Properties

Label 820.2.bv.c.207.21
Level $820$
Weight $2$
Character 820.207
Analytic conductor $6.548$
Analytic rank $0$
Dimension $960$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [820,2,Mod(103,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 7])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.103"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 820.bv (of order \(20\), degree \(8\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [960,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.54773296574\)
Analytic rank: \(0\)
Dimension: \(960\)
Relative dimension: \(120\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 207.21
Character \(\chi\) \(=\) 820.207
Dual form 820.2.bv.c.103.21

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.20856 - 0.734432i) q^{2} -3.28938 q^{3} +(0.921218 + 1.77521i) q^{4} +(-0.479772 + 2.18399i) q^{5} +(3.97540 + 2.41583i) q^{6} +(1.14493 + 0.372010i) q^{7} +(0.190425 - 2.82201i) q^{8} +7.82003 q^{9} +(2.18383 - 2.28712i) q^{10} +(-0.512928 - 3.23850i) q^{11} +(-3.03024 - 5.83933i) q^{12} +(-2.12858 + 0.691618i) q^{13} +(-1.11050 - 1.29047i) q^{14} +(1.57815 - 7.18398i) q^{15} +(-2.30272 + 3.27070i) q^{16} +(0.391645 - 0.539053i) q^{17} +(-9.45094 - 5.74328i) q^{18} +(-3.18160 + 1.62111i) q^{19} +(-4.31901 + 1.16024i) q^{20} +(-3.76611 - 1.22368i) q^{21} +(-1.75856 + 4.29062i) q^{22} +(1.59211 - 3.12469i) q^{23} +(-0.626381 + 9.28266i) q^{24} +(-4.53964 - 2.09563i) q^{25} +(3.08046 + 0.727440i) q^{26} -15.8549 q^{27} +(0.394335 + 2.37519i) q^{28} +(10.1164 + 1.60228i) q^{29} +(-7.18343 + 7.52320i) q^{30} +(1.82004 - 2.50507i) q^{31} +(5.18507 - 2.26164i) q^{32} +(1.68722 + 10.6527i) q^{33} +(-0.869223 + 0.363839i) q^{34} +(-1.36177 + 2.32204i) q^{35} +(7.20395 + 13.8822i) q^{36} +(-5.35660 - 0.848402i) q^{37} +(5.03574 + 0.377472i) q^{38} +(7.00171 - 2.27500i) q^{39} +(6.07188 + 1.76981i) q^{40} +(6.33814 - 0.909921i) q^{41} +(3.65284 + 4.24484i) q^{42} +(0.819384 + 0.417497i) q^{43} +(5.27649 - 3.89392i) q^{44} +(-3.75183 + 17.0789i) q^{45} +(-4.21902 + 2.60706i) q^{46} +(-1.76309 - 5.42624i) q^{47} +(7.57451 - 10.7586i) q^{48} +(-4.49065 - 3.26265i) q^{49} +(3.94731 + 5.86675i) q^{50} +(-1.28827 + 1.77315i) q^{51} +(-3.18865 - 3.14154i) q^{52} +(1.83504 + 2.52572i) q^{53} +(19.1615 + 11.6444i) q^{54} +(7.31895 + 0.433510i) q^{55} +(1.26784 - 3.16016i) q^{56} +(10.4655 - 5.33244i) q^{57} +(-11.0495 - 9.36625i) q^{58} +(3.94585 + 12.1441i) q^{59} +(14.2069 - 3.81647i) q^{60} +(0.620962 + 0.201763i) q^{61} +(-4.03942 + 1.69082i) q^{62} +(8.95338 + 2.90913i) q^{63} +(-7.92748 - 1.07476i) q^{64} +(-0.489255 - 4.98062i) q^{65} +(5.78457 - 14.1135i) q^{66} +(9.04522 - 6.57174i) q^{67} +(1.31772 + 0.198665i) q^{68} +(-5.23705 + 10.2783i) q^{69} +(3.35116 - 1.80618i) q^{70} +(0.734882 + 4.63986i) q^{71} +(1.48913 - 22.0682i) q^{72} +(2.04839 + 2.04839i) q^{73} +(5.85066 + 4.95941i) q^{74} +(14.9326 + 6.89334i) q^{75} +(-5.80875 - 4.15461i) q^{76} +(0.617489 - 3.89867i) q^{77} +(-10.1328 - 2.39283i) q^{78} +(-3.29665 + 3.29665i) q^{79} +(-6.03841 - 6.59830i) q^{80} +28.6927 q^{81} +(-8.32828 - 3.55525i) q^{82} +(7.50211 + 7.50211i) q^{83} +(-1.29712 - 7.81290i) q^{84} +(0.989387 + 1.11397i) q^{85} +(-0.683649 - 1.10635i) q^{86} +(-33.2767 - 5.27051i) q^{87} +(-9.23676 + 0.830796i) q^{88} +(0.0119906 - 0.00610950i) q^{89} +(17.0776 - 17.8853i) q^{90} -2.69436 q^{91} +(7.01364 - 0.0521983i) q^{92} +(-5.98679 + 8.24012i) q^{93} +(-1.85441 + 7.85279i) q^{94} +(-2.01404 - 7.72635i) q^{95} +(-17.0557 + 7.43940i) q^{96} +(9.55353 + 13.1493i) q^{97} +(3.03101 + 7.24117i) q^{98} +(-4.01111 - 25.3252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/820\mathbb{Z}\right)^\times\).

\(n\) \(411\) \(621\) \(657\)
\(\chi(n)\) \(-1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{4}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20856 0.734432i −0.854579 0.519322i
\(3\) −3.28938 −1.89912 −0.949562 0.313578i \(-0.898472\pi\)
−0.949562 + 0.313578i \(0.898472\pi\)
\(4\) 0.921218 + 1.77521i 0.460609 + 0.887603i
\(5\) −0.479772 + 2.18399i −0.214560 + 0.976711i
\(6\) 3.97540 + 2.41583i 1.62295 + 0.986258i
\(7\) 1.14493 + 0.372010i 0.432743 + 0.140607i 0.517285 0.855813i \(-0.326943\pi\)
−0.0845422 + 0.996420i \(0.526943\pi\)
\(8\) 0.190425 2.82201i 0.0673255 0.997731i
\(9\) 7.82003 2.60668
\(10\) 2.18383 2.28712i 0.690586 0.723250i
\(11\) −0.512928 3.23850i −0.154654 0.976445i −0.935911 0.352236i \(-0.885421\pi\)
0.781257 0.624209i \(-0.214579\pi\)
\(12\) −3.03024 5.83933i −0.874754 1.68567i
\(13\) −2.12858 + 0.691618i −0.590362 + 0.191820i −0.588937 0.808179i \(-0.700454\pi\)
−0.00142488 + 0.999999i \(0.500454\pi\)
\(14\) −1.11050 1.29047i −0.296792 0.344892i
\(15\) 1.57815 7.18398i 0.407477 1.85490i
\(16\) −2.30272 + 3.27070i −0.575679 + 0.817676i
\(17\) 0.391645 0.539053i 0.0949879 0.130740i −0.758878 0.651233i \(-0.774252\pi\)
0.853866 + 0.520494i \(0.174252\pi\)
\(18\) −9.45094 5.74328i −2.22761 1.35370i
\(19\) −3.18160 + 1.62111i −0.729909 + 0.371907i −0.779115 0.626881i \(-0.784331\pi\)
0.0492055 + 0.998789i \(0.484331\pi\)
\(20\) −4.31901 + 1.16024i −0.965760 + 0.259437i
\(21\) −3.76611 1.22368i −0.821832 0.267029i
\(22\) −1.75856 + 4.29062i −0.374926 + 0.914764i
\(23\) 1.59211 3.12469i 0.331977 0.651542i −0.663328 0.748329i \(-0.730857\pi\)
0.995305 + 0.0967869i \(0.0308565\pi\)
\(24\) −0.626381 + 9.28266i −0.127859 + 1.89482i
\(25\) −4.53964 2.09563i −0.907928 0.419127i
\(26\) 3.08046 + 0.727440i 0.604128 + 0.142663i
\(27\) −15.8549 −3.05128
\(28\) 0.394335 + 2.37519i 0.0745223 + 0.448868i
\(29\) 10.1164 + 1.60228i 1.87857 + 0.297536i 0.987656 0.156641i \(-0.0500664\pi\)
0.890912 + 0.454176i \(0.150066\pi\)
\(30\) −7.18343 + 7.52320i −1.31151 + 1.37354i
\(31\) 1.82004 2.50507i 0.326888 0.449923i −0.613666 0.789565i \(-0.710306\pi\)
0.940555 + 0.339642i \(0.110306\pi\)
\(32\) 5.18507 2.26164i 0.916600 0.399806i
\(33\) 1.68722 + 10.6527i 0.293707 + 1.85439i
\(34\) −0.869223 + 0.363839i −0.149071 + 0.0623979i
\(35\) −1.36177 + 2.32204i −0.230181 + 0.392496i
\(36\) 7.20395 + 13.8822i 1.20066 + 2.31369i
\(37\) −5.35660 0.848402i −0.880620 0.139477i −0.300280 0.953851i \(-0.597080\pi\)
−0.580340 + 0.814374i \(0.697080\pi\)
\(38\) 5.03574 + 0.377472i 0.816905 + 0.0612340i
\(39\) 7.00171 2.27500i 1.12117 0.364291i
\(40\) 6.07188 + 1.76981i 0.960049 + 0.279831i
\(41\) 6.33814 0.909921i 0.989851 0.142106i
\(42\) 3.65284 + 4.24484i 0.563646 + 0.654993i
\(43\) 0.819384 + 0.417497i 0.124955 + 0.0636677i 0.515350 0.856980i \(-0.327662\pi\)
−0.390396 + 0.920647i \(0.627662\pi\)
\(44\) 5.27649 3.89392i 0.795461 0.587031i
\(45\) −3.75183 + 17.0789i −0.559289 + 2.54597i
\(46\) −4.21902 + 2.60706i −0.622061 + 0.384391i
\(47\) −1.76309 5.42624i −0.257173 0.791498i −0.993394 0.114756i \(-0.963391\pi\)
0.736220 0.676742i \(-0.236609\pi\)
\(48\) 7.57451 10.7586i 1.09329 1.55287i
\(49\) −4.49065 3.26265i −0.641521 0.466092i
\(50\) 3.94731 + 5.86675i 0.558234 + 0.829684i
\(51\) −1.28827 + 1.77315i −0.180394 + 0.248291i
\(52\) −3.18865 3.14154i −0.442187 0.435653i
\(53\) 1.83504 + 2.52572i 0.252062 + 0.346934i 0.916232 0.400648i \(-0.131215\pi\)
−0.664170 + 0.747582i \(0.731215\pi\)
\(54\) 19.1615 + 11.6444i 2.60756 + 1.58460i
\(55\) 7.31895 + 0.433510i 0.986887 + 0.0584545i
\(56\) 1.26784 3.16016i 0.169422 0.422294i
\(57\) 10.4655 5.33244i 1.38619 0.706299i
\(58\) −11.0495 9.36625i −1.45087 1.22985i
\(59\) 3.94585 + 12.1441i 0.513705 + 1.58102i 0.785625 + 0.618703i \(0.212341\pi\)
−0.271920 + 0.962320i \(0.587659\pi\)
\(60\) 14.2069 3.81647i 1.83410 0.492704i
\(61\) 0.620962 + 0.201763i 0.0795060 + 0.0258331i 0.348500 0.937309i \(-0.386691\pi\)
−0.268994 + 0.963142i \(0.586691\pi\)
\(62\) −4.03942 + 1.69082i −0.513007 + 0.214734i
\(63\) 8.95338 + 2.90913i 1.12802 + 0.366516i
\(64\) −7.92748 1.07476i −0.990935 0.134345i
\(65\) −0.489255 4.98062i −0.0606846 0.617770i
\(66\) 5.78457 14.1135i 0.712031 1.73725i
\(67\) 9.04522 6.57174i 1.10505 0.802866i 0.123173 0.992385i \(-0.460693\pi\)
0.981877 + 0.189520i \(0.0606931\pi\)
\(68\) 1.31772 + 0.198665i 0.159797 + 0.0240917i
\(69\) −5.23705 + 10.2783i −0.630466 + 1.23736i
\(70\) 3.35116 1.80618i 0.400540 0.215880i
\(71\) 0.734882 + 4.63986i 0.0872144 + 0.550650i 0.992145 + 0.125091i \(0.0399224\pi\)
−0.904931 + 0.425559i \(0.860078\pi\)
\(72\) 1.48913 22.0682i 0.175496 2.60076i
\(73\) 2.04839 + 2.04839i 0.239746 + 0.239746i 0.816745 0.576999i \(-0.195776\pi\)
−0.576999 + 0.816745i \(0.695776\pi\)
\(74\) 5.85066 + 4.95941i 0.680126 + 0.576519i
\(75\) 14.9326 + 6.89334i 1.72427 + 0.795974i
\(76\) −5.80875 4.15461i −0.666309 0.476566i
\(77\) 0.617489 3.89867i 0.0703694 0.444295i
\(78\) −10.1328 2.39283i −1.14731 0.270934i
\(79\) −3.29665 + 3.29665i −0.370902 + 0.370902i −0.867806 0.496903i \(-0.834470\pi\)
0.496903 + 0.867806i \(0.334470\pi\)
\(80\) −6.03841 6.59830i −0.675115 0.737712i
\(81\) 28.6927 3.18808
\(82\) −8.32828 3.55525i −0.919705 0.392611i
\(83\) 7.50211 + 7.50211i 0.823464 + 0.823464i 0.986603 0.163139i \(-0.0521619\pi\)
−0.163139 + 0.986603i \(0.552162\pi\)
\(84\) −1.29712 7.81290i −0.141527 0.852457i
\(85\) 0.989387 + 1.11397i 0.107314 + 0.120827i
\(86\) −0.683649 1.10635i −0.0737197 0.119301i
\(87\) −33.2767 5.27051i −3.56763 0.565058i
\(88\) −9.23676 + 0.830796i −0.984642 + 0.0885632i
\(89\) 0.0119906 0.00610950i 0.00127100 0.000647605i −0.453355 0.891330i \(-0.649773\pi\)
0.454626 + 0.890682i \(0.349773\pi\)
\(90\) 17.0776 17.8853i 1.80013 1.88528i
\(91\) −2.69436 −0.282446
\(92\) 7.01364 0.0521983i 0.731222 0.00544205i
\(93\) −5.98679 + 8.24012i −0.620802 + 0.854460i
\(94\) −1.85441 + 7.85279i −0.191268 + 0.809953i
\(95\) −2.01404 7.72635i −0.206636 0.792707i
\(96\) −17.0557 + 7.43940i −1.74074 + 0.759281i
\(97\) 9.55353 + 13.1493i 0.970014 + 1.33511i 0.942040 + 0.335502i \(0.108906\pi\)
0.0279747 + 0.999609i \(0.491094\pi\)
\(98\) 3.03101 + 7.24117i 0.306178 + 0.731469i
\(99\) −4.01111 25.3252i −0.403132 2.54528i
\(100\) −0.461813 9.98933i −0.0461813 0.998933i
\(101\) −3.00023 + 1.52870i −0.298534 + 0.152111i −0.596842 0.802359i \(-0.703578\pi\)
0.298307 + 0.954470i \(0.403578\pi\)
\(102\) 2.85921 1.19681i 0.283104 0.118501i
\(103\) 7.90780 + 15.5199i 0.779178 + 1.52922i 0.847040 + 0.531529i \(0.178382\pi\)
−0.0678617 + 0.997695i \(0.521618\pi\)
\(104\) 1.54642 + 6.13858i 0.151639 + 0.601937i
\(105\) 4.47938 7.63806i 0.437143 0.745398i
\(106\) −0.362782 4.40019i −0.0352365 0.427384i
\(107\) 6.51491 + 12.7862i 0.629821 + 1.23609i 0.956714 + 0.291031i \(0.0939983\pi\)
−0.326893 + 0.945061i \(0.606002\pi\)
\(108\) −14.6058 28.1457i −1.40545 2.70832i
\(109\) 1.30643 1.30643i 0.125133 0.125133i −0.641767 0.766900i \(-0.721798\pi\)
0.766900 + 0.641767i \(0.221798\pi\)
\(110\) −8.52698 5.89920i −0.813016 0.562466i
\(111\) 17.6199 + 2.79072i 1.67241 + 0.264883i
\(112\) −3.85318 + 2.88809i −0.364091 + 0.272899i
\(113\) 13.1496 2.08269i 1.23701 0.195923i 0.496541 0.868013i \(-0.334603\pi\)
0.740470 + 0.672090i \(0.234603\pi\)
\(114\) −16.5645 1.24165i −1.55140 0.116291i
\(115\) 6.06044 + 4.97628i 0.565139 + 0.464041i
\(116\) 6.47503 + 19.4347i 0.601191 + 1.80447i
\(117\) −16.6456 + 5.40847i −1.53888 + 0.500013i
\(118\) 4.15022 17.5747i 0.382058 1.61789i
\(119\) 0.648939 0.471482i 0.0594881 0.0432207i
\(120\) −19.9727 5.82157i −1.82325 0.531434i
\(121\) 0.236821 0.0769480i 0.0215292 0.00699527i
\(122\) −0.602286 0.699896i −0.0545284 0.0633656i
\(123\) −20.8486 + 2.99308i −1.87985 + 0.269877i
\(124\) 6.12366 + 0.923230i 0.549921 + 0.0829085i
\(125\) 6.75484 8.90911i 0.604171 0.796855i
\(126\) −8.68410 10.0915i −0.773641 0.899022i
\(127\) −2.93916 + 18.5571i −0.260808 + 1.64668i 0.415160 + 0.909749i \(0.363726\pi\)
−0.675968 + 0.736931i \(0.736274\pi\)
\(128\) 8.79146 + 7.12111i 0.777063 + 0.629423i
\(129\) −2.69527 1.37331i −0.237305 0.120913i
\(130\) −3.06664 + 6.37869i −0.268962 + 0.559448i
\(131\) −12.1521 8.82905i −1.06174 0.771397i −0.0873282 0.996180i \(-0.527833\pi\)
−0.974409 + 0.224782i \(0.927833\pi\)
\(132\) −17.3564 + 12.8086i −1.51068 + 1.11484i
\(133\) −4.24578 + 0.672465i −0.368155 + 0.0583101i
\(134\) −15.7582 + 1.29921i −1.36130 + 0.112235i
\(135\) 7.60673 34.6270i 0.654683 2.98021i
\(136\) −1.44663 1.20788i −0.124048 0.103574i
\(137\) 5.76817i 0.492808i 0.969167 + 0.246404i \(0.0792489\pi\)
−0.969167 + 0.246404i \(0.920751\pi\)
\(138\) 13.8780 8.57563i 1.18137 0.730006i
\(139\) −4.78897 + 14.7389i −0.406195 + 1.25014i 0.513698 + 0.857971i \(0.328275\pi\)
−0.919893 + 0.392169i \(0.871725\pi\)
\(140\) −5.37658 0.278324i −0.454404 0.0235227i
\(141\) 5.79948 + 17.8490i 0.488404 + 1.50315i
\(142\) 2.51952 6.14726i 0.211433 0.515866i
\(143\) 3.33162 + 6.53867i 0.278604 + 0.546791i
\(144\) −18.0073 + 25.5770i −1.50061 + 2.13142i
\(145\) −8.35292 + 21.3254i −0.693673 + 1.77098i
\(146\) −0.971192 3.98000i −0.0803765 0.329388i
\(147\) 14.7714 + 10.7321i 1.21833 + 0.885168i
\(148\) −3.42851 10.2906i −0.281822 0.845885i
\(149\) 1.71620 10.8356i 0.140596 0.887691i −0.812045 0.583595i \(-0.801646\pi\)
0.952641 0.304096i \(-0.0983543\pi\)
\(150\) −12.9842 19.2980i −1.06016 1.57567i
\(151\) 7.66317 15.0398i 0.623620 1.22392i −0.335797 0.941934i \(-0.609006\pi\)
0.959418 0.281989i \(-0.0909942\pi\)
\(152\) 3.96892 + 9.28721i 0.321922 + 0.753292i
\(153\) 3.06267 4.21541i 0.247603 0.340796i
\(154\) −3.60958 + 4.25826i −0.290868 + 0.343140i
\(155\) 4.59784 + 5.17681i 0.369307 + 0.415811i
\(156\) 10.4887 + 10.3337i 0.839767 + 0.827360i
\(157\) 5.52386 17.0007i 0.440852 1.35680i −0.446117 0.894975i \(-0.647193\pi\)
0.886969 0.461829i \(-0.152807\pi\)
\(158\) 6.40536 1.56302i 0.509583 0.124347i
\(159\) −6.03615 8.30805i −0.478698 0.658871i
\(160\) 2.45176 + 12.4092i 0.193828 + 0.981035i
\(161\) 2.98526 2.98526i 0.235272 0.235272i
\(162\) −34.6768 21.0729i −2.72446 1.65564i
\(163\) 8.22960 + 8.22960i 0.644592 + 0.644592i 0.951681 0.307089i \(-0.0993550\pi\)
−0.307089 + 0.951681i \(0.599355\pi\)
\(164\) 7.45411 + 10.4133i 0.582068 + 0.813140i
\(165\) −24.0748 1.42598i −1.87422 0.111012i
\(166\) −3.55693 14.5765i −0.276072 1.13136i
\(167\) 11.3541i 0.878609i 0.898338 + 0.439304i \(0.144775\pi\)
−0.898338 + 0.439304i \(0.855225\pi\)
\(168\) −4.17041 + 10.3950i −0.321754 + 0.801990i
\(169\) −6.46470 + 4.69688i −0.497284 + 0.361298i
\(170\) −0.377593 2.07294i −0.0289601 0.158987i
\(171\) −24.8802 + 12.6771i −1.90264 + 0.969442i
\(172\) 0.0136879 + 1.83918i 0.00104369 + 0.140236i
\(173\) 1.03076 + 1.03076i 0.0783670 + 0.0783670i 0.745204 0.666837i \(-0.232352\pi\)
−0.666837 + 0.745204i \(0.732352\pi\)
\(174\) 36.3459 + 30.8092i 2.75538 + 2.33564i
\(175\) −4.41797 4.08814i −0.333967 0.309035i
\(176\) 11.7733 + 5.77971i 0.887447 + 0.435662i
\(177\) −12.9794 39.9465i −0.975591 3.00256i
\(178\) −0.0189783 0.00142259i −0.00142248 0.000106627i
\(179\) −21.7885 3.45096i −1.62855 0.257937i −0.725737 0.687973i \(-0.758501\pi\)
−0.902812 + 0.430036i \(0.858501\pi\)
\(180\) −33.7748 + 9.07309i −2.51742 + 0.676269i
\(181\) −2.33600 14.7489i −0.173633 1.09628i −0.908445 0.418005i \(-0.862729\pi\)
0.734811 0.678271i \(-0.237271\pi\)
\(182\) 3.25629 + 1.97883i 0.241372 + 0.146681i
\(183\) −2.04258 0.663674i −0.150992 0.0490602i
\(184\) −8.51472 5.08796i −0.627713 0.375089i
\(185\) 4.42285 11.2917i 0.325174 0.830185i
\(186\) 13.2872 5.56175i 0.974264 0.407807i
\(187\) −1.94661 0.991848i −0.142350 0.0725311i
\(188\) 8.00850 8.12860i 0.584080 0.592839i
\(189\) −18.1527 5.89818i −1.32042 0.429030i
\(190\) −3.24040 + 10.8169i −0.235083 + 0.784741i
\(191\) 8.51456 8.51456i 0.616092 0.616092i −0.328435 0.944527i \(-0.606521\pi\)
0.944527 + 0.328435i \(0.106521\pi\)
\(192\) 26.0765 + 3.53531i 1.88191 + 0.255139i
\(193\) −13.5424 18.6395i −0.974803 1.34170i −0.939583 0.342321i \(-0.888787\pi\)
−0.0352197 0.999380i \(-0.511213\pi\)
\(194\) −1.88871 22.9081i −0.135601 1.64471i
\(195\) 1.60935 + 16.3832i 0.115248 + 1.17322i
\(196\) 1.65501 10.9774i 0.118215 0.784102i
\(197\) −10.9839 + 1.73968i −0.782572 + 0.123947i −0.534921 0.844902i \(-0.679659\pi\)
−0.247651 + 0.968849i \(0.579659\pi\)
\(198\) −13.7520 + 33.5528i −0.977310 + 2.38449i
\(199\) −0.871702 + 1.71081i −0.0617933 + 0.121276i −0.919837 0.392300i \(-0.871680\pi\)
0.858044 + 0.513576i \(0.171680\pi\)
\(200\) −6.77836 + 12.4118i −0.479303 + 0.877650i
\(201\) −29.7532 + 21.6169i −2.09863 + 1.52474i
\(202\) 4.74868 + 0.355954i 0.334116 + 0.0250448i
\(203\) 10.9865 + 5.59790i 0.771101 + 0.392895i
\(204\) −4.33449 0.653486i −0.303475 0.0457532i
\(205\) −1.05360 + 14.2790i −0.0735867 + 0.997289i
\(206\) 1.84132 24.5645i 0.128291 1.71149i
\(207\) 12.4503 24.4351i 0.865357 1.69836i
\(208\) 2.63944 8.55456i 0.183012 0.593152i
\(209\) 6.88189 + 9.47211i 0.476030 + 0.655200i
\(210\) −11.0232 + 5.94122i −0.760675 + 0.409983i
\(211\) 12.5686 + 6.40402i 0.865259 + 0.440871i 0.829512 0.558490i \(-0.188619\pi\)
0.0357471 + 0.999361i \(0.488619\pi\)
\(212\) −2.79320 + 5.58432i −0.191838 + 0.383532i
\(213\) −2.41731 15.2623i −0.165631 1.04575i
\(214\) 1.51699 20.2377i 0.103699 1.38342i
\(215\) −1.30493 + 1.58922i −0.0889953 + 0.108384i
\(216\) −3.01917 + 44.7427i −0.205429 + 3.04435i
\(217\) 3.01572 2.19105i 0.204721 0.148738i
\(218\) −2.53837 + 0.619409i −0.171920 + 0.0419516i
\(219\) −6.73794 6.73794i −0.455308 0.455308i
\(220\) 5.97278 + 13.3920i 0.402685 + 0.902889i
\(221\) −0.460829 + 1.41829i −0.0309987 + 0.0954043i
\(222\) −19.2451 16.3134i −1.29164 1.09488i
\(223\) −8.19188 + 16.0775i −0.548569 + 1.07663i 0.435724 + 0.900080i \(0.356492\pi\)
−0.984292 + 0.176546i \(0.943508\pi\)
\(224\) 6.77789 0.660521i 0.452867 0.0441329i
\(225\) −35.5001 16.3879i −2.36667 1.09253i
\(226\) −17.4216 7.14045i −1.15887 0.474975i
\(227\) 4.79454 14.7561i 0.318225 0.979396i −0.656181 0.754603i \(-0.727829\pi\)
0.974407 0.224793i \(-0.0721706\pi\)
\(228\) 19.1072 + 13.6661i 1.26540 + 0.905058i
\(229\) −13.0361 + 2.06472i −0.861450 + 0.136440i −0.571500 0.820602i \(-0.693638\pi\)
−0.289949 + 0.957042i \(0.593638\pi\)
\(230\) −3.66964 10.4651i −0.241969 0.690048i
\(231\) −2.03116 + 12.8242i −0.133640 + 0.843771i
\(232\) 6.44806 28.2435i 0.423336 1.85427i
\(233\) 13.2236 4.29660i 0.866305 0.281479i 0.158045 0.987432i \(-0.449481\pi\)
0.708259 + 0.705952i \(0.249481\pi\)
\(234\) 24.0893 + 5.68860i 1.57476 + 0.371875i
\(235\) 12.6967 1.24722i 0.828244 0.0813598i
\(236\) −17.9232 + 18.1920i −1.16670 + 1.18420i
\(237\) 10.8439 10.8439i 0.704390 0.704390i
\(238\) −1.13055 + 0.0932105i −0.0732827 + 0.00604194i
\(239\) 0.472376 + 0.927089i 0.0305554 + 0.0599684i 0.905780 0.423749i \(-0.139286\pi\)
−0.875224 + 0.483718i \(0.839286\pi\)
\(240\) 19.8626 + 21.7043i 1.28213 + 1.40101i
\(241\) 11.9281 + 16.4176i 0.768357 + 1.05755i 0.996473 + 0.0839189i \(0.0267437\pi\)
−0.228115 + 0.973634i \(0.573256\pi\)
\(242\) −0.342725 0.0809334i −0.0220312 0.00520260i
\(243\) −46.8166 −3.00329
\(244\) 0.213871 + 1.28820i 0.0136917 + 0.0824687i
\(245\) 9.28008 8.24221i 0.592882 0.526576i
\(246\) 27.3949 + 11.6946i 1.74663 + 0.745618i
\(247\) 5.65111 5.65111i 0.359572 0.359572i
\(248\) −6.72274 5.61319i −0.426894 0.356438i
\(249\) −24.6773 24.6773i −1.56386 1.56386i
\(250\) −14.7067 + 5.80619i −0.930136 + 0.367215i
\(251\) 23.1444 16.8154i 1.46086 1.06138i 0.477722 0.878511i \(-0.341463\pi\)
0.983138 0.182866i \(-0.0585373\pi\)
\(252\) 3.08371 + 18.5740i 0.194255 + 1.17005i
\(253\) −10.9359 3.55330i −0.687536 0.223394i
\(254\) 17.1811 20.2687i 1.07804 1.27177i
\(255\) −3.25447 3.66428i −0.203803 0.229466i
\(256\) −5.39501 15.0630i −0.337188 0.941437i
\(257\) 10.2376 + 7.43807i 0.638606 + 0.463974i 0.859371 0.511353i \(-0.170855\pi\)
−0.220765 + 0.975327i \(0.570855\pi\)
\(258\) 2.24878 + 3.63921i 0.140003 + 0.226567i
\(259\) −5.81732 2.96407i −0.361470 0.184178i
\(260\) 8.39092 5.45677i 0.520383 0.338414i
\(261\) 79.1105 + 12.5299i 4.89681 + 0.775579i
\(262\) 8.20221 + 19.5953i 0.506734 + 1.21060i
\(263\) 14.2643 19.6331i 0.879574 1.21063i −0.0969642 0.995288i \(-0.530913\pi\)
0.976539 0.215342i \(-0.0690868\pi\)
\(264\) 30.3832 2.73281i 1.86996 0.168193i
\(265\) −6.39655 + 2.79595i −0.392937 + 0.171754i
\(266\) 5.62514 + 2.30552i 0.344900 + 0.141361i
\(267\) −0.0394415 + 0.0200965i −0.00241378 + 0.00122988i
\(268\) 19.9988 + 10.0031i 1.22162 + 0.611039i
\(269\) −0.666358 + 0.216513i −0.0406285 + 0.0132010i −0.329261 0.944239i \(-0.606800\pi\)
0.288632 + 0.957440i \(0.406800\pi\)
\(270\) −34.6243 + 36.2620i −2.10717 + 2.20684i
\(271\) 12.1838 + 3.95877i 0.740116 + 0.240478i 0.654723 0.755869i \(-0.272785\pi\)
0.0853930 + 0.996347i \(0.472785\pi\)
\(272\) 0.861236 + 2.52224i 0.0522201 + 0.152933i
\(273\) 8.86279 0.536400
\(274\) 4.23633 6.97115i 0.255926 0.421143i
\(275\) −4.45821 + 15.7765i −0.268840 + 0.951361i
\(276\) −23.0705 + 0.171700i −1.38868 + 0.0103351i
\(277\) 2.63386 + 16.6295i 0.158253 + 0.999172i 0.931149 + 0.364639i \(0.118807\pi\)
−0.772896 + 0.634533i \(0.781193\pi\)
\(278\) 16.6125 14.2957i 0.996351 0.857396i
\(279\) 14.2327 19.5897i 0.852092 1.17280i
\(280\) 6.29349 + 4.28511i 0.376108 + 0.256084i
\(281\) −6.57910 + 12.9122i −0.392476 + 0.770278i −0.999706 0.0242485i \(-0.992281\pi\)
0.607230 + 0.794526i \(0.292281\pi\)
\(282\) 6.09986 25.8308i 0.363241 1.53820i
\(283\) 11.9570 + 1.89380i 0.710767 + 0.112575i 0.501341 0.865250i \(-0.332840\pi\)
0.209427 + 0.977824i \(0.432840\pi\)
\(284\) −7.55973 + 5.57889i −0.448587 + 0.331046i
\(285\) 6.62495 + 25.4149i 0.392428 + 1.50545i
\(286\) 0.775761 10.3492i 0.0458717 0.611961i
\(287\) 7.59522 + 1.31606i 0.448332 + 0.0776844i
\(288\) 40.5474 17.6861i 2.38928 1.04216i
\(289\) 5.11610 + 15.7457i 0.300947 + 0.926219i
\(290\) 25.7570 19.6383i 1.51251 1.15320i
\(291\) −31.4252 43.2531i −1.84218 2.53554i
\(292\) −1.74930 + 5.52334i −0.102370 + 0.323229i
\(293\) 0.0349019 + 0.107417i 0.00203899 + 0.00627537i 0.952071 0.305878i \(-0.0989498\pi\)
−0.950032 + 0.312153i \(0.898950\pi\)
\(294\) −9.97014 23.8190i −0.581470 1.38915i
\(295\) −28.4156 + 2.79132i −1.65442 + 0.162517i
\(296\) −3.41423 + 14.9548i −0.198448 + 0.869232i
\(297\) 8.13243 + 51.3461i 0.471891 + 2.97940i
\(298\) −10.0322 + 11.8351i −0.581148 + 0.685587i
\(299\) −1.22784 + 7.75228i −0.0710078 + 0.448326i
\(300\) 1.51908 + 32.8587i 0.0877040 + 1.89710i
\(301\) 0.782824 + 0.782824i 0.0451212 + 0.0451212i
\(302\) −20.3071 + 12.5484i −1.16854 + 0.722079i
\(303\) 9.86891 5.02846i 0.566954 0.288878i
\(304\) 2.02416 14.1390i 0.116094 0.810928i
\(305\) −0.738568 + 1.25937i −0.0422903 + 0.0721116i
\(306\) −6.79735 + 2.84523i −0.388579 + 0.162651i
\(307\) −11.3136 + 5.76456i −0.645700 + 0.329001i −0.745990 0.665958i \(-0.768023\pi\)
0.100289 + 0.994958i \(0.468023\pi\)
\(308\) 7.48979 2.49536i 0.426770 0.142186i
\(309\) −26.0118 51.0509i −1.47976 2.90419i
\(310\) −1.75474 9.63327i −0.0996624 0.547133i
\(311\) −19.0139 + 3.01151i −1.07818 + 0.170767i −0.670168 0.742209i \(-0.733778\pi\)
−0.408012 + 0.912976i \(0.633778\pi\)
\(312\) −5.08676 20.1921i −0.287981 1.14315i
\(313\) −5.36402 + 3.89719i −0.303192 + 0.220282i −0.728970 0.684546i \(-0.760001\pi\)
0.425778 + 0.904828i \(0.360001\pi\)
\(314\) −19.1618 + 16.4894i −1.08136 + 0.930551i
\(315\) −10.6491 + 18.1584i −0.600008 + 1.02311i
\(316\) −8.88917 2.81530i −0.500055 0.158373i
\(317\) 3.82261 + 2.77729i 0.214699 + 0.155988i 0.689937 0.723869i \(-0.257638\pi\)
−0.475238 + 0.879857i \(0.657638\pi\)
\(318\) 1.19333 + 14.4739i 0.0669186 + 0.811656i
\(319\) 33.5838i 1.88033i
\(320\) 6.15065 16.7979i 0.343832 0.939031i
\(321\) −21.4300 42.0588i −1.19611 2.34749i
\(322\) −5.80034 + 1.41539i −0.323240 + 0.0788764i
\(323\) −0.372196 + 2.34995i −0.0207095 + 0.130755i
\(324\) 26.4322 + 50.9355i 1.46846 + 2.82975i
\(325\) 11.1124 + 1.32103i 0.616403 + 0.0732777i
\(326\) −3.90185 15.9900i −0.216103 0.885605i
\(327\) −4.29734 + 4.29734i −0.237643 + 0.237643i
\(328\) −1.36086 18.0596i −0.0751412 0.997173i
\(329\) 6.86855i 0.378675i
\(330\) 28.0485 + 19.4047i 1.54402 + 1.06819i
\(331\) 2.44851 + 2.44851i 0.134582 + 0.134582i 0.771189 0.636607i \(-0.219662\pi\)
−0.636607 + 0.771189i \(0.719662\pi\)
\(332\) −6.40672 + 20.2289i −0.351614 + 1.11020i
\(333\) −41.8888 6.63453i −2.29549 0.363570i
\(334\) 8.33884 13.7221i 0.456281 0.750840i
\(335\) 10.0130 + 22.9076i 0.547068 + 1.25158i
\(336\) 12.6746 9.50003i 0.691455 0.518269i
\(337\) 0.0591917 0.0591917i 0.00322438 0.00322438i −0.705493 0.708717i \(-0.749274\pi\)
0.708717 + 0.705493i \(0.249274\pi\)
\(338\) 11.2625 0.928559i 0.612599 0.0505069i
\(339\) −43.2541 + 6.85077i −2.34924 + 0.372083i
\(340\) −1.06609 + 2.78258i −0.0578168 + 0.150906i
\(341\) −9.04621 4.60927i −0.489880 0.249606i
\(342\) 39.3796 + 2.95184i 2.12940 + 0.159617i
\(343\) −8.88097 12.2236i −0.479527 0.660013i
\(344\) 1.33421 2.23281i 0.0719359 0.120385i
\(345\) −19.9351 16.3689i −1.07327 0.881271i
\(346\) −0.488707 2.00275i −0.0262730 0.107668i
\(347\) 1.09477 3.36935i 0.0587702 0.180876i −0.917362 0.398055i \(-0.869685\pi\)
0.976132 + 0.217179i \(0.0696854\pi\)
\(348\) −21.2988 63.9283i −1.14174 3.42691i
\(349\) −5.95153 + 18.3169i −0.318578 + 0.980483i 0.655678 + 0.755041i \(0.272383\pi\)
−0.974256 + 0.225443i \(0.927617\pi\)
\(350\) 2.33690 + 8.18545i 0.124912 + 0.437531i
\(351\) 33.7484 10.9655i 1.80136 0.585297i
\(352\) −9.98390 15.6318i −0.532144 0.833178i
\(353\) −0.223762 0.439158i −0.0119097 0.0233740i 0.884975 0.465638i \(-0.154175\pi\)
−0.896885 + 0.442264i \(0.854175\pi\)
\(354\) −13.6516 + 57.8100i −0.725577 + 3.07257i
\(355\) −10.4860 0.621098i −0.556539 0.0329645i
\(356\) 0.0218915 + 0.0156575i 0.00116025 + 0.000829848i
\(357\) −2.13461 + 1.55088i −0.112975 + 0.0820814i
\(358\) 23.7981 + 20.1729i 1.25777 + 1.06617i
\(359\) 26.7732 + 19.4519i 1.41304 + 1.02663i 0.992872 + 0.119183i \(0.0380275\pi\)
0.420164 + 0.907448i \(0.361973\pi\)
\(360\) 47.4823 + 13.8399i 2.50254 + 0.729429i
\(361\) −3.67332 + 5.05589i −0.193333 + 0.266100i
\(362\) −8.00888 + 19.5405i −0.420938 + 1.02703i
\(363\) −0.778996 + 0.253111i −0.0408867 + 0.0132849i
\(364\) −2.48210 4.78305i −0.130097 0.250700i
\(365\) −5.45643 + 3.49091i −0.285603 + 0.182723i
\(366\) 1.98115 + 2.30222i 0.103556 + 0.120339i
\(367\) 8.44671 16.5776i 0.440915 0.865344i −0.558444 0.829542i \(-0.688601\pi\)
0.999359 0.0358019i \(-0.0113985\pi\)
\(368\) 6.55375 + 12.4026i 0.341638 + 0.646529i
\(369\) 49.5644 7.11561i 2.58022 0.370424i
\(370\) −13.6383 + 10.3984i −0.709020 + 0.540588i
\(371\) 1.16140 + 3.57442i 0.0602969 + 0.185575i
\(372\) −20.1430 3.03685i −1.04437 0.157454i
\(373\) 5.33316 33.6723i 0.276141 1.74348i −0.326251 0.945283i \(-0.605785\pi\)
0.602392 0.798201i \(-0.294215\pi\)
\(374\) 1.62414 + 2.62836i 0.0839825 + 0.135909i
\(375\) −22.2192 + 29.3054i −1.14740 + 1.51333i
\(376\) −15.6486 + 3.94217i −0.807017 + 0.203302i
\(377\) −22.6417 + 3.58610i −1.16611 + 0.184693i
\(378\) 17.6068 + 20.4602i 0.905596 + 1.05236i
\(379\) 29.8298 + 21.6726i 1.53226 + 1.11325i 0.954969 + 0.296707i \(0.0958885\pi\)
0.577287 + 0.816541i \(0.304111\pi\)
\(380\) 11.8605 10.6930i 0.608431 0.548539i
\(381\) 9.66802 61.0415i 0.495308 3.12725i
\(382\) −16.5437 + 4.03696i −0.846449 + 0.206549i
\(383\) 21.1431i 1.08036i −0.841549 0.540181i \(-0.818356\pi\)
0.841549 0.540181i \(-0.181644\pi\)
\(384\) −28.9185 23.4240i −1.47574 1.19535i
\(385\) 8.21841 + 3.21906i 0.418849 + 0.164059i
\(386\) 2.67729 + 32.4729i 0.136270 + 1.65283i
\(387\) 6.40761 + 3.26484i 0.325717 + 0.165961i
\(388\) −14.5419 + 29.0729i −0.738251 + 1.47595i
\(389\) 6.46871 19.9086i 0.327977 1.00941i −0.642102 0.766619i \(-0.721938\pi\)
0.970079 0.242789i \(-0.0780624\pi\)
\(390\) 10.0873 20.9819i 0.510792 1.06246i
\(391\) −1.06083 2.08200i −0.0536485 0.105291i
\(392\) −10.0624 + 12.0514i −0.508225 + 0.608686i
\(393\) 39.9730 + 29.0421i 2.01637 + 1.46498i
\(394\) 14.5524 + 5.96444i 0.733138 + 0.300484i
\(395\) −5.61822 8.78150i −0.282683 0.441845i
\(396\) 41.2623 30.4506i 2.07351 1.53020i
\(397\) 2.85730 + 8.79386i 0.143404 + 0.441351i 0.996802 0.0799076i \(-0.0254625\pi\)
−0.853399 + 0.521259i \(0.825463\pi\)
\(398\) 2.30998 1.42741i 0.115789 0.0715494i
\(399\) 13.9660 2.21199i 0.699173 0.110738i
\(400\) 17.3077 10.0222i 0.865385 0.501108i
\(401\) 29.3822i 1.46728i −0.679539 0.733639i \(-0.737820\pi\)
0.679539 0.733639i \(-0.262180\pi\)
\(402\) 51.8346 4.27361i 2.58527 0.213148i
\(403\) −2.14155 + 6.59101i −0.106678 + 0.328321i
\(404\) −5.47762 3.91777i −0.272522 0.194916i
\(405\) −13.7660 + 62.6647i −0.684036 + 3.11383i
\(406\) −9.16652 14.8342i −0.454927 0.736210i
\(407\) 17.7825i 0.881448i
\(408\) 4.75853 + 3.97316i 0.235582 + 0.196701i
\(409\) 2.55811i 0.126490i 0.997998 + 0.0632451i \(0.0201450\pi\)
−0.997998 + 0.0632451i \(0.979855\pi\)
\(410\) 11.7603 16.4832i 0.580800 0.814046i
\(411\) 18.9737i 0.935903i
\(412\) −20.2663 + 28.3352i −0.998447 + 1.39598i
\(413\) 15.3720i 0.756406i
\(414\) −32.9929 + 20.3873i −1.62151 + 1.00198i
\(415\) −19.9839 + 12.7853i −0.980969 + 0.627603i
\(416\) −9.47266 + 8.40018i −0.464435 + 0.411853i
\(417\) 15.7527 48.4819i 0.771415 2.37417i
\(418\) −1.36053 16.5019i −0.0665457 0.807133i
\(419\) 21.9886i 1.07421i −0.843515 0.537106i \(-0.819517\pi\)
0.843515 0.537106i \(-0.180483\pi\)
\(420\) 17.6856 + 0.915514i 0.862970 + 0.0446725i
\(421\) 11.2644 1.78411i 0.548993 0.0869520i 0.124225 0.992254i \(-0.460356\pi\)
0.424768 + 0.905302i \(0.360356\pi\)
\(422\) −10.4865 16.9704i −0.510477 0.826107i
\(423\) −13.7874 42.4333i −0.670367 2.06318i
\(424\) 7.47704 4.69755i 0.363117 0.228133i
\(425\) −2.90759 + 1.62636i −0.141039 + 0.0788901i
\(426\) −8.28766 + 20.2207i −0.401538 + 0.979694i
\(427\) 0.635899 + 0.462008i 0.0307733 + 0.0223581i
\(428\) −16.6966 + 23.3442i −0.807059 + 1.12839i
\(429\) −10.9590 21.5082i −0.529103 1.03842i
\(430\) 2.74426 0.962287i 0.132340 0.0464056i
\(431\) −9.02667 + 27.7812i −0.434799 + 1.33817i 0.458493 + 0.888698i \(0.348390\pi\)
−0.893292 + 0.449477i \(0.851610\pi\)
\(432\) 36.5093 51.8567i 1.75656 2.49496i
\(433\) 32.7708 + 16.6976i 1.57486 + 0.802433i 0.999876 0.0157288i \(-0.00500683\pi\)
0.574988 + 0.818162i \(0.305007\pi\)
\(434\) −5.25385 + 0.433164i −0.252193 + 0.0207926i
\(435\) 27.4759 70.1473i 1.31737 3.36331i
\(436\) 3.52268 + 1.11567i 0.168706 + 0.0534311i
\(437\) 12.5225i 0.599031i
\(438\) 3.19462 + 13.0918i 0.152645 + 0.625548i
\(439\) −1.25115 + 7.89948i −0.0597143 + 0.377022i 0.939675 + 0.342070i \(0.111128\pi\)
−0.999389 + 0.0349520i \(0.988872\pi\)
\(440\) 2.61708 20.5716i 0.124765 0.980712i
\(441\) −35.1170 25.5140i −1.67224 1.21495i
\(442\) 1.59857 1.37563i 0.0760364 0.0654322i
\(443\) 12.1733 1.92806i 0.578372 0.0916051i 0.139607 0.990207i \(-0.455416\pi\)
0.438765 + 0.898602i \(0.355416\pi\)
\(444\) 11.2777 + 33.8498i 0.535215 + 1.60644i
\(445\) 0.00759036 + 0.0291185i 0.000359817 + 0.00138035i
\(446\) 21.7082 13.4141i 1.02791 0.635178i
\(447\) −5.64523 + 35.6426i −0.267010 + 1.68584i
\(448\) −8.67658 4.17963i −0.409930 0.197469i
\(449\) 2.21355 + 6.81259i 0.104464 + 0.321506i 0.989604 0.143818i \(-0.0459379\pi\)
−0.885141 + 0.465324i \(0.845938\pi\)
\(450\) 30.8680 + 45.8781i 1.45513 + 2.16272i
\(451\) −6.19779 20.0594i −0.291843 0.944558i
\(452\) 15.8109 + 21.4247i 0.743680 + 1.00773i
\(453\) −25.2071 + 49.4717i −1.18433 + 2.32438i
\(454\) −16.6318 + 14.3123i −0.780571 + 0.671710i
\(455\) 1.29268 5.88447i 0.0606018 0.275868i
\(456\) −13.0553 30.5492i −0.611370 1.43060i
\(457\) 10.4973 3.41077i 0.491042 0.159549i −0.0530212 0.998593i \(-0.516885\pi\)
0.544063 + 0.839044i \(0.316885\pi\)
\(458\) 17.2713 + 7.07881i 0.807033 + 0.330771i
\(459\) −6.20949 + 8.54663i −0.289834 + 0.398923i
\(460\) −3.25094 + 15.3428i −0.151576 + 0.715360i
\(461\) 14.7193 + 10.6942i 0.685547 + 0.498079i 0.875193 0.483773i \(-0.160734\pi\)
−0.189646 + 0.981852i \(0.560734\pi\)
\(462\) 11.8733 14.0070i 0.552395 0.651666i
\(463\) 0.916595 0.665945i 0.0425978 0.0309491i −0.566283 0.824211i \(-0.691619\pi\)
0.608880 + 0.793262i \(0.291619\pi\)
\(464\) −28.5358 + 29.3981i −1.32474 + 1.36477i
\(465\) −15.1240 17.0285i −0.701361 0.789677i
\(466\) −19.1370 4.51914i −0.886504 0.209345i
\(467\) −1.86918 3.66848i −0.0864955 0.169757i 0.843707 0.536804i \(-0.180369\pi\)
−0.930202 + 0.367047i \(0.880369\pi\)
\(468\) −24.9353 24.5669i −1.15264 1.13561i
\(469\) 12.8009 4.15926i 0.591090 0.192057i
\(470\) −16.2607 7.81756i −0.750052 0.360597i
\(471\) −18.1701 + 55.9218i −0.837234 + 2.57674i
\(472\) 35.0221 8.82268i 1.61202 0.406097i
\(473\) 0.931780 2.86772i 0.0428433 0.131858i
\(474\) −21.0697 + 5.14137i −0.967762 + 0.236151i
\(475\) 17.8406 0.691765i 0.818581 0.0317404i
\(476\) 1.43479 + 0.717663i 0.0657636 + 0.0328940i
\(477\) 14.3501 + 19.7512i 0.657045 + 0.904345i
\(478\) 0.109992 1.46737i 0.00503091 0.0671158i
\(479\) 8.67147 + 4.41833i 0.396209 + 0.201879i 0.640732 0.767765i \(-0.278631\pi\)
−0.244522 + 0.969644i \(0.578631\pi\)
\(480\) −8.06476 40.8187i −0.368104 1.86311i
\(481\) 11.9887 1.89883i 0.546639 0.0865792i
\(482\) −2.35815 28.6020i −0.107411 1.30279i
\(483\) −9.81967 + 9.81967i −0.446810 + 0.446810i
\(484\) 0.354763 + 0.349521i 0.0161256 + 0.0158873i
\(485\) −33.3015 + 14.5562i −1.51214 + 0.660962i
\(486\) 56.5805 + 34.3836i 2.56654 + 1.55967i
\(487\) −19.5190 3.09150i −0.884490 0.140089i −0.302368 0.953191i \(-0.597777\pi\)
−0.582122 + 0.813102i \(0.697777\pi\)
\(488\) 0.687623 1.71394i 0.0311272 0.0775864i
\(489\) −27.0703 27.0703i −1.22416 1.22416i
\(490\) −17.2688 + 3.14559i −0.780127 + 0.142103i
\(491\) 15.8487i 0.715240i −0.933867 0.357620i \(-0.883588\pi\)
0.933867 0.357620i \(-0.116412\pi\)
\(492\) −24.5194 34.2532i −1.10542 1.54425i
\(493\) 4.82575 4.82575i 0.217341 0.217341i
\(494\) −10.9800 + 2.67933i −0.494016 + 0.120549i
\(495\) 57.2344 + 3.39006i 2.57249 + 0.152372i
\(496\) 4.00230 + 11.7213i 0.179709 + 0.526300i
\(497\) −0.884687 + 5.58570i −0.0396837 + 0.250553i
\(498\) 11.7001 + 47.9477i 0.524294 + 2.14859i
\(499\) 2.85821 + 5.60956i 0.127951 + 0.251118i 0.946091 0.323901i \(-0.104994\pi\)
−0.818140 + 0.575019i \(0.804994\pi\)
\(500\) 22.0382 + 3.78400i 0.985577 + 0.169226i
\(501\) 37.3480i 1.66859i
\(502\) −40.3210 + 3.32435i −1.79962 + 0.148373i
\(503\) −11.4501 8.31900i −0.510535 0.370926i 0.302491 0.953152i \(-0.402182\pi\)
−0.813027 + 0.582226i \(0.802182\pi\)
\(504\) 9.91454 24.7125i 0.441629 1.10078i
\(505\) −1.89923 7.28591i −0.0845147 0.324219i
\(506\) 10.6070 + 12.3261i 0.471540 + 0.547961i
\(507\) 21.2649 15.4498i 0.944405 0.686151i
\(508\) −35.6504 + 11.8775i −1.58173 + 0.526981i
\(509\) 33.6604 5.33129i 1.49197 0.236305i 0.643459 0.765480i \(-0.277499\pi\)
0.848513 + 0.529175i \(0.177499\pi\)
\(510\) 1.24205 + 6.81868i 0.0549988 + 0.301936i
\(511\) 1.58324 + 3.10729i 0.0700385 + 0.137458i
\(512\) −4.54258 + 22.1668i −0.200756 + 0.979641i
\(513\) 50.4440 25.7025i 2.22716 1.13479i
\(514\) −6.90999 16.5082i −0.304787 0.728145i
\(515\) −37.6893 + 9.82454i −1.66079 + 0.432921i
\(516\) −0.0450248 6.04977i −0.00198211 0.266326i
\(517\) −16.6685 + 8.49305i −0.733082 + 0.373524i
\(518\) 4.85365 + 7.85467i 0.213257 + 0.345115i
\(519\) −3.39055 3.39055i −0.148829 0.148829i
\(520\) −14.1485 + 0.432246i −0.620454 + 0.0189553i
\(521\) −0.610428 + 3.85409i −0.0267433 + 0.168851i −0.997445 0.0714365i \(-0.977242\pi\)
0.970702 + 0.240287i \(0.0772417\pi\)
\(522\) −86.4071 73.2443i −3.78194 3.20582i
\(523\) −3.10912 19.6302i −0.135952 0.858368i −0.957543 0.288291i \(-0.906913\pi\)
0.821591 0.570078i \(-0.193087\pi\)
\(524\) 4.47861 29.7060i 0.195649 1.29771i
\(525\) 14.5324 + 13.4475i 0.634245 + 0.586895i
\(526\) −31.6584 + 13.2516i −1.38037 + 0.577796i
\(527\) −0.637555 1.96219i −0.0277723 0.0854745i
\(528\) −38.7269 19.0117i −1.68537 0.827377i
\(529\) 6.29021 + 8.65773i 0.273487 + 0.376423i
\(530\) 9.78403 + 1.31877i 0.424991 + 0.0572838i
\(531\) 30.8566 + 94.9669i 1.33906 + 4.12121i
\(532\) −5.10505 6.91764i −0.221332 0.299918i
\(533\) −12.8619 + 6.32041i −0.557112 + 0.273768i
\(534\) 0.0624268 + 0.00467943i 0.00270147 + 0.000202499i
\(535\) −31.0507 + 8.09404i −1.34244 + 0.349936i
\(536\) −16.8231 26.7771i −0.726646 1.15660i
\(537\) 71.6706 + 11.3515i 3.09282 + 0.489854i
\(538\) 0.964345 + 0.227727i 0.0415759 + 0.00981800i
\(539\) −8.26271 + 16.2165i −0.355900 + 0.698493i
\(540\) 68.4775 18.3955i 2.94680 0.791615i
\(541\) 0.236475 0.325480i 0.0101669 0.0139935i −0.803903 0.594760i \(-0.797247\pi\)
0.814070 + 0.580767i \(0.197247\pi\)
\(542\) −11.8174 13.7326i −0.507601 0.589866i
\(543\) 7.68398 + 48.5147i 0.329751 + 2.08197i
\(544\) 0.811563 3.68079i 0.0347955 0.157813i
\(545\) 2.22644 + 3.48001i 0.0953702 + 0.149067i
\(546\) −10.7112 6.50912i −0.458396 0.278565i
\(547\) −2.23544 −0.0955807 −0.0477903 0.998857i \(-0.515218\pi\)
−0.0477903 + 0.998857i \(0.515218\pi\)
\(548\) −10.2397 + 5.31374i −0.437418 + 0.226992i
\(549\) 4.85594 + 1.57779i 0.207246 + 0.0673384i
\(550\) 16.9748 15.7926i 0.723808 0.673398i
\(551\) −34.7838 + 11.3019i −1.48184 + 0.481479i
\(552\) 28.0081 + 16.7362i 1.19211 + 0.712341i
\(553\) −5.00082 + 2.54805i −0.212657 + 0.108354i
\(554\) 9.03010 22.0321i 0.383652 0.936055i
\(555\) −14.5484 + 37.1428i −0.617547 + 1.57662i
\(556\) −30.5763 + 5.07636i −1.29672 + 0.215286i
\(557\) −13.0777 + 17.9999i −0.554120 + 0.762680i −0.990564 0.137051i \(-0.956238\pi\)
0.436444 + 0.899731i \(0.356238\pi\)
\(558\) −31.5884 + 13.2223i −1.33724 + 0.559743i
\(559\) −2.03287 0.321976i −0.0859814 0.0136181i
\(560\) −4.45892 9.80094i −0.188424 0.414165i
\(561\) 6.40314 + 3.26256i 0.270341 + 0.137746i
\(562\) 17.4344 10.7732i 0.735424 0.454441i
\(563\) 8.70325 + 6.32328i 0.366798 + 0.266495i 0.755882 0.654708i \(-0.227208\pi\)
−0.389084 + 0.921202i \(0.627208\pi\)
\(564\) −26.3430 + 26.7381i −1.10924 + 1.12588i
\(565\) −1.76022 + 29.7178i −0.0740532 + 1.25024i
\(566\) −13.0598 11.0703i −0.548944 0.465321i
\(567\) 32.8511 + 10.6740i 1.37962 + 0.448265i
\(568\) 13.2337 1.19030i 0.555273 0.0499438i
\(569\) −7.86210 + 5.71215i −0.329596 + 0.239466i −0.740259 0.672321i \(-0.765297\pi\)
0.410663 + 0.911787i \(0.365297\pi\)
\(570\) 10.6589 35.5809i 0.446453 1.49032i
\(571\) −0.904667 0.904667i −0.0378591 0.0378591i 0.687924 0.725783i \(-0.258522\pi\)
−0.725783 + 0.687924i \(0.758522\pi\)
\(572\) −8.53834 + 11.9378i −0.357006 + 0.499146i
\(573\) −28.0076 + 28.0076i −1.17004 + 1.17004i
\(574\) −8.21270 7.16871i −0.342792 0.299216i
\(575\) −13.7758 + 10.8485i −0.574490 + 0.452412i
\(576\) −61.9931 8.40468i −2.58304 0.350195i
\(577\) −29.2521 −1.21778 −0.608890 0.793254i \(-0.708385\pi\)
−0.608890 + 0.793254i \(0.708385\pi\)
\(578\) 5.38108 22.7870i 0.223823 0.947815i
\(579\) 44.5461 + 61.3124i 1.85127 + 2.54806i
\(580\) −45.5518 + 4.81717i −1.89144 + 0.200022i
\(581\) 5.79853 + 11.3803i 0.240563 + 0.472132i
\(582\) 6.21267 + 75.3535i 0.257523 + 3.12350i
\(583\) 7.23830 7.23830i 0.299780 0.299780i
\(584\) 6.17065 5.39052i 0.255343 0.223061i
\(585\) −3.82599 38.9486i −0.158185 1.61033i
\(586\) 0.0367096 0.155453i 0.00151646 0.00642169i
\(587\) 29.1723 9.47864i 1.20407 0.391225i 0.362812 0.931862i \(-0.381817\pi\)
0.841256 + 0.540637i \(0.181817\pi\)
\(588\) −5.44394 + 36.1090i −0.224504 + 1.48911i
\(589\) −1.72965 + 10.9206i −0.0712691 + 0.449975i
\(590\) 36.3919 + 17.4959i 1.49823 + 0.720295i
\(591\) 36.1303 5.72248i 1.48620 0.235391i
\(592\) 15.1096 15.5662i 0.621001 0.639768i
\(593\) 4.21735 12.9797i 0.173186 0.533011i −0.826360 0.563142i \(-0.809593\pi\)
0.999546 + 0.0301312i \(0.00959251\pi\)
\(594\) 27.8818 68.0274i 1.14400 2.79120i
\(595\) 0.718370 + 1.64348i 0.0294503 + 0.0673762i
\(596\) 20.8165 6.93539i 0.852677 0.284085i
\(597\) 2.86736 5.62751i 0.117353 0.230319i
\(598\) 7.17744 8.46730i 0.293507 0.346254i
\(599\) 13.6280 41.9427i 0.556825 1.71373i −0.134248 0.990948i \(-0.542862\pi\)
0.691074 0.722784i \(-0.257138\pi\)
\(600\) 22.2966 40.8273i 0.910255 1.66677i
\(601\) −21.4047 21.4047i −0.873117 0.873117i 0.119694 0.992811i \(-0.461809\pi\)
−0.992811 + 0.119694i \(0.961809\pi\)
\(602\) −0.371156 1.52102i −0.0151272 0.0619921i
\(603\) 70.7339 51.3912i 2.88051 2.09281i
\(604\) 33.7582 0.251242i 1.37360 0.0102229i
\(605\) 0.0544335 + 0.554134i 0.00221304 + 0.0225287i
\(606\) −15.6202 1.17087i −0.634527 0.0475633i
\(607\) −0.888786 5.61158i −0.0360747 0.227767i 0.963063 0.269275i \(-0.0867839\pi\)
−0.999138 + 0.0415077i \(0.986784\pi\)
\(608\) −12.8305 + 15.6012i −0.520344 + 0.632712i
\(609\) −36.1388 18.4136i −1.46442 0.746157i
\(610\) 1.81753 0.979598i 0.0735895 0.0396628i
\(611\) 7.50577 + 10.3308i 0.303651 + 0.417940i
\(612\) 10.3046 + 1.55357i 0.416539 + 0.0627993i
\(613\) 14.8914 29.2261i 0.601460 1.18043i −0.366757 0.930317i \(-0.619532\pi\)
0.968216 0.250114i \(-0.0804681\pi\)
\(614\) 17.9068 + 1.34227i 0.722659 + 0.0541695i
\(615\) 3.46569 46.9691i 0.139750 1.89398i
\(616\) −10.8845 2.48496i −0.438549 0.100122i
\(617\) −11.2259 5.71989i −0.451938 0.230274i 0.213179 0.977013i \(-0.431618\pi\)
−0.665117 + 0.746739i \(0.731618\pi\)
\(618\) −6.05679 + 80.8018i −0.243640 + 3.25033i
\(619\) 12.8250 9.31793i 0.515482 0.374519i −0.299417 0.954122i \(-0.596792\pi\)
0.814899 + 0.579603i \(0.196792\pi\)
\(620\) −4.95428 + 12.9311i −0.198969 + 0.519325i
\(621\) −25.2427 + 49.5416i −1.01295 + 1.98803i
\(622\) 25.1911 + 10.3249i 1.01007 + 0.413989i
\(623\) 0.0160011 0.00253433i 0.000641072 0.000101536i
\(624\) −8.68212 + 28.1392i −0.347563 + 1.12647i
\(625\) 16.2166 + 19.0268i 0.648665 + 0.761074i
\(626\) 9.34494 0.770463i 0.373499 0.0307939i
\(627\) −22.6372 31.1574i −0.904041 1.24431i
\(628\) 35.2684 5.85536i 1.40736 0.233654i
\(629\) −2.55522 + 2.55522i −0.101883 + 0.101883i
\(630\) 26.2061 14.1244i 1.04408 0.562729i
\(631\) −31.1163 10.1103i −1.23872 0.402484i −0.384854 0.922978i \(-0.625748\pi\)
−0.853866 + 0.520493i \(0.825748\pi\)
\(632\) 8.67542 + 9.93095i 0.345090 + 0.395032i
\(633\) −41.3429 21.0653i −1.64323 0.837270i
\(634\) −2.58011 6.16396i −0.102469 0.244802i
\(635\) −39.1185 15.3223i −1.55237 0.608047i
\(636\) 9.18789 18.3689i 0.364324 0.728376i
\(637\) 11.8152 + 3.83900i 0.468136 + 0.152107i
\(638\) −24.6650 + 40.5879i −0.976499 + 1.60689i
\(639\) 5.74679 + 36.2838i 0.227340 + 1.43537i
\(640\) −19.7703 + 15.7840i −0.781491 + 0.623916i
\(641\) 0.268588 + 0.0425401i 0.0106086 + 0.00168023i 0.161736 0.986834i \(-0.448291\pi\)
−0.151128 + 0.988514i \(0.548291\pi\)
\(642\) −4.98995 + 66.5694i −0.196938 + 2.62728i
\(643\) −0.255199 0.785422i −0.0100641 0.0309740i 0.945898 0.324463i \(-0.105184\pi\)
−0.955962 + 0.293489i \(0.905184\pi\)
\(644\) 8.04954 + 2.54938i 0.317196 + 0.100460i
\(645\) 4.29240 5.22757i 0.169013 0.205835i
\(646\) 2.17570 2.56670i 0.0856017 0.100985i
\(647\) −22.9749 22.9749i −0.903236 0.903236i 0.0924785 0.995715i \(-0.470521\pi\)
−0.995715 + 0.0924785i \(0.970521\pi\)
\(648\) 5.46382 80.9711i 0.214639 3.18085i
\(649\) 37.3046 19.0077i 1.46434 0.746116i
\(650\) −12.4597 9.75783i −0.488710 0.382733i
\(651\) −9.91986 + 7.20720i −0.388790 + 0.282473i
\(652\) −7.02798 + 22.1905i −0.275237 + 0.869046i
\(653\) 31.9818i 1.25155i 0.780006 + 0.625773i \(0.215216\pi\)
−0.780006 + 0.625773i \(0.784784\pi\)
\(654\) 8.34968 2.03747i 0.326498 0.0796714i
\(655\) 25.1128 22.3042i 0.981239 0.871499i
\(656\) −11.6189 + 22.8255i −0.453640 + 0.891185i
\(657\) 16.0185 + 16.0185i 0.624941 + 0.624941i
\(658\) −5.04448 + 8.30103i −0.196654 + 0.323608i
\(659\) 17.6120 17.6120i 0.686066 0.686066i −0.275294 0.961360i \(-0.588775\pi\)
0.961360 + 0.275294i \(0.0887752\pi\)
\(660\) −19.6467 44.0514i −0.764748 1.71470i
\(661\) 22.8024 + 31.3848i 0.886910 + 1.22073i 0.974459 + 0.224566i \(0.0720966\pi\)
−0.0875489 + 0.996160i \(0.527903\pi\)
\(662\) −1.16090 4.75743i −0.0451195 0.184903i
\(663\) 1.51584 4.66529i 0.0588705 0.181185i
\(664\) 22.5996 19.7424i 0.877036 0.766156i
\(665\) 0.568345 9.59537i 0.0220395 0.372092i
\(666\) 45.7523 + 38.7827i 1.77287 + 1.50280i
\(667\) 21.1130 29.0596i 0.817499 1.12519i
\(668\) −20.1559 + 10.4596i −0.779856 + 0.404695i
\(669\) 26.9462 52.8849i 1.04180 2.04465i
\(670\) 4.72285 35.0390i 0.182460 1.35368i
\(671\) 0.334900 2.11448i 0.0129287 0.0816284i
\(672\) −22.2951 + 2.17270i −0.860051 + 0.0838139i
\(673\) −16.0700 11.6756i −0.619455 0.450060i 0.233276 0.972411i \(-0.425055\pi\)
−0.852731 + 0.522350i \(0.825055\pi\)
\(674\) −0.115009 + 0.0280642i −0.00442998 + 0.00108099i
\(675\) 71.9755 + 33.2261i 2.77034 + 1.27887i
\(676\) −14.2933 7.14932i −0.549743 0.274974i
\(677\) −10.6252 20.8532i −0.408361 0.801453i 0.591628 0.806211i \(-0.298485\pi\)
−0.999989 + 0.00475812i \(0.998485\pi\)
\(678\) 57.3064 + 23.4876i 2.20084 + 0.902038i
\(679\) 6.04644 + 18.6090i 0.232041 + 0.714149i
\(680\) 3.33204 2.57993i 0.127778 0.0989359i
\(681\) −15.7711 + 48.5384i −0.604349 + 1.86000i
\(682\) 7.54766 + 12.2144i 0.289015 + 0.467714i
\(683\) 25.3108i 0.968489i 0.874933 + 0.484245i \(0.160905\pi\)
−0.874933 + 0.484245i \(0.839095\pi\)
\(684\) −45.4245 32.4891i −1.73685 1.24225i
\(685\) −12.5976 2.76740i −0.481330 0.105737i
\(686\) 1.75574 + 21.2954i 0.0670345 + 0.813062i
\(687\) 42.8807 6.79163i 1.63600 0.259117i
\(688\) −3.25232 + 1.71859i −0.123993 + 0.0655205i
\(689\) −5.65287 4.10705i −0.215357 0.156466i
\(690\) 12.0708 + 34.4237i 0.459529 + 1.31049i
\(691\) −28.6000 14.5724i −1.08800 0.554361i −0.184445 0.982843i \(-0.559049\pi\)
−0.903551 + 0.428481i \(0.859049\pi\)
\(692\) −0.880255 + 2.77936i −0.0334623 + 0.105655i
\(693\) 4.82878 30.4877i 0.183430 1.15813i
\(694\) −3.79765 + 3.26802i −0.144157 + 0.124052i
\(695\) −29.8921 17.5304i −1.13387 0.664965i
\(696\) −21.2101 + 92.9035i −0.803968 + 3.52150i
\(697\) 1.99181 3.77296i 0.0754450 0.142911i
\(698\) 20.6453 17.7661i 0.781437 0.672455i
\(699\) −43.4973 + 14.1331i −1.64522 + 0.534565i
\(700\) 3.18739 11.6089i 0.120472 0.438774i
\(701\) −27.5926 + 20.0472i −1.04216 + 0.757172i −0.970705 0.240273i \(-0.922763\pi\)
−0.0714517 + 0.997444i \(0.522763\pi\)
\(702\) −48.8403 11.5335i −1.84336 0.435303i
\(703\) 18.4179 5.98435i 0.694645 0.225704i
\(704\) 0.585604 + 26.2244i 0.0220708 + 0.988370i
\(705\) −41.7644 + 4.10259i −1.57294 + 0.154512i
\(706\) −0.0521027 + 0.695086i −0.00196091 + 0.0261599i
\(707\) −4.00375 + 0.634131i −0.150576 + 0.0238489i
\(708\) 58.9563 59.8405i 2.21572 2.24894i
\(709\) 3.65116 + 0.578288i 0.137122 + 0.0217181i 0.224618 0.974447i \(-0.427886\pi\)
−0.0874959 + 0.996165i \(0.527886\pi\)
\(710\) 12.2168 + 8.45189i 0.458487 + 0.317194i
\(711\) −25.7799 + 25.7799i −0.966822 + 0.966822i
\(712\) −0.0149578 0.0350009i −0.000560566 0.00131171i
\(713\) −4.92985 9.67538i −0.184624 0.362346i
\(714\) 3.71881 0.306605i 0.139173 0.0114744i
\(715\) −15.8788 + 4.13916i −0.593834 + 0.154796i
\(716\) −13.9458 41.8582i −0.521179 1.56431i
\(717\) −1.55382 3.04955i −0.0580286 0.113888i
\(718\) −18.0709 43.1718i −0.674398 1.61116i
\(719\) 15.2548 7.77271i 0.568908 0.289873i −0.145779 0.989317i \(-0.546569\pi\)
0.714687 + 0.699444i \(0.246569\pi\)
\(720\) −47.2205 51.5989i −1.75981 1.92298i
\(721\) 3.28030 + 20.7110i 0.122165 + 0.771318i
\(722\) 8.15263 3.41253i 0.303409 0.127001i
\(723\) −39.2361 54.0039i −1.45921 2.00843i
\(724\) 24.0304 17.7338i 0.893082 0.659072i
\(725\) −42.5670 28.4740i −1.58090 1.05750i
\(726\) 1.12735 + 0.266221i 0.0418400 + 0.00988038i
\(727\) −25.1723 + 34.6467i −0.933588 + 1.28497i 0.0248559 + 0.999691i \(0.492087\pi\)
−0.958444 + 0.285282i \(0.907913\pi\)
\(728\) −0.513075 + 7.60352i −0.0190158 + 0.281805i
\(729\) 67.9194 2.51553
\(730\) 9.15825 0.211583i 0.338962 0.00783102i
\(731\) 0.545961 0.278181i 0.0201931 0.0102889i
\(732\) −0.703502 4.23739i −0.0260022 0.156618i
\(733\) −30.5515 4.83888i −1.12844 0.178728i −0.435825 0.900032i \(-0.643543\pi\)
−0.692619 + 0.721304i \(0.743543\pi\)
\(734\) −22.3835 + 13.8314i −0.826189 + 0.510528i
\(735\) −30.5257 + 27.1118i −1.12596 + 1.00003i
\(736\) 1.18827 19.8025i 0.0438002 0.729930i
\(737\) −25.9221 25.9221i −0.954854 0.954854i
\(738\) −65.1273 27.8021i −2.39737 1.02341i
\(739\) −40.5634 −1.49215 −0.746074 0.665864i \(-0.768063\pi\)
−0.746074 + 0.665864i \(0.768063\pi\)
\(740\) 24.1196 2.55068i 0.886653 0.0937648i
\(741\) −18.5887 + 18.5887i −0.682871 + 0.682871i
\(742\) 1.22155 5.17286i 0.0448447 0.189902i
\(743\) −0.638530 + 4.03152i −0.0234254 + 0.147902i −0.996629 0.0820443i \(-0.973855\pi\)
0.973203 + 0.229946i \(0.0738551\pi\)
\(744\) 22.1137 + 18.4639i 0.810726 + 0.676920i
\(745\) 22.8416 + 8.94680i 0.836851 + 0.327785i
\(746\) −31.1754 + 36.7780i −1.14141 + 1.34654i
\(747\) 58.6667 + 58.6667i 2.14650 + 2.14650i
\(748\) −0.0325184 4.36934i −0.00118899 0.159759i
\(749\) 2.70251 + 17.0630i 0.0987474 + 0.623467i
\(750\) 48.3761 19.0988i 1.76644 0.697388i
\(751\) 1.50677 2.95720i 0.0549828 0.107910i −0.861880 0.507112i \(-0.830713\pi\)
0.916863 + 0.399202i \(0.130713\pi\)
\(752\) 21.8075 + 6.72853i 0.795238 + 0.245364i
\(753\) −76.1306 + 55.3122i −2.77436 + 2.01569i
\(754\) 29.9976 + 12.2948i 1.09245 + 0.447751i
\(755\) 29.1703 + 23.9520i 1.06161 + 0.871702i
\(756\) −6.25214 37.6584i −0.227388 1.36962i
\(757\) 35.3756 + 11.4942i 1.28575 + 0.417765i 0.870602 0.491989i \(-0.163730\pi\)
0.415148 + 0.909754i \(0.363730\pi\)
\(758\) −20.1339 48.1006i −0.731298 1.74709i
\(759\) 35.9725 + 11.6882i 1.30572 + 0.424253i
\(760\) −22.1874 + 4.21235i −0.804820 + 0.152798i
\(761\) −6.39414 19.6791i −0.231787 0.713368i −0.997531 0.0702227i \(-0.977629\pi\)
0.765744 0.643146i \(-0.222371\pi\)
\(762\) −56.5152 + 66.6716i −2.04733 + 2.41526i
\(763\) 1.98177 1.00976i 0.0717449 0.0365559i
\(764\) 22.9589 + 7.27134i 0.830623 + 0.263068i
\(765\) 7.73703 + 8.71129i 0.279733 + 0.314957i
\(766\) −15.5282 + 25.5526i −0.561056 + 0.923254i
\(767\) −16.7981 23.1206i −0.606545 0.834837i
\(768\) 17.7462 + 49.5479i 0.640362 + 1.78791i
\(769\) 14.2535 19.6183i 0.513995 0.707454i −0.470591 0.882351i \(-0.655959\pi\)
0.984587 + 0.174898i \(0.0559594\pi\)
\(770\) −7.56823 9.92629i −0.272740 0.357718i
\(771\) −33.6755 24.4667i −1.21279 0.881145i
\(772\) 20.6135 41.2116i 0.741895 1.48324i
\(773\) 5.04757 + 15.5348i 0.181549 + 0.558749i 0.999872 0.0160092i \(-0.00509610\pi\)
−0.818323 + 0.574758i \(0.805096\pi\)
\(774\) −5.34615 8.65169i −0.192163 0.310979i
\(775\) −13.5120 + 7.55796i −0.485366 + 0.271490i
\(776\) 38.9267 24.4562i 1.39739 0.877927i
\(777\) 19.1354 + 9.74996i 0.686478 + 0.349778i
\(778\) −22.4394 + 19.3099i −0.804490 + 0.692293i
\(779\) −18.6904 + 13.1698i −0.669652 + 0.471857i
\(780\) −27.6009 + 17.9494i −0.988272 + 0.642691i
\(781\) 14.6493 4.75983i 0.524192 0.170320i
\(782\) −0.247013 + 3.29532i −0.00883315 + 0.117840i
\(783\) −160.394 25.4040i −5.73203 0.907864i
\(784\) 21.0118 7.17463i 0.750423 0.256237i
\(785\) 34.4792 + 20.2205i 1.23062 + 0.721702i
\(786\) −26.9802 64.4565i −0.962351 2.29909i
\(787\) −3.96799 25.0529i −0.141444 0.893040i −0.951714 0.306985i \(-0.900680\pi\)
0.810271 0.586056i \(-0.199320\pi\)
\(788\) −13.2069 17.8961i −0.470476 0.637522i
\(789\) −46.9207 + 64.5808i −1.67042 + 2.29914i
\(790\) 0.340518 + 14.7391i 0.0121151 + 0.524395i
\(791\) 15.8302 + 2.50725i 0.562855 + 0.0891475i
\(792\) −72.2317 + 6.49685i −2.56664 + 0.230855i
\(793\) −1.46131 −0.0518926
\(794\) 3.00529 12.7264i 0.106654 0.451642i
\(795\) 21.0407 9.19694i 0.746236 0.326182i
\(796\) −3.84007 + 0.0285793i −0.136108 + 0.00101297i
\(797\) −0.904827 + 1.77582i −0.0320506 + 0.0629028i −0.906477 0.422256i \(-0.861238\pi\)
0.874426 + 0.485159i \(0.161238\pi\)
\(798\) −18.5032 7.58375i −0.655007 0.268462i
\(799\) −3.61554 1.17476i −0.127909 0.0415600i
\(800\) −28.2779 0.598980i −0.999776 0.0211771i
\(801\) 0.0937665 0.0477764i 0.00331308 0.00168810i
\(802\) −21.5793 + 35.5101i −0.761990 + 1.25390i
\(803\) 5.58305 7.68440i 0.197021 0.271177i
\(804\) −65.7837 32.9041i −2.32001 1.16044i
\(805\) 5.08755 + 7.95204i 0.179312 + 0.280272i
\(806\) 7.42883 6.39278i 0.261669 0.225176i
\(807\) 2.19190 0.712193i 0.0771587 0.0250704i
\(808\) 3.74267 + 8.75779i 0.131667 + 0.308098i
\(809\) −4.29045 27.0888i −0.150844 0.952392i −0.940734 0.339144i \(-0.889863\pi\)
0.789890 0.613248i \(-0.210137\pi\)
\(810\) 62.6599 65.6236i 2.20164 2.30578i
\(811\) 26.0890 0.916109 0.458055 0.888924i \(-0.348546\pi\)
0.458055 + 0.888924i \(0.348546\pi\)
\(812\) 0.183531 + 24.6602i 0.00644067 + 0.865403i
\(813\) −40.0773 13.0219i −1.40557 0.456698i
\(814\) 13.0601 21.4912i 0.457755 0.753266i
\(815\) −21.9217 + 14.0250i −0.767883 + 0.491276i
\(816\) −2.83293 8.29661i −0.0991725 0.290439i
\(817\) −3.28376 −0.114884
\(818\) 1.87876 3.09162i 0.0656892 0.108096i
\(819\) −21.0700 −0.736245
\(820\) −26.3188 + 11.2837i −0.919091 + 0.394044i
\(821\) −4.63363 −0.161715 −0.0808573 0.996726i \(-0.525766\pi\)
−0.0808573 + 0.996726i \(0.525766\pi\)
\(822\) −13.9349 + 22.9308i −0.486035 + 0.799803i
\(823\) −0.172990 −0.00603003 −0.00301502 0.999995i \(-0.500960\pi\)
−0.00301502 + 0.999995i \(0.500960\pi\)
\(824\) 45.3032 19.3605i 1.57821 0.674455i
\(825\) 14.6647 51.8950i 0.510561 1.80675i
\(826\) 11.2897 18.5779i 0.392818 0.646408i
\(827\) −40.5710 13.1823i −1.41079 0.458394i −0.498128 0.867103i \(-0.665979\pi\)
−0.912665 + 0.408709i \(0.865979\pi\)
\(828\) 54.8468 0.408192i 1.90606 0.0141856i
\(829\) −44.4426 −1.54356 −0.771778 0.635892i \(-0.780632\pi\)
−0.771778 + 0.635892i \(0.780632\pi\)
\(830\) 33.5415 0.774908i 1.16424 0.0268975i
\(831\) −8.66376 54.7009i −0.300543 1.89755i
\(832\) 17.6176 3.19506i 0.610781 0.110769i
\(833\) −3.51748 + 1.14290i −0.121873 + 0.0395991i
\(834\) −54.6448 + 47.0239i −1.89219 + 1.62830i
\(835\) −24.7973 5.44739i −0.858146 0.188515i
\(836\) −10.4752 + 20.9427i −0.362293 + 0.724317i
\(837\) −28.8565 + 39.7176i −0.997427 + 1.37284i
\(838\) −16.1491 + 26.5744i −0.557862 + 0.917999i
\(839\) −20.0330 + 10.2073i −0.691615 + 0.352395i −0.764211 0.644966i \(-0.776871\pi\)
0.0725966 + 0.997361i \(0.476871\pi\)
\(840\) −20.7017 14.0953i −0.714276 0.486336i
\(841\) 72.1935 + 23.4571i 2.48943 + 0.808865i
\(842\) −14.9240 6.11675i −0.514314 0.210797i
\(843\) 21.6412 42.4732i 0.745361 1.46285i
\(844\) 0.209960 + 28.2114i 0.00722713 + 0.971076i
\(845\) −7.15636 16.3723i −0.246186 0.563223i
\(846\) −14.5015 + 61.4090i −0.498573 + 2.11129i
\(847\) 0.299769 0.0103002
\(848\) −12.4865 + 0.185869i −0.428787 + 0.00638276i
\(849\) −39.3310 6.22942i −1.34984 0.213793i
\(850\) 4.70843 + 0.169875i 0.161498 + 0.00582667i
\(851\) −11.1793 + 15.3870i −0.383221 + 0.527458i
\(852\) 24.8668 18.3511i 0.851923 0.628698i
\(853\) −3.31324 20.9190i −0.113443 0.716252i −0.977196 0.212337i \(-0.931893\pi\)
0.863753 0.503915i \(-0.168107\pi\)
\(854\) −0.429207 1.02539i −0.0146872 0.0350881i
\(855\) −15.7499 60.4203i −0.538634 2.06633i
\(856\) 37.3235 15.9503i 1.27569 0.545171i
\(857\) 27.4913 + 4.35420i 0.939086 + 0.148737i 0.607170 0.794572i \(-0.292305\pi\)
0.331916 + 0.943309i \(0.392305\pi\)
\(858\) −2.55177 + 34.0424i −0.0871161 + 1.16219i
\(859\) 16.3031 5.29719i 0.556254 0.180738i −0.0173809 0.999849i \(-0.505533\pi\)
0.573635 + 0.819111i \(0.305533\pi\)
\(860\) −4.02332 0.852493i −0.137194 0.0290698i
\(861\) −24.9836 4.32901i −0.851438 0.147532i
\(862\) 31.3127 26.9457i 1.06651 0.917775i
\(863\) −15.1617 7.72527i −0.516110 0.262971i 0.176478 0.984305i \(-0.443530\pi\)
−0.692588 + 0.721333i \(0.743530\pi\)
\(864\) −82.2088 + 35.8581i −2.79680 + 1.21992i
\(865\) −2.74569 + 1.75664i −0.0933563 + 0.0597274i
\(866\) −27.3421 44.2479i −0.929124 1.50360i
\(867\) −16.8288 51.7937i −0.571536 1.75901i
\(868\) 6.66771 + 3.33510i 0.226317 + 0.113201i
\(869\) 12.3672 + 8.98527i 0.419527 + 0.304804i
\(870\) −84.7247 + 64.5978i −2.87244 + 2.19007i
\(871\) −14.7084 + 20.2443i −0.498374 + 0.685953i
\(872\) −3.43797 3.93553i −0.116424 0.133274i
\(873\) 74.7089 + 102.828i 2.52851 + 3.48020i
\(874\) 9.19691 15.1341i 0.311090 0.511919i
\(875\) 11.0481 7.68743i 0.373494 0.259883i
\(876\) 5.75413 18.1684i 0.194414 0.613852i
\(877\) 7.63213 3.88876i 0.257719 0.131314i −0.320358 0.947296i \(-0.603803\pi\)
0.578077 + 0.815982i \(0.303803\pi\)
\(878\) 7.31372 8.62808i 0.246826 0.291184i
\(879\) −0.114806 0.353335i −0.00387230 0.0119177i
\(880\) −18.2713 + 22.9399i −0.615927 + 0.773303i
\(881\) −21.1679 6.87786i −0.713163 0.231721i −0.0701068 0.997539i \(-0.522334\pi\)
−0.643057 + 0.765819i \(0.722334\pi\)
\(882\) 23.7026 + 56.6261i 0.798107 + 1.90670i
\(883\) 30.7250 + 9.98317i 1.03398 + 0.335960i 0.776363 0.630287i \(-0.217063\pi\)
0.257617 + 0.966247i \(0.417063\pi\)
\(884\) −2.94228 + 0.488484i −0.0989595 + 0.0164295i
\(885\) 93.4699 9.18170i 3.14195 0.308639i
\(886\) −16.1282 6.61030i −0.541837 0.222078i
\(887\) −25.2413 + 18.3388i −0.847518 + 0.615758i −0.924461 0.381277i \(-0.875484\pi\)
0.0769423 + 0.997036i \(0.475484\pi\)
\(888\) 11.2307 49.1921i 0.376878 1.65078i
\(889\) −10.2686 + 20.1532i −0.344397 + 0.675917i
\(890\) 0.0122122 0.0407659i 0.000409353 0.00136648i
\(891\) −14.7173 92.9214i −0.493048 3.11299i
\(892\) −36.0873 + 0.268576i −1.20829 + 0.00899259i
\(893\) 14.4060 + 14.4060i 0.482077 + 0.482077i
\(894\) 32.9996 38.9300i 1.10367 1.30201i
\(895\) 17.9904 45.9302i 0.601352 1.53528i
\(896\) 7.41648 + 11.4237i 0.247767 + 0.381638i
\(897\) 4.03883 25.5002i 0.134853 0.851427i
\(898\) 2.32819 9.85910i 0.0776928 0.329003i
\(899\) 22.4260 22.4260i 0.747950 0.747950i
\(900\) −3.61139 78.1168i −0.120380 2.60389i
\(901\) 2.08018 0.0693009
\(902\) −7.24186 + 28.7947i −0.241128 + 0.958760i
\(903\) −2.57501 2.57501i −0.0856908 0.0856908i
\(904\) −3.37336 37.5049i −0.112196 1.24739i
\(905\) 33.3322 + 1.97431i 1.10800 + 0.0656282i
\(906\) 66.7978 41.2764i 2.21921 1.37132i
\(907\) −13.6348 2.15954i −0.452737 0.0717064i −0.0740978 0.997251i \(-0.523608\pi\)
−0.378639 + 0.925545i \(0.623608\pi\)
\(908\) 30.6119 5.08227i 1.01589 0.168661i
\(909\) −23.4619 + 11.9544i −0.778182 + 0.396504i
\(910\) −5.88402 + 6.16233i −0.195053 + 0.204279i
\(911\) 19.6269 0.650267 0.325134 0.945668i \(-0.394591\pi\)
0.325134 + 0.945668i \(0.394591\pi\)
\(912\) −6.65823 + 46.5086i −0.220476 + 1.54005i
\(913\) 20.4476 28.1437i 0.676716 0.931419i
\(914\) −15.1915 3.58743i −0.502492 0.118662i
\(915\) 2.42943 4.14256i 0.0803145 0.136949i
\(916\) −15.6744 21.2397i −0.517896 0.701780i
\(917\) −10.6288 14.6294i −0.350995 0.483104i
\(918\) 13.7814 5.76864i 0.454856 0.190393i
\(919\) −0.238166 1.50372i −0.00785637 0.0496032i 0.983449 0.181187i \(-0.0579938\pi\)
−0.991305 + 0.131584i \(0.957994\pi\)
\(920\) 15.1972 16.1550i 0.501036 0.532615i
\(921\) 37.2147 18.9618i 1.22627 0.624814i
\(922\) −9.93495 23.7349i −0.327190 0.781667i
\(923\) −4.77327 9.36807i −0.157114 0.308354i
\(924\) −24.6368 + 8.20817i −0.810490 + 0.270029i
\(925\) 22.5391 + 15.0769i 0.741081 + 0.495726i
\(926\) −1.59685 + 0.131655i −0.0524757 + 0.00432647i
\(927\) 61.8392 + 121.366i 2.03106 + 3.98619i
\(928\) 56.0780 14.5717i 1.84085 0.478340i
\(929\) 0.857957 0.857957i 0.0281486 0.0281486i −0.692892 0.721041i \(-0.743664\pi\)
0.721041 + 0.692892i \(0.243664\pi\)
\(930\) 5.77200 + 31.6875i 0.189271 + 1.03907i
\(931\) 19.5765 + 3.10062i 0.641595 + 0.101619i
\(932\) 19.8091 + 19.5165i 0.648870 + 0.639283i
\(933\) 62.5440 9.90600i 2.04760 0.324308i
\(934\) −0.435236 + 5.80635i −0.0142414 + 0.189990i
\(935\) 3.10012 3.77552i 0.101385 0.123473i
\(936\) 12.0930 + 48.0038i 0.395273 + 1.56905i
\(937\) 28.5759 9.28486i 0.933533 0.303323i 0.197526 0.980298i \(-0.436709\pi\)
0.736007 + 0.676974i \(0.236709\pi\)
\(938\) −18.5253 4.37469i −0.604872 0.142839i
\(939\) 17.6443 12.8193i 0.575800 0.418343i
\(940\) 13.9105 + 21.3904i 0.453712 + 0.697677i
\(941\) −41.2840 + 13.4140i −1.34582 + 0.437284i −0.891285 0.453444i \(-0.850195\pi\)
−0.454536 + 0.890728i \(0.650195\pi\)
\(942\) 63.0304 54.2399i 2.05364 1.76723i
\(943\) 7.24778 21.2534i 0.236020 0.692106i
\(944\) −48.8058 15.0586i −1.58849 0.490117i
\(945\) 21.5907 36.8156i 0.702347 1.19761i
\(946\) −3.23226 + 2.78148i −0.105090 + 0.0904336i
\(947\) 0.433985 2.74007i 0.0141026 0.0890404i −0.979633 0.200796i \(-0.935647\pi\)
0.993736 + 0.111755i \(0.0356473\pi\)
\(948\) 29.2399 + 9.26060i 0.949667 + 0.300770i
\(949\) −5.77688 2.94347i −0.187525 0.0955489i
\(950\) −22.0694 12.2667i −0.716025 0.397983i
\(951\) −12.5740 9.13556i −0.407740 0.296241i
\(952\) −1.20695 1.92109i −0.0391175 0.0622630i
\(953\) 0.784452 0.124245i 0.0254109 0.00402469i −0.143716 0.989619i \(-0.545905\pi\)
0.169127 + 0.985594i \(0.445905\pi\)
\(954\) −2.83697 34.4096i −0.0918502 1.11405i
\(955\) 14.5107 + 22.6808i 0.469555 + 0.733933i
\(956\) −1.21061 + 1.69262i −0.0391541 + 0.0547431i
\(957\) 110.470i 3.57099i
\(958\) −7.23499 11.7084i −0.233752 0.378282i
\(959\) −2.14582 + 6.60414i −0.0692920 + 0.213259i
\(960\) −20.2318 + 55.2547i −0.652980 + 1.78334i
\(961\) 6.61671 + 20.3641i 0.213442 + 0.656907i
\(962\) −15.8836 6.51007i −0.512109 0.209893i
\(963\) 50.9468 + 99.9887i 1.64174 + 3.22209i
\(964\) −18.1563 + 36.2991i −0.584775 + 1.16911i
\(965\) 47.2058 20.6338i 1.51961 0.664224i
\(966\) 19.0795 4.65574i 0.613873 0.149796i
\(967\) −35.4037 25.7223i −1.13851 0.827173i −0.151596 0.988443i \(-0.548441\pi\)
−0.986910 + 0.161269i \(0.948441\pi\)
\(968\) −0.172051 0.682965i −0.00552993 0.0219513i
\(969\) 1.22429 7.72988i 0.0393300 0.248320i
\(970\) 50.9373 + 6.86575i 1.63550 + 0.220446i
\(971\) 1.62120 3.18179i 0.0520269 0.102109i −0.863529 0.504299i \(-0.831751\pi\)
0.915556 + 0.402190i \(0.131751\pi\)
\(972\) −43.1283 83.1091i −1.38334 2.66573i
\(973\) −10.9661 + 15.0935i −0.351556 + 0.483875i
\(974\) 21.3193 + 18.0716i 0.683115 + 0.579053i
\(975\) −36.5528 4.34538i −1.17063 0.139164i
\(976\) −2.08980 + 1.56638i −0.0668930 + 0.0501386i
\(977\) −9.54591 + 29.3793i −0.305401 + 0.939926i 0.674127 + 0.738616i \(0.264520\pi\)
−0.979527 + 0.201311i \(0.935480\pi\)
\(978\) 12.8347 + 52.5972i 0.410407 + 1.68187i
\(979\) −0.0259359 0.0356977i −0.000828916 0.00114090i
\(980\) 23.1806 + 8.88118i 0.740477 + 0.283699i
\(981\) 10.2163 10.2163i 0.326181 0.326181i
\(982\) −11.6398 + 19.1540i −0.371440 + 0.611229i
\(983\) −12.7616 12.7616i −0.407032 0.407032i 0.473670 0.880702i \(-0.342929\pi\)
−0.880702 + 0.473670i \(0.842929\pi\)
\(984\) 4.47640 + 59.4048i 0.142702 + 1.89376i
\(985\) 1.47032 24.8234i 0.0468484 0.790940i
\(986\) −9.37638 + 2.28800i −0.298605 + 0.0728649i
\(987\) 22.5933i 0.719152i
\(988\) 15.2378 + 4.82598i 0.484779 + 0.153535i
\(989\) 2.60909 1.89562i 0.0829644 0.0602771i
\(990\) −66.6812 46.1319i −2.11927 1.46617i
\(991\) −30.2050 + 15.3902i −0.959493 + 0.488886i −0.862310 0.506381i \(-0.830983\pi\)
−0.0971827 + 0.995267i \(0.530983\pi\)
\(992\) 3.77146 17.1052i 0.119744 0.543091i
\(993\) −8.05408 8.05408i −0.255588 0.255588i
\(994\) 5.17151 6.10089i 0.164030 0.193508i
\(995\) −3.31818 2.72459i −0.105193 0.0863753i
\(996\) 21.0741 66.5405i 0.667760 2.10842i
\(997\) 1.94646 + 5.99060i 0.0616452 + 0.189724i 0.977136 0.212614i \(-0.0681976\pi\)
−0.915491 + 0.402338i \(0.868198\pi\)
\(998\) 0.665530 8.87863i 0.0210670 0.281048i
\(999\) 84.9284 + 13.4513i 2.68702 + 0.425581i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 820.2.bv.c.207.21 yes 960
4.3 odd 2 inner 820.2.bv.c.207.16 yes 960
5.3 odd 4 820.2.bk.c.43.40 960
20.3 even 4 820.2.bk.c.43.47 yes 960
41.21 even 20 820.2.bk.c.267.47 yes 960
164.103 odd 20 820.2.bk.c.267.40 yes 960
205.103 odd 20 inner 820.2.bv.c.103.16 yes 960
820.103 even 20 inner 820.2.bv.c.103.21 yes 960
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
820.2.bk.c.43.40 960 5.3 odd 4
820.2.bk.c.43.47 yes 960 20.3 even 4
820.2.bk.c.267.40 yes 960 164.103 odd 20
820.2.bk.c.267.47 yes 960 41.21 even 20
820.2.bv.c.103.16 yes 960 205.103 odd 20 inner
820.2.bv.c.103.21 yes 960 820.103 even 20 inner
820.2.bv.c.207.16 yes 960 4.3 odd 2 inner
820.2.bv.c.207.21 yes 960 1.1 even 1 trivial