Properties

Label 105.2.d.b.64.6
Level 105
Weight 2
Character 105.64
Analytic conductor 0.838
Analytic rank 0
Dimension 6
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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 64.6
Root \(-0.854638 - 0.854638i\) of \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Character \(\chi\) \(=\) 105.64
Dual form 105.2.d.b.64.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.70928i q^{2} +1.00000i q^{3} -5.34017 q^{4} +(2.17009 + 0.539189i) q^{5} -2.70928 q^{6} -1.00000i q^{7} -9.04945i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+2.70928i q^{2} +1.00000i q^{3} -5.34017 q^{4} +(2.17009 + 0.539189i) q^{5} -2.70928 q^{6} -1.00000i q^{7} -9.04945i q^{8} -1.00000 q^{9} +(-1.46081 + 5.87936i) q^{10} +2.00000 q^{11} -5.34017i q^{12} +0.921622i q^{13} +2.70928 q^{14} +(-0.539189 + 2.17009i) q^{15} +13.8371 q^{16} -1.07838i q^{17} -2.70928i q^{18} -3.07838 q^{19} +(-11.5886 - 2.87936i) q^{20} +1.00000 q^{21} +5.41855i q^{22} +2.34017i q^{23} +9.04945 q^{24} +(4.41855 + 2.34017i) q^{25} -2.49693 q^{26} -1.00000i q^{27} +5.34017i q^{28} +6.68035 q^{29} +(-5.87936 - 1.46081i) q^{30} -7.75872 q^{31} +19.3896i q^{32} +2.00000i q^{33} +2.92162 q^{34} +(0.539189 - 2.17009i) q^{35} +5.34017 q^{36} -10.8371i q^{37} -8.34017i q^{38} -0.921622 q^{39} +(4.87936 - 19.6381i) q^{40} +6.49693 q^{41} +2.70928i q^{42} -6.52359i q^{43} -10.6803 q^{44} +(-2.17009 - 0.539189i) q^{45} -6.34017 q^{46} -4.68035i q^{47} +13.8371i q^{48} -1.00000 q^{49} +(-6.34017 + 11.9711i) q^{50} +1.07838 q^{51} -4.92162i q^{52} +3.75872i q^{53} +2.70928 q^{54} +(4.34017 + 1.07838i) q^{55} -9.04945 q^{56} -3.07838i q^{57} +18.0989i q^{58} -10.5236 q^{59} +(2.87936 - 11.5886i) q^{60} -4.15676 q^{61} -21.0205i q^{62} +1.00000i q^{63} -24.8576 q^{64} +(-0.496928 + 2.00000i) q^{65} -5.41855 q^{66} -4.68035i q^{67} +5.75872i q^{68} -2.34017 q^{69} +(5.87936 + 1.46081i) q^{70} +2.00000 q^{71} +9.04945i q^{72} +7.07838i q^{73} +29.3607 q^{74} +(-2.34017 + 4.41855i) q^{75} +16.4391 q^{76} -2.00000i q^{77} -2.49693i q^{78} -6.15676 q^{79} +(30.0277 + 7.46081i) q^{80} +1.00000 q^{81} +17.6020i q^{82} +6.83710i q^{83} -5.34017 q^{84} +(0.581449 - 2.34017i) q^{85} +17.6742 q^{86} +6.68035i q^{87} -18.0989i q^{88} -8.34017 q^{89} +(1.46081 - 5.87936i) q^{90} +0.921622 q^{91} -12.4969i q^{92} -7.75872i q^{93} +12.6803 q^{94} +(-6.68035 - 1.65983i) q^{95} -19.3896 q^{96} +8.43907i q^{97} -2.70928i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 10q^{4} + 2q^{5} - 2q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 10q^{4} + 2q^{5} - 2q^{6} - 6q^{9} - 12q^{10} + 12q^{11} + 2q^{14} + 26q^{16} - 12q^{19} - 30q^{20} + 6q^{21} + 18q^{24} - 2q^{25} + 20q^{26} - 4q^{29} - 10q^{30} + 4q^{31} + 24q^{34} + 10q^{36} - 12q^{39} + 4q^{40} + 4q^{41} - 20q^{44} - 2q^{45} - 16q^{46} - 6q^{49} - 16q^{50} + 2q^{54} + 4q^{55} - 18q^{56} - 32q^{59} - 8q^{60} - 12q^{61} - 26q^{64} + 32q^{65} - 4q^{66} + 8q^{69} + 10q^{70} + 12q^{71} + 88q^{74} + 8q^{75} + 4q^{76} - 24q^{79} + 46q^{80} + 6q^{81} - 10q^{84} + 32q^{85} - 8q^{86} - 28q^{89} + 12q^{90} + 12q^{91} + 32q^{94} + 4q^{95} - 58q^{96} - 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.70928i 1.91575i 0.287190 + 0.957873i \(0.407279\pi\)
−0.287190 + 0.957873i \(0.592721\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −5.34017 −2.67009
\(5\) 2.17009 + 0.539189i 0.970492 + 0.241133i
\(6\) −2.70928 −1.10606
\(7\) 1.00000i 0.377964i
\(8\) 9.04945i 3.19946i
\(9\) −1.00000 −0.333333
\(10\) −1.46081 + 5.87936i −0.461949 + 1.85922i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 5.34017i 1.54158i
\(13\) 0.921622i 0.255612i 0.991799 + 0.127806i \(0.0407935\pi\)
−0.991799 + 0.127806i \(0.959207\pi\)
\(14\) 2.70928 0.724084
\(15\) −0.539189 + 2.17009i −0.139218 + 0.560314i
\(16\) 13.8371 3.45928
\(17\) 1.07838i 0.261545i −0.991412 0.130773i \(-0.958254\pi\)
0.991412 0.130773i \(-0.0417457\pi\)
\(18\) 2.70928i 0.638582i
\(19\) −3.07838 −0.706228 −0.353114 0.935580i \(-0.614877\pi\)
−0.353114 + 0.935580i \(0.614877\pi\)
\(20\) −11.5886 2.87936i −2.59130 0.643845i
\(21\) 1.00000 0.218218
\(22\) 5.41855i 1.15524i
\(23\) 2.34017i 0.487960i 0.969780 + 0.243980i \(0.0784531\pi\)
−0.969780 + 0.243980i \(0.921547\pi\)
\(24\) 9.04945 1.84721
\(25\) 4.41855 + 2.34017i 0.883710 + 0.468035i
\(26\) −2.49693 −0.489688
\(27\) 1.00000i 0.192450i
\(28\) 5.34017i 1.00920i
\(29\) 6.68035 1.24051 0.620255 0.784401i \(-0.287029\pi\)
0.620255 + 0.784401i \(0.287029\pi\)
\(30\) −5.87936 1.46081i −1.07342 0.266706i
\(31\) −7.75872 −1.39351 −0.696754 0.717310i \(-0.745373\pi\)
−0.696754 + 0.717310i \(0.745373\pi\)
\(32\) 19.3896i 3.42763i
\(33\) 2.00000i 0.348155i
\(34\) 2.92162 0.501054
\(35\) 0.539189 2.17009i 0.0911396 0.366812i
\(36\) 5.34017 0.890029
\(37\) 10.8371i 1.78161i −0.454387 0.890804i \(-0.650142\pi\)
0.454387 0.890804i \(-0.349858\pi\)
\(38\) 8.34017i 1.35295i
\(39\) −0.921622 −0.147578
\(40\) 4.87936 19.6381i 0.771495 3.10505i
\(41\) 6.49693 1.01465 0.507325 0.861755i \(-0.330634\pi\)
0.507325 + 0.861755i \(0.330634\pi\)
\(42\) 2.70928i 0.418050i
\(43\) 6.52359i 0.994838i −0.867510 0.497419i \(-0.834281\pi\)
0.867510 0.497419i \(-0.165719\pi\)
\(44\) −10.6803 −1.61012
\(45\) −2.17009 0.539189i −0.323497 0.0803775i
\(46\) −6.34017 −0.934808
\(47\) 4.68035i 0.682699i −0.939937 0.341349i \(-0.889116\pi\)
0.939937 0.341349i \(-0.110884\pi\)
\(48\) 13.8371i 1.99721i
\(49\) −1.00000 −0.142857
\(50\) −6.34017 + 11.9711i −0.896636 + 1.69297i
\(51\) 1.07838 0.151003
\(52\) 4.92162i 0.682506i
\(53\) 3.75872i 0.516300i 0.966105 + 0.258150i \(0.0831129\pi\)
−0.966105 + 0.258150i \(0.916887\pi\)
\(54\) 2.70928 0.368686
\(55\) 4.34017 + 1.07838i 0.585229 + 0.145408i
\(56\) −9.04945 −1.20928
\(57\) 3.07838i 0.407741i
\(58\) 18.0989i 2.37650i
\(59\) −10.5236 −1.37005 −0.685027 0.728517i \(-0.740210\pi\)
−0.685027 + 0.728517i \(0.740210\pi\)
\(60\) 2.87936 11.5886i 0.371724 1.49609i
\(61\) −4.15676 −0.532218 −0.266109 0.963943i \(-0.585738\pi\)
−0.266109 + 0.963943i \(0.585738\pi\)
\(62\) 21.0205i 2.66961i
\(63\) 1.00000i 0.125988i
\(64\) −24.8576 −3.10720
\(65\) −0.496928 + 2.00000i −0.0616364 + 0.248069i
\(66\) −5.41855 −0.666977
\(67\) 4.68035i 0.571795i −0.958260 0.285898i \(-0.907708\pi\)
0.958260 0.285898i \(-0.0922917\pi\)
\(68\) 5.75872i 0.698348i
\(69\) −2.34017 −0.281724
\(70\) 5.87936 + 1.46081i 0.702718 + 0.174600i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 9.04945i 1.06649i
\(73\) 7.07838i 0.828461i 0.910172 + 0.414231i \(0.135949\pi\)
−0.910172 + 0.414231i \(0.864051\pi\)
\(74\) 29.3607 3.41311
\(75\) −2.34017 + 4.41855i −0.270220 + 0.510210i
\(76\) 16.4391 1.88569
\(77\) 2.00000i 0.227921i
\(78\) 2.49693i 0.282721i
\(79\) −6.15676 −0.692689 −0.346345 0.938107i \(-0.612577\pi\)
−0.346345 + 0.938107i \(0.612577\pi\)
\(80\) 30.0277 + 7.46081i 3.35720 + 0.834144i
\(81\) 1.00000 0.111111
\(82\) 17.6020i 1.94381i
\(83\) 6.83710i 0.750469i 0.926930 + 0.375235i \(0.122438\pi\)
−0.926930 + 0.375235i \(0.877562\pi\)
\(84\) −5.34017 −0.582661
\(85\) 0.581449 2.34017i 0.0630670 0.253827i
\(86\) 17.6742 1.90586
\(87\) 6.68035i 0.716208i
\(88\) 18.0989i 1.92935i
\(89\) −8.34017 −0.884057 −0.442028 0.897001i \(-0.645741\pi\)
−0.442028 + 0.897001i \(0.645741\pi\)
\(90\) 1.46081 5.87936i 0.153983 0.619739i
\(91\) 0.921622 0.0966123
\(92\) 12.4969i 1.30289i
\(93\) 7.75872i 0.804542i
\(94\) 12.6803 1.30788
\(95\) −6.68035 1.65983i −0.685389 0.170295i
\(96\) −19.3896 −1.97894
\(97\) 8.43907i 0.856858i 0.903576 + 0.428429i \(0.140933\pi\)
−0.903576 + 0.428429i \(0.859067\pi\)
\(98\) 2.70928i 0.273678i
\(99\) −2.00000 −0.201008
\(100\) −23.5958 12.4969i −2.35958 1.24969i
\(101\) −5.81658 −0.578772 −0.289386 0.957213i \(-0.593451\pi\)
−0.289386 + 0.957213i \(0.593451\pi\)
\(102\) 2.92162i 0.289284i
\(103\) 2.15676i 0.212511i −0.994339 0.106256i \(-0.966114\pi\)
0.994339 0.106256i \(-0.0338862\pi\)
\(104\) 8.34017 0.817821
\(105\) 2.17009 + 0.539189i 0.211779 + 0.0526194i
\(106\) −10.1834 −0.989101
\(107\) 16.4969i 1.59482i 0.603439 + 0.797409i \(0.293797\pi\)
−0.603439 + 0.797409i \(0.706203\pi\)
\(108\) 5.34017i 0.513858i
\(109\) 12.8371 1.22957 0.614786 0.788694i \(-0.289243\pi\)
0.614786 + 0.788694i \(0.289243\pi\)
\(110\) −2.92162 + 11.7587i −0.278566 + 1.12115i
\(111\) 10.8371 1.02861
\(112\) 13.8371i 1.30748i
\(113\) 5.23513i 0.492480i −0.969209 0.246240i \(-0.920805\pi\)
0.969209 0.246240i \(-0.0791951\pi\)
\(114\) 8.34017 0.781129
\(115\) −1.26180 + 5.07838i −0.117663 + 0.473561i
\(116\) −35.6742 −3.31227
\(117\) 0.921622i 0.0852040i
\(118\) 28.5113i 2.62468i
\(119\) −1.07838 −0.0988547
\(120\) 19.6381 + 4.87936i 1.79270 + 0.445423i
\(121\) −7.00000 −0.636364
\(122\) 11.2618i 1.01960i
\(123\) 6.49693i 0.585808i
\(124\) 41.4329 3.72079
\(125\) 8.32684 + 7.46081i 0.744775 + 0.667315i
\(126\) −2.70928 −0.241361
\(127\) 1.84324i 0.163562i −0.996650 0.0817808i \(-0.973939\pi\)
0.996650 0.0817808i \(-0.0260607\pi\)
\(128\) 28.5669i 2.52498i
\(129\) 6.52359 0.574370
\(130\) −5.41855 1.34632i −0.475238 0.118080i
\(131\) 1.47641 0.128995 0.0644973 0.997918i \(-0.479456\pi\)
0.0644973 + 0.997918i \(0.479456\pi\)
\(132\) 10.6803i 0.929605i
\(133\) 3.07838i 0.266929i
\(134\) 12.6803 1.09542
\(135\) 0.539189 2.17009i 0.0464060 0.186771i
\(136\) −9.75872 −0.836804
\(137\) 4.43907i 0.379255i −0.981856 0.189628i \(-0.939272\pi\)
0.981856 0.189628i \(-0.0607281\pi\)
\(138\) 6.34017i 0.539711i
\(139\) −13.6020 −1.15370 −0.576852 0.816849i \(-0.695719\pi\)
−0.576852 + 0.816849i \(0.695719\pi\)
\(140\) −2.87936 + 11.5886i −0.243350 + 0.979419i
\(141\) 4.68035 0.394156
\(142\) 5.41855i 0.454715i
\(143\) 1.84324i 0.154140i
\(144\) −13.8371 −1.15309
\(145\) 14.4969 + 3.60197i 1.20390 + 0.299127i
\(146\) −19.1773 −1.58712
\(147\) 1.00000i 0.0824786i
\(148\) 57.8720i 4.75705i
\(149\) −15.6742 −1.28408 −0.642040 0.766671i \(-0.721912\pi\)
−0.642040 + 0.766671i \(0.721912\pi\)
\(150\) −11.9711 6.34017i −0.977434 0.517673i
\(151\) 5.84324 0.475516 0.237758 0.971324i \(-0.423587\pi\)
0.237758 + 0.971324i \(0.423587\pi\)
\(152\) 27.8576i 2.25955i
\(153\) 1.07838i 0.0871817i
\(154\) 5.41855 0.436639
\(155\) −16.8371 4.18342i −1.35239 0.336020i
\(156\) 4.92162 0.394045
\(157\) 4.92162i 0.392788i −0.980525 0.196394i \(-0.937077\pi\)
0.980525 0.196394i \(-0.0629232\pi\)
\(158\) 16.6803i 1.32702i
\(159\) −3.75872 −0.298086
\(160\) −10.4547 + 42.0772i −0.826514 + 3.32649i
\(161\) 2.34017 0.184431
\(162\) 2.70928i 0.212861i
\(163\) 9.84324i 0.770982i −0.922712 0.385491i \(-0.874032\pi\)
0.922712 0.385491i \(-0.125968\pi\)
\(164\) −34.6947 −2.70920
\(165\) −1.07838 + 4.34017i −0.0839516 + 0.337882i
\(166\) −18.5236 −1.43771
\(167\) 19.2039i 1.48605i 0.669266 + 0.743023i \(0.266609\pi\)
−0.669266 + 0.743023i \(0.733391\pi\)
\(168\) 9.04945i 0.698180i
\(169\) 12.1506 0.934662
\(170\) 6.34017 + 1.57531i 0.486269 + 0.120820i
\(171\) 3.07838 0.235409
\(172\) 34.8371i 2.65630i
\(173\) 22.4391i 1.70601i −0.521902 0.853005i \(-0.674777\pi\)
0.521902 0.853005i \(-0.325223\pi\)
\(174\) −18.0989 −1.37207
\(175\) 2.34017 4.41855i 0.176900 0.334011i
\(176\) 27.6742 2.08602
\(177\) 10.5236i 0.791001i
\(178\) 22.5958i 1.69363i
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 11.5886 + 2.87936i 0.863766 + 0.214615i
\(181\) −8.52359 −0.633553 −0.316777 0.948500i \(-0.602601\pi\)
−0.316777 + 0.948500i \(0.602601\pi\)
\(182\) 2.49693i 0.185085i
\(183\) 4.15676i 0.307276i
\(184\) 21.1773 1.56121
\(185\) 5.84324 23.5174i 0.429604 1.72904i
\(186\) 21.0205 1.54130
\(187\) 2.15676i 0.157718i
\(188\) 24.9939i 1.82286i
\(189\) −1.00000 −0.0727393
\(190\) 4.49693 18.0989i 0.326241 1.31303i
\(191\) 15.3607 1.11146 0.555730 0.831363i \(-0.312439\pi\)
0.555730 + 0.831363i \(0.312439\pi\)
\(192\) 24.8576i 1.79394i
\(193\) 8.36683i 0.602258i 0.953583 + 0.301129i \(0.0973635\pi\)
−0.953583 + 0.301129i \(0.902637\pi\)
\(194\) −22.8638 −1.64152
\(195\) −2.00000 0.496928i −0.143223 0.0355858i
\(196\) 5.34017 0.381441
\(197\) 11.7587i 0.837774i 0.908038 + 0.418887i \(0.137580\pi\)
−0.908038 + 0.418887i \(0.862420\pi\)
\(198\) 5.41855i 0.385080i
\(199\) 22.5958 1.60178 0.800888 0.598814i \(-0.204361\pi\)
0.800888 + 0.598814i \(0.204361\pi\)
\(200\) 21.1773 39.9854i 1.49746 2.82740i
\(201\) 4.68035 0.330126
\(202\) 15.7587i 1.10878i
\(203\) 6.68035i 0.468868i
\(204\) −5.75872 −0.403191
\(205\) 14.0989 + 3.50307i 0.984710 + 0.244665i
\(206\) 5.84324 0.407118
\(207\) 2.34017i 0.162653i
\(208\) 12.7526i 0.884232i
\(209\) −6.15676 −0.425872
\(210\) −1.46081 + 5.87936i −0.100806 + 0.405715i
\(211\) −13.6742 −0.941371 −0.470685 0.882301i \(-0.655993\pi\)
−0.470685 + 0.882301i \(0.655993\pi\)
\(212\) 20.0722i 1.37857i
\(213\) 2.00000i 0.137038i
\(214\) −44.6947 −3.05527
\(215\) 3.51745 14.1568i 0.239888 0.965483i
\(216\) −9.04945 −0.615737
\(217\) 7.75872i 0.526696i
\(218\) 34.7792i 2.35555i
\(219\) −7.07838 −0.478312
\(220\) −23.1773 5.75872i −1.56261 0.388253i
\(221\) 0.993857 0.0668541
\(222\) 29.3607i 1.97056i
\(223\) 21.6742i 1.45141i −0.688005 0.725706i \(-0.741513\pi\)
0.688005 0.725706i \(-0.258487\pi\)
\(224\) 19.3896 1.29552
\(225\) −4.41855 2.34017i −0.294570 0.156012i
\(226\) 14.1834 0.943467
\(227\) 11.5174i 0.764440i 0.924071 + 0.382220i \(0.124840\pi\)
−0.924071 + 0.382220i \(0.875160\pi\)
\(228\) 16.4391i 1.08870i
\(229\) −12.8371 −0.848300 −0.424150 0.905592i \(-0.639427\pi\)
−0.424150 + 0.905592i \(0.639427\pi\)
\(230\) −13.7587 3.41855i −0.907223 0.225413i
\(231\) 2.00000 0.131590
\(232\) 60.4534i 3.96896i
\(233\) 6.76487i 0.443181i −0.975140 0.221591i \(-0.928875\pi\)
0.975140 0.221591i \(-0.0711248\pi\)
\(234\) 2.49693 0.163229
\(235\) 2.52359 10.1568i 0.164621 0.662554i
\(236\) 56.1978 3.65816
\(237\) 6.15676i 0.399924i
\(238\) 2.92162i 0.189381i
\(239\) 23.3607 1.51108 0.755539 0.655104i \(-0.227375\pi\)
0.755539 + 0.655104i \(0.227375\pi\)
\(240\) −7.46081 + 30.0277i −0.481593 + 1.93828i
\(241\) −14.6803 −0.945644 −0.472822 0.881158i \(-0.656765\pi\)
−0.472822 + 0.881158i \(0.656765\pi\)
\(242\) 18.9649i 1.21911i
\(243\) 1.00000i 0.0641500i
\(244\) 22.1978 1.42107
\(245\) −2.17009 0.539189i −0.138642 0.0344475i
\(246\) −17.6020 −1.12226
\(247\) 2.83710i 0.180520i
\(248\) 70.2122i 4.45848i
\(249\) −6.83710 −0.433284
\(250\) −20.2134 + 22.5597i −1.27841 + 1.42680i
\(251\) 9.16290 0.578357 0.289179 0.957275i \(-0.406618\pi\)
0.289179 + 0.957275i \(0.406618\pi\)
\(252\) 5.34017i 0.336399i
\(253\) 4.68035i 0.294251i
\(254\) 4.99386 0.313342
\(255\) 2.34017 + 0.581449i 0.146547 + 0.0364118i
\(256\) 27.6803 1.73002
\(257\) 5.07838i 0.316781i 0.987377 + 0.158390i \(0.0506304\pi\)
−0.987377 + 0.158390i \(0.949370\pi\)
\(258\) 17.6742i 1.10035i
\(259\) −10.8371 −0.673385
\(260\) 2.65368 10.6803i 0.164574 0.662367i
\(261\) −6.68035 −0.413503
\(262\) 4.00000i 0.247121i
\(263\) 5.65983i 0.349000i 0.984657 + 0.174500i \(0.0558309\pi\)
−0.984657 + 0.174500i \(0.944169\pi\)
\(264\) 18.0989 1.11391
\(265\) −2.02666 + 8.15676i −0.124497 + 0.501066i
\(266\) −8.34017 −0.511369
\(267\) 8.34017i 0.510410i
\(268\) 24.9939i 1.52674i
\(269\) 27.8576 1.69851 0.849255 0.527984i \(-0.177052\pi\)
0.849255 + 0.527984i \(0.177052\pi\)
\(270\) 5.87936 + 1.46081i 0.357807 + 0.0889021i
\(271\) 25.1194 1.52590 0.762948 0.646460i \(-0.223751\pi\)
0.762948 + 0.646460i \(0.223751\pi\)
\(272\) 14.9216i 0.904756i
\(273\) 0.921622i 0.0557791i
\(274\) 12.0267 0.726557
\(275\) 8.83710 + 4.68035i 0.532897 + 0.282235i
\(276\) 12.4969 0.752227
\(277\) 28.1978i 1.69424i 0.531401 + 0.847121i \(0.321666\pi\)
−0.531401 + 0.847121i \(0.678334\pi\)
\(278\) 36.8515i 2.21020i
\(279\) 7.75872 0.464503
\(280\) −19.6381 4.87936i −1.17360 0.291598i
\(281\) −20.3545 −1.21425 −0.607125 0.794606i \(-0.707677\pi\)
−0.607125 + 0.794606i \(0.707677\pi\)
\(282\) 12.6803i 0.755104i
\(283\) 23.5174i 1.39797i 0.715138 + 0.698984i \(0.246364\pi\)
−0.715138 + 0.698984i \(0.753636\pi\)
\(284\) −10.6803 −0.633762
\(285\) 1.65983 6.68035i 0.0983197 0.395710i
\(286\) −4.99386 −0.295293
\(287\) 6.49693i 0.383502i
\(288\) 19.3896i 1.14254i
\(289\) 15.8371 0.931594
\(290\) −9.75872 + 39.2762i −0.573052 + 2.30638i
\(291\) −8.43907 −0.494707
\(292\) 37.7998i 2.21206i
\(293\) 2.92162i 0.170683i −0.996352 0.0853415i \(-0.972802\pi\)
0.996352 0.0853415i \(-0.0271981\pi\)
\(294\) 2.70928 0.158008
\(295\) −22.8371 5.67420i −1.32963 0.330365i
\(296\) −98.0698 −5.70019
\(297\) 2.00000i 0.116052i
\(298\) 42.4657i 2.45997i
\(299\) −2.15676 −0.124728
\(300\) 12.4969 23.5958i 0.721511 1.36231i
\(301\) −6.52359 −0.376014
\(302\) 15.8310i 0.910969i
\(303\) 5.81658i 0.334154i
\(304\) −42.5958 −2.44304
\(305\) −9.02052 2.24128i −0.516513 0.128335i
\(306\) −2.92162 −0.167018
\(307\) 10.4703i 0.597570i 0.954321 + 0.298785i \(0.0965813\pi\)
−0.954321 + 0.298785i \(0.903419\pi\)
\(308\) 10.6803i 0.608569i
\(309\) 2.15676 0.122694
\(310\) 11.3340 45.6163i 0.643730 2.59083i
\(311\) 23.8310 1.35133 0.675665 0.737209i \(-0.263857\pi\)
0.675665 + 0.737209i \(0.263857\pi\)
\(312\) 8.34017i 0.472169i
\(313\) 32.7526i 1.85129i 0.378399 + 0.925643i \(0.376475\pi\)
−0.378399 + 0.925643i \(0.623525\pi\)
\(314\) 13.3340 0.752483
\(315\) −0.539189 + 2.17009i −0.0303799 + 0.122271i
\(316\) 32.8781 1.84954
\(317\) 17.9155i 1.00623i 0.864218 + 0.503117i \(0.167813\pi\)
−0.864218 + 0.503117i \(0.832187\pi\)
\(318\) 10.1834i 0.571058i
\(319\) 13.3607 0.748055
\(320\) −53.9432 13.4030i −3.01552 0.749248i
\(321\) −16.4969 −0.920769
\(322\) 6.34017i 0.353324i
\(323\) 3.31965i 0.184710i
\(324\) −5.34017 −0.296676
\(325\) −2.15676 + 4.07223i −0.119635 + 0.225887i
\(326\) 26.6681 1.47701
\(327\) 12.8371i 0.709893i
\(328\) 58.7936i 3.24633i
\(329\) −4.68035 −0.258036
\(330\) −11.7587 2.92162i −0.647296 0.160830i
\(331\) −1.36069 −0.0747904 −0.0373952 0.999301i \(-0.511906\pi\)
−0.0373952 + 0.999301i \(0.511906\pi\)
\(332\) 36.5113i 2.00382i
\(333\) 10.8371i 0.593870i
\(334\) −52.0288 −2.84689
\(335\) 2.52359 10.1568i 0.137878 0.554923i
\(336\) 13.8371 0.754876
\(337\) 25.3607i 1.38148i 0.723101 + 0.690742i \(0.242716\pi\)
−0.723101 + 0.690742i \(0.757284\pi\)
\(338\) 32.9194i 1.79058i
\(339\) 5.23513 0.284333
\(340\) −3.10504 + 12.4969i −0.168394 + 0.677741i
\(341\) −15.5174 −0.840317
\(342\) 8.34017i 0.450985i
\(343\) 1.00000i 0.0539949i
\(344\) −59.0349 −3.18295
\(345\) −5.07838 1.26180i −0.273411 0.0679328i
\(346\) 60.7936 3.26829
\(347\) 16.8638i 0.905294i −0.891690 0.452647i \(-0.850480\pi\)
0.891690 0.452647i \(-0.149520\pi\)
\(348\) 35.6742i 1.91234i
\(349\) −9.51745 −0.509457 −0.254729 0.967013i \(-0.581986\pi\)
−0.254729 + 0.967013i \(0.581986\pi\)
\(350\) 11.9711 + 6.34017i 0.639881 + 0.338897i
\(351\) 0.921622 0.0491926
\(352\) 38.7792i 2.06694i
\(353\) 35.7998i 1.90543i −0.303867 0.952715i \(-0.598278\pi\)
0.303867 0.952715i \(-0.401722\pi\)
\(354\) 28.5113 1.51536
\(355\) 4.34017 + 1.07838i 0.230352 + 0.0572343i
\(356\) 44.5380 2.36051
\(357\) 1.07838i 0.0570738i
\(358\) 27.0928i 1.43190i
\(359\) 22.3135 1.17766 0.588831 0.808256i \(-0.299588\pi\)
0.588831 + 0.808256i \(0.299588\pi\)
\(360\) −4.87936 + 19.6381i −0.257165 + 1.03502i
\(361\) −9.52359 −0.501242
\(362\) 23.0928i 1.21373i
\(363\) 7.00000i 0.367405i
\(364\) −4.92162 −0.257963
\(365\) −3.81658 + 15.3607i −0.199769 + 0.804015i
\(366\) 11.2618 0.588663
\(367\) 20.3135i 1.06036i −0.847886 0.530178i \(-0.822125\pi\)
0.847886 0.530178i \(-0.177875\pi\)
\(368\) 32.3812i 1.68799i
\(369\) −6.49693 −0.338217
\(370\) 63.7152 + 15.8310i 3.31240 + 0.823012i
\(371\) 3.75872 0.195143
\(372\) 41.4329i 2.14820i
\(373\) 16.0000i 0.828449i −0.910175 0.414224i \(-0.864053\pi\)
0.910175 0.414224i \(-0.135947\pi\)
\(374\) 5.84324 0.302147
\(375\) −7.46081 + 8.32684i −0.385275 + 0.429996i
\(376\) −42.3545 −2.18427
\(377\) 6.15676i 0.317089i
\(378\) 2.70928i 0.139350i
\(379\) −6.15676 −0.316251 −0.158126 0.987419i \(-0.550545\pi\)
−0.158126 + 0.987419i \(0.550545\pi\)
\(380\) 35.6742 + 8.86376i 1.83005 + 0.454701i
\(381\) 1.84324 0.0944323
\(382\) 41.6163i 2.12928i
\(383\) 26.8371i 1.37131i 0.727926 + 0.685656i \(0.240485\pi\)
−0.727926 + 0.685656i \(0.759515\pi\)
\(384\) 28.5669 1.45780
\(385\) 1.07838 4.34017i 0.0549592 0.221196i
\(386\) −22.6681 −1.15377
\(387\) 6.52359i 0.331613i
\(388\) 45.0661i 2.28788i
\(389\) 5.63317 0.285613 0.142806 0.989751i \(-0.454387\pi\)
0.142806 + 0.989751i \(0.454387\pi\)
\(390\) 1.34632 5.41855i 0.0681734 0.274379i
\(391\) 2.52359 0.127623
\(392\) 9.04945i 0.457066i
\(393\) 1.47641i 0.0744750i
\(394\) −31.8576 −1.60496
\(395\) −13.3607 3.31965i −0.672249 0.167030i
\(396\) 10.6803 0.536708
\(397\) 37.7998i 1.89712i −0.316604 0.948558i \(-0.602543\pi\)
0.316604 0.948558i \(-0.397457\pi\)
\(398\) 61.2183i 3.06860i
\(399\) −3.07838 −0.154112
\(400\) 61.1399 + 32.3812i 3.05700 + 1.61906i
\(401\) −13.6332 −0.680808 −0.340404 0.940279i \(-0.610564\pi\)
−0.340404 + 0.940279i \(0.610564\pi\)
\(402\) 12.6803i 0.632438i
\(403\) 7.15061i 0.356197i
\(404\) 31.0616 1.54537
\(405\) 2.17009 + 0.539189i 0.107832 + 0.0267925i
\(406\) 18.0989 0.898233
\(407\) 21.6742i 1.07435i
\(408\) 9.75872i 0.483129i
\(409\) −12.3545 −0.610893 −0.305447 0.952209i \(-0.598806\pi\)
−0.305447 + 0.952209i \(0.598806\pi\)
\(410\) −9.49079 + 38.1978i −0.468716 + 1.88645i
\(411\) 4.43907 0.218963
\(412\) 11.5174i 0.567424i
\(413\) 10.5236i 0.517832i
\(414\) 6.34017 0.311603
\(415\) −3.68649 + 14.8371i −0.180963 + 0.728325i
\(416\) −17.8699 −0.876144
\(417\) 13.6020i 0.666091i
\(418\) 16.6803i 0.815862i
\(419\) −28.9939 −1.41644 −0.708221 0.705991i \(-0.750502\pi\)
−0.708221 + 0.705991i \(0.750502\pi\)
\(420\) −11.5886 2.87936i −0.565468 0.140498i
\(421\) −15.1629 −0.738994 −0.369497 0.929232i \(-0.620470\pi\)
−0.369497 + 0.929232i \(0.620470\pi\)
\(422\) 37.0472i 1.80343i
\(423\) 4.68035i 0.227566i
\(424\) 34.0144 1.65188
\(425\) 2.52359 4.76487i 0.122412 0.231130i
\(426\) −5.41855 −0.262530
\(427\) 4.15676i 0.201159i
\(428\) 88.0965i 4.25830i
\(429\) −1.84324 −0.0889927
\(430\) 38.3545 + 9.52973i 1.84962 + 0.459565i
\(431\) −10.3135 −0.496784 −0.248392 0.968660i \(-0.579902\pi\)
−0.248392 + 0.968660i \(0.579902\pi\)
\(432\) 13.8371i 0.665738i
\(433\) 20.4391i 0.982239i 0.871092 + 0.491120i \(0.163412\pi\)
−0.871092 + 0.491120i \(0.836588\pi\)
\(434\) −21.0205 −1.00902
\(435\) −3.60197 + 14.4969i −0.172701 + 0.695075i
\(436\) −68.5523 −3.28306
\(437\) 7.20394i 0.344611i
\(438\) 19.1773i 0.916326i
\(439\) 16.9216 0.807625 0.403812 0.914842i \(-0.367685\pi\)
0.403812 + 0.914842i \(0.367685\pi\)
\(440\) 9.75872 39.2762i 0.465229 1.87242i
\(441\) 1.00000 0.0476190
\(442\) 2.69263i 0.128075i
\(443\) 12.8104i 0.608642i −0.952569 0.304321i \(-0.901570\pi\)
0.952569 0.304321i \(-0.0984296\pi\)
\(444\) −57.8720 −2.74648
\(445\) −18.0989 4.49693i −0.857970 0.213175i
\(446\) 58.7214 2.78054
\(447\) 15.6742i 0.741364i
\(448\) 24.8576i 1.17441i
\(449\) 14.6270 0.690292 0.345146 0.938549i \(-0.387829\pi\)
0.345146 + 0.938549i \(0.387829\pi\)
\(450\) 6.34017 11.9711i 0.298879 0.564322i
\(451\) 12.9939 0.611857
\(452\) 27.9565i 1.31496i
\(453\) 5.84324i 0.274540i
\(454\) −31.2039 −1.46447
\(455\) 2.00000 + 0.496928i 0.0937614 + 0.0232964i
\(456\) −27.8576 −1.30455
\(457\) 14.1568i 0.662225i −0.943591 0.331113i \(-0.892576\pi\)
0.943591 0.331113i \(-0.107424\pi\)
\(458\) 34.7792i 1.62513i
\(459\) −1.07838 −0.0503344
\(460\) 6.73820 27.1194i 0.314170 1.26445i
\(461\) 0.340173 0.0158434 0.00792172 0.999969i \(-0.497478\pi\)
0.00792172 + 0.999969i \(0.497478\pi\)
\(462\) 5.41855i 0.252094i
\(463\) 9.84324i 0.457454i −0.973491 0.228727i \(-0.926544\pi\)
0.973491 0.228727i \(-0.0734564\pi\)
\(464\) 92.4366 4.29126
\(465\) 4.18342 16.8371i 0.194001 0.780802i
\(466\) 18.3279 0.849023
\(467\) 11.5174i 0.532964i 0.963840 + 0.266482i \(0.0858613\pi\)
−0.963840 + 0.266482i \(0.914139\pi\)
\(468\) 4.92162i 0.227502i
\(469\) −4.68035 −0.216118
\(470\) 27.5174 + 6.83710i 1.26929 + 0.315372i
\(471\) 4.92162 0.226776
\(472\) 95.2327i 4.38344i
\(473\) 13.0472i 0.599910i
\(474\) 16.6803 0.766154
\(475\) −13.6020 7.20394i −0.624101 0.330539i
\(476\) 5.75872 0.263951
\(477\) 3.75872i 0.172100i
\(478\) 63.2905i 2.89484i
\(479\) 19.5174 0.891775 0.445887 0.895089i \(-0.352888\pi\)
0.445887 + 0.895089i \(0.352888\pi\)
\(480\) −42.0772 10.4547i −1.92055 0.477188i
\(481\) 9.98771 0.455401
\(482\) 39.7731i 1.81162i
\(483\) 2.34017i 0.106482i
\(484\) 37.3812 1.69915
\(485\) −4.55025 + 18.3135i −0.206616 + 0.831574i
\(486\) −2.70928 −0.122895
\(487\) 23.1506i 1.04905i −0.851394 0.524527i \(-0.824242\pi\)
0.851394 0.524527i \(-0.175758\pi\)
\(488\) 37.6163i 1.70281i
\(489\) 9.84324 0.445127
\(490\) 1.46081 5.87936i 0.0659927 0.265602i
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) 34.6947i 1.56416i
\(493\) 7.20394i 0.324449i
\(494\) 7.68649 0.345831
\(495\) −4.34017 1.07838i −0.195076 0.0484695i
\(496\) −107.358 −4.82053
\(497\) 2.00000i 0.0897123i
\(498\) 18.5236i 0.830062i
\(499\) −27.2039 −1.21782 −0.608908 0.793241i \(-0.708392\pi\)
−0.608908 + 0.793241i \(0.708392\pi\)
\(500\) −44.4668 39.8420i −1.98861 1.78179i
\(501\) −19.2039 −0.857969
\(502\) 24.8248i 1.10799i
\(503\) 18.8371i 0.839905i −0.907546 0.419952i \(-0.862047\pi\)
0.907546 0.419952i \(-0.137953\pi\)
\(504\) 9.04945 0.403094
\(505\) −12.6225 3.13624i −0.561693 0.139561i
\(506\) −12.6803 −0.563710
\(507\) 12.1506i 0.539628i
\(508\) 9.84324i 0.436723i
\(509\) −6.81044 −0.301867 −0.150934 0.988544i \(-0.548228\pi\)
−0.150934 + 0.988544i \(0.548228\pi\)
\(510\) −1.57531 + 6.34017i −0.0697557 + 0.280748i
\(511\) 7.07838 0.313129
\(512\) 17.8599i 0.789303i
\(513\) 3.07838i 0.135914i
\(514\) −13.7587 −0.606871
\(515\) 1.16290 4.68035i 0.0512434 0.206241i
\(516\) −34.8371 −1.53362
\(517\) 9.36069i 0.411683i
\(518\) 29.3607i 1.29003i
\(519\) 22.4391 0.984966
\(520\) 18.0989 + 4.49693i 0.793689 + 0.197203i
\(521\) −25.8166 −1.13105 −0.565523 0.824733i \(-0.691325\pi\)
−0.565523 + 0.824733i \(0.691325\pi\)
\(522\) 18.0989i 0.792167i
\(523\) 4.00000i 0.174908i 0.996169 + 0.0874539i \(0.0278730\pi\)
−0.996169 + 0.0874539i \(0.972127\pi\)
\(524\) −7.88428 −0.344426
\(525\) 4.41855 + 2.34017i 0.192841 + 0.102134i
\(526\) −15.3340 −0.668595
\(527\) 8.36683i 0.364465i
\(528\) 27.6742i 1.20437i
\(529\) 17.5236 0.761895
\(530\) −22.0989 5.49079i −0.959915 0.238504i
\(531\) 10.5236 0.456685
\(532\) 16.4391i 0.712724i
\(533\) 5.98771i 0.259357i
\(534\) 22.5958 0.977817
\(535\) −8.89496 + 35.7998i −0.384563 + 1.54776i
\(536\) −42.3545 −1.82944
\(537\) 10.0000i 0.431532i
\(538\) 75.4740i 3.25391i
\(539\) −2.00000 −0.0861461
\(540\) −2.87936 + 11.5886i −0.123908 + 0.498696i
\(541\) 25.8843 1.11285 0.556426 0.830897i \(-0.312172\pi\)
0.556426 + 0.830897i \(0.312172\pi\)
\(542\) 68.0554i 2.92323i
\(543\) 8.52359i 0.365782i
\(544\) 20.9093 0.896480
\(545\) 27.8576 + 6.92162i 1.19329 + 0.296490i
\(546\) −2.49693 −0.106859
\(547\) 11.3197i 0.483993i −0.970277 0.241997i \(-0.922198\pi\)
0.970277 0.241997i \(-0.0778023\pi\)
\(548\) 23.7054i 1.01264i
\(549\) 4.15676 0.177406
\(550\) −12.6803 + 23.9421i −0.540692 + 1.02090i
\(551\) −20.5646 −0.876083
\(552\) 21.1773i 0.901365i
\(553\) 6.15676i 0.261812i
\(554\) −76.3956 −3.24574
\(555\) 23.5174 + 5.84324i 0.998260 + 0.248032i
\(556\) 72.6369 3.08049
\(557\) 26.6491i 1.12916i 0.825378 + 0.564580i \(0.190962\pi\)
−0.825378 + 0.564580i \(0.809038\pi\)
\(558\) 21.0205i 0.889870i
\(559\) 6.01229 0.254293
\(560\) 7.46081 30.0277i 0.315277 1.26890i
\(561\) 2.15676 0.0910583
\(562\) 55.1461i 2.32620i
\(563\) 46.3545i 1.95361i 0.214128 + 0.976806i \(0.431309\pi\)
−0.214128 + 0.976806i \(0.568691\pi\)
\(564\) −24.9939 −1.05243
\(565\) 2.82273 11.3607i 0.118753 0.477948i
\(566\) −63.7152 −2.67815
\(567\) 1.00000i 0.0419961i
\(568\) 18.0989i 0.759413i
\(569\) 14.3668 0.602289 0.301145 0.953579i \(-0.402631\pi\)
0.301145 + 0.953579i \(0.402631\pi\)
\(570\) 18.0989 + 4.49693i 0.758079 + 0.188356i
\(571\) 38.7214 1.62044 0.810220 0.586126i \(-0.199348\pi\)
0.810220 + 0.586126i \(0.199348\pi\)
\(572\) 9.84324i 0.411567i
\(573\) 15.3607i 0.641702i
\(574\) 17.6020 0.734692
\(575\) −5.47641 + 10.3402i −0.228382 + 0.431215i
\(576\) 24.8576 1.03573
\(577\) 43.4740i 1.80984i −0.425577 0.904922i \(-0.639929\pi\)
0.425577 0.904922i \(-0.360071\pi\)
\(578\) 42.9071i 1.78470i
\(579\) −8.36683 −0.347714
\(580\) −77.4161 19.2351i −3.21453 0.798695i
\(581\) 6.83710 0.283651
\(582\) 22.8638i 0.947733i
\(583\) 7.51745i 0.311341i
\(584\) 64.0554 2.65063
\(585\) 0.496928 2.00000i 0.0205455 0.0826898i
\(586\) 7.91548 0.326985
\(587\) 36.0288i 1.48707i −0.668699 0.743533i \(-0.733149\pi\)
0.668699 0.743533i \(-0.266851\pi\)
\(588\) 5.34017i 0.220225i
\(589\) 23.8843 0.984135
\(590\) 15.3730 61.8720i 0.632895 2.54723i
\(591\) −11.7587 −0.483689
\(592\) 149.954i 6.16307i
\(593\) 31.4863i 1.29299i 0.762920 + 0.646493i \(0.223765\pi\)
−0.762920 + 0.646493i \(0.776235\pi\)
\(594\) 5.41855 0.222326
\(595\) −2.34017 0.581449i −0.0959377 0.0238371i
\(596\) 83.7030 3.42861
\(597\) 22.5958i 0.924786i
\(598\) 5.84324i 0.238948i
\(599\) −29.0349 −1.18633 −0.593167 0.805080i \(-0.702123\pi\)
−0.593167 + 0.805080i \(0.702123\pi\)
\(600\) 39.9854 + 21.1773i 1.63240 + 0.864559i
\(601\) 15.3607 0.626576 0.313288 0.949658i \(-0.398570\pi\)
0.313288 + 0.949658i \(0.398570\pi\)
\(602\) 17.6742i 0.720347i
\(603\) 4.68035i 0.190598i
\(604\) −31.2039 −1.26967
\(605\) −15.1906 3.77432i −0.617586 0.153448i
\(606\) 15.7587 0.640154
\(607\) 13.0472i 0.529569i 0.964308 + 0.264784i \(0.0853008\pi\)
−0.964308 + 0.264784i \(0.914699\pi\)
\(608\) 59.6886i 2.42069i
\(609\) 6.68035 0.270701
\(610\) 6.07223 24.4391i 0.245858 0.989509i
\(611\) 4.31351 0.174506
\(612\) 5.75872i 0.232783i
\(613\) 15.5174i 0.626744i −0.949630 0.313372i \(-0.898541\pi\)
0.949630 0.313372i \(-0.101459\pi\)
\(614\) −28.3668 −1.14479
\(615\) −3.50307 + 14.0989i −0.141257 + 0.568522i
\(616\) −18.0989 −0.729225
\(617\) 22.7649i 0.916479i 0.888829 + 0.458240i \(0.151520\pi\)
−0.888829 + 0.458240i \(0.848480\pi\)
\(618\) 5.84324i 0.235050i
\(619\) −7.92777 −0.318644 −0.159322 0.987227i \(-0.550931\pi\)
−0.159322 + 0.987227i \(0.550931\pi\)
\(620\) 89.9130 + 22.3402i 3.61099 + 0.897203i
\(621\) 2.34017 0.0939079
\(622\) 64.5646i 2.58881i
\(623\) 8.34017i 0.334142i
\(624\) −12.7526 −0.510512
\(625\) 14.0472 + 20.6803i 0.561887 + 0.827214i
\(626\) −88.7358 −3.54659
\(627\) 6.15676i 0.245877i
\(628\) 26.2823i 1.04878i
\(629\) −11.6865 −0.465971
\(630\) −5.87936 1.46081i −0.234239 0.0582001i
\(631\) 19.2039 0.764497 0.382248 0.924060i \(-0.375150\pi\)
0.382248 + 0.924060i \(0.375150\pi\)
\(632\) 55.7152i 2.21623i
\(633\) 13.6742i 0.543501i
\(634\) −48.5380 −1.92769
\(635\) 0.993857 4.00000i 0.0394400 0.158735i
\(636\) 20.0722 0.795916
\(637\) 0.921622i 0.0365160i
\(638\) 36.1978i 1.43308i
\(639\) −2.00000 −0.0791188
\(640\) 15.4030 61.9926i 0.608855 2.45047i
\(641\) −5.94668 −0.234880 −0.117440 0.993080i \(-0.537469\pi\)
−0.117440 + 0.993080i \(0.537469\pi\)
\(642\) 44.6947i 1.76396i
\(643\) 30.8904i 1.21820i −0.793094 0.609100i \(-0.791531\pi\)
0.793094 0.609100i \(-0.208469\pi\)
\(644\) −12.4969 −0.492448
\(645\) 14.1568 + 3.51745i 0.557422 + 0.138499i
\(646\) −8.99386 −0.353859
\(647\) 19.2039i 0.754985i 0.926013 + 0.377492i \(0.123214\pi\)
−0.926013 + 0.377492i \(0.876786\pi\)
\(648\) 9.04945i 0.355496i
\(649\) −21.0472 −0.826174
\(650\) −11.0328 5.84324i −0.432742 0.229191i
\(651\) −7.75872 −0.304088
\(652\) 52.5646i 2.05859i
\(653\) 28.5548i 1.11744i −0.829358 0.558718i \(-0.811294\pi\)
0.829358 0.558718i \(-0.188706\pi\)
\(654\) −34.7792 −1.35998
\(655\) 3.20394 + 0.796064i 0.125188 + 0.0311048i
\(656\) 89.8987 3.50995
\(657\) 7.07838i 0.276154i
\(658\) 12.6803i 0.494331i
\(659\) 27.9877 1.09025 0.545123 0.838356i \(-0.316483\pi\)
0.545123 + 0.838356i \(0.316483\pi\)
\(660\) 5.75872 23.1773i 0.224158 0.902174i
\(661\) −22.1445 −0.861320 −0.430660 0.902514i \(-0.641719\pi\)
−0.430660 + 0.902514i \(0.641719\pi\)
\(662\) 3.68649i 0.143279i
\(663\) 0.993857i 0.0385982i
\(664\) 61.8720 2.40110
\(665\) −1.65983 + 6.68035i −0.0643653 + 0.259053i
\(666\) −29.3607 −1.13770
\(667\) 15.6332i 0.605319i
\(668\) 102.552i 3.96787i
\(669\) 21.6742 0.837973
\(670\) 27.5174 + 6.83710i 1.06309 + 0.264140i
\(671\) −8.31351 −0.320940
\(672\) 19.3896i 0.747971i
\(673\) 2.21008i 0.0851923i 0.999092 + 0.0425962i \(0.0135629\pi\)
−0.999092 + 0.0425962i \(0.986437\pi\)
\(674\) −68.7091 −2.64658
\(675\) 2.34017 4.41855i 0.0900733 0.170070i
\(676\) −64.8864 −2.49563
\(677\) 19.5486i 0.751315i −0.926758 0.375658i \(-0.877417\pi\)
0.926758 0.375658i \(-0.122583\pi\)
\(678\) 14.1834i 0.544711i
\(679\) 8.43907 0.323862
\(680\) −21.1773 5.26180i −0.812111 0.201781i
\(681\) −11.5174 −0.441350
\(682\) 42.0410i 1.60983i
\(683\) 11.8166i 0.452149i 0.974110 + 0.226074i \(0.0725893\pi\)
−0.974110 + 0.226074i \(0.927411\pi\)
\(684\) −16.4391 −0.628564
\(685\) 2.39350 9.63317i 0.0914508 0.368064i
\(686\) −2.70928 −0.103441
\(687\) 12.8371i 0.489766i
\(688\) 90.2676i 3.44142i
\(689\) −3.46412 −0.131973
\(690\) 3.41855 13.7587i 0.130142 0.523786i
\(691\) 11.7587 0.447323 0.223661 0.974667i \(-0.428199\pi\)
0.223661 + 0.974667i \(0.428199\pi\)
\(692\) 119.829i 4.55520i
\(693\) 2.00000i 0.0759737i
\(694\) 45.6886 1.73431
\(695\) −29.5174 7.33403i −1.11966 0.278196i
\(696\) 60.4534 2.29148
\(697\) 7.00614i 0.265377i
\(698\) 25.7854i 0.975991i
\(699\) 6.76487 0.255871
\(700\) −12.4969 + 23.5958i −0.472339 + 0.891838i
\(701\) 9.94668 0.375681 0.187840 0.982200i \(-0.439851\pi\)
0.187840 + 0.982200i \(0.439851\pi\)
\(702\) 2.49693i 0.0942405i
\(703\) 33.3607i 1.25822i
\(704\) −49.7152 −1.87371
\(705\) 10.1568 + 2.52359i 0.382526 + 0.0950439i
\(706\) 96.9914 3.65032
\(707\) 5.81658i 0.218755i
\(708\) 56.1978i 2.11204i
\(709\) 11.0472 0.414886 0.207443 0.978247i \(-0.433486\pi\)
0.207443 + 0.978247i \(0.433486\pi\)
\(710\) −2.92162 + 11.7587i −0.109647 + 0.441297i
\(711\) 6.15676 0.230896
\(712\) 75.4740i 2.82851i
\(713\) 18.1568i 0.679976i
\(714\) 2.92162 0.109339
\(715\) −0.993857 + 4.00000i −0.0371681 + 0.149592i
\(716\) 53.4017 1.99572
\(717\) 23.3607i 0.872421i
\(718\) 60.4534i 2.25610i
\(719\) 6.15676 0.229608 0.114804 0.993388i \(-0.463376\pi\)
0.114804 + 0.993388i \(0.463376\pi\)
\(720\) −30.0277 7.46081i −1.11907 0.278048i
\(721\) −2.15676 −0.0803218
\(722\) 25.8020i 0.960252i
\(723\) 14.6803i 0.545968i
\(724\) 45.5174 1.69164
\(725\) 29.5174 + 15.6332i 1.09625 + 0.580601i
\(726\) 18.9649 0.703854
\(727\) 2.89043i 0.107200i −0.998562 0.0536000i \(-0.982930\pi\)
0.998562 0.0536000i \(-0.0170696\pi\)
\(728\) 8.34017i 0.309107i
\(729\) −1.00000 −0.0370370
\(730\) −41.6163 10.3402i −1.54029 0.382707i
\(731\) −7.03489 −0.260195
\(732\) 22.1978i 0.820454i
\(733\) 25.7998i 0.952936i −0.879192 0.476468i \(-0.841917\pi\)
0.879192 0.476468i \(-0.158083\pi\)
\(734\) 55.0349 2.03138
\(735\) 0.539189 2.17009i 0.0198883 0.0800448i
\(736\) −45.3751 −1.67255
\(737\) 9.36069i 0.344806i
\(738\) 17.6020i 0.647937i
\(739\) 1.04718 0.0385212 0.0192606 0.999814i \(-0.493869\pi\)
0.0192606 + 0.999814i \(0.493869\pi\)
\(740\) −31.2039 + 125.587i −1.14708 + 4.61668i
\(741\) 2.83710 0.104224
\(742\) 10.1834i 0.373845i
\(743\) 9.97334i 0.365886i −0.983123 0.182943i \(-0.941438\pi\)
0.983123 0.182943i \(-0.0585624\pi\)
\(744\) −70.2122 −2.57410
\(745\) −34.0144 8.45136i −1.24619 0.309634i
\(746\) 43.3484 1.58710
\(747\) 6.83710i 0.250156i
\(748\) 11.5174i 0.421120i
\(749\) 16.4969 0.602785
\(750\) −22.5597 20.2134i −0.823764 0.738089i
\(751\) 3.26633 0.119190 0.0595950 0.998223i \(-0.481019\pi\)
0.0595950 + 0.998223i \(0.481019\pi\)
\(752\) 64.7624i 2.36164i
\(753\) 9.16290i 0.333915i
\(754\) −16.6803 −0.607462
\(755\) 12.6803 + 3.15061i 0.461485 + 0.114663i
\(756\) 5.34017 0.194220
\(757\) 49.9877i 1.81683i 0.418065 + 0.908417i \(0.362708\pi\)
−0.418065 + 0.908417i \(0.637292\pi\)
\(758\) 16.6803i 0.605857i
\(759\) −4.68035 −0.169886
\(760\) −15.0205 + 60.4534i −0.544851 + 2.19288i
\(761\) 2.61265 0.0947083 0.0473542 0.998878i \(-0.484921\pi\)
0.0473542 + 0.998878i \(0.484921\pi\)
\(762\) 4.99386i 0.180908i
\(763\) 12.8371i 0.464734i
\(764\) −82.0288 −2.96770
\(765\) −0.581449 + 2.34017i −0.0210223 + 0.0846091i
\(766\) −72.7091 −2.62709
\(767\) 9.69878i 0.350202i
\(768\) 27.6803i 0.998828i
\(769\) 15.6742 0.565226 0.282613 0.959234i \(-0.408799\pi\)
0.282613 + 0.959234i \(0.408799\pi\)
\(770\) 11.7587 + 2.92162i 0.423755 + 0.105288i
\(771\) −5.07838 −0.182893
\(772\) 44.6803i 1.60808i
\(773\) 5.81205i 0.209045i 0.994523 + 0.104522i \(0.0333314\pi\)
−0.994523 + 0.104522i \(0.966669\pi\)
\(774\) −17.6742 −0.635286
\(775\) −34.2823 18.1568i −1.23146 0.652210i
\(776\) 76.3689 2.74148
\(777\) 10.8371i 0.388779i
\(778\) 15.2618i 0.547162i
\(779\) −20.0000 −0.716574
\(780\) 10.6803 + 2.65368i 0.382418 + 0.0950171i
\(781\) 4.00000 0.143131
\(782\) 6.83710i 0.244494i
\(783\) 6.68035i 0.238736i
\(784\) −13.8371 −0.494182
\(785\) 2.65368 10.6803i 0.0947140 0.381198i
\(786\) −4.00000 −0.142675
\(787\) 39.3484i 1.40262i −0.712857 0.701310i \(-0.752599\pi\)
0.712857 0.701310i \(-0.247401\pi\)
\(788\) 62.7936i 2.23693i
\(789\) −5.65983 −0.201495
\(790\) 8.99386 36.1978i 0.319987 1.28786i
\(791\) −5.23513 −0.186140