LMFDB - Embedded newform 425.3.u.a.401.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.126"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,0,0,16,-16,8,0,40,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
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			401.1
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	425.401
Dual form			425.3.u.a.301.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.324423 + 0.783227i) q^{2} +(1.35595 + 0.906019i) q^{3} +(2.32023 + 2.32023i) q^{4} +(-1.14952 + 0.768086i) q^{6} +(-0.886687 - 0.176373i) q^{7} +(-5.70292 + 2.36223i) q^{8} +(-2.42641 - 5.85788i) q^{9} +(3.73690 + 5.59267i) q^{11} +(1.04395 + 5.24830i) q^{12} +(-10.5602 + 10.5602i) q^{13} +(0.425802 - 0.637258i) q^{14} +7.89218i q^{16} +(14.7921 + 8.37823i) q^{17} +5.37523 q^{18} +(-12.9821 + 31.3415i) q^{19} +(-1.04251 - 1.04251i) q^{21} +(-5.59267 + 1.11245i) q^{22} +(-15.4758 + 10.3406i) q^{23} +(-9.87311 - 1.96388i) q^{24} +(-4.84504 - 11.6970i) q^{26} +(4.88061 - 24.5365i) q^{27} +(-1.64809 - 2.46655i) q^{28} +(4.13027 + 20.7643i) q^{29} +(21.1305 - 31.6240i) q^{31} +(-28.9930 - 12.0093i) q^{32} +10.9691i q^{33} +(-11.3609 + 8.86746i) q^{34} +(7.96180 - 19.2215i) q^{36} +(33.3284 + 22.2693i) q^{37} +(-20.3359 - 20.3359i) q^{38} +(-23.8868 + 4.75138i) q^{39} +(-3.70199 - 0.736372i) q^{41} +(1.15474 - 0.478307i) q^{42} +(5.21542 + 12.5911i) q^{43} +(-4.30581 + 21.6468i) q^{44} +(-3.07832 - 15.4758i) q^{46} +(9.20504 - 9.20504i) q^{47} +(-7.15046 + 10.7014i) q^{48} +(-44.5150 - 18.4387i) q^{49} +(12.4665 + 24.7624i) q^{51} -49.0040 q^{52} +(-0.763466 + 1.84317i) q^{53} +(17.6343 + 11.7828i) q^{54} +(5.47334 - 1.08871i) q^{56} +(-45.9991 + 30.7356i) q^{57} +(-17.6031 - 3.50147i) q^{58} +(31.7838 - 13.1653i) q^{59} +(6.92641 - 34.8214i) q^{61} +(17.9136 + 26.8096i) q^{62} +(1.11830 + 5.62206i) q^{63} +(-3.51042 + 3.51042i) q^{64} +(-8.59130 - 3.55863i) q^{66} -31.9912i q^{67} +(14.8816 + 53.7605i) q^{68} -30.3532 q^{69} +(86.1606 + 57.5707i) q^{71} +(27.6752 + 27.6752i) q^{72} +(-61.7546 + 12.2837i) q^{73} +(-28.2544 + 18.8790i) q^{74} +(-102.841 + 42.5982i) q^{76} +(-2.32707 - 5.61804i) q^{77} +(4.02802 - 20.2502i) q^{78} +(-36.2984 - 54.3244i) q^{79} +(-11.5024 + 11.5024i) q^{81} +(1.77776 - 2.66060i) q^{82} +(39.7149 + 16.4505i) q^{83} -4.83773i q^{84} -11.5537 q^{86} +(-13.2124 + 31.8975i) q^{87} +(-34.5224 - 23.0671i) q^{88} +(49.5695 + 49.5695i) q^{89} +(11.2261 - 7.50103i) q^{91} +(-59.9000 - 11.9148i) q^{92} +(57.3040 - 23.7361i) q^{93} +(4.22331 + 10.1960i) q^{94} +(-28.4325 - 42.5523i) q^{96} +(-24.9233 - 125.298i) q^{97} +(28.8834 - 28.8834i) q^{98} +(23.6939 - 35.4604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 16 q^{7} - 16 q^{8} + 8 q^{9} + 40 q^{11} - 40 q^{12} + 16 q^{14} + 16 q^{17} + 136 q^{18} - 32 q^{19} - 64 q^{21} + 8 q^{23} + 24 q^{24} - 96 q^{27} - 80 q^{28} + 24 q^{29} + 32 q^{31}+ \cdots + 136 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 16 * q^7 - 16 * q^8 + 8 * q^9 + 40 * q^11 - 40 * q^12 + 16 * q^14 + 16 * q^17 + 136 * q^18 - 32 * q^19 - 64 * q^21 + 8 * q^23 + 24 * q^24 - 96 * q^27 - 80 * q^28 + 24 * q^29 + 32 * q^31 + 24 * q^32 + 64 * q^34 - 104 * q^36 + 168 * q^37 - 8 * q^38 - 72 * q^39 + 72 * q^42 - 96 * q^43 - 96 * q^44 + 80 * q^47 - 88 * q^48 + 8 * q^49 - 176 * q^51 - 240 * q^52 - 96 * q^53 + 208 * q^54 + 72 * q^56 - 248 * q^57 + 8 * q^59 + 264 * q^61 + 136 * q^62 - 8 * q^63 - 120 * q^64 + 8 * q^66 + 176 * q^68 - 208 * q^69 + 32 * q^71 - 24 * q^72 - 24 * q^73 + 176 * q^74 - 80 * q^76 + 216 * q^77 + 368 * q^78 - 96 * q^79 - 224 * q^81 + 408 * q^82 + 88 * q^83 + 288 * q^86 - 312 * q^87 - 176 * q^88 + 288 * q^89 - 24 * q^91 - 336 * q^92 - 280 * q^93 - 8 * q^94 + 328 * q^96 + 344 * q^97 - 16 * q^98 + 136 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	−0.324423	+	0.783227i	−0.162212	+	0.391614i	−0.983997	−	0.178183i	$-0.942978\pi$
$2$	−0.324423	+	0.783227i	−0.162212	+	0.391614i	0.821786	+	0.569797i	$0.192978\pi$
$3$	1.35595	+	0.906019i	0.451984	+	0.302006i	0.760648	−	0.649165i	$-0.224882\pi$
$3$	1.35595	+	0.906019i	0.451984	+	0.302006i	−0.308663	+	0.951171i	$0.599882\pi$
$4$	2.32023	+	2.32023i	0.580058	+	0.580058i
$5$		0			0
$5$		0			0
$6$	−1.14952	+	0.768086i	−0.191587	+	0.128014i
$7$	−0.886687	−	0.176373i	−0.126670	−	0.0251962i	0.131348	−	0.991336i	$-0.458069\pi$
$7$	−0.886687	−	0.176373i	−0.126670	−	0.0251962i	−0.258018	+	0.966140i	$0.583069\pi$
$8$	−5.70292	+	2.36223i	−0.712865	+	0.295278i
$9$	−2.42641	−	5.85788i	−0.269601	−	0.650875i
$10$		0			0
$11$	3.73690	+	5.59267i	0.339718	+	0.508424i	0.961514	−	0.274755i	$-0.0885967\pi$
$11$	3.73690	+	5.59267i	0.339718	+	0.508424i	−0.621796	+	0.783179i	$0.713597\pi$
$12$	1.04395	+	5.24830i	0.0869960	+	0.437359i
$13$	−10.5602	+	10.5602i	−0.812320	+	0.812320i	−0.984981	−	0.172662i	$-0.944763\pi$
$13$	−10.5602	+	10.5602i	−0.812320	+	0.812320i	0.172662	+	0.984981i	$0.444763\pi$
$14$	0.425802	−	0.637258i	0.0304144	−	0.0455184i
$15$		0			0
$16$			7.89218i			0.493261i
$17$	14.7921	+	8.37823i	0.870122	+	0.492837i
$17$	14.7921	+	8.37823i	0.870122	+	0.492837i
$18$	5.37523			0.298624
$19$	−12.9821	+	31.3415i	−0.683268	+	1.64955i	0.0746542	+	0.997209i	$0.476215\pi$
$19$	−12.9821	+	31.3415i	−0.683268	+	1.64955i	−0.757922	+	0.652345i	$0.773785\pi$
$20$		0			0
$21$	−1.04251	−	1.04251i	−0.0496433	−	0.0496433i
$22$	−5.59267	+	1.11245i	−0.254212	+	0.0505659i
$23$	−15.4758	+	10.3406i	−0.672860	+	0.449590i	−0.844490	−	0.535571i	$-0.820096\pi$
$23$	−15.4758	+	10.3406i	−0.672860	+	0.449590i	0.171631	+	0.985161i	$0.445096\pi$
$24$	−9.87311	−	1.96388i	−0.411380	−	0.0818285i
$25$		0			0
$26$	−4.84504	−	11.6970i	−0.186348	−	0.449883i
$27$	4.88061	−	24.5365i	0.180763	−	0.908759i
$28$	−1.64809	−	2.46655i	−0.0588605	−	0.0880910i
$29$	4.13027	+	20.7643i	0.142423	+	0.716009i	0.984323	+	0.176376i	$0.0564373\pi$
$29$	4.13027	+	20.7643i	0.142423	+	0.716009i	−0.841900	+	0.539634i	$0.818563\pi$
$30$		0			0
$31$	21.1305	−	31.6240i	0.681629	−	1.02013i	−0.315825	−	0.948818i	$-0.602281\pi$
$31$	21.1305	−	31.6240i	0.681629	−	1.02013i	0.997454	−	0.0713127i	$-0.0227188\pi$
$32$	−28.9930	−	12.0093i	−0.906032	−	0.375291i
$33$			10.9691i			0.332397i
$34$	−11.3609	+	8.86746i	−0.334146	+	0.260808i
$35$		0			0
$36$	7.96180	−	19.2215i	0.221161	−	0.533930i
$37$	33.3284	+	22.2693i	0.900767	+	0.601873i	0.917390	−	0.397988i	$-0.130292\pi$
$37$	33.3284	+	22.2693i	0.900767	+	0.601873i	−0.0166233	+	0.999862i	$0.505292\pi$
$38$	−20.3359	−	20.3359i	−0.535154	−	0.535154i
$39$	−23.8868	+	4.75138i	−0.612482	+	0.121830i
$40$		0			0
$41$	−3.70199	−	0.736372i	−0.0902925	−	0.0179603i	0.149737	−	0.988726i	$-0.452157\pi$
$41$	−3.70199	−	0.736372i	−0.0902925	−	0.0179603i	−0.240030	+	0.970766i	$0.577157\pi$
$42$	1.15474	−	0.478307i	0.0274937	−	0.0113883i
$43$	5.21542	+	12.5911i	0.121289	+	0.292817i	0.972849	−	0.231439i	$-0.0743434\pi$
$43$	5.21542	+	12.5911i	0.121289	+	0.292817i	−0.851561	+	0.524256i	$0.824343\pi$
$44$	−4.30581	+	21.6468i	−0.0978593	+	0.491972i
$45$		0			0
$46$	−3.07832	−	15.4758i	−0.0669201	−	0.336430i
$47$	9.20504	−	9.20504i	0.195852	−	0.195852i	−0.602367	−	0.798219i	$-0.705776\pi$
$47$	9.20504	−	9.20504i	0.195852	−	0.195852i	0.798219	+	0.602367i	$0.205776\pi$
$48$	−7.15046	+	10.7014i	−0.148968	+	0.222946i
$49$	−44.5150	−	18.4387i	−0.908469	−	0.376300i
$50$		0			0
$51$	12.4665	+	24.7624i	0.244442	+	0.485537i
$52$	−49.0040			−0.942385
$53$	−0.763466	+	1.84317i	−0.0144050	+	0.0347768i	−0.930918	−	0.365227i	$-0.880991\pi$
$53$	−0.763466	+	1.84317i	−0.0144050	+	0.0347768i	0.916513	+	0.400004i	$0.130991\pi$
$54$	17.6343	+	11.7828i	0.326560	+	0.218201i
$55$		0			0
$56$	5.47334	−	1.08871i	0.0977381	−	0.0194413i
$57$	−45.9991	+	30.7356i	−0.807002	+	0.539222i
$58$	−17.6031	−	3.50147i	−0.303502	−	0.0603703i
$59$	31.7838	−	13.1653i	0.538708	−	0.223140i	−0.0967043	−	0.995313i	$-0.530830\pi$
$59$	31.7838	−	13.1653i	0.538708	−	0.223140i	0.635412	+	0.772173i	$0.280830\pi$
$60$		0			0
$61$	6.92641	−	34.8214i	0.113548	−	0.570843i	−0.881562	−	0.472068i	$-0.843508\pi$
$61$	6.92641	−	34.8214i	0.113548	−	0.570843i	0.995110	−	0.0987749i	$-0.0314924\pi$
$62$	17.9136	+	26.8096i	0.288929	+	0.432412i
$63$	1.11830	+	5.62206i	0.0177507	+	0.0892390i
$64$	−3.51042	+	3.51042i	−0.0548503	+	0.0548503i
$65$		0			0
$66$	−8.59130	−	3.55863i	−0.130171	−	0.0539187i
$67$		−	31.9912i		−	0.477480i	−0.971084	−	0.238740i	$-0.923266\pi$
$67$		−	31.9912i		−	0.477480i	0.971084	−	0.238740i	$-0.0767344\pi$
$68$	14.8816	+	53.7605i	0.218847	+	0.790595i
$69$	−30.3532			−0.439901
$70$		0			0
$71$	86.1606	+	57.5707i	1.21353	+	0.810854i	0.986616	−	0.163061i	$-0.0521366\pi$
$71$	86.1606	+	57.5707i	1.21353	+	0.810854i	0.226913	+	0.973915i	$0.427137\pi$
$72$	27.6752	+	27.6752i	0.384378	+	0.384378i
$73$	−61.7546	+	12.2837i	−0.845953	+	0.168270i	−0.598992	−	0.800755i	$-0.704432\pi$
$73$	−61.7546	+	12.2837i	−0.845953	+	0.168270i	−0.246961	+	0.969025i	$0.579432\pi$
$74$	−28.2544	+	18.8790i	−0.381817	+	0.255122i
$75$		0			0
$76$	−102.841	+	42.5982i	−1.35317	+	0.560502i
$77$	−2.32707	−	5.61804i	−0.0302216	−	0.0729615i
$78$	4.02802	−	20.2502i	0.0516413	−	0.259618i
$79$	−36.2984	−	54.3244i	−0.459474	−	0.687651i	0.527314	−	0.849671i	$-0.323199\pi$
$79$	−36.2984	−	54.3244i	−0.459474	−	0.687651i	−0.986788	+	0.162020i	$0.948199\pi$
$80$		0			0
$81$	−11.5024	+	11.5024i	−0.142005	+	0.142005i
$82$	1.77776	−	2.66060i	0.0216800	−	0.0324464i
$83$	39.7149	+	16.4505i	0.478493	+	0.198198i	0.608876	−	0.793265i	$-0.291621\pi$
$83$	39.7149	+	16.4505i	0.478493	+	0.198198i	−0.130383	+	0.991464i	$0.541621\pi$
$84$		−	4.83773i		−	0.0575920i
$85$		0			0
$86$	−11.5537			−0.134346
$87$	−13.2124	+	31.8975i	−0.151866	+	0.366638i
$88$	−34.5224	−	23.0671i	−0.392300	−	0.262126i
$89$	49.5695	+	49.5695i	0.556961	+	0.556961i	0.928441	−	0.371480i	$-0.121150\pi$
$89$	49.5695	+	49.5695i	0.556961	+	0.556961i	−0.371480	+	0.928441i	$0.621150\pi$
$90$		0			0
$91$	11.2261	−	7.50103i	0.123364	−	0.0824289i
$92$	−59.9000	−	11.9148i	−0.651086	−	0.129509i
$93$	57.3040	−	23.7361i	0.616172	−	0.255227i
$94$	4.22331	+	10.1960i	0.0449288	+	0.108468i
$95$		0			0
$96$	−28.4325	−	42.5523i	−0.296172	−	0.443253i
$97$	−24.9233	−	125.298i	−0.256941	−	1.29173i	−0.866574	−	0.499048i	$-0.833683\pi$
$97$	−24.9233	−	125.298i	−0.256941	−	1.29173i	0.609633	−	0.792684i	$-0.291317\pi$
$98$	28.8834	−	28.8834i	0.294729	−	0.294729i
$99$	23.6939	−	35.4604i	0.239332	−	0.358186i
$100$		0			0
$101$			37.1128i			0.367453i	0.982977	+	0.183727i	$0.0588162\pi$
$101$			37.1128i			0.367453i	−0.982977	+	0.183727i	$0.941184\pi$
$102$	−23.4390	+	1.73062i	−0.229794	+	0.0169669i
$103$	54.9138			0.533144			0.266572	−	0.963815i	$-0.414109\pi$
$103$	54.9138			0.533144			0.266572	+	0.963815i	$0.414109\pi$
$104$	35.2782	−	85.1691i	0.339214	−	0.818934i
$105$		0			0
$106$	−1.19594	−	1.19594i	−0.0112824	−	0.0112824i
$107$	145.657	−	28.9729i	1.36128	−	0.270775i	0.540173	−	0.841554i	$-0.318359\pi$
$107$	145.657	−	28.9729i	1.36128	−	0.270775i	0.821104	+	0.570779i	$0.193359\pi$
$108$	68.2545	−	45.6062i	0.631986	−	0.422280i
$109$	23.4177	+	4.65808i	0.214842	+	0.0427347i	0.301338	−	0.953518i	$-0.402567\pi$
$109$	23.4177	+	4.65808i	0.214842	+	0.0427347i	−0.0864958	+	0.996252i	$0.527567\pi$
$110$		0			0
$111$	25.0153	+	60.3923i	0.225363	+	0.544075i
$112$	1.39197	−	6.99789i	0.0124283	−	0.0624812i
$113$	26.9507	+	40.3346i	0.238502	+	0.356943i	0.931341	−	0.364149i	$-0.118640\pi$
$113$	26.9507	+	40.3346i	0.238502	+	0.356943i	−0.692839	+	0.721093i	$0.743640\pi$
$114$	−9.14980	−	45.9991i	−0.0802614	−	0.403501i
$115$		0			0
$116$	−38.5948	+	57.7611i	−0.332713	+	0.497941i
$117$	87.4834	+	36.2368i	0.747721	+	0.309716i
$118$			29.1650i			0.247161i
$119$	−11.6382	−	10.0378i	−0.0978004	−	0.0843512i
$120$		0			0
$121$	28.9912	−	69.9909i	0.239597	−	0.578437i
$122$	25.0260	+	16.7218i	0.205131	+	0.137064i
$123$	−4.35256	−	4.35256i	−0.0353867	−	0.0353867i
$124$	122.403	−	24.3474i	0.987120	−	0.196350i
$125$		0			0
$126$	−4.76615	−	0.948046i	−0.0378266	−	0.00752418i
$127$	−44.5892	+	18.4694i	−0.351096	+	0.145429i	−0.551260	−	0.834334i	$-0.685853\pi$
$127$	−44.5892	+	18.4694i	−0.351096	+	0.145429i	0.200164	+	0.979762i	$0.435853\pi$
$128$	−49.6478	−	119.860i	−0.387874	−	0.936410i
$129$	−4.33594	+	21.7982i	−0.0336119	+	0.168979i
$130$		0			0
$131$	0.637092	+	3.20288i	0.00486330	+	0.0244495i	0.983141	−	0.182850i	$-0.0585324\pi$
$131$	0.637092	+	3.20288i	0.00486330	+	0.0244495i	−0.978277	+	0.207300i	$0.933532\pi$
$132$	−25.4509	+	25.4509i	−0.192810	+	0.192810i
$133$	17.0389	−	25.5004i	0.128112	−	0.191733i
$134$	25.0563	+	10.3787i	0.186988	+	0.0774528i
$135$		0			0
$136$	−104.149	−	12.8381i	−0.765803	−	0.0943981i
$137$	89.9517			0.656581			0.328291	−	0.944577i	$-0.393527\pi$
$137$	89.9517			0.656581			0.328291	+	0.944577i	$0.393527\pi$
$138$	9.84728	−	23.7734i	0.0713571	−	0.172271i
$139$	108.219	+	72.3095i	0.778553	+	0.520212i	0.880197	−	0.474608i	$-0.157410\pi$
$139$	108.219	+	72.3095i	0.778553	+	0.520212i	−0.101644	+	0.994821i	$0.532410\pi$
$140$		0			0
$141$	20.8216	−	4.14166i	0.147671	−	0.0293735i
$142$	−73.0434	+	48.8061i	−0.514390	+	0.343705i
$143$	−98.5217	−	19.5972i	−0.688963	−	0.137043i
$144$	46.2314	−	19.1497i	0.321051	−	0.132984i
$145$		0			0
$146$	10.4137	−	52.3530i	0.0713264	−	0.358582i
$147$	−43.6544	−	65.3335i	−0.296969	−	0.444445i
$148$	25.6596	+	129.000i	0.173376	+	0.871619i
$149$	149.894	−	149.894i	1.00600	−	1.00600i	0.00602015	−	0.999982i	$-0.498084\pi$
$149$	149.894	−	149.894i	1.00600	−	1.00600i	0.999982	−	0.00602015i	$-0.00191628\pi$
$150$		0			0
$151$	−55.2876	−	22.9009i	−0.366143	−	0.151661i	0.192023	−	0.981390i	$-0.438495\pi$
$151$	−55.2876	−	22.9009i	−0.366143	−	0.151661i	−0.558167	+	0.829729i	$0.688495\pi$
$152$		−	209.405i		−	1.37766i
$153$	13.1870	−	106.979i	0.0861894	−	0.699210i
$154$	5.15515			0.0334750
$155$		0			0
$156$	−66.4472	−	44.3986i	−0.425944	−	0.284606i
$157$	104.330	+	104.330i	0.664524	+	0.664524i	0.956443	−	0.291919i	$-0.0942937\pi$
$157$	104.330	+	104.330i	0.664524	+	0.664524i	−0.291919	+	0.956443i	$0.594294\pi$
$158$	54.3244	−	10.8058i	0.343826	−	0.0683912i
$159$	−2.70517	+	1.80754i	−0.0170137	+	0.0113682i
$160$		0			0
$161$	15.5460	−	6.43935i	0.0965588	−	0.0399960i
$162$	−5.27735	−	12.7406i	−0.0325762	−	0.0786460i
$163$	63.2704	−	318.082i	0.388162	−	1.95142i	0.0944348	−	0.995531i	$-0.469896\pi$
$163$	63.2704	−	318.082i	0.388162	−	1.95142i	0.293727	−	0.955889i	$-0.405104\pi$
$164$	−6.88093	−	10.2980i	−0.0419569	−	0.0627929i
$165$		0			0
$166$	−25.7689	+	25.7689i	−0.155234	+	0.155234i
$167$	−87.6108	+	131.119i	−0.524615	+	0.785142i	−0.995267	−	0.0971767i	$-0.969019\pi$
$167$	−87.6108	+	131.119i	−0.524615	+	0.785142i	0.470652	+	0.882319i	$0.344019\pi$
$168$	8.40798	+	3.48270i	0.0500475	+	0.0207304i
$169$		−	54.0337i		−	0.319726i
$170$		0			0
$171$	215.095			1.25786
$172$	−17.1134	+	41.3153i	−0.0994963	+	0.240205i
$173$	136.654	+	91.3096i	0.789910	+	0.527801i	0.883846	−	0.467777i	$-0.154945\pi$
$173$	136.654	+	91.3096i	0.789910	+	0.527801i	−0.0939363	+	0.995578i	$0.529945\pi$
$174$	−20.6966	−	20.6966i	−0.118946	−	0.118946i
$175$		0			0
$176$	−44.1383	+	29.4923i	−0.250786	+	0.167570i
$177$	55.0253	+	10.9452i	0.310877	+	0.0618374i
$178$	−54.9057	+	22.7427i	−0.308459	+	0.127768i
$179$	−74.2691	−	179.301i	−0.414911	−	1.00168i	−0.983800	−	0.179269i	$-0.942627\pi$
$179$	−74.2691	−	179.301i	−0.414911	−	1.00168i	0.568889	−	0.822414i	$-0.307373\pi$
$180$		0			0
$181$	27.7497	+	41.5304i	0.153313	+	0.229450i	0.900173	−	0.435532i	$-0.143440\pi$
$181$	27.7497	+	41.5304i	0.153313	+	0.229450i	−0.746860	+	0.664981i	$0.768440\pi$
$182$	2.23301	+	11.2261i	0.0122693	+	0.0616818i
$183$	40.9408	−	40.9408i	0.223720	−	0.223720i
$184$	63.8303	−	95.5287i	0.346904	−	0.519178i
$185$		0			0
$186$			52.5826i			0.282702i
$187$	8.41985	+	114.036i	0.0450259	+	0.609817i
$188$	42.7157			0.227211
$189$	−8.65515	+	20.8954i	−0.0457944	+	0.110558i
$190$		0			0
$191$	210.946	+	210.946i	1.10443	+	1.10443i	0.993869	+	0.110561i	$0.0352646\pi$
$191$	210.946	+	210.946i	1.10443	+	1.10443i	0.110561	+	0.993869i	$0.464735\pi$
$192$	−7.94047	+	1.57946i	−0.0413566	+	0.00822634i
$193$	−46.8606	+	31.3112i	−0.242801	+	0.162234i	−0.671017	−	0.741442i	$-0.734142\pi$
$193$	−46.8606	+	31.3112i	−0.242801	+	0.162234i	0.428216	+	0.903676i	$0.359142\pi$
$194$	106.223	+	21.1290i	0.547539	+	0.108912i
$195$		0			0
$196$	−60.5030	−	146.067i	−0.308689	−	0.745241i
$197$	−0.730502	+	3.67248i	−0.00370813	+	0.0186420i	−0.982595	−	0.185760i	$-0.940525\pi$
$197$	−0.730502	+	3.67248i	−0.00370813	+	0.0186420i	0.978887	+	0.204403i	$0.0655251\pi$
$198$	20.0867	+	30.0619i	0.101448	+	0.151828i
$199$	29.0628	+	146.108i	0.146044	+	0.734213i	0.982512	+	0.186198i	$0.0596165\pi$
$199$	29.0628	+	146.108i	0.146044	+	0.734213i	−0.836468	+	0.548016i	$0.815383\pi$
$200$		0			0
$201$	28.9846	−	43.3785i	0.144202	−	0.215814i
$202$	−29.0678	−	12.0403i	−0.143900	−	0.0596052i
$203$		−	19.1399i		−	0.0942851i
$204$	−28.5293	+	86.3797i	−0.139849	+	0.423430i
$205$		0			0
$206$	−17.8153	+	43.0100i	−0.0864821	+	0.208786i
$207$	98.1244	+	65.5647i	0.474031	+	0.316737i
$208$	−83.3426	−	83.3426i	−0.400686	−	0.400686i
$209$	−223.796	+	44.5157i	−1.07079	+	0.212994i
$210$		0			0
$211$	−291.187	−	57.9207i	−1.38003	−	0.274506i	−0.551374	−	0.834258i	$-0.685896\pi$
$211$	−291.187	−	57.9207i	−1.38003	−	0.274506i	−0.828660	+	0.559752i	$0.810896\pi$
$212$	−6.04800	+	2.50517i	−0.0285283	+	0.0118168i
$213$	64.6696	+	156.126i	0.303613	+	0.732987i
$214$	−24.5620	+	123.482i	−0.114776	+	0.577017i
$215$		0			0
$216$	30.1270	+	151.459i	0.139477	+	0.701197i
$217$	−24.3138	+	24.3138i	−0.112045	+	0.112045i
$218$	−11.2456	+	16.8302i	−0.0515853	+	0.0772029i
$219$	−94.8656	−	39.2946i	−0.433176	−	0.179428i
$220$		0			0
$221$	−244.682	+	67.7311i	−1.10716	+	0.306476i
$222$	−55.4165			−0.249624
$223$	34.4629	−	83.2008i	0.154542	−	0.373098i	−0.827579	−	0.561350i	$-0.810282\pi$
$223$	34.4629	−	83.2008i	0.154542	−	0.373098i	0.982121	+	0.188252i	$0.0602822\pi$
$224$	23.5896	+	15.7621i	0.105311	+	0.0703665i
$225$		0			0
$226$	−40.3346	+	8.02305i	−0.178472	+	0.0355002i
$227$	124.031	−	82.8747i	0.546391	−	0.365087i	−0.251529	−	0.967850i	$-0.580934\pi$
$227$	124.031	−	82.8747i	0.546391	−	0.365087i	0.797920	+	0.602763i	$0.205934\pi$
$228$	−178.043	−	35.4149i	−0.780888	−	0.155328i
$229$	126.494	−	52.3955i	0.552375	−	0.228801i	−0.0889961	−	0.996032i	$-0.528366\pi$
$229$	126.494	−	52.3955i	0.552375	−	0.228801i	0.641371	+	0.767231i	$0.278366\pi$
$230$		0			0
$231$	1.93465	−	9.72616i	0.00837512	−	0.0421046i
$232$	−72.6045	−	108.660i	−0.312950	−	0.468363i
$233$	69.6099	+	349.953i	0.298755	+	1.50194i	0.780235	+	0.625486i	$0.215099\pi$
$233$	69.6099	+	349.953i	0.298755	+	1.50194i	−0.481480	+	0.876457i	$0.659901\pi$
$234$	−56.7633	+	56.7633i	−0.242578	+	0.242578i
$235$		0			0
$236$	104.292	+	43.1993i	0.441916	+	0.183048i
$237$		−	106.548i		−	0.449572i
$238$	11.6376	−	5.85890i	0.0488974	−	0.0246172i
$239$	−398.078			−1.66560			−0.832800	−	0.553574i	$-0.813264\pi$
$239$	−398.078			−1.66560			−0.832800	+	0.553574i	$0.813264\pi$
$240$		0			0
$241$	−65.9725	−	44.0814i	−0.273745	−	0.182910i	0.411119	−	0.911582i	$-0.365138\pi$
$241$	−65.9725	−	44.0814i	−0.273745	−	0.182910i	−0.684863	+	0.728671i	$0.740138\pi$
$242$	45.4134	+	45.4134i	0.187659	+	0.187659i
$243$	−246.847	+	49.1008i	−1.01583	+	0.202061i
$244$	96.8647	−	64.7229i	0.396987	−	0.265258i
$245$		0			0
$246$	4.82112	−	1.99697i	0.0195980	−	0.00811777i
$247$	−193.879	−	468.064i	−0.784934	−	1.89500i
$248$	−45.8024	+	230.264i	−0.184687	+	0.928485i
$249$	38.9471	+	58.2885i	0.156414	+	0.234090i
$250$		0			0
$251$	320.583	−	320.583i	1.27722	−	1.27722i	0.335010	−	0.942215i	$-0.391260\pi$
$251$	320.583	−	320.583i	1.27722	−	1.27722i	0.942215	−	0.335010i	$-0.108740\pi$
$252$	−10.4498	+	15.6392i	−0.0414674	+	0.0620603i
$253$	−115.663	−	47.9091i	−0.457166	−	0.189364i
$254$		−	40.9154i		−	0.161084i
$255$		0			0
$256$	90.1270			0.352058
$257$	−37.6834	+	90.9757i	−0.146628	+	0.353991i	−0.980081	−	0.198600i	$-0.936361\pi$
$257$	−37.6834	+	90.9757i	−0.146628	+	0.353991i	0.833453	+	0.552591i	$0.186361\pi$
$258$	−15.6663	−	10.4679i	−0.0607221	−	0.0405732i
$259$	−25.6241	−	25.6241i	−0.0989349	−	0.0989349i
$260$		0			0
$261$	111.613	−	74.5773i	0.427635	−	0.285737i
$262$	−2.71527	−	0.540101i	−0.0103636	−	0.00206145i
$263$	83.1206	−	34.4297i	0.316048	−	0.130911i	−0.219020	−	0.975720i	$-0.570286\pi$
$263$	83.1206	−	34.4297i	0.316048	−	0.130911i	0.535068	+	0.844809i	$0.320286\pi$
$264$	−25.9115	−	62.5559i	−0.0981496	−	0.236954i
$265$		0			0
$266$	14.4448	+	21.6182i	0.0543039	+	0.0812716i
$267$	22.3030	+	112.125i	0.0835319	+	0.419943i
$268$	74.2269	−	74.2269i	0.276966	−	0.276966i
$269$	−262.976	+	393.571i	−0.977605	+	1.46309i	−0.0936016	+	0.995610i	$0.529838\pi$
$269$	−262.976	+	393.571i	−0.977605	+	1.46309i	−0.884004	+	0.467480i	$0.845162\pi$
$270$		0			0
$271$			61.4406i			0.226718i	0.993554	+	0.113359i	$0.0361611\pi$
$271$			61.4406i			0.226718i	−0.993554	+	0.113359i	$0.963839\pi$
$272$	−66.1225	+	116.742i	−0.243097	+	0.429197i
$273$	22.0181			0.0806524
$274$	−29.1824	+	70.4526i	−0.106505	+	0.257126i
$275$		0			0
$276$	−70.4265	−	70.4265i	−0.255168	−	0.255168i
$277$	−146.302	+	29.1012i	−0.528165	+	0.105058i	−0.451968	−	0.892034i	$-0.649278\pi$
$277$	−146.302	+	29.1012i	−0.528165	+	0.105058i	−0.0761970	+	0.997093i	$0.524278\pi$
$278$	−91.7435	+	61.3011i	−0.330013	+	0.220507i
$279$	−236.521	−	47.0470i	−0.847746	−	0.168627i
$280$		0			0
$281$	−12.9932	−	31.3685i	−0.0462393	−	0.111632i	0.899072	−	0.437800i	$-0.144242\pi$
$281$	−12.9932	−	31.3685i	−0.0462393	−	0.111632i	−0.945312	+	0.326169i	$0.894242\pi$
$282$	−3.51113	+	17.6517i	−0.0124508	+	0.0625945i
$283$	105.039	+	157.202i	0.371162	+	0.555484i	0.969291	−	0.245916i	$-0.0790889\pi$
$283$	105.039	+	157.202i	0.371162	+	0.555484i	−0.598129	+	0.801400i	$0.704089\pi$
$284$	66.3353	+	333.490i	0.233575	+	1.17426i
$285$		0			0
$286$	47.3118	−	70.8071i	0.165426	−	0.247577i
$287$	3.15263	+	1.30586i	0.0109848	+	0.00455005i
$288$			198.977i			0.690893i
$289$	148.611	+	247.863i	0.514223	+	0.857656i
$290$		0			0
$291$	79.7275	−	192.479i	0.273978	−	0.661441i
$292$	−171.786	−	114.784i	−0.588309	−	0.393095i
$293$	−125.147	−	125.147i	−0.427121	−	0.427121i	0.460525	−	0.887647i	$-0.347661\pi$
$293$	−125.147	−	125.147i	−0.427121	−	0.427121i	−0.887647	+	0.460525i	$0.847661\pi$
$294$	65.3335	−	12.9956i	0.222223	−	0.0442028i
$295$		0			0
$296$	−242.674	−	48.2709i	−0.819845	−	0.163077i
$297$	155.463	−	64.3948i	0.523444	−	0.216817i
$298$	68.7721	+	166.031i	0.230779	+	0.557149i
$299$	54.2284	−	272.625i	0.181366	−	0.911788i
$300$		0			0
$301$	−2.40371	−	12.0843i	−0.00798574	−	0.0401470i
$302$	35.8732	−	35.8732i	0.118785	−	0.118785i
$303$	−33.6249	+	50.3232i	−0.110973	+	0.166083i
$304$	−247.353	−	102.457i	−0.813661	−	0.337029i
$305$		0			0
$306$	79.5108	+	45.0349i	0.259839	+	0.147173i
$307$	−368.138			−1.19914			−0.599572	−	0.800320i	$-0.704663\pi$
$307$	−368.138			−1.19914			−0.599572	+	0.800320i	$0.704663\pi$
$308$	7.63581	−	18.4345i	0.0247916	−	0.0598522i
$309$	74.4606	+	49.7530i	0.240973	+	0.161013i
$310$		0			0
$311$	103.068	−	20.5015i	0.331408	−	0.0659211i	−0.0265819	−	0.999647i	$-0.508462\pi$
$311$	103.068	−	20.5015i	0.331408	−	0.0659211i	0.357990	+	0.933726i	$0.383462\pi$
$312$	125.000	−	83.5227i	0.400643	−	0.267701i
$313$	−425.555	−	84.6482i	−1.35960	−	0.270441i	−0.539175	−	0.842194i	$-0.681264\pi$
$313$	−425.555	−	84.6482i	−1.35960	−	0.270441i	−0.820426	+	0.571752i	$0.806264\pi$
$314$	−115.562	+	47.8672i	−0.368030	+	0.152443i
$315$		0			0
$316$	41.8245	−	210.266i	0.132356	−	0.665399i
$317$	291.124	+	435.698i	0.918372	+	1.37444i	0.927235	+	0.374480i	$0.122179\pi$
$317$	291.124	+	435.698i	0.918372	+	1.37444i	−0.00886288	+	0.999961i	$0.502821\pi$
$318$	−0.538092	−	2.70517i	−0.00169211	−	0.00850683i
$319$	−100.693	+	100.693i	−0.315653	+	0.315653i
$320$		0			0
$321$	223.754	+	92.6818i	0.697052	+	0.288728i
$322$			14.2651i			0.0443016i
$323$	−454.619	+	354.839i	−1.40749	+	1.09857i
$324$	−53.3765			−0.164742
$325$		0			0
$326$	228.604	+	152.748i	0.701238	+	0.468553i
$327$	27.5331	+	27.5331i	0.0841990	+	0.0841990i
$328$	22.8516	−	4.54547i	0.0696696	−	0.0138581i
$329$	−9.78551	+	6.53847i	−0.0297432	+	0.0198738i
$330$		0			0
$331$	−325.078	+	134.652i	−0.982109	+	0.406803i	−0.815206	−	0.579171i	$-0.803377\pi$
$331$	−325.078	+	134.652i	−0.982109	+	0.406803i	−0.166903	+	0.985973i	$0.553377\pi$
$332$	53.9790	+	130.317i	0.162587	+	0.392520i
$333$	49.5825	−	249.268i	0.148896	−	0.748553i
$334$	−74.2728	−	111.157i	−0.222374	−	0.332806i
$335$		0			0
$336$	8.22767	−	8.22767i	0.0244871	−	0.0244871i
$337$	86.3544	−	129.239i	0.256245	−	0.383497i	−0.680935	−	0.732344i	$-0.738427\pi$
$337$	86.3544	−	129.239i	0.256245	−	0.383497i	0.937180	+	0.348846i	$0.113427\pi$
$338$	42.3207	+	17.5298i	0.125209	+	0.0518633i
$339$			79.1097i			0.233362i
$340$		0			0
$341$	255.825			0.750221
$342$	−69.7818	+	168.468i	−0.204040	+	0.492597i
$343$	73.0519	+	48.8117i	0.212979	+	0.142308i
$344$	−59.4862	−	59.4862i	−0.172925	−	0.172925i
$345$		0			0
$346$	−115.850	+	77.4085i	−0.334827	+	0.223724i
$347$	262.388	+	52.1922i	0.756161	+	0.150410i	0.558093	−	0.829779i	$-0.311533\pi$
$347$	262.388	+	52.1922i	0.756161	+	0.150410i	0.198068	+	0.980188i	$0.436533\pi$
$348$	−104.665	+	43.3538i	−0.300763	+	0.124580i
$349$	75.5583	+	182.414i	0.216499	+	0.522676i	0.994396	−	0.105716i	$-0.0337135\pi$
$349$	75.5583	+	182.414i	0.216499	+	0.522676i	−0.777897	+	0.628392i	$0.783713\pi$
$350$		0			0
$351$	207.569	+	310.649i	0.591365	+	0.885040i
$352$	−41.1800	−	207.026i	−0.116989	−	0.588142i
$353$	303.609	−	303.609i	0.860081	−	0.860081i	−0.131266	−	0.991347i	$-0.541904\pi$
$353$	303.609	−	303.609i	0.860081	−	0.860081i	0.991347	+	0.131266i	$0.0419041\pi$
$354$	−26.4241	+	39.5464i	−0.0746443	+	0.111713i
$355$		0			0
$356$			230.026i			0.646139i
$357$	−6.68649	−	24.1552i	−0.0187297	−	0.0676618i
$358$	164.528			0.459576
$359$	21.7296	−	52.4599i	0.0605281	−	0.146128i	−0.890722	−	0.454549i	$-0.849801\pi$
$359$	21.7296	−	52.4599i	0.0605281	−	0.146128i	0.951250	+	0.308421i	$0.0998005\pi$
$360$		0			0
$361$	−558.492	−	558.492i	−1.54707	−	1.54707i
$362$	−41.5304	+	8.26091i	−0.114725	+	0.0228202i
$363$	102.724	−	68.6379i	0.282986	−	0.189085i
$364$	43.4512	+	8.64299i	0.119372	+	0.0237445i
$365$		0			0
$366$	18.7838	+	45.3481i	0.0513218	+	0.123902i
$367$	−44.3636	+	223.031i	−0.120882	+	0.607714i	0.872088	+	0.489348i	$0.162765\pi$
$367$	−44.3636	+	223.031i	−0.120882	+	0.607714i	−0.992970	+	0.118365i	$0.962235\pi$
$368$	−81.6097	−	122.138i	−0.221766	−	0.331896i
$369$	4.66898	+	23.4726i	0.0126531	+	0.0636113i
$370$		0			0
$371$	1.00204	−	1.49966i	0.00270092	−	0.00404221i
$372$	188.032	+	77.8853i	0.505462	+	0.209369i
$373$			460.172i			1.23370i	0.787079	+	0.616852i	$0.211592\pi$
$373$			460.172i			1.23370i	−0.787079	+	0.616852i	$0.788408\pi$
$374$	−92.0475	−	30.4012i	−0.246116	−	0.0812866i
$375$		0			0
$376$	−30.7512	+	74.2400i	−0.0817851	+	0.197447i
$377$	−262.890	−	175.658i	−0.697322	−	0.465935i
$378$	−13.5579	−	13.5579i	−0.0358675	−	0.0358675i
$379$	60.3712	−	12.0086i	0.159291	−	0.0316849i	−0.114801	−	0.993389i	$-0.536623\pi$
$379$	60.3712	−	12.0086i	0.159291	−	0.0316849i	0.274091	+	0.961704i	$0.411623\pi$
$380$		0			0
$381$	−77.1945	−	15.3549i	−0.202610	−	0.0403017i
$382$	−233.655	+	96.7829i	−0.611661	+	0.253358i
$383$	−235.671	−	568.960i	−0.615329	−	1.48554i	−0.857073	−	0.515196i	$-0.827719\pi$
$383$	−235.671	−	568.960i	−0.615329	−	1.48554i	0.241744	−	0.970340i	$-0.422281\pi$
$384$	41.2757	−	207.507i	0.107489	−	0.540383i
$385$		0			0
$386$	−9.32115	−	46.8606i	−0.0241481	−	0.121400i
$387$	61.1025	−	61.1025i	0.157888	−	0.157888i
$388$	232.893	−	348.548i	0.600239	−	0.898321i
$389$	336.723	+	139.475i	0.865613	+	0.358549i	0.770900	−	0.636956i	$-0.219807\pi$
$389$	336.723	+	139.475i	0.865613	+	0.358549i	0.0947127	+	0.995505i	$0.469807\pi$
$390$		0			0
$391$	−315.554	+	23.2990i	−0.807045	+	0.0595883i
$392$	297.422			0.758729
$393$	−2.03800	+	4.92017i	−0.00518576	+	0.0125195i
$394$	−2.63940	−	1.76359i	−0.00669898	−	0.00447611i
$395$		0			0
$396$	137.252	−	27.3011i	0.346595	−	0.0689421i
$397$	50.0566	−	33.4467i	0.126087	−	0.0842487i	−0.490927	−	0.871200i	$-0.663342\pi$
$397$	50.0566	−	33.4467i	0.126087	−	0.0842487i	0.617015	+	0.786952i	$0.288342\pi$
$398$	−123.865	−	24.6382i	−0.311218	−	0.0619051i
$399$	46.2078	−	19.1399i	0.115809	−	0.0479697i
$400$		0			0
$401$	3.79806	−	19.0941i	0.00947147	−	0.0476163i	−0.975761	−	0.218841i	$-0.929772\pi$
$401$	3.79806	−	19.0941i	0.00947147	−	0.0476163i	0.985232	+	0.171225i	$0.0547724\pi$
$402$	24.5720	+	36.7745i	0.0611243	+	0.0914789i
$403$	110.813	+	557.096i	0.274971	+	1.38237i
$404$	−86.1103	+	86.1103i	−0.213144	+	0.213144i
$405$		0			0
$406$	14.9909	+	6.20943i	0.0369233	+	0.0152942i
$407$			269.613i			0.662439i
$408$	−129.590	−	111.769i	−0.317622	−	0.273944i
$409$	434.868			1.06325			0.531623	−	0.846981i	$-0.321582\pi$
$409$	434.868			1.06325			0.531623	+	0.846981i	$0.321582\pi$
$410$		0			0
$411$	121.970	+	81.4979i	0.296765	+	0.198292i
$412$	127.413	+	127.413i	0.309254	+	0.309254i
$413$	−30.5043	+	6.06768i	−0.0738602	+	0.0146917i
$414$	−83.1859	+	55.5830i	−0.200932	+	0.134259i
$415$		0			0
$416$	432.991	−	179.351i	1.04084	−	0.431132i
$417$	81.2259	+	196.097i	0.194786	+	0.470256i
$418$	37.7386	−	189.725i	0.0902837	−	0.453887i
$419$	−44.9826	−	67.3212i	−0.107357	−	0.160671i	0.773901	−	0.633307i	$-0.218303\pi$
$419$	−44.9826	−	67.3212i	−0.107357	−	0.160671i	−0.881258	+	0.472635i	$0.843303\pi$
$420$		0			0
$421$	211.099	−	211.099i	0.501423	−	0.501423i	−0.410457	−	0.911880i	$-0.634631\pi$
$421$	211.099	−	211.099i	0.501423	−	0.501423i	0.911880	+	0.410457i	$0.134631\pi$
$422$	139.833	−	209.275i	0.331358	−	0.495912i
$423$	−76.2572	−	31.5868i	−0.180277	−	0.0746732i
$424$		−	12.3149i		−	0.0290446i
$425$		0			0
$426$	−143.263			−0.336297
$427$	−12.2831	+	29.6541i	−0.0287661	+	0.0694475i
$428$	405.181	+	270.733i	0.946685	+	0.632555i
$429$	−115.835	−	115.835i	−0.270013	−	0.270013i
$430$		0			0
$431$	−499.936	+	334.047i	−1.15994	+	0.775050i	−0.978071	−	0.208272i	$-0.933216\pi$
$431$	−499.936	+	334.047i	−1.15994	+	0.775050i	−0.181873	+	0.983322i	$0.558216\pi$
$432$	193.646	+	38.5187i	0.448255	+	0.0891635i
$433$	405.728	−	168.058i	0.937017	−	0.388125i	0.138681	−	0.990337i	$-0.455714\pi$
$433$	405.728	−	168.058i	0.937017	−	0.388125i	0.798336	+	0.602212i	$0.205714\pi$
$434$	−11.1553	−	26.9312i	−0.0257034	−	0.0620534i
$435$		0			0
$436$	43.5268	+	65.1425i	0.0998321	+	0.149409i
$437$	−123.182	−	619.277i	−0.281881	−	1.41711i
$438$	61.5532	−	61.5532i	0.140533	−	0.140533i
$439$	354.911	−	531.162i	0.808453	−	1.20994i	−0.166173	−	0.986097i	$-0.553141\pi$
$439$	354.911	−	531.162i	0.808453	−	1.20994i	0.974626	−	0.223839i	$-0.0718589\pi$
$440$		0			0
$441$			305.503i			0.692751i
$442$	26.3317	−	213.615i	0.0595739	−	0.483292i
$443$	79.9030			0.180368			0.0901839	−	0.995925i	$-0.471255\pi$
$443$	79.9030			0.180368			0.0901839	+	0.995925i	$0.471255\pi$
$444$	−82.0829	+	198.166i	−0.184871	+	0.446319i
$445$		0			0
$446$	53.9846	+	53.9846i	0.121042	+	0.121042i
$447$	339.057	−	67.4426i	0.758516	−	0.150878i
$448$	3.73178	−	2.49350i	0.00832987	−	0.00556584i
$449$	144.414	+	28.7257i	0.321634	+	0.0639770i	0.353267	−	0.935523i	$-0.385071\pi$
$449$	144.414	+	28.7257i	0.321634	+	0.0639770i	−0.0316329	+	0.999500i	$0.510071\pi$
$450$		0			0
$451$	−9.71569	−	23.4558i	−0.0215426	−	0.0520083i
$452$	−31.0537	+	156.118i	−0.0687029	+	0.345393i
$453$	−54.2188	−	81.1442i	−0.119688	−	0.179126i
$454$	24.6712	+	124.031i	0.0543420	+	0.273195i
$455$		0			0
$456$	189.725	−	283.943i	0.416063	−	0.622682i
$457$	−595.804	−	246.790i	−1.30373	−	0.540022i	−0.380681	−	0.924706i	$-0.624310\pi$
$457$	−595.804	−	246.790i	−1.30373	−	0.540022i	−0.923048	+	0.384684i	$0.874310\pi$
$458$			116.072i			0.253432i
$459$	277.767	−	322.055i	0.605156	−	0.701644i
$460$		0			0
$461$	98.1211	−	236.885i	0.212844	−	0.513851i	−0.781014	−	0.624513i	$-0.785297\pi$
$461$	98.1211	−	236.885i	0.212844	−	0.513851i	0.993858	+	0.110663i	$0.0352973\pi$
$462$	6.99015	+	4.67067i	0.0151302	+	0.0101097i
$463$	−422.873	−	422.873i	−0.913332	−	0.913332i	0.0832008	−	0.996533i	$-0.473486\pi$
$463$	−422.873	−	422.873i	−0.913332	−	0.913332i	−0.996533	+	0.0832008i	$0.973486\pi$
$464$	−163.875	+	32.5968i	−0.353180	+	0.0702518i
$465$		0			0
$466$	−296.676	−	59.0124i	−0.636643	−	0.126636i
$467$	−469.394	+	194.429i	−1.00513	+	0.416337i	−0.823674	−	0.567063i	$-0.808080\pi$
$467$	−469.394	+	194.429i	−1.00513	+	0.416337i	−0.181452	+	0.983400i	$0.558080\pi$
$468$	118.904	+	287.060i	0.254068	+	0.613375i
$469$	−5.64238	+	28.3661i	−0.0120307	+	0.0604822i
$470$		0			0
$471$	46.9418	+	235.992i	0.0996641	+	0.501045i
$472$	−150.161	+	150.161i	−0.318137	+	0.318137i
$473$	−50.9285	+	76.2199i	−0.107671	+	0.161141i
$474$	83.4517	+	34.5668i	0.176058	+	0.0729258i
$475$		0			0
$476$	−3.71343	−	50.2934i	−0.00780131	−	0.105658i
$477$	12.6495			0.0265190
$478$	129.146	−	311.786i	0.270180	−	0.652272i
$479$	−329.863	−	220.407i	−0.688649	−	0.460141i	0.161369	−	0.986894i	$-0.448409\pi$
$479$	−329.863	−	220.407i	−0.688649	−	0.460141i	−0.850018	+	0.526753i	$0.823409\pi$
$480$		0			0
$481$	−587.120	+	116.785i	−1.22062	+	0.242797i
$482$	55.9288	−	37.3704i	0.116035	−	0.0775320i
$483$	26.9138	+	5.35349i	0.0557221	+	0.0110838i
$484$	229.662	−	95.1289i	0.474507	−	0.196547i
$485$		0			0
$486$	41.6257	−	209.266i	0.0856495	−	0.430589i
$487$	−214.400	−	320.872i	−0.440246	−	0.658875i	0.543299	−	0.839539i	$-0.317175\pi$
$487$	−214.400	−	320.872i	−0.440246	−	0.658875i	−0.983545	+	0.180665i	$0.942175\pi$
$488$	42.7553	+	214.945i	0.0876133	+	0.440462i
$489$	373.980	−	373.980i	0.764784	−	0.764784i
$490$		0			0
$491$	430.764	+	178.428i	0.877319	+	0.363398i	0.775457	−	0.631401i	$-0.217520\pi$
$491$	430.764	+	178.428i	0.877319	+	0.363398i	0.101863	+	0.994798i	$0.467520\pi$
$492$		−	20.1979i		−	0.0410527i
$493$	−112.873	+	341.751i	−0.228950	+	0.693207i
$494$	429.499			0.869432
$495$		0			0
$496$	249.583	+	166.766i	0.503191	+	0.336221i
$497$	−66.2436	−	66.2436i	−0.133287	−	0.133287i
$498$	−58.2885	+	11.5943i	−0.117045	+	0.0232817i
$499$	152.031	−	101.584i	0.304671	−	0.203574i	−0.393831	−	0.919183i	$-0.628850\pi$
$499$	152.031	−	101.584i	0.304671	−	0.203574i	0.698502	+	0.715608i	$0.253850\pi$
$500$		0			0
$501$	−237.592	+	98.4139i	−0.474236	+	0.196435i
$502$	147.085	+	355.094i	0.292998	+	0.707359i
$503$	125.290	−	629.877i	0.249086	−	1.25224i	−0.630383	−	0.776284i	$-0.717102\pi$
$503$	125.290	−	629.877i	0.249086	−	1.25224i	0.879469	−	0.475956i	$-0.157898\pi$
$504$	−19.6581	−	29.4205i	−0.0390042	−	0.0583739i
$505$		0			0
$506$	75.0475	−	75.0475i	0.148315	−	0.148315i
$507$	48.9556	−	73.2672i	0.0965593	−	0.144511i
$508$	−146.311	−	60.6039i	−0.288013	−	0.119299i
$509$		−	177.040i		−	0.347819i	−0.984762	−	0.173909i	$-0.944360\pi$
$509$		−	177.040i		−	0.347819i	0.984762	−	0.173909i	$-0.0556400\pi$
$510$		0			0
$511$	56.9235			0.111396
$512$	169.352	−	408.852i	0.330766	−	0.798539i
$513$	705.651	+	471.501i	1.37554	+	0.919105i
$514$	−59.0293	−	59.0293i	−0.114843	−	0.114843i
$515$		0			0
$516$	−60.6374	+	40.5166i	−0.117514	+	0.0785206i
$517$	85.8791	+	17.0824i	0.166110	+	0.0330414i
$518$	28.3826	−	11.7565i	0.0547927	−	0.0226959i
$519$	102.569	+	247.623i	0.197628	+	0.477116i
$520$		0			0
$521$	−169.681	−	253.946i	−0.325684	−	0.487420i	0.632109	−	0.774879i	$-0.282189\pi$
$521$	−169.681	−	253.946i	−0.325684	−	0.487420i	−0.957793	+	0.287459i	$0.907189\pi$
$522$	22.2012	+	111.613i	0.0425310	+	0.213818i
$523$	291.958	−	291.958i	0.558238	−	0.558238i	−0.370568	−	0.928806i	$-0.620837\pi$
$523$	291.958	−	291.958i	0.558238	−	0.558238i	0.928806	+	0.370568i	$0.120837\pi$
$524$	−5.95322	+	8.90963i	−0.0113611	+	0.0170031i
$525$		0			0
$526$			76.2721i			0.145004i
$527$	577.517	−	290.749i	1.09586	−	0.551705i
$528$	−86.5701			−0.163959
$529$	−69.8676	+	168.675i	−0.132075	+	0.318857i
$530$		0			0
$531$	−154.241	−	154.241i	−0.290473	−	0.290473i
$532$	98.7011	−	19.6329i	0.185528	−	0.0369039i
$533$	46.8698	−	31.3174i	0.0879359	−	0.0587569i
$534$	−95.0549	−	18.9076i	−0.178005	−	0.0354075i
$535$		0			0
$536$	75.5703	+	182.443i	0.140989	+	0.340379i
$537$	61.7451	−	310.413i	0.114982	−	0.578051i
$538$	−222.940	−	333.653i	−0.414387	−	0.620174i
$539$	−63.2265	−	317.861i	−0.117303	−	0.589724i
$540$		0			0
$541$	−397.133	+	594.351i	−0.734072	+	1.09862i	0.257145	+	0.966373i	$0.417218\pi$
$541$	−397.133	+	594.351i	−0.734072	+	1.09862i	−0.991217	+	0.132243i	$0.957782\pi$
$542$	−48.1220	−	19.9328i	−0.0887859	−	0.0367763i
$543$			81.4550i			0.150009i
$544$	−328.250	−	420.553i	−0.603401	−	0.773075i
$545$		0			0
$546$	−7.14319	+	17.2452i	−0.0130828	+	0.0315846i
$547$	−251.742	−	168.209i	−0.460223	−	0.307511i	0.303759	−	0.952749i	$-0.401758\pi$
$547$	−251.742	−	168.209i	−0.460223	−	0.307511i	−0.763982	+	0.645238i	$0.776758\pi$
$548$	208.709	+	208.709i	0.380855	+	0.380855i
$549$	−220.786	+	43.9171i	−0.402160	+	0.0799946i
$550$		0			0
$551$	−704.404	−	140.115i	−1.27841	−	0.254292i
$552$	173.102	−	71.7011i	0.313590	−	0.129893i
$553$	22.6040	+	54.5708i	0.0408752	+	0.0986815i
$554$	24.6708	−	124.029i	0.0445321	−	0.223878i
$555$		0			0
$556$	83.3180	+	418.868i	0.149853	+	0.753360i
$557$	−708.431	+	708.431i	−1.27187	+	1.27187i	−0.326762	+	0.945107i	$0.605958\pi$
$557$	−708.431	+	708.431i	−1.27187	+	1.27187i	−0.945107	+	0.326762i	$0.894042\pi$
$558$	113.581	−	169.987i	0.203551	−	0.304635i
$559$	−188.040	−	77.8887i	−0.336386	−	0.139336i
$560$		0			0
$561$	−91.9016	+	162.256i	−0.163818	+	0.289226i
$562$	28.7839			0.0512170
$563$	314.331	−	758.863i	0.558315	−	1.34789i	−0.352784	−	0.935705i	$-0.614765\pi$
$563$	314.331	−	758.863i	0.558315	−	1.34789i	0.911099	−	0.412187i	$-0.135235\pi$
$564$	57.9205	+	38.7012i	0.102696	+	0.0686192i
$565$		0			0
$566$	−157.202	+	31.2694i	−0.277742	+	0.0552463i
$567$	12.2278	−	8.17032i	0.0215657	−	0.0144097i
$568$	−627.361	−	124.790i	−1.10451	−	0.219701i
$569$	395.568	−	163.849i	0.695198	−	0.287960i	−0.00696604	−	0.999976i	$-0.502217\pi$
$569$	395.568	−	163.849i	0.695198	−	0.287960i	0.702164	+	0.712015i	$0.252217\pi$
$570$		0			0
$571$	78.3724	−	394.005i	0.137255	−	0.690026i	−0.849472	−	0.527634i	$-0.823079\pi$
$571$	78.3724	−	394.005i	0.137255	−	0.690026i	0.986726	−	0.162392i	$-0.0519208\pi$
$572$	−183.123	−	274.063i	−0.320145	−	0.479132i
$573$	94.9119	+	477.154i	0.165640	+	0.832730i
$574$	−2.04558	+	2.04558i	−0.00356372	+	0.00356372i
$575$		0			0
$576$	29.0813	+	12.0459i	0.0504884	+	0.0209130i
$577$			324.254i			0.561965i	0.959713	+	0.280982i	$0.0906602\pi$
$577$			324.254i			0.561965i	−0.959713	+	0.280982i	$0.909340\pi$
$578$	−242.346	+	35.9834i	−0.419283	+	0.0622550i
$579$	−91.9094			−0.158738
$580$		0			0
$581$	−32.3133	−	21.5910i	−0.0556167	−	0.0371619i
$582$	124.890	+	124.890i	0.214587	+	0.214587i
$583$	−13.1612	+	2.61793i	−0.0225750	+	0.00449045i
$584$	323.164	−	215.931i	0.553363	−	0.369745i
$585$		0			0
$586$	138.619	−	57.4177i	0.236551	−	0.0979825i
$587$	103.107	+	248.922i	0.175651	+	0.424058i	0.987046	−	0.160440i	$-0.0512914\pi$
$587$	103.107	+	248.922i	0.175651	+	0.424058i	−0.811395	+	0.584498i	$0.801291\pi$
$588$	50.3004	−	252.877i	0.0855449	−	0.430063i
$589$	716.828	+	1072.81i	1.21703	+	1.82141i
$590$		0			0
$591$	−4.31787	+	4.31787i	−0.00730603	+	0.00730603i
$592$	−175.753	+	263.034i	−0.296881	+	0.444313i
$593$	662.174	+	274.282i	1.11665	+	0.462532i	0.863223	−	0.504822i	$-0.168442\pi$
$593$	662.174	+	274.282i	1.11665	+	0.462532i	0.253428	+	0.967354i	$0.418442\pi$
$594$			142.654i			0.240158i
$595$		0			0
$596$	695.579			1.16708
$597$	−92.9693	+	224.448i	−0.155727	+	0.375959i
$598$	195.934	+	130.919i	0.327649	+	0.218928i
$599$	−330.421	−	330.421i	−0.551622	−	0.551622i	0.375287	−	0.926909i	$-0.377544\pi$
$599$	−330.421	−	330.421i	−0.551622	−	0.551622i	−0.926909	+	0.375287i	$0.877544\pi$
$600$		0			0
$601$	−26.7271	+	17.8585i	−0.0444710	+	0.0297146i	−0.577607	−	0.816315i	$-0.696013\pi$
$601$	−26.7271	+	17.8585i	−0.0444710	+	0.0297146i	0.533136	+	0.846030i	$0.321013\pi$
$602$	10.2445	+	2.03776i	0.0170175	+	0.00338499i
$603$	−187.400	+	77.6237i	−0.310780	+	0.128729i
$604$	−75.1448	−	181.416i	−0.124412	−	0.300357i
$605$		0			0
$606$	−28.5058	−	42.6620i	−0.0470393	−	0.0703993i
$607$	51.7408	+	260.119i	0.0852402	+	0.428531i	0.999715	+	0.0238877i	$0.00760442\pi$
$607$	51.7408	+	260.119i	0.0852402	+	0.428531i	−0.914474	+	0.404644i	$0.867396\pi$
$608$	752.780	−	752.780i	1.23813	−	1.23813i
$609$	17.3411	−	25.9528i	0.0284747	−	0.0426154i
$610$		0			0
$611$			194.413i			0.318189i
$612$	278.813	−	217.620i	0.455577	−	0.355588i
$613$	700.076			1.14205			0.571025	−	0.820933i	$-0.306546\pi$
$613$	700.076			1.14205			0.571025	+	0.820933i	$0.306546\pi$
$614$	119.432	−	288.335i	0.194515	−	0.469602i
$615$		0			0
$616$	26.5421	+	26.5421i	0.0430879	+	0.0430879i
$617$	−703.990	+	140.032i	−1.14099	+	0.226957i	−0.729185	−	0.684316i	$-0.760101\pi$
$617$	−703.990	+	140.032i	−1.14099	+	0.226957i	−0.411803	+	0.911273i	$0.635101\pi$
$618$	−63.1246	+	42.1785i	−0.102143	+	0.0682500i
$619$	−898.874	−	178.797i	−1.45214	−	0.288848i	−0.594913	−	0.803790i	$-0.702814\pi$
$619$	−898.874	−	178.797i	−1.45214	−	0.288848i	−0.857225	+	0.514941i	$0.827814\pi$
$620$		0			0
$621$	178.190	+	430.190i	0.286941	+	0.692737i
$622$	−17.3803	+	87.3767i	−0.0279426	+	0.140477i
$623$	−35.2099	−	52.6954i	−0.0565167	−	0.0845833i
$624$	−37.4987	−	188.519i	−0.0600941	−	0.302113i
$625$		0			0
$626$	204.359	−	305.845i	0.326452	−	0.488570i
$627$	−343.788	−	142.402i	−0.548307	−	0.227116i
$628$			484.141i			0.770926i
$629$	306.418	+	608.642i	0.487152	+	0.967634i
$630$		0			0
$631$	313.464	−	756.768i	0.496773	−	1.19932i	−0.454439	−	0.890778i	$-0.650160\pi$
$631$	313.464	−	756.768i	0.496773	−	1.19932i	0.951212	−	0.308538i	$-0.0998397\pi$
$632$	335.333	+	224.063i	0.530591	+	0.354529i
$633$	−342.359	−	342.359i	−0.540852	−	0.540852i
$634$	−435.698	+	86.6657i	−0.687220	+	0.136697i
$635$		0			0
$636$	−10.4705	−	2.08272i	−0.0164631	−	0.00327472i
$637$	664.801	−	275.370i	1.04364	−	0.432291i
$638$	−46.1985	−	111.533i	−0.0724114	−	0.174817i
$639$	128.181	−	644.408i	0.200596	−	1.00846i
$640$		0			0
$641$	206.112	+	1036.19i	0.321547	+	1.61653i	0.716337	+	0.697754i	$0.245817\pi$
$641$	206.112	+	1036.19i	0.321547	+	1.61653i	−0.394790	+	0.918771i	$0.629183\pi$
$642$	−145.182	+	145.182i	−0.226140	+	0.226140i
$643$	−198.642	+	297.289i	−0.308931	+	0.462347i	−0.953152	−	0.302492i	$-0.902182\pi$
$643$	−198.642	+	297.289i	−0.308931	+	0.462347i	0.644221	+	0.764839i	$0.277182\pi$
$644$	51.0111	+	21.1295i	0.0792097	+	0.0328097i
$645$		0			0
$646$	−130.431	−	471.188i	−0.201905	−	0.729393i
$647$	−414.046			−0.639947			−0.319973	−	0.947427i	$-0.603674\pi$
$647$	−414.046			−0.639947			−0.319973	+	0.947427i	$0.603674\pi$
$648$	38.4260	−	92.7686i	0.0592994	−	0.143161i
$649$	192.402	+	128.559i	0.296459	+	0.198088i
$650$		0			0
$651$	−54.9971	+	10.9396i	−0.0844810	+	0.0168043i
$652$	884.825	−	591.221i	1.35709	−	0.906781i
$653$	−714.568	−	142.136i	−1.09428	−	0.217667i	−0.385230	−	0.922821i	$-0.625878\pi$
$653$	−714.568	−	142.136i	−1.09428	−	0.217667i	−0.709054	+	0.705154i	$0.750878\pi$
$654$	−30.4970	+	12.6323i	−0.0466315	+	0.0193154i
$655$		0			0
$656$	5.81158	−	29.2168i	0.00885911	−	0.0445378i
$657$	221.799	+	331.945i	0.337593	+	0.505244i
$658$	−1.94646	−	9.78551i	−0.00295815	−	0.0148716i
$659$	−310.871	+	310.871i	−0.471731	+	0.471731i	−0.902474	−	0.430743i	$-0.858251\pi$
$659$	−310.871	+	310.871i	−0.471731	+	0.471731i	0.430743	+	0.902474i	$0.358251\pi$
$660$		0			0
$661$	−163.337	−	67.6563i	−0.247105	−	0.102354i	0.255693	−	0.966758i	$-0.417696\pi$
$661$	−163.337	−	67.6563i	−0.247105	−	0.102354i	−0.502799	+	0.864404i	$0.667696\pi$
$662$		−	298.294i		−	0.450595i
$663$	−393.143	−	129.846i	−0.592976	−	0.195846i
$664$	−265.351			−0.399624
$665$		0			0
$666$	179.148	+	119.703i	0.268991	+	0.179734i
$667$	−278.634	−	278.634i	−0.417742	−	0.417742i
$668$	−507.503	+	100.949i	−0.759736	+	0.151121i
$669$	122.112	−	81.5924i	0.182529	−	0.121962i
$670$		0			0
$671$	220.628	−	91.3871i	0.328805	−	0.136195i
$672$	17.7057	+	42.7453i	0.0263478	+	0.0636091i
$673$	−121.389	+	610.263i	−0.180370	+	0.906780i	0.779515	+	0.626384i	$0.215466\pi$
$673$	−121.389	+	610.263i	−0.180370	+	0.906780i	−0.959884	+	0.280396i	$0.909534\pi$
$674$	73.2077	+	109.563i	0.108617	+	0.162557i
$675$		0			0
$676$	125.371	−	125.371i	0.185460	−	0.185460i
$677$	26.5471	−	39.7306i	0.0392129	−	0.0586862i	−0.811345	−	0.584567i	$-0.801264\pi$
$677$	26.5471	−	39.7306i	0.0392129	−	0.0586862i	0.850558	+	0.525881i	$0.176264\pi$
$678$	−61.9609	−	25.6650i	−0.0913878	−	0.0378540i
$679$			115.496i			0.170097i
$680$		0			0
$681$	243.266			0.357219
$682$	−82.9957	+	200.369i	−0.121695	+	0.293797i
$683$	−618.830	−	413.489i	−0.906048	−	0.605402i	0.0128416	−	0.999918i	$-0.495912\pi$
$683$	−618.830	−	413.489i	−0.906048	−	0.605402i	−0.918889	+	0.394516i	$0.870912\pi$
$684$	499.070	+	499.070i	0.729634	+	0.729634i
$685$		0			0
$686$	−61.9304	+	41.3806i	−0.0902776	+	0.0603216i
$687$	218.991	+	43.5600i	0.318764	+	0.0634062i
$688$	−99.3714	+	41.1610i	−0.144435	+	0.0598270i
$689$	−11.4018	−	27.5265i	−0.0165484	−	0.0399514i
$690$		0			0
$691$	−713.306	−	1067.54i	−1.03228	−	1.54492i	−0.823792	−	0.566893i	$-0.808145\pi$
$691$	−713.306	−	1067.54i	−1.03228	−	1.54492i	−0.208489	−	0.978025i	$-0.566855\pi$
$692$	105.211	+	528.930i	0.152038	+	0.764349i
$693$	−27.2633	+	27.2633i	−0.0393410	+	0.0393410i
$694$	−126.003	+	188.577i	−0.181561	+	0.271725i
$695$		0			0
$696$		−	213.119i		−	0.306206i
$697$	−48.5906	−	41.9086i	−0.0697140	−	0.0601271i
$698$	−167.384			−0.239806
$699$	−222.676	+	537.588i	−0.318564	+	0.769081i
$700$		0			0
$701$	−895.228	−	895.228i	−1.27707	−	1.27707i	−0.942298	−	0.334774i	$-0.891340\pi$
$701$	−895.228	−	895.228i	−1.27707	−	1.27707i	−0.334774	−	0.942298i	$-0.608660\pi$
$702$	−310.649	+	61.7920i	−0.442520	+	0.0880227i
$703$	−1130.63	+	755.461i	−1.60829	+	1.07462i
$704$	−32.7507	−	6.51451i	−0.0465208	−	0.00925357i
$705$		0			0
$706$	139.297	+	336.292i	0.197304	+	0.476335i
$707$	6.54570	−	32.9074i	0.00925841	−	0.0465452i
$708$	102.276	+	153.067i	0.144458	+	0.216196i
$709$	145.154	+	729.738i	0.204730	+	1.02925i	0.937291	+	0.348547i	$0.113325\pi$
$709$	145.154	+	729.738i	0.204730	+	1.02925i	−0.732561	+	0.680702i	$0.761675\pi$
$710$		0			0
$711$	−230.151	+	344.445i	−0.323700	+	0.484452i
$712$	−399.785	−	165.596i	−0.561496	−	0.232579i
$713$			707.908i			0.992859i
$714$	21.0883	+	2.59949i	0.0295354	+	0.00364074i
$715$		0			0
$716$	243.699	−	588.342i	0.340362	−	0.821707i
$717$	−539.776	−	360.667i	−0.752826	−	0.503022i
$718$	34.0384	+	34.0384i	0.0474073	+	0.0474073i
$719$	141.631	−	28.1722i	0.196984	−	0.0391825i	−0.0956124	−	0.995419i	$-0.530481\pi$
$719$	141.631	−	28.1722i	0.196984	−	0.0391825i	0.292596	+	0.956236i	$0.405481\pi$
$720$		0			0
$721$	−48.6914	−	9.68532i	−0.0675331	−	0.0134332i
$722$	618.614	−	256.238i	0.856806	−	0.354901i
$723$	−49.5170	−	119.545i	−0.0684883	−	0.165345i
$724$	−31.9744	+	160.746i	−0.0441635	+	0.222025i
$725$		0			0
$726$	20.4330	+	102.724i	0.0281447	+	0.141493i
$727$	−33.3667	+	33.3667i	−0.0458965	+	0.0458965i	−0.729683	−	0.683786i	$-0.760332\pi$
$727$	−33.3667	+	33.3667i	−0.0458965	+	0.0458965i	0.683786	+	0.729683i	$0.260332\pi$
$728$	−46.3023	+	69.2963i	−0.0636020	+	0.0951872i
$729$	−243.941	−	101.044i	−0.334624	−	0.138606i
$730$		0			0
$731$	−28.3446	+	229.945i	−0.0387750	+	0.314562i
$732$	189.984			0.259541
$733$	250.284	−	604.239i	0.341452	−	0.824337i	−0.656118	−	0.754658i	$-0.727803\pi$
$733$	250.284	−	604.239i	0.341452	−	0.824337i	0.997569	−	0.0696787i	$-0.0221974\pi$
$734$	−160.291	−	107.103i	−0.218381	−	0.145917i
$735$		0			0
$736$	572.873	−	113.951i	0.778360	−	0.154825i
$737$	178.916	−	119.548i	0.242762	−	0.162209i
$738$	−19.8991	−	3.95817i	−0.0269635	−	0.00536338i
$739$	−1135.07	+	470.162i	−1.53596	+	0.636214i	−0.980709	−	0.195472i	$-0.937376\pi$
$739$	−1135.07	+	470.162i	−1.53596	+	0.636214i	−0.555247	+	0.831685i	$0.687376\pi$
$740$		0			0
$741$	161.185	−	810.331i	0.217523	−	1.09356i
$742$	0.849490	+	1.27135i	0.00114486	+	0.00171341i
$743$	219.382	+	1102.91i	0.295266	+	1.48440i	0.788787	+	0.614667i	$0.210710\pi$
$743$	219.382	+	1102.91i	0.295266	+	1.48440i	−0.493521	+	0.869734i	$0.664290\pi$
$744$	−270.730	+	270.730i	−0.363884	+	0.363884i
$745$		0			0
$746$	−360.419	−	149.290i	−0.483135	−	0.200121i
$747$		−	272.561i		−	0.364874i
$748$	−245.053	+	284.125i	−0.327612	+	0.379847i
$749$	−134.262			−0.179255
$750$		0			0
$751$	1063.32	+	710.490i	1.41588	+	0.946059i	0.999317	+	0.0369501i	$0.0117643\pi$
$751$	1063.32	+	710.490i	1.41588	+	0.946059i	0.416560	+	0.909108i	$0.363236\pi$
$752$	72.6478	+	72.6478i	0.0966061	+	0.0966061i
$753$	725.151	−	144.241i	0.963016	−	0.191556i
$754$	222.868	−	148.915i	0.295580	−	0.197500i
$755$		0			0
$756$	−68.5641	+	28.4002i	−0.0906933	+	0.0375664i
$757$	75.7752	+	182.937i	0.100099	+	0.241661i	0.965994	−	0.258566i	$-0.0832499\pi$
$757$	75.7752	+	182.937i	0.100099	+	0.241661i	−0.865894	+	0.500227i	$0.833250\pi$
$758$	−10.1804	+	51.1802i	−0.0134306	+	0.0675201i
$759$	−113.427	−	169.755i	−0.149443	−	0.223657i
$760$		0			0
$761$	380.948	−	380.948i	0.500588	−	0.500588i	−0.411032	−	0.911621i	$-0.634832\pi$
$761$	380.948	−	380.948i	0.500588	−	0.500588i	0.911621	+	0.411032i	$0.134832\pi$
$762$	37.0701	−	55.4793i	0.0486484	−	0.0728075i
$763$	−19.9427	−	8.26052i	−0.0261372	−	0.0108264i
$764$			978.888i			1.28127i
$765$		0			0
$766$	522.082			0.681570
$767$	−196.614	+	474.669i	−0.256342	+	0.618864i
$768$	122.208	+	81.6568i	0.159125	+	0.106324i
$769$	−90.3571	−	90.3571i	−0.117500	−	0.117500i	0.645912	−	0.763412i	$-0.276477\pi$
$769$	−90.3571	−	90.3571i	−0.117500	−	0.117500i	−0.763412	+	0.645912i	$0.776477\pi$
$770$		0			0
$771$	−133.523	+	89.2169i	−0.173181	+	0.115716i
$772$	−181.377	−	36.0781i	−0.234944	−	0.0467333i
$773$	−134.981	+	55.9110i	−0.174620	+	0.0723298i	−0.468281	−	0.883580i	$-0.655126\pi$
$773$	−134.981	+	55.9110i	−0.174620	+	0.0723298i	0.293661	+	0.955910i	$0.405126\pi$
$774$	28.0341	+	67.6802i	0.0362197	+	0.0874422i
$775$		0			0
$776$	438.118	+	655.689i	0.564585	+	0.844961i
$777$	−11.5292	−	57.9611i	−0.0148381	−	0.0745960i
$778$	−218.482	+	218.482i	−0.280825	+	0.280825i
$779$	71.1386	−	106.466i	0.0913204	−	0.136671i
$780$		0			0
$781$			697.003i			0.892450i
$782$	84.1248	−	254.710i	0.107576	−	0.325716i
$783$	529.641			0.676425
$784$	145.522	−	351.320i	0.185614	−	0.448113i
$785$		0			0
$786$	−3.19244	−	3.19244i	−0.00406163	−	0.00406163i
$787$	678.506	−	134.963i	0.862142	−	0.171491i	0.255834	−	0.966721i	$-0.417650\pi$
$787$	678.506	−	134.963i	0.862142	−	0.171491i	0.606308	+	0.795230i	$0.292650\pi$
$788$	−10.2159	+	6.82608i	−0.0129644	+	0.00866254i
$789$	143.902	+	28.6238i	0.182385	+	0.0362786i
$790$		0			0
$791$	−16.7829	−	40.5176i	−0.0212174	−	0.0512232i
$792$	−51.3588	+	258.198i	−0.0648470	+	0.326008i
$793$	294.576	+	440.864i	0.371470	+	0.555944i
$794$	9.95687	+	50.0566i	0.0125401	+	0.0630436i
$795$		0			0
$796$	−271.573	+	406.438i	−0.341172	+	0.510601i
$797$	997.012	+	412.976i	1.25096	+	0.518163i	0.907122	−	0.420867i	$-0.138274\pi$
$797$	997.012	+	412.976i	1.25096	+	0.518163i	0.343834	+	0.939030i	$0.388274\pi$
$798$			42.4006i			0.0531336i
$799$	213.284	−	59.0397i	0.266938	−	0.0738919i
$800$		0			0
$801$	170.096	−	410.648i	0.212355	−	0.512669i
$802$	13.7229	+	9.16932i	0.0171108	+	0.0114331i
$803$	−299.470	−	299.470i	−0.372938	−	0.372938i
$804$	167.899	−	33.3972i	0.208830	−	0.0415389i
$805$		0			0
$806$	−472.283	−	93.9430i	−0.585959	−	0.116555i
$807$	−713.166	+	295.403i	−0.883725	+	0.366051i
$808$	−87.6688	−	211.651i	−0.108501	−	0.261945i
$809$	−111.178	+	558.928i	−0.137426	+	0.690887i	0.849224	+	0.528033i	$0.177070\pi$
$809$	−111.178	+	558.928i	−0.137426	+	0.690887i	−0.986650	+	0.162855i	$0.947930\pi$
$810$		0			0
$811$	221.750	+	1114.81i	0.273428	+	1.37461i	0.836392	+	0.548132i	$0.184661\pi$
$811$	221.750	+	1114.81i	0.273428	+	1.37461i	−0.562964	+	0.826481i	$0.690339\pi$
$812$	44.4090	−	44.4090i	0.0546909	−	0.0546909i
$813$	−55.6664	+	83.3106i	−0.0684703	+	0.102473i
$814$	−211.168	−	87.4687i	−0.259420	−	0.107455i
$815$		0			0
$816$	−195.429	+	98.3880i	−0.239497	+	0.120574i
$817$	−462.332			−0.565890
$818$	−141.081	+	340.600i	−0.172471	+	0.416382i
$819$	−71.1792	−	47.5604i	−0.0869099	−	0.0580713i
$820$		0			0
$821$	−20.5375	+	4.08517i	−0.0250153	+	0.00497585i	−0.207582	−	0.978218i	$-0.566559\pi$
$821$	−20.5375	+	4.08517i	−0.0250153	+	0.00497585i	0.182567	+	0.983193i	$0.441559\pi$
$822$	−103.401	+	69.0906i	−0.125792	+	0.0840518i
$823$	−1543.55	−	307.031i	−1.87551	−	0.373063i	−0.880606	−	0.473850i	$-0.842864\pi$
$823$	−1543.55	−	307.031i	−1.87551	−	0.373063i	−0.994908	+	0.100787i	$0.967864\pi$
$824$	−313.169	+	129.719i	−0.380059	+	0.157426i
$825$		0			0
$826$	5.14393	−	25.8603i	0.00622752	−	0.0313078i
$827$	−299.622	−	448.417i	−0.362300	−	0.542221i	0.604878	−	0.796318i	$-0.293222\pi$
$827$	−299.622	−	448.417i	−0.362300	−	0.542221i	−0.967179	+	0.254097i	$0.918222\pi$
$828$	75.5463	+	379.797i	0.0912395	+	0.458692i
$829$	−145.931	+	145.931i	−0.176032	+	0.176032i	−0.789624	−	0.613591i	$-0.789724\pi$
$829$	−145.931	+	145.931i	−0.176032	+	0.176032i	0.613591	+	0.789624i	$0.289724\pi$
$830$		0			0
$831$	−224.744	−	93.0922i	−0.270451	−	0.112024i
$832$		−	74.1411i		−	0.0891119i
$833$	−503.985	−	645.703i	−0.605024	−	0.775154i
$834$	−179.940			−0.215755
$835$		0			0
$836$	−622.545	−	415.971i	−0.744671	−	0.497573i
$837$	−672.813	−	672.813i	−0.803839	−	0.803839i
$838$	67.3212	−	13.3910i	0.0803355	−	0.0159797i
$839$	−587.153	+	392.323i	−0.699824	+	0.467608i	−0.853890	−	0.520453i	$-0.825763\pi$
$839$	−587.153	+	392.323i	−0.699824	+	0.467608i	0.154066	+	0.988061i	$0.450763\pi$
$840$		0			0
$841$	362.887	−	150.313i	0.431494	−	0.178731i
$842$	96.8532	+	233.824i	0.115028	+	0.277701i
$843$	10.8022	−	54.3063i	0.0128140	−	0.0644203i
$844$	−541.233	−	810.012i	−0.641271	−	0.959730i
$845$		0			0
$846$	49.4792	−	49.4792i	0.0584861	−	0.0584861i
$847$	−38.0506	+	56.9468i	−0.0449240	+	0.0672335i
$848$	−14.5466	−	6.02541i	−0.0171540	−	0.00710544i
$849$			308.326i			0.363163i
$850$		0			0
$851$	−746.060			−0.876686
$852$	−212.201	+	512.298i	−0.249062	+	0.601289i
$853$	940.733	+	628.578i	1.10285	+	0.736903i	0.967241	−	0.253860i	$-0.0817001\pi$
$853$	940.733	+	628.578i	1.10285	+	0.736903i	0.135612	+	0.990762i	$0.456700\pi$
$854$	−19.2410	−	19.2410i	−0.0225304	−	0.0225304i
$855$		0			0
$856$	−762.227	+	509.304i	−0.890452	+	0.594981i
$857$	1477.19	+	293.831i	1.72368	+	0.342860i	0.954961	−	0.296732i	$-0.0958967\pi$
$857$	1477.19	+	293.831i	1.72368	+	0.342860i	0.768715	+	0.639592i	$0.220897\pi$
$858$	128.305	−	53.1457i	0.149540	−	0.0619414i
$859$	−39.2673	−	94.7998i	−0.0457129	−	0.110361i	0.899374	−	0.437181i	$-0.144023\pi$
$859$	−39.2673	−	94.7998i	−0.0457129	−	0.110361i	−0.945087	+	0.326820i	$0.894023\pi$
$860$		0			0
$861$	3.09169	+	4.62704i	0.00359081	+	0.00537403i
$862$	−99.4434	−	499.936i	−0.115364	−	0.579972i
$863$	533.064	−	533.064i	0.617687	−	0.617687i	−0.327250	−	0.944938i	$-0.606122\pi$
$863$	533.064	−	533.064i	0.617687	−	0.617687i	0.944938	+	0.327250i	$0.106122\pi$
$864$	−436.170	+	652.774i	−0.504826	+	0.755526i
$865$		0			0
$866$			372.300i			0.429907i
$867$	−23.0593	+	470.734i	−0.0265966	+	0.542946i
$868$	−112.827			−0.129985
$869$	168.175	−	406.010i	0.193527	−	0.467215i
$870$		0			0
$871$	337.832	+	337.832i	0.387866	+	0.387866i
$872$	−144.553	+	28.7534i	−0.165772	+	0.0329740i
$873$	−673.506	+	450.022i	−0.771484	+	0.515489i
$874$	524.998	+	104.429i	0.600684	+	0.119483i
$875$		0			0
$876$	−128.938	−	311.283i	−0.147189	−	0.355346i
$877$	−173.231	+	870.893i	−0.197527	+	0.993036i	0.747055	+	0.664762i	$0.231467\pi$
$877$	−173.231	+	870.893i	−0.197527	+	0.993036i	−0.944582	+	0.328274i	$0.893533\pi$
$878$	300.879	+	450.297i	0.342687	+	0.512867i
$879$	−56.3077	−	283.078i	−0.0640589	−	0.322046i
$880$		0			0
$881$	850.061	−	1272.21i	0.964882	−	1.44405i	0.0701022	−	0.997540i	$-0.477667\pi$
$881$	850.061	−	1272.21i	0.964882	−	1.44405i	0.894780	−	0.446508i	$-0.147333\pi$
$882$	−239.278	−	99.1124i	−0.271291	−	0.112372i
$883$		−	625.063i		−	0.707885i	−0.935267	−	0.353943i	$-0.884841\pi$
$883$		−	625.063i		−	0.707885i	0.935267	−	0.353943i	$-0.115159\pi$
$884$	−724.871	−	410.567i	−0.819990	−	0.464442i
$885$		0			0
$886$	−25.9224	+	62.5822i	−0.0292578	+	0.0706345i
$887$	24.3095	+	16.2431i	0.0274064	+	0.0183124i	0.569198	−	0.822200i	$-0.307254\pi$
$887$	24.3095	+	16.2431i	0.0274064	+	0.0183124i	−0.541792	+	0.840513i	$0.682254\pi$
$888$	−285.320	−	285.320i	−0.321307	−	0.321307i
$889$	42.7942	−	8.51229i	0.0481374	−	0.00957513i
$890$		0			0
$891$	−107.313	−	21.3458i	−0.120441	−	0.0239571i
$892$	273.007	−	113.083i	0.306062	−	0.126775i
$893$	168.999	+	408.001i	0.189249	+	0.456888i
$894$	−57.1751	+	287.438i	−0.0639542	+	0.321520i
$895$		0			0
$896$	22.8819	+	115.035i	0.0255379	+	0.128388i
$897$	320.534	−	320.534i	0.357340	−	0.357340i
$898$	−69.3499	+	103.789i	−0.0772271	+	0.115578i
$899$	743.925	+	308.144i	0.827503	+	0.342763i
$900$		0			0
$901$	−26.7357	+	20.8678i	−0.0296734	+	0.0231607i
$902$	21.5232			0.0238616
$903$	7.68925	−	18.5635i	0.00851522	−	0.0205576i
$904$	−248.977	−	166.361i	−0.275417	−	0.184028i
$905$		0			0
$906$	81.1442	−	16.1406i	0.0895631	−	0.0178152i
$907$	−848.139	+	566.708i	−0.935104	+	0.624816i	−0.926964	−	0.375151i	$-0.877591\pi$
$907$	−848.139	+	566.708i	−0.935104	+	0.624816i	−0.00813978	+	0.999967i	$0.502591\pi$
$908$	480.069	+	95.4916i	0.528710	+	0.105167i
$909$	217.402	−	90.0509i	0.239166	−	0.0990659i
$910$		0			0
$911$	−281.322	+	1414.30i	−0.308805	+	1.55247i	0.445097	+	0.895483i	$0.353169\pi$
$911$	−281.322	+	1414.30i	−0.308805	+	1.55247i	−0.753902	+	0.656987i	$0.771831\pi$
$912$	−242.571	−	363.033i	−0.265977	−	0.398063i
$913$	56.4088	+	283.586i	0.0617840	+	0.310609i
$914$	386.586	−	386.586i	0.422960	−	0.422960i
$915$		0			0
$916$	415.065	+	171.926i	0.453128	+	0.187692i
$917$		−	2.95232i		−	0.00321954i
$918$	162.128	+	322.036i	0.176610	+	0.350802i
$919$	811.637			0.883175			0.441587	−	0.897218i	$-0.354416\pi$
$919$	811.637			0.883175			0.441587	+	0.897218i	$0.354416\pi$
$920$		0			0
$921$	−499.177	−	333.540i	−0.541995	−	0.362149i
$922$	153.702	+	153.702i	0.166705	+	0.166705i
$923$	−1517.82	+	301.914i	−1.64445	+	0.327101i
$924$	27.0558	−	18.0781i	0.0292812	−	0.0195651i
$925$		0			0
$926$	468.395	−	194.016i	0.505826	−	0.209520i
$927$	−133.244	−	321.678i	−0.143736	−	0.347010i
$928$	129.615	−	651.621i	0.139672	−	0.702178i
$929$	−32.1049	−	48.0484i	−0.0345586	−	0.0517206i	0.813788	−	0.581162i	$-0.197402\pi$
$929$	−32.1049	−	48.0484i	−0.0345586	−	0.0517206i	−0.848347	+	0.529441i	$0.822402\pi$
$930$		0			0
$931$	1155.80	−	1155.80i	1.24146	−	1.24146i
$932$	−650.461	+	973.483i	−0.697919	+	1.04451i
$933$	158.330	+	65.5824i	0.169700	+	0.0702920i
$934$		−	430.720i		−	0.461156i
$935$		0			0
$936$	−584.510			−0.624476
$937$	571.943	−	1380.79i	0.610398	−	1.47363i	−0.252167	−	0.967684i	$-0.581143\pi$
$937$	571.943	−	1380.79i	0.610398	−	1.47363i	0.862565	−	0.505946i	$-0.168857\pi$
$938$	−20.3866	−	13.6219i	−0.0217341	−	0.0145223i
$939$	−500.340	−	500.340i	−0.532844	−	0.532844i
$940$		0			0
$941$	834.402	−	557.530i	0.886719	−	0.592487i	−0.0266387	−	0.999645i	$-0.508480\pi$
$941$	834.402	−	557.530i	0.886719	−	0.592487i	0.913357	+	0.407159i	$0.133480\pi$
$942$	−200.065	−	39.7953i	−0.212383	−	0.0422456i
$943$	64.9057	−	26.8848i	0.0688290	−	0.0285099i
$944$	103.903	+	250.843i	0.110066	+	0.265724i
$945$		0			0
$946$	−43.1751	−	64.6161i	−0.0456396	−	0.0683045i
$947$	−271.675	−	1365.80i	−0.286879	−	1.44224i	−0.808215	−	0.588888i	$-0.799566\pi$
$947$	−271.675	−	1365.80i	−0.286879	−	1.44224i	0.521336	−	0.853352i	$-0.325434\pi$
$948$	247.217	−	247.217i	0.260778	−	0.260778i
$949$	522.419	−	781.856i	0.550495	−	0.823873i
$950$		0			0
$951$			854.550i			0.898580i
$952$	90.0835	+	29.7525i	0.0946255	+	0.0312527i
$953$	1378.59			1.44658			0.723292	−	0.690543i	$-0.242628\pi$
$953$	1378.59			1.44658			0.723292	+	0.690543i	$0.242628\pi$
$954$	−4.10381	+	9.90747i	−0.00430169	+	0.0103852i
$955$		0			0
$956$	−923.635	−	923.635i	−0.966145	−	0.966145i
$957$	−227.765	+	45.3054i	−0.237999	+	0.0473410i
$958$	279.644	−	186.852i	0.291904	−	0.195044i
$959$	−79.7590	−	15.8650i	−0.0831689	−	0.0165433i
$960$		0			0
$961$	−185.823	−	448.616i	−0.193364	−	0.466822i
$962$	99.0060	−	497.737i	0.102917	−	0.517398i
$963$	−523.143	−	782.938i	−0.543243	−	0.813020i
$964$	−50.7924	−	255.351i	−0.0526892	−	0.264887i
$965$		0			0
$966$	−12.9245	+	19.3428i	−0.0133794	+	0.0200236i
$967$	964.483	+	399.502i	0.997398	+	0.413136i	0.820842	−	0.571155i	$-0.193505\pi$
$967$	964.483	+	399.502i	0.997398	+	0.413136i	0.176555	+	0.984291i	$0.443505\pi$
$968$			467.636i			0.483095i
$969$	−937.933	+	69.2524i	−0.967939	+	0.0714679i
$970$		0			0
$971$	−68.3025	+	164.897i	−0.0703424	+	0.169822i	−0.955141	−	0.296153i	$-0.904296\pi$
$971$	−68.3025	+	164.897i	−0.0703424	+	0.169822i	0.884798	+	0.465975i	$0.154296\pi$
$972$	−686.667	−	458.816i	−0.706447	−	0.472033i
$973$	−83.2028	−	83.2028i	−0.0855116	−	0.0855116i
$974$	320.872	−	63.8254i	0.329437	−	0.0655292i
$975$		0			0
$976$	274.817	+	54.6645i	0.281575	+	0.0560087i
$977$	−1094.70	+	453.439i	−1.12047	+	0.464113i	−0.864531	−	0.502580i	$-0.832384\pi$
$977$	−1094.70	+	453.439i	−1.12047	+	0.464113i	−0.255938	+	0.966693i	$0.582384\pi$
$978$	171.583	+	414.239i	0.175443	+	0.423557i
$979$	−91.9894	+	462.462i	−0.0939626	+	0.472382i
$980$		0			0
$981$	−29.5346	−	148.481i	−0.0301067	−	0.151356i
$982$	−279.500	+	279.500i	−0.284623	+	0.284623i
$983$	876.560	−	1311.86i	0.891719	−	1.33455i	−0.0502093	−	0.998739i	$-0.515989\pi$
$983$	876.560	−	1311.86i	0.891719	−	1.33455i	0.941929	−	0.335813i	$-0.109011\pi$
$984$	35.1040	+	14.5406i	0.0356748	+	0.0147770i
$985$		0			0
$986$	−231.050	−	199.277i	−0.234331	−	0.202106i
$987$	−19.1927			−0.0194455
$988$	636.175	−	1535.86i	0.643902	−	1.55452i
$989$	−210.912	−	140.927i	−0.213258	−	0.142494i
$990$		0			0
$991$	−891.097	+	177.250i	−0.899190	+	0.178860i	−0.622980	−	0.782238i	$-0.714078\pi$
$991$	−891.097	+	177.250i	−0.899190	+	0.178860i	−0.276209	+	0.961098i	$0.589078\pi$
$992$	−992.420	+	663.114i	−1.00042	+	0.668462i
$993$	−562.788	−	111.945i	−0.566755	−	0.112735i
$994$	73.3747	−	30.3928i	0.0738176	−	0.0305763i
$995$		0			0
$996$	−44.8765	+	225.609i	−0.0450567	+	0.226515i
$997$	965.850	+	1445.50i	0.968757	+	1.44985i	0.891598	+	0.452828i	$0.149585\pi$
$997$	965.850	+	1445.50i	0.968757	+	1.44985i	0.0771586	+	0.997019i	$0.475415\pi$
$998$	30.2408	+	152.031i	0.0303014	+	0.152335i
$999$	709.074	−	709.074i	0.709783	−	0.709783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.a.401.1		8
5.2	odd	4		425.3.t.b.299.1		8
5.3	odd	4		425.3.t.d.299.1		8
5.4	even	2		17.3.e.b.10.1	✓	8
15.14	odd	2		153.3.p.a.10.1		8
17.12	odd	16	inner	425.3.u.a.301.1		8
20.19	odd	2		272.3.bh.b.129.1		8
85.4	even	4		289.3.e.h.75.1		8
85.9	even	8		289.3.e.a.249.1		8
85.12	even	16		425.3.t.d.199.1		8
85.14	odd	16		289.3.e.f.158.1		8
85.19	even	8		289.3.e.j.40.1		8
85.24	odd	16		289.3.e.a.65.1		8
85.29	odd	16		17.3.e.b.12.1	yes	8
85.39	odd	16		289.3.e.g.131.1		8
85.44	odd	16		289.3.e.e.65.1		8
85.49	even	8		289.3.e.n.40.1		8
85.54	odd	16		289.3.e.h.158.1		8
85.59	even	8		289.3.e.e.249.1		8
85.63	even	16		425.3.t.b.199.1		8
85.64	even	4		289.3.e.f.75.1		8
85.74	odd	16		289.3.e.j.224.1		8
85.79	odd	16		289.3.e.n.224.1		8
85.84	even	2		289.3.e.g.214.1		8
255.29	even	16		153.3.p.a.46.1		8
340.199	even	16		272.3.bh.b.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.10.1	✓	8	5.4	even	2
17.3.e.b.12.1	yes	8	85.29	odd	16
153.3.p.a.10.1		8	15.14	odd	2
153.3.p.a.46.1		8	255.29	even	16
272.3.bh.b.97.1		8	340.199	even	16
272.3.bh.b.129.1		8	20.19	odd	2
289.3.e.a.65.1		8	85.24	odd	16
289.3.e.a.249.1		8	85.9	even	8
289.3.e.e.65.1		8	85.44	odd	16
289.3.e.e.249.1		8	85.59	even	8
289.3.e.f.75.1		8	85.64	even	4
289.3.e.f.158.1		8	85.14	odd	16
289.3.e.g.131.1		8	85.39	odd	16
289.3.e.g.214.1		8	85.84	even	2
289.3.e.h.75.1		8	85.4	even	4
289.3.e.h.158.1		8	85.54	odd	16
289.3.e.j.40.1		8	85.19	even	8
289.3.e.j.224.1		8	85.74	odd	16
289.3.e.n.40.1		8	85.49	even	8
289.3.e.n.224.1		8	85.79	odd	16
425.3.t.b.199.1		8	85.63	even	16
425.3.t.b.299.1		8	5.2	odd	4
425.3.t.d.199.1		8	85.12	even	16
425.3.t.d.299.1		8	5.3	odd	4
425.3.u.a.301.1		8	17.12	odd	16	inner
425.3.u.a.401.1		8	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.324423 + 0.783227i) q^{2} +(1.35595 + 0.906019i) q^{3} +(2.32023 + 2.32023i) q^{4} +(-1.14952 + 0.768086i) q^{6} +(-0.886687 - 0.176373i) q^{7} +(-5.70292 + 2.36223i) q^{8} +(-2.42641 - 5.85788i) q^{9} +(3.73690 + 5.59267i) q^{11} +(1.04395 + 5.24830i) q^{12} +(-10.5602 + 10.5602i) q^{13} +(0.425802 - 0.637258i) q^{14} +7.89218i q^{16} +(14.7921 + 8.37823i) q^{17} +5.37523 q^{18} +(-12.9821 + 31.3415i) q^{19} +(-1.04251 - 1.04251i) q^{21} +(-5.59267 + 1.11245i) q^{22} +(-15.4758 + 10.3406i) q^{23} +(-9.87311 - 1.96388i) q^{24} +(-4.84504 - 11.6970i) q^{26} +(4.88061 - 24.5365i) q^{27} +(-1.64809 - 2.46655i) q^{28} +(4.13027 + 20.7643i) q^{29} +(21.1305 - 31.6240i) q^{31} +(-28.9930 - 12.0093i) q^{32} +10.9691i q^{33} +(-11.3609 + 8.86746i) q^{34} +(7.96180 - 19.2215i) q^{36} +(33.3284 + 22.2693i) q^{37} +(-20.3359 - 20.3359i) q^{38} +(-23.8868 + 4.75138i) q^{39} +(-3.70199 - 0.736372i) q^{41} +(1.15474 - 0.478307i) q^{42} +(5.21542 + 12.5911i) q^{43} +(-4.30581 + 21.6468i) q^{44} +(-3.07832 - 15.4758i) q^{46} +(9.20504 - 9.20504i) q^{47} +(-7.15046 + 10.7014i) q^{48} +(-44.5150 - 18.4387i) q^{49} +(12.4665 + 24.7624i) q^{51} -49.0040 q^{52} +(-0.763466 + 1.84317i) q^{53} +(17.6343 + 11.7828i) q^{54} +(5.47334 - 1.08871i) q^{56} +(-45.9991 + 30.7356i) q^{57} +(-17.6031 - 3.50147i) q^{58} +(31.7838 - 13.1653i) q^{59} +(6.92641 - 34.8214i) q^{61} +(17.9136 + 26.8096i) q^{62} +(1.11830 + 5.62206i) q^{63} +(-3.51042 + 3.51042i) q^{64} +(-8.59130 - 3.55863i) q^{66} -31.9912i q^{67} +(14.8816 + 53.7605i) q^{68} -30.3532 q^{69} +(86.1606 + 57.5707i) q^{71} +(27.6752 + 27.6752i) q^{72} +(-61.7546 + 12.2837i) q^{73} +(-28.2544 + 18.8790i) q^{74} +(-102.841 + 42.5982i) q^{76} +(-2.32707 - 5.61804i) q^{77} +(4.02802 - 20.2502i) q^{78} +(-36.2984 - 54.3244i) q^{79} +(-11.5024 + 11.5024i) q^{81} +(1.77776 - 2.66060i) q^{82} +(39.7149 + 16.4505i) q^{83} -4.83773i q^{84} -11.5537 q^{86} +(-13.2124 + 31.8975i) q^{87} +(-34.5224 - 23.0671i) q^{88} +(49.5695 + 49.5695i) q^{89} +(11.2261 - 7.50103i) q^{91} +(-59.9000 - 11.9148i) q^{92} +(57.3040 - 23.7361i) q^{93} +(4.22331 + 10.1960i) q^{94} +(-28.4325 - 42.5523i) q^{96} +(-24.9233 - 125.298i) q^{97} +(28.8834 - 28.8834i) q^{98} +(23.6939 - 35.4604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 16 q^{7} - 16 q^{8} + 8 q^{9} + 40 q^{11} - 40 q^{12} + 16 q^{14} + 16 q^{17} + 136 q^{18} - 32 q^{19} - 64 q^{21} + 8 q^{23} + 24 q^{24} - 96 q^{27} - 80 q^{28} + 24 q^{29} + 32 q^{31}+ \cdots + 136 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 16 * q^7 - 16 * q^8 + 8 * q^9 + 40 * q^11 - 40 * q^12 + 16 * q^14 + 16 * q^17 + 136 * q^18 - 32 * q^19 - 64 * q^21 + 8 * q^23 + 24 * q^24 - 96 * q^27 - 80 * q^28 + 24 * q^29 + 32 * q^31 + 24 * q^32 + 64 * q^34 - 104 * q^36 + 168 * q^37 - 8 * q^38 - 72 * q^39 + 72 * q^42 - 96 * q^43 - 96 * q^44 + 80 * q^47 - 88 * q^48 + 8 * q^49 - 176 * q^51 - 240 * q^52 - 96 * q^53 + 208 * q^54 + 72 * q^56 - 248 * q^57 + 8 * q^59 + 264 * q^61 + 136 * q^62 - 8 * q^63 - 120 * q^64 + 8 * q^66 + 176 * q^68 - 208 * q^69 + 32 * q^71 - 24 * q^72 - 24 * q^73 + 176 * q^74 - 80 * q^76 + 216 * q^77 + 368 * q^78 - 96 * q^79 - 224 * q^81 + 408 * q^82 + 88 * q^83 + 288 * q^86 - 312 * q^87 - 176 * q^88 + 288 * q^89 - 24 * q^91 - 336 * q^92 - 280 * q^93 - 8 * q^94 + 328 * q^96 + 344 * q^97 - 16 * q^98 + 136 * q^99

Introduction

L-functions

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