LMFDB - Embedded newform 896.2.z.a.31.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(31,896)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("896.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,-6] 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.12
Character	$\chi$	$=$	896.31
Dual form			896.2.z.a.607.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.524583 + 1.95777i) q^{3} +(-2.48890 - 0.666898i) q^{5} +(2.38027 - 1.15512i) q^{7} +(-0.959602 + 0.554026i) q^{9} +(-1.35371 - 5.05213i) q^{11} +(-0.848888 - 0.848888i) q^{13} -5.22253i q^{15} +(-2.23951 - 1.29298i) q^{17} +(-4.72466 - 1.26597i) q^{19} +(3.51010 + 4.05408i) q^{21} +(-3.15967 - 5.47271i) q^{23} +(1.41973 + 0.819681i) q^{25} +(2.71152 + 2.71152i) q^{27} +(3.92758 - 3.92758i) q^{29} +(-0.585390 + 1.01392i) q^{31} +(9.18077 - 5.30052i) q^{33} +(-6.69460 + 1.28757i) q^{35} +(-1.61869 + 6.04104i) q^{37} +(1.21662 - 2.10724i) q^{39} +4.77063 q^{41} +(4.80121 - 4.80121i) q^{43} +(2.75783 - 0.738958i) q^{45} +(-3.39263 - 5.87622i) q^{47} +(4.33141 - 5.49899i) q^{49} +(1.35655 - 5.06272i) q^{51} +(7.35887 - 1.97180i) q^{53} +13.4770i q^{55} -9.91391i q^{57} +(-0.809319 + 0.216856i) q^{59} +(-1.17253 + 4.37595i) q^{61} +(-1.64415 + 2.42719i) q^{63} +(1.54667 + 2.67892i) q^{65} +(0.376913 - 0.100994i) q^{67} +(9.05679 - 9.05679i) q^{69} -3.83330 q^{71} +(-4.84591 + 8.39335i) q^{73} +(-0.859981 + 3.20949i) q^{75} +(-9.05801 - 10.4618i) q^{77} +(-0.954167 + 0.550889i) q^{79} +(-5.54819 + 9.60974i) q^{81} +(9.73434 - 9.73434i) q^{83} +(4.71162 + 4.71162i) q^{85} +(9.74964 + 5.62896i) q^{87} +(7.91117 + 13.7025i) q^{89} +(-3.00115 - 1.04002i) q^{91} +(-2.29212 - 0.614171i) q^{93} +(10.9149 + 6.30174i) q^{95} +1.12228i q^{97} +(4.09804 + 4.09804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	0.524583	+	1.95777i	0.302868	+	1.13032i	0.934765	+	0.355267i	$0.115610\pi$
$3$	0.524583	+	1.95777i	0.302868	+	1.13032i	−0.631897	+	0.775053i	$0.717723\pi$
$4$		0			0
$5$	−2.48890	−	0.666898i	−1.11307	−	0.298246i	−0.344993	−	0.938605i	$-0.612119\pi$
$5$	−2.48890	−	0.666898i	−1.11307	−	0.298246i	−0.768075	+	0.640359i	$0.778785\pi$
$6$		0			0
$7$	2.38027	−	1.15512i	0.899659	−	0.436593i
$7$	2.38027	−	1.15512i	0.899659	−	0.436593i
$8$		0			0
$9$	−0.959602	+	0.554026i	−0.319867	+	0.184675i
$10$		0			0
$11$	−1.35371	−	5.05213i	−0.408160	−	1.52327i	−0.798152	−	0.602456i	$-0.794189\pi$
$11$	−1.35371	−	5.05213i	−0.408160	−	1.52327i	0.389992	−	0.920818i	$-0.372478\pi$
$12$		0			0
$13$	−0.848888	−	0.848888i	−0.235439	−	0.235439i	0.579519	−	0.814958i	$-0.303240\pi$
$13$	−0.848888	−	0.848888i	−0.235439	−	0.235439i	−0.814958	+	0.579519i	$0.803240\pi$
$14$		0			0
$15$		−	5.22253i		−	1.34845i
$16$		0			0
$17$	−2.23951	−	1.29298i	−0.543161	−	0.313594i	0.203198	−	0.979138i	$-0.434866\pi$
$17$	−2.23951	−	1.29298i	−0.543161	−	0.313594i	−0.746359	+	0.665544i	$0.768200\pi$
$18$		0			0
$19$	−4.72466	−	1.26597i	−1.08391	−	0.290433i	−0.327714	−	0.944777i	$-0.606278\pi$
$19$	−4.72466	−	1.26597i	−1.08391	−	0.290433i	−0.756197	+	0.654343i	$0.772945\pi$
$20$		0			0
$21$	3.51010	+	4.05408i	0.765968	+	0.884672i
$22$		0			0
$23$	−3.15967	−	5.47271i	−0.658836	−	1.14114i	−0.980917	−	0.194426i	$-0.937716\pi$
$23$	−3.15967	−	5.47271i	−0.658836	−	1.14114i	0.322081	−	0.946712i	$-0.395618\pi$
$24$		0			0
$25$	1.41973	+	0.819681i	0.283946	+	0.163936i
$26$		0			0
$27$	2.71152	+	2.71152i	0.521831	+	0.521831i
$28$		0			0
$29$	3.92758	−	3.92758i	0.729333	−	0.729333i	−0.241154	−	0.970487i	$-0.577526\pi$
$29$	3.92758	−	3.92758i	0.729333	−	0.729333i	0.970487	+	0.241154i	$0.0775258\pi$
$30$		0			0
$31$	−0.585390	+	1.01392i	−0.105139	+	0.182106i	−0.913795	−	0.406176i	$-0.866862\pi$
$31$	−0.585390	+	1.01392i	−0.105139	+	0.182106i	0.808656	+	0.588282i	$0.200195\pi$
$32$		0			0
$33$	9.18077	−	5.30052i	1.59817	−	0.922703i
$34$		0			0
$35$	−6.69460	+	1.28757i	−1.13159	+	0.217638i
$36$		0			0
$37$	−1.61869	+	6.04104i	−0.266111	+	0.993141i	0.695455	+	0.718569i	$0.255203\pi$
$37$	−1.61869	+	6.04104i	−0.266111	+	0.993141i	−0.961567	+	0.274571i	$0.911464\pi$
$38$		0			0
$39$	1.21662	−	2.10724i	0.194814	−	0.337428i
$40$		0			0
$41$	4.77063			0.745047			0.372523	−	0.928023i	$-0.378493\pi$
$41$	4.77063			0.745047			0.372523	+	0.928023i	$0.378493\pi$
$42$		0			0
$43$	4.80121	−	4.80121i	0.732177	−	0.732177i	−0.238873	−	0.971051i	$-0.576778\pi$
$43$	4.80121	−	4.80121i	0.732177	−	0.732177i	0.971051	+	0.238873i	$0.0767781\pi$
$44$		0			0
$45$	2.75783	−	0.738958i	0.411113	−	0.110157i
$46$		0			0
$47$	−3.39263	−	5.87622i	−0.494867	−	0.857134i	0.505116	−	0.863052i	$-0.331450\pi$
$47$	−3.39263	−	5.87622i	−0.494867	−	0.857134i	−0.999982	+	0.00591740i	$0.998116\pi$
$48$		0			0
$49$	4.33141	−	5.49899i	0.618773	−	0.785570i
$50$		0			0
$51$	1.35655	−	5.06272i	0.189955	−	0.708923i
$52$		0			0
$53$	7.35887	−	1.97180i	1.01082	−	0.270848i	0.284847	−	0.958573i	$-0.408057\pi$
$53$	7.35887	−	1.97180i	1.01082	−	0.270848i	0.725971	+	0.687725i	$0.241390\pi$
$54$		0			0
$55$			13.4770i			1.81724i
$56$		0			0
$57$		−	9.91391i		−	1.31313i
$58$		0			0
$59$	−0.809319	+	0.216856i	−0.105364	+	0.0282323i	−0.311116	−	0.950372i	$-0.600703\pi$
$59$	−0.809319	+	0.216856i	−0.105364	+	0.0282323i	0.205752	+	0.978604i	$0.434036\pi$
$60$		0			0
$61$	−1.17253	+	4.37595i	−0.150127	+	0.560283i	0.849346	+	0.527836i	$0.176997\pi$
$61$	−1.17253	+	4.37595i	−0.150127	+	0.560283i	−0.999473	+	0.0324466i	$0.989670\pi$
$62$		0			0
$63$	−1.64415	+	2.42719i	−0.207143	+	0.305797i
$64$		0			0
$65$	1.54667	+	2.67892i	0.191841	+	0.332279i
$66$		0			0
$67$	0.376913	−	0.100994i	0.0460473	−	0.0123383i	−0.235722	−	0.971821i	$-0.575745\pi$
$67$	0.376913	−	0.100994i	0.0460473	−	0.0123383i	0.281769	+	0.959482i	$0.409079\pi$
$68$		0			0
$69$	9.05679	−	9.05679i	1.09031	−	1.09031i
$70$		0			0
$71$	−3.83330			−0.454929			−0.227465	−	0.973786i	$-0.573044\pi$
$71$	−3.83330			−0.454929			−0.227465	+	0.973786i	$0.573044\pi$
$72$		0			0
$73$	−4.84591	+	8.39335i	−0.567170	+	0.982368i	0.429674	+	0.902984i	$0.358629\pi$
$73$	−4.84591	+	8.39335i	−0.567170	+	0.982368i	−0.996844	+	0.0793836i	$0.974705\pi$
$74$		0			0
$75$	−0.859981	+	3.20949i	−0.0993021	+	0.370600i
$76$		0			0
$77$	−9.05801	−	10.4618i	−1.03226	−	1.19223i
$78$		0			0
$79$	−0.954167	+	0.550889i	−0.107352	+	0.0619798i	−0.552715	−	0.833370i	$-0.686408\pi$
$79$	−0.954167	+	0.550889i	−0.107352	+	0.0619798i	0.445363	+	0.895350i	$0.353075\pi$
$80$		0			0
$81$	−5.54819	+	9.60974i	−0.616465	+	1.06775i
$82$		0			0
$83$	9.73434	−	9.73434i	1.06848	−	1.06848i	0.0710068	−	0.997476i	$-0.477379\pi$
$83$	9.73434	−	9.73434i	1.06848	−	1.06848i	0.997476	−	0.0710068i	$-0.0226212\pi$
$84$		0			0
$85$	4.71162	+	4.71162i	0.511047	+	0.511047i
$86$		0			0
$87$	9.74964	+	5.62896i	1.04527	+	0.603488i
$88$		0			0
$89$	7.91117	+	13.7025i	0.838582	+	1.45247i	0.891080	+	0.453846i	$0.149948\pi$
$89$	7.91117	+	13.7025i	0.838582	+	1.45247i	−0.0524979	+	0.998621i	$0.516718\pi$
$90$		0			0
$91$	−3.00115	−	1.04002i	−0.314606	−	0.109024i
$92$		0			0
$93$	−2.29212	−	0.614171i	−0.237682	−	0.0636866i
$94$		0			0
$95$	10.9149	+	6.30174i	1.11985	+	0.646544i
$96$		0			0
$97$			1.12228i			0.113950i	0.998376	+	0.0569750i	$0.0181455\pi$
$97$			1.12228i			0.113950i	−0.998376	+	0.0569750i	$0.981854\pi$
$98$		0			0
$99$	4.09804	+	4.09804i	0.411868	+	0.411868i
$100$		0			0
$101$	−3.75591	−	14.0172i	−0.373727	−	1.39477i	−0.855196	−	0.518304i	$-0.826564\pi$
$101$	−3.75591	−	14.0172i	−0.373727	−	1.39477i	0.481470	−	0.876463i	$-0.340103\pi$
$102$		0			0
$103$	−0.741916	+	0.428345i	−0.0731031	+	0.0422061i	−0.536106	−	0.844151i	$-0.680105\pi$
$103$	−0.741916	+	0.428345i	−0.0731031	+	0.0422061i	0.463003	+	0.886357i	$0.346772\pi$
$104$		0			0
$105$	−6.03263	−	12.4311i	−0.588725	−	1.21315i
$106$		0			0
$107$	−5.09589	−	1.36544i	−0.492639	−	0.132002i	0.00394288	−	0.999992i	$-0.498745\pi$
$107$	−5.09589	−	1.36544i	−0.492639	−	0.132002i	−0.496581	+	0.867990i	$0.665412\pi$
$108$		0			0
$109$	3.58485	+	13.3788i	0.343367	+	1.28146i	0.894509	+	0.447050i	$0.147525\pi$
$109$	3.58485	+	13.3788i	0.343367	+	1.28146i	−0.551142	+	0.834411i	$0.685808\pi$
$110$		0			0
$111$	−12.6761			−1.20316
$112$		0			0
$113$	−8.67774			−0.816333			−0.408167	−	0.912907i	$-0.633832\pi$
$113$	−8.67774			−0.816333			−0.408167	+	0.912907i	$0.633832\pi$
$114$		0			0
$115$	4.21435	+	15.7282i	0.392990	+	1.46666i
$116$		0			0
$117$	1.28490	+	0.344288i	0.118789	+	0.0318294i
$118$		0			0
$119$	−6.82419	−	0.490756i	−0.625572	−	0.0449875i
$120$		0			0
$121$	−14.1652	+	8.17828i	−1.28774	+	0.743480i
$122$		0			0
$123$	2.50259	+	9.33979i	0.225651	+	0.842141i
$124$		0			0
$125$	6.12308	+	6.12308i	0.547665	+	0.547665i
$126$		0			0
$127$		−	14.0559i		−	1.24726i	−0.781721	−	0.623628i	$-0.785658\pi$
$127$		−	14.0559i		−	1.24726i	0.781721	−	0.623628i	$-0.214342\pi$
$128$		0			0
$129$	11.9183	+	6.88103i	1.04935	+	0.605841i
$130$		0			0
$131$	−14.5921	−	3.90994i	−1.27492	−	0.341613i	−0.443004	−	0.896520i	$-0.646087\pi$
$131$	−14.5921	−	3.90994i	−1.27492	−	0.341613i	−0.831913	+	0.554907i	$0.812754\pi$
$132$		0			0
$133$	−12.7083	+	2.44418i	−1.10195	+	0.211937i
$134$		0			0
$135$	−4.94038	−	8.55699i	−0.425200	−	0.736468i
$136$		0			0
$137$	−4.37058	−	2.52336i	−0.373404	−	0.215585i	0.301541	−	0.953453i	$-0.402499\pi$
$137$	−4.37058	−	2.52336i	−0.373404	−	0.215585i	−0.674945	+	0.737868i	$0.735832\pi$
$138$		0			0
$139$	−3.77959	−	3.77959i	−0.320581	−	0.320581i	0.528409	−	0.848990i	$-0.322789\pi$
$139$	−3.77959	−	3.77959i	−0.320581	−	0.320581i	−0.848990	+	0.528409i	$0.822789\pi$
$140$		0			0
$141$	9.72456	−	9.72456i	0.818956	−	0.818956i
$142$		0			0
$143$	−3.13954	+	5.43784i	−0.262541	+	0.454735i
$144$		0			0
$145$	−12.3946	+	7.15605i	−1.02932	+	0.594277i
$146$		0			0
$147$	13.0379	+	5.59523i	1.07535	+	0.461487i
$148$		0			0
$149$	−0.0705758	+	0.263393i	−0.00578180	+	0.0215780i	−0.968756	−	0.248014i	$-0.920222\pi$
$149$	−0.0705758	+	0.263393i	−0.00578180	+	0.0215780i	0.962975	+	0.269592i	$0.0868888\pi$
$150$		0			0
$151$	4.58028	−	7.93328i	0.372738	−	0.645601i	−0.617248	−	0.786769i	$-0.711752\pi$
$151$	4.58028	−	7.93328i	0.372738	−	0.645601i	0.989986	+	0.141168i	$0.0450857\pi$
$152$		0			0
$153$	2.86538			0.231652
$154$		0			0
$155$	2.13316	−	2.13316i	0.171340	−	0.171340i
$156$		0			0
$157$	−14.3922	+	3.85638i	−1.14862	+	0.307772i	−0.782413	−	0.622760i	$-0.786011\pi$
$157$	−14.3922	+	3.85638i	−1.14862	+	0.307772i	−0.366209	+	0.930533i	$0.619345\pi$
$158$		0			0
$159$	7.72068	+	13.3726i	0.612290	+	1.06052i
$160$		0			0
$161$	−13.8425	−	9.37676i	−1.09094	−	0.738992i
$162$		0			0
$163$	4.99953	−	18.6585i	0.391593	−	1.46145i	−0.435912	−	0.899989i	$-0.643574\pi$
$163$	4.99953	−	18.6585i	0.391593	−	1.46145i	0.827506	−	0.561457i	$-0.189759\pi$
$164$		0			0
$165$	−26.3849	+	7.06982i	−2.05406	+	0.550384i
$166$		0			0
$167$		−	3.48341i		−	0.269554i	−0.990876	−	0.134777i	$-0.956968\pi$
$167$		−	3.48341i		−	0.269554i	0.990876	−	0.134777i	$-0.0430318\pi$
$168$		0			0
$169$		−	11.5588i		−	0.889137i
$170$		0			0
$171$	5.23517	−	1.40276i	0.400344	−	0.107272i
$172$		0			0
$173$	−0.0189557	+	0.0707438i	−0.00144118	+	0.00537855i	−0.966643	−	0.256129i	$-0.917553\pi$
$173$	−0.0189557	+	0.0707438i	−0.00144118	+	0.00537855i	0.965201	+	0.261507i	$0.0842196\pi$
$174$		0			0
$175$	4.32617	+	0.311113i	0.327028	+	0.0235179i
$176$		0			0
$177$	−0.849110	−	1.47070i	−0.0638230	−	0.110545i
$178$		0			0
$179$	−3.00622	+	0.805515i	−0.224696	+	0.0602070i	−0.369410	−	0.929266i	$-0.620440\pi$
$179$	−3.00622	+	0.805515i	−0.224696	+	0.0602070i	0.144715	+	0.989473i	$0.453774\pi$
$180$		0			0
$181$	−3.34414	+	3.34414i	−0.248568	+	0.248568i	−0.820383	−	0.571815i	$-0.806240\pi$
$181$	−3.34414	+	3.34414i	−0.248568	+	0.248568i	0.571815	+	0.820383i	$0.306240\pi$
$182$		0			0
$183$	−9.18219			−0.678767
$184$		0			0
$185$	8.05751	−	13.9560i	0.592400	−	1.02607i
$186$		0			0
$187$	−3.50065	+	13.0646i	−0.255993	+	0.955379i
$188$		0			0
$189$	9.58627	+	3.32203i	0.697298	+	0.241642i
$190$		0			0
$191$	−0.271101	+	0.156520i	−0.0196162	+	0.0113254i	−0.509776	−	0.860307i	$-0.670272\pi$
$191$	−0.271101	+	0.156520i	−0.0196162	+	0.0113254i	0.490160	+	0.871633i	$0.336938\pi$
$192$		0			0
$193$	5.17806	−	8.96866i	0.372725	−	0.645578i	−0.617259	−	0.786760i	$-0.711757\pi$
$193$	5.17806	−	8.96866i	0.372725	−	0.645578i	0.989984	+	0.141182i	$0.0450902\pi$
$194$		0			0
$195$	−4.43334	+	4.43334i	−0.317478	+	0.317478i
$196$		0			0
$197$	−0.112804	−	0.112804i	−0.00803695	−	0.00803695i	0.703077	−	0.711114i	$-0.251809\pi$
$197$	−0.112804	−	0.112804i	−0.00803695	−	0.00803695i	−0.711114	+	0.703077i	$0.751809\pi$
$198$		0			0
$199$	18.4737	+	10.6658i	1.30957	+	0.756078i	0.982023	−	0.188759i	$-0.0604464\pi$
$199$	18.4737	+	10.6658i	1.30957	+	0.756078i	0.327542	+	0.944837i	$0.393780\pi$
$200$		0			0
$201$	0.395444	+	0.684930i	0.0278925	+	0.0483112i
$202$		0			0
$203$	4.81190	−	13.8855i	0.337730	−	0.974573i
$204$		0			0
$205$	−11.8736	−	3.18152i	−0.829288	−	0.222207i
$206$		0			0
$207$	6.06405	+	3.50108i	0.421480	+	0.243342i
$208$		0			0
$209$			25.5834i			1.76964i
$210$		0			0
$211$	7.71946	+	7.71946i	0.531430	+	0.531430i	0.920998	−	0.389568i	$-0.127376\pi$
$211$	7.71946	+	7.71946i	0.531430	+	0.531430i	−0.389568	+	0.920998i	$0.627376\pi$
$212$		0			0
$213$	−2.01088	−	7.50472i	−0.137784	−	0.514215i
$214$		0			0
$215$	−15.1516	+	8.74780i	−1.03333	+	0.596595i
$216$		0			0
$217$	−0.222187	+	3.08961i	−0.0150830	+	0.209737i
$218$		0			0
$219$	−18.9743	−	5.08416i	−1.28217	−	0.343556i
$220$		0			0
$221$	0.803496	+	2.99869i	0.0540490	+	0.201714i
$222$		0			0
$223$	9.74121			0.652319			0.326160	−	0.945315i	$-0.394245\pi$
$223$	9.74121			0.652319			0.326160	+	0.945315i	$0.394245\pi$
$224$		0			0
$225$	−1.81650			−0.121100
$226$		0			0
$227$	0.269850	+	1.00710i	0.0179106	+	0.0668433i	0.974303	−	0.225242i	$-0.0723174\pi$
$227$	0.269850	+	1.00710i	0.0179106	+	0.0668433i	−0.956392	+	0.292086i	$0.905651\pi$
$228$		0			0
$229$	5.19372	+	1.39165i	0.343210	+	0.0919630i	0.426307	−	0.904579i	$-0.359814\pi$
$229$	5.19372	+	1.39165i	0.343210	+	0.0919630i	−0.0830966	+	0.996541i	$0.526481\pi$
$230$		0			0
$231$	15.7300	−	23.2216i	1.03496	−	1.52787i
$232$		0			0
$233$	11.0720	−	6.39244i	0.725352	−	0.418782i	−0.0913671	−	0.995817i	$-0.529124\pi$
$233$	11.0720	−	6.39244i	0.725352	−	0.418782i	0.816720	+	0.577035i	$0.195790\pi$
$234$		0			0
$235$	4.52508	+	16.8878i	0.295184	+	1.10164i
$236$		0			0
$237$	−1.57905	−	1.57905i	−0.102571	−	0.102571i
$238$		0			0
$239$			26.2285i			1.69658i	0.529530	+	0.848291i	$0.322368\pi$
$239$			26.2285i			1.69658i	−0.529530	+	0.848291i	$0.677632\pi$
$240$		0			0
$241$	−19.0929	−	11.0233i	−1.22988	−	0.710072i	−0.262875	−	0.964830i	$-0.584671\pi$
$241$	−19.0929	−	11.0233i	−1.22988	−	0.710072i	−0.967005	+	0.254758i	$0.918004\pi$
$242$		0			0
$243$	−10.6122	−	2.84352i	−0.680771	−	0.182412i
$244$		0			0
$245$	−14.4477	+	10.7978i	−0.923030	+	0.689846i
$246$		0			0
$247$	2.93604	+	5.08537i	0.186816	+	0.323575i
$248$		0			0
$249$	24.1641	+	13.9511i	1.53134	+	0.884117i
$250$		0			0
$251$	15.4991	+	15.4991i	0.978295	+	0.978295i	0.999769	−	0.0214744i	$-0.00683604\pi$
$251$	15.4991	+	15.4991i	0.978295	+	0.978295i	−0.0214744	+	0.999769i	$0.506836\pi$
$252$		0			0
$253$	−23.3715	+	23.3715i	−1.46936	+	1.46936i
$254$		0			0
$255$	−6.75264	+	11.6959i	−0.422866	+	0.732426i
$256$		0			0
$257$	1.64001	−	0.946858i	0.102301	−	0.0590633i	−0.447977	−	0.894045i	$-0.647855\pi$
$257$	1.64001	−	0.946858i	0.102301	−	0.0590633i	0.550277	+	0.834982i	$0.314522\pi$
$258$		0			0
$259$	3.12517	+	16.2491i	0.194189	+	1.00967i
$260$		0			0
$261$	−1.59293	+	5.94489i	−0.0985998	+	0.367980i
$262$		0			0
$263$	−4.67609	+	8.09923i	−0.288340	+	0.499420i	−0.973414	−	0.229054i	$-0.926437\pi$
$263$	−4.67609	+	8.09923i	−0.288340	+	0.499420i	0.685073	+	0.728474i	$0.259770\pi$
$264$		0			0
$265$	−19.6305			−1.20589
$266$		0			0
$267$	−22.6764	+	22.6764i	−1.38777	+	1.38777i
$268$		0			0
$269$	25.7633	−	6.90325i	1.57082	−	0.420899i	0.634748	−	0.772719i	$-0.281104\pi$
$269$	25.7633	−	6.90325i	1.57082	−	0.420899i	0.936067	+	0.351820i	$0.114437\pi$
$270$		0			0
$271$	4.30075	+	7.44912i	0.261252	+	0.452502i	0.966575	−	0.256384i	$-0.0825313\pi$
$271$	4.30075	+	7.44912i	0.261252	+	0.452502i	−0.705323	+	0.708886i	$0.749198\pi$
$272$		0			0
$273$	0.461771	−	6.42114i	0.0279477	−	0.388625i
$274$		0			0
$275$	2.21923	−	8.28227i	0.133824	−	0.499440i
$276$		0			0
$277$	24.7551	−	6.63310i	1.48739	−	0.398544i	0.578533	−	0.815659i	$-0.303625\pi$
$277$	24.7551	−	6.63310i	1.48739	−	0.398544i	0.908854	+	0.417114i	$0.136959\pi$
$278$		0			0
$279$		−	1.29729i		−	0.0776664i
$280$		0			0
$281$			23.2859i			1.38912i	0.719434	+	0.694561i	$0.244401\pi$
$281$			23.2859i			1.38912i	−0.719434	+	0.694561i	$0.755599\pi$
$282$		0			0
$283$	9.80680	−	2.62772i	0.582954	−	0.156202i	0.0447228	−	0.998999i	$-0.485760\pi$
$283$	9.80680	−	2.62772i	0.582954	−	0.156202i	0.538231	+	0.842797i	$0.319093\pi$
$284$		0			0
$285$	−6.61157	+	24.6747i	−0.391635	+	1.46160i
$286$		0			0
$287$	11.3554	−	5.51063i	0.670288	−	0.325282i
$288$		0			0
$289$	−5.15640	−	8.93115i	−0.303318	−	0.525362i
$290$		0			0
$291$	−2.19716	+	0.588728i	−0.128800	+	0.0345118i
$292$		0			0
$293$	−0.0961358	+	0.0961358i	−0.00561631	+	0.00561631i	−0.709909	−	0.704293i	$-0.751264\pi$
$293$	−0.0961358	+	0.0961358i	−0.00561631	+	0.00561631i	0.704293	+	0.709909i	$0.251264\pi$
$294$		0			0
$295$	2.15893			0.125698
$296$		0			0
$297$	10.0283	−	17.3695i	0.581902	−	1.00788i
$298$		0			0
$299$	−1.96351	+	7.32792i	−0.113553	+	0.423784i
$300$		0			0
$301$	5.88224	−	16.9741i	0.339047	−	0.978374i
$302$		0			0
$303$	25.4722	−	14.7064i	1.46334	−	0.844861i
$304$		0			0
$305$	5.83662	−	10.1093i	0.334204	−	0.578858i
$306$		0			0
$307$	−16.2451	+	16.2451i	−0.927157	+	0.927157i	−0.997521	−	0.0703642i	$-0.977584\pi$
$307$	−16.2451	+	16.2451i	−0.927157	+	0.927157i	0.0703642	+	0.997521i	$0.477584\pi$
$308$		0			0
$309$	−1.22780	−	1.22780i	−0.0698470	−	0.0698470i
$310$		0			0
$311$	−12.3134	−	7.10914i	−0.698228	−	0.403122i	0.108459	−	0.994101i	$-0.465408\pi$
$311$	−12.3134	−	7.10914i	−0.698228	−	0.403122i	−0.806687	+	0.590979i	$0.798742\pi$
$312$		0			0
$313$	13.4403	+	23.2792i	0.759689	+	1.31582i	0.943009	+	0.332766i	$0.107982\pi$
$313$	13.4403	+	23.2792i	0.759689	+	1.31582i	−0.183321	+	0.983053i	$0.558685\pi$
$314$		0			0
$315$	5.71081	−	4.94454i	0.321767	−	0.278593i
$316$		0			0
$317$	−15.4978	−	4.15263i	−0.870445	−	0.233235i	−0.204165	−	0.978936i	$-0.565448\pi$
$317$	−15.4978	−	4.15263i	−0.870445	−	0.233235i	−0.666280	+	0.745701i	$0.732115\pi$
$318$		0			0
$319$	−25.1595	−	14.5258i	−1.40866	−	0.813290i
$320$		0			0
$321$		−	10.6929i		−	0.596818i
$322$		0			0
$323$	8.94405	+	8.94405i	0.497660	+	0.497660i
$324$		0			0
$325$	−0.509373	−	1.90101i	−0.0282549	−	0.105449i
$326$		0			0
$327$	−24.3122	+	14.0366i	−1.34447	+	0.776228i
$328$		0			0
$329$	−14.8631	−	10.0681i	−0.819430	−	0.555073i
$330$		0			0
$331$	18.3460	+	4.91579i	1.00839	+	0.270196i	0.724955	−	0.688796i	$-0.241861\pi$
$331$	18.3460	+	4.91579i	1.00839	+	0.270196i	0.283431	+	0.958993i	$0.408527\pi$
$332$		0			0
$333$	−1.79360	−	6.69379i	−0.0982884	−	0.366817i
$334$		0			0
$335$	−1.00545			−0.0549336
$336$		0			0
$337$	15.6500			0.852513			0.426256	−	0.904602i	$-0.359832\pi$
$337$	15.6500			0.852513			0.426256	+	0.904602i	$0.359832\pi$
$338$		0			0
$339$	−4.55220	−	16.9890i	−0.247241	−	0.922717i
$340$		0			0
$341$	5.91493	+	1.58490i	0.320311	+	0.0858272i
$342$		0			0
$343$	3.95798	−	18.0924i	0.213711	−	0.976897i
$344$		0			0
$345$	−28.5814	+	16.5015i	−1.53877	+	0.888409i
$346$		0			0
$347$	−5.07381	−	18.9357i	−0.272376	−	1.01652i	−0.957579	−	0.288170i	$-0.906953\pi$
$347$	−5.07381	−	18.9357i	−0.272376	−	1.01652i	0.685203	−	0.728352i	$-0.259714\pi$
$348$		0			0
$349$	7.34147	+	7.34147i	0.392980	+	0.392980i	0.875748	−	0.482768i	$-0.160369\pi$
$349$	7.34147	+	7.34147i	0.392980	+	0.392980i	−0.482768	+	0.875748i	$0.660369\pi$
$350$		0			0
$351$		−	4.60354i		−	0.245719i
$352$		0			0
$353$	10.4533	+	6.03519i	0.556371	+	0.321221i	0.751687	−	0.659519i	$-0.229240\pi$
$353$	10.4533	+	6.03519i	0.556371	+	0.321221i	−0.195317	+	0.980740i	$0.562574\pi$
$354$		0			0
$355$	9.54069	+	2.55642i	0.506367	+	0.135681i
$356$		0			0
$357$	−2.61907	−	13.6176i	−0.138616	−	0.720722i
$358$		0			0
$359$	−0.868374	−	1.50407i	−0.0458310	−	0.0793816i	0.842200	−	0.539165i	$-0.181260\pi$
$359$	−0.868374	−	1.50407i	−0.0458310	−	0.0793816i	−0.888031	+	0.459784i	$0.847927\pi$
$360$		0			0
$361$	4.26528	+	2.46256i	0.224488	+	0.129608i
$362$		0			0
$363$	−23.4420	−	23.4420i	−1.23039	−	1.23039i
$364$		0			0
$365$	17.6585	−	17.6585i	0.924287	−	0.924287i
$366$		0			0
$367$	5.21754	−	9.03704i	0.272353	−	0.471730i	−0.697111	−	0.716963i	$-0.745531\pi$
$367$	5.21754	−	9.03704i	0.272353	−	0.471730i	0.969464	+	0.245234i	$0.0788648\pi$
$368$		0			0
$369$	−4.57790	+	2.64305i	−0.238316	+	0.137592i
$370$		0			0
$371$	15.2385	−	13.1938i	0.791142	−	0.684987i
$372$		0			0
$373$	2.84184	−	10.6059i	0.147145	−	0.549153i	−0.852505	−	0.522718i	$-0.824918\pi$
$373$	2.84184	−	10.6059i	0.147145	−	0.549153i	0.999651	−	0.0264347i	$-0.00841541\pi$
$374$		0			0
$375$	−8.77552	+	15.1996i	−0.453166	+	0.784907i
$376$		0			0
$377$	−6.66815			−0.343427
$378$		0			0
$379$	19.3486	−	19.3486i	0.993870	−	0.993870i	−0.00611151	−	0.999981i	$-0.501945\pi$
$379$	19.3486	−	19.3486i	0.993870	−	0.993870i	0.999981	+	0.00611151i	$0.00194537\pi$
$380$		0			0
$381$	27.5182	−	7.37347i	1.40980	−	0.377754i
$382$		0			0
$383$	−8.91313	−	15.4380i	−0.455440	−	0.788844i	0.543274	−	0.839556i	$-0.317185\pi$
$383$	−8.91313	−	15.4380i	−0.455440	−	0.788844i	−0.998713	+	0.0507112i	$0.983851\pi$
$384$		0			0
$385$	15.5675	+	32.0790i	0.793395	+	1.63490i
$386$		0			0
$387$	−1.94725	+	7.26724i	−0.0989844	+	0.369415i
$388$		0			0
$389$	−6.02818	+	1.61525i	−0.305641	+	0.0818963i	−0.408380	−	0.912812i	$-0.633906\pi$
$389$	−6.02818	+	1.61525i	−0.305641	+	0.0818963i	0.102739	+	0.994708i	$0.467239\pi$
$390$		0			0
$391$			16.3416i			0.826429i
$392$		0			0
$393$		−	30.6190i		−	1.54453i
$394$		0			0
$395$	2.74221	−	0.734773i	0.137976	−	0.0369705i
$396$		0			0
$397$	1.82783	−	6.82155i	0.0917361	−	0.342364i	−0.904768	−	0.425904i	$-0.859956\pi$
$397$	1.82783	−	6.82155i	0.0917361	−	0.342364i	0.996504	+	0.0835403i	$0.0266227\pi$
$398$		0			0
$399$	−11.4517	−	23.5978i	−0.573303	−	1.18137i
$400$		0			0
$401$	10.4950	+	18.1779i	0.524096	+	0.907761i	0.999606	+	0.0280512i	$0.00893014\pi$
$401$	10.4950	+	18.1779i	0.524096	+	0.907761i	−0.475510	+	0.879710i	$0.657737\pi$
$402$		0			0
$403$	1.35764	−	0.363778i	0.0676288	−	0.0181211i
$404$		0			0
$405$	20.2176	−	20.2176i	1.00462	−	1.00462i
$406$		0			0
$407$	32.7114			1.62144
$408$		0			0
$409$	18.0958	−	31.3428i	0.894780	−	1.54980i	0.0607027	−	0.998156i	$-0.480666\pi$
$409$	18.0958	−	31.3428i	0.894780	−	1.54980i	0.834077	−	0.551648i	$-0.186001\pi$
$410$		0			0
$411$	2.64742	−	9.88031i	0.130588	−	0.487360i
$412$		0			0
$413$	−1.67591	+	1.45103i	−0.0824660	+	0.0714008i
$414$		0			0
$415$	−30.7196	+	17.7360i	−1.50797	+	0.870624i
$416$		0			0
$417$	5.41686	−	9.38228i	0.265265	−	0.459452i
$418$		0			0
$419$	5.15413	−	5.15413i	0.251796	−	0.251796i	−0.569911	−	0.821707i	$-0.693022\pi$
$419$	5.15413	−	5.15413i	0.251796	−	0.251796i	0.821707	+	0.569911i	$0.193022\pi$
$420$		0			0
$421$	7.75876	+	7.75876i	0.378139	+	0.378139i	0.870430	−	0.492292i	$-0.163841\pi$
$421$	7.75876	+	7.75876i	0.378139	+	0.378139i	−0.492292	+	0.870430i	$0.663841\pi$
$422$		0			0
$423$	6.51116	+	3.75922i	0.316583	+	0.182779i
$424$		0			0
$425$	−2.11966	−	3.67137i	−0.102819	−	0.178087i
$426$		0			0
$427$	2.26378	+	11.7704i	0.109552	+	0.569608i
$428$		0			0
$429$	−12.2930	−	3.29390i	−0.593511	−	0.159031i
$430$		0			0
$431$	−21.4746	−	12.3984i	−1.03440	−	0.597209i	−0.116156	−	0.993231i	$-0.537057\pi$
$431$	−21.4746	−	12.3984i	−1.03440	−	0.597209i	−0.918241	+	0.396022i	$0.870391\pi$
$432$		0			0
$433$		−	4.84981i		−	0.233067i	−0.993187	−	0.116534i	$-0.962822\pi$
$433$		−	4.84981i		−	0.233067i	0.993187	−	0.116534i	$-0.0371782\pi$
$434$		0			0
$435$	−20.5119	−	20.5119i	−0.983471	−	0.983471i
$436$		0			0
$437$	8.00009	+	29.8567i	0.382696	+	1.42824i
$438$		0			0
$439$	32.2458	−	18.6171i	1.53901	−	0.888546i	0.540109	−	0.841595i	$-0.318383\pi$
$439$	32.2458	−	18.6171i	1.53901	−	0.888546i	0.998897	−	0.0469506i	$-0.0149503\pi$
$440$		0			0
$441$	−1.10985	+	7.67655i	−0.0528498	+	0.365550i
$442$		0			0
$443$	−24.3077	−	6.51323i	−1.15489	−	0.309453i	−0.369969	−	0.929044i	$-0.620632\pi$
$443$	−24.3077	−	6.51323i	−1.15489	−	0.309453i	−0.784925	+	0.619591i	$0.787298\pi$
$444$		0			0
$445$	−10.5519	−	39.3802i	−0.500207	−	1.86680i
$446$		0			0
$447$	−0.552685			−0.0261411
$448$		0			0
$449$	0.885883			0.0418074			0.0209037	−	0.999781i	$-0.493346\pi$
$449$	0.885883			0.0418074			0.0209037	+	0.999781i	$0.493346\pi$
$450$		0			0
$451$	−6.45806	−	24.1018i	−0.304098	−	1.13491i
$452$		0			0
$453$	17.9343	+	4.80548i	0.842626	+	0.225781i
$454$		0			0
$455$	6.77596	+	4.58997i	0.317662	+	0.215181i
$456$		0			0
$457$	−30.0308	+	17.3383i	−1.40478	+	0.811052i	−0.994879	−	0.101077i	$-0.967771\pi$
$457$	−30.0308	+	17.3383i	−1.40478	+	0.811052i	−0.409904	+	0.912129i	$0.634438\pi$
$458$		0			0
$459$	−2.56653	−	9.57840i	−0.119795	−	0.447082i
$460$		0			0
$461$	−4.11212	−	4.11212i	−0.191520	−	0.191520i	0.604832	−	0.796353i	$-0.293240\pi$
$461$	−4.11212	−	4.11212i	−0.191520	−	0.191520i	−0.796353	+	0.604832i	$0.793240\pi$
$462$		0			0
$463$			11.6892i			0.543245i	0.962404	+	0.271623i	$0.0875603\pi$
$463$			11.6892i			0.543245i	−0.962404	+	0.271623i	$0.912440\pi$
$464$		0			0
$465$	5.29526	+	3.05722i	0.245562	+	0.141775i
$466$		0			0
$467$	−24.3284	−	6.51878i	−1.12579	−	0.301653i	−0.352563	−	0.935788i	$-0.614690\pi$
$467$	−24.3284	−	6.51878i	−1.12579	−	0.301653i	−0.773222	+	0.634135i	$0.781356\pi$
$468$		0			0
$469$	0.780497	−	0.675771i	0.0360400	−	0.0312042i
$470$		0			0
$471$	−15.0998	−	26.1536i	−0.695762	−	1.20509i
$472$		0			0
$473$	−30.7558	−	17.7569i	−1.41415	−	0.816461i
$474$		0			0
$475$	−5.67005	−	5.67005i	−0.260160	−	0.260160i
$476$		0			0
$477$	−5.96915	+	5.96915i	−0.273309	+	0.273309i
$478$		0			0
$479$	12.1539	−	21.0512i	0.555328	−	0.961856i	−0.442550	−	0.896744i	$-0.645926\pi$
$479$	12.1539	−	21.0512i	0.555328	−	0.961856i	0.997878	−	0.0651122i	$-0.0207405\pi$
$480$		0			0
$481$	6.50225	−	3.75408i	0.296477	−	0.171171i
$482$		0			0
$483$	11.0960	−	32.0193i	0.504886	−	1.45693i
$484$		0			0
$485$	0.748444	−	2.79323i	0.0339851	−	0.126834i
$486$		0			0
$487$	−15.5000	+	26.8468i	−0.702373	+	1.21655i	0.265258	+	0.964177i	$0.414543\pi$
$487$	−15.5000	+	26.8468i	−0.702373	+	1.21655i	−0.967631	+	0.252369i	$0.918790\pi$
$488$		0			0
$489$	39.1517			1.77050
$490$		0			0
$491$	8.29080	−	8.29080i	0.374159	−	0.374159i	−0.494831	−	0.868989i	$-0.664770\pi$
$491$	8.29080	−	8.29080i	0.374159	−	0.374159i	0.868989	+	0.494831i	$0.164770\pi$
$492$		0			0
$493$	−13.8741	+	3.71756i	−0.624860	+	0.167431i
$494$		0			0
$495$	−7.46662	−	12.9326i	−0.335600	−	0.581276i
$496$		0			0
$497$	−9.12431	+	4.42791i	−0.409281	+	0.198619i
$498$		0			0
$499$	−6.15379	+	22.9663i	−0.275482	+	1.02811i	0.680036	+	0.733178i	$0.261964\pi$
$499$	−6.15379	+	22.9663i	−0.275482	+	1.02811i	−0.955518	+	0.294933i	$0.904703\pi$
$500$		0			0
$501$	6.81971	−	1.82734i	0.304682	−	0.0816394i
$502$		0			0
$503$		−	3.42708i		−	0.152806i	−0.997077	−	0.0764029i	$-0.975656\pi$
$503$		−	3.42708i		−	0.152806i	0.997077	−	0.0764029i	$-0.0243435\pi$
$504$		0			0
$505$			37.3923i			1.66393i
$506$		0			0
$507$	22.6294	−	6.06354i	1.00501	−	0.269291i
$508$		0			0
$509$	−9.52030	+	35.5302i	−0.421980	+	1.57485i	0.348451	+	0.937327i	$0.386708\pi$
$509$	−9.52030	+	35.5302i	−0.421980	+	1.57485i	−0.770431	+	0.637523i	$0.779959\pi$
$510$		0			0
$511$	−1.83928	+	25.5761i	−0.0813651	+	1.13142i
$512$		0			0
$513$	−9.37830	−	16.2437i	−0.414062	−	0.717177i
$514$		0			0
$515$	2.13221	−	0.571325i	0.0939566	−	0.0251756i
$516$		0			0
$517$	−25.0947	+	25.0947i	−1.10367	+	1.10367i
$518$		0			0
$519$	−0.148444			−0.00651597
$520$		0			0
$521$	−6.82432	+	11.8201i	−0.298979	+	0.517846i	−0.975903	−	0.218207i	$-0.929979\pi$
$521$	−6.82432	+	11.8201i	−0.298979	+	0.517846i	0.676924	+	0.736053i	$0.263313\pi$
$522$		0			0
$523$	4.93451	−	18.4158i	0.215771	−	0.805269i	−0.770123	−	0.637896i	$-0.779805\pi$
$523$	4.93451	−	18.4158i	0.215771	−	0.805269i	0.985894	−	0.167373i	$-0.0535283\pi$
$524$		0			0
$525$	1.66035	+	8.63285i	0.0724635	+	0.376769i
$526$		0			0
$527$	2.62197	−	1.51380i	0.114215	−	0.0659420i
$528$		0			0
$529$	−8.46701	+	14.6653i	−0.368131	+	0.637621i
$530$		0			0
$531$	0.656479	−	0.656479i	0.0284888	−	0.0284888i
$532$		0			0
$533$	−4.04973	−	4.04973i	−0.175413	−	0.175413i
$534$		0			0
$535$	11.7725	+	6.79688i	0.508971	+	0.293855i
$536$		0			0
$537$	−3.15403	−	5.46293i	−0.136106	−	0.235743i
$538$		0			0
$539$	−33.6451	−	14.4388i	−1.44920	−	0.621923i
$540$		0			0
$541$	−0.455845	−	0.122143i	−0.0195983	−	0.00525135i	0.249007	−	0.968502i	$-0.419896\pi$
$541$	−0.455845	−	0.122143i	−0.0195983	−	0.00525135i	−0.268605	+	0.963250i	$0.586563\pi$
$542$		0			0
$543$	−8.30133	−	4.79278i	−0.356244	−	0.205678i
$544$		0			0
$545$		−	35.6893i		−	1.52876i
$546$		0			0
$547$	9.02908	+	9.02908i	0.386056	+	0.386056i	0.873278	−	0.487222i	$-0.161990\pi$
$547$	9.02908	+	9.02908i	0.386056	+	0.386056i	−0.487222	+	0.873278i	$0.661990\pi$
$548$		0			0
$549$	−1.29923	−	4.84878i	−0.0554497	−	0.206941i
$550$		0			0
$551$	−23.5287	+	13.5843i	−1.00236	+	0.578710i
$552$		0			0
$553$	−1.63484	+	2.41344i	−0.0695204	+	0.102630i
$554$		0			0
$555$	31.5495	+	8.45367i	1.33920	+	0.358838i
$556$		0			0
$557$	−1.79973	−	6.71669i	−0.0762570	−	0.284595i	0.917258	−	0.398293i	$-0.130397\pi$
$557$	−1.79973	−	6.71669i	−0.0762570	−	0.284595i	−0.993515	+	0.113698i	$0.963731\pi$
$558$		0			0
$559$	−8.15137			−0.344766
$560$		0			0
$561$	−27.4139			−1.15742
$562$		0			0
$563$	7.95972	+	29.7061i	0.335462	+	1.25196i	0.903367	+	0.428868i	$0.141087\pi$
$563$	7.95972	+	29.7061i	0.335462	+	1.25196i	−0.567905	+	0.823094i	$0.692246\pi$
$564$		0			0
$565$	21.5980	+	5.78717i	0.908635	+	0.243468i
$566$		0			0
$567$	−2.10584	+	29.2826i	−0.0884369	+	1.22975i
$568$		0			0
$569$	33.8726	−	19.5564i	1.42002	−	0.819846i	0.423716	−	0.905795i	$-0.360726\pi$
$569$	33.8726	−	19.5564i	1.42002	−	0.819846i	0.996300	+	0.0859489i	$0.0273922\pi$
$570$		0			0
$571$	1.41986	+	5.29899i	0.0594193	+	0.221756i	0.989251	−	0.146230i	$-0.0467141\pi$
$571$	1.41986	+	5.29899i	0.0594193	+	0.221756i	−0.929831	+	0.367986i	$0.880047\pi$
$572$		0			0
$573$	−0.448646	−	0.448646i	−0.0187425	−	0.0187425i
$574$		0			0
$575$		−	10.3597i		−	0.432028i
$576$		0			0
$577$	30.0825	+	17.3681i	1.25235	+	0.723044i	0.971576	−	0.236729i	$-0.0760755\pi$
$577$	30.0825	+	17.3681i	1.25235	+	0.723044i	0.280774	+	0.959774i	$0.409409\pi$
$578$		0			0
$579$	20.2749	+	5.43264i	0.842596	+	0.225773i
$580$		0			0
$581$	11.9261	−	34.4147i	0.494778	−	1.42776i
$582$		0			0
$583$	−19.9236	−	34.5087i	−0.825152	−	1.42920i
$584$		0			0
$585$	−2.96838	−	1.71379i	−0.122727	−	0.0708567i
$586$		0			0
$587$	25.6897	+	25.6897i	1.06033	+	1.06033i	0.998059	+	0.0622695i	$0.0198338\pi$
$587$	25.6897	+	25.6897i	1.06033	+	1.06033i	0.0622695	+	0.998059i	$0.480166\pi$
$588$		0			0
$589$	4.04937	−	4.04937i	0.166851	−	0.166851i
$590$		0			0
$591$	0.161669	−	0.280019i	0.00665018	−	0.0115185i
$592$		0			0
$593$	21.1335	−	12.2015i	0.867850	−	0.501054i	0.00121701	−	0.999999i	$-0.499613\pi$
$593$	21.1335	−	12.2015i	0.867850	−	0.501054i	0.866633	+	0.498946i	$0.166279\pi$
$594$		0			0
$595$	16.6574	+	5.77248i	0.682888	+	0.236649i
$596$		0			0
$597$	−11.1902	+	41.7623i	−0.457984	+	1.70922i
$598$		0			0
$599$	13.3779	−	23.1712i	0.546606	−	0.946750i	−0.451898	−	0.892070i	$-0.649253\pi$
$599$	13.3779	−	23.1712i	0.546606	−	0.946750i	0.998504	−	0.0546799i	$-0.0174138\pi$
$600$		0			0
$601$	16.1853			0.660212			0.330106	−	0.943944i	$-0.392915\pi$
$601$	16.1853			0.660212			0.330106	+	0.943944i	$0.392915\pi$
$602$		0			0
$603$	−0.305733	+	0.305733i	−0.0124504	+	0.0124504i
$604$		0			0
$605$	40.7098	−	10.9082i	1.65509	−	0.443479i
$606$		0			0
$607$	−2.51647	−	4.35866i	−0.102141	−	0.176913i	0.810426	−	0.585841i	$-0.199236\pi$
$607$	−2.51647	−	4.35866i	−0.102141	−	0.176913i	−0.912566	+	0.408929i	$0.865902\pi$
$608$		0			0
$609$	29.7089	+	2.13649i	1.20387	+	0.0865751i
$610$		0			0
$611$	−2.10828	+	7.86821i	−0.0852919	+	0.318314i
$612$		0			0
$613$	−0.439011	+	0.117633i	−0.0177315	+	0.00475113i	−0.267674	−	0.963510i	$-0.586255\pi$
$613$	−0.439011	+	0.117633i	−0.0177315	+	0.00475113i	0.249942	+	0.968261i	$0.419588\pi$
$614$		0			0
$615$		−	24.9147i		−	1.00466i
$616$		0			0
$617$		−	4.35363i		−	0.175271i	−0.996153	−	0.0876353i	$-0.972069\pi$
$617$		−	4.35363i		−	0.175271i	0.996153	−	0.0876353i	$-0.0279310\pi$
$618$		0			0
$619$	−4.74521	+	1.27148i	−0.190726	+	0.0511049i	−0.352918	−	0.935654i	$-0.614810\pi$
$619$	−4.74521	+	1.27148i	−0.190726	+	0.0511049i	0.162191	+	0.986759i	$0.448144\pi$
$620$		0			0
$621$	6.27184	−	23.4068i	0.251680	−	0.939283i
$622$		0			0
$623$	34.6588	+	23.4775i	1.38858	+	0.940606i
$624$		0			0
$625$	−15.2547	−	26.4218i	−0.610186	−	1.05687i
$626$		0			0
$627$	−50.0864	+	13.4206i	−2.00026	+	0.535967i
$628$		0			0
$629$	11.4360	−	11.4360i	0.455984	−	0.455984i
$630$		0			0
$631$	22.0158			0.876434			0.438217	−	0.898869i	$-0.355610\pi$
$631$	22.0158			0.876434			0.438217	+	0.898869i	$0.355610\pi$
$632$		0			0
$633$	−11.0634	+	19.1624i	−0.439732	+	0.761638i
$634$		0			0
$635$	−9.37383	+	34.9836i	−0.371989	+	1.38828i
$636$		0			0
$637$	−8.34491	+	0.991141i	−0.330637	+	0.0392704i
$638$		0			0
$639$	3.67844	−	2.12375i	0.145517	−	0.0840142i
$640$		0			0
$641$	11.9837	−	20.7564i	0.473328	−	0.819828i	−0.526206	−	0.850357i	$-0.676386\pi$
$641$	11.9837	−	20.7564i	0.473328	−	0.819828i	0.999534	+	0.0305295i	$0.00971934\pi$
$642$		0			0
$643$	−30.4232	+	30.4232i	−1.19977	+	1.19977i	−0.225537	+	0.974235i	$0.572414\pi$
$643$	−30.4232	+	30.4232i	−1.19977	+	1.19977i	−0.974235	+	0.225537i	$0.927586\pi$
$644$		0			0
$645$	−25.0745	−	25.0745i	−0.987306	−	0.987306i
$646$		0			0
$647$	−5.45353	−	3.14859i	−0.214400	−	0.123784i	0.388954	−	0.921257i	$-0.372836\pi$
$647$	−5.45353	−	3.14859i	−0.214400	−	0.123784i	−0.603355	+	0.797473i	$0.706170\pi$
$648$		0			0
$649$	2.19117	+	3.79522i	0.0860110	+	0.148975i
$650$		0			0
$651$	−6.16531	+	1.18577i	−0.241638	+	0.0464739i
$652$		0			0
$653$	30.7763	+	8.24649i	1.20437	+	0.322710i	0.804551	−	0.593884i	$-0.202406\pi$
$653$	30.7763	+	8.24649i	1.20437	+	0.322710i	0.399819	+	0.916594i	$0.369073\pi$
$654$		0			0
$655$	33.7107	+	19.4629i	1.31719	+	0.760477i
$656$		0			0
$657$		−	10.7390i		−	0.418970i
$658$		0			0
$659$	−3.27251	−	3.27251i	−0.127479	−	0.127479i	0.640489	−	0.767968i	$-0.278732\pi$
$659$	−3.27251	−	3.27251i	−0.127479	−	0.127479i	−0.767968	+	0.640489i	$0.778732\pi$
$660$		0			0
$661$	3.83925	+	14.3283i	0.149329	+	0.557305i	0.999524	+	0.0308372i	$0.00981733\pi$
$661$	3.83925	+	14.3283i	0.149329	+	0.557305i	−0.850195	+	0.526468i	$0.823516\pi$
$662$		0			0
$663$	−5.44924	+	3.14612i	−0.211631	+	0.122185i
$664$		0			0
$665$	33.2598	+	2.39185i	1.28976	+	0.0927519i
$666$		0			0
$667$	−33.9043	−	9.08464i	−1.31278	−	0.351759i
$668$		0			0
$669$	5.11007	+	19.0710i	0.197567	+	0.737329i
$670$		0			0
$671$	23.6951			0.914740
$672$		0			0
$673$	1.09724			0.0422955			0.0211478	−	0.999776i	$-0.493268\pi$
$673$	1.09724			0.0422955			0.0211478	+	0.999776i	$0.493268\pi$
$674$		0			0
$675$	1.62704	+	6.07219i	0.0626248	+	0.233719i
$676$		0			0
$677$	−16.0585	−	4.30288i	−0.617180	−	0.165373i	−0.0633346	−	0.997992i	$-0.520174\pi$
$677$	−16.0585	−	4.30288i	−0.617180	−	0.165373i	−0.553846	+	0.832619i	$0.686840\pi$
$678$		0			0
$679$	1.29636	+	2.67133i	0.0497498	+	0.102516i
$680$		0			0
$681$	−1.83010	+	1.05661i	−0.0701297	+	0.0404894i
$682$		0			0
$683$	5.03528	+	18.7919i	0.192670	+	0.719053i	0.992858	+	0.119304i	$0.0380663\pi$
$683$	5.03528	+	18.7919i	0.192670	+	0.719053i	−0.800188	+	0.599749i	$0.795267\pi$
$684$		0			0
$685$	9.19511	+	9.19511i	0.351327	+	0.351327i
$686$		0			0
$687$			10.8981i			0.415790i
$688$		0			0
$689$	−7.92069	−	4.57301i	−0.301754	−	0.174218i
$690$		0			0
$691$	−1.24774	−	0.334331i	−0.0474663	−	0.0127186i	0.235008	−	0.971993i	$-0.424488\pi$
$691$	−1.24774	−	0.334331i	−0.0474663	−	0.0127186i	−0.282474	+	0.959275i	$0.591155\pi$
$692$		0			0
$693$	14.4882	+	5.02074i	0.550360	+	0.190722i
$694$		0			0
$695$	6.88641	+	11.9276i	0.261216	+	0.452440i
$696$		0			0
$697$	−10.6839	−	6.16833i	−0.404680	−	0.233642i
$698$		0			0
$699$	18.3231	+	18.3231i	0.693044	+	0.693044i
$700$		0			0
$701$	−4.42004	+	4.42004i	−0.166942	+	0.166942i	−0.785634	−	0.618692i	$-0.787663\pi$
$701$	−4.42004	+	4.42004i	−0.166942	+	0.166942i	0.618692	+	0.785634i	$0.287663\pi$
$702$		0			0
$703$	15.2955	−	26.4927i	0.576882	−	0.999189i
$704$		0			0
$705$	−30.6887	+	17.7181i	−1.15580	+	0.667304i
$706$		0			0
$707$	−25.1316	−	29.0263i	−0.945172	−	1.09165i
$708$		0			0
$709$	−5.94273	+	22.1786i	−0.223184	+	0.832934i	0.759940	+	0.649993i	$0.225228\pi$
$709$	−5.94273	+	22.1786i	−0.223184	+	0.832934i	−0.983124	+	0.182941i	$0.941438\pi$
$710$		0			0
$711$	0.610414	−	1.05727i	0.0228923	−	0.0396506i
$712$		0			0
$713$	7.39855			0.277078
$714$		0			0
$715$	11.4405	−	11.4405i	0.427849	−	0.427849i
$716$		0			0
$717$	−51.3494	+	13.7590i	−1.91768	+	0.513841i
$718$		0			0
$719$	−3.53562	−	6.12387i	−0.131856	−	0.228382i	0.792536	−	0.609825i	$-0.208760\pi$
$719$	−3.53562	−	6.12387i	−0.131856	−	0.228382i	−0.924392	+	0.381444i	$0.875427\pi$
$720$		0			0
$721$	−1.27117	+	1.87658i	−0.0473410	+	0.0698874i
$722$		0			0
$723$	11.5652	−	43.1621i	0.430116	−	1.60522i
$724$		0			0
$725$	8.79546	−	2.35674i	0.326655	−	0.0875270i
$726$		0			0
$727$			21.2964i			0.789838i	0.918716	+	0.394919i	$0.129227\pi$
$727$			21.2964i			0.789838i	−0.918716	+	0.394919i	$0.870773\pi$
$728$		0			0
$729$			11.0213i			0.408196i
$730$		0			0
$731$	−16.9602	+	4.54448i	−0.627296	+	0.168084i
$732$		0			0
$733$	7.20760	−	26.8991i	0.266219	−	0.993543i	−0.695281	−	0.718738i	$-0.744720\pi$
$733$	7.20760	−	26.8991i	0.266219	−	0.993543i	0.961500	−	0.274805i	$-0.0886132\pi$
$734$		0			0
$735$	−28.7186	−	22.6209i	−1.05930	−	0.834386i
$736$		0			0
$737$	−1.02047	−	1.76750i	−0.0375893	−	0.0651066i
$738$		0			0
$739$	26.8289	−	7.18877i	0.986916	−	0.264443i	0.270961	−	0.962590i	$-0.412658\pi$
$739$	26.8289	−	7.18877i	0.986916	−	0.264443i	0.715954	+	0.698147i	$0.245992\pi$
$740$		0			0
$741$	−8.41580	+	8.41580i	−0.309162	+	0.309162i
$742$		0			0
$743$	4.98267			0.182796			0.0913982	−	0.995814i	$-0.470866\pi$
$743$	4.98267			0.182796			0.0913982	+	0.995814i	$0.470866\pi$
$744$		0			0
$745$	0.351312	−	0.608490i	0.0128711	−	0.0222934i
$746$		0			0
$747$	−3.94801	+	14.7342i	−0.144450	+	0.539095i
$748$		0			0
$749$	−13.7069	+	2.63623i	−0.500838	+	0.0963256i
$750$		0			0
$751$	14.1452	−	8.16676i	0.516167	−	0.298009i	−0.219198	−	0.975680i	$-0.570344\pi$
$751$	14.1452	−	8.16676i	0.516167	−	0.298009i	0.735365	+	0.677671i	$0.237011\pi$
$752$		0			0
$753$	−22.2131	+	38.4743i	−0.809491	+	1.40208i
$754$		0			0
$755$	−16.6905	+	16.6905i	−0.607431	+	0.607431i
$756$		0			0
$757$	−38.1458	−	38.1458i	−1.38643	−	1.38643i	−0.832685	−	0.553747i	$-0.813198\pi$
$757$	−38.1458	−	38.1458i	−1.38643	−	1.38643i	−0.553747	−	0.832685i	$-0.686802\pi$
$758$		0			0
$759$	−58.0164	−	33.4958i	−2.10586	−	1.21582i
$760$		0			0
$761$	−16.5068	−	28.5906i	−0.598371	−	1.03641i	−0.993062	−	0.117595i	$-0.962481\pi$
$761$	−16.5068	−	28.5906i	−0.598371	−	1.03641i	0.394690	−	0.918814i	$-0.370852\pi$
$762$		0			0
$763$	23.9871	+	27.7044i	0.868390	+	1.00297i
$764$		0			0
$765$	−7.13164	−	1.91092i	−0.257845	−	0.0690894i
$766$		0			0
$767$	0.871107	+	0.502934i	0.0314539	+	0.0181599i
$768$		0			0
$769$			18.6850i			0.673800i	0.941540	+	0.336900i	$0.109378\pi$
$769$			18.6850i			0.673800i	−0.941540	+	0.336900i	$0.890622\pi$
$770$		0			0
$771$	2.71405	+	2.71405i	0.0977441	+	0.0977441i
$772$		0			0
$773$	−9.03958	−	33.7362i	−0.325131	−	1.21341i	−0.914180	−	0.405309i	$-0.867164\pi$
$773$	−9.03958	−	33.7362i	−0.325131	−	1.21341i	0.589049	−	0.808097i	$-0.299503\pi$
$774$		0			0
$775$	−1.66219	+	0.959666i	−0.0597076	+	0.0344722i
$776$		0			0
$777$	−30.1726	+	14.6424i	−1.08244	+	0.525292i
$778$		0			0
$779$	−22.5396	−	6.03947i	−0.807565	−	0.216386i
$780$		0			0
$781$	5.18919	+	19.3663i	0.185684	+	0.692982i
$782$		0			0
$783$	21.2994			0.761178
$784$		0			0
$785$	38.3925			1.37029
$786$		0			0
$787$	6.30807	+	23.5420i	0.224858	+	0.839183i	0.982461	+	0.186467i	$0.0597038\pi$
$787$	6.30807	+	23.5420i	0.224858	+	0.839183i	−0.757603	+	0.652716i	$0.773630\pi$
$788$		0			0
$789$	−18.3094	−	4.90600i	−0.651833	−	0.174658i
$790$		0			0
$791$	−20.6554	+	10.0238i	−0.734422	+	0.356405i
$792$		0			0
$793$	4.71004	−	2.71934i	0.167258	−	0.0965666i
$794$		0			0
$795$	−10.2978	−	38.4319i	−0.365226	−	1.36304i
$796$		0			0
$797$	−25.8769	−	25.8769i	−0.916608	−	0.916608i	0.0801732	−	0.996781i	$-0.474453\pi$
$797$	−25.8769	−	25.8769i	−0.916608	−	0.916608i	−0.996781	+	0.0801732i	$0.974453\pi$
$798$		0			0
$799$			17.5465i			0.620749i
$800$		0			0
$801$	−15.1831	−	8.76599i	−0.536470	−	0.309731i
$802$		0			0
$803$	48.9643	+	13.1199i	1.72791	+	0.462993i
$804$		0			0
$805$	28.1992	+	32.5693i	0.993891	+	1.14792i
$806$		0			0
$807$	27.0300	+	46.8173i	0.951500	+	1.64805i
$808$		0			0
$809$	19.9357	+	11.5099i	0.700901	+	0.404665i	0.807683	−	0.589617i	$-0.200721\pi$
$809$	19.9357	+	11.5099i	0.700901	+	0.404665i	−0.106782	+	0.994282i	$0.534055\pi$
$810$		0			0
$811$	−8.31612	−	8.31612i	−0.292019	−	0.292019i	0.545859	−	0.837877i	$-0.316204\pi$
$811$	−8.31612	−	8.31612i	−0.292019	−	0.292019i	−0.837877	+	0.545859i	$0.816204\pi$
$812$		0			0
$813$	−12.3276	+	12.3276i	−0.432347	+	0.432347i
$814$		0			0
$815$	−24.8866	+	43.1049i	−0.871741	+	1.50990i
$816$		0			0
$817$	−28.7623	+	16.6059i	−1.00626	+	0.580967i
$818$		0			0
$819$	3.45611	−	0.664709i	0.120766	−	0.0232268i
$820$		0			0
$821$	0.583745	−	2.17857i	0.0203728	−	0.0760325i	−0.954991	−	0.296635i	$-0.904136\pi$
$821$	0.583745	−	2.17857i	0.0203728	−	0.0760325i	0.975364	+	0.220602i	$0.0708023\pi$
$822$		0			0
$823$	4.37272	−	7.57377i	0.152423	−	0.264005i	−0.779694	−	0.626160i	$-0.784626\pi$
$823$	4.37272	−	7.57377i	0.152423	−	0.264005i	0.932118	+	0.362155i	$0.117959\pi$
$824$		0			0
$825$	17.3789			0.605057
$826$		0			0
$827$	−2.25129	+	2.25129i	−0.0782850	+	0.0782850i	−0.745165	−	0.666880i	$-0.767629\pi$
$827$	−2.25129	+	2.25129i	−0.0782850	+	0.0782850i	0.666880	+	0.745165i	$0.267629\pi$
$828$		0			0
$829$	6.26518	−	1.67875i	0.217599	−	0.0583054i	−0.148373	−	0.988932i	$-0.547403\pi$
$829$	6.26518	−	1.67875i	0.217599	−	0.0583054i	0.365971	+	0.930626i	$0.380737\pi$
$830$		0			0
$831$	25.9722	+	44.9851i	0.900965	+	1.56052i
$832$		0			0
$833$	−16.8103	+	6.71460i	−0.582443	+	0.232647i
$834$		0			0
$835$	−2.32308	+	8.66985i	−0.0803934	+	0.300032i
$836$		0			0
$837$	−4.33657	+	1.16198i	−0.149894	+	0.0401639i
$838$		0			0
$839$		−	15.8804i		−	0.548253i	−0.961694	−	0.274126i	$-0.911611\pi$
$839$		−	15.8804i		−	0.548253i	0.961694	−	0.274126i	$-0.0883886\pi$
$840$		0			0
$841$		−	1.85175i		−	0.0638536i
$842$		0			0
$843$	−45.5885	+	12.2154i	−1.57015	+	0.420721i
$844$		0			0
$845$	−7.70853	+	28.7686i	−0.265181	+	0.989670i
$846$		0			0
$847$	−24.2702	+	35.8290i	−0.833933	+	1.23110i
$848$		0			0
$849$	10.2890	+	17.8210i	0.353116	+	0.611615i
$850$		0			0
$851$	38.1754	−	10.2291i	1.30863	−	0.350648i
$852$		0			0
$853$	−31.2018	+	31.2018i	−1.06833	+	1.06833i	−0.0708400	+	0.997488i	$0.522568\pi$
$853$	−31.2018	+	31.2018i	−1.06833	+	1.06833i	−0.997488	+	0.0708400i	$0.977432\pi$
$854$		0			0
$855$	−13.9653			−0.477603
$856$		0			0
$857$	0.256772	−	0.444743i	0.00877118	−	0.0151921i	−0.861607	−	0.507577i	$-0.830541\pi$
$857$	0.256772	−	0.444743i	0.00877118	−	0.0151921i	0.870378	+	0.492385i	$0.163875\pi$
$858$		0			0
$859$	5.48453	−	20.4685i	0.187130	−	0.698377i	−0.807035	−	0.590504i	$-0.798929\pi$
$859$	5.48453	−	20.4685i	0.187130	−	0.698377i	0.994165	−	0.107874i	$-0.0344042\pi$
$860$		0			0
$861$	16.7454	+	19.3405i	0.570682	+	0.659122i
$862$		0			0
$863$	−41.4589	+	23.9363i	−1.41128	+	0.814801i	−0.995509	−	0.0946697i	$-0.969821\pi$
$863$	−41.4589	+	23.9363i	−1.41128	+	0.814801i	−0.415768	+	0.909471i	$0.636487\pi$
$864$		0			0
$865$	0.0943578	−	0.163433i	0.00320826	−	0.00555687i
$866$		0			0
$867$	14.7802	−	14.7802i	0.501961	−	0.501961i
$868$		0			0
$869$	4.07483	+	4.07483i	0.138229	+	0.138229i
$870$		0			0
$871$	−0.405689	−	0.234225i	−0.0137463	−	0.00793640i
$872$		0			0
$873$	−0.621771	−	1.07694i	−0.0210438	−	0.0364489i
$874$		0			0
$875$	21.6475	+	7.50174i	0.731818	+	0.253605i
$876$		0			0
$877$	21.8607	+	5.85755i	0.738182	+	0.197795i	0.608270	−	0.793730i	$-0.291864\pi$
$877$	21.8607	+	5.85755i	0.738182	+	0.197795i	0.129912	+	0.991525i	$0.458530\pi$
$878$		0			0
$879$	−0.238643	−	0.137781i	−0.00804923	−	0.00464722i
$880$		0			0
$881$		−	17.7026i		−	0.596417i	−0.954501	−	0.298209i	$-0.903611\pi$
$881$		−	17.7026i		−	0.596417i	0.954501	−	0.298209i	$-0.0963891\pi$
$882$		0			0
$883$	−13.2141	−	13.2141i	−0.444691	−	0.444691i	0.448894	−	0.893585i	$-0.351818\pi$
$883$	−13.2141	−	13.2141i	−0.444691	−	0.444691i	−0.893585	+	0.448894i	$0.851818\pi$
$884$		0			0
$885$	1.13254	+	4.22669i	0.0380699	+	0.142079i
$886$		0			0
$887$	44.3615	−	25.6121i	1.48951	−	0.859970i	0.489584	−	0.871956i	$-0.337149\pi$
$887$	44.3615	−	25.6121i	1.48951	−	0.859970i	0.999928	+	0.0119857i	$0.00381526\pi$
$888$		0			0
$889$	−16.2362	−	33.4568i	−0.544543	−	1.12211i
$890$		0			0
$891$	56.0603	+	15.0213i	1.87809	+	0.503233i
$892$		0			0
$893$	8.58994	+	32.0581i	0.287452	+	1.07278i
$894$		0			0
$895$	8.01938			0.268058
$896$		0			0
$897$	−15.3764			−0.513403
$898$		0			0
$899$	1.68311	+	6.28144i	0.0561347	+	0.209498i
$900$		0			0
$901$	−19.0298	−	5.09901i	−0.633973	−	0.169873i
$902$		0			0
$903$	36.3172	+	2.61172i	1.20856	+	0.0869127i
$904$		0			0
$905$	10.5534	−	6.09302i	0.350807	−	0.202539i
$906$		0			0
$907$	−2.19909	−	8.20711i	−0.0730195	−	0.272512i	0.919757	−	0.392487i	$-0.128385\pi$
$907$	−2.19909	−	8.20711i	−0.0730195	−	0.272512i	−0.992777	+	0.119975i	$0.961719\pi$
$908$		0			0
$909$	11.3701	+	11.3701i	0.377122	+	0.377122i
$910$		0			0
$911$		−	19.6850i		−	0.652192i	−0.945337	−	0.326096i	$-0.894267\pi$
$911$		−	19.6850i		−	0.652192i	0.945337	−	0.326096i	$-0.105733\pi$
$912$		0			0
$913$	−62.3567	−	36.0016i	−2.06370	−	1.19148i
$914$		0			0
$915$	22.8535	+	6.12359i	0.755515	+	0.202440i
$916$		0			0
$917$	−39.2496	+	7.54884i	−1.29614	+	0.249285i
$918$		0			0
$919$	17.7313	+	30.7116i	0.584903	+	1.01308i	0.994888	+	0.100989i	$0.0322006\pi$
$919$	17.7313	+	30.7116i	0.584903	+	1.01308i	−0.409985	+	0.912092i	$0.634466\pi$
$920$		0			0
$921$	−40.3261	−	23.2823i	−1.32879	−	0.767177i
$922$		0			0
$923$	3.25404	+	3.25404i	0.107108	+	0.107108i
$924$		0			0
$925$	−7.24983	+	7.24983i	−0.238373	+	0.238373i
$926$		0			0
$927$	0.474629	−	0.822082i	0.0155889	−	0.0270007i
$928$		0			0
$929$	−38.0765	+	21.9835i	−1.24925	+	0.721255i	−0.970960	−	0.239242i	$-0.923101\pi$
$929$	−38.0765	+	21.9835i	−1.24925	+	0.721255i	−0.278290	+	0.960497i	$0.589768\pi$
$930$		0			0
$931$	−27.4260	+	20.4974i	−0.898851	+	0.671776i
$932$		0			0
$933$	7.45867	−	27.8361i	0.244186	−	0.911314i
$934$		0			0
$935$	17.4255	−	30.1819i	0.569876	−	0.987054i
$936$		0			0
$937$	−32.7634			−1.07033			−0.535167	−	0.844746i	$-0.679751\pi$
$937$	−32.7634			−1.07033			−0.535167	+	0.844746i	$0.679751\pi$
$938$		0			0
$939$	−38.5248	+	38.5248i	−1.25721	+	1.25721i
$940$		0			0
$941$	−29.6051	+	7.93265i	−0.965098	+	0.258597i	−0.706757	−	0.707457i	$-0.749842\pi$
$941$	−29.6051	+	7.93265i	−0.965098	+	0.258597i	−0.258341	+	0.966054i	$0.583176\pi$
$942$		0			0
$943$	−15.0736	−	26.1082i	−0.490864	−	0.850201i
$944$		0			0
$945$	−21.6438	−	14.6613i	−0.704072	−	0.476931i
$946$		0			0
$947$	−2.97785	+	11.1135i	−0.0967672	+	0.361140i	−0.997281	−	0.0736863i	$-0.976524\pi$
$947$	−2.97785	+	11.1135i	−0.0967672	+	0.361140i	0.900514	+	0.434826i	$0.143190\pi$
$948$		0			0
$949$	11.2386	−	3.01139i	0.364822	−	0.0977537i
$950$		0			0
$951$		−	32.5196i		−	1.05452i
$952$		0			0
$953$		−	31.6828i		−	1.02631i	−0.858297	−	0.513153i	$-0.828477\pi$
$953$		−	31.6828i		−	1.02631i	0.858297	−	0.513153i	$-0.171523\pi$
$954$		0			0
$955$	0.779126	−	0.208766i	0.0252119	−	0.00675552i
$956$		0			0
$957$	15.2400	−	56.8764i	0.492639	−	1.83855i
$958$		0			0
$959$	−13.3180	−	0.957750i	−0.430059	−	0.0309274i
$960$		0			0
$961$	14.8146	+	25.6597i	0.477892	+	0.827732i
$962$		0			0
$963$	5.64652	−	1.51298i	0.181956	−	0.0487551i
$964$		0			0
$965$	−18.8688	+	18.8688i	−0.607409	+	0.607409i
$966$		0			0
$967$	−15.2574			−0.490645			−0.245322	−	0.969442i	$-0.578894\pi$
$967$	−15.2574			−0.490645			−0.245322	+	0.969442i	$0.578894\pi$
$968$		0			0
$969$	−12.8185	+	22.2023i	−0.411790	+	0.713240i
$970$		0			0
$971$	7.84283	−	29.2698i	0.251688	−	0.939314i	−0.718215	−	0.695822i	$-0.755040\pi$
$971$	7.84283	−	29.2698i	0.251688	−	0.939314i	0.969903	−	0.243492i	$-0.0782930\pi$
$972$		0			0
$973$	−13.3623	−	4.63059i	−0.428377	−	0.148450i
$974$		0			0
$975$	3.45453	−	1.99447i	0.110633	−	0.0638742i
$976$		0			0
$977$	−25.1720	+	43.5992i	−0.805325	+	1.39486i	0.110747	+	0.993849i	$0.464676\pi$
$977$	−25.1720	+	43.5992i	−0.805325	+	1.39486i	−0.916072	+	0.401015i	$0.868658\pi$
$978$		0			0
$979$	58.5176	−	58.5176i	1.87023	−	1.87023i
$980$		0			0
$981$	−10.8523	−	10.8523i	−0.346486	−	0.346486i
$982$		0			0
$983$	−8.64540	−	4.99143i	−0.275746	−	0.159202i	0.355750	−	0.934581i	$-0.384225\pi$
$983$	−8.64540	−	4.99143i	−0.275746	−	0.159202i	−0.631496	+	0.775379i	$0.717559\pi$
$984$		0			0
$985$	0.205529	+	0.355986i	0.00654869	+	0.0113427i
$986$		0			0
$987$	11.9141	−	34.3801i	0.379231	−	1.09433i
$988$		0			0
$989$	−41.4458	−	11.1054i	−1.31790	−	0.353130i
$990$		0			0
$991$	40.8868	+	23.6060i	1.29881	+	0.749869i	0.980199	−	0.198016i	$-0.0634500\pi$
$991$	40.8868	+	23.6060i	1.29881	+	0.749869i	0.318612	+	0.947885i	$0.396783\pi$
$992$		0			0
$993$			38.4959i			1.22163i
$994$		0			0
$995$	−38.8661	−	38.8661i	−1.23214	−	1.23214i
$996$		0			0
$997$	−9.00216	−	33.5965i	−0.285101	−	1.06401i	−0.948765	−	0.315982i	$-0.897666\pi$
$997$	−9.00216	−	33.5965i	−0.285101	−	1.06401i	0.663664	−	0.748031i	$-0.269001\pi$
$998$		0			0
$999$	−20.7695	+	11.9913i	−0.657117	+	0.379387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.z.a.31.12		56
4.3	odd	2		896.2.z.b.31.3		56
7.5	odd	6	inner	896.2.z.a.159.12		56
8.3	odd	2		112.2.v.a.59.10	yes	56
8.5	even	2		448.2.z.a.143.3		56
16.3	odd	4	inner	896.2.z.a.479.12		56
16.5	even	4		112.2.v.a.3.1	✓	56
16.11	odd	4		448.2.z.a.367.3		56
16.13	even	4		896.2.z.b.479.3		56
28.19	even	6		896.2.z.b.159.3		56
56.3	even	6		784.2.j.a.587.17		56
56.5	odd	6		448.2.z.a.271.3		56
56.11	odd	6		784.2.j.a.587.18		56
56.19	even	6		112.2.v.a.75.1	yes	56
56.27	even	2		784.2.w.f.619.10		56
56.51	odd	6		784.2.w.f.411.1		56
112.5	odd	12		112.2.v.a.19.10	yes	56
112.19	even	12	inner	896.2.z.a.607.12		56
112.37	even	12		784.2.w.f.19.10		56
112.53	even	12		784.2.j.a.195.17		56
112.61	odd	12		896.2.z.b.607.3		56
112.69	odd	4		784.2.w.f.227.1		56
112.75	even	12		448.2.z.a.47.3		56
112.101	odd	12		784.2.j.a.195.18		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.1	✓	56	16.5	even	4
112.2.v.a.19.10	yes	56	112.5	odd	12
112.2.v.a.59.10	yes	56	8.3	odd	2
112.2.v.a.75.1	yes	56	56.19	even	6
448.2.z.a.47.3		56	112.75	even	12
448.2.z.a.143.3		56	8.5	even	2
448.2.z.a.271.3		56	56.5	odd	6
448.2.z.a.367.3		56	16.11	odd	4
784.2.j.a.195.17		56	112.53	even	12
784.2.j.a.195.18		56	112.101	odd	12
784.2.j.a.587.17		56	56.3	even	6
784.2.j.a.587.18		56	56.11	odd	6
784.2.w.f.19.10		56	112.37	even	12
784.2.w.f.227.1		56	112.69	odd	4
784.2.w.f.411.1		56	56.51	odd	6
784.2.w.f.619.10		56	56.27	even	2
896.2.z.a.31.12		56	1.1	even	1	trivial
896.2.z.a.159.12		56	7.5	odd	6	inner
896.2.z.a.479.12		56	16.3	odd	4	inner
896.2.z.a.607.12		56	112.19	even	12	inner
896.2.z.b.31.3		56	4.3	odd	2
896.2.z.b.159.3		56	28.19	even	6
896.2.z.b.479.3		56	16.13	even	4
896.2.z.b.607.3		56	112.61	odd	12

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.524583 + 1.95777i) q^{3} +(-2.48890 - 0.666898i) q^{5} +(2.38027 - 1.15512i) q^{7} +(-0.959602 + 0.554026i) q^{9} +(-1.35371 - 5.05213i) q^{11} +(-0.848888 - 0.848888i) q^{13} -5.22253i q^{15} +(-2.23951 - 1.29298i) q^{17} +(-4.72466 - 1.26597i) q^{19} +(3.51010 + 4.05408i) q^{21} +(-3.15967 - 5.47271i) q^{23} +(1.41973 + 0.819681i) q^{25} +(2.71152 + 2.71152i) q^{27} +(3.92758 - 3.92758i) q^{29} +(-0.585390 + 1.01392i) q^{31} +(9.18077 - 5.30052i) q^{33} +(-6.69460 + 1.28757i) q^{35} +(-1.61869 + 6.04104i) q^{37} +(1.21662 - 2.10724i) q^{39} +4.77063 q^{41} +(4.80121 - 4.80121i) q^{43} +(2.75783 - 0.738958i) q^{45} +(-3.39263 - 5.87622i) q^{47} +(4.33141 - 5.49899i) q^{49} +(1.35655 - 5.06272i) q^{51} +(7.35887 - 1.97180i) q^{53} +13.4770i q^{55} -9.91391i q^{57} +(-0.809319 + 0.216856i) q^{59} +(-1.17253 + 4.37595i) q^{61} +(-1.64415 + 2.42719i) q^{63} +(1.54667 + 2.67892i) q^{65} +(0.376913 - 0.100994i) q^{67} +(9.05679 - 9.05679i) q^{69} -3.83330 q^{71} +(-4.84591 + 8.39335i) q^{73} +(-0.859981 + 3.20949i) q^{75} +(-9.05801 - 10.4618i) q^{77} +(-0.954167 + 0.550889i) q^{79} +(-5.54819 + 9.60974i) q^{81} +(9.73434 - 9.73434i) q^{83} +(4.71162 + 4.71162i) q^{85} +(9.74964 + 5.62896i) q^{87} +(7.91117 + 13.7025i) q^{89} +(-3.00115 - 1.04002i) q^{91} +(-2.29212 - 0.614171i) q^{93} +(10.9149 + 6.30174i) q^{95} +1.12228i q^{97} +(4.09804 + 4.09804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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