LMFDB - Embedded newform 360.2.w.d.163.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(163,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("360.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{12} + 28x^{8} + 80x^{4} + 256 $ x^16 + 5x^12 + 28x^8 + 80*x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.5
Root			$1.31813 - 0.512386i$ of defining polynomial
Character	$\chi$	$=$	360.163
Dual form			360.2.w.d.307.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.512386 + 1.31813i) q^{2} +(-1.47492 + 1.35078i) q^{4} +(-1.83051 - 1.28422i) q^{5} +(-2.94984 - 2.94984i) q^{7} +(-2.53623 - 1.25201i) q^{8} +O(q^{10})$	\(q+(0.512386 + 1.31813i) q^{2} +(-1.47492 + 1.35078i) q^{4} +(-1.83051 - 1.28422i) q^{5} +(-2.94984 - 2.94984i) q^{7} +(-2.53623 - 1.25201i) q^{8} +(0.754834 - 3.07087i) q^{10} -1.61148 q^{11} +(2.50967 - 2.50967i) q^{13} +(2.37681 - 5.39972i) q^{14} +(0.350781 - 3.98459i) q^{16} +(-4.59398 + 4.59398i) q^{17} -4.00000i q^{19} +(4.43456 - 0.578502i) q^{20} +(-0.825702 - 2.12414i) q^{22} +(-1.09259 + 1.09259i) q^{23} +(1.70156 + 4.70156i) q^{25} +(4.59398 + 2.02214i) q^{26} +(8.33537 + 0.366192i) q^{28} -4.75362 q^{29} +5.01934i q^{31} +(5.43193 - 1.57927i) q^{32} +(-8.40935 - 3.70156i) q^{34} +(1.61148 + 9.18797i) q^{35} +(-2.50967 - 2.50967i) q^{37} +(5.27251 - 2.04955i) q^{38} +(3.03475 + 5.54890i) q^{40} +9.18797 q^{41} +(-7.40312 - 7.40312i) q^{43} +(2.37681 - 2.17676i) q^{44} +(-2.00000 - 0.880344i) q^{46} +(-7.32206 - 7.32206i) q^{47} +10.4031i q^{49} +(-5.32540 + 4.65189i) q^{50} +(-0.311549 + 7.09158i) q^{52} +(3.11473 - 3.11473i) q^{53} +(2.94984 + 2.06950i) q^{55} +(3.78824 + 11.1747i) q^{56} +(-2.43569 - 6.26587i) q^{58} -1.61148i q^{59} +6.78003i q^{61} +(-6.61613 + 2.57184i) q^{62} +(4.86493 + 6.35078i) q^{64} +(-7.81695 + 1.37102i) q^{65} +(7.40312 - 7.40312i) q^{67} +(0.570295 - 12.9812i) q^{68} +(-11.2852 + 6.83193i) q^{70} +(5.00000 + 5.00000i) q^{73} +(2.02214 - 4.59398i) q^{74} +(5.40312 + 5.89968i) q^{76} +(4.75362 + 4.75362i) q^{77} -5.01934 q^{79} +(-5.75920 + 6.84337i) q^{80} +(4.70779 + 12.1109i) q^{82} +(-7.57648 - 7.57648i) q^{83} +(14.3090 - 2.50967i) q^{85} +(5.96500 - 13.5515i) q^{86} +(4.08709 + 2.01759i) q^{88} -2.74204i q^{89} -14.8062 q^{91} +(0.135633 - 3.08733i) q^{92} +(5.89968 - 13.4031i) q^{94} +(-5.13688 + 7.32206i) q^{95} +(2.40312 - 2.40312i) q^{97} +(-13.7126 + 5.33042i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{10} - 20 q^{16} + 36 q^{22} - 24 q^{25} + 44 q^{28} + 32 q^{40} - 16 q^{43} - 32 q^{46} - 8 q^{52} - 44 q^{58} + 16 q^{67} - 44 q^{70} + 80 q^{73} - 16 q^{76} - 8 q^{82} - 28 q^{88} - 32 q^{91} - 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^10 - 20 * q^16 + 36 * q^22 - 24 * q^25 + 44 * q^28 + 32 * q^40 - 16 * q^43 - 32 * q^46 - 8 * q^52 - 44 * q^58 + 16 * q^67 - 44 * q^70 + 80 * q^73 - 16 * q^76 - 8 * q^82 - 28 * q^88 - 32 * q^91 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	0.512386	+	1.31813i	0.362312	+	0.932057i
$2$	0.512386	+	1.31813i	0.362312	+	0.932057i
$3$		0			0
$3$		0			0
$4$	−1.47492	+	1.35078i	−0.737460	+	0.675391i
$5$	−1.83051	−	1.28422i	−0.818631	−	0.574320i
$5$	−1.83051	−	1.28422i	−0.818631	−	0.574320i
$6$		0			0
$7$	−2.94984	−	2.94984i	−1.11494	−	1.11494i	−0.992473	−	0.122462i	$-0.960921\pi$
$7$	−2.94984	−	2.94984i	−1.11494	−	1.11494i	−0.122462	−	0.992473i	$-0.539079\pi$
$8$	−2.53623	−	1.25201i	−0.896693	−	0.442653i
$9$		0			0
$10$	0.754834	−	3.07087i	0.238700	−	0.971093i
$11$	−1.61148			−0.485880			−0.242940	−	0.970041i	$-0.578112\pi$
$11$	−1.61148			−0.485880			−0.242940	+	0.970041i	$0.578112\pi$
$12$		0			0
$13$	2.50967	−	2.50967i	0.696057	−	0.696057i	−0.267501	−	0.963558i	$-0.586198\pi$
$13$	2.50967	−	2.50967i	0.696057	−	0.696057i	0.963558	+	0.267501i	$0.0861978\pi$
$14$	2.37681	−	5.39972i	0.635229	−	1.44314i
$15$		0			0
$16$	0.350781	−	3.98459i	0.0876953	−	0.996147i
$17$	−4.59398	+	4.59398i	−1.11420	+	1.11420i	−0.121629	+	0.992576i	$0.538812\pi$
$17$	−4.59398	+	4.59398i	−1.11420	+	1.11420i	−0.992576	+	0.121629i	$0.961188\pi$
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	4.43456	−	0.578502i	0.991598	−	0.129357i
$21$		0			0
$22$	−0.825702	−	2.12414i	−0.176040	−	0.452868i
$23$	−1.09259	+	1.09259i	−0.227821	+	0.227821i	−0.811782	−	0.583961i	$-0.801502\pi$
$23$	−1.09259	+	1.09259i	−0.227821	+	0.227821i	0.583961	+	0.811782i	$0.301502\pi$
$24$		0			0
$25$	1.70156	+	4.70156i	0.340312	+	0.940312i
$26$	4.59398	+	2.02214i	0.900954	+	0.396575i
$27$		0			0
$28$	8.33537	+	0.366192i	1.57524	+	0.0692037i
$29$	−4.75362			−0.882725			−0.441362	−	0.897329i	$-0.645505\pi$
$29$	−4.75362			−0.882725			−0.441362	+	0.897329i	$0.645505\pi$
$30$		0			0
$31$			5.01934i			0.901500i	0.892650	+	0.450750i	$0.148843\pi$
$31$			5.01934i			0.901500i	−0.892650	+	0.450750i	$0.851157\pi$
$32$	5.43193	−	1.57927i	0.960239	−	0.279179i
$33$		0			0
$34$	−8.40935	−	3.70156i	−1.44219	−	0.634813i
$35$	1.61148	+	9.18797i	0.272390	+	1.55305i
$36$		0			0
$37$	−2.50967	−	2.50967i	−0.412587	−	0.412587i	0.470052	−	0.882639i	$-0.344235\pi$
$37$	−2.50967	−	2.50967i	−0.412587	−	0.412587i	−0.882639	+	0.470052i	$0.844235\pi$
$38$	5.27251	−	2.04955i	0.855314	−	0.332480i
$39$		0			0
$40$	3.03475	+	5.54890i	0.479836	+	0.877358i
$41$	9.18797			1.43492			0.717460	−	0.696600i	$-0.245305\pi$
$41$	9.18797			1.43492			0.717460	+	0.696600i	$0.245305\pi$
$42$		0			0
$43$	−7.40312	−	7.40312i	−1.12897	−	1.12897i	−0.990346	−	0.138620i	$-0.955733\pi$
$43$	−7.40312	−	7.40312i	−1.12897	−	1.12897i	−0.138620	−	0.990346i	$-0.544267\pi$
$44$	2.37681	−	2.17676i	0.358317	−	0.328159i
$45$		0			0
$46$	−2.00000	−	0.880344i	−0.294884	−	0.129800i
$47$	−7.32206	−	7.32206i	−1.06803	−	1.06803i	−0.997510	−	0.0705213i	$-0.977534\pi$
$47$	−7.32206	−	7.32206i	−1.06803	−	1.06803i	−0.0705213	−	0.997510i	$-0.522466\pi$
$48$		0			0
$49$			10.4031i			1.48616i
$50$	−5.32540	+	4.65189i	−0.753125	+	0.657877i
$51$		0			0
$52$	−0.311549	+	7.09158i	−0.0432041	+	0.983425i
$53$	3.11473	−	3.11473i	0.427841	−	0.427841i	−0.460051	−	0.887892i	$-0.652169\pi$
$53$	3.11473	−	3.11473i	0.427841	−	0.427841i	0.887892	+	0.460051i	$0.152169\pi$
$54$		0			0
$55$	2.94984	+	2.06950i	0.397756	+	0.279051i
$56$	3.78824	+	11.1747i	0.506225	+	1.49328i
$57$		0			0
$58$	−2.43569	−	6.26587i	−0.319822	−	0.822750i
$59$		−	1.61148i		−	0.209797i	−0.994483	−	0.104899i	$-0.966548\pi$
$59$		−	1.61148i		−	0.209797i	0.994483	−	0.104899i	$-0.0334518\pi$
$60$		0			0
$61$			6.78003i			0.868093i	0.900890	+	0.434047i	$0.142915\pi$
$61$			6.78003i			0.868093i	−0.900890	+	0.434047i	$0.857085\pi$
$62$	−6.61613	+	2.57184i	−0.840249	+	0.326624i
$63$		0			0
$64$	4.86493	+	6.35078i	0.608117	+	0.793848i
$65$	−7.81695	+	1.37102i	−0.969573	+	0.170054i
$66$		0			0
$67$	7.40312	−	7.40312i	0.904436	−	0.904436i	−0.0913805	−	0.995816i	$-0.529128\pi$
$67$	7.40312	−	7.40312i	0.904436	−	0.904436i	0.995816	+	0.0913805i	$0.0291279\pi$
$68$	0.570295	−	12.9812i	0.0691584	−	1.57421i
$69$		0			0
$70$	−11.2852	+	6.83193i	−1.34884	+	0.816572i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	5.00000	+	5.00000i	0.585206	+	0.585206i	0.936329	−	0.351123i	$-0.114200\pi$
$73$	5.00000	+	5.00000i	0.585206	+	0.585206i	−0.351123	+	0.936329i	$0.614200\pi$
$74$	2.02214	−	4.59398i	0.235069	−	0.534040i
$75$		0			0
$76$	5.40312	+	5.89968i	0.619781	+	0.676740i
$77$	4.75362	+	4.75362i	0.541725	+	0.541725i
$78$		0			0
$79$	−5.01934			−0.564720			−0.282360	−	0.959309i	$-0.591117\pi$
$79$	−5.01934			−0.564720			−0.282360	+	0.959309i	$0.591117\pi$
$80$	−5.75920	+	6.84337i	−0.643898	+	0.765112i
$81$		0			0
$82$	4.70779	+	12.1109i	0.519888	+	1.33743i
$83$	−7.57648	−	7.57648i	−0.831627	−	0.831627i	0.156112	−	0.987739i	$-0.450104\pi$
$83$	−7.57648	−	7.57648i	−0.831627	−	0.831627i	−0.987739	+	0.156112i	$0.950104\pi$
$84$		0			0
$85$	14.3090	−	2.50967i	1.55203	−	0.272212i
$86$	5.96500	−	13.5515i	0.643223	−	1.46130i
$87$		0			0
$88$	4.08709	+	2.01759i	0.435685	+	0.215076i
$89$		−	2.74204i		−	0.290655i	−0.989384	−	0.145328i	$-0.953576\pi$
$89$		−	2.74204i		−	0.290655i	0.989384	−	0.145328i	$-0.0464236\pi$
$90$		0			0
$91$	−14.8062			−1.55212
$92$	0.135633	−	3.08733i	0.0141408	−	0.321877i
$93$		0			0
$94$	5.89968	−	13.4031i	0.608506	−	1.38243i
$95$	−5.13688	+	7.32206i	−0.527032	+	0.751227i
$96$		0			0
$97$	2.40312	−	2.40312i	0.244000	−	0.244000i	−0.574503	−	0.818503i	$-0.694804\pi$
$97$	2.40312	−	2.40312i	0.244000	−	0.244000i	0.818503	+	0.574503i	$0.194804\pi$
$98$	−13.7126	+	5.33042i	−1.38519	+	0.538454i
$99$		0			0
$100$	−8.86045	−	4.63599i	−0.886045	−	0.463599i
$101$			8.79790i			0.875424i	0.899115	+	0.437712i	$0.144211\pi$
$101$			8.79790i			0.875424i	−0.899115	+	0.437712i	$0.855789\pi$
$102$		0			0
$103$	−7.96918	+	7.96918i	−0.785227	+	0.785227i	−0.980707	−	0.195481i	$-0.937373\pi$
$103$	−7.96918	+	7.96918i	−0.785227	+	0.785227i	0.195481	+	0.980707i	$0.437373\pi$
$104$	−9.50723	+	3.22296i	−0.932261	+	0.316038i
$105$		0			0
$106$	5.70156	+	2.50967i	0.553785	+	0.243761i
$107$	−1.61148	+	1.61148i	−0.155788	+	0.155788i	−0.780697	−	0.624909i	$-0.785136\pi$
$107$	−1.61148	+	1.61148i	−0.155788	+	0.155788i	0.624909	+	0.780697i	$0.285136\pi$
$108$		0			0
$109$	11.7994			1.13017			0.565087	−	0.825031i	$-0.308843\pi$
$109$	11.7994			1.13017			0.565087	+	0.825031i	$0.308843\pi$
$110$	−1.21640	+	4.94865i	−0.115979	+	0.471835i
$111$		0			0
$112$	−12.7887	+	10.7192i	−1.20841	+	1.01287i
$113$	−4.59398	−	4.59398i	−0.432166	−	0.432166i	0.457199	−	0.889364i	$-0.348853\pi$
$113$	−4.59398	−	4.59398i	−0.432166	−	0.432166i	−0.889364	+	0.457199i	$0.848853\pi$
$114$		0			0
$115$	3.40312	−	0.596876i	0.317343	−	0.0556590i
$116$	7.01121	−	6.42110i	0.650974	−	0.596184i
$117$		0			0
$118$	2.12414	−	0.825702i	0.195543	−	0.0760120i
$119$	27.1030			2.48453
$120$		0			0
$121$	−8.40312			−0.763920
$122$	−8.93694	+	3.47399i	−0.809112	+	0.314521i
$123$		0			0
$124$	−6.78003	−	7.40312i	−0.608864	−	0.664820i
$125$	2.92310	−	10.7915i	0.261450	−	0.965217i
$126$		0			0
$127$	−3.83019	−	3.83019i	−0.339874	−	0.339874i	0.516446	−	0.856320i	$-0.327255\pi$
$127$	−3.83019	−	3.83019i	−0.339874	−	0.339874i	−0.856320	+	0.516446i	$0.827255\pi$
$128$	−5.87841	+	9.66666i	−0.519583	+	0.854420i
$129$		0			0
$130$	−5.81248	−	9.60124i	−0.509788	−	0.842085i
$131$	13.5415			1.18313			0.591563	−	0.806259i	$-0.298511\pi$
$131$	13.5415			1.18313			0.591563	+	0.806259i	$0.298511\pi$
$132$		0			0
$133$	−11.7994	+	11.7994i	−1.02313	+	1.02313i
$134$	13.5515	+	5.96500i	1.17067	+	0.515298i
$135$		0			0
$136$	17.4031	−	5.89968i	1.49231	−	0.505894i
$137$	11.0399	−	11.0399i	0.943203	−	0.943203i	−0.0552681	−	0.998472i	$-0.517601\pi$
$137$	11.0399	−	11.0399i	0.943203	−	0.943203i	0.998472	+	0.0552681i	$0.0176013\pi$
$138$		0			0
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$	−14.7877	−	11.3748i	−1.24979	−	0.961343i
$141$		0			0
$142$		0			0
$143$	−4.04429	+	4.04429i	−0.338200	+	0.338200i
$144$		0			0
$145$	8.70156	+	6.10469i	0.722625	+	0.506967i
$146$	−4.02871	+	9.15257i	−0.333418	+	0.757472i
$147$		0			0
$148$	7.09158	+	0.311549i	0.582924	+	0.0256092i
$149$	−8.79790			−0.720752			−0.360376	−	0.932807i	$-0.617352\pi$
$149$	−8.79790			−0.720752			−0.360376	+	0.932807i	$0.617352\pi$
$150$		0			0
$151$			0.880344i			0.0716414i	0.999358	+	0.0358207i	$0.0114045\pi$
$151$			0.880344i			0.0716414i	−0.999358	+	0.0358207i	$0.988595\pi$
$152$	−5.00805	+	10.1449i	−0.406206	+	0.822862i
$153$		0			0
$154$	−3.83019	+	8.70156i	−0.308645	+	0.701192i
$155$	6.44593	−	9.18797i	0.517750	−	0.737995i
$156$		0			0
$157$	−9.28970	−	9.28970i	−0.741398	−	0.741398i	0.231449	−	0.972847i	$-0.425653\pi$
$157$	−9.28970	−	9.28970i	−0.741398	−	0.741398i	−0.972847	+	0.231449i	$0.925653\pi$
$158$	−2.57184	−	6.61613i	−0.204605	−	0.526351i
$159$		0			0
$160$	−11.9714	−	4.08491i	−0.946419	−	0.322940i
$161$	6.44593			0.508010
$162$		0			0
$163$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$163$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$164$	−13.5515	+	12.4109i	−1.05820	+	0.969131i
$165$		0			0
$166$	6.10469	−	13.8689i	0.473816	−	1.07643i
$167$	7.32206	+	7.32206i	0.566598	+	0.566598i	0.931174	−	0.364576i	$-0.118786\pi$
$167$	7.32206	+	7.32206i	0.566598	+	0.566598i	−0.364576	+	0.931174i	$0.618786\pi$
$168$		0			0
$169$			0.403124i			0.0310096i
$170$	10.6398	+	17.5752i	0.816037	+	1.34796i
$171$		0			0
$172$	20.9190	+	0.919020i	1.59506	+	0.0700746i
$173$	7.86835	−	7.86835i	0.598220	−	0.598220i	−0.341619	−	0.939839i	$-0.610975\pi$
$173$	7.86835	−	7.86835i	0.598220	−	0.598220i	0.939839	+	0.341619i	$0.110975\pi$
$174$		0			0
$175$	8.84952	−	18.8882i	0.668961	−	1.42781i
$176$	−0.565278	+	6.42110i	−0.0426094	+	0.484008i
$177$		0			0
$178$	3.61436	−	1.40498i	0.270907	−	0.105308i
$179$		−	26.4333i		−	1.97572i	−0.155343	−	0.987861i	$-0.549648\pi$
$179$		−	26.4333i		−	1.97572i	0.155343	−	0.987861i	$-0.450352\pi$
$180$		0			0
$181$		−	11.7994i		−	0.877040i	−0.898721	−	0.438520i	$-0.855503\pi$
$181$		−	11.7994i		−	0.877040i	0.898721	−	0.438520i	$-0.144497\pi$
$182$	−7.58652	−	19.5165i	−0.562350	−	1.44666i
$183$		0			0
$184$	4.13899	−	1.40312i	0.305131	−	0.103440i
$185$	1.37102	+	7.81695i	0.100799	+	0.574713i
$186$		0			0
$187$	7.40312	−	7.40312i	0.541370	−	0.541370i
$188$	20.6899	+	0.908956i	1.50897	+	0.0662924i
$189$		0			0
$190$	−12.2835	−	3.01934i	−0.891136	−	0.219046i
$191$		−	19.0145i		−	1.37584i	−0.725787	−	0.687919i	$-0.758524\pi$
$191$		−	19.0145i		−	1.37584i	0.725787	−	0.687919i	$-0.241476\pi$
$192$		0			0
$193$	−12.4031	−	12.4031i	−0.892796	−	0.892796i	0.101989	−	0.994786i	$-0.467479\pi$
$193$	−12.4031	−	12.4031i	−0.892796	−	0.892796i	−0.994786	+	0.101989i	$0.967479\pi$
$194$	4.39895	+	1.93630i	0.315826	+	0.139018i
$195$		0			0
$196$	−14.0523	−	15.3438i	−1.00374	−	1.09598i
$197$	9.34420	+	9.34420i	0.665747	+	0.665747i	0.956729	−	0.290982i	$-0.0939820\pi$
$197$	9.34420	+	9.34420i	0.665747	+	0.665747i	−0.290982	+	0.956729i	$0.593982\pi$
$198$		0			0
$199$	20.9577			1.48565			0.742826	−	0.669485i	$-0.233485\pi$
$199$	20.9577			1.48565			0.742826	+	0.669485i	$0.233485\pi$
$200$	1.57086	−	14.0546i	0.111076	−	0.993812i
$201$		0			0
$202$	−11.5968	+	4.50793i	−0.815945	+	0.317177i
$203$	14.0224	+	14.0224i	0.984181	+	0.984181i
$204$		0			0
$205$	−16.8187	−	11.7994i	−1.17467	−	0.824103i
$206$	−14.5877	−	6.42110i	−1.01637	−	0.447379i
$207$		0			0
$208$	−9.11966	−	10.8803i	−0.632334	−	0.754416i
$209$			6.44593i			0.445874i
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	−0.386661	+	8.80131i	−0.0265560	+	0.604476i
$213$		0			0
$214$	−2.94984	−	1.29844i	−0.201647	−	0.0887594i
$215$	4.04429	+	23.0588i	0.275818	+	1.57259i
$216$		0			0
$217$	14.8062	−	14.8062i	1.00511	−	1.00511i
$218$	6.04583	+	15.5531i	0.409475	+	1.05339i
$219$		0			0
$220$	−7.14622	+	0.932246i	−0.481798	+	0.0628520i
$221$			23.0588i			1.55110i
$222$		0			0
$223$	−3.83019	+	3.83019i	−0.256488	+	0.256488i	−0.823624	−	0.567136i	$-0.808051\pi$
$223$	−3.83019	+	3.83019i	−0.256488	+	0.256488i	0.567136	+	0.823624i	$0.308051\pi$
$224$	−20.6819	−	11.3647i	−1.38187	−	0.759338i
$225$		0			0
$226$	3.70156	−	8.40935i	0.246224	−	0.559382i
$227$	−15.6339	+	15.6339i	−1.03766	+	1.03766i	−0.0383956	+	0.999263i	$0.512225\pi$
$227$	−15.6339	+	15.6339i	−1.03766	+	1.03766i	−0.999263	+	0.0383956i	$0.987775\pi$
$228$		0			0
$229$	−6.78003			−0.448037			−0.224018	−	0.974585i	$-0.571918\pi$
$229$	−6.78003			−0.448037			−0.224018	+	0.974585i	$0.571918\pi$
$230$	2.53047	+	4.17992i	0.166854	+	0.275616i
$231$		0			0
$232$	12.0563	+	5.95158i	0.791533	+	0.390741i
$233$	−11.0399	−	11.0399i	−0.723249	−	0.723249i	0.246017	−	0.969266i	$-0.420878\pi$
$233$	−11.0399	−	11.0399i	−0.723249	−	0.723249i	−0.969266	+	0.246017i	$0.920878\pi$
$234$		0			0
$235$	4.00000	+	22.8062i	0.260931	+	1.48772i
$236$	2.17676	+	2.37681i	0.141695	+	0.154717i
$237$		0			0
$238$	13.8872	+	35.7253i	0.900175	+	2.31573i
$239$	−8.08857			−0.523206			−0.261603	−	0.965176i	$-0.584251\pi$
$239$	−8.08857			−0.523206			−0.261603	+	0.965176i	$0.584251\pi$
$240$		0			0
$241$	−6.80625			−0.438429			−0.219215	−	0.975677i	$-0.570349\pi$
$241$	−6.80625			−0.438429			−0.219215	+	0.975677i	$0.570349\pi$
$242$	−4.30565	−	11.0764i	−0.276777	−	0.712017i
$243$		0			0
$244$	−9.15833	−	10.0000i	−0.586302	−	0.640184i
$245$	13.3599	−	19.0431i	0.853532	−	1.21662i
$246$		0			0
$247$	−10.0387	−	10.0387i	−0.638746	−	0.638746i
$248$	6.28427	−	12.7302i	0.399051	−	0.808368i
$249$		0			0
$250$	15.7223	−	1.67637i	0.994364	−	0.106023i
$251$	−19.9874			−1.26159			−0.630797	−	0.775948i	$-0.717272\pi$
$251$	−19.9874			−1.26159			−0.630797	+	0.775948i	$0.717272\pi$
$252$		0			0
$253$	1.76069	−	1.76069i	0.110694	−	0.110694i
$254$	3.08614	−	7.01121i	0.193642	−	0.439922i
$255$		0			0
$256$	−15.7539	−	2.79544i	−0.984619	−	0.174715i
$257$	13.7820	−	13.7820i	0.859694	−	0.859694i	−0.131607	−	0.991302i	$-0.542014\pi$
$257$	13.7820	−	13.7820i	0.859694	−	0.859694i	0.991302	+	0.131607i	$0.0420138\pi$
$258$		0			0
$259$			14.8062i			0.920016i
$260$	9.67743	−	12.5811i	0.600169	−	0.780249i
$261$		0			0
$262$	6.93847	+	17.8494i	0.428660	+	1.10274i
$263$	2.95170	−	2.95170i	0.182009	−	0.182009i	−0.610221	−	0.792231i	$-0.708920\pi$
$263$	2.95170	−	2.95170i	0.182009	−	0.182009i	0.792231	+	0.610221i	$0.208920\pi$
$264$		0			0
$265$	−9.70156	+	1.70156i	−0.595962	+	0.104526i
$266$	−21.5989	−	9.50723i	−1.32431	−	0.582926i
$267$		0			0
$268$	−0.919020	+	20.9190i	−0.0561381	+	1.27783i
$269$	−18.3051			−1.11608			−0.558042	−	0.829813i	$-0.688447\pi$
$269$	−18.3051			−1.11608			−0.558042	+	0.829813i	$0.688447\pi$
$270$		0			0
$271$			12.6797i			0.770237i	0.922867	+	0.385119i	$0.125840\pi$
$271$			12.6797i			0.770237i	−0.922867	+	0.385119i	$0.874160\pi$
$272$	16.6937	+	19.9166i	1.01220	+	1.20762i
$273$		0			0
$274$	20.2087	+	8.89531i	1.22085	+	0.537386i
$275$	−2.74204	−	7.57648i	−0.165351	−	0.456879i
$276$		0			0
$277$	7.52901	+	7.52901i	0.452374	+	0.452374i	0.896142	−	0.443768i	$-0.146358\pi$
$277$	7.52901	+	7.52901i	0.452374	+	0.452374i	−0.443768	+	0.896142i	$0.646358\pi$
$278$	−5.27251	+	2.04955i	−0.316224	+	0.122924i
$279$		0			0
$280$	7.41635	−	25.3204i	0.443212	−	1.51318i
$281$	−27.5639			−1.64432			−0.822162	−	0.569253i	$-0.807232\pi$
$281$	−27.5639			−1.64432			−0.822162	+	0.569253i	$0.807232\pi$
$282$		0			0
$283$	7.40312	+	7.40312i	0.440070	+	0.440070i	0.892035	−	0.451965i	$-0.149277\pi$
$283$	7.40312	+	7.40312i	0.440070	+	0.440070i	−0.451965	+	0.892035i	$0.649277\pi$
$284$		0			0
$285$		0			0
$286$	−7.40312	−	3.25865i	−0.437756	−	0.192688i
$287$	−27.1030	−	27.1030i	−1.59984	−	1.59984i
$288$		0			0
$289$		−	25.2094i		−	1.48290i
$290$	−3.58819	+	14.5977i	−0.210706	+	0.857208i
$291$		0			0
$292$	−14.1285	−	0.620697i	−0.826808	−	0.0363236i
$293$	−3.11473	+	3.11473i	−0.181965	+	0.181965i	−0.792211	−	0.610247i	$-0.791070\pi$
$293$	−3.11473	+	3.11473i	−0.181965	+	0.181965i	0.610247	+	0.792211i	$0.291070\pi$
$294$		0			0
$295$	−2.06950	+	2.94984i	−0.120491	+	0.171746i
$296$	3.22296	+	9.50723i	0.187331	+	0.552597i
$297$		0			0
$298$	−4.50793	−	11.5968i	−0.261137	−	0.671782i
$299$			5.48408i			0.317152i
$300$		0			0
$301$			43.6761i			2.51745i
$302$	−1.16041	+	0.451076i	−0.0667739	+	0.0259565i
$303$		0			0
$304$	−15.9384	−	1.40312i	−0.914128	−	0.0804747i
$305$	8.70704	−	12.4109i	0.498564	−	0.710648i
$306$		0			0
$307$	−20.0000	+	20.0000i	−1.14146	+	1.14146i	−0.153277	+	0.988183i	$0.548983\pi$
$307$	−20.0000	+	20.0000i	−1.14146	+	1.14146i	−0.988183	+	0.153277i	$0.951017\pi$
$308$	−13.4323	−	0.590111i	−0.765377	−	0.0336247i
$309$		0			0
$310$	15.4137	+	3.78877i	0.875440	+	0.215188i
$311$		−	8.08857i		−	0.458661i	−0.973349	−	0.229330i	$-0.926346\pi$
$311$		−	8.08857i		−	0.458661i	0.973349	−	0.229330i	$-0.0736537\pi$
$312$		0			0
$313$	−19.8062	−	19.8062i	−1.11952	−	1.11952i	−0.991812	−	0.127703i	$-0.959240\pi$
$313$	−19.8062	−	19.8062i	−1.11952	−	1.11952i	−0.127703	−	0.991812i	$-0.540760\pi$
$314$	7.48509	−	17.0049i	0.422408	−	0.959643i
$315$		0			0
$316$	7.40312	−	6.78003i	0.416458	−	0.381406i
$317$	4.59058	+	4.59058i	0.257833	+	0.257833i	0.824172	−	0.566339i	$-0.191641\pi$
$317$	4.59058	+	4.59058i	0.257833	+	0.257833i	−0.566339	+	0.824172i	$0.691641\pi$
$318$		0			0
$319$	7.66037			0.428898
$320$	−0.749534	−	17.8728i	−0.0419002	−	0.999122i
$321$		0			0
$322$	3.30281	+	8.49656i	0.184058	+	0.473495i
$323$	18.3759	+	18.3759i	1.02246	+	1.02246i
$324$		0			0
$325$	16.0697	+	7.52901i	0.891388	+	0.417634i
$326$		0			0
$327$		0			0
$328$	−23.3028	−	11.5034i	−1.28668	−	0.635171i
$329$			43.1978i			2.38157i
$330$		0			0
$331$	2.80625			0.154245			0.0771227	−	0.997022i	$-0.475427\pi$
$331$	2.80625			0.154245			0.0771227	+	0.997022i	$0.475427\pi$
$332$	21.4089	+	0.940541i	1.17497	+	0.0516189i
$333$		0			0
$334$	−5.89968	+	13.4031i	−0.322816	+	0.733386i
$335$	−23.0588	+	4.04429i	−1.25983	+	0.220963i
$336$		0			0
$337$	−2.40312	+	2.40312i	−0.130907	+	0.130907i	−0.769524	−	0.638618i	$-0.779507\pi$
$337$	−2.40312	+	2.40312i	−0.130907	+	0.130907i	0.638618	+	0.769524i	$0.279507\pi$
$338$	−0.531369	+	0.206555i	−0.0289027	+	0.0112351i
$339$		0			0
$340$	−17.7147	+	23.0299i	−0.960713	+	1.24897i
$341$		−	8.08857i		−	0.438021i
$342$		0			0
$343$	10.0387	−	10.0387i	0.542038	−	0.542038i
$344$	9.50723	+	28.0448i	0.512596	+	1.51208i
$345$		0			0
$346$	14.4031	+	6.33985i	0.774317	+	0.340833i
$347$	2.74204	−	2.74204i	0.147200	−	0.147200i	−0.629666	−	0.776866i	$-0.716808\pi$
$347$	2.74204	−	2.74204i	0.147200	−	0.147200i	0.776866	+	0.629666i	$0.216808\pi$
$348$		0			0
$349$	6.78003			0.362926			0.181463	−	0.983398i	$-0.441917\pi$
$349$	6.78003			0.362926			0.181463	+	0.983398i	$0.441917\pi$
$350$	29.4314	+	1.98675i	1.57318	+	0.106196i
$351$		0			0
$352$	−8.75346	+	2.54497i	−0.466561	+	0.135648i
$353$	13.7820	+	13.7820i	0.733539	+	0.733539i	0.971319	−	0.237780i	$-0.0764197\pi$
$353$	13.7820	+	13.7820i	0.733539	+	0.733539i	−0.237780	+	0.971319i	$0.576420\pi$
$354$		0			0
$355$		0			0
$356$	3.70389	+	4.04429i	0.196306	+	0.214347i
$357$		0			0
$358$	34.8425	−	13.5441i	1.84148	−	0.715827i
$359$	35.1916			1.85734			0.928671	−	0.370904i	$-0.120952\pi$
$359$	35.1916			1.85734			0.928671	+	0.370904i	$0.120952\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	15.5531	−	6.04583i	0.817451	−	0.317762i
$363$		0			0
$364$	21.8380	−	20.0000i	1.14462	−	1.04828i
$365$	−2.73147	−	15.5737i	−0.142972	−	0.815163i
$366$		0			0
$367$	14.7492	+	14.7492i	0.769902	+	0.769902i	0.978089	−	0.208187i	$-0.0667562\pi$
$367$	14.7492	+	14.7492i	0.769902	+	0.769902i	−0.208187	+	0.978089i	$0.566756\pi$
$368$	3.97026	+	4.73678i	0.206964	+	0.246922i
$369$		0			0
$370$	−9.60124	+	5.81248i	−0.499145	+	0.302176i
$371$	−18.3759			−0.954031
$372$		0			0
$373$	−14.3090	+	14.3090i	−0.740894	+	0.740894i	−0.972750	−	0.231856i	$-0.925520\pi$
$373$	−14.3090	+	14.3090i	−0.740894	+	0.740894i	0.231856	+	0.972750i	$0.425520\pi$
$374$	13.5515	+	5.96500i	0.700733	+	0.308443i
$375$		0			0
$376$	9.40312	+	27.7377i	0.484929	+	1.43046i
$377$	−11.9300	+	11.9300i	−0.614427	+	0.614427i
$378$		0			0
$379$			18.8062i			0.966012i	0.875617	+	0.483006i	$0.160455\pi$
$379$			18.8062i			0.966012i	−0.875617	+	0.483006i	$0.839545\pi$
$380$	−2.31401	−	17.7382i	−0.118706	−	0.909953i
$381$		0			0
$382$	25.0635	−	9.74275i	1.28236	−	0.498483i
$383$	−26.0105	+	26.0105i	−1.32907	+	1.32907i	−0.422892	+	0.906180i	$0.638985\pi$
$383$	−26.0105	+	26.0105i	−1.32907	+	1.32907i	−0.906180	+	0.422892i	$0.861015\pi$
$384$		0			0
$385$	−2.59688	−	14.8062i	−0.132349	−	0.754596i
$386$	9.99371	−	22.7041i	0.508666	−	1.15561i
$387$		0			0
$388$	−0.298323	+	6.79051i	−0.0151450	+	0.344736i
$389$	−37.3196			−1.89218			−0.946090	−	0.323905i	$-0.895004\pi$
$389$	−37.3196			−1.89218			−0.946090	+	0.323905i	$0.895004\pi$
$390$		0			0
$391$		−	10.0387i		−	0.507678i
$392$	13.0248	−	26.3847i	0.657853	−	1.33263i
$393$		0			0
$394$	−7.52901	+	17.1047i	−0.379306	+	0.861722i
$395$	9.18797	+	6.44593i	0.462297	+	0.324330i
$396$		0			0
$397$	−19.3284	−	19.3284i	−0.970063	−	0.970063i	0.0295016	−	0.999565i	$-0.490608\pi$
$397$	−19.3284	−	19.3284i	−0.970063	−	0.970063i	−0.999565	+	0.0295016i	$0.990608\pi$
$398$	10.7384	+	27.6249i	0.538269	+	1.38471i
$399$		0			0
$400$	19.3307	−	5.13081i	0.966534	−	0.256540i
$401$	12.8919			0.643789			0.321894	−	0.946776i	$-0.395680\pi$
$401$	12.8919			0.643789			0.321894	+	0.946776i	$0.395680\pi$
$402$		0			0
$403$	12.5969	+	12.5969i	0.627495	+	0.627495i
$404$	−11.8840	−	12.9762i	−0.591253	−	0.645591i
$405$		0			0
$406$	−11.2984	+	25.6682i	−0.560732	+	1.27389i
$407$	4.04429	+	4.04429i	0.200468	+	0.200468i
$408$		0			0
$409$		−	3.40312i		−	0.168274i	−0.996454	−	0.0841368i	$-0.973187\pi$
$409$		−	3.40312i		−	0.168274i	0.996454	−	0.0841368i	$-0.0268133\pi$
$410$	6.93539	−	28.2150i	0.342515	−	1.39344i
$411$		0			0
$412$	0.989290	−	22.5185i	0.0487388	−	1.10941i
$413$	−4.75362	+	4.75362i	−0.233910	+	0.233910i
$414$		0			0
$415$	4.13899	+	23.5987i	0.203175	+	1.15842i
$416$	9.66889	−	17.5958i	0.474057	−	0.862706i
$417$		0			0
$418$	−8.49656	+	3.30281i	−0.415580	+	0.161546i
$419$			31.9174i			1.55927i	0.626235	+	0.779634i	$0.284595\pi$
$419$			31.9174i			1.55927i	−0.626235	+	0.779634i	$0.715405\pi$
$420$		0			0
$421$		−	30.3788i		−	1.48057i	−0.672293	−	0.740285i	$-0.734691\pi$
$421$		−	30.3788i		−	1.48057i	0.672293	−	0.740285i	$-0.265309\pi$
$422$	6.14864	+	15.8175i	0.299311	+	0.769985i
$423$		0			0
$424$	−11.7994	+	4.00000i	−0.573028	+	0.194257i
$425$	−29.4158	−	13.7820i	−1.42688	−	0.668523i
$426$		0			0
$427$	20.0000	−	20.0000i	0.967868	−	0.967868i
$428$	0.200049	−	4.55357i	0.00966971	−	0.220105i
$429$		0			0
$430$	−28.3221	+	17.1459i	−1.36582	+	0.826848i
$431$		−	27.1030i		−	1.30551i	−0.757570	−	0.652754i	$-0.773614\pi$
$431$		−	27.1030i		−	1.30551i	0.757570	−	0.652754i	$-0.226386\pi$
$432$		0			0
$433$	12.4031	+	12.4031i	0.596056	+	0.596056i	0.939261	−	0.343205i	$-0.111512\pi$
$433$	12.4031	+	12.4031i	0.596056	+	0.596056i	−0.343205	+	0.939261i	$0.611512\pi$
$434$	27.1030	+	11.9300i	1.30099	+	0.572659i
$435$		0			0
$436$	−17.4031	+	15.9384i	−0.833458	+	0.763309i
$437$	4.37036	+	4.37036i	0.209063	+	0.209063i
$438$		0			0
$439$	−10.9190			−0.521136			−0.260568	−	0.965455i	$-0.583910\pi$
$439$	−10.9190			−0.521136			−0.260568	+	0.965455i	$0.583910\pi$
$440$	−4.89044	−	8.94196i	−0.233143	−	0.426291i
$441$		0			0
$442$	−30.3944	+	11.8150i	−1.44571	+	0.561982i
$443$	−15.6339	−	15.6339i	−0.742789	−	0.742789i	0.230325	−	0.973114i	$-0.426021\pi$
$443$	−15.6339	−	15.6339i	−0.742789	−	0.742789i	−0.973114	+	0.230325i	$0.926021\pi$
$444$		0			0
$445$	−3.52138	+	5.01934i	−0.166929	+	0.237939i
$446$	−7.01121	−	3.08614i	−0.331990	−	0.146133i
$447$		0			0
$448$	4.38301	−	33.0846i	0.207078	−	1.56310i
$449$			6.44593i			0.304202i	0.988365	+	0.152101i	$0.0486039\pi$
$449$			6.44593i			0.304202i	−0.988365	+	0.152101i	$0.951396\pi$
$450$		0			0
$451$	−14.8062			−0.697199
$452$	12.9812	+	0.570295i	0.610586	+	0.0268244i
$453$		0			0
$454$	−28.6181	−	12.5969i	−1.34311	−	0.591201i
$455$	27.1030	+	19.0145i	1.27061	+	0.891412i
$456$		0			0
$457$	−9.80625	+	9.80625i	−0.458717	+	0.458717i	−0.898234	−	0.439517i	$-0.855150\pi$
$457$	−9.80625	+	9.80625i	−0.458717	+	0.458717i	0.439517	+	0.898234i	$0.355150\pi$
$458$	−3.47399	−	8.93694i	−0.162329	−	0.417596i
$459$		0			0
$460$	−4.21309	+	5.47722i	−0.196436	+	0.255377i
$461$		−	18.3051i		−	0.852555i	−0.904592	−	0.426278i	$-0.859825\pi$
$461$		−	18.3051i		−	0.852555i	0.904592	−	0.426278i	$-0.140175\pi$
$462$		0			0
$463$	14.7492	−	14.7492i	0.685454	−	0.685454i	−0.275770	−	0.961224i	$-0.588933\pi$
$463$	14.7492	−	14.7492i	0.685454	−	0.685454i	0.961224	+	0.275770i	$0.0889328\pi$
$464$	−1.66748	+	18.9412i	−0.0774108	+	0.879324i
$465$		0			0
$466$	8.89531	−	20.2087i	0.412067	−	0.936151i
$467$	10.7994	−	10.7994i	0.499739	−	0.499739i	−0.411618	−	0.911357i	$-0.635036\pi$
$467$	10.7994	−	10.7994i	0.499739	−	0.499739i	0.911357	+	0.411618i	$0.135036\pi$
$468$		0			0
$469$	−43.6761			−2.01677
$470$	−28.0120	+	16.9581i	−1.29210	+	0.782220i
$471$		0			0
$472$	−2.01759	+	4.08709i	−0.0928673	+	0.188124i
$473$	11.9300	+	11.9300i	0.548542	+	0.548542i
$474$		0			0
$475$	18.8062	−	6.80625i	0.862890	−	0.312292i
$476$	−39.9748	+	36.6103i	−1.83224	+	1.67803i
$477$		0			0
$478$	−4.14448	−	10.6618i	−0.189564	−	0.487658i
$479$	−8.08857			−0.369576			−0.184788	−	0.982778i	$-0.559160\pi$
$479$	−8.08857			−0.369576			−0.184788	+	0.982778i	$0.559160\pi$
$480$		0			0
$481$	−12.5969			−0.574368
$482$	−3.48743	−	8.97150i	−0.158848	−	0.408641i
$483$		0			0
$484$	12.3939	−	11.3508i	0.563361	−	0.515945i
$485$	−7.48509	+	1.31281i	−0.339880	+	0.0596118i
$486$		0			0
$487$	2.06950	+	2.06950i	0.0937778	+	0.0937778i	0.752439	−	0.658662i	$-0.228877\pi$
$487$	2.06950	+	2.06950i	0.0937778	+	0.0937778i	−0.658662	+	0.752439i	$0.728877\pi$
$488$	8.48867	−	17.1957i	0.384264	−	0.778413i
$489$		0			0
$490$	31.9466	+	7.85264i	1.44320	+	0.354746i
$491$	−11.2804			−0.509076			−0.254538	−	0.967063i	$-0.581923\pi$
$491$	−11.2804			−0.509076			−0.254538	+	0.967063i	$0.581923\pi$
$492$		0			0
$493$	21.8380	−	21.8380i	0.983536	−	0.983536i
$494$	8.08857	−	18.3759i	0.363922	−	0.826772i
$495$		0			0
$496$	20.0000	+	1.76069i	0.898027	+	0.0790573i
$497$		0			0
$498$		0			0
$499$		−	18.8062i		−	0.841883i	−0.907088	−	0.420942i	$-0.861700\pi$
$499$		−	18.8062i		−	0.841883i	0.907088	−	0.420942i	$-0.138300\pi$
$500$	10.2655	+	19.8650i	0.459089	+	0.888390i
$501$		0			0
$502$	−10.2413	−	26.3460i	−0.457091	−	1.17588i
$503$	5.13688	−	5.13688i	0.229042	−	0.229042i	−0.583250	−	0.812292i	$-0.698219\pi$
$503$	5.13688	−	5.13688i	0.229042	−	0.229042i	0.812292	+	0.583250i	$0.198219\pi$
$504$		0			0
$505$	11.2984	−	16.1047i	0.502774	−	0.716649i
$506$	3.22296	+	1.41866i	0.143278	+	0.0630671i
$507$		0			0
$508$	10.8230	+	0.475477i	0.480191	+	0.0210959i
$509$	−12.8422			−0.569220			−0.284610	−	0.958643i	$-0.591864\pi$
$509$	−12.8422			−0.569220			−0.284610	+	0.958643i	$0.591864\pi$
$510$		0			0
$511$		−	29.4984i		−	1.30493i
$512$	−4.38734	−	22.1980i	−0.193895	−	0.981022i
$513$		0			0
$514$	25.2281	+	11.1047i	1.11276	+	0.489807i
$515$	24.8219	−	4.35352i	1.09378	−	0.191839i
$516$		0			0
$517$	11.7994	+	11.7994i	0.518935	+	0.518935i
$518$	−19.5165	+	7.58652i	−0.857507	+	0.333333i
$519$		0			0
$520$	21.5421	+	6.30969i	0.944684	+	0.276698i
$521$	6.44593			0.282401			0.141201	−	0.989981i	$-0.454904\pi$
$521$	6.44593			0.282401			0.141201	+	0.989981i	$0.454904\pi$
$522$		0			0
$523$	−5.19375	−	5.19375i	−0.227107	−	0.227107i	0.584376	−	0.811483i	$-0.301339\pi$
$523$	−5.19375	−	5.19375i	−0.227107	−	0.227107i	−0.811483	+	0.584376i	$0.801339\pi$
$524$	−19.9726	+	18.2916i	−0.872508	+	0.799072i
$525$		0			0
$526$	5.40312	+	2.37830i	0.235587	+	0.103699i
$527$	−23.0588	−	23.0588i	−1.00446	−	1.00446i
$528$		0			0
$529$			20.6125i			0.896196i
$530$	−7.21382	−	11.9160i	−0.313348	−	0.517600i
$531$		0			0
$532$	1.46477	−	33.3415i	0.0635057	−	1.44554i
$533$	23.0588	−	23.0588i	0.998786	−	0.998786i
$534$		0			0
$535$	5.01934	−	0.880344i	0.217005	−	0.0380606i
$536$	−28.0448	+	9.50723i	−1.21135	+	0.410650i
$537$		0			0
$538$	−9.37930	−	24.1285i	−0.404370	−	1.04025i
$539$		−	16.7645i		−	0.722096i
$540$		0			0
$541$		−	8.27799i		−	0.355898i	−0.984040	−	0.177949i	$-0.943054\pi$
$541$		−	8.27799i		−	0.355898i	0.984040	−	0.177949i	$-0.0569463\pi$
$542$	−16.7135	+	6.49691i	−0.717905	+	0.279066i
$543$		0			0
$544$	−17.6990	+	32.2094i	−0.758840	+	1.38097i
$545$	−21.5989	−	15.1530i	−0.925195	−	0.649082i
$546$		0			0
$547$	−22.2094	+	22.2094i	−0.949604	+	0.949604i	−0.998790	−	0.0491855i	$-0.984337\pi$
$547$	−22.2094	+	22.2094i	−0.949604	+	0.949604i	0.0491855	+	0.998790i	$0.484337\pi$
$548$	−1.37049	+	31.1955i	−0.0585444	+	1.33261i
$549$		0			0
$550$	8.58179	−	7.49644i	0.365929	−	0.319649i
$551$			19.0145i			0.810044i
$552$		0			0
$553$	14.8062	+	14.8062i	0.629626	+	0.629626i
$554$	−6.06643	+	13.7820i	−0.257738	+	0.585539i
$555$		0			0
$556$	−5.40312	−	5.89968i	−0.229144	−	0.250202i
$557$	13.7146	+	13.7146i	0.581104	+	0.581104i	0.935207	−	0.354102i	$-0.115214\pi$
$557$	13.7146	+	13.7146i	0.581104	+	0.581104i	−0.354102	+	0.935207i	$0.615214\pi$
$558$		0			0
$559$	−37.1588			−1.57165
$560$	37.1756	−	3.19813i	1.57095	−	0.135146i
$561$		0			0
$562$	−14.1234	−	36.3327i	−0.595758	−	1.53260i
$563$	−2.74204	−	2.74204i	−0.115563	−	0.115563i	0.646960	−	0.762524i	$-0.276040\pi$
$563$	−2.74204	−	2.74204i	−0.115563	−	0.115563i	−0.762524	+	0.646960i	$0.776040\pi$
$564$		0			0
$565$	2.50967	+	14.3090i	0.105583	+	0.601986i
$566$	−5.96500	+	13.5515i	−0.250728	+	0.569613i
$567$		0			0
$568$		0			0
$569$		−	36.7519i		−	1.54072i	−0.637610	−	0.770359i	$-0.720077\pi$
$569$		−	36.7519i		−	1.54072i	0.637610	−	0.770359i	$-0.279923\pi$
$570$		0			0
$571$	17.6125			0.737060			0.368530	−	0.929616i	$-0.379861\pi$
$571$	17.6125			0.737060			0.368530	+	0.929616i	$0.379861\pi$
$572$	0.502056	−	11.4279i	0.0209920	−	0.477827i
$573$		0			0
$574$	21.8380	−	49.6125i	0.911502	−	2.07079i
$575$	−6.99599	−	3.27777i	−0.291753	−	0.136692i
$576$		0			0
$577$	12.4031	−	12.4031i	0.516349	−	0.516349i	−0.400116	−	0.916465i	$-0.631030\pi$
$577$	12.4031	−	12.4031i	0.516349	−	0.516349i	0.916465	+	0.400116i	$0.131030\pi$
$578$	33.2292	−	12.9169i	1.38215	−	0.537274i
$579$		0			0
$580$	−21.0802	+	2.74998i	−0.875308	+	0.114187i
$581$			44.6989i			1.85442i
$582$		0			0
$583$	−5.01934	+	5.01934i	−0.207880	+	0.207880i
$584$	−6.42110	−	18.9412i	−0.265707	−	0.783793i
$585$		0			0
$586$	−5.70156	−	2.50967i	−0.235529	−	0.103673i
$587$	1.61148	−	1.61148i	0.0665130	−	0.0665130i	−0.673068	−	0.739581i	$-0.735024\pi$
$587$	1.61148	−	1.61148i	0.0665130	−	0.0665130i	0.739581	+	0.673068i	$0.235024\pi$
$588$		0			0
$589$	20.0774			0.827273
$590$	−4.94865	−	1.21640i	−0.203733	−	0.0500785i
$591$		0			0
$592$	−10.8803	+	9.11966i	−0.447179	+	0.374816i
$593$	4.59398	+	4.59398i	0.188652	+	0.188652i	0.795113	−	0.606461i	$-0.207411\pi$
$593$	4.59398	+	4.59398i	0.188652	+	0.188652i	−0.606461	+	0.795113i	$0.707411\pi$
$594$		0			0
$595$	−49.6125	−	34.8062i	−2.03391	−	1.42692i
$596$	12.9762	−	11.8840i	0.531526	−	0.486789i
$597$		0			0
$598$	−7.22871	+	2.80997i	−0.295604	+	0.114908i
$599$	27.1030			1.10740			0.553700	−	0.832716i	$-0.313215\pi$
$599$	27.1030			1.10740			0.553700	+	0.832716i	$0.313215\pi$
$600$		0			0
$601$	20.2094			0.824358			0.412179	−	0.911103i	$-0.364768\pi$
$601$	20.2094			0.824358			0.412179	+	0.911103i	$0.364768\pi$
$602$	−57.5706	+	22.3790i	−2.34640	+	0.912101i
$603$		0			0
$604$	−1.18915	−	1.29844i	−0.0483859	−	0.0528327i
$605$	15.3820	+	10.7915i	0.625369	+	0.438735i
$606$		0			0
$607$	−18.8882	−	18.8882i	−0.766648	−	0.766648i	0.210867	−	0.977515i	$-0.432371\pi$
$607$	−18.8882	−	18.8882i	−0.766648	−	0.766648i	−0.977515	+	0.210867i	$0.932371\pi$
$608$	−6.31710	−	21.7277i	−0.256192	−	0.881176i
$609$		0			0
$610$	20.8206	+	5.11780i	0.843000	+	0.207214i
$611$	−36.7519			−1.48682
$612$		0			0
$613$	19.3284	−	19.3284i	0.780666	−	0.780666i	−0.199278	−	0.979943i	$-0.563860\pi$
$613$	19.3284	−	19.3284i	0.780666	−	0.780666i	0.979943	+	0.199278i	$0.0638595\pi$
$614$	−36.6103	−	16.1148i	−1.47747	−	0.650341i
$615$		0			0
$616$	−6.10469	−	18.0079i	−0.245965	−	0.725557i
$617$	7.33602	−	7.33602i	0.295337	−	0.295337i	−0.543847	−	0.839184i	$-0.683033\pi$
$617$	7.33602	−	7.33602i	0.295337	−	0.295337i	0.839184	+	0.543847i	$0.183033\pi$
$618$		0			0
$619$		−	10.8062i		−	0.434340i	−0.976134	−	0.217170i	$-0.930317\pi$
$619$		−	10.8062i		−	0.434340i	0.976134	−	0.217170i	$-0.0696826\pi$
$620$	2.90370	+	22.2586i	0.116615	+	0.893925i
$621$		0			0
$622$	10.6618	−	4.14448i	0.427498	−	0.166178i
$623$	−8.08857	+	8.08857i	−0.324062	+	0.324062i
$624$		0			0
$625$	−19.2094	+	16.0000i	−0.768375	+	0.640000i
$626$	15.9587	−	36.2556i	0.637838	−	1.44907i
$627$		0			0
$628$	26.2499	+	1.15322i	1.04749	+	0.0460184i
$629$	23.0588			0.919413
$630$		0			0
$631$			25.0967i			0.999083i	0.866290	+	0.499542i	$0.166498\pi$
$631$			25.0967i			0.999083i	−0.866290	+	0.499542i	$0.833502\pi$
$632$	12.7302	+	6.28427i	0.506380	+	0.249975i
$633$		0			0
$634$	−3.69882	+	8.40312i	−0.146899	+	0.333731i
$635$	2.09241	+	11.9300i	0.0830348	+	0.473428i
$636$		0			0
$637$	26.1084	+	26.1084i	1.03445	+	1.03445i
$638$	3.92507	+	10.0973i	0.155395	+	0.399758i
$639$		0			0
$640$	23.1746	−	10.1458i	0.916057	−	0.401047i
$641$	2.74204			0.108304			0.0541520	−	0.998533i	$-0.482754\pi$
$641$	2.74204			0.108304			0.0541520	+	0.998533i	$0.482754\pi$
$642$		0			0
$643$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$643$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$644$	−9.50723	+	8.70704i	−0.374638	+	0.343105i
$645$		0			0
$646$	−14.8062	+	33.6374i	−0.582544	+	1.32345i
$647$	19.7810	+	19.7810i	0.777671	+	0.777671i	0.979434	−	0.201763i	$-0.0646672\pi$
$647$	19.7810	+	19.7810i	0.777671	+	0.777671i	−0.201763	+	0.979434i	$0.564667\pi$
$648$		0			0
$649$			2.59688i			0.101936i
$650$	−1.69029	+	25.0397i	−0.0662985	+	0.982138i
$651$		0			0
$652$		0			0
$653$	15.1904	−	15.1904i	0.594447	−	0.594447i	−0.344383	−	0.938829i	$-0.611912\pi$
$653$	15.1904	−	15.1904i	0.594447	−	0.594447i	0.938829	+	0.344383i	$0.111912\pi$
$654$		0			0
$655$	−24.7879	−	17.3902i	−0.968543	−	0.679493i
$656$	3.22296	−	36.6103i	0.125836	−	1.42939i
$657$		0			0
$658$	−56.9402	+	22.1340i	−2.21976	+	0.862872i
$659$		−	4.83445i		−	0.188323i	−0.995557	−	0.0941617i	$-0.969983\pi$
$659$		−	4.83445i		−	0.188323i	0.995557	−	0.0941617i	$-0.0300171\pi$
$660$		0			0
$661$		−	26.8574i		−	1.04463i	−0.852752	−	0.522315i	$-0.825068\pi$
$661$		−	26.8574i		−	1.04463i	0.852752	−	0.522315i	$-0.174932\pi$
$662$	1.43788	+	3.69899i	0.0558849	+	0.143765i
$663$		0			0
$664$	9.72987	+	28.7016i	0.377592	+	1.11384i
$665$	36.7519	−	6.44593i	1.42518	−	0.249962i
$666$		0			0
$667$	5.19375	−	5.19375i	0.201103	−	0.201103i
$668$	−20.6899	−	0.908956i	−0.800518	−	0.0351686i
$669$		0			0
$670$	−17.1459	−	28.3221i	−0.662403	−	1.09418i
$671$		−	10.9259i		−	0.421789i
$672$		0			0
$673$	15.0000	+	15.0000i	0.578208	+	0.578208i	0.934409	−	0.356202i	$-0.115928\pi$
$673$	15.0000	+	15.0000i	0.578208	+	0.578208i	−0.356202	+	0.934409i	$0.615928\pi$
$674$	−4.39895	−	1.93630i	−0.169441	−	0.0745833i
$675$		0			0
$676$	−0.544533	−	0.594576i	−0.0209436	−	0.0228683i
$677$	18.1421	+	18.1421i	0.697258	+	0.697258i	0.963818	−	0.266560i	$-0.0858872\pi$
$677$	18.1421	+	18.1421i	0.697258	+	0.697258i	−0.266560	+	0.963818i	$0.585887\pi$
$678$		0			0
$679$	−14.1777			−0.544089
$680$	−39.4331	−	11.5500i	−1.51219	−	0.442921i
$681$		0			0
$682$	10.6618	−	4.14448i	0.408260	−	0.158700i
$683$	−1.13056	−	1.13056i	−0.0432595	−	0.0432595i	0.685146	−	0.728406i	$-0.259738\pi$
$683$	−1.13056	−	1.13056i	−0.0432595	−	0.0432595i	−0.728406	+	0.685146i	$0.759738\pi$
$684$		0			0
$685$	−34.3864	+	6.03105i	−1.31384	+	0.230434i
$686$	18.3759	+	8.08857i	0.701596	+	0.308823i
$687$		0			0
$688$	−32.0953	+	26.9015i	−1.22362	+	1.02561i
$689$		−	15.6339i		−	0.595604i
$690$		0			0
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$	−0.976773	+	22.2336i	−0.0371313	+	0.845195i
$693$		0			0
$694$	5.01934	+	2.20937i	0.190531	+	0.0838666i
$695$	5.13688	−	7.32206i	0.194853	−	0.277741i
$696$		0			0
$697$	−42.2094	+	42.2094i	−1.59879	+	1.59879i
$698$	3.47399	+	8.93694i	0.131493	+	0.338268i
$699$		0			0
$700$	12.4615	+	39.8124i	0.471000	+	1.50477i
$701$			3.33496i			0.125960i	0.998015	+	0.0629798i	$0.0200604\pi$
$701$			3.33496i			0.125960i	−0.998015	+	0.0629798i	$0.979940\pi$
$702$		0			0
$703$	−10.0387	+	10.0387i	−0.378616	+	0.378616i
$704$	−7.83976	−	10.2342i	−0.295472	−	0.385715i
$705$		0			0
$706$	−11.1047	+	25.2281i	−0.417930	+	0.949470i
$707$	25.9524	−	25.9524i	0.976041	−	0.976041i
$708$		0			0
$709$	26.8574			1.00865			0.504325	−	0.863514i	$-0.331741\pi$
$709$	26.8574			1.00865			0.504325	+	0.863514i	$0.331741\pi$
$710$		0			0
$711$		0			0
$712$	−3.43306	+	6.95444i	−0.128659	+	0.260629i
$713$	−5.48408	−	5.48408i	−0.205380	−	0.205380i
$714$		0			0
$715$	12.5969	−	2.20937i	0.471096	−	0.0826259i
$716$	35.7057	+	38.9871i	1.33438	+	1.45702i
$717$		0			0
$718$	18.0317	+	46.3870i	0.672937	+	1.73115i
$719$	−8.08857			−0.301653			−0.150826	−	0.988560i	$-0.548193\pi$
$719$	−8.08857			−0.301653			−0.150826	+	0.988560i	$0.548193\pi$
$720$		0			0
$721$	47.0156			1.75095
$722$	1.53716	+	3.95438i	0.0572071	+	0.147167i
$723$		0			0
$724$	15.9384	+	17.4031i	0.592344	+	0.646782i
$725$	−8.08857	−	22.3494i	−0.300402	−	0.830037i
$726$		0			0
$727$	35.7069	+	35.7069i	1.32430	+	1.32430i	0.910261	+	0.414034i	$0.135881\pi$
$727$	35.7069	+	35.7069i	1.32430	+	1.32430i	0.414034	+	0.910261i	$0.364119\pi$
$728$	37.5521	+	18.5376i	1.39177	+	0.687049i
$729$		0			0
$730$	19.1285	−	11.5802i	0.707978	−	0.428601i
$731$	68.0197			2.51580
$732$		0			0
$733$	2.50967	−	2.50967i	0.0926967	−	0.0926967i	−0.659238	−	0.751935i	$-0.729121\pi$
$733$	2.50967	−	2.50967i	0.0926967	−	0.0926967i	0.751935	+	0.659238i	$0.229121\pi$
$734$	−11.8840	+	26.9986i	−0.438648	+	0.996537i
$735$		0			0
$736$	−4.20937	+	7.66037i	−0.155160	+	0.282365i
$737$	−11.9300	+	11.9300i	−0.439447	+	0.439447i
$738$		0			0
$739$		−	48.4187i		−	1.78111i	−0.454873	−	0.890556i	$-0.650315\pi$
$739$		−	48.4187i		−	1.78111i	0.454873	−	0.890556i	$-0.349685\pi$
$740$	−12.5811	−	9.67743i	−0.462492	−	0.355749i
$741$		0			0
$742$	−9.41558	−	24.2218i	−0.345657	−	0.889211i
$743$	9.18116	−	9.18116i	0.336824	−	0.336824i	−0.518346	−	0.855171i	$-0.673452\pi$
$743$	9.18116	−	9.18116i	0.336824	−	0.336824i	0.855171	+	0.518346i	$0.173452\pi$
$744$		0			0
$745$	16.1047	+	11.2984i	0.590030	+	0.413943i
$746$	−26.1929	−	11.5294i	−0.958990	−	0.422121i
$747$		0			0
$748$	−0.919020	+	20.9190i	−0.0336027	+	0.764875i
$749$	9.50723			0.347387
$750$		0			0
$751$			15.0580i			0.549475i	0.961519	+	0.274737i	$0.0885909\pi$
$751$			15.0580i			0.549475i	−0.961519	+	0.274737i	$0.911409\pi$
$752$	−31.7438	+	26.6069i	−1.15758	+	0.970256i
$753$		0			0
$754$	−21.8380	−	9.61250i	−0.795294	−	0.350066i
$755$	1.13056	−	1.61148i	0.0411451	−	0.0586479i
$756$		0			0
$757$	11.0504	+	11.0504i	0.401633	+	0.401633i	0.878808	−	0.477175i	$-0.158339\pi$
$757$	11.0504	+	11.0504i	0.401633	+	0.401633i	−0.477175	+	0.878808i	$0.658339\pi$
$758$	−24.7890	+	9.63606i	−0.900378	+	0.349998i
$759$		0			0
$760$	22.1956	−	12.1390i	0.805119	−	0.440328i
$761$	43.1978			1.56592			0.782960	−	0.622073i	$-0.213709\pi$
$761$	43.1978			1.56592			0.782960	+	0.622073i	$0.213709\pi$
$762$		0			0
$763$	−34.8062	−	34.8062i	−1.26007	−	1.26007i
$764$	25.6844	+	28.0448i	0.929228	+	1.01463i
$765$		0			0
$766$	−47.6125	−	20.9577i	−1.72031	−	0.757232i
$767$	−4.04429	−	4.04429i	−0.146031	−	0.146031i
$768$		0			0
$769$		−	1.40312i		−	0.0505980i	−0.999680	−	0.0252990i	$-0.991946\pi$
$769$		−	1.40312i		−	0.0505980i	0.999680	−	0.0252990i	$-0.00805377\pi$
$770$	18.1859	−	11.0095i	0.655375	−	0.396756i
$771$		0			0
$772$	35.0475	+	1.53972i	1.26139	+	0.0554156i
$773$	−25.4642	+	25.4642i	−0.915882	+	0.915882i	−0.996727	−	0.0808446i	$-0.974238\pi$
$773$	−25.4642	+	25.4642i	−0.915882	+	0.915882i	0.0808446	+	0.996727i	$0.474238\pi$
$774$		0			0
$775$	−23.5987	+	8.54071i	−0.847691	+	0.306792i
$776$	−9.10362	+	3.08614i	−0.326801	+	0.110786i
$777$		0			0
$778$	−19.1221	−	49.1920i	−0.685559	−	1.76362i
$779$		−	36.7519i		−	1.31677i
$780$		0			0
$781$		0			0
$782$	13.2323	−	5.14368i	0.473184	−	0.183938i
$783$		0			0
$784$	41.4522	+	3.64922i	1.48043	+	0.130329i
$785$	5.07491	+	28.9349i	0.181131	+	1.03273i
$786$		0			0
$787$	−20.0000	+	20.0000i	−0.712923	+	0.712923i	−0.967146	−	0.254223i	$-0.918180\pi$
$787$	−20.0000	+	20.0000i	−0.712923	+	0.712923i	0.254223	+	0.967146i	$0.418180\pi$
$788$	−26.4039	−	1.15998i	−0.940601	−	0.0413227i
$789$		0			0
$790$	−3.78877	+	15.4137i	−0.134798	+	0.548396i
$791$			27.1030i			0.963673i
$792$		0			0
$793$	17.0156	+	17.0156i	0.604242	+	0.604242i
$794$	15.5737	−	35.3809i	0.552689	−	1.25562i
$795$		0			0
$796$	−30.9109	+	28.3093i	−1.09561	+	1.00340i
$797$	−6.00924	−	6.00924i	−0.212858	−	0.212858i	0.592622	−	0.805481i	$-0.298093\pi$
$797$	−6.00924	−	6.00924i	−0.212858	−	0.212858i	−0.805481	+	0.592622i	$0.798093\pi$
$798$		0			0
$799$	67.2748			2.38001
$800$	16.6678	+	22.8513i	0.589297	+	0.807917i
$801$		0			0
$802$	6.60561	+	16.9931i	0.233252	+	0.600048i
$803$	−8.05741	−	8.05741i	−0.284340	−	0.284340i
$804$		0			0
$805$	−11.7994	−	8.27799i	−0.415873	−	0.291761i
$806$	−10.1498	+	23.0588i	−0.357512	+	0.812210i
$807$		0			0
$808$	11.0151	−	22.3135i	0.387509	−	0.784987i
$809$		−	2.74204i		−	0.0964049i	−0.998838	−	0.0482025i	$-0.984651\pi$
$809$		−	2.74204i		−	0.0964049i	0.998838	−	0.0482025i	$-0.0153493\pi$
$810$		0			0
$811$	−42.8062			−1.50313			−0.751565	−	0.659659i	$-0.770701\pi$
$811$	−42.8062			−1.50313			−0.751565	+	0.659659i	$0.770701\pi$
$812$	−39.6232	−	1.74073i	−1.39050	−	0.0610878i
$813$		0			0
$814$	−3.25865	+	7.40312i	−0.114216	+	0.259479i
$815$		0			0
$816$		0			0
$817$	−29.6125	+	29.6125i	−1.03601	+	1.03601i
$818$	4.48575	−	1.74371i	0.156841	−	0.0609675i
$819$		0			0
$820$	40.7446	−	5.31526i	1.42286	−	0.185617i
$821$		−	39.9452i		−	1.39410i	−0.717023	−	0.697049i	$-0.754496\pi$
$821$		−	39.9452i		−	1.39410i	0.717023	−	0.697049i	$-0.245504\pi$
$822$		0			0
$823$	5.59087	−	5.59087i	0.194886	−	0.194886i	−0.602918	−	0.797803i	$-0.705995\pi$
$823$	5.59087	−	5.59087i	0.194886	−	0.194886i	0.797803	+	0.602918i	$0.205995\pi$
$824$	30.1892	−	10.2342i	1.05169	−	0.356524i
$825$		0			0
$826$	−8.70156	−	3.83019i	−0.302766	−	0.133269i
$827$	−36.7519	+	36.7519i	−1.27799	+	1.27799i	−0.336196	+	0.941792i	$0.609140\pi$
$827$	−36.7519	+	36.7519i	−1.27799	+	1.27799i	−0.941792	+	0.336196i	$0.890860\pi$
$828$		0			0
$829$	−8.27799			−0.287506			−0.143753	−	0.989614i	$-0.545917\pi$
$829$	−8.27799			−0.287506			−0.143753	+	0.989614i	$0.545917\pi$
$830$	−28.9854	+	17.5474i	−1.00610	+	0.609079i
$831$		0			0
$832$	28.1477	+	3.72898i	0.975847	+	0.129279i
$833$	−47.7918	−	47.7918i	−1.65589	−	1.65589i
$834$		0			0
$835$	−4.00000	−	22.8062i	−0.138426	−	0.789243i
$836$	−8.70704	−	9.50723i	−0.301139	−	0.328815i
$837$		0			0
$838$	−42.0712	+	16.3541i	−1.45333	+	0.564941i
$839$	27.1030			0.935701			0.467850	−	0.883808i	$-0.345029\pi$
$839$	27.1030			0.935701			0.467850	+	0.883808i	$0.345029\pi$
$840$		0			0
$841$	−6.40312			−0.220797
$842$	40.0431	−	15.5657i	1.37998	−	0.536428i
$843$		0			0
$844$	−17.6990	+	16.2094i	−0.609226	+	0.557950i
$845$	0.517700	−	0.737925i	0.0178094	−	0.0253854i
$846$		0			0
$847$	24.7879	+	24.7879i	0.851722	+	0.851722i
$848$	−11.3183	−	13.5035i	−0.388673	−	0.463713i
$849$		0			0
$850$	3.09409	−	45.8355i	0.106126	−	1.57215i
$851$	5.48408			0.187992
$852$		0			0
$853$	−14.3090	+	14.3090i	−0.489932	+	0.489932i	−0.908285	−	0.418353i	$-0.862608\pi$
$853$	−14.3090	+	14.3090i	−0.489932	+	0.489932i	0.418353	+	0.908285i	$0.362608\pi$
$854$	36.6103	+	16.1148i	1.25278	+	0.551438i
$855$		0			0
$856$	6.10469	−	2.06950i	0.208654	−	0.0707339i
$857$	13.7820	−	13.7820i	0.470782	−	0.470782i	−0.431385	−	0.902168i	$-0.641975\pi$
$857$	13.7820	−	13.7820i	0.470782	−	0.470782i	0.902168	+	0.431385i	$0.141975\pi$
$858$		0			0
$859$		−	25.6125i		−	0.873887i	−0.899489	−	0.436944i	$-0.856061\pi$
$859$		−	25.6125i		−	0.873887i	0.899489	−	0.436944i	$-0.143939\pi$
$860$	−37.1123	−	28.5469i	−1.26552	−	0.973441i
$861$		0			0
$862$	35.7253	−	13.8872i	1.21681	−	0.473001i
$863$	21.9662	−	21.9662i	0.747737	−	0.747737i	−0.226317	−	0.974054i	$-0.572668\pi$
$863$	21.9662	−	21.9662i	0.747737	−	0.747737i	0.974054	+	0.226317i	$0.0726684\pi$
$864$		0			0
$865$	−24.5078	+	4.29844i	−0.833291	+	0.146151i
$866$	−9.99371	+	22.7041i	−0.339600	+	0.771516i
$867$		0			0
$868$	−1.83804	+	41.8380i	−0.0623871	+	1.42008i
$869$	8.08857			0.274386
$870$		0			0
$871$		−	37.1588i		−	1.25908i
$872$	−29.9259	−	14.7729i	−1.01342	−	0.500275i
$873$		0			0
$874$	−3.52138	+	8.00000i	−0.119112	+	0.270604i
$875$	−40.4558	+	23.2104i	−1.36765	+	0.784654i
$876$		0			0
$877$	14.3090	+	14.3090i	0.483182	+	0.483182i	0.906146	−	0.422965i	$-0.139011\pi$
$877$	14.3090	+	14.3090i	0.483182	+	0.483182i	−0.422965	+	0.906146i	$0.639011\pi$
$878$	−5.59476	−	14.3927i	−0.188814	−	0.485729i
$879$		0			0
$880$	9.28084	−	11.0280i	0.312857	−	0.371753i
$881$	−46.9017			−1.58016			−0.790079	−	0.613005i	$-0.789961\pi$
$881$	−46.9017			−1.58016			−0.790079	+	0.613005i	$0.789961\pi$
$882$		0			0
$883$	14.8062	+	14.8062i	0.498270	+	0.498270i	0.910899	−	0.412629i	$-0.135389\pi$
$883$	14.8062	+	14.8062i	0.498270	+	0.498270i	−0.412629	+	0.910899i	$0.635389\pi$
$884$	−31.1473	−	34.0098i	−1.04760	−	1.14387i
$885$		0			0
$886$	12.5969	−	28.6181i	0.423200	−	0.961443i
$887$	26.3365	+	26.3365i	0.884294	+	0.884294i	0.993968	−	0.109674i	$-0.0349806\pi$
$887$	26.3365	+	26.3365i	0.884294	+	0.884294i	−0.109674	+	0.993968i	$0.534981\pi$
$888$		0			0
$889$			22.5969i			0.757875i
$890$	−8.42043	−	2.06978i	−0.282254	−	0.0693793i
$891$		0			0
$892$	0.475477	−	10.8230i	0.0159202	−	0.362380i
$893$	−29.2882	+	29.2882i	−0.980093	+	0.980093i
$894$		0			0
$895$	−33.9462	+	48.3866i	−1.13470	+	1.61739i
$896$	45.8555	−	11.1747i	1.53192	−	0.373321i
$897$		0			0
$898$	−8.49656	+	3.30281i	−0.283534	+	0.110216i
$899$		−	23.8600i		−	0.795776i
$900$		0			0
$901$			28.6181i			0.953406i
$902$	−7.58652	−	19.5165i	−0.252603	−	0.649829i
$903$		0			0
$904$	5.89968	+	17.4031i	0.196221	+	0.578819i
$905$	−15.1530	+	21.5989i	−0.503702	+	0.717972i
$906$		0			0
$907$	12.5969	−	12.5969i	0.418272	−	0.418272i	−0.466336	−	0.884608i	$-0.654426\pi$
$907$	12.5969	−	12.5969i	0.418272	−	0.418272i	0.884608	+	0.466336i	$0.154426\pi$
$908$	1.94078	−	44.1767i	0.0644072	−	1.46606i
$909$		0			0
$910$	−11.1763	+	45.4680i	−0.370490	+	1.50725i
$911$			27.1030i			0.897964i	0.893541	+	0.448982i	$0.148213\pi$
$911$			27.1030i			0.897964i	−0.893541	+	0.448982i	$0.851787\pi$
$912$		0			0
$913$	12.2094	+	12.2094i	0.404071	+	0.404071i
$914$	−17.9505	−	7.90130i	−0.593749	−	0.261352i
$915$		0			0
$916$	10.0000	−	9.15833i	0.330409	−	0.302600i
$917$	−39.9452	−	39.9452i	−1.31911	−	1.31911i
$918$		0			0
$919$	−52.2168			−1.72247			−0.861237	−	0.508204i	$-0.830309\pi$
$919$	−52.2168			−1.72247			−0.861237	+	0.508204i	$0.830309\pi$
$920$	−9.37840	−	2.74694i	−0.309197	−	0.0905638i
$921$		0			0
$922$	24.1285	−	9.37930i	0.794630	−	0.308891i
$923$		0			0
$924$		0			0
$925$	7.52901	−	16.0697i	0.247552	−	0.528369i
$926$	26.9986	+	11.8840i	0.887230	+	0.390534i
$927$		0			0
$928$	−25.8213	+	7.50727i	−0.847627	+	0.246438i
$929$			43.1978i			1.41727i	0.705573	+	0.708637i	$0.250690\pi$
$929$			43.1978i			1.41727i	−0.705573	+	0.708637i	$0.749310\pi$
$930$		0			0
$931$	41.6125			1.36379
$932$	31.1955	+	1.37049i	1.02184	+	0.0448919i
$933$		0			0
$934$	19.7685	+	8.70156i	0.646846	+	0.284724i
$935$	−23.0588	+	4.04429i	−0.754102	+	0.132262i
$936$		0			0
$937$	22.4031	−	22.4031i	0.731878	−	0.731878i	−0.239113	−	0.970992i	$-0.576857\pi$
$937$	22.4031	−	22.4031i	0.731878	−	0.731878i	0.970992	+	0.239113i	$0.0768568\pi$
$938$	−22.3790	−	57.5706i	−0.730701	−	1.87975i
$939$		0			0
$940$	−36.7059	−	28.2343i	−1.19722	−	0.920901i
$941$			10.2166i			0.333050i	0.986037	+	0.166525i	$0.0532547\pi$
$941$			10.2166i			0.333050i	−0.986037	+	0.166525i	$0.946745\pi$
$942$		0			0
$943$	−10.0387	+	10.0387i	−0.326904	+	0.326904i
$944$	−6.42110	−	0.565278i	−0.208989	−	0.0183982i
$945$		0			0
$946$	−9.61250	+	21.8380i	−0.312529	+	0.710016i
$947$	−18.3759	+	18.3759i	−0.597138	+	0.597138i	−0.939550	−	0.342412i	$-0.888756\pi$
$947$	−18.3759	+	18.3759i	−0.597138	+	0.597138i	0.342412	+	0.939550i	$0.388756\pi$
$948$		0			0
$949$	25.0967			0.814673
$950$	18.6076	+	21.3016i	0.603709	+	0.691115i
$951$		0			0
$952$	−68.7396	−	33.9333i	−2.22786	−	1.09979i
$953$	1.85195	+	1.85195i	0.0599904	+	0.0599904i	0.736466	−	0.676475i	$-0.236493\pi$
$953$	1.85195	+	1.85195i	0.0599904	+	0.0599904i	−0.676475	+	0.736466i	$0.736493\pi$
$954$		0			0
$955$	−24.4187	+	34.8062i	−0.790172	+	1.12630i
$956$	11.9300	−	10.9259i	0.385844	−	0.353369i
$957$		0			0
$958$	−4.14448	−	10.6618i	−0.133902	−	0.344466i
$959$	−65.1320			−2.10322
$960$		0			0
$961$	5.80625			0.187298
$962$	−6.45447	−	16.6043i	−0.208100	−	0.535344i
$963$		0			0
$964$	10.0387	−	9.19375i	0.323324	−	0.296111i
$965$	6.77576	+	38.6324i	0.218119	+	1.24362i
$966$		0			0
$967$	2.06950	+	2.06950i	0.0665505	+	0.0665505i	0.739599	−	0.673048i	$-0.235015\pi$
$967$	2.06950	+	2.06950i	0.0665505	+	0.0665505i	−0.673048	+	0.739599i	$0.735015\pi$
$968$	21.3123	+	10.5208i	0.685002	+	0.338152i
$969$		0			0
$970$	−5.56571	−	9.19364i	−0.178704	−	0.295190i
$971$	38.3634			1.23114			0.615569	−	0.788083i	$-0.288926\pi$
$971$	38.3634			1.23114			0.615569	+	0.788083i	$0.288926\pi$
$972$		0			0
$973$	11.7994	−	11.7994i	0.378270	−	0.378270i
$974$	−1.66748	+	3.78824i	−0.0534295	+	0.121383i
$975$		0			0
$976$	27.0156	+	2.37830i	0.864749	+	0.0761277i
$977$	−7.33602	+	7.33602i	−0.234700	+	0.234700i	−0.814651	−	0.579951i	$-0.803072\pi$
$977$	−7.33602	+	7.33602i	−0.234700	+	0.234700i	0.579951	+	0.814651i	$0.303072\pi$
$978$		0			0
$979$			4.41875i			0.141224i
$980$	6.01823	+	46.1333i	0.192245	+	1.47367i
$981$		0			0
$982$	−5.77991	−	14.8690i	−0.184444	−	0.474488i
$983$	9.18116	−	9.18116i	0.292834	−	0.292834i	−0.545365	−	0.838199i	$-0.683609\pi$
$983$	9.18116	−	9.18116i	0.292834	−	0.292834i	0.838199	+	0.545365i	$0.183609\pi$
$984$		0			0
$985$	−5.10469	−	29.1047i	−0.162649	−	0.927352i
$986$	39.9748	+	17.5958i	1.27306	+	0.560365i
$987$		0			0
$988$	28.3663	+	1.24620i	0.902452	+	0.0396468i
$989$	16.1771			0.514403
$990$		0			0
$991$		−	42.7957i		−	1.35945i	−0.733466	−	0.679726i	$-0.762099\pi$
$991$		−	42.7957i		−	1.35945i	0.733466	−	0.679726i	$-0.237901\pi$
$992$	7.92691	+	27.2647i	0.251680	+	0.865655i
$993$		0			0
$994$		0			0
$995$	−38.3634	−	26.9143i	−1.21620	−	0.853240i
$996$		0			0
$997$	−2.50967	−	2.50967i	−0.0794820	−	0.0794820i	0.666248	−	0.745730i	$-0.267899\pi$
$997$	−2.50967	−	2.50967i	−0.0794820	−	0.0794820i	−0.745730	+	0.666248i	$0.767899\pi$
$998$	24.7890	−	9.63606i	0.784683	−	0.305024i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.w.d.163.5	yes	16
3.2	odd	2	inner	360.2.w.d.163.4	yes	16
4.3	odd	2		1440.2.bi.d.1423.2		16
5.2	odd	4	inner	360.2.w.d.307.1	yes	16
8.3	odd	2	inner	360.2.w.d.163.1	✓	16
8.5	even	2		1440.2.bi.d.1423.7		16
12.11	even	2		1440.2.bi.d.1423.8		16
15.2	even	4	inner	360.2.w.d.307.8	yes	16
20.7	even	4		1440.2.bi.d.847.7		16
24.5	odd	2		1440.2.bi.d.1423.1		16
24.11	even	2	inner	360.2.w.d.163.8	yes	16
40.27	even	4	inner	360.2.w.d.307.5	yes	16
40.37	odd	4		1440.2.bi.d.847.2		16
60.47	odd	4		1440.2.bi.d.847.1		16
120.77	even	4		1440.2.bi.d.847.8		16
120.107	odd	4	inner	360.2.w.d.307.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.w.d.163.1	✓	16	8.3	odd	2	inner
360.2.w.d.163.4	yes	16	3.2	odd	2	inner
360.2.w.d.163.5	yes	16	1.1	even	1	trivial
360.2.w.d.163.8	yes	16	24.11	even	2	inner
360.2.w.d.307.1	yes	16	5.2	odd	4	inner
360.2.w.d.307.4	yes	16	120.107	odd	4	inner
360.2.w.d.307.5	yes	16	40.27	even	4	inner
360.2.w.d.307.8	yes	16	15.2	even	4	inner
1440.2.bi.d.847.1		16	60.47	odd	4
1440.2.bi.d.847.2		16	40.37	odd	4
1440.2.bi.d.847.7		16	20.7	even	4
1440.2.bi.d.847.8		16	120.77	even	4
1440.2.bi.d.1423.1		16	24.5	odd	2
1440.2.bi.d.1423.2		16	4.3	odd	2
1440.2.bi.d.1423.7		16	8.5	even	2
1440.2.bi.d.1423.8		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.512386 + 1.31813i) q^{2} +(-1.47492 + 1.35078i) q^{4} +(-1.83051 - 1.28422i) q^{5} +(-2.94984 - 2.94984i) q^{7} +(-2.53623 - 1.25201i) q^{8} +O(q^{10})\)	\(q+(0.512386 + 1.31813i) q^{2} +(-1.47492 + 1.35078i) q^{4} +(-1.83051 - 1.28422i) q^{5} +(-2.94984 - 2.94984i) q^{7} +(-2.53623 - 1.25201i) q^{8} +(0.754834 - 3.07087i) q^{10} -1.61148 q^{11} +(2.50967 - 2.50967i) q^{13} +(2.37681 - 5.39972i) q^{14} +(0.350781 - 3.98459i) q^{16} +(-4.59398 + 4.59398i) q^{17} -4.00000i q^{19} +(4.43456 - 0.578502i) q^{20} +(-0.825702 - 2.12414i) q^{22} +(-1.09259 + 1.09259i) q^{23} +(1.70156 + 4.70156i) q^{25} +(4.59398 + 2.02214i) q^{26} +(8.33537 + 0.366192i) q^{28} -4.75362 q^{29} +5.01934i q^{31} +(5.43193 - 1.57927i) q^{32} +(-8.40935 - 3.70156i) q^{34} +(1.61148 + 9.18797i) q^{35} +(-2.50967 - 2.50967i) q^{37} +(5.27251 - 2.04955i) q^{38} +(3.03475 + 5.54890i) q^{40} +9.18797 q^{41} +(-7.40312 - 7.40312i) q^{43} +(2.37681 - 2.17676i) q^{44} +(-2.00000 - 0.880344i) q^{46} +(-7.32206 - 7.32206i) q^{47} +10.4031i q^{49} +(-5.32540 + 4.65189i) q^{50} +(-0.311549 + 7.09158i) q^{52} +(3.11473 - 3.11473i) q^{53} +(2.94984 + 2.06950i) q^{55} +(3.78824 + 11.1747i) q^{56} +(-2.43569 - 6.26587i) q^{58} -1.61148i q^{59} +6.78003i q^{61} +(-6.61613 + 2.57184i) q^{62} +(4.86493 + 6.35078i) q^{64} +(-7.81695 + 1.37102i) q^{65} +(7.40312 - 7.40312i) q^{67} +(0.570295 - 12.9812i) q^{68} +(-11.2852 + 6.83193i) q^{70} +(5.00000 + 5.00000i) q^{73} +(2.02214 - 4.59398i) q^{74} +(5.40312 + 5.89968i) q^{76} +(4.75362 + 4.75362i) q^{77} -5.01934 q^{79} +(-5.75920 + 6.84337i) q^{80} +(4.70779 + 12.1109i) q^{82} +(-7.57648 - 7.57648i) q^{83} +(14.3090 - 2.50967i) q^{85} +(5.96500 - 13.5515i) q^{86} +(4.08709 + 2.01759i) q^{88} -2.74204i q^{89} -14.8062 q^{91} +(0.135633 - 3.08733i) q^{92} +(5.89968 - 13.4031i) q^{94} +(-5.13688 + 7.32206i) q^{95} +(2.40312 - 2.40312i) q^{97} +(-13.7126 + 5.33042i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{10} - 20 q^{16} + 36 q^{22} - 24 q^{25} + 44 q^{28} + 32 q^{40} - 16 q^{43} - 32 q^{46} - 8 q^{52} - 44 q^{58} + 16 q^{67} - 44 q^{70} + 80 q^{73} - 16 q^{76} - 8 q^{82} - 28 q^{88} - 32 q^{91} - 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^10 - 20 * q^16 + 36 * q^22 - 24 * q^25 + 44 * q^28 + 32 * q^40 - 16 * q^43 - 32 * q^46 - 8 * q^52 - 44 * q^58 + 16 * q^67 - 44 * q^70 + 80 * q^73 - 16 * q^76 - 8 * q^82 - 28 * q^88 - 32 * q^91 - 64 * q^97

Introduction

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