LMFDB - Embedded newform 448.3.o.b.415.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,3,Mod(95,448)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("448.95"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	448.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2071158433$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 34 x^{18} + 755 x^{16} - 9698 x^{14} + 89921 x^{12} - 522048 x^{10} + 2189920 x^{8} + \cdots + 7311616 $ x^20 - 34x^18 + 755x^16 - 9698x^14 + 89921x^12 - 522048x^10 + 2189920x^8 - 5640416x^6 + 10423552x^4 - 10729472*x^2 + 7311616
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.9
Root			$2.85584 + 1.64882i$ of defining polynomial
Character	$\chi$	$=$	448.415
Dual form			448.3.o.b.95.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.20080 + 3.81190i) q^{3} +(3.13426 + 1.80957i) q^{5} +(-4.05500 + 5.70587i) q^{7} +(-5.18704 + 8.98421i) q^{9} +(1.85420 + 3.21157i) q^{11} -15.5806i q^{13} +15.9300i q^{15} +(14.3108 + 24.7871i) q^{17} +(-15.0096 + 25.9974i) q^{19} +(-30.6744 - 2.89977i) q^{21} +(-11.3062 - 6.52765i) q^{23} +(-5.95093 - 10.3073i) q^{25} -6.04813 q^{27} -8.55364i q^{29} +(13.2292 - 7.63786i) q^{31} +(-8.16146 + 14.1361i) q^{33} +(-23.0346 + 10.5459i) q^{35} +(-30.2785 - 17.4813i) q^{37} +(59.3918 - 34.2899i) q^{39} -0.875858 q^{41} +33.4932 q^{43} +(-32.5151 + 18.7726i) q^{45} +(76.1422 + 43.9607i) q^{47} +(-16.1139 - 46.2746i) q^{49} +(-62.9905 + 109.103i) q^{51} +(-19.2041 + 11.0875i) q^{53} +13.4212i q^{55} -132.132 q^{57} +(-48.9999 - 84.8704i) q^{59} +(-34.7686 - 20.0736i) q^{61} +(-30.2293 - 66.0276i) q^{63} +(28.1942 - 48.8338i) q^{65} +(7.33119 + 12.6980i) q^{67} -57.4642i q^{69} +112.733i q^{71} +(56.4171 + 97.7174i) q^{73} +(26.1936 - 45.3686i) q^{75} +(-25.8436 - 2.44310i) q^{77} +(-56.0478 - 32.3592i) q^{79} +(33.3726 + 57.8031i) q^{81} +58.2311 q^{83} +103.586i q^{85} +(32.6056 - 18.8248i) q^{87} +(-22.2291 + 38.5019i) q^{89} +(88.9011 + 63.1795i) q^{91} +(58.2295 + 33.6188i) q^{93} +(-94.0881 + 54.3218i) q^{95} +166.677 q^{97} -38.4713 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{5} - 28 q^{9} + 46 q^{17} - 114 q^{21} + 36 q^{25} + 94 q^{33} + 114 q^{37} - 160 q^{41} - 708 q^{45} - 92 q^{49} - 6 q^{53} + 308 q^{57} + 90 q^{61} + 212 q^{65} + 314 q^{73} - 198 q^{77} - 322 q^{81}+ \cdots - 224 q^{97}+O(q^{100}) $ 20 * q + 6 * q^5 - 28 * q^9 + 46 * q^17 - 114 * q^21 + 36 * q^25 + 94 * q^33 + 114 * q^37 - 160 * q^41 - 708 * q^45 - 92 * q^49 - 6 * q^53 + 308 * q^57 + 90 * q^61 + 212 * q^65 + 314 * q^73 - 198 * q^77 - 322 * q^81 - 206 * q^89 + 1530 * q^93 - 224 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.20080	+	3.81190i	0.733600	+	1.27063i	0.955335	+	0.295525i	$0.0954947\pi$
$3$	2.20080	+	3.81190i	0.733600	+	1.27063i	−0.221735	+	0.975107i	$0.571172\pi$
$4$		0			0
$5$	3.13426	+	1.80957i	0.626853	+	0.361914i	0.779532	−	0.626362i	$-0.215457\pi$
$5$	3.13426	+	1.80957i	0.626853	+	0.361914i	−0.152679	+	0.988276i	$0.548790\pi$
$6$		0			0
$7$	−4.05500	+	5.70587i	−0.579286	+	0.815124i
$7$	−4.05500	+	5.70587i	−0.579286	+	0.815124i
$8$		0			0
$9$	−5.18704	+	8.98421i	−0.576337	+	0.998246i
$10$		0			0
$11$	1.85420	+	3.21157i	0.168564	+	0.291961i	0.937915	−	0.346865i	$-0.112754\pi$
$11$	1.85420	+	3.21157i	0.168564	+	0.291961i	−0.769351	+	0.638826i	$0.779420\pi$
$12$		0			0
$13$		−	15.5806i		−	1.19851i	−0.800558	−	0.599255i	$-0.795463\pi$
$13$		−	15.5806i		−	1.19851i	0.800558	−	0.599255i	$-0.204537\pi$
$14$		0			0
$15$			15.9300i			1.06200i
$16$		0			0
$17$	14.3108	+	24.7871i	0.841814	+	1.45806i	0.888360	+	0.459148i	$0.151845\pi$
$17$	14.3108	+	24.7871i	0.841814	+	1.45806i	−0.0465463	+	0.998916i	$0.514822\pi$
$18$		0			0
$19$	−15.0096	+	25.9974i	−0.789979	+	1.36828i	0.136000	+	0.990709i	$0.456575\pi$
$19$	−15.0096	+	25.9974i	−0.789979	+	1.36828i	−0.925979	+	0.377575i	$0.876758\pi$
$20$		0			0
$21$	−30.6744	−	2.89977i	−1.46069	−	0.138085i
$22$		0			0
$23$	−11.3062	−	6.52765i	−0.491575	−	0.283811i	0.233653	−	0.972320i	$-0.424932\pi$
$23$	−11.3062	−	6.52765i	−0.491575	−	0.283811i	−0.725228	+	0.688509i	$0.758265\pi$
$24$		0			0
$25$	−5.95093	−	10.3073i	−0.238037	−	0.412292i
$26$		0			0
$27$	−6.04813			−0.224005
$28$		0			0
$29$		−	8.55364i		−	0.294953i	−0.989066	−	0.147476i	$-0.952885\pi$
$29$		−	8.55364i		−	0.294953i	0.989066	−	0.147476i	$-0.0471151\pi$
$30$		0			0
$31$	13.2292	−	7.63786i	0.426747	−	0.246383i	−0.271213	−	0.962519i	$-0.587425\pi$
$31$	13.2292	−	7.63786i	0.426747	−	0.246383i	0.697960	+	0.716137i	$0.254091\pi$
$32$		0			0
$33$	−8.16146	+	14.1361i	−0.247317	+	0.428365i
$34$		0			0
$35$	−23.0346	+	10.5459i	−0.658132	+	0.301311i
$36$		0			0
$37$	−30.2785	−	17.4813i	−0.818337	−	0.472467i	0.0315058	−	0.999504i	$-0.489970\pi$
$37$	−30.2785	−	17.4813i	−0.818337	−	0.472467i	−0.849843	+	0.527037i	$0.823303\pi$
$38$		0			0
$39$	59.3918	−	34.2899i	1.52287	−	0.879227i
$40$		0			0
$41$	−0.875858			−0.0213624			−0.0106812	−	0.999943i	$-0.503400\pi$
$41$	−0.875858			−0.0213624			−0.0106812	+	0.999943i	$0.503400\pi$
$42$		0			0
$43$	33.4932			0.778912			0.389456	−	0.921045i	$-0.372663\pi$
$43$	33.4932			0.778912			0.389456	+	0.921045i	$0.372663\pi$
$44$		0			0
$45$	−32.5151	+	18.7726i	−0.722557	+	0.417169i
$46$		0			0
$47$	76.1422	+	43.9607i	1.62005	+	0.935335i	0.986906	+	0.161299i	$0.0515682\pi$
$47$	76.1422	+	43.9607i	1.62005	+	0.935335i	0.633142	+	0.774036i	$0.281765\pi$
$48$		0			0
$49$	−16.1139	−	46.2746i	−0.328855	−	0.944380i
$50$		0			0
$51$	−62.9905	+	109.103i	−1.23511	+	2.13927i
$52$		0			0
$53$	−19.2041	+	11.0875i	−0.362341	+	0.209198i	−0.670107	−	0.742264i	$-0.733752\pi$
$53$	−19.2041	+	11.0875i	−0.362341	+	0.209198i	0.307766	+	0.951462i	$0.400419\pi$
$54$		0			0
$55$			13.4212i			0.244022i
$56$		0			0
$57$	−132.132			−2.31811
$58$		0			0
$59$	−48.9999	−	84.8704i	−0.830507	−	1.43848i	−0.897636	−	0.440737i	$-0.854717\pi$
$59$	−48.9999	−	84.8704i	−0.830507	−	1.43848i	0.0671290	−	0.997744i	$-0.478616\pi$
$60$		0			0
$61$	−34.7686	−	20.0736i	−0.569977	−	0.329076i	0.187163	−	0.982329i	$-0.440071\pi$
$61$	−34.7686	−	20.0736i	−0.569977	−	0.329076i	−0.757140	+	0.653253i	$0.773404\pi$
$62$		0			0
$63$	−30.2293	−	66.0276i	−0.479830	−	1.04806i
$64$		0			0
$65$	28.1942	−	48.8338i	0.433757	−	0.751290i
$66$		0			0
$67$	7.33119	+	12.6980i	0.109421	+	0.189522i	0.915536	−	0.402237i	$-0.131767\pi$
$67$	7.33119	+	12.6980i	0.109421	+	0.189522i	−0.806115	+	0.591759i	$0.798434\pi$
$68$		0			0
$69$		−	57.4642i		−	0.832815i
$70$		0			0
$71$			112.733i			1.58779i	0.608055	+	0.793895i	$0.291950\pi$
$71$			112.733i			1.58779i	−0.608055	+	0.793895i	$0.708050\pi$
$72$		0			0
$73$	56.4171	+	97.7174i	0.772838	+	1.33859i	0.936002	+	0.351995i	$0.114497\pi$
$73$	56.4171	+	97.7174i	0.772838	+	1.33859i	−0.163164	+	0.986599i	$0.552170\pi$
$74$		0			0
$75$	26.1936	−	45.3686i	0.349248	−	0.604915i
$76$		0			0
$77$	−25.8436	−	2.44310i	−0.335631	−	0.0317286i
$78$		0			0
$79$	−56.0478	−	32.3592i	−0.709466	−	0.409611i	0.101397	−	0.994846i	$-0.467669\pi$
$79$	−56.0478	−	32.3592i	−0.709466	−	0.409611i	−0.810863	+	0.585235i	$0.801002\pi$
$80$		0			0
$81$	33.3726	+	57.8031i	0.412008	+	0.713618i
$82$		0			0
$83$	58.2311			0.701580			0.350790	−	0.936454i	$-0.385913\pi$
$83$	58.2311			0.701580			0.350790	+	0.936454i	$0.385913\pi$
$84$		0			0
$85$			103.586i			1.21866i
$86$		0			0
$87$	32.6056	−	18.8248i	0.374777	−	0.216377i
$88$		0			0
$89$	−22.2291	+	38.5019i	−0.249765	+	0.432606i	−0.963461	−	0.267850i	$-0.913687\pi$
$89$	−22.2291	+	38.5019i	−0.249765	+	0.432606i	0.713696	+	0.700456i	$0.247020\pi$
$90$		0			0
$91$	88.9011	+	63.1795i	0.976935	+	0.694281i
$92$		0			0
$93$	58.2295	+	33.6188i	0.626123	+	0.361492i
$94$		0			0
$95$	−94.0881	+	54.3218i	−0.990401	+	0.571808i
$96$		0			0
$97$	166.677			1.71832			0.859159	−	0.511708i	$-0.170987\pi$
$97$	166.677			1.71832			0.859159	+	0.511708i	$0.170987\pi$
$98$		0			0
$99$	−38.4713			−0.388599
$100$		0			0
$101$	99.2204	−	57.2849i	0.982380	−	0.567178i	0.0793924	−	0.996843i	$-0.474702\pi$
$101$	99.2204	−	57.2849i	0.982380	−	0.567178i	0.902988	+	0.429666i	$0.141369\pi$
$102$		0			0
$103$	−17.3025	−	9.98959i	−0.167985	−	0.0969863i	0.413650	−	0.910436i	$-0.364254\pi$
$103$	−17.3025	−	9.98959i	−0.167985	−	0.0969863i	−0.581635	+	0.813450i	$0.697587\pi$
$104$		0			0
$105$	−90.8944	−	64.5961i	−0.865661	−	0.615201i
$106$		0			0
$107$	−18.5115	+	32.0628i	−0.173005	+	0.299653i	−0.939469	−	0.342634i	$-0.888681\pi$
$107$	−18.5115	+	32.0628i	−0.173005	+	0.299653i	0.766464	+	0.642287i	$0.222014\pi$
$108$		0			0
$109$	116.968	−	67.5313i	1.07310	−	0.619553i	0.144072	−	0.989567i	$-0.453980\pi$
$109$	116.968	−	67.5313i	1.07310	−	0.619553i	0.929026	+	0.370014i	$0.120647\pi$
$110$		0			0
$111$		−	153.891i		−	1.38641i
$112$		0			0
$113$	87.7541			0.776585			0.388293	−	0.921536i	$-0.373065\pi$
$113$	87.7541			0.776585			0.388293	+	0.921536i	$0.373065\pi$
$114$		0			0
$115$	−23.6245	−	40.9188i	−0.205430	−	0.355815i
$116$		0			0
$117$	139.980	+	80.8174i	1.19641	+	0.690747i
$118$		0			0
$119$	−199.462	−	18.8560i	−1.67615	−	0.158453i
$120$		0			0
$121$	53.6239	−	92.8793i	0.443172	−	0.767597i
$122$		0			0
$123$	−1.92759	−	3.33868i	−0.0156715	−	0.0271438i
$124$		0			0
$125$		−	133.553i		−	1.06842i
$126$		0			0
$127$			209.424i			1.64901i	0.565853	+	0.824506i	$0.308547\pi$
$127$			209.424i			1.64901i	−0.565853	+	0.824506i	$0.691453\pi$
$128$		0			0
$129$	73.7118	+	127.673i	0.571410	+	0.989711i
$130$		0			0
$131$	76.5681	−	132.620i	0.584489	−	1.01236i	−0.410450	−	0.911883i	$-0.634628\pi$
$131$	76.5681	−	132.620i	0.584489	−	1.01236i	0.994939	−	0.100481i	$-0.0320383\pi$
$132$		0			0
$133$	−87.4738	−	191.062i	−0.657697	−	1.43656i
$134$		0			0
$135$	−18.9564	−	10.9445i	−0.140418	−	0.0810703i
$136$		0			0
$137$	−74.8701	−	129.679i	−0.546497	−	0.946561i	−0.998511	−	0.0545502i	$-0.982628\pi$
$137$	−74.8701	−	129.679i	−0.546497	−	0.946561i	0.452014	−	0.892011i	$-0.350706\pi$
$138$		0			0
$139$	−4.60976			−0.0331637			−0.0165819	−	0.999863i	$-0.505278\pi$
$139$	−4.60976			−0.0331637			−0.0165819	+	0.999863i	$0.505278\pi$
$140$		0			0
$141$			386.995i			2.74465i
$142$		0			0
$143$	50.0384	−	28.8897i	0.349919	−	0.202026i
$144$		0			0
$145$	15.4784	−	26.8093i	0.106747	−	0.184892i
$146$		0			0
$147$	140.931	−	163.266i	0.958712	−	1.11065i
$148$		0			0
$149$	228.911	+	132.162i	1.53632	+	0.886992i	0.999050	+	0.0435793i	$0.0138761\pi$
$149$	228.911	+	132.162i	1.53632	+	0.886992i	0.537266	+	0.843413i	$0.319457\pi$
$150$		0			0
$151$	134.864	−	77.8638i	0.893139	−	0.515654i	0.0181710	−	0.999835i	$-0.494216\pi$
$151$	134.864	−	77.8638i	0.893139	−	0.515654i	0.874968	+	0.484181i	$0.160882\pi$
$152$		0			0
$153$	−296.923			−1.94067
$154$		0			0
$155$	55.2849			0.356677
$156$		0			0
$157$	−136.001	+	78.5200i	−0.866246	+	0.500128i	−0.866099	−	0.499872i	$-0.833380\pi$
$157$	−136.001	+	78.5200i	−0.866246	+	0.500128i	−0.000147402		1.00000i	$0.500047\pi$
$158$		0			0
$159$	−84.5287	−	48.8027i	−0.531627	−	0.306935i
$160$		0			0
$161$	83.0927	−	38.0422i	0.516104	−	0.236287i
$162$		0			0
$163$	68.2863	−	118.275i	0.418934	−	0.725615i	−0.576898	−	0.816816i	$-0.695737\pi$
$163$	68.2863	−	118.275i	0.418934	−	0.725615i	0.995833	+	0.0912008i	$0.0290705\pi$
$164$		0			0
$165$	−51.1603	+	29.5374i	−0.310063	+	0.179015i
$166$		0			0
$167$		−	95.3243i		−	0.570804i	−0.958408	−	0.285402i	$-0.907873\pi$
$167$		−	95.3243i		−	0.570804i	0.958408	−	0.285402i	$-0.0921272\pi$
$168$		0			0
$169$	−73.7564			−0.436428
$170$		0			0
$171$	−155.711	−	269.699i	−0.910589	−	1.57719i
$172$		0			0
$173$	57.9376	+	33.4503i	0.334900	+	0.193354i	0.658014	−	0.753005i	$-0.271397\pi$
$173$	57.9376	+	33.4503i	0.334900	+	0.193354i	−0.323115	+	0.946360i	$0.604730\pi$
$174$		0			0
$175$	82.9432	+	7.84094i	0.473961	+	0.0448054i
$176$		0			0
$177$	215.678	−	373.565i	1.21852	−	2.11054i
$178$		0			0
$179$	−60.9834	−	105.626i	−0.340689	−	0.590091i	0.643872	−	0.765134i	$-0.277327\pi$
$179$	−60.9834	−	105.626i	−0.340689	−	0.590091i	−0.984561	+	0.175042i	$0.943994\pi$
$180$		0			0
$181$			185.859i			1.02685i	0.858136	+	0.513423i	$0.171623\pi$
$181$			185.859i			1.02685i	−0.858136	+	0.513423i	$0.828377\pi$
$182$		0			0
$183$		−	176.712i		−	0.965641i
$184$		0			0
$185$	−63.2671	−	109.582i	−0.341984	−	0.592334i
$186$		0			0
$187$	−53.0704	+	91.9206i	−0.283799	+	0.491554i
$188$		0			0
$189$	24.5252	−	34.5098i	0.129763	−	0.182592i
$190$		0			0
$191$	95.0890	+	54.8997i	0.497848	+	0.287433i	0.727825	−	0.685763i	$-0.240532\pi$
$191$	95.0890	+	54.8997i	0.497848	+	0.287433i	−0.229976	+	0.973196i	$0.573865\pi$
$192$		0			0
$193$	−10.9970	−	19.0474i	−0.0569794	−	0.0986912i	0.836129	−	0.548533i	$-0.184814\pi$
$193$	−10.9970	−	19.0474i	−0.0569794	−	0.0986912i	−0.893108	+	0.449842i	$0.851480\pi$
$194$		0			0
$195$	248.199			1.27282
$196$		0			0
$197$		−	336.582i		−	1.70854i	−0.519830	−	0.854270i	$-0.674005\pi$
$197$		−	336.582i		−	1.70854i	0.519830	−	0.854270i	$-0.325995\pi$
$198$		0			0
$199$	−200.150	+	115.556i	−1.00578	+	0.580686i	−0.909952	−	0.414713i	$-0.863882\pi$
$199$	−200.150	+	115.556i	−1.00578	+	0.580686i	−0.0958246	+	0.995398i	$0.530549\pi$
$200$		0			0
$201$	−32.2689	+	55.8915i	−0.160542	+	0.278067i
$202$		0			0
$203$	48.8059	+	34.6850i	0.240423	+	0.170862i
$204$		0			0
$205$	−2.74517	−	1.58493i	−0.0133911	−	0.00773134i
$206$		0			0
$207$	117.292	−	67.7183i	0.566626	−	0.327142i
$208$		0			0
$209$	−111.323			−0.532648
$210$		0			0
$211$	−63.2914			−0.299959			−0.149980	−	0.988689i	$-0.547921\pi$
$211$	−63.2914			−0.299959			−0.149980	+	0.988689i	$0.547921\pi$
$212$		0			0
$213$	−429.727	+	248.103i	−2.01750	+	1.16480i
$214$		0			0
$215$	104.977	+	60.6082i	0.488263	+	0.281899i
$216$		0			0
$217$	−10.0636	+	106.455i	−0.0463763	+	0.490578i
$218$		0			0
$219$	−248.326	+	430.113i	−1.13391	+	1.96398i
$220$		0			0
$221$	386.199	−	222.972i	1.74751	−	1.00892i
$222$		0			0
$223$		−	128.029i		−	0.574121i	−0.957912	−	0.287061i	$-0.907322\pi$
$223$		−	128.029i		−	0.574121i	0.957912	−	0.287061i	$-0.0926782\pi$
$224$		0			0
$225$	123.471			0.548759
$226$		0			0
$227$	−198.452	−	343.728i	−0.874236	−	1.51422i	−0.857574	−	0.514361i	$-0.828029\pi$
$227$	−198.452	−	343.728i	−0.874236	−	1.51422i	−0.0166626	−	0.999861i	$-0.505304\pi$
$228$		0			0
$229$	180.192	+	104.034i	0.786864	+	0.454296i	0.838857	−	0.544351i	$-0.183224\pi$
$229$	180.192	+	104.034i	0.786864	+	0.454296i	−0.0519935	+	0.998647i	$0.516558\pi$
$230$		0			0
$231$	−47.5638	−	103.890i	−0.205904	−	0.449740i
$232$		0			0
$233$	−74.0856	+	128.320i	−0.317964	+	0.550729i	−0.980063	−	0.198687i	$-0.936332\pi$
$233$	−74.0856	+	128.320i	−0.317964	+	0.550729i	0.662099	+	0.749416i	$0.269666\pi$
$234$		0			0
$235$	159.100	+	275.569i	0.677021	+	1.17263i
$236$		0			0
$237$		−	284.865i		−	1.20196i
$238$		0			0
$239$		−	13.6048i		−	0.0569240i	−0.999595	−	0.0284620i	$-0.990939\pi$
$239$		−	13.6048i		−	0.0569240i	0.999595	−	0.0284620i	$-0.00906096\pi$
$240$		0			0
$241$	145.570	+	252.135i	0.604026	+	1.04620i	0.992205	+	0.124620i	$0.0397711\pi$
$241$	145.570	+	252.135i	0.604026	+	1.04620i	−0.388179	+	0.921584i	$0.626896\pi$
$242$		0			0
$243$	−174.109	+	301.566i	−0.716500	+	1.24101i
$244$		0			0
$245$	33.2319	−	174.196i	0.135640	−	0.711005i
$246$		0			0
$247$	405.056	+	233.859i	1.63990	+	0.946798i
$248$		0			0
$249$	128.155	+	221.971i	0.514679	+	0.891450i
$250$		0			0
$251$	122.061			0.486300			0.243150	−	0.969989i	$-0.421819\pi$
$251$	122.061			0.486300			0.243150	+	0.969989i	$0.421819\pi$
$252$		0			0
$253$		−	48.4144i		−	0.191361i
$254$		0			0
$255$	−394.858	+	227.971i	−1.54846	+	0.894005i
$256$		0			0
$257$	176.424	−	305.575i	0.686473	−	1.18901i	−0.286499	−	0.958081i	$-0.592491\pi$
$257$	176.424	−	305.575i	0.686473	−	1.18901i	0.972971	−	0.230925i	$-0.0741753\pi$
$258$		0			0
$259$	222.525	−	101.878i	0.859170	−	0.393353i
$260$		0			0
$261$	76.8477	+	44.3680i	0.294436	+	0.169992i
$262$		0			0
$263$	−364.152	+	210.243i	−1.38461	+	0.799404i	−0.992701	−	0.120601i	$-0.961518\pi$
$263$	−364.152	+	210.243i	−1.38461	+	0.799404i	−0.391907	+	0.920005i	$0.628185\pi$
$264$		0			0
$265$	−80.2542			−0.302846
$266$		0			0
$267$	−195.687			−0.732910
$268$		0			0
$269$	−246.913	+	142.556i	−0.917894	+	0.529946i	−0.882963	−	0.469443i	$-0.844455\pi$
$269$	−246.913	+	142.556i	−0.917894	+	0.529946i	−0.0349314	+	0.999390i	$0.511121\pi$
$270$		0			0
$271$	−149.590	−	86.3658i	−0.551993	−	0.318693i	0.197933	−	0.980216i	$-0.436577\pi$
$271$	−149.590	−	86.3658i	−0.551993	−	0.318693i	−0.749925	+	0.661523i	$0.769911\pi$
$272$		0			0
$273$	−45.1803	+	477.927i	−0.165496	+	1.75065i
$274$		0			0
$275$	22.0685	−	38.2237i	0.0802489	−	0.138995i
$276$		0			0
$277$	−343.551	+	198.349i	−1.24026	+	0.716063i	−0.969146	−	0.246486i	$-0.920724\pi$
$277$	−343.551	+	198.349i	−1.24026	+	0.716063i	−0.271110	+	0.962548i	$0.587391\pi$
$278$		0			0
$279$			158.471i			0.567998i
$280$		0			0
$281$	184.273			0.655774			0.327887	−	0.944717i	$-0.393663\pi$
$281$	184.273			0.655774			0.327887	+	0.944717i	$0.393663\pi$
$282$		0			0
$283$	27.8791	+	48.2881i	0.0985129	+	0.170629i	0.911069	−	0.412253i	$-0.135258\pi$
$283$	27.8791	+	48.2881i	0.0985129	+	0.170629i	−0.812556	+	0.582883i	$0.801925\pi$
$284$		0			0
$285$	−414.138	−	239.103i	−1.45312	−	0.838957i
$286$		0			0
$287$	3.55161	−	4.99753i	0.0123749	−	0.0174130i
$288$		0			0
$289$	−265.100	+	459.166i	−0.917300	+	1.58881i
$290$		0			0
$291$	366.822	+	635.355i	1.26056	+	2.18335i
$292$		0			0
$293$		−	313.145i		−	1.06875i	−0.845246	−	0.534377i	$-0.820546\pi$
$293$		−	313.145i		−	1.06875i	0.845246	−	0.534377i	$-0.179454\pi$
$294$		0			0
$295$		−	354.675i		−	1.20229i
$296$		0			0
$297$	−11.2145	−	19.4240i	−0.0377591	−	0.0654007i
$298$		0			0
$299$	−101.705	+	176.158i	−0.340150	+	0.589158i
$300$		0			0
$301$	−135.815	+	191.108i	−0.451213	+	0.634910i
$302$		0			0
$303$	436.728	+	252.145i	1.44135	+	0.832163i
$304$		0			0
$305$	−72.6493	−	125.832i	−0.238194	−	0.412565i
$306$		0			0
$307$	18.7354			0.0610272			0.0305136	−	0.999534i	$-0.490286\pi$
$307$	18.7354			0.0610272			0.0305136	+	0.999534i	$0.490286\pi$
$308$		0			0
$309$		−	87.9403i		−	0.284597i
$310$		0			0
$311$	−192.773	+	111.298i	−0.619849	+	0.357870i	−0.776810	−	0.629735i	$-0.783164\pi$
$311$	−192.773	+	111.298i	−0.619849	+	0.357870i	0.156961	+	0.987605i	$0.449830\pi$
$312$		0			0
$313$	−41.0509	+	71.1022i	−0.131153	+	0.227164i	−0.924121	−	0.382099i	$-0.875201\pi$
$313$	−41.0509	+	71.1022i	−0.131153	+	0.227164i	0.792968	+	0.609263i	$0.208535\pi$
$314$		0			0
$315$	24.7348	−	261.650i	0.0785231	−	0.830634i
$316$		0			0
$317$	123.479	+	71.2906i	0.389523	+	0.224891i	0.681954	−	0.731395i	$-0.261131\pi$
$317$	123.479	+	71.2906i	0.389523	+	0.224891i	−0.292430	+	0.956287i	$0.594464\pi$
$318$		0			0
$319$	27.4706	−	15.8602i	0.0861148	−	0.0497184i
$320$		0			0
$321$	−162.960			−0.507664
$322$		0			0
$323$	−859.199			−2.66006
$324$		0			0
$325$	−160.594	+	92.7193i	−0.494137	+	0.285290i
$326$		0			0
$327$	514.845	+	297.246i	1.57445	+	0.909008i
$328$		0			0
$329$	−559.591	+	256.197i	−1.70088	+	0.778713i
$330$		0			0
$331$	−104.981	+	181.832i	−0.317163	+	0.549342i	−0.979895	−	0.199514i	$-0.936064\pi$
$331$	−104.981	+	181.832i	−0.317163	+	0.549342i	0.662732	+	0.748857i	$0.269397\pi$
$332$		0			0
$333$	314.111	−	181.352i	0.943276	−	0.544601i
$334$		0			0
$335$			53.0651i			0.158403i
$336$		0			0
$337$	422.518			1.25376			0.626881	−	0.779115i	$-0.284331\pi$
$337$	422.518			1.25376			0.626881	+	0.779115i	$0.284331\pi$
$338$		0			0
$339$	193.129	+	334.510i	0.569703	+	0.986754i
$340$		0			0
$341$	49.0591	+	28.3243i	0.143868	+	0.0830624i
$342$		0			0
$343$	329.379	+	95.6999i	0.960289	+	0.279008i
$344$		0			0
$345$	103.985	−	180.108i	0.301407	−	0.522052i
$346$		0			0
$347$	−210.317	−	364.280i	−0.606101	−	1.04980i	−0.991876	−	0.127205i	$-0.959399\pi$
$347$	−210.317	−	364.280i	−0.606101	−	1.04980i	0.385775	−	0.922593i	$-0.373934\pi$
$348$		0			0
$349$		−	256.210i		−	0.734126i	−0.930196	−	0.367063i	$-0.880363\pi$
$349$		−	256.210i		−	0.734126i	0.930196	−	0.367063i	$-0.119637\pi$
$350$		0			0
$351$			94.2337i			0.268472i
$352$		0			0
$353$	−230.942	−	400.003i	−0.654226	−	1.13315i	−0.982087	−	0.188426i	$-0.939661\pi$
$353$	−230.942	−	400.003i	−0.654226	−	1.13315i	0.327862	−	0.944726i	$-0.393672\pi$
$354$		0			0
$355$	−203.998	+	353.335i	−0.574643	+	0.995311i
$356$		0			0
$357$	−367.100	−	801.828i	−1.02829	−	2.24602i
$358$		0			0
$359$	−103.906	−	59.9900i	−0.289431	−	0.167103i	0.348254	−	0.937400i	$-0.386775\pi$
$359$	−103.906	−	59.9900i	−0.289431	−	0.167103i	−0.637685	+	0.770297i	$0.720108\pi$
$360$		0			0
$361$	−270.076	−	467.786i	−0.748133	−	1.29581i
$362$		0			0
$363$	472.061			1.30044
$364$		0			0
$365$			408.363i			1.11880i
$366$		0			0
$367$	280.223	−	161.787i	0.763551	−	0.440836i	−0.0670185	−	0.997752i	$-0.521349\pi$
$367$	280.223	−	161.787i	0.763551	−	0.440836i	0.830569	+	0.556916i	$0.188015\pi$
$368$		0			0
$369$	4.54311	−	7.86890i	0.0123120	−	0.0213249i
$370$		0			0
$371$	14.6089	−	154.536i	0.0393770	−	0.416539i
$372$		0			0
$373$	395.712	+	228.465i	1.06089	+	0.612506i	0.925679	−	0.378311i	$-0.123495\pi$
$373$	395.712	+	228.465i	1.06089	+	0.612506i	0.135213	+	0.990817i	$0.456828\pi$
$374$		0			0
$375$	509.090	−	293.923i	1.35757	−	0.783795i
$376$		0			0
$377$	−133.271			−0.353504
$378$		0			0
$379$	−82.7835			−0.218426			−0.109213	−	0.994018i	$-0.534833\pi$
$379$	−82.7835			−0.218426			−0.109213	+	0.994018i	$0.534833\pi$
$380$		0			0
$381$	−798.304	+	460.901i	−2.09529	+	1.20971i
$382$		0			0
$383$	−531.521	−	306.874i	−1.38778	−	0.801237i	−0.394718	−	0.918802i	$-0.629158\pi$
$383$	−531.521	−	306.874i	−1.38778	−	0.801237i	−0.993065	+	0.117565i	$0.962491\pi$
$384$		0			0
$385$	−76.5798	−	54.4231i	−0.198909	−	0.141359i
$386$		0			0
$387$	−173.731	+	300.910i	−0.448916	+	0.777546i
$388$		0			0
$389$	−390.184	+	225.273i	−1.00304	+	0.579108i	−0.909148	−	0.416474i	$-0.863266\pi$
$389$	−390.184	+	225.273i	−1.00304	+	0.579108i	−0.0938970	+	0.995582i	$0.529932\pi$
$390$		0			0
$391$		−	373.664i		−	0.955663i
$392$		0			0
$393$	674.044			1.71512
$394$		0			0
$395$	−117.112	−	202.845i	−0.296487	−	0.513531i
$396$		0			0
$397$	−511.270	−	295.182i	−1.28783	−	0.743532i	−0.309567	−	0.950878i	$-0.600184\pi$
$397$	−511.270	−	295.182i	−1.28783	−	0.743532i	−0.978268	+	0.207346i	$0.933517\pi$
$398$		0			0
$399$	535.798	−	753.931i	1.34285	−	1.88955i
$400$		0			0
$401$	−27.6472	+	47.8864i	−0.0689457	+	0.119417i	−0.898437	−	0.439101i	$-0.855297\pi$
$401$	−27.6472	+	47.8864i	−0.0689457	+	0.119417i	0.829492	+	0.558519i	$0.188630\pi$
$402$		0			0
$403$	−119.003	−	206.119i	−0.295292	−	0.511461i
$404$		0			0
$405$			241.560i			0.596445i
$406$		0			0
$407$		−	129.655i		−	0.318564i
$408$		0			0
$409$	46.3157	+	80.2212i	0.113241	+	0.196140i	0.917075	−	0.398714i	$-0.130543\pi$
$409$	46.3157	+	80.2212i	0.113241	+	0.196140i	−0.803834	+	0.594854i	$0.797210\pi$
$410$		0			0
$411$	329.548	−	570.794i	0.801821	−	1.38879i
$412$		0			0
$413$	682.954	+	64.5623i	1.65364	+	0.156325i
$414$		0			0
$415$	182.512	+	105.373i	0.439787	+	0.253911i
$416$		0			0
$417$	−10.1452	−	17.5719i	−0.0243289	−	0.0421389i
$418$		0			0
$419$	−342.855			−0.818270			−0.409135	−	0.912474i	$-0.634170\pi$
$419$	−342.855			−0.818270			−0.409135	+	0.912474i	$0.634170\pi$
$420$		0			0
$421$		−	147.685i		−	0.350795i	−0.984498	−	0.175398i	$-0.943879\pi$
$421$		−	147.685i		−	0.350795i	0.984498	−	0.175398i	$-0.0561211\pi$
$422$		0			0
$423$	−789.905	+	456.052i	−1.86739	+	1.07814i
$424$		0			0
$425$	170.325	−	295.012i	0.400766	−	0.694147i
$426$		0			0
$427$	255.524	−	116.986i	0.598418	−	0.273973i
$428$		0			0
$429$	220.249	+	127.161i	0.513401	+	0.296412i
$430$		0			0
$431$	68.9402	−	39.8027i	0.159954	−	0.0923495i	−0.417886	−	0.908499i	$-0.637229\pi$
$431$	68.9402	−	39.8027i	0.159954	−	0.0923495i	0.577840	+	0.816150i	$0.303896\pi$
$432$		0			0
$433$	−487.810			−1.12658			−0.563291	−	0.826259i	$-0.690465\pi$
$433$	−487.810			−1.12658			−0.563291	+	0.826259i	$0.690465\pi$
$434$		0			0
$435$	136.259			0.313240
$436$		0			0
$437$	339.404	−	195.955i	0.776668	−	0.448409i
$438$		0			0
$439$	−241.116	−	139.208i	−0.549239	−	0.317103i	0.199576	−	0.979882i	$-0.436044\pi$
$439$	−241.116	−	139.208i	−0.549239	−	0.317103i	−0.748815	+	0.662779i	$0.769377\pi$
$440$		0			0
$441$	499.325	+	95.2575i	1.13226	+	0.216003i
$442$		0			0
$443$	100.954	−	174.857i	0.227887	−	0.394712i	−0.729295	−	0.684200i	$-0.760152\pi$
$443$	100.954	−	174.857i	0.227887	−	0.394712i	0.957182	+	0.289488i	$0.0934849\pi$
$444$		0			0
$445$	−139.344	+	80.4501i	−0.313132	+	0.180787i
$446$		0			0
$447$			1163.45i			2.60279i
$448$		0			0
$449$	−277.311			−0.617619			−0.308809	−	0.951124i	$-0.599931\pi$
$449$	−277.311			−0.617619			−0.308809	+	0.951124i	$0.599931\pi$
$450$		0			0
$451$	−1.62402	−	2.81288i	−0.00360093	−	0.00623699i
$452$		0			0
$453$	593.617	+	342.725i	1.31041	+	0.756567i
$454$		0			0
$455$	164.312	+	358.894i	0.361125	+	0.788778i
$456$		0			0
$457$	−18.9532	+	32.8279i	−0.0414731	+	0.0718335i	−0.886017	−	0.463653i	$-0.846538\pi$
$457$	−18.9532	+	32.8279i	−0.0414731	+	0.0718335i	0.844544	+	0.535487i	$0.179872\pi$
$458$		0			0
$459$	−86.5537	−	149.915i	−0.188570	−	0.326613i
$460$		0			0
$461$		−	220.061i		−	0.477356i	−0.971099	−	0.238678i	$-0.923286\pi$
$461$		−	220.061i		−	0.477356i	0.971099	−	0.238678i	$-0.0767140\pi$
$462$		0			0
$463$		−	73.1168i		−	0.157920i	−0.996878	−	0.0789598i	$-0.974840\pi$
$463$		−	73.1168i		−	0.157920i	0.996878	−	0.0789598i	$-0.0251599\pi$
$464$		0			0
$465$	121.671	+	210.740i	0.261658	+	0.453205i
$466$		0			0
$467$	158.591	−	274.688i	0.339595	−	0.588196i	−0.644761	−	0.764384i	$-0.723043\pi$
$467$	158.591	−	274.688i	0.339595	−	0.588196i	0.984357	+	0.176188i	$0.0563765\pi$
$468$		0			0
$469$	−102.181	−	9.65958i	−0.217870	−	0.0205961i
$470$		0			0
$471$	−598.621	−	345.614i	−1.27096	−	0.733787i
$472$		0			0
$473$	62.1032	+	107.566i	0.131296	+	0.227412i
$474$		0			0
$475$	357.284			0.752177
$476$		0			0
$477$		−	230.045i		−	0.482274i
$478$		0			0
$479$	−426.647	+	246.325i	−0.890704	+	0.514248i	−0.874173	−	0.485615i	$-0.838596\pi$
$479$	−426.647	+	246.325i	−0.890704	+	0.514248i	−0.0165316	+	0.999863i	$0.505262\pi$
$480$		0			0
$481$	−272.369	+	471.758i	−0.566257	+	0.980785i
$482$		0			0
$483$	327.883	+	233.017i	0.678847	+	0.482438i
$484$		0			0
$485$	522.409	+	301.613i	1.07713	+	0.621883i
$486$		0			0
$487$	−23.4016	+	13.5109i	−0.0480525	+	0.0277432i	−0.523834	−	0.851820i	$-0.675499\pi$
$487$	−23.4016	+	13.5109i	−0.0480525	+	0.0277432i	0.475781	+	0.879564i	$0.342165\pi$
$488$		0			0
$489$	601.137			1.22932
$490$		0			0
$491$	140.587			0.286327			0.143164	−	0.989699i	$-0.454272\pi$
$491$	140.587			0.286327			0.143164	+	0.989699i	$0.454272\pi$
$492$		0			0
$493$	212.020	−	122.410i	0.430060	−	0.248295i
$494$		0			0
$495$	−120.579	−	69.6164i	−0.243594	−	0.140639i
$496$		0			0
$497$	−643.240	−	457.133i	−1.29425	−	0.919785i
$498$		0			0
$499$	−332.243	+	575.463i	−0.665819	+	1.15323i	0.313244	+	0.949673i	$0.398584\pi$
$499$	−332.243	+	575.463i	−0.665819	+	1.15323i	−0.979063	+	0.203559i	$0.934749\pi$
$500$		0			0
$501$	363.366	−	209.790i	0.725282	−	0.418742i
$502$		0			0
$503$		−	678.934i		−	1.34977i	−0.737923	−	0.674885i	$-0.764193\pi$
$503$		−	678.934i		−	1.34977i	0.737923	−	0.674885i	$-0.235807\pi$
$504$		0			0
$505$	414.644			0.821077
$506$		0			0
$507$	−162.323	−	281.152i	−0.320164	−	0.554540i
$508$		0			0
$509$	103.197	+	59.5809i	0.202745	+	0.117055i	0.597935	−	0.801544i	$-0.295988\pi$
$509$	103.197	+	59.5809i	0.202745	+	0.117055i	−0.395190	+	0.918599i	$0.629321\pi$
$510$		0			0
$511$	−786.334	−	74.3353i	−1.53881	−	0.145470i
$512$		0			0
$513$	90.7800	−	157.236i	0.176959	−	0.306502i
$514$		0			0
$515$	−36.1537	−	62.6200i	−0.0702013	−	0.121592i
$516$		0			0
$517$			326.048i			0.630655i
$518$		0			0
$519$			294.470i			0.567379i
$520$		0			0
$521$	302.941	+	524.710i	0.581461	+	1.00712i	0.995306	+	0.0967732i	$0.0308522\pi$
$521$	302.941	+	524.710i	0.581461	+	1.00712i	−0.413845	+	0.910347i	$0.635815\pi$
$522$		0			0
$523$	−18.9269	+	32.7823i	−0.0361891	+	0.0626813i	−0.883553	−	0.468332i	$-0.844855\pi$
$523$	−18.9269	+	32.7823i	−0.0361891	+	0.0626813i	0.847364	+	0.531013i	$0.178189\pi$
$524$		0			0
$525$	152.652	+	333.427i	0.290767	+	0.635099i
$526$		0			0
$527$	378.641	+	218.608i	0.718483	+	0.414816i
$528$		0			0
$529$	−179.280	−	310.521i	−0.338903	−	0.586997i
$530$		0			0
$531$	1016.66			1.91461
$532$		0			0
$533$			13.6464i			0.0256031i
$534$		0			0
$535$	−116.040	+	66.9956i	−0.216897	+	0.125225i
$536$		0			0
$537$	268.424	−	464.925i	0.499859	−	0.865782i
$538$		0			0
$539$	118.736	−	137.554i	0.220289	−	0.255201i
$540$		0			0
$541$	514.014	+	296.766i	0.950118	+	0.548551i	0.893118	−	0.449823i	$-0.148513\pi$
$541$	514.014	+	296.766i	0.950118	+	0.548551i	0.0570004	+	0.998374i	$0.481846\pi$
$542$		0			0
$543$	−708.476	+	409.039i	−1.30474	+	0.753294i
$544$		0			0
$545$	488.810			0.896899
$546$		0			0
$547$	532.191			0.972926			0.486463	−	0.873701i	$-0.338287\pi$
$547$	532.191			0.972926			0.486463	+	0.873701i	$0.338287\pi$
$548$		0			0
$549$	360.692	−	208.246i	0.656998	−	0.379318i
$550$		0			0
$551$	222.372	+	128.387i	0.403579	+	0.233007i
$552$		0			0
$553$	411.912	−	188.585i	0.744867	−	0.341022i
$554$		0			0
$555$	278.477	−	482.335i	0.501759	−	0.869073i
$556$		0			0
$557$	797.199	−	460.263i	1.43124	−	0.826325i	0.434022	−	0.900902i	$-0.357094\pi$
$557$	797.199	−	460.263i	1.43124	−	0.826325i	0.997215	+	0.0745774i	$0.0237608\pi$
$558$		0			0
$559$		−	521.846i		−	0.933534i
$560$		0			0
$561$	−467.189			−0.832779
$562$		0			0
$563$	−399.420	−	691.815i	−0.709449	−	1.22880i	−0.965062	−	0.262023i	$-0.915610\pi$
$563$	−399.420	−	691.815i	−0.709449	−	1.22880i	0.255613	−	0.966779i	$-0.417723\pi$
$564$		0			0
$565$	275.045	+	158.797i	0.486804	+	0.281057i
$566$		0			0
$567$	−465.143	−	43.9718i	−0.820358	−	0.0775516i
$568$		0			0
$569$	−138.724	+	240.277i	−0.243803	+	0.422279i	−0.961794	−	0.273773i	$-0.911728\pi$
$569$	−138.724	+	240.277i	−0.243803	+	0.422279i	0.717992	+	0.696052i	$0.245062\pi$
$570$		0			0
$571$	348.159	+	603.029i	0.609735	+	1.05609i	0.991284	+	0.131744i	$0.0420576\pi$
$571$	348.159	+	603.029i	0.609735	+	1.05609i	−0.381549	+	0.924349i	$0.624609\pi$
$572$		0			0
$573$			483.293i			0.843443i
$574$		0			0
$575$			155.382i			0.270230i
$576$		0			0
$577$	−227.366	−	393.809i	−0.394048	−	0.682512i	0.598931	−	0.800801i	$-0.295592\pi$
$577$	−227.366	−	393.809i	−0.394048	−	0.682512i	−0.992979	+	0.118289i	$0.962259\pi$
$578$		0			0
$579$	48.4045	−	83.8390i	0.0836001	−	0.144800i
$580$		0			0
$581$	−236.127	+	332.259i	−0.406415	+	0.571875i
$582$		0			0
$583$	−71.2166	−	41.1169i	−0.122155	−	0.0705264i
$584$		0			0
$585$	292.489	+	506.606i	0.499981	+	0.865993i
$586$		0			0
$587$	−659.220			−1.12303			−0.561517	−	0.827466i	$-0.689782\pi$
$587$	−659.220			−1.12303			−0.561517	+	0.827466i	$0.689782\pi$
$588$		0			0
$589$			458.565i			0.778548i
$590$		0			0
$591$	1283.02	−	740.750i	2.17093	−	1.25338i
$592$		0			0
$593$	200.964	−	348.080i	0.338894	−	0.586982i	−0.645331	−	0.763903i	$-0.723280\pi$
$593$	200.964	−	348.080i	0.338894	−	0.586982i	0.984225	+	0.176921i	$0.0566138\pi$
$594$		0			0
$595$	−591.046	−	420.040i	−0.993355	−	0.705950i
$596$		0			0
$597$	−880.978	−	508.633i	−1.47568	−	0.851982i
$598$		0			0
$599$	139.863	−	80.7499i	0.233494	−	0.134808i	−0.378689	−	0.925524i	$-0.623625\pi$
$599$	139.863	−	80.7499i	0.233494	−	0.134808i	0.612183	+	0.790716i	$0.290292\pi$
$600$		0			0
$601$	645.091			1.07336			0.536681	−	0.843785i	$-0.319678\pi$
$601$	645.091			1.07336			0.536681	+	0.843785i	$0.319678\pi$
$602$		0			0
$603$	−152.109			−0.252253
$604$		0			0
$605$	336.143	−	194.072i	0.555608	−	0.320780i
$606$		0			0
$607$	−219.907	−	126.963i	−0.362285	−	0.209165i	0.307798	−	0.951452i	$-0.400408\pi$
$607$	−219.907	−	126.963i	−0.362285	−	0.209165i	−0.670083	+	0.742287i	$0.733741\pi$
$608$		0			0
$609$	−24.8036	+	262.378i	−0.0407284	+	0.430834i
$610$		0			0
$611$	684.936	−	1186.34i	1.12101	−	1.94164i
$612$		0			0
$613$	−775.160	+	447.539i	−1.26454	+	0.730080i	−0.973949	−	0.226768i	$-0.927184\pi$
$613$	−775.160	+	447.539i	−1.26454	+	0.730080i	−0.290587	+	0.956849i	$0.593851\pi$
$614$		0			0
$615$		−	13.9524i		−	0.0226869i
$616$		0			0
$617$	−847.857			−1.37416			−0.687080	−	0.726582i	$-0.741108\pi$
$617$	−847.857			−1.37416			−0.687080	+	0.726582i	$0.741108\pi$
$618$		0			0
$619$	25.3118	+	43.8414i	0.0408915	+	0.0708261i	0.885747	−	0.464169i	$-0.153647\pi$
$619$	25.3118	+	43.8414i	0.0408915	+	0.0708261i	−0.844855	+	0.534995i	$0.820314\pi$
$620$		0			0
$621$	68.3815	+	39.4801i	0.110115	+	0.0635750i
$622$		0			0
$623$	−129.548	−	282.962i	−0.207942	−	0.454192i
$624$		0			0
$625$	92.8998	−	160.907i	0.148640	−	0.257451i
$626$		0			0
$627$	−245.000	−	424.353i	−0.390750	−	0.676799i
$628$		0			0
$629$		−	1000.69i		−	1.59092i
$630$		0			0
$631$		−	412.200i		−	0.653248i	−0.945154	−	0.326624i	$-0.894089\pi$
$631$		−	412.200i		−	0.653248i	0.945154	−	0.326624i	$-0.105911\pi$
$632$		0			0
$633$	−139.292	−	241.260i	−0.220050	−	0.381138i
$634$		0			0
$635$	−378.968	+	656.392i	−0.596800	+	1.03369i
$636$		0			0
$637$	−720.988	+	251.065i	−1.13185	+	0.394137i
$638$		0			0
$639$	−1012.82	−	584.751i	−1.58500	−	0.915103i
$640$		0			0
$641$	−11.1639	−	19.3365i	−0.0174164	−	0.0301661i	0.857186	−	0.515007i	$-0.172211\pi$
$641$	−11.1639	−	19.3365i	−0.0174164	−	0.0301661i	−0.874602	+	0.484841i	$0.838877\pi$
$642$		0			0
$643$	−707.978			−1.10105			−0.550527	−	0.834817i	$-0.685573\pi$
$643$	−707.978			−1.10105			−0.550527	+	0.834817i	$0.685573\pi$
$644$		0			0
$645$			533.546i			0.827204i
$646$		0			0
$647$	297.181	−	171.577i	0.459321	−	0.265189i	−0.252438	−	0.967613i	$-0.581232\pi$
$647$	297.181	−	171.577i	0.459321	−	0.265189i	0.711759	+	0.702424i	$0.247899\pi$
$648$		0			0
$649$	181.712	−	314.734i	0.279987	−	0.484952i
$650$		0			0
$651$	−427.945	+	195.925i	−0.657366	+	0.300961i
$652$		0			0
$653$	−1097.53	−	633.659i	−1.68075	−	0.970381i	−0.961165	−	0.275976i	$-0.910999\pi$
$653$	−1097.53	−	633.659i	−1.68075	−	0.970381i	−0.719584	−	0.694405i	$-0.755668\pi$
$654$		0			0
$655$	479.969	−	277.110i	0.732777	−	0.423069i
$656$		0			0
$657$	−1170.55			−1.78166
$658$		0			0
$659$	391.748			0.594458			0.297229	−	0.954806i	$-0.403938\pi$
$659$	391.748			0.594458			0.297229	+	0.954806i	$0.403938\pi$
$660$		0			0
$661$	−192.013	+	110.859i	−0.290489	+	0.167714i	−0.638162	−	0.769902i	$-0.720305\pi$
$661$	−192.013	+	110.859i	−0.290489	+	0.167714i	0.347674	+	0.937616i	$0.386972\pi$
$662$		0			0
$663$	1699.89	+	981.433i	2.56394	+	1.48029i
$664$		0			0
$665$	71.5744	−	757.129i	0.107631	−	1.13854i
$666$		0			0
$667$	−55.8351	+	96.7093i	−0.0837109	+	0.144991i
$668$		0			0
$669$	488.034	−	281.766i	0.729497	−	0.421175i
$670$		0			0
$671$		−	148.882i		−	0.221881i
$672$		0			0
$673$	−749.039			−1.11298			−0.556492	−	0.830853i	$-0.687853\pi$
$673$	−749.039			−1.11298			−0.556492	+	0.830853i	$0.687853\pi$
$674$		0			0
$675$	35.9920	+	62.3399i	0.0533214	+	0.0923554i
$676$		0			0
$677$	555.738	+	320.856i	0.820884	+	0.473938i	0.850721	−	0.525617i	$-0.176166\pi$
$677$	555.738	+	320.856i	0.820884	+	0.473938i	−0.0298372	+	0.999555i	$0.509499\pi$
$678$		0			0
$679$	−675.875	+	951.037i	−0.995398	+	1.40064i
$680$		0			0
$681$	873.505	−	1512.95i	1.28268	−	2.22167i
$682$		0			0
$683$	142.757	+	247.262i	0.209014	+	0.362023i	0.951404	−	0.307945i	$-0.0996412\pi$
$683$	142.757	+	247.262i	0.209014	+	0.362023i	−0.742390	+	0.669968i	$0.766308\pi$
$684$		0			0
$685$		−	541.930i		−	0.791139i
$686$		0			0
$687$			915.830i			1.33309i
$688$		0			0
$689$	172.750	+	299.212i	0.250726	+	0.434270i
$690$		0			0
$691$	584.960	−	1013.18i	0.846541	−	1.46625i	−0.0377355	−	0.999288i	$-0.512014\pi$
$691$	584.960	−	1013.18i	0.846541	−	1.46625i	0.884276	−	0.466964i	$-0.154652\pi$
$692$		0			0
$693$	156.001	−	219.512i	0.225110	−	0.316756i
$694$		0			0
$695$	−14.4482	−	8.34167i	−0.0207888	−	0.0120024i
$696$		0			0
$697$	−12.5343	−	21.7100i	−0.0179832	−	0.0311477i
$698$		0			0
$699$	−652.190			−0.933033
$700$		0			0
$701$			779.001i			1.11127i	0.831426	+	0.555635i	$0.187525\pi$
$701$			779.001i			1.11127i	−0.831426	+	0.555635i	$0.812475\pi$
$702$		0			0
$703$	908.935	−	524.774i	1.29294	−	0.746478i
$704$		0			0
$705$	−700.294	+	1212.94i	−0.993325	+	1.72049i
$706$		0			0
$707$	−75.4787	+	798.429i	−0.106759	+	1.12932i
$708$		0			0
$709$	−220.696	−	127.419i	−0.311278	−	0.179716i	0.336220	−	0.941783i	$-0.390851\pi$
$709$	−220.696	−	127.419i	−0.311278	−	0.179716i	−0.647498	+	0.762067i	$0.724185\pi$
$710$		0			0
$711$	581.444	−	335.697i	0.817784	−	0.472148i
$712$		0			0
$713$	−199.429			−0.279704
$714$		0			0
$715$	209.111			0.292463
$716$		0			0
$717$	51.8602	−	29.9415i	0.0723295	−	0.0417594i
$718$		0			0
$719$	−178.500	−	103.057i	−0.248262	−	0.143334i	0.370706	−	0.928750i	$-0.379116\pi$
$719$	−178.500	−	103.057i	−0.248262	−	0.143334i	−0.618968	+	0.785416i	$0.712449\pi$
$720$		0			0
$721$	127.161	−	58.2179i	0.176367	−	0.0807460i
$722$		0			0
$723$	−640.742	+	1109.80i	−0.886227	+	1.53499i
$724$		0			0
$725$	−88.1650	+	50.9021i	−0.121607	+	0.0702097i
$726$		0			0
$727$		−	76.0393i		−	0.104593i	−0.998632	−	0.0522966i	$-0.983346\pi$
$727$		−	76.0393i		−	0.104593i	0.998632	−	0.0522966i	$-0.0166541\pi$
$728$		0			0
$729$	−932.013			−1.27848
$730$		0			0
$731$	479.316	+	830.199i	0.655699	+	1.13570i
$732$		0			0
$733$	257.623	+	148.739i	0.351464	+	0.202918i	0.665330	−	0.746550i	$-0.268291\pi$
$733$	257.623	+	148.739i	0.351464	+	0.202918i	−0.313866	+	0.949467i	$0.601624\pi$
$734$		0			0
$735$	737.154	−	256.694i	1.00293	−	0.349244i
$736$		0			0
$737$	−27.1870	+	47.0893i	−0.0368888	+	0.0638932i
$738$		0			0
$739$	−266.147	−	460.979i	−0.360144	−	0.623788i	0.627840	−	0.778342i	$-0.283939\pi$
$739$	−266.147	−	460.979i	−0.360144	−	0.623788i	−0.987984	+	0.154554i	$0.950606\pi$
$740$		0			0
$741$			2058.71i			2.77828i
$742$		0			0
$743$		−	187.452i		−	0.252291i	−0.992012	−	0.126145i	$-0.959739\pi$
$743$		−	187.452i		−	0.252291i	0.992012	−	0.126145i	$-0.0402606\pi$
$744$		0			0
$745$	478.312	+	828.460i	0.642029	+	1.11203i
$746$		0			0
$747$	−302.047	+	523.161i	−0.404347	+	0.700349i
$748$		0			0
$749$	−107.882	−	235.639i	−0.144035	−	0.314605i
$750$		0			0
$751$	399.197	+	230.476i	0.531554	+	0.306893i	0.741649	−	0.670788i	$-0.234044\pi$
$751$	399.197	+	230.476i	0.531554	+	0.306893i	−0.210095	+	0.977681i	$0.567377\pi$
$752$		0			0
$753$	268.632	+	465.285i	0.356749	+	0.617908i
$754$		0			0
$755$	563.599			0.746489
$756$		0			0
$757$		−	1381.08i		−	1.82441i	−0.409735	−	0.912205i	$-0.634379\pi$
$757$		−	1381.08i		−	1.82441i	0.409735	−	0.912205i	$-0.365621\pi$
$758$		0			0
$759$	184.551	−	106.550i	0.243150	−	0.140382i
$760$		0			0
$761$	−341.816	+	592.043i	−0.449167	+	0.777980i	−0.998332	−	0.0577337i	$-0.981613\pi$
$761$	−341.816	+	592.043i	−0.449167	+	0.777980i	0.549165	+	0.835714i	$0.314946\pi$
$762$		0			0
$763$	−88.9793	+	941.242i	−0.116618	+	1.23361i
$764$		0			0
$765$	−930.636	−	537.303i	−1.21652	−	0.702357i
$766$		0			0
$767$	−1322.33	+	763.450i	−1.72404	+	0.995372i
$768$		0			0
$769$	592.828			0.770907			0.385454	−	0.922727i	$-0.374045\pi$
$769$	592.828			0.770907			0.385454	+	0.922727i	$0.374045\pi$
$770$		0			0
$771$	1553.09			2.01439
$772$		0			0
$773$	43.9419	−	25.3699i	0.0568459	−	0.0328200i	−0.471308	−	0.881969i	$-0.656218\pi$
$773$	43.9419	−	25.3699i	0.0568459	−	0.0328200i	0.528154	+	0.849149i	$0.322885\pi$
$774$		0			0
$775$	−157.452	−	90.9047i	−0.203163	−	0.117296i
$776$		0			0
$777$	878.083	+	624.029i	1.13009	+	0.803126i
$778$		0			0
$779$	13.1463	−	22.7700i	0.0168758	−	0.0292298i
$780$		0			0
$781$	−362.051	+	209.030i	−0.463573	+	0.267644i
$782$		0			0
$783$			51.7335i			0.0660708i
$784$		0			0
$785$	−568.349			−0.724012
$786$		0			0
$787$	216.453	+	374.908i	0.275036	+	0.476376i	0.970144	−	0.242529i	$-0.0779770\pi$
$787$	216.453	+	374.908i	0.275036	+	0.476376i	−0.695109	+	0.718905i	$0.744644\pi$
$788$		0			0
$789$	−1602.85	−	925.407i	−2.03150	−	1.17289i
$790$		0			0
$791$	−355.843	+	500.714i	−0.449865	+	0.633013i
$792$		0			0
$793$	−312.760	+	541.717i	−0.394401	+	0.683123i
$794$		0			0
$795$	−176.623	−	305.921i	−0.222168	−	0.384806i
$796$		0			0
$797$		−	526.301i		−	0.660352i	−0.943919	−	0.330176i	$-0.892892\pi$
$797$		−	526.301i		−	0.660352i	0.943919	−	0.330176i	$-0.107108\pi$
$798$		0			0
$799$			2516.46i			3.14951i
$800$		0			0
$801$	−230.606	−	399.422i	−0.287898	−	0.498654i
$802$		0			0
$803$	−209.218	+	362.376i	−0.260545	+	0.451277i
$804$		0			0
$805$	329.274	+	31.1276i	0.409036	+	0.0386678i
$806$		0			0
$807$	−1086.81	−	627.472i	−1.34673	−	0.777537i
$808$		0			0
$809$	391.649	+	678.356i	0.484115	+	0.838511i	0.999834	−	0.0182466i	$-0.00580838\pi$
$809$	391.649	+	678.356i	0.484115	+	0.838511i	−0.515719	+	0.856758i	$0.672475\pi$
$810$		0			0
$811$	−1526.43			−1.88216			−0.941079	−	0.338188i	$-0.890186\pi$
$811$	−1526.43			−1.88216			−0.941079	+	0.338188i	$0.890186\pi$
$812$		0			0
$813$		−	760.295i		−	0.935173i
$814$		0			0
$815$	428.054	−	247.137i	0.525220	−	0.303236i
$816$		0			0
$817$	−502.720	+	870.736i	−0.615324	+	1.06577i
$818$		0			0
$819$	−1028.75	+	470.992i	−1.25611	+	0.575082i
$820$		0			0
$821$	−311.578	−	179.890i	−0.379511	−	0.219111i	0.298095	−	0.954536i	$-0.403649\pi$
$821$	−311.578	−	179.890i	−0.379511	−	0.219111i	−0.677605	+	0.735426i	$0.736982\pi$
$822$		0			0
$823$	−199.591	+	115.234i	−0.242516	+	0.140017i	−0.616333	−	0.787486i	$-0.711382\pi$
$823$	−199.591	+	115.234i	−0.242516	+	0.140017i	0.373817	+	0.927503i	$0.378049\pi$
$824$		0			0
$825$	194.273			0.235482
$826$		0			0
$827$	−515.503			−0.623340			−0.311670	−	0.950190i	$-0.600888\pi$
$827$	−515.503			−0.623340			−0.311670	+	0.950190i	$0.600888\pi$
$828$		0			0
$829$	1014.52	−	585.733i	1.22379	−	0.706554i	0.258064	−	0.966128i	$-0.416915\pi$
$829$	1014.52	−	585.733i	1.22379	−	0.706554i	0.965723	+	0.259573i	$0.0835820\pi$
$830$		0			0
$831$	−1512.17	−	873.054i	−1.81970	−	1.05061i
$832$		0			0
$833$	916.410	−	1061.65i	1.10013	−	1.27448i
$834$		0			0
$835$	172.496	−	298.772i	0.206582	−	0.357810i
$836$		0			0
$837$	−80.0116	+	46.1947i	−0.0955934	+	0.0551909i
$838$		0			0
$839$			564.433i			0.672745i	0.941729	+	0.336372i	$0.109200\pi$
$839$			564.433i			0.672745i	−0.941729	+	0.336372i	$0.890800\pi$
$840$		0			0
$841$	767.835			0.913003
$842$		0			0
$843$	405.547	+	702.428i	0.481076	+	0.833248i
$844$		0			0
$845$	−231.172	−	133.467i	−0.273576	−	0.157949i
$846$		0			0
$847$	312.512	+	682.596i	0.368963	+	0.805899i
$848$		0			0
$849$	−122.713	+	212.545i	−0.144538	+	0.250347i
$850$		0			0
$851$	228.223	+	395.294i	0.268183	+	0.464506i
$852$		0			0
$853$		−	462.894i		−	0.542666i	−0.962486	−	0.271333i	$-0.912536\pi$
$853$		−	462.894i		−	0.542666i	0.962486	−	0.271333i	$-0.0874644\pi$
$854$		0			0
$855$		−	1127.08i		−	1.31822i
$856$		0			0
$857$	423.274	+	733.131i	0.493902	+	0.855463i	0.999975	−	0.00702758i	$-0.00223697\pi$
$857$	423.274	+	733.131i	0.493902	+	0.855463i	−0.506074	+	0.862490i	$0.668904\pi$
$858$		0			0
$859$	94.2748	−	163.289i	0.109749	−	0.190092i	−0.805919	−	0.592025i	$-0.798328\pi$
$859$	94.2748	−	163.289i	0.109749	−	0.190092i	0.915669	+	0.401934i	$0.131662\pi$
$860$		0			0
$861$	26.8665	+	2.53979i	0.0312038	+	0.00294982i
$862$		0			0
$863$	678.004	+	391.446i	0.785636	+	0.453587i	0.838424	−	0.545018i	$-0.183477\pi$
$863$	678.004	+	391.446i	0.785636	+	0.453587i	−0.0527878	+	0.998606i	$0.516811\pi$
$864$		0			0
$865$	121.061	+	209.684i	0.139955	+	0.242409i
$866$		0			0
$867$	−2333.73			−2.69173
$868$		0			0
$869$		−	240.002i		−	0.276182i
$870$		0			0
$871$	197.843	−	114.225i	0.227144	−	0.131142i
$872$		0			0
$873$	−864.559	+	1497.46i	−0.990331	+	1.71530i
$874$		0			0
$875$	762.035	+	541.557i	0.870897	+	0.618922i
$876$		0			0
$877$	−57.9190	−	33.4395i	−0.0660421	−	0.0381295i	0.466615	−	0.884460i	$-0.345473\pi$
$877$	−57.9190	−	33.4395i	−0.0660421	−	0.0381295i	−0.532657	+	0.846331i	$0.678807\pi$
$878$		0			0
$879$	1193.68	−	689.170i	1.35799	−	0.784038i
$880$		0			0
$881$	1077.23			1.22274			0.611369	−	0.791345i	$-0.290619\pi$
$881$	1077.23			1.22274			0.611369	+	0.791345i	$0.290619\pi$
$882$		0			0
$883$	50.4655			0.0571524			0.0285762	−	0.999592i	$-0.490903\pi$
$883$	50.4655			0.0571524			0.0285762	+	0.999592i	$0.490903\pi$
$884$		0			0
$885$	1351.98	−	780.568i	1.52767	−	0.881998i
$886$		0			0
$887$	798.495	+	461.011i	0.900220	+	0.519742i	0.877272	−	0.479994i	$-0.159361\pi$
$887$	798.495	+	461.011i	0.900220	+	0.519742i	0.0229484	+	0.999737i	$0.492695\pi$
$888$		0			0
$889$	−1194.95	−	849.217i	−1.34415	−	0.955250i
$890$		0			0
$891$	−123.759	+	214.357i	−0.138899	+	0.240581i
$892$		0			0
$893$	−2285.73	+	1319.67i	−2.55961	+	1.47779i
$894$		0			0
$895$		−	441.414i		−	0.493200i
$896$		0			0
$897$	−895.329			−0.998137
$898$		0			0
$899$	−65.3315	−	113.157i	−0.0726713	−	0.125870i
$900$		0			0
$901$	−549.653	−	317.342i	−0.610048	−	0.352211i
$902$		0			0
$903$	−1027.39	−	97.1228i	−1.13775	−	0.107556i
$904$		0			0
$905$	−336.325	+	582.532i	−0.371630	+	0.643682i
$906$		0			0
$907$	130.121	+	225.376i	0.143463	+	0.248485i	0.928798	−	0.370585i	$-0.120843\pi$
$907$	130.121	+	225.376i	0.143463	+	0.248485i	−0.785336	+	0.619070i	$0.787510\pi$
$908$		0			0
$909$			1188.56i			1.30754i
$910$		0			0
$911$		−	143.580i		−	0.157607i	−0.996890	−	0.0788034i	$-0.974890\pi$
$911$		−	143.580i		−	0.157607i	0.996890	−	0.0788034i	$-0.0251099\pi$
$912$		0			0
$913$	107.972	+	187.014i	0.118261	+	0.204834i
$914$		0			0
$915$	319.773	−	553.863i	0.349479	−	0.605315i
$916$		0			0
$917$	446.227	+	974.661i	0.486617	+	1.06288i
$918$		0			0
$919$	511.111	+	295.090i	0.556160	+	0.321099i	0.751603	−	0.659616i	$-0.229281\pi$
$919$	511.111	+	295.090i	0.556160	+	0.321099i	−0.195443	+	0.980715i	$0.562614\pi$
$920$		0			0
$921$	41.2328	+	71.4173i	0.0447696	+	0.0775432i
$922$		0			0
$923$	1756.45			1.90298
$924$		0			0
$925$			416.119i			0.449859i
$926$		0			0
$927$	179.497	−	103.633i	0.193632	−	0.111794i
$928$		0			0
$929$	771.734	−	1336.68i	0.830715	−	1.43884i	−0.0667570	−	0.997769i	$-0.521265\pi$
$929$	771.734	−	1336.68i	0.830715	−	1.43884i	0.897472	−	0.441071i	$-0.145401\pi$
$930$		0			0
$931$	1444.88	+	275.644i	1.55197	+	0.296073i
$932$		0			0
$933$	−848.509	−	489.887i	−0.909442	−	0.525067i
$934$		0			0
$935$	−332.673	+	192.069i	−0.355800	+	0.205421i
$936$		0			0
$937$	430.049			0.458964			0.229482	−	0.973313i	$-0.426297\pi$
$937$	430.049			0.458964			0.229482	+	0.973313i	$0.426297\pi$
$938$		0			0
$939$	−361.379			−0.384855
$940$		0			0
$941$	570.055	−	329.122i	0.605797	−	0.349757i	−0.165522	−	0.986206i	$-0.552931\pi$
$941$	570.055	−	329.122i	0.605797	−	0.349757i	0.771319	+	0.636449i	$0.219597\pi$
$942$		0			0
$943$	9.90265	+	5.71730i	0.0105012	+	0.00606288i
$944$		0			0
$945$	139.316	−	63.7829i	0.147425	−	0.0674952i
$946$		0			0
$947$	−210.844	+	365.192i	−0.222644	+	0.385630i	−0.955610	−	0.294635i	$-0.904802\pi$
$947$	−210.844	+	365.192i	−0.222644	+	0.385630i	0.732966	+	0.680265i	$0.238135\pi$
$948$		0			0
$949$	1522.50	−	879.015i	1.60432	−	0.926254i
$950$		0			0
$951$			627.585i			0.659921i
$952$		0			0
$953$	872.394			0.915419			0.457709	−	0.889102i	$-0.348670\pi$
$953$	872.394			0.915419			0.457709	+	0.889102i	$0.348670\pi$
$954$		0			0
$955$	198.689	+	344.140i	0.208052	+	0.360356i
$956$		0			0
$957$	120.915	+	69.8101i	0.126348	+	0.0729469i
$958$		0			0
$959$	1043.53	+	98.6489i	1.08814	+	0.102866i
$960$		0			0
$961$	−363.826	+	630.165i	−0.378591	+	0.655739i
$962$		0			0
$963$	−192.040	−	332.622i	−0.199418	−	0.345402i
$964$		0			0
$965$		−	79.5994i		−	0.0824865i
$966$		0			0
$967$		−	1130.71i		−	1.16930i	−0.811286	−	0.584649i	$-0.801232\pi$
$967$		−	1130.71i		−	1.16930i	0.811286	−	0.584649i	$-0.198768\pi$
$968$		0			0
$969$	−1890.93	−	3275.18i	−1.95142	−	3.37996i
$970$		0			0
$971$	194.294	−	336.527i	0.200097	−	0.346578i	−0.748463	−	0.663177i	$-0.769208\pi$
$971$	194.294	−	336.527i	0.200097	−	0.346578i	0.948559	+	0.316599i	$0.102541\pi$
$972$		0			0
$973$	18.6926	−	26.3027i	0.0192113	−	0.0270326i
$974$		0			0
$975$	−706.872	−	408.113i	−0.724997	−	0.418577i
$976$		0			0
$977$	−235.013	−	407.055i	−0.240546	−	0.416638i	0.720324	−	0.693638i	$-0.243993\pi$
$977$	−235.013	−	407.055i	−0.240546	−	0.416638i	−0.960870	+	0.277000i	$0.910660\pi$
$978$		0			0
$979$	−164.869			−0.168405
$980$		0			0
$981$			1401.15i			1.42829i
$982$		0			0
$983$	1025.30	−	591.957i	1.04303	−	0.602195i	0.122341	−	0.992488i	$-0.460960\pi$
$983$	1025.30	−	591.957i	1.04303	−	0.602195i	0.920691	+	0.390293i	$0.127626\pi$
$984$		0			0
$985$	609.069	−	1054.94i	0.618344	−	1.07100i
$986$		0			0
$987$	−2208.14	−	1569.27i	−2.23723	−	1.58993i
$988$		0			0
$989$	−378.682	−	218.632i	−0.382894	−	0.221064i
$990$		0			0
$991$	−875.407	+	505.417i	−0.883357	+	0.510007i	−0.871764	−	0.489926i	$-0.837024\pi$
$991$	−875.407	+	505.417i	−0.883357	+	0.510007i	−0.0115934	+	0.999933i	$0.503690\pi$
$992$		0			0
$993$	−924.168			−0.930683
$994$		0			0
$995$	−836.429			−0.840632
$996$		0			0
$997$	518.411	−	299.305i	0.519971	−	0.300205i	−0.216952	−	0.976182i	$-0.569611\pi$
$997$	518.411	−	299.305i	0.519971	−	0.300205i	0.736923	+	0.675977i	$0.236278\pi$
$998$		0			0
$999$	183.128	+	105.729i	0.183311	+	0.105835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.3.o.b.415.9	yes	20
4.3	odd	2	inner	448.3.o.b.415.2	yes	20
7.4	even	3		448.3.o.a.95.9	yes	20
8.3	odd	2		448.3.o.a.415.9	yes	20
8.5	even	2		448.3.o.a.415.2	yes	20
28.11	odd	6		448.3.o.a.95.2	✓	20
56.11	odd	6	inner	448.3.o.b.95.9	yes	20
56.53	even	6	inner	448.3.o.b.95.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
448.3.o.a.95.2	✓	20	28.11	odd	6
448.3.o.a.95.9	yes	20	7.4	even	3
448.3.o.a.415.2	yes	20	8.5	even	2
448.3.o.a.415.9	yes	20	8.3	odd	2
448.3.o.b.95.2	yes	20	56.53	even	6	inner
448.3.o.b.95.9	yes	20	56.11	odd	6	inner
448.3.o.b.415.2	yes	20	4.3	odd	2	inner
448.3.o.b.415.9	yes	20	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.20080 + 3.81190i) q^{3} +(3.13426 + 1.80957i) q^{5} +(-4.05500 + 5.70587i) q^{7} +(-5.18704 + 8.98421i) q^{9} +(1.85420 + 3.21157i) q^{11} -15.5806i q^{13} +15.9300i q^{15} +(14.3108 + 24.7871i) q^{17} +(-15.0096 + 25.9974i) q^{19} +(-30.6744 - 2.89977i) q^{21} +(-11.3062 - 6.52765i) q^{23} +(-5.95093 - 10.3073i) q^{25} -6.04813 q^{27} -8.55364i q^{29} +(13.2292 - 7.63786i) q^{31} +(-8.16146 + 14.1361i) q^{33} +(-23.0346 + 10.5459i) q^{35} +(-30.2785 - 17.4813i) q^{37} +(59.3918 - 34.2899i) q^{39} -0.875858 q^{41} +33.4932 q^{43} +(-32.5151 + 18.7726i) q^{45} +(76.1422 + 43.9607i) q^{47} +(-16.1139 - 46.2746i) q^{49} +(-62.9905 + 109.103i) q^{51} +(-19.2041 + 11.0875i) q^{53} +13.4212i q^{55} -132.132 q^{57} +(-48.9999 - 84.8704i) q^{59} +(-34.7686 - 20.0736i) q^{61} +(-30.2293 - 66.0276i) q^{63} +(28.1942 - 48.8338i) q^{65} +(7.33119 + 12.6980i) q^{67} -57.4642i q^{69} +112.733i q^{71} +(56.4171 + 97.7174i) q^{73} +(26.1936 - 45.3686i) q^{75} +(-25.8436 - 2.44310i) q^{77} +(-56.0478 - 32.3592i) q^{79} +(33.3726 + 57.8031i) q^{81} +58.2311 q^{83} +103.586i q^{85} +(32.6056 - 18.8248i) q^{87} +(-22.2291 + 38.5019i) q^{89} +(88.9011 + 63.1795i) q^{91} +(58.2295 + 33.6188i) q^{93} +(-94.0881 + 54.3218i) q^{95} +166.677 q^{97} -38.4713 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{5} - 28 q^{9} + 46 q^{17} - 114 q^{21} + 36 q^{25} + 94 q^{33} + 114 q^{37} - 160 q^{41} - 708 q^{45} - 92 q^{49} - 6 q^{53} + 308 q^{57} + 90 q^{61} + 212 q^{65} + 314 q^{73} - 198 q^{77} - 322 q^{81}+ \cdots - 224 q^{97}+O(q^{100}) \) 20 * q + 6 * q^5 - 28 * q^9 + 46 * q^17 - 114 * q^21 + 36 * q^25 + 94 * q^33 + 114 * q^37 - 160 * q^41 - 708 * q^45 - 92 * q^49 - 6 * q^53 + 308 * q^57 + 90 * q^61 + 212 * q^65 + 314 * q^73 - 198 * q^77 - 322 * q^81 - 206 * q^89 + 1530 * q^93 - 224 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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