Properties

Label 3150.2.m.g.1457.4
Level 3150
Weight 2
Character 3150.1457
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 1457.4
Root \(-0.965926 - 0.258819i\)
Character \(\chi\) = 3150.1457
Dual form 3150.2.m.g.2843.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.585786i q^{11} +(0.0249440 - 0.0249440i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-1.92152 + 1.92152i) q^{17} +4.87832i q^{19} +(0.414214 + 0.414214i) q^{22} +(5.15660 + 5.15660i) q^{23} -0.0352762i q^{26} +(-0.707107 + 0.707107i) q^{28} +4.58114 q^{29} +9.83839 q^{31} +(-0.707107 + 0.707107i) q^{32} +2.71744i q^{34} +(-2.87832 - 2.87832i) q^{37} +(3.44949 + 3.44949i) q^{38} +0.979336i q^{41} +(4.27463 - 4.27463i) q^{43} +0.585786 q^{44} +7.29253 q^{46} +(6.32780 - 6.32780i) q^{47} +1.00000i q^{49} +(-0.0249440 - 0.0249440i) q^{52} +(1.56084 + 1.56084i) q^{53} +1.00000i q^{56} +(3.23936 - 3.23936i) q^{58} +0.670951 q^{59} +2.35363 q^{61} +(6.95680 - 6.95680i) q^{62} +1.00000i q^{64} +(-5.08516 - 5.08516i) q^{67} +(1.92152 + 1.92152i) q^{68} -2.92820i q^{71} +(-2.51059 + 2.51059i) q^{73} -4.07055 q^{74} +4.87832 q^{76} +(0.414214 - 0.414214i) q^{77} -8.71279i q^{79} +(0.692495 + 0.692495i) q^{82} +(2.99207 + 2.99207i) q^{83} -6.04524i q^{86} +(0.414214 - 0.414214i) q^{88} +9.72741 q^{89} -0.0352762 q^{91} +(5.15660 - 5.15660i) q^{92} -8.94887i q^{94} +(-4.74666 - 4.74666i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 8q^{13} - 8q^{14} - 8q^{16} - 8q^{22} + 16q^{23} + 16q^{37} + 8q^{38} + 8q^{43} + 16q^{44} + 8q^{46} - 8q^{47} + 8q^{52} + 32q^{53} + 8q^{58} - 8q^{59} - 32q^{61} + 32q^{62} - 16q^{67} - 16q^{74} - 8q^{77} + 8q^{82} - 8q^{83} - 8q^{88} + 16q^{89} + 8q^{91} + 16q^{92} - 16q^{97} + O(q^{100}) \)

Character values

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

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

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 \(0.0281468\pi\)
−0.996093 + 0.0883106i \(0.971853\pi\)
\(12\) 0 0
\(13\) 0.0249440 0.0249440i 0.00691823 0.00691823i −0.703639 0.710557i \(-0.748443\pi\)
0.710557 + 0.703639i \(0.248443\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −1.92152 + 1.92152i −0.466037 + 0.466037i −0.900628 0.434591i \(-0.856893\pi\)
0.434591 + 0.900628i \(0.356893\pi\)
\(18\) 0 0
\(19\) 4.87832i 1.11916i 0.828776 + 0.559581i \(0.189038\pi\)
−0.828776 + 0.559581i \(0.810962\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.414214 + 0.414214i 0.0883106 + 0.0883106i
\(23\) 5.15660 + 5.15660i 1.07522 + 1.07522i 0.996930 + 0.0782944i \(0.0249474\pi\)
0.0782944 + 0.996930i \(0.475053\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0.0352762i 0.00691823i
\(27\) 0 0
\(28\) −0.707107 + 0.707107i −0.133631 + 0.133631i
\(29\) 4.58114 0.850697 0.425348 0.905030i \(-0.360152\pi\)
0.425348 + 0.905030i \(0.360152\pi\)
\(30\) 0 0
\(31\) 9.83839 1.76703 0.883514 0.468405i \(-0.155171\pi\)
0.883514 + 0.468405i \(0.155171\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0 0
\(34\) 2.71744i 0.466037i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.87832 2.87832i −0.473192 0.473192i 0.429754 0.902946i \(-0.358600\pi\)
−0.902946 + 0.429754i \(0.858600\pi\)
\(38\) 3.44949 + 3.44949i 0.559581 + 0.559581i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.979336i 0.152947i 0.997072 + 0.0764733i \(0.0243660\pi\)
−0.997072 + 0.0764733i \(0.975634\pi\)
\(42\) 0 0
\(43\) 4.27463 4.27463i 0.651875 0.651875i −0.301569 0.953444i \(-0.597510\pi\)
0.953444 + 0.301569i \(0.0975103\pi\)
\(44\) 0.585786 0.0883106
\(45\) 0 0
\(46\) 7.29253 1.07522
\(47\) 6.32780 6.32780i 0.923005 0.923005i −0.0742355 0.997241i \(-0.523652\pi\)
0.997241 + 0.0742355i \(0.0236517\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.0249440 0.0249440i −0.00345911 0.00345911i
\(53\) 1.56084 + 1.56084i 0.214398 + 0.214398i 0.806133 0.591735i \(-0.201557\pi\)
−0.591735 + 0.806133i \(0.701557\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) 3.23936 3.23936i 0.425348 0.425348i
\(59\) 0.670951 0.0873503 0.0436752 0.999046i \(-0.486093\pi\)
0.0436752 + 0.999046i \(0.486093\pi\)
\(60\) 0 0
\(61\) 2.35363 0.301351 0.150676 0.988583i \(-0.451855\pi\)
0.150676 + 0.988583i \(0.451855\pi\)
\(62\) 6.95680 6.95680i 0.883514 0.883514i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) −5.08516 5.08516i −0.621252 0.621252i 0.324600 0.945851i \(-0.394770\pi\)
−0.945851 + 0.324600i \(0.894770\pi\)
\(68\) 1.92152 + 1.92152i 0.233018 + 0.233018i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.92820i 0.347514i −0.984789 0.173757i \(-0.944409\pi\)
0.984789 0.173757i \(-0.0555907\pi\)
\(72\) 0 0
\(73\) −2.51059 + 2.51059i −0.293842 + 0.293842i −0.838596 0.544754i \(-0.816623\pi\)
0.544754 + 0.838596i \(0.316623\pi\)
\(74\) −4.07055 −0.473192
\(75\) 0 0
\(76\) 4.87832 0.559581
\(77\) 0.414214 0.414214i 0.0472040 0.0472040i
\(78\) 0 0
\(79\) 8.71279i 0.980266i −0.871648 0.490133i \(-0.836948\pi\)
0.871648 0.490133i \(-0.163052\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0.692495 + 0.692495i 0.0764733 + 0.0764733i
\(83\) 2.99207 + 2.99207i 0.328423 + 0.328423i 0.851986 0.523564i \(-0.175398\pi\)
−0.523564 + 0.851986i \(0.675398\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.04524i 0.651875i
\(87\) 0 0
\(88\) 0.414214 0.414214i 0.0441553 0.0441553i
\(89\) 9.72741 1.03110 0.515552 0.856859i \(-0.327587\pi\)
0.515552 + 0.856859i \(0.327587\pi\)
\(90\) 0 0
\(91\) −0.0352762 −0.00369795
\(92\) 5.15660 5.15660i 0.537612 0.537612i
\(93\) 0 0
\(94\) 8.94887i 0.923005i
\(95\) 0 0
\(96\) 0 0
\(97\) −4.74666 4.74666i −0.481951 0.481951i 0.423804 0.905754i \(-0.360695\pi\)
−0.905754 + 0.423804i \(0.860695\pi\)
\(98\) 0.707107 + 0.707107i 0.0714286 + 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 6.18618i 0.615548i 0.951459 + 0.307774i \(0.0995841\pi\)
−0.951459 + 0.307774i \(0.900416\pi\)
\(102\) 0 0
\(103\) 0.272229 0.272229i 0.0268235 0.0268235i −0.693568 0.720391i \(-0.743962\pi\)
0.720391 + 0.693568i \(0.243962\pi\)
\(104\) −0.0352762 −0.00345911
\(105\) 0 0
\(106\) 2.20736 0.214398
\(107\) −3.97934 + 3.97934i −0.384697 + 0.384697i −0.872791 0.488094i \(-0.837692\pi\)
0.488094 + 0.872791i \(0.337692\pi\)
\(108\) 0 0
\(109\) 8.61982i 0.825629i 0.910815 + 0.412814i \(0.135454\pi\)
−0.910815 + 0.412814i \(0.864546\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.707107 + 0.707107i 0.0668153 + 0.0668153i
\(113\) 6.13165 + 6.13165i 0.576817 + 0.576817i 0.934025 0.357208i \(-0.116271\pi\)
−0.357208 + 0.934025i \(0.616271\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 4.58114i 0.425348i
\(117\) 0 0
\(118\) 0.474434 0.474434i 0.0436752 0.0436752i
\(119\) 2.71744 0.249107
\(120\) 0 0
\(121\) 10.6569 0.968805
\(122\) 1.66427 1.66427i 0.150676 0.150676i
\(123\) 0 0
\(124\) 9.83839i 0.883514i
\(125\) 0 0
\(126\) 0 0
\(127\) −14.1356 14.1356i −1.25433 1.25433i −0.953760 0.300569i \(-0.902824\pi\)
−0.300569 0.953760i \(-0.597176\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 19.3843i 1.69361i 0.531903 + 0.846805i \(0.321477\pi\)
−0.531903 + 0.846805i \(0.678523\pi\)
\(132\) 0 0
\(133\) 3.44949 3.44949i 0.299109 0.299109i
\(134\) −7.19151 −0.621252
\(135\) 0 0
\(136\) 2.71744 0.233018
\(137\) 5.29858 5.29858i 0.452688 0.452688i −0.443558 0.896246i \(-0.646284\pi\)
0.896246 + 0.443558i \(0.146284\pi\)
\(138\) 0 0
\(139\) 4.33386i 0.367593i 0.982964 + 0.183796i \(0.0588387\pi\)
−0.982964 + 0.183796i \(0.941161\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2.07055 2.07055i −0.173757 0.173757i
\(143\) 0.0146119 + 0.0146119i 0.00122191 + 0.00122191i
\(144\) 0 0
\(145\) 0 0
\(146\) 3.55051i 0.293842i
\(147\) 0 0
\(148\) −2.87832 + 2.87832i −0.236596 + 0.236596i
\(149\) 16.4083 1.34422 0.672111 0.740450i \(-0.265388\pi\)
0.672111 + 0.740450i \(0.265388\pi\)
\(150\) 0 0
\(151\) 6.19275 0.503959 0.251980 0.967733i \(-0.418918\pi\)
0.251980 + 0.967733i \(0.418918\pi\)
\(152\) 3.44949 3.44949i 0.279791 0.279791i
\(153\) 0 0
\(154\) 0.585786i 0.0472040i
\(155\) 0 0
\(156\) 0 0
\(157\) −6.65561 6.65561i −0.531175 0.531175i 0.389747 0.920922i \(-0.372563\pi\)
−0.920922 + 0.389747i \(0.872563\pi\)
\(158\) −6.16088 6.16088i −0.490133 0.490133i
\(159\) 0 0
\(160\) 0 0
\(161\) 7.29253i 0.574732i
\(162\) 0 0
\(163\) 7.26002 7.26002i 0.568649 0.568649i −0.363101 0.931750i \(-0.618282\pi\)
0.931750 + 0.363101i \(0.118282\pi\)
\(164\) 0.979336 0.0764733
\(165\) 0 0
\(166\) 4.23143 0.328423
\(167\) 0.484766 0.484766i 0.0375123 0.0375123i −0.688102 0.725614i \(-0.741556\pi\)
0.725614 + 0.688102i \(0.241556\pi\)
\(168\) 0 0
\(169\) 12.9988i 0.999904i
\(170\) 0 0
\(171\) 0 0
\(172\) −4.27463 4.27463i −0.325938 0.325938i
\(173\) 15.8126 + 15.8126i 1.20221 + 1.20221i 0.973494 + 0.228714i \(0.0734520\pi\)
0.228714 + 0.973494i \(0.426548\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.585786i 0.0441553i
\(177\) 0 0
\(178\) 6.87832 6.87832i 0.515552 0.515552i
\(179\) 5.14235 0.384357 0.192179 0.981360i \(-0.438445\pi\)
0.192179 + 0.981360i \(0.438445\pi\)
\(180\) 0 0
\(181\) 15.0411 1.11800 0.558999 0.829169i \(-0.311186\pi\)
0.558999 + 0.829169i \(0.311186\pi\)
\(182\) −0.0249440 + 0.0249440i −0.00184897 + 0.00184897i
\(183\) 0 0
\(184\) 7.29253i 0.537612i
\(185\) 0 0
\(186\) 0 0
\(187\) −1.12560 1.12560i −0.0823120 0.0823120i
\(188\) −6.32780 6.32780i −0.461503 0.461503i
\(189\) 0 0
\(190\) 0 0
\(191\) 11.8732i 0.859111i 0.903040 + 0.429556i \(0.141330\pi\)
−0.903040 + 0.429556i \(0.858670\pi\)
\(192\) 0 0
\(193\) −0.0864086 + 0.0864086i −0.00621983 + 0.00621983i −0.710210 0.703990i \(-0.751400\pi\)
0.703990 + 0.710210i \(0.251400\pi\)
\(194\) −6.71279 −0.481951
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 15.3374 15.3374i 1.09275 1.09275i 0.0975106 0.995234i \(-0.468912\pi\)
0.995234 0.0975106i \(-0.0310880\pi\)
\(198\) 0 0
\(199\) 13.4256i 0.951715i −0.879522 0.475857i \(-0.842138\pi\)
0.879522 0.475857i \(-0.157862\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 4.37429 + 4.37429i 0.307774 + 0.307774i
\(203\) −3.23936 3.23936i −0.227358 0.227358i
\(204\) 0 0
\(205\) 0 0
\(206\) 0.384990i 0.0268235i
\(207\) 0 0
\(208\) −0.0249440 + 0.0249440i −0.00172956 + 0.00172956i
\(209\) −2.85765 −0.197668
\(210\) 0 0
\(211\) −16.2263 −1.11706 −0.558531 0.829484i \(-0.688635\pi\)
−0.558531 + 0.829484i \(0.688635\pi\)
\(212\) 1.56084 1.56084i 0.107199 0.107199i
\(213\) 0 0
\(214\) 5.62763i 0.384697i
\(215\) 0 0
\(216\) 0 0
\(217\) −6.95680 6.95680i −0.472258 0.472258i
\(218\) 6.09513 + 6.09513i 0.412814 + 0.412814i
\(219\) 0 0
\(220\) 0 0
\(221\) 0.0958609i 0.00644830i
\(222\) 0 0
\(223\) −11.1919 + 11.1919i −0.749463 + 0.749463i −0.974378 0.224915i \(-0.927790\pi\)
0.224915 + 0.974378i \(0.427790\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 8.67147 0.576817
\(227\) −14.5784 + 14.5784i −0.967601 + 0.967601i −0.999491 0.0318907i \(-0.989847\pi\)
0.0318907 + 0.999491i \(0.489847\pi\)
\(228\) 0 0
\(229\) 16.0905i 1.06329i −0.846967 0.531645i \(-0.821574\pi\)
0.846967 0.531645i \(-0.178426\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.23936 3.23936i −0.212674 0.212674i
\(233\) −13.7162 13.7162i −0.898578 0.898578i 0.0967326 0.995310i \(-0.469161\pi\)
−0.995310 + 0.0967326i \(0.969161\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.670951i 0.0436752i
\(237\) 0 0
\(238\) 1.92152 1.92152i 0.124554 0.124554i
\(239\) 0.485281 0.0313902 0.0156951 0.999877i \(-0.495004\pi\)
0.0156951 + 0.999877i \(0.495004\pi\)
\(240\) 0 0
\(241\) 9.57598 0.616843 0.308422 0.951250i \(-0.400199\pi\)
0.308422 + 0.951250i \(0.400199\pi\)
\(242\) 7.53553 7.53553i 0.484402 0.484402i
\(243\) 0 0
\(244\) 2.35363i 0.150676i
\(245\) 0 0
\(246\) 0 0
\(247\) 0.121685 + 0.121685i 0.00774262 + 0.00774262i
\(248\) −6.95680 6.95680i −0.441757 0.441757i
\(249\) 0 0
\(250\) 0 0
\(251\) 23.8532i 1.50560i 0.658250 + 0.752799i \(0.271297\pi\)
−0.658250 + 0.752799i \(0.728703\pi\)
\(252\) 0 0
\(253\) −3.02066 + 3.02066i −0.189908 + 0.189908i
\(254\) −19.9907 −1.25433
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −4.62095 + 4.62095i −0.288247 + 0.288247i −0.836387 0.548140i \(-0.815336\pi\)
0.548140 + 0.836387i \(0.315336\pi\)
\(258\) 0 0
\(259\) 4.07055i 0.252932i
\(260\) 0 0
\(261\) 0 0
\(262\) 13.7067 + 13.7067i 0.846805 + 0.846805i
\(263\) −7.67183 7.67183i −0.473065 0.473065i 0.429840 0.902905i \(-0.358570\pi\)
−0.902905 + 0.429840i \(0.858570\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.87832i 0.299109i
\(267\) 0 0
\(268\) −5.08516 + 5.08516i −0.310626 + 0.310626i
\(269\) 20.4629 1.24764 0.623821 0.781567i \(-0.285579\pi\)
0.623821 + 0.781567i \(0.285579\pi\)
\(270\) 0 0
\(271\) −23.2500 −1.41233 −0.706167 0.708045i \(-0.749577\pi\)
−0.706167 + 0.708045i \(0.749577\pi\)
\(272\) 1.92152 1.92152i 0.116509 0.116509i
\(273\) 0 0
\(274\) 7.49333i 0.452688i
\(275\) 0 0
\(276\) 0 0
\(277\) −20.3636 20.3636i −1.22353 1.22353i −0.966368 0.257161i \(-0.917213\pi\)
−0.257161 0.966368i \(-0.582787\pi\)
\(278\) 3.06450 + 3.06450i 0.183796 + 0.183796i
\(279\) 0 0
\(280\) 0 0
\(281\) 22.1421i 1.32089i 0.750875 + 0.660445i \(0.229632\pi\)
−0.750875 + 0.660445i \(0.770368\pi\)
\(282\) 0 0
\(283\) 14.4600 14.4600i 0.859556 0.859556i −0.131730 0.991286i \(-0.542053\pi\)
0.991286 + 0.131730i \(0.0420530\pi\)
\(284\) −2.92820 −0.173757
\(285\) 0 0
\(286\) 0.0206643 0.00122191
\(287\) 0.692495 0.692495i 0.0408767 0.0408767i
\(288\) 0 0
\(289\) 9.61553i 0.565619i
\(290\) 0 0
\(291\) 0 0
\(292\) 2.51059 + 2.51059i 0.146921 + 0.146921i
\(293\) 0.442922 + 0.442922i 0.0258758 + 0.0258758i 0.719926 0.694051i \(-0.244176\pi\)
−0.694051 + 0.719926i \(0.744176\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4.07055i 0.236596i
\(297\) 0 0
\(298\) 11.6024 11.6024i 0.672111 0.672111i
\(299\) 0.257253 0.0148773
\(300\) 0 0
\(301\) −6.04524 −0.348442
\(302\) 4.37894 4.37894i 0.251980 0.251980i
\(303\) 0 0
\(304\) 4.87832i 0.279791i
\(305\) 0 0
\(306\) 0 0
\(307\) −14.3696 14.3696i −0.820119 0.820119i 0.166006 0.986125i \(-0.446913\pi\)
−0.986125 + 0.166006i \(0.946913\pi\)
\(308\) −0.414214 0.414214i −0.0236020 0.0236020i
\(309\) 0 0
\(310\) 0 0
\(311\) 17.0892i 0.969042i 0.874780 + 0.484521i \(0.161006\pi\)
−0.874780 + 0.484521i \(0.838994\pi\)
\(312\) 0 0
\(313\) 2.66098 2.66098i 0.150408 0.150408i −0.627892 0.778300i \(-0.716082\pi\)
0.778300 + 0.627892i \(0.216082\pi\)
\(314\) −9.41245 −0.531175
\(315\) 0 0
\(316\) −8.71279 −0.490133
\(317\) −9.56011 + 9.56011i −0.536949 + 0.536949i −0.922632 0.385682i \(-0.873966\pi\)
0.385682 + 0.922632i \(0.373966\pi\)
\(318\) 0 0
\(319\) 2.68357i 0.150251i
\(320\) 0 0
\(321\) 0 0
\(322\) −5.15660 5.15660i −0.287366 0.287366i
\(323\) −9.37378 9.37378i −0.521571 0.521571i
\(324\) 0 0
\(325\) 0 0
\(326\) 10.2672i 0.568649i
\(327\) 0 0
\(328\) 0.692495 0.692495i 0.0382366 0.0382366i
\(329\) −8.94887 −0.493367
\(330\) 0 0
\(331\) 2.71404 0.149177 0.0745885 0.997214i \(-0.476236\pi\)
0.0745885 + 0.997214i \(0.476236\pi\)
\(332\) 2.99207 2.99207i 0.164211 0.164211i
\(333\) 0 0
\(334\) 0.685563i 0.0375123i
\(335\) 0 0
\(336\) 0 0
\(337\) 15.9867 + 15.9867i 0.870851 + 0.870851i 0.992565 0.121714i \(-0.0388391\pi\)
−0.121714 + 0.992565i \(0.538839\pi\)
\(338\) 9.19151 + 9.19151i 0.499952 + 0.499952i
\(339\) 0 0
\(340\) 0 0
\(341\) 5.76320i 0.312095i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) −6.04524 −0.325938
\(345\) 0 0
\(346\) 22.3624 1.20221
\(347\) −18.0228 + 18.0228i −0.967516 + 0.967516i −0.999489 0.0319731i \(-0.989821\pi\)
0.0319731 + 0.999489i \(0.489821\pi\)
\(348\) 0 0
\(349\) 22.6437i 1.21209i 0.795431 + 0.606044i \(0.207244\pi\)
−0.795431 + 0.606044i \(0.792756\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.414214 0.414214i −0.0220777 0.0220777i
\(353\) 14.5266 + 14.5266i 0.773173 + 0.773173i 0.978660 0.205487i \(-0.0658777\pi\)
−0.205487 + 0.978660i \(0.565878\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 9.72741i 0.515552i
\(357\) 0 0
\(358\) 3.63619 3.63619i 0.192179 0.192179i
\(359\) 12.3264 0.650562 0.325281 0.945617i \(-0.394541\pi\)
0.325281 + 0.945617i \(0.394541\pi\)
\(360\) 0 0
\(361\) −4.79796 −0.252524
\(362\) 10.6357 10.6357i 0.558999 0.558999i
\(363\) 0 0
\(364\) 0.0352762i 0.00184897i
\(365\) 0 0
\(366\) 0 0
\(367\) 20.3428 + 20.3428i 1.06188 + 1.06188i 0.997954 + 0.0639302i \(0.0203635\pi\)
0.0639302 + 0.997954i \(0.479637\pi\)
\(368\) −5.15660 5.15660i −0.268806 0.268806i
\(369\) 0 0
\(370\) 0 0
\(371\) 2.20736i 0.114601i
\(372\) 0 0
\(373\) 16.7980 16.7980i 0.869765 0.869765i −0.122681 0.992446i \(-0.539149\pi\)
0.992446 + 0.122681i \(0.0391491\pi\)
\(374\) −1.59184 −0.0823120
\(375\) 0 0
\(376\) −8.94887 −0.461503
\(377\) 0.114272 0.114272i 0.00588531 0.00588531i
\(378\) 0 0
\(379\) 13.5108i 0.694001i 0.937865 + 0.347000i \(0.112800\pi\)
−0.937865 + 0.347000i \(0.887200\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 8.39559 + 8.39559i 0.429556 + 0.429556i
\(383\) −3.84377 3.84377i −0.196407 0.196407i 0.602051 0.798458i \(-0.294351\pi\)
−0.798458 + 0.602051i \(0.794351\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.122200i 0.00621983i
\(387\) 0 0
\(388\) −4.74666 + 4.74666i −0.240975 + 0.240975i
\(389\) −35.9081 −1.82061 −0.910305 0.413937i \(-0.864153\pi\)
−0.910305 + 0.413937i \(0.864153\pi\)
\(390\) 0 0
\(391\) −19.8170 −1.00219
\(392\) 0.707107 0.707107i 0.0357143 0.0357143i
\(393\) 0 0
\(394\) 21.6904i 1.09275i
\(395\) 0 0
\(396\) 0 0
\(397\) 17.9227 + 17.9227i 0.899513 + 0.899513i 0.995393 0.0958795i \(-0.0305663\pi\)
−0.0958795 + 0.995393i \(0.530566\pi\)
\(398\) −9.49333 9.49333i −0.475857 0.475857i
\(399\) 0 0
\(400\) 0 0
\(401\) 33.4042i 1.66813i −0.551669 0.834063i \(-0.686009\pi\)
0.551669 0.834063i \(-0.313991\pi\)
\(402\) 0 0
\(403\) 0.245409 0.245409i 0.0122247 0.0122247i
\(404\) 6.18618 0.307774
\(405\) 0 0
\(406\) −4.58114 −0.227358
\(407\) 1.68608 1.68608i 0.0835758 0.0835758i
\(408\) 0 0
\(409\) 39.4438i 1.95037i −0.221395 0.975184i \(-0.571061\pi\)
0.221395 0.975184i \(-0.428939\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.272229 0.272229i −0.0134118 0.0134118i
\(413\) −0.474434 0.474434i −0.0233454 0.0233454i
\(414\) 0 0
\(415\) 0 0
\(416\) 0.0352762i 0.00172956i
\(417\) 0 0
\(418\) −2.02066 + 2.02066i −0.0988339 + 0.0988339i
\(419\) −32.5989 −1.59256 −0.796281 0.604927i \(-0.793202\pi\)
−0.796281 + 0.604927i \(0.793202\pi\)
\(420\) 0 0
\(421\) −14.6330 −0.713167 −0.356583 0.934264i \(-0.616058\pi\)
−0.356583 + 0.934264i \(0.616058\pi\)
\(422\) −11.4737 + 11.4737i −0.558531 + 0.558531i
\(423\) 0 0
\(424\) 2.20736i 0.107199i
\(425\) 0 0
\(426\) 0 0
\(427\) −1.66427 1.66427i −0.0805395 0.0805395i
\(428\) 3.97934 + 3.97934i 0.192348 + 0.192348i
\(429\) 0 0
\(430\) 0 0
\(431\) 5.88347i 0.283397i −0.989910 0.141699i \(-0.954744\pi\)
0.989910 0.141699i \(-0.0452564\pi\)
\(432\) 0 0
\(433\) −7.55532 + 7.55532i −0.363085 + 0.363085i −0.864948 0.501862i \(-0.832648\pi\)
0.501862 + 0.864948i \(0.332648\pi\)
\(434\) −9.83839 −0.472258
\(435\) 0 0
\(436\) 8.61982 0.412814
\(437\) −25.1555 + 25.1555i −1.20335 + 1.20335i
\(438\) 0 0
\(439\) 21.1614i 1.00998i 0.863126 + 0.504989i \(0.168503\pi\)
−0.863126 + 0.504989i \(0.831497\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0.0677839 + 0.0677839i 0.00322415 + 0.00322415i
\(443\) −4.32640 4.32640i −0.205553 0.205553i 0.596821 0.802374i \(-0.296430\pi\)
−0.802374 + 0.596821i \(0.796430\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 15.8277i 0.749463i
\(447\) 0 0
\(448\) 0.707107 0.707107i 0.0334077 0.0334077i
\(449\) 4.38623 0.206999 0.103500 0.994629i \(-0.466996\pi\)
0.103500 + 0.994629i \(0.466996\pi\)
\(450\) 0 0
\(451\) −0.573682 −0.0270136
\(452\) 6.13165 6.13165i 0.288409 0.288409i
\(453\) 0 0
\(454\) 20.6169i 0.967601i
\(455\) 0 0
\(456\) 0 0
\(457\) 1.36960 + 1.36960i 0.0640672 + 0.0640672i 0.738414 0.674347i \(-0.235575\pi\)
−0.674347 + 0.738414i \(0.735575\pi\)
\(458\) −11.3777 11.3777i −0.531645 0.531645i
\(459\) 0 0
\(460\) 0 0
\(461\) 0.856388i 0.0398860i 0.999801 + 0.0199430i \(0.00634847\pi\)
−0.999801 + 0.0199430i \(0.993652\pi\)
\(462\) 0 0
\(463\) 3.76393 3.76393i 0.174925 0.174925i −0.614215 0.789139i \(-0.710527\pi\)
0.789139 + 0.614215i \(0.210527\pi\)
\(464\) −4.58114 −0.212674
\(465\) 0 0
\(466\) −19.3976 −0.898578
\(467\) 19.3844 19.3844i 0.897002 0.897002i −0.0981679 0.995170i \(-0.531298\pi\)
0.995170 + 0.0981679i \(0.0312982\pi\)
\(468\) 0 0
\(469\) 7.19151i 0.332073i
\(470\) 0 0
\(471\) 0 0
\(472\) −0.474434 0.474434i −0.0218376 0.0218376i
\(473\) 2.50402 + 2.50402i 0.115135 + 0.115135i
\(474\) 0 0
\(475\) 0 0
\(476\) 2.71744i 0.124554i
\(477\) 0 0
\(478\) 0.343146 0.343146i 0.0156951 0.0156951i
\(479\) 27.8192 1.27109 0.635545 0.772064i \(-0.280776\pi\)
0.635545 + 0.772064i \(0.280776\pi\)
\(480\) 0 0
\(481\) −0.143594 −0.00654730
\(482\) 6.77124 6.77124i 0.308422 0.308422i
\(483\) 0 0
\(484\) 10.6569i 0.484402i
\(485\) 0 0
\(486\) 0 0
\(487\) −19.7899 19.7899i −0.896767 0.896767i 0.0983821 0.995149i \(-0.468633\pi\)
−0.995149 + 0.0983821i \(0.968633\pi\)
\(488\) −1.66427 1.66427i −0.0753378 0.0753378i
\(489\) 0 0
\(490\) 0 0
\(491\) 11.2817i 0.509135i −0.967055 0.254567i \(-0.918067\pi\)
0.967055 0.254567i \(-0.0819330\pi\)
\(492\) 0 0
\(493\) −8.80275 + 8.80275i −0.396456 + 0.396456i
\(494\) 0.172088 0.00774262
\(495\) 0 0
\(496\) −9.83839 −0.441757
\(497\) −2.07055 + 2.07055i −0.0928770 + 0.0928770i
\(498\) 0 0
\(499\) 25.0825i 1.12285i −0.827529 0.561423i \(-0.810254\pi\)
0.827529 0.561423i \(-0.189746\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 16.8667 + 16.8667i 0.752799 + 0.752799i
\(503\) −3.68357 3.68357i −0.164242 0.164242i 0.620201 0.784443i \(-0.287051\pi\)
−0.784443 + 0.620201i \(0.787051\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 4.27186i 0.189908i
\(507\) 0 0
\(508\) −14.1356 + 14.1356i −0.627164 + 0.627164i
\(509\) 41.1742 1.82501 0.912507 0.409061i \(-0.134144\pi\)
0.912507 + 0.409061i \(0.134144\pi\)
\(510\) 0 0
\(511\) 3.55051 0.157065
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 6.53501i 0.288247i
\(515\) 0 0
\(516\) 0 0
\(517\) 3.70674 + 3.70674i 0.163022 + 0.163022i
\(518\) 2.87832 + 2.87832i 0.126466 + 0.126466i
\(519\) 0 0
\(520\) 0 0
\(521\) 7.30639i 0.320099i −0.987109 0.160049i \(-0.948835\pi\)
0.987109 0.160049i \(-0.0511654\pi\)
\(522\) 0 0
\(523\) 1.96060 1.96060i 0.0857308 0.0857308i −0.662941 0.748672i \(-0.730692\pi\)
0.748672 + 0.662941i \(0.230692\pi\)
\(524\) 19.3843 0.846805
\(525\) 0 0
\(526\) −10.8496 −0.473065
\(527\) −18.9047 + 18.9047i −0.823500 + 0.823500i
\(528\) 0 0
\(529\) 30.1810i 1.31222i
\(530\) 0 0
\(531\) 0 0
\(532\) −3.44949 3.44949i −0.149554 0.149554i
\(533\) 0.0244286 + 0.0244286i 0.00105812 + 0.00105812i
\(534\) 0 0
\(535\) 0 0
\(536\) 7.19151i 0.310626i
\(537\) 0 0
\(538\) 14.4694 14.4694i 0.623821 0.623821i
\(539\) −0.585786 −0.0252316
\(540\) 0 0
\(541\) −13.5423 −0.582227 −0.291113 0.956689i \(-0.594026\pi\)
−0.291113 + 0.956689i \(0.594026\pi\)
\(542\) −16.4402 + 16.4402i −0.706167 + 0.706167i
\(543\) 0 0
\(544\) 2.71744i 0.116509i
\(545\) 0 0
\(546\) 0 0
\(547\) −17.5392 17.5392i −0.749921 0.749921i 0.224543 0.974464i \(-0.427911\pi\)
−0.974464 + 0.224543i \(0.927911\pi\)
\(548\) −5.29858 5.29858i −0.226344 0.226344i
\(549\) 0 0
\(550\) 0 0
\(551\) 22.3483i 0.952068i
\(552\) 0 0
\(553\) −6.16088 + 6.16088i −0.261987 + 0.261987i
\(554\) −28.7985 −1.22353
\(555\) 0 0
\(556\) 4.33386 0.183796
\(557\) −19.5639 + 19.5639i −0.828948 + 0.828948i −0.987371 0.158423i \(-0.949359\pi\)
0.158423 + 0.987371i \(0.449359\pi\)
\(558\) 0 0
\(559\) 0.213253i 0.00901965i
\(560\) 0 0
\(561\) 0 0
\(562\) 15.6569 + 15.6569i 0.660445 + 0.660445i
\(563\) −9.44156 9.44156i −0.397914 0.397914i 0.479582 0.877497i \(-0.340788\pi\)
−0.877497 + 0.479582i \(0.840788\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 20.4495i 0.859556i
\(567\) 0 0
\(568\) −2.07055 + 2.07055i −0.0868784 + 0.0868784i
\(569\) 17.2613 0.723633 0.361816 0.932249i \(-0.382157\pi\)
0.361816 + 0.932249i \(0.382157\pi\)
\(570\) 0 0
\(571\) −9.88415 −0.413639 −0.206819 0.978379i \(-0.566311\pi\)
−0.206819 + 0.978379i \(0.566311\pi\)
\(572\) 0.0146119 0.0146119i 0.000610953 0.000610953i
\(573\) 0 0
\(574\) 0.979336i 0.0408767i
\(575\) 0 0
\(576\) 0 0
\(577\) 27.5140 + 27.5140i 1.14542 + 1.14542i 0.987442 + 0.157980i \(0.0504982\pi\)
0.157980 + 0.987442i \(0.449502\pi\)
\(578\) 6.79920 + 6.79920i 0.282810 + 0.282810i
\(579\) 0 0
\(580\) 0 0
\(581\) 4.23143i 0.175549i
\(582\) 0 0
\(583\) −0.914320 + 0.914320i −0.0378673 + 0.0378673i
\(584\) 3.55051 0.146921
\(585\) 0 0
\(586\) 0.626386 0.0258758
\(587\) −7.47632 + 7.47632i −0.308581 + 0.308581i −0.844359 0.535778i \(-0.820018\pi\)
0.535778 + 0.844359i \(0.320018\pi\)
\(588\) 0 0
\(589\) 47.9948i 1.97759i
\(590\) 0 0
\(591\) 0 0
\(592\) 2.87832 + 2.87832i 0.118298 + 0.118298i
\(593\) −10.2024 10.2024i −0.418961 0.418961i 0.465884 0.884846i \(-0.345736\pi\)
−0.884846 + 0.465884i \(0.845736\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 16.4083i 0.672111i
\(597\) 0 0
\(598\) 0.181905 0.181905i 0.00743865 0.00743865i
\(599\) −32.7293 −1.33728 −0.668642 0.743584i \(-0.733124\pi\)
−0.668642 + 0.743584i \(0.733124\pi\)
\(600\) 0 0
\(601\) −37.5685 −1.53245 −0.766225 0.642573i \(-0.777867\pi\)
−0.766225 + 0.642573i \(0.777867\pi\)
\(602\) −4.27463 + 4.27463i −0.174221 + 0.174221i
\(603\) 0 0
\(604\) 6.19275i 0.251980i
\(605\) 0 0
\(606\) 0 0
\(607\) 28.4243 + 28.4243i 1.15371 + 1.15371i 0.985803 + 0.167905i \(0.0537003\pi\)
0.167905 + 0.985803i \(0.446300\pi\)
\(608\) −3.44949 3.44949i −0.139895 0.139895i
\(609\) 0 0
\(610\) 0 0
\(611\) 0.315682i 0.0127711i
\(612\) 0 0
\(613\) −32.4894 + 32.4894i −1.31223 + 1.31223i −0.392467 + 0.919766i \(0.628378\pi\)
−0.919766 + 0.392467i \(0.871622\pi\)
\(614\) −20.3218 −0.820119
\(615\) 0 0
\(616\) −0.585786 −0.0236020
\(617\) 14.0451 14.0451i 0.565434 0.565434i −0.365412 0.930846i \(-0.619072\pi\)
0.930846 + 0.365412i \(0.119072\pi\)
\(618\) 0 0
\(619\) 29.1719i 1.17252i −0.810124 0.586259i \(-0.800600\pi\)
0.810124 0.586259i \(-0.199400\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 12.0839 + 12.0839i 0.484521 + 0.484521i
\(623\) −6.87832 6.87832i −0.275574 0.275574i
\(624\) 0 0
\(625\) 0 0
\(626\) 3.76320i 0.150408i
\(627\) 0 0
\(628\) −6.65561 + 6.65561i −0.265588 + 0.265588i
\(629\) 11.0615 0.441050
\(630\) 0 0
\(631\) −36.5826 −1.45633 −0.728165 0.685402i \(-0.759626\pi\)
−0.728165 + 0.685402i \(0.759626\pi\)
\(632\) −6.16088 + 6.16088i −0.245066 + 0.245066i
\(633\) 0 0
\(634\) 13.5200i 0.536949i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.0249440 + 0.0249440i 0.000988318 + 0.000988318i
\(638\) 1.89757 + 1.89757i 0.0751256 + 0.0751256i
\(639\) 0 0
\(640\) 0 0
\(641\) 45.6957i 1.80487i −0.430825 0.902436i \(-0.641777\pi\)
0.430825 0.902436i \(-0.358223\pi\)
\(642\) 0 0
\(643\) −18.3877 + 18.3877i −0.725139 + 0.725139i −0.969647 0.244509i \(-0.921373\pi\)
0.244509 + 0.969647i \(0.421373\pi\)
\(644\) −7.29253 −0.287366
\(645\) 0 0
\(646\) −13.2565 −0.521571
\(647\) −16.5423 + 16.5423i −0.650343 + 0.650343i −0.953076 0.302733i \(-0.902101\pi\)
0.302733 + 0.953076i \(0.402101\pi\)
\(648\) 0 0
\(649\) 0.393034i 0.0154279i
\(650\) 0 0
\(651\) 0 0
\(652\) −7.26002 7.26002i −0.284324 0.284324i
\(653\) 6.67876 + 6.67876i 0.261360 + 0.261360i 0.825607 0.564246i \(-0.190833\pi\)
−0.564246 + 0.825607i \(0.690833\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.979336i 0.0382366i
\(657\) 0 0
\(658\) −6.32780 + 6.32780i −0.246684 + 0.246684i
\(659\) −31.7335 −1.23616 −0.618080 0.786115i \(-0.712089\pi\)
−0.618080 + 0.786115i \(0.712089\pi\)
\(660\) 0 0
\(661\) 42.4019 1.64924 0.824622 0.565684i \(-0.191388\pi\)
0.824622 + 0.565684i \(0.191388\pi\)
\(662\) 1.91912 1.91912i 0.0745885 0.0745885i
\(663\) 0 0
\(664\) 4.23143i 0.164211i
\(665\) 0 0
\(666\) 0 0
\(667\) 23.6231 + 23.6231i 0.914690 + 0.914690i
\(668\) −0.484766 0.484766i −0.0187562 0.0187562i
\(669\) 0 0
\(670\) 0 0
\(671\) 1.37872i 0.0532250i
\(672\) 0 0
\(673\) −27.8748 + 27.8748i −1.07450 + 1.07450i −0.0775032 + 0.996992i \(0.524695\pi\)
−0.996992 + 0.0775032i \(0.975305\pi\)
\(674\) 22.6086 0.870851
\(675\) 0 0
\(676\) 12.9988 0.499952
\(677\) −1.95616 + 1.95616i −0.0751815 + 0.0751815i −0.743698 0.668516i \(-0.766930\pi\)
0.668516 + 0.743698i \(0.266930\pi\)
\(678\) 0 0
\(679\) 6.71279i 0.257613i
\(680\) 0 0
\(681\) 0 0
\(682\) 4.07520 + 4.07520i 0.156047 + 0.156047i
\(683\) −24.5400 24.5400i −0.938996 0.938996i 0.0592472 0.998243i \(-0.481130\pi\)
−0.998243 + 0.0592472i \(0.981130\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) −4.27463 + 4.27463i −0.162969 + 0.162969i
\(689\) 0.0778674 0.00296651
\(690\) 0 0
\(691\) −0.993716 −0.0378027 −0.0189014 0.999821i \(-0.506017\pi\)
−0.0189014 + 0.999821i \(0.506017\pi\)
\(692\) 15.8126 15.8126i 0.601104 0.601104i
\(693\) 0 0
\(694\) 25.4881i 0.967516i
\(695\) 0 0
\(696\) 0 0
\(697\) −1.88181 1.88181i −0.0712787 0.0712787i
\(698\) 16.0115 + 16.0115i 0.606044 + 0.606044i
\(699\) 0 0
\(700\) 0 0
\(701\) 46.4565i 1.75464i −0.479909 0.877318i \(-0.659331\pi\)
0.479909 0.877318i \(-0.340669\pi\)
\(702\) 0 0
\(703\) 14.0413 14.0413i 0.529579 0.529579i
\(704\) −0.585786 −0.0220777
\(705\) 0 0
\(706\) 20.5437 0.773173
\(707\) 4.37429 4.37429i 0.164512 0.164512i
\(708\) 0 0
\(709\) 10.5904i 0.397729i −0.980027 0.198865i \(-0.936275\pi\)
0.980027 0.198865i \(-0.0637254\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −6.87832 6.87832i −0.257776 0.257776i
\(713\) 50.7326 + 50.7326i 1.89995 + 1.89995i
\(714\) 0 0
\(715\) 0 0
\(716\) 5.14235i 0.192179i
\(717\) 0 0
\(718\) 8.71608 8.71608i 0.325281 0.325281i
\(719\) 16.2086 0.604479 0.302240 0.953232i \(-0.402266\pi\)
0.302240 + 0.953232i \(0.402266\pi\)
\(720\) 0 0
\(721\) −0.384990 −0.0143378
\(722\) −3.39267 + 3.39267i −0.126262 + 0.126262i
\(723\) 0 0
\(724\) 15.0411i 0.558999i
\(725\) 0 0
\(726\) 0 0
\(727\) 4.44183 + 4.44183i 0.164738 + 0.164738i 0.784662 0.619924i \(-0.212836\pi\)
−0.619924 + 0.784662i \(0.712836\pi\)
\(728\) 0.0249440 + 0.0249440i 0.000924487 + 0.000924487i
\(729\) 0 0
\(730\) 0 0
\(731\) 16.4276i 0.607596i
\(732\) 0 0
\(733\) −22.9524 + 22.9524i −0.847767 + 0.847767i −0.989854 0.142087i \(-0.954619\pi\)
0.142087 + 0.989854i \(0.454619\pi\)
\(734\) 28.7690 1.06188
\(735\) 0 0
\(736\) −7.29253 −0.268806
\(737\) 2.97882 2.97882i 0.109726 0.109726i
\(738\) 0 0
\(739\) 2.01607i 0.0741623i −0.999312 0.0370812i \(-0.988194\pi\)
0.999312 0.0370812i \(-0.0118060\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.56084 1.56084i −0.0573003 0.0573003i
\(743\) −4.57937 4.57937i −0.168001 0.168001i 0.618099 0.786100i \(-0.287903\pi\)
−0.786100 + 0.618099i \(0.787903\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 23.7559i 0.869765i
\(747\) 0 0
\(748\) −1.12560 + 1.12560i −0.0411560 + 0.0411560i
\(749\) 5.62763 0.205629
\(750\) 0 0
\(751\) 13.5894 0.495882 0.247941 0.968775i \(-0.420246\pi\)
0.247941 + 0.968775i \(0.420246\pi\)
\(752\) −6.32780 + 6.32780i −0.230751 + 0.230751i
\(753\) 0 0
\(754\) 0.161605i 0.00588531i
\(755\) 0 0
\(756\) 0 0
\(757\) −19.4354 19.4354i −0.706391 0.706391i 0.259383 0.965775i \(-0.416481\pi\)
−0.965775 + 0.259383i \(0.916481\pi\)
\(758\) 9.55355 + 9.55355i 0.347000 + 0.347000i
\(759\) 0 0
\(760\) 0 0
\(761\) 4.32354i 0.156728i −0.996925 0.0783641i \(-0.975030\pi\)
0.996925 0.0783641i \(-0.0249697\pi\)
\(762\) 0 0
\(763\) 6.09513 6.09513i 0.220659 0.220659i
\(764\) 11.8732 0.429556
\(765\) 0 0
\(766\) −5.43591 −0.196407
\(767\) 0.0167362 0.0167362i 0.000604310 0.000604310i
\(768\) 0 0
\(769\) 23.5218i 0.848219i −0.905611 0.424109i \(-0.860587\pi\)
0.905611 0.424109i \(-0.139413\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.0864086 + 0.0864086i 0.00310992 + 0.00310992i
\(773\) −20.3027 20.3027i −0.730236 0.730236i 0.240430 0.970666i \(-0.422711\pi\)
−0.970666 + 0.240430i \(0.922711\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 6.71279i 0.240975i
\(777\) 0 0
\(778\) −25.3908 + 25.3908i −0.910305 + 0.910305i
\(779\) −4.77751 −0.171172
\(780\) 0 0
\(781\) 1.71530 0.0613783
\(782\) −14.0127 + 14.0127i −0.501094 + 0.501094i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) 36.8569 + 36.8569i 1.31381 + 1.31381i 0.918586 + 0.395222i \(0.129332\pi\)
0.395222 + 0.918586i \(0.370668\pi\)
\(788\) −15.3374 15.3374i −0.546373 0.546373i
\(789\) 0 0
\(790\) 0 0
\(791\) 8.67147i 0.308322i
\(792\) 0 0
\(793\) 0.0587090 0.0587090i 0.00208482 0.00208482i
\(794\) 25.3465 0.899513
\(795\) 0 0
\(796\) −13.4256 −0.475857
\(797\) 5.72865 5.72865i 0.202919 0.202919i −0.598330 0.801250i \(-0.704169\pi\)
0.801250 + 0.598330i \(0.204169\pi\)
\(798\) 0 0