LMFDB - Embedded newform 1024.2.g.c.897.2

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:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8x^{14} + 32x^{12} - 64x^{10} + 127x^{8} - 576x^{6} + 2592x^{4} - 5832x^{2} + 6561 $ x^16 - 8x^14 + 32x^12 - 64x^10 + 127x^8 - 576x^6 + 2592x^4 - 5832*x^2 + 6561
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			897.2
Root			$-0.639878 - 1.60952i$ of defining polynomial
Character	$\chi$	$=$	1024.897
Dual form			1024.2.g.c.129.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.401639 - 0.969643i) q^{3} +(-3.49877 - 1.44924i) q^{5} +(-3.21904 - 3.21904i) q^{7} +(1.34243 - 1.34243i) q^{9} +O(q^{10})$	\(q+(-0.401639 - 0.969643i) q^{3} +(-3.49877 - 1.44924i) q^{5} +(-3.21904 - 3.21904i) q^{7} +(1.34243 - 1.34243i) q^{9} +(0.363728 - 0.878116i) q^{11} +(-2.37919 + 0.985492i) q^{13} +3.97463i q^{15} +1.34416i q^{17} +(-3.10629 + 1.28667i) q^{19} +(-1.82843 + 4.41421i) q^{21} +(4.30143 - 4.30143i) q^{23} +(6.60559 + 6.60559i) q^{25} +(-4.74977 - 1.96742i) q^{27} +(0.600295 + 1.44924i) q^{29} +3.69552 q^{31} -0.997546 q^{33} +(6.59753 + 15.9279i) q^{35} +(4.03257 + 1.67035i) q^{37} +(1.91115 + 1.91115i) q^{39} +(-5.34171 + 5.34171i) q^{41} +(3.01477 - 7.27829i) q^{43} +(-6.64235 + 2.75135i) q^{45} +1.02878i q^{47} +13.7245i q^{49} +(1.30336 - 0.539868i) q^{51} +(-2.69188 + 6.49877i) q^{53} +(-2.54520 + 2.54520i) q^{55} +(2.49522 + 2.49522i) q^{57} +(-5.90700 - 2.44676i) q^{59} +(1.83444 + 4.42872i) q^{61} -8.64266 q^{63} +9.75245 q^{65} +(-2.58213 - 6.23381i) q^{67} +(-5.89848 - 2.44323i) q^{69} +(-5.75634 - 5.75634i) q^{71} +(-2.94801 + 2.94801i) q^{73} +(3.75200 - 9.05812i) q^{75} +(-3.99755 + 1.65584i) q^{77} +15.4357i q^{79} -0.299657i q^{81} +(11.2627 - 4.66516i) q^{83} +(1.94801 - 4.70292i) q^{85} +(1.16414 - 1.16414i) q^{87} +(-9.04708 - 9.04708i) q^{89} +(10.8310 + 4.48636i) q^{91} +(-1.48427 - 3.58333i) q^{93} +12.7329 q^{95} +8.41176 q^{97} +(-0.690529 - 1.66708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 16 q^{21} + 32 q^{25} + 24 q^{29} + 80 q^{33} - 40 q^{37} + 16 q^{41} - 24 q^{45} + 56 q^{53} + 80 q^{57} - 8 q^{61} + 32 q^{65} - 32 q^{69} + 32 q^{73} + 32 q^{77} - 48 q^{85} - 32 q^{89} + 16 q^{93} + 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 + 16 * q^9 - 24 * q^13 + 16 * q^21 + 32 * q^25 + 24 * q^29 + 80 * q^33 - 40 * q^37 + 16 * q^41 - 24 * q^45 + 56 * q^53 + 80 * q^57 - 8 * q^61 + 32 * q^65 - 32 * q^69 + 32 * q^73 + 32 * q^77 - 48 * q^85 - 32 * q^89 + 16 * q^93 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.401639	−	0.969643i	−0.231887	−	0.559824i	0.764513	−	0.644609i	$-0.222980\pi$
$3$	−0.401639	−	0.969643i	−0.231887	−	0.559824i	−0.996399	+	0.0847850i	$0.972980\pi$
$4$		0			0
$5$	−3.49877	−	1.44924i	−1.56470	−	0.648120i	−0.578801	−	0.815469i	$-0.696479\pi$
$5$	−3.49877	−	1.44924i	−1.56470	−	0.648120i	−0.985898	+	0.167349i	$0.946479\pi$
$6$		0			0
$7$	−3.21904	−	3.21904i	−1.21668	−	1.21668i	−0.968786	−	0.247897i	$-0.920261\pi$
$7$	−3.21904	−	3.21904i	−1.21668	−	1.21668i	−0.247897	−	0.968786i	$-0.579739\pi$
$8$		0			0
$9$	1.34243	−	1.34243i	0.447476	−	0.447476i
$10$		0			0
$11$	0.363728	−	0.878116i	0.109668	−	0.264762i	−0.859512	−	0.511116i	$-0.829232\pi$
$11$	0.363728	−	0.878116i	0.109668	−	0.264762i	0.969180	+	0.246354i	$0.0792324\pi$
$12$		0			0
$13$	−2.37919	+	0.985492i	−0.659868	+	0.273326i	−0.687383	−	0.726295i	$-0.741241\pi$
$13$	−2.37919	+	0.985492i	−0.659868	+	0.273326i	0.0275150	+	0.999621i	$0.491241\pi$
$14$		0			0
$15$			3.97463i			1.02625i
$16$		0			0
$17$			1.34416i			0.326007i	0.986625	+	0.163004i	$0.0521182\pi$
$17$			1.34416i			0.326007i	−0.986625	+	0.163004i	$0.947882\pi$
$18$		0			0
$19$	−3.10629	+	1.28667i	−0.712632	+	0.295182i	−0.709393	−	0.704813i	$-0.751031\pi$
$19$	−3.10629	+	1.28667i	−0.712632	+	0.295182i	−0.00323890	+	0.999995i	$0.501031\pi$
$20$		0			0
$21$	−1.82843	+	4.41421i	−0.398996	+	0.963260i
$22$		0			0
$23$	4.30143	−	4.30143i	0.896911	−	0.896911i	−0.0982508	−	0.995162i	$-0.531325\pi$
$23$	4.30143	−	4.30143i	0.896911	−	0.896911i	0.995162	+	0.0982508i	$0.0313247\pi$
$24$		0			0
$25$	6.60559	+	6.60559i	1.32112	+	1.32112i
$26$		0			0
$27$	−4.74977	−	1.96742i	−0.914095	−	0.378630i
$28$		0			0
$29$	0.600295	+	1.44924i	0.111472	+	0.269117i	0.969764	−	0.244044i	$-0.0784742\pi$
$29$	0.600295	+	1.44924i	0.111472	+	0.269117i	−0.858292	+	0.513161i	$0.828474\pi$
$30$		0			0
$31$	3.69552			0.663735			0.331867	−	0.943326i	$-0.392321\pi$
$31$	3.69552			0.663735			0.331867	+	0.943326i	$0.392321\pi$
$32$		0			0
$33$	−0.997546			−0.173651
$34$		0			0
$35$	6.59753	+	15.9279i	1.11519	+	2.69230i
$36$		0			0
$37$	4.03257	+	1.67035i	0.662951	+	0.274603i	0.688680	−	0.725066i	$-0.258191\pi$
$37$	4.03257	+	1.67035i	0.662951	+	0.274603i	−0.0257289	+	0.999669i	$0.508191\pi$
$38$		0			0
$39$	1.91115	+	1.91115i	0.306029	+	0.306029i
$40$		0			0
$41$	−5.34171	+	5.34171i	−0.834235	+	0.834235i	−0.988093	−	0.153858i	$-0.950830\pi$
$41$	−5.34171	+	5.34171i	−0.834235	+	0.834235i	0.153858	+	0.988093i	$0.450830\pi$
$42$		0			0
$43$	3.01477	−	7.27829i	0.459747	−	1.10993i	−0.508752	−	0.860913i	$-0.669893\pi$
$43$	3.01477	−	7.27829i	0.459747	−	1.10993i	0.968500	−	0.249015i	$-0.0801070\pi$
$44$		0			0
$45$	−6.64235	+	2.75135i	−0.990182	+	0.410147i
$46$		0			0
$47$			1.02878i			0.150063i	0.997181	+	0.0750313i	$0.0239057\pi$
$47$			1.02878i			0.150063i	−0.997181	+	0.0750313i	$0.976094\pi$
$48$		0			0
$49$			13.7245i			1.96064i
$50$		0			0
$51$	1.30336	−	0.539868i	0.182507	−	0.0755967i
$52$		0			0
$53$	−2.69188	+	6.49877i	−0.369758	+	0.892675i	0.624031	+	0.781399i	$0.285494\pi$
$53$	−2.69188	+	6.49877i	−0.369758	+	0.892675i	−0.993790	+	0.111276i	$0.964506\pi$
$54$		0			0
$55$	−2.54520	+	2.54520i	−0.343195	+	0.343195i
$56$		0			0
$57$	2.49522	+	2.49522i	0.330500	+	0.330500i
$58$		0			0
$59$	−5.90700	−	2.44676i	−0.769027	−	0.318541i	−0.0365485	−	0.999332i	$-0.511636\pi$
$59$	−5.90700	−	2.44676i	−0.769027	−	0.318541i	−0.732478	+	0.680791i	$0.761636\pi$
$60$		0			0
$61$	1.83444	+	4.42872i	0.234876	+	0.567040i	0.996739	−	0.0806985i	$-0.0257151\pi$
$61$	1.83444	+	4.42872i	0.234876	+	0.567040i	−0.761863	+	0.647738i	$0.775715\pi$
$62$		0			0
$63$	−8.64266			−1.08887
$64$		0			0
$65$	9.75245			1.20964
$66$		0			0
$67$	−2.58213	−	6.23381i	−0.315457	−	0.761581i	−0.999484	−	0.0321238i	$-0.989773\pi$
$67$	−2.58213	−	6.23381i	−0.315457	−	0.761581i	0.684027	−	0.729457i	$-0.260227\pi$
$68$		0			0
$69$	−5.89848	−	2.44323i	−0.710093	−	0.294130i
$70$		0			0
$71$	−5.75634	−	5.75634i	−0.683152	−	0.683152i	0.277557	−	0.960709i	$-0.410475\pi$
$71$	−5.75634	−	5.75634i	−0.683152	−	0.683152i	−0.960709	+	0.277557i	$0.910475\pi$
$72$		0			0
$73$	−2.94801	+	2.94801i	−0.345039	+	0.345039i	−0.858258	−	0.513219i	$-0.828453\pi$
$73$	−2.94801	+	2.94801i	−0.345039	+	0.345039i	0.513219	+	0.858258i	$0.328453\pi$
$74$		0			0
$75$	3.75200	−	9.05812i	0.433243	−	1.04594i
$76$		0			0
$77$	−3.99755	+	1.65584i	−0.455563	+	0.188700i
$78$		0			0
$79$			15.4357i			1.73665i	0.495996	+	0.868325i	$0.334803\pi$
$79$			15.4357i			1.73665i	−0.495996	+	0.868325i	$0.665197\pi$
$80$		0			0
$81$		−	0.299657i		−	0.0332952i
$82$		0			0
$83$	11.2627	−	4.66516i	1.23624	−	0.512068i	0.333703	−	0.942678i	$-0.391702\pi$
$83$	11.2627	−	4.66516i	1.23624	−	0.512068i	0.902538	+	0.430610i	$0.141702\pi$
$84$		0			0
$85$	1.94801	−	4.70292i	0.211292	−	0.510103i
$86$		0			0
$87$	1.16414	−	1.16414i	0.124809	−	0.124809i
$88$		0			0
$89$	−9.04708	−	9.04708i	−0.958989	−	0.958989i	0.0402029	−	0.999192i	$-0.487200\pi$
$89$	−9.04708	−	9.04708i	−0.958989	−	0.958989i	−0.999192	+	0.0402029i	$0.987200\pi$
$90$		0			0
$91$	10.8310	+	4.48636i	1.13540	+	0.470299i
$92$		0			0
$93$	−1.48427	−	3.58333i	−0.153911	−	0.371574i
$94$		0			0
$95$	12.7329			1.30637
$96$		0			0
$97$	8.41176			0.854085			0.427042	−	0.904232i	$-0.359556\pi$
$97$	8.41176			0.854085			0.427042	+	0.904232i	$0.359556\pi$
$98$		0			0
$99$	−0.690529	−	1.66708i	−0.0694008	−	0.167548i
$100$		0			0
$101$	−8.69188	−	3.60029i	−0.864874	−	0.358243i	−0.0942625	−	0.995547i	$-0.530049\pi$
$101$	−8.69188	−	3.60029i	−0.864874	−	0.358243i	−0.770612	+	0.637305i	$0.780049\pi$
$102$		0			0
$103$	−6.64927	−	6.64927i	−0.655172	−	0.655172i	0.299062	−	0.954234i	$-0.403326\pi$
$103$	−6.64927	−	6.64927i	−0.655172	−	0.655172i	−0.954234	+	0.299062i	$0.903326\pi$
$104$		0			0
$105$	12.7945	−	12.7945i	1.24862	−	1.24862i
$106$		0			0
$107$	−3.19970	+	7.72475i	−0.309326	+	0.746780i	0.690401	+	0.723427i	$0.257434\pi$
$107$	−3.19970	+	7.72475i	−0.309326	+	0.746780i	−0.999727	+	0.0233529i	$0.992566\pi$
$108$		0			0
$109$	−0.670346	+	0.277666i	−0.0642075	+	0.0265956i	−0.414556	−	0.910024i	$-0.636063\pi$
$109$	−0.670346	+	0.277666i	−0.0642075	+	0.0265956i	0.350349	+	0.936619i	$0.386063\pi$
$110$		0			0
$111$		−	4.58103i		−	0.434812i
$112$		0			0
$113$		−	15.8960i		−	1.49537i	−0.664052	−	0.747686i	$-0.731165\pi$
$113$		−	15.8960i		−	1.49537i	0.664052	−	0.747686i	$-0.268835\pi$
$114$		0			0
$115$	−21.2835	+	8.81593i	−1.98470	+	0.822090i
$116$		0			0
$117$	−1.87094	+	4.51684i	−0.172968	+	0.417582i
$118$		0			0
$119$	4.32691	−	4.32691i	0.396647	−	0.396647i
$120$		0			0
$121$	7.13938	+	7.13938i	0.649035	+	0.649035i
$122$		0			0
$123$	7.32499	+	3.03411i	0.660472	+	0.273576i
$124$		0			0
$125$	−6.29217	−	15.1907i	−0.562789	−	1.35869i
$126$		0			0
$127$	−3.43664			−0.304953			−0.152476	−	0.988307i	$-0.548725\pi$
$127$	−3.43664			−0.304953			−0.152476	+	0.988307i	$0.548725\pi$
$128$		0			0
$129$	−8.26819			−0.727973
$130$		0			0
$131$	−1.39250	−	3.36180i	−0.121664	−	0.293722i	0.851300	−	0.524679i	$-0.175815\pi$
$131$	−1.39250	−	3.36180i	−0.121664	−	0.293722i	−0.972964	+	0.230956i	$0.925815\pi$
$132$		0			0
$133$	14.1411	+	5.85744i	1.22619	+	0.507905i
$134$		0			0
$135$	13.7671	+	13.7671i	1.18489	+	1.18489i
$136$		0			0
$137$	−1.79941	+	1.79941i	−0.153734	+	0.153734i	−0.779783	−	0.626049i	$-0.784671\pi$
$137$	−1.79941	+	1.79941i	−0.153734	+	0.153734i	0.626049	+	0.779783i	$0.284671\pi$
$138$		0			0
$139$	−6.67049	+	16.1040i	−0.565784	+	1.36592i	0.339295	+	0.940680i	$0.389811\pi$
$139$	−6.67049	+	16.1040i	−0.565784	+	1.36592i	−0.905079	+	0.425243i	$0.860189\pi$
$140$		0			0
$141$	0.997546	−	0.413197i	0.0840086	−	0.0347975i
$142$		0			0
$143$			2.44765i			0.204683i
$144$		0			0
$145$		−	5.94053i		−	0.493334i
$146$		0			0
$147$	13.3078	−	5.51228i	1.09761	−	0.454645i
$148$		0			0
$149$	6.60029	−	15.9345i	0.540717	−	1.30541i	−0.383500	−	0.923541i	$-0.625282\pi$
$149$	6.60029	−	15.9345i	0.540717	−	1.30541i	0.924218	−	0.381866i	$-0.124718\pi$
$150$		0			0
$151$	−6.89235	+	6.89235i	−0.560892	+	0.560892i	−0.929561	−	0.368669i	$-0.879814\pi$
$151$	−6.89235	+	6.89235i	−0.560892	+	0.560892i	0.368669	+	0.929561i	$0.379814\pi$
$152$		0			0
$153$	1.80444	+	1.80444i	0.145880	+	0.145880i
$154$		0			0
$155$	−12.9298	−	5.35569i	−1.03854	−	0.430179i
$156$		0			0
$157$	2.72090	+	6.56882i	0.217151	+	0.524249i	0.994490	−	0.104833i	$-0.0334308\pi$
$157$	2.72090	+	6.56882i	0.217151	+	0.524249i	−0.777339	+	0.629082i	$0.783431\pi$
$158$		0			0
$159$	7.38265			0.585483
$160$		0			0
$161$	−27.6930			−2.18251
$162$		0			0
$163$	−0.849981	−	2.05204i	−0.0665756	−	0.160728i	0.887090	−	0.461597i	$-0.152723\pi$
$163$	−0.849981	−	2.05204i	−0.0665756	−	0.160728i	−0.953665	+	0.300869i	$0.902723\pi$
$164$		0			0
$165$	3.49019	+	1.44568i	0.271711	+	0.112546i
$166$		0			0
$167$	−1.05426	−	1.05426i	−0.0815808	−	0.0815808i	0.665139	−	0.746720i	$-0.268372\pi$
$167$	−1.05426	−	1.05426i	−0.0815808	−	0.0815808i	−0.746720	+	0.665139i	$0.768372\pi$
$168$		0			0
$169$	−4.50305	+	4.50305i	−0.346388	+	0.346388i
$170$		0			0
$171$	−2.44271	+	5.89723i	−0.186799	+	0.450972i
$172$		0			0
$173$	17.5904	−	7.28617i	1.33737	−	0.553957i	0.404622	−	0.914484i	$-0.367403\pi$
$173$	17.5904	−	7.28617i	1.33737	−	0.553957i	0.932749	+	0.360527i	$0.117403\pi$
$174$		0			0
$175$		−	42.5273i		−	3.21476i
$176$		0			0
$177$			6.71040i			0.504385i
$178$		0			0
$179$	−10.2700	+	4.25395i	−0.767612	+	0.317955i	−0.731905	−	0.681407i	$-0.761368\pi$
$179$	−10.2700	+	4.25395i	−0.767612	+	0.317955i	−0.0357074	+	0.999362i	$0.511368\pi$
$180$		0			0
$181$	−1.12805	+	2.72335i	−0.0838472	+	0.202425i	−0.960242	−	0.279168i	$-0.909941\pi$
$181$	−1.12805	+	2.72335i	−0.0838472	+	0.202425i	0.876395	+	0.481593i	$0.159941\pi$
$182$		0			0
$183$	3.55750	−	3.55750i	0.262978	−	0.262978i
$184$		0			0
$185$	−11.6883	−	11.6883i	−0.859343	−	0.859343i
$186$		0			0
$187$	1.18033	+	0.488909i	0.0863143	+	0.0357526i
$188$		0			0
$189$	8.95651	+	21.6229i	0.651490	+	1.57284i
$190$		0			0
$191$	−21.2674			−1.53885			−0.769426	−	0.638736i	$-0.779458\pi$
$191$	−21.2674			−1.53885			−0.769426	+	0.638736i	$0.779458\pi$
$192$		0			0
$193$	−2.75491			−0.198302			−0.0991512	−	0.995072i	$-0.531613\pi$
$193$	−2.75491			−0.198302			−0.0991512	+	0.995072i	$0.531613\pi$
$194$		0			0
$195$	−3.91697	−	9.45640i	−0.280500	−	0.677187i
$196$		0			0
$197$	5.05309	+	2.09306i	0.360018	+	0.149124i	0.555358	−	0.831611i	$-0.312581\pi$
$197$	5.05309	+	2.09306i	0.360018	+	0.149124i	−0.195340	+	0.980735i	$0.562581\pi$
$198$		0			0
$199$	15.3344	+	15.3344i	1.08702	+	1.08702i	0.995833	+	0.0911915i	$0.0290675\pi$
$199$	15.3344	+	15.3344i	1.08702	+	1.08702i	0.0911915	+	0.995833i	$0.470932\pi$
$200$		0			0
$201$	−5.00748	+	5.00748i	−0.353201	+	0.353201i
$202$		0			0
$203$	2.73279	−	6.59753i	0.191804	−	0.463056i
$204$		0			0
$205$	26.4308	−	10.9480i	1.84601	−	0.764642i
$206$		0			0
$207$		−	11.5487i		−	0.802692i
$208$		0			0
$209$			3.19568i			0.221050i
$210$		0			0
$211$	21.3205	−	8.83123i	1.46776	−	0.607967i	0.501414	−	0.865207i	$-0.332813\pi$
$211$	21.3205	−	8.83123i	1.46776	−	0.607967i	0.966347	+	0.257240i	$0.0828132\pi$
$212$		0			0
$213$	−3.26962	+	7.89357i	−0.224031	+	0.540859i
$214$		0			0
$215$	−21.0960	+	21.0960i	−1.43873	+	1.43873i
$216$		0			0
$217$	−11.8960	−	11.8960i	−0.807555	−	0.807555i
$218$		0			0
$219$	4.04256	+	1.67448i	0.273171	+	0.113151i
$220$		0			0
$221$	−1.32466	−	3.19801i	−0.0891063	−	0.215122i
$222$		0			0
$223$	−12.3493			−0.826973			−0.413487	−	0.910510i	$-0.635689\pi$
$223$	−12.3493			−0.826973			−0.413487	+	0.910510i	$0.635689\pi$
$224$		0			0
$225$	17.7350			1.18234
$226$		0			0
$227$	−1.77697	−	4.28999i	−0.117942	−	0.284736i	0.853873	−	0.520481i	$-0.174247\pi$
$227$	−1.77697	−	4.28999i	−0.117942	−	0.284736i	−0.971815	+	0.235744i	$0.924247\pi$
$228$		0			0
$229$	−4.32720	−	1.79239i	−0.285949	−	0.118444i	0.235098	−	0.971972i	$-0.424459\pi$
$229$	−4.32720	−	1.79239i	−0.285949	−	0.118444i	−0.521048	+	0.853527i	$0.674459\pi$
$230$		0			0
$231$	3.21114	+	3.21114i	0.211278	+	0.211278i
$232$		0			0
$233$	−0.848945	+	0.848945i	−0.0556162	+	0.0556162i	−0.734368	−	0.678752i	$-0.762521\pi$
$233$	−0.848945	+	0.848945i	−0.0556162	+	0.0556162i	0.678752	+	0.734368i	$0.262521\pi$
$234$		0			0
$235$	1.49094	−	3.59946i	0.0972585	−	0.234803i
$236$		0			0
$237$	14.9671	−	6.19957i	0.972217	−	0.402706i
$238$		0			0
$239$		−	1.40395i		−	0.0908141i	−0.998969	−	0.0454070i	$-0.985542\pi$
$239$		−	1.40395i		−	0.0908141i	0.998969	−	0.0454070i	$-0.0144585\pi$
$240$		0			0
$241$		−	17.3343i		−	1.11660i	−0.829638	−	0.558302i	$-0.811453\pi$
$241$		−	17.3343i		−	1.11660i	0.829638	−	0.558302i	$-0.188547\pi$
$242$		0			0
$243$	−14.5399	+	6.02262i	−0.932734	+	0.386351i
$244$		0			0
$245$	19.8900	−	48.0187i	1.27073	−	3.06781i
$246$		0			0
$247$	6.12245	−	6.12245i	0.389562	−	0.389562i
$248$		0			0
$249$	−9.04708	−	9.04708i	−0.573335	−	0.573335i
$250$		0			0
$251$	−4.06378	−	1.68327i	−0.256503	−	0.106247i	0.250726	−	0.968058i	$-0.419331\pi$
$251$	−4.06378	−	1.68327i	−0.256503	−	0.106247i	−0.507230	+	0.861811i	$0.669331\pi$
$252$		0			0
$253$	−2.21261	−	5.34171i	−0.139105	−	0.335830i
$254$		0			0
$255$	−5.34255			−0.334563
$256$		0			0
$257$	−24.5843			−1.53353			−0.766765	−	0.641928i	$-0.778135\pi$
$257$	−24.5843			−1.53353			−0.766765	+	0.641928i	$0.778135\pi$
$258$		0			0
$259$	−7.60410	−	18.3579i	−0.472496	−	1.14071i
$260$		0			0
$261$	2.75135	+	1.13965i	0.170304	+	0.0705423i
$262$		0			0
$263$	−13.4858	−	13.4858i	−0.831572	−	0.831572i	0.156160	−	0.987732i	$-0.450089\pi$
$263$	−13.4858	−	13.4858i	−0.831572	−	0.831572i	−0.987732	+	0.156160i	$0.950089\pi$
$264$		0			0
$265$	18.8366	−	18.8366i	1.15712	−	1.15712i
$266$		0			0
$267$	−5.13877	+	12.4061i	−0.314488	+	0.759241i
$268$		0			0
$269$	−12.0506	+	4.99154i	−0.734740	+	0.304339i	−0.718498	−	0.695529i	$-0.755170\pi$
$269$	−12.0506	+	4.99154i	−0.734740	+	0.304339i	−0.0162420	+	0.999868i	$0.505170\pi$
$270$		0			0
$271$			5.83168i			0.354250i	0.984188	+	0.177125i	$0.0566796\pi$
$271$			5.83168i			0.354250i	−0.984188	+	0.177125i	$0.943320\pi$
$272$		0			0
$273$		−	12.3041i		−	0.744681i
$274$		0			0
$275$	8.20311	−	3.39784i	0.494666	−	0.204897i
$276$		0			0
$277$	−6.57732	+	15.8791i	−0.395193	+	0.954080i	0.593596	+	0.804763i	$0.297708\pi$
$277$	−6.57732	+	15.8791i	−0.395193	+	0.954080i	−0.988789	+	0.149317i	$0.952292\pi$
$278$		0			0
$279$	4.96096	−	4.96096i	0.297005	−	0.297005i
$280$		0			0
$281$	2.49031	+	2.49031i	0.148559	+	0.148559i	0.777474	−	0.628915i	$-0.216501\pi$
$281$	2.49031	+	2.49031i	0.148559	+	0.148559i	−0.628915	+	0.777474i	$0.716501\pi$
$282$		0			0
$283$	23.8218	+	9.86733i	1.41606	+	0.586552i	0.953868	−	0.300227i	$-0.0970626\pi$
$283$	23.8218	+	9.86733i	1.41606	+	0.586552i	0.462193	+	0.886779i	$0.347063\pi$
$284$		0			0
$285$	−5.11403	−	12.3464i	−0.302929	−	0.731336i
$286$		0			0
$287$	34.3904			2.03000
$288$		0			0
$289$	15.1932			0.893719
$290$		0			0
$291$	−3.37849	−	8.15640i	−0.198051	−	0.478137i
$292$		0			0
$293$	26.3258	+	10.9045i	1.53797	+	0.637047i	0.981091	−	0.193548i	$-0.0619996\pi$
$293$	26.3258	+	10.9045i	1.53797	+	0.637047i	0.556877	+	0.830595i	$0.312000\pi$
$294$		0			0
$295$	17.1213	+	17.1213i	0.996842	+	0.996842i
$296$		0			0
$297$	−3.45525	+	3.45525i	−0.200494	+	0.200494i
$298$		0			0
$299$	−5.99489	+	14.4729i	−0.346693	+	0.836992i
$300$		0			0
$301$	−33.1338	+	13.7245i	−1.90980	+	0.791064i
$302$		0			0
$303$			9.87404i			0.567249i
$304$		0			0
$305$		−	18.1536i		−	1.03947i
$306$		0			0
$307$	2.50827	−	1.03896i	0.143155	−	0.0592967i	−0.309956	−	0.950751i	$-0.600314\pi$
$307$	2.50827	−	1.03896i	0.143155	−	0.0592967i	0.453111	+	0.891454i	$0.350314\pi$
$308$		0			0
$309$	−3.77681	+	9.11803i	−0.214855	+	0.518706i
$310$		0			0
$311$	−15.1737	+	15.1737i	−0.860419	+	0.860419i	−0.991387	−	0.130967i	$-0.958192\pi$
$311$	−15.1737	+	15.1737i	−0.860419	+	0.860419i	0.130967	+	0.991387i	$0.458192\pi$
$312$		0			0
$313$	−9.23773	−	9.23773i	−0.522148	−	0.522148i	0.396072	−	0.918219i	$-0.370373\pi$
$313$	−9.23773	−	9.23773i	−0.522148	−	0.522148i	−0.918219	+	0.396072i	$0.870373\pi$
$314$		0			0
$315$	30.2387	+	12.5253i	1.70376	+	0.705719i
$316$		0			0
$317$	−10.4368	−	25.1968i	−0.586192	−	1.41519i	−0.887117	−	0.461545i	$-0.847295\pi$
$317$	−10.4368	−	25.1968i	−0.586192	−	1.41519i	0.300925	−	0.953648i	$-0.402705\pi$
$318$		0			0
$319$	1.49094			0.0834769
$320$		0			0
$321$	8.77537			0.489794
$322$		0			0
$323$	−1.72949	−	4.17536i	−0.0962314	−	0.232323i
$324$		0			0
$325$	−22.2257	−	9.20618i	−1.23286	−	0.510667i
$326$		0			0
$327$	0.538475	+	0.538475i	0.0297777	+	0.0297777i
$328$		0			0
$329$	3.31168	−	3.31168i	0.182579	−	0.182579i
$330$		0			0
$331$	−11.9883	+	28.9422i	−0.658935	+	1.59081i	0.140516	+	0.990078i	$0.455124\pi$
$331$	−11.9883	+	28.9422i	−0.658935	+	1.59081i	−0.799451	+	0.600731i	$0.794876\pi$
$332$		0			0
$333$	7.65575	−	3.17112i	0.419533	−	0.173776i
$334$		0			0
$335$			25.5528i			1.39610i
$336$		0			0
$337$		−	2.82843i		−	0.154074i	−0.997028	−	0.0770371i	$-0.975454\pi$
$337$		−	2.82843i		−	0.154074i	0.997028	−	0.0770371i	$-0.0245460\pi$
$338$		0			0
$339$	−15.4135	+	6.38447i	−0.837145	+	0.346757i
$340$		0			0
$341$	1.34416	−	3.24509i	0.0727905	−	0.175732i
$342$		0			0
$343$	21.6463	−	21.6463i	1.16879	−	1.16879i
$344$		0			0
$345$	17.0966	+	17.0966i	0.920451	+	0.920451i
$346$		0			0
$347$	−13.7464	−	5.69394i	−0.737944	−	0.305667i	−0.0181324	−	0.999836i	$-0.505772\pi$
$347$	−13.7464	−	5.69394i	−0.737944	−	0.305667i	−0.719812	+	0.694169i	$0.755772\pi$
$348$		0			0
$349$	−1.77043	−	4.27420i	−0.0947690	−	0.228792i	0.869385	−	0.494135i	$-0.164515\pi$
$349$	−1.77043	−	4.27420i	−0.0947690	−	0.228792i	−0.964154	+	0.265342i	$0.914515\pi$
$350$		0			0
$351$	13.2395			0.706671
$352$		0			0
$353$	−15.5598			−0.828166			−0.414083	−	0.910239i	$-0.635898\pi$
$353$	−15.5598			−0.828166			−0.414083	+	0.910239i	$0.635898\pi$
$354$		0			0
$355$	11.7978	+	28.4825i	0.626163	+	1.51169i
$356$		0			0
$357$	−5.93342	−	2.45770i	−0.314030	−	0.130075i
$358$		0			0
$359$	−8.89363	−	8.89363i	−0.469388	−	0.469388i	0.432328	−	0.901716i	$-0.357692\pi$
$359$	−8.89363	−	8.89363i	−0.469388	−	0.469388i	−0.901716	+	0.432328i	$0.857692\pi$
$360$		0			0
$361$	−5.44149	+	5.44149i	−0.286394	+	0.286394i
$362$		0			0
$363$	4.05520	−	9.79011i	0.212843	−	0.513848i
$364$		0			0
$365$	14.5868	−	6.04205i	0.763508	−	0.316255i
$366$		0			0
$367$		−	7.25894i		−	0.378914i	−0.981889	−	0.189457i	$-0.939327\pi$
$367$		−	7.25894i		−	0.378914i	0.981889	−	0.189457i	$-0.0606727\pi$
$368$		0			0
$369$			14.3417i			0.746600i
$370$		0			0
$371$	29.5851	−	12.2545i	1.53598	−	0.636224i
$372$		0			0
$373$	1.57978	−	3.81392i	0.0817978	−	0.197477i	−0.877689	−	0.479230i	$-0.840916\pi$
$373$	1.57978	−	3.81392i	0.0817978	−	0.197477i	0.959487	+	0.281753i	$0.0909159\pi$
$374$		0			0
$375$	−12.2023	+	12.2023i	−0.630125	+	0.630125i
$376$		0			0
$377$	−2.85643	−	2.85643i	−0.147113	−	0.147113i
$378$		0			0
$379$	−18.0669	−	7.48355i	−0.928033	−	0.384404i	−0.133101	−	0.991102i	$-0.542494\pi$
$379$	−18.0669	−	7.48355i	−0.928033	−	0.384404i	−0.794932	+	0.606698i	$0.792494\pi$
$380$		0			0
$381$	1.38029	+	3.33232i	0.0707144	+	0.170720i
$382$		0			0
$383$	4.43680			0.226710			0.113355	−	0.993555i	$-0.463840\pi$
$383$	4.43680			0.226710			0.113355	+	0.993555i	$0.463840\pi$
$384$		0			0
$385$	16.3862			0.835119
$386$		0			0
$387$	−5.72347	−	13.8177i	−0.290940	−	0.702392i
$388$		0			0
$389$	17.1002	+	7.08312i	0.867013	+	0.359129i	0.771446	−	0.636294i	$-0.219534\pi$
$389$	17.1002	+	7.08312i	0.867013	+	0.359129i	0.0955668	+	0.995423i	$0.469534\pi$
$390$		0			0
$391$	5.78182	+	5.78182i	0.292399	+	0.292399i
$392$		0			0
$393$	−2.70046	+	2.70046i	−0.136220	+	0.136220i
$394$		0			0
$395$	22.3700	−	54.0059i	1.12556	−	2.71733i
$396$		0			0
$397$	−30.0576	+	12.4503i	−1.50855	+	0.624860i	−0.975257	−	0.221073i	$-0.929044\pi$
$397$	−30.0576	+	12.4503i	−1.50855	+	0.624860i	−0.533289	+	0.845933i	$0.679044\pi$
$398$		0			0
$399$		−	16.0644i		−	0.804227i
$400$		0			0
$401$			38.1068i			1.90296i	0.307708	+	0.951481i	$0.400438\pi$
$401$			38.1068i			1.90296i	−0.307708	+	0.951481i	$0.599562\pi$
$402$		0			0
$403$	−8.79233	+	3.64190i	−0.437977	+	0.181416i
$404$		0			0
$405$	−0.434275	+	1.04843i	−0.0215793	+	0.0520970i
$406$		0			0
$407$	2.93352	−	2.93352i	0.145409	−	0.145409i
$408$		0			0
$409$	−4.45034	−	4.45034i	−0.220055	−	0.220055i	0.588466	−	0.808522i	$-0.299732\pi$
$409$	−4.45034	−	4.45034i	−0.220055	−	0.220055i	−0.808522	+	0.588466i	$0.799732\pi$
$410$		0			0
$411$	2.46750	+	1.02207i	0.121713	+	0.0504151i
$412$		0			0
$413$	11.1387	+	26.8911i	0.548098	+	1.32323i
$414$		0			0
$415$	−46.1666			−2.26623
$416$		0			0
$417$	18.2943			0.895874
$418$		0			0
$419$	8.82067	+	21.2950i	0.430918	+	1.04033i	0.978992	+	0.203899i	$0.0653613\pi$
$419$	8.82067	+	21.2950i	0.430918	+	1.04033i	−0.548074	+	0.836430i	$0.684639\pi$
$420$		0			0
$421$	−15.1182	−	6.26218i	−0.736818	−	0.305200i	−0.0174674	−	0.999847i	$-0.505560\pi$
$421$	−15.1182	−	6.26218i	−0.736818	−	0.305200i	−0.719350	+	0.694648i	$0.755560\pi$
$422$		0			0
$423$	1.38106	+	1.38106i	0.0671494	+	0.0671494i
$424$		0			0
$425$	−8.87898	+	8.87898i	−0.430694	+	0.430694i
$426$		0			0
$427$	8.35111	−	20.1614i	0.404139	−	0.975677i
$428$		0			0
$429$	2.37335	−	0.983074i	0.114586	−	0.0474633i
$430$		0			0
$431$			5.84075i			0.281339i	0.990057	+	0.140670i	$0.0449255\pi$
$431$			5.84075i			0.281339i	−0.990057	+	0.140670i	$0.955074\pi$
$432$		0			0
$433$		−	1.77141i		−	0.0851286i	−0.999094	−	0.0425643i	$-0.986447\pi$
$433$		−	1.77141i		−	0.0851286i	0.999094	−	0.0425643i	$-0.0135527\pi$
$434$		0			0
$435$	−5.76019	+	2.38595i	−0.276180	+	0.114398i
$436$		0			0
$437$	−7.82699	+	18.8960i	−0.374416	+	0.903919i
$438$		0			0
$439$	−5.32755	+	5.32755i	−0.254270	+	0.254270i	−0.822719	−	0.568449i	$-0.807544\pi$
$439$	−5.32755	+	5.32755i	−0.254270	+	0.254270i	0.568449	+	0.822719i	$0.307544\pi$
$440$		0			0
$441$	18.4241	+	18.4241i	0.877337	+	0.877337i
$442$		0			0
$443$	−34.6293	−	14.3439i	−1.64529	−	0.681500i	−0.648471	−	0.761240i	$-0.724591\pi$
$443$	−34.6293	−	14.3439i	−1.64529	−	0.681500i	−0.996816	+	0.0797396i	$0.974591\pi$
$444$		0			0
$445$	18.5423	+	44.7651i	0.878989	+	2.12207i
$446$		0			0
$447$	−18.1017			−0.856183
$448$		0			0
$449$	−12.5278			−0.591225			−0.295612	−	0.955308i	$-0.595524\pi$
$449$	−12.5278			−0.591225			−0.295612	+	0.955308i	$0.595524\pi$
$450$		0			0
$451$	2.74771	+	6.63357i	0.129385	+	0.312363i
$452$		0			0
$453$	9.45136	+	3.91488i	0.444064	+	0.183937i
$454$		0			0
$455$	−31.3935	−	31.3935i	−1.47175	−	1.47175i
$456$		0			0
$457$	−7.04451	+	7.04451i	−0.329528	+	0.329528i	−0.852407	−	0.522879i	$-0.824858\pi$
$457$	−7.04451	+	7.04451i	−0.329528	+	0.329528i	0.522879	+	0.852407i	$0.324858\pi$
$458$		0			0
$459$	2.64453	−	6.38447i	0.123436	−	0.298001i
$460$		0			0
$461$	31.6991	−	13.1302i	1.47637	−	0.611535i	0.508072	−	0.861314i	$-0.330358\pi$
$461$	31.6991	−	13.1302i	1.47637	−	0.611535i	0.968303	+	0.249780i	$0.0803583\pi$
$462$		0			0
$463$			8.90222i			0.413721i	0.978370	+	0.206861i	$0.0663246\pi$
$463$			8.90222i			0.413721i	−0.978370	+	0.206861i	$0.933675\pi$
$464$		0			0
$465$			14.6883i			0.681155i
$466$		0			0
$467$	−22.7108	+	9.40713i	−1.05093	+	0.435310i	−0.840224	−	0.542239i	$-0.817577\pi$
$467$	−22.7108	+	9.40713i	−1.05093	+	0.435310i	−0.210707	+	0.977549i	$0.567577\pi$
$468$		0			0
$469$	−11.7549	+	28.3789i	−0.542791	+	1.31041i
$470$		0			0
$471$	5.27660	−	5.27660i	0.243133	−	0.243133i
$472$		0			0
$473$	−5.29463	−	5.29463i	−0.243447	−	0.243447i
$474$		0			0
$475$	−29.0181	−	12.0197i	−1.33144	−	0.551501i
$476$		0			0
$477$	5.11048	+	12.3378i	0.233993	+	0.564908i
$478$		0			0
$479$	8.80923			0.402504			0.201252	−	0.979540i	$-0.435499\pi$
$479$	8.80923			0.402504			0.201252	+	0.979540i	$0.435499\pi$
$480$		0			0
$481$	−11.2404			−0.512516
$482$		0			0
$483$	11.1226	+	26.8523i	0.506095	+	1.22182i
$484$		0			0
$485$	−29.4308	−	12.1907i	−1.33639	−	0.553549i
$486$		0			0
$487$	5.25173	+	5.25173i	0.237979	+	0.237979i	0.816013	−	0.578034i	$-0.196180\pi$
$487$	5.25173	+	5.25173i	0.237979	+	0.237979i	−0.578034	+	0.816013i	$0.696180\pi$
$488$		0			0
$489$	−1.64836	+	1.64836i	−0.0745412	+	0.0745412i
$490$		0			0
$491$	−4.18136	+	10.0947i	−0.188702	+	0.455568i	−0.989710	−	0.143086i	$-0.954297\pi$
$491$	−4.18136	+	10.0947i	−0.188702	+	0.455568i	0.801008	+	0.598654i	$0.204297\pi$
$492$		0			0
$493$	−1.94801	+	0.806893i	−0.0877341	+	0.0363406i
$494$		0			0
$495$			6.83349i			0.307143i
$496$		0			0
$497$			37.0598i			1.66236i
$498$		0			0
$499$	26.4331	−	10.9489i	1.18331	−	0.490142i	0.297737	−	0.954648i	$-0.403768\pi$
$499$	26.4331	−	10.9489i	1.18331	−	0.490142i	0.885570	+	0.464506i	$0.153768\pi$
$500$		0			0
$501$	−0.598822	+	1.44568i	−0.0267534	+	0.0645884i
$502$		0			0
$503$	19.9802	−	19.9802i	0.890873	−	0.890873i	−0.103733	−	0.994605i	$-0.533079\pi$
$503$	19.9802	−	19.9802i	0.890873	−	0.890873i	0.994605	+	0.103733i	$0.0330786\pi$
$504$		0			0
$505$	25.1932	+	25.1932i	1.12108	+	1.12108i
$506$		0			0
$507$	6.17495	+	2.55775i	0.274239	+	0.113594i
$508$		0			0
$509$	−14.1351	−	34.1252i	−0.626528	−	1.51257i	−0.843910	−	0.536485i	$-0.819752\pi$
$509$	−14.1351	−	34.1252i	−0.626528	−	1.51257i	0.217382	−	0.976087i	$-0.430248\pi$
$510$		0			0
$511$	18.9795			0.839606
$512$		0			0
$513$	17.2856			0.763178
$514$		0			0
$515$	13.6279	+	32.9007i	0.600517	+	1.44978i
$516$		0			0
$517$	0.903386	+	0.374195i	0.0397309	+	0.0164571i
$518$		0			0
$519$	−14.1300	−	14.1300i	−0.620236	−	0.620236i
$520$		0			0
$521$	−28.8690	+	28.8690i	−1.26478	+	1.26478i	−0.316025	+	0.948751i	$0.602348\pi$
$521$	−28.8690	+	28.8690i	−1.26478	+	1.26478i	−0.948751	+	0.316025i	$0.897652\pi$
$522$		0			0
$523$	5.01220	−	12.1005i	0.219168	−	0.529119i	−0.775606	−	0.631217i	$-0.782556\pi$
$523$	5.01220	−	12.1005i	0.219168	−	0.529119i	0.994774	+	0.102098i	$0.0325557\pi$
$524$		0			0
$525$	−41.2363	+	17.0806i	−1.79970	+	0.745460i
$526$		0			0
$527$			4.96738i			0.216382i
$528$		0			0
$529$		−	14.0047i		−	0.608898i
$530$		0			0
$531$	−11.2143	+	4.64512i	−0.486660	+	0.201581i
$532$		0			0
$533$	7.44472	−	17.9731i	0.322467	−	0.778503i
$534$		0			0
$535$	22.3900	−	22.3900i	0.968005	−	0.968005i
$536$		0			0
$537$	8.24963	+	8.24963i	0.355998	+	0.355998i
$538$		0			0
$539$	12.0517	+	4.99196i	0.519102	+	0.215019i
$540$		0			0
$541$	−6.54974	−	15.8125i	−0.281596	−	0.679832i	0.718278	−	0.695757i	$-0.244931\pi$
$541$	−6.54974	−	15.8125i	−0.281596	−	0.679832i	−0.999873	+	0.0159249i	$0.994931\pi$
$542$		0			0
$543$	3.09375			0.132765
$544$		0			0
$545$	2.74779			0.117703
$546$		0			0
$547$	−9.82921	−	23.7298i	−0.420267	−	1.01461i	−0.982269	−	0.187478i	$-0.939969\pi$
$547$	−9.82921	−	23.7298i	−0.420267	−	1.01461i	0.562002	−	0.827136i	$-0.310031\pi$
$548$		0			0
$549$	8.40783	+	3.48264i	0.358838	+	0.148635i
$550$		0			0
$551$	−3.72938	−	3.72938i	−0.158877	−	0.158877i
$552$		0			0
$553$	49.6881	−	49.6881i	2.11295	−	2.11295i
$554$		0			0
$555$	−6.63901	+	16.0280i	−0.281810	+	0.680350i
$556$		0			0
$557$	−27.0732	+	11.2141i	−1.14713	+	0.475156i	−0.873569	−	0.486700i	$-0.838201\pi$
$557$	−27.0732	+	11.2141i	−1.14713	+	0.475156i	−0.273558	+	0.961855i	$0.588201\pi$
$558$		0			0
$559$			20.2874i			0.858067i
$560$		0			0
$561$		−	1.34086i		−	0.0566113i
$562$		0			0
$563$	−27.6272	+	11.4436i	−1.16435	+	0.482289i	−0.879321	−	0.476230i	$-0.842003\pi$
$563$	−27.6272	+	11.4436i	−1.16435	+	0.482289i	−0.285028	+	0.958519i	$0.592003\pi$
$564$		0			0
$565$	−23.0371	+	55.6166i	−0.969180	+	2.33981i
$566$		0			0
$567$	−0.964608	+	0.964608i	−0.0405097	+	0.0405097i
$568$		0			0
$569$	28.0917	+	28.0917i	1.17767	+	1.17767i	0.980337	+	0.197328i	$0.0632264\pi$
$569$	28.0917	+	28.0917i	1.17767	+	1.17767i	0.197328	+	0.980337i	$0.436774\pi$
$570$		0			0
$571$	3.99922	+	1.65653i	0.167362	+	0.0693237i	0.464791	−	0.885420i	$-0.346129\pi$
$571$	3.99922	+	1.65653i	0.167362	+	0.0693237i	−0.297429	+	0.954744i	$0.596129\pi$
$572$		0			0
$573$	8.54181	+	20.6217i	0.356839	+	0.861486i
$574$		0			0
$575$	56.8270			2.36985
$576$		0			0
$577$	−12.9445			−0.538886			−0.269443	−	0.963016i	$-0.586840\pi$
$577$	−12.9445			−0.538886			−0.269443	+	0.963016i	$0.586840\pi$
$578$		0			0
$579$	1.10648	+	2.67127i	0.0459837	+	0.111014i
$580$		0			0
$581$	−51.2724	−	21.2377i	−2.12714	−	0.881090i
$582$		0			0
$583$	4.72757	+	4.72757i	0.195796	+	0.195796i
$584$		0			0
$585$	13.0920	−	13.0920i	0.541286	−	0.541286i
$586$		0			0
$587$	−8.82612	+	21.3081i	−0.364293	+	0.879481i	0.630369	+	0.776295i	$0.282903\pi$
$587$	−8.82612	+	21.3081i	−0.364293	+	0.879481i	−0.994662	+	0.103185i	$0.967097\pi$
$588$		0			0
$589$	−11.4794	+	4.75491i	−0.472999	+	0.195922i
$590$		0			0
$591$		−	5.74035i		−	0.236126i
$592$		0			0
$593$		−	34.4804i		−	1.41594i	−0.706243	−	0.707970i	$-0.749611\pi$
$593$		−	34.4804i		−	1.41594i	0.706243	−	0.707970i	$-0.250389\pi$
$594$		0			0
$595$	−21.4096	+	8.86815i	−0.877709	+	0.363559i
$596$		0			0
$597$	8.70998	−	21.0278i	0.356476	−	0.860609i
$598$		0			0
$599$	−5.59550	+	5.59550i	−0.228626	+	0.228626i	−0.812118	−	0.583493i	$-0.801686\pi$
$599$	−5.59550	+	5.59550i	−0.228626	+	0.228626i	0.583493	+	0.812118i	$0.301686\pi$
$600$		0			0
$601$	27.2303	+	27.2303i	1.11075	+	1.11075i	0.993050	+	0.117695i	$0.0375506\pi$
$601$	27.2303	+	27.2303i	1.11075	+	1.11075i	0.117695	+	0.993050i	$0.462449\pi$
$602$		0			0
$603$	−11.8347	−	4.90211i	−0.481948	−	0.199629i
$604$		0			0
$605$	−14.6324	−	35.3258i	−0.594892	−	1.43620i
$606$		0			0
$607$	−3.74369			−0.151952			−0.0759758	−	0.997110i	$-0.524207\pi$
$607$	−3.74369			−0.151952			−0.0759758	+	0.997110i	$0.524207\pi$
$608$		0			0
$609$	−7.49485			−0.303707
$610$		0			0
$611$	−1.01385	−	2.44765i	−0.0410160	−	0.0990215i
$612$		0			0
$613$	−6.88397	−	2.85143i	−0.278041	−	0.115168i	0.239306	−	0.970944i	$-0.423080\pi$
$613$	−6.88397	−	2.85143i	−0.278041	−	0.115168i	−0.517347	+	0.855776i	$0.673080\pi$
$614$		0			0
$615$	−21.2313	−	21.2313i	−0.856130	−	0.856130i
$616$		0			0
$617$	−6.08913	+	6.08913i	−0.245139	+	0.245139i	−0.818972	−	0.573833i	$-0.805456\pi$
$617$	−6.08913	+	6.08913i	−0.245139	+	0.245139i	0.573833	+	0.818972i	$0.305456\pi$
$618$		0			0
$619$	12.6058	−	30.4332i	0.506672	−	1.22321i	−0.439117	−	0.898430i	$-0.644709\pi$
$619$	12.6058	−	30.4332i	0.506672	−	1.22321i	0.945788	−	0.324783i	$-0.105291\pi$
$620$		0			0
$621$	−28.8936	+	11.9681i	−1.15946	+	0.480264i
$622$		0			0
$623$			58.2458i			2.33357i
$624$		0			0
$625$			15.5590i			0.622359i
$626$		0			0
$627$	3.09867	−	1.28351i	0.123749	−	0.0512585i
$628$		0			0
$629$	−2.24522	+	5.42043i	−0.0895226	+	0.216127i
$630$		0			0
$631$	−12.1982	+	12.1982i	−0.485602	+	0.485602i	−0.906915	−	0.421313i	$-0.861569\pi$
$631$	−12.1982	+	12.1982i	−0.485602	+	0.485602i	0.421313	+	0.906915i	$0.361569\pi$
$632$		0			0
$633$	−17.1263	−	17.1263i	−0.680708	−	0.680708i
$634$		0			0
$635$	12.0240	+	4.98052i	0.477159	+	0.197646i
$636$		0			0
$637$	−13.5253	−	32.6530i	−0.535893	−	1.29376i
$638$		0			0
$639$	−15.4549			−0.611388
$640$		0			0
$641$	35.7157			1.41068			0.705342	−	0.708867i	$-0.250794\pi$
$641$	35.7157			1.41068			0.705342	+	0.708867i	$0.250794\pi$
$642$		0			0
$643$	8.24179	+	19.8975i	0.325025	+	0.784679i	0.998947	+	0.0458768i	$0.0146082\pi$
$643$	8.24179	+	19.8975i	0.325025	+	0.784679i	−0.673922	+	0.738802i	$0.735392\pi$
$644$		0			0
$645$	28.9285	+	11.9826i	1.13906	+	0.471814i
$646$		0			0
$647$	−6.13152	−	6.13152i	−0.241055	−	0.241055i	0.576232	−	0.817286i	$-0.304523\pi$
$647$	−6.13152	−	6.13152i	−0.241055	−	0.241055i	−0.817286	+	0.576232i	$0.804523\pi$
$648$		0			0
$649$	−4.29708	+	4.29708i	−0.168675	+	0.168675i
$650$		0			0
$651$	−6.75699	+	16.3128i	−0.264827	+	0.639349i
$652$		0			0
$653$	19.0482	−	7.89002i	0.745413	−	0.308760i	0.0225445	−	0.999746i	$-0.492823\pi$
$653$	19.0482	−	7.89002i	0.745413	−	0.308760i	0.722868	+	0.690986i	$0.242823\pi$
$654$		0			0
$655$			13.7803i			0.538439i
$656$		0			0
$657$			7.91498i			0.308793i
$658$		0			0
$659$	39.7290	−	16.4563i	1.54762	−	0.641046i	0.564737	−	0.825271i	$-0.308978\pi$
$659$	39.7290	−	16.4563i	1.54762	−	0.641046i	0.982884	+	0.184225i	$0.0589777\pi$
$660$		0			0
$661$	7.09412	−	17.1267i	0.275929	−	0.666153i	−0.723786	−	0.690025i	$-0.757600\pi$
$661$	7.09412	−	17.1267i	0.275929	−	0.666153i	0.999715	+	0.0238723i	$0.00759951\pi$
$662$		0			0
$663$	−2.56890	+	2.56890i	−0.0997676	+	0.0997676i
$664$		0			0
$665$	−40.9877	−	40.9877i	−1.58944	−	1.58944i
$666$		0			0
$667$	8.81593	+	3.65168i	0.341354	+	0.141394i
$668$		0			0
$669$	4.95998	+	11.9745i	0.191764	+	0.462959i
$670$		0			0
$671$	4.55617			0.175889
$672$		0			0
$673$	33.1192			1.27665			0.638326	−	0.769766i	$-0.279627\pi$
$673$	33.1192			1.27665			0.638326	+	0.769766i	$0.279627\pi$
$674$		0			0
$675$	−18.3791	−	44.3710i	−0.707411	−	1.70784i
$676$		0			0
$677$	−6.49374	−	2.68980i	−0.249575	−	0.103377i	0.254389	−	0.967102i	$-0.418126\pi$
$677$	−6.49374	−	2.68980i	−0.249575	−	0.103377i	−0.503964	+	0.863725i	$0.668126\pi$
$678$		0			0
$679$	−27.0778	−	27.0778i	−1.03915	−	1.03915i
$680$		0			0
$681$	−3.44605	+	3.44605i	−0.132053	+	0.132053i
$682$		0			0
$683$	7.44891	−	17.9833i	0.285025	−	0.688110i	−0.714914	−	0.699213i	$-0.753534\pi$
$683$	7.44891	−	17.9833i	0.285025	−	0.688110i	0.999938	+	0.0111024i	$0.00353409\pi$
$684$		0			0
$685$	8.90351	−	3.68795i	0.340186	−	0.140909i
$686$		0			0
$687$			4.91573i			0.187547i
$688$		0			0
$689$		−	18.1146i		−	0.690112i
$690$		0			0
$691$	6.80634	−	2.81928i	0.258926	−	0.107250i	−0.249445	−	0.968389i	$-0.580248\pi$
$691$	6.80634	−	2.81928i	0.258926	−	0.107250i	0.508370	+	0.861139i	$0.330248\pi$
$692$		0			0
$693$	−3.14357	+	7.58926i	−0.119414	+	0.288292i
$694$		0			0
$695$	46.6771	−	46.6771i	1.77056	−	1.77056i
$696$		0			0
$697$	−7.18012	−	7.18012i	−0.271967	−	0.271967i
$698$		0			0
$699$	1.16414	+	0.482204i	0.0440319	+	0.0182386i
$700$		0			0
$701$	17.0726	+	41.2169i	0.644823	+	1.55674i	0.820100	+	0.572221i	$0.193918\pi$
$701$	17.0726	+	41.2169i	0.644823	+	1.55674i	−0.175277	+	0.984519i	$0.556082\pi$
$702$		0			0
$703$	−14.6755			−0.553498
$704$		0			0
$705$	−4.08901			−0.154001
$706$		0			0
$707$	16.3900	+	39.5690i	0.616410	+	1.48815i
$708$		0			0
$709$	−1.11345	−	0.461208i	−0.0418167	−	0.0173210i	0.361677	−	0.932303i	$-0.382204\pi$
$709$	−1.11345	−	0.461208i	−0.0418167	−	0.0173210i	−0.403494	+	0.914982i	$0.632204\pi$
$710$		0			0
$711$	20.7213	+	20.7213i	0.777108	+	0.777108i
$712$		0			0
$713$	15.8960	−	15.8960i	0.595311	−	0.595311i
$714$		0			0
$715$	3.54724	−	8.56379i	0.132659	−	0.320267i
$716$		0			0
$717$	−1.36133	+	0.563882i	−0.0508398	+	0.0210586i
$718$		0			0
$719$		−	47.3791i		−	1.76694i	−0.468487	−	0.883470i	$-0.655201\pi$
$719$		−	47.3791i		−	1.76694i	0.468487	−	0.883470i	$-0.344799\pi$
$720$		0			0
$721$			42.8086i			1.59427i
$722$		0			0
$723$	−16.8081	+	6.96215i	−0.625101	+	0.258925i
$724$		0			0
$725$	−5.60778	+	13.5384i	−0.208268	+	0.502802i
$726$		0			0
$727$	−32.0891	+	32.0891i	−1.19012	+	1.19012i	−0.213086	+	0.977034i	$0.568351\pi$
$727$	−32.0891	+	32.0891i	−1.19012	+	1.19012i	−0.977034	+	0.213086i	$0.931649\pi$
$728$		0			0
$729$	11.0439	+	11.0439i	0.409034	+	0.409034i
$730$		0			0
$731$	9.78320	+	4.05233i	0.361845	+	0.149881i
$732$		0			0
$733$	15.8815	+	38.3414i	0.586597	+	1.41617i	0.886736	+	0.462276i	$0.152967\pi$
$733$	15.8815	+	38.3414i	0.586597	+	1.41617i	−0.300139	+	0.953895i	$0.597033\pi$
$734$		0			0
$735$	−54.5496			−2.01209
$736$		0			0
$737$	−6.41320			−0.236233
$738$		0			0
$739$	−17.6166	−	42.5302i	−0.648036	−	1.56450i	−0.815587	−	0.578634i	$-0.803586\pi$
$739$	−17.6166	−	42.5302i	−0.648036	−	1.56450i	0.167551	−	0.985863i	$-0.446414\pi$
$740$		0			0
$741$	−8.39561	−	3.47757i	−0.308420	−	0.127752i
$742$		0			0
$743$	21.8955	+	21.8955i	0.803267	+	0.803267i	0.983605	−	0.180337i	$-0.0577190\pi$
$743$	21.8955	+	21.8955i	0.803267	+	0.803267i	−0.180337	+	0.983605i	$0.557719\pi$
$744$		0			0
$745$	−46.1859	+	46.1859i	−1.69212	+	1.69212i
$746$		0			0
$747$	8.85671	−	21.3820i	0.324050	−	0.782326i
$748$		0			0
$749$	35.1662	−	14.5663i	1.28495	−	0.532242i
$750$		0			0
$751$		−	11.9637i		−	0.436561i	−0.975886	−	0.218281i	$-0.929955\pi$
$751$		−	11.9637i		−	0.436561i	0.975886	−	0.218281i	$-0.0700448\pi$
$752$		0			0
$753$			4.61648i			0.168234i
$754$		0			0
$755$	34.1034	−	14.1261i	1.24115	−	0.514102i
$756$		0			0
$757$	17.7520	−	42.8571i	0.645207	−	1.55767i	−0.174358	−	0.984682i	$-0.555785\pi$
$757$	17.7520	−	42.8571i	0.645207	−	1.55767i	0.819565	−	0.572986i	$-0.194215\pi$
$758$		0			0
$759$	−4.29088	+	4.29088i	−0.155749	+	0.155749i
$760$		0			0
$761$	−26.2473	−	26.2473i	−0.951464	−	0.951464i	0.0474116	−	0.998875i	$-0.484903\pi$
$761$	−26.2473	−	26.2473i	−0.951464	−	0.951464i	−0.998875	+	0.0474116i	$0.984903\pi$
$762$		0			0
$763$	3.05169	+	1.26405i	0.110479	+	0.0457618i
$764$		0			0
$765$	−3.69826	−	8.92839i	−0.133711	−	0.322807i
$766$		0			0
$767$	16.4651			0.594522
$768$		0			0
$769$	14.5470			0.524577			0.262288	−	0.964990i	$-0.415523\pi$
$769$	14.5470			0.524577			0.262288	+	0.964990i	$0.415523\pi$
$770$		0			0
$771$	9.87404	+	23.8380i	0.355605	+	0.858506i
$772$		0			0
$773$	3.52868	+	1.46163i	0.126918	+	0.0525711i	0.445239	−	0.895412i	$-0.353119\pi$
$773$	3.52868	+	1.46163i	0.126918	+	0.0525711i	−0.318321	+	0.947983i	$0.603119\pi$
$774$		0			0
$775$	24.4111	+	24.4111i	0.876871	+	0.876871i
$776$		0			0
$777$	−14.7465	+	14.7465i	−0.529029	+	0.529029i
$778$		0			0
$779$	9.71990	−	23.4659i	0.348252	−	0.840754i
$780$		0			0
$781$	−7.14848	+	2.96100i	−0.255793	+	0.105953i
$782$		0			0
$783$		−	8.06459i		−	0.288205i
$784$		0			0
$785$		−	26.9261i		−	0.961032i
$786$		0			0
$787$	−11.4346	+	4.73636i	−0.407599	+	0.168833i	−0.577056	−	0.816705i	$-0.695799\pi$
$787$	−11.4346	+	4.73636i	−0.407599	+	0.168833i	0.169457	+	0.985538i	$0.445799\pi$
$788$		0			0
$789$	−7.66000	+	18.4929i	−0.272703	+	0.658364i
$790$		0			0
$791$	−51.1700	+	51.1700i	−1.81939	+	1.81939i
$792$		0			0
$793$	−8.72894	−	8.72894i	−0.309974	−	0.309974i
$794$		0			0
$795$	−25.8302	−	10.6992i	−0.916104	−	0.379463i
$796$		0			0
$797$	−0.560326	−	1.35275i	−0.0198478	−	0.0479167i	0.913645	−	0.406513i	$-0.133255\pi$
$797$	−0.560326	−	1.35275i	−0.0198478	−	0.0479167i	−0.933493	+	0.358596i	$0.883255\pi$
$798$		0			0
$799$	−1.38284			−0.0489215
$800$		0			0
$801$	−24.2901			−0.858248
$802$		0			0
$803$	1.51642	+	3.66097i	0.0535134	+	0.129193i
$804$		0			0
$805$	96.8915	+	40.1338i	3.41498	+	1.41453i
$806$		0			0
$807$	9.68002	+	9.68002i	0.340753	+	0.340753i
$808$		0			0
$809$	−3.15363	+	3.15363i	−0.110876	+	0.110876i	−0.760368	−	0.649492i	$-0.774981\pi$
$809$	−3.15363	+	3.15363i	−0.110876	+	0.110876i	0.649492	+	0.760368i	$0.274981\pi$
$810$		0			0
$811$	−8.61166	+	20.7904i	−0.302396	+	0.730049i	0.697513	+	0.716572i	$0.254290\pi$
$811$	−8.61166	+	20.7904i	−0.302396	+	0.730049i	−0.999909	+	0.0134769i	$0.995710\pi$
$812$		0			0
$813$	5.65465	−	2.34223i	0.198317	−	0.0821457i
$814$		0			0
$815$			8.41143i			0.294640i
$816$		0			0
$817$			26.4875i			0.926680i
$818$		0			0
$819$	20.5625	−	8.51727i	0.718512	−	0.297617i
$820$		0			0
$821$	1.63781	−	3.95402i	0.0571599	−	0.137996i	−0.892719	−	0.450613i	$-0.851205\pi$
$821$	1.63781	−	3.95402i	0.0571599	−	0.137996i	0.949879	+	0.312617i	$0.101205\pi$
$822$		0			0
$823$	−6.07415	+	6.07415i	−0.211731	+	0.211731i	−0.805003	−	0.593271i	$-0.797836\pi$
$823$	−6.07415	+	6.07415i	−0.211731	+	0.211731i	0.593271	+	0.805003i	$0.297836\pi$
$824$		0			0
$825$	−6.58938	−	6.58938i	−0.229413	−	0.229413i
$826$		0			0
$827$	−25.1075	−	10.3999i	−0.873074	−	0.361639i	−0.0992672	−	0.995061i	$-0.531650\pi$
$827$	−25.1075	−	10.3999i	−0.873074	−	0.361639i	−0.773807	+	0.633422i	$0.781650\pi$
$828$		0			0
$829$	−10.3361	−	24.9536i	−0.358988	−	0.866674i	−0.995443	−	0.0953602i	$-0.969600\pi$
$829$	−10.3361	−	24.9536i	−0.358988	−	0.866674i	0.636455	−	0.771314i	$-0.280400\pi$
$830$		0			0
$831$	18.0387			0.625757
$832$		0			0
$833$	−18.4479			−0.639181
$834$		0			0
$835$	2.16073	+	5.21648i	0.0747753	+	0.180524i
$836$		0			0
$837$	−17.5529	−	7.27064i	−0.606716	−	0.251310i
$838$		0			0
$839$	19.6105	+	19.6105i	0.677028	+	0.677028i	0.959327	−	0.282298i	$-0.0910968\pi$
$839$	19.6105	+	19.6105i	0.677028	+	0.677028i	−0.282298	+	0.959327i	$0.591097\pi$
$840$		0			0
$841$	18.7662	−	18.7662i	0.647109	−	0.647109i
$842$		0			0
$843$	1.41451	−	3.41492i	0.0487181	−	0.117616i
$844$		0			0
$845$	22.2811	−	9.22915i	0.766494	−	0.317492i
$846$		0			0
$847$		−	45.9639i		−	1.57934i
$848$		0			0
$849$		−	27.0618i		−	0.928758i
$850$		0			0
$851$	24.5307	−	10.1610i	0.840902	−	0.348313i
$852$		0			0
$853$	9.24721	−	22.3247i	0.316619	−	0.764385i	−0.682810	−	0.730596i	$-0.739243\pi$
$853$	9.24721	−	22.3247i	0.316619	−	0.764385i	0.999429	−	0.0337892i	$-0.0107575\pi$
$854$		0			0
$855$	17.0930	−	17.0930i	0.584568	−	0.584568i
$856$		0			0
$857$	21.5074	+	21.5074i	0.734677	+	0.734677i	0.971543	−	0.236865i	$-0.0761200\pi$
$857$	21.5074	+	21.5074i	0.734677	+	0.734677i	−0.236865	+	0.971543i	$0.576120\pi$
$858$		0			0
$859$	29.5057	+	12.2217i	1.00672	+	0.416998i	0.824258	−	0.566215i	$-0.191593\pi$
$859$	29.5057	+	12.2217i	1.00672	+	0.416998i	0.182464	+	0.983212i	$0.441593\pi$
$860$		0			0
$861$	−13.8125	−	33.3464i	−0.470729	−	1.13644i
$862$		0			0
$863$	−26.4436			−0.900151			−0.450076	−	0.892990i	$-0.648603\pi$
$863$	−26.4436			−0.900151			−0.450076	+	0.892990i	$0.648603\pi$
$864$		0			0
$865$	−72.1041			−2.45161
$866$		0			0
$867$	−6.10220	−	14.7320i	−0.207241	−	0.500325i
$868$		0			0
$869$	13.5543	+	5.61438i	0.459799	+	0.190455i
$870$		0			0
$871$	12.2867	+	12.2867i	0.416320	+	0.416320i
$872$		0			0
$873$	11.2922	−	11.2922i	0.382182	−	0.382182i
$874$		0			0
$875$	−28.6446	+	69.1541i	−0.968363	+	2.33784i
$876$		0			0
$877$	30.5345	−	12.6478i	1.03108	−	0.427086i	0.197975	−	0.980207i	$-0.436563\pi$
$877$	30.5345	−	12.6478i	1.03108	−	0.427086i	0.833101	+	0.553121i	$0.186563\pi$
$878$		0			0
$879$		−	29.9063i		−	1.00871i
$880$		0			0
$881$			13.9951i			0.471507i	0.971813	+	0.235753i	$0.0757557\pi$
$881$			13.9951i			0.471507i	−0.971813	+	0.235753i	$0.924244\pi$
$882$		0			0
$883$	−44.4774	+	18.4231i	−1.49678	+	0.619987i	−0.972780	−	0.231730i	$-0.925561\pi$
$883$	−44.4774	+	18.4231i	−1.49678	+	0.619987i	−0.524002	+	0.851717i	$0.675561\pi$
$884$		0			0
$885$	9.72498	−	23.4782i	0.326902	−	0.789210i
$886$		0			0
$887$	11.0611	−	11.0611i	0.371395	−	0.371395i	−0.496590	−	0.867985i	$-0.665415\pi$
$887$	11.0611	−	11.0611i	0.371395	−	0.371395i	0.867985	+	0.496590i	$0.165415\pi$
$888$		0			0
$889$	11.0627	+	11.0627i	0.371031	+	0.371031i
$890$		0			0
$891$	−0.263134	−	0.108994i	−0.00881531	−	0.00365142i
$892$		0			0
$893$	−1.32369	−	3.19568i	−0.0442958	−	0.106939i
$894$		0			0
$895$	42.0972			1.40716
$896$		0			0
$897$	16.4414			0.548961
$898$		0			0
$899$	2.21840	+	5.35569i	0.0739878	+	0.178622i
$900$		0			0
$901$	−8.73540	−	3.61832i	−0.291019	−	0.120544i
$902$		0			0
$903$	26.6156	+	26.6156i	0.885713	+	0.885713i
$904$		0			0
$905$	7.89357	−	7.89357i	0.262391	−	0.262391i
$906$		0			0
$907$	−20.5034	+	49.4995i	−0.680803	+	1.64360i	0.0817295	+	0.996655i	$0.473956\pi$
$907$	−20.5034	+	49.4995i	−0.680803	+	1.64360i	−0.762533	+	0.646950i	$0.776044\pi$
$908$		0			0
$909$	−16.5013	+	6.83508i	−0.547315	+	0.226705i
$910$		0			0
$911$		−	45.3750i		−	1.50334i	−0.659539	−	0.751670i	$-0.729248\pi$
$911$		−	45.3750i		−	1.50334i	0.659539	−	0.751670i	$-0.270752\pi$
$912$		0			0
$913$		−	11.5868i		−	0.383467i
$914$		0			0
$915$	−17.6025	+	7.29121i	−0.581922	+	0.241040i
$916$		0			0
$917$	−6.33925	+	15.3043i	−0.209341	+	0.505393i
$918$		0			0
$919$	9.90286	−	9.90286i	0.326665	−	0.326665i	−0.524652	−	0.851317i	$-0.675804\pi$
$919$	9.90286	−	9.90286i	0.326665	−	0.326665i	0.851317	+	0.524652i	$0.175804\pi$
$920$		0			0
$921$	−2.01484	−	2.01484i	−0.0663913	−	0.0663913i
$922$		0			0
$923$	19.3683	+	8.02259i	0.637514	+	0.264067i
$924$		0			0
$925$	15.6039	+	37.6711i	0.513053	+	1.23862i
$926$		0			0
$927$	−17.8523			−0.586347
$928$		0			0
$929$	1.64137			0.0538515			0.0269257	−	0.999637i	$-0.491428\pi$
$929$	1.64137			0.0538515			0.0269257	+	0.999637i	$0.491428\pi$
$930$		0			0
$931$	−17.6588	−	42.6322i	−0.578744	−	1.39721i
$932$		0			0
$933$	20.8074	+	8.61869i	0.681203	+	0.282163i
$934$		0			0
$935$	−3.42116	−	3.42116i	−0.111884	−	0.111884i
$936$		0			0
$937$	0.172711	−	0.172711i	0.00564221	−	0.00564221i	−0.704280	−	0.709922i	$-0.748730\pi$
$937$	0.172711	−	0.172711i	0.00564221	−	0.00564221i	0.709922	+	0.704280i	$0.248730\pi$
$938$		0			0
$939$	−5.24707	+	12.6675i	−0.171232	+	0.413389i
$940$		0			0
$941$	−39.8801	+	16.5189i	−1.30005	+	0.538500i	−0.921966	−	0.387270i	$-0.873418\pi$
$941$	−39.8801	+	16.5189i	−1.30005	+	0.538500i	−0.378087	+	0.925770i	$0.623418\pi$
$942$		0			0
$943$			45.9540i			1.49647i
$944$		0			0
$945$		−	88.6339i		−	2.88326i
$946$		0			0
$947$	20.0171	−	8.29136i	0.650469	−	0.269433i	−0.0329528	−	0.999457i	$-0.510491\pi$
$947$	20.0171	−	8.29136i	0.650469	−	0.269433i	0.683422	+	0.730024i	$0.260491\pi$
$948$		0			0
$949$	4.10863	−	9.91912i	0.133372	−	0.321988i
$950$		0			0
$951$	−20.2400	+	20.2400i	−0.656328	+	0.656328i
$952$		0			0
$953$	−35.0721	−	35.0721i	−1.13610	−	1.13610i	−0.989144	−	0.146953i	$-0.953053\pi$
$953$	−35.0721	−	35.0721i	−1.13610	−	1.13610i	−0.146953	−	0.989144i	$-0.546947\pi$
$954$		0			0
$955$	74.4097	+	30.8215i	2.40784	+	0.997360i
$956$		0			0
$957$	−0.598822	−	1.44568i	−0.0193572	−	0.0467323i
$958$		0			0
$959$	11.5848			0.374091
$960$		0			0
$961$	−17.3431			−0.559456
$962$		0			0
$963$	6.07456	+	14.6653i	0.195750	+	0.472582i
$964$		0			0
$965$	9.63879	+	3.99252i	0.310284	+	0.128524i
$966$		0			0
$967$	−17.5945	−	17.5945i	−0.565802	−	0.565802i	0.365148	−	0.930950i	$-0.381019\pi$
$967$	−17.5945	−	17.5945i	−0.565802	−	0.565802i	−0.930950	+	0.365148i	$0.881019\pi$
$968$		0			0
$969$	−3.35398	+	3.35398i	−0.107745	+	0.107745i
$970$		0			0
$971$	0.858080	−	2.07159i	0.0275371	−	0.0664804i	−0.909513	−	0.415676i	$-0.863545\pi$
$971$	0.858080	−	2.07159i	0.0275371	−	0.0664804i	0.937050	+	0.349195i	$0.113545\pi$
$972$		0			0
$973$	73.3120	−	30.3668i	2.35028	−	0.973516i
$974$		0			0
$975$			25.2485i			0.808600i
$976$		0			0
$977$		−	39.3535i		−	1.25903i	−0.776989	−	0.629515i	$-0.783254\pi$
$977$		−	39.3535i		−	1.25903i	0.776989	−	0.629515i	$-0.216746\pi$
$978$		0			0
$979$	−11.2351	+	4.65371i	−0.359074	+	0.148733i
$980$		0			0
$981$	−0.527144	+	1.27264i	−0.0168304	+	0.0406322i
$982$		0			0
$983$	30.0511	−	30.0511i	0.958481	−	0.958481i	−0.0406903	−	0.999172i	$-0.512956\pi$
$983$	30.0511	−	30.0511i	0.958481	−	0.958481i	0.999172	+	0.0406903i	$0.0129557\pi$
$984$		0			0
$985$	−14.6463	−	14.6463i	−0.466669	−	0.466669i
$986$		0			0
$987$	−4.54124	−	1.88104i	−0.144549	−	0.0598743i
$988$		0			0
$989$	−18.3393	−	44.2749i	−0.583154	−	1.40786i
$990$		0			0
$991$	37.5749			1.19360			0.596802	−	0.802388i	$-0.296438\pi$
$991$	37.5749			1.19360			0.596802	+	0.802388i	$0.296438\pi$
$992$		0			0
$993$	32.8786			1.04337
$994$		0			0
$995$	−31.4283	−	75.8747i	−0.996345	−	2.40539i
$996$		0			0
$997$	−52.6516	−	21.8090i	−1.66749	−	0.690698i	−0.668881	−	0.743369i	$-0.733227\pi$
$997$	−52.6516	−	21.8090i	−1.66749	−	0.690698i	−0.998612	+	0.0526708i	$0.983227\pi$
$998$		0			0
$999$	−15.8675	−	15.8675i	−0.502027	−	0.502027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.g.c.897.2	yes	16
4.3	odd	2	inner	1024.2.g.c.897.3	yes	16
8.3	odd	2		1024.2.g.h.897.2	yes	16
8.5	even	2		1024.2.g.h.897.3	yes	16
16.3	odd	4		1024.2.g.e.385.2	yes	16
16.5	even	4		1024.2.g.b.385.2	✓	16
16.11	odd	4		1024.2.g.b.385.3	yes	16
16.13	even	4		1024.2.g.e.385.3	yes	16
32.3	odd	8		1024.2.g.h.129.2	yes	16
32.5	even	8		1024.2.g.e.641.3	yes	16
32.11	odd	8		1024.2.g.b.641.3	yes	16
32.13	even	8	inner	1024.2.g.c.129.2	yes	16
32.19	odd	8	inner	1024.2.g.c.129.3	yes	16
32.21	even	8		1024.2.g.b.641.2	yes	16
32.27	odd	8		1024.2.g.e.641.2	yes	16
32.29	even	8		1024.2.g.h.129.3	yes	16
64.13	even	16		4096.2.a.n.1.3		8
64.19	odd	16		4096.2.a.n.1.4		8
64.45	even	16		4096.2.a.o.1.6		8
64.51	odd	16		4096.2.a.o.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.b.385.2	✓	16	16.5	even	4
1024.2.g.b.385.3	yes	16	16.11	odd	4
1024.2.g.b.641.2	yes	16	32.21	even	8
1024.2.g.b.641.3	yes	16	32.11	odd	8
1024.2.g.c.129.2	yes	16	32.13	even	8	inner
1024.2.g.c.129.3	yes	16	32.19	odd	8	inner
1024.2.g.c.897.2	yes	16	1.1	even	1	trivial
1024.2.g.c.897.3	yes	16	4.3	odd	2	inner
1024.2.g.e.385.2	yes	16	16.3	odd	4
1024.2.g.e.385.3	yes	16	16.13	even	4
1024.2.g.e.641.2	yes	16	32.27	odd	8
1024.2.g.e.641.3	yes	16	32.5	even	8
1024.2.g.h.129.2	yes	16	32.3	odd	8
1024.2.g.h.129.3	yes	16	32.29	even	8
1024.2.g.h.897.2	yes	16	8.3	odd	2
1024.2.g.h.897.3	yes	16	8.5	even	2
4096.2.a.n.1.3		8	64.13	even	16
4096.2.a.n.1.4		8	64.19	odd	16
4096.2.a.o.1.5		8	64.51	odd	16
4096.2.a.o.1.6		8	64.45	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)

\(f(q)\)	\(=\)	\(q+(-0.401639 - 0.969643i) q^{3} +(-3.49877 - 1.44924i) q^{5} +(-3.21904 - 3.21904i) q^{7} +(1.34243 - 1.34243i) q^{9} +O(q^{10})\)	\(q+(-0.401639 - 0.969643i) q^{3} +(-3.49877 - 1.44924i) q^{5} +(-3.21904 - 3.21904i) q^{7} +(1.34243 - 1.34243i) q^{9} +(0.363728 - 0.878116i) q^{11} +(-2.37919 + 0.985492i) q^{13} +3.97463i q^{15} +1.34416i q^{17} +(-3.10629 + 1.28667i) q^{19} +(-1.82843 + 4.41421i) q^{21} +(4.30143 - 4.30143i) q^{23} +(6.60559 + 6.60559i) q^{25} +(-4.74977 - 1.96742i) q^{27} +(0.600295 + 1.44924i) q^{29} +3.69552 q^{31} -0.997546 q^{33} +(6.59753 + 15.9279i) q^{35} +(4.03257 + 1.67035i) q^{37} +(1.91115 + 1.91115i) q^{39} +(-5.34171 + 5.34171i) q^{41} +(3.01477 - 7.27829i) q^{43} +(-6.64235 + 2.75135i) q^{45} +1.02878i q^{47} +13.7245i q^{49} +(1.30336 - 0.539868i) q^{51} +(-2.69188 + 6.49877i) q^{53} +(-2.54520 + 2.54520i) q^{55} +(2.49522 + 2.49522i) q^{57} +(-5.90700 - 2.44676i) q^{59} +(1.83444 + 4.42872i) q^{61} -8.64266 q^{63} +9.75245 q^{65} +(-2.58213 - 6.23381i) q^{67} +(-5.89848 - 2.44323i) q^{69} +(-5.75634 - 5.75634i) q^{71} +(-2.94801 + 2.94801i) q^{73} +(3.75200 - 9.05812i) q^{75} +(-3.99755 + 1.65584i) q^{77} +15.4357i q^{79} -0.299657i q^{81} +(11.2627 - 4.66516i) q^{83} +(1.94801 - 4.70292i) q^{85} +(1.16414 - 1.16414i) q^{87} +(-9.04708 - 9.04708i) q^{89} +(10.8310 + 4.48636i) q^{91} +(-1.48427 - 3.58333i) q^{93} +12.7329 q^{95} +8.41176 q^{97} +(-0.690529 - 1.66708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q - 8 * q^5 + 16 * q^9	\( 16 q - 8 q^{5} + 16 q^{9} - 24 q^{13} + 16 q^{21} + 32 q^{25} + 24 q^{29} + 80 q^{33} - 40 q^{37} + 16 q^{41} - 24 q^{45} + 56 q^{53} + 80 q^{57} - 8 q^{61} + 32 q^{65} - 32 q^{69} + 32 q^{73} + 32 q^{77} - 48 q^{85} - 32 q^{89} + 16 q^{93} + 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 + 16 * q^9 - 24 * q^13 + 16 * q^21 + 32 * q^25 + 24 * q^29 + 80 * q^33 - 40 * q^37 + 16 * q^41 - 24 * q^45 + 56 * q^53 + 80 * q^57 - 8 * q^61 + 32 * q^65 - 32 * q^69 + 32 * q^73 + 32 * q^77 - 48 * q^85 - 32 * q^89 + 16 * q^93 + 16 * q^97

Introduction

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Database

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