$
$920$		0			0
$921$	17.2127			0.567177
$922$		0			0
$923$	−12.4203	+	10.7622i	−0.408818	+	0.354243i
$924$		0			0
$925$	49.3639	−	1.41794i	1.62307	−	0.0466215i
$926$		0			0
$927$	−18.8730	−	8.61901i	−0.619871	−	0.283086i
$928$		0			0
$929$	−2.73370	+	19.0133i	−0.0896897	+	0.623806i	0.894550	+	0.446967i	$0.147496\pi$
$929$	−2.73370	+	19.0133i	−0.0896897	+	0.623806i	−0.984240	+	0.176838i	$0.943413\pi$
$930$		0			0
$931$	7.69256	+	2.25874i	0.252114	+	0.0740272i
$932$		0			0
$933$	24.6156	−	11.2415i	0.805877	−	0.368032i
$934$		0			0
$935$	−4.35649	+	4.48343i	−0.142473	+	0.146624i
$936$		0			0
$937$	−17.6880	+	27.5231i	−0.577842	+	0.899139i	−0.999973	−	0.00739585i	$-0.997646\pi$
$937$	−17.6880	+	27.5231i	−0.577842	+	0.899139i	0.422131	+	0.906535i	$0.361282\pi$
$938$		0			0
$939$	−1.77296	+	1.13941i	−0.0578583	+	0.0371832i
$940$		0			0
$941$	13.6687	−	4.01350i	0.445587	−	0.130836i	−0.0512387	−	0.998686i	$-0.516317\pi$
$941$	13.6687	−	4.01350i	0.445587	−	0.130836i	0.496826	+	0.867850i	$0.334499\pi$
$942$		0			0
$943$	−10.9815	−	48.3014i	−0.357607	−	1.57291i
$944$		0			0
$945$	0.883239	+	3.79688i	0.0287318	+	0.123512i
$946$		0			0
$947$	25.7802	+	40.1147i	0.837743	+	1.30355i	0.950750	+	0.309959i	$0.100315\pi$
$947$	25.7802	+	40.1147i	0.837743	+	1.30355i	−0.113007	+	0.993594i	$0.536048\pi$
$948$		0			0
$949$	−10.7216	−	6.89035i	−0.348038	−	0.223670i
$950$		0			0
$951$	−41.2428	+	47.5967i	−1.33739	+	1.54343i
$952$		0			0
$953$	19.1912	−	8.76433i	0.621664	−	0.283905i	−0.0795769	−	0.996829i	$-0.525357\pi$
$953$	19.1912	−	8.76433i	0.621664	−	0.283905i	0.701241	+	0.712924i	$0.252630\pi$
$954$		0			0
$955$	−20.4239	+	57.2562i	−0.660903	+	1.85277i
$956$		0			0
$957$	6.53915	+	0.940188i	0.211381	+	0.0303920i
$958$		0			0
$959$	−4.93953	+	10.8161i	−0.159506	+	0.349269i
$960$		0			0
$961$	4.15448	+	28.8950i	0.134016	+	0.932098i
$962$		0			0
$963$	4.19419	−	3.63429i	0.135156	−	0.117113i
$964$		0			0
$965$	41.8713	+	2.39100i	1.34788	+	0.0769691i
$966$		0			0
$967$		−	44.6587i		−	1.43613i	−0.695978	−	0.718063i	$-0.745029\pi$
$967$		−	44.6587i		−	1.43613i	0.695978	−	0.718063i	$-0.254971\pi$
$968$		0			0
$969$	−26.3157	−	30.3700i	−0.845383	−	0.975624i
$970$		0			0
$971$	4.41115	+	30.6802i	0.141561	+	0.984576i	0.929500	+	0.368823i	$0.120239\pi$
$971$	4.41115	+	30.6802i	0.141561	+	0.984576i	−0.787939	+	0.615753i	$0.788852\pi$
$972$		0			0
$973$	−36.5629	−	16.6977i	−1.17215	−	0.535304i
$974$		0			0
$975$	−7.52579	+	28.6493i	−0.241018	+	0.917512i
$976$		0			0
$977$	−4.85511	+	16.5350i	−0.155329	+	0.529002i	−0.999980	−	0.00631551i	$-0.997990\pi$
$977$	−4.85511	+	16.5350i	−0.155329	+	0.529002i	0.844651	+	0.535317i	$0.179808\pi$
$978$		0			0
$979$	−2.33481	−	5.11251i	−0.0746207	−	0.163397i
$980$		0			0
$981$	27.9128	−	32.2130i	0.891186	−	1.02848i
$982$		0			0
$983$	5.48098	−	8.52858i	0.174816	−	0.272019i	−0.742778	−	0.669538i	$-0.766492\pi$
$983$	5.48098	−	8.52858i	0.174816	−	0.272019i	0.917594	+	0.397519i	$0.130129\pi$
$984$		0			0
$985$	36.5988	−	20.6721i	1.16613	−	0.658667i
$986$		0			0
$987$	−8.11776	−	27.6465i	−0.258391	−	0.879999i
$988$		0			0
$989$	−20.9565	+	21.3523i	−0.666379	+	0.678964i
$990$		0			0
$991$	9.79410	−	2.87581i	0.311120	−	0.0913530i	−0.122445	−	0.992475i	$-0.539074\pi$
$991$	9.79410	−	2.87581i	0.311120	−	0.0913530i	0.433565	+	0.901122i	$0.357255\pi$
$992$		0			0
$993$	7.04482	+	10.9620i	0.223561	+	0.347867i
$994$		0			0
$995$	−4.84214	+	6.66573i	−0.153506	+	0.211318i
$996$		0			0
$997$	10.4077	+	9.01829i	0.329614	+	0.285612i	0.803907	−	0.594755i	$-0.202751\pi$
$997$	10.4077	+	9.01829i	0.329614	+	0.285612i	−0.474293	+	0.880367i	$0.657296\pi$
$998$		0			0
$999$	3.32528	+	7.28135i	0.105207	+	0.230372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.s.a.9.2	✓	120
5.4	even	2	inner	460.2.s.a.9.11	yes	120
23.18	even	11	inner	460.2.s.a.409.11	yes	120
115.64	even	22	inner	460.2.s.a.409.2	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.s.a.9.2	✓	120	1.1	even	1	trivial
460.2.s.a.9.11	yes	120	5.4	even	2	inner
460.2.s.a.409.2	yes	120	115.64	even	22	inner
460.2.s.a.409.11	yes	120	23.18	even	11	inner

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.90027 + 1.64660i) q^{3} +(-2.22785 + 0.191526i) q^{5} +(-1.95670 - 0.893593i) q^{7} +(0.472816 - 3.28851i) q^{9} +O(q^{10})\)	\(q+(-1.90027 + 1.64660i) q^{3} +(-2.22785 + 0.191526i) q^{5} +(-1.95670 - 0.893593i) q^{7} +(0.472816 - 3.28851i) q^{9} +(0.567111 + 0.166519i) q^{11} +(2.14319 - 0.978763i) q^{13} +(3.91816 - 4.03232i) q^{15} +(2.55726 - 3.97918i) q^{17} +(-2.84242 + 1.82671i) q^{19} +(5.18964 - 1.52382i) q^{21} +(4.78020 - 0.386862i) q^{23} +(4.92664 - 0.853381i) q^{25} +(0.438164 + 0.681796i) q^{27} +(-3.73961 - 2.40330i) q^{29} +(0.880493 - 1.01614i) q^{31} +(-1.35186 + 0.617372i) q^{33} +(4.53037 + 1.61603i) q^{35} +(9.77632 + 1.40562i) q^{37} +(-2.46102 + 5.38889i) q^{39} +(-1.46991 - 10.2234i) q^{41} +(-4.71465 + 4.08527i) q^{43} +(-0.423529 + 7.41685i) q^{45} -5.32725i q^{47} +(-1.55388 - 1.79327i) q^{49} +(1.69260 + 11.7723i) q^{51} +(-5.18487 - 2.36785i) q^{53} +(-1.29533 - 0.262363i) q^{55} +(2.39352 - 8.15158i) q^{57} +(-2.79321 - 6.11627i) q^{59} +(4.07329 - 4.70083i) q^{61} +(-3.86374 + 6.01210i) q^{63} +(-4.58725 + 2.59101i) q^{65} +(-1.22613 - 4.17582i) q^{67} +(-8.44669 + 8.60621i) q^{69} +(-6.69267 + 1.96514i) q^{71} +(-2.92446 - 4.55055i) q^{73} +(-7.95678 + 9.73384i) q^{75} +(-0.960864 - 0.832593i) q^{77} +(6.76581 + 14.8151i) q^{79} +(7.60796 + 2.23390i) q^{81} +(-7.46383 - 1.07314i) q^{83} +(-4.93509 + 9.35480i) q^{85} +(11.0636 - 1.59070i) q^{87} +(-6.22717 - 7.18654i) q^{89} -5.06819 q^{91} +3.38077i q^{93} +(5.98263 - 4.61404i) q^{95} +(-5.01954 + 0.721701i) q^{97} +(0.815737 - 1.78622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{9}+O(q^{10}) \) 120 * q + 20 * q^9	\( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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