LMFDB - Embedded newform 1440.2.q.m.961.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1440,2,Mod(481,1440)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1440.481"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1440, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,4,0,0,0,0] 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:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.4
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1440.961
Dual form			1440.2.q.m.481.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.67303 + 0.448288i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.258819 + 0.448288i) q^{7} +(2.59808 + 1.50000i) q^{9} +(0.189469 - 0.328169i) q^{11} +(0.366025 + 0.633975i) q^{13} +(0.448288 + 1.67303i) q^{15} +2.73205 q^{17} +2.44949 q^{19} +(-0.633975 + 0.633975i) q^{21} +(-0.258819 - 0.448288i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.67423 + 3.67423i) q^{27} +(-1.50000 + 2.59808i) q^{29} +(0.189469 + 0.328169i) q^{31} +(0.464102 - 0.464102i) q^{33} -0.517638 q^{35} +0.732051 q^{37} +(0.328169 + 1.22474i) q^{39} +(2.33013 + 4.03590i) q^{41} +(2.12132 - 3.67423i) q^{43} +3.00000i q^{45} +(-3.41542 + 5.91567i) q^{47} +(3.36603 + 5.83013i) q^{49} +(4.57081 + 1.22474i) q^{51} +2.53590 q^{53} +0.378937 q^{55} +(4.09808 + 1.09808i) q^{57} +(-6.17449 - 10.6945i) q^{59} +(-3.33013 + 5.76795i) q^{61} +(-1.34486 + 0.776457i) q^{63} +(-0.366025 + 0.633975i) q^{65} +(1.86250 + 3.22595i) q^{67} +(-0.232051 - 0.866025i) q^{69} -9.89949 q^{71} +4.39230 q^{73} +(-1.22474 + 1.22474i) q^{75} +(0.0980762 + 0.169873i) q^{77} +(5.27792 - 9.14162i) q^{79} +(4.50000 + 7.79423i) q^{81} +(0.637756 - 1.10463i) q^{83} +(1.36603 + 2.36603i) q^{85} +(-3.67423 + 3.67423i) q^{87} +9.39230 q^{89} -0.378937 q^{91} +(0.169873 + 0.633975i) q^{93} +(1.22474 + 2.12132i) q^{95} +(5.46410 - 9.46410i) q^{97} +(0.984508 - 0.568406i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} - 4 q^{13} + 8 q^{17} - 12 q^{21} - 4 q^{25} - 12 q^{29} - 24 q^{33} - 8 q^{37} - 16 q^{41} + 20 q^{49} + 48 q^{53} + 12 q^{57} + 8 q^{61} + 4 q^{65} + 12 q^{69} - 48 q^{73} - 20 q^{77} + 36 q^{81}+ \cdots + 16 q^{97}+O(q^{100}) $ 8 * q + 4 * q^5 - 4 * q^13 + 8 * q^17 - 12 * q^21 - 4 * q^25 - 12 * q^29 - 24 * q^33 - 8 * q^37 - 16 * q^41 + 20 * q^49 + 48 * q^53 + 12 * q^57 + 8 * q^61 + 4 * q^65 + 12 * q^69 - 48 * q^73 - 20 * q^77 + 36 * q^81 + 4 * q^85 - 8 * q^89 + 36 * q^93 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	1.67303	+	0.448288i	0.965926	+	0.258819i
$3$	1.67303	+	0.448288i	0.965926	+	0.258819i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.258819	+	0.448288i	−0.0978244	+	0.169437i	−0.910784	−	0.412883i	$-0.864522\pi$
$7$	−0.258819	+	0.448288i	−0.0978244	+	0.169437i	0.812959	+	0.582320i	$0.197855\pi$
$8$		0			0
$9$	2.59808	+	1.50000i	0.866025	+	0.500000i
$10$		0			0
$11$	0.189469	−	0.328169i	0.0571270	−	0.0989468i	−0.836048	−	0.548657i	$-0.815139\pi$
$11$	0.189469	−	0.328169i	0.0571270	−	0.0989468i	0.893175	+	0.449710i	$0.148473\pi$
$12$		0			0
$13$	0.366025	+	0.633975i	0.101517	+	0.175833i	0.912310	−	0.409500i	$-0.134297\pi$
$13$	0.366025	+	0.633975i	0.101517	+	0.175833i	−0.810793	+	0.585333i	$0.800964\pi$
$14$		0			0
$15$	0.448288	+	1.67303i	0.115747	+	0.431975i
$16$		0			0
$17$	2.73205			0.662620			0.331310	−	0.943522i	$-0.392509\pi$
$17$	2.73205			0.662620			0.331310	+	0.943522i	$0.392509\pi$
$18$		0			0
$19$	2.44949			0.561951			0.280976	−	0.959715i	$-0.409342\pi$
$19$	2.44949			0.561951			0.280976	+	0.959715i	$0.409342\pi$
$20$		0			0
$21$	−0.633975	+	0.633975i	−0.138345	+	0.138345i
$22$		0			0
$23$	−0.258819	−	0.448288i	−0.0539675	−	0.0934745i	0.837780	−	0.546009i	$-0.183853\pi$
$23$	−0.258819	−	0.448288i	−0.0539675	−	0.0934745i	−0.891747	+	0.452534i	$0.850520\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	3.67423	+	3.67423i	0.707107	+	0.707107i
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	0.189469	+	0.328169i	0.0340296	+	0.0589410i	0.882539	−	0.470240i	$-0.155833\pi$
$31$	0.189469	+	0.328169i	0.0340296	+	0.0589410i	−0.848509	+	0.529181i	$0.822499\pi$
$32$		0			0
$33$	0.464102	−	0.464102i	0.0807897	−	0.0807897i
$34$		0			0
$35$	−0.517638			−0.0874968
$36$		0			0
$37$	0.732051			0.120348			0.0601742	−	0.998188i	$-0.480834\pi$
$37$	0.732051			0.120348			0.0601742	+	0.998188i	$0.480834\pi$
$38$		0			0
$39$	0.328169	+	1.22474i	0.0525492	+	0.196116i
$40$		0			0
$41$	2.33013	+	4.03590i	0.363905	+	0.630301i	0.988600	−	0.150567i	$-0.0481100\pi$
$41$	2.33013	+	4.03590i	0.363905	+	0.630301i	−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$	2.12132	−	3.67423i	0.323498	−	0.560316i	−0.657709	−	0.753272i	$-0.728474\pi$
$43$	2.12132	−	3.67423i	0.323498	−	0.560316i	0.981207	+	0.192957i	$0.0618077\pi$
$44$		0			0
$45$			3.00000i			0.447214i
$46$		0			0
$47$	−3.41542	+	5.91567i	−0.498190	+	0.862890i	−0.999998	−	0.00208925i	$-0.999335\pi$
$47$	−3.41542	+	5.91567i	−0.498190	+	0.862890i	0.501808	+	0.864979i	$0.332668\pi$
$48$		0			0
$49$	3.36603	+	5.83013i	0.480861	+	0.832875i
$50$		0			0
$51$	4.57081	+	1.22474i	0.640041	+	0.171499i
$52$		0			0
$53$	2.53590			0.348332			0.174166	−	0.984716i	$-0.444277\pi$
$53$	2.53590			0.348332			0.174166	+	0.984716i	$0.444277\pi$
$54$		0			0
$55$	0.378937			0.0510959
$56$		0			0
$57$	4.09808	+	1.09808i	0.542803	+	0.145444i
$58$		0			0
$59$	−6.17449	−	10.6945i	−0.803850	−	1.39231i	−0.917064	−	0.398739i	$-0.869448\pi$
$59$	−6.17449	−	10.6945i	−0.803850	−	1.39231i	0.113214	−	0.993571i	$-0.463885\pi$
$60$		0			0
$61$	−3.33013	+	5.76795i	−0.426379	+	0.738510i	−0.996548	−	0.0830172i	$-0.973544\pi$
$61$	−3.33013	+	5.76795i	−0.426379	+	0.738510i	0.570169	+	0.821527i	$0.306878\pi$
$62$		0			0
$63$	−1.34486	+	0.776457i	−0.169437	+	0.0978244i
$64$		0			0
$65$	−0.366025	+	0.633975i	−0.0453999	+	0.0786349i
$66$		0			0
$67$	1.86250	+	3.22595i	0.227541	+	0.394112i	0.957079	−	0.289828i	$-0.0935982\pi$
$67$	1.86250	+	3.22595i	0.227541	+	0.394112i	−0.729538	+	0.683940i	$0.760265\pi$
$68$		0			0
$69$	−0.232051	−	0.866025i	−0.0279356	−	0.104257i
$70$		0			0
$71$	−9.89949			−1.17485			−0.587427	−	0.809277i	$-0.699859\pi$
$71$	−9.89949			−1.17485			−0.587427	+	0.809277i	$0.699859\pi$
$72$		0			0
$73$	4.39230			0.514080			0.257040	−	0.966401i	$-0.417253\pi$
$73$	4.39230			0.514080			0.257040	+	0.966401i	$0.417253\pi$
$74$		0			0
$75$	−1.22474	+	1.22474i	−0.141421	+	0.141421i
$76$		0			0
$77$	0.0980762	+	0.169873i	0.0111768	+	0.0193588i
$78$		0			0
$79$	5.27792	−	9.14162i	0.593812	−	1.02851i	−0.399901	−	0.916558i	$-0.630956\pi$
$79$	5.27792	−	9.14162i	0.593812	−	1.02851i	0.993713	−	0.111954i	$-0.0357111\pi$
$80$		0			0
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$		0			0
$83$	0.637756	−	1.10463i	0.0700029	−	0.121249i	−0.828899	−	0.559398i	$-0.811032\pi$
$83$	0.637756	−	1.10463i	0.0700029	−	0.121249i	0.898902	+	0.438149i	$0.144366\pi$
$84$		0			0
$85$	1.36603	+	2.36603i	0.148166	+	0.256631i
$86$		0			0
$87$	−3.67423	+	3.67423i	−0.393919	+	0.393919i
$88$		0			0
$89$	9.39230			0.995582			0.497791	−	0.867297i	$-0.334145\pi$
$89$	9.39230			0.995582			0.497791	+	0.867297i	$0.334145\pi$
$90$		0			0
$91$	−0.378937			−0.0397234
$92$		0			0
$93$	0.169873	+	0.633975i	0.0176150	+	0.0657401i
$94$		0			0
$95$	1.22474	+	2.12132i	0.125656	+	0.217643i
$96$		0			0
$97$	5.46410	−	9.46410i	0.554795	−	0.960934i	−0.443124	−	0.896460i	$-0.646130\pi$
$97$	5.46410	−	9.46410i	0.554795	−	0.960934i	0.997919	−	0.0644736i	$-0.0205368\pi$
$98$		0			0
$99$	0.984508	−	0.568406i	0.0989468	−	0.0571270i
$100$		0			0
$101$	−6.19615	+	10.7321i	−0.616540	+	1.06788i	0.373572	+	0.927601i	$0.378133\pi$
$101$	−6.19615	+	10.7321i	−0.616540	+	1.06788i	−0.990112	+	0.140278i	$0.955200\pi$
$102$		0			0
$103$	−8.05558	−	13.9527i	−0.793739	−	1.37480i	−0.923637	−	0.383270i	$-0.874798\pi$
$103$	−8.05558	−	13.9527i	−0.793739	−	1.37480i	0.129897	−	0.991527i	$-0.458535\pi$
$104$		0			0
$105$	−0.866025	−	0.232051i	−0.0845154	−	0.0226458i
$106$		0			0
$107$	−14.1793			−1.37076			−0.685382	−	0.728183i	$-0.740365\pi$
$107$	−14.1793			−1.37076			−0.685382	+	0.728183i	$0.740365\pi$
$108$		0			0
$109$	−1.73205			−0.165900			−0.0829502	−	0.996554i	$-0.526434\pi$
$109$	−1.73205			−0.165900			−0.0829502	+	0.996554i	$0.526434\pi$
$110$		0			0
$111$	1.22474	+	0.328169i	0.116248	+	0.0311485i
$112$		0			0
$113$	1.00000	+	1.73205i	0.0940721	+	0.162938i	0.909221	−	0.416314i	$-0.136678\pi$
$113$	1.00000	+	1.73205i	0.0940721	+	0.162938i	−0.815149	+	0.579252i	$0.803345\pi$
$114$		0			0
$115$	0.258819	−	0.448288i	0.0241350	−	0.0418030i
$116$		0			0
$117$			2.19615i			0.203034i
$118$		0			0
$119$	−0.707107	+	1.22474i	−0.0648204	+	0.112272i
$120$		0			0
$121$	5.42820	+	9.40192i	0.493473	+	0.854720i
$122$		0			0
$123$	2.08913	+	7.79676i	0.188371	+	0.703010i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.34658			0.740639			0.370320	−	0.928904i	$-0.379248\pi$
$127$	8.34658			0.740639			0.370320	+	0.928904i	$0.379248\pi$
$128$		0			0
$129$	5.19615	−	5.19615i	0.457496	−	0.457496i
$130$		0			0
$131$	−5.65685	−	9.79796i	−0.494242	−	0.856052i	0.505736	−	0.862688i	$-0.331221\pi$
$131$	−5.65685	−	9.79796i	−0.494242	−	0.856052i	−0.999978	+	0.00663646i	$0.997888\pi$
$132$		0			0
$133$	−0.633975	+	1.09808i	−0.0549726	+	0.0952153i
$134$		0			0
$135$	−1.34486	+	5.01910i	−0.115747	+	0.431975i
$136$		0			0
$137$	3.92820	−	6.80385i	0.335609	−	0.581292i	−0.647993	−	0.761647i	$-0.724391\pi$
$137$	3.92820	−	6.80385i	0.335609	−	0.581292i	0.983602	+	0.180355i	$0.0577246\pi$
$138$		0			0
$139$	−6.31319	−	10.9348i	−0.535478	−	0.927475i	−0.999140	−	0.0414630i	$-0.986798\pi$
$139$	−6.31319	−	10.9348i	−0.535478	−	0.927475i	0.463662	−	0.886012i	$-0.346535\pi$
$140$		0			0
$141$	−8.36603	+	8.36603i	−0.704546	+	0.704546i
$142$		0			0
$143$	0.277401			0.0231975
$144$		0			0
$145$	−3.00000			−0.249136
$146$		0			0
$147$	3.01790	+	11.2629i	0.248912	+	0.928952i
$148$		0			0
$149$	−9.33013	−	16.1603i	−0.764354	−	1.32390i	−0.940588	−	0.339551i	$-0.889725\pi$
$149$	−9.33013	−	16.1603i	−0.764354	−	1.32390i	0.176234	−	0.984348i	$-0.443609\pi$
$150$		0			0
$151$	8.57321	−	14.8492i	0.697678	−	1.20841i	−0.271591	−	0.962413i	$-0.587550\pi$
$151$	8.57321	−	14.8492i	0.697678	−	1.20841i	0.969269	−	0.246001i	$-0.0791168\pi$
$152$		0			0
$153$	7.09808	+	4.09808i	0.573845	+	0.331310i
$154$		0			0
$155$	−0.189469	+	0.328169i	−0.0152185	+	0.0263592i
$156$		0			0
$157$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$157$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$158$		0			0
$159$	4.24264	+	1.13681i	0.336463	+	0.0901551i
$160$		0			0
$161$	0.267949			0.0211174
$162$		0			0
$163$	5.00052			0.391671			0.195835	−	0.980637i	$-0.437258\pi$
$163$	5.00052			0.391671			0.195835	+	0.980637i	$0.437258\pi$
$164$		0			0
$165$	0.633975	+	0.169873i	0.0493549	+	0.0132246i
$166$		0			0
$167$	0.965926	+	1.67303i	0.0747456	+	0.129463i	0.900976	−	0.433870i	$-0.142852\pi$
$167$	0.965926	+	1.67303i	0.0747456	+	0.129463i	−0.826230	+	0.563333i	$0.809519\pi$
$168$		0			0
$169$	6.23205	−	10.7942i	0.479389	−	0.830325i
$170$		0			0
$171$	6.36396	+	3.67423i	0.486664	+	0.280976i
$172$		0			0
$173$	−4.00000	+	6.92820i	−0.304114	+	0.526742i	−0.977064	−	0.212947i	$-0.931694\pi$
$173$	−4.00000	+	6.92820i	−0.304114	+	0.526742i	0.672949	+	0.739689i	$0.265027\pi$
$174$		0			0
$175$	−0.258819	−	0.448288i	−0.0195649	−	0.0338874i
$176$		0			0
$177$	−5.53590	−	20.6603i	−0.416104	−	1.55292i
$178$		0			0
$179$	−16.8690			−1.26085			−0.630425	−	0.776250i	$-0.717119\pi$
$179$	−16.8690			−1.26085			−0.630425	+	0.776250i	$0.717119\pi$
$180$		0			0
$181$	−8.85641			−0.658292			−0.329146	−	0.944279i	$-0.606761\pi$
$181$	−8.85641			−0.658292			−0.329146	+	0.944279i	$0.606761\pi$
$182$		0			0
$183$	−8.15711	+	8.15711i	−0.602991	+	0.602991i
$184$		0			0
$185$	0.366025	+	0.633975i	0.0269107	+	0.0466107i
$186$		0			0
$187$	0.517638	−	0.896575i	0.0378534	−	0.0655641i
$188$		0			0
$189$	−2.59808	+	0.696152i	−0.188982	+	0.0506376i
$190$		0			0
$191$	−7.67664	+	13.2963i	−0.555462	+	0.962089i	0.442405	+	0.896815i	$0.354125\pi$
$191$	−7.67664	+	13.2963i	−0.555462	+	0.962089i	−0.997867	+	0.0652733i	$0.979208\pi$
$192$		0			0
$193$	−1.09808	−	1.90192i	−0.0790413	−	0.136903i	0.823795	−	0.566887i	$-0.191853\pi$
$193$	−1.09808	−	1.90192i	−0.0790413	−	0.136903i	−0.902837	+	0.429984i	$0.858519\pi$
$194$		0			0
$195$	−0.896575	+	0.896575i	−0.0642051	+	0.0642051i
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	13.7632			0.975647			0.487824	−	0.872942i	$-0.337791\pi$
$199$	13.7632			0.975647			0.487824	+	0.872942i	$0.337791\pi$
$200$		0			0
$201$	1.66987	+	6.23205i	0.117784	+	0.439575i
$202$		0			0
$203$	−0.776457	−	1.34486i	−0.0544966	−	0.0943909i
$204$		0			0
$205$	−2.33013	+	4.03590i	−0.162743	+	0.281879i
$206$		0			0
$207$		−	1.55291i		−	0.107935i
$208$		0			0
$209$	0.464102	−	0.803848i	0.0321026	−	0.0556033i
$210$		0			0
$211$	7.91688	+	13.7124i	0.545020	+	0.944003i	0.998606	+	0.0527898i	$0.0168113\pi$
$211$	7.91688	+	13.7124i	0.545020	+	0.944003i	−0.453585	+	0.891213i	$0.649855\pi$
$212$		0			0
$213$	−16.5622	−	4.43782i	−1.13482	−	0.304075i
$214$		0			0
$215$	4.24264			0.289346
$216$		0			0
$217$	−0.196152			−0.0133157
$218$		0			0
$219$	7.34847	+	1.96902i	0.496564	+	0.133054i
$220$		0			0
$221$	1.00000	+	1.73205i	0.0672673	+	0.116510i
$222$		0			0
$223$	13.8325	−	23.9587i	0.926296	−	1.60439i	0.136832	−	0.990594i	$-0.456308\pi$
$223$	13.8325	−	23.9587i	0.926296	−	1.60439i	0.789464	−	0.613797i	$-0.210359\pi$
$224$		0			0
$225$	−2.59808	+	1.50000i	−0.173205	+	0.100000i
$226$		0			0
$227$	−2.91636	+	5.05128i	−0.193566	+	0.335265i	−0.946429	−	0.322911i	$-0.895339\pi$
$227$	−2.91636	+	5.05128i	−0.193566	+	0.335265i	0.752864	+	0.658176i	$0.228672\pi$
$228$		0			0
$229$	−9.89230	−	17.1340i	−0.653702	−	1.13224i	−0.982218	−	0.187746i	$-0.939882\pi$
$229$	−9.89230	−	17.1340i	−0.653702	−	1.13224i	0.328516	−	0.944499i	$-0.393452\pi$
$230$		0			0
$231$	0.0879327	+	0.328169i	0.00578555	+	0.0215920i
$232$		0			0
$233$	12.7321			0.834104			0.417052	−	0.908883i	$-0.363063\pi$
$233$	12.7321			0.834104			0.417052	+	0.908883i	$0.363063\pi$
$234$		0			0
$235$	−6.83083			−0.445594
$236$		0			0
$237$	12.9282	−	12.9282i	0.839777	−	0.839777i
$238$		0			0
$239$	7.48717	+	12.9682i	0.484305	+	0.838840i	0.999837	−	0.0180295i	$-0.00573926\pi$
$239$	7.48717	+	12.9682i	0.484305	+	0.838840i	−0.515533	+	0.856870i	$0.672406\pi$
$240$		0			0
$241$	−3.59808	+	6.23205i	−0.231772	+	0.401442i	−0.958330	−	0.285664i	$-0.907786\pi$
$241$	−3.59808	+	6.23205i	−0.231772	+	0.401442i	0.726557	+	0.687106i	$0.241119\pi$
$242$		0			0
$243$	4.03459	+	15.0573i	0.258819	+	0.965926i
$244$		0			0
$245$	−3.36603	+	5.83013i	−0.215047	+	0.372473i
$246$		0			0
$247$	0.896575	+	1.55291i	0.0570477	+	0.0988096i
$248$		0			0
$249$	1.56218	−	1.56218i	0.0989990	−	0.0989990i
$250$		0			0
$251$	−13.2827			−0.838398			−0.419199	−	0.907894i	$-0.637689\pi$
$251$	−13.2827			−0.838398			−0.419199	+	0.907894i	$0.637689\pi$
$252$		0			0
$253$	−0.196152			−0.0123320
$254$		0			0
$255$	1.22474	+	4.57081i	0.0766965	+	0.286235i
$256$		0			0
$257$	−14.8564	−	25.7321i	−0.926717	−	1.60512i	−0.788776	−	0.614681i	$-0.789285\pi$
$257$	−14.8564	−	25.7321i	−0.926717	−	1.60512i	−0.137941	−	0.990440i	$-0.544049\pi$
$258$		0			0
$259$	−0.189469	+	0.328169i	−0.0117730	+	0.0203915i
$260$		0			0
$261$	−7.79423	+	4.50000i	−0.482451	+	0.278543i
$262$		0			0
$263$	1.36345	−	2.36156i	0.0840737	−	0.145620i	−0.820922	−	0.571040i	$-0.806540\pi$
$263$	1.36345	−	2.36156i	0.0840737	−	0.145620i	0.904996	+	0.425420i	$0.139874\pi$
$264$		0			0
$265$	1.26795	+	2.19615i	0.0778895	+	0.134909i
$266$		0			0
$267$	15.7136	+	4.21046i	0.961659	+	0.257676i
$268$		0			0
$269$	3.33975			0.203628			0.101814	−	0.994803i	$-0.467535\pi$
$269$	3.33975			0.203628			0.101814	+	0.994803i	$0.467535\pi$
$270$		0			0
$271$	23.0064			1.39754			0.698768	−	0.715348i	$-0.253732\pi$
$271$	23.0064			1.39754			0.698768	+	0.715348i	$0.253732\pi$
$272$		0			0
$273$	−0.633975	−	0.169873i	−0.0383699	−	0.0102812i
$274$		0			0
$275$	0.189469	+	0.328169i	0.0114254	+	0.0197894i
$276$		0			0
$277$	2.29423	−	3.97372i	0.137847	−	0.238758i	−0.788835	−	0.614606i	$-0.789315\pi$
$277$	2.29423	−	3.97372i	0.137847	−	0.238758i	0.926681	+	0.375848i	$0.122648\pi$
$278$		0			0
$279$			1.13681i			0.0680592i
$280$		0			0
$281$	−12.5263	+	21.6962i	−0.747255	+	1.29428i	0.201879	+	0.979411i	$0.435295\pi$
$281$	−12.5263	+	21.6962i	−0.747255	+	1.29428i	−0.949134	+	0.314873i	$0.898038\pi$
$282$		0			0
$283$	−5.91567	−	10.2462i	−0.351650	−	0.609076i	0.634888	−	0.772604i	$-0.281046\pi$
$283$	−5.91567	−	10.2462i	−0.351650	−	0.609076i	−0.986539	+	0.163528i	$0.947713\pi$
$284$		0			0
$285$	1.09808	+	4.09808i	0.0650444	+	0.242749i
$286$		0			0
$287$	−2.41233			−0.142395
$288$		0			0
$289$	−9.53590			−0.560935
$290$		0			0
$291$	13.3843	−	13.3843i	0.784599	−	0.784599i
$292$		0			0
$293$	−15.5622	−	26.9545i	−0.909152	−	1.57470i	−0.815245	−	0.579117i	$-0.803398\pi$
$293$	−15.5622	−	26.9545i	−0.909152	−	1.57470i	−0.0939075	−	0.995581i	$-0.529936\pi$
$294$		0			0
$295$	6.17449	−	10.6945i	0.359493	−	0.622660i
$296$		0			0
$297$	1.90192	−	0.509619i	0.110361	−	0.0295711i
$298$		0			0
$299$	0.189469	−	0.328169i	0.0109573	−	0.0189785i
$300$		0			0
$301$	1.09808	+	1.90192i	0.0632921	+	0.109625i
$302$		0			0
$303$	−15.1774	+	15.1774i	−0.871920	+	0.871920i
$304$		0			0
$305$	−6.66025			−0.381365
$306$		0			0
$307$	7.20977			0.411483			0.205742	−	0.978606i	$-0.434039\pi$
$307$	7.20977			0.411483			0.205742	+	0.978606i	$0.434039\pi$
$308$		0			0
$309$	−7.22243	−	26.9545i	−0.410870	−	1.53339i
$310$		0			0
$311$	−7.77817	−	13.4722i	−0.441060	−	0.763938i	0.556709	−	0.830708i	$-0.312064\pi$
$311$	−7.77817	−	13.4722i	−0.441060	−	0.763938i	−0.997768	+	0.0667698i	$0.978731\pi$
$312$		0			0
$313$	0.633975	−	1.09808i	0.0358344	−	0.0620669i	−0.847552	−	0.530712i	$-0.821924\pi$
$313$	0.633975	−	1.09808i	0.0358344	−	0.0620669i	0.883386	+	0.468645i	$0.155258\pi$
$314$		0			0
$315$	−1.34486	−	0.776457i	−0.0757745	−	0.0437484i
$316$		0			0
$317$	2.83013	−	4.90192i	0.158956	−	0.275319i	−0.775537	−	0.631303i	$-0.782521\pi$
$317$	2.83013	−	4.90192i	0.158956	−	0.275319i	0.934492	+	0.355983i	$0.115854\pi$
$318$		0			0
$319$	0.568406	+	0.984508i	0.0318246	+	0.0551219i
$320$		0			0
$321$	−23.7224	−	6.35641i	−1.32406	−	0.354780i
$322$		0			0
$323$	6.69213			0.372360
$324$		0			0
$325$	−0.732051			−0.0406069
$326$		0			0
$327$	−2.89778	−	0.776457i	−0.160247	−	0.0429382i
$328$		0			0
$329$	−1.76795	−	3.06218i	−0.0974702	−	0.168823i
$330$		0			0
$331$	−13.5230	+	23.4225i	−0.743289	+	1.28741i	0.207701	+	0.978192i	$0.433402\pi$
$331$	−13.5230	+	23.4225i	−0.743289	+	1.28741i	−0.950990	+	0.309222i	$0.899931\pi$
$332$		0			0
$333$	1.90192	+	1.09808i	0.104225	+	0.0601742i
$334$		0			0
$335$	−1.86250	+	3.22595i	−0.101759	+	0.176252i
$336$		0			0
$337$	−15.5885	−	27.0000i	−0.849157	−	1.47078i	−0.881961	−	0.471322i	$-0.843777\pi$
$337$	−15.5885	−	27.0000i	−0.849157	−	1.47078i	0.0328039	−	0.999462i	$-0.489556\pi$
$338$		0			0
$339$	0.896575	+	3.34607i	0.0486953	+	0.181733i
$340$		0			0
$341$	0.143594			0.00777603
$342$		0			0
$343$	−7.10823			−0.383808
$344$		0			0
$345$	0.633975	−	0.633975i	0.0341320	−	0.0341320i
$346$		0			0
$347$	−14.8492	−	25.7196i	−0.797149	−	1.38070i	−0.921466	−	0.388460i	$-0.873007\pi$
$347$	−14.8492	−	25.7196i	−0.797149	−	1.38070i	0.124316	−	0.992243i	$-0.460326\pi$
$348$		0			0
$349$	2.42820	−	4.20577i	0.129979	−	0.225130i	−0.793689	−	0.608323i	$-0.791842\pi$
$349$	2.42820	−	4.20577i	0.129979	−	0.225130i	0.923668	+	0.383194i	$0.125176\pi$
$350$		0			0
$351$	−0.984508	+	3.67423i	−0.0525492	+	0.196116i
$352$		0			0
$353$	−3.46410	+	6.00000i	−0.184376	+	0.319348i	−0.943366	−	0.331754i	$-0.892360\pi$
$353$	−3.46410	+	6.00000i	−0.184376	+	0.319348i	0.758990	+	0.651102i	$0.225693\pi$
$354$		0			0
$355$	−4.94975	−	8.57321i	−0.262705	−	0.455019i
$356$		0			0
$357$	−1.73205	+	1.73205i	−0.0916698	+	0.0916698i
$358$		0			0
$359$	0.859411			0.0453580			0.0226790	−	0.999743i	$-0.492780\pi$
$359$	0.859411			0.0453580			0.0226790	+	0.999743i	$0.492780\pi$
$360$		0			0
$361$	−13.0000			−0.684211
$362$		0			0
$363$	4.86679	+	18.1631i	0.255440	+	0.953317i
$364$		0			0
$365$	2.19615	+	3.80385i	0.114952	+	0.199102i
$366$		0			0
$367$	5.88349	−	10.1905i	0.307116	−	0.531940i	−0.670615	−	0.741806i	$-0.733970\pi$
$367$	5.88349	−	10.1905i	0.307116	−	0.531940i	0.977730	+	0.209866i	$0.0673029\pi$
$368$		0			0
$369$			13.9808i			0.727809i
$370$		0			0
$371$	−0.656339	+	1.13681i	−0.0340754	+	0.0590203i
$372$		0			0
$373$	−16.1962	−	28.0526i	−0.838605	−	1.45251i	−0.891061	−	0.453883i	$-0.850038\pi$
$373$	−16.1962	−	28.0526i	−0.838605	−	1.45251i	0.0524562	−	0.998623i	$-0.483295\pi$
$374$		0			0
$375$	−1.67303	−	0.448288i	−0.0863950	−	0.0231495i
$376$		0			0
$377$	−2.19615			−0.113108
$378$		0			0
$379$	−14.1421			−0.726433			−0.363216	−	0.931705i	$-0.618321\pi$
$379$	−14.1421			−0.726433			−0.363216	+	0.931705i	$0.618321\pi$
$380$		0			0
$381$	13.9641	+	3.74167i	0.715403	+	0.191692i
$382$		0			0
$383$	9.57133	+	16.5780i	0.489072	+	0.847097i	0.999921	−	0.0125731i	$-0.00400223\pi$
$383$	9.57133	+	16.5780i	0.489072	+	0.847097i	−0.510849	+	0.859670i	$0.670669\pi$
$384$		0			0
$385$	−0.0980762	+	0.169873i	−0.00499843	+	0.00865753i
$386$		0			0
$387$	11.0227	−	6.36396i	0.560316	−	0.323498i
$388$		0			0
$389$	3.52628	−	6.10770i	0.178789	−	0.309672i	−0.762677	−	0.646780i	$-0.776115\pi$
$389$	3.52628	−	6.10770i	0.178789	−	0.309672i	0.941466	+	0.337107i	$0.109449\pi$
$390$		0			0
$391$	−0.707107	−	1.22474i	−0.0357599	−	0.0619380i
$392$		0			0
$393$	−5.07180	−	18.9282i	−0.255838	−	0.954802i
$394$		0			0
$395$	10.5558			0.531122
$396$		0			0
$397$	22.7846			1.14353			0.571763	−	0.820419i	$-0.306260\pi$
$397$	22.7846			1.14353			0.571763	+	0.820419i	$0.306260\pi$
$398$		0			0
$399$	−1.55291	+	1.55291i	−0.0777430	+	0.0777430i
$400$		0			0
$401$	−8.00000	−	13.8564i	−0.399501	−	0.691956i	0.594163	−	0.804344i	$-0.297483\pi$
$401$	−8.00000	−	13.8564i	−0.399501	−	0.691956i	−0.993664	+	0.112388i	$0.964150\pi$
$402$		0			0
$403$	−0.138701	+	0.240237i	−0.00690917	+	0.0119670i
$404$		0			0
$405$	−4.50000	+	7.79423i	−0.223607	+	0.387298i
$406$		0			0
$407$	0.138701	−	0.240237i	0.00687514	−	0.0119081i
$408$		0			0
$409$	13.1962	+	22.8564i	0.652508	+	1.13018i	0.982512	+	0.186197i	$0.0596163\pi$
$409$	13.1962	+	22.8564i	0.652508	+	1.13018i	−0.330005	+	0.943979i	$0.607050\pi$
$410$		0			0
$411$	9.62209	−	9.62209i	0.474623	−	0.474623i
$412$		0			0
$413$	6.39230			0.314545
$414$		0			0
$415$	1.27551			0.0626125
$416$		0			0
$417$	−5.66025	−	21.1244i	−0.277184	−	1.03446i
$418$		0			0
$419$	−9.33109	−	16.1619i	−0.455854	−	0.789561i	0.542883	−	0.839808i	$-0.317333\pi$
$419$	−9.33109	−	16.1619i	−0.455854	−	0.789561i	−0.998737	+	0.0502467i	$0.983999\pi$
$420$		0			0
$421$	−11.7321	+	20.3205i	−0.571785	+	0.990361i	0.424598	+	0.905382i	$0.360416\pi$
$421$	−11.7321	+	20.3205i	−0.571785	+	0.990361i	−0.996383	+	0.0849788i	$0.972918\pi$
$422$		0			0
$423$	−17.7470	+	10.2462i	−0.862890	+	0.498190i
$424$		0			0
$425$	−1.36603	+	2.36603i	−0.0662620	+	0.114769i
$426$		0			0
$427$	−1.72380	−	2.98571i	−0.0834206	−	0.144489i
$428$		0			0
$429$	0.464102	+	0.124356i	0.0224070	+	0.00600395i
$430$		0			0
$431$	−39.3949			−1.89759			−0.948793	−	0.315899i	$-0.897694\pi$
$431$	−39.3949			−1.89759			−0.948793	+	0.315899i	$0.897694\pi$
$432$		0			0
$433$	3.41154			0.163948			0.0819741	−	0.996634i	$-0.473878\pi$
$433$	3.41154			0.163948			0.0819741	+	0.996634i	$0.473878\pi$
$434$		0			0
$435$	−5.01910	−	1.34486i	−0.240647	−	0.0644813i
$436$		0			0
$437$	−0.633975	−	1.09808i	−0.0303271	−	0.0525281i
$438$		0			0
$439$	−6.83083	+	11.8313i	−0.326018	+	0.564679i	−0.981718	−	0.190342i	$-0.939040\pi$
$439$	−6.83083	+	11.8313i	−0.326018	+	0.564679i	0.655700	+	0.755022i	$0.272374\pi$
$440$		0			0
$441$			20.1962i			0.961722i
$442$		0			0
$443$	11.0041	−	19.0597i	0.522822	−	0.905554i	−0.476826	−	0.878998i	$-0.658213\pi$
$443$	11.0041	−	19.0597i	0.522822	−	0.905554i	0.999647	−	0.0265557i	$-0.00845394\pi$
$444$		0			0
$445$	4.69615	+	8.13397i	0.222619	+	0.385587i
$446$		0			0
$447$	−8.36516	−	31.2192i	−0.395659	−	1.47662i
$448$		0			0
$449$	9.07180			0.428125			0.214062	−	0.976820i	$-0.431330\pi$
$449$	9.07180			0.428125			0.214062	+	0.976820i	$0.431330\pi$
$450$		0			0
$451$	1.76594			0.0831551
$452$		0			0
$453$	21.0000	−	21.0000i	0.986666	−	0.986666i
$454$		0			0
$455$	−0.189469	−	0.328169i	−0.00888243	−	0.0153848i
$456$		0			0
$457$	6.56218	−	11.3660i	0.306966	−	0.531680i	−0.670731	−	0.741700i	$-0.734020\pi$
$457$	6.56218	−	11.3660i	0.306966	−	0.531680i	0.977697	+	0.210020i	$0.0673530\pi$
$458$		0			0
$459$	10.0382	+	10.0382i	0.468543	+	0.468543i
$460$		0			0
$461$	−7.96410	+	13.7942i	−0.370925	+	0.642461i	−0.989708	−	0.143101i	$-0.954293\pi$
$461$	−7.96410	+	13.7942i	−0.370925	+	0.642461i	0.618783	+	0.785562i	$0.287626\pi$
$462$		0			0
$463$	−9.22955	−	15.9861i	−0.428934	−	0.742935i	0.567845	−	0.823135i	$-0.307777\pi$
$463$	−9.22955	−	15.9861i	−0.428934	−	0.742935i	−0.996779	+	0.0802005i	$0.974444\pi$
$464$		0			0
$465$	−0.464102	+	0.464102i	−0.0215222	+	0.0215222i
$466$		0			0
$467$	−25.3543			−1.17326			−0.586629	−	0.809856i	$-0.699545\pi$
$467$	−25.3543			−1.17326			−0.586629	+	0.809856i	$0.699545\pi$
$468$		0			0
$469$	−1.92820			−0.0890362
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.803848	−	1.39230i	−0.0369610	−	0.0640182i
$474$		0			0
$475$	−1.22474	+	2.12132i	−0.0561951	+	0.0973329i
$476$		0			0
$477$	6.58846	+	3.80385i	0.301665	+	0.174166i
$478$		0			0
$479$	−7.82894	+	13.5601i	−0.357714	+	0.619578i	−0.987578	−	0.157127i	$-0.949777\pi$
$479$	−7.82894	+	13.5601i	−0.357714	+	0.619578i	0.629865	+	0.776705i	$0.283110\pi$
$480$		0			0
$481$	0.267949	+	0.464102i	0.0122174	+	0.0211612i
$482$		0			0
$483$	0.448288	+	0.120118i	0.0203978	+	0.00546557i
$484$		0			0
$485$	10.9282			0.496224
$486$		0			0
$487$	−12.4505			−0.564187			−0.282093	−	0.959387i	$-0.591029\pi$
$487$	−12.4505			−0.564187			−0.282093	+	0.959387i	$0.591029\pi$
$488$		0			0
$489$	8.36603	+	2.24167i	0.378325	+	0.101372i
$490$		0			0
$491$	1.27551	+	2.20925i	0.0575631	+	0.0997022i	0.893371	−	0.449320i	$-0.148334\pi$
$491$	1.27551	+	2.20925i	0.0575631	+	0.0997022i	−0.835808	+	0.549022i	$0.815000\pi$
$492$		0			0
$493$	−4.09808	+	7.09808i	−0.184568	+	0.319681i
$494$		0			0
$495$	0.984508	+	0.568406i	0.0442504	+	0.0255480i
$496$		0			0
$497$	2.56218	−	4.43782i	0.114929	−	0.199064i
$498$		0			0
$499$	14.2808	+	24.7351i	0.639298	+	1.10730i	0.985587	+	0.169169i	$0.0541083\pi$
$499$	14.2808	+	24.7351i	0.639298	+	1.10730i	−0.346289	+	0.938128i	$0.612558\pi$
$500$		0			0
$501$	0.866025	+	3.23205i	0.0386912	+	0.144397i
$502$		0			0
$503$	35.6699			1.59044			0.795221	−	0.606319i	$-0.207355\pi$
$503$	35.6699			1.59044			0.795221	+	0.606319i	$0.207355\pi$
$504$		0			0
$505$	−12.3923			−0.551450
$506$		0			0
$507$	15.2653	−	15.2653i	0.677958	−	0.677958i
$508$		0			0
$509$	−4.69615	−	8.13397i	−0.208153	−	0.360532i	0.742980	−	0.669314i	$-0.233412\pi$
$509$	−4.69615	−	8.13397i	−0.208153	−	0.360532i	−0.951133	+	0.308782i	$0.900079\pi$
$510$		0			0
$511$	−1.13681	+	1.96902i	−0.0502896	+	0.0871042i
$512$		0			0
$513$	9.00000	+	9.00000i	0.397360	+	0.397360i
$514$		0			0
$515$	8.05558	−	13.9527i	0.354971	−	0.614828i
$516$		0			0
$517$	1.29423	+	2.24167i	0.0569201	+	0.0985885i
$518$		0			0
$519$	−9.79796	+	9.79796i	−0.430083	+	0.430083i
$520$		0			0
$521$	12.6077			0.552353			0.276177	−	0.961107i	$-0.410933\pi$
$521$	12.6077			0.552353			0.276177	+	0.961107i	$0.410933\pi$
$522$		0			0
$523$	−28.4973			−1.24610			−0.623050	−	0.782182i	$-0.714107\pi$
$523$	−28.4973			−1.24610			−0.623050	+	0.782182i	$0.714107\pi$
$524$		0			0
$525$	−0.232051	−	0.866025i	−0.0101275	−	0.0377964i
$526$		0			0
$527$	0.517638	+	0.896575i	0.0225487	+	0.0390554i
$528$		0			0
$529$	11.3660	−	19.6865i	0.494175	−	0.855936i
$530$		0			0
$531$		−	37.0470i		−	1.60770i
$532$		0			0
$533$	−1.70577	+	2.95448i	−0.0738852	+	0.127973i
$534$		0			0
$535$	−7.08965	−	12.2796i	−0.306512	−	0.530895i
$536$		0			0
$537$	−28.2224	−	7.56218i	−1.21789	−	0.326332i
$538$		0			0
$539$	2.55103			0.109880
$540$		0			0
$541$	27.3923			1.17769			0.588844	−	0.808247i	$-0.299583\pi$
$541$	27.3923			1.17769			0.588844	+	0.808247i	$0.299583\pi$
$542$		0			0
$543$	−14.8171	−	3.97022i	−0.635861	−	0.170378i
$544$		0			0
$545$	−0.866025	−	1.50000i	−0.0370965	−	0.0642529i
$546$		0			0
$547$	2.32937	−	4.03459i	0.0995967	−	0.172507i	−0.811921	−	0.583767i	$-0.801578\pi$
$547$	2.32937	−	4.03459i	0.0995967	−	0.172507i	0.911518	+	0.411261i	$0.134911\pi$
$548$		0			0
$549$	−17.3038	+	9.99038i	−0.738510	+	0.426379i
$550$		0			0
$551$	−3.67423	+	6.36396i	−0.156528	+	0.271114i
$552$		0			0
$553$	2.73205	+	4.73205i	0.116179	+	0.201227i
$554$		0			0
$555$	0.328169	+	1.22474i	0.0139300	+	0.0519875i
$556$		0			0
$557$	40.2487			1.70539			0.852696	−	0.522407i	$-0.174966\pi$
$557$	40.2487			1.70539			0.852696	+	0.522407i	$0.174966\pi$
$558$		0			0
$559$	3.10583			0.131363
$560$		0			0
$561$	1.26795	−	1.26795i	0.0535329	−	0.0535329i
$562$		0			0
$563$	9.31251	+	16.1297i	0.392475	+	0.679787i	0.992775	−	0.119988i	$-0.0382855\pi$
$563$	9.31251	+	16.1297i	0.392475	+	0.679787i	−0.600300	+	0.799775i	$0.704952\pi$
$564$		0			0
$565$	−1.00000	+	1.73205i	−0.0420703	+	0.0728679i
$566$		0			0
$567$	−4.65874			−0.195649
$568$		0			0
$569$	−13.9282	+	24.1244i	−0.583901	+	1.01135i	0.411111	+	0.911585i	$0.365141\pi$
$569$	−13.9282	+	24.1244i	−0.583901	+	1.01135i	−0.995012	+	0.0997602i	$0.968192\pi$
$570$		0			0
$571$	19.9749	+	34.5975i	0.835922	+	1.44786i	0.893278	+	0.449505i	$0.148400\pi$
$571$	19.9749	+	34.5975i	0.835922	+	1.44786i	−0.0573561	+	0.998354i	$0.518267\pi$
$572$		0			0
$573$	−18.8038	+	18.8038i	−0.785542	+	0.785542i
$574$		0			0
$575$	0.517638			0.0215870
$576$		0			0
$577$	−26.9282			−1.12104			−0.560518	−	0.828142i	$-0.689398\pi$
$577$	−26.9282			−1.12104			−0.560518	+	0.828142i	$0.689398\pi$
$578$		0			0
$579$	−0.984508	−	3.67423i	−0.0409148	−	0.152696i
$580$		0			0
$581$	0.330127	+	0.571797i	0.0136960	+	0.0237221i
$582$		0			0
$583$	0.480473	−	0.832204i	0.0198992	−	0.0344664i
$584$		0			0
$585$	−1.90192	+	1.09808i	−0.0786349	+	0.0453999i
$586$		0			0
$587$	10.8147	−	18.7315i	0.446368	−	0.773133i	−0.551778	−	0.833991i	$-0.686050\pi$
$587$	10.8147	−	18.7315i	0.446368	−	0.773133i	0.998146	+	0.0608582i	$0.0193837\pi$
$588$		0			0
$589$	0.464102	+	0.803848i	0.0191230	+	0.0331220i
$590$		0			0
$591$	10.0382	+	2.68973i	0.412916	+	0.110641i
$592$		0			0
$593$	−9.80385			−0.402596			−0.201298	−	0.979530i	$-0.564516\pi$
$593$	−9.80385			−0.402596			−0.201298	+	0.979530i	$0.564516\pi$
$594$		0			0
$595$	−1.41421			−0.0579771
$596$		0			0
$597$	23.0263	+	6.16987i	0.942403	+	0.252516i
$598$		0			0
$599$	5.65685	+	9.79796i	0.231133	+	0.400334i	0.958142	−	0.286294i	$-0.0924235\pi$
$599$	5.65685	+	9.79796i	0.231133	+	0.400334i	−0.727009	+	0.686628i	$0.759090\pi$
$600$		0			0
$601$	−12.3205	+	21.3397i	−0.502564	+	0.870466i	0.497432	+	0.867503i	$0.334277\pi$
$601$	−12.3205	+	21.3397i	−0.502564	+	0.870466i	−0.999996	+	0.00296319i	$0.999057\pi$
$602$		0			0
$603$			11.1750i			0.455081i
$604$		0			0
$605$	−5.42820	+	9.40192i	−0.220688	+	0.382243i
$606$		0			0
$607$	8.07416	+	13.9849i	0.327720	+	0.567628i	0.982059	−	0.188574i	$-0.0603864\pi$
$607$	8.07416	+	13.9849i	0.327720	+	0.567628i	−0.654339	+	0.756201i	$0.727053\pi$
$608$		0			0
$609$	−0.696152	−	2.59808i	−0.0282095	−	0.105279i
$610$		0			0
$611$	−5.00052			−0.202299
$612$		0			0
$613$	36.1962			1.46195			0.730974	−	0.682405i	$-0.239066\pi$
$613$	36.1962			1.46195			0.730974	+	0.682405i	$0.239066\pi$
$614$		0			0
$615$	−5.70762	+	5.70762i	−0.230154	+	0.230154i
$616$		0			0
$617$	−10.4641	−	18.1244i	−0.421269	−	0.729659i	0.574795	−	0.818297i	$-0.305082\pi$
$617$	−10.4641	−	18.1244i	−0.421269	−	0.729659i	−0.996064	+	0.0886384i	$0.971748\pi$
$618$		0			0
$619$	−5.36585	+	9.29392i	−0.215672	+	0.373554i	−0.953480	−	0.301456i	$-0.902527\pi$
$619$	−5.36585	+	9.29392i	−0.215672	+	0.373554i	0.737808	+	0.675010i	$0.235861\pi$
$620$		0			0
$621$	0.696152	−	2.59808i	0.0279356	−	0.104257i
$622$		0			0
$623$	−2.43091	+	4.21046i	−0.0973922	+	0.168688i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	1.13681	−	1.13681i	0.0453999	−	0.0453999i
$628$		0			0
$629$	2.00000			0.0797452
$630$		0			0
$631$	8.00481			0.318666			0.159333	−	0.987225i	$-0.449066\pi$
$631$	8.00481			0.318666			0.159333	+	0.987225i	$0.449066\pi$
$632$		0			0
$633$	7.09808	+	26.4904i	0.282123	+	1.05290i
$634$		0			0
$635$	4.17329	+	7.22835i	0.165612	+	0.286848i
$636$		0			0
$637$	−2.46410	+	4.26795i	−0.0976313	+	0.169102i
$638$		0			0
$639$	−25.7196	−	14.8492i	−1.01745	−	0.587427i
$640$		0			0
$641$	−9.93782	+	17.2128i	−0.392520	+	0.679865i	−0.992781	−	0.119939i	$-0.961730\pi$
$641$	−9.93782	+	17.2128i	−0.392520	+	0.679865i	0.600261	+	0.799804i	$0.295063\pi$
$642$		0			0
$643$	−16.1433	−	27.9611i	−0.636631	−	1.10268i	−0.986167	−	0.165754i	$-0.946994\pi$
$643$	−16.1433	−	27.9611i	−0.636631	−	1.10268i	0.349536	−	0.936923i	$-0.386339\pi$
$644$		0			0
$645$	7.09808	+	1.90192i	0.279486	+	0.0748882i
$646$		0			0
$647$	28.4230			1.11742			0.558711	−	0.829362i	$-0.311296\pi$
$647$	28.4230			1.11742			0.558711	+	0.829362i	$0.311296\pi$
$648$		0			0
$649$	−4.67949			−0.183686
$650$		0			0
$651$	−0.328169	−	0.0879327i	−0.0128620	−	0.00344636i
$652$		0			0
$653$	2.56218	+	4.43782i	0.100266	+	0.173665i	0.911794	−	0.410648i	$-0.134697\pi$
$653$	2.56218	+	4.43782i	0.100266	+	0.173665i	−0.811528	+	0.584313i	$0.801364\pi$
$654$		0			0
$655$	5.65685	−	9.79796i	0.221032	−	0.382838i
$656$		0			0
$657$	11.4115	+	6.58846i	0.445207	+	0.257040i
$658$		0			0
$659$	−9.55772	+	16.5545i	−0.372316	+	0.644870i	−0.989921	−	0.141618i	$-0.954770\pi$
$659$	−9.55772	+	16.5545i	−0.372316	+	0.644870i	0.617605	+	0.786488i	$0.288103\pi$
$660$		0			0
$661$	−5.33975	−	9.24871i	−0.207692	−	0.359733i	0.743295	−	0.668964i	$-0.233262\pi$
$661$	−5.33975	−	9.24871i	−0.207692	−	0.359733i	−0.950987	+	0.309231i	$0.899929\pi$
$662$		0			0
$663$	0.896575	+	3.34607i	0.0348201	+	0.129950i
$664$		0			0
$665$	−1.26795			−0.0491690
$666$		0			0
$667$	1.55291			0.0601291
$668$		0			0
$669$	33.8827	−	33.8827i	1.30998	−	1.30998i
$670$		0			0
$671$	1.26191	+	2.18569i	0.0487155	+	0.0843777i
$672$		0			0
$673$	−17.5622	+	30.4186i	−0.676972	+	1.17255i	0.298916	+	0.954279i	$0.403375\pi$
$673$	−17.5622	+	30.4186i	−0.676972	+	1.17255i	−0.975888	+	0.218271i	$0.929958\pi$
$674$		0			0
$675$	−5.01910	+	1.34486i	−0.193185	+	0.0517638i
$676$		0			0
$677$	−8.63397	+	14.9545i	−0.331831	+	0.574747i	−0.982871	−	0.184296i	$-0.941000\pi$
$677$	−8.63397	+	14.9545i	−0.331831	+	0.574747i	0.651040	+	0.759043i	$0.274333\pi$
$678$		0			0
$679$	2.82843	+	4.89898i	0.108545	+	0.188006i
$680$		0			0
$681$	−7.14359	+	7.14359i	−0.273743	+	0.273743i
$682$		0			0
$683$	47.2239			1.80697			0.903485	−	0.428619i	$-0.141000\pi$
$683$	47.2239			1.80697			0.903485	+	0.428619i	$0.141000\pi$
$684$		0			0
$685$	7.85641			0.300178
$686$		0			0
$687$	−8.86920	−	33.1003i	−0.338381	−	1.26286i
$688$		0			0
$689$	0.928203	+	1.60770i	0.0353617	+	0.0612483i
$690$		0			0
$691$	−22.9048	+	39.6723i	−0.871340	+	1.50921i	−0.0107296	+	0.999942i	$0.503415\pi$
$691$	−22.9048	+	39.6723i	−0.871340	+	1.50921i	−0.860611	+	0.509263i	$0.829918\pi$
$692$		0			0
$693$			0.588457i			0.0223536i
$694$		0			0
$695$	6.31319	−	10.9348i	0.239473	−	0.414780i
$696$		0			0
$697$	6.36603	+	11.0263i	0.241130	+	0.417650i
$698$		0			0
$699$	21.3011	+	5.70762i	0.805683	+	0.215882i
$700$		0			0
$701$	15.0526			0.568527			0.284264	−	0.958746i	$-0.408251\pi$
$701$	15.0526			0.568527			0.284264	+	0.958746i	$0.408251\pi$
$702$		0			0
$703$	1.79315			0.0676300
$704$		0			0
$705$	−11.4282	−	3.06218i	−0.430411	−	0.115328i
$706$		0			0
$707$	−3.20736	−	5.55532i	−0.120625	−	0.208929i
$708$		0			0
$709$	7.76795	−	13.4545i	0.291731	−	0.505294i	−0.682488	−	0.730897i	$-0.739102\pi$
$709$	7.76795	−	13.4545i	0.291731	−	0.505294i	0.974219	+	0.225603i	$0.0724353\pi$
$710$		0			0
$711$	27.4249	−	15.8338i	1.02851	−	0.593812i
$712$		0			0
$713$	0.0980762	−	0.169873i	0.00367298	−	0.00636179i
$714$		0			0
$715$	0.138701	+	0.240237i	0.00518711	+	0.00898434i
$716$		0			0
$717$	6.71281	+	25.0526i	0.250695	+	0.935605i
$718$		0			0
$719$	17.0449			0.635667			0.317834	−	0.948147i	$-0.397045\pi$
$719$	17.0449			0.635667			0.317834	+	0.948147i	$0.397045\pi$
$720$		0			0
$721$	8.33975			0.310588
$722$		0			0
$723$	−8.81345	+	8.81345i	−0.327776	+	0.327776i
$724$		0			0
$725$	−1.50000	−	2.59808i	−0.0557086	−	0.0964901i
$726$		0			0
$727$	−16.0418	+	27.7852i	−0.594957	+	1.03050i	0.398595	+	0.917127i	$0.369498\pi$
$727$	−16.0418	+	27.7852i	−0.594957	+	1.03050i	−0.993553	+	0.113370i	$0.963836\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$	5.79555	−	10.0382i	0.214356	−	0.371276i
$732$		0			0
$733$	5.73205	+	9.92820i	0.211718	+	0.366707i	0.952252	−	0.305312i	$-0.0987608\pi$
$733$	5.73205	+	9.92820i	0.211718	+	0.366707i	−0.740534	+	0.672019i	$0.765427\pi$
$734$		0			0
$735$	−8.24504	+	8.24504i	−0.304123	+	0.304123i
$736$		0			0
$737$	1.41154			0.0519948
$738$		0			0
$739$	17.2480			0.634477			0.317238	−	0.948346i	$-0.397244\pi$
$739$	17.2480			0.634477			0.317238	+	0.948346i	$0.397244\pi$
$740$		0			0
$741$	0.803848	+	3.00000i	0.0295301	+	0.110208i
$742$		0			0
$743$	23.9215	+	41.4333i	0.877595	+	1.52004i	0.853972	+	0.520318i	$0.174187\pi$
$743$	23.9215	+	41.4333i	0.877595	+	1.52004i	0.0236229	+	0.999721i	$0.492480\pi$
$744$		0			0
$745$	9.33013	−	16.1603i	0.341829	−	0.592066i
$746$		0			0
$747$	3.31388	−	1.91327i	0.121249	−	0.0700029i
$748$		0			0
$749$	3.66987	−	6.35641i	0.134094	−	0.232258i
$750$		0			0
$751$	14.1929	+	24.5828i	0.517906	+	0.897040i	0.999784	+	0.0208015i	$0.00662179\pi$
$751$	14.1929	+	24.5828i	0.517906	+	0.897040i	−0.481877	+	0.876239i	$0.660045\pi$
$752$		0			0
$753$	−22.2224	−	5.95448i	−0.809830	−	0.216993i
$754$		0			0
$755$	17.1464			0.624022
$756$		0			0
$757$	34.1962			1.24288			0.621440	−	0.783462i	$-0.286548\pi$
$757$	34.1962			1.24288			0.621440	+	0.783462i	$0.286548\pi$
$758$		0			0
$759$	−0.328169	−	0.0879327i	−0.0119118	−	0.00319176i
$760$		0			0
$761$	5.16025	+	8.93782i	0.187059	+	0.323996i	0.944268	−	0.329176i	$-0.106771\pi$
$761$	5.16025	+	8.93782i	0.187059	+	0.323996i	−0.757209	+	0.653172i	$0.773438\pi$
$762$		0			0
$763$	0.448288	−	0.776457i	0.0162291	−	0.0281096i
$764$		0			0
$765$			8.19615i			0.296333i
$766$		0			0
$767$	4.52004	−	7.82894i	0.163209	−	0.282687i
$768$		0			0
$769$	13.6244	+	23.5981i	0.491307	+	0.850968i	0.999950	−	0.0100091i	$-0.00318604\pi$
$769$	13.6244	+	23.5981i	0.491307	+	0.850968i	−0.508643	+	0.860977i	$0.669853\pi$
$770$		0			0
$771$	−13.3199	−	49.7105i	−0.479704	−	1.79028i
$772$		0			0
$773$	26.5359			0.954430			0.477215	−	0.878787i	$-0.341646\pi$
$773$	26.5359			0.954430			0.477215	+	0.878787i	$0.341646\pi$
$774$		0			0
$775$	−0.378937			−0.0136118
$776$		0			0
$777$	−0.464102	+	0.464102i	−0.0166496	+	0.0166496i
$778$		0			0
$779$	5.70762	+	9.88589i	0.204497	+	0.354199i
$780$		0			0
$781$	−1.87564	+	3.24871i	−0.0671158	+	0.116248i
$782$		0			0
$783$	−15.0573	+	4.03459i	−0.538104	+	0.144184i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	14.8492	+	25.7196i	0.529318	+	0.916806i	0.999415	+	0.0341915i	$0.0108856\pi$
$787$	14.8492	+	25.7196i	0.529318	+	0.916806i	−0.470097	+	0.882615i	$0.655781\pi$
$788$		0			0
$789$	3.33975	−	3.33975i	0.118898	−	0.118898i
$790$		0			0
$791$	−1.03528			−0.0368102
$792$		0			0
$793$	−4.87564			−0.173139
$794$		0			0
$795$	1.13681	+	4.24264i	0.0403186	+	0.150471i
$796$		0			0
$797$	10.6865	+	18.5096i	0.378536	+	0.655644i	0.990850	−	0.134971i	$-0.0430941\pi$
$797$	10.6865	+	18.5096i	0.378536	+	0.655644i	−0.612313	+	0.790615i	$0.709761\pi$
$798$		0			0
$799$	−9.33109	+	16.1619i	−0.330110	+	0.571768i
$800$		0			0
$801$	24.4019	+	14.0885i	0.862200	+	0.497791i
$802$		0			0
$803$	0.832204	−	1.44142i	0.0293679	−	0.0508666i
$804$		0			0
$805$	0.133975	+	0.232051i	0.00472198	+	0.00817872i
$806$		0			0
$807$	5.58750	+	1.49717i	0.196689	+	0.0527028i
$808$		0			0
$809$	23.3205			0.819905			0.409953	−	0.912107i	$-0.365545\pi$
$809$	23.3205			0.819905			0.409953	+	0.912107i	$0.365545\pi$
$810$		0			0
$811$	−26.2137			−0.920488			−0.460244	−	0.887792i	$-0.652238\pi$
$811$	−26.2137			−0.920488			−0.460244	+	0.887792i	$0.652238\pi$
$812$		0			0
$813$	38.4904	+	10.3135i	1.34992	+	0.361709i
$814$		0			0
$815$	2.50026	+	4.33057i	0.0875802	+	0.151693i
$816$		0			0
$817$	5.19615	−	9.00000i	0.181790	−	0.314870i
$818$		0			0
$819$	−0.984508	−	0.568406i	−0.0344015	−	0.0198617i
$820$		0			0
$821$	2.66987	−	4.62436i	0.0931792	−	0.161391i	−0.815668	−	0.578520i	$-0.803630\pi$
$821$	2.66987	−	4.62436i	0.0931792	−	0.161391i	0.908847	+	0.417129i	$0.136964\pi$
$822$		0			0
$823$	−10.7267	−	18.5792i	−0.373910	−	0.647631i	0.616253	−	0.787548i	$-0.288650\pi$
$823$	−10.7267	−	18.5792i	−0.373910	−	0.647631i	−0.990163	+	0.139917i	$0.955316\pi$
$824$		0			0
$825$	0.169873	+	0.633975i	0.00591422	+	0.0220722i
$826$		0			0
$827$	−14.5582			−0.506240			−0.253120	−	0.967435i	$-0.581457\pi$
$827$	−14.5582			−0.506240			−0.253120	+	0.967435i	$0.581457\pi$
$828$		0			0
$829$	−13.8756			−0.481921			−0.240961	−	0.970535i	$-0.577462\pi$
$829$	−13.8756			−0.481921			−0.240961	+	0.970535i	$0.577462\pi$
$830$		0			0
$831$	5.61969	−	5.61969i	0.194945	−	0.194945i
$832$		0			0
$833$	9.19615	+	15.9282i	0.318628	+	0.551880i
$834$		0			0
$835$	−0.965926	+	1.67303i	−0.0334272	+	0.0578977i
$836$		0			0
$837$	−0.509619	+	1.90192i	−0.0176150	+	0.0657401i
$838$		0			0
$839$	19.1290	−	33.1325i	0.660408	−	1.14386i	−0.320100	−	0.947384i	$-0.603717\pi$
$839$	19.1290	−	33.1325i	0.660408	−	1.14386i	0.980508	−	0.196477i	$-0.0629500\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	−30.6830	+	30.6830i	−1.05678	+	1.05678i
$844$		0			0
$845$	12.4641			0.428778
$846$		0			0
$847$	−5.61969			−0.193095
$848$		0			0
$849$	−5.30385	−	19.7942i	−0.182028	−	0.679336i
$850$		0			0
$851$	−0.189469	−	0.328169i	−0.00649490	−	0.0112495i
$852$		0			0
$853$	−8.97372	+	15.5429i	−0.307254	+	0.532180i	−0.977761	−	0.209724i	$-0.932744\pi$
$853$	−8.97372	+	15.5429i	−0.307254	+	0.532180i	0.670506	+	0.741904i	$0.266077\pi$
$854$		0			0
$855$			7.34847i			0.251312i
$856$		0			0
$857$	−14.9545	+	25.9019i	−0.510835	+	0.884793i	0.489086	+	0.872236i	$0.337331\pi$
$857$	−14.9545	+	25.9019i	−0.510835	+	0.884793i	−0.999921	+	0.0125572i	$0.996003\pi$
$858$		0			0
$859$	1.64085	+	2.84203i	0.0559850	+	0.0969688i	0.892660	−	0.450731i	$-0.148837\pi$
$859$	1.64085	+	2.84203i	0.0559850	+	0.0969688i	−0.836675	+	0.547700i	$0.815503\pi$
$860$		0			0
$861$	−4.03590	−	1.08142i	−0.137543	−	0.0368545i
$862$		0			0
$863$	55.2658			1.88127			0.940635	−	0.339419i	$-0.110230\pi$
$863$	55.2658			1.88127			0.940635	+	0.339419i	$0.110230\pi$
$864$		0			0
$865$	−8.00000			−0.272008
$866$		0			0
$867$	−15.9539	−	4.27483i	−0.541822	−	0.145181i
$868$		0			0
$869$	−2.00000	−	3.46410i	−0.0678454	−	0.117512i
$870$		0			0
$871$	−1.36345	+	2.36156i	−0.0461986	+	0.0800183i
$872$		0			0
$873$	28.3923	−	16.3923i	0.960934	−	0.554795i
$874$		0			0
$875$	0.258819	−	0.448288i	0.00874968	−	0.0151549i
$876$		0			0
$877$	6.02628	+	10.4378i	0.203493	+	0.352460i	0.949652	−	0.313308i	$-0.101437\pi$
$877$	6.02628	+	10.4378i	0.203493	+	0.352460i	−0.746159	+	0.665768i	$0.768104\pi$
$878$		0			0
$879$	−13.9527	−	52.0721i	−0.470612	−	1.75635i
$880$		0			0
$881$	14.6603			0.493917			0.246958	−	0.969026i	$-0.420569\pi$
$881$	14.6603			0.493917			0.246958	+	0.969026i	$0.420569\pi$
$882$		0			0
$883$	−21.2504			−0.715132			−0.357566	−	0.933888i	$-0.616393\pi$
$883$	−21.2504			−0.715132			−0.357566	+	0.933888i	$0.616393\pi$
$884$		0			0
$885$	15.1244	−	15.1244i	0.508400	−	0.508400i
$886$		0			0
$887$	15.2282	+	26.3760i	0.511312	+	0.885619i	0.999914	+	0.0131119i	$0.00417376\pi$
$887$	15.2282	+	26.3760i	0.511312	+	0.885619i	−0.488602	+	0.872507i	$0.662493\pi$
$888$		0			0
$889$	−2.16025	+	3.74167i	−0.0724526	+	0.125492i
$890$		0			0
$891$	3.41044			0.114254
$892$		0			0
$893$	−8.36603	+	14.4904i	−0.279958	+	0.484902i
$894$		0			0
$895$	−8.43451	−	14.6090i	−0.281935	−	0.488325i
$896$		0			0
$897$	0.464102	−	0.464102i	0.0154959	−	0.0154959i
$898$		0			0
$899$	−1.13681			−0.0379148
$900$		0			0
$901$	6.92820			0.230812
$902$		0			0
$903$	0.984508	+	3.67423i	0.0327624	+	0.122271i
$904$		0			0
$905$	−4.42820	−	7.66987i	−0.147198	−	0.254955i
$906$		0			0
$907$	2.00120	−	3.46618i	0.0664488	−	0.115093i	−0.830887	−	0.556441i	$-0.812166\pi$
$907$	2.00120	−	3.46618i	0.0664488	−	0.115093i	0.897336	+	0.441349i	$0.145500\pi$
$908$		0			0
$909$	−32.1962	+	18.5885i	−1.06788	+	0.616540i
$910$		0			0
$911$	−17.6641	+	30.5951i	−0.585237	+	1.01366i	0.409609	+	0.912261i	$0.365665\pi$
$911$	−17.6641	+	30.5951i	−0.585237	+	1.01366i	−0.994846	+	0.101399i	$0.967668\pi$
$912$		0			0
$913$	−0.241670	−	0.418584i	−0.00799810	−	0.0138531i
$914$		0			0
$915$	−11.1428	−	2.98571i	−0.368370	−	0.0987045i
$916$		0			0
$917$	5.85641			0.193396
$918$		0			0
$919$	−30.3548			−1.00131			−0.500657	−	0.865646i	$-0.666908\pi$
$919$	−30.3548			−1.00131			−0.500657	+	0.865646i	$0.666908\pi$
$920$		0			0
$921$	12.0622	+	3.23205i	0.397462	+	0.106500i
$922$		0			0
$923$	−3.62347	−	6.27603i	−0.119268	−	0.206578i
$924$		0			0
$925$	−0.366025	+	0.633975i	−0.0120348	+	0.0208450i
$926$		0			0
$927$		−	48.3335i		−	1.58748i
$928$		0			0
$929$	−2.12436	+	3.67949i	−0.0696978	+	0.120720i	−0.898768	−	0.438424i	$-0.855537\pi$
$929$	−2.12436	+	3.67949i	−0.0696978	+	0.120720i	0.829070	+	0.559144i	$0.188870\pi$
$930$		0			0
$931$	8.24504	+	14.2808i	0.270220	+	0.468036i
$932$		0			0
$933$	−6.97372	−	26.0263i	−0.228309	−	0.852062i
$934$		0			0
$935$	1.03528			0.0338572
$936$		0			0
$937$	−18.3923			−0.600850			−0.300425	−	0.953805i	$-0.597129\pi$
$937$	−18.3923			−0.600850			−0.300425	+	0.953805i	$0.597129\pi$
$938$		0			0
$939$	1.55291	−	1.55291i	0.0506774	−	0.0506774i
$940$		0			0
$941$	−6.50000	−	11.2583i	−0.211894	−	0.367011i	0.740413	−	0.672152i	$-0.234630\pi$
$941$	−6.50000	−	11.2583i	−0.211894	−	0.367011i	−0.952307	+	0.305141i	$0.901296\pi$
$942$		0			0
$943$	1.20616	−	2.08913i	0.0392781	−	0.0680316i
$944$		0			0
$945$	−1.90192	−	1.90192i	−0.0618696	−	0.0618696i
$946$		0			0
$947$	−20.9408	+	36.2705i	−0.680484	+	1.17863i	0.294349	+	0.955698i	$0.404897\pi$
$947$	−20.9408	+	36.2705i	−0.680484	+	1.17863i	−0.974833	+	0.222935i	$0.928436\pi$
$948$		0			0
$949$	1.60770	+	2.78461i	0.0521880	+	0.0903923i
$950$		0			0
$951$	6.93237	−	6.93237i	0.224797	−	0.224797i
$952$		0			0
$953$	3.80385			0.123219			0.0616094	−	0.998100i	$-0.480377\pi$
$953$	3.80385			0.123219			0.0616094	+	0.998100i	$0.480377\pi$
$954$		0			0
$955$	−15.3533			−0.496820
$956$		0			0
$957$	0.509619	+	1.90192i	0.0164736	+	0.0614805i
$958$		0			0
$959$	2.03339	+	3.52193i	0.0656615	+	0.113729i
$960$		0			0
$961$	15.4282	−	26.7224i	0.497684	−	0.862014i
$962$		0			0
$963$	−36.8389	−	21.2690i	−1.18712	−	0.685382i
$964$		0			0
$965$	1.09808	−	1.90192i	0.0353483	−	0.0612251i
$966$		0			0
$967$	14.5768	+	25.2478i	0.468759	+	0.811914i	0.999362	−	0.0357059i	$-0.0113680\pi$
$967$	14.5768	+	25.2478i	0.468759	+	0.811914i	−0.530603	+	0.847620i	$0.678035\pi$
$968$		0			0
$969$	11.1962	+	3.00000i	0.359672	+	0.0963739i
$970$		0			0
$971$	25.0769			0.804756			0.402378	−	0.915474i	$-0.368184\pi$
$971$	25.0769			0.804756			0.402378	+	0.915474i	$0.368184\pi$
$972$		0			0
$973$	6.53590			0.209531
$974$		0			0
$975$	−1.22474	−	0.328169i	−0.0392232	−	0.0105098i
$976$		0			0
$977$	−13.5622	−	23.4904i	−0.433893	−	0.751524i	0.563312	−	0.826244i	$-0.309527\pi$
$977$	−13.5622	−	23.4904i	−0.433893	−	0.751524i	−0.997205	+	0.0747204i	$0.976194\pi$
$978$		0			0
$979$	1.77955	−	3.08227i	0.0568746	−	0.0985097i
$980$		0			0
$981$	−4.50000	−	2.59808i	−0.143674	−	0.0829502i
$982$		0			0
$983$	16.8876	−	29.2502i	0.538631	−	0.932936i	−0.460347	−	0.887739i	$-0.652275\pi$
$983$	16.8876	−	29.2502i	0.538631	−	0.932936i	0.998978	−	0.0451973i	$-0.0143917\pi$
$984$		0			0
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$		0			0
$987$	−1.58510	−	5.91567i	−0.0504543	−	0.188298i
$988$		0			0
$989$	−2.19615			−0.0698336
$990$		0			0
$991$	36.0860			1.14631			0.573155	−	0.819447i	$-0.305719\pi$
$991$	36.0860			1.14631			0.573155	+	0.819447i	$0.305719\pi$
$992$		0			0
$993$	−33.1244	+	33.1244i	−1.05117	+	1.05117i
$994$		0			0
$995$	6.88160	+	11.9193i	0.218161	+	0.377867i
$996$		0			0
$997$	−27.3205	+	47.3205i	−0.865249	+	1.49866i	0.00155038	+	0.999999i	$0.499506\pi$
$997$	−27.3205	+	47.3205i	−0.865249	+	1.49866i	−0.866800	+	0.498657i	$0.833827\pi$
$998$		0			0
$999$	2.68973	+	2.68973i	0.0850992	+	0.0850992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.q.m.961.4	yes	8
3.2	odd	2		4320.2.q.j.2881.2		8
4.3	odd	2	inner	1440.2.q.m.961.1	yes	8
9.4	even	3	inner	1440.2.q.m.481.4	yes	8
9.5	odd	6		4320.2.q.j.1441.2		8
12.11	even	2		4320.2.q.j.2881.3		8
36.23	even	6		4320.2.q.j.1441.3		8
36.31	odd	6	inner	1440.2.q.m.481.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1440.2.q.m.481.1	✓	8	36.31	odd	6	inner
1440.2.q.m.481.4	yes	8	9.4	even	3	inner
1440.2.q.m.961.1	yes	8	4.3	odd	2	inner
1440.2.q.m.961.4	yes	8	1.1	even	1	trivial
4320.2.q.j.1441.2		8	9.5	odd	6
4320.2.q.j.1441.3		8	36.23	even	6
4320.2.q.j.2881.2		8	3.2	odd	2
4320.2.q.j.2881.3		8	12.11	even	2

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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.67303 + 0.448288i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.258819 + 0.448288i) q^{7} +(2.59808 + 1.50000i) q^{9} +(0.189469 - 0.328169i) q^{11} +(0.366025 + 0.633975i) q^{13} +(0.448288 + 1.67303i) q^{15} +2.73205 q^{17} +2.44949 q^{19} +(-0.633975 + 0.633975i) q^{21} +(-0.258819 - 0.448288i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.67423 + 3.67423i) q^{27} +(-1.50000 + 2.59808i) q^{29} +(0.189469 + 0.328169i) q^{31} +(0.464102 - 0.464102i) q^{33} -0.517638 q^{35} +0.732051 q^{37} +(0.328169 + 1.22474i) q^{39} +(2.33013 + 4.03590i) q^{41} +(2.12132 - 3.67423i) q^{43} +3.00000i q^{45} +(-3.41542 + 5.91567i) q^{47} +(3.36603 + 5.83013i) q^{49} +(4.57081 + 1.22474i) q^{51} +2.53590 q^{53} +0.378937 q^{55} +(4.09808 + 1.09808i) q^{57} +(-6.17449 - 10.6945i) q^{59} +(-3.33013 + 5.76795i) q^{61} +(-1.34486 + 0.776457i) q^{63} +(-0.366025 + 0.633975i) q^{65} +(1.86250 + 3.22595i) q^{67} +(-0.232051 - 0.866025i) q^{69} -9.89949 q^{71} +4.39230 q^{73} +(-1.22474 + 1.22474i) q^{75} +(0.0980762 + 0.169873i) q^{77} +(5.27792 - 9.14162i) q^{79} +(4.50000 + 7.79423i) q^{81} +(0.637756 - 1.10463i) q^{83} +(1.36603 + 2.36603i) q^{85} +(-3.67423 + 3.67423i) q^{87} +9.39230 q^{89} -0.378937 q^{91} +(0.169873 + 0.633975i) q^{93} +(1.22474 + 2.12132i) q^{95} +(5.46410 - 9.46410i) q^{97} +(0.984508 - 0.568406i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} - 4 q^{13} + 8 q^{17} - 12 q^{21} - 4 q^{25} - 12 q^{29} - 24 q^{33} - 8 q^{37} - 16 q^{41} + 20 q^{49} + 48 q^{53} + 12 q^{57} + 8 q^{61} + 4 q^{65} + 12 q^{69} - 48 q^{73} - 20 q^{77} + 36 q^{81}+ \cdots + 16 q^{97}+O(q^{100}) \) 8 * q + 4 * q^5 - 4 * q^13 + 8 * q^17 - 12 * q^21 - 4 * q^25 - 12 * q^29 - 24 * q^33 - 8 * q^37 - 16 * q^41 + 20 * q^49 + 48 * q^53 + 12 * q^57 + 8 * q^61 + 4 * q^65 + 12 * q^69 - 48 * q^73 - 20 * q^77 + 36 * q^81 + 4 * q^85 - 8 * q^89 + 36 * q^93 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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