LMFDB - Embedded newform 384.3.i.d.353.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,3,Mod(161,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("384.161");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	384.i (of order $4$, degree $2$, not 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:	$10.4632421514$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 $ x^20 - 2x^18 + 6x^16 - 24x^14 - 24x^12 + 1216x^10 - 384x^8 - 6144x^6 + 24576x^4 - 131072*x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{23} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			353.9
Root			$1.85381 + 0.750590i$ of defining polynomial
Character	$\chi$	$=$	384.353
Dual form			384.3.i.d.161.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.59524 + 1.50491i) q^{3} +(-2.59897 + 2.59897i) q^{5} +7.30027i q^{7} +(4.47050 + 7.81118i) q^{9} +O(q^{10})$	\(q+(2.59524 + 1.50491i) q^{3} +(-2.59897 + 2.59897i) q^{5} +7.30027i q^{7} +(4.47050 + 7.81118i) q^{9} +(11.3161 - 11.3161i) q^{11} +(0.746462 - 0.746462i) q^{13} +(-10.6561 + 2.83373i) q^{15} +6.67452i q^{17} +(-22.1936 + 22.1936i) q^{19} +(-10.9862 + 18.9459i) q^{21} -21.4389 q^{23} +11.4908i q^{25} +(-0.153096 + 26.9996i) q^{27} +(1.54272 + 1.54272i) q^{29} -14.6082 q^{31} +(46.3976 - 12.3382i) q^{33} +(-18.9732 - 18.9732i) q^{35} +(50.1010 + 50.1010i) q^{37} +(3.06060 - 0.813888i) q^{39} +15.0731 q^{41} +(-26.3634 - 26.3634i) q^{43} +(-31.9197 - 8.68231i) q^{45} -36.6067i q^{47} -4.29399 q^{49} +(-10.0445 + 17.3220i) q^{51} +(50.9270 - 50.9270i) q^{53} +58.8202i q^{55} +(-90.9971 + 24.1983i) q^{57} +(-12.1683 + 12.1683i) q^{59} +(27.5789 - 27.5789i) q^{61} +(-57.0238 + 32.6359i) q^{63} +3.88006i q^{65} +(4.84214 - 4.84214i) q^{67} +(-55.6391 - 32.2636i) q^{69} +74.9072 q^{71} -3.47110i q^{73} +(-17.2925 + 29.8212i) q^{75} +(82.6105 + 82.6105i) q^{77} +103.463 q^{79} +(-41.0292 + 69.8399i) q^{81} +(-31.7254 - 31.7254i) q^{83} +(-17.3469 - 17.3469i) q^{85} +(1.68207 + 6.32538i) q^{87} +78.2605 q^{89} +(5.44937 + 5.44937i) q^{91} +(-37.9118 - 21.9840i) q^{93} -115.361i q^{95} -61.5651 q^{97} +(138.981 + 37.8034i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{3}+O(q^{10}) $ 20 * q + 6 * q^3	$ 20 q + 6 q^{3} - 92 q^{13} - 116 q^{15} + 52 q^{19} - 48 q^{21} - 18 q^{27} - 80 q^{31} + 60 q^{33} + 116 q^{37} - 172 q^{43} - 60 q^{45} - 364 q^{49} - 128 q^{51} + 244 q^{61} + 296 q^{63} - 356 q^{67} + 20 q^{69} + 146 q^{75} + 384 q^{79} - 188 q^{81} - 48 q^{85} - 136 q^{91} + 132 q^{93} + 472 q^{97} + 452 q^{99}+O(q^{100}) $ 20 * q + 6 * q^3 - 92 * q^13 - 116 * q^15 + 52 * q^19 - 48 * q^21 - 18 * q^27 - 80 * q^31 + 60 * q^33 + 116 * q^37 - 172 * q^43 - 60 * q^45 - 364 * q^49 - 128 * q^51 + 244 * q^61 + 296 * q^63 - 356 * q^67 + 20 * q^69 + 146 * q^75 + 384 * q^79 - 188 * q^81 - 48 * q^85 - 136 * q^91 + 132 * q^93 + 472 * q^97 + 452 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.59524	+	1.50491i	0.865079	+	0.501636i
$3$	2.59524	+	1.50491i	0.865079	+	0.501636i
$4$		0			0
$5$	−2.59897	+	2.59897i	−0.519793	+	0.519793i	−0.917509	−	0.397716i	$-0.869803\pi$
$5$	−2.59897	+	2.59897i	−0.519793	+	0.519793i	0.397716	+	0.917509i	$0.369803\pi$
$6$		0			0
$7$			7.30027i			1.04290i	0.853283	+	0.521448i	$0.174608\pi$
$7$			7.30027i			1.04290i	−0.853283	+	0.521448i	$0.825392\pi$
$8$		0			0
$9$	4.47050	+	7.81118i	0.496723	+	0.867909i
$10$		0			0
$11$	11.3161	−	11.3161i	1.02873	−	1.02873i	0.0291601	−	0.999575i	$-0.490717\pi$
$11$	11.3161	−	11.3161i	1.02873	−	1.02873i	0.999575	−	0.0291601i	$-0.00928328\pi$
$12$		0			0
$13$	0.746462	−	0.746462i	0.0574201	−	0.0574201i	−0.677814	−	0.735234i	$-0.737072\pi$
$13$	0.746462	−	0.746462i	0.0574201	−	0.0574201i	0.735234	+	0.677814i	$0.237072\pi$
$14$		0			0
$15$	−10.6561	+	2.83373i	−0.710409	+	0.188915i
$16$		0			0
$17$			6.67452i			0.392619i	0.980542	+	0.196310i	$0.0628957\pi$
$17$			6.67452i			0.392619i	−0.980542	+	0.196310i	$0.937104\pi$
$18$		0			0
$19$	−22.1936	+	22.1936i	−1.16809	+	1.16809i	−0.185428	+	0.982658i	$0.559367\pi$
$19$	−22.1936	+	22.1936i	−1.16809	+	1.16809i	−0.982658	+	0.185428i	$0.940633\pi$
$20$		0			0
$21$	−10.9862	+	18.9459i	−0.523154	+	0.902187i
$22$		0			0
$23$	−21.4389			−0.932128			−0.466064	−	0.884751i	$-0.654328\pi$
$23$	−21.4389			−0.932128			−0.466064	+	0.884751i	$0.654328\pi$
$24$		0			0
$25$			11.4908i			0.459630i
$26$		0			0
$27$	−0.153096	+	26.9996i	−0.00567024	+	0.999984i
$28$		0			0
$29$	1.54272	+	1.54272i	0.0531973	+	0.0531973i	0.733205	−	0.680008i	$-0.238024\pi$
$29$	1.54272	+	1.54272i	0.0531973	+	0.0531973i	−0.680008	+	0.733205i	$0.738024\pi$
$30$		0			0
$31$	−14.6082			−0.471233			−0.235616	−	0.971846i	$-0.575711\pi$
$31$	−14.6082			−0.471233			−0.235616	+	0.971846i	$0.575711\pi$
$32$		0			0
$33$	46.3976	−	12.3382i	1.40599	−	0.373886i
$34$		0			0
$35$	−18.9732	−	18.9732i	−0.542090	−	0.542090i
$36$		0			0
$37$	50.1010	+	50.1010i	1.35408	+	1.35408i	0.881041	+	0.473039i	$0.156843\pi$
$37$	50.1010	+	50.1010i	1.35408	+	1.35408i	0.473039	+	0.881041i	$0.343157\pi$
$38$		0			0
$39$	3.06060	−	0.813888i	0.0784769	−	0.0208689i
$40$		0			0
$41$	15.0731			0.367637			0.183819	−	0.982960i	$-0.441154\pi$
$41$	15.0731			0.367637			0.183819	+	0.982960i	$0.441154\pi$
$42$		0			0
$43$	−26.3634	−	26.3634i	−0.613102	−	0.613102i	0.330651	−	0.943753i	$-0.392732\pi$
$43$	−26.3634	−	26.3634i	−0.613102	−	0.613102i	−0.943753	+	0.330651i	$0.892732\pi$
$44$		0			0
$45$	−31.9197	−	8.68231i	−0.709326	−	0.192940i
$46$		0			0
$47$		−	36.6067i		−	0.778866i	−0.921055	−	0.389433i	$-0.872671\pi$
$47$		−	36.6067i		−	0.778866i	0.921055	−	0.389433i	$-0.127329\pi$
$48$		0			0
$49$	−4.29399			−0.0876325
$50$		0			0
$51$	−10.0445	+	17.3220i	−0.196952	+	0.339646i
$52$		0			0
$53$	50.9270	−	50.9270i	0.960887	−	0.960887i	−0.0383765	−	0.999263i	$-0.512219\pi$
$53$	50.9270	−	50.9270i	0.960887	−	0.960887i	0.999263	+	0.0383765i	$0.0122186\pi$
$54$		0			0
$55$			58.8202i			1.06946i
$56$		0			0
$57$	−90.9971	+	24.1983i	−1.59644	+	0.424532i
$58$		0			0
$59$	−12.1683	+	12.1683i	−0.206242	+	0.206242i	−0.802668	−	0.596426i	$-0.796587\pi$
$59$	−12.1683	+	12.1683i	−0.206242	+	0.206242i	0.596426	+	0.802668i	$0.296587\pi$
$60$		0			0
$61$	27.5789	−	27.5789i	0.452113	−	0.452113i	−0.443943	−	0.896055i	$-0.646421\pi$
$61$	27.5789	−	27.5789i	0.452113	−	0.452113i	0.896055	+	0.443943i	$0.146421\pi$
$62$		0			0
$63$	−57.0238	+	32.6359i	−0.905139	+	0.518030i
$64$		0			0
$65$			3.88006i			0.0596932i
$66$		0			0
$67$	4.84214	−	4.84214i	0.0722707	−	0.0722707i	−0.670047	−	0.742318i	$-0.733726\pi$
$67$	4.84214	−	4.84214i	0.0722707	−	0.0722707i	0.742318	+	0.670047i	$0.233726\pi$
$68$		0			0
$69$	−55.6391	−	32.2636i	−0.806364	−	0.467589i
$70$		0			0
$71$	74.9072			1.05503			0.527515	−	0.849546i	$-0.323124\pi$
$71$	74.9072			1.05503			0.527515	+	0.849546i	$0.323124\pi$
$72$		0			0
$73$		−	3.47110i		−	0.0475494i	−0.999717	−	0.0237747i	$-0.992432\pi$
$73$		−	3.47110i		−	0.0475494i	0.999717	−	0.0237747i	$-0.00756843\pi$
$74$		0			0
$75$	−17.2925	+	29.8212i	−0.230567	+	0.397616i
$76$		0			0
$77$	82.6105	+	82.6105i	1.07286	+	1.07286i
$78$		0			0
$79$	103.463			1.30966			0.654831	−	0.755775i	$-0.272740\pi$
$79$	103.463			1.30966			0.654831	+	0.755775i	$0.272740\pi$
$80$		0			0
$81$	−41.0292	+	69.8399i	−0.506533	+	0.862221i
$82$		0			0
$83$	−31.7254	−	31.7254i	−0.382233	−	0.382233i	0.489673	−	0.871906i	$-0.337116\pi$
$83$	−31.7254	−	31.7254i	−0.382233	−	0.382233i	−0.871906	+	0.489673i	$0.837116\pi$
$84$		0			0
$85$	−17.3469	−	17.3469i	−0.204081	−	0.204081i
$86$		0			0
$87$	1.68207	+	6.32538i	0.0193342	+	0.0727056i
$88$		0			0
$89$	78.2605			0.879331			0.439666	−	0.898162i	$-0.355097\pi$
$89$	78.2605			0.879331			0.439666	+	0.898162i	$0.355097\pi$
$90$		0			0
$91$	5.44937	+	5.44937i	0.0598832	+	0.0598832i
$92$		0			0
$93$	−37.9118	−	21.9840i	−0.407653	−	0.236387i
$94$		0			0
$95$		−	115.361i		−	1.21433i
$96$		0			0
$97$	−61.5651			−0.634692			−0.317346	−	0.948310i	$-0.602792\pi$
$97$	−61.5651			−0.634692			−0.317346	+	0.948310i	$0.602792\pi$
$98$		0			0
$99$	138.981	+	37.8034i	1.40384	+	0.381853i
$100$		0			0
$101$	−56.9675	+	56.9675i	−0.564034	+	0.564034i	−0.930451	−	0.366417i	$-0.880585\pi$
$101$	−56.9675	+	56.9675i	−0.564034	+	0.564034i	0.366417	+	0.930451i	$0.380585\pi$
$102$		0			0
$103$		−	153.944i		−	1.49460i	−0.664485	−	0.747301i	$-0.731349\pi$
$103$		−	153.944i		−	1.49460i	0.664485	−	0.747301i	$-0.268651\pi$
$104$		0			0
$105$	−20.6870	−	77.7927i	−0.197019	−	0.740883i
$106$		0			0
$107$	76.9344	−	76.9344i	0.719013	−	0.719013i	−0.249390	−	0.968403i	$-0.580230\pi$
$107$	76.9344	−	76.9344i	0.719013	−	0.719013i	0.968403	+	0.249390i	$0.0802300\pi$
$108$		0			0
$109$	−74.1271	+	74.1271i	−0.680065	+	0.680065i	−0.960015	−	0.279949i	$-0.909682\pi$
$109$	−74.1271	+	74.1271i	−0.680065	+	0.680065i	0.279949	+	0.960015i	$0.409682\pi$
$110$		0			0
$111$	54.6265	+	205.421i	0.492131	+	1.85064i
$112$		0			0
$113$		−	38.3909i		−	0.339742i	−0.985466	−	0.169871i	$-0.945665\pi$
$113$		−	38.3909i		−	0.339742i	0.985466	−	0.169871i	$-0.0543352\pi$
$114$		0			0
$115$	55.7191	−	55.7191i	0.484514	−	0.484514i
$116$		0			0
$117$	9.16781	+	2.49369i	0.0783573	+	0.0213136i
$118$		0			0
$119$	−48.7259			−0.409461
$120$		0			0
$121$		−	135.108i		−	1.11659i
$122$		0			0
$123$	39.1184	+	22.6837i	0.318035	+	0.184420i
$124$		0			0
$125$	−94.8382	−	94.8382i	−0.758706	−	0.758706i
$126$		0			0
$127$	−43.3417			−0.341273			−0.170636	−	0.985334i	$-0.554582\pi$
$127$	−43.3417			−0.341273			−0.170636	+	0.985334i	$0.554582\pi$
$128$		0			0
$129$	−28.7447	−	108.094i	−0.222827	−	0.837935i
$130$		0			0
$131$	1.21414	+	1.21414i	0.00926827	+	0.00926827i	0.711726	−	0.702457i	$-0.247914\pi$
$131$	1.21414	+	1.21414i	0.00926827	+	0.00926827i	−0.702457	+	0.711726i	$0.747914\pi$
$132$		0			0
$133$	−162.020	−	162.020i	−1.21819	−	1.21819i
$134$		0			0
$135$	−69.7730	−	70.5688i	−0.516837	−	0.522732i
$136$		0			0
$137$	238.227			1.73889			0.869443	−	0.494033i	$-0.164478\pi$
$137$	238.227			1.73889			0.869443	+	0.494033i	$0.164478\pi$
$138$		0			0
$139$	26.5704	+	26.5704i	0.191154	+	0.191154i	0.796195	−	0.605041i	$-0.206843\pi$
$139$	26.5704	+	26.5704i	0.191154	+	0.191154i	−0.605041	+	0.796195i	$0.706843\pi$
$140$		0			0
$141$	55.0897	−	95.0030i	0.390707	−	0.673780i
$142$		0			0
$143$		−	16.8940i		−	0.118140i
$144$		0			0
$145$	−8.01896			−0.0553032
$146$		0			0
$147$	−11.1439	−	6.46207i	−0.0758090	−	0.0439596i
$148$		0			0
$149$	133.254	−	133.254i	0.894321	−	0.894321i	−0.100605	−	0.994926i	$-0.532078\pi$
$149$	133.254	−	133.254i	0.894321	−	0.894321i	0.994926	+	0.100605i	$0.0320779\pi$
$150$		0			0
$151$		−	23.3716i		−	0.154779i	−0.997001	−	0.0773895i	$-0.975342\pi$
$151$		−	23.3716i		−	0.154779i	0.997001	−	0.0773895i	$-0.0246585\pi$
$152$		0			0
$153$	−52.1359	+	29.8385i	−0.340758	+	0.195023i
$154$		0			0
$155$	37.9662	−	37.9662i	0.244943	−	0.244943i
$156$		0			0
$157$	95.8780	−	95.8780i	0.610688	−	0.610688i	−0.332438	−	0.943125i	$-0.607871\pi$
$157$	95.8780	−	95.8780i	0.610688	−	0.610688i	0.943125	+	0.332438i	$0.107871\pi$
$158$		0			0
$159$	208.808	−	55.5272i	1.31326	−	0.349227i
$160$		0			0
$161$		−	156.510i		−	0.972113i
$162$		0			0
$163$	103.379	−	103.379i	0.634230	−	0.634230i	−0.314896	−	0.949126i	$-0.601970\pi$
$163$	103.379	−	103.379i	0.634230	−	0.634230i	0.949126	+	0.314896i	$0.101970\pi$
$164$		0			0
$165$	−88.5190	+	152.652i	−0.536479	+	0.925166i
$166$		0			0
$167$	−113.980			−0.682515			−0.341258	−	0.939970i	$-0.610853\pi$
$167$	−113.980			−0.682515			−0.341258	+	0.939970i	$0.610853\pi$
$168$		0			0
$169$			167.886i			0.993406i
$170$		0			0
$171$	−272.575	−	74.1418i	−1.59401	−	0.433578i
$172$		0			0
$173$	144.265	+	144.265i	0.833901	+	0.833901i	0.988048	−	0.154147i	$-0.0492630\pi$
$173$	144.265	+	144.265i	0.833901	+	0.833901i	−0.154147	+	0.988048i	$0.549263\pi$
$174$		0			0
$175$	−83.8857			−0.479347
$176$		0			0
$177$	−49.8918	+	13.2674i	−0.281875	+	0.0749573i
$178$		0			0
$179$	−16.8240	−	16.8240i	−0.0939888	−	0.0939888i	0.658549	−	0.752538i	$-0.271171\pi$
$179$	−16.8240	−	16.8240i	−0.0939888	−	0.0939888i	−0.752538	+	0.658549i	$0.771171\pi$
$180$		0			0
$181$	−34.2037	−	34.2037i	−0.188971	−	0.188971i	0.606280	−	0.795251i	$-0.292661\pi$
$181$	−34.2037	−	34.2037i	−0.188971	−	0.188971i	−0.795251	+	0.606280i	$0.792661\pi$
$182$		0			0
$183$	113.077	−	30.0700i	0.617909	−	0.164317i
$184$		0			0
$185$	−260.421			−1.40768
$186$		0			0
$187$	75.5295	+	75.5295i	0.403901	+	0.403901i
$188$		0			0
$189$	−197.104	−	1.11765i	−1.04288	−	0.00591347i
$190$		0			0
$191$			150.160i			0.786177i	0.919501	+	0.393088i	$0.128593\pi$
$191$			150.160i			0.786177i	−0.919501	+	0.393088i	$0.871407\pi$
$192$		0			0
$193$	117.637			0.609518			0.304759	−	0.952429i	$-0.401424\pi$
$193$	117.637			0.609518			0.304759	+	0.952429i	$0.401424\pi$
$194$		0			0
$195$	−5.83913	+	10.0697i	−0.0299442	+	0.0516393i
$196$		0			0
$197$	31.8524	−	31.8524i	0.161688	−	0.161688i	−0.621626	−	0.783314i	$-0.713528\pi$
$197$	31.8524	−	31.8524i	0.161688	−	0.161688i	0.783314	+	0.621626i	$0.213528\pi$
$198$		0			0
$199$			128.347i			0.644959i	0.946576	+	0.322480i	$0.104516\pi$
$199$			128.347i			0.644959i	−0.946576	+	0.322480i	$0.895484\pi$
$200$		0			0
$201$	19.8535	−	5.27952i	0.0987735	−	0.0262663i
$202$		0			0
$203$	−11.2623	+	11.2623i	−0.0554793	+	0.0554793i
$204$		0			0
$205$	−39.1746	+	39.1746i	−0.191095	+	0.191095i
$206$		0			0
$207$	−95.8429	−	167.464i	−0.463009	−	0.809003i
$208$		0			0
$209$			502.290i			2.40330i
$210$		0			0
$211$	−78.8045	+	78.8045i	−0.373481	+	0.373481i	−0.868743	−	0.495262i	$-0.835072\pi$
$211$	−78.8045	+	78.8045i	−0.373481	+	0.373481i	0.495262	+	0.868743i	$0.335072\pi$
$212$		0			0
$213$	194.402	+	112.728i	0.912685	+	0.529241i
$214$		0			0
$215$	137.035			0.637372
$216$		0			0
$217$		−	106.644i		−	0.491447i
$218$		0			0
$219$	5.22369	−	9.00834i	0.0238525	−	0.0411340i
$220$		0			0
$221$	4.98228	+	4.98228i	0.0225442	+	0.0225442i
$222$		0			0
$223$	−153.748			−0.689455			−0.344727	−	0.938703i	$-0.612029\pi$
$223$	−153.748			−0.689455			−0.344727	+	0.938703i	$0.612029\pi$
$224$		0			0
$225$	−89.7564	+	51.3695i	−0.398917	+	0.228309i
$226$		0			0
$227$	−43.6518	−	43.6518i	−0.192299	−	0.192299i	0.604390	−	0.796689i	$-0.293417\pi$
$227$	−43.6518	−	43.6518i	−0.192299	−	0.192299i	−0.796689	+	0.604390i	$0.793417\pi$
$228$		0			0
$229$	111.882	+	111.882i	0.488566	+	0.488566i	0.907853	−	0.419288i	$-0.137720\pi$
$229$	111.882	+	111.882i	0.488566	+	0.488566i	−0.419288	+	0.907853i	$0.637720\pi$
$230$		0			0
$231$	90.0726	+	338.715i	0.389925	+	1.46630i
$232$		0			0
$233$	32.4793			0.139396			0.0696980	−	0.997568i	$-0.477796\pi$
$233$	32.4793			0.139396			0.0696980	+	0.997568i	$0.477796\pi$
$234$		0			0
$235$	95.1395	+	95.1395i	0.404849	+	0.404849i
$236$		0			0
$237$	268.512	+	155.703i	1.13296	+	0.656974i
$238$		0			0
$239$		−	133.305i		−	0.557762i	−0.960326	−	0.278881i	$-0.910036\pi$
$239$		−	133.305i		−	0.557762i	0.960326	−	0.278881i	$-0.0899636\pi$
$240$		0			0
$241$	159.670			0.662532			0.331266	−	0.943537i	$-0.392524\pi$
$241$	159.670			0.662532			0.331266	+	0.943537i	$0.392524\pi$
$242$		0			0
$243$	−211.583	+	119.506i	−0.870712	+	0.491793i
$244$		0			0
$245$	11.1599	−	11.1599i	0.0455508	−	0.0455508i
$246$		0			0
$247$			33.1334i			0.134143i
$248$		0			0
$249$	−34.5911	−	130.079i	−0.138920	−	0.522404i
$250$		0			0
$251$	−106.711	+	106.711i	−0.425141	+	0.425141i	−0.886969	−	0.461828i	$-0.847194\pi$
$251$	−106.711	+	106.711i	−0.425141	+	0.425141i	0.461828	+	0.886969i	$0.347194\pi$
$252$		0			0
$253$	−242.605	+	242.605i	−0.958913	+	0.958913i
$254$		0			0
$255$	−18.9138	−	71.1246i	−0.0741717	−	0.278920i
$256$		0			0
$257$		−	343.816i		−	1.33781i	−0.743350	−	0.668903i	$-0.766764\pi$
$257$		−	343.816i		−	1.33781i	0.743350	−	0.668903i	$-0.233236\pi$
$258$		0			0
$259$	−365.751	+	365.751i	−1.41217	+	1.41217i
$260$		0			0
$261$	−5.15374	+	18.9472i	−0.0197461	+	0.0725948i
$262$		0			0
$263$	266.255			1.01238			0.506188	−	0.862423i	$-0.331054\pi$
$263$	266.255			1.01238			0.506188	+	0.862423i	$0.331054\pi$
$264$		0			0
$265$			264.715i			0.998925i
$266$		0			0
$267$	203.104	+	117.775i	0.760691	+	0.441104i
$268$		0			0
$269$	−102.194	−	102.194i	−0.379904	−	0.379904i	0.491164	−	0.871067i	$-0.336572\pi$
$269$	−102.194	−	102.194i	−0.379904	−	0.379904i	−0.871067	+	0.491164i	$0.836572\pi$
$270$		0			0
$271$	−38.5636			−0.142301			−0.0711505	−	0.997466i	$-0.522667\pi$
$271$	−38.5636			−0.142301			−0.0711505	+	0.997466i	$0.522667\pi$
$272$		0			0
$273$	5.94161	+	22.3432i	0.0217641	+	0.0818433i
$274$		0			0
$275$	130.030	+	130.030i	0.472838	+	0.472838i
$276$		0			0
$277$	277.306	+	277.306i	1.00111	+	1.00111i	0.999999	+	0.00110593i	$0.000352027\pi$
$277$	277.306	+	277.306i	1.00111	+	1.00111i	0.00110593	+	0.999999i	$0.499648\pi$
$278$		0			0
$279$	−65.3061	−	114.107i	−0.234072	−	0.408987i
$280$		0			0
$281$	−458.765			−1.63262			−0.816308	−	0.577617i	$-0.803983\pi$
$281$	−458.765			−1.63262			−0.816308	+	0.577617i	$0.803983\pi$
$282$		0			0
$283$	−276.746	−	276.746i	−0.977900	−	0.977900i	0.0218614	−	0.999761i	$-0.493041\pi$
$283$	−276.746	−	276.746i	−0.977900	−	0.977900i	−0.999761	+	0.0218614i	$0.993041\pi$
$284$		0			0
$285$	173.608	−	299.389i	0.609149	−	1.05049i
$286$		0			0
$287$			110.038i			0.383408i
$288$		0			0
$289$	244.451			0.845850
$290$		0			0
$291$	−159.776	−	92.6499i	−0.549059	−	0.318384i
$292$		0			0
$293$	−306.513	+	306.513i	−1.04612	+	1.04612i	−0.0472370	+	0.998884i	$0.515042\pi$
$293$	−306.513	+	306.513i	−1.04612	+	1.04612i	−0.998884	+	0.0472370i	$0.984958\pi$
$294$		0			0
$295$		−	63.2500i		−	0.214407i
$296$		0			0
$297$	303.797	+	307.262i	1.02289	+	1.03455i
$298$		0			0
$299$	−16.0033	+	16.0033i	−0.0535229	+	0.0535229i
$300$		0			0
$301$	192.460	−	192.460i	0.639401	−	0.639401i
$302$		0			0
$303$	−233.575	+	62.1133i	−0.770874	+	0.204994i
$304$		0			0
$305$			143.353i			0.470010i
$306$		0			0
$307$	359.692	−	359.692i	1.17163	−	1.17163i	0.189814	−	0.981820i	$-0.439211\pi$
$307$	359.692	−	359.692i	1.17163	−	1.17163i	0.981820	−	0.189814i	$-0.0607886\pi$
$308$		0			0
$309$	231.672	−	399.521i	0.749746	−	1.29295i
$310$		0			0
$311$	−572.008			−1.83925			−0.919626	−	0.392794i	$-0.871508\pi$
$311$	−572.008			−1.83925			−0.919626	+	0.392794i	$0.871508\pi$
$312$		0			0
$313$			333.314i			1.06490i	0.846461	+	0.532450i	$0.178729\pi$
$313$			333.314i			1.06490i	−0.846461	+	0.532450i	$0.821271\pi$
$314$		0			0
$315$	63.3832	−	233.022i	0.201217	−	0.739754i
$316$		0			0
$317$	−266.382	−	266.382i	−0.840322	−	0.840322i	0.148578	−	0.988901i	$-0.452530\pi$
$317$	−266.382	−	266.382i	−0.840322	−	0.840322i	−0.988901	+	0.148578i	$0.952530\pi$
$318$		0			0
$319$	34.9151			0.109452
$320$		0			0
$321$	315.442	−	83.8838i	0.982686	−	0.261320i
$322$		0			0
$323$	−148.132	−	148.132i	−0.458613	−	0.458613i
$324$		0			0
$325$	8.57741	+	8.57741i	0.0263920	+	0.0263920i
$326$		0			0
$327$	−303.932	+	80.8229i	−0.929455	+	0.247165i
$328$		0			0
$329$	267.239			0.812276
$330$		0			0
$331$	212.431	+	212.431i	0.641787	+	0.641787i	0.950995	−	0.309208i	$-0.100064\pi$
$331$	212.431	+	212.431i	0.641787	+	0.641787i	−0.309208	+	0.950995i	$0.600064\pi$
$332$		0			0
$333$	−167.371	+	615.325i	−0.502617	+	1.84782i
$334$		0			0
$335$			25.1691i			0.0751317i
$336$		0			0
$337$	−207.477			−0.615658			−0.307829	−	0.951442i	$-0.599602\pi$
$337$	−207.477			−0.615658			−0.307829	+	0.951442i	$0.599602\pi$
$338$		0			0
$339$	57.7748	−	99.6335i	0.170427	−	0.293904i
$340$		0			0
$341$	−165.308	+	165.308i	−0.484773	+	0.484773i
$342$		0			0
$343$			326.366i			0.951505i
$344$		0			0
$345$	228.456	−	60.7521i	0.662192	−	0.176093i
$346$		0			0
$347$	−98.4692	+	98.4692i	−0.283773	+	0.283773i	−0.834612	−	0.550839i	$-0.814308\pi$
$347$	−98.4692	+	98.4692i	−0.283773	+	0.283773i	0.550839	+	0.834612i	$0.314308\pi$
$348$		0			0
$349$	337.382	−	337.382i	0.966711	−	0.966711i	−0.0327527	−	0.999463i	$-0.510427\pi$
$349$	337.382	−	337.382i	0.966711	−	0.966711i	0.999463	+	0.0327527i	$0.0104274\pi$
$350$		0			0
$351$	20.0399	+	20.2684i	0.0570936	+	0.0577448i
$352$		0			0
$353$		−	293.330i		−	0.830964i	−0.909601	−	0.415482i	$-0.863613\pi$
$353$		−	293.330i		−	0.830964i	0.909601	−	0.415482i	$-0.136387\pi$
$354$		0			0
$355$	−194.681	+	194.681i	−0.548398	+	0.548398i
$356$		0			0
$357$	−126.455	−	73.3279i	−0.354216	−	0.205400i
$358$		0			0
$359$	−305.954			−0.852239			−0.426119	−	0.904667i	$-0.640120\pi$
$359$	−305.954			−0.852239			−0.426119	+	0.904667i	$0.640120\pi$
$360$		0			0
$361$		−	624.114i		−	1.72885i
$362$		0			0
$363$	203.324	−	350.636i	0.560122	−	0.965939i
$364$		0			0
$365$	9.02128	+	9.02128i	0.0247158	+	0.0247158i
$366$		0			0
$367$	221.149			0.602585			0.301292	−	0.953532i	$-0.402582\pi$
$367$	221.149			0.602585			0.301292	+	0.953532i	$0.402582\pi$
$368$		0			0
$369$	67.3845	+	117.739i	0.182614	+	0.319076i
$370$		0			0
$371$	371.781	+	371.781i	1.00211	+	1.00211i
$372$		0			0
$373$	−147.216	−	147.216i	−0.394682	−	0.394682i	0.481671	−	0.876352i	$-0.340030\pi$
$373$	−147.216	−	147.216i	−0.394682	−	0.394682i	−0.876352	+	0.481671i	$0.840030\pi$
$374$		0			0
$375$	−103.405	−	388.850i	−0.275746	−	1.03693i
$376$		0			0
$377$	2.30317			0.00610919
$378$		0			0
$379$	−298.572	−	298.572i	−0.787790	−	0.787790i	0.193342	−	0.981131i	$-0.438067\pi$
$379$	−298.572	−	298.572i	−0.787790	−	0.787790i	−0.981131	+	0.193342i	$0.938067\pi$
$380$		0			0
$381$	−112.482	−	65.2252i	−0.295228	−	0.171195i
$382$		0			0
$383$			427.326i			1.11573i	0.829931	+	0.557866i	$0.188380\pi$
$383$			427.326i			1.11573i	−0.829931	+	0.557866i	$0.811620\pi$
$384$		0			0
$385$	−429.404			−1.11533
$386$		0			0
$387$	88.0716	−	323.787i	0.227575	−	0.836658i
$388$		0			0
$389$	−314.075	+	314.075i	−0.807391	+	0.807391i	−0.984238	−	0.176847i	$-0.943410\pi$
$389$	−314.075	+	314.075i	−0.807391	+	0.807391i	0.176847	+	0.984238i	$0.443410\pi$
$390$		0			0
$391$		−	143.095i		−	0.365971i
$392$		0			0
$393$	1.32382	+	4.97816i	0.00336849	+	0.0126671i
$394$		0			0
$395$	−268.898	+	268.898i	−0.680753	+	0.680753i
$396$		0			0
$397$	−189.839	+	189.839i	−0.478185	+	0.478185i	−0.904551	−	0.426366i	$-0.859794\pi$
$397$	−189.839	+	189.839i	−0.478185	+	0.478185i	0.426366	+	0.904551i	$0.359794\pi$
$398$		0			0
$399$	−176.655	−	664.304i	−0.442743	−	1.66492i
$400$		0			0
$401$		−	268.223i		−	0.668886i	−0.942416	−	0.334443i	$-0.891452\pi$
$401$		−	268.223i		−	0.668886i	0.942416	−	0.334443i	$-0.108548\pi$
$402$		0			0
$403$	−10.9045	+	10.9045i	−0.0270582	+	0.0270582i
$404$		0			0
$405$	−74.8780	−	288.145i	−0.184884	−	0.711469i
$406$		0			0
$407$	1133.89			2.78598
$408$		0			0
$409$		−	25.8478i		−	0.0631976i	−0.999501	−	0.0315988i	$-0.989940\pi$
$409$		−	25.8478i		−	0.0631976i	0.999501	−	0.0315988i	$-0.0100599\pi$
$410$		0			0
$411$	618.257	+	358.510i	1.50427	+	0.872288i
$412$		0			0
$413$	−88.8319	−	88.8319i	−0.215089	−	0.215089i
$414$		0			0
$415$	164.906			0.397365
$416$		0			0
$417$	28.9705	+	108.942i	0.0694735	+	0.261253i
$418$		0			0
$419$	243.361	+	243.361i	0.580813	+	0.580813i	0.935127	−	0.354313i	$-0.115285\pi$
$419$	243.361	+	243.361i	0.580813	+	0.580813i	−0.354313	+	0.935127i	$0.615285\pi$
$420$		0			0
$421$	−115.847	−	115.847i	−0.275171	−	0.275171i	0.556007	−	0.831178i	$-0.312333\pi$
$421$	−115.847	−	115.847i	−0.275171	−	0.275171i	−0.831178	+	0.556007i	$0.812333\pi$
$422$		0			0
$423$	285.942	−	163.650i	0.675985	−	0.386880i
$424$		0			0
$425$	−76.6953			−0.180460
$426$		0			0
$427$	201.333	+	201.333i	0.471507	+	0.471507i
$428$		0			0
$429$	25.4240	−	43.8440i	0.0592634	−	0.102201i
$430$		0			0
$431$			568.037i			1.31795i	0.752165	+	0.658975i	$0.229010\pi$
$431$			568.037i			1.31795i	−0.752165	+	0.658975i	$0.770990\pi$
$432$		0			0
$433$	−647.222			−1.49474			−0.747370	−	0.664408i	$-0.768684\pi$
$433$	−647.222			−1.49474			−0.747370	+	0.664408i	$0.768684\pi$
$434$		0			0
$435$	−20.8111	−	12.0678i	−0.0478416	−	0.0277421i
$436$		0			0
$437$	475.808	−	475.808i	1.08881	−	1.08881i
$438$		0			0
$439$		−	486.389i		−	1.10795i	−0.832534	−	0.553973i	$-0.813111\pi$
$439$		−	486.389i		−	1.10795i	0.832534	−	0.553973i	$-0.186889\pi$
$440$		0			0
$441$	−19.1963	−	33.5412i	−0.0435291	−	0.0760571i
$442$		0			0
$443$	258.469	−	258.469i	0.583451	−	0.583451i	−0.352399	−	0.935850i	$-0.614634\pi$
$443$	258.469	−	258.469i	0.583451	−	0.583451i	0.935850	+	0.352399i	$0.114634\pi$
$444$		0			0
$445$	−203.396	+	203.396i	−0.457070	+	0.457070i
$446$		0			0
$447$	546.360	−	145.290i	1.22228	−	0.325035i
$448$		0			0
$449$			498.015i			1.10916i	0.832129	+	0.554582i	$0.187122\pi$
$449$			498.015i			1.10916i	−0.832129	+	0.554582i	$0.812878\pi$
$450$		0			0
$451$	170.569	−	170.569i	0.378201	−	0.378201i
$452$		0			0
$453$	35.1721	−	60.6549i	0.0776427	−	0.133896i
$454$		0			0
$455$	−28.3255			−0.0622538
$456$		0			0
$457$		−	466.468i		−	1.02072i	−0.859961	−	0.510359i	$-0.829513\pi$
$457$		−	466.468i		−	1.02072i	0.859961	−	0.510359i	$-0.170487\pi$
$458$		0			0
$459$	−180.209	−	1.02185i	−0.392613	−	0.00222624i
$460$		0			0
$461$	389.251	+	389.251i	0.844362	+	0.844362i	0.989423	−	0.145061i	$-0.0463378\pi$
$461$	389.251	+	389.251i	0.844362	+	0.844362i	−0.145061	+	0.989423i	$0.546338\pi$
$462$		0			0
$463$	500.857			1.08177			0.540883	−	0.841098i	$-0.318090\pi$
$463$	500.857			1.08177			0.540883	+	0.841098i	$0.318090\pi$
$464$		0			0
$465$	155.667	−	41.3957i	0.334768	−	0.0890229i
$466$		0			0
$467$	−188.836	−	188.836i	−0.404359	−	0.404359i	0.475407	−	0.879766i	$-0.342301\pi$
$467$	−188.836	−	188.836i	−0.404359	−	0.404359i	−0.879766	+	0.475407i	$0.842301\pi$
$468$		0			0
$469$	35.3489	+	35.3489i	0.0753709	+	0.0753709i
$470$		0			0
$471$	393.113	−	104.538i	0.834636	−	0.221950i
$472$		0			0
$473$	−596.660			−1.26144
$474$		0			0
$475$	−255.022	−	255.022i	−0.536888	−	0.536888i
$476$		0			0
$477$	625.470	+	170.131i	1.31126	+	0.356668i
$478$		0			0
$479$		−	326.344i		−	0.681303i	−0.940190	−	0.340652i	$-0.889352\pi$
$479$		−	326.344i		−	0.681303i	0.940190	−	0.340652i	$-0.110648\pi$
$480$		0			0
$481$	74.7969			0.155503
$482$		0			0
$483$	235.533	−	406.181i	0.487647	−	0.840954i
$484$		0			0
$485$	160.006	−	160.006i	0.329909	−	0.329909i
$486$		0			0
$487$			196.238i			0.402952i	0.979493	+	0.201476i	$0.0645739\pi$
$487$			196.238i			0.402952i	−0.979493	+	0.201476i	$0.935426\pi$
$488$		0			0
$489$	423.871	−	112.718i	0.866812	−	0.230506i
$490$		0			0
$491$	−349.172	+	349.172i	−0.711144	+	0.711144i	−0.966774	−	0.255631i	$-0.917717\pi$
$491$	−349.172	+	349.172i	−0.711144	+	0.711144i	0.255631	+	0.966774i	$0.417717\pi$
$492$		0			0
$493$	−10.2969	+	10.2969i	−0.0208863	+	0.0208863i
$494$		0			0
$495$	−459.456	+	262.956i	−0.928193	+	0.531224i
$496$		0			0
$497$			546.843i			1.10029i
$498$		0			0
$499$	321.326	−	321.326i	0.643940	−	0.643940i	−0.307582	−	0.951522i	$-0.599520\pi$
$499$	321.326	−	321.326i	0.643940	−	0.643940i	0.951522	+	0.307582i	$0.0995198\pi$
$500$		0			0
$501$	−295.805	−	171.530i	−0.590430	−	0.342374i
$502$		0			0
$503$	−623.698			−1.23996			−0.619978	−	0.784619i	$-0.712858\pi$
$503$	−623.698			−1.23996			−0.619978	+	0.784619i	$0.712858\pi$
$504$		0			0
$505$		−	296.113i		−	0.586362i
$506$		0			0
$507$	−252.652	+	435.703i	−0.498328	+	0.859374i
$508$		0			0
$509$	−452.448	−	452.448i	−0.888897	−	0.888897i	0.105520	−	0.994417i	$-0.466349\pi$
$509$	−452.448	−	452.448i	−0.888897	−	0.888897i	−0.994417	+	0.105520i	$0.966349\pi$
$510$		0			0
$511$	25.3400			0.0495891
$512$		0			0
$513$	−595.821	−	602.616i	−1.16144	−	1.17469i
$514$		0			0
$515$	400.095	+	400.095i	0.776884	+	0.776884i
$516$		0			0
$517$	−414.244	−	414.244i	−0.801247	−	0.801247i
$518$		0			0
$519$	157.296	+	591.506i	0.303075	+	1.13970i
$520$		0			0
$521$	−444.986			−0.854100			−0.427050	−	0.904228i	$-0.640447\pi$
$521$	−444.986			−0.854100			−0.427050	+	0.904228i	$0.640447\pi$
$522$		0			0
$523$	−399.942	−	399.942i	−0.764707	−	0.764707i	0.212462	−	0.977169i	$-0.431852\pi$
$523$	−399.942	−	399.942i	−0.764707	−	0.764707i	−0.977169	+	0.212462i	$0.931852\pi$
$524$		0			0
$525$	−217.703	−	126.240i	−0.414673	−	0.240458i
$526$		0			0
$527$		−	97.5029i		−	0.185015i
$528$		0			0
$529$	−69.3715			−0.131137
$530$		0			0
$531$	−149.447	−	40.6504i	−0.281445	−	0.0765544i
$532$		0			0
$533$	11.2515	−	11.2515i	0.0211098	−	0.0211098i
$534$		0			0
$535$			399.900i			0.747476i
$536$		0			0
$537$	−18.3437	−	68.9808i	−0.0341595	−	0.128456i
$538$		0			0
$539$	−48.5912	+	48.5912i	−0.0901506	+	0.0901506i
$540$		0			0
$541$	116.940	−	116.940i	0.216155	−	0.216155i	−0.590721	−	0.806876i	$-0.701156\pi$
$541$	116.940	−	116.940i	0.216155	−	0.216155i	0.806876	+	0.590721i	$0.201156\pi$
$542$		0			0
$543$	−37.2932	−	140.240i	−0.0686800	−	0.258269i
$544$		0			0
$545$		−	385.308i		−	0.706987i
$546$		0			0
$547$	−85.6914	+	85.6914i	−0.156657	+	0.156657i	−0.781084	−	0.624427i	$-0.785333\pi$
$547$	−85.6914	+	85.6914i	−0.156657	+	0.156657i	0.624427	+	0.781084i	$0.285333\pi$
$548$		0			0
$549$	338.715	+	92.1322i	0.616968	+	0.167818i
$550$		0			0
$551$	−68.4772			−0.124278
$552$		0			0
$553$			755.311i			1.36584i
$554$		0			0
$555$	−675.855	−	391.910i	−1.21776	−	0.706145i
$556$		0			0
$557$	−104.194	−	104.194i	−0.187062	−	0.187062i	0.607363	−	0.794425i	$-0.292228\pi$
$557$	−104.194	−	104.194i	−0.187062	−	0.187062i	−0.794425	+	0.607363i	$0.792228\pi$
$558$		0			0
$559$	−39.3585			−0.0704087
$560$		0			0
$561$	82.3519	+	309.682i	0.146795	+	0.552017i
$562$		0			0
$563$	−776.673	−	776.673i	−1.37953	−	1.37953i	−0.845414	−	0.534111i	$-0.820646\pi$
$563$	−776.673	−	776.673i	−1.37953	−	1.37953i	−0.534111	−	0.845414i	$-0.679354\pi$
$564$		0			0
$565$	99.7766	+	99.7766i	0.176596	+	0.176596i
$566$		0			0
$567$	−509.850	−	299.524i	−0.899207	−	0.528261i
$568$		0			0
$569$	456.546			0.802366			0.401183	−	0.915998i	$-0.368599\pi$
$569$	456.546			0.802366			0.401183	+	0.915998i	$0.368599\pi$
$570$		0			0
$571$	475.108	+	475.108i	0.832062	+	0.832062i	0.987799	−	0.155736i	$-0.0497750\pi$
$571$	475.108	+	475.108i	0.832062	+	0.832062i	−0.155736	+	0.987799i	$0.549775\pi$
$572$		0			0
$573$	−225.977	+	389.700i	−0.394375	+	0.680105i
$574$		0			0
$575$		−	246.350i		−	0.428434i
$576$		0			0
$577$	1127.70			1.95443			0.977213	−	0.212262i	$-0.0680832\pi$
$577$	1127.70			1.95443			0.977213	+	0.212262i	$0.0680832\pi$
$578$		0			0
$579$	305.296	+	177.033i	0.527281	+	0.305756i
$580$		0			0
$581$	231.604	−	231.604i	0.398630	−	0.398630i
$582$		0			0
$583$		−	1152.59i		−	1.97700i
$584$		0			0
$585$	−30.3078	+	17.3458i	−0.0518082	+	0.0296509i
$586$		0			0
$587$	584.236	−	584.236i	0.995292	−	0.995292i	−0.00469688	−	0.999989i	$-0.501495\pi$
$587$	584.236	−	584.236i	0.995292	−	0.995292i	0.999989	+	0.00469688i	$0.00149507\pi$
$588$		0			0
$589$	324.209	−	324.209i	0.550440	−	0.550440i
$590$		0			0
$591$	130.600	−	34.7296i	0.220981	−	0.0587642i
$592$		0			0
$593$		−	870.906i		−	1.46864i	−0.678801	−	0.734322i	$-0.737500\pi$
$593$		−	870.906i		−	1.46864i	0.678801	−	0.734322i	$-0.262500\pi$
$594$		0			0
$595$	126.637	−	126.637i	0.212835	−	0.212835i
$596$		0			0
$597$	−193.150	+	333.090i	−0.323535	+	0.557940i
$598$		0			0
$599$	224.305			0.374466			0.187233	−	0.982316i	$-0.440048\pi$
$599$	224.305			0.374466			0.187233	+	0.982316i	$0.440048\pi$
$600$		0			0
$601$			234.358i			0.389946i	0.980809	+	0.194973i	$0.0624620\pi$
$601$			234.358i			0.389946i	−0.980809	+	0.194973i	$0.937538\pi$
$602$		0			0
$603$	59.4697	+	16.1760i	0.0986230	+	0.0268259i
$604$		0			0
$605$	351.140	+	351.140i	0.580396	+	0.580396i
$606$		0			0
$607$	−620.755			−1.02266			−0.511330	−	0.859384i	$-0.670847\pi$
$607$	−620.755			−1.02266			−0.511330	+	0.859384i	$0.670847\pi$
$608$		0			0
$609$	−46.1770	+	12.2796i	−0.0758244	+	0.0201635i
$610$		0			0
$611$	−27.3255	−	27.3255i	−0.0447226	−	0.0447226i
$612$		0			0
$613$	645.945	+	645.945i	1.05374	+	1.05374i	0.998471	+	0.0552724i	$0.0176027\pi$
$613$	645.945	+	645.945i	1.05374	+	1.05374i	0.0552724	+	0.998471i	$0.482397\pi$
$614$		0			0
$615$	−160.621	+	42.7131i	−0.261173	+	0.0694523i
$616$		0			0
$617$	169.883			0.275337			0.137669	−	0.990478i	$-0.456039\pi$
$617$	169.883			0.275337			0.137669	+	0.990478i	$0.456039\pi$
$618$		0			0
$619$	647.603	+	647.603i	1.04621	+	1.04621i	0.998879	+	0.0473286i	$0.0150708\pi$
$619$	647.603	+	647.603i	1.04621	+	1.04621i	0.0473286	+	0.998879i	$0.484929\pi$
$620$		0			0
$621$	3.28222	−	578.842i	0.00528539	−	0.932113i
$622$		0			0
$623$			571.323i			0.917051i
$624$		0			0
$625$	205.694			0.329110
$626$		0			0
$627$	−755.900	+	1303.56i	−1.20558	+	2.07904i
$628$		0			0
$629$	−334.400	+	334.400i	−0.531638	+	0.531638i
$630$		0			0
$631$			975.374i			1.54576i	0.634553	+	0.772880i	$0.281184\pi$
$631$			975.374i			1.54576i	−0.634553	+	0.772880i	$0.718816\pi$
$632$		0			0
$633$	−323.110	+	85.9228i	−0.510442	+	0.135739i
$634$		0			0
$635$	112.643	−	112.643i	0.177391	−	0.177391i
$636$		0			0
$637$	−3.20530	+	3.20530i	−0.00503187	+	0.00503187i
$638$		0			0
$639$	334.873	+	585.114i	0.524058	+	0.915671i
$640$		0			0
$641$			771.555i			1.20367i	0.798619	+	0.601837i	$0.205564\pi$
$641$			771.555i			1.20367i	−0.798619	+	0.601837i	$0.794436\pi$
$642$		0			0
$643$	−319.214	+	319.214i	−0.496445	+	0.496445i	−0.910330	−	0.413884i	$-0.864172\pi$
$643$	−319.214	+	319.214i	−0.496445	+	0.496445i	0.413884	+	0.910330i	$0.364172\pi$
$644$		0			0
$645$	355.638	+	206.225i	0.551377	+	0.319729i
$646$		0			0
$647$	−360.720			−0.557527			−0.278764	−	0.960360i	$-0.589925\pi$
$647$	−360.720			−0.557527			−0.278764	+	0.960360i	$0.589925\pi$
$648$		0			0
$649$			275.395i			0.424338i
$650$		0			0
$651$	160.489	−	276.766i	0.246527	−	0.425140i
$652$		0			0
$653$	−415.043	−	415.043i	−0.635595	−	0.635595i	0.313871	−	0.949466i	$-0.398374\pi$
$653$	−415.043	−	415.043i	−0.635595	−	0.635595i	−0.949466	+	0.313871i	$0.898374\pi$
$654$		0			0
$655$	−6.31104			−0.00963517
$656$		0			0
$657$	27.1134	−	15.5176i	0.0412685	−	0.0236189i
$658$		0			0
$659$	363.535	+	363.535i	0.551646	+	0.551646i	0.926916	−	0.375269i	$-0.122450\pi$
$659$	363.535	+	363.535i	0.551646	+	0.551646i	−0.375269	+	0.926916i	$0.622450\pi$
$660$		0			0
$661$	151.997	+	151.997i	0.229951	+	0.229951i	0.812672	−	0.582721i	$-0.198012\pi$
$661$	151.997	+	151.997i	0.229951	+	0.229951i	−0.582721	+	0.812672i	$0.698012\pi$
$662$		0			0
$663$	5.43232	+	20.4280i	0.00819354	+	0.0308115i
$664$		0			0
$665$	842.166			1.26642
$666$		0			0
$667$	−33.0743	−	33.0743i	−0.0495867	−	0.0495867i
$668$		0			0
$669$	−399.013	−	231.377i	−0.596433	−	0.345855i
$670$		0			0
$671$		−	624.170i		−	0.930208i
$672$		0			0
$673$	−271.149			−0.402896			−0.201448	−	0.979499i	$-0.564565\pi$
$673$	−271.149			−0.402896			−0.201448	+	0.979499i	$0.564565\pi$
$674$		0			0
$675$	−310.245	−	1.75919i	−0.459623	−	0.00260621i
$676$		0			0
$677$	−639.750	+	639.750i	−0.944978	+	0.944978i	−0.998563	−	0.0535849i	$-0.982935\pi$
$677$	−639.750	+	639.750i	−0.944978	+	0.944978i	0.0535849	+	0.998563i	$0.482935\pi$
$678$		0			0
$679$		−	449.442i		−	0.661918i
$680$		0			0
$681$	−47.5948	−	178.979i	−0.0698895	−	0.262817i
$682$		0			0
$683$	93.1730	−	93.1730i	0.136417	−	0.136417i	−0.635601	−	0.772018i	$-0.719248\pi$
$683$	93.1730	−	93.1730i	0.136417	−	0.136417i	0.772018	+	0.635601i	$0.219248\pi$
$684$		0			0
$685$	−619.145	+	619.145i	−0.903861	+	0.903861i
$686$		0			0
$687$	121.988	+	458.731i	0.177566	+	0.667730i
$688$		0			0
$689$		−	76.0301i		−	0.110348i
$690$		0			0
$691$	−303.844	+	303.844i	−0.439716	+	0.439716i	−0.891916	−	0.452200i	$-0.850639\pi$
$691$	−303.844	+	303.844i	−0.439716	+	0.439716i	0.452200	+	0.891916i	$0.350639\pi$
$692$		0			0
$693$	−275.975	+	1014.60i	−0.398233	+	1.46406i
$694$		0			0
$695$	−138.111			−0.198721
$696$		0			0
$697$			100.606i			0.144341i
$698$		0			0
$699$	84.2914	+	48.8783i	0.120589	+	0.0699261i
$700$		0			0
$701$	797.170	+	797.170i	1.13719	+	1.13719i	0.988952	+	0.148238i	$0.0473601\pi$
$701$	797.170	+	797.170i	1.13719	+	1.13719i	0.148238	+	0.988952i	$0.452640\pi$
$702$		0			0
$703$	−2223.85			−3.16336
$704$		0			0
$705$	103.733	+	390.086i	0.147140	+	0.553313i
$706$		0			0
$707$	−415.878	−	415.878i	−0.588229	−	0.588229i
$708$		0			0
$709$	−592.848	−	592.848i	−0.836176	−	0.836176i	0.152178	−	0.988353i	$-0.451371\pi$
$709$	−592.848	−	592.848i	−0.836176	−	0.836176i	−0.988353	+	0.152178i	$0.951371\pi$
$710$		0			0
$711$	462.533	+	808.171i	0.650539	+	1.13667i
$712$		0			0
$713$	313.185			0.439249
$714$		0			0
$715$	43.9070	+	43.9070i	0.0614084	+	0.0614084i
$716$		0			0
$717$	200.612	−	345.959i	0.279794	−	0.482508i
$718$		0			0
$719$		−	1252.89i		−	1.74255i	−0.490799	−	0.871273i	$-0.663295\pi$
$719$		−	1252.89i		−	1.74255i	0.490799	−	0.871273i	$-0.336705\pi$
$720$		0			0
$721$	1123.83			1.55872
$722$		0			0
$723$	414.382	+	240.289i	0.573142	+	0.332350i
$724$		0			0
$725$	−17.7270	+	17.7270i	−0.0244511	+	0.0244511i
$726$		0			0
$727$			1182.91i			1.62711i	0.581490	+	0.813553i	$0.302470\pi$
$727$			1182.91i			1.62711i	−0.581490	+	0.813553i	$0.697530\pi$
$728$		0			0
$729$	−728.953	−	8.26707i	−0.999936	−	0.0113403i
$730$		0			0
$731$	175.963	−	175.963i	0.240715	−	0.240715i
$732$		0			0
$733$	−679.023	+	679.023i	−0.926361	+	0.926361i	−0.997469	−	0.0711072i	$-0.977347\pi$
$733$	−679.023	+	679.023i	−0.926361	+	0.926361i	0.0711072	+	0.997469i	$0.477347\pi$
$734$		0			0
$735$	45.7574	−	12.1680i	0.0622549	−	0.0165551i
$736$		0			0
$737$		−	109.588i		−	0.148695i
$738$		0			0
$739$	−408.587	+	408.587i	−0.552892	+	0.552892i	−0.927274	−	0.374383i	$-0.877855\pi$
$739$	−408.587	+	408.587i	−0.552892	+	0.552892i	0.374383	+	0.927274i	$0.377855\pi$
$740$		0			0
$741$	−49.8627	+	85.9889i	−0.0672911	+	0.116044i
$742$		0			0
$743$	228.202			0.307137			0.153568	−	0.988138i	$-0.450923\pi$
$743$	228.202			0.307137			0.153568	+	0.988138i	$0.450923\pi$
$744$		0			0
$745$			692.644i			0.929724i
$746$		0			0
$747$	105.984	−	389.641i	0.141880	−	0.521608i
$748$		0			0
$749$	561.642	+	561.642i	0.749856	+	0.749856i
$750$		0			0
$751$	835.943			1.11311			0.556553	−	0.830812i	$-0.312124\pi$
$751$	835.943			1.11311			0.556553	+	0.830812i	$0.312124\pi$
$752$		0			0
$753$	−437.528	+	116.350i	−0.581047	+	0.154515i
$754$		0			0
$755$	60.7421	+	60.7421i	0.0804530	+	0.0804530i
$756$		0			0
$757$	−144.017	−	144.017i	−0.190247	−	0.190247i	0.605556	−	0.795803i	$-0.292951\pi$
$757$	−144.017	−	144.017i	−0.190247	−	0.190247i	−0.795803	+	0.605556i	$0.792951\pi$
$758$		0			0
$759$	−994.715	+	264.519i	−1.31056	+	0.348510i
$760$		0			0
$761$	1238.49			1.62745			0.813727	−	0.581247i	$-0.197435\pi$
$761$	1238.49			1.62745			0.813727	+	0.581247i	$0.197435\pi$
$762$		0			0
$763$	−541.148	−	541.148i	−0.709238	−	0.709238i
$764$		0			0
$765$	57.9503	−	213.049i	0.0757520	−	0.278495i
$766$		0			0
$767$			18.1663i			0.0236849i
$768$		0			0
$769$	−906.729			−1.17910			−0.589551	−	0.807732i	$-0.700695\pi$
$769$	−906.729			−1.17910			−0.589551	+	0.807732i	$0.700695\pi$
$770$		0			0
$771$	517.411	−	892.284i	0.671091	−	1.15731i
$772$		0			0
$773$	989.152	−	989.152i	1.27963	−	1.27963i	0.338752	−	0.940876i	$-0.389995\pi$
$773$	989.152	−	989.152i	1.27963	−	1.27963i	0.940876	−	0.338752i	$-0.110005\pi$
$774$		0			0
$775$		−	167.859i		−	0.216593i
$776$		0			0
$777$	−1499.63	+	398.789i	−1.93003	+	0.513241i
$778$		0			0
$779$	−334.528	+	334.528i	−0.429432	+	0.429432i
$780$		0			0
$781$	847.656	−	847.656i	1.08535	−	1.08535i
$782$		0			0
$783$	−41.8890	+	41.4166i	−0.0534981	+	0.0528948i
$784$		0			0
$785$			498.367i			0.634862i
$786$		0			0
$787$	−100.012	+	100.012i	−0.127080	+	0.127080i	−0.767786	−	0.640706i	$-0.778642\pi$
$787$	−100.012	+	100.012i	−0.127080	+	0.127080i	0.640706	+	0.767786i	$0.278642\pi$
$788$		0			0
$789$	690.994	+	400.689i	0.875785	+	0.507844i
$790$		0			0
$791$	280.264			0.354316
$792$		0			0
$793$		−	41.1731i		−	0.0519207i
$794$		0			0
$795$	−398.372	+	686.998i	−0.501097	+	0.864149i
$796$		0			0
$797$	−264.491	−	264.491i	−0.331858	−	0.331858i	0.521433	−	0.853292i	$-0.325397\pi$
$797$	−264.491	−	264.491i	−0.331858	−	0.331858i	−0.853292	+	0.521433i	$0.825397\pi$
$798$		0			0
$799$	244.332			0.305798
$800$		0			0
$801$	349.864	+	611.307i	0.436784	+	0.763180i
$802$		0			0
$803$	−39.2793	−	39.2793i	−0.0489157	−	0.0489157i
$804$		0			0
$805$	406.765	+	406.765i	0.505298	+	0.505298i
$806$		0			0
$807$	−111.425	−	419.011i	−0.138073	−	0.519220i
$808$		0			0
$809$	−1041.53			−1.28743			−0.643717	−	0.765264i	$-0.722609\pi$
$809$	−1041.53			−1.28743			−0.643717	+	0.765264i	$0.722609\pi$
$810$		0			0
$811$	442.482	+	442.482i	0.545600	+	0.545600i	0.925165	−	0.379565i	$-0.123926\pi$
$811$	442.482	+	442.482i	0.545600	+	0.545600i	−0.379565	+	0.925165i	$0.623926\pi$
$812$		0			0
$813$	−100.082	−	58.0346i	−0.123102	−	0.0713833i
$814$		0			0
$815$			537.359i			0.659337i
$816$		0			0
$817$	1170.20			1.43231
$818$		0			0
$819$	−18.2046	+	66.9275i	−0.0222279	+	0.0817186i
$820$		0			0
$821$	−104.027	+	104.027i	−0.126708	+	0.126708i	−0.767617	−	0.640909i	$-0.778558\pi$
$821$	−104.027	+	104.027i	−0.126708	+	0.126708i	0.640909	+	0.767617i	$0.278558\pi$
$822$		0			0
$823$		−	349.420i		−	0.424568i	−0.977208	−	0.212284i	$-0.931910\pi$
$823$		−	349.420i		−	0.424568i	0.977208	−	0.212284i	$-0.0680902\pi$
$824$		0			0
$825$	141.776	+	533.143i	0.171850	+	0.646234i
$826$		0			0
$827$	−554.122	+	554.122i	−0.670038	+	0.670038i	−0.957725	−	0.287686i	$-0.907114\pi$
$827$	−554.122	+	554.122i	−0.670038	+	0.670038i	0.287686	+	0.957725i	$0.407114\pi$
$828$		0			0
$829$	583.639	−	583.639i	0.704027	−	0.704027i	−0.261245	−	0.965272i	$-0.584133\pi$
$829$	583.639	−	583.639i	0.704027	−	0.704027i	0.965272	+	0.261245i	$0.0841331\pi$
$830$		0			0
$831$	302.355	+	1137.00i	0.363845	+	1.36823i
$832$		0			0
$833$		−	28.6604i		−	0.0344062i
$834$		0			0
$835$	296.230	−	296.230i	0.354767	−	0.354767i
$836$		0			0
$837$	2.23646	−	394.415i	0.00267200	−	0.471225i
$838$		0			0
$839$	1235.55			1.47264			0.736322	−	0.676632i	$-0.236561\pi$
$839$	1235.55			1.47264			0.736322	+	0.676632i	$0.236561\pi$
$840$		0			0
$841$		−	836.240i		−	0.994340i
$842$		0			0
$843$	−1190.60	−	690.399i	−1.41234	−	0.818979i
$844$		0			0
$845$	−436.329	−	436.329i	−0.516365	−	0.516365i
$846$		0			0
$847$	986.322			1.16449
$848$		0			0
$849$	−301.744	−	1134.70i	−0.355411	−	1.33651i
$850$		0			0
$851$	−1074.11	−	1074.11i	−1.26218	−	1.26218i
$852$		0			0
$853$	−535.104	−	535.104i	−0.627320	−	0.627320i	0.320073	−	0.947393i	$-0.396293\pi$
$853$	−535.104	−	535.104i	−0.627320	−	0.627320i	−0.947393	+	0.320073i	$0.896293\pi$
$854$		0			0
$855$	901.105	−	515.722i	1.05392	−	0.603183i
$856$		0			0
$857$	−261.325			−0.304929			−0.152465	−	0.988309i	$-0.548721\pi$
$857$	−261.325			−0.304929			−0.152465	+	0.988309i	$0.548721\pi$
$858$		0			0
$859$	81.4524	+	81.4524i	0.0948224	+	0.0948224i	0.752927	−	0.658104i	$-0.228641\pi$
$859$	81.4524	+	81.4524i	0.0948224	+	0.0948224i	−0.658104	+	0.752927i	$0.728641\pi$
$860$		0			0
$861$	−165.597	+	285.575i	−0.192331	+	0.331678i
$862$		0			0
$863$		−	1250.31i		−	1.44879i	−0.689383	−	0.724397i	$-0.742118\pi$
$863$		−	1250.31i		−	1.44879i	0.689383	−	0.724397i	$-0.257882\pi$
$864$		0			0
$865$	−749.878			−0.866911
$866$		0			0
$867$	634.407	+	367.876i	0.731727	+	0.424309i
$868$		0			0
$869$	1170.80	−	1170.80i	1.34730	−	1.34730i
$870$		0			0
$871$		−	7.22894i		−	0.00829959i
$872$		0			0
$873$	−275.227	−	480.897i	−0.315266	−	0.550855i
$874$		0			0
$875$	692.345	−	692.345i	0.791251	−	0.791251i
$876$		0			0
$877$	−288.263	+	288.263i	−0.328692	+	0.328692i	−0.852089	−	0.523397i	$-0.824664\pi$
$877$	−288.263	+	288.263i	−0.328692	+	0.328692i	0.523397	+	0.852089i	$0.324664\pi$
$878$		0			0
$879$	−1256.75	+	334.200i	−1.42975	+	0.380205i
$880$		0			0
$881$		−	1682.63i		−	1.90991i	−0.296744	−	0.954957i	$-0.595901\pi$
$881$		−	1682.63i		−	1.90991i	0.296744	−	0.954957i	$-0.404099\pi$
$882$		0			0
$883$	477.885	−	477.885i	0.541206	−	0.541206i	−0.382676	−	0.923882i	$-0.624998\pi$
$883$	477.885	−	477.885i	0.541206	−	0.541206i	0.923882	+	0.382676i	$0.124998\pi$
$884$		0			0
$885$	95.1854	−	164.149i	0.107554	−	0.185479i
$886$		0			0
$887$	−1366.70			−1.54081			−0.770405	−	0.637555i	$-0.779946\pi$
$887$	−1366.70			−1.54081			−0.770405	+	0.637555i	$0.779946\pi$
$888$		0			0
$889$		−	316.406i		−	0.355912i
$890$		0			0
$891$	326.024	+	1254.60i	0.365908	+	1.40808i
$892$		0			0
$893$	812.435	+	812.435i	0.909782	+	0.909782i
$894$		0			0
$895$	87.4499			0.0977094
$896$		0			0
$897$	−65.6160	+	17.4489i	−0.0731506	+	0.0194525i
$898$		0			0
$899$	−22.5364	−	22.5364i	−0.0250683	−	0.0250683i
$900$		0			0
$901$	339.914	+	339.914i	0.377263	+	0.377263i
$902$		0			0
$903$	789.113	−	209.844i	0.873879	−	0.232386i
$904$		0			0
$905$	177.788			0.196451
$906$		0			0
$907$	−330.495	−	330.495i	−0.364383	−	0.364383i	0.501041	−	0.865424i	$-0.332951\pi$
$907$	−330.495	−	330.495i	−0.364383	−	0.364383i	−0.865424	+	0.501041i	$0.832951\pi$
$908$		0			0
$909$	−699.657	−	190.310i	−0.769699	−	0.209362i
$910$		0			0
$911$		−	1633.72i		−	1.79332i	−0.442715	−	0.896662i	$-0.645985\pi$
$911$		−	1633.72i		−	1.79332i	0.442715	−	0.896662i	$-0.354015\pi$
$912$		0			0
$913$	−718.014			−0.786434
$914$		0			0
$915$	−215.733	+	372.035i	−0.235774	+	0.406596i
$916$		0			0
$917$	−8.86358	+	8.86358i	−0.00966585	+	0.00966585i
$918$		0			0
$919$		−	765.918i		−	0.833426i	−0.909038	−	0.416713i	$-0.863182\pi$
$919$		−	765.918i		−	0.833426i	0.909038	−	0.416713i	$-0.136818\pi$
$920$		0			0
$921$	1474.79	−	392.182i	1.60129	−	0.425822i
$922$		0			0
$923$	55.9153	−	55.9153i	0.0605800	−	0.0605800i
$924$		0			0
$925$	−575.698	+	575.698i	−0.622377	+	0.622377i
$926$		0			0
$927$	1202.49	−	688.208i	1.29718	−	0.742403i
$928$		0			0
$929$			1283.88i			1.38200i	0.722855	+	0.691000i	$0.242830\pi$
$929$			1283.88i			1.38200i	−0.722855	+	0.691000i	$0.757170\pi$
$930$		0			0
$931$	95.2993	−	95.2993i	0.102362	−	0.102362i
$932$		0			0
$933$	−1484.50	−	860.819i	−1.59110	−	0.922635i
$934$		0			0
$935$	−392.597			−0.419890
$936$		0			0
$937$		−	1617.33i		−	1.72607i	−0.505141	−	0.863037i	$-0.668560\pi$
$937$		−	1617.33i		−	1.72607i	0.505141	−	0.863037i	$-0.331440\pi$
$938$		0			0
$939$	−501.607	+	865.029i	−0.534193	+	0.921223i
$940$		0			0
$941$	−721.542	−	721.542i	−0.766782	−	0.766782i	0.210757	−	0.977539i	$-0.432407\pi$
$941$	−721.542	−	721.542i	−0.766782	−	0.766782i	−0.977539	+	0.210757i	$0.932407\pi$
$942$		0			0
$943$	−323.152			−0.342685
$944$		0			0
$945$	515.172	−	509.362i	0.545155	−	0.539008i
$946$		0			0
$947$	442.411	+	442.411i	0.467171	+	0.467171i	0.900997	−	0.433826i	$-0.142837\pi$
$947$	442.411	+	442.411i	0.467171	+	0.467171i	−0.433826	+	0.900997i	$0.642837\pi$
$948$		0			0
$949$	−2.59105	−	2.59105i	−0.00273029	−	0.00273029i
$950$		0			0
$951$	−290.444	−	1092.21i	−0.305409	−	1.14848i
$952$		0			0
$953$	66.7031			0.0699928			0.0349964	−	0.999387i	$-0.488858\pi$
$953$	66.7031			0.0699928			0.0349964	+	0.999387i	$0.488858\pi$
$954$		0			0
$955$	−390.260	−	390.260i	−0.408649	−	0.408649i
$956$		0			0
$957$	90.6131	+	52.5441i	0.0946845	+	0.0549050i
$958$		0			0
$959$			1739.13i			1.81348i
$960$		0			0
$961$	−747.600			−0.777940
$962$		0			0
$963$	944.885	+	257.013i	0.981189	+	0.266888i
$964$		0			0
$965$	−305.735	+	305.735i	−0.316823	+	0.316823i
$966$		0			0
$967$			81.7617i			0.0845519i	0.999106	+	0.0422759i	$0.0134609\pi$
$967$			81.7617i			0.0845519i	−0.999106	+	0.0422759i	$0.986539\pi$
$968$		0			0
$969$	−161.512	−	607.362i	−0.166679	−	0.626793i
$970$		0			0
$971$	558.759	−	558.759i	0.575447	−	0.575447i	−0.358198	−	0.933646i	$-0.616609\pi$
$971$	558.759	−	558.759i	0.575447	−	0.575447i	0.933646	+	0.358198i	$0.116609\pi$
$972$		0			0
$973$	−193.971	+	193.971i	−0.199354	+	0.199354i
$974$		0			0
$975$	9.35219	+	35.1686i	0.00959199	+	0.0360704i
$976$		0			0
$977$			250.154i			0.256043i	0.991771	+	0.128021i	$0.0408626\pi$
$977$			250.154i			0.256043i	−0.991771	+	0.128021i	$0.959137\pi$
$978$		0			0
$979$	885.602	−	885.602i	0.904599	−	0.904599i
$980$		0			0
$981$	−910.406	−	247.635i	−0.928039	−	0.252431i
$982$		0			0
$983$	1147.26			1.16710			0.583551	−	0.812077i	$-0.301663\pi$
$983$	1147.26			1.16710			0.583551	+	0.812077i	$0.301663\pi$
$984$		0			0
$985$			165.567i			0.168088i
$986$		0			0
$987$	693.548	+	402.170i	0.702683	+	0.407467i
$988$		0			0
$989$	565.203	+	565.203i	0.571489	+	0.571489i
$990$		0			0
$991$	1364.34			1.37673			0.688364	−	0.725365i	$-0.258329\pi$
$991$	1364.34			1.37673			0.688364	+	0.725365i	$0.258329\pi$
$992$		0			0
$993$	231.620	+	871.000i	0.233253	+	0.877140i
$994$		0			0
$995$	−333.569	−	333.569i	−0.335245	−	0.335245i
$996$		0			0
$997$	328.128	+	328.128i	0.329115	+	0.329115i	0.852250	−	0.523135i	$-0.175238\pi$
$997$	328.128	+	328.128i	0.329115	+	0.329115i	−0.523135	+	0.852250i	$0.675238\pi$
$998$		0			0
$999$	−1360.38	+	1345.03i	−1.36174	+	1.34638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.3.i.d.353.9		20
3.2	odd	2	inner	384.3.i.d.353.3		20
4.3	odd	2		384.3.i.c.353.2		20
8.3	odd	2		192.3.i.b.113.9		20
8.5	even	2		48.3.i.b.5.9	yes	20
12.11	even	2		384.3.i.c.353.8		20
16.3	odd	4		384.3.i.c.161.8		20
16.5	even	4		48.3.i.b.29.2	yes	20
16.11	odd	4		192.3.i.b.17.3		20
16.13	even	4	inner	384.3.i.d.161.3		20
24.5	odd	2		48.3.i.b.5.2	✓	20
24.11	even	2		192.3.i.b.113.3		20
48.5	odd	4		48.3.i.b.29.9	yes	20
48.11	even	4		192.3.i.b.17.9		20
48.29	odd	4	inner	384.3.i.d.161.9		20
48.35	even	4		384.3.i.c.161.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.b.5.2	✓	20	24.5	odd	2
48.3.i.b.5.9	yes	20	8.5	even	2
48.3.i.b.29.2	yes	20	16.5	even	4
48.3.i.b.29.9	yes	20	48.5	odd	4
192.3.i.b.17.3		20	16.11	odd	4
192.3.i.b.17.9		20	48.11	even	4
192.3.i.b.113.3		20	24.11	even	2
192.3.i.b.113.9		20	8.3	odd	2
384.3.i.c.161.2		20	48.35	even	4
384.3.i.c.161.8		20	16.3	odd	4
384.3.i.c.353.2		20	4.3	odd	2
384.3.i.c.353.8		20	12.11	even	2
384.3.i.d.161.3		20	16.13	even	4	inner
384.3.i.d.161.9		20	48.29	odd	4	inner
384.3.i.d.353.3		20	3.2	odd	2	inner
384.3.i.d.353.9		20	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	384.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.59524 + 1.50491i) q^{3} +(-2.59897 + 2.59897i) q^{5} +7.30027i q^{7} +(4.47050 + 7.81118i) q^{9} +O(q^{10})\)	\(q+(2.59524 + 1.50491i) q^{3} +(-2.59897 + 2.59897i) q^{5} +7.30027i q^{7} +(4.47050 + 7.81118i) q^{9} +(11.3161 - 11.3161i) q^{11} +(0.746462 - 0.746462i) q^{13} +(-10.6561 + 2.83373i) q^{15} +6.67452i q^{17} +(-22.1936 + 22.1936i) q^{19} +(-10.9862 + 18.9459i) q^{21} -21.4389 q^{23} +11.4908i q^{25} +(-0.153096 + 26.9996i) q^{27} +(1.54272 + 1.54272i) q^{29} -14.6082 q^{31} +(46.3976 - 12.3382i) q^{33} +(-18.9732 - 18.9732i) q^{35} +(50.1010 + 50.1010i) q^{37} +(3.06060 - 0.813888i) q^{39} +15.0731 q^{41} +(-26.3634 - 26.3634i) q^{43} +(-31.9197 - 8.68231i) q^{45} -36.6067i q^{47} -4.29399 q^{49} +(-10.0445 + 17.3220i) q^{51} +(50.9270 - 50.9270i) q^{53} +58.8202i q^{55} +(-90.9971 + 24.1983i) q^{57} +(-12.1683 + 12.1683i) q^{59} +(27.5789 - 27.5789i) q^{61} +(-57.0238 + 32.6359i) q^{63} +3.88006i q^{65} +(4.84214 - 4.84214i) q^{67} +(-55.6391 - 32.2636i) q^{69} +74.9072 q^{71} -3.47110i q^{73} +(-17.2925 + 29.8212i) q^{75} +(82.6105 + 82.6105i) q^{77} +103.463 q^{79} +(-41.0292 + 69.8399i) q^{81} +(-31.7254 - 31.7254i) q^{83} +(-17.3469 - 17.3469i) q^{85} +(1.68207 + 6.32538i) q^{87} +78.2605 q^{89} +(5.44937 + 5.44937i) q^{91} +(-37.9118 - 21.9840i) q^{93} -115.361i q^{95} -61.5651 q^{97} +(138.981 + 37.8034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{3}+O(q^{10}) \) 20 * q + 6 * q^3	\( 20 q + 6 q^{3} - 92 q^{13} - 116 q^{15} + 52 q^{19} - 48 q^{21} - 18 q^{27} - 80 q^{31} + 60 q^{33} + 116 q^{37} - 172 q^{43} - 60 q^{45} - 364 q^{49} - 128 q^{51} + 244 q^{61} + 296 q^{63} - 356 q^{67} + 20 q^{69} + 146 q^{75} + 384 q^{79} - 188 q^{81} - 48 q^{85} - 136 q^{91} + 132 q^{93} + 472 q^{97} + 452 q^{99}+O(q^{100}) \) 20 * q + 6 * q^3 - 92 * q^13 - 116 * q^15 + 52 * q^19 - 48 * q^21 - 18 * q^27 - 80 * q^31 + 60 * q^33 + 116 * q^37 - 172 * q^43 - 60 * q^45 - 364 * q^49 - 128 * q^51 + 244 * q^61 + 296 * q^63 - 356 * q^67 + 20 * q^69 + 146 * q^75 + 384 * q^79 - 188 * q^81 - 48 * q^85 - 136 * q^91 + 132 * q^93 + 472 * q^97 + 452 * q^99

Introduction

L-functions

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