LMFDB - Embedded newform 1920.2.w.i.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(127,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))

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

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

chi := DirichletCharacter("1920.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 71x^{8} + 158x^{6} + 149x^{4} + 52x^{2} + 4 $ x^12 + 14x^10 + 71x^8 + 158x^6 + 149x^4 + 52*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.4
Root			$1.04757i$ of defining polynomial
Character	$\chi$	$=$	1920.127
Dual form			1920.2.w.i.1663.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(-2.15008 + 0.614127i) q^{5} +(1.55919 - 1.55919i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{3} +(-2.15008 + 0.614127i) q^{5} +(1.55919 - 1.55919i) q^{7} +1.00000i q^{9} +0.205022i q^{11} +(-0.131493 + 0.131493i) q^{13} +(-1.95459 - 1.08608i) q^{15} +(-4.22663 - 4.22663i) q^{17} +6.79513 q^{19} +2.20502 q^{21} +(-5.78165 - 5.78165i) q^{23} +(4.24570 - 2.64085i) q^{25} +(-0.707107 + 0.707107i) q^{27} -1.33719i q^{29} -2.55165i q^{31} +(-0.144972 + 0.144972i) q^{33} +(-2.39484 + 4.30991i) q^{35} +(-1.10826 - 1.10826i) q^{37} -0.185959 q^{39} +10.9367 q^{41} +(4.09514 + 4.09514i) q^{43} +(-0.614127 - 2.15008i) q^{45} +(0.628395 - 0.628395i) q^{47} +2.13788i q^{49} -5.97736i q^{51} +(7.32736 - 7.32736i) q^{53} +(-0.125910 - 0.440814i) q^{55} +(4.80488 + 4.80488i) q^{57} -5.21446 q^{59} +1.15712 q^{61} +(1.55919 + 1.55919i) q^{63} +(0.201967 - 0.363474i) q^{65} +(-1.62808 + 1.62808i) q^{67} -8.17649i q^{69} -8.09386i q^{71} +(6.05811 - 6.05811i) q^{73} +(4.86952 + 1.13480i) q^{75} +(0.319667 + 0.319667i) q^{77} -12.1156 q^{79} -1.00000 q^{81} +(1.32339 + 1.32339i) q^{83} +(11.6833 + 6.49191i) q^{85} +(0.945534 - 0.945534i) q^{87} -9.82628i q^{89} +0.410044i q^{91} +(1.80429 - 1.80429i) q^{93} +(-14.6101 + 4.17307i) q^{95} +(-7.56544 - 7.56544i) q^{97} -0.205022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) $ 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	−2.15008	+	0.614127i	−0.961545	+	0.274646i
$5$	−2.15008	+	0.614127i	−0.961545	+	0.274646i
$6$		0			0
$7$	1.55919	−	1.55919i	0.589317	−	0.589317i	−0.348130	−	0.937446i	$-0.613183\pi$
$7$	1.55919	−	1.55919i	0.589317	−	0.589317i	0.937446	+	0.348130i	$0.113183\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$			0.205022i			0.0618165i	0.999522	+	0.0309082i	$0.00983996\pi$
$11$			0.205022i			0.0618165i	−0.999522	+	0.0309082i	$0.990160\pi$
$12$		0			0
$13$	−0.131493	+	0.131493i	−0.0364696	+	0.0364696i	−0.725106	−	0.688637i	$-0.758209\pi$
$13$	−0.131493	+	0.131493i	−0.0364696	+	0.0364696i	0.688637	+	0.725106i	$0.258209\pi$
$14$		0			0
$15$	−1.95459	−	1.08608i	−0.504673	−	0.280425i
$16$		0			0
$17$	−4.22663	−	4.22663i	−1.02511	−	1.02511i	−0.999677	−	0.0254325i	$-0.991904\pi$
$17$	−4.22663	−	4.22663i	−1.02511	−	1.02511i	−0.0254325	−	0.999677i	$-0.508096\pi$
$18$		0			0
$19$	6.79513			1.55891			0.779455	−	0.626459i	$-0.215496\pi$
$19$	6.79513			1.55891			0.779455	+	0.626459i	$0.215496\pi$
$20$		0			0
$21$	2.20502			0.481175
$22$		0			0
$23$	−5.78165	−	5.78165i	−1.20556	−	1.20556i	−0.972451	−	0.233106i	$-0.925111\pi$
$23$	−5.78165	−	5.78165i	−1.20556	−	1.20556i	−0.233106	−	0.972451i	$-0.574889\pi$
$24$		0			0
$25$	4.24570	−	2.64085i	0.849139	−	0.528169i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	1.33719i		−	0.248309i	−0.992263	−	0.124155i	$-0.960378\pi$
$29$		−	1.33719i		−	0.248309i	0.992263	−	0.124155i	$-0.0396219\pi$
$30$		0			0
$31$		−	2.55165i		−	0.458290i	−0.973392	−	0.229145i	$-0.926407\pi$
$31$		−	2.55165i		−	0.458290i	0.973392	−	0.229145i	$-0.0735929\pi$
$32$		0			0
$33$	−0.144972	+	0.144972i	−0.0252365	+	0.0252365i
$34$		0			0
$35$	−2.39484	+	4.30991i	−0.404801	+	0.728509i
$36$		0			0
$37$	−1.10826	−	1.10826i	−0.182197	−	0.182197i	0.610116	−	0.792312i	$-0.291123\pi$
$37$	−1.10826	−	1.10826i	−0.182197	−	0.182197i	−0.792312	+	0.610116i	$0.791123\pi$
$38$		0			0
$39$	−0.185959			−0.0297773
$40$		0			0
$41$	10.9367			1.70803			0.854015	−	0.520248i	$-0.174160\pi$
$41$	10.9367			1.70803			0.854015	+	0.520248i	$0.174160\pi$
$42$		0			0
$43$	4.09514	+	4.09514i	0.624503	+	0.624503i	0.946680	−	0.322177i	$-0.104414\pi$
$43$	4.09514	+	4.09514i	0.624503	+	0.624503i	−0.322177	+	0.946680i	$0.604414\pi$
$44$		0			0
$45$	−0.614127	−	2.15008i	−0.0915487	−	0.320515i
$46$		0			0
$47$	0.628395	−	0.628395i	0.0916608	−	0.0916608i	−0.659790	−	0.751450i	$-0.729355\pi$
$47$	0.628395	−	0.628395i	0.0916608	−	0.0916608i	0.751450	+	0.659790i	$0.229355\pi$
$48$		0			0
$49$			2.13788i			0.305411i
$50$		0			0
$51$		−	5.97736i		−	0.836998i
$52$		0			0
$53$	7.32736	−	7.32736i	1.00649	−	1.00649i	0.00651092	−	0.999979i	$-0.497927\pi$
$53$	7.32736	−	7.32736i	1.00649	−	1.00649i	0.999979	−	0.00651092i	$-0.00207251\pi$
$54$		0			0
$55$	−0.125910	−	0.440814i	−0.0169776	−	0.0594393i
$56$		0			0
$57$	4.80488	+	4.80488i	0.636422	+	0.636422i
$58$		0			0
$59$	−5.21446			−0.678865			−0.339433	−	0.940630i	$-0.610235\pi$
$59$	−5.21446			−0.678865			−0.339433	+	0.940630i	$0.610235\pi$
$60$		0			0
$61$	1.15712			0.148155			0.0740773	−	0.997253i	$-0.476399\pi$
$61$	1.15712			0.148155			0.0740773	+	0.997253i	$0.476399\pi$
$62$		0			0
$63$	1.55919	+	1.55919i	0.196439	+	0.196439i
$64$		0			0
$65$	0.201967	−	0.363474i	0.0250509	−	0.0450834i
$66$		0			0
$67$	−1.62808	+	1.62808i	−0.198902	+	0.198902i	−0.799529	−	0.600627i	$-0.794918\pi$
$67$	−1.62808	+	1.62808i	−0.198902	+	0.198902i	0.600627	+	0.799529i	$0.294918\pi$
$68$		0			0
$69$		−	8.17649i		−	0.984333i
$70$		0			0
$71$		−	8.09386i		−	0.960564i	−0.877114	−	0.480282i	$-0.840534\pi$
$71$		−	8.09386i		−	0.960564i	0.877114	−	0.480282i	$-0.159466\pi$
$72$		0			0
$73$	6.05811	−	6.05811i	0.709049	−	0.709049i	−0.257286	−	0.966335i	$-0.582828\pi$
$73$	6.05811	−	6.05811i	0.709049	−	0.709049i	0.966335	+	0.257286i	$0.0828284\pi$
$74$		0			0
$75$	4.86952	+	1.13480i	0.562284	+	0.131035i
$76$		0			0
$77$	0.319667	+	0.319667i	0.0364295	+	0.0364295i
$78$		0			0
$79$	−12.1156			−1.36311			−0.681554	−	0.731768i	$-0.738696\pi$
$79$	−12.1156			−1.36311			−0.681554	+	0.731768i	$0.738696\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	1.32339	+	1.32339i	0.145261	+	0.145261i	0.775997	−	0.630736i	$-0.217247\pi$
$83$	1.32339	+	1.32339i	0.145261	+	0.145261i	−0.630736	+	0.775997i	$0.717247\pi$
$84$		0			0
$85$	11.6833	+	6.49191i	1.26723	+	0.704147i
$86$		0			0
$87$	0.945534	−	0.945534i	0.101372	−	0.101372i
$88$		0			0
$89$		−	9.82628i		−	1.04158i	−0.853684	−	0.520792i	$-0.825637\pi$
$89$		−	9.82628i		−	1.04158i	0.853684	−	0.520792i	$-0.174363\pi$
$90$		0			0
$91$			0.410044i			0.0429843i
$92$		0			0
$93$	1.80429	−	1.80429i	0.187096	−	0.187096i
$94$		0			0
$95$	−14.6101	+	4.17307i	−1.49896	+	0.428148i
$96$		0			0
$97$	−7.56544	−	7.56544i	−0.768154	−	0.768154i	0.209627	−	0.977781i	$-0.432775\pi$
$97$	−7.56544	−	7.56544i	−0.768154	−	0.768154i	−0.977781	+	0.209627i	$0.932775\pi$
$98$		0			0
$99$	−0.205022			−0.0206055
$100$		0			0
$101$	13.3909			1.33245			0.666225	−	0.745751i	$-0.267909\pi$
$101$	13.3909			1.33245			0.666225	+	0.745751i	$0.267909\pi$
$102$		0			0
$103$	12.6173	+	12.6173i	1.24322	+	1.24322i	0.958658	+	0.284562i	$0.0918481\pi$
$103$	12.6173	+	12.6173i	1.24322	+	1.24322i	0.284562	+	0.958658i	$0.408152\pi$
$104$		0			0
$105$	−4.74098	+	1.35416i	−0.462672	+	0.132153i
$106$		0			0
$107$	−3.42306	+	3.42306i	−0.330920	+	0.330920i	−0.852936	−	0.522016i	$-0.825180\pi$
$107$	−3.42306	+	3.42306i	−0.330920	+	0.330920i	0.522016	+	0.852936i	$0.325180\pi$
$108$		0			0
$109$		−	16.2572i		−	1.55716i	−0.627548	−	0.778578i	$-0.715942\pi$
$109$		−	16.2572i		−	1.55716i	0.627548	−	0.778578i	$-0.284058\pi$
$110$		0			0
$111$		−	1.56732i		−	0.148763i
$112$		0			0
$113$	12.9391	−	12.9391i	1.21721	−	1.21721i	0.248607	−	0.968605i	$-0.420027\pi$
$113$	12.9391	−	12.9391i	1.21721	−	1.21721i	0.968605	−	0.248607i	$-0.0799726\pi$
$114$		0			0
$115$	15.9817	+	8.88035i	1.49030	+	0.828096i
$116$		0			0
$117$	−0.131493	−	0.131493i	−0.0121565	−	0.0121565i
$118$		0			0
$119$	−13.1802			−1.20823
$120$		0			0
$121$	10.9580			0.996179
$122$		0			0
$123$	7.73344	+	7.73344i	0.697301	+	0.697301i
$124$		0			0
$125$	−7.50677	+	8.28543i	−0.671426	+	0.741071i
$126$		0			0
$127$	10.0839	−	10.0839i	0.894799	−	0.894799i	−0.100171	−	0.994970i	$-0.531939\pi$
$127$	10.0839	−	10.0839i	0.894799	−	0.894799i	0.994970	+	0.100171i	$0.0319390\pi$
$128$		0			0
$129$			5.79140i			0.509905i
$130$		0			0
$131$		−	4.71608i		−	0.412045i	−0.978547	−	0.206023i	$-0.933948\pi$
$131$		−	4.71608i		−	0.412045i	0.978547	−	0.206023i	$-0.0660521\pi$
$132$		0			0
$133$	10.5949	−	10.5949i	0.918692	−	0.918692i
$134$		0			0
$135$	1.08608	−	1.95459i	0.0934752	−	0.168224i
$136$		0			0
$137$	−4.77956	−	4.77956i	−0.408346	−	0.408346i	0.472816	−	0.881161i	$-0.343238\pi$
$137$	−4.77956	−	4.77956i	−0.408346	−	0.408346i	−0.881161	+	0.472816i	$0.843238\pi$
$138$		0			0
$139$	4.12076			0.349518			0.174759	−	0.984611i	$-0.444085\pi$
$139$	4.12076			0.349518			0.174759	+	0.984611i	$0.444085\pi$
$140$		0			0
$141$	0.888684			0.0748407
$142$		0			0
$143$	−0.0269590	−	0.0269590i	−0.00225442	−	0.00225442i
$144$		0			0
$145$	0.821203	+	2.87506i	0.0681972	+	0.238761i
$146$		0			0
$147$	−1.51171	+	1.51171i	−0.124684	+	0.124684i
$148$		0			0
$149$			17.9020i			1.46659i	0.679911	+	0.733295i	$0.262018\pi$
$149$			17.9020i			1.46659i	−0.679911	+	0.733295i	$0.737982\pi$
$150$		0			0
$151$		−	2.49267i		−	0.202851i	−0.994843	−	0.101425i	$-0.967660\pi$
$151$		−	2.49267i		−	0.202851i	0.994843	−	0.101425i	$-0.0323403\pi$
$152$		0			0
$153$	4.22663	−	4.22663i	0.341703	−	0.341703i
$154$		0			0
$155$	1.56704	+	5.48625i	0.125867	+	0.440666i
$156$		0			0
$157$	−8.09819	−	8.09819i	−0.646306	−	0.646306i	0.305792	−	0.952098i	$-0.401079\pi$
$157$	−8.09819	−	8.09819i	−0.646306	−	0.646306i	−0.952098	+	0.305792i	$0.901079\pi$
$158$		0			0
$159$	10.3624			0.821795
$160$		0			0
$161$	−18.0293			−1.42091
$162$		0			0
$163$	−5.90486	−	5.90486i	−0.462504	−	0.462504i	0.436971	−	0.899476i	$-0.356051\pi$
$163$	−5.90486	−	5.90486i	−0.462504	−	0.462504i	−0.899476	+	0.436971i	$0.856051\pi$
$164$		0			0
$165$	0.222671	−	0.400734i	0.0173349	−	0.0311971i
$166$		0			0
$167$	−3.21621	+	3.21621i	−0.248878	+	0.248878i	−0.820510	−	0.571632i	$-0.806310\pi$
$167$	−3.21621	+	3.21621i	−0.248878	+	0.248878i	0.571632	+	0.820510i	$0.306310\pi$
$168$		0			0
$169$			12.9654i			0.997340i
$170$		0			0
$171$			6.79513i			0.519636i
$172$		0			0
$173$	−7.96393	+	7.96393i	−0.605486	+	0.605486i	−0.941763	−	0.336277i	$-0.890832\pi$
$173$	−7.96393	+	7.96393i	−0.605486	+	0.605486i	0.336277	+	0.941763i	$0.390832\pi$
$174$		0			0
$175$	2.50226	−	10.7374i	0.189153	−	0.811671i
$176$		0			0
$177$	−3.68718	−	3.68718i	−0.277146	−	0.277146i
$178$		0			0
$179$	0.111165			0.00830884			0.00415442	−	0.999991i	$-0.498678\pi$
$179$	0.111165			0.00830884			0.00415442	+	0.999991i	$0.498678\pi$
$180$		0			0
$181$	9.33308			0.693722			0.346861	−	0.937916i	$-0.387247\pi$
$181$	9.33308			0.693722			0.346861	+	0.937916i	$0.387247\pi$
$182$		0			0
$183$	0.818210	+	0.818210i	0.0604838	+	0.0604838i
$184$		0			0
$185$	3.06346	+	1.70224i	0.225230	+	0.125151i
$186$		0			0
$187$	0.866553	−	0.866553i	0.0633686	−	0.0633686i
$188$		0			0
$189$			2.20502i			0.160392i
$190$		0			0
$191$			14.9159i			1.07928i	0.841897	+	0.539638i	$0.181439\pi$
$191$			14.9159i			1.07928i	−0.841897	+	0.539638i	$0.818561\pi$
$192$		0			0
$193$	−12.5495	+	12.5495i	−0.903333	+	0.903333i	−0.995723	−	0.0923897i	$-0.970549\pi$
$193$	−12.5495	+	12.5495i	−0.903333	+	0.903333i	0.0923897	+	0.995723i	$0.470549\pi$
$194$		0			0
$195$	0.399827	−	0.114203i	0.0286322	−	0.00817822i
$196$		0			0
$197$	11.2803	+	11.2803i	0.803686	+	0.803686i	0.983670	−	0.179984i	$-0.0576046\pi$
$197$	11.2803	+	11.2803i	0.803686	+	0.803686i	−0.179984	+	0.983670i	$0.557605\pi$
$198$		0			0
$199$	−3.49987			−0.248099			−0.124050	−	0.992276i	$-0.539588\pi$
$199$	−3.49987			−0.248099			−0.124050	+	0.992276i	$0.539588\pi$
$200$		0			0
$201$	−2.30246			−0.162403
$202$		0			0
$203$	−2.08492	−	2.08492i	−0.146333	−	0.146333i
$204$		0			0
$205$	−23.5149	+	6.71655i	−1.64235	+	0.469104i
$206$		0			0
$207$	5.78165	−	5.78165i	0.401852	−	0.401852i
$208$		0			0
$209$			1.39315i			0.0963663i
$210$		0			0
$211$			18.5728i			1.27860i	0.768956	+	0.639302i	$0.220777\pi$
$211$			18.5728i			1.27860i	−0.768956	+	0.639302i	$0.779223\pi$
$212$		0			0
$213$	5.72322	−	5.72322i	0.392149	−	0.392149i
$214$		0			0
$215$	−11.3198	−	6.28994i	−0.772005	−	0.428971i
$216$		0			0
$217$	−3.97849	−	3.97849i	−0.270078	−	0.270078i
$218$		0			0
$219$	8.56747			0.578936
$220$		0			0
$221$	1.11155			0.0747706
$222$		0			0
$223$	−13.8990	−	13.8990i	−0.930745	−	0.930745i	0.0670071	−	0.997753i	$-0.478655\pi$
$223$	−13.8990	−	13.8990i	−0.930745	−	0.930745i	−0.997753	+	0.0670071i	$0.978655\pi$
$224$		0			0
$225$	2.64085	+	4.24570i	0.176056	+	0.283046i
$226$		0			0
$227$	−15.7606	+	15.7606i	−1.04607	+	1.04607i	−0.0471796	+	0.998886i	$0.515023\pi$
$227$	−15.7606	+	15.7606i	−1.04607	+	1.04607i	−0.998886	+	0.0471796i	$0.984977\pi$
$228$		0			0
$229$		−	6.83572i		−	0.451717i	−0.974160	−	0.225859i	$-0.927481\pi$
$229$		−	6.83572i		−	0.451717i	0.974160	−	0.225859i	$-0.0725188\pi$
$230$		0			0
$231$			0.452078i			0.0297446i
$232$		0			0
$233$	12.5277	−	12.5277i	0.820720	−	0.820720i	−0.165491	−	0.986211i	$-0.552921\pi$
$233$	12.5277	−	12.5277i	0.820720	−	0.820720i	0.986211	+	0.165491i	$0.0529210\pi$
$234$		0			0
$235$	−0.965185	+	1.73701i	−0.0629617	+	0.113310i
$236$		0			0
$237$	−8.56700	−	8.56700i	−0.556487	−	0.556487i
$238$		0			0
$239$	−11.7722			−0.761477			−0.380739	−	0.924683i	$-0.624330\pi$
$239$	−11.7722			−0.761477			−0.380739	+	0.924683i	$0.624330\pi$
$240$		0			0
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−1.31293	−	4.59661i	−0.0838800	−	0.293667i
$246$		0			0
$247$	−0.893512	+	0.893512i	−0.0568528	+	0.0568528i
$248$		0			0
$249$			1.87156i			0.118605i
$250$		0			0
$251$		−	18.8794i		−	1.19166i	−0.803112	−	0.595828i	$-0.796824\pi$
$251$		−	18.8794i		−	1.19166i	0.803112	−	0.595828i	$-0.203176\pi$
$252$		0			0
$253$	1.18537	−	1.18537i	0.0745233	−	0.0745233i
$254$		0			0
$255$	3.67086	+	12.8518i	0.229878	+	0.804812i
$256$		0			0
$257$	−10.0213	−	10.0213i	−0.625110	−	0.625110i	0.321724	−	0.946834i	$-0.395738\pi$
$257$	−10.0213	−	10.0213i	−0.625110	−	0.625110i	−0.946834	+	0.321724i	$0.895738\pi$
$258$		0			0
$259$	−3.45597			−0.214743
$260$		0			0
$261$	1.33719			0.0827698
$262$		0			0
$263$	−0.736701	−	0.736701i	−0.0454269	−	0.0454269i	0.684028	−	0.729455i	$-0.260226\pi$
$263$	−0.736701	−	0.736701i	−0.0454269	−	0.0454269i	−0.729455	+	0.684028i	$0.760226\pi$
$264$		0			0
$265$	−11.2545	+	20.2543i	−0.691357	+	1.24421i
$266$		0			0
$267$	6.94823	−	6.94823i	0.425225	−	0.425225i
$268$		0			0
$269$			9.78405i			0.596544i	0.954481	+	0.298272i	$0.0964103\pi$
$269$			9.78405i			0.596544i	−0.954481	+	0.298272i	$0.903590\pi$
$270$		0			0
$271$			22.1172i			1.34352i	0.740768	+	0.671761i	$0.234462\pi$
$271$			22.1172i			1.34352i	−0.740768	+	0.671761i	$0.765538\pi$
$272$		0			0
$273$	−0.289945	+	0.289945i	−0.0175483	+	0.0175483i
$274$		0			0
$275$	0.541432	+	0.870461i	0.0326496	+	0.0524908i
$276$		0			0
$277$	−12.2731	−	12.2731i	−0.737419	−	0.737419i	0.234659	−	0.972078i	$-0.424603\pi$
$277$	−12.2731	−	12.2731i	−0.737419	−	0.737419i	−0.972078	+	0.234659i	$0.924603\pi$
$278$		0			0
$279$	2.55165			0.152763
$280$		0			0
$281$	17.9273			1.06945			0.534726	−	0.845025i	$-0.320415\pi$
$281$	17.9273			1.06945			0.534726	+	0.845025i	$0.320415\pi$
$282$		0			0
$283$	−22.0291	−	22.0291i	−1.30949	−	1.30949i	−0.921781	−	0.387712i	$-0.873266\pi$
$283$	−22.0291	−	22.0291i	−1.30949	−	1.30949i	−0.387712	−	0.921781i	$-0.626734\pi$
$284$		0			0
$285$	−13.2817	−	7.38008i	−0.786740	−	0.437158i
$286$		0			0
$287$	17.0524	−	17.0524i	1.00657	−	1.00657i
$288$		0			0
$289$			18.7288i			1.10170i
$290$		0			0
$291$		−	10.6991i		−	0.627195i
$292$		0			0
$293$	−14.7914	+	14.7914i	−0.864123	+	0.864123i	−0.991814	−	0.127691i	$-0.959243\pi$
$293$	−14.7914	+	14.7914i	−0.864123	+	0.864123i	0.127691	+	0.991814i	$0.459243\pi$
$294$		0			0
$295$	11.2115	−	3.20234i	0.652760	−	0.186448i
$296$		0			0
$297$	−0.144972	−	0.144972i	−0.00841216	−	0.00841216i
$298$		0			0
$299$	1.52049			0.0879324
$300$		0			0
$301$	12.7702			0.736060
$302$		0			0
$303$	9.46883	+	9.46883i	0.543970	+	0.543970i
$304$		0			0
$305$	−2.48791	+	0.710621i	−0.142457	+	0.0406901i
$306$		0			0
$307$	14.3122	−	14.3122i	0.816842	−	0.816842i	−0.168807	−	0.985649i	$-0.553992\pi$
$307$	14.3122	−	14.3122i	0.816842	−	0.816842i	0.985649	+	0.168807i	$0.0539916\pi$
$308$		0			0
$309$			17.8436i			1.01508i
$310$		0			0
$311$			8.25912i			0.468332i	0.972197	+	0.234166i	$0.0752358\pi$
$311$			8.25912i			0.468332i	−0.972197	+	0.234166i	$0.924764\pi$
$312$		0			0
$313$	−12.5626	+	12.5626i	−0.710083	+	0.710083i	−0.966552	−	0.256470i	$-0.917441\pi$
$313$	−12.5626	+	12.5626i	−0.710083	+	0.710083i	0.256470	+	0.966552i	$0.417441\pi$
$314$		0			0
$315$	−4.30991	−	2.39484i	−0.242836	−	0.134934i
$316$		0			0
$317$	−6.31094	−	6.31094i	−0.354458	−	0.354458i	0.507307	−	0.861765i	$-0.330641\pi$
$317$	−6.31094	−	6.31094i	−0.354458	−	0.354458i	−0.861765	+	0.507307i	$0.830641\pi$
$318$		0			0
$319$	0.274153			0.0153496
$320$		0			0
$321$	−4.84094			−0.270195
$322$		0			0
$323$	−28.7205	−	28.7205i	−1.59805	−	1.59805i
$324$		0			0
$325$	−0.211026	+	0.905532i	−0.0117056	+	0.0502299i
$326$		0			0
$327$	11.4956	−	11.4956i	0.635706	−	0.635706i
$328$		0			0
$329$		−	1.95957i		−	0.108035i
$330$		0			0
$331$		−	33.7039i		−	1.85253i	−0.376871	−	0.926266i	$-0.623000\pi$
$331$		−	33.7039i		−	1.85253i	0.376871	−	0.926266i	$-0.377000\pi$
$332$		0			0
$333$	1.10826	−	1.10826i	0.0607323	−	0.0607323i
$334$		0			0
$335$	2.50066	−	4.50036i	0.136626	−	0.245881i
$336$		0			0
$337$	−13.2700	−	13.2700i	−0.722865	−	0.722865i	0.246323	−	0.969188i	$-0.420778\pi$
$337$	−13.2700	−	13.2700i	−0.722865	−	0.722865i	−0.969188	+	0.246323i	$0.920778\pi$
$338$		0			0
$339$	18.2987			0.993849
$340$		0			0
$341$	0.523144			0.0283298
$342$		0			0
$343$	14.2477	+	14.2477i	0.769301	+	0.769301i
$344$		0			0
$345$	5.02140	+	17.5801i	0.270343	+	0.946481i
$346$		0			0
$347$	−25.2076	+	25.2076i	−1.35322	+	1.35322i	−0.471180	+	0.882037i	$0.656172\pi$
$347$	−25.2076	+	25.2076i	−1.35322	+	1.35322i	−0.882037	+	0.471180i	$0.843828\pi$
$348$		0			0
$349$			5.80934i			0.310967i	0.987838	+	0.155484i	$0.0496936\pi$
$349$			5.80934i			0.310967i	−0.987838	+	0.155484i	$0.950306\pi$
$350$		0			0
$351$		−	0.185959i		−	0.00992577i
$352$		0			0
$353$	8.69148	−	8.69148i	0.462601	−	0.462601i	−0.436906	−	0.899507i	$-0.643926\pi$
$353$	8.69148	−	8.69148i	0.462601	−	0.462601i	0.899507	+	0.436906i	$0.143926\pi$
$354$		0			0
$355$	4.97066	+	17.4024i	0.263815	+	0.923626i
$356$		0			0
$357$	−9.31982	−	9.31982i	−0.493257	−	0.493257i
$358$		0			0
$359$	−19.2666			−1.01685			−0.508427	−	0.861105i	$-0.669773\pi$
$359$	−19.2666			−1.01685			−0.508427	+	0.861105i	$0.669773\pi$
$360$		0			0
$361$	27.1738			1.43020
$362$		0			0
$363$	7.74845	+	7.74845i	0.406688	+	0.406688i
$364$		0			0
$365$	−9.30498	+	16.7459i	−0.487045	+	0.876520i
$366$		0			0
$367$	9.63261	−	9.63261i	0.502818	−	0.502818i	−0.409494	−	0.912313i	$-0.634295\pi$
$367$	9.63261	−	9.63261i	0.502818	−	0.502818i	0.912313	+	0.409494i	$0.134295\pi$
$368$		0			0
$369$			10.9367i			0.569344i
$370$		0			0
$371$		−	22.8494i		−	1.18628i
$372$		0			0
$373$	6.62130	−	6.62130i	0.342838	−	0.342838i	−0.514595	−	0.857433i	$-0.672058\pi$
$373$	6.62130	−	6.62130i	0.342838	−	0.342838i	0.857433	+	0.514595i	$0.172058\pi$
$374$		0			0
$375$	−11.1668	+	0.550594i	−0.576650	+	0.0284325i
$376$		0			0
$377$	0.175831	+	0.175831i	0.00905574	+	0.00905574i
$378$		0			0
$379$	−29.1221			−1.49590			−0.747950	−	0.663755i	$-0.768962\pi$
$379$	−29.1221			−1.49590			−0.747950	+	0.663755i	$0.768962\pi$
$380$		0			0
$381$	14.2608			0.730601
$382$		0			0
$383$	22.7472	+	22.7472i	1.16233	+	1.16233i	0.983965	+	0.178360i	$0.0570792\pi$
$383$	22.7472	+	22.7472i	1.16233	+	1.16233i	0.178360	+	0.983965i	$0.442921\pi$
$384$		0			0
$385$	−0.883627	−	0.490994i	−0.0450338	−	0.0250234i
$386$		0			0
$387$	−4.09514	+	4.09514i	−0.208168	+	0.208168i
$388$		0			0
$389$			38.1622i			1.93490i	0.253063	+	0.967450i	$0.418562\pi$
$389$			38.1622i			1.93490i	−0.253063	+	0.967450i	$0.581438\pi$
$390$		0			0
$391$			48.8738i			2.47166i
$392$		0			0
$393$	3.33477	−	3.33477i	0.168217	−	0.168217i
$394$		0			0
$395$	26.0495	−	7.44050i	1.31069	−	0.374372i
$396$		0			0
$397$	5.65056	+	5.65056i	0.283593	+	0.283593i	0.834540	−	0.550947i	$-0.185733\pi$
$397$	5.65056	+	5.65056i	0.283593	+	0.283593i	−0.550947	+	0.834540i	$0.685733\pi$
$398$		0			0
$399$	14.9834			0.750109
$400$		0			0
$401$	−18.7037			−0.934019			−0.467009	−	0.884252i	$-0.654669\pi$
$401$	−18.7037			−0.934019			−0.467009	+	0.884252i	$0.654669\pi$
$402$		0			0
$403$	0.335524	+	0.335524i	0.0167136	+	0.0167136i
$404$		0			0
$405$	2.15008	−	0.614127i	0.106838	−	0.0305162i
$406$		0			0
$407$	0.227218	−	0.227218i	0.0112628	−	0.0112628i
$408$		0			0
$409$		−	22.1457i		−	1.09503i	−0.836795	−	0.547517i	$-0.815573\pi$
$409$		−	22.1457i		−	1.09503i	0.836795	−	0.547517i	$-0.184427\pi$
$410$		0			0
$411$		−	6.75932i		−	0.333413i
$412$		0			0
$413$	−8.13032	+	8.13032i	−0.400067	+	0.400067i
$414$		0			0
$415$	−3.65814	−	2.03267i	−0.179571	−	0.0997799i
$416$		0			0
$417$	2.91381	+	2.91381i	0.142690	+	0.142690i
$418$		0			0
$419$	−35.9608			−1.75680			−0.878401	−	0.477924i	$-0.841389\pi$
$419$	−35.9608			−1.75680			−0.878401	+	0.477924i	$0.841389\pi$
$420$		0			0
$421$	−26.4602			−1.28959			−0.644796	−	0.764354i	$-0.723058\pi$
$421$	−26.4602			−1.28959			−0.644796	+	0.764354i	$0.723058\pi$
$422$		0			0
$423$	0.628395	+	0.628395i	0.0305536	+	0.0305536i
$424$		0			0
$425$	−29.1069	−	6.78311i	−1.41189	−	0.329029i
$426$		0			0
$427$	1.80417	−	1.80417i	0.0873100	−	0.0873100i
$428$		0			0
$429$		−	0.0381257i		−	0.00184073i
$430$		0			0
$431$			1.32339i			0.0637453i	0.999492	+	0.0318726i	$0.0101471\pi$
$431$			1.32339i			0.0637453i	−0.999492	+	0.0318726i	$0.989853\pi$
$432$		0			0
$433$	4.65108	−	4.65108i	0.223517	−	0.223517i	−0.586461	−	0.809978i	$-0.699479\pi$
$433$	4.65108	−	4.65108i	0.223517	−	0.223517i	0.809978	+	0.586461i	$0.199479\pi$
$434$		0			0
$435$	−1.45230	+	2.61365i	−0.0696323	+	0.125315i
$436$		0			0
$437$	−39.2871	−	39.2871i	−1.87935	−	1.87935i
$438$		0			0
$439$	18.6739			0.891257			0.445628	−	0.895218i	$-0.352980\pi$
$439$	18.6739			0.891257			0.445628	+	0.895218i	$0.352980\pi$
$440$		0			0
$441$	−2.13788			−0.101804
$442$		0			0
$443$	1.25473	+	1.25473i	0.0596142	+	0.0596142i	0.736285	−	0.676671i	$-0.236578\pi$
$443$	1.25473	+	1.25473i	0.0596142	+	0.0596142i	−0.676671	+	0.736285i	$0.736578\pi$
$444$		0			0
$445$	6.03459	+	21.1273i	0.286067	+	1.00153i
$446$		0			0
$447$	−12.6586	+	12.6586i	−0.598732	+	0.598732i
$448$		0			0
$449$			5.75134i			0.271422i	0.990748	+	0.135711i	$0.0433319\pi$
$449$			5.75134i			0.271422i	−0.990748	+	0.135711i	$0.956668\pi$
$450$		0			0
$451$			2.24227i			0.105584i
$452$		0			0
$453$	1.76259	−	1.76259i	0.0828135	−	0.0828135i
$454$		0			0
$455$	−0.251819	−	0.881628i	−0.0118055	−	0.0413314i
$456$		0			0
$457$	23.7835	+	23.7835i	1.11254	+	1.11254i	0.992806	+	0.119737i	$0.0382052\pi$
$457$	23.7835	+	23.7835i	1.11254	+	1.11254i	0.119737	+	0.992806i	$0.461795\pi$
$458$		0			0
$459$	5.97736			0.278999
$460$		0			0
$461$	3.61134			0.168197			0.0840984	−	0.996457i	$-0.473199\pi$
$461$	3.61134			0.168197			0.0840984	+	0.996457i	$0.473199\pi$
$462$		0			0
$463$	0.961103	+	0.961103i	0.0446662	+	0.0446662i	0.729087	−	0.684421i	$-0.239945\pi$
$463$	0.961103	+	0.961103i	0.0446662	+	0.0446662i	−0.684421	+	0.729087i	$0.739945\pi$
$464$		0			0
$465$	−2.77130	+	4.98743i	−0.128516	+	0.231286i
$466$		0			0
$467$	7.43870	−	7.43870i	0.344222	−	0.344222i	−0.513730	−	0.857952i	$-0.671737\pi$
$467$	7.43870	−	7.43870i	0.344222	−	0.344222i	0.857952	+	0.513730i	$0.171737\pi$
$468$		0			0
$469$			5.07696i			0.234432i
$470$		0			0
$471$		−	11.4526i		−	0.527707i
$472$		0			0
$473$	−0.839594	+	0.839594i	−0.0386046	+	0.0386046i
$474$		0			0
$475$	28.8500	−	17.9449i	1.32373	−	0.823368i
$476$		0			0
$477$	7.32736	+	7.32736i	0.335497	+	0.335497i
$478$		0			0
$479$	1.09457			0.0500122			0.0250061	−	0.999687i	$-0.492039\pi$
$479$	1.09457			0.0500122			0.0250061	+	0.999687i	$0.492039\pi$
$480$		0			0
$481$	0.291457			0.0132893
$482$		0			0
$483$	−12.7487	−	12.7487i	−0.580084	−	0.580084i
$484$		0			0
$485$	20.9125	+	11.6202i	0.949586	+	0.527645i
$486$		0			0
$487$	22.1812	−	22.1812i	1.00513	−	1.00513i	0.00514049	−	0.999987i	$-0.498364\pi$
$487$	22.1812	−	22.1812i	1.00513	−	1.00513i	0.999987	−	0.00514049i	$-0.00163628\pi$
$488$		0			0
$489$		−	8.35073i		−	0.377633i
$490$		0			0
$491$			8.31873i			0.375419i	0.982225	+	0.187709i	$0.0601063\pi$
$491$			8.31873i			0.375419i	−0.982225	+	0.187709i	$0.939894\pi$
$492$		0			0
$493$	−5.65180	+	5.65180i	−0.254544	+	0.254544i
$494$		0			0
$495$	0.440814	−	0.125910i	0.0198131	−	0.00565922i
$496$		0			0
$497$	−12.6198	−	12.6198i	−0.566077	−	0.566077i
$498$		0			0
$499$	40.4167			1.80930			0.904649	−	0.426157i	$-0.140133\pi$
$499$	40.4167			1.80930			0.904649	+	0.426157i	$0.140133\pi$
$500$		0			0
$501$	−4.54841			−0.203208
$502$		0			0
$503$	18.9544	+	18.9544i	0.845135	+	0.845135i	0.989521	−	0.144386i	$-0.0461207\pi$
$503$	18.9544	+	18.9544i	0.845135	+	0.845135i	−0.144386	+	0.989521i	$0.546121\pi$
$504$		0			0
$505$	−28.7916	+	8.22375i	−1.28121	+	0.365952i
$506$		0			0
$507$	−9.16794	+	9.16794i	−0.407162	+	0.407162i
$508$		0			0
$509$		−	17.0259i		−	0.754661i	−0.926079	−	0.377331i	$-0.876842\pi$
$509$		−	17.0259i		−	0.754661i	0.926079	−	0.377331i	$-0.123158\pi$
$510$		0			0
$511$		−	18.8915i		−	0.835709i
$512$		0			0
$513$	−4.80488	+	4.80488i	−0.212141	+	0.212141i
$514$		0			0
$515$	−34.8768	−	19.3796i	−1.53686	−	0.853967i
$516$		0			0
$517$	0.128835	+	0.128835i	0.00566615	+	0.00566615i
$518$		0			0
$519$	−11.2627			−0.494377
$520$		0			0
$521$	−31.6529			−1.38674			−0.693369	−	0.720583i	$-0.743874\pi$
$521$	−31.6529			−1.38674			−0.693369	+	0.720583i	$0.743874\pi$
$522$		0			0
$523$	−15.6241	−	15.6241i	−0.683194	−	0.683194i	0.277525	−	0.960718i	$-0.410486\pi$
$523$	−15.6241	−	15.6241i	−0.683194	−	0.683194i	−0.960718	+	0.277525i	$0.910486\pi$
$524$		0			0
$525$	9.36185	−	5.82312i	0.408585	−	0.254142i
$526$		0			0
$527$	−10.7849	+	10.7849i	−0.469797	+	0.469797i
$528$		0			0
$529$			43.8549i			1.90674i
$530$		0			0
$531$		−	5.21446i		−	0.226288i
$532$		0			0
$533$	−1.43810	+	1.43810i	−0.0622912	+	0.0622912i
$534$		0			0
$535$	5.25766	−	9.46205i	0.227309	−	0.409080i
$536$		0			0
$537$	0.0786053	+	0.0786053i	0.00339207	+	0.00339207i
$538$		0			0
$539$	−0.438312			−0.0188794
$540$		0			0
$541$	−20.5838			−0.884967			−0.442484	−	0.896777i	$-0.645903\pi$
$541$	−20.5838			−0.884967			−0.442484	+	0.896777i	$0.645903\pi$
$542$		0			0
$543$	6.59948	+	6.59948i	0.283211	+	0.283211i
$544$		0			0
$545$	9.98397	+	34.9542i	0.427667	+	1.49728i
$546$		0			0
$547$	−27.9566	+	27.9566i	−1.19534	+	1.19534i	−0.219789	+	0.975547i	$0.570537\pi$
$547$	−27.9566	+	27.9566i	−1.19534	+	1.19534i	−0.975547	+	0.219789i	$0.929463\pi$
$548$		0			0
$549$			1.15712i			0.0493849i
$550$		0			0
$551$		−	9.08636i		−	0.387092i
$552$		0			0
$553$	−18.8904	+	18.8904i	−0.803303	+	0.803303i
$554$		0			0
$555$	0.962532	+	3.36986i	0.0408572	+	0.143043i
$556$		0			0
$557$	16.5928	+	16.5928i	0.703059	+	0.703059i	0.965066	−	0.262007i	$-0.0843844\pi$
$557$	16.5928	+	16.5928i	0.703059	+	0.703059i	−0.262007	+	0.965066i	$0.584384\pi$
$558$		0			0
$559$	−1.07696			−0.0455507
$560$		0			0
$561$	1.22549			0.0517403
$562$		0			0
$563$	12.0583	+	12.0583i	0.508199	+	0.508199i	0.913973	−	0.405774i	$-0.132998\pi$
$563$	12.0583	+	12.0583i	0.508199	+	0.508199i	−0.405774	+	0.913973i	$0.632998\pi$
$564$		0			0
$565$	−19.8739	+	35.7665i	−0.836102	+	1.50471i
$566$		0			0
$567$	−1.55919	+	1.55919i	−0.0654797	+	0.0654797i
$568$		0			0
$569$		−	3.07472i		−	0.128899i	−0.997921	−	0.0644496i	$-0.979471\pi$
$569$		−	3.07472i		−	0.128899i	0.997921	−	0.0644496i	$-0.0205292\pi$
$570$		0			0
$571$			28.6472i			1.19885i	0.800432	+	0.599424i	$0.204604\pi$
$571$			28.6472i			1.19885i	−0.800432	+	0.599424i	$0.795396\pi$
$572$		0			0
$573$	−10.5471	+	10.5471i	−0.440612	+	0.440612i
$574$		0			0
$575$	−39.8156	−	9.27868i	−1.66042	−	0.386948i
$576$		0			0
$577$	−27.8106	−	27.8106i	−1.15777	−	1.15777i	−0.984954	−	0.172818i	$-0.944713\pi$
$577$	−27.8106	−	27.8106i	−1.15777	−	1.15777i	−0.172818	−	0.984954i	$-0.555287\pi$
$578$		0			0
$579$	−17.7477			−0.737568
$580$		0			0
$581$	4.12684			0.171210
$582$		0			0
$583$	1.50227	+	1.50227i	0.0622176	+	0.0622176i
$584$		0			0
$585$	0.363474	+	0.201967i	0.0150278	+	0.00835031i
$586$		0			0
$587$	−25.4111	+	25.4111i	−1.04883	+	1.04883i	−0.0500851	+	0.998745i	$0.515949\pi$
$587$	−25.4111	+	25.4111i	−1.04883	+	1.04883i	−0.998745	+	0.0500851i	$0.984051\pi$
$588$		0			0
$589$		−	17.3388i		−	0.714432i
$590$		0			0
$591$			15.9527i			0.656207i
$592$		0			0
$593$	2.85804	−	2.85804i	0.117366	−	0.117366i	−0.645985	−	0.763350i	$-0.723553\pi$
$593$	2.85804	−	2.85804i	0.117366	−	0.117366i	0.763350	+	0.645985i	$0.223553\pi$
$594$		0			0
$595$	28.3385	−	8.09433i	1.16177	−	0.331835i
$596$		0			0
$597$	−2.47478	−	2.47478i	−0.101286	−	0.101286i
$598$		0			0
$599$	30.6342			1.25168			0.625841	−	0.779951i	$-0.284756\pi$
$599$	30.6342			1.25168			0.625841	+	0.779951i	$0.284756\pi$
$600$		0			0
$601$	0.145077			0.00591783			0.00295892	−	0.999996i	$-0.499058\pi$
$601$	0.145077			0.00591783			0.00295892	+	0.999996i	$0.499058\pi$
$602$		0			0
$603$	−1.62808	−	1.62808i	−0.0663006	−	0.0663006i
$604$		0			0
$605$	−23.5605	+	6.72958i	−0.957871	+	0.273597i
$606$		0			0
$607$	−14.8214	+	14.8214i	−0.601581	+	0.601581i	−0.940732	−	0.339151i	$-0.889860\pi$
$607$	−14.8214	+	14.8214i	−0.601581	+	0.601581i	0.339151	+	0.940732i	$0.389860\pi$
$608$		0			0
$609$		−	2.94853i		−	0.119480i
$610$		0			0
$611$			0.165259i			0.00668566i
$612$		0			0
$613$	13.1947	−	13.1947i	0.532930	−	0.532930i	−0.388513	−	0.921443i	$-0.627011\pi$
$613$	13.1947	−	13.1947i	0.532930	−	0.532930i	0.921443	+	0.388513i	$0.127011\pi$
$614$		0			0
$615$	−21.3768	−	11.8782i	−0.861997	−	0.478975i
$616$		0			0
$617$	−0.425078	−	0.425078i	−0.0171130	−	0.0171130i	0.698499	−	0.715612i	$-0.253852\pi$
$617$	−0.425078	−	0.425078i	−0.0171130	−	0.0171130i	−0.715612	+	0.698499i	$0.753852\pi$
$618$		0			0
$619$	−2.35875			−0.0948062			−0.0474031	−	0.998876i	$-0.515095\pi$
$619$	−2.35875			−0.0948062			−0.0474031	+	0.998876i	$0.515095\pi$
$620$		0			0
$621$	8.17649			0.328111
$622$		0			0
$623$	−15.3210	−	15.3210i	−0.613823	−	0.613823i
$624$		0			0
$625$	11.0519	−	22.4245i	0.442074	−	0.896978i
$626$		0			0
$627$	−0.985107	+	0.985107i	−0.0393414	+	0.0393414i
$628$		0			0
$629$			9.36842i			0.373543i
$630$		0			0
$631$			49.7173i			1.97921i	0.143803	+	0.989606i	$0.454067\pi$
$631$			49.7173i			1.97921i	−0.143803	+	0.989606i	$0.545933\pi$
$632$		0			0
$633$	−13.1330	+	13.1330i	−0.521988	+	0.521988i
$634$		0			0
$635$	−15.4884	+	27.8739i	−0.614637	+	1.10614i
$636$		0			0
$637$	−0.281116	−	0.281116i	−0.0111382	−	0.0111382i
$638$		0			0
$639$	8.09386			0.320188
$640$		0			0
$641$	38.0162			1.50155			0.750776	−	0.660557i	$-0.229680\pi$
$641$	38.0162			1.50155			0.750776	+	0.660557i	$0.229680\pi$
$642$		0			0
$643$	6.91064	+	6.91064i	0.272529	+	0.272529i	0.830118	−	0.557588i	$-0.188273\pi$
$643$	6.91064	+	6.91064i	0.272529	+	0.272529i	−0.557588	+	0.830118i	$0.688273\pi$
$644$		0			0
$645$	−3.55666	−	12.4520i	−0.140043	−	0.490296i
$646$		0			0
$647$	−13.2727	+	13.2727i	−0.521802	+	0.521802i	−0.918115	−	0.396313i	$-0.870289\pi$
$647$	−13.2727	+	13.2727i	−0.521802	+	0.521802i	0.396313	+	0.918115i	$0.370289\pi$
$648$		0			0
$649$		−	1.06908i		−	0.0419650i
$650$		0			0
$651$		−	5.62644i		−	0.220518i
$652$		0			0
$653$	26.3413	−	26.3413i	1.03082	−	1.03082i	0.0313060	−	0.999510i	$-0.490033\pi$
$653$	26.3413	−	26.3413i	1.03082	−	1.03082i	0.999510	−	0.0313060i	$-0.00996664\pi$
$654$		0			0
$655$	2.89627	+	10.1399i	0.113167	+	0.396200i
$656$		0			0
$657$	6.05811	+	6.05811i	0.236350	+	0.236350i
$658$		0			0
$659$	35.3377			1.37656			0.688280	−	0.725445i	$-0.258366\pi$
$659$	35.3377			1.37656			0.688280	+	0.725445i	$0.258366\pi$
$660$		0			0
$661$	−16.3644			−0.636503			−0.318251	−	0.948006i	$-0.603096\pi$
$661$	−16.3644			−0.636503			−0.318251	+	0.948006i	$0.603096\pi$
$662$		0			0
$663$	0.785981	+	0.785981i	0.0305250	+	0.0305250i
$664$		0			0
$665$	−16.2732	+	29.2864i	−0.631049	+	1.13568i
$666$		0			0
$667$	−7.73114	+	7.73114i	−0.299351	+	0.299351i
$668$		0			0
$669$		−	19.6561i		−	0.759950i
$670$		0			0
$671$			0.237236i			0.00915839i
$672$		0			0
$673$	22.2256	−	22.2256i	0.856735	−	0.856735i	−0.134217	−	0.990952i	$-0.542852\pi$
$673$	22.2256	−	22.2256i	0.856735	−	0.856735i	0.990952	+	0.134217i	$0.0428518\pi$
$674$		0			0
$675$	−1.13480	+	4.86952i	−0.0436785	+	0.187428i
$676$		0			0
$677$	−25.7146	−	25.7146i	−0.988294	−	0.988294i	0.0116384	−	0.999932i	$-0.496295\pi$
$677$	−25.7146	−	25.7146i	−0.988294	−	0.988294i	−0.999932	+	0.0116384i	$0.996295\pi$
$678$		0			0
$679$	−23.5919			−0.905373
$680$		0			0
$681$	−22.2888			−0.854109
$682$		0			0
$683$	0.597163	+	0.597163i	0.0228498	+	0.0228498i	0.718439	−	0.695590i	$-0.244857\pi$
$683$	0.597163	+	0.597163i	0.0228498	+	0.0228498i	−0.695590	+	0.718439i	$0.744857\pi$
$684$		0			0
$685$	13.2117	+	7.34119i	0.504793	+	0.280492i
$686$		0			0
$687$	4.83359	−	4.83359i	0.184413	−	0.184413i
$688$		0			0
$689$			1.92699i			0.0734125i
$690$		0			0
$691$			0.200281i			0.00761906i	0.999993	+	0.00380953i	$0.00121261\pi$
$691$			0.200281i			0.00761906i	−0.999993	+	0.00380953i	$0.998787\pi$
$692$		0			0
$693$	−0.319667	+	0.319667i	−0.0121432	+	0.0121432i
$694$		0			0
$695$	−8.85996	+	2.53067i	−0.336077	+	0.0959937i
$696$		0			0
$697$	−46.2256	−	46.2256i	−1.75092	−	1.75092i
$698$		0			0
$699$	17.7169			0.670115
$700$		0			0
$701$	45.3405			1.71249			0.856243	−	0.516573i	$-0.172792\pi$
$701$	45.3405			1.71249			0.856243	+	0.516573i	$0.172792\pi$
$702$		0			0
$703$	−7.53077	−	7.53077i	−0.284029	−	0.284029i
$704$		0			0
$705$	−1.91074	+	0.545765i	−0.0719628	+	0.0205547i
$706$		0			0
$707$	20.8790	−	20.8790i	0.785235	−	0.785235i
$708$		0			0
$709$			39.0284i			1.46574i	0.680368	+	0.732871i	$0.261820\pi$
$709$			39.0284i			1.46574i	−0.680368	+	0.732871i	$0.738180\pi$
$710$		0			0
$711$		−	12.1156i		−	0.454369i
$712$		0			0
$713$	−14.7527	+	14.7527i	−0.552494	+	0.552494i
$714$		0			0
$715$	0.0745202	+	0.0414077i	0.00278690	+	0.00154856i
$716$		0			0
$717$	−8.32417	−	8.32417i	−0.310872	−	0.310872i
$718$		0			0
$719$	26.4416			0.986106			0.493053	−	0.869999i	$-0.335881\pi$
$719$	26.4416			0.986106			0.493053	+	0.869999i	$0.335881\pi$
$720$		0			0
$721$	39.3454			1.46530
$722$		0			0
$723$	2.82843	+	2.82843i	0.105190	+	0.105190i
$724$		0			0
$725$	−3.53130	−	5.67729i	−0.131149	−	0.210849i
$726$		0			0
$727$	31.7281	−	31.7281i	1.17673	−	1.17673i	0.196155	−	0.980573i	$-0.437154\pi$
$727$	31.7281	−	31.7281i	1.17673	−	1.17673i	0.980573	−	0.196155i	$-0.0628457\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		−	34.6173i		−	1.28037i
$732$		0			0
$733$	32.0186	−	32.0186i	1.18263	−	1.18263i	0.203574	−	0.979059i	$-0.434744\pi$
$733$	32.0186	−	32.0186i	1.18263	−	1.18263i	0.979059	−	0.203574i	$-0.0652559\pi$
$734$		0			0
$735$	2.32191	−	4.17868i	0.0856451	−	0.154133i
$736$		0			0
$737$	−0.333793	−	0.333793i	−0.0122954	−	0.0122954i
$738$		0			0
$739$	−2.47991			−0.0912251			−0.0456126	−	0.998959i	$-0.514524\pi$
$739$	−2.47991			−0.0912251			−0.0456126	+	0.998959i	$0.514524\pi$
$740$		0			0
$741$	−1.26362			−0.0464201
$742$		0			0
$743$	−18.1503	−	18.1503i	−0.665871	−	0.665871i	0.290887	−	0.956758i	$-0.406050\pi$
$743$	−18.1503	−	18.1503i	−0.665871	−	0.665871i	−0.956758	+	0.290887i	$0.906050\pi$
$744$		0			0
$745$	−10.9941	−	38.4908i	−0.402793	−	1.41019i
$746$		0			0
$747$	−1.32339	+	1.32339i	−0.0484205	+	0.0484205i
$748$		0			0
$749$			10.6744i			0.390033i
$750$		0			0
$751$			16.2121i			0.591589i	0.955252	+	0.295795i	$0.0955844\pi$
$751$			16.2121i			0.591589i	−0.955252	+	0.295795i	$0.904416\pi$
$752$		0			0
$753$	13.3497	−	13.3497i	0.486492	−	0.486492i
$754$		0			0
$755$	1.53082	+	5.35945i	0.0557122	+	0.195050i
$756$		0			0
$757$	−1.75773	−	1.75773i	−0.0638858	−	0.0638858i	0.674442	−	0.738328i	$-0.264384\pi$
$757$	−1.75773	−	1.75773i	−0.0638858	−	0.0638858i	−0.738328	+	0.674442i	$0.764384\pi$
$758$		0			0
$759$	1.67636			0.0608480
$760$		0			0
$761$	40.9867			1.48577			0.742884	−	0.669421i	$-0.233458\pi$
$761$	40.9867			1.48577			0.742884	+	0.669421i	$0.233458\pi$
$762$		0			0
$763$	−25.3480	−	25.3480i	−0.917658	−	0.917658i
$764$		0			0
$765$	−6.49191	+	11.6833i	−0.234716	+	0.422410i
$766$		0			0
$767$	0.685665	−	0.685665i	0.0247579	−	0.0247579i
$768$		0			0
$769$			17.3181i			0.624508i	0.949999	+	0.312254i	$0.101084\pi$
$769$			17.3181i			0.624508i	−0.949999	+	0.312254i	$0.898916\pi$
$770$		0			0
$771$		−	14.1722i		−	0.510400i
$772$		0			0
$773$	5.25694	−	5.25694i	0.189079	−	0.189079i	−0.606219	−	0.795298i	$-0.707314\pi$
$773$	5.25694	−	5.25694i	0.189079	−	0.189079i	0.795298	+	0.606219i	$0.207314\pi$
$774$		0			0
$775$	−6.73851	−	10.8335i	−0.242054	−	0.389152i
$776$		0			0
$777$	−2.44374	−	2.44374i	−0.0876687	−	0.0876687i
$778$		0			0
$779$	74.3165			2.66267
$780$		0			0
$781$	1.65942			0.0593787
$782$		0			0
$783$	0.945534	+	0.945534i	0.0337906	+	0.0337906i
$784$		0			0
$785$	22.3851	+	12.4385i	0.798958	+	0.443947i
$786$		0			0
$787$	−15.8569	+	15.8569i	−0.565238	+	0.565238i	−0.930791	−	0.365553i	$-0.880880\pi$
$787$	−15.8569	+	15.8569i	−0.565238	+	0.565238i	0.365553	+	0.930791i	$0.380880\pi$
$788$		0			0
$789$		−	1.04185i		−	0.0370909i
$790$		0			0
$791$		−	40.3490i		−	1.43465i
$792$		0			0
$793$	−0.152154	+	0.152154i	−0.00540314	+	0.00540314i
$794$		0			0
$795$	−22.2801	+	6.36386i	−0.790194	+	0.225703i
$796$		0			0
$797$	11.1413	+	11.1413i	0.394644	+	0.394644i	0.876339	−	0.481695i	$-0.159979\pi$
$797$	11.1413	+	11.1413i	0.394644	+	0.394644i	−0.481695	+	0.876339i	$0.659979\pi$
$798$		0			0
$799$	−5.31199			−0.187925
$800$		0			0
$801$	9.82628			0.347195
$802$		0			0
$803$	1.24205	+	1.24205i	0.0438309	+	0.0438309i
$804$		0			0
$805$	38.7645	−	11.0723i	1.36627	−	0.390247i
$806$		0			0
$807$	−6.91837	+	6.91837i	−0.243538	+	0.243538i
$808$		0			0
$809$		−	30.0815i		−	1.05761i	−0.848743	−	0.528805i	$-0.822640\pi$
$809$		−	30.0815i		−	1.05761i	0.848743	−	0.528805i	$-0.177360\pi$
$810$		0			0
$811$			17.7763i			0.624210i	0.950048	+	0.312105i	$0.101034\pi$
$811$			17.7763i			0.624210i	−0.950048	+	0.312105i	$0.898966\pi$
$812$		0			0
$813$	−15.6392	+	15.6392i	−0.548491	+	0.548491i
$814$		0			0
$815$	16.3223	+	9.06959i	0.571744	+	0.317694i
$816$		0			0
$817$	27.8270	+	27.8270i	0.973544	+	0.973544i
$818$		0			0
$819$	−0.410044			−0.0143281
$820$		0			0
$821$	6.65072			0.232112			0.116056	−	0.993243i	$-0.462975\pi$
$821$	6.65072			0.232112			0.116056	+	0.993243i	$0.462975\pi$
$822$		0			0
$823$	9.06860	+	9.06860i	0.316111	+	0.316111i	0.847271	−	0.531160i	$-0.178244\pi$
$823$	9.06860	+	9.06860i	0.316111	+	0.316111i	−0.531160	+	0.847271i	$0.678244\pi$
$824$		0			0
$825$	−0.232659	+	0.998359i	−0.00810015	+	0.0347584i
$826$		0			0
$827$	7.97916	−	7.97916i	0.277462	−	0.277462i	−0.554633	−	0.832095i	$-0.687141\pi$
$827$	7.97916	−	7.97916i	0.277462	−	0.277462i	0.832095	+	0.554633i	$0.187141\pi$
$828$		0			0
$829$			7.48595i			0.259998i	0.991514	+	0.129999i	$0.0414974\pi$
$829$			7.48595i			0.259998i	−0.991514	+	0.129999i	$0.958503\pi$
$830$		0			0
$831$		−	17.3568i		−	0.602100i
$832$		0			0
$833$	9.03602	−	9.03602i	0.313080	−	0.313080i
$834$		0			0
$835$	4.93995	−	8.89027i	0.170954	−	0.307660i
$836$		0			0
$837$	1.80429	+	1.80429i	0.0623653	+	0.0623653i
$838$		0			0
$839$	17.2157			0.594353			0.297177	−	0.954823i	$-0.403955\pi$
$839$	17.2157			0.594353			0.297177	+	0.954823i	$0.403955\pi$
$840$		0			0
$841$	27.2119			0.938342
$842$		0			0
$843$	12.6765	+	12.6765i	0.436602	+	0.436602i
$844$		0			0
$845$	−7.96242	−	27.8767i	−0.273915	−	0.958988i
$846$		0			0
$847$	17.0855	−	17.0855i	0.587065	−	0.587065i
$848$		0			0
$849$		−	31.1538i		−	1.06920i
$850$		0			0
$851$			12.8151i			0.439298i
$852$		0			0
$853$	20.1658	−	20.1658i	0.690463	−	0.690463i	−0.271871	−	0.962334i	$-0.587642\pi$
$853$	20.1658	−	20.1658i	0.690463	−	0.690463i	0.962334	+	0.271871i	$0.0876423\pi$
$854$		0			0
$855$	−4.17307	−	14.6101i	−0.142716	−	0.499654i
$856$		0			0
$857$	7.92995	+	7.92995i	0.270882	+	0.270882i	0.829455	−	0.558573i	$-0.188651\pi$
$857$	7.92995	+	7.92995i	0.270882	+	0.270882i	−0.558573	+	0.829455i	$0.688651\pi$
$858$		0			0
$859$	−20.2821			−0.692018			−0.346009	−	0.938231i	$-0.612463\pi$
$859$	−20.2821			−0.692018			−0.346009	+	0.938231i	$0.612463\pi$
$860$		0			0
$861$	24.1157			0.821862
$862$		0			0
$863$	26.1273	+	26.1273i	0.889383	+	0.889383i	0.994464	−	0.105081i	$-0.0335100\pi$
$863$	26.1273	+	26.1273i	0.889383	+	0.889383i	−0.105081	+	0.994464i	$0.533510\pi$
$864$		0			0
$865$	12.2322	−	22.0140i	0.415908	−	0.748497i
$866$		0			0
$867$	−13.2433	+	13.2433i	−0.449766	+	0.449766i
$868$		0			0
$869$		−	2.48396i		−	0.0842626i
$870$		0			0
$871$		−	0.428163i		−	0.0145077i
$872$		0			0
$873$	7.56544	−	7.56544i	0.256051	−	0.256051i
$874$		0			0
$875$	1.21407	+	24.6230i	0.0410431	+	0.832409i
$876$		0			0
$877$	19.2918	+	19.2918i	0.651437	+	0.651437i	0.953339	−	0.301902i	$-0.0976216\pi$
$877$	19.2918	+	19.2918i	0.651437	+	0.651437i	−0.301902	+	0.953339i	$0.597622\pi$
$878$		0			0
$879$	−20.9182			−0.705554
$880$		0			0
$881$	10.9071			0.367470			0.183735	−	0.982976i	$-0.441181\pi$
$881$	10.9071			0.367470			0.183735	+	0.982976i	$0.441181\pi$
$882$		0			0
$883$	23.2958	+	23.2958i	0.783966	+	0.783966i	0.980497	−	0.196532i	$-0.0629679\pi$
$883$	23.2958	+	23.2958i	0.783966	+	0.783966i	−0.196532	+	0.980497i	$0.562968\pi$
$884$		0			0
$885$	10.1921	+	5.66334i	0.342605	+	0.190371i
$886$		0			0
$887$	−11.7744	+	11.7744i	−0.395344	+	0.395344i	−0.876587	−	0.481243i	$-0.840185\pi$
$887$	−11.7744	+	11.7744i	−0.395344	+	0.395344i	0.481243	+	0.876587i	$0.340185\pi$
$888$		0			0
$889$		−	31.4453i		−	1.05464i
$890$		0			0
$891$		−	0.205022i		−	0.00686850i
$892$		0			0
$893$	4.27002	−	4.27002i	0.142891	−	0.142891i
$894$		0			0
$895$	−0.239013	+	0.0682693i	−0.00798933	+	0.00228199i
$896$		0			0
$897$	1.07515	+	1.07515i	0.0358982	+	0.0358982i
$898$		0			0
$899$	−3.41203			−0.113798
$900$		0			0
$901$	−61.9401			−2.06352
$902$		0			0
$903$	9.02987	+	9.02987i	0.300495	+	0.300495i
$904$		0			0
$905$	−20.0669	+	5.73170i	−0.667046	+	0.190528i
$906$		0			0
$907$	10.8698	−	10.8698i	0.360927	−	0.360927i	−0.503227	−	0.864154i	$-0.667854\pi$
$907$	10.8698	−	10.8698i	0.360927	−	0.360927i	0.864154	+	0.503227i	$0.167854\pi$
$908$		0			0
$909$			13.3909i			0.444150i
$910$		0			0
$911$			51.4593i			1.70492i	0.522791	+	0.852461i	$0.324891\pi$
$911$			51.4593i			1.70492i	−0.522791	+	0.852461i	$0.675109\pi$
$912$		0			0
$913$	−0.271325	+	0.271325i	−0.00897955	+	0.00897955i
$914$		0			0
$915$	−2.26170	−	1.25673i	−0.0747696	−	0.0415463i
$916$		0			0
$917$	−7.35324	−	7.35324i	−0.242825	−	0.242825i
$918$		0			0
$919$	−33.2936			−1.09825			−0.549127	−	0.835739i	$-0.685040\pi$
$919$	−33.2936			−1.09825			−0.549127	+	0.835739i	$0.685040\pi$
$920$		0			0
$921$	20.2405			0.666948
$922$		0			0
$923$	1.06429	+	1.06429i	0.0350314	+	0.0350314i
$924$		0			0
$925$	−7.63208	−	1.77859i	−0.250941	−	0.0584797i
$926$		0			0
$927$	−12.6173	+	12.6173i	−0.414407	+	0.414407i
$928$		0			0
$929$		−	1.96003i		−	0.0643065i	−0.999483	−	0.0321532i	$-0.989764\pi$
$929$		−	1.96003i		−	0.0643065i	0.999483	−	0.0321532i	$-0.0102365\pi$
$930$		0			0
$931$			14.5272i			0.476108i
$932$		0			0
$933$	−5.84008	+	5.84008i	−0.191196	+	0.191196i
$934$		0			0
$935$	−1.33099	+	2.39533i	−0.0435279	+	0.0783357i
$936$		0			0
$937$	18.9164	+	18.9164i	0.617972	+	0.617972i	0.945011	−	0.327039i	$-0.106051\pi$
$937$	18.9164	+	18.9164i	0.617972	+	0.617972i	−0.327039	+	0.945011i	$0.606051\pi$
$938$		0			0
$939$	−17.7663			−0.579780
$940$		0			0
$941$	13.7658			0.448751			0.224376	−	0.974503i	$-0.427966\pi$
$941$	13.7658			0.448751			0.224376	+	0.974503i	$0.427966\pi$
$942$		0			0
$943$	−63.2324	−	63.2324i	−2.05913	−	2.05913i
$944$		0			0
$945$	−1.35416	−	4.74098i	−0.0440510	−	0.154224i
$946$		0			0
$947$	21.2333	−	21.2333i	0.689988	−	0.689988i	−0.272241	−	0.962229i	$-0.587765\pi$
$947$	21.2333	−	21.2333i	0.689988	−	0.689988i	0.962229	+	0.272241i	$0.0877648\pi$
$948$		0			0
$949$			1.59320i			0.0517174i
$950$		0			0
$951$		−	8.92502i		−	0.289414i
$952$		0			0
$953$	−11.6224	+	11.6224i	−0.376486	+	0.376486i	−0.869833	−	0.493346i	$-0.835773\pi$
$953$	−11.6224	+	11.6224i	−0.376486	+	0.376486i	0.493346	+	0.869833i	$0.335773\pi$
$954$		0			0
$955$	−9.16025	−	32.0704i	−0.296419	−	1.03777i
$956$		0			0
$957$	0.193855	+	0.193855i	0.00626645	+	0.00626645i
$958$		0			0
$959$	−14.9045			−0.481290
$960$		0			0
$961$	24.4891			0.789971
$962$		0			0
$963$	−3.42306	−	3.42306i	−0.110307	−	0.110307i
$964$		0			0
$965$	19.2755	−	34.6894i	0.620499	−	1.11669i
$966$		0			0
$967$	−0.631750	+	0.631750i	−0.0203157	+	0.0203157i	−0.717192	−	0.696876i	$-0.754573\pi$
$967$	−0.631750	+	0.631750i	−0.0203157	+	0.0203157i	0.696876	+	0.717192i	$0.254573\pi$
$968$		0			0
$969$		−	40.6169i		−	1.30480i
$970$		0			0
$971$		−	22.2608i		−	0.714385i	−0.934031	−	0.357192i	$-0.883734\pi$
$971$		−	22.2608i		−	0.714385i	0.934031	−	0.357192i	$-0.116266\pi$
$972$		0			0
$973$	6.42502	−	6.42502i	0.205977	−	0.205977i
$974$		0			0
$975$	−0.789526	+	0.491090i	−0.0252851	+	0.0157275i
$976$		0			0
$977$	6.80590	+	6.80590i	0.217740	+	0.217740i	0.807545	−	0.589805i	$-0.200796\pi$
$977$	6.80590	+	6.80590i	0.217740	+	0.217740i	−0.589805	+	0.807545i	$0.700796\pi$
$978$		0			0
$979$	2.01460			0.0643871
$980$		0			0
$981$	16.2572			0.519052
$982$		0			0
$983$	−9.81843	−	9.81843i	−0.313159	−	0.313159i	0.532973	−	0.846132i	$-0.321075\pi$
$983$	−9.81843	−	9.81843i	−0.313159	−	0.313159i	−0.846132	+	0.532973i	$0.821075\pi$
$984$		0			0
$985$	−31.1810	−	17.3260i	−0.993509	−	0.552051i
$986$		0			0
$987$	1.38562	−	1.38562i	0.0441049	−	0.0441049i
$988$		0			0
$989$		−	47.3533i		−	1.50575i
$990$		0			0
$991$		−	50.2632i		−	1.59666i	−0.602218	−	0.798331i	$-0.705716\pi$
$991$		−	50.2632i		−	1.59666i	0.602218	−	0.798331i	$-0.294284\pi$
$992$		0			0
$993$	23.8322	−	23.8322i	0.756293	−	0.756293i
$994$		0			0
$995$	7.52501	−	2.14937i	0.238559	−	0.0681395i
$996$		0			0
$997$	−31.9681	−	31.9681i	−1.01244	−	1.01244i	−0.999922	−	0.0125171i	$-0.996016\pi$
$997$	−31.9681	−	31.9681i	−1.01244	−	1.01244i	−0.0125171	−	0.999922i	$-0.503984\pi$
$998$		0			0
$999$	1.56732			0.0495877

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.w.i.127.4	✓	12
4.3	odd	2		1920.2.w.j.127.1	yes	12
5.3	odd	4		1920.2.w.j.1663.1	yes	12
8.3	odd	2		1920.2.w.l.127.6	yes	12
8.5	even	2		1920.2.w.k.127.3	yes	12
20.3	even	4	inner	1920.2.w.i.1663.4	yes	12
40.3	even	4		1920.2.w.k.1663.3	yes	12
40.13	odd	4		1920.2.w.l.1663.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1920.2.w.i.127.4	✓	12	1.1	even	1	trivial
1920.2.w.i.1663.4	yes	12	20.3	even	4	inner
1920.2.w.j.127.1	yes	12	4.3	odd	2
1920.2.w.j.1663.1	yes	12	5.3	odd	4
1920.2.w.k.127.3	yes	12	8.5	even	2
1920.2.w.k.1663.3	yes	12	40.3	even	4
1920.2.w.l.127.6	yes	12	8.3	odd	2
1920.2.w.l.1663.6	yes	12	40.13	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-2.15008 + 0.614127i) q^{5} +(1.55919 - 1.55919i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(-2.15008 + 0.614127i) q^{5} +(1.55919 - 1.55919i) q^{7} +1.00000i q^{9} +0.205022i q^{11} +(-0.131493 + 0.131493i) q^{13} +(-1.95459 - 1.08608i) q^{15} +(-4.22663 - 4.22663i) q^{17} +6.79513 q^{19} +2.20502 q^{21} +(-5.78165 - 5.78165i) q^{23} +(4.24570 - 2.64085i) q^{25} +(-0.707107 + 0.707107i) q^{27} -1.33719i q^{29} -2.55165i q^{31} +(-0.144972 + 0.144972i) q^{33} +(-2.39484 + 4.30991i) q^{35} +(-1.10826 - 1.10826i) q^{37} -0.185959 q^{39} +10.9367 q^{41} +(4.09514 + 4.09514i) q^{43} +(-0.614127 - 2.15008i) q^{45} +(0.628395 - 0.628395i) q^{47} +2.13788i q^{49} -5.97736i q^{51} +(7.32736 - 7.32736i) q^{53} +(-0.125910 - 0.440814i) q^{55} +(4.80488 + 4.80488i) q^{57} -5.21446 q^{59} +1.15712 q^{61} +(1.55919 + 1.55919i) q^{63} +(0.201967 - 0.363474i) q^{65} +(-1.62808 + 1.62808i) q^{67} -8.17649i q^{69} -8.09386i q^{71} +(6.05811 - 6.05811i) q^{73} +(4.86952 + 1.13480i) q^{75} +(0.319667 + 0.319667i) q^{77} -12.1156 q^{79} -1.00000 q^{81} +(1.32339 + 1.32339i) q^{83} +(11.6833 + 6.49191i) q^{85} +(0.945534 - 0.945534i) q^{87} -9.82628i q^{89} +0.410044i q^{91} +(1.80429 - 1.80429i) q^{93} +(-14.6101 + 4.17307i) q^{95} +(-7.56544 - 7.56544i) q^{97} -0.205022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) \) 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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