Properties

Label 105.2.d.b.64.2
Level 105
Weight 2
Character 105.64
Analytic conductor 0.838
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.2
Root \(1.45161 + 1.45161i\)
Character \(\chi\) = 105.64
Dual form 105.2.d.b.64.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.90321i q^{2} +1.00000i q^{3} -1.62222 q^{4} +(0.311108 - 2.21432i) q^{5} +1.90321 q^{6} -1.00000i q^{7} -0.719004i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.90321i q^{2} +1.00000i q^{3} -1.62222 q^{4} +(0.311108 - 2.21432i) q^{5} +1.90321 q^{6} -1.00000i q^{7} -0.719004i q^{8} -1.00000 q^{9} +(-4.21432 - 0.592104i) q^{10} +2.00000 q^{11} -1.62222i q^{12} +6.42864i q^{13} -1.90321 q^{14} +(2.21432 + 0.311108i) q^{15} -4.61285 q^{16} +4.42864i q^{17} +1.90321i q^{18} +2.42864 q^{19} +(-0.504684 + 3.59210i) q^{20} +1.00000 q^{21} -3.80642i q^{22} -1.37778i q^{23} +0.719004 q^{24} +(-4.80642 - 1.37778i) q^{25} +12.2351 q^{26} -1.00000i q^{27} +1.62222i q^{28} -0.755569 q^{29} +(0.592104 - 4.21432i) q^{30} +5.18421 q^{31} +7.34122i q^{32} +2.00000i q^{33} +8.42864 q^{34} +(-2.21432 - 0.311108i) q^{35} +1.62222 q^{36} +7.61285i q^{37} -4.62222i q^{38} -6.42864 q^{39} +(-1.59210 - 0.223688i) q^{40} -8.23506 q^{41} -1.90321i q^{42} -10.1017i q^{43} -3.24443 q^{44} +(-0.311108 + 2.21432i) q^{45} -2.62222 q^{46} +2.75557i q^{47} -4.61285i q^{48} -1.00000 q^{49} +(-2.62222 + 9.14764i) q^{50} -4.42864 q^{51} -10.4286i q^{52} -9.18421i q^{53} -1.90321 q^{54} +(0.622216 - 4.42864i) q^{55} -0.719004 q^{56} +2.42864i q^{57} +1.43801i q^{58} -14.1017 q^{59} +(-3.59210 - 0.504684i) q^{60} +6.85728 q^{61} -9.86665i q^{62} +1.00000i q^{63} +4.74620 q^{64} +(14.2351 + 2.00000i) q^{65} +3.80642 q^{66} +2.75557i q^{67} -7.18421i q^{68} +1.37778 q^{69} +(-0.592104 + 4.21432i) q^{70} +2.00000 q^{71} +0.719004i q^{72} +1.57136i q^{73} +14.4889 q^{74} +(1.37778 - 4.80642i) q^{75} -3.93978 q^{76} -2.00000i q^{77} +12.2351i q^{78} +4.85728 q^{79} +(-1.43509 + 10.2143i) q^{80} +1.00000 q^{81} +15.6731i q^{82} -11.6128i q^{83} -1.62222 q^{84} +(9.80642 + 1.37778i) q^{85} -19.2257 q^{86} -0.755569i q^{87} -1.43801i q^{88} -4.62222 q^{89} +(4.21432 + 0.592104i) q^{90} +6.42864 q^{91} +2.23506i q^{92} +5.18421i q^{93} +5.24443 q^{94} +(0.755569 - 5.37778i) q^{95} -7.34122 q^{96} -11.9398i q^{97} +1.90321i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 10q^{4} + 2q^{5} - 2q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 10q^{4} + 2q^{5} - 2q^{6} - 6q^{9} - 12q^{10} + 12q^{11} + 2q^{14} + 26q^{16} - 12q^{19} - 30q^{20} + 6q^{21} + 18q^{24} - 2q^{25} + 20q^{26} - 4q^{29} - 10q^{30} + 4q^{31} + 24q^{34} + 10q^{36} - 12q^{39} + 4q^{40} + 4q^{41} - 20q^{44} - 2q^{45} - 16q^{46} - 6q^{49} - 16q^{50} + 2q^{54} + 4q^{55} - 18q^{56} - 32q^{59} - 8q^{60} - 12q^{61} - 26q^{64} + 32q^{65} - 4q^{66} + 8q^{69} + 10q^{70} + 12q^{71} + 88q^{74} + 8q^{75} + 4q^{76} - 24q^{79} + 46q^{80} + 6q^{81} - 10q^{84} + 32q^{85} - 8q^{86} - 28q^{89} + 12q^{90} + 12q^{91} + 32q^{94} + 4q^{95} - 58q^{96} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90321i 1.34577i −0.739745 0.672887i \(-0.765054\pi\)
0.739745 0.672887i \(-0.234946\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −1.62222 −0.811108
\(5\) 0.311108 2.21432i 0.139132 0.990274i
\(6\) 1.90321 0.776983
\(7\) 1.00000i 0.377964i
\(8\) 0.719004i 0.254206i
\(9\) −1.00000 −0.333333
\(10\) −4.21432 0.592104i −1.33268 0.187240i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.62222i 0.468293i
\(13\) 6.42864i 1.78298i 0.453037 + 0.891492i \(0.350341\pi\)
−0.453037 + 0.891492i \(0.649659\pi\)
\(14\) −1.90321 −0.508655
\(15\) 2.21432 + 0.311108i 0.571735 + 0.0803277i
\(16\) −4.61285 −1.15321
\(17\) 4.42864i 1.07410i 0.843550 + 0.537051i \(0.180462\pi\)
−0.843550 + 0.537051i \(0.819538\pi\)
\(18\) 1.90321i 0.448591i
\(19\) 2.42864 0.557168 0.278584 0.960412i \(-0.410135\pi\)
0.278584 + 0.960412i \(0.410135\pi\)
\(20\) −0.504684 + 3.59210i −0.112851 + 0.803219i
\(21\) 1.00000 0.218218
\(22\) 3.80642i 0.811532i
\(23\) 1.37778i 0.287288i −0.989629 0.143644i \(-0.954118\pi\)
0.989629 0.143644i \(-0.0458820\pi\)
\(24\) 0.719004 0.146766
\(25\) −4.80642 1.37778i −0.961285 0.275557i
\(26\) 12.2351 2.39949
\(27\) 1.00000i 0.192450i
\(28\) 1.62222i 0.306570i
\(29\) −0.755569 −0.140306 −0.0701528 0.997536i \(-0.522349\pi\)
−0.0701528 + 0.997536i \(0.522349\pi\)
\(30\) 0.592104 4.21432i 0.108103 0.769426i
\(31\) 5.18421 0.931111 0.465556 0.885019i \(-0.345855\pi\)
0.465556 + 0.885019i \(0.345855\pi\)
\(32\) 7.34122i 1.29776i
\(33\) 2.00000i 0.348155i
\(34\) 8.42864 1.44550
\(35\) −2.21432 0.311108i −0.374288 0.0525868i
\(36\) 1.62222 0.270369
\(37\) 7.61285i 1.25154i 0.780006 + 0.625772i \(0.215216\pi\)
−0.780006 + 0.625772i \(0.784784\pi\)
\(38\) 4.62222i 0.749822i
\(39\) −6.42864 −1.02941
\(40\) −1.59210 0.223688i −0.251734 0.0353681i
\(41\) −8.23506 −1.28610 −0.643050 0.765824i \(-0.722331\pi\)
−0.643050 + 0.765824i \(0.722331\pi\)
\(42\) 1.90321i 0.293672i
\(43\) 10.1017i 1.54050i −0.637744 0.770248i \(-0.720132\pi\)
0.637744 0.770248i \(-0.279868\pi\)
\(44\) −3.24443 −0.489116
\(45\) −0.311108 + 2.21432i −0.0463772 + 0.330091i
\(46\) −2.62222 −0.386625
\(47\) 2.75557i 0.401941i 0.979597 + 0.200971i \(0.0644095\pi\)
−0.979597 + 0.200971i \(0.935590\pi\)
\(48\) 4.61285i 0.665807i
\(49\) −1.00000 −0.142857
\(50\) −2.62222 + 9.14764i −0.370837 + 1.29367i
\(51\) −4.42864 −0.620134
\(52\) 10.4286i 1.44619i
\(53\) 9.18421i 1.26155i −0.775967 0.630774i \(-0.782737\pi\)
0.775967 0.630774i \(-0.217263\pi\)
\(54\) −1.90321 −0.258994
\(55\) 0.622216 4.42864i 0.0838995 0.597158i
\(56\) −0.719004 −0.0960809
\(57\) 2.42864i 0.321681i
\(58\) 1.43801i 0.188820i
\(59\) −14.1017 −1.83589 −0.917943 0.396712i \(-0.870151\pi\)
−0.917943 + 0.396712i \(0.870151\pi\)
\(60\) −3.59210 0.504684i −0.463739 0.0651544i
\(61\) 6.85728 0.877985 0.438992 0.898491i \(-0.355336\pi\)
0.438992 + 0.898491i \(0.355336\pi\)
\(62\) 9.86665i 1.25307i
\(63\) 1.00000i 0.125988i
\(64\) 4.74620 0.593275
\(65\) 14.2351 + 2.00000i 1.76564 + 0.248069i
\(66\) 3.80642 0.468538
\(67\) 2.75557i 0.336646i 0.985732 + 0.168323i \(0.0538352\pi\)
−0.985732 + 0.168323i \(0.946165\pi\)
\(68\) 7.18421i 0.871213i
\(69\) 1.37778 0.165866
\(70\) −0.592104 + 4.21432i −0.0707700 + 0.503708i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0.719004i 0.0847354i
\(73\) 1.57136i 0.183914i 0.995763 + 0.0919569i \(0.0293122\pi\)
−0.995763 + 0.0919569i \(0.970688\pi\)
\(74\) 14.4889 1.68430
\(75\) 1.37778 4.80642i 0.159093 0.554998i
\(76\) −3.93978 −0.451923
\(77\) 2.00000i 0.227921i
\(78\) 12.2351i 1.38535i
\(79\) 4.85728 0.546487 0.273243 0.961945i \(-0.411904\pi\)
0.273243 + 0.961945i \(0.411904\pi\)
\(80\) −1.43509 + 10.2143i −0.160448 + 1.14200i
\(81\) 1.00000 0.111111
\(82\) 15.6731i 1.73080i
\(83\) 11.6128i 1.27468i −0.770585 0.637338i \(-0.780036\pi\)
0.770585 0.637338i \(-0.219964\pi\)
\(84\) −1.62222 −0.176998
\(85\) 9.80642 + 1.37778i 1.06366 + 0.149442i
\(86\) −19.2257 −2.07316
\(87\) 0.755569i 0.0810055i
\(88\) 1.43801i 0.153292i
\(89\) −4.62222 −0.489954 −0.244977 0.969529i \(-0.578780\pi\)
−0.244977 + 0.969529i \(0.578780\pi\)
\(90\) 4.21432 + 0.592104i 0.444228 + 0.0624133i
\(91\) 6.42864 0.673905
\(92\) 2.23506i 0.233021i
\(93\) 5.18421i 0.537577i
\(94\) 5.24443 0.540922
\(95\) 0.755569 5.37778i 0.0775197 0.551749i
\(96\) −7.34122 −0.749260
\(97\) 11.9398i 1.21230i −0.795350 0.606150i \(-0.792713\pi\)
0.795350 0.606150i \(-0.207287\pi\)
\(98\) 1.90321i 0.192253i
\(99\) −2.00000 −0.201008
\(100\) 7.79706 + 2.23506i 0.779706 + 0.223506i
\(101\) 1.47949 0.147215 0.0736076 0.997287i \(-0.476549\pi\)
0.0736076 + 0.997287i \(0.476549\pi\)
\(102\) 8.42864i 0.834560i
\(103\) 8.85728i 0.872734i 0.899769 + 0.436367i \(0.143735\pi\)
−0.899769 + 0.436367i \(0.856265\pi\)
\(104\) 4.62222 0.453246
\(105\) 0.311108 2.21432i 0.0303610 0.216095i
\(106\) −17.4795 −1.69776
\(107\) 1.76494i 0.170623i 0.996354 + 0.0853114i \(0.0271885\pi\)
−0.996354 + 0.0853114i \(0.972811\pi\)
\(108\) 1.62222i 0.156098i
\(109\) −5.61285 −0.537613 −0.268807 0.963194i \(-0.586629\pi\)
−0.268807 + 0.963194i \(0.586629\pi\)
\(110\) −8.42864 1.18421i −0.803639 0.112910i
\(111\) −7.61285 −0.722580
\(112\) 4.61285i 0.435873i
\(113\) 11.2859i 1.06169i 0.847469 + 0.530845i \(0.178125\pi\)
−0.847469 + 0.530845i \(0.821875\pi\)
\(114\) 4.62222 0.432910
\(115\) −3.05086 0.428639i −0.284494 0.0399708i
\(116\) 1.22570 0.113803
\(117\) 6.42864i 0.594328i
\(118\) 26.8385i 2.47069i
\(119\) 4.42864 0.405973
\(120\) 0.223688 1.59210i 0.0204198 0.145339i
\(121\) −7.00000 −0.636364
\(122\) 13.0509i 1.18157i
\(123\) 8.23506i 0.742531i
\(124\) −8.40990 −0.755232
\(125\) −4.54617 + 10.2143i −0.406622 + 0.913597i
\(126\) 1.90321 0.169552
\(127\) 12.8573i 1.14090i −0.821333 0.570450i \(-0.806769\pi\)
0.821333 0.570450i \(-0.193231\pi\)
\(128\) 5.64941i 0.499342i
\(129\) 10.1017 0.889406
\(130\) 3.80642 27.0923i 0.333845 2.37616i
\(131\) −2.10171 −0.183627 −0.0918136 0.995776i \(-0.529266\pi\)
−0.0918136 + 0.995776i \(0.529266\pi\)
\(132\) 3.24443i 0.282391i
\(133\) 2.42864i 0.210590i
\(134\) 5.24443 0.453050
\(135\) −2.21432 0.311108i −0.190578 0.0267759i
\(136\) 3.18421 0.273044
\(137\) 15.9398i 1.36183i 0.732364 + 0.680914i \(0.238417\pi\)
−0.732364 + 0.680914i \(0.761583\pi\)
\(138\) 2.62222i 0.223218i
\(139\) −11.6731 −0.990097 −0.495048 0.868865i \(-0.664850\pi\)
−0.495048 + 0.868865i \(0.664850\pi\)
\(140\) 3.59210 + 0.504684i 0.303588 + 0.0426536i
\(141\) −2.75557 −0.232061
\(142\) 3.80642i 0.319428i
\(143\) 12.8573i 1.07518i
\(144\) 4.61285 0.384404
\(145\) −0.235063 + 1.67307i −0.0195209 + 0.138941i
\(146\) 2.99063 0.247506
\(147\) 1.00000i 0.0824786i
\(148\) 12.3497i 1.01514i
\(149\) 21.2257 1.73888 0.869438 0.494041i \(-0.164481\pi\)
0.869438 + 0.494041i \(0.164481\pi\)
\(150\) −9.14764 2.62222i −0.746902 0.214103i
\(151\) 16.8573 1.37183 0.685913 0.727684i \(-0.259403\pi\)
0.685913 + 0.727684i \(0.259403\pi\)
\(152\) 1.74620i 0.141636i
\(153\) 4.42864i 0.358034i
\(154\) −3.80642 −0.306730
\(155\) 1.61285 11.4795i 0.129547 0.922055i
\(156\) 10.4286 0.834959
\(157\) 10.4286i 0.832296i −0.909297 0.416148i \(-0.863380\pi\)
0.909297 0.416148i \(-0.136620\pi\)
\(158\) 9.24443i 0.735447i
\(159\) 9.18421 0.728355
\(160\) 16.2558 + 2.28391i 1.28513 + 0.180559i
\(161\) −1.37778 −0.108585
\(162\) 1.90321i 0.149530i
\(163\) 20.8573i 1.63367i −0.576873 0.816834i \(-0.695727\pi\)
0.576873 0.816834i \(-0.304273\pi\)
\(164\) 13.3590 1.04317
\(165\) 4.42864 + 0.622216i 0.344769 + 0.0484394i
\(166\) −22.1017 −1.71543
\(167\) 15.3461i 1.18752i 0.804642 + 0.593760i \(0.202357\pi\)
−0.804642 + 0.593760i \(0.797643\pi\)
\(168\) 0.719004i 0.0554723i
\(169\) −28.3274 −2.17903
\(170\) 2.62222 18.6637i 0.201115 1.43144i
\(171\) −2.42864 −0.185723
\(172\) 16.3872i 1.24951i
\(173\) 2.06022i 0.156636i −0.996928 0.0783179i \(-0.975045\pi\)
0.996928 0.0783179i \(-0.0249549\pi\)
\(174\) −1.43801 −0.109015
\(175\) −1.37778 + 4.80642i −0.104151 + 0.363331i
\(176\) −9.22570 −0.695413
\(177\) 14.1017i 1.05995i
\(178\) 8.79706i 0.659367i
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 0.504684 3.59210i 0.0376169 0.267740i
\(181\) −12.1017 −0.899513 −0.449757 0.893151i \(-0.648489\pi\)
−0.449757 + 0.893151i \(0.648489\pi\)
\(182\) 12.2351i 0.906923i
\(183\) 6.85728i 0.506905i
\(184\) −0.990632 −0.0730304
\(185\) 16.8573 + 2.36842i 1.23937 + 0.174129i
\(186\) 9.86665 0.723458
\(187\) 8.85728i 0.647708i
\(188\) 4.47013i 0.326017i
\(189\) −1.00000 −0.0727393
\(190\) −10.2351 1.43801i −0.742530 0.104324i
\(191\) 0.488863 0.0353729 0.0176864 0.999844i \(-0.494370\pi\)
0.0176864 + 0.999844i \(0.494370\pi\)
\(192\) 4.74620i 0.342528i
\(193\) 22.9590i 1.65262i 0.563212 + 0.826312i \(0.309565\pi\)
−0.563212 + 0.826312i \(0.690435\pi\)
\(194\) −22.7239 −1.63148
\(195\) −2.00000 + 14.2351i −0.143223 + 1.01939i
\(196\) 1.62222 0.115873
\(197\) 1.18421i 0.0843713i −0.999110 0.0421857i \(-0.986568\pi\)
0.999110 0.0421857i \(-0.0134321\pi\)
\(198\) 3.80642i 0.270511i
\(199\) −8.79706 −0.623607 −0.311803 0.950147i \(-0.600933\pi\)
−0.311803 + 0.950147i \(0.600933\pi\)
\(200\) −0.990632 + 3.45584i −0.0700483 + 0.244365i
\(201\) −2.75557 −0.194363
\(202\) 2.81579i 0.198118i
\(203\) 0.755569i 0.0530305i
\(204\) 7.18421 0.502995
\(205\) −2.56199 + 18.2351i −0.178937 + 1.27359i
\(206\) 16.8573 1.17450
\(207\) 1.37778i 0.0957626i
\(208\) 29.6543i 2.05616i
\(209\) 4.85728 0.335985
\(210\) −4.21432 0.592104i −0.290816 0.0408591i
\(211\) 23.2257 1.59892 0.799461 0.600717i \(-0.205118\pi\)
0.799461 + 0.600717i \(0.205118\pi\)
\(212\) 14.8988i 1.02325i
\(213\) 2.00000i 0.137038i
\(214\) 3.35905 0.229620
\(215\) −22.3684 3.14272i −1.52551 0.214332i
\(216\) −0.719004 −0.0489220
\(217\) 5.18421i 0.351927i
\(218\) 10.6824i 0.723506i
\(219\) −1.57136 −0.106183
\(220\) −1.00937 + 7.18421i −0.0680516 + 0.484359i
\(221\) −28.4701 −1.91511
\(222\) 14.4889i 0.972429i
\(223\) 15.2257i 1.01959i 0.860297 + 0.509794i \(0.170278\pi\)
−0.860297 + 0.509794i \(0.829722\pi\)
\(224\) 7.34122 0.490506
\(225\) 4.80642 + 1.37778i 0.320428 + 0.0918523i
\(226\) 21.4795 1.42879
\(227\) 14.3684i 0.953665i −0.878994 0.476833i \(-0.841785\pi\)
0.878994 0.476833i \(-0.158215\pi\)
\(228\) 3.93978i 0.260918i
\(229\) 5.61285 0.370907 0.185454 0.982653i \(-0.440625\pi\)
0.185454 + 0.982653i \(0.440625\pi\)
\(230\) −0.815792 + 5.80642i −0.0537917 + 0.382864i
\(231\) 2.00000 0.131590
\(232\) 0.543257i 0.0356666i
\(233\) 23.2859i 1.52551i −0.646687 0.762756i \(-0.723846\pi\)
0.646687 0.762756i \(-0.276154\pi\)
\(234\) −12.2351 −0.799831
\(235\) 6.10171 + 0.857279i 0.398032 + 0.0559227i
\(236\) 22.8760 1.48910
\(237\) 4.85728i 0.315514i
\(238\) 8.42864i 0.546348i
\(239\) 8.48886 0.549099 0.274549 0.961573i \(-0.411471\pi\)
0.274549 + 0.961573i \(0.411471\pi\)
\(240\) −10.2143 1.43509i −0.659332 0.0926349i
\(241\) −7.24443 −0.466655 −0.233327 0.972398i \(-0.574961\pi\)
−0.233327 + 0.972398i \(0.574961\pi\)
\(242\) 13.3225i 0.856402i
\(243\) 1.00000i 0.0641500i
\(244\) −11.1240 −0.712140
\(245\) −0.311108 + 2.21432i −0.0198759 + 0.141468i
\(246\) −15.6731 −0.999278
\(247\) 15.6128i 0.993422i
\(248\) 3.72746i 0.236694i
\(249\) 11.6128 0.735934
\(250\) 19.4400 + 8.65233i 1.22949 + 0.547221i
\(251\) 27.6128 1.74291 0.871454 0.490478i \(-0.163178\pi\)
0.871454 + 0.490478i \(0.163178\pi\)
\(252\) 1.62222i 0.102190i
\(253\) 2.75557i 0.173241i
\(254\) −24.4701 −1.53539
\(255\) −1.37778 + 9.80642i −0.0862802 + 0.614102i
\(256\) 20.2444 1.26528
\(257\) 0.428639i 0.0267378i −0.999911 0.0133689i \(-0.995744\pi\)
0.999911 0.0133689i \(-0.00425558\pi\)
\(258\) 19.2257i 1.19694i
\(259\) 7.61285 0.473039
\(260\) −23.0923 3.24443i −1.43213 0.201211i
\(261\) 0.755569 0.0467685
\(262\) 4.00000i 0.247121i
\(263\) 9.37778i 0.578259i 0.957290 + 0.289129i \(0.0933658\pi\)
−0.957290 + 0.289129i \(0.906634\pi\)
\(264\) 1.43801 0.0885032
\(265\) −20.3368 2.85728i −1.24928 0.175521i
\(266\) −4.62222 −0.283406
\(267\) 4.62222i 0.282875i
\(268\) 4.47013i 0.273056i
\(269\) −1.74620 −0.106468 −0.0532339 0.998582i \(-0.516953\pi\)
−0.0532339 + 0.998582i \(0.516953\pi\)
\(270\) −0.592104 + 4.21432i −0.0360343 + 0.256475i
\(271\) −2.69535 −0.163731 −0.0818653 0.996643i \(-0.526088\pi\)
−0.0818653 + 0.996643i \(0.526088\pi\)
\(272\) 20.4286i 1.23867i
\(273\) 6.42864i 0.389079i
\(274\) 30.3368 1.83271
\(275\) −9.61285 2.75557i −0.579677 0.166167i
\(276\) −2.23506 −0.134535
\(277\) 5.12399i 0.307870i −0.988081 0.153935i \(-0.950805\pi\)
0.988081 0.153935i \(-0.0491947\pi\)
\(278\) 22.2163i 1.33245i
\(279\) −5.18421 −0.310370
\(280\) −0.223688 + 1.59210i −0.0133679 + 0.0951464i
\(281\) 23.9813 1.43060 0.715301 0.698816i \(-0.246290\pi\)
0.715301 + 0.698816i \(0.246290\pi\)
\(282\) 5.24443i 0.312301i
\(283\) 2.36842i 0.140788i −0.997519 0.0703939i \(-0.977574\pi\)
0.997519 0.0703939i \(-0.0224256\pi\)
\(284\) −3.24443 −0.192522
\(285\) 5.37778 + 0.755569i 0.318552 + 0.0447560i
\(286\) 24.4701 1.44695
\(287\) 8.23506i 0.486100i
\(288\) 7.34122i 0.432585i
\(289\) −2.61285 −0.153697
\(290\) 3.18421 + 0.447375i 0.186983 + 0.0262708i
\(291\) 11.9398 0.699922
\(292\) 2.54909i 0.149174i
\(293\) 8.42864i 0.492406i −0.969218 0.246203i \(-0.920817\pi\)
0.969218 0.246203i \(-0.0791831\pi\)
\(294\) −1.90321 −0.110998
\(295\) −4.38715 + 31.2257i −0.255430 + 1.81803i
\(296\) 5.47367 0.318150
\(297\) 2.00000i 0.116052i
\(298\) 40.3970i 2.34014i
\(299\) 8.85728 0.512230
\(300\) −2.23506 + 7.79706i −0.129041 + 0.450163i
\(301\) −10.1017 −0.582253
\(302\) 32.0830i 1.84617i
\(303\) 1.47949i 0.0849947i
\(304\) −11.2029 −0.642533
\(305\) 2.13335 15.1842i 0.122155 0.869445i
\(306\) −8.42864 −0.481833
\(307\) 22.5718i 1.28824i −0.764923 0.644121i \(-0.777223\pi\)
0.764923 0.644121i \(-0.222777\pi\)
\(308\) 3.24443i 0.184869i
\(309\) −8.85728 −0.503873
\(310\) −21.8479 3.06959i −1.24088 0.174341i
\(311\) −24.0830 −1.36562 −0.682810 0.730596i \(-0.739242\pi\)
−0.682810 + 0.730596i \(0.739242\pi\)
\(312\) 4.62222i 0.261681i
\(313\) 9.65433i 0.545695i −0.962057 0.272848i \(-0.912035\pi\)
0.962057 0.272848i \(-0.0879655\pi\)
\(314\) −19.8479 −1.12008
\(315\) 2.21432 + 0.311108i 0.124763 + 0.0175289i
\(316\) −7.87955 −0.443260
\(317\) 6.04149i 0.339324i −0.985502 0.169662i \(-0.945732\pi\)
0.985502 0.169662i \(-0.0542676\pi\)
\(318\) 17.4795i 0.980201i
\(319\) −1.51114 −0.0846075
\(320\) 1.47658 10.5096i 0.0825433 0.587505i
\(321\) −1.76494 −0.0985092
\(322\) 2.62222i 0.146130i
\(323\) 10.7556i 0.598456i
\(324\) −1.62222 −0.0901231
\(325\) 8.85728 30.8988i 0.491313 1.71396i
\(326\) −39.6958 −2.19855
\(327\) 5.61285i 0.310391i
\(328\) 5.92104i 0.326935i
\(329\) 2.75557 0.151919
\(330\) 1.18421 8.42864i 0.0651885 0.463981i
\(331\) 13.5111 0.742639 0.371320 0.928505i \(-0.378905\pi\)
0.371320 + 0.928505i \(0.378905\pi\)
\(332\) 18.8385i 1.03390i
\(333\) 7.61285i 0.417181i
\(334\) 29.2070 1.59813
\(335\) 6.10171 + 0.857279i 0.333372 + 0.0468382i
\(336\) −4.61285 −0.251651
\(337\) 10.4889i 0.571365i 0.958324 + 0.285682i \(0.0922202\pi\)
−0.958324 + 0.285682i \(0.907780\pi\)
\(338\) 53.9131i 2.93248i
\(339\) −11.2859 −0.612967
\(340\) −15.9081 2.23506i −0.862740 0.121213i
\(341\) 10.3684 0.561481
\(342\) 4.62222i 0.249941i
\(343\) 1.00000i 0.0539949i
\(344\) −7.26317 −0.391604
\(345\) 0.428639 3.05086i 0.0230772 0.164253i
\(346\) −3.92104 −0.210796
\(347\) 16.7239i 0.897787i −0.893585 0.448894i \(-0.851818\pi\)
0.893585 0.448894i \(-0.148182\pi\)
\(348\) 1.22570i 0.0657042i
\(349\) 16.3684 0.876181 0.438091 0.898931i \(-0.355655\pi\)
0.438091 + 0.898931i \(0.355655\pi\)
\(350\) 9.14764 + 2.62222i 0.488962 + 0.140163i
\(351\) 6.42864 0.343135
\(352\) 14.6824i 0.782577i
\(353\) 0.549086i 0.0292249i −0.999893 0.0146124i \(-0.995349\pi\)
0.999893 0.0146124i \(-0.00465145\pi\)
\(354\) −26.8385 −1.42645
\(355\) 0.622216 4.42864i 0.0330238 0.235048i
\(356\) 7.49823 0.397405
\(357\) 4.42864i 0.234388i
\(358\) 19.0321i 1.00588i
\(359\) 0.285442 0.0150651 0.00753253 0.999972i \(-0.497602\pi\)
0.00753253 + 0.999972i \(0.497602\pi\)
\(360\) 1.59210 + 0.223688i 0.0839113 + 0.0117894i
\(361\) −13.1017 −0.689564
\(362\) 23.0321i 1.21054i
\(363\) 7.00000i 0.367405i
\(364\) −10.4286 −0.546609
\(365\) 3.47949 + 0.488863i 0.182125 + 0.0255882i
\(366\) 13.0509 0.682179
\(367\) 1.71456i 0.0894992i 0.998998 + 0.0447496i \(0.0142490\pi\)
−0.998998 + 0.0447496i \(0.985751\pi\)
\(368\) 6.35551i 0.331304i
\(369\) 8.23506 0.428700
\(370\) 4.50760 32.0830i 0.234339 1.66791i
\(371\) −9.18421 −0.476820
\(372\) 8.40990i 0.436033i
\(373\) 16.0000i 0.828449i −0.910175 0.414224i \(-0.864053\pi\)
0.910175 0.414224i \(-0.135947\pi\)
\(374\) 16.8573 0.871669
\(375\) −10.2143 4.54617i −0.527465 0.234763i
\(376\) 1.98126 0.102176
\(377\) 4.85728i 0.250163i
\(378\) 1.90321i 0.0978907i
\(379\) 4.85728 0.249502 0.124751 0.992188i \(-0.460187\pi\)
0.124751 + 0.992188i \(0.460187\pi\)
\(380\) −1.22570 + 8.72393i −0.0628768 + 0.447528i
\(381\) 12.8573 0.658698
\(382\) 0.930409i 0.0476039i
\(383\) 8.38715i 0.428563i 0.976772 + 0.214282i \(0.0687411\pi\)
−0.976772 + 0.214282i \(0.931259\pi\)
\(384\) −5.64941 −0.288295
\(385\) −4.42864 0.622216i −0.225704 0.0317110i
\(386\) 43.6958 2.22406
\(387\) 10.1017i 0.513499i
\(388\) 19.3689i 0.983307i
\(389\) −8.95899 −0.454239 −0.227119 0.973867i \(-0.572931\pi\)
−0.227119 + 0.973867i \(0.572931\pi\)
\(390\) 27.0923 + 3.80642i 1.37187 + 0.192746i
\(391\) 6.10171 0.308577
\(392\) 0.719004i 0.0363152i
\(393\) 2.10171i 0.106017i
\(394\) −2.25380 −0.113545
\(395\) 1.51114 10.7556i 0.0760336 0.541171i
\(396\) 3.24443 0.163039
\(397\) 2.54909i 0.127935i −0.997952 0.0639675i \(-0.979625\pi\)
0.997952 0.0639675i \(-0.0203754\pi\)
\(398\) 16.7427i 0.839234i
\(399\) 2.42864 0.121584
\(400\) 22.1713 + 6.35551i 1.10857 + 0.317775i
\(401\) 0.958989 0.0478896 0.0239448 0.999713i \(-0.492377\pi\)
0.0239448 + 0.999713i \(0.492377\pi\)
\(402\) 5.24443i 0.261568i
\(403\) 33.3274i 1.66016i
\(404\) −2.40006 −0.119407
\(405\) 0.311108 2.21432i 0.0154591 0.110030i
\(406\) 1.43801 0.0713671
\(407\) 15.2257i 0.754710i
\(408\) 3.18421i 0.157642i
\(409\) 31.9813 1.58137 0.790686 0.612222i \(-0.209724\pi\)
0.790686 + 0.612222i \(0.209724\pi\)
\(410\) 34.7052 + 4.87601i 1.71397 + 0.240809i
\(411\) −15.9398 −0.786251
\(412\) 14.3684i 0.707881i
\(413\) 14.1017i 0.693900i
\(414\) 2.62222 0.128875
\(415\) −25.7146 3.61285i −1.26228 0.177348i
\(416\) −47.1941 −2.31388
\(417\) 11.6731i 0.571633i
\(418\) 9.24443i 0.452160i
\(419\) 0.470127 0.0229672 0.0114836 0.999934i \(-0.496345\pi\)
0.0114836 + 0.999934i \(0.496345\pi\)
\(420\) −0.504684 + 3.59210i −0.0246261 + 0.175277i
\(421\) −33.6128 −1.63819 −0.819095 0.573658i \(-0.805524\pi\)
−0.819095 + 0.573658i \(0.805524\pi\)
\(422\) 44.2034i 2.15179i
\(423\) 2.75557i 0.133980i
\(424\) −6.60348 −0.320693
\(425\) 6.10171 21.2859i 0.295976 1.03252i
\(426\) 3.80642 0.184422
\(427\) 6.85728i 0.331847i
\(428\) 2.86311i 0.138394i
\(429\) −12.8573 −0.620755
\(430\) −5.98126 + 42.5718i −0.288442 + 2.05300i
\(431\) 11.7146 0.564270 0.282135 0.959375i \(-0.408957\pi\)
0.282135 + 0.959375i \(0.408957\pi\)
\(432\) 4.61285i 0.221936i
\(433\) 0.0602231i 0.00289414i 0.999999 + 0.00144707i \(0.000460616\pi\)
−0.999999 + 0.00144707i \(0.999539\pi\)
\(434\) −9.86665 −0.473614
\(435\) −1.67307 0.235063i −0.0802176 0.0112704i
\(436\) 9.10525 0.436062
\(437\) 3.34614i 0.160068i
\(438\) 2.99063i 0.142898i
\(439\) 22.4286 1.07046 0.535230 0.844706i \(-0.320225\pi\)
0.535230 + 0.844706i \(0.320225\pi\)
\(440\) −3.18421 0.447375i −0.151801 0.0213278i
\(441\) 1.00000 0.0476190
\(442\) 54.1847i 2.57730i
\(443\) 23.9496i 1.13788i 0.822379 + 0.568940i \(0.192647\pi\)
−0.822379 + 0.568940i \(0.807353\pi\)
\(444\) 12.3497 0.586090
\(445\) −1.43801 + 10.2351i −0.0681681 + 0.485189i
\(446\) 28.9777 1.37214
\(447\) 21.2257i 1.00394i
\(448\) 4.74620i 0.224237i
\(449\) −29.4291 −1.38885 −0.694423 0.719567i \(-0.744340\pi\)
−0.694423 + 0.719567i \(0.744340\pi\)
\(450\) 2.62222 9.14764i 0.123612 0.431224i
\(451\) −16.4701 −0.775548
\(452\) 18.3082i 0.861145i
\(453\) 16.8573i 0.792024i
\(454\) −27.3461 −1.28342
\(455\) 2.00000 14.2351i 0.0937614 0.667350i
\(456\) 1.74620 0.0817733
\(457\) 3.14272i 0.147010i −0.997295 0.0735051i \(-0.976581\pi\)
0.997295 0.0735051i \(-0.0234185\pi\)
\(458\) 10.6824i 0.499158i
\(459\) 4.42864 0.206711
\(460\) 4.94914 + 0.695346i 0.230755 + 0.0324207i
\(461\) −3.37778 −0.157319 −0.0786596 0.996902i \(-0.525064\pi\)
−0.0786596 + 0.996902i \(0.525064\pi\)
\(462\) 3.80642i 0.177091i
\(463\) 20.8573i 0.969320i −0.874703 0.484660i \(-0.838943\pi\)
0.874703 0.484660i \(-0.161057\pi\)
\(464\) 3.48532 0.161802
\(465\) 11.4795 + 1.61285i 0.532349 + 0.0747940i
\(466\) −44.3180 −2.05299
\(467\) 14.3684i 0.664891i −0.943122 0.332446i \(-0.892126\pi\)
0.943122 0.332446i \(-0.107874\pi\)
\(468\) 10.4286i 0.482064i
\(469\) 2.75557 0.127240
\(470\) 1.63158 11.6128i 0.0752593 0.535661i
\(471\) 10.4286 0.480526
\(472\) 10.1392i 0.466694i
\(473\) 20.2034i 0.928954i
\(474\) 9.24443 0.424611
\(475\) −11.6731 3.34614i −0.535597 0.153532i
\(476\) −7.18421 −0.329288
\(477\) 9.18421i 0.420516i
\(478\) 16.1561i 0.738963i
\(479\) −6.36842 −0.290980 −0.145490 0.989360i \(-0.546476\pi\)
−0.145490 + 0.989360i \(0.546476\pi\)
\(480\) −2.28391 + 16.2558i −0.104246 + 0.741973i
\(481\) −48.9403 −2.23148
\(482\) 13.7877i 0.628012i
\(483\) 1.37778i 0.0626914i
\(484\) 11.3555 0.516160
\(485\) −26.4385 3.71456i −1.20051 0.168669i
\(486\) 1.90321 0.0863314
\(487\) 17.3274i 0.785180i 0.919714 + 0.392590i \(0.128421\pi\)
−0.919714 + 0.392590i \(0.871579\pi\)
\(488\) 4.93041i 0.223189i
\(489\) 20.8573 0.943199
\(490\) 4.21432 + 0.592104i 0.190384 + 0.0267485i
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) 13.3590i 0.602272i
\(493\) 3.34614i 0.150703i
\(494\) 29.7146 1.33692
\(495\) −0.622216 + 4.42864i −0.0279665 + 0.199053i
\(496\) −23.9140 −1.07377
\(497\) 2.00000i 0.0897123i
\(498\) 22.1017i 0.990401i
\(499\) −23.3461 −1.04512 −0.522558 0.852603i \(-0.675022\pi\)
−0.522558 + 0.852603i \(0.675022\pi\)
\(500\) 7.37487 16.5698i 0.329814 0.741025i
\(501\) −15.3461 −0.685615
\(502\) 52.5531i 2.34556i
\(503\) 0.387152i 0.0172623i −0.999963 0.00863113i \(-0.997253\pi\)
0.999963 0.00863113i \(-0.00274741\pi\)
\(504\) 0.719004 0.0320270
\(505\) 0.460282 3.27607i 0.0204823 0.145783i
\(506\) −5.24443 −0.233143
\(507\) 28.3274i 1.25806i
\(508\) 20.8573i 0.925392i
\(509\) 29.9496 1.32749 0.663747 0.747957i \(-0.268965\pi\)
0.663747 + 0.747957i \(0.268965\pi\)
\(510\) 18.6637 + 2.62222i 0.826443 + 0.116114i
\(511\) 1.57136 0.0695129
\(512\) 27.2306i 1.20343i
\(513\) 2.42864i 0.107227i
\(514\) −0.815792 −0.0359830
\(515\) 19.6128 + 2.75557i 0.864245 + 0.121425i
\(516\) −16.3872 −0.721404
\(517\) 5.51114i 0.242380i
\(518\) 14.4889i 0.636604i
\(519\) 2.06022 0.0904338
\(520\) 1.43801 10.2351i 0.0630608 0.448837i
\(521\) −18.5205 −0.811398 −0.405699 0.914007i \(-0.632972\pi\)
−0.405699 + 0.914007i \(0.632972\pi\)
\(522\) 1.43801i 0.0629399i
\(523\) 4.00000i 0.174908i 0.996169 + 0.0874539i \(0.0278730\pi\)
−0.996169 + 0.0874539i \(0.972127\pi\)
\(524\) 3.40943 0.148942
\(525\) −4.80642 1.37778i −0.209770 0.0601314i
\(526\) 17.8479 0.778206
\(527\) 22.9590i 1.00011i
\(528\) 9.22570i 0.401497i
\(529\) 21.1017 0.917466
\(530\) −5.43801 + 38.7052i −0.236212 + 1.68125i
\(531\) 14.1017 0.611962
\(532\) 3.93978i 0.170811i
\(533\) 52.9403i 2.29310i
\(534\) −8.79706 −0.380686
\(535\) 3.90813 + 0.549086i 0.168963 + 0.0237390i
\(536\) 1.98126 0.0855776
\(537\) 10.0000i 0.431532i
\(538\) 3.32339i 0.143282i
\(539\) −2.00000 −0.0861461
\(540\) 3.59210 + 0.504684i 0.154580 + 0.0217181i
\(541\) 14.5906 0.627298 0.313649 0.949539i \(-0.398449\pi\)
0.313649 + 0.949539i \(0.398449\pi\)
\(542\) 5.12981i 0.220344i
\(543\) 12.1017i 0.519334i
\(544\) −32.5116 −1.39392
\(545\) −1.74620 + 12.4286i −0.0747990 + 0.532384i
\(546\) 12.2351 0.523612
\(547\) 18.7556i 0.801930i −0.916093 0.400965i \(-0.868675\pi\)
0.916093 0.400965i \(-0.131325\pi\)
\(548\) 25.8578i 1.10459i
\(549\) −6.85728 −0.292662
\(550\) −5.24443 + 18.2953i −0.223623 + 0.780114i
\(551\) −1.83500 −0.0781738
\(552\) 0.990632i 0.0421641i
\(553\) 4.85728i 0.206553i
\(554\) −9.75203 −0.414324
\(555\) −2.36842 + 16.8573i −0.100534 + 0.715552i
\(556\) 18.9362 0.803075
\(557\) 31.8765i 1.35065i 0.737520 + 0.675325i \(0.235997\pi\)
−0.737520 + 0.675325i \(0.764003\pi\)
\(558\) 9.86665i 0.417688i
\(559\) 64.9403 2.74668
\(560\) 10.2143 + 1.43509i 0.431634 + 0.0606437i
\(561\) −8.85728 −0.373955
\(562\) 45.6414i 1.92527i
\(563\) 2.01874i 0.0850796i 0.999095 + 0.0425398i \(0.0135449\pi\)
−0.999095 + 0.0425398i \(0.986455\pi\)
\(564\) 4.47013 0.188226
\(565\) 24.9906 + 3.51114i 1.05136 + 0.147715i
\(566\) −4.50760 −0.189468
\(567\) 1.00000i 0.0419961i
\(568\) 1.43801i 0.0603375i
\(569\) 28.9590 1.21402 0.607012 0.794693i \(-0.292368\pi\)
0.607012 + 0.794693i \(0.292368\pi\)
\(570\) 1.43801 10.2351i 0.0602315 0.428700i
\(571\) 8.97773 0.375706 0.187853 0.982197i \(-0.439847\pi\)
0.187853 + 0.982197i \(0.439847\pi\)
\(572\) 20.8573i 0.872087i
\(573\) 0.488863i 0.0204225i
\(574\) 15.6731 0.654181
\(575\) −1.89829 + 6.62222i −0.0791642 + 0.276165i
\(576\) −4.74620 −0.197758
\(577\) 28.6766i 1.19382i 0.802307 + 0.596911i \(0.203606\pi\)
−0.802307 + 0.596911i \(0.796394\pi\)
\(578\) 4.97280i 0.206841i
\(579\) −22.9590 −0.954143
\(580\) 0.381323 2.71408i 0.0158336 0.112696i
\(581\) −11.6128 −0.481782
\(582\) 22.7239i 0.941937i
\(583\) 18.3684i 0.760742i
\(584\) 1.12981 0.0467520
\(585\) −14.2351 2.00000i −0.588547 0.0826898i
\(586\) −16.0415 −0.662668
\(587\) 45.2070i 1.86589i 0.360018 + 0.932945i \(0.382771\pi\)
−0.360018 + 0.932945i \(0.617229\pi\)
\(588\) 1.62222i 0.0668990i
\(589\) 12.5906 0.518786
\(590\) 59.4291 + 8.34968i 2.44666 + 0.343751i
\(591\) 1.18421 0.0487118
\(592\) 35.1169i 1.44330i
\(593\) 18.2636i 0.749998i 0.927025 + 0.374999i \(0.122357\pi\)
−0.927025 + 0.374999i \(0.877643\pi\)
\(594\) −3.80642 −0.156179
\(595\) 1.37778 9.80642i 0.0564837 0.402024i
\(596\) −34.4327 −1.41042
\(597\) 8.79706i 0.360040i
\(598\) 16.8573i 0.689345i
\(599\) 22.7368 0.929002 0.464501 0.885573i \(-0.346234\pi\)
0.464501 + 0.885573i \(0.346234\pi\)
\(600\) −3.45584 0.990632i −0.141084 0.0404424i
\(601\) 0.488863 0.0199411 0.00997056 0.999950i \(-0.496826\pi\)
0.00997056 + 0.999950i \(0.496826\pi\)
\(602\) 19.2257i 0.783581i
\(603\) 2.75557i 0.112215i
\(604\) −27.3461 −1.11270
\(605\) −2.17775 + 15.5002i −0.0885383 + 0.630174i
\(606\) 2.81579 0.114384
\(607\) 20.2034i 0.820032i 0.912078 + 0.410016i \(0.134477\pi\)
−0.912078 + 0.410016i \(0.865523\pi\)
\(608\) 17.8292i 0.723069i
\(609\) −0.755569 −0.0306172
\(610\) −28.8988 4.06022i −1.17008 0.164394i
\(611\) −17.7146 −0.716654
\(612\) 7.18421i 0.290404i
\(613\) 10.3684i 0.418776i 0.977833 + 0.209388i \(0.0671472\pi\)
−0.977833 + 0.209388i \(0.932853\pi\)
\(614\) −42.9590 −1.73368
\(615\) −18.2351 2.56199i −0.735309 0.103310i
\(616\) −1.43801 −0.0579390
\(617\) 39.2859i 1.58159i 0.612080 + 0.790796i \(0.290333\pi\)
−0.612080 + 0.790796i \(0.709667\pi\)
\(618\) 16.8573i 0.678099i
\(619\) −42.8988 −1.72425 −0.862123 0.506698i \(-0.830866\pi\)
−0.862123 + 0.506698i \(0.830866\pi\)
\(620\) −2.61639 + 18.6222i −0.105077 + 0.747886i
\(621\) −1.37778 −0.0552886
\(622\) 45.8350i 1.83782i
\(623\) 4.62222i 0.185185i
\(624\) 29.6543 1.18712
\(625\) 21.2034 + 13.2444i 0.848137 + 0.529777i
\(626\) −18.3742 −0.734383
\(627\) 4.85728i 0.193981i
\(628\) 16.9175i 0.675082i
\(629\) −33.7146 −1.34429
\(630\) 0.592104 4.21432i 0.0235900 0.167903i
\(631\) 15.3461 0.610920 0.305460 0.952205i \(-0.401190\pi\)
0.305460 + 0.952205i \(0.401190\pi\)
\(632\) 3.49240i 0.138920i
\(633\) 23.2257i 0.923139i
\(634\) −11.4982 −0.456653
\(635\) −28.4701 4.00000i −1.12980 0.158735i
\(636\) −14.8988 −0.590775
\(637\) 6.42864i 0.254712i
\(638\) 2.87601i 0.113863i
\(639\) −2.00000 −0.0791188
\(640\) 12.5096 + 1.75758i 0.494486 + 0.0694743i
\(641\) 30.6735 1.21153 0.605766 0.795643i \(-0.292867\pi\)
0.605766 + 0.795643i \(0.292867\pi\)
\(642\) 3.35905i 0.132571i
\(643\) 49.0607i 1.93477i −0.253320 0.967383i \(-0.581523\pi\)
0.253320 0.967383i \(-0.418477\pi\)
\(644\) 2.23506 0.0880738
\(645\) 3.14272 22.3684i 0.123745 0.880756i
\(646\) 20.4701 0.805386
\(647\) 15.3461i 0.603319i 0.953416 + 0.301660i \(0.0975406\pi\)
−0.953416 + 0.301660i \(0.902459\pi\)
\(648\) 0.719004i 0.0282451i
\(649\) −28.2034 −1.10708
\(650\) −58.8069 16.8573i −2.30660 0.661197i
\(651\) 5.18421 0.203185
\(652\) 33.8350i 1.32508i
\(653\) 19.4697i 0.761906i −0.924594 0.380953i \(-0.875596\pi\)
0.924594 0.380953i \(-0.124404\pi\)
\(654\) −10.6824 −0.417716
\(655\) −0.653858 + 4.65386i −0.0255484 + 0.181841i
\(656\) 37.9871 1.48315
\(657\) 1.57136i 0.0613046i
\(658\) 5.24443i 0.204449i
\(659\) −30.9403 −1.20526 −0.602631 0.798020i \(-0.705881\pi\)
−0.602631 + 0.798020i \(0.705881\pi\)
\(660\) −7.18421 1.00937i −0.279645 0.0392896i
\(661\) 47.7975 1.85911 0.929554 0.368685i \(-0.120192\pi\)
0.929554 + 0.368685i \(0.120192\pi\)
\(662\) 25.7146i 0.999425i
\(663\) 28.4701i 1.10569i
\(664\) −8.34968 −0.324030
\(665\) −5.37778 0.755569i −0.208542 0.0292997i
\(666\) −14.4889 −0.561432
\(667\) 1.04101i 0.0403081i
\(668\) 24.8948i 0.963207i
\(669\) −15.2257 −0.588659
\(670\) 1.63158 11.6128i 0.0630336 0.448643i
\(671\) 13.7146 0.529445
\(672\) 7.34122i 0.283194i
\(673\) 27.8163i 1.07224i 0.844142 + 0.536119i \(0.180110\pi\)
−0.844142 + 0.536119i \(0.819890\pi\)
\(674\) 19.9625 0.768928
\(675\) −1.37778 + 4.80642i −0.0530309 + 0.184999i
\(676\) 45.9532 1.76743
\(677\) 19.0005i 0.730248i 0.930959 + 0.365124i \(0.118973\pi\)
−0.930959 + 0.365124i \(0.881027\pi\)
\(678\) 21.4795i 0.824915i
\(679\) −11.9398 −0.458207
\(680\) 0.990632 7.05086i 0.0379890 0.270388i
\(681\) 14.3684 0.550599
\(682\) 19.7333i 0.755627i
\(683\) 4.52051i 0.172972i 0.996253 + 0.0864862i \(0.0275638\pi\)
−0.996253 + 0.0864862i \(0.972436\pi\)
\(684\) 3.93978 0.150641
\(685\) 35.2958 + 4.95899i 1.34858 + 0.189473i
\(686\) 1.90321 0.0726650
\(687\) 5.61285i 0.214143i
\(688\) 46.5977i 1.77652i
\(689\) 59.0420 2.24932
\(690\) −5.80642 0.815792i −0.221047 0.0310567i
\(691\) −1.18421 −0.0450494 −0.0225247 0.999746i \(-0.507170\pi\)
−0.0225247 + 0.999746i \(0.507170\pi\)
\(692\) 3.34213i 0.127049i
\(693\) 2.00000i 0.0759737i
\(694\) −31.8292 −1.20822
\(695\) −3.63158 + 25.8479i −0.137754 + 0.980467i
\(696\) −0.543257 −0.0205921
\(697\) 36.4701i 1.38140i
\(698\) 31.1526i 1.17914i
\(699\) 23.2859 0.880754
\(700\) 2.23506 7.79706i 0.0844775 0.294701i
\(701\) −26.6735 −1.00745 −0.503723 0.863865i \(-0.668037\pi\)
−0.503723 + 0.863865i \(0.668037\pi\)
\(702\) 12.2351i 0.461783i
\(703\) 18.4889i 0.697321i
\(704\) 9.49240 0.357758
\(705\) −0.857279 + 6.10171i −0.0322870 + 0.229804i
\(706\) −1.04503 −0.0393301
\(707\) 1.47949i 0.0556421i
\(708\) 22.8760i 0.859733i
\(709\) 18.2034 0.683644 0.341822 0.939765i \(-0.388956\pi\)
0.341822 + 0.939765i \(0.388956\pi\)
\(710\) −8.42864 1.18421i −0.316321 0.0444425i
\(711\) −4.85728 −0.182162
\(712\) 3.32339i 0.124549i
\(713\) 7.14272i 0.267497i
\(714\) 8.42864 0.315434
\(715\) 28.4701 + 4.00000i 1.06472 + 0.149592i
\(716\) 16.2222 0.606250
\(717\) 8.48886i 0.317022i
\(718\) 0.543257i 0.0202742i
\(719\) −4.85728 −0.181146 −0.0905730 0.995890i \(-0.528870\pi\)
−0.0905730 + 0.995890i \(0.528870\pi\)
\(720\) 1.43509 10.2143i 0.0534828 0.380665i
\(721\) 8.85728 0.329862
\(722\) 24.9353i 0.927997i
\(723\) 7.24443i 0.269423i
\(724\) 19.6316 0.729602
\(725\) 3.63158 + 1.04101i 0.134874 + 0.0386622i
\(726\) −13.3225 −0.494444
\(727\) 21.0607i 0.781098i −0.920582 0.390549i \(-0.872285\pi\)
0.920582 0.390549i \(-0.127715\pi\)
\(728\) 4.62222i 0.171311i
\(729\) −1.00000 −0.0370370
\(730\) 0.930409 6.62222i 0.0344360 0.245099i
\(731\) 44.7368 1.65465
\(732\) 11.1240i 0.411154i
\(733\) 9.45091i 0.349077i 0.984650 + 0.174539i \(0.0558434\pi\)
−0.984650 + 0.174539i \(0.944157\pi\)
\(734\) 3.26317 0.120446
\(735\) −2.21432 0.311108i −0.0816764 0.0114754i
\(736\) 10.1146 0.372830
\(737\) 5.51114i 0.203005i
\(738\) 15.6731i 0.576934i
\(739\) 8.20342 0.301768 0.150884 0.988551i \(-0.451788\pi\)
0.150884 + 0.988551i \(0.451788\pi\)
\(740\) −27.3461 3.84208i −1.00526 0.141238i
\(741\) −15.6128 −0.573552
\(742\) 17.4795i 0.641692i
\(743\) 8.33677i 0.305847i 0.988238 + 0.152923i \(0.0488687\pi\)
−0.988238 + 0.152923i \(0.951131\pi\)
\(744\) 3.72746 0.136655
\(745\) 6.60348 47.0005i 0.241933 1.72196i
\(746\) −30.4514 −1.11490
\(747\) 11.6128i 0.424892i
\(748\) 14.3684i 0.525361i
\(749\) 1.76494 0.0644894
\(750\) −8.65233 + 19.4400i −0.315938 + 0.709849i
\(751\) −25.9180 −0.945760 −0.472880 0.881127i \(-0.656786\pi\)
−0.472880 + 0.881127i \(0.656786\pi\)
\(752\) 12.7110i 0.463523i
\(753\) 27.6128i 1.00627i
\(754\) −9.24443 −0.336662
\(755\) 5.24443 37.3274i 0.190864 1.35848i
\(756\) 1.62222 0.0589994
\(757\) 8.94025i 0.324939i −0.986714 0.162470i \(-0.948054\pi\)
0.986714 0.162470i \(-0.0519459\pi\)
\(758\) 9.24443i 0.335773i
\(759\) 2.75557 0.100021
\(760\) −3.86665 0.543257i −0.140258 0.0197060i
\(761\) −0.825636 −0.0299293 −0.0149646 0.999888i \(-0.504764\pi\)
−0.0149646 + 0.999888i \(0.504764\pi\)
\(762\) 24.4701i 0.886459i
\(763\) 5.61285i 0.203199i
\(764\) −0.793040 −0.0286912
\(765\) −9.80642 1.37778i −0.354552 0.0498139i
\(766\) 15.9625 0.576750
\(767\) 90.6548i 3.27336i
\(768\) 20.2444i 0.730508i
\(769\) −21.2257 −0.765418 −0.382709 0.923869i \(-0.625009\pi\)
−0.382709 + 0.923869i \(0.625009\pi\)
\(770\) −1.18421 + 8.42864i −0.0426759 + 0.303747i
\(771\) 0.428639 0.0154371
\(772\) 37.2444i 1.34046i
\(773\) 29.4893i 1.06066i 0.847792 + 0.530329i \(0.177932\pi\)
−0.847792 + 0.530329i \(0.822068\pi\)
\(774\) 19.2257 0.691053
\(775\) −24.9175 7.14272i −0.895063 0.256574i
\(776\) −8.58474 −0.308174
\(777\) 7.61285i 0.273109i
\(778\) 17.0509i 0.611303i
\(779\) −20.0000 −0.716574
\(780\) 3.24443 23.0923i 0.116169 0.826838i
\(781\) 4.00000 0.143131
\(782\) 11.6128i 0.415275i
\(783\) 0.755569i 0.0270018i
\(784\) 4.61285 0.164745
\(785\) −23.0923 3.24443i −0.824201 0.115799i
\(786\) −4.00000 −0.142675
\(787\) 34.4514i 1.22806i 0.789283 + 0.614030i \(0.210453\pi\)
−0.789283 + 0.614030i \(0.789547\pi\)
\(788\) 1.92104i 0.0684343i
\(789\) −9.37778 −0.333858
\(790\) −20.4701 2.87601i −0.728294 0.102324i
\(791\) 11.2859 0.401281