LMFDB - Embedded newform 1024.2.g.d.129.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1024,2,Mod(129,1024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1024, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("1024.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1024 = 2^{10} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1024.g (of order $8$, degree $4$, 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:	$8.17668116698$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			129.2
Root			$-0.608761 - 0.793353i$ of defining polynomial
Character	$\chi$	$=$	1024.129
Dual form			1024.2.g.d.897.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.356604 + 0.860919i) q^{3} +(0.883663 - 0.366025i) q^{5} +(-2.35207 + 2.35207i) q^{7} +(1.50731 + 1.50731i) q^{9} +O(q^{10})$	\(q+(-0.356604 + 0.860919i) q^{3} +(0.883663 - 0.366025i) q^{5} +(-2.35207 + 2.35207i) q^{7} +(1.50731 + 1.50731i) q^{9} +(0.752787 + 1.81739i) q^{11} +(2.04819 + 0.848387i) q^{13} +0.891289i q^{15} -6.00997i q^{17} +(3.73510 + 1.54713i) q^{19} +(-1.18618 - 2.86370i) q^{21} +(-2.91236 - 2.91236i) q^{23} +(-2.88865 + 2.88865i) q^{25} +(-4.41794 + 1.82997i) q^{27} +(-4.01532 + 9.69383i) q^{29} -7.52140 q^{31} -1.83307 q^{33} +(-1.21752 + 2.93936i) q^{35} +(2.40130 - 0.994652i) q^{37} +(-1.46078 + 1.46078i) q^{39} +(1.37894 + 1.37894i) q^{41} +(4.50046 + 10.8651i) q^{43} +(1.88366 + 0.780239i) q^{45} +3.33173i q^{47} -4.06450i q^{49} +(5.17409 + 2.14318i) q^{51} +(-3.32611 - 8.02993i) q^{53} +(1.33042 + 1.33042i) q^{55} +(-2.66390 + 2.66390i) q^{57} +(11.3694 - 4.70936i) q^{59} +(-0.0688525 + 0.166225i) q^{61} -7.09059 q^{63} +2.12044 q^{65} +(-3.47786 + 8.39629i) q^{67} +(3.54587 - 1.46875i) q^{69} +(-7.92235 + 7.92235i) q^{71} +(5.84544 + 5.84544i) q^{73} +(-1.45679 - 3.51699i) q^{75} +(-6.04524 - 2.50402i) q^{77} -1.80100i q^{79} +1.93890i q^{81} +(-4.79049 - 1.98429i) q^{83} +(-2.19980 - 5.31079i) q^{85} +(-6.91372 - 6.91372i) q^{87} +(-6.38134 + 6.38134i) q^{89} +(-6.81296 + 2.82202i) q^{91} +(2.68216 - 6.47531i) q^{93} +3.86686 q^{95} +0.874915 q^{97} +(-1.60468 + 3.87404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q - 8 * q^5 + 16 * q^9	$ 16 q - 8 q^{5} + 16 q^{9} + 24 q^{13} - 48 q^{21} + 32 q^{25} - 8 q^{29} - 80 q^{33} + 8 q^{37} + 16 q^{41} + 8 q^{45} + 40 q^{53} + 16 q^{57} + 8 q^{61} - 32 q^{65} - 32 q^{73} + 32 q^{77} - 32 q^{85} - 32 q^{89} + 48 q^{93} - 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 + 16 * q^9 + 24 * q^13 - 48 * q^21 + 32 * q^25 - 8 * q^29 - 80 * q^33 + 8 * q^37 + 16 * q^41 + 8 * q^45 + 40 * q^53 + 16 * q^57 + 8 * q^61 - 32 * q^65 - 32 * q^73 + 32 * q^77 - 32 * q^85 - 32 * q^89 + 48 * q^93 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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
$3$	−0.356604	+	0.860919i	−0.205886	+	0.497052i	−0.992768	−	0.120052i	$-0.961694\pi$
$3$	−0.356604	+	0.860919i	−0.205886	+	0.497052i	0.786882	+	0.617103i	$0.211694\pi$
$4$		0			0
$5$	0.883663	−	0.366025i	0.395186	−	0.163692i	−0.176236	−	0.984348i	$-0.556392\pi$
$5$	0.883663	−	0.366025i	0.395186	−	0.163692i	0.571422	+	0.820656i	$0.306392\pi$
$6$		0			0
$7$	−2.35207	+	2.35207i	−0.889000	+	0.889000i	−0.994427	−	0.105427i	$-0.966379\pi$
$7$	−2.35207	+	2.35207i	−0.889000	+	0.889000i	0.105427	+	0.994427i	$0.466379\pi$
$8$		0			0
$9$	1.50731	+	1.50731i	0.502435	+	0.502435i
$10$		0			0
$11$	0.752787	+	1.81739i	0.226974	+	0.547963i	0.995806	−	0.0914869i	$-0.0291620\pi$
$11$	0.752787	+	1.81739i	0.226974	+	0.547963i	−0.768832	+	0.639450i	$0.779162\pi$
$12$		0			0
$13$	2.04819	+	0.848387i	0.568065	+	0.235300i	0.648182	−	0.761485i	$-0.275529\pi$
$13$	2.04819	+	0.848387i	0.568065	+	0.235300i	−0.0801172	+	0.996785i	$0.525529\pi$
$14$		0			0
$15$			0.891289i			0.230130i
$16$		0			0
$17$		−	6.00997i		−	1.45763i	−0.684710	−	0.728816i	$-0.740071\pi$
$17$		−	6.00997i		−	1.45763i	0.684710	−	0.728816i	$-0.259929\pi$
$18$		0			0
$19$	3.73510	+	1.54713i	0.856890	+	0.354935i	0.767490	−	0.641060i	$-0.221505\pi$
$19$	3.73510	+	1.54713i	0.856890	+	0.354935i	0.0893996	+	0.995996i	$0.471505\pi$
$20$		0			0
$21$	−1.18618	−	2.86370i	−0.258847	−	0.624911i
$22$		0			0
$23$	−2.91236	−	2.91236i	−0.607269	−	0.607269i	0.334962	−	0.942232i	$-0.391276\pi$
$23$	−2.91236	−	2.91236i	−0.607269	−	0.607269i	−0.942232	+	0.334962i	$0.891276\pi$
$24$		0			0
$25$	−2.88865	+	2.88865i	−0.577729	+	0.577729i
$26$		0			0
$27$	−4.41794	+	1.82997i	−0.850232	+	0.352178i
$28$		0			0
$29$	−4.01532	+	9.69383i	−0.745625	+	1.80010i	−0.164332	+	0.986405i	$0.552547\pi$
$29$	−4.01532	+	9.69383i	−0.745625	+	1.80010i	−0.581293	+	0.813694i	$0.697453\pi$
$30$		0			0
$31$	−7.52140			−1.35088			−0.675442	−	0.737413i	$-0.736047\pi$
$31$	−7.52140			−1.35088			−0.675442	+	0.737413i	$0.736047\pi$
$32$		0			0
$33$	−1.83307			−0.319097
$34$		0			0
$35$	−1.21752	+	2.93936i	−0.205799	+	0.496843i
$36$		0			0
$37$	2.40130	−	0.994652i	0.394772	−	0.163520i	−0.176462	−	0.984308i	$-0.556465\pi$
$37$	2.40130	−	0.994652i	0.394772	−	0.163520i	0.571233	+	0.820788i	$0.306465\pi$
$38$		0			0
$39$	−1.46078	+	1.46078i	−0.233913	+	0.233913i
$40$		0			0
$41$	1.37894	+	1.37894i	0.215354	+	0.215354i	0.806537	−	0.591183i	$-0.201339\pi$
$41$	1.37894	+	1.37894i	0.215354	+	0.215354i	−0.591183	+	0.806537i	$0.701339\pi$
$42$		0			0
$43$	4.50046	+	10.8651i	0.686314	+	1.65691i	0.752078	+	0.659074i	$0.229052\pi$
$43$	4.50046	+	10.8651i	0.686314	+	1.65691i	−0.0657637	+	0.997835i	$0.520948\pi$
$44$		0			0
$45$	1.88366	+	0.780239i	0.280800	+	0.116311i
$46$		0			0
$47$			3.33173i			0.485983i	0.970028	+	0.242991i	$0.0781286\pi$
$47$			3.33173i			0.485983i	−0.970028	+	0.242991i	$0.921871\pi$
$48$		0			0
$49$		−	4.06450i		−	0.580643i
$50$		0			0
$51$	5.17409	+	2.14318i	0.724518	+	0.300105i
$52$		0			0
$53$	−3.32611	−	8.02993i	−0.456876	−	1.10300i	−0.969656	−	0.244475i	$-0.921384\pi$
$53$	−3.32611	−	8.02993i	−0.456876	−	1.10300i	0.512780	−	0.858520i	$-0.328616\pi$
$54$		0			0
$55$	1.33042	+	1.33042i	0.179394	+	0.179394i
$56$		0			0
$57$	−2.66390	+	2.66390i	−0.352843	+	0.352843i
$58$		0			0
$59$	11.3694	−	4.70936i	1.48017	−	0.613106i	0.511017	−	0.859570i	$-0.329269\pi$
$59$	11.3694	−	4.70936i	1.48017	−	0.613106i	0.969152	+	0.246464i	$0.0792688\pi$
$60$		0			0
$61$	−0.0688525	+	0.166225i	−0.00881566	+	0.0212829i	−0.928226	−	0.372017i	$-0.878666\pi$
$61$	−0.0688525	+	0.166225i	−0.00881566	+	0.0212829i	0.919410	+	0.393299i	$0.128666\pi$
$62$		0			0
$63$	−7.09059			−0.893330
$64$		0			0
$65$	2.12044			0.263008
$66$		0			0
$67$	−3.47786	+	8.39629i	−0.424888	+	1.02577i	0.555997	+	0.831184i	$0.312336\pi$
$67$	−3.47786	+	8.39629i	−0.424888	+	1.02577i	−0.980885	+	0.194587i	$0.937664\pi$
$68$		0			0
$69$	3.54587	−	1.46875i	0.426872	−	0.176816i
$70$		0			0
$71$	−7.92235	+	7.92235i	−0.940210	+	0.940210i	−0.998311	−	0.0581008i	$-0.981496\pi$
$71$	−7.92235	+	7.92235i	−0.940210	+	0.940210i	0.0581008	+	0.998311i	$0.481496\pi$
$72$		0			0
$73$	5.84544	+	5.84544i	0.684157	+	0.684157i	0.960934	−	0.276777i	$-0.0892663\pi$
$73$	5.84544	+	5.84544i	0.684157	+	0.684157i	−0.276777	+	0.960934i	$0.589266\pi$
$74$		0			0
$75$	−1.45679	−	3.51699i	−0.168215	−	0.406108i
$76$		0			0
$77$	−6.04524	−	2.50402i	−0.688919	−	0.285360i
$78$		0			0
$79$		−	1.80100i		−	0.202628i	−0.994855	−	0.101314i	$-0.967695\pi$
$79$		−	1.80100i		−	0.202628i	0.994855	−	0.101314i	$-0.0323046\pi$
$80$		0			0
$81$			1.93890i			0.215433i
$82$		0			0
$83$	−4.79049	−	1.98429i	−0.525825	−	0.217804i	0.103949	−	0.994583i	$-0.466852\pi$
$83$	−4.79049	−	1.98429i	−0.525825	−	0.217804i	−0.629773	+	0.776779i	$0.716852\pi$
$84$		0			0
$85$	−2.19980	−	5.31079i	−0.238602	−	0.576036i
$86$		0			0
$87$	−6.91372	−	6.91372i	−0.741229	−	0.741229i
$88$		0			0
$89$	−6.38134	+	6.38134i	−0.676421	+	0.676421i	−0.959188	−	0.282768i	$-0.908747\pi$
$89$	−6.38134	+	6.38134i	−0.676421	+	0.676421i	0.282768	+	0.959188i	$0.408747\pi$
$90$		0			0
$91$	−6.81296	+	2.82202i	−0.714192	+	0.295828i
$92$		0			0
$93$	2.68216	−	6.47531i	0.278127	−	0.671459i
$94$		0			0
$95$	3.86686			0.396731
$96$		0			0
$97$	0.874915			0.0888342			0.0444171	−	0.999013i	$-0.485857\pi$
$97$	0.874915			0.0888342			0.0444171	+	0.999013i	$0.485857\pi$
$98$		0			0
$99$	−1.60468	+	3.87404i	−0.161276	+	0.389356i
$100$		0			0
$101$	0.00169989		0.000704119i	0.000169146		7.00625e-5i	−0.382599	−	0.923915i	$-0.624971\pi$
$101$	0.00169989		0.000704119i	0.000169146		7.00625e-5i	0.382768	+	0.923844i	$0.374971\pi$
$102$		0			0
$103$	8.93098	−	8.93098i	0.879996	−	0.879996i	−0.113538	−	0.993534i	$-0.536218\pi$
$103$	8.93098	−	8.93098i	0.879996	−	0.879996i	0.993534	+	0.113538i	$0.0362184\pi$
$104$		0			0
$105$	−2.09638	−	2.09638i	−0.204585	−	0.204585i
$106$		0			0
$107$	1.27489	+	3.07786i	0.123248	+	0.297548i	0.973446	−	0.228915i	$-0.0735178\pi$
$107$	1.27489	+	3.07786i	0.123248	+	0.297548i	−0.850198	+	0.526463i	$0.823518\pi$
$108$		0			0
$109$	7.71209	+	3.19445i	0.738684	+	0.305973i	0.720115	−	0.693855i	$-0.244089\pi$
$109$	7.71209	+	3.19445i	0.738684	+	0.305973i	0.0185691	+	0.999828i	$0.494089\pi$
$110$		0			0
$111$			2.42202i			0.229888i
$112$		0			0
$113$		−	7.03528i		−	0.661823i	−0.943662	−	0.330912i	$-0.892644\pi$
$113$		−	7.03528i		−	0.661823i	0.943662	−	0.330912i	$-0.107356\pi$
$114$		0			0
$115$	−3.63955	−	1.50755i	−0.339389	−	0.140580i
$116$		0			0
$117$	1.80847	+	4.36603i	0.167193	+	0.403639i
$118$		0			0
$119$	14.1359	+	14.1359i	1.29583	+	1.29583i
$120$		0			0
$121$	5.04196	−	5.04196i	0.458360	−	0.458360i
$122$		0			0
$123$	−1.67889	+	0.695418i	−0.151380	+	0.0627037i
$124$		0			0
$125$	−3.32540	+	8.02823i	−0.297433	+	0.718067i
$126$		0			0
$127$	−1.09821			−0.0974502			−0.0487251	−	0.998812i	$-0.515516\pi$
$127$	−1.09821			−0.0974502			−0.0487251	+	0.998812i	$0.515516\pi$
$128$		0			0
$129$	−10.9588			−0.964872
$130$		0			0
$131$	7.06683	−	17.0608i	0.617431	−	1.49061i	−0.237245	−	0.971450i	$-0.576244\pi$
$131$	7.06683	−	17.0608i	0.617431	−	1.49061i	0.854676	−	0.519161i	$-0.173756\pi$
$132$		0			0
$133$	−12.4242	+	5.14626i	−1.07731	+	0.446238i
$134$		0			0
$135$	−3.23415	+	3.23415i	−0.278352	+	0.278352i
$136$		0			0
$137$	−5.83183	−	5.83183i	−0.498247	−	0.498247i	0.412645	−	0.910892i	$-0.364605\pi$
$137$	−5.83183	−	5.83183i	−0.498247	−	0.498247i	−0.910892	+	0.412645i	$0.864605\pi$
$138$		0			0
$139$	−5.13991	−	12.4088i	−0.435961	−	1.05250i	−0.977331	−	0.211719i	$-0.932094\pi$
$139$	−5.13991	−	12.4088i	−0.435961	−	1.05250i	0.541369	−	0.840785i	$-0.317906\pi$
$140$		0			0
$141$	−2.86835	−	1.18811i	−0.241558	−	0.100057i
$142$		0			0
$143$			4.36101i			0.364686i
$144$		0			0
$145$			10.0358i			0.833427i
$146$		0			0
$147$	3.49920	+	1.44942i	0.288609	+	0.119546i
$148$		0			0
$149$	6.88366	+	16.6186i	0.563932	+	1.36145i	0.906598	+	0.421994i	$0.138670\pi$
$149$	6.88366	+	16.6186i	0.563932	+	1.36145i	−0.342667	+	0.939457i	$0.611330\pi$
$150$		0			0
$151$	−8.54877	−	8.54877i	−0.695689	−	0.695689i	0.267789	−	0.963478i	$-0.413707\pi$
$151$	−8.54877	−	8.54877i	−0.695689	−	0.695689i	−0.963478	+	0.267789i	$0.913707\pi$
$152$		0			0
$153$	9.05886	−	9.05886i	0.732365	−	0.732365i
$154$		0			0
$155$	−6.64639	+	2.75302i	−0.533851	+	0.221128i
$156$		0			0
$157$	2.26500	−	5.46821i	0.180767	−	0.436410i	−0.807358	−	0.590062i	$-0.799103\pi$
$157$	2.26500	−	5.46821i	0.180767	−	0.436410i	0.988125	+	0.153652i	$0.0491033\pi$
$158$		0			0
$159$	8.09922			0.642310
$160$		0			0
$161$	13.7002			1.07973
$162$		0			0
$163$	2.96694	−	7.16282i	0.232388	−	0.561035i	−0.764069	−	0.645135i	$-0.776801\pi$
$163$	2.96694	−	7.16282i	0.232388	−	0.561035i	0.996457	+	0.0840992i	$0.0268013\pi$
$164$		0			0
$165$	−1.61982	+	0.670951i	−0.126103	+	0.0522334i
$166$		0			0
$167$	14.5948	−	14.5948i	1.12938	−	1.12938i	0.139100	−	0.990278i	$-0.455579\pi$
$167$	14.5948	−	14.5948i	1.12938	−	1.12938i	0.990278	−	0.139100i	$-0.0444209\pi$
$168$		0			0
$169$	−5.71707	−	5.71707i	−0.439775	−	0.439775i
$170$		0			0
$171$	3.29794	+	7.96193i	0.252200	+	0.608864i
$172$		0			0
$173$	−6.63397	−	2.74788i	−0.504372	−	0.208918i	0.115965	−	0.993253i	$-0.463004\pi$
$173$	−6.63397	−	2.74788i	−0.504372	−	0.208918i	−0.620337	+	0.784336i	$0.713004\pi$
$174$		0			0
$175$		−	13.5886i		−	1.02720i
$176$		0			0
$177$			11.4675i			0.861950i
$178$		0			0
$179$	−0.804946	−	0.333419i	−0.0601645	−	0.0249209i	0.352398	−	0.935850i	$-0.385366\pi$
$179$	−0.804946	−	0.333419i	−0.0601645	−	0.0249209i	−0.412563	+	0.910929i	$0.635366\pi$
$180$		0			0
$181$	6.60110	+	15.9365i	0.490656	+	1.18455i	0.954387	+	0.298572i	$0.0965105\pi$
$181$	6.60110	+	15.9365i	0.490656	+	1.18455i	−0.463731	+	0.885976i	$0.653490\pi$
$182$		0			0
$183$	−0.118553	−	0.118553i	−0.00876367	−	0.00876367i
$184$		0			0
$185$	1.75787	−	1.75787i	0.129242	−	0.129242i
$186$		0			0
$187$	10.9225	−	4.52423i	0.798729	−	0.330844i
$188$		0			0
$189$	6.08709	−	14.6955i	0.442770	−	1.06894i
$190$		0			0
$191$	21.7629			1.57471			0.787356	−	0.616499i	$-0.211449\pi$
$191$	21.7629			1.57471			0.787356	+	0.616499i	$0.211449\pi$
$192$		0			0
$193$	0.640834			0.0461283			0.0230641	−	0.999734i	$-0.492658\pi$
$193$	0.640834			0.0461283			0.0230641	+	0.999734i	$0.492658\pi$
$194$		0			0
$195$	−0.756158	+	1.82553i	−0.0541496	+	0.130729i
$196$		0			0
$197$	19.1156	−	7.91794i	1.36193	−	0.564130i	0.422342	−	0.906436i	$-0.361208\pi$
$197$	19.1156	−	7.91794i	1.36193	−	0.564130i	0.939588	+	0.342306i	$0.111208\pi$
$198$		0			0
$199$	−7.96053	+	7.96053i	−0.564307	+	0.564307i	−0.930528	−	0.366221i	$-0.880651\pi$
$199$	−7.96053	+	7.96053i	−0.564307	+	0.564307i	0.366221	+	0.930528i	$0.380651\pi$
$200$		0			0
$201$	−5.98831	−	5.98831i	−0.422383	−	0.422383i
$202$		0			0
$203$	−13.3563	−	32.2449i	−0.937427	−	2.26315i
$204$		0			0
$205$	1.72324	+	0.713791i	0.120356	+	0.0498533i
$206$		0			0
$207$		−	8.77964i		−	0.610227i
$208$		0			0
$209$			7.95278i			0.550105i
$210$		0			0
$211$	−5.49696	−	2.27691i	−0.378426	−	0.156749i	0.185359	−	0.982671i	$-0.440655\pi$
$211$	−5.49696	−	2.27691i	−0.378426	−	0.156749i	−0.563785	+	0.825922i	$0.690655\pi$
$212$		0			0
$213$	−3.99536	−	9.64564i	−0.273757	−	0.660909i
$214$		0			0
$215$	7.95379	+	7.95379i	0.542444	+	0.542444i
$216$		0			0
$217$	17.6909	−	17.6909i	1.20094	−	1.20094i
$218$		0			0
$219$	−7.11696	+	2.94794i	−0.480920	+	0.199203i
$220$		0			0
$221$	5.09878	−	12.3095i	0.342981	−	0.828030i
$222$		0			0
$223$	15.3054			1.02493			0.512464	−	0.858709i	$-0.328733\pi$
$223$	15.3054			1.02493			0.512464	+	0.858709i	$0.328733\pi$
$224$		0			0
$225$	−8.70815			−0.580543
$226$		0			0
$227$	6.67827	−	16.1228i	0.443252	−	1.07011i	−0.531548	−	0.847028i	$-0.678390\pi$
$227$	6.67827	−	16.1228i	0.443252	−	1.07011i	0.974801	−	0.223078i	$-0.0716105\pi$
$228$		0			0
$229$	−14.1151	+	5.84666i	−0.932752	+	0.386358i	−0.796722	−	0.604346i	$-0.793434\pi$
$229$	−14.1151	+	5.84666i	−0.932752	+	0.386358i	−0.136030	+	0.990705i	$0.543434\pi$
$230$		0			0
$231$	4.31152	−	4.31152i	0.283677	−	0.283677i
$232$		0			0
$233$	8.21582	+	8.21582i	0.538236	+	0.538236i	0.923011	−	0.384774i	$-0.125721\pi$
$233$	8.21582	+	8.21582i	0.538236	+	0.538236i	−0.384774	+	0.923011i	$0.625721\pi$
$234$		0			0
$235$	1.21950	+	2.94413i	0.0795512	+	0.192054i
$236$		0			0
$237$	1.55051	+	0.642242i	0.100716	+	0.0417181i
$238$		0			0
$239$		−	4.21394i		−	0.272577i	−0.990669	−	0.136289i	$-0.956483\pi$
$239$		−	4.21394i		−	0.272577i	0.990669	−	0.136289i	$-0.0435175\pi$
$240$		0			0
$241$			20.9382i			1.34875i	0.738391	+	0.674373i	$0.235586\pi$
$241$			20.9382i			1.34875i	−0.738391	+	0.674373i	$0.764414\pi$
$242$		0			0
$243$	−14.9230	−	6.18133i	−0.957314	−	0.396532i
$244$		0			0
$245$	−1.48771	−	3.59165i	−0.0950463	−	0.229462i
$246$		0			0
$247$	6.33762	+	6.33762i	0.403253	+	0.403253i
$248$		0			0
$249$	3.41662	−	3.41662i	0.216519	−	0.216519i
$250$		0			0
$251$	16.8538	−	6.98106i	1.06380	−	0.440641i	0.219002	−	0.975724i	$-0.429720\pi$
$251$	16.8538	−	6.98106i	1.06380	−	0.440641i	0.844799	+	0.535084i	$0.179720\pi$
$252$		0			0
$253$	3.10051	−	7.48528i	0.194927	−	0.470596i
$254$		0			0
$255$	5.35662			0.335444
$256$		0			0
$257$	15.7839			0.984570			0.492285	−	0.870434i	$-0.336162\pi$
$257$	15.7839			0.984570			0.492285	+	0.870434i	$0.336162\pi$
$258$		0			0
$259$	−3.30854	+	7.98753i	−0.205583	+	0.496321i
$260$		0			0
$261$	−20.6639	+	8.55926i	−1.27906	+	0.529805i
$262$		0			0
$263$	15.7140	−	15.7140i	0.968967	−	0.968967i	−0.0305653	−	0.999533i	$-0.509731\pi$
$263$	15.7140	−	15.7140i	0.968967	−	0.968967i	0.999533	+	0.0305653i	$0.00973076\pi$
$264$		0			0
$265$	−5.87832	−	5.87832i	−0.361102	−	0.361102i
$266$		0			0
$267$	−3.21820	−	7.76943i	−0.196951	−	0.475481i
$268$		0			0
$269$	8.75253	+	3.62542i	0.533651	+	0.221045i	0.633201	−	0.773987i	$-0.281740\pi$
$269$	8.75253	+	3.62542i	0.533651	+	0.221045i	−0.0995505	+	0.995033i	$0.531740\pi$
$270$		0			0
$271$			6.69345i			0.406598i	0.979117	+	0.203299i	$0.0651664\pi$
$271$			6.69345i			0.406598i	−0.979117	+	0.203299i	$0.934834\pi$
$272$		0			0
$273$		−	6.87175i		−	0.415897i
$274$		0			0
$275$	−7.42433	−	3.07526i	−0.447704	−	0.185445i
$276$		0			0
$277$	9.67781	+	23.3643i	0.581483	+	1.40382i	0.891468	+	0.453083i	$0.149676\pi$
$277$	9.67781	+	23.3643i	0.581483	+	1.40382i	−0.309985	+	0.950741i	$0.600324\pi$
$278$		0			0
$279$	−11.3371	−	11.3371i	−0.678731	−	0.678731i
$280$		0			0
$281$	−13.6559	+	13.6559i	−0.814640	+	0.814640i	−0.985326	−	0.170685i	$-0.945402\pi$
$281$	−13.6559	+	13.6559i	−0.814640	+	0.814640i	0.170685	+	0.985326i	$0.445402\pi$
$282$		0			0
$283$	−12.7490	+	5.28083i	−0.757852	+	0.313913i	−0.727941	−	0.685640i	$-0.759522\pi$
$283$	−12.7490	+	5.28083i	−0.757852	+	0.313913i	−0.0299113	+	0.999553i	$0.509522\pi$
$284$		0			0
$285$	−1.37894	+	3.32905i	−0.0816812	+	0.197196i
$286$		0			0
$287$	−6.48672			−0.382899
$288$		0			0
$289$	−19.1197			−1.12469
$290$		0			0
$291$	−0.311998	+	0.753231i	−0.0182897	+	0.0441552i
$292$		0			0
$293$	14.8571	−	6.15402i	0.867962	−	0.359521i	0.0961455	−	0.995367i	$-0.469349\pi$
$293$	14.8571	−	6.15402i	0.867962	−	0.359521i	0.771816	+	0.635846i	$0.219349\pi$
$294$		0			0
$295$	8.32298	−	8.32298i	0.484582	−	0.484582i
$296$		0			0
$297$	−6.65153	−	6.65153i	−0.385961	−	0.385961i
$298$		0			0
$299$	−3.49425	−	8.43587i	−0.202078	−	0.487859i
$300$		0			0
$301$	−36.1409	−	14.9700i	−2.08313	−	0.862859i
$302$		0			0
$303$			0.00171456i			9.84990e-5i
$304$		0			0
$305$			0.172088i			0.00985375i
$306$		0			0
$307$	−6.40896	−	2.65468i	−0.365779	−	0.151511i	0.192221	−	0.981352i	$-0.438431\pi$
$307$	−6.40896	−	2.65468i	−0.365779	−	0.151511i	−0.558000	+	0.829841i	$0.688431\pi$
$308$		0			0
$309$	4.50402	+	10.8737i	0.256225	+	0.618582i
$310$		0			0
$311$	21.7524	+	21.7524i	1.23347	+	1.23347i	0.962624	+	0.270841i	$0.0873018\pi$
$311$	21.7524	+	21.7524i	1.23347	+	1.23347i	0.270841	+	0.962624i	$0.412698\pi$
$312$		0			0
$313$	−2.78658	+	2.78658i	−0.157507	+	0.157507i	−0.781461	−	0.623954i	$-0.785525\pi$
$313$	−2.78658	+	2.78658i	−0.157507	+	0.157507i	0.623954	+	0.781461i	$0.285525\pi$
$314$		0			0
$315$	−6.26569	+	2.59534i	−0.353032	+	0.146231i
$316$		0			0
$317$	−1.61984	+	3.91065i	−0.0909794	+	0.219644i	−0.962819	−	0.270148i	$-0.912927\pi$
$317$	−1.61984	+	3.91065i	−0.0909794	+	0.219644i	0.871839	+	0.489792i	$0.162927\pi$
$318$		0			0
$319$	−20.6401			−1.15563
$320$		0			0
$321$	−3.10442			−0.173272
$322$		0			0
$323$	9.29819	−	22.4478i	0.517365	−	1.24903i
$324$		0			0
$325$	−8.36719	+	3.46580i	−0.464128	+	0.192248i
$326$		0			0
$327$	−5.50033	+	5.50033i	−0.304169	+	0.304169i
$328$		0			0
$329$	−7.83647	−	7.83647i	−0.432039	−	0.432039i
$330$		0			0
$331$	6.19790	+	14.9631i	0.340668	+	0.822444i	0.997649	+	0.0685372i	$0.0218332\pi$
$331$	6.19790	+	14.9631i	0.340668	+	0.822444i	−0.656981	+	0.753907i	$0.728167\pi$
$332$		0			0
$333$	5.11874	+	2.12025i	0.280505	+	0.116189i
$334$		0			0
$335$			8.69248i			0.474921i
$336$		0			0
$337$		−	2.16071i		−	0.117702i	−0.998267	−	0.0588508i	$-0.981256\pi$
$337$		−	2.16071i		−	0.117702i	0.998267	−	0.0588508i	$-0.0187436\pi$
$338$		0			0
$339$	6.05680	+	2.50881i	0.328960	+	0.136260i
$340$		0			0
$341$	−5.66201	−	13.6693i	−0.306615	−	0.740235i
$342$		0			0
$343$	−6.90451	−	6.90451i	−0.372809	−	0.372809i
$344$		0			0
$345$	2.59575	−	2.59575i	0.139751	−	0.139751i
$346$		0			0
$347$	8.12222	−	3.36433i	0.436024	−	0.180607i	−0.153864	−	0.988092i	$-0.549172\pi$
$347$	8.12222	−	3.36433i	0.436024	−	0.180607i	0.589888	+	0.807485i	$0.299172\pi$
$348$		0			0
$349$	6.13095	−	14.8014i	0.328182	−	0.792302i	−0.670545	−	0.741869i	$-0.733940\pi$
$349$	6.13095	−	14.8014i	0.328182	−	0.792302i	0.998727	−	0.0504332i	$-0.0160602\pi$
$350$		0			0
$351$	−10.6013			−0.565855
$352$		0			0
$353$	−2.59235			−0.137977			−0.0689885	−	0.997617i	$-0.521977\pi$
$353$	−2.59235			−0.137977			−0.0689885	+	0.997617i	$0.521977\pi$
$354$		0			0
$355$	−4.10091	+	9.90047i	−0.217654	+	0.525463i
$356$		0			0
$357$	−17.2108	+	7.12893i	−0.910890	+	0.377303i
$358$		0			0
$359$	4.94678	−	4.94678i	0.261081	−	0.261081i	−0.564412	−	0.825493i	$-0.690897\pi$
$359$	4.94678	−	4.94678i	0.261081	−	0.261081i	0.825493	+	0.564412i	$0.190897\pi$
$360$		0			0
$361$	−1.87768	−	1.87768i	−0.0988255	−	0.0988255i
$362$		0			0
$363$	2.54273	+	6.13870i	0.133459	+	0.322198i
$364$		0			0
$365$	7.30499	+	3.02582i	0.382360	+	0.158379i
$366$		0			0
$367$			19.5663i			1.02135i	0.859774	+	0.510675i	$0.170605\pi$
$367$			19.5663i			1.02135i	−0.859774	+	0.510675i	$0.829395\pi$
$368$		0			0
$369$			4.15696i			0.216403i
$370$		0			0
$371$	26.7102	+	11.0637i	1.38673	+	0.574401i
$372$		0			0
$373$	−8.43606	−	20.3665i	−0.436803	−	1.05454i	−0.977046	−	0.213026i	$-0.931668\pi$
$373$	−8.43606	−	20.3665i	−0.436803	−	1.05454i	0.540244	−	0.841509i	$-0.318332\pi$
$374$		0			0
$375$	−5.72580	−	5.72580i	−0.295679	−	0.295679i
$376$		0			0
$377$	−16.4482	+	16.4482i	−0.847128	+	0.847128i
$378$		0			0
$379$	3.88618	−	1.60971i	0.199620	−	0.0826851i	−0.280634	−	0.959815i	$-0.590545\pi$
$379$	3.88618	−	1.60971i	0.199620	−	0.0826851i	0.480253	+	0.877130i	$0.340545\pi$
$380$		0			0
$381$	0.391626	−	0.945468i	0.0200636	−	0.0484378i
$382$		0			0
$383$	20.6568			1.05552			0.527758	−	0.849395i	$-0.323033\pi$
$383$	20.6568			1.05552			0.527758	+	0.849395i	$0.323033\pi$
$384$		0			0
$385$	−6.25850			−0.318963
$386$		0			0
$387$	−9.59343	+	23.1606i	−0.487661	+	1.17732i
$388$		0			0
$389$	15.8994	−	6.58576i	0.806133	−	0.333911i	0.0587232	−	0.998274i	$-0.481297\pi$
$389$	15.8994	−	6.58576i	0.806133	−	0.333911i	0.747410	+	0.664363i	$0.231297\pi$
$390$		0			0
$391$	−17.5032	+	17.5032i	−0.885175	+	0.885175i
$392$		0			0
$393$	12.1679	+	12.1679i	0.613791	+	0.613791i
$394$		0			0
$395$	−0.659210	−	1.59147i	−0.0331685	−	0.0800757i
$396$		0			0
$397$	17.8218	+	7.38205i	0.894452	+	0.370494i	0.782084	−	0.623172i	$-0.214157\pi$
$397$	17.8218	+	7.38205i	0.894452	+	0.370494i	0.112368	+	0.993667i	$0.464157\pi$
$398$		0			0
$399$		−	12.5314i		−	0.627354i
$400$		0			0
$401$			0.119032i			0.00594418i	0.999996	+	0.00297209i	$0.000946048\pi$
$401$			0.119032i			0.00594418i	−0.999996	+	0.00297209i	$0.999054\pi$
$402$		0			0
$403$	−15.4052	−	6.38106i	−0.767390	−	0.317863i
$404$		0			0
$405$	0.709687	+	1.71334i	0.0352646	+	0.0851363i
$406$		0			0
$407$	3.61534	+	3.61534i	0.179206	+	0.179206i
$408$		0			0
$409$	10.5505	−	10.5505i	0.521689	−	0.521689i	−0.396392	−	0.918081i	$-0.629738\pi$
$409$	10.5505	−	10.5505i	0.521689	−	0.521689i	0.918081	+	0.396392i	$0.129738\pi$
$410$		0			0
$411$	7.10038	−	2.94107i	0.350236	−	0.145073i
$412$		0			0
$413$	−15.6649	+	37.8184i	−0.770819	+	1.86092i
$414$		0			0
$415$	−4.95948			−0.243451
$416$		0			0
$417$	12.5159			0.612907
$418$		0			0
$419$	−3.49762	+	8.44401i	−0.170870	+	0.412517i	−0.985996	−	0.166766i	$-0.946667\pi$
$419$	−3.49762	+	8.44401i	−0.170870	+	0.412517i	0.815126	+	0.579283i	$0.196667\pi$
$420$		0			0
$421$	25.2227	−	10.4476i	1.22928	−	0.509184i	0.328930	−	0.944354i	$-0.393312\pi$
$421$	25.2227	−	10.4476i	1.22928	−	0.509184i	0.900348	+	0.435171i	$0.143312\pi$
$422$		0			0
$423$	−5.02193	+	5.02193i	−0.244175	+	0.244175i
$424$		0			0
$425$	17.3607	+	17.3607i	0.842117	+	0.842117i
$426$		0			0
$427$	−0.229026	−	0.552918i	−0.0110834	−	0.0267576i
$428$		0			0
$429$	−3.75447	−	1.55515i	−0.181268	−	0.0750836i
$430$		0			0
$431$		−	3.31726i		−	0.159787i	−0.996803	−	0.0798934i	$-0.974542\pi$
$431$		−	3.31726i		−	0.159787i	0.996803	−	0.0798934i	$-0.0254580\pi$
$432$		0			0
$433$		−	22.3224i		−	1.07275i	−0.843981	−	0.536374i	$-0.819794\pi$
$433$		−	22.3224i		−	1.07275i	0.843981	−	0.536374i	$-0.180206\pi$
$434$		0			0
$435$	−8.64000	−	3.57881i	−0.414256	−	0.171591i
$436$		0			0
$437$	−6.37216	−	15.3837i	−0.304822	−	0.735904i
$438$		0			0
$439$	−21.1260	−	21.1260i	−1.00829	−	1.00829i	−0.999965	−	0.00832228i	$-0.997351\pi$
$439$	−21.1260	−	21.1260i	−1.00829	−	1.00829i	−0.00832228	−	0.999965i	$-0.502649\pi$
$440$		0			0
$441$	6.12644	−	6.12644i	0.291735	−	0.291735i
$442$		0			0
$443$	0.221149	−	0.0916028i	0.0105071	−	0.00435218i	−0.377424	−	0.926041i	$-0.623190\pi$
$443$	0.221149	−	0.0916028i	0.0105071	−	0.00435218i	0.387931	+	0.921689i	$0.373190\pi$
$444$		0			0
$445$	−3.30323	+	7.97469i	−0.156588	+	0.378037i
$446$		0			0
$447$	−16.7620			−0.792817
$448$		0			0
$449$	21.5081			1.01503			0.507515	−	0.861643i	$-0.330564\pi$
$449$	21.5081			1.01503			0.507515	+	0.861643i	$0.330564\pi$
$450$		0			0
$451$	−1.46802	+	3.54411i	−0.0691263	+	0.166886i
$452$		0			0
$453$	10.4083	−	4.31127i	0.489026	−	0.202561i
$454$		0			0
$455$	−4.98743	+	4.98743i	−0.233814	+	0.233814i
$456$		0			0
$457$	9.73721	+	9.73721i	0.455487	+	0.455487i	0.897171	−	0.441683i	$-0.145619\pi$
$457$	9.73721	+	9.73721i	0.455487	+	0.455487i	−0.441683	+	0.897171i	$0.645619\pi$
$458$		0			0
$459$	10.9981	+	26.5516i	0.513345	+	1.23932i
$460$		0			0
$461$	−27.2925	−	11.3049i	−1.27114	−	0.526523i	−0.357828	−	0.933787i	$-0.616483\pi$
$461$	−27.2925	−	11.3049i	−1.27114	−	0.526523i	−0.913310	+	0.407265i	$0.866483\pi$
$462$		0			0
$463$		−	39.6338i		−	1.84194i	−0.389635	−	0.920969i	$-0.627399\pi$
$463$		−	39.6338i		−	1.84194i	0.389635	−	0.920969i	$-0.372601\pi$
$464$		0			0
$465$		−	6.70374i		−	0.310878i
$466$		0			0
$467$	19.7102	+	8.16422i	0.912077	+	0.377795i	0.788852	−	0.614584i	$-0.210676\pi$
$467$	19.7102	+	8.16422i	0.912077	+	0.377795i	0.123226	+	0.992379i	$0.460676\pi$
$468$		0			0
$469$	−11.5685	−	27.9289i	−0.534185	−	1.28964i
$470$		0			0
$471$	3.89997	+	3.89997i	0.179701	+	0.179701i
$472$		0			0
$473$	−16.3582	+	16.3582i	−0.752150	+	0.752150i
$474$		0			0
$475$	−15.2585	+	6.32027i	−0.700107	+	0.289994i
$476$		0			0
$477$	7.09010	−	17.1170i	0.324633	−	0.783734i
$478$		0			0
$479$	3.07863			0.140666			0.0703331	−	0.997524i	$-0.477594\pi$
$479$	3.07863			0.140666			0.0703331	+	0.997524i	$0.477594\pi$
$480$		0			0
$481$	5.76217			0.262732
$482$		0			0
$483$	−4.88554	+	11.7947i	−0.222300	+	0.536679i
$484$		0			0
$485$	0.773131	−	0.320241i	0.0351061	−	0.0145414i
$486$		0			0
$487$	−21.0643	+	21.0643i	−0.954517	+	0.954517i	−0.999010	−	0.0444931i	$-0.985833\pi$
$487$	−21.0643	+	21.0643i	−0.954517	+	0.954517i	0.0444931	+	0.999010i	$0.485833\pi$
$488$		0			0
$489$	5.10858	+	5.10858i	0.231018	+	0.231018i
$490$		0			0
$491$	6.66130	+	16.0818i	0.300620	+	0.725761i	0.999940	+	0.0109525i	$0.00348635\pi$
$491$	6.66130	+	16.0818i	0.300620	+	0.725761i	−0.699320	+	0.714809i	$0.746514\pi$
$492$		0			0
$493$	58.2596	+	24.1319i	2.62388	+	1.08685i
$494$		0			0
$495$			4.01070i			0.180268i
$496$		0			0
$497$		−	37.2679i		−	1.67169i
$498$		0			0
$499$	18.5877	+	7.69930i	0.832102	+	0.344668i	0.757734	−	0.652563i	$-0.226306\pi$
$499$	18.5877	+	7.69930i	0.832102	+	0.344668i	0.0743674	+	0.997231i	$0.476306\pi$
$500$		0			0
$501$	7.36036	+	17.7695i	0.328837	+	0.793882i
$502$		0			0
$503$	−11.0921	−	11.0921i	−0.494572	−	0.494572i	0.415172	−	0.909743i	$-0.363722\pi$
$503$	−11.0921	−	11.0921i	−0.494572	−	0.494572i	−0.909743	+	0.415172i	$0.863722\pi$
$504$		0			0
$505$	0.00124441	−	0.00124441i	5.53755e−5	−	5.53755e-5i
$506$		0			0
$507$	6.96067	−	2.88320i	0.309134	−	0.128048i
$508$		0			0
$509$	−13.9012	+	33.5605i	−0.616160	+	1.48754i	0.239970	+	0.970780i	$0.422862\pi$
$509$	−13.9012	+	33.5605i	−0.616160	+	1.48754i	−0.856130	+	0.516761i	$0.827138\pi$
$510$		0			0
$511$	−27.4978			−1.21643
$512$		0			0
$513$	−19.3326			−0.853556
$514$		0			0
$515$	4.62301	−	11.1609i	0.203714	−	0.491810i
$516$		0			0
$517$	−6.05505	+	2.50808i	−0.266301	+	0.110305i
$518$		0			0
$519$	4.73141	−	4.73141i	0.207686	−	0.207686i
$520$		0			0
$521$	−5.27400	−	5.27400i	−0.231058	−	0.231058i	0.582076	−	0.813134i	$-0.302241\pi$
$521$	−5.27400	−	5.27400i	−0.231058	−	0.231058i	−0.813134	+	0.582076i	$0.802241\pi$
$522$		0			0
$523$	2.35226	+	5.67885i	0.102857	+	0.248319i	0.966927	−	0.255053i	$-0.0820928\pi$
$523$	2.35226	+	5.67885i	0.102857	+	0.248319i	−0.864070	+	0.503371i	$0.832093\pi$
$524$		0			0
$525$	11.6987	+	4.84576i	0.510573	+	0.211486i
$526$		0			0
$527$			45.2034i			1.96909i
$528$		0			0
$529$		−	6.03631i		−	0.262448i
$530$		0			0
$531$	24.2356	+	10.0387i	1.05174	+	0.435643i
$532$		0			0
$533$	1.65445	+	3.99420i	0.0716622	+	0.173008i
$534$		0			0
$535$	2.25315	+	2.25315i	0.0974122	+	0.0974122i
$536$		0			0
$537$	0.574094	−	0.574094i	0.0247740	−	0.0247740i
$538$		0			0
$539$	7.38678	−	3.05970i	0.318171	−	0.131791i
$540$		0			0
$541$	−8.08295	+	19.5140i	−0.347513	+	0.838971i	0.649399	+	0.760448i	$0.275020\pi$
$541$	−8.08295	+	19.5140i	−0.347513	+	0.838971i	−0.996912	+	0.0785232i	$0.974980\pi$
$542$		0			0
$543$	−16.0740			−0.689801
$544$		0			0
$545$	7.98414			0.342003
$546$		0			0
$547$	−1.49376	+	3.60625i	−0.0638684	+	0.154192i	−0.952591	−	0.304253i	$-0.901593\pi$
$547$	−1.49376	+	3.60625i	−0.0638684	+	0.154192i	0.888723	+	0.458445i	$0.151593\pi$
$548$		0			0
$549$	−0.354333	+	0.146770i	−0.0151226	+	0.00626397i
$550$		0			0
$551$	−29.9952	+	29.9952i	−1.27784	+	1.27784i
$552$		0			0
$553$	4.23607	+	4.23607i	0.180136	+	0.180136i
$554$		0			0
$555$	0.886522	+	2.14025i	0.0376308	+	0.0908487i
$556$		0			0
$557$	−17.6668	−	7.31781i	−0.748565	−	0.310066i	−0.0244089	−	0.999702i	$-0.507770\pi$
$557$	−17.6668	−	7.31781i	−0.748565	−	0.310066i	−0.724156	+	0.689636i	$0.757770\pi$
$558$		0			0
$559$			26.0719i			1.10272i
$560$		0			0
$561$			11.0167i			0.465125i
$562$		0			0
$563$	2.71884	+	1.12618i	0.114585	+	0.0474628i	0.439240	−	0.898370i	$-0.355248\pi$
$563$	2.71884	+	1.12618i	0.114585	+	0.0474628i	−0.324654	+	0.945833i	$0.605248\pi$
$564$		0			0
$565$	−2.57509	−	6.21682i	−0.108335	−	0.261543i
$566$		0			0
$567$	−4.56044	−	4.56044i	−0.191520	−	0.191520i
$568$		0			0
$569$	−10.4042	+	10.4042i	−0.436169	+	0.436169i	−0.890720	−	0.454552i	$-0.849799\pi$
$569$	−10.4042	+	10.4042i	−0.436169	+	0.436169i	0.454552	+	0.890720i	$0.349799\pi$
$570$		0			0
$571$	−37.7960	+	15.6556i	−1.58171	+	0.655167i	−0.988684	−	0.150013i	$-0.952068\pi$
$571$	−37.7960	+	15.6556i	−1.58171	+	0.655167i	−0.593030	+	0.805181i	$0.702068\pi$
$572$		0			0
$573$	−7.76076	+	18.7361i	−0.324210	+	0.782713i
$574$		0			0
$575$	16.8256			0.701675
$576$		0			0
$577$	−30.1981			−1.25716			−0.628582	−	0.777744i	$-0.716364\pi$
$577$	−30.1981			−1.25716			−0.628582	+	0.777744i	$0.716364\pi$
$578$		0			0
$579$	−0.228524	+	0.551706i	−0.00949714	+	0.0229281i
$580$		0			0
$581$	15.9348	−	6.60040i	0.661086	−	0.273831i
$582$		0			0
$583$	12.0897	−	12.0897i	0.500702	−	0.500702i
$584$		0			0
$585$	3.19615	+	3.19615i	0.132145	+	0.132145i
$586$		0			0
$587$	8.32558	+	20.0997i	0.343634	+	0.829605i	0.997342	+	0.0728586i	$0.0232122\pi$
$587$	8.32558	+	20.0997i	0.343634	+	0.829605i	−0.653709	+	0.756746i	$0.726788\pi$
$588$		0			0
$589$	−28.0932	−	11.6366i	−1.15756	−	0.479476i
$590$		0			0
$591$			19.2806i			0.793096i
$592$		0			0
$593$		−	38.2715i		−	1.57162i	−0.618468	−	0.785810i	$-0.712246\pi$
$593$		−	38.2715i		−	1.57162i	0.618468	−	0.785810i	$-0.287754\pi$
$594$		0			0
$595$	17.6655	+	7.31727i	0.724213	+	0.299979i
$596$		0			0
$597$	−4.01461	−	9.69213i	−0.164307	−	0.396672i
$598$		0			0
$599$	2.76223	+	2.76223i	0.112862	+	0.112862i	0.761282	−	0.648421i	$-0.224570\pi$
$599$	2.76223	+	2.76223i	0.112862	+	0.112862i	−0.648421	+	0.761282i	$0.724570\pi$
$600$		0			0
$601$	−20.7961	+	20.7961i	−0.848289	+	0.848289i	−0.989920	−	0.141630i	$-0.954766\pi$
$601$	−20.7961	+	20.7961i	−0.848289	+	0.848289i	0.141630	+	0.989920i	$0.454766\pi$
$602$		0			0
$603$	−17.8980	+	7.41359i	−0.728862	+	0.301905i
$604$		0			0
$605$	2.60991	−	6.30088i	0.106108	−	0.256167i
$606$		0			0
$607$	−18.7402			−0.760642			−0.380321	−	0.924855i	$-0.624187\pi$
$607$	−18.7402			−0.760642			−0.380321	+	0.924855i	$0.624187\pi$
$608$		0			0
$609$	32.5232			1.31790
$610$		0			0
$611$	−2.82660	+	6.82401i	−0.114352	+	0.276070i
$612$		0			0
$613$	−14.9560	+	6.19497i	−0.604066	+	0.250212i	−0.663689	−	0.748009i	$-0.731010\pi$
$613$	−14.9560	+	6.19497i	−0.604066	+	0.250212i	0.0596229	+	0.998221i	$0.481010\pi$
$614$		0			0
$615$	−1.22903	+	1.22903i	−0.0495593	+	0.0495593i
$616$		0			0
$617$	−25.7897	−	25.7897i	−1.03825	−	1.03825i	−0.999239	−	0.0390142i	$-0.987578\pi$
$617$	−25.7897	−	25.7897i	−1.03825	−	1.03825i	−0.0390142	−	0.999239i	$-0.512422\pi$
$618$		0			0
$619$	2.21236	+	5.34111i	0.0889222	+	0.214677i	0.962084	−	0.272753i	$-0.0879342\pi$
$619$	2.21236	+	5.34111i	0.0889222	+	0.214677i	−0.873162	+	0.487431i	$0.837934\pi$
$620$		0			0
$621$	18.1962	+	7.53709i	0.730186	+	0.302453i
$622$		0			0
$623$		−	30.0188i		−	1.20268i
$624$		0			0
$625$		−	12.1144i		−	0.484576i
$626$		0			0
$627$	−6.84670	−	2.83600i	−0.273431	−	0.113259i
$628$		0			0
$629$	−5.97782	−	14.4317i	−0.238351	−	0.575431i
$630$		0			0
$631$	−5.43699	−	5.43699i	−0.216443	−	0.216443i	0.590555	−	0.806998i	$-0.298909\pi$
$631$	−5.43699	−	5.43699i	−0.216443	−	0.216443i	−0.806998	+	0.590555i	$0.798909\pi$
$632$		0			0
$633$	3.92048	−	3.92048i	0.155825	−	0.155825i
$634$		0			0
$635$	−0.970446	+	0.401972i	−0.0385110	+	0.0159518i
$636$		0			0
$637$	3.44827	−	8.32486i	0.136625	−	0.329843i
$638$		0			0
$639$	−23.8828			−0.944789
$640$		0			0
$641$	11.1732			0.441315			0.220658	−	0.975351i	$-0.429180\pi$
$641$	11.1732			0.441315			0.220658	+	0.975351i	$0.429180\pi$
$642$		0			0
$643$	−14.8270	+	35.7957i	−0.584722	+	1.41164i	0.303768	+	0.952746i	$0.401755\pi$
$643$	−14.8270	+	35.7957i	−0.584722	+	1.41164i	−0.888490	+	0.458897i	$0.848245\pi$
$644$		0			0
$645$	−9.68392	+	4.01121i	−0.381304	+	0.157941i
$646$		0			0
$647$	−3.05035	+	3.05035i	−0.119922	+	0.119922i	−0.764521	−	0.644599i	$-0.777024\pi$
$647$	−3.05035	+	3.05035i	−0.119922	+	0.119922i	0.644599	+	0.764521i	$0.277024\pi$
$648$		0			0
$649$	17.1175	+	17.1175i	0.671920	+	0.671920i
$650$		0			0
$651$	8.92177	+	21.5391i	0.349672	+	0.844182i
$652$		0			0
$653$	15.5810	+	6.45384i	0.609730	+	0.252558i	0.666113	−	0.745851i	$-0.267957\pi$
$653$	15.5810	+	6.45384i	0.609730	+	0.252558i	−0.0563832	+	0.998409i	$0.517957\pi$
$654$		0			0
$655$		−	17.6627i		−	0.690138i
$656$		0			0
$657$			17.6217i			0.687490i
$658$		0			0
$659$	−38.7490	−	16.0504i	−1.50945	−	0.625233i	−0.534003	−	0.845483i	$-0.679313\pi$
$659$	−38.7490	−	16.0504i	−1.50945	−	0.625233i	−0.975444	+	0.220250i	$0.929313\pi$
$660$		0			0
$661$	9.39102	+	22.6719i	0.365268	+	0.881836i	0.994512	+	0.104627i	$0.0333649\pi$
$661$	9.39102	+	22.6719i	0.365268	+	0.881836i	−0.629243	+	0.777208i	$0.716635\pi$
$662$		0			0
$663$	8.77927	+	8.77927i	0.340959	+	0.340959i
$664$		0			0
$665$	−9.09513	+	9.09513i	−0.352694	+	0.352694i
$666$		0			0
$667$	39.9260	−	16.5379i	1.54594	−	0.640349i
$668$		0			0
$669$	−5.45798	+	13.1767i	−0.211018	+	0.509442i
$670$		0			0
$671$	−0.353926			−0.0136632
$672$		0			0
$673$	−19.5003			−0.751680			−0.375840	−	0.926685i	$-0.622646\pi$
$673$	−19.5003			−0.751680			−0.375840	+	0.926685i	$0.622646\pi$
$674$		0			0
$675$	7.47572	−	18.0480i	0.287741	−	0.694668i
$676$		0			0
$677$	15.5588	−	6.44466i	0.597972	−	0.247688i	−0.0631039	−	0.998007i	$-0.520100\pi$
$677$	15.5588	−	6.44466i	0.597972	−	0.247688i	0.661076	+	0.750319i	$0.270100\pi$
$678$		0			0
$679$	−2.05787	+	2.05787i	−0.0789736	+	0.0789736i
$680$		0			0
$681$	11.4989	+	11.4989i	0.440639	+	0.440639i
$682$		0			0
$683$	−18.7811	−	45.3415i	−0.718638	−	1.73495i	−0.677193	−	0.735805i	$-0.736804\pi$
$683$	−18.7811	−	45.3415i	−0.718638	−	1.73495i	−0.0414451	−	0.999141i	$-0.513196\pi$
$684$		0			0
$685$	−7.28797	−	3.01878i	−0.278459	−	0.115341i
$686$		0			0
$687$		−	14.2369i		−	0.543171i
$688$		0			0
$689$		−	19.2686i		−	0.734076i
$690$		0			0
$691$	8.12311	+	3.36470i	0.309018	+	0.127999i	0.531803	−	0.846868i	$-0.321515\pi$
$691$	8.12311	+	3.36470i	0.309018	+	0.127999i	−0.222785	+	0.974868i	$0.571515\pi$
$692$		0			0
$693$	−5.33770	−	12.8864i	−0.202763	−	0.489512i
$694$		0			0
$695$	−9.08390	−	9.08390i	−0.344572	−	0.344572i
$696$		0			0
$697$	8.28737	−	8.28737i	0.313906	−	0.313906i
$698$		0			0
$699$	−10.0029	+	4.14336i	−0.378346	+	0.156716i
$700$		0			0
$701$	10.6060	−	25.6052i	0.400584	−	0.967094i	−0.586941	−	0.809630i	$-0.699668\pi$
$701$	10.6060	−	25.6052i	0.400584	−	0.967094i	0.987525	−	0.157465i	$-0.0503320\pi$
$702$		0			0
$703$	10.5079			0.396315
$704$		0			0
$705$	−2.96953			−0.111839
$706$		0			0
$707$	−0.00234214	+	0.00565442i	−8.80851e−5	+	0.000212656i
$708$		0			0
$709$	20.5899	−	8.52863i	0.773271	−	0.320299i	0.0390744	−	0.999236i	$-0.487559\pi$
$709$	20.5899	−	8.52863i	0.773271	−	0.320299i	0.734197	+	0.678937i	$0.237559\pi$
$710$		0			0
$711$	2.71465	−	2.71465i	0.101807	−	0.101807i
$712$		0			0
$713$	21.9050	+	21.9050i	0.820350	+	0.820350i
$714$		0			0
$715$	1.59624	+	3.85367i	0.0596960	+	0.144119i
$716$		0			0
$717$	3.62786	+	1.50271i	0.135485	+	0.0561197i
$718$		0			0
$719$			33.6036i			1.25320i	0.779340	+	0.626601i	$0.215555\pi$
$719$			33.6036i			1.25320i	−0.779340	+	0.626601i	$0.784445\pi$
$720$		0			0
$721$			42.0126i			1.56463i
$722$		0			0
$723$	−18.0261	−	7.46664i	−0.670396	−	0.277687i
$724$		0			0
$725$	−16.4032	−	39.6009i	−0.609200	−	1.47074i
$726$		0			0
$727$	6.49728	+	6.49728i	0.240971	+	0.240971i	0.817252	−	0.576281i	$-0.195497\pi$
$727$	6.49728	+	6.49728i	0.240971	+	0.240971i	−0.576281	+	0.817252i	$0.695497\pi$
$728$		0			0
$729$	6.53021	−	6.53021i	0.241860	−	0.241860i
$730$		0			0
$731$	65.2988	−	27.0476i	2.41516	−	1.00039i
$732$		0			0
$733$	5.96344	−	14.3970i	0.220265	−	0.531766i	−0.774661	−	0.632376i	$-0.782080\pi$
$733$	5.96344	−	14.3970i	0.220265	−	0.531766i	0.994926	+	0.100611i	$0.0320797\pi$
$734$		0			0
$735$	3.62264			0.133623
$736$		0			0
$737$	−17.8774			−0.658523
$738$		0			0
$739$	3.80567	−	9.18771i	0.139994	−	0.337975i	−0.838296	−	0.545215i	$-0.816448\pi$
$739$	3.80567	−	9.18771i	0.139994	−	0.337975i	0.978290	+	0.207240i	$0.0664480\pi$
$740$		0			0
$741$	−7.71619	+	3.19615i	−0.283461	+	0.117414i
$742$		0			0
$743$	3.28243	−	3.28243i	0.120421	−	0.120421i	−0.644328	−	0.764749i	$-0.722863\pi$
$743$	3.28243	−	3.28243i	0.120421	−	0.120421i	0.764749	+	0.644328i	$0.222863\pi$
$744$		0			0
$745$	12.1657	+	12.1657i	0.445716	+	0.445716i
$746$		0			0
$747$	−4.22981	−	10.2117i	−0.154761	−	0.373625i
$748$		0			0
$749$	−10.2380	−	4.24072i	−0.374088	−	0.154952i
$750$		0			0
$751$			5.40568i			0.197256i	0.995124	+	0.0986280i	$0.0314454\pi$
$751$			5.40568i			0.197256i	−0.995124	+	0.0986280i	$0.968555\pi$
$752$		0			0
$753$			16.9992i			0.619485i
$754$		0			0
$755$	−10.6833	−	4.42517i	−0.388805	−	0.161048i
$756$		0			0
$757$	0.220757	+	0.532954i	0.00802354	+	0.0193705i	0.927841	−	0.372977i	$-0.121663\pi$
$757$	0.220757	+	0.532954i	0.00802354	+	0.0193705i	−0.919817	+	0.392348i	$0.871663\pi$
$758$		0			0
$759$	5.33857	+	5.33857i	0.193778	+	0.193778i
$760$		0			0
$761$	3.74202	−	3.74202i	0.135648	−	0.135648i	−0.636022	−	0.771671i	$-0.719421\pi$
$761$	3.74202	−	3.74202i	0.135648	−	0.135648i	0.771671	+	0.636022i	$0.219421\pi$
$762$		0			0
$763$	−25.6530	+	10.6258i	−0.928701	+	0.384680i
$764$		0			0
$765$	4.68921	−	11.3208i	0.169539	−	0.409303i
$766$		0			0
$767$	27.2820			0.985097
$768$		0			0
$769$	43.7699			1.57838			0.789192	−	0.614146i	$-0.210499\pi$
$769$	43.7699			1.57838			0.789192	+	0.614146i	$0.210499\pi$
$770$		0			0
$771$	−5.62859	+	13.5886i	−0.202709	+	0.489382i
$772$		0			0
$773$	−44.0963	+	18.2653i	−1.58603	+	0.656956i	−0.989355	−	0.145525i	$-0.953513\pi$
$773$	−44.0963	+	18.2653i	−1.58603	+	0.656956i	−0.596678	+	0.802481i	$0.703513\pi$
$774$		0			0
$775$	21.7267	−	21.7267i	0.780445	−	0.780445i
$776$		0			0
$777$	−5.69677	−	5.69677i	−0.204371	−	0.204371i
$778$		0			0
$779$	3.01707	+	7.28386i	0.108098	+	0.260971i
$780$		0			0
$781$	−20.3618	−	8.43415i	−0.728604	−	0.301798i
$782$		0			0
$783$		−	50.1746i		−	1.79309i
$784$		0			0
$785$		−	5.66110i		−	0.202053i
$786$		0			0
$787$	35.7769	+	14.8193i	1.27531	+	0.528250i	0.914574	−	0.404418i	$-0.132526\pi$
$787$	35.7769	+	14.8193i	1.27531	+	0.528250i	0.360735	+	0.932668i	$0.382526\pi$
$788$		0			0
$789$	7.92480	+	19.1322i	0.282130	+	0.681123i
$790$		0			0
$791$	16.5475	+	16.5475i	0.588361	+	0.588361i
$792$		0			0
$793$	−0.282046	+	0.282046i	−0.0100157	+	0.0100157i
$794$		0			0
$795$	7.15698	−	2.96452i	0.253832	−	0.105141i
$796$		0			0
$797$	−10.8601	+	26.2186i	−0.384684	+	0.928709i	0.606362	+	0.795188i	$0.292628\pi$
$797$	−10.8601	+	26.2186i	−0.384684	+	0.928709i	−0.991046	+	0.133520i	$0.957372\pi$
$798$		0			0
$799$	20.0236			0.708383
$800$		0			0
$801$	−19.2373			−0.679715
$802$		0			0
$803$	−6.22307	+	15.0238i	−0.219607	+	0.530179i
$804$		0			0
$805$	12.1063	−	5.01461i	0.426693	−	0.176742i
$806$		0			0
$807$	−6.24238	+	6.24238i	−0.219742	+	0.219742i
$808$		0			0
$809$	−36.1908	−	36.1908i	−1.27240	−	1.27240i	−0.944825	−	0.327575i	$-0.893769\pi$
$809$	−36.1908	−	36.1908i	−1.27240	−	1.27240i	−0.327575	−	0.944825i	$-0.606231\pi$
$810$		0			0
$811$	−1.87355	−	4.52316i	−0.0657893	−	0.158829i	0.887565	−	0.460682i	$-0.152395\pi$
$811$	−1.87355	−	4.52316i	−0.0657893	−	0.158829i	−0.953355	+	0.301852i	$0.902395\pi$
$812$		0			0
$813$	−5.76252	−	2.38691i	−0.202100	−	0.0837127i
$814$		0			0
$815$		−	7.41550i		−	0.259754i
$816$		0			0
$817$			47.5449i			1.66339i
$818$		0			0
$819$	−14.5229	−	6.01557i	−0.507470	−	0.210201i
$820$		0			0
$821$	11.3409	+	27.3794i	0.395801	+	0.955549i	0.988650	+	0.150235i	$0.0480030\pi$
$821$	11.3409	+	27.3794i	0.395801	+	0.955549i	−0.592849	+	0.805314i	$0.701997\pi$
$822$		0			0
$823$	−17.6023	−	17.6023i	−0.613576	−	0.613576i	0.330300	−	0.943876i	$-0.392850\pi$
$823$	−17.6023	−	17.6023i	−0.613576	−	0.613576i	−0.943876	+	0.330300i	$0.892850\pi$
$824$		0			0
$825$	5.29510	−	5.29510i	0.184352	−	0.184352i
$826$		0			0
$827$	−21.9487	+	9.09145i	−0.763231	+	0.316141i	−0.730127	−	0.683311i	$-0.760539\pi$
$827$	−21.9487	+	9.09145i	−0.763231	+	0.316141i	−0.0331040	+	0.999452i	$0.510539\pi$
$828$		0			0
$829$	19.0679	−	46.0340i	0.662256	−	1.59883i	−0.132004	−	0.991249i	$-0.542141\pi$
$829$	19.0679	−	46.0340i	0.662256	−	1.59883i	0.794260	−	0.607578i	$-0.207859\pi$
$830$		0			0
$831$	−23.5659			−0.817492
$832$		0			0
$833$	−24.4275			−0.846363
$834$		0			0
$835$	7.55482	−	18.2389i	0.261445	−	0.631185i
$836$		0			0
$837$	33.2291	−	13.7639i	1.14856	−	0.475751i
$838$		0			0
$839$	32.6558	−	32.6558i	1.12740	−	1.12740i	0.136807	−	0.990598i	$-0.456316\pi$
$839$	32.6558	−	32.6558i	1.12740	−	1.12740i	0.990598	−	0.136807i	$-0.0436841\pi$
$840$		0			0
$841$	−57.3415	−	57.3415i	−1.97729	−	1.97729i
$842$		0			0
$843$	−6.88685	−	16.6263i	−0.237196	−	0.572641i
$844$		0			0
$845$	−7.14456	−	2.95938i	−0.245780	−	0.101806i
$846$		0			0
$847$			23.7181i			0.814964i
$848$		0			0
$849$		−	12.8591i		−	0.441322i
$850$		0			0
$851$	−9.89024	−	4.09667i	−0.339033	−	0.140432i
$852$		0			0
$853$	−0.105373	−	0.254393i	−0.00360790	−	0.00871025i	0.922065	−	0.387034i	$-0.126501\pi$
$853$	−0.105373	−	0.254393i	−0.00360790	−	0.00871025i	−0.925673	+	0.378324i	$0.876501\pi$
$854$		0			0
$855$	5.82854	+	5.82854i	0.199332	+	0.199332i
$856$		0			0
$857$	15.7107	−	15.7107i	0.536666	−	0.536666i	−0.385882	−	0.922548i	$-0.626103\pi$
$857$	15.7107	−	15.7107i	0.536666	−	0.536666i	0.922548	+	0.385882i	$0.126103\pi$
$858$		0			0
$859$	0.496502	−	0.205658i	0.0169404	−	0.00701695i	−0.374197	−	0.927349i	$-0.622082\pi$
$859$	0.496502	−	0.205658i	0.0169404	−	0.00701695i	0.391138	+	0.920332i	$0.372082\pi$
$860$		0			0
$861$	2.31319	−	5.58454i	0.0788334	−	0.190321i
$862$		0			0
$863$	11.3841			0.387520			0.193760	−	0.981049i	$-0.437932\pi$
$863$	11.3841			0.387520			0.193760	+	0.981049i	$0.437932\pi$
$864$		0			0
$865$	−6.86800			−0.233519
$866$		0			0
$867$	6.81817	−	16.4605i	0.231557	−	0.559028i
$868$		0			0
$869$	3.27311	−	1.35577i	0.111033	−	0.0459912i
$870$		0			0
$871$	−14.2466	+	14.2466i	−0.482728	+	0.482728i
$872$		0			0
$873$	1.31877	+	1.31877i	0.0446334	+	0.0446334i
$874$		0			0
$875$	−11.0614	−	26.7046i	−0.373943	−	0.902779i
$876$		0			0
$877$	−4.25139	−	1.76098i	−0.143559	−	0.0594642i	0.309747	−	0.950819i	$-0.399756\pi$
$877$	−4.25139	−	1.76098i	−0.143559	−	0.0594642i	−0.453306	+	0.891355i	$0.649756\pi$
$878$		0			0
$879$			14.9853i			0.505442i
$880$		0			0
$881$			41.1185i			1.38532i	0.721266	+	0.692658i	$0.243561\pi$
$881$			41.1185i			1.38532i	−0.721266	+	0.692658i	$0.756439\pi$
$882$		0			0
$883$	−28.8046	−	11.9313i	−0.969353	−	0.401519i	−0.158881	−	0.987298i	$-0.550789\pi$
$883$	−28.8046	−	11.9313i	−0.969353	−	0.401519i	−0.810471	+	0.585779i	$0.800789\pi$
$884$		0			0
$885$	4.19740	+	10.1334i	0.141094	+	0.340631i
$886$		0			0
$887$	−8.97107	−	8.97107i	−0.301219	−	0.301219i	0.540272	−	0.841491i	$-0.318321\pi$
$887$	−8.97107	−	8.97107i	−0.301219	−	0.301219i	−0.841491	+	0.540272i	$0.818321\pi$
$888$		0			0
$889$	2.58307	−	2.58307i	0.0866333	−	0.0866333i
$890$		0			0
$891$	−3.52374	+	1.45958i	−0.118050	+	0.0488977i
$892$		0			0
$893$	−5.15461	+	12.4443i	−0.172492	+	0.416434i
$894$		0			0
$895$	−0.833341			−0.0278555
$896$		0			0
$897$	8.50867			0.284096
$898$		0			0
$899$	30.2008	−	72.9112i	1.00725	−	2.43172i
$900$		0			0
$901$	−48.2596	+	19.9898i	−1.60776	+	0.665956i
$902$		0			0
$903$	25.7760	−	25.7760i	0.857771	−	0.857771i
$904$		0			0
$905$	11.6663	+	11.6663i	0.387801	+	0.387801i
$906$		0			0
$907$	2.44502	+	5.90281i	0.0811857	+	0.196000i	0.959260	−	0.282525i	$-0.0911719\pi$
$907$	2.44502	+	5.90281i	0.0811857	+	0.196000i	−0.878074	+	0.478524i	$0.841172\pi$
$908$		0			0
$909$	0.00362358	+	0.00150094i	0.000120187	+	4.97830e-5i
$910$		0			0
$911$			2.93353i			0.0971921i	0.998819	+	0.0485961i	$0.0154747\pi$
$911$			2.93353i			0.0971921i	−0.998819	+	0.0485961i	$0.984525\pi$
$912$		0			0
$913$		−	10.1999i		−	0.337568i
$914$		0			0
$915$	−0.148154	−	0.0613674i	−0.00489782	−	0.00202874i
$916$		0			0
$917$	23.5066	+	56.7500i	0.776257	+	1.87405i
$918$		0			0
$919$	31.0406	+	31.0406i	1.02393	+	1.02393i	0.999706	+	0.0242270i	$0.00771244\pi$
$919$	31.0406	+	31.0406i	1.02393	+	1.02393i	0.0242270	+	0.999706i	$0.492288\pi$
$920$		0			0
$921$	4.57093	−	4.57093i	0.150617	−	0.150617i
$922$		0			0
$923$	−22.9477	+	9.50524i	−0.755332	+	0.312869i
$924$		0			0
$925$	−4.06332	+	9.80971i	−0.133601	+	0.322541i
$926$		0			0
$927$	26.9234			0.884282
$928$		0			0
$929$	−11.7583			−0.385776			−0.192888	−	0.981221i	$-0.561785\pi$
$929$	−11.7583			−0.385776			−0.192888	+	0.981221i	$0.561785\pi$
$930$		0			0
$931$	6.28830	−	15.1813i	0.206091	−	0.497547i
$932$		0			0
$933$	−26.4840	+	10.9700i	−0.867048	+	0.359143i
$934$		0			0
$935$	7.99579	−	7.99579i	0.261490	−	0.261490i
$936$		0			0
$937$	1.46723	+	1.46723i	0.0479325	+	0.0479325i	0.730667	−	0.682734i	$-0.239209\pi$
$937$	1.46723	+	1.46723i	0.0479325	+	0.0479325i	−0.682734	+	0.730667i	$0.739209\pi$
$938$		0			0
$939$	−1.40531	−	3.39273i	−0.0458607	−	0.110718i
$940$		0			0
$941$	−9.34561	−	3.87108i	−0.304658	−	0.126194i	0.225117	−	0.974332i	$-0.427724\pi$
$941$	−9.34561	−	3.87108i	−0.304658	−	0.126194i	−0.529775	+	0.848138i	$0.677724\pi$
$942$		0			0
$943$		−	8.03193i		−	0.261556i
$944$		0			0
$945$		−	15.2139i		−	0.494909i
$946$		0			0
$947$	33.0365	+	13.6842i	1.07354	+	0.444676i	0.848240	−	0.529613i	$-0.177663\pi$
$947$	33.0365	+	13.6842i	1.07354	+	0.444676i	0.225303	+	0.974289i	$0.427663\pi$
$948$		0			0
$949$	7.01337	+	16.9318i	0.227664	+	0.549628i
$950$		0			0
$951$	−2.78911	−	2.78911i	−0.0904430	−	0.0904430i
$952$		0			0
$953$	11.2740	−	11.2740i	0.365201	−	0.365201i	−0.500523	−	0.865723i	$-0.666859\pi$
$953$	11.2740	−	11.2740i	0.365201	−	0.365201i	0.865723	+	0.500523i	$0.166859\pi$
$954$		0			0
$955$	19.2311	−	7.96579i	0.622305	−	0.257767i
$956$		0			0
$957$	7.36036	−	17.7695i	0.237927	−	0.574406i
$958$		0			0
$959$	27.4338			0.885883
$960$		0			0
$961$	25.5715			0.824886
$962$		0			0
$963$	−2.71763	+	6.56093i	−0.0875743	+	0.211423i
$964$		0			0
$965$	0.566282	−	0.234562i	0.0182293	−	0.00755080i
$966$		0			0
$967$	25.1865	−	25.1865i	0.809944	−	0.809944i	−0.174681	−	0.984625i	$-0.555889\pi$
$967$	25.1865	−	25.1865i	0.809944	−	0.809944i	0.984625	+	0.174681i	$0.0558893\pi$
$968$		0			0
$969$	16.0100	+	16.0100i	0.514314	+	0.514314i
$970$		0			0
$971$	−2.92168	−	7.05357i	−0.0937613	−	0.226360i	0.870040	−	0.492981i	$-0.164093\pi$
$971$	−2.92168	−	7.05357i	−0.0937613	−	0.226360i	−0.963801	+	0.266621i	$0.914093\pi$
$972$		0			0
$973$	41.2759	+	17.0971i	1.32325	+	0.548106i
$974$		0			0
$975$		−	8.43939i		−	0.270277i
$976$		0			0
$977$			21.0511i			0.673484i	0.941597	+	0.336742i	$0.109325\pi$
$977$			21.0511i			0.673484i	−0.941597	+	0.336742i	$0.890675\pi$
$978$		0			0
$979$	−16.4012	−	6.79359i	−0.524184	−	0.217124i
$980$		0			0
$981$	6.80946	+	16.4395i	0.217409	+	0.524873i
$982$		0			0
$983$	23.6221	+	23.6221i	0.753429	+	0.753429i	0.975117	−	0.221689i	$-0.0711569\pi$
$983$	23.6221	+	23.6221i	0.753429	+	0.753429i	−0.221689	+	0.975117i	$0.571157\pi$
$984$		0			0
$985$	13.9936	−	13.9936i	0.445873	−	0.445873i
$986$		0			0
$987$	9.54108	−	3.95205i	0.303696	−	0.125795i
$988$		0			0
$989$	18.5361	−	44.7500i	0.589412	−	1.42297i
$990$		0			0
$991$	27.0358			0.858822			0.429411	−	0.903109i	$-0.358721\pi$
$991$	27.0358			0.858822			0.429411	+	0.903109i	$0.358721\pi$
$992$		0			0
$993$	−15.0922			−0.478936
$994$		0			0
$995$	−4.12067	+	9.94819i	−0.130634	+	0.315379i
$996$		0			0
$997$	−32.4278	+	13.4320i	−1.02700	+	0.425397i	−0.831628	−	0.555333i	$-0.812591\pi$
$997$	−32.4278	+	13.4320i	−1.02700	+	0.425397i	−0.195371	+	0.980729i	$0.562591\pi$
$998$		0			0
$999$	−8.78861	+	8.78861i	−0.278059	+	0.278059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.g.d.129.2	yes	16
4.3	odd	2	inner	1024.2.g.d.129.3	yes	16
8.3	odd	2		1024.2.g.g.129.2	yes	16
8.5	even	2		1024.2.g.g.129.3	yes	16
16.3	odd	4		1024.2.g.f.641.3	yes	16
16.5	even	4		1024.2.g.a.641.3	yes	16
16.11	odd	4		1024.2.g.a.641.2	yes	16
16.13	even	4		1024.2.g.f.641.2	yes	16
32.3	odd	8		1024.2.g.f.385.3	yes	16
32.5	even	8	inner	1024.2.g.d.897.2	yes	16
32.11	odd	8		1024.2.g.g.897.2	yes	16
32.13	even	8		1024.2.g.a.385.3	yes	16
32.19	odd	8		1024.2.g.a.385.2	✓	16
32.21	even	8		1024.2.g.g.897.3	yes	16
32.27	odd	8	inner	1024.2.g.d.897.3	yes	16
32.29	even	8		1024.2.g.f.385.2	yes	16
64.5	even	16		4096.2.a.s.1.2		8
64.27	odd	16		4096.2.a.s.1.1		8
64.37	even	16		4096.2.a.i.1.7		8
64.59	odd	16		4096.2.a.i.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.a.385.2	✓	16	32.19	odd	8
1024.2.g.a.385.3	yes	16	32.13	even	8
1024.2.g.a.641.2	yes	16	16.11	odd	4
1024.2.g.a.641.3	yes	16	16.5	even	4
1024.2.g.d.129.2	yes	16	1.1	even	1	trivial
1024.2.g.d.129.3	yes	16	4.3	odd	2	inner
1024.2.g.d.897.2	yes	16	32.5	even	8	inner
1024.2.g.d.897.3	yes	16	32.27	odd	8	inner
1024.2.g.f.385.2	yes	16	32.29	even	8
1024.2.g.f.385.3	yes	16	32.3	odd	8
1024.2.g.f.641.2	yes	16	16.13	even	4
1024.2.g.f.641.3	yes	16	16.3	odd	4
1024.2.g.g.129.2	yes	16	8.3	odd	2
1024.2.g.g.129.3	yes	16	8.5	even	2
1024.2.g.g.897.2	yes	16	32.11	odd	8
1024.2.g.g.897.3	yes	16	32.21	even	8
4096.2.a.i.1.7		8	64.37	even	16
4096.2.a.i.1.8		8	64.59	odd	16
4096.2.a.s.1.1		8	64.27	odd	16
4096.2.a.s.1.2		8	64.5	even	16

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:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1024.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.356604 + 0.860919i) q^{3} +(0.883663 - 0.366025i) q^{5} +(-2.35207 + 2.35207i) q^{7} +(1.50731 + 1.50731i) q^{9} +O(q^{10})\)	\(q+(-0.356604 + 0.860919i) q^{3} +(0.883663 - 0.366025i) q^{5} +(-2.35207 + 2.35207i) q^{7} +(1.50731 + 1.50731i) q^{9} +(0.752787 + 1.81739i) q^{11} +(2.04819 + 0.848387i) q^{13} +0.891289i q^{15} -6.00997i q^{17} +(3.73510 + 1.54713i) q^{19} +(-1.18618 - 2.86370i) q^{21} +(-2.91236 - 2.91236i) q^{23} +(-2.88865 + 2.88865i) q^{25} +(-4.41794 + 1.82997i) q^{27} +(-4.01532 + 9.69383i) q^{29} -7.52140 q^{31} -1.83307 q^{33} +(-1.21752 + 2.93936i) q^{35} +(2.40130 - 0.994652i) q^{37} +(-1.46078 + 1.46078i) q^{39} +(1.37894 + 1.37894i) q^{41} +(4.50046 + 10.8651i) q^{43} +(1.88366 + 0.780239i) q^{45} +3.33173i q^{47} -4.06450i q^{49} +(5.17409 + 2.14318i) q^{51} +(-3.32611 - 8.02993i) q^{53} +(1.33042 + 1.33042i) q^{55} +(-2.66390 + 2.66390i) q^{57} +(11.3694 - 4.70936i) q^{59} +(-0.0688525 + 0.166225i) q^{61} -7.09059 q^{63} +2.12044 q^{65} +(-3.47786 + 8.39629i) q^{67} +(3.54587 - 1.46875i) q^{69} +(-7.92235 + 7.92235i) q^{71} +(5.84544 + 5.84544i) q^{73} +(-1.45679 - 3.51699i) q^{75} +(-6.04524 - 2.50402i) q^{77} -1.80100i q^{79} +1.93890i q^{81} +(-4.79049 - 1.98429i) q^{83} +(-2.19980 - 5.31079i) q^{85} +(-6.91372 - 6.91372i) q^{87} +(-6.38134 + 6.38134i) q^{89} +(-6.81296 + 2.82202i) q^{91} +(2.68216 - 6.47531i) q^{93} +3.86686 q^{95} +0.874915 q^{97} +(-1.60468 + 3.87404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q - 8 * q^5 + 16 * q^9	\( 16 q - 8 q^{5} + 16 q^{9} + 24 q^{13} - 48 q^{21} + 32 q^{25} - 8 q^{29} - 80 q^{33} + 8 q^{37} + 16 q^{41} + 8 q^{45} + 40 q^{53} + 16 q^{57} + 8 q^{61} - 32 q^{65} - 32 q^{73} + 32 q^{77} - 32 q^{85} - 32 q^{89} + 48 q^{93} - 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 + 16 * q^9 + 24 * q^13 - 48 * q^21 + 32 * q^25 - 8 * q^29 - 80 * q^33 + 8 * q^37 + 16 * q^41 + 8 * q^45 + 40 * q^53 + 16 * q^57 + 8 * q^61 - 32 * q^65 - 32 * q^73 + 32 * q^77 - 32 * q^85 - 32 * q^89 + 48 * q^93 - 16 * q^97

Introduction

L-functions

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Database

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