LMFDB - Embedded newform 1620.2.e.a.971.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(971,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1620.971");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.e (of order $2$, degree $1$, 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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.28
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.a.971.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.478649 + 1.33075i) q^{2} +(-1.54179 + 1.27393i) q^{4} -1.00000i q^{5} -2.36914i q^{7} +(-2.43325 - 1.44197i) q^{8} +O(q^{10})$	\(q+(0.478649 + 1.33075i) q^{2} +(-1.54179 + 1.27393i) q^{4} -1.00000i q^{5} -2.36914i q^{7} +(-2.43325 - 1.44197i) q^{8} +(1.33075 - 0.478649i) q^{10} -3.15463 q^{11} +1.48542 q^{13} +(3.15273 - 1.13399i) q^{14} +(0.754230 - 3.92825i) q^{16} +3.53381i q^{17} +8.30447i q^{19} +(1.27393 + 1.54179i) q^{20} +(-1.50996 - 4.19802i) q^{22} +2.03336 q^{23} -1.00000 q^{25} +(0.710997 + 1.97673i) q^{26} +(3.01811 + 3.65271i) q^{28} -0.315544i q^{29} +6.46028i q^{31} +(5.58853 - 0.876563i) q^{32} +(-4.70262 + 1.69146i) q^{34} -2.36914 q^{35} +7.56172 q^{37} +(-11.0512 + 3.97493i) q^{38} +(-1.44197 + 2.43325i) q^{40} +6.32639i q^{41} +9.58083i q^{43} +(4.86377 - 4.01876i) q^{44} +(0.973268 + 2.70590i) q^{46} +3.63739 q^{47} +1.38718 q^{49} +(-0.478649 - 1.33075i) q^{50} +(-2.29021 + 1.89232i) q^{52} +12.3129i q^{53} +3.15463i q^{55} +(-3.41623 + 5.76471i) q^{56} +(0.419910 - 0.151035i) q^{58} -6.81205 q^{59} +5.64652 q^{61} +(-8.59702 + 3.09221i) q^{62} +(3.84143 + 7.01736i) q^{64} -1.48542i q^{65} -7.60671i q^{67} +(-4.50181 - 5.44839i) q^{68} +(-1.13399 - 3.15273i) q^{70} -5.95154 q^{71} +10.3219 q^{73} +(3.61941 + 10.0628i) q^{74} +(-10.5793 - 12.8038i) q^{76} +7.47375i q^{77} -5.96218i q^{79} +(-3.92825 - 0.754230i) q^{80} +(-8.41885 + 3.02812i) q^{82} -5.34367 q^{83} +3.53381 q^{85} +(-12.7497 + 4.58586i) q^{86} +(7.67600 + 4.54889i) q^{88} +3.28812i q^{89} -3.51918i q^{91} +(-3.13502 + 2.59035i) q^{92} +(1.74103 + 4.84045i) q^{94} +8.30447 q^{95} -2.42098 q^{97} +(0.663972 + 1.84599i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) $ 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.478649	+	1.33075i	0.338456	+	0.940982i
$2$	0.478649	+	1.33075i	0.338456	+	0.940982i
$3$		0			0
$3$		0			0
$4$	−1.54179	+	1.27393i	−0.770895	+	0.636963i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$		−	2.36914i		−	0.895451i	−0.894171	−	0.447725i	$-0.852234\pi$
$7$		−	2.36914i		−	0.895451i	0.894171	−	0.447725i	$-0.147766\pi$
$8$	−2.43325	−	1.44197i	−0.860285	−	0.509814i
$9$		0			0
$10$	1.33075	−	0.478649i	0.420820	−	0.151362i
$11$	−3.15463			−0.951156			−0.475578	−	0.879674i	$-0.657761\pi$
$11$	−3.15463			−0.951156			−0.475578	+	0.879674i	$0.657761\pi$
$12$		0			0
$13$	1.48542			0.411982			0.205991	−	0.978554i	$-0.433958\pi$
$13$	1.48542			0.411982			0.205991	+	0.978554i	$0.433958\pi$
$14$	3.15273	−	1.13399i	0.842603	−	0.303071i
$15$		0			0
$16$	0.754230	−	3.92825i	0.188557	−	0.982062i
$17$			3.53381i			0.857075i	0.903524	+	0.428538i	$0.140971\pi$
$17$			3.53381i			0.857075i	−0.903524	+	0.428538i	$0.859029\pi$
$18$		0			0
$19$			8.30447i			1.90518i	0.304261	+	0.952589i	$0.401590\pi$
$19$			8.30447i			1.90518i	−0.304261	+	0.952589i	$0.598410\pi$
$20$	1.27393	+	1.54179i	0.284858	+	0.344755i
$21$		0			0
$22$	−1.50996	−	4.19802i	−0.321925	−	0.895021i
$23$	2.03336			0.423986			0.211993	−	0.977271i	$-0.432005\pi$
$23$	2.03336			0.423986			0.211993	+	0.977271i	$0.432005\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	0.710997	+	1.97673i	0.139438	+	0.387668i
$27$		0			0
$28$	3.01811	+	3.65271i	0.570369	+	0.690298i
$29$		−	0.315544i		−	0.0585950i	−0.999571	−	0.0292975i	$-0.990673\pi$
$29$		−	0.315544i		−	0.0585950i	0.999571	−	0.0292975i	$-0.00932702\pi$
$30$		0			0
$31$			6.46028i			1.16030i	0.814509	+	0.580150i	$0.197006\pi$
$31$			6.46028i			1.16030i	−0.814509	+	0.580150i	$0.802994\pi$
$32$	5.58853	−	0.876563i	0.987921	−	0.154956i
$33$		0			0
$34$	−4.70262	+	1.69146i	−0.806493	+	0.290083i
$35$	−2.36914			−0.400458
$36$		0			0
$37$	7.56172			1.24314			0.621570	−	0.783359i	$-0.286495\pi$
$37$	7.56172			1.24314			0.621570	+	0.783359i	$0.286495\pi$
$38$	−11.0512	+	3.97493i	−1.79274	+	0.644819i
$39$		0			0
$40$	−1.44197	+	2.43325i	−0.227996	+	0.384731i
$41$			6.32639i			0.988017i	0.869457	+	0.494008i	$0.164469\pi$
$41$			6.32639i			0.988017i	−0.869457	+	0.494008i	$0.835531\pi$
$42$		0			0
$43$			9.58083i			1.46106i	0.682879	+	0.730532i	$0.260728\pi$
$43$			9.58083i			1.46106i	−0.682879	+	0.730532i	$0.739272\pi$
$44$	4.86377	−	4.01876i	0.733241	−	0.605851i
$45$		0			0
$46$	0.973268	+	2.70590i	0.143501	+	0.398963i
$47$	3.63739			0.530568			0.265284	−	0.964170i	$-0.414534\pi$
$47$	3.63739			0.530568			0.265284	+	0.964170i	$0.414534\pi$
$48$		0			0
$49$	1.38718			0.198168
$50$	−0.478649	−	1.33075i	−0.0676912	−	0.188196i
$51$		0			0
$52$	−2.29021	+	1.89232i	−0.317595	+	0.262417i
$53$			12.3129i			1.69131i	0.533732	+	0.845654i	$0.320789\pi$
$53$			12.3129i			1.69131i	−0.533732	+	0.845654i	$0.679211\pi$
$54$		0			0
$55$			3.15463i			0.425370i
$56$	−3.41623	+	5.76471i	−0.456513	+	0.770342i
$57$		0			0
$58$	0.419910	−	0.151035i	0.0551369	−	0.0198319i
$59$	−6.81205			−0.886854			−0.443427	−	0.896311i	$-0.646237\pi$
$59$	−6.81205			−0.886854			−0.443427	+	0.896311i	$0.646237\pi$
$60$		0			0
$61$	5.64652			0.722963			0.361482	−	0.932379i	$-0.382271\pi$
$61$	5.64652			0.722963			0.361482	+	0.932379i	$0.382271\pi$
$62$	−8.59702	+	3.09221i	−1.09182	+	0.392711i
$63$		0			0
$64$	3.84143	+	7.01736i	0.480179	+	0.877171i
$65$		−	1.48542i		−	0.184244i
$66$		0			0
$67$		−	7.60671i		−	0.929307i	−0.885493	−	0.464654i	$-0.846179\pi$
$67$		−	7.60671i		−	0.929307i	0.885493	−	0.464654i	$-0.153821\pi$
$68$	−4.50181	−	5.44839i	−0.545925	−	0.660715i
$69$		0			0
$70$	−1.13399	−	3.15273i	−0.135537	−	0.376824i
$71$	−5.95154			−0.706317			−0.353159	−	0.935563i	$-0.614892\pi$
$71$	−5.95154			−0.706317			−0.353159	+	0.935563i	$0.614892\pi$
$72$		0			0
$73$	10.3219			1.20809			0.604045	−	0.796950i	$-0.293555\pi$
$73$	10.3219			1.20809			0.604045	+	0.796950i	$0.293555\pi$
$74$	3.61941	+	10.0628i	0.420748	+	1.16977i
$75$		0			0
$76$	−10.5793	−	12.8038i	−1.21353	−	1.46869i
$77$			7.47375i			0.851713i
$78$		0			0
$79$		−	5.96218i		−	0.670797i	−0.942076	−	0.335399i	$-0.891129\pi$
$79$		−	5.96218i		−	0.670797i	0.942076	−	0.335399i	$-0.108871\pi$
$80$	−3.92825	−	0.754230i	−0.439192	−	0.0843254i
$81$		0			0
$82$	−8.41885	+	3.02812i	−0.929706	+	0.334400i
$83$	−5.34367			−0.586544			−0.293272	−	0.956029i	$-0.594744\pi$
$83$	−5.34367			−0.586544			−0.293272	+	0.956029i	$0.594744\pi$
$84$		0			0
$85$	3.53381			0.383296
$86$	−12.7497	+	4.58586i	−1.37483	+	0.494506i
$87$		0			0
$88$	7.67600	+	4.54889i	0.818265	+	0.484913i
$89$			3.28812i			0.348540i	0.984698	+	0.174270i	$0.0557566\pi$
$89$			3.28812i			0.348540i	−0.984698	+	0.174270i	$0.944243\pi$
$90$		0			0
$91$		−	3.51918i		−	0.368910i
$92$	−3.13502	+	2.59035i	−0.326848	+	0.270063i
$93$		0			0
$94$	1.74103	+	4.84045i	0.179574	+	0.499255i
$95$	8.30447			0.852021
$96$		0			0
$97$	−2.42098			−0.245813			−0.122907	−	0.992418i	$-0.539222\pi$
$97$	−2.42098			−0.245813			−0.122907	+	0.992418i	$0.539222\pi$
$98$	0.663972	+	1.84599i	0.0670713	+	0.186473i
$99$		0			0
$100$	1.54179	−	1.27393i	0.154179	−	0.127393i
$101$		−	18.2856i		−	1.81948i	−0.415178	−	0.909740i	$-0.636281\pi$
$101$		−	18.2856i		−	1.81948i	0.415178	−	0.909740i	$-0.363719\pi$
$102$		0			0
$103$		−	11.2751i		−	1.11097i	−0.831526	−	0.555485i	$-0.812533\pi$
$103$		−	11.2751i		−	1.11097i	0.831526	−	0.555485i	$-0.187467\pi$
$104$	−3.61441	−	2.14194i	−0.354422	−	0.210034i
$105$		0			0
$106$	−16.3854	+	5.89357i	−1.59149	+	0.572434i
$107$	−15.3721			−1.48607			−0.743036	−	0.669251i	$-0.766615\pi$
$107$	−15.3721			−1.48607			−0.743036	+	0.669251i	$0.766615\pi$
$108$		0			0
$109$	18.6304			1.78447			0.892233	−	0.451575i	$-0.149138\pi$
$109$	18.6304			1.78447			0.892233	+	0.451575i	$0.149138\pi$
$110$	−4.19802	+	1.50996i	−0.400265	+	0.143969i
$111$		0			0
$112$	−9.30657	−	1.78688i	−0.879388	−	0.168844i
$113$			3.23643i			0.304458i	0.988345	+	0.152229i	$0.0486451\pi$
$113$			3.23643i			0.304458i	−0.988345	+	0.152229i	$0.951355\pi$
$114$		0			0
$115$		−	2.03336i		−	0.189612i
$116$	0.401979	+	0.486502i	0.0373228	+	0.0451706i
$117$		0			0
$118$	−3.26059	−	9.06514i	−0.300161	−	0.834514i
$119$	8.37209			0.767469
$120$		0			0
$121$	−1.04832			−0.0953022
$122$	2.70271	+	7.51411i	0.244691	+	0.680296i
$123$		0			0
$124$	−8.22992	−	9.96040i	−0.739068	−	0.894470i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	1.54603i		−	0.137188i	−0.997645	−	0.0685941i	$-0.978149\pi$
$127$		−	1.54603i		−	0.137188i	0.997645	−	0.0685941i	$-0.0218513\pi$
$128$	−7.49966	+	8.47084i	−0.662882	+	0.748724i
$129$		0			0
$130$	1.97673	−	0.710997i	0.173370	−	0.0623586i
$131$	−13.7281			−1.19943			−0.599713	−	0.800215i	$-0.704719\pi$
$131$	−13.7281			−1.19943			−0.599713	+	0.800215i	$0.704719\pi$
$132$		0			0
$133$	19.6745			1.70599
$134$	10.1226	−	3.64095i	0.874461	−	0.314530i
$135$		0			0
$136$	5.09566	−	8.59866i	0.436949	−	0.737329i
$137$		−	11.1943i		−	0.956392i	−0.878253	−	0.478196i	$-0.841291\pi$
$137$		−	11.1943i		−	0.956392i	0.878253	−	0.478196i	$-0.158709\pi$
$138$		0			0
$139$			11.0010i			0.933094i	0.884497	+	0.466547i	$0.154502\pi$
$139$			11.0010i			0.933094i	−0.884497	+	0.466547i	$0.845498\pi$
$140$	3.65271	−	3.01811i	0.308711	−	0.255077i
$141$		0			0
$142$	−2.84870	−	7.92000i	−0.239058	−	0.664632i
$143$	−4.68596			−0.391859
$144$		0			0
$145$	−0.315544			−0.0262045
$146$	4.94059	+	13.7359i	0.408886	+	1.13679i
$147$		0			0
$148$	−11.6586	+	9.63307i	−0.958330	+	0.791833i
$149$			11.2523i			0.921825i	0.887446	+	0.460912i	$0.152478\pi$
$149$			11.2523i			0.921825i	−0.887446	+	0.460912i	$0.847522\pi$
$150$		0			0
$151$			0.943526i			0.0767831i	0.999263	+	0.0383915i	$0.0122234\pi$
$151$			0.943526i			0.0767831i	−0.999263	+	0.0383915i	$0.987777\pi$
$152$	11.9748	−	20.2069i	0.971286	−	1.63899i
$153$		0			0
$154$	−9.94569	+	3.57731i	−0.801447	+	0.288268i
$155$	6.46028			0.518902
$156$		0			0
$157$	−9.76628			−0.779434			−0.389717	−	0.920935i	$-0.627427\pi$
$157$	−9.76628			−0.779434			−0.389717	+	0.920935i	$0.627427\pi$
$158$	7.93416	−	2.85379i	0.631208	−	0.227036i
$159$		0			0
$160$	−0.876563	−	5.58853i	−0.0692984	−	0.441812i
$161$		−	4.81732i		−	0.379658i
$162$		0			0
$163$			18.0212i			1.41153i	0.708444	+	0.705767i	$0.249397\pi$
$163$			18.0212i			1.41153i	−0.708444	+	0.705767i	$0.750603\pi$
$164$	−8.05935	−	9.75397i	−0.629330	−	0.761657i
$165$		0			0
$166$	−2.55774	−	7.11109i	−0.198519	−	0.551927i
$167$	−20.2085			−1.56378			−0.781889	−	0.623418i	$-0.785744\pi$
$167$	−20.2085			−1.56378			−0.781889	+	0.623418i	$0.785744\pi$
$168$		0			0
$169$	−10.7935			−0.830271
$170$	1.69146	+	4.70262i	0.129729	+	0.360674i
$171$		0			0
$172$	−12.2053	−	14.7716i	−0.930642	−	1.12633i
$173$			5.66833i			0.430955i	0.976509	+	0.215478i	$0.0691308\pi$
$173$			5.66833i			0.430955i	−0.976509	+	0.215478i	$0.930869\pi$
$174$		0			0
$175$			2.36914i			0.179090i
$176$	−2.37931	+	12.3922i	−0.179347	+	0.934094i
$177$		0			0
$178$	−4.37566	+	1.57386i	−0.327970	+	0.117966i
$179$	21.7810			1.62799			0.813993	−	0.580874i	$-0.197289\pi$
$179$	21.7810			1.62799			0.813993	+	0.580874i	$0.197289\pi$
$180$		0			0
$181$	−23.5686			−1.75184			−0.875919	−	0.482457i	$-0.839744\pi$
$181$	−23.5686			−1.75184			−0.875919	+	0.482457i	$0.839744\pi$
$182$	4.68314	−	1.68445i	0.347138	−	0.124860i
$183$		0			0
$184$	−4.94769	−	2.93205i	−0.364748	−	0.216154i
$185$		−	7.56172i		−	0.555949i
$186$		0			0
$187$		−	11.1479i		−	0.815212i
$188$	−5.60809	+	4.63376i	−0.409012	+	0.337952i
$189$		0			0
$190$	3.97493	+	11.0512i	0.288372	+	0.801737i
$191$	14.2915			1.03410			0.517049	−	0.855956i	$-0.327030\pi$
$191$	14.2915			1.03410			0.517049	+	0.855956i	$0.327030\pi$
$192$		0			0
$193$	15.6303			1.12509			0.562546	−	0.826766i	$-0.309822\pi$
$193$	15.6303			1.12509			0.562546	+	0.826766i	$0.309822\pi$
$194$	−1.15880	−	3.22172i	−0.0831970	−	0.231306i
$195$		0			0
$196$	−2.13874	+	1.76716i	−0.152767	+	0.126226i
$197$			13.6558i			0.972935i	0.873699	+	0.486468i	$0.161715\pi$
$197$			13.6558i			0.972935i	−0.873699	+	0.486468i	$0.838285\pi$
$198$		0			0
$199$		−	1.10119i		−	0.0780612i	−0.999238	−	0.0390306i	$-0.987573\pi$
$199$		−	1.10119i		−	0.0780612i	0.999238	−	0.0390306i	$-0.0124270\pi$
$200$	2.43325	+	1.44197i	0.172057	+	0.101963i
$201$		0			0
$202$	24.3335	−	8.75237i	1.71210	−	0.615815i
$203$	−0.747568			−0.0524690
$204$		0			0
$205$	6.32639			0.441854
$206$	15.0044	−	5.39683i	1.04540	−	0.376015i
$207$		0			0
$208$	1.12035	−	5.83511i	0.0776823	−	0.404592i
$209$		−	26.1975i		−	1.81212i
$210$		0			0
$211$		−	16.4674i		−	1.13366i	−0.823835	−	0.566830i	$-0.808170\pi$
$211$		−	16.4674i		−	1.13366i	0.823835	−	0.566830i	$-0.191830\pi$
$212$	−15.6857	−	18.9839i	−1.07730	−	1.30382i
$213$		0			0
$214$	−7.35782	−	20.4564i	−0.502970	−	1.39837i
$215$	9.58083			0.653407
$216$		0			0
$217$	15.3053			1.03899
$218$	8.91742	+	24.7924i	0.603964	+	1.67915i
$219$		0			0
$220$	−4.01876	−	4.86377i	−0.270945	−	0.327915i
$221$			5.24921i			0.353100i
$222$		0			0
$223$			20.3784i			1.36464i	0.731054	+	0.682319i	$0.239029\pi$
$223$			20.3784i			1.36464i	−0.731054	+	0.682319i	$0.760971\pi$
$224$	−2.07670	−	13.2400i	−0.138755	−	0.884635i
$225$		0			0
$226$	−4.30688	+	1.54912i	−0.286490	+	0.103046i
$227$	2.31493			0.153648			0.0768238	−	0.997045i	$-0.475522\pi$
$227$	2.31493			0.153648			0.0768238	+	0.997045i	$0.475522\pi$
$228$		0			0
$229$	0.377653			0.0249560			0.0124780	−	0.999922i	$-0.496028\pi$
$229$	0.377653			0.0249560			0.0124780	+	0.999922i	$0.496028\pi$
$230$	2.70590	−	0.973268i	0.178422	−	0.0641754i
$231$		0			0
$232$	−0.455006	+	0.767798i	−0.0298726	+	0.0504084i
$233$			1.15686i			0.0757882i	0.999282	+	0.0378941i	$0.0120649\pi$
$233$			1.15686i			0.0757882i	−0.999282	+	0.0378941i	$0.987935\pi$
$234$		0			0
$235$		−	3.63739i		−	0.237277i
$236$	10.5028	−	8.67805i	0.683671	−	0.564893i
$237$		0			0
$238$	4.00730	+	11.1412i	0.259755	+	0.722174i
$239$	20.8679			1.34983			0.674916	−	0.737895i	$-0.264180\pi$
$239$	20.8679			1.34983			0.674916	+	0.737895i	$0.264180\pi$
$240$		0			0
$241$	0.181836			0.0117131			0.00585654	−	0.999983i	$-0.498136\pi$
$241$	0.181836			0.0117131			0.00585654	+	0.999983i	$0.498136\pi$
$242$	−0.501780	−	1.39506i	−0.0322556	−	0.0896777i
$243$		0			0
$244$	−8.70575	+	7.19325i	−0.557329	+	0.460501i
$245$		−	1.38718i		−	0.0886235i
$246$		0			0
$247$			12.3357i			0.784899i
$248$	9.31555	−	15.7195i	0.591538	−	0.998189i
$249$		0			0
$250$	−1.33075	+	0.478649i	−0.0841640	+	0.0302724i
$251$	15.6805			0.989746			0.494873	−	0.868965i	$-0.335215\pi$
$251$	15.6805			0.989746			0.494873	+	0.868965i	$0.335215\pi$
$252$		0			0
$253$	−6.41451			−0.403277
$254$	2.05738	−	0.740007i	0.129092	−	0.0464322i
$255$		0			0
$256$	−14.8623	−	5.92560i	−0.928892	−	0.370350i
$257$			23.7232i			1.47981i	0.672711	+	0.739905i	$0.265130\pi$
$257$			23.7232i			1.47981i	−0.672711	+	0.739905i	$0.734870\pi$
$258$		0			0
$259$		−	17.9148i		−	1.11317i
$260$	1.89232	+	2.29021i	0.117357	+	0.142033i
$261$		0			0
$262$	−6.57093	−	18.2686i	−0.405953	−	1.12864i
$263$	−2.52352			−0.155607			−0.0778034	−	0.996969i	$-0.524791\pi$
$263$	−2.52352			−0.155607			−0.0778034	+	0.996969i	$0.524791\pi$
$264$		0			0
$265$	12.3129			0.756376
$266$	9.41717	+	26.1818i	0.577404	+	1.60531i
$267$		0			0
$268$	9.69038	+	11.7279i	0.591934	+	0.716398i
$269$			5.37246i			0.327565i	0.986496	+	0.163782i	$0.0523695\pi$
$269$			5.37246i			0.327565i	−0.986496	+	0.163782i	$0.947631\pi$
$270$		0			0
$271$		−	26.6779i		−	1.62057i	−0.586037	−	0.810284i	$-0.699313\pi$
$271$		−	26.6779i		−	1.62057i	0.586037	−	0.810284i	$-0.300687\pi$
$272$	13.8817	+	2.66531i	0.841701	+	0.161608i
$273$		0			0
$274$	14.8968	−	5.35814i	0.899948	−	0.323697i
$275$	3.15463			0.190231
$276$		0			0
$277$	−0.180895			−0.0108689			−0.00543447	−	0.999985i	$-0.501730\pi$
$277$	−0.180895			−0.0108689			−0.00543447	+	0.999985i	$0.501730\pi$
$278$	−14.6396	+	5.26563i	−0.878024	+	0.315811i
$279$		0			0
$280$	5.76471	+	3.41623i	0.344508	+	0.204159i
$281$		−	28.4550i		−	1.69748i	−0.528807	−	0.848742i	$-0.677360\pi$
$281$		−	28.4550i		−	1.69748i	0.528807	−	0.848742i	$-0.322640\pi$
$282$		0			0
$283$			29.1214i			1.73109i	0.500835	+	0.865543i	$0.333026\pi$
$283$			29.1214i			1.73109i	−0.500835	+	0.865543i	$0.666974\pi$
$284$	9.17602	−	7.58181i	0.544496	−	0.449898i
$285$		0			0
$286$	−2.24293	−	6.23584i	−0.132627	−	0.368733i
$287$	14.9881			0.884720
$288$		0			0
$289$	4.51217			0.265422
$290$	−0.151035	−	0.419910i	−0.00886908	−	0.0246580i
$291$		0			0
$292$	−15.9142	+	13.1494i	−0.931311	+	0.769508i
$293$		−	26.4071i		−	1.54272i	−0.636400	−	0.771359i	$-0.719577\pi$
$293$		−	26.4071i		−	1.54272i	0.636400	−	0.771359i	$-0.280423\pi$
$294$		0			0
$295$			6.81205i			0.396613i
$296$	−18.3996	−	10.9038i	−1.06945	−	0.633770i
$297$		0			0
$298$	−14.9740	+	5.38591i	−0.867421	+	0.311997i
$299$	3.02041			0.174675
$300$		0			0
$301$	22.6983			1.30831
$302$	−1.25560	+	0.451618i	−0.0722515	+	0.0259877i
$303$		0			0
$304$	32.6220	+	6.26348i	1.87100	+	0.359235i
$305$		−	5.64652i		−	0.323319i
$306$		0			0
$307$			4.20312i			0.239884i	0.992781	+	0.119942i	$0.0382709\pi$
$307$			4.20312i			0.239884i	−0.992781	+	0.119942i	$0.961729\pi$
$308$	−9.52100	−	11.5230i	−0.542509	−	0.656581i
$309$		0			0
$310$	3.09221	+	8.59702i	0.175626	+	0.488278i
$311$	−18.0189			−1.02176			−0.510878	−	0.859653i	$-0.670680\pi$
$311$	−18.0189			−1.02176			−0.510878	+	0.859653i	$0.670680\pi$
$312$		0			0
$313$	5.70921			0.322704			0.161352	−	0.986897i	$-0.448415\pi$
$313$	5.70921			0.322704			0.161352	+	0.986897i	$0.448415\pi$
$314$	−4.67462	−	12.9965i	−0.263804	−	0.733433i
$315$		0			0
$316$	7.59537	+	9.19242i	0.427273	+	0.517114i
$317$			13.1252i			0.737186i	0.929591	+	0.368593i	$0.120160\pi$
$317$			13.1252i			0.737186i	−0.929591	+	0.368593i	$0.879840\pi$
$318$		0			0
$319$			0.995424i			0.0557330i
$320$	7.01736	−	3.84143i	0.392283	−	0.214743i
$321$		0			0
$322$	6.41065	−	2.30581i	0.357252	−	0.128498i
$323$	−29.3465			−1.63288
$324$		0			0
$325$	−1.48542			−0.0823965
$326$	−23.9818	+	8.62586i	−1.32823	+	0.477742i
$327$		0			0
$328$	9.12248	−	15.3937i	0.503705	−	0.849975i
$329$		−	8.61748i		−	0.475097i
$330$		0			0
$331$			11.1802i			0.614518i	0.951626	+	0.307259i	$0.0994118\pi$
$331$			11.1802i			0.614518i	−0.951626	+	0.307259i	$0.900588\pi$
$332$	8.23881	−	6.80744i	0.452164	−	0.373607i
$333$		0			0
$334$	−9.67277	−	26.8924i	−0.529271	−	1.47149i
$335$	−7.60671			−0.415599
$336$		0			0
$337$	−12.2346			−0.666461			−0.333231	−	0.942845i	$-0.608139\pi$
$337$	−12.2346			−0.666461			−0.333231	+	0.942845i	$0.608139\pi$
$338$	−5.16631	−	14.3635i	−0.281010	−	0.781270i
$339$		0			0
$340$	−5.44839	+	4.50181i	−0.295481	+	0.244145i
$341$		−	20.3798i		−	1.10363i
$342$		0			0
$343$		−	19.8704i		−	1.07290i
$344$	13.8153	−	23.3126i	0.744871	−	1.25693i
$345$		0			0
$346$	−7.54313	+	2.71314i	−0.405521	+	0.145860i
$347$	21.3695			1.14717			0.573587	−	0.819145i	$-0.305552\pi$
$347$	21.3695			1.14717			0.573587	+	0.819145i	$0.305552\pi$
$348$		0			0
$349$	1.80245			0.0964830			0.0482415	−	0.998836i	$-0.484638\pi$
$349$	1.80245			0.0964830			0.0482415	+	0.998836i	$0.484638\pi$
$350$	−3.15273	+	1.13399i	−0.168521	+	0.0606142i
$351$		0			0
$352$	−17.6297	+	2.76523i	−0.939667	+	0.147387i
$353$			13.4061i			0.713535i	0.934193	+	0.356768i	$0.116121\pi$
$353$			13.4061i			0.713535i	−0.934193	+	0.356768i	$0.883879\pi$
$354$		0			0
$355$			5.95154i			0.315875i
$356$	−4.18882	−	5.06959i	−0.222007	−	0.268688i
$357$		0			0
$358$	10.4255	+	28.9850i	0.551002	+	1.53191i
$359$	−34.7904			−1.83617			−0.918084	−	0.396386i	$-0.870264\pi$
$359$	−34.7904			−1.83617			−0.918084	+	0.396386i	$0.870264\pi$
$360$		0			0
$361$	−49.9643			−2.62970
$362$	−11.2811	−	31.3639i	−0.592921	−	1.64845i
$363$		0			0
$364$	4.48317	+	5.42583i	0.234982	+	0.284391i
$365$		−	10.3219i		−	0.540275i
$366$		0			0
$367$			28.0523i			1.46432i	0.681133	+	0.732160i	$0.261488\pi$
$367$			28.0523i			1.46432i	−0.681133	+	0.732160i	$0.738512\pi$
$368$	1.53362	−	7.98756i	0.0799456	−	0.416380i
$369$		0			0
$370$	10.0628	−	3.61941i	0.523138	−	0.188164i
$371$	29.1710			1.51448
$372$		0			0
$373$	0.0675921			0.00349979			0.00174989	−	0.999998i	$-0.499443\pi$
$373$	0.0675921			0.00349979			0.00174989	+	0.999998i	$0.499443\pi$
$374$	14.8350	−	5.33592i	0.767100	−	0.275914i
$375$		0			0
$376$	−8.85069	−	5.24501i	−0.456439	−	0.270491i
$377$		−	0.468716i		−	0.0241401i
$378$		0			0
$379$			5.02345i			0.258037i	0.991642	+	0.129019i	$0.0411827\pi$
$379$			5.02345i			0.258037i	−0.991642	+	0.129019i	$0.958817\pi$
$380$	−12.8038	+	10.5793i	−0.656819	+	0.542706i
$381$		0			0
$382$	6.84063	+	19.0184i	0.349997	+	0.973068i
$383$	27.9197			1.42663			0.713316	−	0.700843i	$-0.247192\pi$
$383$	27.9197			1.42663			0.713316	+	0.700843i	$0.247192\pi$
$384$		0			0
$385$	7.47375			0.380898
$386$	7.48142	+	20.8000i	0.380794	+	1.05869i
$387$		0			0
$388$	3.73264	−	3.08414i	0.189496	−	0.156574i
$389$			20.8700i			1.05815i	0.848576	+	0.529074i	$0.177461\pi$
$389$			20.8700i			1.05815i	−0.848576	+	0.529074i	$0.822539\pi$
$390$		0			0
$391$			7.18553i			0.363388i
$392$	−3.37535	−	2.00027i	−0.170481	−	0.101029i
$393$		0			0
$394$	−18.1725	+	6.53634i	−0.915515	+	0.329296i
$395$	−5.96218			−0.299990
$396$		0			0
$397$	−6.07508			−0.304899			−0.152450	−	0.988311i	$-0.548716\pi$
$397$	−6.07508			−0.304899			−0.152450	+	0.988311i	$0.548716\pi$
$398$	1.46541	−	0.527084i	0.0734542	−	0.0264203i
$399$		0			0
$400$	−0.754230	+	3.92825i	−0.0377115	+	0.196412i
$401$		−	17.0359i		−	0.850731i	−0.905022	−	0.425366i	$-0.860146\pi$
$401$		−	17.0359i		−	0.850731i	0.905022	−	0.425366i	$-0.139854\pi$
$402$		0			0
$403$			9.59625i			0.478024i
$404$	23.2944	+	28.1925i	1.15894	+	1.40263i
$405$		0			0
$406$	−0.357823	−	0.994825i	−0.0177584	−	0.0493724i
$407$	−23.8544			−1.18242
$408$		0			0
$409$	11.5135			0.569306			0.284653	−	0.958631i	$-0.408122\pi$
$409$	11.5135			0.569306			0.284653	+	0.958631i	$0.408122\pi$
$410$	3.02812	+	8.41885i	0.149548	+	0.415777i
$411$		0			0
$412$	14.3637	+	17.3839i	0.707647	+	0.856441i
$413$			16.1387i			0.794134i
$414$		0			0
$415$			5.34367i			0.262310i
$416$	8.30133	−	1.30207i	0.407006	−	0.0638391i
$417$		0			0
$418$	34.8623	−	12.5394i	1.70517	−	0.613324i
$419$	−11.3706			−0.555488			−0.277744	−	0.960655i	$-0.589587\pi$
$419$	−11.3706			−0.555488			−0.277744	+	0.960655i	$0.589587\pi$
$420$		0			0
$421$	32.9752			1.60711			0.803556	−	0.595229i	$-0.202939\pi$
$421$	32.9752			1.60711			0.803556	+	0.595229i	$0.202939\pi$
$422$	21.9139	−	7.88209i	1.06675	−	0.383694i
$423$		0			0
$424$	17.7549	−	29.9604i	0.862253	−	1.45501i
$425$		−	3.53381i		−	0.171415i
$426$		0			0
$427$		−	13.3774i		−	0.647378i
$428$	23.7005	−	19.5828i	1.14561	−	0.946572i
$429$		0			0
$430$	4.58586	+	12.7497i	0.221150	+	0.614845i
$431$	22.1229			1.06562			0.532811	−	0.846234i	$-0.321136\pi$
$431$	22.1229			1.06562			0.532811	+	0.846234i	$0.321136\pi$
$432$		0			0
$433$	32.6530			1.56921			0.784603	−	0.619999i	$-0.212867\pi$
$433$	32.6530			1.56921			0.784603	+	0.619999i	$0.212867\pi$
$434$	7.32588	+	20.3675i	0.351653	+	0.977673i
$435$		0			0
$436$	−28.7241	+	23.7337i	−1.37564	+	1.13664i
$437$			16.8860i			0.807768i
$438$		0			0
$439$		−	2.33537i		−	0.111461i	−0.998446	−	0.0557307i	$-0.982251\pi$
$439$		−	2.33537i		−	0.111461i	0.998446	−	0.0557307i	$-0.0177488\pi$
$440$	4.54889	−	7.67600i	0.216860	−	0.365939i
$441$		0			0
$442$	−6.98538	+	2.51253i	−0.332261	+	0.119509i
$443$	−26.3999			−1.25430			−0.627148	−	0.778900i	$-0.715778\pi$
$443$	−26.3999			−1.25430			−0.627148	+	0.778900i	$0.715778\pi$
$444$		0			0
$445$	3.28812			0.155872
$446$	−27.1186	+	9.75411i	−1.28410	+	0.461871i
$447$		0			0
$448$	16.6251	−	9.10089i	0.785463	−	0.429977i
$449$		−	14.8990i		−	0.703129i	−0.936164	−	0.351565i	$-0.885650\pi$
$449$		−	14.8990i		−	0.703129i	0.936164	−	0.351565i	$-0.114350\pi$
$450$		0			0
$451$		−	19.9574i		−	0.939758i
$452$	−4.12297	−	4.98990i	−0.193928	−	0.234705i
$453$		0			0
$454$	1.10804	+	3.08060i	0.0520030	+	0.144580i
$455$	−3.51918			−0.164981
$456$		0			0
$457$	−30.6917			−1.43570			−0.717848	−	0.696200i	$-0.754873\pi$
$457$	−30.6917			−1.43570			−0.717848	+	0.696200i	$0.754873\pi$
$458$	0.180763	+	0.502562i	0.00844652	+	0.0234832i
$459$		0			0
$460$	2.59035	+	3.13502i	0.120776	+	0.146171i
$461$			9.50819i			0.442841i	0.975178	+	0.221420i	$0.0710693\pi$
$461$			9.50819i			0.442841i	−0.975178	+	0.221420i	$0.928931\pi$
$462$		0			0
$463$		−	0.500514i		−	0.0232609i	−0.999932	−	0.0116304i	$-0.996298\pi$
$463$		−	0.500514i		−	0.0232609i	0.999932	−	0.0116304i	$-0.00370217\pi$
$464$	−1.23954	−	0.237993i	−0.0575440	−	0.0110485i
$465$		0			0
$466$	−1.53949	+	0.553729i	−0.0713153	+	0.0256510i
$467$	9.26967			0.428949			0.214475	−	0.976730i	$-0.431196\pi$
$467$	9.26967			0.428949			0.214475	+	0.976730i	$0.431196\pi$
$468$		0			0
$469$	−18.0214			−0.832149
$470$	4.84045	−	1.74103i	0.223274	−	0.0803079i
$471$		0			0
$472$	16.5754	+	9.82279i	0.762947	+	0.452131i
$473$		−	30.2240i		−	1.38970i
$474$		0			0
$475$		−	8.30447i		−	0.381035i
$476$	−12.9080	+	10.6654i	−0.591638	+	0.488849i
$477$		0			0
$478$	9.98841	+	27.7699i	0.456859	+	1.27017i
$479$	−9.92660			−0.453558			−0.226779	−	0.973946i	$-0.572820\pi$
$479$	−9.92660			−0.453558			−0.226779	+	0.973946i	$0.572820\pi$
$480$		0			0
$481$	11.2324			0.512151
$482$	0.0870357	+	0.241978i	0.00396437	+	0.0110218i
$483$		0			0
$484$	1.61630	−	1.33549i	0.0734680	−	0.0607039i
$485$			2.42098i			0.109931i
$486$		0			0
$487$			26.9101i			1.21941i	0.792627	+	0.609706i	$0.208713\pi$
$487$			26.9101i			1.21941i	−0.792627	+	0.609706i	$0.791287\pi$
$488$	−13.7394	−	8.14213i	−0.621954	−	0.368577i
$489$		0			0
$490$	1.84599	−	0.663972i	0.0833932	−	0.0299952i
$491$	37.4663			1.69083			0.845416	−	0.534108i	$-0.179352\pi$
$491$	37.4663			1.69083			0.845416	+	0.534108i	$0.179352\pi$
$492$		0			0
$493$	1.11507			0.0502204
$494$	−16.4157	+	5.90446i	−0.738576	+	0.265654i
$495$		0			0
$496$	25.3776	+	4.87254i	1.13949	+	0.218783i
$497$			14.1000i			0.632472i
$498$		0			0
$499$		−	38.3596i		−	1.71721i	−0.512637	−	0.858605i	$-0.671331\pi$
$499$		−	38.3596i		−	1.71721i	0.512637	−	0.858605i	$-0.328669\pi$
$500$	−1.27393	−	1.54179i	−0.0569717	−	0.0689509i
$501$		0			0
$502$	7.50548	+	20.8669i	0.334986	+	0.931333i
$503$	8.67550			0.386821			0.193411	−	0.981118i	$-0.438045\pi$
$503$	8.67550			0.386821			0.193411	+	0.981118i	$0.438045\pi$
$504$		0			0
$505$	−18.2856			−0.813696
$506$	−3.07030	−	8.53610i	−0.136491	−	0.379476i
$507$		0			0
$508$	1.96953	+	2.38366i	0.0873837	+	0.105758i
$509$			3.60986i			0.160004i	0.996795	+	0.0800020i	$0.0254927\pi$
$509$			3.60986i			0.160004i	−0.996795	+	0.0800020i	$0.974507\pi$
$510$		0			0
$511$		−	24.4541i		−	1.08179i
$512$	0.771674	−	22.6143i	0.0341035	−	0.999418i
$513$		0			0
$514$	−31.5696	+	11.3551i	−1.39247	+	0.500851i
$515$	−11.2751			−0.496841
$516$		0			0
$517$	−11.4746			−0.504653
$518$	23.8401	−	8.57490i	1.04747	−	0.376759i
$519$		0			0
$520$	−2.14194	+	3.61441i	−0.0939303	+	0.158502i
$521$		−	41.7010i		−	1.82696i	−0.406889	−	0.913478i	$-0.633386\pi$
$521$		−	41.7010i		−	1.82696i	0.406889	−	0.913478i	$-0.366614\pi$
$522$		0			0
$523$		−	23.4977i		−	1.02748i	−0.857946	−	0.513740i	$-0.828259\pi$
$523$		−	23.4977i		−	1.02748i	0.857946	−	0.513740i	$-0.171741\pi$
$524$	21.1658	−	17.4885i	0.924631	−	0.763990i
$525$		0			0
$526$	−1.20788	−	3.35817i	−0.0526661	−	0.146423i
$527$	−22.8294			−0.994465
$528$		0			0
$529$	−18.8654			−0.820236
$530$	5.89357	+	16.3854i	0.256000	+	0.711736i
$531$		0			0
$532$	−30.3339	+	25.0638i	−1.31514	+	1.08665i
$533$			9.39737i			0.407045i
$534$		0			0
$535$			15.3721i			0.664592i
$536$	−10.9687	+	18.5090i	−0.473774	+	0.799469i
$537$		0			0
$538$	−7.14940	+	2.57152i	−0.308233	+	0.110866i
$539$	−4.37603			−0.188489
$540$		0			0
$541$	−32.2001			−1.38439			−0.692196	−	0.721709i	$-0.743357\pi$
$541$	−32.2001			−1.38439			−0.692196	+	0.721709i	$0.743357\pi$
$542$	35.5016	−	12.7694i	1.52493	−	0.548491i
$543$		0			0
$544$	3.09761	+	19.7488i	0.132809	+	0.846723i
$545$		−	18.6304i		−	0.798038i
$546$		0			0
$547$		−	7.52052i		−	0.321554i	−0.986991	−	0.160777i	$-0.948600\pi$
$547$		−	7.52052i		−	0.321554i	0.986991	−	0.160777i	$-0.0514000\pi$
$548$	14.2607	+	17.2592i	0.609186	+	0.737277i
$549$		0			0
$550$	1.50996	+	4.19802i	0.0643849	+	0.179004i
$551$	2.62043			0.111634
$552$		0			0
$553$	−14.1252			−0.600666
$554$	−0.0865854	−	0.240726i	−0.00367866	−	0.0102275i
$555$		0			0
$556$	−14.0145	−	16.9612i	−0.594346	−	0.719317i
$557$		−	15.6594i		−	0.663510i	−0.943366	−	0.331755i	$-0.892359\pi$
$557$		−	15.6594i		−	0.663510i	0.943366	−	0.331755i	$-0.107641\pi$
$558$		0			0
$559$			14.2316i			0.601932i
$560$	−1.78688	+	9.30657i	−0.0755093	+	0.393274i
$561$		0			0
$562$	37.8665	−	13.6200i	1.59730	−	0.574524i
$563$	32.8848			1.38593			0.692964	−	0.720972i	$-0.256304\pi$
$563$	32.8848			1.38593			0.692964	+	0.720972i	$0.256304\pi$
$564$		0			0
$565$	3.23643			0.136158
$566$	−38.7533	+	13.9389i	−1.62892	+	0.585897i
$567$		0			0
$568$	14.4816	+	8.58195i	0.607634	+	0.360091i
$569$			29.5509i			1.23884i	0.785061	+	0.619418i	$0.212631\pi$
$569$			29.5509i			1.23884i	−0.785061	+	0.619418i	$0.787369\pi$
$570$		0			0
$571$			7.85568i			0.328750i	0.986398	+	0.164375i	$0.0525607\pi$
$571$			7.85568i			0.328750i	−0.986398	+	0.164375i	$0.947439\pi$
$572$	7.22476	−	5.96956i	0.302082	−	0.249600i
$573$		0			0
$574$	7.17405	+	19.9454i	0.299439	+	0.832506i
$575$	−2.03336			−0.0847971
$576$		0			0
$577$	47.4804			1.97663			0.988317	−	0.152411i	$-0.0487037\pi$
$577$	47.4804			1.97663			0.988317	+	0.152411i	$0.0487037\pi$
$578$	2.15975	+	6.00457i	0.0898336	+	0.249757i
$579$		0			0
$580$	0.486502	−	0.401979i	0.0202009	−	0.0166913i
$581$			12.6599i			0.525221i
$582$		0			0
$583$		−	38.8426i		−	1.60870i
$584$	−25.1159	−	14.8839i	−1.03930	−	0.615902i
$585$		0			0
$586$	35.1412	−	12.6397i	1.45167	−	0.522143i
$587$	20.4641			0.844646			0.422323	−	0.906445i	$-0.361215\pi$
$587$	20.4641			0.844646			0.422323	+	0.906445i	$0.361215\pi$
$588$		0			0
$589$	−53.6493			−2.21058
$590$	−9.06514	+	3.26059i	−0.373206	+	0.134236i
$591$		0			0
$592$	5.70327	−	29.7043i	0.234403	−	1.22084i
$593$		−	5.44069i		−	0.223422i	−0.993741	−	0.111711i	$-0.964367\pi$
$593$		−	5.44069i		−	0.223422i	0.993741	−	0.111711i	$-0.0356332\pi$
$594$		0			0
$595$		−	8.37209i		−	0.343222i
$596$	−14.3346	−	17.3487i	−0.587168	−	0.710630i
$597$		0			0
$598$	1.44572	+	4.01940i	0.0591197	+	0.164366i
$599$	12.3889			0.506197			0.253098	−	0.967441i	$-0.418550\pi$
$599$	12.3889			0.506197			0.253098	+	0.967441i	$0.418550\pi$
$600$		0			0
$601$	−47.5475			−1.93950			−0.969751	−	0.244096i	$-0.921509\pi$
$601$	−47.5475			−1.93950			−0.969751	+	0.244096i	$0.921509\pi$
$602$	10.8645	+	30.2058i	0.442806	+	1.23110i
$603$		0			0
$604$	−1.20198	−	1.45472i	−0.0489079	−	0.0591917i
$605$			1.04832i			0.0426204i
$606$		0			0
$607$		−	17.9444i		−	0.728339i	−0.931333	−	0.364170i	$-0.881353\pi$
$607$		−	17.9444i		−	0.728339i	0.931333	−	0.364170i	$-0.118647\pi$
$608$	7.27940	+	46.4098i	0.295219	+	1.88217i
$609$		0			0
$610$	7.51411	−	2.70271i	0.304237	−	0.109429i
$611$	5.40306			0.218585
$612$		0			0
$613$	−17.3002			−0.698748			−0.349374	−	0.936983i	$-0.613606\pi$
$613$	−17.3002			−0.698748			−0.349374	+	0.936983i	$0.613606\pi$
$614$	−5.59329	+	2.01182i	−0.225727	+	0.0811904i
$615$		0			0
$616$	10.7769	−	18.1855i	0.434216	−	0.732716i
$617$		−	12.5470i		−	0.505122i	−0.967581	−	0.252561i	$-0.918727\pi$
$617$		−	12.5470i		−	0.505122i	0.967581	−	0.252561i	$-0.0812728\pi$
$618$		0			0
$619$			27.1772i			1.09234i	0.837673	+	0.546172i	$0.183916\pi$
$619$			27.1772i			1.09234i	−0.837673	+	0.546172i	$0.816084\pi$
$620$	−9.96040	+	8.22992i	−0.400019	+	0.330521i
$621$		0			0
$622$	−8.62472	−	23.9786i	−0.345820	−	0.961454i
$623$	7.79002			0.312100
$624$		0			0
$625$	1.00000			0.0400000
$626$	2.73271	+	7.59753i	0.109221	+	0.303658i
$627$		0			0
$628$	15.0575	−	12.4415i	0.600861	−	0.496470i
$629$			26.7217i			1.06546i
$630$		0			0
$631$		−	5.25157i		−	0.209062i	−0.994522	−	0.104531i	$-0.966666\pi$
$631$		−	5.25157i		−	0.209062i	0.994522	−	0.104531i	$-0.0333341\pi$
$632$	−8.59729	+	14.5075i	−0.341982	+	0.577076i
$633$		0			0
$634$	−17.4664	+	6.28238i	−0.693679	+	0.249505i
$635$	−1.54603			−0.0613524
$636$		0			0
$637$	2.06055			0.0816418
$638$	−1.32466	+	0.476459i	−0.0524438	+	0.0188632i
$639$		0			0
$640$	8.47084	+	7.49966i	0.334839	+	0.296450i
$641$		−	22.8806i		−	0.903728i	−0.892087	−	0.451864i	$-0.850759\pi$
$641$		−	22.8806i		−	0.903728i	0.892087	−	0.451864i	$-0.149241\pi$
$642$		0			0
$643$			31.3970i			1.23818i	0.785321	+	0.619089i	$0.212498\pi$
$643$			31.3970i			1.23818i	−0.785321	+	0.619089i	$0.787502\pi$
$644$	6.13691	+	7.42730i	0.241828	+	0.292677i
$645$		0			0
$646$	−14.0467	−	39.0528i	−0.552659	−	1.53651i
$647$	27.4398			1.07877			0.539385	−	0.842059i	$-0.318657\pi$
$647$	27.4398			1.07877			0.539385	+	0.842059i	$0.318657\pi$
$648$		0			0
$649$	21.4895			0.843536
$650$	−0.710997	−	1.97673i	−0.0278876	−	0.0775336i
$651$		0			0
$652$	−22.9577	−	27.7850i	−0.899094	−	1.08814i
$653$			0.667266i			0.0261121i	0.999915	+	0.0130561i	$0.00415599\pi$
$653$			0.667266i			0.0261121i	−0.999915	+	0.0130561i	$0.995844\pi$
$654$		0			0
$655$			13.7281i			0.536400i
$656$	24.8516	+	4.77155i	0.970294	+	0.186298i
$657$		0			0
$658$	11.4677	−	4.12475i	0.447058	−	0.160800i
$659$	11.4489			0.445985			0.222993	−	0.974820i	$-0.428417\pi$
$659$	11.4489			0.445985			0.222993	+	0.974820i	$0.428417\pi$
$660$		0			0
$661$	−13.4904			−0.524716			−0.262358	−	0.964971i	$-0.584500\pi$
$661$	−13.4904			−0.524716			−0.262358	+	0.964971i	$0.584500\pi$
$662$	−14.8780	+	5.35138i	−0.578251	+	0.207987i
$663$		0			0
$664$	13.0025	+	7.70542i	0.504595	+	0.299028i
$665$		−	19.6745i		−	0.762943i
$666$		0			0
$667$		−	0.641616i		−	0.0248435i
$668$	31.1572	−	25.7441i	1.20551	−	0.996068i
$669$		0			0
$670$	−3.64095	−	10.1226i	−0.140662	−	0.391071i
$671$	−17.8127			−0.687651
$672$		0			0
$673$	−14.3425			−0.552862			−0.276431	−	0.961034i	$-0.589152\pi$
$673$	−14.3425			−0.552862			−0.276431	+	0.961034i	$0.589152\pi$
$674$	−5.85609	−	16.2812i	−0.225568	−	0.627128i
$675$		0			0
$676$	16.6413	−	13.7501i	0.640051	−	0.528851i
$677$			44.9951i			1.72930i	0.502374	+	0.864651i	$0.332460\pi$
$677$			44.9951i			1.72930i	−0.502374	+	0.864651i	$0.667540\pi$
$678$		0			0
$679$			5.73563i			0.220113i
$680$	−8.59866	−	5.09566i	−0.329743	−	0.195410i
$681$		0			0
$682$	27.1204	−	9.75477i	1.03849	−	0.373530i
$683$	7.31143			0.279764			0.139882	−	0.990168i	$-0.455328\pi$
$683$	7.31143			0.279764			0.139882	+	0.990168i	$0.455328\pi$
$684$		0			0
$685$	−11.1943			−0.427711
$686$	26.4425	−	9.51095i	1.00958	−	0.363130i
$687$		0			0
$688$	37.6359	+	7.22615i	1.43485	+	0.275494i
$689$			18.2899i			0.696789i
$690$		0			0
$691$			22.3660i			0.850842i	0.904996	+	0.425421i	$0.139874\pi$
$691$			22.3660i			0.850842i	−0.904996	+	0.425421i	$0.860126\pi$
$692$	−7.22103	−	8.73937i	−0.274502	−	0.332221i
$693$		0			0
$694$	10.2285	+	28.4374i	0.388268	+	1.07947i
$695$	11.0010			0.417292
$696$		0			0
$697$	−22.3563			−0.846805
$698$	0.862742	+	2.39861i	0.0326553	+	0.0907888i
$699$		0			0
$700$	−3.01811	−	3.65271i	−0.114074	−	0.138060i
$701$		−	15.5381i		−	0.586865i	−0.955980	−	0.293433i	$-0.905202\pi$
$701$		−	15.5381i		−	0.586865i	0.955980	−	0.293433i	$-0.0947976\pi$
$702$		0			0
$703$			62.7961i			2.36840i
$704$	−12.1183	−	22.1372i	−0.456725	−	0.834326i
$705$		0			0
$706$	−17.8402	+	6.41683i	−0.671424	+	0.241500i
$707$	−43.3210			−1.62925
$708$		0			0
$709$	4.65057			0.174656			0.0873279	−	0.996180i	$-0.472167\pi$
$709$	4.65057			0.174656			0.0873279	+	0.996180i	$0.472167\pi$
$710$	−7.92000	+	2.84870i	−0.297232	+	0.106910i
$711$		0			0
$712$	4.74138	−	8.00083i	0.177691	−	0.299844i
$713$			13.1361i			0.491951i
$714$		0			0
$715$			4.68596i			0.175245i
$716$	−33.5817	+	27.7473i	−1.25501	+	1.03697i
$717$		0			0
$718$	−16.6524	−	46.2973i	−0.621462	−	1.72780i
$719$	9.56589			0.356747			0.178374	−	0.983963i	$-0.442916\pi$
$719$	9.56589			0.356747			0.178374	+	0.983963i	$0.442916\pi$
$720$		0			0
$721$	−26.7123			−0.994819
$722$	−23.9154	−	66.4900i	−0.890038	−	2.47450i
$723$		0			0
$724$	36.3378	−	30.0246i	1.35048	−	1.11586i
$725$			0.315544i			0.0117190i
$726$		0			0
$727$		−	46.1516i		−	1.71167i	−0.517250	−	0.855834i	$-0.673044\pi$
$727$		−	46.1516i		−	1.71167i	0.517250	−	0.855834i	$-0.326956\pi$
$728$	−5.07455	+	8.56304i	−0.188075	+	0.317367i
$729$		0			0
$730$	13.7359	−	4.94059i	0.508389	−	0.182859i
$731$	−33.8569			−1.25224
$732$		0			0
$733$	−8.52019			−0.314701			−0.157350	−	0.987543i	$-0.550295\pi$
$733$	−8.52019			−0.314701			−0.157350	+	0.987543i	$0.550295\pi$
$734$	−37.3306	+	13.4272i	−1.37790	+	0.495608i
$735$		0			0
$736$	11.3635	−	1.78237i	0.418865	−	0.0656991i
$737$			23.9963i			0.883916i
$738$		0			0
$739$		−	48.7789i		−	1.79436i	−0.441663	−	0.897181i	$-0.645611\pi$
$739$		−	48.7789i		−	1.79436i	0.441663	−	0.897181i	$-0.354389\pi$
$740$	9.63307	+	11.6586i	0.354119	+	0.428578i
$741$		0			0
$742$	13.9627	+	38.8193i	0.512586	+	1.42510i
$743$	−40.8081			−1.49710			−0.748552	−	0.663076i	$-0.769251\pi$
$743$	−40.8081			−1.49710			−0.748552	+	0.663076i	$0.769251\pi$
$744$		0			0
$745$	11.2523			0.412253
$746$	0.0323529	+	0.0899482i	0.00118453	+	0.00329324i
$747$		0			0
$748$	14.2015	+	17.1877i	0.519260	+	0.628443i
$749$			36.4185i			1.33070i
$750$		0			0
$751$		−	29.1059i		−	1.06209i	−0.847343	−	0.531045i	$-0.821799\pi$
$751$		−	29.1059i		−	1.06209i	0.847343	−	0.531045i	$-0.178201\pi$
$752$	2.74343	−	14.2886i	0.100042	−	0.521051i
$753$		0			0
$754$	0.623744	−	0.224351i	0.0227154	−	0.00817037i
$755$	0.943526			0.0343384
$756$		0			0
$757$	25.9592			0.943501			0.471751	−	0.881732i	$-0.343622\pi$
$757$	25.9592			0.943501			0.471751	+	0.881732i	$0.343622\pi$
$758$	−6.68496	+	2.40447i	−0.242809	+	0.0873344i
$759$		0			0
$760$	−20.2069	−	11.9748i	−0.732981	−	0.434372i
$761$		−	44.9146i		−	1.62815i	−0.580758	−	0.814076i	$-0.697244\pi$
$761$		−	44.9146i		−	1.62815i	0.580758	−	0.814076i	$-0.302756\pi$
$762$		0			0
$763$		−	44.1380i		−	1.59790i
$764$	−22.0345	+	18.2063i	−0.797181	+	0.658682i
$765$		0			0
$766$	13.3638	+	37.1542i	0.482852	+	1.34244i
$767$	−10.1188			−0.365368
$768$		0			0
$769$	−33.1302			−1.19471			−0.597353	−	0.801978i	$-0.703781\pi$
$769$	−33.1302			−1.19471			−0.597353	+	0.801978i	$0.703781\pi$
$770$	3.57731	+	9.94569i	0.128917	+	0.358418i
$771$		0			0
$772$	−24.0986	+	19.9118i	−0.867328	+	0.716642i
$773$		−	7.20425i		−	0.259119i	−0.991572	−	0.129559i	$-0.958644\pi$
$773$		−	7.20425i		−	0.259119i	0.991572	−	0.129559i	$-0.0413563\pi$
$774$		0			0
$775$		−	6.46028i		−	0.232060i
$776$	5.89085	+	3.49098i	0.211469	+	0.125319i
$777$		0			0
$778$	−27.7727	+	9.98939i	−0.995699	+	0.358137i
$779$	−52.5374			−1.88235
$780$		0			0
$781$	18.7749			0.671818
$782$	−9.56214	+	3.43935i	−0.341941	+	0.122991i
$783$		0			0
$784$	1.04625	−	5.44918i	0.0373661	−	0.194614i
$785$			9.76628i			0.348573i
$786$		0			0
$787$		−	33.0244i		−	1.17719i	−0.808428	−	0.588596i	$-0.799681\pi$
$787$		−	33.0244i		−	1.17719i	0.808428	−	0.588596i	$-0.200319\pi$
$788$	−17.3965	−	21.0544i	−0.619723	−	0.750031i
$789$		0			0
$790$	−2.85379	−	7.93416i	−0.101533	−	0.282285i
$791$	7.66756			0.272627
$792$		0			0
$793$	8.38748			0.297848
$794$	−2.90783	−	8.08441i	−0.103195	−	0.286905i
$795$		0			0
$796$	1.40283	+	1.69780i	0.0497221	+	0.0601770i
$797$			34.6664i			1.22795i	0.789327	+	0.613973i	$0.210430\pi$
$797$			34.6664i			1.22795i	−0.789327	+	0.613973i	$0.789570\pi$
$798$		0			0
$799$			12.8539i			0.454737i
$800$	−5.58853	+	0.876563i	−0.197584	+	0.0309912i
$801$		0			0
$802$	22.6705	−	8.15421i	0.800523	−	0.287935i
$803$	−32.5618			−1.14908
$804$		0			0
$805$	−4.81732			−0.169788
$806$	−12.7702	+	4.59324i	−0.449812	+	0.161790i
$807$		0			0
$808$	−26.3673	+	44.4934i	−0.927597	+	1.56527i
$809$		−	13.9551i		−	0.490636i	−0.969443	−	0.245318i	$-0.921108\pi$
$809$		−	13.9551i		−	0.490636i	0.969443	−	0.245318i	$-0.0788924\pi$
$810$		0			0
$811$			20.3355i			0.714075i	0.934090	+	0.357038i	$0.116213\pi$
$811$			20.3355i			0.714075i	−0.934090	+	0.357038i	$0.883787\pi$
$812$	1.15259	−	0.952345i	0.0404480	−	0.0334208i
$813$		0			0
$814$	−11.4179	−	31.7443i	−0.400197	−	1.11264i
$815$	18.0212			0.631257
$816$		0			0
$817$	−79.5638			−2.78358
$818$	5.51093	+	15.3216i	0.192685	+	0.535707i
$819$		0			0
$820$	−9.75397	+	8.05935i	−0.340623	+	0.281445i
$821$		−	13.6503i		−	0.476400i	−0.971216	−	0.238200i	$-0.923443\pi$
$821$		−	13.6503i		−	0.476400i	0.971216	−	0.238200i	$-0.0765574\pi$
$822$		0			0
$823$		−	37.6521i		−	1.31247i	−0.754557	−	0.656234i	$-0.772148\pi$
$823$		−	37.6521i		−	1.31247i	0.754557	−	0.656234i	$-0.227852\pi$
$824$	−16.2584	+	27.4352i	−0.566388	+	0.955751i
$825$		0			0
$826$	−21.4766	+	7.72478i	−0.747266	+	0.268780i
$827$	−18.4787			−0.642569			−0.321285	−	0.946983i	$-0.604115\pi$
$827$	−18.4787			−0.642569			−0.321285	+	0.946983i	$0.604115\pi$
$828$		0			0
$829$	1.18064			0.0410052			0.0205026	−	0.999790i	$-0.493473\pi$
$829$	1.18064			0.0410052			0.0205026	+	0.999790i	$0.493473\pi$
$830$	−7.11109	+	2.55774i	−0.246829	+	0.0887806i
$831$		0			0
$832$	5.70615	+	10.4238i	0.197825	+	0.361379i
$833$			4.90203i			0.169845i
$834$		0			0
$835$			20.2085i			0.699343i
$836$	33.3737	+	40.3911i	1.15425	+	1.39695i
$837$		0			0
$838$	−5.44251	−	15.1314i	−0.188009	−	0.522705i
$839$	−39.3261			−1.35769			−0.678843	−	0.734283i	$-0.737518\pi$
$839$	−39.3261			−1.35769			−0.678843	+	0.734283i	$0.737518\pi$
$840$		0			0
$841$	28.9004			0.996567
$842$	15.7836	+	43.8817i	0.543937	+	1.51226i
$843$		0			0
$844$	20.9782	+	25.3892i	0.722099	+	0.873933i
$845$			10.7935i			0.371308i
$846$		0			0
$847$			2.48363i			0.0853384i
$848$	48.3682	+	9.28676i	1.66097	+	0.318909i
$849$		0			0
$850$	4.70262	−	1.69146i	0.161299	−	0.0580165i
$851$	15.3757			0.527073
$852$		0			0
$853$	−11.0443			−0.378148			−0.189074	−	0.981963i	$-0.560549\pi$
$853$	−11.0443			−0.378148			−0.189074	+	0.981963i	$0.560549\pi$
$854$	17.8020	−	6.40309i	0.609171	−	0.219109i
$855$		0			0
$856$	37.4041	+	22.1661i	1.27844	+	0.757621i
$857$			13.3618i			0.456429i	0.973611	+	0.228214i	$0.0732887\pi$
$857$			13.3618i			0.456429i	−0.973611	+	0.228214i	$0.926711\pi$
$858$		0			0
$859$		−	10.2714i		−	0.350456i	−0.984528	−	0.175228i	$-0.943934\pi$
$859$		−	10.2714i		−	0.350456i	0.984528	−	0.175228i	$-0.0560663\pi$
$860$	−14.7716	+	12.2053i	−0.503708	+	0.416196i
$861$		0			0
$862$	10.5891	+	29.4400i	0.360666	+	1.00273i
$863$	3.91660			0.133323			0.0666614	−	0.997776i	$-0.478765\pi$
$863$	3.91660			0.133323			0.0666614	+	0.997776i	$0.478765\pi$
$864$		0			0
$865$	5.66833			0.192729
$866$	15.6294	+	43.4530i	0.531107	+	1.47659i
$867$		0			0
$868$	−23.5976	+	19.4978i	−0.800954	+	0.661799i
$869$			18.8084i			0.638033i
$870$		0			0
$871$		−	11.2992i		−	0.382858i
$872$	−45.3324	−	26.8645i	−1.53515	−	0.909746i
$873$		0			0
$874$	−22.4711	+	8.08248i	−0.760095	+	0.273394i
$875$	2.36914			0.0800915
$876$		0			0
$877$	−54.9852			−1.85672			−0.928360	−	0.371683i	$-0.878781\pi$
$877$	−54.9852			−1.85672			−0.928360	+	0.371683i	$0.878781\pi$
$878$	3.10780	−	1.11783i	0.104883	−	0.0377248i
$879$		0			0
$880$	12.3922	+	2.37931i	0.417740	+	0.0802066i
$881$		−	3.67165i		−	0.123701i	−0.998085	−	0.0618505i	$-0.980300\pi$
$881$		−	3.67165i		−	0.123701i	0.998085	−	0.0618505i	$-0.0197002\pi$
$882$		0			0
$883$			25.1322i			0.845767i	0.906184	+	0.422883i	$0.138982\pi$
$883$			25.1322i			0.845767i	−0.906184	+	0.422883i	$0.861018\pi$
$884$	−6.68710	−	8.09317i	−0.224911	−	0.272203i
$885$		0			0
$886$	−12.6363	−	35.1317i	−0.424525	−	1.18027i
$887$	35.4515			1.19035			0.595173	−	0.803597i	$-0.297083\pi$
$887$	35.4515			1.19035			0.595173	+	0.803597i	$0.297083\pi$
$888$		0			0
$889$	−3.66276			−0.122845
$890$	1.57386	+	4.37566i	0.0527558	+	0.146673i
$891$		0			0
$892$	−25.9606	−	31.4192i	−0.869224	−	1.05199i
$893$			30.2066i			1.01083i
$894$		0			0
$895$		−	21.7810i		−	0.728058i
$896$	20.0686	+	17.7677i	0.670445	+	0.593578i
$897$		0			0
$898$	19.8269	−	7.13142i	0.661632	−	0.237978i
$899$	2.03850			0.0679879
$900$		0			0
$901$	−43.5115			−1.44958
$902$	26.5583	−	9.55260i	0.884295	−	0.318067i
$903$		0			0
$904$	4.66685	−	7.87506i	0.155217	−	0.261921i
$905$			23.5686i			0.783446i
$906$		0			0
$907$		−	4.14318i		−	0.137572i	−0.997631	−	0.0687859i	$-0.978087\pi$
$907$		−	4.14318i		−	0.137572i	0.997631	−	0.0687859i	$-0.0219126\pi$
$908$	−3.56914	+	2.94905i	−0.118446	+	0.0978678i
$909$		0			0
$910$	−1.68445	−	4.68314i	−0.0558390	−	0.155245i
$911$	0.864260			0.0286342			0.0143171	−	0.999898i	$-0.495443\pi$
$911$	0.864260			0.0286342			0.0143171	+	0.999898i	$0.495443\pi$
$912$		0			0
$913$	16.8573			0.557895
$914$	−14.6905	−	40.8429i	−0.485920	−	1.35096i
$915$		0			0
$916$	−0.582262	+	0.481102i	−0.0192385	+	0.0158960i
$917$			32.5237i			1.07403i
$918$		0			0
$919$		−	5.51108i		−	0.181794i	−0.995860	−	0.0908969i	$-0.971027\pi$
$919$		−	5.51108i		−	0.181794i	0.995860	−	0.0908969i	$-0.0289734\pi$
$920$	−2.93205	+	4.94769i	−0.0966670	+	0.163120i
$921$		0			0
$922$	−12.6530	+	4.55109i	−0.416705	+	0.149882i
$923$	−8.84055			−0.290990
$924$		0			0
$925$	−7.56172			−0.248628
$926$	0.666059	−	0.239571i	0.0218881	−	0.00787279i
$927$		0			0
$928$	−0.276594	−	1.76343i	−0.00907965	−	0.0578873i
$929$			28.2634i			0.927291i	0.886021	+	0.463646i	$0.153459\pi$
$929$			28.2634i			0.927291i	−0.886021	+	0.463646i	$0.846541\pi$
$930$		0			0
$931$			11.5198i			0.377546i
$932$	−1.47375	−	1.78363i	−0.0482742	−	0.0584247i
$933$		0			0
$934$	4.43692	+	12.3356i	0.145181	+	0.403634i
$935$	−11.1479			−0.364574
$936$		0			0
$937$	0.790755			0.0258328			0.0129164	−	0.999917i	$-0.495888\pi$
$937$	0.790755			0.0258328			0.0129164	+	0.999917i	$0.495888\pi$
$938$	−8.62591	−	23.9819i	−0.281646	−	0.783037i
$939$		0			0
$940$	4.63376	+	5.60809i	0.151137	+	0.182916i
$941$			8.85723i			0.288737i	0.989524	+	0.144369i	$0.0461151\pi$
$941$			8.85723i			0.288737i	−0.989524	+	0.144369i	$0.953885\pi$
$942$		0			0
$943$			12.8639i			0.418905i
$944$	−5.13785	+	26.7594i	−0.167223	+	0.870945i
$945$		0			0
$946$	40.2205	−	14.4667i	1.30768	−	0.470352i
$947$	−15.7223			−0.510908			−0.255454	−	0.966821i	$-0.582225\pi$
$947$	−15.7223			−0.510908			−0.255454	+	0.966821i	$0.582225\pi$
$948$		0			0
$949$	15.3324			0.497712
$950$	11.0512	−	3.97493i	0.358548	−	0.128964i
$951$		0			0
$952$	−20.3714	−	12.0723i	−0.660241	−	0.391266i
$953$		−	49.1552i		−	1.59229i	−0.605105	−	0.796146i	$-0.706869\pi$
$953$		−	49.1552i		−	1.59229i	0.605105	−	0.796146i	$-0.293131\pi$
$954$		0			0
$955$		−	14.2915i		−	0.462463i
$956$	−32.1739	+	26.5841i	−1.04058	+	0.859793i
$957$		0			0
$958$	−4.75136	−	13.2098i	−0.153510	−	0.426790i
$959$	−26.5208			−0.856402
$960$		0			0
$961$	−10.7352			−0.346298
$962$	5.37636	+	14.9475i	0.173341	+	0.481925i
$963$		0			0
$964$	−0.280353	+	0.231645i	−0.00902955	+	0.00746080i
$965$		−	15.6303i		−	0.503156i
$966$		0			0
$967$			5.75890i			0.185194i	0.995704	+	0.0925968i	$0.0295168\pi$
$967$			5.75890i			0.185194i	−0.995704	+	0.0925968i	$0.970483\pi$
$968$	2.55084	+	1.51165i	0.0819870	+	0.0485864i
$969$		0			0
$970$	−3.22172	+	1.15880i	−0.103443	+	0.0372068i
$971$	−16.1635			−0.518713			−0.259356	−	0.965782i	$-0.583510\pi$
$971$	−16.1635			−0.518713			−0.259356	+	0.965782i	$0.583510\pi$
$972$		0			0
$973$	26.0629			0.835539
$974$	−35.8106	+	12.8805i	−1.14745	+	0.412718i
$975$		0			0
$976$	4.25878	−	22.1810i	0.136320	−	0.709995i
$977$		−	11.0248i		−	0.352715i	−0.984326	−	0.176358i	$-0.943568\pi$
$977$		−	11.0248i		−	0.352715i	0.984326	−	0.176358i	$-0.0564315\pi$
$978$		0			0
$979$		−	10.3728i		−	0.331516i
$980$	1.76716	+	2.13874i	0.0564499	+	0.0683194i
$981$		0			0
$982$	17.9332	+	49.8583i	0.572273	+	1.59104i
$983$	43.0362			1.37264			0.686321	−	0.727299i	$-0.259225\pi$
$983$	43.0362			1.37264			0.686321	+	0.727299i	$0.259225\pi$
$984$		0			0
$985$	13.6558			0.435110
$986$	0.533729	+	1.48388i	0.0169974	+	0.0472565i
$987$		0			0
$988$	−15.7147	−	19.0190i	−0.499951	−	0.605075i
$989$			19.4813i			0.619470i
$990$		0			0
$991$		−	5.97281i		−	0.189732i	−0.995490	−	0.0948662i	$-0.969758\pi$
$991$		−	5.97281i		−	0.189732i	0.995490	−	0.0948662i	$-0.0302423\pi$
$992$	5.66285	+	36.1035i	0.179796	+	1.14629i
$993$		0			0
$994$	−18.7636	+	6.74897i	−0.595145	+	0.214064i
$995$	−1.10119			−0.0349100
$996$		0			0
$997$	22.8768			0.724516			0.362258	−	0.932078i	$-0.382006\pi$
$997$	22.8768			0.724516			0.362258	+	0.932078i	$0.382006\pi$
$998$	51.0470	−	18.3608i	1.61586	−	0.581201i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.a.971.28	yes	48
3.2	odd	2	inner	1620.2.e.a.971.21	✓	48
4.3	odd	2	inner	1620.2.e.a.971.22	yes	48
12.11	even	2	inner	1620.2.e.a.971.27	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.2.e.a.971.21	✓	48	3.2	odd	2	inner
1620.2.e.a.971.22	yes	48	4.3	odd	2	inner
1620.2.e.a.971.27	yes	48	12.11	even	2	inner
1620.2.e.a.971.28	yes	48	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.478649 + 1.33075i) q^{2} +(-1.54179 + 1.27393i) q^{4} -1.00000i q^{5} -2.36914i q^{7} +(-2.43325 - 1.44197i) q^{8} +O(q^{10})\)	\(q+(0.478649 + 1.33075i) q^{2} +(-1.54179 + 1.27393i) q^{4} -1.00000i q^{5} -2.36914i q^{7} +(-2.43325 - 1.44197i) q^{8} +(1.33075 - 0.478649i) q^{10} -3.15463 q^{11} +1.48542 q^{13} +(3.15273 - 1.13399i) q^{14} +(0.754230 - 3.92825i) q^{16} +3.53381i q^{17} +8.30447i q^{19} +(1.27393 + 1.54179i) q^{20} +(-1.50996 - 4.19802i) q^{22} +2.03336 q^{23} -1.00000 q^{25} +(0.710997 + 1.97673i) q^{26} +(3.01811 + 3.65271i) q^{28} -0.315544i q^{29} +6.46028i q^{31} +(5.58853 - 0.876563i) q^{32} +(-4.70262 + 1.69146i) q^{34} -2.36914 q^{35} +7.56172 q^{37} +(-11.0512 + 3.97493i) q^{38} +(-1.44197 + 2.43325i) q^{40} +6.32639i q^{41} +9.58083i q^{43} +(4.86377 - 4.01876i) q^{44} +(0.973268 + 2.70590i) q^{46} +3.63739 q^{47} +1.38718 q^{49} +(-0.478649 - 1.33075i) q^{50} +(-2.29021 + 1.89232i) q^{52} +12.3129i q^{53} +3.15463i q^{55} +(-3.41623 + 5.76471i) q^{56} +(0.419910 - 0.151035i) q^{58} -6.81205 q^{59} +5.64652 q^{61} +(-8.59702 + 3.09221i) q^{62} +(3.84143 + 7.01736i) q^{64} -1.48542i q^{65} -7.60671i q^{67} +(-4.50181 - 5.44839i) q^{68} +(-1.13399 - 3.15273i) q^{70} -5.95154 q^{71} +10.3219 q^{73} +(3.61941 + 10.0628i) q^{74} +(-10.5793 - 12.8038i) q^{76} +7.47375i q^{77} -5.96218i q^{79} +(-3.92825 - 0.754230i) q^{80} +(-8.41885 + 3.02812i) q^{82} -5.34367 q^{83} +3.53381 q^{85} +(-12.7497 + 4.58586i) q^{86} +(7.67600 + 4.54889i) q^{88} +3.28812i q^{89} -3.51918i q^{91} +(-3.13502 + 2.59035i) q^{92} +(1.74103 + 4.84045i) q^{94} +8.30447 q^{95} -2.42098 q^{97} +(0.663972 + 1.84599i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) \) 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

Introduction

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Database

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