LMFDB - Embedded newform 1120.2.x.f.127.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1120,2,Mod(127,1120)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1120, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1120.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.x (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,-4,0,0,0,0,0,0,0,-12,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

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

Self dual:	no
Analytic conductor:	$8.94324502638$
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} - 4 x^{19} + 4 x^{18} + 16 x^{17} - 56 x^{16} - 24 x^{15} + 512 x^{14} + 856 x^{13} + 402 x^{12} + \cdots + 5000 $ x^20 - 4x^19 + 4x^18 + 16x^17 - 56x^16 - 24x^15 + 512x^14 + 856x^13 + 402x^12 - 2696x^11 - 2776x^10 + 4912x^9 + 9744x^8 + 15176x^7 + 40928x^6 + 42808x^5 + 48369x^4 + 34460x^3 + 24900x^2 + 16000*x + 5000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.10
Root			$0.458613 + 1.10719i$ of defining polynomial
Character	$\chi$	$=$	1120.127
Dual form			1120.2.x.f.1023.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.27923 + 2.27923i) q^{3} +(2.07423 - 0.835201i) q^{5} +(-0.707107 + 0.707107i) q^{7} +7.38979i q^{9} +3.68262i q^{11} +(-0.712298 + 0.712298i) q^{13} +(6.63127 + 2.82404i) q^{15} +(-2.90079 - 2.90079i) q^{17} -6.77624 q^{19} -3.22332 q^{21} +(5.17244 + 5.17244i) q^{23} +(3.60488 - 3.46480i) q^{25} +(-10.0053 + 10.0053i) q^{27} -6.87275i q^{29} -5.20801i q^{31} +(-8.39355 + 8.39355i) q^{33} +(-0.876127 + 2.05728i) q^{35} +(2.61952 + 2.61952i) q^{37} -3.24698 q^{39} +3.63583 q^{41} +(5.92367 + 5.92367i) q^{43} +(6.17196 + 15.3281i) q^{45} +(7.11278 - 7.11278i) q^{47} -1.00000i q^{49} -13.2232i q^{51} +(1.56467 - 1.56467i) q^{53} +(3.07573 + 7.63861i) q^{55} +(-15.4446 - 15.4446i) q^{57} +9.98237 q^{59} -2.37399 q^{61} +(-5.22537 - 5.22537i) q^{63} +(-0.882559 + 2.07238i) q^{65} +(3.74159 - 3.74159i) q^{67} +23.5784i q^{69} +1.23688i q^{71} +(4.22679 - 4.22679i) q^{73} +(16.1134 + 0.319262i) q^{75} +(-2.60401 - 2.60401i) q^{77} +6.23911 q^{79} -23.4396 q^{81} +(-4.78446 - 4.78446i) q^{83} +(-8.43966 - 3.59417i) q^{85} +(15.6646 - 15.6646i) q^{87} +11.3619i q^{89} -1.00734i q^{91} +(11.8703 - 11.8703i) q^{93} +(-14.0555 + 5.65952i) q^{95} +(-11.4341 - 11.4341i) q^{97} -27.2138 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} - 12 q^{13} + 8 q^{15} - 4 q^{17} - 24 q^{19} + 8 q^{23} + 4 q^{25} - 16 q^{33} - 4 q^{35} + 4 q^{37} + 8 q^{39} + 32 q^{41} - 8 q^{43} + 32 q^{45} + 24 q^{47} + 28 q^{53} + 24 q^{59} + 24 q^{61}+ \cdots + 4 q^{97}+O(q^{100}) $ 20 * q - 4 * q^5 - 12 * q^13 + 8 * q^15 - 4 * q^17 - 24 * q^19 + 8 * q^23 + 4 * q^25 - 16 * q^33 - 4 * q^35 + 4 * q^37 + 8 * q^39 + 32 * q^41 - 8 * q^43 + 32 * q^45 + 24 * q^47 + 28 * q^53 + 24 * q^59 + 24 * q^61 - 8 * q^63 - 12 * q^65 - 8 * q^67 + 20 * q^73 + 72 * q^75 + 8 * q^77 - 24 * q^79 - 20 * q^81 - 48 * q^83 - 20 * q^85 + 56 * q^87 - 8 * q^93 - 8 * q^95 + 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	2.27923	+	2.27923i	1.31591	+	1.31591i	0.916979	+	0.398936i	$0.130620\pi$
$3$	2.27923	+	2.27923i	1.31591	+	1.31591i	0.398936	+	0.916979i	$0.369380\pi$
$4$		0			0
$5$	2.07423	−	0.835201i	0.927625	−	0.373513i
$5$	2.07423	−	0.835201i	0.927625	−	0.373513i
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		0			0
$9$			7.38979i			2.46326i
$10$		0			0
$11$			3.68262i			1.11035i	0.831733	+	0.555176i	$0.187349\pi$
$11$			3.68262i			1.11035i	−0.831733	+	0.555176i	$0.812651\pi$
$12$		0			0
$13$	−0.712298	+	0.712298i	−0.197556	+	0.197556i	−0.798951	−	0.601396i	$-0.794612\pi$
$13$	−0.712298	+	0.712298i	−0.197556	+	0.197556i	0.601396	+	0.798951i	$0.294612\pi$
$14$		0			0
$15$	6.63127	+	2.82404i	1.71219	+	0.729163i
$16$		0			0
$17$	−2.90079	−	2.90079i	−0.703546	−	0.703546i	0.261624	−	0.965170i	$-0.415742\pi$
$17$	−2.90079	−	2.90079i	−0.703546	−	0.703546i	−0.965170	+	0.261624i	$0.915742\pi$
$18$		0			0
$19$	−6.77624			−1.55458			−0.777288	−	0.629146i	$-0.783405\pi$
$19$	−6.77624			−1.55458			−0.777288	+	0.629146i	$0.783405\pi$
$20$		0			0
$21$	−3.22332			−0.703386
$22$		0			0
$23$	5.17244	+	5.17244i	1.07853	+	1.07853i	0.996642	+	0.0818861i	$0.0260944\pi$
$23$	5.17244	+	5.17244i	1.07853	+	1.07853i	0.0818861	+	0.996642i	$0.473906\pi$
$24$		0			0
$25$	3.60488	−	3.46480i	0.720975	−	0.692961i
$26$		0			0
$27$	−10.0053	+	10.0053i	−1.92553	+	1.92553i
$28$		0			0
$29$		−	6.87275i		−	1.27624i	−0.769938	−	0.638119i	$-0.779713\pi$
$29$		−	6.87275i		−	1.27624i	0.769938	−	0.638119i	$-0.220287\pi$
$30$		0			0
$31$		−	5.20801i		−	0.935387i	−0.883891	−	0.467694i	$-0.845085\pi$
$31$		−	5.20801i		−	0.935387i	0.883891	−	0.467694i	$-0.154915\pi$
$32$		0			0
$33$	−8.39355	+	8.39355i	−1.46113	+	1.46113i
$34$		0			0
$35$	−0.876127	+	2.05728i	−0.148092	+	0.347744i
$36$		0			0
$37$	2.61952	+	2.61952i	0.430647	+	0.430647i	0.888848	−	0.458202i	$-0.151506\pi$
$37$	2.61952	+	2.61952i	0.430647	+	0.430647i	−0.458202	+	0.888848i	$0.651506\pi$
$38$		0			0
$39$	−3.24698			−0.519933
$40$		0			0
$41$	3.63583			0.567821			0.283911	−	0.958851i	$-0.408368\pi$
$41$	3.63583			0.567821			0.283911	+	0.958851i	$0.408368\pi$
$42$		0			0
$43$	5.92367	+	5.92367i	0.903351	+	0.903351i	0.995724	−	0.0923738i	$-0.0294455\pi$
$43$	5.92367	+	5.92367i	0.903351	+	0.903351i	−0.0923738	+	0.995724i	$0.529445\pi$
$44$		0			0
$45$	6.17196	+	15.3281i	0.920062	+	2.28498i
$46$		0			0
$47$	7.11278	−	7.11278i	1.03751	−	1.03751i	0.0382366	−	0.999269i	$-0.487826\pi$
$47$	7.11278	−	7.11278i	1.03751	−	1.03751i	0.999269	−	0.0382366i	$-0.0121741\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$		−	13.2232i		−	1.85161i
$52$		0			0
$53$	1.56467	−	1.56467i	0.214924	−	0.214924i	−0.591431	−	0.806355i	$-0.701437\pi$
$53$	1.56467	−	1.56467i	0.214924	−	0.214924i	0.806355	+	0.591431i	$0.201437\pi$
$54$		0			0
$55$	3.07573	+	7.63861i	0.414732	+	1.02999i
$56$		0			0
$57$	−15.4446	−	15.4446i	−2.04569	−	2.04569i
$58$		0			0
$59$	9.98237			1.29959			0.649797	−	0.760108i	$-0.274854\pi$
$59$	9.98237			1.29959			0.649797	+	0.760108i	$0.274854\pi$
$60$		0			0
$61$	−2.37399			−0.303958			−0.151979	−	0.988384i	$-0.548565\pi$
$61$	−2.37399			−0.303958			−0.151979	+	0.988384i	$0.548565\pi$
$62$		0			0
$63$	−5.22537	−	5.22537i	−0.658335	−	0.658335i
$64$		0			0
$65$	−0.882559	+	2.07238i	−0.109468	+	0.257048i
$66$		0			0
$67$	3.74159	−	3.74159i	0.457108	−	0.457108i	−0.440597	−	0.897705i	$-0.645233\pi$
$67$	3.74159	−	3.74159i	0.457108	−	0.457108i	0.897705	+	0.440597i	$0.145233\pi$
$68$		0			0
$69$			23.5784i			2.83850i
$70$		0			0
$71$			1.23688i			0.146791i	0.997303	+	0.0733956i	$0.0233836\pi$
$71$			1.23688i			0.146791i	−0.997303	+	0.0733956i	$0.976616\pi$
$72$		0			0
$73$	4.22679	−	4.22679i	0.494708	−	0.494708i	−0.415078	−	0.909786i	$-0.636246\pi$
$73$	4.22679	−	4.22679i	0.494708	−	0.494708i	0.909786	+	0.415078i	$0.136246\pi$
$74$		0			0
$75$	16.1134	+	0.319262i	1.86062	+	0.0368651i
$76$		0			0
$77$	−2.60401	−	2.60401i	−0.296754	−	0.296754i
$78$		0			0
$79$	6.23911			0.701955			0.350978	−	0.936384i	$-0.385849\pi$
$79$	6.23911			0.701955			0.350978	+	0.936384i	$0.385849\pi$
$80$		0			0
$81$	−23.4396			−2.60440
$82$		0			0
$83$	−4.78446	−	4.78446i	−0.525163	−	0.525163i	0.393963	−	0.919126i	$-0.371104\pi$
$83$	−4.78446	−	4.78446i	−0.525163	−	0.525163i	−0.919126	+	0.393963i	$0.871104\pi$
$84$		0			0
$85$	−8.43966	−	3.59417i	−0.915410	−	0.389843i
$86$		0			0
$87$	15.6646	−	15.6646i	1.67942	−	1.67942i
$88$		0			0
$89$			11.3619i			1.20436i	0.798359	+	0.602182i	$0.205702\pi$
$89$			11.3619i			1.20436i	−0.798359	+	0.602182i	$0.794298\pi$
$90$		0			0
$91$		−	1.00734i		−	0.105598i
$92$		0			0
$93$	11.8703	−	11.8703i	1.23089	−	1.23089i
$94$		0			0
$95$	−14.0555	+	5.65952i	−1.44206	+	0.580655i
$96$		0			0
$97$	−11.4341	−	11.4341i	−1.16095	−	1.16095i	−0.984267	−	0.176688i	$-0.943462\pi$
$97$	−11.4341	−	11.4341i	−1.16095	−	1.16095i	−0.176688	−	0.984267i	$-0.556538\pi$
$98$		0			0
$99$	−27.2138			−2.73509
$100$		0			0
$101$	−4.78624			−0.476249			−0.238124	−	0.971235i	$-0.576533\pi$
$101$	−4.78624			−0.476249			−0.238124	+	0.971235i	$0.576533\pi$
$102$		0			0
$103$	−11.3805	−	11.3805i	−1.12135	−	1.12135i	−0.991538	−	0.129814i	$-0.958562\pi$
$103$	−11.3805	−	11.3805i	−1.12135	−	1.12135i	−0.129814	−	0.991538i	$-0.541438\pi$
$104$		0			0
$105$	−6.68591	+	2.69212i	−0.652478	+	0.262724i
$106$		0			0
$107$	−2.39737	+	2.39737i	−0.231763	+	0.231763i	−0.813428	−	0.581665i	$-0.802401\pi$
$107$	−2.39737	+	2.39737i	−0.231763	+	0.231763i	0.581665	+	0.813428i	$0.302401\pi$
$108$		0			0
$109$		−	4.04707i		−	0.387639i	−0.981037	−	0.193820i	$-0.937912\pi$
$109$		−	4.04707i		−	0.387639i	0.981037	−	0.193820i	$-0.0620876\pi$
$110$		0			0
$111$			11.9410i			1.13339i
$112$		0			0
$113$	−8.37492	+	8.37492i	−0.787846	+	0.787846i	−0.981141	−	0.193295i	$-0.938083\pi$
$113$	−8.37492	+	8.37492i	−0.787846	+	0.787846i	0.193295	+	0.981141i	$0.438083\pi$
$114$		0			0
$115$	15.0489	+	6.40881i	1.40331	+	0.597625i
$116$		0			0
$117$	−5.26373	−	5.26373i	−0.486632	−	0.486632i
$118$		0			0
$119$	4.10234			0.376061
$120$		0			0
$121$	−2.56171			−0.232883
$122$		0			0
$123$	8.28690	+	8.28690i	0.747204	+	0.747204i
$124$		0			0
$125$	4.58354	−	10.1976i	0.409965	−	0.912101i
$126$		0			0
$127$	−8.03325	+	8.03325i	−0.712836	+	0.712836i	−0.967128	−	0.254292i	$-0.918158\pi$
$127$	−8.03325	+	8.03325i	−0.712836	+	0.712836i	0.254292	+	0.967128i	$0.418158\pi$
$128$		0			0
$129$			27.0028i			2.37746i
$130$		0			0
$131$			4.17997i			0.365206i	0.983187	+	0.182603i	$0.0584523\pi$
$131$			4.17997i			0.365206i	−0.983187	+	0.182603i	$0.941548\pi$
$132$		0			0
$133$	4.79152	−	4.79152i	0.415478	−	0.415478i
$134$		0			0
$135$	−12.3969	+	29.1099i	−1.06696	+	2.50538i
$136$		0			0
$137$	−7.68028	−	7.68028i	−0.656171	−	0.656171i	0.298301	−	0.954472i	$-0.403580\pi$
$137$	−7.68028	−	7.68028i	−0.656171	−	0.656171i	−0.954472	+	0.298301i	$0.903580\pi$
$138$		0			0
$139$	1.23092			0.104405			0.0522027	−	0.998637i	$-0.483376\pi$
$139$	1.23092			0.104405			0.0522027	+	0.998637i	$0.483376\pi$
$140$		0			0
$141$	32.4233			2.73054
$142$		0			0
$143$	−2.62312	−	2.62312i	−0.219357	−	0.219357i
$144$		0			0
$145$	−5.74013	−	14.2557i	−0.476692	−	1.18387i
$146$		0			0
$147$	2.27923	−	2.27923i	0.187988	−	0.187988i
$148$		0			0
$149$			0.759549i			0.0622247i	0.999516	+	0.0311123i	$0.00990497\pi$
$149$			0.759549i			0.0622247i	−0.999516	+	0.0311123i	$0.990095\pi$
$150$		0			0
$151$		−	8.03907i		−	0.654210i	−0.944988	−	0.327105i	$-0.893927\pi$
$151$		−	8.03907i		−	0.654210i	0.944988	−	0.327105i	$-0.106073\pi$
$152$		0			0
$153$	21.4362	−	21.4362i	1.73302	−	1.73302i
$154$		0			0
$155$	−4.34974	−	10.8026i	−0.349380	−	0.867688i
$156$		0			0
$157$	11.2712	+	11.2712i	0.899542	+	0.899542i	0.995395	−	0.0958535i	$-0.0305580\pi$
$157$	11.2712	+	11.2712i	0.899542	+	0.899542i	−0.0958535	+	0.995395i	$0.530558\pi$
$158$		0			0
$159$	7.13249			0.565643
$160$		0			0
$161$	−7.31493			−0.576497
$162$		0			0
$163$	8.10511	+	8.10511i	0.634841	+	0.634841i	0.949278	−	0.314437i	$-0.101816\pi$
$163$	8.10511	+	8.10511i	0.634841	+	0.634841i	−0.314437	+	0.949278i	$0.601816\pi$
$164$		0			0
$165$	−10.3999	+	24.4205i	−0.809628	+	1.90113i
$166$		0			0
$167$	−2.12870	+	2.12870i	−0.164724	+	0.164724i	−0.784656	−	0.619932i	$-0.787160\pi$
$167$	−2.12870	+	2.12870i	−0.164724	+	0.164724i	0.619932	+	0.784656i	$0.287160\pi$
$168$		0			0
$169$			11.9853i			0.921943i
$170$		0			0
$171$		−	50.0749i		−	3.82933i
$172$		0			0
$173$	13.0460	−	13.0460i	0.991869	−	0.991869i	−0.00809802	−	0.999967i	$-0.502578\pi$
$173$	13.0460	−	13.0460i	0.991869	−	0.991869i	0.999967	+	0.00809802i	$0.00257771\pi$
$174$		0			0
$175$	−0.0990474	+	4.99902i	−0.00748728	+	0.377890i
$176$		0			0
$177$	22.7521	+	22.7521i	1.71015	+	1.71015i
$178$		0			0
$179$	0.810771			0.0605999			0.0302999	−	0.999541i	$-0.490354\pi$
$179$	0.810771			0.0605999			0.0302999	+	0.999541i	$0.490354\pi$
$180$		0			0
$181$	8.55923			0.636203			0.318101	−	0.948057i	$-0.396955\pi$
$181$	8.55923			0.636203			0.318101	+	0.948057i	$0.396955\pi$
$182$		0			0
$183$	−5.41087	−	5.41087i	−0.399983	−	0.399983i
$184$		0			0
$185$	7.62132	+	3.24567i	0.560331	+	0.238626i
$186$		0			0
$187$	10.6825	−	10.6825i	0.781184	−	0.781184i
$188$		0			0
$189$		−	14.1497i		−	1.02924i
$190$		0			0
$191$		−	3.65130i		−	0.264199i	−0.991236	−	0.132099i	$-0.957828\pi$
$191$		−	3.65130i		−	0.264199i	0.991236	−	0.132099i	$-0.0421718\pi$
$192$		0			0
$193$	17.5323	−	17.5323i	1.26201	−	1.26201i	0.311886	−	0.950120i	$-0.399039\pi$
$193$	17.5323	−	17.5323i	1.26201	−	1.26201i	0.950120	−	0.311886i	$-0.100961\pi$
$194$		0			0
$195$	−6.73500	+	2.71189i	−0.482303	+	0.194202i
$196$		0			0
$197$	−10.5902	−	10.5902i	−0.754520	−	0.754520i	0.220799	−	0.975319i	$-0.429133\pi$
$197$	−10.5902	−	10.5902i	−0.754520	−	0.754520i	−0.975319	+	0.220799i	$0.929133\pi$
$198$		0			0
$199$	−0.686117			−0.0486376			−0.0243188	−	0.999704i	$-0.507742\pi$
$199$	−0.686117			−0.0486376			−0.0243188	+	0.999704i	$0.507742\pi$
$200$		0			0
$201$	17.0559			1.20303
$202$		0			0
$203$	4.85977	+	4.85977i	0.341089	+	0.341089i
$204$		0			0
$205$	7.54155	−	3.03665i	0.526725	−	0.212089i
$206$		0			0
$207$	−38.2232	+	38.2232i	−2.65670	+	2.65670i
$208$		0			0
$209$		−	24.9543i		−	1.72613i
$210$		0			0
$211$			9.42776i			0.649034i	0.945880	+	0.324517i	$0.105202\pi$
$211$			9.42776i			0.649034i	−0.945880	+	0.324517i	$0.894798\pi$
$212$		0			0
$213$	−2.81914	+	2.81914i	−0.193165	+	0.193165i
$214$		0			0
$215$	17.2345	+	7.33960i	1.17538	+	0.500557i
$216$		0			0
$217$	3.68262	+	3.68262i	0.249993	+	0.249993i
$218$		0			0
$219$	19.2677			1.30199
$220$		0			0
$221$	4.13246			0.277979
$222$		0			0
$223$	−13.9869	−	13.9869i	−0.936632	−	0.936632i	0.0614768	−	0.998109i	$-0.480419\pi$
$223$	−13.9869	−	13.9869i	−0.936632	−	0.936632i	−0.998109	+	0.0614768i	$0.980419\pi$
$224$		0			0
$225$	25.6042	+	26.6393i	1.70694	+	1.77595i
$226$		0			0
$227$	−17.7213	+	17.7213i	−1.17621	+	1.17621i	−0.195503	+	0.980703i	$0.562634\pi$
$227$	−17.7213	+	17.7213i	−1.17621	+	1.17621i	−0.980703	+	0.195503i	$0.937366\pi$
$228$		0			0
$229$			17.9700i			1.18749i	0.804653	+	0.593745i	$0.202351\pi$
$229$			17.9700i			1.18749i	−0.804653	+	0.593745i	$0.797649\pi$
$230$		0			0
$231$		−	11.8703i		−	0.781006i
$232$		0			0
$233$	10.9130	−	10.9130i	0.714932	−	0.714932i	−0.252631	−	0.967563i	$-0.581296\pi$
$233$	10.9130	−	10.9130i	0.714932	−	0.714932i	0.967563	+	0.252631i	$0.0812958\pi$
$234$		0			0
$235$	8.81295	−	20.6942i	0.574893	−	1.34994i
$236$		0			0
$237$	14.2204	+	14.2204i	0.923713	+	0.923713i
$238$		0			0
$239$	−11.5532			−0.747316			−0.373658	−	0.927567i	$-0.621897\pi$
$239$	−11.5532			−0.747316			−0.373658	+	0.927567i	$0.621897\pi$
$240$		0			0
$241$	−2.53775			−0.163471			−0.0817355	−	0.996654i	$-0.526046\pi$
$241$	−2.53775			−0.163471			−0.0817355	+	0.996654i	$0.526046\pi$
$242$		0			0
$243$	−23.4082	−	23.4082i	−1.50164	−	1.50164i
$244$		0			0
$245$	−0.835201	−	2.07423i	−0.0533591	−	0.132518i
$246$		0			0
$247$	4.82670	−	4.82670i	0.307116	−	0.307116i
$248$		0			0
$249$		−	21.8098i		−	1.38214i
$250$		0			0
$251$			26.5266i			1.67434i	0.546940	+	0.837172i	$0.315792\pi$
$251$			26.5266i			1.67434i	−0.546940	+	0.837172i	$0.684208\pi$
$252$		0			0
$253$	−19.0481	+	19.0481i	−1.19755	+	1.19755i
$254$		0			0
$255$	−11.0440	−	27.4279i	−0.691602	−	1.71760i
$256$		0			0
$257$	−14.3115	−	14.3115i	−0.892726	−	0.892726i	0.102053	−	0.994779i	$-0.467459\pi$
$257$	−14.3115	−	14.3115i	−0.892726	−	0.892726i	−0.994779	+	0.102053i	$0.967459\pi$
$258$		0			0
$259$	−3.70456			−0.230190
$260$		0			0
$261$	50.7882			3.14371
$262$		0			0
$263$	−17.0790	−	17.0790i	−1.05313	−	1.05313i	−0.998507	−	0.0546278i	$-0.982603\pi$
$263$	−17.0790	−	17.0790i	−1.05313	−	1.05313i	−0.0546278	−	0.998507i	$-0.517397\pi$
$264$		0			0
$265$	1.93867	−	4.55230i	0.119092	−	0.279646i
$266$		0			0
$267$	−25.8965	+	25.8965i	−1.58484	+	1.58484i
$268$		0			0
$269$		−	18.8904i		−	1.15177i	−0.817531	−	0.575885i	$-0.804658\pi$
$269$		−	18.8904i		−	1.15177i	0.817531	−	0.575885i	$-0.195342\pi$
$270$		0			0
$271$			13.3859i			0.813137i	0.913620	+	0.406569i	$0.133275\pi$
$271$			13.3859i			0.813137i	−0.913620	+	0.406569i	$0.866725\pi$
$272$		0			0
$273$	2.29596	−	2.29596i	0.138958	−	0.138958i
$274$		0			0
$275$	12.7596	+	13.2754i	0.769431	+	0.800537i
$276$		0			0
$277$	−16.0468	−	16.0468i	−0.964159	−	0.964159i	0.0352201	−	0.999380i	$-0.488787\pi$
$277$	−16.0468	−	16.0468i	−0.964159	−	0.964159i	−0.999380	+	0.0352201i	$0.988787\pi$
$278$		0			0
$279$	38.4861			2.30410
$280$		0			0
$281$	5.07634			0.302829			0.151415	−	0.988470i	$-0.451617\pi$
$281$	5.07634			0.302829			0.151415	+	0.988470i	$0.451617\pi$
$282$		0			0
$283$	−4.37366	−	4.37366i	−0.259987	−	0.259987i	0.565062	−	0.825049i	$-0.308852\pi$
$283$	−4.37366	−	4.37366i	−0.259987	−	0.259987i	−0.825049	+	0.565062i	$0.808852\pi$
$284$		0			0
$285$	−44.9351	−	19.1363i	−2.66172	−	1.13354i
$286$		0			0
$287$	−2.57092	+	2.57092i	−0.151757	+	0.151757i
$288$		0			0
$289$		−	0.170802i		−	0.0100472i
$290$		0			0
$291$		−	52.1218i		−	3.05543i
$292$		0			0
$293$	−13.5546	+	13.5546i	−0.791871	+	0.791871i	−0.981798	−	0.189928i	$-0.939175\pi$
$293$	−13.5546	+	13.5546i	−0.791871	+	0.791871i	0.189928	+	0.981798i	$0.439175\pi$
$294$		0			0
$295$	20.7058	−	8.33729i	1.20554	−	0.485416i
$296$		0			0
$297$	−36.8459	−	36.8459i	−2.13801	−	2.13801i
$298$		0			0
$299$	−7.36864			−0.426139
$300$		0			0
$301$	−8.37733			−0.482861
$302$		0			0
$303$	−10.9089	−	10.9089i	−0.626702	−	0.626702i
$304$		0			0
$305$	−4.92421	+	1.98276i	−0.281959	+	0.113533i
$306$		0			0
$307$	9.29603	−	9.29603i	0.530553	−	0.530553i	−0.390184	−	0.920737i	$-0.627589\pi$
$307$	9.29603	−	9.29603i	0.530553	−	0.530553i	0.920737	+	0.390184i	$0.127589\pi$
$308$		0			0
$309$		−	51.8775i		−	2.95121i
$310$		0			0
$311$			7.99492i			0.453350i	0.973970	+	0.226675i	$0.0727856\pi$
$311$			7.99492i			0.453350i	−0.973970	+	0.226675i	$0.927214\pi$
$312$		0			0
$313$	−3.25463	+	3.25463i	−0.183963	+	0.183963i	−0.793080	−	0.609117i	$-0.791524\pi$
$313$	−3.25463	+	3.25463i	−0.183963	+	0.183963i	0.609117	+	0.793080i	$0.291524\pi$
$314$		0			0
$315$	−15.2029	−	6.47439i	−0.856584	−	0.364791i
$316$		0			0
$317$	−6.39843	−	6.39843i	−0.359372	−	0.359372i	0.504210	−	0.863581i	$-0.331784\pi$
$317$	−6.39843	−	6.39843i	−0.359372	−	0.359372i	−0.863581	+	0.504210i	$0.831784\pi$
$318$		0			0
$319$	25.3098			1.41707
$320$		0			0
$321$	−10.9283			−0.609960
$322$		0			0
$323$	19.6565	+	19.6565i	1.09371	+	1.09371i
$324$		0			0
$325$	−0.0997746	+	5.03572i	−0.00553450	+	0.279331i
$326$		0			0
$327$	9.22421	−	9.22421i	0.510100	−	0.510100i
$328$		0			0
$329$			10.0590i			0.554570i
$330$		0			0
$331$			27.9861i			1.53826i	0.639094	+	0.769129i	$0.279309\pi$
$331$			27.9861i			1.53826i	−0.639094	+	0.769129i	$0.720691\pi$
$332$		0			0
$333$	−19.3577	+	19.3577i	−1.06080	+	1.06080i
$334$		0			0
$335$	4.63595	−	10.8859i	0.253289	−	0.594761i
$336$		0			0
$337$	19.1004	+	19.1004i	1.04047	+	1.04047i	0.999146	+	0.0413193i	$0.0131561\pi$
$337$	19.1004	+	19.1004i	1.04047	+	1.04047i	0.0413193	+	0.999146i	$0.486844\pi$
$338$		0			0
$339$	−38.1767			−2.07348
$340$		0			0
$341$	19.1792			1.03861
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		0			0
$345$	19.6927	+	48.9070i	1.06022	+	2.63306i
$346$		0			0
$347$	4.12958	−	4.12958i	0.221688	−	0.221688i	−0.587521	−	0.809209i	$-0.699896\pi$
$347$	4.12958	−	4.12958i	0.221688	−	0.221688i	0.809209	+	0.587521i	$0.199896\pi$
$348$		0			0
$349$			7.72536i			0.413529i	0.978391	+	0.206765i	$0.0662934\pi$
$349$			7.72536i			0.413529i	−0.978391	+	0.206765i	$0.933707\pi$
$350$		0			0
$351$		−	14.2536i		−	0.760799i
$352$		0			0
$353$	−11.8654	+	11.8654i	−0.631531	+	0.631531i	−0.948452	−	0.316921i	$-0.897351\pi$
$353$	−11.8654	+	11.8654i	−0.631531	+	0.631531i	0.316921	+	0.948452i	$0.397351\pi$
$354$		0			0
$355$	1.03305	+	2.56558i	0.0548285	+	0.136167i
$356$		0			0
$357$	9.35018	+	9.35018i	0.494864	+	0.494864i
$358$		0			0
$359$	−30.5278			−1.61120			−0.805599	−	0.592462i	$-0.798156\pi$
$359$	−30.5278			−1.61120			−0.805599	+	0.592462i	$0.798156\pi$
$360$		0			0
$361$	26.9174			1.41670
$362$		0			0
$363$	−5.83872	−	5.83872i	−0.306454	−	0.306454i
$364$		0			0
$365$	5.23712	−	12.2976i	0.274123	−	0.643684i
$366$		0			0
$367$	21.2481	−	21.2481i	1.10914	−	1.10914i	0.115876	−	0.993264i	$-0.463033\pi$
$367$	21.2481	−	21.2481i	1.10914	−	1.10914i	0.993264	−	0.115876i	$-0.0369675\pi$
$368$		0			0
$369$			26.8680i			1.39869i
$370$		0			0
$371$			2.21278i			0.114882i
$372$		0			0
$373$	0.640653	−	0.640653i	0.0331717	−	0.0331717i	−0.690326	−	0.723498i	$-0.742533\pi$
$373$	0.640653	−	0.640653i	0.0331717	−	0.0331717i	0.723498	+	0.690326i	$0.242533\pi$
$374$		0			0
$375$	33.6896	−	12.7957i	1.73973	−	0.660769i
$376$		0			0
$377$	4.89545	+	4.89545i	0.252128	+	0.252128i
$378$		0			0
$379$	12.4232			0.638135			0.319068	−	0.947732i	$-0.396630\pi$
$379$	12.4232			0.638135			0.319068	+	0.947732i	$0.396630\pi$
$380$		0			0
$381$	−36.6193			−1.87606
$382$		0			0
$383$	−22.3365	−	22.3365i	−1.14134	−	1.14134i	−0.988205	−	0.153136i	$-0.951063\pi$
$383$	−22.3365	−	22.3365i	−1.14134	−	1.14134i	−0.153136	−	0.988205i	$-0.548937\pi$
$384$		0			0
$385$	−7.57619	−	3.22644i	−0.386118	−	0.164435i
$386$		0			0
$387$	−43.7746	+	43.7746i	−2.22519	+	2.22519i
$388$		0			0
$389$		−	10.0840i		−	0.511279i	−0.966772	−	0.255640i	$-0.917714\pi$
$389$		−	10.0840i		−	0.511279i	0.966772	−	0.255640i	$-0.0822861\pi$
$390$		0			0
$391$		−	30.0083i		−	1.51759i
$392$		0			0
$393$	−9.52712	+	9.52712i	−0.480580	+	0.480580i
$394$		0			0
$395$	12.9414	−	5.21092i	0.651151	−	0.262190i
$396$		0			0
$397$	12.2703	+	12.2703i	0.615830	+	0.615830i	0.944459	−	0.328629i	$-0.106587\pi$
$397$	12.2703	+	12.2703i	0.615830	+	0.615830i	−0.328629	+	0.944459i	$0.606587\pi$
$398$		0			0
$399$	21.8420			1.09347
$400$		0			0
$401$	−20.6196			−1.02970			−0.514848	−	0.857282i	$-0.672152\pi$
$401$	−20.6196			−1.02970			−0.514848	+	0.857282i	$0.672152\pi$
$402$		0			0
$403$	3.70966	+	3.70966i	0.184791	+	0.184791i
$404$		0			0
$405$	−48.6191	+	19.5768i	−2.41590	+	0.972778i
$406$		0			0
$407$	−9.64671	+	9.64671i	−0.478170	+	0.478170i
$408$		0			0
$409$		−	22.3852i		−	1.10688i	−0.832890	−	0.553439i	$-0.813315\pi$
$409$		−	22.3852i		−	1.10688i	0.832890	−	0.553439i	$-0.186685\pi$
$410$		0			0
$411$		−	35.0103i		−	1.72693i
$412$		0			0
$413$	−7.05860	+	7.05860i	−0.347331	+	0.347331i
$414$		0			0
$415$	−13.9201	−	5.92810i	−0.683310	−	0.290999i
$416$		0			0
$417$	2.80556	+	2.80556i	0.137389	+	0.137389i
$418$		0			0
$419$	−1.08794			−0.0531491			−0.0265746	−	0.999647i	$-0.508460\pi$
$419$	−1.08794			−0.0531491			−0.0265746	+	0.999647i	$0.508460\pi$
$420$		0			0
$421$	19.6617			0.958252			0.479126	−	0.877746i	$-0.340954\pi$
$421$	19.6617			0.958252			0.479126	+	0.877746i	$0.340954\pi$
$422$		0			0
$423$	52.5619	+	52.5619i	2.55565	+	2.55565i
$424$		0			0
$425$	−20.5077	−	0.406326i	−0.994768	−	0.0197097i
$426$		0			0
$427$	1.67866	−	1.67866i	0.0812363	−	0.0812363i
$428$		0			0
$429$		−	11.9574i		−	0.577309i
$430$		0			0
$431$		−	15.1755i		−	0.730978i	−0.930816	−	0.365489i	$-0.880902\pi$
$431$		−	15.1755i		−	0.730978i	0.930816	−	0.365489i	$-0.119098\pi$
$432$		0			0
$433$	18.4880	−	18.4880i	0.888474	−	0.888474i	−0.105902	−	0.994377i	$-0.533773\pi$
$433$	18.4880	−	18.4880i	0.888474	−	0.888474i	0.994377	+	0.105902i	$0.0337731\pi$
$434$		0			0
$435$	19.4089	−	45.5751i	0.930586	−	2.18516i
$436$		0			0
$437$	−35.0497	−	35.0497i	−1.67665	−	1.67665i
$438$		0			0
$439$	−2.24408			−0.107104			−0.0535521	−	0.998565i	$-0.517054\pi$
$439$	−2.24408			−0.107104			−0.0535521	+	0.998565i	$0.517054\pi$
$440$		0			0
$441$	7.38979			0.351895
$442$		0			0
$443$	−4.47050	−	4.47050i	−0.212400	−	0.212400i	0.592886	−	0.805286i	$-0.297988\pi$
$443$	−4.47050	−	4.47050i	−0.212400	−	0.212400i	−0.805286	+	0.592886i	$0.797988\pi$
$444$		0			0
$445$	9.48951	+	23.5673i	0.449846	+	1.11720i
$446$		0			0
$447$	−1.73119	+	1.73119i	−0.0818824	+	0.0818824i
$448$		0			0
$449$		−	34.7341i		−	1.63920i	−0.572934	−	0.819602i	$-0.694195\pi$
$449$		−	34.7341i		−	1.63920i	0.572934	−	0.819602i	$-0.305805\pi$
$450$		0			0
$451$			13.3894i			0.630482i
$452$		0			0
$453$	18.3229	−	18.3229i	0.860884	−	0.860884i
$454$		0			0
$455$	−0.841333	−	2.08946i	−0.0394423	−	0.0979554i
$456$		0			0
$457$	0.136442	+	0.136442i	0.00638250	+	0.00638250i	0.710291	−	0.703908i	$-0.248563\pi$
$457$	0.136442	+	0.136442i	0.00638250	+	0.00638250i	−0.703908	+	0.710291i	$0.748563\pi$
$458$		0			0
$459$	58.0468			2.70939
$460$		0			0
$461$	18.4678			0.860130			0.430065	−	0.902798i	$-0.358491\pi$
$461$	18.4678			0.860130			0.430065	+	0.902798i	$0.358491\pi$
$462$		0			0
$463$	4.19082	+	4.19082i	0.194764	+	0.194764i	0.797751	−	0.602987i	$-0.206023\pi$
$463$	4.19082	+	4.19082i	0.194764	+	0.194764i	−0.602987	+	0.797751i	$0.706023\pi$
$464$		0			0
$465$	14.7076	−	34.5358i	0.682050	−	1.60156i
$466$		0			0
$467$	−1.78605	+	1.78605i	−0.0826487	+	0.0826487i	−0.747223	−	0.664574i	$-0.768613\pi$
$467$	−1.78605	+	1.78605i	−0.0826487	+	0.0826487i	0.664574	+	0.747223i	$0.268613\pi$
$468$		0			0
$469$			5.29141i			0.244335i
$470$		0			0
$471$			51.3795i			2.36744i
$472$		0			0
$473$	−21.8146	+	21.8146i	−1.00304	+	1.00304i
$474$		0			0
$475$	−24.4275	+	23.4783i	−1.12081	+	1.07726i
$476$		0			0
$477$	11.5626	+	11.5626i	0.529414	+	0.529414i
$478$		0			0
$479$	−2.85552			−0.130472			−0.0652360	−	0.997870i	$-0.520780\pi$
$479$	−2.85552			−0.130472			−0.0652360	+	0.997870i	$0.520780\pi$
$480$		0			0
$481$	−3.73176			−0.170154
$482$		0			0
$483$	−16.6724	−	16.6724i	−0.758621	−	0.758621i
$484$		0			0
$485$	−33.2667	−	14.1672i	−1.51056	−	0.643298i
$486$		0			0
$487$	−6.08351	+	6.08351i	−0.275670	+	0.275670i	−0.831378	−	0.555708i	$-0.812447\pi$
$487$	−6.08351	+	6.08351i	−0.275670	+	0.275670i	0.555708	+	0.831378i	$0.312447\pi$
$488$		0			0
$489$			36.9468i			1.67079i
$490$		0			0
$491$			27.9165i			1.25985i	0.776654	+	0.629927i	$0.216915\pi$
$491$			27.9165i			1.25985i	−0.776654	+	0.629927i	$0.783085\pi$
$492$		0			0
$493$	−19.9364	+	19.9364i	−0.897892	+	0.897892i
$494$		0			0
$495$	−56.4477	+	22.7290i	−2.53714	+	1.02159i
$496$		0			0
$497$	−0.874609	−	0.874609i	−0.0392316	−	0.0392316i
$498$		0			0
$499$	−4.56538			−0.204375			−0.102187	−	0.994765i	$-0.532584\pi$
$499$	−4.56538			−0.204375			−0.102187	+	0.994765i	$0.532584\pi$
$500$		0			0
$501$	−9.70361			−0.433525
$502$		0			0
$503$	−9.55537	−	9.55537i	−0.426053	−	0.426053i	0.461229	−	0.887281i	$-0.347409\pi$
$503$	−9.55537	−	9.55537i	−0.426053	−	0.426053i	−0.887281	+	0.461229i	$0.847409\pi$
$504$		0			0
$505$	−9.92777	+	3.99747i	−0.441780	+	0.177885i
$506$		0			0
$507$	−27.3172	+	27.3172i	−1.21320	+	1.21320i
$508$		0			0
$509$		−	6.60247i		−	0.292649i	−0.989237	−	0.146325i	$-0.953256\pi$
$509$		−	6.60247i		−	0.292649i	0.989237	−	0.146325i	$-0.0467444\pi$
$510$		0			0
$511$			5.97758i			0.264433i
$512$		0			0
$513$	67.7985	−	67.7985i	2.99338	−	2.99338i
$514$		0			0
$515$	−33.1108	−	14.1008i	−1.45903	−	0.621354i
$516$		0			0
$517$	26.1937	+	26.1937i	1.15200	+	1.15200i
$518$		0			0
$519$	59.4697			2.61043
$520$		0			0
$521$	30.3514			1.32972			0.664859	−	0.746969i	$-0.268491\pi$
$521$	30.3514			1.32972			0.664859	+	0.746969i	$0.268491\pi$
$522$		0			0
$523$	−7.04232	−	7.04232i	−0.307939	−	0.307939i	0.536171	−	0.844110i	$-0.319870\pi$
$523$	−7.04232	−	7.04232i	−0.307939	−	0.307939i	−0.844110	+	0.536171i	$0.819870\pi$
$524$		0			0
$525$	−11.6197	+	11.1682i	−0.507124	+	0.487419i
$526$		0			0
$527$	−15.1074	+	15.1074i	−0.658087	+	0.658087i
$528$		0			0
$529$			30.5082i			1.32644i
$530$		0			0
$531$			73.7676i			3.20124i
$532$		0			0
$533$	−2.58979	+	2.58979i	−0.112176	+	0.112176i
$534$		0			0
$535$	−2.97042	+	6.97499i	−0.128422	+	0.301555i
$536$		0			0
$537$	1.84794	+	1.84794i	0.0797443	+	0.0797443i
$538$		0			0
$539$	3.68262			0.158622
$540$		0			0
$541$	8.36610			0.359687			0.179843	−	0.983695i	$-0.442441\pi$
$541$	8.36610			0.359687			0.179843	+	0.983695i	$0.442441\pi$
$542$		0			0
$543$	19.5085	+	19.5085i	0.837189	+	0.837189i
$544$		0			0
$545$	−3.38012	−	8.39456i	−0.144788	−	0.359584i
$546$		0			0
$547$	8.80941	−	8.80941i	0.376663	−	0.376663i	−0.493234	−	0.869897i	$-0.664185\pi$
$547$	8.80941	−	8.80941i	0.376663	−	0.376663i	0.869897	+	0.493234i	$0.164185\pi$
$548$		0			0
$549$		−	17.5433i		−	0.748729i
$550$		0			0
$551$			46.5714i			1.98401i
$552$		0			0
$553$	−4.41172	+	4.41172i	−0.187605	+	0.187605i
$554$		0			0
$555$	9.97313	+	24.7684i	0.423336	+	1.05136i
$556$		0			0
$557$	22.9600	+	22.9600i	0.972845	+	0.972845i	0.999641	−	0.0267960i	$-0.00853044\pi$
$557$	22.9600	+	22.9600i	0.972845	+	0.972845i	−0.0267960	+	0.999641i	$0.508530\pi$
$558$		0			0
$559$	−8.43883			−0.356925
$560$		0			0
$561$	48.6959			2.05594
$562$		0			0
$563$	−22.2509	−	22.2509i	−0.937765	−	0.937765i	0.0604087	−	0.998174i	$-0.480760\pi$
$563$	−22.2509	−	22.2509i	−0.937765	−	0.937765i	−0.998174	+	0.0604087i	$0.980760\pi$
$564$		0			0
$565$	−10.3768	+	24.3663i	−0.436554	+	1.02510i
$566$		0			0
$567$	16.5743	−	16.5743i	0.696055	−	0.696055i
$568$		0			0
$569$			37.0951i			1.55511i	0.628817	+	0.777553i	$0.283539\pi$
$569$			37.0951i			1.55511i	−0.628817	+	0.777553i	$0.716461\pi$
$570$		0			0
$571$			35.4236i			1.48243i	0.671267	+	0.741216i	$0.265751\pi$
$571$			35.4236i			1.48243i	−0.671267	+	0.741216i	$0.734249\pi$
$572$		0			0
$573$	8.32215	−	8.32215i	0.347663	−	0.347663i
$574$		0			0
$575$	36.5675	+	0.724525i	1.52497	+	0.0302148i
$576$		0			0
$577$	−6.41565	−	6.41565i	−0.267087	−	0.267087i	0.560838	−	0.827925i	$-0.310479\pi$
$577$	−6.41565	−	6.41565i	−0.267087	−	0.267087i	−0.827925	+	0.560838i	$0.810479\pi$
$578$		0			0
$579$	79.9205			3.32138
$580$		0			0
$581$	6.76625			0.280712
$582$		0			0
$583$	5.76209	+	5.76209i	0.238641	+	0.238641i
$584$		0			0
$585$	−15.3145	−	6.52192i	−0.633176	−	0.269648i
$586$		0			0
$587$	11.2565	−	11.2565i	0.464606	−	0.464606i	−0.435555	−	0.900162i	$-0.643448\pi$
$587$	11.2565	−	11.2565i	0.464606	−	0.464606i	0.900162	+	0.435555i	$0.143448\pi$
$588$		0			0
$589$			35.2907i			1.45413i
$590$		0			0
$591$		−	48.2750i		−	1.98577i
$592$		0			0
$593$	−15.1597	+	15.1597i	−0.622532	+	0.622532i	−0.946178	−	0.323646i	$-0.895091\pi$
$593$	−15.1597	+	15.1597i	−0.622532	+	0.622532i	0.323646	+	0.946178i	$0.395091\pi$
$594$		0			0
$595$	8.50921	−	3.42628i	0.348843	−	0.140464i
$596$		0			0
$597$	−1.56382	−	1.56382i	−0.0640029	−	0.0640029i
$598$		0			0
$599$	−46.0807			−1.88281			−0.941403	−	0.337285i	$-0.890492\pi$
$599$	−46.0807			−1.88281			−0.941403	+	0.337285i	$0.890492\pi$
$600$		0			0
$601$	10.3744			0.423180			0.211590	−	0.977358i	$-0.432136\pi$
$601$	10.3744			0.423180			0.211590	+	0.977358i	$0.432136\pi$
$602$		0			0
$603$	27.6496	+	27.6496i	1.12598	+	1.12598i
$604$		0			0
$605$	−5.31358	+	2.13954i	−0.216028	+	0.0869848i
$606$		0			0
$607$	−6.71022	+	6.71022i	−0.272360	+	0.272360i	−0.830049	−	0.557690i	$-0.811688\pi$
$607$	−6.71022	+	6.71022i	−0.272360	+	0.272360i	0.557690	+	0.830049i	$0.311688\pi$
$608$		0			0
$609$			22.1531i			0.897688i
$610$		0			0
$611$			10.1328i			0.409931i
$612$		0			0
$613$	9.74236	−	9.74236i	0.393490	−	0.393490i	−0.482439	−	0.875929i	$-0.660249\pi$
$613$	9.74236	−	9.74236i	0.393490	−	0.393490i	0.875929	+	0.482439i	$0.160249\pi$
$614$		0			0
$615$	24.1102	+	10.2677i	0.972216	+	0.414034i
$616$		0			0
$617$	1.08042	+	1.08042i	0.0434961	+	0.0434961i	0.728520	−	0.685024i	$-0.240208\pi$
$617$	1.08042	+	1.08042i	0.0434961	+	0.0434961i	−0.685024	+	0.728520i	$0.740208\pi$
$618$		0			0
$619$	−11.1417			−0.447823			−0.223912	−	0.974609i	$-0.571883\pi$
$619$	−11.1417			−0.447823			−0.223912	+	0.974609i	$0.571883\pi$
$620$		0			0
$621$	−103.504			−4.15347
$622$		0			0
$623$	−8.03410	−	8.03410i	−0.321880	−	0.321880i
$624$		0			0
$625$	0.990280	−	24.9804i	0.0396112	−	0.999215i
$626$		0			0
$627$	56.8767	−	56.8767i	2.27143	−	2.27143i
$628$		0			0
$629$		−	15.1974i		−	0.605959i
$630$		0			0
$631$		−	31.0072i		−	1.23438i	−0.786815	−	0.617189i	$-0.788271\pi$
$631$		−	31.0072i		−	1.23438i	0.786815	−	0.617189i	$-0.211729\pi$
$632$		0			0
$633$	−21.4880	+	21.4880i	−0.854073	+	0.854073i
$634$		0			0
$635$	−9.95345	+	23.3722i	−0.394990	+	0.927498i
$636$		0			0
$637$	0.712298	+	0.712298i	0.0282223	+	0.0282223i
$638$		0			0
$639$	−9.14031			−0.361585
$640$		0			0
$641$	41.7539			1.64918			0.824590	−	0.565731i	$-0.191406\pi$
$641$	41.7539			1.64918			0.824590	+	0.565731i	$0.191406\pi$
$642$		0			0
$643$	−28.9640	−	28.9640i	−1.14223	−	1.14223i	−0.988042	−	0.154187i	$-0.950724\pi$
$643$	−28.9640	−	28.9640i	−1.14223	−	1.14223i	−0.154187	−	0.988042i	$-0.549276\pi$
$644$		0			0
$645$	22.5528	+	56.0101i	0.888015	+	2.20539i
$646$		0			0
$647$	−30.2277	+	30.2277i	−1.18837	+	1.18837i	−0.210854	+	0.977518i	$0.567625\pi$
$647$	−30.2277	+	30.2277i	−1.18837	+	1.18837i	−0.977518	+	0.210854i	$0.932375\pi$
$648$		0			0
$649$			36.7613i			1.44301i
$650$		0			0
$651$			16.7871i			0.657938i
$652$		0			0
$653$	−31.0360	+	31.0360i	−1.21453	+	1.21453i	−0.245015	+	0.969519i	$0.578793\pi$
$653$	−31.0360	+	31.0360i	−1.21453	+	1.21453i	−0.969519	+	0.245015i	$0.921207\pi$
$654$		0			0
$655$	3.49112	+	8.67023i	0.136409	+	0.338774i
$656$		0			0
$657$	31.2351	+	31.2351i	1.21860	+	1.21860i
$658$		0			0
$659$	−22.4635			−0.875054			−0.437527	−	0.899205i	$-0.644145\pi$
$659$	−22.4635			−0.875054			−0.437527	+	0.899205i	$0.644145\pi$
$660$		0			0
$661$	−22.8870			−0.890200			−0.445100	−	0.895481i	$-0.646832\pi$
$661$	−22.8870			−0.890200			−0.445100	+	0.895481i	$0.646832\pi$
$662$		0			0
$663$	9.41883	+	9.41883i	0.365797	+	0.365797i
$664$		0			0
$665$	5.93684	−	13.9406i	0.230221	−	0.540594i
$666$		0			0
$667$	35.5489	−	35.5489i	1.37646	−	1.37646i
$668$		0			0
$669$		−	63.7587i		−	2.46505i
$670$		0			0
$671$		−	8.74251i		−	0.337501i
$672$		0			0
$673$	−31.4642	+	31.4642i	−1.21285	+	1.21285i	−0.242771	+	0.970084i	$0.578057\pi$
$673$	−31.4642	+	31.4642i	−1.21285	+	1.21285i	−0.970084	+	0.242771i	$0.921943\pi$
$674$		0			0
$675$	−1.40149	+	70.7345i	−0.0539434	+	2.72257i
$676$		0			0
$677$	−2.66330	−	2.66330i	−0.102359	−	0.102359i	0.654073	−	0.756432i	$-0.273059\pi$
$677$	−2.66330	−	2.66330i	−0.102359	−	0.102359i	−0.756432	+	0.654073i	$0.773059\pi$
$678$		0			0
$679$	16.1702			0.620556
$680$		0			0
$681$	−80.7820			−3.09557
$682$		0			0
$683$	−5.39335	−	5.39335i	−0.206371	−	0.206371i	0.596352	−	0.802723i	$-0.296616\pi$
$683$	−5.39335	−	5.39335i	−0.206371	−	0.206371i	−0.802723	+	0.596352i	$0.796616\pi$
$684$		0			0
$685$	−22.3453	−	9.51611i	−0.853769	−	0.363592i
$686$		0			0
$687$	−40.9578	+	40.9578i	−1.56264	+	1.56264i
$688$		0			0
$689$			2.22902i			0.0849190i
$690$		0			0
$691$			1.99731i			0.0759811i	0.999278	+	0.0379906i	$0.0120957\pi$
$691$			1.99731i			0.0759811i	−0.999278	+	0.0379906i	$0.987904\pi$
$692$		0			0
$693$	19.2431	−	19.2431i	0.730983	−	0.730983i
$694$		0			0
$695$	2.55322	−	1.02807i	0.0968491	−	0.0389968i
$696$		0			0
$697$	−10.5468	−	10.5468i	−0.399488	−	0.399488i
$698$		0			0
$699$	49.7463			1.88158
$700$		0			0
$701$	−26.4607			−0.999408			−0.499704	−	0.866196i	$-0.666558\pi$
$701$	−26.4607			−0.999408			−0.499704	+	0.866196i	$0.666558\pi$
$702$		0			0
$703$	−17.7505	−	17.7505i	−0.669473	−	0.669473i
$704$		0			0
$705$	67.2535	−	27.0800i	2.53291	−	1.01989i
$706$		0			0
$707$	3.38438	−	3.38438i	0.127283	−	0.127283i
$708$		0			0
$709$			44.4017i			1.66754i	0.552112	+	0.833770i	$0.313822\pi$
$709$			44.4017i			1.66754i	−0.552112	+	0.833770i	$0.686178\pi$
$710$		0			0
$711$			46.1057i			1.72910i
$712$		0			0
$713$	26.9381	−	26.9381i	1.00884	−	1.00884i
$714$		0			0
$715$	−7.63181	−	3.25013i	−0.285413	−	0.121548i
$716$		0			0
$717$	−26.3325	−	26.3325i	−0.983404	−	0.983404i
$718$		0			0
$719$	−11.5712			−0.431534			−0.215767	−	0.976445i	$-0.569225\pi$
$719$	−11.5712			−0.431534			−0.215767	+	0.976445i	$0.569225\pi$
$720$		0			0
$721$	16.0944			0.599388
$722$		0			0
$723$	−5.78412	−	5.78412i	−0.215114	−	0.215114i
$724$		0			0
$725$	−23.8127	−	24.7754i	−0.884383	−	0.920137i
$726$		0			0
$727$	−2.66972	+	2.66972i	−0.0990145	+	0.0990145i	−0.754879	−	0.655864i	$-0.772304\pi$
$727$	−2.66972	+	2.66972i	−0.0990145	+	0.0990145i	0.655864	+	0.754879i	$0.272304\pi$
$728$		0			0
$729$		−	36.3867i		−	1.34766i
$730$		0			0
$731$		−	34.3667i		−	1.27110i
$732$		0			0
$733$	16.0058	−	16.0058i	0.591187	−	0.591187i	−0.346765	−	0.937952i	$-0.612720\pi$
$733$	16.0058	−	16.0058i	0.591187	−	0.591187i	0.937952	+	0.346765i	$0.112720\pi$
$734$		0			0
$735$	2.82404	−	6.63127i	0.104166	−	0.244598i
$736$		0			0
$737$	13.7789	+	13.7789i	0.507551	+	0.507551i
$738$		0			0
$739$	6.62288			0.243626			0.121813	−	0.992553i	$-0.461129\pi$
$739$	6.62288			0.243626			0.121813	+	0.992553i	$0.461129\pi$
$740$		0			0
$741$	22.0023			0.808276
$742$		0			0
$743$	17.5061	+	17.5061i	0.642235	+	0.642235i	0.951104	−	0.308869i	$-0.0999506\pi$
$743$	17.5061	+	17.5061i	0.642235	+	0.642235i	−0.308869	+	0.951104i	$0.599951\pi$
$744$		0			0
$745$	0.634376	+	1.57548i	0.0232418	+	0.0577212i
$746$		0			0
$747$	35.3562	−	35.3562i	1.29361	−	1.29361i
$748$		0			0
$749$		−	3.39040i		−	0.123882i
$750$		0			0
$751$			36.6569i			1.33763i	0.743430	+	0.668814i	$0.233198\pi$
$751$			36.6569i			1.33763i	−0.743430	+	0.668814i	$0.766802\pi$
$752$		0			0
$753$	−60.4602	+	60.4602i	−2.20329	+	2.20329i
$754$		0			0
$755$	−6.71424	−	16.6749i	−0.244356	−	0.606861i
$756$		0			0
$757$	−12.5751	−	12.5751i	−0.457051	−	0.457051i	0.440635	−	0.897686i	$-0.354753\pi$
$757$	−12.5751	−	12.5751i	−0.457051	−	0.457051i	−0.897686	+	0.440635i	$0.854753\pi$
$758$		0			0
$759$	−86.8302			−3.15174
$760$		0			0
$761$	−53.5135			−1.93986			−0.969932	−	0.243377i	$-0.921745\pi$
$761$	−53.5135			−1.93986			−0.969932	+	0.243377i	$0.921745\pi$
$762$		0			0
$763$	2.86171	+	2.86171i	0.103601	+	0.103601i
$764$		0			0
$765$	26.5602	−	62.3673i	0.960285	−	2.25490i
$766$		0			0
$767$	−7.11042	+	7.11042i	−0.256743	+	0.256743i
$768$		0			0
$769$			17.6971i			0.638176i	0.947725	+	0.319088i	$0.103376\pi$
$769$			17.6971i			0.638176i	−0.947725	+	0.319088i	$0.896624\pi$
$770$		0			0
$771$		−	65.2383i		−	2.34950i
$772$		0			0
$773$	31.3291	−	31.3291i	1.12683	−	1.12683i	0.136140	−	0.990690i	$-0.456530\pi$
$773$	31.3291	−	31.3291i	1.12683	−	1.12683i	0.990690	−	0.136140i	$-0.0434697\pi$
$774$		0			0
$775$	−18.0447	−	18.7743i	−0.648186	−	0.674391i
$776$		0			0
$777$	−8.44355	−	8.44355i	−0.302911	−	0.302911i
$778$		0			0
$779$	−24.6372			−0.882721
$780$		0			0
$781$	−4.55498			−0.162990
$782$		0			0
$783$	68.7642	+	68.7642i	2.45743	+	2.45743i
$784$		0			0
$785$	32.7929	+	13.9654i	1.17043	+	0.498446i
$786$		0			0
$787$	−10.6190	+	10.6190i	−0.378527	+	0.378527i	−0.870571	−	0.492044i	$-0.836250\pi$
$787$	−10.6190	+	10.6190i	−0.378527	+	0.378527i	0.492044	+	0.870571i	$0.336250\pi$
$788$		0			0
$789$		−	77.8538i		−	2.77167i
$790$		0			0
$791$		−	11.8439i		−	0.421121i
$792$		0			0
$793$	1.69099	−	1.69099i	0.0600488	−	0.0600488i
$794$		0			0
$795$	14.7944	−	5.95707i	0.524705	−	0.211275i
$796$		0			0
$797$	−0.106374	−	0.106374i	−0.00376796	−	0.00376796i	0.705220	−	0.708988i	$-0.250848\pi$
$797$	−0.106374	−	0.106374i	−0.00376796	−	0.00376796i	−0.708988	+	0.705220i	$0.750848\pi$
$798$		0			0
$799$	−41.2654			−1.45986
$800$		0			0
$801$	−83.9623			−2.96666
$802$		0			0
$803$	15.5657	+	15.5657i	0.549300	+	0.549300i
$804$		0			0
$805$	−15.1729	+	6.10944i	−0.534773	+	0.215330i
$806$		0			0
$807$	43.0556	−	43.0556i	1.51563	−	1.51563i
$808$		0			0
$809$			30.0550i			1.05668i	0.849033	+	0.528339i	$0.177185\pi$
$809$			30.0550i			1.05668i	−0.849033	+	0.528339i	$0.822815\pi$
$810$		0			0
$811$		−	46.8320i		−	1.64449i	−0.569131	−	0.822247i	$-0.692720\pi$
$811$		−	46.8320i		−	1.64449i	0.569131	−	0.822247i	$-0.307280\pi$
$812$		0			0
$813$	−30.5096	+	30.5096i	−1.07002	+	1.07002i
$814$		0			0
$815$	23.5813	+	10.0425i	0.826016	+	0.351773i
$816$		0			0
$817$	−40.1402	−	40.1402i	−1.40433	−	1.40433i
$818$		0			0
$819$	7.44404			0.260116
$820$		0			0
$821$	5.48543			0.191443			0.0957214	−	0.995408i	$-0.469484\pi$
$821$	5.48543			0.191443			0.0957214	+	0.995408i	$0.469484\pi$
$822$		0			0
$823$	−13.8581	−	13.8581i	−0.483063	−	0.483063i	0.423046	−	0.906108i	$-0.360961\pi$
$823$	−13.8581	−	13.8581i	−0.483063	−	0.483063i	−0.906108	+	0.423046i	$0.860961\pi$
$824$		0			0
$825$	−1.17572	+	59.3397i	−0.0409333	+	2.06594i
$826$		0			0
$827$	−12.9702	+	12.9702i	−0.451019	+	0.451019i	−0.895693	−	0.444673i	$-0.853320\pi$
$827$	−12.9702	+	12.9702i	−0.451019	+	0.451019i	0.444673	+	0.895693i	$0.353320\pi$
$828$		0			0
$829$			18.8729i			0.655484i	0.944767	+	0.327742i	$0.106288\pi$
$829$			18.8729i			0.655484i	−0.944767	+	0.327742i	$0.893712\pi$
$830$		0			0
$831$		−	73.1488i		−	2.53750i
$832$		0			0
$833$	−2.90079	+	2.90079i	−0.100507	+	0.100507i
$834$		0			0
$835$	−2.63753	+	6.19332i	−0.0912754	+	0.214329i
$836$		0			0
$837$	52.1079	+	52.1079i	1.80111	+	1.80111i
$838$		0			0
$839$	−1.87606			−0.0647687			−0.0323844	−	0.999475i	$-0.510310\pi$
$839$	−1.87606			−0.0647687			−0.0323844	+	0.999475i	$0.510310\pi$
$840$		0			0
$841$	−18.2348			−0.628785
$842$		0			0
$843$	11.5702	+	11.5702i	0.398497	+	0.398497i
$844$		0			0
$845$	10.0101	+	24.8602i	0.344358	+	0.855217i
$846$		0			0
$847$	1.81140	−	1.81140i	0.0622405	−	0.0622405i
$848$		0			0
$849$		−	19.9372i		−	0.684242i
$850$		0			0
$851$			27.0986i			0.928929i
$852$		0			0
$853$	15.7976	−	15.7976i	0.540899	−	0.540899i	−0.382893	−	0.923793i	$-0.625072\pi$
$853$	15.7976	−	15.7976i	0.540899	−	0.540899i	0.923793	+	0.382893i	$0.125072\pi$
$854$		0			0
$855$	−41.8227	−	103.867i	−1.43030	−	3.55218i
$856$		0			0
$857$	−21.8544	−	21.8544i	−0.746531	−	0.746531i	0.227295	−	0.973826i	$-0.427012\pi$
$857$	−21.8544	−	21.8544i	−0.746531	−	0.746531i	−0.973826	+	0.227295i	$0.927012\pi$
$858$		0			0
$859$	19.0170			0.648850			0.324425	−	0.945911i	$-0.394829\pi$
$859$	19.0170			0.648850			0.324425	+	0.945911i	$0.394829\pi$
$860$		0			0
$861$	−11.7194			−0.399397
$862$		0			0
$863$	23.1915	+	23.1915i	0.789449	+	0.789449i	0.981404	−	0.191955i	$-0.0614826\pi$
$863$	23.1915	+	23.1915i	0.789449	+	0.789449i	−0.191955	+	0.981404i	$0.561483\pi$
$864$		0			0
$865$	16.1644	−	37.9565i	0.549606	−	1.29056i
$866$		0			0
$867$	0.389296	−	0.389296i	0.0132212	−	0.0132212i
$868$		0			0
$869$			22.9763i			0.779418i
$870$		0			0
$871$			5.33026i			0.180609i
$872$		0			0
$873$	84.4954	−	84.4954i	2.85974	−	2.85974i
$874$		0			0
$875$	3.96974	+	10.4518i	0.134202	+	0.353337i
$876$		0			0
$877$	−9.38349	−	9.38349i	−0.316858	−	0.316858i	0.530701	−	0.847559i	$-0.321929\pi$
$877$	−9.38349	−	9.38349i	−0.316858	−	0.316858i	−0.847559	+	0.530701i	$0.821929\pi$
$878$		0			0
$879$	−61.7883			−2.08407
$880$		0			0
$881$	−22.3516			−0.753044			−0.376522	−	0.926408i	$-0.622880\pi$
$881$	−22.3516			−0.753044			−0.376522	+	0.926408i	$0.622880\pi$
$882$		0			0
$883$	−15.8373	−	15.8373i	−0.532967	−	0.532967i	0.388487	−	0.921454i	$-0.372998\pi$
$883$	−15.8373	−	15.8373i	−0.532967	−	0.532967i	−0.921454	+	0.388487i	$0.872998\pi$
$884$		0			0
$885$	66.1958	+	28.1906i	2.22515	+	0.947616i
$886$		0			0
$887$	−16.9639	+	16.9639i	−0.569593	+	0.569593i	−0.932014	−	0.362421i	$-0.881950\pi$
$887$	−16.9639	+	16.9639i	−0.569593	+	0.569593i	0.362421	+	0.932014i	$0.381950\pi$
$888$		0			0
$889$		−	11.3607i		−	0.381027i
$890$		0			0
$891$		−	86.3192i		−	2.89180i
$892$		0			0
$893$	−48.1979	+	48.1979i	−1.61288	+	1.61288i
$894$		0			0
$895$	1.68173	−	0.677157i	0.0562140	−	0.0226349i
$896$		0			0
$897$	−16.7948	−	16.7948i	−0.560763	−	0.560763i
$898$		0			0
$899$	−35.7934			−1.19378
$900$		0			0
$901$	−9.07757			−0.302418
$902$		0			0
$903$	−19.0939	−	19.0939i	−0.635404	−	0.635404i
$904$		0			0
$905$	17.7538	−	7.14868i	0.590158	−	0.237630i
$906$		0			0
$907$	6.71530	−	6.71530i	0.222978	−	0.222978i	−0.586773	−	0.809751i	$-0.699602\pi$
$907$	6.71530	−	6.71530i	0.222978	−	0.222978i	0.809751	+	0.586773i	$0.199602\pi$
$908$		0			0
$909$		−	35.3693i		−	1.17313i
$910$		0			0
$911$		−	12.9346i		−	0.428541i	−0.976774	−	0.214271i	$-0.931263\pi$
$911$		−	12.9346i		−	0.428541i	0.976774	−	0.214271i	$-0.0687374\pi$
$912$		0			0
$913$	17.6194	−	17.6194i	0.583116	−	0.583116i
$914$		0			0
$915$	−15.7426	−	6.70424i	−0.520433	−	0.221635i
$916$		0			0
$917$	−2.95569	−	2.95569i	−0.0976053	−	0.0976053i
$918$		0			0
$919$	59.0749			1.94870			0.974350	−	0.225039i	$-0.0722509\pi$
$919$	59.0749			1.94870			0.974350	+	0.225039i	$0.0722509\pi$
$920$		0			0
$921$	42.3756			1.39632
$922$		0			0
$923$	−0.881030	−	0.881030i	−0.0289995	−	0.0289995i
$924$		0			0
$925$	18.5192	+	0.366927i	0.608907	+	0.0120645i
$926$		0			0
$927$	84.0994	−	84.0994i	2.76219	−	2.76219i
$928$		0			0
$929$		−	21.2077i		−	0.695801i	−0.937531	−	0.347901i	$-0.886895\pi$
$929$		−	21.2077i		−	0.695801i	0.937531	−	0.347901i	$-0.113105\pi$
$930$		0			0
$931$			6.77624i			0.222082i
$932$		0			0
$933$	−18.2223	+	18.2223i	−0.596570	+	0.596570i
$934$		0			0
$935$	13.2360	−	31.0801i	0.432863	−	1.01643i
$936$		0			0
$937$	25.8581	+	25.8581i	0.844746	+	0.844746i	0.989472	−	0.144726i	$-0.0462300\pi$
$937$	25.8581	+	25.8581i	0.844746	+	0.844746i	−0.144726	+	0.989472i	$0.546230\pi$
$938$		0			0
$939$	−14.8361			−0.484158
$940$		0			0
$941$	47.5143			1.54892			0.774460	−	0.632622i	$-0.218021\pi$
$941$	47.5143			1.54892			0.774460	+	0.632622i	$0.218021\pi$
$942$		0			0
$943$	18.8061	+	18.8061i	0.612411	+	0.612411i
$944$		0			0
$945$	−11.8178	−	29.3497i	−0.384434	−	0.954747i
$946$		0			0
$947$	19.1768	−	19.1768i	0.623161	−	0.623161i	−0.323177	−	0.946338i	$-0.604751\pi$
$947$	19.1768	−	19.1768i	0.623161	−	0.623161i	0.946338	+	0.323177i	$0.104751\pi$
$948$		0			0
$949$			6.02147i			0.195465i
$950$		0			0
$951$		−	29.1670i		−	0.945805i
$952$		0			0
$953$	−7.21221	+	7.21221i	−0.233626	+	0.233626i	−0.814205	−	0.580578i	$-0.802827\pi$
$953$	−7.21221	+	7.21221i	−0.233626	+	0.233626i	0.580578	+	0.814205i	$0.302827\pi$
$954$		0			0
$955$	−3.04957	−	7.57364i	−0.0986818	−	0.245077i
$956$		0			0
$957$	57.6868	+	57.6868i	1.86475	+	1.86475i
$958$		0			0
$959$	10.8616			0.350738
$960$		0			0
$961$	3.87658			0.125051
$962$		0			0
$963$	−17.7161	−	17.7161i	−0.570892	−	0.570892i
$964$		0			0
$965$	21.7231	−	51.0092i	0.699291	−	1.64204i
$966$		0			0
$967$	12.3264	−	12.3264i	0.396390	−	0.396390i	−0.480567	−	0.876958i	$-0.659569\pi$
$967$	12.3264	−	12.3264i	0.396390	−	0.396390i	0.876958	+	0.480567i	$0.159569\pi$
$968$		0			0
$969$			89.6032i			2.87847i
$970$		0			0
$971$		−	20.4678i		−	0.656842i	−0.944531	−	0.328421i	$-0.893484\pi$
$971$		−	20.4678i		−	0.656842i	0.944531	−	0.328421i	$-0.106516\pi$
$972$		0			0
$973$	−0.870394	+	0.870394i	−0.0279035	+	0.0279035i
$974$		0			0
$975$	−11.7050	+	11.2502i	−0.374859	+	0.360293i
$976$		0			0
$977$	−2.67796	−	2.67796i	−0.0856756	−	0.0856756i	0.662970	−	0.748646i	$-0.269296\pi$
$977$	−2.67796	−	2.67796i	−0.0856756	−	0.0856756i	−0.748646	+	0.662970i	$0.769296\pi$
$978$		0			0
$979$	−41.8417			−1.33727
$980$		0			0
$981$	29.9070			0.954857
$982$		0			0
$983$	25.4156	+	25.4156i	0.810633	+	0.810633i	0.984729	−	0.174096i	$-0.0557003\pi$
$983$	25.4156	+	25.4156i	0.810633	+	0.810633i	−0.174096	+	0.984729i	$0.555700\pi$
$984$		0			0
$985$	−30.8115	−	13.1216i	−0.981735	−	0.418088i
$986$		0			0
$987$	−22.9268	+	22.9268i	−0.729767	+	0.729767i
$988$		0			0
$989$			61.2796i			1.94858i
$990$		0			0
$991$			9.43569i			0.299734i	0.988706	+	0.149867i	$0.0478846\pi$
$991$			9.43569i			0.299734i	−0.988706	+	0.149867i	$0.952115\pi$
$992$		0			0
$993$	−63.7869	+	63.7869i	−2.02421	+	2.02421i
$994$		0			0
$995$	−1.42317	+	0.573046i	−0.0451174	+	0.0181668i
$996$		0			0
$997$	18.2530	+	18.2530i	0.578078	+	0.578078i	0.934373	−	0.356295i	$-0.115960\pi$
$997$	18.2530	+	18.2530i	0.578078	+	0.578078i	−0.356295	+	0.934373i	$0.615960\pi$
$998$		0			0
$999$	−52.4184			−1.65844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.x.f.127.10	yes	20
4.3	odd	2		1120.2.x.e.127.1	✓	20
5.3	odd	4		1120.2.x.e.1023.1	yes	20
20.3	even	4	inner	1120.2.x.f.1023.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1120.2.x.e.127.1	✓	20	4.3	odd	2
1120.2.x.e.1023.1	yes	20	5.3	odd	4
1120.2.x.f.127.10	yes	20	1.1	even	1	trivial
1120.2.x.f.1023.10	yes	20	20.3	even	4	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.27923 + 2.27923i) q^{3} +(2.07423 - 0.835201i) q^{5} +(-0.707107 + 0.707107i) q^{7} +7.38979i q^{9} +3.68262i q^{11} +(-0.712298 + 0.712298i) q^{13} +(6.63127 + 2.82404i) q^{15} +(-2.90079 - 2.90079i) q^{17} -6.77624 q^{19} -3.22332 q^{21} +(5.17244 + 5.17244i) q^{23} +(3.60488 - 3.46480i) q^{25} +(-10.0053 + 10.0053i) q^{27} -6.87275i q^{29} -5.20801i q^{31} +(-8.39355 + 8.39355i) q^{33} +(-0.876127 + 2.05728i) q^{35} +(2.61952 + 2.61952i) q^{37} -3.24698 q^{39} +3.63583 q^{41} +(5.92367 + 5.92367i) q^{43} +(6.17196 + 15.3281i) q^{45} +(7.11278 - 7.11278i) q^{47} -1.00000i q^{49} -13.2232i q^{51} +(1.56467 - 1.56467i) q^{53} +(3.07573 + 7.63861i) q^{55} +(-15.4446 - 15.4446i) q^{57} +9.98237 q^{59} -2.37399 q^{61} +(-5.22537 - 5.22537i) q^{63} +(-0.882559 + 2.07238i) q^{65} +(3.74159 - 3.74159i) q^{67} +23.5784i q^{69} +1.23688i q^{71} +(4.22679 - 4.22679i) q^{73} +(16.1134 + 0.319262i) q^{75} +(-2.60401 - 2.60401i) q^{77} +6.23911 q^{79} -23.4396 q^{81} +(-4.78446 - 4.78446i) q^{83} +(-8.43966 - 3.59417i) q^{85} +(15.6646 - 15.6646i) q^{87} +11.3619i q^{89} -1.00734i q^{91} +(11.8703 - 11.8703i) q^{93} +(-14.0555 + 5.65952i) q^{95} +(-11.4341 - 11.4341i) q^{97} -27.2138 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} - 12 q^{13} + 8 q^{15} - 4 q^{17} - 24 q^{19} + 8 q^{23} + 4 q^{25} - 16 q^{33} - 4 q^{35} + 4 q^{37} + 8 q^{39} + 32 q^{41} - 8 q^{43} + 32 q^{45} + 24 q^{47} + 28 q^{53} + 24 q^{59} + 24 q^{61}+ \cdots + 4 q^{97}+O(q^{100}) \) 20 * q - 4 * q^5 - 12 * q^13 + 8 * q^15 - 4 * q^17 - 24 * q^19 + 8 * q^23 + 4 * q^25 - 16 * q^33 - 4 * q^35 + 4 * q^37 + 8 * q^39 + 32 * q^41 - 8 * q^43 + 32 * q^45 + 24 * q^47 + 28 * q^53 + 24 * q^59 + 24 * q^61 - 8 * q^63 - 12 * q^65 - 8 * q^67 + 20 * q^73 + 72 * q^75 + 8 * q^77 - 24 * q^79 - 20 * q^81 - 48 * q^83 - 20 * q^85 + 56 * q^87 - 8 * q^93 - 8 * q^95 + 4 * q^97

Introduction

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