LMFDB - Embedded newform 1040.2.da.b.641.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (of order $6$, degree $2$, not 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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			641.4
Root			$1.40994 + 0.109843i$ of defining polynomial
Character	$\chi$	$=$	1040.641
Dual form			1040.2.da.b.881.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16612 - 2.01978i) q^{3} +1.00000i q^{5} +(-3.11786 + 1.80010i) q^{7} +(-1.21969 - 2.11256i) q^{9} +O(q^{10})$	\(q+(1.16612 - 2.01978i) q^{3} +1.00000i q^{5} +(-3.11786 + 1.80010i) q^{7} +(-1.21969 - 2.11256i) q^{9} +(4.65213 + 2.68591i) q^{11} +(1.81988 + 3.11256i) q^{13} +(2.01978 + 1.16612i) q^{15} +(-0.565928 - 0.980215i) q^{17} +(1.96410 - 1.13397i) q^{19} +8.39654i q^{21} +(1.94644 - 3.37133i) q^{23} -1.00000 q^{25} +1.30752 q^{27} +(0.0123639 - 0.0214150i) q^{29} +5.46410i q^{31} +(10.8499 - 6.26420i) q^{33} +(-1.80010 - 3.11786i) q^{35} +(7.53794 + 4.35203i) q^{37} +(8.40891 - 0.0461428i) q^{39} +(3.23205 + 1.86603i) q^{41} +(0.565928 + 0.980215i) q^{43} +(2.11256 - 1.21969i) q^{45} -2.58535i q^{47} +(2.98070 - 5.16273i) q^{49} -2.63977 q^{51} -4.43937 q^{53} +(-2.68591 + 4.65213i) q^{55} -5.28942i q^{57} +(0.148458 - 0.0857123i) q^{59} +(-1.68012 - 2.91005i) q^{61} +(7.60563 + 4.39111i) q^{63} +(-3.11256 + 1.81988i) q^{65} +(-5.54239 - 3.19990i) q^{67} +(-4.53957 - 7.86276i) q^{69} +(-9.35076 + 5.39866i) q^{71} -4.70308i q^{73} +(-1.16612 + 2.01978i) q^{75} -19.3396 q^{77} +11.9826 q^{79} +(5.18379 - 8.97859i) q^{81} -12.1286i q^{83} +(0.980215 - 0.565928i) q^{85} +(-0.0288357 - 0.0499450i) q^{87} +(13.9898 + 8.07702i) q^{89} +(-11.2771 - 6.42856i) q^{91} +(11.0363 + 6.37182i) q^{93} +(1.13397 + 1.96410i) q^{95} +(-10.5379 + 6.08408i) q^{97} -13.1039i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9	$ 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 6 q^{15} - 2 q^{17} - 12 q^{19} + 10 q^{23} - 8 q^{25} + 4 q^{27} - 8 q^{29} + 42 q^{33} - 10 q^{35} + 6 q^{37} + 12 q^{41} + 2 q^{43} + 12 q^{49} + 8 q^{51} - 24 q^{53} + 12 q^{59} - 28 q^{61} + 24 q^{63} - 8 q^{65} - 6 q^{67} - 16 q^{69} + 2 q^{75} - 36 q^{77} + 16 q^{79} + 8 q^{81} + 18 q^{85} - 22 q^{87} + 24 q^{89} - 28 q^{91} + 16 q^{95} - 30 q^{97}+O(q^{100}) $ 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9 + 6 * q^15 - 2 * q^17 - 12 * q^19 + 10 * q^23 - 8 * q^25 + 4 * q^27 - 8 * q^29 + 42 * q^33 - 10 * q^35 + 6 * q^37 + 12 * q^41 + 2 * q^43 + 12 * q^49 + 8 * q^51 - 24 * q^53 + 12 * q^59 - 28 * q^61 + 24 * q^63 - 8 * q^65 - 6 * q^67 - 16 * q^69 + 2 * q^75 - 36 * q^77 + 16 * q^79 + 8 * q^81 + 18 * q^85 - 22 * q^87 + 24 * q^89 - 28 * q^91 + 16 * q^95 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.16612	−	2.01978i	0.673262	−	1.16612i	−0.303712	−	0.952764i	$-0.598226\pi$
$3$	1.16612	−	2.01978i	0.673262	−	1.16612i	0.976974	−	0.213359i	$-0.0684405\pi$
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−3.11786	+	1.80010i	−1.17844	+	0.680373i	−0.955653	−	0.294494i	$-0.904849\pi$
$7$	−3.11786	+	1.80010i	−1.17844	+	0.680373i	−0.222787	+	0.974867i	$0.571516\pi$
$8$		0			0
$9$	−1.21969	−	2.11256i	−0.406562	−	0.704187i
$10$		0			0
$11$	4.65213	+	2.68591i	1.40267	+	0.809832i	0.994666	−	0.103149i	$-0.0328917\pi$
$11$	4.65213	+	2.68591i	1.40267	+	0.809832i	0.408004	+	0.912980i	$0.366225\pi$
$12$		0			0
$13$	1.81988	+	3.11256i	0.504745	+	0.863269i
$13$	1.81988	+	3.11256i	0.504745	+	0.863269i
$14$		0			0
$15$	2.01978	+	1.16612i	0.521506	+	0.301092i
$16$		0			0
$17$	−0.565928	−	0.980215i	−0.137258	−	0.237737i	0.789200	−	0.614136i	$-0.210495\pi$
$17$	−0.565928	−	0.980215i	−0.137258	−	0.237737i	−0.926458	+	0.376399i	$0.877162\pi$
$18$		0			0
$19$	1.96410	−	1.13397i	0.450596	−	0.260152i	−0.257486	−	0.966282i	$-0.582894\pi$
$19$	1.96410	−	1.13397i	0.450596	−	0.260152i	0.708082	+	0.706130i	$0.249561\pi$
$20$		0			0
$21$			8.39654i			1.83228i
$22$		0			0
$23$	1.94644	−	3.37133i	0.405860	−	0.702970i	−0.588561	−	0.808453i	$-0.700305\pi$
$23$	1.94644	−	3.37133i	0.405860	−	0.702970i	0.994421	+	0.105483i	$0.0336387\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	1.30752			0.251632
$28$		0			0
$29$	0.0123639	−	0.0214150i	0.00229593	−	0.00397666i	−0.864875	−	0.501987i	$-0.832603\pi$
$29$	0.0123639	−	0.0214150i	0.00229593	−	0.00397666i	0.867171	+	0.498010i	$0.165936\pi$
$30$		0			0
$31$			5.46410i			0.981382i	0.871334	+	0.490691i	$0.163256\pi$
$31$			5.46410i			0.981382i	−0.871334	+	0.490691i	$0.836744\pi$
$32$		0			0
$33$	10.8499	−	6.26420i	1.88873	−	1.09046i
$34$		0			0
$35$	−1.80010	−	3.11786i	−0.304272	−	0.527015i
$36$		0			0
$37$	7.53794	+	4.35203i	1.23923	+	0.715470i	0.968937	−	0.247309i	$-0.0795462\pi$
$37$	7.53794	+	4.35203i	1.23923	+	0.715470i	0.270293	+	0.962778i	$0.412879\pi$
$38$		0			0
$39$	8.40891	−	0.0461428i	1.34650	−	0.00738877i
$40$		0			0
$41$	3.23205	+	1.86603i	0.504762	+	0.291424i	0.730678	−	0.682723i	$-0.239204\pi$
$41$	3.23205	+	1.86603i	0.504762	+	0.291424i	−0.225916	+	0.974147i	$0.572538\pi$
$42$		0			0
$43$	0.565928	+	0.980215i	0.0863031	+	0.149481i	0.905946	−	0.423394i	$-0.139161\pi$
$43$	0.565928	+	0.980215i	0.0863031	+	0.149481i	−0.819643	+	0.572875i	$0.805828\pi$
$44$		0			0
$45$	2.11256	−	1.21969i	0.314922	−	0.181820i
$46$		0			0
$47$		−	2.58535i		−	0.377113i	−0.982062	−	0.188556i	$-0.939619\pi$
$47$		−	2.58535i		−	0.377113i	0.982062	−	0.188556i	$-0.0603808\pi$
$48$		0			0
$49$	2.98070	−	5.16273i	0.425815	−	0.737533i
$50$		0			0
$51$	−2.63977			−0.369641
$52$		0			0
$53$	−4.43937			−0.609795			−0.304897	−	0.952385i	$-0.598622\pi$
$53$	−4.43937			−0.609795			−0.304897	+	0.952385i	$0.598622\pi$
$54$		0			0
$55$	−2.68591	+	4.65213i	−0.362168	+	0.627293i
$56$		0			0
$57$		−	5.28942i		−	0.700600i
$58$		0			0
$59$	0.148458	−	0.0857123i	0.0193276	−	0.0111588i	−0.490305	−	0.871551i	$-0.663115\pi$
$59$	0.148458	−	0.0857123i	0.0193276	−	0.0111588i	0.509633	+	0.860392i	$0.329781\pi$
$60$		0			0
$61$	−1.68012	−	2.91005i	−0.215117	−	0.372594i	0.738192	−	0.674591i	$-0.235680\pi$
$61$	−1.68012	−	2.91005i	−0.215117	−	0.372594i	−0.953309	+	0.301997i	$0.902347\pi$
$62$		0			0
$63$	7.60563	+	4.39111i	0.958219	+	0.553228i
$64$		0			0
$65$	−3.11256	+	1.81988i	−0.386066	+	0.225729i
$66$		0			0
$67$	−5.54239	−	3.19990i	−0.677111	−	0.390930i	0.121655	−	0.992572i	$-0.461180\pi$
$67$	−5.54239	−	3.19990i	−0.677111	−	0.390930i	−0.798766	+	0.601642i	$0.794513\pi$
$68$		0			0
$69$	−4.53957	−	7.86276i	−0.546500	−	0.946566i
$70$		0			0
$71$	−9.35076	+	5.39866i	−1.10973	+	0.640703i	−0.938760	−	0.344573i	$-0.888024\pi$
$71$	−9.35076	+	5.39866i	−1.10973	+	0.640703i	−0.170971	+	0.985276i	$0.554691\pi$
$72$		0			0
$73$		−	4.70308i		−	0.550454i	−0.961379	−	0.275227i	$-0.911247\pi$
$73$		−	4.70308i		−	0.550454i	0.961379	−	0.275227i	$-0.0887531\pi$
$74$		0			0
$75$	−1.16612	+	2.01978i	−0.134652	+	0.233225i
$76$		0			0
$77$	−19.3396			−2.20395
$78$		0			0
$79$	11.9826			1.34815			0.674075	−	0.738663i	$-0.264543\pi$
$79$	11.9826			1.34815			0.674075	+	0.738663i	$0.264543\pi$
$80$		0			0
$81$	5.18379	−	8.97859i	0.575976	−	0.997621i
$82$		0			0
$83$		−	12.1286i		−	1.33129i	−0.746270	−	0.665643i	$-0.768157\pi$
$83$		−	12.1286i		−	1.33129i	0.746270	−	0.665643i	$-0.231843\pi$
$84$		0			0
$85$	0.980215	−	0.565928i	0.106319	−	0.0613835i
$86$		0			0
$87$	−0.0288357	−	0.0499450i	−0.00309152	−	0.00535466i
$88$		0			0
$89$	13.9898	+	8.07702i	1.48292	+	0.856162i	0.999812	−	0.0194001i	$-0.00617565\pi$
$89$	13.9898	+	8.07702i	1.48292	+	0.856162i	0.483105	+	0.875562i	$0.339509\pi$
$90$		0			0
$91$	−11.2771	−	6.42856i	−1.18216	−	0.673896i
$92$		0			0
$93$	11.0363	+	6.37182i	1.14441	+	0.660727i
$94$		0			0
$95$	1.13397	+	1.96410i	0.116343	+	0.201513i
$96$		0			0
$97$	−10.5379	+	6.08408i	−1.06997	+	0.617745i	−0.928172	−	0.372151i	$-0.878620\pi$
$97$	−10.5379	+	6.08408i	−1.06997	+	0.617745i	−0.141794	+	0.989896i	$0.545287\pi$
$98$		0			0
$99$		−	13.1039i		−	1.31699i
$100$		0			0
$101$	−2.02721	+	3.51122i	−0.201714	+	0.349380i	−0.949081	−	0.315032i	$-0.897985\pi$
$101$	−2.02721	+	3.51122i	−0.201714	+	0.349380i	0.747366	+	0.664412i	$0.231318\pi$
$102$		0			0
$103$	−17.9035			−1.76408			−0.882041	−	0.471173i	$-0.843831\pi$
$103$	−17.9035			−1.76408			−0.882041	+	0.471173i	$0.843831\pi$
$104$		0			0
$105$	−8.39654			−0.819419
$106$		0			0
$107$	−4.56593	+	7.90842i	−0.441405	+	0.764536i	−0.997794	−	0.0663862i	$-0.978853\pi$
$107$	−4.56593	+	7.90842i	−0.441405	+	0.764536i	0.556389	+	0.830922i	$0.312186\pi$
$108$		0			0
$109$		−	7.37605i		−	0.706498i	−0.935529	−	0.353249i	$-0.885077\pi$
$109$		−	7.37605i		−	0.706498i	0.935529	−	0.353249i	$-0.114923\pi$
$110$		0			0
$111$	17.5803	−	10.1500i	1.66865	−	0.963396i
$112$		0			0
$113$	−3.53794	−	6.12789i	−0.332821	−	0.576463i	0.650243	−	0.759727i	$-0.274667\pi$
$113$	−3.53794	−	6.12789i	−0.332821	−	0.576463i	−0.983064	+	0.183263i	$0.941334\pi$
$114$		0			0
$115$	3.37133	+	1.94644i	0.314378	+	0.181506i
$116$		0			0
$117$	4.35578	−	7.64096i	0.402692	−	0.706407i
$118$		0			0
$119$	3.52897	+	2.03745i	0.323500	+	0.186773i
$120$		0			0
$121$	8.92820	+	15.4641i	0.811655	+	1.40583i
$122$		0			0
$123$	7.53794	−	4.35203i	0.679673	−	0.392409i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	5.71806	−	9.90396i	0.507395	−	0.878835i	−0.492568	−	0.870274i	$-0.663942\pi$
$127$	5.71806	−	9.90396i	0.507395	−	0.878835i	0.999963	−	0.00856072i	$-0.00272499\pi$
$128$		0			0
$129$	2.63977			0.232418
$130$		0			0
$131$	10.5680			0.923328			0.461664	−	0.887055i	$-0.347253\pi$
$131$	10.5680			0.923328			0.461664	+	0.887055i	$0.347253\pi$
$132$		0			0
$133$	−4.08253	+	7.07115i	−0.354000	+	0.613146i
$134$		0			0
$135$			1.30752i			0.112533i
$136$		0			0
$137$	3.27940	−	1.89336i	0.280178	−	0.161761i	−0.353326	−	0.935500i	$-0.614949\pi$
$137$	3.27940	−	1.89336i	0.280178	−	0.161761i	0.633504	+	0.773739i	$0.281616\pi$
$138$		0			0
$139$	1.00693	+	1.74406i	0.0854068	+	0.147929i	0.905564	−	0.424209i	$-0.139448\pi$
$139$	1.00693	+	1.74406i	0.0854068	+	0.147929i	−0.820158	+	0.572138i	$0.806114\pi$
$140$		0			0
$141$	−5.22186	−	3.01484i	−0.439760	−	0.253895i
$142$		0			0
$143$	0.106280	+	19.3681i	0.00888757	+	1.61964i
$144$		0			0
$145$	0.0214150	+	0.0123639i	0.00177842	+	0.00102677i
$146$		0			0
$147$	−6.95174	−	12.0408i	−0.573370	−	0.993105i
$148$		0			0
$149$	4.77855	−	2.75890i	0.391474	−	0.226018i	−0.291324	−	0.956624i	$-0.594096\pi$
$149$	4.77855	−	2.75890i	0.391474	−	0.226018i	0.682799	+	0.730607i	$0.260763\pi$
$150$		0			0
$151$			4.88961i			0.397911i	0.980009	+	0.198956i	$0.0637549\pi$
$151$			4.88961i			0.397911i	−0.980009	+	0.198956i	$0.936245\pi$
$152$		0			0
$153$	−1.38051	+	2.39111i	−0.111608	+	0.193310i
$154$		0			0
$155$	−5.46410			−0.438887
$156$		0			0
$157$	10.0405			0.801323			0.400661	−	0.916226i	$-0.368780\pi$
$157$	10.0405			0.801323			0.400661	+	0.916226i	$0.368780\pi$
$158$		0			0
$159$	−5.17686	+	8.96658i	−0.410551	+	0.711096i
$160$		0			0
$161$			14.0151i			1.10454i
$162$		0			0
$163$	−5.87273	+	3.39062i	−0.459988	+	0.265574i	−0.712039	−	0.702140i	$-0.752228\pi$
$163$	−5.87273	+	3.39062i	−0.459988	+	0.265574i	0.252051	+	0.967714i	$0.418895\pi$
$164$		0			0
$165$	6.26420	+	10.8499i	0.487667	+	0.844664i
$166$		0			0
$167$	9.08444	+	5.24490i	0.702975	+	0.405863i	0.808455	−	0.588559i	$-0.200304\pi$
$167$	9.08444	+	5.24490i	0.702975	+	0.405863i	−0.105479	+	0.994421i	$0.533638\pi$
$168$		0			0
$169$	−6.37605	+	11.3290i	−0.490466	+	0.871460i
$170$		0			0
$171$	−4.79118	−	2.76619i	−0.366391	−	0.211536i
$172$		0			0
$173$	−2.22923	−	3.86113i	−0.169485	−	0.293557i	0.768754	−	0.639545i	$-0.220877\pi$
$173$	−2.22923	−	3.86113i	−0.169485	−	0.293557i	−0.938239	+	0.345988i	$0.887544\pi$
$174$		0			0
$175$	3.11786	−	1.80010i	0.235688	−	0.136075i
$176$		0			0
$177$		−	0.399804i		−	0.0300511i
$178$		0			0
$179$	−9.31564	+	16.1352i	−0.696284	+	1.20600i	0.273462	+	0.961883i	$0.411831\pi$
$179$	−9.31564	+	16.1352i	−0.696284	+	1.20600i	−0.969746	+	0.244116i	$0.921502\pi$
$180$		0			0
$181$	−18.0900			−1.34462			−0.672310	−	0.740270i	$-0.734698\pi$
$181$	−18.0900			−1.34462			−0.672310	+	0.740270i	$0.734698\pi$
$182$		0			0
$183$	−7.83690			−0.579320
$184$		0			0
$185$	−4.35203	+	7.53794i	−0.319968	+	0.554200i
$186$		0			0
$187$		−	6.08012i		−	0.444622i
$188$		0			0
$189$	−4.07666	+	2.35366i	−0.296533	+	0.171204i
$190$		0			0
$191$	13.6682	+	23.6740i	0.988994	+	1.71299i	0.622632	+	0.782515i	$0.286063\pi$
$191$	13.6682	+	23.6740i	0.988994	+	1.71299i	0.366361	+	0.930473i	$0.380603\pi$
$192$		0			0
$193$	−18.8511	−	10.8837i	−1.35693	−	0.783425i	−0.367723	−	0.929935i	$-0.619863\pi$
$193$	−18.8511	−	10.8837i	−1.35693	−	0.783425i	−0.989209	+	0.146510i	$0.953196\pi$
$194$		0			0
$195$	0.0461428	+	8.40891i	0.00330436	+	0.602174i
$196$		0			0
$197$	−1.46940	−	0.848360i	−0.104691	−	0.0604432i	0.446741	−	0.894664i	$-0.352585\pi$
$197$	−1.46940	−	0.848360i	−0.104691	−	0.0604432i	−0.551431	+	0.834220i	$0.685918\pi$
$198$		0			0
$199$	−12.6627	−	21.9325i	−0.897637	−	1.55475i	−0.830506	−	0.557009i	$-0.811949\pi$
$199$	−12.6627	−	21.9325i	−0.897637	−	1.55475i	−0.0671309	−	0.997744i	$-0.521385\pi$
$200$		0			0
$201$	−12.9262	+	7.46296i	−0.911746	+	0.526397i
$202$		0			0
$203$			0.0890252i			0.00624834i
$204$		0			0
$205$	−1.86603	+	3.23205i	−0.130329	+	0.225736i
$206$		0			0
$207$	−9.49617			−0.660030
$208$		0			0
$209$	12.1830			0.842716
$210$		0			0
$211$	−0.167753	+	0.290558i	−0.0115486	+	0.0200028i	−0.871742	−	0.489965i	$-0.837009\pi$
$211$	−0.167753	+	0.290558i	−0.0115486	+	0.0200028i	0.860193	+	0.509968i	$0.170343\pi$
$212$		0			0
$213$			25.1820i			1.72544i
$214$		0			0
$215$	−0.980215	+	0.565928i	−0.0668501	+	0.0385959i
$216$		0			0
$217$	−9.83592	−	17.0363i	−0.667706	−	1.15650i
$218$		0			0
$219$	−9.49922	−	5.48438i	−0.641898	−	0.370600i
$220$		0			0
$221$	2.02106	−	3.54536i	0.135951	−	0.238487i
$222$		0			0
$223$	10.6493	+	6.14838i	0.713130	+	0.411726i	0.812219	−	0.583353i	$-0.198259\pi$
$223$	10.6493	+	6.14838i	0.713130	+	0.411726i	−0.0990887	+	0.995079i	$0.531593\pi$
$224$		0			0
$225$	1.21969	+	2.11256i	0.0813125	+	0.140837i
$226$		0			0
$227$	−6.60974	+	3.81613i	−0.438704	+	0.253286i	−0.703048	−	0.711143i	$-0.748178\pi$
$227$	−6.60974	+	3.81613i	−0.438704	+	0.253286i	0.264344	+	0.964428i	$0.414845\pi$
$228$		0			0
$229$		−	14.4008i		−	0.951631i	−0.879545	−	0.475815i	$-0.842153\pi$
$229$		−	14.4008i		−	0.951631i	0.879545	−	0.475815i	$-0.157847\pi$
$230$		0			0
$231$	−22.5523	+	39.0618i	−1.48384	+	2.57008i
$232$		0			0
$233$	−9.49617			−0.622115			−0.311057	−	0.950391i	$-0.600683\pi$
$233$	−9.49617			−0.622115			−0.311057	+	0.950391i	$0.600683\pi$
$234$		0			0
$235$	2.58535			0.168650
$236$		0			0
$237$	13.9732	−	24.2023i	0.907657	−	1.57211i
$238$		0			0
$239$		−	19.9143i		−	1.28815i	−0.764962	−	0.644076i	$-0.777242\pi$
$239$		−	19.9143i		−	1.28815i	0.764962	−	0.644076i	$-0.222758\pi$
$240$		0			0
$241$	20.1493	−	11.6332i	1.29793	−	0.749360i	0.317883	−	0.948130i	$-0.397028\pi$
$241$	20.1493	−	11.6332i	1.29793	−	0.749360i	0.980046	+	0.198770i	$0.0636947\pi$
$242$		0			0
$243$	−10.1286	−	17.5432i	−0.649750	−	1.12540i
$244$		0			0
$245$	5.16273	+	2.98070i	0.329835	+	0.190430i
$246$		0			0
$247$	7.10400	+	4.04968i	0.452017	+	0.257675i
$248$		0			0
$249$	−24.4972	−	14.1434i	−1.55244	−	0.896304i
$250$		0			0
$251$	−5.92008	−	10.2539i	−0.373672	−	0.647219i	0.616455	−	0.787390i	$-0.288568\pi$
$251$	−5.92008	−	10.2539i	−0.373672	−	0.647219i	−0.990127	+	0.140171i	$0.955235\pi$
$252$		0			0
$253$	18.1101	−	10.4559i	1.13858	−	0.657357i
$254$		0			0
$255$		−	2.63977i		−	0.165309i
$256$		0			0
$257$	−2.77501	+	4.80646i	−0.173100	+	0.299819i	−0.939502	−	0.342543i	$-0.888712\pi$
$257$	−2.77501	+	4.80646i	−0.173100	+	0.299819i	0.766402	+	0.642361i	$0.222045\pi$
$258$		0			0
$259$	−31.3363			−1.94714
$260$		0			0
$261$	−0.0603205			−0.00373375
$262$		0			0
$263$	3.42983	−	5.94065i	0.211493	−	0.366316i	−0.740689	−	0.671848i	$-0.765501\pi$
$263$	3.42983	−	5.94065i	0.211493	−	0.366316i	0.952182	+	0.305532i	$0.0988342\pi$
$264$		0			0
$265$		−	4.43937i		−	0.272709i
$266$		0			0
$267$	32.6277	−	18.8376i	1.99678	−	1.15284i
$268$		0			0
$269$	0.710994	+	1.23148i	0.0433501	+	0.0750845i	0.886886	−	0.461988i	$-0.152864\pi$
$269$	0.710994	+	1.23148i	0.0433501	+	0.0750845i	−0.843536	+	0.537072i	$0.819530\pi$
$270$		0			0
$271$	−8.63381	−	4.98473i	−0.524467	−	0.302801i	0.214294	−	0.976769i	$-0.431255\pi$
$271$	−8.63381	−	4.98473i	−0.524467	−	0.302801i	−0.738760	+	0.673968i	$0.764588\pi$
$272$		0			0
$273$	−26.1347	+	15.2807i	−1.58175	+	0.924831i
$274$		0			0
$275$	−4.65213	−	2.68591i	−0.280534	−	0.161966i
$276$		0			0
$277$	−8.76187	−	15.1760i	−0.526449	−	0.911837i	−0.999525	−	0.0308154i	$-0.990190\pi$
$277$	−8.76187	−	15.1760i	−0.526449	−	0.911837i	0.473076	−	0.881022i	$-0.343144\pi$
$278$		0			0
$279$	11.5432	−	6.66449i	0.691076	−	0.398993i
$280$		0			0
$281$			10.7352i			0.640406i	0.947349	+	0.320203i	$0.103751\pi$
$281$			10.7352i			0.640406i	−0.947349	+	0.320203i	$0.896249\pi$
$282$		0			0
$283$	−0.659192	+	1.14175i	−0.0391849	+	0.0678702i	−0.884953	−	0.465681i	$-0.845809\pi$
$283$	−0.659192	+	1.14175i	−0.0391849	+	0.0678702i	0.845768	+	0.533551i	$0.179143\pi$
$284$		0			0
$285$	5.28942			0.313318
$286$		0			0
$287$	−13.4361			−0.793109
$288$		0			0
$289$	7.85945	−	13.6130i	0.462321	−	0.800763i
$290$		0			0
$291$			28.3792i			1.66362i
$292$		0			0
$293$	16.2316	−	9.37133i	0.948261	−	0.547479i	0.0557207	−	0.998446i	$-0.482254\pi$
$293$	16.2316	−	9.37133i	0.948261	−	0.547479i	0.892540	+	0.450968i	$0.148921\pi$
$294$		0			0
$295$	0.0857123	+	0.148458i	0.00499036	+	0.00864356i
$296$		0			0
$297$	6.08275	+	3.51187i	0.352957	+	0.203780i
$298$		0			0
$299$	14.0357	−	0.0770194i	0.811708	−	0.00445415i
$300$		0			0
$301$	−3.52897	−	2.03745i	−0.203406	−	0.117437i
$302$		0			0
$303$	4.72794	+	8.18904i	0.271613	+	0.470448i
$304$		0			0
$305$	2.91005	−	1.68012i	0.166629	−	0.0962032i
$306$		0			0
$307$		−	14.3043i		−	0.816387i	−0.912895	−	0.408194i	$-0.866159\pi$
$307$		−	14.3043i		−	0.816387i	0.912895	−	0.408194i	$-0.133841\pi$
$308$		0			0
$309$	−20.8777	+	36.1612i	−1.18769	+	2.05714i
$310$		0			0
$311$	2.76102			0.156563			0.0782815	−	0.996931i	$-0.475057\pi$
$311$	2.76102			0.156563			0.0782815	+	0.996931i	$0.475057\pi$
$312$		0			0
$313$	−16.3858			−0.926179			−0.463090	−	0.886311i	$-0.653259\pi$
$313$	−16.3858			−0.926179			−0.463090	+	0.886311i	$0.653259\pi$
$314$		0			0
$315$	−4.39111	+	7.60563i	−0.247411	+	0.428529i
$316$		0			0
$317$		−	1.78575i		−	0.100297i	−0.998742	−	0.0501487i	$-0.984030\pi$
$317$		−	1.78575i		−	0.100297i	0.998742	−	0.0501487i	$-0.0159695\pi$
$318$		0			0
$319$	0.115037	−	0.0664168i	0.00644085	−	0.00371863i
$320$		0			0
$321$	10.6489	+	18.4444i	0.594362	+	1.02946i
$322$		0			0
$323$	−2.22308	−	1.28349i	−0.123695	−	0.0714156i
$324$		0			0
$325$	−1.81988	−	3.11256i	−0.100949	−	0.172654i
$326$		0			0
$327$	−14.8980	−	8.60139i	−0.823864	−	0.475658i
$328$		0			0
$329$	4.65389	+	8.06077i	0.256577	+	0.444405i
$330$		0			0
$331$	6.25652	−	3.61220i	0.343889	−	0.198545i	−0.318101	−	0.948057i	$-0.603045\pi$
$331$	6.25652	−	3.61220i	0.343889	−	0.198545i	0.661991	+	0.749512i	$0.269712\pi$
$332$		0			0
$333$		−	21.2325i		−	1.16353i
$334$		0			0
$335$	3.19990	−	5.54239i	0.174829	−	0.302813i
$336$		0			0
$337$	4.36219			0.237624			0.118812	−	0.992917i	$-0.462091\pi$
$337$	4.36219			0.237624			0.118812	+	0.992917i	$0.462091\pi$
$338$		0			0
$339$	−16.5027			−0.896303
$340$		0			0
$341$	−14.6761	+	25.4197i	−0.794754	+	1.37655i
$342$		0			0
$343$		−	3.73913i		−	0.201894i
$344$		0			0
$345$	7.86276	−	4.53957i	0.423317	−	0.244402i
$346$		0			0
$347$	−13.3536	−	23.1291i	−0.716858	−	1.24163i	−0.962239	−	0.272207i	$-0.912246\pi$
$347$	−13.3536	−	23.1291i	−0.716858	−	1.24163i	0.245381	−	0.969427i	$-0.421087\pi$
$348$		0			0
$349$	−20.4131	−	11.7855i	−1.09269	−	0.630865i	−0.158399	−	0.987375i	$-0.550633\pi$
$349$	−20.4131	−	11.7855i	−1.09269	−	0.630865i	−0.934292	+	0.356510i	$0.883967\pi$
$350$		0			0
$351$	2.37953	+	4.06973i	0.127010	+	0.217226i
$352$		0			0
$353$	4.96862	+	2.86863i	0.264453	+	0.152682i	0.626364	−	0.779531i	$-0.284542\pi$
$353$	4.96862	+	2.86863i	0.264453	+	0.152682i	−0.361911	+	0.932213i	$0.617876\pi$
$354$		0			0
$355$	−5.39866	−	9.35076i	−0.286531	−	0.496287i
$356$		0			0
$357$	8.23042	−	4.75184i	0.435600	−	0.251494i
$358$		0			0
$359$			24.7583i			1.30669i	0.757059	+	0.653347i	$0.226636\pi$
$359$			24.7583i			1.30669i	−0.757059	+	0.653347i	$0.773364\pi$
$360$		0			0
$361$	−6.92820	+	12.0000i	−0.364642	+	0.631579i
$362$		0			0
$363$	41.6455			2.18582
$364$		0			0
$365$	4.70308			0.246171
$366$		0			0
$367$	13.0268	−	22.5630i	0.679992	−	1.17778i	−0.294991	−	0.955500i	$-0.595317\pi$
$367$	13.0268	−	22.5630i	0.679992	−	1.17778i	0.974983	−	0.222280i	$-0.0713500\pi$
$368$		0			0
$369$		−	9.10387i		−	0.473928i
$370$		0			0
$371$	13.8413	−	7.99131i	0.718607	−	0.414888i
$372$		0			0
$373$	−6.60224	−	11.4354i	−0.341851	−	0.592103i	0.642926	−	0.765929i	$-0.277720\pi$
$373$	−6.60224	−	11.4354i	−0.341851	−	0.592103i	−0.984776	+	0.173826i	$0.944387\pi$
$374$		0			0
$375$	−2.01978	−	1.16612i	−0.104301	−	0.0602183i
$376$		0			0
$377$	0.0891563		0.000489234i	0.00459178		2.51968e-5i
$378$		0			0
$379$	−22.5147	−	12.9989i	−1.15650	−	0.667707i	−0.206039	−	0.978544i	$-0.566057\pi$
$379$	−22.5147	−	12.9989i	−1.15650	−	0.667707i	−0.950463	+	0.310837i	$0.899391\pi$
$380$		0			0
$381$	−13.3359	−	23.0985i	−0.683220	−	1.18337i
$382$		0			0
$383$	−8.31401	+	4.80010i	−0.424826	+	0.245274i	−0.697140	−	0.716935i	$-0.745544\pi$
$383$	−8.31401	+	4.80010i	−0.424826	+	0.245274i	0.272314	+	0.962208i	$0.412211\pi$
$384$		0			0
$385$		−	19.3396i		−	0.985637i
$386$		0			0
$387$	1.38051	−	2.39111i	0.0701752	−	0.121547i
$388$		0			0
$389$	−5.63129			−0.285518			−0.142759	−	0.989758i	$-0.545597\pi$
$389$	−5.63129			−0.285518			−0.142759	+	0.989758i	$0.545597\pi$
$390$		0			0
$391$	−4.40617			−0.222829
$392$		0			0
$393$	12.3236	−	21.3450i	0.621641	−	1.07671i
$394$		0			0
$395$			11.9826i			0.602911i
$396$		0			0
$397$	−14.5196	+	8.38291i	−0.728719	+	0.420726i	−0.817953	−	0.575285i	$-0.804891\pi$
$397$	−14.5196	+	8.38291i	−0.728719	+	0.420726i	0.0892344	+	0.996011i	$0.471558\pi$
$398$		0			0
$399$	9.52147	+	16.4917i	0.476670	+	0.825616i
$400$		0			0
$401$	12.0187	+	6.93902i	0.600187	+	0.346518i	0.769115	−	0.639110i	$-0.220697\pi$
$401$	12.0187	+	6.93902i	0.600187	+	0.346518i	−0.168928	+	0.985628i	$0.554031\pi$
$402$		0			0
$403$	−17.0073	+	9.94402i	−0.847196	+	0.495347i
$404$		0			0
$405$	8.97859	+	5.18379i	0.446149	+	0.257585i
$406$		0			0
$407$	23.3783	+	40.4924i	1.15882	+	2.00713i
$408$		0			0
$409$	−25.4829	+	14.7125i	−1.26005	+	0.727489i	−0.973083	−	0.230453i	$-0.925979\pi$
$409$	−25.4829	+	14.7125i	−1.26005	+	0.727489i	−0.286964	+	0.957941i	$0.592646\pi$
$410$		0			0
$411$		−	8.83157i		−	0.435629i
$412$		0			0
$413$	−0.308581	+	0.534478i	−0.0151843	+	0.0262999i
$414$		0			0
$415$	12.1286			0.595369
$416$		0			0
$417$	4.69683			0.230005
$418$		0			0
$419$	3.48397	−	6.03440i	0.170203	−	0.294800i	−0.768288	−	0.640104i	$-0.778891\pi$
$419$	3.48397	−	6.03440i	0.170203	−	0.294800i	0.938491	+	0.345305i	$0.112224\pi$
$420$		0			0
$421$		−	7.12125i		−	0.347069i	−0.984828	−	0.173534i	$-0.944481\pi$
$421$		−	7.12125i		−	0.347069i	0.984828	−	0.173534i	$-0.0555188\pi$
$422$		0			0
$423$	−5.46171	+	3.15332i	−0.265558	+	0.153320i
$424$		0			0
$425$	0.565928	+	0.980215i	0.0274515	+	0.0475474i
$426$		0			0
$427$	10.4767	+	6.04875i	0.507005	+	0.292720i
$428$		0			0
$429$	39.2433	+	22.3709i	1.89468	+	1.08008i
$430$		0			0
$431$	−26.1664	−	15.1072i	−1.26039	−	0.727687i	−0.287241	−	0.957858i	$-0.592738\pi$
$431$	−26.1664	−	15.1072i	−1.26039	−	0.727687i	−0.973150	+	0.230171i	$0.926071\pi$
$432$		0			0
$433$	0.600065	+	1.03934i	0.0288373	+	0.0499476i	0.880084	−	0.474818i	$-0.157486\pi$
$433$	0.600065	+	1.03934i	0.0288373	+	0.0499476i	−0.851247	+	0.524766i	$0.824153\pi$
$434$		0			0
$435$	0.0499450	−	0.0288357i	0.00239468	−	0.00138257i
$436$		0			0
$437$		−	8.82884i		−	0.422341i
$438$		0			0
$439$	8.27705	−	14.3363i	0.395042	−	0.684233i	−0.598064	−	0.801448i	$-0.704063\pi$
$439$	8.27705	−	14.3363i	0.395042	−	0.684233i	0.993107	+	0.117215i	$0.0373966\pi$
$440$		0			0
$441$	−14.5421			−0.692481
$442$		0			0
$443$	−4.55949			−0.216628			−0.108314	−	0.994117i	$-0.534545\pi$
$443$	−4.55949			−0.216628			−0.108314	+	0.994117i	$0.534545\pi$
$444$		0			0
$445$	−8.07702	+	13.9898i	−0.382887	+	0.663180i
$446$		0			0
$447$		−	12.8689i		−	0.608676i
$448$		0			0
$449$	11.9963	−	6.92608i	0.566142	−	0.326862i	−0.189465	−	0.981887i	$-0.560675\pi$
$449$	11.9963	−	6.92608i	0.566142	−	0.326862i	0.755607	+	0.655025i	$0.227342\pi$
$450$		0			0
$451$	10.0239	+	17.3620i	0.472009	+	0.817544i
$452$		0			0
$453$	9.87596	+	5.70189i	0.464013	+	0.267898i
$454$		0			0
$455$	6.42856	−	11.2771i	0.301376	−	0.528676i
$456$		0			0
$457$	34.7402	+	20.0573i	1.62508	+	0.938240i	0.985532	+	0.169489i	$0.0542117\pi$
$457$	34.7402	+	20.0573i	1.62508	+	0.938240i	0.639548	+	0.768751i	$0.279122\pi$
$458$		0			0
$459$	−0.739961	−	1.28165i	−0.0345384	−	0.0598223i
$460$		0			0
$461$	6.52897	−	3.76950i	0.304084	−	0.175563i	−0.340192	−	0.940356i	$-0.610492\pi$
$461$	6.52897	−	3.76950i	0.304084	−	0.175563i	0.644276	+	0.764793i	$0.277159\pi$
$462$		0			0
$463$		−	23.3031i		−	1.08299i	−0.840705	−	0.541494i	$-0.817859\pi$
$463$		−	23.3031i		−	1.08299i	0.840705	−	0.541494i	$-0.182141\pi$
$464$		0			0
$465$	−6.37182	+	11.0363i	−0.295486	+	0.511797i
$466$		0			0
$467$	−22.6297			−1.04718			−0.523589	−	0.851971i	$-0.675407\pi$
$467$	−22.6297			−1.04718			−0.523589	+	0.851971i	$0.675407\pi$
$468$		0			0
$469$	23.0405			1.06391
$470$		0			0
$471$	11.7085	−	20.2797i	0.539500	−	0.934441i
$472$		0			0
$473$			6.08012i			0.279564i
$474$		0			0
$475$	−1.96410	+	1.13397i	−0.0901192	+	0.0520303i
$476$		0			0
$477$	5.41465	+	9.37844i	0.247920	+	0.429409i
$478$		0			0
$479$	17.8789	+	10.3224i	0.816910	+	0.471643i	0.849350	−	0.527831i	$-0.176994\pi$
$479$	17.8789	+	10.3224i	0.816910	+	0.471643i	−0.0324399	+	0.999474i	$0.510328\pi$
$480$		0			0
$481$	0.172207	+	31.3825i	0.00785198	+	1.43092i
$482$		0			0
$483$	28.3075	+	16.3433i	1.28804	+	0.743648i
$484$		0			0
$485$	−6.08408	−	10.5379i	−0.276264	−	0.478503i
$486$		0			0
$487$	2.62929	−	1.51802i	0.119145	−	0.0687882i	−0.439243	−	0.898368i	$-0.644753\pi$
$487$	2.62929	−	1.51802i	0.119145	−	0.0687882i	0.558388	+	0.829580i	$0.311420\pi$
$488$		0			0
$489$			15.8155i			0.715203i
$490$		0			0
$491$	−5.33401	+	9.23877i	−0.240720	+	0.416940i	−0.960920	−	0.276827i	$-0.910717\pi$
$491$	−5.33401	+	9.23877i	−0.240720	+	0.416940i	0.720199	+	0.693767i	$0.244050\pi$
$492$		0			0
$493$	−0.0279884			−0.00126053
$494$		0			0
$495$	13.1039			0.588975
$496$		0			0
$497$	19.4362	−	33.6646i	0.871835	−	1.51006i
$498$		0			0
$499$			33.9143i			1.51821i	0.650966	+	0.759107i	$0.274364\pi$
$499$			33.9143i			1.51821i	−0.650966	+	0.759107i	$0.725636\pi$
$500$		0			0
$501$	21.1872	−	12.2324i	0.946572	−	0.546504i
$502$		0			0
$503$	−6.31380	−	10.9358i	−0.281518	−	0.487604i	0.690241	−	0.723580i	$-0.257505\pi$
$503$	−6.31380	−	10.9358i	−0.281518	−	0.487604i	−0.971759	+	0.235976i	$0.924171\pi$
$504$		0			0
$505$	−3.51122	−	2.02721i	−0.156247	−	0.0902095i
$506$		0			0
$507$	15.4468	+	26.0893i	0.686019	+	1.15866i
$508$		0			0
$509$	−20.9168	−	12.0763i	−0.927120	−	0.535273i	−0.0412201	−	0.999150i	$-0.513124\pi$
$509$	−20.9168	−	12.0763i	−0.927120	−	0.535273i	−0.885899	+	0.463877i	$0.846458\pi$
$510$		0			0
$511$	8.46601	+	14.6636i	0.374514	+	0.648678i
$512$		0			0
$513$	2.56810	−	1.48269i	0.113384	−	0.0654625i
$514$		0			0
$515$		−	17.9035i		−	0.788921i
$516$		0			0
$517$	6.94402	−	12.0274i	0.305398	−	0.528964i
$518$		0			0
$519$	−10.3982			−0.456431
$520$		0			0
$521$	−24.7521			−1.08441			−0.542205	−	0.840246i	$-0.682410\pi$
$521$	−24.7521			−1.08441			−0.542205	+	0.840246i	$0.682410\pi$
$522$		0			0
$523$	18.5163	−	32.0712i	0.809662	−	1.40238i	−0.103436	−	0.994636i	$-0.532984\pi$
$523$	18.5163	−	32.0712i	0.809662	−	1.40238i	0.913098	−	0.407739i	$-0.133683\pi$
$524$		0			0
$525$		−	8.39654i		−	0.366455i
$526$		0			0
$527$	5.35600	−	3.09229i	0.233311	−	0.134702i
$528$		0			0
$529$	3.92277	+	6.79444i	0.170555	+	0.295410i
$530$		0			0
$531$	−0.362145	−	0.209084i	−0.0157157	−	0.00907348i
$532$		0			0
$533$	0.0738376	+	13.4559i	0.00319826	+	0.582840i
$534$		0			0
$535$	−7.90842	−	4.56593i	−0.341911	−	0.197402i
$536$		0			0
$537$	21.7264	+	37.6312i	0.937562	+	1.62391i
$538$		0			0
$539$	27.7332	−	16.0118i	1.19456	−	0.689677i
$540$		0			0
$541$		−	8.38144i		−	0.360346i	−0.983635	−	0.180173i	$-0.942334\pi$
$541$		−	8.38144i		−	0.360346i	0.983635	−	0.180173i	$-0.0576658\pi$
$542$		0			0
$543$	−21.0952	+	36.5379i	−0.905281	+	1.56799i
$544$		0			0
$545$	7.37605			0.315955
$546$		0			0
$547$	22.7842			0.974181			0.487091	−	0.873351i	$-0.338058\pi$
$547$	22.7842			0.974181			0.487091	+	0.873351i	$0.338058\pi$
$548$		0			0
$549$	−4.09843	+	7.09870i	−0.174917	+	0.302965i
$550$		0			0
$551$		−	0.0560816i		−	0.00238915i
$552$		0			0
$553$	−37.3601	+	21.5699i	−1.58871	+	0.917245i
$554$		0			0
$555$	10.1500	+	17.5803i	0.430844	+	0.746244i
$556$		0			0
$557$	24.3810	+	14.0764i	1.03306	+	0.596435i	0.917858	−	0.396908i	$-0.129917\pi$
$557$	24.3810	+	14.0764i	1.03306	+	0.596435i	0.115197	+	0.993343i	$0.463250\pi$
$558$		0			0
$559$	−2.02106	+	3.54536i	−0.0854816	+	0.149953i
$560$		0			0
$561$	−12.2805	−	7.09017i	−0.518484	−	0.299347i
$562$		0			0
$563$	9.06514	+	15.7013i	0.382050	+	0.661731i	0.991355	−	0.131206i	$-0.0418848\pi$
$563$	9.06514	+	15.7013i	0.382050	+	0.661731i	−0.609305	+	0.792936i	$0.708551\pi$
$564$		0			0
$565$	6.12789	−	3.53794i	0.257802	−	0.148842i
$566$		0			0
$567$			37.3253i			1.56752i
$568$		0			0
$569$	20.2992	−	35.1593i	0.850988	−	1.47395i	−0.0293292	−	0.999570i	$-0.509337\pi$
$569$	20.2992	−	35.1593i	0.850988	−	1.47395i	0.880317	−	0.474385i	$-0.157330\pi$
$570$		0			0
$571$	24.7159			1.03433			0.517164	−	0.855886i	$-0.326988\pi$
$571$	24.7159			1.03433			0.517164	+	0.855886i	$0.326988\pi$
$572$		0			0
$573$	63.7551			2.66341
$574$		0			0
$575$	−1.94644	+	3.37133i	−0.0811720	+	0.140594i
$576$		0			0
$577$		−	23.0691i		−	0.960379i	−0.877165	−	0.480189i	$-0.840568\pi$
$577$		−	23.0691i		−	0.960379i	0.877165	−	0.480189i	$-0.159432\pi$
$578$		0			0
$579$	−43.9654	+	25.3834i	−1.82714	+	1.05490i
$580$		0			0
$581$	21.8327	+	37.8153i	0.905771	+	1.56884i
$582$		0			0
$583$	−20.6525	−	11.9237i	−0.855341	−	0.493831i
$584$		0			0
$585$	7.64096	+	4.35578i	0.315915	+	0.180089i
$586$		0			0
$587$	17.6256	+	10.1762i	0.727487	+	0.420015i	0.817502	−	0.575926i	$-0.195358\pi$
$587$	17.6256	+	10.1762i	0.727487	+	0.420015i	−0.0900152	+	0.995940i	$0.528692\pi$
$588$		0			0
$589$	6.19615	+	10.7321i	0.255308	+	0.442206i
$590$		0			0
$591$	−3.42701	+	1.97859i	−0.140968	+	0.0813881i
$592$		0			0
$593$			10.3834i			0.426395i	0.977009	+	0.213198i	$0.0683878\pi$
$593$			10.3834i			0.426395i	−0.977009	+	0.213198i	$0.931612\pi$
$594$		0			0
$595$	−2.03745	+	3.52897i	−0.0835273	+	0.144674i
$596$		0			0
$597$	−59.0652			−2.41738
$598$		0			0
$599$	31.5965			1.29100			0.645499	−	0.763761i	$-0.276649\pi$
$599$	31.5965			1.29100			0.645499	+	0.763761i	$0.276649\pi$
$600$		0			0
$601$	21.9423	−	38.0051i	0.895044	−	1.55026i	0.0612928	−	0.998120i	$-0.480478\pi$
$601$	21.9423	−	38.0051i	0.895044	−	1.55026i	0.833751	−	0.552141i	$-0.186189\pi$
$602$		0			0
$603$			15.6115i			0.635750i
$604$		0			0
$605$	−15.4641	+	8.92820i	−0.628705	+	0.362983i
$606$		0			0
$607$	1.08770	+	1.88395i	0.0441484	+	0.0764673i	0.887255	−	0.461279i	$-0.152609\pi$
$607$	1.08770	+	1.88395i	0.0441484	+	0.0764673i	−0.843107	+	0.537746i	$0.819276\pi$
$608$		0			0
$609$	0.179812	+	0.103814i	0.00728634	+	0.00420677i
$610$		0			0
$611$	8.04707	−	4.70504i	0.325550	−	0.190346i
$612$		0			0
$613$	−12.7843	−	7.38100i	−0.516352	−	0.298116i	0.219089	−	0.975705i	$-0.429691\pi$
$613$	−12.7843	−	7.38100i	−0.516352	−	0.298116i	−0.735441	+	0.677589i	$0.763025\pi$
$614$		0			0
$615$	4.35203	+	7.53794i	0.175491	+	0.303959i
$616$		0			0
$617$	17.5779	−	10.1486i	0.707659	−	0.408567i	−0.102535	−	0.994729i	$-0.532695\pi$
$617$	17.5779	−	10.1486i	0.707659	−	0.408567i	0.810194	+	0.586162i	$0.199362\pi$
$618$		0			0
$619$		−	9.94207i		−	0.399605i	−0.979836	−	0.199803i	$-0.935970\pi$
$619$		−	9.94207i		−	0.399605i	0.979836	−	0.199803i	$-0.0640301\pi$
$620$		0			0
$621$	2.54500	−	4.40807i	0.102127	−	0.176890i
$622$		0			0
$623$	−58.1577			−2.33004
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	14.2069	−	24.6070i	0.567368	−	0.982711i
$628$		0			0
$629$		−	9.85174i		−	0.392815i
$630$		0			0
$631$	−0.843006	+	0.486710i	−0.0335596	+	0.0193756i	−0.516686	−	0.856175i	$-0.672835\pi$
$631$	−0.843006	+	0.486710i	−0.0335596	+	0.0193756i	0.483126	+	0.875551i	$0.339501\pi$
$632$		0			0
$633$	0.391243	+	0.677652i	0.0155505	+	0.0269342i
$634$		0			0
$635$	9.90396	+	5.71806i	0.393027	+	0.226914i
$636$		0			0
$637$	21.4938	−	0.117945i	0.851617	−	0.00467314i
$638$		0			0
$639$	22.8100	+	13.1694i	0.902350	+	0.520972i
$640$		0			0
$641$	−6.31047	−	10.9301i	−0.249249	−	0.431711i	0.714069	−	0.700075i	$-0.246850\pi$
$641$	−6.31047	−	10.9301i	−0.249249	−	0.431711i	−0.963318	+	0.268364i	$0.913517\pi$
$642$		0			0
$643$	8.62599	−	4.98022i	0.340176	−	0.196401i	−0.320174	−	0.947359i	$-0.603741\pi$
$643$	8.62599	−	4.98022i	0.340176	−	0.196401i	0.660350	+	0.750958i	$0.270408\pi$
$644$		0			0
$645$			2.63977i			0.103941i
$646$		0			0
$647$	18.1381	−	31.4162i	0.713084	−	1.23510i	−0.250610	−	0.968088i	$-0.580631\pi$
$647$	18.1381	−	31.4162i	0.713084	−	1.23510i	0.963694	−	0.267009i	$-0.0860354\pi$
$648$		0			0
$649$	0.920861			0.0361470
$650$		0			0
$651$	−45.8796			−1.79816
$652$		0			0
$653$	−6.87769	+	11.9125i	−0.269145	+	0.466172i	−0.968641	−	0.248464i	$-0.920074\pi$
$653$	−6.87769	+	11.9125i	−0.269145	+	0.466172i	0.699497	+	0.714636i	$0.253408\pi$
$654$		0			0
$655$			10.5680i			0.412925i
$656$		0			0
$657$	−9.93555	+	5.73629i	−0.387623	+	0.223794i
$658$		0			0
$659$	−1.29092	−	2.23593i	−0.0502869	−	0.0870995i	0.839786	−	0.542917i	$-0.182680\pi$
$659$	−1.29092	−	2.23593i	−0.0502869	−	0.0870995i	−0.890073	+	0.455818i	$0.849347\pi$
$660$		0			0
$661$	−21.5437	−	12.4382i	−0.837951	−	0.483791i	0.0186163	−	0.999827i	$-0.494074\pi$
$661$	−21.5437	−	12.4382i	−0.837951	−	0.483791i	−0.856567	+	0.516036i	$0.827407\pi$
$662$		0			0
$663$	−4.80406	−	8.21643i	−0.186574	−	0.319100i
$664$		0			0
$665$	−7.07115	−	4.08253i	−0.274207	−	0.158314i
$666$		0			0
$667$	−0.0481312	−	0.0833657i	−0.00186365	−	0.00322793i
$668$		0			0
$669$	24.8368	−	14.3395i	0.960246	−	0.554398i
$670$		0			0
$671$		−	18.0506i		−	0.696834i
$672$		0			0
$673$	21.6611	−	37.5181i	0.834974	−	1.44622i	−0.0590774	−	0.998253i	$-0.518816\pi$
$673$	21.6611	−	37.5181i	0.834974	−	1.44622i	0.894052	−	0.447964i	$-0.147851\pi$
$674$		0			0
$675$	−1.30752			−0.0503264
$676$		0			0
$677$	−41.3625			−1.58969			−0.794845	−	0.606813i	$-0.792448\pi$
$677$	−41.3625			−1.58969			−0.794845	+	0.606813i	$0.792448\pi$
$678$		0			0
$679$	21.9039	−	37.9386i	0.840594	−	1.45595i
$680$		0			0
$681$			17.8003i			0.682110i
$682$		0			0
$683$	−2.27495	+	1.31344i	−0.0870484	+	0.0502574i	−0.542892	−	0.839802i	$-0.682671\pi$
$683$	−2.27495	+	1.31344i	−0.0870484	+	0.0502574i	0.455844	+	0.890060i	$0.349338\pi$
$684$		0			0
$685$	1.89336	+	3.27940i	0.0723416	+	0.125299i
$686$		0			0
$687$	−29.0865	−	16.7931i	−1.10972	−	0.640696i
$688$		0			0
$689$	−8.07914	−	13.8178i	−0.307791	−	0.526417i
$690$		0			0
$691$	13.2288	+	7.63765i	0.503247	+	0.290550i	0.730053	−	0.683390i	$-0.239495\pi$
$691$	13.2288	+	7.63765i	0.503247	+	0.290550i	−0.226806	+	0.973940i	$0.572828\pi$
$692$		0			0
$693$	23.5882	+	40.8560i	0.896043	+	1.55199i
$694$		0			0
$695$	−1.74406	+	1.00693i	−0.0661558	+	0.0381951i
$696$		0			0
$697$		−	4.22414i		−	0.160001i
$698$		0			0
$699$	−11.0737	+	19.1802i	−0.418846	+	0.725463i
$700$		0			0
$701$	48.1947			1.82029			0.910144	−	0.414292i	$-0.135971\pi$
$701$	48.1947			1.82029			0.910144	+	0.414292i	$0.135971\pi$
$702$		0			0
$703$	19.7404			0.744522
$704$		0			0
$705$	3.01484	−	5.22186i	0.113546	−	0.196667i
$706$		0			0
$707$		−	14.5967i		−	0.548964i
$708$		0			0
$709$	−33.6624	+	19.4350i	−1.26422	+	0.729896i	−0.973887	−	0.227031i	$-0.927098\pi$
$709$	−33.6624	+	19.4350i	−1.26422	+	0.729896i	−0.290329	+	0.956927i	$0.593765\pi$
$710$		0			0
$711$	−14.6150	−	25.3140i	−0.548107	−	0.949349i
$712$		0			0
$713$	18.4213	+	10.6355i	0.689882	+	0.398304i
$714$		0			0
$715$	−19.3681	+	0.106280i	−0.724325	+	0.00397464i
$716$		0			0
$717$	−40.2227	−	23.2226i	−1.50214	−	0.867263i
$718$		0			0
$719$	−3.30830	−	5.73015i	−0.123379	−	0.213698i	0.797719	−	0.603029i	$-0.206040\pi$
$719$	−3.30830	−	5.73015i	−0.123379	−	0.213698i	−0.921098	+	0.389331i	$0.872706\pi$
$720$		0			0
$721$	55.8205	−	32.2280i	2.07887	−	1.20023i
$722$		0			0
$723$		−	54.2629i		−	2.01806i
$724$		0			0
$725$	−0.0123639	+	0.0214150i	−0.000459185	+	0.000795332i
$726$		0			0
$727$	−18.3735			−0.681435			−0.340717	−	0.940166i	$-0.610670\pi$
$727$	−18.3735			−0.681435			−0.340717	+	0.940166i	$0.610670\pi$
$728$		0			0
$729$	−16.1420			−0.597853
$730$		0			0
$731$	0.640548	−	1.10946i	0.0236915	−	0.0410349i
$732$		0			0
$733$		−	0.791131i		−	0.0292211i	−0.999893	−	0.0146105i	$-0.995349\pi$
$733$		−	0.791131i		−	0.0292211i	0.999893	−	0.0146105i	$-0.00465084\pi$
$734$		0			0
$735$	12.0408	−	6.95174i	0.444130	−	0.256419i
$736$		0			0
$737$	−17.1893	−	29.7727i	−0.633175	−	1.09669i
$738$		0			0
$739$	27.0073	+	15.5926i	0.993478	+	0.573585i	0.906312	−	0.422609i	$-0.138886\pi$
$739$	27.0073	+	15.5926i	0.993478	+	0.573585i	0.0871658	+	0.996194i	$0.472219\pi$
$740$		0			0
$741$	16.4636	−	9.62612i	0.604806	−	0.353624i
$742$		0			0
$743$	−4.81773	−	2.78152i	−0.176745	−	0.102044i	0.409017	−	0.912527i	$-0.365872\pi$
$743$	−4.81773	−	2.78152i	−0.176745	−	0.102044i	−0.585763	+	0.810483i	$0.699205\pi$
$744$		0			0
$745$	2.75890	+	4.77855i	0.101078	+	0.175073i
$746$		0			0
$747$	−25.6224	+	14.7931i	−0.937474	+	0.541251i
$748$		0			0
$749$		−	32.8765i		−	1.20128i
$750$		0			0
$751$	17.6048	−	30.4925i	0.642410	−	1.11269i	−0.342483	−	0.939524i	$-0.611268\pi$
$751$	17.6048	−	30.4925i	0.642410	−	1.11269i	0.984893	−	0.173163i	$-0.0553987\pi$
$752$		0			0
$753$	−27.6142			−1.00632
$754$		0			0
$755$	−4.88961			−0.177951
$756$		0			0
$757$	−25.0223	+	43.3399i	−0.909451	+	1.57522i	−0.0946237	+	0.995513i	$0.530165\pi$
$757$	−25.0223	+	43.3399i	−0.909451	+	1.57522i	−0.814828	+	0.579703i	$0.803169\pi$
$758$		0			0
$759$		−	48.7715i		−	1.77029i
$760$		0			0
$761$	38.8161	−	22.4105i	1.40708	−	0.812379i	0.411975	−	0.911195i	$-0.364839\pi$
$761$	38.8161	−	22.4105i	1.40708	−	0.812379i	0.995106	+	0.0988165i	$0.0315057\pi$
$762$		0			0
$763$	13.2776	+	22.9975i	0.480682	+	0.832566i
$764$		0			0
$765$	−2.39111	−	1.38051i	−0.0864508	−	0.0499124i
$766$		0			0
$767$	0.536961	+	0.306098i	0.0193885	+	0.0110526i
$768$		0			0
$769$	−34.0897	−	19.6817i	−1.22930	−	0.709739i	−0.262420	−	0.964954i	$-0.584521\pi$
$769$	−34.0897	−	19.6817i	−1.22930	−	0.709739i	−0.966884	+	0.255215i	$0.917854\pi$
$770$		0			0
$771$	6.47201	+	11.2099i	0.233084	+	0.403713i
$772$		0			0
$773$	−42.2452	+	24.3902i	−1.51945	+	0.877256i	−0.519715	+	0.854340i	$0.673962\pi$
$773$	−42.2452	+	24.3902i	−1.51945	+	0.877256i	−0.999737	+	0.0229167i	$0.992705\pi$
$774$		0			0
$775$		−	5.46410i		−	0.196276i
$776$		0			0
$777$	−36.5420	+	63.2926i	−1.31094	+	2.27061i
$778$		0			0
$779$	8.46410			0.303258
$780$		0			0
$781$	−58.0013			−2.07545
$782$		0			0
$783$	0.0161661	−	0.0280005i	0.000577728	−	0.00100066i
$784$		0			0
$785$			10.0405i			0.358363i
$786$		0			0
$787$	−34.5204	+	19.9304i	−1.23052	+	0.710442i	−0.967139	−	0.254250i	$-0.918171\pi$
$787$	−34.5204	+	19.9304i	−1.23052	+	0.710442i	−0.263382	+	0.964692i	$0.584838\pi$
$788$		0			0
$789$	−7.99922	−	13.8551i	−0.284780	−	0.493253i
$790$		0			0
$791$	22.0616	+	12.7373i	0.784420	+	0.452885i
$792$		0			0
$793$	6.00008	−	10.5254i	0.213069	−	0.373768i
$794$		0			0
$795$	−8.96658	−	5.17686i	−0.318012	−	0.183604i
$796$		0			0
$797$	13.1059	+	22.7001i	0.464235	+	0.804079i	0.999167	−	0.0408167i	$-0.0129960\pi$
$797$	13.1059	+	22.7001i	0.464235	+	0.804079i	−0.534932	+	0.844895i	$0.679663\pi$
$798$		0			0
$799$	−2.53420	+	1.46312i	−0.0896537	+	0.0517616i
$800$		0			0
$801$		−	39.4057i		−	1.39233i
$802$		0			0
$803$	12.6321	−	21.8794i	0.445775	−	0.772106i
$804$		0			0
$805$	−14.0151			−0.493968
$806$		0			0
$807$	3.31643			0.116744
$808$		0			0
$809$	−11.1068	+	19.2376i	−0.390495	+	0.676357i	−0.992515	−	0.122124i	$-0.961029\pi$
$809$	−11.1068	+	19.2376i	−0.390495	+	0.676357i	0.602020	+	0.798481i	$0.294363\pi$
$810$		0			0
$811$			19.0950i			0.670515i	0.942127	+	0.335257i	$0.108823\pi$
$811$			19.0950i			0.670515i	−0.942127	+	0.335257i	$0.891177\pi$
$812$		0			0
$813$	−20.1362	+	11.6256i	−0.706207	+	0.407729i
$814$		0			0
$815$	−3.39062	−	5.87273i	−0.118768	−	0.205713i
$816$		0			0
$817$	2.22308	+	1.28349i	0.0777757	+	0.0449038i
$818$		0			0
$819$	0.173754	+	31.6643i	0.00607145	+	1.10644i
$820$		0			0
$821$	−29.5820	−	17.0792i	−1.03242	−	0.596068i	−0.114743	−	0.993395i	$-0.536604\pi$
$821$	−29.5820	−	17.0792i	−1.03242	−	0.596068i	−0.917677	+	0.397327i	$0.869938\pi$
$822$		0			0
$823$	−2.03970	−	3.53286i	−0.0710995	−	0.123148i	0.828284	−	0.560309i	$-0.189317\pi$
$823$	−2.03970	−	3.53286i	−0.0710995	−	0.123148i	−0.899383	+	0.437161i	$0.855984\pi$
$824$		0			0
$825$	−10.8499	+	6.26420i	−0.377745	+	0.218091i
$826$		0			0
$827$			54.8780i			1.90830i	0.299337	+	0.954148i	$0.403235\pi$
$827$			54.8780i			1.90830i	−0.299337	+	0.954148i	$0.596765\pi$
$828$		0			0
$829$	4.07475	−	7.05768i	0.141522	−	0.245123i	−0.786548	−	0.617529i	$-0.788134\pi$
$829$	4.07475	−	7.05768i	0.141522	−	0.245123i	0.928070	+	0.372406i	$0.121467\pi$
$830$		0			0
$831$	−40.8697			−1.41775
$832$		0			0
$833$	−6.74745			−0.233785
$834$		0			0
$835$	−5.24490	+	9.08444i	−0.181507	+	0.314380i
$836$		0			0
$837$			7.14441i			0.246947i
$838$		0			0
$839$	18.9543	−	10.9433i	0.654374	−	0.377803i	−0.135756	−	0.990742i	$-0.543346\pi$
$839$	18.9543	−	10.9433i	0.654374	−	0.377803i	0.790130	+	0.612939i	$0.210013\pi$
$840$		0			0
$841$	14.4997	+	25.1142i	0.499989	+	0.866007i
$842$		0			0
$843$	21.6827	+	12.5185i	0.746792	+	0.431160i
$844$		0			0
$845$	−11.3290	−	6.37605i	−0.389729	−	0.219343i
$846$		0			0
$847$	−55.6738	−	32.1433i	−1.91297	−	1.10446i
$848$		0			0
$849$	1.53740	+	2.66285i	0.0527633	+	0.0913888i
$850$		0			0
$851$	29.3442	−	16.9419i	1.00591	−	0.580761i
$852$		0			0
$853$		−	19.2240i		−	0.658217i	−0.944292	−	0.329108i	$-0.893252\pi$
$853$		−	19.2240i		−	0.658217i	0.944292	−	0.329108i	$-0.106748\pi$
$854$		0			0
$855$	2.76619	−	4.79118i	0.0946016	−	0.163855i
$856$		0			0
$857$	27.8197			0.950302			0.475151	−	0.879904i	$-0.342393\pi$
$857$	27.8197			0.950302			0.475151	+	0.879904i	$0.342393\pi$
$858$		0			0
$859$	−45.7355			−1.56048			−0.780238	−	0.625482i	$-0.784902\pi$
$859$	−45.7355			−1.56048			−0.780238	+	0.625482i	$0.784902\pi$
$860$		0			0
$861$	−15.6682	+	27.1381i	−0.533970	+	0.924862i
$862$		0			0
$863$			54.8186i			1.86605i	0.359814	+	0.933024i	$0.382840\pi$
$863$			54.8186i			1.86605i	−0.359814	+	0.933024i	$0.617160\pi$
$864$		0			0
$865$	3.86113	−	2.22923i	0.131283	−	0.0757960i
$866$		0			0
$867$	−18.3302	−	31.7488i	−0.622526	−	1.07825i
$868$		0			0
$869$	55.7447	+	32.1842i	1.89101	+	1.09177i
$870$		0			0
$871$	−0.126618	−	23.0745i	−0.00429030	−	0.781849i
$872$		0			0
$873$	25.7060	+	14.8413i	0.870015	+	0.502304i
$874$		0			0
$875$	1.80010	+	3.11786i	0.0608544	+	0.105403i
$876$		0			0
$877$	23.7113	−	13.6897i	0.800673	−	0.462269i	−0.0430336	−	0.999074i	$-0.513702\pi$
$877$	23.7113	−	13.6897i	0.800673	−	0.462269i	0.843706	+	0.536805i	$0.180369\pi$
$878$		0			0
$879$		−	43.7125i		−	1.47439i
$880$		0			0
$881$	−17.2213	+	29.8282i	−0.580200	+	1.00494i	0.415255	+	0.909705i	$0.363692\pi$
$881$	−17.2213	+	29.8282i	−0.580200	+	1.00494i	−0.995455	+	0.0952310i	$0.969641\pi$
$882$		0			0
$883$	−17.3592			−0.584183			−0.292092	−	0.956390i	$-0.594351\pi$
$883$	−17.3592			−0.584183			−0.292092	+	0.956390i	$0.594351\pi$
$884$		0			0
$885$	0.399804			0.0134393
$886$		0			0
$887$	−15.5714	+	26.9704i	−0.522835	+	0.905577i	0.476812	+	0.879005i	$0.341792\pi$
$887$	−15.5714	+	26.9704i	−0.522835	+	0.905577i	−0.999647	+	0.0265716i	$0.991541\pi$
$888$		0			0
$889$			41.1722i			1.38087i
$890$		0			0
$891$	48.2313	−	27.8464i	1.61581	−	0.932888i
$892$		0			0
$893$	−2.93173	−	5.07790i	−0.0981065	−	0.169925i
$894$		0			0
$895$	−16.1352	−	9.31564i	−0.539339	−	0.311388i
$896$		0			0
$897$	16.2118	−	28.4390i	0.541298	−	0.949550i
$898$		0			0
$899$	0.117014	+	0.0675578i	0.00390262	+	0.00225318i
$900$		0			0
$901$	2.51236	+	4.35154i	0.0836990	+	0.144971i
$902$		0			0
$903$	−8.23042	+	4.75184i	−0.273891	+	0.158131i
$904$		0			0
$905$		−	18.0900i		−	0.601332i
$906$		0			0
$907$	−8.80284	+	15.2470i	−0.292294	+	0.506267i	−0.974352	−	0.225031i	$-0.927752\pi$
$907$	−8.80284	+	15.2470i	−0.292294	+	0.506267i	0.682058	+	0.731298i	$0.261085\pi$
$908$		0			0
$909$	9.89022			0.328038
$910$		0			0
$911$	−50.0232			−1.65734			−0.828671	−	0.559737i	$-0.810902\pi$
$911$	−50.0232			−1.65734			−0.828671	+	0.559737i	$0.810902\pi$
$912$		0			0
$913$	32.5763	−	56.4238i	1.07812	−	1.86735i
$914$		0			0
$915$		−	7.83690i		−	0.259080i
$916$		0			0
$917$	−32.9495	+	19.0234i	−1.08809	+	0.628207i
$918$		0			0
$919$	−3.80778	−	6.59527i	−0.125607	−	0.217558i	0.796363	−	0.604819i	$-0.206755\pi$
$919$	−3.80778	−	6.59527i	−0.125607	−	0.217558i	−0.921970	+	0.387261i	$0.873421\pi$
$920$		0			0
$921$	−28.8915	−	16.6805i	−0.952008	−	0.549642i
$922$		0			0
$923$	−33.8209	−	19.2799i	−1.11323	−	0.634604i
$924$		0			0
$925$	−7.53794	−	4.35203i	−0.247846	−	0.143094i
$926$		0			0
$927$	21.8366	+	37.8222i	0.717209	+	1.24224i
$928$		0			0
$929$	12.2317	−	7.06196i	0.401308	−	0.231695i	−0.285740	−	0.958307i	$-0.592239\pi$
$929$	12.2317	−	7.06196i	0.401308	−	0.231695i	0.687048	+	0.726612i	$0.258906\pi$
$930$		0			0
$931$		−	13.5202i		−	0.443106i
$932$		0			0
$933$	3.21969	−	5.57666i	0.105408	−	0.182572i
$934$		0			0
$935$	6.08012			0.198841
$936$		0			0
$937$	−23.9317			−0.781815			−0.390908	−	0.920430i	$-0.627839\pi$
$937$	−23.9317			−0.781815			−0.390908	+	0.920430i	$0.627839\pi$
$938$		0			0
$939$	−19.1078	+	33.0958i	−0.623561	+	1.08004i
$940$		0			0
$941$			25.3591i			0.826683i	0.910576	+	0.413342i	$0.135638\pi$
$941$			25.3591i			0.826683i	−0.910576	+	0.413342i	$0.864362\pi$
$942$		0			0
$943$	12.5820	−	7.26420i	0.409725	−	0.236555i
$944$		0			0
$945$	−2.35366	−	4.07666i	−0.0765646	−	0.132614i
$946$		0			0
$947$	35.8727	+	20.7111i	1.16571	+	0.673021i	0.952665	−	0.304022i	$-0.0983296\pi$
$947$	35.8727	+	20.7111i	1.16571	+	0.673021i	0.213042	+	0.977043i	$0.431663\pi$
$948$		0			0
$949$	14.6386	−	8.55906i	0.475190	−	0.277839i
$950$		0			0
$951$	−3.60682	−	2.08240i	−0.116959	−	0.0675264i
$952$		0			0
$953$	12.1513	+	21.0466i	0.393619	+	0.681767i	0.992924	−	0.118753i	$-0.0378897\pi$
$953$	12.1513	+	21.0466i	0.393619	+	0.681767i	−0.599305	+	0.800521i	$0.704556\pi$
$954$		0			0
$955$	−23.6740	+	13.6682i	−0.766071	+	0.442291i
$956$		0			0
$957$		−	0.309801i		−	0.0100144i
$958$		0			0
$959$	−6.81647	+	11.8065i	−0.220115	+	0.381251i
$960$		0			0
$961$	1.14359			0.0368901
$962$		0			0
$963$	22.2760			0.717834
$964$		0			0
$965$	10.8837	−	18.8511i	0.350358	−	0.606839i
$966$		0			0
$967$			23.6784i			0.761445i	0.924689	+	0.380722i	$0.124325\pi$
$967$			23.6784i			0.761445i	−0.924689	+	0.380722i	$0.875675\pi$
$968$		0			0
$969$	−5.18477	+	2.99343i	−0.166559	+	0.0961627i
$970$		0			0
$971$	−8.48609	−	14.6983i	−0.272332	−	0.471692i	0.697127	−	0.716948i	$-0.254461\pi$
$971$	−8.48609	−	14.6983i	−0.272332	−	0.471692i	−0.969458	+	0.245256i	$0.921128\pi$
$972$		0			0
$973$	−6.27895	−	3.62515i	−0.201294	−	0.116217i
$974$		0			0
$975$	−8.40891	+	0.0461428i	−0.269301	+	0.00147775i
$976$		0			0
$977$	21.6501	+	12.4997i	0.692649	+	0.399901i	0.804604	−	0.593812i	$-0.202378\pi$
$977$	21.6501	+	12.4997i	0.692649	+	0.399901i	−0.111955	+	0.993713i	$0.535711\pi$
$978$		0			0
$979$	43.3883	+	75.1507i	1.38669	+	2.40183i
$980$		0			0
$981$	−15.5824	+	8.99648i	−0.497506	+	0.287235i
$982$		0			0
$983$			27.3418i			0.872068i	0.899930	+	0.436034i	$0.143617\pi$
$983$			27.3418i			0.872068i	−0.899930	+	0.436034i	$0.856383\pi$
$984$		0			0
$985$	0.848360	−	1.46940i	0.0270310	−	0.0468191i
$986$		0			0
$987$	21.7080			0.690975
$988$		0			0
$989$	4.40617			0.140108
$990$		0			0
$991$	8.03802	−	13.9223i	0.255336	−	0.442255i	−0.709651	−	0.704554i	$-0.751147\pi$
$991$	8.03802	−	13.9223i	0.255336	−	0.442255i	0.964987	+	0.262299i	$0.0844805\pi$
$992$		0			0
$993$		−	16.8491i		−	0.534690i
$994$		0			0
$995$	21.9325	−	12.6627i	0.695307	−	0.401436i
$996$		0			0
$997$	17.2806	+	29.9309i	0.547282	+	0.947920i	0.998459	+	0.0554858i	$0.0176708\pi$
$997$	17.2806	+	29.9309i	0.547282	+	0.947920i	−0.451178	+	0.892434i	$0.648996\pi$
$998$		0			0
$999$	9.85600	+	5.69036i	0.311830	+	0.180035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.b.641.4		8
4.3	odd	2		65.2.m.a.56.3	yes	8
12.11	even	2		585.2.bu.c.316.2		8
13.10	even	6	inner	1040.2.da.b.881.4		8
20.3	even	4		325.2.m.c.199.3		8
20.7	even	4		325.2.m.b.199.2		8
20.19	odd	2		325.2.n.d.251.2		8
52.3	odd	6		845.2.m.g.361.2		8
52.7	even	12		845.2.a.m.1.3		4
52.11	even	12		845.2.e.m.146.2		8
52.15	even	12		845.2.e.n.146.3		8
52.19	even	12		845.2.a.l.1.2		4
52.23	odd	6		65.2.m.a.36.3	✓	8
52.31	even	4		845.2.e.n.191.3		8
52.35	odd	6		845.2.c.g.506.3		8
52.43	odd	6		845.2.c.g.506.6		8
52.47	even	4		845.2.e.m.191.2		8
52.51	odd	2		845.2.m.g.316.2		8
156.23	even	6		585.2.bu.c.361.2		8
156.59	odd	12		7605.2.a.cf.1.2		4
156.71	odd	12		7605.2.a.cj.1.3		4
260.19	even	12		4225.2.a.bl.1.3		4
260.23	even	12		325.2.m.b.49.2		8
260.59	even	12		4225.2.a.bi.1.2		4
260.127	even	12		325.2.m.c.49.3		8
260.179	odd	6		325.2.n.d.101.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	52.23	odd	6
65.2.m.a.56.3	yes	8	4.3	odd	2
325.2.m.b.49.2		8	260.23	even	12
325.2.m.b.199.2		8	20.7	even	4
325.2.m.c.49.3		8	260.127	even	12
325.2.m.c.199.3		8	20.3	even	4
325.2.n.d.101.2		8	260.179	odd	6
325.2.n.d.251.2		8	20.19	odd	2
585.2.bu.c.316.2		8	12.11	even	2
585.2.bu.c.361.2		8	156.23	even	6
845.2.a.l.1.2		4	52.19	even	12
845.2.a.m.1.3		4	52.7	even	12
845.2.c.g.506.3		8	52.35	odd	6
845.2.c.g.506.6		8	52.43	odd	6
845.2.e.m.146.2		8	52.11	even	12
845.2.e.m.191.2		8	52.47	even	4
845.2.e.n.146.3		8	52.15	even	12
845.2.e.n.191.3		8	52.31	even	4
845.2.m.g.316.2		8	52.51	odd	2
845.2.m.g.361.2		8	52.3	odd	6
1040.2.da.b.641.4		8	1.1	even	1	trivial
1040.2.da.b.881.4		8	13.10	even	6	inner
4225.2.a.bi.1.2		4	260.59	even	12
4225.2.a.bl.1.3		4	260.19	even	12
7605.2.a.cf.1.2		4	156.59	odd	12
7605.2.a.cj.1.3		4	156.71	odd	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.16612 - 2.01978i) q^{3} +1.00000i q^{5} +(-3.11786 + 1.80010i) q^{7} +(-1.21969 - 2.11256i) q^{9} +O(q^{10})\)	\(q+(1.16612 - 2.01978i) q^{3} +1.00000i q^{5} +(-3.11786 + 1.80010i) q^{7} +(-1.21969 - 2.11256i) q^{9} +(4.65213 + 2.68591i) q^{11} +(1.81988 + 3.11256i) q^{13} +(2.01978 + 1.16612i) q^{15} +(-0.565928 - 0.980215i) q^{17} +(1.96410 - 1.13397i) q^{19} +8.39654i q^{21} +(1.94644 - 3.37133i) q^{23} -1.00000 q^{25} +1.30752 q^{27} +(0.0123639 - 0.0214150i) q^{29} +5.46410i q^{31} +(10.8499 - 6.26420i) q^{33} +(-1.80010 - 3.11786i) q^{35} +(7.53794 + 4.35203i) q^{37} +(8.40891 - 0.0461428i) q^{39} +(3.23205 + 1.86603i) q^{41} +(0.565928 + 0.980215i) q^{43} +(2.11256 - 1.21969i) q^{45} -2.58535i q^{47} +(2.98070 - 5.16273i) q^{49} -2.63977 q^{51} -4.43937 q^{53} +(-2.68591 + 4.65213i) q^{55} -5.28942i q^{57} +(0.148458 - 0.0857123i) q^{59} +(-1.68012 - 2.91005i) q^{61} +(7.60563 + 4.39111i) q^{63} +(-3.11256 + 1.81988i) q^{65} +(-5.54239 - 3.19990i) q^{67} +(-4.53957 - 7.86276i) q^{69} +(-9.35076 + 5.39866i) q^{71} -4.70308i q^{73} +(-1.16612 + 2.01978i) q^{75} -19.3396 q^{77} +11.9826 q^{79} +(5.18379 - 8.97859i) q^{81} -12.1286i q^{83} +(0.980215 - 0.565928i) q^{85} +(-0.0288357 - 0.0499450i) q^{87} +(13.9898 + 8.07702i) q^{89} +(-11.2771 - 6.42856i) q^{91} +(11.0363 + 6.37182i) q^{93} +(1.13397 + 1.96410i) q^{95} +(-10.5379 + 6.08408i) q^{97} -13.1039i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9	\( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 6 q^{15} - 2 q^{17} - 12 q^{19} + 10 q^{23} - 8 q^{25} + 4 q^{27} - 8 q^{29} + 42 q^{33} - 10 q^{35} + 6 q^{37} + 12 q^{41} + 2 q^{43} + 12 q^{49} + 8 q^{51} - 24 q^{53} + 12 q^{59} - 28 q^{61} + 24 q^{63} - 8 q^{65} - 6 q^{67} - 16 q^{69} + 2 q^{75} - 36 q^{77} + 16 q^{79} + 8 q^{81} + 18 q^{85} - 22 q^{87} + 24 q^{89} - 28 q^{91} + 16 q^{95} - 30 q^{97}+O(q^{100}) \) 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9 + 6 * q^15 - 2 * q^17 - 12 * q^19 + 10 * q^23 - 8 * q^25 + 4 * q^27 - 8 * q^29 + 42 * q^33 - 10 * q^35 + 6 * q^37 + 12 * q^41 + 2 * q^43 + 12 * q^49 + 8 * q^51 - 24 * q^53 + 12 * q^59 - 28 * q^61 + 24 * q^63 - 8 * q^65 - 6 * q^67 - 16 * q^69 + 2 * q^75 - 36 * q^77 + 16 * q^79 + 8 * q^81 + 18 * q^85 - 22 * q^87 + 24 * q^89 - 28 * q^91 + 16 * q^95 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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