LMFDB - Embedded newform 192.3.i.b.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,3,Mod(17,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, 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("192.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	192.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:	$5.23162107572$
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			17.2
Root			$-0.312316 - 1.97546i$ of defining polynomial
Character	$\chi$	$=$	192.17
Dual form			192.3.i.b.113.2

$q$-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 $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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	0.708092	−	0.706120i	$-0.249556\pi$
$5$	0.00985921	+	0.00985921i	0.00197184	+	0.00197184i	−0.706120	+	0.708092i	$0.749556\pi$
$6$		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	0.986780	−	0.162065i	$-0.0518155\pi$
$11$	9.07186	+	9.07186i	0.824715	+	0.824715i	−0.162065	+	0.986780i	$0.551815\pi$
$12$		0			0
$13$	12.6098	+	12.6098i	0.969987	+	0.969987i	0.999563	−	0.0295753i	$-0.00941548\pi$
$13$	12.6098	+	12.6098i	0.969987	+	0.969987i	−0.0295753	+	0.999563i	$0.509415\pi$
$14$		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	0.759519	−	0.650485i	$-0.225434\pi$
$19$	2.07165	+	2.07165i	0.109034	+	0.109034i	−0.650485	+	0.759519i	$0.725434\pi$
$20$		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	−0.487695	−	0.873014i	$-0.662162\pi$
$29$	11.1742	−	11.1742i	0.385319	−	0.385319i	0.873014	+	0.487695i	$0.162162\pi$
$30$		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	−0.569741	−	0.821824i	$-0.692957\pi$
$37$	9.32707	−	9.32707i	0.252083	−	0.252083i	0.821824	+	0.569741i	$0.192957\pi$
$38$		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	−0.929585	−	0.368607i	$-0.879835\pi$
$43$	−24.1220	+	24.1220i	−0.560978	+	0.560978i	0.368607	+	0.929585i	$0.379835\pi$
$44$		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	0.485041	−	0.874491i	$-0.338805\pi$
$53$	−20.6409	−	20.6409i	−0.389450	−	0.389450i	−0.874491	+	0.485041i	$0.838805\pi$
$54$		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	$-0.992613\pi$
$59$	−60.3533	−	60.3533i	−1.02294	−	1.02294i	−0.0232062	−	0.999731i	$-0.507387\pi$
$60$		0			0
$61$	48.0230	+	48.0230i	0.787262	+	0.787262i	0.981045	−	0.193782i	$-0.0620755\pi$
$61$	48.0230	+	48.0230i	0.787262	+	0.787262i	−0.193782	+	0.981045i	$0.562076\pi$
$62$		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	0.861921	−	0.507043i	$-0.169262\pi$
$67$	23.7768	+	23.7768i	0.354878	+	0.354878i	−0.507043	+	0.861921i	$0.669262\pi$
$68$		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	−0.989804	−	0.142433i	$-0.954507\pi$
$83$	−70.3318	+	70.3318i	−0.847372	+	0.847372i	0.142433	+	0.989804i	$0.454507\pi$
$84$		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	0.427106	−	0.904202i	$-0.359533\pi$
$101$	−48.1867	−	48.1867i	−0.477096	−	0.477096i	−0.904202	+	0.427106i	$0.859533\pi$
$102$		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	0.489390	−	0.872065i	$-0.337219\pi$
$107$	−40.9462	−	40.9462i	−0.382674	−	0.382674i	−0.872065	+	0.489390i	$0.837219\pi$
$108$		0			0
$109$	−120.437	−	120.437i	−1.10493	−	1.10493i	−0.993807	−	0.111123i	$-0.964555\pi$
$109$	−120.437	−	120.437i	−1.10493	−	1.10493i	−0.111123	−	0.993807i	$-0.535445\pi$
$110$		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	−0.577662	−	0.816276i	$-0.696035\pi$
$131$	31.2584	−	31.2584i	0.238614	−	0.238614i	0.816276	+	0.577662i	$0.196035\pi$
$132$		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	−0.517110	−	0.855919i	$-0.672992\pi$
$139$	47.0945	−	47.0945i	0.338809	−	0.338809i	0.855919	+	0.517110i	$0.172992\pi$
$140$		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	0.993815	−	0.111049i	$-0.0354210\pi$
$149$	131.532	+	131.532i	0.882766	+	0.882766i	−0.111049	+	0.993815i	$0.535421\pi$
$150$		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	0.508875	−	0.860840i	$-0.330062\pi$
$157$	−55.2586	−	55.2586i	−0.351966	−	0.351966i	−0.860840	+	0.508875i	$0.830062\pi$
$158$		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	0.456499	−	0.889724i	$-0.349103\pi$
$163$	−70.6156	−	70.6156i	−0.433225	−	0.433225i	−0.889724	+	0.456499i	$0.849103\pi$
$164$		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	−0.518448	−	0.855109i	$-0.673490\pi$
$173$	58.2425	−	58.2425i	0.336662	−	0.336662i	0.855109	+	0.518448i	$0.173490\pi$
$174$		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	−0.652258	−	0.757997i	$-0.726178\pi$
$179$	18.9272	−	18.9272i	0.105738	−	0.105738i	0.757997	+	0.652258i	$0.226178\pi$
$180$		0			0
$181$	24.5109	−	24.5109i	0.135420	−	0.135420i	−0.636148	−	0.771567i	$-0.719473\pi$
$181$	24.5109	−	24.5109i	0.135420	−	0.135420i	0.771567	+	0.636148i	$0.219473\pi$
$182$		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	$-0.905663\pi$
$197$	−245.945	−	245.945i	−1.24845	−	1.24845i	−0.292050	−	0.956403i	$-0.594337\pi$
$198$		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	0.726951	−	0.686690i	$-0.240937\pi$
$211$	8.49504	+	8.49504i	0.0402609	+	0.0402609i	−0.686690	+	0.726951i	$0.740937\pi$
$212$		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	−0.892045	−	0.451946i	$-0.850730\pi$
$227$	−99.9027	+	99.9027i	−0.440100	+	0.440100i	0.451946	+	0.892045i	$0.350730\pi$
$228$		0			0
$229$	−231.857	+	231.857i	−1.01248	+	1.01248i	−0.0125555	+	0.999921i	$0.503997\pi$
$229$	−231.857	+	231.857i	−1.01248	+	1.01248i	−0.999921	+	0.0125555i	$0.996003\pi$
$230$		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	0.915451	−	0.402430i	$-0.131834\pi$
$251$	128.768	+	128.768i	0.513021	+	0.513021i	−0.402430	+	0.915451i	$0.631834\pi$
$252$		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	$-0.465345\pi$
$269$	296.636	−	296.636i	1.10274	−	1.10274i	0.994079	−	0.108658i	$-0.0346555\pi$
$270$		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	−0.807297	−	0.590145i	$-0.799071\pi$
$277$	−60.1513	+	60.1513i	−0.217153	+	0.217153i	0.590145	+	0.807297i	$0.299071\pi$
$278$		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	$0.504508\pi$
$283$	−286.980	+	286.980i	−1.01406	+	1.01406i	−0.999900	+	0.0141627i	$0.995492\pi$
$284$		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	0.940947	−	0.338553i	$-0.109938\pi$
$293$	176.501	+	176.501i	0.602394	+	0.602394i	−0.338553	+	0.940947i	$0.609938\pi$
$294$		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	0.595165	−	0.803603i	$-0.297087\pi$
$307$	−63.9904	−	63.9904i	−0.208438	−	0.208438i	−0.803603	+	0.595165i	$0.797087\pi$
$308$		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	−0.920683	−	0.390312i	$-0.872367\pi$
$317$	−168.127	+	168.127i	−0.530370	+	0.530370i	0.390312	+	0.920683i	$0.372367\pi$
$318$		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	−0.240504	−	0.970648i	$-0.577313\pi$
$331$	241.678	−	241.678i	0.730144	−	0.730144i	0.970648	+	0.240504i	$0.0773127\pi$
$332$		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	0.760496	−	0.649343i	$-0.224956\pi$
$347$	38.5699	+	38.5699i	0.111153	+	0.111153i	−0.649343	+	0.760496i	$0.724956\pi$
$348$		0			0
$349$	10.4065	+	10.4065i	0.0298180	+	0.0298180i	0.721859	−	0.692041i	$-0.243288\pi$
$349$	10.4065	+	10.4065i	0.0298180	+	0.0298180i	−0.692041	+	0.721859i	$0.743288\pi$
$350$		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	−0.0563743	−	0.998410i	$-0.517954\pi$
$373$	351.379	−	351.379i	0.942035	−	0.942035i	0.998410	+	0.0563743i	$0.0179540\pi$
$374$		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	−0.445435	−	0.895315i	$-0.646951\pi$
$379$	170.505	−	170.505i	0.449880	−	0.449880i	0.895315	+	0.445435i	$0.146951\pi$
$380$		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	0.0323468	−	0.999477i	$-0.489702\pi$
$389$	−376.214	−	376.214i	−0.967130	−	0.967130i	−0.999477	+	0.0323468i	$0.989702\pi$
$390$		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	0.193021	−	0.981195i	$-0.438172\pi$
$397$	−312.905	−	312.905i	−0.788174	−	0.788174i	−0.981195	+	0.193021i	$0.938172\pi$
$398$		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	−0.383007	−	0.923745i	$-0.625112\pi$
$419$	226.569	−	226.569i	0.540738	−	0.540738i	0.923745	+	0.383007i	$0.125112\pi$
$420$		0			0
$421$	−498.861	+	498.861i	−1.18494	+	1.18494i	−0.206495	+	0.978448i	$0.566206\pi$
$421$	−498.861	+	498.861i	−1.18494	+	1.18494i	−0.978448	+	0.206495i	$0.933794\pi$
$422$		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	0.808593	−	0.588368i	$-0.200229\pi$
$443$	97.5600	+	97.5600i	0.220226	+	0.220226i	−0.588368	+	0.808593i	$0.700229\pi$
$444$		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	−0.999991	−	0.00415179i	$-0.998678\pi$
$461$	−459.082	+	459.082i	−0.995840	+	0.995840i	0.00415179	+	0.999991i	$0.498678\pi$
$462$		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	−0.604750	−	0.796415i	$-0.706727\pi$
$467$	89.5077	−	89.5077i	0.191665	−	0.191665i	0.796415	+	0.604750i	$0.206727\pi$
$468$		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	0.239286	−	0.970949i	$-0.423087\pi$
$491$	−359.246	−	359.246i	−0.731663	−	0.731663i	−0.970949	+	0.239286i	$0.923087\pi$
$492$		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	0.768747	−	0.639553i	$-0.220880\pi$
$499$	64.4682	+	64.4682i	0.129195	+	0.129195i	−0.639553	+	0.768747i	$0.720880\pi$
$500$		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	−0.259350	−	0.965783i	$-0.583508\pi$
$509$	359.574	−	359.574i	0.706433	−	0.706433i	0.965783	+	0.259350i	$0.0835084\pi$
$510$		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	−0.417908	−	0.908489i	$-0.637237\pi$
$523$	256.574	−	256.574i	0.490581	−	0.490581i	0.908489	+	0.417908i	$0.137237\pi$
$524$		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	0.185167	−	0.982707i	$-0.440717\pi$
$541$	−431.469	−	431.469i	−0.797540	−	0.797540i	−0.982707	+	0.185167i	$0.940717\pi$
$542$		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	0.330632	−	0.943760i	$-0.392738\pi$
$547$	−335.381	−	335.381i	−0.613127	−	0.613127i	−0.943760	+	0.330632i	$0.892738\pi$
$548$		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	−0.592540	−	0.805541i	$-0.701875\pi$
$557$	118.642	−	118.642i	0.213001	−	0.213001i	0.805541	+	0.592540i	$0.201875\pi$
$558$		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	−0.400039	−	0.916498i	$-0.631003\pi$
$563$	290.766	−	290.766i	0.516459	−	0.516459i	0.916498	+	0.400039i	$0.131003\pi$
$564$		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	−0.982589	−	0.185792i	$-0.940515\pi$
$571$	−454.971	+	454.971i	−0.796798	+	0.796798i	0.185792	+	0.982589i	$0.440515\pi$
$572$		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	0.957842	−	0.287297i	$-0.0927566\pi$
$587$	393.610	+	393.610i	0.670545	+	0.670545i	−0.287297	+	0.957842i	$0.592757\pi$
$588$		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	−0.443636	−	0.896207i	$-0.646312\pi$
$613$	277.427	−	277.427i	0.452572	−	0.452572i	0.896207	+	0.443636i	$0.146312\pi$
$614$		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	$0.555740\pi$
$619$	−717.374	+	717.374i	−1.15892	+	1.15892i	−0.984707	+	0.174218i	$0.944260\pi$
$620$		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	0.931992	−	0.362479i	$-0.118069\pi$
$643$	366.197	+	366.197i	0.569514	+	0.569514i	−0.362479	+	0.931992i	$0.618069\pi$
$644$		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	−0.447985	−	0.894041i	$-0.647858\pi$
$653$	291.274	−	291.274i	0.446056	−	0.446056i	0.894041	+	0.447985i	$0.147858\pi$
$654$		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	$0.590827\pi$
$659$	−817.853	+	817.853i	−1.24105	+	1.24105i	−0.959565	+	0.281486i	$0.909173\pi$
$660$		0			0
$661$	−673.995	+	673.995i	−1.01966	+	1.01966i	−0.0198568	+	0.999803i	$0.506321\pi$
$661$	−673.995	+	673.995i	−1.01966	+	1.01966i	−0.999803	+	0.0198568i	$0.993679\pi$
$662$		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	0.805204	−	0.592998i	$-0.202056\pi$
$677$	143.663	+	143.663i	0.212205	+	0.212205i	−0.592998	+	0.805204i	$0.702056\pi$
$678$		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	0.669073	−	0.743196i	$-0.266691\pi$
$683$	−50.6262	−	50.6262i	−0.0741232	−	0.0741232i	−0.743196	+	0.669073i	$0.766691\pi$
$684$		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	0.359712	−	0.933063i	$-0.382875\pi$
$691$	−396.186	−	396.186i	−0.573351	−	0.573351i	−0.933063	+	0.359712i	$0.882875\pi$
$692$		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	−0.224321	−	0.974515i	$-0.572016\pi$
$701$	525.886	−	525.886i	0.750195	−	0.750195i	0.974515	+	0.224321i	$0.0720164\pi$
$702$		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	−0.773726	−	0.633520i	$-0.781609\pi$
$709$	−99.4062	+	99.4062i	−0.140206	+	0.140206i	0.633520	+	0.773726i	$0.281609\pi$
$710$		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	0.941363	−	0.337395i	$-0.109546\pi$
$733$	442.709	+	442.709i	0.603968	+	0.603968i	−0.337395	+	0.941363i	$0.609546\pi$
$734$		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	0.488871	−	0.872356i	$-0.337409\pi$
$739$	−283.395	−	283.395i	−0.383485	−	0.383485i	−0.872356	+	0.488871i	$0.837409\pi$
$740$		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	−0.893213	−	0.449634i	$-0.851554\pi$
$757$	−335.789	+	335.789i	−0.443578	+	0.443578i	0.449634	+	0.893213i	$0.351554\pi$
$758$		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	0.820965	−	0.570979i	$-0.193436\pi$
$773$	193.239	+	193.239i	0.249986	+	0.249986i	−0.570979	+	0.820965i	$0.693436\pi$
$774$		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	0.329345	−	0.944210i	$-0.393172\pi$
$787$	−483.899	−	483.899i	−0.614865	−	0.614865i	−0.944210	+	0.329345i	$0.893172\pi$
$788$		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	$-0.468285\pi$
$797$	872.325	−	872.325i	1.09451	−	1.09451i	0.995041	−	0.0994694i	$-0.0317145\pi$
$798$		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	−0.436898	−	0.899511i	$-0.643923\pi$
$811$	375.179	−	375.179i	0.462613	−	0.462613i	0.899511	+	0.436898i	$0.143923\pi$
$812$		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	0.168259	−	0.985743i	$-0.446186\pi$
$821$	−671.154	−	671.154i	−0.817484	−	0.817484i	−0.985743	+	0.168259i	$0.946186\pi$
$822$		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	$-0.893843\pi$
$827$	−1052.16	−	1052.16i	−1.27226	−	1.27226i	−0.327355	−	0.944901i	$-0.606157\pi$
$828$		0			0
$829$	−95.3529	−	95.3529i	−0.115022	−	0.115022i	0.647253	−	0.762275i	$-0.275918\pi$
$829$	−95.3529	−	95.3529i	−0.115022	−	0.115022i	−0.762275	+	0.647253i	$0.775918\pi$
$830$		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	−0.265866	−	0.964010i	$-0.585658\pi$
$853$	595.516	−	595.516i	0.698143	−	0.698143i	0.964010	+	0.265866i	$0.0856580\pi$
$854$		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	−0.861392	−	0.507941i	$-0.830407\pi$
$859$	−303.614	+	303.614i	−0.353451	+	0.353451i	0.507941	+	0.861392i	$0.330407\pi$
$860$		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	0.341550	−	0.939864i	$-0.389048\pi$
$877$	−524.721	−	524.721i	−0.598314	−	0.598314i	−0.939864	+	0.341550i	$0.889048\pi$
$878$		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	$0.0194154\pi$
$883$	935.183	+	935.183i	1.05910	+	1.05910i	0.0609574	+	0.998140i	$0.480585\pi$
$884$		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	$-0.426094\pi$
$907$	1091.36	−	1091.36i	1.20327	−	1.20327i	0.973167	−	0.230101i	$-0.0739056\pi$
$908$		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	−0.738168	−	0.674617i	$-0.764309\pi$
$941$	−59.8023	+	59.8023i	−0.0635518	+	0.0635518i	0.674617	+	0.738168i	$0.264309\pi$
$942$		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	−0.899637	−	0.436639i	$-0.856169\pi$
$947$	−438.459	+	438.459i	−0.462998	+	0.462998i	0.436639	+	0.899637i	$0.356169\pi$
$948$		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	0.368060	−	0.929802i	$-0.380022\pi$
$971$	−545.451	−	545.451i	−0.561742	−	0.561742i	−0.929802	+	0.368060i	$0.880022\pi$
$972$		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	−0.495883	−	0.868390i	$-0.665155\pi$
$997$	371.389	−	371.389i	0.372507	−	0.372507i	0.868390	+	0.495883i	$0.165155\pi$
$998$		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	192.3.i.b.17.2		20
3.2	odd	2	inner	192.3.i.b.17.6		20
4.3	odd	2		48.3.i.b.29.6	yes	20
8.3	odd	2		384.3.i.d.161.2		20
8.5	even	2		384.3.i.c.161.9		20
12.11	even	2		48.3.i.b.29.5	yes	20
16.3	odd	4		384.3.i.d.353.6		20
16.5	even	4	inner	192.3.i.b.113.6		20
16.11	odd	4		48.3.i.b.5.5	✓	20
16.13	even	4		384.3.i.c.353.5		20
24.5	odd	2		384.3.i.c.161.5		20
24.11	even	2		384.3.i.d.161.6		20
48.5	odd	4	inner	192.3.i.b.113.2		20
48.11	even	4		48.3.i.b.5.6	yes	20
48.29	odd	4		384.3.i.c.353.9		20
48.35	even	4		384.3.i.d.353.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.b.5.5	✓	20	16.11	odd	4
48.3.i.b.5.6	yes	20	48.11	even	4
48.3.i.b.29.5	yes	20	12.11	even	2
48.3.i.b.29.6	yes	20	4.3	odd	2
192.3.i.b.17.2		20	1.1	even	1	trivial
192.3.i.b.17.6		20	3.2	odd	2	inner
192.3.i.b.113.2		20	48.5	odd	4	inner
192.3.i.b.113.6		20	16.5	even	4	inner
384.3.i.c.161.5		20	24.5	odd	2
384.3.i.c.161.9		20	8.5	even	2
384.3.i.c.353.5		20	16.13	even	4
384.3.i.c.353.9		20	48.29	odd	4
384.3.i.d.161.2		20	8.3	odd	2
384.3.i.d.161.6		20	24.11	even	2
384.3.i.d.353.2		20	48.35	even	4
384.3.i.d.353.6		20	16.3	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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	192.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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more