LMFDB - Embedded newform 1040.2.dh.b.289.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(289,1040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.dh (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.5
Root			$0.550552 + 0.147520i$ of defining polynomial
Character	$\chi$	$=$	1040.289
Dual form			1040.2.dh.b.529.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.45071 - 0.837565i) q^{3} +(-1.67513 - 1.48119i) q^{5} +(1.56410 + 0.903032i) q^{7} +(-0.0969683 + 0.167954i) q^{9} +(3.22179 + 5.58031i) q^{11} +(1.98082 - 3.01270i) q^{13} +(-3.67072 - 0.745746i) q^{15} +(-0.416726 - 0.240597i) q^{17} +(3.14363 - 5.44492i) q^{19} +3.02539 q^{21} +(6.16499 - 3.55936i) q^{23} +(0.612127 + 4.96239i) q^{25} +5.35026i q^{27} +(1.15633 + 2.00281i) q^{29} -3.25694 q^{31} +(9.34774 + 5.39692i) q^{33} +(-1.28250 - 3.82943i) q^{35} +(2.65264 - 1.53150i) q^{37} +(0.350262 - 6.02961i) q^{39} +(-3.75329 - 6.50089i) q^{41} +(1.73205 + 1.00000i) q^{43} +(0.411207 - 0.137716i) q^{45} -2.19394i q^{47} +(-1.86907 - 3.23732i) q^{49} -0.806063 q^{51} +0.906679i q^{53} +(2.86860 - 14.1198i) q^{55} -10.5320i q^{57} +(-3.28726 + 5.69370i) q^{59} +(5.47508 - 9.48313i) q^{61} +(-0.303336 + 0.175131i) q^{63} +(-7.78053 + 2.11268i) q^{65} +(-0.562690 + 0.324869i) q^{67} +(5.96239 - 10.3272i) q^{69} +(1.83146 - 3.17217i) q^{71} +2.60720i q^{73} +(5.04434 + 6.68627i) q^{75} +11.6375i q^{77} -2.29455 q^{79} +(4.19029 + 7.25779i) q^{81} +13.3380i q^{83} +(0.341700 + 1.02028i) q^{85} +(3.35498 + 1.93700i) q^{87} +(-0.578163 - 1.00141i) q^{89} +(5.81876 - 2.92340i) q^{91} +(-4.72486 + 2.72790i) q^{93} +(-13.3310 + 4.46464i) q^{95} +(-11.9784 - 6.91573i) q^{97} -1.24965 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{9} + 6 q^{11} - 4 q^{15} + 26 q^{19} - 24 q^{21} + 4 q^{25} - 28 q^{29} - 24 q^{31} + 6 q^{35} - 36 q^{39} - 4 q^{41} + 12 q^{45} - 4 q^{49} - 8 q^{51} - 12 q^{55} - 16 q^{59} - 8 q^{61} - 10 q^{65}+ \cdots + 52 q^{99}+O(q^{100}) $ 12 * q - 2 * q^9 + 6 * q^11 - 4 * q^15 + 26 * q^19 - 24 * q^21 + 4 * q^25 - 28 * q^29 - 24 * q^31 + 6 * q^35 - 36 * q^39 - 4 * q^41 + 12 * q^45 - 4 * q^49 - 8 * q^51 - 12 * q^55 - 16 * q^59 - 8 * q^61 - 10 * q^65 + 28 * q^69 - 40 * q^71 + 8 * q^75 - 56 * q^79 + 26 * q^81 - 16 * q^85 + 14 * q^89 + 38 * q^91 + 8 * q^95 + 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	1.45071	−	0.837565i	0.837565	−	0.483569i	−0.0188705	−	0.999822i	$-0.506007\pi$
$3$	1.45071	−	0.837565i	0.837565	−	0.483569i	0.856436	+	0.516253i	$0.172674\pi$
$4$		0			0
$5$	−1.67513	−	1.48119i	−0.749141	−	0.662410i
$5$	−1.67513	−	1.48119i	−0.749141	−	0.662410i
$6$		0			0
$7$	1.56410	+	0.903032i	0.591173	+	0.341314i	0.765561	−	0.643363i	$-0.222461\pi$
$7$	1.56410	+	0.903032i	0.591173	+	0.341314i	−0.174388	+	0.984677i	$0.555795\pi$
$8$		0			0
$9$	−0.0969683	+	0.167954i	−0.0323228	+	0.0559847i
$10$		0			0
$11$	3.22179	+	5.58031i	0.971407	+	1.68253i	0.691317	+	0.722552i	$0.257031\pi$
$11$	3.22179	+	5.58031i	0.971407	+	1.68253i	0.280090	+	0.959974i	$0.409636\pi$
$12$		0			0
$13$	1.98082	−	3.01270i	0.549382	−	0.835572i
$13$	1.98082	−	3.01270i	0.549382	−	0.835572i
$14$		0			0
$15$	−3.67072	−	0.745746i	−0.947776	−	0.192551i
$16$		0			0
$17$	−0.416726	−	0.240597i	−0.101071	−	0.0583534i	0.448612	−	0.893726i	$-0.351918\pi$
$17$	−0.416726	−	0.240597i	−0.101071	−	0.0583534i	−0.549684	+	0.835373i	$0.685252\pi$
$18$		0			0
$19$	3.14363	−	5.44492i	0.721198	−	1.24915i	−0.239322	−	0.970940i	$-0.576925\pi$
$19$	3.14363	−	5.44492i	0.721198	−	1.24915i	0.960520	−	0.278211i	$-0.0897415\pi$
$20$		0			0
$21$	3.02539			0.660195
$22$		0			0
$23$	6.16499	−	3.55936i	1.28549	−	0.742177i	0.307642	−	0.951502i	$-0.400460\pi$
$23$	6.16499	−	3.55936i	1.28549	−	0.742177i	0.977846	+	0.209325i	$0.0671266\pi$
$24$		0			0
$25$	0.612127	+	4.96239i	0.122425	+	0.992478i
$26$		0			0
$27$			5.35026i			1.02966i
$28$		0			0
$29$	1.15633	+	2.00281i	0.214724	+	0.371913i	0.953187	−	0.302381i	$-0.0977814\pi$
$29$	1.15633	+	2.00281i	0.214724	+	0.371913i	−0.738463	+	0.674294i	$0.764448\pi$
$30$		0			0
$31$	−3.25694			−0.584964			−0.292482	−	0.956271i	$-0.594481\pi$
$31$	−3.25694			−0.584964			−0.292482	+	0.956271i	$0.594481\pi$
$32$		0			0
$33$	9.34774	+	5.39692i	1.62723	+	0.939484i
$34$		0			0
$35$	−1.28250	−	3.82943i	−0.216782	−	0.647291i
$36$		0			0
$37$	2.65264	−	1.53150i	0.436091	−	0.251777i	−0.265847	−	0.964015i	$-0.585652\pi$
$37$	2.65264	−	1.53150i	0.436091	−	0.251777i	0.701938	+	0.712238i	$0.252318\pi$
$38$		0			0
$39$	0.350262	−	6.02961i	0.0560868	−	0.965510i
$40$		0			0
$41$	−3.75329	−	6.50089i	−0.586166	−	1.01527i	−0.994729	−	0.102539i	$-0.967303\pi$
$41$	−3.75329	−	6.50089i	−0.586166	−	1.01527i	0.408563	−	0.912730i	$-0.366030\pi$
$42$		0			0
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	0.626219	−	0.779647i	$-0.284601\pi$
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	−0.362084	+	0.932145i	$0.617935\pi$
$44$		0			0
$45$	0.411207	−	0.137716i	0.0612991	−	0.0205295i
$46$		0			0
$47$		−	2.19394i		−	0.320019i	−0.987116	−	0.160009i	$-0.948848\pi$
$47$		−	2.19394i		−	0.320019i	0.987116	−	0.160009i	$-0.0511524\pi$
$48$		0			0
$49$	−1.86907	−	3.23732i	−0.267010	−	0.462474i
$50$		0			0
$51$	−0.806063			−0.112871
$52$		0			0
$53$			0.906679i			0.124542i	0.998059	+	0.0622710i	$0.0198343\pi$
$53$			0.906679i			0.124542i	−0.998059	+	0.0622710i	$0.980166\pi$
$54$		0			0
$55$	2.86860	−	14.1198i	0.386801	−	1.90392i
$56$		0			0
$57$		−	10.5320i		−	1.39499i
$58$		0			0
$59$	−3.28726	+	5.69370i	−0.427965	+	0.741256i	−0.996692	−	0.0812696i	$-0.974103\pi$
$59$	−3.28726	+	5.69370i	−0.427965	+	0.741256i	0.568728	+	0.822526i	$0.307436\pi$
$60$		0			0
$61$	5.47508	−	9.48313i	0.701013	−	1.21419i	−0.267098	−	0.963669i	$-0.586065\pi$
$61$	5.47508	−	9.48313i	0.701013	−	1.21419i	0.968111	−	0.250521i	$-0.0806018\pi$
$62$		0			0
$63$	−0.303336	+	0.175131i	−0.0382167	+	0.0220644i
$64$		0			0
$65$	−7.78053	+	2.11268i	−0.965056	+	0.262045i
$66$		0			0
$67$	−0.562690	+	0.324869i	−0.0687435	+	0.0396891i	−0.533978	−	0.845499i	$-0.679303\pi$
$67$	−0.562690	+	0.324869i	−0.0687435	+	0.0396891i	0.465234	+	0.885188i	$0.345970\pi$
$68$		0			0
$69$	5.96239	−	10.3272i	0.717787	−	1.24324i
$70$		0			0
$71$	1.83146	−	3.17217i	0.217354	−	0.376468i	−0.736644	−	0.676280i	$-0.763591\pi$
$71$	1.83146	−	3.17217i	0.217354	−	0.376468i	0.953998	+	0.299812i	$0.0969241\pi$
$72$		0			0
$73$			2.60720i			0.305150i	0.988292	+	0.152575i	$0.0487566\pi$
$73$			2.60720i			0.305150i	−0.988292	+	0.152575i	$0.951243\pi$
$74$		0			0
$75$	5.04434	+	6.68627i	0.582470	+	0.772064i
$76$		0			0
$77$			11.6375i			1.32622i
$78$		0			0
$79$	−2.29455			−0.258157			−0.129079	−	0.991634i	$-0.541202\pi$
$79$	−2.29455			−0.258157			−0.129079	+	0.991634i	$0.541202\pi$
$80$		0			0
$81$	4.19029	+	7.25779i	0.465588	+	0.806422i
$82$		0			0
$83$			13.3380i			1.46404i	0.681283	+	0.732020i	$0.261422\pi$
$83$			13.3380i			1.46404i	−0.681283	+	0.732020i	$0.738578\pi$
$84$		0			0
$85$	0.341700	+	1.02028i	0.0370626	+	0.110665i
$86$		0			0
$87$	3.35498	+	1.93700i	0.359691	+	0.207668i
$88$		0			0
$89$	−0.578163	−	1.00141i	−0.0612851	−	0.106149i	0.833755	−	0.552135i	$-0.186187\pi$
$89$	−0.578163	−	1.00141i	−0.0612851	−	0.106149i	−0.895040	+	0.445986i	$0.852853\pi$
$90$		0			0
$91$	5.81876	−	2.92340i	0.609972	−	0.306456i
$92$		0			0
$93$	−4.72486	+	2.72790i	−0.489945	+	0.282870i
$94$		0			0
$95$	−13.3310	+	4.46464i	−1.36773	+	0.458062i
$96$		0			0
$97$	−11.9784	−	6.91573i	−1.21622	−	0.702186i	−0.252114	−	0.967698i	$-0.581126\pi$
$97$	−11.9784	−	6.91573i	−1.21622	−	0.702186i	−0.964108	+	0.265512i	$0.914459\pi$
$98$		0			0
$99$	−1.24965			−0.125594
$100$		0			0
$101$	4.79995	+	8.31376i	0.477613	+	0.827250i	0.999671	−	0.0256599i	$-0.00816868\pi$
$101$	4.79995	+	8.31376i	0.477613	+	0.827250i	−0.522057	+	0.852910i	$0.674835\pi$
$102$		0			0
$103$			3.07522i			0.303011i	0.988456	+	0.151505i	$0.0484121\pi$
$103$			3.07522i			0.303011i	−0.988456	+	0.151505i	$0.951588\pi$
$104$		0			0
$105$	−5.06793	−	4.48119i	−0.494579	−	0.437320i
$106$		0			0
$107$	1.45071	−	0.837565i	0.140245	−	0.0809705i	−0.428236	−	0.903667i	$-0.640865\pi$
$107$	1.45071	−	0.837565i	0.140245	−	0.0809705i	0.568481	+	0.822697i	$0.307531\pi$
$108$		0			0
$109$	−10.8872			−1.04280			−0.521401	−	0.853312i	$-0.674590\pi$
$109$	−10.8872			−1.04280			−0.521401	+	0.853312i	$0.674590\pi$
$110$		0			0
$111$	2.56547	−	4.44352i	0.243503	−	0.421760i
$112$		0			0
$113$	12.1244	+	7.00000i	1.14056	+	0.658505i	0.946570	−	0.322498i	$-0.104523\pi$
$113$	12.1244	+	7.00000i	1.14056	+	0.658505i	0.193993	+	0.981003i	$0.437856\pi$
$114$		0			0
$115$	−15.5993	−	3.16915i	−1.45464	−	0.295525i
$116$		0			0
$117$	0.313917	+	0.624823i	0.0290217	+	0.0577649i
$118$		0			0
$119$	−0.434534	−	0.752634i	−0.0398336	−	0.0689939i
$120$		0			0
$121$	−15.2599	+	26.4309i	−1.38726	+	2.40281i
$122$		0			0
$123$	−10.8898	−	6.28726i	−0.981905	−	0.566903i
$124$		0			0
$125$	6.32487	−	9.21933i	0.565713	−	0.824602i
$126$		0			0
$127$	4.49176	−	2.59332i	0.398580	−	0.230120i	−0.287291	−	0.957843i	$-0.592755\pi$
$127$	4.49176	−	2.59332i	0.398580	−	0.230120i	0.685871	+	0.727723i	$0.259421\pi$
$128$		0			0
$129$	3.35026			0.294974
$130$		0			0
$131$	10.8011			0.943700			0.471850	−	0.881679i	$-0.343586\pi$
$131$	10.8011			0.943700			0.471850	+	0.881679i	$0.343586\pi$
$132$		0			0
$133$	9.83388	−	5.67759i	0.852706	−	0.492310i
$134$		0			0
$135$	7.92478	−	8.96239i	0.682056	−	0.771360i
$136$		0			0
$137$	5.32095	+	3.07205i	0.454600	+	0.262463i	0.709771	−	0.704433i	$-0.248798\pi$
$137$	5.32095	+	3.07205i	0.454600	+	0.262463i	−0.255171	+	0.966896i	$0.582132\pi$
$138$		0			0
$139$	−5.16902	+	8.95301i	−0.438431	+	0.759384i	−0.997569	−	0.0696904i	$-0.977799\pi$
$139$	−5.16902	+	8.95301i	−0.438431	+	0.759384i	0.559138	+	0.829075i	$0.311132\pi$
$140$		0			0
$141$	−1.83757	−	3.18276i	−0.154751	−	0.268036i
$142$		0			0
$143$	23.1936	+	1.34732i	1.93954	+	0.112669i
$144$		0			0
$145$	1.02956	−	5.06772i	0.0855004	−	0.420851i
$146$		0			0
$147$	−5.42293	−	3.13093i	−0.447276	−	0.258235i
$148$		0			0
$149$	−8.02539	+	13.9004i	−0.657466	+	1.13876i	0.323804	+	0.946124i	$0.395038\pi$
$149$	−8.02539	+	13.9004i	−0.657466	+	1.13876i	−0.981270	+	0.192640i	$0.938295\pi$
$150$		0			0
$151$	−9.31757			−0.758253			−0.379127	−	0.925345i	$-0.623776\pi$
$151$	−9.31757			−0.758253			−0.379127	+	0.925345i	$0.623776\pi$
$152$		0			0
$153$	0.0808185	−	0.0466606i	0.00653379	−	0.00377228i
$154$		0			0
$155$	5.45580	+	4.82416i	0.438221	+	0.387486i
$156$		0			0
$157$		−	14.7562i		−	1.17768i	−0.808251	−	0.588838i	$-0.799586\pi$
$157$		−	14.7562i		−	1.17768i	0.808251	−	0.588838i	$-0.200414\pi$
$158$		0			0
$159$	0.759403	+	1.31532i	0.0602246	+	0.104312i
$160$		0			0
$161$	12.8568			1.01326
$162$		0			0
$163$	11.7127	+	6.76234i	0.917411	+	0.529668i	0.882808	−	0.469734i	$-0.155650\pi$
$163$	11.7127	+	6.76234i	0.917411	+	0.529668i	0.0346029	+	0.999401i	$0.488983\pi$
$164$		0			0
$165$	−7.66480	−	22.8864i	−0.596704	−	1.78170i
$166$		0			0
$167$	−20.2858	+	11.7120i	−1.56977	+	0.906304i	−0.573570	+	0.819157i	$0.694442\pi$
$167$	−20.2858	+	11.7120i	−1.56977	+	0.906304i	−0.996195	+	0.0871479i	$0.972225\pi$
$168$		0			0
$169$	−5.15268	−	11.9352i	−0.396360	−	0.918095i
$170$		0			0
$171$	0.609665	+	1.05597i	0.0466222	+	0.0807520i
$172$		0			0
$173$	−4.00480	−	2.31217i	−0.304479	−	0.175791i	0.339974	−	0.940435i	$-0.389582\pi$
$173$	−4.00480	−	2.31217i	−0.304479	−	0.175791i	−0.644453	+	0.764644i	$0.722915\pi$
$174$		0			0
$175$	−3.52377	+	8.31443i	−0.266372	+	0.628512i
$176$		0			0
$177$			11.0132i			0.827801i
$178$		0			0
$179$	4.15633	+	7.19897i	0.310658	+	0.538076i	0.978505	−	0.206223i	$-0.0661172\pi$
$179$	4.15633	+	7.19897i	0.310658	+	0.538076i	−0.667847	+	0.744299i	$0.732784\pi$
$180$		0			0
$181$	−1.02539			−0.0762168			−0.0381084	−	0.999274i	$-0.512133\pi$
$181$	−1.02539			−0.0762168			−0.0381084	+	0.999274i	$0.512133\pi$
$182$		0			0
$183$		−	18.3430i		−	1.35595i
$184$		0			0
$185$	−6.71197	−	1.36361i	−0.493474	−	0.100254i
$186$		0			0
$187$		−	3.10062i		−	0.226739i
$188$		0			0
$189$	−4.83146	+	8.36833i	−0.351437	+	0.608706i
$190$		0			0
$191$	0.177593	−	0.307600i	0.0128502	−	0.0222572i	−0.859529	−	0.511087i	$-0.829243\pi$
$191$	0.177593	−	0.307600i	0.0128502	−	0.0222572i	0.872379	+	0.488830i	$0.162576\pi$
$192$		0			0
$193$	−12.1244	+	7.00000i	−0.872730	+	0.503871i	−0.868255	−	0.496119i	$-0.834758\pi$
$193$	−12.1244	+	7.00000i	−0.872730	+	0.503871i	−0.00447566	+	0.999990i	$0.501425\pi$
$194$		0			0
$195$	−9.51775	+	9.58157i	−0.681580	+	0.686151i
$196$		0			0
$197$	−12.2166	+	7.05325i	−0.870396	+	0.502523i	−0.867480	−	0.497473i	$-0.834261\pi$
$197$	−12.2166	+	7.05325i	−0.870396	+	0.502523i	−0.00291585	+	0.999996i	$0.500928\pi$
$198$		0			0
$199$	1.57452	−	2.72714i	0.111614	−	0.193322i	−0.804807	−	0.593537i	$-0.797731\pi$
$199$	1.57452	−	2.72714i	0.111614	−	0.193322i	0.916421	+	0.400215i	$0.131065\pi$
$200$		0			0
$201$	−0.544198	+	0.942579i	−0.0383848	+	0.0664844i
$202$		0			0
$203$			4.17679i			0.293153i
$204$		0			0
$205$	−3.34183	+	16.4492i	−0.233404	+	1.14886i
$206$		0			0
$207$			1.38058i			0.0959569i
$208$		0			0
$209$	40.5125			2.80231
$210$		0			0
$211$	1.54666	+	2.67889i	0.106477	+	0.184423i	0.914340	−	0.404946i	$-0.132710\pi$
$211$	1.54666	+	2.67889i	0.106477	+	0.184423i	−0.807864	+	0.589369i	$0.799376\pi$
$212$		0			0
$213$		−	6.13586i		−	0.420422i
$214$		0			0
$215$	−1.42022	−	4.24063i	−0.0968580	−	0.289209i
$216$		0			0
$217$	−5.09417	−	2.94112i	−0.345815	−	0.199656i
$218$		0			0
$219$	2.18370	+	3.78228i	0.147561	+	0.255583i
$220$		0			0
$221$	−1.55031	+	0.778890i	−0.104285	+	0.0523938i
$222$		0			0
$223$	19.2205	−	11.0970i	1.28710	−	0.743108i	0.308965	−	0.951074i	$-0.400018\pi$
$223$	19.2205	−	11.0970i	1.28710	−	0.743108i	0.978136	+	0.207966i	$0.0666842\pi$
$224$		0			0
$225$	−0.892810	−	0.378385i	−0.0595207	−	0.0252257i
$226$		0			0
$227$	−11.5490	−	6.66784i	−0.766536	−	0.442560i	0.0651014	−	0.997879i	$-0.479263\pi$
$227$	−11.5490	−	6.66784i	−0.766536	−	0.442560i	−0.831638	+	0.555319i	$0.812596\pi$
$228$		0			0
$229$	−26.1744			−1.72965			−0.864827	−	0.502069i	$-0.832572\pi$
$229$	−26.1744			−1.72965			−0.864827	+	0.502069i	$0.832572\pi$
$230$		0			0
$231$	9.74718	+	16.8826i	0.641318	+	1.11079i
$232$		0			0
$233$		−	20.8691i		−	1.36718i	−0.729867	−	0.683589i	$-0.760418\pi$
$233$		−	20.8691i		−	1.36718i	0.729867	−	0.683589i	$-0.239582\pi$
$234$		0			0
$235$	−3.24965	+	3.67513i	−0.211984	+	0.239739i
$236$		0			0
$237$	−3.32872	+	1.92184i	−0.216224	+	0.124837i
$238$		0			0
$239$	−15.2931			−0.989231			−0.494615	−	0.869112i	$-0.664691\pi$
$239$	−15.2931			−0.989231			−0.494615	+	0.869112i	$0.664691\pi$
$240$		0			0
$241$	6.38423	−	11.0578i	0.411244	−	0.712296i	−0.583782	−	0.811910i	$-0.698428\pi$
$241$	6.38423	−	11.0578i	0.411244	−	0.712296i	0.995026	+	0.0996147i	$0.0317610\pi$
$242$		0			0
$243$	−1.74263	−	1.00611i	−0.111790	−	0.0645419i
$244$		0			0
$245$	−1.66417	+	8.19139i	−0.106320	+	0.523328i
$246$		0			0
$247$	−10.1769	−	20.2562i	−0.647543	−	1.28887i
$248$		0			0
$249$	11.1715	+	19.3496i	0.707964	+	1.22623i
$250$		0			0
$251$	−2.10602	+	3.64773i	−0.132931	+	0.230243i	−0.924805	−	0.380441i	$-0.875772\pi$
$251$	−2.10602	+	3.64773i	−0.132931	+	0.230243i	0.791874	+	0.610684i	$0.209105\pi$
$252$		0			0
$253$	39.7246	+	22.9350i	2.49746	+	1.44191i
$254$		0			0
$255$	1.35026	+	1.19394i	0.0845567	+	0.0747672i
$256$		0			0
$257$	16.1300	−	9.31265i	1.00616	−	0.580907i	0.0960955	−	0.995372i	$-0.469365\pi$
$257$	16.1300	−	9.31265i	1.00616	−	0.580907i	0.910065	+	0.414465i	$0.136031\pi$
$258$		0			0
$259$	5.53198			0.343740
$260$		0			0
$261$	−0.448507			−0.0277619
$262$		0			0
$263$	−19.9363	+	11.5102i	−1.22933	+	0.709751i	−0.966889	−	0.255198i	$-0.917859\pi$
$263$	−19.9363	+	11.5102i	−1.22933	+	0.709751i	−0.262437	+	0.964949i	$0.584526\pi$
$264$		0			0
$265$	1.34297	−	1.51881i	0.0824978	−	0.0932995i
$266$		0			0
$267$	−1.67749	−	0.968498i	−0.102661	−	0.0592711i
$268$		0			0
$269$	−6.73695	+	11.6687i	−0.410759	+	0.711456i	−0.994973	−	0.100144i	$-0.968070\pi$
$269$	−6.73695	+	11.6687i	−0.410759	+	0.711456i	0.584214	+	0.811600i	$0.301403\pi$
$270$		0			0
$271$	−8.95017	−	15.5021i	−0.543684	−	0.941688i	−0.998688	−	0.0511993i	$-0.983696\pi$
$271$	−8.95017	−	15.5021i	−0.543684	−	0.941688i	0.455004	−	0.890489i	$-0.349638\pi$
$272$		0			0
$273$	5.99277	−	9.11459i	0.362699	−	0.551640i
$274$		0			0
$275$	−25.7195	+	19.4036i	−1.55094	+	1.17008i
$276$		0			0
$277$	−7.35125	−	4.24424i	−0.441694	−	0.255012i	0.262622	−	0.964899i	$-0.415413\pi$
$277$	−7.35125	−	4.24424i	−0.441694	−	0.255012i	−0.704316	+	0.709887i	$0.748746\pi$
$278$		0			0
$279$	0.315820	−	0.547016i	0.0189076	−	0.0327490i
$280$		0			0
$281$	−16.5296			−0.986074			−0.493037	−	0.870008i	$-0.664113\pi$
$281$	−16.5296			−0.986074			−0.493037	+	0.870008i	$0.664113\pi$
$282$		0			0
$283$	1.33100	−	0.768452i	0.0791196	−	0.0456797i	−0.459918	−	0.887961i	$-0.652121\pi$
$283$	1.33100	−	0.768452i	0.0791196	−	0.0456797i	0.539038	+	0.842282i	$0.318788\pi$
$284$		0			0
$285$	−15.5999	+	17.6424i	−0.924059	+	1.04505i
$286$		0			0
$287$		−	13.5574i		−	0.800266i
$288$		0			0
$289$	−8.38423	−	14.5219i	−0.493190	−	0.854230i
$290$		0			0
$291$	−23.1695			−1.35822
$292$		0			0
$293$	5.13527	+	2.96485i	0.300006	+	0.173208i	0.642446	−	0.766331i	$-0.277920\pi$
$293$	5.13527	+	2.96485i	0.300006	+	0.173208i	−0.342440	+	0.939540i	$0.611253\pi$
$294$		0			0
$295$	13.9401	−	4.66862i	0.811622	−	0.271818i
$296$		0			0
$297$	−29.8561	+	17.2374i	−1.73243	+	1.00022i
$298$		0			0
$299$	1.48849	−	25.6237i	0.0860815	−	1.48186i
$300$		0			0
$301$	1.80606	+	3.12819i	0.104100	+	0.180306i
$302$		0			0
$303$	13.9266	+	8.04055i	0.800065	+	0.461918i
$304$		0			0
$305$	−23.2178	+	7.77581i	−1.32945	+	0.445242i
$306$		0			0
$307$		−	17.9756i		−	1.02592i	−0.858413	−	0.512960i	$-0.828549\pi$
$307$		−	17.9756i		−	1.02592i	0.858413	−	0.512960i	$-0.171451\pi$
$308$		0			0
$309$	2.57570	+	4.46124i	0.146526	+	0.253791i
$310$		0			0
$311$	−15.9575			−0.904865			−0.452432	−	0.891799i	$-0.649444\pi$
$311$	−15.9575			−0.904865			−0.452432	+	0.891799i	$0.649444\pi$
$312$		0			0
$313$		−	23.4372i		−	1.32475i	−0.749172	−	0.662376i	$-0.769548\pi$
$313$		−	23.4372i		−	1.32475i	0.749172	−	0.662376i	$-0.230452\pi$
$314$		0			0
$315$	0.767530	+	0.155932i	0.0432454	+	0.00878576i
$316$		0			0
$317$			20.6507i			1.15986i	0.814667	+	0.579929i	$0.196920\pi$
$317$			20.6507i			1.15986i	−0.814667	+	0.579929i	$0.803080\pi$
$318$		0			0
$319$	−7.45088	+	12.9053i	−0.417169	+	0.722558i
$320$		0			0
$321$	1.40303	−	2.43012i	0.0783096	−	0.135636i
$322$		0			0
$323$	−2.62007	+	1.51270i	−0.145784	+	0.0841687i
$324$		0			0
$325$	16.1627	+	7.98546i	0.896544	+	0.442954i
$326$		0			0
$327$	−15.7941	+	9.11871i	−0.873414	+	0.504266i
$328$		0			0
$329$	1.98119	−	3.43153i	0.109227	−	0.189186i
$330$		0			0
$331$	−13.3380	+	23.1022i	−0.733125	+	1.26981i	0.222416	+	0.974952i	$0.428606\pi$
$331$	−13.3380	+	23.1022i	−0.733125	+	1.26981i	−0.955541	+	0.294858i	$0.904728\pi$
$332$		0			0
$333$			0.594028i			0.0325526i
$334$		0			0
$335$	1.42377	+	0.289255i	0.0777891	+	0.0158037i
$336$		0			0
$337$			8.40597i			0.457902i	0.973438	+	0.228951i	$0.0735296\pi$
$337$			8.40597i			0.457902i	−0.973438	+	0.228951i	$0.926470\pi$
$338$		0			0
$339$	23.4518			1.27373
$340$		0			0
$341$	−10.4932	−	18.1747i	−0.568238	−	0.984217i
$342$		0			0
$343$		−	19.3938i		−	1.04716i
$344$		0			0
$345$	−25.2843	+	8.46789i	−1.36126	+	0.455896i
$346$		0			0
$347$	18.3177	+	10.5757i	0.983343	+	0.567733i	0.903278	−	0.429056i	$-0.141154\pi$
$347$	18.3177	+	10.5757i	0.983343	+	0.567733i	0.0800652	+	0.996790i	$0.474487\pi$
$348$		0			0
$349$	2.73695	+	4.74054i	0.146506	+	0.253755i	0.929934	−	0.367727i	$-0.119864\pi$
$349$	2.73695	+	4.74054i	0.146506	+	0.253755i	−0.783428	+	0.621482i	$0.786531\pi$
$350$		0			0
$351$	16.1187	+	10.5979i	0.860353	+	0.565675i
$352$		0			0
$353$	−26.1056	+	15.0721i	−1.38946	+	0.802204i	−0.993254	−	0.115958i	$-0.963006\pi$
$353$	−26.1056	+	15.0721i	−1.38946	+	0.802204i	−0.396205	+	0.918162i	$0.629673\pi$
$354$		0			0
$355$	−7.76654	+	2.60107i	−0.412205	+	0.138050i
$356$		0			0
$357$	−1.26076	−	0.727901i	−0.0667266	−	0.0385246i
$358$		0			0
$359$	−8.38787			−0.442695			−0.221348	−	0.975195i	$-0.571046\pi$
$359$	−8.38787			−0.442695			−0.221348	+	0.975195i	$0.571046\pi$
$360$		0			0
$361$	−10.2648	−	17.7792i	−0.540253	−	0.935745i
$362$		0			0
$363$			51.1246i			2.68335i
$364$		0			0
$365$	3.86177	−	4.36741i	0.202134	−	0.228600i
$366$		0			0
$367$	−16.8983	+	9.75623i	−0.882084	+	0.509271i	−0.871345	−	0.490671i	$-0.836752\pi$
$367$	−16.8983	+	9.75623i	−0.882084	+	0.509271i	−0.0107388	+	0.999942i	$0.503418\pi$
$368$		0			0
$369$	1.45580			0.0757860
$370$		0			0
$371$	−0.818760	+	1.41813i	−0.0425079	+	0.0736258i
$372$		0			0
$373$	7.37324	+	4.25694i	0.381772	+	0.220416i	0.678589	−	0.734518i	$-0.262592\pi$
$373$	7.37324	+	4.25694i	0.381772	+	0.220416i	−0.296817	+	0.954934i	$0.595925\pi$
$374$		0			0
$375$	1.45373	−	18.6720i	0.0750705	−	0.964219i
$376$		0			0
$377$	8.32435	+	0.483564i	0.428726	+	0.0249048i
$378$		0			0
$379$	9.85931	+	17.0768i	0.506439	+	0.877178i	0.999972	+	0.00745089i	$0.00237172\pi$
$379$	9.85931	+	17.0768i	0.506439	+	0.877178i	−0.493533	+	0.869727i	$0.664295\pi$
$380$		0			0
$381$	4.34415	−	7.52429i	0.222558	−	0.385481i
$382$		0			0
$383$	24.0059	+	13.8598i	1.22664	+	0.708202i	0.966326	−	0.257321i	$-0.0828399\pi$
$383$	24.0059	+	13.8598i	1.22664	+	0.708202i	0.260316	+	0.965523i	$0.416173\pi$
$384$		0			0
$385$	17.2374	−	19.4944i	0.878501	−	0.993525i
$386$		0			0
$387$	−0.335908	+	0.193937i	−0.0170752	+	0.00985835i
$388$		0			0
$389$	−9.15140			−0.463994			−0.231997	−	0.972716i	$-0.574526\pi$
$389$	−9.15140			−0.463994			−0.231997	+	0.972716i	$0.574526\pi$
$390$		0			0
$391$	−3.42548			−0.173234
$392$		0			0
$393$	15.6693	−	9.04666i	0.790410	−	0.456344i
$394$		0			0
$395$	3.84367	+	3.39868i	0.193396	+	0.171006i
$396$		0			0
$397$	1.23877	+	0.715205i	0.0621721	+	0.0358951i	0.530764	−	0.847520i	$-0.321905\pi$
$397$	1.23877	+	0.715205i	0.0621721	+	0.0358951i	−0.468592	+	0.883415i	$0.655238\pi$
$398$		0			0
$399$	9.51071	−	16.4730i	0.476131	−	0.824683i
$400$		0			0
$401$	−10.8351	−	18.7669i	−0.541079	−	0.937177i	−0.998842	−	0.0481025i	$-0.984683\pi$
$401$	−10.8351	−	18.7669i	−0.541079	−	0.937177i	0.457763	−	0.889074i	$-0.348651\pi$
$402$		0			0
$403$	−6.45142	+	9.81217i	−0.321368	+	0.488779i
$404$		0			0
$405$	3.73092	−	18.3644i	0.185391	−	0.912534i
$406$		0			0
$407$	17.0925	+	9.86836i	0.847244	+	0.489156i
$408$		0			0
$409$	4.54055	−	7.86447i	0.224516	−	0.388873i	−0.731658	−	0.681672i	$-0.761253\pi$
$409$	4.54055	−	7.86447i	0.224516	−	0.388873i	0.956174	+	0.292799i	$0.0945866\pi$
$410$		0			0
$411$	10.2922			0.507676
$412$		0			0
$413$	−10.2832	+	5.93700i	−0.506002	+	0.292140i
$414$		0			0
$415$	19.7562	−	22.3430i	0.969795	−	1.09677i
$416$		0			0
$417$			17.3176i			0.848045i
$418$		0			0
$419$	7.77139	+	13.4604i	0.379657	+	0.657586i	0.991012	−	0.133771i	$-0.0427086\pi$
$419$	7.77139	+	13.4604i	0.379657	+	0.657586i	−0.611355	+	0.791356i	$0.709375\pi$
$420$		0			0
$421$	−4.96476			−0.241968			−0.120984	−	0.992654i	$-0.538605\pi$
$421$	−4.96476			−0.241968			−0.120984	+	0.992654i	$0.538605\pi$
$422$		0			0
$423$	0.368480	+	0.212742i	0.0179161	+	0.0103439i
$424$		0			0
$425$	0.938847	−	2.21523i	0.0455408	−	0.107455i
$426$		0			0
$427$	17.1271	−	9.88835i	0.828840	−	0.478531i
$428$		0			0
$429$	34.7755	−	17.4716i	1.67898	−	0.843535i
$430$		0			0
$431$	−16.4853	−	28.5534i	−0.794070	−	1.37537i	−0.923428	−	0.383771i	$-0.874625\pi$
$431$	−16.4853	−	28.5534i	−0.794070	−	1.37537i	0.129358	−	0.991598i	$-0.458708\pi$
$432$		0			0
$433$	13.9529	+	8.05571i	0.670534	+	0.387133i	0.796279	−	0.604930i	$-0.206799\pi$
$433$	13.9529	+	8.05571i	0.670534	+	0.387133i	−0.125745	+	0.992063i	$0.540132\pi$
$434$		0			0
$435$	−2.75096	−	8.21409i	−0.131898	−	0.393836i
$436$		0			0
$437$		−	44.7572i		−	2.14103i
$438$		0			0
$439$	0.0417360	+	0.0722889i	0.00199195	+	0.00345016i	0.867020	−	0.498274i	$-0.166033\pi$
$439$	0.0417360	+	0.0722889i	0.00199195	+	0.00345016i	−0.865028	+	0.501724i	$0.832699\pi$
$440$		0			0
$441$	0.724961			0.0345220
$442$		0			0
$443$		−	40.9135i		−	1.94386i	−0.235271	−	0.971930i	$-0.575598\pi$
$443$		−	40.9135i		−	1.94386i	0.235271	−	0.971930i	$-0.424402\pi$
$444$		0			0
$445$	−0.514780	+	2.53386i	−0.0244029	+	0.120116i
$446$		0			0
$447$			26.8872i			1.27172i
$448$		0			0
$449$	−14.5659	+	25.2290i	−0.687409	+	1.19063i	0.285264	+	0.958449i	$0.407919\pi$
$449$	−14.5659	+	25.2290i	−0.687409	+	1.19063i	−0.972673	+	0.232179i	$0.925415\pi$
$450$		0			0
$451$	24.1847	−	41.8891i	1.13881	−	1.97248i
$452$		0			0
$453$	−13.5171	+	7.80408i	−0.635087	+	0.366668i
$454$		0			0
$455$	−14.0773	−	3.72163i	−0.659955	−	0.174473i
$456$		0			0
$457$	28.2912	−	16.3339i	1.32341	−	0.764068i	0.339135	−	0.940738i	$-0.389866\pi$
$457$	28.2912	−	16.3339i	1.32341	−	0.764068i	0.984270	+	0.176669i	$0.0565323\pi$
$458$		0			0
$459$	1.28726	−	2.22960i	0.0600840	−	0.104069i
$460$		0			0
$461$	9.55031	−	16.5416i	0.444802	−	0.770420i	−0.553236	−	0.833024i	$-0.686607\pi$
$461$	9.55031	−	16.5416i	0.444802	−	0.770420i	0.998038	+	0.0626044i	$0.0199407\pi$
$462$		0			0
$463$		−	8.29218i		−	0.385370i	−0.981261	−	0.192685i	$-0.938280\pi$
$463$		−	8.29218i		−	0.385370i	0.981261	−	0.192685i	$-0.0617196\pi$
$464$		0			0
$465$	11.9553	+	2.42885i	0.554414	+	0.112635i
$466$		0			0
$467$		−	23.5369i		−	1.08916i	−0.838710	−	0.544579i	$-0.816689\pi$
$467$		−	23.5369i		−	1.08916i	0.838710	−	0.544579i	$-0.183311\pi$
$468$		0			0
$469$	−1.17347			−0.0541857
$470$		0			0
$471$	−12.3593	−	21.4070i	−0.569487	−	0.986380i
$472$		0			0
$473$			12.8872i			0.592553i
$474$		0			0
$475$	28.9441	+	12.2669i	1.32805	+	0.562845i
$476$		0			0
$477$	−0.152280	−	0.0879191i	−0.00697244	−	0.00402554i
$478$		0			0
$479$	−3.27821	−	5.67802i	−0.149785	−	0.259436i	0.781363	−	0.624077i	$-0.214525\pi$
$479$	−3.27821	−	5.67802i	−0.149785	−	0.259436i	−0.931148	+	0.364642i	$0.881192\pi$
$480$		0			0
$481$	0.640459	−	11.0252i	0.0292024	−	0.502707i
$482$		0			0
$483$	18.6515	−	10.7685i	0.848673	−	0.489982i
$484$		0			0
$485$	9.82184	+	29.3271i	0.445987	+	1.33167i
$486$		0			0
$487$	11.7432	+	6.77996i	0.532137	+	0.307229i	0.741886	−	0.670526i	$-0.233931\pi$
$487$	11.7432	+	6.77996i	0.532137	+	0.307229i	−0.209749	+	0.977755i	$0.567265\pi$
$488$		0			0
$489$	22.6556			1.02452
$490$		0			0
$491$	2.47873	+	4.29329i	0.111864	+	0.193753i	0.916522	−	0.399985i	$-0.130985\pi$
$491$	2.47873	+	4.29329i	0.111864	+	0.193753i	−0.804658	+	0.593739i	$0.797651\pi$
$492$		0			0
$493$		−	1.11283i		−	0.0501195i
$494$		0			0
$495$	2.09332	+	1.85097i	0.0940878	+	0.0831949i
$496$		0			0
$497$	5.72915	−	3.30773i	0.256987	−	0.148372i
$498$		0			0
$499$	−13.8700			−0.620907			−0.310454	−	0.950588i	$-0.600481\pi$
$499$	−13.8700			−0.620907			−0.310454	+	0.950588i	$0.600481\pi$
$500$		0			0
$501$	−19.6192	+	33.9814i	−0.876521	+	1.51818i
$502$		0			0
$503$	−2.98650	−	1.72425i	−0.133161	−	0.0768807i	0.431940	−	0.901903i	$-0.357829\pi$
$503$	−2.98650	−	1.72425i	−0.133161	−	0.0768807i	−0.565101	+	0.825022i	$0.691163\pi$
$504$		0			0
$505$	4.27375	−	21.0363i	0.190179	−	0.936103i
$506$		0			0
$507$	−17.4716	−	12.9988i	−0.775939	−	0.577298i
$508$		0			0
$509$	−15.4812	−	26.8142i	−0.686192	−	1.18852i	−0.973061	−	0.230549i	$-0.925948\pi$
$509$	−15.4812	−	26.8142i	−0.686192	−	1.18852i	0.286869	−	0.957970i	$-0.407386\pi$
$510$		0			0
$511$	−2.35439	+	4.07792i	−0.104152	+	0.180396i
$512$		0			0
$513$	29.1318	+	16.8192i	1.28620	+	0.742587i
$514$		0			0
$515$	4.55500	−	5.15140i	0.200717	−	0.226998i
$516$		0			0
$517$	12.2428	−	7.06841i	0.538439	−	0.310868i
$518$		0			0
$519$	−7.74638			−0.340029
$520$		0			0
$521$	14.2506			0.624330			0.312165	−	0.950028i	$-0.398946\pi$
$521$	14.2506			0.624330			0.312165	+	0.950028i	$0.398946\pi$
$522$		0			0
$523$	−9.10529	+	5.25694i	−0.398146	+	0.229870i	−0.685684	−	0.727899i	$-0.740497\pi$
$523$	−9.10529	+	5.25694i	−0.398146	+	0.229870i	0.287537	+	0.957769i	$0.407163\pi$
$524$		0			0
$525$	1.85192	+	15.0132i	0.0808246	+	0.655229i
$526$		0			0
$527$	1.35725	+	0.783611i	0.0591229	+	0.0341346i
$528$		0			0
$529$	13.8380	−	23.9682i	0.601654	−	1.04210i
$530$		0			0
$531$	−0.637519	−	1.10422i	−0.0276660	−	0.0479189i
$532$		0			0
$533$	−27.0198	−	1.56959i	−1.17036	−	0.0679865i
$534$		0			0
$535$	−3.67072	−	0.745746i	−0.158699	−	0.0322414i
$536$		0			0
$537$	12.0592	+	6.96239i	0.520393	+	0.300449i
$538$		0			0
$539$	12.0435	−	20.8599i	0.518750	−	0.898501i
$540$		0			0
$541$	15.5345			0.667882			0.333941	−	0.942594i	$-0.391621\pi$
$541$	15.5345			0.667882			0.333941	+	0.942594i	$0.391621\pi$
$542$		0			0
$543$	−1.48754	+	0.858833i	−0.0638366	+	0.0368561i
$544$		0			0
$545$	18.2374	+	16.1260i	0.781206	+	0.690762i
$546$		0			0
$547$			23.5515i			1.00699i	0.863998	+	0.503495i	$0.167953\pi$
$547$			23.5515i			1.00699i	−0.863998	+	0.503495i	$0.832047\pi$
$548$		0			0
$549$	1.06182	+	1.83912i	0.0453173	+	0.0784919i
$550$		0			0
$551$	14.5402			0.619435
$552$		0			0
$553$	−3.58890	−	2.07205i	−0.152616	−	0.0881127i
$554$		0			0
$555$	−10.8792	+	3.64352i	−0.461797	+	0.154659i
$556$		0			0
$557$	17.3602	−	10.0229i	0.735576	−	0.424685i	−0.0848824	−	0.996391i	$-0.527051\pi$
$557$	17.3602	−	10.0229i	0.735576	−	0.424685i	0.820459	+	0.571706i	$0.193718\pi$
$558$		0			0
$559$	6.44358	−	3.23732i	0.272535	−	0.136924i
$560$		0			0
$561$	−2.59697	−	4.49808i	−0.109644	−	0.189909i
$562$		0			0
$563$	10.8898	+	6.28726i	0.458952	+	0.264976i	0.711604	−	0.702581i	$-0.247969\pi$
$563$	10.8898	+	6.28726i	0.458952	+	0.264976i	−0.252651	+	0.967557i	$0.581303\pi$
$564$		0			0
$565$	−9.94152	−	29.6844i	−0.418243	−	1.24883i
$566$		0			0
$567$			15.1359i			0.635646i
$568$		0			0
$569$	2.14481	+	3.71493i	0.0899153	+	0.155738i	0.907475	−	0.420106i	$-0.138007\pi$
$569$	2.14481	+	3.71493i	0.0899153	+	0.155738i	−0.817560	+	0.575844i	$0.804674\pi$
$570$		0			0
$571$	−6.39280			−0.267530			−0.133765	−	0.991013i	$-0.542707\pi$
$571$	−6.39280			−0.267530			−0.133765	+	0.991013i	$0.542707\pi$
$572$		0			0
$573$		−	0.594984i		−	0.0248558i
$574$		0			0
$575$	21.4367	+	28.4143i	0.893971	+	1.18496i
$576$		0			0
$577$			37.8169i			1.57434i	0.616738	+	0.787168i	$0.288454\pi$
$577$			37.8169i			1.57434i	−0.616738	+	0.787168i	$0.711546\pi$
$578$		0			0
$579$	−11.7259	+	20.3099i	−0.487312	+	0.844050i
$580$		0			0
$581$	−12.0447	+	20.8620i	−0.499697	+	0.865501i
$582$		0			0
$583$	−5.05955	+	2.92113i	−0.209545	+	0.120981i
$584$		0			0
$585$	0.399632	−	1.51163i	0.0165227	−	0.0624983i
$586$		0			0
$587$	19.5289	−	11.2750i	0.806046	−	0.465371i	−0.0395351	−	0.999218i	$-0.512588\pi$
$587$	19.5289	−	11.2750i	0.806046	−	0.465371i	0.845581	+	0.533848i	$0.179254\pi$
$588$		0			0
$589$	−10.2386	+	17.7338i	−0.421875	+	0.730708i
$590$		0			0
$591$	−11.8151	+	20.4644i	−0.486009	+	0.841792i
$592$		0			0
$593$			8.38787i			0.344449i	0.985058	+	0.172224i	$0.0550954\pi$
$593$			8.38787i			0.344449i	−0.985058	+	0.172224i	$0.944905\pi$
$594$		0			0
$595$	−0.386897	+	1.90439i	−0.0158612	+	0.0780724i
$596$		0			0
$597$		−	5.27504i		−	0.215893i
$598$		0			0
$599$	29.0884			1.18852			0.594260	−	0.804273i	$-0.297445\pi$
$599$	29.0884			1.18852			0.594260	+	0.804273i	$0.297445\pi$
$600$		0			0
$601$	21.5059	+	37.2493i	0.877243	+	1.51943i	0.854354	+	0.519692i	$0.173953\pi$
$601$	21.5059	+	37.2493i	0.877243	+	1.51943i	0.0228892	+	0.999738i	$0.492713\pi$
$602$		0			0
$603$		−	0.126008i		−	0.00513144i
$604$		0			0
$605$	64.7116	−	21.6723i	2.63090	−	0.881106i
$606$		0			0
$607$	−18.8372	−	10.8757i	−0.764578	−	0.441429i	0.0663591	−	0.997796i	$-0.478862\pi$
$607$	−18.8372	−	10.8757i	−0.764578	−	0.441429i	−0.830937	+	0.556367i	$0.812195\pi$
$608$		0			0
$609$	3.49834	+	6.05930i	0.141760	+	0.245535i
$610$		0			0
$611$	−6.60966	−	4.34580i	−0.267398	−	0.175812i
$612$		0			0
$613$	26.6848	−	15.4064i	1.07779	−	0.622261i	0.147488	−	0.989064i	$-0.452881\pi$
$613$	26.6848	−	15.4064i	1.07779	−	0.622261i	0.930299	+	0.366803i	$0.119548\pi$
$614$		0			0
$615$	8.92927	+	26.6620i	0.360063	+	1.07511i
$616$		0			0
$617$	−39.9125	−	23.0435i	−1.60682	−	0.927696i	−0.990077	−	0.140529i	$-0.955120\pi$
$617$	−39.9125	−	23.0435i	−1.60682	−	0.927696i	−0.616740	−	0.787167i	$-0.711547\pi$
$618$		0			0
$619$	−13.5564			−0.544878			−0.272439	−	0.962173i	$-0.587830\pi$
$619$	−13.5564			−0.544878			−0.272439	+	0.962173i	$0.587830\pi$
$620$		0			0
$621$	19.0435	+	32.9843i	0.764189	+	1.32361i
$622$		0			0
$623$		−	2.08840i		−	0.0836698i
$624$		0			0
$625$	−24.2506	+	6.07522i	−0.970024	+	0.243009i
$626$		0			0
$627$	58.7717	−	33.9318i	2.34711	−	1.35511i
$628$		0			0
$629$	−1.47390			−0.0587682
$630$		0			0
$631$	−2.67513	+	4.63346i	−0.106495	+	0.184455i	−0.914348	−	0.404929i	$-0.867296\pi$
$631$	−2.67513	+	4.63346i	−0.106495	+	0.184455i	0.807853	+	0.589384i	$0.200630\pi$
$632$		0			0
$633$	4.48750	+	2.59086i	0.178362	+	0.102977i
$634$		0			0
$635$	−11.3655	−	2.30902i	−0.451026	−	0.0916308i
$636$		0			0
$637$	−13.4554	−	0.781626i	−0.533121	−	0.0309691i
$638$		0			0
$639$	0.355186	+	0.615201i	0.0140510	+	0.0243370i
$640$		0			0
$641$	−6.19029	+	10.7219i	−0.244502	+	0.423489i	−0.961991	−	0.273080i	$-0.911958\pi$
$641$	−6.19029	+	10.7219i	−0.244502	+	0.423489i	0.717490	+	0.696569i	$0.245291\pi$
$642$		0			0
$643$	9.98067	+	5.76234i	0.393599	+	0.227245i	0.683718	−	0.729746i	$-0.260362\pi$
$643$	9.98067	+	5.76234i	0.393599	+	0.227245i	−0.290119	+	0.956991i	$0.593695\pi$
$644$		0			0
$645$	−5.61213	−	4.96239i	−0.220977	−	0.195394i
$646$		0			0
$647$	−3.17849	+	1.83510i	−0.124959	+	0.0721453i	−0.561177	−	0.827696i	$-0.689651\pi$
$647$	−3.17849	+	1.83510i	−0.124959	+	0.0721453i	0.436217	+	0.899841i	$0.356318\pi$
$648$		0			0
$649$	−42.3634			−1.66291
$650$		0			0
$651$	−9.85352			−0.386190
$652$		0			0
$653$	−7.02043	+	4.05325i	−0.274731	+	0.158616i	−0.631036	−	0.775754i	$-0.717370\pi$
$653$	−7.02043	+	4.05325i	−0.274731	+	0.158616i	0.356305	+	0.934370i	$0.384036\pi$
$654$		0			0
$655$	−18.0933	−	15.9986i	−0.706965	−	0.625116i
$656$		0			0
$657$	−0.437890	−	0.252816i	−0.0170837	−	0.00986329i
$658$		0			0
$659$	−9.27210	+	16.0597i	−0.361190	+	0.625599i	−0.988157	−	0.153447i	$-0.950963\pi$
$659$	−9.27210	+	16.0597i	−0.361190	+	0.625599i	0.626967	+	0.779046i	$0.284296\pi$
$660$		0			0
$661$	−23.2059	−	40.1938i	−0.902606	−	1.56336i	−0.824099	−	0.566446i	$-0.808318\pi$
$661$	−23.2059	−	40.1938i	−0.902606	−	1.56336i	−0.0785068	−	0.996914i	$-0.525015\pi$
$662$		0			0
$663$	−1.59667	+	2.42842i	−0.0620095	+	0.0943122i
$664$		0			0
$665$	−24.8827	−	5.05518i	−0.964908	−	0.196031i
$666$		0			0
$667$	14.2575	+	8.23155i	0.552051	+	0.318727i
$668$		0			0
$669$	18.5889	−	32.1969i	0.718687	−	1.24480i
$670$		0			0
$671$	70.5583			2.72387
$672$		0			0
$673$	34.9956	−	20.2047i	1.34898	−	0.778836i	0.360877	−	0.932613i	$-0.382477\pi$
$673$	34.9956	−	20.2047i	1.34898	−	0.778836i	0.988105	+	0.153778i	$0.0491440\pi$
$674$		0			0
$675$	−26.5501	+	3.27504i	−1.02191	+	0.126056i
$676$		0			0
$677$		−	14.2473i		−	0.547567i	−0.961791	−	0.273784i	$-0.911725\pi$
$677$		−	14.2473i		−	0.547567i	0.961791	−	0.273784i	$-0.0882752\pi$
$678$		0			0
$679$	−12.4902	−	21.6337i	−0.479332	−	0.830227i
$680$		0			0
$681$	−22.3390			−0.856032
$682$		0			0
$683$	−5.02599	−	2.90175i	−0.192314	−	0.111033i	0.400751	−	0.916187i	$-0.368749\pi$
$683$	−5.02599	−	2.90175i	−0.192314	−	0.111033i	−0.593065	+	0.805154i	$0.702082\pi$
$684$		0			0
$685$	−4.36298	−	13.0275i	−0.166701	−	0.497753i
$686$		0			0
$687$	−37.9714	+	21.9228i	−1.44870	+	0.836407i
$688$		0			0
$689$	2.73155	+	1.79597i	0.104064	+	0.0684210i
$690$		0			0
$691$	−9.61990	−	16.6622i	−0.365958	−	0.633858i	0.622971	−	0.782245i	$-0.285925\pi$
$691$	−9.61990	−	16.6622i	−0.365958	−	0.633858i	−0.988929	+	0.148387i	$0.952592\pi$
$692$		0			0
$693$	−1.95457	−	1.12847i	−0.0742479	−	0.0428670i
$694$		0			0
$695$	21.9199	−	7.34113i	0.831470	−	0.278465i
$696$		0			0
$697$			3.61213i			0.136819i
$698$		0			0
$699$	−17.4792	−	30.2749i	−0.661124	−	1.14510i
$700$		0			0
$701$	45.3742			1.71376			0.856881	−	0.515515i	$-0.172399\pi$
$701$	45.3742			1.71376			0.856881	+	0.515515i	$0.172399\pi$
$702$		0			0
$703$		−	19.2579i		−	0.726325i
$704$		0			0
$705$	−1.63612	+	8.05333i	−0.0616198	+	0.303306i
$706$		0			0
$707$			17.3380i			0.652064i
$708$		0			0
$709$	1.98660	−	3.44089i	0.0746082	−	0.129225i	−0.826308	−	0.563219i	$-0.809563\pi$
$709$	1.98660	−	3.44089i	0.0746082	−	0.129225i	0.900916	+	0.433994i	$0.142896\pi$
$710$		0			0
$711$	0.222499	−	0.385379i	0.00834436	−	0.0144528i
$712$		0			0
$713$	−20.0790	+	11.5926i	−0.751964	+	0.434147i
$714$		0			0
$715$	−36.8566	−	36.6111i	−1.37836	−	1.36918i
$716$		0			0
$717$	−22.1858	+	12.8090i	−0.828546	+	0.478361i
$718$		0			0
$719$	−22.8496	+	39.5766i	−0.852145	+	1.47596i	0.0271244	+	0.999632i	$0.491365\pi$
$719$	−22.8496	+	39.5766i	−0.852145	+	1.47596i	−0.879269	+	0.476326i	$0.841968\pi$
$720$		0			0
$721$	−2.77702	+	4.80995i	−0.103422	+	0.179132i
$722$		0			0
$723$		−	21.3888i		−	0.795459i
$724$		0			0
$725$	−9.23092	+	6.96411i	−0.342828	+	0.258641i
$726$		0			0
$727$			24.7948i			0.919588i	0.888026	+	0.459794i	$0.152077\pi$
$727$			24.7948i			0.919588i	−0.888026	+	0.459794i	$0.847923\pi$
$728$		0			0
$729$	−28.5125			−1.05602
$730$		0			0
$731$	−0.481194	−	0.833453i	−0.0177976	−	0.0308264i
$732$		0			0
$733$		−	45.8651i		−	1.69407i	−0.531540	−	0.847033i	$-0.678387\pi$
$733$		−	45.8651i		−	1.69407i	0.531540	−	0.847033i	$-0.321613\pi$
$734$		0			0
$735$	4.44661	+	13.2771i	0.164016	+	0.489735i
$736$		0			0
$737$	−3.62574	−	2.09332i	−0.133556	−	0.0771085i
$738$		0			0
$739$	−17.4817	−	30.2791i	−0.643074	−	1.11384i	−0.984743	−	0.174016i	$-0.944326\pi$
$739$	−17.4817	−	30.2791i	−0.643074	−	1.11384i	0.341669	−	0.939820i	$-0.389008\pi$
$740$		0			0
$741$	−31.7297	−	20.8620i	−1.16562	−	0.766384i
$742$		0			0
$743$	−5.94673	+	3.43335i	−0.218165	+	0.125957i	−0.605100	−	0.796149i	$-0.706867\pi$
$743$	−5.94673	+	3.43335i	−0.218165	+	0.125957i	0.386936	+	0.922107i	$0.373534\pi$
$744$		0			0
$745$	34.0328	−	11.3978i	1.24686	−	0.417583i
$746$		0			0
$747$	−2.24018	−	1.29337i	−0.0819638	−	0.0473218i
$748$		0			0
$749$	3.02539			0.110545
$750$		0			0
$751$	2.40009	+	4.15708i	0.0875806	+	0.151694i	0.906488	−	0.422232i	$-0.138753\pi$
$751$	2.40009	+	4.15708i	0.0875806	+	0.151694i	−0.818907	+	0.573926i	$0.805420\pi$
$752$		0			0
$753$			7.05571i			0.257124i
$754$		0			0
$755$	15.6082	+	13.8011i	0.568039	+	0.502275i
$756$		0			0
$757$	−24.0541	+	13.8876i	−0.874261	+	0.504755i	−0.868762	−	0.495230i	$-0.835084\pi$
$757$	−24.0541	+	13.8876i	−0.874261	+	0.504755i	−0.00549931	+	0.999985i	$0.501750\pi$
$758$		0			0
$759$	76.8383			2.78905
$760$		0			0
$761$	1.58110	−	2.73855i	0.0573149	−	0.0992723i	−0.835944	−	0.548814i	$-0.815079\pi$
$761$	1.58110	−	2.73855i	0.0573149	−	0.0992723i	0.893259	+	0.449542i	$0.148413\pi$
$762$		0			0
$763$	−17.0286	−	9.83146i	−0.616476	−	0.355923i
$764$		0			0
$765$	−0.204495	−	0.0415453i	−0.00739353	−	0.00150207i
$766$		0			0
$767$	10.6419	+	21.1817i	0.384257	+	0.764828i
$768$		0			0
$769$	4.07816	+	7.06358i	0.147062	+	0.254719i	0.930140	−	0.367204i	$-0.119685\pi$
$769$	4.07816	+	7.06358i	0.147062	+	0.254719i	−0.783078	+	0.621923i	$0.786352\pi$
$770$		0			0
$771$	15.5999	−	27.0198i	0.561817	−	0.973096i
$772$		0			0
$773$	5.09129	+	2.93946i	0.183121	+	0.105725i	0.588758	−	0.808309i	$-0.299617\pi$
$773$	5.09129	+	2.93946i	0.183121	+	0.105725i	−0.405637	+	0.914034i	$0.632950\pi$
$774$		0			0
$775$	−1.99366	−	16.1622i	−0.0716144	−	0.580564i
$776$		0			0
$777$	8.02528	−	4.63339i	0.287905	−	0.166222i
$778$		0			0
$779$	−47.1958			−1.69097
$780$		0			0
$781$	23.6023			0.844556
$782$		0			0
$783$	−10.7156	+	6.18664i	−0.382944	+	0.221093i
$784$		0			0
$785$	−21.8568	+	24.7186i	−0.780104	+	0.882245i
$786$		0			0
$787$	20.5261	+	11.8507i	0.731676	+	0.422433i	0.819035	−	0.573744i	$-0.194509\pi$
$787$	20.5261	+	11.8507i	0.731676	+	0.422433i	−0.0873591	+	0.996177i	$0.527843\pi$
$788$		0			0
$789$	−19.2811	+	33.3959i	−0.686427	+	1.18893i
$790$		0			0
$791$	12.6424	+	21.8974i	0.449514	+	0.778580i
$792$		0			0
$793$	−17.7246	−	35.2792i	−0.629419	−	1.25280i
$794$		0			0
$795$	0.676152	−	3.32816i	0.0239806	−	0.118038i
$796$		0			0
$797$	42.0193	+	24.2599i	1.48840	+	0.859329i	0.999912	−	0.0132409i	$-0.00421482\pi$
$797$	42.0193	+	24.2599i	1.48840	+	0.859329i	0.488489	+	0.872570i	$0.337548\pi$
$798$		0			0
$799$	−0.527855	+	0.914271i	−0.0186742	+	0.0323446i
$800$		0			0
$801$	0.224254			0.00792362
$802$		0			0
$803$	−14.5490	+	8.39986i	−0.513423	+	0.296425i
$804$		0			0
$805$	−21.5369	−	19.0435i	−0.759076	−	0.671195i
$806$		0			0
$807$			22.5705i			0.794521i
$808$		0			0
$809$	−8.55936	−	14.8252i	−0.300931	−	0.521228i	0.675416	−	0.737437i	$-0.263964\pi$
$809$	−8.55936	−	14.8252i	−0.300931	−	0.521228i	−0.976347	+	0.216209i	$0.930631\pi$
$810$		0			0
$811$	7.67372			0.269461			0.134730	−	0.990882i	$-0.456983\pi$
$811$	7.67372			0.269461			0.134730	+	0.990882i	$0.456983\pi$
$812$		0			0
$813$	−25.9681	−	14.9927i	−0.910742	−	0.525817i
$814$		0			0
$815$	−9.60400	−	28.6766i	−0.336413	−	1.00450i
$816$		0			0
$817$	10.8898	−	6.28726i	0.380988	−	0.219963i
$818$		0			0
$819$	−0.0732380	+	1.26076i	−0.00255914	+	0.0440546i
$820$		0			0
$821$	26.8933	+	46.5805i	0.938582	+	1.62567i	0.768119	+	0.640307i	$0.221193\pi$
$821$	26.8933	+	46.5805i	0.938582	+	1.62567i	0.170463	+	0.985364i	$0.445474\pi$
$822$		0			0
$823$	−8.46604	−	4.88787i	−0.295108	−	0.170381i	0.345135	−	0.938553i	$-0.387833\pi$
$823$	−8.46604	−	4.88787i	−0.295108	−	0.170381i	−0.640243	+	0.768172i	$0.721166\pi$
$824$		0			0
$825$	−21.0596	+	49.6907i	−0.733202	+	1.73001i
$826$		0			0
$827$		−	28.1598i		−	0.979213i	−0.871943	−	0.489607i	$-0.837140\pi$
$827$		−	28.1598i		−	0.979213i	0.871943	−	0.489607i	$-0.162860\pi$
$828$		0			0
$829$	10.1065	+	17.5050i	0.351013	+	0.607972i	0.986427	−	0.164199i	$-0.0525039\pi$
$829$	10.1065	+	17.5050i	0.351013	+	0.607972i	−0.635414	+	0.772172i	$0.719171\pi$
$830$		0			0
$831$	−14.2193			−0.493263
$832$		0			0
$833$			1.79877i			0.0623237i
$834$		0			0
$835$	51.3292	+	10.4281i	1.77632	+	0.360879i
$836$		0			0
$837$		−	17.4255i		−	0.602313i
$838$		0			0
$839$	−6.29631	+	10.9055i	−0.217373	+	0.376500i	−0.954004	−	0.299794i	$-0.903082\pi$
$839$	−6.29631	+	10.9055i	−0.217373	+	0.376500i	0.736631	+	0.676295i	$0.236415\pi$
$840$		0			0
$841$	11.8258	−	20.4829i	0.407787	−	0.706308i
$842$		0			0
$843$	−23.9796	+	13.8446i	−0.825901	+	0.476834i
$844$		0			0
$845$	−9.04700	+	27.6252i	−0.311226	+	0.950336i
$846$		0			0
$847$	−47.7359	+	27.5603i	−1.64022	+	0.946984i
$848$		0			0
$849$	1.28726	−	2.22960i	0.0441786	−	0.0765195i
$850$		0			0
$851$	10.9023	−	18.8834i	0.373727	−	0.647314i
$852$		0			0
$853$			45.7704i			1.56715i	0.621299	+	0.783574i	$0.286605\pi$
$853$			45.7704i			1.56715i	−0.621299	+	0.783574i	$0.713395\pi$
$854$		0			0
$855$	0.542829	−	2.67192i	0.0185644	−	0.0913777i
$856$		0			0
$857$		−	27.8169i		−	0.950206i	−0.879930	−	0.475103i	$-0.842411\pi$
$857$		−	27.8169i		−	0.950206i	0.879930	−	0.475103i	$-0.157589\pi$
$858$		0			0
$859$	25.9706			0.886107			0.443053	−	0.896495i	$-0.353895\pi$
$859$	25.9706			0.886107			0.443053	+	0.896495i	$0.353895\pi$
$860$		0			0
$861$	−11.3552	−	19.6678i	−0.386984	−	0.670275i
$862$		0			0
$863$			18.7210i			0.637270i	0.947877	+	0.318635i	$0.103224\pi$
$863$			18.7210i			0.637270i	−0.947877	+	0.318635i	$0.896776\pi$
$864$		0			0
$865$	3.28379	+	9.80508i	0.111652	+	0.333383i
$866$		0			0
$867$	−24.3261	−	14.0447i	−0.826157	−	0.476982i
$868$		0			0
$869$	−7.39257	−	12.8043i	−0.250776	−	0.434356i
$870$		0			0
$871$	−0.135857	+	2.33872i	−0.00460334	+	0.0792446i
$872$		0			0
$873$	2.32305	−	1.34121i	0.0786233	−	0.0453932i
$874$		0			0
$875$	18.2181	−	8.70837i	0.615883	−	0.294397i
$876$		0			0
$877$	19.6466	+	11.3430i	0.663418	+	0.383025i	0.793578	−	0.608468i	$-0.208216\pi$
$877$	19.6466	+	11.3430i	0.663418	+	0.383025i	−0.130160	+	0.991493i	$0.541549\pi$
$878$		0			0
$879$	9.93303			0.335033
$880$		0			0
$881$	1.23813	+	2.14451i	0.0417138	+	0.0722505i	0.886129	−	0.463440i	$-0.153385\pi$
$881$	1.23813	+	2.14451i	0.0417138	+	0.0722505i	−0.844415	+	0.535690i	$0.820052\pi$
$882$		0			0
$883$		−	31.4641i		−	1.05885i	−0.848357	−	0.529425i	$-0.822408\pi$
$883$		−	31.4641i		−	1.05885i	0.848357	−	0.529425i	$-0.177592\pi$
$884$		0			0
$885$	16.3127	−	18.4485i	0.548344	−	0.620140i
$886$		0			0
$887$	−34.3953	+	19.8581i	−1.15488	+	0.666771i	−0.950072	−	0.312031i	$-0.898991\pi$
$887$	−34.3953	+	19.8581i	−1.15488	+	0.666771i	−0.204809	+	0.978802i	$0.565657\pi$
$888$		0			0
$889$	9.36741			0.314173
$890$		0			0
$891$	−27.0005	+	46.7662i	−0.904550	+	1.56673i
$892$		0			0
$893$	−11.9458	−	6.89692i	−0.399752	−	0.230797i
$894$		0			0
$895$	3.70068	−	18.2155i	0.123700	−	0.608878i
$896$		0			0
$897$	−19.3022	−	38.4191i	−0.644480	−	1.28278i
$898$		0			0
$899$	−3.76608	−	6.52305i	−0.125606	−	0.217556i
$900$		0			0
$901$	0.218144	−	0.377837i	0.00726744	−	0.0125876i
$902$		0			0
$903$	5.24013	+	3.02539i	0.174381	+	0.100679i
$904$		0			0
$905$	1.71767	+	1.51881i	0.0570972	+	0.0504868i
$906$		0			0
$907$	46.3977	−	26.7877i	1.54061	−	0.889472i	0.541811	−	0.840500i	$-0.317739\pi$
$907$	46.3977	−	26.7877i	1.54061	−	0.889472i	0.998800	−	0.0489717i	$-0.0155944\pi$
$908$		0			0
$909$	−1.86177			−0.0617511
$910$		0			0
$911$	−14.6253			−0.484558			−0.242279	−	0.970207i	$-0.577895\pi$
$911$	−14.6253			−0.484558			−0.242279	+	0.970207i	$0.577895\pi$
$912$		0			0
$913$	−74.4304	+	42.9724i	−2.46329	+	1.42218i
$914$		0			0
$915$	−27.1695	+	30.7269i	−0.898196	+	1.01580i
$916$		0			0
$917$	16.8940	+	9.75377i	0.557890	+	0.322098i
$918$		0			0
$919$	−26.5247	+	45.9421i	−0.874969	+	1.51549i	−0.0181725	+	0.999835i	$0.505785\pi$
$919$	−26.5247	+	45.9421i	−0.874969	+	1.51549i	−0.856796	+	0.515655i	$0.827549\pi$
$920$		0			0
$921$	−15.0557	−	26.0773i	−0.496103	−	0.859275i
$922$		0			0
$923$	−5.92901	−	11.8011i	−0.195156	−	0.388439i
$924$		0			0
$925$	9.22366	+	12.2260i	0.303272	+	0.401987i
$926$		0			0
$927$	−0.516496	−	0.298199i	−0.0169640	−	0.00979414i
$928$		0			0
$929$	−5.22521	+	9.05033i	−0.171434	+	0.296932i	−0.938921	−	0.344132i	$-0.888173\pi$
$929$	−5.22521	+	9.05033i	−0.171434	+	0.296932i	0.767488	+	0.641064i	$0.221507\pi$
$930$		0			0
$931$	−23.5026			−0.770267
$932$		0			0
$933$	−23.1496	+	13.3654i	−0.757883	+	0.437564i
$934$		0			0
$935$	−4.59261	+	5.19394i	−0.150195	+	0.169860i
$936$		0			0
$937$			10.5745i			0.345454i	0.984970	+	0.172727i	$0.0552579\pi$
$937$			10.5745i			0.345454i	−0.984970	+	0.172727i	$0.944742\pi$
$938$		0			0
$939$	−19.6302	−	34.0005i	−0.640608	−	1.10957i
$940$		0			0
$941$	−16.6107			−0.541494			−0.270747	−	0.962651i	$-0.587271\pi$
$941$	−16.6107			−0.541494			−0.270747	+	0.962651i	$0.587271\pi$
$942$		0			0
$943$	−46.2780	−	26.7186i	−1.50702	−	0.870078i
$944$		0			0
$945$	20.4884	−	6.86172i	0.666489	−	0.223212i
$946$		0			0
$947$	36.7949	−	21.2435i	1.19567	−	0.690322i	0.236086	−	0.971732i	$-0.424135\pi$
$947$	36.7949	−	21.2435i	1.19567	−	0.690322i	0.959588	+	0.281410i	$0.0908021\pi$
$948$		0			0
$949$	7.85471	+	5.16441i	0.254975	+	0.167644i
$950$		0			0
$951$	17.2963	+	29.9581i	0.560871	+	0.971457i
$952$		0			0
$953$	−38.9897	−	22.5107i	−1.26300	−	0.729193i	−0.289346	−	0.957224i	$-0.593438\pi$
$953$	−38.9897	−	22.5107i	−1.26300	−	0.729193i	−0.973654	+	0.228031i	$0.926771\pi$
$954$		0			0
$955$	−0.753108	+	0.252221i	−0.0243700	+	0.00816168i
$956$		0			0
$957$			24.9624i			0.806919i
$958$		0			0
$959$	5.54832	+	9.60998i	0.179165	+	0.310322i
$960$		0			0
$961$	−20.3923			−0.657817
$962$		0			0
$963$			0.324869i			0.0104688i
$964$		0			0
$965$	30.6782	+	6.23261i	0.987568	+	0.200635i
$966$		0			0
$967$		−	24.4763i		−	0.787104i	−0.919302	−	0.393552i	$-0.871246\pi$
$967$		−	24.4763i		−	0.787104i	0.919302	−	0.393552i	$-0.128754\pi$
$968$		0			0
$969$	−2.53396	+	4.38895i	−0.0814027	+	0.140994i
$970$		0			0
$971$	−28.2023	+	48.8478i	−0.905054	+	1.56760i	−0.0842097	+	0.996448i	$0.526837\pi$
$971$	−28.2023	+	48.8478i	−0.905054	+	1.56760i	−0.820844	+	0.571152i	$0.806497\pi$
$972$		0			0
$973$	−16.1697	+	9.33558i	−0.518377	+	0.299285i
$974$		0			0
$975$	30.1356	−	1.95275i	0.965113	−	0.0625380i
$976$		0			0
$977$	11.7021	−	6.75623i	0.374385	−	0.216151i	−0.300988	−	0.953628i	$-0.597316\pi$
$977$	11.7021	−	6.75623i	0.374385	−	0.216151i	0.675372	+	0.737477i	$0.263983\pi$
$978$		0			0
$979$	3.72544	−	6.45265i	0.119066	−	0.206228i
$980$		0			0
$981$	1.05571	−	1.82854i	0.0337062	−	0.0583809i
$982$		0			0
$983$			30.1187i			0.960638i	0.877094	+	0.480319i	$0.159479\pi$
$983$			30.1187i			0.960638i	−0.877094	+	0.480319i	$0.840521\pi$
$984$		0			0
$985$	30.9116	+	6.28002i	0.984926	+	0.200098i
$986$		0			0
$987$		−	6.63752i		−	0.211275i
$988$		0			0
$989$	14.2374			0.452724
$990$		0			0
$991$	17.6629	+	30.5931i	0.561081	+	0.971821i	0.997402	+	0.0720298i	$0.0229477\pi$
$991$	17.6629	+	30.5931i	0.561081	+	0.971821i	−0.436322	+	0.899791i	$0.643719\pi$
$992$		0			0
$993$			44.6859i			1.41807i
$994$		0			0
$995$	−6.67694	+	2.23615i	−0.211673	+	0.0708909i
$996$		0			0
$997$	−14.5638	−	8.40843i	−0.461241	−	0.266298i	0.251325	−	0.967903i	$-0.419134\pi$
$997$	−14.5638	−	8.40843i	−0.461241	−	0.266298i	−0.712566	+	0.701605i	$0.752467\pi$
$998$		0			0
$999$	8.19394	+	14.1923i	0.259245	+	0.449025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.dh.b.289.5		12
4.3	odd	2		130.2.n.a.29.1	yes	12
5.4	even	2	inner	1040.2.dh.b.289.2		12
12.11	even	2		1170.2.bp.h.289.6		12
13.9	even	3	inner	1040.2.dh.b.529.2		12
20.3	even	4		650.2.e.k.601.1		6
20.7	even	4		650.2.e.j.601.3		6
20.19	odd	2		130.2.n.a.29.6	yes	12
52.3	odd	6		1690.2.b.c.339.1		6
52.11	even	12		1690.2.c.c.1689.2		6
52.15	even	12		1690.2.c.b.1689.2		6
52.23	odd	6		1690.2.b.b.339.4		6
52.35	odd	6		130.2.n.a.9.6	yes	12
60.59	even	2		1170.2.bp.h.289.3		12
65.9	even	6	inner	1040.2.dh.b.529.5		12
156.35	even	6		1170.2.bp.h.919.3		12
260.3	even	12		8450.2.a.bu.1.3		3
260.23	even	12		8450.2.a.ca.1.3		3
260.87	even	12		650.2.e.j.451.3		6
260.107	even	12		8450.2.a.cb.1.1		3
260.119	even	12		1690.2.c.c.1689.5		6
260.127	even	12		8450.2.a.bt.1.1		3
260.139	odd	6		130.2.n.a.9.1	✓	12
260.159	odd	6		1690.2.b.c.339.6		6
260.179	odd	6		1690.2.b.b.339.3		6
260.219	even	12		1690.2.c.b.1689.5		6
260.243	even	12		650.2.e.k.451.1		6
780.659	even	6		1170.2.bp.h.919.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.1	✓	12	260.139	odd	6
130.2.n.a.9.6	yes	12	52.35	odd	6
130.2.n.a.29.1	yes	12	4.3	odd	2
130.2.n.a.29.6	yes	12	20.19	odd	2
650.2.e.j.451.3		6	260.87	even	12
650.2.e.j.601.3		6	20.7	even	4
650.2.e.k.451.1		6	260.243	even	12
650.2.e.k.601.1		6	20.3	even	4
1040.2.dh.b.289.2		12	5.4	even	2	inner
1040.2.dh.b.289.5		12	1.1	even	1	trivial
1040.2.dh.b.529.2		12	13.9	even	3	inner
1040.2.dh.b.529.5		12	65.9	even	6	inner
1170.2.bp.h.289.3		12	60.59	even	2
1170.2.bp.h.289.6		12	12.11	even	2
1170.2.bp.h.919.3		12	156.35	even	6
1170.2.bp.h.919.6		12	780.659	even	6
1690.2.b.b.339.3		6	260.179	odd	6
1690.2.b.b.339.4		6	52.23	odd	6
1690.2.b.c.339.1		6	52.3	odd	6
1690.2.b.c.339.6		6	260.159	odd	6
1690.2.c.b.1689.2		6	52.15	even	12
1690.2.c.b.1689.5		6	260.219	even	12
1690.2.c.c.1689.2		6	52.11	even	12
1690.2.c.c.1689.5		6	260.119	even	12
8450.2.a.bt.1.1		3	260.127	even	12
8450.2.a.bu.1.3		3	260.3	even	12
8450.2.a.ca.1.3		3	260.23	even	12
8450.2.a.cb.1.1		3	260.107	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.dh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.45071 - 0.837565i) q^{3} +(-1.67513 - 1.48119i) q^{5} +(1.56410 + 0.903032i) q^{7} +(-0.0969683 + 0.167954i) q^{9} +(3.22179 + 5.58031i) q^{11} +(1.98082 - 3.01270i) q^{13} +(-3.67072 - 0.745746i) q^{15} +(-0.416726 - 0.240597i) q^{17} +(3.14363 - 5.44492i) q^{19} +3.02539 q^{21} +(6.16499 - 3.55936i) q^{23} +(0.612127 + 4.96239i) q^{25} +5.35026i q^{27} +(1.15633 + 2.00281i) q^{29} -3.25694 q^{31} +(9.34774 + 5.39692i) q^{33} +(-1.28250 - 3.82943i) q^{35} +(2.65264 - 1.53150i) q^{37} +(0.350262 - 6.02961i) q^{39} +(-3.75329 - 6.50089i) q^{41} +(1.73205 + 1.00000i) q^{43} +(0.411207 - 0.137716i) q^{45} -2.19394i q^{47} +(-1.86907 - 3.23732i) q^{49} -0.806063 q^{51} +0.906679i q^{53} +(2.86860 - 14.1198i) q^{55} -10.5320i q^{57} +(-3.28726 + 5.69370i) q^{59} +(5.47508 - 9.48313i) q^{61} +(-0.303336 + 0.175131i) q^{63} +(-7.78053 + 2.11268i) q^{65} +(-0.562690 + 0.324869i) q^{67} +(5.96239 - 10.3272i) q^{69} +(1.83146 - 3.17217i) q^{71} +2.60720i q^{73} +(5.04434 + 6.68627i) q^{75} +11.6375i q^{77} -2.29455 q^{79} +(4.19029 + 7.25779i) q^{81} +13.3380i q^{83} +(0.341700 + 1.02028i) q^{85} +(3.35498 + 1.93700i) q^{87} +(-0.578163 - 1.00141i) q^{89} +(5.81876 - 2.92340i) q^{91} +(-4.72486 + 2.72790i) q^{93} +(-13.3310 + 4.46464i) q^{95} +(-11.9784 - 6.91573i) q^{97} -1.24965 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{9} + 6 q^{11} - 4 q^{15} + 26 q^{19} - 24 q^{21} + 4 q^{25} - 28 q^{29} - 24 q^{31} + 6 q^{35} - 36 q^{39} - 4 q^{41} + 12 q^{45} - 4 q^{49} - 8 q^{51} - 12 q^{55} - 16 q^{59} - 8 q^{61} - 10 q^{65}+ \cdots + 52 q^{99}+O(q^{100}) \) 12 * q - 2 * q^9 + 6 * q^11 - 4 * q^15 + 26 * q^19 - 24 * q^21 + 4 * q^25 - 28 * q^29 - 24 * q^31 + 6 * q^35 - 36 * q^39 - 4 * q^41 + 12 * q^45 - 4 * q^49 - 8 * q^51 - 12 * q^55 - 16 * q^59 - 8 * q^61 - 10 * q^65 + 28 * q^69 - 40 * q^71 + 8 * q^75 - 56 * q^79 + 26 * q^81 - 16 * q^85 + 14 * q^89 + 38 * q^91 + 8 * q^95 + 52 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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