Properties

Label 3150.2.m.k.2843.2
Level 3150
Weight 2
Character 3150.2843
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{24})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2843.2
Root \(0.258819 - 0.965926i\)
Character \(\chi\) = 3150.2843
Dual form 3150.2.m.k.1457.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -0.585786i q^{11} +(3.43916 + 3.43916i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(0.906908 + 0.906908i) q^{17} +2.04989i q^{19} +(-0.414214 + 0.414214i) q^{22} +(-0.257617 + 0.257617i) q^{23} -4.86370i q^{26} +(0.707107 + 0.707107i) q^{28} -1.75272 q^{29} +1.47531 q^{31} +(0.707107 + 0.707107i) q^{32} -1.28256i q^{34} +(-4.04989 + 4.04989i) q^{37} +(1.44949 - 1.44949i) q^{38} -3.84909i q^{41} +(5.10306 + 5.10306i) q^{43} +0.585786 q^{44} +0.364326 q^{46} +(5.49938 + 5.49938i) q^{47} -1.00000i q^{49} +(-3.43916 + 3.43916i) q^{52} +(-5.02494 + 5.02494i) q^{53} -1.00000i q^{56} +(1.23936 + 1.23936i) q^{58} -11.1562 q^{59} +3.78851 q^{61} +(-1.04320 - 1.04320i) q^{62} -1.00000i q^{64} +(-6.74202 + 6.74202i) q^{67} +(-0.906908 + 0.906908i) q^{68} -10.9282i q^{71} +(5.97469 + 5.97469i) q^{73} +5.72741 q^{74} -2.04989 q^{76} +(-0.414214 - 0.414214i) q^{77} +0.944060i q^{79} +(-2.72172 + 2.72172i) q^{82} +(7.82050 - 7.82050i) q^{83} -7.21682i q^{86} +(-0.414214 - 0.414214i) q^{88} -0.0705524 q^{89} +4.86370 q^{91} +(-0.257617 - 0.257617i) q^{92} -7.77729i q^{94} +(-0.746663 + 0.746663i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 8q^{13} - 8q^{14} - 8q^{16} + 8q^{22} - 16q^{23} - 16q^{37} - 8q^{38} - 8q^{43} + 16q^{44} + 8q^{46} + 8q^{47} - 8q^{52} - 32q^{53} - 8q^{58} - 8q^{59} - 32q^{61} - 32q^{62} + 16q^{67} - 16q^{74} + 8q^{77} - 8q^{82} + 8q^{83} + 8q^{88} + 16q^{89} + 8q^{91} - 16q^{92} + 16q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 0.585786i 0.176621i −0.996093 0.0883106i \(-0.971853\pi\)
0.996093 0.0883106i \(-0.0281468\pi\)
\(12\) 0 0
\(13\) 3.43916 + 3.43916i 0.953851 + 0.953851i 0.998981 0.0451304i \(-0.0143703\pi\)
−0.0451304 + 0.998981i \(0.514370\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 0.906908 + 0.906908i 0.219957 + 0.219957i 0.808480 0.588523i \(-0.200290\pi\)
−0.588523 + 0.808480i \(0.700290\pi\)
\(18\) 0 0
\(19\) 2.04989i 0.470277i 0.971962 + 0.235138i \(0.0755543\pi\)
−0.971962 + 0.235138i \(0.924446\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.414214 + 0.414214i −0.0883106 + 0.0883106i
\(23\) −0.257617 + 0.257617i −0.0537169 + 0.0537169i −0.733455 0.679738i \(-0.762093\pi\)
0.679738 + 0.733455i \(0.262093\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 4.86370i 0.953851i
\(27\) 0 0
\(28\) 0.707107 + 0.707107i 0.133631 + 0.133631i
\(29\) −1.75272 −0.325471 −0.162736 0.986670i \(-0.552032\pi\)
−0.162736 + 0.986670i \(0.552032\pi\)
\(30\) 0 0
\(31\) 1.47531 0.264974 0.132487 0.991185i \(-0.457704\pi\)
0.132487 + 0.991185i \(0.457704\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 0 0
\(34\) 1.28256i 0.219957i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.04989 + 4.04989i −0.665797 + 0.665797i −0.956740 0.290943i \(-0.906031\pi\)
0.290943 + 0.956740i \(0.406031\pi\)
\(38\) 1.44949 1.44949i 0.235138 0.235138i
\(39\) 0 0
\(40\) 0 0
\(41\) 3.84909i 0.601127i −0.953762 0.300564i \(-0.902825\pi\)
0.953762 0.300564i \(-0.0971747\pi\)
\(42\) 0 0
\(43\) 5.10306 + 5.10306i 0.778209 + 0.778209i 0.979526 0.201317i \(-0.0645221\pi\)
−0.201317 + 0.979526i \(0.564522\pi\)
\(44\) 0.585786 0.0883106
\(45\) 0 0
\(46\) 0.364326 0.0537169
\(47\) 5.49938 + 5.49938i 0.802167 + 0.802167i 0.983434 0.181267i \(-0.0580199\pi\)
−0.181267 + 0.983434i \(0.558020\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −3.43916 + 3.43916i −0.476925 + 0.476925i
\(53\) −5.02494 + 5.02494i −0.690229 + 0.690229i −0.962282 0.272053i \(-0.912297\pi\)
0.272053 + 0.962282i \(0.412297\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) 1.23936 + 1.23936i 0.162736 + 0.162736i
\(59\) −11.1562 −1.45242 −0.726209 0.687474i \(-0.758719\pi\)
−0.726209 + 0.687474i \(0.758719\pi\)
\(60\) 0 0
\(61\) 3.78851 0.485069 0.242534 0.970143i \(-0.422021\pi\)
0.242534 + 0.970143i \(0.422021\pi\)
\(62\) −1.04320 1.04320i −0.132487 0.132487i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) −6.74202 + 6.74202i −0.823669 + 0.823669i −0.986632 0.162963i \(-0.947895\pi\)
0.162963 + 0.986632i \(0.447895\pi\)
\(68\) −0.906908 + 0.906908i −0.109979 + 0.109979i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.9282i 1.29694i −0.761241 0.648470i \(-0.775409\pi\)
0.761241 0.648470i \(-0.224591\pi\)
\(72\) 0 0
\(73\) 5.97469 + 5.97469i 0.699285 + 0.699285i 0.964256 0.264971i \(-0.0853626\pi\)
−0.264971 + 0.964256i \(0.585363\pi\)
\(74\) 5.72741 0.665797
\(75\) 0 0
\(76\) −2.04989 −0.235138
\(77\) −0.414214 0.414214i −0.0472040 0.0472040i
\(78\) 0 0
\(79\) 0.944060i 0.106215i 0.998589 + 0.0531075i \(0.0169126\pi\)
−0.998589 + 0.0531075i \(0.983087\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −2.72172 + 2.72172i −0.300564 + 0.300564i
\(83\) 7.82050 7.82050i 0.858411 0.858411i −0.132740 0.991151i \(-0.542377\pi\)
0.991151 + 0.132740i \(0.0423774\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 7.21682i 0.778209i
\(87\) 0 0
\(88\) −0.414214 0.414214i −0.0441553 0.0441553i
\(89\) −0.0705524 −0.00747854 −0.00373927 0.999993i \(-0.501190\pi\)
−0.00373927 + 0.999993i \(0.501190\pi\)
\(90\) 0 0
\(91\) 4.86370 0.509855
\(92\) −0.257617 0.257617i −0.0268584 0.0268584i
\(93\) 0 0
\(94\) 7.77729i 0.802167i
\(95\) 0 0
\(96\) 0 0
\(97\) −0.746663 + 0.746663i −0.0758121 + 0.0758121i −0.743996 0.668184i \(-0.767072\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(98\) −0.707107 + 0.707107i −0.0714286 + 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 4.15696i 0.413633i −0.978380 0.206817i \(-0.933690\pi\)
0.978380 0.206817i \(-0.0663103\pi\)
\(102\) 0 0
\(103\) −3.14198 3.14198i −0.309589 0.309589i 0.535161 0.844750i \(-0.320251\pi\)
−0.844750 + 0.535161i \(0.820251\pi\)
\(104\) 4.86370 0.476925
\(105\) 0 0
\(106\) 7.10634 0.690229
\(107\) 6.84909 + 6.84909i 0.662127 + 0.662127i 0.955881 0.293754i \(-0.0949047\pi\)
−0.293754 + 0.955881i \(0.594905\pi\)
\(108\) 0 0
\(109\) 19.9335i 1.90929i 0.297753 + 0.954643i \(0.403763\pi\)
−0.297753 + 0.954643i \(0.596237\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.707107 + 0.707107i −0.0668153 + 0.0668153i
\(113\) −4.69677 + 4.69677i −0.441835 + 0.441835i −0.892628 0.450793i \(-0.851141\pi\)
0.450793 + 0.892628i \(0.351141\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.75272i 0.162736i
\(117\) 0 0
\(118\) 7.88865 + 7.88865i 0.726209 + 0.726209i
\(119\) 1.28256 0.117572
\(120\) 0 0
\(121\) 10.6569 0.968805
\(122\) −2.67888 2.67888i −0.242534 0.242534i
\(123\) 0 0
\(124\) 1.47531i 0.132487i
\(125\) 0 0
\(126\) 0 0
\(127\) 5.17814 5.17814i 0.459486 0.459486i −0.439001 0.898487i \(-0.644668\pi\)
0.898487 + 0.439001i \(0.144668\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 9.58630i 0.837559i −0.908088 0.418780i \(-0.862458\pi\)
0.908088 0.418780i \(-0.137542\pi\)
\(132\) 0 0
\(133\) 1.44949 + 1.44949i 0.125687 + 0.125687i
\(134\) 9.53465 0.823669
\(135\) 0 0
\(136\) 1.28256 0.109979
\(137\) 2.47015 + 2.47015i 0.211040 + 0.211040i 0.804709 0.593669i \(-0.202321\pi\)
−0.593669 + 0.804709i \(0.702321\pi\)
\(138\) 0 0
\(139\) 8.33386i 0.706869i 0.935459 + 0.353434i \(0.114986\pi\)
−0.935459 + 0.353434i \(0.885014\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −7.72741 + 7.72741i −0.648470 + 0.648470i
\(143\) 2.01461 2.01461i 0.168470 0.168470i
\(144\) 0 0
\(145\) 0 0
\(146\) 8.44949i 0.699285i
\(147\) 0 0
\(148\) −4.04989 4.04989i −0.332899 0.332899i
\(149\) −13.5799 −1.11251 −0.556254 0.831012i \(-0.687762\pi\)
−0.556254 + 0.831012i \(0.687762\pi\)
\(150\) 0 0
\(151\) 13.1210 1.06777 0.533884 0.845558i \(-0.320732\pi\)
0.533884 + 0.845558i \(0.320732\pi\)
\(152\) 1.44949 + 1.44949i 0.117569 + 0.117569i
\(153\) 0 0
\(154\) 0.585786i 0.0472040i
\(155\) 0 0
\(156\) 0 0
\(157\) −16.9988 + 16.9988i −1.35665 + 1.35665i −0.478634 + 0.878015i \(0.658868\pi\)
−0.878015 + 0.478634i \(0.841132\pi\)
\(158\) 0.667551 0.667551i 0.0531075 0.0531075i
\(159\) 0 0
\(160\) 0 0
\(161\) 0.364326i 0.0287129i
\(162\) 0 0
\(163\) 0.0884482 + 0.0884482i 0.00692780 + 0.00692780i 0.710562 0.703634i \(-0.248441\pi\)
−0.703634 + 0.710562i \(0.748441\pi\)
\(164\) 3.84909 0.300564
\(165\) 0 0
\(166\) −11.0599 −0.858411
\(167\) 9.31319 + 9.31319i 0.720677 + 0.720677i 0.968743 0.248066i \(-0.0797951\pi\)
−0.248066 + 0.968743i \(0.579795\pi\)
\(168\) 0 0
\(169\) 10.6556i 0.819662i
\(170\) 0 0
\(171\) 0 0
\(172\) −5.10306 + 5.10306i −0.389105 + 0.389105i
\(173\) 5.81257 5.81257i 0.441922 0.441922i −0.450736 0.892657i \(-0.648838\pi\)
0.892657 + 0.450736i \(0.148838\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.585786i 0.0441553i
\(177\) 0 0
\(178\) 0.0498881 + 0.0498881i 0.00373927 + 0.00373927i
\(179\) 9.20080 0.687700 0.343850 0.939025i \(-0.388269\pi\)
0.343850 + 0.939025i \(0.388269\pi\)
\(180\) 0 0
\(181\) 5.24316 0.389721 0.194860 0.980831i \(-0.437575\pi\)
0.194860 + 0.980831i \(0.437575\pi\)
\(182\) −3.43916 3.43916i −0.254927 0.254927i
\(183\) 0 0
\(184\) 0.364326i 0.0268584i
\(185\) 0 0
\(186\) 0 0
\(187\) 0.531254 0.531254i 0.0388492 0.0388492i
\(188\) −5.49938 + 5.49938i −0.401083 + 0.401083i
\(189\) 0 0
\(190\) 0 0
\(191\) 11.1869i 0.809453i 0.914438 + 0.404727i \(0.132633\pi\)
−0.914438 + 0.404727i \(0.867367\pi\)
\(192\) 0 0
\(193\) 11.9136 + 11.9136i 0.857559 + 0.857559i 0.991050 0.133491i \(-0.0426187\pi\)
−0.133491 + 0.991050i \(0.542619\pi\)
\(194\) 1.05594 0.0758121
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 11.7811 + 11.7811i 0.839366 + 0.839366i 0.988775 0.149410i \(-0.0477373\pi\)
−0.149410 + 0.988775i \(0.547737\pi\)
\(198\) 0 0
\(199\) 2.11188i 0.149707i −0.997195 0.0748536i \(-0.976151\pi\)
0.997195 0.0748536i \(-0.0238490\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −2.93942 + 2.93942i −0.206817 + 0.206817i
\(203\) −1.23936 + 1.23936i −0.0869858 + 0.0869858i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.44344i 0.309589i
\(207\) 0 0
\(208\) −3.43916 3.43916i −0.238463 0.238463i
\(209\) 1.20080 0.0830608
\(210\) 0 0
\(211\) 15.1968 1.04619 0.523097 0.852273i \(-0.324777\pi\)
0.523097 + 0.852273i \(0.324777\pi\)
\(212\) −5.02494 5.02494i −0.345115 0.345115i
\(213\) 0 0
\(214\) 9.68608i 0.662127i
\(215\) 0 0
\(216\) 0 0
\(217\) 1.04320 1.04320i 0.0708173 0.0708173i
\(218\) 14.0951 14.0951i 0.954643 0.954643i
\(219\) 0 0
\(220\) 0 0
\(221\) 6.23800i 0.419613i
\(222\) 0 0
\(223\) 1.39391 + 1.39391i 0.0933434 + 0.0933434i 0.752237 0.658893i \(-0.228975\pi\)
−0.658893 + 0.752237i \(0.728975\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 6.64224 0.441835
\(227\) 13.5638 + 13.5638i 0.900258 + 0.900258i 0.995458 0.0951997i \(-0.0303490\pi\)
−0.0951997 + 0.995458i \(0.530349\pi\)
\(228\) 0 0
\(229\) 10.4336i 0.689474i −0.938699 0.344737i \(-0.887968\pi\)
0.938699 0.344737i \(-0.112032\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.23936 + 1.23936i −0.0813678 + 0.0813678i
\(233\) −11.3730 + 11.3730i −0.745073 + 0.745073i −0.973549 0.228476i \(-0.926626\pi\)
0.228476 + 0.973549i \(0.426626\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 11.1562i 0.726209i
\(237\) 0 0
\(238\) −0.906908 0.906908i −0.0587861 0.0587861i
\(239\) 0.485281 0.0313902 0.0156951 0.999877i \(-0.495004\pi\)
0.0156951 + 0.999877i \(0.495004\pi\)
\(240\) 0 0
\(241\) −12.8897 −0.830298 −0.415149 0.909753i \(-0.636271\pi\)
−0.415149 + 0.909753i \(0.636271\pi\)
\(242\) −7.53553 7.53553i −0.484402 0.484402i
\(243\) 0 0
\(244\) 3.78851i 0.242534i
\(245\) 0 0
\(246\) 0 0
\(247\) −7.04989 + 7.04989i −0.448574 + 0.448574i
\(248\) 1.04320 1.04320i 0.0662435 0.0662435i
\(249\) 0 0
\(250\) 0 0
\(251\) 17.3679i 1.09625i 0.836396 + 0.548126i \(0.184658\pi\)
−0.836396 + 0.548126i \(0.815342\pi\)
\(252\) 0 0
\(253\) 0.150909 + 0.150909i 0.00948754 + 0.00948754i
\(254\) −7.32300 −0.459486
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 21.5212 + 21.5212i 1.34245 + 1.34245i 0.893609 + 0.448846i \(0.148165\pi\)
0.448846 + 0.893609i \(0.351835\pi\)
\(258\) 0 0
\(259\) 5.72741i 0.355884i
\(260\) 0 0
\(261\) 0 0
\(262\) −6.77854 + 6.77854i −0.418780 + 0.418780i
\(263\) 12.5708 12.5708i 0.775149 0.775149i −0.203852 0.979002i \(-0.565346\pi\)
0.979002 + 0.203852i \(0.0653462\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.04989i 0.125687i
\(267\) 0 0
\(268\) −6.74202 6.74202i −0.411834 0.411834i
\(269\) −10.1197 −0.617010 −0.308505 0.951223i \(-0.599829\pi\)
−0.308505 + 0.951223i \(0.599829\pi\)
\(270\) 0 0
\(271\) 1.59310 0.0967740 0.0483870 0.998829i \(-0.484592\pi\)
0.0483870 + 0.998829i \(0.484592\pi\)
\(272\) −0.906908 0.906908i −0.0549894 0.0549894i
\(273\) 0 0
\(274\) 3.49333i 0.211040i
\(275\) 0 0
\(276\) 0 0
\(277\) 13.4354 13.4354i 0.807255 0.807255i −0.176963 0.984218i \(-0.556627\pi\)
0.984218 + 0.176963i \(0.0566273\pi\)
\(278\) 5.89293 5.89293i 0.353434 0.353434i
\(279\) 0 0
\(280\) 0 0
\(281\) 22.1421i 1.32089i −0.750875 0.660445i \(-0.770368\pi\)
0.750875 0.660445i \(-0.229632\pi\)
\(282\) 0 0
\(283\) −10.9959 10.9959i −0.653637 0.653637i 0.300230 0.953867i \(-0.402937\pi\)
−0.953867 + 0.300230i \(0.902937\pi\)
\(284\) 10.9282 0.648470
\(285\) 0 0
\(286\) −2.84909 −0.168470
\(287\) −2.72172 2.72172i −0.160658 0.160658i
\(288\) 0 0
\(289\) 15.3550i 0.903237i
\(290\) 0 0
\(291\) 0 0
\(292\) −5.97469 + 5.97469i −0.349642 + 0.349642i
\(293\) 13.4135 13.4135i 0.783624 0.783624i −0.196816 0.980440i \(-0.563060\pi\)
0.980440 + 0.196816i \(0.0630602\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 5.72741i 0.332899i
\(297\) 0 0
\(298\) 9.60244 + 9.60244i 0.556254 + 0.556254i
\(299\) −1.77197 −0.102476
\(300\) 0 0
\(301\) 7.21682 0.415970
\(302\) −9.27792 9.27792i −0.533884 0.533884i
\(303\) 0 0
\(304\) 2.04989i 0.117569i
\(305\) 0 0
\(306\) 0 0
\(307\) 6.60091 6.60091i 0.376734 0.376734i −0.493188 0.869922i \(-0.664169\pi\)
0.869922 + 0.493188i \(0.164169\pi\)
\(308\) 0.414214 0.414214i 0.0236020 0.0236020i
\(309\) 0 0
\(310\) 0 0
\(311\) 33.0892i 1.87632i 0.346204 + 0.938159i \(0.387471\pi\)
−0.346204 + 0.938159i \(0.612529\pi\)
\(312\) 0 0
\(313\) 0.803119 + 0.803119i 0.0453949 + 0.0453949i 0.729440 0.684045i \(-0.239781\pi\)
−0.684045 + 0.729440i \(0.739781\pi\)
\(314\) 24.0399 1.35665
\(315\) 0 0
\(316\) −0.944060 −0.0531075
\(317\) −0.832191 0.832191i −0.0467405 0.0467405i 0.683350 0.730091i \(-0.260522\pi\)
−0.730091 + 0.683350i \(0.760522\pi\)
\(318\) 0 0
\(319\) 1.02672i 0.0574851i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.257617 0.257617i 0.0143564 0.0143564i
\(323\) −1.85906 + 1.85906i −0.103441 + 0.103441i
\(324\) 0 0
\(325\) 0 0
\(326\) 0.125085i 0.00692780i
\(327\) 0 0
\(328\) −2.72172 2.72172i −0.150282 0.150282i
\(329\) 7.77729 0.428776
\(330\) 0 0
\(331\) 18.5997 1.02233 0.511165 0.859483i \(-0.329214\pi\)
0.511165 + 0.859483i \(0.329214\pi\)
\(332\) 7.82050 + 7.82050i 0.429206 + 0.429206i
\(333\) 0 0
\(334\) 13.1708i 0.720677i
\(335\) 0 0
\(336\) 0 0
\(337\) 15.0161 15.0161i 0.817981 0.817981i −0.167834 0.985815i \(-0.553677\pi\)
0.985815 + 0.167834i \(0.0536773\pi\)
\(338\) 7.53465 7.53465i 0.409831 0.409831i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.864219i 0.0468001i
\(342\) 0 0
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 7.21682 0.389105
\(345\) 0 0
\(346\) −8.22022 −0.441922
\(347\) −25.8218 25.8218i −1.38619 1.38619i −0.833169 0.553018i \(-0.813476\pi\)
−0.553018 0.833169i \(-0.686524\pi\)
\(348\) 0 0
\(349\) 30.1584i 1.61434i 0.590318 + 0.807171i \(0.299002\pi\)
−0.590318 + 0.807171i \(0.700998\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.414214 0.414214i 0.0220777 0.0220777i
\(353\) −8.78710 + 8.78710i −0.467690 + 0.467690i −0.901165 0.433475i \(-0.857287\pi\)
0.433475 + 0.901165i \(0.357287\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.0705524i 0.00373927i
\(357\) 0 0
\(358\) −6.50595 6.50595i −0.343850 0.343850i
\(359\) 7.67360 0.404997 0.202499 0.979283i \(-0.435094\pi\)
0.202499 + 0.979283i \(0.435094\pi\)
\(360\) 0 0
\(361\) 14.7980 0.778840
\(362\) −3.70747 3.70747i −0.194860 0.194860i
\(363\) 0 0
\(364\) 4.86370i 0.254927i
\(365\) 0 0
\(366\) 0 0
\(367\) −13.4146 + 13.4146i −0.700235 + 0.700235i −0.964461 0.264226i \(-0.914884\pi\)
0.264226 + 0.964461i \(0.414884\pi\)
\(368\) 0.257617 0.257617i 0.0134292 0.0134292i
\(369\) 0 0
\(370\) 0 0
\(371\) 7.10634i 0.368943i
\(372\) 0 0
\(373\) 2.79796 + 2.79796i 0.144873 + 0.144873i 0.775823 0.630950i \(-0.217335\pi\)
−0.630950 + 0.775823i \(0.717335\pi\)
\(374\) −0.751307 −0.0388492
\(375\) 0 0
\(376\) 7.77729 0.401083
\(377\) −6.02786 6.02786i −0.310451 0.310451i
\(378\) 0 0
\(379\) 13.8539i 0.711627i 0.934557 + 0.355814i \(0.115796\pi\)
−0.934557 + 0.355814i \(0.884204\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 7.91031 7.91031i 0.404727 0.404727i
\(383\) 15.6710 15.6710i 0.800748 0.800748i −0.182464 0.983212i \(-0.558407\pi\)
0.983212 + 0.182464i \(0.0584074\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 16.8484i 0.857559i
\(387\) 0 0
\(388\) −0.746663 0.746663i −0.0379061 0.0379061i
\(389\) −34.7194 −1.76034 −0.880171 0.474657i \(-0.842572\pi\)
−0.880171 + 0.474657i \(0.842572\pi\)
\(390\) 0 0
\(391\) −0.467270 −0.0236308
\(392\) −0.707107 0.707107i −0.0357143 0.0357143i
\(393\) 0 0
\(394\) 16.6609i 0.839366i
\(395\) 0 0
\(396\) 0 0
\(397\) 18.9937 18.9937i 0.953269 0.953269i −0.0456870 0.998956i \(-0.514548\pi\)
0.998956 + 0.0456870i \(0.0145477\pi\)
\(398\) −1.49333 + 1.49333i −0.0748536 + 0.0748536i
\(399\) 0 0
\(400\) 0 0
\(401\) 6.88008i 0.343575i 0.985134 + 0.171787i \(0.0549542\pi\)
−0.985134 + 0.171787i \(0.945046\pi\)
\(402\) 0 0
\(403\) 5.07384 + 5.07384i 0.252746 + 0.252746i
\(404\) 4.15696 0.206817
\(405\) 0 0
\(406\) 1.75272 0.0869858
\(407\) 2.37237 + 2.37237i 0.117594 + 0.117594i
\(408\) 0 0
\(409\) 26.2722i 1.29908i −0.760329 0.649538i \(-0.774962\pi\)
0.760329 0.649538i \(-0.225038\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 3.14198 3.14198i 0.154794 0.154794i
\(413\) −7.88865 + 7.88865i −0.388175 + 0.388175i
\(414\) 0 0
\(415\) 0 0
\(416\) 4.86370i 0.238463i
\(417\) 0 0
\(418\) −0.849091 0.849091i −0.0415304 0.0415304i
\(419\) −2.85690 −0.139569 −0.0697844 0.997562i \(-0.522231\pi\)
−0.0697844 + 0.997562i \(0.522231\pi\)
\(420\) 0 0
\(421\) −3.99446 −0.194678 −0.0973391 0.995251i \(-0.531033\pi\)
−0.0973391 + 0.995251i \(0.531033\pi\)
\(422\) −10.7458 10.7458i −0.523097 0.523097i
\(423\) 0 0
\(424\) 7.10634i 0.345115i
\(425\) 0 0
\(426\) 0 0
\(427\) 2.67888 2.67888i 0.129640 0.129640i
\(428\) −6.84909 + 6.84909i −0.331063 + 0.331063i
\(429\) 0 0
\(430\) 0 0
\(431\) 15.0871i 0.726719i 0.931649 + 0.363360i \(0.118370\pi\)
−0.931649 + 0.363360i \(0.881630\pi\)
\(432\) 0 0
\(433\) −12.0406 12.0406i −0.578634 0.578634i 0.355893 0.934527i \(-0.384177\pi\)
−0.934527 + 0.355893i \(0.884177\pi\)
\(434\) −1.47531 −0.0708173
\(435\) 0 0
\(436\) −19.9335 −0.954643
\(437\) −0.528086 0.528086i −0.0252618 0.0252618i
\(438\) 0 0
\(439\) 25.4660i 1.21543i −0.794156 0.607714i \(-0.792087\pi\)
0.794156 0.607714i \(-0.207913\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.41093 4.41093i 0.209807 0.209807i
\(443\) −0.326397 + 0.326397i −0.0155076 + 0.0155076i −0.714818 0.699310i \(-0.753491\pi\)
0.699310 + 0.714818i \(0.253491\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 1.97129i 0.0933434i
\(447\) 0 0
\(448\) −0.707107 0.707107i −0.0334077 0.0334077i
\(449\) 32.0990 1.51485 0.757424 0.652924i \(-0.226458\pi\)
0.757424 + 0.652924i \(0.226458\pi\)
\(450\) 0 0
\(451\) −2.25475 −0.106172
\(452\) −4.69677 4.69677i −0.220918 0.220918i
\(453\) 0 0
\(454\) 19.1821i 0.900258i
\(455\) 0 0
\(456\) 0 0
\(457\) −2.63040 + 2.63040i −0.123045 + 0.123045i −0.765948 0.642903i \(-0.777730\pi\)
0.642903 + 0.765948i \(0.277730\pi\)
\(458\) −7.37769 + 7.37769i −0.344737 + 0.344737i
\(459\) 0 0
\(460\) 0 0
\(461\) 20.8005i 0.968774i −0.874854 0.484387i \(-0.839043\pi\)
0.874854 0.484387i \(-0.160957\pi\)
\(462\) 0 0
\(463\) −12.7214 12.7214i −0.591211 0.591211i 0.346747 0.937959i \(-0.387286\pi\)
−0.937959 + 0.346747i \(0.887286\pi\)
\(464\) 1.75272 0.0813678
\(465\) 0 0
\(466\) 16.0839 0.745073
\(467\) 12.2128 + 12.2128i 0.565141 + 0.565141i 0.930763 0.365622i \(-0.119144\pi\)
−0.365622 + 0.930763i \(0.619144\pi\)
\(468\) 0 0
\(469\) 9.53465i 0.440269i
\(470\) 0 0
\(471\) 0 0
\(472\) −7.88865 + 7.88865i −0.363104 + 0.363104i
\(473\) 2.98930 2.98930i 0.137448 0.137448i
\(474\) 0 0
\(475\) 0 0
\(476\) 1.28256i 0.0587861i
\(477\) 0 0
\(478\) −0.343146 0.343146i −0.0156951 0.0156951i
\(479\) −32.5054 −1.48521 −0.742606 0.669729i \(-0.766410\pi\)
−0.742606 + 0.669729i \(0.766410\pi\)
\(480\) 0 0
\(481\) −27.8564 −1.27014
\(482\) 9.11439 + 9.11439i 0.415149 + 0.415149i
\(483\) 0 0
\(484\) 10.6569i 0.484402i
\(485\) 0 0
\(486\) 0 0
\(487\) 11.1806 11.1806i 0.506644 0.506644i −0.406851 0.913495i \(-0.633373\pi\)
0.913495 + 0.406851i \(0.133373\pi\)
\(488\) 2.67888 2.67888i 0.121267 0.121267i
\(489\) 0 0
\(490\) 0 0
\(491\) 29.6889i 1.33984i 0.742433 + 0.669921i \(0.233672\pi\)
−0.742433 + 0.669921i \(0.766328\pi\)
\(492\) 0 0
\(493\) −1.58955 1.58955i −0.0715898 0.0715898i
\(494\) 9.97005 0.448574
\(495\) 0 0
\(496\) −1.47531 −0.0662435
\(497\) −7.72741 7.72741i −0.346622 0.346622i
\(498\) 0 0
\(499\) 38.1119i 1.70612i −0.521810 0.853061i \(-0.674743\pi\)
0.521810 0.853061i \(-0.325257\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 12.2810 12.2810i 0.548126 0.548126i
\(503\) −0.0267167 + 0.0267167i −0.00119124 + 0.00119124i −0.707702 0.706511i \(-0.750268\pi\)
0.706511 + 0.707702i \(0.250268\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0.213417i 0.00948754i
\(507\) 0 0
\(508\) 5.17814 + 5.17814i 0.229743 + 0.229743i
\(509\) −24.8899 −1.10323 −0.551613 0.834100i \(-0.685988\pi\)
−0.551613 + 0.834100i \(0.685988\pi\)
\(510\) 0 0
\(511\) 8.44949 0.373783
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) 30.4356i 1.34245i
\(515\) 0 0
\(516\) 0 0
\(517\) 3.22146 3.22146i 0.141680 0.141680i
\(518\) 4.04989 4.04989i 0.177942 0.177942i
\(519\) 0 0
\(520\) 0 0
\(521\) 32.1495i 1.40849i 0.709956 + 0.704247i \(0.248715\pi\)
−0.709956 + 0.704247i \(0.751285\pi\)
\(522\) 0 0
\(523\) −10.3237 10.3237i −0.451423 0.451423i 0.444404 0.895827i \(-0.353416\pi\)
−0.895827 + 0.444404i \(0.853416\pi\)
\(524\) 9.58630 0.418780
\(525\) 0 0
\(526\) −17.7778 −0.775149
\(527\) 1.33797 + 1.33797i 0.0582830 + 0.0582830i
\(528\) 0 0
\(529\) 22.8673i 0.994229i
\(530\) 0 0
\(531\) 0 0
\(532\) −1.44949 + 1.44949i −0.0628434 + 0.0628434i
\(533\) 13.2376 13.2376i 0.573385 0.573385i
\(534\) 0 0
\(535\) 0 0
\(536\) 9.53465i 0.411834i
\(537\) 0 0
\(538\) 7.15572 + 7.15572i 0.308505 + 0.308505i
\(539\) −0.585786 −0.0252316
\(540\) 0 0
\(541\) −25.3694 −1.09072 −0.545359 0.838203i \(-0.683607\pi\)
−0.545359 + 0.838203i \(0.683607\pi\)
\(542\) −1.12649 1.12649i −0.0483870 0.0483870i
\(543\) 0 0
\(544\) 1.28256i 0.0549894i
\(545\) 0 0
\(546\) 0 0
\(547\) 28.9461 28.9461i 1.23765 1.23765i 0.276685 0.960961i \(-0.410764\pi\)
0.960961 0.276685i \(-0.0892359\pi\)
\(548\) −2.47015 + 2.47015i −0.105520 + 0.105520i
\(549\) 0 0
\(550\) 0 0
\(551\) 3.59287i 0.153061i
\(552\) 0 0
\(553\) 0.667551 + 0.667551i 0.0283872 + 0.0283872i
\(554\) −19.0005 −0.807255
\(555\) 0 0
\(556\) −8.33386 −0.353434
\(557\) −1.22073 1.22073i −0.0517241 0.0517241i 0.680772 0.732496i \(-0.261645\pi\)
−0.732496 + 0.680772i \(0.761645\pi\)
\(558\) 0 0
\(559\) 35.1005i 1.48459i
\(560\) 0 0
\(561\) 0 0
\(562\) −15.6569 + 15.6569i −0.660445 + 0.660445i
\(563\) −6.26999 + 6.26999i −0.264249 + 0.264249i −0.826778 0.562529i \(-0.809828\pi\)
0.562529 + 0.826778i \(0.309828\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 15.5505i 0.653637i
\(567\) 0 0
\(568\) −7.72741 7.72741i −0.324235 0.324235i
\(569\) −23.1192 −0.969207 −0.484604 0.874734i \(-0.661036\pi\)
−0.484604 + 0.874734i \(0.661036\pi\)
\(570\) 0 0
\(571\) 1.94303 0.0813132 0.0406566 0.999173i \(-0.487055\pi\)
0.0406566 + 0.999173i \(0.487055\pi\)
\(572\) 2.01461 + 2.01461i 0.0842352 + 0.0842352i
\(573\) 0 0
\(574\) 3.84909i 0.160658i
\(575\) 0 0
\(576\) 0 0
\(577\) −13.6576 + 13.6576i −0.568573 + 0.568573i −0.931728 0.363156i \(-0.881699\pi\)
0.363156 + 0.931728i \(0.381699\pi\)
\(578\) −10.8577 + 10.8577i −0.451619 + 0.451619i
\(579\) 0 0
\(580\) 0 0
\(581\) 11.0599i 0.458840i
\(582\) 0 0
\(583\) 2.94354 + 2.94354i 0.121909 + 0.121909i
\(584\) 8.44949 0.349642
\(585\) 0 0
\(586\) −18.9695 −0.783624
\(587\) −22.9322 22.9322i −0.946512 0.946512i 0.0521286 0.998640i \(-0.483399\pi\)
−0.998640 + 0.0521286i \(0.983399\pi\)
\(588\) 0 0
\(589\) 3.02423i 0.124611i
\(590\) 0 0
\(591\) 0 0
\(592\) 4.04989 4.04989i 0.166449 0.166449i
\(593\) −31.8592 + 31.8592i −1.30830 + 1.30830i −0.385661 + 0.922641i \(0.626027\pi\)
−0.922641 + 0.385661i \(0.873973\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 13.5799i 0.556254i
\(597\) 0 0
\(598\) 1.25297 + 1.25297i 0.0512379 + 0.0512379i
\(599\) 22.1019 0.903060 0.451530 0.892256i \(-0.350878\pi\)
0.451530 + 0.892256i \(0.350878\pi\)
\(600\) 0 0
\(601\) −35.8874 −1.46388 −0.731939 0.681371i \(-0.761384\pi\)
−0.731939 + 0.681371i \(0.761384\pi\)
\(602\) −5.10306 5.10306i −0.207985 0.207985i
\(603\) 0 0
\(604\) 13.1210i 0.533884i
\(605\) 0 0
\(606\) 0 0
\(607\) 10.7675 10.7675i 0.437039 0.437039i −0.453975 0.891014i \(-0.649995\pi\)
0.891014 + 0.453975i \(0.149995\pi\)
\(608\) −1.44949 + 1.44949i −0.0587846 + 0.0587846i
\(609\) 0 0
\(610\) 0 0
\(611\) 37.8265i 1.53029i
\(612\) 0 0
\(613\) −5.86194 5.86194i −0.236762 0.236762i 0.578746 0.815508i \(-0.303542\pi\)
−0.815508 + 0.578746i \(0.803542\pi\)
\(614\) −9.33510 −0.376734
\(615\) 0 0
\(616\) −0.585786 −0.0236020
\(617\) −31.6118 31.6118i −1.27264 1.27264i −0.944697 0.327945i \(-0.893644\pi\)
−0.327945 0.944697i \(-0.606356\pi\)
\(618\) 0 0
\(619\) 32.4856i 1.30571i −0.757484 0.652853i \(-0.773572\pi\)
0.757484 0.652853i \(-0.226428\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 23.3976 23.3976i 0.938159 0.938159i
\(623\) −0.0498881 + 0.0498881i −0.00199872 + 0.00199872i
\(624\) 0 0
\(625\) 0 0
\(626\) 1.13578i 0.0453949i
\(627\) 0 0
\(628\) −16.9988 16.9988i −0.678324 0.678324i
\(629\) −7.34575 −0.292894
\(630\) 0 0
\(631\) 24.5826 0.978617 0.489308 0.872111i \(-0.337249\pi\)
0.489308 + 0.872111i \(0.337249\pi\)
\(632\) 0.667551 + 0.667551i 0.0265537 + 0.0265537i
\(633\) 0 0
\(634\) 1.17690i 0.0467405i
\(635\) 0 0
\(636\) 0 0
\(637\) 3.43916 3.43916i 0.136264 0.136264i
\(638\) 0.725998 0.725998i 0.0287426 0.0287426i
\(639\) 0 0
\(640\) 0 0
\(641\) 7.35255i 0.290408i −0.989402 0.145204i \(-0.953616\pi\)
0.989402 0.145204i \(-0.0463839\pi\)
\(642\) 0 0
\(643\) −8.73081 8.73081i −0.344309 0.344309i 0.513675 0.857985i \(-0.328284\pi\)
−0.857985 + 0.513675i \(0.828284\pi\)
\(644\) −0.364326 −0.0143564
\(645\) 0 0
\(646\) 2.62911 0.103441
\(647\) 28.3694 + 28.3694i 1.11532 + 1.11532i 0.992419 + 0.122898i \(0.0392189\pi\)
0.122898 + 0.992419i \(0.460781\pi\)
\(648\) 0 0
\(649\) 6.53517i 0.256528i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.0884482 + 0.0884482i −0.00346390 + 0.00346390i
\(653\) −27.4634 + 27.4634i −1.07472 + 1.07472i −0.0777521 + 0.996973i \(0.524774\pi\)
−0.996973 + 0.0777521i \(0.975226\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.84909i 0.150282i
\(657\) 0 0
\(658\) −5.49938 5.49938i −0.214388 0.214388i
\(659\) 26.5619 1.03470 0.517352 0.855772i \(-0.326918\pi\)
0.517352 + 0.855772i \(0.326918\pi\)
\(660\) 0 0
\(661\) −27.3725 −1.06467 −0.532333 0.846535i \(-0.678685\pi\)
−0.532333 + 0.846535i \(0.678685\pi\)
\(662\) −13.1520 13.1520i −0.511165 0.511165i
\(663\) 0 0
\(664\) 11.0599i 0.429206i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.451529 0.451529i 0.0174833 0.0174833i
\(668\) −9.31319 + 9.31319i −0.360338 + 0.360338i
\(669\) 0 0
\(670\) 0 0
\(671\) 2.21926i 0.0856734i
\(672\) 0 0
\(673\) 12.4095 + 12.4095i 0.478349 + 0.478349i 0.904603 0.426254i \(-0.140167\pi\)
−0.426254 + 0.904603i \(0.640167\pi\)
\(674\) −21.2360 −0.817981
\(675\) 0 0
\(676\) −10.6556 −0.409831
\(677\) 8.04384 + 8.04384i 0.309150 + 0.309150i 0.844580 0.535430i \(-0.179850\pi\)
−0.535430 + 0.844580i \(0.679850\pi\)
\(678\) 0 0
\(679\) 1.05594i 0.0405233i
\(680\) 0 0
\(681\) 0 0
\(682\) −0.611095 + 0.611095i −0.0234000 + 0.0234000i
\(683\) −6.88312 + 6.88312i −0.263375 + 0.263375i −0.826424 0.563048i \(-0.809628\pi\)
0.563048 + 0.826424i \(0.309628\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) −5.10306 5.10306i −0.194552 0.194552i
\(689\) −34.5631 −1.31675
\(690\) 0 0
\(691\) −45.4327 −1.72834 −0.864171 0.503199i \(-0.832156\pi\)
−0.864171 + 0.503199i \(0.832156\pi\)
\(692\) 5.81257 + 5.81257i 0.220961 + 0.220961i
\(693\) 0 0
\(694\) 36.5176i 1.38619i
\(695\) 0 0
\(696\) 0 0
\(697\) 3.49077 3.49077i 0.132222 0.132222i
\(698\) 21.3252 21.3252i 0.807171 0.807171i
\(699\) 0 0
\(700\) 0 0
\(701\) 23.9123i 0.903155i −0.892232 0.451578i \(-0.850861\pi\)
0.892232 0.451578i \(-0.149139\pi\)
\(702\) 0 0
\(703\) −8.30182 8.30182i −0.313109 0.313109i
\(704\) −0.585786 −0.0220777
\(705\) 0 0
\(706\) 12.4268 0.467690
\(707\) −2.93942 2.93942i −0.110548 0.110548i
\(708\) 0 0
\(709\) 29.6939i 1.11518i 0.830117 + 0.557589i \(0.188273\pi\)
−0.830117 + 0.557589i \(0.811727\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.0498881 + 0.0498881i −0.00186963 + 0.00186963i
\(713\) −0.380066 + 0.380066i −0.0142336 + 0.0142336i
\(714\) 0 0
\(715\) 0 0
\(716\) 9.20080i 0.343850i
\(717\) 0 0
\(718\) −5.42606 5.42606i −0.202499 0.202499i
\(719\) 44.7620 1.66934 0.834670 0.550751i \(-0.185659\pi\)
0.834670 + 0.550751i \(0.185659\pi\)
\(720\) 0 0
\(721\) −4.44344 −0.165482
\(722\) −10.4637 10.4637i −0.389420 0.389420i
\(723\) 0 0
\(724\) 5.24316i 0.194860i
\(725\) 0 0
\(726\) 0 0
\(727\) 30.1992 30.1992i 1.12003 1.12003i 0.128289 0.991737i \(-0.459051\pi\)
0.991737 0.128289i \(-0.0409485\pi\)
\(728\) 3.43916 3.43916i 0.127464 0.127464i
\(729\) 0 0
\(730\) 0 0
\(731\) 9.25601i 0.342346i
\(732\) 0 0
\(733\) −8.22450 8.22450i −0.303779 0.303779i 0.538712 0.842490i \(-0.318911\pi\)
−0.842490 + 0.538712i \(0.818911\pi\)
\(734\) 18.9711 0.700235
\(735\) 0 0
\(736\) −0.364326 −0.0134292
\(737\) 3.94938 + 3.94938i 0.145477 + 0.145477i
\(738\) 0 0
\(739\) 27.6997i 1.01895i 0.860486 + 0.509474i \(0.170160\pi\)
−0.860486 + 0.509474i \(0.829840\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 5.02494 5.02494i 0.184471 0.184471i
\(743\) −1.50830 + 1.50830i −0.0553342 + 0.0553342i −0.734232 0.678898i \(-0.762458\pi\)
0.678898 + 0.734232i \(0.262458\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 3.95691i 0.144873i
\(747\) 0 0
\(748\) 0.531254 + 0.531254i 0.0194246 + 0.0194246i
\(749\) 9.68608 0.353922
\(750\) 0 0
\(751\) −34.5599 −1.26111 −0.630555 0.776145i \(-0.717172\pi\)
−0.630555 + 0.776145i \(0.717172\pi\)
\(752\) −5.49938 5.49938i −0.200542 0.200542i
\(753\) 0 0
\(754\) 8.52469i 0.310451i
\(755\) 0 0
\(756\) 0 0
\(757\) 26.3636 26.3636i 0.958201 0.958201i −0.0409596 0.999161i \(-0.513041\pi\)
0.999161 + 0.0409596i \(0.0130415\pi\)
\(758\) 9.79619 9.79619i 0.355814 0.355814i
\(759\) 0 0
\(760\) 0 0
\(761\) 40.6078i 1.47203i −0.676964 0.736016i \(-0.736705\pi\)
0.676964 0.736016i \(-0.263295\pi\)
\(762\) 0 0
\(763\) 14.0951 + 14.0951i 0.510278 + 0.510278i
\(764\) −11.1869 −0.404727
\(765\) 0 0
\(766\) −22.1621 −0.800748
\(767\) −38.3680 38.3680i −1.38539 1.38539i
\(768\) 0 0
\(769\) 5.37968i 0.193996i −0.995285 0.0969982i \(-0.969076\pi\)
0.995285 0.0969982i \(-0.0309241\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −11.9136 + 11.9136i −0.428780 + 0.428780i
\(773\) −25.8174 + 25.8174i −0.928587 + 0.928587i −0.997615 0.0690281i \(-0.978010\pi\)
0.0690281 + 0.997615i \(0.478010\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.05594i 0.0379061i
\(777\) 0 0
\(778\) 24.5503 + 24.5503i 0.880171 + 0.880171i
\(779\) 7.89021 0.282696
\(780\) 0 0
\(781\) −6.40159 −0.229067
\(782\) 0.330410 + 0.330410i 0.0118154 + 0.0118154i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) −18.9421 + 18.9421i −0.675212 + 0.675212i −0.958913 0.283701i \(-0.908438\pi\)
0.283701 + 0.958913i \(0.408438\pi\)
\(788\) −11.7811 + 11.7811i −0.419683 + 0.419683i
\(789\) 0 0
\(790\) 0 0
\(791\) 6.64224i 0.236171i
\(792\) 0 0
\(793\) 13.0293 + 13.0293i 0.462683 + 0.462683i
\(794\) −26.8612 −0.953269
\(795\) 0 0
\(796\) 2.11188 0.0748536
\(797\) −19.5851 19.5851i −0.693738 0.693738i 0.269314 0.963052i \(-0.413203\pi\)
−0.963052 + 0.269314i \(0.913203\pi\)
\(798\) 0 0