LMFDB - Embedded newform 384.3.i.c.161.9

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			161.9
Root			$0.312316 + 1.97546i$ of defining polynomial
Character	$\chi$	$=$	384.161
Dual form			384.3.i.c.353.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.75602 - 1.18505i) q^{3} +(-0.00985921 - 0.00985921i) q^{5} -6.42277i q^{7} +(6.19134 - 6.53203i) q^{9} +O(q^{10})$	\(q+(2.75602 - 1.18505i) q^{3} +(-0.00985921 - 0.00985921i) q^{5} -6.42277i q^{7} +(6.19134 - 6.53203i) q^{9} +(-9.07186 - 9.07186i) q^{11} +(-12.6098 - 12.6098i) q^{13} +(-0.0388558 - 0.0154886i) q^{15} +19.0155i q^{17} +(-2.07165 - 2.07165i) q^{19} +(-7.61127 - 17.7013i) q^{21} +19.5712 q^{23} -24.9998i q^{25} +(9.32272 - 25.3394i) q^{27} +(-11.1742 + 11.1742i) q^{29} +59.9385 q^{31} +(-35.7528 - 14.2517i) q^{33} +(-0.0633234 + 0.0633234i) q^{35} +(-9.32707 + 9.32707i) q^{37} +(-49.6962 - 19.8098i) q^{39} -47.2639 q^{41} +(24.1220 - 24.1220i) q^{43} +(-0.125442 + 0.00335893i) q^{45} -6.29702i q^{47} +7.74808 q^{49} +(22.5343 + 52.4073i) q^{51} +(20.6409 + 20.6409i) q^{53} +0.178883i q^{55} +(-8.16452 - 3.25452i) q^{57} +(60.3533 + 60.3533i) q^{59} +(-48.0230 - 48.0230i) q^{61} +(-41.9537 - 39.7655i) q^{63} +0.248646i q^{65} +(-23.7768 - 23.7768i) q^{67} +(53.9388 - 23.1928i) q^{69} +13.5743 q^{71} +31.4516i q^{73} +(-29.6259 - 68.9001i) q^{75} +(-58.2665 + 58.2665i) q^{77} -47.4718 q^{79} +(-4.33472 - 80.8839i) q^{81} +(70.3318 - 70.3318i) q^{83} +(0.187478 - 0.187478i) q^{85} +(-17.5545 + 44.0385i) q^{87} +95.1729 q^{89} +(-80.9900 + 80.9900i) q^{91} +(165.192 - 71.0298i) q^{93} +0.0408497i q^{95} +61.6218 q^{97} +(-115.425 + 3.09069i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	2.75602	−	1.18505i	0.918675	−	0.395015i
$3$	2.75602	−	1.18505i	0.918675	−	0.395015i
$4$		0			0
$5$	−0.00985921	−	0.00985921i	−0.00197184	−	0.00197184i	0.706120	−	0.708092i	$-0.250444\pi$
$5$	−0.00985921	−	0.00985921i	−0.00197184	−	0.00197184i	−0.708092	+	0.706120i	$0.750444\pi$
$6$		0			0
$7$		−	6.42277i		−	0.917538i	−0.888556	−	0.458769i	$-0.848291\pi$
$7$		−	6.42277i		−	0.917538i	0.888556	−	0.458769i	$-0.151709\pi$
$8$		0			0
$9$	6.19134	−	6.53203i	0.687926	−	0.725781i
$10$		0			0
$11$	−9.07186	−	9.07186i	−0.824715	−	0.824715i	0.162065	−	0.986780i	$-0.448185\pi$
$11$	−9.07186	−	9.07186i	−0.824715	−	0.824715i	−0.986780	+	0.162065i	$0.948185\pi$
$12$		0			0
$13$	−12.6098	−	12.6098i	−0.969987	−	0.969987i	0.0295753	−	0.999563i	$-0.490585\pi$
$13$	−12.6098	−	12.6098i	−0.969987	−	0.969987i	−0.999563	+	0.0295753i	$0.990585\pi$
$14$		0			0
$15$	−0.0388558	−	0.0154886i	−0.00259039	−	0.00103257i
$16$		0			0
$17$			19.0155i			1.11856i	0.828978	+	0.559281i	$0.188923\pi$
$17$			19.0155i			1.11856i	−0.828978	+	0.559281i	$0.811077\pi$
$18$		0			0
$19$	−2.07165	−	2.07165i	−0.109034	−	0.109034i	0.650485	−	0.759519i	$-0.274566\pi$
$19$	−2.07165	−	2.07165i	−0.109034	−	0.109034i	−0.759519	+	0.650485i	$0.774566\pi$
$20$		0			0
$21$	−7.61127	−	17.7013i	−0.362441	−	0.842919i
$22$		0			0
$23$	19.5712			0.850923			0.425461	−	0.904977i	$-0.360112\pi$
$23$	19.5712			0.850923			0.425461	+	0.904977i	$0.360112\pi$
$24$		0			0
$25$		−	24.9998i		−	0.999992i
$26$		0			0
$27$	9.32272	−	25.3394i	0.345286	−	0.938497i
$28$		0			0
$29$	−11.1742	+	11.1742i	−0.385319	+	0.385319i	−0.873014	−	0.487695i	$-0.837838\pi$
$29$	−11.1742	+	11.1742i	−0.385319	+	0.385319i	0.487695	+	0.873014i	$0.337838\pi$
$30$		0			0
$31$	59.9385			1.93350			0.966750	−	0.255725i	$-0.0823142\pi$
$31$	59.9385			1.93350			0.966750	+	0.255725i	$0.0823142\pi$
$32$		0			0
$33$	−35.7528	−	14.2517i	−1.08342	−	0.431870i
$34$		0			0
$35$	−0.0633234	+	0.0633234i	−0.00180924	+	0.00180924i
$36$		0			0
$37$	−9.32707	+	9.32707i	−0.252083	+	0.252083i	−0.821824	−	0.569741i	$-0.807043\pi$
$37$	−9.32707	+	9.32707i	−0.252083	+	0.252083i	0.569741	+	0.821824i	$0.307043\pi$
$38$		0			0
$39$	−49.6962	−	19.8098i	−1.27426	−	0.507943i
$40$		0			0
$41$	−47.2639			−1.15278			−0.576389	−	0.817176i	$-0.695539\pi$
$41$	−47.2639			−1.15278			−0.576389	+	0.817176i	$0.695539\pi$
$42$		0			0
$43$	24.1220	−	24.1220i	0.560978	−	0.560978i	−0.368607	−	0.929585i	$-0.620165\pi$
$43$	24.1220	−	24.1220i	0.560978	−	0.560978i	0.929585	+	0.368607i	$0.120165\pi$
$44$		0			0
$45$	−0.125442	+	0.00335893i	−0.00278761	+	7.46430e-5i
$46$		0			0
$47$		−	6.29702i		−	0.133979i	−0.997754	−	0.0669896i	$-0.978661\pi$
$47$		−	6.29702i		−	0.133979i	0.997754	−	0.0669896i	$-0.0213394\pi$
$48$		0			0
$49$	7.74808			0.158124
$50$		0			0
$51$	22.5343	+	52.4073i	0.441849	+	1.02759i
$52$		0			0
$53$	20.6409	+	20.6409i	0.389450	+	0.389450i	0.874491	−	0.485041i	$-0.161195\pi$
$53$	20.6409	+	20.6409i	0.389450	+	0.389450i	−0.485041	+	0.874491i	$0.661195\pi$
$54$		0			0
$55$			0.178883i			0.00325242i
$56$		0			0
$57$	−8.16452	−	3.25452i	−0.143237	−	0.0570968i
$58$		0			0
$59$	60.3533	+	60.3533i	1.02294	+	1.02294i	0.999731	+	0.0232062i	$0.00738742\pi$
$59$	60.3533	+	60.3533i	1.02294	+	1.02294i	0.0232062	+	0.999731i	$0.492613\pi$
$60$		0			0
$61$	−48.0230	−	48.0230i	−0.787262	−	0.787262i	0.193782	−	0.981045i	$-0.437924\pi$
$61$	−48.0230	−	48.0230i	−0.787262	−	0.787262i	−0.981045	+	0.193782i	$0.937924\pi$
$62$		0			0
$63$	−41.9537	−	39.7655i	−0.665931	−	0.631198i
$64$		0			0
$65$			0.248646i			0.00382532i
$66$		0			0
$67$	−23.7768	−	23.7768i	−0.354878	−	0.354878i	0.507043	−	0.861921i	$-0.330738\pi$
$67$	−23.7768	−	23.7768i	−0.354878	−	0.354878i	−0.861921	+	0.507043i	$0.830738\pi$
$68$		0			0
$69$	53.9388	−	23.1928i	0.781721	−	0.336127i
$70$		0			0
$71$	13.5743			0.191188			0.0955938	−	0.995420i	$-0.469525\pi$
$71$	13.5743			0.191188			0.0955938	+	0.995420i	$0.469525\pi$
$72$		0			0
$73$			31.4516i			0.430844i	0.976521	+	0.215422i	$0.0691127\pi$
$73$			31.4516i			0.430844i	−0.976521	+	0.215422i	$0.930887\pi$
$74$		0			0
$75$	−29.6259	−	68.9001i	−0.395012	−	0.918668i
$76$		0			0
$77$	−58.2665	+	58.2665i	−0.756707	+	0.756707i
$78$		0			0
$79$	−47.4718			−0.600909			−0.300455	−	0.953796i	$-0.597138\pi$
$79$	−47.4718			−0.600909			−0.300455	+	0.953796i	$0.597138\pi$
$80$		0			0
$81$	−4.33472	−	80.8839i	−0.0535151	−	0.998567i
$82$		0			0
$83$	70.3318	−	70.3318i	0.847372	−	0.847372i	−0.142433	−	0.989804i	$-0.545493\pi$
$83$	70.3318	−	70.3318i	0.847372	−	0.847372i	0.989804	+	0.142433i	$0.0454925\pi$
$84$		0			0
$85$	0.187478	−	0.187478i	0.00220563	−	0.00220563i
$86$		0			0
$87$	−17.5545	+	44.0385i	−0.201776	+	0.506189i
$88$		0			0
$89$	95.1729			1.06936			0.534679	−	0.845055i	$-0.320432\pi$
$89$	95.1729			1.06936			0.534679	+	0.845055i	$0.320432\pi$
$90$		0			0
$91$	−80.9900	+	80.9900i	−0.890000	+	0.890000i
$92$		0			0
$93$	165.192	−	71.0298i	1.77626	−	0.763761i
$94$		0			0
$95$			0.0408497i			0.000429997i
$96$		0			0
$97$	61.6218			0.635276			0.317638	−	0.948212i	$-0.397110\pi$
$97$	61.6218			0.635276			0.317638	+	0.948212i	$0.397110\pi$
$98$		0			0
$99$	−115.425	+	3.09069i	−1.16591	+	0.0312191i
$100$		0			0
$101$	48.1867	+	48.1867i	0.477096	+	0.477096i	0.904202	−	0.427106i	$-0.140467\pi$
$101$	48.1867	+	48.1867i	0.477096	+	0.477096i	−0.427106	+	0.904202i	$0.640467\pi$
$102$		0			0
$103$			4.73669i			0.0459873i	0.999736	+	0.0229936i	$0.00731975\pi$
$103$			4.73669i			0.0459873i	−0.999736	+	0.0229936i	$0.992680\pi$
$104$		0			0
$105$	−0.0994797	+	0.249562i	−0.000947426	+	0.00237678i
$106$		0			0
$107$	40.9462	+	40.9462i	0.382674	+	0.382674i	0.872065	−	0.489390i	$-0.162781\pi$
$107$	40.9462	+	40.9462i	0.382674	+	0.382674i	−0.489390	+	0.872065i	$0.662781\pi$
$108$		0			0
$109$	120.437	+	120.437i	1.10493	+	1.10493i	0.993807	+	0.111123i	$0.0354447\pi$
$109$	120.437	+	120.437i	1.10493	+	1.10493i	0.111123	+	0.993807i	$0.464555\pi$
$110$		0			0
$111$	−14.6526	+	36.7586i	−0.132006	+	0.331159i
$112$		0			0
$113$			205.193i			1.81587i	0.419110	+	0.907936i	$0.362342\pi$
$113$			205.193i			1.81587i	−0.419110	+	0.907936i	$0.637658\pi$
$114$		0			0
$115$	−0.192957	−	0.192957i	−0.00167789	−	0.00167789i
$116$		0			0
$117$	−160.439	+	4.29604i	−1.37128	+	0.0367183i
$118$		0			0
$119$	122.132			1.02632
$120$		0			0
$121$			43.5974i			0.360309i
$122$		0			0
$123$	−130.260	+	56.0098i	−1.05903	+	0.455365i
$124$		0			0
$125$	−0.492959	+	0.492959i	−0.00394367	+	0.00394367i
$126$		0			0
$127$	−54.1458			−0.426345			−0.213173	−	0.977015i	$-0.568380\pi$
$127$	−54.1458			−0.426345			−0.213173	+	0.977015i	$0.568380\pi$
$128$		0			0
$129$	37.8952	−	95.0666i	0.293761	−	0.736951i
$130$		0			0
$131$	−31.2584	+	31.2584i	−0.238614	+	0.238614i	−0.816276	−	0.577662i	$-0.803965\pi$
$131$	−31.2584	+	31.2584i	−0.238614	+	0.238614i	0.577662	+	0.816276i	$0.303965\pi$
$132$		0			0
$133$	−13.3057	+	13.3057i	−0.100043	+	0.100043i
$134$		0			0
$135$	−0.341742	+	0.157912i	−0.00253142	+	0.00116972i
$136$		0			0
$137$	−42.9176			−0.313267			−0.156633	−	0.987657i	$-0.550064\pi$
$137$	−42.9176			−0.313267			−0.156633	+	0.987657i	$0.550064\pi$
$138$		0			0
$139$	−47.0945	+	47.0945i	−0.338809	+	0.338809i	−0.855919	−	0.517110i	$-0.827008\pi$
$139$	−47.0945	+	47.0945i	−0.338809	+	0.338809i	0.517110	+	0.855919i	$0.327008\pi$
$140$		0			0
$141$	−7.46225	−	17.3547i	−0.0529238	−	0.123083i
$142$		0			0
$143$			228.789i			1.59993i
$144$		0			0
$145$	0.220339			0.00151958
$146$		0			0
$147$	21.3539	−	9.18183i	0.145265	−	0.0624614i
$148$		0			0
$149$	−131.532	−	131.532i	−0.882766	−	0.882766i	0.111049	−	0.993815i	$-0.464579\pi$
$149$	−131.532	−	131.532i	−0.882766	−	0.882766i	−0.993815	+	0.111049i	$0.964579\pi$
$150$		0			0
$151$			145.908i			0.966281i	0.875543	+	0.483140i	$0.160504\pi$
$151$			145.908i			0.966281i	−0.875543	+	0.483140i	$0.839496\pi$
$152$		0			0
$153$	124.210	+	117.732i	0.811830	+	0.769488i
$154$		0			0
$155$	−0.590946	−	0.590946i	−0.00381256	−	0.00381256i
$156$		0			0
$157$	55.2586	+	55.2586i	0.351966	+	0.351966i	0.860840	−	0.508875i	$-0.169938\pi$
$157$	55.2586	+	55.2586i	0.351966	+	0.351966i	−0.508875	+	0.860840i	$0.669938\pi$
$158$		0			0
$159$	81.3470	+	32.4263i	0.511617	+	0.203939i
$160$		0			0
$161$		−	125.701i		−	0.780754i
$162$		0			0
$163$	70.6156	+	70.6156i	0.433225	+	0.433225i	0.889724	−	0.456499i	$-0.150897\pi$
$163$	70.6156	+	70.6156i	0.433225	+	0.433225i	−0.456499	+	0.889724i	$0.650897\pi$
$164$		0			0
$165$	0.211984	+	0.493006i	0.00128475	+	0.00298791i
$166$		0			0
$167$	86.2013			0.516176			0.258088	−	0.966121i	$-0.416908\pi$
$167$	86.2013			0.516176			0.258088	+	0.966121i	$0.416908\pi$
$168$		0			0
$169$			149.016i			0.881751i
$170$		0			0
$171$	−26.3584	+	0.705790i	−0.154142	+	0.00412743i
$172$		0			0
$173$	−58.2425	+	58.2425i	−0.336662	+	0.336662i	−0.855109	−	0.518448i	$-0.826510\pi$
$173$	−58.2425	+	58.2425i	−0.336662	+	0.336662i	0.518448	+	0.855109i	$0.326510\pi$
$174$		0			0
$175$	−160.568			−0.917531
$176$		0			0
$177$	237.856	+	94.8137i	1.34382	+	0.535671i
$178$		0			0
$179$	−18.9272	+	18.9272i	−0.105738	+	0.105738i	−0.757997	−	0.652258i	$-0.773822\pi$
$179$	−18.9272	+	18.9272i	−0.105738	+	0.105738i	0.652258	+	0.757997i	$0.273822\pi$
$180$		0			0
$181$	−24.5109	+	24.5109i	−0.135420	+	0.135420i	−0.771567	−	0.636148i	$-0.780527\pi$
$181$	−24.5109	+	24.5109i	−0.135420	+	0.135420i	0.636148	+	0.771567i	$0.280527\pi$
$182$		0			0
$183$	−189.262	−	75.4431i	−1.03422	−	0.412257i
$184$		0			0
$185$	0.183915			0.000994136
$186$		0			0
$187$	172.506	−	172.506i	0.922494	−	0.922494i
$188$		0			0
$189$	−162.749	−	59.8777i	−0.861107	−	0.316813i
$190$		0			0
$191$		−	156.422i		−	0.818962i	−0.912319	−	0.409481i	$-0.865710\pi$
$191$		−	156.422i		−	0.818962i	0.912319	−	0.409481i	$-0.134290\pi$
$192$		0			0
$193$	−217.972			−1.12939			−0.564695	−	0.825299i	$-0.691006\pi$
$193$	−217.972			−1.12939			−0.564695	+	0.825299i	$0.691006\pi$
$194$		0			0
$195$	0.294657	+	0.685275i	0.00151106	+	0.00351423i
$196$		0			0
$197$	245.945	+	245.945i	1.24845	+	1.24845i	0.956403	+	0.292050i	$0.0943374\pi$
$197$	245.945	+	245.945i	1.24845	+	1.24845i	0.292050	+	0.956403i	$0.405663\pi$
$198$		0			0
$199$		−	233.190i		−	1.17181i	−0.810379	−	0.585905i	$-0.800739\pi$
$199$		−	233.190i		−	1.17181i	0.810379	−	0.585905i	$-0.199261\pi$
$200$		0			0
$201$	−93.7060	−	37.3528i	−0.466199	−	0.185835i
$202$		0			0
$203$	71.7695	+	71.7695i	0.353545	+	0.353545i
$204$		0			0
$205$	0.465985	+	0.465985i	0.00227310	+	0.00227310i
$206$		0			0
$207$	121.172	−	127.840i	0.585372	−	0.617583i
$208$		0			0
$209$			37.5875i			0.179844i
$210$		0			0
$211$	−8.49504	−	8.49504i	−0.0402609	−	0.0402609i	0.686690	−	0.726951i	$-0.259063\pi$
$211$	−8.49504	−	8.49504i	−0.0402609	−	0.0402609i	−0.726951	+	0.686690i	$0.759063\pi$
$212$		0			0
$213$	37.4111	−	16.0862i	0.175639	−	0.0755220i
$214$		0			0
$215$	−0.475649			−0.00221232
$216$		0			0
$217$		−	384.971i		−	1.77406i
$218$		0			0
$219$	37.2716	+	86.6814i	0.170190	+	0.395806i
$220$		0			0
$221$	239.783	−	239.783i	1.08499	−	1.08499i
$222$		0			0
$223$	10.9290			0.0490090			0.0245045	−	0.999700i	$-0.492199\pi$
$223$	10.9290			0.0490090			0.0245045	+	0.999700i	$0.492199\pi$
$224$		0			0
$225$	−163.299	−	154.782i	−0.725775	−	0.687921i
$226$		0			0
$227$	99.9027	−	99.9027i	0.440100	−	0.440100i	−0.451946	−	0.892045i	$-0.649270\pi$
$227$	99.9027	−	99.9027i	0.440100	−	0.440100i	0.892045	+	0.451946i	$0.149270\pi$
$228$		0			0
$229$	231.857	−	231.857i	1.01248	−	1.01248i	0.0125555	−	0.999921i	$-0.496003\pi$
$229$	231.857	−	231.857i	1.01248	−	1.01248i	0.999921	−	0.0125555i	$-0.00399663\pi$
$230$		0			0
$231$	−91.5354	+	229.632i	−0.396257	+	0.994079i
$232$		0			0
$233$	−316.641			−1.35897			−0.679486	−	0.733688i	$-0.737797\pi$
$233$	−316.641			−1.35897			−0.679486	+	0.733688i	$0.737797\pi$
$234$		0			0
$235$	−0.0620836	+	0.0620836i	−0.000264186	+	0.000264186i
$236$		0			0
$237$	−130.833	+	56.2562i	−0.552040	+	0.237368i
$238$		0			0
$239$		−	382.691i		−	1.60122i	−0.599187	−	0.800609i	$-0.704509\pi$
$239$		−	382.691i		−	1.60122i	0.599187	−	0.800609i	$-0.295491\pi$
$240$		0			0
$241$	−91.3157			−0.378903			−0.189452	−	0.981890i	$-0.560671\pi$
$241$	−91.3157			−0.378903			−0.189452	+	0.981890i	$0.560671\pi$
$242$		0			0
$243$	−107.798	−	217.781i	−0.443612	−	0.896219i
$244$		0			0
$245$	−0.0763900	−	0.0763900i	−0.000311796	−	0.000311796i
$246$		0			0
$247$			52.2463i			0.211524i
$248$		0			0
$249$	110.490	−	277.183i	0.443734	−	1.11318i
$250$		0			0
$251$	−128.768	−	128.768i	−0.513021	−	0.513021i	0.402430	−	0.915451i	$-0.368166\pi$
$251$	−128.768	−	128.768i	−0.513021	−	0.513021i	−0.915451	+	0.402430i	$0.868166\pi$
$252$		0			0
$253$	−177.547	−	177.547i	−0.701769	−	0.701769i
$254$		0			0
$255$	0.294524	−	0.738865i	0.00115500	−	0.00289751i
$256$		0			0
$257$		−	123.915i		−	0.482159i	−0.970505	−	0.241079i	$-0.922499\pi$
$257$		−	123.915i		−	0.482159i	0.970505	−	0.241079i	$-0.0775014\pi$
$258$		0			0
$259$	59.9056	+	59.9056i	0.231296	+	0.231296i
$260$		0			0
$261$	3.80695	+	142.174i	0.0145860	+	0.544728i
$262$		0			0
$263$	−194.379			−0.739085			−0.369542	−	0.929214i	$-0.620486\pi$
$263$	−194.379			−0.739085			−0.369542	+	0.929214i	$0.620486\pi$
$264$		0			0
$265$		−	0.407005i		−	0.00153587i
$266$		0			0
$267$	262.299	−	112.784i	0.982393	−	0.422413i
$268$		0			0
$269$	−296.636	+	296.636i	−1.10274	+	1.10274i	−0.108658	+	0.994079i	$0.534655\pi$
$269$	−296.636	+	296.636i	−1.10274	+	1.10274i	−0.994079	+	0.108658i	$0.965345\pi$
$270$		0			0
$271$	278.227			1.02667			0.513334	−	0.858189i	$-0.328410\pi$
$271$	278.227			1.02667			0.513334	+	0.858189i	$0.328410\pi$
$272$		0			0
$273$	−127.234	+	319.187i	−0.466057	+	1.16918i
$274$		0			0
$275$	−226.795	+	226.795i	−0.824709	+	0.824709i
$276$		0			0
$277$	60.1513	−	60.1513i	0.217153	−	0.217153i	−0.590145	−	0.807297i	$-0.700929\pi$
$277$	60.1513	−	60.1513i	0.217153	−	0.217153i	0.807297	+	0.590145i	$0.200929\pi$
$278$		0			0
$279$	371.099	−	391.520i	1.33010	−	1.40330i
$280$		0			0
$281$	313.645			1.11617			0.558087	−	0.829782i	$-0.311535\pi$
$281$	313.645			1.11617			0.558087	+	0.829782i	$0.311535\pi$
$282$		0			0
$283$	286.980	−	286.980i	1.01406	−	1.01406i	0.0141627	−	0.999900i	$-0.495492\pi$
$283$	286.980	−	286.980i	1.01406	−	1.01406i	0.999900	−	0.0141627i	$-0.00450829\pi$
$284$		0			0
$285$	0.0484087	+	0.112583i	0.000169855	+	0.000395027i
$286$		0			0
$287$			303.565i			1.05772i
$288$		0			0
$289$	−72.5910			−0.251180
$290$		0			0
$291$	169.831	−	73.0246i	0.583612	−	0.250944i
$292$		0			0
$293$	−176.501	−	176.501i	−0.602394	−	0.602394i	0.338553	−	0.940947i	$-0.390062\pi$
$293$	−176.501	−	176.501i	−0.602394	−	0.602394i	−0.940947	+	0.338553i	$0.890062\pi$
$294$		0			0
$295$		−	1.19007i		−	0.00403414i
$296$		0			0
$297$	−314.450	+	145.301i	−1.05876	+	0.489230i
$298$		0			0
$299$	−246.790	−	246.790i	−0.825384	−	0.825384i
$300$		0			0
$301$	−154.930	−	154.930i	−0.514718	−	0.514718i
$302$		0			0
$303$	189.907	+	75.7002i	0.626756	+	0.249836i
$304$		0			0
$305$			0.946938i			0.00310471i
$306$		0			0
$307$	63.9904	+	63.9904i	0.208438	+	0.208438i	0.803603	−	0.595165i	$-0.202913\pi$
$307$	63.9904	+	63.9904i	0.208438	+	0.208438i	−0.595165	+	0.803603i	$0.702913\pi$
$308$		0			0
$309$	5.61319	+	13.0544i	0.0181657	+	0.0422473i
$310$		0			0
$311$	−532.288			−1.71154			−0.855769	−	0.517359i	$-0.826915\pi$
$311$	−532.288			−1.71154			−0.855769	+	0.517359i	$0.826915\pi$
$312$		0			0
$313$			185.676i			0.593215i	0.954999	+	0.296607i	$0.0958553\pi$
$313$			185.676i			0.593215i	−0.954999	+	0.296607i	$0.904145\pi$
$314$		0			0
$315$	0.0215736	+	0.805687i	6.84878e−5	+	0.00255774i
$316$		0			0
$317$	168.127	−	168.127i	0.530370	−	0.530370i	−0.390312	−	0.920683i	$-0.627633\pi$
$317$	168.127	−	168.127i	0.530370	−	0.530370i	0.920683	+	0.390312i	$0.127633\pi$
$318$		0			0
$319$	202.742			0.635556
$320$		0			0
$321$	161.372	+	64.3256i	0.502715	+	0.200391i
$322$		0			0
$323$	39.3936	−	39.3936i	0.121962	−	0.121962i
$324$		0			0
$325$	−315.243	+	315.243i	−0.969980	+	0.969980i
$326$		0			0
$327$	474.652	+	189.204i	1.45153	+	0.578607i
$328$		0			0
$329$	−40.4443			−0.122931
$330$		0			0
$331$	−241.678	+	241.678i	−0.730144	+	0.730144i	−0.970648	−	0.240504i	$-0.922687\pi$
$331$	−241.678	+	241.678i	−0.730144	+	0.730144i	0.240504	+	0.970648i	$0.422687\pi$
$332$		0			0
$333$	3.17764	+	118.672i	0.00954245	+	0.356371i
$334$		0			0
$335$			0.468841i			0.00139953i
$336$		0			0
$337$	396.856			1.17762			0.588808	−	0.808273i	$-0.299598\pi$
$337$	396.856			1.17762			0.588808	+	0.808273i	$0.299598\pi$
$338$		0			0
$339$	243.163	+	565.518i	0.717296	+	1.66819i
$340$		0			0
$341$	−543.754	−	543.754i	−1.59459	−	1.59459i
$342$		0			0
$343$		−	364.480i		−	1.06262i
$344$		0			0
$345$	−0.760456	−	0.303131i	−0.00220422	−	0.000878641i
$346$		0			0
$347$	−38.5699	−	38.5699i	−0.111153	−	0.111153i	0.649343	−	0.760496i	$-0.275044\pi$
$347$	−38.5699	−	38.5699i	−0.111153	−	0.111153i	−0.760496	+	0.649343i	$0.775044\pi$
$348$		0			0
$349$	−10.4065	−	10.4065i	−0.0298180	−	0.0298180i	0.692041	−	0.721859i	$-0.256712\pi$
$349$	−10.4065	−	10.4065i	−0.0298180	−	0.0298180i	−0.721859	+	0.692041i	$0.756712\pi$
$350$		0			0
$351$	−437.084	+	201.968i	−1.24525	+	0.575408i
$352$		0			0
$353$		−	209.294i		−	0.592900i	−0.955048	−	0.296450i	$-0.904197\pi$
$353$		−	209.294i		−	0.592900i	0.955048	−	0.296450i	$-0.0958028\pi$
$354$		0			0
$355$	−0.133832	−	0.133832i	−0.000376992	−	0.000376992i
$356$		0			0
$357$	336.600	−	144.732i	0.942857	−	0.405413i
$358$		0			0
$359$	42.6682			0.118853			0.0594264	−	0.998233i	$-0.481073\pi$
$359$	42.6682			0.118853			0.0594264	+	0.998233i	$0.481073\pi$
$360$		0			0
$361$		−	352.417i		−	0.976223i
$362$		0			0
$363$	51.6649	+	120.156i	0.142328	+	0.331007i
$364$		0			0
$365$	0.310088	−	0.310088i	0.000849557	−	0.000849557i
$366$		0			0
$367$	16.2444			0.0442627			0.0221313	−	0.999755i	$-0.492955\pi$
$367$	16.2444			0.0442627			0.0221313	+	0.999755i	$0.492955\pi$
$368$		0			0
$369$	−292.627	+	308.729i	−0.793026	+	0.836664i
$370$		0			0
$371$	132.571	−	132.571i	0.357335	−	0.357335i
$372$		0			0
$373$	−351.379	+	351.379i	−0.942035	+	0.942035i	−0.998410	−	0.0563743i	$-0.982046\pi$
$373$	−351.379	+	351.379i	−0.942035	+	0.942035i	0.0563743	+	0.998410i	$0.482046\pi$
$374$		0			0
$375$	−0.774428	+	1.94278i	−0.00206514	+	0.00518076i
$376$		0			0
$377$	281.811			0.747509
$378$		0			0
$379$	−170.505	+	170.505i	−0.449880	+	0.449880i	−0.895315	−	0.445435i	$-0.853049\pi$
$379$	−170.505	+	170.505i	−0.449880	+	0.449880i	0.445435	+	0.895315i	$0.353049\pi$
$380$		0			0
$381$	−149.227	+	64.1653i	−0.391673	+	0.168413i
$382$		0			0
$383$			256.234i			0.669017i	0.942393	+	0.334509i	$0.108570\pi$
$383$			256.234i			0.669017i	−0.942393	+	0.334509i	$0.891430\pi$
$384$		0			0
$385$	1.14892			0.00298422
$386$		0			0
$387$	−8.21813	−	306.913i	−0.0212355	−	0.793058i
$388$		0			0
$389$	376.214	+	376.214i	0.967130	+	0.967130i	0.999477	−	0.0323468i	$-0.0102981\pi$
$389$	376.214	+	376.214i	0.967130	+	0.967130i	−0.0323468	+	0.999477i	$0.510298\pi$
$390$		0			0
$391$			372.158i			0.951810i
$392$		0			0
$393$	−49.1063	+	123.192i	−0.124953	+	0.313465i
$394$		0			0
$395$	0.468035	+	0.468035i	0.00118490	+	0.00118490i
$396$		0			0
$397$	312.905	+	312.905i	0.788174	+	0.788174i	0.981195	−	0.193021i	$-0.0618284\pi$
$397$	312.905	+	312.905i	0.788174	+	0.788174i	−0.193021	+	0.981195i	$0.561828\pi$
$398$		0			0
$399$	−20.9030	+	52.4388i	−0.0523885	+	0.131426i
$400$		0			0
$401$		−	9.22373i		−	0.0230018i	−0.999934	−	0.0115009i	$-0.996339\pi$
$401$		−	9.22373i		−	0.0230018i	0.999934	−	0.0115009i	$-0.00366093\pi$
$402$		0			0
$403$	−755.814	−	755.814i	−1.87547	−	1.87547i
$404$		0			0
$405$	−0.754715	+	0.840189i	−0.00186349	+	0.00207454i
$406$		0			0
$407$	169.228			0.415793
$408$		0			0
$409$			322.436i			0.788352i	0.919035	+	0.394176i	$0.128970\pi$
$409$			322.436i			0.788352i	−0.919035	+	0.394176i	$0.871030\pi$
$410$		0			0
$411$	−118.282	+	50.8592i	−0.287790	+	0.123745i
$412$		0			0
$413$	387.635	−	387.635i	0.938583	−	0.938583i
$414$		0			0
$415$	−1.38683			−0.00334177
$416$		0			0
$417$	−73.9845	+	185.603i	−0.177421	+	0.445090i
$418$		0			0
$419$	−226.569	+	226.569i	−0.540738	+	0.540738i	−0.923745	−	0.383007i	$-0.874888\pi$
$419$	−226.569	+	226.569i	−0.540738	+	0.540738i	0.383007	+	0.923745i	$0.374888\pi$
$420$		0			0
$421$	498.861	−	498.861i	1.18494	−	1.18494i	0.206495	−	0.978448i	$-0.433794\pi$
$421$	498.861	−	498.861i	1.18494	−	1.18494i	0.978448	−	0.206495i	$-0.0662058\pi$
$422$		0			0
$423$	−41.1323	−	38.9870i	−0.0972394	−	0.0921677i
$424$		0			0
$425$	475.385			1.11855
$426$		0			0
$427$	−308.440	+	308.440i	−0.722343	+	0.722343i
$428$		0			0
$429$	271.126	+	630.549i	0.631995	+	1.46981i
$430$		0			0
$431$		−	452.283i		−	1.04938i	−0.851293	−	0.524690i	$-0.824181\pi$
$431$		−	452.283i		−	1.04938i	0.851293	−	0.524690i	$-0.175819\pi$
$432$		0			0
$433$	379.557			0.876574			0.438287	−	0.898835i	$-0.355585\pi$
$433$	379.557			0.876574			0.438287	+	0.898835i	$0.355585\pi$
$434$		0			0
$435$	0.607258	−	0.261111i	0.00139600	−	0.000600255i
$436$		0			0
$437$	−40.5447	−	40.5447i	−0.0927797	−	0.0927797i
$438$		0			0
$439$			689.509i			1.57063i	0.619094	+	0.785317i	$0.287500\pi$
$439$			689.509i			1.57063i	−0.619094	+	0.785317i	$0.712500\pi$
$440$		0			0
$441$	47.9710	−	50.6107i	0.108778	−	0.114763i
$442$		0			0
$443$	−97.5600	−	97.5600i	−0.220226	−	0.220226i	0.588368	−	0.808593i	$-0.299771\pi$
$443$	−97.5600	−	97.5600i	−0.220226	−	0.220226i	−0.808593	+	0.588368i	$0.799771\pi$
$444$		0			0
$445$	−0.938330	−	0.938330i	−0.00210861	−	0.00210861i
$446$		0			0
$447$	−518.377	−	206.634i	−1.15968	−	0.462269i
$448$		0			0
$449$		−	718.711i		−	1.60069i	−0.599538	−	0.800347i	$-0.704649\pi$
$449$		−	718.711i		−	1.60069i	0.599538	−	0.800347i	$-0.295351\pi$
$450$		0			0
$451$	428.772	+	428.772i	0.950713	+	0.950713i
$452$		0			0
$453$	172.908	+	402.127i	0.381695	+	0.887698i
$454$		0			0
$455$	1.59700			0.00350988
$456$		0			0
$457$			489.021i			1.07007i	0.844830	+	0.535034i	$0.179701\pi$
$457$			489.021i			1.07007i	−0.844830	+	0.535034i	$0.820299\pi$
$458$		0			0
$459$	481.843	+	177.277i	1.04977	+	0.386224i
$460$		0			0
$461$	459.082	−	459.082i	0.995840	−	0.995840i	−0.00415179	−	0.999991i	$-0.501322\pi$
$461$	459.082	−	459.082i	0.995840	−	0.995840i	0.999991	+	0.00415179i	$0.00132156\pi$
$462$		0			0
$463$	−587.611			−1.26914			−0.634569	−	0.772866i	$-0.718822\pi$
$463$	−587.611			−1.26914			−0.634569	+	0.772866i	$0.718822\pi$
$464$		0			0
$465$	−2.32896	−	0.928364i	−0.00500852	−	0.00199648i
$466$		0			0
$467$	−89.5077	+	89.5077i	−0.191665	+	0.191665i	−0.796415	−	0.604750i	$-0.793273\pi$
$467$	−89.5077	+	89.5077i	−0.191665	+	0.191665i	0.604750	+	0.796415i	$0.293273\pi$
$468$		0			0
$469$	−152.713	+	152.713i	−0.325614	+	0.325614i
$470$		0			0
$471$	217.778	+	86.8101i	0.462374	+	0.184310i
$472$		0			0
$473$	−437.664			−0.925293
$474$		0			0
$475$	−51.7909	+	51.7909i	−0.109033	+	0.109033i
$476$		0			0
$477$	262.621	−	7.03213i	0.550568	−	0.0147424i
$478$		0			0
$479$		−	439.291i		−	0.917101i	−0.888668	−	0.458550i	$-0.848369\pi$
$479$		−	439.291i		−	0.917101i	0.888668	−	0.458550i	$-0.151631\pi$
$480$		0			0
$481$	235.226			0.489034
$482$		0			0
$483$	−148.962	−	346.436i	−0.308410	−	0.717259i
$484$		0			0
$485$	−0.607542	−	0.607542i	−0.00125266	−	0.00125266i
$486$		0			0
$487$		−	499.716i		−	1.02611i	−0.858355	−	0.513056i	$-0.828513\pi$
$487$		−	499.716i		−	1.02611i	0.858355	−	0.513056i	$-0.171487\pi$
$488$		0			0
$489$	278.301	+	110.936i	0.569123	+	0.226862i
$490$		0			0
$491$	359.246	+	359.246i	0.731663	+	0.731663i	0.970949	−	0.239286i	$-0.0769134\pi$
$491$	359.246	+	359.246i	0.731663	+	0.731663i	−0.239286	+	0.970949i	$0.576913\pi$
$492$		0			0
$493$	−212.484	−	212.484i	−0.431003	−	0.431003i
$494$		0			0
$495$	1.16847	+	1.10752i	0.00236054	+	0.00223742i
$496$		0			0
$497$		−	87.1846i		−	0.175422i
$498$		0			0
$499$	−64.4682	−	64.4682i	−0.129195	−	0.129195i	0.639553	−	0.768747i	$-0.279120\pi$
$499$	−64.4682	−	64.4682i	−0.129195	−	0.129195i	−0.768747	+	0.639553i	$0.779120\pi$
$500$		0			0
$501$	237.573	−	102.152i	0.474197	−	0.203897i
$502$		0			0
$503$	−597.277			−1.18743			−0.593714	−	0.804676i	$-0.702339\pi$
$503$	−597.277			−1.18743			−0.593714	+	0.804676i	$0.702339\pi$
$504$		0			0
$505$		−	0.950165i		−	0.00188151i
$506$		0			0
$507$	176.591	+	410.691i	0.348305	+	0.810042i
$508$		0			0
$509$	−359.574	+	359.574i	−0.706433	+	0.706433i	−0.965783	−	0.259350i	$-0.916492\pi$
$509$	−359.574	+	359.574i	−0.706433	+	0.706433i	0.259350	+	0.965783i	$0.416492\pi$
$510$		0			0
$511$	202.006			0.395316
$512$		0			0
$513$	−71.8079	+	33.1810i	−0.139976	+	0.0646804i
$514$		0			0
$515$	0.0467000	−	0.0467000i	9.06796e−5	−	9.06796e-5i
$516$		0			0
$517$	−57.1257	+	57.1257i	−0.110495	+	0.110495i
$518$		0			0
$519$	−91.4977	+	229.538i	−0.176296	+	0.442269i
$520$		0			0
$521$	−862.399			−1.65528			−0.827639	−	0.561261i	$-0.810316\pi$
$521$	−862.399			−1.65528			−0.827639	+	0.561261i	$0.810316\pi$
$522$		0			0
$523$	−256.574	+	256.574i	−0.490581	+	0.490581i	−0.908489	−	0.417908i	$-0.862763\pi$
$523$	−256.574	+	256.574i	−0.490581	+	0.490581i	0.417908	+	0.908489i	$0.362763\pi$
$524$		0			0
$525$	−442.529	+	190.280i	−0.842912	+	0.362438i
$526$		0			0
$527$			1139.76i			2.16274i
$528$		0			0
$529$	−145.967			−0.275930
$530$		0			0
$531$	767.897	−	20.5617i	1.44613	−	0.0387227i
$532$		0			0
$533$	595.990	+	595.990i	1.11818	+	1.11818i
$534$		0			0
$535$		−	0.807394i		−	0.00150915i
$536$		0			0
$537$	−29.7342	+	74.5933i	−0.0553709	+	0.138907i
$538$		0			0
$539$	−70.2895	−	70.2895i	−0.130407	−	0.130407i
$540$		0			0
$541$	431.469	+	431.469i	0.797540	+	0.797540i	0.982707	−	0.185167i	$-0.0592826\pi$
$541$	431.469	+	431.469i	0.797540	+	0.797540i	−0.185167	+	0.982707i	$0.559283\pi$
$542$		0			0
$543$	−38.5062	+	96.5993i	−0.0709137	+	0.177899i
$544$		0			0
$545$		−	2.37483i		−	0.00435749i
$546$		0			0
$547$	335.381	+	335.381i	0.613127	+	0.613127i	0.943760	−	0.330632i	$-0.107262\pi$
$547$	335.381	+	335.381i	0.613127	+	0.613127i	−0.330632	+	0.943760i	$0.607262\pi$
$548$		0			0
$549$	−611.014	+	16.3609i	−1.11296	+	0.0298014i
$550$		0			0
$551$	46.2983			0.0840259
$552$		0			0
$553$			304.900i			0.551357i
$554$		0			0
$555$	0.506874	−	0.217948i	0.000913287	−	0.000392699i
$556$		0			0
$557$	−118.642	+	118.642i	−0.213001	+	0.213001i	−0.805541	−	0.592540i	$-0.798125\pi$
$557$	−118.642	+	118.642i	−0.213001	+	0.213001i	0.592540	+	0.805541i	$0.298125\pi$
$558$		0			0
$559$	−608.350			−1.08828
$560$		0			0
$561$	271.004	−	679.860i	0.483073	−	1.21187i
$562$		0			0
$563$	−290.766	+	290.766i	−0.516459	+	0.516459i	−0.916498	−	0.400039i	$-0.868997\pi$
$563$	−290.766	+	290.766i	−0.516459	+	0.516459i	0.400039	+	0.916498i	$0.368997\pi$
$564$		0			0
$565$	2.02305	−	2.02305i	0.00358061	−	0.00358061i
$566$		0			0
$567$	−519.499	+	27.8409i	−0.916223	+	0.0491021i
$568$		0			0
$569$	669.398			1.17645			0.588223	−	0.808699i	$-0.299828\pi$
$569$	669.398			1.17645			0.588223	+	0.808699i	$0.299828\pi$
$570$		0			0
$571$	454.971	−	454.971i	0.796798	−	0.796798i	−0.185792	−	0.982589i	$-0.559485\pi$
$571$	454.971	−	454.971i	0.796798	−	0.796798i	0.982589	+	0.185792i	$0.0594849\pi$
$572$		0			0
$573$	−185.367	−	431.102i	−0.323502	−	0.752359i
$574$		0			0
$575$		−	489.277i		−	0.850916i
$576$		0			0
$577$	−288.393			−0.499814			−0.249907	−	0.968270i	$-0.580400\pi$
$577$	−288.393			−0.499814			−0.249907	+	0.968270i	$0.580400\pi$
$578$		0			0
$579$	−600.737	+	258.307i	−1.03754	+	0.446126i
$580$		0			0
$581$	−451.725	−	451.725i	−0.777496	−	0.777496i
$582$		0			0
$583$		−	374.502i		−	0.642371i
$584$		0			0
$585$	1.62416	+	1.53945i	0.00277635	+	0.00263154i
$586$		0			0
$587$	−393.610	−	393.610i	−0.670545	−	0.670545i	0.287297	−	0.957842i	$-0.407243\pi$
$587$	−393.610	−	393.610i	−0.670545	−	0.670545i	−0.957842	+	0.287297i	$0.907243\pi$
$588$		0			0
$589$	−124.172	−	124.172i	−0.210818	−	0.210818i
$590$		0			0
$591$	969.287	+	386.375i	1.64008	+	0.653764i
$592$		0			0
$593$			707.638i			1.19332i	0.802495	+	0.596659i	$0.203506\pi$
$593$			707.638i			1.19332i	−0.802495	+	0.596659i	$0.796494\pi$
$594$		0			0
$595$	−1.20413	−	1.20413i	−0.00202375	−	0.00202375i
$596$		0			0
$597$	−276.341	−	642.678i	−0.462883	−	1.07651i
$598$		0			0
$599$	996.581			1.66374			0.831870	−	0.554970i	$-0.187270\pi$
$599$	996.581			1.66374			0.831870	+	0.554970i	$0.187270\pi$
$600$		0			0
$601$		−	214.386i		−	0.356716i	−0.983966	−	0.178358i	$-0.942921\pi$
$601$		−	214.386i		−	0.356716i	0.983966	−	0.178358i	$-0.0570785\pi$
$602$		0			0
$603$	−302.521	+	8.10051i	−0.501693	+	0.0134337i
$604$		0			0
$605$	0.429836	−	0.429836i	0.000710474	−	0.000710474i
$606$		0			0
$607$	989.981			1.63094			0.815470	−	0.578799i	$-0.196478\pi$
$607$	989.981			1.63094			0.815470	+	0.578799i	$0.196478\pi$
$608$		0			0
$609$	282.849	+	112.748i	0.464448	+	0.185137i
$610$		0			0
$611$	−79.4044	+	79.4044i	−0.129958	+	0.129958i
$612$		0			0
$613$	−277.427	+	277.427i	−0.452572	+	0.452572i	−0.896207	−	0.443636i	$-0.853688\pi$
$613$	−277.427	+	277.427i	−0.452572	+	0.452572i	0.443636	+	0.896207i	$0.353688\pi$
$614$		0			0
$615$	1.83648	+	0.732052i	0.00298614	+	0.00119033i
$616$		0			0
$617$	−294.951			−0.478040			−0.239020	−	0.971015i	$-0.576826\pi$
$617$	−294.951			−0.478040			−0.239020	+	0.971015i	$0.576826\pi$
$618$		0			0
$619$	717.374	−	717.374i	1.15892	−	1.15892i	0.174218	−	0.984707i	$-0.444260\pi$
$619$	717.374	−	717.374i	1.15892	−	1.15892i	0.984707	−	0.174218i	$-0.0557396\pi$
$620$		0			0
$621$	182.457	−	495.924i	0.293812	−	0.798589i
$622$		0			0
$623$		−	611.273i		−	0.981177i
$624$		0			0
$625$	−624.985			−0.999977
$626$		0			0
$627$	44.5428	+	103.592i	0.0710412	+	0.165218i
$628$		0			0
$629$	−177.359	−	177.359i	−0.281970	−	0.281970i
$630$		0			0
$631$			526.114i			0.833779i	0.908957	+	0.416889i	$0.136880\pi$
$631$			526.114i			0.833779i	−0.908957	+	0.416889i	$0.863120\pi$
$632$		0			0
$633$	−33.4795	−	13.3455i	−0.0528903	−	0.0210830i
$634$		0			0
$635$	0.533835	+	0.533835i	0.000840686	+	0.000840686i
$636$		0			0
$637$	−97.7020	−	97.7020i	−0.153378	−	0.153378i
$638$		0			0
$639$	84.0431	−	88.6678i	0.131523	−	0.138760i
$640$		0			0
$641$			1025.84i			1.60037i	0.599754	+	0.800184i	$0.295265\pi$
$641$			1025.84i			1.60037i	−0.599754	+	0.800184i	$0.704735\pi$
$642$		0			0
$643$	−366.197	−	366.197i	−0.569514	−	0.569514i	0.362479	−	0.931992i	$-0.381931\pi$
$643$	−366.197	−	366.197i	−0.569514	−	0.569514i	−0.931992	+	0.362479i	$0.881931\pi$
$644$		0			0
$645$	−1.31090	+	0.563665i	−0.00203240	+	0.000873900i
$646$		0			0
$647$	90.9084			0.140508			0.0702538	−	0.997529i	$-0.477619\pi$
$647$	90.9084			0.140508			0.0702538	+	0.997529i	$0.477619\pi$
$648$		0			0
$649$		−	1095.03i		−	1.68726i
$650$		0			0
$651$	−456.208	−	1060.99i	−0.700780	−	1.62978i
$652$		0			0
$653$	−291.274	+	291.274i	−0.446056	+	0.446056i	−0.894041	−	0.447985i	$-0.852142\pi$
$653$	−291.274	+	291.274i	−0.446056	+	0.446056i	0.447985	+	0.894041i	$0.352142\pi$
$654$		0			0
$655$	0.616367			0.000941019
$656$		0			0
$657$	205.443	+	194.728i	0.312698	+	0.296389i
$658$		0			0
$659$	817.853	−	817.853i	1.24105	−	1.24105i	0.281486	−	0.959565i	$-0.409173\pi$
$659$	817.853	−	817.853i	1.24105	−	1.24105i	0.959565	−	0.281486i	$-0.0908273\pi$
$660$		0			0
$661$	673.995	−	673.995i	1.01966	−	1.01966i	0.0198568	−	0.999803i	$-0.493679\pi$
$661$	673.995	−	673.995i	1.01966	−	1.01966i	0.999803	−	0.0198568i	$-0.00632103\pi$
$662$		0			0
$663$	376.694	−	945.001i	0.568166	−	1.42534i
$664$		0			0
$665$	0.262368			0.000394538
$666$		0			0
$667$	−218.694	+	218.694i	−0.327877	+	0.327877i
$668$		0			0
$669$	30.1206	−	12.9514i	0.0450233	−	0.0193593i
$670$		0			0
$671$			871.316i			1.29853i
$672$		0			0
$673$	−526.059			−0.781662			−0.390831	−	0.920462i	$-0.627812\pi$
$673$	−526.059			−0.781662			−0.390831	+	0.920462i	$0.627812\pi$
$674$		0			0
$675$	−633.481	−	233.066i	−0.938490	−	0.345283i
$676$		0			0
$677$	−143.663	−	143.663i	−0.212205	−	0.212205i	0.592998	−	0.805204i	$-0.297944\pi$
$677$	−143.663	−	143.663i	−0.212205	−	0.212205i	−0.805204	+	0.592998i	$0.797944\pi$
$678$		0			0
$679$		−	395.782i		−	0.582890i
$680$		0			0
$681$	156.945	−	393.723i	0.230462	−	0.578155i
$682$		0			0
$683$	50.6262	+	50.6262i	0.0741232	+	0.0741232i	0.743196	−	0.669073i	$-0.233309\pi$
$683$	50.6262	+	50.6262i	0.0741232	+	0.0741232i	−0.669073	+	0.743196i	$0.733309\pi$
$684$		0			0
$685$	0.423133	+	0.423133i	0.000617713	+	0.000617713i
$686$		0			0
$687$	364.243	−	913.765i	0.530193	−	1.33008i
$688$		0			0
$689$		−	520.556i		−	0.755523i
$690$		0			0
$691$	396.186	+	396.186i	0.573351	+	0.573351i	0.933063	−	0.359712i	$-0.117125\pi$
$691$	396.186	+	396.186i	0.573351	+	0.573351i	−0.359712	+	0.933063i	$0.617125\pi$
$692$		0			0
$693$	19.8508	+	741.345i	0.0286447	+	1.06976i
$694$		0			0
$695$	0.928629			0.00133616
$696$		0			0
$697$		−	898.749i		−	1.28945i
$698$		0			0
$699$	−872.669	+	375.233i	−1.24845	+	0.536815i
$700$		0			0
$701$	−525.886	+	525.886i	−0.750195	+	0.750195i	−0.974515	−	0.224321i	$-0.927984\pi$
$701$	−525.886	+	525.886i	−0.750195	+	0.750195i	0.224321	+	0.974515i	$0.427984\pi$
$702$		0			0
$703$	38.6449			0.0549713
$704$		0			0
$705$	−0.0975321	+	0.244676i	−0.000138343	+	0.000347058i
$706$		0			0
$707$	309.492	−	309.492i	0.437753	−	0.437753i
$708$		0			0
$709$	99.4062	−	99.4062i	0.140206	−	0.140206i	−0.633520	−	0.773726i	$-0.718391\pi$
$709$	99.4062	−	99.4062i	0.140206	−	0.140206i	0.773726	+	0.633520i	$0.218391\pi$
$710$		0			0
$711$	−293.914	+	310.087i	−0.413381	+	0.436128i
$712$		0			0
$713$	1173.07			1.64526
$714$		0			0
$715$	2.25568	−	2.25568i	0.00315480	−	0.00315480i
$716$		0			0
$717$	−453.506	−	1054.71i	−0.632505	−	1.47100i
$718$		0			0
$719$			551.765i			0.767406i	0.923456	+	0.383703i	$0.125351\pi$
$719$			551.765i			0.767406i	−0.923456	+	0.383703i	$0.874649\pi$
$720$		0			0
$721$	30.4226			0.0421951
$722$		0			0
$723$	−251.668	+	108.213i	−0.348089	+	0.149673i
$724$		0			0
$725$	279.354	+	279.354i	0.385316	+	0.385316i
$726$		0			0
$727$			75.0947i			0.103294i	0.998665	+	0.0516470i	$0.0164471\pi$
$727$			75.0947i			0.103294i	−0.998665	+	0.0516470i	$0.983553\pi$
$728$		0			0
$729$	−555.174	−	472.465i	−0.761555	−	0.648100i
$730$		0			0
$731$	458.694	+	458.694i	0.627488	+	0.627488i
$732$		0			0
$733$	−442.709	−	442.709i	−0.603968	−	0.603968i	0.337395	−	0.941363i	$-0.390454\pi$
$733$	−442.709	−	442.709i	−0.603968	−	0.603968i	−0.941363	+	0.337395i	$0.890454\pi$
$734$		0			0
$735$	−0.301058	−	0.120007i	−0.000409603	−	0.000163275i
$736$		0			0
$737$			431.400i			0.585346i
$738$		0			0
$739$	283.395	+	283.395i	0.383485	+	0.383485i	0.872356	−	0.488871i	$-0.162591\pi$
$739$	283.395	+	283.395i	0.383485	+	0.383485i	−0.488871	+	0.872356i	$0.662591\pi$
$740$		0			0
$741$	61.9143	+	143.992i	0.0835550	+	0.194321i
$742$		0			0
$743$	−835.949			−1.12510			−0.562550	−	0.826763i	$-0.690180\pi$
$743$	−835.949			−1.12510			−0.562550	+	0.826763i	$0.690180\pi$
$744$		0			0
$745$			2.59361i			0.00348135i
$746$		0			0
$747$	−23.9613	−	894.857i	−0.0320768	−	1.19794i
$748$		0			0
$749$	262.988	−	262.988i	0.351118	−	0.351118i
$750$		0			0
$751$	−753.712			−1.00361			−0.501806	−	0.864980i	$-0.667331\pi$
$751$	−753.712			−1.00361			−0.501806	+	0.864980i	$0.667331\pi$
$752$		0			0
$753$	−507.485	−	202.292i	−0.673951	−	0.268648i
$754$		0			0
$755$	1.43854	−	1.43854i	0.00190535	−	0.00190535i
$756$		0			0
$757$	335.789	−	335.789i	0.443578	−	0.443578i	−0.449634	−	0.893213i	$-0.648446\pi$
$757$	335.789	−	335.789i	0.443578	−	0.443578i	0.893213	+	0.449634i	$0.148446\pi$
$758$		0			0
$759$	−699.727	−	278.923i	−0.921906	−	0.367488i
$760$		0			0
$761$	−1094.53			−1.43828			−0.719138	−	0.694868i	$-0.755463\pi$
$761$	−1094.53			−1.43828			−0.719138	+	0.694868i	$0.755463\pi$
$762$		0			0
$763$	773.541	−	773.541i	1.01381	−	1.01381i
$764$		0			0
$765$	−0.0638720	−	2.38535i	−8.34928e−5	−	0.00311811i
$766$		0			0
$767$		−	1522.09i		−	1.98447i
$768$		0			0
$769$	290.367			0.377590			0.188795	−	0.982016i	$-0.439542\pi$
$769$	290.367			0.377590			0.188795	+	0.982016i	$0.439542\pi$
$770$		0			0
$771$	−146.845	−	341.512i	−0.190460	−	0.442947i
$772$		0			0
$773$	−193.239	−	193.239i	−0.249986	−	0.249986i	0.570979	−	0.820965i	$-0.306564\pi$
$773$	−193.239	−	193.239i	−0.249986	−	0.249986i	−0.820965	+	0.570979i	$0.806564\pi$
$774$		0			0
$775$		−	1498.45i		−	1.93348i
$776$		0			0
$777$	236.092	+	94.1104i	0.303851	+	0.121120i
$778$		0			0
$779$	97.9143	+	97.9143i	0.125692	+	0.125692i
$780$		0			0
$781$	−123.144	−	123.144i	−0.157675	−	0.157675i
$782$		0			0
$783$	178.975	+	387.323i	0.228575	+	0.494666i
$784$		0			0
$785$		−	1.08961i		−	0.00138804i
$786$		0			0
$787$	483.899	+	483.899i	0.614865	+	0.614865i	0.944210	−	0.329345i	$-0.106828\pi$
$787$	483.899	+	483.899i	0.614865	+	0.614865i	−0.329345	+	0.944210i	$0.606828\pi$
$788$		0			0
$789$	−535.714	+	230.348i	−0.678979	+	0.291950i
$790$		0			0
$791$	1317.91			1.66613
$792$		0			0
$793$			1211.12i			1.52727i
$794$		0			0
$795$	−0.482320	−	1.12172i	−0.000606691	−	0.00141096i
$796$		0			0
$797$	−872.325	+	872.325i	−1.09451	+	1.09451i	−0.0994694	+	0.995041i	$0.531715\pi$
$797$	−872.325	+	872.325i	−1.09451	+	1.09451i	−0.995041	+	0.0994694i	$0.968285\pi$
$798$		0			0
$799$	119.741			0.149864
$800$		0			0
$801$	589.248	−	621.672i	0.735640	−	0.776120i
$802$		0			0
$803$	285.325	−	285.325i	0.355324	−	0.355324i
$804$		0			0
$805$	−1.23932	+	1.23932i	−0.00153952	+	0.00153952i
$806$		0			0
$807$	−466.009	+	1169.06i	−0.577459	+	1.44865i
$808$		0			0
$809$	146.162			0.180670			0.0903349	−	0.995911i	$-0.471206\pi$
$809$	146.162			0.180670			0.0903349	+	0.995911i	$0.471206\pi$
$810$		0			0
$811$	−375.179	+	375.179i	−0.462613	+	0.462613i	−0.899511	−	0.436898i	$-0.856077\pi$
$811$	−375.179	+	375.179i	−0.462613	+	0.462613i	0.436898	+	0.899511i	$0.356077\pi$
$812$		0			0
$813$	766.800	−	329.711i	0.943173	−	0.405549i
$814$		0			0
$815$		−	1.39243i		−	0.00170850i
$816$		0			0
$817$	−99.9449			−0.122332
$818$		0			0
$819$	27.5925	+	1030.47i	0.0336904	+	1.25820i
$820$		0			0
$821$	671.154	+	671.154i	0.817484	+	0.817484i	0.985743	−	0.168259i	$-0.0538144\pi$
$821$	671.154	+	671.154i	0.817484	+	0.817484i	−0.168259	+	0.985743i	$0.553814\pi$
$822$		0			0
$823$			675.121i			0.820317i	0.912014	+	0.410159i	$0.134527\pi$
$823$			675.121i			0.820317i	−0.912014	+	0.410159i	$0.865473\pi$
$824$		0			0
$825$	−356.290	+	893.814i	−0.431867	+	1.08341i
$826$		0			0
$827$	1052.16	+	1052.16i	1.27226	+	1.27226i	0.944901	+	0.327355i	$0.106157\pi$
$827$	1052.16	+	1052.16i	1.27226	+	1.27226i	0.327355	+	0.944901i	$0.393843\pi$
$828$		0			0
$829$	95.3529	+	95.3529i	0.115022	+	0.115022i	0.762275	−	0.647253i	$-0.224082\pi$
$829$	95.3529	+	95.3529i	0.115022	+	0.115022i	−0.647253	+	0.762275i	$0.724082\pi$
$830$		0			0
$831$	94.4964	−	237.060i	0.113714	−	0.285271i
$832$		0			0
$833$			147.334i			0.176872i
$834$		0			0
$835$	−0.849877	−	0.849877i	−0.00101782	−	0.00101782i
$836$		0			0
$837$	558.790	−	1518.81i	0.667610	−	1.81458i
$838$		0			0
$839$	581.969			0.693646			0.346823	−	0.937931i	$-0.387260\pi$
$839$	581.969			0.693646			0.346823	+	0.937931i	$0.387260\pi$
$840$		0			0
$841$			591.273i			0.703059i
$842$		0			0
$843$	864.413	−	371.684i	1.02540	−	0.440906i
$844$		0			0
$845$	1.46918	−	1.46918i	0.00173867	−	0.00173867i
$846$		0			0
$847$	280.016			0.330598
$848$		0			0
$849$	450.839	−	1131.01i	0.531024	−	1.33216i
$850$		0			0
$851$	−182.542	+	182.542i	−0.214503	+	0.214503i
$852$		0			0
$853$	−595.516	+	595.516i	−0.698143	+	0.698143i	−0.964010	−	0.265866i	$-0.914342\pi$
$853$	−595.516	+	595.516i	−0.698143	+	0.698143i	0.265866	+	0.964010i	$0.414342\pi$
$854$		0			0
$855$	0.266831	+	0.252914i	0.000312083	+	0.000295806i
$856$		0			0
$857$	−731.802			−0.853912			−0.426956	−	0.904273i	$-0.640414\pi$
$857$	−731.802			−0.853912			−0.426956	+	0.904273i	$0.640414\pi$
$858$		0			0
$859$	303.614	−	303.614i	0.353451	−	0.353451i	−0.507941	−	0.861392i	$-0.669593\pi$
$859$	303.614	−	303.614i	0.353451	−	0.353451i	0.861392	+	0.507941i	$0.169593\pi$
$860$		0			0
$861$	359.738	+	836.632i	0.417814	+	0.971698i
$862$		0			0
$863$			1423.90i			1.64995i	0.565173	+	0.824973i	$0.308810\pi$
$863$			1423.90i			1.64995i	−0.565173	+	0.824973i	$0.691190\pi$
$864$		0			0
$865$	1.14845			0.00132769
$866$		0			0
$867$	−200.062	+	86.0236i	−0.230753	+	0.0992198i
$868$		0			0
$869$	430.658	+	430.658i	0.495579	+	0.495579i
$870$		0			0
$871$			599.643i			0.688453i
$872$		0			0
$873$	381.521	−	402.515i	0.437023	−	0.461071i
$874$		0			0
$875$	3.16616	+	3.16616i	0.00361847	+	0.00361847i
$876$		0			0
$877$	524.721	+	524.721i	0.598314	+	0.598314i	0.939864	−	0.341550i	$-0.110952\pi$
$877$	524.721	+	524.721i	0.598314	+	0.598314i	−0.341550	+	0.939864i	$0.610952\pi$
$878$		0			0
$879$	−695.604	−	277.280i	−0.791358	−	0.315449i
$880$		0			0
$881$			51.0313i			0.0579243i	0.999581	+	0.0289622i	$0.00922023\pi$
$881$			51.0313i			0.0579243i	−0.999581	+	0.0289622i	$0.990780\pi$
$882$		0			0
$883$	−935.183	−	935.183i	−1.05910	−	1.05910i	−0.998140	−	0.0609574i	$-0.980585\pi$
$883$	−935.183	−	935.183i	−1.05910	−	1.05910i	−0.0609574	−	0.998140i	$-0.519415\pi$
$884$		0			0
$885$	−1.41029	−	3.27987i	−0.00159355	−	0.00370606i
$886$		0			0
$887$	−1077.88			−1.21520			−0.607598	−	0.794245i	$-0.707867\pi$
$887$	−1077.88			−1.21520			−0.607598	+	0.794245i	$0.707867\pi$
$888$		0			0
$889$			347.766i			0.391188i
$890$		0			0
$891$	−694.444	+	773.092i	−0.779398	+	0.867668i
$892$		0			0
$893$	−13.0452	+	13.0452i	−0.0146083	+	0.0146083i
$894$		0			0
$895$	0.373214			0.000416999
$896$		0			0
$897$	−972.616	−	387.702i	−1.08430	−	0.432220i
$898$		0			0
$899$	−669.767	+	669.767i	−0.745013	+	0.745013i
$900$		0			0
$901$	−392.497	+	392.497i	−0.435624	+	0.435624i
$902$		0			0
$903$	−610.591	−	243.392i	−0.676180	−	0.269537i
$904$		0			0
$905$	0.483317			0.000534052
$906$		0			0
$907$	−1091.36	+	1091.36i	−1.20327	+	1.20327i	−0.230101	+	0.973167i	$0.573906\pi$
$907$	−1091.36	+	1091.36i	−1.20327	+	1.20327i	−0.973167	+	0.230101i	$0.926094\pi$
$908$		0			0
$909$	613.096	−	16.4167i	0.674473	−	0.0180602i
$910$		0			0
$911$		−	599.270i		−	0.657816i	−0.944362	−	0.328908i	$-0.893319\pi$
$911$		−	599.270i		−	0.657816i	0.944362	−	0.328908i	$-0.106681\pi$
$912$		0			0
$913$	−1276.08			−1.39768
$914$		0			0
$915$	1.12216	+	2.60978i	0.00122641	+	0.00285222i
$916$		0			0
$917$	200.766	+	200.766i	0.218937	+	0.218937i
$918$		0			0
$919$			1271.46i			1.38353i	0.722123	+	0.691765i	$0.243166\pi$
$919$			1271.46i			1.38353i	−0.722123	+	0.691765i	$0.756834\pi$
$920$		0			0
$921$	252.190	+	100.528i	0.273822	+	0.109150i
$922$		0			0
$923$	−171.170	−	171.170i	−0.185449	−	0.185449i
$924$		0			0
$925$	233.175	+	233.175i	0.252081	+	0.252081i
$926$		0			0
$927$	30.9402	+	29.3264i	0.0333767	+	0.0316358i
$928$		0			0
$929$			1274.81i			1.37224i	0.727488	+	0.686120i	$0.240688\pi$
$929$			1274.81i			1.37224i	−0.727488	+	0.686120i	$0.759312\pi$
$930$		0			0
$931$	−16.0513	−	16.0513i	−0.0172409	−	0.0172409i
$932$		0			0
$933$	−1467.00	+	630.785i	−1.57235	+	0.676083i
$934$		0			0
$935$	−3.40156			−0.00363803
$936$		0			0
$937$		−	416.118i		−	0.444096i	−0.975036	−	0.222048i	$-0.928726\pi$
$937$		−	416.118i		−	0.444096i	0.975036	−	0.222048i	$-0.0712742\pi$
$938$		0			0
$939$	220.035	+	511.728i	0.234329	+	0.544971i
$940$		0			0
$941$	59.8023	−	59.8023i	0.0635518	−	0.0635518i	−0.674617	−	0.738168i	$-0.735691\pi$
$941$	59.8023	−	59.8023i	0.0635518	−	0.0635518i	0.738168	+	0.674617i	$0.235691\pi$
$942$		0			0
$943$	−925.012			−0.980925
$944$		0			0
$945$	1.01423	+	2.19493i	0.00107326	+	0.00232267i
$946$		0			0
$947$	438.459	−	438.459i	0.462998	−	0.462998i	−0.436639	−	0.899637i	$-0.643831\pi$
$947$	438.459	−	438.459i	0.462998	−	0.462998i	0.899637	+	0.436639i	$0.143831\pi$
$948$		0			0
$949$	396.600	−	396.600i	0.417913	−	0.417913i
$950$		0			0
$951$	264.125	−	662.602i	0.277733	−	0.696742i
$952$		0			0
$953$	−874.202			−0.917316			−0.458658	−	0.888613i	$-0.651670\pi$
$953$	−874.202			−0.917316			−0.458658	+	0.888613i	$0.651670\pi$
$954$		0			0
$955$	−1.54219	+	1.54219i	−0.00161486	+	0.00161486i
$956$		0			0
$957$	558.763	−	240.259i	0.583869	−	0.251054i
$958$		0			0
$959$			275.649i			0.287434i
$960$		0			0
$961$	2631.62			2.73842
$962$		0			0
$963$	520.973	−	13.9499i	0.540989	−	0.0144859i
$964$		0			0
$965$	2.14904	+	2.14904i	0.00222698	+	0.00222698i
$966$		0			0
$967$		−	78.0123i		−	0.0806746i	−0.999186	−	0.0403373i	$-0.987157\pi$
$967$		−	78.0123i		−	0.0806746i	0.999186	−	0.0403373i	$-0.0128432\pi$
$968$		0			0
$969$	61.8865	−	155.253i	0.0638663	−	0.160220i
$970$		0			0
$971$	545.451	+	545.451i	0.561742	+	0.561742i	0.929802	−	0.368060i	$-0.119978\pi$
$971$	545.451	+	545.451i	0.561742	+	0.561742i	−0.368060	+	0.929802i	$0.619978\pi$
$972$		0			0
$973$	302.477	+	302.477i	0.310870	+	0.310870i
$974$		0			0
$975$	−495.241	+	1242.40i	−0.507939	+	1.27425i
$976$		0			0
$977$		−	1711.35i		−	1.75164i	−0.482640	−	0.875819i	$-0.660322\pi$
$977$		−	1711.35i		−	1.75164i	0.482640	−	0.875819i	$-0.339678\pi$
$978$		0			0
$979$	−863.396	−	863.396i	−0.881916	−	0.881916i
$980$		0			0
$981$	1532.37	−	41.0318i	1.56205	−	0.0418265i
$982$		0			0
$983$	1349.18			1.37252			0.686259	−	0.727358i	$-0.259252\pi$
$983$	1349.18			1.37252			0.686259	+	0.727358i	$0.259252\pi$
$984$		0			0
$985$		−	4.84965i		−	0.00492351i
$986$		0			0
$987$	−111.465	+	47.9283i	−0.112934	+	0.0485596i
$988$		0			0
$989$	472.098	−	472.098i	0.477349	−	0.477349i
$990$		0			0
$991$	923.093			0.931476			0.465738	−	0.884923i	$-0.345789\pi$
$991$	923.093			0.931476			0.465738	+	0.884923i	$0.345789\pi$
$992$		0			0
$993$	−379.671	+	952.469i	−0.382347	+	0.959183i
$994$		0			0
$995$	−2.29907	+	2.29907i	−0.00231063	+	0.00231063i
$996$		0			0
$997$	−371.389	+	371.389i	−0.372507	+	0.372507i	−0.868390	−	0.495883i	$-0.834845\pi$
$997$	−371.389	+	371.389i	−0.372507	+	0.372507i	0.495883	+	0.868390i	$0.334845\pi$
$998$		0			0
$999$	149.389	+	323.296i	0.149538	+	0.323620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.3.i.c.161.9		20
3.2	odd	2	inner	384.3.i.c.161.5		20
4.3	odd	2		384.3.i.d.161.2		20
8.3	odd	2		48.3.i.b.29.6	yes	20
8.5	even	2		192.3.i.b.17.2		20
12.11	even	2		384.3.i.d.161.6		20
16.3	odd	4		48.3.i.b.5.5	✓	20
16.5	even	4	inner	384.3.i.c.353.5		20
16.11	odd	4		384.3.i.d.353.6		20
16.13	even	4		192.3.i.b.113.6		20
24.5	odd	2		192.3.i.b.17.6		20
24.11	even	2		48.3.i.b.29.5	yes	20
48.5	odd	4	inner	384.3.i.c.353.9		20
48.11	even	4		384.3.i.d.353.2		20
48.29	odd	4		192.3.i.b.113.2		20
48.35	even	4		48.3.i.b.5.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.b.5.5	✓	20	16.3	odd	4
48.3.i.b.5.6	yes	20	48.35	even	4
48.3.i.b.29.5	yes	20	24.11	even	2
48.3.i.b.29.6	yes	20	8.3	odd	2
192.3.i.b.17.2		20	8.5	even	2
192.3.i.b.17.6		20	24.5	odd	2
192.3.i.b.113.2		20	48.29	odd	4
192.3.i.b.113.6		20	16.13	even	4
384.3.i.c.161.5		20	3.2	odd	2	inner
384.3.i.c.161.9		20	1.1	even	1	trivial
384.3.i.c.353.5		20	16.5	even	4	inner
384.3.i.c.353.9		20	48.5	odd	4	inner
384.3.i.d.161.2		20	4.3	odd	2
384.3.i.d.161.6		20	12.11	even	2
384.3.i.d.353.2		20	48.11	even	4
384.3.i.d.353.6		20	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	384.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.75602 - 1.18505i) q^{3} +(-0.00985921 - 0.00985921i) q^{5} -6.42277i q^{7} +(6.19134 - 6.53203i) q^{9} +O(q^{10})\)	\(q+(2.75602 - 1.18505i) q^{3} +(-0.00985921 - 0.00985921i) q^{5} -6.42277i q^{7} +(6.19134 - 6.53203i) q^{9} +(-9.07186 - 9.07186i) q^{11} +(-12.6098 - 12.6098i) q^{13} +(-0.0388558 - 0.0154886i) q^{15} +19.0155i q^{17} +(-2.07165 - 2.07165i) q^{19} +(-7.61127 - 17.7013i) q^{21} +19.5712 q^{23} -24.9998i q^{25} +(9.32272 - 25.3394i) q^{27} +(-11.1742 + 11.1742i) q^{29} +59.9385 q^{31} +(-35.7528 - 14.2517i) q^{33} +(-0.0633234 + 0.0633234i) q^{35} +(-9.32707 + 9.32707i) q^{37} +(-49.6962 - 19.8098i) q^{39} -47.2639 q^{41} +(24.1220 - 24.1220i) q^{43} +(-0.125442 + 0.00335893i) q^{45} -6.29702i q^{47} +7.74808 q^{49} +(22.5343 + 52.4073i) q^{51} +(20.6409 + 20.6409i) q^{53} +0.178883i q^{55} +(-8.16452 - 3.25452i) q^{57} +(60.3533 + 60.3533i) q^{59} +(-48.0230 - 48.0230i) q^{61} +(-41.9537 - 39.7655i) q^{63} +0.248646i q^{65} +(-23.7768 - 23.7768i) q^{67} +(53.9388 - 23.1928i) q^{69} +13.5743 q^{71} +31.4516i q^{73} +(-29.6259 - 68.9001i) q^{75} +(-58.2665 + 58.2665i) q^{77} -47.4718 q^{79} +(-4.33472 - 80.8839i) q^{81} +(70.3318 - 70.3318i) q^{83} +(0.187478 - 0.187478i) q^{85} +(-17.5545 + 44.0385i) q^{87} +95.1729 q^{89} +(-80.9900 + 80.9900i) q^{91} +(165.192 - 71.0298i) q^{93} +0.0408497i q^{95} +61.6218 q^{97} +(-115.425 + 3.09069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3}+O(q^{10}) \) 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

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