LMFDB - Embedded newform 1860.2.s.a.1177.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1860,2,Mod(433,1860)] 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("1860.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1860, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1860.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$14.8521747760$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1177.32
Character	$\chi$	$=$	1860.1177
Dual form			1860.2.s.a.433.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{3} +(-2.16858 - 0.545223i) q^{5} +(-3.45556 - 3.45556i) q^{7} +1.00000i q^{9} +4.89678i q^{11} +(3.25243 + 3.25243i) q^{13} +(-1.14789 - 1.91895i) q^{15} +(-1.38440 + 1.38440i) q^{17} -7.75672i q^{19} -4.88691i q^{21} +(-2.52755 - 2.52755i) q^{23} +(4.40546 + 2.36472i) q^{25} +(-0.707107 + 0.707107i) q^{27} +6.32793 q^{29} +(4.39095 - 3.42339i) q^{31} +(-3.46254 + 3.46254i) q^{33} +(5.60961 + 9.37772i) q^{35} +(-1.06608 + 1.06608i) q^{37} +4.59963i q^{39} -0.549352 q^{41} +(4.48876 + 4.48876i) q^{43} +(0.545223 - 2.16858i) q^{45} +(2.44703 + 2.44703i) q^{47} +16.8819i q^{49} -1.95783 q^{51} +(8.49714 + 8.49714i) q^{53} +(2.66984 - 10.6190i) q^{55} +(5.48483 - 5.48483i) q^{57} -7.41481i q^{59} -11.9378i q^{61} +(3.45556 - 3.45556i) q^{63} +(-5.27985 - 8.82646i) q^{65} +(-0.0563954 - 0.0563954i) q^{67} -3.57449i q^{69} +12.8374 q^{71} +(8.55320 + 8.55320i) q^{73} +(1.44302 + 4.78724i) q^{75} +(16.9211 - 16.9211i) q^{77} +11.4113 q^{79} -1.00000 q^{81} +(1.53224 + 1.53224i) q^{83} +(3.75697 - 2.24737i) q^{85} +(4.47452 + 4.47452i) q^{87} -13.0869 q^{89} -22.4780i q^{91} +(5.52557 + 0.684169i) q^{93} +(-4.22914 + 16.8211i) q^{95} +(-7.79226 - 7.79226i) q^{97} -4.89678 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

$n$	$931$	$1117$	$1241$	$1801$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	−2.16858	−	0.545223i	−0.969818	−	0.243831i
$5$	−2.16858	−	0.545223i	−0.969818	−	0.243831i
$6$		0			0
$7$	−3.45556	−	3.45556i	−1.30608	−	1.30608i	−0.924220	−	0.381861i	$-0.875283\pi$
$7$	−3.45556	−	3.45556i	−1.30608	−	1.30608i	−0.381861	−	0.924220i	$-0.624717\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$			4.89678i			1.47643i	0.674563	+	0.738217i	$0.264332\pi$
$11$			4.89678i			1.47643i	−0.674563	+	0.738217i	$0.735668\pi$
$12$		0			0
$13$	3.25243	+	3.25243i	0.902063	+	0.902063i	0.995614	−	0.0935519i	$-0.0298221\pi$
$13$	3.25243	+	3.25243i	0.902063	+	0.902063i	−0.0935519	+	0.995614i	$0.529822\pi$
$14$		0			0
$15$	−1.14789	−	1.91895i	−0.296383	−	0.495470i
$16$		0			0
$17$	−1.38440	+	1.38440i	−0.335765	+	0.335765i	−0.854771	−	0.519006i	$-0.826302\pi$
$17$	−1.38440	+	1.38440i	−0.335765	+	0.335765i	0.519006	+	0.854771i	$0.326302\pi$
$18$		0			0
$19$		−	7.75672i		−	1.77951i	−0.456435	−	0.889757i	$-0.650874\pi$
$19$		−	7.75672i		−	1.77951i	0.456435	−	0.889757i	$-0.349126\pi$
$20$		0			0
$21$		−	4.88691i		−	1.06641i
$22$		0			0
$23$	−2.52755	−	2.52755i	−0.527030	−	0.527030i	0.392656	−	0.919685i	$-0.371556\pi$
$23$	−2.52755	−	2.52755i	−0.527030	−	0.527030i	−0.919685	+	0.392656i	$0.871556\pi$
$24$		0			0
$25$	4.40546	+	2.36472i	0.881093	+	0.472944i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	6.32793			1.17507			0.587534	−	0.809200i	$-0.300099\pi$
$29$	6.32793			1.17507			0.587534	+	0.809200i	$0.300099\pi$
$30$		0			0
$31$	4.39095	−	3.42339i	0.788637	−	0.614858i
$31$	4.39095	−	3.42339i	0.788637	−	0.614858i
$32$		0			0
$33$	−3.46254	+	3.46254i	−0.602752	+	0.602752i
$34$		0			0
$35$	5.60961	+	9.37772i	0.948197	+	1.58512i
$36$		0			0
$37$	−1.06608	+	1.06608i	−0.175262	+	0.175262i	−0.789287	−	0.614025i	$-0.789549\pi$
$37$	−1.06608	+	1.06608i	−0.175262	+	0.175262i	0.614025	+	0.789287i	$0.289549\pi$
$38$		0			0
$39$			4.59963i			0.736531i
$40$		0			0
$41$	−0.549352			−0.0857944			−0.0428972	−	0.999079i	$-0.513659\pi$
$41$	−0.549352			−0.0857944			−0.0428972	+	0.999079i	$0.513659\pi$
$42$		0			0
$43$	4.48876	+	4.48876i	0.684530	+	0.684530i	0.961017	−	0.276488i	$-0.0891705\pi$
$43$	4.48876	+	4.48876i	0.684530	+	0.684530i	−0.276488	+	0.961017i	$0.589171\pi$
$44$		0			0
$45$	0.545223	−	2.16858i	0.0812771	−	0.323273i
$46$		0			0
$47$	2.44703	+	2.44703i	0.356937	+	0.356937i	0.862683	−	0.505746i	$-0.168783\pi$
$47$	2.44703	+	2.44703i	0.356937	+	0.356937i	−0.505746	+	0.862683i	$0.668783\pi$
$48$		0			0
$49$			16.8819i			2.41169i
$50$		0			0
$51$	−1.95783			−0.274151
$52$		0			0
$53$	8.49714	+	8.49714i	1.16717	+	1.16717i	0.982870	+	0.184303i	$0.0590026\pi$
$53$	8.49714	+	8.49714i	1.16717	+	1.16717i	0.184303	+	0.982870i	$0.440997\pi$
$54$		0			0
$55$	2.66984	−	10.6190i	0.360001	−	1.43187i
$56$		0			0
$57$	5.48483	−	5.48483i	0.726483	−	0.726483i
$58$		0			0
$59$		−	7.41481i		−	0.965326i	−0.875806	−	0.482663i	$-0.839670\pi$
$59$		−	7.41481i		−	0.965326i	0.875806	−	0.482663i	$-0.160330\pi$
$60$		0			0
$61$		−	11.9378i		−	1.52848i	−0.644932	−	0.764240i	$-0.723114\pi$
$61$		−	11.9378i		−	1.52848i	0.644932	−	0.764240i	$-0.276886\pi$
$62$		0			0
$63$	3.45556	−	3.45556i	0.435360	−	0.435360i
$64$		0			0
$65$	−5.27985	−	8.82646i	−0.654885	−	1.09479i
$66$		0			0
$67$	−0.0563954	−	0.0563954i	−0.00688980	−	0.00688980i	0.703653	−	0.710543i	$-0.251551\pi$
$67$	−0.0563954	−	0.0563954i	−0.00688980	−	0.00688980i	−0.710543	+	0.703653i	$0.751551\pi$
$68$		0			0
$69$		−	3.57449i		−	0.430318i
$70$		0			0
$71$	12.8374			1.52352			0.761761	−	0.647858i	$-0.224335\pi$
$71$	12.8374			1.52352			0.761761	+	0.647858i	$0.224335\pi$
$72$		0			0
$73$	8.55320	+	8.55320i	1.00108	+	1.00108i	0.999999	+	0.00107691i	$0.000342791\pi$
$73$	8.55320	+	8.55320i	1.00108	+	1.00108i	0.00107691	+	0.999999i	$0.499657\pi$
$74$		0			0
$75$	1.44302	+	4.78724i	0.166626	+	0.552783i
$76$		0			0
$77$	16.9211	−	16.9211i	1.92834	−	1.92834i
$78$		0			0
$79$	11.4113			1.28387			0.641937	−	0.766758i	$-0.278131\pi$
$79$	11.4113			1.28387			0.641937	+	0.766758i	$0.278131\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	1.53224	+	1.53224i	0.168185	+	0.168185i	0.786181	−	0.617996i	$-0.212055\pi$
$83$	1.53224	+	1.53224i	0.168185	+	0.168185i	−0.617996	+	0.786181i	$0.712055\pi$
$84$		0			0
$85$	3.75697	−	2.24737i	0.407501	−	0.243761i
$86$		0			0
$87$	4.47452	+	4.47452i	0.479719	+	0.479719i
$88$		0			0
$89$	−13.0869			−1.38721			−0.693604	−	0.720357i	$-0.743978\pi$
$89$	−13.0869			−1.38721			−0.693604	+	0.720357i	$0.743978\pi$
$90$		0			0
$91$		−	22.4780i		−	2.35633i
$92$		0			0
$93$	5.52557	+	0.684169i	0.572975	+	0.0709450i
$94$		0			0
$95$	−4.22914	+	16.8211i	−0.433901	+	1.72580i
$96$		0			0
$97$	−7.79226	−	7.79226i	−0.791184	−	0.791184i	0.190502	−	0.981687i	$-0.438988\pi$
$97$	−7.79226	−	7.79226i	−0.791184	−	0.791184i	−0.981687	+	0.190502i	$0.938988\pi$
$98$		0			0
$99$	−4.89678			−0.492145
$100$		0			0
$101$	17.2863			1.72005			0.860026	−	0.510251i	$-0.170447\pi$
$101$	17.2863			1.72005			0.860026	+	0.510251i	$0.170447\pi$
$102$		0			0
$103$	−2.90798	+	2.90798i	−0.286531	+	0.286531i	−0.835707	−	0.549176i	$-0.814942\pi$
$103$	−2.90798	+	2.90798i	−0.286531	+	0.286531i	0.549176	+	0.835707i	$0.314942\pi$
$104$		0			0
$105$	−2.66446	+	10.5976i	−0.260024	+	1.03422i
$106$		0			0
$107$	6.58266	+	6.58266i	0.636370	+	0.636370i	0.949658	−	0.313288i	$-0.101431\pi$
$107$	6.58266	+	6.58266i	0.636370	+	0.636370i	−0.313288	+	0.949658i	$0.601431\pi$
$108$		0			0
$109$		−	2.19756i		−	0.210488i	−0.994446	−	0.105244i	$-0.966438\pi$
$109$		−	2.19756i		−	0.210488i	0.994446	−	0.105244i	$-0.0335624\pi$
$110$		0			0
$111$	−1.50766			−0.143101
$112$		0			0
$113$	6.18137	−	6.18137i	0.581494	−	0.581494i	−0.353819	−	0.935314i	$-0.615117\pi$
$113$	6.18137	−	6.18137i	0.581494	−	0.581494i	0.935314	+	0.353819i	$0.115117\pi$
$114$		0			0
$115$	4.10310	+	6.85926i	0.382616	+	0.639629i
$116$		0			0
$117$	−3.25243	+	3.25243i	−0.300688	+	0.300688i
$118$		0			0
$119$	9.56774			0.877073
$120$		0			0
$121$	−12.9784			−1.17986
$122$		0			0
$123$	−0.388451	−	0.388451i	−0.0350254	−	0.0350254i
$124$		0			0
$125$	−8.26429	−	7.53004i	−0.739181	−	0.673507i
$126$		0			0
$127$	5.76550	−	5.76550i	0.511606	−	0.511606i	−0.403412	−	0.915018i	$-0.632176\pi$
$127$	5.76550	−	5.76550i	0.511606	−	0.511606i	0.915018	+	0.403412i	$0.132176\pi$
$128$		0			0
$129$			6.34807i			0.558916i
$130$		0			0
$131$	11.0306			0.963750			0.481875	−	0.876240i	$-0.339956\pi$
$131$	11.0306			0.963750			0.481875	+	0.876240i	$0.339956\pi$
$132$		0			0
$133$	−26.8038	+	26.8038i	−2.32419	+	2.32419i
$134$		0			0
$135$	1.91895	−	1.14789i	0.165157	−	0.0987942i
$136$		0			0
$137$	−6.54010	+	6.54010i	−0.558758	+	0.558758i	−0.928954	−	0.370195i	$-0.879291\pi$
$137$	−6.54010	+	6.54010i	−0.558758	+	0.558758i	0.370195	+	0.928954i	$0.379291\pi$
$138$		0			0
$139$	−13.8817			−1.17743			−0.588713	−	0.808342i	$-0.700365\pi$
$139$	−13.8817			−1.17743			−0.588713	+	0.808342i	$0.700365\pi$
$140$		0			0
$141$			3.46063i			0.291438i
$142$		0			0
$143$	−15.9264	+	15.9264i	−1.33184	+	1.33184i
$144$		0			0
$145$	−13.7226	−	3.45014i	−1.13960	−	0.286518i
$146$		0			0
$147$	−11.9373	+	11.9373i	−0.984570	+	0.984570i
$148$		0			0
$149$			7.50236i			0.614617i	0.951610	+	0.307309i	$0.0994284\pi$
$149$			7.50236i			0.614617i	−0.951610	+	0.307309i	$0.900572\pi$
$150$		0			0
$151$		−	0.0322435i		−	0.00262394i	−0.999999	−	0.00131197i	$-0.999582\pi$
$151$		−	0.0322435i		−	0.00262394i	0.999999	−	0.00131197i	$-0.000417613\pi$
$152$		0			0
$153$	−1.38440	−	1.38440i	−0.111922	−	0.111922i
$154$		0			0
$155$	−11.3886	+	5.02984i	−0.914756	+	0.404006i
$156$		0			0
$157$	1.46603	+	1.46603i	0.117002	+	0.117002i	0.763183	−	0.646182i	$-0.223635\pi$
$157$	1.46603	+	1.46603i	0.117002	+	0.117002i	−0.646182	+	0.763183i	$0.723635\pi$
$158$		0			0
$159$			12.0168i			0.952992i
$160$		0			0
$161$			17.4682i			1.37669i
$162$		0			0
$163$	1.53082	−	1.53082i	0.119903	−	0.119903i	−0.644609	−	0.764512i	$-0.722980\pi$
$163$	1.53082	−	1.53082i	0.119903	−	0.119903i	0.764512	+	0.644609i	$0.222980\pi$
$164$		0			0
$165$	9.39666	−	5.62094i	0.731529	−	0.437590i
$166$		0			0
$167$	−13.2302	+	13.2302i	−1.02378	+	1.02378i	−0.0240724	+	0.999710i	$0.507663\pi$
$167$	−13.2302	+	13.2302i	−1.02378	+	1.02378i	−0.999710	+	0.0240724i	$0.992337\pi$
$168$		0			0
$169$			8.15664i			0.627434i
$170$		0			0
$171$	7.75672			0.593171
$172$		0			0
$173$	5.17247	−	5.17247i	0.393256	−	0.393256i	−0.482590	−	0.875846i	$-0.660304\pi$
$173$	5.17247	−	5.17247i	0.393256	−	0.393256i	0.875846	+	0.482590i	$0.160304\pi$
$174$		0			0
$175$	−7.05193	−	23.3948i	−0.533076	−	1.76848i
$176$		0			0
$177$	5.24306	−	5.24306i	0.394093	−	0.394093i
$178$		0			0
$179$	14.5872			1.09030			0.545149	−	0.838339i	$-0.316473\pi$
$179$	14.5872			1.09030			0.545149	+	0.838339i	$0.316473\pi$
$180$		0			0
$181$		−	11.4683i		−	0.852430i	−0.904622	−	0.426215i	$-0.859847\pi$
$181$		−	11.4683i		−	0.852430i	0.904622	−	0.426215i	$-0.140153\pi$
$182$		0			0
$183$	8.44130	−	8.44130i	0.623999	−	0.623999i
$184$		0			0
$185$	2.89312	−	1.73062i	0.212706	−	0.127238i
$186$		0			0
$187$	−6.77908	−	6.77908i	−0.495735	−	0.495735i
$188$		0			0
$189$	4.88691			0.355470
$190$		0			0
$191$	7.85426			0.568315			0.284157	−	0.958778i	$-0.408286\pi$
$191$	7.85426			0.568315			0.284157	+	0.958778i	$0.408286\pi$
$192$		0			0
$193$	−0.841265	+	0.841265i	−0.0605556	+	0.0605556i	−0.736736	−	0.676180i	$-0.763634\pi$
$193$	−0.841265	+	0.841265i	−0.0605556	+	0.0605556i	0.676180	+	0.736736i	$0.263634\pi$
$194$		0			0
$195$	2.50783	−	9.97467i	0.179589	−	0.714301i
$196$		0			0
$197$	−7.79831	+	7.79831i	−0.555607	+	0.555607i	−0.928054	−	0.372447i	$-0.878519\pi$
$197$	−7.79831	+	7.79831i	−0.555607	+	0.555607i	0.372447	+	0.928054i	$0.378519\pi$
$198$		0			0
$199$	−1.59890			−0.113343			−0.0566715	−	0.998393i	$-0.518049\pi$
$199$	−1.59890			−0.113343			−0.0566715	+	0.998393i	$0.518049\pi$
$200$		0			0
$201$		−	0.0797552i		−	0.00562550i
$202$		0			0
$203$	−21.8666	−	21.8666i	−1.53473	−	1.53473i
$204$		0			0
$205$	1.19131	+	0.299519i	0.0832049	+	0.0209193i
$206$		0			0
$207$	2.52755	−	2.52755i	0.175677	−	0.175677i
$208$		0			0
$209$	37.9829			2.62733
$210$		0			0
$211$	−1.96835			−0.135507			−0.0677535	−	0.997702i	$-0.521583\pi$
$211$	−1.96835			−0.135507			−0.0677535	+	0.997702i	$0.521583\pi$
$212$		0			0
$213$	9.07743	+	9.07743i	0.621975	+	0.621975i
$214$		0			0
$215$	−7.28685	−	12.1816i	−0.496959	−	0.830779i
$216$		0			0
$217$	−27.0029	−	3.34347i	−1.83308	−	0.226969i
$218$		0			0
$219$			12.0961i			0.817375i
$220$		0			0
$221$	−9.00531			−0.605762
$222$		0			0
$223$	−8.52099	−	8.52099i	−0.570608	−	0.570608i	0.361691	−	0.932298i	$-0.382200\pi$
$223$	−8.52099	−	8.52099i	−0.570608	−	0.570608i	−0.932298	+	0.361691i	$0.882200\pi$
$224$		0			0
$225$	−2.36472	+	4.40546i	−0.157648	+	0.293698i
$226$		0			0
$227$	−0.864339	−	0.864339i	−0.0573682	−	0.0573682i	0.677841	−	0.735209i	$-0.262916\pi$
$227$	−0.864339	−	0.864339i	−0.0573682	−	0.0573682i	−0.735209	+	0.677841i	$0.762916\pi$
$228$		0			0
$229$	−6.87180			−0.454102			−0.227051	−	0.973883i	$-0.572908\pi$
$229$	−6.87180			−0.454102			−0.227051	+	0.973883i	$0.572908\pi$
$230$		0			0
$231$	23.9301			1.57448
$232$		0			0
$233$	−5.13678	+	5.13678i	−0.336521	+	0.336521i	−0.855056	−	0.518535i	$-0.826478\pi$
$233$	−5.13678	+	5.13678i	−0.336521	+	0.336521i	0.518535	+	0.855056i	$0.326478\pi$
$234$		0			0
$235$	−3.97241	−	6.64077i	−0.259131	−	0.433196i
$236$		0			0
$237$	8.06902	+	8.06902i	0.524139	+	0.524139i
$238$		0			0
$239$	2.47579			0.160146			0.0800729	−	0.996789i	$-0.474485\pi$
$239$	2.47579			0.160146			0.0800729	+	0.996789i	$0.474485\pi$
$240$		0			0
$241$			22.5414i			1.45202i	0.687686	+	0.726009i	$0.258627\pi$
$241$			22.5414i			1.45202i	−0.687686	+	0.726009i	$0.741373\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	9.20438	−	36.6096i	0.588046	−	2.33890i
$246$		0			0
$247$	25.2282	−	25.2282i	1.60523	−	1.60523i
$248$		0			0
$249$			2.16692i			0.137323i
$250$		0			0
$251$		−	7.55545i		−	0.476896i	−0.971155	−	0.238448i	$-0.923361\pi$
$251$		−	7.55545i		−	0.476896i	0.971155	−	0.238448i	$-0.0766386\pi$
$252$		0			0
$253$	12.3768	−	12.3768i	0.778124	−	0.778124i
$254$		0			0
$255$	4.24571	+	1.06745i	0.265877	+	0.0668466i
$256$		0			0
$257$	6.44599	+	6.44599i	0.402090	+	0.402090i	0.878969	−	0.476879i	$-0.158232\pi$
$257$	6.44599	+	6.44599i	0.402090	+	0.402090i	−0.476879	+	0.878969i	$0.658232\pi$
$258$		0			0
$259$	7.36779			0.457812
$260$		0			0
$261$			6.32793i			0.391689i
$262$		0			0
$263$	−6.65661	−	6.65661i	−0.410464	−	0.410464i	0.471436	−	0.881900i	$-0.343736\pi$
$263$	−6.65661	−	6.65661i	−0.410464	−	0.410464i	−0.881900	+	0.471436i	$0.843736\pi$
$264$		0			0
$265$	−13.7939	−	23.0596i	−0.847351	−	1.41654i
$266$		0			0
$267$	−9.25383	−	9.25383i	−0.566325	−	0.566325i
$268$		0			0
$269$	−9.08425			−0.553877			−0.276938	−	0.960888i	$-0.589320\pi$
$269$	−9.08425			−0.553877			−0.276938	+	0.960888i	$0.589320\pi$
$270$		0			0
$271$			7.47607i			0.454139i	0.973879	+	0.227070i	$0.0729145\pi$
$271$			7.47607i			0.454139i	−0.973879	+	0.227070i	$0.927086\pi$
$272$		0			0
$273$	15.8943	−	15.8943i	0.961969	−	0.961969i
$274$		0			0
$275$	−11.5795	+	21.5726i	−0.698270	+	1.30088i
$276$		0			0
$277$	22.8243	−	22.8243i	1.37138	−	1.37138i	0.512984	−	0.858398i	$-0.328540\pi$
$277$	22.8243	−	22.8243i	1.37138	−	1.37138i	0.858398	−	0.512984i	$-0.171460\pi$
$278$		0			0
$279$	3.42339	+	4.39095i	0.204953	+	0.262879i
$280$		0			0
$281$	−22.3125			−1.33105			−0.665526	−	0.746374i	$-0.731793\pi$
$281$	−22.3125			−1.33105			−0.665526	+	0.746374i	$0.731793\pi$
$282$		0			0
$283$	4.02813	−	4.02813i	0.239448	−	0.239448i	−0.577174	−	0.816621i	$-0.695844\pi$
$283$	4.02813	−	4.02813i	0.239448	−	0.239448i	0.816621	+	0.577174i	$0.195844\pi$
$284$		0			0
$285$	−14.8847	+	8.90382i	−0.881696	+	0.527417i
$286$		0			0
$287$	1.89832	+	1.89832i	0.112054	+	0.112054i
$288$		0			0
$289$			13.1669i			0.774523i
$290$		0			0
$291$		−	11.0199i		−	0.645999i
$292$		0			0
$293$	−15.2778	+	15.2778i	−0.892540	+	0.892540i	−0.994762	−	0.102222i	$-0.967405\pi$
$293$	−15.2778	+	15.2778i	−0.892540	+	0.892540i	0.102222	+	0.994762i	$0.467405\pi$
$294$		0			0
$295$	−4.04273	+	16.0796i	−0.235377	+	0.936191i
$296$		0			0
$297$	−3.46254	−	3.46254i	−0.200917	−	0.200917i
$298$		0			0
$299$		−	16.4413i		−	0.950827i
$300$		0			0
$301$		−	31.0224i		−	1.78810i
$302$		0			0
$303$	12.2233	+	12.2233i	0.702208	+	0.702208i
$304$		0			0
$305$	−6.50877	+	25.8881i	−0.372691	+	1.48235i
$306$		0			0
$307$	−9.43636	−	9.43636i	−0.538561	−	0.538561i	0.384545	−	0.923106i	$-0.374358\pi$
$307$	−9.43636	−	9.43636i	−0.538561	−	0.538561i	−0.923106	+	0.384545i	$0.874358\pi$
$308$		0			0
$309$	−4.11250			−0.233952
$310$		0			0
$311$	28.0760			1.59205			0.796023	−	0.605267i	$-0.206934\pi$
$311$	28.0760			1.59205			0.796023	+	0.605267i	$0.206934\pi$
$312$		0			0
$313$	−7.01601	−	7.01601i	−0.396569	−	0.396569i	0.480452	−	0.877021i	$-0.340473\pi$
$313$	−7.01601	−	7.01601i	−0.396569	−	0.396569i	−0.877021	+	0.480452i	$0.840473\pi$
$314$		0			0
$315$	−9.37772	+	5.60961i	−0.528374	+	0.316066i
$316$		0			0
$317$	−20.0745	−	20.0745i	−1.12749	−	1.12749i	−0.990583	−	0.136911i	$-0.956283\pi$
$317$	−20.0745	−	20.0745i	−1.12749	−	1.12749i	−0.136911	−	0.990583i	$-0.543717\pi$
$318$		0			0
$319$			30.9865i			1.73491i
$320$		0			0
$321$			9.30929i			0.519594i
$322$		0			0
$323$	10.7384	+	10.7384i	0.597499	+	0.597499i
$324$		0			0
$325$	6.63739	+	22.0196i	0.368176	+	1.22143i
$326$		0			0
$327$	1.55391	−	1.55391i	0.0859314	−	0.0859314i
$328$		0			0
$329$		−	16.9118i		−	0.932376i
$330$		0			0
$331$			9.46469i			0.520227i	0.965578	+	0.260113i	$0.0837599\pi$
$331$			9.46469i			0.520227i	−0.965578	+	0.260113i	$0.916240\pi$
$332$		0			0
$333$	−1.06608	−	1.06608i	−0.0584206	−	0.0584206i
$334$		0			0
$335$	0.0915498	+	0.153046i	0.00500190	+	0.00836179i
$336$		0			0
$337$	−23.9610	+	23.9610i	−1.30524	+	1.30524i	−0.380430	+	0.924810i	$0.624224\pi$
$337$	−23.9610	+	23.9610i	−1.30524	+	1.30524i	−0.924810	+	0.380430i	$0.875776\pi$
$338$		0			0
$339$	8.74178			0.474788
$340$		0			0
$341$	16.7636	+	21.5015i	0.907798	+	1.16437i
$342$		0			0
$343$	34.1474	−	34.1474i	1.84379	−	1.84379i
$344$		0			0
$345$	−1.94889	+	7.75156i	−0.104925	+	0.417330i
$346$		0			0
$347$	−10.6386	+	10.6386i	−0.571108	+	0.571108i	−0.932438	−	0.361330i	$-0.882323\pi$
$347$	−10.6386	+	10.6386i	−0.571108	+	0.571108i	0.361330	+	0.932438i	$0.382323\pi$
$348$		0			0
$349$			7.28805i			0.390120i	0.980791	+	0.195060i	$0.0624902\pi$
$349$			7.28805i			0.390120i	−0.980791	+	0.195060i	$0.937510\pi$
$350$		0			0
$351$	−4.59963			−0.245510
$352$		0			0
$353$	6.91692	+	6.91692i	0.368151	+	0.368151i	0.866802	−	0.498652i	$-0.166171\pi$
$353$	6.91692	+	6.91692i	0.368151	+	0.368151i	−0.498652	+	0.866802i	$0.666171\pi$
$354$		0			0
$355$	−27.8390	−	6.99926i	−1.47754	−	0.371482i
$356$		0			0
$357$	6.76541	+	6.76541i	0.358064	+	0.358064i
$358$		0			0
$359$		−	3.51255i		−	0.185385i	−0.995695	−	0.0926925i	$-0.970453\pi$
$359$		−	3.51255i		−	0.185385i	0.995695	−	0.0926925i	$-0.0295474\pi$
$360$		0			0
$361$	−41.1667			−2.16667
$362$		0			0
$363$	−9.17713	−	9.17713i	−0.481675	−	0.481675i
$364$		0			0
$365$	−13.8849	−	23.2117i	−0.726768	−	1.21496i
$366$		0			0
$367$	10.6423	−	10.6423i	0.555524	−	0.555524i	−0.372506	−	0.928030i	$-0.621501\pi$
$367$	10.6423	−	10.6423i	0.555524	−	0.555524i	0.928030	+	0.372506i	$0.121501\pi$
$368$		0			0
$369$		−	0.549352i		−	0.0285981i
$370$		0			0
$371$		−	58.7248i		−	3.04884i
$372$		0			0
$373$	0.579797	−	0.579797i	0.0300207	−	0.0300207i	−0.691937	−	0.721958i	$-0.743242\pi$
$373$	0.579797	−	0.579797i	0.0300207	−	0.0300207i	0.721958	+	0.691937i	$0.243242\pi$
$374$		0			0
$375$	−0.519196	−	11.1683i	−0.0268112	−	0.576727i
$376$		0			0
$377$	20.5812	+	20.5812i	1.05998	+	1.05998i
$378$		0			0
$379$		−	28.3112i		−	1.45425i	−0.686505	−	0.727125i	$-0.740856\pi$
$379$		−	28.3112i		−	1.45425i	0.686505	−	0.727125i	$-0.259144\pi$
$380$		0			0
$381$	8.15366			0.417724
$382$		0			0
$383$	−7.05626	−	7.05626i	−0.360558	−	0.360558i	0.503460	−	0.864018i	$-0.332060\pi$
$383$	−7.05626	−	7.05626i	−0.360558	−	0.360558i	−0.864018	+	0.503460i	$0.832060\pi$
$384$		0			0
$385$	−45.9206	+	27.4690i	−2.34033	+	1.39995i
$386$		0			0
$387$	−4.48876	+	4.48876i	−0.228177	+	0.228177i
$388$		0			0
$389$	17.6401			0.894387			0.447193	−	0.894437i	$-0.352424\pi$
$389$	17.6401			0.894387			0.447193	+	0.894437i	$0.352424\pi$
$390$		0			0
$391$	6.99824			0.353916
$392$		0			0
$393$	7.79983	+	7.79983i	0.393449	+	0.393449i
$394$		0			0
$395$	−24.7463	−	6.22171i	−1.24512	−	0.313048i
$396$		0			0
$397$	−7.53894	−	7.53894i	−0.378368	−	0.378368i	0.492145	−	0.870513i	$-0.336213\pi$
$397$	−7.53894	−	7.53894i	−0.378368	−	0.378368i	−0.870513	+	0.492145i	$0.836213\pi$
$398$		0			0
$399$	−37.9064			−1.89769
$400$		0			0
$401$			3.41386i			0.170480i	0.996360	+	0.0852401i	$0.0271657\pi$
$401$			3.41386i			0.170480i	−0.996360	+	0.0852401i	$0.972834\pi$
$402$		0			0
$403$	25.4156	+	3.14693i	1.26604	+	0.156760i
$404$		0			0
$405$	2.16858	+	0.545223i	0.107758	+	0.0270924i
$406$		0			0
$407$	−5.22034	−	5.22034i	−0.258762	−	0.258762i
$408$		0			0
$409$	31.5783			1.56145			0.780724	−	0.624876i	$-0.214850\pi$
$409$	31.5783			1.56145			0.780724	+	0.624876i	$0.214850\pi$
$410$		0			0
$411$	−9.24910			−0.456224
$412$		0			0
$413$	−25.6224	+	25.6224i	−1.26079	+	1.26079i
$414$		0			0
$415$	−2.48737	−	4.15820i	−0.122100	−	0.204118i
$416$		0			0
$417$	−9.81581	−	9.81581i	−0.480682	−	0.480682i
$418$		0			0
$419$			22.0057i			1.07505i	0.843248	+	0.537525i	$0.180640\pi$
$419$			22.0057i			1.07505i	−0.843248	+	0.537525i	$0.819360\pi$
$420$		0			0
$421$	39.7439			1.93700			0.968498	−	0.249020i	$-0.0801084\pi$
$421$	39.7439			1.93700			0.968498	+	0.249020i	$0.0801084\pi$
$422$		0			0
$423$	−2.44703	+	2.44703i	−0.118979	+	0.118979i
$424$		0			0
$425$	−9.37261	+	2.82520i	−0.454638	+	0.137042i
$426$		0			0
$427$	−41.2519	+	41.2519i	−1.99632	+	1.99632i
$428$		0			0
$429$	−22.5234			−1.08744
$430$		0			0
$431$	−12.4241			−0.598447			−0.299224	−	0.954183i	$-0.596728\pi$
$431$	−12.4241			−0.598447			−0.299224	+	0.954183i	$0.596728\pi$
$432$		0			0
$433$	21.3312	+	21.3312i	1.02511	+	1.02511i	0.999677	+	0.0254333i	$0.00809655\pi$
$433$	21.3312	+	21.3312i	1.02511	+	1.02511i	0.0254333	+	0.999677i	$0.491903\pi$
$434$		0			0
$435$	−7.26374	−	12.1430i	−0.348270	−	0.582211i
$436$		0			0
$437$	−19.6055	+	19.6055i	−0.937856	+	0.937856i
$438$		0			0
$439$		−	36.1648i		−	1.72605i	−0.505159	−	0.863026i	$-0.668566\pi$
$439$		−	36.1648i		−	1.72605i	0.505159	−	0.863026i	$-0.331434\pi$
$440$		0			0
$441$	−16.8819			−0.803898
$442$		0			0
$443$	8.63713	−	8.63713i	0.410362	−	0.410362i	−0.471502	−	0.881865i	$-0.656288\pi$
$443$	8.63713	−	8.63713i	0.410362	−	0.410362i	0.881865	+	0.471502i	$0.156288\pi$
$444$		0			0
$445$	28.3799	+	7.13528i	1.34534	+	0.338245i
$446$		0			0
$447$	−5.30497	+	5.30497i	−0.250916	+	0.250916i
$448$		0			0
$449$	30.3951			1.43443			0.717216	−	0.696851i	$-0.245416\pi$
$449$	30.3951			1.43443			0.717216	+	0.696851i	$0.245416\pi$
$450$		0			0
$451$		−	2.69005i		−	0.126670i
$452$		0			0
$453$	0.0227996	−	0.0227996i	0.00107122	−	0.00107122i
$454$		0			0
$455$	−12.2555	+	48.7453i	−0.574548	+	2.28521i
$456$		0			0
$457$	21.7509	−	21.7509i	1.01747	−	1.01747i	0.0176210	−	0.999845i	$-0.494391\pi$
$457$	21.7509	−	21.7509i	1.01747	−	1.01747i	0.999845	−	0.0176210i	$-0.00560923\pi$
$458$		0			0
$459$		−	1.95783i		−	0.0913837i
$460$		0			0
$461$			41.1546i			1.91676i	0.285494	+	0.958381i	$0.407842\pi$
$461$			41.1546i			1.91676i	−0.285494	+	0.958381i	$0.592158\pi$
$462$		0			0
$463$	12.2736	+	12.2736i	0.570403	+	0.570403i	0.932241	−	0.361838i	$-0.117851\pi$
$463$	12.2736	+	12.2736i	0.570403	+	0.570403i	−0.361838	+	0.932241i	$0.617851\pi$
$464$		0			0
$465$	−11.6096	−	4.49634i	−0.538383	−	0.208513i
$466$		0			0
$467$	−5.31236	−	5.31236i	−0.245827	−	0.245827i	0.573429	−	0.819255i	$-0.305613\pi$
$467$	−5.31236	−	5.31236i	−0.245827	−	0.245827i	−0.819255	+	0.573429i	$0.805613\pi$
$468$		0			0
$469$			0.389756i			0.0179973i
$470$		0			0
$471$			2.07327i			0.0955314i
$472$		0			0
$473$	−21.9805	+	21.9805i	−1.01066	+	1.01066i
$474$		0			0
$475$	18.3425	−	34.1719i	0.841610	−	1.56792i
$476$		0			0
$477$	−8.49714	+	8.49714i	−0.389057	+	0.389057i
$478$		0			0
$479$		−	28.1222i		−	1.28494i	−0.766312	−	0.642469i	$-0.777910\pi$
$479$		−	28.1222i		−	1.28494i	0.766312	−	0.642469i	$-0.222090\pi$
$480$		0			0
$481$	−6.93468			−0.316194
$482$		0			0
$483$	−12.3519	+	12.3519i	−0.562030	+	0.562030i
$484$		0			0
$485$	12.6496	+	21.1467i	0.574389	+	0.960220i
$486$		0			0
$487$	3.73712	−	3.73712i	0.169345	−	0.169345i	−0.617346	−	0.786691i	$-0.711792\pi$
$487$	3.73712	−	3.73712i	0.169345	−	0.169345i	0.786691	+	0.617346i	$0.211792\pi$
$488$		0			0
$489$	2.16490			0.0979002
$490$		0			0
$491$		−	35.2715i		−	1.59178i	−0.605441	−	0.795890i	$-0.707003\pi$
$491$		−	35.2715i		−	1.59178i	0.605441	−	0.795890i	$-0.292997\pi$
$492$		0			0
$493$	−8.76036	+	8.76036i	−0.394547	+	0.394547i
$494$		0			0
$495$	10.6190	+	2.66984i	0.477291	+	0.120000i
$496$		0			0
$497$	−44.3606	−	44.3606i	−1.98984	−	1.98984i
$498$		0			0
$499$	−8.55558			−0.383001			−0.191500	−	0.981493i	$-0.561335\pi$
$499$	−8.55558			−0.383001			−0.191500	+	0.981493i	$0.561335\pi$
$500$		0			0
$501$	−18.7103			−0.835915
$502$		0			0
$503$	13.4456	−	13.4456i	0.599509	−	0.599509i	−0.340673	−	0.940182i	$-0.610655\pi$
$503$	13.4456	−	13.4456i	0.599509	−	0.599509i	0.940182	+	0.340673i	$0.110655\pi$
$504$		0			0
$505$	−37.4867	−	9.42489i	−1.66814	−	0.419402i
$506$		0			0
$507$	−5.76761	+	5.76761i	−0.256149	+	0.256149i
$508$		0			0
$509$	−3.06081			−0.135668			−0.0678340	−	0.997697i	$-0.521609\pi$
$509$	−3.06081			−0.135668			−0.0678340	+	0.997697i	$0.521609\pi$
$510$		0			0
$511$		−	59.1123i		−	2.61497i
$512$		0			0
$513$	5.48483	+	5.48483i	0.242161	+	0.242161i
$514$		0			0
$515$	7.89167	−	4.72068i	0.347749	−	0.208018i
$516$		0			0
$517$	−11.9826	+	11.9826i	−0.526993	+	0.526993i
$518$		0			0
$519$	7.31498			0.321092
$520$		0			0
$521$	42.7863			1.87450			0.937250	−	0.348658i	$-0.113362\pi$
$521$	42.7863			1.87450			0.937250	+	0.348658i	$0.113362\pi$
$522$		0			0
$523$	11.3231	+	11.3231i	0.495126	+	0.495126i	0.909917	−	0.414791i	$-0.136145\pi$
$523$	11.3231	+	11.3231i	0.495126	+	0.495126i	−0.414791	+	0.909917i	$0.636145\pi$
$524$		0			0
$525$	11.5562	−	21.5291i	0.504352	−	0.939606i
$526$		0			0
$527$	−1.33949	+	10.8181i	−0.0583489	+	0.471245i
$528$		0			0
$529$		−	10.2230i		−	0.444479i
$530$		0			0
$531$	7.41481			0.321775
$532$		0			0
$533$	−1.78673	−	1.78673i	−0.0773919	−	0.0773919i
$534$		0			0
$535$	−10.6860	−	17.8640i	−0.461996	−	0.772329i
$536$		0			0
$537$	10.3147	+	10.3147i	0.445113	+	0.445113i
$538$		0			0
$539$	−82.6667			−3.56071
$540$		0			0
$541$	−19.2669			−0.828350			−0.414175	−	0.910197i	$-0.635930\pi$
$541$	−19.2669			−0.828350			−0.414175	+	0.910197i	$0.635930\pi$
$542$		0			0
$543$	8.10930	−	8.10930i	0.348003	−	0.348003i
$544$		0			0
$545$	−1.19816	+	4.76558i	−0.0513236	+	0.204135i
$546$		0			0
$547$	28.5347	+	28.5347i	1.22006	+	1.22006i	0.967612	+	0.252443i	$0.0812341\pi$
$547$	28.5347	+	28.5347i	1.22006	+	1.22006i	0.252443	+	0.967612i	$0.418766\pi$
$548$		0			0
$549$	11.9378			0.509493
$550$		0			0
$551$		−	49.0840i		−	2.09105i
$552$		0			0
$553$	−39.4325	−	39.4325i	−1.67684	−	1.67684i
$554$		0			0
$555$	3.26948	+	0.822011i	0.138782	+	0.0348924i
$556$		0			0
$557$	16.5408	−	16.5408i	0.700857	−	0.700857i	−0.263738	−	0.964594i	$-0.584955\pi$
$557$	16.5408	−	16.5408i	0.700857	−	0.700857i	0.964594	+	0.263738i	$0.0849554\pi$
$558$		0			0
$559$			29.1988i			1.23498i
$560$		0			0
$561$		−	9.58706i		−	0.404766i
$562$		0			0
$563$	7.01144	−	7.01144i	0.295497	−	0.295497i	−0.543750	−	0.839247i	$-0.682996\pi$
$563$	7.01144	−	7.01144i	0.295497	−	0.295497i	0.839247	+	0.543750i	$0.182996\pi$
$564$		0			0
$565$	−16.7750	+	10.0346i	−0.705730	+	0.422157i
$566$		0			0
$567$	3.45556	+	3.45556i	0.145120	+	0.145120i
$568$		0			0
$569$	20.8064			0.872250			0.436125	−	0.899886i	$-0.356351\pi$
$569$	20.8064			0.872250			0.436125	+	0.899886i	$0.356351\pi$
$570$		0			0
$571$			40.6599i			1.70156i	0.525519	+	0.850782i	$0.323871\pi$
$571$			40.6599i			1.70156i	−0.525519	+	0.850782i	$0.676129\pi$
$572$		0			0
$573$	5.55380	+	5.55380i	0.232013	+	0.232013i
$574$		0			0
$575$	−5.15808	−	17.1119i	−0.215107	−	0.713617i
$576$		0			0
$577$	26.3995	+	26.3995i	1.09903	+	1.09903i	0.994525	+	0.104502i	$0.0333249\pi$
$577$	26.3995	+	26.3995i	1.09903	+	1.09903i	0.104502	+	0.994525i	$0.466675\pi$
$578$		0			0
$579$	−1.18973			−0.0494434
$580$		0			0
$581$		−	10.5895i		−	0.439328i
$582$		0			0
$583$	−41.6086	+	41.6086i	−1.72325	+	1.72325i
$584$		0			0
$585$	8.82646	−	5.27985i	0.364929	−	0.218295i
$586$		0			0
$587$	9.52719	−	9.52719i	0.393229	−	0.393229i	−0.482607	−	0.875837i	$-0.660310\pi$
$587$	9.52719	−	9.52719i	0.393229	−	0.393229i	0.875837	+	0.482607i	$0.160310\pi$
$588$		0			0
$589$	−26.5543	−	34.0593i	−1.09415	−	1.40339i
$590$		0			0
$591$	−11.0285			−0.453651
$592$		0			0
$593$	−3.70145	+	3.70145i	−0.152000	+	0.152000i	−0.779011	−	0.627011i	$-0.784278\pi$
$593$	−3.70145	+	3.70145i	−0.152000	+	0.152000i	0.627011	+	0.779011i	$0.284278\pi$
$594$		0			0
$595$	−20.7484	−	5.21655i	−0.850601	−	0.213858i
$596$		0			0
$597$	−1.13059	−	1.13059i	−0.0462721	−	0.0462721i
$598$		0			0
$599$		−	7.27677i		−	0.297321i	−0.988888	−	0.148660i	$-0.952504\pi$
$599$		−	7.27677i		−	0.297321i	0.988888	−	0.148660i	$-0.0474961\pi$
$600$		0			0
$601$		−	27.9458i		−	1.13993i	−0.821668	−	0.569966i	$-0.806956\pi$
$601$		−	27.9458i		−	1.13993i	0.821668	−	0.569966i	$-0.193044\pi$
$602$		0			0
$603$	0.0563954	−	0.0563954i	0.00229660	−	0.00229660i
$604$		0			0
$605$	28.1447	+	7.07614i	1.14425	+	0.287686i
$606$		0			0
$607$	−2.94856	−	2.94856i	−0.119678	−	0.119678i	0.644731	−	0.764409i	$-0.276969\pi$
$607$	−2.94856	−	2.94856i	−0.119678	−	0.119678i	−0.764409	+	0.644731i	$0.776969\pi$
$608$		0			0
$609$		−	30.9240i		−	1.25310i
$610$		0			0
$611$			15.9176i			0.643958i
$612$		0			0
$613$	−7.25229	−	7.25229i	−0.292917	−	0.292917i	0.545314	−	0.838232i	$-0.316410\pi$
$613$	−7.25229	−	7.25229i	−0.292917	−	0.292917i	−0.838232	+	0.545314i	$0.816410\pi$
$614$		0			0
$615$	0.630593	+	1.05418i	0.0254280	+	0.0425085i
$616$		0			0
$617$	24.7603	+	24.7603i	0.996812	+	0.996812i	0.999995	−	0.00318330i	$-0.00101328\pi$
$617$	24.7603	+	24.7603i	0.996812	+	0.996812i	−0.00318330	+	0.999995i	$0.501013\pi$
$618$		0			0
$619$	−34.7040			−1.39487			−0.697437	−	0.716647i	$-0.745676\pi$
$619$	−34.7040			−1.39487			−0.697437	+	0.716647i	$0.745676\pi$
$620$		0			0
$621$	3.57449			0.143439
$622$		0			0
$623$	45.2226	+	45.2226i	1.81181	+	1.81181i
$624$		0			0
$625$	13.8162	+	20.8354i	0.552649	+	0.833414i
$626$		0			0
$627$	26.8580	+	26.8580i	1.07260	+	1.07260i
$628$		0			0
$629$		−	2.95174i		−	0.117694i
$630$		0			0
$631$		−	41.3611i		−	1.64656i	−0.567635	−	0.823280i	$-0.692142\pi$
$631$		−	41.3611i		−	1.64656i	0.567635	−	0.823280i	$-0.307858\pi$
$632$		0			0
$633$	−1.39184	−	1.39184i	−0.0553205	−	0.0553205i
$634$		0			0
$635$	−15.6464	+	9.35946i	−0.620910	+	0.371419i
$636$		0			0
$637$	−54.9071	+	54.9071i	−2.17550	+	2.17550i
$638$		0			0
$639$			12.8374i			0.507841i
$640$		0			0
$641$			33.2226i			1.31221i	0.754668	+	0.656107i	$0.227798\pi$
$641$			33.2226i			1.31221i	−0.754668	+	0.656107i	$0.772202\pi$
$642$		0			0
$643$	−17.7653	−	17.7653i	−0.700596	−	0.700596i	0.263943	−	0.964538i	$-0.414977\pi$
$643$	−17.7653	−	17.7653i	−0.700596	−	0.700596i	−0.964538	+	0.263943i	$0.914977\pi$
$644$		0			0
$645$	3.46111	−	13.7663i	0.136281	−	0.542047i
$646$		0			0
$647$	−12.0055	+	12.0055i	−0.471985	+	0.471985i	−0.902557	−	0.430571i	$-0.858312\pi$
$647$	−12.0055	+	12.0055i	−0.471985	+	0.471985i	0.430571	+	0.902557i	$0.358312\pi$
$648$		0			0
$649$	36.3087			1.42524
$650$		0			0
$651$	−16.7298	−	21.4582i	−0.655691	−	0.841011i
$652$		0			0
$653$	−23.2656	+	23.2656i	−0.910454	+	0.910454i	−0.996308	−	0.0858533i	$-0.972638\pi$
$653$	−23.2656	+	23.2656i	−0.910454	+	0.910454i	0.0858533	+	0.996308i	$0.472638\pi$
$654$		0			0
$655$	−23.9208	−	6.01415i	−0.934662	−	0.234992i
$656$		0			0
$657$	−8.55320	+	8.55320i	−0.333692	+	0.333692i
$658$		0			0
$659$			19.2928i			0.751543i	0.926712	+	0.375771i	$0.122622\pi$
$659$			19.2928i			0.751543i	−0.926712	+	0.375771i	$0.877378\pi$
$660$		0			0
$661$	11.6552			0.453336			0.226668	−	0.973972i	$-0.427217\pi$
$661$	11.6552			0.453336			0.226668	+	0.973972i	$0.427217\pi$
$662$		0			0
$663$	−6.36771	−	6.36771i	−0.247301	−	0.247301i
$664$		0			0
$665$	72.7403	−	43.5122i	2.82075	−	1.68733i
$666$		0			0
$667$	−15.9941	−	15.9941i	−0.619295	−	0.619295i
$668$		0			0
$669$		−	12.0505i		−	0.465899i
$670$		0			0
$671$	58.4568			2.25670
$672$		0			0
$673$	−5.90308	−	5.90308i	−0.227547	−	0.227547i	0.584120	−	0.811667i	$-0.301440\pi$
$673$	−5.90308	−	5.90308i	−0.227547	−	0.227547i	−0.811667	+	0.584120i	$0.801440\pi$
$674$		0			0
$675$	−4.78724	+	1.44302i	−0.184261	+	0.0555420i
$676$		0			0
$677$	0.318677	−	0.318677i	0.0122477	−	0.0122477i	−0.700956	−	0.713204i	$-0.747243\pi$
$677$	0.318677	−	0.318677i	0.0122477	−	0.0122477i	0.713204	+	0.700956i	$0.247243\pi$
$678$		0			0
$679$			53.8533i			2.06670i
$680$		0			0
$681$		−	1.22236i		−	0.0468409i
$682$		0			0
$683$	−11.8614	+	11.8614i	−0.453864	+	0.453864i	−0.896635	−	0.442771i	$-0.853995\pi$
$683$	−11.8614	+	11.8614i	−0.453864	+	0.453864i	0.442771	+	0.896635i	$0.353995\pi$
$684$		0			0
$685$	17.7485	−	10.6169i	0.678137	−	0.405651i
$686$		0			0
$687$	−4.85910	−	4.85910i	−0.185386	−	0.185386i
$688$		0			0
$689$			55.2728i			2.10572i
$690$		0			0
$691$	−18.9159			−0.719593			−0.359797	−	0.933031i	$-0.617154\pi$
$691$	−18.9159			−0.719593			−0.359797	+	0.933031i	$0.617154\pi$
$692$		0			0
$693$	16.9211	+	16.9211i	0.642781	+	0.642781i
$694$		0			0
$695$	30.1035	+	7.56860i	1.14189	+	0.287093i
$696$		0			0
$697$	0.760520	−	0.760520i	0.0288068	−	0.0288068i
$698$		0			0
$699$	−7.26450			−0.274769
$700$		0			0
$701$	−1.13129			−0.0427284			−0.0213642	−	0.999772i	$-0.506801\pi$
$701$	−1.13129			−0.0427284			−0.0213642	+	0.999772i	$0.506801\pi$
$702$		0			0
$703$	8.26925	+	8.26925i	0.311881	+	0.311881i
$704$		0			0
$705$	1.88682	−	7.50465i	0.0710616	−	0.282641i
$706$		0			0
$707$	−59.7339	−	59.7339i	−2.24653	−	2.24653i
$708$		0			0
$709$	24.6940			0.927402			0.463701	−	0.885992i	$-0.346521\pi$
$709$	24.6940			0.927402			0.463701	+	0.885992i	$0.346521\pi$
$710$		0			0
$711$			11.4113i			0.427958i
$712$		0			0
$713$	−19.7511	−	2.44555i	−0.739684	−	0.0915867i
$714$		0			0
$715$	43.2212	−	25.8543i	1.61638	−	0.966895i
$716$		0			0
$717$	1.75065	+	1.75065i	0.0653792	+	0.0653792i
$718$		0			0
$719$	15.2440			0.568507			0.284253	−	0.958749i	$-0.408254\pi$
$719$	15.2440			0.568507			0.284253	+	0.958749i	$0.408254\pi$
$720$		0			0
$721$	20.0974			0.748466
$722$		0			0
$723$	−15.9392	+	15.9392i	−0.592784	+	0.592784i
$724$		0			0
$725$	27.8775	+	14.9638i	1.03534	+	0.555741i
$726$		0			0
$727$	−14.6099	−	14.6099i	−0.541852	−	0.541852i	0.382220	−	0.924072i	$-0.375160\pi$
$727$	−14.6099	−	14.6099i	−0.541852	−	0.541852i	−0.924072	+	0.382220i	$0.875160\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−12.4284			−0.459683
$732$		0			0
$733$	−33.8807	+	33.8807i	−1.25141	+	1.25141i	−0.296325	+	0.955087i	$0.595761\pi$
$733$	−33.8807	+	33.8807i	−1.25141	+	1.25141i	−0.955087	+	0.296325i	$0.904239\pi$
$734$		0			0
$735$	32.3954	−	19.3784i	1.19492	−	0.714784i
$736$		0			0
$737$	0.276156	−	0.276156i	0.0101723	−	0.0101723i
$738$		0			0
$739$	21.3105			0.783920			0.391960	−	0.919982i	$-0.371797\pi$
$739$	21.3105			0.783920			0.391960	+	0.919982i	$0.371797\pi$
$740$		0			0
$741$	35.6781			1.31067
$742$		0			0
$743$	21.4350	+	21.4350i	0.786373	+	0.786373i	0.980898	−	0.194525i	$-0.0623165\pi$
$743$	21.4350	+	21.4350i	0.786373	+	0.786373i	−0.194525	+	0.980898i	$0.562316\pi$
$744$		0			0
$745$	4.09046	−	16.2695i	0.149863	−	0.596067i
$746$		0			0
$747$	−1.53224	+	1.53224i	−0.0560618	+	0.0560618i
$748$		0			0
$749$		−	45.4936i		−	1.66230i
$750$		0			0
$751$	−29.3802			−1.07210			−0.536049	−	0.844187i	$-0.680084\pi$
$751$	−29.3802			−1.07210			−0.536049	+	0.844187i	$0.680084\pi$
$752$		0			0
$753$	5.34251	−	5.34251i	0.194692	−	0.194692i
$754$		0			0
$755$	−0.0175799	+	0.0699226i	−0.000639798	+	0.00254474i
$756$		0			0
$757$	−11.9078	+	11.9078i	−0.432796	+	0.432796i	−0.889578	−	0.456783i	$-0.849002\pi$
$757$	−11.9078	+	11.9078i	−0.432796	+	0.432796i	0.456783	+	0.889578i	$0.349002\pi$
$758$		0			0
$759$	17.5035			0.635336
$760$		0			0
$761$		−	9.76514i		−	0.353986i	−0.984212	−	0.176993i	$-0.943363\pi$
$761$		−	9.76514i		−	0.353986i	0.984212	−	0.176993i	$-0.0566370\pi$
$762$		0			0
$763$	−7.59381	+	7.59381i	−0.274914	+	0.274914i
$764$		0			0
$765$	2.24737	+	3.75697i	0.0812537	+	0.135834i
$766$		0			0
$767$	24.1162	−	24.1162i	0.870785	−	0.870785i
$768$		0			0
$769$			32.1135i			1.15804i	0.815313	+	0.579021i	$0.196565\pi$
$769$			32.1135i			1.15804i	−0.815313	+	0.579021i	$0.803435\pi$
$770$		0			0
$771$			9.11601i			0.328305i
$772$		0			0
$773$	4.82343	+	4.82343i	0.173487	+	0.173487i	0.788509	−	0.615023i	$-0.210853\pi$
$773$	4.82343	+	4.82343i	0.173487	+	0.173487i	−0.615023	+	0.788509i	$0.710853\pi$
$774$		0			0
$775$	27.4395	−	4.69825i	0.985656	−	0.168766i
$776$		0			0
$777$	5.20981	+	5.20981i	0.186901	+	0.186901i
$778$		0			0
$779$			4.26117i			0.152672i
$780$		0			0
$781$			62.8620i			2.24938i
$782$		0			0
$783$	−4.47452	+	4.47452i	−0.159906	+	0.159906i
$784$		0			0
$785$	−2.37988	−	3.97850i	−0.0849416	−	0.141999i
$786$		0			0
$787$	−4.31437	+	4.31437i	−0.153791	+	0.153791i	−0.779809	−	0.626018i	$-0.784684\pi$
$787$	−4.31437	+	4.31437i	−0.153791	+	0.153791i	0.626018	+	0.779809i	$0.284684\pi$
$788$		0			0
$789$		−	9.41387i		−	0.335143i
$790$		0			0
$791$	−42.7203			−1.51896
$792$		0			0
$793$	38.8269	−	38.8269i	1.37878	−	1.37878i
$794$		0			0
$795$	6.55182	−	26.0593i	0.232369	−	0.924229i
$796$		0			0
$797$	−19.2281	+	19.2281i	−0.681094	+	0.681094i	−0.960247	−	0.279152i	$-0.909947\pi$
$797$	−19.2281	+	19.2281i	−0.681094	+	0.681094i	0.279152	+	0.960247i	$0.409947\pi$
$798$		0			0
$799$	−6.77533			−0.239694
$800$		0			0
$801$		−	13.0869i		−	0.462403i
$802$		0			0
$803$	−41.8831	+	41.8831i	−1.47802	+	1.47802i
$804$		0			0
$805$	9.52407	−	37.8811i	0.335679	−	1.33514i
$806$		0			0
$807$	−6.42354	−	6.42354i	−0.226119	−	0.226119i
$808$		0			0
$809$	−13.2550			−0.466022			−0.233011	−	0.972474i	$-0.574858\pi$
$809$	−13.2550			−0.466022			−0.233011	+	0.972474i	$0.574858\pi$
$810$		0			0
$811$	−4.16919			−0.146400			−0.0732001	−	0.997317i	$-0.523321\pi$
$811$	−4.16919			−0.146400			−0.0732001	+	0.997317i	$0.523321\pi$
$812$		0			0
$813$	−5.28638	+	5.28638i	−0.185401	+	0.185401i
$814$		0			0
$815$	−4.15433	+	2.48506i	−0.145520	+	0.0870478i
$816$		0			0
$817$	34.8181	−	34.8181i	1.21813	−	1.21813i
$818$		0			0
$819$	22.4780			0.785444
$820$		0			0
$821$			0.400642i			0.0139825i	0.999976	+	0.00699125i	$0.00222540\pi$
$821$			0.400642i			0.0139825i	−0.999976	+	0.00699125i	$0.997775\pi$
$822$		0			0
$823$	3.00912	+	3.00912i	0.104891	+	0.104891i	0.757605	−	0.652713i	$-0.226369\pi$
$823$	3.00912	+	3.00912i	0.104891	+	0.104891i	−0.652713	+	0.757605i	$0.726369\pi$
$824$		0			0
$825$	−23.4421	+	7.06617i	−0.816148	+	0.246012i
$826$		0			0
$827$	18.8781	−	18.8781i	0.656455	−	0.656455i	−0.298085	−	0.954539i	$-0.596348\pi$
$827$	18.8781	−	18.8781i	0.656455	−	0.656455i	0.954539	+	0.298085i	$0.0963478\pi$
$828$		0			0
$829$	16.0434			0.557211			0.278606	−	0.960406i	$-0.410128\pi$
$829$	16.0434			0.557211			0.278606	+	0.960406i	$0.410128\pi$
$830$		0			0
$831$	32.2785			1.11973
$832$		0			0
$833$	−23.3712	−	23.3712i	−0.809763	−	0.809763i
$834$		0			0
$835$	35.9041	−	21.4773i	1.24251	−	0.743252i
$836$		0			0
$837$	−0.684169	+	5.52557i	−0.0236483	+	0.190992i
$838$		0			0
$839$		−	17.6178i		−	0.608234i	−0.952635	−	0.304117i	$-0.901639\pi$
$839$		−	17.6178i		−	0.608234i	0.952635	−	0.304117i	$-0.0983614\pi$
$840$		0			0
$841$	11.0427			0.380783
$842$		0			0
$843$	−15.7773	−	15.7773i	−0.543400	−	0.543400i
$844$		0			0
$845$	4.44719	−	17.6883i	0.152988	−	0.608496i
$846$		0			0
$847$	44.8478	+	44.8478i	1.54099	+	1.54099i
$848$		0			0
$849$	5.69664			0.195508
$850$		0			0
$851$	5.38911			0.184736
$852$		0			0
$853$	2.83296	−	2.83296i	0.0969988	−	0.0969988i	−0.656942	−	0.753941i	$-0.728150\pi$
$853$	2.83296	−	2.83296i	0.0969988	−	0.0969988i	0.753941	+	0.656942i	$0.228150\pi$
$854$		0			0
$855$	−16.8211	−	4.22914i	−0.575268	−	0.144634i
$856$		0			0
$857$	−30.4896	−	30.4896i	−1.04150	−	1.04150i	−0.999101	−	0.0424041i	$-0.986498\pi$
$857$	−30.4896	−	30.4896i	−1.04150	−	1.04150i	−0.0424041	−	0.999101i	$-0.513502\pi$
$858$		0			0
$859$	45.0258			1.53626			0.768131	−	0.640293i	$-0.221187\pi$
$859$	45.0258			1.53626			0.768131	+	0.640293i	$0.221187\pi$
$860$		0			0
$861$			2.68463i			0.0914920i
$862$		0			0
$863$	−6.99688	−	6.99688i	−0.238177	−	0.238177i	0.577918	−	0.816095i	$-0.303865\pi$
$863$	−6.99688	−	6.99688i	−0.238177	−	0.238177i	−0.816095	+	0.577918i	$0.803865\pi$
$864$		0			0
$865$	−14.0371	+	8.39676i	−0.477274	+	0.285498i
$866$		0			0
$867$	−9.31040	+	9.31040i	−0.316198	+	0.316198i
$868$		0			0
$869$			55.8787i			1.89555i
$870$		0			0
$871$		−	0.366845i		−	0.0124301i
$872$		0			0
$873$	7.79226	−	7.79226i	0.263728	−	0.263728i
$874$		0			0
$875$	2.53726	+	54.5783i	0.0857752	+	1.84508i
$876$		0			0
$877$	−16.0767	−	16.0767i	−0.542871	−	0.542871i	0.381498	−	0.924370i	$-0.375408\pi$
$877$	−16.0767	−	16.0767i	−0.542871	−	0.542871i	−0.924370	+	0.381498i	$0.875408\pi$
$878$		0			0
$879$	−21.6061			−0.728756
$880$		0			0
$881$		−	57.7504i		−	1.94566i	−0.231520	−	0.972830i	$-0.574370\pi$
$881$		−	57.7504i		−	1.94566i	0.231520	−	0.972830i	$-0.425630\pi$
$882$		0			0
$883$	26.5193	+	26.5193i	0.892444	+	0.892444i	0.994753	−	0.102309i	$-0.0326230\pi$
$883$	26.5193	+	26.5193i	0.892444	+	0.892444i	−0.102309	+	0.994753i	$0.532623\pi$
$884$		0			0
$885$	−14.2286	+	8.51136i	−0.478290	+	0.286106i
$886$		0			0
$887$	34.8453	+	34.8453i	1.16999	+	1.16999i	0.982211	+	0.187778i	$0.0601286\pi$
$887$	34.8453	+	34.8453i	1.16999	+	1.16999i	0.187778	+	0.982211i	$0.439871\pi$
$888$		0			0
$889$	−39.8462			−1.33640
$890$		0			0
$891$		−	4.89678i		−	0.164048i
$892$		0			0
$893$	18.9810	−	18.9810i	0.635174	−	0.635174i
$894$		0			0
$895$	−31.6335	−	7.95328i	−1.05739	−	0.265849i
$896$		0			0
$897$	11.6258	−	11.6258i	0.388174	−	0.388174i
$898$		0			0
$899$	27.7856	−	21.6630i	0.926702	−	0.722500i
$900$		0			0
$901$	−23.5268			−0.783792
$902$		0			0
$903$	21.9362	−	21.9362i	0.729990	−	0.729990i
$904$		0			0
$905$	−6.25277	+	24.8699i	−0.207849	+	0.826702i
$906$		0			0
$907$	29.5016	+	29.5016i	0.979585	+	0.979585i	0.999796	−	0.0202110i	$-0.00643380\pi$
$907$	29.5016	+	29.5016i	0.979585	+	0.979585i	−0.0202110	+	0.999796i	$0.506434\pi$
$908$		0			0
$909$			17.2863i			0.573351i
$910$		0			0
$911$			38.8492i			1.28713i	0.765391	+	0.643566i	$0.222546\pi$
$911$			38.8492i			1.28713i	−0.765391	+	0.643566i	$0.777454\pi$
$912$		0			0
$913$	−7.50305	+	7.50305i	−0.248315	+	0.248315i
$914$		0			0
$915$	−22.9080	+	13.7032i	−0.757316	+	0.453015i
$916$		0			0
$917$	−38.1170	−	38.1170i	−1.25874	−	1.25874i
$918$		0			0
$919$		−	10.5864i		−	0.349214i	−0.984638	−	0.174607i	$-0.944134\pi$
$919$		−	10.5864i		−	0.349214i	0.984638	−	0.174607i	$-0.0558655\pi$
$920$		0			0
$921$		−	13.3450i		−	0.439734i
$922$		0			0
$923$	41.7529	+	41.7529i	1.37431	+	1.37431i
$924$		0			0
$925$	−7.21753	+	2.17559i	−0.237311	+	0.0715329i
$926$		0			0
$927$	−2.90798	−	2.90798i	−0.0955105	−	0.0955105i
$928$		0			0
$929$	15.4991			0.508508			0.254254	−	0.967138i	$-0.418170\pi$
$929$	15.4991			0.508508			0.254254	+	0.967138i	$0.418170\pi$
$930$		0			0
$931$	130.948			4.29164
$932$		0			0
$933$	19.8527	+	19.8527i	0.649950	+	0.649950i
$934$		0			0
$935$	11.0048	+	18.3971i	0.359897	+	0.601648i
$936$		0			0
$937$	31.0188	+	31.0188i	1.01334	+	1.01334i	0.999910	+	0.0134292i	$0.00427478\pi$
$937$	31.0188	+	31.0188i	1.01334	+	1.01334i	0.0134292	+	0.999910i	$0.495725\pi$
$938$		0			0
$939$		−	9.92214i		−	0.323797i
$940$		0			0
$941$		−	30.1329i		−	0.982306i	−0.871073	−	0.491153i	$-0.836576\pi$
$941$		−	30.1329i		−	0.982306i	0.871073	−	0.491153i	$-0.163424\pi$
$942$		0			0
$943$	1.38851	+	1.38851i	0.0452162	+	0.0452162i
$944$		0			0
$945$	−10.5976	−	2.66446i	−0.344741	−	0.0866747i
$946$		0			0
$947$	8.64543	−	8.64543i	0.280939	−	0.280939i	−0.552545	−	0.833483i	$-0.686343\pi$
$947$	8.64543	−	8.64543i	0.280939	−	0.280939i	0.833483	+	0.552545i	$0.186343\pi$
$948$		0			0
$949$			55.6374i			1.80607i
$950$		0			0
$951$		−	28.3896i		−	0.920595i
$952$		0			0
$953$	−42.9489	−	42.9489i	−1.39125	−	1.39125i	−0.822534	−	0.568716i	$-0.807441\pi$
$953$	−42.9489	−	42.9489i	−1.39125	−	1.39125i	−0.568716	−	0.822534i	$-0.692559\pi$
$954$		0			0
$955$	−17.0326	−	4.28233i	−0.551162	−	0.138573i
$956$		0			0
$957$	−21.9107	+	21.9107i	−0.708274	+	0.708274i
$958$		0			0
$959$	45.1995			1.45957
$960$		0			0
$961$	7.56084	−	30.0638i	0.243898	−	0.969801i
$962$		0			0
$963$	−6.58266	+	6.58266i	−0.212123	+	0.212123i
$964$		0			0
$965$	2.28303	−	1.36567i	0.0734932	−	0.0439625i
$966$		0			0
$967$	15.5563	−	15.5563i	0.500258	−	0.500258i	−0.411260	−	0.911518i	$-0.634911\pi$
$967$	15.5563	−	15.5563i	0.500258	−	0.500258i	0.911518	+	0.411260i	$0.134911\pi$
$968$		0			0
$969$			15.1863i			0.487856i
$970$		0			0
$971$	−27.6524			−0.887408			−0.443704	−	0.896173i	$-0.646336\pi$
$971$	−27.6524			−0.887408			−0.443704	+	0.896173i	$0.646336\pi$
$972$		0			0
$973$	47.9690	+	47.9690i	1.53781	+	1.53781i
$974$		0			0
$975$	−10.8768	+	20.2635i	−0.348338	+	0.648952i
$976$		0			0
$977$	−17.2983	−	17.2983i	−0.553422	−	0.553422i	0.374005	−	0.927427i	$-0.377984\pi$
$977$	−17.2983	−	17.2983i	−0.553422	−	0.553422i	−0.927427	+	0.374005i	$0.877984\pi$
$978$		0			0
$979$		−	64.0836i		−	2.04812i
$980$		0			0
$981$	2.19756			0.0701627
$982$		0			0
$983$	−18.0115	−	18.0115i	−0.574479	−	0.574479i	0.358898	−	0.933377i	$-0.383153\pi$
$983$	−18.0115	−	18.0115i	−0.574479	−	0.574479i	−0.933377	+	0.358898i	$0.883153\pi$
$984$		0			0
$985$	21.1631	−	12.6594i	0.674312	−	0.403363i
$986$		0			0
$987$	11.9584	−	11.9584i	0.380641	−	0.380641i
$988$		0			0
$989$		−	22.6911i		−	0.721535i
$990$		0			0
$991$			26.7453i			0.849593i	0.905289	+	0.424796i	$0.139654\pi$
$991$			26.7453i			0.849593i	−0.905289	+	0.424796i	$0.860346\pi$
$992$		0			0
$993$	−6.69255	+	6.69255i	−0.212382	+	0.212382i
$994$		0			0
$995$	3.46734	+	0.871758i	0.109922	+	0.0276366i
$996$		0			0
$997$	−15.3742	−	15.3742i	−0.486906	−	0.486906i	0.420422	−	0.907328i	$-0.361882\pi$
$997$	−15.3742	−	15.3742i	−0.486906	−	0.486906i	−0.907328	+	0.420422i	$0.861882\pi$
$998$		0			0
$999$		−	1.50766i		−	0.0477002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.2.s.a.1177.32	yes	64
5.3	odd	4	inner	1860.2.s.a.433.11	✓	64
31.30	odd	2	inner	1860.2.s.a.1177.11	yes	64
155.123	even	4	inner	1860.2.s.a.433.32	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.s.a.433.11	✓	64	5.3	odd	4	inner
1860.2.s.a.433.32	yes	64	155.123	even	4	inner
1860.2.s.a.1177.11	yes	64	31.30	odd	2	inner
1860.2.s.a.1177.32	yes	64	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-2.16858 - 0.545223i) q^{5} +(-3.45556 - 3.45556i) q^{7} +1.00000i q^{9} +4.89678i q^{11} +(3.25243 + 3.25243i) q^{13} +(-1.14789 - 1.91895i) q^{15} +(-1.38440 + 1.38440i) q^{17} -7.75672i q^{19} -4.88691i q^{21} +(-2.52755 - 2.52755i) q^{23} +(4.40546 + 2.36472i) q^{25} +(-0.707107 + 0.707107i) q^{27} +6.32793 q^{29} +(4.39095 - 3.42339i) q^{31} +(-3.46254 + 3.46254i) q^{33} +(5.60961 + 9.37772i) q^{35} +(-1.06608 + 1.06608i) q^{37} +4.59963i q^{39} -0.549352 q^{41} +(4.48876 + 4.48876i) q^{43} +(0.545223 - 2.16858i) q^{45} +(2.44703 + 2.44703i) q^{47} +16.8819i q^{49} -1.95783 q^{51} +(8.49714 + 8.49714i) q^{53} +(2.66984 - 10.6190i) q^{55} +(5.48483 - 5.48483i) q^{57} -7.41481i q^{59} -11.9378i q^{61} +(3.45556 - 3.45556i) q^{63} +(-5.27985 - 8.82646i) q^{65} +(-0.0563954 - 0.0563954i) q^{67} -3.57449i q^{69} +12.8374 q^{71} +(8.55320 + 8.55320i) q^{73} +(1.44302 + 4.78724i) q^{75} +(16.9211 - 16.9211i) q^{77} +11.4113 q^{79} -1.00000 q^{81} +(1.53224 + 1.53224i) q^{83} +(3.75697 - 2.24737i) q^{85} +(4.47452 + 4.47452i) q^{87} -13.0869 q^{89} -22.4780i q^{91} +(5.52557 + 0.684169i) q^{93} +(-4.22914 + 16.8211i) q^{95} +(-7.79226 - 7.79226i) q^{97} -4.89678 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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