LMFDB - Embedded newform 289.3.e.n.224.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,3,Mod(40,289)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([15])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("289.40"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,8,8,-16] 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:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			224.1
Root			$0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.224
Dual form			289.3.e.n.40.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.783227 - 0.324423i) q^{2} +(1.59946 + 0.318152i) q^{3} +(-2.32023 + 2.32023i) q^{4} +(-3.79690 - 5.68246i) q^{5} +(1.35595 - 0.269716i) q^{6} +(0.502268 - 0.751697i) q^{7} +(-2.36223 + 5.70292i) q^{8} +(-5.85788 - 2.42641i) q^{9} +(-4.81736 - 3.21885i) q^{10} +(1.31223 + 6.59700i) q^{11} +(-4.44930 + 2.97292i) q^{12} +(-10.5602 - 10.5602i) q^{13} +(0.149522 - 0.751697i) q^{14} +(-4.26509 - 10.2968i) q^{15} -7.89218i q^{16} -5.37523 q^{18} +(-31.3415 + 12.9821i) q^{19} +(21.9943 + 4.37494i) q^{20} +(1.04251 - 1.04251i) q^{21} +(3.16799 + 4.74123i) q^{22} +(-18.2549 + 3.63113i) q^{23} +(-5.59267 + 8.37002i) q^{24} +(-8.30682 + 20.0544i) q^{25} +(-11.6970 - 4.84504i) q^{26} +(-20.8010 - 13.8988i) q^{27} +(0.578734 + 2.90949i) q^{28} +(17.6031 - 11.7620i) q^{29} +(-6.68107 - 6.68107i) q^{30} +(7.42005 - 37.3031i) q^{31} +(-12.0093 - 28.9930i) q^{32} +10.9691i q^{33} -6.17855 q^{35} +(19.2215 - 7.96180i) q^{36} +(39.3135 + 7.81994i) q^{37} +(-20.3359 + 20.3359i) q^{38} +(-13.5308 - 20.2502i) q^{39} +(41.3757 - 8.23014i) q^{40} +(-2.09701 + 3.13840i) q^{41} +(0.478307 - 1.15474i) q^{42} +(-12.5911 - 5.21542i) q^{43} +(-18.3512 - 12.2619i) q^{44} +(8.45377 + 42.5000i) q^{45} +(-13.1197 + 8.76632i) q^{46} +(9.20504 + 9.20504i) q^{47} +(2.51091 - 12.6232i) q^{48} +(18.4387 + 44.5150i) q^{49} +18.4021i q^{50} +49.0040 q^{52} +(1.84317 - 0.763466i) q^{53} +(-20.8010 - 4.13758i) q^{54} +(32.5048 - 32.5048i) q^{55} +(3.10040 + 4.64007i) q^{56} +(-54.2597 + 10.7929i) q^{57} +(9.97136 - 14.9232i) q^{58} +(-13.1653 + 31.7838i) q^{59} +(33.7870 + 13.9951i) q^{60} +(29.5202 + 19.7248i) q^{61} +(-6.29041 - 31.6240i) q^{62} +(-4.76615 + 3.18464i) q^{63} +(3.51042 + 3.51042i) q^{64} +(-19.9118 + 100.103i) q^{65} +(3.55863 + 8.59130i) q^{66} -31.9912i q^{67} -30.3532 q^{69} +(-4.83921 + 2.00446i) q^{70} +(-101.633 - 20.2161i) q^{71} +(27.6752 - 27.6752i) q^{72} +(34.9811 + 52.3530i) q^{73} +(33.3284 - 6.62943i) q^{74} +(-19.6667 + 29.4333i) q^{75} +(42.5982 - 102.841i) q^{76} +(5.61804 + 2.32707i) q^{77} +(-17.1673 - 11.4708i) q^{78} +(-12.7463 - 64.0800i) q^{79} +(-44.8470 + 29.9658i) q^{80} +(11.5024 + 11.5024i) q^{81} +(-0.624266 + 3.13840i) q^{82} +(16.4505 + 39.7149i) q^{83} +4.83773i q^{84} -11.5537 q^{86} +(31.8975 - 13.2124i) q^{87} +(-40.7219 - 8.10009i) q^{88} +(-49.5695 + 49.5695i) q^{89} +(20.4092 + 30.5445i) q^{90} +(-13.2421 + 2.63401i) q^{91} +(33.9306 - 50.7807i) q^{92} +(23.7361 - 57.3040i) q^{93} +(10.1960 + 4.22331i) q^{94} +(192.771 + 128.805i) q^{95} +(-9.98418 - 50.1939i) q^{96} +(106.223 - 70.9756i) q^{97} +(28.8834 + 28.8834i) q^{98} +(8.32019 - 41.8284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 16 q^{5} + 8 q^{7} + 8 q^{8} - 56 q^{9} - 48 q^{10} + 24 q^{11} + 24 q^{12} - 8 q^{14} - 80 q^{15} - 136 q^{18} - 80 q^{19} + 48 q^{20} + 64 q^{21} - 16 q^{22} - 104 q^{23}+ \cdots + 120 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 16 * q^5 + 8 * q^7 + 8 * q^8 - 56 * q^9 - 48 * q^10 + 24 * q^11 + 24 * q^12 - 8 * q^14 - 80 * q^15 - 136 * q^18 - 80 * q^19 + 48 * q^20 + 64 * q^21 - 16 * q^22 - 104 * q^23 - 136 * q^25 + 40 * q^26 + 32 * q^27 - 168 * q^30 + 144 * q^31 + 16 * q^32 + 80 * q^35 - 72 * q^36 + 48 * q^37 - 8 * q^38 - 96 * q^39 + 8 * q^40 + 208 * q^41 + 88 * q^42 + 48 * q^43 - 56 * q^44 + 48 * q^45 - 80 * q^46 + 80 * q^47 - 256 * q^48 + 72 * q^49 + 240 * q^52 + 88 * q^53 + 32 * q^54 + 8 * q^55 - 8 * q^56 + 40 * q^57 - 120 * q^58 - 40 * q^59 - 96 * q^60 - 16 * q^61 + 256 * q^62 + 96 * q^63 + 120 * q^64 - 72 * q^65 - 120 * q^66 - 208 * q^69 + 96 * q^70 - 328 * q^71 - 24 * q^72 + 160 * q^73 + 168 * q^74 - 264 * q^75 + 192 * q^76 + 120 * q^77 - 168 * q^78 - 352 * q^79 - 328 * q^80 + 224 * q^81 + 320 * q^82 + 504 * q^83 + 288 * q^86 + 216 * q^87 - 56 * q^88 - 288 * q^89 + 392 * q^90 + 32 * q^91 - 200 * q^92 + 248 * q^93 + 72 * q^94 + 800 * q^95 - 408 * q^96 + 504 * q^97 - 16 * q^98 + 120 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{16}\right)$

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 $

$2$	0.783227	−	0.324423i	0.391614	−	0.162212i	−0.178183	−	0.983997i	$-0.557022\pi$
$2$	0.783227	−	0.324423i	0.391614	−	0.162212i	0.569797	+	0.821786i	$0.307022\pi$
$3$	1.59946	+	0.318152i	0.533152	+	0.106051i	0.454322	−	0.890838i	$-0.349882\pi$
$3$	1.59946	+	0.318152i	0.533152	+	0.106051i	0.0788300	+	0.996888i	$0.474882\pi$
$4$	−2.32023	+	2.32023i	−0.580058	+	0.580058i
$5$	−3.79690	−	5.68246i	−0.759379	−	1.13649i	−0.986681	−	0.162667i	$-0.947990\pi$
$5$	−3.79690	−	5.68246i	−0.759379	−	1.13649i	0.227302	−	0.973824i	$-0.427010\pi$
$6$	1.35595	−	0.269716i	0.225992	−	0.0449527i
$7$	0.502268	−	0.751697i	0.0717526	−	0.107385i	−0.793858	−	0.608103i	$-0.791931\pi$
$7$	0.502268	−	0.751697i	0.0717526	−	0.107385i	0.865610	+	0.500718i	$0.166931\pi$
$8$	−2.36223	+	5.70292i	−0.295278	+	0.712865i
$9$	−5.85788	−	2.42641i	−0.650875	−	0.269601i
$10$	−4.81736	−	3.21885i	−0.481736	−	0.321885i
$11$	1.31223	+	6.59700i	0.119293	+	0.599727i	0.993468	+	0.114115i	$0.0364033\pi$
$11$	1.31223	+	6.59700i	0.119293	+	0.599727i	−0.874174	+	0.485612i	$0.838597\pi$
$12$	−4.44930	+	2.97292i	−0.370775	+	0.247744i
$13$	−10.5602	−	10.5602i	−0.812320	−	0.812320i	0.172662	−	0.984981i	$-0.444763\pi$
$13$	−10.5602	−	10.5602i	−0.812320	−	0.812320i	−0.984981	+	0.172662i	$0.944763\pi$
$14$	0.149522	−	0.751697i	0.0106801	−	0.0536927i
$15$	−4.26509	−	10.2968i	−0.284339	−	0.686455i
$16$		−	7.89218i		−	0.493261i
$17$		0			0
$17$		0			0
$18$	−5.37523			−0.298624
$19$	−31.3415	+	12.9821i	−1.64955	+	0.683268i	−0.997209	−	0.0746542i	$-0.976215\pi$
$19$	−31.3415	+	12.9821i	−1.64955	+	0.683268i	−0.652345	+	0.757922i	$0.726215\pi$
$20$	21.9943	+	4.37494i	1.09972	+	0.218747i
$21$	1.04251	−	1.04251i	0.0496433	−	0.0496433i
$22$	3.16799	+	4.74123i	0.144000	+	0.215511i
$23$	−18.2549	+	3.63113i	−0.793692	+	0.157875i	−0.575253	−	0.817975i	$-0.695096\pi$
$23$	−18.2549	+	3.63113i	−0.793692	+	0.157875i	−0.218439	+	0.975851i	$0.570096\pi$
$24$	−5.59267	+	8.37002i	−0.233028	+	0.348751i
$25$	−8.30682	+	20.0544i	−0.332273	+	0.802177i
$26$	−11.6970	−	4.84504i	−0.449883	−	0.186348i
$27$	−20.8010	−	13.8988i	−0.770409	−	0.514771i
$28$	0.578734	+	2.90949i	0.0206691	+	0.103910i
$29$	17.6031	−	11.7620i	0.607004	−	0.405587i	−0.213734	−	0.976892i	$-0.568563\pi$
$29$	17.6031	−	11.7620i	0.607004	−	0.405587i	0.820738	+	0.571305i	$0.193563\pi$
$30$	−6.68107	−	6.68107i	−0.222702	−	0.222702i
$31$	7.42005	−	37.3031i	0.239356	−	1.20333i	−0.654881	−	0.755732i	$-0.727281\pi$
$31$	7.42005	−	37.3031i	0.239356	−	1.20333i	0.894237	−	0.447593i	$-0.147719\pi$
$32$	−12.0093	−	28.9930i	−0.375291	−	0.906032i
$33$			10.9691i			0.332397i
$34$		0			0
$35$	−6.17855			−0.176530
$36$	19.2215	−	7.96180i	0.533930	−	0.221161i
$37$	39.3135	+	7.81994i	1.06253	+	0.211350i	0.695255	−	0.718764i	$-0.255292\pi$
$37$	39.3135	+	7.81994i	1.06253	+	0.211350i	0.367273	+	0.930113i	$0.380292\pi$
$38$	−20.3359	+	20.3359i	−0.535154	+	0.535154i
$39$	−13.5308	−	20.2502i	−0.346943	−	0.519237i
$40$	41.3757	−	8.23014i	1.03439	−	0.205753i
$41$	−2.09701	+	3.13840i	−0.0511466	+	0.0765463i	−0.856162	−	0.516708i	$-0.827157\pi$
$41$	−2.09701	+	3.13840i	−0.0511466	+	0.0765463i	0.805015	+	0.593254i	$0.202157\pi$
$42$	0.478307	−	1.15474i	0.0113883	−	0.0274937i
$43$	−12.5911	−	5.21542i	−0.292817	−	0.121289i	0.231439	−	0.972849i	$-0.425657\pi$
$43$	−12.5911	−	5.21542i	−0.292817	−	0.121289i	−0.524256	+	0.851561i	$0.675657\pi$
$44$	−18.3512	−	12.2619i	−0.417074	−	0.278680i
$45$	8.45377	+	42.5000i	0.187862	+	0.944444i
$46$	−13.1197	+	8.76632i	−0.285211	+	0.190572i
$47$	9.20504	+	9.20504i	0.195852	+	0.195852i	0.798219	−	0.602367i	$-0.205776\pi$
$47$	9.20504	+	9.20504i	0.195852	+	0.195852i	−0.602367	+	0.798219i	$0.705776\pi$
$48$	2.51091	−	12.6232i	0.0523106	−	0.262983i
$49$	18.4387	+	44.5150i	0.376300	+	0.908469i
$50$			18.4021i			0.368042i
$51$		0			0
$52$	49.0040			0.942385
$53$	1.84317	−	0.763466i	0.0347768	−	0.0144050i	−0.365227	−	0.930918i	$-0.619009\pi$
$53$	1.84317	−	0.763466i	0.0347768	−	0.0144050i	0.400004	+	0.916513i	$0.369009\pi$
$54$	−20.8010	−	4.13758i	−0.385204	−	0.0766219i
$55$	32.5048	−	32.5048i	0.590996	−	0.590996i
$56$	3.10040	+	4.64007i	0.0553642	+	0.0828584i
$57$	−54.2597	+	10.7929i	−0.951924	+	0.189350i
$58$	9.97136	−	14.9232i	0.171920	−	0.257296i
$59$	−13.1653	+	31.7838i	−0.223140	+	0.538708i	−0.995313	−	0.0967043i	$-0.969170\pi$
$59$	−13.1653	+	31.7838i	−0.223140	+	0.538708i	0.772173	+	0.635412i	$0.219170\pi$
$60$	33.7870	+	13.9951i	0.563117	+	0.233251i
$61$	29.5202	+	19.7248i	0.483937	+	0.323357i	0.773493	−	0.633804i	$-0.218508\pi$
$61$	29.5202	+	19.7248i	0.483937	+	0.323357i	−0.289556	+	0.957161i	$0.593508\pi$
$62$	−6.29041	−	31.6240i	−0.101458	−	0.510065i
$63$	−4.76615	+	3.18464i	−0.0756532	+	0.0505498i
$64$	3.51042	+	3.51042i	0.0548503	+	0.0548503i
$65$	−19.9118	+	100.103i	−0.306336	+	1.54005i
$66$	3.55863	+	8.59130i	0.0539187	+	0.130171i
$67$		−	31.9912i		−	0.477480i	−0.971084	−	0.238740i	$-0.923266\pi$
$67$		−	31.9912i		−	0.477480i	0.971084	−	0.238740i	$-0.0767344\pi$
$68$		0			0
$69$	−30.3532			−0.439901
$70$	−4.83921	+	2.00446i	−0.0691315	+	0.0286352i
$71$	−101.633	−	20.2161i	−1.43146	−	0.284734i	−0.582342	−	0.812944i	$-0.697863\pi$
$71$	−101.633	−	20.2161i	−1.43146	−	0.284734i	−0.849114	+	0.528210i	$0.822863\pi$
$72$	27.6752	−	27.6752i	0.384378	−	0.384378i
$73$	34.9811	+	52.3530i	0.479194	+	0.717164i	0.989771	−	0.142668i	$-0.0455681\pi$
$73$	34.9811	+	52.3530i	0.479194	+	0.717164i	−0.510577	+	0.859832i	$0.670568\pi$
$74$	33.3284	−	6.62943i	0.450384	−	0.0895869i
$75$	−19.6667	+	29.4333i	−0.262223	+	0.392445i
$76$	42.5982	−	102.841i	0.560502	−	1.35317i
$77$	5.61804	+	2.32707i	0.0729615	+	0.0302216i
$78$	−17.1673	−	11.4708i	−0.220094	−	0.147062i
$79$	−12.7463	−	64.0800i	−0.161346	−	0.811140i	−0.973675	−	0.227941i	$-0.926801\pi$
$79$	−12.7463	−	64.0800i	−0.161346	−	0.811140i	0.812329	−	0.583199i	$-0.198199\pi$
$80$	−44.8470	+	29.9658i	−0.560587	+	0.374572i
$81$	11.5024	+	11.5024i	0.142005	+	0.142005i
$82$	−0.624266	+	3.13840i	−0.00761300	+	0.0382731i
$83$	16.4505	+	39.7149i	0.198198	+	0.478493i	0.991464	−	0.130383i	$-0.0416207\pi$
$83$	16.4505	+	39.7149i	0.198198	+	0.478493i	−0.793265	+	0.608876i	$0.791621\pi$
$84$			4.83773i			0.0575920i
$85$		0			0
$86$	−11.5537			−0.134346
$87$	31.8975	−	13.2124i	0.366638	−	0.151866i
$88$	−40.7219	−	8.10009i	−0.462749	−	0.0920465i
$89$	−49.5695	+	49.5695i	−0.556961	+	0.556961i	−0.928441	−	0.371480i	$-0.878850\pi$
$89$	−49.5695	+	49.5695i	−0.556961	+	0.556961i	0.371480	+	0.928441i	$0.378850\pi$
$90$	20.4092	+	30.5445i	0.226769	+	0.339384i
$91$	−13.2421	+	2.63401i	−0.145517	+	0.0289452i
$92$	33.9306	−	50.7807i	0.368811	−	0.551964i
$93$	23.7361	−	57.3040i	0.255227	−	0.616172i
$94$	10.1960	+	4.22331i	0.108468	+	0.0449288i
$95$	192.771	+	128.805i	2.02917	+	1.35585i
$96$	−9.98418	−	50.1939i	−0.104002	−	0.522853i
$97$	106.223	−	70.9756i	1.09508	−	0.731707i	0.129437	−	0.991588i	$-0.458683\pi$
$97$	106.223	−	70.9756i	1.09508	−	0.731707i	0.965641	+	0.259880i	$0.0836831\pi$
$98$	28.8834	+	28.8834i	0.294729	+	0.294729i
$99$	8.32019	−	41.8284i	0.0840423	−	0.422509i
$100$	−27.2572	−	65.8047i	−0.272572	−	0.658047i
$101$		−	37.1128i		−	0.367453i	−0.982977	−	0.183727i	$-0.941184\pi$
$101$		−	37.1128i		−	0.367453i	0.982977	−	0.183727i	$-0.0588162\pi$
$102$		0			0
$103$	−54.9138			−0.533144			−0.266572	−	0.963815i	$-0.585891\pi$
$103$	−54.9138			−0.533144			−0.266572	+	0.963815i	$0.585891\pi$
$104$	85.1691	−	35.2782i	0.818934	−	0.339214i
$105$	−9.88232	−	1.96571i	−0.0941173	−	0.0187211i
$106$	1.19594	−	1.19594i	0.0112824	−	0.0112824i
$107$	−82.5078	−	123.482i	−0.771101	−	1.15403i	−0.984210	−	0.177006i	$-0.943359\pi$
$107$	−82.5078	−	123.482i	−0.771101	−	1.15403i	0.213109	−	0.977029i	$-0.431641\pi$
$108$	80.5117	−	16.0148i	0.745479	−	0.148285i
$109$	13.2651	−	19.8526i	0.121698	−	0.182134i	−0.765618	−	0.643295i	$-0.777567\pi$
$109$	13.2651	−	19.8526i	0.121698	−	0.182134i	0.887317	+	0.461161i	$0.152567\pi$
$110$	14.9133	−	36.0040i	0.135576	−	0.327309i
$111$	60.3923	+	25.0153i	0.544075	+	0.225363i
$112$	−5.93253	−	3.96399i	−0.0529690	−	0.0353928i
$113$	−9.46384	−	47.5779i	−0.0837508	−	0.421044i	−0.999800	−	0.0199786i	$-0.993640\pi$
$113$	−9.46384	−	47.5779i	−0.0837508	−	0.421044i	0.916050	−	0.401065i	$-0.131360\pi$
$114$	−38.9962	+	26.0564i	−0.342072	+	0.228565i
$115$	89.9458	+	89.9458i	0.782137	+	0.782137i
$116$	−13.5527	+	68.1339i	−0.116833	+	0.587361i
$117$	36.2368	+	87.4834i	0.309716	+	0.747721i
$118$			29.1650i			0.247161i
$119$		0			0
$120$	68.7971			0.573309
$121$	69.9909	−	28.9912i	0.578437	−	0.239597i
$122$	29.5202	+	5.87193i	0.241969	+	0.0481306i
$123$	−4.35256	+	4.35256i	−0.0353867	+	0.0353867i
$124$	69.3356	+	103.768i	0.559158	+	0.836840i
$125$	−22.0743	+	4.39086i	−0.176595	+	0.0351269i
$126$	−2.69981	+	4.04055i	−0.0214270	+	0.0320678i
$127$	−18.4694	+	44.5892i	−0.145429	+	0.351096i	−0.979762	−	0.200164i	$-0.935853\pi$
$127$	−18.4694	+	44.5892i	−0.145429	+	0.351096i	0.834334	+	0.551260i	$0.185853\pi$
$128$	119.860	+	49.6478i	0.936410	+	0.387874i
$129$	−18.4797	−	12.3477i	−0.143253	−	0.0957187i
$130$	16.8804	+	84.8636i	0.129849	+	0.652797i
$131$	2.71527	−	1.81429i	0.0207273	−	0.0138495i	−0.545163	−	0.838330i	$-0.683532\pi$
$131$	2.71527	−	1.81429i	0.0207273	−	0.0138495i	0.565891	+	0.824480i	$0.308532\pi$
$132$	−25.4509	−	25.4509i	−0.192810	−	0.192810i
$133$	−5.98325	+	30.0798i	−0.0449868	+	0.226164i
$134$	−10.3787	−	25.0563i	−0.0774528	−	0.186988i
$135$			170.973i			1.26647i
$136$		0			0
$137$	−89.9517			−0.656581			−0.328291	−	0.944577i	$-0.606473\pi$
$137$	−89.9517			−0.656581			−0.328291	+	0.944577i	$0.606473\pi$
$138$	−23.7734	+	9.84728i	−0.172271	+	0.0713571i
$139$	−127.653	−	25.3917i	−0.918366	−	0.182674i	−0.286795	−	0.957992i	$-0.592590\pi$
$139$	−127.653	−	25.3917i	−0.918366	−	0.182674i	−0.631571	+	0.775318i	$0.717590\pi$
$140$	14.3357	−	14.3357i	0.102398	−	0.102398i
$141$	11.7945	+	17.6517i	0.0836487	+	0.125189i
$142$	−86.1606	+	17.1384i	−0.606765	+	0.120693i
$143$	55.8081	−	83.5227i	0.390266	−	0.584074i
$144$	−19.1497	+	46.2314i	−0.132984	+	0.321051i
$145$	−133.674	−	55.3697i	−0.921892	−	0.381860i
$146$	44.3827	+	29.6556i	0.303991	+	0.203120i
$147$	15.3294	+	77.0661i	0.104282	+	0.524259i
$148$	−109.361	+	73.0724i	−0.738923	+	0.493732i
$149$	−149.894	−	149.894i	−1.00600	−	1.00600i	−0.999982	−	0.00602015i	$-0.998084\pi$
$149$	−149.894	−	149.894i	−1.00600	−	1.00600i	−0.00602015	−	0.999982i	$-0.501916\pi$
$150$	−5.85466	+	29.4333i	−0.0390310	+	0.196222i
$151$	22.9009	+	55.2876i	0.151661	+	0.366143i	0.981390	−	0.192023i	$-0.0615050\pi$
$151$	22.9009	+	55.2876i	0.151661	+	0.366143i	−0.829729	+	0.558167i	$0.811505\pi$
$152$		−	209.405i		−	1.37766i
$153$		0			0
$154$	5.15515			0.0334750
$155$	−240.146	+	99.4719i	−1.54933	+	0.641754i
$156$	78.3798	+	15.5907i	0.502435	+	0.0999405i
$157$	104.330	−	104.330i	0.664524	−	0.664524i	−0.291919	−	0.956443i	$-0.594294\pi$
$157$	104.330	−	104.330i	0.664524	−	0.664524i	0.956443	+	0.291919i	$0.0942937\pi$
$158$	−30.7723	−	46.0540i	−0.194762	−	0.291481i
$159$	3.19097	−	0.634723i	0.0200690	−	0.00399197i
$160$	−119.154	+	178.326i	−0.744710	+	1.11454i
$161$	−6.43935	+	15.5460i	−0.0399960	+	0.0965588i
$162$	12.7406	+	5.27735i	0.0786460	+	0.0325762i
$163$	−269.657	−	180.179i	−1.65433	−	1.10539i	−0.883612	−	0.468220i	$-0.844896\pi$
$163$	−269.657	−	180.179i	−1.65433	−	1.10539i	−0.770722	−	0.637171i	$-0.780104\pi$
$164$	−2.41626	−	12.1474i	−0.0147333	−	0.0740693i
$165$	62.3315	−	41.6485i	0.377766	−	0.252415i
$166$	25.7689	+	25.7689i	0.155234	+	0.155234i
$167$	30.7648	−	154.665i	0.184220	−	0.926138i	−0.772474	−	0.635046i	$-0.780981\pi$
$167$	30.7648	−	154.665i	0.184220	−	0.926138i	0.956695	−	0.291093i	$-0.0940188\pi$
$168$	3.48270	+	8.40798i	0.0207304	+	0.0500475i
$169$			54.0337i			0.319726i
$170$		0			0
$171$	215.095			1.25786
$172$	41.3153	−	17.1134i	0.240205	−	0.0994963i
$173$	161.195	+	32.0637i	0.931763	+	0.185339i	0.637557	−	0.770403i	$-0.279945\pi$
$173$	161.195	+	32.0637i	0.931763	+	0.185339i	0.294205	+	0.955742i	$0.404945\pi$
$174$	20.6966	−	20.6966i	0.118946	−	0.118946i
$175$	10.9026	+	16.3169i	0.0623006	+	0.0932395i
$176$	52.0647	−	10.3563i	0.295822	−	0.0588427i
$177$	−31.1693	+	46.6482i	−0.176098	+	0.263549i
$178$	−22.7427	+	54.9057i	−0.127768	+	0.308459i
$179$	−179.301	−	74.2691i	−1.00168	−	0.414911i	−0.179269	−	0.983800i	$-0.557373\pi$
$179$	−179.301	−	74.2691i	−1.00168	−	0.414911i	−0.822414	+	0.568889i	$0.807373\pi$
$180$	−118.225	−	78.9951i	−0.656803	−	0.438862i
$181$	9.74440	+	48.9884i	0.0538365	+	0.270654i	0.998323	−	0.0578972i	$-0.0184396\pi$
$181$	9.74440	+	48.9884i	0.0538365	+	0.270654i	−0.944486	+	0.328551i	$0.893440\pi$
$182$	−9.51701	+	6.35906i	−0.0522913	+	0.0349399i
$183$	40.9408	+	40.9408i	0.223720	+	0.223720i
$184$	22.4142	−	112.684i	0.121816	−	0.612412i
$185$	−104.833	−	253.089i	−0.566664	−	1.36805i
$186$		−	52.5826i		−	0.282702i
$187$		0			0
$188$	−42.7157			−0.227211
$189$	−20.8954	+	8.65515i	−0.110558	+	0.0457944i
$190$	192.771	+	38.3445i	1.01458	+	0.201813i
$191$	−210.946	+	210.946i	−1.10443	+	1.10443i	−0.110561	+	0.993869i	$0.535265\pi$
$191$	−210.946	+	210.946i	−1.10443	+	1.10443i	−0.993869	+	0.110561i	$0.964735\pi$
$192$	4.49791	+	6.73160i	0.0234266	+	0.0350604i
$193$	−55.2758	+	10.9950i	−0.286403	+	0.0569692i	−0.336201	−	0.941790i	$-0.609142\pi$
$193$	−55.2758	+	10.9950i	−0.286403	+	0.0569692i	0.0497980	+	0.998759i	$0.484142\pi$
$194$	60.1702	−	90.0511i	0.310156	−	0.464181i
$195$	−63.6961	+	153.776i	−0.326647	+	0.788595i
$196$	−146.067	−	60.5030i	−0.745241	−	0.308689i
$197$	3.11338	+	2.08029i	0.0158040	+	0.0105599i	0.563447	−	0.826152i	$-0.309475\pi$
$197$	3.11338	+	2.08029i	0.0158040	+	0.0105599i	−0.547643	+	0.836712i	$0.684475\pi$
$198$	−7.05352	−	35.4604i	−0.0356238	−	0.179093i
$199$	123.865	−	82.7638i	0.622436	−	0.415898i	−0.203967	−	0.978978i	$-0.565383\pi$
$199$	123.865	−	82.7638i	0.622436	−	0.415898i	0.826403	+	0.563079i	$0.190383\pi$
$200$	−94.7461	−	94.7461i	−0.473731	−	0.473731i
$201$	10.1780	−	51.1685i	0.0506370	−	0.254569i
$202$	−12.0403	−	29.0678i	−0.0596052	−	0.143900i
$203$		−	19.1399i		−	0.0942851i
$204$		0			0
$205$	25.7959			0.125834
$206$	−43.0100	+	17.8153i	−0.208786	+	0.0864821i
$207$	115.746	+	23.0232i	0.559158	+	0.111223i
$208$	−83.3426	+	83.3426i	−0.400686	+	0.400686i
$209$	−126.770	−	189.725i	−0.606555	−	0.907774i
$210$	−8.37782	+	1.66645i	−0.0398944	+	0.00793549i
$211$	−164.944	+	246.857i	−0.781727	+	1.16994i	0.200029	+	0.979790i	$0.435896\pi$
$211$	−164.944	+	246.857i	−0.781727	+	1.16994i	−0.981756	+	0.190147i	$0.939104\pi$
$212$	−2.50517	+	6.04800i	−0.0118168	+	0.0285283i
$213$	−156.126	−	64.6696i	−0.732987	−	0.303613i
$214$	−104.683	−	69.9468i	−0.489172	−	0.326854i
$215$	18.1708	+	91.3509i	0.0845155	+	0.424888i
$216$	128.400	−	85.7944i	0.594446	−	0.397196i
$217$	−24.3138	−	24.3138i	−0.112045	−	0.112045i
$218$	3.94893	−	19.8526i	0.0181144	−	0.0910670i
$219$	39.2946	+	94.8656i	0.179428	+	0.433176i
$220$			150.837i			0.685625i
$221$		0			0
$222$	55.4165			0.249624
$223$	−83.2008	+	34.4629i	−0.373098	+	0.154542i	−0.561350	−	0.827579i	$-0.689718\pi$
$223$	−83.2008	+	34.4629i	−0.373098	+	0.154542i	0.188252	+	0.982121i	$0.439718\pi$
$224$	−27.8259	−	5.53491i	−0.124223	−	0.0247094i
$225$	97.3206	−	97.3206i	0.432536	−	0.432536i
$226$	−22.8477	−	34.1940i	−0.101096	−	0.151301i
$227$	146.304	−	29.1017i	0.644512	−	0.128201i	0.137997	−	0.990433i	$-0.455934\pi$
$227$	146.304	−	29.1017i	0.644512	−	0.128201i	0.506515	+	0.862231i	$0.330934\pi$
$228$	100.853	−	150.937i	0.442338	−	0.662005i
$229$	−52.3955	+	126.494i	−0.228801	+	0.552375i	−0.996032	−	0.0889961i	$-0.971634\pi$
$229$	−52.3955	+	126.494i	−0.228801	+	0.552375i	0.767231	+	0.641371i	$0.221634\pi$
$230$	99.6285	+	41.2675i	0.433167	+	0.179424i
$231$	8.24544	+	5.50943i	0.0356946	+	0.0238503i
$232$	25.4953	+	128.174i	0.109894	+	0.552472i
$233$	−296.676	+	198.232i	−1.27329	+	0.850782i	−0.993995	−	0.109424i	$-0.965099\pi$
$233$	−296.676	+	198.232i	−1.27329	+	0.850782i	−0.279291	+	0.960207i	$0.590099\pi$
$234$	56.7633	+	56.7633i	0.242578	+	0.242578i
$235$	17.3567	−	87.2579i	0.0738582	−	0.371310i
$236$	−43.1993	−	104.292i	−0.183048	−	0.441916i
$237$		−	106.548i		−	0.449572i
$238$		0			0
$239$	−398.078			−1.66560			−0.832800	−	0.553574i	$-0.813264\pi$
$239$	−398.078			−1.66560			−0.832800	+	0.553574i	$0.813264\pi$
$240$	−81.2644	+	33.6608i	−0.338602	+	0.140253i
$241$	77.8198	+	15.4793i	0.322904	+	0.0642296i	0.353881	−	0.935291i	$-0.384862\pi$
$241$	77.8198	+	15.4793i	0.322904	+	0.0642296i	−0.0309769	+	0.999520i	$0.509862\pi$
$242$	45.4134	−	45.4134i	0.187659	−	0.187659i
$243$	139.827	+	209.266i	0.575421	+	0.861179i
$244$	−114.260	+	22.7277i	−0.468278	+	0.0931462i
$245$	182.945	−	273.796i	0.746713	−	1.11753i
$246$	−1.99697	+	4.82112i	−0.00811777	+	0.0195980i
$247$	468.064	+	193.879i	1.89500	+	0.784934i
$248$	195.209	+	130.434i	0.787131	+	0.525944i
$249$	13.6764	+	68.7560i	0.0549254	+	0.276129i
$250$	−15.8647	+	10.6005i	−0.0634589	+	0.0424019i
$251$	−320.583	−	320.583i	−1.27722	−	1.27722i	−0.942215	−	0.335010i	$-0.891260\pi$
$251$	−320.583	−	320.583i	−1.27722	−	1.27722i	−0.335010	−	0.942215i	$-0.608740\pi$
$252$	3.66947	−	18.4477i	0.0145614	−	0.0732051i
$253$	−47.9091	−	115.663i	−0.189364	−	0.457166i
$254$			40.9154i			0.161084i
$255$		0			0
$256$	90.1270			0.352058
$257$	90.9757	−	37.6834i	0.353991	−	0.146628i	−0.198600	−	0.980081i	$-0.563639\pi$
$257$	90.9757	−	37.6834i	0.353991	−	0.146628i	0.552591	+	0.833453i	$0.313639\pi$
$258$	−18.4797	−	3.67583i	−0.0716266	−	0.0142474i
$259$	25.6241	−	25.6241i	0.0989349	−	0.0989349i
$260$	−186.063	−	278.463i	−0.715628	−	1.07101i
$261$	−131.656	+	26.1881i	−0.504430	+	0.100337i
$262$	1.53808	−	2.30190i	0.00587052	−	0.00878586i
$263$	34.4297	−	83.1206i	0.130911	−	0.316048i	−0.844809	−	0.535068i	$-0.820286\pi$
$263$	34.4297	−	83.1206i	0.130911	−	0.316048i	0.975720	+	0.219020i	$0.0702860\pi$
$264$	−62.5559	−	25.9115i	−0.236954	−	0.0981496i
$265$	−11.3367	−	7.57494i	−0.0427800	−	0.0285847i
$266$	5.07235	+	25.5004i	0.0190690	+	0.0958663i
$267$	−95.0549	+	63.5136i	−0.356011	+	0.237879i
$268$	74.2269	+	74.2269i	0.276966	+	0.276966i
$269$	−92.3448	+	464.249i	−0.343289	+	1.72583i	0.294527	+	0.955643i	$0.404838\pi$
$269$	−92.3448	+	464.249i	−0.343289	+	1.72583i	−0.637816	+	0.770189i	$0.720162\pi$
$270$	55.4677	+	133.911i	0.205436	+	0.495967i
$271$		−	61.4406i		−	0.226718i	−0.993554	−	0.113359i	$-0.963839\pi$
$271$		−	61.4406i		−	0.226718i	0.993554	−	0.113359i	$-0.0361611\pi$
$272$		0			0
$273$	−22.0181			−0.0806524
$274$	−70.4526	+	29.1824i	−0.257126	+	0.106505i
$275$	−143.199	−	28.4841i	−0.520725	−	0.103579i
$276$	70.4265	−	70.4265i	0.255168	−	0.255168i
$277$	82.8732	+	124.029i	0.299181	+	0.447756i	0.950353	−	0.311174i	$-0.100722\pi$
$277$	82.8732	+	124.029i	0.299181	+	0.447756i	−0.651172	+	0.758930i	$0.725722\pi$
$278$	−108.219	+	21.5261i	−0.389276	+	0.0774319i
$279$	−133.978	+	200.513i	−0.480209	+	0.718684i
$280$	14.5951	−	35.2357i	0.0521254	−	0.125842i
$281$	−31.3685	−	12.9932i	−0.111632	−	0.0462393i	0.326169	−	0.945312i	$-0.394242\pi$
$281$	−31.3685	−	12.9932i	−0.111632	−	0.0462393i	−0.437800	+	0.899072i	$0.644242\pi$
$282$	14.9644	+	9.99886i	0.0530651	+	0.0354570i
$283$	−36.8848	−	185.432i	−0.130335	−	0.655238i	−0.989616	−	0.143734i	$-0.954089\pi$
$283$	−36.8848	−	185.432i	−0.130335	−	0.655238i	0.859281	−	0.511503i	$-0.170911\pi$
$284$	282.719	−	188.907i	0.995490	−	0.665165i
$285$	267.349	+	267.349i	0.938066	+	0.938066i
$286$	16.6137	−	83.5227i	0.0580898	−	0.292037i
$287$	1.30586	+	3.15263i	0.00455005	+	0.0109848i
$288$			198.977i			0.690893i
$289$		0			0
$290$	−122.661			−0.422968
$291$	192.479	−	79.7275i	0.661441	−	0.273978i
$292$	−202.636	−	40.3067i	−0.693957	−	0.138037i
$293$	−125.147	+	125.147i	−0.427121	+	0.427121i	−0.887647	−	0.460525i	$-0.847661\pi$
$293$	−125.147	+	125.147i	−0.427121	+	0.427121i	0.460525	+	0.887647i	$0.347661\pi$
$294$	37.0084	+	55.3870i	0.125879	+	0.188391i
$295$	230.597	−	45.8686i	0.781685	−	0.155487i
$296$	−137.464	+	205.729i	−0.464405	+	0.695031i
$297$	64.3948	−	155.463i	0.216817	−	0.523444i
$298$	−166.031	−	68.7721i	−0.557149	−	0.230779i
$299$	231.120	+	154.429i	0.772977	+	0.516487i
$300$	−22.6608	−	113.924i	−0.0755361	−	0.379745i
$301$	−10.2445	+	6.84518i	−0.0340350	+	0.0227415i
$302$	35.8732	+	35.8732i	0.118785	+	0.118785i
$303$	11.8075	−	59.3603i	0.0389686	−	0.195909i
$304$	102.457	+	247.353i	0.337029	+	0.813661i
$305$		−	242.640i		−	0.795541i
$306$		0			0
$307$	368.138			1.19914			0.599572	−	0.800320i	$-0.295337\pi$
$307$	368.138			1.19914			0.599572	+	0.800320i	$0.295337\pi$
$308$	−18.4345	+	7.63581i	−0.0598522	+	0.0247916i
$309$	−87.8322	−	17.4709i	−0.284247	−	0.0565402i
$310$	−155.818	+	155.818i	−0.502639	+	0.502639i
$311$	58.3833	+	87.3767i	0.187728	+	0.280954i	0.913381	−	0.407107i	$-0.133462\pi$
$311$	58.3833	+	87.3767i	0.187728	+	0.280954i	−0.725653	+	0.688061i	$0.758462\pi$
$312$	147.448	−	29.3293i	0.472590	−	0.0940040i
$313$	241.058	−	360.768i	0.770152	−	1.15261i	−0.214267	−	0.976775i	$-0.568736\pi$
$313$	241.058	−	360.768i	0.770152	−	1.15261i	0.984419	−	0.175839i	$-0.0562638\pi$
$314$	47.8672	−	115.562i	0.152443	−	0.368030i
$315$	36.1932	+	14.9917i	0.114899	+	0.0475927i
$316$	178.255	+	119.106i	0.564098	+	0.376918i
$317$	−102.229	−	513.941i	−0.322489	−	1.62126i	−0.713346	−	0.700812i	$-0.752821\pi$
$317$	−102.229	−	513.941i	−0.322489	−	1.62126i	0.390857	−	0.920452i	$-0.372179\pi$
$318$	2.29333	−	1.53236i	0.00721174	−	0.00481873i
$319$	100.693	+	100.693i	0.315653	+	0.315653i
$320$	6.61910	−	33.2765i	0.0206847	−	0.103989i
$321$	−92.6818	−	223.754i	−0.288728	−	0.697052i
$322$			14.2651i			0.0443016i
$323$		0			0
$324$	−53.3765			−0.164742
$325$	299.499	−	124.057i	0.921536	−	0.381713i
$326$	−269.657	−	53.6380i	−0.827167	−	0.164534i
$327$	27.5331	−	27.5331i	0.0841990	−	0.0841990i
$328$	−12.9444	−	19.3727i	−0.0394647	−	0.0590630i
$329$	11.5428	−	2.29601i	0.0350845	−	0.00697874i
$330$	35.3079	−	52.8421i	0.106994	−	0.160127i
$331$	134.652	−	325.078i	0.406803	−	0.982109i	−0.579171	−	0.815206i	$-0.696623\pi$
$331$	134.652	−	325.078i	0.406803	−	0.982109i	0.985973	−	0.166903i	$-0.0533765\pi$
$332$	−130.317	−	53.9790i	−0.392520	−	0.162587i
$333$	−211.319	−	141.199i	−0.634592	−	0.424021i
$334$	−26.0811	−	131.119i	−0.0780873	−	0.392571i
$335$	−181.788	+	121.467i	−0.542652	+	0.362588i
$336$	−8.22767	−	8.22767i	−0.0244871	−	0.0244871i
$337$	−30.3236	+	152.447i	−0.0899811	+	0.452366i	0.909358	+	0.416015i	$0.136573\pi$
$337$	−30.3236	+	152.447i	−0.0899811	+	0.452366i	−0.999339	+	0.0363511i	$0.988427\pi$
$338$	17.5298	+	42.3207i	0.0518633	+	0.125209i
$339$		−	79.1097i		−	0.233362i
$340$		0			0
$341$	255.825			0.750221
$342$	168.468	−	69.7818i	0.492597	−	0.204040i
$343$	86.1706	+	17.1404i	0.251226	+	0.0499720i
$344$	59.4862	−	59.4862i	0.172925	−	0.172925i
$345$	115.248	+	172.481i	0.334052	+	0.499944i
$346$	136.654	−	27.1823i	0.394955	−	0.0785614i
$347$	−148.631	+	222.442i	−0.428331	+	0.641042i	−0.981373	−	0.192111i	$-0.938467\pi$
$347$	−148.631	+	222.442i	−0.428331	+	0.641042i	0.553043	+	0.833153i	$0.313467\pi$
$348$	−43.3538	+	104.665i	−0.124580	+	0.300763i
$349$	182.414	+	75.5583i	0.522676	+	0.216499i	0.628392	−	0.777897i	$-0.283713\pi$
$349$	182.414	+	75.5583i	0.522676	+	0.216499i	−0.105716	+	0.994396i	$0.533713\pi$
$350$	13.8328	+	9.24278i	0.0395223	+	0.0264080i
$351$	72.8886	+	366.436i	0.207660	+	1.04398i
$352$	175.508	−	117.271i	0.498603	−	0.333156i
$353$	303.609	+	303.609i	0.860081	+	0.860081i	0.991347	−	0.131266i	$-0.0419041\pi$
$353$	303.609	+	303.609i	0.860081	+	0.860081i	−0.131266	+	0.991347i	$0.541904\pi$
$354$	−9.27891	+	46.6482i	−0.0262116	+	0.131775i
$355$	271.014	+	654.286i	0.763420	+	1.84306i
$356$		−	230.026i		−	0.646139i
$357$		0			0
$358$	−164.528			−0.459576
$359$	52.4599	−	21.7296i	0.146128	−	0.0605281i	−0.308421	−	0.951250i	$-0.599801\pi$
$359$	52.4599	−	21.7296i	0.146128	−	0.0605281i	0.454549	+	0.890722i	$0.349801\pi$
$360$	−262.343	−	52.1834i	−0.728732	−	0.144954i
$361$	558.492	−	558.492i	1.54707	−	1.54707i
$362$	23.5251	+	35.2078i	0.0649864	+	0.0972590i
$363$	121.171	−	24.1024i	0.333804	−	0.0663978i
$364$	24.6132	−	36.8362i	0.0676186	−	0.101198i
$365$	164.674	−	397.558i	0.451161	−	1.08920i
$366$	45.3481	+	18.7838i	0.123902	+	0.0513218i
$367$	189.076	+	126.337i	0.515195	+	0.344242i	0.785833	−	0.618439i	$-0.212235\pi$
$367$	189.076	+	126.337i	0.515195	+	0.344242i	−0.270638	+	0.962681i	$0.587235\pi$
$368$	28.6575	+	144.071i	0.0778737	+	0.391497i
$369$	19.8991	−	13.2961i	0.0539270	−	0.0360329i
$370$	−164.216	−	164.216i	−0.443827	−	0.443827i
$371$	0.351870	−	1.76897i	0.000948437	−	0.00476811i
$372$	77.8853	+	188.032i	0.209369	+	0.505462i
$373$			460.172i			1.23370i	0.787079	+	0.616852i	$0.211592\pi$
$373$			460.172i			1.23370i	−0.787079	+	0.616852i	$0.788408\pi$
$374$		0			0
$375$	−36.7039			−0.0978771
$376$	−74.2400	+	30.7512i	−0.197447	+	0.0817851i
$377$	−310.100	−	61.6828i	−0.822547	−	0.163615i
$378$	−13.5579	+	13.5579i	−0.0358675	+	0.0358675i
$379$	34.1975	+	51.1802i	0.0902309	+	0.135040i	0.873839	−	0.486215i	$-0.161623\pi$
$379$	34.1975	+	51.1802i	0.0902309	+	0.135040i	−0.783608	+	0.621255i	$0.786623\pi$
$380$	−746.131	+	148.415i	−1.96350	+	0.390565i
$381$	−43.7272	+	65.4423i	−0.114769	+	0.171765i
$382$	−96.7829	+	233.655i	−0.253358	+	0.611661i
$383$	568.960	+	235.671i	1.48554	+	0.615329i	0.970340	−	0.241744i	$-0.0777193\pi$
$383$	568.960	+	235.671i	1.48554	+	0.615329i	0.515196	+	0.857073i	$0.327719\pi$
$384$	175.916	+	117.543i	0.458115	+	0.306102i
$385$	−8.10764	−	40.7599i	−0.0210588	−	0.105870i
$386$	−39.7265	+	26.5444i	−0.102918	+	0.0687678i
$387$	61.1025	+	61.1025i	0.157888	+	0.157888i
$388$	−81.7810	+	411.141i	−0.210776	+	1.05964i
$389$	−139.475	−	336.723i	−0.358549	−	0.865613i	−0.995505	−	0.0947127i	$-0.969807\pi$
$389$	−139.475	−	336.723i	−0.358549	−	0.865613i	0.636956	−	0.770900i	$-0.280193\pi$
$390$			141.106i			0.361811i
$391$		0			0
$392$	−297.422			−0.758729
$393$	4.92017	−	2.03800i	0.0125195	−	0.00518576i
$394$	3.11338	+	0.619290i	0.00790198	+	0.00157180i
$395$	−315.736	+	315.736i	−0.799331	+	0.799331i
$396$	77.7469	+	116.356i	0.196331	+	0.293829i
$397$	59.0458	−	11.7449i	0.148730	−	0.0295842i	−0.120164	−	0.992754i	$-0.538342\pi$
$397$	59.0458	−	11.7449i	0.148730	−	0.0295842i	0.268894	+	0.963170i	$0.413342\pi$
$398$	70.1638	−	105.007i	0.176291	−	0.263838i
$399$	−19.1399	+	46.2078i	−0.0479697	+	0.115809i
$400$	158.273	+	65.5589i	0.395683	+	0.163897i
$401$	16.1872	+	10.8160i	0.0403671	+	0.0269725i	0.575590	−	0.817738i	$-0.304772\pi$
$401$	16.1872	+	10.8160i	0.0403671	+	0.0269725i	−0.535223	+	0.844711i	$0.679772\pi$
$402$	−8.62852	−	43.3785i	−0.0214640	−	0.107907i
$403$	−472.283	+	315.570i	−1.17192	+	0.783051i
$404$	86.1103	+	86.1103i	0.213144	+	0.213144i
$405$	21.6885	−	109.035i	0.0535518	−	0.269223i
$406$	−6.20943	−	14.9909i	−0.0152942	−	0.0369233i
$407$			269.613i			0.662439i
$408$		0			0
$409$	434.868			1.06325			0.531623	−	0.846981i	$-0.321582\pi$
$409$	434.868			1.06325			0.531623	+	0.846981i	$0.321582\pi$
$410$	20.2041	−	8.36881i	0.0492783	−	0.0204117i
$411$	−143.874	−	28.6183i	−0.350058	−	0.0696308i
$412$	127.413	−	127.413i	0.309254	−	0.309254i
$413$	17.2793	+	25.8603i	0.0418385	+	0.0626157i
$414$	98.1244	−	19.5182i	0.237016	−	0.0471453i
$415$	163.218	−	244.272i	0.393296	−	0.588608i
$416$	−179.351	+	432.991i	−0.431132	+	1.04084i
$417$	−196.097	−	81.2259i	−0.470256	−	0.194786i
$418$	−160.841	−	107.470i	−0.384787	−	0.257106i
$419$	−15.7958	−	79.4107i	−0.0376988	−	0.189524i	0.957347	−	0.288940i	$-0.0933027\pi$
$419$	−15.7958	−	79.4107i	−0.0376988	−	0.189524i	−0.995046	+	0.0994154i	$0.968303\pi$
$420$	27.4902	−	18.3684i	0.0654528	−	0.0437342i
$421$	−211.099	−	211.099i	−0.501423	−	0.501423i	0.410457	−	0.911880i	$-0.365369\pi$
$421$	−211.099	−	211.099i	−0.501423	−	0.501423i	−0.911880	+	0.410457i	$0.865369\pi$
$422$	−49.1028	+	246.857i	−0.116357	+	0.584968i
$423$	−31.5868	−	76.2572i	−0.0746732	−	0.180277i
$424$			12.3149i			0.0290446i
$425$		0			0
$426$	−143.263			−0.336297
$427$	29.6541	−	12.2831i	0.0694475	−	0.0287661i
$428$	477.944	+	95.0689i	1.11669	+	0.222124i
$429$	115.835	−	115.835i	0.270013	−	0.270013i
$430$	43.8683	+	65.6535i	0.102019	+	0.152683i
$431$	589.715	−	117.302i	1.36825	−	0.272161i	0.544330	−	0.838871i	$-0.316784\pi$
$431$	589.715	−	117.302i	1.36825	−	0.272161i	0.823917	+	0.566710i	$0.191784\pi$
$432$	−109.692	+	164.165i	−0.253916	+	0.380013i
$433$	168.058	−	405.728i	0.388125	−	0.937017i	−0.602212	−	0.798336i	$-0.705714\pi$
$433$	168.058	−	405.728i	0.388125	−	0.937017i	0.990337	−	0.138681i	$-0.0442862\pi$
$434$	−26.9312	−	11.1553i	−0.0620534	−	0.0257034i
$435$	−196.190	−	131.090i	−0.451012	−	0.301357i
$436$	15.2846	+	76.8408i	0.0350564	+	0.176240i
$437$	524.998	−	350.792i	1.20137	−	0.802728i
$438$	61.5532	+	61.5532i	0.140533	+	0.140533i
$439$	124.628	−	626.548i	0.283891	−	1.42722i	−0.530887	−	0.847443i	$-0.678141\pi$
$439$	124.628	−	626.548i	0.283891	−	1.42722i	0.814778	−	0.579773i	$-0.196859\pi$
$440$	108.588	+	262.156i	0.246792	+	0.595809i
$441$		−	305.503i		−	0.692751i
$442$		0			0
$443$	−79.9030			−0.180368			−0.0901839	−	0.995925i	$-0.528745\pi$
$443$	−79.9030			−0.180368			−0.0901839	+	0.995925i	$0.528745\pi$
$444$	−198.166	+	82.0829i	−0.446319	+	0.184871i
$445$	469.887	+	93.4663i	1.05593	+	0.210037i
$446$	−53.9846	+	53.9846i	−0.121042	+	0.121042i
$447$	−192.060	−	287.438i	−0.429665	−	0.643039i
$448$	4.40194	−	0.875600i	0.00982576	−	0.00195446i
$449$	81.8038	−	122.428i	0.182191	−	0.272668i	−0.729121	−	0.684385i	$-0.760071\pi$
$449$	81.8038	−	122.428i	0.182191	−	0.272668i	0.911312	+	0.411717i	$0.135071\pi$
$450$	44.6511	−	107.797i	0.0992246	−	0.239549i
$451$	−23.4558	−	9.71569i	−0.0520083	−	0.0215426i
$452$	132.350	+	88.4335i	0.292810	+	0.195649i
$453$	19.0391	+	95.7161i	0.0420289	+	0.211294i
$454$	105.148	−	70.2578i	0.231604	−	0.154753i
$455$	65.2464	+	65.2464i	0.143399	+	0.143399i
$456$	66.6225	−	334.934i	0.146102	−	0.734504i
$457$	−246.790	−	595.804i	−0.540022	−	1.30373i	−0.924706	−	0.380681i	$-0.875690\pi$
$457$	−246.790	−	595.804i	−0.540022	−	1.30373i	0.384684	−	0.923048i	$-0.374310\pi$
$458$			116.072i			0.253432i
$459$		0			0
$460$	−417.390			−0.907370
$461$	236.885	−	98.1211i	0.513851	−	0.212844i	−0.110663	−	0.993858i	$-0.535297\pi$
$461$	236.885	−	98.1211i	0.513851	−	0.212844i	0.624513	+	0.781014i	$0.285297\pi$
$462$	8.24544	+	1.64012i	0.0178473	+	0.00355004i
$463$	−422.873	+	422.873i	−0.913332	+	0.913332i	−0.996533	−	0.0832008i	$-0.973486\pi$
$463$	−422.873	+	422.873i	−0.913332	+	0.913332i	0.0832008	+	0.996533i	$0.473486\pi$
$464$	−92.8279	−	138.927i	−0.200060	−	0.299411i
$465$	−415.751	+	82.6980i	−0.894088	+	0.177845i
$466$	−168.053	+	251.509i	−0.360629	+	0.539720i
$467$	−194.429	+	469.394i	−0.416337	+	1.00513i	0.567063	+	0.823674i	$0.308080\pi$
$467$	−194.429	+	469.394i	−0.416337	+	1.00513i	−0.983400	+	0.181452i	$0.941920\pi$
$468$	−287.060	−	118.904i	−0.613375	−	0.254068i
$469$	−24.0477	−	16.0681i	−0.0512743	−	0.0342604i
$470$	−14.7143	−	73.9736i	−0.0313070	−	0.157391i
$471$	200.065	−	133.679i	0.424766	−	0.283819i
$472$	−150.161	−	150.161i	−0.318137	−	0.318137i
$473$	17.8837	−	89.9075i	0.0378091	−	0.190079i
$474$	−34.5668	−	83.4517i	−0.0729258	−	0.176058i
$475$		−	736.376i		−	1.55027i
$476$		0			0
$477$	−12.6495			−0.0265190
$478$	−311.786	+	129.146i	−0.652272	+	0.270180i
$479$	389.100	+	77.3968i	0.812317	+	0.161580i	0.583735	−	0.811944i	$-0.301591\pi$
$479$	389.100	+	77.3968i	0.812317	+	0.161580i	0.228583	+	0.973524i	$0.426591\pi$
$480$	−247.316	+	247.316i	−0.515241	+	0.515241i
$481$	−332.577	−	497.737i	−0.691428	−	1.03480i
$482$	65.9725	−	13.1227i	0.136872	−	0.0272256i
$483$	−15.2454	+	22.8164i	−0.0315641	+	0.0472389i
$484$	−95.1289	+	229.662i	−0.196547	+	0.474507i
$485$	−806.632	−	334.118i	−1.66316	−	0.688903i
$486$	177.407	+	118.540i	0.365036	+	0.243909i
$487$	75.2872	+	378.494i	0.154594	+	0.777196i	0.977814	+	0.209474i	$0.0671751\pi$
$487$	75.2872	+	378.494i	0.154594	+	0.777196i	−0.823220	+	0.567722i	$0.807825\pi$
$488$	−182.222	+	121.757i	−0.373406	+	0.249502i
$489$	−373.980	−	373.980i	−0.764784	−	0.764784i
$490$	54.4614	−	273.796i	0.111146	−	0.558767i
$491$	−178.428	−	430.764i	−0.363398	−	0.877319i	−0.994798	−	0.101863i	$-0.967520\pi$
$491$	−178.428	−	430.764i	−0.363398	−	0.877319i	0.631401	−	0.775457i	$-0.282480\pi$
$492$		−	20.1979i		−	0.0410527i
$493$		0			0
$494$	429.499			0.869432
$495$	−269.279	+	111.539i	−0.543998	+	0.225331i
$496$	−294.403	−	58.5603i	−0.593554	−	0.118065i
$497$	−66.2436	+	66.2436i	−0.133287	+	0.133287i
$498$	33.0178	+	49.4146i	0.0663008	+	0.0992262i
$499$	−179.332	+	35.6714i	−0.359384	+	0.0714858i	−0.371480	−	0.928441i	$-0.621150\pi$
$499$	−179.332	+	35.6714i	−0.359384	+	0.0714858i	0.0120963	+	0.999927i	$0.496150\pi$
$500$	41.0298	−	61.4054i	0.0820596	−	0.122811i
$501$	98.4139	−	237.592i	0.196435	−	0.474236i
$502$	−355.094	−	147.085i	−0.707359	−	0.292998i
$503$	−533.984	−	356.797i	−1.06160	−	0.709337i	−0.103168	−	0.994664i	$-0.532898\pi$
$503$	−533.984	−	356.797i	−1.06160	−	0.709337i	−0.958430	+	0.285327i	$0.907898\pi$
$504$	−6.90301	−	34.7038i	−0.0136965	−	0.0688567i
$505$	−210.892	+	140.913i	−0.417608	+	0.279037i
$506$	−75.0475	−	75.0475i	−0.148315	−	0.148315i
$507$	−17.1909	+	86.4246i	−0.0339071	+	0.170463i
$508$	−60.6039	−	146.311i	−0.119299	−	0.288013i
$509$			177.040i			0.347819i	0.984762	+	0.173909i	$0.0556400\pi$
$509$			177.040i			0.347819i	−0.984762	+	0.173909i	$0.944360\pi$
$510$		0			0
$511$	56.9235			0.111396
$512$	−408.852	+	169.352i	−0.798539	+	0.330766i
$513$	832.372	+	165.569i	1.62256	+	0.322747i
$514$	59.0293	−	59.0293i	0.114843	−	0.114843i
$515$	208.502	+	312.045i	0.404858	+	0.605913i
$516$	71.5267	−	14.2275i	0.138618	−	0.0275728i
$517$	−48.6466	+	72.8048i	−0.0940940	+	0.140822i
$518$	11.7565	−	28.3826i	0.0226959	−	0.0547927i
$519$	247.623	+	102.569i	0.477116	+	0.197628i
$520$	−523.845	−	350.022i	−1.00739	−	0.673120i
$521$	−59.5841	−	299.550i	−0.114365	−	0.574951i	−0.994891	−	0.100954i	$-0.967811\pi$
$521$	−59.5841	−	299.550i	−0.114365	−	0.574951i	0.880526	−	0.473997i	$-0.157189\pi$
$522$	−94.6208	+	63.2236i	−0.181266	+	0.121118i
$523$	291.958	+	291.958i	0.558238	+	0.558238i	0.928806	−	0.370568i	$-0.120837\pi$
$523$	291.958	+	291.958i	0.558238	+	0.558238i	−0.370568	+	0.928806i	$0.620837\pi$
$524$	−2.09049	+	10.5096i	−0.00398949	+	0.0200565i
$525$	12.2470	+	29.5669i	0.0233276	+	0.0563178i
$526$		−	76.2721i		−	0.145004i
$527$		0			0
$528$	86.5701			0.163959
$529$	−168.675	+	69.8676i	−0.318857	+	0.132075i
$530$	−11.3367	−	2.25501i	−0.0213900	−	0.00425473i
$531$	154.241	−	154.241i	0.290473	−	0.290473i
$532$	−55.9097	−	83.6747i	−0.105093	−	0.157283i
$533$	55.2867	−	10.9972i	0.103727	−	0.0206327i
$534$	−53.8443	+	80.5836i	−0.100832	+	0.150906i
$535$	−388.406	+	937.695i	−0.725992	+	1.75270i
$536$	182.443	+	75.5703i	0.340379	+	0.140989i
$537$	−263.156	−	175.835i	−0.490048	−	0.327440i
$538$	78.2862	+	393.571i	0.145513	+	0.731545i
$539$	−269.470	+	180.054i	−0.499944	+	0.334052i
$540$	−396.698	−	396.698i	−0.734626	−	0.734626i
$541$	−139.455	+	701.085i	−0.257772	+	1.29591i	0.607386	+	0.794407i	$0.292218\pi$
$541$	−139.455	+	701.085i	−0.257772	+	1.29591i	−0.865158	+	0.501499i	$0.832782\pi$
$542$	−19.9328	−	48.1220i	−0.0367763	−	0.0887859i
$543$			81.4550i			0.150009i
$544$		0			0
$545$	−163.178			−0.299409
$546$	−17.2452	+	7.14319i	−0.0315846	+	0.0130828i
$547$	−296.950	−	59.0670i	−0.542870	−	0.107984i	−0.0839647	−	0.996469i	$-0.526758\pi$
$547$	−296.950	−	59.0670i	−0.542870	−	0.107984i	−0.458905	+	0.888485i	$0.651758\pi$
$548$	208.709	−	208.709i	0.380855	−	0.380855i
$549$	−125.065	−	187.173i	−0.227805	−	0.340935i
$550$	−121.399	+	24.1477i	−0.220725	+	0.0439049i
$551$	−399.013	+	597.165i	−0.724161	+	1.08378i
$552$	71.7011	−	173.102i	0.129893	−	0.313590i
$553$	−54.5708	−	22.6040i	−0.0986815	−	0.0408752i
$554$	105.146	+	70.2565i	0.189795	+	0.126817i
$555$	−87.1549	−	438.157i	−0.157036	−	0.789473i
$556$	355.099	−	237.270i	0.638667	−	0.426744i
$557$	−708.431	−	708.431i	−1.27187	−	1.27187i	−0.945107	−	0.326762i	$-0.894042\pi$
$557$	−708.431	−	708.431i	−1.27187	−	1.27187i	−0.326762	−	0.945107i	$-0.605958\pi$
$558$	−39.8845	+	200.513i	−0.0714776	+	0.359342i
$559$	77.8887	+	188.040i	0.139336	+	0.336386i
$560$			48.7622i			0.0870753i
$561$		0			0
$562$	−28.7839			−0.0512170
$563$	−758.863	+	314.331i	−1.34789	+	0.558315i	−0.935705	−	0.352784i	$-0.885235\pi$
$563$	−758.863	+	314.331i	−1.34789	+	0.558315i	−0.412187	+	0.911099i	$0.635235\pi$
$564$	−68.3219	−	13.5901i	−0.121138	−	0.0240959i
$565$	−234.426	+	234.426i	−0.414914	+	0.414914i
$566$	−89.0477	−	133.269i	−0.157328	−	0.235458i
$567$	14.4236	−	2.86904i	0.0254385	−	0.00506003i
$568$	355.372	−	531.851i	0.625654	−	0.936358i
$569$	−163.849	+	395.568i	−0.287960	+	0.695198i	−0.999976	−	0.00696604i	$-0.997783\pi$
$569$	−163.849	+	395.568i	−0.287960	+	0.695198i	0.712015	+	0.702164i	$0.247783\pi$
$570$	296.129	+	122.661i	0.519525	+	0.215194i
$571$	334.021	+	223.186i	0.584976	+	0.390868i	0.812549	−	0.582893i	$-0.198079\pi$
$571$	334.021	+	223.186i	0.584976	+	0.390868i	−0.227574	+	0.973761i	$0.573079\pi$
$572$	64.3043	+	323.280i	0.112420	+	0.565174i
$573$	−404.512	+	270.286i	−0.705954	+	0.471704i
$574$	2.04558	+	2.04558i	0.00356372	+	0.00356372i
$575$	78.8200	−	396.255i	0.137078	−	0.689139i
$576$	−12.0459	−	29.0813i	−0.0209130	−	0.0504884i
$577$			324.254i			0.561965i	0.959713	+	0.280982i	$0.0906602\pi$
$577$			324.254i			0.561965i	−0.959713	+	0.280982i	$0.909340\pi$
$578$		0			0
$579$	−91.9094			−0.158738
$580$	438.626	−	181.685i	0.756252	−	0.313250i
$581$	38.1161	+	7.58177i	0.0656043	+	0.0130495i
$582$	124.890	−	124.890i	0.214587	−	0.214587i
$583$	7.45524	+	11.1576i	0.0127877	+	0.0191382i
$584$	−381.198	+	75.8250i	−0.652736	+	0.129837i
$585$	359.533	−	538.079i	0.614587	−	0.919794i
$586$	−57.4177	+	138.619i	−0.0979825	+	0.236551i
$587$	−248.922	−	103.107i	−0.424058	−	0.175651i	0.160440	−	0.987046i	$-0.448709\pi$
$587$	−248.922	−	103.107i	−0.424058	−	0.175651i	−0.584498	+	0.811395i	$0.698709\pi$
$588$	−214.379	−	143.243i	−0.364590	−	0.243611i
$589$	251.716	+	1265.46i	0.427362	+	2.14850i
$590$	165.729	−	110.737i	0.280897	−	0.187689i
$591$	4.31787	+	4.31787i	0.00730603	+	0.00730603i
$592$	61.7164	−	310.269i	0.104251	−	0.524103i
$593$	274.282	+	662.174i	0.462532	+	1.11665i	0.967354	+	0.253428i	$0.0815581\pi$
$593$	274.282	+	662.174i	0.462532	+	1.11665i	−0.504822	+	0.863223i	$0.668442\pi$
$594$		−	142.654i		−	0.240158i
$595$		0			0
$596$	695.579			1.16708
$597$	224.448	−	92.9693i	0.375959	−	0.155727i
$598$	231.120	+	45.9726i	0.386488	+	0.0768773i
$599$	330.421	−	330.421i	0.551622	−	0.551622i	−0.375287	−	0.926909i	$-0.622456\pi$
$599$	330.421	−	330.421i	0.551622	−	0.551622i	0.926909	+	0.375287i	$0.122456\pi$
$600$	−121.399	−	181.686i	−0.202331	−	0.302810i
$601$	31.5267	−	6.27105i	0.0524571	−	0.0104344i	−0.168792	−	0.985652i	$-0.553987\pi$
$601$	31.5267	−	6.27105i	0.0524571	−	0.0104344i	0.221249	+	0.975217i	$0.428987\pi$
$602$	−5.80306	+	8.68490i	−0.00963964	+	0.0144267i
$603$	−77.6237	+	187.400i	−0.128729	+	0.310780i
$604$	−181.416	−	75.1448i	−0.300357	−	0.124412i
$605$	−430.490	−	287.644i	−0.711553	−	0.475445i
$606$	−10.0099	−	50.3232i	−0.0165180	−	0.0830416i
$607$	−220.518	+	147.345i	−0.363291	+	0.242744i	−0.723796	−	0.690014i	$-0.757604\pi$
$607$	−220.518	+	147.345i	−0.363291	+	0.242744i	0.360505	+	0.932757i	$0.382604\pi$
$608$	752.780	+	752.780i	1.23813	+	1.23813i
$609$	6.08939	−	30.6134i	0.00999899	−	0.0502683i
$610$	−78.7181	−	190.042i	−0.129046	−	0.311545i
$611$		−	194.413i		−	0.318189i
$612$		0			0
$613$	−700.076			−1.14205			−0.571025	−	0.820933i	$-0.693454\pi$
$613$	−700.076			−1.14205			−0.571025	+	0.820933i	$0.693454\pi$
$614$	288.335	−	119.432i	0.469602	−	0.194515i
$615$	41.2595	+	8.20702i	0.0670886	+	0.0133447i
$616$	−26.5421	+	26.5421i	−0.0430879	+	0.0430879i
$617$	398.778	+	596.814i	0.646318	+	0.967283i	0.999497	+	0.0317273i	$0.0101008\pi$
$617$	398.778	+	596.814i	0.646318	+	0.967283i	−0.353179	+	0.935556i	$0.614899\pi$
$618$	−74.4606	+	14.8111i	−0.120486	+	0.0239662i
$619$	−509.171	+	762.028i	−0.822570	+	1.23106i	0.147698	+	0.989033i	$0.452814\pi$
$619$	−509.171	+	762.028i	−0.822570	+	1.23106i	−0.970268	+	0.242031i	$0.922186\pi$
$620$	326.398	−	787.994i	0.526448	−	1.27096i
$621$	430.190	+	178.190i	0.692737	+	0.286941i
$622$	74.0744	+	49.4949i	0.119091	+	0.0795738i
$623$	12.3641	+	62.1584i	0.0198460	+	0.0997727i
$624$	−159.818	+	106.787i	−0.256119	+	0.171133i
$625$	492.490	+	492.490i	0.787984	+	0.787984i
$626$	71.7613	−	360.768i	0.114635	−	0.576307i
$627$	−142.402	−	343.788i	−0.227116	−	0.548307i
$628$			484.141i			0.770926i
$629$		0			0
$630$	33.2111			0.0527161
$631$	756.768	−	313.464i	1.19932	−	0.496773i	0.308538	−	0.951212i	$-0.400160\pi$
$631$	756.768	−	313.464i	1.19932	−	0.496773i	0.890778	+	0.454439i	$0.150160\pi$
$632$	395.553	+	78.6803i	0.625875	+	0.124494i
$633$	−342.359	+	342.359i	−0.540852	+	0.540852i
$634$	−246.803	−	369.367i	−0.389279	−	0.582597i
$635$	323.503	−	64.3487i	0.509453	−	0.101336i
$636$	−5.93108	+	8.87650i	−0.00932560	+	0.0139568i
$637$	275.370	−	664.801i	0.432291	−	1.04364i
$638$	111.533	+	46.1985i	0.174817	+	0.0724114i
$639$	546.303	+	365.028i	0.854934	+	0.571249i
$640$	−172.976	−	869.610i	−0.270275	−	1.35877i
$641$	878.442	−	586.956i	1.37042	−	0.915688i	0.370510	−	0.928828i	$-0.379183\pi$
$641$	878.442	−	586.956i	1.37042	−	0.915688i	0.999914	+	0.0131402i	$0.00418276\pi$
$642$	−145.182	−	145.182i	−0.226140	−	0.226140i
$643$	69.7539	−	350.677i	0.108482	−	0.545376i	−0.887874	−	0.460086i	$-0.847818\pi$
$643$	69.7539	−	350.677i	0.108482	−	0.545376i	0.996356	−	0.0852895i	$-0.0271815\pi$
$644$	−21.1295	−	51.0111i	−0.0328097	−	0.0792097i
$645$			151.893i			0.235493i
$646$		0			0
$647$	414.046			0.639947			0.319973	−	0.947427i	$-0.396326\pi$
$647$	414.046			0.639947			0.319973	+	0.947427i	$0.396326\pi$
$648$	−92.7686	+	38.4260i	−0.143161	+	0.0592994i
$649$	−226.953	−	45.1438i	−0.349697	−	0.0695591i
$650$	194.329	−	194.329i	0.298968	−	0.298968i
$651$	−31.1534	−	46.6243i	−0.0478546	−	0.0716195i
$652$	1043.72	−	207.609i	1.60080	−	0.318419i
$653$	404.770	−	605.781i	0.619862	−	0.927690i	−0.380134	−	0.924932i	$-0.624122\pi$
$653$	404.770	−	605.781i	0.619862	−	0.927690i	0.999996	−	0.00275813i	$-0.000877940\pi$
$654$	12.6323	−	30.4970i	0.0193154	−	0.0466315i
$655$	−20.6192	−	8.54075i	−0.0314797	−	0.0130393i
$656$	24.7688	+	16.5500i	0.0377573	+	0.0252286i
$657$	−77.8853	−	391.556i	−0.118547	−	0.595976i
$658$	8.29576	−	5.54305i	0.0126075	−	0.00842409i
$659$	310.871	+	310.871i	0.471731	+	0.471731i	0.902474	−	0.430743i	$-0.141749\pi$
$659$	310.871	+	310.871i	0.471731	+	0.471731i	−0.430743	+	0.902474i	$0.641749\pi$
$660$	−47.9892	+	241.258i	−0.0727109	+	0.365542i
$661$	67.6563	+	163.337i	0.102354	+	0.247105i	0.966758	−	0.255693i	$-0.0823037\pi$
$661$	67.6563	+	163.337i	0.102354	+	0.247105i	−0.864404	+	0.502799i	$0.832304\pi$
$662$		−	298.294i		−	0.450595i
$663$		0			0
$664$	−265.351			−0.399624
$665$	193.645	−	80.2104i	0.291196	−	0.120617i
$666$	−211.319	−	42.0340i	−0.317296	−	0.0631141i
$667$	−278.634	+	278.634i	−0.417742	+	0.417742i
$668$	287.478	+	430.241i	0.430356	+	0.644073i
$669$	−144.041	+	28.6514i	−0.215307	+	0.0428273i
$670$	−102.975	+	154.113i	−0.153694	+	0.230019i
$671$	−91.3871	+	220.628i	−0.136195	+	0.328805i
$672$	−42.7453	−	17.7057i	−0.0636091	−	0.0263478i
$673$	517.356	+	345.686i	0.768731	+	0.513650i	0.877011	−	0.480471i	$-0.159534\pi$
$673$	517.356	+	345.686i	0.768731	+	0.513650i	−0.108280	+	0.994120i	$0.534534\pi$
$674$	25.7071	+	129.239i	0.0381412	+	0.191749i
$675$	451.523	−	301.698i	0.668923	−	0.446960i
$676$	−125.371	−	125.371i	−0.185460	−	0.185460i
$677$	−9.32211	+	46.8654i	−0.0137697	+	0.0692251i	−0.987059	−	0.160356i	$-0.948736\pi$
$677$	−9.32211	+	46.8654i	−0.0137697	+	0.0692251i	0.973289	+	0.229581i	$0.0737357\pi$
$678$	−25.6650	−	61.9609i	−0.0378540	−	0.0913878i
$679$		−	115.496i		−	0.170097i
$680$		0			0
$681$	243.266			0.357219
$682$	200.369	−	82.9957i	0.293797	−	0.121695i
$683$	−729.960	−	145.198i	−1.06876	−	0.212589i	−0.370788	−	0.928718i	$-0.620912\pi$
$683$	−729.960	−	145.198i	−1.06876	−	0.212589i	−0.697968	+	0.716129i	$0.745912\pi$
$684$	−499.070	+	499.070i	−0.729634	+	0.729634i
$685$	341.537	+	511.146i	0.498594	+	0.746199i
$686$	73.0519	−	14.5309i	0.106490	−	0.0211821i
$687$	−124.049	+	185.652i	−0.180566	+	0.270235i
$688$	−41.1610	+	99.3714i	−0.0598270	+	0.144435i
$689$	−27.5265	−	11.4018i	−0.0399514	−	0.0165484i
$690$	146.222	+	97.7025i	0.211916	+	0.141598i
$691$	−250.480	−	1259.25i	−0.362489	−	1.82235i	−0.544144	−	0.838992i	$-0.683145\pi$
$691$	−250.480	−	1259.25i	−0.362489	−	1.82235i	0.181655	−	0.983362i	$-0.441855\pi$
$692$	−448.405	+	299.615i	−0.647984	+	0.432969i
$693$	−27.2633	−	27.2633i	−0.0393410	−	0.0393410i
$694$	−44.2464	+	222.442i	−0.0637556	+	0.320521i
$695$	340.397	+	821.792i	0.489780	+	1.18243i
$696$			213.119i			0.306206i
$697$		0			0
$698$	167.384			0.239806
$699$	−537.588	+	222.676i	−0.769081	+	0.318564i
$700$	−63.1556	−	12.5624i	−0.0902223	−	0.0179463i
$701$	895.228	−	895.228i	1.27707	−	1.27707i	0.334774	−	0.942298i	$-0.391340\pi$
$701$	895.228	−	895.228i	1.27707	−	1.27707i	0.942298	−	0.334774i	$-0.108660\pi$
$702$	175.969	+	263.356i	0.250668	+	0.375150i
$703$	−1333.66	+	265.282i	−1.89711	+	0.377358i
$704$	−18.5518	+	27.7647i	−0.0263519	+	0.0394385i
$705$	55.5225	−	134.043i	0.0787553	−	0.190132i
$706$	336.292	+	139.297i	0.476335	+	0.197304i
$707$	−27.8976	−	18.6406i	−0.0394591	−	0.0263657i
$708$	−35.9146	−	180.555i	−0.0507268	−	0.255021i
$709$	618.642	−	413.363i	0.872555	−	0.583023i	−0.0366699	−	0.999327i	$-0.511675\pi$
$709$	618.642	−	413.363i	0.872555	−	0.583023i	0.909225	+	0.416305i	$0.136675\pi$
$710$	424.531	+	424.531i	0.597931	+	0.597931i
$711$	−80.8182	+	406.301i	−0.113668	+	0.571450i
$712$	−165.596	−	399.785i	−0.232579	−	0.561496i
$713$			707.908i			0.992859i
$714$		0			0
$715$	−686.511			−0.960156
$716$	588.342	−	243.699i	0.821707	−	0.340362i
$717$	−636.709	−	126.649i	−0.888018	−	0.176638i
$718$	34.0384	−	34.0384i	0.0474073	−	0.0474073i
$719$	80.2276	+	120.069i	0.111582	+	0.166995i	0.883058	−	0.469265i	$-0.155481\pi$
$719$	80.2276	+	120.069i	0.111582	+	0.166995i	−0.771475	+	0.636259i	$0.780481\pi$
$720$	335.417	−	66.7187i	0.465857	−	0.0926648i
$721$	−27.5814	+	41.2786i	−0.0382544	+	0.0572518i
$722$	256.238	−	618.614i	0.354901	−	0.856806i
$723$	119.545	+	49.5170i	0.165345	+	0.0684883i
$724$	−136.274	−	91.0553i	−0.188224	−	0.125767i
$725$	89.6548	+	450.725i	0.123662	+	0.621690i
$726$	87.0851	−	58.1884i	0.119952	−	0.0801493i
$727$	−33.3667	−	33.3667i	−0.0458965	−	0.0458965i	0.683786	−	0.729683i	$-0.260332\pi$
$727$	−33.3667	−	33.3667i	−0.0458965	−	0.0458965i	−0.729683	+	0.683786i	$0.760332\pi$
$728$	16.2592	−	81.7405i	0.0223341	−	0.112281i
$729$	101.044	+	243.941i	0.138606	+	0.334624i
$730$		−	364.802i		−	0.499729i
$731$		0			0
$732$	−189.984			−0.259541
$733$	−604.239	+	250.284i	−0.824337	+	0.341452i	−0.754658	−	0.656118i	$-0.772197\pi$
$733$	−604.239	+	250.284i	−0.824337	+	0.341452i	−0.0696787	+	0.997569i	$0.522197\pi$
$734$	189.076	+	37.6097i	0.257597	+	0.0512393i
$735$	379.721	−	379.721i	0.516627	−	0.516627i
$736$	324.506	+	485.658i	0.440905	+	0.659862i
$737$	211.046	−	41.9796i	0.286358	−	0.0569601i
$738$	11.2719	−	16.8696i	0.0152736	−	0.0228586i
$739$	470.162	−	1135.07i	0.636214	−	1.53596i	−0.195472	−	0.980709i	$-0.562624\pi$
$739$	470.162	−	1135.07i	0.636214	−	1.53596i	0.831685	−	0.555247i	$-0.187376\pi$
$740$	830.462	+	343.988i	1.12225	+	0.464849i
$741$	686.966	+	459.016i	0.927079	+	0.619454i
$742$	−0.298301	−	1.49966i	−0.000402023	−	0.00202111i
$743$	−935.002	+	624.748i	−1.25841	+	0.840845i	−0.992392	−	0.123121i	$-0.960710\pi$
$743$	−935.002	+	624.748i	−1.25841	+	0.840845i	−0.266022	+	0.963967i	$0.585710\pi$
$744$	270.730	+	270.730i	0.363884	+	0.363884i
$745$	−282.635	+	1420.90i	−0.379376	+	1.90725i
$746$	149.290	+	360.419i	0.200121	+	0.483135i
$747$		−	272.561i		−	0.364874i
$748$		0			0
$749$	−134.262			−0.179255
$750$	−28.7475	+	11.9076i	−0.0383300	+	0.0158768i
$751$	−1254.28	−	249.491i	−1.67014	−	0.332212i	−0.732752	−	0.680496i	$-0.761764\pi$
$751$	−1254.28	−	249.491i	−1.67014	−	0.332212i	−0.937389	+	0.348285i	$0.886764\pi$
$752$	72.6478	−	72.6478i	0.0966061	−	0.0966061i
$753$	−410.765	−	614.753i	−0.545505	−	0.816405i
$754$	−262.890	+	52.2921i	−0.348661	+	0.0693529i
$755$	227.217	−	340.055i	0.300950	−	0.450404i
$756$	28.4002	−	68.5641i	0.0375664	−	0.0906933i
$757$	−182.937	−	75.7752i	−0.241661	−	0.100099i	0.258566	−	0.965994i	$-0.416750\pi$
$757$	−182.937	−	75.7752i	−0.241661	−	0.100099i	−0.500227	+	0.865894i	$0.666750\pi$
$758$	43.3885	+	28.9913i	0.0572407	+	0.0382470i
$759$	−39.8302	−	200.240i	−0.0524772	−	0.263821i
$760$	−1189.93	+	795.088i	−1.56570	+	1.04617i
$761$	−380.948	−	380.948i	−0.500588	−	0.500588i	0.411032	−	0.911621i	$-0.365168\pi$
$761$	−380.948	−	380.948i	−0.500588	−	0.500588i	−0.911621	+	0.411032i	$0.865168\pi$
$762$	−13.0173	+	65.4423i	−0.0170831	+	0.0858823i
$763$	−8.26052	−	19.9427i	−0.0108264	−	0.0261372i
$764$		−	978.888i		−	1.28127i
$765$		0			0
$766$	522.082			0.681570
$767$	474.669	−	196.614i	0.618864	−	0.256342i
$768$	144.154	+	28.6740i	0.187701	+	0.0373360i
$769$	90.3571	−	90.3571i	0.117500	−	0.117500i	−0.645912	−	0.763412i	$-0.723523\pi$
$769$	90.3571	−	90.3571i	0.117500	−	0.117500i	0.763412	+	0.645912i	$0.223523\pi$
$770$	−19.5736	−	29.2939i	−0.0254202	−	0.0380441i
$771$	157.501	−	31.3288i	0.204281	−	0.0406340i
$772$	102.742	−	153.764i	0.133085	−	0.199176i
$773$	−55.9110	+	134.981i	−0.0723298	+	0.174620i	−0.955910	−	0.293661i	$-0.905126\pi$
$773$	−55.9110	+	134.981i	−0.0723298	+	0.174620i	0.883580	+	0.468281i	$0.155126\pi$
$774$	67.6802	+	28.0341i	0.0874422	+	0.0362197i
$775$	686.455	+	458.675i	0.885749	+	0.591838i
$776$	153.846	+	773.438i	0.198256	+	0.996699i
$777$	49.1371	−	32.8323i	0.0632395	−	0.0422553i
$778$	−218.482	−	218.482i	−0.280825	−	0.280825i
$779$	24.9806	−	125.586i	0.0320675	−	0.161214i
$780$	−209.006	−	504.586i	−0.267957	−	0.646905i
$781$		−	697.003i		−	0.892450i
$782$		0			0
$783$	−529.641			−0.676425
$784$	351.320	−	145.522i	0.448113	−	0.185614i
$785$	−988.984	−	196.721i	−1.25985	−	0.250600i
$786$	3.19244	−	3.19244i	0.00406163	−	0.00406163i
$787$	−384.343	−	575.209i	−0.488364	−	0.730889i	0.502673	−	0.864477i	$-0.332350\pi$
$787$	−384.343	−	575.209i	−0.488364	−	0.730889i	−0.991037	+	0.133588i	$0.957350\pi$
$788$	−12.0505	+	2.39700i	−0.0152926	+	0.00304188i
$789$	81.5137	−	121.994i	0.103313	−	0.154618i
$790$	−144.861	+	349.725i	−0.183368	+	0.442690i
$791$	−40.5176	−	16.7829i	−0.0512232	−	0.0212174i
$792$	218.890	+	146.257i	0.276376	+	0.184669i
$793$	−103.441	−	520.034i	−0.130443	−	0.655781i
$794$	42.4359	−	28.3548i	0.0534457	−	0.0357113i
$795$	−15.7226	−	15.7226i	−0.0197768	−	0.0197768i
$796$	−95.3638	+	479.426i	−0.119804	+	0.602294i
$797$	412.976	+	997.012i	0.518163	+	1.25096i	0.939030	+	0.343834i	$0.111726\pi$
$797$	412.976	+	997.012i	0.518163	+	1.25096i	−0.420867	+	0.907122i	$0.638274\pi$
$798$			42.4006i			0.0531336i
$799$		0			0
$800$	681.198			0.851497
$801$	410.648	−	170.096i	0.512669	−	0.212355i
$802$	16.1872	+	3.21984i	0.0201836	+	0.00401476i
$803$	−299.470	+	299.470i	−0.372938	+	0.372938i
$804$	95.1073	+	142.338i	0.118293	+	0.177037i
$805$	112.789	−	22.4351i	0.140110	−	0.0278697i
$806$	−267.527	+	400.382i	−0.331919	+	0.496752i
$807$	−295.403	+	713.166i	−0.366051	+	0.883725i
$808$	211.651	+	87.6688i	0.261945	+	0.108501i
$809$	−473.836	−	316.607i	−0.585706	−	0.391356i	0.227117	−	0.973868i	$-0.427070\pi$
$809$	−473.836	−	316.607i	−0.585706	−	0.391356i	−0.812822	+	0.582511i	$0.802070\pi$
$810$	−18.3866	−	92.4358i	−0.0226995	−	0.114118i
$811$	945.092	−	631.490i	1.16534	−	0.778656i	0.186335	−	0.982486i	$-0.440339\pi$
$811$	945.092	−	631.490i	1.16534	−	0.778656i	0.979006	+	0.203830i	$0.0653391\pi$
$812$	44.4090	+	44.4090i	0.0546909	+	0.0546909i
$813$	19.5474	−	98.2716i	0.0240436	−	0.120875i
$814$	87.4687	+	211.168i	0.107455	+	0.259420i
$815$			2216.43i			2.71955i
$816$		0			0
$817$	462.332			0.565890
$818$	340.600	−	141.081i	0.416382	−	0.172471i
$819$	83.9616	+	16.7010i	0.102517	+	0.0203919i
$820$	−59.8526	+	59.8526i	−0.0729910	+	0.0729910i
$821$	−11.6336	−	17.4109i	−0.0141700	−	0.0212069i	0.824317	−	0.566129i	$-0.191559\pi$
$821$	−11.6336	−	17.4109i	−0.0141700	−	0.0212069i	−0.838487	+	0.544922i	$0.816559\pi$
$822$	−121.970	+	24.2614i	−0.148382	+	0.0295151i
$823$	874.350	−	1308.56i	1.06239	−	1.58998i	0.287620	−	0.957745i	$-0.407136\pi$
$823$	874.350	−	1308.56i	1.06239	−	1.58998i	0.774774	−	0.632239i	$-0.217864\pi$
$824$	129.719	−	313.169i	0.157426	−	0.380059i
$825$	−219.979	−	91.1183i	−0.266641	−	0.110446i
$826$	21.9233	+	14.6487i	0.0265415	+	0.0177345i
$827$	105.213	+	528.944i	0.127223	+	0.639593i	0.990795	+	0.135368i	$0.0432217\pi$
$827$	105.213	+	528.944i	0.127223	+	0.639593i	−0.863572	+	0.504225i	$0.831778\pi$
$828$	−321.976	+	215.138i	−0.388860	+	0.259828i
$829$	145.931	+	145.931i	0.176032	+	0.176032i	0.789624	−	0.613591i	$-0.210276\pi$
$829$	145.931	+	145.931i	0.176032	+	0.176032i	−0.613591	+	0.789624i	$0.710276\pi$
$830$	48.5888	−	244.272i	0.0585407	−	0.294304i
$831$	93.0922	+	224.744i	0.112024	+	0.270451i
$832$		−	74.1411i		−	0.0891119i
$833$		0			0
$834$	−179.940			−0.215755
$835$	−995.689	+	412.428i	−1.19244	+	0.493926i
$836$	734.341	+	146.070i	0.878399	+	0.174724i
$837$	−672.813	+	672.813i	−0.803839	+	0.803839i
$838$	−38.1344	−	57.0721i	−0.0455064	−	0.0681052i
$839$	692.594	−	137.765i	0.825499	−	0.164202i	0.235776	−	0.971807i	$-0.424237\pi$
$839$	692.594	−	137.765i	0.825499	−	0.164202i	0.589723	+	0.807605i	$0.299237\pi$
$840$	34.5546	−	51.7146i	0.0411364	−	0.0615649i
$841$	−150.313	+	362.887i	−0.178731	+	0.431494i
$842$	−233.824	−	96.8532i	−0.277701	−	0.115028i
$843$	−46.0386	−	30.7620i	−0.0546129	−	0.0364912i
$844$	−190.056	−	955.474i	−0.225184	−	1.13208i
$845$	307.044	−	205.160i	0.363366	−	0.242793i
$846$	−49.4792	−	49.4792i	−0.0584861	−	0.0584861i
$847$	13.3616	−	67.1733i	0.0157752	−	0.0793074i
$848$	−6.02541	−	14.5466i	−0.00710544	−	0.0171540i
$849$		−	308.326i		−	0.363163i
$850$		0			0
$851$	−746.060			−0.876686
$852$	512.298	−	212.201i	0.601289	−	0.249062i
$853$	1109.67	+	220.727i	1.30090	+	0.258766i	0.796466	−	0.604683i	$-0.206700\pi$
$853$	1109.67	+	220.727i	1.30090	+	0.258766i	0.504437	+	0.863449i	$0.331700\pi$
$854$	19.2410	−	19.2410i	0.0225304	−	0.0225304i
$855$	−816.693	−	1222.27i	−0.955196	−	1.42955i
$856$	899.108	−	178.844i	1.05036	−	0.208930i
$857$	−836.761	+	1252.30i	−0.976384	+	1.46126i	−0.0913035	+	0.995823i	$0.529103\pi$
$857$	−836.761	+	1252.30i	−0.976384	+	1.46126i	−0.885080	+	0.465438i	$0.845897\pi$
$858$	53.1457	−	128.305i	0.0619414	−	0.149540i
$859$	−94.7998	−	39.2673i	−0.110361	−	0.0457129i	0.326820	−	0.945087i	$-0.394023\pi$
$859$	−94.7998	−	39.2673i	−0.110361	−	0.0457129i	−0.437181	+	0.899374i	$0.644023\pi$
$860$	−254.116	−	169.795i	−0.295484	−	0.197436i
$861$	1.08566	+	5.45796i	0.00126092	+	0.00633909i
$862$	423.825	−	283.191i	0.491677	−	0.328528i
$863$	533.064	+	533.064i	0.617687	+	0.617687i	0.944938	−	0.327250i	$-0.106122\pi$
$863$	533.064	+	533.064i	0.617687	+	0.617687i	−0.327250	+	0.944938i	$0.606122\pi$
$864$	−153.163	+	770.000i	−0.177271	+	0.891204i
$865$	−429.840	−	1037.73i	−0.496925	−	1.19968i
$866$		−	372.300i		−	0.429907i
$867$		0			0
$868$	112.827			0.129985
$869$	406.010	−	168.175i	0.467215	−	0.193527i
$870$	−196.190	−	39.0247i	−0.225506	−	0.0448559i
$871$	−337.832	+	337.832i	−0.387866	+	0.387866i
$872$	81.8826	+	122.546i	0.0939021	+	0.140534i
$873$	−794.454	+	158.027i	−0.910028	+	0.181016i
$874$	297.387	−	445.071i	0.340260	−	0.509235i
$875$	−7.78664	+	18.7986i	−0.00889902	+	0.0214841i
$876$	−311.283	−	128.938i	−0.355346	−	0.147189i
$877$	738.307	+	493.321i	0.841856	+	0.562510i	0.900046	−	0.435796i	$-0.143533\pi$
$877$	738.307	+	493.321i	0.841856	+	0.562510i	−0.0581900	+	0.998306i	$0.518533\pi$
$878$	−105.655	−	531.162i	−0.120336	−	0.604968i
$879$	−239.982	+	160.351i	−0.273017	+	0.182424i
$880$	−256.534	−	256.534i	−0.291516	−	0.291516i
$881$	298.502	−	1500.67i	0.338821	−	1.70337i	−0.316976	−	0.948434i	$-0.602667\pi$
$881$	298.502	−	1500.67i	0.338821	−	1.70337i	0.655797	−	0.754937i	$-0.272333\pi$
$882$	−99.1124	−	239.278i	−0.112372	−	0.271291i
$883$		−	625.063i		−	0.707885i	−0.935267	−	0.353943i	$-0.884841\pi$
$883$		−	625.063i		−	0.707885i	0.935267	−	0.353943i	$-0.115159\pi$
$884$		0			0
$885$	383.423			0.433247
$886$	−62.5822	+	25.9224i	−0.0706345	+	0.0292578i
$887$	28.6750	+	5.70381i	0.0323281	+	0.00643045i	0.211228	−	0.977437i	$-0.432254\pi$
$887$	28.6750	+	5.70381i	0.0323281	+	0.00643045i	−0.178900	+	0.983867i	$0.557254\pi$
$888$	−285.320	+	285.320i	−0.321307	+	0.321307i
$889$	24.2409	+	36.2791i	0.0272677	+	0.0408089i
$890$	398.351	−	79.2369i	0.447585	−	0.0890302i
$891$	−60.7877	+	90.9752i	−0.0682241	+	0.102105i
$892$	113.083	−	273.007i	0.126775	−	0.306062i
$893$	−408.001	−	168.999i	−0.456888	−	0.189249i
$894$	−243.679	−	162.821i	−0.272571	−	0.182126i
$895$	258.758	+	1300.86i	0.289115	+	1.45348i
$896$	97.5222	−	65.1622i	0.108842	−	0.0727257i
$897$	320.534	+	320.534i	0.357340	+	0.357340i
$898$	24.3524	−	122.428i	0.0271185	−	0.136334i
$899$	−308.144	−	743.925i	−0.342763	−	0.827503i
$900$			451.613i			0.501792i
$901$		0			0
$902$	−21.5232			−0.0238616
$903$	−18.5635	+	7.68925i	−0.0205576	+	0.00851522i
$904$	293.689	+	58.4183i	0.324877	+	0.0646220i
$905$	241.376	−	241.376i	0.266714	−	0.266714i
$906$	45.9645	+	68.7907i	0.0507334	+	0.0759279i
$907$	−1000.45	+	199.002i	−1.10303	+	0.219406i	−0.712839	−	0.701328i	$-0.752591\pi$
$907$	−1000.45	+	199.002i	−1.10303	+	0.219406i	−0.390191	+	0.920734i	$0.627591\pi$
$908$	−271.937	+	406.983i	−0.299490	+	0.448219i
$909$	−90.0509	+	217.402i	−0.0990659	+	0.239166i
$910$	72.2702	+	29.9353i	0.0794178	+	0.0328959i
$911$	−1198.99	−	801.136i	−1.31612	−	0.879403i	−0.318471	−	0.947933i	$-0.603169\pi$
$911$	−1198.99	−	801.136i	−1.31612	−	0.879403i	−0.997649	+	0.0685293i	$0.978169\pi$
$912$	85.1797	+	428.227i	0.0933988	+	0.469547i
$913$	−240.413	+	160.639i	−0.263322	+	0.175946i
$914$	−386.586	−	386.586i	−0.422960	−	0.422960i
$915$	77.1963	−	388.092i	0.0843676	−	0.424144i
$916$	−171.926	−	415.065i	−0.187692	−	0.453128i
$917$		−	2.95232i		−	0.00321954i
$918$		0			0
$919$	811.637			0.883175			0.441587	−	0.897218i	$-0.354416\pi$
$919$	811.637			0.883175			0.441587	+	0.897218i	$0.354416\pi$
$920$	−725.426	+	300.481i	−0.788506	+	0.326610i
$921$	588.820	+	117.124i	0.639327	+	0.127170i
$922$	153.702	−	153.702i	0.166705	−	0.166705i
$923$	859.778	+	1286.75i	0.931504	+	1.39409i
$924$	−31.9145	+	6.34819i	−0.0345395	+	0.00687033i
$925$	−483.395	+	723.451i	−0.522589	+	0.782109i
$926$	−194.016	+	468.395i	−0.209520	+	0.505826i
$927$	321.678	+	133.244i	0.347010	+	0.143736i
$928$	−552.418	−	369.114i	−0.595278	−	0.397752i
$929$	−11.2737	−	56.6770i	−0.0121354	−	0.0610086i	0.974243	−	0.225500i	$-0.0724016\pi$
$929$	−11.2737	−	56.6770i	−0.0121354	−	0.0610086i	−0.986378	+	0.164492i	$0.947402\pi$
$930$	−298.798	+	199.651i	−0.321288	+	0.214678i
$931$	−1155.80	−	1155.80i	−1.24146	−	1.24146i
$932$	228.411	−	1148.30i	0.245077	−	1.23208i
$933$	65.5824	+	158.330i	0.0702920	+	0.169700i
$934$			430.720i			0.461156i
$935$		0			0
$936$	−584.510			−0.624476
$937$	−1380.79	+	571.943i	−1.47363	+	0.610398i	−0.967684	−	0.252167i	$-0.918857\pi$
$937$	−1380.79	+	571.943i	−1.47363	+	0.610398i	−0.505946	+	0.862565i	$0.668857\pi$
$938$	−24.0477	−	4.78338i	−0.0256372	−	0.00509955i
$939$	500.340	−	500.340i	0.532844	−	0.532844i
$940$	162.187	+	242.730i	0.172539	+	0.258223i
$941$	−984.245	+	195.778i	−1.04596	+	0.208054i	−0.688019	−	0.725692i	$-0.741520\pi$
$941$	−984.245	+	195.778i	−1.04596	+	0.208054i	−0.357937	+	0.933746i	$0.616520\pi$
$942$	113.328	−	169.607i	0.120305	−	0.180049i
$943$	26.8848	−	64.9057i	0.0285099	−	0.0688290i
$944$	250.843	+	103.903i	0.265724	+	0.110066i
$945$	128.520	+	85.8744i	0.136000	+	0.0908724i
$946$	−15.1611	−	76.2199i	−0.0160265	−	0.0805707i
$947$	1157.87	−	773.664i	1.22267	−	0.816963i	0.234771	−	0.972051i	$-0.424566\pi$
$947$	1157.87	−	773.664i	1.22267	−	0.816963i	0.987901	+	0.155088i	$0.0495660\pi$
$948$	247.217	+	247.217i	0.260778	+	0.260778i
$949$	183.449	−	922.262i	0.193308	−	0.971825i
$950$	−238.898	−	576.750i	−0.251471	−	0.607105i
$951$		−	854.550i		−	0.898580i
$952$		0			0
$953$	−1378.59			−1.44658			−0.723292	−	0.690543i	$-0.757372\pi$
$953$	−1378.59			−1.44658			−0.723292	+	0.690543i	$0.757372\pi$
$954$	−9.90747	+	4.10381i	−0.0103852	+	0.00430169i
$955$	1999.63	+	397.752i	2.09386	+	0.416494i
$956$	923.635	−	923.635i	0.966145	−	0.966145i
$957$	129.019	+	193.090i	0.134816	+	0.201766i
$958$	329.863	−	65.6139i	0.344325	−	0.0684904i
$959$	−45.1798	+	67.6164i	−0.0471114	+	0.0705072i
$960$	21.1739	−	51.1184i	0.0220562	−	0.0532483i
$961$	−448.616	−	185.823i	−0.466822	−	0.193364i
$962$	−421.961	−	281.945i	−0.438629	−	0.293082i
$963$	183.703	+	923.538i	0.190761	+	0.959022i
$964$	−216.476	+	144.644i	−0.224560	+	0.150046i
$965$	272.356	+	272.356i	0.282234	+	0.282234i
$966$	−4.53847	+	22.8164i	−0.00469820	+	0.0236195i
$967$	399.502	+	964.483i	0.413136	+	0.997398i	0.984291	+	0.176555i	$0.0564955\pi$
$967$	399.502	+	964.483i	0.413136	+	0.997398i	−0.571155	+	0.820842i	$0.693505\pi$
$968$			467.636i			0.483095i
$969$		0			0
$970$	−740.172			−0.763064
$971$	−164.897	+	68.3025i	−0.169822	+	0.0703424i	−0.465975	−	0.884798i	$-0.654296\pi$
$971$	−164.897	+	68.3025i	−0.169822	+	0.0703424i	0.296153	+	0.955141i	$0.404296\pi$
$972$	−809.979	−	161.115i	−0.833311	−	0.165756i
$973$	−83.2028	+	83.2028i	−0.0855116	+	0.0855116i
$974$	181.759	+	272.022i	0.186611	+	0.279283i
$975$	518.504	−	103.137i	0.531799	−	0.105781i
$976$	155.671	−	232.979i	0.159499	−	0.238708i
$977$	−453.439	+	1094.70i	−0.464113	+	1.12047i	0.502580	+	0.864531i	$0.332384\pi$
$977$	−453.439	+	1094.70i	−0.464113	+	1.12047i	−0.966693	+	0.255938i	$0.917616\pi$
$978$	−414.239	−	171.583i	−0.423557	−	0.175443i
$979$	−392.056	−	261.964i	−0.400466	−	0.267583i
$980$	210.796	+	1059.74i	0.215098	+	1.08137i
$981$	−125.876	+	84.1076i	−0.128314	+	0.0857366i
$982$	−279.500	−	279.500i	−0.284623	−	0.284623i
$983$	−307.807	+	1547.45i	−0.313130	+	1.57421i	0.428588	+	0.903500i	$0.359011\pi$
$983$	−307.807	+	1547.45i	−0.313130	+	1.57421i	−0.741718	+	0.670712i	$0.765989\pi$
$984$	−14.5406	−	35.1040i	−0.0147770	−	0.0356748i
$985$		−	25.5903i		−	0.0259800i
$986$		0			0
$987$	19.1927			0.0194455
$988$	−1535.86	+	636.175i	−1.55452	+	0.643902i
$989$	248.788	+	49.4870i	0.251555	+	0.0500374i
$990$	−174.721	+	174.721i	−0.176486	+	0.176486i
$991$	−504.766	−	755.435i	−0.509350	−	0.762296i	0.484289	−	0.874908i	$-0.339078\pi$
$991$	−504.766	−	755.435i	−0.509350	−	0.762296i	−0.993639	+	0.112612i	$0.964078\pi$
$992$	−1170.64	+	232.855i	−1.18008	+	0.234733i
$993$	318.794	−	477.108i	0.321041	−	0.480472i
$994$	−30.3928	+	73.3747i	−0.0305763	+	0.0738176i
$995$	−940.604	−	389.611i	−0.945330	−	0.391569i
$996$	−191.262	−	127.797i	−0.192031	−	0.128311i
$997$	−339.162	−	1705.08i	−0.340182	−	1.71021i	−0.650439	−	0.759558i	$-0.725415\pi$
$997$	−339.162	−	1705.08i	−0.340182	−	1.71021i	0.310257	−	0.950653i	$-0.399585\pi$
$998$	−128.885	+	86.1185i	−0.129144	+	0.0862911i
$999$	−709.074	−	709.074i	−0.709783	−	0.709783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.n.224.1		8
17.2	even	8		289.3.e.g.131.1		8
17.3	odd	16		289.3.e.g.214.1		8
17.4	even	4		289.3.e.e.65.1		8
17.5	odd	16		289.3.e.h.75.1		8
17.6	odd	16	inner	289.3.e.n.40.1		8
17.7	odd	16		289.3.e.a.249.1		8
17.8	even	8		289.3.e.h.158.1		8
17.9	even	8		289.3.e.f.158.1		8
17.10	odd	16		289.3.e.e.249.1		8
17.11	odd	16		289.3.e.j.40.1		8
17.12	odd	16		289.3.e.f.75.1		8
17.13	even	4		289.3.e.a.65.1		8
17.14	odd	16		17.3.e.b.10.1	✓	8
17.15	even	8		17.3.e.b.12.1	yes	8
17.16	even	2		289.3.e.j.224.1		8
51.14	even	16		153.3.p.a.10.1		8
51.32	odd	8		153.3.p.a.46.1		8
68.15	odd	8		272.3.bh.b.97.1		8
68.31	even	16		272.3.bh.b.129.1		8
85.14	odd	16		425.3.u.a.401.1		8
85.32	odd	8		425.3.t.b.199.1		8
85.48	even	16		425.3.t.b.299.1		8
85.49	even	8		425.3.u.a.301.1		8
85.82	even	16		425.3.t.d.299.1		8
85.83	odd	8		425.3.t.d.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.10.1	✓	8	17.14	odd	16
17.3.e.b.12.1	yes	8	17.15	even	8
153.3.p.a.10.1		8	51.14	even	16
153.3.p.a.46.1		8	51.32	odd	8
272.3.bh.b.97.1		8	68.15	odd	8
272.3.bh.b.129.1		8	68.31	even	16
289.3.e.a.65.1		8	17.13	even	4
289.3.e.a.249.1		8	17.7	odd	16
289.3.e.e.65.1		8	17.4	even	4
289.3.e.e.249.1		8	17.10	odd	16
289.3.e.f.75.1		8	17.12	odd	16
289.3.e.f.158.1		8	17.9	even	8
289.3.e.g.131.1		8	17.2	even	8
289.3.e.g.214.1		8	17.3	odd	16
289.3.e.h.75.1		8	17.5	odd	16
289.3.e.h.158.1		8	17.8	even	8
289.3.e.j.40.1		8	17.11	odd	16
289.3.e.j.224.1		8	17.16	even	2
289.3.e.n.40.1		8	17.6	odd	16	inner
289.3.e.n.224.1		8	1.1	even	1	trivial
425.3.t.b.199.1		8	85.32	odd	8
425.3.t.b.299.1		8	85.48	even	16
425.3.t.d.199.1		8	85.83	odd	8
425.3.t.d.299.1		8	85.82	even	16
425.3.u.a.301.1		8	85.49	even	8
425.3.u.a.401.1		8	85.14	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.783227 - 0.324423i) q^{2} +(1.59946 + 0.318152i) q^{3} +(-2.32023 + 2.32023i) q^{4} +(-3.79690 - 5.68246i) q^{5} +(1.35595 - 0.269716i) q^{6} +(0.502268 - 0.751697i) q^{7} +(-2.36223 + 5.70292i) q^{8} +(-5.85788 - 2.42641i) q^{9} +(-4.81736 - 3.21885i) q^{10} +(1.31223 + 6.59700i) q^{11} +(-4.44930 + 2.97292i) q^{12} +(-10.5602 - 10.5602i) q^{13} +(0.149522 - 0.751697i) q^{14} +(-4.26509 - 10.2968i) q^{15} -7.89218i q^{16} -5.37523 q^{18} +(-31.3415 + 12.9821i) q^{19} +(21.9943 + 4.37494i) q^{20} +(1.04251 - 1.04251i) q^{21} +(3.16799 + 4.74123i) q^{22} +(-18.2549 + 3.63113i) q^{23} +(-5.59267 + 8.37002i) q^{24} +(-8.30682 + 20.0544i) q^{25} +(-11.6970 - 4.84504i) q^{26} +(-20.8010 - 13.8988i) q^{27} +(0.578734 + 2.90949i) q^{28} +(17.6031 - 11.7620i) q^{29} +(-6.68107 - 6.68107i) q^{30} +(7.42005 - 37.3031i) q^{31} +(-12.0093 - 28.9930i) q^{32} +10.9691i q^{33} -6.17855 q^{35} +(19.2215 - 7.96180i) q^{36} +(39.3135 + 7.81994i) q^{37} +(-20.3359 + 20.3359i) q^{38} +(-13.5308 - 20.2502i) q^{39} +(41.3757 - 8.23014i) q^{40} +(-2.09701 + 3.13840i) q^{41} +(0.478307 - 1.15474i) q^{42} +(-12.5911 - 5.21542i) q^{43} +(-18.3512 - 12.2619i) q^{44} +(8.45377 + 42.5000i) q^{45} +(-13.1197 + 8.76632i) q^{46} +(9.20504 + 9.20504i) q^{47} +(2.51091 - 12.6232i) q^{48} +(18.4387 + 44.5150i) q^{49} +18.4021i q^{50} +49.0040 q^{52} +(1.84317 - 0.763466i) q^{53} +(-20.8010 - 4.13758i) q^{54} +(32.5048 - 32.5048i) q^{55} +(3.10040 + 4.64007i) q^{56} +(-54.2597 + 10.7929i) q^{57} +(9.97136 - 14.9232i) q^{58} +(-13.1653 + 31.7838i) q^{59} +(33.7870 + 13.9951i) q^{60} +(29.5202 + 19.7248i) q^{61} +(-6.29041 - 31.6240i) q^{62} +(-4.76615 + 3.18464i) q^{63} +(3.51042 + 3.51042i) q^{64} +(-19.9118 + 100.103i) q^{65} +(3.55863 + 8.59130i) q^{66} -31.9912i q^{67} -30.3532 q^{69} +(-4.83921 + 2.00446i) q^{70} +(-101.633 - 20.2161i) q^{71} +(27.6752 - 27.6752i) q^{72} +(34.9811 + 52.3530i) q^{73} +(33.3284 - 6.62943i) q^{74} +(-19.6667 + 29.4333i) q^{75} +(42.5982 - 102.841i) q^{76} +(5.61804 + 2.32707i) q^{77} +(-17.1673 - 11.4708i) q^{78} +(-12.7463 - 64.0800i) q^{79} +(-44.8470 + 29.9658i) q^{80} +(11.5024 + 11.5024i) q^{81} +(-0.624266 + 3.13840i) q^{82} +(16.4505 + 39.7149i) q^{83} +4.83773i q^{84} -11.5537 q^{86} +(31.8975 - 13.2124i) q^{87} +(-40.7219 - 8.10009i) q^{88} +(-49.5695 + 49.5695i) q^{89} +(20.4092 + 30.5445i) q^{90} +(-13.2421 + 2.63401i) q^{91} +(33.9306 - 50.7807i) q^{92} +(23.7361 - 57.3040i) q^{93} +(10.1960 + 4.22331i) q^{94} +(192.771 + 128.805i) q^{95} +(-9.98418 - 50.1939i) q^{96} +(106.223 - 70.9756i) q^{97} +(28.8834 + 28.8834i) q^{98} +(8.32019 - 41.8284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 16 q^{5} + 8 q^{7} + 8 q^{8} - 56 q^{9} - 48 q^{10} + 24 q^{11} + 24 q^{12} - 8 q^{14} - 80 q^{15} - 136 q^{18} - 80 q^{19} + 48 q^{20} + 64 q^{21} - 16 q^{22} - 104 q^{23}+ \cdots + 120 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 16 * q^5 + 8 * q^7 + 8 * q^8 - 56 * q^9 - 48 * q^10 + 24 * q^11 + 24 * q^12 - 8 * q^14 - 80 * q^15 - 136 * q^18 - 80 * q^19 + 48 * q^20 + 64 * q^21 - 16 * q^22 - 104 * q^23 - 136 * q^25 + 40 * q^26 + 32 * q^27 - 168 * q^30 + 144 * q^31 + 16 * q^32 + 80 * q^35 - 72 * q^36 + 48 * q^37 - 8 * q^38 - 96 * q^39 + 8 * q^40 + 208 * q^41 + 88 * q^42 + 48 * q^43 - 56 * q^44 + 48 * q^45 - 80 * q^46 + 80 * q^47 - 256 * q^48 + 72 * q^49 + 240 * q^52 + 88 * q^53 + 32 * q^54 + 8 * q^55 - 8 * q^56 + 40 * q^57 - 120 * q^58 - 40 * q^59 - 96 * q^60 - 16 * q^61 + 256 * q^62 + 96 * q^63 + 120 * q^64 - 72 * q^65 - 120 * q^66 - 208 * q^69 + 96 * q^70 - 328 * q^71 - 24 * q^72 + 160 * q^73 + 168 * q^74 - 264 * q^75 + 192 * q^76 + 120 * q^77 - 168 * q^78 - 352 * q^79 - 328 * q^80 + 224 * q^81 + 320 * q^82 + 504 * q^83 + 288 * q^86 + 216 * q^87 - 56 * q^88 - 288 * q^89 + 392 * q^90 + 32 * q^91 - 200 * q^92 + 248 * q^93 + 72 * q^94 + 800 * q^95 - 408 * q^96 + 504 * q^97 - 16 * q^98 + 120 * q^99

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