LMFDB - Embedded newform 985.2.b.a.789.33

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [985,2,Mod(789,985)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("985.789"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(985, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 985 = 5 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	985.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.86526459910$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			789.33
Character	$\chi$	$=$	985.789
Dual form			985.2.b.a.789.66

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.18293i q^{2} -0.672647i q^{3} +0.600670 q^{4} +(1.81029 + 1.31258i) q^{5} -0.795696 q^{6} -3.32812i q^{7} -3.07642i q^{8} +2.54755 q^{9} +(1.55269 - 2.14145i) q^{10} -4.01450 q^{11} -0.404039i q^{12} -0.365360i q^{13} -3.93695 q^{14} +(0.882900 - 1.21769i) q^{15} -2.43785 q^{16} -5.21648i q^{17} -3.01358i q^{18} -2.16257 q^{19} +(1.08739 + 0.788425i) q^{20} -2.23865 q^{21} +4.74888i q^{22} +7.86503i q^{23} -2.06934 q^{24} +(1.55429 + 4.75228i) q^{25} -0.432196 q^{26} -3.73154i q^{27} -1.99911i q^{28} +7.24543 q^{29} +(-1.44044 - 1.04441i) q^{30} -3.93707 q^{31} -3.26902i q^{32} +2.70034i q^{33} -6.17075 q^{34} +(4.36841 - 6.02487i) q^{35} +1.53023 q^{36} -3.21046i q^{37} +2.55817i q^{38} -0.245758 q^{39} +(4.03803 - 5.56921i) q^{40} +4.57854 q^{41} +2.64818i q^{42} -8.31813i q^{43} -2.41139 q^{44} +(4.61179 + 3.34385i) q^{45} +9.30380 q^{46} +3.03063i q^{47} +1.63982i q^{48} -4.07641 q^{49} +(5.62163 - 1.83862i) q^{50} -3.50885 q^{51} -0.219461i q^{52} +4.72562i q^{53} -4.41416 q^{54} +(-7.26740 - 5.26933i) q^{55} -10.2387 q^{56} +1.45464i q^{57} -8.57085i q^{58} +5.78433 q^{59} +(0.530332 - 0.731428i) q^{60} -6.30248 q^{61} +4.65729i q^{62} -8.47855i q^{63} -8.74274 q^{64} +(0.479563 - 0.661407i) q^{65} +3.19432 q^{66} +11.0069i q^{67} -3.13339i q^{68} +5.29039 q^{69} +(-7.12701 - 5.16754i) q^{70} -9.14673 q^{71} -7.83731i q^{72} -1.79241i q^{73} -3.79776 q^{74} +(3.19661 - 1.04549i) q^{75} -1.29899 q^{76} +13.3607i q^{77} +0.290716i q^{78} +14.4163 q^{79} +(-4.41322 - 3.19987i) q^{80} +5.13263 q^{81} -5.41610i q^{82} +2.56116i q^{83} -1.34469 q^{84} +(6.84703 - 9.44334i) q^{85} -9.83978 q^{86} -4.87362i q^{87} +12.3503i q^{88} +13.7724 q^{89} +(3.95554 - 5.45544i) q^{90} -1.21596 q^{91} +4.72429i q^{92} +2.64826i q^{93} +3.58503 q^{94} +(-3.91487 - 2.83853i) q^{95} -2.19890 q^{96} +4.69428i q^{97} +4.82212i q^{98} -10.2271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q - 98 q^{4} - 2 q^{5} + 4 q^{6} - 102 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{14} - 2 q^{15} + 98 q^{16} - 8 q^{19} - 2 q^{20} + 20 q^{21} + 10 q^{25} - 4 q^{26} - 12 q^{29} - 10 q^{30} - 4 q^{31} + 24 q^{34}+ \cdots - 44 q^{99}+O(q^{100}) $ 98 * q - 98 * q^4 - 2 * q^5 + 4 * q^6 - 102 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^14 - 2 * q^15 + 98 * q^16 - 8 * q^19 - 2 * q^20 + 20 * q^21 + 10 * q^25 - 4 * q^26 - 12 * q^29 - 10 * q^30 - 4 * q^31 + 24 * q^34 + 4 * q^35 + 86 * q^36 + 12 * q^40 - 4 * q^41 + 16 * q^44 - 16 * q^45 - 44 * q^46 - 130 * q^49 + 28 * q^50 + 32 * q^51 - 84 * q^54 + 14 * q^55 - 44 * q^56 - 16 * q^59 + 38 * q^60 + 32 * q^61 - 110 * q^64 + 30 * q^65 + 84 * q^66 + 12 * q^69 + 38 * q^70 + 48 * q^74 + 38 * q^75 - 8 * q^76 - 20 * q^79 - 4 * q^80 + 82 * q^81 - 84 * q^84 - 40 * q^85 - 56 * q^86 - 8 * q^89 + 30 * q^90 + 16 * q^94 + 18 * q^95 - 68 * q^96 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/985\mathbb{Z}\right)^\times$.

$n$	$396$	$592$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.18293i		−	0.836460i	−0.908341	−	0.418230i	$-0.862651\pi$
$2$		−	1.18293i		−	0.836460i	0.908341	−	0.418230i	$-0.137349\pi$
$3$		−	0.672647i		−	0.388353i	−0.980967	−	0.194177i	$-0.937797\pi$
$3$		−	0.672647i		−	0.388353i	0.980967	−	0.194177i	$-0.0622035\pi$
$4$	0.600670			0.300335
$5$	1.81029	+	1.31258i	0.809586	+	0.587002i
$5$	1.81029	+	1.31258i	0.809586	+	0.587002i
$6$	−0.795696			−0.324842
$7$		−	3.32812i		−	1.25791i	−0.777441	−	0.628956i	$-0.783482\pi$
$7$		−	3.32812i		−	1.25791i	0.777441	−	0.628956i	$-0.216518\pi$
$8$		−	3.07642i		−	1.08768i
$9$	2.54755			0.849182
$10$	1.55269	−	2.14145i	0.491003	−	0.677186i
$11$	−4.01450			−1.21042			−0.605208	−	0.796067i	$-0.706910\pi$
$11$	−4.01450			−1.21042			−0.605208	+	0.796067i	$0.706910\pi$
$12$		−	0.404039i		−	0.116636i
$13$		−	0.365360i		−	0.101333i	−0.998716	−	0.0506663i	$-0.983865\pi$
$13$		−	0.365360i		−	0.101333i	0.998716	−	0.0506663i	$-0.0161345\pi$
$14$	−3.93695			−1.05219
$15$	0.882900	−	1.21769i	0.227964	−	0.314405i
$16$	−2.43785			−0.609464
$17$		−	5.21648i		−	1.26518i	−0.774486	−	0.632591i	$-0.781991\pi$
$17$		−	5.21648i		−	1.26518i	0.774486	−	0.632591i	$-0.218009\pi$
$18$		−	3.01358i		−	0.710306i
$19$	−2.16257			−0.496127			−0.248063	−	0.968744i	$-0.579794\pi$
$19$	−2.16257			−0.496127			−0.248063	+	0.968744i	$0.579794\pi$
$20$	1.08739	+	0.788425i	0.243147	+	0.176297i
$21$	−2.23865			−0.488514
$22$			4.74888i			1.01246i
$23$			7.86503i			1.63997i	0.572384	+	0.819986i	$0.306019\pi$
$23$			7.86503i			1.63997i	−0.572384	+	0.819986i	$0.693981\pi$
$24$	−2.06934			−0.422403
$25$	1.55429	+	4.75228i	0.310858	+	0.950456i
$26$	−0.432196			−0.0847607
$27$		−	3.73154i		−	0.718136i
$28$		−	1.99911i		−	0.377795i
$29$	7.24543			1.34544			0.672721	−	0.739896i	$-0.265125\pi$
$29$	7.24543			1.34544			0.672721	+	0.739896i	$0.265125\pi$
$30$	−1.44044	−	1.04441i	−0.262987	−	0.190683i
$31$	−3.93707			−0.707119			−0.353560	−	0.935412i	$-0.615029\pi$
$31$	−3.93707			−0.707119			−0.353560	+	0.935412i	$0.615029\pi$
$32$		−	3.26902i		−	0.577886i
$33$			2.70034i			0.470069i
$34$	−6.17075			−1.05827
$35$	4.36841	−	6.02487i	0.738397	−	1.01839i
$36$	1.53023			0.255039
$37$		−	3.21046i		−	0.527797i	−0.964551	−	0.263898i	$-0.914992\pi$
$37$		−	3.21046i		−	0.527797i	0.964551	−	0.263898i	$-0.0850083\pi$
$38$			2.55817i			0.414990i
$39$	−0.245758			−0.0393529
$40$	4.03803	−	5.56921i	0.638469	−	0.880569i
$41$	4.57854			0.715048			0.357524	−	0.933904i	$-0.383621\pi$
$41$	4.57854			0.715048			0.357524	+	0.933904i	$0.383621\pi$
$42$			2.64818i			0.408623i
$43$		−	8.31813i		−	1.26850i	−0.773127	−	0.634251i	$-0.781308\pi$
$43$		−	8.31813i		−	1.26850i	0.773127	−	0.634251i	$-0.218692\pi$
$44$	−2.41139			−0.363530
$45$	4.61179	+	3.34385i	0.687486	+	0.498471i
$46$	9.30380			1.37177
$47$			3.03063i			0.442063i	0.975267	+	0.221031i	$0.0709423\pi$
$47$			3.03063i			0.442063i	−0.975267	+	0.221031i	$0.929058\pi$
$48$			1.63982i			0.236687i
$49$	−4.07641			−0.582345
$50$	5.62163	−	1.83862i	0.795018	−	0.260021i
$51$	−3.50885			−0.491338
$52$		−	0.219461i		−	0.0304338i
$53$			4.72562i			0.649113i	0.945866	+	0.324557i	$0.105215\pi$
$53$			4.72562i			0.649113i	−0.945866	+	0.324557i	$0.894785\pi$
$54$	−4.41416			−0.600691
$55$	−7.26740	−	5.26933i	−0.979936	−	0.710516i
$56$	−10.2387			−1.36820
$57$			1.45464i			0.192672i
$58$		−	8.57085i		−	1.12541i
$59$	5.78433			0.753055			0.376528	−	0.926405i	$-0.377118\pi$
$59$	5.78433			0.753055			0.376528	+	0.926405i	$0.377118\pi$
$60$	0.530332	−	0.731428i	0.0684656	−	0.0944269i
$61$	−6.30248			−0.806949			−0.403475	−	0.914991i	$-0.632198\pi$
$61$	−6.30248			−0.806949			−0.403475	+	0.914991i	$0.632198\pi$
$62$			4.65729i			0.591477i
$63$		−	8.47855i		−	1.06820i
$64$	−8.74274			−1.09284
$65$	0.479563	−	0.661407i	0.0594824	−	0.0820375i
$66$	3.19432			0.393194
$67$			11.0069i			1.34470i	0.740232	+	0.672351i	$0.234715\pi$
$67$			11.0069i			1.34470i	−0.740232	+	0.672351i	$0.765285\pi$
$68$		−	3.13339i		−	0.379979i
$69$	5.29039			0.636888
$70$	−7.12701	−	5.16754i	−0.851841	−	0.617639i
$71$	−9.14673			−1.08552			−0.542758	−	0.839889i	$-0.682620\pi$
$71$	−9.14673			−1.08552			−0.542758	+	0.839889i	$0.682620\pi$
$72$		−	7.83731i		−	0.923636i
$73$		−	1.79241i		−	0.209786i	−0.994484	−	0.104893i	$-0.966550\pi$
$73$		−	1.79241i		−	0.209786i	0.994484	−	0.104893i	$-0.0334499\pi$
$74$	−3.79776			−0.441481
$75$	3.19661	−	1.04549i	0.369113	−	0.120723i
$76$	−1.29899			−0.149004
$77$			13.3607i			1.52260i
$78$			0.290716i			0.0329171i
$79$	14.4163			1.62196			0.810982	−	0.585071i	$-0.198933\pi$
$79$	14.4163			1.62196			0.810982	+	0.585071i	$0.198933\pi$
$80$	−4.41322	−	3.19987i	−0.493413	−	0.357756i
$81$	5.13263			0.570292
$82$		−	5.41610i		−	0.598108i
$83$			2.56116i			0.281124i	0.990072	+	0.140562i	$0.0448909\pi$
$83$			2.56116i			0.281124i	−0.990072	+	0.140562i	$0.955109\pi$
$84$	−1.34469			−0.146718
$85$	6.84703	−	9.44334i	0.742664	−	1.02427i
$86$	−9.83978			−1.06105
$87$		−	4.87362i		−	0.522507i
$88$			12.3503i			1.31654i
$89$	13.7724			1.45987			0.729937	−	0.683514i	$-0.239549\pi$
$89$	13.7724			1.45987			0.729937	+	0.683514i	$0.239549\pi$
$90$	3.95554	−	5.45544i	0.416951	−	0.575054i
$91$	−1.21596			−0.127468
$92$			4.72429i			0.492541i
$93$			2.64826i			0.274612i
$94$	3.58503			0.369768
$95$	−3.91487	−	2.83853i	−0.401657	−	0.291227i
$96$	−2.19890			−0.224424
$97$			4.69428i			0.476632i	0.971188	+	0.238316i	$0.0765954\pi$
$97$			4.69428i			0.476632i	−0.971188	+	0.238316i	$0.923405\pi$
$98$			4.82212i			0.487108i
$99$	−10.2271			−1.02786
$100$	0.933617	+	2.85455i	0.0933617	+	0.285455i
$101$	−10.7288			−1.06756			−0.533779	−	0.845624i	$-0.679229\pi$
$101$	−10.7288			−1.06756			−0.533779	+	0.845624i	$0.679229\pi$
$102$			4.15074i			0.410984i
$103$			5.27161i			0.519427i	0.965686	+	0.259713i	$0.0836281\pi$
$103$			5.27161i			0.519427i	−0.965686	+	0.259713i	$0.916372\pi$
$104$	−1.12400			−0.110217
$105$	−4.05261	−	2.93840i	−0.395494	−	0.286759i
$106$	5.59009			0.542957
$107$		−	4.45979i		−	0.431144i	−0.976488	−	0.215572i	$-0.930838\pi$
$107$		−	4.45979i		−	0.431144i	0.976488	−	0.215572i	$-0.0691616\pi$
$108$		−	2.24143i		−	0.215681i
$109$	−10.2412			−0.980929			−0.490465	−	0.871461i	$-0.663173\pi$
$109$	−10.2412			−0.980929			−0.490465	+	0.871461i	$0.663173\pi$
$110$	−6.23326	+	8.59684i	−0.594318	+	0.819677i
$111$	−2.15951			−0.204971
$112$			8.11348i			0.766652i
$113$		−	10.5620i		−	0.993593i	−0.867867	−	0.496796i	$-0.834510\pi$
$113$		−	10.5620i		−	0.993593i	0.867867	−	0.496796i	$-0.165490\pi$
$114$	1.72075			0.161163
$115$	−10.3234	+	14.2380i	−0.962666	+	1.32770i
$116$	4.35211			0.404084
$117$		−	0.930772i		−	0.0860499i
$118$		−	6.84247i		−	0.629900i
$119$	−17.3611			−1.59149
$120$	−3.74611	−	2.71617i	−0.341972	−	0.247951i
$121$	5.11618			0.465107
$122$			7.45541i			0.674981i
$123$		−	3.07974i		−	0.277691i
$124$	−2.36488			−0.212373
$125$	−3.42401	+	10.6431i	−0.306253	+	0.951950i
$126$	−10.0296			−0.893504
$127$			13.5115i			1.19895i	0.800392	+	0.599477i	$0.204625\pi$
$127$			13.5115i			1.19895i	−0.800392	+	0.599477i	$0.795375\pi$
$128$			3.80403i			0.336232i
$129$	−5.59517			−0.492627
$130$	−0.782400	−	0.567290i	−0.0686211	−	0.0497547i
$131$	11.8689			1.03699			0.518495	−	0.855081i	$-0.326492\pi$
$131$	11.8689			1.03699			0.518495	+	0.855081i	$0.326492\pi$
$132$			1.62201i			0.141178i
$133$			7.19729i			0.624084i
$134$	13.0204			1.12479
$135$	4.89793	−	6.75517i	0.421547	−	0.581392i
$136$	−16.0481			−1.37611
$137$			18.3633i			1.56888i	0.620205	+	0.784440i	$0.287050\pi$
$137$			18.3633i			1.56888i	−0.620205	+	0.784440i	$0.712950\pi$
$138$		−	6.25818i		−	0.532731i
$139$	−11.5674			−0.981132			−0.490566	−	0.871404i	$-0.663210\pi$
$139$	−11.5674			−0.981132			−0.490566	+	0.871404i	$0.663210\pi$
$140$	2.62398	−	3.61896i	0.221766	−	0.305858i
$141$	2.03854			0.171676
$142$			10.8200i			0.907991i
$143$			1.46674i			0.122655i
$144$	−6.21055			−0.517546
$145$	13.1163	+	9.51017i	1.08925	+	0.789777i
$146$	−2.12030			−0.175477
$147$			2.74199i			0.226155i
$148$		−	1.92843i		−	0.158516i
$149$	16.3235			1.33727			0.668637	−	0.743589i	$-0.266878\pi$
$149$	16.3235			1.33727			0.668637	+	0.743589i	$0.266878\pi$
$150$	−1.23674	−	3.78137i	−0.100980	−	0.308748i
$151$	−15.6126			−1.27054			−0.635269	−	0.772291i	$-0.719111\pi$
$151$	−15.6126			−1.27054			−0.635269	+	0.772291i	$0.719111\pi$
$152$			6.65296i			0.539626i
$153$		−	13.2892i		−	1.07437i
$154$	15.8049			1.27359
$155$	−7.12724	−	5.16770i	−0.572474	−	0.415080i
$156$	−0.147620			−0.0118190
$157$		−	14.6540i		−	1.16951i	−0.811208	−	0.584757i	$-0.801190\pi$
$157$		−	14.6540i		−	1.16951i	0.811208	−	0.584757i	$-0.198810\pi$
$158$		−	17.0535i		−	1.35671i
$159$	3.17867			0.252085
$160$	4.29083	−	5.91787i	0.339220	−	0.467848i
$161$	26.1758			2.06294
$162$		−	6.07155i		−	0.477026i
$163$			3.42042i			0.267908i	0.990988	+	0.133954i	$0.0427675\pi$
$163$			3.42042i			0.267908i	−0.990988	+	0.133954i	$0.957233\pi$
$164$	2.75019			0.214754
$165$	−3.54440	+	4.88840i	−0.275931	+	0.380561i
$166$	3.02968			0.235149
$167$		−	0.265125i		−	0.0205160i	−0.999947	−	0.0102580i	$-0.996735\pi$
$167$		−	0.265125i		−	0.0205160i	0.999947	−	0.0102580i	$-0.00326527\pi$
$168$			6.88703i			0.531346i
$169$	12.8665			0.989732
$170$	−11.1708	−	8.09957i	−0.856764	−	0.621209i
$171$	−5.50924			−0.421302
$172$		−	4.99645i		−	0.380976i
$173$		−	11.3576i		−	0.863500i	−0.901993	−	0.431750i	$-0.857896\pi$
$173$		−	11.3576i		−	0.863500i	0.901993	−	0.431750i	$-0.142104\pi$
$174$	−5.76516			−0.437056
$175$	15.8162	−	5.17288i	1.19559	−	0.391033i
$176$	9.78676			0.737705
$177$		−	3.89081i		−	0.292451i
$178$		−	16.2918i		−	1.22113i
$179$	10.6177			0.793606			0.396803	−	0.917904i	$-0.370120\pi$
$179$	10.6177			0.793606			0.396803	+	0.917904i	$0.370120\pi$
$180$	2.77017	+	2.00855i	0.206476	+	0.149708i
$181$	18.6295			1.38472			0.692360	−	0.721552i	$-0.256571\pi$
$181$	18.6295			1.38472			0.692360	+	0.721552i	$0.256571\pi$
$182$			1.43840i			0.106622i
$183$			4.23934i			0.313381i
$184$	24.1961			1.78376
$185$	4.21397	−	5.81186i	0.309817	−	0.427297i
$186$	3.13272			0.229702
$187$			20.9415i			1.53140i
$188$			1.82041i			0.132767i
$189$	−12.4190			−0.903352
$190$	−3.35779	+	4.63103i	−0.243600	+	0.335970i
$191$	5.78207			0.418376			0.209188	−	0.977875i	$-0.432918\pi$
$191$	5.78207			0.418376			0.209188	+	0.977875i	$0.432918\pi$
$192$			5.88078i			0.424409i
$193$		−	0.502765i		−	0.0361898i	−0.999836	−	0.0180949i	$-0.994240\pi$
$193$		−	0.502765i		−	0.0361898i	0.999836	−	0.0180949i	$-0.00576011\pi$
$194$	5.55302			0.398684
$195$	−0.444894	−	0.322577i	−0.0318595	−	0.0231002i
$196$	−2.44858			−0.174899
$197$		−	1.00000i		−	0.0712470i
$197$		−	1.00000i		−	0.0712470i
$198$			12.0980i			0.859766i
$199$	−14.3755			−1.01905			−0.509527	−	0.860455i	$-0.670180\pi$
$199$	−14.3755			−1.01905			−0.509527	+	0.860455i	$0.670180\pi$
$200$	14.6200	−	4.78165i	1.03379	−	0.338114i
$201$	7.40374			0.522219
$202$			12.6915i			0.892970i
$203$		−	24.1137i		−	1.69245i
$204$	−2.10766			−0.147566
$205$	8.28848	+	6.00968i	0.578892	+	0.419734i
$206$	6.23596			0.434480
$207$			20.0365i			1.39263i
$208$			0.890695i			0.0617586i
$209$	8.68162			0.600520
$210$	−3.47593	+	4.79397i	−0.239862	+	0.330815i
$211$	−5.40187			−0.371880			−0.185940	−	0.982561i	$-0.559533\pi$
$211$	−5.40187			−0.371880			−0.185940	+	0.982561i	$0.559533\pi$
$212$			2.83854i			0.194952i
$213$			6.15252i			0.421564i
$214$	−5.27563			−0.360634
$215$	10.9182	−	15.0582i	0.744613	−	1.02696i
$216$	−11.4798			−0.781100
$217$			13.1031i			0.889494i
$218$			12.1147i			0.820508i
$219$	−1.20566			−0.0814709
$220$	−4.36531	−	3.16513i	−0.294309	−	0.213393i
$221$	−1.90589			−0.128204
$222$			2.55455i			0.171450i
$223$			16.1807i			1.08354i	0.840526	+	0.541771i	$0.182246\pi$
$223$			16.1807i			1.08354i	−0.840526	+	0.541771i	$0.817754\pi$
$224$	−10.8797			−0.726930
$225$	3.95963	+	12.1067i	0.263975	+	0.807110i
$226$	−12.4942			−0.831101
$227$			7.37366i			0.489407i	0.969598	+	0.244704i	$0.0786907\pi$
$227$			7.37366i			0.489407i	−0.969598	+	0.244704i	$0.921309\pi$
$228$			0.873762i			0.0578663i
$229$	19.8853			1.31405			0.657027	−	0.753867i	$-0.271814\pi$
$229$	19.8853			1.31405			0.657027	+	0.753867i	$0.271814\pi$
$230$	16.8426	+	12.2119i	1.11057	+	0.805231i
$231$	8.98707			0.591306
$232$		−	22.2900i		−	1.46341i
$233$			11.1333i			0.729369i	0.931131	+	0.364684i	$0.118823\pi$
$233$			11.1333i			0.729369i	−0.931131	+	0.364684i	$0.881177\pi$
$234$	−1.10104			−0.0719772
$235$	−3.97793	+	5.48631i	−0.259491	+	0.357888i
$236$	3.47447			0.226169
$237$		−	9.69710i		−	0.629895i
$238$			20.5370i			1.33122i
$239$	5.92300			0.383127			0.191563	−	0.981480i	$-0.438644\pi$
$239$	5.92300			0.383127			0.191563	+	0.981480i	$0.438644\pi$
$240$	−2.15238	+	2.96854i	−0.138936	+	0.191619i
$241$	11.3665			0.732183			0.366091	−	0.930579i	$-0.380696\pi$
$241$	11.3665			0.732183			0.366091	+	0.930579i	$0.380696\pi$
$242$		−	6.05209i		−	0.389043i
$243$		−	14.6471i		−	0.939610i
$244$	−3.78571			−0.242355
$245$	−7.37948	−	5.35060i	−0.471458	−	0.341837i
$246$	−3.64313			−0.232277
$247$			0.790116i			0.0502739i
$248$			12.1121i			0.769118i
$249$	1.72276			0.109175
$250$	12.5901	+	4.05037i	0.796268	+	0.256168i
$251$	27.7984			1.75462			0.877311	−	0.479923i	$-0.159335\pi$
$251$	27.7984			1.75462			0.877311	+	0.479923i	$0.159335\pi$
$252$		−	5.09281i		−	0.320817i
$253$		−	31.5741i		−	1.98505i
$254$	15.9832			1.00288
$255$	−6.35204	−	4.60563i	−0.397780	−	0.288416i
$256$	−12.9856			−0.811597
$257$			12.6874i			0.791418i	0.918376	+	0.395709i	$0.129501\pi$
$257$			12.6874i			0.791418i	−0.918376	+	0.395709i	$0.870499\pi$
$258$			6.61870i			0.412063i
$259$	−10.6848			−0.663922
$260$	0.288059	−	0.397288i	0.0178647	−	0.0246387i
$261$	18.4581			1.14253
$262$		−	14.0401i		−	0.867401i
$263$			29.2878i			1.80596i	0.429678	+	0.902982i	$0.358627\pi$
$263$			29.2878i			1.80596i	−0.429678	+	0.902982i	$0.641373\pi$
$264$	8.30737			0.511283
$265$	−6.20273	+	8.55473i	−0.381031	+	0.525513i
$266$	8.51391			0.522021
$267$		−	9.26398i		−	0.566947i
$268$			6.61149i			0.403861i
$269$	6.77642			0.413166			0.206583	−	0.978429i	$-0.433766\pi$
$269$	6.77642			0.413166			0.206583	+	0.978429i	$0.433766\pi$
$270$	−7.99091	−	5.79392i	−0.486311	−	0.352607i
$271$	−24.4544			−1.48550			−0.742748	−	0.669571i	$-0.766478\pi$
$271$	−24.4544			−1.48550			−0.742748	+	0.669571i	$0.766478\pi$
$272$			12.7170i			0.771083i
$273$			0.817915i			0.0495025i
$274$	21.7225			1.31230
$275$	−6.23970	−	19.0780i	−0.376268	−	1.15045i
$276$	3.17778			0.191280
$277$		−	1.64895i		−	0.0990758i	−0.998772	−	0.0495379i	$-0.984225\pi$
$277$		−	1.64895i		−	0.0990758i	0.998772	−	0.0495379i	$-0.0157749\pi$
$278$			13.6834i			0.820677i
$279$	−10.0299			−0.600473
$280$	−18.5350	−	13.4391i	−1.10768	−	0.803138i
$281$	−15.2800			−0.911530			−0.455765	−	0.890100i	$-0.650634\pi$
$281$	−15.2800			−0.911530			−0.455765	+	0.890100i	$0.650634\pi$
$282$		−	2.41146i		−	0.143600i
$283$		−	14.2874i		−	0.849300i	−0.905358	−	0.424650i	$-0.860397\pi$
$283$		−	14.2874i		−	0.849300i	0.905358	−	0.424650i	$-0.139603\pi$
$284$	−5.49417			−0.326019
$285$	−1.90933	+	2.63333i	−0.113099	+	0.155985i
$286$	1.73505			0.102596
$287$		−	15.2379i		−	0.899467i
$288$		−	8.32797i		−	0.490730i
$289$	−10.2117			−0.600688
$290$	11.2499	−	15.5157i	0.660616	−	0.911115i
$291$	3.15760			0.185102
$292$		−	1.07665i		−	0.0630060i
$293$			9.81819i			0.573585i	0.957993	+	0.286792i	$0.0925890\pi$
$293$			9.81819i			0.573585i	−0.957993	+	0.286792i	$0.907411\pi$
$294$	3.24359			0.189170
$295$	10.4713	+	7.59236i	0.609663	+	0.442044i
$296$	−9.87672			−0.574073
$297$			14.9803i			0.869243i
$298$		−	19.3096i		−	1.11858i
$299$	2.87357			0.166183
$300$	1.92011	−	0.627995i	0.110857	−	0.0362573i
$301$	−27.6838			−1.59567
$302$			18.4687i			1.06275i
$303$			7.21672i			0.414590i
$304$	5.27202			0.302371
$305$	−11.4093	−	8.27248i	−0.653295	−	0.473681i
$306$	−15.7203			−0.898668
$307$			18.4502i			1.05301i	0.850172	+	0.526505i	$0.176498\pi$
$307$			18.4502i			1.05301i	−0.850172	+	0.526505i	$0.823502\pi$
$308$			8.02540i			0.457290i
$309$	3.54593			0.201721
$310$	−6.11305	+	8.43104i	−0.347198	+	0.478851i
$311$	34.6643			1.96563			0.982815	−	0.184593i	$-0.0590967\pi$
$311$	34.6643			1.96563			0.982815	+	0.184593i	$0.0590967\pi$
$312$			0.756056i			0.0428032i
$313$			12.3956i			0.700641i	0.936630	+	0.350320i	$0.113927\pi$
$313$			12.3956i			0.700641i	−0.936630	+	0.350320i	$0.886073\pi$
$314$	−17.3347			−0.978252
$315$	11.1287	−	15.3486i	0.627033	−	0.864797i
$316$	8.65946			0.487133
$317$			22.1635i			1.24482i	0.782690	+	0.622412i	$0.213847\pi$
$317$			22.1635i			1.24482i	−0.782690	+	0.622412i	$0.786153\pi$
$318$		−	3.76016i		−	0.210859i
$319$	−29.0867			−1.62854
$320$	−15.8269	−	11.4755i	−0.884750	−	0.641500i
$321$	−2.99986			−0.167436
$322$		−	30.9642i		−	1.72557i
$323$			11.2810i			0.627691i
$324$	3.08302			0.171279
$325$	1.73629	−	0.567876i	0.0963123	−	0.0315001i
$326$	4.04613			0.224095
$327$			6.88872i			0.380947i
$328$		−	14.0855i		−	0.777741i
$329$	10.0863			0.556076
$330$	5.78264	+	4.19279i	0.318324	+	0.230805i
$331$	−27.4133			−1.50677			−0.753386	−	0.657578i	$-0.771581\pi$
$331$	−27.4133			−1.50677			−0.753386	+	0.657578i	$0.771581\pi$
$332$			1.53841i			0.0844314i
$333$		−	8.17880i		−	0.448195i
$334$	−0.313624			−0.0171608
$335$	−14.4473	+	19.9256i	−0.789342	+	1.08865i
$336$	5.45751			0.297732
$337$			6.31336i			0.343910i	0.985105	+	0.171955i	$0.0550084\pi$
$337$			6.31336i			0.343910i	−0.985105	+	0.171955i	$0.944992\pi$
$338$		−	15.2202i		−	0.827871i
$339$	−7.10453			−0.385865
$340$	4.11281	−	5.67233i	0.223048	−	0.307625i
$341$	15.8054			0.855908
$342$			6.51706i			0.352402i
$343$		−	9.73006i		−	0.525374i
$344$	−25.5900			−1.37972
$345$	9.57714	+	6.94404i	0.515616	+	0.373854i
$346$	−13.4352			−0.722283
$347$			14.9294i			0.801451i	0.916198	+	0.400726i	$0.131242\pi$
$347$			14.9294i			0.801451i	−0.916198	+	0.400726i	$0.868758\pi$
$348$		−	2.92744i		−	0.156927i
$349$	−21.8095			−1.16743			−0.583717	−	0.811957i	$-0.698402\pi$
$349$	−21.8095			−1.16743			−0.583717	+	0.811957i	$0.698402\pi$
$350$	−6.11917	−	18.7095i	−0.327083	−	1.00006i
$351$	−1.36336			−0.0727706
$352$			13.1235i			0.699483i
$353$			9.32850i			0.496506i	0.968695	+	0.248253i	$0.0798564\pi$
$353$			9.32850i			0.496506i	−0.968695	+	0.248253i	$0.920144\pi$
$354$	−4.60257			−0.244624
$355$	−16.5582	−	12.0058i	−0.878819	−	0.637200i
$356$	8.27268			0.438451
$357$			11.6779i			0.618060i
$358$		−	12.5601i		−	0.663819i
$359$	−14.1641			−0.747554			−0.373777	−	0.927519i	$-0.621937\pi$
$359$	−14.1641			−0.747554			−0.373777	+	0.927519i	$0.621937\pi$
$360$	10.2871	−	14.1878i	0.542176	−	0.747763i
$361$	−14.3233			−0.753858
$362$		−	22.0374i		−	1.15826i
$363$		−	3.44138i		−	0.180626i
$364$	−0.730393			−0.0382830
$365$	2.35267	−	3.24478i	0.123144	−	0.169839i
$366$	5.01486			0.262131
$367$		−	7.47147i		−	0.390008i	−0.980802	−	0.195004i	$-0.937528\pi$
$367$		−	7.47147i		−	0.390008i	0.980802	−	0.195004i	$-0.0624719\pi$
$368$		−	19.1738i		−	0.999503i
$369$	11.6640			0.607205
$370$	−6.87504	−	4.98485i	−0.357416	−	0.259150i
$371$	15.7274			0.816528
$372$			1.59073i			0.0824756i
$373$		−	28.3484i		−	1.46782i	−0.679245	−	0.733912i	$-0.737693\pi$
$373$		−	28.3484i		−	1.46782i	0.679245	−	0.733912i	$-0.262307\pi$
$374$	24.7724			1.28095
$375$	7.15907	+	2.30315i	0.369693	+	0.118934i
$376$	9.32348			0.480822
$377$		−	2.64719i		−	0.136337i
$378$			14.6909i			0.755617i
$379$	24.3013			1.24827			0.624136	−	0.781316i	$-0.285451\pi$
$379$	24.3013			1.24827			0.624136	+	0.781316i	$0.285451\pi$
$380$	−2.35155	−	1.70502i	−0.120632	−	0.0874658i
$381$	9.08849			0.465617
$382$		−	6.83981i		−	0.349955i
$383$		−	0.942323i		−	0.0481505i	−0.999710	−	0.0240752i	$-0.992336\pi$
$383$		−	0.942323i		−	0.0481505i	0.999710	−	0.0240752i	$-0.00766412\pi$
$384$	2.55877			0.130577
$385$	−17.5370	+	24.1868i	−0.893767	+	1.23267i
$386$	−0.594738			−0.0302713
$387$		−	21.1908i		−	1.07719i
$388$			2.81972i			0.143149i
$389$	−4.36844			−0.221489			−0.110744	−	0.993849i	$-0.535323\pi$
$389$	−4.36844			−0.221489			−0.110744	+	0.993849i	$0.535323\pi$
$390$	−0.381586	+	0.526280i	−0.0193224	+	0.0266492i
$391$	41.0278			2.07486
$392$			12.5407i			0.633403i
$393$		−	7.98358i		−	0.402718i
$394$	−1.18293			−0.0595953
$395$	26.0977	+	18.9225i	1.31312	+	0.952095i
$396$	−6.14312			−0.308703
$397$		−	17.5141i		−	0.879009i	−0.898240	−	0.439504i	$-0.855154\pi$
$397$		−	17.5141i		−	0.879009i	0.898240	−	0.439504i	$-0.144846\pi$
$398$			17.0053i			0.852398i
$399$	4.84124			0.242365
$400$	−3.78914	−	11.5854i	−0.189457	−	0.579269i
$401$	−35.5964			−1.77760			−0.888800	−	0.458294i	$-0.848461\pi$
$401$	−35.5964			−1.77760			−0.888800	+	0.458294i	$0.848461\pi$
$402$		−	8.75812i		−	0.436815i
$403$			1.43845i			0.0716543i
$404$	−6.44449			−0.320625
$405$	9.29154	+	6.73696i	0.461700	+	0.334762i
$406$	−28.5249			−1.41567
$407$			12.8884i			0.638853i
$408$			10.7947i			0.534417i
$409$	−20.2533			−1.00146			−0.500730	−	0.865603i	$-0.666935\pi$
$409$	−20.2533			−1.00146			−0.500730	+	0.865603i	$0.666935\pi$
$410$	7.10904	−	9.80471i	0.351091	−	0.484220i
$411$	12.3520			0.609279
$412$			3.16650i			0.156002i
$413$		−	19.2510i		−	0.947278i
$414$	23.7019			1.16488
$415$	−3.36172	+	4.63644i	−0.165020	+	0.227594i
$416$	−1.19437			−0.0585587
$417$			7.78076i			0.381025i
$418$		−	10.2698i		−	0.502311i
$419$	12.5680			0.613985			0.306992	−	0.951712i	$-0.400677\pi$
$419$	12.5680			0.613985			0.306992	+	0.951712i	$0.400677\pi$
$420$	−2.43428	−	1.76501i	−0.118781	−	0.0861237i
$421$	−24.6205			−1.19993			−0.599964	−	0.800027i	$-0.704818\pi$
$421$	−24.6205			−1.19993			−0.599964	+	0.800027i	$0.704818\pi$
$422$			6.39005i			0.311063i
$423$			7.72067i			0.375392i
$424$	14.5380			0.706026
$425$	24.7902	−	8.10794i	1.20250	−	0.393293i
$426$	7.27802			0.352621
$427$			20.9754i			1.01507i
$428$		−	2.67886i		−	0.129488i
$429$	0.986596			0.0476333
$430$	−17.8129	−	12.9155i	−0.859012	−	0.622839i
$431$	25.8545			1.24537			0.622685	−	0.782473i	$-0.286042\pi$
$431$	25.8545			1.24537			0.622685	+	0.782473i	$0.286042\pi$
$432$			9.09696i			0.437678i
$433$			14.5312i			0.698326i	0.937062	+	0.349163i	$0.113534\pi$
$433$			14.5312i			0.698326i	−0.937062	+	0.349163i	$0.886466\pi$
$434$	15.5000			0.744026
$435$	6.39699	−	8.82266i	0.306712	−	0.423014i
$436$	−6.15159			−0.294608
$437$		−	17.0087i		−	0.813634i
$438$			1.42621i			0.0681471i
$439$	−14.7262			−0.702843			−0.351421	−	0.936217i	$-0.614302\pi$
$439$	−14.7262			−0.702843			−0.351421	+	0.936217i	$0.614302\pi$
$440$	−16.2107	+	22.3576i	−0.772813	+	1.06585i
$441$	−10.3848			−0.494516
$442$			2.25455i			0.107238i
$443$		−	16.8930i		−	0.802611i	−0.915944	−	0.401306i	$-0.868557\pi$
$443$		−	16.8930i		−	0.802611i	0.915944	−	0.401306i	$-0.131443\pi$
$444$	−1.29715			−0.0615601
$445$	24.9321	+	18.0773i	1.18189	+	0.856948i
$446$	19.1407			0.906340
$447$		−	10.9800i		−	0.519335i
$448$			29.0969i			1.37470i
$449$	−40.2353			−1.89882			−0.949412	−	0.314034i	$-0.898319\pi$
$449$	−40.2353			−1.89882			−0.949412	+	0.314034i	$0.898319\pi$
$450$	14.3214	−	4.68398i	0.675115	−	0.220805i
$451$	−18.3805			−0.865505
$452$		−	6.34430i		−	0.298411i
$453$			10.5018i			0.493417i
$454$	8.72255			0.409369
$455$	−2.20125	−	1.59604i	−0.103196	−	0.0748237i
$456$	4.47509			0.209566
$457$			23.9328i			1.11953i	0.828652	+	0.559764i	$0.189108\pi$
$457$			23.9328i			1.11953i	−0.828652	+	0.559764i	$0.810892\pi$
$458$		−	23.5229i		−	1.09915i
$459$	−19.4655			−0.908573
$460$	−6.20099	+	8.55233i	−0.289122	+	0.398754i
$461$	−36.4943			−1.69971			−0.849855	−	0.527017i	$-0.823310\pi$
$461$	−36.4943			−1.69971			−0.849855	+	0.527017i	$0.823310\pi$
$462$		−	10.6311i		−	0.494603i
$463$		−	22.8528i		−	1.06206i	−0.847353	−	0.531030i	$-0.821805\pi$
$463$		−	22.8528i		−	1.06206i	0.847353	−	0.531030i	$-0.178195\pi$
$464$	−17.6633			−0.819998
$465$	−3.47604	+	4.79412i	−0.161198	+	0.222322i
$466$	13.1700			0.610087
$467$		−	27.0948i		−	1.25380i	−0.779101	−	0.626898i	$-0.784324\pi$
$467$		−	27.0948i		−	1.25380i	0.779101	−	0.626898i	$-0.215676\pi$
$468$		−	0.559087i		−	0.0258438i
$469$	36.6322			1.69152
$470$	6.48994	+	4.70562i	0.299359	+	0.217054i
$471$	−9.85695			−0.454184
$472$		−	17.7950i		−	0.819081i
$473$			33.3931i			1.53542i
$474$	−11.4710			−0.526881
$475$	−3.36126	−	10.2771i	−0.154225	−	0.471547i
$476$	−10.4283			−0.477980
$477$			12.0387i			0.551215i
$478$		−	7.00651i		−	0.320470i
$479$	9.83837			0.449527			0.224763	−	0.974413i	$-0.427839\pi$
$479$	9.83837			0.449527			0.224763	+	0.974413i	$0.427839\pi$
$480$	−3.98064	−	2.88622i	−0.181690	−	0.131737i
$481$	−1.17297			−0.0534830
$482$		−	13.4458i		−	0.612441i
$483$		−	17.6071i		−	0.801150i
$484$	3.07313			0.139688
$485$	−6.16160	+	8.49801i	−0.279784	+	0.385875i
$486$	−17.3265			−0.785946
$487$			21.7301i			0.984685i	0.870402	+	0.492342i	$0.163859\pi$
$487$			21.7301i			0.984685i	−0.870402	+	0.492342i	$0.836141\pi$
$488$			19.3891i			0.877701i
$489$	2.30074			0.104043
$490$	−6.32940	+	8.72943i	−0.285933	+	0.394356i
$491$	9.92067			0.447714			0.223857	−	0.974622i	$-0.428135\pi$
$491$	9.92067			0.447714			0.223857	+	0.974622i	$0.428135\pi$
$492$		−	1.84991i		−	0.0834003i
$493$		−	37.7957i		−	1.70223i
$494$	0.934654			0.0420521
$495$	−18.5140	−	13.4239i	−0.832144	−	0.603357i
$496$	9.59801			0.430963
$497$			30.4414i			1.36549i
$498$		−	2.03791i		−	0.0913208i
$499$	−5.40678			−0.242041			−0.121020	−	0.992650i	$-0.538617\pi$
$499$	−5.40678			−0.242041			−0.121020	+	0.992650i	$0.538617\pi$
$500$	−2.05670	+	6.39301i	−0.0919784	+	0.285904i
$501$	−0.178335			−0.00796743
$502$		−	32.8837i		−	1.46767i
$503$		−	4.66981i		−	0.208216i	−0.994566	−	0.104108i	$-0.966801\pi$
$503$		−	4.66981i		−	0.208216i	0.994566	−	0.104108i	$-0.0331988\pi$
$504$	−26.0836			−1.16185
$505$	−19.4223	−	14.0824i	−0.864280	−	0.626658i
$506$	−37.3501			−1.66041
$507$		−	8.65462i		−	0.384365i
$508$			8.11597i			0.360088i
$509$	21.1778			0.938690			0.469345	−	0.883015i	$-0.344490\pi$
$509$	21.1778			0.938690			0.469345	+	0.883015i	$0.344490\pi$
$510$	−5.44815	+	7.51403i	−0.241248	+	0.332727i
$511$	−5.96536			−0.263892
$512$			22.9691i			1.01510i
$513$			8.06971i			0.356286i
$514$	15.0083			0.661989
$515$	−6.91938	+	9.54313i	−0.304904	+	0.420521i
$516$	−3.36085			−0.147953
$517$		−	12.1664i		−	0.535080i
$518$			12.6394i			0.555344i
$519$	−7.63964			−0.335343
$520$	−2.03477	−	1.47534i	−0.0892304	−	0.0646977i
$521$	12.2704			0.537577			0.268789	−	0.963199i	$-0.413377\pi$
$521$	12.2704			0.537577			0.268789	+	0.963199i	$0.413377\pi$
$522$		−	21.8346i		−	0.955676i
$523$		−	7.41074i		−	0.324049i	−0.986787	−	0.162024i	$-0.948198\pi$
$523$		−	7.41074i		−	0.324049i	0.986787	−	0.162024i	$-0.0518023\pi$
$524$	7.12929			0.311445
$525$	−3.47952	−	10.6387i	−0.151859	−	0.464311i
$526$	34.6455			1.51062
$527$			20.5377i			0.894635i
$528$		−	6.58304i		−	0.286490i
$529$	−38.8587			−1.68951
$530$	10.1197	+	7.33741i	0.439571	+	0.318717i
$531$	14.7358			0.639481
$532$			4.32320i			0.187434i
$533$		−	1.67282i		−	0.0724577i
$534$	−10.9587			−0.474228
$535$	5.85381	−	8.07350i	0.253082	−	0.349048i
$536$	33.8617			1.46260
$537$		−	7.14198i		−	0.308199i
$538$		−	8.01605i		−	0.345596i
$539$	16.3647			0.704879
$540$	2.94204	−	4.05763i	0.126605	−	0.174613i
$541$	−4.41764			−0.189929			−0.0949647	−	0.995481i	$-0.530274\pi$
$541$	−4.41764			−0.189929			−0.0949647	+	0.995481i	$0.530274\pi$
$542$			28.9279i			1.24256i
$543$		−	12.5311i		−	0.537760i
$544$	−17.0528			−0.731132
$545$	−18.5395	−	13.4424i	−0.794147	−	0.575807i
$546$	0.967538			0.0414068
$547$		−	7.34172i		−	0.313909i	−0.987606	−	0.156955i	$-0.949832\pi$
$547$		−	7.34172i		−	0.313909i	0.987606	−	0.156955i	$-0.0501677\pi$
$548$			11.0303i			0.471190i
$549$	−16.0558			−0.685247
$550$	−22.5680	+	7.38114i	−0.962303	+	0.314733i
$551$	−15.6687			−0.667510
$552$		−	16.2755i		−	0.692729i
$553$		−	47.9793i		−	2.04029i
$554$	−1.95060			−0.0828729
$555$	−3.90933	−	2.83452i	−0.165942	−	0.120319i
$556$	−6.94818			−0.294668
$557$			3.51847i			0.149082i	0.997218	+	0.0745412i	$0.0237492\pi$
$557$			3.51847i			0.149082i	−0.997218	+	0.0745412i	$0.976251\pi$
$558$			11.8647i			0.502271i
$559$	−3.03911			−0.128541
$560$	−10.6496	+	14.6878i	−0.450026	+	0.620671i
$561$	14.0863			0.594723
$562$			18.0752i			0.762458i
$563$		−	26.4829i		−	1.11612i	−0.829800	−	0.558060i	$-0.811546\pi$
$563$		−	26.4829i		−	1.11612i	0.829800	−	0.558060i	$-0.188454\pi$
$564$	1.22449			0.0515605
$565$	13.8635	−	19.1203i	0.583241	−	0.804399i
$566$	−16.9011			−0.710405
$567$		−	17.0820i		−	0.717377i
$568$			28.1392i			1.18069i
$569$	−32.0339			−1.34293			−0.671466	−	0.741036i	$-0.734335\pi$
$569$	−32.0339			−1.34293			−0.671466	+	0.741036i	$0.734335\pi$
$570$	3.11505	+	2.25861i	0.130475	+	0.0946028i
$571$	−30.6558			−1.28290			−0.641452	−	0.767163i	$-0.721668\pi$
$571$	−30.6558			−1.28290			−0.641452	+	0.767163i	$0.721668\pi$
$572$			0.881025i			0.0368375i
$573$		−	3.88930i		−	0.162478i
$574$	−18.0255			−0.752368
$575$	−37.3768	+	12.2246i	−1.55872	+	0.509799i
$576$	−22.2725			−0.928022
$577$		−	27.1211i		−	1.12907i	−0.825410	−	0.564533i	$-0.809056\pi$
$577$		−	27.1211i		−	1.12907i	0.825410	−	0.564533i	$-0.190944\pi$
$578$			12.0797i			0.502451i
$579$	−0.338184			−0.0140544
$580$	7.87858	+	5.71248i	0.327140	+	0.237198i
$581$	8.52386			0.353629
$582$		−	3.73522i		−	0.154830i
$583$		−	18.9710i		−	0.785697i
$584$	−5.51420			−0.228179
$585$	1.22171	−	1.68497i	0.0505114	−	0.0696647i
$586$	11.6143			0.479780
$587$		−	35.1593i		−	1.45118i	−0.688128	−	0.725589i	$-0.741567\pi$
$587$		−	35.1593i		−	1.45118i	0.688128	−	0.725589i	$-0.258433\pi$
$588$			1.64703i			0.0679224i
$589$	8.51418			0.350821
$590$	8.98126	−	12.3868i	0.369752	−	0.509958i
$591$	−0.672647			−0.0276690
$592$			7.82664i			0.321673i
$593$			40.0424i			1.64435i	0.569238	+	0.822173i	$0.307238\pi$
$593$			40.0424i			1.64435i	−0.569238	+	0.822173i	$0.692762\pi$
$594$	17.7206			0.727087
$595$	−31.4286	−	22.7878i	−1.28845	−	0.934207i
$596$	9.80505			0.401630
$597$			9.66966i			0.395753i
$598$		−	3.39924i		−	0.139005i
$599$	−6.08575			−0.248657			−0.124329	−	0.992241i	$-0.539678\pi$
$599$	−6.08575			−0.248657			−0.124329	+	0.992241i	$0.539678\pi$
$600$	−3.21637	−	9.83411i	−0.131308	−	0.401476i
$601$	15.5884			0.635866			0.317933	−	0.948113i	$-0.397011\pi$
$601$	15.5884			0.635866			0.317933	+	0.948113i	$0.397011\pi$
$602$			32.7480i			1.33471i
$603$			28.0405i			1.14190i
$604$	−9.37804			−0.381587
$605$	9.26176	+	6.71537i	0.376544	+	0.273018i
$606$	8.53689			0.346788
$607$			43.0843i			1.74874i	0.485263	+	0.874368i	$0.338724\pi$
$607$			43.0843i			1.74874i	−0.485263	+	0.874368i	$0.661276\pi$
$608$			7.06947i			0.286705i
$609$	−16.2200			−0.657268
$610$	−9.78578	+	13.4964i	−0.396215	+	0.546455i
$611$	1.10727			0.0447954
$612$		−	7.98244i		−	0.322671i
$613$		−	9.83189i		−	0.397106i	−0.980090	−	0.198553i	$-0.936376\pi$
$613$		−	9.83189i		−	0.397106i	0.980090	−	0.198553i	$-0.0636243\pi$
$614$	21.8254			0.880801
$615$	4.04239	−	5.57522i	0.163005	−	0.224815i
$616$	41.1032			1.65610
$617$		−	40.8672i		−	1.64525i	−0.568583	−	0.822626i	$-0.692508\pi$
$617$		−	40.8672i		−	1.64525i	0.568583	−	0.822626i	$-0.307492\pi$
$618$		−	4.19460i		−	0.168732i
$619$	35.8404			1.44055			0.720274	−	0.693689i	$-0.244016\pi$
$619$	35.8404			1.44055			0.720274	+	0.693689i	$0.244016\pi$
$620$	−4.28112	−	3.10409i	−0.171934	−	0.124663i
$621$	29.3487			1.17772
$622$		−	41.0055i		−	1.64417i
$623$		−	45.8363i		−	1.83639i
$624$	0.599124			0.0239841
$625$	−20.1684	+	14.7729i	−0.806734	+	0.590915i
$626$	14.6632			0.586058
$627$		−	5.83966i		−	0.233214i
$628$		−	8.80220i		−	0.351246i
$629$	−16.7473			−0.667759
$630$	−18.1564	−	13.1645i	−0.723368	−	0.524488i
$631$	−5.16698			−0.205694			−0.102847	−	0.994697i	$-0.532795\pi$
$631$	−5.16698			−0.205694			−0.102847	+	0.994697i	$0.532795\pi$
$632$		−	44.3507i		−	1.76417i
$633$			3.63355i			0.144421i
$634$	26.2179			1.04125
$635$	−17.7349	+	24.4598i	−0.703788	+	0.970656i
$636$	1.90933			0.0757100
$637$			1.48936i			0.0590105i
$638$			34.4077i			1.36221i
$639$	−23.3017			−0.921801
$640$	−4.99308	+	6.88640i	−0.197369	+	0.272209i
$641$	23.3893			0.923822			0.461911	−	0.886926i	$-0.347164\pi$
$641$	23.3893			0.923822			0.461911	+	0.886926i	$0.347164\pi$
$642$			3.54864i			0.140053i
$643$		−	48.9826i		−	1.93168i	−0.259130	−	0.965842i	$-0.583436\pi$
$643$		−	48.9826i		−	1.93168i	0.259130	−	0.965842i	$-0.416564\pi$
$644$	15.7230			0.619574
$645$	−10.1289	−	7.34408i	−0.398824	−	0.289173i
$646$	13.3447			0.525038
$647$		−	44.2948i		−	1.74141i	−0.491809	−	0.870703i	$-0.663664\pi$
$647$		−	44.2948i		−	1.74141i	0.491809	−	0.870703i	$-0.336336\pi$
$648$		−	15.7901i		−	0.620294i
$649$	−23.2212			−0.911510
$650$	−0.671759	−	2.05392i	−0.0263486	−	0.0805613i
$651$	8.81374			0.345438
$652$			2.05455i			0.0804623i
$653$			20.8680i			0.816629i	0.912841	+	0.408315i	$0.133883\pi$
$653$			20.8680i			0.816629i	−0.912841	+	0.408315i	$0.866117\pi$
$654$	8.14889			0.318647
$655$	21.4861	+	15.5788i	0.839533	+	0.608715i
$656$	−11.1618			−0.435796
$657$		−	4.56624i		−	0.178146i
$658$		−	11.9314i		−	0.465135i
$659$	16.4987			0.642697			0.321349	−	0.946961i	$-0.395864\pi$
$659$	16.4987			0.642697			0.321349	+	0.946961i	$0.395864\pi$
$660$	−2.12902	+	2.93631i	−0.0828718	+	0.114296i
$661$	−35.2710			−1.37188			−0.685941	−	0.727658i	$-0.740609\pi$
$661$	−35.2710			−1.37188			−0.685941	+	0.727658i	$0.740609\pi$
$662$			32.4281i			1.26035i
$663$			1.28199i			0.0497886i
$664$	7.87920			0.305772
$665$	−9.44699	+	13.0292i	−0.366338	+	0.505250i
$666$	−9.67496			−0.374897
$667$			56.9855i			2.20649i
$668$		−	0.159252i		−	0.00616166i
$669$	10.8839			0.420797
$670$	23.5706	+	17.0902i	0.910613	+	0.660253i
$671$	25.3013			0.976745
$672$			7.31820i			0.282306i
$673$			41.8981i			1.61505i	0.589830	+	0.807527i	$0.299195\pi$
$673$			41.8981i			1.61505i	−0.589830	+	0.807527i	$0.700805\pi$
$674$	7.46828			0.287667
$675$	17.7333	−	5.79991i	0.682556	−	0.223238i
$676$	7.72853			0.297251
$677$		−	16.8927i		−	0.649240i	−0.945845	−	0.324620i	$-0.894764\pi$
$677$		−	16.8927i		−	0.649240i	0.945845	−	0.324620i	$-0.105236\pi$
$678$			8.40418i			0.322760i
$679$	15.6232			0.599562
$680$	−29.0517	−	21.0643i	−1.11408	−	0.807780i
$681$	4.95987			0.190063
$682$		−	18.6967i		−	0.715933i
$683$		−	34.9194i		−	1.33615i	−0.744093	−	0.668077i	$-0.767118\pi$
$683$		−	34.9194i		−	1.33615i	0.744093	−	0.668077i	$-0.232882\pi$
$684$	−3.30923			−0.126532
$685$	−24.1032	+	33.2428i	−0.920935	+	1.27014i
$686$	−11.5100			−0.439454
$687$		−	13.3758i		−	0.510317i
$688$			20.2784i			0.773106i
$689$	1.72655			0.0657764
$690$	8.21433	−	11.3291i	0.312714	−	0.431292i
$691$	37.2958			1.41880			0.709399	−	0.704807i	$-0.248966\pi$
$691$	37.2958			1.41880			0.709399	+	0.704807i	$0.248966\pi$
$692$		−	6.82215i		−	0.259339i
$693$			34.0371i			1.29296i
$694$	17.6605			0.670382
$695$	−20.9403	−	15.1830i	−0.794310	−	0.575926i
$696$	−14.9933			−0.568319
$697$		−	23.8839i		−	0.904666i
$698$			25.7991i			0.976512i
$699$	7.48880			0.283253
$700$	9.50031	−	3.10719i	0.359078	−	0.117441i
$701$	5.44329			0.205590			0.102795	−	0.994703i	$-0.467221\pi$
$701$	5.44329			0.205590			0.102795	+	0.994703i	$0.467221\pi$
$702$			1.61276i			0.0608697i
$703$			6.94284i			0.261854i
$704$	35.0977			1.32279
$705$	3.69035	+	2.67574i	0.138987	+	0.100774i
$706$	11.0350			0.415307
$707$			35.7069i			1.34290i
$708$		−	2.33709i		−	0.0878334i
$709$	8.83117			0.331661			0.165831	−	0.986154i	$-0.446969\pi$
$709$	8.83117			0.331661			0.165831	+	0.986154i	$0.446969\pi$
$710$	−14.2020	+	19.5873i	−0.532992	+	0.735097i
$711$	36.7263			1.37734
$712$		−	42.3697i		−	1.58787i
$713$		−	30.9652i		−	1.15966i
$714$	13.8142			0.516982
$715$	−1.92520	+	2.65522i	−0.0719985	+	0.0992995i
$716$	6.37775			0.238348
$717$		−	3.98409i		−	0.148788i
$718$			16.7552i			0.625299i
$719$	−7.51607			−0.280302			−0.140151	−	0.990130i	$-0.544759\pi$
$719$	−7.51607			−0.280302			−0.140151	+	0.990130i	$0.544759\pi$
$720$	−11.2429	−	8.15181i	−0.418998	−	0.303800i
$721$	17.5446			0.653394
$722$			16.9435i			0.630572i
$723$		−	7.64567i		−	0.284345i
$724$	11.1902			0.415880
$725$	11.2615	+	34.4323i	0.418242	+	1.27878i
$726$	−4.07092			−0.151086
$727$		−	9.35179i		−	0.346839i	−0.984848	−	0.173419i	$-0.944518\pi$
$727$		−	9.35179i		−	0.346839i	0.984848	−	0.173419i	$-0.0554816\pi$
$728$			3.74081i			0.138644i
$729$	5.54556			0.205391
$730$	−3.83835	−	2.78305i	−0.142064	−	0.103005i
$731$	−43.3914			−1.60489
$732$			2.54645i			0.0941194i
$733$			8.95136i			0.330626i	0.986241	+	0.165313i	$0.0528634\pi$
$733$			8.95136i			0.330626i	−0.986241	+	0.165313i	$0.947137\pi$
$734$	−8.83825			−0.326226
$735$	−3.59907	+	4.96379i	−0.132754	+	0.183092i
$736$	25.7109			0.947717
$737$		−	44.1870i		−	1.62765i
$738$		−	13.7978i		−	0.507903i
$739$	−39.4888			−1.45262			−0.726309	−	0.687368i	$-0.758766\pi$
$739$	−39.4888			−1.45262			−0.726309	+	0.687368i	$0.758766\pi$
$740$	2.53121	−	3.49101i	0.0930490	−	0.128332i
$741$	0.531469			0.0195240
$742$		−	18.6045i		−	0.682993i
$743$			12.2083i			0.447879i	0.974603	+	0.223939i	$0.0718917\pi$
$743$			12.2083i			0.447879i	−0.974603	+	0.223939i	$0.928108\pi$
$744$	8.14716			0.298689
$745$	29.5503	+	21.4258i	1.08264	+	0.784982i
$746$	−33.5342			−1.22778
$747$			6.52467i			0.238725i
$748$			12.5790i			0.459932i
$749$	−14.8427			−0.542341
$750$	2.72447	−	8.46870i	0.0994837	−	0.309233i
$751$	31.3797			1.14506			0.572531	−	0.819883i	$-0.305962\pi$
$751$	31.3797			1.14506			0.572531	+	0.819883i	$0.305962\pi$
$752$		−	7.38823i		−	0.269421i
$753$		−	18.6985i		−	0.681413i
$754$	−3.13145			−0.114041
$755$	−28.2634	−	20.4927i	−1.02861	−	0.745807i
$756$	−7.45974			−0.271308
$757$			28.2134i			1.02544i	0.858557	+	0.512718i	$0.171361\pi$
$757$			28.2134i			1.02544i	−0.858557	+	0.512718i	$0.828639\pi$
$758$		−	28.7468i		−	1.04413i
$759$	−21.2383			−0.770900
$760$	−8.73251	+	12.0438i	−0.316761	+	0.436874i
$761$	35.6534			1.29243			0.646217	−	0.763154i	$-0.276350\pi$
$761$	35.6534			1.29243			0.646217	+	0.763154i	$0.276350\pi$
$762$		−	10.7511i		−	0.389470i
$763$			34.0840i			1.23392i
$764$	3.47312			0.125653
$765$	17.4431	−	24.0573i	0.630657	−	0.869795i
$766$	−1.11470			−0.0402759
$767$		−	2.11336i		−	0.0763091i
$768$			8.73470i			0.315186i
$769$	−45.2644			−1.63228			−0.816139	−	0.577856i	$-0.803890\pi$
$769$	−45.2644			−1.63228			−0.816139	+	0.577856i	$0.803890\pi$
$770$	28.6114	+	20.7451i	1.03108	+	0.747600i
$771$	8.53414			0.307350
$772$		−	0.301996i		−	0.0108691i
$773$			24.4364i			0.878915i	0.898263	+	0.439457i	$0.144829\pi$
$773$			24.4364i			0.878915i	−0.898263	+	0.439457i	$0.855171\pi$
$774$	−25.0673			−0.901026
$775$	−6.11936	−	18.7101i	−0.219814	−	0.672086i
$776$	14.4416			0.518422
$777$			7.18711i			0.257836i
$778$			5.16757i			0.185266i
$779$	−9.90139			−0.354754
$780$	−0.267235	−	0.193762i	−0.00956853	−	0.00693780i
$781$	36.7195			1.31393
$782$		−	48.5331i		−	1.73554i
$783$		−	27.0366i		−	0.966210i
$784$	9.93770			0.354918
$785$	19.2344	−	26.5279i	0.686507	−	0.946822i
$786$	−9.44404			−0.336858
$787$		−	8.26001i		−	0.294437i	−0.989104	−	0.147219i	$-0.952968\pi$
$787$		−	8.26001i		−	0.294437i	0.989104	−	0.147219i	$-0.0470321\pi$
$788$		−	0.600670i		−	0.0213980i
$789$	19.7004			0.701352
$790$	22.3841	−	30.8718i	0.796389	−	1.09837i
$791$	−35.1518			−1.24985
$792$			31.4629i			1.11798i
$793$			2.30267i			0.0817703i
$794$	−20.7180			−0.735256
$795$	5.75432	+	4.17225i	0.204085	+	0.147974i
$796$	−8.63495			−0.306058
$797$		−	6.32888i		−	0.224180i	−0.993698	−	0.112090i	$-0.964245\pi$
$797$		−	6.32888i		−	0.224180i	0.993698	−	0.112090i	$-0.0357546\pi$
$798$		−	5.72686i		−	0.202729i
$799$	15.8092			0.559290
$800$	15.5353	−	5.08101i	0.549255	−	0.179641i
$801$	35.0859			1.23970
$802$			42.1082i			1.48689i
$803$			7.19562i			0.253928i
$804$	4.44720			0.156841
$805$	47.3858	+	34.3577i	1.67013	+	1.21095i
$806$	1.70159			0.0599359
$807$		−	4.55814i		−	0.160454i
$808$			33.0064i			1.16116i
$809$	−0.743242			−0.0261310			−0.0130655	−	0.999915i	$-0.504159\pi$
$809$	−0.743242			−0.0261310			−0.0130655	+	0.999915i	$0.504159\pi$
$810$	7.96937	−	10.9913i	0.280015	−	0.386194i
$811$	−35.0526			−1.23086			−0.615431	−	0.788191i	$-0.711018\pi$
$811$	−35.0526			−1.23086			−0.615431	+	0.788191i	$0.711018\pi$
$812$		−	14.4844i		−	0.508302i
$813$			16.4492i			0.576897i
$814$	15.2461			0.534375
$815$	−4.48957	+	6.19196i	−0.157263	+	0.216895i
$816$	8.55407			0.299452
$817$			17.9885i			0.629338i
$818$			23.9583i			0.837681i
$819$	−3.09772			−0.108243
$820$	4.97864	+	3.60983i	0.173862	+	0.126061i
$821$	−29.8090			−1.04034			−0.520171	−	0.854062i	$-0.674132\pi$
$821$	−29.8090			−1.04034			−0.520171	+	0.854062i	$0.674132\pi$
$822$		−	14.6116i		−	0.509638i
$823$		−	20.0698i		−	0.699591i	−0.936826	−	0.349795i	$-0.886251\pi$
$823$		−	20.0698i		−	0.699591i	0.936826	−	0.349795i	$-0.113749\pi$
$824$	16.2177			0.564969
$825$	−12.8328	+	4.19712i	−0.446780	+	0.146125i
$826$	−22.7726			−0.792360
$827$		−	18.9685i		−	0.659598i	−0.944051	−	0.329799i	$-0.893019\pi$
$827$		−	18.9685i		−	0.659598i	0.944051	−	0.329799i	$-0.106981\pi$
$828$			12.0353i			0.418257i
$829$	−20.7884			−0.722011			−0.361005	−	0.932564i	$-0.617566\pi$
$829$	−20.7884			−0.722011			−0.361005	+	0.932564i	$0.617566\pi$
$830$	5.48460	+	3.97668i	0.190373	+	0.138033i
$831$	−1.10916			−0.0384764
$832$			3.19425i			0.110741i
$833$			21.2645i			0.736772i
$834$	9.20412			0.318712
$835$	0.347996	−	0.479952i	0.0120429	−	0.0166094i
$836$	5.21479			0.180357
$837$			14.6914i			0.507807i
$838$		−	14.8670i		−	0.513573i
$839$	−52.9766			−1.82896			−0.914478	−	0.404636i	$-0.867398\pi$
$839$	−52.9766			−1.82896			−0.914478	+	0.404636i	$0.867398\pi$
$840$	−9.03975	+	12.4675i	−0.311901	+	0.430170i
$841$	23.4962			0.810215
$842$			29.1243i			1.00369i
$843$			10.2781i			0.353996i
$844$	−3.24474			−0.111689
$845$	23.2921	+	16.8883i	0.801273	+	0.580974i
$846$	9.13303			0.314000
$847$		−	17.0273i		−	0.585064i
$848$		−	11.5204i		−	0.395611i
$849$	−9.61040			−0.329828
$850$	−9.59114	−	29.3251i	−0.328974	−	1.00584i
$851$	25.2504			0.865572
$852$			3.69564i			0.126610i
$853$			23.3978i			0.801126i	0.916269	+	0.400563i	$0.131185\pi$
$853$			23.3978i			0.801126i	−0.916269	+	0.400563i	$0.868815\pi$
$854$	24.8125			0.849067
$855$	−9.97331	−	7.23129i	−0.341080	−	0.247305i
$856$	−13.7202			−0.468946
$857$		−	24.1325i		−	0.824349i	−0.911105	−	0.412175i	$-0.864769\pi$
$857$		−	24.1325i		−	0.824349i	0.911105	−	0.412175i	$-0.135231\pi$
$858$		−	1.16708i		−	0.0398434i
$859$	−4.08951			−0.139532			−0.0697661	−	0.997563i	$-0.522225\pi$
$859$	−4.08951			−0.139532			−0.0697661	+	0.997563i	$0.522225\pi$
$860$	6.55822	−	9.04502i	0.223633	−	0.308433i
$861$	−10.2498			−0.349311
$862$		−	30.5842i		−	1.04170i
$863$			44.4527i			1.51319i	0.653885	+	0.756594i	$0.273138\pi$
$863$			44.4527i			1.51319i	−0.653885	+	0.756594i	$0.726862\pi$
$864$	−12.1985			−0.415001
$865$	14.9077	−	20.5605i	0.506876	−	0.699077i
$866$	17.1895			0.584122
$867$			6.86887i			0.233279i
$868$			7.87062i			0.267146i
$869$	−57.8743			−1.96325
$870$	−10.4366	−	7.56721i	−0.353834	−	0.256552i
$871$	4.02147			0.136262
$872$			31.5062i			1.06694i
$873$			11.9589i			0.404747i
$874$	−20.1201			−0.680572
$875$	35.4217	+	11.3955i	1.19747	+	0.385239i
$876$	−0.724203			−0.0244686
$877$			14.4263i			0.487142i	0.969883	+	0.243571i	$0.0783189\pi$
$877$			14.4263i			0.487142i	−0.969883	+	0.243571i	$0.921681\pi$
$878$			17.4201i			0.587900i
$879$	6.60418			0.222753
$880$	17.7169	+	12.8459i	0.597235	+	0.433034i
$881$	−15.8712			−0.534715			−0.267357	−	0.963597i	$-0.586150\pi$
$881$	−15.8712			−0.534715			−0.267357	+	0.963597i	$0.586150\pi$
$882$			12.2846i			0.413643i
$883$			4.89293i			0.164660i	0.996605	+	0.0823301i	$0.0262362\pi$
$883$			4.89293i			0.164660i	−0.996605	+	0.0823301i	$0.973764\pi$
$884$	−1.14481			−0.0385043
$885$	5.10698	−	7.04349i	0.171669	−	0.236764i
$886$	−19.9833			−0.671352
$887$		−	26.0584i		−	0.874955i	−0.899229	−	0.437477i	$-0.855872\pi$
$887$		−	26.0584i		−	0.874955i	0.899229	−	0.437477i	$-0.144128\pi$
$888$			6.64355i			0.222943i
$889$	44.9680			1.50818
$890$	21.3843	−	29.4930i	0.716803	−	0.988606i
$891$	−20.6049			−0.690290
$892$			9.71929i			0.325426i
$893$		−	6.55394i		−	0.219319i
$894$	−12.9886			−0.434402
$895$	19.2211	+	13.9366i	0.642492	+	0.465848i
$896$	12.6603			0.422951
$897$		−	1.93290i		−	0.0645376i
$898$			47.5957i			1.58829i
$899$	−28.5258			−0.951388
$900$	2.37843	+	7.27211i	0.0792811	+	0.242404i
$901$	24.6511			0.821247
$902$			21.7429i			0.723960i
$903$			18.6214i			0.619682i
$904$	−32.4932			−1.08071
$905$	33.7248	+	24.4526i	1.12105	+	0.812833i
$906$	12.4229			0.412723
$907$		−	57.2778i		−	1.90188i	−0.309376	−	0.950940i	$-0.600120\pi$
$907$		−	57.2778i		−	1.90188i	0.309376	−	0.950940i	$-0.399880\pi$
$908$			4.42914i			0.146986i
$909$	−27.3322			−0.906551
$910$	−1.88801	+	2.60393i	−0.0625870	+	0.0863193i
$911$	−29.9179			−0.991225			−0.495613	−	0.868544i	$-0.665056\pi$
$911$	−29.9179			−0.991225			−0.495613	+	0.868544i	$0.665056\pi$
$912$		−	3.54621i		−	0.117427i
$913$		−	10.2818i		−	0.340277i
$914$	28.3109			0.936441
$915$	−5.56446	+	7.67444i	−0.183955	+	0.253709i
$916$	11.9445			0.394657
$917$		−	39.5012i		−	1.30444i
$918$			23.0264i			0.759985i
$919$	41.7005			1.37557			0.687786	−	0.725913i	$-0.258583\pi$
$919$	41.7005			1.37557			0.687786	+	0.725913i	$0.258583\pi$
$920$	43.8020	+	31.7592i	1.44411	+	1.04707i
$921$	12.4105			0.408940
$922$			43.1703i			1.42174i
$923$			3.34185i			0.109998i
$924$	5.39826			0.177590
$925$	15.2570	−	4.98999i	0.501647	−	0.164070i
$926$	−27.0333			−0.888371
$927$			13.4297i			0.441088i
$928$		−	23.6854i		−	0.777512i
$929$	28.6930			0.941387			0.470694	−	0.882297i	$-0.344004\pi$
$929$	28.6930			0.941387			0.470694	+	0.882297i	$0.344004\pi$
$930$	5.67112	+	4.11192i	0.185963	+	0.134835i
$931$	8.81551			0.288917
$932$			6.68746i			0.219055i
$933$		−	23.3168i		−	0.763359i
$934$	−32.0513			−1.04875
$935$	−27.4874	+	37.9103i	−0.898933	+	1.23980i
$936$	−2.86344			−0.0935945
$937$		−	38.1640i		−	1.24676i	−0.781917	−	0.623382i	$-0.785758\pi$
$937$		−	38.1640i		−	1.24676i	0.781917	−	0.623382i	$-0.214242\pi$
$938$		−	43.3334i		−	1.41489i
$939$	8.33787			0.272096
$940$	−2.38942	+	3.29547i	−0.0779344	+	0.107486i
$941$	−51.7782			−1.68792			−0.843961	−	0.536404i	$-0.819782\pi$
$941$	−51.7782			−1.68792			−0.843961	+	0.536404i	$0.819782\pi$
$942$			11.6601i			0.379907i
$943$			36.0103i			1.17266i
$944$	−14.1013			−0.458960
$945$	−22.4820	−	16.3009i	−0.731341	−	0.530269i
$946$	39.5018			1.28431
$947$			1.35453i			0.0440164i	0.999758	+	0.0220082i	$0.00700599\pi$
$947$			1.35453i			0.0440164i	−0.999758	+	0.0220082i	$0.992994\pi$
$948$		−	5.82476i		−	0.189179i
$949$	−0.654875			−0.0212581
$950$	−12.1571	+	3.97614i	−0.394430	+	0.129003i
$951$	14.9082			0.483431
$952$			53.4100i			1.73103i
$953$			23.2905i			0.754452i	0.926121	+	0.377226i	$0.123122\pi$
$953$			23.2905i			0.754452i	−0.926121	+	0.377226i	$0.876878\pi$
$954$	14.2410			0.461069
$955$	10.4672	+	7.58941i	0.338711	+	0.245587i
$956$	3.55777			0.115066
$957$			19.5651i			0.632450i
$958$		−	11.6381i		−	0.376011i
$959$	61.1152			1.97351
$960$	−7.71896	+	10.6459i	−0.249129	+	0.343595i
$961$	−15.4995			−0.499982
$962$			1.38755i			0.0447364i
$963$		−	11.3615i		−	0.366120i
$964$	6.82754			0.219900
$965$	0.659917	−	0.910151i	0.0212435	−	0.0292988i
$966$	−20.8280			−0.670130
$967$		−	6.69207i		−	0.215203i	−0.994194	−	0.107601i	$-0.965683\pi$
$967$		−	6.69207i		−	0.215203i	0.994194	−	0.107601i	$-0.0343170\pi$
$968$		−	15.7395i		−	0.505887i
$969$	7.58813			0.243766
$970$	10.0526	+	7.28876i	0.322769	+	0.234028i
$971$	−41.7616			−1.34019			−0.670097	−	0.742274i	$-0.733748\pi$
$971$	−41.7616			−1.34019			−0.670097	+	0.742274i	$0.733748\pi$
$972$		−	8.79806i		−	0.282198i
$973$			38.4976i			1.23418i
$974$	25.7052			0.823649
$975$	−0.381980	−	1.16791i	−0.0122332	−	0.0374032i
$976$	15.3645			0.491806
$977$			18.8391i			0.602715i	0.953511	+	0.301357i	$0.0974397\pi$
$977$			18.8391i			0.602715i	−0.953511	+	0.301357i	$0.902560\pi$
$978$		−	2.72162i		−	0.0870278i
$979$	−55.2893			−1.76705
$980$	−4.43264	−	3.21395i	−0.141595	−	0.102666i
$981$	−26.0899			−0.832987
$982$		−	11.7355i		−	0.374494i
$983$		−	41.7654i		−	1.33211i	−0.745903	−	0.666055i	$-0.767982\pi$
$983$		−	41.7654i		−	1.33211i	0.745903	−	0.666055i	$-0.232018\pi$
$984$	−9.47457			−0.302038
$985$	1.31258	−	1.81029i	0.0418221	−	0.0576806i
$986$	−44.7097			−1.42385
$987$		−	6.78453i		−	0.215954i
$988$			0.474599i			0.0150990i
$989$	65.4223			2.08031
$990$	−15.8795	+	21.9008i	−0.504684	+	0.696055i
$991$	−31.3931			−0.997235			−0.498617	−	0.866822i	$-0.666159\pi$
$991$	−31.3931			−0.997235			−0.498617	+	0.866822i	$0.666159\pi$
$992$			12.8704i			0.408634i
$993$			18.4395i			0.585160i
$994$	36.0102			1.14217
$995$	−26.0239	−	18.8690i	−0.825012	−	0.598187i
$996$	1.03481			0.0327892
$997$		−	12.4169i		−	0.393247i	−0.980479	−	0.196623i	$-0.937002\pi$
$997$		−	12.4169i		−	0.393247i	0.980479	−	0.196623i	$-0.0629976\pi$
$998$			6.39586i			0.202457i
$999$	−11.9800			−0.379029

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	985.2.b.a.789.33	✓	98
5.2	odd	4		4925.2.a.r.1.34		49
5.3	odd	4		4925.2.a.s.1.16		49
5.4	even	2	inner	985.2.b.a.789.66	yes	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
985.2.b.a.789.33	✓	98	1.1	even	1	trivial
985.2.b.a.789.66	yes	98	5.4	even	2	inner
4925.2.a.r.1.34		49	5.2	odd	4
4925.2.a.s.1.16		49	5.3	odd	4

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:	\( N \)	\(=\)	\( 985 = 5 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	985.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.18293i q^{2} -0.672647i q^{3} +0.600670 q^{4} +(1.81029 + 1.31258i) q^{5} -0.795696 q^{6} -3.32812i q^{7} -3.07642i q^{8} +2.54755 q^{9} +(1.55269 - 2.14145i) q^{10} -4.01450 q^{11} -0.404039i q^{12} -0.365360i q^{13} -3.93695 q^{14} +(0.882900 - 1.21769i) q^{15} -2.43785 q^{16} -5.21648i q^{17} -3.01358i q^{18} -2.16257 q^{19} +(1.08739 + 0.788425i) q^{20} -2.23865 q^{21} +4.74888i q^{22} +7.86503i q^{23} -2.06934 q^{24} +(1.55429 + 4.75228i) q^{25} -0.432196 q^{26} -3.73154i q^{27} -1.99911i q^{28} +7.24543 q^{29} +(-1.44044 - 1.04441i) q^{30} -3.93707 q^{31} -3.26902i q^{32} +2.70034i q^{33} -6.17075 q^{34} +(4.36841 - 6.02487i) q^{35} +1.53023 q^{36} -3.21046i q^{37} +2.55817i q^{38} -0.245758 q^{39} +(4.03803 - 5.56921i) q^{40} +4.57854 q^{41} +2.64818i q^{42} -8.31813i q^{43} -2.41139 q^{44} +(4.61179 + 3.34385i) q^{45} +9.30380 q^{46} +3.03063i q^{47} +1.63982i q^{48} -4.07641 q^{49} +(5.62163 - 1.83862i) q^{50} -3.50885 q^{51} -0.219461i q^{52} +4.72562i q^{53} -4.41416 q^{54} +(-7.26740 - 5.26933i) q^{55} -10.2387 q^{56} +1.45464i q^{57} -8.57085i q^{58} +5.78433 q^{59} +(0.530332 - 0.731428i) q^{60} -6.30248 q^{61} +4.65729i q^{62} -8.47855i q^{63} -8.74274 q^{64} +(0.479563 - 0.661407i) q^{65} +3.19432 q^{66} +11.0069i q^{67} -3.13339i q^{68} +5.29039 q^{69} +(-7.12701 - 5.16754i) q^{70} -9.14673 q^{71} -7.83731i q^{72} -1.79241i q^{73} -3.79776 q^{74} +(3.19661 - 1.04549i) q^{75} -1.29899 q^{76} +13.3607i q^{77} +0.290716i q^{78} +14.4163 q^{79} +(-4.41322 - 3.19987i) q^{80} +5.13263 q^{81} -5.41610i q^{82} +2.56116i q^{83} -1.34469 q^{84} +(6.84703 - 9.44334i) q^{85} -9.83978 q^{86} -4.87362i q^{87} +12.3503i q^{88} +13.7724 q^{89} +(3.95554 - 5.45544i) q^{90} -1.21596 q^{91} +4.72429i q^{92} +2.64826i q^{93} +3.58503 q^{94} +(-3.91487 - 2.83853i) q^{95} -2.19890 q^{96} +4.69428i q^{97} +4.82212i q^{98} -10.2271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 98 q^{4} - 2 q^{5} + 4 q^{6} - 102 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{14} - 2 q^{15} + 98 q^{16} - 8 q^{19} - 2 q^{20} + 20 q^{21} + 10 q^{25} - 4 q^{26} - 12 q^{29} - 10 q^{30} - 4 q^{31} + 24 q^{34}+ \cdots - 44 q^{99}+O(q^{100}) \) 98 * q - 98 * q^4 - 2 * q^5 + 4 * q^6 - 102 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^14 - 2 * q^15 + 98 * q^16 - 8 * q^19 - 2 * q^20 + 20 * q^21 + 10 * q^25 - 4 * q^26 - 12 * q^29 - 10 * q^30 - 4 * q^31 + 24 * q^34 + 4 * q^35 + 86 * q^36 + 12 * q^40 - 4 * q^41 + 16 * q^44 - 16 * q^45 - 44 * q^46 - 130 * q^49 + 28 * q^50 + 32 * q^51 - 84 * q^54 + 14 * q^55 - 44 * q^56 - 16 * q^59 + 38 * q^60 + 32 * q^61 - 110 * q^64 + 30 * q^65 + 84 * q^66 + 12 * q^69 + 38 * q^70 + 48 * q^74 + 38 * q^75 - 8 * q^76 - 20 * q^79 - 4 * q^80 + 82 * q^81 - 84 * q^84 - 40 * q^85 - 56 * q^86 - 8 * q^89 + 30 * q^90 + 16 * q^94 + 18 * q^95 - 68 * q^96 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more