LMFDB - Embedded newform 425.3.u.b.126.1

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			126.1
Root			$-0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	425.126
Dual form			425.3.u.b.226.1

$q$-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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{11}{16}\right)$

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	−0.561385	−	0.827555i	$-0.689731\pi$
$2$	0.841487	−	2.03153i	0.420744	−	1.01577i	0.982129	−	0.188210i	$-0.0602687\pi$
$3$	−0.0897902	+	0.134381i	−0.0299301	+	0.0447935i	−0.846133	−	0.532972i	$-0.821075\pi$
$3$	−0.0897902	+	0.134381i	−0.0299301	+	0.0447935i	0.816203	+	0.577765i	$0.196075\pi$
$4$	−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	0.790800	+	0.612075i	$0.209665\pi$
$7$	−1.21824	+	6.12453i	−0.174035	+	0.874933i	−0.964835	+	0.262858i	$0.915335\pi$
$8$	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	−0.967463	−	0.253014i	$-0.918578\pi$
$11$	−12.1433	+	8.11392i	−1.10394	+	0.737629i	−0.136478	+	0.990643i	$0.543578\pi$
$12$	0.132392	−	0.0263345i	0.0110327	−	0.00219454i
$13$	−4.79884	+	4.79884i	−0.369141	+	0.369141i	−0.867164	−	0.498023i	$-0.834060\pi$
$13$	−4.79884	+	4.79884i	−0.369141	+	0.369141i	0.498023	+	0.867164i	$0.334060\pi$
$14$	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	0.444454	+	0.895802i	$0.353398\pi$
$19$	−9.56175	+	23.0841i	−0.503250	+	1.21495i	−0.947704	+	0.319151i	$0.896602\pi$
$20$		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	0.638873	−	0.769312i	$-0.279401\pi$
$23$	−7.27639	−	10.8899i	−0.316365	−	0.473474i	−0.955238	+	0.295839i	$0.904401\pi$
$24$	−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	0.398228	−	0.917287i	$-0.369625\pi$
$29$	32.3980	−	6.44436i	1.11717	−	0.222219i	0.718945	+	0.695067i	$0.244625\pi$
$30$		0			0
$31$	−1.00960	−	0.674593i	−0.0325678	−	0.0217611i	0.539180	−	0.842191i	$-0.318734\pi$
$31$	−1.00960	−	0.674593i	−0.0325678	−	0.0217611i	−0.571748	+	0.820430i	$0.693734\pi$
$32$	−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	−0.298002	−	0.954565i	$-0.596320\pi$
$37$	25.8238	−	38.6481i	0.697941	−	1.04454i	0.995944	−	0.0899781i	$-0.0286797\pi$
$38$	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	−0.830949	−	0.556348i	$-0.812202\pi$
$41$	6.13577	−	30.8466i	0.149653	−	0.752356i	0.980602	−	0.196008i	$-0.0627979\pi$
$42$	−2.05027	+	0.849251i	−0.0488161	+	0.0202203i
$43$	27.8948	+	67.3441i	0.648717	+	1.56614i	0.814617	+	0.579999i	$0.196947\pi$
$43$	27.8948	+	67.3441i	0.648717	+	1.56614i	−0.165901	+	0.986142i	$0.553053\pi$
$44$	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	−0.586672	−	0.809825i	$-0.699562\pi$
$47$	10.4882	−	10.4882i	0.223153	−	0.223153i	0.809825	+	0.586672i	$0.199562\pi$
$48$	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	−0.904116	−	0.427287i	$-0.859469\pi$
$53$	1.97838	−	4.77624i	0.0373280	−	0.0901178i	0.941444	+	0.337169i	$0.109469\pi$
$54$	−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	−0.150356	−	0.988632i	$-0.548042\pi$
$59$	26.1013	−	10.8115i	0.442394	−	0.183246i	0.592751	+	0.805386i	$0.298042\pi$
$60$		0			0
$61$	−81.0541	−	16.1227i	−1.32876	−	0.264306i	−0.520866	−	0.853639i	$-0.674391\pi$
$61$	−81.0541	−	16.1227i	−1.32876	−	0.264306i	−0.807891	+	0.589332i	$0.799391\pi$
$62$	−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	$-0.892165\pi$
$67$		−	44.5324i		−	0.664663i	0.943163	−	0.332332i	$-0.107835\pi$
$68$	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	−0.532323	−	0.846541i	$-0.678681\pi$
$71$	32.1978	−	48.1875i	0.453491	−	0.678697i	0.985813	+	0.167845i	$0.0536807\pi$
$72$	44.1588	+	44.1588i	0.613317	+	0.613317i
$73$	0.262865	+	1.32151i	0.00360089	+	0.0181029i	0.982544	−	0.186031i	$-0.0595623\pi$
$73$	0.262865	+	1.32151i	0.00360089	+	0.0181029i	−0.978943	+	0.204133i	$0.934562\pi$
$74$	−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	−0.702062	−	0.712116i	$-0.747737\pi$
$79$	−24.7128	+	16.5125i	−0.312820	+	0.209020i	0.389242	+	0.921136i	$0.372737\pi$
$80$		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	0.724863	−	0.688893i	$-0.241903\pi$
$83$	62.2748	+	25.7951i	0.750298	+	0.310784i	0.0254351	+	0.999676i	$0.491903\pi$
$84$			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	0.999917	+	0.0128890i	$0.00410281\pi$
$89$	90.1397	+	90.1397i	1.01281	+	1.01281i	0.0128890	+	0.999917i	$0.495897\pi$
$90$		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	0.159091	−	0.987264i	$-0.449144\pi$
$97$	66.3366	−	13.1952i	0.683882	−	0.136033i	0.524791	+	0.851231i	$0.324144\pi$
$98$	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	$0.0548573\pi$
$101$			34.6405i			0.342975i	−0.985186	+	0.171488i	$0.945143\pi$
$102$	−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	0.988506	−	0.151183i	$-0.0483083\pi$
$107$	1.86075	+	9.35463i	0.0173902	+	0.0874264i	−0.971116	+	0.238610i	$0.923308\pi$
$108$	1.34794	+	2.01733i	0.0124809	+	0.0186790i
$109$	22.6951	−	114.096i	0.208212	−	1.04675i	−0.725362	−	0.688368i	$-0.758327\pi$
$109$	22.6951	−	114.096i	0.208212	−	1.04675i	0.933574	−	0.358385i	$-0.116673\pi$
$110$		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	−0.288751	−	0.957404i	$-0.593240\pi$
$113$	54.8360	−	36.6403i	0.485274	−	0.324250i	0.774026	+	0.633154i	$0.218240\pi$
$114$	−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	−0.702059	−	0.712119i	$-0.747736\pi$
$127$	−88.2580	+	36.5576i	−0.694945	+	0.287855i	0.00711395	+	0.999975i	$0.497736\pi$
$128$	−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	−0.0318711	−	0.999492i	$-0.510147\pi$
$131$	42.0736	−	8.36897i	0.321173	−	0.0638852i	0.353044	+	0.935607i	$0.385147\pi$
$132$	−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	−0.238632	+	0.971110i	$0.576699\pi$
$139$	−145.186	+	217.286i	−1.04450	+	1.56321i	−0.805868	+	0.592095i	$0.798301\pi$
$140$		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	−0.929614	−	0.368534i	$-0.879860\pi$
$149$	−83.6010	+	83.6010i	−0.561080	+	0.561080i	0.368534	+	0.929614i	$0.379860\pi$
$150$		0			0
$151$	25.5851	+	10.5977i	0.169437	+	0.0701833i	0.465790	−	0.884895i	$-0.345770\pi$
$151$	25.5851	+	10.5977i	0.169437	+	0.0701833i	−0.296352	+	0.955079i	$0.595770\pi$
$152$			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	0.862345	−	0.506321i	$-0.168995\pi$
$157$	55.8958	+	55.8958i	0.356024	+	0.356024i	−0.506321	+	0.862345i	$0.668995\pi$
$158$	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	0.359262	−	0.933237i	$-0.383029\pi$
$163$	54.4489	+	10.8306i	0.334042	+	0.0664451i	−0.0252196	+	0.999682i	$0.508029\pi$
$164$	−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	0.677489	−	0.735533i	$-0.263068\pi$
$167$	42.9537	+	28.7008i	0.257208	+	0.171861i	−0.420281	+	0.907394i	$0.638068\pi$
$168$	−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	−0.800625	−	0.599166i	$-0.795499\pi$
$173$	10.2620	−	15.3581i	0.0593178	−	0.0887754i	0.859943	+	0.510390i	$0.170499\pi$
$174$	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	0.976604	−	0.215046i	$-0.0689900\pi$
$179$	23.9825	+	57.8989i	0.133980	+	0.323457i	−0.842624	+	0.538503i	$0.818990\pi$
$180$		0			0
$181$	86.9711	−	58.1122i	0.480503	−	0.321062i	−0.291621	−	0.956534i	$-0.594194\pi$
$181$	86.9711	−	58.1122i	0.480503	−	0.321062i	0.772124	+	0.635472i	$0.219194\pi$
$182$	−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	0.246897	−	0.969042i	$-0.420589\pi$
$191$	−137.930	−	137.930i	−0.722145	−	0.722145i	−0.969042	+	0.246897i	$0.920589\pi$
$192$	1.43899	+	7.23428i	0.00749473	+	0.0376785i
$193$	−49.1142	−	73.5045i	−0.254478	−	0.380853i	0.682131	−	0.731230i	$-0.261053\pi$
$193$	−49.1142	−	73.5045i	−0.254478	−	0.380853i	−0.936609	+	0.350377i	$0.886053\pi$
$194$	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	−0.492972	−	0.870045i	$-0.664089\pi$
$197$	−252.430	−	50.2114i	−1.28137	−	0.254880i	−0.788398	+	0.615165i	$0.789089\pi$
$198$	−239.622	+	160.110i	−1.21021	+	0.808637i
$199$	223.079	−	44.3732i	1.12100	−	0.222981i	0.400406	−	0.916338i	$-0.368869\pi$
$199$	223.079	−	44.3732i	1.12100	−	0.222981i	0.720594	+	0.693357i	$0.243869\pi$
$200$		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	−0.976866	−	0.213852i	$-0.931399\pi$
$211$	1.57784	−	7.93236i	0.00747794	−	0.0375941i	0.984344	+	0.176257i	$0.0563991\pi$
$212$	−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	−0.960372	−	0.278720i	$-0.910090\pi$
$223$	−18.7769	+	45.3315i	−0.0842014	+	0.203280i	0.876171	+	0.482001i	$0.160090\pi$
$224$	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	0.978062	−	0.208312i	$-0.0667969\pi$
$227$	93.3694	+	139.737i	0.411319	+	0.615582i	−0.566743	+	0.823894i	$0.691797\pi$
$228$	−0.657994	+	3.30796i	−0.00288594	+	0.0145086i
$229$	114.723	−	47.5197i	0.500972	−	0.207510i	−0.117864	−	0.993030i	$-0.537605\pi$
$229$	114.723	−	47.5197i	0.500972	−	0.207510i	0.618836	+	0.785520i	$0.287605\pi$
$230$		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	0.615791	−	0.787910i	$-0.288837\pi$
$233$	346.291	−	68.8815i	1.48623	−	0.295629i	0.870436	+	0.492281i	$0.163837\pi$
$234$	−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	−0.334691	−	0.942328i	$-0.608632\pi$
$241$	160.021	−	239.488i	0.663988	−	0.993728i	0.998678	−	0.0513996i	$-0.0163682\pi$
$242$	−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	−0.215227	−	0.976564i	$-0.569049\pi$
$251$	191.096	−	191.096i	0.761337	−	0.761337i	0.976564	+	0.215227i	$0.0690490\pi$
$252$	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	−0.879680	−	0.475565i	$-0.842244\pi$
$257$	20.2061	−	48.7819i	0.0786230	−	0.189813i	0.958303	+	0.285753i	$0.0922436\pi$
$258$	−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	0.790970	−	0.611854i	$-0.209576\pi$
$263$	468.907	−	194.228i	1.78292	−	0.738509i	0.991947	−	0.126654i	$-0.0404239\pi$
$264$	−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	0.797310	−	0.603570i	$-0.206256\pi$
$269$	146.551	+	97.9225i	0.544801	+	0.364024i	−0.252509	+	0.967595i	$0.581256\pi$
$270$		0			0
$271$		−	464.255i		−	1.71312i	−0.516050	−	0.856559i	$-0.672598\pi$
$271$		−	464.255i		−	1.71312i	0.516050	−	0.856559i	$-0.327402\pi$
$272$	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	−0.991812	−	0.127704i	$-0.959239\pi$
$277$	−34.4498	−	173.191i	−0.124368	−	0.625238i	0.867445	−	0.497534i	$-0.165761\pi$
$278$	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	0.921851	+	0.387545i	$0.126677\pi$
$281$	152.875	+	369.073i	0.544040	+	1.31343i	−0.377811	+	0.925883i	$0.623323\pi$
$282$	5.16995	+	1.02837i	0.0183332	+	0.00364669i
$283$	−297.348	+	198.682i	−1.05070	+	0.702055i	−0.955975	−	0.293448i	$-0.905197\pi$
$283$	−297.348	+	198.682i	−1.05070	+	0.702055i	−0.0947249	+	0.995503i	$0.530197\pi$
$284$	−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	0.934020	−	0.357220i	$-0.116275\pi$
$293$	169.002	+	169.002i	0.576800	+	0.576800i	−0.357220	+	0.934020i	$0.616275\pi$
$294$	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	0.987332	+	0.158670i	$0.0507207\pi$
$311$	42.2576	+	212.443i	0.135877	+	0.683098i	−0.851455	+	0.524428i	$0.824279\pi$
$312$	−4.24064	−	6.34657i	−0.0135918	−	0.0203416i
$313$	92.3584	−	464.317i	0.295075	−	1.48344i	−0.494171	−	0.869365i	$-0.664528\pi$
$313$	92.3584	−	464.317i	0.295075	−	1.48344i	0.789246	−	0.614077i	$-0.210472\pi$
$314$	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	−0.844322	−	0.535836i	$-0.819997\pi$
$317$	−213.145	+	142.419i	−0.672383	+	0.449272i	0.171939	+	0.985108i	$0.444997\pi$
$318$	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	−0.0446663	−	0.999002i	$-0.514222\pi$
$331$	208.580	−	86.3966i	0.630151	−	0.261017i	0.674817	+	0.737985i	$0.264222\pi$
$332$	−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	0.914601	−	0.404357i	$-0.132505\pi$
$337$	300.276	+	200.638i	0.891027	+	0.595365i	−0.0235742	+	0.999722i	$0.507505\pi$
$338$	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	−0.984987	−	0.172628i	$-0.944774\pi$
$347$	−3.09377	+	15.5534i	−0.00891575	+	0.0448225i	0.976071	+	0.217451i	$0.0697741\pi$
$348$	4.11954	−	1.70637i	0.0118377	−	0.00490336i
$349$	−121.062	−	292.270i	−0.346883	−	0.837448i	−0.996984	−	0.0776015i	$-0.975274\pi$
$349$	−121.062	−	292.270i	−0.346883	−	0.837448i	0.650102	−	0.759847i	$-0.274726\pi$
$350$		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	−0.924352	−	0.381540i	$-0.875394\pi$
$353$	−191.613	+	191.613i	−0.542812	+	0.542812i	0.381540	+	0.924352i	$0.375394\pi$
$354$	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	−0.816757	−	0.576981i	$-0.804231\pi$
$359$	60.5865	−	146.269i	0.168765	−	0.407434i	0.985522	+	0.169547i	$0.0542305\pi$
$360$		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	0.798892	−	0.601474i	$-0.205420\pi$
$367$	479.595	+	95.3974i	1.30680	+	0.259938i	0.507906	+	0.861413i	$0.330420\pi$
$368$	−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	$-0.720902\pi$
$373$		−	573.453i		−	1.53741i	0.639605	−	0.768704i	$-0.279098\pi$
$374$	−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	0.550641	+	0.834742i	$0.314383\pi$
$379$	136.954	+	688.516i	0.361357	+	1.81666i	−0.189284	+	0.981922i	$0.560617\pi$
$380$		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	0.999765	+	0.0216830i	$0.00690247\pi$
$383$	118.024	+	284.935i	0.308157	+	0.743956i	−0.691608	+	0.722273i	$0.743098\pi$
$384$	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	0.694604	−	0.719392i	$-0.255580\pi$
$389$	263.382	+	109.097i	0.677076	+	0.280454i	−0.0175282	+	0.999846i	$0.505580\pi$
$390$		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	0.734202	−	0.678931i	$-0.237556\pi$
$397$	−69.0841	−	103.392i	−0.174015	−	0.260432i	−0.908217	+	0.418499i	$0.862556\pi$
$398$	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	−0.357014	−	0.934099i	$-0.616205\pi$
$401$	−418.770	−	83.2986i	−1.04432	−	0.207727i	−0.687302	+	0.726372i	$0.741205\pi$
$402$	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	−0.989504	−	0.144503i	$-0.953842\pi$
$419$	−517.326	+	345.666i	−1.23467	+	0.824979i	−0.245164	+	0.969482i	$0.578842\pi$
$420$		0			0
$421$	−36.3708	+	36.3708i	−0.0863916	+	0.0863916i	−0.748982	−	0.662590i	$-0.769457\pi$
$421$	−36.3708	+	36.3708i	−0.0863916	+	0.0863916i	0.662590	+	0.748982i	$0.269457\pi$
$422$	−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	0.999934	−	0.0115175i	$-0.00366621\pi$
$431$	261.460	+	391.302i	0.606635	+	0.907893i	−0.393299	+	0.919411i	$0.628666\pi$
$432$	−10.5655	+	53.1163i	−0.0244572	+	0.122954i
$433$	594.595	−	246.289i	1.37320	−	0.568798i	0.430545	−	0.902569i	$-0.358321\pi$
$433$	594.595	−	246.289i	1.37320	−	0.568798i	0.942654	+	0.333772i	$0.108321\pi$
$434$	−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	−0.969389	−	0.245530i	$-0.921038\pi$
$439$	−688.000	−	459.707i	−1.56720	−	1.04717i	−0.597809	−	0.801638i	$-0.703962\pi$
$440$		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	−0.303692	−	0.952770i	$-0.598220\pi$
$449$	153.330	−	770.842i	0.341492	−	1.71680i	0.645185	−	0.764027i	$-0.276780\pi$
$450$		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	0.0289968	−	0.999580i	$-0.490769\pi$
$457$	−300.390	−	124.426i	−0.657309	−	0.272266i	−0.686306	+	0.727313i	$0.740769\pi$
$458$		−	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	−0.992522	−	0.122064i	$-0.961049\pi$
$461$	−94.2242	+	227.477i	−0.204391	+	0.493444i	0.788131	+	0.615507i	$0.211049\pi$
$462$	18.0064	−	26.9485i	0.0389749	−	0.0583301i
$463$	248.069	+	248.069i	0.535786	+	0.535786i	0.922288	−	0.386503i	$-0.126317\pi$
$463$	248.069	+	248.069i	0.535786	+	0.535786i	−0.386503	+	0.922288i	$0.626317\pi$
$464$	−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	−0.155526	−	0.987832i	$-0.549707\pi$
$467$	202.212	−	83.7591i	0.433003	−	0.179356i	0.588529	+	0.808476i	$0.299707\pi$
$468$	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	−0.999318	−	0.0369135i	$-0.988247\pi$
$479$	−279.157	+	417.789i	−0.582792	+	0.872210i	0.416526	+	0.909124i	$0.363247\pi$
$480$		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	−0.321745	−	0.946826i	$-0.604269\pi$
$487$	209.352	−	139.885i	0.429882	−	0.287238i	0.751627	+	0.659589i	$0.229269\pi$
$488$	−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	0.159423	−	0.987210i	$-0.449037\pi$
$491$	−209.123	−	86.6215i	−0.425912	−	0.176418i	−0.585334	+	0.810792i	$0.699037\pi$
$492$		−	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	0.691631	−	0.722251i	$-0.256893\pi$
$499$	−119.919	−	179.471i	−0.240318	−	0.359662i	−0.931949	+	0.362590i	$0.881893\pi$
$500$		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	−0.766698	−	0.642008i	$-0.778102\pi$
$503$	−865.523	−	172.163i	−1.72072	−	0.342273i	−0.954023	+	0.299735i	$0.903102\pi$
$504$	−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	$-0.850952\pi$
$509$		−	459.446i		−	0.902645i	0.892361	−	0.451323i	$-0.149048\pi$
$510$		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	−0.472241	−	0.881470i	$-0.656555\pi$
$521$	84.0959	−	56.1911i	0.161412	−	0.107852i	0.633653	+	0.773617i	$0.281555\pi$
$522$	639.303	−	127.165i	1.22472	−	0.243611i
$523$	−395.099	+	395.099i	−0.755448	+	0.755448i	−0.975490	−	0.220042i	$-0.929380\pi$
$523$	−395.099	+	395.099i	−0.755448	+	0.755448i	0.220042	+	0.975490i	$0.429380\pi$
$524$	−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	0.523804	−	0.851839i	$-0.324513\pi$
$541$	−33.9436	−	22.6804i	−0.0627423	−	0.0419230i	−0.586546	+	0.809916i	$0.699513\pi$
$542$	−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	−0.795280	−	0.606243i	$-0.792676\pi$
$547$	37.8284	−	56.6142i	0.0691562	−	0.103500i	0.864436	+	0.502743i	$0.167676\pi$
$548$	−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	−0.494365	−	0.869255i	$-0.664599\pi$
$557$	208.814	−	208.814i	0.374890	−	0.374890i	0.869255	+	0.494365i	$0.164599\pi$
$558$	−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	0.699551	+	0.714583i	$0.253384\pi$
$563$	−169.121	+	408.295i	−0.300393	+	0.725212i	−0.999944	+	0.0106294i	$0.996616\pi$
$564$	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	0.207882	−	0.978154i	$-0.433343\pi$
$569$	595.479	−	246.656i	1.04654	−	0.433490i	0.838654	+	0.544664i	$0.183343\pi$
$570$		0			0
$571$	−117.482	−	23.3687i	−0.205748	−	0.0409259i	0.0911400	−	0.995838i	$-0.470949\pi$
$571$	−117.482	−	23.3687i	−0.205748	−	0.0409259i	−0.296888	+	0.954912i	$0.595949\pi$
$572$	−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	$-0.950982\pi$
$577$		−	177.008i		−	0.306773i	0.988166	−	0.153387i	$-0.0490180\pi$
$578$	−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	0.985794	+	0.167956i	$0.0537168\pi$
$587$	239.200	+	577.480i	0.407496	+	0.983781i	−0.578299	+	0.815825i	$0.696283\pi$
$588$	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	0.496434	−	0.868074i	$-0.334642\pi$
$593$	138.551	+	57.3899i	0.233645	+	0.0967789i	−0.262789	+	0.964853i	$0.584642\pi$
$594$		−	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	0.502210	−	0.864746i	$-0.332520\pi$
$599$	−217.159	−	217.159i	−0.362536	−	0.362536i	−0.864746	+	0.502210i	$0.832520\pi$
$600$		0			0
$601$	225.714	+	337.804i	0.375564	+	0.562071i	0.970317	−	0.241838i	$-0.0777502\pi$
$601$	225.714	+	337.804i	0.375564	+	0.562071i	−0.594753	+	0.803908i	$0.702750\pi$
$602$	−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	−0.939274	−	0.343167i	$-0.888500\pi$
$607$	−1017.17	+	202.327i	−1.67573	+	0.333323i	−0.736452	+	0.676490i	$0.763500\pi$
$608$	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	−0.999917	−	0.0128460i	$-0.995911\pi$
$617$	−49.9956	−	251.345i	−0.0810302	−	0.407366i	0.918887	−	0.394520i	$-0.129089\pi$
$618$	−29.8464	−	44.6683i	−0.0482951	−	0.0722788i
$619$	−17.9310	+	90.1450i	−0.0289676	+	0.145630i	−0.992562	−	0.121737i	$-0.961154\pi$
$619$	−17.9310	+	90.1450i	−0.0289676	+	0.145630i	0.963595	+	0.267367i	$0.0861536\pi$
$620$		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	−0.648364	−	0.761331i	$-0.724546\pi$
$631$	219.866	−	530.804i	0.348441	−	0.841210i	0.996805	−	0.0798795i	$-0.0254536\pi$
$632$	−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	−0.878555	−	0.477641i	$-0.841492\pi$
$641$	−966.275	+	192.204i	−1.50745	+	0.299850i	−0.628894	+	0.777491i	$0.716492\pi$
$642$	−2.39682	+	2.39682i	−0.00373337	+	0.00373337i
$643$	29.4169	+	19.6558i	0.0457495	+	0.0305688i	0.578235	−	0.815870i	$-0.303742\pi$
$643$	29.4169	+	19.6558i	0.0457495	+	0.0305688i	−0.532485	+	0.846439i	$0.678742\pi$
$644$	−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	−0.761482	−	0.648186i	$-0.775528\pi$
$653$	124.126	−	624.023i	0.190086	−	0.955625i	0.951568	−	0.307439i	$-0.0994720\pi$
$654$	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	−0.602831	−	0.797869i	$-0.705961\pi$
$659$	128.530	−	128.530i	0.195037	−	0.195037i	0.797869	+	0.602831i	$0.205961\pi$
$660$		0			0
$661$	1075.49	+	445.481i	1.62706	+	0.673950i	0.994898	−	0.100887i	$-0.0321681\pi$
$661$	1075.49	+	445.481i	1.62706	+	0.673950i	0.632161	+	0.774837i	$0.282168\pi$
$662$		−	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	0.116267	−	0.993218i	$-0.462907\pi$
$673$	−105.260	−	20.9375i	−0.156404	−	0.0311106i	−0.272671	+	0.962107i	$0.587907\pi$
$674$	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	0.996043	−	0.0888773i	$-0.0283279\pi$
$677$	876.782	+	585.847i	1.29510	+	0.865358i	0.299057	+	0.954235i	$0.403328\pi$
$678$	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	−0.495265	−	0.868742i	$-0.664929\pi$
$683$	339.367	−	507.899i	0.496877	−	0.743629i	0.992143	+	0.125113i	$0.0399292\pi$
$684$	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	−0.981520	−	0.191362i	$-0.938710\pi$
$691$	−815.612	+	544.975i	−1.18034	+	0.788675i	−0.198816	+	0.980037i	$0.563710\pi$
$692$	−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	0.743751	−	0.668457i	$-0.233045\pi$
$701$	52.7814	+	52.7814i	0.0752944	+	0.0752944i	−0.668457	+	0.743751i	$0.733045\pi$
$702$	−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	−0.694821	−	0.719183i	$-0.744516\pi$
$709$	−752.626	+	149.707i	−1.06153	+	0.211152i	−0.366711	+	0.930335i	$0.619516\pi$
$710$		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	0.742606	+	0.669729i	$0.233590\pi$
$719$	224.919	+	1130.74i	0.312822	+	1.57266i	−0.429785	+	0.902931i	$0.641410\pi$
$720$		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	−0.828914	−	0.559376i	$-0.811041\pi$
$727$	−195.955	+	195.955i	−0.269539	+	0.269539i	0.559376	+	0.828914i	$0.311041\pi$
$728$	−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	−0.996352	−	0.0853397i	$-0.972802\pi$
$733$	−169.675	+	409.632i	−0.231480	+	0.558843i	0.764871	+	0.644183i	$0.222802\pi$
$734$	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	−0.315291	−	0.948995i	$-0.602102\pi$
$739$	98.1432	−	40.6523i	0.132805	−	0.0550098i	0.448096	+	0.893985i	$0.352102\pi$
$740$		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	−0.762355	−	0.647159i	$-0.775957\pi$
$743$	−905.734	+	180.162i	−1.21902	+	0.242479i	−0.456668	+	0.889637i	$0.650957\pi$
$744$	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	−0.113610	−	0.993525i	$-0.536241\pi$
$751$	636.671	−	952.846i	0.847765	−	1.26877i	0.961374	−	0.275244i	$-0.0887587\pi$
$752$	−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	0.906800	−	0.421561i	$-0.138518\pi$
$757$	−24.5973	−	59.3832i	−0.0324932	−	0.0784455i	−0.939293	+	0.343116i	$0.888518\pi$
$758$	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	−0.811668	−	0.584120i	$-0.801440\pi$
$761$	−173.164	+	173.164i	−0.227548	+	0.227548i	0.584120	+	0.811668i	$0.301440\pi$
$762$	−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	0.967712	−	0.252057i	$-0.0811072\pi$
$769$	550.339	+	550.339i	0.715655	+	0.715655i	−0.252057	+	0.967712i	$0.581107\pi$
$770$		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	−0.625837	−	0.779953i	$-0.715243\pi$
$773$	−399.534	+	165.492i	−0.516861	+	0.214091i	0.108976	+	0.994044i	$0.465243\pi$
$774$	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	0.817884	+	0.575383i	$0.195147\pi$
$787$	222.286	+	1117.51i	0.282447	+	1.41996i	−0.535437	+	0.844575i	$0.679853\pi$
$788$	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	0.316429	−	0.948616i	$-0.397516\pi$
$797$	−104.084	−	43.1132i	−0.130595	−	0.0540943i	−0.447024	+	0.894522i	$0.647516\pi$
$798$		−	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	0.573014	−	0.819546i	$-0.305774\pi$
$809$	638.126	+	126.931i	0.788783	+	0.156899i	0.215769	+	0.976444i	$0.430774\pi$
$810$		0			0
$811$	−631.322	+	125.578i	−0.778449	+	0.154843i	−0.568294	−	0.822825i	$-0.692397\pi$
$811$	−631.322	+	125.578i	−0.778449	+	0.154843i	−0.210154	+	0.977668i	$0.567397\pi$
$812$	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	−0.928902	−	0.370325i	$-0.879246\pi$
$821$	−174.401	−	876.775i	−0.212426	−	1.06794i	0.716477	−	0.697611i	$-0.245754\pi$
$822$	12.6013	+	18.8592i	0.0153300	+	0.0229430i
$823$	−180.424	+	907.053i	−0.219227	+	1.10213i	0.701723	+	0.712450i	$0.252414\pi$
$823$	−180.424	+	907.053i	−0.219227	+	1.10213i	−0.920950	+	0.389680i	$0.872586\pi$
$824$	−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	−0.0508208	−	0.998708i	$-0.516184\pi$
$827$	704.948	−	471.032i	0.852417	−	0.569567i	0.903237	+	0.429141i	$0.141184\pi$
$828$	−96.2787	+	19.1510i	−0.116279	+	0.0231292i
$829$	862.801	−	862.801i	1.04077	−	1.04077i	0.0416400	−	0.999133i	$-0.486742\pi$
$829$	862.801	−	862.801i	1.04077	−	1.04077i	0.999133	−	0.0416400i	$-0.0132583\pi$
$830$		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	0.682085	−	0.731273i	$-0.261073\pi$
$839$	−213.563	−	319.620i	−0.254545	−	0.380954i	−0.936631	+	0.350319i	$0.886073\pi$
$840$		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	−0.429566	−	0.903036i	$-0.641333\pi$
$853$	485.458	−	726.539i	0.569118	−	0.851745i	0.998684	+	0.0512903i	$0.0163334\pi$
$854$	−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	−0.456332	−	0.889810i	$-0.650837\pi$
$857$	262.053	−	1317.43i	0.305779	−	1.53726i	0.762111	−	0.647446i	$-0.224163\pi$
$858$	32.5429	−	13.4797i	0.0379288	−	0.0157106i
$859$	−97.9655	−	236.510i	−0.114046	−	0.275331i	0.856542	−	0.516077i	$-0.172608\pi$
$859$	−97.9655	−	236.510i	−0.114046	−	0.275331i	−0.970588	+	0.240745i	$0.922608\pi$
$860$		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	0.403612	−	0.914930i	$-0.367755\pi$
$863$	1137.90	−	1137.90i	1.31854	−	1.31854i	0.914930	−	0.403612i	$-0.132245\pi$
$864$	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	0.462902	−	0.886409i	$-0.346808\pi$
$877$	483.538	+	96.1816i	0.551354	+	0.109671i	0.0884519	+	0.996080i	$0.471808\pi$
$878$	−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	0.351155	−	0.936317i	$-0.385789\pi$
$881$	−334.347	−	223.404i	−0.379508	−	0.253579i	−0.730663	+	0.682738i	$0.760789\pi$
$882$	182.417	+	75.5597i	0.206822	+	0.0856686i
$883$		−	907.327i		−	1.02755i	−0.857925	−	0.513775i	$-0.828246\pi$
$883$		−	907.327i		−	1.02755i	0.857925	−	0.513775i	$-0.171754\pi$
$884$	−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	−0.182294	−	0.983244i	$-0.558352\pi$
$887$	705.933	−	1056.50i	0.795866	−	1.19110i	0.978160	−	0.207854i	$-0.0666478\pi$
$888$	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	−0.913522	−	0.406788i	$-0.866649\pi$
$907$	−852.359	−	1275.64i	−0.939756	−	1.40644i	−0.0262336	−	0.999656i	$-0.508351\pi$
$908$	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	0.388269	−	0.921546i	$-0.373073\pi$
$911$	359.228	+	71.4549i	0.394323	+	0.0784357i	0.00605352	+	0.999982i	$0.498073\pi$
$912$	−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	−0.0387126	−	0.999250i	$-0.512326\pi$
$929$	807.914	−	539.831i	0.869660	−	0.581088i	0.908372	+	0.418162i	$0.137326\pi$
$930$		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	−0.752678	−	0.658389i	$-0.771238\pi$
$937$	229.656	−	554.438i	0.245097	−	0.591716i	0.997775	+	0.0666728i	$0.0212384\pi$
$938$	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	0.999686	+	0.0250777i	$0.00798332\pi$
$941$	602.514	+	901.726i	0.640291	+	0.958263i	−0.359394	+	0.933186i	$0.617017\pi$
$942$	−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	−0.542219	−	0.840237i	$-0.682416\pi$
$947$	−683.372	+	135.931i	−0.721618	+	0.143539i	−0.179400	+	0.983776i	$0.557416\pi$
$948$	−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	0.652071	−	0.758158i	$-0.273901\pi$
$967$	558.012	+	231.136i	0.577055	+	0.239024i	−0.0750154	+	0.997182i	$0.523901\pi$
$968$		−	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	−0.544168	−	0.838976i	$-0.683155\pi$
$971$	421.281	−	1017.06i	0.433863	−	1.04744i	0.978031	−	0.208461i	$-0.0668454\pi$
$972$	−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	−0.834884	−	0.550426i	$-0.814465\pi$
$977$	−1012.20	+	419.266i	−1.03603	+	0.429136i	−0.201142	+	0.979562i	$0.564465\pi$
$978$	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	0.953433	−	0.301604i	$-0.0975219\pi$
$983$	1021.98	+	682.863i	1.03965	+	0.694673i	0.0862178	+	0.996276i	$0.472522\pi$
$984$	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	−0.983025	−	0.183473i	$-0.941266\pi$
$991$	−143.735	−	722.604i	−0.145040	−	0.729167i	0.837985	−	0.545694i	$-0.183734\pi$
$992$	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	−0.626230	−	0.779638i	$-0.715403\pi$
$997$	−145.149	+	96.9855i	−0.145586	+	0.0972774i	0.480644	+	0.876916i	$0.340403\pi$
$998$	−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.126.1		8
5.2	odd	4		425.3.t.c.24.1		8
5.3	odd	4		425.3.t.a.24.1		8
5.4	even	2		17.3.e.a.7.1	yes	8
15.14	odd	2		153.3.p.b.109.1		8
17.5	odd	16	inner	425.3.u.b.226.1		8
20.19	odd	2		272.3.bh.c.177.1		8
85.4	even	4		289.3.e.i.214.1		8
85.9	even	8		289.3.e.k.40.1		8
85.14	odd	16		289.3.e.i.131.1		8
85.19	even	8		289.3.e.d.249.1		8
85.22	even	16		425.3.t.a.124.1		8
85.24	odd	16		289.3.e.l.224.1		8
85.29	odd	16		289.3.e.c.158.1		8
85.39	odd	16		17.3.e.a.5.1	✓	8
85.44	odd	16		289.3.e.k.224.1		8
85.49	even	8		289.3.e.b.249.1		8
85.54	odd	16		289.3.e.m.131.1		8
85.59	even	8		289.3.e.l.40.1		8
85.64	even	4		289.3.e.m.214.1		8
85.73	even	16		425.3.t.c.124.1		8
85.74	odd	16		289.3.e.b.65.1		8
85.79	odd	16		289.3.e.d.65.1		8
85.84	even	2		289.3.e.c.75.1		8
255.209	even	16		153.3.p.b.73.1		8
340.39	even	16		272.3.bh.c.209.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.5.1	✓	8	85.39	odd	16
17.3.e.a.7.1	yes	8	5.4	even	2
153.3.p.b.73.1		8	255.209	even	16
153.3.p.b.109.1		8	15.14	odd	2
272.3.bh.c.177.1		8	20.19	odd	2
272.3.bh.c.209.1		8	340.39	even	16
289.3.e.b.65.1		8	85.74	odd	16
289.3.e.b.249.1		8	85.49	even	8
289.3.e.c.75.1		8	85.84	even	2
289.3.e.c.158.1		8	85.29	odd	16
289.3.e.d.65.1		8	85.79	odd	16
289.3.e.d.249.1		8	85.19	even	8
289.3.e.i.131.1		8	85.14	odd	16
289.3.e.i.214.1		8	85.4	even	4
289.3.e.k.40.1		8	85.9	even	8
289.3.e.k.224.1		8	85.44	odd	16
289.3.e.l.40.1		8	85.59	even	8
289.3.e.l.224.1		8	85.24	odd	16
289.3.e.m.131.1		8	85.54	odd	16
289.3.e.m.214.1		8	85.64	even	4
425.3.t.a.24.1		8	5.3	odd	4
425.3.t.a.124.1		8	85.22	even	16
425.3.t.c.24.1		8	5.2	odd	4
425.3.t.c.124.1		8	85.73	even	16
425.3.u.b.126.1		8	1.1	even	1	trivial
425.3.u.b.226.1		8	17.5	odd	16	inner

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more