LMFDB - Embedded newform 1156.2.h.f.1001.1

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			1001.1
Root			$-0.793353 - 0.608761i$ of defining polynomial
Character	$\chi$	$=$	1156.1001
Dual form			1156.2.h.f.977.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	$-0.835767\pi$
$3$	−1.04551	−	2.52409i	−0.603626	−	1.45728i	0.266198	−	0.963918i	$-0.414233\pi$
$4$		0			0
$5$	3.20041	−	1.32565i	1.43127	−	0.592851i	0.473604	−	0.880738i	$-0.342953\pi$
$5$	3.20041	−	1.32565i	1.43127	−	0.592851i	0.957664	+	0.287887i	$0.0929529\pi$
$6$		0			0
$7$	2.52409	+	1.04551i	0.954015	+	0.395166i	0.804738	−	0.593630i	$-0.202306\pi$
$7$	2.52409	+	1.04551i	0.954015	+	0.395166i	0.149276	+	0.988796i	$0.452306\pi$
$8$		0			0
$9$	−3.15660	+	3.15660i	−1.05220	+	1.05220i
$10$		0			0
$11$	−0.485223	+	1.17143i	−0.146300	+	0.353200i	−0.979994	−	0.199027i	$-0.936222\pi$
$11$	−0.485223	+	1.17143i	−0.146300	+	0.353200i	0.833694	+	0.552227i	$0.186222\pi$
$12$		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	−0.865184	−	0.501455i	$-0.832798\pi$
$23$	0.485223	−	1.17143i	0.101176	−	0.244261i	0.966360	+	0.257195i	$0.0827982\pi$
$24$		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	−0.0651984	−	0.997872i	$-0.520768\pi$
$29$	3.20041	−	1.32565i	0.594302	−	0.246168i	0.659500	+	0.751704i	$0.270768\pi$
$30$		0			0
$31$	1.60580	+	3.87674i	0.288410	+	0.696283i	0.999980	−	0.00633216i	$-0.00201560\pi$
$31$	1.60580	+	3.87674i	0.288410	+	0.696283i	−0.711570	+	0.702615i	$0.752016\pi$
$32$		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	0.714578	−	0.699556i	$-0.246619\pi$
$37$	−1.73581	−	4.19062i	−0.285366	−	0.688934i	−0.999944	+	0.0106218i	$0.996619\pi$
$38$		0			0
$39$	−13.7919	+	5.71278i	−2.20847	+	0.914776i
$40$		0			0
$41$	5.54328	+	2.29610i	0.865714	+	0.358591i	0.770940	−	0.636908i	$-0.219787\pi$
$41$	5.54328	+	2.29610i	0.865714	+	0.358591i	0.0947747	+	0.995499i	$0.469787\pi$
$42$		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	0.350762	−	0.936465i	$-0.385923\pi$
$61$	−0.495106	−	0.205079i	−0.0633918	−	0.0262577i	−0.414154	+	0.910207i	$0.635923\pi$
$62$		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	$0.0366728\pi$
$71$	3.13653	+	7.57226i	0.372238	+	0.898662i	−0.621133	+	0.783705i	$0.713327\pi$
$72$		0			0
$73$	−1.84776	+	0.765367i	−0.216264	+	0.0895794i	−0.488185	−	0.872740i	$-0.662341\pi$
$73$	−1.84776	+	0.765367i	−0.216264	+	0.0895794i	0.271921	+	0.962319i	$0.412341\pi$
$74$		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	$0.365673\pi$
$79$	−4.66727	+	11.2678i	−0.525108	+	1.26772i	−0.934694	+	0.355452i	$0.884327\pi$
$80$		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	−0.601660	−	0.798753i	$-0.705494\pi$
$97$	−4.55307	+	1.88594i	−0.462294	+	0.191488i	0.139366	+	0.990241i	$0.455494\pi$
$98$		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	−0.806431	−	0.591329i	$-0.798604\pi$
$107$	−9.91512	+	4.10698i	−0.958531	+	0.397037i	−0.152100	+	0.988365i	$0.548604\pi$
$108$		0			0
$109$	13.2968	+	5.50770i	1.27360	+	0.527542i	0.914056	−	0.405587i	$-0.132933\pi$
$109$	13.2968	+	5.50770i	1.27360	+	0.527542i	0.359542	+	0.933129i	$0.382933\pi$
$110$		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	$-0.491323\pi$
$113$	7.59872	−	18.3449i	0.714827	−	1.72575i	0.687571	−	0.726117i	$-0.258677\pi$
$114$		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	−0.142353	−	0.989816i	$-0.545467\pi$
$131$	5.22939	−	2.16609i	0.456894	−	0.189252i	0.599247	+	0.800564i	$0.295467\pi$
$132$		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	$0.0898106\pi$
$139$	5.63771	+	13.6106i	0.478184	+	1.15444i	−0.482275	+	0.876020i	$0.660189\pi$
$140$		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	0.971286	−	0.237913i	$-0.0764634\pi$
$163$	19.0213	+	7.87886i	1.48986	+	0.617120i	0.518573	+	0.855033i	$0.326463\pi$
$164$		0			0
$165$	11.0866	−	4.59220i	0.863087	−	0.357502i
$166$		0			0
$167$	2.16609	+	5.22939i	0.167617	+	0.404663i	0.985260	−	0.171062i	$-0.0547199\pi$
$167$	2.16609	+	5.22939i	0.167617	+	0.404663i	−0.817643	+	0.575725i	$0.804720\pi$
$168$		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	$0.0750282\pi$
$173$	5.91786	+	14.2870i	0.449926	+	1.08622i	−0.522423	+	0.852686i	$0.674972\pi$
$174$		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	−0.846147	−	0.532950i	$-0.821083\pi$
$181$	1.73581	−	4.19062i	0.129022	−	0.311487i	0.975169	+	0.221463i	$0.0710834\pi$
$182$		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	$0.396502\pi$
$193$	−8.00888	+	19.3351i	−0.576492	+	1.39177i	−0.895942	+	0.444171i	$0.853498\pi$
$194$		0			0
$195$	−36.5665	+	36.5665i	−2.61858	+	2.61858i
$196$		0			0
$197$	3.20041	+	1.32565i	0.228020	+	0.0944490i	0.493768	−	0.869593i	$-0.335619\pi$
$197$	3.20041	+	1.32565i	0.228020	+	0.0944490i	−0.265748	+	0.964042i	$0.585619\pi$
$198$		0			0
$199$	3.87674	−	1.60580i	0.274815	−	0.113832i	−0.241020	−	0.970520i	$-0.577482\pi$
$199$	3.87674	−	1.60580i	0.274815	−	0.113832i	0.515835	+	0.856688i	$0.327482\pi$
$200$		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	0.307033	−	0.951699i	$-0.400664\pi$
$211$	−2.16164	−	0.895382i	−0.148814	−	0.0616406i	−0.455847	+	0.890058i	$0.650664\pi$
$212$		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	$-0.641194\pi$
$227$	7.72873	−	18.6588i	0.512974	−	1.23843i	0.942145	−	0.335206i	$-0.108806\pi$
$228$		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	−0.193644	−	0.981072i	$-0.562031\pi$
$233$	5.54328	−	2.29610i	0.363152	−	0.150423i	0.556796	+	0.830649i	$0.312031\pi$
$234$		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	0.897310	−	0.441401i	$-0.145518\pi$
$241$	−0.765367	−	1.84776i	−0.0493016	−	0.119025i	−0.946612	+	0.322376i	$0.895518\pi$
$242$		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	$-0.809157\pi$
$269$	−10.5101	−	25.3735i	−0.640809	−	1.54705i	0.184780	−	0.982780i	$-0.440843\pi$
$270$		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	−0.552981	−	0.833194i	$-0.686510\pi$
$277$	−5.90572	+	2.44623i	−0.354840	+	0.146980i	0.198141	+	0.980174i	$0.436510\pi$
$278$		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	$-0.665394\pi$
$283$	7.87886	−	19.0213i	0.468350	−	1.13070i	0.964883	−	0.262679i	$-0.0846059\pi$
$284$		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	−0.299339	−	0.954147i	$-0.596766\pi$
$311$	2.88653	−	1.19564i	0.163680	−	0.0677985i	0.463019	+	0.886348i	$0.346766\pi$
$312$		0			0
$313$	−19.3351	−	8.00888i	−1.09289	−	0.452688i	−0.237874	−	0.971296i	$-0.576451\pi$
$313$	−19.3351	−	8.00888i	−1.09289	−	0.452688i	−0.855012	+	0.518607i	$0.826451\pi$
$314$		0			0
$315$	−29.8744	+	29.8744i	−1.68323	+	1.68323i
$316$		0			0
$317$	3.26655	−	7.88614i	0.183468	−	0.442930i	−0.805209	−	0.592991i	$-0.797947\pi$
$317$	3.26655	−	7.88614i	0.183468	−	0.442930i	0.988677	+	0.150061i	$0.0479470\pi$
$318$		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	0.837252	−	0.546817i	$-0.184161\pi$
$337$	−2.59636	−	6.26816i	−0.141433	−	0.341449i	−0.978685	+	0.205369i	$0.934161\pi$
$338$		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	0.999687	−	0.0250126i	$-0.00796259\pi$
$347$	31.4605	+	13.0314i	1.68889	+	0.699560i	0.689199	+	0.724572i	$0.257963\pi$
$348$		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	0.438388	−	0.898786i	$-0.355550\pi$
$367$	2.16164	+	0.895382i	0.112837	+	0.0467386i	−0.325551	+	0.945525i	$0.605550\pi$
$368$		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	−0.254165	−	0.967161i	$-0.581801\pi$
$379$	4.86695	−	2.01596i	0.249998	−	0.103553i	0.504164	+	0.863608i	$0.331801\pi$
$380$		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	−0.860835	−	0.508885i	$-0.830058\pi$
$397$	2.14597	−	5.18083i	0.107703	−	0.260019i	0.968538	+	0.248866i	$0.0800579\pi$
$398$		0			0
$399$	7.72741	−	7.72741i	0.386854	−	0.386854i
$400$		0			0
$401$	29.4315	+	12.1909i	1.46974	+	0.608785i	0.966799	−	0.255537i	$-0.0822521\pi$
$401$	29.4315	+	12.1909i	1.46974	+	0.608785i	0.502939	+	0.864322i	$0.332252\pi$
$402$		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	$0.330076\pi$
$419$	−9.40960	+	22.7168i	−0.459689	+	1.10979i	−0.968523	+	0.248923i	$0.919924\pi$
$420$		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	$0.264843\pi$
$431$	−6.75829	+	16.3159i	−0.325535	+	0.785912i	−0.998913	+	0.0466130i	$0.985157\pi$
$432$		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	$-0.929064\pi$
$439$	−9.25947	−	22.3543i	−0.441930	−	1.06691i	0.533341	−	0.845901i	$-0.320936\pi$
$440$		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	0.248027	−	0.968753i	$-0.420218\pi$
$449$	−5.54328	−	2.29610i	−0.261603	−	0.108360i	−0.509630	+	0.860393i	$0.670218\pi$
$450$		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	$0.00719213\pi$
$479$	6.75829	+	16.3159i	0.308794	+	0.745495i	−0.690951	+	0.722902i	$0.742808\pi$
$480$		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	−0.862672	−	0.505763i	$-0.831211\pi$
$487$	2.31621	−	5.59184i	0.104958	−	0.253390i	0.967630	+	0.252373i	$0.0812110\pi$
$488$		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	$0.313871\pi$
$499$	−9.55972	+	23.0792i	−0.427952	+	1.03317i	−0.979936	+	0.199313i	$0.936129\pi$
$500$		0			0
$501$	10.9348	−	10.9348i	0.488530	−	0.488530i
$502$		0			0
$503$	25.0596	+	10.3800i	1.11735	+	0.462823i	0.863464	−	0.504410i	$-0.168290\pi$
$503$	25.0596	+	10.3800i	1.11735	+	0.462823i	0.253890	+	0.967233i	$0.418290\pi$
$504$		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	−0.966162	−	0.257936i	$-0.916958\pi$
$521$	−2.29610	+	5.54328i	−0.100594	+	0.242855i	0.865568	+	0.500791i	$0.166958\pi$
$522$		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	$0.00438483\pi$
$541$	7.03843	+	16.9923i	0.302606	+	0.730555i	−0.697299	+	0.716780i	$0.745615\pi$
$542$		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	$-0.758333\pi$
$547$	−16.3528	−	39.4793i	−0.699197	−	1.68801i	0.0261774	−	0.999657i	$-0.491667\pi$
$548$		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	0.587223	−	0.809425i	$-0.300221\pi$
$571$	10.2776	+	4.25711i	0.430103	+	0.178154i	−0.157120	+	0.987579i	$0.550221\pi$
$572$		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	−0.985427	−	0.170098i	$-0.945592\pi$
$601$	−4.12709	+	9.96368i	−0.168348	+	0.406427i	0.817080	+	0.576525i	$0.195592\pi$
$602$		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	−0.962773	−	0.270311i	$-0.912873\pi$
$607$	−35.7837	+	14.8221i	−1.45242	+	0.601611i	−0.489645	+	0.871922i	$0.662873\pi$
$608$		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	0.394322	−	0.918972i	$-0.370980\pi$
$617$	32.8617	−	13.6118i	1.32296	−	0.547988i	0.928639	+	0.370984i	$0.120980\pi$
$618$		0			0
$619$	−10.9053	−	4.51714i	−0.438322	−	0.181559i	0.152599	−	0.988288i	$-0.451236\pi$
$619$	−10.9053	−	4.51714i	−0.438322	−	0.181559i	−0.590921	+	0.806729i	$0.701236\pi$
$620$		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	−0.605882	−	0.795554i	$-0.707180\pi$
$641$	−11.9441	+	4.94741i	−0.471764	+	0.195411i	0.134119	+	0.990965i	$0.457180\pi$
$642$		0			0
$643$	12.4711	+	30.1078i	0.491811	+	1.18734i	0.953798	+	0.300449i	$0.0971367\pi$
$643$	12.4711	+	30.1078i	0.491811	+	1.18734i	−0.461987	+	0.886887i	$0.652863\pi$
$644$		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	0.562551	−	0.826763i	$-0.309820\pi$
$653$	9.60124	+	3.97696i	0.375725	+	0.155631i	−0.186826	+	0.982393i	$0.559820\pi$
$654$		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	0.385239	−	0.922817i	$-0.374119\pi$
$673$	0.132663	+	0.0549509i	0.00511379	+	0.00211820i	−0.380125	+	0.924935i	$0.624119\pi$
$674$		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	$-0.970703\pi$
$677$	−9.27958	−	22.4029i	−0.356643	−	0.861013i	0.639124	−	0.769104i	$-0.279297\pi$
$678$		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	$0.218180\pi$
$683$	17.6236	+	42.5470i	0.674346	+	1.62802i	−0.0997983	+	0.995008i	$0.531820\pi$
$684$		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	$0.366723\pi$
$691$	−13.8517	+	33.4409i	−0.526942	+	1.27215i	−0.933517	+	0.358534i	$0.883277\pi$
$692$		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	−0.646326	−	0.763061i	$-0.723695\pi$
$709$	−15.0119	+	6.21811i	−0.563782	+	0.233526i	0.0825442	+	0.996587i	$0.473695\pi$
$710$		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	−0.973330	−	0.229409i	$-0.926321\pi$
$719$	−40.2042	+	16.6531i	−1.49936	+	0.621056i	−0.526032	+	0.850465i	$0.676321\pi$
$720$		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	0.0612665	−	0.998121i	$-0.480486\pi$
$743$	22.0890	−	9.14956i	0.810367	−	0.335665i	0.749100	+	0.662456i	$0.230486\pi$
$744$		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	0.737456	−	0.675395i	$-0.236027\pi$
$751$	−7.16845	−	17.3062i	−0.261580	−	0.631511i	−0.999037	+	0.0438841i	$0.986027\pi$
$752$		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	−0.729444	−	0.684041i	$-0.760221\pi$
$787$	−21.3641	+	8.84931i	−0.761549	+	0.315444i	−0.0321048	+	0.999485i	$0.510221\pi$
$788$		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	0.251421	−	0.967878i	$-0.419102\pi$
$809$	−7.25837	−	3.00652i	−0.255191	−	0.105703i	−0.506612	+	0.862174i	$0.669102\pi$
$810$		0			0
$811$	−34.5282	+	14.3021i	−1.21245	+	0.502213i	−0.895002	−	0.446063i	$-0.852826\pi$
$811$	−34.5282	+	14.3021i	−1.21245	+	0.502213i	−0.317448	+	0.948276i	$0.602826\pi$
$812$		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	−0.962683	−	0.270632i	$-0.912767\pi$
$821$	−41.6054	+	17.2335i	−1.45204	+	0.601454i	−0.489354	+	0.872085i	$0.662767\pi$
$822$		0			0
$823$	−1.53387	−	0.635352i	−0.0534675	−	0.0221470i	0.355789	−	0.934566i	$-0.384212\pi$
$823$	−1.53387	−	0.635352i	−0.0534675	−	0.0221470i	−0.409257	+	0.912419i	$0.634212\pi$
$824$		0			0
$825$	17.1464	−	17.1464i	0.596962	−	0.596962i
$826$		0			0
$827$	−7.46870	+	18.0310i	−0.259712	+	0.627001i	−0.998919	−	0.0464774i	$-0.985200\pi$
$827$	−7.46870	+	18.0310i	−0.259712	+	0.627001i	0.739207	+	0.673478i	$0.235200\pi$
$828$		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	−0.950725	−	0.310036i	$-0.899659\pi$
$839$	−1.71570	+	4.14207i	−0.0592325	+	0.143000i	0.891492	+	0.453036i	$0.149659\pi$
$840$		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	0.860581	−	0.509314i	$-0.170101\pi$
$853$	−3.15665	−	7.62082i	−0.108081	−	0.260932i	−0.968662	+	0.248383i	$0.920101\pi$
$854$		0			0
$855$	−20.9176	+	8.66434i	−0.715366	+	0.296314i
$856$		0			0
$857$	−15.3743	−	6.36824i	−0.525176	−	0.217535i	0.104313	−	0.994545i	$-0.466736\pi$
$857$	−15.3743	−	6.36824i	−0.525176	−	0.217535i	−0.629489	+	0.777010i	$0.716736\pi$
$858$		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	0.527482	−	0.849566i	$-0.323136\pi$
$877$	8.87635	+	3.67671i	0.299733	+	0.124154i	−0.227748	+	0.973720i	$0.573136\pi$
$878$		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	$-0.898366\pi$
$881$	−14.8422	−	35.8323i	−0.500047	−	1.20722i	0.449410	−	0.893326i	$-0.351634\pi$
$882$		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	0.833451	−	0.552593i	$-0.186361\pi$
$887$	−4.36701	−	10.5429i	−0.146630	−	0.353996i	−0.980081	+	0.198597i	$0.936361\pi$
$888$		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	$0.318779\pi$
$907$	−13.1815	+	31.8229i	−0.437684	+	1.05666i	−0.976747	+	0.214397i	$0.931221\pi$
$908$		0			0
$909$	−8.00481	+	8.00481i	−0.265503	+	0.265503i
$910$		0			0
$911$	−14.6009	−	6.04787i	−0.483748	−	0.200375i	0.127462	−	0.991843i	$-0.459317\pi$
$911$	−14.6009	−	6.04787i	−0.483748	−	0.200375i	−0.611210	+	0.791469i	$0.709317\pi$
$912$		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	−0.973051	−	0.230590i	$-0.925935\pi$
$929$	−3.71693	+	8.97347i	−0.121949	+	0.294410i	0.851102	+	0.525000i	$0.175935\pi$
$930$		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	$0.360212\pi$
$941$	−15.8127	+	38.1752i	−0.515478	+	1.24448i	−0.940655	+	0.339365i	$0.889788\pi$
$942$		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	0.510206	−	0.860052i	$-0.329569\pi$
$947$	45.5176	−	18.8540i	1.47912	−	0.612674i	0.968919	+	0.247379i	$0.0795692\pi$
$948$		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	$-0.930912\pi$
$983$	−13.7418	−	33.1756i	−0.438294	−	1.05814i	0.538243	−	0.842789i	$-0.319088\pi$
$984$		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	−0.379803	−	0.925067i	$-0.624008\pi$
$991$	0.181221	−	0.0750643i	0.00575668	−	0.00238450i	0.385560	+	0.922683i	$0.374008\pi$
$992$		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	−0.737176	−	0.675701i	$-0.763841\pi$
$997$	8.26891	−	19.9629i	0.261879	−	0.632232i	0.999055	+	0.0434693i	$0.0138411\pi$
$998$		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.1001.1		16
17.2	even	8	inner	1156.2.h.f.757.1		16
17.3	odd	16		1156.2.b.c.577.1		4
17.4	even	4	inner	1156.2.h.f.733.1		16
17.5	odd	16		68.2.a.a.1.2	✓	2
17.6	odd	16		1156.2.e.d.829.1		8
17.7	odd	16		1156.2.e.d.905.1		8
17.8	even	8	inner	1156.2.h.f.977.1		16
17.9	even	8	inner	1156.2.h.f.977.4		16
17.10	odd	16		1156.2.e.d.905.4		8
17.11	odd	16		1156.2.e.d.829.4		8
17.12	odd	16		1156.2.a.a.1.1		2
17.13	even	4	inner	1156.2.h.f.733.4		16
17.14	odd	16		1156.2.b.c.577.4		4
17.15	even	8	inner	1156.2.h.f.757.4		16
17.16	even	2	inner	1156.2.h.f.1001.4		16
51.5	even	16		612.2.a.e.1.2		2
68.39	even	16		272.2.a.e.1.1		2
68.63	even	16		4624.2.a.x.1.2		2
85.22	even	16		1700.2.e.c.749.1		4
85.39	odd	16		1700.2.a.d.1.1		2
85.73	even	16		1700.2.e.c.749.4		4
119.90	even	16		3332.2.a.h.1.1		2
136.5	odd	16		1088.2.a.p.1.1		2
136.107	even	16		1088.2.a.t.1.2		2
187.175	even	16		8228.2.a.k.1.2		2
204.107	odd	16		2448.2.a.y.1.2		2
340.39	even	16		6800.2.a.bh.1.2		2
408.5	even	16		9792.2.a.cr.1.1		2
408.107	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	17.5	odd	16
272.2.a.e.1.1		2	68.39	even	16
612.2.a.e.1.2		2	51.5	even	16
1088.2.a.p.1.1		2	136.5	odd	16
1088.2.a.t.1.2		2	136.107	even	16
1156.2.a.a.1.1		2	17.12	odd	16
1156.2.b.c.577.1		4	17.3	odd	16
1156.2.b.c.577.4		4	17.14	odd	16
1156.2.e.d.829.1		8	17.6	odd	16
1156.2.e.d.829.4		8	17.11	odd	16
1156.2.e.d.905.1		8	17.7	odd	16
1156.2.e.d.905.4		8	17.10	odd	16
1156.2.h.f.733.1		16	17.4	even	4	inner
1156.2.h.f.733.4		16	17.13	even	4	inner
1156.2.h.f.757.1		16	17.2	even	8	inner
1156.2.h.f.757.4		16	17.15	even	8	inner
1156.2.h.f.977.1		16	17.8	even	8	inner
1156.2.h.f.977.4		16	17.9	even	8	inner
1156.2.h.f.1001.1		16	1.1	even	1	trivial
1156.2.h.f.1001.4		16	17.16	even	2	inner
1700.2.a.d.1.1		2	85.39	odd	16
1700.2.e.c.749.1		4	85.22	even	16
1700.2.e.c.749.4		4	85.73	even	16
2448.2.a.y.1.2		2	204.107	odd	16
3332.2.a.h.1.1		2	119.90	even	16
4624.2.a.x.1.2		2	68.63	even	16
6800.2.a.bh.1.2		2	340.39	even	16
8228.2.a.k.1.2		2	187.175	even	16
9792.2.a.cr.1.1		2	408.5	even	16
9792.2.a.cs.1.1		2	408.107	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)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more