LMFDB - Embedded newform 1040.2.da.b.881.4

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			881.4
Root			$1.40994 - 0.109843i$ of defining polynomial
Character	$\chi$	$=$	1040.881
Dual form			1040.2.da.b.641.4

$q$-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 $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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	0.976974	+	0.213359i	$0.0684405\pi$
$3$	1.16612	+	2.01978i	0.673262	+	1.16612i	−0.303712	+	0.952764i	$0.598226\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−3.11786	−	1.80010i	−1.17844	−	0.680373i	−0.222787	−	0.974867i	$-0.571516\pi$
$7$	−3.11786	−	1.80010i	−1.17844	−	0.680373i	−0.955653	+	0.294494i	$0.904849\pi$
$8$		0			0
$9$	−1.21969	+	2.11256i	−0.406562	+	0.704187i
$10$		0			0
$11$	4.65213	−	2.68591i	1.40267	−	0.809832i	0.408004	−	0.912980i	$-0.366225\pi$
$11$	4.65213	−	2.68591i	1.40267	−	0.809832i	0.994666	+	0.103149i	$0.0328917\pi$
$12$		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	−0.926458	−	0.376399i	$-0.877162\pi$
$17$	−0.565928	+	0.980215i	−0.137258	+	0.237737i	0.789200	+	0.614136i	$0.210495\pi$
$18$		0			0
$19$	1.96410	+	1.13397i	0.450596	+	0.260152i	0.708082	−	0.706130i	$-0.249561\pi$
$19$	1.96410	+	1.13397i	0.450596	+	0.260152i	−0.257486	+	0.966282i	$0.582894\pi$
$20$		0			0
$21$		−	8.39654i		−	1.83228i
$22$		0			0
$23$	1.94644	+	3.37133i	0.405860	+	0.702970i	0.994421	−	0.105483i	$-0.0336387\pi$
$23$	1.94644	+	3.37133i	0.405860	+	0.702970i	−0.588561	+	0.808453i	$0.700305\pi$
$24$		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	0.867171	−	0.498010i	$-0.165936\pi$
$29$	0.0123639	+	0.0214150i	0.00229593	+	0.00397666i	−0.864875	+	0.501987i	$0.832603\pi$
$30$		0			0
$31$		−	5.46410i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$		−	5.46410i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$		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	0.270293	−	0.962778i	$-0.412879\pi$
$37$	7.53794	−	4.35203i	1.23923	−	0.715470i	0.968937	+	0.247309i	$0.0795462\pi$
$38$		0			0
$39$	8.40891	+	0.0461428i	1.34650	+	0.00738877i
$40$		0			0
$41$	3.23205	−	1.86603i	0.504762	−	0.291424i	−0.225916	−	0.974147i	$-0.572538\pi$
$41$	3.23205	−	1.86603i	0.504762	−	0.291424i	0.730678	+	0.682723i	$0.239204\pi$
$42$		0			0
$43$	0.565928	−	0.980215i	0.0863031	−	0.149481i	−0.819643	−	0.572875i	$-0.805828\pi$
$43$	0.565928	−	0.980215i	0.0863031	−	0.149481i	0.905946	+	0.423394i	$0.139161\pi$
$44$		0			0
$45$	2.11256	+	1.21969i	0.314922	+	0.181820i
$46$		0			0
$47$			2.58535i			0.377113i	0.982062	+	0.188556i	$0.0603808\pi$
$47$			2.58535i			0.377113i	−0.982062	+	0.188556i	$0.939619\pi$
$48$		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	0.509633	−	0.860392i	$-0.329781\pi$
$59$	0.148458	+	0.0857123i	0.0193276	+	0.0111588i	−0.490305	+	0.871551i	$0.663115\pi$
$60$		0			0
$61$	−1.68012	+	2.91005i	−0.215117	+	0.372594i	−0.953309	−	0.301997i	$-0.902347\pi$
$61$	−1.68012	+	2.91005i	−0.215117	+	0.372594i	0.738192	+	0.674591i	$0.235680\pi$
$62$		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	−0.798766	−	0.601642i	$-0.794513\pi$
$67$	−5.54239	+	3.19990i	−0.677111	+	0.390930i	0.121655	+	0.992572i	$0.461180\pi$
$68$		0			0
$69$	−4.53957	+	7.86276i	−0.546500	+	0.946566i
$70$		0			0
$71$	−9.35076	−	5.39866i	−1.10973	−	0.640703i	−0.170971	−	0.985276i	$-0.554691\pi$
$71$	−9.35076	−	5.39866i	−1.10973	−	0.640703i	−0.938760	+	0.344573i	$0.888024\pi$
$72$		0			0
$73$			4.70308i			0.550454i	0.961379	+	0.275227i	$0.0887531\pi$
$73$			4.70308i			0.550454i	−0.961379	+	0.275227i	$0.911247\pi$
$74$		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	$0.231843\pi$
$83$			12.1286i			1.33129i	−0.746270	+	0.665643i	$0.768157\pi$
$84$		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	0.483105	−	0.875562i	$-0.339509\pi$
$89$	13.9898	−	8.07702i	1.48292	−	0.856162i	0.999812	+	0.0194001i	$0.00617565\pi$
$90$		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	−0.141794	−	0.989896i	$-0.545287\pi$
$97$	−10.5379	−	6.08408i	−1.06997	−	0.617745i	−0.928172	+	0.372151i	$0.878620\pi$
$98$		0			0
$99$			13.1039i			1.31699i
$100$		0			0
$101$	−2.02721	−	3.51122i	−0.201714	−	0.349380i	0.747366	−	0.664412i	$-0.231318\pi$
$101$	−2.02721	−	3.51122i	−0.201714	−	0.349380i	−0.949081	+	0.315032i	$0.897985\pi$
$102$		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	0.556389	−	0.830922i	$-0.312186\pi$
$107$	−4.56593	−	7.90842i	−0.441405	−	0.764536i	−0.997794	+	0.0663862i	$0.978853\pi$
$108$		0			0
$109$			7.37605i			0.706498i	0.935529	+	0.353249i	$0.114923\pi$
$109$			7.37605i			0.706498i	−0.935529	+	0.353249i	$0.885077\pi$
$110$		0			0
$111$	17.5803	+	10.1500i	1.66865	+	0.963396i
$112$		0			0
$113$	−3.53794	+	6.12789i	−0.332821	+	0.576463i	−0.983064	−	0.183263i	$-0.941334\pi$
$113$	−3.53794	+	6.12789i	−0.332821	+	0.576463i	0.650243	+	0.759727i	$0.274667\pi$
$114$		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	0.999963	+	0.00856072i	$0.00272499\pi$
$127$	5.71806	+	9.90396i	0.507395	+	0.878835i	−0.492568	+	0.870274i	$0.663942\pi$
$128$		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	0.633504	−	0.773739i	$-0.281616\pi$
$137$	3.27940	+	1.89336i	0.280178	+	0.161761i	−0.353326	+	0.935500i	$0.614949\pi$
$138$		0			0
$139$	1.00693	−	1.74406i	0.0854068	−	0.147929i	−0.820158	−	0.572138i	$-0.806114\pi$
$139$	1.00693	−	1.74406i	0.0854068	−	0.147929i	0.905564	+	0.424209i	$0.139448\pi$
$140$		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	0.682799	−	0.730607i	$-0.260763\pi$
$149$	4.77855	+	2.75890i	0.391474	+	0.226018i	−0.291324	+	0.956624i	$0.594096\pi$
$150$		0			0
$151$		−	4.88961i		−	0.397911i	−0.980009	−	0.198956i	$-0.936245\pi$
$151$		−	4.88961i		−	0.397911i	0.980009	−	0.198956i	$-0.0637549\pi$
$152$		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	0.252051	−	0.967714i	$-0.418895\pi$
$163$	−5.87273	−	3.39062i	−0.459988	−	0.265574i	−0.712039	+	0.702140i	$0.752228\pi$
$164$		0			0
$165$	6.26420	−	10.8499i	0.487667	−	0.844664i
$166$		0			0
$167$	9.08444	−	5.24490i	0.702975	−	0.405863i	−0.105479	−	0.994421i	$-0.533638\pi$
$167$	9.08444	−	5.24490i	0.702975	−	0.405863i	0.808455	+	0.588559i	$0.200304\pi$
$168$		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	−0.938239	−	0.345988i	$-0.887544\pi$
$173$	−2.22923	+	3.86113i	−0.169485	+	0.293557i	0.768754	+	0.639545i	$0.220877\pi$
$174$		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	−0.969746	−	0.244116i	$-0.921502\pi$
$179$	−9.31564	−	16.1352i	−0.696284	−	1.20600i	0.273462	−	0.961883i	$-0.411831\pi$
$180$		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	0.366361	−	0.930473i	$-0.380603\pi$
$191$	13.6682	−	23.6740i	0.988994	−	1.71299i	0.622632	−	0.782515i	$-0.286063\pi$
$192$		0			0
$193$	−18.8511	+	10.8837i	−1.35693	+	0.783425i	−0.989209	−	0.146510i	$-0.953196\pi$
$193$	−18.8511	+	10.8837i	−1.35693	+	0.783425i	−0.367723	+	0.929935i	$0.619863\pi$
$194$		0			0
$195$	0.0461428	−	8.40891i	0.00330436	−	0.602174i
$196$		0			0
$197$	−1.46940	+	0.848360i	−0.104691	+	0.0604432i	−0.551431	−	0.834220i	$-0.685918\pi$
$197$	−1.46940	+	0.848360i	−0.104691	+	0.0604432i	0.446741	+	0.894664i	$0.352585\pi$
$198$		0			0
$199$	−12.6627	+	21.9325i	−0.897637	+	1.55475i	−0.0671309	+	0.997744i	$0.521385\pi$
$199$	−12.6627	+	21.9325i	−0.897637	+	1.55475i	−0.830506	+	0.557009i	$0.811949\pi$
$200$		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	0.860193	−	0.509968i	$-0.170343\pi$
$211$	−0.167753	−	0.290558i	−0.0115486	−	0.0200028i	−0.871742	+	0.489965i	$0.837009\pi$
$212$		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	−0.0990887	−	0.995079i	$-0.531593\pi$
$223$	10.6493	−	6.14838i	0.713130	−	0.411726i	0.812219	+	0.583353i	$0.198259\pi$
$224$		0			0
$225$	1.21969	−	2.11256i	0.0813125	−	0.140837i
$226$		0			0
$227$	−6.60974	−	3.81613i	−0.438704	−	0.253286i	0.264344	−	0.964428i	$-0.414845\pi$
$227$	−6.60974	−	3.81613i	−0.438704	−	0.253286i	−0.703048	+	0.711143i	$0.748178\pi$
$228$		0			0
$229$			14.4008i			0.951631i	0.879545	+	0.475815i	$0.157847\pi$
$229$			14.4008i			0.951631i	−0.879545	+	0.475815i	$0.842153\pi$
$230$		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	$0.222758\pi$
$239$			19.9143i			1.28815i	−0.764962	+	0.644076i	$0.777242\pi$
$240$		0			0
$241$	20.1493	+	11.6332i	1.29793	+	0.749360i	0.980046	−	0.198770i	$-0.0636947\pi$
$241$	20.1493	+	11.6332i	1.29793	+	0.749360i	0.317883	+	0.948130i	$0.397028\pi$
$242$		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	−0.990127	−	0.140171i	$-0.955235\pi$
$251$	−5.92008	+	10.2539i	−0.373672	+	0.647219i	0.616455	+	0.787390i	$0.288568\pi$
$252$		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	0.766402	−	0.642361i	$-0.222045\pi$
$257$	−2.77501	−	4.80646i	−0.173100	−	0.299819i	−0.939502	+	0.342543i	$0.888712\pi$
$258$		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	0.952182	−	0.305532i	$-0.0988342\pi$
$263$	3.42983	+	5.94065i	0.211493	+	0.366316i	−0.740689	+	0.671848i	$0.765501\pi$
$264$		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	−0.843536	−	0.537072i	$-0.819530\pi$
$269$	0.710994	−	1.23148i	0.0433501	−	0.0750845i	0.886886	+	0.461988i	$0.152864\pi$
$270$		0			0
$271$	−8.63381	+	4.98473i	−0.524467	+	0.302801i	−0.738760	−	0.673968i	$-0.764588\pi$
$271$	−8.63381	+	4.98473i	−0.524467	+	0.302801i	0.214294	+	0.976769i	$0.431255\pi$
$272$		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	0.473076	+	0.881022i	$0.343144\pi$
$277$	−8.76187	+	15.1760i	−0.526449	+	0.911837i	−0.999525	+	0.0308154i	$0.990190\pi$
$278$		0			0
$279$	11.5432	+	6.66449i	0.691076	+	0.398993i
$280$		0			0
$281$		−	10.7352i		−	0.640406i	−0.947349	−	0.320203i	$-0.896249\pi$
$281$		−	10.7352i		−	0.640406i	0.947349	−	0.320203i	$-0.103751\pi$
$282$		0			0
$283$	−0.659192	−	1.14175i	−0.0391849	−	0.0678702i	0.845768	−	0.533551i	$-0.179143\pi$
$283$	−0.659192	−	1.14175i	−0.0391849	−	0.0678702i	−0.884953	+	0.465681i	$0.845809\pi$
$284$		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	0.892540	−	0.450968i	$-0.148921\pi$
$293$	16.2316	+	9.37133i	0.948261	+	0.547479i	0.0557207	+	0.998446i	$0.482254\pi$
$294$		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	$0.133841\pi$
$307$			14.3043i			0.816387i	−0.912895	+	0.408194i	$0.866159\pi$
$308$		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	$0.0159695\pi$
$317$			1.78575i			0.100297i	−0.998742	+	0.0501487i	$0.984030\pi$
$318$		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	0.661991	−	0.749512i	$-0.269712\pi$
$331$	6.25652	+	3.61220i	0.343889	+	0.198545i	−0.318101	+	0.948057i	$0.603045\pi$
$332$		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	0.245381	+	0.969427i	$0.421087\pi$
$347$	−13.3536	+	23.1291i	−0.716858	+	1.24163i	−0.962239	+	0.272207i	$0.912246\pi$
$348$		0			0
$349$	−20.4131	+	11.7855i	−1.09269	+	0.630865i	−0.934292	−	0.356510i	$-0.883967\pi$
$349$	−20.4131	+	11.7855i	−1.09269	+	0.630865i	−0.158399	+	0.987375i	$0.550633\pi$
$350$		0			0
$351$	2.37953	−	4.06973i	0.127010	−	0.217226i
$352$		0			0
$353$	4.96862	−	2.86863i	0.264453	−	0.152682i	−0.361911	−	0.932213i	$-0.617876\pi$
$353$	4.96862	−	2.86863i	0.264453	−	0.152682i	0.626364	+	0.779531i	$0.284542\pi$
$354$		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	$-0.773364\pi$
$359$		−	24.7583i		−	1.30669i	0.757059	−	0.653347i	$-0.226636\pi$
$360$		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	0.974983	+	0.222280i	$0.0713500\pi$
$367$	13.0268	+	22.5630i	0.679992	+	1.17778i	−0.294991	+	0.955500i	$0.595317\pi$
$368$		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	−0.984776	−	0.173826i	$-0.944387\pi$
$373$	−6.60224	+	11.4354i	−0.341851	+	0.592103i	0.642926	+	0.765929i	$0.277720\pi$
$374$		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	−0.950463	−	0.310837i	$-0.899391\pi$
$379$	−22.5147	+	12.9989i	−1.15650	+	0.667707i	−0.206039	+	0.978544i	$0.566057\pi$
$380$		0			0
$381$	−13.3359	+	23.0985i	−0.683220	+	1.18337i
$382$		0			0
$383$	−8.31401	−	4.80010i	−0.424826	−	0.245274i	0.272314	−	0.962208i	$-0.412211\pi$
$383$	−8.31401	−	4.80010i	−0.424826	−	0.245274i	−0.697140	+	0.716935i	$0.745544\pi$
$384$		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	0.0892344	−	0.996011i	$-0.471558\pi$
$397$	−14.5196	−	8.38291i	−0.728719	−	0.420726i	−0.817953	+	0.575285i	$0.804891\pi$
$398$		0			0
$399$	9.52147	−	16.4917i	0.476670	−	0.825616i
$400$		0			0
$401$	12.0187	−	6.93902i	0.600187	−	0.346518i	−0.168928	−	0.985628i	$-0.554031\pi$
$401$	12.0187	−	6.93902i	0.600187	−	0.346518i	0.769115	+	0.639110i	$0.220697\pi$
$402$		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	−0.286964	−	0.957941i	$-0.592646\pi$
$409$	−25.4829	−	14.7125i	−1.26005	−	0.727489i	−0.973083	+	0.230453i	$0.925979\pi$
$410$		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	0.938491	−	0.345305i	$-0.112224\pi$
$419$	3.48397	+	6.03440i	0.170203	+	0.294800i	−0.768288	+	0.640104i	$0.778891\pi$
$420$		0			0
$421$			7.12125i			0.347069i	0.984828	+	0.173534i	$0.0555188\pi$
$421$			7.12125i			0.347069i	−0.984828	+	0.173534i	$0.944481\pi$
$422$		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	−0.973150	−	0.230171i	$-0.926071\pi$
$431$	−26.1664	+	15.1072i	−1.26039	+	0.727687i	−0.287241	+	0.957858i	$0.592738\pi$
$432$		0			0
$433$	0.600065	−	1.03934i	0.0288373	−	0.0499476i	−0.851247	−	0.524766i	$-0.824153\pi$
$433$	0.600065	−	1.03934i	0.0288373	−	0.0499476i	0.880084	+	0.474818i	$0.157486\pi$
$434$		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	0.993107	−	0.117215i	$-0.0373966\pi$
$439$	8.27705	+	14.3363i	0.395042	+	0.684233i	−0.598064	+	0.801448i	$0.704063\pi$
$440$		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	0.755607	−	0.655025i	$-0.227342\pi$
$449$	11.9963	+	6.92608i	0.566142	+	0.326862i	−0.189465	+	0.981887i	$0.560675\pi$
$450$		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	0.639548	−	0.768751i	$-0.279122\pi$
$457$	34.7402	−	20.0573i	1.62508	−	0.938240i	0.985532	−	0.169489i	$-0.0542117\pi$
$458$		0			0
$459$	−0.739961	+	1.28165i	−0.0345384	+	0.0598223i
$460$		0			0
$461$	6.52897	+	3.76950i	0.304084	+	0.175563i	0.644276	−	0.764793i	$-0.277159\pi$
$461$	6.52897	+	3.76950i	0.304084	+	0.175563i	−0.340192	+	0.940356i	$0.610492\pi$
$462$		0			0
$463$			23.3031i			1.08299i	0.840705	+	0.541494i	$0.182141\pi$
$463$			23.3031i			1.08299i	−0.840705	+	0.541494i	$0.817859\pi$
$464$		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	−0.0324399	−	0.999474i	$-0.510328\pi$
$479$	17.8789	−	10.3224i	0.816910	−	0.471643i	0.849350	+	0.527831i	$0.176994\pi$
$480$		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	0.558388	−	0.829580i	$-0.311420\pi$
$487$	2.62929	+	1.51802i	0.119145	+	0.0687882i	−0.439243	+	0.898368i	$0.644753\pi$
$488$		0			0
$489$		−	15.8155i		−	0.715203i
$490$		0			0
$491$	−5.33401	−	9.23877i	−0.240720	−	0.416940i	0.720199	−	0.693767i	$-0.244050\pi$
$491$	−5.33401	−	9.23877i	−0.240720	−	0.416940i	−0.960920	+	0.276827i	$0.910717\pi$
$492$		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	$-0.725636\pi$
$499$		−	33.9143i		−	1.51821i	0.650966	−	0.759107i	$-0.274364\pi$
$500$		0			0
$501$	21.1872	+	12.2324i	0.946572	+	0.546504i
$502$		0			0
$503$	−6.31380	+	10.9358i	−0.281518	+	0.487604i	−0.971759	−	0.235976i	$-0.924171\pi$
$503$	−6.31380	+	10.9358i	−0.281518	+	0.487604i	0.690241	+	0.723580i	$0.257505\pi$
$504$		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	−0.885899	−	0.463877i	$-0.846458\pi$
$509$	−20.9168	+	12.0763i	−0.927120	+	0.535273i	−0.0412201	+	0.999150i	$0.513124\pi$
$510$		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	0.913098	+	0.407739i	$0.133683\pi$
$523$	18.5163	+	32.0712i	0.809662	+	1.40238i	−0.103436	+	0.994636i	$0.532984\pi$
$524$		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	$0.0576658\pi$
$541$			8.38144i			0.360346i	−0.983635	+	0.180173i	$0.942334\pi$
$542$		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	0.115197	−	0.993343i	$-0.463250\pi$
$557$	24.3810	−	14.0764i	1.03306	−	0.596435i	0.917858	+	0.396908i	$0.129917\pi$
$558$		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	−0.609305	−	0.792936i	$-0.708551\pi$
$563$	9.06514	−	15.7013i	0.382050	−	0.661731i	0.991355	+	0.131206i	$0.0418848\pi$
$564$		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	0.880317	+	0.474385i	$0.157330\pi$
$569$	20.2992	+	35.1593i	0.850988	+	1.47395i	−0.0293292	+	0.999570i	$0.509337\pi$
$570$		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	$0.159432\pi$
$577$			23.0691i			0.960379i	−0.877165	+	0.480189i	$0.840568\pi$
$578$		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	−0.0900152	−	0.995940i	$-0.528692\pi$
$587$	17.6256	−	10.1762i	0.727487	−	0.420015i	0.817502	+	0.575926i	$0.195358\pi$
$588$		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	$-0.931612\pi$
$593$		−	10.3834i		−	0.426395i	0.977009	−	0.213198i	$-0.0683878\pi$
$594$		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	0.833751	+	0.552141i	$0.186189\pi$
$601$	21.9423	+	38.0051i	0.895044	+	1.55026i	0.0612928	+	0.998120i	$0.480478\pi$
$602$		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	−0.843107	−	0.537746i	$-0.819276\pi$
$607$	1.08770	−	1.88395i	0.0441484	−	0.0764673i	0.887255	+	0.461279i	$0.152609\pi$
$608$		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	−0.735441	−	0.677589i	$-0.763025\pi$
$613$	−12.7843	+	7.38100i	−0.516352	+	0.298116i	0.219089	+	0.975705i	$0.429691\pi$
$614$		0			0
$615$	4.35203	−	7.53794i	0.175491	−	0.303959i
$616$		0			0
$617$	17.5779	+	10.1486i	0.707659	+	0.408567i	0.810194	−	0.586162i	$-0.199362\pi$
$617$	17.5779	+	10.1486i	0.707659	+	0.408567i	−0.102535	+	0.994729i	$0.532695\pi$
$618$		0			0
$619$			9.94207i			0.399605i	0.979836	+	0.199803i	$0.0640301\pi$
$619$			9.94207i			0.399605i	−0.979836	+	0.199803i	$0.935970\pi$
$620$		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	0.483126	−	0.875551i	$-0.339501\pi$
$631$	−0.843006	−	0.486710i	−0.0335596	−	0.0193756i	−0.516686	+	0.856175i	$0.672835\pi$
$632$		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	−0.963318	−	0.268364i	$-0.913517\pi$
$641$	−6.31047	+	10.9301i	−0.249249	+	0.431711i	0.714069	+	0.700075i	$0.246850\pi$
$642$		0			0
$643$	8.62599	+	4.98022i	0.340176	+	0.196401i	0.660350	−	0.750958i	$-0.270408\pi$
$643$	8.62599	+	4.98022i	0.340176	+	0.196401i	−0.320174	+	0.947359i	$0.603741\pi$
$644$		0			0
$645$		−	2.63977i		−	0.103941i
$646$		0			0
$647$	18.1381	+	31.4162i	0.713084	+	1.23510i	0.963694	+	0.267009i	$0.0860354\pi$
$647$	18.1381	+	31.4162i	0.713084	+	1.23510i	−0.250610	+	0.968088i	$0.580631\pi$
$648$		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	0.699497	−	0.714636i	$-0.253408\pi$
$653$	−6.87769	−	11.9125i	−0.269145	−	0.466172i	−0.968641	+	0.248464i	$0.920074\pi$
$654$		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	−0.890073	−	0.455818i	$-0.849347\pi$
$659$	−1.29092	+	2.23593i	−0.0502869	+	0.0870995i	0.839786	+	0.542917i	$0.182680\pi$
$660$		0			0
$661$	−21.5437	+	12.4382i	−0.837951	+	0.483791i	−0.856567	−	0.516036i	$-0.827407\pi$
$661$	−21.5437	+	12.4382i	−0.837951	+	0.483791i	0.0186163	+	0.999827i	$0.494074\pi$
$662$		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	0.894052	+	0.447964i	$0.147851\pi$
$673$	21.6611	+	37.5181i	0.834974	+	1.44622i	−0.0590774	+	0.998253i	$0.518816\pi$
$674$		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	0.455844	−	0.890060i	$-0.349338\pi$
$683$	−2.27495	−	1.31344i	−0.0870484	−	0.0502574i	−0.542892	+	0.839802i	$0.682671\pi$
$684$		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	−0.226806	−	0.973940i	$-0.572828\pi$
$691$	13.2288	−	7.63765i	0.503247	−	0.290550i	0.730053	+	0.683390i	$0.239495\pi$
$692$		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	−0.290329	−	0.956927i	$-0.593765\pi$
$709$	−33.6624	−	19.4350i	−1.26422	−	0.729896i	−0.973887	+	0.227031i	$0.927098\pi$
$710$		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	−0.921098	−	0.389331i	$-0.872706\pi$
$719$	−3.30830	+	5.73015i	−0.123379	+	0.213698i	0.797719	+	0.603029i	$0.206040\pi$
$720$		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	$0.00465084\pi$
$733$			0.791131i			0.0292211i	−0.999893	+	0.0146105i	$0.995349\pi$
$734$		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	0.0871658	−	0.996194i	$-0.472219\pi$
$739$	27.0073	−	15.5926i	0.993478	−	0.573585i	0.906312	+	0.422609i	$0.138886\pi$
$740$		0			0
$741$	16.4636	+	9.62612i	0.604806	+	0.353624i
$742$		0			0
$743$	−4.81773	+	2.78152i	−0.176745	+	0.102044i	−0.585763	−	0.810483i	$-0.699205\pi$
$743$	−4.81773	+	2.78152i	−0.176745	+	0.102044i	0.409017	+	0.912527i	$0.365872\pi$
$744$		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	0.984893	+	0.173163i	$0.0553987\pi$
$751$	17.6048	+	30.4925i	0.642410	+	1.11269i	−0.342483	+	0.939524i	$0.611268\pi$
$752$		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	−0.814828	−	0.579703i	$-0.803169\pi$
$757$	−25.0223	−	43.3399i	−0.909451	−	1.57522i	−0.0946237	−	0.995513i	$-0.530165\pi$
$758$		0			0
$759$			48.7715i			1.77029i
$760$		0			0
$761$	38.8161	+	22.4105i	1.40708	+	0.812379i	0.995106	−	0.0988165i	$-0.0315057\pi$
$761$	38.8161	+	22.4105i	1.40708	+	0.812379i	0.411975	+	0.911195i	$0.364839\pi$
$762$		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	−0.966884	−	0.255215i	$-0.917854\pi$
$769$	−34.0897	+	19.6817i	−1.22930	+	0.709739i	−0.262420	+	0.964954i	$0.584521\pi$
$770$		0			0
$771$	6.47201	−	11.2099i	0.233084	−	0.403713i
$772$		0			0
$773$	−42.2452	−	24.3902i	−1.51945	−	0.877256i	−0.999737	−	0.0229167i	$-0.992705\pi$
$773$	−42.2452	−	24.3902i	−1.51945	−	0.877256i	−0.519715	−	0.854340i	$-0.673962\pi$
$774$		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	−0.263382	−	0.964692i	$-0.584838\pi$
$787$	−34.5204	−	19.9304i	−1.23052	−	0.710442i	−0.967139	+	0.254250i	$0.918171\pi$
$788$		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	−0.534932	−	0.844895i	$-0.679663\pi$
$797$	13.1059	−	22.7001i	0.464235	−	0.804079i	0.999167	+	0.0408167i	$0.0129960\pi$
$798$		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	0.602020	−	0.798481i	$-0.294363\pi$
$809$	−11.1068	−	19.2376i	−0.390495	−	0.676357i	−0.992515	+	0.122124i	$0.961029\pi$
$810$		0			0
$811$		−	19.0950i		−	0.670515i	−0.942127	−	0.335257i	$-0.891177\pi$
$811$		−	19.0950i		−	0.670515i	0.942127	−	0.335257i	$-0.108823\pi$
$812$		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	−0.917677	−	0.397327i	$-0.869938\pi$
$821$	−29.5820	+	17.0792i	−1.03242	+	0.596068i	−0.114743	+	0.993395i	$0.536604\pi$
$822$		0			0
$823$	−2.03970	+	3.53286i	−0.0710995	+	0.123148i	−0.899383	−	0.437161i	$-0.855984\pi$
$823$	−2.03970	+	3.53286i	−0.0710995	+	0.123148i	0.828284	+	0.560309i	$0.189317\pi$
$824$		0			0
$825$	−10.8499	−	6.26420i	−0.377745	−	0.218091i
$826$		0			0
$827$		−	54.8780i		−	1.90830i	−0.299337	−	0.954148i	$-0.596765\pi$
$827$		−	54.8780i		−	1.90830i	0.299337	−	0.954148i	$-0.403235\pi$
$828$		0			0
$829$	4.07475	+	7.05768i	0.141522	+	0.245123i	0.928070	−	0.372406i	$-0.121467\pi$
$829$	4.07475	+	7.05768i	0.141522	+	0.245123i	−0.786548	+	0.617529i	$0.788134\pi$
$830$		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	0.790130	−	0.612939i	$-0.210013\pi$
$839$	18.9543	+	10.9433i	0.654374	+	0.377803i	−0.135756	+	0.990742i	$0.543346\pi$
$840$		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	$0.106748\pi$
$853$			19.2240i			0.658217i	−0.944292	+	0.329108i	$0.893252\pi$
$854$		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	$-0.617160\pi$
$863$		−	54.8186i		−	1.86605i	0.359814	−	0.933024i	$-0.382840\pi$
$864$		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	0.843706	−	0.536805i	$-0.180369\pi$
$877$	23.7113	+	13.6897i	0.800673	+	0.462269i	−0.0430336	+	0.999074i	$0.513702\pi$
$878$		0			0
$879$			43.7125i			1.47439i
$880$		0			0
$881$	−17.2213	−	29.8282i	−0.580200	−	1.00494i	−0.995455	−	0.0952310i	$-0.969641\pi$
$881$	−17.2213	−	29.8282i	−0.580200	−	1.00494i	0.415255	−	0.909705i	$-0.363692\pi$
$882$		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	−0.999647	−	0.0265716i	$-0.991541\pi$
$887$	−15.5714	−	26.9704i	−0.522835	−	0.905577i	0.476812	−	0.879005i	$-0.341792\pi$
$888$		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	0.682058	−	0.731298i	$-0.261085\pi$
$907$	−8.80284	−	15.2470i	−0.292294	−	0.506267i	−0.974352	+	0.225031i	$0.927752\pi$
$908$		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	−0.921970	−	0.387261i	$-0.873421\pi$
$919$	−3.80778	+	6.59527i	−0.125607	+	0.217558i	0.796363	+	0.604819i	$0.206755\pi$
$920$		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	0.687048	−	0.726612i	$-0.258906\pi$
$929$	12.2317	+	7.06196i	0.401308	+	0.231695i	−0.285740	+	0.958307i	$0.592239\pi$
$930$		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	$-0.864362\pi$
$941$		−	25.3591i		−	0.826683i	0.910576	−	0.413342i	$-0.135638\pi$
$942$		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	0.213042	−	0.977043i	$-0.431663\pi$
$947$	35.8727	−	20.7111i	1.16571	−	0.673021i	0.952665	+	0.304022i	$0.0983296\pi$
$948$		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	−0.599305	−	0.800521i	$-0.704556\pi$
$953$	12.1513	−	21.0466i	0.393619	−	0.681767i	0.992924	+	0.118753i	$0.0378897\pi$
$954$		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	$-0.875675\pi$
$967$		−	23.6784i		−	0.761445i	0.924689	−	0.380722i	$-0.124325\pi$
$968$		0			0
$969$	−5.18477	−	2.99343i	−0.166559	−	0.0961627i
$970$		0			0
$971$	−8.48609	+	14.6983i	−0.272332	+	0.471692i	−0.969458	−	0.245256i	$-0.921128\pi$
$971$	−8.48609	+	14.6983i	−0.272332	+	0.471692i	0.697127	+	0.716948i	$0.254461\pi$
$972$		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	−0.111955	−	0.993713i	$-0.535711\pi$
$977$	21.6501	−	12.4997i	0.692649	−	0.399901i	0.804604	+	0.593812i	$0.202378\pi$
$978$		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	$-0.856383\pi$
$983$		−	27.3418i		−	0.872068i	0.899930	−	0.436034i	$-0.143617\pi$
$984$		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	0.964987	−	0.262299i	$-0.0844805\pi$
$991$	8.03802	+	13.9223i	0.255336	+	0.442255i	−0.709651	+	0.704554i	$0.751147\pi$
$992$		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	−0.451178	−	0.892434i	$-0.648996\pi$
$997$	17.2806	−	29.9309i	0.547282	−	0.947920i	0.998459	−	0.0554858i	$-0.0176708\pi$
$998$		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.881.4		8
4.3	odd	2		65.2.m.a.36.3	✓	8
12.11	even	2		585.2.bu.c.361.2		8
13.4	even	6	inner	1040.2.da.b.641.4		8
20.3	even	4		325.2.m.b.49.2		8
20.7	even	4		325.2.m.c.49.3		8
20.19	odd	2		325.2.n.d.101.2		8
52.3	odd	6		845.2.c.g.506.6		8
52.7	even	12		845.2.e.n.191.3		8
52.11	even	12		845.2.a.l.1.2		4
52.15	even	12		845.2.a.m.1.3		4
52.19	even	12		845.2.e.m.191.2		8
52.23	odd	6		845.2.c.g.506.3		8
52.31	even	4		845.2.e.m.146.2		8
52.35	odd	6		845.2.m.g.316.2		8
52.43	odd	6		65.2.m.a.56.3	yes	8
52.47	even	4		845.2.e.n.146.3		8
52.51	odd	2		845.2.m.g.361.2		8
156.11	odd	12		7605.2.a.cj.1.3		4
156.95	even	6		585.2.bu.c.316.2		8
156.119	odd	12		7605.2.a.cf.1.2		4
260.43	even	12		325.2.m.c.199.3		8
260.119	even	12		4225.2.a.bi.1.2		4
260.147	even	12		325.2.m.b.199.2		8
260.199	odd	6		325.2.n.d.251.2		8
260.219	even	12		4225.2.a.bl.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	4.3	odd	2
65.2.m.a.56.3	yes	8	52.43	odd	6
325.2.m.b.49.2		8	20.3	even	4
325.2.m.b.199.2		8	260.147	even	12
325.2.m.c.49.3		8	20.7	even	4
325.2.m.c.199.3		8	260.43	even	12
325.2.n.d.101.2		8	20.19	odd	2
325.2.n.d.251.2		8	260.199	odd	6
585.2.bu.c.316.2		8	156.95	even	6
585.2.bu.c.361.2		8	12.11	even	2
845.2.a.l.1.2		4	52.11	even	12
845.2.a.m.1.3		4	52.15	even	12
845.2.c.g.506.3		8	52.23	odd	6
845.2.c.g.506.6		8	52.3	odd	6
845.2.e.m.146.2		8	52.31	even	4
845.2.e.m.191.2		8	52.19	even	12
845.2.e.n.146.3		8	52.47	even	4
845.2.e.n.191.3		8	52.7	even	12
845.2.m.g.316.2		8	52.35	odd	6
845.2.m.g.361.2		8	52.51	odd	2
1040.2.da.b.641.4		8	13.4	even	6	inner
1040.2.da.b.881.4		8	1.1	even	1	trivial
4225.2.a.bi.1.2		4	260.119	even	12
4225.2.a.bl.1.3		4	260.219	even	12
7605.2.a.cf.1.2		4	156.119	odd	12
7605.2.a.cj.1.3		4	156.11	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

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Representations

Groups

Database

Properties

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