LMFDB - Embedded newform 1156.2.h.f.733.4

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			733.4
Root			$0.608761 - 0.793353i$ of defining polynomial
Character	$\chi$	$=$	1156.733
Dual form			1156.2.h.f.757.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.52409 - 1.04551i) q^{3} +(1.32565 + 3.20041i) q^{5} +(1.04551 - 2.52409i) q^{7} +(3.15660 - 3.15660i) q^{9} +O(q^{10})$	\(q+(2.52409 - 1.04551i) q^{3} +(1.32565 + 3.20041i) q^{5} +(1.04551 - 2.52409i) q^{7} +(3.15660 - 3.15660i) q^{9} +(1.17143 + 0.485223i) q^{11} -5.46410i q^{13} +(6.69213 + 6.69213i) q^{15} +(-1.03528 - 1.03528i) q^{19} -7.46410i q^{21} +(-1.17143 - 0.485223i) q^{23} +(-4.94975 + 4.94975i) q^{25} +(1.53073 - 3.69552i) q^{27} +(1.32565 + 3.20041i) q^{29} +(-3.87674 + 1.60580i) q^{31} +3.46410 q^{33} +9.46410 q^{35} +(4.19062 - 1.73581i) q^{37} +(-5.71278 - 13.7919i) q^{39} +(2.29610 - 5.54328i) q^{41} +(-5.93426 + 5.93426i) q^{43} +(14.2870 + 5.91786i) q^{45} +6.92820i q^{47} +(-0.328169 - 0.328169i) q^{49} +(9.14162 + 9.14162i) q^{53} +4.39230i q^{55} +(-3.69552 - 1.53073i) q^{57} +(-1.79315 + 1.79315i) q^{59} +(-0.205079 + 0.495106i) q^{61} +(-4.66727 - 11.2678i) q^{63} +(17.4874 - 7.24351i) q^{65} -14.9282 q^{67} -3.46410 q^{69} +(-7.57226 + 3.13653i) q^{71} +(-0.765367 - 1.84776i) q^{73} +(-7.31857 + 17.6686i) q^{75} +(2.44949 - 2.44949i) q^{77} +(11.2678 + 4.66727i) q^{79} +2.46410i q^{81} +(1.79315 + 1.79315i) q^{83} +(6.69213 + 6.69213i) q^{87} +2.53590i q^{89} +(-13.7919 - 5.71278i) q^{91} +(-8.10634 + 8.10634i) q^{93} +(1.94089 - 4.68573i) q^{95} +(-1.88594 - 4.55307i) q^{97} +(5.22939 - 2.16609i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 96 q^{35} - 128 q^{67}+O(q^{100}) $ 16 * q + 96 * q^35 - 128 * q^67

Display 100 coefficients 10 coefficients

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
$3$	2.52409	−	1.04551i	1.45728	−	0.603626i	0.493363	−	0.869823i	$-0.335767\pi$
$3$	2.52409	−	1.04551i	1.45728	−	0.603626i	0.963918	+	0.266198i	$0.0857674\pi$
$4$		0			0
$5$	1.32565	+	3.20041i	0.592851	+	1.43127i	0.880738	+	0.473604i	$0.157047\pi$
$5$	1.32565	+	3.20041i	0.592851	+	1.43127i	−0.287887	+	0.957664i	$0.592953\pi$
$6$		0			0
$7$	1.04551	−	2.52409i	0.395166	−	0.954015i	−0.593630	−	0.804738i	$-0.702306\pi$
$7$	1.04551	−	2.52409i	0.395166	−	0.954015i	0.988796	−	0.149276i	$-0.0476944\pi$
$8$		0			0
$9$	3.15660	−	3.15660i	1.05220	−	1.05220i
$10$		0			0
$11$	1.17143	+	0.485223i	0.353200	+	0.146300i	0.552227	−	0.833694i	$-0.313778\pi$
$11$	1.17143	+	0.485223i	0.353200	+	0.146300i	−0.199027	+	0.979994i	$0.563778\pi$
$12$		0			0
$13$		−	5.46410i		−	1.51547i	−0.652563	−	0.757735i	$-0.726306\pi$
$13$		−	5.46410i		−	1.51547i	0.652563	−	0.757735i	$-0.273694\pi$
$14$		0			0
$15$	6.69213	+	6.69213i	1.72790	+	1.72790i
$16$		0			0
$17$		0			0
$17$		0			0
$18$		0			0
$19$	−1.03528	−	1.03528i	−0.237509	−	0.237509i	0.578309	−	0.815818i	$-0.303713\pi$
$19$	−1.03528	−	1.03528i	−0.237509	−	0.237509i	−0.815818	+	0.578309i	$0.803713\pi$
$20$		0			0
$21$		−	7.46410i		−	1.62880i
$22$		0			0
$23$	−1.17143	−	0.485223i	−0.244261	−	0.101176i	0.257195	−	0.966360i	$-0.417202\pi$
$23$	−1.17143	−	0.485223i	−0.244261	−	0.101176i	−0.501455	+	0.865184i	$0.667202\pi$
$24$		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	0.997872	−	0.0651984i	$-0.0207680\pi$
$29$	1.32565	+	3.20041i	0.246168	+	0.594302i	−0.751704	+	0.659500i	$0.770768\pi$
$30$		0			0
$31$	−3.87674	+	1.60580i	−0.696283	+	0.288410i	−0.702615	−	0.711570i	$-0.747984\pi$
$31$	−3.87674	+	1.60580i	−0.696283	+	0.288410i	0.00633216	+	0.999980i	$0.497984\pi$
$32$		0			0
$33$	3.46410			0.603023
$34$		0			0
$35$	9.46410			1.59973
$36$		0			0
$37$	4.19062	−	1.73581i	0.688934	−	0.285366i	−0.0106218	−	0.999944i	$-0.503381\pi$
$37$	4.19062	−	1.73581i	0.688934	−	0.285366i	0.699556	+	0.714578i	$0.253381\pi$
$38$		0			0
$39$	−5.71278	−	13.7919i	−0.914776	−	2.20847i
$40$		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
$43$	−5.93426	+	5.93426i	−0.904966	+	0.904966i	−0.995860	−	0.0908950i	$-0.971027\pi$
$43$	−5.93426	+	5.93426i	−0.904966	+	0.904966i	0.0908950	+	0.995860i	$0.471027\pi$
$44$		0			0
$45$	14.2870	+	5.91786i	2.12978	+	0.882182i
$46$		0			0
$47$			6.92820i			1.01058i	0.862949	+	0.505291i	$0.168615\pi$
$47$			6.92820i			1.01058i	−0.862949	+	0.505291i	$0.831385\pi$
$48$		0			0
$49$	−0.328169	−	0.328169i	−0.0468813	−	0.0468813i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	9.14162	+	9.14162i	1.25570	+	1.25570i	0.953127	+	0.302571i	$0.0978451\pi$
$53$	9.14162	+	9.14162i	1.25570	+	1.25570i	0.302571	+	0.953127i	$0.402155\pi$
$54$		0			0
$55$			4.39230i			0.592258i
$56$		0			0
$57$	−3.69552	−	1.53073i	−0.489483	−	0.202751i
$58$		0			0
$59$	−1.79315	+	1.79315i	−0.233448	+	0.233448i	−0.814130	−	0.580682i	$-0.802786\pi$
$59$	−1.79315	+	1.79315i	−0.233448	+	0.233448i	0.580682	+	0.814130i	$0.302786\pi$
$60$		0			0
$61$	−0.205079	+	0.495106i	−0.0262577	+	0.0633918i	−0.936465	−	0.350762i	$-0.885923\pi$
$61$	−0.205079	+	0.495106i	−0.0262577	+	0.0633918i	0.910207	+	0.414154i	$0.135923\pi$
$62$		0			0
$63$	−4.66727	−	11.2678i	−0.588020	−	1.41961i
$64$		0			0
$65$	17.4874	−	7.24351i	2.16904	−	0.898447i
$66$		0			0
$67$	−14.9282			−1.82377			−0.911885	−	0.410445i	$-0.865373\pi$
$67$	−14.9282			−1.82377			−0.911885	+	0.410445i	$0.865373\pi$
$68$		0			0
$69$	−3.46410			−0.417029
$70$		0			0
$71$	−7.57226	+	3.13653i	−0.898662	+	0.372238i	−0.783705	−	0.621133i	$-0.786673\pi$
$71$	−7.57226	+	3.13653i	−0.898662	+	0.372238i	−0.114956	+	0.993371i	$0.536673\pi$
$72$		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
$75$	−7.31857	+	17.6686i	−0.845076	+	2.04019i
$76$		0			0
$77$	2.44949	−	2.44949i	0.279145	−	0.279145i
$78$		0			0
$79$	11.2678	+	4.66727i	1.26772	+	0.525108i	0.912271	−	0.409586i	$-0.134327\pi$
$79$	11.2678	+	4.66727i	1.26772	+	0.525108i	0.355452	+	0.934694i	$0.384327\pi$
$80$		0			0
$81$			2.46410i			0.273789i
$82$		0			0
$83$	1.79315	+	1.79315i	0.196824	+	0.196824i	0.798637	−	0.601813i	$-0.205555\pi$
$83$	1.79315	+	1.79315i	0.196824	+	0.196824i	−0.601813	+	0.798637i	$0.705555\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.69213	+	6.69213i	0.717472	+	0.717472i
$88$		0			0
$89$			2.53590i			0.268805i	0.990927	+	0.134402i	$0.0429115\pi$
$89$			2.53590i			0.268805i	−0.990927	+	0.134402i	$0.957089\pi$
$90$		0			0
$91$	−13.7919	−	5.71278i	−1.44578	−	0.598862i
$92$		0			0
$93$	−8.10634	+	8.10634i	−0.840589	+	0.840589i
$94$		0			0
$95$	1.94089	−	4.68573i	0.199131	−	0.480746i
$96$		0			0
$97$	−1.88594	−	4.55307i	−0.191488	−	0.462294i	0.798753	−	0.601660i	$-0.205494\pi$
$97$	−1.88594	−	4.55307i	−0.191488	−	0.462294i	−0.990241	+	0.139366i	$0.955494\pi$
$98$		0			0
$99$	5.22939	−	2.16609i	0.525574	−	0.217700i
$100$		0			0
$101$	2.53590			0.252331			0.126166	−	0.992009i	$-0.459733\pi$
$101$	2.53590			0.252331			0.126166	+	0.992009i	$0.459733\pi$
$102$		0			0
$103$	−10.9282			−1.07679			−0.538394	−	0.842693i	$-0.680969\pi$
$103$	−10.9282			−1.07679			−0.538394	+	0.842693i	$0.680969\pi$
$104$		0			0
$105$	23.8882	−	9.89482i	2.33125	−	0.965635i
$106$		0			0
$107$	−4.10698	−	9.91512i	−0.397037	−	0.958531i	−0.988365	−	0.152100i	$-0.951396\pi$
$107$	−4.10698	−	9.91512i	−0.397037	−	0.958531i	0.591329	−	0.806431i	$-0.298604\pi$
$108$		0			0
$109$	5.50770	−	13.2968i	0.527542	−	1.27360i	−0.405587	−	0.914056i	$-0.632933\pi$
$109$	5.50770	−	13.2968i	0.527542	−	1.27360i	0.933129	−	0.359542i	$-0.117067\pi$
$110$		0			0
$111$	8.76268	−	8.76268i	0.831717	−	0.831717i
$112$		0			0
$113$	−18.3449	−	7.59872i	−1.72575	−	0.714827i	−0.999628	−	0.0272562i	$-0.991323\pi$
$113$	−18.3449	−	7.59872i	−1.72575	−	0.714827i	−0.726117	−	0.687571i	$-0.758677\pi$
$114$		0			0
$115$		−	4.39230i		−	0.409585i
$116$		0			0
$117$	−17.2480	−	17.2480i	−1.59457	−	1.59457i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−6.64136	−	6.64136i	−0.603760	−	0.603760i
$122$		0			0
$123$		−	16.3923i		−	1.47804i
$124$		0			0
$125$	−6.40083	−	2.65131i	−0.572507	−	0.237140i
$126$		0			0
$127$	−0.277401	+	0.277401i	−0.0246154	+	0.0246154i	−0.719307	−	0.694692i	$-0.755541\pi$
$127$	−0.277401	+	0.277401i	−0.0246154	+	0.0246154i	0.694692	+	0.719307i	$0.255541\pi$
$128$		0			0
$129$	−8.77424	+	21.1829i	−0.772529	+	1.86505i
$130$		0			0
$131$	2.16609	+	5.22939i	0.189252	+	0.456894i	0.989816	−	0.142353i	$-0.0454668\pi$
$131$	2.16609	+	5.22939i	0.189252	+	0.456894i	−0.800564	+	0.599247i	$0.795467\pi$
$132$		0			0
$133$	−3.69552	+	1.53073i	−0.320442	+	0.132731i
$134$		0			0
$135$	13.8564			1.19257
$136$		0			0
$137$	2.53590			0.216656			0.108328	−	0.994115i	$-0.465450\pi$
$137$	2.53590			0.216656			0.108328	+	0.994115i	$0.465450\pi$
$138$		0			0
$139$	−13.6106	+	5.63771i	−1.15444	+	0.478184i	−0.876020	−	0.482275i	$-0.839811\pi$
$139$	−13.6106	+	5.63771i	−1.15444	+	0.478184i	−0.278420	+	0.960460i	$0.589811\pi$
$140$		0			0
$141$	7.24351	+	17.4874i	0.610014	+	1.47270i
$142$		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
$147$	−1.17143	−	0.485223i	−0.0966181	−	0.0400205i
$148$		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
$151$	9.52056	+	9.52056i	0.774772	+	0.774772i	0.978937	−	0.204165i	$-0.0654478\pi$
$151$	9.52056	+	9.52056i	0.774772	+	0.774772i	−0.204165	+	0.978937i	$0.565448\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.2784	−	10.2784i	−0.825584	−	0.825584i
$156$		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
$159$	32.6319	+	13.5166i	2.58788	+	1.07193i
$160$		0			0
$161$	−2.44949	+	2.44949i	−0.193047	+	0.193047i
$162$		0			0
$163$	7.87886	−	19.0213i	0.617120	−	1.48986i	−0.237913	−	0.971286i	$-0.576463\pi$
$163$	7.87886	−	19.0213i	0.617120	−	1.48986i	0.855033	−	0.518573i	$-0.173537\pi$
$164$		0			0
$165$	4.59220	+	11.0866i	0.357502	+	0.863087i
$166$		0			0
$167$	−5.22939	+	2.16609i	−0.404663	+	0.167617i	−0.575725	−	0.817643i	$-0.695280\pi$
$167$	−5.22939	+	2.16609i	−0.404663	+	0.167617i	0.171062	+	0.985260i	$0.445280\pi$
$168$		0			0
$169$	−16.8564			−1.29665
$170$		0			0
$171$	−6.53590			−0.499813
$172$		0			0
$173$	−14.2870	+	5.91786i	−1.08622	+	0.449926i	−0.852686	−	0.522423i	$-0.825028\pi$
$173$	−14.2870	+	5.91786i	−1.08622	+	0.449926i	−0.233532	+	0.972349i	$0.575028\pi$
$174$		0			0
$175$	7.31857	+	17.6686i	0.553232	+	1.33562i
$176$		0			0
$177$	−2.65131	+	6.40083i	−0.199285	+	0.481115i
$178$		0			0
$179$	10.2784	−	10.2784i	0.768246	−	0.768246i	−0.209552	−	0.977798i	$-0.567200\pi$
$179$	10.2784	−	10.2784i	0.768246	−	0.768246i	0.977798	+	0.209552i	$0.0672004\pi$
$180$		0			0
$181$	−4.19062	−	1.73581i	−0.311487	−	0.129022i	0.221463	−	0.975169i	$-0.428917\pi$
$181$	−4.19062	−	1.73581i	−0.311487	−	0.129022i	−0.532950	+	0.846147i	$0.678917\pi$
$182$		0			0
$183$			1.46410i			0.108230i
$184$		0			0
$185$	11.1106	+	11.1106i	0.816870	+	0.816870i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−7.72741	−	7.72741i	−0.562086	−	0.562086i
$190$		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
$193$	19.3351	+	8.00888i	1.39177	+	0.576492i	0.947603	−	0.319451i	$-0.103498\pi$
$193$	19.3351	+	8.00888i	1.39177	+	0.576492i	0.444171	+	0.895942i	$0.353498\pi$
$194$		0			0
$195$	36.5665	−	36.5665i	2.61858	−	2.61858i
$196$		0			0
$197$	1.32565	−	3.20041i	0.0944490	−	0.228020i	−0.869593	−	0.493768i	$-0.835619\pi$
$197$	1.32565	−	3.20041i	0.0944490	−	0.228020i	0.964042	+	0.265748i	$0.0856191\pi$
$198$		0			0
$199$	1.60580	+	3.87674i	0.113832	+	0.274815i	0.970520	−	0.241020i	$-0.0774819\pi$
$199$	1.60580	+	3.87674i	0.113832	+	0.274815i	−0.856688	+	0.515835i	$0.827482\pi$
$200$		0			0
$201$	−37.6801	+	15.6076i	−2.65775	+	1.10087i
$202$		0			0
$203$	9.46410			0.664250
$204$		0			0
$205$	20.7846			1.45166
$206$		0			0
$207$	−5.22939	+	2.16609i	−0.363468	+	0.150553i
$208$		0			0
$209$	−0.710416	−	1.71510i	−0.0491405	−	0.118636i
$210$		0			0
$211$	−0.895382	+	2.16164i	−0.0616406	+	0.148814i	−0.951699	−	0.307033i	$-0.900664\pi$
$211$	−0.895382	+	2.16164i	−0.0616406	+	0.148814i	0.890058	+	0.455847i	$0.150664\pi$
$212$		0			0
$213$	−15.8338	+	15.8338i	−1.08491	+	1.08491i
$214$		0			0
$215$	−26.8588	−	11.1253i	−1.83176	−	0.758739i
$216$		0			0
$217$			11.4641i			0.778234i
$218$		0			0
$219$	−3.86370	−	3.86370i	−0.261085	−	0.261085i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	8.76268	+	8.76268i	0.586793	+	0.586793i	0.936761	−	0.349969i	$-0.113808\pi$
$223$	8.76268	+	8.76268i	0.586793	+	0.586793i	−0.349969	+	0.936761i	$0.613808\pi$
$224$		0			0
$225$			31.2487i			2.08325i
$226$		0			0
$227$	−18.6588	−	7.72873i	−1.23843	−	0.512974i	−0.335206	−	0.942145i	$-0.608806\pi$
$227$	−18.6588	−	7.72873i	−1.23843	−	0.512974i	−0.903223	+	0.429171i	$0.858806\pi$
$228$		0			0
$229$	14.4195	−	14.4195i	0.952870	−	0.952870i	−0.0460685	−	0.998938i	$-0.514669\pi$
$229$	14.4195	−	14.4195i	0.952870	−	0.952870i	0.998938	+	0.0460685i	$0.0146692\pi$
$230$		0			0
$231$	3.62175	−	8.74369i	0.238294	−	0.575293i
$232$		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
$237$	33.3205			2.16440
$238$		0			0
$239$	20.7846			1.34444			0.672222	−	0.740349i	$-0.265340\pi$
$239$	20.7846			1.34444			0.672222	+	0.740349i	$0.265340\pi$
$240$		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
$243$	7.16845	+	17.3062i	0.459856	+	1.11019i
$244$		0			0
$245$	0.615238	−	1.48532i	0.0393061	−	0.0948934i
$246$		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	$-0.929834\pi$
$251$		−	6.92820i		−	0.437304i	0.975803	−	0.218652i	$-0.0701660\pi$
$252$		0			0
$253$	−1.13681	−	1.13681i	−0.0714708	−	0.0714708i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−20.0764	−	20.0764i	−1.25233	−	1.25233i	−0.954672	−	0.297658i	$-0.903794\pi$
$257$	−20.0764	−	20.0764i	−1.25233	−	1.25233i	−0.297658	−	0.954672i	$-0.596206\pi$
$258$		0			0
$259$		−	12.3923i		−	0.770020i
$260$		0			0
$261$	14.2870	+	5.91786i	0.884341	+	0.366306i
$262$		0			0
$263$	−8.00481	+	8.00481i	−0.493598	+	0.493598i	−0.909438	−	0.415840i	$-0.863488\pi$
$263$	−8.00481	+	8.00481i	−0.493598	+	0.493598i	0.415840	+	0.909438i	$0.363488\pi$
$264$		0			0
$265$	−17.1383	+	41.3756i	−1.05280	+	2.54168i
$266$		0			0
$267$	2.65131	+	6.40083i	0.162257	+	0.391724i
$268$		0			0
$269$	25.3735	−	10.5101i	1.54705	−	0.640809i	0.564271	−	0.825590i	$-0.309157\pi$
$269$	25.3735	−	10.5101i	1.54705	−	0.640809i	0.982780	+	0.184780i	$0.0591573\pi$
$270$		0			0
$271$	−1.07180			−0.0651070			−0.0325535	−	0.999470i	$-0.510364\pi$
$271$	−1.07180			−0.0651070			−0.0325535	+	0.999470i	$0.510364\pi$
$272$		0			0
$273$	−40.7846			−2.46840
$274$		0			0
$275$	−8.20003	+	3.39656i	−0.494480	+	0.204820i
$276$		0			0
$277$	−2.44623	−	5.90572i	−0.146980	−	0.354840i	0.833194	−	0.552981i	$-0.186510\pi$
$277$	−2.44623	−	5.90572i	−0.146980	−	0.354840i	−0.980174	+	0.198141i	$0.936510\pi$
$278$		0			0
$279$	−7.16845	+	17.3062i	−0.429164	+	1.03609i
$280$		0			0
$281$	−14.0406	+	14.0406i	−0.837592	+	0.837592i	−0.988541	−	0.150950i	$-0.951767\pi$
$281$	−14.0406	+	14.0406i	−0.837592	+	0.837592i	0.150950	+	0.988541i	$0.451767\pi$
$282$		0			0
$283$	−19.0213	−	7.87886i	−1.13070	−	0.468350i	−0.262679	−	0.964883i	$-0.584606\pi$
$283$	−19.0213	−	7.87886i	−1.13070	−	0.468350i	−0.868017	+	0.496534i	$0.834606\pi$
$284$		0			0
$285$		−	13.8564i		−	0.820783i
$286$		0			0
$287$	−11.5911	−	11.5911i	−0.684202	−	0.684202i
$288$		0			0
$289$		0			0
$290$		0			0
$291$	−9.52056	−	9.52056i	−0.558105	−	0.558105i
$292$		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
$295$	−8.11592	−	3.36172i	−0.472527	−	0.195727i
$296$		0			0
$297$	3.58630	−	3.58630i	0.208098	−	0.208098i
$298$		0			0
$299$	−2.65131	+	6.40083i	−0.153329	+	0.370169i
$300$		0			0
$301$	8.77424	+	21.1829i	0.505739	+	1.22096i
$302$		0			0
$303$	6.40083	−	2.65131i	0.367718	−	0.152314i
$304$		0			0
$305$	−1.85641			−0.106298
$306$		0			0
$307$	−24.7846			−1.41453			−0.707266	−	0.706947i	$-0.750072\pi$
$307$	−24.7846			−1.41453			−0.707266	+	0.706947i	$0.750072\pi$
$308$		0			0
$309$	−27.5837	+	11.4256i	−1.56918	+	0.649977i
$310$		0			0
$311$	1.19564	+	2.88653i	0.0677985	+	0.163680i	0.954147	−	0.299339i	$-0.0967662\pi$
$311$	1.19564	+	2.88653i	0.0677985	+	0.163680i	−0.886348	+	0.463019i	$0.846766\pi$
$312$		0			0
$313$	−8.00888	+	19.3351i	−0.452688	+	1.09289i	0.518607	+	0.855012i	$0.326451\pi$
$313$	−8.00888	+	19.3351i	−0.452688	+	1.09289i	−0.971296	+	0.237874i	$0.923549\pi$
$314$		0			0
$315$	29.8744	−	29.8744i	1.68323	−	1.68323i
$316$		0			0
$317$	−7.88614	−	3.26655i	−0.442930	−	0.183468i	0.150061	−	0.988677i	$-0.452053\pi$
$317$	−7.88614	−	3.26655i	−0.442930	−	0.183468i	−0.592991	+	0.805209i	$0.702053\pi$
$318$		0			0
$319$			4.39230i			0.245922i
$320$		0			0
$321$	−20.7327	−	20.7327i	−1.15719	−	1.15719i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	27.0459	+	27.0459i	1.50024	+	1.50024i
$326$		0			0
$327$		−	39.3205i		−	2.17443i
$328$		0			0
$329$	17.4874	+	7.24351i	0.964110	+	0.399348i
$330$		0			0
$331$	−13.6617	+	13.6617i	−0.750913	+	0.750913i	−0.974650	−	0.223737i	$-0.928174\pi$
$331$	−13.6617	+	13.6617i	−0.750913	+	0.750913i	0.223737	+	0.974650i	$0.428174\pi$
$332$		0			0
$333$	7.74885	−	18.7074i	0.424634	−	1.02516i
$334$		0			0
$335$	−19.7896	−	47.7764i	−1.08122	−	2.61030i
$336$		0			0
$337$	6.26816	−	2.59636i	0.341449	−	0.141433i	−0.205369	−	0.978685i	$-0.565839\pi$
$337$	6.26816	−	2.59636i	0.341449	−	0.141433i	0.546817	+	0.837252i	$0.315839\pi$
$338$		0			0
$339$	−54.2487			−2.94639
$340$		0			0
$341$	−5.32051			−0.288122
$342$		0			0
$343$	16.4972	−	6.83335i	0.890763	−	0.368966i
$344$		0			0
$345$	−4.59220	−	11.0866i	−0.247236	−	0.596880i
$346$		0			0
$347$	13.0314	−	31.4605i	0.699560	−	1.68889i	−0.0250126	−	0.999687i	$-0.507963\pi$
$347$	13.0314	−	31.4605i	0.699560	−	1.68889i	0.724572	−	0.689199i	$-0.242037\pi$
$348$		0			0
$349$	7.62587	−	7.62587i	0.408203	−	0.408203i	−0.472908	−	0.881112i	$-0.656796\pi$
$349$	7.62587	−	7.62587i	0.408203	−	0.408203i	0.881112	+	0.472908i	$0.156796\pi$
$350$		0			0
$351$	−20.1927	−	8.36408i	−1.07781	−	0.446442i
$352$		0			0
$353$			19.8564i			1.05685i	0.848980	+	0.528425i	$0.177217\pi$
$353$			19.8564i			1.05685i	−0.848980	+	0.528425i	$0.822783\pi$
$354$		0			0
$355$	−20.0764	−	20.0764i	−1.06554	−	1.06554i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−16.4901	−	16.4901i	−0.870314	−	0.870314i	0.122193	−	0.992506i	$-0.461007\pi$
$359$	−16.4901	−	16.4901i	−0.870314	−	0.870314i	−0.992506	+	0.122193i	$0.961007\pi$
$360$		0			0
$361$		−	16.8564i		−	0.887179i
$362$		0			0
$363$	−23.7070	−	9.81975i	−1.24429	−	0.515403i
$364$		0			0
$365$	4.89898	−	4.89898i	0.256424	−	0.256424i
$366$		0			0
$367$	0.895382	−	2.16164i	0.0467386	−	0.112837i	−0.898786	−	0.438388i	$-0.855550\pi$
$367$	0.895382	−	2.16164i	0.0467386	−	0.112837i	0.945525	+	0.325551i	$0.105550\pi$
$368$		0			0
$369$	−10.2500	−	24.7458i	−0.533595	−	1.28821i
$370$		0			0
$371$	32.6319	−	13.5166i	1.69416	−	0.701746i
$372$		0			0
$373$	8.39230			0.434537			0.217269	−	0.976112i	$-0.430285\pi$
$373$	8.39230			0.434537			0.217269	+	0.976112i	$0.430285\pi$
$374$		0			0
$375$	−18.9282			−0.977448
$376$		0			0
$377$	17.4874	−	7.24351i	0.900646	−	0.373060i
$378$		0			0
$379$	2.01596	+	4.86695i	0.103553	+	0.249998i	0.967161	−	0.254165i	$-0.0818008\pi$
$379$	2.01596	+	4.86695i	0.103553	+	0.249998i	−0.863608	+	0.504164i	$0.831801\pi$
$380$		0			0
$381$	−0.410159	+	0.990211i	−0.0210131	+	0.0507301i
$382$		0			0
$383$	−1.79315	+	1.79315i	−0.0916257	+	0.0916257i	−0.751434	−	0.659808i	$-0.770637\pi$
$383$	−1.79315	+	1.79315i	−0.0916257	+	0.0916257i	0.659808	+	0.751434i	$0.270637\pi$
$384$		0			0
$385$	11.0866	+	4.59220i	0.565023	+	0.234040i
$386$		0			0
$387$			37.4641i			1.90441i
$388$		0			0
$389$	−26.2880	−	26.2880i	−1.33286	−	1.33286i	−0.902803	−	0.430054i	$-0.858495\pi$
$389$	−26.2880	−	26.2880i	−1.33286	−	1.33286i	−0.430054	−	0.902803i	$-0.641505\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	10.9348	+	10.9348i	0.551586	+	0.551586i
$394$		0			0
$395$			42.2487i			2.12576i
$396$		0			0
$397$	−5.18083	−	2.14597i	−0.260019	−	0.107703i	0.248866	−	0.968538i	$-0.419942\pi$
$397$	−5.18083	−	2.14597i	−0.260019	−	0.107703i	−0.508885	+	0.860835i	$0.669942\pi$
$398$		0			0
$399$	−7.72741	+	7.72741i	−0.386854	+	0.386854i
$400$		0			0
$401$	12.1909	−	29.4315i	0.608785	−	1.46974i	−0.255537	−	0.966799i	$-0.582252\pi$
$401$	12.1909	−	29.4315i	0.608785	−	1.46974i	0.864322	−	0.502939i	$-0.167748\pi$
$402$		0			0
$403$	8.77424	+	21.1829i	0.437076	+	1.05520i
$404$		0			0
$405$	−7.88614	+	3.26655i	−0.391866	+	0.162316i
$406$		0			0
$407$	5.75129			0.285081
$408$		0			0
$409$	17.7128			0.875842			0.437921	−	0.899013i	$-0.355715\pi$
$409$	17.7128			0.875842			0.437921	+	0.899013i	$0.355715\pi$
$410$		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
$415$	−3.36172	+	8.11592i	−0.165021	+	0.398395i
$416$		0			0
$417$	−28.4601	+	28.4601i	−1.39370	+	1.39370i
$418$		0			0
$419$	22.7168	+	9.40960i	1.10979	+	0.459689i	0.860864	−	0.508835i	$-0.169924\pi$
$419$	22.7168	+	9.40960i	1.10979	+	0.459689i	0.248923	+	0.968523i	$0.419924\pi$
$420$		0			0
$421$			22.2487i			1.08434i	0.840270	+	0.542168i	$0.182396\pi$
$421$			22.2487i			1.08434i	−0.840270	+	0.542168i	$0.817604\pi$
$422$		0			0
$423$	21.8695	+	21.8695i	1.06333	+	1.06333i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.03528	+	1.03528i	0.0501005	+	0.0501005i
$428$		0			0
$429$		−	18.9282i		−	0.913862i
$430$		0			0
$431$	16.3159	+	6.75829i	0.785912	+	0.325535i	0.739299	−	0.673378i	$-0.235157\pi$
$431$	16.3159	+	6.75829i	0.785912	+	0.325535i	0.0466130	+	0.998913i	$0.485157\pi$
$432$		0			0
$433$	−2.55103	+	2.55103i	−0.122594	+	0.122594i	−0.765742	−	0.643148i	$-0.777628\pi$
$433$	−2.55103	+	2.55103i	−0.122594	+	0.122594i	0.643148	+	0.765742i	$0.277628\pi$
$434$		0			0
$435$	−12.5461	+	30.2890i	−0.601541	+	1.45225i
$436$		0			0
$437$	0.710416	+	1.71510i	0.0339838	+	0.0820442i
$438$		0			0
$439$	22.3543	−	9.25947i	1.06691	−	0.441930i	0.221013	−	0.975271i	$-0.429064\pi$
$439$	22.3543	−	9.25947i	1.06691	−	0.441930i	0.845901	+	0.533341i	$0.179064\pi$
$440$		0			0
$441$	−2.07180			−0.0986570
$442$		0			0
$443$	−20.7846			−0.987507			−0.493753	−	0.869602i	$-0.664375\pi$
$443$	−20.7846			−0.987507			−0.493753	+	0.869602i	$0.664375\pi$
$444$		0			0
$445$	−8.11592	+	3.36172i	−0.384732	+	0.159361i
$446$		0			0
$447$	−6.27306	−	15.1445i	−0.296706	−	0.716311i
$448$		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
$451$	5.37945	−	5.37945i	0.253309	−	0.253309i
$452$		0			0
$453$	33.9845	+	14.0769i	1.59673	+	0.661389i
$454$		0			0
$455$		−	51.7128i		−	2.42433i
$456$		0			0
$457$	14.4195	+	14.4195i	0.674517	+	0.674517i	0.958754	−	0.284237i	$-0.0917401\pi$
$457$	14.4195	+	14.4195i	0.674517	+	0.674517i	−0.284237	+	0.958754i	$0.591740\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	18.9396	+	18.9396i	0.882104	+	0.882104i	0.993748	−	0.111644i	$-0.0356117\pi$
$461$	18.9396	+	18.9396i	0.882104	+	0.882104i	−0.111644	+	0.993748i	$0.535612\pi$
$462$		0			0
$463$		−	2.14359i		−	0.0996212i	−0.998759	−	0.0498106i	$-0.984138\pi$
$463$		−	2.14359i		−	0.0996212i	0.998759	−	0.0498106i	$-0.0158618\pi$
$464$		0			0
$465$	−36.6899	−	15.1974i	−1.70145	−	0.704764i
$466$		0			0
$467$	−10.2784	+	10.2784i	−0.475629	+	0.475629i	−0.903731	−	0.428102i	$-0.859183\pi$
$467$	−10.2784	+	10.2784i	−0.475629	+	0.475629i	0.428102	+	0.903731i	$0.359183\pi$
$468$		0			0
$469$	−15.6076	+	37.6801i	−0.720692	+	1.73990i
$470$		0			0
$471$	2.09102	+	5.04817i	0.0963492	+	0.232607i
$472$		0			0
$473$	−9.83102	+	4.07214i	−0.452031	+	0.187237i
$474$		0			0
$475$	10.2487			0.470243
$476$		0			0
$477$	57.7128			2.64249
$478$		0			0
$479$	−16.3159	+	6.75829i	−0.745495	+	0.308794i	−0.722902	−	0.690951i	$-0.757192\pi$
$479$	−16.3159	+	6.75829i	−0.745495	+	0.308794i	−0.0225928	+	0.999745i	$0.507192\pi$
$480$		0			0
$481$	−9.48466	−	22.8980i	−0.432463	−	1.04406i
$482$		0			0
$483$	−3.62175	+	8.74369i	−0.164796	+	0.397852i
$484$		0			0
$485$	12.0716	−	12.0716i	0.548142	−	0.548142i
$486$		0			0
$487$	−5.59184	−	2.31621i	−0.253390	−	0.104958i	0.252373	−	0.967630i	$-0.418789\pi$
$487$	−5.59184	−	2.31621i	−0.253390	−	0.104958i	−0.505763	+	0.862672i	$0.668789\pi$
$488$		0			0
$489$		−	56.2487i		−	2.54365i
$490$		0			0
$491$	26.2880	+	26.2880i	1.18636	+	1.18636i	0.978066	+	0.208298i	$0.0667922\pi$
$491$	26.2880	+	26.2880i	1.18636	+	1.18636i	0.208298	+	0.978066i	$0.433208\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	13.8647	+	13.8647i	0.623173	+	0.623173i
$496$		0			0
$497$			22.3923i			1.00443i
$498$		0			0
$499$	23.0792	+	9.55972i	1.03317	+	0.427952i	0.833855	−	0.551984i	$-0.186129\pi$
$499$	23.0792	+	9.55972i	1.03317	+	0.427952i	0.199313	+	0.979936i	$0.436129\pi$
$500$		0			0
$501$	−10.9348	+	10.9348i	−0.488530	+	0.488530i
$502$		0			0
$503$	10.3800	−	25.0596i	0.462823	−	1.11735i	−0.504410	−	0.863464i	$-0.668290\pi$
$503$	10.3800	−	25.0596i	0.462823	−	1.11735i	0.967233	−	0.253890i	$-0.0817100\pi$
$504$		0			0
$505$	3.36172	+	8.11592i	0.149595	+	0.361154i
$506$		0			0
$507$	−42.5470	+	17.6236i	−1.88958	+	0.782689i
$508$		0			0
$509$	21.7128			0.962404			0.481202	−	0.876610i	$-0.340200\pi$
$509$	21.7128			0.962404			0.481202	+	0.876610i	$0.340200\pi$
$510$		0			0
$511$	−5.46410			−0.241718
$512$		0			0
$513$	−5.41061	+	2.24115i	−0.238884	+	0.0989492i
$514$		0			0
$515$	−14.4870	−	34.9748i	−0.638374	−	1.54117i
$516$		0			0
$517$	−3.36172	+	8.11592i	−0.147848	+	0.356938i
$518$		0			0
$519$	−29.8744	+	29.8744i	−1.31134	+	1.31134i
$520$		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
$523$			12.7846i			0.559032i	0.960141	+	0.279516i	$0.0901740\pi$
$523$			12.7846i			0.559032i	−0.960141	+	0.279516i	$0.909826\pi$
$524$		0			0
$525$	36.9454	+	36.9454i	1.61243	+	1.61243i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−15.1266	−	15.1266i	−0.657680	−	0.657680i
$530$		0			0
$531$			11.3205i			0.491268i
$532$		0			0
$533$	−30.2890	−	12.5461i	−1.31196	−	0.543433i
$534$		0			0
$535$	26.2880	−	26.2880i	1.13653	−	1.13653i
$536$		0			0
$537$	15.1974	−	36.6899i	0.655818	−	1.58328i
$538$		0			0
$539$	−0.225193	−	0.543664i	−0.00969974	−	0.0234173i
$540$		0			0
$541$	−16.9923	+	7.03843i	−0.730555	+	0.302606i	−0.716780	−	0.697299i	$-0.754385\pi$
$541$	−16.9923	+	7.03843i	−0.730555	+	0.302606i	−0.0137749	+	0.999905i	$0.504385\pi$
$542$		0			0
$543$	−12.3923			−0.531805
$544$		0			0
$545$	49.8564			2.13561
$546$		0			0
$547$	39.4793	−	16.3528i	1.68801	−	0.699197i	0.688354	−	0.725375i	$-0.258333\pi$
$547$	39.4793	−	16.3528i	1.68801	−	0.699197i	0.999657	+	0.0261774i	$0.00833347\pi$
$548$		0			0
$549$	0.915495	+	2.21020i	0.0390724	+	0.0943291i
$550$		0			0
$551$	1.94089	−	4.68573i	0.0826848	−	0.199619i
$552$		0			0
$553$	23.5612	−	23.5612i	1.00192	−	1.00192i
$554$		0			0
$555$	39.6605	+	16.4279i	1.68349	+	0.697326i
$556$		0			0
$557$			26.5359i			1.12436i	0.827014	+	0.562181i	$0.190038\pi$
$557$			26.5359i			1.12436i	−0.827014	+	0.562181i	$0.809962\pi$
$558$		0			0
$559$	32.4254	+	32.4254i	1.37145	+	1.37145i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−24.9754	−	24.9754i	−1.05259	−	1.05259i	−0.998538	−	0.0540480i	$-0.982788\pi$
$563$	−24.9754	−	24.9754i	−1.05259	−	1.05259i	−0.0540480	−	0.998538i	$-0.517212\pi$
$564$		0			0
$565$		−	68.7846i		−	2.89379i
$566$		0			0
$567$	6.21960	+	2.57624i	0.261199	+	0.108192i
$568$		0			0
$569$	5.55532	−	5.55532i	0.232891	−	0.232891i	−0.581007	−	0.813898i	$-0.697341\pi$
$569$	5.55532	−	5.55532i	0.232891	−	0.232891i	0.813898	+	0.581007i	$0.197341\pi$
$570$		0			0
$571$	4.25711	−	10.2776i	0.178154	−	0.430103i	−0.809425	−	0.587223i	$-0.800221\pi$
$571$	4.25711	−	10.2776i	0.178154	−	0.430103i	0.987579	+	0.157120i	$0.0502211\pi$
$572$		0			0
$573$	12.5461	+	30.2890i	0.524122	+	1.26534i
$574$		0			0
$575$	8.20003	−	3.39656i	0.341965	−	0.141646i
$576$		0			0
$577$	13.4641			0.560518			0.280259	−	0.959924i	$-0.409580\pi$
$577$	13.4641			0.560518			0.280259	+	0.959924i	$0.409580\pi$
$578$		0			0
$579$	57.1769			2.37619
$580$		0			0
$581$	6.40083	−	2.65131i	0.265551	−	0.109995i
$582$		0			0
$583$	6.27306	+	15.1445i	0.259804	+	0.627222i
$584$		0			0
$585$	32.3358	−	78.0654i	1.33692	−	3.22761i
$586$		0			0
$587$	20.0764	−	20.0764i	0.828641	−	0.828641i	−0.158688	−	0.987329i	$-0.550726\pi$
$587$	20.0764	−	20.0764i	0.828641	−	0.828641i	0.987329	+	0.158688i	$0.0507262\pi$
$588$		0			0
$589$	5.67594	+	2.35105i	0.233873	+	0.0968734i
$590$		0			0
$591$		−	9.46410i		−	0.389301i
$592$		0			0
$593$	2.92996	+	2.92996i	0.120319	+	0.120319i	0.764703	−	0.644383i	$-0.222886\pi$
$593$	2.92996	+	2.92996i	0.120319	+	0.120319i	−0.644383	+	0.764703i	$0.722886\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.10634	+	8.10634i	0.331771	+	0.331771i
$598$		0			0
$599$		−	27.7128i		−	1.13231i	−0.824297	−	0.566157i	$-0.808429\pi$
$599$		−	27.7128i		−	1.13231i	0.824297	−	0.566157i	$-0.191571\pi$
$600$		0			0
$601$	9.96368	+	4.12709i	0.406427	+	0.168348i	0.576525	−	0.817080i	$-0.304408\pi$
$601$	9.96368	+	4.12709i	0.406427	+	0.168348i	−0.170098	+	0.985427i	$0.554408\pi$
$602$		0			0
$603$	−47.1223	+	47.1223i	−1.91897	+	1.91897i
$604$		0			0
$605$	12.4509	−	30.0593i	0.506203	−	1.22208i
$606$		0			0
$607$	−14.8221	−	35.7837i	−0.601611	−	1.45242i	−0.871922	−	0.489645i	$-0.837127\pi$
$607$	−14.8221	−	35.7837i	−0.601611	−	1.45242i	0.270311	−	0.962773i	$-0.412873\pi$
$608$		0			0
$609$	23.8882	−	9.89482i	0.967999	−	0.400958i
$610$		0			0
$611$	37.8564			1.53151
$612$		0			0
$613$	−47.8564			−1.93290			−0.966451	−	0.256851i	$-0.917315\pi$
$613$	−47.8564			−1.93290			−0.966451	+	0.256851i	$0.917315\pi$
$614$		0			0
$615$	52.4621	−	21.7305i	2.11548	−	0.876260i
$616$		0			0
$617$	13.6118	+	32.8617i	0.547988	+	1.32296i	0.918972	+	0.394322i	$0.129020\pi$
$617$	13.6118	+	32.8617i	0.547988	+	1.32296i	−0.370984	+	0.928639i	$0.620980\pi$
$618$		0			0
$619$	−4.51714	+	10.9053i	−0.181559	+	0.438322i	−0.988288	−	0.152599i	$-0.951236\pi$
$619$	−4.51714	+	10.9053i	−0.181559	+	0.438322i	0.806729	+	0.590921i	$0.201236\pi$
$620$		0			0
$621$	−3.58630	+	3.58630i	−0.143913	+	0.143913i
$622$		0			0
$623$	6.40083	+	2.65131i	0.256444	+	0.106222i
$624$		0			0
$625$			11.0000i			0.440000i
$626$		0			0
$627$	−3.58630	−	3.58630i	−0.143223	−	0.143223i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	29.3195	+	29.3195i	1.16719	+	1.16719i	0.982865	+	0.184328i	$0.0590109\pi$
$631$	29.3195	+	29.3195i	1.16719	+	1.16719i	0.184328	+	0.982865i	$0.440989\pi$
$632$		0			0
$633$			6.39230i			0.254071i
$634$		0			0
$635$	−1.25554	−	0.520061i	−0.0498245	−	0.0206380i
$636$		0			0
$637$	−1.79315	+	1.79315i	−0.0710472	+	0.0710472i
$638$		0			0
$639$	−14.0018	+	33.8033i	−0.553903	+	1.33724i
$640$		0			0
$641$	−4.94741	−	11.9441i	−0.195411	−	0.471764i	0.795554	−	0.605882i	$-0.207180\pi$
$641$	−4.94741	−	11.9441i	−0.195411	−	0.471764i	−0.990965	+	0.134119i	$0.957180\pi$
$642$		0			0
$643$	−30.1078	+	12.4711i	−1.18734	+	0.491811i	−0.886887	−	0.461987i	$-0.847137\pi$
$643$	−30.1078	+	12.4711i	−1.18734	+	0.491811i	−0.300449	+	0.953798i	$0.597137\pi$
$644$		0			0
$645$	−79.4256			−3.12738
$646$		0			0
$647$	17.0718			0.671162			0.335581	−	0.942011i	$-0.391067\pi$
$647$	17.0718			0.671162			0.335581	+	0.942011i	$0.391067\pi$
$648$		0			0
$649$	−2.97063	+	1.23048i	−0.116608	+	0.0483004i
$650$		0			0
$651$	11.9858	+	28.9364i	0.469762	+	1.13411i
$652$		0			0
$653$	3.97696	−	9.60124i	0.155631	−	0.375725i	−0.826763	−	0.562551i	$-0.809820\pi$
$653$	3.97696	−	9.60124i	0.155631	−	0.375725i	0.982393	+	0.186826i	$0.0598199\pi$
$654$		0			0
$655$	−13.8647	+	13.8647i	−0.541740	+	0.541740i
$656$		0			0
$657$	−8.24858	−	3.41668i	−0.321808	−	0.133297i
$658$		0			0
$659$		−	42.9282i		−	1.67225i	−0.548542	−	0.836123i	$-0.684817\pi$
$659$		−	42.9282i		−	1.67225i	0.548542	−	0.836123i	$-0.315183\pi$
$660$		0			0
$661$	10.6574	+	10.6574i	0.414524	+	0.414524i	0.883311	−	0.468787i	$-0.155309\pi$
$661$	10.6574	+	10.6574i	0.414524	+	0.414524i	−0.468787	+	0.883311i	$0.655309\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−9.79796	−	9.79796i	−0.379949	−	0.379949i
$666$		0			0
$667$		−	4.39230i		−	0.170071i
$668$		0			0
$669$	31.2792	+	12.9563i	1.20933	+	0.500919i
$670$		0			0
$671$	−0.480473	+	0.480473i	−0.0185485	+	0.0185485i
$672$		0			0
$673$	0.0549509	−	0.132663i	0.00211820	−	0.00511379i	−0.922817	−	0.385239i	$-0.874119\pi$
$673$	0.0549509	−	0.132663i	0.00211820	−	0.00511379i	0.924935	+	0.380125i	$0.124119\pi$
$674$		0			0
$675$	10.7151	+	25.8686i	0.412426	+	0.995684i
$676$		0			0
$677$	22.4029	−	9.27958i	0.861013	−	0.356643i	0.0919093	−	0.995767i	$-0.470703\pi$
$677$	22.4029	−	9.27958i	0.861013	−	0.356643i	0.769104	+	0.639124i	$0.220703\pi$
$678$		0			0
$679$	−13.4641			−0.516705
$680$		0			0
$681$	−55.1769			−2.11438
$682$		0			0
$683$	−42.5470	+	17.6236i	−1.62802	+	0.674346i	−0.995008	−	0.0997983i	$-0.968180\pi$
$683$	−42.5470	+	17.6236i	−1.62802	+	0.674346i	−0.633009	+	0.774145i	$0.718180\pi$
$684$		0			0
$685$	3.36172	+	8.11592i	0.128445	+	0.310093i
$686$		0			0
$687$	21.3204	−	51.4719i	0.813423	−	1.96378i
$688$		0			0
$689$	49.9507	−	49.9507i	1.90297	−	1.90297i
$690$		0			0
$691$	33.4409	+	13.8517i	1.27215	+	0.526942i	0.913618	−	0.406575i	$-0.133277\pi$
$691$	33.4409	+	13.8517i	1.27215	+	0.526942i	0.358534	+	0.933517i	$0.383277\pi$
$692$		0			0
$693$		−	15.4641i		−	0.587433i
$694$		0			0
$695$	−36.0860	−	36.0860i	−1.36882	−	1.36882i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	11.5911	+	11.5911i	0.438416	+	0.438416i
$700$		0			0
$701$		−	16.3923i		−	0.619129i	−0.950878	−	0.309564i	$-0.899817\pi$
$701$		−	16.3923i		−	0.619129i	0.950878	−	0.309564i	$-0.100183\pi$
$702$		0			0
$703$	−6.13550	−	2.54141i	−0.231405	−	0.0958510i
$704$		0			0
$705$	−46.3644	+	46.3644i	−1.74619	+	1.74619i
$706$		0			0
$707$	2.65131	−	6.40083i	0.0997127	−	0.240728i
$708$		0			0
$709$	−6.21811	−	15.0119i	−0.233526	−	0.563782i	0.763061	−	0.646326i	$-0.223695\pi$
$709$	−6.21811	−	15.0119i	−0.233526	−	0.563782i	−0.996587	+	0.0825442i	$0.973695\pi$
$710$		0			0
$711$	50.3005	−	20.8351i	1.88642	−	0.781379i
$712$		0			0
$713$	5.32051			0.199255
$714$		0			0
$715$	24.0000			0.897549
$716$		0			0
$717$	52.4621	−	21.7305i	1.95923	−	0.811541i
$718$		0			0
$719$	−16.6531	−	40.2042i	−0.621056	−	1.49936i	−0.850465	−	0.526032i	$-0.823679\pi$
$719$	−16.6531	−	40.2042i	−0.621056	−	1.49936i	0.229409	−	0.973330i	$-0.426321\pi$
$720$		0			0
$721$	−11.4256	+	27.5837i	−0.425510	+	1.02727i
$722$		0			0
$723$	3.86370	−	3.86370i	0.143693	−	0.143693i
$724$		0			0
$725$	−22.4029	−	9.27958i	−0.832022	−	0.344635i
$726$		0			0
$727$		−	4.78461i		−	0.177451i	−0.996056	−	0.0887257i	$-0.971721\pi$
$727$		−	4.78461i		−	0.177451i	0.996056	−	0.0887257i	$-0.0282794\pi$
$728$		0			0
$729$	30.9604	+	30.9604i	1.14668	+	1.14668i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−13.2827	−	13.2827i	−0.490609	−	0.490609i	0.417889	−	0.908498i	$-0.362770\pi$
$733$	−13.2827	−	13.2827i	−0.490609	−	0.490609i	−0.908498	+	0.417889i	$0.862770\pi$
$734$		0			0
$735$		−	4.39230i		−	0.162013i
$736$		0			0
$737$	−17.4874	−	7.24351i	−0.644156	−	0.266818i
$738$		0			0
$739$	−8.76268	+	8.76268i	−0.322340	+	0.322340i	−0.849664	−	0.527324i	$-0.823195\pi$
$739$	−8.76268	+	8.76268i	−0.322340	+	0.322340i	0.527324	+	0.849664i	$0.323195\pi$
$740$		0			0
$741$	−8.36408	+	20.1927i	−0.307262	+	0.741797i
$742$		0			0
$743$	9.14956	+	22.0890i	0.335665	+	0.810367i	0.998121	+	0.0612665i	$0.0195140\pi$
$743$	9.14956	+	22.0890i	0.335665	+	0.810367i	−0.662456	+	0.749100i	$0.730486\pi$
$744$		0			0
$745$	19.2025	−	7.95393i	0.703524	−	0.291409i
$746$		0			0
$747$	11.3205			0.414196
$748$		0			0
$749$	−29.3205			−1.07135
$750$		0			0
$751$	17.3062	−	7.16845i	0.631511	−	0.261580i	−0.0438841	−	0.999037i	$-0.513973\pi$
$751$	17.3062	−	7.16845i	0.631511	−	0.261580i	0.675395	+	0.737456i	$0.263973\pi$
$752$		0			0
$753$	−7.24351	−	17.4874i	−0.263968	−	0.637276i
$754$		0			0
$755$	−17.8487	+	43.0907i	−0.649582	+	1.56823i
$756$		0			0
$757$	12.3490	−	12.3490i	0.448831	−	0.448831i	−0.446134	−	0.894966i	$-0.647200\pi$
$757$	12.3490	−	12.3490i	0.448831	−	0.448831i	0.894966	+	0.446134i	$0.147200\pi$
$758$		0			0
$759$	−4.05796	−	1.68086i	−0.147295	−	0.0610114i
$760$		0			0
$761$		−	16.3923i		−	0.594221i	−0.954843	−	0.297110i	$-0.903977\pi$
$761$		−	16.3923i		−	0.594221i	0.954843	−	0.297110i	$-0.0960229\pi$
$762$		0			0
$763$	−27.8038	−	27.8038i	−1.00657	−	1.00657i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.79796	+	9.79796i	0.353784	+	0.353784i
$768$		0			0
$769$			0.392305i			0.0141469i	0.999975	+	0.00707344i	$0.00225156\pi$
$769$			0.392305i			0.0141469i	−0.999975	+	0.00707344i	$0.997748\pi$
$770$		0			0
$771$	−71.6646	−	29.6845i	−2.58094	−	1.06906i
$772$		0			0
$773$	0.480473	−	0.480473i	0.0172814	−	0.0172814i	−0.698413	−	0.715695i	$-0.746110\pi$
$773$	0.480473	−	0.480473i	0.0172814	−	0.0172814i	0.715695	+	0.698413i	$0.246110\pi$
$774$		0			0
$775$	11.2406	−	27.1372i	0.403774	−	0.974796i
$776$		0			0
$777$	−12.9563	−	31.2792i	−0.464804	−	1.12214i
$778$		0			0
$779$	−8.11592	+	3.36172i	−0.290783	+	0.120446i
$780$		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
$787$	−8.84931	−	21.3641i	−0.315444	−	0.761549i	−0.999485	−	0.0321048i	$-0.989779\pi$
$787$	−8.84931	−	21.3641i	−0.315444	−	0.761549i	0.684041	−	0.729444i	$-0.260221\pi$
$788$		0			0
$789$	−11.8357	+	28.5739i	−0.421362	+	1.01726i
$790$		0			0
$791$	−38.3596	+	38.3596i	−1.36391	+	1.36391i
$792$		0			0
$793$	2.70531	+	1.12057i	0.0960683	+	0.0397928i
$794$		0			0
$795$			122.354i			4.33944i
$796$		0			0
$797$	1.96902	+	1.96902i	0.0697461	+	0.0697461i	0.741119	−	0.671373i	$-0.234295\pi$
$797$	1.96902	+	1.96902i	0.0697461	+	0.0697461i	−0.671373	+	0.741119i	$0.734295\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	8.00481	+	8.00481i	0.282836	+	0.282836i
$802$		0			0
$803$		−	2.53590i		−	0.0894899i
$804$		0			0
$805$	−11.0866	−	4.59220i	−0.390750	−	0.161854i
$806$		0			0
$807$	53.0566	−	53.0566i	1.86768	−	1.86768i
$808$		0			0
$809$	−3.00652	+	7.25837i	−0.105703	+	0.255191i	−0.967878	−	0.251421i	$-0.919102\pi$
$809$	−3.00652	+	7.25837i	−0.105703	+	0.255191i	0.862174	+	0.506612i	$0.169102\pi$
$810$		0			0
$811$	−14.3021	−	34.5282i	−0.502213	−	1.21245i	−0.948276	−	0.317448i	$-0.897174\pi$
$811$	−14.3021	−	34.5282i	−0.502213	−	1.21245i	0.446063	−	0.895002i	$-0.352826\pi$
$812$		0			0
$813$	−2.70531	+	1.12057i	−0.0948793	+	0.0393003i
$814$		0			0
$815$	71.3205			2.49825
$816$		0			0
$817$	12.2872			0.429874
$818$		0			0
$819$	−61.5683	+	25.5024i	−2.15137	+	0.891126i
$820$		0			0
$821$	−17.2335	−	41.6054i	−0.601454	−	1.45204i	−0.872085	−	0.489354i	$-0.837233\pi$
$821$	−17.2335	−	41.6054i	−0.601454	−	1.45204i	0.270632	−	0.962683i	$-0.412767\pi$
$822$		0			0
$823$	−0.635352	+	1.53387i	−0.0221470	+	0.0534675i	−0.934566	−	0.355789i	$-0.884212\pi$
$823$	−0.635352	+	1.53387i	−0.0221470	+	0.0534675i	0.912419	+	0.409257i	$0.134212\pi$
$824$		0			0
$825$	−17.1464	+	17.1464i	−0.596962	+	0.596962i
$826$		0			0
$827$	18.0310	+	7.46870i	0.627001	+	0.259712i	0.673478	−	0.739207i	$-0.264800\pi$
$827$	18.0310	+	7.46870i	0.627001	+	0.259712i	−0.0464774	+	0.998919i	$0.514800\pi$
$828$		0			0
$829$		−	39.8564i		−	1.38427i	−0.721768	−	0.692135i	$-0.756670\pi$
$829$		−	39.8564i		−	1.38427i	0.721768	−	0.692135i	$-0.243330\pi$
$830$		0			0
$831$	−12.3490	−	12.3490i	−0.428382	−	0.428382i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−13.8647	−	13.8647i	−0.479809	−	0.479809i
$836$		0			0
$837$			16.7846i			0.580161i
$838$		0			0
$839$	4.14207	+	1.71570i	0.143000	+	0.0592325i	0.453036	−	0.891492i	$-0.350341\pi$
$839$	4.14207	+	1.71570i	0.143000	+	0.0592325i	−0.310036	+	0.950725i	$0.600341\pi$
$840$		0			0
$841$	12.0208	−	12.0208i	0.414511	−	0.414511i
$842$		0			0
$843$	−20.7601	+	50.1193i	−0.715015	+	1.72620i
$844$		0			0
$845$	−22.3458	−	53.9475i	−0.768718	−	1.85585i
$846$		0			0
$847$	−23.7070	+	9.81975i	−0.814582	+	0.337411i
$848$		0			0
$849$	−56.2487			−1.93045
$850$		0			0
$851$	−5.75129			−0.197152
$852$		0			0
$853$	7.62082	−	3.15665i	0.260932	−	0.108081i	−0.248383	−	0.968662i	$-0.579899\pi$
$853$	7.62082	−	3.15665i	0.260932	−	0.108081i	0.509314	+	0.860581i	$0.329899\pi$
$854$		0			0
$855$	−8.66434	−	20.9176i	−0.296314	−	0.715366i
$856$		0			0
$857$	−6.36824	+	15.3743i	−0.217535	+	0.525176i	−0.994545	−	0.104313i	$-0.966736\pi$
$857$	−6.36824	+	15.3743i	−0.217535	+	0.525176i	0.777010	+	0.629489i	$0.216736\pi$
$858$		0			0
$859$	−19.3185	+	19.3185i	−0.659139	+	0.659139i	−0.955176	−	0.296037i	$-0.904335\pi$
$859$	−19.3185	+	19.3185i	−0.659139	+	0.659139i	0.296037	+	0.955176i	$0.404335\pi$
$860$		0			0
$861$	−41.3756	−	17.1383i	−1.41008	−	0.584073i
$862$		0			0
$863$		−	10.1436i		−	0.345292i	−0.984984	−	0.172646i	$-0.944768\pi$
$863$		−	10.1436i		−	0.345292i	0.984984	−	0.172646i	$-0.0552317\pi$
$864$		0			0
$865$	−37.8792	−	37.8792i	−1.28793	−	1.28793i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.9348	+	10.9348i	0.370937	+	0.370937i
$870$		0			0
$871$			81.5692i			2.76387i
$872$		0			0
$873$	−20.3253	−	8.41904i	−0.687909	−	0.284941i
$874$		0			0
$875$	−13.3843	+	13.3843i	−0.452471	+	0.452471i
$876$		0			0
$877$	3.67671	−	8.87635i	0.124154	−	0.299733i	−0.849566	−	0.527482i	$-0.823136\pi$
$877$	3.67671	−	8.87635i	0.124154	−	0.299733i	0.973720	+	0.227748i	$0.0731364\pi$
$878$		0			0
$879$	31.3653	+	75.7226i	1.05793	+	2.55406i
$880$		0			0
$881$	35.8323	−	14.8422i	1.20722	−	0.500047i	0.313896	−	0.949458i	$-0.398366\pi$
$881$	35.8323	−	14.8422i	1.20722	−	0.500047i	0.893326	+	0.449410i	$0.148366\pi$
$882$		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
$887$	10.5429	−	4.36701i	0.353996	−	0.146630i	−0.198597	−	0.980081i	$-0.563639\pi$
$887$	10.5429	−	4.36701i	0.353996	−	0.146630i	0.552593	+	0.833451i	$0.313639\pi$
$888$		0			0
$889$	0.410159	+	0.990211i	0.0137563	+	0.0332106i
$890$		0			0
$891$	−1.19564	+	2.88653i	−0.0400554	+	0.0967023i
$892$		0			0
$893$	7.17260	−	7.17260i	0.240022	−	0.240022i
$894$		0			0
$895$	46.5209	+	19.2696i	1.55502	+	0.644111i
$896$		0			0
$897$			18.9282i			0.631994i
$898$		0			0
$899$	−10.2784	−	10.2784i	−0.342805	−	0.342805i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	44.2939	+	44.2939i	1.47401	+	1.47401i
$904$		0			0
$905$		−	15.7128i		−	0.522312i
$906$		0			0
$907$	31.8229	+	13.1815i	1.05666	+	0.437684i	0.842266	−	0.539063i	$-0.181221\pi$
$907$	31.8229	+	13.1815i	1.05666	+	0.437684i	0.214397	+	0.976747i	$0.431221\pi$
$908$		0			0
$909$	8.00481	−	8.00481i	0.265503	−	0.265503i
$910$		0			0
$911$	−6.04787	+	14.6009i	−0.200375	+	0.483748i	−0.991843	−	0.127462i	$-0.959317\pi$
$911$	−6.04787	+	14.6009i	−0.200375	+	0.483748i	0.791469	+	0.611210i	$0.209317\pi$
$912$		0			0
$913$	1.23048	+	2.97063i	0.0407228	+	0.0983136i
$914$		0			0
$915$	−4.68573	+	1.94089i	−0.154905	+	0.0641639i
$916$		0			0
$917$	15.4641			0.510670
$918$		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
$921$	−62.5585	+	25.9126i	−2.06137	+	0.853848i
$922$		0			0
$923$	17.1383	+	41.3756i	0.564115	+	1.36189i
$924$		0			0
$925$	−12.1507	+	29.3344i	−0.399512	+	0.964508i
$926$		0			0
$927$	−34.4959	+	34.4959i	−1.13299	+	1.13299i
$928$		0			0
$929$	8.97347	+	3.71693i	0.294410	+	0.121949i	0.525000	−	0.851102i	$-0.324065\pi$
$929$	8.97347	+	3.71693i	0.294410	+	0.121949i	−0.230590	+	0.973051i	$0.574065\pi$
$930$		0			0
$931$			0.679492i			0.0222694i
$932$		0			0
$933$	6.03579	+	6.03579i	0.197603	+	0.197603i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	0.101536	+	0.101536i	0.00331704	+	0.00331704i	0.708763	−	0.705446i	$-0.249253\pi$
$937$	0.101536	+	0.101536i	0.00331704	+	0.00331704i	−0.705446	+	0.708763i	$0.749253\pi$
$938$		0			0
$939$			57.1769i			1.86590i
$940$		0			0
$941$	38.1752	+	15.8127i	1.24448	+	0.515478i	0.905110	−	0.425176i	$-0.139788\pi$
$941$	38.1752	+	15.8127i	1.24448	+	0.515478i	0.339365	+	0.940655i	$0.389788\pi$
$942$		0			0
$943$	−5.37945	+	5.37945i	−0.175179	+	0.175179i
$944$		0			0
$945$	14.4870	−	34.9748i	0.471263	−	1.13773i
$946$		0			0
$947$	18.8540	+	45.5176i	0.612674	+	1.47912i	0.860052	+	0.510206i	$0.170431\pi$
$947$	18.8540	+	45.5176i	0.612674	+	1.47912i	−0.247379	+	0.968919i	$0.579569\pi$
$948$		0			0
$949$	−10.0963	+	4.18204i	−0.327741	+	0.135755i
$950$		0			0
$951$	−23.3205			−0.756219
$952$		0			0
$953$	6.24871			0.202416			0.101208	−	0.994865i	$-0.467729\pi$
$953$	6.24871			0.202416			0.101208	+	0.994865i	$0.467729\pi$
$954$		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
$961$	−9.46979	+	9.46979i	−0.305477	+	0.305477i
$962$		0			0
$963$	−44.2621	−	18.3340i	−1.42633	−	0.590804i
$964$		0			0
$965$			72.4974i			2.33377i
$966$		0			0
$967$	−19.5216	−	19.5216i	−0.627772	−	0.627772i	0.319735	−	0.947507i	$-0.396406\pi$
$967$	−19.5216	−	19.5216i	−0.627772	−	0.627772i	−0.947507	+	0.319735i	$0.896406\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.2165	+	14.2165i	0.456228	+	0.456228i	0.897415	−	0.441187i	$-0.145442\pi$
$971$	14.2165	+	14.2165i	0.456228	+	0.456228i	−0.441187	+	0.897415i	$0.645442\pi$
$972$		0			0
$973$			40.2487i			1.29031i
$974$		0			0
$975$	96.5430	+	39.9894i	3.09185	+	1.28069i
$976$		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
$979$	−1.23048	+	2.97063i	−0.0393262	+	0.0949419i
$980$		0			0
$981$	−24.5869	−	59.3581i	−0.785000	−	1.89516i
$982$		0			0
$983$	33.1756	−	13.7418i	1.05814	−	0.438294i	0.215347	−	0.976538i	$-0.430912\pi$
$983$	33.1756	−	13.7418i	1.05814	−	0.438294i	0.842789	+	0.538243i	$0.180912\pi$
$984$		0			0
$985$	12.0000			0.382352
$986$		0			0
$987$	51.7128			1.64604
$988$		0			0
$989$	9.83102	−	4.07214i	0.312608	−	0.129487i
$990$		0			0
$991$	0.0750643	+	0.181221i	0.00238450	+	0.00575668i	0.925067	−	0.379803i	$-0.124008\pi$
$991$	0.0750643	+	0.181221i	0.00238450	+	0.00575668i	−0.922683	+	0.385560i	$0.874008\pi$
$992$		0			0
$993$	−20.1998	+	48.7666i	−0.641021	+	1.54756i
$994$		0			0
$995$	−10.2784	+	10.2784i	−0.325848	+	0.325848i
$996$		0			0
$997$	−19.9629	−	8.26891i	−0.632232	−	0.261879i	0.0434693	−	0.999055i	$-0.486159\pi$
$997$	−19.9629	−	8.26891i	−0.632232	−	0.261879i	−0.675701	+	0.737176i	$0.736159\pi$
$998$		0			0
$999$		−	18.1436i		−	0.574038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1156.2.h.f.733.4		16
17.2	even	8	inner	1156.2.h.f.977.4		16
17.3	odd	16		68.2.a.a.1.2	✓	2
17.4	even	4	inner	1156.2.h.f.1001.1		16
17.5	odd	16		1156.2.b.c.577.4		4
17.6	odd	16		1156.2.e.d.905.4		8
17.7	odd	16		1156.2.e.d.829.1		8
17.8	even	8	inner	1156.2.h.f.757.1		16
17.9	even	8	inner	1156.2.h.f.757.4		16
17.10	odd	16		1156.2.e.d.829.4		8
17.11	odd	16		1156.2.e.d.905.1		8
17.12	odd	16		1156.2.b.c.577.1		4
17.13	even	4	inner	1156.2.h.f.1001.4		16
17.14	odd	16		1156.2.a.a.1.1		2
17.15	even	8	inner	1156.2.h.f.977.1		16
17.16	even	2	inner	1156.2.h.f.733.1		16
51.20	even	16		612.2.a.e.1.2		2
68.3	even	16		272.2.a.e.1.1		2
68.31	even	16		4624.2.a.x.1.2		2
85.3	even	16		1700.2.e.c.749.4		4
85.37	even	16		1700.2.e.c.749.1		4
85.54	odd	16		1700.2.a.d.1.1		2
119.20	even	16		3332.2.a.h.1.1		2
136.3	even	16		1088.2.a.t.1.2		2
136.37	odd	16		1088.2.a.p.1.1		2
187.54	even	16		8228.2.a.k.1.2		2
204.71	odd	16		2448.2.a.y.1.2		2
340.139	even	16		6800.2.a.bh.1.2		2
408.173	even	16		9792.2.a.cr.1.1		2
408.275	odd	16		9792.2.a.cs.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.a.a.1.2	✓	2	17.3	odd	16
272.2.a.e.1.1		2	68.3	even	16
612.2.a.e.1.2		2	51.20	even	16
1088.2.a.p.1.1		2	136.37	odd	16
1088.2.a.t.1.2		2	136.3	even	16
1156.2.a.a.1.1		2	17.14	odd	16
1156.2.b.c.577.1		4	17.12	odd	16
1156.2.b.c.577.4		4	17.5	odd	16
1156.2.e.d.829.1		8	17.7	odd	16
1156.2.e.d.829.4		8	17.10	odd	16
1156.2.e.d.905.1		8	17.11	odd	16
1156.2.e.d.905.4		8	17.6	odd	16
1156.2.h.f.733.1		16	17.16	even	2	inner
1156.2.h.f.733.4		16	1.1	even	1	trivial
1156.2.h.f.757.1		16	17.8	even	8	inner
1156.2.h.f.757.4		16	17.9	even	8	inner
1156.2.h.f.977.1		16	17.15	even	8	inner
1156.2.h.f.977.4		16	17.2	even	8	inner
1156.2.h.f.1001.1		16	17.4	even	4	inner
1156.2.h.f.1001.4		16	17.13	even	4	inner
1700.2.a.d.1.1		2	85.54	odd	16
1700.2.e.c.749.1		4	85.37	even	16
1700.2.e.c.749.4		4	85.3	even	16
2448.2.a.y.1.2		2	204.71	odd	16
3332.2.a.h.1.1		2	119.20	even	16
4624.2.a.x.1.2		2	68.31	even	16
6800.2.a.bh.1.2		2	340.139	even	16
8228.2.a.k.1.2		2	187.54	even	16
9792.2.a.cr.1.1		2	408.173	even	16
9792.2.a.cs.1.1		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)

\(f(q)\)	\(=\)	\(q+(2.52409 - 1.04551i) q^{3} +(1.32565 + 3.20041i) q^{5} +(1.04551 - 2.52409i) q^{7} +(3.15660 - 3.15660i) q^{9} +O(q^{10})\)	\(q+(2.52409 - 1.04551i) q^{3} +(1.32565 + 3.20041i) q^{5} +(1.04551 - 2.52409i) q^{7} +(3.15660 - 3.15660i) q^{9} +(1.17143 + 0.485223i) q^{11} -5.46410i q^{13} +(6.69213 + 6.69213i) q^{15} +(-1.03528 - 1.03528i) q^{19} -7.46410i q^{21} +(-1.17143 - 0.485223i) q^{23} +(-4.94975 + 4.94975i) q^{25} +(1.53073 - 3.69552i) q^{27} +(1.32565 + 3.20041i) q^{29} +(-3.87674 + 1.60580i) q^{31} +3.46410 q^{33} +9.46410 q^{35} +(4.19062 - 1.73581i) q^{37} +(-5.71278 - 13.7919i) q^{39} +(2.29610 - 5.54328i) q^{41} +(-5.93426 + 5.93426i) q^{43} +(14.2870 + 5.91786i) q^{45} +6.92820i q^{47} +(-0.328169 - 0.328169i) q^{49} +(9.14162 + 9.14162i) q^{53} +4.39230i q^{55} +(-3.69552 - 1.53073i) q^{57} +(-1.79315 + 1.79315i) q^{59} +(-0.205079 + 0.495106i) q^{61} +(-4.66727 - 11.2678i) q^{63} +(17.4874 - 7.24351i) q^{65} -14.9282 q^{67} -3.46410 q^{69} +(-7.57226 + 3.13653i) q^{71} +(-0.765367 - 1.84776i) q^{73} +(-7.31857 + 17.6686i) q^{75} +(2.44949 - 2.44949i) q^{77} +(11.2678 + 4.66727i) q^{79} +2.46410i q^{81} +(1.79315 + 1.79315i) q^{83} +(6.69213 + 6.69213i) q^{87} +2.53590i q^{89} +(-13.7919 - 5.71278i) q^{91} +(-8.10634 + 8.10634i) q^{93} +(1.94089 - 4.68573i) q^{95} +(-1.88594 - 4.55307i) q^{97} +(5.22939 - 2.16609i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * 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

Varieties

Fields

Representations

Groups

Database

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