Properties

Label 76.2.d.a.75.7
Level $76$
Weight $2$
Character 76.75
Analytic conductor $0.607$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.606863055362\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.14453810176.1
Defining polynomial: \(x^{8} + 3 x^{6} + 6 x^{4} + 12 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 75.7
Root \(1.06789 - 0.927153i\) of defining polynomial
Character \(\chi\) \(=\) 76.75
Dual form 76.2.d.a.75.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.06789 - 0.927153i) q^{2} -1.19935 q^{3} +(0.280776 - 1.98019i) q^{4} +1.56155 q^{5} +(-1.28078 + 1.11198i) q^{6} +0.868210i q^{7} +(-1.53610 - 2.37495i) q^{8} -1.56155 q^{9} +O(q^{10})\) \(q+(1.06789 - 0.927153i) q^{2} -1.19935 q^{3} +(0.280776 - 1.98019i) q^{4} +1.56155 q^{5} +(-1.28078 + 1.11198i) q^{6} +0.868210i q^{7} +(-1.53610 - 2.37495i) q^{8} -1.56155 q^{9} +(1.66757 - 1.44780i) q^{10} +3.09218i q^{11} +(-0.336750 + 2.37495i) q^{12} +4.74990i q^{13} +(0.804963 + 0.927153i) q^{14} -1.87285 q^{15} +(-3.84233 - 1.11198i) q^{16} -1.00000 q^{17} +(-1.66757 + 1.44780i) q^{18} +(3.07221 - 3.09218i) q^{19} +(0.438447 - 3.09218i) q^{20} -1.04129i q^{21} +(2.86692 + 3.30210i) q^{22} -3.96039i q^{23} +(1.84233 + 2.84840i) q^{24} -2.56155 q^{25} +(4.40388 + 5.07237i) q^{26} +5.47091 q^{27} +(1.71922 + 0.243773i) q^{28} -8.45851i q^{29} +(-2.00000 + 1.73642i) q^{30} -4.27156 q^{31} +(-5.13416 + 2.37495i) q^{32} -3.70861i q^{33} +(-1.06789 + 0.927153i) q^{34} +1.35576i q^{35} +(-0.438447 + 3.09218i) q^{36} +3.70861i q^{37} +(0.413858 - 6.15051i) q^{38} -5.69681i q^{39} +(-2.39871 - 3.70861i) q^{40} -3.70861i q^{41} +(-0.965435 - 1.11198i) q^{42} +11.0129i q^{43} +(6.12311 + 0.868210i) q^{44} -2.43845 q^{45} +(-3.67188 - 4.22926i) q^{46} -9.27653i q^{47} +(4.60831 + 1.33366i) q^{48} +6.24621 q^{49} +(-2.73546 + 2.37495i) q^{50} +1.19935 q^{51} +(9.40572 + 1.33366i) q^{52} +1.04129i q^{53} +(5.84233 - 5.07237i) q^{54} +4.82860i q^{55} +(2.06196 - 1.33366i) q^{56} +(-3.68466 + 3.70861i) q^{57} +(-7.84233 - 9.03276i) q^{58} +11.6153 q^{59} +(-0.525853 + 3.70861i) q^{60} -0.684658 q^{61} +(-4.56155 + 3.96039i) q^{62} -1.35576i q^{63} +(-3.28078 + 7.29634i) q^{64} +7.41722i q^{65} +(-3.43845 - 3.96039i) q^{66} -9.74247 q^{67} +(-0.280776 + 1.98019i) q^{68} +4.74990i q^{69} +(1.25699 + 1.44780i) q^{70} -10.9418 q^{71} +(2.39871 + 3.70861i) q^{72} +8.12311 q^{73} +(3.43845 + 3.96039i) q^{74} +3.07221 q^{75} +(-5.26050 - 6.95177i) q^{76} -2.68466 q^{77} +(-5.28181 - 6.08356i) q^{78} -8.01726 q^{79} +(-6.00000 - 1.73642i) q^{80} -1.87689 q^{81} +(-3.43845 - 3.96039i) q^{82} +9.65719i q^{83} +(-2.06196 - 0.292370i) q^{84} -1.56155 q^{85} +(10.2107 + 11.7606i) q^{86} +10.1447i q^{87} +(7.34376 - 4.74990i) q^{88} -5.79119i q^{89} +(-2.60399 + 2.26081i) q^{90} -4.12391 q^{91} +(-7.84233 - 1.11198i) q^{92} +5.12311 q^{93} +(-8.60076 - 9.90631i) q^{94} +(4.79741 - 4.82860i) q^{95} +(6.15767 - 2.84840i) q^{96} +16.9170i q^{97} +(6.67026 - 5.79119i) q^{98} -4.82860i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 6q^{4} - 4q^{5} - 2q^{6} + 4q^{9} + O(q^{10}) \) \( 8q - 6q^{4} - 4q^{5} - 2q^{6} + 4q^{9} - 6q^{16} - 8q^{17} + 20q^{20} - 10q^{24} - 4q^{25} - 6q^{26} + 22q^{28} - 16q^{30} - 20q^{36} + 18q^{38} + 50q^{42} + 16q^{44} - 36q^{45} - 16q^{49} + 22q^{54} + 20q^{57} - 38q^{58} + 44q^{61} - 20q^{62} - 18q^{64} - 44q^{66} + 6q^{68} + 32q^{73} + 44q^{74} - 16q^{76} + 28q^{77} - 48q^{80} - 48q^{81} - 44q^{82} + 4q^{85} - 38q^{92} + 8q^{93} + 74q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(-1\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.06789 0.927153i 0.755112 0.655596i
\(3\) −1.19935 −0.692447 −0.346223 0.938152i \(-0.612536\pi\)
−0.346223 + 0.938152i \(0.612536\pi\)
\(4\) 0.280776 1.98019i 0.140388 0.990097i
\(5\) 1.56155 0.698348 0.349174 0.937058i \(-0.386462\pi\)
0.349174 + 0.937058i \(0.386462\pi\)
\(6\) −1.28078 + 1.11198i −0.522875 + 0.453965i
\(7\) 0.868210i 0.328153i 0.986448 + 0.164076i \(0.0524643\pi\)
−0.986448 + 0.164076i \(0.947536\pi\)
\(8\) −1.53610 2.37495i −0.543094 0.839672i
\(9\) −1.56155 −0.520518
\(10\) 1.66757 1.44780i 0.527331 0.457834i
\(11\) 3.09218i 0.932326i 0.884699 + 0.466163i \(0.154364\pi\)
−0.884699 + 0.466163i \(0.845636\pi\)
\(12\) −0.336750 + 2.37495i −0.0972113 + 0.685589i
\(13\) 4.74990i 1.31739i 0.752412 + 0.658693i \(0.228890\pi\)
−0.752412 + 0.658693i \(0.771110\pi\)
\(14\) 0.804963 + 0.927153i 0.215135 + 0.247792i
\(15\) −1.87285 −0.483569
\(16\) −3.84233 1.11198i −0.960582 0.277996i
\(17\) −1.00000 −0.242536 −0.121268 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) −1.66757 + 1.44780i −0.393049 + 0.341249i
\(19\) 3.07221 3.09218i 0.704812 0.709394i
\(20\) 0.438447 3.09218i 0.0980398 0.691432i
\(21\) 1.04129i 0.227228i
\(22\) 2.86692 + 3.30210i 0.611229 + 0.704011i
\(23\) 3.96039i 0.825798i −0.910777 0.412899i \(-0.864516\pi\)
0.910777 0.412899i \(-0.135484\pi\)
\(24\) 1.84233 + 2.84840i 0.376064 + 0.581428i
\(25\) −2.56155 −0.512311
\(26\) 4.40388 + 5.07237i 0.863672 + 0.994773i
\(27\) 5.47091 1.05288
\(28\) 1.71922 + 0.243773i 0.324903 + 0.0460687i
\(29\) 8.45851i 1.57071i −0.619048 0.785353i \(-0.712481\pi\)
0.619048 0.785353i \(-0.287519\pi\)
\(30\) −2.00000 + 1.73642i −0.365148 + 0.317025i
\(31\) −4.27156 −0.767195 −0.383597 0.923500i \(-0.625315\pi\)
−0.383597 + 0.923500i \(0.625315\pi\)
\(32\) −5.13416 + 2.37495i −0.907600 + 0.419836i
\(33\) 3.70861i 0.645586i
\(34\) −1.06789 + 0.927153i −0.183142 + 0.159005i
\(35\) 1.35576i 0.229165i
\(36\) −0.438447 + 3.09218i −0.0730745 + 0.515363i
\(37\) 3.70861i 0.609692i 0.952402 + 0.304846i \(0.0986050\pi\)
−0.952402 + 0.304846i \(0.901395\pi\)
\(38\) 0.413858 6.15051i 0.0671366 0.997744i
\(39\) 5.69681i 0.912219i
\(40\) −2.39871 3.70861i −0.379269 0.586383i
\(41\) 3.70861i 0.579188i −0.957150 0.289594i \(-0.906480\pi\)
0.957150 0.289594i \(-0.0935202\pi\)
\(42\) −0.965435 1.11198i −0.148970 0.171583i
\(43\) 11.0129i 1.67946i 0.543005 + 0.839729i \(0.317286\pi\)
−0.543005 + 0.839729i \(0.682714\pi\)
\(44\) 6.12311 + 0.868210i 0.923093 + 0.130888i
\(45\) −2.43845 −0.363502
\(46\) −3.67188 4.22926i −0.541389 0.623570i
\(47\) 9.27653i 1.35312i −0.736387 0.676560i \(-0.763470\pi\)
0.736387 0.676560i \(-0.236530\pi\)
\(48\) 4.60831 + 1.33366i 0.665152 + 0.192497i
\(49\) 6.24621 0.892316
\(50\) −2.73546 + 2.37495i −0.386852 + 0.335869i
\(51\) 1.19935 0.167943
\(52\) 9.40572 + 1.33366i 1.30434 + 0.184945i
\(53\) 1.04129i 0.143032i 0.997439 + 0.0715161i \(0.0227837\pi\)
−0.997439 + 0.0715161i \(0.977216\pi\)
\(54\) 5.84233 5.07237i 0.795040 0.690262i
\(55\) 4.82860i 0.651088i
\(56\) 2.06196 1.33366i 0.275540 0.178218i
\(57\) −3.68466 + 3.70861i −0.488045 + 0.491217i
\(58\) −7.84233 9.03276i −1.02975 1.18606i
\(59\) 11.6153 1.51219 0.756093 0.654464i \(-0.227106\pi\)
0.756093 + 0.654464i \(0.227106\pi\)
\(60\) −0.525853 + 3.70861i −0.0678873 + 0.478780i
\(61\) −0.684658 −0.0876615 −0.0438308 0.999039i \(-0.513956\pi\)
−0.0438308 + 0.999039i \(0.513956\pi\)
\(62\) −4.56155 + 3.96039i −0.579318 + 0.502970i
\(63\) 1.35576i 0.170809i
\(64\) −3.28078 + 7.29634i −0.410097 + 0.912042i
\(65\) 7.41722i 0.919993i
\(66\) −3.43845 3.96039i −0.423244 0.487490i
\(67\) −9.74247 −1.19023 −0.595116 0.803640i \(-0.702894\pi\)
−0.595116 + 0.803640i \(0.702894\pi\)
\(68\) −0.280776 + 1.98019i −0.0340491 + 0.240134i
\(69\) 4.74990i 0.571821i
\(70\) 1.25699 + 1.44780i 0.150239 + 0.173045i
\(71\) −10.9418 −1.29856 −0.649278 0.760551i \(-0.724929\pi\)
−0.649278 + 0.760551i \(0.724929\pi\)
\(72\) 2.39871 + 3.70861i 0.282690 + 0.437064i
\(73\) 8.12311 0.950738 0.475369 0.879787i \(-0.342315\pi\)
0.475369 + 0.879787i \(0.342315\pi\)
\(74\) 3.43845 + 3.96039i 0.399711 + 0.460386i
\(75\) 3.07221 0.354748
\(76\) −5.26050 6.95177i −0.603421 0.797423i
\(77\) −2.68466 −0.305945
\(78\) −5.28181 6.08356i −0.598047 0.688828i
\(79\) −8.01726 −0.902013 −0.451006 0.892521i \(-0.648935\pi\)
−0.451006 + 0.892521i \(0.648935\pi\)
\(80\) −6.00000 1.73642i −0.670820 0.194138i
\(81\) −1.87689 −0.208544
\(82\) −3.43845 3.96039i −0.379713 0.437351i
\(83\) 9.65719i 1.06001i 0.847993 + 0.530007i \(0.177811\pi\)
−0.847993 + 0.530007i \(0.822189\pi\)
\(84\) −2.06196 0.292370i −0.224978 0.0319002i
\(85\) −1.56155 −0.169374
\(86\) 10.2107 + 11.7606i 1.10105 + 1.26818i
\(87\) 10.1447i 1.08763i
\(88\) 7.34376 4.74990i 0.782848 0.506341i
\(89\) 5.79119i 0.613865i −0.951731 0.306932i \(-0.900697\pi\)
0.951731 0.306932i \(-0.0993026\pi\)
\(90\) −2.60399 + 2.26081i −0.274485 + 0.238311i
\(91\) −4.12391 −0.432303
\(92\) −7.84233 1.11198i −0.817619 0.115932i
\(93\) 5.12311 0.531241
\(94\) −8.60076 9.90631i −0.887100 1.02176i
\(95\) 4.79741 4.82860i 0.492204 0.495404i
\(96\) 6.15767 2.84840i 0.628465 0.290714i
\(97\) 16.9170i 1.71766i 0.512258 + 0.858832i \(0.328809\pi\)
−0.512258 + 0.858832i \(0.671191\pi\)
\(98\) 6.67026 5.79119i 0.673798 0.584999i
\(99\) 4.82860i 0.485292i
\(100\) −0.719224 + 5.07237i −0.0719224 + 0.507237i
\(101\) 8.24621 0.820529 0.410264 0.911967i \(-0.365436\pi\)
0.410264 + 0.911967i \(0.365436\pi\)
\(102\) 1.28078 1.11198i 0.126816 0.110103i
\(103\) 3.74571 0.369075 0.184538 0.982825i \(-0.440921\pi\)
0.184538 + 0.982825i \(0.440921\pi\)
\(104\) 11.2808 7.29634i 1.10617 0.715465i
\(105\) 1.62603i 0.158684i
\(106\) 0.965435 + 1.11198i 0.0937713 + 0.108005i
\(107\) 7.86962 0.760785 0.380392 0.924825i \(-0.375789\pi\)
0.380392 + 0.924825i \(0.375789\pi\)
\(108\) 1.53610 10.8335i 0.147812 1.04245i
\(109\) 15.8757i 1.52062i −0.649561 0.760310i \(-0.725047\pi\)
0.649561 0.760310i \(-0.274953\pi\)
\(110\) 4.47685 + 5.15641i 0.426850 + 0.491644i
\(111\) 4.44793i 0.422179i
\(112\) 0.965435 3.33595i 0.0912250 0.315218i
\(113\) 3.70861i 0.348877i 0.984668 + 0.174438i \(0.0558110\pi\)
−0.984668 + 0.174438i \(0.944189\pi\)
\(114\) −0.496361 + 7.37663i −0.0464885 + 0.690884i
\(115\) 6.18435i 0.576694i
\(116\) −16.7495 2.37495i −1.55515 0.220509i
\(117\) 7.41722i 0.685722i
\(118\) 12.4039 10.7692i 1.14187 0.991383i
\(119\) 0.868210i 0.0795887i
\(120\) 2.87689 + 4.44793i 0.262623 + 0.406039i
\(121\) 1.43845 0.130768
\(122\) −0.731140 + 0.634783i −0.0661943 + 0.0574705i
\(123\) 4.44793i 0.401057i
\(124\) −1.19935 + 8.45851i −0.107705 + 0.759597i
\(125\) −11.8078 −1.05612
\(126\) −1.25699 1.44780i −0.111982 0.128980i
\(127\) 1.87285 0.166189 0.0830944 0.996542i \(-0.473520\pi\)
0.0830944 + 0.996542i \(0.473520\pi\)
\(128\) 3.26131 + 10.8335i 0.288262 + 0.957552i
\(129\) 13.2084i 1.16294i
\(130\) 6.87689 + 7.92077i 0.603144 + 0.694698i
\(131\) 4.82860i 0.421876i −0.977499 0.210938i \(-0.932348\pi\)
0.977499 0.210938i \(-0.0676519\pi\)
\(132\) −7.34376 1.04129i −0.639193 0.0906327i
\(133\) 2.68466 + 2.66732i 0.232789 + 0.231286i
\(134\) −10.4039 + 9.03276i −0.898759 + 0.780311i
\(135\) 8.54312 0.735274
\(136\) 1.53610 + 2.37495i 0.131720 + 0.203650i
\(137\) −3.87689 −0.331225 −0.165613 0.986191i \(-0.552960\pi\)
−0.165613 + 0.986191i \(0.552960\pi\)
\(138\) 4.40388 + 5.07237i 0.374883 + 0.431789i
\(139\) 0.380664i 0.0322875i −0.999870 0.0161438i \(-0.994861\pi\)
0.999870 0.0161438i \(-0.00513894\pi\)
\(140\) 2.68466 + 0.380664i 0.226895 + 0.0321720i
\(141\) 11.1258i 0.936964i
\(142\) −11.6847 + 10.1447i −0.980555 + 0.851328i
\(143\) −14.6875 −1.22823
\(144\) 6.00000 + 1.73642i 0.500000 + 0.144702i
\(145\) 13.2084i 1.09690i
\(146\) 8.67458 7.53136i 0.717913 0.623300i
\(147\) −7.49141 −0.617881
\(148\) 7.34376 + 1.04129i 0.603654 + 0.0855935i
\(149\) −17.8078 −1.45887 −0.729434 0.684051i \(-0.760217\pi\)
−0.729434 + 0.684051i \(0.760217\pi\)
\(150\) 3.28078 2.84840i 0.267874 0.232571i
\(151\) 24.2824 1.97607 0.988035 0.154231i \(-0.0492900\pi\)
0.988035 + 0.154231i \(0.0492900\pi\)
\(152\) −12.0630 2.54643i −0.978437 0.206543i
\(153\) 1.56155 0.126244
\(154\) −2.86692 + 2.48909i −0.231023 + 0.200576i
\(155\) −6.67026 −0.535769
\(156\) −11.2808 1.59953i −0.903185 0.128065i
\(157\) 6.00000 0.478852 0.239426 0.970915i \(-0.423041\pi\)
0.239426 + 0.970915i \(0.423041\pi\)
\(158\) −8.56155 + 7.43323i −0.681121 + 0.591356i
\(159\) 1.24887i 0.0990422i
\(160\) −8.01726 + 3.70861i −0.633820 + 0.293191i
\(161\) 3.43845 0.270988
\(162\) −2.00432 + 1.74017i −0.157474 + 0.136720i
\(163\) 10.6323i 0.832785i −0.909185 0.416392i \(-0.863294\pi\)
0.909185 0.416392i \(-0.136706\pi\)
\(164\) −7.34376 1.04129i −0.573452 0.0813111i
\(165\) 5.79119i 0.450844i
\(166\) 8.95369 + 10.3128i 0.694941 + 0.800430i
\(167\) 0.525853 0.0406917 0.0203459 0.999793i \(-0.493523\pi\)
0.0203459 + 0.999793i \(0.493523\pi\)
\(168\) −2.47301 + 1.59953i −0.190797 + 0.123406i
\(169\) −9.56155 −0.735504
\(170\) −1.66757 + 1.44780i −0.127896 + 0.111041i
\(171\) −4.79741 + 4.82860i −0.366867 + 0.369252i
\(172\) 21.8078 + 3.09218i 1.66283 + 0.235776i
\(173\) 16.9170i 1.28618i 0.765792 + 0.643089i \(0.222347\pi\)
−0.765792 + 0.643089i \(0.777653\pi\)
\(174\) 9.40572 + 10.8335i 0.713046 + 0.821283i
\(175\) 2.22397i 0.168116i
\(176\) 3.43845 11.8812i 0.259183 0.895576i
\(177\) −13.9309 −1.04711
\(178\) −5.36932 6.18435i −0.402447 0.463537i
\(179\) 9.06897 0.677847 0.338923 0.940814i \(-0.389937\pi\)
0.338923 + 0.940814i \(0.389937\pi\)
\(180\) −0.684658 + 4.82860i −0.0510314 + 0.359902i
\(181\) 2.08258i 0.154797i 0.997000 + 0.0773985i \(0.0246614\pi\)
−0.997000 + 0.0773985i \(0.975339\pi\)
\(182\) −4.40388 + 3.82349i −0.326437 + 0.283416i
\(183\) 0.821147 0.0607009
\(184\) −9.40572 + 6.08356i −0.693399 + 0.448486i
\(185\) 5.79119i 0.425777i
\(186\) 5.47091 4.74990i 0.401147 0.348280i
\(187\) 3.09218i 0.226122i
\(188\) −18.3693 2.60463i −1.33972 0.189962i
\(189\) 4.74990i 0.345504i
\(190\) 0.646260 9.60434i 0.0468847 0.696772i
\(191\) 8.78898i 0.635948i 0.948099 + 0.317974i \(0.103003\pi\)
−0.948099 + 0.317974i \(0.896997\pi\)
\(192\) 3.93481 8.75088i 0.283970 0.631540i
\(193\) 3.70861i 0.266952i −0.991052 0.133476i \(-0.957386\pi\)
0.991052 0.133476i \(-0.0426138\pi\)
\(194\) 15.6847 + 18.0655i 1.12609 + 1.29703i
\(195\) 8.89586i 0.637046i
\(196\) 1.75379 12.3687i 0.125271 0.883479i
\(197\) 10.4924 0.747554 0.373777 0.927519i \(-0.378063\pi\)
0.373777 + 0.927519i \(0.378063\pi\)
\(198\) −4.47685 5.15641i −0.318156 0.366450i
\(199\) 13.2369i 0.938340i 0.883108 + 0.469170i \(0.155447\pi\)
−0.883108 + 0.469170i \(0.844553\pi\)
\(200\) 3.93481 + 6.08356i 0.278233 + 0.430173i
\(201\) 11.6847 0.824172
\(202\) 8.80604 7.64550i 0.619591 0.537935i
\(203\) 7.34376 0.515431
\(204\) 0.336750 2.37495i 0.0235772 0.166280i
\(205\) 5.79119i 0.404474i
\(206\) 4.00000 3.47284i 0.278693 0.241964i
\(207\) 6.18435i 0.429842i
\(208\) 5.28181 18.2507i 0.366228 1.26546i
\(209\) 9.56155 + 9.49980i 0.661386 + 0.657115i
\(210\) −1.50758 1.73642i −0.104033 0.119824i
\(211\) −2.02050 −0.139097 −0.0695485 0.997579i \(-0.522156\pi\)
−0.0695485 + 0.997579i \(0.522156\pi\)
\(212\) 2.06196 + 0.292370i 0.141616 + 0.0200800i
\(213\) 13.1231 0.899180
\(214\) 8.40388 7.29634i 0.574478 0.498767i
\(215\) 17.1973i 1.17285i
\(216\) −8.40388 12.9931i −0.571812 0.884071i
\(217\) 3.70861i 0.251757i
\(218\) −14.7192 16.9535i −0.996912 1.14824i
\(219\) −9.74247 −0.658335
\(220\) 9.56155 + 1.35576i 0.644640 + 0.0914050i
\(221\) 4.74990i 0.319513i
\(222\) −4.12391 4.74990i −0.276779 0.318792i
\(223\) −16.2651 −1.08919 −0.544595 0.838699i \(-0.683317\pi\)
−0.544595 + 0.838699i \(0.683317\pi\)
\(224\) −2.06196 4.45753i −0.137770 0.297831i
\(225\) 4.00000 0.266667
\(226\) 3.43845 + 3.96039i 0.228722 + 0.263441i
\(227\) −17.4644 −1.15916 −0.579578 0.814917i \(-0.696783\pi\)
−0.579578 + 0.814917i \(0.696783\pi\)
\(228\) 6.30920 + 8.33763i 0.417837 + 0.552173i
\(229\) −2.43845 −0.161137 −0.0805686 0.996749i \(-0.525674\pi\)
−0.0805686 + 0.996749i \(0.525674\pi\)
\(230\) −5.73384 6.60421i −0.378078 0.435468i
\(231\) 3.21985 0.211851
\(232\) −20.0885 + 12.9931i −1.31888 + 0.853042i
\(233\) −9.80776 −0.642528 −0.321264 0.946990i \(-0.604108\pi\)
−0.321264 + 0.946990i \(0.604108\pi\)
\(234\) −6.87689 7.92077i −0.449557 0.517797i
\(235\) 14.4858i 0.944949i
\(236\) 3.26131 23.0006i 0.212293 1.49721i
\(237\) 9.61553 0.624596
\(238\) −0.804963 0.927153i −0.0521780 0.0600984i
\(239\) 19.4213i 1.25626i −0.778110 0.628129i \(-0.783821\pi\)
0.778110 0.628129i \(-0.216179\pi\)
\(240\) 7.19612 + 2.08258i 0.464507 + 0.134430i
\(241\) 15.2910i 0.984979i 0.870318 + 0.492490i \(0.163913\pi\)
−0.870318 + 0.492490i \(0.836087\pi\)
\(242\) 1.53610 1.33366i 0.0987444 0.0857309i
\(243\) −14.1617 −0.908472
\(244\) −0.192236 + 1.35576i −0.0123066 + 0.0867934i
\(245\) 9.75379 0.623147
\(246\) 4.12391 + 4.74990i 0.262931 + 0.302843i
\(247\) 14.6875 + 14.5927i 0.934545 + 0.928509i
\(248\) 6.56155 + 10.1447i 0.416659 + 0.644192i
\(249\) 11.5824i 0.734004i
\(250\) −12.6094 + 10.9476i −0.797488 + 0.692387i
\(251\) 22.4066i 1.41429i 0.707069 + 0.707145i \(0.250017\pi\)
−0.707069 + 0.707145i \(0.749983\pi\)
\(252\) −2.68466 0.380664i −0.169118 0.0239796i
\(253\) 12.2462 0.769913
\(254\) 2.00000 1.73642i 0.125491 0.108953i
\(255\) 1.87285 0.117283
\(256\) 13.5270 + 8.54521i 0.845437 + 0.534076i
\(257\) 18.9996i 1.18516i −0.805511 0.592581i \(-0.798109\pi\)
0.805511 0.592581i \(-0.201891\pi\)
\(258\) −12.2462 14.1051i −0.762416 0.878147i
\(259\) −3.21985 −0.200072
\(260\) 14.6875 + 2.08258i 0.910882 + 0.129156i
\(261\) 13.2084i 0.817580i
\(262\) −4.47685 5.15641i −0.276580 0.318564i
\(263\) 6.56502i 0.404816i 0.979301 + 0.202408i \(0.0648768\pi\)
−0.979301 + 0.202408i \(0.935123\pi\)
\(264\) −8.80776 + 5.69681i −0.542080 + 0.350614i
\(265\) 1.62603i 0.0998862i
\(266\) 5.33993 + 0.359315i 0.327412 + 0.0220310i
\(267\) 6.94568i 0.425069i
\(268\) −2.73546 + 19.2920i −0.167095 + 1.17844i
\(269\) 3.70861i 0.226118i −0.993588 0.113059i \(-0.963935\pi\)
0.993588 0.113059i \(-0.0360649\pi\)
\(270\) 9.12311 7.92077i 0.555215 0.482043i
\(271\) 15.3540i 0.932689i −0.884603 0.466345i \(-0.845571\pi\)
0.884603 0.466345i \(-0.154429\pi\)
\(272\) 3.84233 + 1.11198i 0.232975 + 0.0674239i
\(273\) 4.94602 0.299347
\(274\) −4.14010 + 3.59447i −0.250112 + 0.217150i
\(275\) 7.92077i 0.477641i
\(276\) 9.40572 + 1.33366i 0.566158 + 0.0802769i
\(277\) −24.0540 −1.44526 −0.722632 0.691233i \(-0.757068\pi\)
−0.722632 + 0.691233i \(0.757068\pi\)
\(278\) −0.352934 0.406507i −0.0211676 0.0243807i
\(279\) 6.67026 0.399338
\(280\) 3.21985 2.08258i 0.192423 0.124458i
\(281\) 11.5824i 0.690947i 0.938429 + 0.345473i \(0.112282\pi\)
−0.938429 + 0.345473i \(0.887718\pi\)
\(282\) 10.3153 + 11.8812i 0.614270 + 0.707513i
\(283\) 4.82860i 0.287030i −0.989648 0.143515i \(-0.954159\pi\)
0.989648 0.143515i \(-0.0458406\pi\)
\(284\) −3.07221 + 21.6669i −0.182302 + 1.28570i
\(285\) −5.75379 + 5.79119i −0.340825 + 0.343041i
\(286\) −15.6847 + 13.6176i −0.927453 + 0.805224i
\(287\) 3.21985 0.190062
\(288\) 8.01726 3.70861i 0.472422 0.218532i
\(289\) −16.0000 −0.941176
\(290\) −12.2462 14.1051i −0.719122 0.828281i
\(291\) 20.2895i 1.18939i
\(292\) 2.28078 16.0853i 0.133472 0.941322i
\(293\) 4.74990i 0.277492i −0.990328 0.138746i \(-0.955693\pi\)
0.990328 0.138746i \(-0.0443072\pi\)
\(294\) −8.00000 + 6.94568i −0.466569 + 0.405080i
\(295\) 18.1379 1.05603
\(296\) 8.80776 5.69681i 0.511941 0.331120i
\(297\) 16.9170i 0.981625i
\(298\) −19.0167 + 16.5105i −1.10161 + 0.956428i
\(299\) 18.8114 1.08789
\(300\) 0.862603 6.08356i 0.0498024 0.351235i
\(301\) −9.56155 −0.551119
\(302\) 25.9309 22.5134i 1.49215 1.29550i
\(303\) −9.89012 −0.568172
\(304\) −15.2429 + 8.46492i −0.874239 + 0.485496i
\(305\) −1.06913 −0.0612182
\(306\) 1.66757 1.44780i 0.0953284 0.0827651i
\(307\) −8.01726 −0.457569 −0.228785 0.973477i \(-0.573475\pi\)
−0.228785 + 0.973477i \(0.573475\pi\)
\(308\) −0.753789 + 5.31614i −0.0429511 + 0.302915i
\(309\) −4.49242 −0.255565
\(310\) −7.12311 + 6.18435i −0.404565 + 0.351248i
\(311\) 0.868210i 0.0492317i 0.999697 + 0.0246158i \(0.00783626\pi\)
−0.999697 + 0.0246158i \(0.992164\pi\)
\(312\) −13.5296 + 8.75088i −0.765965 + 0.495421i
\(313\) −4.56155 −0.257834 −0.128917 0.991655i \(-0.541150\pi\)
−0.128917 + 0.991655i \(0.541150\pi\)
\(314\) 6.40734 5.56292i 0.361587 0.313933i
\(315\) 2.11708i 0.119284i
\(316\) −2.25106 + 15.8757i −0.126632 + 0.893080i
\(317\) 4.74990i 0.266781i 0.991064 + 0.133390i \(0.0425864\pi\)
−0.991064 + 0.133390i \(0.957414\pi\)
\(318\) −1.15790 1.33366i −0.0649316 0.0747879i
\(319\) 26.1552 1.46441
\(320\) −5.12311 + 11.3936i −0.286390 + 0.636922i
\(321\) −9.43845 −0.526803
\(322\) 3.67188 3.18796i 0.204626 0.177658i
\(323\) −3.07221 + 3.09218i −0.170942 + 0.172053i
\(324\) −0.526988 + 3.71661i −0.0292771 + 0.206479i
\(325\) 12.1671i 0.674910i
\(326\) −9.85775 11.3541i −0.545970 0.628846i
\(327\) 19.0406i 1.05295i
\(328\) −8.80776 + 5.69681i −0.486327 + 0.314554i
\(329\) 8.05398 0.444030
\(330\) −5.36932 6.18435i −0.295571 0.340437i
\(331\) 2.25106 0.123729 0.0618647 0.998085i \(-0.480295\pi\)
0.0618647 + 0.998085i \(0.480295\pi\)
\(332\) 19.1231 + 2.71151i 1.04952 + 0.148814i
\(333\) 5.79119i 0.317355i
\(334\) 0.561553 0.487546i 0.0307268 0.0266773i
\(335\) −15.2134 −0.831196
\(336\) −1.15790 + 4.00098i −0.0631685 + 0.218271i
\(337\) 26.4168i 1.43902i −0.694484 0.719508i \(-0.744367\pi\)
0.694484 0.719508i \(-0.255633\pi\)
\(338\) −10.2107 + 8.86502i −0.555388 + 0.482193i
\(339\) 4.44793i 0.241579i
\(340\) −0.438447 + 3.09218i −0.0237781 + 0.167697i
\(341\) 13.2084i 0.715276i
\(342\) −0.646260 + 9.60434i −0.0349458 + 0.519343i
\(343\) 11.5005i 0.620968i
\(344\) 26.1552 16.9170i 1.41019 0.912105i
\(345\) 7.41722i 0.399330i
\(346\) 15.6847 + 18.0655i 0.843212 + 0.971208i
\(347\) 24.1430i 1.29606i −0.761613 0.648032i \(-0.775592\pi\)
0.761613 0.648032i \(-0.224408\pi\)
\(348\) 20.0885 + 2.84840i 1.07686 + 0.152690i
\(349\) −28.0540 −1.50169 −0.750847 0.660476i \(-0.770355\pi\)
−0.750847 + 0.660476i \(0.770355\pi\)
\(350\) −2.06196 2.37495i −0.110216 0.126946i
\(351\) 25.9863i 1.38705i
\(352\) −7.34376 15.8757i −0.391424 0.846179i
\(353\) 6.31534 0.336132 0.168066 0.985776i \(-0.446248\pi\)
0.168066 + 0.985776i \(0.446248\pi\)
\(354\) −14.8766 + 12.9160i −0.790684 + 0.686480i
\(355\) −17.0862 −0.906843
\(356\) −11.4677 1.62603i −0.607786 0.0861794i
\(357\) 1.04129i 0.0551109i
\(358\) 9.68466 8.40832i 0.511850 0.444393i
\(359\) 27.3420i 1.44306i −0.692384 0.721529i \(-0.743440\pi\)
0.692384 0.721529i \(-0.256560\pi\)
\(360\) 3.74571 + 5.79119i 0.197416 + 0.305223i
\(361\) −0.123106 18.9996i −0.00647924 0.999979i
\(362\) 1.93087 + 2.22397i 0.101484 + 0.116889i
\(363\) −1.72521 −0.0905498
\(364\) −1.15790 + 8.16614i −0.0606903 + 0.428022i
\(365\) 12.6847 0.663945
\(366\) 0.876894 0.761329i 0.0458360 0.0397953i
\(367\) 14.1051i 0.736282i −0.929770 0.368141i \(-0.879994\pi\)
0.929770 0.368141i \(-0.120006\pi\)
\(368\) −4.40388 + 15.2171i −0.229568 + 0.793247i
\(369\) 5.79119i 0.301477i
\(370\) 5.36932 + 6.18435i 0.279137 + 0.321509i
\(371\) −0.904059 −0.0469364
\(372\) 1.43845 10.1447i 0.0745800 0.525980i
\(373\) 12.1671i 0.629990i −0.949093 0.314995i \(-0.897997\pi\)
0.949093 0.314995i \(-0.102003\pi\)
\(374\) −2.86692 3.30210i −0.148245 0.170748i
\(375\) 14.1617 0.731306
\(376\) −22.0313 + 14.2497i −1.13618 + 0.734872i
\(377\) 40.1771 2.06922
\(378\) 4.40388 + 5.07237i 0.226511 + 0.260895i
\(379\) 6.81791 0.350213 0.175106 0.984550i \(-0.443973\pi\)
0.175106 + 0.984550i \(0.443973\pi\)
\(380\) −8.21455 10.8556i −0.421398 0.556878i
\(381\) −2.24621 −0.115077
\(382\) 8.14873 + 9.38566i 0.416925 + 0.480212i
\(383\) 16.2651 0.831107 0.415554 0.909569i \(-0.363588\pi\)
0.415554 + 0.909569i \(0.363588\pi\)
\(384\) −3.91146 12.9931i −0.199606 0.663053i
\(385\) −4.19224 −0.213656
\(386\) −3.43845 3.96039i −0.175012 0.201578i
\(387\) 17.1973i 0.874188i
\(388\) 33.4990 + 4.74990i 1.70065 + 0.241140i
\(389\) −5.80776 −0.294465 −0.147233 0.989102i \(-0.547037\pi\)
−0.147233 + 0.989102i \(0.547037\pi\)
\(390\) −8.24782 9.49980i −0.417645 0.481041i
\(391\) 3.96039i 0.200285i
\(392\) −9.59482 14.8344i −0.484612 0.749252i
\(393\) 5.79119i 0.292127i
\(394\) 11.2047 9.72808i 0.564487 0.490093i
\(395\) −12.5194 −0.629918
\(396\) −9.56155 1.35576i −0.480486 0.0681293i
\(397\) 24.9309 1.25124 0.625622 0.780126i \(-0.284845\pi\)
0.625622 + 0.780126i \(0.284845\pi\)
\(398\) 12.2726 + 14.1356i 0.615172 + 0.708552i
\(399\) −3.21985 3.19906i −0.161194 0.160153i
\(400\) 9.84233 + 2.84840i 0.492116 + 0.142420i
\(401\) 20.6256i 1.02999i −0.857192 0.514997i \(-0.827793\pi\)
0.857192 0.514997i \(-0.172207\pi\)
\(402\) 12.4779 10.8335i 0.622342 0.540324i
\(403\) 20.2895i 1.01069i
\(404\) 2.31534 16.3291i 0.115193 0.812403i
\(405\) −2.93087 −0.145636
\(406\) 7.84233 6.80879i 0.389208 0.337915i
\(407\) −11.4677 −0.568432
\(408\) −1.84233 2.84840i −0.0912089 0.141017i
\(409\) 18.5431i 0.916895i 0.888722 + 0.458447i \(0.151594\pi\)
−0.888722 + 0.458447i \(0.848406\pi\)
\(410\) −5.36932 6.18435i −0.265172 0.305423i
\(411\) 4.64976 0.229356
\(412\) 1.05171 7.41722i 0.0518138 0.365420i
\(413\) 10.0845i 0.496228i
\(414\) 5.73384 + 6.60421i 0.281803 + 0.324579i
\(415\) 15.0802i 0.740259i
\(416\) −11.2808 24.3868i −0.553086 1.19566i
\(417\) 0.456551i 0.0223574i
\(418\) 19.0184 + 1.27972i 0.930223 + 0.0625932i
\(419\) 27.4489i 1.34097i 0.741924 + 0.670484i \(0.233913\pi\)
−0.741924 + 0.670484i \(0.766087\pi\)
\(420\) −3.21985 0.456551i −0.157113 0.0222774i
\(421\) 23.2930i 1.13523i 0.823294 + 0.567614i \(0.192134\pi\)
−0.823294 + 0.567614i \(0.807866\pi\)
\(422\) −2.15767 + 1.87331i −0.105034 + 0.0911914i
\(423\) 14.4858i 0.704323i
\(424\) 2.47301 1.59953i 0.120100 0.0776800i
\(425\) 2.56155 0.124254
\(426\) 14.0140 12.1671i 0.678982 0.589499i
\(427\) 0.594427i 0.0287664i
\(428\) 2.20960 15.5834i 0.106805 0.753250i
\(429\) 17.6155 0.850486
\(430\) 15.9445 + 18.3648i 0.768913 + 0.885630i
\(431\) −17.0862 −0.823015 −0.411507 0.911406i \(-0.634998\pi\)
−0.411507 + 0.911406i \(0.634998\pi\)
\(432\) −21.0210 6.08356i −1.01138 0.292695i
\(433\) 28.0429i 1.34765i 0.738889 + 0.673827i \(0.235351\pi\)
−0.738889 + 0.673827i \(0.764649\pi\)
\(434\) −3.43845 3.96039i −0.165051 0.190105i
\(435\) 15.8415i 0.759544i
\(436\) −31.4370 4.45753i −1.50556 0.213477i
\(437\) −12.2462 12.1671i −0.585816 0.582032i
\(438\) −10.4039 + 9.03276i −0.497117 + 0.431602i
\(439\) −24.8082 −1.18403 −0.592015 0.805927i \(-0.701668\pi\)
−0.592015 + 0.805927i \(0.701668\pi\)
\(440\) 11.4677 7.41722i 0.546700 0.353602i
\(441\) −9.75379 −0.464466
\(442\) −4.40388 5.07237i −0.209471 0.241268i
\(443\) 34.7753i 1.65222i 0.563507 + 0.826111i \(0.309452\pi\)
−0.563507 + 0.826111i \(0.690548\pi\)
\(444\) −8.80776 1.24887i −0.417998 0.0592690i
\(445\) 9.04325i 0.428691i
\(446\) −17.3693 + 15.0802i −0.822461 + 0.714069i
\(447\) 21.3578 1.01019
\(448\) −6.33475 2.84840i −0.299289 0.134574i
\(449\) 35.9166i 1.69501i 0.530787 + 0.847505i \(0.321896\pi\)
−0.530787 + 0.847505i \(0.678104\pi\)
\(450\) 4.27156 3.70861i 0.201363 0.174826i
\(451\) 11.4677 0.539992
\(452\) 7.34376 + 1.04129i 0.345422 + 0.0489782i
\(453\) −29.1231 −1.36832
\(454\) −18.6501 + 16.1922i −0.875292 + 0.759938i
\(455\) −6.43971 −0.301898
\(456\) 14.4678 + 3.05407i 0.677516 + 0.143020i
\(457\) 12.1231 0.567095 0.283547 0.958958i \(-0.408489\pi\)
0.283547 + 0.958958i \(0.408489\pi\)
\(458\) −2.60399 + 2.26081i −0.121677 + 0.105641i
\(459\) −5.47091 −0.255360
\(460\) −12.2462 1.73642i −0.570983 0.0809610i
\(461\) 19.3153 0.899605 0.449803 0.893128i \(-0.351494\pi\)
0.449803 + 0.893128i \(0.351494\pi\)
\(462\) 3.43845 2.98529i 0.159971 0.138888i
\(463\) 21.6452i 1.00594i −0.864304 0.502970i \(-0.832241\pi\)
0.864304 0.502970i \(-0.167759\pi\)
\(464\) −9.40572 + 32.5004i −0.436650 + 1.50879i
\(465\) 8.00000 0.370991
\(466\) −10.4736 + 9.09329i −0.485181 + 0.421239i
\(467\) 3.09218i 0.143089i 0.997437 + 0.0715444i \(0.0227928\pi\)
−0.997437 + 0.0715444i \(0.977207\pi\)
\(468\) −14.6875 2.08258i −0.678931 0.0962673i
\(469\) 8.45851i 0.390578i
\(470\) −13.4305 15.4692i −0.619504 0.713542i
\(471\) −7.19612 −0.331580
\(472\) −17.8423 27.5858i −0.821260 1.26974i
\(473\) −34.0540 −1.56580
\(474\) 10.2683 8.91506i 0.471640 0.409482i
\(475\) −7.86962 + 7.92077i −0.361083 + 0.363430i
\(476\) −1.71922 0.243773i −0.0788005 0.0111733i
\(477\) 1.62603i 0.0744508i
\(478\) −18.0065 20.7398i −0.823597 0.948615i
\(479\) 8.68210i 0.396695i 0.980132 + 0.198348i \(0.0635575\pi\)
−0.980132 + 0.198348i \(0.936442\pi\)
\(480\) 9.61553 4.44793i 0.438887 0.203019i
\(481\) −17.6155 −0.803199
\(482\) 14.1771 + 16.3291i 0.645748 + 0.743770i
\(483\) −4.12391 −0.187644
\(484\) 0.403882 2.84840i 0.0183583 0.129473i
\(485\) 26.4168i 1.19953i
\(486\) −15.1231 + 13.1300i −0.685998 + 0.595590i
\(487\) −9.59482 −0.434783 −0.217391 0.976085i \(-0.569755\pi\)
−0.217391 + 0.976085i \(0.569755\pi\)
\(488\) 1.05171 + 1.62603i 0.0476085 + 0.0736069i
\(489\) 12.7519i 0.576659i
\(490\) 10.4160 9.04325i 0.470546 0.408532i
\(491\) 2.71151i 0.122369i 0.998126 + 0.0611844i \(0.0194878\pi\)
−0.998126 + 0.0611844i \(0.980512\pi\)
\(492\) 8.80776 + 1.24887i 0.397085 + 0.0563036i
\(493\) 8.45851i 0.380952i
\(494\) 29.2143 + 1.96578i 1.31441 + 0.0884447i
\(495\) 7.54011i 0.338903i
\(496\) 16.4127 + 4.74990i 0.736953 + 0.213277i
\(497\) 9.49980i 0.426124i
\(498\) −10.7386 12.3687i −0.481210 0.554255i
\(499\) 11.0129i 0.493007i 0.969142 + 0.246504i \(0.0792817\pi\)
−0.969142 + 0.246504i \(0.920718\pi\)
\(500\) −3.31534 + 23.3817i −0.148267 + 1.04566i
\(501\) −0.630683 −0.0281768
\(502\) 20.7743 + 23.9277i 0.927202 + 1.06795i
\(503\) 35.6435i 1.58926i −0.607091 0.794632i \(-0.707664\pi\)
0.607091 0.794632i \(-0.292336\pi\)
\(504\) −3.21985 + 2.08258i −0.143424 + 0.0927655i
\(505\) 12.8769 0.573014
\(506\) 13.0776 11.3541i 0.581370 0.504752i
\(507\) 11.4677 0.509297
\(508\) 0.525853 3.70861i 0.0233309 0.164543i
\(509\) 9.49980i 0.421071i −0.977586 0.210536i \(-0.932479\pi\)
0.977586 0.210536i \(-0.0675208\pi\)
\(510\) 2.00000 1.73642i 0.0885615 0.0768900i
\(511\) 7.05256i 0.311987i
\(512\) 22.3680 3.41624i 0.988537 0.150978i
\(513\) 16.8078 16.9170i 0.742081 0.746905i
\(514\) −17.6155 20.2895i −0.776988 0.894930i
\(515\) 5.84912 0.257743
\(516\) −26.1552 3.70861i −1.15142 0.163262i
\(517\) 28.6847 1.26155
\(518\) −3.43845 + 2.98529i −0.151077 + 0.131166i
\(519\) 20.2895i 0.890609i
\(520\) 17.6155 11.3936i 0.772492 0.499643i
\(521\) 15.2910i 0.669910i −0.942234 0.334955i \(-0.891279\pi\)
0.942234 0.334955i \(-0.108721\pi\)
\(522\) 12.2462 + 14.1051i 0.536002 + 0.617365i
\(523\) 33.4990 1.46481 0.732404 0.680871i \(-0.238398\pi\)
0.732404 + 0.680871i \(0.238398\pi\)
\(524\) −9.56155 1.35576i −0.417698 0.0592265i
\(525\) 2.66732i 0.116411i
\(526\) 6.08677 + 7.01071i 0.265396 + 0.305682i
\(527\) 4.27156 0.186072
\(528\) −4.12391 + 14.2497i −0.179470 + 0.620139i
\(529\) 7.31534 0.318058
\(530\) 1.50758 + 1.73642i 0.0654850 + 0.0754253i
\(531\) −18.1379 −0.787120
\(532\) 6.03560 4.56722i 0.261676 0.198014i
\(533\) 17.6155 0.763013
\(534\) 6.43971 + 7.41722i 0.278673 + 0.320975i
\(535\) 12.2888 0.531292
\(536\) 14.9654 + 23.1379i 0.646408 + 0.999404i
\(537\) −10.8769 −0.469373
\(538\) −3.43845 3.96039i −0.148242 0.170744i
\(539\) 19.3144i 0.831929i
\(540\) 2.39871 16.9170i 0.103224 0.727993i
\(541\) −12.1922 −0.524185 −0.262093 0.965043i \(-0.584413\pi\)
−0.262093 + 0.965043i \(0.584413\pi\)
\(542\) −14.2355 16.3964i −0.611467 0.704285i
\(543\) 2.49775i 0.107189i
\(544\) 5.13416 2.37495i 0.220125 0.101825i
\(545\) 24.7908i 1.06192i
\(546\) 5.28181 4.58572i 0.226041 0.196251i
\(547\) 19.4849 0.833116 0.416558 0.909109i \(-0.363236\pi\)
0.416558 + 0.909109i \(0.363236\pi\)
\(548\) −1.08854 + 7.67700i −0.0465001 + 0.327945i
\(549\) 1.06913 0.0456294
\(550\) −7.34376 8.45851i −0.313139 0.360672i
\(551\) −26.1552 25.9863i −1.11425 1.10705i
\(552\) 11.2808 7.29634i 0.480142 0.310553i
\(553\) 6.96067i 0.295998i
\(554\) −25.6870 + 22.3017i −1.09134 + 0.947509i
\(555\) 6.94568i 0.294828i
\(556\) −0.753789 0.106882i −0.0319678 0.00453279i
\(557\) −18.9309 −0.802127 −0.401063 0.916050i \(-0.631359\pi\)
−0.401063 + 0.916050i \(0.631359\pi\)
\(558\) 7.12311 6.18435i 0.301545 0.261805i
\(559\) −52.3104 −2.21249
\(560\) 1.50758 5.20926i 0.0637068 0.220131i
\(561\) 3.70861i 0.156578i
\(562\) 10.7386 + 12.3687i 0.452982 + 0.521742i
\(563\) 33.6466 1.41804 0.709018 0.705191i \(-0.249139\pi\)
0.709018 + 0.705191i \(0.249139\pi\)
\(564\) 22.0313 + 3.12387i 0.927685 + 0.131539i
\(565\) 5.79119i 0.243637i
\(566\) −4.47685 5.15641i −0.188176 0.216740i
\(567\) 1.62954i 0.0684342i
\(568\) 16.8078 + 25.9863i 0.705238 + 1.09036i
\(569\) 12.7519i 0.534586i −0.963615 0.267293i \(-0.913871\pi\)
0.963615 0.267293i \(-0.0861291\pi\)
\(570\) −0.775094 + 11.5190i −0.0324651 + 0.482477i
\(571\) 17.5780i 0.735615i −0.929902 0.367807i \(-0.880109\pi\)
0.929902 0.367807i \(-0.119891\pi\)
\(572\) −4.12391 + 29.0841i −0.172429 + 1.21607i
\(573\) 10.5411i 0.440360i
\(574\) 3.43845 2.98529i 0.143518 0.124604i
\(575\) 10.1447i 0.423065i
\(576\) 5.12311 11.3936i 0.213463 0.474734i
\(577\) 27.0000 1.12402 0.562012 0.827129i \(-0.310027\pi\)
0.562012 + 0.827129i \(0.310027\pi\)
\(578\) −17.0862 + 14.8344i −0.710694 + 0.617031i
\(579\) 4.44793i 0.184850i
\(580\) −26.1552 3.70861i −1.08604 0.153992i
\(581\) −8.38447 −0.347847
\(582\) −18.8114 21.6669i −0.779759 0.898123i
\(583\) −3.21985 −0.133353
\(584\) −12.4779 19.2920i −0.516340 0.798307i
\(585\) 11.5824i 0.478873i
\(586\) −4.40388 5.07237i −0.181923 0.209538i
\(587\) 4.82860i 0.199297i −0.995023 0.0996487i \(-0.968228\pi\)
0.995023 0.0996487i \(-0.0317719\pi\)
\(588\) −2.10341 + 14.8344i −0.0867432 + 0.611762i
\(589\) −13.1231 + 13.2084i −0.540728 + 0.544243i
\(590\) 19.3693 16.8166i 0.797422 0.692330i
\(591\) −12.5841 −0.517641
\(592\) 4.12391 14.2497i 0.169492 0.585659i
\(593\) −36.7386 −1.50867 −0.754337 0.656487i \(-0.772042\pi\)
−0.754337 + 0.656487i \(0.772042\pi\)
\(594\) 15.6847 + 18.0655i 0.643549 + 0.741237i
\(595\) 1.35576i 0.0555806i
\(596\) −5.00000 + 35.2628i −0.204808 + 1.44442i
\(597\) 15.8757i 0.649750i
\(598\) 20.0885 17.4411i 0.821482 0.713219i
\(599\) 7.72197 0.315511 0.157756 0.987478i \(-0.449574\pi\)
0.157756 + 0.987478i \(0.449574\pi\)
\(600\) −4.71922 7.29634i −0.192661 0.297872i
\(601\) 39.1687i 1.59772i −0.601514 0.798862i \(-0.705436\pi\)
0.601514 0.798862i \(-0.294564\pi\)
\(602\) −10.2107 + 8.86502i −0.416156 + 0.361311i
\(603\) 15.2134 0.619537
\(604\) 6.81791 48.0837i 0.277417 1.95650i
\(605\) 2.24621 0.0913215
\(606\) −10.5616 + 9.16965i −0.429034 + 0.372491i
\(607\) 13.6358 0.553461 0.276730 0.960948i \(-0.410749\pi\)
0.276730 + 0.960948i \(0.410749\pi\)
\(608\) −8.42943 + 23.1721i −0.341859 + 0.939751i
\(609\) −8.80776 −0.356909
\(610\) −1.14171 + 0.991247i −0.0462266 + 0.0401344i
\(611\) 44.0626 1.78258
\(612\) 0.438447 3.09218i 0.0177232 0.124994i
\(613\) 24.3002 0.981475 0.490738 0.871307i \(-0.336727\pi\)
0.490738 + 0.871307i \(0.336727\pi\)
\(614\) −8.56155 + 7.43323i −0.345516 + 0.299981i
\(615\) 6.94568i 0.280077i
\(616\) 4.12391 + 6.37593i 0.166157 + 0.256894i
\(617\) −28.5464 −1.14923 −0.574617 0.818422i \(-0.694849\pi\)
−0.574617 + 0.818422i \(0.694849\pi\)
\(618\) −4.79741 + 4.16516i −0.192980 + 0.167547i
\(619\) 34.3946i 1.38244i 0.722646 + 0.691218i \(0.242926\pi\)
−0.722646 + 0.691218i \(0.757074\pi\)
\(620\) −1.87285 + 13.2084i −0.0752156 + 0.530463i
\(621\) 21.6669i 0.869464i
\(622\) 0.804963 + 0.927153i 0.0322761 + 0.0371754i
\(623\) 5.02797 0.201441
\(624\) −6.33475 + 21.8890i −0.253593 + 0.876262i
\(625\) −5.63068 −0.225227
\(626\) −4.87123 + 4.22926i −0.194694 + 0.169035i
\(627\) −11.4677 11.3936i −0.457975 0.455017i
\(628\) 1.68466 11.8812i 0.0672252 0.474110i
\(629\) 3.70861i 0.147872i
\(630\) −1.96286 2.26081i −0.0782022 0.0900729i
\(631\) 12.7494i 0.507544i −0.967264 0.253772i \(-0.918329\pi\)
0.967264 0.253772i \(-0.0816713\pi\)
\(632\) 12.3153 + 19.0406i 0.489878 + 0.757394i
\(633\) 2.42329 0.0963172
\(634\) 4.40388 + 5.07237i 0.174900 + 0.201450i
\(635\) 2.92456 0.116058
\(636\) −2.47301 0.350654i −0.0980613 0.0139044i
\(637\) 29.6689i 1.17552i
\(638\) 27.9309 24.2499i 1.10579 0.960061i
\(639\) 17.0862 0.675921
\(640\) 5.09271 + 16.9170i 0.201307 + 0.668704i
\(641\) 48.6685i 1.92229i 0.276045 + 0.961145i \(0.410976\pi\)
−0.276045 + 0.961145i \(0.589024\pi\)
\(642\) −10.0792 + 8.75088i −0.397795 + 0.345370i
\(643\) 6.56502i 0.258899i 0.991586 + 0.129449i \(0.0413210\pi\)
−0.991586 + 0.129449i \(0.958679\pi\)
\(644\) 0.965435 6.80879i 0.0380435 0.268304i
\(645\) 20.6256i 0.812133i
\(646\) −0.413858 + 6.15051i −0.0162830 + 0.241988i
\(647\) 36.2379i 1.42466i −0.701845 0.712329i \(-0.747640\pi\)
0.701845 0.712329i \(-0.252360\pi\)
\(648\) 2.88310 + 4.45753i 0.113259 + 0.175108i
\(649\) 35.9166i 1.40985i
\(650\) −11.2808 12.9931i −0.442468 0.509633i
\(651\) 4.44793i 0.174328i
\(652\) −21.0540 2.98529i −0.824537 0.116913i
\(653\) −45.8078 −1.79260 −0.896298 0.443452i \(-0.853754\pi\)
−0.896298 + 0.443452i \(0.853754\pi\)
\(654\) 17.6535 + 20.3333i 0.690308 + 0.795093i
\(655\) 7.54011i 0.294616i
\(656\) −4.12391 + 14.2497i −0.161012 + 0.556357i
\(657\) −12.6847 −0.494876
\(658\) 8.60076 7.46726i 0.335292 0.291104i
\(659\) 3.36750 0.131179 0.0655896 0.997847i \(-0.479107\pi\)
0.0655896 + 0.997847i \(0.479107\pi\)
\(660\) −11.4677 1.62603i −0.446379 0.0632931i
\(661\) 17.5018i 0.680740i 0.940292 + 0.340370i \(0.110552\pi\)
−0.940292 + 0.340370i \(0.889448\pi\)
\(662\) 2.40388 2.08707i 0.0934295 0.0811165i
\(663\) 5.69681i 0.221246i
\(664\) 22.9354 14.8344i 0.890064 0.575688i
\(665\) 4.19224 + 4.16516i 0.162568 + 0.161518i
\(666\) −5.36932 6.18435i −0.208057 0.239639i
\(667\) −33.4990 −1.29709
\(668\) 0.147647 1.04129i 0.00571264 0.0402887i
\(669\) 19.5076 0.754207
\(670\) −16.2462 + 14.1051i −0.627646 + 0.544928i
\(671\) 2.11708i 0.0817291i
\(672\) 2.47301 + 5.34615i 0.0953985 + 0.206232i
\(673\) 31.7515i 1.22393i −0.790885 0.611964i \(-0.790380\pi\)
0.790885 0.611964i \(-0.209620\pi\)
\(674\) −24.4924 28.2102i −0.943413 1.08662i
\(675\) −14.0140 −0.539400
\(676\) −2.68466 + 18.9337i −0.103256 + 0.728220i
\(677\) 4.29335i 0.165007i 0.996591 + 0.0825034i \(0.0262915\pi\)
−0.996591 + 0.0825034i \(0.973708\pi\)
\(678\) −4.12391 4.74990i −0.158378 0.182419i
\(679\) −14.6875 −0.563656
\(680\) 2.39871 + 3.70861i 0.0919862 + 0.142219i
\(681\) 20.9460 0.802653
\(682\) −12.2462 14.1051i −0.468932 0.540113i
\(683\) −13.6358 −0.521760 −0.260880 0.965371i \(-0.584013\pi\)
−0.260880 + 0.965371i \(0.584013\pi\)
\(684\) 8.21455 + 10.8556i 0.314091 + 0.415073i
\(685\) −6.05398 −0.231311
\(686\) 10.6627 + 12.2813i 0.407104 + 0.468901i
\(687\) 2.92456 0.111579
\(688\) 12.2462 42.3154i 0.466882 1.61326i
\(689\) −4.94602 −0.188429
\(690\) 6.87689 + 7.92077i 0.261799 + 0.301539i
\(691\) 23.3817i 0.889480i 0.895660 + 0.444740i \(0.146704\pi\)
−0.895660 + 0.444740i \(0.853296\pi\)
\(692\) 33.4990 + 4.74990i 1.27344 + 0.180564i
\(693\) 4.19224 0.159250
\(694\) −22.3842 25.7820i −0.849694 0.978673i
\(695\) 0.594427i 0.0225479i
\(696\) 24.0932 15.5834i 0.913252 0.590686i
\(697\) 3.70861i 0.140474i
\(698\) −29.9585 + 26.0103i −1.13395 + 0.984505i
\(699\) 11.7630 0.444916
\(700\) −4.40388 0.624437i −0.166451 0.0236015i
\(701\) 29.3693 1.10926 0.554632 0.832096i \(-0.312859\pi\)
0.554632 + 0.832096i \(0.312859\pi\)
\(702\) 24.0932 + 27.7505i 0.909341 + 1.04737i
\(703\) 11.4677 + 11.3936i 0.432512 + 0.429718i
\(704\) −22.5616 10.1447i −0.850321 0.382344i
\(705\) 17.3736i 0.654327i
\(706\) 6.74409 5.85528i 0.253817 0.220367i
\(707\) 7.15944i 0.269259i
\(708\) −3.91146 + 27.5858i −0.147002 + 1.03674i
\(709\) 37.3693 1.40343 0.701717 0.712456i \(-0.252417\pi\)
0.701717 + 0.712456i \(0.252417\pi\)
\(710\) −18.2462 + 15.8415i −0.684768 + 0.594523i
\(711\) 12.5194 0.469513
\(712\) −13.7538 + 8.89586i −0.515445 + 0.333387i
\(713\) 16.9170i 0.633547i
\(714\) 0.965435 + 1.11198i 0.0361305 + 0.0416149i
\(715\) −22.9354 −0.857733
\(716\) 2.54635 17.9583i 0.0951617 0.671134i
\(717\) 23.2930i 0.869891i
\(718\) −25.3502 29.1983i −0.946063 1.08967i
\(719\) 15.9484i 0.594776i −0.954757 0.297388i \(-0.903885\pi\)
0.954757 0.297388i \(-0.0961155\pi\)
\(720\) 9.36932 + 2.71151i 0.349174 + 0.101052i
\(721\) 3.25206i 0.121113i
\(722\) −17.7470 20.1753i −0.660475 0.750848i
\(723\) 18.3393i 0.682046i
\(724\) 4.12391 + 0.584739i 0.153264 + 0.0217317i
\(725\) 21.6669i 0.804689i
\(726\) −1.84233 + 1.59953i −0.0683753 + 0.0593641i
\(727\) 23.6554i 0.877332i 0.898650 + 0.438666i \(0.144549\pi\)
−0.898650 + 0.438666i \(0.855451\pi\)
\(728\) 6.33475 + 9.79408i 0.234782 + 0.362993i
\(729\) 22.6155 0.837612
\(730\) 13.5458 11.7606i 0.501353 0.435280i
\(731\) 11.0129i 0.407329i
\(732\) 0.230559 1.62603i 0.00852170 0.0600998i
\(733\) 3.12311 0.115355 0.0576773 0.998335i \(-0.481631\pi\)
0.0576773 + 0.998335i \(0.481631\pi\)
\(734\) −13.0776 15.0627i −0.482703 0.555975i
\(735\) −11.6982 −0.431496
\(736\) 9.40572 + 20.3333i 0.346699 + 0.749494i
\(737\) 30.1254i 1.10968i
\(738\) 5.36932 + 6.18435i 0.197647 + 0.227649i
\(739\) 30.3273i 1.11561i 0.829972 + 0.557804i \(0.188356\pi\)
−0.829972 + 0.557804i \(0.811644\pi\)
\(740\) 11.4677 + 1.62603i 0.421560 + 0.0597740i
\(741\) −17.6155 17.5018i −0.647123 0.642943i
\(742\) −0.965435 + 0.838200i −0.0354422 + 0.0307713i
\(743\) −38.4440 −1.41037 −0.705187 0.709021i \(-0.749137\pi\)
−0.705187 + 0.709021i \(0.749137\pi\)
\(744\) −7.86962 12.1671i −0.288514 0.446068i
\(745\) −27.8078 −1.01880
\(746\) −11.2808 12.9931i −0.413019 0.475713i
\(747\) 15.0802i 0.551756i
\(748\) −6.12311 0.868210i −0.223883 0.0317449i
\(749\) 6.83248i 0.249653i
\(750\) 15.1231 13.1300i 0.552218 0.479441i
\(751\) −8.24782 −0.300967 −0.150484 0.988612i \(-0.548083\pi\)
−0.150484 + 0.988612i \(0.548083\pi\)
\(752\) −10.3153 + 35.6435i −0.376162 + 1.29978i
\(753\) 26.8734i 0.979320i
\(754\) 42.9047 37.2503i 1.56250 1.35658i
\(755\) 37.9182 1.37998
\(756\) 9.40572 + 1.33366i 0.342083 + 0.0485047i
\(757\) −24.1922 −0.879282 −0.439641 0.898174i \(-0.644894\pi\)
−0.439641 + 0.898174i \(0.644894\pi\)
\(758\) 7.28078 6.32124i 0.264450 0.229598i
\(759\) −14.6875 −0.533123
\(760\) −18.8370 3.97639i −0.683290 0.144239i
\(761\) −10.6155 −0.384813 −0.192406 0.981315i \(-0.561629\pi\)
−0.192406 + 0.981315i \(0.561629\pi\)
\(762\) −2.39871 + 2.08258i −0.0868959 + 0.0754439i
\(763\) 13.7835 0.498995
\(764\) 17.4039 + 2.46774i 0.629650 + 0.0892797i
\(765\) 2.43845 0.0881622
\(766\) 17.3693 15.0802i 0.627579 0.544870i
\(767\) 55.1716i 1.99213i
\(768\) −16.2236 10.2487i −0.585420 0.369819i
\(769\) 54.2311 1.95562 0.977811 0.209489i \(-0.0671801\pi\)
0.977811 + 0.209489i \(0.0671801\pi\)
\(770\) −4.47685 + 3.88684i −0.161334 + 0.140072i
\(771\) 22.7872i 0.820662i
\(772\) −7.34376 1.04129i −0.264308 0.0374769i
\(773\) 25.8321i 0.929115i 0.885543 + 0.464558i \(0.153787\pi\)
−0.885543 + 0.464558i \(0.846213\pi\)
\(774\) −15.9445 18.3648i −0.573114 0.660110i
\(775\) 10.9418 0.393042
\(776\) 40.1771 25.9863i 1.44227 0.932853i
\(777\) 3.86174 0.138539
\(778\) −6.20205 + 5.38468i −0.222354 + 0.193050i
\(779\) −11.4677 11.3936i −0.410872 0.408219i
\(780\) −17.6155 2.49775i −0.630737 0.0894337i
\(781\) 33.8340i 1.21068i