Properties

Label 735.2.d.b.589.6
Level $735$
Weight $2$
Character 735.589
Analytic conductor $5.869$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 589.6
Root \(-0.854638 - 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 735.589
Dual form 735.2.d.b.589.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(7\) 0 0
\(8\) 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 \(-0.959207\pi\)
0.991799 0.127806i \(-0.0407935\pi\)
\(14\) 0 0
\(15\) −0.539189 + 2.17009i −0.139218 + 0.560314i
\(16\) 13.8371 3.45928
\(17\) 1.07838i 0.261545i 0.991412 + 0.130773i \(0.0417457\pi\)
−0.991412 + 0.130773i \(0.958254\pi\)
\(18\) 2.70928i 0.638582i
\(19\) 3.07838 0.706228 0.353114 0.935580i \(-0.385123\pi\)
0.353114 + 0.935580i \(0.385123\pi\)
\(20\) 11.5886 + 2.87936i 2.59130 + 0.643845i
\(21\) 0 0
\(22\) 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
\(28\) 0 0
\(29\) 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 \(-0.254627\pi\)
0.696754 + 0.717310i \(0.254627\pi\)
\(32\) 19.3896i 3.42763i
\(33\) 2.00000i 0.348155i
\(34\) −2.92162 −0.501054
\(35\) 0 0
\(36\) 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 \(-0.669366\pi\)
−0.507325 + 0.861755i \(0.669366\pi\)
\(42\) 0 0
\(43\) 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 \(0.110884\pi\)
−0.939937 + 0.341349i \(0.889116\pi\)
\(48\) 13.8371i 1.99721i
\(49\) 0 0
\(50\) −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
\(56\) 0 0
\(57\) 3.07838i 0.407741i
\(58\) 18.0989i 2.37650i
\(59\) 10.5236 1.37005 0.685027 0.728517i \(-0.259790\pi\)
0.685027 + 0.728517i \(0.259790\pi\)
\(60\) 2.87936 11.5886i 0.371724 1.49609i
\(61\) 4.15676 0.532218 0.266109 0.963943i \(-0.414262\pi\)
0.266109 + 0.963943i \(0.414262\pi\)
\(62\) 21.0205i 2.66961i
\(63\) 0 0
\(64\) −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
\(70\) 0 0
\(71\) 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 \(-0.864051\pi\)
0.910172 0.414231i \(-0.135949\pi\)
\(74\) 29.3607 3.41311
\(75\) 2.34017 4.41855i 0.270220 0.510210i
\(76\) −16.4391 −1.88569
\(77\) 0 0
\(78\) 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 \(-0.877562\pi\)
0.926930 0.375235i \(-0.122438\pi\)
\(84\) 0 0
\(85\) 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 \(-0.354259\pi\)
0.442028 + 0.897001i \(0.354259\pi\)
\(90\) −1.46081 + 5.87936i −0.153983 + 0.619739i
\(91\) 0 0
\(92\) 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 \(-0.859067\pi\)
0.903576 0.428429i \(-0.140933\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) −23.5958 12.4969i −2.35958 1.24969i
\(101\) 5.81658 0.578772 0.289386 0.957213i \(-0.406549\pi\)
0.289386 + 0.957213i \(0.406549\pi\)
\(102\) 2.92162i 0.289284i
\(103\) 2.15676i 0.212511i 0.994339 + 0.106256i \(0.0338862\pi\)
−0.994339 + 0.106256i \(0.966114\pi\)
\(104\) −8.34017 −0.817821
\(105\) 0 0
\(106\) −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
\(112\) 0 0
\(113\) 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
\(119\) 0 0
\(120\) 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
\(126\) 0 0
\(127\) 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 \(-0.520544\pi\)
−0.0644973 + 0.997918i \(0.520544\pi\)
\(132\) 10.6803i 0.929605i
\(133\) 0 0
\(134\) 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 \(-0.304281\pi\)
0.576852 + 0.816849i \(0.304281\pi\)
\(140\) 0 0
\(141\) 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
\(147\) 0 0
\(148\) 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
\(154\) 0 0
\(155\) −16.8371 4.18342i −1.35239 0.336020i
\(156\) 4.92162 0.394045
\(157\) 4.92162i 0.392788i 0.980525 + 0.196394i \(0.0629232\pi\)
−0.980525 + 0.196394i \(0.937077\pi\)
\(158\) 16.6803i 1.32702i
\(159\) 3.75872 0.298086
\(160\) 10.4547 42.0772i 0.826514 3.32649i
\(161\) 0 0
\(162\) 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 \(-0.733391\pi\)
0.669266 0.743023i \(-0.266609\pi\)
\(168\) 0 0
\(169\) 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 \(0.325223\pi\)
−0.521902 + 0.853005i \(0.674777\pi\)
\(174\) 18.0989 1.37207
\(175\) 0 0
\(176\) 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 \(-0.397399\pi\)
0.316777 + 0.948500i \(0.397399\pi\)
\(182\) 0 0
\(183\) 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
\(189\) 0 0
\(190\) 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
\(196\) 0 0
\(197\) 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 \(-0.795639\pi\)
−0.800888 + 0.598814i \(0.795639\pi\)
\(200\) 21.1773 39.9854i 1.49746 2.82740i
\(201\) −4.68035 −0.330126
\(202\) 15.7587i 1.10878i
\(203\) 0 0
\(204\) −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
\(210\) 0 0
\(211\) −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
\(217\) 0 0
\(218\) 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 \(0.258487\pi\)
−0.688005 + 0.725706i \(0.741513\pi\)
\(224\) 0 0
\(225\) −4.41855 2.34017i −0.294570 0.156012i
\(226\) 14.1834 0.943467
\(227\) 11.5174i 0.764440i −0.924071 0.382220i \(-0.875160\pi\)
0.924071 0.382220i \(-0.124840\pi\)
\(228\) 16.4391i 1.08870i
\(229\) 12.8371 0.848300 0.424150 0.905592i \(-0.360573\pi\)
0.424150 + 0.905592i \(0.360573\pi\)
\(230\) 13.7587 + 3.41855i 0.907223 + 0.225413i
\(231\) 0 0
\(232\) 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
\(238\) 0 0
\(239\) 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 \(-0.343235\pi\)
0.472822 + 0.881158i \(0.343235\pi\)
\(242\) 18.9649i 1.21911i
\(243\) 1.00000i 0.0641500i
\(244\) −22.1978 −1.42107
\(245\) 0 0
\(246\) −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 \(-0.593382\pi\)
−0.289179 + 0.957275i \(0.593382\pi\)
\(252\) 0 0
\(253\) 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 \(-0.949370\pi\)
0.987377 0.158390i \(-0.0506304\pi\)
\(258\) 17.6742i 1.10035i
\(259\) 0 0
\(260\) 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
\(266\) 0 0
\(267\) 8.34017i 0.510410i
\(268\) 24.9939i 1.52674i
\(269\) −27.8576 −1.69851 −0.849255 0.527984i \(-0.822948\pi\)
−0.849255 + 0.527984i \(0.822948\pi\)
\(270\) 5.87936 + 1.46081i 0.357807 + 0.0889021i
\(271\) −25.1194 −1.52590 −0.762948 0.646460i \(-0.776249\pi\)
−0.762948 + 0.646460i \(0.776249\pi\)
\(272\) 14.9216i 0.904756i
\(273\) 0 0
\(274\) 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
\(280\) 0 0
\(281\) −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 \(-0.753636\pi\)
0.715138 0.698984i \(-0.246364\pi\)
\(284\) −10.6803 −0.633762
\(285\) −1.65983 + 6.68035i −0.0983197 + 0.395710i
\(286\) 4.99386 0.295293
\(287\) 0 0
\(288\) 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 \(0.0271981\pi\)
−0.996352 + 0.0853415i \(0.972802\pi\)
\(294\) 0 0
\(295\) −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
\(301\) 0 0
\(302\) 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 \(-0.903419\pi\)
0.954321 0.298785i \(-0.0965813\pi\)
\(308\) 0 0
\(309\) 2.15676 0.122694
\(310\) 11.3340 45.6163i 0.643730 2.59083i
\(311\) −23.8310 −1.35133 −0.675665 0.737209i \(-0.736143\pi\)
−0.675665 + 0.737209i \(0.736143\pi\)
\(312\) 8.34017i 0.472169i
\(313\) 32.7526i 1.85129i −0.378399 0.925643i \(-0.623525\pi\)
0.378399 0.925643i \(-0.376475\pi\)
\(314\) −13.3340 −0.752483
\(315\) 0 0
\(316\) 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
\(322\) 0 0
\(323\) 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
\(329\) 0 0
\(330\) −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
\(336\) 0 0
\(337\) 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
\(343\) 0 0
\(344\) −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 \(-0.418014\pi\)
0.254729 + 0.967013i \(0.418014\pi\)
\(350\) 0 0
\(351\) 0.921622 0.0491926
\(352\) 38.7792i 2.06694i
\(353\) 35.7998i 1.90543i 0.303867 + 0.952715i \(0.401722\pi\)
−0.303867 + 0.952715i \(0.598278\pi\)
\(354\) 28.5113 1.51536
\(355\) −4.34017 1.07838i −0.230352 0.0572343i
\(356\) −44.5380 −2.36051
\(357\) 0 0
\(358\) 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
\(364\) 0 0
\(365\) −3.81658 + 15.3607i −0.199769 + 0.804015i
\(366\) 11.2618 0.588663
\(367\) 20.3135i 1.06036i 0.847886 + 0.530178i \(0.177875\pi\)
−0.847886 + 0.530178i \(0.822125\pi\)
\(368\) 32.3812i 1.68799i
\(369\) 6.49693 0.338217
\(370\) −63.7152 15.8310i −3.31240 0.823012i
\(371\) 0 0
\(372\) 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
\(378\) 0 0
\(379\) −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 \(-0.759515\pi\)
0.727926 0.685656i \(-0.240485\pi\)
\(384\) −28.5669 −1.45780
\(385\) 0 0
\(386\) −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
\(392\) 0 0
\(393\) 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 \(0.397457\pi\)
−0.316604 + 0.948558i \(0.602543\pi\)
\(398\) 61.2183i 3.06860i
\(399\) 0 0
\(400\) 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
\(406\) 0 0
\(407\) 21.6742i 1.07435i
\(408\) 9.75872i 0.483129i
\(409\) 12.3545 0.610893 0.305447 0.952209i \(-0.401194\pi\)
0.305447 + 0.952209i \(0.401194\pi\)
\(410\) −9.49079 + 38.1978i −0.468716 + 1.88645i
\(411\) −4.43907 −0.218963
\(412\) 11.5174i 0.567424i
\(413\) 0 0
\(414\) 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 \(-0.249498\pi\)
0.708221 + 0.705991i \(0.249498\pi\)
\(420\) 0 0
\(421\) −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
\(427\) 0 0
\(428\) 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 \(-0.836588\pi\)
0.871092 0.491120i \(-0.163412\pi\)
\(434\) 0 0
\(435\) −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 \(-0.632315\pi\)
−0.403812 + 0.914842i \(0.632315\pi\)
\(440\) −9.75872 + 39.2762i −0.465229 + 1.87242i
\(441\) 0 0
\(442\) 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
\(448\) 0 0
\(449\) 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
\(455\) 0 0
\(456\) −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 \(-0.502522\pi\)
−0.00792172 + 0.999969i \(0.502522\pi\)
\(462\) 0 0
\(463\) 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 \(-0.914139\pi\)
0.963840 0.266482i \(-0.0858613\pi\)
\(468\) 4.92162i 0.227502i
\(469\) 0 0
\(470\) 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
\(476\) 0 0
\(477\) 3.75872i 0.172100i
\(478\) 63.2905i 2.89484i
\(479\) −19.5174 −0.891775 −0.445887 0.895089i \(-0.647112\pi\)
−0.445887 + 0.895089i \(0.647112\pi\)
\(480\) −42.0772 10.4547i −1.92055 0.477188i
\(481\) −9.98771 −0.455401
\(482\) 39.7731i 1.81162i
\(483\) 0 0
\(484\) 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
\(490\) 0 0
\(491\) 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
\(497\) 0 0
\(498\) 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 \(0.137953\pi\)
−0.907546 + 0.419952i \(0.862047\pi\)
\(504\) 0 0
\(505\) −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 \(-0.451772\pi\)
0.150934 + 0.988544i \(0.451772\pi\)
\(510\) 1.57531 6.34017i 0.0697557 0.280748i
\(511\) 0 0
\(512\) 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
\(518\) 0 0
\(519\) 22.4391 0.984966
\(520\) 18.0989 + 4.49693i 0.793689 + 0.197203i
\(521\) 25.8166 1.13105 0.565523 0.824733i \(-0.308675\pi\)
0.565523 + 0.824733i \(0.308675\pi\)
\(522\) 18.0989i 0.792167i
\(523\) 4.00000i 0.174908i −0.996169 0.0874539i \(-0.972127\pi\)
0.996169 0.0874539i \(-0.0278730\pi\)
\(524\) 7.88428 0.344426
\(525\) 0 0
\(526\) −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
\(532\) 0 0
\(533\) 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
\(539\) 0 0
\(540\) −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
\(546\) 0 0
\(547\) 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
\(553\) 0 0
\(554\) −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
\(560\) 0 0
\(561\) 2.15676 0.0910583
\(562\) 55.1461i 2.32620i
\(563\) 46.3545i 1.95361i −0.214128 0.976806i \(-0.568691\pi\)
0.214128 0.976806i \(-0.431309\pi\)
\(564\) −24.9939 −1.05243
\(565\) −2.82273 + 11.3607i −0.118753 + 0.477948i
\(566\) 63.7152 2.67815
\(567\) 0 0
\(568\) 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
\(574\) 0 0
\(575\) −5.47641 + 10.3402i −0.228382 + 0.431215i
\(576\) 24.8576 1.03573
\(577\) 43.4740i 1.80984i 0.425577 + 0.904922i \(0.360071\pi\)
−0.425577 + 0.904922i \(0.639929\pi\)
\(578\) 42.9071i 1.78470i
\(579\) 8.36683 0.347714
\(580\) 77.4161 + 19.2351i 3.21453 + 0.798695i
\(581\) 0 0
\(582\) 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 \(0.266851\pi\)
−0.668699 + 0.743533i \(0.733149\pi\)
\(588\) 0 0
\(589\) 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 \(-0.776235\pi\)
0.762920 0.646493i \(-0.223765\pi\)
\(594\) −5.41855 −0.222326
\(595\) 0 0
\(596\) 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 \(-0.601430\pi\)
−0.313288 + 0.949658i \(0.601430\pi\)
\(602\) 0 0
\(603\) 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 \(-0.914699\pi\)
0.964308 0.264784i \(-0.0853008\pi\)
\(608\) 59.6886i 2.42069i
\(609\) 0 0
\(610\) 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
\(616\) 0 0
\(617\) 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 \(-0.449069\pi\)
0.159322 + 0.987227i \(0.449069\pi\)
\(620\) 89.9130 + 22.3402i 3.61099 + 0.897203i
\(621\) −2.34017 −0.0939079
\(622\) 64.5646i 2.58881i
\(623\) 0 0
\(624\) −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
\(630\) 0 0
\(631\) 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 0
\(638\) 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 \(0.208469\pi\)
−0.793094 + 0.609100i \(0.791531\pi\)
\(644\) 0 0
\(645\) 14.1568 + 3.51745i 0.557422 + 0.138499i
\(646\) −8.99386 −0.353859
\(647\) 19.2039i 0.754985i −0.926013 0.377492i \(-0.876786\pi\)
0.926013 0.377492i \(-0.123214\pi\)
\(648\) 9.04945i 0.355496i
\(649\) 21.0472 0.826174
\(650\) 11.0328 + 5.84324i 0.432742 + 0.229191i
\(651\) 0 0
\(652\) 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
\(658\) 0 0
\(659\) 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 \(-0.358281\pi\)
0.430660 + 0.902514i \(0.358281\pi\)
\(662\) 3.68649i 0.143279i
\(663\) 0.993857i 0.0385982i
\(664\) −61.8720 −2.40110
\(665\) 0 0
\(666\) −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
\(672\) 0 0
\(673\) 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 \(0.122583\pi\)
−0.926758 + 0.375658i \(0.877417\pi\)
\(678\) 14.1834i 0.544711i
\(679\) 0 0
\(680\) −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
\(686\) 0 0
\(687\) 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 \(-0.571801\pi\)
−0.223661 + 0.974667i \(0.571801\pi\)
\(692\) 119.829i 4.55520i
\(693\) 0 0
\(694\) 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
\(700\) 0 0
\(701\) 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
\(707\) 0 0
\(708\) 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
\(714\) 0 0
\(715\) −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 \(-0.536624\pi\)
−0.114804 + 0.993388i \(0.536624\pi\)
\(720\) 30.0277 + 7.46081i 1.11907 + 0.278048i
\(721\) 0 0
\(722\) 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 \(0.0170696\pi\)
−0.998562 + 0.0536000i \(0.982930\pi\)
\(728\) 0 0
\(729\) −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 \(0.158083\pi\)
−0.879192 + 0.476468i \(0.841917\pi\)
\(734\) −55.0349 −2.03138
\(735\) 0 0
\(736\) −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
\(742\) 0 0
\(743\) 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
\(749\) 0 0
\(750\) −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
\(756\) 0 0
\(757\) 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 \(-0.515079\pi\)
−0.0473542 + 0.998878i \(0.515079\pi\)
\(762\) 4.99386i 0.180908i
\(763\) 0 0
\(764\) −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 \(-0.591201\pi\)
−0.282613 + 0.959234i \(0.591201\pi\)
\(770\) 0 0
\(771\) −5.07838 −0.182893
\(772\) 44.6803i 1.60808i
\(773\) 5.81205i 0.209045i −0.994523 0.104522i \(-0.966669\pi\)
0.994523 0.104522i \(-0.0333314\pi\)
\(774\) −17.6742 −0.635286
\(775\) 34.2823 + 18.1568i 1.23146 + 0.652210i
\(776\) −76.3689 −2.74148
\(777\) 0 0
\(778\) 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
\(784\) 0 0
\(785\) 2.65368 10.6803i 0.0947140 0.381198i
\(786\) −4.00000 −0.142675
\(787\) 39.3484i 1.40262i 0.712857 + 0.701310i \(0.247401\pi\)
−0.712857 + 0.701310i \(0.752599\pi\)
\(788\) 62.7936i 2.23693i
\(789\) 5.65983 0.201495