LMFDB - Embedded newform 1024.2.g.e.385.2

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			385.2
Root			$-0.639878 - 1.60952i$ of defining polynomial
Character	$\chi$	$=$	1024.385
Dual form			1024.2.g.e.641.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.969643 + 0.401639i) q^{3} +(-1.44924 + 3.49877i) q^{5} +(-3.21904 - 3.21904i) q^{7} +(-1.34243 + 1.34243i) q^{9} +O(q^{10})$	\(q+(-0.969643 + 0.401639i) q^{3} +(-1.44924 + 3.49877i) q^{5} +(-3.21904 - 3.21904i) q^{7} +(-1.34243 + 1.34243i) q^{9} +(0.878116 + 0.363728i) q^{11} +(-0.985492 - 2.37919i) q^{13} -3.97463i q^{15} +1.34416i q^{17} +(1.28667 + 3.10629i) q^{19} +(4.41421 + 1.82843i) q^{21} +(4.30143 - 4.30143i) q^{23} +(-6.60559 - 6.60559i) q^{25} +(1.96742 - 4.74977i) q^{27} +(-1.44924 + 0.600295i) q^{29} -3.69552 q^{31} -0.997546 q^{33} +(15.9279 - 6.59753i) q^{35} +(1.67035 - 4.03257i) q^{37} +(1.91115 + 1.91115i) q^{39} +(5.34171 - 5.34171i) q^{41} +(7.27829 + 3.01477i) q^{43} +(-2.75135 - 6.64235i) q^{45} -1.02878i q^{47} +13.7245i q^{49} +(-0.539868 - 1.30336i) q^{51} +(6.49877 + 2.69188i) q^{53} +(-2.54520 + 2.54520i) q^{55} +(-2.49522 - 2.49522i) q^{57} +(2.44676 - 5.90700i) q^{59} +(-4.42872 + 1.83444i) q^{61} +8.64266 q^{63} +9.75245 q^{65} +(-6.23381 + 2.58213i) q^{67} +(-2.44323 + 5.89848i) q^{69} +(-5.75634 - 5.75634i) q^{71} +(2.94801 - 2.94801i) q^{73} +(9.05812 + 3.75200i) q^{75} +(-1.65584 - 3.99755i) q^{77} -15.4357i q^{79} -0.299657i q^{81} +(-4.66516 - 11.2627i) q^{83} +(-4.70292 - 1.94801i) q^{85} +(1.16414 - 1.16414i) q^{87} +(9.04708 + 9.04708i) q^{89} +(-4.48636 + 10.8310i) q^{91} +(3.58333 - 1.48427i) q^{93} -12.7329 q^{95} +8.41176 q^{97} +(-1.66708 + 0.690529i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 24 q^{37} - 16 q^{41} - 104 q^{45} + 56 q^{53} - 80 q^{57} - 40 q^{61} + 32 q^{65} - 32 q^{73} - 32 q^{77} + 32 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 + 48 * q^21 - 32 * q^25 + 8 * q^29 + 80 * q^33 + 24 * q^37 - 16 * q^41 - 104 * q^45 + 56 * q^53 - 80 * q^57 - 40 * q^61 + 32 * q^65 - 32 * q^73 - 32 * q^77 + 32 * 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 $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

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

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
$3$	−0.969643	+	0.401639i	−0.559824	+	0.231887i	−0.644609	−	0.764513i	$-0.722980\pi$
$3$	−0.969643	+	0.401639i	−0.559824	+	0.231887i	0.0847850	+	0.996399i	$0.472980\pi$
$4$		0			0
$5$	−1.44924	+	3.49877i	−0.648120	+	1.56470i	0.167349	+	0.985898i	$0.446479\pi$
$5$	−1.44924	+	3.49877i	−0.648120	+	1.56470i	−0.815469	+	0.578801i	$0.803521\pi$
$6$		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
$11$	0.878116	+	0.363728i	0.264762	+	0.109668i	0.511116	−	0.859512i	$-0.329232\pi$
$11$	0.878116	+	0.363728i	0.264762	+	0.109668i	−0.246354	+	0.969180i	$0.579232\pi$
$12$		0			0
$13$	−0.985492	−	2.37919i	−0.273326	−	0.659868i	0.726295	−	0.687383i	$-0.241241\pi$
$13$	−0.985492	−	2.37919i	−0.273326	−	0.659868i	−0.999621	+	0.0275150i	$0.991241\pi$
$14$		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
$19$	1.28667	+	3.10629i	0.295182	+	0.712632i	0.999995	+	0.00323890i	$0.00103098\pi$
$19$	1.28667	+	3.10629i	0.295182	+	0.712632i	−0.704813	+	0.709393i	$0.748969\pi$
$20$		0			0
$21$	4.41421	+	1.82843i	0.963260	+	0.398996i
$22$		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
$27$	1.96742	−	4.74977i	0.378630	−	0.914095i
$28$		0			0
$29$	−1.44924	+	0.600295i	−0.269117	+	0.111472i	−0.513161	−	0.858292i	$-0.671526\pi$
$29$	−1.44924	+	0.600295i	−0.269117	+	0.111472i	0.244044	+	0.969764i	$0.421526\pi$
$30$		0			0
$31$	−3.69552			−0.663735			−0.331867	−	0.943326i	$-0.607679\pi$
$31$	−3.69552			−0.663735			−0.331867	+	0.943326i	$0.607679\pi$
$32$		0			0
$33$	−0.997546			−0.173651
$34$		0			0
$35$	15.9279	−	6.59753i	2.69230	−	1.11519i
$36$		0			0
$37$	1.67035	−	4.03257i	0.274603	−	0.662951i	−0.725066	−	0.688680i	$-0.758191\pi$
$37$	1.67035	−	4.03257i	0.274603	−	0.662951i	0.999669	+	0.0257289i	$0.00819066\pi$
$38$		0			0
$39$	1.91115	+	1.91115i	0.306029	+	0.306029i
$40$		0			0
$41$	5.34171	−	5.34171i	0.834235	−	0.834235i	−0.153858	−	0.988093i	$-0.549170\pi$
$41$	5.34171	−	5.34171i	0.834235	−	0.834235i	0.988093	+	0.153858i	$0.0491699\pi$
$42$		0			0
$43$	7.27829	+	3.01477i	1.10993	+	0.459747i	0.860913	−	0.508752i	$-0.169893\pi$
$43$	7.27829	+	3.01477i	1.10993	+	0.459747i	0.249015	+	0.968500i	$0.419893\pi$
$44$		0			0
$45$	−2.75135	−	6.64235i	−0.410147	−	0.990182i
$46$		0			0
$47$		−	1.02878i		−	0.150063i	−0.997181	−	0.0750313i	$-0.976094\pi$
$47$		−	1.02878i		−	0.150063i	0.997181	−	0.0750313i	$-0.0239057\pi$
$48$		0			0
$49$			13.7245i			1.96064i
$50$		0			0
$51$	−0.539868	−	1.30336i	−0.0755967	−	0.182507i
$52$		0			0
$53$	6.49877	+	2.69188i	0.892675	+	0.369758i	0.781399	−	0.624031i	$-0.214506\pi$
$53$	6.49877	+	2.69188i	0.892675	+	0.369758i	0.111276	+	0.993790i	$0.464506\pi$
$54$		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
$59$	2.44676	−	5.90700i	0.318541	−	0.769027i	−0.680791	−	0.732478i	$-0.738364\pi$
$59$	2.44676	−	5.90700i	0.318541	−	0.769027i	0.999332	−	0.0365485i	$-0.0116363\pi$
$60$		0			0
$61$	−4.42872	+	1.83444i	−0.567040	+	0.234876i	−0.647738	−	0.761863i	$-0.724285\pi$
$61$	−4.42872	+	1.83444i	−0.567040	+	0.234876i	0.0806985	+	0.996739i	$0.474285\pi$
$62$		0			0
$63$	8.64266			1.08887
$64$		0			0
$65$	9.75245			1.20964
$66$		0			0
$67$	−6.23381	+	2.58213i	−0.761581	+	0.315457i	−0.729457	−	0.684027i	$-0.760227\pi$
$67$	−6.23381	+	2.58213i	−0.761581	+	0.315457i	−0.0321238	+	0.999484i	$0.510227\pi$
$68$		0			0
$69$	−2.44323	+	5.89848i	−0.294130	+	0.710093i
$70$		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	−0.513219	−	0.858258i	$-0.671547\pi$
$73$	2.94801	−	2.94801i	0.345039	−	0.345039i	0.858258	+	0.513219i	$0.171547\pi$
$74$		0			0
$75$	9.05812	+	3.75200i	1.04594	+	0.433243i
$76$		0			0
$77$	−1.65584	−	3.99755i	−0.188700	−	0.455563i
$78$		0			0
$79$		−	15.4357i		−	1.73665i	−0.495996	−	0.868325i	$-0.665197\pi$
$79$		−	15.4357i		−	1.73665i	0.495996	−	0.868325i	$-0.334803\pi$
$80$		0			0
$81$		−	0.299657i		−	0.0332952i
$82$		0			0
$83$	−4.66516	−	11.2627i	−0.512068	−	1.23624i	−0.942678	−	0.333703i	$-0.891702\pi$
$83$	−4.66516	−	11.2627i	−0.512068	−	1.23624i	0.430610	−	0.902538i	$-0.358298\pi$
$84$		0			0
$85$	−4.70292	−	1.94801i	−0.510103	−	0.211292i
$86$		0			0
$87$	1.16414	−	1.16414i	0.124809	−	0.124809i
$88$		0			0
$89$	9.04708	+	9.04708i	0.958989	+	0.958989i	0.999192	−	0.0402029i	$-0.0128004\pi$
$89$	9.04708	+	9.04708i	0.958989	+	0.958989i	−0.0402029	+	0.999192i	$0.512800\pi$
$90$		0			0
$91$	−4.48636	+	10.8310i	−0.470299	+	1.13540i
$92$		0			0
$93$	3.58333	−	1.48427i	0.371574	−	0.153911i
$94$		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
$99$	−1.66708	+	0.690529i	−0.167548	+	0.0694008i
$100$		0			0
$101$	−3.60029	+	8.69188i	−0.358243	+	0.864874i	0.637305	+	0.770612i	$0.280049\pi$
$101$	−3.60029	+	8.69188i	−0.358243	+	0.864874i	−0.995547	+	0.0942625i	$0.969951\pi$
$102$		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
$107$	−7.72475	−	3.19970i	−0.746780	−	0.309326i	−0.0233529	−	0.999727i	$-0.507434\pi$
$107$	−7.72475	−	3.19970i	−0.746780	−	0.309326i	−0.723427	+	0.690401i	$0.757434\pi$
$108$		0			0
$109$	−0.277666	−	0.670346i	−0.0265956	−	0.0642075i	0.910024	−	0.414556i	$-0.136063\pi$
$109$	−0.277666	−	0.670346i	−0.0265956	−	0.0642075i	−0.936619	+	0.350349i	$0.886063\pi$
$110$		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
$115$	8.81593	+	21.2835i	0.822090	+	1.98470i
$116$		0			0
$117$	4.51684	+	1.87094i	0.417582	+	0.172968i
$118$		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
$123$	−3.03411	+	7.32499i	−0.273576	+	0.660472i
$124$		0			0
$125$	15.1907	−	6.29217i	1.35869	−	0.562789i
$126$		0			0
$127$	3.43664			0.304953			0.152476	−	0.988307i	$-0.451275\pi$
$127$	3.43664			0.304953			0.152476	+	0.988307i	$0.451275\pi$
$128$		0			0
$129$	−8.26819			−0.727973
$130$		0			0
$131$	−3.36180	+	1.39250i	−0.293722	+	0.121664i	−0.524679	−	0.851300i	$-0.675815\pi$
$131$	−3.36180	+	1.39250i	−0.293722	+	0.121664i	0.230956	+	0.972964i	$0.425815\pi$
$132$		0			0
$133$	5.85744	−	14.1411i	0.507905	−	1.22619i
$134$		0			0
$135$	13.7671	+	13.7671i	1.18489	+	1.18489i
$136$		0			0
$137$	1.79941	−	1.79941i	0.153734	−	0.153734i	−0.626049	−	0.779783i	$-0.715329\pi$
$137$	1.79941	−	1.79941i	0.153734	−	0.153734i	0.779783	+	0.626049i	$0.215329\pi$
$138$		0			0
$139$	−16.1040	−	6.67049i	−1.36592	−	0.565784i	−0.425243	−	0.905079i	$-0.639811\pi$
$139$	−16.1040	−	6.67049i	−1.36592	−	0.565784i	−0.940680	+	0.339295i	$0.889811\pi$
$140$		0			0
$141$	0.413197	+	0.997546i	0.0347975	+	0.0840086i
$142$		0			0
$143$		−	2.44765i		−	0.204683i
$144$		0			0
$145$		−	5.94053i		−	0.493334i
$146$		0			0
$147$	−5.51228	−	13.3078i	−0.454645	−	1.09761i
$148$		0			0
$149$	−15.9345	−	6.60029i	−1.30541	−	0.540717i	−0.381866	−	0.924218i	$-0.624718\pi$
$149$	−15.9345	−	6.60029i	−1.30541	−	0.540717i	−0.923541	+	0.383500i	$0.874718\pi$
$150$		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
$155$	5.35569	−	12.9298i	0.430179	−	1.03854i
$156$		0			0
$157$	−6.56882	+	2.72090i	−0.524249	+	0.217151i	−0.629082	−	0.777339i	$-0.716569\pi$
$157$	−6.56882	+	2.72090i	−0.524249	+	0.217151i	0.104833	+	0.994490i	$0.466569\pi$
$158$		0			0
$159$	−7.38265			−0.585483
$160$		0			0
$161$	−27.6930			−2.18251
$162$		0			0
$163$	−2.05204	+	0.849981i	−0.160728	+	0.0665756i	−0.461597	−	0.887090i	$-0.652723\pi$
$163$	−2.05204	+	0.849981i	−0.160728	+	0.0665756i	0.300869	+	0.953665i	$0.402723\pi$
$164$		0			0
$165$	1.44568	−	3.49019i	0.112546	−	0.271711i
$166$		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
$171$	−5.89723	−	2.44271i	−0.450972	−	0.186799i
$172$		0			0
$173$	7.28617	+	17.5904i	0.553957	+	1.33737i	0.914484	+	0.404622i	$0.132597\pi$
$173$	7.28617	+	17.5904i	0.553957	+	1.33737i	−0.360527	+	0.932749i	$0.617403\pi$
$174$		0			0
$175$			42.5273i			3.21476i
$176$		0			0
$177$			6.71040i			0.504385i
$178$		0			0
$179$	4.25395	+	10.2700i	0.317955	+	0.767612i	0.999362	+	0.0357074i	$0.0113684\pi$
$179$	4.25395	+	10.2700i	0.317955	+	0.767612i	−0.681407	+	0.731905i	$0.738632\pi$
$180$		0			0
$181$	2.72335	+	1.12805i	0.202425	+	0.0838472i	0.481593	−	0.876395i	$-0.340059\pi$
$181$	2.72335	+	1.12805i	0.202425	+	0.0838472i	−0.279168	+	0.960242i	$0.590059\pi$
$182$		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
$187$	−0.488909	+	1.18033i	−0.0357526	+	0.0863143i
$188$		0			0
$189$	−21.6229	+	8.95651i	−1.57284	+	0.651490i
$190$		0			0
$191$	21.2674			1.53885			0.769426	−	0.638736i	$-0.220542\pi$
$191$	21.2674			1.53885			0.769426	+	0.638736i	$0.220542\pi$
$192$		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
$195$	−9.45640	+	3.91697i	−0.677187	+	0.280500i
$196$		0			0
$197$	2.09306	−	5.05309i	0.149124	−	0.360018i	−0.831611	−	0.555358i	$-0.812581\pi$
$197$	2.09306	−	5.05309i	0.149124	−	0.360018i	0.980735	+	0.195340i	$0.0625812\pi$
$198$		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
$203$	6.59753	+	2.73279i	0.463056	+	0.191804i
$204$		0			0
$205$	10.9480	+	26.4308i	0.764642	+	1.84601i
$206$		0			0
$207$			11.5487i			0.802692i
$208$		0			0
$209$			3.19568i			0.221050i
$210$		0			0
$211$	−8.83123	−	21.3205i	−0.607967	−	1.46776i	−0.865207	−	0.501414i	$-0.832813\pi$
$211$	−8.83123	−	21.3205i	−0.607967	−	1.46776i	0.257240	−	0.966347i	$-0.417187\pi$
$212$		0			0
$213$	7.89357	+	3.26962i	0.540859	+	0.224031i
$214$		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
$219$	−1.67448	+	4.04256i	−0.113151	+	0.273171i
$220$		0			0
$221$	3.19801	−	1.32466i	0.215122	−	0.0891063i
$222$		0			0
$223$	12.3493			0.826973			0.413487	−	0.910510i	$-0.364311\pi$
$223$	12.3493			0.826973			0.413487	+	0.910510i	$0.364311\pi$
$224$		0			0
$225$	17.7350			1.18234
$226$		0			0
$227$	−4.28999	+	1.77697i	−0.284736	+	0.117942i	−0.520481	−	0.853873i	$-0.674247\pi$
$227$	−4.28999	+	1.77697i	−0.284736	+	0.117942i	0.235744	+	0.971815i	$0.424247\pi$
$228$		0			0
$229$	−1.79239	+	4.32720i	−0.118444	+	0.285949i	−0.971972	−	0.235098i	$-0.924459\pi$
$229$	−1.79239	+	4.32720i	−0.118444	+	0.285949i	0.853527	+	0.521048i	$0.174459\pi$
$230$		0			0
$231$	3.21114	+	3.21114i	0.211278	+	0.211278i
$232$		0			0
$233$	0.848945	−	0.848945i	0.0556162	−	0.0556162i	−0.678752	−	0.734368i	$-0.737479\pi$
$233$	0.848945	−	0.848945i	0.0556162	−	0.0556162i	0.734368	+	0.678752i	$0.237479\pi$
$234$		0			0
$235$	3.59946	+	1.49094i	0.234803	+	0.0972585i
$236$		0			0
$237$	6.19957	+	14.9671i	0.402706	+	0.972217i
$238$		0			0
$239$			1.40395i			0.0908141i	0.998969	+	0.0454070i	$0.0144585\pi$
$239$			1.40395i			0.0908141i	−0.998969	+	0.0454070i	$0.985542\pi$
$240$		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
$243$	6.02262	+	14.5399i	0.386351	+	0.932734i
$244$		0			0
$245$	−48.0187	−	19.8900i	−3.06781	−	1.27073i
$246$		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
$251$	1.68327	−	4.06378i	0.106247	−	0.256503i	−0.861811	−	0.507230i	$-0.830669\pi$
$251$	1.68327	−	4.06378i	0.106247	−	0.256503i	0.968058	+	0.250726i	$0.0806695\pi$
$252$		0			0
$253$	5.34171	−	2.21261i	0.335830	−	0.139105i
$254$		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
$259$	−18.3579	+	7.60410i	−1.14071	+	0.472496i
$260$		0			0
$261$	1.13965	−	2.75135i	0.0705423	−	0.170304i
$262$		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
$267$	−12.4061	−	5.13877i	−0.759241	−	0.314488i
$268$		0			0
$269$	−4.99154	−	12.0506i	−0.304339	−	0.734740i	−0.999868	−	0.0162420i	$-0.994830\pi$
$269$	−4.99154	−	12.0506i	−0.304339	−	0.734740i	0.695529	−	0.718498i	$-0.255170\pi$
$270$		0			0
$271$		−	5.83168i		−	0.354250i	−0.984188	−	0.177125i	$-0.943320\pi$
$271$		−	5.83168i		−	0.354250i	0.984188	−	0.177125i	$-0.0566796\pi$
$272$		0			0
$273$		−	12.3041i		−	0.744681i
$274$		0			0
$275$	−3.39784	−	8.20311i	−0.204897	−	0.494666i
$276$		0			0
$277$	15.8791	+	6.57732i	0.954080	+	0.395193i	0.804763	−	0.593596i	$-0.202292\pi$
$277$	15.8791	+	6.57732i	0.954080	+	0.395193i	0.149317	+	0.988789i	$0.452292\pi$
$278$		0			0
$279$	4.96096	−	4.96096i	0.297005	−	0.297005i
$280$		0			0
$281$	−2.49031	−	2.49031i	−0.148559	−	0.148559i	0.628915	−	0.777474i	$-0.283499\pi$
$281$	−2.49031	−	2.49031i	−0.148559	−	0.148559i	−0.777474	+	0.628915i	$0.783499\pi$
$282$		0			0
$283$	−9.86733	+	23.8218i	−0.586552	+	1.41606i	0.300227	+	0.953868i	$0.402937\pi$
$283$	−9.86733	+	23.8218i	−0.586552	+	1.41606i	−0.886779	+	0.462193i	$0.847063\pi$
$284$		0			0
$285$	12.3464	−	5.11403i	0.731336	−	0.302929i
$286$		0			0
$287$	−34.3904			−2.03000
$288$		0			0
$289$	15.1932			0.893719
$290$		0			0
$291$	−8.15640	+	3.37849i	−0.478137	+	0.198051i
$292$		0			0
$293$	10.9045	−	26.3258i	0.637047	−	1.53797i	−0.193548	−	0.981091i	$-0.562000\pi$
$293$	10.9045	−	26.3258i	0.637047	−	1.53797i	0.830595	−	0.556877i	$-0.188000\pi$
$294$		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
$299$	−14.4729	−	5.99489i	−0.836992	−	0.346693i
$300$		0			0
$301$	−13.7245	−	33.1338i	−0.791064	−	1.90980i
$302$		0			0
$303$		−	9.87404i		−	0.567249i
$304$		0			0
$305$		−	18.1536i		−	1.03947i
$306$		0			0
$307$	−1.03896	−	2.50827i	−0.0592967	−	0.143155i	0.891454	−	0.453111i	$-0.149686\pi$
$307$	−1.03896	−	2.50827i	−0.0592967	−	0.143155i	−0.950751	+	0.309956i	$0.899686\pi$
$308$		0			0
$309$	9.11803	+	3.77681i	0.518706	+	0.214855i
$310$		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	0.918219	−	0.396072i	$-0.129627\pi$
$313$	9.23773	+	9.23773i	0.522148	+	0.522148i	−0.396072	+	0.918219i	$0.629627\pi$
$314$		0			0
$315$	−12.5253	+	30.2387i	−0.705719	+	1.70376i
$316$		0			0
$317$	25.1968	−	10.4368i	1.41519	−	0.586192i	0.461545	−	0.887117i	$-0.347295\pi$
$317$	25.1968	−	10.4368i	1.41519	−	0.586192i	0.953648	+	0.300925i	$0.0972954\pi$
$318$		0			0
$319$	−1.49094			−0.0834769
$320$		0			0
$321$	8.77537			0.489794
$322$		0			0
$323$	−4.17536	+	1.72949i	−0.232323	+	0.0962314i
$324$		0			0
$325$	−9.20618	+	22.2257i	−0.510667	+	1.23286i
$326$		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
$331$	−28.9422	−	11.9883i	−1.59081	−	0.658935i	−0.600731	−	0.799451i	$-0.705124\pi$
$331$	−28.9422	−	11.9883i	−1.59081	−	0.658935i	−0.990078	+	0.140516i	$0.955124\pi$
$332$		0			0
$333$	3.17112	+	7.65575i	0.173776	+	0.419533i
$334$		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
$339$	6.38447	+	15.4135i	0.346757	+	0.837145i
$340$		0			0
$341$	−3.24509	−	1.34416i	−0.175732	−	0.0727905i
$342$		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
$347$	5.69394	−	13.7464i	0.305667	−	0.737944i	−0.694169	−	0.719812i	$-0.744228\pi$
$347$	5.69394	−	13.7464i	0.305667	−	0.737944i	0.999836	−	0.0181324i	$-0.00577204\pi$
$348$		0			0
$349$	4.27420	−	1.77043i	0.228792	−	0.0947690i	−0.265342	−	0.964154i	$-0.585485\pi$
$349$	4.27420	−	1.77043i	0.228792	−	0.0947690i	0.494135	+	0.869385i	$0.335485\pi$
$350$		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
$355$	28.4825	−	11.7978i	1.51169	−	0.626163i
$356$		0			0
$357$	−2.45770	+	5.93342i	−0.130075	+	0.314030i
$358$		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
$363$	9.79011	+	4.05520i	0.513848	+	0.212843i
$364$		0			0
$365$	6.04205	+	14.5868i	0.316255	+	0.763508i
$366$		0			0
$367$			7.25894i			0.378914i	0.981889	+	0.189457i	$0.0606727\pi$
$367$			7.25894i			0.378914i	−0.981889	+	0.189457i	$0.939327\pi$
$368$		0			0
$369$			14.3417i			0.746600i
$370$		0			0
$371$	−12.2545	−	29.5851i	−0.636224	−	1.53598i
$372$		0			0
$373$	−3.81392	−	1.57978i	−0.197477	−	0.0817978i	0.281753	−	0.959487i	$-0.409084\pi$
$373$	−3.81392	−	1.57978i	−0.197477	−	0.0817978i	−0.479230	+	0.877689i	$0.659084\pi$
$374$		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
$379$	7.48355	−	18.0669i	0.384404	−	0.928033i	−0.606698	−	0.794932i	$-0.707506\pi$
$379$	7.48355	−	18.0669i	0.384404	−	0.928033i	0.991102	−	0.133101i	$-0.0424936\pi$
$380$		0			0
$381$	−3.33232	+	1.38029i	−0.170720	+	0.0707144i
$382$		0			0
$383$	−4.43680			−0.226710			−0.113355	−	0.993555i	$-0.536160\pi$
$383$	−4.43680			−0.226710			−0.113355	+	0.993555i	$0.536160\pi$
$384$		0			0
$385$	16.3862			0.835119
$386$		0			0
$387$	−13.8177	+	5.72347i	−0.702392	+	0.290940i
$388$		0			0
$389$	7.08312	−	17.1002i	0.359129	−	0.867013i	−0.636294	−	0.771446i	$-0.719534\pi$
$389$	7.08312	−	17.1002i	0.359129	−	0.867013i	0.995423	−	0.0955668i	$-0.0304663\pi$
$390$		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
$395$	54.0059	+	22.3700i	2.71733	+	1.12556i
$396$		0			0
$397$	−12.4503	−	30.0576i	−0.624860	−	1.50855i	−0.845933	−	0.533289i	$-0.820956\pi$
$397$	−12.4503	−	30.0576i	−0.624860	−	1.50855i	0.221073	−	0.975257i	$-0.429044\pi$
$398$		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
$403$	3.64190	+	8.79233i	0.181416	+	0.437977i
$404$		0			0
$405$	1.04843	+	0.434275i	0.0520970	+	0.0215793i
$406$		0			0
$407$	2.93352	−	2.93352i	0.145409	−	0.145409i
$408$		0			0
$409$	4.45034	+	4.45034i	0.220055	+	0.220055i	0.808522	−	0.588466i	$-0.200268\pi$
$409$	4.45034	+	4.45034i	0.220055	+	0.220055i	−0.588466	+	0.808522i	$0.700268\pi$
$410$		0			0
$411$	−1.02207	+	2.46750i	−0.0504151	+	0.121713i
$412$		0			0
$413$	−26.8911	+	11.1387i	−1.32323	+	0.548098i
$414$		0			0
$415$	46.1666			2.26623
$416$		0			0
$417$	18.2943			0.895874
$418$		0			0
$419$	21.2950	−	8.82067i	1.04033	−	0.430918i	0.203899	−	0.978992i	$-0.434639\pi$
$419$	21.2950	−	8.82067i	1.04033	−	0.430918i	0.836430	+	0.548074i	$0.184639\pi$
$420$		0			0
$421$	−6.26218	+	15.1182i	−0.305200	+	0.736818i	0.694648	+	0.719350i	$0.255560\pi$
$421$	−6.26218	+	15.1182i	−0.305200	+	0.736818i	−0.999847	+	0.0174674i	$0.994440\pi$
$422$		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
$427$	20.1614	+	8.35111i	0.975677	+	0.404139i
$428$		0			0
$429$	0.983074	+	2.37335i	0.0474633	+	0.114586i
$430$		0			0
$431$		−	5.84075i		−	0.281339i	−0.990057	−	0.140670i	$-0.955074\pi$
$431$		−	5.84075i		−	0.281339i	0.990057	−	0.140670i	$-0.0449255\pi$
$432$		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
$435$	2.38595	+	5.76019i	0.114398	+	0.276180i
$436$		0			0
$437$	18.8960	+	7.82699i	0.903919	+	0.374416i
$438$		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
$443$	14.3439	−	34.6293i	0.681500	−	1.64529i	−0.0797396	−	0.996816i	$-0.525409\pi$
$443$	14.3439	−	34.6293i	0.681500	−	1.64529i	0.761240	−	0.648471i	$-0.224591\pi$
$444$		0			0
$445$	−44.7651	+	18.5423i	−2.12207	+	0.878989i
$446$		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
$451$	6.63357	−	2.74771i	0.312363	−	0.129385i
$452$		0			0
$453$	3.91488	−	9.45136i	0.183937	−	0.444064i
$454$		0			0
$455$	−31.3935	−	31.3935i	−1.47175	−	1.47175i
$456$		0			0
$457$	7.04451	−	7.04451i	0.329528	−	0.329528i	−0.522879	−	0.852407i	$-0.675142\pi$
$457$	7.04451	−	7.04451i	0.329528	−	0.329528i	0.852407	+	0.522879i	$0.175142\pi$
$458$		0			0
$459$	6.38447	+	2.64453i	0.298001	+	0.123436i
$460$		0			0
$461$	13.1302	+	31.6991i	0.611535	+	1.47637i	0.861314	+	0.508072i	$0.169642\pi$
$461$	13.1302	+	31.6991i	0.611535	+	1.47637i	−0.249780	+	0.968303i	$0.580358\pi$
$462$		0			0
$463$		−	8.90222i		−	0.413721i	−0.978370	−	0.206861i	$-0.933675\pi$
$463$		−	8.90222i		−	0.413721i	0.978370	−	0.206861i	$-0.0663246\pi$
$464$		0			0
$465$			14.6883i			0.681155i
$466$		0			0
$467$	9.40713	+	22.7108i	0.435310	+	1.05093i	0.977549	+	0.210707i	$0.0675767\pi$
$467$	9.40713	+	22.7108i	0.435310	+	1.05093i	−0.542239	+	0.840224i	$0.682423\pi$
$468$		0			0
$469$	28.3789	+	11.7549i	1.31041	+	0.542791i
$470$		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
$475$	12.0197	−	29.0181i	0.551501	−	1.33144i
$476$		0			0
$477$	−12.3378	+	5.11048i	−0.564908	+	0.233993i
$478$		0			0
$479$	−8.80923			−0.402504			−0.201252	−	0.979540i	$-0.564501\pi$
$479$	−8.80923			−0.402504			−0.201252	+	0.979540i	$0.564501\pi$
$480$		0			0
$481$	−11.2404			−0.512516
$482$		0			0
$483$	26.8523	−	11.1226i	1.22182	−	0.506095i
$484$		0			0
$485$	−12.1907	+	29.4308i	−0.553549	+	1.33639i
$486$		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
$491$	−10.0947	−	4.18136i	−0.455568	−	0.188702i	0.143086	−	0.989710i	$-0.454297\pi$
$491$	−10.0947	−	4.18136i	−0.455568	−	0.188702i	−0.598654	+	0.801008i	$0.704297\pi$
$492$		0			0
$493$	−0.806893	−	1.94801i	−0.0363406	−	0.0877341i
$494$		0			0
$495$		−	6.83349i		−	0.307143i
$496$		0			0
$497$			37.0598i			1.66236i
$498$		0			0
$499$	−10.9489	−	26.4331i	−0.490142	−	1.18331i	−0.954648	−	0.297737i	$-0.903768\pi$
$499$	−10.9489	−	26.4331i	−0.490142	−	1.18331i	0.464506	−	0.885570i	$-0.346232\pi$
$500$		0			0
$501$	1.44568	+	0.598822i	0.0645884	+	0.0267534i
$502$		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
$507$	−2.55775	+	6.17495i	−0.113594	+	0.274239i
$508$		0			0
$509$	34.1252	−	14.1351i	1.51257	−	0.626528i	0.536485	−	0.843910i	$-0.319752\pi$
$509$	34.1252	−	14.1351i	1.51257	−	0.626528i	0.976087	+	0.217382i	$0.0697517\pi$
$510$		0			0
$511$	−18.9795			−0.839606
$512$		0			0
$513$	17.2856			0.763178
$514$		0			0
$515$	32.9007	−	13.6279i	1.44978	−	0.600517i
$516$		0			0
$517$	0.374195	−	0.903386i	0.0164571	−	0.0397309i
$518$		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	$-0.397652\pi$
$521$	28.8690	−	28.8690i	1.26478	−	1.26478i	0.948751	−	0.316025i	$-0.102348\pi$
$522$		0			0
$523$	12.1005	+	5.01220i	0.529119	+	0.219168i	0.631217	−	0.775606i	$-0.282556\pi$
$523$	12.1005	+	5.01220i	0.529119	+	0.219168i	−0.102098	+	0.994774i	$0.532556\pi$
$524$		0			0
$525$	−17.0806	−	41.2363i	−0.745460	−	1.79970i
$526$		0			0
$527$		−	4.96738i		−	0.216382i
$528$		0			0
$529$		−	14.0047i		−	0.608898i
$530$		0			0
$531$	4.64512	+	11.2143i	0.201581	+	0.486660i
$532$		0			0
$533$	−17.9731	−	7.44472i	−0.778503	−	0.322467i
$534$		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
$539$	−4.99196	+	12.0517i	−0.215019	+	0.519102i
$540$		0			0
$541$	15.8125	−	6.54974i	0.679832	−	0.281596i	−0.0159249	−	0.999873i	$-0.505069\pi$
$541$	15.8125	−	6.54974i	0.679832	−	0.281596i	0.695757	+	0.718278i	$0.255069\pi$
$542$		0			0
$543$	−3.09375			−0.132765
$544$		0			0
$545$	2.74779			0.117703
$546$		0			0
$547$	−23.7298	+	9.82921i	−1.01461	+	0.420267i	−0.827136	−	0.562002i	$-0.810031\pi$
$547$	−23.7298	+	9.82921i	−1.01461	+	0.420267i	−0.187478	+	0.982269i	$0.560031\pi$
$548$		0			0
$549$	3.48264	−	8.40783i	0.148635	−	0.358838i
$550$		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
$555$	−16.0280	−	6.63901i	−0.680350	−	0.281810i
$556$		0			0
$557$	−11.2141	−	27.0732i	−0.475156	−	1.14713i	−0.961855	−	0.273558i	$-0.911799\pi$
$557$	−11.2141	−	27.0732i	−0.475156	−	1.14713i	0.486700	−	0.873569i	$-0.338201\pi$
$558$		0			0
$559$		−	20.2874i		−	0.858067i
$560$		0			0
$561$		−	1.34086i		−	0.0566113i
$562$		0			0
$563$	11.4436	+	27.6272i	0.482289	+	1.16435i	0.958519	+	0.285028i	$0.0920030\pi$
$563$	11.4436	+	27.6272i	0.482289	+	1.16435i	−0.476230	+	0.879321i	$0.657997\pi$
$564$		0			0
$565$	55.6166	+	23.0371i	2.33981	+	0.969180i
$566$		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	$-0.936774\pi$
$569$	−28.0917	−	28.0917i	−1.17767	−	1.17767i	−0.197328	−	0.980337i	$-0.563226\pi$
$570$		0			0
$571$	−1.65653	+	3.99922i	−0.0693237	+	0.167362i	−0.954744	−	0.297429i	$-0.903871\pi$
$571$	−1.65653	+	3.99922i	−0.0693237	+	0.167362i	0.885420	+	0.464791i	$0.153871\pi$
$572$		0			0
$573$	−20.6217	+	8.54181i	−0.861486	+	0.356839i
$574$		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
$579$	2.67127	−	1.10648i	0.111014	−	0.0459837i
$580$		0			0
$581$	−21.2377	+	51.2724i	−0.881090	+	2.12714i
$582$		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
$587$	−21.3081	−	8.82612i	−0.879481	−	0.364293i	−0.103185	−	0.994662i	$-0.532903\pi$
$587$	−21.3081	−	8.82612i	−0.879481	−	0.364293i	−0.776295	+	0.630369i	$0.782903\pi$
$588$		0			0
$589$	−4.75491	−	11.4794i	−0.195922	−	0.472999i
$590$		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
$595$	8.86815	+	21.4096i	0.363559	+	0.877709i
$596$		0			0
$597$	−21.0278	−	8.70998i	−0.860609	−	0.356476i
$598$		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	$-0.962449\pi$
$601$	−27.2303	−	27.2303i	−1.11075	−	1.11075i	−0.117695	−	0.993050i	$-0.537551\pi$
$602$		0			0
$603$	4.90211	−	11.8347i	0.199629	−	0.481948i
$604$		0			0
$605$	35.3258	−	14.6324i	1.43620	−	0.594892i
$606$		0			0
$607$	3.74369			0.151952			0.0759758	−	0.997110i	$-0.475793\pi$
$607$	3.74369			0.151952			0.0759758	+	0.997110i	$0.475793\pi$
$608$		0			0
$609$	−7.49485			−0.303707
$610$		0			0
$611$	−2.44765	+	1.01385i	−0.0990215	+	0.0410160i
$612$		0			0
$613$	−2.85143	+	6.88397i	−0.115168	+	0.278041i	−0.970944	−	0.239306i	$-0.923080\pi$
$613$	−2.85143	+	6.88397i	−0.115168	+	0.278041i	0.855776	+	0.517347i	$0.173080\pi$
$614$		0			0
$615$	−21.2313	−	21.2313i	−0.856130	−	0.856130i
$616$		0			0
$617$	6.08913	−	6.08913i	0.245139	−	0.245139i	−0.573833	−	0.818972i	$-0.694544\pi$
$617$	6.08913	−	6.08913i	0.245139	−	0.245139i	0.818972	+	0.573833i	$0.194544\pi$
$618$		0			0
$619$	30.4332	+	12.6058i	1.22321	+	0.506672i	0.898430	−	0.439117i	$-0.144709\pi$
$619$	30.4332	+	12.6058i	1.22321	+	0.506672i	0.324783	+	0.945788i	$0.394709\pi$
$620$		0			0
$621$	−11.9681	−	28.8936i	−0.480264	−	1.15946i
$622$		0			0
$623$		−	58.2458i		−	2.33357i
$624$		0			0
$625$			15.5590i			0.622359i
$626$		0			0
$627$	−1.28351	−	3.09867i	−0.0512585	−	0.123749i
$628$		0			0
$629$	5.42043	+	2.24522i	0.216127	+	0.0895226i
$630$		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
$635$	−4.98052	+	12.0240i	−0.197646	+	0.477159i
$636$		0			0
$637$	32.6530	−	13.5253i	1.29376	−	0.535893i
$638$		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
$643$	19.8975	−	8.24179i	0.784679	−	0.325025i	0.0458768	−	0.998947i	$-0.485392\pi$
$643$	19.8975	−	8.24179i	0.784679	−	0.325025i	0.738802	+	0.673922i	$0.235392\pi$
$644$		0			0
$645$	11.9826	−	28.9285i	0.471814	−	1.13906i
$646$		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
$651$	−16.3128	−	6.75699i	−0.639349	−	0.264827i
$652$		0			0
$653$	7.89002	+	19.0482i	0.308760	+	0.745413i	0.999746	+	0.0225445i	$0.00717676\pi$
$653$	7.89002	+	19.0482i	0.308760	+	0.745413i	−0.690986	+	0.722868i	$0.742823\pi$
$654$		0			0
$655$		−	13.7803i		−	0.538439i
$656$		0			0
$657$			7.91498i			0.308793i
$658$		0			0
$659$	−16.4563	−	39.7290i	−0.641046	−	1.54762i	−0.825271	−	0.564737i	$-0.808978\pi$
$659$	−16.4563	−	39.7290i	−0.641046	−	1.54762i	0.184225	−	0.982884i	$-0.441022\pi$
$660$		0			0
$661$	−17.1267	−	7.09412i	−0.666153	−	0.275929i	0.0238723	−	0.999715i	$-0.492400\pi$
$661$	−17.1267	−	7.09412i	−0.666153	−	0.275929i	−0.690025	+	0.723786i	$0.742400\pi$
$662$		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
$667$	−3.65168	+	8.81593i	−0.141394	+	0.341354i
$668$		0			0
$669$	−11.9745	+	4.95998i	−0.462959	+	0.191764i
$670$		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
$675$	−44.3710	+	18.3791i	−1.70784	+	0.707411i
$676$		0			0
$677$	−2.68980	+	6.49374i	−0.103377	+	0.249575i	−0.967102	−	0.254389i	$-0.918126\pi$
$677$	−2.68980	+	6.49374i	−0.103377	+	0.249575i	0.863725	+	0.503964i	$0.168126\pi$
$678$		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
$683$	17.9833	+	7.44891i	0.688110	+	0.285025i	0.699213	−	0.714914i	$-0.253534\pi$
$683$	17.9833	+	7.44891i	0.688110	+	0.285025i	−0.0111024	+	0.999938i	$0.503534\pi$
$684$		0			0
$685$	3.68795	+	8.90351i	0.140909	+	0.340186i
$686$		0			0
$687$		−	4.91573i		−	0.187547i
$688$		0			0
$689$		−	18.1146i		−	0.690112i
$690$		0			0
$691$	−2.81928	−	6.80634i	−0.107250	−	0.258926i	0.861139	−	0.508370i	$-0.169752\pi$
$691$	−2.81928	−	6.80634i	−0.107250	−	0.258926i	−0.968389	+	0.249445i	$0.919752\pi$
$692$		0			0
$693$	7.58926	+	3.14357i	0.288292	+	0.119414i
$694$		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
$699$	−0.482204	+	1.16414i	−0.0182386	+	0.0440319i
$700$		0			0
$701$	−41.2169	+	17.0726i	−1.55674	+	0.644823i	−0.984519	−	0.175277i	$-0.943918\pi$
$701$	−41.2169	+	17.0726i	−1.55674	+	0.644823i	−0.572221	+	0.820100i	$0.693918\pi$
$702$		0			0
$703$	14.6755			0.553498
$704$		0			0
$705$	−4.08901			−0.154001
$706$		0			0
$707$	39.5690	−	16.3900i	1.48815	−	0.616410i
$708$		0			0
$709$	−0.461208	+	1.11345i	−0.0173210	+	0.0418167i	−0.932303	−	0.361677i	$-0.882204\pi$
$709$	−0.461208	+	1.11345i	−0.0173210	+	0.0418167i	0.914982	+	0.403494i	$0.132204\pi$
$710$		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
$715$	8.56379	+	3.54724i	0.320267	+	0.132659i
$716$		0			0
$717$	−0.563882	−	1.36133i	−0.0210586	−	0.0508398i
$718$		0			0
$719$			47.3791i			1.76694i	0.468487	+	0.883470i	$0.344799\pi$
$719$			47.3791i			1.76694i	−0.468487	+	0.883470i	$0.655201\pi$
$720$		0			0
$721$			42.8086i			1.59427i
$722$		0			0
$723$	6.96215	+	16.8081i	0.258925	+	0.625101i
$724$		0			0
$725$	13.5384	+	5.60778i	0.502802	+	0.208268i
$726$		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
$731$	−4.05233	+	9.78320i	−0.149881	+	0.361845i
$732$		0			0
$733$	−38.3414	+	15.8815i	−1.41617	+	0.586597i	−0.953895	−	0.300139i	$-0.902967\pi$
$733$	−38.3414	+	15.8815i	−1.41617	+	0.586597i	−0.462276	+	0.886736i	$0.652967\pi$
$734$		0			0
$735$	54.5496			2.01209
$736$		0			0
$737$	−6.41320			−0.236233
$738$		0			0
$739$	−42.5302	+	17.6166i	−1.56450	+	0.648036i	−0.985863	−	0.167551i	$-0.946414\pi$
$739$	−42.5302	+	17.6166i	−1.56450	+	0.648036i	−0.578634	+	0.815587i	$0.696414\pi$
$740$		0			0
$741$	−3.47757	+	8.39561i	−0.127752	+	0.308420i
$742$		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
$747$	21.3820	+	8.85671i	0.782326	+	0.324050i
$748$		0			0
$749$	14.5663	+	35.1662i	0.532242	+	1.28495i
$750$		0			0
$751$			11.9637i			0.436561i	0.975886	+	0.218281i	$0.0700448\pi$
$751$			11.9637i			0.436561i	−0.975886	+	0.218281i	$0.929955\pi$
$752$		0			0
$753$			4.61648i			0.168234i
$754$		0			0
$755$	−14.1261	−	34.1034i	−0.514102	−	1.24115i
$756$		0			0
$757$	−42.8571	−	17.7520i	−1.55767	−	0.645207i	−0.572986	−	0.819565i	$-0.694215\pi$
$757$	−42.8571	−	17.7520i	−1.55767	−	0.645207i	−0.984682	+	0.174358i	$0.944215\pi$
$758$		0			0
$759$	−4.29088	+	4.29088i	−0.155749	+	0.155749i
$760$		0			0
$761$	26.2473	+	26.2473i	0.951464	+	0.951464i	0.998875	−	0.0474116i	$-0.0150972\pi$
$761$	26.2473	+	26.2473i	0.951464	+	0.951464i	−0.0474116	+	0.998875i	$0.515097\pi$
$762$		0			0
$763$	−1.26405	+	3.05169i	−0.0457618	+	0.110479i
$764$		0			0
$765$	8.92839	−	3.69826i	0.322807	−	0.133711i
$766$		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
$771$	23.8380	−	9.87404i	0.858506	−	0.355605i
$772$		0			0
$773$	1.46163	−	3.52868i	0.0525711	−	0.126918i	−0.895412	−	0.445239i	$-0.853119\pi$
$773$	1.46163	−	3.52868i	0.0525711	−	0.126918i	0.947983	+	0.318321i	$0.103119\pi$
$774$		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
$779$	23.4659	+	9.71990i	0.840754	+	0.348252i
$780$		0			0
$781$	−2.96100	−	7.14848i	−0.105953	−	0.255793i
$782$		0			0
$783$			8.06459i			0.288205i
$784$		0			0
$785$		−	26.9261i		−	0.961032i
$786$		0			0
$787$	4.73636	+	11.4346i	0.168833	+	0.407599i	0.985538	−	0.169457i	$-0.0542015\pi$
$787$	4.73636	+	11.4346i	0.168833	+	0.407599i	−0.816705	+	0.577056i	$0.804201\pi$
$788$		0			0
$789$	18.4929	+	7.66000i	0.658364	+	0.272703i
$790$		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
$795$	10.6992	−	25.8302i	0.379463	−	0.916104i
$796$		0			0
$797$	1.35275	−	0.560326i	0.0479167	−	0.0198478i	−0.358596	−	0.933493i	$-0.616745\pi$
$797$	1.35275	−	0.560326i	0.0479167	−	0.0198478i	0.406513	+	0.913645i	$0.366745\pi$
$798$		0			0
$799$	1.38284			0.0489215
$800$		0			0
$801$	−24.2901			−0.858248
$802$		0			0
$803$	3.66097	−	1.51642i	0.129193	−	0.0535134i
$804$		0			0
$805$	40.1338	−	96.8915i	1.41453	−	3.41498i
$806$		0			0
$807$	9.68002	+	9.68002i	0.340753	+	0.340753i
$808$		0			0
$809$	3.15363	−	3.15363i	0.110876	−	0.110876i	−0.649492	−	0.760368i	$-0.725019\pi$
$809$	3.15363	−	3.15363i	0.110876	−	0.110876i	0.760368	+	0.649492i	$0.225019\pi$
$810$		0			0
$811$	−20.7904	−	8.61166i	−0.730049	−	0.302396i	−0.0134769	−	0.999909i	$-0.504290\pi$
$811$	−20.7904	−	8.61166i	−0.730049	−	0.302396i	−0.716572	+	0.697513i	$0.754290\pi$
$812$		0			0
$813$	2.34223	+	5.65465i	0.0821457	+	0.198317i
$814$		0			0
$815$		−	8.41143i		−	0.294640i
$816$		0			0
$817$			26.4875i			0.926680i
$818$		0			0
$819$	−8.51727	−	20.5625i	−0.297617	−	0.718512i
$820$		0			0
$821$	−3.95402	−	1.63781i	−0.137996	−	0.0571599i	0.312617	−	0.949879i	$-0.398795\pi$
$821$	−3.95402	−	1.63781i	−0.137996	−	0.0571599i	−0.450613	+	0.892719i	$0.648795\pi$
$822$		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
$827$	10.3999	−	25.1075i	0.361639	−	0.873074i	−0.633422	−	0.773807i	$-0.718350\pi$
$827$	10.3999	−	25.1075i	0.361639	−	0.873074i	0.995061	−	0.0992672i	$-0.0316498\pi$
$828$		0			0
$829$	24.9536	−	10.3361i	0.866674	−	0.358988i	0.0953602	−	0.995443i	$-0.469600\pi$
$829$	24.9536	−	10.3361i	0.866674	−	0.358988i	0.771314	+	0.636455i	$0.219600\pi$
$830$		0			0
$831$	−18.0387			−0.625757
$832$		0			0
$833$	−18.4479			−0.639181
$834$		0			0
$835$	5.21648	−	2.16073i	0.180524	−	0.0747753i
$836$		0			0
$837$	−7.27064	+	17.5529i	−0.251310	+	0.606716i
$838$		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
$843$	3.41492	+	1.41451i	0.117616	+	0.0487181i
$844$		0			0
$845$	9.22915	+	22.2811i	0.317492	+	0.766494i
$846$		0			0
$847$			45.9639i			1.57934i
$848$		0			0
$849$		−	27.0618i		−	0.928758i
$850$		0			0
$851$	−10.1610	−	24.5307i	−0.348313	−	0.840902i
$852$		0			0
$853$	−22.3247	−	9.24721i	−0.764385	−	0.316619i	−0.0337892	−	0.999429i	$-0.510757\pi$
$853$	−22.3247	−	9.24721i	−0.764385	−	0.316619i	−0.730596	+	0.682810i	$0.760757\pi$
$854$		0			0
$855$	17.0930	−	17.0930i	0.584568	−	0.584568i
$856$		0			0
$857$	−21.5074	−	21.5074i	−0.734677	−	0.734677i	0.236865	−	0.971543i	$-0.423880\pi$
$857$	−21.5074	−	21.5074i	−0.734677	−	0.734677i	−0.971543	+	0.236865i	$0.923880\pi$
$858$		0			0
$859$	−12.2217	+	29.5057i	−0.416998	+	1.00672i	0.566215	+	0.824258i	$0.308407\pi$
$859$	−12.2217	+	29.5057i	−0.416998	+	1.00672i	−0.983212	+	0.182464i	$0.941593\pi$
$860$		0			0
$861$	33.3464	−	13.8125i	1.13644	−	0.470729i
$862$		0			0
$863$	26.4436			0.900151			0.450076	−	0.892990i	$-0.351397\pi$
$863$	26.4436			0.900151			0.450076	+	0.892990i	$0.351397\pi$
$864$		0			0
$865$	−72.1041			−2.45161
$866$		0			0
$867$	−14.7320	+	6.10220i	−0.500325	+	0.207241i
$868$		0			0
$869$	5.61438	−	13.5543i	0.190455	−	0.459799i
$870$		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
$875$	−69.1541	−	28.6446i	−2.33784	−	0.968363i
$876$		0			0
$877$	12.6478	+	30.5345i	0.427086	+	1.03108i	0.980207	+	0.197975i	$0.0634366\pi$
$877$	12.6478	+	30.5345i	0.427086	+	1.03108i	−0.553121	+	0.833101i	$0.686563\pi$
$878$		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
$883$	18.4231	+	44.4774i	0.619987	+	1.49678i	0.851717	+	0.524002i	$0.175561\pi$
$883$	18.4231	+	44.4774i	0.619987	+	1.49678i	−0.231730	+	0.972780i	$0.574439\pi$
$884$		0			0
$885$	−23.4782	−	9.72498i	−0.789210	−	0.326902i
$886$		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
$891$	0.108994	−	0.263134i	0.00365142	−	0.00881531i
$892$		0			0
$893$	3.19568	−	1.32369i	0.106939	−	0.0442958i
$894$		0			0
$895$	−42.0972			−1.40716
$896$		0			0
$897$	16.4414			0.548961
$898$		0			0
$899$	5.35569	−	2.21840i	0.178622	−	0.0739878i
$900$		0			0
$901$	−3.61832	+	8.73540i	−0.120544	+	0.291019i
$902$		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
$907$	−49.4995	−	20.5034i	−1.64360	−	0.680803i	−0.646950	−	0.762533i	$-0.723956\pi$
$907$	−49.4995	−	20.5034i	−1.64360	−	0.680803i	−0.996655	+	0.0817295i	$0.973956\pi$
$908$		0			0
$909$	−6.83508	−	16.5013i	−0.226705	−	0.547315i
$910$		0			0
$911$			45.3750i			1.50334i	0.659539	+	0.751670i	$0.270752\pi$
$911$			45.3750i			1.50334i	−0.659539	+	0.751670i	$0.729248\pi$
$912$		0			0
$913$		−	11.5868i		−	0.383467i
$914$		0			0
$915$	7.29121	+	17.6025i	0.241040	+	0.581922i
$916$		0			0
$917$	15.3043	+	6.33925i	0.505393	+	0.209341i
$918$		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
$923$	−8.02259	+	19.3683i	−0.264067	+	0.637514i
$924$		0			0
$925$	−37.6711	+	15.6039i	−1.23862	+	0.513053i
$926$		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
$931$	−42.6322	+	17.6588i	−1.39721	+	0.578744i
$932$		0			0
$933$	8.61869	−	20.8074i	0.282163	−	0.681203i
$934$		0			0
$935$	−3.42116	−	3.42116i	−0.111884	−	0.111884i
$936$		0			0
$937$	−0.172711	+	0.172711i	−0.00564221	+	0.00564221i	−0.709922	−	0.704280i	$-0.751270\pi$
$937$	−0.172711	+	0.172711i	−0.00564221	+	0.00564221i	0.704280	+	0.709922i	$0.251270\pi$
$938$		0			0
$939$	−12.6675	−	5.24707i	−0.413389	−	0.171232i
$940$		0			0
$941$	−16.5189	−	39.8801i	−0.538500	−	1.30005i	−0.925770	−	0.378087i	$-0.876582\pi$
$941$	−16.5189	−	39.8801i	−0.538500	−	1.30005i	0.387270	−	0.921966i	$-0.373418\pi$
$942$		0			0
$943$		−	45.9540i		−	1.49647i
$944$		0			0
$945$		−	88.6339i		−	2.88326i
$946$		0			0
$947$	−8.29136	−	20.0171i	−0.269433	−	0.650469i	0.730024	−	0.683422i	$-0.239509\pi$
$947$	−8.29136	−	20.0171i	−0.269433	−	0.650469i	−0.999457	+	0.0329528i	$0.989509\pi$
$948$		0			0
$949$	−9.91912	−	4.10863i	−0.321988	−	0.133372i
$950$		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	$0.0469465\pi$
$953$	35.0721	+	35.0721i	1.13610	+	1.13610i	0.146953	+	0.989144i	$0.453053\pi$
$954$		0			0
$955$	−30.8215	+	74.4097i	−0.997360	+	2.40784i
$956$		0			0
$957$	1.44568	−	0.598822i	0.0467323	−	0.0193572i
$958$		0			0
$959$	−11.5848			−0.374091
$960$		0			0
$961$	−17.3431			−0.559456
$962$		0			0
$963$	14.6653	−	6.07456i	0.472582	−	0.195750i
$964$		0			0
$965$	3.99252	−	9.63879i	0.128524	−	0.310284i
$966$		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
$971$	2.07159	+	0.858080i	0.0664804	+	0.0275371i	0.415676	−	0.909513i	$-0.363545\pi$
$971$	2.07159	+	0.858080i	0.0664804	+	0.0275371i	−0.349195	+	0.937050i	$0.613545\pi$
$972$		0			0
$973$	30.3668	+	73.3120i	0.973516	+	2.35028i
$974$		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
$979$	4.65371	+	11.2351i	0.148733	+	0.359074i
$980$		0			0
$981$	1.27264	+	0.527144i	0.0406322	+	0.0168304i
$982$		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
$987$	1.88104	−	4.54124i	0.0598743	−	0.144549i
$988$		0			0
$989$	44.2749	−	18.3393i	1.40786	−	0.583154i
$990$		0			0
$991$	−37.5749			−1.19360			−0.596802	−	0.802388i	$-0.703562\pi$
$991$	−37.5749			−1.19360			−0.596802	+	0.802388i	$0.703562\pi$
$992$		0			0
$993$	32.8786			1.04337
$994$		0			0
$995$	−75.8747	+	31.4283i	−2.40539	+	0.996345i
$996$		0			0
$997$	−21.8090	+	52.6516i	−0.690698	+	1.66749i	0.0526708	+	0.998612i	$0.483227\pi$
$997$	−21.8090	+	52.6516i	−0.690698	+	1.66749i	−0.743369	+	0.668881i	$0.766773\pi$
$998$		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.e.385.2	yes	16
4.3	odd	2	inner	1024.2.g.e.385.3	yes	16
8.3	odd	2		1024.2.g.b.385.2	✓	16
8.5	even	2		1024.2.g.b.385.3	yes	16
16.3	odd	4		1024.2.g.h.897.3	yes	16
16.5	even	4		1024.2.g.c.897.3	yes	16
16.11	odd	4		1024.2.g.c.897.2	yes	16
16.13	even	4		1024.2.g.h.897.2	yes	16
32.3	odd	8	inner	1024.2.g.e.641.3	yes	16
32.5	even	8		1024.2.g.c.129.3	yes	16
32.11	odd	8		1024.2.g.h.129.3	yes	16
32.13	even	8		1024.2.g.b.641.3	yes	16
32.19	odd	8		1024.2.g.b.641.2	yes	16
32.21	even	8		1024.2.g.h.129.2	yes	16
32.27	odd	8		1024.2.g.c.129.2	yes	16
32.29	even	8	inner	1024.2.g.e.641.2	yes	16
64.3	odd	16		4096.2.a.n.1.3		8
64.29	even	16		4096.2.a.n.1.4		8
64.35	odd	16		4096.2.a.o.1.6		8
64.61	even	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	8.3	odd	2
1024.2.g.b.385.3	yes	16	8.5	even	2
1024.2.g.b.641.2	yes	16	32.19	odd	8
1024.2.g.b.641.3	yes	16	32.13	even	8
1024.2.g.c.129.2	yes	16	32.27	odd	8
1024.2.g.c.129.3	yes	16	32.5	even	8
1024.2.g.c.897.2	yes	16	16.11	odd	4
1024.2.g.c.897.3	yes	16	16.5	even	4
1024.2.g.e.385.2	yes	16	1.1	even	1	trivial
1024.2.g.e.385.3	yes	16	4.3	odd	2	inner
1024.2.g.e.641.2	yes	16	32.29	even	8	inner
1024.2.g.e.641.3	yes	16	32.3	odd	8	inner
1024.2.g.h.129.2	yes	16	32.21	even	8
1024.2.g.h.129.3	yes	16	32.11	odd	8
1024.2.g.h.897.2	yes	16	16.13	even	4
1024.2.g.h.897.3	yes	16	16.3	odd	4
4096.2.a.n.1.3		8	64.3	odd	16
4096.2.a.n.1.4		8	64.29	even	16
4096.2.a.o.1.5		8	64.61	even	16
4096.2.a.o.1.6		8	64.35	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.969643 + 0.401639i) q^{3} +(-1.44924 + 3.49877i) q^{5} +(-3.21904 - 3.21904i) q^{7} +(-1.34243 + 1.34243i) q^{9} +O(q^{10})\)	\(q+(-0.969643 + 0.401639i) q^{3} +(-1.44924 + 3.49877i) q^{5} +(-3.21904 - 3.21904i) q^{7} +(-1.34243 + 1.34243i) q^{9} +(0.878116 + 0.363728i) q^{11} +(-0.985492 - 2.37919i) q^{13} -3.97463i q^{15} +1.34416i q^{17} +(1.28667 + 3.10629i) q^{19} +(4.41421 + 1.82843i) q^{21} +(4.30143 - 4.30143i) q^{23} +(-6.60559 - 6.60559i) q^{25} +(1.96742 - 4.74977i) q^{27} +(-1.44924 + 0.600295i) q^{29} -3.69552 q^{31} -0.997546 q^{33} +(15.9279 - 6.59753i) q^{35} +(1.67035 - 4.03257i) q^{37} +(1.91115 + 1.91115i) q^{39} +(5.34171 - 5.34171i) q^{41} +(7.27829 + 3.01477i) q^{43} +(-2.75135 - 6.64235i) q^{45} -1.02878i q^{47} +13.7245i q^{49} +(-0.539868 - 1.30336i) q^{51} +(6.49877 + 2.69188i) q^{53} +(-2.54520 + 2.54520i) q^{55} +(-2.49522 - 2.49522i) q^{57} +(2.44676 - 5.90700i) q^{59} +(-4.42872 + 1.83444i) q^{61} +8.64266 q^{63} +9.75245 q^{65} +(-6.23381 + 2.58213i) q^{67} +(-2.44323 + 5.89848i) q^{69} +(-5.75634 - 5.75634i) q^{71} +(2.94801 - 2.94801i) q^{73} +(9.05812 + 3.75200i) q^{75} +(-1.65584 - 3.99755i) q^{77} -15.4357i q^{79} -0.299657i q^{81} +(-4.66516 - 11.2627i) q^{83} +(-4.70292 - 1.94801i) q^{85} +(1.16414 - 1.16414i) q^{87} +(9.04708 + 9.04708i) q^{89} +(-4.48636 + 10.8310i) q^{91} +(3.58333 - 1.48427i) q^{93} -12.7329 q^{95} +8.41176 q^{97} +(-1.66708 + 0.690529i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} - 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^5 - 16 * q^9	\( 16 q + 8 q^{5} - 16 q^{9} - 24 q^{13} + 48 q^{21} - 32 q^{25} + 8 q^{29} + 80 q^{33} + 24 q^{37} - 16 q^{41} - 104 q^{45} + 56 q^{53} - 80 q^{57} - 40 q^{61} + 32 q^{65} - 32 q^{73} - 32 q^{77} + 32 q^{85} + 32 q^{89} - 16 q^{93} + 16 q^{97}+O(q^{100}) \) 16 * q + 8 * q^5 - 16 * q^9 - 24 * q^13 + 48 * q^21 - 32 * q^25 + 8 * q^29 + 80 * q^33 + 24 * q^37 - 16 * q^41 - 104 * q^45 + 56 * q^53 - 80 * q^57 - 40 * q^61 + 32 * q^65 - 32 * q^73 - 32 * q^77 + 32 * q^85 + 32 * q^89 - 16 * q^93 + 16 * q^97

Introduction

L-functions

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Database

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