LMFDB - Embedded newform 1156.2.h.f.733.1

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			733.1
Root			$-0.608761 + 0.793353i$ of defining polynomial
Character	$\chi$	$=$	1156.733
Dual form			1156.2.h.f.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.52409 + 1.04551i) q^{3} +(-1.32565 - 3.20041i) q^{5} +(-1.04551 + 2.52409i) q^{7} +(3.15660 - 3.15660i) q^{9} +(-1.17143 - 0.485223i) q^{11} -5.46410i q^{13} +(6.69213 + 6.69213i) q^{15} +(-1.03528 - 1.03528i) q^{19} -7.46410i q^{21} +(1.17143 + 0.485223i) q^{23} +(-4.94975 + 4.94975i) q^{25} +(-1.53073 + 3.69552i) q^{27} +(-1.32565 - 3.20041i) q^{29} +(3.87674 - 1.60580i) q^{31} +3.46410 q^{33} +9.46410 q^{35} +(-4.19062 + 1.73581i) q^{37} +(5.71278 + 13.7919i) q^{39} +(-2.29610 + 5.54328i) q^{41} +(-5.93426 + 5.93426i) q^{43} +(-14.2870 - 5.91786i) q^{45} +6.92820i q^{47} +(-0.328169 - 0.328169i) q^{49} +(9.14162 + 9.14162i) q^{53} +4.39230i q^{55} +(3.69552 + 1.53073i) q^{57} +(-1.79315 + 1.79315i) q^{59} +(0.205079 - 0.495106i) q^{61} +(4.66727 + 11.2678i) q^{63} +(-17.4874 + 7.24351i) q^{65} -14.9282 q^{67} -3.46410 q^{69} +(7.57226 - 3.13653i) q^{71} +(0.765367 + 1.84776i) q^{73} +(7.31857 - 17.6686i) q^{75} +(2.44949 - 2.44949i) q^{77} +(-11.2678 - 4.66727i) q^{79} +2.46410i q^{81} +(1.79315 + 1.79315i) q^{83} +(6.69213 + 6.69213i) q^{87} +2.53590i q^{89} +(13.7919 + 5.71278i) q^{91} +(-8.10634 + 8.10634i) q^{93} +(-1.94089 + 4.68573i) q^{95} +(1.88594 + 4.55307i) q^{97} +(-5.22939 + 2.16609i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 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
$3$	−2.52409	+	1.04551i	−1.45728	+	0.603626i	−0.963918	−	0.266198i	$-0.914233\pi$
$3$	−2.52409	+	1.04551i	−1.45728	+	0.603626i	−0.493363	+	0.869823i	$0.664233\pi$
$4$		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
$7$	−1.04551	+	2.52409i	−0.395166	+	0.954015i	0.593630	+	0.804738i	$0.297694\pi$
$7$	−1.04551	+	2.52409i	−0.395166	+	0.954015i	−0.988796	+	0.149276i	$0.952306\pi$
$8$		0			0
$9$	3.15660	−	3.15660i	1.05220	−	1.05220i
$10$		0			0
$11$	−1.17143	−	0.485223i	−0.353200	−	0.146300i	0.199027	−	0.979994i	$-0.436222\pi$
$11$	−1.17143	−	0.485223i	−0.353200	−	0.146300i	−0.552227	+	0.833694i	$0.686222\pi$
$12$		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	0.501455	−	0.865184i	$-0.332798\pi$
$23$	1.17143	+	0.485223i	0.244261	+	0.101176i	−0.257195	+	0.966360i	$0.582798\pi$
$24$		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
$31$	3.87674	−	1.60580i	0.696283	−	0.288410i	−0.00633216	−	0.999980i	$-0.502016\pi$
$31$	3.87674	−	1.60580i	0.696283	−	0.288410i	0.702615	+	0.711570i	$0.252016\pi$
$32$		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	−0.699556	−	0.714578i	$-0.746619\pi$
$37$	−4.19062	+	1.73581i	−0.688934	+	0.285366i	0.0106218	+	0.999944i	$0.496619\pi$
$38$		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	$0.280213\pi$
$41$	−2.29610	+	5.54328i	−0.358591	+	0.865714i	−0.995499	+	0.0947747i	$0.969787\pi$
$42$		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	−0.910207	−	0.414154i	$-0.864077\pi$
$61$	0.205079	−	0.495106i	0.0262577	−	0.0633918i	0.936465	+	0.350762i	$0.114077\pi$
$62$		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	0.114956	−	0.993371i	$-0.463327\pi$
$71$	7.57226	−	3.13653i	0.898662	−	0.372238i	0.783705	+	0.621133i	$0.213327\pi$
$72$		0			0
$73$	0.765367	+	1.84776i	0.0895794	+	0.216264i	0.962319	−	0.271921i	$-0.0876591\pi$
$73$	0.765367	+	1.84776i	0.0895794	+	0.216264i	−0.872740	+	0.488185i	$0.837659\pi$
$74$		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	−0.355452	−	0.934694i	$-0.615673\pi$
$79$	−11.2678	−	4.66727i	−1.26772	−	0.525108i	−0.912271	+	0.409586i	$0.865673\pi$
$80$		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	0.990241	−	0.139366i	$-0.0445064\pi$
$97$	1.88594	+	4.55307i	0.191488	+	0.462294i	−0.798753	+	0.601660i	$0.794506\pi$
$98$		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	$0.0486037\pi$
$107$	4.10698	+	9.91512i	0.397037	+	0.958531i	−0.591329	+	0.806431i	$0.701396\pi$
$108$		0			0
$109$	−5.50770	+	13.2968i	−0.527542	+	1.27360i	0.405587	+	0.914056i	$0.367067\pi$
$109$	−5.50770	+	13.2968i	−0.527542	+	1.27360i	−0.933129	+	0.359542i	$0.882933\pi$
$110$		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	$0.00867700\pi$
$113$	18.3449	+	7.59872i	1.72575	+	0.714827i	0.726117	+	0.687571i	$0.241323\pi$
$114$		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	0.800564	−	0.599247i	$-0.204533\pi$
$131$	−2.16609	−	5.22939i	−0.189252	−	0.456894i	−0.989816	+	0.142353i	$0.954533\pi$
$132$		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	0.278420	−	0.960460i	$-0.410189\pi$
$139$	13.6106	−	5.63771i	1.15444	−	0.478184i	0.876020	+	0.482275i	$0.160189\pi$
$140$		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	$0.423537\pi$
$163$	−7.87886	+	19.0213i	−0.617120	+	1.48986i	−0.855033	+	0.518573i	$0.826463\pi$
$164$		0			0
$165$	−4.59220	−	11.0866i	−0.357502	−	0.863087i
$166$		0			0
$167$	5.22939	−	2.16609i	0.404663	−	0.167617i	−0.171062	−	0.985260i	$-0.554720\pi$
$167$	5.22939	−	2.16609i	0.404663	−	0.167617i	0.575725	+	0.817643i	$0.304720\pi$
$168$		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	0.233532	−	0.972349i	$-0.424972\pi$
$173$	14.2870	−	5.91786i	1.08622	−	0.449926i	0.852686	+	0.522423i	$0.174972\pi$
$174$		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	0.532950	−	0.846147i	$-0.321083\pi$
$181$	4.19062	+	1.73581i	0.311487	+	0.129022i	−0.221463	+	0.975169i	$0.571083\pi$
$182$		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	−0.444171	−	0.895942i	$-0.646502\pi$
$193$	−19.3351	−	8.00888i	−1.39177	−	0.576492i	−0.947603	+	0.319451i	$0.896502\pi$
$194$		0			0
$195$	36.5665	−	36.5665i	2.61858	−	2.61858i
$196$		0			0
$197$	−1.32565	+	3.20041i	−0.0944490	+	0.228020i	−0.964042	−	0.265748i	$-0.914381\pi$
$197$	−1.32565	+	3.20041i	−0.0944490	+	0.228020i	0.869593	+	0.493768i	$0.164381\pi$
$198$		0			0
$199$	−1.60580	−	3.87674i	−0.113832	−	0.274815i	0.856688	−	0.515835i	$-0.172518\pi$
$199$	−1.60580	−	3.87674i	−0.113832	−	0.274815i	−0.970520	+	0.241020i	$0.922518\pi$
$200$		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	−0.890058	−	0.455847i	$-0.849336\pi$
$211$	0.895382	−	2.16164i	0.0616406	−	0.148814i	0.951699	+	0.307033i	$0.0993364\pi$
$212$		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	0.903223	−	0.429171i	$-0.141194\pi$
$227$	18.6588	+	7.72873i	1.23843	+	0.512974i	0.335206	+	0.942145i	$0.391194\pi$
$228$		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	0.830649	−	0.556796i	$-0.187969\pi$
$233$	−2.29610	−	5.54328i	−0.150423	−	0.363152i	−0.981072	+	0.193644i	$0.937969\pi$
$234$		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	−0.441401	−	0.897310i	$-0.645518\pi$
$241$	−1.84776	+	0.765367i	−0.119025	+	0.0493016i	0.322376	+	0.946612i	$0.395518\pi$
$242$		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	−0.982780	−	0.184780i	$-0.940843\pi$
$269$	−25.3735	+	10.5101i	−1.54705	+	0.640809i	−0.564271	+	0.825590i	$0.690843\pi$
$270$		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	0.980174	−	0.198141i	$-0.0634903\pi$
$277$	2.44623	+	5.90572i	0.146980	+	0.354840i	−0.833194	+	0.552981i	$0.813490\pi$
$278$		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	0.868017	−	0.496534i	$-0.165394\pi$
$283$	19.0213	+	7.87886i	1.13070	+	0.468350i	0.262679	+	0.964883i	$0.415394\pi$
$284$		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	0.886348	−	0.463019i	$-0.153234\pi$
$311$	−1.19564	−	2.88653i	−0.0677985	−	0.163680i	−0.954147	+	0.299339i	$0.903234\pi$
$312$		0			0
$313$	8.00888	−	19.3351i	0.452688	−	1.09289i	−0.518607	−	0.855012i	$-0.673549\pi$
$313$	8.00888	−	19.3351i	0.452688	−	1.09289i	0.971296	−	0.237874i	$-0.0764506\pi$
$314$		0			0
$315$	29.8744	−	29.8744i	1.68323	−	1.68323i
$316$		0			0
$317$	7.88614	+	3.26655i	0.442930	+	0.183468i	0.592991	−	0.805209i	$-0.297947\pi$
$317$	7.88614	+	3.26655i	0.442930	+	0.183468i	−0.150061	+	0.988677i	$0.547947\pi$
$318$		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	−0.546817	−	0.837252i	$-0.684161\pi$
$337$	−6.26816	+	2.59636i	−0.341449	+	0.141433i	0.205369	+	0.978685i	$0.434161\pi$
$338$		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	$0.492037\pi$
$347$	−13.0314	+	31.4605i	−0.699560	+	1.68889i	−0.724572	+	0.689199i	$0.757963\pi$
$348$		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	−0.945525	−	0.325551i	$-0.894450\pi$
$367$	−0.895382	+	2.16164i	−0.0467386	+	0.112837i	0.898786	+	0.438388i	$0.144450\pi$
$368$		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	0.863608	−	0.504164i	$-0.168199\pi$
$379$	−2.01596	−	4.86695i	−0.103553	−	0.249998i	−0.967161	+	0.254165i	$0.918199\pi$
$380$		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	0.508885	−	0.860835i	$-0.330058\pi$
$397$	5.18083	+	2.14597i	0.260019	+	0.107703i	−0.248866	+	0.968538i	$0.580058\pi$
$398$		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	$0.417748\pi$
$401$	−12.1909	+	29.4315i	−0.608785	+	1.46974i	−0.864322	+	0.502939i	$0.832252\pi$
$402$		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	−0.248923	−	0.968523i	$-0.580076\pi$
$419$	−22.7168	−	9.40960i	−1.10979	−	0.459689i	−0.860864	+	0.508835i	$0.830076\pi$
$420$		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	−0.0466130	−	0.998913i	$-0.514843\pi$
$431$	−16.3159	−	6.75829i	−0.785912	−	0.325535i	−0.739299	+	0.673378i	$0.764843\pi$
$432$		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	−0.845901	−	0.533341i	$-0.820936\pi$
$439$	−22.3543	+	9.25947i	−1.06691	+	0.441930i	−0.221013	+	0.975271i	$0.570936\pi$
$440$		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	−0.860393	−	0.509630i	$-0.829782\pi$
$449$	2.29610	−	5.54328i	0.108360	−	0.261603i	0.968753	+	0.248027i	$0.0797822\pi$
$450$		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	0.0225928	−	0.999745i	$-0.492808\pi$
$479$	16.3159	−	6.75829i	0.745495	−	0.308794i	0.722902	+	0.690951i	$0.242808\pi$
$480$		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	0.505763	−	0.862672i	$-0.331211\pi$
$487$	5.59184	+	2.31621i	0.253390	+	0.104958i	−0.252373	+	0.967630i	$0.581211\pi$
$488$		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	−0.199313	−	0.979936i	$-0.563871\pi$
$499$	−23.0792	−	9.55972i	−1.03317	−	0.427952i	−0.833855	+	0.551984i	$0.813871\pi$
$500$		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	$0.331710\pi$
$503$	−10.3800	+	25.0596i	−0.462823	+	1.11735i	−0.967233	+	0.253890i	$0.918290\pi$
$504$		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	0.257936	−	0.966162i	$-0.416958\pi$
$521$	−5.54328	−	2.29610i	−0.242855	−	0.100594i	−0.500791	+	0.865568i	$0.666958\pi$
$522$		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	0.0137749	−	0.999905i	$-0.495615\pi$
$541$	16.9923	−	7.03843i	0.730555	−	0.302606i	0.716780	+	0.697299i	$0.245615\pi$
$542$		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	−0.999657	−	0.0261774i	$-0.991667\pi$
$547$	−39.4793	+	16.3528i	−1.68801	+	0.699197i	−0.688354	+	0.725375i	$0.741667\pi$
$548$		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	−0.987579	−	0.157120i	$-0.949779\pi$
$571$	−4.25711	+	10.2776i	−0.178154	+	0.430103i	0.809425	+	0.587223i	$0.199779\pi$
$572$		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	0.170098	−	0.985427i	$-0.445592\pi$
$601$	−9.96368	−	4.12709i	−0.406427	−	0.168348i	−0.576525	+	0.817080i	$0.695592\pi$
$602$		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	$0.162873\pi$
$607$	14.8221	+	35.7837i	0.601611	+	1.45242i	−0.270311	+	0.962773i	$0.587127\pi$
$608$		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	$-0.870980\pi$
$617$	−13.6118	−	32.8617i	−0.547988	−	1.32296i	0.370984	−	0.928639i	$-0.379020\pi$
$618$		0			0
$619$	4.51714	−	10.9053i	0.181559	−	0.438322i	−0.806729	−	0.590921i	$-0.798764\pi$
$619$	4.51714	−	10.9053i	0.181559	−	0.438322i	0.988288	+	0.152599i	$0.0487643\pi$
$620$		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	0.990965	−	0.134119i	$-0.0428203\pi$
$641$	4.94741	+	11.9441i	0.195411	+	0.471764i	−0.795554	+	0.605882i	$0.792820\pi$
$642$		0			0
$643$	30.1078	−	12.4711i	1.18734	−	0.491811i	0.300449	−	0.953798i	$-0.402863\pi$
$643$	30.1078	−	12.4711i	1.18734	−	0.491811i	0.886887	+	0.461987i	$0.152863\pi$
$644$		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	−0.982393	−	0.186826i	$-0.940180\pi$
$653$	−3.97696	+	9.60124i	−0.155631	+	0.375725i	0.826763	+	0.562551i	$0.190180\pi$
$654$		0			0
$655$	−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	−0.924935	−	0.380125i	$-0.875881\pi$
$673$	−0.0549509	+	0.132663i	−0.00211820	+	0.00511379i	0.922817	+	0.385239i	$0.125881\pi$
$674$		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
$679$	−13.4641			−0.516705
$680$		0			0
$681$	−55.1769			−2.11438
$682$		0			0
$683$	42.5470	−	17.6236i	1.62802	−	0.674346i	0.633009	−	0.774145i	$-0.281820\pi$
$683$	42.5470	−	17.6236i	1.62802	−	0.674346i	0.995008	+	0.0997983i	$0.0318197\pi$
$684$		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	−0.358534	−	0.933517i	$-0.616723\pi$
$691$	−33.4409	−	13.8517i	−1.27215	−	0.526942i	−0.913618	+	0.406575i	$0.866723\pi$
$692$		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	0.996587	−	0.0825442i	$-0.0263046\pi$
$709$	6.21811	+	15.0119i	0.233526	+	0.563782i	−0.763061	+	0.646326i	$0.776305\pi$
$710$		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	$0.176321\pi$
$719$	16.6531	+	40.2042i	0.621056	+	1.49936i	−0.229409	+	0.973330i	$0.573679\pi$
$720$		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	$-0.980486\pi$
$743$	−9.14956	−	22.0890i	−0.335665	−	0.810367i	0.662456	−	0.749100i	$-0.269514\pi$
$744$		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	−0.675395	−	0.737456i	$-0.736027\pi$
$751$	−17.3062	+	7.16845i	−0.631511	+	0.261580i	0.0438841	+	0.999037i	$0.486027\pi$
$752$		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	$0.0102210\pi$
$787$	8.84931	+	21.3641i	0.315444	+	0.761549i	−0.684041	+	0.729444i	$0.739779\pi$
$788$		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	−0.862174	−	0.506612i	$-0.830898\pi$
$809$	3.00652	−	7.25837i	0.105703	−	0.255191i	0.967878	+	0.251421i	$0.0808978\pi$
$810$		0			0
$811$	14.3021	+	34.5282i	0.502213	+	1.21245i	0.948276	+	0.317448i	$0.102826\pi$
$811$	14.3021	+	34.5282i	0.502213	+	1.21245i	−0.446063	+	0.895002i	$0.647174\pi$
$812$		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	$0.162767\pi$
$821$	17.2335	+	41.6054i	0.601454	+	1.45204i	−0.270632	+	0.962683i	$0.587233\pi$
$822$		0			0
$823$	0.635352	−	1.53387i	0.0221470	−	0.0534675i	−0.912419	−	0.409257i	$-0.865788\pi$
$823$	0.635352	−	1.53387i	0.0221470	−	0.0534675i	0.934566	+	0.355789i	$0.115788\pi$
$824$		0			0
$825$	−17.1464	+	17.1464i	−0.596962	+	0.596962i
$826$		0			0
$827$	−18.0310	−	7.46870i	−0.627001	−	0.259712i	0.0464774	−	0.998919i	$-0.485200\pi$
$827$	−18.0310	−	7.46870i	−0.627001	−	0.259712i	−0.673478	+	0.739207i	$0.735200\pi$
$828$		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	0.310036	−	0.950725i	$-0.399659\pi$
$839$	−4.14207	−	1.71570i	−0.143000	−	0.0592325i	−0.453036	+	0.891492i	$0.649659\pi$
$840$		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	−0.509314	−	0.860581i	$-0.670101\pi$
$853$	−7.62082	+	3.15665i	−0.260932	+	0.108081i	0.248383	+	0.968662i	$0.420101\pi$
$854$		0			0
$855$	8.66434	+	20.9176i	0.296314	+	0.715366i
$856$		0			0
$857$	6.36824	−	15.3743i	0.217535	−	0.525176i	−0.777010	−	0.629489i	$-0.783264\pi$
$857$	6.36824	−	15.3743i	0.217535	−	0.525176i	0.994545	+	0.104313i	$0.0332643\pi$
$858$		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	−0.973720	−	0.227748i	$-0.926864\pi$
$877$	−3.67671	+	8.87635i	−0.124154	+	0.299733i	0.849566	+	0.527482i	$0.176864\pi$
$878$		0			0
$879$	−31.3653	−	75.7226i	−1.05793	−	2.55406i
$880$		0			0
$881$	−35.8323	+	14.8422i	−1.20722	+	0.500047i	−0.893326	−	0.449410i	$-0.851634\pi$
$881$	−35.8323	+	14.8422i	−1.20722	+	0.500047i	−0.313896	+	0.949458i	$0.601634\pi$
$882$		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	−0.552593	−	0.833451i	$-0.686361\pi$
$887$	−10.5429	+	4.36701i	−0.353996	+	0.146630i	0.198597	+	0.980081i	$0.436361\pi$
$888$		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	−0.214397	−	0.976747i	$-0.568779\pi$
$907$	−31.8229	−	13.1815i	−1.05666	−	0.437684i	−0.842266	+	0.539063i	$0.818779\pi$
$908$		0			0
$909$	8.00481	−	8.00481i	0.265503	−	0.265503i
$910$		0			0
$911$	6.04787	−	14.6009i	0.200375	−	0.483748i	−0.791469	−	0.611210i	$-0.790683\pi$
$911$	6.04787	−	14.6009i	0.200375	−	0.483748i	0.991843	+	0.127462i	$0.0406831\pi$
$912$		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	0.230590	−	0.973051i	$-0.425935\pi$
$929$	−8.97347	−	3.71693i	−0.294410	−	0.121949i	−0.525000	+	0.851102i	$0.675935\pi$
$930$		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	−0.339365	−	0.940655i	$-0.610212\pi$
$941$	−38.1752	−	15.8127i	−1.24448	−	0.515478i	−0.905110	+	0.425176i	$0.860212\pi$
$942$		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	$-0.829569\pi$
$947$	−18.8540	−	45.5176i	−0.612674	−	1.47912i	0.247379	−	0.968919i	$-0.420431\pi$
$948$		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	−0.842789	−	0.538243i	$-0.819088\pi$
$983$	−33.1756	+	13.7418i	−1.05814	+	0.438294i	−0.215347	+	0.976538i	$0.569088\pi$
$984$		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	0.922683	−	0.385560i	$-0.125992\pi$
$991$	−0.0750643	−	0.181221i	−0.00238450	−	0.00575668i	−0.925067	+	0.379803i	$0.875992\pi$
$992$		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	0.675701	−	0.737176i	$-0.263841\pi$
$997$	19.9629	+	8.26891i	0.632232	+	0.261879i	−0.0434693	+	0.999055i	$0.513841\pi$
$998$		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.733.1		16
17.2	even	8	inner	1156.2.h.f.977.1		16
17.3	odd	16		1156.2.a.a.1.1		2
17.4	even	4	inner	1156.2.h.f.1001.4		16
17.5	odd	16		1156.2.b.c.577.1		4
17.6	odd	16		1156.2.e.d.905.1		8
17.7	odd	16		1156.2.e.d.829.4		8
17.8	even	8	inner	1156.2.h.f.757.4		16
17.9	even	8	inner	1156.2.h.f.757.1		16
17.10	odd	16		1156.2.e.d.829.1		8
17.11	odd	16		1156.2.e.d.905.4		8
17.12	odd	16		1156.2.b.c.577.4		4
17.13	even	4	inner	1156.2.h.f.1001.1		16
17.14	odd	16		68.2.a.a.1.2	✓	2
17.15	even	8	inner	1156.2.h.f.977.4		16
17.16	even	2	inner	1156.2.h.f.733.4		16
51.14	even	16		612.2.a.e.1.2		2
68.3	even	16		4624.2.a.x.1.2		2
68.31	even	16		272.2.a.e.1.1		2
85.14	odd	16		1700.2.a.d.1.1		2
85.48	even	16		1700.2.e.c.749.4		4
85.82	even	16		1700.2.e.c.749.1		4
119.48	even	16		3332.2.a.h.1.1		2
136.99	even	16		1088.2.a.t.1.2		2
136.133	odd	16		1088.2.a.p.1.1		2
187.65	even	16		8228.2.a.k.1.2		2
204.167	odd	16		2448.2.a.y.1.2		2
340.99	even	16		6800.2.a.bh.1.2		2
408.269	even	16		9792.2.a.cr.1.1		2
408.371	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	17.14	odd	16
272.2.a.e.1.1		2	68.31	even	16
612.2.a.e.1.2		2	51.14	even	16
1088.2.a.p.1.1		2	136.133	odd	16
1088.2.a.t.1.2		2	136.99	even	16
1156.2.a.a.1.1		2	17.3	odd	16
1156.2.b.c.577.1		4	17.5	odd	16
1156.2.b.c.577.4		4	17.12	odd	16
1156.2.e.d.829.1		8	17.10	odd	16
1156.2.e.d.829.4		8	17.7	odd	16
1156.2.e.d.905.1		8	17.6	odd	16
1156.2.e.d.905.4		8	17.11	odd	16
1156.2.h.f.733.1		16	1.1	even	1	trivial
1156.2.h.f.733.4		16	17.16	even	2	inner
1156.2.h.f.757.1		16	17.9	even	8	inner
1156.2.h.f.757.4		16	17.8	even	8	inner
1156.2.h.f.977.1		16	17.2	even	8	inner
1156.2.h.f.977.4		16	17.15	even	8	inner
1156.2.h.f.1001.1		16	17.13	even	4	inner
1156.2.h.f.1001.4		16	17.4	even	4	inner
1700.2.a.d.1.1		2	85.14	odd	16
1700.2.e.c.749.1		4	85.82	even	16
1700.2.e.c.749.4		4	85.48	even	16
2448.2.a.y.1.2		2	204.167	odd	16
3332.2.a.h.1.1		2	119.48	even	16
4624.2.a.x.1.2		2	68.3	even	16
6800.2.a.bh.1.2		2	340.99	even	16
8228.2.a.k.1.2		2	187.65	even	16
9792.2.a.cr.1.1		2	408.269	even	16
9792.2.a.cs.1.1		2	408.371	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)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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