LMFDB - Embedded newform 1156.2.h.f.1001.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1156,2,Mod(733,1156)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(33)] == traces)

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			1001.4
Root			$0.793353 + 0.608761i$ of defining polynomial
Character	$\chi$	$=$	1156.1001
Dual form			1156.2.h.f.977.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04551 + 2.52409i) q^{3} +(-3.20041 + 1.32565i) q^{5} +(-2.52409 - 1.04551i) q^{7} +(-3.15660 + 3.15660i) q^{9} +(0.485223 - 1.17143i) q^{11} -5.46410i q^{13} +(-6.69213 - 6.69213i) q^{15} +(1.03528 + 1.03528i) q^{19} -7.46410i q^{21} +(-0.485223 + 1.17143i) q^{23} +(4.94975 - 4.94975i) q^{25} +(-3.69552 - 1.53073i) q^{27} +(-3.20041 + 1.32565i) q^{29} +(-1.60580 - 3.87674i) q^{31} +3.46410 q^{33} +9.46410 q^{35} +(1.73581 + 4.19062i) q^{37} +(13.7919 - 5.71278i) q^{39} +(-5.54328 - 2.29610i) q^{41} +(5.93426 - 5.93426i) q^{43} +(5.91786 - 14.2870i) q^{45} +6.92820i q^{47} +(0.328169 + 0.328169i) q^{49} +(-9.14162 - 9.14162i) q^{53} +4.39230i q^{55} +(-1.53073 + 3.69552i) q^{57} +(1.79315 - 1.79315i) q^{59} +(0.495106 + 0.205079i) q^{61} +(11.2678 - 4.66727i) q^{63} +(7.24351 + 17.4874i) q^{65} -14.9282 q^{67} -3.46410 q^{69} +(-3.13653 - 7.57226i) q^{71} +(1.84776 - 0.765367i) q^{73} +(17.6686 + 7.31857i) q^{75} +(-2.44949 + 2.44949i) q^{77} +(4.66727 - 11.2678i) q^{79} +2.46410i q^{81} +(-1.79315 - 1.79315i) q^{83} +(-6.69213 - 6.69213i) q^{87} +2.53590i q^{89} +(-5.71278 + 13.7919i) q^{91} +(8.10634 - 8.10634i) q^{93} +(-4.68573 - 1.94089i) q^{95} +(4.55307 - 1.88594i) q^{97} +(2.16609 + 5.22939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times$.

$n$	$579$	$581$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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
$3$	1.04551	+	2.52409i	0.603626	+	1.45728i	0.869823	+	0.493363i	$0.164233\pi$
$3$	1.04551	+	2.52409i	0.603626	+	1.45728i	−0.266198	+	0.963918i	$0.585767\pi$
$4$		0			0
$5$	−3.20041	+	1.32565i	−1.43127	+	0.592851i	−0.957664	−	0.287887i	$-0.907047\pi$
$5$	−3.20041	+	1.32565i	−1.43127	+	0.592851i	−0.473604	+	0.880738i	$0.657047\pi$
$6$		0			0
$7$	−2.52409	−	1.04551i	−0.954015	−	0.395166i	−0.149276	−	0.988796i	$-0.547694\pi$
$7$	−2.52409	−	1.04551i	−0.954015	−	0.395166i	−0.804738	+	0.593630i	$0.797694\pi$
$8$		0			0
$9$	−3.15660	+	3.15660i	−1.05220	+	1.05220i
$10$		0			0
$11$	0.485223	−	1.17143i	0.146300	−	0.353200i	−0.833694	−	0.552227i	$-0.813778\pi$
$11$	0.485223	−	1.17143i	0.146300	−	0.353200i	0.979994	+	0.199027i	$0.0637781\pi$
$12$		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	0.815818	−	0.578309i	$-0.196287\pi$
$19$	1.03528	+	1.03528i	0.237509	+	0.237509i	−0.578309	+	0.815818i	$0.696287\pi$
$20$		0			0
$21$		−	7.46410i		−	1.62880i
$22$		0			0
$23$	−0.485223	+	1.17143i	−0.101176	+	0.244261i	−0.966360	−	0.257195i	$-0.917202\pi$
$23$	−0.485223	+	1.17143i	−0.101176	+	0.244261i	0.865184	+	0.501455i	$0.167202\pi$
$24$		0			0
$25$	4.94975	−	4.94975i	0.989949	−	0.989949i
$26$		0			0
$27$	−3.69552	−	1.53073i	−0.711203	−	0.294590i
$28$		0			0
$29$	−3.20041	+	1.32565i	−0.594302	+	0.246168i	−0.659500	−	0.751704i	$-0.729232\pi$
$29$	−3.20041	+	1.32565i	−0.594302	+	0.246168i	0.0651984	+	0.997872i	$0.479232\pi$
$30$		0			0
$31$	−1.60580	−	3.87674i	−0.288410	−	0.696283i	0.711570	−	0.702615i	$-0.247984\pi$
$31$	−1.60580	−	3.87674i	−0.288410	−	0.696283i	−0.999980	+	0.00633216i	$0.997984\pi$
$32$		0			0
$33$	3.46410			0.603023
$34$		0			0
$35$	9.46410			1.59973
$36$		0			0
$37$	1.73581	+	4.19062i	0.285366	+	0.688934i	0.999944	−	0.0106218i	$-0.00338110\pi$
$37$	1.73581	+	4.19062i	0.285366	+	0.688934i	−0.714578	+	0.699556i	$0.753381\pi$
$38$		0			0
$39$	13.7919	−	5.71278i	2.20847	−	0.914776i
$40$		0			0
$41$	−5.54328	−	2.29610i	−0.865714	−	0.358591i	−0.0947747	−	0.995499i	$-0.530213\pi$
$41$	−5.54328	−	2.29610i	−0.865714	−	0.358591i	−0.770940	+	0.636908i	$0.780213\pi$
$42$		0			0
$43$	5.93426	−	5.93426i	0.904966	−	0.904966i	−0.0908950	−	0.995860i	$-0.528973\pi$
$43$	5.93426	−	5.93426i	0.904966	−	0.904966i	0.995860	+	0.0908950i	$0.0289728\pi$
$44$		0			0
$45$	5.91786	−	14.2870i	0.882182	−	2.12978i
$46$		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	$-0.902155\pi$
$53$	−9.14162	−	9.14162i	−1.25570	−	1.25570i	−0.302571	−	0.953127i	$-0.597845\pi$
$54$		0			0
$55$			4.39230i			0.592258i
$56$		0			0
$57$	−1.53073	+	3.69552i	−0.202751	+	0.489483i
$58$		0			0
$59$	1.79315	−	1.79315i	0.233448	−	0.233448i	−0.580682	−	0.814130i	$-0.697214\pi$
$59$	1.79315	−	1.79315i	0.233448	−	0.233448i	0.814130	+	0.580682i	$0.197214\pi$
$60$		0			0
$61$	0.495106	+	0.205079i	0.0633918	+	0.0262577i	0.414154	−	0.910207i	$-0.364077\pi$
$61$	0.495106	+	0.205079i	0.0633918	+	0.0262577i	−0.350762	+	0.936465i	$0.614077\pi$
$62$		0			0
$63$	11.2678	−	4.66727i	1.41961	−	0.588020i
$64$		0			0
$65$	7.24351	+	17.4874i	0.898447	+	2.16904i
$66$		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
$71$	−3.13653	−	7.57226i	−0.372238	−	0.898662i	−0.993371	−	0.114956i	$-0.963327\pi$
$71$	−3.13653	−	7.57226i	−0.372238	−	0.898662i	0.621133	−	0.783705i	$-0.286673\pi$
$72$		0			0
$73$	1.84776	−	0.765367i	0.216264	−	0.0895794i	−0.271921	−	0.962319i	$-0.587659\pi$
$73$	1.84776	−	0.765367i	0.216264	−	0.0895794i	0.488185	+	0.872740i	$0.337659\pi$
$74$		0			0
$75$	17.6686	+	7.31857i	2.04019	+	0.845076i
$76$		0			0
$77$	−2.44949	+	2.44949i	−0.279145	+	0.279145i
$78$		0			0
$79$	4.66727	−	11.2678i	0.525108	−	1.26772i	−0.409586	−	0.912271i	$-0.634327\pi$
$79$	4.66727	−	11.2678i	0.525108	−	1.26772i	0.934694	−	0.355452i	$-0.115673\pi$
$80$		0			0
$81$			2.46410i			0.273789i
$82$		0			0
$83$	−1.79315	−	1.79315i	−0.196824	−	0.196824i	0.601813	−	0.798637i	$-0.294445\pi$
$83$	−1.79315	−	1.79315i	−0.196824	−	0.196824i	−0.798637	+	0.601813i	$0.794445\pi$
$84$		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
$91$	−5.71278	+	13.7919i	−0.598862	+	1.44578i
$92$		0			0
$93$	8.10634	−	8.10634i	0.840589	−	0.840589i
$94$		0			0
$95$	−4.68573	−	1.94089i	−0.480746	−	0.199131i
$96$		0			0
$97$	4.55307	−	1.88594i	0.462294	−	0.191488i	−0.139366	−	0.990241i	$-0.544506\pi$
$97$	4.55307	−	1.88594i	0.462294	−	0.191488i	0.601660	+	0.798753i	$0.294506\pi$
$98$		0			0
$99$	2.16609	+	5.22939i	0.217700	+	0.525574i
$100$		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
$105$	9.89482	+	23.8882i	0.965635	+	2.33125i
$106$		0			0
$107$	9.91512	−	4.10698i	0.958531	−	0.397037i	0.152100	−	0.988365i	$-0.451396\pi$
$107$	9.91512	−	4.10698i	0.958531	−	0.397037i	0.806431	+	0.591329i	$0.201396\pi$
$108$		0			0
$109$	−13.2968	−	5.50770i	−1.27360	−	0.527542i	−0.359542	−	0.933129i	$-0.617067\pi$
$109$	−13.2968	−	5.50770i	−1.27360	−	0.527542i	−0.914056	+	0.405587i	$0.867067\pi$
$110$		0			0
$111$	−8.76268	+	8.76268i	−0.831717	+	0.831717i
$112$		0			0
$113$	−7.59872	+	18.3449i	−0.714827	+	1.72575i	−0.0272562	+	0.999628i	$0.508677\pi$
$113$	−7.59872	+	18.3449i	−0.714827	+	1.72575i	−0.687571	+	0.726117i	$0.741323\pi$
$114$		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
$125$	−2.65131	+	6.40083i	−0.237140	+	0.572507i
$126$		0			0
$127$	0.277401	−	0.277401i	0.0246154	−	0.0246154i	−0.694692	−	0.719307i	$-0.744459\pi$
$127$	0.277401	−	0.277401i	0.0246154	−	0.0246154i	0.719307	+	0.694692i	$0.244459\pi$
$128$		0			0
$129$	21.1829	+	8.77424i	1.86505	+	0.772529i
$130$		0			0
$131$	−5.22939	+	2.16609i	−0.456894	+	0.189252i	−0.599247	−	0.800564i	$-0.704533\pi$
$131$	−5.22939	+	2.16609i	−0.456894	+	0.189252i	0.142353	+	0.989816i	$0.454533\pi$
$132$		0			0
$133$	−1.53073	−	3.69552i	−0.132731	−	0.320442i
$134$		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
$139$	−5.63771	−	13.6106i	−0.478184	−	1.15444i	−0.960460	−	0.278420i	$-0.910189\pi$
$139$	−5.63771	−	13.6106i	−0.478184	−	1.15444i	0.482275	−	0.876020i	$-0.339811\pi$
$140$		0			0
$141$	−17.4874	+	7.24351i	−1.47270	+	0.610014i
$142$		0			0
$143$	−6.40083	−	2.65131i	−0.535264	−	0.221714i
$144$		0			0
$145$	8.48528	−	8.48528i	0.704664	−	0.704664i
$146$		0			0
$147$	−0.485223	+	1.17143i	−0.0400205	+	0.0966181i
$148$		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	0.204165	−	0.978937i	$-0.434552\pi$
$151$	−9.52056	−	9.52056i	−0.774772	−	0.774772i	−0.978937	+	0.204165i	$0.934552\pi$
$152$		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
$159$	13.5166	−	32.6319i	1.07193	−	2.58788i
$160$		0			0
$161$	2.44949	−	2.44949i	0.193047	−	0.193047i
$162$		0			0
$163$	−19.0213	−	7.87886i	−1.48986	−	0.617120i	−0.518573	−	0.855033i	$-0.673537\pi$
$163$	−19.0213	−	7.87886i	−1.48986	−	0.617120i	−0.971286	+	0.237913i	$0.923537\pi$
$164$		0			0
$165$	−11.0866	+	4.59220i	−0.863087	+	0.357502i
$166$		0			0
$167$	−2.16609	−	5.22939i	−0.167617	−	0.404663i	0.817643	−	0.575725i	$-0.195280\pi$
$167$	−2.16609	−	5.22939i	−0.167617	−	0.404663i	−0.985260	+	0.171062i	$0.945280\pi$
$168$		0			0
$169$	−16.8564			−1.29665
$170$		0			0
$171$	−6.53590			−0.499813
$172$		0			0
$173$	−5.91786	−	14.2870i	−0.449926	−	1.08622i	−0.972349	−	0.233532i	$-0.924972\pi$
$173$	−5.91786	−	14.2870i	−0.449926	−	1.08622i	0.522423	−	0.852686i	$-0.325028\pi$
$174$		0			0
$175$	−17.6686	+	7.31857i	−1.33562	+	0.553232i
$176$		0			0
$177$	6.40083	+	2.65131i	0.481115	+	0.199285i
$178$		0			0
$179$	−10.2784	+	10.2784i	−0.768246	+	0.768246i	−0.977798	−	0.209552i	$-0.932800\pi$
$179$	−10.2784	+	10.2784i	−0.768246	+	0.768246i	0.209552	+	0.977798i	$0.432800\pi$
$180$		0			0
$181$	−1.73581	+	4.19062i	−0.129022	+	0.311487i	−0.975169	−	0.221463i	$-0.928917\pi$
$181$	−1.73581	+	4.19062i	−0.129022	+	0.311487i	0.846147	+	0.532950i	$0.178917\pi$
$182$		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
$193$	8.00888	−	19.3351i	0.576492	−	1.39177i	−0.319451	−	0.947603i	$-0.603498\pi$
$193$	8.00888	−	19.3351i	0.576492	−	1.39177i	0.895942	−	0.444171i	$-0.146502\pi$
$194$		0			0
$195$	−36.5665	+	36.5665i	−2.61858	+	2.61858i
$196$		0			0
$197$	−3.20041	−	1.32565i	−0.228020	−	0.0944490i	0.265748	−	0.964042i	$-0.414381\pi$
$197$	−3.20041	−	1.32565i	−0.228020	−	0.0944490i	−0.493768	+	0.869593i	$0.664381\pi$
$198$		0			0
$199$	−3.87674	+	1.60580i	−0.274815	+	0.113832i	−0.515835	−	0.856688i	$-0.672518\pi$
$199$	−3.87674	+	1.60580i	−0.274815	+	0.113832i	0.241020	+	0.970520i	$0.422518\pi$
$200$		0			0
$201$	−15.6076	−	37.6801i	−1.10087	−	2.65775i
$202$		0			0
$203$	9.46410			0.664250
$204$		0			0
$205$	20.7846			1.45166
$206$		0			0
$207$	−2.16609	−	5.22939i	−0.150553	−	0.363468i
$208$		0			0
$209$	1.71510	−	0.710416i	0.118636	−	0.0491405i
$210$		0			0
$211$	2.16164	+	0.895382i	0.148814	+	0.0616406i	0.455847	−	0.890058i	$-0.349336\pi$
$211$	2.16164	+	0.895382i	0.148814	+	0.0616406i	−0.307033	+	0.951699i	$0.599336\pi$
$212$		0			0
$213$	15.8338	−	15.8338i	1.08491	−	1.08491i
$214$		0			0
$215$	−11.1253	+	26.8588i	−0.758739	+	1.83176i
$216$		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	0.349969	−	0.936761i	$-0.386192\pi$
$223$	−8.76268	−	8.76268i	−0.586793	−	0.586793i	−0.936761	+	0.349969i	$0.886192\pi$
$224$		0			0
$225$			31.2487i			2.08325i
$226$		0			0
$227$	−7.72873	+	18.6588i	−0.512974	+	1.23843i	0.429171	+	0.903223i	$0.358806\pi$
$227$	−7.72873	+	18.6588i	−0.512974	+	1.23843i	−0.942145	+	0.335206i	$0.891194\pi$
$228$		0			0
$229$	−14.4195	+	14.4195i	−0.952870	+	0.952870i	−0.998938	−	0.0460685i	$-0.985331\pi$
$229$	−14.4195	+	14.4195i	−0.952870	+	0.952870i	0.0460685	+	0.998938i	$0.485331\pi$
$230$		0			0
$231$	−8.74369	−	3.62175i	−0.575293	−	0.238294i
$232$		0			0
$233$	−5.54328	+	2.29610i	−0.363152	+	0.150423i	−0.556796	−	0.830649i	$-0.687969\pi$
$233$	−5.54328	+	2.29610i	−0.363152	+	0.150423i	0.193644	+	0.981072i	$0.437969\pi$
$234$		0			0
$235$	−9.18440	−	22.1731i	−0.599124	−	1.44641i
$236$		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
$241$	0.765367	+	1.84776i	0.0493016	+	0.119025i	0.946612	−	0.322376i	$-0.104482\pi$
$241$	0.765367	+	1.84776i	0.0493016	+	0.119025i	−0.897310	+	0.441401i	$0.854482\pi$
$242$		0			0
$243$	−17.3062	+	7.16845i	−1.11019	+	0.459856i
$244$		0			0
$245$	−1.48532	−	0.615238i	−0.0948934	−	0.0393061i
$246$		0			0
$247$	5.65685	−	5.65685i	0.359937	−	0.359937i
$248$		0			0
$249$	2.65131	−	6.40083i	0.168020	−	0.405636i
$250$		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	$0.0962057\pi$
$257$	20.0764	+	20.0764i	1.25233	+	1.25233i	0.297658	+	0.954672i	$0.403794\pi$
$258$		0			0
$259$		−	12.3923i		−	0.770020i
$260$		0			0
$261$	5.91786	−	14.2870i	0.366306	−	0.884341i
$262$		0			0
$263$	8.00481	−	8.00481i	0.493598	−	0.493598i	−0.415840	−	0.909438i	$-0.636512\pi$
$263$	8.00481	−	8.00481i	0.493598	−	0.493598i	0.909438	+	0.415840i	$0.136512\pi$
$264$		0			0
$265$	41.3756	+	17.1383i	2.54168	+	1.05280i
$266$		0			0
$267$	−6.40083	+	2.65131i	−0.391724	+	0.162257i
$268$		0			0
$269$	10.5101	+	25.3735i	0.640809	+	1.54705i	0.825590	+	0.564271i	$0.190843\pi$
$269$	10.5101	+	25.3735i	0.640809	+	1.54705i	−0.184780	+	0.982780i	$0.559157\pi$
$270$		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
$275$	−3.39656	−	8.20003i	−0.204820	−	0.494480i
$276$		0			0
$277$	5.90572	−	2.44623i	0.354840	−	0.146980i	−0.198141	−	0.980174i	$-0.563490\pi$
$277$	5.90572	−	2.44623i	0.354840	−	0.146980i	0.552981	+	0.833194i	$0.313490\pi$
$278$		0			0
$279$	17.3062	+	7.16845i	1.03609	+	0.429164i
$280$		0			0
$281$	14.0406	−	14.0406i	0.837592	−	0.837592i	−0.150950	−	0.988541i	$-0.548233\pi$
$281$	14.0406	−	14.0406i	0.837592	−	0.837592i	0.988541	+	0.150950i	$0.0482331\pi$
$282$		0			0
$283$	−7.87886	+	19.0213i	−0.468350	+	1.13070i	0.496534	+	0.868017i	$0.334606\pi$
$283$	−7.87886	+	19.0213i	−0.468350	+	1.13070i	−0.964883	+	0.262679i	$0.915394\pi$
$284$		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
$295$	−3.36172	+	8.11592i	−0.195727	+	0.472527i
$296$		0			0
$297$	−3.58630	+	3.58630i	−0.208098	+	0.208098i
$298$		0			0
$299$	6.40083	+	2.65131i	0.370169	+	0.153329i
$300$		0			0
$301$	−21.1829	+	8.77424i	−1.22096	+	0.505739i
$302$		0			0
$303$	2.65131	+	6.40083i	0.152314	+	0.367718i
$304$		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
$309$	−11.4256	−	27.5837i	−0.649977	−	1.56918i
$310$		0			0
$311$	−2.88653	+	1.19564i	−0.163680	+	0.0677985i	−0.463019	−	0.886348i	$-0.653234\pi$
$311$	−2.88653	+	1.19564i	−0.163680	+	0.0677985i	0.299339	+	0.954147i	$0.403234\pi$
$312$		0			0
$313$	19.3351	+	8.00888i	1.09289	+	0.452688i	0.855012	−	0.518607i	$-0.173549\pi$
$313$	19.3351	+	8.00888i	1.09289	+	0.452688i	0.237874	+	0.971296i	$0.423549\pi$
$314$		0			0
$315$	−29.8744	+	29.8744i	−1.68323	+	1.68323i
$316$		0			0
$317$	−3.26655	+	7.88614i	−0.183468	+	0.442930i	−0.988677	−	0.150061i	$-0.952053\pi$
$317$	−3.26655	+	7.88614i	−0.183468	+	0.442930i	0.805209	+	0.592991i	$0.202053\pi$
$318$		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
$329$	7.24351	−	17.4874i	0.399348	−	0.964110i
$330$		0			0
$331$	13.6617	−	13.6617i	0.750913	−	0.750913i	−0.223737	−	0.974650i	$-0.571826\pi$
$331$	13.6617	−	13.6617i	0.750913	−	0.750913i	0.974650	+	0.223737i	$0.0718256\pi$
$332$		0			0
$333$	−18.7074	−	7.74885i	−1.02516	−	0.424634i
$334$		0			0
$335$	47.7764	−	19.7896i	2.61030	−	1.08122i
$336$		0			0
$337$	2.59636	+	6.26816i	0.141433	+	0.341449i	0.978685	−	0.205369i	$-0.0658393\pi$
$337$	2.59636	+	6.26816i	0.141433	+	0.341449i	−0.837252	+	0.546817i	$0.815839\pi$
$338$		0			0
$339$	−54.2487			−2.94639
$340$		0			0
$341$	−5.32051			−0.288122
$342$		0			0
$343$	6.83335	+	16.4972i	0.368966	+	0.890763i
$344$		0			0
$345$	11.0866	−	4.59220i	0.596880	−	0.247236i
$346$		0			0
$347$	−31.4605	−	13.0314i	−1.68889	−	0.699560i	−0.689199	−	0.724572i	$-0.742037\pi$
$347$	−31.4605	−	13.0314i	−1.68889	−	0.699560i	−0.999687	+	0.0250126i	$0.992037\pi$
$348$		0			0
$349$	−7.62587	+	7.62587i	−0.408203	+	0.408203i	−0.881112	−	0.472908i	$-0.843204\pi$
$349$	−7.62587	+	7.62587i	−0.408203	+	0.408203i	0.472908	+	0.881112i	$0.343204\pi$
$350$		0			0
$351$	−8.36408	+	20.1927i	−0.446442	+	1.07781i
$352$		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	0.992506	−	0.122193i	$-0.0389926\pi$
$359$	16.4901	+	16.4901i	0.870314	+	0.870314i	−0.122193	+	0.992506i	$0.538993\pi$
$360$		0			0
$361$		−	16.8564i		−	0.887179i
$362$		0			0
$363$	−9.81975	+	23.7070i	−0.515403	+	1.24429i
$364$		0			0
$365$	−4.89898	+	4.89898i	−0.256424	+	0.256424i
$366$		0			0
$367$	−2.16164	−	0.895382i	−0.112837	−	0.0467386i	0.325551	−	0.945525i	$-0.394450\pi$
$367$	−2.16164	−	0.895382i	−0.112837	−	0.0467386i	−0.438388	+	0.898786i	$0.644450\pi$
$368$		0			0
$369$	24.7458	−	10.2500i	1.28821	−	0.533595i
$370$		0			0
$371$	13.5166	+	32.6319i	0.701746	+	1.69416i
$372$		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
$377$	7.24351	+	17.4874i	0.373060	+	0.900646i
$378$		0			0
$379$	−4.86695	+	2.01596i	−0.249998	+	0.103553i	−0.504164	−	0.863608i	$-0.668199\pi$
$379$	−4.86695	+	2.01596i	−0.249998	+	0.103553i	0.254165	+	0.967161i	$0.418199\pi$
$380$		0			0
$381$	0.990211	+	0.410159i	0.0507301	+	0.0210131i
$382$		0			0
$383$	1.79315	−	1.79315i	0.0916257	−	0.0916257i	−0.659808	−	0.751434i	$-0.729363\pi$
$383$	1.79315	−	1.79315i	0.0916257	−	0.0916257i	0.751434	+	0.659808i	$0.229363\pi$
$384$		0			0
$385$	4.59220	−	11.0866i	0.234040	−	0.565023i
$386$		0			0
$387$			37.4641i			1.90441i
$388$		0			0
$389$	26.2880	+	26.2880i	1.33286	+	1.33286i	0.902803	+	0.430054i	$0.141505\pi$
$389$	26.2880	+	26.2880i	1.33286	+	1.33286i	0.430054	+	0.902803i	$0.358495\pi$
$390$		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
$397$	−2.14597	+	5.18083i	−0.107703	+	0.260019i	−0.968538	−	0.248866i	$-0.919942\pi$
$397$	−2.14597	+	5.18083i	−0.107703	+	0.260019i	0.860835	+	0.508885i	$0.169942\pi$
$398$		0			0
$399$	7.72741	−	7.72741i	0.386854	−	0.386854i
$400$		0			0
$401$	−29.4315	−	12.1909i	−1.46974	−	0.608785i	−0.502939	−	0.864322i	$-0.667748\pi$
$401$	−29.4315	−	12.1909i	−1.46974	−	0.608785i	−0.966799	+	0.255537i	$0.917748\pi$
$402$		0			0
$403$	−21.1829	+	8.77424i	−1.05520	+	0.437076i
$404$		0			0
$405$	−3.26655	−	7.88614i	−0.162316	−	0.391866i
$406$		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
$411$	2.65131	+	6.40083i	0.130779	+	0.315729i
$412$		0			0
$413$	−6.40083	+	2.65131i	−0.314964	+	0.130462i
$414$		0			0
$415$	8.11592	+	3.36172i	0.398395	+	0.165021i
$416$		0			0
$417$	28.4601	−	28.4601i	1.39370	−	1.39370i
$418$		0			0
$419$	9.40960	−	22.7168i	0.459689	−	1.10979i	−0.508835	−	0.860864i	$-0.669924\pi$
$419$	9.40960	−	22.7168i	0.459689	−	1.10979i	0.968523	−	0.248923i	$-0.0800765\pi$
$420$		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
$431$	6.75829	−	16.3159i	0.325535	−	0.785912i	−0.673378	−	0.739299i	$-0.735157\pi$
$431$	6.75829	−	16.3159i	0.325535	−	0.785912i	0.998913	−	0.0466130i	$-0.0148428\pi$
$432$		0			0
$433$	2.55103	−	2.55103i	0.122594	−	0.122594i	−0.643148	−	0.765742i	$-0.722372\pi$
$433$	2.55103	−	2.55103i	0.122594	−	0.122594i	0.765742	+	0.643148i	$0.222372\pi$
$434$		0			0
$435$	30.2890	+	12.5461i	1.45225	+	0.601541i
$436$		0			0
$437$	−1.71510	+	0.710416i	−0.0820442	+	0.0339838i
$438$		0			0
$439$	9.25947	+	22.3543i	0.441930	+	1.06691i	0.975271	+	0.221013i	$0.0709364\pi$
$439$	9.25947	+	22.3543i	0.441930	+	1.06691i	−0.533341	+	0.845901i	$0.679064\pi$
$440$		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
$445$	−3.36172	−	8.11592i	−0.159361	−	0.384732i
$446$		0			0
$447$	15.1445	−	6.27306i	0.716311	−	0.296706i
$448$		0			0
$449$	5.54328	+	2.29610i	0.261603	+	0.108360i	0.509630	−	0.860393i	$-0.329782\pi$
$449$	5.54328	+	2.29610i	0.261603	+	0.108360i	−0.248027	+	0.968753i	$0.579782\pi$
$450$		0			0
$451$	−5.37945	+	5.37945i	−0.253309	+	0.253309i
$452$		0			0
$453$	14.0769	−	33.9845i	0.661389	−	1.59673i
$454$		0			0
$455$		−	51.7128i		−	2.42433i
$456$		0			0
$457$	−14.4195	−	14.4195i	−0.674517	−	0.674517i	0.284237	−	0.958754i	$-0.408260\pi$
$457$	−14.4195	−	14.4195i	−0.674517	−	0.674517i	−0.958754	+	0.284237i	$0.908260\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.9396	−	18.9396i	−0.882104	−	0.882104i	0.111644	−	0.993748i	$-0.464388\pi$
$461$	−18.9396	−	18.9396i	−0.882104	−	0.882104i	−0.993748	+	0.111644i	$0.964388\pi$
$462$		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
$465$	−15.1974	+	36.6899i	−0.704764	+	1.70145i
$466$		0			0
$467$	10.2784	−	10.2784i	0.475629	−	0.475629i	−0.428102	−	0.903731i	$-0.640817\pi$
$467$	10.2784	−	10.2784i	0.475629	−	0.475629i	0.903731	+	0.428102i	$0.140817\pi$
$468$		0			0
$469$	37.6801	+	15.6076i	1.73990	+	0.720692i
$470$		0			0
$471$	−5.04817	+	2.09102i	−0.232607	+	0.0963492i
$472$		0			0
$473$	−4.07214	−	9.83102i	−0.187237	−	0.452031i
$474$		0			0
$475$	10.2487			0.470243
$476$		0			0
$477$	57.7128			2.64249
$478$		0			0
$479$	−6.75829	−	16.3159i	−0.308794	−	0.745495i	−0.999745	−	0.0225928i	$-0.992808\pi$
$479$	−6.75829	−	16.3159i	−0.308794	−	0.745495i	0.690951	−	0.722902i	$-0.257192\pi$
$480$		0			0
$481$	22.8980	−	9.48466i	1.04406	−	0.432463i
$482$		0			0
$483$	8.74369	+	3.62175i	0.397852	+	0.164796i
$484$		0			0
$485$	−12.0716	+	12.0716i	−0.548142	+	0.548142i
$486$		0			0
$487$	−2.31621	+	5.59184i	−0.104958	+	0.253390i	−0.967630	−	0.252373i	$-0.918789\pi$
$487$	−2.31621	+	5.59184i	−0.104958	+	0.253390i	0.862672	+	0.505763i	$0.168789\pi$
$488$		0			0
$489$		−	56.2487i		−	2.54365i
$490$		0			0
$491$	−26.2880	−	26.2880i	−1.18636	−	1.18636i	−0.978066	−	0.208298i	$-0.933208\pi$
$491$	−26.2880	−	26.2880i	−1.18636	−	1.18636i	−0.208298	−	0.978066i	$-0.566792\pi$
$492$		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
$499$	9.55972	−	23.0792i	0.427952	−	1.03317i	−0.551984	−	0.833855i	$-0.686129\pi$
$499$	9.55972	−	23.0792i	0.427952	−	1.03317i	0.979936	−	0.199313i	$-0.0638710\pi$
$500$		0			0
$501$	10.9348	−	10.9348i	0.488530	−	0.488530i
$502$		0			0
$503$	−25.0596	−	10.3800i	−1.11735	−	0.462823i	−0.253890	−	0.967233i	$-0.581710\pi$
$503$	−25.0596	−	10.3800i	−1.11735	−	0.462823i	−0.863464	+	0.504410i	$0.831710\pi$
$504$		0			0
$505$	−8.11592	+	3.36172i	−0.361154	+	0.149595i
$506$		0			0
$507$	−17.6236	−	42.5470i	−0.782689	−	1.88958i
$508$		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
$513$	−2.24115	−	5.41061i	−0.0989492	−	0.238884i
$514$		0			0
$515$	34.9748	−	14.4870i	1.54117	−	0.638374i
$516$		0			0
$517$	8.11592	+	3.36172i	0.356938	+	0.147848i
$518$		0			0
$519$	29.8744	−	29.8744i	1.31134	−	1.31134i
$520$		0			0
$521$	2.29610	−	5.54328i	0.100594	−	0.242855i	−0.865568	−	0.500791i	$-0.833042\pi$
$521$	2.29610	−	5.54328i	0.100594	−	0.242855i	0.966162	+	0.257936i	$0.0830424\pi$
$522$		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
$533$	−12.5461	+	30.2890i	−0.543433	+	1.31196i
$534$		0			0
$535$	−26.2880	+	26.2880i	−1.13653	+	1.13653i
$536$		0			0
$537$	−36.6899	−	15.1974i	−1.58328	−	0.655818i
$538$		0			0
$539$	0.543664	−	0.225193i	0.0234173	−	0.00969974i
$540$		0			0
$541$	−7.03843	−	16.9923i	−0.302606	−	0.730555i	−0.999905	−	0.0137749i	$-0.995615\pi$
$541$	−7.03843	−	16.9923i	−0.302606	−	0.730555i	0.697299	−	0.716780i	$-0.254385\pi$
$542$		0			0
$543$	−12.3923			−0.531805
$544$		0			0
$545$	49.8564			2.13561
$546$		0			0
$547$	16.3528	+	39.4793i	0.699197	+	1.68801i	0.725375	+	0.688354i	$0.241667\pi$
$547$	16.3528	+	39.4793i	0.699197	+	1.68801i	−0.0261774	+	0.999657i	$0.508333\pi$
$548$		0			0
$549$	−2.21020	+	0.915495i	−0.0943291	+	0.0390724i
$550$		0			0
$551$	−4.68573	−	1.94089i	−0.199619	−	0.0826848i
$552$		0			0
$553$	−23.5612	+	23.5612i	−1.00192	+	1.00192i
$554$		0			0
$555$	16.4279	−	39.6605i	0.697326	−	1.68349i
$556$		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	$0.0172124\pi$
$563$	24.9754	+	24.9754i	1.05259	+	1.05259i	0.0540480	+	0.998538i	$0.482788\pi$
$564$		0			0
$565$		−	68.7846i		−	2.89379i
$566$		0			0
$567$	2.57624	−	6.21960i	0.108192	−	0.261199i
$568$		0			0
$569$	−5.55532	+	5.55532i	−0.232891	+	0.232891i	−0.813898	−	0.581007i	$-0.802659\pi$
$569$	−5.55532	+	5.55532i	−0.232891	+	0.232891i	0.581007	+	0.813898i	$0.302659\pi$
$570$		0			0
$571$	−10.2776	−	4.25711i	−0.430103	−	0.178154i	0.157120	−	0.987579i	$-0.449779\pi$
$571$	−10.2776	−	4.25711i	−0.430103	−	0.178154i	−0.587223	+	0.809425i	$0.699779\pi$
$572$		0			0
$573$	−30.2890	+	12.5461i	−1.26534	+	0.524122i
$574$		0			0
$575$	3.39656	+	8.20003i	0.141646	+	0.341965i
$576$		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
$581$	2.65131	+	6.40083i	0.109995	+	0.265551i
$582$		0			0
$583$	−15.1445	+	6.27306i	−0.627222	+	0.259804i
$584$		0			0
$585$	−78.0654	−	32.3358i	−3.22761	−	1.33692i
$586$		0			0
$587$	−20.0764	+	20.0764i	−0.828641	+	0.828641i	−0.987329	−	0.158688i	$-0.949274\pi$
$587$	−20.0764	+	20.0764i	−0.828641	+	0.828641i	0.158688	+	0.987329i	$0.449274\pi$
$588$		0			0
$589$	2.35105	−	5.67594i	0.0968734	−	0.233873i
$590$		0			0
$591$		−	9.46410i		−	0.389301i
$592$		0			0
$593$	−2.92996	−	2.92996i	−0.120319	−	0.120319i	0.644383	−	0.764703i	$-0.277114\pi$
$593$	−2.92996	−	2.92996i	−0.120319	−	0.120319i	−0.764703	+	0.644383i	$0.777114\pi$
$594$		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
$601$	4.12709	−	9.96368i	0.168348	−	0.406427i	−0.817080	−	0.576525i	$-0.804408\pi$
$601$	4.12709	−	9.96368i	0.168348	−	0.406427i	0.985427	+	0.170098i	$0.0544084\pi$
$602$		0			0
$603$	47.1223	−	47.1223i	1.91897	−	1.91897i
$604$		0			0
$605$	−30.0593	−	12.4509i	−1.22208	−	0.506203i
$606$		0			0
$607$	35.7837	−	14.8221i	1.45242	−	0.601611i	0.489645	−	0.871922i	$-0.337127\pi$
$607$	35.7837	−	14.8221i	1.45242	−	0.601611i	0.962773	+	0.270311i	$0.0871266\pi$
$608$		0			0
$609$	9.89482	+	23.8882i	0.400958	+	0.967999i
$610$		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
$615$	21.7305	+	52.4621i	0.876260	+	2.11548i
$616$		0			0
$617$	−32.8617	+	13.6118i	−1.32296	+	0.547988i	−0.928639	−	0.370984i	$-0.879020\pi$
$617$	−32.8617	+	13.6118i	−1.32296	+	0.547988i	−0.394322	+	0.918972i	$0.629020\pi$
$618$		0			0
$619$	10.9053	+	4.51714i	0.438322	+	0.181559i	0.590921	−	0.806729i	$-0.298764\pi$
$619$	10.9053	+	4.51714i	0.438322	+	0.181559i	−0.152599	+	0.988288i	$0.548764\pi$
$620$		0			0
$621$	3.58630	−	3.58630i	0.143913	−	0.143913i
$622$		0			0
$623$	2.65131	−	6.40083i	0.106222	−	0.256444i
$624$		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	$-0.940989\pi$
$631$	−29.3195	−	29.3195i	−1.16719	−	1.16719i	−0.184328	−	0.982865i	$-0.559011\pi$
$632$		0			0
$633$			6.39230i			0.254071i
$634$		0			0
$635$	−0.520061	+	1.25554i	−0.0206380	+	0.0498245i
$636$		0			0
$637$	1.79315	−	1.79315i	0.0710472	−	0.0710472i
$638$		0			0
$639$	33.8033	+	14.0018i	1.33724	+	0.553903i
$640$		0			0
$641$	11.9441	−	4.94741i	0.471764	−	0.195411i	−0.134119	−	0.990965i	$-0.542820\pi$
$641$	11.9441	−	4.94741i	0.471764	−	0.195411i	0.605882	+	0.795554i	$0.292820\pi$
$642$		0			0
$643$	−12.4711	−	30.1078i	−0.491811	−	1.18734i	−0.953798	−	0.300449i	$-0.902863\pi$
$643$	−12.4711	−	30.1078i	−0.491811	−	1.18734i	0.461987	−	0.886887i	$-0.347137\pi$
$644$		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
$649$	−1.23048	−	2.97063i	−0.0483004	−	0.116608i
$650$		0			0
$651$	−28.9364	+	11.9858i	−1.13411	+	0.469762i
$652$		0			0
$653$	−9.60124	−	3.97696i	−0.375725	−	0.155631i	0.186826	−	0.982393i	$-0.440180\pi$
$653$	−9.60124	−	3.97696i	−0.375725	−	0.155631i	−0.562551	+	0.826763i	$0.690180\pi$
$654$		0			0
$655$	13.8647	−	13.8647i	0.541740	−	0.541740i
$656$		0			0
$657$	−3.41668	+	8.24858i	−0.133297	+	0.321808i
$658$		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	0.468787	−	0.883311i	$-0.344691\pi$
$661$	−10.6574	−	10.6574i	−0.414524	−	0.414524i	−0.883311	+	0.468787i	$0.844691\pi$
$662$		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
$669$	12.9563	−	31.2792i	0.500919	−	1.20933i
$670$		0			0
$671$	0.480473	−	0.480473i	0.0185485	−	0.0185485i
$672$		0			0
$673$	−0.132663	−	0.0549509i	−0.00511379	−	0.00211820i	0.380125	−	0.924935i	$-0.375881\pi$
$673$	−0.132663	−	0.0549509i	−0.00511379	−	0.00211820i	−0.385239	+	0.922817i	$0.625881\pi$
$674$		0			0
$675$	−25.8686	+	10.7151i	−0.995684	+	0.412426i
$676$		0			0
$677$	9.27958	+	22.4029i	0.356643	+	0.861013i	0.995767	+	0.0919093i	$0.0292970\pi$
$677$	9.27958	+	22.4029i	0.356643	+	0.861013i	−0.639124	+	0.769104i	$0.720703\pi$
$678$		0			0
$679$	−13.4641			−0.516705
$680$		0			0
$681$	−55.1769			−2.11438
$682$		0			0
$683$	−17.6236	−	42.5470i	−0.674346	−	1.62802i	−0.774145	−	0.633009i	$-0.781820\pi$
$683$	−17.6236	−	42.5470i	−0.674346	−	1.62802i	0.0997983	−	0.995008i	$-0.468180\pi$
$684$		0			0
$685$	−8.11592	+	3.36172i	−0.310093	+	0.128445i
$686$		0			0
$687$	−51.4719	−	21.3204i	−1.96378	−	0.813423i
$688$		0			0
$689$	−49.9507	+	49.9507i	−1.90297	+	1.90297i
$690$		0			0
$691$	13.8517	−	33.4409i	0.526942	−	1.27215i	−0.406575	−	0.913618i	$-0.633277\pi$
$691$	13.8517	−	33.4409i	0.526942	−	1.27215i	0.933517	−	0.358534i	$-0.116723\pi$
$692$		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
$703$	−2.54141	+	6.13550i	−0.0958510	+	0.231405i
$704$		0			0
$705$	46.3644	−	46.3644i	1.74619	−	1.74619i
$706$		0			0
$707$	−6.40083	−	2.65131i	−0.240728	−	0.0997127i
$708$		0			0
$709$	15.0119	−	6.21811i	0.563782	−	0.233526i	−0.0825442	−	0.996587i	$-0.526305\pi$
$709$	15.0119	−	6.21811i	0.563782	−	0.233526i	0.646326	+	0.763061i	$0.276305\pi$
$710$		0			0
$711$	20.8351	+	50.3005i	0.781379	+	1.88642i
$712$		0			0
$713$	5.32051			0.199255
$714$		0			0
$715$	24.0000			0.897549
$716$		0			0
$717$	21.7305	+	52.4621i	0.811541	+	1.95923i
$718$		0			0
$719$	40.2042	−	16.6531i	1.49936	−	0.621056i	0.526032	−	0.850465i	$-0.323679\pi$
$719$	40.2042	−	16.6531i	1.49936	−	0.621056i	0.973330	+	0.229409i	$0.0736793\pi$
$720$		0			0
$721$	27.5837	+	11.4256i	1.02727	+	0.425510i
$722$		0			0
$723$	−3.86370	+	3.86370i	−0.143693	+	0.143693i
$724$		0			0
$725$	−9.27958	+	22.4029i	−0.344635	+	0.832022i
$726$		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	0.908498	−	0.417889i	$-0.137230\pi$
$733$	13.2827	+	13.2827i	0.490609	+	0.490609i	−0.417889	+	0.908498i	$0.637230\pi$
$734$		0			0
$735$		−	4.39230i		−	0.162013i
$736$		0			0
$737$	−7.24351	+	17.4874i	−0.266818	+	0.644156i
$738$		0			0
$739$	8.76268	−	8.76268i	0.322340	−	0.322340i	−0.527324	−	0.849664i	$-0.676805\pi$
$739$	8.76268	−	8.76268i	0.322340	−	0.322340i	0.849664	+	0.527324i	$0.176805\pi$
$740$		0			0
$741$	20.1927	+	8.36408i	0.741797	+	0.307262i
$742$		0			0
$743$	−22.0890	+	9.14956i	−0.810367	+	0.335665i	−0.749100	−	0.662456i	$-0.769514\pi$
$743$	−22.0890	+	9.14956i	−0.810367	+	0.335665i	−0.0612665	+	0.998121i	$0.519514\pi$
$744$		0			0
$745$	7.95393	+	19.2025i	0.291409	+	0.703524i
$746$		0			0
$747$	11.3205			0.414196
$748$		0			0
$749$	−29.3205			−1.07135
$750$		0			0
$751$	7.16845	+	17.3062i	0.261580	+	0.631511i	0.999037	−	0.0438841i	$-0.0139732\pi$
$751$	7.16845	+	17.3062i	0.261580	+	0.631511i	−0.737456	+	0.675395i	$0.763973\pi$
$752$		0			0
$753$	17.4874	−	7.24351i	0.637276	−	0.263968i
$754$		0			0
$755$	43.0907	+	17.8487i	1.56823	+	0.649582i
$756$		0			0
$757$	−12.3490	+	12.3490i	−0.448831	+	0.448831i	−0.894966	−	0.446134i	$-0.852800\pi$
$757$	−12.3490	+	12.3490i	−0.448831	+	0.448831i	0.446134	+	0.894966i	$0.352800\pi$
$758$		0			0
$759$	−1.68086	+	4.05796i	−0.0610114	+	0.147295i
$760$		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
$771$	−29.6845	+	71.6646i	−1.06906	+	2.58094i
$772$		0			0
$773$	−0.480473	+	0.480473i	−0.0172814	+	0.0172814i	−0.715695	−	0.698413i	$-0.753890\pi$
$773$	−0.480473	+	0.480473i	−0.0172814	+	0.0172814i	0.698413	+	0.715695i	$0.253890\pi$
$774$		0			0
$775$	−27.1372	−	11.2406i	−0.974796	−	0.403774i
$776$		0			0
$777$	31.2792	−	12.9563i	1.12214	−	0.464804i
$778$		0			0
$779$	−3.36172	−	8.11592i	−0.120446	−	0.290783i
$780$		0			0
$781$	−10.3923			−0.371866
$782$		0			0
$783$	13.8564			0.495188
$784$		0			0
$785$	−2.65131	−	6.40083i	−0.0946293	−	0.228455i
$786$		0			0
$787$	21.3641	−	8.84931i	0.761549	−	0.315444i	0.0321048	−	0.999485i	$-0.489779\pi$
$787$	21.3641	−	8.84931i	0.761549	−	0.315444i	0.729444	+	0.684041i	$0.239779\pi$
$788$		0			0
$789$	28.5739	+	11.8357i	1.01726	+	0.421362i
$790$		0			0
$791$	38.3596	−	38.3596i	1.36391	−	1.36391i
$792$		0			0
$793$	1.12057	−	2.70531i	0.0397928	−	0.0960683i
$794$		0			0
$795$			122.354i			4.33944i
$796$		0			0
$797$	−1.96902	−	1.96902i	−0.0697461	−	0.0697461i	0.671373	−	0.741119i	$-0.265705\pi$
$797$	−1.96902	−	1.96902i	−0.0697461	−	0.0697461i	−0.741119	+	0.671373i	$0.765705\pi$
$798$		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
$805$	−4.59220	+	11.0866i	−0.161854	+	0.390750i
$806$		0			0
$807$	−53.0566	+	53.0566i	−1.86768	+	1.86768i
$808$		0			0
$809$	7.25837	+	3.00652i	0.255191	+	0.105703i	0.506612	−	0.862174i	$-0.330898\pi$
$809$	7.25837	+	3.00652i	0.255191	+	0.105703i	−0.251421	+	0.967878i	$0.580898\pi$
$810$		0			0
$811$	34.5282	−	14.3021i	1.21245	−	0.502213i	0.317448	−	0.948276i	$-0.397174\pi$
$811$	34.5282	−	14.3021i	1.21245	−	0.502213i	0.895002	+	0.446063i	$0.147174\pi$
$812$		0			0
$813$	−1.12057	−	2.70531i	−0.0393003	−	0.0948793i
$814$		0			0
$815$	71.3205			2.49825
$816$		0			0
$817$	12.2872			0.429874
$818$		0			0
$819$	−25.5024	−	61.5683i	−0.891126	−	2.15137i
$820$		0			0
$821$	41.6054	−	17.2335i	1.45204	−	0.601454i	0.489354	−	0.872085i	$-0.337233\pi$
$821$	41.6054	−	17.2335i	1.45204	−	0.601454i	0.962683	+	0.270632i	$0.0872325\pi$
$822$		0			0
$823$	1.53387	+	0.635352i	0.0534675	+	0.0221470i	0.409257	−	0.912419i	$-0.365788\pi$
$823$	1.53387	+	0.635352i	0.0534675	+	0.0221470i	−0.355789	+	0.934566i	$0.615788\pi$
$824$		0			0
$825$	17.1464	−	17.1464i	0.596962	−	0.596962i
$826$		0			0
$827$	7.46870	−	18.0310i	0.259712	−	0.627001i	−0.739207	−	0.673478i	$-0.764800\pi$
$827$	7.46870	−	18.0310i	0.259712	−	0.627001i	0.998919	+	0.0464774i	$0.0147995\pi$
$828$		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
$839$	1.71570	−	4.14207i	0.0592325	−	0.143000i	−0.891492	−	0.453036i	$-0.850341\pi$
$839$	1.71570	−	4.14207i	0.0592325	−	0.143000i	0.950725	+	0.310036i	$0.100341\pi$
$840$		0			0
$841$	−12.0208	+	12.0208i	−0.414511	+	0.414511i
$842$		0			0
$843$	50.1193	+	20.7601i	1.72620	+	0.715015i
$844$		0			0
$845$	53.9475	−	22.3458i	1.85585	−	0.768718i
$846$		0			0
$847$	−9.81975	−	23.7070i	−0.337411	−	0.814582i
$848$		0			0
$849$	−56.2487			−1.93045
$850$		0			0
$851$	−5.75129			−0.197152
$852$		0			0
$853$	3.15665	+	7.62082i	0.108081	+	0.260932i	0.968662	−	0.248383i	$-0.0798990\pi$
$853$	3.15665	+	7.62082i	0.108081	+	0.260932i	−0.860581	+	0.509314i	$0.829899\pi$
$854$		0			0
$855$	20.9176	−	8.66434i	0.715366	−	0.296314i
$856$		0			0
$857$	15.3743	+	6.36824i	0.525176	+	0.217535i	0.629489	−	0.777010i	$-0.283264\pi$
$857$	15.3743	+	6.36824i	0.525176	+	0.217535i	−0.104313	+	0.994545i	$0.533264\pi$
$858$		0			0
$859$	19.3185	−	19.3185i	0.659139	−	0.659139i	−0.296037	−	0.955176i	$-0.595665\pi$
$859$	19.3185	−	19.3185i	0.659139	−	0.659139i	0.955176	+	0.296037i	$0.0956652\pi$
$860$		0			0
$861$	−17.1383	+	41.3756i	−0.584073	+	1.41008i
$862$		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
$873$	−8.41904	+	20.3253i	−0.284941	+	0.687909i
$874$		0			0
$875$	13.3843	−	13.3843i	0.452471	−	0.452471i
$876$		0			0
$877$	−8.87635	−	3.67671i	−0.299733	−	0.124154i	0.227748	−	0.973720i	$-0.426864\pi$
$877$	−8.87635	−	3.67671i	−0.299733	−	0.124154i	−0.527482	+	0.849566i	$0.676864\pi$
$878$		0			0
$879$	−75.7226	+	31.3653i	−2.55406	+	1.05793i
$880$		0			0
$881$	14.8422	+	35.8323i	0.500047	+	1.20722i	0.949458	+	0.313896i	$0.101634\pi$
$881$	14.8422	+	35.8323i	0.500047	+	1.20722i	−0.449410	+	0.893326i	$0.648366\pi$
$882$		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
$887$	4.36701	+	10.5429i	0.146630	+	0.353996i	0.980081	−	0.198597i	$-0.0636385\pi$
$887$	4.36701	+	10.5429i	0.146630	+	0.353996i	−0.833451	+	0.552593i	$0.813639\pi$
$888$		0			0
$889$	−0.990211	+	0.410159i	−0.0332106	+	0.0137563i
$890$		0			0
$891$	2.88653	+	1.19564i	0.0967023	+	0.0400554i
$892$		0			0
$893$	−7.17260	+	7.17260i	−0.240022	+	0.240022i
$894$		0			0
$895$	19.2696	−	46.5209i	0.644111	−	1.55502i
$896$		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
$907$	13.1815	−	31.8229i	0.437684	−	1.05666i	−0.539063	−	0.842266i	$-0.681221\pi$
$907$	13.1815	−	31.8229i	0.437684	−	1.05666i	0.976747	−	0.214397i	$-0.0687785\pi$
$908$		0			0
$909$	−8.00481	+	8.00481i	−0.265503	+	0.265503i
$910$		0			0
$911$	14.6009	+	6.04787i	0.483748	+	0.200375i	0.611210	−	0.791469i	$-0.290683\pi$
$911$	14.6009	+	6.04787i	0.483748	+	0.200375i	−0.127462	+	0.991843i	$0.540683\pi$
$912$		0			0
$913$	−2.97063	+	1.23048i	−0.0983136	+	0.0407228i
$914$		0			0
$915$	−1.94089	−	4.68573i	−0.0641639	−	0.154905i
$916$		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
$921$	−25.9126	−	62.5585i	−0.853848	−	2.06137i
$922$		0			0
$923$	−41.3756	+	17.1383i	−1.36189	+	0.564115i
$924$		0			0
$925$	29.3344	+	12.1507i	0.964508	+	0.399512i
$926$		0			0
$927$	34.4959	−	34.4959i	1.13299	−	1.13299i
$928$		0			0
$929$	3.71693	−	8.97347i	0.121949	−	0.294410i	−0.851102	−	0.525000i	$-0.824065\pi$
$929$	3.71693	−	8.97347i	0.121949	−	0.294410i	0.973051	+	0.230590i	$0.0740655\pi$
$930$		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	0.705446	−	0.708763i	$-0.250747\pi$
$937$	−0.101536	−	0.101536i	−0.00331704	−	0.00331704i	−0.708763	+	0.705446i	$0.750747\pi$
$938$		0			0
$939$			57.1769i			1.86590i
$940$		0			0
$941$	15.8127	−	38.1752i	0.515478	−	1.24448i	−0.425176	−	0.905110i	$-0.639788\pi$
$941$	15.8127	−	38.1752i	0.515478	−	1.24448i	0.940655	−	0.339365i	$-0.110212\pi$
$942$		0			0
$943$	5.37945	−	5.37945i	0.175179	−	0.175179i
$944$		0			0
$945$	−34.9748	−	14.4870i	−1.13773	−	0.471263i
$946$		0			0
$947$	−45.5176	+	18.8540i	−1.47912	+	0.612674i	−0.968919	−	0.247379i	$-0.920431\pi$
$947$	−45.5176	+	18.8540i	−1.47912	+	0.612674i	−0.510206	+	0.860052i	$0.670431\pi$
$948$		0			0
$949$	−4.18204	−	10.0963i	−0.135755	−	0.327741i
$950$		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
$955$	−15.9079	−	38.4050i	−0.514766	−	1.24276i
$956$		0			0
$957$	−11.0866	+	4.59220i	−0.358377	+	0.148445i
$958$		0			0
$959$	−6.40083	−	2.65131i	−0.206693	−	0.0856152i
$960$		0			0
$961$	9.46979	−	9.46979i	0.305477	−	0.305477i
$962$		0			0
$963$	−18.3340	+	44.2621i	−0.590804	+	1.42633i
$964$		0			0
$965$			72.4974i			2.33377i
$966$		0			0
$967$	19.5216	+	19.5216i	0.627772	+	0.627772i	0.947507	−	0.319735i	$-0.103594\pi$
$967$	19.5216	+	19.5216i	0.627772	+	0.627772i	−0.319735	+	0.947507i	$0.603594\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−14.2165	−	14.2165i	−0.456228	−	0.456228i	0.441187	−	0.897415i	$-0.354558\pi$
$971$	−14.2165	−	14.2165i	−0.456228	−	0.456228i	−0.897415	+	0.441187i	$0.854558\pi$
$972$		0			0
$973$			40.2487i			1.29031i
$974$		0			0
$975$	39.9894	−	96.5430i	1.28069	−	3.09185i
$976$		0			0
$977$	−29.6985	+	29.6985i	−0.950139	+	0.950139i	−0.998815	−	0.0486759i	$-0.984500\pi$
$977$	−29.6985	+	29.6985i	−0.950139	+	0.950139i	0.0486759	+	0.998815i	$0.484500\pi$
$978$		0			0
$979$	2.97063	+	1.23048i	0.0949419	+	0.0393262i
$980$		0			0
$981$	59.3581	−	24.5869i	1.89516	−	0.785000i
$982$		0			0
$983$	13.7418	+	33.1756i	0.438294	+	1.05814i	0.976538	+	0.215347i	$0.0690881\pi$
$983$	13.7418	+	33.1756i	0.438294	+	1.05814i	−0.538243	+	0.842789i	$0.680912\pi$
$984$		0			0
$985$	12.0000			0.382352
$986$		0			0
$987$	51.7128			1.64604
$988$		0			0
$989$	4.07214	+	9.83102i	0.129487	+	0.312608i
$990$		0			0
$991$	−0.181221	+	0.0750643i	−0.00575668	+	0.00238450i	−0.385560	−	0.922683i	$-0.625992\pi$
$991$	−0.181221	+	0.0750643i	−0.00575668	+	0.00238450i	0.379803	+	0.925067i	$0.375992\pi$
$992$		0			0
$993$	48.7666	+	20.1998i	1.54756	+	0.641021i
$994$		0			0
$995$	10.2784	−	10.2784i	0.325848	−	0.325848i
$996$		0			0
$997$	−8.26891	+	19.9629i	−0.261879	+	0.632232i	−0.999055	−	0.0434693i	$-0.986159\pi$
$997$	−8.26891	+	19.9629i	−0.261879	+	0.632232i	0.737176	+	0.675701i	$0.236159\pi$
$998$		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.1001.4		16
17.2	even	8	inner	1156.2.h.f.757.4		16
17.3	odd	16		1156.2.b.c.577.4		4
17.4	even	4	inner	1156.2.h.f.733.4		16
17.5	odd	16		1156.2.a.a.1.1		2
17.6	odd	16		1156.2.e.d.829.4		8
17.7	odd	16		1156.2.e.d.905.4		8
17.8	even	8	inner	1156.2.h.f.977.4		16
17.9	even	8	inner	1156.2.h.f.977.1		16
17.10	odd	16		1156.2.e.d.905.1		8
17.11	odd	16		1156.2.e.d.829.1		8
17.12	odd	16		68.2.a.a.1.2	✓	2
17.13	even	4	inner	1156.2.h.f.733.1		16
17.14	odd	16		1156.2.b.c.577.1		4
17.15	even	8	inner	1156.2.h.f.757.1		16
17.16	even	2	inner	1156.2.h.f.1001.1		16
51.29	even	16		612.2.a.e.1.2		2
68.39	even	16		4624.2.a.x.1.2		2
68.63	even	16		272.2.a.e.1.1		2
85.12	even	16		1700.2.e.c.749.1		4
85.29	odd	16		1700.2.a.d.1.1		2
85.63	even	16		1700.2.e.c.749.4		4
119.97	even	16		3332.2.a.h.1.1		2
136.29	odd	16		1088.2.a.p.1.1		2
136.131	even	16		1088.2.a.t.1.2		2
187.131	even	16		8228.2.a.k.1.2		2
204.131	odd	16		2448.2.a.y.1.2		2
340.199	even	16		6800.2.a.bh.1.2		2
408.29	even	16		9792.2.a.cr.1.1		2
408.131	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	17.12	odd	16
272.2.a.e.1.1		2	68.63	even	16
612.2.a.e.1.2		2	51.29	even	16
1088.2.a.p.1.1		2	136.29	odd	16
1088.2.a.t.1.2		2	136.131	even	16
1156.2.a.a.1.1		2	17.5	odd	16
1156.2.b.c.577.1		4	17.14	odd	16
1156.2.b.c.577.4		4	17.3	odd	16
1156.2.e.d.829.1		8	17.11	odd	16
1156.2.e.d.829.4		8	17.6	odd	16
1156.2.e.d.905.1		8	17.10	odd	16
1156.2.e.d.905.4		8	17.7	odd	16
1156.2.h.f.733.1		16	17.13	even	4	inner
1156.2.h.f.733.4		16	17.4	even	4	inner
1156.2.h.f.757.1		16	17.15	even	8	inner
1156.2.h.f.757.4		16	17.2	even	8	inner
1156.2.h.f.977.1		16	17.9	even	8	inner
1156.2.h.f.977.4		16	17.8	even	8	inner
1156.2.h.f.1001.1		16	17.16	even	2	inner
1156.2.h.f.1001.4		16	1.1	even	1	trivial
1700.2.a.d.1.1		2	85.29	odd	16
1700.2.e.c.749.1		4	85.12	even	16
1700.2.e.c.749.4		4	85.63	even	16
2448.2.a.y.1.2		2	204.131	odd	16
3332.2.a.h.1.1		2	119.97	even	16
4624.2.a.x.1.2		2	68.39	even	16
6800.2.a.bh.1.2		2	340.199	even	16
8228.2.a.k.1.2		2	187.131	even	16
9792.2.a.cr.1.1		2	408.29	even	16
9792.2.a.cs.1.1		2	408.131	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 $\F_{q}$
Belyi maps

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more