LMFDB - Embedded newform 1156.2.h.f.733.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1156,2,Mod(733,1156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1156, 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("1156.733");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1156 = 2^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1156.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.23070647366$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	no (minimal twist has level 68)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			733.2
Root			$-0.991445 - 0.130526i$ of defining polynomial
Character	$\chi$	$=$	1156.733
Dual form			1156.2.h.f.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.676327 + 0.280144i) q^{3} +(-1.32565 - 3.20041i) q^{5} +(-0.280144 + 0.676327i) q^{7} +(-1.74238 + 1.74238i) q^{9} +(4.37184 + 1.81088i) q^{11} +1.46410i q^{13} +(1.79315 + 1.79315i) q^{15} +(3.86370 + 3.86370i) q^{19} -0.535898i q^{21} +(-4.37184 - 1.81088i) q^{23} +(-4.94975 + 4.94975i) q^{25} +(1.53073 - 3.69552i) q^{27} +(-1.32565 - 3.20041i) q^{29} +(5.72450 - 2.37116i) q^{31} -3.46410 q^{33} +2.53590 q^{35} +(10.5914 - 4.38712i) q^{37} +(-0.410159 - 0.990211i) q^{39} +(2.29610 - 5.54328i) q^{41} +(8.76268 - 8.76268i) q^{43} +(7.88614 + 3.26655i) q^{45} -6.92820i q^{47} +(4.57081 + 4.57081i) q^{49} +(-0.656339 - 0.656339i) q^{53} -16.3923i q^{55} +(-3.69552 - 1.53073i) q^{57} +(-6.69213 + 6.69213i) q^{59} +(-2.85639 + 6.89593i) q^{61} +(-0.690303 - 1.66654i) q^{63} +(4.68573 - 1.94089i) q^{65} -1.07180 q^{67} +3.46410 q^{69} +(2.02898 - 0.840431i) q^{71} +(-0.765367 - 1.84776i) q^{73} +(1.96101 - 4.73429i) q^{75} +(-2.44949 + 2.44949i) q^{77} +(1.66654 + 0.690303i) q^{79} -4.46410i q^{81} +(6.69213 + 6.69213i) q^{83} +(1.79315 + 1.79315i) q^{87} +9.46410i q^{89} +(-0.990211 - 0.410159i) q^{91} +(-3.20736 + 3.20736i) q^{93} +(7.24351 - 17.4874i) q^{95} +(3.41668 + 8.24858i) q^{97} +(-10.7727 + 4.46219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 96 q^{35} - 128 q^{67}+O(q^{100}) $ 16 * q + 96 * q^35 - 128 * q^67

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times$.

$n$	$579$	$581$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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
$3$	−0.676327	+	0.280144i	−0.390477	+	0.161741i	−0.569280	−	0.822144i	$-0.692778\pi$
$3$	−0.676327	+	0.280144i	−0.390477	+	0.161741i	0.178802	+	0.983885i	$0.442778\pi$
$4$		0			0
$5$	−1.32565	−	3.20041i	−0.592851	−	1.43127i	−0.880738	−	0.473604i	$-0.842953\pi$
$5$	−1.32565	−	3.20041i	−0.592851	−	1.43127i	0.287887	−	0.957664i	$-0.407047\pi$
$6$		0			0
$7$	−0.280144	+	0.676327i	−0.105884	+	0.255627i	−0.967938	−	0.251190i	$-0.919178\pi$
$7$	−0.280144	+	0.676327i	−0.105884	+	0.255627i	0.862053	+	0.506817i	$0.169178\pi$
$8$		0			0
$9$	−1.74238	+	1.74238i	−0.580794	+	0.580794i
$10$		0			0
$11$	4.37184	+	1.81088i	1.31816	+	0.546000i	0.927255	−	0.374431i	$-0.122162\pi$
$11$	4.37184	+	1.81088i	1.31816	+	0.546000i	0.390906	+	0.920431i	$0.372162\pi$
$12$		0			0
$13$			1.46410i			0.406069i	0.979172	+	0.203034i	$0.0650803\pi$
$13$			1.46410i			0.406069i	−0.979172	+	0.203034i	$0.934920\pi$
$14$		0			0
$15$	1.79315	+	1.79315i	0.462990	+	0.462990i
$16$		0			0
$17$		0			0
$17$		0			0
$18$		0			0
$19$	3.86370	+	3.86370i	0.886394	+	0.886394i	0.994175	−	0.107780i	$-0.0343743\pi$
$19$	3.86370	+	3.86370i	0.886394	+	0.886394i	−0.107780	+	0.994175i	$0.534374\pi$
$20$		0			0
$21$		−	0.535898i		−	0.116943i
$22$		0			0
$23$	−4.37184	−	1.81088i	−0.911593	−	0.377594i	−0.122927	−	0.992416i	$-0.539228\pi$
$23$	−4.37184	−	1.81088i	−0.911593	−	0.377594i	−0.788666	+	0.614822i	$0.789228\pi$
$24$		0			0
$25$	−4.94975	+	4.94975i	−0.989949	+	0.989949i
$26$		0			0
$27$	1.53073	−	3.69552i	0.294590	−	0.711203i
$28$		0			0
$29$	−1.32565	−	3.20041i	−0.246168	−	0.594302i	0.751704	−	0.659500i	$-0.229232\pi$
$29$	−1.32565	−	3.20041i	−0.246168	−	0.594302i	−0.997872	+	0.0651984i	$0.979232\pi$
$30$		0			0
$31$	5.72450	−	2.37116i	1.02815	−	0.425874i	0.196106	−	0.980583i	$-0.437170\pi$
$31$	5.72450	−	2.37116i	1.02815	−	0.425874i	0.832044	+	0.554709i	$0.187170\pi$
$32$		0			0
$33$	−3.46410			−0.603023
$34$		0			0
$35$	2.53590			0.428645
$36$		0			0
$37$	10.5914	−	4.38712i	1.74122	−	0.721238i	0.742548	−	0.669793i	$-0.233617\pi$
$37$	10.5914	−	4.38712i	1.74122	−	0.721238i	0.998676	−	0.0514451i	$-0.0163827\pi$
$38$		0			0
$39$	−0.410159	−	0.990211i	−0.0656780	−	0.158561i
$40$		0			0
$41$	2.29610	−	5.54328i	0.358591	−	0.865714i	−0.636908	−	0.770940i	$-0.719787\pi$
$41$	2.29610	−	5.54328i	0.358591	−	0.865714i	0.995499	−	0.0947747i	$-0.0302131\pi$
$42$		0			0
$43$	8.76268	−	8.76268i	1.33630	−	1.33630i	0.436679	−	0.899617i	$-0.356154\pi$
$43$	8.76268	−	8.76268i	1.33630	−	1.33630i	0.899617	−	0.436679i	$-0.143846\pi$
$44$		0			0
$45$	7.88614	+	3.26655i	1.17560	+	0.486948i
$46$		0			0
$47$		−	6.92820i		−	1.01058i	−0.862949	−	0.505291i	$-0.831385\pi$
$47$		−	6.92820i		−	1.01058i	0.862949	−	0.505291i	$-0.168615\pi$
$48$		0			0
$49$	4.57081	+	4.57081i	0.652973	+	0.652973i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.656339	−	0.656339i	−0.0901551	−	0.0901551i	0.660591	−	0.750746i	$-0.270306\pi$
$53$	−0.656339	−	0.656339i	−0.0901551	−	0.0901551i	−0.750746	+	0.660591i	$0.770306\pi$
$54$		0			0
$55$		−	16.3923i		−	2.21034i
$56$		0			0
$57$	−3.69552	−	1.53073i	−0.489483	−	0.202751i
$58$		0			0
$59$	−6.69213	+	6.69213i	−0.871241	+	0.871241i	−0.992608	−	0.121367i	$-0.961272\pi$
$59$	−6.69213	+	6.69213i	−0.871241	+	0.871241i	0.121367	+	0.992608i	$0.461272\pi$
$60$		0			0
$61$	−2.85639	+	6.89593i	−0.365723	+	0.882933i	0.628718	+	0.777634i	$0.283580\pi$
$61$	−2.85639	+	6.89593i	−0.365723	+	0.882933i	−0.994441	+	0.105300i	$0.966420\pi$
$62$		0			0
$63$	−0.690303	−	1.66654i	−0.0869700	−	0.209964i
$64$		0			0
$65$	4.68573	−	1.94089i	0.581193	−	0.240738i
$66$		0			0
$67$	−1.07180			−0.130941			−0.0654704	−	0.997855i	$-0.520855\pi$
$67$	−1.07180			−0.130941			−0.0654704	+	0.997855i	$0.520855\pi$
$68$		0			0
$69$	3.46410			0.417029
$70$		0			0
$71$	2.02898	−	0.840431i	0.240796	−	0.0997408i	−0.259022	−	0.965871i	$-0.583400\pi$
$71$	2.02898	−	0.840431i	0.240796	−	0.0997408i	0.499818	+	0.866131i	$0.333400\pi$
$72$		0			0
$73$	−0.765367	−	1.84776i	−0.0895794	−	0.216264i	0.872740	−	0.488185i	$-0.162341\pi$
$73$	−0.765367	−	1.84776i	−0.0895794	−	0.216264i	−0.962319	+	0.271921i	$0.912341\pi$
$74$		0			0
$75$	1.96101	−	4.73429i	0.226437	−	0.546668i
$76$		0			0
$77$	−2.44949	+	2.44949i	−0.279145	+	0.279145i
$78$		0			0
$79$	1.66654	+	0.690303i	0.187500	+	0.0776651i	0.474458	−	0.880278i	$-0.342644\pi$
$79$	1.66654	+	0.690303i	0.187500	+	0.0776651i	−0.286958	+	0.957943i	$0.592644\pi$
$80$		0			0
$81$		−	4.46410i		−	0.496011i
$82$		0			0
$83$	6.69213	+	6.69213i	0.734557	+	0.734557i	0.971519	−	0.236962i	$-0.0761517\pi$
$83$	6.69213	+	6.69213i	0.734557	+	0.734557i	−0.236962	+	0.971519i	$0.576152\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.79315	+	1.79315i	0.192246	+	0.192246i
$88$		0			0
$89$			9.46410i			1.00319i	0.865102	+	0.501596i	$0.167254\pi$
$89$			9.46410i			1.00319i	−0.865102	+	0.501596i	$0.832746\pi$
$90$		0			0
$91$	−0.990211	−	0.410159i	−0.103802	−	0.0429963i
$92$		0			0
$93$	−3.20736	+	3.20736i	−0.332588	+	0.332588i
$94$		0			0
$95$	7.24351	−	17.4874i	0.743168	−	1.79417i
$96$		0			0
$97$	3.41668	+	8.24858i	0.346911	+	0.837517i	0.996981	+	0.0776429i	$0.0247394\pi$
$97$	3.41668	+	8.24858i	0.346911	+	0.837517i	−0.650070	+	0.759874i	$0.725261\pi$
$98$		0			0
$99$	−10.7727	+	4.46219i	−1.08269	+	0.448467i
$100$		0			0
$101$	9.46410			0.941713			0.470857	−	0.882210i	$-0.343945\pi$
$101$	9.46410			0.941713			0.470857	+	0.882210i	$0.343945\pi$
$102$		0			0
$103$	2.92820			0.288524			0.144262	−	0.989539i	$-0.453919\pi$
$103$	2.92820			0.288524			0.144262	+	0.989539i	$0.453919\pi$
$104$		0			0
$105$	−1.71510	+	0.710416i	−0.167376	+	0.0693295i
$106$		0			0
$107$	−2.78132	−	6.71471i	−0.268881	−	0.649135i	0.730550	−	0.682859i	$-0.239264\pi$
$107$	−2.78132	−	6.71471i	−0.268881	−	0.649135i	−0.999431	+	0.0337232i	$0.989264\pi$
$108$		0			0
$109$	−2.44623	+	5.90572i	−0.234306	+	0.565665i	−0.996675	−	0.0814773i	$-0.974036\pi$
$109$	−2.44623	+	5.90572i	−0.234306	+	0.565665i	0.762369	+	0.647143i	$0.224036\pi$
$110$		0			0
$111$	−5.93426	+	5.93426i	−0.563255	+	0.563255i
$112$		0			0
$113$	7.25837	+	3.00652i	0.682810	+	0.282829i	0.697001	−	0.717070i	$-0.254517\pi$
$113$	7.25837	+	3.00652i	0.682810	+	0.282829i	−0.0141908	+	0.999899i	$0.504517\pi$
$114$		0			0
$115$			16.3923i			1.52859i
$116$		0			0
$117$	−2.55103	−	2.55103i	−0.235842	−	0.235842i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	8.05558	+	8.05558i	0.732325	+	0.732325i
$122$		0			0
$123$			4.39230i			0.396041i
$124$		0			0
$125$	6.40083	+	2.65131i	0.572507	+	0.237140i
$126$		0			0
$127$	14.4195	−	14.4195i	1.27953	−	1.27953i	0.338595	−	0.940932i	$-0.390048\pi$
$127$	14.4195	−	14.4195i	1.27953	−	1.27953i	0.940932	−	0.338595i	$-0.109952\pi$
$128$		0			0
$129$	−3.47163	+	8.38125i	−0.305660	+	0.737928i
$130$		0			0
$131$	−4.46219	−	10.7727i	−0.389863	−	0.941213i	−0.989968	−	0.141291i	$-0.954875\pi$
$131$	−4.46219	−	10.7727i	−0.389863	−	0.941213i	0.600105	−	0.799921i	$-0.295125\pi$
$132$		0			0
$133$	−3.69552	+	1.53073i	−0.320442	+	0.132731i
$134$		0			0
$135$	−13.8564			−1.19257
$136$		0			0
$137$	9.46410			0.808573			0.404286	−	0.914632i	$-0.367520\pi$
$137$	9.46410			0.808573			0.404286	+	0.914632i	$0.367520\pi$
$138$		0			0
$139$	−10.4102	+	4.31206i	−0.882984	+	0.365744i	−0.777653	−	0.628693i	$-0.783590\pi$
$139$	−10.4102	+	4.31206i	−0.882984	+	0.365744i	−0.105331	+	0.994437i	$0.533590\pi$
$140$		0			0
$141$	1.94089	+	4.68573i	0.163453	+	0.394610i
$142$		0			0
$143$	−2.65131	+	6.40083i	−0.221714	+	0.535264i
$144$		0			0
$145$	−8.48528	+	8.48528i	−0.704664	+	0.704664i
$146$		0			0
$147$	−4.37184	−	1.81088i	−0.360584	−	0.149359i
$148$		0			0
$149$		−	6.00000i		−	0.491539i	−0.969328	−	0.245770i	$-0.920959\pi$
$149$		−	6.00000i		−	0.491539i	0.969328	−	0.245770i	$-0.0790407\pi$
$150$		0			0
$151$	4.62158	+	4.62158i	0.376099	+	0.376099i	0.869693	−	0.493594i	$-0.164317\pi$
$151$	4.62158	+	4.62158i	0.376099	+	0.376099i	−0.493594	+	0.869693i	$0.664317\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−15.1774	−	15.1774i	−1.21908	−	1.21908i
$156$		0			0
$157$			2.00000i			0.159617i	0.996810	+	0.0798087i	$0.0254309\pi$
$157$			2.00000i			0.159617i	−0.996810	+	0.0798087i	$0.974569\pi$
$158$		0			0
$159$	0.627769	+	0.260030i	0.0497853	+	0.0206217i
$160$		0			0
$161$	2.44949	−	2.44949i	0.193047	−	0.193047i
$162$		0			0
$163$	−4.05203	+	9.78246i	−0.317379	+	0.766221i	0.682012	+	0.731341i	$0.261105\pi$
$163$	−4.05203	+	9.78246i	−0.317379	+	0.766221i	−0.999391	+	0.0348805i	$0.988895\pi$
$164$		0			0
$165$	4.59220	+	11.0866i	0.357502	+	0.863087i
$166$		0			0
$167$	10.7727	−	4.46219i	0.833614	−	0.345294i	0.0752818	−	0.997162i	$-0.476014\pi$
$167$	10.7727	−	4.46219i	0.833614	−	0.345294i	0.758332	+	0.651868i	$0.226014\pi$
$168$		0			0
$169$	10.8564			0.835108
$170$		0			0
$171$	−13.4641			−1.02963
$172$		0			0
$173$	−7.88614	+	3.26655i	−0.599572	+	0.248351i	−0.661763	−	0.749713i	$-0.730191\pi$
$173$	−7.88614	+	3.26655i	−0.599572	+	0.248351i	0.0621905	+	0.998064i	$0.480191\pi$
$174$		0			0
$175$	−1.96101	−	4.73429i	−0.148238	−	0.357878i
$176$		0			0
$177$	2.65131	−	6.40083i	0.199285	−	0.481115i
$178$		0			0
$179$	15.1774	−	15.1774i	1.13441	−	1.13441i	0.144978	−	0.989435i	$-0.453689\pi$
$179$	15.1774	−	15.1774i	1.13441	−	1.13441i	0.989435	−	0.144978i	$-0.0463112\pi$
$180$		0			0
$181$	−10.5914	−	4.38712i	−0.787256	−	0.326092i	−0.0474163	−	0.998875i	$-0.515099\pi$
$181$	−10.5914	−	4.38712i	−0.787256	−	0.326092i	−0.739840	+	0.672783i	$0.765099\pi$
$182$		0			0
$183$		−	5.46410i		−	0.403918i
$184$		0			0
$185$	−28.0812	−	28.0812i	−2.06457	−	2.06457i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.07055	+	2.07055i	0.150611	+	0.150611i
$190$		0			0
$191$			12.0000i			0.868290i	0.900843	+	0.434145i	$0.142949\pi$
$191$			12.0000i			0.868290i	−0.900843	+	0.434145i	$0.857051\pi$
$192$		0			0
$193$	6.53349	+	2.70626i	0.470291	+	0.194801i	0.605226	−	0.796054i	$-0.293083\pi$
$193$	6.53349	+	2.70626i	0.470291	+	0.194801i	−0.134935	+	0.990854i	$0.543083\pi$
$194$		0			0
$195$	−2.62536	+	2.62536i	−0.188006	+	0.188006i
$196$		0			0
$197$	−1.32565	+	3.20041i	−0.0944490	+	0.228020i	−0.964042	−	0.265748i	$-0.914381\pi$
$197$	−1.32565	+	3.20041i	−0.0944490	+	0.228020i	0.869593	+	0.493768i	$0.164381\pi$
$198$		0			0
$199$	−2.37116	−	5.72450i	−0.168087	−	0.405799i	0.817280	−	0.576240i	$-0.195481\pi$
$199$	−2.37116	−	5.72450i	−0.168087	−	0.405799i	−0.985368	+	0.170441i	$0.945481\pi$
$200$		0			0
$201$	0.724885	−	0.300257i	0.0511294	−	0.0211785i
$202$		0			0
$203$	2.53590			0.177985
$204$		0			0
$205$	−20.7846			−1.45166
$206$		0			0
$207$	10.7727	−	4.46219i	0.748752	−	0.310143i
$208$		0			0
$209$	9.89482	+	23.8882i	0.684439	+	1.65238i
$210$		0			0
$211$	−7.52365	+	18.1637i	−0.517950	+	1.25044i	0.421211	+	0.906963i	$0.361605\pi$
$211$	−7.52365	+	18.1637i	−0.517950	+	1.25044i	−0.939161	+	0.343478i	$0.888395\pi$
$212$		0			0
$213$	−1.13681	+	1.13681i	−0.0778931	+	0.0778931i
$214$		0			0
$215$	−39.6605	−	16.4279i	−2.70482	−	1.12037i
$216$		0			0
$217$			4.53590i			0.307917i
$218$		0			0
$219$	1.03528	+	1.03528i	0.0699575	+	0.0699575i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−5.93426	−	5.93426i	−0.397387	−	0.397387i	0.479923	−	0.877310i	$-0.340664\pi$
$223$	−5.93426	−	5.93426i	−0.397387	−	0.397387i	−0.877310	+	0.479923i	$0.840664\pi$
$224$		0			0
$225$		−	17.2487i		−	1.14991i
$226$		0			0
$227$	−9.05757	−	3.75177i	−0.601172	−	0.249014i	0.0612766	−	0.998121i	$-0.480483\pi$
$227$	−9.05757	−	3.75177i	−0.601172	−	0.249014i	−0.662449	+	0.749107i	$0.730483\pi$
$228$		0			0
$229$	−0.277401	+	0.277401i	−0.0183312	+	0.0183312i	−0.716213	−	0.697882i	$-0.754126\pi$
$229$	−0.277401	+	0.277401i	−0.0183312	+	0.0183312i	0.697882	+	0.716213i	$0.254126\pi$
$230$		0			0
$231$	0.970446	−	2.34286i	0.0638507	−	0.154149i
$232$		0			0
$233$	2.29610	+	5.54328i	0.150423	+	0.363152i	0.981072	−	0.193644i	$-0.0620306\pi$
$233$	2.29610	+	5.54328i	0.150423	+	0.363152i	−0.830649	+	0.556796i	$0.812031\pi$
$234$		0			0
$235$	−22.1731	+	9.18440i	−1.44641	+	0.599124i
$236$		0			0
$237$	−1.32051			−0.0857762
$238$		0			0
$239$	−20.7846			−1.34444			−0.672222	−	0.740349i	$-0.734660\pi$
$239$	−20.7846			−1.34444			−0.672222	+	0.740349i	$0.734660\pi$
$240$		0			0
$241$	1.84776	−	0.765367i	0.119025	−	0.0493016i	−0.322376	−	0.946612i	$-0.604482\pi$
$241$	1.84776	−	0.765367i	0.119025	−	0.0493016i	0.441401	+	0.897310i	$0.354482\pi$
$242$		0			0
$243$	5.84279	+	14.1057i	0.374815	+	0.904884i
$244$		0			0
$245$	8.56916	−	20.6878i	0.547464	−	1.32169i
$246$		0			0
$247$	−5.65685	+	5.65685i	−0.359937	+	0.359937i
$248$		0			0
$249$	−6.40083	−	2.65131i	−0.405636	−	0.168020i
$250$		0			0
$251$			6.92820i			0.437304i	0.975803	+	0.218652i	$0.0701660\pi$
$251$			6.92820i			0.437304i	−0.975803	+	0.218652i	$0.929834\pi$
$252$		0			0
$253$	−15.8338	−	15.8338i	−0.995459	−	0.995459i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.37945	−	5.37945i	−0.335561	−	0.335561i	0.519133	−	0.854694i	$-0.326255\pi$
$257$	−5.37945	−	5.37945i	−0.335561	−	0.335561i	−0.854694	+	0.519133i	$0.826255\pi$
$258$		0			0
$259$			8.39230i			0.521472i
$260$		0			0
$261$	7.88614	+	3.26655i	0.488140	+	0.202194i
$262$		0			0
$263$	16.4901	−	16.4901i	1.01682	−	1.01682i	0.0169664	−	0.999856i	$-0.494599\pi$
$263$	16.4901	−	16.4901i	1.01682	−	1.01682i	0.999856	−	0.0169664i	$-0.00540084\pi$
$264$		0			0
$265$	−1.23048	+	2.97063i	−0.0755876	+	0.182485i
$266$		0			0
$267$	−2.65131	−	6.40083i	−0.162257	−	0.391724i
$268$		0			0
$269$	18.9727	−	7.85875i	1.15679	−	0.479156i	0.279982	−	0.960005i	$-0.409671\pi$
$269$	18.9727	−	7.85875i	1.15679	−	0.479156i	0.876803	+	0.480849i	$0.159671\pi$
$270$		0			0
$271$	−14.9282			−0.906824			−0.453412	−	0.891301i	$-0.649793\pi$
$271$	−14.9282			−0.906824			−0.453412	+	0.891301i	$0.649793\pi$
$272$		0			0
$273$	0.784610			0.0474867
$274$		0			0
$275$	−30.6029	+	12.6761i	−1.84543	+	0.764400i
$276$		0			0
$277$	5.50770	+	13.2968i	0.330925	+	0.798925i	0.998519	+	0.0543990i	$0.0173243\pi$
$277$	5.50770	+	13.2968i	0.330925	+	0.798925i	−0.667594	+	0.744526i	$0.732676\pi$
$278$		0			0
$279$	−5.84279	+	14.1057i	−0.349799	+	0.844489i
$280$		0			0
$281$	5.55532	−	5.55532i	0.331403	−	0.331403i	−0.521716	−	0.853119i	$-0.674708\pi$
$281$	5.55532	−	5.55532i	0.331403	−	0.331403i	0.853119	+	0.521716i	$0.174708\pi$
$282$		0			0
$283$	9.78246	+	4.05203i	0.581507	+	0.240868i	0.653992	−	0.756501i	$-0.273093\pi$
$283$	9.78246	+	4.05203i	0.581507	+	0.240868i	−0.0724852	+	0.997369i	$0.523093\pi$
$284$		0			0
$285$			13.8564i			0.820783i
$286$		0			0
$287$	3.10583	+	3.10583i	0.183331	+	0.183331i
$288$		0			0
$289$		0			0
$290$		0			0
$291$	−4.62158	−	4.62158i	−0.270922	−	0.270922i
$292$		0			0
$293$			30.0000i			1.75262i	0.481749	+	0.876309i	$0.340002\pi$
$293$			30.0000i			1.75262i	−0.481749	+	0.876309i	$0.659998\pi$
$294$		0			0
$295$	30.2890	+	12.5461i	1.76350	+	0.730464i
$296$		0			0
$297$	13.3843	−	13.3843i	0.776634	−	0.776634i
$298$		0			0
$299$	2.65131	−	6.40083i	0.153329	−	0.370169i
$300$		0			0
$301$	3.47163	+	8.38125i	0.200101	+	0.483087i
$302$		0			0
$303$	−6.40083	+	2.65131i	−0.367718	+	0.152314i
$304$		0			0
$305$	25.8564			1.48053
$306$		0			0
$307$	16.7846			0.957948			0.478974	−	0.877829i	$-0.341009\pi$
$307$	16.7846			0.957948			0.478974	+	0.877829i	$0.341009\pi$
$308$		0			0
$309$	−1.98042	+	0.820318i	−0.112662	+	0.0466662i
$310$		0			0
$311$	−8.08394	−	19.5164i	−0.458398	−	1.10667i	−0.969046	−	0.246881i	$-0.920594\pi$
$311$	−8.08394	−	19.5164i	−0.458398	−	1.10667i	0.510648	−	0.859790i	$-0.329406\pi$
$312$		0			0
$313$	−2.70626	+	6.53349i	−0.152967	+	0.369295i	−0.981723	−	0.190315i	$-0.939049\pi$
$313$	−2.70626	+	6.53349i	−0.152967	+	0.369295i	0.828756	+	0.559610i	$0.189049\pi$
$314$		0			0
$315$	−4.41851	+	4.41851i	−0.248955	+	0.248955i
$316$		0			0
$317$	−14.2870	−	5.91786i	−0.802436	−	0.332380i	−0.0565043	−	0.998402i	$-0.517995\pi$
$317$	−14.2870	−	5.91786i	−0.802436	−	0.332380i	−0.745932	+	0.666022i	$0.767995\pi$
$318$		0			0
$319$		−	16.3923i		−	0.917793i
$320$		0			0
$321$	3.76217	+	3.76217i	0.209984	+	0.209984i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−7.24693	−	7.24693i	−0.401988	−	0.401988i
$326$		0			0
$327$		−	4.67949i		−	0.258776i
$328$		0			0
$329$	4.68573	+	1.94089i	0.258333	+	0.107005i
$330$		0			0
$331$	10.8332	−	10.8332i	0.595448	−	0.595448i	−0.343650	−	0.939098i	$-0.611663\pi$
$331$	10.8332	−	10.8332i	0.595448	−	0.595448i	0.939098	+	0.343650i	$0.111663\pi$
$332$		0			0
$333$	−10.8103	+	26.0984i	−0.592402	+	1.43018i
$334$		0			0
$335$	1.42083	+	3.43019i	0.0776283	+	0.187411i
$336$		0			0
$337$	−32.1368	+	13.3115i	−1.75060	+	0.725123i	−0.752844	+	0.658199i	$0.771319\pi$
$337$	−32.1368	+	13.3115i	−1.75060	+	0.725123i	−0.997758	+	0.0669248i	$0.978681\pi$
$338$		0			0
$339$	−5.75129			−0.312367
$340$		0			0
$341$	29.3205			1.58779
$342$		0			0
$343$	−9.10613	+	3.77188i	−0.491685	+	0.203663i
$344$		0			0
$345$	−4.59220	−	11.0866i	−0.247236	−	0.596880i
$346$		0			0
$347$	−1.55085	+	3.74408i	−0.0832538	+	0.200993i	−0.960024	−	0.279916i	$-0.909693\pi$
$347$	−1.55085	+	3.74408i	−0.0832538	+	0.200993i	0.876771	+	0.480909i	$0.159693\pi$
$348$		0			0
$349$	−21.7680	+	21.7680i	−1.16521	+	1.16521i	−0.181897	+	0.983318i	$0.558224\pi$
$349$	−21.7680	+	21.7680i	−1.16521	+	1.16521i	−0.983318	+	0.181897i	$0.941776\pi$
$350$		0			0
$351$	5.41061	+	2.24115i	0.288797	+	0.119624i
$352$		0			0
$353$		−	7.85641i		−	0.418154i	−0.977899	−	0.209077i	$-0.932954\pi$
$353$		−	7.85641i		−	0.418154i	0.977899	−	0.209077i	$-0.0670460\pi$
$354$		0			0
$355$	−5.37945	−	5.37945i	−0.285512	−	0.285512i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.00481	+	8.00481i	0.422478	+	0.422478i	0.886056	−	0.463578i	$-0.153435\pi$
$359$	8.00481	+	8.00481i	0.422478	+	0.422478i	−0.463578	+	0.886056i	$0.653435\pi$
$360$		0			0
$361$			10.8564i			0.571390i
$362$		0			0
$363$	−7.70492	−	3.19148i	−0.404403	−	0.167509i
$364$		0			0
$365$	−4.89898	+	4.89898i	−0.256424	+	0.256424i
$366$		0			0
$367$	7.52365	−	18.1637i	0.392732	−	0.948138i	−0.596611	−	0.802531i	$-0.703486\pi$
$367$	7.52365	−	18.1637i	0.392732	−	0.948138i	0.989342	−	0.145607i	$-0.0465136\pi$
$368$		0			0
$369$	5.65783	+	13.6592i	0.294535	+	0.711069i
$370$		0			0
$371$	0.627769	−	0.260030i	0.0325921	−	0.0135001i
$372$		0			0
$373$	−12.3923			−0.641649			−0.320825	−	0.947139i	$-0.603960\pi$
$373$	−12.3923			−0.641649			−0.320825	+	0.947139i	$0.603960\pi$
$374$		0			0
$375$	−5.07180			−0.261906
$376$		0			0
$377$	4.68573	−	1.94089i	0.241327	−	0.0999611i
$378$		0			0
$379$	3.34161	+	8.06736i	0.171647	+	0.414393i	0.986170	−	0.165739i	$-0.0530010\pi$
$379$	3.34161	+	8.06736i	0.171647	+	0.414393i	−0.814523	+	0.580132i	$0.803001\pi$
$380$		0			0
$381$	−5.71278	+	13.7919i	−0.292674	+	0.706578i
$382$		0			0
$383$	−6.69213	+	6.69213i	−0.341952	+	0.341952i	−0.857101	−	0.515149i	$-0.827737\pi$
$383$	−6.69213	+	6.69213i	−0.341952	+	0.341952i	0.515149	+	0.857101i	$0.327737\pi$
$384$		0			0
$385$	11.0866	+	4.59220i	0.565023	+	0.234040i
$386$		0			0
$387$			30.5359i			1.55223i
$388$		0			0
$389$	17.8028	+	17.8028i	0.902636	+	0.902636i	0.995664	−	0.0930274i	$-0.0296544\pi$
$389$	17.8028	+	17.8028i	0.902636	+	0.902636i	−0.0930274	+	0.995664i	$0.529654\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	6.03579	+	6.03579i	0.304465	+	0.304465i
$394$		0			0
$395$		−	6.24871i		−	0.314407i
$396$		0			0
$397$	−24.3833	−	10.0999i	−1.22376	−	0.506899i	−0.325159	−	0.945659i	$-0.605418\pi$
$397$	−24.3833	−	10.0999i	−1.22376	−	0.506899i	−0.898604	+	0.438760i	$0.855418\pi$
$398$		0			0
$399$	2.07055	−	2.07055i	0.103657	−	0.103657i
$400$		0			0
$401$	1.58568	−	3.82818i	0.0791853	−	0.191170i	−0.879329	−	0.476215i	$-0.842008\pi$
$401$	1.58568	−	3.82818i	0.0791853	−	0.191170i	0.958514	+	0.285045i	$0.0920084\pi$
$402$		0			0
$403$	3.47163	+	8.38125i	0.172934	+	0.417500i
$404$		0			0
$405$	−14.2870	+	5.91786i	−0.709925	+	0.294061i
$406$		0			0
$407$	54.2487			2.68901
$408$		0			0
$409$	−37.7128			−1.86478			−0.932389	−	0.361456i	$-0.882280\pi$
$409$	−37.7128			−1.86478			−0.932389	+	0.361456i	$0.882280\pi$
$410$		0			0
$411$	−6.40083	+	2.65131i	−0.315729	+	0.130779i
$412$		0			0
$413$	−2.65131	−	6.40083i	−0.130462	−	0.314964i
$414$		0			0
$415$	12.5461	−	30.2890i	0.615865	−	1.48683i
$416$		0			0
$417$	5.83272	−	5.83272i	0.285630	−	0.285630i
$418$		0			0
$419$	−6.08694	−	2.52129i	−0.297367	−	0.123173i	0.229012	−	0.973424i	$-0.426450\pi$
$419$	−6.08694	−	2.52129i	−0.297367	−	0.123173i	−0.526379	+	0.850250i	$0.676450\pi$
$420$		0			0
$421$		−	26.2487i		−	1.27928i	−0.768673	−	0.639642i	$-0.779083\pi$
$421$		−	26.2487i		−	1.27928i	0.768673	−	0.639642i	$-0.220917\pi$
$422$		0			0
$423$	12.0716	+	12.0716i	0.586940	+	0.586940i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.86370	−	3.86370i	−0.186978	−	0.186978i
$428$		0			0
$429$		−	5.07180i		−	0.244869i
$430$		0			0
$431$	0.313884	+	0.130015i	0.0151193	+	0.00626261i	0.390230	−	0.920717i	$-0.372395\pi$
$431$	0.313884	+	0.130015i	0.0151193	+	0.00626261i	−0.375111	+	0.926980i	$0.622395\pi$
$432$		0			0
$433$	−17.2480	+	17.2480i	−0.828884	+	0.828884i	−0.987362	−	0.158478i	$-0.949341\pi$
$433$	−17.2480	+	17.2480i	−0.828884	+	0.828884i	0.158478	+	0.987362i	$0.449341\pi$
$434$		0			0
$435$	3.36172	−	8.11592i	0.161182	−	0.389129i
$436$		0			0
$437$	−9.89482	−	23.8882i	−0.473333	−	1.14273i
$438$		0			0
$439$	12.7531	−	5.28250i	0.608672	−	0.252120i	−0.0569887	−	0.998375i	$-0.518150\pi$
$439$	12.7531	−	5.28250i	0.608672	−	0.252120i	0.665661	+	0.746255i	$0.268150\pi$
$440$		0			0
$441$	−15.9282			−0.758486
$442$		0			0
$443$	20.7846			0.987507			0.493753	−	0.869602i	$-0.335625\pi$
$443$	20.7846			0.987507			0.493753	+	0.869602i	$0.335625\pi$
$444$		0			0
$445$	30.2890	−	12.5461i	1.43584	−	0.594743i
$446$		0			0
$447$	1.68086	+	4.05796i	0.0795021	+	0.191935i
$448$		0			0
$449$	−2.29610	+	5.54328i	−0.108360	+	0.261603i	−0.968753	−	0.248027i	$-0.920218\pi$
$449$	−2.29610	+	5.54328i	−0.108360	+	0.261603i	0.860393	+	0.509630i	$0.170218\pi$
$450$		0			0
$451$	20.0764	−	20.0764i	0.945360	−	0.945360i
$452$		0			0
$453$	−4.42040	−	1.83099i	−0.207689	−	0.0860275i
$454$		0			0
$455$			3.71281i			0.174059i
$456$		0			0
$457$	−0.277401	−	0.277401i	−0.0129763	−	0.0129763i	0.700589	−	0.713565i	$-0.252921\pi$
$457$	−0.277401	−	0.277401i	−0.0129763	−	0.0129763i	−0.713565	+	0.700589i	$0.752921\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.4543	−	10.4543i	−0.486905	−	0.486905i	0.420423	−	0.907328i	$-0.361882\pi$
$461$	−10.4543	−	10.4543i	−0.486905	−	0.486905i	−0.907328	+	0.420423i	$0.861882\pi$
$462$		0			0
$463$		−	29.8564i		−	1.38754i	−0.720194	−	0.693772i	$-0.755947\pi$
$463$		−	29.8564i		−	1.38754i	0.720194	−	0.693772i	$-0.244053\pi$
$464$		0			0
$465$	14.5167	+	6.01303i	0.673198	+	0.278848i
$466$		0			0
$467$	−15.1774	+	15.1774i	−0.702327	+	0.702327i	−0.964910	−	0.262583i	$-0.915426\pi$
$467$	−15.1774	+	15.1774i	−0.702327	+	0.702327i	0.262583	+	0.964910i	$0.415426\pi$
$468$		0			0
$469$	0.300257	−	0.724885i	0.0138646	−	0.0334721i
$470$		0			0
$471$	−0.560287	−	1.35265i	−0.0258167	−	0.0623270i
$472$		0			0
$473$	54.1772	−	22.4409i	2.49107	−	1.03184i
$474$		0			0
$475$	−38.2487			−1.75497
$476$		0			0
$477$	2.28719			0.104723
$478$		0			0
$479$	−0.313884	+	0.130015i	−0.0143417	+	0.00594054i	−0.389843	−	0.920881i	$-0.627471\pi$
$479$	−0.313884	+	0.130015i	−0.0143417	+	0.00594054i	0.375501	+	0.926822i	$0.377471\pi$
$480$		0			0
$481$	6.42319	+	15.5070i	0.292872	+	0.707056i
$482$		0			0
$483$	−0.970446	+	2.34286i	−0.0441568	+	0.106604i
$484$		0			0
$485$	21.8695	−	21.8695i	0.993045	−	0.993045i
$486$		0			0
$487$	29.6127	+	12.2660i	1.34188	+	0.555825i	0.934020	−	0.357220i	$-0.116275\pi$
$487$	29.6127	+	12.2660i	1.34188	+	0.555825i	0.407859	+	0.913045i	$0.366275\pi$
$488$		0			0
$489$		−	7.75129i		−	0.350525i
$490$		0			0
$491$	−17.8028	−	17.8028i	−0.803428	−	0.803428i	0.180202	−	0.983630i	$-0.442325\pi$
$491$	−17.8028	−	17.8028i	−0.803428	−	0.803428i	−0.983630	+	0.180202i	$0.942325\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	28.5617	+	28.5617i	1.28375	+	1.28375i
$496$		0			0
$497$			1.60770i			0.0721150i
$498$		0			0
$499$	−24.9270	−	10.3251i	−1.11588	−	0.462215i	−0.252924	−	0.967486i	$-0.581392\pi$
$499$	−24.9270	−	10.3251i	−1.11588	−	0.462215i	−0.862960	+	0.505272i	$0.831392\pi$
$500$		0			0
$501$	−6.03579	+	6.03579i	−0.269659	+	0.269659i
$502$		0			0
$503$	1.10046	−	2.65675i	0.0490672	−	0.118459i	−0.897445	−	0.441125i	$-0.854579\pi$
$503$	1.10046	−	2.65675i	0.0490672	−	0.118459i	0.946513	+	0.322667i	$0.104579\pi$
$504$		0			0
$505$	−12.5461	−	30.2890i	−0.558295	−	1.34784i
$506$		0			0
$507$	−7.34248	+	3.04135i	−0.326091	+	0.135071i
$508$		0			0
$509$	−33.7128			−1.49429			−0.747147	−	0.664659i	$-0.768577\pi$
$509$	−33.7128			−1.49429			−0.747147	+	0.664659i	$0.768577\pi$
$510$		0			0
$511$	1.46410			0.0647680
$512$		0			0
$513$	20.1927	−	8.36408i	0.891529	−	0.369283i
$514$		0			0
$515$	−3.88179	−	9.37146i	−0.171052	−	0.412956i
$516$		0			0
$517$	12.5461	−	30.2890i	0.551778	−	1.33211i
$518$		0			0
$519$	4.41851	−	4.41851i	0.193951	−	0.193951i
$520$		0			0
$521$	5.54328	+	2.29610i	0.242855	+	0.100594i	0.500791	−	0.865568i	$-0.333042\pi$
$521$	5.54328	+	2.29610i	0.242855	+	0.100594i	−0.257936	+	0.966162i	$0.583042\pi$
$522$		0			0
$523$		−	28.7846i		−	1.25866i	−0.777137	−	0.629332i	$-0.783329\pi$
$523$		−	28.7846i		−	1.25866i	0.777137	−	0.629332i	$-0.216671\pi$
$524$		0			0
$525$	2.65256	+	2.65256i	0.115767	+	0.115767i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.429705	−	0.429705i	−0.0186828	−	0.0186828i
$530$		0			0
$531$		−	23.3205i		−	1.01202i
$532$		0			0
$533$	8.11592	+	3.36172i	0.351540	+	0.145612i
$534$		0			0
$535$	−17.8028	+	17.8028i	−0.769681	+	0.769681i
$536$		0			0
$537$	−6.01303	+	14.5167i	−0.259482	+	0.626444i
$538$		0			0
$539$	11.7057	+	28.2600i	0.504200	+	1.21725i
$540$		0			0
$541$	2.21020	−	0.915495i	0.0950240	−	0.0393602i	−0.334665	−	0.942337i	$-0.608623\pi$
$541$	2.21020	−	0.915495i	0.0950240	−	0.0393602i	0.429689	+	0.902977i	$0.358623\pi$
$542$		0			0
$543$	8.39230			0.360148
$544$		0			0
$545$	22.1436			0.948527
$546$		0			0
$547$	36.2789	−	15.0272i	1.55117	−	0.642516i	0.567644	−	0.823274i	$-0.307855\pi$
$547$	36.2789	−	15.0272i	1.55117	−	0.642516i	0.983528	+	0.180758i	$0.0578550\pi$
$548$		0			0
$549$	−7.03843	−	16.9923i	−0.300393	−	0.725213i
$550$		0			0
$551$	7.24351	−	17.4874i	0.308584	−	0.744987i
$552$		0			0
$553$	−0.933740	+	0.933740i	−0.0397067	+	0.0397067i
$554$		0			0
$555$	26.8588	+	11.1253i	1.14009	+	0.472242i
$556$		0			0
$557$			33.4641i			1.41792i	0.705249	+	0.708960i	$0.250835\pi$
$557$			33.4641i			1.41792i	−0.705249	+	0.708960i	$0.749165\pi$
$558$		0			0
$559$	12.8295	+	12.8295i	0.542628	+	0.542628i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.480473	−	0.480473i	−0.0202495	−	0.0202495i	0.696910	−	0.717159i	$-0.254558\pi$
$563$	−0.480473	−	0.480473i	−0.0202495	−	0.0202495i	−0.717159	+	0.696910i	$0.754558\pi$
$564$		0			0
$565$		−	27.2154i		−	1.14496i
$566$		0			0
$567$	3.01919	+	1.25059i	0.126794	+	0.0525198i
$568$		0			0
$569$	−14.0406	+	14.0406i	−0.588613	+	0.588613i	−0.937256	−	0.348643i	$-0.886643\pi$
$569$	−14.0406	+	14.0406i	−0.588613	+	0.588613i	0.348643	+	0.937256i	$0.386643\pi$
$570$		0			0
$571$	−5.02247	+	12.1253i	−0.210184	+	0.507429i	−0.993451	−	0.114256i	$-0.963552\pi$
$571$	−5.02247	+	12.1253i	−0.210184	+	0.507429i	0.783267	+	0.621685i	$0.213552\pi$
$572$		0			0
$573$	−3.36172	−	8.11592i	−0.140438	−	0.339047i
$574$		0			0
$575$	30.6029	−	12.6761i	1.27623	−	0.528632i
$576$		0			0
$577$	6.53590			0.272093			0.136047	−	0.990702i	$-0.456560\pi$
$577$	6.53590			0.272093			0.136047	+	0.990702i	$0.456560\pi$
$578$		0			0
$579$	−5.17691			−0.215145
$580$		0			0
$581$	−6.40083	+	2.65131i	−0.265551	+	0.109995i
$582$		0			0
$583$	−1.68086	−	4.05796i	−0.0696142	−	0.168064i
$584$		0			0
$585$	−4.78256	+	11.5461i	−0.197734	+	0.477373i
$586$		0			0
$587$	5.37945	−	5.37945i	0.222034	−	0.222034i	−0.587321	−	0.809354i	$-0.699817\pi$
$587$	5.37945	−	5.37945i	0.222034	−	0.222034i	0.809354	+	0.587321i	$0.199817\pi$
$588$		0			0
$589$	31.2792	+	12.9563i	1.28884	+	0.533854i
$590$		0			0
$591$		−	2.53590i		−	0.104313i
$592$		0			0
$593$	22.5259	+	22.5259i	0.925027	+	0.925027i	0.997379	−	0.0723521i	$-0.0230505\pi$
$593$	22.5259	+	22.5259i	0.925027	+	0.925027i	−0.0723521	+	0.997379i	$0.523051\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.20736	+	3.20736i	0.131269	+	0.131269i
$598$		0			0
$599$			27.7128i			1.13231i	0.824297	+	0.566157i	$0.191571\pi$
$599$			27.7128i			1.13231i	−0.824297	+	0.566157i	$0.808429\pi$
$600$		0			0
$601$	−28.4413	−	11.7808i	−1.16014	−	0.480547i	−0.282221	−	0.959349i	$-0.591071\pi$
$601$	−28.4413	−	11.7808i	−1.16014	−	0.480547i	−0.877923	+	0.478802i	$0.841071\pi$
$602$		0			0
$603$	1.86748	−	1.86748i	0.0760497	−	0.0760497i
$604$		0			0
$605$	15.1023	−	36.4601i	0.613994	−	1.48231i
$606$		0			0
$607$	−13.4965	−	32.5833i	−0.547804	−	1.32252i	−0.919108	−	0.394005i	$-0.871089\pi$
$607$	−13.4965	−	32.5833i	−0.547804	−	1.32252i	0.371304	−	0.928511i	$-0.378911\pi$
$608$		0			0
$609$	−1.71510	+	0.710416i	−0.0694992	+	0.0287875i
$610$		0			0
$611$	10.1436			0.410366
$612$		0			0
$613$	−20.1436			−0.813592			−0.406796	−	0.913519i	$-0.633354\pi$
$613$	−20.1436			−0.813592			−0.406796	+	0.913519i	$0.633354\pi$
$614$		0			0
$615$	14.0572	−	5.82268i	0.566841	−	0.234793i
$616$		0			0
$617$	−18.2040	−	43.9482i	−0.732864	−	1.76929i	−0.632810	−	0.774307i	$-0.718099\pi$
$617$	−18.2040	−	43.9482i	−0.732864	−	1.76929i	−0.100053	−	0.994982i	$-0.531901\pi$
$618$		0			0
$619$	−8.49410	+	20.5066i	−0.341407	+	0.824229i	0.656167	+	0.754615i	$0.272177\pi$
$619$	−8.49410	+	20.5066i	−0.341407	+	0.824229i	−0.997574	+	0.0696133i	$0.977823\pi$
$620$		0			0
$621$	−13.3843	+	13.3843i	−0.537092	+	0.537092i
$622$		0			0
$623$	−6.40083	−	2.65131i	−0.256444	−	0.106222i
$624$		0			0
$625$			11.0000i			0.440000i
$626$		0			0
$627$	−13.3843	−	13.3843i	−0.534516	−	0.534516i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	24.4206	+	24.4206i	0.972167	+	0.972167i	0.999623	−	0.0274556i	$-0.00874048\pi$
$631$	24.4206	+	24.4206i	0.972167	+	0.972167i	−0.0274556	+	0.999623i	$0.508740\pi$
$632$		0			0
$633$		−	14.3923i		−	0.572043i
$634$		0			0
$635$	−65.2638	−	27.0331i	−2.58991	−	1.07278i
$636$		0			0
$637$	−6.69213	+	6.69213i	−0.265152	+	0.265152i
$638$		0			0
$639$	−2.07091	+	4.99961i	−0.0819238	+	0.197782i
$640$		0			0
$641$	0.355208	+	0.857548i	0.0140299	+	0.0338711i	0.930739	−	0.365684i	$-0.119165\pi$
$641$	0.355208	+	0.857548i	0.0140299	+	0.0338711i	−0.916709	+	0.399555i	$0.869165\pi$
$642$		0			0
$643$	−1.30410	+	0.540174i	−0.0514285	+	0.0213024i	−0.408249	−	0.912870i	$-0.633861\pi$
$643$	−1.30410	+	0.540174i	−0.0514285	+	0.0213024i	0.356821	+	0.934173i	$0.383861\pi$
$644$		0			0
$645$	31.4256			1.23738
$646$		0			0
$647$	30.9282			1.21591			0.607957	−	0.793970i	$-0.291989\pi$
$647$	30.9282			1.21591			0.607957	+	0.793970i	$0.291989\pi$
$648$		0			0
$649$	−41.3756	+	17.1383i	−1.62413	+	0.672738i
$650$		0			0
$651$	−1.27070	−	3.06775i	−0.0498028	−	0.120235i
$652$		0			0
$653$	−3.97696	+	9.60124i	−0.155631	+	0.375725i	−0.982393	−	0.186826i	$-0.940180\pi$
$653$	−3.97696	+	9.60124i	−0.155631	+	0.375725i	0.826763	+	0.562551i	$0.190180\pi$
$654$		0			0
$655$	−28.5617	+	28.5617i	−1.11600	+	1.11600i
$656$		0			0
$657$	4.55307	+	1.88594i	0.177632	+	0.0735776i
$658$		0			0
$659$		−	29.0718i		−	1.13248i	−0.824242	−	0.566238i	$-0.808398\pi$
$659$		−	29.0718i		−	1.13248i	0.824242	−	0.566238i	$-0.191602\pi$
$660$		0			0
$661$	20.4553	+	20.4553i	0.795620	+	0.795620i	0.982401	−	0.186781i	$-0.0598056\pi$
$661$	20.4553	+	20.4553i	0.795620	+	0.795620i	−0.186781	+	0.982401i	$0.559806\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	9.79796	+	9.79796i	0.379949	+	0.379949i
$666$		0			0
$667$			16.3923i			0.634713i
$668$		0			0
$669$	5.67594	+	2.35105i	0.219445	+	0.0908969i
$670$		0			0
$671$	−24.9754	+	24.9754i	−0.964163	+	0.964163i
$672$		0			0
$673$	10.6602	−	25.7360i	0.410920	−	0.992048i	−0.573971	−	0.818875i	$-0.694598\pi$
$673$	10.6602	−	25.7360i	0.410920	−	0.992048i	0.984891	−	0.173173i	$-0.0554020\pi$
$674$		0			0
$675$	10.7151	+	25.8686i	0.412426	+	0.995684i
$676$		0			0
$677$	−22.4029	+	9.27958i	−0.861013	+	0.356643i	−0.769104	−	0.639124i	$-0.779297\pi$
$677$	−22.4029	+	9.27958i	−0.861013	+	0.356643i	−0.0919093	+	0.995767i	$0.529297\pi$
$678$		0			0
$679$	−6.53590			−0.250825
$680$		0			0
$681$	7.17691			0.275020
$682$		0			0
$683$	−7.34248	+	3.04135i	−0.280952	+	0.116374i	−0.518710	−	0.854950i	$-0.673588\pi$
$683$	−7.34248	+	3.04135i	−0.280952	+	0.116374i	0.237758	+	0.971324i	$0.423588\pi$
$684$		0			0
$685$	−12.5461	−	30.2890i	−0.479363	−	1.15728i
$686$		0			0
$687$	0.109902	−	0.265326i	0.00419301	−	0.0101228i
$688$		0			0
$689$	0.960947	−	0.960947i	0.0366092	−	0.0366092i
$690$		0			0
$691$	23.8396	+	9.87470i	0.906903	+	0.375651i	0.786870	−	0.617118i	$-0.211700\pi$
$691$	23.8396	+	9.87470i	0.906903	+	0.375651i	0.120033	+	0.992770i	$0.461700\pi$
$692$		0			0
$693$		−	8.53590i		−	0.324252i
$694$		0			0
$695$	27.6007	+	27.6007i	1.04696	+	1.04696i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−3.10583	−	3.10583i	−0.117473	−	0.117473i
$700$		0			0
$701$			4.39230i			0.165895i	0.996554	+	0.0829475i	$0.0264334\pi$
$701$			4.39230i			0.165895i	−0.996554	+	0.0829475i	$0.973567\pi$
$702$		0			0
$703$	57.8728	+	23.9717i	2.18271	+	0.904109i
$704$		0			0
$705$	12.4233	−	12.4233i	0.467889	−	0.467889i
$706$		0			0
$707$	−2.65131	+	6.40083i	−0.0997127	+	0.240728i
$708$		0			0
$709$	12.3410	+	29.7939i	0.463478	+	1.11893i	0.966960	+	0.254929i	$0.0820520\pi$
$709$	12.3410	+	29.7939i	0.463478	+	1.11893i	−0.503482	+	0.864006i	$0.667948\pi$
$710$		0			0
$711$	−4.10652	+	1.70098i	−0.154006	+	0.0637916i
$712$		0			0
$713$	−29.3205			−1.09806
$714$		0			0
$715$	24.0000			0.897549
$716$		0			0
$717$	14.0572	−	5.82268i	0.524975	−	0.217452i
$718$		0			0
$719$	0.580401	+	1.40121i	0.0216453	+	0.0522564i	0.934333	−	0.356402i	$-0.115997\pi$
$719$	0.580401	+	1.40121i	0.0216453	+	0.0522564i	−0.912687	+	0.408659i	$0.865997\pi$
$720$		0			0
$721$	−0.820318	+	1.98042i	−0.0305502	+	0.0737548i
$722$		0			0
$723$	−1.03528	+	1.03528i	−0.0385023	+	0.0385023i
$724$		0			0
$725$	22.4029	+	9.27958i	0.832022	+	0.344635i
$726$		0			0
$727$			36.7846i			1.36427i	0.731228	+	0.682133i	$0.238947\pi$
$727$			36.7846i			1.36427i	−0.731228	+	0.682133i	$0.761053\pi$
$728$		0			0
$729$	1.56652	+	1.56652i	0.0580192	+	0.0580192i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	16.1112	+	16.1112i	0.595079	+	0.595079i	0.938999	−	0.343920i	$-0.111755\pi$
$733$	16.1112	+	16.1112i	0.595079	+	0.595079i	−0.343920	+	0.938999i	$0.611755\pi$
$734$		0			0
$735$			16.3923i			0.604639i
$736$		0			0
$737$	−4.68573	−	1.94089i	−0.172601	−	0.0714937i
$738$		0			0
$739$	5.93426	−	5.93426i	0.218295	−	0.218295i	−0.589485	−	0.807780i	$-0.700669\pi$
$739$	5.93426	−	5.93426i	0.218295	−	0.218295i	0.807780	+	0.589485i	$0.200669\pi$
$740$		0			0
$741$	2.24115	−	5.41061i	0.0823307	−	0.198764i
$742$		0			0
$743$	−16.0379	−	38.7188i	−0.588372	−	1.42046i	−0.885058	−	0.465481i	$-0.845881\pi$
$743$	−16.0379	−	38.7188i	−0.588372	−	1.42046i	0.296686	−	0.954975i	$-0.404119\pi$
$744$		0			0
$745$	−19.2025	+	7.95393i	−0.703524	+	0.291409i
$746$		0			0
$747$	−23.3205			−0.853253
$748$		0			0
$749$	5.32051			0.194407
$750$		0			0
$751$	14.1057	−	5.84279i	0.514726	−	0.213206i	−0.110173	−	0.993912i	$-0.535140\pi$
$751$	14.1057	−	5.84279i	0.514726	−	0.213206i	0.624899	+	0.780706i	$0.285140\pi$
$752$		0			0
$753$	−1.94089	−	4.68573i	−0.0707301	−	0.170757i
$754$		0			0
$755$	8.66434	−	20.9176i	0.315328	−	0.761268i
$756$		0			0
$757$	7.45001	−	7.45001i	0.270775	−	0.270775i	−0.558637	−	0.829412i	$-0.688676\pi$
$757$	7.45001	−	7.45001i	0.270775	−	0.270775i	0.829412	+	0.558637i	$0.188676\pi$
$758$		0			0
$759$	15.1445	+	6.27306i	0.549711	+	0.227698i
$760$		0			0
$761$			4.39230i			0.159221i	0.996826	+	0.0796105i	$0.0253676\pi$
$761$			4.39230i			0.159221i	−0.996826	+	0.0796105i	$0.974632\pi$
$762$		0			0
$763$	−3.30890	−	3.30890i	−0.119790	−	0.119790i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.79796	−	9.79796i	−0.353784	−	0.353784i
$768$		0			0
$769$		−	20.3923i		−	0.735365i	−0.929951	−	0.367683i	$-0.880151\pi$
$769$		−	20.3923i		−	0.735365i	0.929951	−	0.367683i	$-0.119849\pi$
$770$		0			0
$771$	5.14529	+	2.13125i	0.185303	+	0.0767550i
$772$		0			0
$773$	24.9754	−	24.9754i	0.898302	−	0.898302i	−0.0969843	−	0.995286i	$-0.530920\pi$
$773$	24.9754	−	24.9754i	0.898302	−	0.898302i	0.995286	+	0.0969843i	$0.0309197\pi$
$774$		0			0
$775$	−16.5982	+	40.0715i	−0.596223	+	1.43941i
$776$		0			0
$777$	−2.35105	−	5.67594i	−0.0843435	−	0.203623i
$778$		0			0
$779$	30.2890	−	12.5461i	1.08522	−	0.449512i
$780$		0			0
$781$	10.3923			0.371866
$782$		0			0
$783$	−13.8564			−0.495188
$784$		0			0
$785$	6.40083	−	2.65131i	0.228455	−	0.0946293i
$786$		0			0
$787$	0.430272	+	1.03877i	0.0153376	+	0.0370281i	0.931363	−	0.364093i	$-0.118621\pi$
$787$	0.430272	+	1.03877i	0.0153376	+	0.0370281i	−0.916025	+	0.401121i	$0.868621\pi$
$788$		0			0
$789$	−6.53309	+	15.7723i	−0.232584	+	0.561508i
$790$		0			0
$791$	−4.06678	+	4.06678i	−0.144598	+	0.144598i
$792$		0			0
$793$	−10.0963	−	4.18204i	−0.358532	−	0.148509i
$794$		0			0
$795$		−	2.35383i		−	0.0834817i
$796$		0			0
$797$	−27.4249	−	27.4249i	−0.971438	−	0.971438i	0.0281649	−	0.999603i	$-0.491034\pi$
$797$	−27.4249	−	27.4249i	−0.971438	−	0.971438i	−0.999603	+	0.0281649i	$0.991034\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−16.4901	−	16.4901i	−0.582649	−	0.582649i
$802$		0			0
$803$		−	9.46410i		−	0.333981i
$804$		0			0
$805$	−11.0866	−	4.59220i	−0.390750	−	0.161854i
$806$		0			0
$807$	−10.6302	+	10.6302i	−0.374199	+	0.374199i
$808$		0			0
$809$	7.59872	−	18.3449i	0.267157	−	0.644973i	−0.732191	−	0.681100i	$-0.761502\pi$
$809$	7.59872	−	18.3449i	0.267157	−	0.644973i	0.999347	+	0.0361266i	$0.0115019\pi$
$810$		0			0
$811$	13.5367	+	32.6805i	0.475337	+	1.14757i	0.961773	+	0.273849i	$0.0882969\pi$
$811$	13.5367	+	32.6805i	0.475337	+	1.14757i	−0.486435	+	0.873717i	$0.661703\pi$
$812$		0			0
$813$	10.0963	−	4.18204i	0.354094	−	0.146671i
$814$		0			0
$815$	36.6795			1.28483
$816$		0			0
$817$	67.7128			2.36897
$818$		0			0
$819$	2.43998	−	1.01067i	0.0852598	−	0.0353158i
$820$		0			0
$821$	17.2335	+	41.6054i	0.601454	+	1.45204i	0.872085	+	0.489354i	$0.162767\pi$
$821$	17.2335	+	41.6054i	0.601454	+	1.45204i	−0.270632	+	0.962683i	$0.587233\pi$
$822$		0			0
$823$	5.99292	−	14.4682i	0.208900	−	0.504329i	−0.784350	−	0.620318i	$-0.787004\pi$
$823$	5.99292	−	14.4682i	0.208900	−	0.504329i	0.993251	+	0.115989i	$0.0370036\pi$
$824$		0			0
$825$	17.1464	−	17.1464i	0.596962	−	0.596962i
$826$		0			0
$827$	−23.5743	−	9.76480i	−0.819759	−	0.339555i	−0.0669189	−	0.997758i	$-0.521317\pi$
$827$	−23.5743	−	9.76480i	−0.819759	−	0.339555i	−0.752841	+	0.658203i	$0.771317\pi$
$828$		0			0
$829$		−	12.1436i		−	0.421764i	−0.977511	−	0.210882i	$-0.932366\pi$
$829$		−	12.1436i		−	0.421764i	0.977511	−	0.210882i	$-0.0676337\pi$
$830$		0			0
$831$	−7.45001	−	7.45001i	−0.258438	−	0.258438i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−28.5617	−	28.5617i	−0.988417	−	0.988417i
$836$		0			0
$837$		−	24.7846i		−	0.856681i
$838$		0			0
$839$	45.7474	+	18.9492i	1.57938	+	0.654199i	0.988315	−	0.152427i	$-0.0487089\pi$
$839$	45.7474	+	18.9492i	1.57938	+	0.654199i	0.591062	+	0.806626i	$0.298709\pi$
$840$		0			0
$841$	12.0208	−	12.0208i	0.414511	−	0.414511i
$842$		0			0
$843$	−2.20092	+	5.31350i	−0.0758038	+	0.183007i
$844$		0			0
$845$	−14.3918	−	34.7450i	−0.495094	−	1.19526i
$846$		0			0
$847$	−7.70492	+	3.19148i	−0.264744	+	0.109661i
$848$		0			0
$849$	−7.75129			−0.266024
$850$		0			0
$851$	−54.2487			−1.85962
$852$		0			0
$853$	−37.1850	+	15.4025i	−1.27319	+	0.527372i	−0.913932	−	0.405867i	$-0.866970\pi$
$853$	−37.1850	+	15.4025i	−1.27319	+	0.527372i	−0.359257	+	0.933239i	$0.616970\pi$
$854$		0			0
$855$	17.8487	+	43.0907i	0.610414	+	1.47367i
$856$		0			0
$857$	20.1448	−	48.6340i	0.688135	−	1.66130i	−0.0603709	−	0.998176i	$-0.519228\pi$
$857$	20.1448	−	48.6340i	0.688135	−	1.66130i	0.748506	−	0.663128i	$-0.230772\pi$
$858$		0			0
$859$	5.17638	−	5.17638i	0.176616	−	0.176616i	−0.613263	−	0.789879i	$-0.710143\pi$
$859$	5.17638	−	5.17638i	0.176616	−	0.176616i	0.789879	+	0.613263i	$0.210143\pi$
$860$		0			0
$861$	−2.97063	−	1.23048i	−0.101239	−	0.0419345i
$862$		0			0
$863$		−	37.8564i		−	1.28865i	−0.764753	−	0.644324i	$-0.777139\pi$
$863$		−	37.8564i		−	1.28865i	0.764753	−	0.644324i	$-0.222861\pi$
$864$		0			0
$865$	20.9086	+	20.9086i	0.710914	+	0.710914i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	6.03579	+	6.03579i	0.204750	+	0.204750i
$870$		0			0
$871$		−	1.56922i		−	0.0531710i
$872$		0			0
$873$	−20.3253	−	8.41904i	−0.687909	−	0.284941i
$874$		0			0
$875$	−3.58630	+	3.58630i	−0.121239	+	0.121239i
$876$		0			0
$877$	11.6306	−	28.0788i	0.392739	−	0.948155i	−0.596602	−	0.802537i	$-0.703483\pi$
$877$	11.6306	−	28.0788i	0.392739	−	0.948155i	0.989341	−	0.145618i	$-0.0465170\pi$
$878$		0			0
$879$	−8.40431	−	20.2898i	−0.283470	−	0.684358i
$880$		0			0
$881$	−2.57264	+	1.06562i	−0.0866746	+	0.0359018i	−0.425599	−	0.904912i	$-0.639937\pi$
$881$	−2.57264	+	1.06562i	−0.0866746	+	0.0359018i	0.338925	+	0.940813i	$0.389937\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	−24.0000			−0.806751
$886$		0			0
$887$	39.3466	−	16.2979i	1.32113	−	0.547230i	0.393018	−	0.919531i	$-0.371431\pi$
$887$	39.3466	−	16.2979i	1.32113	−	0.547230i	0.928112	+	0.372301i	$0.121431\pi$
$888$		0			0
$889$	5.71278	+	13.7919i	0.191600	+	0.462564i
$890$		0			0
$891$	8.08394	−	19.5164i	0.270822	−	0.653823i
$892$		0			0
$893$	26.7685	−	26.7685i	0.895774	−	0.895774i
$894$		0			0
$895$	−68.6940	−	28.4540i	−2.29619	−	0.951112i
$896$		0			0
$897$			5.07180i			0.169342i
$898$		0			0
$899$	−15.1774	−	15.1774i	−0.506195	−	0.506195i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−4.69591	−	4.69591i	−0.156270	−	0.156270i
$904$		0			0
$905$			39.7128i			1.32010i
$906$		0			0
$907$	−22.5841	−	9.35464i	−0.749893	−	0.310616i	−0.0251951	−	0.999683i	$-0.508021\pi$
$907$	−22.5841	−	9.35464i	−0.749893	−	0.310616i	−0.724698	+	0.689067i	$0.758021\pi$
$908$		0			0
$909$	−16.4901	+	16.4901i	−0.546942	+	0.546942i
$910$		0			0
$911$	−10.0248	+	24.2021i	−0.332138	+	0.801851i	0.666285	+	0.745698i	$0.267884\pi$
$911$	−10.0248	+	24.2021i	−0.332138	+	0.801851i	−0.998422	+	0.0561534i	$0.982116\pi$
$912$		0			0
$913$	17.1383	+	41.3756i	0.567196	+	1.36933i
$914$		0			0
$915$	−17.4874	+	7.24351i	−0.578115	+	0.239463i
$916$		0			0
$917$	8.53590			0.281880
$918$		0			0
$919$	−52.0000			−1.71532			−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000			−1.71532			−0.857661	+	0.514216i	$0.828083\pi$
$920$		0			0
$921$	−11.3519	+	4.70210i	−0.374057	+	0.154940i
$922$		0			0
$923$	1.23048	+	2.97063i	0.0405016	+	0.0977796i
$924$		0			0
$925$	−30.7099	+	74.1401i	−1.00973	+	2.43771i
$926$		0			0
$927$	−5.10205	+	5.10205i	−0.167573	+	0.167573i
$928$		0			0
$929$	−42.2331	−	17.4935i	−1.38562	−	0.573944i	−0.439645	−	0.898172i	$-0.644896\pi$
$929$	−42.2331	−	17.4935i	−1.38562	−	0.573944i	−0.945979	+	0.324227i	$0.894896\pi$
$930$		0			0
$931$			35.3205i			1.15758i
$932$		0			0
$933$	10.9348	+	10.9348i	0.357988	+	0.357988i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	19.6975	+	19.6975i	0.643488	+	0.643488i	0.951411	−	0.307923i	$-0.0996340\pi$
$937$	19.6975	+	19.6975i	0.643488	+	0.643488i	−0.307923	+	0.951411i	$0.599634\pi$
$938$		0			0
$939$		−	5.17691i		−	0.168942i
$940$		0			0
$941$	6.17105	+	2.55613i	0.201170	+	0.0833275i	0.480994	−	0.876724i	$-0.340276\pi$
$941$	6.17105	+	2.55613i	0.201170	+	0.0833275i	−0.279823	+	0.960051i	$0.590276\pi$
$942$		0			0
$943$	−20.0764	+	20.0764i	−0.653777	+	0.653777i
$944$		0			0
$945$	3.88179	−	9.37146i	0.126274	−	0.304854i
$946$		0			0
$947$	20.1797	+	48.7181i	0.655752	+	1.58312i	0.804303	+	0.594220i	$0.202539\pi$
$947$	20.1797	+	48.7181i	0.655752	+	1.58312i	−0.148551	+	0.988905i	$0.547461\pi$
$948$		0			0
$949$	2.70531	−	1.12057i	0.0878180	−	0.0363754i
$950$		0			0
$951$	11.3205			0.367093
$952$		0			0
$953$	−42.2487			−1.36857			−0.684285	−	0.729215i	$-0.739886\pi$
$953$	−42.2487			−1.36857			−0.684285	+	0.729215i	$0.739886\pi$
$954$		0			0
$955$	38.4050	−	15.9079i	1.24276	−	0.514766i
$956$		0			0
$957$	4.59220	+	11.0866i	0.148445	+	0.358377i
$958$		0			0
$959$	−2.65131	+	6.40083i	−0.0856152	+	0.206693i
$960$		0			0
$961$	5.22715	−	5.22715i	0.168618	−	0.168618i
$962$		0			0
$963$	16.5457	+	6.85346i	0.533179	+	0.220850i
$964$		0			0
$965$		−	24.4974i		−	0.788600i
$966$		0			0
$967$	−34.2185	−	34.2185i	−1.10039	−	1.10039i	−0.994363	−	0.106031i	$-0.966186\pi$
$967$	−34.2185	−	34.2185i	−1.10039	−	1.10039i	−0.106031	−	0.994363i	$-0.533814\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−39.6723	−	39.6723i	−1.27314	−	1.27314i	−0.944429	−	0.328716i	$-0.893384\pi$
$971$	−39.6723	−	39.6723i	−1.27314	−	1.27314i	−0.328716	−	0.944429i	$-0.606616\pi$
$972$		0			0
$973$		−	8.24871i		−	0.264442i
$974$		0			0
$975$	6.93148	+	2.87111i	0.221985	+	0.0919492i
$976$		0			0
$977$	29.6985	−	29.6985i	0.950139	−	0.950139i	−0.0486759	−	0.998815i	$-0.515500\pi$
$977$	29.6985	−	29.6985i	0.950139	−	0.950139i	0.998815	+	0.0486759i	$0.0155002\pi$
$978$		0			0
$979$	−17.1383	+	41.3756i	−0.547743	+	1.32237i
$980$		0			0
$981$	−6.02776	−	14.5523i	−0.192451	−	0.464619i
$982$		0			0
$983$	−27.6323	+	11.4457i	−0.881333	+	0.365060i	−0.777014	−	0.629484i	$-0.783266\pi$
$983$	−27.6323	+	11.4457i	−0.881333	+	0.365060i	−0.104319	+	0.994544i	$0.533266\pi$
$984$		0			0
$985$	12.0000			0.382352
$986$		0			0
$987$	−3.71281			−0.118180
$988$		0			0
$989$	−54.1772	+	22.4409i	−1.72274	+	0.713581i
$990$		0			0
$991$	−3.90190	−	9.42002i	−0.123948	−	0.299237i	0.849710	−	0.527250i	$-0.176777\pi$
$991$	−3.90190	−	9.42002i	−0.123948	−	0.299237i	−0.973658	+	0.228014i	$0.926777\pi$
$992$		0			0
$993$	−4.29194	+	10.3617i	−0.136201	+	0.328818i
$994$		0			0
$995$	−15.1774	+	15.1774i	−0.481156	+	0.481156i
$996$		0			0
$997$	−39.1654	−	16.2228i	−1.24038	−	0.513782i	−0.336547	−	0.941667i	$-0.609259\pi$
$997$	−39.1654	−	16.2228i	−1.24038	−	0.513782i	−0.903833	+	0.427885i	$0.859259\pi$
$998$		0			0
$999$		−	45.8564i		−	1.45083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1156.2.h.f.733.2		16
17.2	even	8	inner	1156.2.h.f.977.2		16
17.3	odd	16		68.2.a.a.1.1	✓	2
17.4	even	4	inner	1156.2.h.f.1001.3		16
17.5	odd	16		1156.2.b.c.577.2		4
17.6	odd	16		1156.2.e.d.905.2		8
17.7	odd	16		1156.2.e.d.829.3		8
17.8	even	8	inner	1156.2.h.f.757.3		16
17.9	even	8	inner	1156.2.h.f.757.2		16
17.10	odd	16		1156.2.e.d.829.2		8
17.11	odd	16		1156.2.e.d.905.3		8
17.12	odd	16		1156.2.b.c.577.3		4
17.13	even	4	inner	1156.2.h.f.1001.2		16
17.14	odd	16		1156.2.a.a.1.2		2
17.15	even	8	inner	1156.2.h.f.977.3		16
17.16	even	2	inner	1156.2.h.f.733.3		16
51.20	even	16		612.2.a.e.1.1		2
68.3	even	16		272.2.a.e.1.2		2
68.31	even	16		4624.2.a.x.1.1		2
85.3	even	16		1700.2.e.c.749.2		4
85.37	even	16		1700.2.e.c.749.3		4
85.54	odd	16		1700.2.a.d.1.2		2
119.20	even	16		3332.2.a.h.1.2		2
136.3	even	16		1088.2.a.t.1.1		2
136.37	odd	16		1088.2.a.p.1.2		2
187.54	even	16		8228.2.a.k.1.1		2
204.71	odd	16		2448.2.a.y.1.1		2
340.139	even	16		6800.2.a.bh.1.1		2
408.173	even	16		9792.2.a.cr.1.2		2
408.275	odd	16		9792.2.a.cs.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.a.a.1.1	✓	2	17.3	odd	16
272.2.a.e.1.2		2	68.3	even	16
612.2.a.e.1.1		2	51.20	even	16
1088.2.a.p.1.2		2	136.37	odd	16
1088.2.a.t.1.1		2	136.3	even	16
1156.2.a.a.1.2		2	17.14	odd	16
1156.2.b.c.577.2		4	17.5	odd	16
1156.2.b.c.577.3		4	17.12	odd	16
1156.2.e.d.829.2		8	17.10	odd	16
1156.2.e.d.829.3		8	17.7	odd	16
1156.2.e.d.905.2		8	17.6	odd	16
1156.2.e.d.905.3		8	17.11	odd	16
1156.2.h.f.733.2		16	1.1	even	1	trivial
1156.2.h.f.733.3		16	17.16	even	2	inner
1156.2.h.f.757.2		16	17.9	even	8	inner
1156.2.h.f.757.3		16	17.8	even	8	inner
1156.2.h.f.977.2		16	17.2	even	8	inner
1156.2.h.f.977.3		16	17.15	even	8	inner
1156.2.h.f.1001.2		16	17.13	even	4	inner
1156.2.h.f.1001.3		16	17.4	even	4	inner
1700.2.a.d.1.2		2	85.54	odd	16
1700.2.e.c.749.2		4	85.3	even	16
1700.2.e.c.749.3		4	85.37	even	16
2448.2.a.y.1.1		2	204.71	odd	16
3332.2.a.h.1.2		2	119.20	even	16
4624.2.a.x.1.1		2	68.31	even	16
6800.2.a.bh.1.1		2	340.139	even	16
8228.2.a.k.1.1		2	187.54	even	16
9792.2.a.cr.1.2		2	408.173	even	16
9792.2.a.cs.1.2		2	408.275	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:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1156.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.676327 + 0.280144i) q^{3} +(-1.32565 - 3.20041i) q^{5} +(-0.280144 + 0.676327i) q^{7} +(-1.74238 + 1.74238i) q^{9} +(4.37184 + 1.81088i) q^{11} +1.46410i q^{13} +(1.79315 + 1.79315i) q^{15} +(3.86370 + 3.86370i) q^{19} -0.535898i q^{21} +(-4.37184 - 1.81088i) q^{23} +(-4.94975 + 4.94975i) q^{25} +(1.53073 - 3.69552i) q^{27} +(-1.32565 - 3.20041i) q^{29} +(5.72450 - 2.37116i) q^{31} -3.46410 q^{33} +2.53590 q^{35} +(10.5914 - 4.38712i) q^{37} +(-0.410159 - 0.990211i) q^{39} +(2.29610 - 5.54328i) q^{41} +(8.76268 - 8.76268i) q^{43} +(7.88614 + 3.26655i) q^{45} -6.92820i q^{47} +(4.57081 + 4.57081i) q^{49} +(-0.656339 - 0.656339i) q^{53} -16.3923i q^{55} +(-3.69552 - 1.53073i) q^{57} +(-6.69213 + 6.69213i) q^{59} +(-2.85639 + 6.89593i) q^{61} +(-0.690303 - 1.66654i) q^{63} +(4.68573 - 1.94089i) q^{65} -1.07180 q^{67} +3.46410 q^{69} +(2.02898 - 0.840431i) q^{71} +(-0.765367 - 1.84776i) q^{73} +(1.96101 - 4.73429i) q^{75} +(-2.44949 + 2.44949i) q^{77} +(1.66654 + 0.690303i) q^{79} -4.46410i q^{81} +(6.69213 + 6.69213i) q^{83} +(1.79315 + 1.79315i) q^{87} +9.46410i q^{89} +(-0.990211 - 0.410159i) q^{91} +(-3.20736 + 3.20736i) q^{93} +(7.24351 - 17.4874i) q^{95} +(3.41668 + 8.24858i) q^{97} +(-10.7727 + 4.46219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 96 q^{35} - 128 q^{67}+O(q^{100}) \) 16 * q + 96 * q^35 - 128 * q^67

Introduction

L-functions

Modular forms

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Database

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