LMFDB - Embedded newform 425.3.u.b.226.1

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 = [8,8,8,0,0,-8,-8,24,-16,0,-8,-48] 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			226.1
Root			$-0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	425.226
Dual form			425.3.u.b.126.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.841487 + 2.03153i) q^{2} +(-0.0897902 - 0.134381i) q^{3} +(-0.590587 + 0.590587i) q^{4} +(0.197441 - 0.295491i) q^{6} +(-1.21824 - 6.12453i) q^{7} +(6.42935 + 2.66313i) q^{8} +(3.43416 - 8.29078i) q^{9} +(-12.1433 - 8.11392i) q^{11} +(0.132392 + 0.0263345i) q^{12} +(-4.79884 - 4.79884i) q^{13} +(11.4170 - 7.62861i) q^{14} +18.6433i q^{16} +(-6.50562 - 15.7060i) q^{17} +19.7328 q^{18} +(-9.56175 - 23.0841i) q^{19} +(-0.713631 + 0.713631i) q^{21} +(6.26521 - 31.4973i) q^{22} +(-7.27639 + 10.8899i) q^{23} +(-0.219421 - 1.10310i) q^{24} +(5.71082 - 13.7871i) q^{26} +(-2.84909 + 0.566719i) q^{27} +(4.33654 + 2.89759i) q^{28} +(32.3980 + 6.44436i) q^{29} +(-1.00960 + 0.674593i) q^{31} +(-12.1570 + 5.03558i) q^{32} +2.36038i q^{33} +(26.4327 - 26.4327i) q^{34} +(2.86826 + 6.92459i) q^{36} +(25.8238 + 38.6481i) q^{37} +(38.8500 - 38.8500i) q^{38} +(-0.213982 + 1.07576i) q^{39} +(6.13577 + 30.8466i) q^{41} +(-2.05027 - 0.849251i) q^{42} +(27.8948 - 67.3441i) q^{43} +(11.9637 - 2.37972i) q^{44} +(-28.2461 - 5.61851i) q^{46} +(10.4882 + 10.4882i) q^{47} +(2.50529 - 1.67398i) q^{48} +(9.24438 - 3.82915i) q^{49} +(-1.52643 + 2.28447i) q^{51} +5.66826 q^{52} +(1.97838 + 4.77624i) q^{53} +(-3.54878 - 5.31112i) q^{54} +(8.47786 - 42.6211i) q^{56} +(-2.24350 + 3.35764i) q^{57} +(14.1706 + 71.2404i) q^{58} +(26.1013 + 10.8115i) q^{59} +(-81.0541 + 16.1227i) q^{61} +(-2.22002 - 1.48337i) q^{62} +(-54.9608 - 10.9324i) q^{63} +(32.2713 + 32.2713i) q^{64} +(-4.79518 + 1.98623i) q^{66} +44.5324i q^{67} +(13.1179 + 5.43359i) q^{68} +2.11674 q^{69} +(32.1978 + 48.1875i) q^{71} +(44.1588 - 44.1588i) q^{72} +(0.262865 - 1.32151i) q^{73} +(-56.7843 + 84.9838i) q^{74} +(19.2802 + 7.98612i) q^{76} +(-34.9004 + 84.2570i) q^{77} +(-2.36550 + 0.470527i) q^{78} +(-24.7128 - 16.5125i) q^{79} +(-56.7774 - 56.7774i) q^{81} +(-57.5026 + 38.4220i) q^{82} +(62.2748 - 25.7951i) q^{83} -0.842922i q^{84} +160.285 q^{86} +(-2.04303 - 4.93230i) q^{87} +(-56.4655 - 84.5065i) q^{88} +(90.1397 - 90.1397i) q^{89} +(-23.5444 + 35.2368i) q^{91} +(-2.13408 - 10.7288i) q^{92} +(0.181304 + 0.0750988i) q^{93} +(-12.4814 + 30.1327i) q^{94} +(1.76826 + 1.18151i) q^{96} +(66.3366 + 13.1952i) q^{97} +(15.5581 + 15.5581i) q^{98} +(-108.973 + 72.8134i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} - 8 q^{6} - 8 q^{7} + 24 q^{8} - 16 q^{9} - 8 q^{11} - 48 q^{12} - 16 q^{13} + 8 q^{14} - 56 q^{18} - 64 q^{21} + 104 q^{22} + 56 q^{23} - 80 q^{24} + 176 q^{26} - 40 q^{27} - 152 q^{28}+ \cdots - 224 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 - 8 * q^6 - 8 * q^7 + 24 * q^8 - 16 * q^9 - 8 * q^11 - 48 * q^12 - 16 * q^13 + 8 * q^14 - 56 * q^18 - 64 * q^21 + 104 * q^22 + 56 * q^23 - 80 * q^24 + 176 * q^26 - 40 * q^27 - 152 * q^28 + 48 * q^29 + 24 * q^31 - 88 * q^32 - 136 * q^34 - 128 * q^36 - 32 * q^37 + 120 * q^38 + 48 * q^39 + 48 * q^41 - 16 * q^42 + 232 * q^43 + 120 * q^44 - 88 * q^46 - 192 * q^47 - 136 * q^48 + 16 * q^49 + 136 * q^51 + 384 * q^52 + 32 * q^53 + 8 * q^54 - 120 * q^56 - 24 * q^57 - 240 * q^58 - 48 * q^59 - 160 * q^61 + 168 * q^62 - 56 * q^63 - 64 * q^64 - 8 * q^66 - 272 * q^68 + 240 * q^69 + 40 * q^71 - 40 * q^72 - 48 * q^73 - 160 * q^74 + 80 * q^76 + 48 * q^77 + 400 * q^78 - 136 * q^79 - 424 * q^81 + 64 * q^82 + 264 * q^83 + 832 * q^86 - 208 * q^87 - 264 * q^88 + 160 * q^89 + 320 * q^91 - 24 * q^92 + 64 * q^93 + 32 * q^94 - 56 * q^96 - 48 * q^97 + 120 * q^98 - 224 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{5}{16}\right)$

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 $

$2$	0.841487	+	2.03153i	0.420744	+	1.01577i	0.982129	+	0.188210i	$0.0602687\pi$
$2$	0.841487	+	2.03153i	0.420744	+	1.01577i	−0.561385	+	0.827555i	$0.689731\pi$
$3$	−0.0897902	−	0.134381i	−0.0299301	−	0.0447935i	0.816203	−	0.577765i	$-0.196075\pi$
$3$	−0.0897902	−	0.134381i	−0.0299301	−	0.0447935i	−0.846133	+	0.532972i	$0.821075\pi$
$4$	−0.590587	+	0.590587i	−0.147647	+	0.147647i
$5$		0			0
$5$		0			0
$6$	0.197441	−	0.295491i	0.0329068	−	0.0492485i
$7$	−1.21824	−	6.12453i	−0.174035	−	0.874933i	−0.964835	−	0.262858i	$-0.915335\pi$
$7$	−1.21824	−	6.12453i	−0.174035	−	0.874933i	0.790800	−	0.612075i	$-0.209665\pi$
$8$	6.42935	+	2.66313i	0.803669	+	0.332891i
$9$	3.43416	−	8.29078i	0.381573	−	0.921198i
$10$		0			0
$11$	−12.1433	−	8.11392i	−1.10394	−	0.737629i	−0.136478	−	0.990643i	$-0.543578\pi$
$11$	−12.1433	−	8.11392i	−1.10394	−	0.737629i	−0.967463	+	0.253014i	$0.918578\pi$
$12$	0.132392	+	0.0263345i	0.0110327	+	0.00219454i
$13$	−4.79884	−	4.79884i	−0.369141	−	0.369141i	0.498023	−	0.867164i	$-0.334060\pi$
$13$	−4.79884	−	4.79884i	−0.369141	−	0.369141i	−0.867164	+	0.498023i	$0.834060\pi$
$14$	11.4170	−	7.62861i	0.815502	−	0.544901i
$15$		0			0
$16$			18.6433i			1.16520i
$17$	−6.50562	−	15.7060i	−0.382683	−	0.923880i
$17$	−6.50562	−	15.7060i	−0.382683	−	0.923880i
$18$	19.7328			1.09627
$19$	−9.56175	−	23.0841i	−0.503250	−	1.21495i	−0.947704	−	0.319151i	$-0.896602\pi$
$19$	−9.56175	−	23.0841i	−0.503250	−	1.21495i	0.444454	−	0.895802i	$-0.353398\pi$
$20$		0			0
$21$	−0.713631	+	0.713631i	−0.0339824	+	0.0339824i
$22$	6.26521	−	31.4973i	0.284782	−	1.43170i
$23$	−7.27639	+	10.8899i	−0.316365	+	0.473474i	−0.955238	−	0.295839i	$-0.904401\pi$
$23$	−7.27639	+	10.8899i	−0.316365	+	0.473474i	0.638873	+	0.769312i	$0.279401\pi$
$24$	−0.219421	−	1.10310i	−0.00914253	−	0.0459626i
$25$		0			0
$26$	5.71082	−	13.7871i	0.219647	−	0.530274i
$27$	−2.84909	+	0.566719i	−0.105522	+	0.0209896i
$28$	4.33654	+	2.89759i	0.154877	+	0.103485i
$29$	32.3980	+	6.44436i	1.11717	+	0.222219i	0.718945	−	0.695067i	$-0.244625\pi$
$29$	32.3980	+	6.44436i	1.11717	+	0.222219i	0.398228	+	0.917287i	$0.369625\pi$
$30$		0			0
$31$	−1.00960	+	0.674593i	−0.0325678	+	0.0217611i	−0.571748	−	0.820430i	$-0.693734\pi$
$31$	−1.00960	+	0.674593i	−0.0325678	+	0.0217611i	0.539180	+	0.842191i	$0.318734\pi$
$32$	−12.1570	+	5.03558i	−0.379905	+	0.157362i
$33$			2.36038i			0.0715267i
$34$	26.4327	−	26.4327i	0.777433	−	0.777433i
$35$		0			0
$36$	2.86826	+	6.92459i	0.0796739	+	0.192350i
$37$	25.8238	+	38.6481i	0.697941	+	1.04454i	0.995944	+	0.0899781i	$0.0286797\pi$
$37$	25.8238	+	38.6481i	0.697941	+	1.04454i	−0.298002	+	0.954565i	$0.596320\pi$
$38$	38.8500	−	38.8500i	1.02237	−	1.02237i
$39$	−0.213982	+	1.07576i	−0.00548671	+	0.0275836i
$40$		0			0
$41$	6.13577	+	30.8466i	0.149653	+	0.752356i	0.980602	+	0.196008i	$0.0627979\pi$
$41$	6.13577	+	30.8466i	0.149653	+	0.752356i	−0.830949	+	0.556348i	$0.812202\pi$
$42$	−2.05027	−	0.849251i	−0.0488161	−	0.0202203i
$43$	27.8948	−	67.3441i	0.648717	−	1.56614i	−0.165901	−	0.986142i	$-0.553053\pi$
$43$	27.8948	−	67.3441i	0.648717	−	1.56614i	0.814617	−	0.579999i	$-0.196947\pi$
$44$	11.9637	−	2.37972i	0.271902	−	0.0540846i
$45$		0			0
$46$	−28.2461	−	5.61851i	−0.614047	−	0.122141i
$47$	10.4882	+	10.4882i	0.223153	+	0.223153i	0.809825	−	0.586672i	$-0.199562\pi$
$47$	10.4882	+	10.4882i	0.223153	+	0.223153i	−0.586672	+	0.809825i	$0.699562\pi$
$48$	2.50529	−	1.67398i	0.0521936	−	0.0348747i
$49$	9.24438	−	3.82915i	0.188661	−	0.0781458i
$50$		0			0
$51$	−1.52643	+	2.28447i	−0.0299301	+	0.0447935i
$52$	5.66826			0.109005
$53$	1.97838	+	4.77624i	0.0373280	+	0.0901178i	0.941444	−	0.337169i	$-0.109469\pi$
$53$	1.97838	+	4.77624i	0.0373280	+	0.0901178i	−0.904116	+	0.427287i	$0.859469\pi$
$54$	−3.54878	−	5.31112i	−0.0657181	−	0.0983541i
$55$		0			0
$56$	8.47786	−	42.6211i	0.151390	−	0.761091i
$57$	−2.24350	+	3.35764i	−0.0393597	+	0.0589059i
$58$	14.1706	+	71.2404i	0.244321	+	1.22828i
$59$	26.1013	+	10.8115i	0.442394	+	0.183246i	0.592751	−	0.805386i	$-0.298042\pi$
$59$	26.1013	+	10.8115i	0.442394	+	0.183246i	−0.150356	+	0.988632i	$0.548042\pi$
$60$		0			0
$61$	−81.0541	+	16.1227i	−1.32876	+	0.264306i	−0.807891	−	0.589332i	$-0.799391\pi$
$61$	−81.0541	+	16.1227i	−1.32876	+	0.264306i	−0.520866	+	0.853639i	$0.674391\pi$
$62$	−2.22002	−	1.48337i	−0.0358068	−	0.0239254i
$63$	−54.9608	−	10.9324i	−0.872393	−	0.173530i
$64$	32.2713	+	32.2713i	0.504239	+	0.504239i
$65$		0			0
$66$	−4.79518	+	1.98623i	−0.0726543	+	0.0300944i
$67$			44.5324i			0.664663i	0.943163	+	0.332332i	$0.107835\pi$
$67$			44.5324i			0.664663i	−0.943163	+	0.332332i	$0.892165\pi$
$68$	13.1179	+	5.43359i	0.192910	+	0.0799058i
$69$	2.11674			0.0306774
$70$		0			0
$71$	32.1978	+	48.1875i	0.453491	+	0.678697i	0.985813	−	0.167845i	$-0.0536807\pi$
$71$	32.1978	+	48.1875i	0.453491	+	0.678697i	−0.532323	+	0.846541i	$0.678681\pi$
$72$	44.1588	−	44.1588i	0.613317	−	0.613317i
$73$	0.262865	−	1.32151i	0.00360089	−	0.0181029i	−0.978943	−	0.204133i	$-0.934562\pi$
$73$	0.262865	−	1.32151i	0.00360089	−	0.0181029i	0.982544	+	0.186031i	$0.0595623\pi$
$74$	−56.7843	+	84.9838i	−0.767356	+	1.14843i
$75$		0			0
$76$	19.2802	+	7.98612i	0.253687	+	0.105081i
$77$	−34.9004	+	84.2570i	−0.453252	+	1.09425i
$78$	−2.36550	+	0.470527i	−0.0303269	+	0.00603240i
$79$	−24.7128	−	16.5125i	−0.312820	−	0.209020i	0.389242	−	0.921136i	$-0.372737\pi$
$79$	−24.7128	−	16.5125i	−0.312820	−	0.209020i	−0.702062	+	0.712116i	$0.747737\pi$
$80$		0			0
$81$	−56.7774	−	56.7774i	−0.700956	−	0.700956i
$82$	−57.5026	+	38.4220i	−0.701252	+	0.468561i
$83$	62.2748	−	25.7951i	0.750298	−	0.310784i	0.0254351	−	0.999676i	$-0.491903\pi$
$83$	62.2748	−	25.7951i	0.750298	−	0.310784i	0.724863	+	0.688893i	$0.241903\pi$
$84$		−	0.842922i		−	0.0100348i
$85$		0			0
$86$	160.285			1.86377
$87$	−2.04303	−	4.93230i	−0.0234831	−	0.0566931i
$88$	−56.4655	−	84.5065i	−0.641653	−	0.960302i
$89$	90.1397	−	90.1397i	1.01281	−	1.01281i	0.0128890	−	0.999917i	$-0.495897\pi$
$89$	90.1397	−	90.1397i	1.01281	−	1.01281i	0.999917	−	0.0128890i	$-0.00410281\pi$
$90$		0			0
$91$	−23.5444	+	35.2368i	−0.258730	+	0.387217i
$92$	−2.13408	−	10.7288i	−0.0231966	−	0.116617i
$93$	0.181304	+	0.0750988i	0.00194951	+	0.000807514i
$94$	−12.4814	+	30.1327i	−0.132781	+	0.320561i
$95$		0			0
$96$	1.76826	+	1.18151i	0.0184194	+	0.0123074i
$97$	66.3366	+	13.1952i	0.683882	+	0.136033i	0.524791	−	0.851231i	$-0.324144\pi$
$97$	66.3366	+	13.1952i	0.683882	+	0.136033i	0.159091	+	0.987264i	$0.449144\pi$
$98$	15.5581	+	15.5581i	0.158756	+	0.158756i
$99$	−108.973	+	72.8134i	−1.10074	+	0.735489i
$100$		0			0
$101$		−	34.6405i		−	0.342975i	−0.985186	−	0.171488i	$-0.945143\pi$
$101$		−	34.6405i		−	0.342975i	0.985186	−	0.171488i	$-0.0548573\pi$
$102$	−5.92544	−	1.17864i	−0.0580926	−	0.0115553i
$103$	−151.166			−1.46763			−0.733817	−	0.679347i	$-0.762263\pi$
$103$	−151.166			−1.46763			−0.733817	+	0.679347i	$0.762263\pi$
$104$	−18.0735	−	43.6333i	−0.173784	−	0.419551i
$105$		0			0
$106$	−8.03830	+	8.03830i	−0.0758330	+	0.0758330i
$107$	1.86075	−	9.35463i	0.0173902	−	0.0874264i	−0.971116	−	0.238610i	$-0.923308\pi$
$107$	1.86075	−	9.35463i	0.0173902	−	0.0874264i	0.988506	+	0.151183i	$0.0483083\pi$
$108$	1.34794	−	2.01733i	0.0124809	−	0.0186790i
$109$	22.6951	+	114.096i	0.208212	+	1.04675i	0.933574	+	0.358385i	$0.116673\pi$
$109$	22.6951	+	114.096i	0.208212	+	1.04675i	−0.725362	+	0.688368i	$0.758327\pi$
$110$		0			0
$111$	2.87483	−	6.94044i	0.0258993	−	0.0625265i
$112$	114.181	−	22.7121i	1.01948	−	0.202786i
$113$	54.8360	+	36.6403i	0.485274	+	0.324250i	0.774026	−	0.633154i	$-0.218240\pi$
$113$	54.8360	+	36.6403i	0.485274	+	0.324250i	−0.288751	+	0.957404i	$0.593240\pi$
$114$	−8.70902	−	1.73233i	−0.0763949	−	0.0151959i
$115$		0			0
$116$	−22.9398	+	15.3279i	−0.197757	+	0.132137i
$117$	−56.2660	+	23.3062i	−0.480906	+	0.199198i
$118$			62.1233i			0.526468i
$119$	−88.2661	+	58.9775i	−0.741732	+	0.495609i
$120$		0			0
$121$	35.3203	+	85.2709i	0.291904	+	0.704718i
$122$	−100.960	−	151.097i	−0.827539	−	1.23850i
$123$	3.59425	−	3.59425i	0.0292216	−	0.0292216i
$124$	0.197851	−	0.994662i	0.00159557	−	0.00802147i
$125$		0			0
$126$	−24.0393	−	120.854i	−0.190788	−	0.959158i
$127$	−88.2580	−	36.5576i	−0.694945	−	0.287855i	0.00711395	−	0.999975i	$-0.497736\pi$
$127$	−88.2580	−	36.5576i	−0.694945	−	0.287855i	−0.702059	+	0.712119i	$0.747736\pi$
$128$	−58.5465	+	141.344i	−0.457395	+	1.10425i
$129$	−11.5544	+	2.29832i	−0.0895691	+	0.0178164i
$130$		0			0
$131$	42.0736	+	8.36897i	0.321173	+	0.0638852i	0.353044	−	0.935607i	$-0.385147\pi$
$131$	42.0736	+	8.36897i	0.321173	+	0.0638852i	−0.0318711	+	0.999492i	$0.510147\pi$
$132$	−1.39401	−	1.39401i	−0.0105607	−	0.0105607i
$133$	−129.731	+	86.6833i	−0.975419	+	0.651754i
$134$	−90.4690	+	37.4735i	−0.675142	+	0.279653i
$135$		0			0
$136$		−	118.304i		−	0.869885i
$137$	63.8232			0.465863			0.232931	−	0.972493i	$-0.425168\pi$
$137$	63.8232			0.465863			0.232931	+	0.972493i	$0.425168\pi$
$138$	1.78121	+	4.30022i	0.0129073	+	0.0311610i
$139$	−145.186	−	217.286i	−1.04450	−	1.56321i	−0.805868	−	0.592095i	$-0.798301\pi$
$139$	−145.186	−	217.286i	−1.04450	−	1.56321i	−0.238632	−	0.971110i	$-0.576699\pi$
$140$		0			0
$141$	0.467671	−	2.35114i	0.00331682	−	0.0166748i
$142$	−70.8002	+	105.960i	−0.498593	+	0.746197i
$143$	19.3365	+	97.2113i	0.135220	+	0.679799i
$144$	154.567	+	64.0239i	1.07338	+	0.444610i
$145$		0			0
$146$	2.90589	−	0.578017i	0.0199033	−	0.00395902i
$147$	−1.34462	−	0.898445i	−0.00914706	−	0.00611187i
$148$	−38.0763	−	7.57384i	−0.257272	−	0.0511746i
$149$	−83.6010	−	83.6010i	−0.561080	−	0.561080i	0.368534	−	0.929614i	$-0.379860\pi$
$149$	−83.6010	−	83.6010i	−0.561080	−	0.561080i	−0.929614	+	0.368534i	$0.879860\pi$
$150$		0			0
$151$	25.5851	−	10.5977i	0.169437	−	0.0701833i	−0.296352	−	0.955079i	$-0.595770\pi$
$151$	25.5851	−	10.5977i	0.169437	−	0.0701833i	0.465790	+	0.884895i	$0.345770\pi$
$152$		−	173.880i		−	1.14395i
$153$	−152.556			−0.997098
$154$	−200.539			−1.30220
$155$		0			0
$156$	−0.508954	−	0.761703i	−0.00326252	−	0.00488271i
$157$	55.8958	−	55.8958i	0.356024	−	0.356024i	−0.506321	−	0.862345i	$-0.668995\pi$
$157$	55.8958	−	55.8958i	0.356024	−	0.356024i	0.862345	+	0.506321i	$0.168995\pi$
$158$	12.7503	−	64.0998i	0.0806978	−	0.405695i
$159$	0.464195	−	0.694716i	0.00291946	−	0.00436929i
$160$		0			0
$161$	75.5599	+	31.2979i	0.469316	+	0.194397i
$162$	67.5676	−	163.123i	0.417084	−	1.00693i
$163$	54.4489	−	10.8306i	0.334042	−	0.0664451i	−0.0252196	−	0.999682i	$-0.508029\pi$
$163$	54.4489	−	10.8306i	0.334042	−	0.0664451i	0.359262	+	0.933237i	$0.383029\pi$
$164$	−21.8413	−	14.5939i	−0.133179	−	0.0889871i
$165$		0			0
$166$	104.807	+	104.807i	0.631367	+	0.631367i
$167$	42.9537	−	28.7008i	0.257208	−	0.171861i	−0.420281	−	0.907394i	$-0.638068\pi$
$167$	42.9537	−	28.7008i	0.257208	−	0.171861i	0.677489	+	0.735533i	$0.263068\pi$
$168$	−6.48868	+	2.68770i	−0.0386231	+	0.0159982i
$169$		−	122.942i		−	0.727470i
$170$		0			0
$171$	−224.222			−1.31124
$172$	23.2982	+	56.2468i	0.135455	+	0.327016i
$173$	10.2620	+	15.3581i	0.0593178	+	0.0887754i	0.859943	−	0.510390i	$-0.170499\pi$
$173$	10.2620	+	15.3581i	0.0593178	+	0.0887754i	−0.800625	+	0.599166i	$0.795499\pi$
$174$	8.30094	−	8.30094i	0.0477066	−	0.0477066i
$175$		0			0
$176$	151.270	−	226.392i	0.859489	−	1.28632i
$177$	−0.890783	−	4.47827i	−0.00503267	−	0.0253010i
$178$	258.973	+	107.270i	1.45490	+	0.602641i
$179$	23.9825	−	57.8989i	0.133980	−	0.323457i	−0.842624	−	0.538503i	$-0.818990\pi$
$179$	23.9825	−	57.8989i	0.133980	−	0.323457i	0.976604	+	0.215046i	$0.0689900\pi$
$180$		0			0
$181$	86.9711	+	58.1122i	0.480503	+	0.321062i	0.772124	−	0.635472i	$-0.219194\pi$
$181$	86.9711	+	58.1122i	0.480503	+	0.321062i	−0.291621	+	0.956534i	$0.594194\pi$
$182$	−91.3969	−	18.1800i	−0.502181	−	0.0998899i
$183$	9.44444	+	9.44444i	0.0516090	+	0.0516090i
$184$	−75.7837	+	50.6370i	−0.411868	+	0.275201i
$185$		0			0
$186$			0.431520i			0.00232000i
$187$	−48.4369	+	243.509i	−0.259021	+	1.30219i
$188$	−12.3883			−0.0658954
$189$	6.94177	+	16.7589i	0.0367289	+	0.0886715i
$190$		0			0
$191$	−137.930	+	137.930i	−0.722145	+	0.722145i	−0.969042	−	0.246897i	$-0.920589\pi$
$191$	−137.930	+	137.930i	−0.722145	+	0.722145i	0.246897	+	0.969042i	$0.420589\pi$
$192$	1.43899	−	7.23428i	0.00749473	−	0.0376785i
$193$	−49.1142	+	73.5045i	−0.254478	+	0.380853i	−0.936609	−	0.350377i	$-0.886053\pi$
$193$	−49.1142	+	73.5045i	−0.254478	+	0.380853i	0.682131	+	0.731230i	$0.261053\pi$
$194$	29.0150	+	145.868i	0.149562	+	0.751899i
$195$		0			0
$196$	−3.19816	+	7.72105i	−0.0163172	+	0.0393931i
$197$	−252.430	+	50.2114i	−1.28137	+	0.254880i	−0.788398	−	0.615165i	$-0.789089\pi$
$197$	−252.430	+	50.2114i	−1.28137	+	0.254880i	−0.492972	+	0.870045i	$0.664089\pi$
$198$	−239.622	−	160.110i	−1.21021	−	0.808637i
$199$	223.079	+	44.3732i	1.12100	+	0.222981i	0.720594	−	0.693357i	$-0.243869\pi$
$199$	223.079	+	44.3732i	1.12100	+	0.222981i	0.400406	+	0.916338i	$0.368869\pi$
$200$		0			0
$201$	5.98429	−	3.99858i	0.0297726	−	0.0198934i
$202$	70.3732	−	29.1495i	0.348382	−	0.144305i
$203$		−	206.273i		−	1.01612i
$204$	−0.447686	−	2.25067i	−0.00219454	−	0.0110327i
$205$		0			0
$206$	−127.204	−	307.099i	−0.617498	−	1.49077i
$207$	65.2975	+	97.7246i	0.315447	+	0.472100i
$208$	89.4660	−	89.4660i	0.430125	−	0.430125i
$209$	−71.1910	+	357.901i	−0.340627	+	1.71245i
$210$		0			0
$211$	1.57784	+	7.93236i	0.00747794	+	0.0375941i	0.984344	−	0.176257i	$-0.0563991\pi$
$211$	1.57784	+	7.93236i	0.00747794	+	0.0375941i	−0.976866	+	0.213852i	$0.931399\pi$
$212$	−3.98919	−	1.65238i	−0.0188169	−	0.00779423i
$213$	3.58441	−	8.65353i	0.0168282	−	0.0406269i
$214$	20.5700	−	4.09163i	0.0961215	−	0.0191198i
$215$		0			0
$216$	−19.8270	−	3.94384i	−0.0917918	−	0.0182585i
$217$	5.36151	+	5.36151i	0.0247074	+	0.0247074i
$218$	−212.692	+	142.116i	−0.975651	+	0.651909i
$219$	−0.201188	+	0.0833348i	−0.000918667	+	0.000380524i
$220$		0			0
$221$	−44.1509	+	106.590i	−0.199778	+	0.482306i
$222$	16.5188			0.0744092
$223$	−18.7769	−	45.3315i	−0.0842014	−	0.203280i	0.876171	−	0.482001i	$-0.160090\pi$
$223$	−18.7769	−	45.3315i	−0.0842014	−	0.203280i	−0.960372	+	0.278720i	$0.910090\pi$
$224$	45.6507	+	68.3211i	0.203798	+	0.305005i
$225$		0			0
$226$	−28.2920	+	142.233i	−0.125186	+	0.629351i
$227$	93.3694	−	139.737i	0.411319	−	0.615582i	−0.566743	−	0.823894i	$-0.691797\pi$
$227$	93.3694	−	139.737i	0.411319	−	0.615582i	0.978062	+	0.208312i	$0.0667969\pi$
$228$	−0.657994	−	3.30796i	−0.00288594	−	0.0145086i
$229$	114.723	+	47.5197i	0.500972	+	0.207510i	0.618836	−	0.785520i	$-0.287605\pi$
$229$	114.723	+	47.5197i	0.500972	+	0.207510i	−0.117864	+	0.993030i	$0.537605\pi$
$230$		0			0
$231$	14.4562	−	2.87552i	0.0625810	−	0.0124481i
$232$	191.136	+	127.713i	0.823863	+	0.550487i
$233$	346.291	+	68.8815i	1.48623	+	0.295629i	0.870436	−	0.492281i	$-0.163837\pi$
$233$	346.291	+	68.8815i	1.48623	+	0.295629i	0.615791	+	0.787910i	$0.288837\pi$
$234$	−94.6943	−	94.6943i	−0.404677	−	0.404677i
$235$		0			0
$236$	−21.8002	+	9.02993i	−0.0923737	+	0.0382624i
$237$			4.80358i			0.0202683i
$238$	−194.089	−	129.686i	−0.815502	−	0.544901i
$239$	206.527			0.864131			0.432066	−	0.901842i	$-0.357785\pi$
$239$	206.527			0.864131			0.432066	+	0.901842i	$0.357785\pi$
$240$		0			0
$241$	160.021	+	239.488i	0.663988	+	0.993728i	0.998678	+	0.0513996i	$0.0163682\pi$
$241$	160.021	+	239.488i	0.663988	+	0.993728i	−0.334691	+	0.942328i	$0.608632\pi$
$242$	−143.509	+	143.509i	−0.593011	+	0.593011i
$243$	−7.63219	+	38.3696i	−0.0314082	+	0.157900i
$244$	38.3477	−	57.3913i	0.157163	−	0.235210i
$245$		0			0
$246$	10.3263	+	4.27731i	0.0419770	+	0.0173875i
$247$	−64.8915	+	156.662i	−0.262719	+	0.634259i
$248$	−8.28761	+	1.64851i	−0.0334178	+	0.00664721i
$249$	−9.05802	−	6.05237i	−0.0363776	−	0.0243067i
$250$		0			0
$251$	191.096	+	191.096i	0.761337	+	0.761337i	0.976564	−	0.215227i	$-0.0690490\pi$
$251$	191.096	+	191.096i	0.761337	+	0.761337i	−0.215227	+	0.976564i	$0.569049\pi$
$252$	38.9156	−	26.0026i	0.154427	−	0.103185i
$253$	176.720	−	73.1996i	0.698496	−	0.289327i
$254$		−	210.062i		−	0.827014i
$255$		0			0
$256$	−153.856			−0.601002
$257$	20.2061	+	48.7819i	0.0786230	+	0.189813i	0.958303	−	0.285753i	$-0.0922436\pi$
$257$	20.2061	+	48.7819i	0.0786230	+	0.189813i	−0.879680	+	0.475565i	$0.842244\pi$
$258$	−14.3920	−	21.5391i	−0.0557829	−	0.0834850i
$259$	205.242	−	205.242i	0.792439	−	0.792439i
$260$		0			0
$261$	164.689	−	246.474i	0.630991	−	0.944345i
$262$	18.4026	+	92.5162i	0.0702390	+	0.353115i
$263$	468.907	+	194.228i	1.78292	+	0.738509i	0.991947	+	0.126654i	$0.0404239\pi$
$263$	468.907	+	194.228i	1.78292	+	0.738509i	0.790970	+	0.611854i	$0.209576\pi$
$264$	−6.28599	+	15.1757i	−0.0238106	+	0.0574838i
$265$		0			0
$266$	−285.266	−	190.609i	−1.07243	−	0.716575i
$267$	−20.2067	−	4.01936i	−0.0756805	−	0.0150538i
$268$	−26.3003	−	26.3003i	−0.0981353	−	0.0981353i
$269$	146.551	−	97.9225i	0.544801	−	0.364024i	−0.252509	−	0.967595i	$-0.581256\pi$
$269$	146.551	−	97.9225i	0.544801	−	0.364024i	0.797310	+	0.603570i	$0.206256\pi$
$270$		0			0
$271$			464.255i			1.71312i	0.516050	+	0.856559i	$0.327402\pi$
$271$			464.255i			1.71312i	−0.516050	+	0.856559i	$0.672598\pi$
$272$	292.810	−	121.286i	1.07651	−	0.445905i
$273$	6.84919			0.0250886
$274$	53.7064	+	129.659i	0.196009	+	0.473207i
$275$		0			0
$276$	−1.25012	+	1.25012i	−0.00452941	+	0.00452941i
$277$	−34.4498	+	173.191i	−0.124368	+	0.625238i	0.867445	+	0.497534i	$0.165761\pi$
$277$	−34.4498	+	173.191i	−0.124368	+	0.625238i	−0.991812	+	0.127704i	$0.959239\pi$
$278$	319.250	−	477.792i	1.14838	−	1.71868i
$279$	2.12578	+	10.6870i	0.00761930	+	0.0383048i
$280$		0			0
$281$	152.875	−	369.073i	0.544040	−	1.31343i	−0.377811	−	0.925883i	$-0.623323\pi$
$281$	152.875	−	369.073i	0.544040	−	1.31343i	0.921851	−	0.387545i	$-0.126677\pi$
$282$	5.16995	−	1.02837i	0.0183332	−	0.00364669i
$283$	−297.348	−	198.682i	−1.05070	−	0.702055i	−0.0947249	−	0.995503i	$-0.530197\pi$
$283$	−297.348	−	198.682i	−1.05070	−	0.702055i	−0.955975	+	0.293448i	$0.905197\pi$
$284$	−47.4745	−	9.44326i	−0.167164	−	0.0332509i
$285$		0			0
$286$	−181.216	+	121.085i	−0.633623	+	0.423373i
$287$	181.446	−	75.1574i	0.632216	−	0.261872i
$288$			118.084i			0.410013i
$289$	−204.354	+	204.354i	−0.707107	+	0.707107i
$290$		0			0
$291$	−4.18320	−	10.0991i	−0.0143753	−	0.0347050i
$292$	0.625222	+	0.935711i	0.00214117	+	0.00320449i
$293$	169.002	−	169.002i	0.576800	−	0.576800i	−0.357220	−	0.934020i	$-0.616275\pi$
$293$	169.002	−	169.002i	0.576800	−	0.576800i	0.934020	+	0.357220i	$0.116275\pi$
$294$	0.693739	−	3.48766i	0.00235966	−	0.0118628i
$295$		0			0
$296$	63.1058	+	317.254i	0.213195	+	1.07181i
$297$	39.1958	+	16.2354i	0.131972	+	0.0546647i
$298$	99.4888	−	240.187i	0.333855	−	0.805997i
$299$	87.1770	−	17.3406i	0.291562	−	0.0579953i
$300$		0			0
$301$	−446.433	−	88.8011i	−1.48317	−	0.295020i
$302$	43.0590	+	43.0590i	0.142579	+	0.142579i
$303$	−4.65501	+	3.11038i	−0.0153631	+	0.0102653i
$304$	430.363	−	178.262i	1.41567	−	0.586389i
$305$		0			0
$306$	−128.374	−	309.922i	−0.419523	−	1.01282i
$307$	−409.955			−1.33536			−0.667679	−	0.744450i	$-0.732712\pi$
$307$	−409.955			−1.33536			−0.667679	+	0.744450i	$0.732712\pi$
$308$	−29.1493	−	70.3727i	−0.0946407	−	0.228483i
$309$	13.5733	+	20.3138i	0.0439264	+	0.0657405i
$310$		0			0
$311$	42.2576	−	212.443i	0.135877	−	0.683098i	−0.851455	−	0.524428i	$-0.824279\pi$
$311$	42.2576	−	212.443i	0.135877	−	0.683098i	0.987332	−	0.158670i	$-0.0507207\pi$
$312$	−4.24064	+	6.34657i	−0.0135918	+	0.0203416i
$313$	92.3584	+	464.317i	0.295075	+	1.48344i	0.789246	+	0.614077i	$0.210472\pi$
$313$	92.3584	+	464.317i	0.295075	+	1.48344i	−0.494171	+	0.869365i	$0.664528\pi$
$314$	160.590	+	66.5184i	0.511432	+	0.211842i
$315$		0			0
$316$	24.3471	−	4.84294i	0.0770479	−	0.0153258i
$317$	−213.145	−	142.419i	−0.672383	−	0.449272i	0.171939	−	0.985108i	$-0.444997\pi$
$317$	−213.145	−	142.419i	−0.672383	−	0.449272i	−0.844322	+	0.535836i	$0.819997\pi$
$318$	1.80195	+	0.358430i	0.00566651	+	0.00112714i
$319$	−341.131	−	341.131i	−1.06938	−	1.06938i
$320$		0			0
$321$	−1.42416	+	0.589905i	−0.00443663	+	0.00183771i
$322$			179.839i			0.558506i
$323$	−300.353	+	300.353i	−0.929884	+	0.929884i
$324$	67.0640			0.206988
$325$		0			0
$326$	67.8206	+	101.501i	0.208039	+	0.311352i
$327$	13.2945	−	13.2945i	0.0406560	−	0.0406560i
$328$	−42.6993	+	214.664i	−0.130181	+	0.654464i
$329$	51.4579	−	77.0122i	0.156407	−	0.234080i
$330$		0			0
$331$	208.580	+	86.3966i	0.630151	+	0.261017i	0.674817	−	0.737985i	$-0.264222\pi$
$331$	208.580	+	86.3966i	0.630151	+	0.261017i	−0.0446663	+	0.999002i	$0.514222\pi$
$332$	−21.5444	+	52.0129i	−0.0648929	+	0.156665i
$333$	409.106	−	81.3763i	1.22855	−	0.244373i
$334$	94.4515	+	63.1105i	0.282789	+	0.188954i
$335$		0			0
$336$	−13.3044	−	13.3044i	−0.0395965	−	0.0395965i
$337$	300.276	−	200.638i	0.891027	−	0.595365i	−0.0235742	−	0.999722i	$-0.507505\pi$
$337$	300.276	−	200.638i	0.891027	−	0.595365i	0.914601	+	0.404357i	$0.132505\pi$
$338$	249.761	−	103.454i	0.738938	−	0.306078i
$339$		−	10.6588i		−	0.0314420i
$340$		0			0
$341$	17.7335			0.0520045
$342$	−188.680	−	455.513i	−0.551695	−	1.33191i
$343$	−204.708	−	306.367i	−0.596815	−	0.893197i
$344$	358.691	−	358.691i	1.04271	−	1.04271i
$345$		0			0
$346$	−22.5652	+	33.7712i	−0.0652173	+	0.0976046i
$347$	−3.09377	−	15.5534i	−0.00891575	−	0.0448225i	0.976071	−	0.217451i	$-0.0697741\pi$
$347$	−3.09377	−	15.5534i	−0.00891575	−	0.0448225i	−0.984987	+	0.172628i	$0.944774\pi$
$348$	4.11954	+	1.70637i	0.0118377	+	0.00490336i
$349$	−121.062	+	292.270i	−0.346883	+	0.837448i	0.650102	+	0.759847i	$0.274726\pi$
$349$	−121.062	+	292.270i	−0.346883	+	0.837448i	−0.996984	+	0.0776015i	$0.975274\pi$
$350$		0			0
$351$	16.3919	+	10.9527i	0.0467005	+	0.0312043i
$352$	188.484	+	37.4919i	0.535467	+	0.106511i
$353$	−191.613	−	191.613i	−0.542812	−	0.542812i	0.381540	−	0.924352i	$-0.375394\pi$
$353$	−191.613	−	191.613i	−0.542812	−	0.542812i	−0.924352	+	0.381540i	$0.875394\pi$
$354$	8.34816	−	5.57806i	0.0235824	−	0.0157572i
$355$		0			0
$356$			106.471i			0.299075i
$357$	15.8509	+	6.56564i	0.0444002	+	0.0183912i
$358$	137.804			0.384928
$359$	60.5865	+	146.269i	0.168765	+	0.407434i	0.985522	−	0.169547i	$-0.0542305\pi$
$359$	60.5865	+	146.269i	0.168765	+	0.407434i	−0.816757	+	0.576981i	$0.804231\pi$
$360$		0			0
$361$	−186.183	+	186.183i	−0.515743	+	0.515743i
$362$	−44.8717	+	225.585i	−0.123955	+	0.623163i
$363$	8.28732	−	12.4029i	0.0228301	−	0.0341676i
$364$	−6.90532	−	34.7154i	−0.0189707	−	0.0953719i
$365$		0			0
$366$	−11.2393	+	27.1340i	−0.0307084	+	0.0741367i
$367$	479.595	−	95.3974i	1.30680	−	0.259938i	0.507906	−	0.861413i	$-0.330420\pi$
$367$	479.595	−	95.3974i	1.30680	−	0.259938i	0.798892	+	0.601474i	$0.205420\pi$
$368$	−203.023	−	135.656i	−0.551694	−	0.368630i
$369$	276.814	+	55.0617i	0.750173	+	0.149219i
$370$		0			0
$371$	26.8421	−	17.9353i	0.0723506	−	0.0483431i
$372$	−0.151428	+	0.0627237i	−0.000407065	+	0.000168612i
$373$			573.453i			1.53741i	0.639605	+	0.768704i	$0.279098\pi$
$373$			573.453i			1.53741i	−0.639605	+	0.768704i	$0.720902\pi$
$374$	−535.455	+	106.509i	−1.43170	+	0.284782i
$375$		0			0
$376$	39.5008	+	95.3635i	0.105055	+	0.253626i
$377$	−124.547	−	186.398i	−0.330364	−	0.494425i
$378$	−28.2048	+	28.2048i	−0.0746159	+	0.0746159i
$379$	136.954	−	688.516i	0.361357	−	1.81666i	−0.189284	−	0.981922i	$-0.560617\pi$
$379$	136.954	−	688.516i	0.361357	−	1.81666i	0.550641	−	0.834742i	$-0.314383\pi$
$380$		0			0
$381$	3.01206	+	15.1427i	0.00790568	+	0.0397445i
$382$	−396.274	−	164.142i	−1.03737	−	0.429692i
$383$	118.024	−	284.935i	0.308157	−	0.743956i	−0.691608	−	0.722273i	$-0.743098\pi$
$383$	118.024	−	284.935i	0.308157	−	0.743956i	0.999765	−	0.0216830i	$-0.00690247\pi$
$384$	24.2508	−	4.82378i	0.0631530	−	0.0125619i
$385$		0			0
$386$	−190.656	−	37.9238i	−0.493927	−	0.0982481i
$387$	−462.540	−	462.540i	−1.19519	−	1.19519i
$388$	−46.9704	+	31.3846i	−0.121058	+	0.0808882i
$389$	263.382	−	109.097i	0.677076	−	0.280454i	−0.0175282	−	0.999846i	$-0.505580\pi$
$389$	263.382	−	109.097i	0.677076	−	0.280454i	0.694604	+	0.719392i	$0.255580\pi$
$390$		0			0
$391$	218.374	+	43.4372i	0.558500	+	0.111093i
$392$	69.6329			0.177635
$393$	−2.65317	−	6.40533i	−0.00675108	−	0.0162986i
$394$	−314.423	−	470.567i	−0.798027	−	1.19433i
$395$		0			0
$396$	21.3553	−	107.361i	0.0539276	−	0.271112i
$397$	−69.0841	+	103.392i	−0.174015	+	0.260432i	−0.908217	−	0.418499i	$-0.862556\pi$
$397$	−69.0841	+	103.392i	−0.174015	+	0.260432i	0.734202	+	0.678931i	$0.237556\pi$
$398$	97.5727	+	490.531i	0.245158	+	1.23249i
$399$	23.2971	+	9.64997i	0.0583887	+	0.0241854i
$400$		0			0
$401$	−418.770	+	83.2986i	−1.04432	+	0.207727i	−0.687302	−	0.726372i	$-0.741205\pi$
$401$	−418.770	+	83.2986i	−1.04432	+	0.207727i	−0.357014	+	0.934099i	$0.616205\pi$
$402$	13.1589	+	8.79252i	0.0327337	+	0.0218719i
$403$	8.08217	+	1.60764i	0.0200550	+	0.00398919i
$404$	20.4582	+	20.4582i	0.0506391	+	0.0506391i
$405$		0			0
$406$	419.050	−	173.576i	1.03214	−	0.427528i
$407$		−	678.850i		−	1.66794i
$408$	−15.8978	+	10.6226i	−0.0389652	+	0.0260357i
$409$	−215.550			−0.527018			−0.263509	−	0.964657i	$-0.584880\pi$
$409$	−215.550			−0.527018			−0.263509	+	0.964657i	$0.584880\pi$
$410$		0			0
$411$	−5.73070	−	8.57659i	−0.0139433	−	0.0208676i
$412$	89.2768	−	89.2768i	0.216691	−	0.216691i
$413$	34.4176	−	173.029i	0.0833356	−	0.418956i
$414$	−143.583	+	214.888i	−0.346820	+	0.519053i
$415$		0			0
$416$	82.5042	+	34.1743i	0.198327	+	0.0821499i
$417$	−16.1627	+	39.0202i	−0.0387595	+	0.0935737i
$418$	−786.994	+	156.543i	−1.88276	+	0.374504i
$419$	−517.326	−	345.666i	−1.23467	−	0.824979i	−0.245164	−	0.969482i	$-0.578842\pi$
$419$	−517.326	−	345.666i	−1.23467	−	0.824979i	−0.989504	+	0.144503i	$0.953842\pi$
$420$		0			0
$421$	−36.3708	−	36.3708i	−0.0863916	−	0.0863916i	0.662590	−	0.748982i	$-0.269457\pi$
$421$	−36.3708	−	36.3708i	−0.0863916	−	0.0863916i	−0.748982	+	0.662590i	$0.769457\pi$
$422$	−14.7871	+	9.88042i	−0.0350405	+	0.0234133i
$423$	122.973	−	50.9371i	0.290717	−	0.120419i
$424$			35.9769i			0.0848511i
$425$		0			0
$426$	20.5961			0.0483477
$427$	197.488	+	476.777i	0.462500	+	1.11657i
$428$	4.42578	+	6.62365i	0.0103406	+	0.0154758i
$429$	11.3271	−	11.3271i	0.0264034	−	0.0264034i
$430$		0			0
$431$	261.460	−	391.302i	0.606635	−	0.907893i	−0.393299	−	0.919411i	$-0.628666\pi$
$431$	261.460	−	391.302i	0.606635	−	0.907893i	0.999934	+	0.0115175i	$0.00366621\pi$
$432$	−10.5655	−	53.1163i	−0.0244572	−	0.122954i
$433$	594.595	+	246.289i	1.37320	+	0.568798i	0.942654	−	0.333772i	$-0.108321\pi$
$433$	594.595	+	246.289i	1.37320	+	0.568798i	0.430545	+	0.902569i	$0.358321\pi$
$434$	−6.38042	+	15.4037i	−0.0147014	+	0.0354924i
$435$		0			0
$436$	−80.7871	−	53.9802i	−0.185291	−	0.123808i
$437$	320.958	+	63.8426i	0.734459	+	0.146093i
$438$	−0.338594	−	0.338594i	−0.000773047	−	0.000773047i
$439$	−688.000	+	459.707i	−1.56720	+	1.04717i	−0.597809	+	0.801638i	$0.703962\pi$
$439$	−688.000	+	459.707i	−1.56720	+	1.04717i	−0.969389	+	0.245530i	$0.921038\pi$
$440$		0			0
$441$		−	89.7930i		−	0.203612i
$442$	−253.693			−0.573965
$443$	−354.430			−0.800068			−0.400034	−	0.916500i	$-0.631002\pi$
$443$	−354.430			−0.800068			−0.400034	+	0.916500i	$0.631002\pi$
$444$	2.40110	+	5.79677i	0.00540788	+	0.0130558i
$445$		0			0
$446$	76.2917	−	76.2917i	0.171058	−	0.171058i
$447$	−3.72780	+	18.7409i	−0.00833959	+	0.0419259i
$448$	158.332	−	236.961i	0.353420	−	0.528930i
$449$	153.330	+	770.842i	0.341492	+	1.71680i	0.645185	+	0.764027i	$0.276780\pi$
$449$	153.330	+	770.842i	0.341492	+	1.71680i	−0.303692	+	0.952770i	$0.598220\pi$
$450$		0			0
$451$	175.778	−	424.366i	0.389752	−	0.940945i
$452$	−54.0247	+	10.7462i	−0.119524	+	0.0237747i
$453$	−3.72141	−	2.48657i	−0.00821503	−	0.00548911i
$454$	362.450	+	72.0957i	0.798347	+	0.158801i
$455$		0			0
$456$	−23.3661	+	15.6127i	−0.0512414	+	0.0342384i
$457$	−300.390	+	124.426i	−0.657309	+	0.272266i	−0.686306	−	0.727313i	$-0.740769\pi$
$457$	−300.390	+	124.426i	−0.657309	+	0.272266i	0.0289968	+	0.999580i	$0.490769\pi$
$458$			273.050i			0.596178i
$459$	27.4359	+	41.0608i	0.0597733	+	0.0894570i
$460$		0			0
$461$	−94.2242	−	227.477i	−0.204391	−	0.493444i	0.788131	−	0.615507i	$-0.211049\pi$
$461$	−94.2242	−	227.477i	−0.204391	−	0.493444i	−0.992522	+	0.122064i	$0.961049\pi$
$462$	18.0064	+	26.9485i	0.0389749	+	0.0583301i
$463$	248.069	−	248.069i	0.535786	−	0.535786i	−0.386503	−	0.922288i	$-0.626317\pi$
$463$	248.069	−	248.069i	0.535786	−	0.535786i	0.922288	+	0.386503i	$0.126317\pi$
$464$	−120.144	+	604.005i	−0.258931	+	1.30174i
$465$		0			0
$466$	151.464	+	761.463i	0.325031	+	1.63404i
$467$	202.212	+	83.7591i	0.433003	+	0.179356i	0.588529	−	0.808476i	$-0.299707\pi$
$467$	202.212	+	83.7591i	0.433003	+	0.179356i	−0.155526	+	0.987832i	$0.549707\pi$
$468$	19.4657	−	46.9943i	0.0415933	−	0.100415i
$469$	272.740	−	54.2514i	0.581536	−	0.115675i
$470$		0			0
$471$	−12.5302	−	2.49241i	−0.0266034	−	0.00529174i
$472$	139.022	+	139.022i	0.294538	+	0.294538i
$473$	−885.161	+	591.446i	−1.87138	+	1.25041i
$474$	−9.75862	+	4.04215i	−0.0205878	+	0.00852775i
$475$		0			0
$476$	17.2974	−	86.9601i	0.0363392	−	0.182689i
$477$	46.3929			0.0972597
$478$	173.790	+	419.566i	0.363578	+	0.877754i
$479$	−279.157	−	417.789i	−0.582792	−	0.872210i	0.416526	−	0.909124i	$-0.363247\pi$
$479$	−279.157	−	417.789i	−0.582792	−	0.872210i	−0.999318	+	0.0369135i	$0.988247\pi$
$480$		0			0
$481$	61.5415	−	309.390i	0.127945	−	0.643223i
$482$	−351.872	+	526.614i	−0.730025	+	1.09256i
$483$	−2.57871	−	12.9640i	−0.00533893	−	0.0268406i
$484$	−71.2196	−	29.5001i	−0.147148	−	0.0609506i
$485$		0			0
$486$	−84.3715	+	16.7825i	−0.173604	+	0.0345319i
$487$	209.352	+	139.885i	0.429882	+	0.287238i	0.751627	−	0.659589i	$-0.229269\pi$
$487$	209.352	+	139.885i	0.429882	+	0.287238i	−0.321745	+	0.946826i	$0.604269\pi$
$488$	−564.063	−	112.199i	−1.15587	−	0.229916i
$489$	−6.34439	−	6.34439i	−0.0129742	−	0.0129742i
$490$		0			0
$491$	−209.123	+	86.6215i	−0.425912	+	0.176418i	−0.585334	−	0.810792i	$-0.699037\pi$
$491$	−209.123	+	86.6215i	−0.425912	+	0.176418i	0.159423	+	0.987210i	$0.449037\pi$
$492$			4.24543i			0.00862893i
$493$	−109.554	−	550.766i	−0.222219	−	1.11717i
$494$	−372.869			−0.754796
$495$		0			0
$496$	−12.5766	−	18.8223i	−0.0253561	−	0.0379481i
$497$	255.901	−	255.901i	0.514891	−	0.514891i
$498$	4.67337	−	23.4946i	0.00938428	−	0.0471780i
$499$	−119.919	+	179.471i	−0.240318	+	0.359662i	−0.931949	−	0.362590i	$-0.881893\pi$
$499$	−119.919	+	179.471i	−0.240318	+	0.359662i	0.691631	+	0.722251i	$0.256893\pi$
$500$		0			0
$501$	−7.71365	−	3.19510i	−0.0153965	−	0.00637744i
$502$	−227.412	+	549.021i	−0.453012	+	1.09367i
$503$	−865.523	+	172.163i	−1.72072	+	0.342273i	−0.954023	−	0.299735i	$-0.903102\pi$
$503$	−865.523	+	172.163i	−1.72072	+	0.342273i	−0.766698	+	0.642008i	$0.778102\pi$
$504$	−324.248	−	216.656i	−0.643349	−	0.429872i
$505$		0			0
$506$	297.414	+	297.414i	0.587776	+	0.587776i
$507$	−16.5211	+	11.0390i	−0.0325859	+	0.0217732i
$508$	73.7144	−	30.5335i	0.145107	−	0.0601053i
$509$			459.446i			0.902645i	0.892361	+	0.451323i	$0.149048\pi$
$509$			459.446i			0.902645i	−0.892361	+	0.451323i	$0.850952\pi$
$510$		0			0
$511$	−8.41386			−0.0164655
$512$	104.718	+	252.811i	0.204527	+	0.493772i
$513$	40.3244	+	60.3498i	0.0786052	+	0.117641i
$514$	−82.0986	+	82.0986i	−0.159725	+	0.159725i
$515$		0			0
$516$	5.46653	−	8.18124i	0.0105940	−	0.0158551i
$517$	−42.2612	−	212.462i	−0.0817432	−	0.410951i
$518$	589.663	+	244.246i	1.13835	+	0.471518i
$519$	1.14241	−	2.75802i	0.00220117	−	0.00531411i
$520$		0			0
$521$	84.0959	+	56.1911i	0.161412	+	0.107852i	0.633653	−	0.773617i	$-0.281555\pi$
$521$	84.0959	+	56.1911i	0.161412	+	0.107852i	−0.472241	+	0.881470i	$0.656555\pi$
$522$	639.303	+	127.165i	1.22472	+	0.243611i
$523$	−395.099	−	395.099i	−0.755448	−	0.755448i	0.220042	−	0.975490i	$-0.429380\pi$
$523$	−395.099	−	395.099i	−0.755448	−	0.755448i	−0.975490	+	0.220042i	$0.929380\pi$
$524$	−29.7907	+	19.9055i	−0.0568525	+	0.0379876i
$525$		0			0
$526$			1116.04i			2.12175i
$527$	17.1632	+	11.4681i	0.0325678	+	0.0217611i
$528$	−44.0052			−0.0833432
$529$	136.796	+	330.254i	0.258593	+	0.624299i
$530$		0			0
$531$	179.272	−	179.272i	0.337611	−	0.337611i
$532$	25.4232	−	127.811i	0.0477880	−	0.240247i
$533$	118.583	−	177.472i	0.222483	−	0.332969i
$534$	−8.83822	−	44.4327i	−0.0165510	−	0.0832074i
$535$		0			0
$536$	−118.596	+	286.315i	−0.221260	+	0.534170i
$537$	−9.93388	+	1.97597i	−0.0184988	+	0.00367965i
$538$	322.254	+	215.323i	0.598985	+	0.400229i
$539$	−143.327	−	28.5095i	−0.265913	−	0.0528934i
$540$		0			0
$541$	−33.9436	+	22.6804i	−0.0627423	+	0.0419230i	−0.586546	−	0.809916i	$-0.699513\pi$
$541$	−33.9436	+	22.6804i	−0.0627423	+	0.0419230i	0.523804	+	0.851839i	$0.324513\pi$
$542$	−943.148	+	390.665i	−1.74012	+	0.720783i
$543$		−	16.9051i		−	0.0311328i
$544$	158.177	+	158.177i	0.290767	+	0.290767i
$545$		0			0
$546$	5.76351	+	13.9143i	0.0105559	+	0.0254841i
$547$	37.8284	+	56.6142i	0.0691562	+	0.103500i	0.864436	−	0.502743i	$-0.167676\pi$
$547$	37.8284	+	56.6142i	0.0691562	+	0.103500i	−0.795280	+	0.606243i	$0.792676\pi$
$548$	−37.6931	+	37.6931i	−0.0687830	+	0.0687830i
$549$	−144.683	+	727.370i	−0.263539	+	1.32490i
$550$		0			0
$551$	−161.019	−	809.498i	−0.292231	−	1.46914i
$552$	13.6093	+	5.63714i	0.0246545	+	0.0102122i
$553$	−71.0254	+	171.470i	−0.128436	+	0.310073i
$554$	−380.832	+	75.7521i	−0.687422	+	0.136737i
$555$		0			0
$556$	214.071	+	42.5813i	0.385019	+	0.0765850i
$557$	208.814	+	208.814i	0.374890	+	0.374890i	0.869255	−	0.494365i	$-0.164599\pi$
$557$	208.814	+	208.814i	0.374890	+	0.374890i	−0.494365	+	0.869255i	$0.664599\pi$
$558$	−19.9222	+	13.3116i	−0.0357029	+	0.0238559i
$559$	−457.036	+	189.310i	−0.817595	+	0.338659i
$560$		0			0
$561$	37.0720	−	15.3557i	0.0660820	−	0.0273721i
$562$	878.426			1.56304
$563$	−169.121	−	408.295i	−0.300393	−	0.725212i	−0.999944	−	0.0106294i	$-0.996616\pi$
$563$	−169.121	−	408.295i	−0.300393	−	0.725212i	0.699551	−	0.714583i	$-0.253384\pi$
$564$	1.11235	+	1.66475i	0.00197226	+	0.00295169i
$565$		0			0
$566$	153.413	−	771.260i	0.271048	−	1.36265i
$567$	−278.566	+	416.904i	−0.491298	+	0.735280i
$568$	78.6820	+	395.561i	0.138525	+	0.696411i
$569$	595.479	+	246.656i	1.04654	+	0.433490i	0.838654	−	0.544664i	$-0.183343\pi$
$569$	595.479	+	246.656i	1.04654	+	0.433490i	0.207882	+	0.978154i	$0.433343\pi$
$570$		0			0
$571$	−117.482	+	23.3687i	−0.205748	+	0.0409259i	−0.296888	−	0.954912i	$-0.595949\pi$
$571$	−117.482	+	23.3687i	−0.205748	+	0.0409259i	0.0911400	+	0.995838i	$0.470949\pi$
$572$	−68.8316	−	45.9918i	−0.120335	−	0.0804052i
$573$	30.9198	+	6.15033i	0.0539613	+	0.0107336i
$574$	305.369	+	305.369i	0.532002	+	0.532002i
$575$		0			0
$576$	378.379	−	156.730i	0.656908	−	0.272100i
$577$			177.008i			0.306773i	0.988166	+	0.153387i	$0.0490180\pi$
$577$			177.008i			0.306773i	−0.988166	+	0.153387i	$0.950982\pi$
$578$	−587.112	−	243.190i	−1.01577	−	0.420744i
$579$	14.2876			0.0246763
$580$		0			0
$581$	−233.848	−	349.979i	−0.402493	−	0.602373i
$582$	16.9966	−	16.9966i	0.0292038	−	0.0292038i
$583$	14.7299	−	74.0520i	0.0252656	−	0.127019i
$584$	5.20940	−	7.79642i	0.00892021	−	0.0133500i
$585$		0			0
$586$	485.547	+	201.120i	0.828578	+	0.343208i
$587$	239.200	−	577.480i	0.407496	−	0.983781i	−0.578299	−	0.815825i	$-0.696283\pi$
$587$	239.200	−	577.480i	0.407496	−	0.983781i	0.985794	−	0.167956i	$-0.0537168\pi$
$588$	1.32472	−	0.263504i	0.00225293	−	0.000448135i
$589$	25.2259	+	16.8554i	0.0428284	+	0.0286170i
$590$		0			0
$591$	29.4132	+	29.4132i	0.0497685	+	0.0497685i
$592$	−720.527	+	481.441i	−1.21711	+	0.813245i
$593$	138.551	−	57.3899i	0.233645	−	0.0967789i	−0.262789	−	0.964853i	$-0.584642\pi$
$593$	138.551	−	57.3899i	0.233645	−	0.0967789i	0.496434	+	0.868074i	$0.334642\pi$
$594$			93.2893i			0.157053i
$595$		0			0
$596$	98.7472			0.165683
$597$	−14.0674	−	33.9618i	−0.0235635	−	0.0568874i
$598$	108.586	+	162.511i	0.181582	+	0.271757i
$599$	−217.159	+	217.159i	−0.362536	+	0.362536i	−0.864746	−	0.502210i	$-0.832520\pi$
$599$	−217.159	+	217.159i	−0.362536	+	0.362536i	0.502210	+	0.864746i	$0.332520\pi$
$600$		0			0
$601$	225.714	−	337.804i	0.375564	−	0.562071i	−0.594753	−	0.803908i	$-0.702750\pi$
$601$	225.714	−	337.804i	0.375564	−	0.562071i	0.970317	+	0.241838i	$0.0777502\pi$
$602$	−195.266	−	981.668i	−0.324362	−	1.63068i
$603$	369.209	+	152.931i	0.612287	+	0.253617i
$604$	−8.85135	+	21.3690i	−0.0146545	+	0.0353792i
$605$		0			0
$606$	−10.2360	−	6.83945i	−0.0168910	−	0.0112862i
$607$	−1017.17	−	202.327i	−1.67573	−	0.333323i	−0.736452	−	0.676490i	$-0.763500\pi$
$607$	−1017.17	−	202.327i	−1.67573	−	0.333323i	−0.939274	+	0.343167i	$0.888500\pi$
$608$	232.484	+	232.484i	0.382374	+	0.382374i
$609$	−27.7191	+	18.5213i	−0.0455158	+	0.0304127i
$610$		0			0
$611$		−	100.662i		−	0.164750i
$612$	90.0975	−	90.0975i	0.147218	−	0.147218i
$613$	−132.402			−0.215991			−0.107995	−	0.994151i	$-0.534443\pi$
$613$	−132.402			−0.215991			−0.107995	+	0.994151i	$0.534443\pi$
$614$	−344.972	−	832.835i	−0.561843	−	1.35641i
$615$		0			0
$616$	−448.774	+	448.774i	−0.728529	+	0.728529i
$617$	−49.9956	+	251.345i	−0.0810302	+	0.407366i	0.918887	+	0.394520i	$0.129089\pi$
$617$	−49.9956	+	251.345i	−0.0810302	+	0.407366i	−0.999917	+	0.0128460i	$0.995911\pi$
$618$	−29.8464	+	44.6683i	−0.0482951	+	0.0722788i
$619$	−17.9310	−	90.1450i	−0.0289676	−	0.145630i	0.963595	−	0.267367i	$-0.0861536\pi$
$619$	−17.9310	−	90.1450i	−0.0289676	−	0.145630i	−0.992562	+	0.121737i	$0.961154\pi$
$620$		0			0
$621$	14.5596	−	35.1499i	0.0234454	−	0.0566021i
$622$	467.145	−	92.9208i	0.751036	−	0.149390i
$623$	−661.875	−	442.251i	−1.06240	−	0.709873i
$624$	−20.0557	−	3.98932i	−0.0321405	−	0.00639314i
$625$		0			0
$626$	−865.556	+	578.346i	−1.38268	+	0.923875i
$627$	54.4872	−	22.5694i	0.0869015	−	0.0359958i
$628$			66.0226i			0.105131i
$629$	439.005	−	657.018i	0.697941	−	1.04454i
$630$		0			0
$631$	219.866	+	530.804i	0.348441	+	0.841210i	0.996805	+	0.0798795i	$0.0254536\pi$
$631$	219.866	+	530.804i	0.348441	+	0.841210i	−0.648364	+	0.761331i	$0.724546\pi$
$632$	−114.912	−	171.978i	−0.181823	−	0.272117i
$633$	0.924280	−	0.924280i	0.00146016	−	0.00146016i
$634$	109.970	−	552.855i	0.173454	−	0.872012i
$635$		0			0
$636$	0.136143	+	0.684437i	0.000214061	+	0.00107616i
$637$	−62.7377	−	25.9868i	−0.0984893	−	0.0407956i
$638$	405.961	−	980.076i	0.636302	−	1.53617i
$639$	510.084	−	101.462i	0.798254	−	0.158783i
$640$		0			0
$641$	−966.275	−	192.204i	−1.50745	−	0.299850i	−0.628894	−	0.777491i	$-0.716492\pi$
$641$	−966.275	−	192.204i	−1.50745	−	0.299850i	−0.878555	+	0.477641i	$0.841492\pi$
$642$	−2.39682	−	2.39682i	−0.00373337	−	0.00373337i
$643$	29.4169	−	19.6558i	0.0457495	−	0.0305688i	−0.532485	−	0.846439i	$-0.678742\pi$
$643$	29.4169	−	19.6558i	0.0457495	−	0.0305688i	0.578235	+	0.815870i	$0.303742\pi$
$644$	−63.1088	+	26.1405i	−0.0979950	+	0.0405909i
$645$		0			0
$646$	−862.919	−	357.433i	−1.33579	−	0.553301i
$647$	472.176			0.729793			0.364897	−	0.931048i	$-0.381104\pi$
$647$	472.176			0.729793			0.364897	+	0.931048i	$0.381104\pi$
$648$	−213.837	−	516.248i	−0.329995	−	0.796679i
$649$	−229.233	−	343.071i	−0.353210	−	0.528615i
$650$		0			0
$651$	0.239071	−	1.20189i	0.000367237	−	0.00184623i
$652$	−25.7604	+	38.5532i	−0.0395098	+	0.0591306i
$653$	124.126	+	624.023i	0.190086	+	0.955625i	0.951568	+	0.307439i	$0.0994720\pi$
$653$	124.126	+	624.023i	0.190086	+	0.955625i	−0.761482	+	0.648186i	$0.775528\pi$
$654$	38.1953	+	15.8210i	0.0584026	+	0.0241912i
$655$		0			0
$656$	−575.082	+	114.391i	−0.876649	+	0.174376i
$657$	−10.0536	−	6.71763i	−0.0153023	−	0.0102247i
$658$	199.754	+	39.7335i	0.303577	+	0.0603853i
$659$	128.530	+	128.530i	0.195037	+	0.195037i	0.797869	−	0.602831i	$-0.205961\pi$
$659$	128.530	+	128.530i	0.195037	+	0.195037i	−0.602831	+	0.797869i	$0.705961\pi$
$660$		0			0
$661$	1075.49	−	445.481i	1.62706	−	0.673950i	0.632161	−	0.774837i	$-0.282168\pi$
$661$	1075.49	−	445.481i	1.62706	−	0.673950i	0.994898	+	0.100887i	$0.0321681\pi$
$662$			496.438i			0.749906i
$663$	18.2879	−	3.63769i	0.0275836	−	0.00548671i
$664$	469.082			0.706449
$665$		0			0
$666$	509.576	+	762.634i	0.765129	+	1.14510i
$667$	−305.919	+	305.919i	−0.458649	+	0.458649i
$668$	−8.41761	+	42.3182i	−0.0126012	+	0.0633506i
$669$	−4.40568	+	6.59357i	−0.00658548	+	0.00985586i
$670$		0			0
$671$	1115.09	+	461.884i	1.66183	+	0.688352i
$672$	5.08204	−	12.2691i	0.00756256	−	0.0182576i
$673$	−105.260	+	20.9375i	−0.156404	+	0.0311106i	−0.272671	−	0.962107i	$-0.587907\pi$
$673$	−105.260	+	20.9375i	−0.156404	+	0.0311106i	0.116267	+	0.993218i	$0.462907\pi$
$674$	660.281	+	441.186i	0.979645	+	0.654578i
$675$		0			0
$676$	72.6081	+	72.6081i	0.107408	+	0.107408i
$677$	876.782	−	585.847i	1.29510	−	0.865358i	0.299057	−	0.954235i	$-0.403328\pi$
$677$	876.782	−	585.847i	1.29510	−	0.865358i	0.996043	+	0.0888773i	$0.0283279\pi$
$678$	21.6537	−	8.96927i	0.0319377	−	0.0132290i
$679$		−	422.355i		−	0.622025i
$680$		0			0
$681$	−27.1616			−0.0398849
$682$	14.9225	+	36.0262i	0.0218805	+	0.0528243i
$683$	339.367	+	507.899i	0.496877	+	0.743629i	0.992143	−	0.125113i	$-0.0399292\pi$
$683$	339.367	+	507.899i	0.496877	+	0.743629i	−0.495265	+	0.868742i	$0.664929\pi$
$684$	132.422	−	132.422i	0.193600	−	0.193600i
$685$		0			0
$686$	450.134	−	673.673i	0.656172	−	0.982031i
$687$	−3.91525	−	19.6833i	−0.00569906	−	0.0286511i
$688$	1255.51	+	520.051i	1.82488	+	0.755888i
$689$	13.4265	−	32.4143i	0.0194869	−	0.0470455i
$690$		0			0
$691$	−815.612	−	544.975i	−1.18034	−	0.788675i	−0.198816	−	0.980037i	$-0.563710\pi$
$691$	−815.612	−	544.975i	−1.18034	−	0.788675i	−0.981520	+	0.191362i	$0.938710\pi$
$692$	−15.1309	−	3.00972i	−0.0218655	−	0.00434931i
$693$	578.703	+	578.703i	0.835069	+	0.835069i
$694$	28.9939	−	19.3731i	0.0417779	−	0.0279151i
$695$		0			0
$696$		−	37.1524i		−	0.0533798i
$697$	444.558	−	297.044i	0.637817	−	0.426176i
$698$	−695.626			−0.996600
$699$	−21.8372	−	52.7196i	−0.0312406	−	0.0754215i
$700$		0			0
$701$	52.7814	−	52.7814i	0.0752944	−	0.0752944i	−0.668457	−	0.743751i	$-0.733045\pi$
$701$	52.7814	−	52.7814i	0.0752944	−	0.0752944i	0.743751	+	0.668457i	$0.233045\pi$
$702$	−8.45719	+	42.5172i	−0.0120473	+	0.0605658i
$703$	645.236	−	965.663i	0.917832	−	1.37363i
$704$	−130.035	−	653.728i	−0.184708	−	0.928591i
$705$		0			0
$706$	228.027	−	550.507i	0.322985	−	0.779755i
$707$	−212.157	+	42.2006i	−0.300080	+	0.0596896i
$708$	3.17089	+	2.11872i	0.00447866	+	0.00299254i
$709$	−752.626	−	149.707i	−1.06153	−	0.211152i	−0.366711	−	0.930335i	$-0.619516\pi$
$709$	−752.626	−	149.707i	−1.06153	−	0.211152i	−0.694821	+	0.719183i	$0.744516\pi$
$710$		0			0
$711$	−221.769	+	148.182i	−0.311912	+	0.208413i
$712$	819.594	−	339.487i	1.15111	−	0.476807i
$713$		−	15.9030i		−	0.0223044i
$714$			37.7264i			0.0528381i
$715$		0			0
$716$	20.0306	+	48.3580i	0.0279756	+	0.0675392i
$717$	−18.5441	−	27.7533i	−0.0258635	−	0.0387075i
$718$	−246.167	+	246.167i	−0.342851	+	0.342851i
$719$	224.919	−	1130.74i	0.312822	−	1.57266i	−0.429785	−	0.902931i	$-0.641410\pi$
$719$	224.919	−	1130.74i	0.312822	−	1.57266i	0.742606	−	0.669729i	$-0.233590\pi$
$720$		0			0
$721$	184.157	+	925.822i	0.255419	+	1.28408i
$722$	−534.907	−	221.566i	−0.740869	−	0.306878i
$723$	17.8143	−	43.0074i	0.0246394	−	0.0594847i
$724$	−85.6842	+	17.0437i	−0.118348	+	0.0235410i
$725$		0			0
$726$	32.1705	+	6.39910i	0.0443119	+	0.00881419i
$727$	−195.955	−	195.955i	−0.269539	−	0.269539i	0.559376	−	0.828914i	$-0.311041\pi$
$727$	−195.955	−	195.955i	−0.269539	−	0.269539i	−0.828914	+	0.559376i	$0.811041\pi$
$728$	−245.216	+	163.848i	−0.336834	+	0.225066i
$729$	−661.808	+	274.130i	−0.907830	+	0.376036i
$730$		0			0
$731$	−1239.18			−1.69518
$732$	−11.1555			−0.0152398
$733$	−169.675	−	409.632i	−0.231480	−	0.558843i	0.764871	−	0.644183i	$-0.222802\pi$
$733$	−169.675	−	409.632i	−0.231480	−	0.558843i	−0.996352	+	0.0853397i	$0.972802\pi$
$734$	597.376	+	894.036i	0.813863	+	1.21803i
$735$		0			0
$736$	33.6219	−	169.029i	0.0456820	−	0.229659i
$737$	361.333	−	540.773i	0.490275	−	0.733749i
$738$	121.076	+	608.689i	0.164059	+	0.824782i
$739$	98.1432	+	40.6523i	0.132805	+	0.0550098i	0.448096	−	0.893985i	$-0.352102\pi$
$739$	98.1432	+	40.6523i	0.132805	+	0.0550098i	−0.315291	+	0.948995i	$0.602102\pi$
$740$		0			0
$741$	26.8790	−	5.34656i	0.0362739	−	0.00721533i
$742$	59.0234	+	39.4382i	0.0795463	+	0.0531512i
$743$	−905.734	−	180.162i	−1.21902	−	0.242479i	−0.456668	−	0.889637i	$-0.650957\pi$
$743$	−905.734	−	180.162i	−1.21902	−	0.242479i	−0.762355	+	0.647159i	$0.775957\pi$
$744$	0.965673	+	0.965673i	0.00129795	+	0.00129795i
$745$		0			0
$746$	−1164.99	+	482.554i	−1.56165	+	0.646855i
$747$		−	604.891i		−	0.809760i
$748$	−115.207	−	172.419i	−0.154020	−	0.230507i
$749$	−59.5595			−0.0795187
$750$		0			0
$751$	636.671	+	952.846i	0.847765	+	1.26877i	0.961374	+	0.275244i	$0.0887587\pi$
$751$	636.671	+	952.846i	0.847765	+	1.26877i	−0.113610	+	0.993525i	$0.536241\pi$
$752$	−195.534	+	195.534i	−0.260018	+	0.260018i
$753$	8.52102	−	42.8381i	0.0113161	−	0.0568899i
$754$	273.869	−	409.873i	0.363221	−	0.543598i
$755$		0			0
$756$	−13.9973	−	5.79787i	−0.0185150	−	0.00766915i
$757$	−24.5973	+	59.3832i	−0.0324932	+	0.0784455i	−0.939293	−	0.343116i	$-0.888518\pi$
$757$	−24.5973	+	59.3832i	−0.0324932	+	0.0784455i	0.906800	+	0.421561i	$0.138518\pi$
$758$	1513.99	−	301.151i	1.99734	−	0.397296i
$759$	−25.7043	−	17.1751i	−0.0338660	−	0.0226285i
$760$		0			0
$761$	−173.164	−	173.164i	−0.227548	−	0.227548i	0.584120	−	0.811668i	$-0.301440\pi$
$761$	−173.164	−	173.164i	−0.227548	−	0.227548i	−0.811668	+	0.584120i	$0.801440\pi$
$762$	−28.2282	+	18.8615i	−0.0370449	+	0.0247526i
$763$	671.137	−	277.994i	0.879602	−	0.364343i
$764$		−	162.919i		−	0.213245i
$765$		0			0
$766$	678.170			0.885339
$767$	−73.3731	−	177.138i	−0.0956624	−	0.230950i
$768$	13.8148	+	20.6753i	0.0179880	+	0.0269210i
$769$	550.339	−	550.339i	0.715655	−	0.715655i	−0.252057	−	0.967712i	$-0.581107\pi$
$769$	550.339	−	550.339i	0.715655	−	0.715655i	0.967712	+	0.252057i	$0.0811072\pi$
$770$		0			0
$771$	4.74102	−	7.09544i	0.00614919	−	0.00920291i
$772$	−14.4046	−	72.4170i	−0.0186588	−	0.0938044i
$773$	−399.534	−	165.492i	−0.516861	−	0.214091i	0.108976	−	0.994044i	$-0.465243\pi$
$773$	−399.534	−	165.492i	−0.516861	−	0.214091i	−0.625837	+	0.779953i	$0.715243\pi$
$774$	550.442	−	1328.89i	0.711166	−	1.71691i
$775$		0			0
$776$	391.361	+	261.499i	0.504331	+	0.336983i
$777$	−46.0092	−	9.15179i	−0.0592139	−	0.0117784i
$778$	443.266	+	443.266i	0.569751	+	0.569751i
$779$	653.397	−	436.586i	0.838764	−	0.560444i
$780$		0			0
$781$		−	846.408i		−	1.08375i
$782$	95.5146	+	480.184i	0.122141	+	0.614047i
$783$	−95.9569			−0.122550
$784$	71.3878	+	172.345i	0.0910559	+	0.219828i
$785$		0			0
$786$	10.7800	−	10.7800i	0.0137150	−	0.0137150i
$787$	222.286	−	1117.51i	0.282447	−	1.41996i	−0.535437	−	0.844575i	$-0.679853\pi$
$787$	222.286	−	1117.51i	0.282447	−	1.41996i	0.817884	−	0.575383i	$-0.195147\pi$
$788$	119.428	−	178.736i	0.151558	−	0.226822i
$789$	−16.0029	−	80.4518i	−0.0202824	−	0.101967i
$790$		0			0
$791$	157.601	−	380.481i	0.199242	−	0.481013i
$792$	−894.537	+	177.934i	−1.12947	+	0.224665i
$793$	466.336	+	311.595i	0.588065	+	0.392932i
$794$	−268.177	−	53.3436i	−0.337754	−	0.0671834i
$795$		0			0
$796$	−157.954	+	105.541i	−0.198434	+	0.132590i
$797$	−104.084	+	43.1132i	−0.130595	+	0.0540943i	−0.447024	−	0.894522i	$-0.647516\pi$
$797$	−104.084	+	43.1132i	−0.130595	+	0.0540943i	0.316429	+	0.948616i	$0.397516\pi$
$798$			55.4491i			0.0694850i
$799$	96.4946	−	232.959i	0.120769	−	0.291563i
$800$		0			0
$801$	−437.775	−	1056.88i	−0.546536	−	1.31945i
$802$	−521.614	−	780.650i	−0.650391	−	0.973379i
$803$	−13.9147	+	13.9147i	−0.0173284	+	0.0173284i
$804$	−1.17274	+	5.89575i	−0.00145863	+	0.00733302i
$805$		0			0
$806$	3.53507	+	17.7720i	0.00438594	+	0.0220496i
$807$	−26.3178	−	10.9012i	−0.0326119	−	0.0135083i
$808$	92.2520	−	222.716i	0.114173	−	0.275639i
$809$	638.126	−	126.931i	0.788783	−	0.156899i	0.215769	−	0.976444i	$-0.430774\pi$
$809$	638.126	−	126.931i	0.788783	−	0.156899i	0.573014	+	0.819546i	$0.305774\pi$
$810$		0			0
$811$	−631.322	−	125.578i	−0.778449	−	0.154843i	−0.210154	−	0.977668i	$-0.567397\pi$
$811$	−631.322	−	125.578i	−0.778449	−	0.154843i	−0.568294	+	0.822825i	$0.692397\pi$
$812$	121.822	+	121.822i	0.150027	+	0.150027i
$813$	62.3868	−	41.6855i	0.0767366	−	0.0512737i
$814$	1379.10	−	571.243i	1.69423	−	0.701773i
$815$		0			0
$816$	−42.5900	−	28.4577i	−0.0521936	−	0.0348747i
$817$	−1821.30			−2.22925
$818$	−181.383	−	437.897i	−0.221739	−	0.535326i
$819$	211.285	+	316.210i	0.257979	+	0.386093i
$820$		0			0
$821$	−174.401	+	876.775i	−0.212426	+	1.06794i	0.716477	+	0.697611i	$0.245754\pi$
$821$	−174.401	+	876.775i	−0.212426	+	1.06794i	−0.928902	+	0.370325i	$0.879246\pi$
$822$	12.6013	−	18.8592i	0.0153300	−	0.0229430i
$823$	−180.424	−	907.053i	−0.219227	−	1.10213i	−0.920950	−	0.389680i	$-0.872586\pi$
$823$	−180.424	−	907.053i	−0.219227	−	1.10213i	0.701723	−	0.712450i	$-0.252414\pi$
$824$	−971.901	−	402.575i	−1.17949	−	0.488562i
$825$		0			0
$826$	380.476	−	75.6813i	0.460624	−	0.0916239i
$827$	704.948	+	471.032i	0.852417	+	0.569567i	0.903237	−	0.429141i	$-0.141184\pi$
$827$	704.948	+	471.032i	0.852417	+	0.569567i	−0.0508208	+	0.998708i	$0.516184\pi$
$828$	−96.2787	−	19.1510i	−0.116279	−	0.0231292i
$829$	862.801	+	862.801i	1.04077	+	1.04077i	0.999133	+	0.0416400i	$0.0132583\pi$
$829$	862.801	+	862.801i	1.04077	+	1.04077i	0.0416400	+	0.999133i	$0.486742\pi$
$830$		0			0
$831$	26.3667	−	10.9215i	0.0317289	−	0.0131426i
$832$		−	309.729i		−	0.372271i
$833$	−120.281	−	120.281i	−0.144395	−	0.144395i
$834$	−92.8715			−0.111357
$835$		0			0
$836$	−169.327	−	253.416i	−0.202545	−	0.303129i
$837$	2.49414	−	2.49414i	0.00297985	−	0.00297985i
$838$	266.908	−	1341.84i	0.318506	−	1.60124i
$839$	−213.563	+	319.620i	−0.254545	+	0.380954i	−0.936631	−	0.350319i	$-0.886073\pi$
$839$	−213.563	+	319.620i	−0.254545	+	0.380954i	0.682085	+	0.731273i	$0.261073\pi$
$840$		0			0
$841$	231.119	+	95.7324i	0.274814	+	0.113832i
$842$	43.2829	−	104.494i	0.0514048	−	0.124102i
$843$	−63.3230	+	12.5957i	−0.0751162	+	0.0149415i
$844$	−5.61660	−	3.75289i	−0.00665474	−	0.00444655i
$845$		0			0
$846$	206.961	+	206.961i	0.244634	+	0.244634i
$847$	479.215	−	320.201i	0.565779	−	0.378042i
$848$	−89.0448	+	36.8836i	−0.105006	+	0.0434948i
$849$			57.7975i			0.0680771i
$850$		0			0
$851$	−608.778			−0.715368
$852$	2.99375	+	7.22756i	0.00351380	+	0.00848305i
$853$	485.458	+	726.539i	0.569118	+	0.851745i	0.998684	−	0.0512903i	$-0.0163334\pi$
$853$	485.458	+	726.539i	0.569118	+	0.851745i	−0.429566	+	0.903036i	$0.641333\pi$
$854$	−802.404	+	802.404i	−0.939583	+	0.939583i
$855$		0			0
$856$	36.8760	−	55.1888i	0.0430794	−	0.0644729i
$857$	262.053	+	1317.43i	0.305779	+	1.53726i	0.762111	+	0.647446i	$0.224163\pi$
$857$	262.053	+	1317.43i	0.305779	+	1.53726i	−0.456332	+	0.889810i	$0.650837\pi$
$858$	32.5429	+	13.4797i	0.0379288	+	0.0157106i
$859$	−97.9655	+	236.510i	−0.114046	+	0.275331i	−0.970588	−	0.240745i	$-0.922608\pi$
$859$	−97.9655	+	236.510i	−0.114046	+	0.275331i	0.856542	+	0.516077i	$0.172608\pi$
$860$		0			0
$861$	−26.3918	−	17.6344i	−0.0306525	−	0.0204813i
$862$	1014.96	+	201.887i	1.17744	+	0.234208i
$863$	1137.90	+	1137.90i	1.31854	+	1.31854i	0.914930	+	0.403612i	$0.132245\pi$
$863$	1137.90	+	1137.90i	1.31854	+	1.31854i	0.403612	+	0.914930i	$0.367755\pi$
$864$	31.7825	−	21.2364i	0.0367853	−	0.0245791i
$865$		0			0
$866$			1415.19i			1.63417i
$867$	45.8102	+	9.11221i	0.0528376	+	0.0105100i
$868$	−6.33287			−0.00729593
$869$	166.114	+	401.035i	0.191156	+	0.461490i
$870$		0			0
$871$	213.704	−	213.704i	0.245355	−	0.245355i
$872$	−157.937	+	794.004i	−0.181121	+	0.910555i
$873$	337.208	−	504.668i	0.386264	−	0.578085i
$874$	140.384	+	705.760i	0.160623	+	0.807505i
$875$		0			0
$876$	0.0696025	−	0.168035i	7.94550e−5	−	0.000191821i
$877$	483.538	−	96.1816i	0.551354	−	0.109671i	0.0884519	−	0.996080i	$-0.471808\pi$
$877$	483.538	−	96.1816i	0.551354	−	0.109671i	0.462902	+	0.886409i	$0.346808\pi$
$878$	−1512.85	−	1010.86i	−1.72307	−	1.15132i
$879$	−37.8854	−	7.53588i	−0.0431006	−	0.00857324i
$880$		0			0
$881$	−334.347	+	223.404i	−0.379508	+	0.253579i	−0.730663	−	0.682738i	$-0.760789\pi$
$881$	−334.347	+	223.404i	−0.379508	+	0.253579i	0.351155	+	0.936317i	$0.385789\pi$
$882$	182.417	−	75.5597i	0.206822	−	0.0856686i
$883$			907.327i			1.02755i	0.857925	+	0.513775i	$0.171754\pi$
$883$			907.327i			1.02755i	−0.857925	+	0.513775i	$0.828246\pi$
$884$	−36.8755	−	89.0253i	−0.0417144	−	0.100707i
$885$		0			0
$886$	−298.248	−	720.035i	−0.336624	−	0.812681i
$887$	705.933	+	1056.50i	0.795866	+	1.19110i	0.978160	+	0.207854i	$0.0666478\pi$
$887$	705.933	+	1056.50i	0.795866	+	1.19110i	−0.182294	+	0.983244i	$0.558352\pi$
$888$	36.9665	−	36.9665i	0.0416290	−	0.0416290i
$889$	−116.379	+	585.074i	−0.130910	+	0.658127i
$890$		0			0
$891$	228.780	+	1150.16i	0.256768	+	1.29086i
$892$	37.8615	+	15.6828i	0.0424457	+	0.0175816i
$893$	141.825	−	342.395i	0.158818	−	0.383421i
$894$	−41.2096	+	8.19710i	−0.0460957	+	0.00916901i
$895$		0			0
$896$	936.988	+	186.379i	1.04575	+	0.208012i
$897$	−10.1579	−	10.1579i	−0.0113243	−	0.0113243i
$898$	−1436.96	+	960.148i	−1.60018	+	1.06921i
$899$	−37.0564	+	15.3493i	−0.0412195	+	0.0170737i
$900$		0			0
$901$	62.1448	−	62.1448i	0.0689732	−	0.0689732i
$902$	1010.03			1.11976
$903$	28.1522	+	67.9654i	0.0311763	+	0.0752663i
$904$	254.983	+	381.608i	0.282060	+	0.422133i
$905$		0			0
$906$	1.92002	−	9.65257i	0.00211922	−	0.0106541i
$907$	−852.359	+	1275.64i	−0.939756	+	1.40644i	−0.0262336	+	0.999656i	$0.508351\pi$
$907$	−852.359	+	1275.64i	−0.939756	+	1.40644i	−0.913522	+	0.406788i	$0.866649\pi$
$908$	27.3842	+	137.670i	0.0301588	+	0.151619i
$909$	−287.197	−	118.961i	−0.315948	−	0.130870i
$910$		0			0
$911$	359.228	−	71.4549i	0.394323	−	0.0784357i	0.00605352	−	0.999982i	$-0.498073\pi$
$911$	359.228	−	71.4549i	0.394323	−	0.0784357i	0.388269	+	0.921546i	$0.373073\pi$
$912$	−62.5974	−	41.8262i	−0.0686375	−	0.0458621i
$913$	−965.523	−	192.054i	−1.05753	−	0.210355i
$914$	−505.549	−	505.549i	−0.553117	−	0.553117i
$915$		0			0
$916$	−95.8181	+	39.6892i	−0.104605	+	0.0433288i
$917$		−	267.877i		−	0.292123i
$918$	−60.3292	+	90.2891i	−0.0657181	+	0.0983541i
$919$	−944.655			−1.02792			−0.513958	−	0.857815i	$-0.671821\pi$
$919$	−944.655			−1.02792			−0.513958	+	0.857815i	$0.671821\pi$
$920$		0			0
$921$	36.8099	+	55.0899i	0.0399673	+	0.0598153i
$922$	382.839	−	382.839i	0.415226	−	0.415226i
$923$	76.7316	−	385.756i	0.0831328	−	0.417937i
$924$	−6.83940	+	10.2359i	−0.00740195	+	0.0110778i
$925$		0			0
$926$	712.706	+	295.212i	0.769661	+	0.318804i
$927$	−519.128	+	1253.29i	−0.560009	+	1.35198i
$928$	−426.312	+	84.7988i	−0.459388	+	0.0913780i
$929$	807.914	+	539.831i	0.869660	+	0.581088i	0.908372	−	0.418162i	$-0.137326\pi$
$929$	807.914	+	539.831i	0.869660	+	0.581088i	−0.0387126	+	0.999250i	$0.512326\pi$
$930$		0			0
$931$	−176.785	−	176.785i	−0.189887	−	0.189887i
$932$	−245.195	+	163.834i	−0.263085	+	0.175788i
$933$	−32.3426	+	13.3967i	−0.0346652	+	0.0143588i
$934$			481.282i			0.515292i
$935$		0			0
$936$	−423.822			−0.452801
$937$	229.656	+	554.438i	0.245097	+	0.591716i	0.997775	−	0.0666728i	$-0.0212384\pi$
$937$	229.656	+	554.438i	0.245097	+	0.591716i	−0.752678	+	0.658389i	$0.771238\pi$
$938$	339.721	+	508.428i	0.362176	+	0.542034i
$939$	54.1023	−	54.1023i	0.0576170	−	0.0576170i
$940$		0			0
$941$	602.514	−	901.726i	0.640291	−	0.958263i	−0.359394	−	0.933186i	$-0.617017\pi$
$941$	602.514	−	901.726i	0.640291	−	0.958263i	0.999686	−	0.0250777i	$-0.00798332\pi$
$942$	−5.48059	−	27.5528i	−0.00581804	−	0.0292493i
$943$	−380.563	−	157.634i	−0.403566	−	0.167162i
$944$	−201.562	+	486.613i	−0.213519	+	0.515480i
$945$		0			0
$946$	−1946.39	−	1300.54i	−2.05750	−	1.37478i
$947$	−683.372	−	135.931i	−0.721618	−	0.143539i	−0.179400	−	0.983776i	$-0.557416\pi$
$947$	−683.372	−	135.931i	−0.721618	−	0.143539i	−0.542219	+	0.840237i	$0.682416\pi$
$948$	−2.83693	−	2.83693i	−0.00299254	−	0.00299254i
$949$	−7.60316	+	5.08027i	−0.00801176	+	0.00535329i
$950$		0			0
$951$			41.4305i			0.0435651i
$952$	−724.559	+	144.124i	−0.761091	+	0.151390i
$953$	1779.95			1.86774			0.933868	−	0.357618i	$-0.116411\pi$
$953$	1779.95			1.86774			0.933868	+	0.357618i	$0.116411\pi$
$954$	39.0390	+	94.2485i	0.0409214	+	0.0987930i
$955$		0			0
$956$	−121.972	+	121.972i	−0.127586	+	0.127586i
$957$	−15.2111	+	76.4716i	−0.0158946	+	0.0799076i
$958$	613.843	−	918.681i	0.640754	−	0.958957i
$959$	−77.7522	−	390.887i	−0.0810763	−	0.407598i
$960$		0			0
$961$	−367.195	+	886.486i	−0.382096	+	0.922462i
$962$	680.322	−	135.324i	0.707195	−	0.140670i
$963$	−71.1671	−	47.5523i	−0.0739015	−	0.0493794i
$964$	−235.945	−	46.9324i	−0.244756	−	0.0486850i
$965$		0			0
$966$	24.1669	−	16.1478i	0.0250175	−	0.0167161i
$967$	558.012	−	231.136i	0.577055	−	0.239024i	−0.0750154	−	0.997182i	$-0.523901\pi$
$967$	558.012	−	231.136i	0.577055	−	0.239024i	0.652071	+	0.758158i	$0.273901\pi$
$968$			642.299i			0.663532i
$969$	67.3303	+	13.3928i	0.0694843	+	0.0138213i
$970$		0			0
$971$	421.281	+	1017.06i	0.433863	+	1.04744i	0.978031	+	0.208461i	$0.0668454\pi$
$971$	421.281	+	1017.06i	0.433863	+	1.04744i	−0.544168	+	0.838976i	$0.683155\pi$
$972$	−18.1531	−	27.1681i	−0.0186760	−	0.0279507i
$973$	−1153.90	+	1153.90i	−1.18592	+	1.18592i
$974$	−108.013	+	543.017i	−0.110896	+	0.557512i
$975$		0			0
$976$	−300.579	−	1511.11i	−0.307971	−	1.54827i
$977$	−1012.20	−	419.266i	−1.03603	−	0.429136i	−0.201142	−	0.979562i	$-0.564465\pi$
$977$	−1012.20	−	419.266i	−1.03603	−	0.429136i	−0.834884	+	0.550426i	$0.814465\pi$
$978$	7.55010	−	18.2276i	0.00771994	−	0.0186376i
$979$	−1825.98	+	363.211i	−1.86515	+	0.371002i
$980$		0			0
$981$	1023.88	+	203.663i	1.04372	+	0.207608i
$982$	−351.948	−	351.948i	−0.358399	−	0.358399i
$983$	1021.98	−	682.863i	1.03965	−	0.694673i	0.0862178	−	0.996276i	$-0.472522\pi$
$983$	1021.98	−	682.863i	1.03965	−	0.694673i	0.953433	+	0.301604i	$0.0975219\pi$
$984$	32.6807	−	13.5368i	0.0332121	−	0.0137569i
$985$		0			0
$986$	1026.71	−	686.025i	1.04129	−	0.695766i
$987$	−14.9694			−0.0151665
$988$	−54.1984	−	130.847i	−0.0548567	−	0.132436i
$989$	530.396	+	793.794i	0.536295	+	0.802623i
$990$		0			0
$991$	−143.735	+	722.604i	−0.145040	+	0.729167i	0.837985	+	0.545694i	$0.183734\pi$
$991$	−143.735	+	722.604i	−0.145040	+	0.729167i	−0.983025	+	0.183473i	$0.941266\pi$
$992$	8.87670	−	13.2849i	0.00894829	−	0.0133921i
$993$	−7.11841	−	35.7867i	−0.00716859	−	0.0360389i
$994$	735.207	+	304.533i	0.739645	+	0.306371i
$995$		0			0
$996$	8.92400	−	1.77509i	0.00895984	−	0.00178222i
$997$	−145.149	−	96.9855i	−0.145586	−	0.0972774i	0.480644	−	0.876916i	$-0.340403\pi$
$997$	−145.149	−	96.9855i	−0.145586	−	0.0972774i	−0.626230	+	0.779638i	$0.715403\pi$
$998$	−465.511	−	92.5960i	−0.466444	−	0.0927815i
$999$	−95.4770	−	95.4770i	−0.0955725	−	0.0955725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.b.226.1		8
5.2	odd	4		425.3.t.a.124.1		8
5.3	odd	4		425.3.t.c.124.1		8
5.4	even	2		17.3.e.a.5.1	✓	8
15.14	odd	2		153.3.p.b.73.1		8
17.7	odd	16	inner	425.3.u.b.126.1		8
20.19	odd	2		272.3.bh.c.209.1		8
85.4	even	4		289.3.e.m.131.1		8
85.7	even	16		425.3.t.c.24.1		8
85.9	even	8		289.3.e.d.65.1		8
85.14	odd	16		289.3.e.d.249.1		8
85.19	even	8		289.3.e.k.224.1		8
85.24	odd	16		17.3.e.a.7.1	yes	8
85.29	odd	16		289.3.e.k.40.1		8
85.39	odd	16		289.3.e.l.40.1		8
85.44	odd	16		289.3.e.c.75.1		8
85.49	even	8		289.3.e.l.224.1		8
85.54	odd	16		289.3.e.b.249.1		8
85.58	even	16		425.3.t.a.24.1		8
85.59	even	8		289.3.e.b.65.1		8
85.64	even	4		289.3.e.i.131.1		8
85.74	odd	16		289.3.e.m.214.1		8
85.79	odd	16		289.3.e.i.214.1		8
85.84	even	2		289.3.e.c.158.1		8
255.194	even	16		153.3.p.b.109.1		8
340.279	even	16		272.3.bh.c.177.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.5.1	✓	8	5.4	even	2
17.3.e.a.7.1	yes	8	85.24	odd	16
153.3.p.b.73.1		8	15.14	odd	2
153.3.p.b.109.1		8	255.194	even	16
272.3.bh.c.177.1		8	340.279	even	16
272.3.bh.c.209.1		8	20.19	odd	2
289.3.e.b.65.1		8	85.59	even	8
289.3.e.b.249.1		8	85.54	odd	16
289.3.e.c.75.1		8	85.44	odd	16
289.3.e.c.158.1		8	85.84	even	2
289.3.e.d.65.1		8	85.9	even	8
289.3.e.d.249.1		8	85.14	odd	16
289.3.e.i.131.1		8	85.64	even	4
289.3.e.i.214.1		8	85.79	odd	16
289.3.e.k.40.1		8	85.29	odd	16
289.3.e.k.224.1		8	85.19	even	8
289.3.e.l.40.1		8	85.39	odd	16
289.3.e.l.224.1		8	85.49	even	8
289.3.e.m.131.1		8	85.4	even	4
289.3.e.m.214.1		8	85.74	odd	16
425.3.t.a.24.1		8	85.58	even	16
425.3.t.a.124.1		8	5.2	odd	4
425.3.t.c.24.1		8	85.7	even	16
425.3.t.c.124.1		8	5.3	odd	4
425.3.u.b.126.1		8	17.7	odd	16	inner
425.3.u.b.226.1		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+(0.841487 + 2.03153i) q^{2} +(-0.0897902 - 0.134381i) q^{3} +(-0.590587 + 0.590587i) q^{4} +(0.197441 - 0.295491i) q^{6} +(-1.21824 - 6.12453i) q^{7} +(6.42935 + 2.66313i) q^{8} +(3.43416 - 8.29078i) q^{9} +(-12.1433 - 8.11392i) q^{11} +(0.132392 + 0.0263345i) q^{12} +(-4.79884 - 4.79884i) q^{13} +(11.4170 - 7.62861i) q^{14} +18.6433i q^{16} +(-6.50562 - 15.7060i) q^{17} +19.7328 q^{18} +(-9.56175 - 23.0841i) q^{19} +(-0.713631 + 0.713631i) q^{21} +(6.26521 - 31.4973i) q^{22} +(-7.27639 + 10.8899i) q^{23} +(-0.219421 - 1.10310i) q^{24} +(5.71082 - 13.7871i) q^{26} +(-2.84909 + 0.566719i) q^{27} +(4.33654 + 2.89759i) q^{28} +(32.3980 + 6.44436i) q^{29} +(-1.00960 + 0.674593i) q^{31} +(-12.1570 + 5.03558i) q^{32} +2.36038i q^{33} +(26.4327 - 26.4327i) q^{34} +(2.86826 + 6.92459i) q^{36} +(25.8238 + 38.6481i) q^{37} +(38.8500 - 38.8500i) q^{38} +(-0.213982 + 1.07576i) q^{39} +(6.13577 + 30.8466i) q^{41} +(-2.05027 - 0.849251i) q^{42} +(27.8948 - 67.3441i) q^{43} +(11.9637 - 2.37972i) q^{44} +(-28.2461 - 5.61851i) q^{46} +(10.4882 + 10.4882i) q^{47} +(2.50529 - 1.67398i) q^{48} +(9.24438 - 3.82915i) q^{49} +(-1.52643 + 2.28447i) q^{51} +5.66826 q^{52} +(1.97838 + 4.77624i) q^{53} +(-3.54878 - 5.31112i) q^{54} +(8.47786 - 42.6211i) q^{56} +(-2.24350 + 3.35764i) q^{57} +(14.1706 + 71.2404i) q^{58} +(26.1013 + 10.8115i) q^{59} +(-81.0541 + 16.1227i) q^{61} +(-2.22002 - 1.48337i) q^{62} +(-54.9608 - 10.9324i) q^{63} +(32.2713 + 32.2713i) q^{64} +(-4.79518 + 1.98623i) q^{66} +44.5324i q^{67} +(13.1179 + 5.43359i) q^{68} +2.11674 q^{69} +(32.1978 + 48.1875i) q^{71} +(44.1588 - 44.1588i) q^{72} +(0.262865 - 1.32151i) q^{73} +(-56.7843 + 84.9838i) q^{74} +(19.2802 + 7.98612i) q^{76} +(-34.9004 + 84.2570i) q^{77} +(-2.36550 + 0.470527i) q^{78} +(-24.7128 - 16.5125i) q^{79} +(-56.7774 - 56.7774i) q^{81} +(-57.5026 + 38.4220i) q^{82} +(62.2748 - 25.7951i) q^{83} -0.842922i q^{84} +160.285 q^{86} +(-2.04303 - 4.93230i) q^{87} +(-56.4655 - 84.5065i) q^{88} +(90.1397 - 90.1397i) q^{89} +(-23.5444 + 35.2368i) q^{91} +(-2.13408 - 10.7288i) q^{92} +(0.181304 + 0.0750988i) q^{93} +(-12.4814 + 30.1327i) q^{94} +(1.76826 + 1.18151i) q^{96} +(66.3366 + 13.1952i) q^{97} +(15.5581 + 15.5581i) q^{98} +(-108.973 + 72.8134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} - 8 q^{6} - 8 q^{7} + 24 q^{8} - 16 q^{9} - 8 q^{11} - 48 q^{12} - 16 q^{13} + 8 q^{14} - 56 q^{18} - 64 q^{21} + 104 q^{22} + 56 q^{23} - 80 q^{24} + 176 q^{26} - 40 q^{27} - 152 q^{28}+ \cdots - 224 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 - 8 * q^6 - 8 * q^7 + 24 * q^8 - 16 * q^9 - 8 * q^11 - 48 * q^12 - 16 * q^13 + 8 * q^14 - 56 * q^18 - 64 * q^21 + 104 * q^22 + 56 * q^23 - 80 * q^24 + 176 * q^26 - 40 * q^27 - 152 * q^28 + 48 * q^29 + 24 * q^31 - 88 * q^32 - 136 * q^34 - 128 * q^36 - 32 * q^37 + 120 * q^38 + 48 * q^39 + 48 * q^41 - 16 * q^42 + 232 * q^43 + 120 * q^44 - 88 * q^46 - 192 * q^47 - 136 * q^48 + 16 * q^49 + 136 * q^51 + 384 * q^52 + 32 * q^53 + 8 * q^54 - 120 * q^56 - 24 * q^57 - 240 * q^58 - 48 * q^59 - 160 * q^61 + 168 * q^62 - 56 * q^63 - 64 * q^64 - 8 * q^66 - 272 * q^68 + 240 * q^69 + 40 * q^71 - 40 * q^72 - 48 * q^73 - 160 * q^74 + 80 * q^76 + 48 * q^77 + 400 * q^78 - 136 * q^79 - 424 * q^81 + 64 * q^82 + 264 * q^83 + 832 * q^86 - 208 * q^87 - 264 * q^88 + 160 * q^89 + 320 * q^91 - 24 * q^92 + 64 * q^93 + 32 * q^94 - 56 * q^96 - 48 * q^97 + 120 * q^98 - 224 * q^99

Introduction

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Modular forms

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