LMFDB - Embedded newform 448.2.z.a.271.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,2,Mod(47,448)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("448.47"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.57729801055$
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			271.3
Character	$\chi$	$=$	448.271
Dual form			448.2.z.a.367.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.95777 - 0.524583i) q^{3} +(0.666898 + 2.48890i) q^{5} +(2.38027 + 1.15512i) q^{7} +(0.959602 + 0.554026i) q^{9} +(-5.05213 - 1.35371i) q^{11} +(-0.848888 - 0.848888i) q^{13} -5.22253i q^{15} +(-2.23951 + 1.29298i) q^{17} +(1.26597 + 4.72466i) q^{19} +(-4.05408 - 3.51010i) q^{21} +(-3.15967 + 5.47271i) q^{23} +(-1.41973 + 0.819681i) q^{25} +(2.71152 + 2.71152i) q^{27} +(-3.92758 + 3.92758i) q^{29} +(0.585390 + 1.01392i) q^{31} +(9.18077 + 5.30052i) q^{33} +(-1.28757 + 6.69460i) q^{35} +(-6.04104 + 1.61869i) q^{37} +(1.21662 + 2.10724i) q^{39} -4.77063 q^{41} +(-4.80121 + 4.80121i) q^{43} +(-0.738958 + 2.75783i) q^{45} +(3.39263 - 5.87622i) q^{47} +(4.33141 + 5.49899i) q^{49} +(5.06272 - 1.35655i) q^{51} +(1.97180 - 7.35887i) q^{53} -13.4770i q^{55} -9.91391i q^{57} +(0.216856 - 0.809319i) q^{59} +(4.37595 - 1.17253i) q^{61} +(1.64415 + 2.42719i) q^{63} +(1.54667 - 2.67892i) q^{65} +(0.100994 - 0.376913i) q^{67} +(9.05679 - 9.05679i) q^{69} -3.83330 q^{71} +(4.84591 + 8.39335i) q^{73} +(3.20949 - 0.859981i) q^{75} +(-10.4618 - 9.05801i) q^{77} +(0.954167 + 0.550889i) q^{79} +(-5.54819 - 9.60974i) q^{81} +(9.73434 - 9.73434i) q^{83} +(-4.71162 - 4.71162i) q^{85} +(9.74964 - 5.62896i) q^{87} +(-7.91117 + 13.7025i) q^{89} +(-1.04002 - 3.00115i) q^{91} +(-0.614171 - 2.29212i) q^{93} +(-10.9149 + 6.30174i) q^{95} -1.12228i q^{97} +(-4.09804 - 4.09804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.95777	−	0.524583i	−1.13032	−	0.302868i	−0.355267	−	0.934765i	$-0.615610\pi$
$3$	−1.95777	−	0.524583i	−1.13032	−	0.302868i	−0.775053	+	0.631897i	$0.782277\pi$
$4$		0			0
$5$	0.666898	+	2.48890i	0.298246	+	1.11307i	0.938605	+	0.344993i	$0.112119\pi$
$5$	0.666898	+	2.48890i	0.298246	+	1.11307i	−0.640359	+	0.768075i	$0.721215\pi$
$6$		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
$11$	−5.05213	−	1.35371i	−1.52327	−	0.408160i	−0.602456	−	0.798152i	$-0.705811\pi$
$11$	−5.05213	−	1.35371i	−1.52327	−	0.408160i	−0.920818	+	0.389992i	$0.872478\pi$
$12$		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	−0.746359	−	0.665544i	$-0.768200\pi$
$17$	−2.23951	+	1.29298i	−0.543161	+	0.313594i	0.203198	+	0.979138i	$0.434866\pi$
$18$		0			0
$19$	1.26597	+	4.72466i	0.290433	+	1.08391i	0.944777	+	0.327714i	$0.106278\pi$
$19$	1.26597	+	4.72466i	0.290433	+	1.08391i	−0.654343	+	0.756197i	$0.727055\pi$
$20$		0			0
$21$	−4.05408	−	3.51010i	−0.884672	−	0.765968i
$22$		0			0
$23$	−3.15967	+	5.47271i	−0.658836	+	1.14114i	0.322081	+	0.946712i	$0.395618\pi$
$23$	−3.15967	+	5.47271i	−0.658836	+	1.14114i	−0.980917	+	0.194426i	$0.937716\pi$
$24$		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	−0.970487	−	0.241154i	$-0.922474\pi$
$29$	−3.92758	+	3.92758i	−0.729333	+	0.729333i	0.241154	+	0.970487i	$0.422474\pi$
$30$		0			0
$31$	0.585390	+	1.01392i	0.105139	+	0.182106i	0.913795	−	0.406176i	$-0.133138\pi$
$31$	0.585390	+	1.01392i	0.105139	+	0.182106i	−0.808656	+	0.588282i	$0.799805\pi$
$32$		0			0
$33$	9.18077	+	5.30052i	1.59817	+	0.922703i
$34$		0			0
$35$	−1.28757	+	6.69460i	−0.217638	+	1.13159i
$36$		0			0
$37$	−6.04104	+	1.61869i	−0.993141	+	0.266111i	−0.718569	−	0.695455i	$-0.755203\pi$
$37$	−6.04104	+	1.61869i	−0.993141	+	0.266111i	−0.274571	+	0.961567i	$0.588536\pi$
$38$		0			0
$39$	1.21662	+	2.10724i	0.194814	+	0.337428i
$40$		0			0
$41$	−4.77063			−0.745047			−0.372523	−	0.928023i	$-0.621507\pi$
$41$	−4.77063			−0.745047			−0.372523	+	0.928023i	$0.621507\pi$
$42$		0			0
$43$	−4.80121	+	4.80121i	−0.732177	+	0.732177i	−0.971051	−	0.238873i	$-0.923222\pi$
$43$	−4.80121	+	4.80121i	−0.732177	+	0.732177i	0.238873	+	0.971051i	$0.423222\pi$
$44$		0			0
$45$	−0.738958	+	2.75783i	−0.110157	+	0.411113i
$46$		0			0
$47$	3.39263	−	5.87622i	0.494867	−	0.857134i	−0.505116	−	0.863052i	$-0.668550\pi$
$47$	3.39263	−	5.87622i	0.494867	−	0.857134i	0.999982	+	0.00591740i	$0.00188358\pi$
$48$		0			0
$49$	4.33141	+	5.49899i	0.618773	+	0.785570i
$50$		0			0
$51$	5.06272	−	1.35655i	0.708923	−	0.189955i
$52$		0			0
$53$	1.97180	−	7.35887i	0.270848	−	1.01082i	−0.687725	−	0.725971i	$-0.741390\pi$
$53$	1.97180	−	7.35887i	0.270848	−	1.01082i	0.958573	−	0.284847i	$-0.0919429\pi$
$54$		0			0
$55$		−	13.4770i		−	1.81724i
$56$		0			0
$57$		−	9.91391i		−	1.31313i
$58$		0			0
$59$	0.216856	−	0.809319i	0.0282323	−	0.105364i	−0.950372	−	0.311116i	$-0.899297\pi$
$59$	0.216856	−	0.809319i	0.0282323	−	0.105364i	0.978604	+	0.205752i	$0.0659639\pi$
$60$		0			0
$61$	4.37595	−	1.17253i	0.560283	−	0.150127i	0.0324466	−	0.999473i	$-0.489670\pi$
$61$	4.37595	−	1.17253i	0.560283	−	0.150127i	0.527836	+	0.849346i	$0.323003\pi$
$62$		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
$67$	0.100994	−	0.376913i	0.0123383	−	0.0460473i	−0.959482	−	0.281769i	$-0.909079\pi$
$67$	0.100994	−	0.376913i	0.0123383	−	0.0460473i	0.971821	+	0.235722i	$0.0757454\pi$
$68$		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	0.996844	+	0.0793836i	$0.0252952\pi$
$73$	4.84591	+	8.39335i	0.567170	+	0.982368i	−0.429674	+	0.902984i	$0.641371\pi$
$74$		0			0
$75$	3.20949	−	0.859981i	0.370600	−	0.0993021i
$76$		0			0
$77$	−10.4618	−	9.05801i	−1.19223	−	1.03226i
$78$		0			0
$79$	0.954167	+	0.550889i	0.107352	+	0.0619798i	0.552715	−	0.833370i	$-0.313592\pi$
$79$	0.954167	+	0.550889i	0.107352	+	0.0619798i	−0.445363	+	0.895350i	$0.646925\pi$
$80$		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	0.0524979	+	0.998621i	$0.483282\pi$
$89$	−7.91117	+	13.7025i	−0.838582	+	1.45247i	−0.891080	+	0.453846i	$0.850052\pi$
$90$		0			0
$91$	−1.04002	−	3.00115i	−0.109024	−	0.314606i
$92$		0			0
$93$	−0.614171	−	2.29212i	−0.0636866	−	0.237682i
$94$		0			0
$95$	−10.9149	+	6.30174i	−1.11985	+	0.646544i
$96$		0			0
$97$		−	1.12228i		−	0.113950i	−0.998376	−	0.0569750i	$-0.981854\pi$
$97$		−	1.12228i		−	0.113950i	0.998376	−	0.0569750i	$-0.0181455\pi$
$98$		0			0
$99$	−4.09804	−	4.09804i	−0.411868	−	0.411868i
$100$		0			0
$101$	14.0172	+	3.75591i	1.39477	+	0.373727i	0.876463	−	0.481470i	$-0.159897\pi$
$101$	14.0172	+	3.75591i	1.39477	+	0.373727i	0.518304	+	0.855196i	$0.326564\pi$
$102$		0			0
$103$	−0.741916	−	0.428345i	−0.0731031	−	0.0422061i	0.463003	−	0.886357i	$-0.346772\pi$
$103$	−0.741916	−	0.428345i	−0.0731031	−	0.0422061i	−0.536106	+	0.844151i	$0.680105\pi$
$104$		0			0
$105$	6.03263	−	12.4311i	0.588725	−	1.21315i
$106$		0			0
$107$	−1.36544	−	5.09589i	−0.132002	−	0.492639i	0.867990	−	0.496581i	$-0.165412\pi$
$107$	−1.36544	−	5.09589i	−0.132002	−	0.492639i	−0.999992	+	0.00394288i	$0.998745\pi$
$108$		0			0
$109$	13.3788	+	3.58485i	1.28146	+	0.343367i	0.834411	−	0.551142i	$-0.185808\pi$
$109$	13.3788	+	3.58485i	1.28146	+	0.343367i	0.447050	+	0.894509i	$0.352475\pi$
$110$		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
$115$	−15.7282	−	4.21435i	−1.46666	−	0.392990i
$116$		0			0
$117$	−0.344288	−	1.28490i	−0.0318294	−	0.118789i
$118$		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
$123$	9.33979	+	2.50259i	0.842141	+	0.225651i
$124$		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
$131$	3.90994	+	14.5921i	0.341613	+	1.27492i	0.896520	+	0.443004i	$0.146087\pi$
$131$	3.90994	+	14.5921i	0.341613	+	1.27492i	−0.554907	+	0.831913i	$0.687246\pi$
$132$		0			0
$133$	−2.44418	+	12.7083i	−0.211937	+	1.10195i
$134$		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	$-0.597501\pi$
$137$	4.37058	−	2.52336i	0.373404	−	0.215585i	0.674945	+	0.737868i	$0.264168\pi$
$138$		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
$147$	−5.59523	−	13.0379i	−0.461487	−	1.07535i
$148$		0			0
$149$	−0.263393	+	0.0705758i	−0.0215780	+	0.00578180i	−0.269592	−	0.962975i	$-0.586889\pi$
$149$	−0.263393	+	0.0705758i	−0.0215780	+	0.00578180i	0.248014	+	0.968756i	$0.420222\pi$
$150$		0			0
$151$	4.58028	+	7.93328i	0.372738	+	0.645601i	0.989986	−	0.141168i	$-0.0450857\pi$
$151$	4.58028	+	7.93328i	0.372738	+	0.645601i	−0.617248	+	0.786769i	$0.711752\pi$
$152$		0			0
$153$	−2.86538			−0.231652
$154$		0			0
$155$	−2.13316	+	2.13316i	−0.171340	+	0.171340i
$156$		0			0
$157$	3.85638	−	14.3922i	0.307772	−	1.14862i	−0.622760	−	0.782413i	$-0.713989\pi$
$157$	3.85638	−	14.3922i	0.307772	−	1.14862i	0.930533	−	0.366209i	$-0.119345\pi$
$158$		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
$163$	18.6585	−	4.99953i	1.46145	−	0.391593i	0.561457	−	0.827506i	$-0.310241\pi$
$163$	18.6585	−	4.99953i	1.46145	−	0.391593i	0.899989	+	0.435912i	$0.143574\pi$
$164$		0			0
$165$	−7.06982	+	26.3849i	−0.550384	+	2.05406i
$166$		0			0
$167$			3.48341i			0.269554i	0.990876	+	0.134777i	$0.0430318\pi$
$167$			3.48341i			0.269554i	−0.990876	+	0.134777i	$0.956968\pi$
$168$		0			0
$169$		−	11.5588i		−	0.889137i
$170$		0			0
$171$	−1.40276	+	5.23517i	−0.107272	+	0.400344i
$172$		0			0
$173$	0.0707438	−	0.0189557i	0.00537855	−	0.00144118i	−0.256129	−	0.966643i	$-0.582447\pi$
$173$	0.0707438	−	0.0189557i	0.00537855	−	0.00144118i	0.261507	+	0.965201i	$0.415780\pi$
$174$		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
$179$	−0.805515	+	3.00622i	−0.0602070	+	0.224696i	−0.989473	−	0.144715i	$-0.953774\pi$
$179$	−0.805515	+	3.00622i	−0.0602070	+	0.224696i	0.929266	+	0.369410i	$0.120440\pi$
$180$		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
$187$	13.0646	−	3.50065i	0.955379	−	0.255993i
$188$		0			0
$189$	3.32203	+	9.58627i	0.241642	+	0.697298i
$190$		0			0
$191$	0.271101	+	0.156520i	0.0196162	+	0.0113254i	0.509776	−	0.860307i	$-0.329728\pi$
$191$	0.271101	+	0.156520i	0.0196162	+	0.0113254i	−0.490160	+	0.871633i	$0.663062\pi$
$192$		0			0
$193$	5.17806	+	8.96866i	0.372725	+	0.645578i	0.989984	−	0.141182i	$-0.0450902\pi$
$193$	5.17806	+	8.96866i	0.372725	+	0.645578i	−0.617259	+	0.786760i	$0.711757\pi$
$194$		0			0
$195$	−4.43334	+	4.43334i	−0.317478	+	0.317478i
$196$		0			0
$197$	0.112804	+	0.112804i	0.00803695	+	0.00803695i	0.711114	−	0.703077i	$-0.248191\pi$
$197$	0.112804	+	0.112804i	0.00803695	+	0.00803695i	−0.703077	+	0.711114i	$0.748191\pi$
$198$		0			0
$199$	18.4737	−	10.6658i	1.30957	−	0.756078i	0.327542	−	0.944837i	$-0.393780\pi$
$199$	18.4737	−	10.6658i	1.30957	−	0.756078i	0.982023	+	0.188759i	$0.0604464\pi$
$200$		0			0
$201$	−0.395444	+	0.684930i	−0.0278925	+	0.0483112i
$202$		0			0
$203$	−13.8855	+	4.81190i	−0.974573	+	0.337730i
$204$		0			0
$205$	−3.18152	−	11.8736i	−0.222207	−	0.829288i
$206$		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	0.389568	−	0.920998i	$-0.372624\pi$
$211$	−7.71946	−	7.71946i	−0.531430	−	0.531430i	−0.920998	+	0.389568i	$0.872624\pi$
$212$		0			0
$213$	7.50472	+	2.01088i	0.514215	+	0.137784i
$214$		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
$219$	−5.08416	−	18.9743i	−0.343556	−	1.28217i
$220$		0			0
$221$	2.99869	+	0.803496i	0.201714	+	0.0540490i
$222$		0			0
$223$	−9.74121			−0.652319			−0.326160	−	0.945315i	$-0.605755\pi$
$223$	−9.74121			−0.652319			−0.326160	+	0.945315i	$0.605755\pi$
$224$		0			0
$225$	−1.81650			−0.121100
$226$		0			0
$227$	−1.00710	−	0.269850i	−0.0668433	−	0.0179106i	0.225242	−	0.974303i	$-0.427683\pi$
$227$	−1.00710	−	0.269850i	−0.0668433	−	0.0179106i	−0.292086	+	0.956392i	$0.594349\pi$
$228$		0			0
$229$	−1.39165	−	5.19372i	−0.0919630	−	0.343210i	0.904579	−	0.426307i	$-0.140186\pi$
$229$	−1.39165	−	5.19372i	−0.0919630	−	0.343210i	−0.996541	+	0.0830966i	$0.973519\pi$
$230$		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	$-0.470876\pi$
$233$	−11.0720	−	6.39244i	−0.725352	−	0.418782i	−0.816720	+	0.577035i	$0.804210\pi$
$234$		0			0
$235$	16.8878	+	4.52508i	1.10164	+	0.295184i
$236$		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	−0.967005	−	0.254758i	$-0.918004\pi$
$241$	−19.0929	+	11.0233i	−1.22988	+	0.710072i	−0.262875	+	0.964830i	$0.584671\pi$
$242$		0			0
$243$	2.84352	+	10.6122i	0.182412	+	0.680771i
$244$		0			0
$245$	−10.7978	+	14.4477i	−0.689846	+	0.923030i
$246$		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	0.550277	−	0.834982i	$-0.314522\pi$
$257$	1.64001	+	0.946858i	0.102301	+	0.0590633i	−0.447977	+	0.894045i	$0.647855\pi$
$258$		0			0
$259$	−16.2491	−	3.12517i	−1.00967	−	0.194189i
$260$		0			0
$261$	−5.94489	+	1.59293i	−0.367980	+	0.0985998i
$262$		0			0
$263$	−4.67609	−	8.09923i	−0.288340	−	0.499420i	0.685073	−	0.728474i	$-0.259770\pi$
$263$	−4.67609	−	8.09923i	−0.288340	−	0.499420i	−0.973414	+	0.229054i	$0.926437\pi$
$264$		0			0
$265$	19.6305			1.20589
$266$		0			0
$267$	22.6764	−	22.6764i	1.38777	−	1.38777i
$268$		0			0
$269$	−6.90325	+	25.7633i	−0.420899	+	1.57082i	0.351820	+	0.936067i	$0.385563\pi$
$269$	−6.90325	+	25.7633i	−0.420899	+	1.57082i	−0.772719	+	0.634748i	$0.781104\pi$
$270$		0			0
$271$	−4.30075	+	7.44912i	−0.261252	+	0.452502i	−0.966575	−	0.256384i	$-0.917469\pi$
$271$	−4.30075	+	7.44912i	−0.261252	+	0.452502i	0.705323	+	0.708886i	$0.250802\pi$
$272$		0			0
$273$	0.461771	+	6.42114i	0.0279477	+	0.388625i
$274$		0			0
$275$	8.28227	−	2.21923i	0.499440	−	0.133824i
$276$		0			0
$277$	6.63310	−	24.7551i	0.398544	−	1.48739i	−0.417114	−	0.908854i	$-0.636959\pi$
$277$	6.63310	−	24.7551i	0.398544	−	1.48739i	0.815659	−	0.578533i	$-0.196375\pi$
$278$		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
$283$	−2.62772	+	9.80680i	−0.156202	+	0.582954i	0.842797	+	0.538231i	$0.180907\pi$
$283$	−2.62772	+	9.80680i	−0.156202	+	0.582954i	−0.998999	+	0.0447228i	$0.985760\pi$
$284$		0			0
$285$	24.6747	−	6.61157i	1.46160	−	0.391635i
$286$		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
$291$	−0.588728	+	2.19716i	−0.0345118	+	0.128800i
$292$		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
$299$	7.32792	−	1.96351i	0.423784	−	0.113553i
$300$		0			0
$301$	−16.9741	+	5.88224i	−0.978374	+	0.339047i
$302$		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	−0.806687	−	0.590979i	$-0.798742\pi$
$311$	−12.3134	+	7.10914i	−0.698228	+	0.403122i	0.108459	+	0.994101i	$0.465408\pi$
$312$		0			0
$313$	−13.4403	+	23.2792i	−0.759689	+	1.31582i	0.183321	+	0.983053i	$0.441315\pi$
$313$	−13.4403	+	23.2792i	−0.759689	+	1.31582i	−0.943009	+	0.332766i	$0.892018\pi$
$314$		0			0
$315$	−4.94454	+	5.71081i	−0.278593	+	0.321767i
$316$		0			0
$317$	−4.15263	−	15.4978i	−0.233235	−	0.870445i	−0.978936	−	0.204165i	$-0.934552\pi$
$317$	−4.15263	−	15.4978i	−0.233235	−	0.870445i	0.745701	−	0.666280i	$-0.232115\pi$
$318$		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
$325$	1.90101	+	0.509373i	0.105449	+	0.0282549i
$326$		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
$331$	4.91579	+	18.3460i	0.270196	+	1.00839i	0.958993	+	0.283431i	$0.0914727\pi$
$331$	4.91579	+	18.3460i	0.270196	+	1.00839i	−0.688796	+	0.724955i	$0.741861\pi$
$332$		0			0
$333$	−6.69379	−	1.79360i	−0.366817	−	0.0982884i
$334$		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
$339$	16.9890	+	4.55220i	0.922717	+	0.247241i
$340$		0			0
$341$	−1.58490	−	5.91493i	−0.0858272	−	0.320311i
$342$		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
$347$	−18.9357	−	5.07381i	−1.01652	−	0.272376i	−0.288170	−	0.957579i	$-0.593047\pi$
$347$	−18.9357	−	5.07381i	−1.01652	−	0.272376i	−0.728352	+	0.685203i	$0.759714\pi$
$348$		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	−0.195317	−	0.980740i	$-0.562574\pi$
$353$	10.4533	−	6.03519i	0.556371	−	0.321221i	0.751687	+	0.659519i	$0.229240\pi$
$354$		0			0
$355$	−2.55642	−	9.54069i	−0.135681	−	0.506367i
$356$		0			0
$357$	13.6176	+	2.61907i	0.720722	+	0.138616i
$358$		0			0
$359$	−0.868374	+	1.50407i	−0.0458310	+	0.0793816i	−0.888031	−	0.459784i	$-0.847927\pi$
$359$	−0.868374	+	1.50407i	−0.0458310	+	0.0793816i	0.842200	+	0.539165i	$0.181260\pi$
$360$		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	$-0.254469\pi$
$367$	−5.21754	−	9.03704i	−0.272353	−	0.471730i	−0.969464	+	0.245234i	$0.921135\pi$
$368$		0			0
$369$	−4.57790	−	2.64305i	−0.238316	−	0.137592i
$370$		0			0
$371$	13.1938	−	15.2385i	0.684987	−	0.791142i
$372$		0			0
$373$	10.6059	−	2.84184i	0.549153	−	0.147145i	0.0264347	−	0.999651i	$-0.491585\pi$
$373$	10.6059	−	2.84184i	0.549153	−	0.147145i	0.522718	+	0.852505i	$0.324918\pi$
$374$		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	−0.999981	−	0.00611151i	$-0.998055\pi$
$379$	−19.3486	+	19.3486i	−0.993870	+	0.993870i	0.00611151	+	0.999981i	$0.498055\pi$
$380$		0			0
$381$	−7.37347	+	27.5182i	−0.377754	+	1.40980i
$382$		0			0
$383$	8.91313	−	15.4380i	0.455440	−	0.788844i	−0.543274	−	0.839556i	$-0.682815\pi$
$383$	8.91313	−	15.4380i	0.455440	−	0.788844i	0.998713	+	0.0507112i	$0.0161488\pi$
$384$		0			0
$385$	15.5675	−	32.0790i	0.793395	−	1.63490i
$386$		0			0
$387$	−7.26724	+	1.94725i	−0.369415	+	0.0989844i
$388$		0			0
$389$	−1.61525	+	6.02818i	−0.0818963	+	0.305641i	−0.994708	−	0.102739i	$-0.967239\pi$
$389$	−1.61525	+	6.02818i	−0.0818963	+	0.305641i	0.912812	+	0.408380i	$0.133906\pi$
$390$		0			0
$391$		−	16.3416i		−	0.826429i
$392$		0			0
$393$		−	30.6190i		−	1.54453i
$394$		0			0
$395$	−0.734773	+	2.74221i	−0.0369705	+	0.137976i
$396$		0			0
$397$	−6.82155	+	1.82783i	−0.342364	+	0.0917361i	−0.425904	−	0.904768i	$-0.640044\pi$
$397$	−6.82155	+	1.82783i	−0.342364	+	0.0917361i	0.0835403	+	0.996504i	$0.473377\pi$
$398$		0			0
$399$	11.4517	−	23.5978i	0.573303	−	1.18137i
$400$		0			0
$401$	10.4950	−	18.1779i	0.524096	−	0.907761i	−0.475510	−	0.879710i	$-0.657737\pi$
$401$	10.4950	−	18.1779i	0.524096	−	0.907761i	0.999606	−	0.0280512i	$-0.00893014\pi$
$402$		0			0
$403$	0.363778	−	1.35764i	0.0181211	−	0.0676288i
$404$		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	−0.834077	−	0.551648i	$-0.813999\pi$
$409$	−18.0958	−	31.3428i	−0.894780	−	1.54980i	−0.0607027	−	0.998156i	$-0.519334\pi$
$410$		0			0
$411$	−9.88031	+	2.64742i	−0.487360	+	0.130588i
$412$		0			0
$413$	1.45103	−	1.67591i	0.0714008	−	0.0824660i
$414$		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	0.492292	−	0.870430i	$-0.336159\pi$
$421$	−7.75876	−	7.75876i	−0.378139	−	0.378139i	−0.870430	+	0.492292i	$0.836159\pi$
$422$		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
$427$	11.7704	+	2.26378i	0.569608	+	0.109552i
$428$		0			0
$429$	−3.29390	−	12.2930i	−0.159031	−	0.593511i
$430$		0			0
$431$	21.4746	−	12.3984i	1.03440	−	0.597209i	0.116156	−	0.993231i	$-0.462943\pi$
$431$	21.4746	−	12.3984i	1.03440	−	0.597209i	0.918241	+	0.396022i	$0.129609\pi$
$432$		0			0
$433$			4.84981i			0.233067i	0.993187	+	0.116534i	$0.0371782\pi$
$433$			4.84981i			0.233067i	−0.993187	+	0.116534i	$0.962822\pi$
$434$		0			0
$435$	20.5119	+	20.5119i	0.983471	+	0.983471i
$436$		0			0
$437$	−29.8567	−	8.00009i	−1.42824	−	0.382696i
$438$		0			0
$439$	32.2458	+	18.6171i	1.53901	+	0.888546i	0.998897	+	0.0469506i	$0.0149503\pi$
$439$	32.2458	+	18.6171i	1.53901	+	0.888546i	0.540109	+	0.841595i	$0.318383\pi$
$440$		0			0
$441$	1.10985	+	7.67655i	0.0528498	+	0.365550i
$442$		0			0
$443$	−6.51323	−	24.3077i	−0.309453	−	1.15489i	−0.929044	−	0.369969i	$-0.879368\pi$
$443$	−6.51323	−	24.3077i	−0.309453	−	1.15489i	0.619591	−	0.784925i	$-0.287298\pi$
$444$		0			0
$445$	−39.3802	−	10.5519i	−1.86680	−	0.500207i
$446$		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
$451$	24.1018	+	6.45806i	1.13491	+	0.304098i
$452$		0			0
$453$	−4.80548	−	17.9343i	−0.225781	−	0.842626i
$454$		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	$-0.0322289\pi$
$457$	30.0308	+	17.3383i	1.40478	+	0.811052i	0.409904	+	0.912129i	$0.365562\pi$
$458$		0			0
$459$	−9.57840	−	2.56653i	−0.447082	−	0.119795i
$460$		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
$467$	6.51878	+	24.3284i	0.301653	+	1.12579i	0.935788	+	0.352563i	$0.114690\pi$
$467$	6.51878	+	24.3284i	0.301653	+	1.12579i	−0.634135	+	0.773222i	$0.718644\pi$
$468$		0			0
$469$	0.675771	−	0.780497i	0.0312042	−	0.0360400i
$470$		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	−0.997878	−	0.0651122i	$-0.979259\pi$
$479$	−12.1539	−	21.0512i	−0.555328	−	0.961856i	0.442550	−	0.896744i	$-0.354074\pi$
$480$		0			0
$481$	6.50225	+	3.75408i	0.296477	+	0.171171i
$482$		0			0
$483$	32.0193	−	11.0960i	1.45693	−	0.504886i
$484$		0			0
$485$	2.79323	−	0.748444i	0.126834	−	0.0339851i
$486$		0			0
$487$	−15.5000	−	26.8468i	−0.702373	−	1.21655i	−0.967631	−	0.252369i	$-0.918790\pi$
$487$	−15.5000	−	26.8468i	−0.702373	−	1.21655i	0.265258	−	0.964177i	$-0.414543\pi$
$488$		0			0
$489$	−39.1517			−1.77050
$490$		0			0
$491$	−8.29080	+	8.29080i	−0.374159	+	0.374159i	−0.868989	−	0.494831i	$-0.835230\pi$
$491$	−8.29080	+	8.29080i	−0.374159	+	0.374159i	0.494831	+	0.868989i	$0.335230\pi$
$492$		0			0
$493$	3.71756	−	13.8741i	0.167431	−	0.624860i
$494$		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
$499$	−22.9663	+	6.15379i	−1.02811	+	0.275482i	−0.733178	−	0.680036i	$-0.761964\pi$
$499$	−22.9663	+	6.15379i	−1.02811	+	0.275482i	−0.294933	+	0.955518i	$0.595297\pi$
$500$		0			0
$501$	1.82734	−	6.81971i	0.0816394	−	0.304682i
$502$		0			0
$503$			3.42708i			0.152806i	0.997077	+	0.0764029i	$0.0243435\pi$
$503$			3.42708i			0.152806i	−0.997077	+	0.0764029i	$0.975656\pi$
$504$		0			0
$505$			37.3923i			1.66393i
$506$		0			0
$507$	−6.06354	+	22.6294i	−0.269291	+	1.00501i
$508$		0			0
$509$	35.5302	−	9.52030i	1.57485	−	0.421980i	0.637523	−	0.770431i	$-0.279959\pi$
$509$	35.5302	−	9.52030i	1.57485	−	0.421980i	0.937327	+	0.348451i	$0.113292\pi$
$510$		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
$515$	0.571325	−	2.13221i	0.0251756	−	0.0939566i
$516$		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	$-0.0700207\pi$
$521$	6.82432	+	11.8201i	0.298979	+	0.517846i	−0.676924	+	0.736053i	$0.736687\pi$
$522$		0			0
$523$	−18.4158	+	4.93451i	−0.805269	+	0.215771i	−0.637896	−	0.770123i	$-0.720195\pi$
$523$	−18.4158	+	4.93451i	−0.805269	+	0.215771i	−0.167373	+	0.985894i	$0.553528\pi$
$524$		0			0
$525$	8.63285	+	1.66035i	0.376769	+	0.0724635i
$526$		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
$539$	−14.4388	−	33.6451i	−0.621923	−	1.44920i
$540$		0			0
$541$	−0.122143	−	0.455845i	−0.00525135	−	0.0195983i	0.963250	−	0.268605i	$-0.0865626\pi$
$541$	−0.122143	−	0.455845i	−0.00525135	−	0.0195983i	−0.968502	+	0.249007i	$0.919896\pi$
$542$		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	0.487222	−	0.873278i	$-0.338010\pi$
$547$	−9.02908	−	9.02908i	−0.386056	−	0.386056i	−0.873278	+	0.487222i	$0.838010\pi$
$548$		0			0
$549$	4.84878	+	1.29923i	0.206941	+	0.0554497i
$550$		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
$555$	8.45367	+	31.5495i	0.358838	+	1.33920i
$556$		0			0
$557$	−6.71669	−	1.79973i	−0.284595	−	0.0762570i	0.113698	−	0.993515i	$-0.463731\pi$
$557$	−6.71669	−	1.79973i	−0.284595	−	0.0762570i	−0.398293	+	0.917258i	$0.630397\pi$
$558$		0			0
$559$	8.15137			0.344766
$560$		0			0
$561$	−27.4139			−1.15742
$562$		0			0
$563$	−29.7061	−	7.95972i	−1.25196	−	0.335462i	−0.428868	−	0.903367i	$-0.641087\pi$
$563$	−29.7061	−	7.95972i	−1.25196	−	0.335462i	−0.823094	+	0.567905i	$0.807754\pi$
$564$		0			0
$565$	−5.78717	−	21.5980i	−0.243468	−	0.908635i
$566$		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	$-0.639274\pi$
$569$	−33.8726	−	19.5564i	−1.42002	−	0.819846i	−0.996300	+	0.0859489i	$0.972608\pi$
$570$		0			0
$571$	5.29899	+	1.41986i	0.221756	+	0.0594193i	0.367986	−	0.929831i	$-0.380047\pi$
$571$	5.29899	+	1.41986i	0.221756	+	0.0594193i	−0.146230	+	0.989251i	$0.546714\pi$
$572$		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	0.280774	−	0.959774i	$-0.409409\pi$
$577$	30.0825	−	17.3681i	1.25235	−	0.723044i	0.971576	+	0.236729i	$0.0760755\pi$
$578$		0			0
$579$	−5.43264	−	20.2749i	−0.225773	−	0.842596i
$580$		0			0
$581$	34.4147	−	11.9261i	1.42776	−	0.494778i
$582$		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	0.866633	−	0.498946i	$-0.166279\pi$
$593$	21.1335	+	12.2015i	0.867850	+	0.501054i	0.00121701	+	0.999999i	$0.499613\pi$
$594$		0			0
$595$	−5.77248	−	16.6574i	−0.236649	−	0.682888i
$596$		0			0
$597$	−41.7623	+	11.1902i	−1.70922	+	0.457984i
$598$		0			0
$599$	13.3779	+	23.1712i	0.546606	+	0.946750i	0.998504	+	0.0546799i	$0.0174138\pi$
$599$	13.3779	+	23.1712i	0.546606	+	0.946750i	−0.451898	+	0.892070i	$0.649253\pi$
$600$		0			0
$601$	−16.1853			−0.660212			−0.330106	−	0.943944i	$-0.607085\pi$
$601$	−16.1853			−0.660212			−0.330106	+	0.943944i	$0.607085\pi$
$602$		0			0
$603$	0.305733	−	0.305733i	0.0124504	−	0.0124504i
$604$		0			0
$605$	−10.9082	+	40.7098i	−0.443479	+	1.65509i
$606$		0			0
$607$	2.51647	−	4.35866i	0.102141	−	0.176913i	−0.810426	−	0.585841i	$-0.800764\pi$
$607$	2.51647	−	4.35866i	0.102141	−	0.176913i	0.912566	+	0.408929i	$0.134098\pi$
$608$		0			0
$609$	29.7089	−	2.13649i	1.20387	−	0.0865751i
$610$		0			0
$611$	−7.86821	+	2.10828i	−0.318314	+	0.0852919i
$612$		0			0
$613$	−0.117633	+	0.439011i	−0.00475113	+	0.0177315i	−0.968261	−	0.249942i	$-0.919588\pi$
$613$	−0.117633	+	0.439011i	−0.00475113	+	0.0177315i	0.963510	+	0.267674i	$0.0862550\pi$
$614$		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
$619$	1.27148	−	4.74521i	0.0511049	−	0.190726i	−0.935654	−	0.352918i	$-0.885190\pi$
$619$	1.27148	−	4.74521i	0.0511049	−	0.190726i	0.986759	+	0.162191i	$0.0518562\pi$
$620$		0			0
$621$	−23.4068	+	6.27184i	−0.939283	+	0.251680i
$622$		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
$627$	−13.4206	+	50.0864i	−0.535967	+	2.00026i
$628$		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
$635$	34.9836	−	9.37383i	1.38828	−	0.371989i
$636$		0			0
$637$	0.991141	−	8.34491i	0.0392704	−	0.330637i
$638$		0			0
$639$	−3.67844	−	2.12375i	−0.145517	−	0.0840142i
$640$		0			0
$641$	11.9837	+	20.7564i	0.473328	+	0.819828i	0.999534	−	0.0305295i	$-0.00971934\pi$
$641$	11.9837	+	20.7564i	0.473328	+	0.819828i	−0.526206	+	0.850357i	$0.676386\pi$
$642$		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	−0.603355	−	0.797473i	$-0.706170\pi$
$647$	−5.45353	+	3.14859i	−0.214400	+	0.123784i	0.388954	+	0.921257i	$0.372836\pi$
$648$		0			0
$649$	−2.19117	+	3.79522i	−0.0860110	+	0.148975i
$650$		0			0
$651$	1.18577	−	6.16531i	0.0464739	−	0.241638i
$652$		0			0
$653$	8.24649	+	30.7763i	0.322710	+	1.20437i	0.916594	+	0.399819i	$0.130927\pi$
$653$	8.24649	+	30.7763i	0.322710	+	1.20437i	−0.593884	+	0.804551i	$0.702406\pi$
$654$		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	0.767968	−	0.640489i	$-0.221268\pi$
$659$	3.27251	+	3.27251i	0.127479	+	0.127479i	−0.640489	+	0.767968i	$0.721268\pi$
$660$		0			0
$661$	−14.3283	−	3.83925i	−0.557305	−	0.149329i	−0.0308372	−	0.999524i	$-0.509817\pi$
$661$	−14.3283	−	3.83925i	−0.557305	−	0.149329i	−0.526468	+	0.850195i	$0.676484\pi$
$662$		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
$667$	−9.08464	−	33.9043i	−0.351759	−	1.31278i
$668$		0			0
$669$	19.0710	+	5.11007i	0.737329	+	0.197567i
$670$		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
$675$	−6.07219	−	1.62704i	−0.233719	−	0.0626248i
$676$		0			0
$677$	4.30288	+	16.0585i	0.165373	+	0.617180i	0.997992	+	0.0633346i	$0.0201735\pi$
$677$	4.30288	+	16.0585i	0.165373	+	0.617180i	−0.832619	+	0.553846i	$0.813160\pi$
$678$		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
$683$	18.7919	+	5.03528i	0.719053	+	0.192670i	0.599749	−	0.800188i	$-0.295267\pi$
$683$	18.7919	+	5.03528i	0.719053	+	0.192670i	0.119304	+	0.992858i	$0.461934\pi$
$684$		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
$691$	0.334331	+	1.24774i	0.0127186	+	0.0474663i	0.971993	−	0.235008i	$-0.0755116\pi$
$691$	0.334331	+	1.24774i	0.0127186	+	0.0474663i	−0.959275	+	0.282474i	$0.908845\pi$
$692$		0			0
$693$	−5.02074	−	14.4882i	−0.190722	−	0.550360i
$694$		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	−0.618692	−	0.785634i	$-0.712337\pi$
$701$	4.42004	−	4.42004i	0.166942	−	0.166942i	0.785634	+	0.618692i	$0.212337\pi$
$702$		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
$707$	29.0263	+	25.1316i	1.09165	+	0.945172i
$708$		0			0
$709$	−22.1786	+	5.94273i	−0.832934	+	0.223184i	−0.649993	−	0.759940i	$-0.725228\pi$
$709$	−22.1786	+	5.94273i	−0.832934	+	0.223184i	−0.182941	+	0.983124i	$0.558562\pi$
$710$		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
$717$	13.7590	−	51.3494i	0.513841	−	1.91768i
$718$		0			0
$719$	3.53562	−	6.12387i	0.131856	−	0.228382i	−0.792536	−	0.609825i	$-0.791240\pi$
$719$	3.53562	−	6.12387i	0.131856	−	0.228382i	0.924392	+	0.381444i	$0.124573\pi$
$720$		0			0
$721$	−1.27117	−	1.87658i	−0.0473410	−	0.0698874i
$722$		0			0
$723$	43.1621	−	11.5652i	1.60522	−	0.430116i
$724$		0			0
$725$	2.35674	−	8.79546i	0.0875270	−	0.326655i
$726$		0			0
$727$		−	21.2964i		−	0.789838i	−0.918716	−	0.394919i	$-0.870773\pi$
$727$		−	21.2964i		−	0.789838i	0.918716	−	0.394919i	$-0.129227\pi$
$728$		0			0
$729$			11.0213i			0.408196i
$730$		0			0
$731$	4.54448	−	16.9602i	0.168084	−	0.627296i
$732$		0			0
$733$	−26.8991	+	7.20760i	−0.993543	+	0.266219i	−0.718738	−	0.695281i	$-0.755280\pi$
$733$	−26.8991	+	7.20760i	−0.993543	+	0.266219i	−0.274805	+	0.961500i	$0.588613\pi$
$734$		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
$739$	7.18877	−	26.8289i	0.264443	−	0.986916i	−0.698147	−	0.715954i	$-0.745992\pi$
$739$	7.18877	−	26.8289i	0.264443	−	0.986916i	0.962590	−	0.270961i	$-0.0873415\pi$
$740$		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
$747$	14.7342	−	3.94801i	0.539095	−	0.144450i
$748$		0			0
$749$	2.63623	−	13.7069i	0.0963256	−	0.500838i
$750$		0			0
$751$	−14.1452	−	8.16676i	−0.516167	−	0.298009i	0.219198	−	0.975680i	$-0.429656\pi$
$751$	−14.1452	−	8.16676i	−0.516167	−	0.298009i	−0.735365	+	0.677671i	$0.762989\pi$
$752$		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	$0.186802\pi$
$757$	38.1458	+	38.1458i	1.38643	+	1.38643i	0.553747	+	0.832685i	$0.313198\pi$
$758$		0			0
$759$	−58.0164	+	33.4958i	−2.10586	+	1.21582i
$760$		0			0
$761$	16.5068	−	28.5906i	0.598371	−	1.03641i	−0.394690	−	0.918814i	$-0.629148\pi$
$761$	16.5068	−	28.5906i	0.598371	−	1.03641i	0.993062	−	0.117595i	$-0.0375186\pi$
$762$		0			0
$763$	27.7044	+	23.9871i	1.00297	+	0.868390i
$764$		0			0
$765$	−1.91092	−	7.13164i	−0.0690894	−	0.257845i
$766$		0			0
$767$	−0.871107	+	0.502934i	−0.0314539	+	0.0181599i
$768$		0			0
$769$		−	18.6850i		−	0.673800i	−0.941540	−	0.336900i	$-0.890622\pi$
$769$		−	18.6850i		−	0.673800i	0.941540	−	0.336900i	$-0.109378\pi$
$770$		0			0
$771$	−2.71405	−	2.71405i	−0.0977441	−	0.0977441i
$772$		0			0
$773$	33.7362	+	9.03958i	1.21341	+	0.325131i	0.808097	−	0.589049i	$-0.200497\pi$
$773$	33.7362	+	9.03958i	1.21341	+	0.325131i	0.405309	+	0.914180i	$0.367164\pi$
$774$		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
$779$	−6.03947	−	22.5396i	−0.216386	−	0.807565i
$780$		0			0
$781$	19.3663	+	5.18919i	0.692982	+	0.185684i
$782$		0			0
$783$	−21.2994			−0.761178
$784$		0			0
$785$	38.3925			1.37029
$786$		0			0
$787$	−23.5420	−	6.30807i	−0.839183	−	0.224858i	−0.186467	−	0.982461i	$-0.559704\pi$
$787$	−23.5420	−	6.30807i	−0.839183	−	0.224858i	−0.652716	+	0.757603i	$0.726370\pi$
$788$		0			0
$789$	4.90600	+	18.3094i	0.174658	+	0.651833i
$790$		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
$795$	−38.4319	−	10.2978i	−1.36304	−	0.365226i
$796$		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
$803$	−13.1199	−	48.9643i	−0.462993	−	1.72791i
$804$		0			0
$805$	−32.5693	−	28.1992i	−1.14792	−	0.993891i
$806$		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	$-0.799279\pi$
$809$	−19.9357	+	11.5099i	−0.700901	+	0.404665i	0.106782	+	0.994282i	$0.465945\pi$
$810$		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
$819$	0.664709	−	3.45611i	0.0232268	−	0.120766i
$820$		0			0
$821$	2.17857	−	0.583745i	0.0760325	−	0.0203728i	−0.220602	−	0.975364i	$-0.570802\pi$
$821$	2.17857	−	0.583745i	0.0760325	−	0.0203728i	0.296635	+	0.954991i	$0.404136\pi$
$822$		0			0
$823$	4.37272	+	7.57377i	0.152423	+	0.264005i	0.932118	−	0.362155i	$-0.117959\pi$
$823$	4.37272	+	7.57377i	0.152423	+	0.264005i	−0.779694	+	0.626160i	$0.784626\pi$
$824$		0			0
$825$	−17.3789			−0.605057
$826$		0			0
$827$	2.25129	−	2.25129i	0.0782850	−	0.0782850i	−0.666880	−	0.745165i	$-0.732371\pi$
$827$	2.25129	−	2.25129i	0.0782850	−	0.0782850i	0.745165	+	0.666880i	$0.232371\pi$
$828$		0			0
$829$	−1.67875	+	6.26518i	−0.0583054	+	0.217599i	−0.988932	−	0.148373i	$-0.952597\pi$
$829$	−1.67875	+	6.26518i	−0.0583054	+	0.217599i	0.930626	+	0.365971i	$0.119263\pi$
$830$		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
$835$	−8.66985	+	2.32308i	−0.300032	+	0.0803934i
$836$		0			0
$837$	−1.16198	+	4.33657i	−0.0401639	+	0.149894i
$838$		0			0
$839$			15.8804i			0.548253i	0.961694	+	0.274126i	$0.0883886\pi$
$839$			15.8804i			0.548253i	−0.961694	+	0.274126i	$0.911611\pi$
$840$		0			0
$841$		−	1.85175i		−	0.0638536i
$842$		0			0
$843$	12.2154	−	45.5885i	0.420721	−	1.57015i
$844$		0			0
$845$	28.7686	−	7.70853i	0.989670	−	0.265181i
$846$		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
$851$	10.2291	−	38.1754i	0.350648	−	1.30863i
$852$		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	$-0.169459\pi$
$857$	−0.256772	−	0.444743i	−0.00877118	−	0.0151921i	−0.870378	+	0.492385i	$0.836125\pi$
$858$		0			0
$859$	−20.4685	+	5.48453i	−0.698377	+	0.187130i	−0.590504	−	0.807035i	$-0.701071\pi$
$859$	−20.4685	+	5.48453i	−0.698377	+	0.187130i	−0.107874	+	0.994165i	$0.534404\pi$
$860$		0			0
$861$	19.3405	+	16.7454i	0.659122	+	0.570682i
$862$		0			0
$863$	41.4589	+	23.9363i	1.41128	+	0.814801i	0.995509	−	0.0946697i	$-0.0301795\pi$
$863$	41.4589	+	23.9363i	1.41128	+	0.814801i	0.415768	+	0.909471i	$0.363513\pi$
$864$		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
$875$	7.50174	+	21.6475i	0.253605	+	0.731818i
$876$		0			0
$877$	5.85755	+	21.8607i	0.197795	+	0.738182i	0.991525	+	0.129912i	$0.0414696\pi$
$877$	5.85755	+	21.8607i	0.197795	+	0.738182i	−0.793730	+	0.608270i	$0.791864\pi$
$878$		0			0
$879$	0.238643	−	0.137781i	0.00804923	−	0.00464722i
$880$		0			0
$881$			17.7026i			0.596417i	0.954501	+	0.298209i	$0.0963891\pi$
$881$			17.7026i			0.596417i	−0.954501	+	0.298209i	$0.903611\pi$
$882$		0			0
$883$	13.2141	+	13.2141i	0.444691	+	0.444691i	0.893585	−	0.448894i	$-0.148182\pi$
$883$	13.2141	+	13.2141i	0.444691	+	0.444691i	−0.448894	+	0.893585i	$0.648182\pi$
$884$		0			0
$885$	−4.22669	−	1.13254i	−0.142079	−	0.0380699i
$886$		0			0
$887$	44.3615	+	25.6121i	1.48951	+	0.859970i	0.999928	−	0.0119857i	$-0.00381526\pi$
$887$	44.3615	+	25.6121i	1.48951	+	0.859970i	0.489584	+	0.871956i	$0.337149\pi$
$888$		0			0
$889$	16.2362	−	33.4568i	0.544543	−	1.12211i
$890$		0			0
$891$	15.0213	+	56.0603i	0.503233	+	1.87809i
$892$		0			0
$893$	32.0581	+	8.58994i	1.07278	+	0.287452i
$894$		0			0
$895$	−8.01938			−0.268058
$896$		0			0
$897$	−15.3764			−0.513403
$898$		0			0
$899$	−6.28144	−	1.68311i	−0.209498	−	0.0561347i
$900$		0			0
$901$	5.09901	+	19.0298i	0.169873	+	0.633973i
$902$		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
$907$	−8.20711	−	2.19909i	−0.272512	−	0.0730195i	0.119975	−	0.992777i	$-0.461719\pi$
$907$	−8.20711	−	2.19909i	−0.272512	−	0.0730195i	−0.392487	+	0.919757i	$0.628385\pi$
$908$		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
$915$	−6.12359	−	22.8535i	−0.202440	−	0.755515i
$916$		0			0
$917$	−7.54884	+	39.2496i	−0.249285	+	1.29614i
$918$		0			0
$919$	17.7313	−	30.7116i	0.584903	−	1.01308i	−0.409985	−	0.912092i	$-0.634466\pi$
$919$	17.7313	−	30.7116i	0.584903	−	1.01308i	0.994888	−	0.100989i	$-0.0322006\pi$
$920$		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	−0.278290	−	0.960497i	$-0.589768\pi$
$929$	−38.0765	−	21.9835i	−1.24925	−	0.721255i	−0.970960	+	0.239242i	$0.923101\pi$
$930$		0			0
$931$	−20.4974	+	27.4260i	−0.671776	+	0.898851i
$932$		0			0
$933$	27.8361	−	7.45867i	0.911314	−	0.244186i
$934$		0			0
$935$	17.4255	+	30.1819i	0.569876	+	0.987054i
$936$		0			0
$937$	32.7634			1.07033			0.535167	−	0.844746i	$-0.320249\pi$
$937$	32.7634			1.07033			0.535167	+	0.844746i	$0.320249\pi$
$938$		0			0
$939$	38.5248	−	38.5248i	1.25721	−	1.25721i
$940$		0			0
$941$	7.93265	−	29.6051i	0.258597	−	0.965098i	−0.707457	−	0.706757i	$-0.750158\pi$
$941$	7.93265	−	29.6051i	0.258597	−	0.965098i	0.966054	−	0.258341i	$-0.0831758\pi$
$942$		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
$947$	−11.1135	+	2.97785i	−0.361140	+	0.0967672i	−0.434826	−	0.900514i	$-0.643190\pi$
$947$	−11.1135	+	2.97785i	−0.361140	+	0.0967672i	0.0736863	+	0.997281i	$0.476524\pi$
$948$		0			0
$949$	3.01139	−	11.2386i	0.0977537	−	0.364822i
$950$		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
$955$	−0.208766	+	0.779126i	−0.00675552	+	0.0252119i
$956$		0			0
$957$	−56.8764	+	15.2400i	−1.83855	+	0.492639i
$958$		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
$963$	1.51298	−	5.64652i	0.0487551	−	0.181956i
$964$		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
$971$	−29.2698	+	7.84283i	−0.939314	+	0.251688i	−0.695822	−	0.718215i	$-0.744960\pi$
$971$	−29.2698	+	7.84283i	−0.939314	+	0.251688i	−0.243492	+	0.969903i	$0.578293\pi$
$972$		0			0
$973$	−4.63059	−	13.3623i	−0.148450	−	0.428377i
$974$		0			0
$975$	−3.45453	−	1.99447i	−0.110633	−	0.0638742i
$976$		0			0
$977$	−25.1720	−	43.5992i	−0.805325	−	1.39486i	−0.916072	−	0.401015i	$-0.868658\pi$
$977$	−25.1720	−	43.5992i	−0.805325	−	1.39486i	0.110747	−	0.993849i	$-0.464676\pi$
$978$		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	−0.631496	−	0.775379i	$-0.717559\pi$
$983$	−8.64540	+	4.99143i	−0.275746	+	0.159202i	0.355750	+	0.934581i	$0.384225\pi$
$984$		0			0
$985$	−0.205529	+	0.355986i	−0.00654869	+	0.0113427i
$986$		0			0
$987$	−34.3801	+	11.9141i	−1.09433	+	0.379231i
$988$		0			0
$989$	−11.1054	−	41.4458i	−0.353130	−	1.31790i
$990$		0			0
$991$	−40.8868	+	23.6060i	−1.29881	+	0.749869i	−0.980199	−	0.198016i	$-0.936550\pi$
$991$	−40.8868	+	23.6060i	−1.29881	+	0.749869i	−0.318612	+	0.947885i	$0.603217\pi$
$992$		0			0
$993$		−	38.4959i		−	1.22163i
$994$		0			0
$995$	38.8661	+	38.8661i	1.23214	+	1.23214i
$996$		0			0
$997$	33.5965	+	9.00216i	1.06401	+	0.285101i	0.748031	−	0.663664i	$-0.230999\pi$
$997$	33.5965	+	9.00216i	1.06401	+	0.285101i	0.315982	+	0.948765i	$0.397666\pi$
$998$		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	448.2.z.a.271.3		56
4.3	odd	2		112.2.v.a.75.1	yes	56
7.3	odd	6	inner	448.2.z.a.143.3		56
8.3	odd	2		896.2.z.b.159.3		56
8.5	even	2		896.2.z.a.159.12		56
16.3	odd	4	inner	448.2.z.a.47.3		56
16.5	even	4		896.2.z.b.607.3		56
16.11	odd	4		896.2.z.a.607.12		56
16.13	even	4		112.2.v.a.19.10	yes	56
28.3	even	6		112.2.v.a.59.10	yes	56
28.11	odd	6		784.2.w.f.619.10		56
28.19	even	6		784.2.j.a.587.18		56
28.23	odd	6		784.2.j.a.587.17		56
28.27	even	2		784.2.w.f.411.1		56
56.3	even	6		896.2.z.b.31.3		56
56.45	odd	6		896.2.z.a.31.12		56
112.3	even	12	inner	448.2.z.a.367.3		56
112.13	odd	4		784.2.w.f.19.10		56
112.45	odd	12		112.2.v.a.3.1	✓	56
112.59	even	12		896.2.z.a.479.12		56
112.61	odd	12		784.2.j.a.195.17		56
112.93	even	12		784.2.j.a.195.18		56
112.101	odd	12		896.2.z.b.479.3		56
112.109	even	12		784.2.w.f.227.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.1	✓	56	112.45	odd	12
112.2.v.a.19.10	yes	56	16.13	even	4
112.2.v.a.59.10	yes	56	28.3	even	6
112.2.v.a.75.1	yes	56	4.3	odd	2
448.2.z.a.47.3		56	16.3	odd	4	inner
448.2.z.a.143.3		56	7.3	odd	6	inner
448.2.z.a.271.3		56	1.1	even	1	trivial
448.2.z.a.367.3		56	112.3	even	12	inner
784.2.j.a.195.17		56	112.61	odd	12
784.2.j.a.195.18		56	112.93	even	12
784.2.j.a.587.17		56	28.23	odd	6
784.2.j.a.587.18		56	28.19	even	6
784.2.w.f.19.10		56	112.13	odd	4
784.2.w.f.227.1		56	112.109	even	12
784.2.w.f.411.1		56	28.27	even	2
784.2.w.f.619.10		56	28.11	odd	6
896.2.z.a.31.12		56	56.45	odd	6
896.2.z.a.159.12		56	8.5	even	2
896.2.z.a.479.12		56	112.59	even	12
896.2.z.a.607.12		56	16.11	odd	4
896.2.z.b.31.3		56	56.3	even	6
896.2.z.b.159.3		56	8.3	odd	2
896.2.z.b.479.3		56	112.101	odd	12
896.2.z.b.607.3		56	16.5	even	4

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.z (of order \(12\), degree \(4\), not minimal)

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