LMFDB - Embedded newform 289.3.e.d.65.1

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			65.1
Root			$-0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.65
Dual form			289.3.e.d.249.1

$q$-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 $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{16}\right)$

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	−0.827555	−	0.561385i	$-0.810269\pi$
$2$	−2.03153	+	0.841487i	−1.01577	+	0.420744i	−0.188210	+	0.982129i	$0.560269\pi$
$3$	−0.0315301	+	0.158513i	−0.0105100	+	0.0528376i	−0.985684	−	0.168601i	$-0.946075\pi$
$3$	−0.0315301	+	0.158513i	−0.0105100	+	0.0528376i	0.975174	+	0.221438i	$0.0710751\pi$
$4$	0.590587	−	0.590587i	0.147647	−	0.147647i
$5$	4.46088	−	2.98067i	0.892177	−	0.596134i	−0.0227553	−	0.999741i	$-0.507244\pi$
$5$	4.46088	−	2.98067i	0.892177	−	0.596134i	0.914932	+	0.403607i	$0.132244\pi$
$6$	−0.0693320	−	0.348555i	−0.0115553	−	0.0580926i
$7$	−5.19212	−	3.46927i	−0.741732	−	0.495609i	0.126378	−	0.991982i	$-0.459665\pi$
$7$	−5.19212	−	3.46927i	−0.741732	−	0.495609i	−0.868109	+	0.496373i	$0.834665\pi$
$8$	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	−0.796995	−	0.603986i	$-0.793578\pi$
$11$	−14.3240	+	2.84923i	−1.30219	+	0.259021i	−0.505192	+	0.863007i	$0.668578\pi$
$12$	0.0749942	+	0.112237i	0.00624952	+	0.00935306i
$13$	−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	$0.834060\pi$
$14$	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	−0.895802	−	0.444454i	$-0.853398\pi$
$19$	−23.0841	+	9.56175i	−1.21495	+	0.503250i	−0.319151	+	0.947704i	$0.603398\pi$
$20$	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	−0.995737	−	0.0922345i	$-0.970599\pi$
$23$	−2.55513	−	12.8455i	−0.111093	−	0.558500i	0.884645	−	0.466266i	$-0.154401\pi$
$24$	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	−0.999857	−	0.0168842i	$-0.994625\pi$
$29$	−18.3520	−	27.4657i	−0.632828	−	0.947093i	0.367030	−	0.930209i	$-0.380375\pi$
$30$	−1.34821	−	1.34821i	−0.0449403	−	0.0449403i
$31$	−1.19090	−	0.236886i	−0.0384163	−	0.00764147i	0.175845	−	0.984418i	$-0.443734\pi$
$31$	−1.19090	−	0.236886i	−0.0384163	−	0.00764147i	−0.214261	+	0.976776i	$0.568734\pi$
$32$	−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	−0.640614	−	0.767863i	$-0.721320\pi$
$37$	9.06812	−	45.5885i	0.245084	−	1.23212i	0.885699	−	0.464260i	$-0.153680\pi$
$38$	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	0.194172	−	0.980967i	$-0.437798\pi$
$41$	−26.1505	−	17.4732i	−0.637817	−	0.426176i	−0.831989	+	0.554792i	$0.812798\pi$
$42$	−0.849251	+	2.05027i	−0.0202203	+	0.0488161i
$43$	−67.3441	−	27.8948i	−1.56614	−	0.648717i	−0.579999	−	0.814617i	$-0.696947\pi$
$43$	−67.3441	−	27.8948i	−1.56614	−	0.648717i	−0.986142	+	0.165901i	$0.946947\pi$
$44$	−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	0.809825	−	0.586672i	$-0.199562\pi$
$47$	10.4882	+	10.4882i	0.223153	+	0.223153i	−0.586672	+	0.809825i	$0.699562\pi$
$48$	−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	−0.427287	−	0.904116i	$-0.640531\pi$
$53$	−4.77624	+	1.97838i	−0.0901178	+	0.0373280i	0.337169	+	0.941444i	$0.390531\pi$
$54$	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	−0.988632	−	0.150356i	$-0.951958\pi$
$59$	−10.8115	+	26.1013i	−0.183246	+	0.442394i	0.805386	+	0.592751i	$0.201958\pi$
$60$	0.669081	+	0.277142i	0.0111513	+	0.00461904i
$61$	45.9135	−	68.7144i	0.752680	−	1.12647i	−0.235306	−	0.971921i	$-0.575609\pi$
$61$	45.9135	−	68.7144i	0.752680	−	1.12647i	0.987986	−	0.154544i	$-0.0493908\pi$
$62$	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	$-0.892165\pi$
$67$		−	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
$71$	−11.3064	+	56.8410i	−0.159245	+	0.800577i	0.815759	+	0.578391i	$0.196319\pi$
$71$	−11.3064	+	56.8410i	−0.159245	+	0.800577i	−0.975004	+	0.222186i	$0.928681\pi$
$72$	44.1588	−	44.1588i	0.613317	−	0.613317i
$73$	1.12032	−	0.748576i	0.0153469	−	0.0102545i	−0.547873	−	0.836561i	$-0.684562\pi$
$73$	1.12032	−	0.748576i	0.0153469	−	0.0102545i	0.563220	+	0.826307i	$0.309562\pi$
$74$	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	−0.376106	−	0.926577i	$-0.622737\pi$
$79$	−29.1507	+	5.79844i	−0.368996	+	0.0733979i	0.00710935	+	0.999975i	$0.497737\pi$
$80$	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	0.999676	+	0.0254351i	$0.00809712\pi$
$83$	25.7951	+	62.2748i	0.310784	+	0.750298i	−0.688893	+	0.724863i	$0.741903\pi$
$84$		−	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	−0.0128890	+	0.999917i	$0.504103\pi$
$89$	−90.1397	+	90.1397i	−1.01281	+	1.01281i	−0.999917	+	0.0128890i	$0.995897\pi$
$90$	−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	0.972995	−	0.230828i	$-0.0741435\pi$
$97$	37.5767	+	56.2374i	0.387388	+	0.579767i	−0.585606	+	0.810596i	$0.699144\pi$
$98$	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	$-0.945143\pi$
$101$		−	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
$105$	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	−0.517960	−	0.855405i	$-0.673308\pi$
$107$	7.93047	−	5.29897i	0.0741166	−	0.0495231i	0.592076	+	0.805882i	$0.298308\pi$
$108$	0.473332	+	2.37960i	0.00438271	+	0.0220334i
$109$	−96.7260	−	64.6303i	−0.887395	−	0.592938i	0.0261584	−	0.999658i	$-0.491673\pi$
$109$	−96.7260	−	64.6303i	−0.887395	−	0.592938i	−0.913553	+	0.406720i	$0.866673\pi$
$110$	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	−0.472809	−	0.881165i	$-0.656760\pi$
$113$	−64.6835	+	12.8663i	−0.572420	+	0.113861i	−0.0996113	+	0.995026i	$0.531760\pi$
$114$	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	−0.999975	−	0.00711395i	$-0.997736\pi$
$127$	−36.5576	+	88.2580i	−0.287855	+	0.694945i	0.712119	+	0.702059i	$0.247736\pi$
$128$	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	0.729284	−	0.684211i	$-0.239853\pi$
$131$	−23.8328	−	35.6683i	−0.181930	−	0.272277i	−0.911214	+	0.411934i	$0.864853\pi$
$132$	−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	−0.151160	−	0.988509i	$-0.548301\pi$
$139$	50.9824	−	256.306i	0.366780	−	1.84393i	0.517940	−	0.855417i	$-0.326699\pi$
$140$	−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	0.929614	−	0.368534i	$-0.120140\pi$
$149$	83.6010	+	83.6010i	0.561080	+	0.561080i	−0.368534	+	0.929614i	$0.620140\pi$
$150$	−1.31889	−	0.262344i	−0.00879261	−	0.00174896i
$151$	−10.5977	−	25.5851i	−0.0701833	−	0.169437i	0.884895	−	0.465790i	$-0.154230\pi$
$151$	−10.5977	−	25.5851i	−0.0701833	−	0.169437i	−0.955079	+	0.296352i	$0.904230\pi$
$152$			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	−0.506321	−	0.862345i	$-0.668995\pi$
$157$	55.8958	−	55.8958i	0.356024	−	0.356024i	0.862345	+	0.506321i	$0.168995\pi$
$158$	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	−0.724715	−	0.689049i	$-0.758029\pi$
$163$	30.8428	−	46.1595i	0.189220	−	0.283187i	0.913935	+	0.405862i	$0.133029\pi$
$164$	−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	0.0410439	−	0.999157i	$-0.486932\pi$
$167$	−50.6674	−	10.0784i	−0.303398	−	0.0603495i	−0.344441	+	0.938808i	$0.611932\pi$
$168$	−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	−0.968972	−	0.247171i	$-0.920499\pi$
$173$	3.60353	−	18.1162i	0.0208296	−	0.104718i	0.989802	+	0.142453i	$0.0454991\pi$
$174$	−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	0.538503	−	0.842624i	$-0.318990\pi$
$179$	57.8989	+	23.9825i	0.323457	+	0.133980i	−0.215046	+	0.976604i	$0.568990\pi$
$180$	22.3405	−	33.4349i	0.124114	−	0.185749i
$181$	102.589	−	20.4063i	0.566792	−	0.112742i	0.0966274	−	0.995321i	$-0.469194\pi$
$181$	102.589	−	20.4063i	0.566792	−	0.112742i	0.470165	+	0.882579i	$0.344194\pi$
$182$	−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	−0.246897	−	0.969042i	$-0.579411\pi$
$191$	137.930	−	137.930i	0.722145	−	0.722145i	0.969042	+	0.246897i	$0.0794109\pi$
$192$	6.13293	−	4.09789i	0.0319423	−	0.0213432i
$193$	−17.2466	−	86.7045i	−0.0893606	−	0.449246i	−0.999397	−	0.0347181i	$-0.988947\pi$
$193$	−17.2466	−	86.7045i	−0.0893606	−	0.449246i	0.910037	−	0.414528i	$-0.136053\pi$
$194$	−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	0.266631	+	0.963799i	$0.414089\pi$
$197$	−142.990	+	214.000i	−0.725838	+	1.08629i	−0.992469	+	0.122495i	$0.960911\pi$
$198$	282.653	−	56.2232i	1.42754	−	0.283956i
$199$	−126.364	−	189.117i	−0.634996	−	0.950338i	−0.999815	−	0.0192597i	$-0.993869\pi$
$199$	−126.364	−	189.117i	−0.634996	−	0.950338i	0.364819	−	0.931079i	$-0.381131\pi$
$200$	−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	0.539533	−	0.841965i	$-0.318601\pi$
$211$	−6.72473	−	4.49332i	−0.0318708	−	0.0212954i	−0.571404	+	0.820669i	$0.693601\pi$
$212$	−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	−0.278720	−	0.960372i	$-0.589910\pi$
$223$	45.3315	−	18.7769i	0.203280	−	0.0842014i	0.482001	+	0.876171i	$0.339910\pi$
$224$	−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	0.983329	+	0.181833i	$0.0582031\pi$
$227$	32.7870	+	164.831i	0.144436	+	0.726129i	−0.838893	+	0.544296i	$0.816797\pi$
$228$	−2.80435	−	1.87381i	−0.0122998	−	0.00821846i
$229$	−47.5197	+	114.723i	−0.207510	+	0.500972i	−0.993030	−	0.117864i	$-0.962395\pi$
$229$	−47.5197	+	114.723i	−0.207510	+	0.500972i	0.785520	+	0.618836i	$0.212395\pi$
$230$	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	0.963587	+	0.267396i	$0.0861632\pi$
$233$	196.158	+	293.571i	0.841880	+	1.25996i	−0.121707	+	0.992566i	$0.538837\pi$
$234$	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	0.669827	+	0.742517i	$0.266368\pi$
$241$	−56.1919	+	282.496i	−0.233161	+	1.17218i	−0.902989	+	0.429665i	$0.858632\pi$
$242$	−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	0.215227	−	0.976564i	$-0.430951\pi$
$251$	−191.096	−	191.096i	−0.761337	−	0.761337i	−0.976564	+	0.215227i	$0.930951\pi$
$252$	−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	−0.475565	−	0.879680i	$-0.657756\pi$
$257$	−48.7819	+	20.2061i	−0.189813	+	0.0786230i	0.285753	+	0.958303i	$0.407756\pi$
$258$	−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	0.126654	−	0.991947i	$-0.459576\pi$
$263$	194.228	−	468.907i	0.738509	−	1.78292i	0.611854	−	0.790970i	$-0.290424\pi$
$264$	−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	0.505642	−	0.862743i	$-0.331256\pi$
$269$	172.869	+	34.3858i	0.642637	+	0.127828i	0.136995	+	0.990572i	$0.456256\pi$
$270$	−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
$275$	−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	−0.791618	−	0.611017i	$-0.790761\pi$
$277$	−146.824	+	98.1048i	−0.530051	+	0.354169i	0.261567	+	0.965185i	$0.415761\pi$
$278$	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	0.925883	−	0.377811i	$-0.123323\pi$
$281$	369.073	+	152.875i	1.31343	+	0.544040i	0.387545	+	0.921851i	$0.373323\pi$
$282$	2.92854	−	4.38287i	0.0103849	−	0.0155421i
$283$	350.746	−	69.7677i	1.23938	−	0.246529i	0.468477	−	0.883476i	$-0.344803\pi$
$283$	350.746	−	69.7677i	1.23938	−	0.246529i	0.770908	+	0.636947i	$0.219803\pi$
$284$	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	−0.357220	−	0.934020i	$-0.616275\pi$
$293$	169.002	−	169.002i	0.576800	−	0.576800i	0.934020	+	0.357220i	$0.116275\pi$
$294$	−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	−0.810346	−	0.585952i	$-0.800721\pi$
$311$	−180.101	+	120.340i	−0.579103	+	0.386944i	0.231243	+	0.972896i	$0.425721\pi$
$312$	−1.48912	−	7.48629i	−0.00477281	−	0.0239945i
$313$	393.629	+	263.015i	1.25760	+	0.840302i	0.992299	−	0.123863i	$-0.0395284\pi$
$313$	393.629	+	263.015i	1.25760	+	0.840302i	0.265302	+	0.964165i	$0.414528\pi$
$314$	−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	0.218133	−	0.975919i	$-0.430003\pi$
$317$	251.422	−	50.0110i	0.793130	−	0.157763i	0.574997	+	0.818156i	$0.305003\pi$
$318$	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	−0.999002	−	0.0446663i	$-0.985778\pi$
$331$	−86.3966	+	208.580i	−0.261017	+	0.630151i	0.737985	+	0.674817i	$0.235778\pi$
$332$	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	−0.360797	−	0.932644i	$-0.617495\pi$
$337$	−354.200	−	70.4547i	−1.05104	−	0.209064i	−0.690241	+	0.723580i	$0.742495\pi$
$338$	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	0.536426	−	0.843947i	$-0.319774\pi$
$347$	−13.1855	−	8.81030i	−0.0379987	−	0.0253899i	−0.574425	+	0.818558i	$0.694774\pi$
$348$	1.70637	−	4.11954i	0.00490336	−	0.0118377i
$349$	−292.270	−	121.062i	−0.837448	−	0.346883i	−0.0776015	−	0.996984i	$-0.524726\pi$
$349$	−292.270	−	121.062i	−0.837448	−	0.346883i	−0.759847	+	0.650102i	$0.774726\pi$
$350$	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	0.381540	−	0.924352i	$-0.375394\pi$
$353$	−191.613	−	191.613i	−0.542812	−	0.542812i	−0.924352	+	0.381540i	$0.875394\pi$
$354$	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	−0.169547	−	0.985522i	$-0.554231\pi$
$359$	146.269	−	60.5865i	0.407434	−	0.168765i	0.576981	+	0.816757i	$0.304231\pi$
$360$	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	−0.249967	−	0.968254i	$-0.580420\pi$
$367$	271.669	−	406.581i	0.740242	−	1.10785i	0.990209	−	0.139596i	$-0.0445803\pi$
$368$	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	$-0.720902\pi$
$373$		−	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
$377$	−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	−0.560480	+	0.828168i	$0.689383\pi$
$379$	−583.696	+	390.013i	−1.54009	+	1.02906i	−0.979614	+	0.200890i	$0.935617\pi$
$380$	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	−0.0216830	−	0.999765i	$-0.506902\pi$
$383$	−284.935	−	118.024i	−0.743956	−	0.308157i	−0.722273	+	0.691608i	$0.756902\pi$
$384$	−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	0.719392	−	0.694604i	$-0.244420\pi$
$389$	−109.097	−	263.382i	−0.280454	−	0.677076i	−0.999846	+	0.0175282i	$0.994420\pi$
$390$			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	0.938130	−	0.346283i	$-0.112556\pi$
$397$	−24.2591	−	121.959i	−0.0611061	−	0.307201i	−0.999236	+	0.0390826i	$0.987556\pi$
$398$	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	−0.408061	−	0.912955i	$-0.633795\pi$
$401$	237.214	−	355.016i	0.591557	−	0.885328i	0.999618	+	0.0276268i	$0.00879500\pi$
$402$	−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	−0.858884	−	0.512170i	$-0.828842\pi$
$419$	−610.227	+	121.382i	−1.45639	+	0.289694i	−0.597506	+	0.801864i	$0.703842\pi$
$420$	−2.51247	−	3.76018i	−0.00598207	−	0.00895280i
$421$	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	$0.730543\pi$
$422$	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	−0.928226	−	0.372017i	$-0.878666\pi$
$431$	−91.8124	−	461.572i	−0.213022	−	1.07093i	0.715204	−	0.698916i	$-0.246334\pi$
$432$	−45.0299	−	30.0880i	−0.104236	−	0.0696481i
$433$	246.289	−	594.595i	0.568798	−	1.37320i	−0.333772	−	0.942654i	$-0.608321\pi$
$433$	246.289	−	594.595i	0.568798	−	1.37320i	0.902569	−	0.430545i	$-0.141679\pi$
$434$	−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	−0.859077	−	0.511846i	$-0.828962\pi$
$439$	−811.551	−	161.428i	−1.84864	−	0.367717i	−0.989559	+	0.144129i	$0.953962\pi$
$440$	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	−0.996463	−	0.0840341i	$-0.973220\pi$
$449$	−653.488	−	436.647i	−1.45543	−	0.972487i	−0.458967	−	0.888453i	$-0.651780\pi$
$450$	−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	0.727313	−	0.686306i	$-0.240769\pi$
$457$	−124.426	−	300.390i	−0.272266	−	0.657309i	−0.999580	+	0.0289968i	$0.990769\pi$
$458$		−	273.050i		−	0.596178i
$459$		0			0
$460$	−58.6882			−0.127583
$461$	−227.477	+	94.2242i	−0.493444	+	0.204391i	−0.615507	−	0.788131i	$-0.711049\pi$
$461$	−227.477	+	94.2242i	−0.493444	+	0.204391i	0.122064	+	0.992522i	$0.461049\pi$
$462$	6.32302	−	31.7879i	0.0136862	−	0.0688051i
$463$	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	$0.126317\pi$
$464$	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	−0.808476	−	0.588529i	$-0.799707\pi$
$467$	83.7591	−	202.212i	0.179356	−	0.433003i	0.987832	+	0.155526i	$0.0497073\pi$
$468$	−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	−0.732727	−	0.680523i	$-0.761753\pi$
$479$	98.0271	−	492.815i	0.204649	−	1.02884i	0.937376	−	0.348319i	$-0.113247\pi$
$480$	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	−0.441999	−	0.897016i	$-0.645731\pi$
$487$	−246.948	+	49.1210i	−0.507080	+	0.100864i	−0.0650809	+	0.997880i	$0.520731\pi$
$488$	−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	0.987210	−	0.159423i	$-0.0509632\pi$
$491$	86.6215	+	209.123i	0.176418	+	0.425912i	−0.810792	+	0.585334i	$0.800963\pi$
$492$		−	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	0.999766	+	0.0216522i	$0.00689266\pi$
$499$	42.1099	+	211.701i	0.0843886	+	0.424250i	−0.915377	+	0.402598i	$0.868107\pi$
$500$	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	−0.0881697	+	0.996105i	$0.528102\pi$
$503$	−490.279	+	733.755i	−0.974710	+	1.45876i	−0.886540	+	0.462651i	$0.846898\pi$
$504$	−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	$0.149048\pi$
$509$			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
$513$	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	−0.0989697	−	0.995090i	$-0.531555\pi$
$521$	99.1978	−	19.7317i	0.190399	−	0.0378727i	0.289369	+	0.957218i	$0.406555\pi$
$522$	362.136	+	541.975i	0.693747	+	1.03827i
$523$	−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	$0.929380\pi$
$524$	−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	0.157947	−	0.987448i	$-0.449513\pi$
$541$	−40.0392	−	7.96429i	−0.0740095	−	0.0147214i	−0.231956	+	0.972726i	$0.574513\pi$
$542$	−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	−0.966742	−	0.255755i	$-0.917676\pi$
$547$	13.2836	−	66.7811i	0.0242844	−	0.122086i	0.991026	+	0.133669i	$0.0426759\pi$
$548$	−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	0.869255	−	0.494365i	$-0.164599\pi$
$557$	208.814	+	208.814i	0.374890	+	0.374890i	−0.494365	+	0.869255i	$0.664599\pi$
$558$	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	0.0106294	−	0.999944i	$-0.496616\pi$
$563$	408.295	−	169.121i	0.725212	−	0.300393i	0.714583	+	0.699551i	$0.246616\pi$
$564$	−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	0.544664	+	0.838654i	$0.316657\pi$
$569$	−246.656	+	595.479i	−0.433490	+	1.04654i	−0.978154	+	0.207882i	$0.933343\pi$
$570$	44.0135	+	18.2310i	0.0772166	+	0.0319842i
$571$	66.5484	−	99.5967i	0.116547	−	0.174425i	−0.768610	−	0.639718i	$-0.779051\pi$
$571$	66.5484	−	99.5967i	0.116547	−	0.174425i	0.885157	+	0.465293i	$0.154051\pi$
$572$	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	$-0.950982\pi$
$577$		−	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
$581$	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	−0.167956	−	0.985794i	$-0.553717\pi$
$587$	−577.480	−	239.200i	−0.983781	−	0.407496i	−0.815825	+	0.578299i	$0.803717\pi$
$588$	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	0.964853	−	0.262789i	$-0.0846424\pi$
$593$	57.3899	+	138.551i	0.0967789	+	0.233645i	−0.868074	+	0.496434i	$0.834642\pi$
$594$			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	−0.502210	−	0.864746i	$-0.667480\pi$
$599$	217.159	−	217.159i	0.362536	−	0.362536i	0.864746	+	0.502210i	$0.167480\pi$
$600$	3.53855	−	2.36438i	0.00589759	−	0.00394064i
$601$	−79.2601	−	398.467i	−0.131880	−	0.663007i	−0.989003	−	0.147895i	$-0.952750\pi$
$601$	−79.2601	−	398.467i	−0.131880	−	0.663007i	0.857123	−	0.515112i	$-0.172250\pi$
$602$	−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	−0.906823	−	0.421511i	$-0.861500\pi$
$607$	−576.178	−	862.312i	−0.949223	−	1.42061i	−0.0423995	−	0.999101i	$-0.513500\pi$
$608$	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	−0.716132	−	0.697965i	$-0.754089\pi$
$617$	−213.080	+	142.375i	−0.345348	+	0.230754i	0.370784	+	0.928719i	$0.379089\pi$
$618$	−10.4807	−	52.6898i	−0.0169590	−	0.0852586i
$619$	76.4213	+	51.0630i	0.123459	+	0.0824928i	0.615767	−	0.787929i	$-0.288846\pi$
$619$	76.4213	+	51.0630i	0.123459	+	0.0824928i	−0.492307	+	0.870421i	$0.663846\pi$
$620$	−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	0.0798795	−	0.996805i	$-0.474546\pi$
$631$	530.804	−	219.866i	0.841210	−	0.348441i	0.761331	+	0.648364i	$0.224546\pi$
$632$	−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	0.958975	+	0.283489i	$0.0914921\pi$
$641$	547.351	+	819.168i	0.853901	+	1.27795i	−0.105074	+	0.994464i	$0.533508\pi$
$642$	−2.39682	−	2.39682i	−0.00373337	−	0.00373337i
$643$	−34.6996	−	6.90218i	−0.0539652	−	0.0107343i	0.168034	−	0.985781i	$-0.446258\pi$
$643$	−34.6996	−	6.90218i	−0.0539652	−	0.0107343i	−0.221999	+	0.975047i	$0.571258\pi$
$644$	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	0.890252	−	0.455468i	$-0.150528\pi$
$653$	529.021	+	353.481i	0.810140	+	0.541318i	−0.0801126	+	0.996786i	$0.525528\pi$
$654$	−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	0.602831	−	0.797869i	$-0.294039\pi$
$659$	−128.530	−	128.530i	−0.195037	−	0.195037i	−0.797869	+	0.602831i	$0.794039\pi$
$660$	−10.3736	−	2.06344i	−0.0157176	−	0.00312642i
$661$	−445.481	−	1075.49i	−0.673950	−	1.62706i	−0.774837	−	0.632161i	$-0.782168\pi$
$661$	−445.481	−	1075.49i	−0.673950	−	1.62706i	0.100887	−	0.994898i	$-0.467832\pi$
$662$		−	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	−0.873120	−	0.487505i	$-0.837907\pi$
$673$	−59.6248	+	89.2349i	−0.0885956	+	0.132593i	0.784525	+	0.620098i	$0.212907\pi$
$674$	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	−0.641463	−	0.767154i	$-0.721672\pi$
$677$	−1034.24	−	205.722i	−1.52767	−	0.303873i	−0.886211	+	0.463281i	$0.846672\pi$
$678$	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	−0.790019	−	0.613083i	$-0.789929\pi$
$683$	119.170	−	599.107i	0.174480	−	0.877170i	0.964499	−	0.264088i	$-0.0850708\pi$
$684$	−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	−0.833575	−	0.552406i	$-0.813710\pi$
$691$	−962.080	+	191.370i	−1.39230	+	0.276946i	−0.558726	+	0.829352i	$0.688710\pi$
$692$	−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	−0.743751	−	0.668457i	$-0.766955\pi$
$701$	−52.7814	+	52.7814i	−0.0752944	+	0.0752944i	0.668457	+	0.743751i	$0.266955\pi$
$702$	−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	0.999852	−	0.0172267i	$-0.00548369\pi$
$709$	426.329	+	638.046i	0.601310	+	0.899923i	−0.398542	+	0.917150i	$0.630484\pi$
$710$	−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	−0.998671	−	0.0515322i	$-0.983590\pi$
$719$	−958.597	+	640.514i	−1.33324	+	0.890840i	−0.334565	+	0.942373i	$0.608590\pi$
$720$	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	0.559376	−	0.828914i	$-0.311041\pi$
$727$	−195.955	−	195.955i	−0.269539	−	0.269539i	−0.828914	+	0.559376i	$0.811041\pi$
$728$	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	−0.0853397	−	0.996352i	$-0.527198\pi$
$733$	409.632	−	169.675i	0.558843	−	0.231480i	0.644183	+	0.764871i	$0.277198\pi$
$734$	−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	−0.948995	−	0.315291i	$-0.897898\pi$
$739$	−40.6523	+	98.1432i	−0.0550098	+	0.132805i	0.893985	+	0.448096i	$0.147898\pi$
$740$	−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	−0.996677	−	0.0814563i	$-0.974043\pi$
$743$	−513.057	−	767.844i	−0.690521	−	1.03344i	0.306156	−	0.951981i	$-0.400957\pi$
$744$	−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	0.485167	+	0.874421i	$0.338759\pi$
$751$	−223.569	+	1123.96i	−0.297695	+	1.49662i	−0.782863	+	0.622195i	$0.786241\pi$
$752$	−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	0.421561	−	0.906800i	$-0.361482\pi$
$757$	59.3832	+	24.5973i	0.0784455	+	0.0324932i	−0.343116	+	0.939293i	$0.611482\pi$
$758$	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	0.811668	−	0.584120i	$-0.198560\pi$
$761$	173.164	+	173.164i	0.227548	+	0.227548i	−0.584120	+	0.811668i	$0.698560\pi$
$762$	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	−0.967712	−	0.252057i	$-0.918893\pi$
$769$	−550.339	+	550.339i	−0.715655	+	0.715655i	0.252057	+	0.967712i	$0.418893\pi$
$770$	−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	−0.994044	−	0.108976i	$-0.965243\pi$
$773$	−165.492	+	399.534i	−0.214091	+	0.516861i	0.779953	+	0.625837i	$0.215243\pi$
$774$	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	0.218594	−	0.975816i	$-0.429853\pi$
$787$	947.377	−	633.017i	1.20378	−	0.804342i	0.985189	+	0.171474i	$0.0548531\pi$
$788$	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	0.894522	−	0.447024i	$-0.147516\pi$
$797$	−43.1132	−	104.084i	−0.0540943	−	0.130595i	−0.948616	+	0.316429i	$0.897516\pi$
$798$		−	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	−0.984688	−	0.174324i	$-0.944226\pi$
$809$	−361.469	+	540.977i	−0.446810	+	0.668698i	0.537878	+	0.843022i	$0.319226\pi$
$810$	−929.068	+	184.803i	−1.14700	+	0.228152i
$811$	357.615	+	535.209i	0.440956	+	0.659937i	0.983670	−	0.179980i	$-0.0576034\pi$
$811$	357.615	+	535.209i	0.440956	+	0.659937i	−0.542715	+	0.839917i	$0.682603\pi$
$812$	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	−0.0133400	−	0.999911i	$-0.504246\pi$
$821$	743.294	−	496.653i	0.905352	−	0.604937i	0.918692	+	0.394974i	$0.129246\pi$
$822$	4.42499	+	22.2459i	0.00538320	+	0.0270632i
$823$	−768.962	−	513.804i	−0.934340	−	0.624306i	−0.00758474	−	0.999971i	$-0.502414\pi$
$823$	−768.962	−	513.804i	−0.934340	−	0.624306i	−0.926756	+	0.375665i	$0.877414\pi$
$824$	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	−0.670257	−	0.742129i	$-0.733816\pi$
$827$	−831.543	+	165.404i	−1.00549	+	0.200005i	−0.335237	+	0.942134i	$0.608816\pi$
$828$	−54.5375	−	81.6211i	−0.0658665	−	0.0985762i
$829$	−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	$-0.513258\pi$
$830$	−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	0.999395	+	0.0347806i	$0.0110732\pi$
$839$	74.9935	+	377.018i	0.0893844	+	0.449366i	−0.910011	+	0.414585i	$0.863927\pi$
$840$	−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	−0.742444	−	0.669908i	$-0.766333\pi$
$853$	170.470	−	857.011i	0.199848	−	1.00470i	0.942291	−	0.334794i	$-0.108667\pi$
$854$	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	0.996708	−	0.0810800i	$-0.0258369\pi$
$857$	1116.86	+	746.263i	1.30322	+	0.870786i	0.306515	+	0.951866i	$0.400837\pi$
$858$	13.4797	−	32.5429i	0.0157106	−	0.0379288i
$859$	−236.510	−	97.9655i	−0.275331	−	0.114046i	0.240745	−	0.970588i	$-0.422608\pi$
$859$	−236.510	−	97.9655i	−0.275331	−	0.114046i	−0.516077	+	0.856542i	$0.672608\pi$
$860$	−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	0.914930	+	0.403612i	$0.132245\pi$
$863$	1137.90	+	1137.90i	1.31854	+	1.31854i	0.403612	+	0.914930i	$0.367755\pi$
$864$	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	−0.641790	−	0.766880i	$-0.721808\pi$
$877$	273.902	−	409.924i	0.312317	−	0.467416i	0.954107	+	0.299465i	$0.0968080\pi$
$878$	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	−0.0338884	−	0.999426i	$-0.510789\pi$
$881$	−394.389	−	78.4489i	−0.447661	−	0.0890453i	−0.413772	+	0.910380i	$0.635789\pi$
$882$	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
$887$	247.891	−	1246.23i	0.279471	−	1.40500i	−0.544689	−	0.838638i	$-0.683352\pi$
$887$	247.891	−	1246.23i	0.279471	−	1.40500i	0.824160	−	0.566357i	$-0.191648\pi$
$888$	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	−0.688313	−	0.725413i	$-0.741649\pi$
$907$	−299.309	−	1504.73i	−0.329998	−	1.65901i	0.358315	−	0.933601i	$-0.383351\pi$
$908$	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	−0.926179	−	0.377084i	$-0.876927\pi$
$911$	−203.486	+	304.539i	−0.223366	+	0.334291i	0.702813	+	0.711374i	$0.251927\pi$
$912$	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	0.346631	−	0.938002i	$-0.387326\pi$
$929$	952.999	−	189.563i	1.02583	−	0.204051i	0.679203	+	0.733951i	$0.262326\pi$
$930$	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	−0.658389	−	0.752678i	$-0.728762\pi$
$937$	−554.438	+	229.656i	−0.591716	+	0.245097i	0.0666728	+	0.997775i	$0.478762\pi$
$938$	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	−0.913992	−	0.405732i	$-0.867017\pi$
$941$	−211.575	−	1063.66i	−0.224840	−	1.13035i	0.689152	−	0.724617i	$-0.257983\pi$
$942$	−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	0.568780	−	0.822490i	$-0.307416\pi$
$947$	−387.099	−	579.335i	−0.408764	−	0.611758i	−0.977544	+	0.210731i	$0.932416\pi$
$948$	−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	0.997182	−	0.0750154i	$-0.0239006\pi$
$967$	231.136	+	558.012i	0.239024	+	0.577055i	−0.758158	+	0.652071i	$0.773901\pi$
$968$		−	642.299i		−	0.663532i
$969$		0			0
$970$	−797.924			−0.822602
$971$	1017.06	−	421.281i	1.04744	−	0.433863i	0.208461	−	0.978031i	$-0.433155\pi$
$971$	1017.06	−	421.281i	1.04744	−	0.433863i	0.838976	+	0.544168i	$0.183155\pi$
$972$	−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	0.550426	+	0.834884i	$0.314465\pi$
$977$	−419.266	+	1012.20i	−0.429136	+	1.03603i	−0.979562	+	0.201142i	$0.935535\pi$
$978$	−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	−0.460913	−	0.887445i	$-0.652478\pi$
$983$	−1205.50	−	239.790i	−1.22635	−	0.243937i	−0.765439	+	0.643509i	$0.777478\pi$
$984$	−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	−0.206681	−	0.978408i	$-0.566266\pi$
$991$	612.594	−	409.322i	0.618158	−	0.413040i	0.824838	+	0.565369i	$0.191266\pi$
$992$	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	−0.108476	−	0.994099i	$-0.534597\pi$
$997$	171.215	−	34.0568i	0.171730	−	0.0341593i	0.280206	+	0.959940i	$0.409597\pi$
$998$	−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.65.1		8
17.2	even	8		17.3.e.a.5.1	✓	8
17.3	odd	16		289.3.e.c.75.1		8
17.4	even	4		289.3.e.k.224.1		8
17.5	odd	16		289.3.e.i.214.1		8
17.6	odd	16		289.3.e.b.249.1		8
17.7	odd	16		289.3.e.k.40.1		8
17.8	even	8		289.3.e.m.131.1		8
17.9	even	8		289.3.e.i.131.1		8
17.10	odd	16		289.3.e.l.40.1		8
17.11	odd	16	inner	289.3.e.d.249.1		8
17.12	odd	16		289.3.e.m.214.1		8
17.13	even	4		289.3.e.l.224.1		8
17.14	odd	16		17.3.e.a.7.1	yes	8
17.15	even	8		289.3.e.c.158.1		8
17.16	even	2		289.3.e.b.65.1		8
51.2	odd	8		153.3.p.b.73.1		8
51.14	even	16		153.3.p.b.109.1		8
68.19	odd	8		272.3.bh.c.209.1		8
68.31	even	16		272.3.bh.c.177.1		8
85.2	odd	8		425.3.t.c.124.1		8
85.14	odd	16		425.3.u.b.126.1		8
85.19	even	8		425.3.u.b.226.1		8
85.48	even	16		425.3.t.c.24.1		8
85.53	odd	8		425.3.t.a.124.1		8
85.82	even	16		425.3.t.a.24.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.5.1	✓	8	17.2	even	8
17.3.e.a.7.1	yes	8	17.14	odd	16
153.3.p.b.73.1		8	51.2	odd	8
153.3.p.b.109.1		8	51.14	even	16
272.3.bh.c.177.1		8	68.31	even	16
272.3.bh.c.209.1		8	68.19	odd	8
289.3.e.b.65.1		8	17.16	even	2
289.3.e.b.249.1		8	17.6	odd	16
289.3.e.c.75.1		8	17.3	odd	16
289.3.e.c.158.1		8	17.15	even	8
289.3.e.d.65.1		8	1.1	even	1	trivial
289.3.e.d.249.1		8	17.11	odd	16	inner
289.3.e.i.131.1		8	17.9	even	8
289.3.e.i.214.1		8	17.5	odd	16
289.3.e.k.40.1		8	17.7	odd	16
289.3.e.k.224.1		8	17.4	even	4
289.3.e.l.40.1		8	17.10	odd	16
289.3.e.l.224.1		8	17.13	even	4
289.3.e.m.131.1		8	17.8	even	8
289.3.e.m.214.1		8	17.12	odd	16
425.3.t.a.24.1		8	85.82	even	16
425.3.t.a.124.1		8	85.53	odd	8
425.3.t.c.24.1		8	85.48	even	16
425.3.t.c.124.1		8	85.2	odd	8
425.3.u.b.126.1		8	85.14	odd	16
425.3.u.b.226.1		8	85.19	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} +(-0.0315301 + 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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