LMFDB - Embedded newform 289.3.e.k.224.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [8,8,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

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

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.03153 - 0.841487i) q^{2} +(0.158513 + 0.0315301i) q^{3} +(0.590587 - 0.590587i) q^{4} +(-2.98067 - 4.46088i) q^{5} +(0.348555 - 0.0693320i) q^{6} +(3.46927 - 5.19212i) q^{7} +(-2.66313 + 6.42935i) q^{8} +(-8.29078 - 3.43416i) q^{9} +(-9.80910 - 6.55423i) q^{10} +(-2.84923 - 14.3240i) q^{11} +(0.112237 - 0.0749942i) q^{12} +(-4.79884 - 4.79884i) q^{13} +(2.67881 - 13.4673i) q^{14} +(-0.331821 - 0.801088i) q^{15} +18.6433i q^{16} -19.7328 q^{18} +(23.0841 - 9.56175i) q^{19} +(-4.39488 - 0.874196i) q^{20} +(0.713631 - 0.713631i) q^{21} +(-17.8418 - 26.7021i) q^{22} +(12.8455 - 2.55513i) q^{23} +(-0.624858 + 0.935165i) q^{24} +(-1.44803 + 3.49585i) q^{25} +(-13.7871 - 5.71082i) q^{26} +(-2.41534 - 1.61388i) q^{27} +(-1.01750 - 5.11530i) q^{28} +(-27.4657 + 18.3520i) q^{29} +(-1.34821 - 1.34821i) q^{30} +(-0.236886 + 1.19090i) q^{31} +(5.03558 + 12.1570i) q^{32} -2.36038i q^{33} -33.5022 q^{35} +(-6.92459 + 2.86826i) q^{36} +(-45.5885 - 9.06812i) q^{37} +(38.8500 - 38.8500i) q^{38} +(-0.609368 - 0.911984i) q^{39} +(36.6185 - 7.28387i) q^{40} +(17.4732 - 26.1505i) q^{41} +(0.849251 - 2.05027i) q^{42} +(67.3441 + 27.8948i) q^{43} +(-10.1423 - 6.77687i) q^{44} +(9.39270 + 47.2203i) q^{45} +(23.9459 - 16.0002i) q^{46} +(10.4882 + 10.4882i) q^{47} +(-0.587825 + 2.95520i) q^{48} +(3.82915 + 9.24438i) q^{49} +8.32041i q^{50} -5.66826 q^{52} +(4.77624 - 1.97838i) q^{53} +(-6.26489 - 1.24616i) q^{54} +(-55.4053 + 55.4053i) q^{55} +(24.1429 + 36.1324i) q^{56} +(3.96061 - 0.787813i) q^{57} +(-40.3544 + 60.3947i) q^{58} +(10.8115 - 26.1013i) q^{59} +(-0.669081 - 0.277142i) q^{60} +(68.7144 + 45.9135i) q^{61} +(0.520891 + 2.61870i) q^{62} +(-46.5935 + 31.1328i) q^{63} +(-32.2713 - 32.2713i) q^{64} +(-7.10332 + 35.7108i) q^{65} +(-1.98623 - 4.79518i) q^{66} -44.5324i q^{67} +2.11674 q^{69} +(-68.0607 + 28.1917i) q^{70} +(56.8410 + 11.3064i) q^{71} +(44.1588 - 44.1588i) q^{72} +(-0.748576 - 1.12032i) q^{73} +(-100.245 + 19.9400i) q^{74} +(-0.339755 + 0.508479i) q^{75} +(7.98612 - 19.2802i) q^{76} +(-84.2570 - 34.9004i) q^{77} +(-2.00537 - 1.33995i) q^{78} +(-5.79844 - 29.1507i) q^{79} +(83.1655 - 55.5694i) q^{80} +(56.7774 + 56.7774i) q^{81} +(13.4920 - 67.8290i) q^{82} +(-25.7951 - 62.2748i) q^{83} -0.842922i q^{84} +160.285 q^{86} +(-4.93230 + 2.04303i) q^{87} +(99.6823 + 19.8280i) q^{88} +(-90.1397 + 90.1397i) q^{89} +(58.8169 + 88.0256i) q^{90} +(-41.5646 + 8.26771i) q^{91} +(6.07736 - 9.09541i) q^{92} +(-0.0750988 + 0.181304i) q^{93} +(30.1327 + 12.4814i) q^{94} +(-111.460 - 74.4751i) q^{95} +(0.414892 + 2.08580i) q^{96} +(56.2374 - 37.5767i) q^{97} +(15.5581 + 15.5581i) q^{98} +(-25.5687 + 128.542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 16 q^{5} - 8 q^{6} + 40 q^{7} + 40 q^{8} - 8 q^{9} - 48 q^{10} - 8 q^{11} + 72 q^{12} - 16 q^{13} + 104 q^{14} + 56 q^{18} + 48 q^{19} - 16 q^{20} + 64 q^{21} - 24 q^{22} + 56 q^{23} + 24 q^{24}+ \cdots + 128 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 16 * q^5 - 8 * q^6 + 40 * q^7 + 40 * q^8 - 8 * q^9 - 48 * q^10 - 8 * q^11 + 72 * q^12 - 16 * q^13 + 104 * q^14 + 56 * q^18 + 48 * q^19 - 16 * q^20 + 64 * q^21 - 24 * q^22 + 56 * q^23 + 24 * q^24 + 32 * q^25 + 48 * q^26 - 24 * q^27 + 8 * q^28 - 128 * q^29 - 16 * q^30 - 40 * q^31 + 88 * q^32 - 160 * q^35 + 24 * q^36 - 96 * q^37 + 120 * q^38 - 96 * q^39 + 112 * q^40 - 48 * q^41 - 128 * q^42 + 112 * q^43 + 120 * q^44 - 112 * q^45 + 72 * q^46 - 192 * q^47 - 136 * q^48 + 80 * q^49 - 384 * q^52 + 128 * q^53 - 64 * q^54 - 224 * q^55 + 200 * q^56 + 48 * q^57 + 120 * q^59 - 48 * q^60 + 288 * q^61 + 8 * q^62 - 120 * q^63 + 64 * q^64 - 64 * q^65 + 96 * q^66 + 240 * q^69 - 480 * q^70 + 344 * q^71 - 40 * q^72 + 200 * q^73 - 208 * q^74 - 104 * q^75 - 160 * q^76 - 80 * q^77 - 512 * q^78 + 328 * q^79 + 64 * q^80 + 424 * q^81 - 64 * q^82 - 336 * q^83 + 832 * q^86 + 80 * q^87 + 8 * q^88 - 160 * q^89 - 224 * q^90 - 544 * q^91 + 24 * q^92 + 208 * q^93 - 432 * q^94 - 192 * q^95 + 64 * q^96 + 240 * q^97 + 120 * q^98 + 128 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	2.03153	−	0.841487i	1.01577	−	0.420744i	0.188210	−	0.982129i	$-0.439731\pi$
$2$	2.03153	−	0.841487i	1.01577	−	0.420744i	0.827555	+	0.561385i	$0.189731\pi$
$3$	0.158513	+	0.0315301i	0.0528376	+	0.0105100i	0.221438	−	0.975174i	$-0.428925\pi$
$3$	0.158513	+	0.0315301i	0.0528376	+	0.0105100i	−0.168601	+	0.985684i	$0.553925\pi$
$4$	0.590587	−	0.590587i	0.147647	−	0.147647i
$5$	−2.98067	−	4.46088i	−0.596134	−	0.892177i	0.403607	−	0.914932i	$-0.367756\pi$
$5$	−2.98067	−	4.46088i	−0.596134	−	0.892177i	−0.999741	+	0.0227553i	$0.992756\pi$
$6$	0.348555	−	0.0693320i	0.0580926	−	0.0115553i
$7$	3.46927	−	5.19212i	0.495609	−	0.741732i	−0.496373	−	0.868109i	$-0.665335\pi$
$7$	3.46927	−	5.19212i	0.495609	−	0.741732i	0.991982	+	0.126378i	$0.0403351\pi$
$8$	−2.66313	+	6.42935i	−0.332891	+	0.803669i
$9$	−8.29078	−	3.43416i	−0.921198	−	0.381573i
$10$	−9.80910	−	6.55423i	−0.980910	−	0.655423i
$11$	−2.84923	−	14.3240i	−0.259021	−	1.30219i	−0.863007	−	0.505192i	$-0.831422\pi$
$11$	−2.84923	−	14.3240i	−0.259021	−	1.30219i	0.603986	−	0.796995i	$-0.293578\pi$
$12$	0.112237	−	0.0749942i	0.00935306	−	0.00624952i
$13$	−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	$0.834060\pi$
$14$	2.67881	−	13.4673i	0.191344	−	0.961950i
$15$	−0.331821	−	0.801088i	−0.0221214	−	0.0534058i
$16$			18.6433i			1.16520i
$17$		0			0
$17$		0			0
$18$	−19.7328			−1.09627
$19$	23.0841	−	9.56175i	1.21495	−	0.503250i	0.319151	−	0.947704i	$-0.396602\pi$
$19$	23.0841	−	9.56175i	1.21495	−	0.503250i	0.895802	+	0.444454i	$0.146602\pi$
$20$	−4.39488	−	0.874196i	−0.219744	−	0.0437098i
$21$	0.713631	−	0.713631i	0.0339824	−	0.0339824i
$22$	−17.8418	−	26.7021i	−0.810991	−	1.21373i
$23$	12.8455	−	2.55513i	0.558500	−	0.111093i	0.0922345	−	0.995737i	$-0.470599\pi$
$23$	12.8455	−	2.55513i	0.558500	−	0.111093i	0.466266	+	0.884645i	$0.345599\pi$
$24$	−0.624858	+	0.935165i	−0.0260357	+	0.0389652i
$25$	−1.44803	+	3.49585i	−0.0579211	+	0.139834i
$26$	−13.7871	−	5.71082i	−0.530274	−	0.219647i
$27$	−2.41534	−	1.61388i	−0.0894570	−	0.0597733i
$28$	−1.01750	−	5.11530i	−0.0363392	−	0.182689i
$29$	−27.4657	+	18.3520i	−0.947093	+	0.632828i	−0.930209	−	0.367030i	$-0.880375\pi$
$29$	−27.4657	+	18.3520i	−0.947093	+	0.632828i	−0.0168842	+	0.999857i	$0.505375\pi$
$30$	−1.34821	−	1.34821i	−0.0449403	−	0.0449403i
$31$	−0.236886	+	1.19090i	−0.00764147	+	0.0384163i	−0.984418	−	0.175845i	$-0.943734\pi$
$31$	−0.236886	+	1.19090i	−0.00764147	+	0.0384163i	0.976776	+	0.214261i	$0.0687343\pi$
$32$	5.03558	+	12.1570i	0.157362	+	0.379905i
$33$		−	2.36038i		−	0.0715267i
$34$		0			0
$35$	−33.5022			−0.957206
$36$	−6.92459	+	2.86826i	−0.192350	+	0.0796739i
$37$	−45.5885	−	9.06812i	−1.23212	−	0.245084i	−0.464260	−	0.885699i	$-0.653680\pi$
$37$	−45.5885	−	9.06812i	−1.23212	−	0.245084i	−0.767863	+	0.640614i	$0.778680\pi$
$38$	38.8500	−	38.8500i	1.02237	−	1.02237i
$39$	−0.609368	−	0.911984i	−0.0156248	−	0.0233842i
$40$	36.6185	−	7.28387i	0.915463	−	0.182097i
$41$	17.4732	−	26.1505i	0.426176	−	0.637817i	−0.554792	−	0.831989i	$-0.687202\pi$
$41$	17.4732	−	26.1505i	0.426176	−	0.637817i	0.980967	+	0.194172i	$0.0622021\pi$
$42$	0.849251	−	2.05027i	0.0202203	−	0.0488161i
$43$	67.3441	+	27.8948i	1.56614	+	0.648717i	0.986142	−	0.165901i	$-0.0530531\pi$
$43$	67.3441	+	27.8948i	1.56614	+	0.648717i	0.579999	+	0.814617i	$0.303053\pi$
$44$	−10.1423	−	6.77687i	−0.230507	−	0.154020i
$45$	9.39270	+	47.2203i	0.208727	+	1.04934i
$46$	23.9459	−	16.0002i	0.520564	−	0.347829i
$47$	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	$0.699562\pi$
$48$	−0.587825	+	2.95520i	−0.0122464	+	0.0615666i
$49$	3.82915	+	9.24438i	0.0781458	+	0.188661i
$50$			8.32041i			0.166408i
$51$		0			0
$52$	−5.66826			−0.109005
$53$	4.77624	−	1.97838i	0.0901178	−	0.0373280i	−0.337169	−	0.941444i	$-0.609469\pi$
$53$	4.77624	−	1.97838i	0.0901178	−	0.0373280i	0.427287	+	0.904116i	$0.359469\pi$
$54$	−6.26489	−	1.24616i	−0.116017	−	0.0230771i
$55$	−55.4053	+	55.4053i	−1.00737	+	1.00737i
$56$	24.1429	+	36.1324i	0.431123	+	0.645222i
$57$	3.96061	−	0.787813i	0.0694843	−	0.0138213i
$58$	−40.3544	+	60.3947i	−0.695766	+	1.04129i
$59$	10.8115	−	26.1013i	0.183246	−	0.442394i	−0.805386	−	0.592751i	$-0.798042\pi$
$59$	10.8115	−	26.1013i	0.183246	−	0.442394i	0.988632	+	0.150356i	$0.0480420\pi$
$60$	−0.669081	−	0.277142i	−0.0111513	−	0.00461904i
$61$	68.7144	+	45.9135i	1.12647	+	0.752680i	0.971921	−	0.235306i	$-0.0756092\pi$
$61$	68.7144	+	45.9135i	1.12647	+	0.752680i	0.154544	+	0.987986i	$0.450609\pi$
$62$	0.520891	+	2.61870i	0.00840147	+	0.0422370i
$63$	−46.5935	+	31.1328i	−0.739579	+	0.494171i
$64$	−32.2713	−	32.2713i	−0.504239	−	0.504239i
$65$	−7.10332	+	35.7108i	−0.109282	+	0.549397i
$66$	−1.98623	−	4.79518i	−0.0300944	−	0.0726543i
$67$		−	44.5324i		−	0.664663i	−0.943163	−	0.332332i	$-0.892165\pi$
$67$		−	44.5324i		−	0.664663i	0.943163	−	0.332332i	$-0.107835\pi$
$68$		0			0
$69$	2.11674			0.0306774
$70$	−68.0607	+	28.1917i	−0.972296	+	0.402738i
$71$	56.8410	+	11.3064i	0.800577	+	0.159245i	0.578391	−	0.815759i	$-0.303681\pi$
$71$	56.8410	+	11.3064i	0.800577	+	0.159245i	0.222186	+	0.975004i	$0.428681\pi$
$72$	44.1588	−	44.1588i	0.613317	−	0.613317i
$73$	−0.748576	−	1.12032i	−0.0102545	−	0.0153469i	0.826307	−	0.563220i	$-0.190438\pi$
$73$	−0.748576	−	1.12032i	−0.0102545	−	0.0153469i	−0.836561	+	0.547873i	$0.815438\pi$
$74$	−100.245	+	19.9400i	−1.35466	+	0.269460i
$75$	−0.339755	+	0.508479i	−0.00453007	+	0.00677973i
$76$	7.98612	−	19.2802i	0.105081	−	0.253687i
$77$	−84.2570	−	34.9004i	−1.09425	−	0.453252i
$78$	−2.00537	−	1.33995i	−0.0257099	−	0.0171788i
$79$	−5.79844	−	29.1507i	−0.0733979	−	0.368996i	0.926577	−	0.376106i	$-0.122737\pi$
$79$	−5.79844	−	29.1507i	−0.0733979	−	0.368996i	−0.999975	+	0.00710935i	$0.997737\pi$
$80$	83.1655	−	55.5694i	1.03957	−	0.694618i
$81$	56.7774	+	56.7774i	0.700956	+	0.700956i
$82$	13.4920	−	67.8290i	0.164537	−	0.827183i
$83$	−25.7951	−	62.2748i	−0.310784	−	0.750298i	−0.999676	−	0.0254351i	$-0.991903\pi$
$83$	−25.7951	−	62.2748i	−0.310784	−	0.750298i	0.688893	−	0.724863i	$-0.258097\pi$
$84$		−	0.842922i		−	0.0100348i
$85$		0			0
$86$	160.285			1.86377
$87$	−4.93230	+	2.04303i	−0.0566931	+	0.0234831i
$88$	99.6823	+	19.8280i	1.13275	+	0.225319i
$89$	−90.1397	+	90.1397i	−1.01281	+	1.01281i	−0.0128890	+	0.999917i	$0.504103\pi$
$89$	−90.1397	+	90.1397i	−1.01281	+	1.01281i	−0.999917	+	0.0128890i	$0.995897\pi$
$90$	58.8169	+	88.0256i	0.653521	+	0.978063i
$91$	−41.5646	+	8.26771i	−0.456754	+	0.0908540i
$92$	6.07736	−	9.09541i	0.0660582	−	0.0988632i
$93$	−0.0750988	+	0.181304i	−0.000807514	+	0.00194951i
$94$	30.1327	+	12.4814i	0.320561	+	0.132781i
$95$	−111.460	−	74.4751i	−1.17326	−	0.783949i
$96$	0.414892	+	2.08580i	0.00432180	+	0.0217271i
$97$	56.2374	−	37.5767i	0.579767	−	0.387388i	−0.230828	−	0.972995i	$-0.574144\pi$
$97$	56.2374	−	37.5767i	0.579767	−	0.387388i	0.810596	+	0.585606i	$0.199144\pi$
$98$	15.5581	+	15.5581i	0.158756	+	0.158756i
$99$	−25.5687	+	128.542i	−0.258269	+	1.29841i
$100$	1.20941	+	2.91979i	0.0120941	+	0.0291979i
$101$		−	34.6405i		−	0.342975i	−0.985186	−	0.171488i	$-0.945143\pi$
$101$		−	34.6405i		−	0.342975i	0.985186	−	0.171488i	$-0.0548573\pi$
$102$		0			0
$103$	151.166			1.46763			0.733817	−	0.679347i	$-0.237737\pi$
$103$	151.166			1.46763			0.733817	+	0.679347i	$0.237737\pi$
$104$	43.6333	−	18.0735i	0.419551	−	0.173784i
$105$	−5.31052	−	1.05633i	−0.0505764	−	0.0100603i
$106$	8.03830	−	8.03830i	0.0758330	−	0.0758330i
$107$	−5.29897	−	7.93047i	−0.0495231	−	0.0741166i	0.805882	−	0.592076i	$-0.201692\pi$
$107$	−5.29897	−	7.93047i	−0.0495231	−	0.0741166i	−0.855405	+	0.517960i	$0.826692\pi$
$108$	−2.37960	+	0.473332i	−0.0220334	+	0.00438271i
$109$	64.6303	−	96.7260i	0.592938	−	0.887395i	−0.406720	−	0.913553i	$-0.633327\pi$
$109$	64.6303	−	96.7260i	0.592938	−	0.887395i	0.999658	+	0.0261584i	$0.00832744\pi$
$110$	−65.9347	+	159.180i	−0.599406	+	1.44710i
$111$	−6.94044	−	2.87483i	−0.0625265	−	0.0258993i
$112$	96.7982	+	64.6785i	0.864270	+	0.577487i
$113$	−12.8663	−	64.6835i	−0.113861	−	0.572420i	−0.995026	−	0.0996113i	$-0.968240\pi$
$113$	−12.8663	−	64.6835i	−0.113861	−	0.572420i	0.881165	−	0.472809i	$-0.156760\pi$
$114$	7.38315	−	4.93327i	0.0647645	−	0.0432743i
$115$	−49.6863	−	49.6863i	−0.432055	−	0.432055i
$116$	−5.38243	+	27.0593i	−0.0464003	+	0.233270i
$117$	23.3062	+	56.2660i	0.199198	+	0.480906i
$118$		−	62.1233i		−	0.526468i
$119$		0			0
$120$	6.03416			0.0502847
$121$	−85.2709	+	35.3203i	−0.704718	+	0.291904i
$122$	178.231	+	35.4523i	1.46091	+	0.290593i
$123$	3.59425	−	3.59425i	0.0292216	−	0.0292216i
$124$	0.563431	+	0.843234i	0.00454380	+	0.00680027i
$125$	−111.639	+	22.2063i	−0.893109	+	0.177650i
$126$	−68.4583	+	102.455i	−0.543319	+	0.813135i
$127$	36.5576	−	88.2580i	0.287855	−	0.694945i	−0.712119	−	0.702059i	$-0.752264\pi$
$127$	36.5576	−	88.2580i	0.287855	−	0.694945i	0.999975	+	0.00711395i	$0.00226446\pi$
$128$	−141.344	−	58.5465i	−1.10425	−	0.457395i
$129$	9.79536	+	6.54505i	0.0759330	+	0.0507368i
$130$	15.6196	+	78.5249i	0.120151	+	0.604038i
$131$	−35.6683	+	23.8328i	−0.272277	+	0.181930i	−0.684211	−	0.729284i	$-0.739853\pi$
$131$	−35.6683	+	23.8328i	−0.272277	+	0.181930i	0.411934	+	0.911214i	$0.364853\pi$
$132$	−1.39401	−	1.39401i	−0.0105607	−	0.0105607i
$133$	30.4391	−	153.028i	0.228866	−	1.15058i
$134$	−37.4735	−	90.4690i	−0.279653	−	0.675142i
$135$			15.5850i			0.115444i
$136$		0			0
$137$	−63.8232			−0.465863			−0.232931	−	0.972493i	$-0.574832\pi$
$137$	−63.8232			−0.465863			−0.232931	+	0.972493i	$0.574832\pi$
$138$	4.30022	−	1.78121i	0.0311610	−	0.0129073i
$139$	−256.306	−	50.9824i	−1.84393	−	0.366780i	−0.855417	−	0.517940i	$-0.826699\pi$
$139$	−256.306	−	50.9824i	−1.84393	−	0.366780i	−0.988509	+	0.151160i	$0.951699\pi$
$140$	−19.7860	+	19.7860i	−0.141328	+	0.141328i
$141$	1.33181	+	1.99320i	0.00944549	+	0.0141362i
$142$	124.988	−	24.8617i	0.880200	−	0.175083i
$143$	−55.0658	+	82.4117i	−0.385075	+	0.576306i
$144$	64.0239	−	154.567i	0.444610	−	1.07338i
$145$	163.732	+	67.8201i	1.12919	+	0.467725i
$146$	−2.46349	−	1.64605i	−0.0168732	−	0.0112743i
$147$	0.315492	+	1.58608i	0.00214620	+	0.0107897i
$148$	−32.2795	+	21.5685i	−0.218105	+	0.145733i
$149$	83.6010	+	83.6010i	0.561080	+	0.561080i	0.929614	−	0.368534i	$-0.120140\pi$
$149$	83.6010	+	83.6010i	0.561080	+	0.561080i	−0.368534	+	0.929614i	$0.620140\pi$
$150$	−0.262344	+	1.31889i	−0.00174896	+	0.00879261i
$151$	10.5977	+	25.5851i	0.0701833	+	0.169437i	0.955079	−	0.296352i	$-0.0957703\pi$
$151$	10.5977	+	25.5851i	0.0701833	+	0.169437i	−0.884895	+	0.465790i	$0.845770\pi$
$152$			173.880i			1.14395i
$153$		0			0
$154$	−200.539			−1.30220
$155$	6.01857	−	2.49297i	0.0388295	−	0.0160837i
$156$	−0.898490	−	0.178721i	−0.00575955	−	0.00114565i
$157$	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	$0.168995\pi$
$158$	−36.3096	−	54.3412i	−0.229808	−	0.343932i
$159$	0.819474	−	0.163003i	0.00515392	−	0.00102518i
$160$	39.2214	−	58.6990i	0.245134	−	0.366869i
$161$	31.2979	−	75.5599i	0.194397	−	0.469316i
$162$	163.123	+	67.5676i	1.00693	+	0.417084i
$163$	46.1595	+	30.8428i	0.283187	+	0.189220i	0.689049	−	0.724715i	$-0.258029\pi$
$163$	46.1595	+	30.8428i	0.283187	+	0.189220i	−0.405862	+	0.913935i	$0.633029\pi$
$164$	−5.12469	−	25.7636i	−0.0312481	−	0.157095i
$165$	−10.5294	+	7.03551i	−0.0638144	+	0.0426394i
$166$	−104.807	−	104.807i	−0.631367	−	0.631367i
$167$	−10.0784	+	50.6674i	−0.0603495	+	0.303398i	−0.999157	−	0.0410439i	$-0.986932\pi$
$167$	−10.0784	+	50.6674i	−0.0603495	+	0.303398i	0.938808	+	0.344441i	$0.111932\pi$
$168$	2.68770	+	6.48868i	0.0159982	+	0.0386231i
$169$		−	122.942i		−	0.727470i
$170$		0			0
$171$	−224.222			−1.31124
$172$	56.2468	−	23.2982i	0.327016	−	0.135455i
$173$	−18.1162	−	3.60353i	−0.104718	−	0.0208296i	0.142453	−	0.989802i	$-0.454501\pi$
$173$	−18.1162	−	3.60353i	−0.104718	−	0.0208296i	−0.247171	+	0.968972i	$0.579501\pi$
$174$	−8.30094	+	8.30094i	−0.0477066	+	0.0477066i
$175$	13.1273	+	19.6464i	0.0750130	+	0.112265i
$176$	267.047	−	53.1190i	1.51731	−	0.301812i
$177$	2.53674	−	3.79649i	0.0143318	−	0.0214491i
$178$	−107.270	+	258.973i	−0.602641	+	1.45490i
$179$	−57.8989	−	23.9825i	−0.323457	−	0.133980i	0.215046	−	0.976604i	$-0.431010\pi$
$179$	−57.8989	−	23.9825i	−0.323457	−	0.133980i	−0.538503	+	0.842624i	$0.681010\pi$
$180$	33.4349	+	22.3405i	0.185749	+	0.124114i
$181$	20.4063	+	102.589i	0.112742	+	0.566792i	0.995321	+	0.0966274i	$0.0308055\pi$
$181$	20.4063	+	102.589i	0.112742	+	0.566792i	−0.882579	+	0.470165i	$0.844194\pi$
$182$	−77.4825	+	51.7722i	−0.425728	+	0.284462i
$183$	9.44444	+	9.44444i	0.0516090	+	0.0516090i
$184$	−17.7814	+	89.3930i	−0.0966378	+	0.485831i
$185$	95.4324	+	230.394i	0.515851	+	1.24537i
$186$			0.431520i			0.00232000i
$187$		0			0
$188$	12.3883			0.0658954
$189$	−16.7589	+	6.94177i	−0.0886715	+	0.0367289i
$190$	−289.104	−	57.5064i	−1.52160	−	0.302665i
$191$	137.930	−	137.930i	0.722145	−	0.722145i	−0.246897	−	0.969042i	$-0.579411\pi$
$191$	137.930	−	137.930i	0.722145	−	0.722145i	0.969042	+	0.246897i	$0.0794109\pi$
$192$	−4.09789	−	6.13293i	−0.0213432	−	0.0319423i
$193$	86.7045	−	17.2466i	0.449246	−	0.0893606i	0.0347181	−	0.999397i	$-0.488947\pi$
$193$	86.7045	−	17.2466i	0.449246	−	0.0893606i	0.414528	+	0.910037i	$0.363947\pi$
$194$	82.6278	−	123.661i	0.425916	−	0.637429i
$195$	−2.25193	+	5.43664i	−0.0115484	+	0.0278802i
$196$	7.72105	+	3.19816i	0.0393931	+	0.0163172i
$197$	−214.000	−	142.990i	−1.08629	−	0.725838i	−0.122495	−	0.992469i	$-0.539089\pi$
$197$	−214.000	−	142.990i	−1.08629	−	0.725838i	−0.963799	+	0.266631i	$0.914089\pi$
$198$	56.2232	+	282.653i	0.283956	+	1.42754i
$199$	−189.117	+	126.364i	−0.950338	+	0.634996i	−0.931079	−	0.364819i	$-0.881131\pi$
$199$	−189.117	+	126.364i	−0.950338	+	0.634996i	−0.0192597	+	0.999815i	$0.506131\pi$
$200$	−18.6198	−	18.6198i	−0.0930988	−	0.0930988i
$201$	1.40411	−	7.05896i	0.00698564	−	0.0351192i
$202$	−29.1495	−	70.3732i	−0.144305	−	0.348382i
$203$			206.273i			1.01612i
$204$		0			0
$205$	−168.736			−0.823103
$206$	307.099	−	127.204i	1.49077	−	0.617498i
$207$	−115.274	−	22.9294i	−0.556879	−	0.110770i
$208$	89.4660	−	89.4660i	0.430125	−	0.430125i
$209$	−202.735	−	303.414i	−0.970023	−	1.45174i
$210$	−11.6774	+	2.32277i	−0.0556065	+	0.0110608i
$211$	4.49332	−	6.72473i	0.0212954	−	0.0318708i	−0.820669	−	0.571404i	$-0.806399\pi$
$211$	4.49332	−	6.72473i	0.0212954	−	0.0318708i	0.841965	+	0.539533i	$0.181399\pi$
$212$	1.65238	−	3.98919i	0.00779423	−	0.0188169i
$213$	8.65353	+	3.58441i	0.0406269	+	0.0168282i
$214$	−17.4384	−	11.6520i	−0.0814879	−	0.0544485i
$215$	−76.2947	−	383.559i	−0.354859	−	1.78400i
$216$	16.8086	−	11.2311i	0.0778174	−	0.0519959i
$217$	5.36151	+	5.36151i	0.0247074	+	0.0247074i
$218$	49.9046	−	250.887i	0.228920	−	1.15086i
$219$	−0.0833348	−	0.201188i	−0.000380524	−	0.000918667i
$220$			65.4433i			0.297469i
$221$		0			0
$222$	−16.5188			−0.0744092
$223$	−45.3315	+	18.7769i	−0.203280	+	0.0842014i	−0.482001	−	0.876171i	$-0.660090\pi$
$223$	−45.3315	+	18.7769i	−0.203280	+	0.0842014i	0.278720	+	0.960372i	$0.410090\pi$
$224$	80.5902	+	16.0304i	0.359778	+	0.0715642i
$225$	24.0106	−	24.0106i	0.106714	−	0.106714i
$226$	−80.5687	−	120.580i	−0.356499	−	0.533538i
$227$	−164.831	+	32.7870i	−0.726129	+	0.144436i	−0.544296	−	0.838893i	$-0.683203\pi$
$227$	−164.831	+	32.7870i	−0.726129	+	0.144436i	−0.181833	+	0.983329i	$0.558203\pi$
$228$	1.87381	−	2.80435i	0.00821846	−	0.0122998i
$229$	47.5197	−	114.723i	0.207510	−	0.500972i	−0.785520	−	0.618836i	$-0.787605\pi$
$229$	47.5197	−	114.723i	0.207510	−	0.500972i	0.993030	+	0.117864i	$0.0376046\pi$
$230$	−142.750	−	59.1289i	−0.620651	−	0.257082i
$231$	−12.2554	−	8.18879i	−0.0530536	−	0.0354493i
$232$	−44.8469	−	225.460i	−0.193305	−	0.971812i
$233$	293.571	−	196.158i	1.25996	−	0.841880i	0.267396	−	0.963587i	$-0.413837\pi$
$233$	293.571	−	196.158i	1.25996	−	0.841880i	0.992566	+	0.121707i	$0.0388368\pi$
$234$	94.6943	+	94.6943i	0.404677	+	0.404677i
$235$	15.5248	−	78.0483i	0.0660628	−	0.332120i
$236$	−9.02993	−	21.8002i	−0.0382624	−	0.0923737i
$237$		−	4.80358i		−	0.0202683i
$238$		0			0
$239$	206.527			0.864131			0.432066	−	0.901842i	$-0.357785\pi$
$239$	206.527			0.864131			0.432066	+	0.901842i	$0.357785\pi$
$240$	14.9349	−	6.18624i	0.0622287	−	0.0257760i
$241$	282.496	+	56.1919i	1.17218	+	0.233161i	0.742517	−	0.669827i	$-0.233632\pi$
$241$	282.496	+	56.1919i	1.17218	+	0.233161i	0.429665	+	0.902989i	$0.358632\pi$
$242$	−143.509	+	143.509i	−0.593011	+	0.593011i
$243$	21.7347	+	32.5282i	0.0894430	+	0.133861i
$244$	67.6977	−	13.4659i	0.277450	−	0.0551881i
$245$	29.8247	−	44.6358i	0.121733	−	0.182187i
$246$	4.27731	−	10.3263i	0.0173875	−	0.0419770i
$247$	−156.662	−	64.8915i	−0.634259	−	0.262719i
$248$	−7.02589	−	4.69455i	−0.0283302	−	0.0189296i
$249$	−2.12531	−	10.6847i	−0.00853539	−	0.0429103i
$250$	−208.111	+	139.055i	−0.832444	+	0.556221i
$251$	−191.096	−	191.096i	−0.761337	−	0.761337i	0.215227	−	0.976564i	$-0.430951\pi$
$251$	−191.096	−	191.096i	−0.761337	−	0.761337i	−0.976564	+	0.215227i	$0.930951\pi$
$252$	−9.13089	+	45.9041i	−0.0362337	+	0.182159i
$253$	−73.1996	−	176.720i	−0.289327	−	0.698496i
$254$		−	210.062i		−	0.827014i
$255$		0			0
$256$	−153.856			−0.601002
$257$	48.7819	−	20.2061i	0.189813	−	0.0786230i	−0.285753	−	0.958303i	$-0.592244\pi$
$257$	48.7819	−	20.2061i	0.189813	−	0.0786230i	0.475565	+	0.879680i	$0.342244\pi$
$258$	25.4071	+	5.05380i	0.0984773	+	0.0195884i
$259$	−205.242	+	205.242i	−0.792439	+	0.792439i
$260$	16.8952	+	25.2854i	0.0649815	+	0.0972517i
$261$	290.736	−	57.8310i	1.11393	−	0.221575i
$262$	−52.4062	+	78.4315i	−0.200024	+	0.299357i
$263$	−194.228	+	468.907i	−0.738509	+	1.78292i	−0.126654	+	0.991947i	$0.540424\pi$
$263$	−194.228	+	468.907i	−0.738509	+	1.78292i	−0.611854	+	0.790970i	$0.709576\pi$
$264$	15.1757	+	6.28599i	0.0574838	+	0.0238106i
$265$	−23.0617	−	15.4094i	−0.0870254	−	0.0581485i
$266$	−66.9329	−	336.495i	−0.251628	−	1.26502i
$267$	−17.1304	+	11.4462i	−0.0641588	+	0.0428696i
$268$	−26.3003	−	26.3003i	−0.0981353	−	0.0981353i
$269$	34.3858	−	172.869i	0.127828	−	0.642637i	−0.862743	−	0.505642i	$-0.831256\pi$
$269$	34.3858	−	172.869i	0.127828	−	0.642637i	0.990572	−	0.136995i	$-0.0437443\pi$
$270$	13.1146	+	31.6614i	0.0485725	+	0.117264i
$271$			464.255i			1.71312i	0.516050	+	0.856559i	$0.327402\pi$
$271$			464.255i			1.71312i	−0.516050	+	0.856559i	$0.672598\pi$
$272$		0			0
$273$	−6.84919			−0.0250886
$274$	−129.659	+	53.7064i	−0.473207	+	0.196009i
$275$	54.2004	+	10.7811i	0.197093	+	0.0392041i
$276$	1.25012	−	1.25012i	0.00452941	−	0.00452941i
$277$	98.1048	+	146.824i	0.354169	+	0.530051i	0.965185	−	0.261567i	$-0.0842391\pi$
$277$	98.1048	+	146.824i	0.354169	+	0.530051i	−0.611017	+	0.791618i	$0.709239\pi$
$278$	−563.594	+	112.106i	−2.02732	+	0.403258i
$279$	6.05372	−	9.06003i	0.0216979	−	0.0324732i
$280$	89.2206	−	215.398i	0.318645	−	0.769277i
$281$	−369.073	−	152.875i	−1.31343	−	0.544040i	−0.387545	−	0.921851i	$-0.626677\pi$
$281$	−369.073	−	152.875i	−1.31343	−	0.544040i	−0.925883	+	0.377811i	$0.876677\pi$
$282$	4.38287	+	2.92854i	0.0155421	+	0.0103849i
$283$	69.7677	+	350.746i	0.246529	+	1.23938i	0.883476	+	0.468477i	$0.155197\pi$
$283$	69.7677	+	350.746i	0.246529	+	1.23938i	−0.636947	+	0.770908i	$0.719803\pi$
$284$	40.2469	−	26.8921i	0.141715	−	0.0946906i
$285$	−15.3196	−	15.3196i	−0.0537530	−	0.0537530i
$286$	−42.5193	+	213.759i	−0.148669	+	0.747409i
$287$	−75.1574	−	181.446i	−0.261872	−	0.632216i
$288$		−	118.084i		−	0.410013i
$289$		0			0
$290$	389.697			1.34378
$291$	10.0991	−	4.18320i	0.0347050	−	0.0143753i
$292$	−1.10375	−	0.219549i	−0.00377995	−	0.000751880i
$293$	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	$0.116275\pi$
$294$	1.97560	+	2.95670i	0.00671973	+	0.0100568i
$295$	−148.660	+	29.5704i	−0.503933	+	0.100239i
$296$	179.710	−	268.955i	0.607129	−	0.908633i
$297$	−16.2354	+	39.1958i	−0.0546647	+	0.131972i
$298$	240.187	+	99.4888i	0.805997	+	0.333855i
$299$	−73.9051	−	49.3818i	−0.247174	−	0.165157i
$300$	0.0996463	+	0.500956i	0.000332154	+	0.00166985i
$301$	378.468	−	252.884i	1.25737	−	0.840147i
$302$	43.0590	+	43.0590i	0.142579	+	0.142579i
$303$	1.09222	−	5.49096i	0.00360468	−	0.0181220i
$304$	178.262	+	430.363i	0.586389	+	1.41567i
$305$		−	443.380i		−	1.45370i
$306$		0			0
$307$	409.955			1.33536			0.667679	−	0.744450i	$-0.267288\pi$
$307$	409.955			1.33536			0.667679	+	0.744450i	$0.267288\pi$
$308$	−70.3727	+	29.1493i	−0.228483	+	0.0946407i
$309$	23.9618	+	4.76629i	0.0775462	+	0.0154249i
$310$	10.1291	−	10.1291i	0.0326745	−	0.0326745i
$311$	120.340	+	180.101i	0.386944	+	0.579103i	0.972896	−	0.231243i	$-0.0742793\pi$
$311$	120.340	+	180.101i	0.386944	+	0.579103i	−0.585952	+	0.810346i	$0.699279\pi$
$312$	7.48629	−	1.48912i	0.0239945	−	0.00477281i
$313$	−263.015	+	393.629i	−0.840302	+	1.25760i	0.123863	+	0.992299i	$0.460472\pi$
$313$	−263.015	+	393.629i	−0.840302	+	1.25760i	−0.964165	+	0.265302i	$0.914528\pi$
$314$	66.5184	−	160.590i	0.211842	−	0.511432i
$315$	277.759	+	115.052i	0.881776	+	0.365244i
$316$	−20.6405	−	13.7915i	−0.0653180	−	0.0436441i
$317$	50.0110	+	251.422i	0.157763	+	0.793130i	0.975919	+	0.218133i	$0.0699967\pi$
$317$	50.0110	+	251.422i	0.157763	+	0.793130i	−0.818156	+	0.574997i	$0.805003\pi$
$318$	1.52762	−	1.02072i	0.00480384	−	0.00320982i
$319$	341.131	+	341.131i	1.06938	+	1.06938i
$320$	−47.7685	+	240.149i	−0.149277	+	0.750464i
$321$	−0.589905	−	1.42416i	−0.00183771	−	0.00443663i
$322$		−	179.839i		−	0.558506i
$323$		0			0
$324$	67.0640			0.206988
$325$	23.7248	−	9.82715i	0.0729995	−	0.0302374i
$326$	119.728	+	23.8154i	0.367265	+	0.0730535i
$327$	13.2945	−	13.2945i	0.0406560	−	0.0406560i
$328$	121.597	+	181.983i	0.370724	+	0.554828i
$329$	90.8421	−	18.0696i	0.276116	−	0.0549229i
$330$	−15.4705	+	23.1532i	−0.0468802	+	0.0701612i
$331$	86.3966	−	208.580i	0.261017	−	0.630151i	−0.737985	−	0.674817i	$-0.764222\pi$
$331$	86.3966	−	208.580i	0.261017	−	0.630151i	0.999002	+	0.0446663i	$0.0142225\pi$
$332$	−52.0129	−	21.5444i	−0.156665	−	0.0648929i
$333$	346.823	+	231.740i	1.04151	+	0.695916i
$334$	22.1615	+	111.413i	0.0663516	+	0.333572i
$335$	−198.654	+	132.736i	−0.592997	+	0.396228i
$336$	13.3044	+	13.3044i	0.0395965	+	0.0395965i
$337$	−70.4547	+	354.200i	−0.209064	+	1.05104i	0.723580	+	0.690241i	$0.242495\pi$
$337$	−70.4547	+	354.200i	−0.209064	+	1.05104i	−0.932644	+	0.360797i	$0.882505\pi$
$338$	−103.454	−	249.761i	−0.306078	−	0.738938i
$339$		−	10.6588i		−	0.0314420i
$340$		0			0
$341$	17.7335			0.0520045
$342$	−455.513	+	188.680i	−1.33191	+	0.551695i
$343$	361.384	+	71.8838i	1.05360	+	0.209574i
$344$	−358.691	+	358.691i	−1.04271	+	1.04271i
$345$	−6.30930	−	9.44253i	−0.0182878	−	0.0273697i
$346$	−39.8358	+	7.92384i	−0.115132	+	0.0229013i
$347$	8.81030	−	13.1855i	0.0253899	−	0.0379987i	−0.818558	−	0.574425i	$-0.805226\pi$
$347$	8.81030	−	13.1855i	0.0253899	−	0.0379987i	0.843947	+	0.536426i	$0.180226\pi$
$348$	−1.70637	+	4.11954i	−0.00490336	+	0.0118377i
$349$	292.270	+	121.062i	0.837448	+	0.346883i	0.759847	−	0.650102i	$-0.225274\pi$
$349$	292.270	+	121.062i	0.837448	+	0.346883i	0.0776015	+	0.996984i	$0.475274\pi$
$350$	43.2006	+	28.8657i	0.123430	+	0.0824735i
$351$	3.84608	+	19.3356i	0.0109575	+	0.0550870i
$352$	159.789	−	106.768i	0.453947	−	0.303318i
$353$	−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	$0.875394\pi$
$354$	1.95875	−	9.84732i	0.00553320	−	0.0278173i
$355$	−118.988	−	287.262i	−0.335177	−	0.809188i
$356$			106.471i			0.299075i
$357$		0			0
$358$	−137.804			−0.384928
$359$	−146.269	+	60.5865i	−0.407434	+	0.168765i	−0.576981	−	0.816757i	$-0.695769\pi$
$359$	−146.269	+	60.5865i	−0.407434	+	0.168765i	0.169547	+	0.985522i	$0.445769\pi$
$360$	−328.610	−	65.3646i	−0.912806	−	0.181568i
$361$	186.183	−	186.183i	0.515743	−	0.515743i
$362$	127.784	+	191.242i	0.352994	+	0.528292i
$363$	−14.6302	+	2.91012i	−0.0403035	+	0.00801686i
$364$	−19.6647	+	29.4303i	−0.0540239	+	0.0808524i
$365$	−2.76638	+	6.67862i	−0.00757911	+	0.0182976i
$366$	27.1340	+	11.2393i	0.0741367	+	0.0307084i
$367$	406.581	+	271.669i	1.10785	+	0.740242i	0.968254	−	0.249967i	$-0.0804197\pi$
$367$	406.581	+	271.669i	1.10785	+	0.740242i	0.139596	+	0.990209i	$0.455420\pi$
$368$	47.6360	+	239.482i	0.129446	+	0.650767i
$369$	−234.671	+	156.802i	−0.635966	+	0.424939i
$370$	387.748	+	387.748i	1.04797	+	1.04797i
$371$	6.29804	−	31.6624i	0.0169759	−	0.0853434i
$372$	0.0627237	+	0.151428i	0.000168612	+	0.000407065i
$373$		−	573.453i		−	1.53741i	−0.639605	−	0.768704i	$-0.720902\pi$
$373$		−	573.453i		−	1.53741i	0.639605	−	0.768704i	$-0.279098\pi$
$374$		0			0
$375$	−18.3963			−0.0490568
$376$	−95.3635	+	39.5008i	−0.253626	+	0.105055i
$377$	219.872	+	43.7352i	0.583214	+	0.116008i
$378$	−28.2048	+	28.2048i	−0.0746159	+	0.0746159i
$379$	390.013	+	583.696i	1.02906	+	1.54009i	0.828168	+	0.560480i	$0.189383\pi$
$379$	390.013	+	583.696i	1.02906	+	1.54009i	0.200890	+	0.979614i	$0.435617\pi$
$380$	−109.811	+	21.8427i	−0.288976	+	0.0574808i
$381$	8.57764	−	12.8373i	0.0225135	−	0.0336938i
$382$	164.142	−	396.274i	0.429692	−	1.03737i
$383$	284.935	+	118.024i	0.743956	+	0.308157i	0.722273	−	0.691608i	$-0.243098\pi$
$383$	284.935	+	118.024i	0.743956	+	0.308157i	0.0216830	+	0.999765i	$0.493098\pi$
$384$	−20.5588	−	13.7370i	−0.0535386	−	0.0357733i
$385$	95.4555	+	479.887i	0.247936	+	1.24646i
$386$	161.630	−	107.998i	0.418731	−	0.279787i
$387$	−462.540	−	462.540i	−1.19519	−	1.19519i
$388$	11.0208	−	55.4053i	0.0284041	−	0.142797i
$389$	109.097	+	263.382i	0.280454	+	0.677076i	0.999846	−	0.0175282i	$-0.00557969\pi$
$389$	109.097	+	263.382i	0.280454	+	0.677076i	−0.719392	+	0.694604i	$0.755580\pi$
$390$			12.9397i			0.0331787i
$391$		0			0
$392$	−69.6329			−0.177635
$393$	−6.40533	+	2.65317i	−0.0162986	+	0.00675108i
$394$	−555.071	−	110.411i	−1.40881	−	0.280230i
$395$	−112.755	+	112.755i	−0.285455	+	0.285455i
$396$	60.8149	+	91.0159i	0.153573	+	0.229838i
$397$	121.959	−	24.2591i	0.307201	−	0.0611061i	−0.0390826	−	0.999236i	$-0.512444\pi$
$397$	121.959	−	24.2591i	0.307201	−	0.0611061i	0.346283	+	0.938130i	$0.387444\pi$
$398$	−277.864	+	415.852i	−0.698150	+	1.04486i
$399$	9.64997	−	23.2971i	0.0241854	−	0.0583887i
$400$	−65.1740	−	26.9960i	−0.162935	−	0.0674899i
$401$	355.016	+	237.214i	0.885328	+	0.591557i	0.912955	−	0.408061i	$-0.133795\pi$
$401$	355.016	+	237.214i	0.885328	+	0.591557i	−0.0276268	+	0.999618i	$0.508795\pi$
$402$	−3.08752	−	15.5220i	−0.00768041	−	0.0386120i
$403$	6.85173	−	4.57818i	0.0170018	−	0.0113602i
$404$	−20.4582	−	20.4582i	−0.0506391	−	0.0506391i
$405$	84.0429	−	422.512i	0.207513	−	1.04324i
$406$	173.576	+	419.050i	0.427528	+	1.03214i
$407$			678.850i			1.66794i
$408$		0			0
$409$	−215.550			−0.527018			−0.263509	−	0.964657i	$-0.584880\pi$
$409$	−215.550			−0.527018			−0.263509	+	0.964657i	$0.584880\pi$
$410$	−342.793	+	141.989i	−0.836079	+	0.346315i
$411$	−10.1168	−	2.01235i	−0.0246150	−	0.00489624i
$412$	89.2768	−	89.2768i	0.216691	−	0.216691i
$413$	−98.0131	−	146.687i	−0.237320	−	0.355174i
$414$	−253.477	+	50.4198i	−0.612264	+	0.121787i
$415$	−200.914	+	300.689i	−0.484130	+	0.724552i
$416$	34.1743	−	82.5042i	0.0821499	−	0.198327i
$417$	−39.0202	−	16.1627i	−0.0935737	−	0.0387595i
$418$	−667.181	−	445.796i	−1.59613	−	1.06650i
$419$	−121.382	−	610.227i	−0.289694	−	1.45639i	−0.801864	−	0.597506i	$-0.796158\pi$
$419$	−121.382	−	610.227i	−0.289694	−	1.45639i	0.512170	−	0.858884i	$-0.328842\pi$
$420$	−3.76018	+	2.51247i	−0.00895280	+	0.00598207i
$421$	36.3708	+	36.3708i	0.0863916	+	0.0863916i	0.748982	−	0.662590i	$-0.230543\pi$
$421$	36.3708	+	36.3708i	0.0863916	+	0.0863916i	−0.662590	+	0.748982i	$0.730543\pi$
$422$	3.46954	−	17.4426i	0.00822166	−	0.0413331i
$423$	−50.9371	−	122.973i	−0.120419	−	0.290717i
$424$			35.9769i			0.0848511i
$425$		0			0
$426$	20.5961			0.0483477
$427$	476.777	−	197.488i	1.11657	−	0.462500i
$428$	−7.81313	−	1.55413i	−0.0182550	−	0.00363114i
$429$	−11.3271	+	11.3271i	−0.0264034	+	0.0264034i
$430$	−477.755	−	715.011i	−1.11106	−	1.66282i
$431$	461.572	−	91.8124i	1.07093	−	0.213022i	0.372017	−	0.928226i	$-0.378666\pi$
$431$	461.572	−	91.8124i	1.07093	−	0.213022i	0.698916	+	0.715204i	$0.253666\pi$
$432$	30.0880	−	45.0299i	0.0696481	−	0.104236i
$433$	−246.289	+	594.595i	−0.568798	+	1.37320i	0.333772	+	0.942654i	$0.391679\pi$
$433$	−246.289	+	594.595i	−0.568798	+	1.37320i	−0.902569	+	0.430545i	$0.858321\pi$
$434$	15.4037	+	6.38042i	0.0354924	+	0.0147014i
$435$	23.8153	+	15.9129i	0.0547477	+	0.0365813i
$436$	−18.9553	−	95.2948i	−0.0434755	−	0.218566i
$437$	272.095	−	181.808i	0.622644	−	0.416037i
$438$	−0.338594	−	0.338594i	−0.000773047	−	0.000773047i
$439$	−161.428	+	811.551i	−0.367717	+	1.84864i	0.144129	+	0.989559i	$0.453962\pi$
$439$	−161.428	+	811.551i	−0.367717	+	1.84864i	−0.511846	+	0.859077i	$0.671038\pi$
$440$	−208.669	−	503.772i	−0.474248	−	1.14494i
$441$		−	89.7930i		−	0.203612i
$442$		0			0
$443$	354.430			0.800068			0.400034	−	0.916500i	$-0.368998\pi$
$443$	354.430			0.800068			0.400034	+	0.916500i	$0.368998\pi$
$444$	−5.79677	+	2.40110i	−0.0130558	+	0.00540788i
$445$	670.780	+	133.426i	1.50737	+	0.299835i
$446$	−76.2917	+	76.2917i	−0.171058	+	0.171058i
$447$	10.6159	+	15.8878i	0.0237491	+	0.0355431i
$448$	−279.514	+	55.5988i	−0.623916	+	0.124105i
$449$	436.647	−	653.488i	0.972487	−	1.45543i	0.0840341	−	0.996463i	$-0.473220\pi$
$449$	436.647	−	653.488i	0.972487	−	1.45543i	0.888453	−	0.458967i	$-0.151780\pi$
$450$	28.5736	−	68.9828i	0.0634969	−	0.153295i
$451$	−424.366	−	175.778i	−0.940945	−	0.389752i
$452$	−45.7999	−	30.6025i	−0.101327	−	0.0677047i
$453$	0.873166	+	4.38970i	0.00192752	+	0.00969029i
$454$	−307.270	+	205.311i	−0.676806	+	0.452227i
$455$	160.772	+	160.772i	0.353344	+	0.353344i
$456$	−5.48246	+	27.5622i	−0.0120229	+	0.0604434i
$457$	124.426	+	300.390i	0.272266	+	0.657309i	0.999580	−	0.0289968i	$-0.00923125\pi$
$457$	124.426	+	300.390i	0.272266	+	0.657309i	−0.727313	+	0.686306i	$0.759231\pi$
$458$		−	273.050i		−	0.596178i
$459$		0			0
$460$	−58.6882			−0.127583
$461$	227.477	−	94.2242i	0.493444	−	0.204391i	−0.122064	−	0.992522i	$-0.538951\pi$
$461$	227.477	−	94.2242i	0.493444	−	0.204391i	0.615507	+	0.788131i	$0.288951\pi$
$462$	−31.7879	−	6.32302i	−0.0688051	−	0.0136862i
$463$	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	$0.126317\pi$
$464$	−342.141	−	512.051i	−0.737374	−	1.10356i
$465$	1.03262	−	0.205401i	0.00222069	−	0.000441724i
$466$	431.334	−	645.537i	0.925610	−	1.38527i
$467$	−83.7591	+	202.212i	−0.179356	+	0.433003i	−0.987832	−	0.155526i	$-0.950293\pi$
$467$	−83.7591	+	202.212i	−0.179356	+	0.433003i	0.808476	+	0.588529i	$0.200293\pi$
$468$	46.9943	+	19.4657i	0.100415	+	0.0415933i
$469$	−231.218	−	154.495i	−0.493002	−	0.329413i
$470$	−34.1376	−	171.621i	−0.0726332	−	0.365152i
$471$	10.6226	−	7.09779i	0.0225533	−	0.0150696i
$472$	139.022	+	139.022i	0.294538	+	0.294538i
$473$	207.688	−	1044.12i	0.439087	−	2.20744i
$474$	−4.04215	−	9.75862i	−0.00852775	−	0.0205878i
$475$			94.5441i			0.199040i
$476$		0			0
$477$	−46.3929			−0.0972597
$478$	419.566	−	173.790i	0.877754	−	0.363578i
$479$	−492.815	−	98.0271i	−1.02884	−	0.204649i	−0.348319	−	0.937376i	$-0.613247\pi$
$479$	−492.815	−	98.0271i	−1.02884	−	0.204649i	−0.680523	+	0.732727i	$0.738247\pi$
$480$	8.06788	−	8.06788i	0.0168081	−	0.0168081i
$481$	175.255	+	262.288i	0.364356	+	0.545298i
$482$	621.183	−	123.561i	1.28876	−	0.256351i
$483$	7.34353	−	10.9904i	0.0152040	−	0.0227544i
$484$	−29.5001	+	71.2196i	−0.0609506	+	0.147148i
$485$	−335.250	−	138.865i	−0.691238	−	0.286320i
$486$	71.5267	+	47.7926i	0.147174	+	0.0983387i
$487$	−49.1210	−	246.948i	−0.100864	−	0.507080i	−0.997880	−	0.0650809i	$-0.979269\pi$
$487$	−49.1210	−	246.948i	−0.100864	−	0.507080i	0.897016	−	0.441999i	$-0.145731\pi$
$488$	−478.189	+	319.516i	−0.979896	+	0.654745i
$489$	6.34439	+	6.34439i	0.0129742	+	0.0129742i
$490$	23.0293	−	115.776i	0.0469986	−	0.236278i
$491$	−86.6215	−	209.123i	−0.176418	−	0.425912i	0.810792	−	0.585334i	$-0.199037\pi$
$491$	−86.6215	−	209.123i	−0.176418	−	0.425912i	−0.987210	+	0.159423i	$0.949037\pi$
$492$		−	4.24543i		−	0.00862893i
$493$		0			0
$494$	−372.869			−0.754796
$495$	649.624	−	269.083i	1.31237	−	0.543602i
$496$	−22.2024	−	4.41633i	−0.0447628	−	0.00890388i
$497$	255.901	−	255.901i	0.514891	−	0.514891i
$498$	−13.3086	−	19.9178i	−0.0267242	−	0.0399956i
$499$	−211.701	+	42.1099i	−0.424250	+	0.0843886i	−0.402598	−	0.915377i	$-0.631893\pi$
$499$	−211.701	+	42.1099i	−0.424250	+	0.0843886i	−0.0216522	+	0.999766i	$0.506893\pi$
$500$	−52.8175	+	79.0470i	−0.105635	+	0.158094i
$501$	−3.19510	+	7.71365i	−0.00637744	+	0.0153965i
$502$	−549.021	−	227.412i	−1.09367	−	0.453012i
$503$	−733.755	−	490.279i	−1.45876	−	0.974710i	−0.996105	−	0.0881697i	$-0.971898\pi$
$503$	−733.755	−	490.279i	−1.45876	−	0.974710i	−0.462651	−	0.886540i	$-0.653102\pi$
$504$	−76.0793	−	382.477i	−0.150951	−	0.758882i
$505$	−154.527	+	103.252i	−0.305994	+	0.204459i
$506$	−297.414	−	297.414i	−0.587776	−	0.587776i
$507$	3.87639	−	19.4879i	0.00764574	−	0.0384377i
$508$	−30.5335	−	73.7144i	−0.0601053	−	0.145107i
$509$			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
$512$	252.811	−	104.718i	0.493772	−	0.204527i
$513$	−71.1874	−	14.1601i	−0.138767	−	0.0276025i
$514$	82.0986	−	82.0986i	0.159725	−	0.159725i
$515$	−450.576	−	674.335i	−0.874906	−	1.30939i
$516$	9.65043	−	1.91959i	0.0187024	−	0.00372013i
$517$	120.350	−	180.116i	0.232785	−	0.348387i
$518$	−244.246	+	589.663i	−0.471518	+	1.13835i
$519$	−2.75802	−	1.14241i	−0.00531411	−	0.00220117i
$520$	−210.680	−	140.772i	−0.405154	−	0.270716i
$521$	19.7317	+	99.1978i	0.0378727	+	0.190399i	0.995090	−	0.0989697i	$-0.0315547\pi$
$521$	19.7317	+	99.1978i	0.0378727	+	0.190399i	−0.957218	+	0.289369i	$0.906555\pi$
$522$	541.975	−	362.136i	1.03827	−	0.693747i
$523$	−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	$0.929380\pi$
$524$	−6.98989	+	35.1406i	−0.0133395	+	0.0670621i
$525$	1.46139	+	3.52810i	0.00278360	+	0.00672019i
$526$			1116.04i			2.12175i
$527$		0			0
$528$	44.0052			0.0833432
$529$	−330.254	+	136.796i	−0.624299	+	0.258593i
$530$	−59.8174	−	11.8984i	−0.112863	−	0.0224499i
$531$	−179.272	+	179.272i	−0.337611	+	0.337611i
$532$	−72.3992	−	108.353i	−0.136089	−	0.203671i
$533$	−209.343	+	41.6409i	−0.392763	+	0.0781255i
$534$	−25.1691	+	37.6683i	−0.0471332	+	0.0705398i
$535$	−19.5824	+	47.2762i	−0.0366027	+	0.0883667i
$536$	286.315	+	118.596i	0.534170	+	0.221260i
$537$	−8.42153	−	5.62709i	−0.0156826	−	0.0104788i
$538$	−75.6114	−	380.124i	−0.140542	−	0.706551i
$539$	121.507	−	81.1882i	0.225430	−	0.150628i
$540$	9.20429	+	9.20429i	0.0170450	+	0.0170450i
$541$	−7.96429	+	40.0392i	−0.0147214	+	0.0740095i	−0.987448	−	0.157947i	$-0.949513\pi$
$541$	−7.96429	+	40.0392i	−0.0147214	+	0.0740095i	0.972726	+	0.231956i	$0.0745126\pi$
$542$	390.665	+	943.148i	0.720783	+	1.74012i
$543$			16.9051i			0.0311328i
$544$		0			0
$545$	−624.125			−1.14518
$546$	−13.9143	+	5.76351i	−0.0254841	+	0.0105559i
$547$	−66.7811	−	13.2836i	−0.122086	−	0.0242844i	0.133669	−	0.991026i	$-0.457324\pi$
$547$	−66.7811	−	13.2836i	−0.122086	−	0.0242844i	−0.255755	+	0.966742i	$0.582324\pi$
$548$	−37.6931	+	37.6931i	−0.0687830	+	0.0687830i
$549$	−412.022	−	616.635i	−0.750496	−	1.12320i
$550$	119.182	−	23.7068i	0.216695	−	0.0431032i
$551$	−458.544	+	686.260i	−0.832203	+	1.24548i
$552$	−5.63714	+	13.6093i	−0.0102122	+	0.0246545i
$553$	−171.470	−	71.0254i	−0.310073	−	0.128436i
$554$	322.853	+	215.724i	0.582768	+	0.389393i
$555$	7.86289	+	39.5294i	0.0141674	+	0.0712242i
$556$	−181.480	+	121.261i	−0.326403	+	0.218096i
$557$	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	$0.664599\pi$
$558$	4.67441	−	23.4999i	0.00837708	−	0.0421144i
$559$	−189.310	−	457.036i	−0.338659	−	0.817595i
$560$		−	624.591i		−	1.11534i
$561$		0			0
$562$	−878.426			−1.56304
$563$	−408.295	+	169.121i	−0.725212	+	0.300393i	−0.714583	−	0.699551i	$-0.753384\pi$
$563$	−408.295	+	169.121i	−0.725212	+	0.300393i	−0.0106294	+	0.999944i	$0.503384\pi$
$564$	1.96371	+	0.390606i	0.00348175	+	0.000692564i
$565$	−250.195	+	250.195i	−0.442824	+	0.442824i
$566$	436.883	+	653.842i	0.771879	+	1.15520i
$567$	491.772	−	97.8195i	0.867322	−	0.172521i
$568$	−224.067	+	335.341i	−0.394485	+	0.590388i
$569$	246.656	−	595.479i	0.433490	−	1.04654i	−0.544664	−	0.838654i	$-0.683343\pi$
$569$	246.656	−	595.479i	0.433490	−	1.04654i	0.978154	−	0.207882i	$-0.0666571\pi$
$570$	−44.0135	−	18.2310i	−0.0772166	−	0.0319842i
$571$	99.5967	+	66.5484i	0.174425	+	0.116547i	0.639718	−	0.768610i	$-0.279051\pi$
$571$	99.5967	+	66.5484i	0.174425	+	0.116547i	−0.465293	+	0.885157i	$0.654051\pi$
$572$	16.1502	+	81.1924i	0.0282346	+	0.141945i
$573$	26.2125	−	17.5147i	0.0457461	−	0.0305666i
$574$	−305.369	−	305.369i	−0.532002	−	0.532002i
$575$	−9.66830	+	48.6058i	−0.0168144	+	0.0845319i
$576$	156.730	+	378.379i	0.272100	+	0.656908i
$577$		−	177.008i		−	0.306773i	−0.988166	−	0.153387i	$-0.950982\pi$
$577$		−	177.008i		−	0.306773i	0.988166	−	0.153387i	$-0.0490180\pi$
$578$		0			0
$579$	14.2876			0.0246763
$580$	136.752	−	56.6444i	0.235779	−	0.0976628i
$581$	−412.828	−	82.1166i	−0.710548	−	0.141337i
$582$	16.9966	−	16.9966i	0.0292038	−	0.0292038i
$583$	−41.9471	−	62.7783i	−0.0719504	−	0.107681i
$584$	9.19651	−	1.82930i	0.0157474	−	0.00313236i
$585$	181.528	−	271.677i	0.310305	−	0.464404i
$586$	201.120	−	485.547i	0.343208	−	0.828578i
$587$	577.480	+	239.200i	0.983781	+	0.407496i	0.815825	−	0.578299i	$-0.196283\pi$
$587$	577.480	+	239.200i	0.983781	+	0.407496i	0.167956	+	0.985794i	$0.446283\pi$
$588$	1.12305	+	0.750395i	0.00190994	+	0.00127618i
$589$	5.91884	+	29.7560i	0.0100490	+	0.0505195i
$590$	−277.125	+	185.169i	−0.469703	+	0.313845i
$591$	−29.4132	−	29.4132i	−0.0497685	−	0.0497685i
$592$	169.060	−	849.920i	0.285574	−	1.43568i
$593$	−57.3899	−	138.551i	−0.0967789	−	0.233645i	0.868074	−	0.496434i	$-0.165358\pi$
$593$	−57.3899	−	138.551i	−0.0967789	−	0.233645i	−0.964853	+	0.262789i	$0.915358\pi$
$594$			93.2893i			0.157053i
$595$		0			0
$596$	98.7472			0.165683
$597$	−33.9618	+	14.0674i	−0.0568874	+	0.0235635i
$598$	−191.695	−	38.1304i	−0.320560	−	0.0637633i
$599$	217.159	−	217.159i	0.362536	−	0.362536i	−0.502210	−	0.864746i	$-0.667480\pi$
$599$	217.159	−	217.159i	0.362536	−	0.362536i	0.864746	+	0.502210i	$0.167480\pi$
$600$	−2.36438	−	3.53855i	−0.00394064	−	0.00589759i
$601$	398.467	−	79.2601i	0.663007	−	0.131880i	0.147895	−	0.989003i	$-0.452750\pi$
$601$	398.467	−	79.2601i	0.663007	−	0.131880i	0.515112	+	0.857123i	$0.327750\pi$
$602$	556.070	−	832.218i	0.923705	−	1.38242i
$603$	−152.931	+	369.209i	−0.253617	+	0.612287i
$604$	21.3690	+	8.85135i	0.0353792	+	0.0146545i
$605$	411.724	+	275.105i	0.680536	+	0.454719i
$606$	−2.40169	−	12.0741i	−0.00396319	−	0.0199243i
$607$	−862.312	+	576.178i	−1.42061	+	0.949223i	−0.421511	+	0.906823i	$0.638500\pi$
$607$	−862.312	+	576.178i	−1.42061	+	0.949223i	−0.999101	+	0.0423995i	$0.986500\pi$
$608$	232.484	+	232.484i	0.382374	+	0.382374i
$609$	−6.50382	+	32.6969i	−0.0106795	+	0.0536895i
$610$	−373.099	−	900.740i	−0.611637	−	1.47662i
$611$		−	100.662i		−	0.164750i
$612$		0			0
$613$	132.402			0.215991			0.107995	−	0.994151i	$-0.465557\pi$
$613$	132.402			0.215991			0.107995	+	0.994151i	$0.465557\pi$
$614$	832.835	−	344.972i	1.35641	−	0.561843i
$615$	−26.7468	−	5.32027i	−0.0434908	−	0.00865085i
$616$	448.774	−	448.774i	0.728529	−	0.728529i
$617$	142.375	+	213.080i	0.230754	+	0.345348i	0.928719	−	0.370784i	$-0.120911\pi$
$617$	142.375	+	213.080i	0.230754	+	0.345348i	−0.697965	+	0.716132i	$0.745911\pi$
$618$	52.6898	−	10.4807i	0.0852586	−	0.0169590i
$619$	−51.0630	+	76.4213i	−0.0824928	+	0.123459i	−0.870421	−	0.492307i	$-0.836154\pi$
$619$	−51.0630	+	76.4213i	−0.0824928	+	0.123459i	0.787929	+	0.615767i	$0.211154\pi$
$620$	2.08217	−	5.02680i	0.00335834	−	0.00810774i
$621$	−35.1499	−	14.5596i	−0.0566021	−	0.0234454i
$622$	396.026	+	264.616i	0.636698	+	0.425428i
$623$	155.298	+	780.735i	0.249274	+	1.25319i
$624$	17.0024	−	11.3606i	0.0272474	−	0.0182061i
$625$	498.708	+	498.708i	0.797932	+	0.797932i
$626$	−203.088	+	1020.99i	−0.324422	+	1.63098i
$627$	−22.5694	−	54.4872i	−0.0359958	−	0.0869015i
$628$		−	66.0226i		−	0.105131i
$629$		0			0
$630$	661.091			1.04935
$631$	−530.804	+	219.866i	−0.841210	+	0.348441i	−0.761331	−	0.648364i	$-0.775454\pi$
$631$	−530.804	+	219.866i	−0.841210	+	0.348441i	−0.0798795	+	0.996805i	$0.525454\pi$
$632$	202.862	+	40.3518i	0.320984	+	0.0638478i
$633$	0.924280	−	0.924280i	0.00146016	−	0.00146016i
$634$	313.167	+	468.688i	0.493955	+	0.739256i
$635$	−502.675	+	99.9882i	−0.791614	+	0.157462i
$636$	0.387703	−	0.580238i	0.000609595	−	0.000912324i
$637$	25.9868	−	62.7377i	0.0407956	−	0.0984893i
$638$	980.076	+	405.961i	1.53617	+	0.636302i
$639$	−432.429	−	288.940i	−0.676727	−	0.452175i
$640$	160.130	+	805.026i	0.250203	+	1.25785i
$641$	819.168	−	547.351i	1.27795	−	0.853901i	0.283489	−	0.958975i	$-0.408508\pi$
$641$	819.168	−	547.351i	1.27795	−	0.853901i	0.994464	+	0.105074i	$0.0335079\pi$
$642$	−2.39682	−	2.39682i	−0.00373337	−	0.00373337i
$643$	−6.90218	+	34.6996i	−0.0107343	+	0.0539652i	−0.985781	−	0.168034i	$-0.946258\pi$
$643$	−6.90218	+	34.6996i	−0.0107343	+	0.0539652i	0.975047	+	0.221999i	$0.0712582\pi$
$644$	−26.1405	−	63.1088i	−0.0405909	−	0.0979950i
$645$		−	63.2046i		−	0.0979916i
$646$		0			0
$647$	−472.176			−0.729793			−0.364897	−	0.931048i	$-0.618896\pi$
$647$	−472.176			−0.729793			−0.364897	+	0.931048i	$0.618896\pi$
$648$	−516.248	+	213.837i	−0.796679	+	0.329995i
$649$	−404.680	−	80.4959i	−0.623544	−	0.124031i
$650$	39.9283	−	39.9283i	0.0614281	−	0.0614281i
$651$	0.680818	+	1.01892i	0.00104580	+	0.00156515i
$652$	45.4766	−	9.04585i	0.0697493	−	0.0138740i
$653$	−353.481	+	529.021i	−0.541318	+	0.810140i	−0.996786	−	0.0801126i	$-0.974472\pi$
$653$	−353.481	+	529.021i	−0.541318	+	0.810140i	0.455468	+	0.890252i	$0.349472\pi$
$654$	15.8210	−	38.1953i	0.0241912	−	0.0584026i
$655$	212.631	+	88.0746i	0.324627	+	0.134465i
$656$	487.531	+	325.758i	0.743187	+	0.496582i
$657$	2.35892	+	11.8591i	0.00359044	+	0.0180504i
$658$	169.343	−	113.151i	0.257360	−	0.171963i
$659$	−128.530	−	128.530i	−0.195037	−	0.195037i	0.602831	−	0.797869i	$-0.294039\pi$
$659$	−128.530	−	128.530i	−0.195037	−	0.195037i	−0.797869	+	0.602831i	$0.794039\pi$
$660$	−2.06344	+	10.3736i	−0.00312642	+	0.0157176i
$661$	445.481	+	1075.49i	0.673950	+	1.62706i	0.774837	+	0.632161i	$0.217832\pi$
$661$	445.481	+	1075.49i	0.673950	+	1.62706i	−0.100887	+	0.994898i	$0.532168\pi$
$662$		−	496.438i		−	0.749906i
$663$		0			0
$664$	469.082			0.706449
$665$	−773.368	+	320.340i	−1.16296	+	0.481714i
$666$	899.588	+	178.939i	1.35073	+	0.268678i
$667$	−305.919	+	305.919i	−0.458649	+	0.458649i
$668$	23.9713	+	35.8756i	0.0358852	+	0.0537060i
$669$	−7.77765	+	1.54707i	−0.0116258	+	0.00231251i
$670$	−291.876	+	436.823i	−0.435635	+	0.651975i
$671$	461.884	−	1115.09i	0.688352	−	1.66183i
$672$	12.2691	+	5.08204i	0.0182576	+	0.00756256i
$673$	−89.2349	−	59.6248i	−0.132593	−	0.0885956i	0.487505	−	0.873120i	$-0.337907\pi$
$673$	−89.2349	−	59.6248i	−0.132593	−	0.0885956i	−0.620098	+	0.784525i	$0.712907\pi$
$674$	154.924	+	778.854i	0.229857	+	1.15557i
$675$	9.13935	−	6.10672i	0.0135398	−	0.00904699i
$676$	−72.6081	−	72.6081i	−0.107408	−	0.107408i
$677$	−205.722	+	1034.24i	−0.303873	+	1.52767i	0.463281	+	0.886211i	$0.346672\pi$
$677$	−205.722	+	1034.24i	−0.303873	+	1.52767i	−0.767154	+	0.641463i	$0.778328\pi$
$678$	−8.96927	−	21.6537i	−0.0132290	−	0.0319377i
$679$		−	422.355i		−	0.622025i
$680$		0			0
$681$	−27.1616			−0.0398849
$682$	36.0262	−	14.9225i	0.0528243	−	0.0218805i
$683$	−599.107	−	119.170i	−0.877170	−	0.174480i	−0.264088	−	0.964499i	$-0.585071\pi$
$683$	−599.107	−	119.170i	−0.877170	−	0.174480i	−0.613083	+	0.790019i	$0.710071\pi$
$684$	−132.422	+	132.422i	−0.193600	+	0.193600i
$685$	190.236	+	284.708i	0.277716	+	0.415632i
$686$	794.652	−	158.066i	1.15838	−	0.230417i
$687$	11.1497	−	16.6867i	0.0162295	−	0.0242892i
$688$	−520.051	+	1255.51i	−0.755888	+	1.82488i
$689$	−32.4143	−	13.4265i	−0.0470455	−	0.0194869i
$690$	−20.7633	−	13.8736i	−0.0300917	−	0.0201067i
$691$	−191.370	−	962.080i	−0.276946	−	1.39230i	−0.829352	−	0.558726i	$-0.811290\pi$
$691$	−191.370	−	962.080i	−0.276946	−	1.39230i	0.552406	−	0.833575i	$-0.313710\pi$
$692$	−12.8274	+	8.57096i	−0.0185366	+	0.0123858i
$693$	578.703	+	578.703i	0.835069	+	0.835069i
$694$	6.80292	−	34.2006i	0.00980248	−	0.0492804i
$695$	536.536	+	1295.31i	0.771994	+	1.86376i
$696$		−	37.1524i		−	0.0533798i
$697$		0			0
$698$	695.626			0.996600
$699$	52.7196	−	21.8372i	0.0754215	−	0.0312406i
$700$	19.3557	+	3.85008i	0.0276510	+	0.00550012i
$701$	−52.7814	+	52.7814i	−0.0752944	+	0.0752944i	−0.743751	−	0.668457i	$-0.766955\pi$
$701$	−52.7814	+	52.7814i	−0.0752944	+	0.0752944i	0.668457	+	0.743751i	$0.266955\pi$
$702$	24.0841	+	36.0443i	0.0343078	+	0.0513452i
$703$	−1139.08	+	226.577i	−1.62031	+	0.322300i
$704$	−370.307	+	554.204i	−0.526005	+	0.787222i
$705$	4.92174	−	11.8821i	0.00698120	−	0.0168541i
$706$	−550.507	−	228.027i	−0.779755	−	0.322985i
$707$	−179.858	−	120.177i	−0.254396	−	0.169982i
$708$	−0.743996	−	3.74032i	−0.00105084	−	0.00528294i
$709$	638.046	−	426.329i	0.899923	−	0.601310i	−0.0172267	−	0.999852i	$-0.505484\pi$
$709$	638.046	−	426.329i	0.899923	−	0.601310i	0.917150	+	0.398542i	$0.130484\pi$
$710$	−483.454	−	483.454i	−0.680921	−	0.680921i
$711$	−52.0345	+	261.595i	−0.0731849	+	0.367925i
$712$	−339.487	−	819.594i	−0.476807	−	1.15111i
$713$			15.9030i			0.0223044i
$714$		0			0
$715$	531.762			0.743723
$716$	−48.3580	+	20.0306i	−0.0675392	+	0.0279756i
$717$	32.7372	+	6.51183i	0.0456586	+	0.00908206i
$718$	−246.167	+	246.167i	−0.342851	+	0.342851i
$719$	640.514	+	958.597i	0.890840	+	1.33324i	0.942373	+	0.334565i	$0.108590\pi$
$719$	640.514	+	958.597i	0.890840	+	1.33324i	−0.0515322	+	0.998671i	$0.516410\pi$
$720$	−880.341	+	175.111i	−1.22270	+	0.243209i
$721$	524.436	−	784.874i	0.727373	−	1.08859i
$722$	221.566	−	534.907i	0.306878	−	0.740869i
$723$	43.0074	+	17.8143i	0.0594847	+	0.0246394i
$724$	72.6396	+	48.5362i	0.100331	+	0.0670390i
$725$	−24.3847	−	122.590i	−0.0336340	−	0.169090i
$726$	−27.2728	+	18.2231i	−0.0375658	+	0.0251007i
$727$	−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	$0.811041\pi$
$728$	57.5357	−	289.251i	0.0790325	−	0.397323i
$729$	−274.130	−	661.808i	−0.376036	−	0.907830i
$730$			15.8957i			0.0217749i
$731$		0			0
$732$	11.1555			0.0152398
$733$	−409.632	+	169.675i	−0.558843	+	0.231480i	−0.644183	−	0.764871i	$-0.722802\pi$
$733$	−409.632	+	169.675i	−0.558843	+	0.231480i	0.0853397	+	0.996352i	$0.472802\pi$
$734$	1054.59	+	209.770i	1.43677	+	0.285791i
$735$	6.13496	−	6.13496i	0.00834689	−	0.00834689i
$736$	95.7472	+	143.296i	0.130091	+	0.194695i
$737$	−637.885	+	126.883i	−0.865515	+	0.172162i
$738$	−344.795	+	516.022i	−0.467201	+	0.699216i
$739$	40.6523	−	98.1432i	0.0550098	−	0.132805i	−0.893985	−	0.448096i	$-0.852102\pi$
$739$	40.6523	−	98.1432i	0.0550098	−	0.132805i	0.948995	+	0.315291i	$0.102102\pi$
$740$	192.429	+	79.7067i	0.260039	+	0.107712i
$741$	−22.7869	−	15.2257i	−0.0307515	−	0.0205475i
$742$	−13.8488	−	69.6228i	−0.0186642	−	0.0938313i
$743$	−767.844	+	513.057i	−1.03344	+	0.690521i	−0.951981	−	0.306156i	$-0.900957\pi$
$743$	−767.844	+	513.057i	−1.03344	+	0.690521i	−0.0814563	+	0.996677i	$0.525957\pi$
$744$	−0.965673	−	0.965673i	−0.00129795	−	0.00129795i
$745$	123.748	−	622.121i	0.166104	−	0.835062i
$746$	−482.554	−	1164.99i	−0.646855	−	1.56165i
$747$			604.891i			0.809760i
$748$		0			0
$749$	−59.5595			−0.0795187
$750$	−37.3727	+	15.4803i	−0.0498302	+	0.0206403i
$751$	1123.96	+	223.569i	1.49662	+	0.297695i	0.874421	−	0.485167i	$-0.161241\pi$
$751$	1123.96	+	223.569i	1.49662	+	0.297695i	0.622195	+	0.782863i	$0.286241\pi$
$752$	−195.534	+	195.534i	−0.260018	+	0.260018i
$753$	−24.2658	−	36.3164i	−0.0322255	−	0.0482289i
$754$	483.478	−	96.1698i	0.641218	−	0.127546i
$755$	82.5438	−	123.536i	0.109330	−	0.163623i
$756$	−5.79787	+	13.9973i	−0.00766915	+	0.0185150i
$757$	−59.3832	−	24.5973i	−0.0784455	−	0.0324932i	0.343116	−	0.939293i	$-0.388518\pi$
$757$	−59.3832	−	24.5973i	−0.0784455	−	0.0324932i	−0.421561	+	0.906800i	$0.638518\pi$
$758$	1283.50	+	857.604i	1.69327	+	1.13140i
$759$	−6.03108	−	30.3203i	−0.00794608	−	0.0399477i
$760$	775.659	−	518.279i	1.02060	−	0.681945i
$761$	173.164	+	173.164i	0.227548	+	0.227548i	0.811668	−	0.584120i	$-0.198560\pi$
$761$	173.164	+	173.164i	0.227548	+	0.227548i	−0.584120	+	0.811668i	$0.698560\pi$
$762$	6.62327	−	33.2974i	0.00869195	−	0.0436974i
$763$	−277.994	−	671.137i	−0.364343	−	0.879602i
$764$		−	162.919i		−	0.213245i
$765$		0			0
$766$	678.170			0.885339
$767$	−177.138	+	73.3731i	−0.230950	+	0.0956624i
$768$	−24.3882	−	4.85111i	−0.0317555	−	0.00631655i
$769$	−550.339	+	550.339i	−0.715655	+	0.715655i	−0.967712	−	0.252057i	$-0.918893\pi$
$769$	−550.339	+	550.339i	−0.715655	+	0.715655i	0.252057	+	0.967712i	$0.418893\pi$
$770$	597.740	+	894.581i	0.776285	+	1.16179i
$771$	8.36964	−	1.66483i	0.0108556	−	0.00215931i
$772$	41.0209	−	61.3921i	0.0531359	−	0.0795235i
$773$	165.492	−	399.534i	0.214091	−	0.516861i	−0.779953	−	0.625837i	$-0.784757\pi$
$773$	165.492	−	399.534i	0.214091	−	0.516861i	0.994044	+	0.108976i	$0.0347573\pi$
$774$	−1328.89	−	550.442i	−1.71691	−	0.711166i
$775$	−3.82020	−	2.55258i	−0.00492929	−	0.00329365i
$776$	91.8263	+	461.642i	0.118333	+	0.594899i
$777$	−39.0047	+	26.0621i	−0.0501991	+	0.0335420i
$778$	443.266	+	443.266i	0.569751	+	0.569751i
$779$	153.309	−	770.735i	0.196802	−	0.989390i
$780$	1.88085	+	4.54077i	0.00241134	+	0.00582150i
$781$		−	846.408i		−	1.08375i
$782$		0			0
$783$	95.9569			0.122550
$784$	−172.345	+	71.3878i	−0.219828	+	0.0910559i
$785$	−415.951	−	82.7379i	−0.529874	−	0.105399i
$786$	−10.7800	+	10.7800i	−0.0137150	+	0.0137150i
$787$	−633.017	−	947.377i	−0.804342	−	1.20378i	−0.975816	−	0.218594i	$-0.929853\pi$
$787$	−633.017	−	947.377i	−0.804342	−	1.20378i	0.171474	−	0.985189i	$-0.445147\pi$
$788$	−210.833	+	41.9374i	−0.267555	+	0.0532200i
$789$	−45.5723	+	68.2037i	−0.0577595	+	0.0864432i
$790$	−134.183	+	323.946i	−0.169852	+	0.410059i
$791$	−380.481	−	157.601i	−0.481013	−	0.199242i
$792$	−758.351	−	506.714i	−0.957515	−	0.639791i
$793$	−109.418	−	550.080i	−0.137980	−	0.693670i
$794$	227.349	−	151.910i	0.286334	−	0.191322i
$795$	−3.16972	−	3.16972i	−0.00398707	−	0.00398707i
$796$	−37.0612	+	186.319i	−0.0465593	+	0.234069i
$797$	43.1132	+	104.084i	0.0540943	+	0.130595i	0.948616	−	0.316429i	$-0.102484\pi$
$797$	43.1132	+	104.084i	0.0540943	+	0.130595i	−0.894522	+	0.447024i	$0.852484\pi$
$798$		−	55.4491i		−	0.0694850i
$799$		0			0
$800$	−49.7905			−0.0622381
$801$	1056.88	−	437.775i	1.31945	−	0.546536i
$802$	920.840	+	183.166i	1.14818	+	0.228387i
$803$	−13.9147	+	13.9147i	−0.0173284	+	0.0173284i
$804$	−3.33967	−	4.99818i	−0.00415382	−	0.00621664i
$805$	−430.353	+	85.6025i	−0.534600	+	0.106338i
$806$	10.0670	−	15.0664i	0.0124901	−	0.0186927i
$807$	10.9012	−	26.3178i	0.0135083	−	0.0326119i
$808$	222.716	+	92.2520i	0.275639	+	0.114173i
$809$	−540.977	−	361.469i	−0.668698	−	0.446810i	0.174324	−	0.984688i	$-0.444226\pi$
$809$	−540.977	−	361.469i	−0.668698	−	0.446810i	−0.843022	+	0.537878i	$0.819226\pi$
$810$	−184.803	−	929.068i	−0.228152	−	1.14700i
$811$	535.209	−	357.615i	0.659937	−	0.440956i	−0.179980	−	0.983670i	$-0.557603\pi$
$811$	535.209	−	357.615i	0.659937	−	0.440956i	0.839917	+	0.542715i	$0.182603\pi$
$812$	121.822	+	121.822i	0.150027	+	0.150027i
$813$	−14.6380	+	73.5903i	−0.0180049	+	0.0905169i
$814$	571.243	+	1379.10i	0.701773	+	1.69423i
$815$		−	297.845i		−	0.365453i
$816$		0			0
$817$	1821.30			2.22925
$818$	−437.897	+	181.383i	−0.535326	+	0.221739i
$819$	372.996	+	74.1934i	0.455428	+	0.0905903i
$820$	−99.6533	+	99.6533i	−0.121528	+	0.121528i
$821$	−496.653	−	743.294i	−0.604937	−	0.905352i	0.394974	−	0.918692i	$-0.370754\pi$
$821$	−496.653	−	743.294i	−0.604937	−	0.905352i	−0.999911	+	0.0133400i	$0.995754\pi$
$822$	−22.2459	+	4.42499i	−0.0270632	+	0.00538320i
$823$	513.804	−	768.962i	0.624306	−	0.934340i	−0.375665	−	0.926756i	$-0.622586\pi$
$823$	513.804	−	768.962i	0.624306	−	0.934340i	0.999971	−	0.00758474i	$-0.00241432\pi$
$824$	−402.575	+	971.901i	−0.488562	+	1.17949i
$825$	8.25153	+	3.41789i	0.0100018	+	0.00414290i
$826$	−322.552	−	215.522i	−0.390498	−	0.260923i
$827$	−165.404	−	831.543i	−0.200005	−	1.00549i	−0.942134	−	0.335237i	$-0.891184\pi$
$827$	−165.404	−	831.543i	−0.200005	−	1.00549i	0.742129	−	0.670257i	$-0.233816\pi$
$828$	−81.6211	+	54.5375i	−0.0985762	+	0.0658665i
$829$	−862.801	−	862.801i	−1.04077	−	1.04077i	−0.999133	−	0.0416400i	$-0.986742\pi$
$829$	−862.801	−	862.801i	−1.04077	−	1.04077i	−0.0416400	−	0.999133i	$-0.513258\pi$
$830$	−155.137	+	779.926i	−0.186912	+	0.939670i
$831$	10.9215	+	26.3667i	0.0131426	+	0.0317289i
$832$			309.729i			0.372271i
$833$		0			0
$834$	−92.8715			−0.111357
$835$	256.062	−	106.064i	0.306661	−	0.127023i
$836$	−298.925	−	59.4598i	−0.357566	−	0.0711242i
$837$	2.49414	−	2.49414i	0.00297985	−	0.00297985i
$838$	−760.089	−	1137.55i	−0.907028	−	1.35746i
$839$	−377.018	+	74.9935i	−0.449366	+	0.0893844i	−0.414585	−	0.910011i	$-0.636073\pi$
$839$	−377.018	+	74.9935i	−0.449366	+	0.0893844i	−0.0347806	+	0.999395i	$0.511073\pi$
$840$	20.9341	−	31.3301i	0.0249216	−	0.0372977i
$841$	95.7324	−	231.119i	0.113832	−	0.274814i
$842$	104.494	+	43.2829i	0.124102	+	0.0514048i
$843$	−53.6826	−	35.8696i	−0.0636804	−	0.0425499i
$844$	−1.31784	−	6.62523i	−0.00156142	−	0.00784980i
$845$	−548.432	+	366.450i	−0.649032	+	0.433669i
$846$	−206.961	−	206.961i	−0.244634	−	0.244634i
$847$	−112.440	+	565.273i	−0.132751	+	0.667382i
$848$	36.8836	+	89.0448i	0.0434948	+	0.105006i
$849$			57.7975i			0.0680771i
$850$		0			0
$851$	−608.778			−0.715368
$852$	7.22756	−	2.99375i	0.00848305	−	0.00351380i
$853$	−857.011	−	170.470i	−1.00470	−	0.199848i	−0.334794	−	0.942291i	$-0.608667\pi$
$853$	−857.011	−	170.470i	−1.00470	−	0.199848i	−0.669908	+	0.742444i	$0.733667\pi$
$854$	802.404	−	802.404i	0.939583	−	0.939583i
$855$	668.331	+	1000.23i	0.781673	+	1.16986i
$856$	65.0997	−	12.9491i	0.0760510	−	0.0151275i
$857$	−746.263	+	1116.86i	−0.870786	+	1.30322i	0.0810800	+	0.996708i	$0.474163\pi$
$857$	−746.263	+	1116.86i	−0.870786	+	1.30322i	−0.951866	+	0.306515i	$0.900837\pi$
$858$	−13.4797	+	32.5429i	−0.0157106	+	0.0379288i
$859$	236.510	+	97.9655i	0.275331	+	0.114046i	0.516077	−	0.856542i	$-0.327392\pi$
$859$	236.510	+	97.9655i	0.275331	+	0.114046i	−0.240745	+	0.970588i	$0.577392\pi$
$860$	−271.584	−	181.466i	−0.315795	−	0.211007i
$861$	−6.19238	−	31.1312i	−0.00719208	−	0.0361570i
$862$	860.439	−	574.927i	0.998189	−	0.666968i
$863$	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	$0.367755\pi$
$864$	7.45722	−	37.4900i	0.00863105	−	0.0433912i
$865$	37.9233	+	91.5550i	0.0438420	+	0.105844i
$866$			1415.19i			1.63417i
$867$		0			0
$868$	6.33287			0.00729593
$869$	−401.035	+	166.114i	−0.461490	+	0.191156i
$870$	61.7719	+	12.2872i	0.0710022	+	0.0141232i
$871$	−213.704	+	213.704i	−0.245355	+	0.245355i
$872$	449.767	+	673.124i	0.515788	+	0.771932i
$873$	−595.296	+	118.412i	−0.681897	+	0.135638i
$874$	399.781	−	598.314i	0.457415	−	0.684570i
$875$	−272.006	+	656.681i	−0.310864	+	0.750493i
$876$	−0.168035	−	0.0696025i	−0.000191821	−	7.94550e-5i
$877$	409.924	+	273.902i	0.467416	+	0.312317i	0.766880	−	0.641790i	$-0.221808\pi$
$877$	409.924	+	273.902i	0.467416	+	0.312317i	−0.299465	+	0.954107i	$0.596808\pi$
$878$	354.965	+	1784.53i	0.404288	+	2.03249i
$879$	32.1177	−	21.4604i	0.0365389	−	0.0244145i
$880$	−1032.94	−	1032.94i	−1.17379	−	1.17379i
$881$	−78.4489	+	394.389i	−0.0890453	+	0.447661i	0.910380	+	0.413772i	$0.135789\pi$
$881$	−78.4489	+	394.389i	−0.0890453	+	0.447661i	−0.999426	+	0.0338884i	$0.989211\pi$
$882$	−75.5597	−	182.417i	−0.0856686	−	0.206822i
$883$		−	907.327i		−	1.02755i	−0.857925	−	0.513775i	$-0.828246\pi$
$883$		−	907.327i		−	1.02755i	0.857925	−	0.513775i	$-0.171754\pi$
$884$		0			0
$885$	−24.4969			−0.0276801
$886$	720.035	−	298.248i	0.812681	−	0.336624i
$887$	−1246.23	−	247.891i	−1.40500	−	0.279471i	−0.566357	−	0.824160i	$-0.691648\pi$
$887$	−1246.23	−	247.891i	−1.40500	−	0.279471i	−0.838638	+	0.544689i	$0.816648\pi$
$888$	36.9665	−	36.9665i	0.0416290	−	0.0416290i
$889$	−331.418	−	496.002i	−0.372799	−	0.557933i
$890$	1474.99	−	293.393i	1.65729	−	0.329655i
$891$	651.511	−	975.055i	0.731213	−	1.09434i
$892$	−15.6828	+	37.8615i	−0.0175816	+	0.0424457i
$893$	342.395	+	141.825i	0.383421	+	0.158818i
$894$	34.9358	+	23.3434i	0.0390781	+	0.0261111i
$895$	65.5942	+	329.764i	0.0732896	+	0.368452i
$896$	−794.340	+	530.761i	−0.886540	+	0.592367i
$897$	−10.1579	−	10.1579i	−0.0113243	−	0.0113243i
$898$	337.159	−	1695.01i	0.375456	−	1.88754i
$899$	−15.3493	−	37.0564i	−0.0170737	−	0.0412195i
$900$		−	28.3606i		−	0.0315118i
$901$		0			0
$902$	−1010.03			−1.11976
$903$	67.9654	−	28.1522i	0.0752663	−	0.0311763i
$904$	450.138	+	89.5380i	0.497940	+	0.0990464i
$905$	396.815	−	396.815i	0.438470	−	0.438470i
$906$	5.46774	+	8.18305i	0.00603503	+	0.00903207i
$907$	1504.73	−	299.309i	1.65901	−	0.329998i	0.725413	−	0.688313i	$-0.241649\pi$
$907$	1504.73	−	299.309i	1.65901	−	0.329998i	0.933601	+	0.358315i	$0.116649\pi$
$908$	−77.9836	+	116.711i	−0.0858850	+	0.128536i
$909$	−118.961	+	287.197i	−0.130870	+	0.315948i
$910$	461.899	+	191.325i	0.507582	+	0.210247i
$911$	−304.539	−	203.486i	−0.334291	−	0.223366i	0.377084	−	0.926179i	$-0.376927\pi$
$911$	−304.539	−	203.486i	−0.334291	−	0.223366i	−0.711374	+	0.702813i	$0.751927\pi$
$912$	14.6874	+	73.8387i	0.0161046	+	0.0809634i
$913$	−818.531	+	546.925i	−0.896529	+	0.599041i
$914$	505.549	+	505.549i	0.553117	+	0.553117i
$915$	13.9798	−	70.2813i	0.0152785	−	0.0768102i
$916$	−39.6892	−	95.8181i	−0.0433288	−	0.104605i
$917$			267.877i			0.292123i
$918$		0			0
$919$	−944.655			−1.02792			−0.513958	−	0.857815i	$-0.671821\pi$
$919$	−944.655			−1.02792			−0.513958	+	0.857815i	$0.671821\pi$
$920$	451.772	−	187.130i	0.491057	−	0.203402i
$921$	64.9830	+	12.9259i	0.0705570	+	0.0140347i
$922$	382.839	−	382.839i	0.415226	−	0.415226i
$923$	−218.513	−	327.028i	−0.236742	−	0.354310i
$924$	−12.0741	+	2.40168i	−0.0130672	+	0.00259922i
$925$	97.7142	−	146.240i	0.105637	−	0.158097i
$926$	295.212	−	712.706i	0.318804	−	0.769661i
$927$	−1253.29	−	519.128i	−1.35198	−	0.560009i
$928$	−361.410	−	241.487i	−0.389451	−	0.260223i
$929$	189.563	+	952.999i	0.204051	+	1.02583i	0.938002	+	0.346631i	$0.112674\pi$
$929$	189.563	+	952.999i	0.204051	+	1.02583i	−0.733951	+	0.679203i	$0.762326\pi$
$930$	1.92496	−	1.28622i	0.00206985	−	0.00138303i
$931$	176.785	+	176.785i	0.189887	+	0.189887i
$932$	57.5309	−	289.228i	0.0617285	−	0.310330i
$933$	13.3967	+	32.3426i	0.0143588	+	0.0346652i
$934$			481.282i			0.515292i
$935$		0			0
$936$	−423.822			−0.452801
$937$	554.438	−	229.656i	0.591716	−	0.245097i	−0.0666728	−	0.997775i	$-0.521238\pi$
$937$	554.438	−	229.656i	0.591716	−	0.245097i	0.658389	+	0.752678i	$0.271238\pi$
$938$	−599.732	−	119.294i	−0.639373	−	0.127179i
$939$	−54.1023	+	54.1023i	−0.0576170	+	0.0576170i
$940$	−36.9255	−	55.2630i	−0.0392825	−	0.0587904i
$941$	1063.66	−	211.575i	1.13035	−	0.224840i	0.405732	−	0.913992i	$-0.367017\pi$
$941$	1063.66	−	211.575i	1.13035	−	0.224840i	0.724617	+	0.689152i	$0.242017\pi$
$942$	15.6074	−	23.3581i	0.0165684	−	0.0247963i
$943$	157.634	−	380.563i	0.167162	−	0.403566i
$944$	486.613	+	201.562i	0.515480	+	0.213519i
$945$	80.9192	+	54.0685i	0.0856288	+	0.0572153i
$946$	−456.688	−	2295.93i	−0.482757	−	2.42698i
$947$	−579.335	+	387.099i	−0.611758	+	0.408764i	−0.822490	−	0.568780i	$-0.807416\pi$
$947$	−579.335	+	387.099i	−0.611758	+	0.408764i	0.210731	+	0.977544i	$0.432416\pi$
$948$	−2.83693	−	2.83693i	−0.00299254	−	0.00299254i
$949$	−1.78395	+	8.96854i	−0.00187982	+	0.00945051i
$950$	79.5577	+	192.069i	0.0837449	+	0.202178i
$951$			41.4305i			0.0435651i
$952$		0			0
$953$	−1779.95			−1.86774			−0.933868	−	0.357618i	$-0.883589\pi$
$953$	−1779.95			−1.86774			−0.933868	+	0.357618i	$0.883589\pi$
$954$	−94.2485	+	39.0390i	−0.0987930	+	0.0409214i
$955$	−1026.41	−	204.166i	−1.07478	−	0.213786i
$956$	121.972	−	121.972i	0.127586	−	0.127586i
$957$	43.3177	+	64.8295i	0.0452640	+	0.0677424i
$958$	−1083.66	+	215.553i	−1.13117	+	0.225003i
$959$	−221.420	+	331.378i	−0.230886	+	0.345545i
$960$	−15.1438	+	36.5604i	−0.0157748	+	0.0380838i
$961$	886.486	+	367.195i	0.922462	+	0.382096i
$962$	576.749	+	385.371i	0.599531	+	0.400594i
$963$	16.6982	+	83.9473i	0.0173397	+	0.0871727i
$964$	200.024	−	133.652i	0.207494	−	0.138643i
$965$	−335.373	−	335.373i	−0.347536	−	0.347536i
$966$	5.67035	−	28.5068i	0.00586992	−	0.0295101i
$967$	−231.136	−	558.012i	−0.239024	−	0.577055i	0.758158	−	0.652071i	$-0.226099\pi$
$967$	−231.136	−	558.012i	−0.239024	−	0.577055i	−0.997182	+	0.0750154i	$0.976099\pi$
$968$		−	642.299i		−	0.663532i
$969$		0			0
$970$	−797.924			−0.822602
$971$	−1017.06	+	421.281i	−1.04744	+	0.433863i	−0.838976	−	0.544168i	$-0.816845\pi$
$971$	−1017.06	+	421.281i	−1.04744	+	0.433863i	−0.208461	+	0.978031i	$0.566845\pi$
$972$	32.0469	+	6.37453i	0.0329701	+	0.00655816i
$973$	−1153.90	+	1153.90i	−1.18592	+	1.18592i
$974$	−307.594	−	460.348i	−0.315805	−	0.472636i
$975$	4.07054	−	0.809680i	0.00417491	−	0.000830441i
$976$	−855.978	+	1281.06i	−0.877026	+	1.31256i
$977$	419.266	−	1012.20i	0.429136	−	1.03603i	−0.550426	−	0.834884i	$-0.685535\pi$
$977$	419.266	−	1012.20i	0.429136	−	1.03603i	0.979562	−	0.201142i	$-0.0644654\pi$
$978$	18.2276	+	7.55010i	0.0186376	+	0.00771994i
$979$	1547.99	+	1034.34i	1.58120	+	1.05652i
$980$	−8.74724	−	43.9754i	−0.00892576	−	0.0448728i
$981$	−868.008	+	579.984i	−0.884819	+	0.591217i
$982$	−351.948	−	351.948i	−0.358399	−	0.358399i
$983$	−239.790	+	1205.50i	−0.243937	+	1.22635i	0.643509	+	0.765439i	$0.277478\pi$
$983$	−239.790	+	1205.50i	−0.243937	+	1.22635i	−0.887445	+	0.460913i	$0.847522\pi$
$984$	13.5368	+	32.6807i	0.0137569	+	0.0332121i
$985$			1380.83i			1.40186i
$986$		0			0
$987$	14.9694			0.0151665
$988$	−130.847	+	54.1984i	−0.132436	+	0.0548567i
$989$	936.344	+	186.250i	0.946758	+	0.188322i
$990$	1093.30	−	1093.30i	1.10434	−	1.10434i
$991$	−409.322	−	612.594i	−0.413040	−	0.618158i	0.565369	−	0.824838i	$-0.308734\pi$
$991$	−409.322	−	612.594i	−0.413040	−	0.618158i	−0.978408	+	0.206681i	$0.933734\pi$
$992$	−15.6706	+	3.11708i	−0.0157970	+	0.00314222i
$993$	20.2715	−	30.3385i	0.0204144	−	0.0305523i
$994$	304.533	−	735.207i	0.306371	−	0.739645i
$995$	1127.39	+	466.981i	1.13306	+	0.469328i
$996$	−7.56540	−	5.05504i	−0.00759578	−	0.00507534i
$997$	34.0568	+	171.215i	0.0341593	+	0.171730i	0.994099	−	0.108476i	$-0.0345971\pi$
$997$	34.0568	+	171.215i	0.0341593	+	0.171730i	−0.959940	+	0.280206i	$0.909597\pi$
$998$	−394.641	+	263.691i	−0.395432	+	0.264219i
$999$	95.4770	+	95.4770i	0.0955725	+	0.0955725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.k.224.1		8
17.2	even	8		289.3.e.m.131.1		8
17.3	odd	16		289.3.e.m.214.1		8
17.4	even	4		289.3.e.b.65.1		8
17.5	odd	16		289.3.e.c.75.1		8
17.6	odd	16	inner	289.3.e.k.40.1		8
17.7	odd	16		289.3.e.d.249.1		8
17.8	even	8		289.3.e.c.158.1		8
17.9	even	8		17.3.e.a.5.1	✓	8
17.10	odd	16		289.3.e.b.249.1		8
17.11	odd	16		289.3.e.l.40.1		8
17.12	odd	16		17.3.e.a.7.1	yes	8
17.13	even	4		289.3.e.d.65.1		8
17.14	odd	16		289.3.e.i.214.1		8
17.15	even	8		289.3.e.i.131.1		8
17.16	even	2		289.3.e.l.224.1		8
51.26	odd	8		153.3.p.b.73.1		8
51.29	even	16		153.3.p.b.109.1		8
68.43	odd	8		272.3.bh.c.209.1		8
68.63	even	16		272.3.bh.c.177.1		8
85.9	even	8		425.3.u.b.226.1		8
85.12	even	16		425.3.t.a.24.1		8
85.29	odd	16		425.3.u.b.126.1		8
85.43	odd	8		425.3.t.a.124.1		8
85.63	even	16		425.3.t.c.24.1		8
85.77	odd	8		425.3.t.c.124.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.5.1	✓	8	17.9	even	8
17.3.e.a.7.1	yes	8	17.12	odd	16
153.3.p.b.73.1		8	51.26	odd	8
153.3.p.b.109.1		8	51.29	even	16
272.3.bh.c.177.1		8	68.63	even	16
272.3.bh.c.209.1		8	68.43	odd	8
289.3.e.b.65.1		8	17.4	even	4
289.3.e.b.249.1		8	17.10	odd	16
289.3.e.c.75.1		8	17.5	odd	16
289.3.e.c.158.1		8	17.8	even	8
289.3.e.d.65.1		8	17.13	even	4
289.3.e.d.249.1		8	17.7	odd	16
289.3.e.i.131.1		8	17.15	even	8
289.3.e.i.214.1		8	17.14	odd	16
289.3.e.k.40.1		8	17.6	odd	16	inner
289.3.e.k.224.1		8	1.1	even	1	trivial
289.3.e.l.40.1		8	17.11	odd	16
289.3.e.l.224.1		8	17.16	even	2
289.3.e.m.131.1		8	17.2	even	8
289.3.e.m.214.1		8	17.3	odd	16
425.3.t.a.24.1		8	85.12	even	16
425.3.t.a.124.1		8	85.43	odd	8
425.3.t.c.24.1		8	85.63	even	16
425.3.t.c.124.1		8	85.77	odd	8
425.3.u.b.126.1		8	85.29	odd	16
425.3.u.b.226.1		8	85.9	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.03153 - 0.841487i) q^{2} +(0.158513 + 0.0315301i) q^{3} +(0.590587 - 0.590587i) q^{4} +(-2.98067 - 4.46088i) q^{5} +(0.348555 - 0.0693320i) q^{6} +(3.46927 - 5.19212i) q^{7} +(-2.66313 + 6.42935i) q^{8} +(-8.29078 - 3.43416i) q^{9} +(-9.80910 - 6.55423i) q^{10} +(-2.84923 - 14.3240i) q^{11} +(0.112237 - 0.0749942i) q^{12} +(-4.79884 - 4.79884i) q^{13} +(2.67881 - 13.4673i) q^{14} +(-0.331821 - 0.801088i) q^{15} +18.6433i q^{16} -19.7328 q^{18} +(23.0841 - 9.56175i) q^{19} +(-4.39488 - 0.874196i) q^{20} +(0.713631 - 0.713631i) q^{21} +(-17.8418 - 26.7021i) q^{22} +(12.8455 - 2.55513i) q^{23} +(-0.624858 + 0.935165i) q^{24} +(-1.44803 + 3.49585i) q^{25} +(-13.7871 - 5.71082i) q^{26} +(-2.41534 - 1.61388i) q^{27} +(-1.01750 - 5.11530i) q^{28} +(-27.4657 + 18.3520i) q^{29} +(-1.34821 - 1.34821i) q^{30} +(-0.236886 + 1.19090i) q^{31} +(5.03558 + 12.1570i) q^{32} -2.36038i q^{33} -33.5022 q^{35} +(-6.92459 + 2.86826i) q^{36} +(-45.5885 - 9.06812i) q^{37} +(38.8500 - 38.8500i) q^{38} +(-0.609368 - 0.911984i) q^{39} +(36.6185 - 7.28387i) q^{40} +(17.4732 - 26.1505i) q^{41} +(0.849251 - 2.05027i) q^{42} +(67.3441 + 27.8948i) q^{43} +(-10.1423 - 6.77687i) q^{44} +(9.39270 + 47.2203i) q^{45} +(23.9459 - 16.0002i) q^{46} +(10.4882 + 10.4882i) q^{47} +(-0.587825 + 2.95520i) q^{48} +(3.82915 + 9.24438i) q^{49} +8.32041i q^{50} -5.66826 q^{52} +(4.77624 - 1.97838i) q^{53} +(-6.26489 - 1.24616i) q^{54} +(-55.4053 + 55.4053i) q^{55} +(24.1429 + 36.1324i) q^{56} +(3.96061 - 0.787813i) q^{57} +(-40.3544 + 60.3947i) q^{58} +(10.8115 - 26.1013i) q^{59} +(-0.669081 - 0.277142i) q^{60} +(68.7144 + 45.9135i) q^{61} +(0.520891 + 2.61870i) q^{62} +(-46.5935 + 31.1328i) q^{63} +(-32.2713 - 32.2713i) q^{64} +(-7.10332 + 35.7108i) q^{65} +(-1.98623 - 4.79518i) q^{66} -44.5324i q^{67} +2.11674 q^{69} +(-68.0607 + 28.1917i) q^{70} +(56.8410 + 11.3064i) q^{71} +(44.1588 - 44.1588i) q^{72} +(-0.748576 - 1.12032i) q^{73} +(-100.245 + 19.9400i) q^{74} +(-0.339755 + 0.508479i) q^{75} +(7.98612 - 19.2802i) q^{76} +(-84.2570 - 34.9004i) q^{77} +(-2.00537 - 1.33995i) q^{78} +(-5.79844 - 29.1507i) q^{79} +(83.1655 - 55.5694i) q^{80} +(56.7774 + 56.7774i) q^{81} +(13.4920 - 67.8290i) q^{82} +(-25.7951 - 62.2748i) q^{83} -0.842922i q^{84} +160.285 q^{86} +(-4.93230 + 2.04303i) q^{87} +(99.6823 + 19.8280i) q^{88} +(-90.1397 + 90.1397i) q^{89} +(58.8169 + 88.0256i) q^{90} +(-41.5646 + 8.26771i) q^{91} +(6.07736 - 9.09541i) q^{92} +(-0.0750988 + 0.181304i) q^{93} +(30.1327 + 12.4814i) q^{94} +(-111.460 - 74.4751i) q^{95} +(0.414892 + 2.08580i) q^{96} +(56.2374 - 37.5767i) q^{97} +(15.5581 + 15.5581i) q^{98} +(-25.5687 + 128.542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 16 q^{5} - 8 q^{6} + 40 q^{7} + 40 q^{8} - 8 q^{9} - 48 q^{10} - 8 q^{11} + 72 q^{12} - 16 q^{13} + 104 q^{14} + 56 q^{18} + 48 q^{19} - 16 q^{20} + 64 q^{21} - 24 q^{22} + 56 q^{23} + 24 q^{24}+ \cdots + 128 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 16 * q^5 - 8 * q^6 + 40 * q^7 + 40 * q^8 - 8 * q^9 - 48 * q^10 - 8 * q^11 + 72 * q^12 - 16 * q^13 + 104 * q^14 + 56 * q^18 + 48 * q^19 - 16 * q^20 + 64 * q^21 - 24 * q^22 + 56 * q^23 + 24 * q^24 + 32 * q^25 + 48 * q^26 - 24 * q^27 + 8 * q^28 - 128 * q^29 - 16 * q^30 - 40 * q^31 + 88 * q^32 - 160 * q^35 + 24 * q^36 - 96 * q^37 + 120 * q^38 - 96 * q^39 + 112 * q^40 - 48 * q^41 - 128 * q^42 + 112 * q^43 + 120 * q^44 - 112 * q^45 + 72 * q^46 - 192 * q^47 - 136 * q^48 + 80 * q^49 - 384 * q^52 + 128 * q^53 - 64 * q^54 - 224 * q^55 + 200 * q^56 + 48 * q^57 + 120 * q^59 - 48 * q^60 + 288 * q^61 + 8 * q^62 - 120 * q^63 + 64 * q^64 - 64 * q^65 + 96 * q^66 + 240 * q^69 - 480 * q^70 + 344 * q^71 - 40 * q^72 + 200 * q^73 - 208 * q^74 - 104 * q^75 - 160 * q^76 - 80 * q^77 - 512 * q^78 + 328 * q^79 + 64 * q^80 + 424 * q^81 - 64 * q^82 - 336 * q^83 + 832 * q^86 + 80 * q^87 + 8 * q^88 - 160 * q^89 - 224 * q^90 - 544 * q^91 + 24 * q^92 + 208 * q^93 - 432 * q^94 - 192 * q^95 + 64 * q^96 + 240 * q^97 + 120 * q^98 + 128 * q^99

Introduction

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