LMFDB - Embedded newform 1280.2.l.d.321.2

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			321.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1280.321
Dual form			1280.2.l.d.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.658919 - 0.658919i) q^{3} +(0.707107 - 0.707107i) q^{5} -2.34607i q^{7} -2.13165i q^{9} +O(q^{10})$	\(q+(-0.658919 - 0.658919i) q^{3} +(0.707107 - 0.707107i) q^{5} -2.34607i q^{7} -2.13165i q^{9} +(1.19980 - 1.19980i) q^{11} +(1.51764 + 1.51764i) q^{13} -0.931852 q^{15} +1.11099 q^{17} +(-1.53225 - 1.53225i) q^{19} +(-1.54587 + 1.54587i) q^{21} -4.83548i q^{23} -1.00000i q^{25} +(-3.38134 + 3.38134i) q^{27} +(5.49938 + 5.49938i) q^{29} -6.29253 q^{31} -1.58114 q^{33} +(-1.65892 - 1.65892i) q^{35} +(-4.59575 + 4.59575i) q^{37} -2.00000i q^{39} -10.0599i q^{41} +(5.14128 - 5.14128i) q^{43} +(-1.50731 - 1.50731i) q^{45} -6.44584 q^{47} +1.49598 q^{49} +(-0.732051 - 0.732051i) q^{51} +(-5.02823 + 5.02823i) q^{53} -1.69677i q^{55} +2.01926i q^{57} +(-1.46170 + 1.46170i) q^{59} +(0.752715 + 0.752715i) q^{61} -5.00100 q^{63} +2.14626 q^{65} +(-11.2975 - 11.2975i) q^{67} +(-3.18618 + 3.18618i) q^{69} +0.399602i q^{71} -6.02406i q^{73} +(-0.658919 + 0.658919i) q^{75} +(-2.81481 - 2.81481i) q^{77} +15.8637 q^{79} -1.93890 q^{81} +(0.312853 + 0.312853i) q^{83} +(0.785587 - 0.785587i) q^{85} -7.24728i q^{87} -16.5558i q^{89} +(3.56048 - 3.56048i) q^{91} +(4.14626 + 4.14626i) q^{93} -2.16693 q^{95} +9.14502 q^{97} +(-2.55756 - 2.55756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.490829	−	0.871256i	$-0.336694\pi$
$3$	−0.658919	−	0.658919i	−0.380427	−	0.380427i	−0.871256	+	0.490829i	$0.836694\pi$
$4$		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	−0.502705	−	0.864458i	$-0.667662\pi$
$11$	1.19980	−	1.19980i	0.361754	−	0.361754i	0.864458	+	0.502705i	$0.167662\pi$
$12$		0			0
$13$	1.51764	+	1.51764i	0.420917	+	0.420917i	0.885519	−	0.464602i	$-0.153803\pi$
$13$	1.51764	+	1.51764i	0.420917	+	0.420917i	−0.464602	+	0.885519i	$0.653803\pi$
$14$		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	0.509153	−	0.860676i	$-0.329959\pi$
$19$	−1.53225	−	1.53225i	−0.351522	−	0.351522i	−0.860676	+	0.509153i	$0.829959\pi$
$20$		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	$0.00682466\pi$
$29$	5.49938	+	5.49938i	1.02121	+	1.02121i	0.0214387	+	0.999770i	$0.493175\pi$
$30$		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	−0.975507	−	0.219969i	$-0.929404\pi$
$37$	−4.59575	+	4.59575i	−0.755537	+	0.755537i	0.219969	+	0.975507i	$0.429404\pi$
$38$		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	−0.196472	−	0.980510i	$-0.562948\pi$
$43$	5.14128	−	5.14128i	0.784038	−	0.784038i	0.980510	+	0.196472i	$0.0629483\pi$
$44$		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	−0.962382	−	0.271701i	$-0.912414\pi$
$53$	−5.02823	+	5.02823i	−0.690680	+	0.690680i	0.271701	+	0.962382i	$0.412414\pi$
$54$		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	−0.795824	−	0.605528i	$-0.792962\pi$
$59$	−1.46170	+	1.46170i	−0.190297	+	0.190297i	0.605528	+	0.795824i	$0.292962\pi$
$60$		0			0
$61$	0.752715	+	0.752715i	0.0963753	+	0.0963753i	0.753651	−	0.657275i	$-0.228291\pi$
$61$	0.752715	+	0.752715i	0.0963753	+	0.0963753i	−0.657275	+	0.753651i	$0.728291\pi$
$62$		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	$-0.819942\pi$
$67$	−11.2975	−	11.2975i	−1.38021	−	1.38021i	−0.535980	−	0.844230i	$-0.680058\pi$
$68$		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	0.724068	−	0.689728i	$-0.242270\pi$
$83$	0.312853	+	0.312853i	0.0343401	+	0.0343401i	−0.689728	+	0.724068i	$0.742270\pi$
$84$		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	−0.798067	−	0.602569i	$-0.794144\pi$
$101$	−1.96472	+	1.96472i	−0.195497	+	0.195497i	0.602569	+	0.798067i	$0.294144\pi$
$102$		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	−0.832313	−	0.554305i	$-0.812984\pi$
$107$	−2.87574	+	2.87574i	−0.278008	+	0.278008i	0.554305	+	0.832313i	$0.312984\pi$
$108$		0			0
$109$	2.74202	+	2.74202i	0.262638	+	0.262638i	0.826125	−	0.563487i	$-0.190541\pi$
$109$	2.74202	+	2.74202i	0.262638	+	0.262638i	−0.563487	+	0.826125i	$0.690541\pi$
$110$		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	0.476206	−	0.879334i	$-0.342012\pi$
$131$	−4.61401	−	4.61401i	−0.403128	−	0.403128i	−0.879334	+	0.476206i	$0.842012\pi$
$132$		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	$-0.496575\pi$
$139$	11.9160	−	11.9160i	1.01070	−	1.01070i	0.999942	−	0.0107594i	$-0.00342490\pi$
$140$		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	−0.203027	−	0.979173i	$-0.565078\pi$
$149$	9.47407	−	9.47407i	0.776146	−	0.776146i	0.979173	+	0.203027i	$0.0650780\pi$
$150$		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	$-0.868874\pi$
$157$	−16.4986	−	16.4986i	−1.31674	−	1.31674i	−0.400391	−	0.916344i	$-0.631126\pi$
$158$		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	0.989771	−	0.142663i	$-0.0455666\pi$
$163$	10.8152	+	10.8152i	0.847108	+	0.847108i	−0.142663	+	0.989771i	$0.545567\pi$
$164$		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	0.803295	−	0.595581i	$-0.203078\pi$
$173$	2.73205	+	2.73205i	0.207714	+	0.207714i	−0.595581	+	0.803295i	$0.703078\pi$
$174$		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	$0.138192\pi$
$179$	17.7656	+	17.7656i	1.32786	+	1.32786i	0.420632	+	0.907231i	$0.361808\pi$
$180$		0			0
$181$	−2.24213	+	2.24213i	−0.166656	+	0.166656i	−0.785508	−	0.618852i	$-0.787598\pi$
$181$	−2.24213	+	2.24213i	−0.166656	+	0.166656i	0.618852	+	0.785508i	$0.287598\pi$
$182$		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	−0.251558	−	0.967842i	$-0.580943\pi$
$197$	10.0535	−	10.0535i	0.716285	−	0.716285i	0.967842	+	0.251558i	$0.0809428\pi$
$198$		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	$0.0816221\pi$
$211$	17.7350	+	17.7350i	1.22093	+	1.22093i	0.253622	+	0.967303i	$0.418378\pi$
$212$		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	0.342841	−	0.939393i	$-0.388611\pi$
$227$	−8.98797	−	8.98797i	−0.596552	−	0.596552i	−0.939393	+	0.342841i	$0.888611\pi$
$228$		0			0
$229$	−1.60645	+	1.60645i	−0.106157	+	0.106157i	−0.758190	−	0.652033i	$-0.773916\pi$
$229$	−1.60645	+	1.60645i	−0.106157	+	0.106157i	0.652033	+	0.758190i	$0.273916\pi$
$230$		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	−0.945738	−	0.324929i	$-0.894660\pi$
$251$	−9.83548	+	9.83548i	−0.620810	+	0.620810i	0.324929	+	0.945738i	$0.394660\pi$
$252$		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	0.996964	−	0.0778580i	$-0.0248081\pi$
$269$	15.0745	+	15.0745i	0.919107	+	0.919107i	−0.0778580	+	0.996964i	$0.524808\pi$
$270$		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	−0.470544	−	0.882376i	$-0.655942\pi$
$277$	6.85425	−	6.85425i	0.411832	−	0.411832i	0.882376	+	0.470544i	$0.155942\pi$
$278$		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	−0.771932	−	0.635705i	$-0.780710\pi$
$283$	−2.29171	+	2.29171i	−0.136228	+	0.136228i	0.635705	+	0.771932i	$0.280710\pi$
$284$		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	$-0.485005\pi$
$293$	17.9043	−	17.9043i	1.04598	−	1.04598i	0.998891	−	0.0470899i	$-0.0149947\pi$
$294$		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	0.881091	−	0.472947i	$-0.156810\pi$
$307$	7.15125	+	7.15125i	0.408143	+	0.408143i	−0.472947	+	0.881091i	$0.656810\pi$
$308$		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	$-0.944655\pi$
$317$	−20.6162	−	20.6162i	−1.15792	−	1.15792i	−0.172997	−	0.984922i	$-0.555345\pi$
$318$		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	−0.370082	−	0.928999i	$-0.620670\pi$
$331$	10.1686	−	10.1686i	0.558917	−	0.558917i	0.928999	+	0.370082i	$0.120670\pi$
$332$		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	$0.526656\pi$
$347$	−20.1208	+	20.1208i	−1.08014	+	1.08014i	−0.996496	+	0.0836444i	$0.973344\pi$
$348$		0			0
$349$	−3.33386	−	3.33386i	−0.178457	−	0.178457i	0.612226	−	0.790683i	$-0.290274\pi$
$349$	−3.33386	−	3.33386i	−0.178457	−	0.178457i	−0.790683	+	0.612226i	$0.790274\pi$
$350$		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	−0.637104	−	0.770778i	$-0.719868\pi$
$373$	2.58166	−	2.58166i	0.133673	−	0.133673i	0.770778	+	0.637104i	$0.219868\pi$
$374$		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	−0.0135436	−	0.999908i	$-0.504311\pi$
$379$	19.2025	−	19.2025i	0.986365	−	0.986365i	0.999908	+	0.0135436i	$0.00431118\pi$
$380$		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	−0.836166	−	0.548477i	$-0.815208\pi$
$389$	−5.67412	+	5.67412i	−0.287689	+	0.287689i	0.548477	+	0.836166i	$0.315208\pi$
$390$		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	0.269803	−	0.962916i	$-0.413041\pi$
$397$	−13.8102	−	13.8102i	−0.693112	−	0.693112i	−0.962916	+	0.269803i	$0.913041\pi$
$398$		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	0.944489	−	0.328542i	$-0.106557\pi$
$419$	12.6081	+	12.6081i	0.615947	+	0.615947i	−0.328542	+	0.944489i	$0.606557\pi$
$420$		0			0
$421$	5.77589	−	5.77589i	0.281499	−	0.281499i	−0.552207	−	0.833707i	$-0.686214\pi$
$421$	5.77589	−	5.77589i	0.281499	−	0.281499i	0.833707	+	0.552207i	$0.186214\pi$
$422$		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	−0.877604	−	0.479386i	$-0.840859\pi$
$443$	−8.38152	+	8.38152i	−0.398218	+	0.398218i	0.479386	+	0.877604i	$0.340859\pi$
$444$		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	0.554427	−	0.832232i	$-0.312937\pi$
$461$	−5.96472	−	5.96472i	−0.277805	−	0.277805i	−0.832232	+	0.554427i	$0.812937\pi$
$462$		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	0.0772800	−	0.997009i	$-0.475376\pi$
$467$	−19.8755	−	19.8755i	−0.919729	−	0.919729i	−0.997009	+	0.0772800i	$0.975376\pi$
$468$		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	$0.524303\pi$
$491$	−23.7841	+	23.7841i	−1.07336	+	1.07336i	−0.997087	+	0.0762760i	$0.975697\pi$
$492$		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	0.748590	−	0.663033i	$-0.230731\pi$
$499$	1.91119	+	1.91119i	0.0855565	+	0.0855565i	−0.663033	+	0.748590i	$0.730731\pi$
$500$		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	0.976853	−	0.213914i	$-0.0686211\pi$
$509$	17.2127	+	17.2127i	0.762939	+	0.762939i	−0.213914	+	0.976853i	$0.568621\pi$
$510$		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	−0.558975	−	0.829185i	$-0.688805\pi$
$523$	6.17948	−	6.17948i	0.270210	−	0.270210i	0.829185	+	0.558975i	$0.188805\pi$
$524$		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	0.420581	−	0.907255i	$-0.361826\pi$
$541$	−11.3198	−	11.3198i	−0.486675	−	0.486675i	−0.907255	+	0.420581i	$0.861826\pi$
$542$		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	0.570147	−	0.821543i	$-0.306886\pi$
$547$	−5.87965	−	5.87965i	−0.251396	−	0.251396i	−0.821543	+	0.570147i	$0.806886\pi$
$548$		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	0.994861	−	0.101250i	$-0.0322843\pi$
$557$	21.0900	+	21.0900i	0.893611	+	0.893611i	−0.101250	+	0.994861i	$0.532284\pi$
$558$		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	$-0.899617\pi$
$563$	−29.9169	−	29.9169i	−1.26084	−	1.26084i	−0.310161	−	0.950684i	$-0.600383\pi$
$564$		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	−0.0502803	−	0.998735i	$-0.516011\pi$
$571$	22.6639	−	22.6639i	0.948455	−	0.948455i	0.998735	+	0.0502803i	$0.0160115\pi$
$572$		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	−0.872166	−	0.489211i	$-0.837285\pi$
$587$	−9.27826	+	9.27826i	−0.382955	+	0.382955i	0.489211	+	0.872166i	$0.337285\pi$
$588$		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	−0.979389	−	0.201981i	$-0.935262\pi$
$613$	−19.2477	+	19.2477i	−0.777408	+	0.777408i	0.201981	+	0.979389i	$0.435262\pi$
$614$		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	−0.736667	−	0.676255i	$-0.763602\pi$
$619$	−1.50303	+	1.50303i	−0.0604117	+	0.0604117i	0.676255	+	0.736667i	$0.263602\pi$
$620$		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	0.996501	−	0.0835832i	$-0.0266364\pi$
$643$	23.1493	+	23.1493i	0.912918	+	0.912918i	−0.0835832	+	0.996501i	$0.526636\pi$
$644$		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	0.725597	−	0.688120i	$-0.241564\pi$
$653$	0.957676	+	0.957676i	0.0374767	+	0.0374767i	−0.688120	+	0.725597i	$0.741564\pi$
$654$		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	0.724746	−	0.689016i	$-0.241957\pi$
$659$	0.917240	+	0.917240i	0.0357306	+	0.0357306i	−0.689016	+	0.724746i	$0.741957\pi$
$660$		0			0
$661$	−11.7481	+	11.7481i	−0.456947	+	0.456947i	−0.897652	−	0.440705i	$-0.854728\pi$
$661$	−11.7481	+	11.7481i	−0.456947	+	0.456947i	0.440705	+	0.897652i	$0.354728\pi$
$662$		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	−0.973446	−	0.228917i	$-0.926481\pi$
$677$	−19.3721	+	19.3721i	−0.744528	+	0.744528i	0.228917	+	0.973446i	$0.426481\pi$
$678$		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	−0.373760	−	0.927525i	$-0.621932\pi$
$683$	14.4723	−	14.4723i	0.553765	−	0.553765i	0.927525	+	0.373760i	$0.121932\pi$
$684$		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	0.265979	−	0.963979i	$-0.414305\pi$
$691$	−18.3482	−	18.3482i	−0.697999	−	0.697999i	−0.963979	+	0.265979i	$0.914305\pi$
$692$		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	0.908181	−	0.418577i	$-0.137471\pi$
$701$	12.9630	+	12.9630i	0.489604	+	0.489604i	−0.418577	+	0.908181i	$0.637471\pi$
$702$		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	−0.812404	−	0.583095i	$-0.801842\pi$
$709$	−6.10583	+	6.10583i	−0.229309	+	0.229309i	0.583095	+	0.812404i	$0.301842\pi$
$710$		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	0.876099	−	0.482130i	$-0.160137\pi$
$733$	10.6663	+	10.6663i	0.393969	+	0.393969i	−0.482130	+	0.876099i	$0.660137\pi$
$734$		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	0.530165	−	0.847895i	$-0.322130\pi$
$739$	−8.63735	−	8.63735i	−0.317730	−	0.317730i	−0.847895	+	0.530165i	$0.822130\pi$
$740$		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	−0.524753	−	0.851255i	$-0.675842\pi$
$757$	8.98325	−	8.98325i	0.326502	−	0.326502i	0.851255	+	0.524753i	$0.175842\pi$
$758$		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	−0.931783	−	0.363017i	$-0.881747\pi$
$773$	−15.8133	+	15.8133i	−0.568766	+	0.568766i	0.363017	+	0.931783i	$0.381747\pi$
$774$		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	0.251091	−	0.967964i	$-0.419211\pi$
$787$	−20.1108	−	20.1108i	−0.716873	−	0.716873i	−0.967964	+	0.251091i	$0.919211\pi$
$788$		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	0.754860	−	0.655886i	$-0.227705\pi$
$797$	2.79415	+	2.79415i	0.0989738	+	0.0989738i	−0.655886	+	0.754860i	$0.727705\pi$
$798$		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	$0.515948\pi$
$811$	−29.8685	+	29.8685i	−1.04883	+	1.04883i	−0.998745	+	0.0500814i	$0.984052\pi$
$812$		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	−0.875819	−	0.482640i	$-0.839678\pi$
$821$	−11.2658	+	11.2658i	−0.393180	+	0.393180i	0.482640	+	0.875819i	$0.339678\pi$
$822$		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	−0.431218	−	0.902248i	$-0.641916\pi$
$827$	13.5457	−	13.5457i	0.471030	−	0.471030i	0.902248	+	0.431218i	$0.141916\pi$
$828$		0			0
$829$	−10.3975	−	10.3975i	−0.361119	−	0.361119i	0.503106	−	0.864225i	$-0.332191\pi$
$829$	−10.3975	−	10.3975i	−0.361119	−	0.361119i	−0.864225	+	0.503106i	$0.832191\pi$
$830$		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	−0.900866	−	0.434097i	$-0.857068\pi$
$853$	−13.6325	+	13.6325i	−0.466769	+	0.466769i	0.434097	+	0.900866i	$0.357068\pi$
$854$		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	−0.429598	−	0.903020i	$-0.641345\pi$
$859$	13.8754	−	13.8754i	0.473422	−	0.473422i	0.903020	+	0.429598i	$0.141345\pi$
$860$		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	0.973273	−	0.229653i	$-0.0737591\pi$
$877$	22.0217	+	22.0217i	0.743620	+	0.743620i	−0.229653	+	0.973273i	$0.573759\pi$
$878$		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	0.502914	−	0.864337i	$-0.332261\pi$
$883$	−10.7398	−	10.7398i	−0.361423	−	0.361423i	−0.864337	+	0.502914i	$0.832261\pi$
$884$		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	−0.766343	−	0.642432i	$-0.777925\pi$
$907$	−3.73175	+	3.73175i	−0.123911	+	0.123911i	0.642432	+	0.766343i	$0.277925\pi$
$908$		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	0.153677	−	0.988121i	$-0.450888\pi$
$941$	−25.5972	−	25.5972i	−0.834444	−	0.834444i	−0.988121	+	0.153677i	$0.950888\pi$
$942$		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	$0.0759382\pi$
$947$	37.1739	+	37.1739i	1.20799	+	1.20799i	0.236310	+	0.971678i	$0.424062\pi$
$948$		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	$0.562860\pi$
$971$	−36.6690	+	36.6690i	−1.17676	+	1.17676i	−0.980564	+	0.196201i	$0.937140\pi$
$972$		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	−0.931907	−	0.362696i	$-0.881856\pi$
$997$	−17.9730	+	17.9730i	−0.569211	+	0.569211i	0.362696	+	0.931907i	$0.381856\pi$
$998$		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.d.321.2	yes	8
4.3	odd	2		1280.2.l.g.321.3	yes	8
8.3	odd	2		1280.2.l.a.321.2	✓	8
8.5	even	2		1280.2.l.f.321.3	yes	8
16.3	odd	4		1280.2.l.a.961.2	yes	8
16.5	even	4	inner	1280.2.l.d.961.2	yes	8
16.11	odd	4		1280.2.l.g.961.3	yes	8
16.13	even	4		1280.2.l.f.961.3	yes	8
32.5	even	8		5120.2.a.b.1.4		4
32.11	odd	8		5120.2.a.a.1.4		4
32.21	even	8		5120.2.a.q.1.1		4
32.27	odd	8		5120.2.a.r.1.1		4

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

Varieties

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Representations

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Database

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