LMFDB - Embedded newform 1280.2.q.a.1089.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(449,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1280.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.q (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1089.2
Root			$0.500000 - 2.00333i$ of defining polynomial
Character	$\chi$	$=$	1280.1089
Dual form			1280.2.q.a.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53819 + 1.53819i) q^{3} +(-0.569800 + 2.16225i) q^{5} -4.20241 q^{7} -1.73205i q^{9} +O(q^{10})$	\(q+(-1.53819 + 1.53819i) q^{3} +(-0.569800 + 2.16225i) q^{5} -4.20241 q^{7} -1.73205i q^{9} +(4.38134 - 4.38134i) q^{11} +(2.17533 - 2.17533i) q^{13} +(-2.44949 - 4.20241i) q^{15} -2.75821i q^{17} +(-1.93185 - 1.93185i) q^{19} +(6.46410 - 6.46410i) q^{21} -3.37810 q^{23} +(-4.35066 - 2.46410i) q^{25} +(-1.95035 - 1.95035i) q^{27} +(4.46410 + 4.46410i) q^{29} +1.03528 q^{31} +13.4787i q^{33} +(2.39453 - 9.08666i) q^{35} +(7.53556 + 7.53556i) q^{37} +6.69213i q^{39} -3.26795i q^{41} +(4.91629 + 4.91629i) q^{43} +(3.74513 + 0.986923i) q^{45} -0.301719i q^{47} +10.6603 q^{49} +(4.24264 + 4.24264i) q^{51} +(-4.93353 - 4.93353i) q^{53} +(6.97707 + 11.9700i) q^{55} +5.94311 q^{57} +(4.76028 - 4.76028i) q^{59} +(-2.00000 - 2.00000i) q^{61} +7.27879i q^{63} +(3.46410 + 5.94311i) q^{65} +(-4.31285 + 4.31285i) q^{67} +(5.19615 - 5.19615i) q^{69} -3.58630i q^{71} +4.77735 q^{73} +(10.4824 - 2.90188i) q^{75} +(-18.4122 + 18.4122i) q^{77} -3.86370 q^{79} +11.1962 q^{81} +(3.48853 - 3.48853i) q^{83} +(5.96393 + 1.57163i) q^{85} -13.7333 q^{87} +7.46410i q^{89} +(-9.14162 + 9.14162i) q^{91} +(-1.59245 + 1.59245i) q^{93} +(5.27792 - 3.07638i) q^{95} -15.8102i q^{97} +(-7.58871 - 7.58871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5}+O(q^{10}) $ 16 * q - 8 * q^5	$ 16 q - 8 q^{5} + 48 q^{21} + 16 q^{29} + 24 q^{45} + 32 q^{49} - 32 q^{61} + 96 q^{81} - 48 q^{85}+O(q^{100}) $ 16 * q - 8 * q^5 + 48 * q^21 + 16 * q^29 + 24 * q^45 + 32 * q^49 - 32 * q^61 + 96 * q^81 - 48 * q^85

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.53819	+	1.53819i	−0.888074	+	0.888074i	−0.994338	−	0.106264i	$-0.966111\pi$
$3$	−1.53819	+	1.53819i	−0.888074	+	0.888074i	0.106264	+	0.994338i	$0.466111\pi$
$4$		0			0
$5$	−0.569800	+	2.16225i	−0.254822	+	0.966988i
$5$	−0.569800	+	2.16225i	−0.254822	+	0.966988i
$6$		0			0
$7$	−4.20241			−1.58836			−0.794181	−	0.607681i	$-0.792100\pi$
$7$	−4.20241			−1.58836			−0.794181	+	0.607681i	$0.792100\pi$
$8$		0			0
$9$		−	1.73205i		−	0.577350i
$10$		0			0
$11$	4.38134	−	4.38134i	1.32102	−	1.32102i	0.408076	−	0.912948i	$-0.366200\pi$
$11$	4.38134	−	4.38134i	1.32102	−	1.32102i	0.912948	−	0.408076i	$-0.133800\pi$
$12$		0			0
$13$	2.17533	−	2.17533i	0.603327	−	0.603327i	−0.337867	−	0.941194i	$-0.609705\pi$
$13$	2.17533	−	2.17533i	0.603327	−	0.603327i	0.941194	+	0.337867i	$0.109705\pi$
$14$		0			0
$15$	−2.44949	−	4.20241i	−0.632456	−	1.08506i
$16$		0			0
$17$		−	2.75821i		−	0.668963i	−0.942402	−	0.334481i	$-0.891439\pi$
$17$		−	2.75821i		−	0.668963i	0.942402	−	0.334481i	$-0.108561\pi$
$18$		0			0
$19$	−1.93185	−	1.93185i	−0.443197	−	0.443197i	0.449888	−	0.893085i	$-0.351464\pi$
$19$	−1.93185	−	1.93185i	−0.443197	−	0.443197i	−0.893085	+	0.449888i	$0.851464\pi$
$20$		0			0
$21$	6.46410	−	6.46410i	1.41058	−	1.41058i
$22$		0			0
$23$	−3.37810			−0.704382			−0.352191	−	0.935928i	$-0.614563\pi$
$23$	−3.37810			−0.704382			−0.352191	+	0.935928i	$0.614563\pi$
$24$		0			0
$25$	−4.35066	−	2.46410i	−0.870131	−	0.492820i
$26$		0			0
$27$	−1.95035	−	1.95035i	−0.375344	−	0.375344i
$28$		0			0
$29$	4.46410	+	4.46410i	0.828963	+	0.828963i	0.987373	−	0.158410i	$-0.0506369\pi$
$29$	4.46410	+	4.46410i	0.828963	+	0.828963i	−0.158410	+	0.987373i	$0.550637\pi$
$30$		0			0
$31$	1.03528			0.185941			0.0929705	−	0.995669i	$-0.470364\pi$
$31$	1.03528			0.185941			0.0929705	+	0.995669i	$0.470364\pi$
$32$		0			0
$33$			13.4787i			2.34633i
$34$		0			0
$35$	2.39453	−	9.08666i	0.404750	−	1.53593i
$36$		0			0
$37$	7.53556	+	7.53556i	1.23884	+	1.23884i	0.960476	+	0.278361i	$0.0897913\pi$
$37$	7.53556	+	7.53556i	1.23884	+	1.23884i	0.278361	+	0.960476i	$0.410209\pi$
$38$		0			0
$39$			6.69213i			1.07160i
$40$		0			0
$41$		−	3.26795i		−	0.510368i	−0.966893	−	0.255184i	$-0.917864\pi$
$41$		−	3.26795i		−	0.510368i	0.966893	−	0.255184i	$-0.0821360\pi$
$42$		0			0
$43$	4.91629	+	4.91629i	0.749727	+	0.749727i	0.974428	−	0.224701i	$-0.0721406\pi$
$43$	4.91629	+	4.91629i	0.749727	+	0.749727i	−0.224701	+	0.974428i	$0.572141\pi$
$44$		0			0
$45$	3.74513	+	0.986923i	0.558291	+	0.147122i
$46$		0			0
$47$		−	0.301719i		−	0.0440103i	−0.999758	−	0.0220052i	$-0.992995\pi$
$47$		−	0.301719i		−	0.0440103i	0.999758	−	0.0220052i	$-0.00700502\pi$
$48$		0			0
$49$	10.6603			1.52289
$50$		0			0
$51$	4.24264	+	4.24264i	0.594089	+	0.594089i
$52$		0			0
$53$	−4.93353	−	4.93353i	−0.677673	−	0.677673i	0.281800	−	0.959473i	$-0.409068\pi$
$53$	−4.93353	−	4.93353i	−0.677673	−	0.677673i	−0.959473	+	0.281800i	$0.909068\pi$
$54$		0			0
$55$	6.97707	+	11.9700i	0.940788	+	1.61404i
$56$		0			0
$57$	5.94311			0.787184
$58$		0			0
$59$	4.76028	−	4.76028i	0.619736	−	0.619736i	−0.325728	−	0.945464i	$-0.605609\pi$
$59$	4.76028	−	4.76028i	0.619736	−	0.619736i	0.945464	+	0.325728i	$0.105609\pi$
$60$		0			0
$61$	−2.00000	−	2.00000i	−0.256074	−	0.256074i	0.567381	−	0.823455i	$-0.307957\pi$
$61$	−2.00000	−	2.00000i	−0.256074	−	0.256074i	−0.823455	+	0.567381i	$0.807957\pi$
$62$		0			0
$63$			7.27879i			0.917041i
$64$		0			0
$65$	3.46410	+	5.94311i	0.429669	+	0.737152i
$66$		0			0
$67$	−4.31285	+	4.31285i	−0.526898	+	0.526898i	−0.919646	−	0.392748i	$-0.871524\pi$
$67$	−4.31285	+	4.31285i	−0.526898	+	0.526898i	0.392748	+	0.919646i	$0.371524\pi$
$68$		0			0
$69$	5.19615	−	5.19615i	0.625543	−	0.625543i
$70$		0			0
$71$		−	3.58630i		−	0.425616i	−0.977094	−	0.212808i	$-0.931739\pi$
$71$		−	3.58630i		−	0.425616i	0.977094	−	0.212808i	$-0.0682608\pi$
$72$		0			0
$73$	4.77735			0.559147			0.279573	−	0.960124i	$-0.409807\pi$
$73$	4.77735			0.559147			0.279573	+	0.960124i	$0.409807\pi$
$74$		0			0
$75$	10.4824	−	2.90188i	1.21040	−	0.335080i
$76$		0			0
$77$	−18.4122	+	18.4122i	−2.09826	+	2.09826i
$78$		0			0
$79$	−3.86370			−0.434701			−0.217350	−	0.976094i	$-0.569741\pi$
$79$	−3.86370			−0.434701			−0.217350	+	0.976094i	$0.569741\pi$
$80$		0			0
$81$	11.1962			1.24402
$82$		0			0
$83$	3.48853	−	3.48853i	0.382916	−	0.382916i	−0.489235	−	0.872152i	$-0.662724\pi$
$83$	3.48853	−	3.48853i	0.382916	−	0.382916i	0.872152	+	0.489235i	$0.162724\pi$
$84$		0			0
$85$	5.96393	+	1.57163i	0.646879	+	0.170467i
$86$		0			0
$87$	−13.7333			−1.47236
$88$		0			0
$89$			7.46410i			0.791193i	0.918424	+	0.395597i	$0.129462\pi$
$89$			7.46410i			0.791193i	−0.918424	+	0.395597i	$0.870538\pi$
$90$		0			0
$91$	−9.14162	+	9.14162i	−0.958302	+	0.958302i
$92$		0			0
$93$	−1.59245	+	1.59245i	−0.165129	+	0.165129i
$94$		0			0
$95$	5.27792	−	3.07638i	0.541503	−	0.315630i
$96$		0			0
$97$		−	15.8102i		−	1.60528i	−0.596464	−	0.802640i	$-0.703428\pi$
$97$		−	15.8102i		−	1.60528i	0.596464	−	0.802640i	$-0.296572\pi$
$98$		0			0
$99$	−7.58871	−	7.58871i	−0.762694	−	0.762694i
$100$		0			0
$101$	5.53590	−	5.53590i	0.550842	−	0.550842i	−0.375841	−	0.926684i	$-0.622646\pi$
$101$	5.53590	−	5.53590i	0.550842	−	0.550842i	0.926684	+	0.375841i	$0.122646\pi$
$102$		0			0
$103$	7.27879			0.717200			0.358600	−	0.933491i	$-0.383254\pi$
$103$	7.27879			0.717200			0.358600	+	0.933491i	$0.383254\pi$
$104$		0			0
$105$	10.2938	+	17.6603i	1.00457	+	1.72346i
$106$		0			0
$107$	6.04232	+	6.04232i	0.584133	+	0.584133i	0.936036	−	0.351903i	$-0.114465\pi$
$107$	6.04232	+	6.04232i	0.584133	+	0.584133i	−0.351903	+	0.936036i	$0.614465\pi$
$108$		0			0
$109$	−7.66025	−	7.66025i	−0.733719	−	0.733719i	0.237635	−	0.971354i	$-0.423628\pi$
$109$	−7.66025	−	7.66025i	−0.733719	−	0.733719i	−0.971354	+	0.237635i	$0.923628\pi$
$110$		0			0
$111$	−23.1822			−2.20036
$112$		0			0
$113$		−	8.70131i		−	0.818550i	−0.912411	−	0.409275i	$-0.865782\pi$
$113$		−	8.70131i		−	0.818550i	0.912411	−	0.409275i	$-0.134218\pi$
$114$		0			0
$115$	1.92484	−	7.30429i	0.179492	−	0.681129i
$116$		0			0
$117$	−3.76778	−	3.76778i	−0.348331	−	0.348331i
$118$		0			0
$119$			11.5911i			1.06256i
$120$		0			0
$121$		−	27.3923i		−	2.49021i
$122$		0			0
$123$	5.02672	+	5.02672i	0.453244	+	0.453244i
$124$		0			0
$125$	7.80701	−	8.00316i	0.698280	−	0.715825i
$126$		0			0
$127$			5.63016i			0.499596i	0.968298	+	0.249798i	$0.0803642\pi$
$127$			5.63016i			0.499596i	−0.968298	+	0.249798i	$0.919636\pi$
$128$		0			0
$129$	−15.1244			−1.33163
$130$		0			0
$131$	5.51815	+	5.51815i	0.482123	+	0.482123i	0.905809	−	0.423686i	$-0.139264\pi$
$131$	5.51815	+	5.51815i	0.482123	+	0.482123i	−0.423686	+	0.905809i	$0.639264\pi$
$132$		0			0
$133$	8.11843	+	8.11843i	0.703957	+	0.703957i
$134$		0			0
$135$	5.32844	−	3.10583i	0.458599	−	0.267307i
$136$		0			0
$137$	4.35066			0.371702			0.185851	−	0.982578i	$-0.440496\pi$
$137$	4.35066			0.371702			0.185851	+	0.982578i	$0.440496\pi$
$138$		0			0
$139$	5.41662	−	5.41662i	0.459432	−	0.459432i	−0.439037	−	0.898469i	$-0.644680\pi$
$139$	5.41662	−	5.41662i	0.459432	−	0.459432i	0.898469	+	0.439037i	$0.144680\pi$
$140$		0			0
$141$	0.464102	+	0.464102i	0.0390844	+	0.0390844i
$142$		0			0
$143$		−	19.0617i		−	1.59402i
$144$		0			0
$145$	−12.1962	+	7.10886i	−1.01284	+	0.590359i
$146$		0			0
$147$	−16.3975	+	16.3975i	−1.35244	+	1.35244i
$148$		0			0
$149$	−9.46410	+	9.46410i	−0.775329	+	0.775329i	−0.979033	−	0.203703i	$-0.934702\pi$
$149$	−9.46410	+	9.46410i	−0.775329	+	0.775329i	0.203703	+	0.979033i	$0.434702\pi$
$150$		0			0
$151$		−	2.55103i		−	0.207600i	−0.994598	−	0.103800i	$-0.966900\pi$
$151$		−	2.55103i		−	0.207600i	0.994598	−	0.103800i	$-0.0331001\pi$
$152$		0			0
$153$	−4.77735			−0.386226
$154$		0			0
$155$	−0.589901	+	2.23853i	−0.0473820	+	0.179803i
$156$		0			0
$157$	9.12801	−	9.12801i	0.728494	−	0.728494i	−0.241826	−	0.970320i	$-0.577746\pi$
$157$	9.12801	−	9.12801i	0.728494	−	0.728494i	0.970320	+	0.241826i	$0.0777462\pi$
$158$		0			0
$159$	15.1774			1.20365
$160$		0			0
$161$	14.1962			1.11881
$162$		0			0
$163$	14.4471	−	14.4471i	1.13159	−	1.13159i	0.141674	−	0.989913i	$-0.454752\pi$
$163$	14.4471	−	14.4471i	1.13159	−	1.13159i	0.989913	−	0.141674i	$-0.0452485\pi$
$164$		0			0
$165$	−29.1442	−	7.68014i	−2.26888	−	0.597898i
$166$		0			0
$167$	1.72947			0.133831			0.0669153	−	0.997759i	$-0.478684\pi$
$167$	1.72947			0.133831			0.0669153	+	0.997759i	$0.478684\pi$
$168$		0			0
$169$			3.53590i			0.271992i
$170$		0			0
$171$	−3.34607	+	3.34607i	−0.255880	+	0.255880i
$172$		0			0
$173$	8.70131	−	8.70131i	0.661548	−	0.661548i	−0.294197	−	0.955745i	$-0.595052\pi$
$173$	8.70131	−	8.70131i	0.661548	−	0.661548i	0.955745	+	0.294197i	$0.0950520\pi$
$174$		0			0
$175$	18.2832	+	10.3552i	1.38208	+	0.782777i
$176$		0			0
$177$			14.6444i			1.10074i
$178$		0			0
$179$	15.9725	+	15.9725i	1.19384	+	1.19384i	0.975981	+	0.217856i	$0.0699064\pi$
$179$	15.9725	+	15.9725i	1.19384	+	1.19384i	0.217856	+	0.975981i	$0.430094\pi$
$180$		0			0
$181$	7.53590	−	7.53590i	0.560139	−	0.560139i	−0.369208	−	0.929347i	$-0.620371\pi$
$181$	7.53590	−	7.53590i	0.560139	−	0.560139i	0.929347	+	0.369208i	$0.120371\pi$
$182$		0			0
$183$	6.15276			0.454825
$184$		0			0
$185$	−20.5875	+	12.0000i	−1.51362	+	0.882258i
$186$		0			0
$187$	−12.0846	−	12.0846i	−0.883716	−	0.883716i
$188$		0			0
$189$	8.19615	+	8.19615i	0.596182	+	0.596182i
$190$		0			0
$191$	4.14110			0.299640			0.149820	−	0.988713i	$-0.452131\pi$
$191$	4.14110			0.299640			0.149820	+	0.988713i	$0.452131\pi$
$192$		0			0
$193$		−	2.44584i		−	0.176056i	−0.996118	−	0.0880278i	$-0.971944\pi$
$193$		−	2.44584i		−	0.176056i	0.996118	−	0.0880278i	$-0.0280564\pi$
$194$		0			0
$195$	−14.4701	−	3.81318i	−1.03622	−	0.273067i
$196$		0			0
$197$	−1.00957	−	1.00957i	−0.0719291	−	0.0719291i	0.670227	−	0.742156i	$-0.266197\pi$
$197$	−1.00957	−	1.00957i	−0.0719291	−	0.0719291i	−0.742156	+	0.670227i	$0.766197\pi$
$198$		0			0
$199$		−	13.9391i		−	0.988114i	−0.869430	−	0.494057i	$-0.835513\pi$
$199$		−	13.9391i		−	0.988114i	0.869430	−	0.494057i	$-0.164487\pi$
$200$		0			0
$201$		−	13.2679i		−	0.935849i
$202$		0			0
$203$	−18.7600	−	18.7600i	−1.31669	−	1.31669i
$204$		0			0
$205$	7.06613	+	1.86208i	0.493520	+	0.130053i
$206$		0			0
$207$			5.85104i			0.406675i
$208$		0			0
$209$	−16.9282			−1.17095
$210$		0			0
$211$	13.2456	+	13.2456i	0.911862	+	0.911862i	0.996419	−	0.0845567i	$-0.0269474\pi$
$211$	13.2456	+	13.2456i	0.911862	+	0.911862i	−0.0845567	+	0.996419i	$0.526947\pi$
$212$		0			0
$213$	5.51641	+	5.51641i	0.377978	+	0.377978i
$214$		0			0
$215$	−13.4315	+	7.82894i	−0.916024	+	0.533929i
$216$		0			0
$217$	−4.35066			−0.295342
$218$		0			0
$219$	−7.34847	+	7.34847i	−0.496564	+	0.496564i
$220$		0			0
$221$	−6.00000	−	6.00000i	−0.403604	−	0.403604i
$222$		0			0
$223$		−	10.5760i		−	0.708224i	−0.935203	−	0.354112i	$-0.884783\pi$
$223$		−	10.5760i		−	0.708224i	0.935203	−	0.354112i	$-0.115217\pi$
$224$		0			0
$225$	−4.26795	+	7.53556i	−0.284530	+	0.502370i
$226$		0			0
$227$	7.69095	−	7.69095i	0.510466	−	0.510466i	−0.404203	−	0.914669i	$-0.632451\pi$
$227$	7.69095	−	7.69095i	0.510466	−	0.510466i	0.914669	+	0.404203i	$0.132451\pi$
$228$		0			0
$229$	−13.9282	+	13.9282i	−0.920402	+	0.920402i	−0.997058	−	0.0766560i	$-0.975576\pi$
$229$	−13.9282	+	13.9282i	−0.920402	+	0.920402i	0.0766560	+	0.997058i	$0.475576\pi$
$230$		0			0
$231$		−	56.6429i		−	3.72683i
$232$		0			0
$233$	−28.5498			−1.87036			−0.935179	−	0.354176i	$-0.884762\pi$
$233$	−28.5498			−1.87036			−0.935179	+	0.354176i	$0.884762\pi$
$234$		0			0
$235$	0.652393	+	0.171920i	0.0425574	+	0.0112148i
$236$		0			0
$237$	5.94311	−	5.94311i	0.386046	−	0.386046i
$238$		0			0
$239$	−18.0058			−1.16470			−0.582350	−	0.812938i	$-0.697867\pi$
$239$	−18.0058			−1.16470			−0.582350	+	0.812938i	$0.697867\pi$
$240$		0			0
$241$	−22.0526			−1.42053			−0.710265	−	0.703934i	$-0.751425\pi$
$241$	−22.0526			−1.42053			−0.710265	+	0.703934i	$0.751425\pi$
$242$		0			0
$243$	−11.3708	+	11.3708i	−0.729435	+	0.729435i
$244$		0			0
$245$	−6.07421	+	23.0501i	−0.388067	+	1.47262i
$246$		0			0
$247$	−8.40482			−0.534786
$248$		0			0
$249$			10.7321i			0.680116i
$250$		0			0
$251$	−14.6598	+	14.6598i	−0.925317	+	0.925317i	−0.997399	−	0.0720820i	$-0.977036\pi$
$251$	−14.6598	+	14.6598i	−0.925317	+	0.925317i	0.0720820	+	0.997399i	$0.477036\pi$
$252$		0			0
$253$	−14.8006	+	14.8006i	−0.930506	+	0.930506i
$254$		0			0
$255$	−11.5911	+	6.75620i	−0.725863	+	0.423089i
$256$		0			0
$257$		−	17.0903i		−	1.06606i	−0.846096	−	0.533031i	$-0.821053\pi$
$257$		−	17.0903i		−	1.06606i	0.846096	−	0.533031i	$-0.178947\pi$
$258$		0			0
$259$	−31.6675	−	31.6675i	−1.96772	−	1.96772i
$260$		0			0
$261$	7.73205	−	7.73205i	0.478602	−	0.478602i
$262$		0			0
$263$	9.30998			0.574078			0.287039	−	0.957919i	$-0.407329\pi$
$263$	9.30998			0.574078			0.287039	+	0.957919i	$0.407329\pi$
$264$		0			0
$265$	13.4787	−	7.85641i	0.827988	−	0.482615i
$266$		0			0
$267$	−11.4812	−	11.4812i	−0.702638	−	0.702638i
$268$		0			0
$269$	4.92820	+	4.92820i	0.300478	+	0.300478i	0.841201	−	0.540723i	$-0.181849\pi$
$269$	4.92820	+	4.92820i	0.300478	+	0.300478i	−0.540723	+	0.841201i	$0.681849\pi$
$270$		0			0
$271$	23.4596			1.42507			0.712535	−	0.701636i	$-0.247547\pi$
$271$	23.4596			1.42507			0.712535	+	0.701636i	$0.247547\pi$
$272$		0			0
$273$		−	28.1231i		−	1.70209i
$274$		0			0
$275$	−29.8578	+	8.26564i	−1.80049	+	0.498437i
$276$		0			0
$277$	−3.18490	−	3.18490i	−0.191362	−	0.191362i	0.604922	−	0.796284i	$-0.293204\pi$
$277$	−3.18490	−	3.18490i	−0.191362	−	0.191362i	−0.796284	+	0.604922i	$0.793204\pi$
$278$		0			0
$279$		−	1.79315i		−	0.107353i
$280$		0			0
$281$			15.5167i			0.925646i	0.886451	+	0.462823i	$0.153164\pi$
$281$			15.5167i			0.925646i	−0.886451	+	0.462823i	$0.846836\pi$
$282$		0			0
$283$	−18.9513	−	18.9513i	−1.12654	−	1.12654i	−0.990736	−	0.135800i	$-0.956640\pi$
$283$	−18.9513	−	18.9513i	−1.12654	−	1.12654i	−0.135800	−	0.990736i	$-0.543360\pi$
$284$		0			0
$285$	−3.38638	+	12.8505i	−0.200592	+	0.761197i
$286$		0			0
$287$			13.7333i			0.810649i
$288$		0			0
$289$	9.39230			0.552489
$290$		0			0
$291$	24.3190	+	24.3190i	1.42561	+	1.42561i
$292$		0			0
$293$	−0.426696	−	0.426696i	−0.0249278	−	0.0249278i	0.694533	−	0.719461i	$-0.255611\pi$
$293$	−0.426696	−	0.426696i	−0.0249278	−	0.0249278i	−0.719461	+	0.694533i	$0.755611\pi$
$294$		0			0
$295$	7.58051	+	13.0053i	0.441354	+	0.757199i
$296$		0			0
$297$	−17.0903			−0.991677
$298$		0			0
$299$	−7.34847	+	7.34847i	−0.424973	+	0.424973i
$300$		0			0
$301$	−20.6603	−	20.6603i	−1.19084	−	1.19084i
$302$		0			0
$303$			17.0305i			0.978378i
$304$		0			0
$305$	5.46410	−	3.18490i	0.312874	−	0.182367i
$306$		0			0
$307$	11.8934	−	11.8934i	0.678790	−	0.678790i	−0.280937	−	0.959726i	$-0.590645\pi$
$307$	11.8934	−	11.8934i	0.678790	−	0.678790i	0.959726	+	0.280937i	$0.0906451\pi$
$308$		0			0
$309$	−11.1962	+	11.1962i	−0.636927	+	0.636927i
$310$		0			0
$311$		−	30.6322i		−	1.73699i	−0.495694	−	0.868497i	$-0.665086\pi$
$311$		−	30.6322i		−	1.73699i	0.495694	−	0.868497i	$-0.334914\pi$
$312$		0			0
$313$	31.3080			1.76963			0.884816	−	0.465941i	$-0.154284\pi$
$313$	31.3080			1.76963			0.884816	+	0.465941i	$0.154284\pi$
$314$		0			0
$315$	−15.7386	−	4.14746i	−0.886768	−	0.233683i
$316$		0			0
$317$	7.69174	−	7.69174i	0.432011	−	0.432011i	−0.457301	−	0.889312i	$-0.651184\pi$
$317$	7.69174	−	7.69174i	0.432011	−	0.432011i	0.889312	+	0.457301i	$0.151184\pi$
$318$		0			0
$319$	39.1175			2.19016
$320$		0			0
$321$	−18.5885			−1.03751
$322$		0			0
$323$	−5.32844	+	5.32844i	−0.296482	+	0.296482i
$324$		0			0
$325$	−14.8243	+	4.10387i	−0.822306	+	0.227642i
$326$		0			0
$327$	23.5658			1.30319
$328$		0			0
$329$			1.26795i			0.0699043i
$330$		0			0
$331$	4.00240	−	4.00240i	0.219992	−	0.219992i	−0.588503	−	0.808495i	$-0.700282\pi$
$331$	4.00240	−	4.00240i	0.219992	−	0.219992i	0.808495	+	0.588503i	$0.200282\pi$
$332$		0			0
$333$	13.0520	−	13.0520i	0.715243	−	0.715243i
$334$		0			0
$335$	−6.86800	−	11.7829i	−0.375239	−	0.643770i
$336$		0			0
$337$			15.3835i			0.837991i	0.907988	+	0.418996i	$0.137618\pi$
$337$			15.3835i			0.837991i	−0.907988	+	0.418996i	$0.862382\pi$
$338$		0			0
$339$	13.3843	+	13.3843i	0.726933	+	0.726933i
$340$		0			0
$341$	4.53590	−	4.53590i	0.245633	−	0.245633i
$342$		0			0
$343$	−15.3819			−0.830544
$344$		0			0
$345$	8.27462	+	14.1962i	0.445490	+	0.764295i
$346$		0			0
$347$	21.9468	+	21.9468i	1.17817	+	1.17817i	0.980211	+	0.197955i	$0.0634300\pi$
$347$	21.9468	+	21.9468i	1.17817	+	1.17817i	0.197955	+	0.980211i	$0.436570\pi$
$348$		0			0
$349$	−21.7846	−	21.7846i	−1.16610	−	1.16610i	−0.983115	−	0.182988i	$-0.941423\pi$
$349$	−21.7846	−	21.7846i	−1.16610	−	1.16610i	−0.182988	−	0.983115i	$-0.558577\pi$
$350$		0			0
$351$	−8.48528			−0.452911
$352$		0			0
$353$			11.8862i			0.632639i	0.948653	+	0.316320i	$0.102447\pi$
$353$			11.8862i			0.632639i	−0.948653	+	0.316320i	$0.897553\pi$
$354$		0			0
$355$	7.75448	+	2.04348i	0.411565	+	0.108456i
$356$		0			0
$357$	−17.8293	−	17.8293i	−0.943628	−	0.943628i
$358$		0			0
$359$			13.1069i			0.691754i	0.938280	+	0.345877i	$0.112418\pi$
$359$			13.1069i			0.691754i	−0.938280	+	0.345877i	$0.887582\pi$
$360$		0			0
$361$		−	11.5359i		−	0.607153i
$362$		0			0
$363$	42.1345	+	42.1345i	2.21149	+	2.21149i
$364$		0			0
$365$	−2.72214	+	10.3298i	−0.142483	+	0.540688i
$366$		0			0
$367$		−	25.1336i		−	1.31196i	−0.754776	−	0.655982i	$-0.772255\pi$
$367$		−	25.1336i		−	1.31196i	0.754776	−	0.655982i	$-0.227745\pi$
$368$		0			0
$369$	−5.66025			−0.294661
$370$		0			0
$371$	20.7327	+	20.7327i	1.07639	+	1.07639i
$372$		0			0
$373$	−26.1039	−	26.1039i	−1.35161	−	1.35161i	−0.883861	−	0.467749i	$-0.845065\pi$
$373$	−26.1039	−	26.1039i	−1.35161	−	1.35161i	−0.467749	−	0.883861i	$-0.654935\pi$
$374$		0			0
$375$	0.301719	+	24.3190i	0.0155807	+	1.25583i
$376$		0			0
$377$	19.4218			1.00027
$378$		0			0
$379$	−11.3509	+	11.3509i	−0.583055	+	0.583055i	−0.935742	−	0.352686i	$-0.885268\pi$
$379$	−11.3509	+	11.3509i	−0.583055	+	0.583055i	0.352686	+	0.935742i	$0.385268\pi$
$380$		0			0
$381$	−8.66025	−	8.66025i	−0.443678	−	0.443678i
$382$		0			0
$383$			9.53085i			0.487004i	0.969900	+	0.243502i	$0.0782962\pi$
$383$			9.53085i			0.487004i	−0.969900	+	0.243502i	$0.921704\pi$
$384$		0			0
$385$	−29.3205	−	50.3031i	−1.49431	−	2.56368i
$386$		0			0
$387$	8.51526	−	8.51526i	0.432855	−	0.432855i
$388$		0			0
$389$	−8.00000	+	8.00000i	−0.405616	+	0.405616i	−0.880207	−	0.474591i	$-0.842596\pi$
$389$	−8.00000	+	8.00000i	−0.405616	+	0.405616i	0.474591	+	0.880207i	$0.342596\pi$
$390$		0			0
$391$			9.31749i			0.471206i
$392$		0			0
$393$	−16.9759			−0.856322
$394$		0			0
$395$	2.20154	−	8.35429i	0.110771	−	0.420350i
$396$		0			0
$397$	17.2464	−	17.2464i	0.865574	−	0.865574i	−0.126405	−	0.991979i	$-0.540344\pi$
$397$	17.2464	−	17.2464i	0.865574	−	0.865574i	0.991979	+	0.126405i	$0.0403438\pi$
$398$		0			0
$399$	−24.9754			−1.25033
$400$		0			0
$401$	17.4641			0.872116			0.436058	−	0.899919i	$-0.356374\pi$
$401$	17.4641			0.872116			0.436058	+	0.899919i	$0.356374\pi$
$402$		0			0
$403$	2.25207	−	2.25207i	0.112183	−	0.112183i
$404$		0			0
$405$	−6.37957	+	24.2089i	−0.317003	+	1.20295i
$406$		0			0
$407$	66.0317			3.27307
$408$		0			0
$409$			4.73205i			0.233985i	0.993133	+	0.116992i	$0.0373253\pi$
$409$			4.73205i			0.233985i	−0.993133	+	0.116992i	$0.962675\pi$
$410$		0			0
$411$	−6.69213	+	6.69213i	−0.330098	+	0.330098i
$412$		0			0
$413$	−20.0046	+	20.0046i	−0.984364	+	0.984364i
$414$		0			0
$415$	5.55532	+	9.53085i	0.272700	+	0.467851i
$416$		0			0
$417$			16.6636i			0.816018i
$418$		0			0
$419$	1.83032	+	1.83032i	0.0894168	+	0.0894168i	0.750400	−	0.660984i	$-0.229861\pi$
$419$	1.83032	+	1.83032i	0.0894168	+	0.0894168i	−0.660984	+	0.750400i	$0.729861\pi$
$420$		0			0
$421$	26.3923	−	26.3923i	1.28628	−	1.28628i	0.349254	−	0.937028i	$-0.386435\pi$
$421$	26.3923	−	26.3923i	1.28628	−	1.28628i	0.937028	−	0.349254i	$-0.113565\pi$
$422$		0			0
$423$	−0.522594			−0.0254094
$424$		0			0
$425$	−6.79650	+	12.0000i	−0.329679	+	0.582086i
$426$		0			0
$427$	8.40482	+	8.40482i	0.406738	+	0.406738i
$428$		0			0
$429$	29.3205	+	29.3205i	1.41561	+	1.41561i
$430$		0			0
$431$	−28.3586			−1.36599			−0.682993	−	0.730425i	$-0.739322\pi$
$431$	−28.3586			−1.36599			−0.682993	+	0.730425i	$0.739322\pi$
$432$		0			0
$433$			0.426696i			0.0205057i	0.999947	+	0.0102528i	$0.00326364\pi$
$433$			0.426696i			0.0205057i	−0.999947	+	0.0102528i	$0.996736\pi$
$434$		0			0
$435$	7.82522	−	29.6948i	0.375190	−	1.42375i
$436$		0			0
$437$	6.52598	+	6.52598i	0.312180	+	0.312180i
$438$		0			0
$439$		−	7.45001i		−	0.355569i	−0.984069	−	0.177785i	$-0.943107\pi$
$439$		−	7.45001i		−	0.355569i	0.984069	−	0.177785i	$-0.0568931\pi$
$440$		0			0
$441$		−	18.4641i		−	0.879243i
$442$		0			0
$443$	−6.26319	−	6.26319i	−0.297573	−	0.297573i	0.542489	−	0.840063i	$-0.317482\pi$
$443$	−6.26319	−	6.26319i	−0.297573	−	0.297573i	−0.840063	+	0.542489i	$0.817482\pi$
$444$		0			0
$445$	−16.1393	−	4.25305i	−0.765074	−	0.201614i
$446$		0			0
$447$		−	29.1152i		−	1.37710i
$448$		0			0
$449$	−4.87564			−0.230096			−0.115048	−	0.993360i	$-0.536702\pi$
$449$	−4.87564			−0.230096			−0.115048	+	0.993360i	$0.536702\pi$
$450$		0			0
$451$	−14.3180	−	14.3180i	−0.674208	−	0.674208i
$452$		0			0
$453$	3.92396	+	3.92396i	0.184364	+	0.184364i
$454$		0			0
$455$	−14.5576	−	24.9754i	−0.682470	−	1.17086i
$456$		0			0
$457$	−5.82877			−0.272659			−0.136329	−	0.990664i	$-0.543531\pi$
$457$	−5.82877			−0.272659			−0.136329	+	0.990664i	$0.543531\pi$
$458$		0			0
$459$	−5.37945	+	5.37945i	−0.251091	+	0.251091i
$460$		0			0
$461$	12.4641	+	12.4641i	0.580511	+	0.580511i	0.935044	−	0.354533i	$-0.115360\pi$
$461$	12.4641	+	12.4641i	0.580511	+	0.580511i	−0.354533	+	0.935044i	$0.615360\pi$
$462$		0			0
$463$			27.7682i			1.29050i	0.763972	+	0.645250i	$0.223247\pi$
$463$			27.7682i			1.29050i	−0.763972	+	0.645250i	$0.776753\pi$
$464$		0			0
$465$	−2.53590	−	4.35066i	−0.117599	−	0.201757i
$466$		0			0
$467$	8.51526	−	8.51526i	0.394039	−	0.394039i	−0.482085	−	0.876124i	$-0.660120\pi$
$467$	8.51526	−	8.51526i	0.394039	−	0.394039i	0.876124	+	0.482085i	$0.160120\pi$
$468$		0			0
$469$	18.1244	−	18.1244i	0.836905	−	0.836905i
$470$		0			0
$471$			28.0812i			1.29391i
$472$		0			0
$473$	43.0799			1.98081
$474$		0			0
$475$	3.64454	+	13.1651i	0.167223	+	0.604056i
$476$		0			0
$477$	−8.54513	+	8.54513i	−0.391255	+	0.391255i
$478$		0			0
$479$	4.89898			0.223840			0.111920	−	0.993717i	$-0.464300\pi$
$479$	4.89898			0.223840			0.111920	+	0.993717i	$0.464300\pi$
$480$		0			0
$481$	32.7846			1.49485
$482$		0			0
$483$	−21.8364	+	21.8364i	−0.993589	+	0.993589i
$484$		0			0
$485$	34.1856	+	9.00864i	1.55229	+	0.409061i
$486$		0			0
$487$	−0.905158			−0.0410166			−0.0205083	−	0.999790i	$-0.506528\pi$
$487$	−0.905158			−0.0410166			−0.0205083	+	0.999790i	$0.506528\pi$
$488$		0			0
$489$			44.4449i			2.00987i
$490$		0			0
$491$	−1.17398	+	1.17398i	−0.0529808	+	0.0529808i	−0.733101	−	0.680120i	$-0.761928\pi$
$491$	−1.17398	+	1.17398i	−0.0529808	+	0.0529808i	0.680120	+	0.733101i	$0.261928\pi$
$492$		0			0
$493$	12.3129	−	12.3129i	0.554545	−	0.554545i
$494$		0			0
$495$	20.7327	−	12.0846i	0.931867	−	0.543164i
$496$		0			0
$497$			15.0711i			0.676032i
$498$		0			0
$499$	−11.3509	−	11.3509i	−0.508135	−	0.508135i	0.405819	−	0.913954i	$-0.366986\pi$
$499$	−11.3509	−	11.3509i	−0.508135	−	0.508135i	−0.913954	+	0.405819i	$0.866986\pi$
$500$		0			0
$501$	−2.66025	+	2.66025i	−0.118851	+	0.118851i
$502$		0			0
$503$	−10.1343			−0.451866			−0.225933	−	0.974143i	$-0.572543\pi$
$503$	−10.1343			−0.451866			−0.225933	+	0.974143i	$0.572543\pi$
$504$		0			0
$505$	8.81564	+	15.1244i	0.392291	+	0.673025i
$506$		0			0
$507$	−5.43888	−	5.43888i	−0.241549	−	0.241549i
$508$		0			0
$509$	−9.00000	−	9.00000i	−0.398918	−	0.398918i	0.478933	−	0.877851i	$-0.341024\pi$
$509$	−9.00000	−	9.00000i	−0.398918	−	0.398918i	−0.877851	+	0.478933i	$0.841024\pi$
$510$		0			0
$511$	−20.0764			−0.888127
$512$		0			0
$513$			7.53556i			0.332703i
$514$		0			0
$515$	−4.14746	+	15.7386i	−0.182759	+	0.693524i
$516$		0			0
$517$	−1.32194	−	1.32194i	−0.0581387	−	0.0581387i
$518$		0			0
$519$			26.7685i			1.17501i
$520$		0			0
$521$		−	41.1769i		−	1.80399i	−0.431743	−	0.901997i	$-0.642101\pi$
$521$		−	41.1769i		−	1.80399i	0.431743	−	0.901997i	$-0.357899\pi$
$522$		0			0
$523$	−19.9965	−	19.9965i	−0.874384	−	0.874384i	0.118563	−	0.992947i	$-0.462171\pi$
$523$	−19.9965	−	19.9965i	−0.874384	−	0.874384i	−0.992947	+	0.118563i	$0.962171\pi$
$524$		0			0
$525$	−44.0513	+	12.1949i	−1.92256	+	0.532228i
$526$		0			0
$527$		−	2.85550i		−	0.124388i
$528$		0			0
$529$	−11.5885			−0.503846
$530$		0			0
$531$	−8.24504	−	8.24504i	−0.357804	−	0.357804i
$532$		0			0
$533$	−7.10886	−	7.10886i	−0.307919	−	0.307919i
$534$		0			0
$535$	−16.5079	+	9.62209i	−0.713700	+	0.415999i
$536$		0			0
$537$	−49.1373			−2.12043
$538$		0			0
$539$	46.7062	−	46.7062i	2.01178	−	2.01178i
$540$		0			0
$541$	2.85641	+	2.85641i	0.122807	+	0.122807i	0.765839	−	0.643032i	$-0.222324\pi$
$541$	2.85641	+	2.85641i	0.122807	+	0.122807i	−0.643032	+	0.765839i	$0.722324\pi$
$542$		0			0
$543$			23.1833i			0.994889i
$544$		0			0
$545$	20.9282	−	12.1986i	0.896466	−	0.522530i
$546$		0			0
$547$	18.9513	−	18.9513i	0.810298	−	0.810298i	−0.174381	−	0.984678i	$-0.555792\pi$
$547$	18.9513	−	18.9513i	0.810298	−	0.810298i	0.984678	+	0.174381i	$0.0557923\pi$
$548$		0			0
$549$	−3.46410	+	3.46410i	−0.147844	+	0.147844i
$550$		0			0
$551$		−	17.2480i		−	0.734788i
$552$		0			0
$553$	16.2369			0.690462
$554$		0			0
$555$	13.2092	−	50.1258i	0.560701	−	2.12772i
$556$		0			0
$557$	−7.96225	+	7.96225i	−0.337371	+	0.337371i	−0.855377	−	0.518006i	$-0.826675\pi$
$557$	−7.96225	+	7.96225i	−0.337371	+	0.337371i	0.518006	+	0.855377i	$0.326675\pi$
$558$		0			0
$559$	21.3891			0.904661
$560$		0			0
$561$	37.1769			1.56961
$562$		0			0
$563$	−27.5770	+	27.5770i	−1.16223	+	1.16223i	−0.178244	+	0.983986i	$0.557042\pi$
$563$	−27.5770	+	27.5770i	−1.16223	+	1.16223i	−0.983986	+	0.178244i	$0.942958\pi$
$564$		0			0
$565$	18.8144	+	4.95801i	0.791528	+	0.208585i
$566$		0			0
$567$	−47.0508			−1.97595
$568$		0			0
$569$		−	33.5167i		−	1.40509i	−0.711639	−	0.702546i	$-0.752047\pi$
$569$		−	33.5167i		−	1.40509i	0.711639	−	0.702546i	$-0.247953\pi$
$570$		0			0
$571$	−8.24504	+	8.24504i	−0.345044	+	0.345044i	−0.858260	−	0.513215i	$-0.828454\pi$
$571$	−8.24504	+	8.24504i	−0.345044	+	0.345044i	0.513215	+	0.858260i	$0.328454\pi$
$572$		0			0
$573$	−6.36980	+	6.36980i	−0.266102	+	0.266102i
$574$		0			0
$575$	14.6969	+	8.32398i	0.612905	+	0.347134i
$576$		0			0
$577$			19.7341i			0.821543i	0.911738	+	0.410771i	$0.134741\pi$
$577$			19.7341i			0.821543i	−0.911738	+	0.410771i	$0.865259\pi$
$578$		0			0
$579$	3.76217	+	3.76217i	0.156350	+	0.156350i
$580$		0			0
$581$	−14.6603	+	14.6603i	−0.608210	+	0.608210i
$582$		0			0
$583$	−43.2310			−1.79044
$584$		0			0
$585$	10.2938	−	6.00000i	0.425595	−	0.248069i
$586$		0			0
$587$	16.3975	+	16.3975i	0.676797	+	0.676797i	0.959274	−	0.282477i	$-0.0911562\pi$
$587$	16.3975	+	16.3975i	0.676797	+	0.676797i	−0.282477	+	0.959274i	$0.591156\pi$
$588$		0			0
$589$	−2.00000	−	2.00000i	−0.0824086	−	0.0824086i
$590$		0			0
$591$	3.10583			0.127757
$592$		0			0
$593$			34.4929i			1.41645i	0.705985	+	0.708226i	$0.250504\pi$
$593$			34.4929i			1.41645i	−0.705985	+	0.708226i	$0.749496\pi$
$594$		0			0
$595$	−25.0629	−	6.60462i	−1.02748	−	0.270763i
$596$		0			0
$597$	21.4409	+	21.4409i	0.877518	+	0.877518i
$598$		0			0
$599$		−	20.3538i		−	0.831633i	−0.909448	−	0.415817i	$-0.863496\pi$
$599$		−	20.3538i		−	0.831633i	0.909448	−	0.415817i	$-0.136504\pi$
$600$		0			0
$601$		−	20.5885i		−	0.839821i	−0.907566	−	0.419910i	$-0.862062\pi$
$601$		−	20.5885i		−	0.839821i	0.907566	−	0.419910i	$-0.137938\pi$
$602$		0			0
$603$	7.47007	+	7.47007i	0.304205	+	0.304205i
$604$		0			0
$605$	59.2290	+	15.6081i	2.40800	+	0.634561i
$606$		0			0
$607$			26.5614i			1.07809i	0.842276	+	0.539046i	$0.181215\pi$
$607$			26.5614i			1.07809i	−0.842276	+	0.539046i	$0.818785\pi$
$608$		0			0
$609$	57.7128			2.33864
$610$		0			0
$611$	−0.656339	−	0.656339i	−0.0265526	−	0.0265526i
$612$		0			0
$613$	18.8389	+	18.8389i	0.760896	+	0.760896i	0.976484	−	0.215589i	$-0.0691670\pi$
$613$	18.8389	+	18.8389i	0.760896	+	0.760896i	−0.215589	+	0.976484i	$0.569167\pi$
$614$		0			0
$615$	−13.7333	+	8.00481i	−0.553779	+	0.322785i
$616$		0			0
$617$	5.08971			0.204904			0.102452	−	0.994738i	$-0.467331\pi$
$617$	5.08971			0.204904			0.102452	+	0.994738i	$0.467331\pi$
$618$		0			0
$619$	−10.8976	+	10.8976i	−0.438012	+	0.438012i	−0.891342	−	0.453331i	$-0.850236\pi$
$619$	−10.8976	+	10.8976i	−0.438012	+	0.438012i	0.453331	+	0.891342i	$0.350236\pi$
$620$		0			0
$621$	6.58846	+	6.58846i	0.264386	+	0.264386i
$622$		0			0
$623$		−	31.3672i		−	1.25670i
$624$		0			0
$625$	12.8564	+	21.4409i	0.514256	+	0.857637i
$626$		0			0
$627$	26.0388	−	26.0388i	1.03989	−	1.03989i
$628$		0			0
$629$	20.7846	−	20.7846i	0.828737	−	0.828737i
$630$		0			0
$631$			2.55103i			0.101555i	0.998710	+	0.0507774i	$0.0161699\pi$
$631$			2.55103i			0.101555i	−0.998710	+	0.0507774i	$0.983830\pi$
$632$		0			0
$633$	−40.7483			−1.61960
$634$		0			0
$635$	−12.1738	−	3.20807i	−0.483103	−	0.127308i
$636$		0			0
$637$	23.1895	−	23.1895i	0.918803	−	0.918803i
$638$		0			0
$639$	−6.21166			−0.245729
$640$		0			0
$641$	−20.5885			−0.813195			−0.406598	−	0.913607i	$-0.633285\pi$
$641$	−20.5885			−0.813195			−0.406598	+	0.913607i	$0.633285\pi$
$642$		0			0
$643$	9.42042	−	9.42042i	0.371505	−	0.371505i	−0.496520	−	0.868025i	$-0.665389\pi$
$643$	9.42042	−	9.42042i	0.371505	−	0.371505i	0.868025	+	0.496520i	$0.165389\pi$
$644$		0			0
$645$	8.61786	−	32.7026i	0.339328	−	1.28767i
$646$		0			0
$647$	7.49966			0.294842			0.147421	−	0.989074i	$-0.452903\pi$
$647$	7.49966			0.294842			0.147421	+	0.989074i	$0.452903\pi$
$648$		0			0
$649$		−	41.7128i		−	1.63737i
$650$		0			0
$651$	6.69213	−	6.69213i	0.262285	−	0.262285i
$652$		0			0
$653$	−2.60202	+	2.60202i	−0.101825	+	0.101825i	−0.756184	−	0.654359i	$-0.772939\pi$
$653$	−2.60202	+	2.60202i	−0.101825	+	0.101825i	0.654359	+	0.756184i	$0.272939\pi$
$654$		0			0
$655$	−15.0759	+	8.78739i	−0.589063	+	0.343352i
$656$		0			0
$657$		−	8.27462i		−	0.322823i
$658$		0			0
$659$	−3.90087	−	3.90087i	−0.151956	−	0.151956i	0.627035	−	0.778991i	$-0.284268\pi$
$659$	−3.90087	−	3.90087i	−0.151956	−	0.151956i	−0.778991	+	0.627035i	$0.784268\pi$
$660$		0			0
$661$	−3.26795	+	3.26795i	−0.127108	+	0.127108i	−0.767799	−	0.640691i	$-0.778648\pi$
$661$	−3.26795	+	3.26795i	−0.127108	+	0.127108i	0.640691	+	0.767799i	$0.278648\pi$
$662$		0			0
$663$	18.4583			0.716860
$664$		0			0
$665$	−22.1800	+	12.9282i	−0.860102	+	0.501334i
$666$		0			0
$667$	−15.0802	−	15.0802i	−0.583907	−	0.583907i
$668$		0			0
$669$	16.2679	+	16.2679i	0.628955	+	0.628955i
$670$		0			0
$671$	−17.5254			−0.676559
$672$		0			0
$673$			17.5170i			0.675229i	0.941284	+	0.337614i	$0.109620\pi$
$673$			17.5170i			0.675229i	−0.941284	+	0.337614i	$0.890380\pi$
$674$		0			0
$675$	3.67943	+	13.2911i	0.141621	+	0.511576i
$676$		0			0
$677$	−15.2273	−	15.2273i	−0.585232	−	0.585232i	0.351104	−	0.936336i	$-0.385806\pi$
$677$	−15.2273	−	15.2273i	−0.585232	−	0.585232i	−0.936336	+	0.351104i	$0.885806\pi$
$678$		0			0
$679$			66.4408i			2.54977i
$680$		0			0
$681$			23.6603i			0.906663i
$682$		0			0
$683$	1.83991	+	1.83991i	0.0704021	+	0.0704021i	0.741431	−	0.671029i	$-0.234147\pi$
$683$	1.83991	+	1.83991i	0.0704021	+	0.0704021i	−0.671029	+	0.741431i	$0.734147\pi$
$684$		0			0
$685$	−2.47900	+	9.40721i	−0.0947179	+	0.359431i
$686$		0			0
$687$		−	42.8484i		−	1.63477i
$688$		0			0
$689$	−21.4641			−0.817717
$690$		0			0
$691$	−15.3161	−	15.3161i	−0.582652	−	0.582652i	0.352979	−	0.935631i	$-0.385169\pi$
$691$	−15.3161	−	15.3161i	−0.582652	−	0.582652i	−0.935631	+	0.352979i	$0.885169\pi$
$692$		0			0
$693$	31.8909	+	31.8909i	1.21143	+	1.21143i
$694$		0			0
$695$	8.62570	+	14.7985i	0.327191	+	0.561338i
$696$		0			0
$697$	−9.01367			−0.341417
$698$		0			0
$699$	43.9149	−	43.9149i	1.66102	−	1.66102i
$700$		0			0
$701$	29.6603	+	29.6603i	1.12025	+	1.12025i	0.991703	+	0.128549i	$0.0410320\pi$
$701$	29.6603	+	29.6603i	1.12025	+	1.12025i	0.128549	+	0.991703i	$0.458968\pi$
$702$		0			0
$703$		−	29.1152i		−	1.09810i
$704$		0			0
$705$	−1.26795	+	0.739059i	−0.0477537	+	0.0278346i
$706$		0			0
$707$	−23.2641	+	23.2641i	−0.874937	+	0.874937i
$708$		0			0
$709$	17.0000	−	17.0000i	0.638448	−	0.638448i	−0.311724	−	0.950173i	$-0.600907\pi$
$709$	17.0000	−	17.0000i	0.638448	−	0.638448i	0.950173	+	0.311724i	$0.100907\pi$
$710$		0			0
$711$			6.69213i			0.250974i
$712$		0			0
$713$	−3.49726			−0.130974
$714$		0			0
$715$	41.2162	+	10.8614i	1.54140	+	0.406192i
$716$		0			0
$717$	27.6964	−	27.6964i	1.03434	−	1.03434i
$718$		0			0
$719$	−49.6733			−1.85250			−0.926251	−	0.376906i	$-0.876988\pi$
$719$	−49.6733			−1.85250			−0.926251	+	0.376906i	$0.876988\pi$
$720$		0			0
$721$	−30.5885			−1.13917
$722$		0			0
$723$	33.9210	−	33.9210i	1.26154	−	1.26154i
$724$		0			0
$725$	−8.42177	−	30.4218i	−0.312777	−	1.12984i
$726$		0			0
$727$	5.85104			0.217003			0.108501	−	0.994096i	$-0.465395\pi$
$727$	5.85104			0.217003			0.108501	+	0.994096i	$0.465395\pi$
$728$		0			0
$729$		−	1.39230i		−	0.0515668i
$730$		0			0
$731$	13.5601	−	13.5601i	0.501539	−	0.501539i
$732$		0			0
$733$	22.6067	−	22.6067i	0.834996	−	0.834996i	−0.153199	−	0.988195i	$-0.548958\pi$
$733$	22.6067	−	22.6067i	0.834996	−	0.834996i	0.988195	+	0.153199i	$0.0489575\pi$
$734$		0			0
$735$	−26.1122	−	44.7988i	−0.963162	−	1.65243i
$736$		0			0
$737$			37.7921i			1.39209i
$738$		0			0
$739$	−18.5235	−	18.5235i	−0.681397	−	0.681397i	0.278918	−	0.960315i	$-0.410024\pi$
$739$	−18.5235	−	18.5235i	−0.681397	−	0.681397i	−0.960315	+	0.278918i	$0.910024\pi$
$740$		0			0
$741$	12.9282	−	12.9282i	0.474929	−	0.474929i
$742$		0			0
$743$	−29.4169			−1.07920			−0.539600	−	0.841921i	$-0.681425\pi$
$743$	−29.4169			−1.07920			−0.539600	+	0.841921i	$0.681425\pi$
$744$		0			0
$745$	−15.0711	−	25.8564i	−0.552163	−	0.947305i
$746$		0			0
$747$	−6.04232	−	6.04232i	−0.221077	−	0.221077i
$748$		0			0
$749$	−25.3923	−	25.3923i	−0.927815	−	0.927815i
$750$		0			0
$751$	37.3244			1.36199			0.680993	−	0.732290i	$-0.261549\pi$
$751$	37.3244			1.36199			0.680993	+	0.732290i	$0.261549\pi$
$752$		0			0
$753$		−	45.0990i		−	1.64350i
$754$		0			0
$755$	5.51596	+	1.45357i	0.200746	+	0.0529010i
$756$		0			0
$757$	20.5875	+	20.5875i	0.748266	+	0.748266i	0.974153	−	0.225887i	$-0.0725281\pi$
$757$	20.5875	+	20.5875i	0.748266	+	0.748266i	−0.225887	+	0.974153i	$0.572528\pi$
$758$		0			0
$759$		−	45.5322i		−	1.65272i
$760$		0			0
$761$			26.3923i			0.956720i	0.878164	+	0.478360i	$0.158769\pi$
$761$			26.3923i			0.956720i	−0.878164	+	0.478360i	$0.841231\pi$
$762$		0			0
$763$	32.1915	+	32.1915i	1.16541	+	1.16541i
$764$		0			0
$765$	2.72214	−	10.3298i	0.0984190	−	0.373476i
$766$		0			0
$767$		−	20.7103i		−	0.747807i
$768$		0			0
$769$	−19.1769			−0.691537			−0.345769	−	0.938320i	$-0.612382\pi$
$769$	−19.1769			−0.691537			−0.345769	+	0.938320i	$0.612382\pi$
$770$		0			0
$771$	26.2880	+	26.2880i	0.946741	+	0.946741i
$772$		0			0
$773$	−2.91439	−	2.91439i	−0.104823	−	0.104823i	0.652750	−	0.757573i	$-0.273615\pi$
$773$	−2.91439	−	2.91439i	−0.104823	−	0.104823i	−0.757573	+	0.652750i	$0.773615\pi$
$774$		0			0
$775$	−4.50413	−	2.55103i	−0.161793	−	0.0916355i
$776$		0			0
$777$	97.4212			3.49497
$778$		0			0
$779$	−6.31319	+	6.31319i	−0.226194	+	0.226194i
$780$		0			0
$781$	−15.7128	−	15.7128i	−0.562249	−	0.562249i
$782$		0			0
$783$		−	17.4131i		−	0.622293i
$784$		0			0
$785$	14.5359	+	24.9382i	0.518808	+	0.890082i
$786$		0			0
$787$	−18.8704	+	18.8704i	−0.672658	+	0.672658i	−0.958328	−	0.285670i	$-0.907784\pi$
$787$	−18.8704	+	18.8704i	−0.672658	+	0.672658i	0.285670	+	0.958328i	$0.407784\pi$
$788$		0			0
$789$	−14.3205	+	14.3205i	−0.509824	+	0.509824i
$790$		0			0
$791$			36.5665i			1.30015i
$792$		0			0
$793$	−8.70131			−0.308993
$794$		0			0
$795$	−8.64809	+	32.8174i	−0.306716	+	1.16391i
$796$		0			0
$797$	−10.1376	+	10.1376i	−0.359092	+	0.359092i	−0.863478	−	0.504386i	$-0.831719\pi$
$797$	−10.1376	+	10.1376i	−0.359092	+	0.359092i	0.504386	+	0.863478i	$0.331719\pi$
$798$		0			0
$799$	−0.832204			−0.0294413
$800$		0			0
$801$	12.9282			0.456796
$802$		0			0
$803$	20.9312	−	20.9312i	0.738646	−	0.738646i
$804$		0			0
$805$	−8.08897	+	30.6956i	−0.285099	+	1.08188i
$806$		0			0
$807$	−15.1610			−0.533693
$808$		0			0
$809$			29.1769i			1.02581i	0.858447	+	0.512903i	$0.171430\pi$
$809$			29.1769i			1.02581i	−0.858447	+	0.512903i	$0.828570\pi$
$810$		0			0
$811$	18.5235	−	18.5235i	0.650447	−	0.650447i	−0.302653	−	0.953101i	$-0.597872\pi$
$811$	18.5235	−	18.5235i	0.650447	−	0.650447i	0.953101	+	0.302653i	$0.0978725\pi$
$812$		0			0
$813$	−36.0853	+	36.0853i	−1.26557	+	1.26557i
$814$		0			0
$815$	23.0064	+	39.4703i	0.805877	+	1.38259i
$816$		0			0
$817$		−	18.9951i		−	0.664553i
$818$		0			0
$819$	15.8338	+	15.8338i	0.553276	+	0.553276i
$820$		0			0
$821$	33.9090	−	33.9090i	1.18343	−	1.18343i	0.204582	−	0.978850i	$-0.434417\pi$
$821$	33.9090	−	33.9090i	1.18343	−	1.18343i	0.978850	−	0.204582i	$-0.0655833\pi$
$822$		0			0
$823$	26.9439			0.939207			0.469603	−	0.882878i	$-0.344397\pi$
$823$	26.9439			0.939207			0.469603	+	0.882878i	$0.344397\pi$
$824$		0			0
$825$	33.2128	−	58.6410i	1.15632	−	2.04162i
$826$		0			0
$827$	21.5051	+	21.5051i	0.747804	+	0.747804i	0.974066	−	0.226262i	$-0.0726507\pi$
$827$	21.5051	+	21.5051i	0.747804	+	0.747804i	−0.226262	+	0.974066i	$0.572651\pi$
$828$		0			0
$829$	19.3205	+	19.3205i	0.671029	+	0.671029i	0.957953	−	0.286924i	$-0.0926328\pi$
$829$	19.3205	+	19.3205i	0.671029	+	0.671029i	−0.286924	+	0.957953i	$0.592633\pi$
$830$		0			0
$831$	9.79796			0.339887
$832$		0			0
$833$		−	29.4032i		−	1.01876i
$834$		0			0
$835$	−0.985453	+	3.73955i	−0.0341030	+	0.129412i
$836$		0			0
$837$	−2.01915	−	2.01915i	−0.0697919	−	0.0697919i
$838$		0			0
$839$			29.3195i			1.01222i	0.862468	+	0.506112i	$0.168918\pi$
$839$			29.3195i			1.01222i	−0.862468	+	0.506112i	$0.831082\pi$
$840$		0			0
$841$			10.8564i			0.374359i
$842$		0			0
$843$	−23.8676	−	23.8676i	−0.822042	−	0.822042i
$844$		0			0
$845$	−7.64550	−	2.01476i	−0.263013	−	0.0693097i
$846$		0			0
$847$			115.114i			3.95535i
$848$		0			0
$849$	58.3013			2.00089
$850$		0			0
$851$	−25.4558	−	25.4558i	−0.872615	−	0.872615i
$852$		0			0
$853$	−33.7957	−	33.7957i	−1.15714	−	1.15714i	−0.985087	−	0.172054i	$-0.944960\pi$
$853$	−33.7957	−	33.7957i	−1.15714	−	1.15714i	−0.172054	−	0.985087i	$-0.555040\pi$
$854$		0			0
$855$	−5.32844	−	9.14162i	−0.182229	−	0.312637i
$856$		0			0
$857$	−17.0903			−0.583792			−0.291896	−	0.956450i	$-0.594286\pi$
$857$	−17.0903			−0.583792			−0.291896	+	0.956450i	$0.594286\pi$
$858$		0			0
$859$	−22.2856	+	22.2856i	−0.760376	+	0.760376i	−0.976390	−	0.216014i	$-0.930694\pi$
$859$	−22.2856	+	22.2856i	−0.760376	+	0.760376i	0.216014	+	0.976390i	$0.430694\pi$
$860$		0			0
$861$	−21.1244	−	21.1244i	−0.719916	−	0.719916i
$862$		0			0
$863$		−	23.8676i		−	0.812461i	−0.913771	−	0.406231i	$-0.866843\pi$
$863$		−	23.8676i		−	0.812461i	0.913771	−	0.406231i	$-0.133157\pi$
$864$		0			0
$865$	13.8564	+	23.7724i	0.471132	+	0.808287i
$866$		0			0
$867$	−14.4471	+	14.4471i	−0.490651	+	0.490651i
$868$		0			0
$869$	−16.9282	+	16.9282i	−0.574250	+	0.574250i
$870$		0			0
$871$			18.7637i			0.635784i
$872$		0			0
$873$	−27.3840			−0.926809
$874$		0			0
$875$	−32.8083	+	33.6326i	−1.10912	+	1.13699i
$876$		0			0
$877$	−30.0279	+	30.0279i	−1.01397	+	1.01397i	−0.0140689	+	0.999901i	$0.504478\pi$
$877$	−30.0279	+	30.0279i	−1.01397	+	1.01397i	−0.999901	+	0.0140689i	$0.995522\pi$
$878$		0			0
$879$	1.31268			0.0442755
$880$		0			0
$881$	45.5167			1.53350			0.766748	−	0.641949i	$-0.221874\pi$
$881$	45.5167			1.53350			0.766748	+	0.641949i	$0.221874\pi$
$882$		0			0
$883$	2.96594	−	2.96594i	0.0998119	−	0.0998119i	−0.655438	−	0.755249i	$-0.727516\pi$
$883$	2.96594	−	2.96594i	0.0998119	−	0.0998119i	0.755249	+	0.655438i	$0.227516\pi$
$884$		0			0
$885$	−31.6649	−	8.34439i	−1.06440	−	0.280494i
$886$		0			0
$887$	−46.0648			−1.54671			−0.773353	−	0.633976i	$-0.781422\pi$
$887$	−46.0648			−1.54671			−0.773353	+	0.633976i	$0.781422\pi$
$888$		0			0
$889$		−	23.6603i		−	0.793539i
$890$		0			0
$891$	49.0542	−	49.0542i	1.64338	−	1.64338i
$892$		0			0
$893$	−0.582877	+	0.582877i	−0.0195052	+	0.0195052i
$894$		0			0
$895$	−43.6375	+	25.4353i	−1.45864	+	0.850210i
$896$		0			0
$897$		−	22.6067i		−	0.754815i
$898$		0			0
$899$	4.62158	+	4.62158i	0.154138	+	0.154138i
$900$		0			0
$901$	−13.6077	+	13.6077i	−0.453338	+	0.453338i
$902$		0			0
$903$	63.5588			2.11510
$904$		0			0
$905$	12.0005	+	20.5885i	0.398912	+	0.684383i
$906$		0			0
$907$	16.9201	+	16.9201i	0.561822	+	0.561822i	0.929825	−	0.368003i	$-0.119958\pi$
$907$	16.9201	+	16.9201i	0.561822	+	0.561822i	−0.368003	+	0.929825i	$0.619958\pi$
$908$		0			0
$909$	−9.58846	−	9.58846i	−0.318029	−	0.318029i
$910$		0			0
$911$	43.2586			1.43322			0.716611	−	0.697473i	$-0.245692\pi$
$911$	43.2586			1.43322			0.716611	+	0.697473i	$0.245692\pi$
$912$		0			0
$913$		−	30.5689i		−	1.01168i
$914$		0			0
$915$	−3.50584	+	13.3038i	−0.115900	+	0.439810i
$916$		0			0
$917$	−23.1895	−	23.1895i	−0.765786	−	0.765786i
$918$		0			0
$919$		−	24.9010i		−	0.821410i	−0.911768	−	0.410705i	$-0.865283\pi$
$919$		−	24.9010i		−	0.821410i	0.911768	−	0.410705i	$-0.134717\pi$
$920$		0			0
$921$			36.5885i			1.20563i
$922$		0			0
$923$	−7.80138	−	7.80138i	−0.256786	−	0.256786i
$924$		0			0
$925$	−14.2162	−	51.3530i	−0.467427	−	1.68848i
$926$		0			0
$927$		−	12.6072i		−	0.414076i
$928$		0			0
$929$	−21.2679			−0.697779			−0.348889	−	0.937164i	$-0.613441\pi$
$929$	−21.2679			−0.697779			−0.348889	+	0.937164i	$0.613441\pi$
$930$		0			0
$931$	−20.5940	−	20.5940i	−0.674942	−	0.674942i
$932$		0			0
$933$	47.1182	+	47.1182i	1.54258	+	1.54258i
$934$		0			0
$935$	33.0158	−	19.2442i	1.07973	−	0.629352i
$936$		0			0
$937$	2.75821			0.0901066			0.0450533	−	0.998985i	$-0.485654\pi$
$937$	2.75821			0.0901066			0.0450533	+	0.998985i	$0.485654\pi$
$938$		0			0
$939$	−48.1576	+	48.1576i	−1.57156	+	1.57156i
$940$		0			0
$941$	−0.0717968	−	0.0717968i	−0.00234051	−	0.00234051i	0.705936	−	0.708276i	$-0.250527\pi$
$941$	−0.0717968	−	0.0717968i	−0.00234051	−	0.00234051i	−0.708276	+	0.705936i	$0.750527\pi$
$942$		0			0
$943$			11.0395i			0.359494i
$944$		0			0
$945$	−22.3923	+	13.0520i	−0.728422	+	0.424581i
$946$		0			0
$947$	−17.4427	+	17.4427i	−0.566811	+	0.566811i	−0.931234	−	0.364423i	$-0.881266\pi$
$947$	−17.4427	+	17.4427i	−0.566811	+	0.566811i	0.364423	+	0.931234i	$0.381266\pi$
$948$		0			0
$949$	10.3923	−	10.3923i	0.337348	−	0.337348i
$950$		0			0
$951$			23.6627i			0.767315i
$952$		0			0
$953$	51.8955			1.68106			0.840530	−	0.541765i	$-0.182244\pi$
$953$	51.8955			1.68106			0.840530	+	0.541765i	$0.182244\pi$
$954$		0			0
$955$	−2.35960	+	8.95411i	−0.0763549	+	0.289748i
$956$		0			0
$957$	−60.1701	+	60.1701i	−1.94502	+	1.94502i
$958$		0			0
$959$	−18.2832			−0.590397
$960$		0			0
$961$	−29.9282			−0.965426
$962$		0			0
$963$	10.4656	−	10.4656i	0.337249	−	0.337249i
$964$		0			0
$965$	5.28852	+	1.39364i	0.170244	+	0.0448629i
$966$		0			0
$967$	−24.6919			−0.794037			−0.397018	−	0.917811i	$-0.629955\pi$
$967$	−24.6919			−0.794037			−0.397018	+	0.917811i	$0.629955\pi$
$968$		0			0
$969$		−	16.3923i		−	0.526597i
$970$		0			0
$971$	−15.8709	+	15.8709i	−0.509322	+	0.509322i	−0.914318	−	0.404996i	$-0.867273\pi$
$971$	−15.8709	+	15.8709i	−0.509322	+	0.509322i	0.404996	+	0.914318i	$0.367273\pi$
$972$		0			0
$973$	−22.7629	+	22.7629i	−0.729743	+	0.729743i
$974$		0			0
$975$	16.4901	−	29.1152i	0.528106	−	0.932431i
$976$		0			0
$977$		−	59.8578i		−	1.91502i	−0.288401	−	0.957510i	$-0.593124\pi$
$977$		−	59.8578i		−	1.91502i	0.288401	−	0.957510i	$-0.406876\pi$
$978$		0			0
$979$	32.7028	+	32.7028i	1.04519	+	1.04519i
$980$		0			0
$981$	−13.2679	+	13.2679i	−0.423613	+	0.423613i
$982$		0			0
$983$	−21.4538			−0.684270			−0.342135	−	0.939651i	$-0.611150\pi$
$983$	−21.4538			−0.684270			−0.342135	+	0.939651i	$0.611150\pi$
$984$		0			0
$985$	2.75821	−	1.60770i	0.0878837	−	0.0512254i
$986$		0			0
$987$	−1.95035	−	1.95035i	−0.0620802	−	0.0620802i
$988$		0			0
$989$	−16.6077	−	16.6077i	−0.528094	−	0.528094i
$990$		0			0
$991$	−32.4254			−1.03003			−0.515013	−	0.857182i	$-0.672213\pi$
$991$	−32.4254			−1.03003			−0.515013	+	0.857182i	$0.672213\pi$
$992$		0			0
$993$			12.3129i			0.390738i
$994$		0			0
$995$	30.1397	+	7.94248i	0.955494	+	0.251794i
$996$		0			0
$997$	11.6157	+	11.6157i	0.367873	+	0.367873i	0.866701	−	0.498828i	$-0.166236\pi$
$997$	11.6157	+	11.6157i	0.367873	+	0.367873i	−0.498828	+	0.866701i	$0.666236\pi$
$998$		0			0
$999$		−	29.3939i		−	0.929981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.q.a.1089.2	yes	16
4.3	odd	2	inner	1280.2.q.a.1089.8	yes	16
5.4	even	2	inner	1280.2.q.a.1089.7	yes	16
8.3	odd	2		1280.2.q.b.1089.1	yes	16
8.5	even	2		1280.2.q.b.1089.7	yes	16
16.3	odd	4		1280.2.q.b.449.8	yes	16
16.5	even	4	inner	1280.2.q.a.449.7	yes	16
16.11	odd	4	inner	1280.2.q.a.449.1	✓	16
16.13	even	4		1280.2.q.b.449.2	yes	16
20.19	odd	2	inner	1280.2.q.a.1089.1	yes	16
40.19	odd	2		1280.2.q.b.1089.8	yes	16
40.29	even	2		1280.2.q.b.1089.2	yes	16
80.19	odd	4		1280.2.q.b.449.1	yes	16
80.29	even	4		1280.2.q.b.449.7	yes	16
80.59	odd	4	inner	1280.2.q.a.449.8	yes	16
80.69	even	4	inner	1280.2.q.a.449.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.q.a.449.1	✓	16	16.11	odd	4	inner
1280.2.q.a.449.2	yes	16	80.69	even	4	inner
1280.2.q.a.449.7	yes	16	16.5	even	4	inner
1280.2.q.a.449.8	yes	16	80.59	odd	4	inner
1280.2.q.a.1089.1	yes	16	20.19	odd	2	inner
1280.2.q.a.1089.2	yes	16	1.1	even	1	trivial
1280.2.q.a.1089.7	yes	16	5.4	even	2	inner
1280.2.q.a.1089.8	yes	16	4.3	odd	2	inner
1280.2.q.b.449.1	yes	16	80.19	odd	4
1280.2.q.b.449.2	yes	16	16.13	even	4
1280.2.q.b.449.7	yes	16	80.29	even	4
1280.2.q.b.449.8	yes	16	16.3	odd	4
1280.2.q.b.1089.1	yes	16	8.3	odd	2
1280.2.q.b.1089.2	yes	16	40.29	even	2
1280.2.q.b.1089.7	yes	16	8.5	even	2
1280.2.q.b.1089.8	yes	16	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53819 + 1.53819i) q^{3} +(-0.569800 + 2.16225i) q^{5} -4.20241 q^{7} -1.73205i q^{9} +O(q^{10})\)	\(q+(-1.53819 + 1.53819i) q^{3} +(-0.569800 + 2.16225i) q^{5} -4.20241 q^{7} -1.73205i q^{9} +(4.38134 - 4.38134i) q^{11} +(2.17533 - 2.17533i) q^{13} +(-2.44949 - 4.20241i) q^{15} -2.75821i q^{17} +(-1.93185 - 1.93185i) q^{19} +(6.46410 - 6.46410i) q^{21} -3.37810 q^{23} +(-4.35066 - 2.46410i) q^{25} +(-1.95035 - 1.95035i) q^{27} +(4.46410 + 4.46410i) q^{29} +1.03528 q^{31} +13.4787i q^{33} +(2.39453 - 9.08666i) q^{35} +(7.53556 + 7.53556i) q^{37} +6.69213i q^{39} -3.26795i q^{41} +(4.91629 + 4.91629i) q^{43} +(3.74513 + 0.986923i) q^{45} -0.301719i q^{47} +10.6603 q^{49} +(4.24264 + 4.24264i) q^{51} +(-4.93353 - 4.93353i) q^{53} +(6.97707 + 11.9700i) q^{55} +5.94311 q^{57} +(4.76028 - 4.76028i) q^{59} +(-2.00000 - 2.00000i) q^{61} +7.27879i q^{63} +(3.46410 + 5.94311i) q^{65} +(-4.31285 + 4.31285i) q^{67} +(5.19615 - 5.19615i) q^{69} -3.58630i q^{71} +4.77735 q^{73} +(10.4824 - 2.90188i) q^{75} +(-18.4122 + 18.4122i) q^{77} -3.86370 q^{79} +11.1962 q^{81} +(3.48853 - 3.48853i) q^{83} +(5.96393 + 1.57163i) q^{85} -13.7333 q^{87} +7.46410i q^{89} +(-9.14162 + 9.14162i) q^{91} +(-1.59245 + 1.59245i) q^{93} +(5.27792 - 3.07638i) q^{95} -15.8102i q^{97} +(-7.58871 - 7.58871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5}+O(q^{10}) \) 16 * q - 8 * q^5	\( 16 q - 8 q^{5} + 48 q^{21} + 16 q^{29} + 24 q^{45} + 32 q^{49} - 32 q^{61} + 96 q^{81} - 48 q^{85}+O(q^{100}) \) 16 * q - 8 * q^5 + 48 * q^21 + 16 * q^29 + 24 * q^45 + 32 * q^49 - 32 * q^61 + 96 * q^81 - 48 * q^85

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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