LMFDB - Embedded newform 896.2.q.d.831.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(703,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("896.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.q (of order $6$, degree $2$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 24x^{14} + 226x^{12} - 972x^{10} + 1575x^{8} + 252x^{6} + 550x^{4} + 156x^{2} + 49 $ x^16 - 24x^14 + 226x^12 - 972x^10 + 1575x^8 + 252x^6 + 550x^4 + 156*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			831.2
Root			$-2.65282 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	896.831
Dual form			896.2.q.d.703.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54741 + 0.893397i) q^{3} +(0.581841 - 1.00778i) q^{5} +(-2.23781 + 1.41146i) q^{7} +(0.0963180 - 0.166828i) q^{9} +O(q^{10})$	\(q+(-1.54741 + 0.893397i) q^{3} +(0.581841 - 1.00778i) q^{5} +(-2.23781 + 1.41146i) q^{7} +(0.0963180 - 0.166828i) q^{9} +(-1.13595 - 1.96752i) q^{11} -1.57988 q^{13} +2.07926i q^{15} +(5.96304 - 3.44276i) q^{17} +(-0.671415 - 0.387642i) q^{19} +(2.20181 - 4.18336i) q^{21} +(1.11497 + 0.643728i) q^{23} +(1.82292 + 3.15739i) q^{25} -5.01618i q^{27} -8.38228i q^{29} +(0.554469 + 0.960369i) q^{31} +(3.51556 + 2.02971i) q^{33} +(0.120392 + 3.07646i) q^{35} +(-5.84739 - 3.37599i) q^{37} +(2.44472 - 1.41146i) q^{39} +1.99371i q^{41} +5.64584 q^{43} +(-0.112084 - 0.194134i) q^{45} +(2.90963 - 5.03963i) q^{47} +(3.01556 - 6.31715i) q^{49} +(-6.15151 + 10.6547i) q^{51} +(-0.317587 + 0.183359i) q^{53} -2.64377 q^{55} +1.38527 q^{57} +(10.6422 - 6.14429i) q^{59} +(3.93386 - 6.81364i) q^{61} +(0.0199296 + 0.509277i) q^{63} +(-0.919239 + 1.59217i) q^{65} +(4.01194 + 6.94889i) q^{67} -2.30042 q^{69} -12.7646i q^{71} +(9.70520 - 5.60330i) q^{73} +(-5.64161 - 3.25719i) q^{75} +(5.31911 + 2.79959i) q^{77} +(-11.6446 - 6.72299i) q^{79} +(4.77040 + 8.26257i) q^{81} +3.15976i q^{83} -8.01256i q^{85} +(7.48870 + 12.9708i) q^{87} +(-2.53111 - 1.46134i) q^{89} +(3.53547 - 2.22994i) q^{91} +(-1.71598 - 0.990723i) q^{93} +(-0.781314 + 0.451092i) q^{95} -0.333655i q^{97} -0.437649 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{3} + 8 q^{9}+O(q^{10}) $ 16 * q + 12 * q^3 + 8 * q^9	$ 16 q + 12 q^{3} + 8 q^{9} - 4 q^{11} - 12 q^{19} - 16 q^{25} + 24 q^{33} + 20 q^{35} + 16 q^{49} - 52 q^{51} + 48 q^{57} + 60 q^{59} + 24 q^{65} + 12 q^{67} - 24 q^{73} - 120 q^{75} - 32 q^{81} + 24 q^{89} + 72 q^{91} + 64 q^{99}+O(q^{100}) $ 16 * q + 12 * q^3 + 8 * q^9 - 4 * q^11 - 12 * q^19 - 16 * q^25 + 24 * q^33 + 20 * q^35 + 16 * q^49 - 52 * q^51 + 48 * q^57 + 60 * q^59 + 24 * q^65 + 12 * q^67 - 24 * q^73 - 120 * q^75 - 32 * q^81 + 24 * q^89 + 72 * q^91 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.54741	+	0.893397i	−0.893397	+	0.515803i	−0.875052	−	0.484028i	$-0.839173\pi$
$3$	−1.54741	+	0.893397i	−0.893397	+	0.515803i	−0.0183452	+	0.999832i	$0.505840\pi$
$4$		0			0
$5$	0.581841	−	1.00778i	0.260207	−	0.450692i	−0.706090	−	0.708123i	$-0.749542\pi$
$5$	0.581841	−	1.00778i	0.260207	−	0.450692i	0.966297	+	0.257430i	$0.0828757\pi$
$6$		0			0
$7$	−2.23781	+	1.41146i	−0.845811	+	0.533482i
$7$	−2.23781	+	1.41146i	−0.845811	+	0.533482i
$8$		0			0
$9$	0.0963180	−	0.166828i	0.0321060	−	0.0556092i
$10$		0			0
$11$	−1.13595	−	1.96752i	−0.342502	−	0.593230i	0.642395	−	0.766374i	$-0.277941\pi$
$11$	−1.13595	−	1.96752i	−0.342502	−	0.593230i	−0.984897	+	0.173144i	$0.944608\pi$
$12$		0			0
$13$	−1.57988			−0.438180			−0.219090	−	0.975705i	$-0.570309\pi$
$13$	−1.57988			−0.438180			−0.219090	+	0.975705i	$0.570309\pi$
$14$		0			0
$15$			2.07926i			0.536863i
$16$		0			0
$17$	5.96304	−	3.44276i	1.44625	−	0.834992i	0.447993	−	0.894037i	$-0.352139\pi$
$17$	5.96304	−	3.44276i	1.44625	−	0.834992i	0.998255	+	0.0590449i	$0.0188055\pi$
$18$		0			0
$19$	−0.671415	−	0.387642i	−0.154033	−	0.0889311i	0.421002	−	0.907060i	$-0.361678\pi$
$19$	−0.671415	−	0.387642i	−0.154033	−	0.0889311i	−0.575035	+	0.818128i	$0.695012\pi$
$20$		0			0
$21$	2.20181	−	4.18336i	0.480474	−	0.912884i
$22$		0			0
$23$	1.11497	+	0.643728i	0.232487	+	0.134227i	0.611719	−	0.791075i	$-0.290478\pi$
$23$	1.11497	+	0.643728i	0.232487	+	0.134227i	−0.379232	+	0.925302i	$0.623812\pi$
$24$		0			0
$25$	1.82292	+	3.15739i	0.364584	+	0.631478i
$26$		0			0
$27$		−	5.01618i		−	0.965365i
$28$		0			0
$29$		−	8.38228i		−	1.55655i	−0.627924	−	0.778275i	$-0.716095\pi$
$29$		−	8.38228i		−	1.55655i	0.627924	−	0.778275i	$-0.283905\pi$
$30$		0			0
$31$	0.554469	+	0.960369i	0.0995856	+	0.172487i	0.911513	−	0.411271i	$-0.134915\pi$
$31$	0.554469	+	0.960369i	0.0995856	+	0.172487i	−0.811928	+	0.583758i	$0.801582\pi$
$32$		0			0
$33$	3.51556	+	2.02971i	0.611980	+	0.353327i
$34$		0			0
$35$	0.120392	+	3.07646i	0.0203499	+	0.520017i
$36$		0			0
$37$	−5.84739	−	3.37599i	−0.961306	−	0.555010i	−0.0647311	−	0.997903i	$-0.520619\pi$
$37$	−5.84739	−	3.37599i	−0.961306	−	0.555010i	−0.896575	+	0.442893i	$0.853952\pi$
$38$		0			0
$39$	2.44472	−	1.41146i	0.391469	−	0.226015i
$40$		0			0
$41$			1.99371i			0.311365i	0.987807	+	0.155683i	$0.0497577\pi$
$41$			1.99371i			0.311365i	−0.987807	+	0.155683i	$0.950242\pi$
$42$		0			0
$43$	5.64584			0.860983			0.430491	−	0.902595i	$-0.358340\pi$
$43$	5.64584			0.860983			0.430491	+	0.902595i	$0.358340\pi$
$44$		0			0
$45$	−0.112084	−	0.194134i	−0.0167084	−	0.0289399i
$46$		0			0
$47$	2.90963	−	5.03963i	0.424413	−	0.735106i	−0.571952	−	0.820287i	$-0.693814\pi$
$47$	2.90963	−	5.03963i	0.424413	−	0.735106i	0.996365	+	0.0851814i	$0.0271470\pi$
$48$		0			0
$49$	3.01556	−	6.31715i	0.430794	−	0.902450i
$50$		0			0
$51$	−6.15151	+	10.6547i	−0.861383	+	1.49196i
$52$		0			0
$53$	−0.317587	+	0.183359i	−0.0436239	+	0.0251863i	−0.521653	−	0.853158i	$-0.674685\pi$
$53$	−0.317587	+	0.183359i	−0.0436239	+	0.0251863i	0.478029	+	0.878344i	$0.341351\pi$
$54$		0			0
$55$	−2.64377			−0.356486
$56$		0			0
$57$	1.38527			0.183484
$58$		0			0
$59$	10.6422	−	6.14429i	1.38550	−	0.799919i	0.392696	−	0.919668i	$-0.371542\pi$
$59$	10.6422	−	6.14429i	1.38550	−	0.799919i	0.992804	+	0.119749i	$0.0382091\pi$
$60$		0			0
$61$	3.93386	−	6.81364i	0.503679	−	0.872398i	−0.496312	−	0.868144i	$-0.665313\pi$
$61$	3.93386	−	6.81364i	0.503679	−	0.872398i	0.999991	−	0.00425345i	$-0.00135392\pi$
$62$		0			0
$63$	0.0199296	+	0.509277i	0.00251090	+	0.0641629i
$64$		0			0
$65$	−0.919239	+	1.59217i	−0.114018	+	0.197484i
$66$		0			0
$67$	4.01194	+	6.94889i	0.490137	+	0.848942i	0.999936	−	0.0113517i	$-0.00361342\pi$
$67$	4.01194	+	6.94889i	0.490137	+	0.848942i	−0.509799	+	0.860294i	$0.670280\pi$
$68$		0			0
$69$	−2.30042			−0.276938
$70$		0			0
$71$		−	12.7646i		−	1.51487i	−0.652909	−	0.757437i	$-0.726451\pi$
$71$		−	12.7646i		−	1.51487i	0.652909	−	0.757437i	$-0.273549\pi$
$72$		0			0
$73$	9.70520	−	5.60330i	1.13591	−	0.655816i	0.190493	−	0.981688i	$-0.438991\pi$
$73$	9.70520	−	5.60330i	1.13591	−	0.655816i	0.945414	+	0.325872i	$0.105658\pi$
$74$		0			0
$75$	−5.64161	−	3.25719i	−0.651437	−	0.376108i
$76$		0			0
$77$	5.31911	+	2.79959i	0.606169	+	0.319042i
$78$		0			0
$79$	−11.6446	−	6.72299i	−1.31012	−	0.756395i	−0.328000	−	0.944678i	$-0.606375\pi$
$79$	−11.6446	−	6.72299i	−1.31012	−	0.756395i	−0.982115	+	0.188282i	$0.939708\pi$
$80$		0			0
$81$	4.77040	+	8.26257i	0.530044	+	0.918064i
$82$		0			0
$83$			3.15976i			0.346829i	0.984849	+	0.173414i	$0.0554800\pi$
$83$			3.15976i			0.346829i	−0.984849	+	0.173414i	$0.944520\pi$
$84$		0			0
$85$		−	8.01256i		−	0.869084i
$86$		0			0
$87$	7.48870	+	12.9708i	0.802873	+	1.39062i
$88$		0			0
$89$	−2.53111	−	1.46134i	−0.268298	−	0.154902i	0.359816	−	0.933023i	$-0.382839\pi$
$89$	−2.53111	−	1.46134i	−0.268298	−	0.154902i	−0.628114	+	0.778122i	$0.716173\pi$
$90$		0			0
$91$	3.53547	−	2.22994i	0.370618	−	0.233761i
$92$		0			0
$93$	−1.71598	−	0.990723i	−0.177939	−	0.102733i
$94$		0			0
$95$	−0.781314	+	0.451092i	−0.0801611	+	0.0462810i
$96$		0			0
$97$		−	0.333655i		−	0.0338776i	−0.999857	−	0.0169388i	$-0.994608\pi$
$97$		−	0.333655i		−	0.0338776i	0.999857	−	0.0169388i	$-0.00539204\pi$
$98$		0			0
$99$	−0.437649			−0.0439854
$100$		0			0
$101$	7.61953	+	13.1974i	0.758172	+	1.31319i	0.943782	+	0.330569i	$0.107241\pi$
$101$	7.61953	+	13.1974i	0.758172	+	1.31319i	−0.185610	+	0.982623i	$0.559426\pi$
$102$		0			0
$103$	6.46329	−	11.1948i	0.636847	−	1.10305i	−0.349273	−	0.937021i	$-0.613572\pi$
$103$	6.46329	−	11.1948i	0.636847	−	1.10305i	0.986121	−	0.166031i	$-0.0530951\pi$
$104$		0			0
$105$	−2.93480	−	4.65299i	−0.286407	−	0.454085i
$106$		0			0
$107$	0.423405	−	0.733358i	0.0409321	−	0.0708964i	−0.844834	−	0.535029i	$-0.820301\pi$
$107$	0.423405	−	0.733358i	0.0409321	−	0.0708964i	0.885766	+	0.464133i	$0.153634\pi$
$108$		0			0
$109$	−17.9692	+	10.3745i	−1.72113	+	0.993697i	−0.804515	+	0.593933i	$0.797575\pi$
$109$	−17.9692	+	10.3745i	−1.72113	+	0.993697i	−0.916618	+	0.399764i	$0.869092\pi$
$110$		0			0
$111$	12.0644			1.14510
$112$		0			0
$113$	−14.5719			−1.37081			−0.685405	−	0.728162i	$-0.740375\pi$
$113$	−14.5719			−1.37081			−0.685405	+	0.728162i	$0.740375\pi$
$114$		0			0
$115$	1.29747	−	0.749095i	0.120990	−	0.0698535i
$116$		0			0
$117$	−0.152171	+	0.263568i	−0.0140682	+	0.0243668i
$118$		0			0
$119$	−8.48480	+	16.1208i	−0.777800	+	1.47779i
$120$		0			0
$121$	2.91924	−	5.05627i	0.265385	−	0.459661i
$122$		0			0
$123$	−1.78118	−	3.08509i	−0.160603	−	0.278173i
$124$		0			0
$125$	10.0610			0.899885
$126$		0			0
$127$			16.7646i			1.48761i	0.668395	+	0.743807i	$0.266982\pi$
$127$			16.7646i			1.48761i	−0.668395	+	0.743807i	$0.733018\pi$
$128$		0			0
$129$	−8.73643	+	5.04398i	−0.769200	+	0.444098i
$130$		0			0
$131$	−12.5630	−	7.25323i	−1.09763	−	0.633718i	−0.162034	−	0.986785i	$-0.551805\pi$
$131$	−12.5630	−	7.25323i	−1.09763	−	0.633718i	−0.935598	+	0.353067i	$0.885139\pi$
$132$		0			0
$133$	2.04964	−	0.0802088i	0.177726	−	0.00695499i
$134$		0			0
$135$	−5.05520	−	2.91862i	−0.435083	−	0.251195i
$136$		0			0
$137$	5.15567	+	8.92989i	0.440479	+	0.762932i	0.997725	−	0.0674157i	$-0.0214754\pi$
$137$	5.15567	+	8.92989i	0.440479	+	0.762932i	−0.557246	+	0.830347i	$0.688142\pi$
$138$		0			0
$139$		−	15.2121i		−	1.29028i	−0.764066	−	0.645138i	$-0.776800\pi$
$139$		−	15.2121i		−	1.29028i	0.764066	−	0.645138i	$-0.223200\pi$
$140$		0			0
$141$			10.3978i			0.875655i
$142$		0			0
$143$	1.79466	+	3.10845i	0.150077	+	0.259941i
$144$		0			0
$145$	−8.44748	−	4.87715i	−0.701525	−	0.405026i
$146$		0			0
$147$	0.977425	+	12.4693i	0.0806166	+	1.02845i
$148$		0			0
$149$	6.48516	+	3.74421i	0.531285	+	0.306738i	0.741540	−	0.670909i	$-0.234096\pi$
$149$	6.48516	+	3.74421i	0.531285	+	0.306738i	−0.210254	+	0.977647i	$0.567429\pi$
$150$		0			0
$151$	2.60529	−	1.50417i	0.212016	−	0.122407i	−0.390232	−	0.920716i	$-0.627605\pi$
$151$	2.60529	−	1.50417i	0.212016	−	0.122407i	0.602248	+	0.798309i	$0.294272\pi$
$152$		0			0
$153$		−	1.32640i		−	0.107233i
$154$		0			0
$155$	1.29045			0.103652
$156$		0			0
$157$	−2.66069	−	4.60845i	−0.212346	−	0.367794i	0.740102	−	0.672494i	$-0.234777\pi$
$157$	−2.66069	−	4.60845i	−0.212346	−	0.367794i	−0.952448	+	0.304700i	$0.901444\pi$
$158$		0			0
$159$	0.327625	−	0.567463i	0.0259823	−	0.0450027i
$160$		0			0
$161$	−3.40368	+	0.133197i	−0.268248	+	0.0104974i
$162$		0			0
$163$	−7.54741	+	13.0725i	−0.591159	+	1.02392i	0.402918	+	0.915236i	$0.367996\pi$
$163$	−7.54741	+	13.0725i	−0.591159	+	1.02392i	−0.994077	+	0.108681i	$0.965337\pi$
$164$		0			0
$165$	4.09099	−	2.36194i	0.318483	−	0.183876i
$166$		0			0
$167$	−8.99109			−0.695751			−0.347876	−	0.937541i	$-0.613097\pi$
$167$	−8.99109			−0.695751			−0.347876	+	0.937541i	$0.613097\pi$
$168$		0			0
$169$	−10.5040			−0.807998
$170$		0			0
$171$	−0.129339	+	0.0746737i	−0.00989078	+	0.00571044i
$172$		0			0
$173$	−3.36549	+	5.82920i	−0.255874	+	0.443186i	−0.965132	−	0.261762i	$-0.915696\pi$
$173$	−3.36549	+	5.82920i	−0.255874	+	0.443186i	0.709259	+	0.704948i	$0.249030\pi$
$174$		0			0
$175$	−8.53588	−	4.49265i	−0.645252	−	0.339613i
$176$		0			0
$177$	−10.9786	+	19.0155i	−0.825202	+	1.42929i
$178$		0			0
$179$	−8.50267	−	14.7271i	−0.635519	−	1.10075i	−0.986405	−	0.164333i	$-0.947453\pi$
$179$	−8.50267	−	14.7271i	−0.635519	−	1.10075i	0.350886	−	0.936418i	$-0.385881\pi$
$180$		0			0
$181$	−19.8668			−1.47669			−0.738346	−	0.674422i	$-0.764393\pi$
$181$	−19.8668			−1.47669			−0.738346	+	0.674422i	$0.764393\pi$
$182$		0			0
$183$			14.0580i			1.03920i
$184$		0			0
$185$	−6.80451	+	3.92859i	−0.500278	+	0.288835i
$186$		0			0
$187$	−13.5474	−	7.82160i	−0.990685	−	0.571972i
$188$		0			0
$189$	7.08015	+	11.2252i	0.515005	+	0.816517i
$190$		0			0
$191$	−14.9064	−	8.60621i	−1.07859	−	0.622724i	−0.148074	−	0.988976i	$-0.547307\pi$
$191$	−14.9064	−	8.60621i	−1.07859	−	0.622724i	−0.930515	+	0.366253i	$0.880641\pi$
$192$		0			0
$193$	−7.97859	−	13.8193i	−0.574312	−	0.994737i	−0.996116	−	0.0880502i	$-0.971936\pi$
$193$	−7.97859	−	13.8193i	−0.574312	−	0.994737i	0.421804	−	0.906687i	$-0.361397\pi$
$194$		0			0
$195$		−	3.28498i		−	0.235243i
$196$		0			0
$197$			7.29468i			0.519725i	0.965646	+	0.259862i	$0.0836772\pi$
$197$			7.29468i			0.519725i	−0.965646	+	0.259862i	$0.916323\pi$
$198$		0			0
$199$	−3.14586	−	5.44879i	−0.223004	−	0.386255i	0.732715	−	0.680536i	$-0.238253\pi$
$199$	−3.14586	−	5.44879i	−0.223004	−	0.386255i	−0.955719	+	0.294281i	$0.904920\pi$
$200$		0			0
$201$	−12.4162	−	7.16852i	−0.875774	−	0.505628i
$202$		0			0
$203$	11.8313	+	18.7579i	0.830391	+	1.31655i
$204$		0			0
$205$	2.00922	+	1.16002i	0.140330	+	0.0810195i
$206$		0			0
$207$	0.214783	−	0.124005i	0.0149285	−	0.00861895i
$208$		0			0
$209$			1.76136i			0.121836i
$210$		0			0
$211$	8.15852			0.561656			0.280828	−	0.959758i	$-0.409391\pi$
$211$	8.15852			0.561656			0.280828	+	0.959758i	$0.409391\pi$
$212$		0			0
$213$	11.4038	+	19.7520i	0.781377	+	1.35338i
$214$		0			0
$215$	3.28498	−	5.68976i	0.224034	−	0.388038i
$216$		0			0
$217$	−2.59632	−	1.36651i	−0.176250	−	0.0927646i
$218$		0			0
$219$	−10.0119	+	17.3412i	−0.676544	+	1.17181i
$220$		0			0
$221$	−9.42088	+	5.43915i	−0.633717	+	0.365877i
$222$		0			0
$223$	26.6002			1.78128			0.890641	−	0.454708i	$-0.150256\pi$
$223$	26.6002			1.78128			0.890641	+	0.454708i	$0.150256\pi$
$224$		0			0
$225$	0.702321			0.0468214
$226$		0			0
$227$	15.1402	−	8.74119i	1.00489	−	0.580173i	0.0951978	−	0.995458i	$-0.469652\pi$
$227$	15.1402	−	8.74119i	1.00489	−	0.580173i	0.909691	+	0.415285i	$0.136318\pi$
$228$		0			0
$229$	−10.1014	+	17.4962i	−0.667522	+	1.15618i	0.311073	+	0.950386i	$0.399312\pi$
$229$	−10.1014	+	17.4962i	−0.667522	+	1.15618i	−0.978595	+	0.205796i	$0.934022\pi$
$230$		0			0
$231$	−10.7320	+	0.419977i	−0.706113	+	0.0276325i
$232$		0			0
$233$	−6.14011	+	10.6350i	−0.402252	+	0.696721i	−0.993997	−	0.109404i	$-0.965106\pi$
$233$	−6.14011	+	10.6350i	−0.402252	+	0.696721i	0.591745	+	0.806125i	$0.298439\pi$
$234$		0			0
$235$	−3.38589	−	5.86453i	−0.220871	−	0.382560i
$236$		0			0
$237$	24.0252			1.56060
$238$		0			0
$239$			4.46876i			0.289060i	0.989500	+	0.144530i	$0.0461671\pi$
$239$			4.46876i			0.289060i	−0.989500	+	0.144530i	$0.953833\pi$
$240$		0			0
$241$	6.92209	−	3.99647i	0.445891	−	0.257435i	−0.260202	−	0.965554i	$-0.583789\pi$
$241$	6.92209	−	3.99647i	0.445891	−	0.257435i	0.706093	+	0.708119i	$0.250456\pi$
$242$		0			0
$243$	−1.73110	−	0.999450i	−0.111050	−	0.0641148i
$244$		0			0
$245$	−4.61172	−	6.71459i	−0.294632	−	0.428980i
$246$		0			0
$247$	1.06075	+	0.612427i	0.0674942	+	0.0389678i
$248$		0			0
$249$	−2.82292	−	4.88944i	−0.178895	−	0.309856i
$250$		0			0
$251$			15.0313i			0.948767i	0.880318	+	0.474384i	$0.157329\pi$
$251$			15.0313i			0.948767i	−0.880318	+	0.474384i	$0.842671\pi$
$252$		0			0
$253$		−	2.92497i		−	0.183891i
$254$		0			0
$255$	7.15840	+	12.3987i	0.448276	+	0.776438i
$256$		0			0
$257$	8.50983	+	4.91315i	0.530829	+	0.306474i	0.741354	−	0.671114i	$-0.234184\pi$
$257$	8.50983	+	4.91315i	0.530829	+	0.306474i	−0.210525	+	0.977588i	$0.567517\pi$
$258$		0			0
$259$	17.8504	−	0.698544i	1.10917	−	0.0434054i
$260$		0			0
$261$	−1.39840	−	0.807364i	−0.0865585	−	0.0499746i
$262$		0			0
$263$	17.4884	−	10.0969i	1.07838	−	0.622604i	0.147922	−	0.988999i	$-0.452742\pi$
$263$	17.4884	−	10.0969i	1.07838	−	0.622604i	0.930459	+	0.366395i	$0.119408\pi$
$264$		0			0
$265$			0.426743i			0.0262146i
$266$		0			0
$267$	5.22223			0.319595
$268$		0			0
$269$	−4.65440	−	8.06165i	−0.283784	−	0.491528i	0.688530	−	0.725208i	$-0.258256\pi$
$269$	−4.65440	−	8.06165i	−0.283784	−	0.491528i	−0.972313	+	0.233680i	$0.924923\pi$
$270$		0			0
$271$	11.1736	−	19.3533i	0.678749	−	1.17563i	−0.296609	−	0.954999i	$-0.595856\pi$
$271$	11.1736	−	19.3533i	0.678749	−	1.17563i	0.975358	−	0.220629i	$-0.0708109\pi$
$272$		0			0
$273$	−3.47859	+	6.60920i	−0.210534	+	0.400007i
$274$		0			0
$275$	4.14149	−	7.17327i	0.249741	−	0.432565i
$276$		0			0
$277$	20.4618	−	11.8136i	1.22943	−	0.709813i	0.262521	−	0.964926i	$-0.415446\pi$
$277$	20.4618	−	11.8136i	1.22943	−	0.709813i	0.966911	+	0.255113i	$0.0821127\pi$
$278$		0			0
$279$	0.213621			0.0127892
$280$		0			0
$281$	−5.42209			−0.323455			−0.161727	−	0.986835i	$-0.551707\pi$
$281$	−5.42209			−0.323455			−0.161727	+	0.986835i	$0.551707\pi$
$282$		0			0
$283$	12.6923	−	7.32791i	0.754479	−	0.435599i	−0.0728308	−	0.997344i	$-0.523203\pi$
$283$	12.6923	−	7.32791i	0.754479	−	0.435599i	0.827310	+	0.561745i	$0.189870\pi$
$284$		0			0
$285$	0.806008	−	1.39605i	0.0477438	−	0.0826947i
$286$		0			0
$287$	−2.81404	−	4.46154i	−0.166108	−	0.263356i
$288$		0			0
$289$	15.2052	−	26.3362i	0.894423	−	1.54919i
$290$		0			0
$291$	0.298087	+	0.516302i	0.0174742	+	0.0302661i
$292$		0			0
$293$	−8.36928			−0.488939			−0.244469	−	0.969657i	$-0.578614\pi$
$293$	−8.36928			−0.488939			−0.244469	+	0.969657i	$0.578614\pi$
$294$		0			0
$295$		−	14.3000i		−	0.832579i
$296$		0			0
$297$	−9.86945	+	5.69813i	−0.572684	+	0.330639i
$298$		0			0
$299$	−1.76152	−	1.01701i	−0.101871	−	0.0588154i
$300$		0			0
$301$	−12.6343	+	7.96889i	−0.728229	+	0.459319i
$302$		0			0
$303$	−23.5811	−	13.6145i	−1.35470	−	0.782135i
$304$		0			0
$305$	−4.57776	−	7.92892i	−0.262122	−	0.454009i
$306$		0			0
$307$		−	12.3058i		−	0.702331i	−0.936313	−	0.351166i	$-0.885785\pi$
$307$		−	12.3058i		−	0.702331i	0.936313	−	0.351166i	$-0.114215\pi$
$308$		0			0
$309$			23.0972i			1.31395i
$310$		0			0
$311$	14.6670	+	25.4040i	0.831691	+	1.44053i	0.896696	+	0.442646i	$0.145960\pi$
$311$	14.6670	+	25.4040i	0.831691	+	1.44053i	−0.0650050	+	0.997885i	$0.520706\pi$
$312$		0			0
$313$	6.39086	+	3.68976i	0.361233	+	0.208558i	0.669621	−	0.742703i	$-0.266456\pi$
$313$	6.39086	+	3.68976i	0.361233	+	0.208558i	−0.308389	+	0.951260i	$0.599790\pi$
$314$		0			0
$315$	0.524835	+	0.276234i	0.0295711	+	0.0155640i
$316$		0			0
$317$	20.1821	+	11.6521i	1.13354	+	0.654448i	0.944822	−	0.327583i	$-0.106234\pi$
$317$	20.1821	+	11.6521i	1.13354	+	0.654448i	0.188716	+	0.982032i	$0.439568\pi$
$318$		0			0
$319$	−16.4923	+	9.52184i	−0.923392	+	0.533121i
$320$		0			0
$321$			1.51307i			0.0844516i
$322$		0			0
$323$	−5.33823			−0.297027
$324$		0			0
$325$	−2.88000	−	4.98830i	−0.159753	−	0.276701i
$326$		0			0
$327$	18.5371	−	32.1072i	1.02510	−	1.77553i
$328$		0			0
$329$	0.602046	+	15.3846i	0.0331919	+	0.848178i
$330$		0			0
$331$	−10.0119	+	17.3412i	−0.550306	+	0.953158i	0.447946	+	0.894061i	$0.352156\pi$
$331$	−10.0119	+	17.3412i	−0.550306	+	0.953158i	−0.998252	+	0.0590977i	$0.981178\pi$
$332$		0			0
$333$	−1.12642	+	0.650338i	−0.0617274	+	0.0356383i
$334$		0			0
$335$	9.33726			0.510149
$336$		0			0
$337$	26.9883			1.47015			0.735073	−	0.677988i	$-0.237148\pi$
$337$	26.9883			1.47015			0.735073	+	0.677988i	$0.237148\pi$
$338$		0			0
$339$	22.5487	−	13.0185i	1.22468	−	0.707068i
$340$		0			0
$341$	1.25970	−	2.18186i	0.0682165	−	0.118154i
$342$		0			0
$343$	2.16818	+	18.3929i	0.117071	+	0.993124i
$344$		0			0
$345$	−1.33848	+	2.31831i	−0.0720613	+	0.124814i
$346$		0			0
$347$	14.6972	+	25.4564i	0.788989	+	1.36657i	0.926587	+	0.376080i	$0.122728\pi$
$347$	14.6972	+	25.4564i	0.788989	+	1.36657i	−0.137598	+	0.990488i	$0.543938\pi$
$348$		0			0
$349$	−20.8919			−1.11832			−0.559160	−	0.829060i	$-0.688876\pi$
$349$	−20.8919			−1.11832			−0.559160	+	0.829060i	$0.688876\pi$
$350$		0			0
$351$			7.92497i			0.423003i
$352$		0			0
$353$	−7.66425	+	4.42496i	−0.407927	+	0.235517i	−0.689899	−	0.723906i	$-0.742345\pi$
$353$	−7.66425	+	4.42496i	−0.407927	+	0.235517i	0.281972	+	0.959423i	$0.409012\pi$
$354$		0			0
$355$	−12.8638	−	7.42694i	−0.682742	−	0.394181i
$356$		0			0
$357$	−1.27284	−	32.5258i	−0.0673658	−	1.72145i
$358$		0			0
$359$	−27.3788	−	15.8072i	−1.44500	−	0.834271i	−0.446823	−	0.894623i	$-0.647444\pi$
$359$	−27.3788	−	15.8072i	−1.44500	−	0.834271i	−0.998177	+	0.0603517i	$0.980778\pi$
$360$		0			0
$361$	−9.19947	−	15.9339i	−0.484183	−	0.838629i
$362$		0			0
$363$			10.4322i			0.547547i
$364$		0			0
$365$		−	13.0409i		−	0.682593i
$366$		0			0
$367$	−0.437113	−	0.757102i	−0.0228171	−	0.0395204i	0.854391	−	0.519630i	$-0.173930\pi$
$367$	−0.437113	−	0.757102i	−0.0228171	−	0.0395204i	−0.877208	+	0.480110i	$0.840597\pi$
$368$		0			0
$369$	0.332606	+	0.192030i	0.0173148	+	0.00999669i
$370$		0			0
$371$	0.451894	−	0.858583i	0.0234612	−	0.0445754i
$372$		0			0
$373$	−22.0441	−	12.7272i	−1.14140	−	0.658987i	−0.194622	−	0.980878i	$-0.562348\pi$
$373$	−22.0441	−	12.7272i	−1.14140	−	0.658987i	−0.946777	+	0.321891i	$0.895682\pi$
$374$		0			0
$375$	−15.5685	+	8.98849i	−0.803955	+	0.464163i
$376$		0			0
$377$			13.2430i			0.682049i
$378$		0			0
$379$	−29.8082			−1.53115			−0.765573	−	0.643349i	$-0.777544\pi$
$379$	−29.8082			−1.53115			−0.765573	+	0.643349i	$0.777544\pi$
$380$		0			0
$381$	−14.9774	−	25.9416i	−0.767316	−	1.32903i
$382$		0			0
$383$	−3.11806	+	5.40064i	−0.159326	+	0.275960i	−0.934626	−	0.355633i	$-0.884265\pi$
$383$	−3.11806	+	5.40064i	−0.159326	+	0.275960i	0.775300	+	0.631593i	$0.217599\pi$
$384$		0			0
$385$	5.91624	−	3.73158i	0.301520	−	0.190179i
$386$		0			0
$387$	0.543796	−	0.941883i	0.0276427	−	0.0478786i
$388$		0			0
$389$	29.4531	−	17.0048i	1.49333	−	0.862177i	0.493363	−	0.869824i	$-0.335767\pi$
$389$	29.4531	−	17.0048i	1.49333	−	0.862177i	0.999971	+	0.00764684i	$0.00243409\pi$
$390$		0			0
$391$	8.86480			0.448312
$392$		0			0
$393$	25.9201			1.30749
$394$		0			0
$395$	−13.5506	+	7.82343i	−0.681803	+	0.393639i
$396$		0			0
$397$	16.3893	−	28.3871i	0.822554	−	1.42471i	−0.0812202	−	0.996696i	$-0.525882\pi$
$397$	16.3893	−	28.3871i	0.822554	−	1.42471i	0.903774	−	0.428009i	$-0.140785\pi$
$398$		0			0
$399$	−3.09997	+	1.95526i	−0.155193	+	0.0978853i
$400$		0			0
$401$	5.34531	−	9.25835i	0.266932	−	0.462340i	−0.701136	−	0.713028i	$-0.747323\pi$
$401$	5.34531	−	9.25835i	0.266932	−	0.462340i	0.968068	+	0.250688i	$0.0806567\pi$
$402$		0			0
$403$	−0.875995	−	1.51727i	−0.0436364	−	0.0755805i
$404$		0			0
$405$	11.1025			0.551686
$406$		0			0
$407$			15.3398i			0.760367i
$408$		0			0
$409$	5.09919	−	2.94402i	0.252139	−	0.145572i	−0.368604	−	0.929586i	$-0.620164\pi$
$409$	5.09919	−	2.94402i	0.252139	−	0.145572i	0.620743	+	0.784014i	$0.286831\pi$
$410$		0			0
$411$	−15.9559	−	9.21213i	−0.787045	−	0.454401i
$412$		0			0
$413$	−15.1428	+	28.7708i	−0.745130	+	1.41572i
$414$		0			0
$415$	3.18434	+	1.83848i	0.156313	+	0.0902474i
$416$		0			0
$417$	13.5905	+	23.5394i	0.665528	+	1.15273i
$418$		0			0
$419$		−	28.4042i		−	1.38764i	−0.720149	−	0.693819i	$-0.755927\pi$
$419$		−	28.4042i		−	1.38764i	0.720149	−	0.693819i	$-0.244073\pi$
$420$		0			0
$421$		−	5.29468i		−	0.258047i	−0.991642	−	0.129024i	$-0.958816\pi$
$421$		−	5.29468i		−	0.258047i	0.991642	−	0.129024i	$-0.0411843\pi$
$422$		0			0
$423$	−0.560500	−	0.970814i	−0.0272524	−	0.0472026i
$424$		0			0
$425$	21.7403	+	12.5518i	1.05456	+	0.608850i
$426$		0			0
$427$	0.813974	+	20.8001i	0.0393910	+	1.00659i
$428$		0			0
$429$	−5.55416	−	3.20669i	−0.268157	−	0.154821i
$430$		0			0
$431$	12.5805	−	7.26338i	0.605984	−	0.349865i	−0.165408	−	0.986225i	$-0.552894\pi$
$431$	12.5805	−	7.26338i	0.605984	−	0.349865i	0.771392	+	0.636360i	$0.219561\pi$
$432$		0			0
$433$		−	20.5096i		−	0.985628i	−0.870135	−	0.492814i	$-0.835968\pi$
$433$		−	20.5096i		−	0.985628i	0.870135	−	0.492814i	$-0.164032\pi$
$434$		0			0
$435$	17.4289			0.835654
$436$		0			0
$437$	−0.499071	−	0.864417i	−0.0238738	−	0.0413507i
$438$		0			0
$439$	−12.6482	+	21.9073i	−0.603666	+	1.04558i	0.388595	+	0.921409i	$0.372961\pi$
$439$	−12.6482	+	21.9073i	−0.603666	+	1.04558i	−0.992261	+	0.124171i	$0.960373\pi$
$440$		0			0
$441$	−0.763423	−	1.11153i	−0.0363535	−	0.0529302i
$442$		0			0
$443$	−15.4913	+	26.8318i	−0.736016	+	1.27482i	0.218261	+	0.975891i	$0.429962\pi$
$443$	−15.4913	+	26.8318i	−0.736016	+	1.27482i	−0.954276	+	0.298926i	$0.903372\pi$
$444$		0			0
$445$	−2.94541	+	1.70054i	−0.139626	+	0.0806131i
$446$		0			0
$447$	−13.3803			−0.632865
$448$		0			0
$449$	−3.63439			−0.171517			−0.0857586	−	0.996316i	$-0.527331\pi$
$449$	−3.63439			−0.171517			−0.0857586	+	0.996316i	$0.527331\pi$
$450$		0			0
$451$	3.92267	−	2.26475i	0.184711	−	0.106643i
$452$		0			0
$453$	−2.68763	+	4.65512i	−0.126276	+	0.218717i
$454$		0			0
$455$	−0.190204	−	4.86044i	−0.00891692	−	0.227861i
$456$		0			0
$457$	10.1469	−	17.5750i	0.474654	−	0.822125i	−0.524925	−	0.851149i	$-0.675906\pi$
$457$	10.1469	−	17.5750i	0.474654	−	0.822125i	0.999579	+	0.0290237i	$0.00923982\pi$
$458$		0			0
$459$	−17.2695	−	29.9117i	−0.806072	−	1.39616i
$460$		0			0
$461$	27.3236			1.27259			0.636293	−	0.771448i	$-0.280467\pi$
$461$	27.3236			1.27259			0.636293	+	0.771448i	$0.280467\pi$
$462$		0			0
$463$			2.51268i			0.116774i	0.998294	+	0.0583871i	$0.0185958\pi$
$463$			2.51268i			0.116774i	−0.998294	+	0.0583871i	$0.981404\pi$
$464$		0			0
$465$	−1.99686	+	1.15289i	−0.0926021	+	0.0534639i
$466$		0			0
$467$	−27.8982	−	16.1070i	−1.29097	−	0.745345i	−0.312148	−	0.950034i	$-0.601048\pi$
$467$	−27.8982	−	16.1070i	−1.29097	−	0.745345i	−0.978827	+	0.204689i	$0.934382\pi$
$468$		0			0
$469$	−18.7860	−	9.88757i	−0.867459	−	0.456566i
$470$		0			0
$471$	8.23435	+	4.75410i	0.379419	+	0.219058i
$472$		0			0
$473$	−6.41339	−	11.1083i	−0.294888	−	0.510761i
$474$		0			0
$475$		−	2.82656i		−	0.129691i
$476$		0			0
$477$			0.0706430i			0.00323452i
$478$		0			0
$479$	6.12964	+	10.6168i	0.280070	+	0.485096i	0.971402	−	0.237442i	$-0.0763089\pi$
$479$	6.12964	+	10.6168i	0.280070	+	0.485096i	−0.691332	+	0.722538i	$0.742976\pi$
$480$		0			0
$481$	9.23818	+	5.33367i	0.421225	+	0.243194i
$482$		0			0
$483$	5.14789	−	3.24695i	0.234237	−	0.147741i
$484$		0			0
$485$	−0.336251	−	0.194134i	−0.0152684	−	0.00881519i
$486$		0			0
$487$	−4.72155	+	2.72599i	−0.213954	+	0.123526i	−0.603148	−	0.797630i	$-0.706087\pi$
$487$	−4.72155	+	2.72599i	−0.213954	+	0.123526i	0.389194	+	0.921156i	$0.372754\pi$
$488$		0			0
$489$		−	26.9713i		−	1.21969i
$490$		0			0
$491$	30.0205			1.35481			0.677404	−	0.735612i	$-0.263105\pi$
$491$	30.0205			1.35481			0.677404	+	0.735612i	$0.263105\pi$
$492$		0			0
$493$	−28.8582	−	49.9838i	−1.29971	−	2.25116i
$494$		0			0
$495$	−0.254642	+	0.441054i	−0.0114453	+	0.0198239i
$496$		0			0
$497$	18.0167	+	28.5646i	0.808158	+	1.28130i
$498$		0			0
$499$	2.17347	−	3.76455i	0.0972977	−	0.168524i	−0.813268	−	0.581890i	$-0.802313\pi$
$499$	2.17347	−	3.76455i	0.0972977	−	0.168524i	0.910565	+	0.413365i	$0.135647\pi$
$500$		0			0
$501$	13.9129	−	8.03261i	0.621582	−	0.358871i
$502$		0			0
$503$	9.75385			0.434903			0.217451	−	0.976071i	$-0.430226\pi$
$503$	9.75385			0.434903			0.217451	+	0.976071i	$0.430226\pi$
$504$		0			0
$505$	17.7334			0.789128
$506$		0			0
$507$	16.2540	−	9.38423i	0.721864	−	0.416768i
$508$		0			0
$509$	−0.998039	+	1.72865i	−0.0442373	+	0.0766212i	−0.887296	−	0.461200i	$-0.847419\pi$
$509$	−0.998039	+	1.72865i	−0.0442373	+	0.0766212i	0.843059	+	0.537821i	$0.180752\pi$
$510$		0			0
$511$	−13.8095	+	26.2376i	−0.610897	+	1.16068i
$512$		0			0
$513$	−1.94448	+	3.36794i	−0.0858510	+	0.148698i
$514$		0			0
$515$	−7.52122	−	13.0271i	−0.331425	−	0.574044i
$516$		0			0
$517$	−13.2208			−0.581449
$518$		0			0
$519$		−	12.0269i		−	0.527922i
$520$		0			0
$521$	−5.45719	+	3.15071i	−0.239084	+	0.138035i	−0.614756	−	0.788718i	$-0.710745\pi$
$521$	−5.45719	+	3.15071i	−0.239084	+	0.138035i	0.375672	+	0.926753i	$0.377412\pi$
$522$		0			0
$523$	1.98699	+	1.14719i	0.0868849	+	0.0501630i	0.542813	−	0.839854i	$-0.317359\pi$
$523$	1.98699	+	1.14719i	0.0868849	+	0.0501630i	−0.455928	+	0.890017i	$0.650693\pi$
$524$		0			0
$525$	17.2222	−	0.673961i	0.751640	−	0.0294141i
$526$		0			0
$527$	6.61264	+	3.81781i	0.288051	+	0.166306i
$528$		0			0
$529$	−10.6712	−	18.4831i	−0.463966	−	0.803614i
$530$		0			0
$531$		−	2.36722i		−	0.102729i
$532$		0			0
$533$		−	3.14982i		−	0.136434i
$534$		0			0
$535$	−0.492709	−	0.853396i	−0.0213017	−	0.0368955i
$536$		0			0
$537$	26.3142	+	15.1925i	1.13554	+	0.655606i
$538$		0			0
$539$	−15.8547	+	1.24279i	−0.682908	+	0.0535307i
$540$		0			0
$541$	9.00219	+	5.19742i	0.387034	+	0.223454i	0.680874	−	0.732400i	$-0.261600\pi$
$541$	9.00219	+	5.19742i	0.387034	+	0.223454i	−0.293840	+	0.955855i	$0.594933\pi$
$542$		0			0
$543$	30.7422	−	17.7490i	1.31927	−	0.761682i
$544$		0			0
$545$			24.1452i			1.03427i
$546$		0			0
$547$	6.13726			0.262410			0.131205	−	0.991355i	$-0.458115\pi$
$547$	6.13726			0.262410			0.131205	+	0.991355i	$0.458115\pi$
$548$		0			0
$549$	−0.757803	−	1.31255i	−0.0323422	−	0.0560184i
$550$		0			0
$551$	−3.24932	+	5.62798i	−0.138426	+	0.239760i
$552$		0			0
$553$	35.5475	−	1.39109i	1.51163	−	0.0591550i
$554$		0			0
$555$	7.01958	−	12.1583i	0.297965	−	0.516090i
$556$		0			0
$557$	0.675593	−	0.390054i	0.0286258	−	0.0165271i	−0.485619	−	0.874171i	$-0.661406\pi$
$557$	0.675593	−	0.390054i	0.0286258	−	0.0165271i	0.514245	+	0.857644i	$0.328072\pi$
$558$		0			0
$559$	−8.91975			−0.377265
$560$		0			0
$561$	27.9512			1.18010
$562$		0			0
$563$	−12.8515	+	7.41983i	−0.541627	+	0.312709i	−0.745738	−	0.666239i	$-0.767903\pi$
$563$	−12.8515	+	7.41983i	−0.541627	+	0.312709i	0.204111	+	0.978948i	$0.434570\pi$
$564$		0			0
$565$	−8.47854	+	14.6853i	−0.356695	+	0.617814i
$566$		0			0
$567$	−22.3375	−	11.7568i	−0.938088	−	0.493740i
$568$		0			0
$569$	8.67408	−	15.0240i	0.363636	−	0.629837i	−0.624920	−	0.780689i	$-0.714868\pi$
$569$	8.67408	−	15.0240i	0.363636	−	0.629837i	0.988556	+	0.150852i	$0.0482017\pi$
$570$		0			0
$571$	10.6684	+	18.4782i	0.446459	+	0.773290i	0.998153	−	0.0607568i	$-0.0193514\pi$
$571$	10.6684	+	18.4782i	0.446459	+	0.773290i	−0.551693	+	0.834047i	$0.686018\pi$
$572$		0			0
$573$	30.7551			1.28481
$574$		0			0
$575$			4.69386i			0.195748i
$576$		0			0
$577$	−5.02714	+	2.90242i	−0.209282	+	0.120829i	−0.600978	−	0.799266i	$-0.705222\pi$
$577$	−5.02714	+	2.90242i	−0.209282	+	0.120829i	0.391695	+	0.920095i	$0.371889\pi$
$578$		0			0
$579$	24.6923	+	14.2561i	1.02618	+	0.592464i
$580$		0			0
$581$	−4.45988	−	7.07093i	−0.185027	−	0.293352i
$582$		0			0
$583$	0.721525	+	0.416573i	0.0298825	+	0.0172527i
$584$		0			0
$585$	0.177079	+	0.306709i	0.00732130	+	0.0126809i
$586$		0			0
$587$			5.98632i			0.247082i	0.992339	+	0.123541i	$0.0394250\pi$
$587$			5.98632i			0.247082i	−0.992339	+	0.123541i	$0.960575\pi$
$588$		0			0
$589$		−	0.859741i		−	0.0354250i
$590$		0			0
$591$	−6.51705	−	11.2879i	−0.268076	−	0.464321i
$592$		0			0
$593$	−28.9786	−	16.7308i	−1.19001	−	0.687052i	−0.231700	−	0.972787i	$-0.574429\pi$
$593$	−28.9786	−	16.7308i	−1.19001	−	0.687052i	−0.958308	+	0.285736i	$0.907762\pi$
$594$		0			0
$595$	11.3094	+	17.9306i	0.463641	+	0.735081i
$596$		0			0
$597$	9.73587	+	5.62101i	0.398463	+	0.230053i
$598$		0			0
$599$	19.2940	−	11.1394i	0.788330	−	0.455143i	−0.0510442	−	0.998696i	$-0.516255\pi$
$599$	19.2940	−	11.1394i	0.788330	−	0.455143i	0.839374	+	0.543554i	$0.182922\pi$
$600$		0			0
$601$		−	9.75431i		−	0.397887i	−0.980011	−	0.198943i	$-0.936249\pi$
$601$		−	9.75431i		−	0.397887i	0.980011	−	0.198943i	$-0.0637509\pi$
$602$		0			0
$603$	1.54569			0.0629454
$604$		0			0
$605$	−3.39707	−	5.88389i	−0.138110	−	0.239214i
$606$		0			0
$607$	20.3810	−	35.3009i	0.827239	−	1.43282i	−0.0729563	−	0.997335i	$-0.523243\pi$
$607$	20.3810	−	35.3009i	0.827239	−	1.43282i	0.900196	−	0.435486i	$-0.143423\pi$
$608$		0			0
$609$	−35.0661	−	18.4562i	−1.42095	−	0.747882i
$610$		0			0
$611$	−4.59687	+	7.96201i	−0.185969	+	0.322109i
$612$		0			0
$613$	12.5353	−	7.23723i	0.506294	−	0.292309i	−0.225015	−	0.974355i	$-0.572243\pi$
$613$	12.5353	−	7.23723i	0.506294	−	0.292309i	0.731309	+	0.682046i	$0.238910\pi$
$614$		0			0
$615$	−4.14545			−0.167160
$616$		0			0
$617$	8.01966			0.322859			0.161430	−	0.986884i	$-0.448390\pi$
$617$	8.01966			0.322859			0.161430	+	0.986884i	$0.448390\pi$
$618$		0			0
$619$	−35.0723	+	20.2490i	−1.40967	+	0.813876i	−0.995357	−	0.0962568i	$-0.969313\pi$
$619$	−35.0723	+	20.2490i	−1.40967	+	0.813876i	−0.414317	+	0.910132i	$0.635980\pi$
$620$		0			0
$621$	3.22906	−	5.59289i	0.129578	−	0.224435i
$622$		0			0
$623$	7.72677	−	0.302373i	0.309566	−	0.0121143i
$624$		0			0
$625$	−3.26069	+	5.64768i	−0.130428	+	0.225907i
$626$		0			0
$627$	−1.57360	−	2.72555i	−0.0628435	−	0.108848i
$628$		0			0
$629$	−46.4910			−1.85372
$630$		0			0
$631$			6.80166i			0.270770i	0.990793	+	0.135385i	$0.0432271\pi$
$631$			6.80166i			0.270770i	−0.990793	+	0.135385i	$0.956773\pi$
$632$		0			0
$633$	−12.6246	+	7.28880i	−0.501782	+	0.289704i
$634$		0			0
$635$	16.8950	+	9.75431i	0.670456	+	0.387088i
$636$		0			0
$637$	−4.76422	+	9.98034i	−0.188765	+	0.395436i
$638$		0			0
$639$	−2.12948	−	1.22946i	−0.0842409	−	0.0486365i
$640$		0			0
$641$	9.07491	+	15.7182i	0.358437	+	0.620832i	0.987700	−	0.156361i	$-0.0499763\pi$
$641$	9.07491	+	15.7182i	0.358437	+	0.620832i	−0.629263	+	0.777193i	$0.716643\pi$
$642$		0			0
$643$			14.1896i			0.559583i	0.960061	+	0.279792i	$0.0902654\pi$
$643$			14.1896i			0.559583i	−0.960061	+	0.279792i	$0.909735\pi$
$644$		0			0
$645$			11.7392i			0.462230i
$646$		0			0
$647$	−5.56278	−	9.63503i	−0.218696	−	0.378792i	0.735714	−	0.677293i	$-0.236847\pi$
$647$	−5.56278	−	9.63503i	−0.218696	−	0.378792i	−0.954409	+	0.298501i	$0.903514\pi$
$648$		0			0
$649$	−24.1781	−	13.9592i	−0.949072	−	0.547947i
$650$		0			0
$651$	5.23840	−	0.204995i	0.205309	−	0.00803440i
$652$		0			0
$653$	0.295831	+	0.170798i	0.0115768	+	0.00668386i	0.505777	−	0.862664i	$-0.331206\pi$
$653$	0.295831	+	0.170798i	0.0115768	+	0.00668386i	−0.494200	+	0.869348i	$0.664539\pi$
$654$		0			0
$655$	−14.6193	+	8.44046i	−0.571224	+	0.329796i
$656$		0			0
$657$		−	2.15879i		−	0.0842226i
$658$		0			0
$659$	5.86660			0.228530			0.114265	−	0.993450i	$-0.463549\pi$
$659$	5.86660			0.228530			0.114265	+	0.993450i	$0.463549\pi$
$660$		0			0
$661$	12.7756	+	22.1280i	0.496913	+	0.860679i	0.999994	−	0.00356071i	$-0.00113341\pi$
$661$	12.7756	+	22.1280i	0.496913	+	0.860679i	−0.503080	+	0.864240i	$0.667800\pi$
$662$		0			0
$663$	9.71864	−	16.8332i	0.377441	−	0.653747i
$664$		0			0
$665$	1.11173	−	2.11225i	0.0431111	−	0.0819095i
$666$		0			0
$667$	5.39590	−	9.34598i	0.208930	−	0.361878i
$668$		0			0
$669$	−41.1614	+	23.7646i	−1.59139	+	0.918791i
$670$		0			0
$671$	−17.8747			−0.690043
$672$		0			0
$673$	−31.2431			−1.20433			−0.602167	−	0.798370i	$-0.705696\pi$
$673$	−31.2431			−1.20433			−0.602167	+	0.798370i	$0.705696\pi$
$674$		0			0
$675$	15.8381	−	9.14411i	0.609607	−	0.351957i
$676$		0			0
$677$	9.71455	−	16.8261i	0.373361	−	0.646679i	−0.616720	−	0.787183i	$-0.711539\pi$
$677$	9.71455	−	16.8261i	0.373361	−	0.646679i	0.990080	+	0.140503i	$0.0448721\pi$
$678$		0			0
$679$	0.470941	+	0.746656i	0.0180731	+	0.0286540i
$680$		0			0
$681$	−15.6187	+	27.0524i	−0.598510	+	1.03665i
$682$		0			0
$683$	2.43063	+	4.20998i	0.0930055	+	0.161090i	0.908774	−	0.417288i	$-0.137019\pi$
$683$	2.43063	+	4.20998i	0.0930055	+	0.161090i	−0.815769	+	0.578378i	$0.803686\pi$
$684$		0			0
$685$	11.9991			0.458463
$686$		0			0
$687$		−	36.0984i		−	1.37724i
$688$		0			0
$689$	0.501749	−	0.289685i	0.0191151	−	0.0110361i
$690$		0			0
$691$	23.0723	+	13.3208i	0.877711	+	0.506747i	0.869903	−	0.493223i	$-0.164181\pi$
$691$	23.0723	+	13.3208i	0.877711	+	0.506747i	0.00780793	+	0.999970i	$0.497515\pi$
$692$		0			0
$693$	0.979375	−	0.617725i	0.0372034	−	0.0234654i
$694$		0			0
$695$	−15.3304	−	8.85104i	−0.581517	−	0.335739i
$696$		0			0
$697$	6.86387	+	11.8886i	0.259987	+	0.450311i
$698$		0			0
$699$		−	21.9422i		−	0.829932i
$700$		0			0
$701$			6.56046i			0.247785i	0.992296	+	0.123893i	$0.0395378\pi$
$701$			6.56046i			0.247785i	−0.992296	+	0.123893i	$0.960462\pi$
$702$		0			0
$703$	2.61735	+	4.53339i	0.0987153	+	0.170980i
$704$		0			0
$705$	10.4787	+	6.04989i	0.394651	+	0.227852i
$706$		0			0
$707$	−35.6787	−	18.7786i	−1.34183	−	0.706242i
$708$		0			0
$709$	7.70421	+	4.44803i	0.289338	+	0.167049i	0.637643	−	0.770332i	$-0.279909\pi$
$709$	7.70421	+	4.44803i	0.289338	+	0.167049i	−0.348305	+	0.937381i	$0.613243\pi$
$710$		0			0
$711$	−2.24316	+	1.29509i	−0.0841251	+	0.0485697i
$712$		0			0
$713$			1.42771i			0.0534681i
$714$		0			0
$715$	4.17684			0.156205
$716$		0			0
$717$	−3.99238	−	6.91501i	−0.149098	−	0.258246i
$718$		0			0
$719$	−4.23335	+	7.33238i	−0.157877	+	0.273452i	−0.934103	−	0.357003i	$-0.883798\pi$
$719$	−4.23335	+	7.33238i	−0.157877	+	0.273452i	0.776226	+	0.630455i	$0.217132\pi$
$720$		0			0
$721$	1.33735	+	34.1744i	0.0498056	+	1.27272i
$722$		0			0
$723$	−7.14088	+	12.3684i	−0.265572	+	0.459984i
$724$		0			0
$725$	26.4661	−	15.2802i	0.982927	−	0.567493i
$726$		0			0
$727$	27.4279			1.01724			0.508621	−	0.860990i	$-0.330155\pi$
$727$	27.4279			1.01724			0.508621	+	0.860990i	$0.330155\pi$
$728$		0			0
$729$	−25.0508			−0.927806
$730$		0			0
$731$	33.6664	−	19.4373i	1.24520	−	0.718914i
$732$		0			0
$733$	−7.27274	+	12.5967i	−0.268625	+	0.465272i	−0.968507	−	0.248987i	$-0.919902\pi$
$733$	−7.27274	+	12.5967i	−0.268625	+	0.465272i	0.699882	+	0.714258i	$0.253236\pi$
$734$		0			0
$735$	13.1350	+	6.27013i	0.484492	+	0.231277i
$736$		0			0
$737$	9.11473	−	15.7872i	0.335745	−	0.581528i
$738$		0			0
$739$	21.0055	+	36.3827i	0.772701	+	1.33836i	0.936077	+	0.351794i	$0.114428\pi$
$739$	21.0055	+	36.3827i	0.772701	+	1.33836i	−0.163376	+	0.986564i	$0.552238\pi$
$740$		0			0
$741$	−2.18856			−0.0803989
$742$		0			0
$743$			20.2063i			0.741297i	0.928773	+	0.370649i	$0.120865\pi$
$743$			20.2063i			0.741297i	−0.928773	+	0.370649i	$0.879135\pi$
$744$		0			0
$745$	7.54667	−	4.35707i	0.276489	−	0.159631i
$746$		0			0
$747$	0.527135	+	0.304342i	0.0192869	+	0.0111353i
$748$		0			0
$749$	0.0876088	+	2.23873i	0.00320115	+	0.0818015i
$750$		0			0
$751$	35.0599	+	20.2418i	1.27935	+	0.738635i	0.976729	−	0.214475i	$-0.0688041\pi$
$751$	35.0599	+	20.2418i	1.27935	+	0.738635i	0.302624	+	0.953110i	$0.402137\pi$
$752$		0			0
$753$	−13.4289	−	23.2596i	−0.489377	−	0.847626i
$754$		0			0
$755$		−	3.50074i		−	0.127405i
$756$		0			0
$757$		−	17.0846i		−	0.620950i	−0.950582	−	0.310475i	$-0.899512\pi$
$757$		−	17.0846i		−	0.620950i	0.950582	−	0.310475i	$-0.100488\pi$
$758$		0			0
$759$	2.61316	+	4.52612i	0.0948517	+	0.164288i
$760$		0			0
$761$	−18.6059	−	10.7421i	−0.674463	−	0.389401i	0.123303	−	0.992369i	$-0.460651\pi$
$761$	−18.6059	−	10.7421i	−0.674463	−	0.389401i	−0.797765	+	0.602968i	$0.793985\pi$
$762$		0			0
$763$	25.5683	−	48.5789i	0.925635	−	1.75867i
$764$		0			0
$765$	−1.33672	−	0.771754i	−0.0483291	−	0.0279028i
$766$		0			0
$767$	−16.8134	+	9.70725i	−0.607098	+	0.350508i
$768$		0			0
$769$			10.3677i			0.373870i	0.982372	+	0.186935i	$0.0598553\pi$
$769$			10.3677i			0.373870i	−0.982372	+	0.186935i	$0.940145\pi$
$770$		0			0
$771$	−17.5576			−0.632321
$772$		0			0
$773$	22.1135	+	38.3017i	0.795367	+	1.37762i	0.922606	+	0.385743i	$0.126055\pi$
$773$	22.1135	+	38.3017i	0.795367	+	1.37762i	−0.127240	+	0.991872i	$0.540612\pi$
$774$		0			0
$775$	−2.02151	+	3.50135i	−0.0726147	+	0.125772i
$776$		0			0
$777$	−26.9978	+	17.0285i	−0.968542	+	0.610892i
$778$		0			0
$779$	0.772845	−	1.33861i	0.0276900	−	0.0479606i
$780$		0			0
$781$	−25.1145	+	14.4999i	−0.898668	+	0.518846i
$782$		0			0
$783$	−42.0470			−1.50264
$784$		0			0
$785$	−6.19239			−0.221016
$786$		0			0
$787$	−39.7993	+	22.9781i	−1.41869	+	0.819082i	−0.996184	−	0.0872780i	$-0.972183\pi$
$787$	−39.7993	+	22.9781i	−1.41869	+	0.819082i	−0.422507	+	0.906360i	$0.638850\pi$
$788$		0			0
$789$	−18.0412	+	31.2482i	−0.642282	+	1.11247i
$790$		0			0
$791$	32.6091	−	20.5677i	1.15945	−	0.731303i
$792$		0			0
$793$	−6.21503	+	10.7647i	−0.220702	+	0.382267i
$794$		0			0
$795$	−0.381251	−	0.660346i	−0.0135216	−	0.0234201i
$796$		0			0
$797$	15.5217			0.549805			0.274903	−	0.961472i	$-0.411354\pi$
$797$	15.5217			0.549805			0.274903	+	0.961472i	$0.411354\pi$
$798$		0			0
$799$		−	40.0687i		−	1.41753i
$800$		0			0
$801$	−0.487584	+	0.281507i	−0.0172279	+	0.00994655i
$802$		0			0
$803$	−22.0492	−	12.7301i	−0.778100	−	0.449236i
$804$		0			0
$805$	−1.84617	+	3.50766i	−0.0650689	+	0.123629i
$806$		0			0
$807$	14.4045	+	8.31646i	0.507063	+	0.292753i
$808$		0			0
$809$	−13.5467	−	23.4635i	−0.476276	−	0.824934i	0.523355	−	0.852115i	$-0.324680\pi$
$809$	−13.5467	−	23.4635i	−0.476276	−	0.824934i	−0.999631	+	0.0271812i	$0.991347\pi$
$810$		0			0
$811$		−	35.5514i		−	1.24838i	−0.781273	−	0.624190i	$-0.785429\pi$
$811$		−	35.5514i		−	1.24838i	0.781273	−	0.624190i	$-0.214571\pi$
$812$		0			0
$813$			39.9299i			1.40040i
$814$		0			0
$815$	8.78279	+	15.2122i	0.307648	+	0.532861i
$816$		0			0
$817$	−3.79070	−	2.18856i	−0.132620	−	0.0765681i
$818$		0			0
$819$	−0.0314864	−	0.804597i	−0.00110022	−	0.0281149i
$820$		0			0
$821$	6.32826	+	3.65362i	0.220858	+	0.127512i	0.606347	−	0.795200i	$-0.292634\pi$
$821$	6.32826	+	3.65362i	0.220858	+	0.127512i	−0.385490	+	0.922712i	$0.625967\pi$
$822$		0			0
$823$	−39.7324	+	22.9395i	−1.38498	+	0.799621i	−0.992745	−	0.120242i	$-0.961633\pi$
$823$	−39.7324	+	22.9395i	−1.38498	+	0.799621i	−0.392240	+	0.919863i	$0.628300\pi$
$824$		0			0
$825$			14.8000i			0.515270i
$826$		0			0
$827$	−1.96289			−0.0682564			−0.0341282	−	0.999417i	$-0.510865\pi$
$827$	−1.96289			−0.0682564			−0.0341282	+	0.999417i	$0.510865\pi$
$828$		0			0
$829$	11.9828	+	20.7549i	0.416181	+	0.720847i	0.995552	−	0.0942175i	$-0.0300349\pi$
$829$	11.9828	+	20.7549i	0.416181	+	0.720847i	−0.579371	+	0.815064i	$0.696702\pi$
$830$		0			0
$831$	−21.1086	+	36.5611i	−0.732248	+	1.26829i
$832$		0			0
$833$	−3.76656	−	48.0512i	−0.130504	−	1.66488i
$834$		0			0
$835$	−5.23139	+	9.06102i	−0.181040	+	0.313570i
$836$		0			0
$837$	4.81739	−	2.78132i	0.166513	−	0.0961365i
$838$		0			0
$839$	28.1193			0.970786			0.485393	−	0.874296i	$-0.338677\pi$
$839$	28.1193			0.970786			0.485393	+	0.874296i	$0.338677\pi$
$840$		0			0
$841$	−41.2625			−1.42285
$842$		0			0
$843$	8.39020	−	4.84408i	0.288974	−	0.166839i
$844$		0			0
$845$	−6.11165	+	10.5857i	−0.210247	+	0.364159i
$846$		0			0
$847$	0.604034	+	15.4353i	0.0207549	+	0.530365i
$848$		0			0
$849$	−13.0935	+	22.6785i	−0.449367	+	0.778326i
$850$		0			0
$851$	−4.34644	−	7.52826i	−0.148994	−	0.258065i
$852$		0			0
$853$	−16.7019			−0.571862			−0.285931	−	0.958250i	$-0.592303\pi$
$853$	−16.7019			−0.571862			−0.285931	+	0.958250i	$0.592303\pi$
$854$		0			0
$855$			0.173793i			0.00594360i
$856$		0			0
$857$	−3.72835	+	2.15257i	−0.127358	+	0.0735302i	−0.562326	−	0.826916i	$-0.690093\pi$
$857$	−3.72835	+	2.15257i	−0.127358	+	0.0735302i	0.434967	+	0.900446i	$0.356760\pi$
$858$		0			0
$859$	−26.1068	−	15.0728i	−0.890752	−	0.514276i	−0.0165639	−	0.999863i	$-0.505273\pi$
$859$	−26.1068	−	15.0728i	−0.890752	−	0.514276i	−0.874189	+	0.485587i	$0.838606\pi$
$860$		0			0
$861$	8.34040	+	4.38977i	0.284240	+	0.149603i
$862$		0			0
$863$	18.5801	+	10.7272i	0.632474	+	0.365159i	0.781709	−	0.623643i	$-0.214348\pi$
$863$	18.5801	+	10.7272i	0.632474	+	0.365159i	−0.149236	+	0.988802i	$0.547681\pi$
$864$		0			0
$865$	3.91636	+	6.78334i	0.133160	+	0.230640i
$866$		0			0
$867$			54.3371i			1.84539i
$868$		0			0
$869$			30.5479i			1.03627i
$870$		0			0
$871$	−6.33839	−	10.9784i	−0.214768	−	0.371989i
$872$		0			0
$873$	−0.0556629	−	0.0321370i	−0.00188391	−	0.00108767i
$874$		0			0
$875$	−22.5146	+	14.2007i	−0.761133	+	0.480072i
$876$		0			0
$877$	8.72762	+	5.03889i	0.294711	+	0.170151i	0.640064	−	0.768321i	$-0.278908\pi$
$877$	8.72762	+	5.03889i	0.294711	+	0.170151i	−0.345354	+	0.938473i	$0.612241\pi$
$878$		0			0
$879$	12.9507	−	7.47709i	0.436817	−	0.252196i
$880$		0			0
$881$		−	7.37180i		−	0.248362i	−0.992260	−	0.124181i	$-0.960370\pi$
$881$		−	7.37180i		−	0.248362i	0.992260	−	0.124181i	$-0.0396304\pi$
$882$		0			0
$883$	−27.5124			−0.925867			−0.462934	−	0.886393i	$-0.653203\pi$
$883$	−27.5124			−0.925867			−0.462934	+	0.886393i	$0.653203\pi$
$884$		0			0
$885$	12.7756	+	22.1280i	0.429447	+	0.743824i
$886$		0			0
$887$	−21.6675	+	37.5293i	−0.727525	+	1.26011i	0.230401	+	0.973096i	$0.425996\pi$
$887$	−21.6675	+	37.5293i	−0.727525	+	1.26011i	−0.957926	+	0.287014i	$0.907337\pi$
$888$		0			0
$889$	−23.6625	−	37.5158i	−0.793615	−	1.25824i
$890$		0			0
$891$	10.8379	−	18.7717i	0.363082	−	0.628877i
$892$		0			0
$893$	−3.90714	+	2.25579i	−0.130747	+	0.0754871i
$894$		0			0
$895$	−19.7888			−0.661467
$896$		0			0
$897$	3.63439			0.121349
$898$		0			0
$899$	8.05008	−	4.64771i	0.268485	−	0.155010i
$900$		0			0
$901$	−1.26252	+	2.18675i	−0.0420607	+	0.0728512i
$902$		0			0
$903$	12.4311	−	23.6186i	0.413680	−	0.785977i
$904$		0			0
$905$	−11.5594	+	20.0214i	−0.384246	+	0.665533i
$906$		0			0
$907$	−15.9506	−	27.6272i	−0.529630	−	0.917346i	−0.999403	−	0.0345589i	$-0.988997\pi$
$907$	−15.9506	−	27.6272i	−0.529630	−	0.917346i	0.469772	−	0.882788i	$-0.344336\pi$
$908$		0			0
$909$	2.93559			0.0973675
$910$		0			0
$911$			4.71677i			0.156274i	0.996943	+	0.0781369i	$0.0248971\pi$
$911$			4.71677i			0.156274i	−0.996943	+	0.0781369i	$0.975103\pi$
$912$		0			0
$913$	6.21690	−	3.58933i	0.205749	−	0.118789i
$914$		0			0
$915$	14.1674	+	8.17952i	0.468358	+	0.270407i
$916$		0			0
$917$	38.3511	−	1.50080i	1.26647	−	0.0495609i
$918$		0			0
$919$	−0.607906	−	0.350974i	−0.0200530	−	0.0115776i	0.489940	−	0.871756i	$-0.337019\pi$
$919$	−0.607906	−	0.350974i	−0.0200530	−	0.0115776i	−0.509993	+	0.860179i	$0.670352\pi$
$920$		0			0
$921$	10.9940	+	19.0422i	0.362265	+	0.627461i
$922$		0			0
$923$			20.1665i			0.663787i
$924$		0			0
$925$		−	24.6167i		−	0.809392i
$926$		0			0
$927$	−1.24506	−	2.15651i	−0.0408932	−	0.0708292i
$928$		0			0
$929$	10.5273	+	6.07791i	0.345388	+	0.199410i	0.662652	−	0.748927i	$-0.269431\pi$
$929$	10.5273	+	6.07791i	0.345388	+	0.199410i	−0.317264	+	0.948337i	$0.602764\pi$
$930$		0			0
$931$	−4.47348	+	3.07247i	−0.146612	+	0.100696i
$932$		0			0
$933$	−45.3918	−	26.2070i	−1.48606	−	0.857978i
$934$		0			0
$935$	−15.7649	+	9.10186i	−0.515567	+	0.297663i
$936$		0			0
$937$			42.3926i			1.38490i	0.721464	+	0.692452i	$0.243470\pi$
$937$			42.3926i			1.38490i	−0.721464	+	0.692452i	$0.756530\pi$
$938$		0			0
$939$	−13.1857			−0.430299
$940$		0			0
$941$	13.6455	+	23.6347i	0.444830	+	0.770468i	0.998040	−	0.0625733i	$-0.0199307\pi$
$941$	13.6455	+	23.6347i	0.444830	+	0.770468i	−0.553210	+	0.833042i	$0.686597\pi$
$942$		0			0
$943$	−1.28341	+	2.22293i	−0.0417935	+	0.0723884i
$944$		0			0
$945$	15.4321	−	0.603907i	0.502006	−	0.0196451i
$946$		0			0
$947$	−0.0119439	+	0.0206875i	−0.000388126	+	0.000672253i	−0.866219	−	0.499664i	$-0.833457\pi$
$947$	−0.0119439	+	0.0206875i	−0.000388126	+	0.000672253i	0.865831	+	0.500336i	$0.166790\pi$
$948$		0			0
$949$	−15.3330	+	8.85254i	−0.497732	+	0.287366i
$950$		0			0
$951$	−41.6399			−1.35027
$952$		0			0
$953$	−29.1946			−0.945706			−0.472853	−	0.881141i	$-0.656776\pi$
$953$	−29.1946			−0.945706			−0.472853	+	0.881141i	$0.656776\pi$
$954$		0			0
$955$	−17.3463	+	10.0149i	−0.561314	+	0.324075i
$956$		0			0
$957$	17.0136	−	29.4684i	0.549971	−	0.952577i
$958$		0			0
$959$	−24.1416	−	12.7063i	−0.779572	−	0.410309i
$960$		0			0
$961$	14.8851	−	25.7818i	0.480165	−	0.831671i
$962$		0			0
$963$	−0.0815630	−	0.141271i	−0.00262833	−	0.00455240i
$964$		0			0
$965$	−18.5691			−0.597760
$966$		0			0
$967$			24.9315i			0.801744i	0.916134	+	0.400872i	$0.131293\pi$
$967$			24.9315i			0.801744i	−0.916134	+	0.400872i	$0.868707\pi$
$968$		0			0
$969$	8.26043	−	4.76916i	0.265363	−	0.153207i
$970$		0			0
$971$	36.3162	+	20.9672i	1.16544	+	0.672868i	0.952602	−	0.304219i	$-0.0983954\pi$
$971$	36.3162	+	20.9672i	1.16544	+	0.672868i	0.212840	+	0.977087i	$0.431729\pi$
$972$		0			0
$973$	21.4713	+	34.0418i	0.688339	+	1.09133i
$974$		0			0
$975$	8.91307	+	5.14596i	0.285447	+	0.164803i
$976$		0			0
$977$	10.0465	+	17.4011i	0.321417	+	0.556710i	0.980781	−	0.195114i	$-0.0625076\pi$
$977$	10.0465	+	17.4011i	0.321417	+	0.556710i	−0.659364	+	0.751824i	$0.729174\pi$
$978$		0			0
$979$			6.64003i			0.212216i
$980$		0			0
$981$			3.99700i			0.127614i
$982$		0			0
$983$	−21.9887	−	38.0855i	−0.701330	−	1.21474i	−0.968000	−	0.250951i	$-0.919257\pi$
$983$	−21.9887	−	38.0855i	−0.701330	−	1.21474i	0.266670	−	0.963788i	$-0.414077\pi$
$984$		0			0
$985$	7.35143	+	4.24435i	0.234236	+	0.135236i
$986$		0			0
$987$	−14.6761	−	23.2683i	−0.467146	−	0.740639i
$988$		0			0
$989$	6.29494	+	3.63439i	0.200167	+	0.115567i
$990$		0			0
$991$	13.3615	−	7.71429i	0.424443	−	0.245052i	−0.272533	−	0.962146i	$-0.587861\pi$
$991$	13.3615	−	7.71429i	0.424443	−	0.245052i	0.696977	+	0.717094i	$0.254528\pi$
$992$		0			0
$993$		−	35.7786i		−	1.13540i
$994$		0			0
$995$	−7.32157			−0.232109
$996$		0			0
$997$	24.4335	+	42.3201i	0.773817	+	1.34029i	0.935457	+	0.353441i	$0.114988\pi$
$997$	24.4335	+	42.3201i	0.773817	+	1.34029i	−0.161640	+	0.986850i	$0.551678\pi$
$998$		0			0
$999$	−16.9346	+	29.3316i	−0.535787	+	0.928011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.q.d.831.2	yes	16
4.3	odd	2		896.2.q.a.831.8	yes	16
7.3	odd	6	inner	896.2.q.d.703.1	yes	16
8.3	odd	2	inner	896.2.q.d.831.1	yes	16
8.5	even	2		896.2.q.a.831.7	yes	16
28.3	even	6		896.2.q.a.703.7	✓	16
56.3	even	6	inner	896.2.q.d.703.2	yes	16
56.45	odd	6		896.2.q.a.703.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.q.a.703.7	✓	16	28.3	even	6
896.2.q.a.703.8	yes	16	56.45	odd	6
896.2.q.a.831.7	yes	16	8.5	even	2
896.2.q.a.831.8	yes	16	4.3	odd	2
896.2.q.d.703.1	yes	16	7.3	odd	6	inner
896.2.q.d.703.2	yes	16	56.3	even	6	inner
896.2.q.d.831.1	yes	16	8.3	odd	2	inner
896.2.q.d.831.2	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54741 + 0.893397i) q^{3} +(0.581841 - 1.00778i) q^{5} +(-2.23781 + 1.41146i) q^{7} +(0.0963180 - 0.166828i) q^{9} +O(q^{10})\)	\(q+(-1.54741 + 0.893397i) q^{3} +(0.581841 - 1.00778i) q^{5} +(-2.23781 + 1.41146i) q^{7} +(0.0963180 - 0.166828i) q^{9} +(-1.13595 - 1.96752i) q^{11} -1.57988 q^{13} +2.07926i q^{15} +(5.96304 - 3.44276i) q^{17} +(-0.671415 - 0.387642i) q^{19} +(2.20181 - 4.18336i) q^{21} +(1.11497 + 0.643728i) q^{23} +(1.82292 + 3.15739i) q^{25} -5.01618i q^{27} -8.38228i q^{29} +(0.554469 + 0.960369i) q^{31} +(3.51556 + 2.02971i) q^{33} +(0.120392 + 3.07646i) q^{35} +(-5.84739 - 3.37599i) q^{37} +(2.44472 - 1.41146i) q^{39} +1.99371i q^{41} +5.64584 q^{43} +(-0.112084 - 0.194134i) q^{45} +(2.90963 - 5.03963i) q^{47} +(3.01556 - 6.31715i) q^{49} +(-6.15151 + 10.6547i) q^{51} +(-0.317587 + 0.183359i) q^{53} -2.64377 q^{55} +1.38527 q^{57} +(10.6422 - 6.14429i) q^{59} +(3.93386 - 6.81364i) q^{61} +(0.0199296 + 0.509277i) q^{63} +(-0.919239 + 1.59217i) q^{65} +(4.01194 + 6.94889i) q^{67} -2.30042 q^{69} -12.7646i q^{71} +(9.70520 - 5.60330i) q^{73} +(-5.64161 - 3.25719i) q^{75} +(5.31911 + 2.79959i) q^{77} +(-11.6446 - 6.72299i) q^{79} +(4.77040 + 8.26257i) q^{81} +3.15976i q^{83} -8.01256i q^{85} +(7.48870 + 12.9708i) q^{87} +(-2.53111 - 1.46134i) q^{89} +(3.53547 - 2.22994i) q^{91} +(-1.71598 - 0.990723i) q^{93} +(-0.781314 + 0.451092i) q^{95} -0.333655i q^{97} -0.437649 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{3} + 8 q^{9}+O(q^{10}) \) 16 * q + 12 * q^3 + 8 * q^9	\( 16 q + 12 q^{3} + 8 q^{9} - 4 q^{11} - 12 q^{19} - 16 q^{25} + 24 q^{33} + 20 q^{35} + 16 q^{49} - 52 q^{51} + 48 q^{57} + 60 q^{59} + 24 q^{65} + 12 q^{67} - 24 q^{73} - 120 q^{75} - 32 q^{81} + 24 q^{89} + 72 q^{91} + 64 q^{99}+O(q^{100}) \) 16 * q + 12 * q^3 + 8 * q^9 - 4 * q^11 - 12 * q^19 - 16 * q^25 + 24 * q^33 + 20 * q^35 + 16 * q^49 - 52 * q^51 + 48 * q^57 + 60 * q^59 + 24 * q^65 + 12 * q^67 - 24 * q^73 - 120 * q^75 - 32 * q^81 + 24 * q^89 + 72 * q^91 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more