LMFDB - Embedded newform 289.3.e.d.249.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			249.1
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.249
Dual form			289.3.e.d.65.1

$q$-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} +(-0.0315301 - 0.158513i) q^{3} +(0.590587 + 0.590587i) q^{4} +(4.46088 + 2.98067i) q^{5} +(-0.0693320 + 0.348555i) q^{6} +(-5.19212 + 3.46927i) q^{7} +(2.66313 + 6.42935i) q^{8} +(8.29078 - 3.43416i) q^{9} +(-6.55423 - 9.80910i) q^{10} +(-14.3240 - 2.84923i) q^{11} +(0.0749942 - 0.112237i) q^{12} +(-4.79884 + 4.79884i) q^{13} +(13.4673 - 2.67881i) q^{14} +(0.331821 - 0.801088i) q^{15} -18.6433i q^{16} -19.7328 q^{18} +(-23.0841 - 9.56175i) q^{19} +(0.874196 + 4.39488i) q^{20} +(0.713631 + 0.713631i) q^{21} +(26.7021 + 17.8418i) q^{22} +(-2.55513 + 12.8455i) q^{23} +(0.935165 - 0.624858i) q^{24} +(1.44803 + 3.49585i) q^{25} +(13.7871 - 5.71082i) q^{26} +(-1.61388 - 2.41534i) q^{27} +(-5.11530 - 1.01750i) q^{28} +(-18.3520 + 27.4657i) q^{29} +(-1.34821 + 1.34821i) q^{30} +(-1.19090 + 0.236886i) q^{31} +(-5.03558 + 12.1570i) q^{32} +2.36038i q^{33} -33.5022 q^{35} +(6.92459 + 2.86826i) q^{36} +(9.06812 + 45.5885i) q^{37} +(38.8500 + 38.8500i) q^{38} +(0.911984 + 0.609368i) q^{39} +(-7.28387 + 36.6185i) q^{40} +(-26.1505 + 17.4732i) q^{41} +(-0.849251 - 2.05027i) q^{42} +(-67.3441 + 27.8948i) q^{43} +(-6.77687 - 10.1423i) q^{44} +(47.2203 + 9.39270i) q^{45} +(16.0002 - 23.9459i) q^{46} +(10.4882 - 10.4882i) q^{47} +(-2.95520 + 0.587825i) q^{48} +(-3.82915 + 9.24438i) q^{49} -8.32041i q^{50} -5.66826 q^{52} +(-4.77624 - 1.97838i) q^{53} +(1.24616 + 6.26489i) q^{54} +(-55.4053 - 55.4053i) q^{55} +(-36.1324 - 24.1429i) q^{56} +(-0.787813 + 3.96061i) q^{57} +(60.3947 - 40.3544i) q^{58} +(-10.8115 - 26.1013i) q^{59} +(0.669081 - 0.277142i) q^{60} +(45.9135 + 68.7144i) q^{61} +(2.61870 + 0.520891i) q^{62} +(-31.1328 + 46.5935i) q^{63} +(-32.2713 + 32.2713i) q^{64} +(-35.7108 + 7.10332i) q^{65} +(1.98623 - 4.79518i) q^{66} +44.5324i q^{67} +2.11674 q^{69} +(68.0607 + 28.1917i) q^{70} +(-11.3064 - 56.8410i) q^{71} +(44.1588 + 44.1588i) q^{72} +(1.12032 + 0.748576i) q^{73} +(19.9400 - 100.245i) q^{74} +(0.508479 - 0.339755i) q^{75} +(-7.98612 - 19.2802i) q^{76} +(84.2570 - 34.9004i) q^{77} +(-1.33995 - 2.00537i) q^{78} +(-29.1507 - 5.79844i) q^{79} +(55.5694 - 83.1655i) q^{80} +(56.7774 - 56.7774i) q^{81} +(67.8290 - 13.4920i) q^{82} +(25.7951 - 62.2748i) q^{83} +0.842922i q^{84} +160.285 q^{86} +(4.93230 + 2.04303i) q^{87} +(-19.8280 - 99.6823i) q^{88} +(-90.1397 - 90.1397i) q^{89} +(-88.0256 - 58.8169i) q^{90} +(8.26771 - 41.5646i) q^{91} +(-9.09541 + 6.07736i) q^{92} +(0.0750988 + 0.181304i) q^{93} +(-30.1327 + 12.4814i) q^{94} +(-74.4751 - 111.460i) q^{95} +(2.08580 + 0.414892i) q^{96} +(37.5767 - 56.2374i) q^{97} +(15.5581 - 15.5581i) q^{98} +(-128.542 + 25.5687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{3} + 32 q^{6} + 8 q^{7} - 40 q^{8} + 8 q^{9} + 32 q^{10} - 24 q^{11} - 8 q^{12} - 16 q^{13} + 24 q^{14} + 56 q^{18} - 48 q^{19} - 80 q^{20} + 64 q^{21} + 48 q^{22} + 24 q^{23} - 120 q^{24}+ \cdots - 216 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^3 + 32 * q^6 + 8 * q^7 - 40 * q^8 + 8 * q^9 + 32 * q^10 - 24 * q^11 - 8 * q^12 - 16 * q^13 + 24 * q^14 + 56 * q^18 - 48 * q^19 - 80 * q^20 + 64 * q^21 + 48 * q^22 + 24 * q^23 - 120 * q^24 - 32 * q^25 - 48 * q^26 + 80 * q^27 - 120 * q^28 + 16 * q^29 - 16 * q^30 - 40 * q^31 - 88 * q^32 - 160 * q^35 - 24 * q^36 + 16 * q^37 + 120 * q^38 + 160 * q^39 + 48 * q^40 - 40 * q^41 + 128 * q^42 - 112 * q^43 - 64 * q^44 + 128 * q^45 - 8 * q^46 - 192 * q^47 - 96 * q^48 - 80 * q^49 - 384 * q^52 - 128 * q^53 - 168 * q^54 - 224 * q^55 - 264 * q^56 - 80 * q^57 + 368 * q^58 - 120 * q^59 + 48 * q^60 - 96 * q^61 + 120 * q^62 - 184 * q^63 + 64 * q^64 - 96 * q^66 + 240 * q^69 + 480 * q^70 + 280 * q^71 - 40 * q^72 + 208 * q^73 - 224 * q^74 - 136 * q^75 + 160 * q^76 + 80 * q^77 - 64 * q^78 + 24 * q^79 + 240 * q^80 + 424 * q^81 + 272 * q^82 + 336 * q^83 + 832 * q^86 - 80 * q^87 + 72 * q^88 - 160 * q^89 - 384 * q^90 - 248 * q^92 - 208 * q^93 + 432 * q^94 - 192 * q^95 - 88 * q^96 + 176 * q^97 + 120 * q^98 - 216 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{16}\right)$

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	$-0.560269\pi$
$2$	−2.03153	−	0.841487i	−1.01577	−	0.420744i	−0.827555	+	0.561385i	$0.810269\pi$
$3$	−0.0315301	−	0.158513i	−0.0105100	−	0.0528376i	0.975174	−	0.221438i	$-0.0710751\pi$
$3$	−0.0315301	−	0.158513i	−0.0105100	−	0.0528376i	−0.985684	+	0.168601i	$0.946075\pi$
$4$	0.590587	+	0.590587i	0.147647	+	0.147647i
$5$	4.46088	+	2.98067i	0.892177	+	0.596134i	0.914932	−	0.403607i	$-0.132244\pi$
$5$	4.46088	+	2.98067i	0.892177	+	0.596134i	−0.0227553	+	0.999741i	$0.507244\pi$
$6$	−0.0693320	+	0.348555i	−0.0115553	+	0.0580926i
$7$	−5.19212	+	3.46927i	−0.741732	+	0.495609i	−0.868109	−	0.496373i	$-0.834665\pi$
$7$	−5.19212	+	3.46927i	−0.741732	+	0.495609i	0.126378	+	0.991982i	$0.459665\pi$
$8$	2.66313	+	6.42935i	0.332891	+	0.803669i
$9$	8.29078	−	3.43416i	0.921198	−	0.381573i
$10$	−6.55423	−	9.80910i	−0.655423	−	0.980910i
$11$	−14.3240	−	2.84923i	−1.30219	−	0.259021i	−0.505192	−	0.863007i	$-0.668578\pi$
$11$	−14.3240	−	2.84923i	−1.30219	−	0.259021i	−0.796995	+	0.603986i	$0.793578\pi$
$12$	0.0749942	−	0.112237i	0.00624952	−	0.00935306i
$13$	−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	$0.334060\pi$
$14$	13.4673	−	2.67881i	0.961950	−	0.191344i
$15$	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	$-0.603398\pi$
$19$	−23.0841	−	9.56175i	−1.21495	−	0.503250i	−0.895802	+	0.444454i	$0.853398\pi$
$20$	0.874196	+	4.39488i	0.0437098	+	0.219744i
$21$	0.713631	+	0.713631i	0.0339824	+	0.0339824i
$22$	26.7021	+	17.8418i	1.21373	+	0.810991i
$23$	−2.55513	+	12.8455i	−0.111093	+	0.558500i	0.884645	+	0.466266i	$0.154401\pi$
$23$	−2.55513	+	12.8455i	−0.111093	+	0.558500i	−0.995737	+	0.0922345i	$0.970599\pi$
$24$	0.935165	−	0.624858i	0.0389652	−	0.0260357i
$25$	1.44803	+	3.49585i	0.0579211	+	0.139834i
$26$	13.7871	−	5.71082i	0.530274	−	0.219647i
$27$	−1.61388	−	2.41534i	−0.0597733	−	0.0894570i
$28$	−5.11530	−	1.01750i	−0.182689	−	0.0363392i
$29$	−18.3520	+	27.4657i	−0.632828	+	0.947093i	0.367030	+	0.930209i	$0.380375\pi$
$29$	−18.3520	+	27.4657i	−0.632828	+	0.947093i	−0.999857	+	0.0168842i	$0.994625\pi$
$30$	−1.34821	+	1.34821i	−0.0449403	+	0.0449403i
$31$	−1.19090	+	0.236886i	−0.0384163	+	0.00764147i	−0.214261	−	0.976776i	$-0.568734\pi$
$31$	−1.19090	+	0.236886i	−0.0384163	+	0.00764147i	0.175845	+	0.984418i	$0.443734\pi$
$32$	−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
$37$	9.06812	+	45.5885i	0.245084	+	1.23212i	0.885699	+	0.464260i	$0.153680\pi$
$37$	9.06812	+	45.5885i	0.245084	+	1.23212i	−0.640614	+	0.767863i	$0.721320\pi$
$38$	38.8500	+	38.8500i	1.02237	+	1.02237i
$39$	0.911984	+	0.609368i	0.0233842	+	0.0156248i
$40$	−7.28387	+	36.6185i	−0.182097	+	0.915463i
$41$	−26.1505	+	17.4732i	−0.637817	+	0.426176i	−0.831989	−	0.554792i	$-0.812798\pi$
$41$	−26.1505	+	17.4732i	−0.637817	+	0.426176i	0.194172	+	0.980967i	$0.437798\pi$
$42$	−0.849251	−	2.05027i	−0.0202203	−	0.0488161i
$43$	−67.3441	+	27.8948i	−1.56614	+	0.648717i	−0.986142	−	0.165901i	$-0.946947\pi$
$43$	−67.3441	+	27.8948i	−1.56614	+	0.648717i	−0.579999	+	0.814617i	$0.696947\pi$
$44$	−6.77687	−	10.1423i	−0.154020	−	0.230507i
$45$	47.2203	+	9.39270i	1.04934	+	0.208727i
$46$	16.0002	−	23.9459i	0.347829	−	0.520564i
$47$	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	$0.199562\pi$
$48$	−2.95520	+	0.587825i	−0.0615666	+	0.0122464i
$49$	−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	$-0.390531\pi$
$53$	−4.77624	−	1.97838i	−0.0901178	−	0.0373280i	−0.427287	+	0.904116i	$0.640531\pi$
$54$	1.24616	+	6.26489i	0.0230771	+	0.116017i
$55$	−55.4053	−	55.4053i	−1.00737	−	1.00737i
$56$	−36.1324	−	24.1429i	−0.645222	−	0.431123i
$57$	−0.787813	+	3.96061i	−0.0138213	+	0.0694843i
$58$	60.3947	−	40.3544i	1.04129	−	0.695766i
$59$	−10.8115	−	26.1013i	−0.183246	−	0.442394i	0.805386	−	0.592751i	$-0.201958\pi$
$59$	−10.8115	−	26.1013i	−0.183246	−	0.442394i	−0.988632	+	0.150356i	$0.951958\pi$
$60$	0.669081	−	0.277142i	0.0111513	−	0.00461904i
$61$	45.9135	+	68.7144i	0.752680	+	1.12647i	0.987986	+	0.154544i	$0.0493908\pi$
$61$	45.9135	+	68.7144i	0.752680	+	1.12647i	−0.235306	+	0.971921i	$0.575609\pi$
$62$	2.61870	+	0.520891i	0.0422370	+	0.00840147i
$63$	−31.1328	+	46.5935i	−0.494171	+	0.739579i
$64$	−32.2713	+	32.2713i	−0.504239	+	0.504239i
$65$	−35.7108	+	7.10332i	−0.549397	+	0.109282i
$66$	1.98623	−	4.79518i	0.0300944	−	0.0726543i
$67$			44.5324i			0.664663i	0.943163	+	0.332332i	$0.107835\pi$
$67$			44.5324i			0.664663i	−0.943163	+	0.332332i	$0.892165\pi$
$68$		0			0
$69$	2.11674			0.0306774
$70$	68.0607	+	28.1917i	0.972296	+	0.402738i
$71$	−11.3064	−	56.8410i	−0.159245	−	0.800577i	−0.975004	−	0.222186i	$-0.928681\pi$
$71$	−11.3064	−	56.8410i	−0.159245	−	0.800577i	0.815759	−	0.578391i	$-0.196319\pi$
$72$	44.1588	+	44.1588i	0.613317	+	0.613317i
$73$	1.12032	+	0.748576i	0.0153469	+	0.0102545i	0.563220	−	0.826307i	$-0.309562\pi$
$73$	1.12032	+	0.748576i	0.0153469	+	0.0102545i	−0.547873	+	0.836561i	$0.684562\pi$
$74$	19.9400	−	100.245i	0.269460	−	1.35466i
$75$	0.508479	−	0.339755i	0.00677973	−	0.00453007i
$76$	−7.98612	−	19.2802i	−0.105081	−	0.253687i
$77$	84.2570	−	34.9004i	1.09425	−	0.453252i
$78$	−1.33995	−	2.00537i	−0.0171788	−	0.0257099i
$79$	−29.1507	−	5.79844i	−0.368996	−	0.0733979i	0.00710935	−	0.999975i	$-0.497737\pi$
$79$	−29.1507	−	5.79844i	−0.368996	−	0.0733979i	−0.376106	+	0.926577i	$0.622737\pi$
$80$	55.5694	−	83.1655i	0.694618	−	1.03957i
$81$	56.7774	−	56.7774i	0.700956	−	0.700956i
$82$	67.8290	−	13.4920i	0.827183	−	0.164537i
$83$	25.7951	−	62.2748i	0.310784	−	0.750298i	−0.688893	−	0.724863i	$-0.741903\pi$
$83$	25.7951	−	62.2748i	0.310784	−	0.750298i	0.999676	−	0.0254351i	$-0.00809712\pi$
$84$			0.842922i			0.0100348i
$85$		0			0
$86$	160.285			1.86377
$87$	4.93230	+	2.04303i	0.0566931	+	0.0234831i
$88$	−19.8280	−	99.6823i	−0.225319	−	1.13275i
$89$	−90.1397	−	90.1397i	−1.01281	−	1.01281i	−0.999917	−	0.0128890i	$-0.995897\pi$
$89$	−90.1397	−	90.1397i	−1.01281	−	1.01281i	−0.0128890	−	0.999917i	$-0.504103\pi$
$90$	−88.0256	−	58.8169i	−0.978063	−	0.653521i
$91$	8.26771	−	41.5646i	0.0908540	−	0.456754i
$92$	−9.09541	+	6.07736i	−0.0988632	+	0.0660582i
$93$	0.0750988	+	0.181304i	0.000807514	+	0.00194951i
$94$	−30.1327	+	12.4814i	−0.320561	+	0.132781i
$95$	−74.4751	−	111.460i	−0.783949	−	1.17326i
$96$	2.08580	+	0.414892i	0.0217271	+	0.00432180i
$97$	37.5767	−	56.2374i	0.387388	−	0.579767i	−0.585606	−	0.810596i	$-0.699144\pi$
$97$	37.5767	−	56.2374i	0.387388	−	0.579767i	0.972995	+	0.230828i	$0.0741435\pi$
$98$	15.5581	−	15.5581i	0.158756	−	0.158756i
$99$	−128.542	+	25.5687i	−1.29841	+	0.258269i
$100$	−1.20941	+	2.91979i	−0.0120941	+	0.0291979i
$101$			34.6405i			0.342975i	0.985186	+	0.171488i	$0.0548573\pi$
$101$			34.6405i			0.342975i	−0.985186	+	0.171488i	$0.945143\pi$
$102$		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
$105$	1.05633	+	5.31052i	0.0100603	+	0.0505764i
$106$	8.03830	+	8.03830i	0.0758330	+	0.0758330i
$107$	7.93047	+	5.29897i	0.0741166	+	0.0495231i	0.592076	−	0.805882i	$-0.298308\pi$
$107$	7.93047	+	5.29897i	0.0741166	+	0.0495231i	−0.517960	+	0.855405i	$0.673308\pi$
$108$	0.473332	−	2.37960i	0.00438271	−	0.0220334i
$109$	−96.7260	+	64.6303i	−0.887395	+	0.592938i	−0.913553	−	0.406720i	$-0.866673\pi$
$109$	−96.7260	+	64.6303i	−0.887395	+	0.592938i	0.0261584	+	0.999658i	$0.491673\pi$
$110$	65.9347	+	159.180i	0.599406	+	1.44710i
$111$	6.94044	−	2.87483i	0.0625265	−	0.0258993i
$112$	64.6785	+	96.7982i	0.577487	+	0.864270i
$113$	−64.6835	−	12.8663i	−0.572420	−	0.113861i	−0.0996113	−	0.995026i	$-0.531760\pi$
$113$	−64.6835	−	12.8663i	−0.572420	−	0.113861i	−0.472809	+	0.881165i	$0.656760\pi$
$114$	4.93327	−	7.38315i	0.0432743	−	0.0647645i
$115$	−49.6863	+	49.6863i	−0.432055	+	0.432055i
$116$	−27.0593	+	5.38243i	−0.233270	+	0.0464003i
$117$	−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
$122$	−35.4523	−	178.231i	−0.290593	−	1.46091i
$123$	3.59425	+	3.59425i	0.0292216	+	0.0292216i
$124$	−0.843234	−	0.563431i	−0.00680027	−	0.00454380i
$125$	22.2063	−	111.639i	0.177650	−	0.893109i
$126$	102.455	−	68.4583i	0.813135	−	0.543319i
$127$	−36.5576	−	88.2580i	−0.287855	−	0.694945i	0.712119	−	0.702059i	$-0.247736\pi$
$127$	−36.5576	−	88.2580i	−0.287855	−	0.694945i	−0.999975	+	0.00711395i	$0.997736\pi$
$128$	141.344	−	58.5465i	1.10425	−	0.457395i
$129$	6.54505	+	9.79536i	0.0507368	+	0.0759330i
$130$	78.5249	+	15.6196i	0.604038	+	0.120151i
$131$	−23.8328	+	35.6683i	−0.181930	+	0.272277i	−0.911214	−	0.411934i	$-0.864853\pi$
$131$	−23.8328	+	35.6683i	−0.181930	+	0.272277i	0.729284	+	0.684211i	$0.239853\pi$
$132$	−1.39401	+	1.39401i	−0.0105607	+	0.0105607i
$133$	153.028	−	30.4391i	1.15058	−	0.228866i
$134$	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
$139$	50.9824	+	256.306i	0.366780	+	1.84393i	0.517940	+	0.855417i	$0.326699\pi$
$139$	50.9824	+	256.306i	0.366780	+	1.84393i	−0.151160	+	0.988509i	$0.548301\pi$
$140$	−19.7860	−	19.7860i	−0.141328	−	0.141328i
$141$	−1.99320	−	1.33181i	−0.0141362	−	0.00944549i
$142$	−24.8617	+	124.988i	−0.175083	+	0.880200i
$143$	82.4117	−	55.0658i	0.576306	−	0.385075i
$144$	−64.0239	−	154.567i	−0.444610	−	1.07338i
$145$	−163.732	+	67.8201i	−1.12919	+	0.467725i
$146$	−1.64605	−	2.46349i	−0.0112743	−	0.0168732i
$147$	1.58608	+	0.315492i	0.0107897	+	0.00214620i
$148$	−21.5685	+	32.2795i	−0.145733	+	0.218105i
$149$	83.6010	−	83.6010i	0.561080	−	0.561080i	−0.368534	−	0.929614i	$-0.620140\pi$
$149$	83.6010	−	83.6010i	0.561080	−	0.561080i	0.929614	+	0.368534i	$0.120140\pi$
$150$	−1.31889	+	0.262344i	−0.00879261	+	0.00174896i
$151$	−10.5977	+	25.5851i	−0.0701833	+	0.169437i	−0.955079	−	0.296352i	$-0.904230\pi$
$151$	−10.5977	+	25.5851i	−0.0701833	+	0.169437i	0.884895	+	0.465790i	$0.154230\pi$
$152$		−	173.880i		−	1.14395i
$153$		0			0
$154$	−200.539			−1.30220
$155$	−6.01857	−	2.49297i	−0.0388295	−	0.0160837i
$156$	0.178721	+	0.898490i	0.00114565	+	0.00575955i
$157$	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	$0.668995\pi$
$158$	54.3412	+	36.3096i	0.343932	+	0.229808i
$159$	−0.163003	+	0.819474i	−0.00102518	+	0.00515392i
$160$	−58.6990	+	39.2214i	−0.366869	+	0.245134i
$161$	−31.2979	−	75.5599i	−0.194397	−	0.469316i
$162$	−163.123	+	67.5676i	−1.00693	+	0.417084i
$163$	30.8428	+	46.1595i	0.189220	+	0.283187i	0.913935	−	0.405862i	$-0.133029\pi$
$163$	30.8428	+	46.1595i	0.189220	+	0.283187i	−0.724715	+	0.689049i	$0.758029\pi$
$164$	−25.7636	−	5.12469i	−0.157095	−	0.0312481i
$165$	−7.03551	+	10.5294i	−0.0426394	+	0.0638144i
$166$	−104.807	+	104.807i	−0.631367	+	0.631367i
$167$	−50.6674	+	10.0784i	−0.303398	+	0.0603495i	−0.344441	−	0.938808i	$-0.611932\pi$
$167$	−50.6674	+	10.0784i	−0.303398	+	0.0603495i	0.0410439	+	0.999157i	$0.486932\pi$
$168$	−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
$173$	3.60353	+	18.1162i	0.0208296	+	0.104718i	0.989802	−	0.142453i	$-0.0454991\pi$
$173$	3.60353	+	18.1162i	0.0208296	+	0.104718i	−0.968972	+	0.247171i	$0.920499\pi$
$174$	−8.30094	−	8.30094i	−0.0477066	−	0.0477066i
$175$	−19.6464	−	13.1273i	−0.112265	−	0.0750130i
$176$	−53.1190	+	267.047i	−0.301812	+	1.51731i
$177$	−3.79649	+	2.53674i	−0.0214491	+	0.0143318i
$178$	107.270	+	258.973i	0.602641	+	1.45490i
$179$	57.8989	−	23.9825i	0.323457	−	0.133980i	−0.215046	−	0.976604i	$-0.568990\pi$
$179$	57.8989	−	23.9825i	0.323457	−	0.133980i	0.538503	+	0.842624i	$0.318990\pi$
$180$	22.3405	+	33.4349i	0.124114	+	0.185749i
$181$	102.589	+	20.4063i	0.566792	+	0.112742i	0.470165	−	0.882579i	$-0.344194\pi$
$181$	102.589	+	20.4063i	0.566792	+	0.112742i	0.0966274	+	0.995321i	$0.469194\pi$
$182$	−51.7722	+	77.4825i	−0.284462	+	0.425728i
$183$	9.44444	−	9.44444i	0.0516090	−	0.0516090i
$184$	−89.3930	+	17.7814i	−0.485831	+	0.0966378i
$185$	−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
$190$	57.5064	+	289.104i	0.302665	+	1.52160i
$191$	137.930	+	137.930i	0.722145	+	0.722145i	0.969042	−	0.246897i	$-0.0794109\pi$
$191$	137.930	+	137.930i	0.722145	+	0.722145i	−0.246897	+	0.969042i	$0.579411\pi$
$192$	6.13293	+	4.09789i	0.0319423	+	0.0213432i
$193$	−17.2466	+	86.7045i	−0.0893606	+	0.449246i	0.910037	+	0.414528i	$0.136053\pi$
$193$	−17.2466	+	86.7045i	−0.0893606	+	0.449246i	−0.999397	+	0.0347181i	$0.988947\pi$
$194$	−123.661	+	82.6278i	−0.637429	+	0.425916i
$195$	2.25193	+	5.43664i	0.0115484	+	0.0278802i
$196$	−7.72105	+	3.19816i	−0.0393931	+	0.0163172i
$197$	−142.990	−	214.000i	−0.725838	−	1.08629i	−0.992469	−	0.122495i	$-0.960911\pi$
$197$	−142.990	−	214.000i	−0.725838	−	1.08629i	0.266631	−	0.963799i	$-0.414089\pi$
$198$	282.653	+	56.2232i	1.42754	+	0.283956i
$199$	−126.364	+	189.117i	−0.634996	+	0.950338i	0.364819	+	0.931079i	$0.381131\pi$
$199$	−126.364	+	189.117i	−0.634996	+	0.950338i	−0.999815	+	0.0192597i	$0.993869\pi$
$200$	−18.6198	+	18.6198i	−0.0930988	+	0.0930988i
$201$	7.05896	−	1.40411i	0.0351192	−	0.00698564i
$202$	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
$207$	22.9294	+	115.274i	0.110770	+	0.556879i
$208$	89.4660	+	89.4660i	0.430125	+	0.430125i
$209$	303.414	+	202.735i	1.45174	+	0.970023i
$210$	2.32277	−	11.6774i	0.0110608	−	0.0556065i
$211$	−6.72473	+	4.49332i	−0.0318708	+	0.0212954i	−0.571404	−	0.820669i	$-0.693601\pi$
$211$	−6.72473	+	4.49332i	−0.0318708	+	0.0212954i	0.539533	+	0.841965i	$0.318601\pi$
$212$	−1.65238	−	3.98919i	−0.00779423	−	0.0188169i
$213$	−8.65353	+	3.58441i	−0.0406269	+	0.0168282i
$214$	−11.6520	−	17.4384i	−0.0544485	−	0.0814879i
$215$	−383.559	−	76.2947i	−1.78400	−	0.354859i
$216$	11.2311	−	16.8086i	0.0519959	−	0.0778174i
$217$	5.36151	−	5.36151i	0.0247074	−	0.0247074i
$218$	250.887	−	49.9046i	1.15086	−	0.228920i
$219$	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	$-0.339910\pi$
$223$	45.3315	+	18.7769i	0.203280	+	0.0842014i	−0.278720	+	0.960372i	$0.589910\pi$
$224$	−16.0304	−	80.5902i	−0.0715642	−	0.359778i
$225$	24.0106	+	24.0106i	0.106714	+	0.106714i
$226$	120.580	+	80.5687i	0.533538	+	0.356499i
$227$	32.7870	−	164.831i	0.144436	−	0.726129i	−0.838893	−	0.544296i	$-0.816797\pi$
$227$	32.7870	−	164.831i	0.144436	−	0.726129i	0.983329	−	0.181833i	$-0.0582031\pi$
$228$	−2.80435	+	1.87381i	−0.0122998	+	0.00821846i
$229$	−47.5197	−	114.723i	−0.207510	−	0.500972i	0.785520	−	0.618836i	$-0.212395\pi$
$229$	−47.5197	−	114.723i	−0.207510	−	0.500972i	−0.993030	+	0.117864i	$0.962395\pi$
$230$	142.750	−	59.1289i	0.620651	−	0.257082i
$231$	−8.18879	−	12.2554i	−0.0354493	−	0.0530536i
$232$	−225.460	−	44.8469i	−0.971812	−	0.193305i
$233$	196.158	−	293.571i	0.841880	−	1.25996i	−0.121707	−	0.992566i	$-0.538837\pi$
$233$	196.158	−	293.571i	0.841880	−	1.25996i	0.963587	−	0.267396i	$-0.0861632\pi$
$234$	94.6943	−	94.6943i	0.404677	−	0.404677i
$235$	78.0483	−	15.5248i	0.332120	−	0.0660628i
$236$	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
$241$	−56.1919	−	282.496i	−0.233161	−	1.17218i	−0.902989	−	0.429665i	$-0.858632\pi$
$241$	−56.1919	−	282.496i	−0.233161	−	1.17218i	0.669827	−	0.742517i	$-0.266368\pi$
$242$	−143.509	−	143.509i	−0.593011	−	0.593011i
$243$	−32.5282	−	21.7347i	−0.133861	−	0.0894430i
$244$	−13.4659	+	67.6977i	−0.0551881	+	0.277450i
$245$	−44.6358	+	29.8247i	−0.182187	+	0.121733i
$246$	−4.27731	−	10.3263i	−0.0173875	−	0.0419770i
$247$	156.662	−	64.8915i	0.634259	−	0.262719i
$248$	−4.69455	−	7.02589i	−0.0189296	−	0.0283302i
$249$	−10.6847	−	2.12531i	−0.0429103	−	0.00853539i
$250$	−139.055	+	208.111i	−0.556221	+	0.832444i
$251$	−191.096	+	191.096i	−0.761337	+	0.761337i	−0.976564	−	0.215227i	$-0.930951\pi$
$251$	−191.096	+	191.096i	−0.761337	+	0.761337i	0.215227	+	0.976564i	$0.430951\pi$
$252$	−45.9041	+	9.13089i	−0.182159	+	0.0362337i
$253$	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	$-0.407756\pi$
$257$	−48.7819	−	20.2061i	−0.189813	−	0.0786230i	−0.475565	+	0.879680i	$0.657756\pi$
$258$	−5.05380	−	25.4071i	−0.0195884	−	0.0984773i
$259$	−205.242	−	205.242i	−0.792439	−	0.792439i
$260$	−25.2854	−	16.8952i	−0.0972517	−	0.0649815i
$261$	−57.8310	+	290.736i	−0.221575	+	1.11393i
$262$	78.4315	−	52.4062i	0.299357	−	0.200024i
$263$	194.228	+	468.907i	0.738509	+	1.78292i	0.611854	+	0.790970i	$0.290424\pi$
$263$	194.228	+	468.907i	0.738509	+	1.78292i	0.126654	+	0.991947i	$0.459576\pi$
$264$	−15.1757	+	6.28599i	−0.0574838	+	0.0238106i
$265$	−15.4094	−	23.0617i	−0.0581485	−	0.0870254i
$266$	−336.495	−	66.9329i	−1.26502	−	0.251628i
$267$	−11.4462	+	17.1304i	−0.0428696	+	0.0641588i
$268$	−26.3003	+	26.3003i	−0.0981353	+	0.0981353i
$269$	172.869	−	34.3858i	0.642637	−	0.127828i	0.136995	−	0.990572i	$-0.456256\pi$
$269$	172.869	−	34.3858i	0.642637	−	0.127828i	0.505642	+	0.862743i	$0.331256\pi$
$270$	−13.1146	+	31.6614i	−0.0485725	+	0.117264i
$271$		−	464.255i		−	1.71312i	−0.516050	−	0.856559i	$-0.672598\pi$
$271$		−	464.255i		−	1.71312i	0.516050	−	0.856559i	$-0.327402\pi$
$272$		0			0
$273$	−6.84919			−0.0250886
$274$	129.659	+	53.7064i	0.473207	+	0.196009i
$275$	−10.7811	−	54.2004i	−0.0392041	−	0.197093i
$276$	1.25012	+	1.25012i	0.00452941	+	0.00452941i
$277$	−146.824	−	98.1048i	−0.530051	−	0.354169i	0.261567	−	0.965185i	$-0.415761\pi$
$277$	−146.824	−	98.1048i	−0.530051	−	0.354169i	−0.791618	+	0.611017i	$0.790761\pi$
$278$	112.106	−	563.594i	0.403258	−	2.02732i
$279$	−9.06003	+	6.05372i	−0.0324732	+	0.0216979i
$280$	−89.2206	−	215.398i	−0.318645	−	0.769277i
$281$	369.073	−	152.875i	1.31343	−	0.544040i	0.387545	−	0.921851i	$-0.373323\pi$
$281$	369.073	−	152.875i	1.31343	−	0.544040i	0.925883	+	0.377811i	$0.123323\pi$
$282$	2.92854	+	4.38287i	0.0103849	+	0.0155421i
$283$	350.746	+	69.7677i	1.23938	+	0.246529i	0.770908	−	0.636947i	$-0.219803\pi$
$283$	350.746	+	69.7677i	1.23938	+	0.246529i	0.468477	+	0.883476i	$0.344803\pi$
$284$	26.8921	−	40.2469i	0.0946906	−	0.141715i
$285$	−15.3196	+	15.3196i	−0.0537530	+	0.0537530i
$286$	−213.759	+	42.5193i	−0.747409	+	0.148669i
$287$	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
$292$	0.219549	+	1.10375i	0.000751880	+	0.00377995i
$293$	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	$0.616275\pi$
$294$	−2.95670	−	1.97560i	−0.0100568	−	0.00671973i
$295$	29.5704	−	148.660i	0.100239	−	0.503933i
$296$	−268.955	+	179.710i	−0.908633	+	0.607129i
$297$	16.2354	+	39.1958i	0.0546647	+	0.131972i
$298$	−240.187	+	99.4888i	−0.805997	+	0.333855i
$299$	−49.3818	−	73.9051i	−0.165157	−	0.247174i
$300$	0.500956	+	0.0996463i	0.00166985	+	0.000332154i
$301$	252.884	−	378.468i	0.840147	−	1.25737i
$302$	43.0590	−	43.0590i	0.142579	−	0.142579i
$303$	5.49096	−	1.09222i	0.0181220	−	0.00360468i
$304$	−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
$309$	−4.76629	−	23.9618i	−0.0154249	−	0.0775462i
$310$	10.1291	+	10.1291i	0.0326745	+	0.0326745i
$311$	−180.101	−	120.340i	−0.579103	−	0.386944i	0.231243	−	0.972896i	$-0.425721\pi$
$311$	−180.101	−	120.340i	−0.579103	−	0.386944i	−0.810346	+	0.585952i	$0.800721\pi$
$312$	−1.48912	+	7.48629i	−0.00477281	+	0.0239945i
$313$	393.629	−	263.015i	1.25760	−	0.840302i	0.265302	−	0.964165i	$-0.414528\pi$
$313$	393.629	−	263.015i	1.25760	−	0.840302i	0.992299	+	0.123863i	$0.0395284\pi$
$314$	−66.5184	−	160.590i	−0.211842	−	0.511432i
$315$	−277.759	+	115.052i	−0.881776	+	0.365244i
$316$	−13.7915	−	20.6405i	−0.0436441	−	0.0653180i
$317$	251.422	+	50.0110i	0.793130	+	0.157763i	0.574997	−	0.818156i	$-0.305003\pi$
$317$	251.422	+	50.0110i	0.793130	+	0.157763i	0.218133	+	0.975919i	$0.430003\pi$
$318$	1.02072	−	1.52762i	0.00320982	−	0.00480384i
$319$	341.131	−	341.131i	1.06938	−	1.06938i
$320$	−240.149	+	47.7685i	−0.750464	+	0.149277i
$321$	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
$326$	−23.8154	−	119.728i	−0.0730535	−	0.367265i
$327$	13.2945	+	13.2945i	0.0406560	+	0.0406560i
$328$	−181.983	−	121.597i	−0.554828	−	0.370724i
$329$	−18.0696	+	90.8421i	−0.0549229	+	0.276116i
$330$	23.1532	−	15.4705i	0.0701612	−	0.0468802i
$331$	−86.3966	−	208.580i	−0.261017	−	0.630151i	0.737985	−	0.674817i	$-0.235778\pi$
$331$	−86.3966	−	208.580i	−0.261017	−	0.630151i	−0.999002	+	0.0446663i	$0.985778\pi$
$332$	52.0129	−	21.5444i	0.156665	−	0.0648929i
$333$	231.740	+	346.823i	0.695916	+	1.04151i
$334$	111.413	+	22.1615i	0.333572	+	0.0663516i
$335$	−132.736	+	198.654i	−0.396228	+	0.592997i
$336$	13.3044	−	13.3044i	0.0395965	−	0.0395965i
$337$	−354.200	+	70.4547i	−1.05104	+	0.209064i	−0.690241	−	0.723580i	$-0.742495\pi$
$337$	−354.200	+	70.4547i	−1.05104	+	0.209064i	−0.360797	+	0.932644i	$0.617495\pi$
$338$	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
$343$	−71.8838	−	361.384i	−0.209574	−	1.05360i
$344$	−358.691	−	358.691i	−1.04271	−	1.04271i
$345$	9.44253	+	6.30930i	0.0273697	+	0.0182878i
$346$	7.92384	−	39.8358i	0.0229013	−	0.115132i
$347$	−13.1855	+	8.81030i	−0.0379987	+	0.0253899i	−0.574425	−	0.818558i	$-0.694774\pi$
$347$	−13.1855	+	8.81030i	−0.0379987	+	0.0253899i	0.536426	+	0.843947i	$0.319774\pi$
$348$	1.70637	+	4.11954i	0.00490336	+	0.0118377i
$349$	−292.270	+	121.062i	−0.837448	+	0.346883i	−0.759847	−	0.650102i	$-0.774726\pi$
$349$	−292.270	+	121.062i	−0.837448	+	0.346883i	−0.0776015	+	0.996984i	$0.524726\pi$
$350$	28.8657	+	43.2006i	0.0824735	+	0.123430i
$351$	19.3356	+	3.84608i	0.0550870	+	0.0109575i
$352$	106.768	−	159.789i	0.303318	−	0.453947i
$353$	−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	$0.375394\pi$
$354$	9.84732	−	1.95875i	0.0278173	−	0.00553320i
$355$	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	$-0.304231\pi$
$359$	146.269	+	60.5865i	0.407434	+	0.168765i	−0.169547	+	0.985522i	$0.554231\pi$
$360$	65.3646	+	328.610i	0.181568	+	0.912806i
$361$	186.183	+	186.183i	0.515743	+	0.515743i
$362$	−191.242	−	127.784i	−0.528292	−	0.352994i
$363$	2.91012	−	14.6302i	0.00801686	−	0.0403035i
$364$	29.4303	−	19.6647i	0.0808524	−	0.0540239i
$365$	2.76638	+	6.67862i	0.00757911	+	0.0182976i
$366$	−27.1340	+	11.2393i	−0.0741367	+	0.0307084i
$367$	271.669	+	406.581i	0.740242	+	1.10785i	0.990209	+	0.139596i	$0.0445803\pi$
$367$	271.669	+	406.581i	0.740242	+	1.10785i	−0.249967	+	0.968254i	$0.580420\pi$
$368$	239.482	+	47.6360i	0.650767	+	0.129446i
$369$	−156.802	+	234.671i	−0.424939	+	0.635966i
$370$	387.748	−	387.748i	1.04797	−	1.04797i
$371$	31.6624	−	6.29804i	0.0853434	−	0.0169759i
$372$	−0.0627237	+	0.151428i	−0.000168612	+	0.000407065i
$373$			573.453i			1.53741i	0.639605	+	0.768704i	$0.279098\pi$
$373$			573.453i			1.53741i	−0.639605	+	0.768704i	$0.720902\pi$
$374$		0			0
$375$	−18.3963			−0.0490568
$376$	95.3635	+	39.5008i	0.253626	+	0.105055i
$377$	−43.7352	−	219.872i	−0.116008	−	0.583214i
$378$	−28.2048	−	28.2048i	−0.0746159	−	0.0746159i
$379$	−583.696	−	390.013i	−1.54009	−	1.02906i	−0.979614	−	0.200890i	$-0.935617\pi$
$379$	−583.696	−	390.013i	−1.54009	−	1.02906i	−0.560480	−	0.828168i	$-0.689383\pi$
$380$	21.8427	−	109.811i	0.0574808	−	0.288976i
$381$	−12.8373	+	8.57764i	−0.0336938	+	0.0225135i
$382$	−164.142	−	396.274i	−0.429692	−	1.03737i
$383$	−284.935	+	118.024i	−0.743956	+	0.308157i	−0.722273	−	0.691608i	$-0.756902\pi$
$383$	−284.935	+	118.024i	−0.743956	+	0.308157i	−0.0216830	+	0.999765i	$0.506902\pi$
$384$	−13.7370	−	20.5588i	−0.0357733	−	0.0535386i
$385$	479.887	+	95.4555i	1.24646	+	0.247936i
$386$	107.998	−	161.630i	0.279787	−	0.418731i
$387$	−462.540	+	462.540i	−1.19519	+	1.19519i
$388$	55.4053	−	11.0208i	0.142797	−	0.0284041i
$389$	−109.097	+	263.382i	−0.280454	+	0.677076i	−0.999846	−	0.0175282i	$-0.994420\pi$
$389$	−109.097	+	263.382i	−0.280454	+	0.677076i	0.719392	+	0.694604i	$0.244420\pi$
$390$		−	12.9397i		−	0.0331787i
$391$		0			0
$392$	−69.6329			−0.177635
$393$	6.40533	+	2.65317i	0.0162986	+	0.00675108i
$394$	110.411	+	555.071i	0.280230	+	1.40881i
$395$	−112.755	−	112.755i	−0.285455	−	0.285455i
$396$	−91.0159	−	60.8149i	−0.229838	−	0.153573i
$397$	−24.2591	+	121.959i	−0.0611061	+	0.307201i	−0.999236	−	0.0390826i	$-0.987556\pi$
$397$	−24.2591	+	121.959i	−0.0611061	+	0.307201i	0.938130	+	0.346283i	$0.112556\pi$
$398$	415.852	−	277.864i	1.04486	−	0.698150i
$399$	−9.64997	−	23.2971i	−0.0241854	−	0.0583887i
$400$	65.1740	−	26.9960i	0.162935	−	0.0674899i
$401$	237.214	+	355.016i	0.591557	+	0.885328i	0.999618	−	0.0276268i	$-0.00879500\pi$
$401$	237.214	+	355.016i	0.591557	+	0.885328i	−0.408061	+	0.912955i	$0.633795\pi$
$402$	−15.5220	−	3.08752i	−0.0386120	−	0.00768041i
$403$	4.57818	−	6.85173i	0.0113602	−	0.0170018i
$404$	−20.4582	+	20.4582i	−0.0506391	+	0.0506391i
$405$	422.512	−	84.0429i	1.04324	−	0.207513i
$406$	−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
$411$	2.01235	+	10.1168i	0.00489624	+	0.0246150i
$412$	89.2768	+	89.2768i	0.216691	+	0.216691i
$413$	146.687	+	98.0131i	0.355174	+	0.237320i
$414$	50.4198	−	253.477i	0.121787	−	0.612264i
$415$	300.689	−	200.914i	0.724552	−	0.484130i
$416$	−34.1743	−	82.5042i	−0.0821499	−	0.198327i
$417$	39.0202	−	16.1627i	0.0935737	−	0.0387595i
$418$	−445.796	−	667.181i	−1.06650	−	1.59613i
$419$	−610.227	−	121.382i	−1.45639	−	0.289694i	−0.597506	−	0.801864i	$-0.703842\pi$
$419$	−610.227	−	121.382i	−1.45639	−	0.289694i	−0.858884	+	0.512170i	$0.828842\pi$
$420$	−2.51247	+	3.76018i	−0.00598207	+	0.00895280i
$421$	36.3708	−	36.3708i	0.0863916	−	0.0863916i	−0.662590	−	0.748982i	$-0.730543\pi$
$421$	36.3708	−	36.3708i	0.0863916	−	0.0863916i	0.748982	+	0.662590i	$0.230543\pi$
$422$	17.4426	−	3.46954i	0.0413331	−	0.00822166i
$423$	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
$428$	1.55413	+	7.81313i	0.00363114	+	0.0182550i
$429$	−11.3271	−	11.3271i	−0.0264034	−	0.0264034i
$430$	715.011	+	477.755i	1.66282	+	1.11106i
$431$	−91.8124	+	461.572i	−0.213022	+	1.07093i	0.715204	+	0.698916i	$0.246334\pi$
$431$	−91.8124	+	461.572i	−0.213022	+	1.07093i	−0.928226	+	0.372017i	$0.878666\pi$
$432$	−45.0299	+	30.0880i	−0.104236	+	0.0696481i
$433$	246.289	+	594.595i	0.568798	+	1.37320i	0.902569	+	0.430545i	$0.141679\pi$
$433$	246.289	+	594.595i	0.568798	+	1.37320i	−0.333772	+	0.942654i	$0.608321\pi$
$434$	−15.4037	+	6.38042i	−0.0354924	+	0.0147014i
$435$	15.9129	+	23.8153i	0.0365813	+	0.0547477i
$436$	−95.2948	−	18.9553i	−0.218566	−	0.0434755i
$437$	181.808	−	272.095i	0.416037	−	0.622644i
$438$	−0.338594	+	0.338594i	−0.000773047	+	0.000773047i
$439$	−811.551	+	161.428i	−1.84864	+	0.367717i	−0.989559	−	0.144129i	$-0.953962\pi$
$439$	−811.551	+	161.428i	−1.84864	+	0.367717i	−0.859077	+	0.511846i	$0.828962\pi$
$440$	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
$445$	−133.426	−	670.780i	−0.299835	−	1.50737i
$446$	−76.2917	−	76.2917i	−0.171058	−	0.171058i
$447$	−15.8878	−	10.6159i	−0.0355431	−	0.0237491i
$448$	55.5988	−	279.514i	0.124105	−	0.623916i
$449$	−653.488	+	436.647i	−1.45543	+	0.972487i	−0.458967	+	0.888453i	$0.651780\pi$
$449$	−653.488	+	436.647i	−1.45543	+	0.972487i	−0.996463	+	0.0840341i	$0.973220\pi$
$450$	−28.5736	−	68.9828i	−0.0634969	−	0.153295i
$451$	424.366	−	175.778i	0.940945	−	0.389752i
$452$	−30.6025	−	45.7999i	−0.0677047	−	0.101327i
$453$	4.38970	+	0.873166i	0.00969029	+	0.00192752i
$454$	−205.311	+	307.270i	−0.452227	+	0.676806i
$455$	160.772	−	160.772i	0.353344	−	0.353344i
$456$	−27.5622	+	5.48246i	−0.0604434	+	0.0120229i
$457$	−124.426	+	300.390i	−0.272266	+	0.657309i	−0.999580	−	0.0289968i	$-0.990769\pi$
$457$	−124.426	+	300.390i	−0.272266	+	0.657309i	0.727313	+	0.686306i	$0.240769\pi$
$458$			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	$-0.461049\pi$
$461$	−227.477	−	94.2242i	−0.493444	−	0.204391i	−0.615507	+	0.788131i	$0.711049\pi$
$462$	6.32302	+	31.7879i	0.0136862	+	0.0688051i
$463$	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	$0.626317\pi$
$464$	512.051	+	342.141i	1.10356	+	0.737374i
$465$	−0.205401	+	1.03262i	−0.000441724	+	0.00222069i
$466$	−645.537	+	431.334i	−1.38527	+	0.925610i
$467$	83.7591	+	202.212i	0.179356	+	0.433003i	0.987832	−	0.155526i	$-0.0497073\pi$
$467$	83.7591	+	202.212i	0.179356	+	0.433003i	−0.808476	+	0.588529i	$0.799707\pi$
$468$	−46.9943	+	19.4657i	−0.100415	+	0.0415933i
$469$	−154.495	−	231.218i	−0.329413	−	0.493002i
$470$	−171.621	−	34.1376i	−0.365152	−	0.0726332i
$471$	7.09779	−	10.6226i	0.0150696	−	0.0225533i
$472$	139.022	−	139.022i	0.294538	−	0.294538i
$473$	1044.12	−	207.688i	2.20744	−	0.439087i
$474$	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
$479$	98.0271	+	492.815i	0.204649	+	1.02884i	0.937376	+	0.348319i	$0.113247\pi$
$479$	98.0271	+	492.815i	0.204649	+	1.02884i	−0.732727	+	0.680523i	$0.761753\pi$
$480$	8.06788	+	8.06788i	0.0168081	+	0.0168081i
$481$	−262.288	−	175.255i	−0.545298	−	0.364356i
$482$	−123.561	+	621.183i	−0.256351	+	1.28876i
$483$	−10.9904	+	7.34353i	−0.0227544	+	0.0152040i
$484$	29.5001	+	71.2196i	0.0609506	+	0.147148i
$485$	335.250	−	138.865i	0.691238	−	0.286320i
$486$	47.7926	+	71.5267i	0.0983387	+	0.147174i
$487$	−246.948	−	49.1210i	−0.507080	−	0.100864i	−0.0650809	−	0.997880i	$-0.520731\pi$
$487$	−246.948	−	49.1210i	−0.507080	−	0.100864i	−0.441999	+	0.897016i	$0.645731\pi$
$488$	−319.516	+	478.189i	−0.654745	+	0.979896i
$489$	6.34439	−	6.34439i	0.0129742	−	0.0129742i
$490$	115.776	−	23.0293i	0.236278	−	0.0469986i
$491$	86.6215	−	209.123i	0.176418	−	0.425912i	−0.810792	−	0.585334i	$-0.800963\pi$
$491$	86.6215	−	209.123i	0.176418	−	0.425912i	0.987210	+	0.159423i	$0.0509632\pi$
$492$			4.24543i			0.00862893i
$493$		0			0
$494$	−372.869			−0.754796
$495$	−649.624	−	269.083i	−1.31237	−	0.543602i
$496$	4.41633	+	22.2024i	0.00890388	+	0.0447628i
$497$	255.901	+	255.901i	0.514891	+	0.514891i
$498$	19.9178	+	13.3086i	0.0399956	+	0.0267242i
$499$	42.1099	−	211.701i	0.0843886	−	0.424250i	−0.915377	−	0.402598i	$-0.868107\pi$
$499$	42.1099	−	211.701i	0.0843886	−	0.424250i	0.999766	−	0.0216522i	$-0.00689266\pi$
$500$	79.0470	−	52.8175i	0.158094	−	0.105635i
$501$	3.19510	+	7.71365i	0.00637744	+	0.0153965i
$502$	549.021	−	227.412i	1.09367	−	0.453012i
$503$	−490.279	−	733.755i	−0.974710	−	1.45876i	−0.886540	−	0.462651i	$-0.846898\pi$
$503$	−490.279	−	733.755i	−0.974710	−	1.45876i	−0.0881697	−	0.996105i	$-0.528102\pi$
$504$	−382.477	−	76.0793i	−0.758882	−	0.150951i
$505$	−103.252	+	154.527i	−0.204459	+	0.305994i
$506$	−297.414	+	297.414i	−0.587776	+	0.587776i
$507$	19.4879	−	3.87639i	0.0384377	−	0.00764574i
$508$	30.5335	−	73.7144i	0.0601053	−	0.145107i
$509$		−	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
$512$	−252.811	−	104.718i	−0.493772	−	0.204527i
$513$	14.1601	+	71.1874i	0.0276025	+	0.138767i
$514$	82.0986	+	82.0986i	0.159725	+	0.159725i
$515$	674.335	+	450.576i	1.30939	+	0.874906i
$516$	−1.91959	+	9.65043i	−0.00372013	+	0.0187024i
$517$	−180.116	+	120.350i	−0.348387	+	0.232785i
$518$	244.246	+	589.663i	0.471518	+	1.13835i
$519$	2.75802	−	1.14241i	0.00531411	−	0.00220117i
$520$	−140.772	−	210.680i	−0.270716	−	0.405154i
$521$	99.1978	+	19.7317i	0.190399	+	0.0378727i	0.289369	−	0.957218i	$-0.406555\pi$
$521$	99.1978	+	19.7317i	0.190399	+	0.0378727i	−0.0989697	+	0.995090i	$0.531555\pi$
$522$	362.136	−	541.975i	0.693747	−	1.03827i
$523$	−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	$0.429380\pi$
$524$	−35.1406	+	6.98989i	−0.0670621	+	0.0133395i
$525$	−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
$530$	11.8984	+	59.8174i	0.0224499	+	0.112863i
$531$	−179.272	−	179.272i	−0.337611	−	0.337611i
$532$	108.353	+	72.3992i	0.203671	+	0.136089i
$533$	41.6409	−	209.343i	0.0781255	−	0.392763i
$534$	37.6683	−	25.1691i	0.0705398	−	0.0471332i
$535$	19.5824	+	47.2762i	0.0366027	+	0.0883667i
$536$	−286.315	+	118.596i	−0.534170	+	0.221260i
$537$	−5.62709	−	8.42153i	−0.0104788	−	0.0156826i
$538$	−380.124	−	75.6114i	−0.706551	−	0.140542i
$539$	81.1882	−	121.507i	0.150628	−	0.225430i
$540$	9.20429	−	9.20429i	0.0170450	−	0.0170450i
$541$	−40.0392	+	7.96429i	−0.0740095	+	0.0147214i	−0.231956	−	0.972726i	$-0.574513\pi$
$541$	−40.0392	+	7.96429i	−0.0740095	+	0.0147214i	0.157947	+	0.987448i	$0.449513\pi$
$542$	−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
$547$	13.2836	+	66.7811i	0.0242844	+	0.122086i	0.991026	−	0.133669i	$-0.0426759\pi$
$547$	13.2836	+	66.7811i	0.0242844	+	0.122086i	−0.966742	+	0.255755i	$0.917676\pi$
$548$	−37.6931	−	37.6931i	−0.0687830	−	0.0687830i
$549$	616.635	+	412.022i	1.12320	+	0.750496i
$550$	−23.7068	+	119.182i	−0.0431032	+	0.216695i
$551$	686.260	−	458.544i	1.24548	−	0.832203i
$552$	5.63714	+	13.6093i	0.0102122	+	0.0246545i
$553$	171.470	−	71.0254i	0.310073	−	0.128436i
$554$	215.724	+	322.853i	0.389393	+	0.582768i
$555$	39.5294	+	7.86289i	0.0712242	+	0.0141674i
$556$	−121.261	+	181.480i	−0.218096	+	0.326403i
$557$	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	$0.164599\pi$
$558$	23.4999	−	4.67441i	0.0421144	−	0.00837708i
$559$	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	$-0.246616\pi$
$563$	408.295	+	169.121i	0.725212	+	0.300393i	0.0106294	+	0.999944i	$0.496616\pi$
$564$	−0.390606	−	1.96371i	−0.000692564	−	0.00348175i
$565$	−250.195	−	250.195i	−0.442824	−	0.442824i
$566$	−653.842	−	436.883i	−1.15520	−	0.771879i
$567$	−97.8195	+	491.772i	−0.172521	+	0.867322i
$568$	335.341	−	224.067i	0.590388	−	0.394485i
$569$	−246.656	−	595.479i	−0.433490	−	1.04654i	−0.978154	−	0.207882i	$-0.933343\pi$
$569$	−246.656	−	595.479i	−0.433490	−	1.04654i	0.544664	−	0.838654i	$-0.316657\pi$
$570$	44.0135	−	18.2310i	0.0772166	−	0.0319842i
$571$	66.5484	+	99.5967i	0.116547	+	0.174425i	0.885157	−	0.465293i	$-0.154051\pi$
$571$	66.5484	+	99.5967i	0.116547	+	0.174425i	−0.768610	+	0.639718i	$0.779051\pi$
$572$	81.1924	+	16.1502i	0.141945	+	0.0282346i
$573$	17.5147	−	26.2125i	0.0305666	−	0.0457461i
$574$	−305.369	+	305.369i	−0.532002	+	0.532002i
$575$	−48.6058	+	9.66830i	−0.0845319	+	0.0168144i
$576$	−156.730	+	378.379i	−0.272100	+	0.656908i
$577$			177.008i			0.306773i	0.988166	+	0.153387i	$0.0490180\pi$
$577$			177.008i			0.306773i	−0.988166	+	0.153387i	$0.950982\pi$
$578$		0			0
$579$	14.2876			0.0246763
$580$	−136.752	−	56.6444i	−0.235779	−	0.0976628i
$581$	82.1166	+	412.828i	0.141337	+	0.710548i
$582$	16.9966	+	16.9966i	0.0292038	+	0.0292038i
$583$	62.7783	+	41.9471i	0.107681	+	0.0719504i
$584$	−1.82930	+	9.19651i	−0.00313236	+	0.0157474i
$585$	−271.677	+	181.528i	−0.464404	+	0.310305i
$586$	−201.120	−	485.547i	−0.343208	−	0.828578i
$587$	−577.480	+	239.200i	−0.983781	+	0.407496i	−0.815825	−	0.578299i	$-0.803717\pi$
$587$	−577.480	+	239.200i	−0.983781	+	0.407496i	−0.167956	+	0.985794i	$0.553717\pi$
$588$	0.750395	+	1.12305i	0.00127618	+	0.00190994i
$589$	29.7560	+	5.91884i	0.0505195	+	0.0100490i
$590$	−185.169	+	277.125i	−0.313845	+	0.469703i
$591$	−29.4132	+	29.4132i	−0.0497685	+	0.0497685i
$592$	849.920	−	169.060i	1.43568	−	0.285574i
$593$	57.3899	−	138.551i	0.0967789	−	0.233645i	−0.868074	−	0.496434i	$-0.834642\pi$
$593$	57.3899	−	138.551i	0.0967789	−	0.233645i	0.964853	+	0.262789i	$0.0846424\pi$
$594$		−	93.2893i		−	0.157053i
$595$		0			0
$596$	98.7472			0.165683
$597$	33.9618	+	14.0674i	0.0568874	+	0.0235635i
$598$	38.1304	+	191.695i	0.0637633	+	0.320560i
$599$	217.159	+	217.159i	0.362536	+	0.362536i	0.864746	−	0.502210i	$-0.167480\pi$
$599$	217.159	+	217.159i	0.362536	+	0.362536i	−0.502210	+	0.864746i	$0.667480\pi$
$600$	3.53855	+	2.36438i	0.00589759	+	0.00394064i
$601$	−79.2601	+	398.467i	−0.131880	+	0.663007i	0.857123	+	0.515112i	$0.172250\pi$
$601$	−79.2601	+	398.467i	−0.131880	+	0.663007i	−0.989003	+	0.147895i	$0.952750\pi$
$602$	−832.218	+	556.070i	−1.38242	+	0.923705i
$603$	152.931	+	369.209i	0.253617	+	0.612287i
$604$	−21.3690	+	8.85135i	−0.0353792	+	0.0146545i
$605$	275.105	+	411.724i	0.454719	+	0.680536i
$606$	−12.0741	−	2.40169i	−0.0199243	−	0.00396319i
$607$	−576.178	+	862.312i	−0.949223	+	1.42061i	−0.0423995	+	0.999101i	$0.513500\pi$
$607$	−576.178	+	862.312i	−0.949223	+	1.42061i	−0.906823	+	0.421511i	$0.861500\pi$
$608$	232.484	−	232.484i	0.382374	−	0.382374i
$609$	−32.6969	+	6.50382i	−0.0536895	+	0.0106795i
$610$	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
$615$	5.32027	+	26.7468i	0.00865085	+	0.0434908i
$616$	448.774	+	448.774i	0.728529	+	0.728529i
$617$	−213.080	−	142.375i	−0.345348	−	0.230754i	0.370784	−	0.928719i	$-0.379089\pi$
$617$	−213.080	−	142.375i	−0.345348	−	0.230754i	−0.716132	+	0.697965i	$0.754089\pi$
$618$	−10.4807	+	52.6898i	−0.0169590	+	0.0852586i
$619$	76.4213	−	51.0630i	0.123459	−	0.0824928i	−0.492307	−	0.870421i	$-0.663846\pi$
$619$	76.4213	−	51.0630i	0.123459	−	0.0824928i	0.615767	+	0.787929i	$0.288846\pi$
$620$	−2.08217	−	5.02680i	−0.00335834	−	0.00810774i
$621$	35.1499	−	14.5596i	0.0566021	−	0.0234454i
$622$	264.616	+	396.026i	0.425428	+	0.636698i
$623$	780.735	+	155.298i	1.25319	+	0.249274i
$624$	11.3606	−	17.0024i	0.0182061	−	0.0272474i
$625$	498.708	−	498.708i	0.797932	−	0.797932i
$626$	−1020.99	+	203.088i	−1.63098	+	0.324422i
$627$	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	$-0.224546\pi$
$631$	530.804	+	219.866i	0.841210	+	0.348441i	0.0798795	+	0.996805i	$0.474546\pi$
$632$	−40.3518	−	202.862i	−0.0638478	−	0.320984i
$633$	0.924280	+	0.924280i	0.00146016	+	0.00146016i
$634$	−468.688	−	313.167i	−0.739256	−	0.493955i
$635$	99.9882	−	502.675i	0.157462	−	0.791614i
$636$	−0.580238	+	0.387703i	−0.000912324	+	0.000609595i
$637$	−25.9868	−	62.7377i	−0.0407956	−	0.0984893i
$638$	−980.076	+	405.961i	−1.53617	+	0.636302i
$639$	−288.940	−	432.429i	−0.452175	−	0.676727i
$640$	805.026	+	160.130i	1.25785	+	0.250203i
$641$	547.351	−	819.168i	0.853901	−	1.27795i	−0.105074	−	0.994464i	$-0.533508\pi$
$641$	547.351	−	819.168i	0.853901	−	1.27795i	0.958975	−	0.283489i	$-0.0914921\pi$
$642$	−2.39682	+	2.39682i	−0.00373337	+	0.00373337i
$643$	−34.6996	+	6.90218i	−0.0539652	+	0.0107343i	−0.221999	−	0.975047i	$-0.571258\pi$
$643$	−34.6996	+	6.90218i	−0.0539652	+	0.0107343i	0.168034	+	0.985781i	$0.446258\pi$
$644$	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
$649$	80.4959	+	404.680i	0.124031	+	0.623544i
$650$	39.9283	+	39.9283i	0.0614281	+	0.0614281i
$651$	−1.01892	−	0.680818i	−0.00156515	−	0.00104580i
$652$	−9.04585	+	45.4766i	−0.0138740	+	0.0697493i
$653$	529.021	−	353.481i	0.810140	−	0.541318i	−0.0801126	−	0.996786i	$-0.525528\pi$
$653$	529.021	−	353.481i	0.810140	−	0.541318i	0.890252	+	0.455468i	$0.150528\pi$
$654$	−15.8210	−	38.1953i	−0.0241912	−	0.0584026i
$655$	−212.631	+	88.0746i	−0.324627	+	0.134465i
$656$	325.758	+	487.531i	0.496582	+	0.743187i
$657$	11.8591	+	2.35892i	0.0180504	+	0.00359044i
$658$	113.151	−	169.343i	0.171963	−	0.257360i
$659$	−128.530	+	128.530i	−0.195037	+	0.195037i	−0.797869	−	0.602831i	$-0.794039\pi$
$659$	−128.530	+	128.530i	−0.195037	+	0.195037i	0.602831	+	0.797869i	$0.294039\pi$
$660$	−10.3736	+	2.06344i	−0.0157176	+	0.00312642i
$661$	−445.481	+	1075.49i	−0.673950	+	1.62706i	0.100887	+	0.994898i	$0.467832\pi$
$661$	−445.481	+	1075.49i	−0.673950	+	1.62706i	−0.774837	+	0.632161i	$0.782168\pi$
$662$			496.438i			0.749906i
$663$		0			0
$664$	469.082			0.706449
$665$	773.368	+	320.340i	1.16296	+	0.481714i
$666$	−178.939	−	899.588i	−0.268678	−	1.35073i
$667$	−305.919	−	305.919i	−0.458649	−	0.458649i
$668$	−35.8756	−	23.9713i	−0.0537060	−	0.0358852i
$669$	1.54707	−	7.77765i	0.00231251	−	0.0116258i
$670$	436.823	−	291.876i	0.651975	−	0.435635i
$671$	−461.884	−	1115.09i	−0.688352	−	1.66183i
$672$	−12.2691	+	5.08204i	−0.0182576	+	0.00756256i
$673$	−59.6248	−	89.2349i	−0.0885956	−	0.132593i	0.784525	−	0.620098i	$-0.212907\pi$
$673$	−59.6248	−	89.2349i	−0.0885956	−	0.132593i	−0.873120	+	0.487505i	$0.837907\pi$
$674$	778.854	+	154.924i	1.15557	+	0.229857i
$675$	6.10672	−	9.13935i	0.00904699	−	0.0135398i
$676$	−72.6081	+	72.6081i	−0.107408	+	0.107408i
$677$	−1034.24	+	205.722i	−1.52767	+	0.303873i	−0.886211	−	0.463281i	$-0.846672\pi$
$677$	−1034.24	+	205.722i	−1.52767	+	0.303873i	−0.641463	+	0.767154i	$0.721672\pi$
$678$	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
$683$	119.170	+	599.107i	0.174480	+	0.877170i	0.964499	+	0.264088i	$0.0850708\pi$
$683$	119.170	+	599.107i	0.174480	+	0.877170i	−0.790019	+	0.613083i	$0.789929\pi$
$684$	−132.422	−	132.422i	−0.193600	−	0.193600i
$685$	−284.708	−	190.236i	−0.415632	−	0.277716i
$686$	−158.066	+	794.652i	−0.230417	+	1.15838i
$687$	−16.6867	+	11.1497i	−0.0242892	+	0.0162295i
$688$	520.051	+	1255.51i	0.755888	+	1.82488i
$689$	32.4143	−	13.4265i	0.0470455	−	0.0194869i
$690$	−13.8736	−	20.7633i	−0.0201067	−	0.0300917i
$691$	−962.080	−	191.370i	−1.39230	−	0.276946i	−0.558726	−	0.829352i	$-0.688710\pi$
$691$	−962.080	−	191.370i	−1.39230	−	0.276946i	−0.833575	+	0.552406i	$0.813710\pi$
$692$	−8.57096	+	12.8274i	−0.0123858	+	0.0185366i
$693$	578.703	−	578.703i	0.835069	−	0.835069i
$694$	34.2006	−	6.80292i	0.0492804	−	0.00980248i
$695$	−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
$700$	−3.85008	−	19.3557i	−0.00550012	−	0.0276510i
$701$	−52.7814	−	52.7814i	−0.0752944	−	0.0752944i	0.668457	−	0.743751i	$-0.266955\pi$
$701$	−52.7814	−	52.7814i	−0.0752944	−	0.0752944i	−0.743751	+	0.668457i	$0.766955\pi$
$702$	−36.0443	−	24.0841i	−0.0513452	−	0.0343078i
$703$	226.577	−	1139.08i	0.322300	−	1.62031i
$704$	554.204	−	370.307i	0.787222	−	0.526005i
$705$	−4.92174	−	11.8821i	−0.00698120	−	0.0168541i
$706$	550.507	−	228.027i	0.779755	−	0.322985i
$707$	−120.177	−	179.858i	−0.169982	−	0.254396i
$708$	−3.74032	−	0.743996i	−0.00528294	−	0.00105084i
$709$	426.329	−	638.046i	0.601310	−	0.899923i	−0.398542	−	0.917150i	$-0.630484\pi$
$709$	426.329	−	638.046i	0.601310	−	0.899923i	0.999852	+	0.0172267i	$0.00548369\pi$
$710$	−483.454	+	483.454i	−0.680921	+	0.680921i
$711$	−261.595	+	52.0345i	−0.367925	+	0.0731849i
$712$	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
$717$	−6.51183	−	32.7372i	−0.00908206	−	0.0456586i
$718$	−246.167	−	246.167i	−0.342851	−	0.342851i
$719$	−958.597	−	640.514i	−1.33324	−	0.890840i	−0.334565	−	0.942373i	$-0.608590\pi$
$719$	−958.597	−	640.514i	−1.33324	−	0.890840i	−0.998671	+	0.0515322i	$0.983590\pi$
$720$	175.111	−	880.341i	0.243209	−	1.22270i
$721$	−784.874	+	524.436i	−1.08859	+	0.727373i
$722$	−221.566	−	534.907i	−0.306878	−	0.740869i
$723$	−43.0074	+	17.8143i	−0.0594847	+	0.0246394i
$724$	48.5362	+	72.6396i	0.0670390	+	0.100331i
$725$	−122.590	−	24.3847i	−0.169090	−	0.0336340i
$726$	−18.2231	+	27.2728i	−0.0251007	+	0.0375658i
$727$	−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	$0.311041\pi$
$728$	289.251	−	57.5357i	0.397323	−	0.0790325i
$729$	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	$-0.277198\pi$
$733$	409.632	+	169.675i	0.558843	+	0.231480i	−0.0853397	+	0.996352i	$0.527198\pi$
$734$	−209.770	−	1054.59i	−0.285791	−	1.43677i
$735$	6.13496	+	6.13496i	0.00834689	+	0.00834689i
$736$	−143.296	−	95.7472i	−0.194695	−	0.130091i
$737$	126.883	−	637.885i	0.172162	−	0.865515i
$738$	516.022	−	344.795i	0.699216	−	0.467201i
$739$	−40.6523	−	98.1432i	−0.0550098	−	0.132805i	0.893985	−	0.448096i	$-0.147898\pi$
$739$	−40.6523	−	98.1432i	−0.0550098	−	0.132805i	−0.948995	+	0.315291i	$0.897898\pi$
$740$	−192.429	+	79.7067i	−0.260039	+	0.107712i
$741$	−15.2257	−	22.7869i	−0.0205475	−	0.0307515i
$742$	−69.6228	−	13.8488i	−0.0938313	−	0.0186642i
$743$	−513.057	+	767.844i	−0.690521	+	1.03344i	0.306156	+	0.951981i	$0.400957\pi$
$743$	−513.057	+	767.844i	−0.690521	+	1.03344i	−0.996677	+	0.0814563i	$0.974043\pi$
$744$	−0.965673	+	0.965673i	−0.00129795	+	0.00129795i
$745$	622.121	−	123.748i	0.835062	−	0.166104i
$746$	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
$751$	−223.569	−	1123.96i	−0.297695	−	1.49662i	−0.782863	−	0.622195i	$-0.786241\pi$
$751$	−223.569	−	1123.96i	−0.297695	−	1.49662i	0.485167	−	0.874421i	$-0.338759\pi$
$752$	−195.534	−	195.534i	−0.260018	−	0.260018i
$753$	36.3164	+	24.2658i	0.0482289	+	0.0322255i
$754$	−96.1698	+	483.478i	−0.127546	+	0.641218i
$755$	−123.536	+	82.5438i	−0.163623	+	0.109330i
$756$	5.79787	+	13.9973i	0.00766915	+	0.0185150i
$757$	59.3832	−	24.5973i	0.0784455	−	0.0324932i	−0.343116	−	0.939293i	$-0.611482\pi$
$757$	59.3832	−	24.5973i	0.0784455	−	0.0324932i	0.421561	+	0.906800i	$0.361482\pi$
$758$	857.604	+	1283.50i	1.13140	+	1.69327i
$759$	−30.3203	−	6.03108i	−0.0399477	−	0.00794608i
$760$	518.279	−	775.659i	0.681945	−	1.02060i
$761$	173.164	−	173.164i	0.227548	−	0.227548i	−0.584120	−	0.811668i	$-0.698560\pi$
$761$	173.164	−	173.164i	0.227548	−	0.227548i	0.811668	+	0.584120i	$0.198560\pi$
$762$	33.2974	−	6.62327i	0.0436974	−	0.00869195i
$763$	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
$768$	4.85111	+	24.3882i	0.00631655	+	0.0317555i
$769$	−550.339	−	550.339i	−0.715655	−	0.715655i	0.252057	−	0.967712i	$-0.418893\pi$
$769$	−550.339	−	550.339i	−0.715655	−	0.715655i	−0.967712	+	0.252057i	$0.918893\pi$
$770$	−894.581	−	597.740i	−1.16179	−	0.776285i
$771$	−1.66483	+	8.36964i	−0.00215931	+	0.0108556i
$772$	−61.3921	+	41.0209i	−0.0795235	+	0.0531359i
$773$	−165.492	−	399.534i	−0.214091	−	0.516861i	0.779953	−	0.625837i	$-0.215243\pi$
$773$	−165.492	−	399.534i	−0.214091	−	0.516861i	−0.994044	+	0.108976i	$0.965243\pi$
$774$	1328.89	−	550.442i	1.71691	−	0.711166i
$775$	−2.55258	−	3.82020i	−0.00329365	−	0.00492929i
$776$	461.642	+	91.8263i	0.594899	+	0.118333i
$777$	−26.0621	+	39.0047i	−0.0335420	+	0.0501991i
$778$	443.266	−	443.266i	0.569751	−	0.569751i
$779$	770.735	−	153.309i	0.989390	−	0.196802i
$780$	−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
$785$	82.7379	+	415.951i	0.105399	+	0.529874i
$786$	−10.7800	−	10.7800i	−0.0137150	−	0.0137150i
$787$	947.377	+	633.017i	1.20378	+	0.804342i	0.985189	−	0.171474i	$-0.0548531\pi$
$787$	947.377	+	633.017i	1.20378	+	0.804342i	0.218594	+	0.975816i	$0.429853\pi$
$788$	41.9374	−	210.833i	0.0532200	−	0.267555i
$789$	68.2037	−	45.5723i	0.0864432	−	0.0577595i
$790$	134.183	+	323.946i	0.169852	+	0.410059i
$791$	380.481	−	157.601i	0.481013	−	0.199242i
$792$	−506.714	−	758.351i	−0.639791	−	0.957515i
$793$	−550.080	−	109.418i	−0.693670	−	0.137980i
$794$	151.910	−	227.349i	0.191322	−	0.286334i
$795$	−3.16972	+	3.16972i	−0.00398707	+	0.00398707i
$796$	−186.319	+	37.0612i	−0.234069	+	0.0465593i
$797$	−43.1132	+	104.084i	−0.0540943	+	0.130595i	−0.948616	−	0.316429i	$-0.897516\pi$
$797$	−43.1132	+	104.084i	−0.0540943	+	0.130595i	0.894522	+	0.447024i	$0.147516\pi$
$798$			55.4491i			0.0694850i
$799$		0			0
$800$	−49.7905			−0.0622381
$801$	−1056.88	−	437.775i	−1.31945	−	0.546536i
$802$	−183.166	−	920.840i	−0.228387	−	1.14818i
$803$	−13.9147	−	13.9147i	−0.0173284	−	0.0173284i
$804$	4.99818	+	3.33967i	0.00621664	+	0.00415382i
$805$	85.6025	−	430.353i	0.106338	−	0.534600i
$806$	−15.0664	+	10.0670i	−0.0186927	+	0.0124901i
$807$	−10.9012	−	26.3178i	−0.0135083	−	0.0326119i
$808$	−222.716	+	92.2520i	−0.275639	+	0.114173i
$809$	−361.469	−	540.977i	−0.446810	−	0.668698i	0.537878	−	0.843022i	$-0.319226\pi$
$809$	−361.469	−	540.977i	−0.446810	−	0.668698i	−0.984688	+	0.174324i	$0.944226\pi$
$810$	−929.068	−	184.803i	−1.14700	−	0.228152i
$811$	357.615	−	535.209i	0.440956	−	0.659937i	−0.542715	−	0.839917i	$-0.682603\pi$
$811$	357.615	−	535.209i	0.440956	−	0.659937i	0.983670	+	0.179980i	$0.0576034\pi$
$812$	121.822	−	121.822i	0.150027	−	0.150027i
$813$	−73.5903	+	14.6380i	−0.0905169	+	0.0180049i
$814$	−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
$819$	−74.1934	−	372.996i	−0.0905903	−	0.455428i
$820$	−99.6533	−	99.6533i	−0.121528	−	0.121528i
$821$	743.294	+	496.653i	0.905352	+	0.604937i	0.918692	−	0.394974i	$-0.129246\pi$
$821$	743.294	+	496.653i	0.905352	+	0.604937i	−0.0133400	+	0.999911i	$0.504246\pi$
$822$	4.42499	−	22.2459i	0.00538320	−	0.0270632i
$823$	−768.962	+	513.804i	−0.934340	+	0.624306i	−0.926756	−	0.375665i	$-0.877414\pi$
$823$	−768.962	+	513.804i	−0.934340	+	0.624306i	−0.00758474	+	0.999971i	$0.502414\pi$
$824$	402.575	+	971.901i	0.488562	+	1.17949i
$825$	−8.25153	+	3.41789i	−0.0100018	+	0.00414290i
$826$	−215.522	−	322.552i	−0.260923	−	0.390498i
$827$	−831.543	−	165.404i	−1.00549	−	0.200005i	−0.335237	−	0.942134i	$-0.608816\pi$
$827$	−831.543	−	165.404i	−1.00549	−	0.200005i	−0.670257	+	0.742129i	$0.733816\pi$
$828$	−54.5375	+	81.6211i	−0.0658665	+	0.0985762i
$829$	−862.801	+	862.801i	−1.04077	+	1.04077i	−0.0416400	+	0.999133i	$0.513258\pi$
$829$	−862.801	+	862.801i	−1.04077	+	1.04077i	−0.999133	+	0.0416400i	$0.986742\pi$
$830$	−779.926	+	155.137i	−0.939670	+	0.186912i
$831$	−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
$836$	59.4598	+	298.925i	0.0711242	+	0.357566i
$837$	2.49414	+	2.49414i	0.00297985	+	0.00297985i
$838$	1137.55	+	760.089i	1.35746	+	0.907028i
$839$	74.9935	−	377.018i	0.0893844	−	0.449366i	−0.910011	−	0.414585i	$-0.863927\pi$
$839$	74.9935	−	377.018i	0.0893844	−	0.449366i	0.999395	−	0.0347806i	$-0.0110732\pi$
$840$	−31.3301	+	20.9341i	−0.0372977	+	0.0249216i
$841$	−95.7324	−	231.119i	−0.113832	−	0.274814i
$842$	−104.494	+	43.2829i	−0.124102	+	0.0514048i
$843$	−35.8696	−	53.6826i	−0.0425499	−	0.0636804i
$844$	−6.62523	−	1.31784i	−0.00784980	−	0.00156142i
$845$	−366.450	+	548.432i	−0.433669	+	0.649032i
$846$	−206.961	+	206.961i	−0.244634	+	0.244634i
$847$	−565.273	+	112.440i	−0.667382	+	0.132751i
$848$	−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
$853$	170.470	+	857.011i	0.199848	+	1.00470i	0.942291	+	0.334794i	$0.108667\pi$
$853$	170.470	+	857.011i	0.199848	+	1.00470i	−0.742444	+	0.669908i	$0.766333\pi$
$854$	802.404	+	802.404i	0.939583	+	0.939583i
$855$	−1000.23	−	668.331i	−1.16986	−	0.781673i
$856$	−12.9491	+	65.0997i	−0.0151275	+	0.0760510i
$857$	1116.86	−	746.263i	1.30322	−	0.870786i	0.306515	−	0.951866i	$-0.400837\pi$
$857$	1116.86	−	746.263i	1.30322	−	0.870786i	0.996708	+	0.0810800i	$0.0258369\pi$
$858$	13.4797	+	32.5429i	0.0157106	+	0.0379288i
$859$	−236.510	+	97.9655i	−0.275331	+	0.114046i	−0.516077	−	0.856542i	$-0.672608\pi$
$859$	−236.510	+	97.9655i	−0.275331	+	0.114046i	0.240745	+	0.970588i	$0.422608\pi$
$860$	−181.466	−	271.584i	−0.211007	−	0.315795i
$861$	−31.1312	−	6.19238i	−0.0361570	−	0.00719208i
$862$	574.927	−	860.439i	0.666968	−	0.998189i
$863$	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	$-0.132245\pi$
$864$	37.4900	−	7.45722i	0.0433912	−	0.00863105i
$865$	−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
$870$	−12.2872	−	61.7719i	−0.0141232	−	0.0710022i
$871$	−213.704	−	213.704i	−0.245355	−	0.245355i
$872$	−673.124	−	449.767i	−0.771932	−	0.515788i
$873$	118.412	−	595.296i	0.135638	−	0.681897i
$874$	−598.314	+	399.781i	−0.684570	+	0.457415i
$875$	272.006	+	656.681i	0.310864	+	0.750493i
$876$	0.168035	−	0.0696025i	0.000191821	−	7.94550e-5i
$877$	273.902	+	409.924i	0.312317	+	0.467416i	0.954107	−	0.299465i	$-0.0968080\pi$
$877$	273.902	+	409.924i	0.312317	+	0.467416i	−0.641790	+	0.766880i	$0.721808\pi$
$878$	1784.53	+	354.965i	2.03249	+	0.404288i
$879$	21.4604	−	32.1177i	0.0244145	−	0.0365389i
$880$	−1032.94	+	1032.94i	−1.17379	+	1.17379i
$881$	−394.389	+	78.4489i	−0.447661	+	0.0890453i	−0.413772	−	0.910380i	$-0.635789\pi$
$881$	−394.389	+	78.4489i	−0.447661	+	0.0890453i	−0.0338884	+	0.999426i	$0.510789\pi$
$882$	75.5597	−	182.417i	0.0856686	−	0.206822i
$883$			907.327i			1.02755i	0.857925	+	0.513775i	$0.171754\pi$
$883$			907.327i			1.02755i	−0.857925	+	0.513775i	$0.828246\pi$
$884$		0			0
$885$	−24.4969			−0.0276801
$886$	−720.035	−	298.248i	−0.812681	−	0.336624i
$887$	247.891	+	1246.23i	0.279471	+	1.40500i	0.824160	+	0.566357i	$0.191648\pi$
$887$	247.891	+	1246.23i	0.279471	+	1.40500i	−0.544689	+	0.838638i	$0.683352\pi$
$888$	36.9665	+	36.9665i	0.0416290	+	0.0416290i
$889$	496.002	+	331.418i	0.557933	+	0.372799i
$890$	−293.393	+	1474.99i	−0.329655	+	1.65729i
$891$	−975.055	+	651.511i	−1.09434	+	0.731213i
$892$	15.6828	+	37.8615i	0.0175816	+	0.0424457i
$893$	−342.395	+	141.825i	−0.383421	+	0.158818i
$894$	23.3434	+	34.9358i	0.0261111	+	0.0390781i
$895$	329.764	+	65.5942i	0.368452	+	0.0732896i
$896$	−530.761	+	794.340i	−0.592367	+	0.886540i
$897$	−10.1579	+	10.1579i	−0.0113243	+	0.0113243i
$898$	1695.01	−	337.159i	1.88754	−	0.375456i
$899$	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
$904$	−89.5380	−	450.138i	−0.0990464	−	0.497940i
$905$	396.815	+	396.815i	0.438470	+	0.438470i
$906$	−8.18305	−	5.46774i	−0.00903207	−	0.00603503i
$907$	−299.309	+	1504.73i	−0.329998	+	1.65901i	0.358315	+	0.933601i	$0.383351\pi$
$907$	−299.309	+	1504.73i	−0.329998	+	1.65901i	−0.688313	+	0.725413i	$0.741649\pi$
$908$	116.711	−	77.9836i	0.128536	−	0.0858850i
$909$	118.961	+	287.197i	0.130870	+	0.315948i
$910$	−461.899	+	191.325i	−0.507582	+	0.210247i
$911$	−203.486	−	304.539i	−0.223366	−	0.334291i	0.702813	−	0.711374i	$-0.251927\pi$
$911$	−203.486	−	304.539i	−0.223366	−	0.334291i	−0.926179	+	0.377084i	$0.876927\pi$
$912$	73.8387	+	14.6874i	0.0809634	+	0.0161046i
$913$	−546.925	+	818.531i	−0.599041	+	0.896529i
$914$	505.549	−	505.549i	0.553117	−	0.553117i
$915$	70.2813	−	13.9798i	0.0768102	−	0.0152785i
$916$	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
$921$	−12.9259	−	64.9830i	−0.0140347	−	0.0705570i
$922$	382.839	+	382.839i	0.415226	+	0.415226i
$923$	327.028	+	218.513i	0.354310	+	0.236742i
$924$	2.40168	−	12.0741i	0.00259922	−	0.0130672i
$925$	−146.240	+	97.7142i	−0.158097	+	0.105637i
$926$	−295.212	−	712.706i	−0.318804	−	0.769661i
$927$	1253.29	−	519.128i	1.35198	−	0.560009i
$928$	−241.487	−	361.410i	−0.260223	−	0.389451i
$929$	952.999	+	189.563i	1.02583	+	0.204051i	0.679203	−	0.733951i	$-0.262326\pi$
$929$	952.999	+	189.563i	1.02583	+	0.204051i	0.346631	+	0.938002i	$0.387326\pi$
$930$	1.28622	−	1.92496i	0.00138303	−	0.00206985i
$931$	176.785	−	176.785i	0.189887	−	0.189887i
$932$	289.228	−	57.5309i	0.310330	−	0.0617285i
$933$	−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	$-0.478762\pi$
$937$	−554.438	−	229.656i	−0.591716	−	0.245097i	−0.658389	+	0.752678i	$0.728762\pi$
$938$	119.294	+	599.732i	0.127179	+	0.639373i
$939$	−54.1023	−	54.1023i	−0.0576170	−	0.0576170i
$940$	55.2630	+	36.9255i	0.0587904	+	0.0392825i
$941$	−211.575	+	1063.66i	−0.224840	+	1.13035i	0.689152	+	0.724617i	$0.257983\pi$
$941$	−211.575	+	1063.66i	−0.224840	+	1.13035i	−0.913992	+	0.405732i	$0.867017\pi$
$942$	−23.3581	+	15.6074i	−0.0247963	+	0.0165684i
$943$	−157.634	−	380.563i	−0.167162	−	0.403566i
$944$	−486.613	+	201.562i	−0.515480	+	0.213519i
$945$	54.0685	+	80.9192i	0.0572153	+	0.0856288i
$946$	−2295.93	−	456.688i	−2.42698	−	0.482757i
$947$	−387.099	+	579.335i	−0.408764	+	0.611758i	−0.977544	−	0.210731i	$-0.932416\pi$
$947$	−387.099	+	579.335i	−0.408764	+	0.611758i	0.568780	+	0.822490i	$0.307416\pi$
$948$	−2.83693	+	2.83693i	−0.00299254	+	0.00299254i
$949$	−8.96854	+	1.78395i	−0.00945051	+	0.00187982i
$950$	−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
$955$	204.166	+	1026.41i	0.213786	+	1.07478i
$956$	121.972	+	121.972i	0.127586	+	0.127586i
$957$	−64.8295	−	43.3177i	−0.0677424	−	0.0452640i
$958$	215.553	−	1083.66i	0.225003	−	1.13117i
$959$	331.378	−	221.420i	0.345545	−	0.230886i
$960$	15.1438	+	36.5604i	0.0157748	+	0.0380838i
$961$	−886.486	+	367.195i	−0.922462	+	0.382096i
$962$	385.371	+	576.749i	0.400594	+	0.599531i
$963$	83.9473	+	16.6982i	0.0871727	+	0.0173397i
$964$	133.652	−	200.024i	0.138643	−	0.207494i
$965$	−335.373	+	335.373i	−0.347536	+	0.347536i
$966$	28.5068	−	5.67035i	0.0295101	−	0.00586992i
$967$	231.136	−	558.012i	0.239024	−	0.577055i	−0.758158	−	0.652071i	$-0.773901\pi$
$967$	231.136	−	558.012i	0.239024	−	0.577055i	0.997182	+	0.0750154i	$0.0239006\pi$
$968$			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	$-0.183155\pi$
$971$	1017.06	+	421.281i	1.04744	+	0.433863i	0.208461	+	0.978031i	$0.433155\pi$
$972$	−6.37453	−	32.0469i	−0.00655816	−	0.0329701i
$973$	−1153.90	−	1153.90i	−1.18592	−	1.18592i
$974$	460.348	+	307.594i	0.472636	+	0.315805i
$975$	−0.809680	+	4.07054i	−0.000830441	+	0.00417491i
$976$	1281.06	−	855.978i	1.31256	−	0.877026i
$977$	−419.266	−	1012.20i	−0.429136	−	1.03603i	−0.979562	−	0.201142i	$-0.935535\pi$
$977$	−419.266	−	1012.20i	−0.429136	−	1.03603i	0.550426	−	0.834884i	$-0.314465\pi$
$978$	−18.2276	+	7.55010i	−0.0186376	+	0.00771994i
$979$	1034.34	+	1547.99i	1.05652	+	1.58120i
$980$	−43.9754	−	8.74724i	−0.0448728	−	0.00892576i
$981$	−579.984	+	868.008i	−0.591217	+	0.884819i
$982$	−351.948	+	351.948i	−0.358399	+	0.358399i
$983$	−1205.50	+	239.790i	−1.22635	+	0.243937i	−0.765439	−	0.643509i	$-0.777478\pi$
$983$	−1205.50	+	239.790i	−1.22635	+	0.243937i	−0.460913	+	0.887445i	$0.652478\pi$
$984$	−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
$989$	−186.250	−	936.344i	−0.188322	−	0.946758i
$990$	1093.30	+	1093.30i	1.10434	+	1.10434i
$991$	612.594	+	409.322i	0.618158	+	0.413040i	0.824838	−	0.565369i	$-0.191266\pi$
$991$	612.594	+	409.322i	0.618158	+	0.413040i	−0.206681	+	0.978408i	$0.566266\pi$
$992$	3.11708	−	15.6706i	0.00314222	−	0.0157970i
$993$	−30.3385	+	20.2715i	−0.0305523	+	0.0204144i
$994$	−304.533	−	735.207i	−0.306371	−	0.739645i
$995$	−1127.39	+	466.981i	−1.13306	+	0.469328i
$996$	−5.05504	−	7.56540i	−0.00507534	−	0.00759578i
$997$	171.215	+	34.0568i	0.171730	+	0.0341593i	0.280206	−	0.959940i	$-0.409597\pi$
$997$	171.215	+	34.0568i	0.171730	+	0.0341593i	−0.108476	+	0.994099i	$0.534597\pi$
$998$	−263.691	+	394.641i	−0.264219	+	0.395432i
$999$	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.d.249.1		8
17.2	even	8		289.3.e.i.214.1		8
17.3	odd	16		289.3.e.b.65.1		8
17.4	even	4		289.3.e.l.40.1		8
17.5	odd	16		289.3.e.k.224.1		8
17.6	odd	16		289.3.e.c.158.1		8
17.7	odd	16		289.3.e.i.131.1		8
17.8	even	8		289.3.e.c.75.1		8
17.9	even	8		17.3.e.a.7.1	yes	8
17.10	odd	16		289.3.e.m.131.1		8
17.11	odd	16		17.3.e.a.5.1	✓	8
17.12	odd	16		289.3.e.l.224.1		8
17.13	even	4		289.3.e.k.40.1		8
17.14	odd	16	inner	289.3.e.d.65.1		8
17.15	even	8		289.3.e.m.214.1		8
17.16	even	2		289.3.e.b.249.1		8
51.11	even	16		153.3.p.b.73.1		8
51.26	odd	8		153.3.p.b.109.1		8
68.11	even	16		272.3.bh.c.209.1		8
68.43	odd	8		272.3.bh.c.177.1		8
85.9	even	8		425.3.u.b.126.1		8
85.28	even	16		425.3.t.a.124.1		8
85.43	odd	8		425.3.t.c.24.1		8
85.62	even	16		425.3.t.c.124.1		8
85.77	odd	8		425.3.t.a.24.1		8
85.79	odd	16		425.3.u.b.226.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.5.1	✓	8	17.11	odd	16
17.3.e.a.7.1	yes	8	17.9	even	8
153.3.p.b.73.1		8	51.11	even	16
153.3.p.b.109.1		8	51.26	odd	8
272.3.bh.c.177.1		8	68.43	odd	8
272.3.bh.c.209.1		8	68.11	even	16
289.3.e.b.65.1		8	17.3	odd	16
289.3.e.b.249.1		8	17.16	even	2
289.3.e.c.75.1		8	17.8	even	8
289.3.e.c.158.1		8	17.6	odd	16
289.3.e.d.65.1		8	17.14	odd	16	inner
289.3.e.d.249.1		8	1.1	even	1	trivial
289.3.e.i.131.1		8	17.7	odd	16
289.3.e.i.214.1		8	17.2	even	8
289.3.e.k.40.1		8	17.13	even	4
289.3.e.k.224.1		8	17.5	odd	16
289.3.e.l.40.1		8	17.4	even	4
289.3.e.l.224.1		8	17.12	odd	16
289.3.e.m.131.1		8	17.10	odd	16
289.3.e.m.214.1		8	17.15	even	8
425.3.t.a.24.1		8	85.77	odd	8
425.3.t.a.124.1		8	85.28	even	16
425.3.t.c.24.1		8	85.43	odd	8
425.3.t.c.124.1		8	85.62	even	16
425.3.u.b.126.1		8	85.9	even	8
425.3.u.b.226.1		8	85.79	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.03153 - 0.841487i) q^{2} +(-0.0315301 - 0.158513i) q^{3} +(0.590587 + 0.590587i) q^{4} +(4.46088 + 2.98067i) q^{5} +(-0.0693320 + 0.348555i) q^{6} +(-5.19212 + 3.46927i) q^{7} +(2.66313 + 6.42935i) q^{8} +(8.29078 - 3.43416i) q^{9} +(-6.55423 - 9.80910i) q^{10} +(-14.3240 - 2.84923i) q^{11} +(0.0749942 - 0.112237i) q^{12} +(-4.79884 + 4.79884i) q^{13} +(13.4673 - 2.67881i) q^{14} +(0.331821 - 0.801088i) q^{15} -18.6433i q^{16} -19.7328 q^{18} +(-23.0841 - 9.56175i) q^{19} +(0.874196 + 4.39488i) q^{20} +(0.713631 + 0.713631i) q^{21} +(26.7021 + 17.8418i) q^{22} +(-2.55513 + 12.8455i) q^{23} +(0.935165 - 0.624858i) q^{24} +(1.44803 + 3.49585i) q^{25} +(13.7871 - 5.71082i) q^{26} +(-1.61388 - 2.41534i) q^{27} +(-5.11530 - 1.01750i) q^{28} +(-18.3520 + 27.4657i) q^{29} +(-1.34821 + 1.34821i) q^{30} +(-1.19090 + 0.236886i) q^{31} +(-5.03558 + 12.1570i) q^{32} +2.36038i q^{33} -33.5022 q^{35} +(6.92459 + 2.86826i) q^{36} +(9.06812 + 45.5885i) q^{37} +(38.8500 + 38.8500i) q^{38} +(0.911984 + 0.609368i) q^{39} +(-7.28387 + 36.6185i) q^{40} +(-26.1505 + 17.4732i) q^{41} +(-0.849251 - 2.05027i) q^{42} +(-67.3441 + 27.8948i) q^{43} +(-6.77687 - 10.1423i) q^{44} +(47.2203 + 9.39270i) q^{45} +(16.0002 - 23.9459i) q^{46} +(10.4882 - 10.4882i) q^{47} +(-2.95520 + 0.587825i) q^{48} +(-3.82915 + 9.24438i) q^{49} -8.32041i q^{50} -5.66826 q^{52} +(-4.77624 - 1.97838i) q^{53} +(1.24616 + 6.26489i) q^{54} +(-55.4053 - 55.4053i) q^{55} +(-36.1324 - 24.1429i) q^{56} +(-0.787813 + 3.96061i) q^{57} +(60.3947 - 40.3544i) q^{58} +(-10.8115 - 26.1013i) q^{59} +(0.669081 - 0.277142i) q^{60} +(45.9135 + 68.7144i) q^{61} +(2.61870 + 0.520891i) q^{62} +(-31.1328 + 46.5935i) q^{63} +(-32.2713 + 32.2713i) q^{64} +(-35.7108 + 7.10332i) q^{65} +(1.98623 - 4.79518i) q^{66} +44.5324i q^{67} +2.11674 q^{69} +(68.0607 + 28.1917i) q^{70} +(-11.3064 - 56.8410i) q^{71} +(44.1588 + 44.1588i) q^{72} +(1.12032 + 0.748576i) q^{73} +(19.9400 - 100.245i) q^{74} +(0.508479 - 0.339755i) q^{75} +(-7.98612 - 19.2802i) q^{76} +(84.2570 - 34.9004i) q^{77} +(-1.33995 - 2.00537i) q^{78} +(-29.1507 - 5.79844i) q^{79} +(55.5694 - 83.1655i) q^{80} +(56.7774 - 56.7774i) q^{81} +(67.8290 - 13.4920i) q^{82} +(25.7951 - 62.2748i) q^{83} +0.842922i q^{84} +160.285 q^{86} +(4.93230 + 2.04303i) q^{87} +(-19.8280 - 99.6823i) q^{88} +(-90.1397 - 90.1397i) q^{89} +(-88.0256 - 58.8169i) q^{90} +(8.26771 - 41.5646i) q^{91} +(-9.09541 + 6.07736i) q^{92} +(0.0750988 + 0.181304i) q^{93} +(-30.1327 + 12.4814i) q^{94} +(-74.4751 - 111.460i) q^{95} +(2.08580 + 0.414892i) q^{96} +(37.5767 - 56.2374i) q^{97} +(15.5581 - 15.5581i) q^{98} +(-128.542 + 25.5687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{3} + 32 q^{6} + 8 q^{7} - 40 q^{8} + 8 q^{9} + 32 q^{10} - 24 q^{11} - 8 q^{12} - 16 q^{13} + 24 q^{14} + 56 q^{18} - 48 q^{19} - 80 q^{20} + 64 q^{21} + 48 q^{22} + 24 q^{23} - 120 q^{24}+ \cdots - 216 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 32 * q^6 + 8 * q^7 - 40 * q^8 + 8 * q^9 + 32 * q^10 - 24 * q^11 - 8 * q^12 - 16 * q^13 + 24 * q^14 + 56 * q^18 - 48 * q^19 - 80 * q^20 + 64 * q^21 + 48 * q^22 + 24 * q^23 - 120 * q^24 - 32 * q^25 - 48 * q^26 + 80 * q^27 - 120 * q^28 + 16 * q^29 - 16 * q^30 - 40 * q^31 - 88 * q^32 - 160 * q^35 - 24 * q^36 + 16 * q^37 + 120 * q^38 + 160 * q^39 + 48 * q^40 - 40 * q^41 + 128 * q^42 - 112 * q^43 - 64 * q^44 + 128 * q^45 - 8 * q^46 - 192 * q^47 - 96 * q^48 - 80 * q^49 - 384 * q^52 - 128 * q^53 - 168 * q^54 - 224 * q^55 - 264 * q^56 - 80 * q^57 + 368 * q^58 - 120 * q^59 + 48 * q^60 - 96 * q^61 + 120 * q^62 - 184 * q^63 + 64 * q^64 - 96 * q^66 + 240 * q^69 + 480 * q^70 + 280 * q^71 - 40 * q^72 + 208 * q^73 - 224 * q^74 - 136 * q^75 + 160 * q^76 + 80 * q^77 - 64 * q^78 + 24 * q^79 + 240 * q^80 + 424 * q^81 + 272 * q^82 + 336 * q^83 + 832 * q^86 - 80 * q^87 + 72 * q^88 - 160 * q^89 - 384 * q^90 - 248 * q^92 - 208 * q^93 + 432 * q^94 - 192 * q^95 - 88 * q^96 + 176 * q^97 + 120 * q^98 - 216 * q^99

Introduction

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