LMFDB - Embedded newform 1056.2.bp.a.271.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1056,2,Mod(79,1056)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1056, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1056.79"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1056 = 2^{5} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1056.bp (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$8.43220245345$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 264)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			271.4
Character	$\chi$	$=$	1056.271
Dual form			1056.2.bp.a.943.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{3} +(-1.03968 - 1.43099i) q^{5} +(0.430909 + 1.32620i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(2.97889 - 1.45816i) q^{11} +(-2.66400 - 1.93551i) q^{13} +(-1.68223 + 0.546590i) q^{15} +(-2.21773 - 3.05245i) q^{17} +(0.399566 + 0.129827i) q^{19} +1.39445 q^{21} +1.44940i q^{23} +(0.578275 - 1.77975i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(-2.45128 - 7.54427i) q^{29} +(-0.816325 + 1.12358i) q^{31} +(-0.466268 - 3.28369i) q^{33} +(1.44978 - 1.99544i) q^{35} +(-8.91884 + 2.89791i) q^{37} +(-2.66400 + 1.93551i) q^{39} +(3.29058 + 1.06918i) q^{41} -3.60336i q^{43} +1.76880i q^{45} +(0.727433 + 0.236357i) q^{47} +(4.08999 - 2.97155i) q^{49} +(-3.58836 + 1.16593i) q^{51} +(2.54374 - 3.50116i) q^{53} +(-5.18369 - 2.74674i) q^{55} +(0.246945 - 0.339891i) q^{57} +(-3.69578 - 11.3745i) q^{59} +(-8.45451 + 6.14256i) q^{61} +(0.430909 - 1.32620i) q^{63} +5.82447i q^{65} -9.95011 q^{67} +(1.37846 + 0.447890i) q^{69} +(-7.57332 - 10.4238i) q^{71} +(-9.14630 + 2.97181i) q^{73} +(-1.51394 - 1.09994i) q^{75} +(3.21744 + 3.32227i) q^{77} +(4.69761 + 3.41302i) q^{79} +(0.309017 + 0.951057i) q^{81} +(8.86730 + 12.2048i) q^{83} +(-2.06230 + 6.34711i) q^{85} -7.93251 q^{87} +10.9210 q^{89} +(1.41893 - 4.36703i) q^{91} +(0.816325 + 1.12358i) q^{93} +(-0.229638 - 0.706752i) q^{95} +(-11.2144 - 8.14771i) q^{97} +(-3.26706 - 0.571268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{3} - 12 q^{9} - 4 q^{11} - 4 q^{25} - 12 q^{27} - 4 q^{33} - 60 q^{41} - 12 q^{49} + 8 q^{59} - 8 q^{67} + 36 q^{75} - 12 q^{81} + 100 q^{83} + 96 q^{89} + 20 q^{91} - 40 q^{97} + 16 q^{99}+O(q^{100}) $ 48 * q - 12 * q^3 - 12 * q^9 - 4 * q^11 - 4 * q^25 - 12 * q^27 - 4 * q^33 - 60 * q^41 - 12 * q^49 + 8 * q^59 - 8 * q^67 + 36 * q^75 - 12 * q^81 + 100 * q^83 + 96 * q^89 + 20 * q^91 - 40 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1056\mathbb{Z}\right)^\times$.

$n$	$133$	$353$	$673$	$991$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$		0			0
$5$	−1.03968	−	1.43099i	−0.464957	−	0.639959i	0.510570	−	0.859836i	$-0.329434\pi$
$5$	−1.03968	−	1.43099i	−0.464957	−	0.639959i	−0.975528	+	0.219877i	$0.929434\pi$
$6$		0			0
$7$	0.430909	+	1.32620i	0.162868	+	0.501257i	0.998873	−	0.0474657i	$-0.0151145\pi$
$7$	0.430909	+	1.32620i	0.162868	+	0.501257i	−0.836005	+	0.548722i	$0.815114\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	2.97889	−	1.45816i	0.898168	−	0.439652i
$11$	2.97889	−	1.45816i	0.898168	−	0.439652i
$12$		0			0
$13$	−2.66400	−	1.93551i	−0.738862	−	0.536815i	0.153493	−	0.988150i	$-0.450948\pi$
$13$	−2.66400	−	1.93551i	−0.738862	−	0.536815i	−0.892355	+	0.451335i	$0.850948\pi$
$14$		0			0
$15$	−1.68223	+	0.546590i	−0.434350	+	0.141129i
$16$		0			0
$17$	−2.21773	−	3.05245i	−0.537879	−	0.740327i	0.450427	−	0.892813i	$-0.351272\pi$
$17$	−2.21773	−	3.05245i	−0.537879	−	0.740327i	−0.988306	+	0.152487i	$0.951272\pi$
$18$		0			0
$19$	0.399566	+	0.129827i	0.0916666	+	0.0297843i	0.354491	−	0.935059i	$-0.384654\pi$
$19$	0.399566	+	0.129827i	0.0916666	+	0.0297843i	−0.262825	+	0.964844i	$0.584654\pi$
$20$		0			0
$21$	1.39445			0.304294
$22$		0			0
$23$			1.44940i			0.302222i	0.988517	+	0.151111i	$0.0482850\pi$
$23$			1.44940i			0.302222i	−0.988517	+	0.151111i	$0.951715\pi$
$24$		0			0
$25$	0.578275	−	1.77975i	0.115655	−	0.355950i
$26$		0			0
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$		0			0
$29$	−2.45128	−	7.54427i	−0.455191	−	1.40094i	−0.870910	−	0.491442i	$-0.836470\pi$
$29$	−2.45128	−	7.54427i	−0.455191	−	1.40094i	0.415719	−	0.909493i	$-0.363530\pi$
$30$		0			0
$31$	−0.816325	+	1.12358i	−0.146616	+	0.201800i	−0.876008	−	0.482296i	$-0.839803\pi$
$31$	−0.816325	+	1.12358i	−0.146616	+	0.201800i	0.729392	+	0.684096i	$0.239803\pi$
$32$		0			0
$33$	−0.466268	−	3.28369i	−0.0811668	−	0.571616i
$34$		0			0
$35$	1.44978	−	1.99544i	0.245057	−	0.337292i
$36$		0			0
$37$	−8.91884	+	2.89791i	−1.46625	+	0.476413i	−0.929972	−	0.367630i	$-0.880169\pi$
$37$	−8.91884	+	2.89791i	−1.46625	+	0.476413i	−0.536276	+	0.844043i	$0.680169\pi$
$38$		0			0
$39$	−2.66400	+	1.93551i	−0.426582	+	0.309930i
$40$		0			0
$41$	3.29058	+	1.06918i	0.513903	+	0.166977i	0.554476	−	0.832199i	$-0.312919\pi$
$41$	3.29058	+	1.06918i	0.513903	+	0.166977i	−0.0405736	+	0.999177i	$0.512919\pi$
$42$		0			0
$43$		−	3.60336i		−	0.549507i	−0.961515	−	0.274753i	$-0.911404\pi$
$43$		−	3.60336i		−	0.549507i	0.961515	−	0.274753i	$-0.0885962\pi$
$44$		0			0
$45$			1.76880i			0.263678i
$46$		0			0
$47$	0.727433	+	0.236357i	0.106107	+	0.0344763i	0.361589	−	0.932337i	$-0.382234\pi$
$47$	0.727433	+	0.236357i	0.106107	+	0.0344763i	−0.255482	+	0.966814i	$0.582234\pi$
$48$		0			0
$49$	4.08999	−	2.97155i	0.584285	−	0.424508i
$50$		0			0
$51$	−3.58836	+	1.16593i	−0.502472	+	0.163263i
$52$		0			0
$53$	2.54374	−	3.50116i	0.349410	−	0.480921i	−0.597751	−	0.801682i	$-0.703939\pi$
$53$	2.54374	−	3.50116i	0.349410	−	0.480921i	0.947160	+	0.320761i	$0.103939\pi$
$54$		0			0
$55$	−5.18369	−	2.74674i	−0.698969	−	0.370371i
$56$		0			0
$57$	0.246945	−	0.339891i	0.0327087	−	0.0450196i
$58$		0			0
$59$	−3.69578	−	11.3745i	−0.481150	−	1.48083i	−0.837480	−	0.546468i	$-0.815972\pi$
$59$	−3.69578	−	11.3745i	−0.481150	−	1.48083i	0.356330	−	0.934360i	$-0.384028\pi$
$60$		0			0
$61$	−8.45451	+	6.14256i	−1.08249	+	0.786474i	−0.978115	−	0.208064i	$-0.933284\pi$
$61$	−8.45451	+	6.14256i	−1.08249	+	0.786474i	−0.104373	+	0.994538i	$0.533284\pi$
$62$		0			0
$63$	0.430909	−	1.32620i	0.0542894	−	0.167086i
$64$		0			0
$65$			5.82447i			0.722437i
$66$		0			0
$67$	−9.95011			−1.21560			−0.607800	−	0.794090i	$-0.707948\pi$
$67$	−9.95011			−1.21560			−0.607800	+	0.794090i	$0.707948\pi$
$68$		0			0
$69$	1.37846	+	0.447890i	0.165948	+	0.0539197i
$70$		0			0
$71$	−7.57332	−	10.4238i	−0.898788	−	1.23708i	−0.970853	−	0.239675i	$-0.922959\pi$
$71$	−7.57332	−	10.4238i	−0.898788	−	1.23708i	0.0720652	−	0.997400i	$-0.477041\pi$
$72$		0			0
$73$	−9.14630	+	2.97181i	−1.07049	+	0.347824i	−0.790680	−	0.612230i	$-0.790273\pi$
$73$	−9.14630	+	2.97181i	−1.07049	+	0.347824i	−0.279814	+	0.960054i	$0.590273\pi$
$74$		0			0
$75$	−1.51394	−	1.09994i	−0.174815	−	0.127011i
$76$		0			0
$77$	3.21744	+	3.32227i	0.366662	+	0.378607i
$78$		0			0
$79$	4.69761	+	3.41302i	0.528523	+	0.383994i	0.819805	−	0.572643i	$-0.194082\pi$
$79$	4.69761	+	3.41302i	0.528523	+	0.383994i	−0.291282	+	0.956637i	$0.594082\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	8.86730	+	12.2048i	0.973313	+	1.33965i	0.940355	+	0.340194i	$0.110493\pi$
$83$	8.86730	+	12.2048i	0.973313	+	1.33965i	0.0329578	+	0.999457i	$0.489507\pi$
$84$		0			0
$85$	−2.06230	+	6.34711i	−0.223688	+	0.688441i
$86$		0			0
$87$	−7.93251			−0.850455
$88$		0			0
$89$	10.9210			1.15763			0.578814	−	0.815460i	$-0.303516\pi$
$89$	10.9210			1.15763			0.578814	+	0.815460i	$0.303516\pi$
$90$		0			0
$91$	1.41893	−	4.36703i	0.148745	−	0.457789i
$92$		0			0
$93$	0.816325	+	1.12358i	0.0846490	+	0.116509i
$94$		0			0
$95$	−0.229638	−	0.706752i	−0.0235603	−	0.0725113i
$96$		0			0
$97$	−11.2144	−	8.14771i	−1.13865	−	0.827275i	−0.151716	−	0.988424i	$-0.548480\pi$
$97$	−11.2144	−	8.14771i	−1.13865	−	0.827275i	−0.986930	+	0.161149i	$0.948480\pi$
$98$		0			0
$99$	−3.26706	−	0.571268i	−0.328351	−	0.0574146i
$100$		0			0
$101$	6.49406	+	4.71821i	0.646183	+	0.469480i	0.861969	−	0.506961i	$-0.169231\pi$
$101$	6.49406	+	4.71821i	0.646183	+	0.469480i	−0.215786	+	0.976441i	$0.569231\pi$
$102$		0			0
$103$	11.7338	−	3.81254i	1.15617	−	0.375661i	0.332703	−	0.943032i	$-0.392039\pi$
$103$	11.7338	−	3.81254i	1.15617	−	0.375661i	0.823463	+	0.567370i	$0.192039\pi$
$104$		0			0
$105$	−1.44978	−	1.99544i	−0.141484	−	0.194735i
$106$		0			0
$107$	6.82340	+	2.21706i	0.659643	+	0.214331i	0.619661	−	0.784869i	$-0.287270\pi$
$107$	6.82340	+	2.21706i	0.659643	+	0.214331i	0.0399817	+	0.999200i	$0.487270\pi$
$108$		0			0
$109$	9.38007			0.898448			0.449224	−	0.893419i	$-0.351700\pi$
$109$	9.38007			0.898448			0.449224	+	0.893419i	$0.351700\pi$
$110$		0			0
$111$			9.37782i			0.890103i
$112$		0			0
$113$	0.566005	−	1.74198i	0.0532452	−	0.163872i	−0.920898	−	0.389804i	$-0.872543\pi$
$113$	0.566005	−	1.74198i	0.0532452	−	0.163872i	0.974143	+	0.225932i	$0.0725427\pi$
$114$		0			0
$115$	2.07408	−	1.50691i	0.193409	−	0.140520i
$116$		0			0
$117$	1.01756	+	3.13173i	0.0940734	+	0.289528i
$118$		0			0
$119$	3.09251	−	4.25648i	0.283490	−	0.390191i
$120$		0			0
$121$	6.74753	−	8.68740i	0.613412	−	0.789763i
$122$		0			0
$123$	2.03369	−	2.79914i	0.183372	−	0.252390i
$124$		0			0
$125$	−11.5592	+	3.75580i	−1.03388	+	0.335929i
$126$		0			0
$127$	−5.77997	+	4.19940i	−0.512890	+	0.372636i	−0.813919	−	0.580979i	$-0.802670\pi$
$127$	−5.77997	+	4.19940i	−0.512890	+	0.372636i	0.301029	+	0.953615i	$0.402670\pi$
$128$		0			0
$129$	−3.42700	−	1.11350i	−0.301730	−	0.0980381i
$130$		0			0
$131$			8.74918i			0.764420i	0.924076	+	0.382210i	$0.124837\pi$
$131$			8.74918i			0.764420i	−0.924076	+	0.382210i	$0.875163\pi$
$132$		0			0
$133$			0.585847i			0.0507994i
$134$		0			0
$135$	1.68223	+	0.546590i	0.144783	+	0.0470430i
$136$		0			0
$137$	6.84644	−	4.97423i	0.584930	−	0.424977i	−0.255568	−	0.966791i	$-0.582262\pi$
$137$	6.84644	−	4.97423i	0.584930	−	0.424977i	0.840498	+	0.541814i	$0.182262\pi$
$138$		0			0
$139$	5.45350	−	1.77195i	0.462560	−	0.150295i	−0.0684604	−	0.997654i	$-0.521809\pi$
$139$	5.45350	−	1.77195i	0.462560	−	0.150295i	0.531021	+	0.847359i	$0.321809\pi$
$140$		0			0
$141$	0.449578	−	0.618791i	0.0378613	−	0.0521116i
$142$		0			0
$143$	−10.7581	−	1.88112i	−0.899634	−	0.157307i
$144$		0			0
$145$	−8.24724	+	11.3514i	−0.684896	+	0.942679i
$146$		0			0
$147$	−1.56224	−	4.80808i	−0.128851	−	0.396563i
$148$		0			0
$149$	15.6781	−	11.3908i	1.28440	−	0.933168i	0.284720	−	0.958611i	$-0.408099\pi$
$149$	15.6781	−	11.3908i	1.28440	−	0.933168i	0.999676	+	0.0254423i	$0.00809940\pi$
$150$		0			0
$151$	3.22214	−	9.91672i	0.262214	−	0.807011i	−0.730108	−	0.683331i	$-0.760530\pi$
$151$	3.22214	−	9.91672i	0.262214	−	0.807011i	0.992322	−	0.123680i	$-0.0394696\pi$
$152$		0			0
$153$			3.77303i			0.305031i
$154$		0			0
$155$	2.45654			0.197314
$156$		0			0
$157$	16.9246	+	5.49914i	1.35073	+	0.438879i	0.892938	−	0.450180i	$-0.148640\pi$
$157$	16.9246	+	5.49914i	1.35073	+	0.438879i	0.457792	+	0.889059i	$0.348640\pi$
$158$		0			0
$159$	−2.54374	−	3.50116i	−0.201732	−	0.277660i
$160$		0			0
$161$	−1.92220	+	0.624560i	−0.151491	+	0.0492223i
$162$		0			0
$163$	4.84269	+	3.51842i	0.379308	+	0.275584i	0.761060	−	0.648681i	$-0.224679\pi$
$163$	4.84269	+	3.51842i	0.379308	+	0.275584i	−0.381752	+	0.924265i	$0.624679\pi$
$164$		0			0
$165$	−4.21416	+	4.08119i	−0.328072	+	0.317721i
$166$		0			0
$167$	−4.20600	−	3.05584i	−0.325470	−	0.236468i	0.413036	−	0.910715i	$-0.364468\pi$
$167$	−4.20600	−	3.05584i	−0.325470	−	0.236468i	−0.738506	+	0.674247i	$0.764468\pi$
$168$		0			0
$169$	−0.666510	−	2.05131i	−0.0512700	−	0.157793i
$170$		0			0
$171$	−0.246945	−	0.339891i	−0.0188844	−	0.0259921i
$172$		0			0
$173$	4.33891	−	13.3538i	0.329881	−	1.01527i	−0.639307	−	0.768951i	$-0.720779\pi$
$173$	4.33891	−	13.3538i	0.329881	−	1.01527i	0.969189	−	0.246319i	$-0.0792212\pi$
$174$		0			0
$175$	2.60949			0.197259
$176$		0			0
$177$	−11.9598			−0.898954
$178$		0			0
$179$	−7.11085	+	21.8849i	−0.531490	+	1.63576i	0.219624	+	0.975585i	$0.429517\pi$
$179$	−7.11085	+	21.8849i	−0.531490	+	1.63576i	−0.751114	+	0.660173i	$0.770483\pi$
$180$		0			0
$181$	−11.4700	−	15.7871i	−0.852559	−	1.17345i	−0.983293	−	0.182030i	$-0.941733\pi$
$181$	−11.4700	−	15.7871i	−0.852559	−	1.17345i	0.130734	−	0.991418i	$-0.458267\pi$
$182$		0			0
$183$	3.22933	+	9.93887i	0.238719	+	0.734702i
$184$		0			0
$185$	13.4196	+	9.74989i	0.986627	+	0.716827i
$186$		0			0
$187$	−11.0573	−	5.85908i	−0.808592	−	0.428458i
$188$		0			0
$189$	−1.12813	−	0.819637i	−0.0820596	−	0.0596198i
$190$		0			0
$191$	24.3481	−	7.91117i	1.76177	−	0.572432i	0.764385	−	0.644760i	$-0.223043\pi$
$191$	24.3481	−	7.91117i	1.76177	−	0.572432i	0.997381	+	0.0723280i	$0.0230428\pi$
$192$		0			0
$193$	12.9917	+	17.8816i	0.935166	+	1.28715i	0.957810	+	0.287402i	$0.0927917\pi$
$193$	12.9917	+	17.8816i	0.935166	+	1.28715i	−0.0226438	+	0.999744i	$0.507208\pi$
$194$		0			0
$195$	5.53940	+	1.79986i	0.396685	+	0.128891i
$196$		0			0
$197$	18.2227			1.29832			0.649158	−	0.760653i	$-0.275121\pi$
$197$	18.2227			1.29832			0.649158	+	0.760653i	$0.275121\pi$
$198$		0			0
$199$			13.2643i			0.940284i	0.882591	+	0.470142i	$0.155797\pi$
$199$			13.2643i			0.940284i	−0.882591	+	0.470142i	$0.844203\pi$
$200$		0			0
$201$	−3.07475	+	9.46312i	−0.216876	+	0.667477i
$202$		0			0
$203$	8.94893	−	6.50178i	0.628092	−	0.456335i
$204$		0			0
$205$	−1.89116	−	5.82039i	−0.132084	−	0.406514i
$206$		0			0
$207$	0.851938	−	1.17259i	0.0592138	−	0.0815008i
$208$		0			0
$209$	1.37957	−	0.195892i	0.0954268	−	0.0135501i
$210$		0			0
$211$	−11.2460	+	15.4787i	−0.774204	+	1.06560i	0.221694	+	0.975116i	$0.428841\pi$
$211$	−11.2460	+	15.4787i	−0.774204	+	1.06560i	−0.995898	+	0.0904841i	$0.971159\pi$
$212$		0			0
$213$	−12.2539	+	3.98153i	−0.839623	+	0.272810i
$214$		0			0
$215$	−5.15637	+	3.74632i	−0.351662	+	0.255497i
$216$		0			0
$217$	−1.84185	−	0.598452i	−0.125033	−	0.0406256i
$218$		0			0
$219$			9.61699i			0.649856i
$220$		0			0
$221$			12.4242i			0.835740i
$222$		0			0
$223$	1.64768	+	0.535364i	0.110337	+	0.0358507i	0.363665	−	0.931530i	$-0.381525\pi$
$223$	1.64768	+	0.535364i	0.110337	+	0.0358507i	−0.253328	+	0.967380i	$0.581525\pi$
$224$		0			0
$225$	−1.51394	+	1.09994i	−0.100930	+	0.0733296i
$226$		0			0
$227$	−5.99045	+	1.94642i	−0.397600	+	0.129188i	−0.500991	−	0.865453i	$-0.667031\pi$
$227$	−5.99045	+	1.94642i	−0.397600	+	0.129188i	0.103390	+	0.994641i	$0.467031\pi$
$228$		0			0
$229$	−2.03611	+	2.80246i	−0.134550	+	0.185192i	−0.870975	−	0.491327i	$-0.836512\pi$
$229$	−2.03611	+	2.80246i	−0.134550	+	0.185192i	0.736426	+	0.676519i	$0.236512\pi$
$230$		0			0
$231$	4.15391	−	2.03333i	0.273307	−	0.133783i
$232$		0			0
$233$	−8.63879	+	11.8903i	−0.565946	+	0.778958i	−0.992067	−	0.125708i	$-0.959880\pi$
$233$	−8.63879	+	11.8903i	−0.565946	+	0.778958i	0.426121	+	0.904666i	$0.359880\pi$
$234$		0			0
$235$	−0.418069	−	1.28669i	−0.0272718	−	0.0839341i
$236$		0			0
$237$	4.69761	−	3.41302i	0.305143	−	0.221699i
$238$		0			0
$239$	6.25422	−	19.2485i	0.404552	−	1.24508i	−0.516717	−	0.856156i	$-0.672846\pi$
$239$	6.25422	−	19.2485i	0.404552	−	1.24508i	0.921269	−	0.388927i	$-0.127154\pi$
$240$		0			0
$241$			8.76302i			0.564476i	0.959344	+	0.282238i	$0.0910768\pi$
$241$			8.76302i			0.564476i	−0.959344	+	0.282238i	$0.908923\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−8.50454	−	2.76329i	−0.543335	−	0.176540i
$246$		0			0
$247$	−0.813163	−	1.11922i	−0.0517403	−	0.0712145i
$248$		0			0
$249$	14.3476	−	4.66182i	0.909242	−	0.295431i
$250$		0			0
$251$	4.24381	+	3.08331i	0.267867	+	0.194617i	0.713608	−	0.700545i	$-0.247060\pi$
$251$	4.24381	+	3.08331i	0.267867	+	0.194617i	−0.445741	+	0.895162i	$0.647060\pi$
$252$		0			0
$253$	2.11346	+	4.31761i	0.132872	+	0.271446i
$254$		0			0
$255$	5.39917	+	3.92273i	0.338109	+	0.245651i
$256$		0			0
$257$	−1.45063	−	4.46459i	−0.0904879	−	0.278493i	0.895564	−	0.444933i	$-0.146773\pi$
$257$	−1.45063	−	4.46459i	−0.0904879	−	0.278493i	−0.986052	+	0.166440i	$0.946773\pi$
$258$		0			0
$259$	−7.68641	−	10.5794i	−0.477610	−	0.657374i
$260$		0			0
$261$	−2.45128	+	7.54427i	−0.151730	+	0.466978i
$262$		0			0
$263$	23.0463			1.42110			0.710548	−	0.703648i	$-0.248447\pi$
$263$	23.0463			1.42110			0.710548	+	0.703648i	$0.248447\pi$
$264$		0			0
$265$	−7.65479			−0.470230
$266$		0			0
$267$	3.37479	−	10.3865i	0.206534	−	0.635645i
$268$		0			0
$269$	−5.66339	−	7.79498i	−0.345303	−	0.475268i	0.600678	−	0.799491i	$-0.294897\pi$
$269$	−5.66339	−	7.79498i	−0.345303	−	0.475268i	−0.945981	+	0.324223i	$0.894897\pi$
$270$		0			0
$271$	7.25330	+	22.3234i	0.440607	+	1.35605i	0.887230	+	0.461326i	$0.152626\pi$
$271$	7.25330	+	22.3234i	0.440607	+	1.35605i	−0.446624	+	0.894722i	$0.647374\pi$
$272$		0			0
$273$	−3.71482	−	2.69897i	−0.224831	−	0.163349i
$274$		0			0
$275$	−0.872544	−	6.14489i	−0.0526164	−	0.370551i
$276$		0			0
$277$	16.1312	+	11.7200i	0.969227	+	0.704185i	0.955275	−	0.295718i	$-0.0955588\pi$
$277$	16.1312	+	11.7200i	0.969227	+	0.704185i	0.0139521	+	0.999903i	$0.495559\pi$
$278$		0			0
$279$	1.32084	−	0.429168i	0.0790767	−	0.0256936i
$280$		0			0
$281$	−3.73754	−	5.14428i	−0.222963	−	0.306882i	0.682851	−	0.730557i	$-0.260740\pi$
$281$	−3.73754	−	5.14428i	−0.222963	−	0.306882i	−0.905814	+	0.423675i	$0.860740\pi$
$282$		0			0
$283$	8.30006	+	2.69685i	0.493387	+	0.160311i	0.545134	−	0.838349i	$-0.316479\pi$
$283$	8.30006	+	2.69685i	0.493387	+	0.160311i	−0.0517465	+	0.998660i	$0.516479\pi$
$284$		0			0
$285$	−0.743124			−0.0440188
$286$		0			0
$287$			4.82469i			0.284792i
$288$		0			0
$289$	0.854199	−	2.62895i	0.0502470	−	0.154644i
$290$		0			0
$291$	−11.2144	+	8.14771i	−0.657398	+	0.477627i
$292$		0			0
$293$	−6.37463	−	19.6191i	−0.372410	−	1.14616i	−0.945209	−	0.326465i	$-0.894143\pi$
$293$	−6.37463	−	19.6191i	−0.372410	−	1.14616i	0.572799	−	0.819696i	$-0.305857\pi$
$294$		0			0
$295$	−12.4343	+	17.1144i	−0.723955	+	0.996438i
$296$		0			0
$297$	−1.55288	+	2.93062i	−0.0901075	+	0.170052i
$298$		0			0
$299$	2.80534	−	3.86122i	0.162237	−	0.223300i
$300$		0			0
$301$	4.77877	−	1.55272i	0.275444	−	0.0894971i
$302$		0			0
$303$	6.49406	−	4.71821i	0.373074	−	0.271054i
$304$		0			0
$305$	17.5799	+	5.71205i	1.00662	+	0.327071i
$306$		0			0
$307$			24.6574i			1.40727i	0.710560	+	0.703637i	$0.248442\pi$
$307$			24.6574i			1.40727i	−0.710560	+	0.703637i	$0.751558\pi$
$308$		0			0
$309$		−	12.3377i		−	0.701864i
$310$		0			0
$311$	24.3504	+	7.91194i	1.38079	+	0.448645i	0.902928	−	0.429792i	$-0.141413\pi$
$311$	24.3504	+	7.91194i	1.38079	+	0.448645i	0.477859	+	0.878437i	$0.341413\pi$
$312$		0			0
$313$	3.15731	−	2.29392i	0.178462	−	0.129660i	−0.494968	−	0.868911i	$-0.664820\pi$
$313$	3.15731	−	2.29392i	0.178462	−	0.129660i	0.673430	+	0.739251i	$0.264820\pi$
$314$		0			0
$315$	−2.34579	+	0.762192i	−0.132170	+	0.0429447i
$316$		0			0
$317$	−3.74958	+	5.16085i	−0.210597	+	0.289862i	−0.901228	−	0.433345i	$-0.857333\pi$
$317$	−3.74958	+	5.16085i	−0.210597	+	0.289862i	0.690631	+	0.723208i	$0.257333\pi$
$318$		0			0
$319$	−18.3028	−	18.8991i	−1.02476	−	1.05815i
$320$		0			0
$321$	4.21709	−	5.80433i	0.235375	−	0.323966i
$322$		0			0
$323$	−0.489840	−	1.50757i	−0.0272554	−	0.0838836i
$324$		0			0
$325$	−4.98525	+	3.62200i	−0.276532	+	0.200912i
$326$		0			0
$327$	2.89860	−	8.92098i	0.160293	−	0.493331i
$328$		0			0
$329$			1.06657i			0.0588019i
$330$		0			0
$331$	4.34773			0.238973			0.119486	−	0.992836i	$-0.461875\pi$
$331$	4.34773			0.238973			0.119486	+	0.992836i	$0.461875\pi$
$332$		0			0
$333$	8.91884	+	2.89791i	0.488749	+	0.158804i
$334$		0			0
$335$	10.3449	+	14.2385i	0.565202	+	0.777934i
$336$		0			0
$337$	9.71778	−	3.15750i	0.529361	−	0.172000i	−0.0321283	−	0.999484i	$-0.510229\pi$
$337$	9.71778	−	3.15750i	0.529361	−	0.172000i	0.561490	+	0.827484i	$0.310229\pi$
$338$		0			0
$339$	−1.48182	−	1.07660i	−0.0804814	−	0.0584731i
$340$		0			0
$341$	−0.793386	+	4.53734i	−0.0429642	+	0.245711i
$342$		0			0
$343$	13.6002	+	9.88114i	0.734343	+	0.533531i
$344$		0			0
$345$	−0.792229	−	2.43823i	−0.0426522	−	0.131270i
$346$		0			0
$347$	−4.37155	−	6.01692i	−0.234677	−	0.323005i	0.675394	−	0.737457i	$-0.263973\pi$
$347$	−4.37155	−	6.01692i	−0.234677	−	0.323005i	−0.910071	+	0.414452i	$0.863973\pi$
$348$		0			0
$349$	1.81469	−	5.58504i	0.0971382	−	0.298961i	−0.890667	−	0.454657i	$-0.849762\pi$
$349$	1.81469	−	5.58504i	0.0971382	−	0.298961i	0.987805	+	0.155696i	$0.0497620\pi$
$350$		0			0
$351$	3.29289			0.175762
$352$		0			0
$353$	−26.3624			−1.40313			−0.701565	−	0.712605i	$-0.747515\pi$
$353$	−26.3624			−1.40313			−0.701565	+	0.712605i	$0.747515\pi$
$354$		0			0
$355$	−7.04254	+	21.6747i	−0.373779	+	1.15037i
$356$		0			0
$357$	−3.09251	−	4.25648i	−0.163673	−	0.225277i
$358$		0			0
$359$	1.23260	+	3.79354i	0.0650539	+	0.200215i	0.978300	−	0.207193i	$-0.0664327\pi$
$359$	1.23260	+	3.79354i	0.0650539	+	0.200215i	−0.913246	+	0.407408i	$0.866433\pi$
$360$		0			0
$361$	−15.2285	−	11.0642i	−0.801501	−	0.582325i
$362$		0			0
$363$	−6.17710	−	9.10183i	−0.324214	−	0.477722i
$364$		0			0
$365$	13.7618	+	9.99855i	0.720327	+	0.523348i
$366$		0			0
$367$	−31.5697	+	10.2576i	−1.64792	+	0.535443i	−0.978288	−	0.207248i	$-0.933549\pi$
$367$	−31.5697	+	10.2576i	−1.64792	+	0.535443i	−0.669634	+	0.742691i	$0.733549\pi$
$368$		0			0
$369$	−2.03369	−	2.79914i	−0.105870	−	0.145717i
$370$		0			0
$371$	5.73936	+	1.86483i	0.297973	+	0.0968171i
$372$		0			0
$373$	30.7237			1.59081			0.795407	−	0.606075i	$-0.207257\pi$
$373$	30.7237			1.59081			0.795407	+	0.606075i	$0.207257\pi$
$374$		0			0
$375$			12.1540i			0.627632i
$376$		0			0
$377$	−8.07180	+	24.8424i	−0.415719	+	1.27945i
$378$		0			0
$379$	29.7001	−	21.5784i	1.52559	−	1.10841i	0.566967	−	0.823741i	$-0.308117\pi$
$379$	29.7001	−	21.5784i	1.52559	−	1.10841i	0.958626	−	0.284667i	$-0.0918832\pi$
$380$		0			0
$381$	2.20775	+	6.79476i	0.113107	+	0.348106i
$382$		0			0
$383$	−7.33813	+	10.1001i	−0.374961	+	0.516090i	−0.954241	−	0.299039i	$-0.903334\pi$
$383$	−7.33813	+	10.1001i	−0.374961	+	0.516090i	0.579280	+	0.815129i	$0.303334\pi$
$384$		0			0
$385$	1.40904	−	8.05821i	0.0718111	−	0.410684i
$386$		0			0
$387$	−2.11800	+	2.91518i	−0.107664	+	0.148187i
$388$		0			0
$389$	−31.6936	+	10.2979i	−1.60693	+	0.522122i	−0.968807	−	0.247815i	$-0.920288\pi$
$389$	−31.6936	+	10.2979i	−1.60693	+	0.522122i	−0.638120	+	0.769937i	$0.720288\pi$
$390$		0			0
$391$	4.42422	−	3.21439i	0.223743	−	0.162559i
$392$		0			0
$393$	8.32097	+	2.70365i	0.419737	+	0.136381i
$394$		0			0
$395$		−	10.2707i		−	0.516774i
$396$		0			0
$397$		−	14.1022i		−	0.707767i	−0.935289	−	0.353884i	$-0.884861\pi$
$397$		−	14.1022i		−	0.707767i	0.935289	−	0.353884i	$-0.115139\pi$
$398$		0			0
$399$	0.557174	+	0.181037i	0.0278936	+	0.00906317i
$400$		0			0
$401$	9.67496	−	7.02927i	0.483145	−	0.351025i	−0.319397	−	0.947621i	$-0.603480\pi$
$401$	9.67496	−	7.02927i	0.483145	−	0.351025i	0.802542	+	0.596596i	$0.203480\pi$
$402$		0			0
$403$	4.34939	−	1.41320i	0.216658	−	0.0703966i
$404$		0			0
$405$	1.03968	−	1.43099i	0.0516619	−	0.0711065i
$406$		0			0
$407$	−22.3426	+	21.6376i	−1.10748	+	1.07254i
$408$		0			0
$409$	−9.59791	+	13.2104i	−0.474586	+	0.653212i	−0.977453	−	0.211152i	$-0.932279\pi$
$409$	−9.59791	+	13.2104i	−0.474586	+	0.653212i	0.502867	+	0.864364i	$0.332279\pi$
$410$		0			0
$411$	−2.61511	−	8.04847i	−0.128994	−	0.397002i
$412$		0			0
$413$	13.4923	−	9.80270i	0.663911	−	0.482359i
$414$		0			0
$415$	8.24584	−	25.3781i	0.404772	−	1.24576i
$416$		0			0
$417$		−	5.73415i		−	0.280803i
$418$		0			0
$419$	−5.36954			−0.262319			−0.131159	−	0.991361i	$-0.541870\pi$
$419$	−5.36954			−0.262319			−0.131159	+	0.991361i	$0.541870\pi$
$420$		0			0
$421$	8.90313	+	2.89280i	0.433912	+	0.140987i	0.517825	−	0.855487i	$-0.326742\pi$
$421$	8.90313	+	2.89280i	0.433912	+	0.140987i	−0.0839132	+	0.996473i	$0.526742\pi$
$422$		0			0
$423$	−0.449578	−	0.618791i	−0.0218592	−	0.0300867i
$424$		0			0
$425$	−6.71504	+	2.18185i	−0.325727	+	0.105835i
$426$		0			0
$427$	−11.7894	−	8.56549i	−0.570528	−	0.414513i
$428$		0			0
$429$	−5.11348	+	9.65022i	−0.246881	+	0.465917i
$430$		0			0
$431$	−30.9429	−	22.4813i	−1.49047	−	1.08289i	−0.973991	−	0.226587i	$-0.927243\pi$
$431$	−30.9429	−	22.4813i	−1.49047	−	1.08289i	−0.516477	−	0.856301i	$-0.672757\pi$
$432$		0			0
$433$	3.07438	+	9.46196i	0.147745	+	0.454713i	0.997354	−	0.0727008i	$-0.0231618\pi$
$433$	3.07438	+	9.46196i	0.147745	+	0.454713i	−0.849609	+	0.527414i	$0.823162\pi$
$434$		0			0
$435$	8.24724	+	11.3514i	0.395425	+	0.544256i
$436$		0			0
$437$	−0.188171	+	0.579132i	−0.00900145	+	0.0277036i
$438$		0			0
$439$	−15.8844			−0.758122			−0.379061	−	0.925372i	$-0.623753\pi$
$439$	−15.8844			−0.758122			−0.379061	+	0.925372i	$0.623753\pi$
$440$		0			0
$441$	−5.05551			−0.240739
$442$		0			0
$443$	1.67612	−	5.15857i	0.0796349	−	0.245091i	−0.903311	−	0.428986i	$-0.858871\pi$
$443$	1.67612	−	5.15857i	0.0796349	−	0.245091i	0.982946	+	0.183895i	$0.0588708\pi$
$444$		0			0
$445$	−11.3543	−	15.6279i	−0.538247	−	0.740834i
$446$		0			0
$447$	−5.98848	−	18.4307i	−0.283246	−	0.871740i
$448$		0			0
$449$	−8.05234	−	5.85037i	−0.380013	−	0.276096i	0.381338	−	0.924436i	$-0.375464\pi$
$449$	−8.05234	−	5.85037i	−0.380013	−	0.276096i	−0.761351	+	0.648340i	$0.775464\pi$
$450$		0			0
$451$	11.3613	−	1.61325i	0.534983	−	0.0759650i
$452$		0			0
$453$	−8.43566	−	6.12887i	−0.396342	−	0.287959i
$454$		0			0
$455$	−7.72442	+	2.50982i	−0.362126	+	0.117662i
$456$		0			0
$457$	−14.7492	−	20.3005i	−0.689939	−	0.949619i	0.310061	−	0.950717i	$-0.399651\pi$
$457$	−14.7492	−	20.3005i	−0.689939	−	0.949619i	−0.999999	+	0.00109777i	$0.999651\pi$
$458$		0			0
$459$	3.58836	+	1.16593i	0.167491	+	0.0544210i
$460$		0			0
$461$	−34.5074			−1.60717			−0.803585	−	0.595190i	$-0.797077\pi$
$461$	−34.5074			−1.60717			−0.803585	+	0.595190i	$0.797077\pi$
$462$		0			0
$463$		−	22.7879i		−	1.05905i	−0.848296	−	0.529523i	$-0.822371\pi$
$463$		−	22.7879i		−	1.05905i	0.848296	−	0.529523i	$-0.177629\pi$
$464$		0			0
$465$	0.759113	−	2.33631i	0.0352030	−	0.108344i
$466$		0			0
$467$	−4.94788	+	3.59484i	−0.228960	+	0.166349i	−0.696351	−	0.717702i	$-0.745194\pi$
$467$	−4.94788	+	3.59484i	−0.228960	+	0.166349i	0.467390	+	0.884051i	$0.345194\pi$
$468$		0			0
$469$	−4.28759	−	13.1958i	−0.197982	−	0.609327i
$470$		0			0
$471$	10.4600	−	14.3969i	0.481970	−	0.663375i
$472$		0			0
$473$	−5.25428	−	10.7340i	−0.241592	−	0.493549i
$474$		0			0
$475$	0.462118	−	0.636050i	0.0212034	−	0.0291840i
$476$		0			0
$477$	−4.11586	+	1.33732i	−0.188452	+	0.0612318i
$478$		0			0
$479$	−2.50936	+	1.82316i	−0.114656	+	0.0833022i	−0.643635	−	0.765332i	$-0.722575\pi$
$479$	−2.50936	+	1.82316i	−0.114656	+	0.0833022i	0.528980	+	0.848634i	$0.322575\pi$
$480$		0			0
$481$	29.3688	+	9.54249i	1.33910	+	0.435100i
$482$		0			0
$483$			2.02112i			0.0919641i
$484$		0			0
$485$			24.5186i			1.11333i
$486$		0			0
$487$	−20.1262	−	6.53939i	−0.912003	−	0.296328i	−0.184821	−	0.982772i	$-0.559171\pi$
$487$	−20.1262	−	6.53939i	−0.912003	−	0.296328i	−0.727182	+	0.686444i	$0.759171\pi$
$488$		0			0
$489$	4.84269	−	3.51842i	0.218994	−	0.159108i
$490$		0			0
$491$	4.96607	−	1.61357i	0.224116	−	0.0728195i	−0.194807	−	0.980842i	$-0.562408\pi$
$491$	4.96607	−	1.61357i	0.224116	−	0.0728195i	0.418922	+	0.908022i	$0.362408\pi$
$492$		0			0
$493$	−17.5922	+	24.2136i	−0.792312	+	1.09052i
$494$		0			0
$495$	2.57920	+	5.26906i	0.115926	+	0.236827i
$496$		0			0
$497$	10.5606	−	14.5354i	0.473708	−	0.652003i
$498$		0			0
$499$	9.84802	+	30.3091i	0.440858	+	1.35682i	0.886963	+	0.461840i	$0.152811\pi$
$499$	9.84802	+	30.3091i	0.440858	+	1.35682i	−0.446105	+	0.894980i	$0.647189\pi$
$500$		0			0
$501$	−4.20600	+	3.05584i	−0.187910	+	0.136525i
$502$		0			0
$503$	4.38495	−	13.4955i	0.195515	−	0.601734i	−0.804455	−	0.594014i	$-0.797542\pi$
$503$	4.38495	−	13.4955i	0.195515	−	0.601734i	0.999970	−	0.00772063i	$-0.00245758\pi$
$504$		0			0
$505$		−	14.1984i		−	0.631819i
$506$		0			0
$507$	−2.15687			−0.0957900
$508$		0			0
$509$	−8.45834	−	2.74828i	−0.374909	−	0.121815i	0.115500	−	0.993307i	$-0.463153\pi$
$509$	−8.45834	−	2.74828i	−0.374909	−	0.121815i	−0.490410	+	0.871492i	$0.663153\pi$
$510$		0			0
$511$	−7.88244	−	10.8492i	−0.348699	−	0.479942i
$512$		0			0
$513$	−0.399566	+	0.129827i	−0.0176412	+	0.00573199i
$514$		0			0
$515$	−17.6551	−	12.8272i	−0.777975	−	0.565232i
$516$		0			0
$517$	2.51159	−	0.356633i	0.110459	−	0.0156847i
$518$		0			0
$519$	−11.3594	−	8.25310i	−0.498623	−	0.362271i
$520$		0			0
$521$	−8.34024	−	25.6686i	−0.365393	−	1.12456i	−0.949735	−	0.313056i	$-0.898647\pi$
$521$	−8.34024	−	25.6686i	−0.365393	−	1.12456i	0.584342	−	0.811507i	$-0.301353\pi$
$522$		0			0
$523$	−25.2868	−	34.8043i	−1.10571	−	1.52188i	−0.827585	−	0.561341i	$-0.810286\pi$
$523$	−25.2868	−	34.8043i	−1.10571	−	1.52188i	−0.278129	−	0.960544i	$-0.589714\pi$
$524$		0			0
$525$	0.806375	−	2.48177i	0.0351931	−	0.108313i
$526$		0			0
$527$	5.24004			0.228260
$528$		0			0
$529$	20.8992			0.908662
$530$		0			0
$531$	−3.69578	+	11.3745i	−0.160383	+	0.493609i
$532$		0			0
$533$	−6.69673	−	9.21726i	−0.290067	−	0.399244i
$534$		0			0
$535$	−3.92154	−	12.0692i	−0.169543	−	0.521799i
$536$		0			0
$537$	18.6164	+	13.5256i	0.803359	+	0.583674i
$538$		0			0
$539$	7.85062	−	14.8158i	0.338150	−	0.638162i
$540$		0			0
$541$	16.3673	+	11.8916i	0.703686	+	0.511258i	0.881131	−	0.472873i	$-0.156783\pi$
$541$	16.3673	+	11.8916i	0.703686	+	0.511258i	−0.177444	+	0.984131i	$0.556783\pi$
$542$		0			0
$543$	−18.5589	+	6.03014i	−0.796437	+	0.258778i
$544$		0			0
$545$	−9.75224	−	13.4228i	−0.417740	−	0.574970i
$546$		0			0
$547$	−13.6380	−	4.43124i	−0.583117	−	0.189466i	0.00257925	−	0.999997i	$-0.499179\pi$
$547$	−13.6380	−	4.43124i	−0.583117	−	0.189466i	−0.585697	+	0.810530i	$0.699179\pi$
$548$		0			0
$549$	10.4503			0.446010
$550$		0			0
$551$		−	3.33267i		−	0.141977i
$552$		0			0
$553$	−2.50210	+	7.70067i	−0.106400	+	0.327466i
$554$		0			0
$555$	13.4196	−	9.74989i	0.569629	−	0.413860i
$556$		0			0
$557$	9.72693	+	29.9364i	0.412143	+	1.26845i	0.914781	+	0.403949i	$0.132363\pi$
$557$	9.72693	+	29.9364i	0.412143	+	1.26845i	−0.502638	+	0.864497i	$0.667637\pi$
$558$		0			0
$559$	−6.97434	+	9.59936i	−0.294983	+	0.406010i
$560$		0			0
$561$	−8.98922	+	8.70559i	−0.379525	+	0.367550i
$562$		0			0
$563$	−11.5320	+	15.8725i	−0.486017	+	0.668946i	−0.979647	−	0.200726i	$-0.935670\pi$
$563$	−11.5320	+	15.8725i	−0.486017	+	0.668946i	0.493630	+	0.869672i	$0.335670\pi$
$564$		0			0
$565$	−3.08122	+	1.00115i	−0.129628	+	0.0421187i
$566$		0			0
$567$	−1.12813	+	0.819637i	−0.0473771	+	0.0344215i
$568$		0			0
$569$	25.2020	+	8.18862i	1.05652	+	0.343285i	0.785225	−	0.619211i	$-0.212547\pi$
$569$	25.2020	+	8.18862i	1.05652	+	0.343285i	0.271297	+	0.962496i	$0.412547\pi$
$570$		0			0
$571$		−	15.2004i		−	0.636116i	−0.948071	−	0.318058i	$-0.896969\pi$
$571$		−	15.2004i		−	0.636116i	0.948071	−	0.318058i	$-0.103031\pi$
$572$		0			0
$573$		−	25.6011i		−	1.06950i
$574$		0			0
$575$	2.57957	+	0.838154i	0.107576	+	0.0349534i
$576$		0			0
$577$	17.6624	−	12.8325i	0.735296	−	0.534224i	−0.155939	−	0.987767i	$-0.549840\pi$
$577$	17.6624	−	12.8325i	0.735296	−	0.534224i	0.891234	+	0.453543i	$0.149840\pi$
$578$		0			0
$579$	21.0211	−	6.83016i	0.873606	−	0.283852i
$580$		0			0
$581$	−12.3650	+	17.0190i	−0.512987	+	0.706066i
$582$		0			0
$583$	2.47226	−	14.1387i	0.102390	−	0.585567i
$584$		0			0
$585$	3.42354	−	4.71210i	0.141546	−	0.194821i
$586$		0			0
$587$	−7.06883	−	21.7556i	−0.291762	−	0.897951i	−0.984290	−	0.176560i	$-0.943503\pi$
$587$	−7.06883	−	21.7556i	−0.291762	−	0.897951i	0.692528	−	0.721391i	$-0.256497\pi$
$588$		0			0
$589$	−0.472045	+	0.342961i	−0.0194503	+	0.0141315i
$590$		0			0
$591$	5.63114	−	17.3309i	0.231634	−	0.712896i
$592$		0			0
$593$		−	13.3772i		−	0.549336i	−0.961539	−	0.274668i	$-0.911432\pi$
$593$		−	13.3772i		−	0.549336i	0.961539	−	0.274668i	$-0.0885679\pi$
$594$		0			0
$595$	−9.30620			−0.381517
$596$		0			0
$597$	12.6151	+	4.09891i	0.516303	+	0.167757i
$598$		0			0
$599$	−13.8109	−	19.0091i	−0.564300	−	0.776692i	0.427565	−	0.903984i	$-0.359371\pi$
$599$	−13.8109	−	19.0091i	−0.564300	−	0.776692i	−0.991865	+	0.127292i	$0.959371\pi$
$600$		0			0
$601$	11.5910	−	3.76616i	0.472809	−	0.153625i	−0.0629138	−	0.998019i	$-0.520039\pi$
$601$	11.5910	−	3.76616i	0.472809	−	0.153625i	0.535722	+	0.844394i	$0.320039\pi$
$602$		0			0
$603$	8.04981	+	5.84853i	0.327814	+	0.238171i
$604$		0			0
$605$	−19.4468	−	0.623576i	−0.790626	−	0.0253520i
$606$		0			0
$607$	33.2882	+	24.1853i	1.35113	+	0.981652i	0.998954	+	0.0457169i	$0.0145572\pi$
$607$	33.2882	+	24.1853i	1.35113	+	0.981652i	0.352173	+	0.935935i	$0.385443\pi$
$608$		0			0
$609$	−3.41819	−	10.5201i	−0.138512	−	0.426296i
$610$		0			0
$611$	−1.48041	−	2.03761i	−0.0598911	−	0.0824330i
$612$		0			0
$613$	−3.01493	+	9.27900i	−0.121772	+	0.374775i	−0.993299	−	0.115572i	$-0.963130\pi$
$613$	−3.01493	+	9.27900i	−0.121772	+	0.374775i	0.871527	+	0.490347i	$0.163130\pi$
$614$		0			0
$615$	−6.11992			−0.246779
$616$		0			0
$617$	−19.8476			−0.799035			−0.399518	−	0.916725i	$-0.630822\pi$
$617$	−19.8476			−0.799035			−0.399518	+	0.916725i	$0.630822\pi$
$618$		0			0
$619$	−0.849909	+	2.61575i	−0.0341607	+	0.105136i	−0.966683	−	0.255977i	$-0.917603\pi$
$619$	−0.849909	+	2.61575i	−0.0341607	+	0.105136i	0.932522	+	0.361113i	$0.117603\pi$
$620$		0			0
$621$	−0.851938	−	1.17259i	−0.0341871	−	0.0470545i
$622$		0			0
$623$	4.70597	+	14.4835i	0.188541	+	0.580269i
$624$		0			0
$625$	9.82260	+	7.13654i	0.392904	+	0.285462i
$626$		0			0
$627$	0.240006	−	1.37258i	0.00958490	−	0.0548156i
$628$		0			0
$629$	28.6253	+	20.7975i	1.14136	+	0.829250i
$630$		0			0
$631$	5.16849	−	1.67934i	0.205754	−	0.0668536i	−0.204327	−	0.978903i	$-0.565500\pi$
$631$	5.16849	−	1.67934i	0.205754	−	0.0668536i	0.410081	+	0.912049i	$0.365500\pi$
$632$		0			0
$633$	11.2460	+	15.4787i	0.446987	+	0.615225i
$634$		0			0
$635$	12.0186	+	3.90508i	0.476943	+	0.154968i
$636$		0			0
$637$	−16.6472			−0.659588
$638$		0			0
$639$			12.8845i			0.509703i
$640$		0			0
$641$	−5.69933	+	17.5407i	−0.225110	+	0.692817i	0.773170	+	0.634198i	$0.218670\pi$
$641$	−5.69933	+	17.5407i	−0.225110	+	0.692817i	−0.998280	+	0.0586191i	$0.981330\pi$
$642$		0			0
$643$	36.3473	−	26.4078i	1.43340	−	1.04142i	0.444024	−	0.896015i	$-0.353551\pi$
$643$	36.3473	−	26.4078i	1.43340	−	1.04142i	0.989372	−	0.145408i	$-0.0464495\pi$
$644$		0			0
$645$	1.96956	+	6.06168i	0.0775513	+	0.238678i
$646$		0			0
$647$	−12.0677	+	16.6098i	−0.474430	+	0.652997i	−0.977423	−	0.211294i	$-0.932232\pi$
$647$	−12.0677	+	16.6098i	−0.474430	+	0.652997i	0.502993	+	0.864291i	$0.332232\pi$
$648$		0			0
$649$	−27.5951	−	28.4942i	−1.08320	−	1.11849i
$650$		0			0
$651$	−1.13832	+	1.56677i	−0.0446144	+	0.0614065i
$652$		0			0
$653$	4.82108	−	1.56646i	0.188664	−	0.0613005i	−0.213161	−	0.977017i	$-0.568376\pi$
$653$	4.82108	−	1.56646i	0.188664	−	0.0613005i	0.401825	+	0.915717i	$0.368376\pi$
$654$		0			0
$655$	12.5200	−	9.09632i	0.489197	−	0.355423i
$656$		0			0
$657$	9.14630	+	2.97181i	0.356831	+	0.115941i
$658$		0			0
$659$		−	24.6770i		−	0.961279i	−0.876918	−	0.480640i	$-0.840405\pi$
$659$		−	24.6770i		−	0.961279i	0.876918	−	0.480640i	$-0.159595\pi$
$660$		0			0
$661$		−	29.9755i		−	1.16591i	−0.812504	−	0.582956i	$-0.801896\pi$
$661$		−	29.9755i		−	1.16591i	0.812504	−	0.582956i	$-0.198104\pi$
$662$		0			0
$663$	11.8161	+	3.83928i	0.458899	+	0.149105i
$664$		0			0
$665$	0.838342	−	0.609091i	0.0325095	−	0.0236196i
$666$		0			0
$667$	10.9347	−	3.55289i	0.423393	−	0.137569i
$668$		0			0
$669$	1.01832	−	1.40160i	0.0393707	−	0.0541891i
$670$		0			0
$671$	−16.2282	+	30.6260i	−0.626482	+	1.18230i
$672$		0			0
$673$	−0.00676354	+	0.00930921i	−0.000260715	+	0.000358844i	−0.809147	−	0.587606i	$-0.800071\pi$
$673$	−0.00676354	+	0.00930921i	−0.000260715	+	0.000358844i	0.808887	+	0.587965i	$0.200071\pi$
$674$		0			0
$675$	0.578275	+	1.77975i	0.0222578	+	0.0685025i
$676$		0			0
$677$	0.292248	−	0.212331i	0.0112320	−	0.00816054i	−0.582155	−	0.813078i	$-0.697790\pi$
$677$	0.292248	−	0.212331i	0.0112320	−	0.00816054i	0.593387	+	0.804917i	$0.297790\pi$
$678$		0			0
$679$	5.97313	−	18.3834i	0.229228	−	0.705491i
$680$		0			0
$681$			6.29873i			0.241368i
$682$		0			0
$683$	−16.8584			−0.645070			−0.322535	−	0.946557i	$-0.604535\pi$
$683$	−16.8584			−0.645070			−0.322535	+	0.946557i	$0.604535\pi$
$684$		0			0
$685$	−14.2362	−	4.62561i	−0.543935	−	0.176735i
$686$		0			0
$687$	2.03611	+	2.80246i	0.0776824	+	0.106921i
$688$		0			0
$689$	−13.5531	+	4.40366i	−0.516331	+	0.167766i
$690$		0			0
$691$	−33.4931	−	24.3341i	−1.27414	−	0.925714i	−0.274777	−	0.961508i	$-0.588604\pi$
$691$	−33.4931	−	24.3341i	−1.27414	−	0.925714i	−0.999359	+	0.0357938i	$0.988604\pi$
$692$		0			0
$693$	−0.650187	−	4.57893i	−0.0246986	−	0.173939i
$694$		0			0
$695$	−8.20552	−	5.96166i	−0.311253	−	0.226139i
$696$		0			0
$697$	−4.03403	−	12.4155i	−0.152800	−	0.470269i
$698$		0			0
$699$	8.63879	+	11.8903i	0.326749	+	0.449732i
$700$		0			0
$701$	9.88537	−	30.4240i	0.373365	−	1.14910i	−0.571210	−	0.820804i	$-0.693526\pi$
$701$	9.88537	−	30.4240i	0.373365	−	1.14910i	0.944575	−	0.328296i	$-0.106474\pi$
$702$		0			0
$703$	−3.93989			−0.148596
$704$		0			0
$705$	−1.35290			−0.0509532
$706$		0			0
$707$	−3.45895	+	10.6455i	−0.130087	+	0.400367i
$708$		0			0
$709$	−20.2031	−	27.8072i	−0.758743	−	1.04432i	−0.997318	−	0.0731963i	$-0.976680\pi$
$709$	−20.2031	−	27.8072i	−0.758743	−	1.04432i	0.238574	−	0.971124i	$-0.423320\pi$
$710$		0			0
$711$	−1.79433	−	5.52238i	−0.0672926	−	0.207105i
$712$		0			0
$713$	−1.62851	−	1.18318i	−0.0609883	−	0.0443106i
$714$		0			0
$715$	8.49302	+	17.3504i	0.317621	+	0.648870i
$716$		0			0
$717$	−16.3738	−	11.8962i	−0.611489	−	0.444273i
$718$		0			0
$719$	−25.4856	+	8.28077i	−0.950452	+	0.308821i	−0.742899	−	0.669403i	$-0.766550\pi$
$719$	−25.4856	+	8.28077i	−0.950452	+	0.308821i	−0.207553	+	0.978224i	$0.566550\pi$
$720$		0			0
$721$	10.1124	+	13.9185i	0.376605	+	0.518353i
$722$		0			0
$723$	8.33413	+	2.70792i	0.309950	+	0.100709i
$724$		0			0
$725$	−14.8444			−0.551307
$726$		0			0
$727$			26.4551i			0.981165i	0.871395	+	0.490583i	$0.163216\pi$
$727$			26.4551i			0.981165i	−0.871395	+	0.490583i	$0.836784\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−10.9990	+	7.99128i	−0.406814	+	0.295568i
$732$		0			0
$733$	0.587267	+	1.80742i	0.0216912	+	0.0667586i	0.961316	−	0.275447i	$-0.0888260\pi$
$733$	0.587267	+	1.80742i	0.0216912	+	0.0667586i	−0.939625	+	0.342206i	$0.888826\pi$
$734$		0			0
$735$	−5.25609	+	7.23439i	−0.193874	+	0.266845i
$736$		0			0
$737$	−29.6403	+	14.5089i	−1.09181	+	0.534441i
$738$		0			0
$739$	−8.35357	+	11.4977i	−0.307291	+	0.422950i	−0.934534	−	0.355874i	$-0.884183\pi$
$739$	−8.35357	+	11.4977i	−0.307291	+	0.422950i	0.627243	+	0.778824i	$0.284183\pi$
$740$		0			0
$741$	−1.31573	+	0.427505i	−0.0483344	+	0.0157048i
$742$		0			0
$743$	−19.8113	+	14.3937i	−0.726806	+	0.528055i	−0.888551	−	0.458777i	$-0.848288\pi$
$743$	−19.8113	+	14.3937i	−0.726806	+	0.528055i	0.161746	+	0.986832i	$0.448288\pi$
$744$		0			0
$745$	−32.6002	−	10.5924i	−1.19438	−	0.388077i
$746$		0			0
$747$		−	15.0860i		−	0.551966i
$748$		0			0
$749$			10.0045i			0.365558i
$750$		0			0
$751$	38.6132	+	12.5462i	1.40901	+	0.457817i	0.912095	−	0.409980i	$-0.134464\pi$
$751$	38.6132	+	12.5462i	1.40901	+	0.457817i	0.496920	+	0.867796i	$0.334464\pi$
$752$		0			0
$753$	4.24381	−	3.08331i	0.154653	−	0.112362i
$754$		0			0
$755$	−17.5407	+	5.69932i	−0.638372	+	0.207420i
$756$		0			0
$757$	−7.32712	+	10.0849i	−0.266309	+	0.366542i	−0.921139	−	0.389233i	$-0.872740\pi$
$757$	−7.32712	+	10.0849i	−0.266309	+	0.366542i	0.654831	+	0.755776i	$0.272740\pi$
$758$		0			0
$759$	4.75939	−	0.675810i	0.172755	−	0.0245304i
$760$		0			0
$761$	19.4146	−	26.7219i	0.703779	−	0.968668i	−0.296130	−	0.955148i	$-0.595696\pi$
$761$	19.4146	−	26.7219i	0.703779	−	0.968668i	0.999909	−	0.0135207i	$-0.00430390\pi$
$762$		0			0
$763$	4.04195	+	12.4399i	0.146329	+	0.450353i
$764$		0			0
$765$	5.39917	−	3.92273i	0.195207	−	0.141827i
$766$		0			0
$767$	−12.1698	+	37.4548i	−0.439427	+	1.35242i
$768$		0			0
$769$			45.9291i			1.65625i	0.560546	+	0.828123i	$0.310591\pi$
$769$			45.9291i			1.65625i	−0.560546	+	0.828123i	$0.689409\pi$
$770$		0			0
$771$	−4.69434			−0.169063
$772$		0			0
$773$	13.4151	+	4.35884i	0.482509	+	0.156777i	0.540164	−	0.841560i	$-0.318362\pi$
$773$	13.4151	+	4.35884i	0.482509	+	0.156777i	−0.0576547	+	0.998337i	$0.518362\pi$
$774$		0			0
$775$	1.52762	+	2.10259i	0.0548737	+	0.0755272i
$776$		0			0
$777$	−12.4369	+	4.04098i	−0.446170	+	0.144969i
$778$		0			0
$779$	1.17600	+	0.854411i	0.0421344	+	0.0306125i
$780$		0			0
$781$	−37.7596	−	20.0081i	−1.35115	−	0.715947i
$782$		0			0
$783$	6.41754	+	4.66261i	0.229344	+	0.166628i
$784$		0			0
$785$	−9.72688	−	29.9363i	−0.347167	−	1.06847i
$786$		0			0
$787$	18.5090	+	25.4755i	0.659776	+	0.908104i	0.999474	−	0.0324309i	$-0.0103249\pi$
$787$	18.5090	+	25.4755i	0.659776	+	0.908104i	−0.339698	+	0.940535i	$0.610325\pi$
$788$		0			0
$789$	7.12170	−	21.9184i	0.253539	−	0.780314i
$790$		0			0
$791$	2.55411			0.0908138
$792$		0			0
$793$	34.4118			1.22200
$794$		0			0
$795$	−2.36546	+	7.28014i	−0.0838943	+	0.258200i
$796$		0			0
$797$	19.3111	+	26.5794i	0.684033	+	0.941490i	0.999973	−	0.00728889i	$-0.00232015\pi$
$797$	19.3111	+	26.5794i	0.684033	+	0.941490i	−0.315941	+	0.948779i	$0.602320\pi$
$798$		0			0
$799$	−0.891783	−	2.74463i	−0.0315490	−	0.0970979i
$800$		0			0
$801$	−8.83531	−	6.41923i	−0.312180	−	0.226812i
$802$		0			0
$803$	−22.9124	+	22.1895i	−0.808561	+	0.783050i
$804$		0			0
$805$	2.89220	+	2.10131i	0.101937	+	0.0740614i
$806$		0			0
$807$	−9.16355	+	2.97742i	−0.322572	+	0.104810i
$808$		0			0
$809$	3.52470	+	4.85134i	0.123922	+	0.170564i	0.866470	−	0.499228i	$-0.166383\pi$
$809$	3.52470	+	4.85134i	0.123922	+	0.170564i	−0.742549	+	0.669792i	$0.766383\pi$
$810$		0			0
$811$	39.0150	+	12.6767i	1.37000	+	0.445140i	0.899369	−	0.437189i	$-0.144026\pi$
$811$	39.0150	+	12.6767i	1.37000	+	0.445140i	0.470632	+	0.882330i	$0.344026\pi$
$812$		0			0
$813$	23.4722			0.823205
$814$		0			0
$815$		−	10.5879i		−	0.370876i
$816$		0			0
$817$	0.467812	−	1.43978i	0.0163667	−	0.0503714i
$818$		0			0
$819$	−3.71482	+	2.69897i	−0.129806	+	0.0943098i
$820$		0			0
$821$	−7.86487	−	24.2056i	−0.274486	−	0.844781i	−0.989355	−	0.145523i	$-0.953514\pi$
$821$	−7.86487	−	24.2056i	−0.274486	−	0.844781i	0.714869	−	0.699258i	$-0.246486\pi$
$822$		0			0
$823$	8.33462	−	11.4716i	0.290526	−	0.399875i	−0.638659	−	0.769490i	$-0.720510\pi$
$823$	8.33462	−	11.4716i	0.290526	−	0.399875i	0.929185	+	0.369615i	$0.120510\pi$
$824$		0			0
$825$	−6.11376	−	1.06903i	−0.212854	−	0.0372190i
$826$		0			0
$827$	−16.3323	+	22.4795i	−0.567931	+	0.781690i	−0.992308	−	0.123796i	$-0.960493\pi$
$827$	−16.3323	+	22.4795i	−0.567931	+	0.781690i	0.424377	+	0.905486i	$0.360493\pi$
$828$		0			0
$829$	47.9834	−	15.5908i	1.66653	−	0.541490i	0.684308	−	0.729193i	$-0.260104\pi$
$829$	47.9834	−	15.5908i	1.66653	−	0.541490i	0.982226	+	0.187703i	$0.0601044\pi$
$830$		0			0
$831$	16.1312	−	11.7200i	0.559584	−	0.406561i
$832$		0			0
$833$	−18.1410	−	5.89437i	−0.628549	−	0.204228i
$834$		0			0
$835$			9.19584i			0.318235i
$836$		0			0
$837$		−	1.38882i		−	0.0480045i
$838$		0			0
$839$	44.3548	+	14.4117i	1.53130	+	0.497548i	0.948959	−	0.315399i	$-0.102138\pi$
$839$	44.3548	+	14.4117i	1.53130	+	0.497548i	0.582337	+	0.812947i	$0.302138\pi$
$840$		0			0
$841$	−27.4457	+	19.9405i	−0.946403	+	0.687602i
$842$		0			0
$843$	−6.04746	+	1.96494i	−0.208286	+	0.0676761i
$844$		0			0
$845$	−2.24245	+	3.08646i	−0.0771425	+	0.106178i
$846$		0			0
$847$	14.4288	+	5.20510i	0.495779	+	0.178849i
$848$		0			0
$849$	5.12972	−	7.06045i	0.176052	−	0.242314i
$850$		0			0
$851$	−4.20023	−	12.9270i	−0.143982	−	0.443132i
$852$		0			0
$853$	−41.5877	+	30.2152i	−1.42394	+	1.03455i	−0.432829	+	0.901476i	$0.642485\pi$
$853$	−41.5877	+	30.2152i	−1.42394	+	1.03455i	−0.991106	+	0.133073i	$0.957515\pi$
$854$		0			0
$855$	−0.229638	+	0.706752i	−0.00785345	+	0.0241704i
$856$		0			0
$857$			17.4541i			0.596221i	0.954531	+	0.298111i	$0.0963565\pi$
$857$			17.4541i			0.596221i	−0.954531	+	0.298111i	$0.903644\pi$
$858$		0			0
$859$	35.3164			1.20498			0.602489	−	0.798127i	$-0.294176\pi$
$859$	35.3164			1.20498			0.602489	+	0.798127i	$0.294176\pi$
$860$		0			0
$861$	4.58855	+	1.49091i	0.156377	+	0.0508101i
$862$		0			0
$863$	3.84304	+	5.28949i	0.130819	+	0.180056i	0.869401	−	0.494106i	$-0.164505\pi$
$863$	3.84304	+	5.28949i	0.130819	+	0.180056i	−0.738583	+	0.674163i	$0.764505\pi$
$864$		0			0
$865$	−23.6202	+	7.67468i	−0.803112	+	0.260947i
$866$		0			0
$867$	−2.23632	−	1.62478i	−0.0759495	−	0.0551805i
$868$		0			0
$869$	18.9704	+	3.31711i	0.643526	+	0.112525i
$870$		0			0
$871$	26.5071	+	19.2586i	0.898160	+	0.652552i
$872$		0			0
$873$	4.28351	+	13.1833i	0.144975	+	0.446186i
$874$		0			0
$875$	−9.96190	−	13.7114i	−0.336774	−	0.463529i
$876$		0			0
$877$	9.06904	−	27.9116i	0.306240	−	0.942509i	−0.672972	−	0.739668i	$-0.734982\pi$
$877$	9.06904	−	27.9116i	0.306240	−	0.942509i	0.979212	−	0.202841i	$-0.0650175\pi$
$878$		0			0
$879$	−20.6288			−0.695790
$880$		0			0
$881$	1.12915			0.0380420			0.0190210	−	0.999819i	$-0.493945\pi$
$881$	1.12915			0.0380420			0.0190210	+	0.999819i	$0.493945\pi$
$882$		0			0
$883$	−4.24530	+	13.0657i	−0.142866	+	0.439695i	−0.996730	−	0.0807999i	$-0.974253\pi$
$883$	−4.24530	+	13.0657i	−0.142866	+	0.439695i	0.853865	+	0.520495i	$0.174253\pi$
$884$		0			0
$885$	12.4343	+	17.1144i	0.417975	+	0.575294i
$886$		0			0
$887$	−1.98190	−	6.09967i	−0.0665458	−	0.204807i	0.912254	−	0.409624i	$-0.134340\pi$
$887$	−1.98190	−	6.09967i	−0.0665458	−	0.204807i	−0.978800	+	0.204817i	$0.934340\pi$
$888$		0			0
$889$	−8.05988	−	5.85584i	−0.270320	−	0.196399i
$890$		0			0
$891$	2.30732	+	2.38249i	0.0772982	+	0.0798165i
$892$		0			0
$893$	0.259972	+	0.188880i	0.00869962	+	0.00632064i
$894$		0			0
$895$	38.7101	−	12.5777i	1.29394	−	0.420426i
$896$		0			0
$897$	−2.80534	−	3.86122i	−0.0936675	−	0.128922i
$898$		0			0
$899$	10.4776	+	3.40438i	0.349447	+	0.113542i
$900$		0			0
$901$	−16.3284			−0.543979
$902$		0			0
$903$		−	5.02470i		−	0.167211i
$904$		0			0
$905$	−10.6661	+	32.8270i	−0.354554	+	1.09121i
$906$		0			0
$907$	−9.91808	+	7.20591i	−0.329325	+	0.239268i	−0.740144	−	0.672448i	$-0.765243\pi$
$907$	−9.91808	+	7.20591i	−0.329325	+	0.239268i	0.410819	+	0.911717i	$0.365243\pi$
$908$		0			0
$909$	−2.48051	−	7.63423i	−0.0822733	−	0.253211i
$910$		0			0
$911$	21.4231	−	29.4864i	0.709779	−	0.976927i	−0.290023	−	0.957020i	$-0.593663\pi$
$911$	21.4231	−	29.4864i	0.709779	−	0.976927i	0.999802	−	0.0199074i	$-0.00633714\pi$
$912$		0			0
$913$	44.2113	+	23.4267i	1.46318	+	0.775312i
$914$		0			0
$915$	10.8650	−	14.9544i	0.359185	−	0.494376i
$916$		0			0
$917$	−11.6032	+	3.77010i	−0.383170	+	0.124500i
$918$		0			0
$919$	10.4315	−	7.57891i	0.344103	−	0.250005i	−0.402288	−	0.915513i	$-0.631785\pi$
$919$	10.4315	−	7.57891i	0.344103	−	0.250005i	0.746391	+	0.665508i	$0.231785\pi$
$920$		0			0
$921$	23.4506	+	7.61956i	0.772724	+	0.251073i
$922$		0			0
$923$			42.4273i			1.39651i
$924$		0			0
$925$			17.5491i			0.577010i
$926$		0			0
$927$	−11.7338	−	3.81254i	−0.385389	−	0.125220i
$928$		0			0
$929$	11.5280	−	8.37561i	0.378223	−	0.274795i	−0.382390	−	0.924001i	$-0.624899\pi$
$929$	11.5280	−	8.37561i	0.378223	−	0.274795i	0.760612	+	0.649206i	$0.224899\pi$
$930$		0			0
$931$	2.02001	−	0.656340i	0.0662031	−	0.0215107i
$932$		0			0
$933$	15.0494	−	20.7137i	0.492695	−	0.678137i
$934$		0			0
$935$	3.11175	+	21.9145i	0.101765	+	0.716680i
$936$		0			0
$937$	−29.3763	+	40.4330i	−0.959681	+	1.32089i	−0.0125913	+	0.999921i	$0.504008\pi$
$937$	−29.3763	+	40.4330i	−0.959681	+	1.32089i	−0.947090	+	0.320967i	$0.895992\pi$
$938$		0			0
$939$	−1.20599	−	3.71165i	−0.0393559	−	0.121125i
$940$		0			0
$941$	−3.47674	+	2.52600i	−0.113338	+	0.0823452i	−0.643011	−	0.765857i	$-0.722315\pi$
$941$	−3.47674	+	2.52600i	−0.113338	+	0.0823452i	0.529672	+	0.848202i	$0.322315\pi$
$942$		0			0
$943$	−1.54967	+	4.76938i	−0.0504641	+	0.155312i
$944$		0			0
$945$			2.46651i			0.0802354i
$946$		0			0
$947$	−0.231238			−0.00751424			−0.00375712	−	0.999993i	$-0.501196\pi$
$947$	−0.231238			−0.00751424			−0.00375712	+	0.999993i	$0.501196\pi$
$948$		0			0
$949$	30.1178	+	9.78586i	0.977664	+	0.317662i
$950$		0			0
$951$	3.74958	+	5.16085i	0.121588	+	0.167352i
$952$		0			0
$953$	50.8341	−	16.5170i	1.64668	−	0.535039i	0.668663	−	0.743566i	$-0.266867\pi$
$953$	50.8341	−	16.5170i	1.64668	−	0.535039i	0.978017	+	0.208527i	$0.0668670\pi$
$954$		0			0
$955$	−36.6349	−	26.6168i	−1.18548	−	0.861301i
$956$		0			0
$957$	−23.6301	+	11.5669i	−0.763851	+	0.373904i
$958$		0			0
$959$	9.54701	+	6.93631i	0.308289	+	0.223985i
$960$		0			0
$961$	8.98349	+	27.6483i	0.289790	+	0.891882i
$962$		0			0
$963$	−4.21709	−	5.80433i	−0.135894	−	0.187042i
$964$		0			0
$965$	12.0812	−	37.1821i	0.388908	−	1.19694i
$966$		0			0
$967$	−1.08508			−0.0348938			−0.0174469	−	0.999848i	$-0.505554\pi$
$967$	−1.08508			−0.0348938			−0.0174469	+	0.999848i	$0.505554\pi$
$968$		0			0
$969$	−1.58516			−0.0509225
$970$		0			0
$971$	10.1034	−	31.0950i	0.324233	−	0.997887i	−0.647552	−	0.762021i	$-0.724207\pi$
$971$	10.1034	−	31.0950i	0.324233	−	0.997887i	0.971786	−	0.235866i	$-0.0757927\pi$
$972$		0			0
$973$	4.69992	+	6.46889i	0.150673	+	0.207383i
$974$		0			0
$975$	1.90420	+	5.86052i	0.0609831	+	0.187687i
$976$		0			0
$977$	−40.9534	−	29.7544i	−1.31021	−	0.951926i	−0.999999	−	0.00125964i	$-0.999599\pi$
$977$	−40.9534	−	29.7544i	−1.31021	−	0.951926i	−0.310215	−	0.950667i	$-0.600401\pi$
$978$		0			0
$979$	32.5325	−	15.9246i	1.03974	−	0.508954i
$980$		0			0
$981$	−7.58864	−	5.51347i	−0.242287	−	0.176032i
$982$		0			0
$983$	−23.1688	+	7.52801i	−0.738971	+	0.240106i	−0.654229	−	0.756297i	$-0.727007\pi$
$983$	−23.1688	+	7.52801i	−0.738971	+	0.240106i	−0.0847421	+	0.996403i	$0.527007\pi$
$984$		0			0
$985$	−18.9457	−	26.0766i	−0.603662	−	0.830869i
$986$		0			0
$987$	1.01437	+	0.329588i	0.0322877	+	0.0104909i
$988$		0			0
$989$	5.22272			0.166073
$990$		0			0
$991$		−	27.0358i		−	0.858821i	−0.903110	−	0.429410i	$-0.858721\pi$
$991$		−	27.0358i		−	0.858821i	0.903110	−	0.429410i	$-0.141279\pi$
$992$		0			0
$993$	1.34352	−	4.13494i	0.0426354	−	0.131218i
$994$		0			0
$995$	18.9812	−	13.7906i	0.601743	−	0.437192i
$996$		0			0
$997$	4.82347	+	14.8451i	0.152761	+	0.470149i	0.997927	−	0.0643542i	$-0.0204987\pi$
$997$	4.82347	+	14.8451i	0.152761	+	0.470149i	−0.845166	+	0.534503i	$0.820499\pi$
$998$		0			0
$999$	5.51214	−	7.58682i	0.174397	−	0.240036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1056.2.bp.a.271.4		48
4.3	odd	2		264.2.z.b.139.1	yes	48
8.3	odd	2	inner	1056.2.bp.a.271.9		48
8.5	even	2		264.2.z.b.139.7	yes	48
11.8	odd	10	inner	1056.2.bp.a.943.9		48
12.11	even	2		792.2.bp.d.667.12		48
24.5	odd	2		792.2.bp.d.667.6		48
44.19	even	10		264.2.z.b.19.7	yes	48
88.19	even	10	inner	1056.2.bp.a.943.4		48
88.85	odd	10		264.2.z.b.19.1	✓	48
132.107	odd	10		792.2.bp.d.19.6		48
264.173	even	10		792.2.bp.d.19.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.z.b.19.1	✓	48	88.85	odd	10
264.2.z.b.19.7	yes	48	44.19	even	10
264.2.z.b.139.1	yes	48	4.3	odd	2
264.2.z.b.139.7	yes	48	8.5	even	2
792.2.bp.d.19.6		48	132.107	odd	10
792.2.bp.d.19.12		48	264.173	even	10
792.2.bp.d.667.6		48	24.5	odd	2
792.2.bp.d.667.12		48	12.11	even	2
1056.2.bp.a.271.4		48	1.1	even	1	trivial
1056.2.bp.a.271.9		48	8.3	odd	2	inner
1056.2.bp.a.943.4		48	88.19	even	10	inner
1056.2.bp.a.943.9		48	11.8	odd	10	inner

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:	\( N \)	\(=\)	\( 1056 = 2^{5} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1056.bp (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{3} +(-1.03968 - 1.43099i) q^{5} +(0.430909 + 1.32620i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(2.97889 - 1.45816i) q^{11} +(-2.66400 - 1.93551i) q^{13} +(-1.68223 + 0.546590i) q^{15} +(-2.21773 - 3.05245i) q^{17} +(0.399566 + 0.129827i) q^{19} +1.39445 q^{21} +1.44940i q^{23} +(0.578275 - 1.77975i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(-2.45128 - 7.54427i) q^{29} +(-0.816325 + 1.12358i) q^{31} +(-0.466268 - 3.28369i) q^{33} +(1.44978 - 1.99544i) q^{35} +(-8.91884 + 2.89791i) q^{37} +(-2.66400 + 1.93551i) q^{39} +(3.29058 + 1.06918i) q^{41} -3.60336i q^{43} +1.76880i q^{45} +(0.727433 + 0.236357i) q^{47} +(4.08999 - 2.97155i) q^{49} +(-3.58836 + 1.16593i) q^{51} +(2.54374 - 3.50116i) q^{53} +(-5.18369 - 2.74674i) q^{55} +(0.246945 - 0.339891i) q^{57} +(-3.69578 - 11.3745i) q^{59} +(-8.45451 + 6.14256i) q^{61} +(0.430909 - 1.32620i) q^{63} +5.82447i q^{65} -9.95011 q^{67} +(1.37846 + 0.447890i) q^{69} +(-7.57332 - 10.4238i) q^{71} +(-9.14630 + 2.97181i) q^{73} +(-1.51394 - 1.09994i) q^{75} +(3.21744 + 3.32227i) q^{77} +(4.69761 + 3.41302i) q^{79} +(0.309017 + 0.951057i) q^{81} +(8.86730 + 12.2048i) q^{83} +(-2.06230 + 6.34711i) q^{85} -7.93251 q^{87} +10.9210 q^{89} +(1.41893 - 4.36703i) q^{91} +(0.816325 + 1.12358i) q^{93} +(-0.229638 - 0.706752i) q^{95} +(-11.2144 - 8.14771i) q^{97} +(-3.26706 - 0.571268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{3} - 12 q^{9} - 4 q^{11} - 4 q^{25} - 12 q^{27} - 4 q^{33} - 60 q^{41} - 12 q^{49} + 8 q^{59} - 8 q^{67} + 36 q^{75} - 12 q^{81} + 100 q^{83} + 96 q^{89} + 20 q^{91} - 40 q^{97} + 16 q^{99}+O(q^{100}) \) 48 * q - 12 * q^3 - 12 * q^9 - 4 * q^11 - 4 * q^25 - 12 * q^27 - 4 * q^33 - 60 * q^41 - 12 * q^49 + 8 * q^59 - 8 * q^67 + 36 * q^75 - 12 * q^81 + 100 * q^83 + 96 * q^89 + 20 * q^91 - 40 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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