LMFDB - Embedded newform 640.2.x.a.81.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(81,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("640.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.x (of order $8$, degree $4$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			81.15
Character	$\chi$	$=$	640.81
Dual form			640.2.x.a.561.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.67164 + 1.10663i) q^{3} +(0.382683 + 0.923880i) q^{5} +(-3.58127 + 3.58127i) q^{7} +(3.79172 + 3.79172i) q^{9} +O(q^{10})$	\(q+(2.67164 + 1.10663i) q^{3} +(0.382683 + 0.923880i) q^{5} +(-3.58127 + 3.58127i) q^{7} +(3.79172 + 3.79172i) q^{9} +(1.44277 - 0.597617i) q^{11} +(1.48141 - 3.57644i) q^{13} +2.89177i q^{15} -1.77217i q^{17} +(-1.36449 + 3.29416i) q^{19} +(-13.5310 + 5.60473i) q^{21} +(3.76499 + 3.76499i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(2.61420 + 6.31124i) q^{27} +(-0.555635 - 0.230151i) q^{29} -4.13645 q^{31} +4.51592 q^{33} +(-4.67915 - 1.93817i) q^{35} +(1.23951 + 2.99244i) q^{37} +(7.91561 - 7.91561i) q^{39} +(1.20035 + 1.20035i) q^{41} +(4.32941 - 1.79330i) q^{43} +(-2.05207 + 4.95413i) q^{45} -6.47426i q^{47} -18.6510i q^{49} +(1.96114 - 4.73462i) q^{51} +(7.99090 - 3.30994i) q^{53} +(1.10425 + 1.10425i) q^{55} +(-7.29084 + 7.29084i) q^{57} +(-2.31884 - 5.59818i) q^{59} +(-0.637370 - 0.264007i) q^{61} -27.1584 q^{63} +3.87112 q^{65} +(5.02905 + 2.08310i) q^{67} +(5.89226 + 14.2252i) q^{69} +(1.19465 - 1.19465i) q^{71} +(0.643585 + 0.643585i) q^{73} +(-2.67164 + 1.10663i) q^{75} +(-3.02674 + 7.30719i) q^{77} -14.7962i q^{79} +3.66742i q^{81} +(-3.70380 + 8.94176i) q^{83} +(1.63728 - 0.678182i) q^{85} +(-1.22976 - 1.22976i) q^{87} +(4.26736 - 4.26736i) q^{89} +(7.50287 + 18.1135i) q^{91} +(-11.0511 - 4.57753i) q^{93} -3.56558 q^{95} +2.38217 q^{97} +(7.73660 + 3.20460i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) $ 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

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
$3$	2.67164	+	1.10663i	1.54247	+	0.638914i	0.981936	−	0.189215i	$-0.0605944\pi$
$3$	2.67164	+	1.10663i	1.54247	+	0.638914i	0.560538	+	0.828129i	$0.310594\pi$
$4$		0			0
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$6$		0			0
$7$	−3.58127	+	3.58127i	−1.35359	+	1.35359i	−0.471986	+	0.881606i	$0.656463\pi$
$7$	−3.58127	+	3.58127i	−1.35359	+	1.35359i	−0.881606	+	0.471986i	$0.843537\pi$
$8$		0			0
$9$	3.79172	+	3.79172i	1.26391	+	1.26391i
$10$		0			0
$11$	1.44277	−	0.597617i	0.435013	−	0.180188i	−0.154420	−	0.988005i	$-0.549351\pi$
$11$	1.44277	−	0.597617i	0.435013	−	0.180188i	0.589433	+	0.807817i	$0.299351\pi$
$12$		0			0
$13$	1.48141	−	3.57644i	0.410870	−	0.991927i	−0.574035	−	0.818831i	$-0.694623\pi$
$13$	1.48141	−	3.57644i	0.410870	−	0.991927i	0.984905	−	0.173097i	$-0.0553773\pi$
$14$		0			0
$15$			2.89177i			0.746651i
$16$		0			0
$17$		−	1.77217i		−	0.429815i	−0.976634	−	0.214908i	$-0.931055\pi$
$17$		−	1.77217i		−	0.429815i	0.976634	−	0.214908i	$-0.0689451\pi$
$18$		0			0
$19$	−1.36449	+	3.29416i	−0.313035	+	0.755733i	0.686555	+	0.727078i	$0.259122\pi$
$19$	−1.36449	+	3.29416i	−0.313035	+	0.755733i	−0.999589	+	0.0286546i	$0.990878\pi$
$20$		0			0
$21$	−13.5310	+	5.60473i	−2.95271	+	1.22305i
$22$		0			0
$23$	3.76499	+	3.76499i	0.785055	+	0.785055i	0.980679	−	0.195624i	$-0.0626732\pi$
$23$	3.76499	+	3.76499i	0.785055	+	0.785055i	−0.195624	+	0.980679i	$0.562673\pi$
$24$		0			0
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$		0			0
$27$	2.61420	+	6.31124i	0.503103	+	1.21460i
$28$		0			0
$29$	−0.555635	−	0.230151i	−0.103179	−	0.0427380i	0.330497	−	0.943807i	$-0.392784\pi$
$29$	−0.555635	−	0.230151i	−0.103179	−	0.0427380i	−0.433676	+	0.901069i	$0.642784\pi$
$30$		0			0
$31$	−4.13645			−0.742929			−0.371464	−	0.928447i	$-0.621144\pi$
$31$	−4.13645			−0.742929			−0.371464	+	0.928447i	$0.621144\pi$
$32$		0			0
$33$	4.51592			0.786121
$34$		0			0
$35$	−4.67915	−	1.93817i	−0.790921	−	0.327610i
$36$		0			0
$37$	1.23951	+	2.99244i	0.203774	+	0.491955i	0.992420	−	0.122893i	$-0.0392173\pi$
$37$	1.23951	+	2.99244i	0.203774	+	0.491955i	−0.788646	+	0.614848i	$0.789217\pi$
$38$		0			0
$39$	7.91561	−	7.91561i	1.26751	−	1.26751i
$40$		0			0
$41$	1.20035	+	1.20035i	0.187463	+	0.187463i	0.794598	−	0.607136i	$-0.207681\pi$
$41$	1.20035	+	1.20035i	0.187463	+	0.187463i	−0.607136	+	0.794598i	$0.707681\pi$
$42$		0			0
$43$	4.32941	−	1.79330i	0.660229	−	0.273476i	−0.0273057	−	0.999627i	$-0.508693\pi$
$43$	4.32941	−	1.79330i	0.660229	−	0.273476i	0.687535	+	0.726151i	$0.258693\pi$
$44$		0			0
$45$	−2.05207	+	4.95413i	−0.305904	+	0.738517i
$46$		0			0
$47$		−	6.47426i		−	0.944368i	−0.881500	−	0.472184i	$-0.843466\pi$
$47$		−	6.47426i		−	0.944368i	0.881500	−	0.472184i	$-0.156534\pi$
$48$		0			0
$49$		−	18.6510i		−	2.66442i
$50$		0			0
$51$	1.96114	−	4.73462i	0.274615	−	0.662979i
$52$		0			0
$53$	7.99090	−	3.30994i	1.09764	−	0.454655i	0.240972	−	0.970532i	$-0.422534\pi$
$53$	7.99090	−	3.30994i	1.09764	−	0.454655i	0.856663	+	0.515877i	$0.172534\pi$
$54$		0			0
$55$	1.10425	+	1.10425i	0.148897	+	0.148897i
$56$		0			0
$57$	−7.29084	+	7.29084i	−0.965696	+	0.965696i
$58$		0			0
$59$	−2.31884	−	5.59818i	−0.301887	−	0.728821i	−0.999919	−	0.0127535i	$-0.995940\pi$
$59$	−2.31884	−	5.59818i	−0.301887	−	0.728821i	0.698031	−	0.716067i	$-0.254060\pi$
$60$		0			0
$61$	−0.637370	−	0.264007i	−0.0816069	−	0.0338027i	0.341507	−	0.939879i	$-0.389063\pi$
$61$	−0.637370	−	0.264007i	−0.0816069	−	0.0338027i	−0.423113	+	0.906077i	$0.639063\pi$
$62$		0			0
$63$	−27.1584			−3.42163
$64$		0			0
$65$	3.87112			0.480153
$66$		0			0
$67$	5.02905	+	2.08310i	0.614397	+	0.254491i	0.668107	−	0.744065i	$-0.267105\pi$
$67$	5.02905	+	2.08310i	0.614397	+	0.254491i	−0.0537105	+	0.998557i	$0.517105\pi$
$68$		0			0
$69$	5.89226	+	14.2252i	0.709345	+	1.71251i
$70$		0			0
$71$	1.19465	−	1.19465i	0.141779	−	0.141779i	−0.632655	−	0.774434i	$-0.718035\pi$
$71$	1.19465	−	1.19465i	0.141779	−	0.141779i	0.774434	+	0.632655i	$0.218035\pi$
$72$		0			0
$73$	0.643585	+	0.643585i	0.0753259	+	0.0753259i	0.743766	−	0.668440i	$-0.233038\pi$
$73$	0.643585	+	0.643585i	0.0753259	+	0.0753259i	−0.668440	+	0.743766i	$0.733038\pi$
$74$		0			0
$75$	−2.67164	+	1.10663i	−0.308495	+	0.127783i
$76$		0			0
$77$	−3.02674	+	7.30719i	−0.344929	+	0.832731i
$78$		0			0
$79$		−	14.7962i		−	1.66470i	−0.554252	−	0.832349i	$-0.686996\pi$
$79$		−	14.7962i		−	1.66470i	0.554252	−	0.832349i	$-0.313004\pi$
$80$		0			0
$81$			3.66742i			0.407491i
$82$		0			0
$83$	−3.70380	+	8.94176i	−0.406545	+	0.981485i	0.579495	+	0.814976i	$0.303250\pi$
$83$	−3.70380	+	8.94176i	−0.406545	+	0.981485i	−0.986040	+	0.166510i	$0.946750\pi$
$84$		0			0
$85$	1.63728	−	0.678182i	0.177587	−	0.0735591i
$86$		0			0
$87$	−1.22976	−	1.22976i	−0.131845	−	0.131845i
$88$		0			0
$89$	4.26736	−	4.26736i	0.452340	−	0.452340i	−0.443791	−	0.896130i	$-0.646367\pi$
$89$	4.26736	−	4.26736i	0.452340	−	0.452340i	0.896130	+	0.443791i	$0.146367\pi$
$90$		0			0
$91$	7.50287	+	18.1135i	0.786515	+	1.89881i
$92$		0			0
$93$	−11.0511	−	4.57753i	−1.14595	−	0.474667i
$94$		0			0
$95$	−3.56558			−0.365820
$96$		0			0
$97$	2.38217			0.241873			0.120937	−	0.992660i	$-0.461410\pi$
$97$	2.38217			0.241873			0.120937	+	0.992660i	$0.461410\pi$
$98$		0			0
$99$	7.73660	+	3.20460i	0.777558	+	0.322075i
$100$		0			0
$101$	1.98285	+	4.78702i	0.197301	+	0.476327i	0.991305	−	0.131586i	$-0.0420070\pi$
$101$	1.98285	+	4.78702i	0.197301	+	0.476327i	−0.794004	+	0.607913i	$0.792007\pi$
$102$		0			0
$103$	12.3064	−	12.3064i	1.21259	−	1.21259i	0.242417	−	0.970172i	$-0.422060\pi$
$103$	12.3064	−	12.3064i	1.21259	−	1.21259i	0.970172	−	0.242417i	$-0.0779402\pi$
$104$		0			0
$105$	−10.3562	−	10.3562i	−1.01066	−	1.01066i
$106$		0			0
$107$	3.65992	−	1.51599i	0.353818	−	0.146556i	−0.198693	−	0.980062i	$-0.563670\pi$
$107$	3.65992	−	1.51599i	0.353818	−	0.146556i	0.552511	+	0.833506i	$0.313670\pi$
$108$		0			0
$109$	2.65821	−	6.41749i	0.254610	−	0.614684i	−0.743955	−	0.668230i	$-0.767052\pi$
$109$	2.65821	−	6.41749i	0.254610	−	0.614684i	0.998565	+	0.0535460i	$0.0170524\pi$
$110$		0			0
$111$			9.36642i			0.889022i
$112$		0			0
$113$			9.72801i			0.915134i	0.889175	+	0.457567i	$0.151279\pi$
$113$			9.72801i			0.915134i	−0.889175	+	0.457567i	$0.848721\pi$
$114$		0			0
$115$	−2.03760	+	4.91920i	−0.190007	+	0.458718i
$116$		0			0
$117$	19.1780	−	7.94379i	1.77301	−	0.734403i
$118$		0			0
$119$	6.34663	+	6.34663i	0.581795	+	0.581795i
$120$		0			0
$121$	−6.05372	+	6.05372i	−0.550338	+	0.550338i
$122$		0			0
$123$	1.87856	+	4.53524i	0.169384	+	0.408929i
$124$		0			0
$125$	−0.923880	−	0.382683i	−0.0826343	−	0.0342282i
$126$		0			0
$127$	12.9947			1.15309			0.576545	−	0.817066i	$-0.304401\pi$
$127$	12.9947			1.15309			0.576545	+	0.817066i	$0.304401\pi$
$128$		0			0
$129$	13.5512			1.19311
$130$		0			0
$131$	−14.2428	−	5.89958i	−1.24440	−	0.515448i	−0.339315	−	0.940673i	$-0.610195\pi$
$131$	−14.2428	−	5.89958i	−1.24440	−	0.515448i	−0.905088	+	0.425225i	$0.860195\pi$
$132$		0			0
$133$	−6.91069	−	16.6839i	−0.599233	−	1.44668i
$134$		0			0
$135$	−4.83041	+	4.83041i	−0.415736	+	0.415736i
$136$		0			0
$137$	−7.44512	−	7.44512i	−0.636080	−	0.636080i	0.313507	−	0.949586i	$-0.398496\pi$
$137$	−7.44512	−	7.44512i	−0.636080	−	0.636080i	−0.949586	+	0.313507i	$0.898496\pi$
$138$		0			0
$139$	−20.1856	+	8.36117i	−1.71212	+	0.709185i	−0.712150	+	0.702027i	$0.752278\pi$
$139$	−20.1856	+	8.36117i	−1.71212	+	0.709185i	−0.999974	+	0.00715788i	$0.997722\pi$
$140$		0			0
$141$	7.16461	−	17.2969i	0.603369	−	1.45666i
$142$		0			0
$143$		−	6.04532i		−	0.505535i
$144$		0			0
$145$		−	0.601415i		−	0.0499448i
$146$		0			0
$147$	20.6397	−	49.8287i	1.70234	−	4.10980i
$148$		0			0
$149$	−14.6495	+	6.06803i	−1.20013	+	0.497112i	−0.891042	−	0.453920i	$-0.850025\pi$
$149$	−14.6495	+	6.06803i	−1.20013	+	0.497112i	−0.309092	+	0.951032i	$0.600025\pi$
$150$		0			0
$151$	−12.1048	−	12.1048i	−0.985071	−	0.985071i	0.0148188	−	0.999890i	$-0.495283\pi$
$151$	−12.1048	−	12.1048i	−0.985071	−	0.985071i	−0.999890	+	0.0148188i	$0.995283\pi$
$152$		0			0
$153$	6.71959	−	6.71959i	0.543247	−	0.543247i
$154$		0			0
$155$	−1.58295	−	3.82158i	−0.127146	−	0.306957i
$156$		0			0
$157$	8.53585	+	3.53566i	0.681235	+	0.282177i	0.696343	−	0.717709i	$-0.254809\pi$
$157$	8.53585	+	3.53566i	0.681235	+	0.282177i	−0.0151081	+	0.999886i	$0.504809\pi$
$158$		0			0
$159$	25.0117			1.98356
$160$		0			0
$161$	−26.9669			−2.12529
$162$		0			0
$163$	0.0791457	+	0.0327832i	0.00619917	+	0.00256778i	0.385781	−	0.922590i	$-0.373932\pi$
$163$	0.0791457	+	0.0327832i	0.00619917	+	0.00256778i	−0.379582	+	0.925158i	$0.623932\pi$
$164$		0			0
$165$	1.72817	+	4.17217i	0.134538	+	0.324803i
$166$		0			0
$167$	−4.55556	+	4.55556i	−0.352520	+	0.352520i	−0.861046	−	0.508527i	$-0.830190\pi$
$167$	−4.55556	+	4.55556i	−0.352520	+	0.352520i	0.508527	+	0.861046i	$0.330190\pi$
$168$		0			0
$169$	−1.40399	−	1.40399i	−0.107999	−	0.107999i
$170$		0			0
$171$	−17.6643	+	7.31680i	−1.35082	+	0.559530i
$172$		0			0
$173$	−5.61219	+	13.5490i	−0.426687	+	1.03011i	0.553645	+	0.832753i	$0.313237\pi$
$173$	−5.61219	+	13.5490i	−0.426687	+	1.03011i	−0.980331	+	0.197359i	$0.936763\pi$
$174$		0			0
$175$		−	5.06468i		−	0.382854i
$176$		0			0
$177$		−	17.5224i		−	1.31707i
$178$		0			0
$179$	−3.31630	+	8.00625i	−0.247872	+	0.598416i	−0.998023	−	0.0628509i	$-0.979981\pi$
$179$	−3.31630	+	8.00625i	−0.247872	+	0.598416i	0.750151	+	0.661266i	$0.229981\pi$
$180$		0			0
$181$	1.13980	−	0.472122i	0.0847209	−	0.0350926i	−0.339921	−	0.940454i	$-0.610400\pi$
$181$	1.13980	−	0.472122i	0.0847209	−	0.0350926i	0.424641	+	0.905362i	$0.360400\pi$
$182$		0			0
$183$	−1.41067	−	1.41067i	−0.104280	−	0.104280i
$184$		0			0
$185$	−2.29032	+	2.29032i	−0.168388	+	0.168388i
$186$		0			0
$187$	−1.05908	−	2.55685i	−0.0774477	−	0.186975i
$188$		0			0
$189$	−31.9644	−	13.2401i	−2.32507	−	0.963075i
$190$		0			0
$191$	−3.99144			−0.288810			−0.144405	−	0.989519i	$-0.546127\pi$
$191$	−3.99144			−0.288810			−0.144405	+	0.989519i	$0.546127\pi$
$192$		0			0
$193$	24.0690			1.73252			0.866262	−	0.499590i	$-0.166516\pi$
$193$	24.0690			1.73252			0.866262	+	0.499590i	$0.166516\pi$
$194$		0			0
$195$	10.3422	+	4.28390i	0.740623	+	0.306776i
$196$		0			0
$197$	0.723996	+	1.74788i	0.0515826	+	0.124531i	0.947570	−	0.319548i	$-0.103531\pi$
$197$	0.723996	+	1.74788i	0.0515826	+	0.124531i	−0.895988	+	0.444079i	$0.853531\pi$
$198$		0			0
$199$	−2.78983	+	2.78983i	−0.197766	+	0.197766i	−0.799041	−	0.601276i	$-0.794659\pi$
$199$	−2.78983	+	2.78983i	−0.197766	+	0.197766i	0.601276	+	0.799041i	$0.294659\pi$
$200$		0			0
$201$	11.1306	+	11.1306i	0.785093	+	0.785093i
$202$		0			0
$203$	2.81411	−	1.16564i	0.197512	−	0.0818121i
$204$		0			0
$205$	−0.649623	+	1.56833i	−0.0453717	+	0.109537i
$206$		0			0
$207$			28.5516i			1.98447i
$208$		0			0
$209$			5.56818i			0.385159i
$210$		0			0
$211$	10.3584	−	25.0075i	0.713105	−	1.72159i	0.0210113	−	0.999779i	$-0.493311\pi$
$211$	10.3584	−	25.0075i	0.713105	−	1.72159i	0.692093	−	0.721808i	$-0.256689\pi$
$212$		0			0
$213$	4.51372	−	1.86964i	0.309275	−	0.128106i
$214$		0			0
$215$	3.31359	+	3.31359i	0.225985	+	0.225985i
$216$		0			0
$217$	14.8137	−	14.8137i	1.00562	−	1.00562i
$218$		0			0
$219$	1.00722	+	2.43164i	0.0680615	+	0.164315i
$220$		0			0
$221$	−6.33808	−	2.62532i	−0.426346	−	0.176598i
$222$		0			0
$223$	−8.45988			−0.566515			−0.283258	−	0.959044i	$-0.591415\pi$
$223$	−8.45988			−0.566515			−0.283258	+	0.959044i	$0.591415\pi$
$224$		0			0
$225$	−5.36231			−0.357487
$226$		0			0
$227$	−24.4413	−	10.1239i	−1.62223	−	0.671949i	−0.627899	−	0.778295i	$-0.716085\pi$
$227$	−24.4413	−	10.1239i	−1.62223	−	0.671949i	−0.994329	+	0.106346i	$0.966085\pi$
$228$		0			0
$229$	−0.348963	−	0.842472i	−0.0230602	−	0.0556721i	0.911930	−	0.410346i	$-0.134592\pi$
$229$	−0.348963	−	0.842472i	−0.0230602	−	0.0556721i	−0.934990	+	0.354674i	$0.884592\pi$
$230$		0			0
$231$	−16.1727	+	16.1727i	−1.06409	+	1.06409i
$232$		0			0
$233$	−13.4810	−	13.4810i	−0.883167	−	0.883167i	0.110688	−	0.993855i	$-0.464695\pi$
$233$	−13.4810	−	13.4810i	−0.883167	−	0.883167i	−0.993855	+	0.110688i	$0.964695\pi$
$234$		0			0
$235$	5.98143	−	2.47759i	0.390186	−	0.161620i
$236$		0			0
$237$	16.3739	−	39.5300i	1.06360	−	2.56775i
$238$		0			0
$239$			22.6901i			1.46770i	0.679311	+	0.733851i	$0.262279\pi$
$239$			22.6901i			1.46770i	−0.679311	+	0.733851i	$0.737721\pi$
$240$		0			0
$241$		−	8.81848i		−	0.568048i	−0.958817	−	0.284024i	$-0.908330\pi$
$241$		−	8.81848i		−	0.568048i	0.958817	−	0.284024i	$-0.0916696\pi$
$242$		0			0
$243$	3.78413	−	9.13570i	0.242752	−	0.586055i
$244$		0			0
$245$	17.2312	−	7.13741i	1.10086	−	0.455993i
$246$		0			0
$247$	9.76003	+	9.76003i	0.621016	+	0.621016i
$248$		0			0
$249$	−19.7904	+	19.7904i	−1.25417	+	1.25417i
$250$		0			0
$251$	6.62699	+	15.9990i	0.418292	+	1.00985i	0.982842	+	0.184447i	$0.0590495\pi$
$251$	6.62699	+	15.9990i	0.418292	+	1.00985i	−0.564551	+	0.825398i	$0.690951\pi$
$252$		0			0
$253$	7.68206	+	3.18201i	0.482967	+	0.200051i
$254$		0			0
$255$	5.12471			0.320922
$256$		0			0
$257$	−1.02689			−0.0640557			−0.0320279	−	0.999487i	$-0.510197\pi$
$257$	−1.02689			−0.0640557			−0.0320279	+	0.999487i	$0.510197\pi$
$258$		0			0
$259$	−15.1558	−	6.27772i	−0.941734	−	0.390079i
$260$		0			0
$261$	−1.23414	−	2.97948i	−0.0763915	−	0.184425i
$262$		0			0
$263$	7.63654	−	7.63654i	0.470889	−	0.470889i	−0.431313	−	0.902202i	$-0.641950\pi$
$263$	7.63654	−	7.63654i	0.470889	−	0.470889i	0.902202	+	0.431313i	$0.141950\pi$
$264$		0			0
$265$	6.11597	+	6.11597i	0.375701	+	0.375701i
$266$		0			0
$267$	16.1233	−	6.67848i	0.986728	−	0.408716i
$268$		0			0
$269$	−4.99718	+	12.0643i	−0.304683	+	0.735571i	0.695177	+	0.718839i	$0.255326\pi$
$269$	−4.99718	+	12.0643i	−0.304683	+	0.735571i	−0.999860	+	0.0167318i	$0.994674\pi$
$270$		0			0
$271$		−	15.2591i		−	0.926922i	−0.886117	−	0.463461i	$-0.846607\pi$
$271$		−	15.2591i		−	0.926922i	0.886117	−	0.463461i	$-0.153393\pi$
$272$		0			0
$273$			56.6958i			3.43139i
$274$		0			0
$275$	−0.597617	+	1.44277i	−0.0360377	+	0.0870026i
$276$		0			0
$277$	−12.5699	+	5.20663i	−0.755253	+	0.312836i	−0.726883	−	0.686762i	$-0.759032\pi$
$277$	−12.5699	+	5.20663i	−0.755253	+	0.312836i	−0.0283700	+	0.999597i	$0.509032\pi$
$278$		0			0
$279$	−15.6843	−	15.6843i	−0.938994	−	0.938994i
$280$		0			0
$281$	−23.2692	+	23.2692i	−1.38812	+	1.38812i	−0.558861	+	0.829262i	$0.688761\pi$
$281$	−23.2692	+	23.2692i	−1.38812	+	1.38812i	−0.829262	+	0.558861i	$0.811239\pi$
$282$		0			0
$283$	−4.08691	−	9.86668i	−0.242942	−	0.586513i	0.754631	−	0.656150i	$-0.227816\pi$
$283$	−4.08691	−	9.86668i	−0.242942	−	0.586513i	−0.997572	+	0.0696364i	$0.977816\pi$
$284$		0			0
$285$	−9.52595	−	3.94578i	−0.564268	−	0.233728i
$286$		0			0
$287$	−8.59753			−0.507496
$288$		0			0
$289$	13.8594			0.815259
$290$		0			0
$291$	6.36432	+	2.63619i	0.373083	+	0.154536i
$292$		0			0
$293$	3.13910	+	7.57847i	0.183388	+	0.442739i	0.988661	−	0.150166i	$-0.0479809\pi$
$293$	3.13910	+	7.57847i	0.183388	+	0.442739i	−0.805272	+	0.592905i	$0.797981\pi$
$294$		0			0
$295$	4.28466	−	4.28466i	0.249463	−	0.249463i
$296$		0			0
$297$	7.54341	+	7.54341i	0.437713	+	0.437713i
$298$		0			0
$299$	19.0428	−	7.88778i	1.10127	−	0.456162i
$300$		0			0
$301$	−9.08250	+	21.9271i	−0.523506	+	1.26386i
$302$		0			0
$303$			14.9835i			0.860780i
$304$		0			0
$305$		−	0.689885i		−	0.0395027i
$306$		0			0
$307$	−9.09448	+	21.9560i	−0.519049	+	1.25310i	0.419439	+	0.907784i	$0.362227\pi$
$307$	−9.09448	+	21.9560i	−0.519049	+	1.25310i	−0.938488	+	0.345312i	$0.887773\pi$
$308$		0			0
$309$	46.4971	−	19.2597i	2.64513	−	1.09565i
$310$		0			0
$311$	5.21696	+	5.21696i	0.295827	+	0.295827i	0.839377	−	0.543550i	$-0.182920\pi$
$311$	5.21696	+	5.21696i	0.295827	+	0.295827i	−0.543550	+	0.839377i	$0.682920\pi$
$312$		0			0
$313$	1.93639	−	1.93639i	0.109451	−	0.109451i	−0.650260	−	0.759711i	$-0.725340\pi$
$313$	1.93639	−	1.93639i	0.109451	−	0.109451i	0.759711	+	0.650260i	$0.225340\pi$
$314$		0			0
$315$	−10.3931	−	25.0910i	−0.585582	−	1.41372i
$316$		0			0
$317$	25.5622	+	10.5882i	1.43572	+	0.594693i	0.958756	−	0.284232i	$-0.0917385\pi$
$317$	25.5622	+	10.5882i	1.43572	+	0.594693i	0.476960	+	0.878925i	$0.341739\pi$
$318$		0			0
$319$	−0.939198			−0.0525850
$320$		0			0
$321$	11.4556			0.639391
$322$		0			0
$323$	5.83783	+	2.41811i	0.324826	+	0.134547i
$324$		0			0
$325$	1.48141	+	3.57644i	0.0821739	+	0.198385i
$326$		0			0
$327$	14.2036	−	14.2036i	0.785459	−	0.785459i
$328$		0			0
$329$	23.1861	+	23.1861i	1.27829	+	1.27829i
$330$		0			0
$331$	−22.0175	+	9.11995i	−1.21019	+	0.501278i	−0.894279	−	0.447510i	$-0.852311\pi$
$331$	−22.0175	+	9.11995i	−1.21019	+	0.501278i	−0.315913	+	0.948788i	$0.602311\pi$
$332$		0			0
$333$	−6.64664	+	16.0464i	−0.364234	+	0.879338i
$334$		0			0
$335$			5.44341i			0.297405i
$336$		0			0
$337$			6.52854i			0.355632i	0.984064	+	0.177816i	$0.0569032\pi$
$337$			6.52854i			0.355632i	−0.984064	+	0.177816i	$0.943097\pi$
$338$		0			0
$339$	−10.7653	+	25.9898i	−0.584692	+	1.41157i
$340$		0			0
$341$	−5.96797	+	2.47201i	−0.323184	+	0.133867i
$342$		0			0
$343$	41.7252	+	41.7252i	2.25295	+	2.25295i
$344$		0			0
$345$	−10.8875	+	10.8875i	−0.586162	+	0.586162i
$346$		0			0
$347$	−8.04690	−	19.4269i	−0.431980	−	1.04289i	−0.978648	−	0.205543i	$-0.934104\pi$
$347$	−8.04690	−	19.4269i	−0.431980	−	1.04289i	0.546668	−	0.837349i	$-0.315896\pi$
$348$		0			0
$349$	−6.21184	−	2.57303i	−0.332512	−	0.137731i	0.210180	−	0.977663i	$-0.432595\pi$
$349$	−6.21184	−	2.57303i	−0.332512	−	0.137731i	−0.542692	+	0.839932i	$0.682595\pi$
$350$		0			0
$351$	26.4445			1.41150
$352$		0			0
$353$	−30.2690			−1.61106			−0.805529	−	0.592556i	$-0.798119\pi$
$353$	−30.2690			−1.61106			−0.805529	+	0.592556i	$0.798119\pi$
$354$		0			0
$355$	1.56089	+	0.646541i	0.0828433	+	0.0343148i
$356$		0			0
$357$	9.93255	+	23.9793i	0.525686	+	1.26912i
$358$		0			0
$359$	−16.5725	+	16.5725i	−0.874663	+	0.874663i	−0.992976	−	0.118313i	$-0.962251\pi$
$359$	−16.5725	+	16.5725i	−0.874663	+	0.874663i	0.118313	+	0.992976i	$0.462251\pi$
$360$		0			0
$361$	4.44534	+	4.44534i	0.233965	+	0.233965i
$362$		0			0
$363$	−22.8726	+	9.47415i	−1.20050	+	0.497264i
$364$		0			0
$365$	−0.348306	+	0.840884i	−0.0182311	+	0.0440139i
$366$		0			0
$367$			7.18520i			0.375064i	0.982258	+	0.187532i	$0.0600489\pi$
$367$			7.18520i			0.375064i	−0.982258	+	0.187532i	$0.939951\pi$
$368$		0			0
$369$			9.10277i			0.473871i
$370$		0			0
$371$	−16.7638	+	40.4714i	−0.870332	+	2.10117i
$372$		0			0
$373$	−28.4632	+	11.7899i	−1.47377	+	0.610455i	−0.967715	−	0.252046i	$-0.918897\pi$
$373$	−28.4632	+	11.7899i	−1.47377	+	0.610455i	−0.506054	+	0.862502i	$0.668897\pi$
$374$		0			0
$375$	−2.04479	−	2.04479i	−0.105592	−	0.105592i
$376$		0			0
$377$	−1.64625	+	1.64625i	−0.0847861	+	0.0847861i
$378$		0			0
$379$	4.77555	+	11.5292i	0.245303	+	0.592215i	0.997794	−	0.0663882i	$-0.0211476\pi$
$379$	4.77555	+	11.5292i	0.245303	+	0.592215i	−0.752490	+	0.658603i	$0.771148\pi$
$380$		0			0
$381$	34.7171	+	14.3803i	1.77861	+	0.736724i
$382$		0			0
$383$	17.8351			0.911333			0.455667	−	0.890150i	$-0.349401\pi$
$383$	17.8351			0.911333			0.455667	+	0.890150i	$0.349401\pi$
$384$		0			0
$385$	−7.90924			−0.403092
$386$		0			0
$387$	23.2156	+	9.61624i	1.18012	+	0.488821i
$388$		0			0
$389$	−9.78830	−	23.6311i	−0.496287	−	1.19814i	−0.951469	−	0.307744i	$-0.900426\pi$
$389$	−9.78830	−	23.6311i	−0.496287	−	1.19814i	0.455183	−	0.890398i	$-0.349574\pi$
$390$		0			0
$391$	6.67222	−	6.67222i	0.337429	−	0.337429i
$392$		0			0
$393$	−31.5231	−	31.5231i	−1.59013	−	1.59013i
$394$		0			0
$395$	13.6699	−	5.66224i	0.687805	−	0.284898i
$396$		0			0
$397$	−0.457502	+	1.10451i	−0.0229614	+	0.0554336i	−0.934944	−	0.354794i	$-0.884551\pi$
$397$	−0.457502	+	1.10451i	−0.0229614	+	0.0554336i	0.911983	+	0.410228i	$0.134551\pi$
$398$		0			0
$399$		−	52.2209i		−	2.61432i
$400$		0			0
$401$		−	12.6359i		−	0.631007i	−0.948924	−	0.315504i	$-0.897827\pi$
$401$		−	12.6359i		−	0.631007i	0.948924	−	0.315504i	$-0.102173\pi$
$402$		0			0
$403$	−6.12779	+	14.7938i	−0.305247	+	0.736931i
$404$		0			0
$405$	−3.38825	+	1.40346i	−0.168363	+	0.0697384i
$406$		0			0
$407$	3.57667	+	3.57667i	0.177289	+	0.177289i
$408$		0			0
$409$	−3.79308	+	3.79308i	−0.187556	+	0.187556i	−0.794639	−	0.607083i	$-0.792340\pi$
$409$	−3.79308	+	3.79308i	−0.187556	+	0.187556i	0.607083	+	0.794639i	$0.292340\pi$
$410$		0			0
$411$	−11.6517	−	28.1297i	−0.574736	−	1.38754i
$412$		0			0
$413$	28.3530	+	11.7442i	1.39516	+	0.577894i
$414$		0			0
$415$	−9.67849			−0.475098
$416$		0			0
$417$	−63.1816			−3.09401
$418$		0			0
$419$	17.1700	+	7.11205i	0.838809	+	0.347446i	0.760384	−	0.649474i	$-0.225011\pi$
$419$	17.1700	+	7.11205i	0.838809	+	0.347446i	0.0784254	+	0.996920i	$0.475011\pi$
$420$		0			0
$421$	−1.28657	−	3.10606i	−0.0627037	−	0.151380i	0.889422	−	0.457087i	$-0.151107\pi$
$421$	−1.28657	−	3.10606i	−0.0627037	−	0.151380i	−0.952126	+	0.305707i	$0.901107\pi$
$422$		0			0
$423$	24.5486	−	24.5486i	1.19359	−	1.19359i
$424$		0			0
$425$	1.25312	+	1.25312i	0.0607851	+	0.0607851i
$426$		0			0
$427$	3.22807	−	1.33711i	0.156217	−	0.0647074i
$428$		0			0
$429$	6.68994	−	16.1509i	0.322993	−	0.779775i
$430$		0			0
$431$			11.2076i			0.539852i	0.962881	+	0.269926i	$0.0869993\pi$
$431$			11.2076i			0.539852i	−0.962881	+	0.269926i	$0.913001\pi$
$432$		0			0
$433$		−	29.1033i		−	1.39862i	−0.714820	−	0.699309i	$-0.753491\pi$
$433$		−	29.1033i		−	1.39862i	0.714820	−	0.699309i	$-0.246509\pi$
$434$		0			0
$435$	0.665544	−	1.60677i	0.0319104	−	0.0770385i
$436$		0			0
$437$	−17.5398	+	7.26522i	−0.839042	+	0.347542i
$438$		0			0
$439$	−25.2635	−	25.2635i	−1.20576	−	1.20576i	−0.972387	−	0.233374i	$-0.925023\pi$
$439$	−25.2635	−	25.2635i	−1.20576	−	1.20576i	−0.233374	−	0.972387i	$-0.574977\pi$
$440$		0			0
$441$	70.7193	−	70.7193i	3.36758	−	3.36758i
$442$		0			0
$443$	8.01806	+	19.3573i	0.380949	+	0.919693i	0.991783	+	0.127934i	$0.0408346\pi$
$443$	8.01806	+	19.3573i	0.380949	+	0.919693i	−0.610833	+	0.791759i	$0.709165\pi$
$444$		0			0
$445$	5.57558	+	2.30948i	0.264308	+	0.109480i
$446$		0			0
$447$	−45.8533			−2.16879
$448$		0			0
$449$	16.0399			0.756968			0.378484	−	0.925608i	$-0.376445\pi$
$449$	16.0399			0.756968			0.378484	+	0.925608i	$0.376445\pi$
$450$		0			0
$451$	2.44918	+	1.01448i	0.115327	+	0.0477701i
$452$		0			0
$453$	−18.9441	−	45.7351i	−0.890071	−	2.14882i
$454$		0			0
$455$	−13.8635	+	13.8635i	−0.649931	+	0.649931i
$456$		0			0
$457$	−19.3203	−	19.3203i	−0.903763	−	0.903763i	0.0919959	−	0.995759i	$-0.470675\pi$
$457$	−19.3203	−	19.3203i	−0.903763	−	0.903763i	−0.995759	+	0.0919959i	$0.970675\pi$
$458$		0			0
$459$	11.1846	−	4.63282i	0.522053	−	0.216242i
$460$		0			0
$461$	9.81020	−	23.6839i	0.456906	−	1.10307i	−0.512737	−	0.858546i	$-0.671368\pi$
$461$	9.81020	−	23.6839i	0.456906	−	1.10307i	0.969643	−	0.244524i	$-0.0786316\pi$
$462$		0			0
$463$		−	30.7713i		−	1.43006i	−0.699093	−	0.715031i	$-0.746413\pi$
$463$		−	30.7713i		−	1.43006i	0.699093	−	0.715031i	$-0.253587\pi$
$464$		0			0
$465$		−	11.9617i		−	0.554708i
$466$		0			0
$467$	−12.1825	+	29.4111i	−0.563738	+	1.36098i	0.343018	+	0.939329i	$0.388551\pi$
$467$	−12.1825	+	29.4111i	−0.563738	+	1.36098i	−0.906756	+	0.421655i	$0.861449\pi$
$468$		0			0
$469$	−25.4705	+	10.5502i	−1.17612	+	0.487165i
$470$		0			0
$471$	18.8921	+	18.8921i	0.870500	+	0.870500i
$472$		0			0
$473$	5.17466	−	5.17466i	0.237931	−	0.237931i
$474$		0			0
$475$	−1.36449	−	3.29416i	−0.0626070	−	0.151147i
$476$		0			0
$477$	42.8497	+	17.7489i	1.96195	+	0.812667i
$478$		0			0
$479$	31.2492			1.42781			0.713906	−	0.700241i	$-0.246924\pi$
$479$	31.2492			1.42781			0.713906	+	0.700241i	$0.246924\pi$
$480$		0			0
$481$	12.5385			0.571708
$482$		0			0
$483$	−72.0459	−	29.8424i	−3.27820	−	1.35788i
$484$		0			0
$485$	0.911619	+	2.20084i	0.0413945	+	0.0999351i
$486$		0			0
$487$	−12.9492	+	12.9492i	−0.586782	+	0.586782i	−0.936759	−	0.349976i	$-0.886190\pi$
$487$	−12.9492	+	12.9492i	−0.586782	+	0.586782i	0.349976	+	0.936759i	$0.386190\pi$
$488$		0			0
$489$	0.175170	+	0.175170i	0.00792147	+	0.00792147i
$490$		0			0
$491$	15.3268	−	6.34858i	0.691690	−	0.286508i	−0.00901392	−	0.999959i	$-0.502869\pi$
$491$	15.3268	−	6.34858i	0.691690	−	0.286508i	0.700704	+	0.713452i	$0.252869\pi$
$492$		0			0
$493$	−0.407868	+	0.984681i	−0.0183695	+	0.0443478i
$494$		0			0
$495$			8.37404i			0.376385i
$496$		0			0
$497$			8.55673i			0.383822i
$498$		0			0
$499$	−1.81479	+	4.38129i	−0.0812411	+	0.196133i	−0.959281	−	0.282455i	$-0.908851\pi$
$499$	−1.81479	+	4.38129i	−0.0812411	+	0.196133i	0.878040	+	0.478588i	$0.158851\pi$
$500$		0			0
$501$	−17.2121	+	7.12951i	−0.768982	+	0.318523i
$502$		0			0
$503$	−29.6810	−	29.6810i	−1.32341	−	1.32341i	−0.910997	−	0.412414i	$-0.864686\pi$
$503$	−29.6810	−	29.6810i	−1.32341	−	1.32341i	−0.412414	−	0.910997i	$-0.635314\pi$
$504$		0			0
$505$	−3.66383	+	3.66383i	−0.163038	+	0.163038i
$506$		0			0
$507$	−2.19726	−	5.30465i	−0.0975836	−	0.235588i
$508$		0			0
$509$	−4.38524	−	1.81643i	−0.194372	−	0.0805117i	0.283374	−	0.959009i	$-0.408546\pi$
$509$	−4.38524	−	1.81643i	−0.194372	−	0.0805117i	−0.477746	+	0.878498i	$0.658546\pi$
$510$		0			0
$511$	−4.60970			−0.203921
$512$		0			0
$513$	−24.3573			−1.07540
$514$		0			0
$515$	16.0791	+	6.66020i	0.708531	+	0.293483i
$516$		0			0
$517$	−3.86913	−	9.34090i	−0.170164	−	0.410812i
$518$		0			0
$519$	−29.9875	+	29.9875i	−1.31631	+	1.31631i
$520$		0			0
$521$	6.91643	+	6.91643i	0.303014	+	0.303014i	0.842192	−	0.539178i	$-0.181265\pi$
$521$	6.91643	+	6.91643i	0.303014	+	0.303014i	−0.539178	+	0.842192i	$0.681265\pi$
$522$		0			0
$523$	28.3471	−	11.7417i	1.23953	−	0.513430i	0.335963	−	0.941875i	$-0.390938\pi$
$523$	28.3471	−	11.7417i	1.23953	−	0.513430i	0.903568	+	0.428445i	$0.140938\pi$
$524$		0			0
$525$	5.60473	−	13.5310i	0.244610	−	0.590542i
$526$		0			0
$527$			7.33051i			0.319322i
$528$		0			0
$529$			5.35033i			0.232623i
$530$		0			0
$531$	12.4343	−	30.0192i	0.539604	−	1.30272i
$532$		0			0
$533$	6.07119	−	2.51477i	0.262972	−	0.108927i
$534$		0			0
$535$	2.80118	+	2.80118i	0.121106	+	0.121106i
$536$		0			0
$537$	−17.7199	+	17.7199i	−0.764672	+	0.764672i
$538$		0			0
$539$	−11.1461	−	26.9091i	−0.480098	−	1.15906i
$540$		0			0
$541$	−14.4946	−	6.00385i	−0.623171	−	0.258126i	0.0486776	−	0.998815i	$-0.484499\pi$
$541$	−14.4946	−	6.00385i	−0.623171	−	0.258126i	−0.671848	+	0.740689i	$0.734499\pi$
$542$		0			0
$543$	3.56761			0.153101
$544$		0			0
$545$	6.94624			0.297544
$546$		0			0
$547$	8.27295	+	3.42677i	0.353726	+	0.146518i	0.552469	−	0.833534i	$-0.313686\pi$
$547$	8.27295	+	3.42677i	0.353726	+	0.146518i	−0.198743	+	0.980052i	$0.563686\pi$
$548$		0			0
$549$	−1.41569	−	3.41777i	−0.0604201	−	0.145867i
$550$		0			0
$551$	1.51631	−	1.51631i	0.0645971	−	0.0645971i
$552$		0			0
$553$	52.9890	+	52.9890i	2.25332	+	2.25332i
$554$		0			0
$555$	−8.65345	+	3.58438i	−0.367318	+	0.152148i
$556$		0			0
$557$	−5.92630	+	14.3073i	−0.251105	+	0.606222i	−0.998294	−	0.0583904i	$-0.981403\pi$
$557$	−5.92630	+	14.3073i	−0.251105	+	0.606222i	0.747189	+	0.664612i	$0.231403\pi$
$558$		0			0
$559$		−	18.1405i		−	0.767263i
$560$		0			0
$561$		−	8.00300i		−	0.337887i
$562$		0			0
$563$	7.70850	−	18.6100i	0.324874	−	0.784316i	−0.674083	−	0.738656i	$-0.735461\pi$
$563$	7.70850	−	18.6100i	0.324874	−	0.784316i	0.998957	−	0.0456603i	$-0.0145392\pi$
$564$		0			0
$565$	−8.98751	+	3.72275i	−0.378107	+	0.156617i
$566$		0			0
$567$	−13.1340	−	13.1340i	−0.551576	−	0.551576i
$568$		0			0
$569$	−23.1752	+	23.1752i	−0.971556	+	0.971556i	−0.999607	−	0.0280502i	$-0.991070\pi$
$569$	−23.1752	+	23.1752i	−0.971556	+	0.971556i	0.0280502	+	0.999607i	$0.491070\pi$
$570$		0			0
$571$	1.61580	+	3.90088i	0.0676189	+	0.163247i	0.954076	−	0.299564i	$-0.0968411\pi$
$571$	1.61580	+	3.90088i	0.0676189	+	0.163247i	−0.886457	+	0.462810i	$0.846841\pi$
$572$		0			0
$573$	−10.6637	−	4.41705i	−0.445482	−	0.184525i
$574$		0			0
$575$	−5.32450			−0.222047
$576$		0			0
$577$	−6.75454			−0.281195			−0.140598	−	0.990067i	$-0.544902\pi$
$577$	−6.75454			−0.281195			−0.140598	+	0.990067i	$0.544902\pi$
$578$		0			0
$579$	64.3037	+	26.6355i	2.67237	+	1.10693i
$580$		0			0
$581$	−18.7585	−	45.2871i	−0.778235	−	1.87883i
$582$		0			0
$583$	9.55100	−	9.55100i	0.395562	−	0.395562i
$584$		0			0
$585$	14.6782	+	14.6782i	0.606869	+	0.606869i
$586$		0			0
$587$	−10.1167	+	4.19048i	−0.417561	+	0.172959i	−0.581564	−	0.813500i	$-0.697559\pi$
$587$	−10.1167	+	4.19048i	−0.417561	+	0.172959i	0.164003	+	0.986460i	$0.447559\pi$
$588$		0			0
$589$	5.64414	−	13.6262i	0.232563	−	0.561456i
$590$		0			0
$591$			5.47091i			0.225043i
$592$		0			0
$593$		−	44.8233i		−	1.84067i	−0.391126	−	0.920337i	$-0.627914\pi$
$593$		−	44.8233i		−	1.84067i	0.391126	−	0.920337i	$-0.372086\pi$
$594$		0			0
$595$	−3.43477	+	8.29227i	−0.140812	+	0.339950i
$596$		0			0
$597$	−10.5407	+	4.36611i	−0.431403	+	0.178693i
$598$		0			0
$599$	−19.9703	−	19.9703i	−0.815963	−	0.815963i	0.169557	−	0.985520i	$-0.445766\pi$
$599$	−19.9703	−	19.9703i	−0.815963	−	0.815963i	−0.985520	+	0.169557i	$0.945766\pi$
$600$		0			0
$601$	5.11580	−	5.11580i	0.208678	−	0.208678i	−0.595028	−	0.803705i	$-0.702859\pi$
$601$	5.11580	−	5.11580i	0.208678	−	0.208678i	0.803705	+	0.595028i	$0.202859\pi$
$602$		0			0
$603$	11.1702	+	26.9673i	0.454887	+	1.09819i
$604$		0			0
$605$	−7.90957	−	3.27625i	−0.321570	−	0.133199i
$606$		0			0
$607$	22.3902			0.908790			0.454395	−	0.890800i	$-0.349855\pi$
$607$	22.3902			0.908790			0.454395	+	0.890800i	$0.349855\pi$
$608$		0			0
$609$	8.80823			0.356928
$610$		0			0
$611$	−23.1548	−	9.59104i	−0.936744	−	0.388012i
$612$		0			0
$613$	12.3276	+	29.7614i	0.497905	+	1.20205i	0.950610	+	0.310389i	$0.100459\pi$
$613$	12.3276	+	29.7614i	0.497905	+	1.20205i	−0.452704	+	0.891661i	$0.649541\pi$
$614$		0			0
$615$	−3.47112	+	3.47112i	−0.139969	+	0.139969i
$616$		0			0
$617$	31.8825	+	31.8825i	1.28354	+	1.28354i	0.938637	+	0.344906i	$0.112089\pi$
$617$	31.8825	+	31.8825i	1.28354	+	1.28354i	0.344906	+	0.938637i	$0.387911\pi$
$618$		0			0
$619$	−3.93246	+	1.62888i	−0.158059	+	0.0654701i	−0.460310	−	0.887758i	$-0.652262\pi$
$619$	−3.93246	+	1.62888i	−0.158059	+	0.0654701i	0.302251	+	0.953228i	$0.402262\pi$
$620$		0			0
$621$	−13.9193	+	33.6042i	−0.558563	+	1.34849i
$622$		0			0
$623$			30.5651i			1.22457i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$		0			0
$627$	−6.16191	+	14.8762i	−0.246083	+	0.594097i
$628$		0			0
$629$	5.30313	−	2.19663i	0.211450	−	0.0875854i
$630$		0			0
$631$	−2.33350	−	2.33350i	−0.0928953	−	0.0928953i	0.659132	−	0.752027i	$-0.270924\pi$
$631$	−2.33350	−	2.33350i	−0.0928953	−	0.0928953i	−0.752027	+	0.659132i	$0.770924\pi$
$632$		0			0
$633$	55.3481	−	55.3481i	2.19989	−	2.19989i
$634$		0			0
$635$	4.97284	+	12.0055i	0.197341	+	0.476424i
$636$		0			0
$637$	−66.7041	−	27.6298i	−2.64291	−	1.09473i
$638$		0			0
$639$	9.05958			0.358391
$640$		0			0
$641$	−10.6572			−0.420935			−0.210468	−	0.977601i	$-0.567499\pi$
$641$	−10.6572			−0.420935			−0.210468	+	0.977601i	$0.567499\pi$
$642$		0			0
$643$	33.5332	+	13.8899i	1.32242	+	0.547764i	0.928483	−	0.371374i	$-0.121113\pi$
$643$	33.5332	+	13.8899i	1.32242	+	0.547764i	0.393936	+	0.919138i	$0.371113\pi$
$644$		0			0
$645$	5.18581	+	12.5196i	0.204191	+	0.492961i
$646$		0			0
$647$	−19.1622	+	19.1622i	−0.753345	+	0.753345i	−0.975102	−	0.221757i	$-0.928821\pi$
$647$	−19.1622	+	19.1622i	−0.753345	+	0.753345i	0.221757	+	0.975102i	$0.428821\pi$
$648$		0			0
$649$	−6.69113	−	6.69113i	−0.262650	−	0.262650i
$650$		0			0
$651$	55.9704	−	23.1837i	2.19365	−	0.908641i
$652$		0			0
$653$	−12.2983	+	29.6907i	−0.481270	+	1.16189i	0.477736	+	0.878503i	$0.341457\pi$
$653$	−12.2983	+	29.6907i	−0.481270	+	1.16189i	−0.959006	+	0.283385i	$0.908543\pi$
$654$		0			0
$655$		−	15.4163i		−	0.602366i
$656$		0			0
$657$			4.88059i			0.190410i
$658$		0			0
$659$	10.3588	−	25.0083i	0.403521	−	0.974186i	−0.583284	−	0.812269i	$-0.698232\pi$
$659$	10.3588	−	25.0083i	0.403521	−	0.974186i	0.986804	−	0.161917i	$-0.0517677\pi$
$660$		0			0
$661$	26.8918	−	11.1390i	1.04597	−	0.433255i	0.207519	−	0.978231i	$-0.433461\pi$
$661$	26.8918	−	11.1390i	1.04597	−	0.433255i	0.838452	+	0.544976i	$0.183461\pi$
$662$		0			0
$663$	−14.0278	−	14.0278i	−0.544796	−	0.544796i
$664$		0			0
$665$	12.7693	−	12.7693i	0.495172	−	0.495172i
$666$		0			0
$667$	−1.22544	−	2.95848i	−0.0474493	−	0.114553i
$668$		0			0
$669$	−22.6018	−	9.36196i	−0.873835	−	0.361954i
$670$		0			0
$671$	−1.07736			−0.0415909
$672$		0			0
$673$	40.7317			1.57009			0.785046	−	0.619437i	$-0.212639\pi$
$673$	40.7317			1.57009			0.785046	+	0.619437i	$0.212639\pi$
$674$		0			0
$675$	−6.31124	−	2.61420i	−0.242920	−	0.100621i
$676$		0			0
$677$	−4.88271	−	11.7879i	−0.187658	−	0.453046i	0.801850	−	0.597525i	$-0.203849\pi$
$677$	−4.88271	−	11.7879i	−0.187658	−	0.453046i	−0.989508	+	0.144479i	$0.953849\pi$
$678$		0			0
$679$	−8.53121	+	8.53121i	−0.327398	+	0.327398i
$680$		0			0
$681$	−54.0951	−	54.0951i	−2.07293	−	2.07293i
$682$		0			0
$683$	6.41400	−	2.65677i	0.245425	−	0.101658i	−0.256580	−	0.966523i	$-0.582596\pi$
$683$	6.41400	−	2.65677i	0.245425	−	0.101658i	0.502005	+	0.864865i	$0.332596\pi$
$684$		0			0
$685$	4.02927	−	9.72752i	0.153950	−	0.371669i
$686$		0			0
$687$		−	2.63696i		−	0.100606i
$688$		0			0
$689$		−	33.4824i		−	1.27558i
$690$		0			0
$691$	0.571505	−	1.37974i	0.0217411	−	0.0524876i	−0.912636	−	0.408773i	$-0.865957\pi$
$691$	0.571505	−	1.37974i	0.0217411	−	0.0524876i	0.934377	+	0.356285i	$0.115957\pi$
$692$		0			0
$693$	−39.1834	+	16.2303i	−1.48845	+	0.616538i
$694$		0			0
$695$	−15.4494	−	15.4494i	−0.586030	−	0.586030i
$696$		0			0
$697$	2.12722	−	2.12722i	0.0805744	−	0.0805744i
$698$		0			0
$699$	−21.0979	−	50.9348i	−0.797995	−	1.92653i
$700$		0			0
$701$	43.4728	+	18.0070i	1.64194	+	0.680115i	0.996492	−	0.0836859i	$-0.0266692\pi$
$701$	43.4728	+	18.0070i	1.64194	+	0.680115i	0.645452	+	0.763801i	$0.276669\pi$
$702$		0			0
$703$	−11.5489			−0.435575
$704$		0			0
$705$	18.7220			0.705113
$706$		0			0
$707$	−24.2447	−	10.0425i	−0.911817	−	0.377687i
$708$		0			0
$709$	8.88934	+	21.4608i	0.333846	+	0.805976i	0.998280	+	0.0586287i	$0.0186728\pi$
$709$	8.88934	+	21.4608i	0.333846	+	0.805976i	−0.664434	+	0.747347i	$0.731327\pi$
$710$		0			0
$711$	56.1029	−	56.1029i	2.10402	−	2.10402i
$712$		0			0
$713$	−15.5737	−	15.5737i	−0.583240	−	0.583240i
$714$		0			0
$715$	5.58515	−	2.31344i	0.208873	−	0.0865179i
$716$		0			0
$717$	−25.1096	+	60.6199i	−0.937734	+	2.26389i
$718$		0			0
$719$			26.5532i			0.990268i	0.868816	+	0.495134i	$0.164881\pi$
$719$			26.5532i			0.990268i	−0.868816	+	0.495134i	$0.835119\pi$
$720$		0			0
$721$			88.1453i			3.28270i
$722$		0			0
$723$	9.75880	−	23.5598i	0.362934	−	0.876199i
$724$		0			0
$725$	0.555635	−	0.230151i	0.0206358	−	0.00854761i
$726$		0			0
$727$	−8.13702	−	8.13702i	−0.301785	−	0.301785i	0.539927	−	0.841712i	$-0.318452\pi$
$727$	−8.13702	−	8.13702i	−0.301785	−	0.301785i	−0.841712	+	0.539927i	$0.818452\pi$
$728$		0			0
$729$	27.9995	−	27.9995i	1.03702	−	1.03702i
$730$		0			0
$731$	−3.17804	−	7.67248i	−0.117544	−	0.283777i
$732$		0			0
$733$	43.2353	+	17.9087i	1.59693	+	0.661472i	0.990978	−	0.134027i	$-0.0427907\pi$
$733$	43.2353	+	17.9087i	1.59693	+	0.661472i	0.605956	+	0.795498i	$0.292791\pi$
$734$		0			0
$735$	53.9342			1.98939
$736$		0			0
$737$	8.50069			0.313127
$738$		0			0
$739$	−8.65398	−	3.58460i	−0.318342	−	0.131862i	0.217790	−	0.975996i	$-0.430115\pi$
$739$	−8.65398	−	3.58460i	−0.318342	−	0.131862i	−0.536132	+	0.844134i	$0.680115\pi$
$740$		0			0
$741$	15.2746	+	36.8760i	0.561125	+	1.35468i
$742$		0			0
$743$	−21.0054	+	21.0054i	−0.770615	+	0.770615i	−0.978214	−	0.207599i	$-0.933435\pi$
$743$	−21.0054	+	21.0054i	−0.770615	+	0.770615i	0.207599	+	0.978214i	$0.433435\pi$
$744$		0			0
$745$	−11.2123	−	11.2123i	−0.410785	−	0.410785i
$746$		0			0
$747$	−47.9484	+	19.8609i	−1.75434	+	0.726672i
$748$		0			0
$749$	−7.67799	+	18.5363i	−0.280548	+	0.677302i
$750$		0			0
$751$		−	6.62510i		−	0.241753i	−0.992668	−	0.120877i	$-0.961429\pi$
$751$		−	6.62510i		−	0.241753i	0.992668	−	0.120877i	$-0.0385706\pi$
$752$		0			0
$753$			50.0771i			1.82491i
$754$		0			0
$755$	6.55105	−	15.8156i	0.238417	−	0.575590i
$756$		0			0
$757$	9.67850	−	4.00897i	0.351771	−	0.145708i	−0.199799	−	0.979837i	$-0.564029\pi$
$757$	9.67850	−	4.00897i	0.351771	−	0.145708i	0.551570	+	0.834129i	$0.314029\pi$
$758$		0			0
$759$	17.0024	+	17.0024i	0.617148	+	0.617148i
$760$		0			0
$761$	7.08924	−	7.08924i	0.256985	−	0.256985i	−0.566842	−	0.823827i	$-0.691835\pi$
$761$	7.08924	−	7.08924i	0.256985	−	0.256985i	0.823827	+	0.566842i	$0.191835\pi$
$762$		0			0
$763$	13.4630	+	32.5025i	0.487392	+	1.17667i
$764$		0			0
$765$	8.77957	+	3.63662i	0.317426	+	0.131482i
$766$		0			0
$767$	−23.4567			−0.846974
$768$		0			0
$769$	0.0753351			0.00271665			0.00135833	−	0.999999i	$-0.499568\pi$
$769$	0.0753351			0.00271665			0.00135833	+	0.999999i	$0.499568\pi$
$770$		0			0
$771$	−2.74349	−	1.13639i	−0.0988043	−	0.0409261i
$772$		0			0
$773$	−5.93405	−	14.3261i	−0.213433	−	0.515273i	0.780513	−	0.625139i	$-0.214958\pi$
$773$	−5.93405	−	14.3261i	−0.213433	−	0.515273i	−0.993946	+	0.109866i	$0.964958\pi$
$774$		0			0
$775$	2.92491	−	2.92491i	0.105066	−	0.105066i
$776$		0			0
$777$	−33.5437	−	33.5437i	−1.20337	−	1.20337i
$778$		0			0
$779$	−5.59200	+	2.31628i	−0.200354	+	0.0829894i
$780$		0			0
$781$	1.00967	−	2.43756i	0.0361288	−	0.0872226i
$782$		0			0
$783$		−	4.10841i		−	0.146822i
$784$		0			0
$785$			9.23914i			0.329759i
$786$		0			0
$787$	5.40326	−	13.0446i	0.192605	−	0.464991i	−0.797845	−	0.602863i	$-0.794026\pi$
$787$	5.40326	−	13.0446i	0.192605	−	0.464991i	0.990450	+	0.137873i	$0.0440264\pi$
$788$		0			0
$789$	28.8529	−	11.9513i	1.02719	−	0.425477i
$790$		0			0
$791$	−34.8386	−	34.8386i	−1.23872	−	1.23872i
$792$		0			0
$793$	−1.88842	+	1.88842i	−0.0670596	+	0.0670596i
$794$		0			0
$795$	9.57157	+	23.1078i	0.339469	+	0.819550i
$796$		0			0
$797$	−17.5140	−	7.25452i	−0.620376	−	0.256968i	0.0502817	−	0.998735i	$-0.483988\pi$
$797$	−17.5140	−	7.25452i	−0.620376	−	0.256968i	−0.670658	+	0.741767i	$0.733988\pi$
$798$		0			0
$799$	−11.4735			−0.405904
$800$		0			0
$801$	32.3613			1.14343
$802$		0			0
$803$	1.31316	+	0.543931i	0.0463406	+	0.0191949i
$804$		0			0
$805$	−10.3198	−	24.9142i	−0.363725	−	0.878109i
$806$		0			0
$807$	−26.7014	+	26.7014i	−0.939932	+	0.939932i
$808$		0			0
$809$	3.90304	+	3.90304i	0.137224	+	0.137224i	0.772382	−	0.635158i	$-0.219065\pi$
$809$	3.90304	+	3.90304i	0.137224	+	0.137224i	−0.635158	+	0.772382i	$0.719065\pi$
$810$		0			0
$811$	21.2460	−	8.80039i	0.746049	−	0.309023i	0.0229205	−	0.999737i	$-0.492704\pi$
$811$	21.2460	−	8.80039i	0.746049	−	0.309023i	0.723128	+	0.690714i	$0.242704\pi$
$812$		0			0
$813$	16.8861	−	40.7667i	0.592223	−	1.42975i
$814$		0			0
$815$			0.0856667i			0.00300077i
$816$		0			0
$817$			16.7087i			0.584565i
$818$		0			0
$819$	−40.2327	+	97.1304i	−1.40584	+	3.39401i
$820$		0			0
$821$	6.24195	−	2.58550i	0.217846	−	0.0902347i	−0.271092	−	0.962554i	$-0.587385\pi$
$821$	6.24195	−	2.58550i	0.217846	−	0.0902347i	0.488937	+	0.872319i	$0.337385\pi$
$822$		0			0
$823$	−16.3101	−	16.3101i	−0.568535	−	0.568535i	0.363183	−	0.931718i	$-0.381690\pi$
$823$	−16.3101	−	16.3101i	−0.568535	−	0.568535i	−0.931718	+	0.363183i	$0.881690\pi$
$824$		0			0
$825$	−3.19324	+	3.19324i	−0.111174	+	0.111174i
$826$		0			0
$827$	−10.3395	−	24.9618i	−0.359540	−	0.868007i	−0.995365	−	0.0961730i	$-0.969340\pi$
$827$	−10.3395	−	24.9618i	−0.359540	−	0.868007i	0.635825	−	0.771834i	$-0.280660\pi$
$828$		0			0
$829$	−47.9293	−	19.8530i	−1.66465	−	0.689522i	−0.666236	−	0.745741i	$-0.732095\pi$
$829$	−47.9293	−	19.8530i	−1.66465	−	0.689522i	−0.998418	+	0.0562191i	$0.982095\pi$
$830$		0			0
$831$	−39.3441			−1.36483
$832$		0			0
$833$	−33.0527			−1.14521
$834$		0			0
$835$	−5.95212	−	2.46545i	−0.205982	−	0.0853204i
$836$		0			0
$837$	−10.8135	−	26.1061i	−0.373770	−	0.902361i
$838$		0			0
$839$	17.1286	−	17.1286i	0.591344	−	0.591344i	−0.346650	−	0.937994i	$-0.612681\pi$
$839$	17.1286	−	17.1286i	0.591344	−	0.591344i	0.937994	+	0.346650i	$0.112681\pi$
$840$		0			0
$841$	−20.2503	−	20.2503i	−0.698287	−	0.698287i
$842$		0			0
$843$	−87.9173	+	36.4165i	−3.02803	+	1.25425i
$844$		0			0
$845$	0.759832	−	1.83440i	0.0261390	−	0.0631052i
$846$		0			0
$847$		−	43.3600i		−	1.48987i
$848$		0			0
$849$		−	30.8830i		−	1.05990i
$850$		0			0
$851$	−6.59978	+	15.9333i	−0.226238	+	0.546186i
$852$		0			0
$853$	−17.6292	+	7.30225i	−0.603612	+	0.250024i	−0.663495	−	0.748181i	$-0.730927\pi$
$853$	−17.6292	+	7.30225i	−0.603612	+	0.250024i	0.0598825	+	0.998205i	$0.480927\pi$
$854$		0			0
$855$	−13.5197	−	13.5197i	−0.462363	−	0.462363i
$856$		0			0
$857$	32.9284	−	32.9284i	1.12481	−	1.12481i	0.133805	−	0.991008i	$-0.457280\pi$
$857$	32.9284	−	32.9284i	1.12481	−	1.12481i	0.991008	−	0.133805i	$-0.0427196\pi$
$858$		0			0
$859$	−2.30057	−	5.55408i	−0.0784946	−	0.189503i	0.879761	−	0.475417i	$-0.157703\pi$
$859$	−2.30057	−	5.55408i	−0.0784946	−	0.189503i	−0.958255	+	0.285914i	$0.907703\pi$
$860$		0			0
$861$	−22.9695	−	9.51429i	−0.782800	−	0.324246i
$862$		0			0
$863$	8.10784			0.275994			0.137997	−	0.990433i	$-0.455934\pi$
$863$	8.10784			0.275994			0.137997	+	0.990433i	$0.455934\pi$
$864$		0			0
$865$	−14.6653			−0.498637
$866$		0			0
$867$	37.0274	+	15.3372i	1.25752	+	0.520880i
$868$		0			0
$869$	−8.84243	−	21.3475i	−0.299959	−	0.724165i
$870$		0			0
$871$	14.9002	−	14.9002i	0.504874	−	0.504874i
$872$		0			0
$873$	9.03255	+	9.03255i	0.305705	+	0.305705i
$874$		0			0
$875$	4.67915	−	1.93817i	0.158184	−	0.0655220i
$876$		0			0
$877$	−17.7091	+	42.7535i	−0.597994	+	1.44368i	0.277629	+	0.960688i	$0.410451\pi$
$877$	−17.7091	+	42.7535i	−0.597994	+	1.44368i	−0.875623	+	0.482996i	$0.839549\pi$
$878$		0			0
$879$			23.7208i			0.800082i
$880$		0			0
$881$			44.5138i			1.49971i	0.661603	+	0.749854i	$0.269876\pi$
$881$			44.5138i			1.49971i	−0.661603	+	0.749854i	$0.730124\pi$
$882$		0			0
$883$	−3.88438	+	9.37772i	−0.130720	+	0.315586i	−0.975665	−	0.219268i	$-0.929633\pi$
$883$	−3.88438	+	9.37772i	−0.130720	+	0.315586i	0.844945	+	0.534853i	$0.179633\pi$
$884$		0			0
$885$	16.1886	−	6.70555i	0.544175	−	0.225404i
$886$		0			0
$887$	25.3802	+	25.3802i	0.852183	+	0.852183i	0.990402	−	0.138218i	$-0.0441376\pi$
$887$	25.3802	+	25.3802i	0.852183	+	0.852183i	−0.138218	+	0.990402i	$0.544138\pi$
$888$		0			0
$889$	−46.5373	+	46.5373i	−1.56081	+	1.56081i
$890$		0			0
$891$	2.19171	+	5.29125i	0.0734250	+	0.177264i
$892$		0			0
$893$	21.3273	+	8.83404i	0.713690	+	0.295620i
$894$		0			0
$895$	−8.66591			−0.289669
$896$		0			0
$897$	59.6044			1.99013
$898$		0			0
$899$	2.29836	+	0.952010i	0.0766545	+	0.0317513i
$900$		0			0
$901$	−5.86579	−	14.1613i	−0.195418	−	0.471780i
$902$		0			0
$903$	−48.5304	+	48.5304i	−1.61499	+	1.61499i
$904$		0			0
$905$	0.872368	+	0.872368i	0.0289985	+	0.0289985i
$906$		0			0
$907$	39.7977	−	16.4847i	1.32146	−	0.547366i	0.393252	−	0.919431i	$-0.371350\pi$
$907$	39.7977	−	16.4847i	1.32146	−	0.547366i	0.928207	+	0.372064i	$0.121350\pi$
$908$		0			0
$909$	−10.6327	+	25.6695i	−0.352663	+	0.851403i
$910$		0			0
$911$		−	43.3520i		−	1.43631i	−0.695881	−	0.718157i	$-0.744986\pi$
$911$		−	43.3520i		−	1.43631i	0.695881	−	0.718157i	$-0.255014\pi$
$912$		0			0
$913$			15.1144i			0.500213i
$914$		0			0
$915$	0.763447	−	1.84313i	0.0252388	−	0.0609318i
$916$		0			0
$917$	72.1354	−	29.8795i	2.38212	−	0.986706i
$918$		0			0
$919$	3.75148	+	3.75148i	0.123750	+	0.123750i	0.766269	−	0.642519i	$-0.222111\pi$
$919$	3.75148	+	3.75148i	0.123750	+	0.123750i	−0.642519	+	0.766269i	$0.722111\pi$
$920$		0			0
$921$	−48.5944	+	48.5944i	−1.60124	+	1.60124i
$922$		0			0
$923$	−2.50283	−	6.04238i	−0.0823818	−	0.198887i
$924$		0			0
$925$	−2.99244	−	1.23951i	−0.0983910	−	0.0407549i
$926$		0			0
$927$	93.3252			3.06520
$928$		0			0
$929$	−50.6423			−1.66152			−0.830760	−	0.556630i	$-0.812094\pi$
$929$	−50.6423			−1.66152			−0.830760	+	0.556630i	$0.812094\pi$
$930$		0			0
$931$	61.4393	+	25.4490i	2.01359	+	0.834057i
$932$		0			0
$933$	8.16461	+	19.7111i	0.267297	+	0.645313i
$934$		0			0
$935$	1.95693	−	1.95693i	0.0639983	−	0.0639983i
$936$		0			0
$937$	−28.0462	−	28.0462i	−0.916230	−	0.916230i	0.0805231	−	0.996753i	$-0.474341\pi$
$937$	−28.0462	−	28.0462i	−0.916230	−	0.916230i	−0.996753	+	0.0805231i	$0.974341\pi$
$938$		0			0
$939$	7.31620	−	3.03047i	0.238755	−	0.0988956i
$940$		0			0
$941$	3.85504	−	9.30689i	0.125671	−	0.303396i	−0.848505	−	0.529188i	$-0.822497\pi$
$941$	3.85504	−	9.30689i	0.125671	−	0.303396i	0.974176	+	0.225791i	$0.0724968\pi$
$942$		0			0
$943$			9.03860i			0.294337i
$944$		0			0
$945$		−	34.5980i		−	1.12547i
$946$		0			0
$947$	11.1300	−	26.8702i	0.361677	−	0.873165i	−0.633379	−	0.773842i	$-0.718332\pi$
$947$	11.1300	−	26.8702i	0.361677	−	0.873165i	0.995055	−	0.0993226i	$-0.0316676\pi$
$948$		0			0
$949$	3.25516	−	1.34833i	0.105667	−	0.0437687i
$950$		0			0
$951$	56.5758	+	56.5758i	1.83460	+	1.83460i
$952$		0			0
$953$	13.9318	−	13.9318i	0.451294	−	0.451294i	−0.444490	−	0.895784i	$-0.646615\pi$
$953$	13.9318	−	13.9318i	0.451294	−	0.451294i	0.895784	+	0.444490i	$0.146615\pi$
$954$		0			0
$955$	−1.52746	−	3.68761i	−0.0494273	−	0.119328i
$956$		0			0
$957$	−2.50920	−	1.03935i	−0.0811110	−	0.0335973i
$958$		0			0
$959$	53.3259			1.72198
$960$		0			0
$961$	−13.8898			−0.448057
$962$		0			0
$963$	19.6256	+	8.12920i	0.632427	+	0.261960i
$964$		0			0
$965$	9.21080	+	22.2368i	0.296506	+	0.715829i
$966$		0			0
$967$	17.4672	−	17.4672i	0.561707	−	0.561707i	−0.368085	−	0.929792i	$-0.619986\pi$
$967$	17.4672	−	17.4672i	0.561707	−	0.561707i	0.929792	+	0.368085i	$0.119986\pi$
$968$		0			0
$969$	12.9206	+	12.9206i	0.415071	+	0.415071i
$970$		0			0
$971$	−3.77355	+	1.56305i	−0.121099	+	0.0501608i	−0.442410	−	0.896813i	$-0.645876\pi$
$971$	−3.77355	+	1.56305i	−0.121099	+	0.0501608i	0.321311	+	0.946974i	$0.395876\pi$
$972$		0			0
$973$	42.3466	−	102.234i	1.35757	−	3.27747i
$974$		0			0
$975$			11.1944i			0.358506i
$976$		0			0
$977$			0.523734i			0.0167557i	0.999965	+	0.00837787i	$0.00266679\pi$
$977$			0.523734i			0.0167557i	−0.999965	+	0.00837787i	$0.997333\pi$
$978$		0			0
$979$	3.60660	−	8.70709i	0.115267	−	0.278280i
$980$		0			0
$981$	34.4125	−	14.2541i	1.09871	−	0.455100i
$982$		0			0
$983$	−17.3514	−	17.3514i	−0.553422	−	0.553422i	0.374005	−	0.927427i	$-0.377984\pi$
$983$	−17.3514	−	17.3514i	−0.553422	−	0.553422i	−0.927427	+	0.374005i	$0.877984\pi$
$984$		0			0
$985$	−1.33777	+	1.33777i	−0.0426249	+	0.0426249i
$986$		0			0
$987$	36.2865	+	87.6032i	1.15501	+	2.78844i
$988$		0			0
$989$	23.0520	+	9.54844i	0.733010	+	0.303623i
$990$		0			0
$991$	−26.5871			−0.844567			−0.422284	−	0.906464i	$-0.638771\pi$
$991$	−26.5871			−0.844567			−0.422284	+	0.906464i	$0.638771\pi$
$992$		0			0
$993$	−68.9153			−2.18696
$994$		0			0
$995$	−3.64508	−	1.50984i	−0.115557	−	0.0478652i
$996$		0			0
$997$	4.34226	+	10.4831i	0.137521	+	0.332004i	0.977604	−	0.210453i	$-0.0674940\pi$
$997$	4.34226	+	10.4831i	0.137521	+	0.332004i	−0.840083	+	0.542457i	$0.817494\pi$
$998$		0			0
$999$	−15.6457	+	15.6457i	−0.495008	+	0.495008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.x.a.81.15		64
4.3	odd	2		160.2.x.a.61.9	yes	64
20.3	even	4		800.2.ba.e.349.16		64
20.7	even	4		800.2.ba.g.349.1		64
20.19	odd	2		800.2.y.c.701.8		64
32.11	odd	8		160.2.x.a.21.9	✓	64
32.21	even	8	inner	640.2.x.a.561.15		64
160.43	even	8		800.2.ba.g.149.1		64
160.107	even	8		800.2.ba.e.149.16		64
160.139	odd	8		800.2.y.c.501.8		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.x.a.21.9	✓	64	32.11	odd	8
160.2.x.a.61.9	yes	64	4.3	odd	2
640.2.x.a.81.15		64	1.1	even	1	trivial
640.2.x.a.561.15		64	32.21	even	8	inner
800.2.y.c.501.8		64	160.139	odd	8
800.2.y.c.701.8		64	20.19	odd	2
800.2.ba.e.149.16		64	160.107	even	8
800.2.ba.e.349.16		64	20.3	even	4
800.2.ba.g.149.1		64	160.43	even	8
800.2.ba.g.349.1		64	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.x (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.67164 + 1.10663i) q^{3} +(0.382683 + 0.923880i) q^{5} +(-3.58127 + 3.58127i) q^{7} +(3.79172 + 3.79172i) q^{9} +O(q^{10})\)	\(q+(2.67164 + 1.10663i) q^{3} +(0.382683 + 0.923880i) q^{5} +(-3.58127 + 3.58127i) q^{7} +(3.79172 + 3.79172i) q^{9} +(1.44277 - 0.597617i) q^{11} +(1.48141 - 3.57644i) q^{13} +2.89177i q^{15} -1.77217i q^{17} +(-1.36449 + 3.29416i) q^{19} +(-13.5310 + 5.60473i) q^{21} +(3.76499 + 3.76499i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(2.61420 + 6.31124i) q^{27} +(-0.555635 - 0.230151i) q^{29} -4.13645 q^{31} +4.51592 q^{33} +(-4.67915 - 1.93817i) q^{35} +(1.23951 + 2.99244i) q^{37} +(7.91561 - 7.91561i) q^{39} +(1.20035 + 1.20035i) q^{41} +(4.32941 - 1.79330i) q^{43} +(-2.05207 + 4.95413i) q^{45} -6.47426i q^{47} -18.6510i q^{49} +(1.96114 - 4.73462i) q^{51} +(7.99090 - 3.30994i) q^{53} +(1.10425 + 1.10425i) q^{55} +(-7.29084 + 7.29084i) q^{57} +(-2.31884 - 5.59818i) q^{59} +(-0.637370 - 0.264007i) q^{61} -27.1584 q^{63} +3.87112 q^{65} +(5.02905 + 2.08310i) q^{67} +(5.89226 + 14.2252i) q^{69} +(1.19465 - 1.19465i) q^{71} +(0.643585 + 0.643585i) q^{73} +(-2.67164 + 1.10663i) q^{75} +(-3.02674 + 7.30719i) q^{77} -14.7962i q^{79} +3.66742i q^{81} +(-3.70380 + 8.94176i) q^{83} +(1.63728 - 0.678182i) q^{85} +(-1.22976 - 1.22976i) q^{87} +(4.26736 - 4.26736i) q^{89} +(7.50287 + 18.1135i) q^{91} +(-11.0511 - 4.57753i) q^{93} -3.56558 q^{95} +2.38217 q^{97} +(7.73660 + 3.20460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) \) 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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