LMFDB - Embedded newform 1280.2.q.a.449.5

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			449.5
Root			$0.500000 - 1.74530i$ of defining polynomial
Character	$\chi$	$=$	1280.449
Dual form			1280.2.q.a.1089.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.796225 + 0.796225i) q^{3} +(-1.17216 + 1.90421i) q^{5} -0.582877 q^{7} -1.73205i q^{9} +O(q^{10})$	\(q+(0.796225 + 0.796225i) q^{3} +(-1.17216 + 1.90421i) q^{5} -0.582877 q^{7} -1.73205i q^{9} +(2.96713 + 2.96713i) q^{11} +(1.12603 + 1.12603i) q^{13} +(-2.44949 + 0.582877i) q^{15} +5.32844i q^{17} +(-0.517638 + 0.517638i) q^{19} +(-0.464102 - 0.464102i) q^{21} -6.52598 q^{23} +(-2.25207 - 4.46410i) q^{25} +(3.76778 - 3.76778i) q^{27} +(-2.46410 + 2.46410i) q^{29} +3.86370 q^{31} +4.72500i q^{33} +(0.683228 - 1.10992i) q^{35} +(-3.90069 + 3.90069i) q^{37} +1.79315i q^{39} +6.73205i q^{41} +(5.72976 - 5.72976i) q^{43} +(3.29820 + 2.03025i) q^{45} +8.11843i q^{47} -6.66025 q^{49} +(-4.24264 + 4.24264i) q^{51} +(-6.45448 + 6.45448i) q^{53} +(-9.12801 + 2.17209i) q^{55} -0.824313 q^{57} +(-2.31079 - 2.31079i) q^{59} +(-2.00000 + 2.00000i) q^{61} +1.00957i q^{63} +(-3.46410 + 0.824313i) q^{65} +(10.5071 + 10.5071i) q^{67} +(-5.19615 - 5.19615i) q^{69} -13.3843i q^{71} -9.22913 q^{73} +(1.76128 - 5.34758i) q^{75} +(-1.72947 - 1.72947i) q^{77} -1.03528 q^{79} +0.803848 q^{81} +(-4.56400 - 4.56400i) q^{83} +(-10.1465 - 6.24581i) q^{85} -3.92396 q^{87} -0.535898i q^{89} +(-0.656339 - 0.656339i) q^{91} +(3.07638 + 3.07638i) q^{93} +(-0.378937 - 1.59245i) q^{95} +12.0846i q^{97} +(5.13922 - 5.13922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.796225	+	0.796225i	0.459701	+	0.459701i	0.898557	−	0.438856i	$-0.144616\pi$
$3$	0.796225	+	0.796225i	0.459701	+	0.459701i	−0.438856	+	0.898557i	$0.644616\pi$
$4$		0			0
$5$	−1.17216	+	1.90421i	−0.524207	+	0.851591i
$5$	−1.17216	+	1.90421i	−0.524207	+	0.851591i
$6$		0			0
$7$	−0.582877			−0.220307			−0.110153	−	0.993915i	$-0.535134\pi$
$7$	−0.582877			−0.220307			−0.110153	+	0.993915i	$0.535134\pi$
$8$		0			0
$9$		−	1.73205i		−	0.577350i
$10$		0			0
$11$	2.96713	+	2.96713i	0.894623	+	0.894623i	0.994954	−	0.100331i	$-0.0319903\pi$
$11$	2.96713	+	2.96713i	0.894623	+	0.894623i	−0.100331	+	0.994954i	$0.531990\pi$
$12$		0			0
$13$	1.12603	+	1.12603i	0.312305	+	0.312305i	0.845802	−	0.533497i	$-0.179122\pi$
$13$	1.12603	+	1.12603i	0.312305	+	0.312305i	−0.533497	+	0.845802i	$0.679122\pi$
$14$		0			0
$15$	−2.44949	+	0.582877i	−0.632456	+	0.150498i
$16$		0			0
$17$			5.32844i			1.29234i	0.763195	+	0.646169i	$0.223630\pi$
$17$			5.32844i			1.29234i	−0.763195	+	0.646169i	$0.776370\pi$
$18$		0			0
$19$	−0.517638	+	0.517638i	−0.118754	+	0.118754i	−0.763987	−	0.645232i	$-0.776761\pi$
$19$	−0.517638	+	0.517638i	−0.118754	+	0.118754i	0.645232	+	0.763987i	$0.276761\pi$
$20$		0			0
$21$	−0.464102	−	0.464102i	−0.101275	−	0.101275i
$22$		0			0
$23$	−6.52598			−1.36076			−0.680381	−	0.732859i	$-0.738186\pi$
$23$	−6.52598			−1.36076			−0.680381	+	0.732859i	$0.738186\pi$
$24$		0			0
$25$	−2.25207	−	4.46410i	−0.450413	−	0.892820i
$26$		0			0
$27$	3.76778	−	3.76778i	0.725109	−	0.725109i
$28$		0			0
$29$	−2.46410	+	2.46410i	−0.457572	+	0.457572i	−0.897858	−	0.440286i	$-0.854877\pi$
$29$	−2.46410	+	2.46410i	−0.457572	+	0.457572i	0.440286	+	0.897858i	$0.354877\pi$
$30$		0			0
$31$	3.86370			0.693942			0.346971	−	0.937876i	$-0.387210\pi$
$31$	3.86370			0.693942			0.346971	+	0.937876i	$0.387210\pi$
$32$		0			0
$33$			4.72500i			0.822518i
$34$		0			0
$35$	0.683228	−	1.10992i	0.115487	−	0.187611i
$36$		0			0
$37$	−3.90069	+	3.90069i	−0.641270	+	0.641270i	−0.950868	−	0.309598i	$-0.899806\pi$
$37$	−3.90069	+	3.90069i	−0.641270	+	0.641270i	0.309598	+	0.950868i	$0.399806\pi$
$38$		0			0
$39$			1.79315i			0.287134i
$40$		0			0
$41$			6.73205i			1.05137i	0.850679	+	0.525685i	$0.176191\pi$
$41$			6.73205i			1.05137i	−0.850679	+	0.525685i	$0.823809\pi$
$42$		0			0
$43$	5.72976	−	5.72976i	0.873780	−	0.873780i	−0.119102	−	0.992882i	$-0.538002\pi$
$43$	5.72976	−	5.72976i	0.873780	−	0.873780i	0.992882	+	0.119102i	$0.0380016\pi$
$44$		0			0
$45$	3.29820	+	2.03025i	0.491666	+	0.302651i
$46$		0			0
$47$			8.11843i			1.18420i	0.805866	+	0.592098i	$0.201700\pi$
$47$			8.11843i			1.18420i	−0.805866	+	0.592098i	$0.798300\pi$
$48$		0			0
$49$	−6.66025			−0.951465
$50$		0			0
$51$	−4.24264	+	4.24264i	−0.594089	+	0.594089i
$52$		0			0
$53$	−6.45448	+	6.45448i	−0.886590	+	0.886590i	−0.994194	−	0.107603i	$-0.965682\pi$
$53$	−6.45448	+	6.45448i	−0.886590	+	0.886590i	0.107603	+	0.994194i	$0.465682\pi$
$54$		0			0
$55$	−9.12801	+	2.17209i	−1.23082	+	0.292884i
$56$		0			0
$57$	−0.824313			−0.109183
$58$		0			0
$59$	−2.31079	−	2.31079i	−0.300839	−	0.300839i	0.540503	−	0.841342i	$-0.318234\pi$
$59$	−2.31079	−	2.31079i	−0.300839	−	0.300839i	−0.841342	+	0.540503i	$0.818234\pi$
$60$		0			0
$61$	−2.00000	+	2.00000i	−0.256074	+	0.256074i	−0.823455	−	0.567381i	$-0.807957\pi$
$61$	−2.00000	+	2.00000i	−0.256074	+	0.256074i	0.567381	+	0.823455i	$0.307957\pi$
$62$		0			0
$63$			1.00957i			0.127194i
$64$		0			0
$65$	−3.46410	+	0.824313i	−0.429669	+	0.102243i
$66$		0			0
$67$	10.5071	+	10.5071i	1.28365	+	1.28365i	0.938577	+	0.345071i	$0.112145\pi$
$67$	10.5071	+	10.5071i	1.28365	+	1.28365i	0.345071	+	0.938577i	$0.387855\pi$
$68$		0			0
$69$	−5.19615	−	5.19615i	−0.625543	−	0.625543i
$70$		0			0
$71$		−	13.3843i		−	1.58842i	−0.607644	−	0.794210i	$-0.707885\pi$
$71$		−	13.3843i		−	1.58842i	0.607644	−	0.794210i	$-0.292115\pi$
$72$		0			0
$73$	−9.22913			−1.08019			−0.540094	−	0.841605i	$-0.681611\pi$
$73$	−9.22913			−1.08019			−0.540094	+	0.841605i	$0.681611\pi$
$74$		0			0
$75$	1.76128	−	5.34758i	0.203375	−	0.617485i
$76$		0			0
$77$	−1.72947	−	1.72947i	−0.197092	−	0.197092i
$78$		0			0
$79$	−1.03528			−0.116478			−0.0582388	−	0.998303i	$-0.518548\pi$
$79$	−1.03528			−0.116478			−0.0582388	+	0.998303i	$0.518548\pi$
$80$		0			0
$81$	0.803848			0.0893164
$82$		0			0
$83$	−4.56400	−	4.56400i	−0.500964	−	0.500964i	0.410773	−	0.911738i	$-0.365259\pi$
$83$	−4.56400	−	4.56400i	−0.500964	−	0.500964i	−0.911738	+	0.410773i	$0.865259\pi$
$84$		0			0
$85$	−10.1465	−	6.24581i	−1.10054	−	0.677453i
$86$		0			0
$87$	−3.92396			−0.420693
$88$		0			0
$89$		−	0.535898i		−	0.0568051i	−0.999597	−	0.0284026i	$-0.990958\pi$
$89$		−	0.535898i		−	0.0568051i	0.999597	−	0.0284026i	$-0.00904203\pi$
$90$		0			0
$91$	−0.656339	−	0.656339i	−0.0688030	−	0.0688030i
$92$		0			0
$93$	3.07638	+	3.07638i	0.319006	+	0.319006i
$94$		0			0
$95$	−0.378937	−	1.59245i	−0.0388782	−	0.163382i
$96$		0			0
$97$			12.0846i			1.22701i	0.789691	+	0.613505i	$0.210241\pi$
$97$			12.0846i			1.22701i	−0.789691	+	0.613505i	$0.789759\pi$
$98$		0			0
$99$	5.13922	−	5.13922i	0.516511	−	0.516511i
$100$		0			0
$101$	12.4641	+	12.4641i	1.24022	+	1.24022i	0.959907	+	0.280317i	$0.0904396\pi$
$101$	12.4641	+	12.4641i	1.24022	+	1.24022i	0.280317	+	0.959907i	$0.409560\pi$
$102$		0			0
$103$	−1.00957			−0.0994762			−0.0497381	−	0.998762i	$-0.515839\pi$
$103$	−1.00957			−0.0994762			−0.0497381	+	0.998762i	$0.515839\pi$
$104$		0			0
$105$	1.42775	−	0.339746i	0.139334	−	0.0331558i
$106$		0			0
$107$	7.90509	−	7.90509i	0.764213	−	0.764213i	−0.212868	−	0.977081i	$-0.568280\pi$
$107$	7.90509	−	7.90509i	0.764213	−	0.764213i	0.977081	+	0.212868i	$0.0682803\pi$
$108$		0			0
$109$	9.66025	−	9.66025i	0.925285	−	0.925285i	−0.0721120	−	0.997397i	$-0.522974\pi$
$109$	9.66025	−	9.66025i	0.925285	−	0.925285i	0.997397	+	0.0721120i	$0.0229739\pi$
$110$		0			0
$111$	−6.21166			−0.589584
$112$		0			0
$113$			4.50413i			0.423713i	0.977301	+	0.211856i	$0.0679509\pi$
$113$			4.50413i			0.423713i	−0.977301	+	0.211856i	$0.932049\pi$
$114$		0			0
$115$	7.64952	−	12.4269i	0.713321	−	1.15881i
$116$		0			0
$117$	1.95035	−	1.95035i	0.180310	−	0.180310i
$118$		0			0
$119$		−	3.10583i		−	0.284711i
$120$		0			0
$121$			6.60770i			0.600700i
$122$		0			0
$123$	−5.36023	+	5.36023i	−0.483316	+	0.483316i
$124$		0			0
$125$	11.1404	+	0.944243i	0.996427	+	0.0844556i
$126$		0			0
$127$		−	10.8766i		−	0.965146i	−0.875856	−	0.482573i	$-0.839702\pi$
$127$		−	10.8766i		−	0.965146i	0.875856	−	0.482573i	$-0.160298\pi$
$128$		0			0
$129$	9.12436			0.803355
$130$		0			0
$131$	−12.8666	+	12.8666i	−1.12416	+	1.12416i	−0.133053	+	0.991109i	$0.542478\pi$
$131$	−12.8666	+	12.8666i	−1.12416	+	1.12416i	−0.991109	+	0.133053i	$0.957522\pi$
$132$		0			0
$133$	0.301719	−	0.301719i	0.0261624	−	0.0261624i
$134$		0			0
$135$	2.75821	+	11.5911i	0.237388	+	0.997604i
$136$		0			0
$137$	2.25207			0.192407			0.0962034	−	0.995362i	$-0.469330\pi$
$137$	2.25207			0.192407			0.0962034	+	0.995362i	$0.469330\pi$
$138$		0			0
$139$	6.83083	+	6.83083i	0.579384	+	0.579384i	0.934733	−	0.355350i	$-0.115638\pi$
$139$	6.83083	+	6.83083i	0.579384	+	0.579384i	−0.355350	+	0.934733i	$0.615638\pi$
$140$		0			0
$141$	−6.46410	+	6.46410i	−0.544376	+	0.544376i
$142$		0			0
$143$			6.68216i			0.558791i
$144$		0			0
$145$	−1.80385	−	7.58051i	−0.149801	−	0.629527i
$146$		0			0
$147$	−5.30306	−	5.30306i	−0.437389	−	0.437389i
$148$		0			0
$149$	−2.53590	−	2.53590i	−0.207749	−	0.207749i	0.595561	−	0.803310i	$-0.296930\pi$
$149$	−2.53590	−	2.53590i	−0.207749	−	0.207749i	−0.803310	+	0.595561i	$0.796930\pi$
$150$		0			0
$151$		−	17.2480i		−	1.40362i	−0.712364	−	0.701810i	$-0.752376\pi$
$151$		−	17.2480i		−	1.40362i	0.712364	−	0.701810i	$-0.247624\pi$
$152$		0			0
$153$	9.22913			0.746131
$154$		0			0
$155$	−4.52889	+	7.35732i	−0.363769	+	0.590954i
$156$		0			0
$157$	−6.97707	−	6.97707i	−0.556831	−	0.556831i	0.371573	−	0.928404i	$-0.378819\pi$
$157$	−6.97707	−	6.97707i	−0.556831	−	0.556831i	−0.928404	+	0.371573i	$0.878819\pi$
$158$		0			0
$159$	−10.2784			−0.815133
$160$		0			0
$161$	3.80385			0.299785
$162$		0			0
$163$	9.07084	+	9.07084i	0.710483	+	0.710483i	0.966636	−	0.256153i	$-0.0824551\pi$
$163$	9.07084	+	9.07084i	0.710483	+	0.710483i	−0.256153	+	0.966636i	$0.582455\pi$
$164$		0			0
$165$	−8.99742	−	5.53848i	−0.700448	−	0.431170i
$166$		0			0
$167$	18.4122			1.42478			0.712389	−	0.701785i	$-0.247613\pi$
$167$	18.4122			1.42478			0.712389	+	0.701785i	$0.247613\pi$
$168$		0			0
$169$		−	10.4641i		−	0.804931i
$170$		0			0
$171$	0.896575	+	0.896575i	0.0685628	+	0.0685628i
$172$		0			0
$173$	4.50413	+	4.50413i	0.342443	+	0.342443i	0.857285	−	0.514842i	$-0.172150\pi$
$173$	4.50413	+	4.50413i	0.342443	+	0.342443i	−0.514842	+	0.857285i	$0.672150\pi$
$174$		0			0
$175$	1.31268	+	2.60202i	0.0992291	+	0.196694i
$176$		0			0
$177$		−	3.67982i		−	0.276592i
$178$		0			0
$179$	6.07296	−	6.07296i	0.453914	−	0.453914i	−0.442737	−	0.896651i	$-0.645993\pi$
$179$	6.07296	−	6.07296i	0.453914	−	0.453914i	0.896651	+	0.442737i	$0.145993\pi$
$180$		0			0
$181$	14.4641	+	14.4641i	1.07511	+	1.07511i	0.996940	+	0.0781680i	$0.0249071\pi$
$181$	14.4641	+	14.4641i	1.07511	+	1.07511i	0.0781680	+	0.996940i	$0.475093\pi$
$182$		0			0
$183$	−3.18490			−0.235435
$184$		0			0
$185$	−2.85550	−	12.0000i	−0.209941	−	0.882258i
$186$		0			0
$187$	−15.8102	+	15.8102i	−1.15615	+	1.15615i
$188$		0			0
$189$	−2.19615	+	2.19615i	−0.159747	+	0.159747i
$190$		0			0
$191$	15.4548			1.11827			0.559136	−	0.829076i	$-0.311133\pi$
$191$	15.4548			1.11827			0.559136	+	0.829076i	$0.311133\pi$
$192$		0			0
$193$		−	26.0388i		−	1.87431i	−0.348910	−	0.937156i	$-0.613448\pi$
$193$		−	26.0388i		−	1.87431i	0.348910	−	0.937156i	$-0.386552\pi$
$194$		0			0
$195$	−3.41454	−	2.10187i	−0.244521	−	0.150518i
$196$		0			0
$197$	7.27879	−	7.27879i	0.518592	−	0.518592i	−0.398553	−	0.917145i	$-0.630488\pi$
$197$	7.27879	−	7.27879i	0.518592	−	0.518592i	0.917145	+	0.398553i	$0.130488\pi$
$198$		0			0
$199$			25.2528i			1.79012i	0.445944	+	0.895061i	$0.352868\pi$
$199$			25.2528i			1.79012i	−0.445944	+	0.895061i	$0.647132\pi$
$200$		0			0
$201$			16.7321i			1.18019i
$202$		0			0
$203$	1.43627	−	1.43627i	0.100806	−	0.100806i
$204$		0			0
$205$	−12.8193	−	7.89106i	−0.895337	−	0.551136i
$206$		0			0
$207$			11.3033i			0.785636i
$208$		0			0
$209$	−3.07180			−0.212481
$210$		0			0
$211$	−10.7961	+	10.7961i	−0.743232	+	0.743232i	−0.973199	−	0.229966i	$-0.926138\pi$
$211$	−10.7961	+	10.7961i	−0.743232	+	0.743232i	0.229966	+	0.973199i	$0.426138\pi$
$212$		0			0
$213$	10.6569	−	10.6569i	0.730198	−	0.730198i
$214$		0			0
$215$	4.19447	+	17.6269i	0.286061	+	1.20214i
$216$		0			0
$217$	−2.25207			−0.152880
$218$		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
$223$		−	24.7820i		−	1.65953i	−0.558116	−	0.829763i	$-0.688476\pi$
$223$		−	24.7820i		−	1.65953i	0.558116	−	0.829763i	$-0.311524\pi$
$224$		0			0
$225$	−7.73205	+	3.90069i	−0.515470	+	0.260046i
$226$		0			0
$227$	−3.98113	−	3.98113i	−0.264237	−	0.264237i	0.562536	−	0.826773i	$-0.309826\pi$
$227$	−3.98113	−	3.98113i	−0.264237	−	0.264237i	−0.826773	+	0.562536i	$0.809826\pi$
$228$		0			0
$229$	−0.0717968	−	0.0717968i	−0.00474446	−	0.00474446i	0.704731	−	0.709475i	$-0.251068\pi$
$229$	−0.0717968	−	0.0717968i	−0.00474446	−	0.00474446i	−0.709475	+	0.704731i	$0.751068\pi$
$230$		0			0
$231$		−	2.75410i		−	0.181206i
$232$		0			0
$233$	12.5264			0.820631			0.410315	−	0.911944i	$-0.365419\pi$
$233$	12.5264			0.820631			0.410315	+	0.911944i	$0.365419\pi$
$234$		0			0
$235$	−15.4592	−	9.51613i	−1.00845	−	0.620764i
$236$		0			0
$237$	−0.824313	−	0.824313i	−0.0535449	−	0.0535449i
$238$		0			0
$239$	13.1069			0.847812			0.423906	−	0.905706i	$-0.360659\pi$
$239$	13.1069			0.847812			0.423906	+	0.905706i	$0.360659\pi$
$240$		0			0
$241$	16.0526			1.03404			0.517018	−	0.855974i	$-0.327042\pi$
$241$	16.0526			1.03404			0.517018	+	0.855974i	$0.327042\pi$
$242$		0			0
$243$	−10.6633	−	10.6633i	−0.684050	−	0.684050i
$244$		0			0
$245$	7.80691	−	12.6826i	0.498765	−	0.810259i
$246$		0			0
$247$	−1.16575			−0.0741752
$248$		0			0
$249$		−	7.26795i		−	0.460588i
$250$		0			0
$251$	12.2103	+	12.2103i	0.770706	+	0.770706i	0.978230	−	0.207524i	$-0.0665404\pi$
$251$	12.2103	+	12.2103i	0.770706	+	0.770706i	−0.207524	+	0.978230i	$0.566540\pi$
$252$		0			0
$253$	−19.3634	−	19.3634i	−1.21737	−	1.21737i
$254$		0			0
$255$	−3.10583	−	13.0520i	−0.194495	−	0.817346i
$256$		0			0
$257$		−	22.3590i		−	1.39471i	−0.716724	−	0.697357i	$-0.754359\pi$
$257$		−	22.3590i		−	1.39471i	0.716724	−	0.697357i	$-0.245641\pi$
$258$		0			0
$259$	2.27362	−	2.27362i	0.141276	−	0.141276i
$260$		0			0
$261$	4.26795	+	4.26795i	0.264179	+	0.264179i
$262$		0			0
$263$	25.5211			1.57370			0.786848	−	0.617147i	$-0.211712\pi$
$263$	25.5211			1.57370			0.786848	+	0.617147i	$0.211712\pi$
$264$		0			0
$265$	−4.72500	−	19.8564i	−0.290255	−	1.21977i
$266$		0			0
$267$	0.426696	−	0.426696i	0.0261134	−	0.0261134i
$268$		0			0
$269$	−8.92820	+	8.92820i	−0.544362	+	0.544362i	−0.924805	−	0.380442i	$-0.875772\pi$
$269$	−8.92820	+	8.92820i	−0.544362	+	0.544362i	0.380442	+	0.924805i	$0.375772\pi$
$270$		0			0
$271$	20.6312			1.25326			0.626628	−	0.779319i	$-0.284435\pi$
$271$	20.6312			1.25326			0.626628	+	0.779319i	$0.284435\pi$
$272$		0			0
$273$		−	1.04519i		−	0.0632576i
$274$		0			0
$275$	6.56340	−	19.9277i	0.395788	−	1.20169i
$276$		0			0
$277$	6.15276	−	6.15276i	0.369683	−	0.369683i	−0.497678	−	0.867362i	$-0.665814\pi$
$277$	6.15276	−	6.15276i	0.369683	−	0.369683i	0.867362	+	0.497678i	$0.165814\pi$
$278$		0			0
$279$		−	6.69213i		−	0.400647i
$280$		0			0
$281$			29.5167i			1.76082i	0.474217	+	0.880408i	$0.342731\pi$
$281$			29.5167i			1.76082i	−0.474217	+	0.880408i	$0.657269\pi$
$282$		0			0
$283$	−17.7722	+	17.7722i	−1.05644	+	1.05644i	−0.0581361	+	0.998309i	$0.518516\pi$
$283$	−17.7722	+	17.7722i	−1.05644	+	1.05644i	−0.998309	+	0.0581361i	$0.981484\pi$
$284$		0			0
$285$	0.966230	−	1.56967i	0.0572345	−	0.0929791i
$286$		0			0
$287$		−	3.92396i		−	0.231624i
$288$		0			0
$289$	−11.3923			−0.670136
$290$		0			0
$291$	−9.62209	+	9.62209i	−0.564057	+	0.564057i
$292$		0			0
$293$	11.4812	−	11.4812i	0.670739	−	0.670739i	−0.287148	−	0.957886i	$-0.592707\pi$
$293$	11.4812	−	11.4812i	0.670739	−	0.670739i	0.957886	+	0.287148i	$0.0927070\pi$
$294$		0			0
$295$	7.10886	−	1.69161i	0.413894	−	0.0984896i
$296$		0			0
$297$	22.3590			1.29740
$298$		0			0
$299$	−7.34847	−	7.34847i	−0.424973	−	0.424973i
$300$		0			0
$301$	−3.33975	+	3.33975i	−0.192500	+	0.192500i
$302$		0			0
$303$			19.8485i			1.14026i
$304$		0			0
$305$	−1.46410	−	6.15276i	−0.0838342	−	0.352306i
$306$		0			0
$307$	−3.39825	−	3.39825i	−0.193948	−	0.193948i	0.603451	−	0.797400i	$-0.293792\pi$
$307$	−3.39825	−	3.39825i	−0.193948	−	0.193948i	−0.797400	+	0.603451i	$0.793792\pi$
$308$		0			0
$309$	−0.803848	−	0.803848i	−0.0457293	−	0.0457293i
$310$		0			0
$311$		−	6.13733i		−	0.348016i	−0.984744	−	0.174008i	$-0.944328\pi$
$311$		−	6.13733i		−	0.348016i	0.984744	−	0.174008i	$-0.0556718\pi$
$312$		0			0
$313$	−7.19794			−0.406852			−0.203426	−	0.979090i	$-0.565208\pi$
$313$	−7.19794			−0.406852			−0.203426	+	0.979090i	$0.565208\pi$
$314$		0			0
$315$	−1.92244	−	1.18338i	−0.108317	−	0.0666762i
$316$		0			0
$317$	11.7829	+	11.7829i	0.661795	+	0.661795i	0.955803	−	0.294008i	$-0.0949893\pi$
$317$	11.7829	+	11.7829i	0.661795	+	0.661795i	−0.294008	+	0.955803i	$0.594989\pi$
$318$		0			0
$319$	−14.6226			−0.818709
$320$		0			0
$321$	12.5885			0.702619
$322$		0			0
$323$	−2.75821	−	2.75821i	−0.153471	−	0.153471i
$324$		0			0
$325$	2.49083	−	7.56262i	0.138166	−	0.419499i
$326$		0			0
$327$	15.3835			0.850708
$328$		0			0
$329$		−	4.73205i		−	0.260886i
$330$		0			0
$331$	8.24504	+	8.24504i	0.453189	+	0.453189i	0.896411	−	0.443223i	$-0.146165\pi$
$331$	8.24504	+	8.24504i	0.453189	+	0.453189i	−0.443223	+	0.896411i	$0.646165\pi$
$332$		0			0
$333$	6.75620	+	6.75620i	0.370237	+	0.370237i
$334$		0			0
$335$	−32.3238	+	7.69174i	−1.76604	+	0.420245i
$336$		0			0
$337$		−	23.5658i		−	1.28371i	−0.766825	−	0.641856i	$-0.778164\pi$
$337$		−	23.5658i		−	1.28371i	0.766825	−	0.641856i	$-0.221836\pi$
$338$		0			0
$339$	−3.58630	+	3.58630i	−0.194781	+	0.194781i
$340$		0			0
$341$	11.4641	+	11.4641i	0.620816	+	0.620816i
$342$		0			0
$343$	7.96225			0.429921
$344$		0			0
$345$	15.9853	−	3.80385i	0.860621	−	0.204792i
$346$		0			0
$347$	−14.1187	+	14.1187i	−0.757932	+	0.757932i	−0.975946	−	0.218014i	$-0.930042\pi$
$347$	−14.1187	+	14.1187i	−0.757932	+	0.757932i	0.218014	+	0.975946i	$0.430042\pi$
$348$		0			0
$349$	19.7846	−	19.7846i	1.05905	−	1.05905i	0.0609021	−	0.998144i	$-0.480602\pi$
$349$	19.7846	−	19.7846i	1.05905	−	1.05905i	0.998144	−	0.0609021i	$-0.0193978\pi$
$350$		0			0
$351$	8.48528			0.452911
$352$		0			0
$353$			1.64863i			0.0877475i	0.999037	+	0.0438738i	$0.0139699\pi$
$353$			1.64863i			0.0877475i	−0.999037	+	0.0438738i	$0.986030\pi$
$354$		0			0
$355$	25.4865	+	15.6885i	1.35268	+	0.832661i
$356$		0			0
$357$	2.47294	−	2.47294i	0.130882	−	0.130882i
$358$		0			0
$359$			18.0058i			0.950312i	0.879902	+	0.475156i	$0.157608\pi$
$359$			18.0058i			0.950312i	−0.879902	+	0.475156i	$0.842392\pi$
$360$		0			0
$361$			18.4641i			0.971795i
$362$		0			0
$363$	−5.26121	+	5.26121i	−0.276142	+	0.276142i
$364$		0			0
$365$	10.8181	−	17.5742i	0.566243	−	0.919878i
$366$		0			0
$367$		−	26.8011i		−	1.39901i	−0.714629	−	0.699504i	$-0.753404\pi$
$367$		−	26.8011i		−	1.39901i	0.714629	−	0.699504i	$-0.246596\pi$
$368$		0			0
$369$	11.6603			0.607009
$370$		0			0
$371$	3.76217	−	3.76217i	0.195322	−	0.195322i
$372$		0			0
$373$	−13.5124	+	13.5124i	−0.699645	+	0.699645i	−0.964334	−	0.264689i	$-0.914731\pi$
$373$	−13.5124	+	13.5124i	−0.699645	+	0.699645i	0.264689	+	0.964334i	$0.414731\pi$
$374$		0			0
$375$	8.11843	+	9.62209i	0.419234	+	0.496883i
$376$		0			0
$377$	−5.54932			−0.285804
$378$		0			0
$379$	−15.5935	−	15.5935i	−0.800985	−	0.800985i	0.182265	−	0.983250i	$-0.441657\pi$
$379$	−15.5935	−	15.5935i	−0.800985	−	0.800985i	−0.983250	+	0.182265i	$0.941657\pi$
$380$		0			0
$381$	8.66025	−	8.66025i	0.443678	−	0.443678i
$382$		0			0
$383$		−	3.34108i		−	0.170721i	−0.996350	−	0.0853607i	$-0.972796\pi$
$383$		−	3.34108i		−	0.170721i	0.996350	−	0.0853607i	$-0.0272042\pi$
$384$		0			0
$385$	5.32051	−	1.26606i	0.271158	−	0.0645244i
$386$		0			0
$387$	−9.92423	−	9.92423i	−0.504477	−	0.504477i
$388$		0			0
$389$	−8.00000	−	8.00000i	−0.405616	−	0.405616i	0.474591	−	0.880207i	$-0.342596\pi$
$389$	−8.00000	−	8.00000i	−0.405616	−	0.405616i	−0.880207	+	0.474591i	$0.842596\pi$
$390$		0			0
$391$		−	34.7733i		−	1.75856i
$392$		0			0
$393$	−20.4895			−1.03356
$394$		0			0
$395$	1.21351	−	1.97139i	0.0610585	−	0.0991913i
$396$		0			0
$397$	−6.67535	−	6.67535i	−0.335026	−	0.335026i	0.519465	−	0.854492i	$-0.326131\pi$
$397$	−6.67535	−	6.67535i	−0.335026	−	0.335026i	−0.854492	+	0.519465i	$0.826131\pi$
$398$		0			0
$399$	0.480473			0.0240538
$400$		0			0
$401$	10.5359			0.526138			0.263069	−	0.964777i	$-0.415265\pi$
$401$	10.5359			0.526138			0.263069	+	0.964777i	$0.415265\pi$
$402$		0			0
$403$	4.35066	+	4.35066i	0.216722	+	0.216722i
$404$		0			0
$405$	−0.942241	+	1.53070i	−0.0468203	+	0.0760610i
$406$		0			0
$407$	−23.1477			−1.14739
$408$		0			0
$409$		−	1.26795i		−	0.0626961i	−0.999509	−	0.0313480i	$-0.990020\pi$
$409$		−	1.26795i		−	0.0626961i	0.999509	−	0.0313480i	$-0.00998002\pi$
$410$		0			0
$411$	1.79315	+	1.79315i	0.0884496	+	0.0884496i
$412$		0			0
$413$	1.34691	+	1.34691i	0.0662769	+	0.0662769i
$414$		0			0
$415$	14.0406	−	3.34108i	0.689226	−	0.164007i
$416$		0			0
$417$			10.8778i			0.532686i
$418$		0			0
$419$	20.2151	−	20.2151i	0.987572	−	0.987572i	−0.0123518	−	0.999924i	$-0.503932\pi$
$419$	20.2151	−	20.2151i	0.987572	−	0.987572i	0.999924	+	0.0123518i	$0.00393181\pi$
$420$		0			0
$421$	5.60770	+	5.60770i	0.273302	+	0.273302i	0.830428	−	0.557126i	$-0.188096\pi$
$421$	5.60770	+	5.60770i	0.273302	+	0.273302i	−0.557126	+	0.830428i	$0.688096\pi$
$422$		0			0
$423$	14.0615			0.683695
$424$		0			0
$425$	23.7867	−	12.0000i	1.15382	−	0.582086i
$426$		0			0
$427$	1.16575	−	1.16575i	0.0564148	−	0.0564148i
$428$		0			0
$429$	−5.32051	+	5.32051i	−0.256877	+	0.256877i
$430$		0			0
$431$	−25.5302			−1.22975			−0.614873	−	0.788626i	$-0.710793\pi$
$431$	−25.5302			−1.22975			−0.614873	+	0.788626i	$0.710793\pi$
$432$		0			0
$433$			11.4812i			0.551751i	0.961193	+	0.275876i	$0.0889678\pi$
$433$			11.4812i			0.551751i	−0.961193	+	0.275876i	$0.911032\pi$
$434$		0			0
$435$	4.59952	−	7.47206i	0.220530	−	0.358258i
$436$		0			0
$437$	3.37810	−	3.37810i	0.161596	−	0.161596i
$438$		0			0
$439$		−	12.3490i		−	0.589385i	−0.955592	−	0.294692i	$-0.904783\pi$
$439$		−	12.3490i		−	0.589385i	0.955592	−	0.294692i	$-0.0952172\pi$
$440$		0			0
$441$			11.5359i			0.549328i
$442$		0			0
$443$	14.2749	−	14.2749i	0.678220	−	0.678220i	−0.281377	−	0.959597i	$-0.590791\pi$
$443$	14.2749	−	14.2749i	0.678220	−	0.678220i	0.959597	+	0.281377i	$0.0907911\pi$
$444$		0			0
$445$	1.02047	+	0.628161i	0.0483747	+	0.0297777i
$446$		0			0
$447$		−	4.03829i		−	0.191005i
$448$		0			0
$449$	−29.1244			−1.37446			−0.687232	−	0.726438i	$-0.741174\pi$
$449$	−29.1244			−1.37446			−0.687232	+	0.726438i	$0.741174\pi$
$450$		0			0
$451$	−19.9749	+	19.9749i	−0.940579	+	0.940579i
$452$		0			0
$453$	13.7333	−	13.7333i	0.645245	−	0.645245i
$454$		0			0
$455$	2.01915	−	0.480473i	0.0946590	−	0.0225249i
$456$		0			0
$457$	−42.0241			−1.96580			−0.982902	−	0.184128i	$-0.941054\pi$
$457$	−42.0241			−1.96580			−0.982902	+	0.184128i	$0.941054\pi$
$458$		0			0
$459$	20.0764	+	20.0764i	0.937086	+	0.937086i
$460$		0			0
$461$	5.53590	−	5.53590i	0.257832	−	0.257832i	−0.566340	−	0.824172i	$-0.691641\pi$
$461$	5.53590	−	5.53590i	0.257832	−	0.257832i	0.824172	+	0.566340i	$0.191641\pi$
$462$		0			0
$463$		−	15.9664i		−	0.742019i	−0.928629	−	0.371010i	$-0.879012\pi$
$463$		−	15.9664i		−	0.742019i	0.928629	−	0.371010i	$-0.120988\pi$
$464$		0			0
$465$	−9.46410	+	2.25207i	−0.438887	+	0.104437i
$466$		0			0
$467$	−9.92423	−	9.92423i	−0.459239	−	0.459239i	0.439167	−	0.898406i	$-0.355274\pi$
$467$	−9.92423	−	9.92423i	−0.459239	−	0.459239i	−0.898406	+	0.439167i	$0.855274\pi$
$468$		0			0
$469$	−6.12436	−	6.12436i	−0.282796	−	0.282796i
$470$		0			0
$471$		−	11.1106i		−	0.511951i
$472$		0			0
$473$	34.0018			1.56341
$474$		0			0
$475$	3.47654	+	1.14503i	0.159515	+	0.0525378i
$476$		0			0
$477$	11.1795	+	11.1795i	0.511873	+	0.511873i
$478$		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
$481$	−8.78461			−0.400544
$482$		0			0
$483$	3.02872	+	3.02872i	0.137812	+	0.137812i
$484$		0			0
$485$	−23.0117	−	14.1652i	−1.04491	−	0.643207i
$486$		0			0
$487$	−24.3553			−1.10364			−0.551822	−	0.833962i	$-0.686067\pi$
$487$	−24.3553			−1.10364			−0.551822	+	0.833962i	$0.686067\pi$
$488$		0			0
$489$			14.4449i			0.653219i
$490$		0			0
$491$	−11.0735	−	11.0735i	−0.499739	−	0.499739i	0.411618	−	0.911357i	$-0.364964\pi$
$491$	−11.0735	−	11.0735i	−0.499739	−	0.499739i	−0.911357	+	0.411618i	$0.864964\pi$
$492$		0			0
$493$	−13.1298	−	13.1298i	−0.591338	−	0.591338i
$494$		0			0
$495$	3.76217	+	15.8102i	0.169097	+	0.710614i
$496$		0			0
$497$			7.80138i			0.349940i
$498$		0			0
$499$	−15.5935	+	15.5935i	−0.698062	+	0.698062i	−0.963992	−	0.265931i	$-0.914321\pi$
$499$	−15.5935	+	15.5935i	−0.698062	+	0.698062i	0.265931	+	0.963992i	$0.414321\pi$
$500$		0			0
$501$	14.6603	+	14.6603i	0.654972	+	0.654972i
$502$		0			0
$503$	−19.5779			−0.872938			−0.436469	−	0.899719i	$-0.643771\pi$
$503$	−19.5779			−0.872938			−0.436469	+	0.899719i	$0.643771\pi$
$504$		0			0
$505$	−38.3443	+	9.12436i	−1.70630	+	0.406028i
$506$		0			0
$507$	8.33178	−	8.33178i	0.370027	−	0.370027i
$508$		0			0
$509$	−9.00000	+	9.00000i	−0.398918	+	0.398918i	−0.877851	−	0.478933i	$-0.841024\pi$
$509$	−9.00000	+	9.00000i	−0.398918	+	0.398918i	0.478933	+	0.877851i	$0.341024\pi$
$510$		0			0
$511$	5.37945			0.237973
$512$		0			0
$513$			3.90069i			0.172220i
$514$		0			0
$515$	1.18338	−	1.92244i	0.0521462	−	0.0847130i
$516$		0			0
$517$	−24.0884	+	24.0884i	−1.05941	+	1.05941i
$518$		0			0
$519$			7.17260i			0.314842i
$520$		0			0
$521$		−	21.1769i		−	0.927777i	−0.885893	−	0.463889i	$-0.846454\pi$
$521$		−	21.1769i		−	0.927777i	0.885893	−	0.463889i	$-0.153546\pi$
$522$		0			0
$523$	10.3509	−	10.3509i	0.452614	−	0.452614i	−0.443607	−	0.896221i	$-0.646301\pi$
$523$	10.3509	−	10.3509i	0.452614	−	0.452614i	0.896221	+	0.443607i	$0.146301\pi$
$524$		0			0
$525$	−1.02661	+	3.11698i	−0.0448049	+	0.136036i
$526$		0			0
$527$			20.5875i			0.896807i
$528$		0			0
$529$	19.5885			0.851672
$530$		0			0
$531$	−4.00240	+	4.00240i	−0.173690	+	0.173690i
$532$		0			0
$533$	−7.58051	+	7.58051i	−0.328348	+	0.328348i
$534$		0			0
$535$	5.78692	+	24.3190i	0.250191	+	1.05140i
$536$		0			0
$537$	9.67088			0.417329
$538$		0			0
$539$	−19.7618	−	19.7618i	−0.851202	−	0.851202i
$540$		0			0
$541$	−24.8564	+	24.8564i	−1.06866	+	1.06866i	−0.0711982	+	0.997462i	$0.522682\pi$
$541$	−24.8564	+	24.8564i	−1.06866	+	1.06866i	−0.997462	+	0.0711982i	$0.977318\pi$
$542$		0			0
$543$			23.0334i			0.988456i
$544$		0			0
$545$	7.07180	+	29.7186i	0.302922	+	1.27300i
$546$		0			0
$547$	17.7722	+	17.7722i	0.759882	+	0.759882i	0.976301	−	0.216418i	$-0.0694375\pi$
$547$	17.7722	+	17.7722i	0.759882	+	0.759882i	−0.216418	+	0.976301i	$0.569438\pi$
$548$		0			0
$549$	3.46410	+	3.46410i	0.147844	+	0.147844i
$550$		0			0
$551$		−	2.55103i		−	0.108677i
$552$		0			0
$553$	0.603439			0.0256608
$554$		0			0
$555$	7.28108	−	11.8283i	0.309065	−	0.502085i
$556$		0			0
$557$	15.3819	+	15.3819i	0.651752	+	0.651752i	0.953415	−	0.301663i	$-0.0975418\pi$
$557$	15.3819	+	15.3819i	0.651752	+	0.651752i	−0.301663	+	0.953415i	$0.597542\pi$
$558$		0			0
$559$	12.9038			0.545772
$560$		0			0
$561$	−25.1769			−1.06297
$562$		0			0
$563$	3.24207	+	3.24207i	0.136637	+	0.136637i	0.772117	−	0.635480i	$-0.219198\pi$
$563$	3.24207	+	3.24207i	0.136637	+	0.136637i	−0.635480	+	0.772117i	$0.719198\pi$
$564$		0			0
$565$	−8.57683	−	5.27958i	−0.360830	−	0.222113i
$566$		0			0
$567$	−0.468545			−0.0196770
$568$		0			0
$569$		−	11.5167i		−	0.482804i	−0.970425	−	0.241402i	$-0.922393\pi$
$569$		−	11.5167i		−	0.482804i	0.970425	−	0.241402i	$-0.0776072\pi$
$570$		0			0
$571$	−4.00240	−	4.00240i	−0.167495	−	0.167495i	0.618382	−	0.785878i	$-0.287788\pi$
$571$	−4.00240	−	4.00240i	−0.167495	−	0.167495i	−0.785878	+	0.618382i	$0.787788\pi$
$572$		0			0
$573$	12.3055	+	12.3055i	0.514070	+	0.514070i
$574$		0			0
$575$	14.6969	+	29.1327i	0.612905	+	1.21492i
$576$		0			0
$577$		−	25.8179i		−	1.07481i	−0.843323	−	0.537407i	$-0.819404\pi$
$577$		−	25.8179i		−	1.07481i	0.843323	−	0.537407i	$-0.180596\pi$
$578$		0			0
$579$	20.7327	−	20.7327i	0.861623	−	0.861623i
$580$		0			0
$581$	2.66025	+	2.66025i	0.110366	+	0.110366i
$582$		0			0
$583$	−38.3025			−1.58633
$584$		0			0
$585$	1.42775	+	6.00000i	0.0590303	+	0.248069i
$586$		0			0
$587$	5.30306	−	5.30306i	0.218881	−	0.218881i	−0.589146	−	0.808027i	$-0.700536\pi$
$587$	5.30306	−	5.30306i	0.218881	−	0.218881i	0.808027	+	0.589146i	$0.200536\pi$
$588$		0			0
$589$	−2.00000	+	2.00000i	−0.0824086	+	0.0824086i
$590$		0			0
$591$	11.5911			0.476795
$592$		0			0
$593$			13.3507i			0.548247i	0.961694	+	0.274124i	$0.0883878\pi$
$593$			13.3507i			0.548247i	−0.961694	+	0.274124i	$0.911612\pi$
$594$		0			0
$595$	5.91416	+	3.64054i	0.242457	+	0.149248i
$596$		0			0
$597$	−20.1069	+	20.1069i	−0.822920	+	0.822920i
$598$		0			0
$599$			9.04008i			0.369368i	0.982798	+	0.184684i	$0.0591261\pi$
$599$			9.04008i			0.369368i	−0.982798	+	0.184684i	$0.940874\pi$
$600$		0			0
$601$		−	10.5885i		−	0.431912i	−0.976403	−	0.215956i	$-0.930713\pi$
$601$		−	10.5885i		−	0.431912i	0.976403	−	0.215956i	$-0.0692868\pi$
$602$		0			0
$603$	18.1988	−	18.1988i	0.741114	−	0.741114i
$604$		0			0
$605$	−12.5825	−	7.74530i	−0.511550	−	0.314891i
$606$		0			0
$607$			16.5074i			0.670014i	0.942216	+	0.335007i	$0.108739\pi$
$607$			16.5074i			0.670014i	−0.942216	+	0.335007i	$0.891261\pi$
$608$		0			0
$609$	2.28719			0.0926815
$610$		0			0
$611$	−9.14162	+	9.14162i	−0.369830	+	0.369830i
$612$		0			0
$613$	−9.75173	+	9.75173i	−0.393869	+	0.393869i	−0.876064	−	0.482195i	$-0.839840\pi$
$613$	−9.75173	+	9.75173i	−0.393869	+	0.393869i	0.482195	+	0.876064i	$0.339840\pi$
$614$		0			0
$615$	−3.92396	−	16.4901i	−0.158229	−	0.664945i
$616$		0			0
$617$	22.1381			0.891246			0.445623	−	0.895221i	$-0.352982\pi$
$617$	22.1381			0.891246			0.445623	+	0.895221i	$0.352982\pi$
$618$		0			0
$619$	32.9430	+	32.9430i	1.32409	+	1.32409i	0.910431	+	0.413660i	$0.135750\pi$
$619$	32.9430	+	32.9430i	1.32409	+	1.32409i	0.413660	+	0.910431i	$0.364250\pi$
$620$		0			0
$621$	−24.5885	+	24.5885i	−0.986701	+	0.986701i
$622$		0			0
$623$			0.312363i			0.0125146i
$624$		0			0
$625$	−14.8564	+	20.1069i	−0.594256	+	0.804276i
$626$		0			0
$627$	−2.44584	−	2.44584i	−0.0976775	−	0.0976775i
$628$		0			0
$629$	−20.7846	−	20.7846i	−0.828737	−	0.828737i
$630$		0			0
$631$			17.2480i			0.686631i	0.939220	+	0.343315i	$0.111550\pi$
$631$			17.2480i			0.686631i	−0.939220	+	0.343315i	$0.888450\pi$
$632$		0			0
$633$	−17.1922			−0.683329
$634$		0			0
$635$	20.7115	+	12.7492i	0.821909	+	0.505937i
$636$		0			0
$637$	−7.49966	−	7.49966i	−0.297147	−	0.297147i
$638$		0			0
$639$	−23.1822			−0.917074
$640$		0			0
$641$	10.5885			0.418219			0.209109	−	0.977892i	$-0.432944\pi$
$641$	10.5885			0.418219			0.209109	+	0.977892i	$0.432944\pi$
$642$		0			0
$643$	14.4311	+	14.4311i	0.569106	+	0.569106i	0.931878	−	0.362772i	$-0.118170\pi$
$643$	14.4311	+	14.4311i	0.569106	+	0.569106i	−0.362772	+	0.931878i	$0.618170\pi$
$644$		0			0
$645$	−10.6952	+	17.3747i	−0.421125	+	0.684129i
$646$		0			0
$647$	−23.1895			−0.911675			−0.455838	−	0.890063i	$-0.650660\pi$
$647$	−23.1895			−0.911675			−0.455838	+	0.890063i	$0.650660\pi$
$648$		0			0
$649$		−	13.7128i		−	0.538275i
$650$		0			0
$651$	−1.79315	−	1.79315i	−0.0702791	−	0.0702791i
$652$		0			0
$653$	10.3552	+	10.3552i	0.405229	+	0.405229i	0.880071	−	0.474842i	$-0.157495\pi$
$653$	10.3552	+	10.3552i	0.405229	+	0.405229i	−0.474842	+	0.880071i	$0.657495\pi$
$654$		0			0
$655$	−9.41902	−	39.5826i	−0.368032	−	1.54662i
$656$		0			0
$657$			15.9853i			0.623647i
$658$		0			0
$659$	−27.9425	+	27.9425i	−1.08849	+	1.08849i	−0.0928005	+	0.995685i	$0.529582\pi$
$659$	−27.9425	+	27.9425i	−1.08849	+	1.08849i	−0.995685	+	0.0928005i	$0.970418\pi$
$660$		0			0
$661$	−6.73205	−	6.73205i	−0.261846	−	0.261846i	0.563957	−	0.825804i	$-0.309278\pi$
$661$	−6.73205	−	6.73205i	−0.261846	−	0.261846i	−0.825804	+	0.563957i	$0.809278\pi$
$662$		0			0
$663$	−9.55470			−0.371074
$664$		0			0
$665$	0.220874	+	0.928203i	0.00856513	+	0.0359942i
$666$		0			0
$667$	16.0807	−	16.0807i	0.622647	−	0.622647i
$668$		0			0
$669$	19.7321	−	19.7321i	0.762885	−	0.762885i
$670$		0			0
$671$	−11.8685			−0.458179
$672$		0			0
$673$			33.8402i			1.30444i	0.758029	+	0.652221i	$0.226163\pi$
$673$			33.8402i			1.30444i	−0.758029	+	0.652221i	$0.773837\pi$
$674$		0			0
$675$	−25.3050	−	8.33446i	−0.973991	−	0.320794i
$676$		0			0
$677$	−7.88223	+	7.88223i	−0.302939	+	0.302939i	−0.842162	−	0.539224i	$-0.818718\pi$
$677$	−7.88223	+	7.88223i	−0.302939	+	0.302939i	0.539224	+	0.842162i	$0.318718\pi$
$678$		0			0
$679$		−	7.04386i		−	0.270319i
$680$		0			0
$681$		−	6.33975i		−	0.242940i
$682$		0			0
$683$	7.32221	−	7.32221i	0.280177	−	0.280177i	−0.553003	−	0.833179i	$-0.686518\pi$
$683$	7.32221	−	7.32221i	0.280177	−	0.280177i	0.833179	+	0.553003i	$0.186518\pi$
$684$		0			0
$685$	−2.63979	+	4.28841i	−0.100861	+	0.163852i
$686$		0			0
$687$		−	0.114333i		−	0.00436207i
$688$		0			0
$689$	−14.5359			−0.553774
$690$		0			0
$691$	3.06866	−	3.06866i	0.116737	−	0.116737i	−0.646325	−	0.763062i	$-0.723695\pi$
$691$	3.06866	−	3.06866i	0.116737	−	0.116737i	0.763062	+	0.646325i	$0.223695\pi$
$692$		0			0
$693$	−2.99553	+	2.99553i	−0.113791	+	0.113791i
$694$		0			0
$695$	−21.0142	+	5.00052i	−0.797115	+	0.189680i
$696$		0			0
$697$	−35.8713			−1.35872
$698$		0			0
$699$	9.97382	+	9.97382i	0.377245	+	0.377245i
$700$		0			0
$701$	12.3397	−	12.3397i	0.466066	−	0.466066i	−0.434572	−	0.900637i	$-0.643100\pi$
$701$	12.3397	−	12.3397i	0.466066	−	0.466066i	0.900637	+	0.434572i	$0.143100\pi$
$702$		0			0
$703$		−	4.03829i		−	0.152307i
$704$		0			0
$705$	−4.73205	−	19.8860i	−0.178219	−	0.748951i
$706$		0			0
$707$	−7.26504	−	7.26504i	−0.273230	−	0.273230i
$708$		0			0
$709$	17.0000	+	17.0000i	0.638448	+	0.638448i	0.950173	−	0.311724i	$-0.100907\pi$
$709$	17.0000	+	17.0000i	0.638448	+	0.638448i	−0.311724	+	0.950173i	$0.600907\pi$
$710$		0			0
$711$			1.79315i			0.0672484i
$712$		0			0
$713$	−25.2145			−0.944289
$714$		0			0
$715$	−12.7243	−	7.83259i	−0.475861	−	0.292922i
$716$		0			0
$717$	10.4360	+	10.4360i	0.389740	+	0.389740i
$718$		0			0
$719$	15.3805			0.573595			0.286798	−	0.957991i	$-0.407409\pi$
$719$	15.3805			0.573595			0.286798	+	0.957991i	$0.407409\pi$
$720$		0			0
$721$	0.588457			0.0219153
$722$		0			0
$723$	12.7815	+	12.7815i	0.475347	+	0.475347i
$724$		0			0
$725$	16.5493	+	5.45068i	0.614626	+	0.202433i
$726$		0			0
$727$	−11.3033			−0.419217			−0.209609	−	0.977785i	$-0.567219\pi$
$727$	−11.3033			−0.419217			−0.209609	+	0.977785i	$0.567219\pi$
$728$		0			0
$729$		−	19.3923i		−	0.718234i
$730$		0			0
$731$	30.5307	+	30.5307i	1.12922	+	1.12922i
$732$		0			0
$733$	−11.7021	−	11.7021i	−0.432226	−	0.432226i	0.457159	−	0.889385i	$-0.348867\pi$
$733$	−11.7021	−	11.7021i	−0.432226	−	0.432226i	−0.889385	+	0.457159i	$0.848867\pi$
$734$		0			0
$735$	16.3142	−	3.88211i	0.601759	−	0.143194i
$736$		0			0
$737$			62.3519i			2.29676i
$738$		0			0
$739$	11.1750	−	11.1750i	0.411079	−	0.411079i	−0.471035	−	0.882114i	$-0.656120\pi$
$739$	11.1750	−	11.1750i	0.411079	−	0.411079i	0.882114	+	0.471035i	$0.156120\pi$
$740$		0			0
$741$	−0.928203	−	0.928203i	−0.0340984	−	0.0340984i
$742$		0			0
$743$	−4.08014			−0.149686			−0.0748429	−	0.997195i	$-0.523846\pi$
$743$	−4.08014			−0.149686			−0.0748429	+	0.997195i	$0.523846\pi$
$744$		0			0
$745$	7.80138	−	1.85641i	0.285821	−	0.0680135i
$746$		0			0
$747$	−7.90509	+	7.90509i	−0.289232	+	0.289232i
$748$		0			0
$749$	−4.60770	+	4.60770i	−0.168362	+	0.168362i
$750$		0			0
$751$	−7.93048			−0.289387			−0.144694	−	0.989477i	$-0.546220\pi$
$751$	−7.93048			−0.289387			−0.144694	+	0.989477i	$0.546220\pi$
$752$		0			0
$753$			19.4443i			0.708589i
$754$		0			0
$755$	32.8438	+	20.2174i	1.19531	+	0.735788i
$756$		0			0
$757$	2.85550	−	2.85550i	0.103785	−	0.103785i	−0.653308	−	0.757093i	$-0.726619\pi$
$757$	2.85550	−	2.85550i	0.103785	−	0.103785i	0.757093	+	0.653308i	$0.226619\pi$
$758$		0			0
$759$		−	30.8353i		−	1.11925i
$760$		0			0
$761$		−	5.60770i		−	0.203279i	−0.994821	−	0.101639i	$-0.967591\pi$
$761$		−	5.60770i		−	0.203279i	0.994821	−	0.101639i	$-0.0324088\pi$
$762$		0			0
$763$	−5.63074	+	5.63074i	−0.203847	+	0.203847i
$764$		0			0
$765$	−10.8181	+	17.5742i	−0.391128	+	0.635398i
$766$		0			0
$767$		−	5.20405i		−	0.187907i
$768$		0			0
$769$	43.1769			1.55700			0.778500	−	0.627645i	$-0.215981\pi$
$769$	43.1769			1.55700			0.778500	+	0.627645i	$0.215981\pi$
$770$		0			0
$771$	17.8028	−	17.8028i	0.641151	−	0.641151i
$772$		0			0
$773$	−21.0121	+	21.0121i	−0.755751	+	0.755751i	−0.975546	−	0.219795i	$-0.929461\pi$
$773$	−21.0121	+	21.0121i	−0.755751	+	0.755751i	0.219795	+	0.975546i	$0.429461\pi$
$774$		0			0
$775$	−8.70131	−	17.2480i	−0.312560	−	0.619565i
$776$		0			0
$777$	3.62063			0.129890
$778$		0			0
$779$	−3.48477	−	3.48477i	−0.124855	−	0.124855i
$780$		0			0
$781$	39.7128	−	39.7128i	1.42104	−	1.42104i
$782$		0			0
$783$			18.5684i			0.663580i
$784$		0			0
$785$	21.4641	−	5.10757i	0.766087	−	0.182297i
$786$		0			0
$787$	12.5263	+	12.5263i	0.446513	+	0.446513i	0.894193	−	0.447681i	$-0.147750\pi$
$787$	12.5263	+	12.5263i	0.446513	+	0.446513i	−0.447681	+	0.894193i	$0.647750\pi$
$788$		0			0
$789$	20.3205	+	20.3205i	0.723429	+	0.723429i
$790$		0			0
$791$		−	2.62536i		−	0.0933469i
$792$		0			0
$793$	−4.50413			−0.159946
$794$		0			0
$795$	12.0480	−	19.5723i	0.427299	−	0.694159i
$796$		0			0
$797$	14.2559	+	14.2559i	0.504968	+	0.504968i	0.912978	−	0.408009i	$-0.133777\pi$
$797$	14.2559	+	14.2559i	0.504968	+	0.504968i	−0.408009	+	0.912978i	$0.633777\pi$
$798$		0			0
$799$	−43.2586			−1.53038
$800$		0			0
$801$	−0.928203			−0.0327964
$802$		0			0
$803$	−27.3840	−	27.3840i	−0.966361	−	0.966361i
$804$		0			0
$805$	−4.45873	+	7.24334i	−0.157150	+	0.255294i
$806$		0			0
$807$	−14.2177			−0.500487
$808$		0			0
$809$			33.1769i			1.16644i	0.812315	+	0.583219i	$0.198207\pi$
$809$			33.1769i			1.16644i	−0.812315	+	0.583219i	$0.801793\pi$
$810$		0			0
$811$	−11.1750	−	11.1750i	−0.392408	−	0.392408i	0.483137	−	0.875545i	$-0.339497\pi$
$811$	−11.1750	−	11.1750i	−0.392408	−	0.392408i	−0.875545	+	0.483137i	$0.839497\pi$
$812$		0			0
$813$	16.4271	+	16.4271i	0.576123	+	0.576123i
$814$		0			0
$815$	−27.9053	+	6.64032i	−0.977481	+	0.232600i
$816$		0			0
$817$			5.93188i			0.207530i
$818$		0			0
$819$	−1.13681	+	1.13681i	−0.0397234	+	0.0397234i
$820$		0			0
$821$	−31.9090	−	31.9090i	−1.11363	−	1.11363i	−0.992656	−	0.120975i	$-0.961398\pi$
$821$	−31.9090	−	31.9090i	−1.11363	−	1.11363i	−0.120975	−	0.992656i	$-0.538602\pi$
$822$		0			0
$823$	21.9095			0.763716			0.381858	−	0.924221i	$-0.375284\pi$
$823$	21.9095			0.763716			0.381858	+	0.924221i	$0.375284\pi$
$824$		0			0
$825$	21.0929	−	10.6410i	0.734360	−	0.370473i
$826$		0			0
$827$	30.2412	−	30.2412i	1.05159	−	1.05159i	0.0529963	−	0.998595i	$-0.483123\pi$
$827$	30.2412	−	30.2412i	1.05159	−	1.05159i	0.998595	−	0.0529963i	$-0.0168771\pi$
$828$		0			0
$829$	−15.3205	+	15.3205i	−0.532103	+	0.532103i	−0.921198	−	0.389095i	$-0.872788\pi$
$829$	−15.3205	+	15.3205i	−0.532103	+	0.532103i	0.389095	+	0.921198i	$0.372788\pi$
$830$		0			0
$831$	9.79796			0.339887
$832$		0			0
$833$		−	35.4888i		−	1.22961i
$834$		0			0
$835$	−21.5821	+	35.0608i	−0.746880	+	1.21333i
$836$		0			0
$837$	14.5576	−	14.5576i	0.503183	−	0.503183i
$838$		0			0
$839$			24.4206i			0.843092i	0.906807	+	0.421546i	$0.138512\pi$
$839$			24.4206i			0.843092i	−0.906807	+	0.421546i	$0.861488\pi$
$840$		0			0
$841$			16.8564i			0.581255i
$842$		0			0
$843$	−23.5019	+	23.5019i	−0.809449	+	0.809449i
$844$		0			0
$845$	19.9259	+	12.2656i	0.685472	+	0.421951i
$846$		0			0
$847$		−	3.85148i		−	0.132338i
$848$		0			0
$849$	−28.3013			−0.971297
$850$		0			0
$851$	25.4558	−	25.4558i	0.872615	−	0.872615i
$852$		0			0
$853$	−25.2953	+	25.2953i	−0.866095	+	0.866095i	−0.992038	−	0.125943i	$-0.959804\pi$
$853$	−25.2953	+	25.2953i	−0.866095	+	0.866095i	0.125943	+	0.992038i	$0.459804\pi$
$854$		0			0
$855$	−2.75821	+	0.656339i	−0.0943286	+	0.0224463i
$856$		0			0
$857$	22.3590			0.763767			0.381884	−	0.924210i	$-0.375275\pi$
$857$	22.3590			0.763767			0.381884	+	0.924210i	$0.375275\pi$
$858$		0			0
$859$	−9.55772	−	9.55772i	−0.326105	−	0.326105i	0.524998	−	0.851103i	$-0.324066\pi$
$859$	−9.55772	−	9.55772i	−0.326105	−	0.326105i	−0.851103	+	0.524998i	$0.824066\pi$
$860$		0			0
$861$	3.12436	−	3.12436i	0.106478	−	0.106478i
$862$		0			0
$863$			23.5019i			0.800014i	0.916512	+	0.400007i	$0.130992\pi$
$863$			23.5019i			0.800014i	−0.916512	+	0.400007i	$0.869008\pi$
$864$		0			0
$865$	−13.8564	+	3.29725i	−0.471132	+	0.112110i
$866$		0			0
$867$	−9.07084	−	9.07084i	−0.308062	−	0.308062i
$868$		0			0
$869$	−3.07180	−	3.07180i	−0.104204	−	0.104204i
$870$		0			0
$871$			23.6627i			0.801780i
$872$		0			0
$873$	20.9312			0.708414
$874$		0			0
$875$	−6.49348	−	0.550378i	−0.219520	−	0.0186062i
$876$		0			0
$877$	−27.2457	−	27.2457i	−0.920020	−	0.920020i	0.0770100	−	0.997030i	$-0.475463\pi$
$877$	−27.2457	−	27.2457i	−0.920020	−	0.920020i	−0.997030	+	0.0770100i	$0.975463\pi$
$878$		0			0
$879$	18.2832			0.616678
$880$		0			0
$881$	0.483340			0.0162841			0.00814206	−	0.999967i	$-0.497408\pi$
$881$	0.483340			0.0162841			0.00814206	+	0.999967i	$0.497408\pi$
$882$		0			0
$883$	9.49754	+	9.49754i	0.319618	+	0.319618i	0.848620	−	0.529003i	$-0.177434\pi$
$883$	9.49754	+	9.49754i	0.319618	+	0.319618i	−0.529003	+	0.848620i	$0.677434\pi$
$884$		0			0
$885$	7.00716	+	4.31335i	0.235543	+	0.144992i
$886$		0			0
$887$	54.1852			1.81936			0.909680	−	0.415310i	$-0.136327\pi$
$887$	54.1852			1.81936			0.909680	+	0.415310i	$0.136327\pi$
$888$		0			0
$889$			6.33975i			0.212628i
$890$		0			0
$891$	2.38512	+	2.38512i	0.0799045	+	0.0799045i
$892$		0			0
$893$	−4.20241	−	4.20241i	−0.140628	−	0.140628i
$894$		0			0
$895$	4.44571	+	18.6827i	0.148604	+	0.624494i
$896$		0			0
$897$		−	11.7021i		−	0.390721i
$898$		0			0
$899$	−9.52056	+	9.52056i	−0.317528	+	0.317528i
$900$		0			0
$901$	−34.3923	−	34.3923i	−1.14577	−	1.14577i
$902$		0			0
$903$	−5.31838			−0.176985
$904$		0			0
$905$	−44.4970	+	10.5885i	−1.47913	+	0.351972i
$906$		0			0
$907$	−8.75848	+	8.75848i	−0.290820	+	0.290820i	−0.837404	−	0.546584i	$-0.815928\pi$
$907$	−8.75848	+	8.75848i	−0.290820	+	0.290820i	0.546584	+	0.837404i	$0.315928\pi$
$908$		0			0
$909$	21.5885	−	21.5885i	0.716044	−	0.716044i
$910$		0			0
$911$	0.832204			0.0275722			0.0137861	−	0.999905i	$-0.495612\pi$
$911$	0.832204			0.0275722			0.0137861	+	0.999905i	$0.495612\pi$
$912$		0			0
$913$		−	27.0840i		−	0.896348i
$914$		0			0
$915$	3.73322	−	6.06473i	0.123417	−	0.200494i
$916$		0			0
$917$	7.49966	−	7.49966i	0.247661	−	0.247661i
$918$		0			0
$919$		−	54.2949i		−	1.79102i	−0.445037	−	0.895512i	$-0.646810\pi$
$919$		−	54.2949i		−	1.79102i	0.445037	−	0.895512i	$-0.353190\pi$
$920$		0			0
$921$		−	5.41154i		−	0.178316i
$922$		0			0
$923$	15.0711	−	15.0711i	0.496072	−	0.496072i
$924$		0			0
$925$	26.1977	+	8.62847i	0.861375	+	0.283702i
$926$		0			0
$927$			1.74863i			0.0574326i
$928$		0			0
$929$	−24.7321			−0.811432			−0.405716	−	0.913999i	$-0.632978\pi$
$929$	−24.7321			−0.811432			−0.405716	+	0.913999i	$0.632978\pi$
$930$		0			0
$931$	3.44760	−	3.44760i	0.112991	−	0.112991i
$932$		0			0
$933$	4.88669	−	4.88669i	0.159983	−	0.159983i
$934$		0			0
$935$	−11.5738	−	48.6381i	−0.378505	−	1.59063i
$936$		0			0
$937$	5.32844			0.174073			0.0870363	−	0.996205i	$-0.472260\pi$
$937$	5.32844			0.174073			0.0870363	+	0.996205i	$0.472260\pi$
$938$		0			0
$939$	−5.73118	−	5.73118i	−0.187030	−	0.187030i
$940$		0			0
$941$	−13.9282	+	13.9282i	−0.454046	+	0.454046i	−0.896695	−	0.442649i	$-0.854039\pi$
$941$	−13.9282	+	13.9282i	−0.454046	+	0.454046i	0.442649	+	0.896695i	$0.354039\pi$
$942$		0			0
$943$		−	43.9333i		−	1.43066i
$944$		0			0
$945$	−1.60770	−	6.75620i	−0.0522983	−	0.219779i
$946$		0			0
$947$	22.8200	+	22.8200i	0.741551	+	0.741551i	0.972876	−	0.231325i	$-0.0743062\pi$
$947$	22.8200	+	22.8200i	0.741551	+	0.741551i	−0.231325	+	0.972876i	$0.574306\pi$
$948$		0			0
$949$	−10.3923	−	10.3923i	−0.337348	−	0.337348i
$950$		0			0
$951$			18.7637i			0.608455i
$952$		0			0
$953$	−4.34244			−0.140665			−0.0703327	−	0.997524i	$-0.522406\pi$
$953$	−4.34244			−0.140665			−0.0703327	+	0.997524i	$0.522406\pi$
$954$		0			0
$955$	−18.1156	+	29.4293i	−0.586206	+	0.952309i
$956$		0			0
$957$	−11.6429	−	11.6429i	−0.376361	−	0.376361i
$958$		0			0
$959$	−1.31268			−0.0423886
$960$		0			0
$961$	−16.0718			−0.518445
$962$		0			0
$963$	−13.6920	−	13.6920i	−0.441219	−	0.441219i
$964$		0			0
$965$	49.5834	+	30.5217i	1.59615	+	0.982528i
$966$		0			0
$967$	−17.5588			−0.564653			−0.282327	−	0.959318i	$-0.591106\pi$
$967$	−17.5588			−0.564653			−0.282327	+	0.959318i	$0.591106\pi$
$968$		0			0
$969$		−	4.39230i		−	0.141101i
$970$		0			0
$971$	−25.7704	−	25.7704i	−0.827012	−	0.827012i	0.160091	−	0.987102i	$-0.448821\pi$
$971$	−25.7704	−	25.7704i	−0.827012	−	0.827012i	−0.987102	+	0.160091i	$0.948821\pi$
$972$		0			0
$973$	−3.98154	−	3.98154i	−0.127642	−	0.127642i
$974$		0			0
$975$	8.00481	−	4.03829i	0.256359	−	0.129329i
$976$		0			0
$977$		−	19.7243i		−	0.631037i	−0.948919	−	0.315519i	$-0.897822\pi$
$977$		−	19.7243i		−	0.631037i	0.948919	−	0.315519i	$-0.102178\pi$
$978$		0			0
$979$	1.59008	−	1.59008i	0.0508191	−	0.0508191i
$980$		0			0
$981$	−16.7321	−	16.7321i	−0.534213	−	0.534213i
$982$		0			0
$983$	41.4456			1.32191			0.660954	−	0.750426i	$-0.270152\pi$
$983$	41.4456			1.32191			0.660954	+	0.750426i	$0.270152\pi$
$984$		0			0
$985$	5.32844	+	22.3923i	0.169778	+	0.713478i
$986$		0			0
$987$	3.76778	−	3.76778i	0.119930	−	0.119930i
$988$		0			0
$989$	−37.3923	+	37.3923i	−1.18901	+	1.18901i
$990$		0			0
$991$	12.8295			0.407541			0.203771	−	0.979019i	$-0.434680\pi$
$991$	12.8295			0.407541			0.203771	+	0.979019i	$0.434680\pi$
$992$		0			0
$993$			13.1298i			0.416662i
$994$		0			0
$995$	−48.0867	−	29.6004i	−1.52445	−	0.938395i
$996$		0			0
$997$	25.5162	−	25.5162i	0.808106	−	0.808106i	−0.176241	−	0.984347i	$-0.556394\pi$
$997$	25.5162	−	25.5162i	0.808106	−	0.808106i	0.984347	+	0.176241i	$0.0563939\pi$
$998$		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.449.5	yes	16
4.3	odd	2	inner	1280.2.q.a.449.3	✓	16
5.4	even	2	inner	1280.2.q.a.449.4	yes	16
8.3	odd	2		1280.2.q.b.449.6	yes	16
8.5	even	2		1280.2.q.b.449.4	yes	16
16.3	odd	4	inner	1280.2.q.a.1089.6	yes	16
16.5	even	4		1280.2.q.b.1089.5	yes	16
16.11	odd	4		1280.2.q.b.1089.3	yes	16
16.13	even	4	inner	1280.2.q.a.1089.4	yes	16
20.19	odd	2	inner	1280.2.q.a.449.6	yes	16
40.19	odd	2		1280.2.q.b.449.3	yes	16
40.29	even	2		1280.2.q.b.449.5	yes	16
80.19	odd	4	inner	1280.2.q.a.1089.3	yes	16
80.29	even	4	inner	1280.2.q.a.1089.5	yes	16
80.59	odd	4		1280.2.q.b.1089.6	yes	16
80.69	even	4		1280.2.q.b.1089.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.q.a.449.3	✓	16	4.3	odd	2	inner
1280.2.q.a.449.4	yes	16	5.4	even	2	inner
1280.2.q.a.449.5	yes	16	1.1	even	1	trivial
1280.2.q.a.449.6	yes	16	20.19	odd	2	inner
1280.2.q.a.1089.3	yes	16	80.19	odd	4	inner
1280.2.q.a.1089.4	yes	16	16.13	even	4	inner
1280.2.q.a.1089.5	yes	16	80.29	even	4	inner
1280.2.q.a.1089.6	yes	16	16.3	odd	4	inner
1280.2.q.b.449.3	yes	16	40.19	odd	2
1280.2.q.b.449.4	yes	16	8.5	even	2
1280.2.q.b.449.5	yes	16	40.29	even	2
1280.2.q.b.449.6	yes	16	8.3	odd	2
1280.2.q.b.1089.3	yes	16	16.11	odd	4
1280.2.q.b.1089.4	yes	16	80.69	even	4
1280.2.q.b.1089.5	yes	16	16.5	even	4
1280.2.q.b.1089.6	yes	16	80.59	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.796225 + 0.796225i) q^{3} +(-1.17216 + 1.90421i) q^{5} -0.582877 q^{7} -1.73205i q^{9} +O(q^{10})\)	\(q+(0.796225 + 0.796225i) q^{3} +(-1.17216 + 1.90421i) q^{5} -0.582877 q^{7} -1.73205i q^{9} +(2.96713 + 2.96713i) q^{11} +(1.12603 + 1.12603i) q^{13} +(-2.44949 + 0.582877i) q^{15} +5.32844i q^{17} +(-0.517638 + 0.517638i) q^{19} +(-0.464102 - 0.464102i) q^{21} -6.52598 q^{23} +(-2.25207 - 4.46410i) q^{25} +(3.76778 - 3.76778i) q^{27} +(-2.46410 + 2.46410i) q^{29} +3.86370 q^{31} +4.72500i q^{33} +(0.683228 - 1.10992i) q^{35} +(-3.90069 + 3.90069i) q^{37} +1.79315i q^{39} +6.73205i q^{41} +(5.72976 - 5.72976i) q^{43} +(3.29820 + 2.03025i) q^{45} +8.11843i q^{47} -6.66025 q^{49} +(-4.24264 + 4.24264i) q^{51} +(-6.45448 + 6.45448i) q^{53} +(-9.12801 + 2.17209i) q^{55} -0.824313 q^{57} +(-2.31079 - 2.31079i) q^{59} +(-2.00000 + 2.00000i) q^{61} +1.00957i q^{63} +(-3.46410 + 0.824313i) q^{65} +(10.5071 + 10.5071i) q^{67} +(-5.19615 - 5.19615i) q^{69} -13.3843i q^{71} -9.22913 q^{73} +(1.76128 - 5.34758i) q^{75} +(-1.72947 - 1.72947i) q^{77} -1.03528 q^{79} +0.803848 q^{81} +(-4.56400 - 4.56400i) q^{83} +(-10.1465 - 6.24581i) q^{85} -3.92396 q^{87} -0.535898i q^{89} +(-0.656339 - 0.656339i) q^{91} +(3.07638 + 3.07638i) q^{93} +(-0.378937 - 1.59245i) q^{95} +12.0846i q^{97} +(5.13922 - 5.13922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5}+O(q^{10}) \) 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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