LMFDB - Embedded newform 1280.2.l.f.321.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(321,1280)]

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, 3, 0]))

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

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

chi := DirichletCharacter("1280.321");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.l (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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			321.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1280.321
Dual form			1280.2.l.f.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.658919 + 0.658919i) q^{3} +(-0.707107 + 0.707107i) q^{5} -2.34607i q^{7} -2.13165i q^{9} +O(q^{10})$	\(q+(0.658919 + 0.658919i) q^{3} +(-0.707107 + 0.707107i) q^{5} -2.34607i q^{7} -2.13165i q^{9} +(-1.19980 + 1.19980i) q^{11} +(-1.51764 - 1.51764i) q^{13} -0.931852 q^{15} +1.11099 q^{17} +(1.53225 + 1.53225i) q^{19} +(1.54587 - 1.54587i) q^{21} -4.83548i q^{23} -1.00000i q^{25} +(3.38134 - 3.38134i) q^{27} +(-5.49938 - 5.49938i) q^{29} -6.29253 q^{31} -1.58114 q^{33} +(1.65892 + 1.65892i) q^{35} +(4.59575 - 4.59575i) q^{37} -2.00000i q^{39} -10.0599i q^{41} +(-5.14128 + 5.14128i) q^{43} +(1.50731 + 1.50731i) q^{45} -6.44584 q^{47} +1.49598 q^{49} +(0.732051 + 0.732051i) q^{51} +(5.02823 - 5.02823i) q^{53} -1.69677i q^{55} +2.01926i q^{57} +(1.46170 - 1.46170i) q^{59} +(-0.752715 - 0.752715i) q^{61} -5.00100 q^{63} +2.14626 q^{65} +(11.2975 + 11.2975i) q^{67} +(3.18618 - 3.18618i) q^{69} +0.399602i q^{71} -6.02406i q^{73} +(0.658919 - 0.658919i) q^{75} +(2.81481 + 2.81481i) q^{77} +15.8637 q^{79} -1.93890 q^{81} +(-0.312853 - 0.312853i) q^{83} +(-0.785587 + 0.785587i) q^{85} -7.24728i q^{87} -16.5558i q^{89} +(-3.56048 + 3.56048i) q^{91} +(-4.14626 - 4.14626i) q^{93} -2.16693 q^{95} +9.14502 q^{97} +(2.55756 + 2.55756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3}+O(q^{10}) $ 8 * q + 4 * q^3	$ 8 q + 4 q^{3} - 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} - 16 q^{21} - 8 q^{27} - 8 q^{29} + 24 q^{33} + 12 q^{35} - 8 q^{37} - 44 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{51} + 16 q^{53} + 16 q^{59} + 8 q^{61} - 48 q^{63} - 8 q^{65} + 12 q^{67} + 40 q^{69} + 4 q^{75} + 16 q^{77} + 96 q^{79} - 16 q^{81} - 28 q^{83} - 16 q^{85} + 8 q^{91} - 8 q^{93} + 8 q^{95} - 24 q^{97} + 56 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 - 16 * q^21 - 8 * q^27 - 8 * q^29 + 24 * q^33 + 12 * q^35 - 8 * q^37 - 44 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^51 + 16 * q^53 + 16 * q^59 + 8 * q^61 - 48 * q^63 - 8 * q^65 + 12 * q^67 + 40 * q^69 + 4 * q^75 + 16 * q^77 + 96 * q^79 - 16 * q^81 - 28 * q^83 - 16 * q^85 + 8 * q^91 - 8 * q^93 + 8 * q^95 - 24 * q^97 + 56 * q^99

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
$3$	0.658919	+	0.658919i	0.380427	+	0.380427i	0.871256	−	0.490829i	$-0.163306\pi$
$3$	0.658919	+	0.658919i	0.380427	+	0.380427i	−0.490829	+	0.871256i	$0.663306\pi$
$4$		0			0
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$		−	2.34607i		−	0.886729i	−0.896341	−	0.443365i	$-0.853785\pi$
$7$		−	2.34607i		−	0.886729i	0.896341	−	0.443365i	$-0.146215\pi$
$8$		0			0
$9$		−	2.13165i		−	0.710551i
$10$		0			0
$11$	−1.19980	+	1.19980i	−0.361754	+	0.361754i	−0.864458	−	0.502705i	$-0.832338\pi$
$11$	−1.19980	+	1.19980i	−0.361754	+	0.361754i	0.502705	+	0.864458i	$0.332338\pi$
$12$		0			0
$13$	−1.51764	−	1.51764i	−0.420917	−	0.420917i	0.464602	−	0.885519i	$-0.346197\pi$
$13$	−1.51764	−	1.51764i	−0.420917	−	0.420917i	−0.885519	+	0.464602i	$0.846197\pi$
$14$		0			0
$15$	−0.931852			−0.240603
$16$		0			0
$17$	1.11099			0.269454			0.134727	−	0.990883i	$-0.456984\pi$
$17$	1.11099			0.269454			0.134727	+	0.990883i	$0.456984\pi$
$18$		0			0
$19$	1.53225	+	1.53225i	0.351522	+	0.351522i	0.860676	−	0.509153i	$-0.170041\pi$
$19$	1.53225	+	1.53225i	0.351522	+	0.351522i	−0.509153	+	0.860676i	$0.670041\pi$
$20$		0			0
$21$	1.54587	−	1.54587i	0.337336	−	0.337336i
$22$		0			0
$23$		−	4.83548i		−	1.00827i	−0.863626	−	0.504133i	$-0.831812\pi$
$23$		−	4.83548i		−	1.00827i	0.863626	−	0.504133i	$-0.168188\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	3.38134	−	3.38134i	0.650739	−	0.650739i
$28$		0			0
$29$	−5.49938	−	5.49938i	−1.02121	−	1.02121i	−0.999770	−	0.0214387i	$-0.993175\pi$
$29$	−5.49938	−	5.49938i	−1.02121	−	1.02121i	−0.0214387	−	0.999770i	$-0.506825\pi$
$30$		0			0
$31$	−6.29253			−1.13017			−0.565086	−	0.825032i	$-0.691157\pi$
$31$	−6.29253			−1.13017			−0.565086	+	0.825032i	$0.691157\pi$
$32$		0			0
$33$	−1.58114			−0.275242
$34$		0			0
$35$	1.65892	+	1.65892i	0.280408	+	0.280408i
$36$		0			0
$37$	4.59575	−	4.59575i	0.755537	−	0.755537i	−0.219969	−	0.975507i	$-0.570596\pi$
$37$	4.59575	−	4.59575i	0.755537	−	0.755537i	0.975507	+	0.219969i	$0.0705958\pi$
$38$		0			0
$39$		−	2.00000i		−	0.320256i
$40$		0			0
$41$		−	10.0599i		−	1.57109i	−0.618807	−	0.785543i	$-0.712384\pi$
$41$		−	10.0599i		−	1.57109i	0.618807	−	0.785543i	$-0.287616\pi$
$42$		0			0
$43$	−5.14128	+	5.14128i	−0.784038	+	0.784038i	−0.980510	−	0.196472i	$-0.937052\pi$
$43$	−5.14128	+	5.14128i	−0.784038	+	0.784038i	0.196472	+	0.980510i	$0.437052\pi$
$44$		0			0
$45$	1.50731	+	1.50731i	0.224696	+	0.224696i
$46$		0			0
$47$	−6.44584			−0.940223			−0.470111	−	0.882607i	$-0.655786\pi$
$47$	−6.44584			−0.940223			−0.470111	+	0.882607i	$0.655786\pi$
$48$		0			0
$49$	1.49598			0.213711
$50$		0			0
$51$	0.732051	+	0.732051i	0.102508	+	0.102508i
$52$		0			0
$53$	5.02823	−	5.02823i	0.690680	−	0.690680i	−0.271701	−	0.962382i	$-0.587586\pi$
$53$	5.02823	−	5.02823i	0.690680	−	0.690680i	0.962382	+	0.271701i	$0.0875863\pi$
$54$		0			0
$55$		−	1.69677i		−	0.228793i
$56$		0			0
$57$			2.01926i			0.267457i
$58$		0			0
$59$	1.46170	−	1.46170i	0.190297	−	0.190297i	−0.605528	−	0.795824i	$-0.707038\pi$
$59$	1.46170	−	1.46170i	0.190297	−	0.190297i	0.795824	+	0.605528i	$0.207038\pi$
$60$		0			0
$61$	−0.752715	−	0.752715i	−0.0963753	−	0.0963753i	0.657275	−	0.753651i	$-0.271709\pi$
$61$	−0.752715	−	0.752715i	−0.0963753	−	0.0963753i	−0.753651	+	0.657275i	$0.771709\pi$
$62$		0			0
$63$	−5.00100			−0.630066
$64$		0			0
$65$	2.14626			0.266211
$66$		0			0
$67$	11.2975	+	11.2975i	1.38021	+	1.38021i	0.844230	+	0.535980i	$0.180058\pi$
$67$	11.2975	+	11.2975i	1.38021	+	1.38021i	0.535980	+	0.844230i	$0.319942\pi$
$68$		0			0
$69$	3.18618	−	3.18618i	0.383572	−	0.383572i
$70$		0			0
$71$			0.399602i			0.0474240i	0.999719	+	0.0237120i	$0.00754847\pi$
$71$			0.399602i			0.0474240i	−0.999719	+	0.0237120i	$0.992452\pi$
$72$		0			0
$73$		−	6.02406i		−	0.705063i	−0.935800	−	0.352532i	$-0.885321\pi$
$73$		−	6.02406i		−	0.705063i	0.935800	−	0.352532i	$-0.114679\pi$
$74$		0			0
$75$	0.658919	−	0.658919i	0.0760854	−	0.0760854i
$76$		0			0
$77$	2.81481	+	2.81481i	0.320777	+	0.320777i
$78$		0			0
$79$	15.8637			1.78481			0.892403	−	0.451239i	$-0.149018\pi$
$79$	15.8637			1.78481			0.892403	+	0.451239i	$0.149018\pi$
$80$		0			0
$81$	−1.93890			−0.215433
$82$		0			0
$83$	−0.312853	−	0.312853i	−0.0343401	−	0.0343401i	0.689728	−	0.724068i	$-0.257730\pi$
$83$	−0.312853	−	0.312853i	−0.0343401	−	0.0343401i	−0.724068	+	0.689728i	$0.757730\pi$
$84$		0			0
$85$	−0.785587	+	0.785587i	−0.0852089	+	0.0852089i
$86$		0			0
$87$		−	7.24728i		−	0.776990i
$88$		0			0
$89$		−	16.5558i		−	1.75491i	−0.479655	−	0.877457i	$-0.659238\pi$
$89$		−	16.5558i		−	1.75491i	0.479655	−	0.877457i	$-0.340762\pi$
$90$		0			0
$91$	−3.56048	+	3.56048i	−0.373240	+	0.373240i
$92$		0			0
$93$	−4.14626	−	4.14626i	−0.429948	−	0.429948i
$94$		0			0
$95$	−2.16693			−0.222322
$96$		0			0
$97$	9.14502			0.928536			0.464268	−	0.885695i	$-0.346317\pi$
$97$	9.14502			0.928536			0.464268	+	0.885695i	$0.346317\pi$
$98$		0			0
$99$	2.55756	+	2.55756i	0.257044	+	0.257044i
$100$		0			0
$101$	1.96472	−	1.96472i	0.195497	−	0.195497i	−0.602569	−	0.798067i	$-0.705856\pi$
$101$	1.96472	−	1.96472i	0.195497	−	0.195497i	0.798067	+	0.602569i	$0.205856\pi$
$102$		0			0
$103$			4.52885i			0.446241i	0.974791	+	0.223120i	$0.0716243\pi$
$103$			4.52885i			0.446241i	−0.974791	+	0.223120i	$0.928376\pi$
$104$		0			0
$105$			2.18618i			0.213350i
$106$		0			0
$107$	2.87574	−	2.87574i	0.278008	−	0.278008i	−0.554305	−	0.832313i	$-0.687016\pi$
$107$	2.87574	−	2.87574i	0.278008	−	0.278008i	0.832313	+	0.554305i	$0.187016\pi$
$108$		0			0
$109$	−2.74202	−	2.74202i	−0.262638	−	0.262638i	0.563487	−	0.826125i	$-0.309459\pi$
$109$	−2.74202	−	2.74202i	−0.262638	−	0.262638i	−0.826125	+	0.563487i	$0.809459\pi$
$110$		0			0
$111$	6.05646			0.574853
$112$		0			0
$113$	−14.3923			−1.35391			−0.676957	−	0.736022i	$-0.736702\pi$
$113$	−14.3923			−1.35391			−0.676957	+	0.736022i	$0.736702\pi$
$114$		0			0
$115$	3.41920	+	3.41920i	0.318842	+	0.318842i
$116$		0			0
$117$	−3.23508	+	3.23508i	−0.299083	+	0.299083i
$118$		0			0
$119$		−	2.60645i		−	0.238933i
$120$		0			0
$121$			8.12096i			0.738269i
$122$		0			0
$123$	6.62863	−	6.62863i	0.597683	−	0.597683i
$124$		0			0
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$	−18.2611			−1.62041			−0.810204	−	0.586148i	$-0.800644\pi$
$127$	−18.2611			−1.62041			−0.810204	+	0.586148i	$0.800644\pi$
$128$		0			0
$129$	−6.77537			−0.596538
$130$		0			0
$131$	4.61401	+	4.61401i	0.403128	+	0.403128i	0.879334	−	0.476206i	$-0.157988\pi$
$131$	4.61401	+	4.61401i	0.403128	+	0.403128i	−0.476206	+	0.879334i	$0.657988\pi$
$132$		0			0
$133$	3.59476	−	3.59476i	0.311705	−	0.311705i
$134$		0			0
$135$			4.78194i			0.411564i
$136$		0			0
$137$			14.4195i			1.23194i	0.787768	+	0.615972i	$0.211237\pi$
$137$			14.4195i			1.23194i	−0.787768	+	0.615972i	$0.788763\pi$
$138$		0			0
$139$	−11.9160	+	11.9160i	−1.01070	+	1.01070i	−0.0107594	+	0.999942i	$0.503425\pi$
$139$	−11.9160	+	11.9160i	−1.01070	+	1.01070i	−0.999942	+	0.0107594i	$0.996575\pi$
$140$		0			0
$141$	−4.24728	−	4.24728i	−0.357686	−	0.357686i
$142$		0			0
$143$	3.64173			0.304537
$144$		0			0
$145$	7.77729			0.645869
$146$		0			0
$147$	0.985728	+	0.985728i	0.0813015	+	0.0813015i
$148$		0			0
$149$	−9.47407	+	9.47407i	−0.776146	+	0.776146i	−0.979173	−	0.203027i	$-0.934922\pi$
$149$	−9.47407	+	9.47407i	−0.776146	+	0.776146i	0.203027	+	0.979173i	$0.434922\pi$
$150$		0			0
$151$		−	10.7062i		−	0.871260i	−0.900126	−	0.435630i	$-0.856526\pi$
$151$		−	10.7062i		−	0.871260i	0.900126	−	0.435630i	$-0.143474\pi$
$152$		0			0
$153$		−	2.36824i		−	0.191461i
$154$		0			0
$155$	4.44949	−	4.44949i	0.357392	−	0.357392i
$156$		0			0
$157$	16.4986	+	16.4986i	1.31674	+	1.31674i	0.916344	+	0.400391i	$0.131126\pi$
$157$	16.4986	+	16.4986i	1.31674	+	1.31674i	0.400391	+	0.916344i	$0.368874\pi$
$158$		0			0
$159$	6.62639			0.525507
$160$		0			0
$161$	−11.3443			−0.894059
$162$		0			0
$163$	−10.8152	−	10.8152i	−0.847108	−	0.847108i	0.142663	−	0.989771i	$-0.454433\pi$
$163$	−10.8152	−	10.8152i	−0.847108	−	0.847108i	−0.989771	+	0.142663i	$0.954433\pi$
$164$		0			0
$165$	1.11804	−	1.11804i	0.0870390	−	0.0870390i
$166$		0			0
$167$			13.9413i			1.07881i	0.842046	+	0.539405i	$0.181351\pi$
$167$			13.9413i			1.07881i	−0.842046	+	0.539405i	$0.818649\pi$
$168$		0			0
$169$		−	8.39355i		−	0.645658i
$170$		0			0
$171$	3.26622	−	3.26622i	0.249774	−	0.249774i
$172$		0			0
$173$	−2.73205	−	2.73205i	−0.207714	−	0.207714i	0.595581	−	0.803295i	$-0.296922\pi$
$173$	−2.73205	−	2.73205i	−0.207714	−	0.207714i	−0.803295	+	0.595581i	$0.796922\pi$
$174$		0			0
$175$	−2.34607			−0.177346
$176$		0			0
$177$	1.92628			0.144788
$178$		0			0
$179$	−17.7656	−	17.7656i	−1.32786	−	1.32786i	−0.907231	−	0.420632i	$-0.861808\pi$
$179$	−17.7656	−	17.7656i	−1.32786	−	1.32786i	−0.420632	−	0.907231i	$-0.638192\pi$
$180$		0			0
$181$	2.24213	−	2.24213i	0.166656	−	0.166656i	−0.618852	−	0.785508i	$-0.712402\pi$
$181$	2.24213	−	2.24213i	0.166656	−	0.166656i	0.785508	+	0.618852i	$0.212402\pi$
$182$		0			0
$183$		−	0.991956i		−	0.0733275i
$184$		0			0
$185$			6.49938i			0.477844i
$186$		0			0
$187$	−1.33296	+	1.33296i	−0.0974760	+	0.0974760i
$188$		0			0
$189$	−7.93285	−	7.93285i	−0.577030	−	0.577030i
$190$		0			0
$191$	−2.60164			−0.188248			−0.0941241	−	0.995560i	$-0.530005\pi$
$191$	−2.60164			−0.188248			−0.0941241	+	0.995560i	$0.530005\pi$
$192$		0			0
$193$	17.0452			1.22694			0.613472	−	0.789717i	$-0.289772\pi$
$193$	17.0452			1.22694			0.613472	+	0.789717i	$0.289772\pi$
$194$		0			0
$195$	1.41421	+	1.41421i	0.101274	+	0.101274i
$196$		0			0
$197$	−10.0535	+	10.0535i	−0.716285	+	0.716285i	−0.967842	−	0.251558i	$-0.919057\pi$
$197$	−10.0535	+	10.0535i	−0.716285	+	0.716285i	0.251558	+	0.967842i	$0.419057\pi$
$198$		0			0
$199$			10.7287i			0.760534i	0.924877	+	0.380267i	$0.124168\pi$
$199$			10.7287i			0.760534i	−0.924877	+	0.380267i	$0.875832\pi$
$200$		0			0
$201$			14.8883i			1.05014i
$202$		0			0
$203$	−12.9019	+	12.9019i	−0.905536	+	0.905536i
$204$		0			0
$205$	7.11339	+	7.11339i	0.496821	+	0.496821i
$206$		0			0
$207$	−10.3076			−0.716424
$208$		0			0
$209$	−3.67679			−0.254329
$210$		0			0
$211$	−17.7350	−	17.7350i	−1.22093	−	1.22093i	−0.967303	−	0.253622i	$-0.918378\pi$
$211$	−17.7350	−	17.7350i	−1.22093	−	1.22093i	−0.253622	−	0.967303i	$-0.581622\pi$
$212$		0			0
$213$	−0.263305	+	0.263305i	−0.0180414	+	0.0180414i
$214$		0			0
$215$		−	7.27087i		−	0.495869i
$216$		0			0
$217$			14.7627i			1.00216i
$218$		0			0
$219$	3.96937	−	3.96937i	0.268225	−	0.268225i
$220$		0			0
$221$	−1.68608	−	1.68608i	−0.113418	−	0.113418i
$222$		0			0
$223$	18.2124			1.21960			0.609798	−	0.792557i	$-0.291251\pi$
$223$	18.2124			1.21960			0.609798	+	0.792557i	$0.291251\pi$
$224$		0			0
$225$	−2.13165			−0.142110
$226$		0			0
$227$	8.98797	+	8.98797i	0.596552	+	0.596552i	0.939393	−	0.342841i	$-0.111389\pi$
$227$	8.98797	+	8.98797i	0.596552	+	0.596552i	−0.342841	+	0.939393i	$0.611389\pi$
$228$		0			0
$229$	1.60645	−	1.60645i	0.106157	−	0.106157i	−0.652033	−	0.758190i	$-0.726084\pi$
$229$	1.60645	−	1.60645i	0.106157	−	0.106157i	0.758190	+	0.652033i	$0.226084\pi$
$230$		0			0
$231$			3.70946i			0.244065i
$232$		0			0
$233$			0.287369i			0.0188262i	0.999956	+	0.00941309i	$0.00299632\pi$
$233$			0.287369i			0.0188262i	−0.999956	+	0.00941309i	$0.997004\pi$
$234$		0			0
$235$	4.55790	−	4.55790i	0.297324	−	0.297324i
$236$		0			0
$237$	10.4529	+	10.4529i	0.678988	+	0.678988i
$238$		0			0
$239$	17.5274			1.13375			0.566875	−	0.823804i	$-0.308152\pi$
$239$	17.5274			1.13375			0.566875	+	0.823804i	$0.308152\pi$
$240$		0			0
$241$	8.39371			0.540687			0.270343	−	0.962764i	$-0.412863\pi$
$241$	8.39371			0.540687			0.270343	+	0.962764i	$0.412863\pi$
$242$		0			0
$243$	−11.4216	−	11.4216i	−0.732696	−	0.732696i
$244$		0			0
$245$	−1.05782	+	1.05782i	−0.0675814	+	0.0675814i
$246$		0			0
$247$		−	4.65080i		−	0.295923i
$248$		0			0
$249$		−	0.412290i		−	0.0261278i
$250$		0			0
$251$	9.83548	−	9.83548i	0.620810	−	0.620810i	−0.324929	−	0.945738i	$-0.605340\pi$
$251$	9.83548	−	9.83548i	0.620810	−	0.620810i	0.945738	+	0.324929i	$0.105340\pi$
$252$		0			0
$253$	5.80161	+	5.80161i	0.364744	+	0.364744i
$254$		0			0
$255$	−1.03528			−0.0648315
$256$		0			0
$257$	18.2054			1.13562			0.567811	−	0.823159i	$-0.307791\pi$
$257$	18.2054			1.13562			0.567811	+	0.823159i	$0.307791\pi$
$258$		0			0
$259$	−10.7819	−	10.7819i	−0.669957	−	0.669957i
$260$		0			0
$261$	−11.7228	+	11.7228i	−0.725621	+	0.725621i
$262$		0			0
$263$			22.5174i			1.38848i	0.719742	+	0.694242i	$0.244260\pi$
$263$			22.5174i			1.38848i	−0.719742	+	0.694242i	$0.755740\pi$
$264$		0			0
$265$			7.11099i			0.436825i
$266$		0			0
$267$	10.9089	−	10.9089i	0.667617	−	0.667617i
$268$		0			0
$269$	−15.0745	−	15.0745i	−0.919107	−	0.919107i	0.0778580	−	0.996964i	$-0.475192\pi$
$269$	−15.0745	−	15.0745i	−0.919107	−	0.919107i	−0.996964	+	0.0778580i	$0.975192\pi$
$270$		0			0
$271$	30.6848			1.86397			0.931985	−	0.362496i	$-0.118075\pi$
$271$	30.6848			1.86397			0.931985	+	0.362496i	$0.118075\pi$
$272$		0			0
$273$	−4.69213			−0.283981
$274$		0			0
$275$	1.19980	+	1.19980i	0.0723507	+	0.0723507i
$276$		0			0
$277$	−6.85425	+	6.85425i	−0.411832	+	0.411832i	−0.882376	−	0.470544i	$-0.844058\pi$
$277$	−6.85425	+	6.85425i	−0.411832	+	0.411832i	0.470544	+	0.882376i	$0.344058\pi$
$278$		0			0
$279$			13.4135i			0.803044i
$280$		0			0
$281$			2.44433i			0.145817i	0.997339	+	0.0729083i	$0.0232280\pi$
$281$			2.44433i			0.145817i	−0.997339	+	0.0729083i	$0.976772\pi$
$282$		0			0
$283$	2.29171	−	2.29171i	0.136228	−	0.136228i	−0.635705	−	0.771932i	$-0.719290\pi$
$283$	2.29171	−	2.29171i	0.136228	−	0.136228i	0.771932	+	0.635705i	$0.219290\pi$
$284$		0			0
$285$	−1.42783	−	1.42783i	−0.0845773	−	0.0845773i
$286$		0			0
$287$	−23.6011			−1.39313
$288$		0			0
$289$	−15.7657			−0.927394
$290$		0			0
$291$	6.02582	+	6.02582i	0.353240	+	0.353240i
$292$		0			0
$293$	−17.9043	+	17.9043i	−1.04598	+	1.04598i	−0.0470899	+	0.998891i	$0.514995\pi$
$293$	−17.9043	+	17.9043i	−1.04598	+	1.04598i	−0.998891	+	0.0470899i	$0.985005\pi$
$294$		0			0
$295$			2.06715i			0.120354i
$296$		0			0
$297$			8.11387i			0.470815i
$298$		0			0
$299$	−7.33850	+	7.33850i	−0.424397	+	0.424397i
$300$		0			0
$301$	12.0618	+	12.0618i	0.695229	+	0.695229i
$302$		0			0
$303$	2.58919			0.148745
$304$		0			0
$305$	1.06450			0.0609531
$306$		0			0
$307$	−7.15125	−	7.15125i	−0.408143	−	0.408143i	0.472947	−	0.881091i	$-0.343190\pi$
$307$	−7.15125	−	7.15125i	−0.408143	−	0.408143i	−0.881091	+	0.472947i	$0.843190\pi$
$308$		0			0
$309$	−2.98414	+	2.98414i	−0.169762	+	0.169762i
$310$		0			0
$311$			23.2114i			1.31620i	0.752930	+	0.658100i	$0.228640\pi$
$311$			23.2114i			1.31620i	−0.752930	+	0.658100i	$0.771360\pi$
$312$		0			0
$313$			5.10686i			0.288657i	0.989530	+	0.144328i	$0.0461022\pi$
$313$			5.10686i			0.288657i	−0.989530	+	0.144328i	$0.953898\pi$
$314$		0			0
$315$	3.53624	−	3.53624i	0.199244	−	0.199244i
$316$		0			0
$317$	20.6162	+	20.6162i	1.15792	+	1.15792i	0.984922	+	0.172997i	$0.0553451\pi$
$317$	20.6162	+	20.6162i	1.15792	+	1.15792i	0.172997	+	0.984922i	$0.444655\pi$
$318$		0			0
$319$	13.1963			0.738852
$320$		0			0
$321$	3.78975			0.211523
$322$		0			0
$323$	1.70231	+	1.70231i	0.0947192	+	0.0947192i
$324$		0			0
$325$	−1.51764	+	1.51764i	−0.0841834	+	0.0841834i
$326$		0			0
$327$		−	3.61353i		−	0.199829i
$328$		0			0
$329$			15.1224i			0.833723i
$330$		0			0
$331$	−10.1686	+	10.1686i	−0.558917	+	0.558917i	−0.928999	−	0.370082i	$-0.879330\pi$
$331$	−10.1686	+	10.1686i	−0.558917	+	0.558917i	0.370082	+	0.928999i	$0.379330\pi$
$332$		0			0
$333$	−9.79655	−	9.79655i	−0.536848	−	0.536848i
$334$		0			0
$335$	−15.9771			−0.872922
$336$		0			0
$337$	13.9542			0.760133			0.380067	−	0.924959i	$-0.375901\pi$
$337$	13.9542			0.760133			0.380067	+	0.924959i	$0.375901\pi$
$338$		0			0
$339$	−9.48336	−	9.48336i	−0.515065	−	0.515065i
$340$		0			0
$341$	7.54978	−	7.54978i	0.408844	−	0.408844i
$342$		0			0
$343$		−	19.9321i		−	1.07623i
$344$		0			0
$345$			4.50595i			0.242592i
$346$		0			0
$347$	20.1208	−	20.1208i	1.08014	−	1.08014i	0.0836444	−	0.996496i	$-0.473344\pi$
$347$	20.1208	−	20.1208i	1.08014	−	1.08014i	0.996496	−	0.0836444i	$-0.0266560\pi$
$348$		0			0
$349$	3.33386	+	3.33386i	0.178457	+	0.178457i	0.790683	−	0.612226i	$-0.209726\pi$
$349$	3.33386	+	3.33386i	0.178457	+	0.178457i	−0.612226	+	0.790683i	$0.709726\pi$
$350$		0			0
$351$	−10.2633			−0.547815
$352$		0			0
$353$	−35.7352			−1.90199			−0.950997	−	0.309199i	$-0.899939\pi$
$353$	−35.7352			−1.90199			−0.950997	+	0.309199i	$0.899939\pi$
$354$		0			0
$355$	−0.282561	−	0.282561i	−0.0149968	−	0.0149968i
$356$		0			0
$357$	1.71744	−	1.71744i	0.0908965	−	0.0908965i
$358$		0			0
$359$			11.2159i			0.591954i	0.955195	+	0.295977i	$0.0956451\pi$
$359$			11.2159i			0.591954i	−0.955195	+	0.295977i	$0.904355\pi$
$360$		0			0
$361$		−	14.3044i		−	0.752864i
$362$		0			0
$363$	−5.35105	+	5.35105i	−0.280857	+	0.280857i
$364$		0			0
$365$	4.25966	+	4.25966i	0.222961	+	0.222961i
$366$		0			0
$367$	13.2867			0.693561			0.346781	−	0.937946i	$-0.387275\pi$
$367$	13.2867			0.693561			0.346781	+	0.937946i	$0.387275\pi$
$368$		0			0
$369$	−21.4441			−1.11634
$370$		0			0
$371$	−11.7966	−	11.7966i	−0.612446	−	0.612446i
$372$		0			0
$373$	−2.58166	+	2.58166i	−0.133673	+	0.133673i	−0.770778	−	0.637104i	$-0.780132\pi$
$373$	−2.58166	+	2.58166i	−0.133673	+	0.133673i	0.637104	+	0.770778i	$0.280132\pi$
$374$		0			0
$375$			0.931852i			0.0481206i
$376$		0			0
$377$			16.6921i			0.859688i
$378$		0			0
$379$	−19.2025	+	19.2025i	−0.986365	+	0.986365i	−0.999908	−	0.0135436i	$-0.995689\pi$
$379$	−19.2025	+	19.2025i	−0.986365	+	0.986365i	0.0135436	+	0.999908i	$0.495689\pi$
$380$		0			0
$381$	−12.0326	−	12.0326i	−0.616447	−	0.616447i
$382$		0			0
$383$	19.5286			0.997867			0.498933	−	0.866640i	$-0.333725\pi$
$383$	19.5286			0.997867			0.498933	+	0.866640i	$0.333725\pi$
$384$		0			0
$385$	−3.98074			−0.202877
$386$		0			0
$387$	10.9594	+	10.9594i	0.557099	+	0.557099i
$388$		0			0
$389$	5.67412	−	5.67412i	0.287689	−	0.287689i	−0.548477	−	0.836166i	$-0.684792\pi$
$389$	5.67412	−	5.67412i	0.287689	−	0.287689i	0.836166	+	0.548477i	$0.184792\pi$
$390$		0			0
$391$		−	5.37216i		−	0.271682i
$392$		0			0
$393$			6.08052i			0.306722i
$394$		0			0
$395$	−11.2173	+	11.2173i	−0.564405	+	0.564405i
$396$		0			0
$397$	13.8102	+	13.8102i	0.693112	+	0.693112i	0.962916	−	0.269803i	$-0.0869586\pi$
$397$	13.8102	+	13.8102i	0.693112	+	0.693112i	−0.269803	+	0.962916i	$0.586959\pi$
$398$		0			0
$399$	4.73731			0.237162
$400$		0			0
$401$	4.06126			0.202810			0.101405	−	0.994845i	$-0.467666\pi$
$401$	4.06126			0.202810			0.101405	+	0.994845i	$0.467666\pi$
$402$		0			0
$403$	9.54978	+	9.54978i	0.475708	+	0.475708i
$404$		0			0
$405$	1.37101	−	1.37101i	0.0681260	−	0.0681260i
$406$		0			0
$407$			11.0280i			0.546637i
$408$		0			0
$409$		−	15.6651i		−	0.774587i	−0.921956	−	0.387294i	$-0.873410\pi$
$409$		−	15.6651i		−	0.774587i	0.921956	−	0.387294i	$-0.126590\pi$
$410$		0			0
$411$	−9.50130	+	9.50130i	−0.468665	+	0.468665i
$412$		0			0
$413$	−3.42924	−	3.42924i	−0.168742	−	0.168742i
$414$		0			0
$415$	0.442442			0.0217186
$416$		0			0
$417$	−15.7033			−0.768996
$418$		0			0
$419$	−12.6081	−	12.6081i	−0.615947	−	0.615947i	0.328542	−	0.944489i	$-0.393443\pi$
$419$	−12.6081	−	12.6081i	−0.615947	−	0.615947i	−0.944489	+	0.328542i	$0.893443\pi$
$420$		0			0
$421$	−5.77589	+	5.77589i	−0.281499	+	0.281499i	−0.833707	−	0.552207i	$-0.813786\pi$
$421$	−5.77589	+	5.77589i	−0.281499	+	0.281499i	0.552207	+	0.833707i	$0.313786\pi$
$422$		0			0
$423$			13.7403i			0.668076i
$424$		0			0
$425$		−	1.11099i		−	0.0538908i
$426$		0			0
$427$	−1.76592	+	1.76592i	−0.0854588	+	0.0854588i
$428$		0			0
$429$	2.39960	+	2.39960i	0.115854	+	0.115854i
$430$		0			0
$431$	−0.928203			−0.0447100			−0.0223550	−	0.999750i	$-0.507116\pi$
$431$	−0.928203			−0.0447100			−0.0223550	+	0.999750i	$0.507116\pi$
$432$		0			0
$433$	24.3730			1.17129			0.585647	−	0.810566i	$-0.300841\pi$
$433$	24.3730			1.17129			0.585647	+	0.810566i	$0.300841\pi$
$434$		0			0
$435$	5.12460	+	5.12460i	0.245706	+	0.245706i
$436$		0			0
$437$	7.40916	−	7.40916i	0.354428	−	0.354428i
$438$		0			0
$439$		−	25.1832i		−	1.20193i	−0.799276	−	0.600964i	$-0.794784\pi$
$439$		−	25.1832i		−	1.20193i	0.799276	−	0.600964i	$-0.205216\pi$
$440$		0			0
$441$		−	3.18891i		−	0.151853i
$442$		0			0
$443$	8.38152	−	8.38152i	0.398218	−	0.398218i	−0.479386	−	0.877604i	$-0.659141\pi$
$443$	8.38152	−	8.38152i	0.398218	−	0.398218i	0.877604	+	0.479386i	$0.159141\pi$
$444$		0			0
$445$	11.7067	+	11.7067i	0.554953	+	0.554953i
$446$		0			0
$447$	−12.4853			−0.590534
$448$		0			0
$449$	6.60607			0.311760			0.155880	−	0.987776i	$-0.450179\pi$
$449$	6.60607			0.311760			0.155880	+	0.987776i	$0.450179\pi$
$450$		0			0
$451$	12.0698	+	12.0698i	0.568346	+	0.568346i
$452$		0			0
$453$	7.05453	−	7.05453i	0.331451	−	0.331451i
$454$		0			0
$455$		−	5.03528i		−	0.236057i
$456$		0			0
$457$			36.6201i			1.71302i	0.516133	+	0.856508i	$0.327371\pi$
$457$			36.6201i			1.71302i	−0.516133	+	0.856508i	$0.672629\pi$
$458$		0			0
$459$	3.75663	−	3.75663i	0.175344	−	0.175344i
$460$		0			0
$461$	5.96472	+	5.96472i	0.277805	+	0.277805i	0.832232	−	0.554427i	$-0.187063\pi$
$461$	5.96472	+	5.96472i	0.277805	+	0.277805i	−0.554427	+	0.832232i	$0.687063\pi$
$462$		0			0
$463$	13.8749			0.644820			0.322410	−	0.946600i	$-0.395507\pi$
$463$	13.8749			0.644820			0.322410	+	0.946600i	$0.395507\pi$
$464$		0			0
$465$	5.86370			0.271923
$466$		0			0
$467$	19.8755	+	19.8755i	0.919729	+	0.919729i	0.997009	−	0.0772800i	$-0.0246235\pi$
$467$	19.8755	+	19.8755i	0.919729	+	0.919729i	−0.0772800	+	0.997009i	$0.524624\pi$
$468$		0			0
$469$	26.5047	−	26.5047i	1.22387	−	1.22387i
$470$		0			0
$471$			21.7425i			1.00184i
$472$		0			0
$473$		−	12.3370i		−	0.567257i
$474$		0			0
$475$	1.53225	−	1.53225i	0.0703044	−	0.0703044i
$476$		0			0
$477$	−10.7184	−	10.7184i	−0.490763	−	0.490763i
$478$		0			0
$479$	−15.5931			−0.712467			−0.356233	−	0.934397i	$-0.615939\pi$
$479$	−15.5931			−0.712467			−0.356233	+	0.934397i	$0.615939\pi$
$480$		0			0
$481$	−13.9494			−0.636037
$482$		0			0
$483$	−7.47500	−	7.47500i	−0.340124	−	0.340124i
$484$		0			0
$485$	−6.46651	+	6.46651i	−0.293629	+	0.293629i
$486$		0			0
$487$		−	14.1319i		−	0.640378i	−0.947354	−	0.320189i	$-0.896254\pi$
$487$		−	14.1319i		−	0.640378i	0.947354	−	0.320189i	$-0.103746\pi$
$488$		0			0
$489$		−	14.2526i		−	0.644525i
$490$		0			0
$491$	23.7841	−	23.7841i	1.07336	−	1.07336i	0.0762760	−	0.997087i	$-0.475697\pi$
$491$	23.7841	−	23.7841i	1.07336	−	1.07336i	0.997087	−	0.0762760i	$-0.0243030\pi$
$492$		0			0
$493$	−6.10974	−	6.10974i	−0.275169	−	0.275169i
$494$		0			0
$495$	−3.61693			−0.162569
$496$		0			0
$497$	0.937492			0.0420522
$498$		0			0
$499$	−1.91119	−	1.91119i	−0.0855565	−	0.0855565i	0.663033	−	0.748590i	$-0.269269\pi$
$499$	−1.91119	−	1.91119i	−0.0855565	−	0.0855565i	−0.748590	+	0.663033i	$0.769269\pi$
$500$		0			0
$501$	−9.18618	+	9.18618i	−0.410408	+	0.410408i
$502$		0			0
$503$		−	20.9343i		−	0.933414i	−0.884412	−	0.466707i	$-0.845440\pi$
$503$		−	20.9343i		−	0.933414i	0.884412	−	0.466707i	$-0.154560\pi$
$504$		0			0
$505$			2.77854i			0.123643i
$506$		0			0
$507$	5.53067	−	5.53067i	0.245625	−	0.245625i
$508$		0			0
$509$	−17.2127	−	17.2127i	−0.762939	−	0.762939i	0.213914	−	0.976853i	$-0.431379\pi$
$509$	−17.2127	−	17.2127i	−0.762939	−	0.762939i	−0.976853	+	0.213914i	$0.931379\pi$
$510$		0			0
$511$	−14.1328			−0.625200
$512$		0			0
$513$	10.3621			0.457499
$514$		0			0
$515$	−3.20238	−	3.20238i	−0.141114	−	0.141114i
$516$		0			0
$517$	7.73373	−	7.73373i	0.340129	−	0.340129i
$518$		0			0
$519$		−	3.60040i		−	0.158040i
$520$		0			0
$521$		−	30.0588i		−	1.31690i	−0.752625	−	0.658449i	$-0.771213\pi$
$521$		−	30.0588i		−	1.31690i	0.752625	−	0.658449i	$-0.228787\pi$
$522$		0			0
$523$	−6.17948	+	6.17948i	−0.270210	+	0.270210i	−0.829185	−	0.558975i	$-0.811195\pi$
$523$	−6.17948	+	6.17948i	−0.270210	+	0.270210i	0.558975	+	0.829185i	$0.311195\pi$
$524$		0			0
$525$	−1.54587	−	1.54587i	−0.0674671	−	0.0674671i
$526$		0			0
$527$	−6.99093			−0.304529
$528$		0			0
$529$	−0.381822			−0.0166009
$530$		0			0
$531$	−3.11583	−	3.11583i	−0.135216	−	0.135216i
$532$		0			0
$533$	−15.2672	+	15.2672i	−0.661297	+	0.661297i
$534$		0			0
$535$			4.06690i			0.175828i
$536$		0			0
$537$		−	23.4122i		−	1.01031i
$538$		0			0
$539$	−1.79488	+	1.79488i	−0.0773108	+	0.0773108i
$540$		0			0
$541$	11.3198	+	11.3198i	0.486675	+	0.486675i	0.907255	−	0.420581i	$-0.138174\pi$
$541$	11.3198	+	11.3198i	0.486675	+	0.486675i	−0.420581	+	0.907255i	$0.638174\pi$
$542$		0			0
$543$	2.95476			0.126801
$544$		0			0
$545$	3.87780			0.166107
$546$		0			0
$547$	5.87965	+	5.87965i	0.251396	+	0.251396i	0.821543	−	0.570147i	$-0.193114\pi$
$547$	5.87965	+	5.87965i	0.251396	+	0.251396i	−0.570147	+	0.821543i	$0.693114\pi$
$548$		0			0
$549$	−1.60453	+	1.60453i	−0.0684795	+	0.0684795i
$550$		0			0
$551$		−	16.8528i		−	0.717955i
$552$		0			0
$553$		−	37.2173i		−	1.58264i
$554$		0			0
$555$	−4.28256	+	4.28256i	−0.181785	+	0.181785i
$556$		0			0
$557$	−21.0900	−	21.0900i	−0.893611	−	0.893611i	0.101250	−	0.994861i	$-0.467716\pi$
$557$	−21.0900	−	21.0900i	−0.893611	−	0.893611i	−0.994861	+	0.101250i	$0.967716\pi$
$558$		0			0
$559$	15.6052			0.660030
$560$		0			0
$561$	−1.75663			−0.0741650
$562$		0			0
$563$	29.9169	+	29.9169i	1.26084	+	1.26084i	0.950684	+	0.310161i	$0.100383\pi$
$563$	29.9169	+	29.9169i	1.26084	+	1.26084i	0.310161	+	0.950684i	$0.399617\pi$
$564$		0			0
$565$	10.1769	−	10.1769i	0.428145	−	0.428145i
$566$		0			0
$567$			4.54879i			0.191031i
$568$		0			0
$569$			4.80990i			0.201641i	0.994905	+	0.100821i	$0.0321469\pi$
$569$			4.80990i			0.201641i	−0.994905	+	0.100821i	$0.967853\pi$
$570$		0			0
$571$	−22.6639	+	22.6639i	−0.948455	+	0.948455i	−0.998735	−	0.0502803i	$-0.983989\pi$
$571$	−22.6639	+	22.6639i	−0.948455	+	0.948455i	0.0502803	+	0.998735i	$0.483989\pi$
$572$		0			0
$573$	−1.71427	−	1.71427i	−0.0716147	−	0.0716147i
$574$		0			0
$575$	−4.83548			−0.201653
$576$		0			0
$577$	45.5463			1.89612			0.948059	−	0.318094i	$-0.103043\pi$
$577$	45.5463			1.89612			0.948059	+	0.318094i	$0.103043\pi$
$578$		0			0
$579$	11.2314	+	11.2314i	0.466762	+	0.466762i
$580$		0			0
$581$	−0.733974	+	0.733974i	−0.0304504	+	0.0304504i
$582$		0			0
$583$			12.0657i			0.499712i
$584$		0			0
$585$		−	4.57509i		−	0.189157i
$586$		0			0
$587$	9.27826	−	9.27826i	0.382955	−	0.382955i	−0.489211	−	0.872166i	$-0.662715\pi$
$587$	9.27826	−	9.27826i	0.382955	−	0.382955i	0.872166	+	0.489211i	$0.162715\pi$
$588$		0			0
$589$	−9.64173	−	9.64173i	−0.397280	−	0.397280i
$590$		0			0
$591$	−13.2489			−0.544988
$592$		0			0
$593$	−3.32677			−0.136614			−0.0683071	−	0.997664i	$-0.521760\pi$
$593$	−3.32677			−0.136614			−0.0683071	+	0.997664i	$0.521760\pi$
$594$		0			0
$595$	1.84304	+	1.84304i	0.0755572	+	0.0755572i
$596$		0			0
$597$	−7.06931	+	7.06931i	−0.289328	+	0.289328i
$598$		0			0
$599$		−	7.52640i		−	0.307520i	−0.988108	−	0.153760i	$-0.950862\pi$
$599$		−	7.52640i		−	0.307520i	0.988108	−	0.153760i	$-0.0491383\pi$
$600$		0			0
$601$		−	9.03188i		−	0.368418i	−0.982887	−	0.184209i	$-0.941028\pi$
$601$		−	9.03188i		−	0.368418i	0.982887	−	0.184209i	$-0.0589723\pi$
$602$		0			0
$603$	24.0824	−	24.0824i	0.980710	−	0.980710i
$604$		0			0
$605$	−5.74238	−	5.74238i	−0.233461	−	0.233461i
$606$		0			0
$607$	−11.7031			−0.475014			−0.237507	−	0.971386i	$-0.576330\pi$
$607$	−11.7031			−0.475014			−0.237507	+	0.971386i	$0.576330\pi$
$608$		0			0
$609$	−17.0026			−0.688980
$610$		0			0
$611$	9.78245	+	9.78245i	0.395756	+	0.395756i
$612$		0			0
$613$	19.2477	−	19.2477i	0.777408	−	0.777408i	−0.201981	−	0.979389i	$-0.564738\pi$
$613$	19.2477	−	19.2477i	0.777408	−	0.777408i	0.979389	+	0.201981i	$0.0647381\pi$
$614$		0			0
$615$			9.37429i			0.378008i
$616$		0			0
$617$		−	13.5963i		−	0.547365i	−0.961820	−	0.273683i	$-0.911758\pi$
$617$		−	13.5963i		−	0.547365i	0.961820	−	0.273683i	$-0.0882418\pi$
$618$		0			0
$619$	1.50303	−	1.50303i	0.0604117	−	0.0604117i	−0.676255	−	0.736667i	$-0.736398\pi$
$619$	1.50303	−	1.50303i	0.0604117	−	0.0604117i	0.736667	+	0.676255i	$0.236398\pi$
$620$		0			0
$621$	−16.3504	−	16.3504i	−0.656119	−	0.656119i
$622$		0			0
$623$	−38.8411			−1.55613
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−2.42271	−	2.42271i	−0.0967535	−	0.0967535i
$628$		0			0
$629$	5.10583	−	5.10583i	0.203583	−	0.203583i
$630$		0			0
$631$		−	27.1399i		−	1.08042i	−0.841530	−	0.540210i	$-0.818345\pi$
$631$		−	27.1399i		−	1.08042i	0.841530	−	0.540210i	$-0.181655\pi$
$632$		0			0
$633$		−	23.3718i		−	0.928946i
$634$		0			0
$635$	12.9125	−	12.9125i	0.512418	−	0.512418i
$636$		0			0
$637$	−2.27035	−	2.27035i	−0.0899547	−	0.0899547i
$638$		0			0
$639$	0.851812			0.0336972
$640$		0			0
$641$	27.5635			1.08869			0.544346	−	0.838861i	$-0.316778\pi$
$641$	27.5635			1.08869			0.544346	+	0.838861i	$0.316778\pi$
$642$		0			0
$643$	−23.1493	−	23.1493i	−0.912918	−	0.912918i	0.0835832	−	0.996501i	$-0.473364\pi$
$643$	−23.1493	−	23.1493i	−0.912918	−	0.912918i	−0.996501	+	0.0835832i	$0.973364\pi$
$644$		0			0
$645$	4.79091	−	4.79091i	0.188642	−	0.188642i
$646$		0			0
$647$		−	28.4410i		−	1.11813i	−0.829123	−	0.559066i	$-0.811160\pi$
$647$		−	28.4410i		−	1.11813i	0.829123	−	0.559066i	$-0.188840\pi$
$648$		0			0
$649$			3.50749i			0.137681i
$650$		0			0
$651$	−9.72741	+	9.72741i	−0.381247	+	0.381247i
$652$		0			0
$653$	−0.957676	−	0.957676i	−0.0374767	−	0.0374767i	0.688120	−	0.725597i	$-0.258436\pi$
$653$	−0.957676	−	0.957676i	−0.0374767	−	0.0374767i	−0.725597	+	0.688120i	$0.758436\pi$
$654$		0			0
$655$	−6.52520			−0.254961
$656$		0			0
$657$	−12.8412			−0.500983
$658$		0			0
$659$	−0.917240	−	0.917240i	−0.0357306	−	0.0357306i	0.689016	−	0.724746i	$-0.258043\pi$
$659$	−0.917240	−	0.917240i	−0.0357306	−	0.0357306i	−0.724746	+	0.689016i	$0.758043\pi$
$660$		0			0
$661$	11.7481	−	11.7481i	0.456947	−	0.456947i	−0.440705	−	0.897652i	$-0.645272\pi$
$661$	11.7481	−	11.7481i	0.456947	−	0.456947i	0.897652	+	0.440705i	$0.145272\pi$
$662$		0			0
$663$		−	2.22198i		−	0.0862944i
$664$		0			0
$665$			5.08376i			0.197140i
$666$		0			0
$667$	−26.5921	+	26.5921i	−1.02965	+	1.02965i
$668$		0			0
$669$	12.0005	+	12.0005i	0.463967	+	0.463967i
$670$		0			0
$671$	1.80622			0.0697282
$672$		0			0
$673$	7.48817			0.288648			0.144324	−	0.989531i	$-0.453899\pi$
$673$	7.48817			0.288648			0.144324	+	0.989531i	$0.453899\pi$
$674$		0			0
$675$	−3.38134	−	3.38134i	−0.130148	−	0.130148i
$676$		0			0
$677$	19.3721	−	19.3721i	0.744528	−	0.744528i	−0.228917	−	0.973446i	$-0.573519\pi$
$677$	19.3721	−	19.3721i	0.744528	−	0.744528i	0.973446	+	0.228917i	$0.0735186\pi$
$678$		0			0
$679$		−	21.4548i		−	0.823360i
$680$		0			0
$681$			11.8447i			0.453889i
$682$		0			0
$683$	−14.4723	+	14.4723i	−0.553765	+	0.553765i	−0.927525	−	0.373760i	$-0.878068\pi$
$683$	−14.4723	+	14.4723i	−0.553765	+	0.553765i	0.373760	+	0.927525i	$0.378068\pi$
$684$		0			0
$685$	−10.1962	−	10.1962i	−0.389575	−	0.389575i
$686$		0			0
$687$	2.11704			0.0807701
$688$		0			0
$689$	−15.2621			−0.581438
$690$		0			0
$691$	18.3482	+	18.3482i	0.697999	+	0.697999i	0.963979	−	0.265979i	$-0.0856953\pi$
$691$	18.3482	+	18.3482i	0.697999	+	0.697999i	−0.265979	+	0.963979i	$0.585695\pi$
$692$		0			0
$693$	6.00020	−	6.00020i	0.227929	−	0.227929i
$694$		0			0
$695$		−	16.8518i		−	0.639224i
$696$		0			0
$697$		−	11.1764i		−	0.423336i
$698$		0			0
$699$	−0.189353	+	0.189353i	−0.00716198	+	0.00716198i
$700$		0			0
$701$	−12.9630	−	12.9630i	−0.489604	−	0.489604i	0.418577	−	0.908181i	$-0.362529\pi$
$701$	−12.9630	−	12.9630i	−0.489604	−	0.489604i	−0.908181	+	0.418577i	$0.862529\pi$
$702$		0			0
$703$	14.0837			0.531176
$704$		0			0
$705$	6.00657			0.226220
$706$		0			0
$707$	−4.60937	−	4.60937i	−0.173353	−	0.173353i
$708$		0			0
$709$	6.10583	−	6.10583i	0.229309	−	0.229309i	−0.583095	−	0.812404i	$-0.698158\pi$
$709$	6.10583	−	6.10583i	0.229309	−	0.229309i	0.812404	+	0.583095i	$0.198158\pi$
$710$		0			0
$711$		−	33.8159i		−	1.26820i
$712$		0			0
$713$			30.4274i			1.13951i
$714$		0			0
$715$	−2.57509	+	2.57509i	−0.0963029	+	0.0963029i
$716$		0			0
$717$	11.5491	+	11.5491i	0.431309	+	0.431309i
$718$		0			0
$719$	−49.9396			−1.86243			−0.931216	−	0.364467i	$-0.881251\pi$
$719$	−49.9396			−1.86243			−0.931216	+	0.364467i	$0.881251\pi$
$720$		0			0
$721$	10.6250			0.395695
$722$		0			0
$723$	5.53077	+	5.53077i	0.205692	+	0.205692i
$724$		0			0
$725$	−5.49938	+	5.49938i	−0.204242	+	0.204242i
$726$		0			0
$727$		−	8.41214i		−	0.311989i	−0.987758	−	0.155994i	$-0.950142\pi$
$727$		−	8.41214i		−	0.311989i	0.987758	−	0.155994i	$-0.0498582\pi$
$728$		0			0
$729$		−	9.23511i		−	0.342041i
$730$		0			0
$731$	−5.71190	+	5.71190i	−0.211262	+	0.211262i
$732$		0			0
$733$	−10.6663	−	10.6663i	−0.393969	−	0.393969i	0.482130	−	0.876099i	$-0.339863\pi$
$733$	−10.6663	−	10.6663i	−0.393969	−	0.393969i	−0.876099	+	0.482130i	$0.839863\pi$
$734$		0			0
$735$	−1.39403			−0.0514196
$736$		0			0
$737$	−27.1095			−0.998592
$738$		0			0
$739$	8.63735	+	8.63735i	0.317730	+	0.317730i	0.847895	−	0.530165i	$-0.177870\pi$
$739$	8.63735	+	8.63735i	0.317730	+	0.317730i	−0.530165	+	0.847895i	$0.677870\pi$
$740$		0			0
$741$	3.06450	−	3.06450i	0.112577	−	0.112577i
$742$		0			0
$743$		−	10.1561i		−	0.372592i	−0.982494	−	0.186296i	$-0.940352\pi$
$743$		−	10.1561i		−	0.372592i	0.982494	−	0.186296i	$-0.0596484\pi$
$744$		0			0
$745$		−	13.3984i		−	0.490878i
$746$		0			0
$747$	−0.666895	+	0.666895i	−0.0244004	+	0.0244004i
$748$		0			0
$749$	−6.74666	−	6.74666i	−0.246518	−	0.246518i
$750$		0			0
$751$	24.3700			0.889272			0.444636	−	0.895711i	$-0.353333\pi$
$751$	24.3700			0.889272			0.444636	+	0.895711i	$0.353333\pi$
$752$		0			0
$753$	12.9616			0.472345
$754$		0			0
$755$	7.57045	+	7.57045i	0.275517	+	0.275517i
$756$		0			0
$757$	−8.98325	+	8.98325i	−0.326502	+	0.326502i	−0.851255	−	0.524753i	$-0.824158\pi$
$757$	−8.98325	+	8.98325i	−0.326502	+	0.326502i	0.524753	+	0.851255i	$0.324158\pi$
$758$		0			0
$759$			7.64557i			0.277517i
$760$		0			0
$761$			4.00929i			0.145337i	0.997356	+	0.0726683i	$0.0231514\pi$
$761$			4.00929i			0.145337i	−0.997356	+	0.0726683i	$0.976849\pi$
$762$		0			0
$763$	−6.43295	+	6.43295i	−0.232889	+	0.232889i
$764$		0			0
$765$	1.67460	+	1.67460i	0.0605453	+	0.0605453i
$766$		0			0
$767$	−4.43666			−0.160198
$768$		0			0
$769$	46.6663			1.68283			0.841414	−	0.540391i	$-0.181724\pi$
$769$	46.6663			1.68283			0.841414	+	0.540391i	$0.181724\pi$
$770$		0			0
$771$	11.9959	+	11.9959i	0.432021	+	0.432021i
$772$		0			0
$773$	15.8133	−	15.8133i	0.568766	−	0.568766i	−0.363017	−	0.931783i	$-0.618253\pi$
$773$	15.8133	−	15.8133i	0.568766	−	0.568766i	0.931783	+	0.363017i	$0.118253\pi$
$774$		0			0
$775$			6.29253i			0.226034i
$776$		0			0
$777$		−	14.2088i		−	0.509739i
$778$		0			0
$779$	15.4142	−	15.4142i	0.552272	−	0.552272i
$780$		0			0
$781$	−0.479442	−	0.479442i	−0.0171558	−	0.0171558i
$782$		0			0
$783$	−37.1905			−1.32908
$784$		0			0
$785$	−23.3326			−0.832777
$786$		0			0
$787$	20.1108	+	20.1108i	0.716873	+	0.716873i	0.967964	−	0.251091i	$-0.0807892\pi$
$787$	20.1108	+	20.1108i	0.716873	+	0.716873i	−0.251091	+	0.967964i	$0.580789\pi$
$788$		0			0
$789$	−14.8372	+	14.8372i	−0.528217	+	0.528217i
$790$		0			0
$791$			33.7653i			1.20056i
$792$		0			0
$793$			2.28470i			0.0811320i
$794$		0			0
$795$	−4.68556	+	4.68556i	−0.166180	+	0.166180i
$796$		0			0
$797$	−2.79415	−	2.79415i	−0.0989738	−	0.0989738i	0.655886	−	0.754860i	$-0.272295\pi$
$797$	−2.79415	−	2.79415i	−0.0989738	−	0.0989738i	−0.754860	+	0.655886i	$0.772295\pi$
$798$		0			0
$799$	−7.16125			−0.253347
$800$		0			0
$801$	−35.2913			−1.24696
$802$		0			0
$803$	7.22768	+	7.22768i	0.255059	+	0.255059i
$804$		0			0
$805$	8.02166	−	8.02166i	0.282726	−	0.282726i
$806$		0			0
$807$		−	19.8657i		−	0.699306i
$808$		0			0
$809$		−	39.9600i		−	1.40492i	−0.711723	−	0.702460i	$-0.752085\pi$
$809$		−	39.9600i		−	1.40492i	0.711723	−	0.702460i	$-0.247915\pi$
$810$		0			0
$811$	29.8685	−	29.8685i	1.04883	−	1.04883i	0.0500814	−	0.998745i	$-0.484052\pi$
$811$	29.8685	−	29.8685i	1.04883	−	1.04883i	0.998745	−	0.0500814i	$-0.0159481\pi$
$812$		0			0
$813$	20.2188	+	20.2188i	0.709105	+	0.709105i
$814$		0			0
$815$	15.2949			0.535758
$816$		0			0
$817$	−15.7555			−0.551214
$818$		0			0
$819$	7.58970	+	7.58970i	0.265206	+	0.265206i
$820$		0			0
$821$	11.2658	−	11.2658i	0.393180	−	0.393180i	−0.482640	−	0.875819i	$-0.660322\pi$
$821$	11.2658	−	11.2658i	0.393180	−	0.393180i	0.875819	+	0.482640i	$0.160322\pi$
$822$		0			0
$823$		−	11.8670i		−	0.413657i	−0.978377	−	0.206828i	$-0.933686\pi$
$823$		−	11.8670i		−	0.413657i	0.978377	−	0.206828i	$-0.0663142\pi$
$824$		0			0
$825$			1.58114i			0.0550483i
$826$		0			0
$827$	−13.5457	+	13.5457i	−0.471030	+	0.471030i	−0.902248	−	0.431218i	$-0.858084\pi$
$827$	−13.5457	+	13.5457i	−0.471030	+	0.471030i	0.431218	+	0.902248i	$0.358084\pi$
$828$		0			0
$829$	10.3975	+	10.3975i	0.361119	+	0.361119i	0.864225	−	0.503106i	$-0.167809\pi$
$829$	10.3975	+	10.3975i	0.361119	+	0.361119i	−0.503106	+	0.864225i	$0.667809\pi$
$830$		0			0
$831$	−9.03279			−0.313344
$832$		0			0
$833$	1.66201			0.0575854
$834$		0			0
$835$	−9.85799	−	9.85799i	−0.341150	−	0.341150i
$836$		0			0
$837$	−21.2772	+	21.2772i	−0.735447	+	0.735447i
$838$		0			0
$839$			2.89168i			0.0998320i	0.998753	+	0.0499160i	$0.0158954\pi$
$839$			2.89168i			0.0998320i	−0.998753	+	0.0499160i	$0.984105\pi$
$840$		0			0
$841$			31.4863i			1.08573i
$842$		0			0
$843$	−1.61061	+	1.61061i	−0.0554725	+	0.0554725i
$844$		0			0
$845$	5.93514	+	5.93514i	0.204175	+	0.204175i
$846$		0			0
$847$	19.0523			0.654645
$848$		0			0
$849$	3.02010			0.103650
$850$		0			0
$851$	−22.2227	−	22.2227i	−0.761783	−	0.761783i
$852$		0			0
$853$	13.6325	−	13.6325i	0.466769	−	0.466769i	−0.434097	−	0.900866i	$-0.642932\pi$
$853$	13.6325	−	13.6325i	0.466769	−	0.466769i	0.900866	+	0.434097i	$0.142932\pi$
$854$		0			0
$855$			4.61914i			0.157971i
$856$		0			0
$857$		−	37.4062i		−	1.27777i	−0.769302	−	0.638886i	$-0.779396\pi$
$857$		−	37.4062i		−	1.27777i	0.769302	−	0.638886i	$-0.220604\pi$
$858$		0			0
$859$	−13.8754	+	13.8754i	−0.473422	+	0.473422i	−0.903020	−	0.429598i	$-0.858655\pi$
$859$	−13.8754	+	13.8754i	−0.473422	+	0.473422i	0.429598	+	0.903020i	$0.358655\pi$
$860$		0			0
$861$	−15.5512	−	15.5512i	−0.529983	−	0.529983i
$862$		0			0
$863$	47.5152			1.61744			0.808718	−	0.588196i	$-0.200162\pi$
$863$	47.5152			1.61744			0.808718	+	0.588196i	$0.200162\pi$
$864$		0			0
$865$	3.86370			0.131370
$866$		0			0
$867$	−10.3883	−	10.3883i	−0.352806	−	0.352806i
$868$		0			0
$869$	−19.0333	+	19.0333i	−0.645660	+	0.645660i
$870$		0			0
$871$		−	34.2911i		−	1.16191i
$872$		0			0
$873$		−	19.4940i		−	0.659772i
$874$		0			0
$875$	1.65892	−	1.65892i	0.0560817	−	0.0560817i
$876$		0			0
$877$	−22.0217	−	22.0217i	−0.743620	−	0.743620i	0.229653	−	0.973273i	$-0.426241\pi$
$877$	−22.0217	−	22.0217i	−0.743620	−	0.743620i	−0.973273	+	0.229653i	$0.926241\pi$
$878$		0			0
$879$	−23.5950			−0.795838
$880$		0			0
$881$	−19.8379			−0.668355			−0.334178	−	0.942510i	$-0.608459\pi$
$881$	−19.8379			−0.668355			−0.334178	+	0.942510i	$0.608459\pi$
$882$		0			0
$883$	10.7398	+	10.7398i	0.361423	+	0.361423i	0.864337	−	0.502914i	$-0.167739\pi$
$883$	10.7398	+	10.7398i	0.361423	+	0.361423i	−0.502914	+	0.864337i	$0.667739\pi$
$884$		0			0
$885$	−1.36209	+	1.36209i	−0.0457860	+	0.0457860i
$886$		0			0
$887$			57.5726i			1.93310i	0.256478	+	0.966550i	$0.417438\pi$
$887$			57.5726i			1.93310i	−0.256478	+	0.966550i	$0.582562\pi$
$888$		0			0
$889$			42.8416i			1.43686i
$890$		0			0
$891$	2.32629	−	2.32629i	0.0779338	−	0.0779338i
$892$		0			0
$893$	−9.87664	−	9.87664i	−0.330509	−	0.330509i
$894$		0			0
$895$	25.1244			0.839815
$896$		0			0
$897$	−9.67095			−0.322904
$898$		0			0
$899$	34.6050	+	34.6050i	1.15414	+	1.15414i
$900$		0			0
$901$	5.58630	−	5.58630i	0.186107	−	0.186107i
$902$		0			0
$903$			15.8955i			0.528968i
$904$		0			0
$905$			3.17084i			0.105402i
$906$		0			0
$907$	3.73175	−	3.73175i	0.123911	−	0.123911i	−0.642432	−	0.766343i	$-0.722075\pi$
$907$	3.73175	−	3.73175i	0.123911	−	0.123911i	0.766343	+	0.642432i	$0.222075\pi$
$908$		0			0
$909$	−4.18811	−	4.18811i	−0.138911	−	0.138911i
$910$		0			0
$911$	11.9590			0.396219			0.198110	−	0.980180i	$-0.436520\pi$
$911$	11.9590			0.396219			0.198110	+	0.980180i	$0.436520\pi$
$912$		0			0
$913$	0.750724			0.0248453
$914$		0			0
$915$	0.701419	+	0.701419i	0.0231882	+	0.0231882i
$916$		0			0
$917$	10.8248	−	10.8248i	0.357466	−	0.357466i
$918$		0			0
$919$			53.6932i			1.77118i	0.464472	+	0.885588i	$0.346244\pi$
$919$			53.6932i			1.77118i	−0.464472	+	0.885588i	$0.653756\pi$
$920$		0			0
$921$		−	9.42418i		−	0.310537i
$922$		0			0
$923$	0.606451	−	0.606451i	0.0199616	−	0.0199616i
$924$		0			0
$925$	−4.59575	−	4.59575i	−0.151107	−	0.151107i
$926$		0			0
$927$	9.65393			0.317077
$928$		0			0
$929$	7.25033			0.237876			0.118938	−	0.992902i	$-0.462051\pi$
$929$	7.25033			0.237876			0.118938	+	0.992902i	$0.462051\pi$
$930$		0			0
$931$	2.29221	+	2.29221i	0.0751242	+	0.0751242i
$932$		0			0
$933$	−15.2945	+	15.2945i	−0.500718	+	0.500718i
$934$		0			0
$935$		−	1.88510i		−	0.0616493i
$936$		0			0
$937$		−	31.3398i		−	1.02383i	−0.859037	−	0.511913i	$-0.828937\pi$
$937$		−	31.3398i		−	1.02383i	0.859037	−	0.511913i	$-0.171063\pi$
$938$		0			0
$939$	−3.36500	+	3.36500i	−0.109813	+	0.109813i
$940$		0			0
$941$	25.5972	+	25.5972i	0.834444	+	0.834444i	0.988121	−	0.153677i	$-0.0491117\pi$
$941$	25.5972	+	25.5972i	0.834444	+	0.834444i	−0.153677	+	0.988121i	$0.549112\pi$
$942$		0			0
$943$	−48.6442			−1.58407
$944$		0			0
$945$	11.2187			0.364946
$946$		0			0
$947$	−37.1739	−	37.1739i	−1.20799	−	1.20799i	−0.971678	−	0.236310i	$-0.924062\pi$
$947$	−37.1739	−	37.1739i	−1.20799	−	1.20799i	−0.236310	−	0.971678i	$-0.575938\pi$
$948$		0			0
$949$	−9.14235	+	9.14235i	−0.296773	+	0.296773i
$950$		0			0
$951$			27.1688i			0.881007i
$952$		0			0
$953$			33.0538i			1.07072i	0.844625	+	0.535358i	$0.179823\pi$
$953$			33.0538i			1.07072i	−0.844625	+	0.535358i	$0.820177\pi$
$954$		0			0
$955$	1.83964	−	1.83964i	0.0595293	−	0.0595293i
$956$		0			0
$957$	8.69530	+	8.69530i	0.281079	+	0.281079i
$958$		0			0
$959$	33.8292			1.09240
$960$		0			0
$961$	8.59592			0.277288
$962$		0			0
$963$	−6.13007	−	6.13007i	−0.197539	−	0.197539i
$964$		0			0
$965$	−12.0528	+	12.0528i	−0.387994	+	0.387994i
$966$		0			0
$967$			19.8952i			0.639785i	0.947454	+	0.319893i	$0.103647\pi$
$967$			19.8952i			0.639785i	−0.947454	+	0.319893i	$0.896353\pi$
$968$		0			0
$969$			2.24337i			0.0720674i
$970$		0			0
$971$	36.6690	−	36.6690i	1.17676	−	1.17676i	0.196201	−	0.980564i	$-0.437140\pi$
$971$	36.6690	−	36.6690i	1.17676	−	1.17676i	0.980564	−	0.196201i	$-0.0628605\pi$
$972$		0			0
$973$	27.9557	+	27.9557i	0.896219	+	0.896219i
$974$		0			0
$975$	−2.00000			−0.0640513
$976$		0			0
$977$	14.8822			0.476124			0.238062	−	0.971250i	$-0.423488\pi$
$977$	14.8822			0.476124			0.238062	+	0.971250i	$0.423488\pi$
$978$		0			0
$979$	19.8637	+	19.8637i	0.634847	+	0.634847i
$980$		0			0
$981$	−5.84503	+	5.84503i	−0.186617	+	0.186617i
$982$		0			0
$983$		−	39.9254i		−	1.27342i	−0.771102	−	0.636711i	$-0.780294\pi$
$983$		−	39.9254i		−	1.27342i	0.771102	−	0.636711i	$-0.219706\pi$
$984$		0			0
$985$		−	14.2178i		−	0.453018i
$986$		0			0
$987$	−9.96441	+	9.96441i	−0.317171	+	0.317171i
$988$		0			0
$989$	24.8605	+	24.8605i	0.790519	+	0.790519i
$990$		0			0
$991$	−2.22646			−0.0707257			−0.0353629	−	0.999375i	$-0.511259\pi$
$991$	−2.22646			−0.0707257			−0.0353629	+	0.999375i	$0.511259\pi$
$992$		0			0
$993$	−13.4006			−0.425254
$994$		0			0
$995$	−7.58630	−	7.58630i	−0.240502	−	0.240502i
$996$		0			0
$997$	17.9730	−	17.9730i	0.569211	−	0.569211i	−0.362696	−	0.931907i	$-0.618144\pi$
$997$	17.9730	−	17.9730i	0.569211	−	0.569211i	0.931907	+	0.362696i	$0.118144\pi$
$998$		0			0
$999$		−	31.0796i		−	0.983316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.l.f.321.3	yes	8
4.3	odd	2		1280.2.l.a.321.2	✓	8
8.3	odd	2		1280.2.l.g.321.3	yes	8
8.5	even	2		1280.2.l.d.321.2	yes	8
16.3	odd	4		1280.2.l.g.961.3	yes	8
16.5	even	4	inner	1280.2.l.f.961.3	yes	8
16.11	odd	4		1280.2.l.a.961.2	yes	8
16.13	even	4		1280.2.l.d.961.2	yes	8
32.5	even	8		5120.2.a.q.1.1		4
32.11	odd	8		5120.2.a.r.1.1		4
32.21	even	8		5120.2.a.b.1.4		4
32.27	odd	8		5120.2.a.a.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.l.a.321.2	✓	8	4.3	odd	2
1280.2.l.a.961.2	yes	8	16.11	odd	4
1280.2.l.d.321.2	yes	8	8.5	even	2
1280.2.l.d.961.2	yes	8	16.13	even	4
1280.2.l.f.321.3	yes	8	1.1	even	1	trivial
1280.2.l.f.961.3	yes	8	16.5	even	4	inner
1280.2.l.g.321.3	yes	8	8.3	odd	2
1280.2.l.g.961.3	yes	8	16.3	odd	4
5120.2.a.a.1.4		4	32.27	odd	8
5120.2.a.b.1.4		4	32.21	even	8
5120.2.a.q.1.1		4	32.5	even	8
5120.2.a.r.1.1		4	32.11	odd	8

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.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.658919 + 0.658919i) q^{3} +(-0.707107 + 0.707107i) q^{5} -2.34607i q^{7} -2.13165i q^{9} +O(q^{10})\)	\(q+(0.658919 + 0.658919i) q^{3} +(-0.707107 + 0.707107i) q^{5} -2.34607i q^{7} -2.13165i q^{9} +(-1.19980 + 1.19980i) q^{11} +(-1.51764 - 1.51764i) q^{13} -0.931852 q^{15} +1.11099 q^{17} +(1.53225 + 1.53225i) q^{19} +(1.54587 - 1.54587i) q^{21} -4.83548i q^{23} -1.00000i q^{25} +(3.38134 - 3.38134i) q^{27} +(-5.49938 - 5.49938i) q^{29} -6.29253 q^{31} -1.58114 q^{33} +(1.65892 + 1.65892i) q^{35} +(4.59575 - 4.59575i) q^{37} -2.00000i q^{39} -10.0599i q^{41} +(-5.14128 + 5.14128i) q^{43} +(1.50731 + 1.50731i) q^{45} -6.44584 q^{47} +1.49598 q^{49} +(0.732051 + 0.732051i) q^{51} +(5.02823 - 5.02823i) q^{53} -1.69677i q^{55} +2.01926i q^{57} +(1.46170 - 1.46170i) q^{59} +(-0.752715 - 0.752715i) q^{61} -5.00100 q^{63} +2.14626 q^{65} +(11.2975 + 11.2975i) q^{67} +(3.18618 - 3.18618i) q^{69} +0.399602i q^{71} -6.02406i q^{73} +(0.658919 - 0.658919i) q^{75} +(2.81481 + 2.81481i) q^{77} +15.8637 q^{79} -1.93890 q^{81} +(-0.312853 - 0.312853i) q^{83} +(-0.785587 + 0.785587i) q^{85} -7.24728i q^{87} -16.5558i q^{89} +(-3.56048 + 3.56048i) q^{91} +(-4.14626 - 4.14626i) q^{93} -2.16693 q^{95} +9.14502 q^{97} +(2.55756 + 2.55756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3}+O(q^{10}) \) 8 * q + 4 * q^3	\( 8 q + 4 q^{3} - 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} - 16 q^{21} - 8 q^{27} - 8 q^{29} + 24 q^{33} + 12 q^{35} - 8 q^{37} - 44 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{51} + 16 q^{53} + 16 q^{59} + 8 q^{61} - 48 q^{63} - 8 q^{65} + 12 q^{67} + 40 q^{69} + 4 q^{75} + 16 q^{77} + 96 q^{79} - 16 q^{81} - 28 q^{83} - 16 q^{85} + 8 q^{91} - 8 q^{93} + 8 q^{95} - 24 q^{97} + 56 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 - 16 * q^21 - 8 * q^27 - 8 * q^29 + 24 * q^33 + 12 * q^35 - 8 * q^37 - 44 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^51 + 16 * q^53 + 16 * q^59 + 8 * q^61 - 48 * q^63 - 8 * q^65 + 12 * q^67 + 40 * q^69 + 4 * q^75 + 16 * q^77 + 96 * q^79 - 16 * q^81 - 28 * q^83 - 16 * q^85 + 8 * q^91 - 8 * q^93 + 8 * q^95 - 24 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

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Database

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