Properties

Label 3150.2.m.g.1457.2
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 1457.2
Root \(0.965926 + 0.258819i\)
Character \(\chi\) = 3150.1457
Dual form 3150.2.m.g.2843.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.41421i q^{11} +(1.43916 - 1.43916i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-1.54258 + 1.54258i) q^{17} +2.04989i q^{19} +(-2.41421 - 2.41421i) q^{22} +(-1.15660 - 1.15660i) q^{23} +2.03528i q^{26} +(0.707107 - 0.707107i) q^{28} -8.04524 q^{29} -6.37429 q^{31} +(0.707107 - 0.707107i) q^{32} -2.18154i q^{34} +(-0.0498881 - 0.0498881i) q^{37} +(-1.44949 - 1.44949i) q^{38} +7.94887i q^{41} +(4.65357 - 4.65357i) q^{43} +3.41421 q^{44} +1.63567 q^{46} +(-1.39960 + 1.39960i) q^{47} +1.00000i q^{49} +(-1.43916 - 1.43916i) q^{52} +(2.97506 + 2.97506i) q^{53} +1.00000i q^{56} +(5.68885 - 5.68885i) q^{58} +4.25725 q^{59} -6.88953 q^{61} +(4.50731 - 4.50731i) q^{62} +1.00000i q^{64} +(-5.84304 - 5.84304i) q^{67} +(1.54258 + 1.54258i) q^{68} -2.92820i q^{71} +(5.97469 - 5.97469i) q^{73} +0.0705524 q^{74} +2.04989 q^{76} +(-2.41421 + 2.41421i) q^{77} +11.6410i q^{79} +(-5.62070 - 5.62070i) q^{82} +(-1.52797 - 1.52797i) q^{83} +6.58114i q^{86} +(-2.41421 + 2.41421i) q^{88} -5.72741 q^{89} +2.03528 q^{91} +(-1.15660 + 1.15660i) q^{92} -1.97934i q^{94} +(-9.64564 - 9.64564i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 8q^{13} - 8q^{14} - 8q^{16} - 8q^{22} + 16q^{23} + 16q^{37} + 8q^{38} + 8q^{43} + 16q^{44} + 8q^{46} - 8q^{47} + 8q^{52} + 32q^{53} + 8q^{58} - 8q^{59} - 32q^{61} + 32q^{62} - 16q^{67} - 16q^{74} - 8q^{77} + 8q^{82} - 8q^{83} - 8q^{88} + 16q^{89} + 8q^{91} + 16q^{92} - 16q^{97} + O(q^{100}) \)

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
\(11\) 3.41421i 1.02942i 0.857363 + 0.514712i \(0.172101\pi\)
−0.857363 + 0.514712i \(0.827899\pi\)
\(12\) 0 0
\(13\) 1.43916 1.43916i 0.399150 0.399150i −0.478783 0.877933i \(-0.658922\pi\)
0.877933 + 0.478783i \(0.158922\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −1.54258 + 1.54258i −0.374131 + 0.374131i −0.868979 0.494848i \(-0.835224\pi\)
0.494848 + 0.868979i \(0.335224\pi\)
\(18\) 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
\(22\) −2.41421 2.41421i −0.514712 0.514712i
\(23\) −1.15660 1.15660i −0.241167 0.241167i 0.576166 0.817333i \(-0.304548\pi\)
−0.817333 + 0.576166i \(0.804548\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.03528i 0.399150i
\(27\) 0 0
\(28\) 0.707107 0.707107i 0.133631 0.133631i
\(29\) −8.04524 −1.49396 −0.746982 0.664844i \(-0.768498\pi\)
−0.746982 + 0.664844i \(0.768498\pi\)
\(30\) 0 0
\(31\) −6.37429 −1.14486 −0.572428 0.819955i \(-0.693999\pi\)
−0.572428 + 0.819955i \(0.693999\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0 0
\(34\) 2.18154i 0.374131i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.0498881 0.0498881i −0.00820155 0.00820155i 0.702994 0.711196i \(-0.251846\pi\)
−0.711196 + 0.702994i \(0.751846\pi\)
\(38\) −1.44949 1.44949i −0.235138 0.235138i
\(39\) 0 0
\(40\) 0 0
\(41\) 7.94887i 1.24140i 0.784046 + 0.620702i \(0.213152\pi\)
−0.784046 + 0.620702i \(0.786848\pi\)
\(42\) 0 0
\(43\) 4.65357 4.65357i 0.709663 0.709663i −0.256801 0.966464i \(-0.582669\pi\)
0.966464 + 0.256801i \(0.0826686\pi\)
\(44\) 3.41421 0.514712
\(45\) 0 0
\(46\) 1.63567 0.241167
\(47\) −1.39960 + 1.39960i −0.204153 + 0.204153i −0.801777 0.597624i \(-0.796112\pi\)
0.597624 + 0.801777i \(0.296112\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.43916 1.43916i −0.199575 0.199575i
\(53\) 2.97506 + 2.97506i 0.408655 + 0.408655i 0.881269 0.472614i \(-0.156690\pi\)
−0.472614 + 0.881269i \(0.656690\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) 5.68885 5.68885i 0.746982 0.746982i
\(59\) 4.25725 0.554247 0.277124 0.960834i \(-0.410619\pi\)
0.277124 + 0.960834i \(0.410619\pi\)
\(60\) 0 0
\(61\) −6.88953 −0.882114 −0.441057 0.897479i \(-0.645396\pi\)
−0.441057 + 0.897479i \(0.645396\pi\)
\(62\) 4.50731 4.50731i 0.572428 0.572428i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) −5.84304 5.84304i −0.713841 0.713841i 0.253496 0.967337i \(-0.418420\pi\)
−0.967337 + 0.253496i \(0.918420\pi\)
\(68\) 1.54258 + 1.54258i 0.187066 + 0.187066i
\(69\) 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
\(73\) 5.97469 5.97469i 0.699285 0.699285i −0.264971 0.964256i \(-0.585363\pi\)
0.964256 + 0.264971i \(0.0853626\pi\)
\(74\) 0.0705524 0.00820155
\(75\) 0 0
\(76\) 2.04989 0.235138
\(77\) −2.41421 + 2.41421i −0.275125 + 0.275125i
\(78\) 0 0
\(79\) 11.6410i 1.30971i 0.755753 + 0.654857i \(0.227271\pi\)
−0.755753 + 0.654857i \(0.772729\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −5.62070 5.62070i −0.620702 0.620702i
\(83\) −1.52797 1.52797i −0.167717 0.167717i 0.618258 0.785975i \(-0.287839\pi\)
−0.785975 + 0.618258i \(0.787839\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.58114i 0.709663i
\(87\) 0 0
\(88\) −2.41421 + 2.41421i −0.257356 + 0.257356i
\(89\) −5.72741 −0.607104 −0.303552 0.952815i \(-0.598173\pi\)
−0.303552 + 0.952815i \(0.598173\pi\)
\(90\) 0 0
\(91\) 2.03528 0.213355
\(92\) −1.15660 + 1.15660i −0.120584 + 0.120584i
\(93\) 0 0
\(94\) 1.97934i 0.204153i
\(95\) 0 0
\(96\) 0 0
\(97\) −9.64564 9.64564i −0.979367 0.979367i 0.0204248 0.999791i \(-0.493498\pi\)
−0.999791 + 0.0204248i \(0.993498\pi\)
\(98\) −0.707107 0.707107i −0.0714286 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 16.7420i 1.66589i 0.553353 + 0.832947i \(0.313348\pi\)
−0.553353 + 0.832947i \(0.686652\pi\)
\(102\) 0 0
\(103\) 8.65597 8.65597i 0.852898 0.852898i −0.137591 0.990489i \(-0.543936\pi\)
0.990489 + 0.137591i \(0.0439359\pi\)
\(104\) 2.03528 0.199575
\(105\) 0 0
\(106\) −4.20736 −0.408655
\(107\) −10.9489 + 10.9489i −1.05847 + 1.05847i −0.0602858 + 0.998181i \(0.519201\pi\)
−0.998181 + 0.0602858i \(0.980799\pi\)
\(108\) 0 0
\(109\) 5.23659i 0.501574i 0.968042 + 0.250787i \(0.0806894\pi\)
−0.968042 + 0.250787i \(0.919311\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.707107 0.707107i −0.0668153 0.0668153i
\(113\) −1.59575 1.59575i −0.150116 0.150116i 0.628054 0.778170i \(-0.283852\pi\)
−0.778170 + 0.628054i \(0.783852\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 8.04524i 0.746982i
\(117\) 0 0
\(118\) −3.01033 + 3.01033i −0.277124 + 0.277124i
\(119\) −2.18154 −0.199981
\(120\) 0 0
\(121\) −0.656854 −0.0597140
\(122\) 4.87163 4.87163i 0.441057 0.441057i
\(123\) 0 0
\(124\) 6.37429i 0.572428i
\(125\) 0 0
\(126\) 0 0
\(127\) −7.72084 7.72084i −0.685114 0.685114i 0.276034 0.961148i \(-0.410980\pi\)
−0.961148 + 0.276034i \(0.910980\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 7.38426i 0.645166i −0.946541 0.322583i \(-0.895449\pi\)
0.946541 0.322583i \(-0.104551\pi\)
\(132\) 0 0
\(133\) −1.44949 + 1.44949i −0.125687 + 0.125687i
\(134\) 8.26330 0.713841
\(135\) 0 0
\(136\) −2.18154 −0.187066
\(137\) −12.2268 + 12.2268i −1.04460 + 1.04460i −0.0456471 + 0.998958i \(0.514535\pi\)
−0.998958 + 0.0456471i \(0.985465\pi\)
\(138\) 0 0
\(139\) 15.2621i 1.29451i −0.762273 0.647256i \(-0.775917\pi\)
0.762273 0.647256i \(-0.224083\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.07055 + 2.07055i 0.173757 + 0.173757i
\(143\) 4.91359 + 4.91359i 0.410895 + 0.410895i
\(144\) 0 0
\(145\) 0 0
\(146\) 8.44949i 0.699285i
\(147\) 0 0
\(148\) −0.0498881 + 0.0498881i −0.00410077 + 0.00410077i
\(149\) −6.01602 −0.492852 −0.246426 0.969162i \(-0.579256\pi\)
−0.246426 + 0.969162i \(0.579256\pi\)
\(150\) 0 0
\(151\) −5.12096 −0.416737 −0.208369 0.978050i \(-0.566815\pi\)
−0.208369 + 0.978050i \(0.566815\pi\)
\(152\) −1.44949 + 1.44949i −0.117569 + 0.117569i
\(153\) 0 0
\(154\) 3.41421i 0.275125i
\(155\) 0 0
\(156\) 0 0
\(157\) 8.79920 + 8.79920i 0.702253 + 0.702253i 0.964894 0.262641i \(-0.0845934\pi\)
−0.262641 + 0.964894i \(0.584593\pi\)
\(158\) −8.23143 8.23143i −0.654857 0.654857i
\(159\) 0 0
\(160\) 0 0
\(161\) 1.63567i 0.128909i
\(162\) 0 0
\(163\) 2.73998 2.73998i 0.214612 0.214612i −0.591611 0.806223i \(-0.701508\pi\)
0.806223 + 0.591611i \(0.201508\pi\)
\(164\) 7.94887 0.620702
\(165\) 0 0
\(166\) 2.16088 0.167717
\(167\) −6.48477 + 6.48477i −0.501806 + 0.501806i −0.911999 0.410193i \(-0.865461\pi\)
0.410193 + 0.911999i \(0.365461\pi\)
\(168\) 0 0
\(169\) 8.85765i 0.681358i
\(170\) 0 0
\(171\) 0 0
\(172\) −4.65357 4.65357i −0.354831 0.354831i
\(173\) 1.11563 + 1.11563i 0.0848200 + 0.0848200i 0.748244 0.663424i \(-0.230897\pi\)
−0.663424 + 0.748244i \(0.730897\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.41421i 0.257356i
\(177\) 0 0
\(178\) 4.04989 4.04989i 0.303552 0.303552i
\(179\) 1.00124 0.0748365 0.0374183 0.999300i \(-0.488087\pi\)
0.0374183 + 0.999300i \(0.488087\pi\)
\(180\) 0 0
\(181\) −23.0411 −1.71263 −0.856316 0.516452i \(-0.827253\pi\)
−0.856316 + 0.516452i \(0.827253\pi\)
\(182\) −1.43916 + 1.43916i −0.106677 + 0.106677i
\(183\) 0 0
\(184\) 1.63567i 0.120584i
\(185\) 0 0
\(186\) 0 0
\(187\) −5.26670 5.26670i −0.385140 0.385140i
\(188\) 1.39960 + 1.39960i 0.102076 + 0.102076i
\(189\) 0 0
\(190\) 0 0
\(191\) 3.59095i 0.259832i 0.991525 + 0.129916i \(0.0414707\pi\)
−0.991525 + 0.129916i \(0.958529\pi\)
\(192\) 0 0
\(193\) −4.98539 + 4.98539i −0.358856 + 0.358856i −0.863391 0.504535i \(-0.831664\pi\)
0.504535 + 0.863391i \(0.331664\pi\)
\(194\) 13.6410 0.979367
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −10.0169 + 10.0169i −0.713675 + 0.713675i −0.967302 0.253627i \(-0.918376\pi\)
0.253627 + 0.967302i \(0.418376\pi\)
\(198\) 0 0
\(199\) 27.2820i 1.93397i 0.254834 + 0.966985i \(0.417979\pi\)
−0.254834 + 0.966985i \(0.582021\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −11.8384 11.8384i −0.832947 0.832947i
\(203\) −5.68885 5.68885i −0.399279 0.399279i
\(204\) 0 0
\(205\) 0 0
\(206\) 12.2414i 0.852898i
\(207\) 0 0
\(208\) −1.43916 + 1.43916i −0.0997876 + 0.0997876i
\(209\) −6.99876 −0.484114
\(210\) 0 0
\(211\) −8.70193 −0.599066 −0.299533 0.954086i \(-0.596831\pi\)
−0.299533 + 0.954086i \(0.596831\pi\)
\(212\) 2.97506 2.97506i 0.204328 0.204328i
\(213\) 0 0
\(214\) 15.4840i 1.05847i
\(215\) 0 0
\(216\) 0 0
\(217\) −4.50731 4.50731i −0.305976 0.305976i
\(218\) −3.70283 3.70283i −0.250787 0.250787i
\(219\) 0 0
\(220\) 0 0
\(221\) 4.44004i 0.298669i
\(222\) 0 0
\(223\) −2.80813 + 2.80813i −0.188046 + 0.188046i −0.794851 0.606805i \(-0.792451\pi\)
0.606805 + 0.794851i \(0.292451\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 2.25674 0.150116
\(227\) −2.88573 + 2.88573i −0.191532 + 0.191532i −0.796358 0.604826i \(-0.793243\pi\)
0.604826 + 0.796358i \(0.293243\pi\)
\(228\) 0 0
\(229\) 9.16228i 0.605461i 0.953076 + 0.302730i \(0.0978982\pi\)
−0.953076 + 0.302730i \(0.902102\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −5.68885 5.68885i −0.373491 0.373491i
\(233\) −4.67611 4.67611i −0.306342 0.306342i 0.537147 0.843489i \(-0.319502\pi\)
−0.843489 + 0.537147i \(0.819502\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 4.25725i 0.277124i
\(237\) 0 0
\(238\) 1.54258 1.54258i 0.0999907 0.0999907i
\(239\) −16.4853 −1.06634 −0.533172 0.846007i \(-0.679000\pi\)
−0.533172 + 0.846007i \(0.679000\pi\)
\(240\) 0 0
\(241\) −8.50419 −0.547803 −0.273901 0.961758i \(-0.588314\pi\)
−0.273901 + 0.961758i \(0.588314\pi\)
\(242\) 0.464466 0.464466i 0.0298570 0.0298570i
\(243\) 0 0
\(244\) 6.88953i 0.441057i
\(245\) 0 0
\(246\) 0 0
\(247\) 2.95011 + 2.95011i 0.187711 + 0.187711i
\(248\) −4.50731 4.50731i −0.286214 0.286214i
\(249\) 0 0
\(250\) 0 0
\(251\) 18.9250i 1.19453i −0.802043 0.597267i \(-0.796253\pi\)
0.802043 0.597267i \(-0.203747\pi\)
\(252\) 0 0
\(253\) 3.94887 3.94887i 0.248263 0.248263i
\(254\) 10.9189 0.685114
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 16.8697 16.8697i 1.05230 1.05230i 0.0537457 0.998555i \(-0.482884\pi\)
0.998555 0.0537457i \(-0.0171160\pi\)
\(258\) 0 0
\(259\) 0.0705524i 0.00438391i
\(260\) 0 0
\(261\) 0 0
\(262\) 5.22146 + 5.22146i 0.322583 + 0.322583i
\(263\) −8.32817 8.32817i −0.513537 0.513537i 0.402071 0.915608i \(-0.368290\pi\)
−0.915608 + 0.402071i \(0.868290\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.04989i 0.125687i
\(267\) 0 0
\(268\) −5.84304 + 5.84304i −0.356920 + 0.356920i
\(269\) 16.3218 0.995155 0.497577 0.867420i \(-0.334223\pi\)
0.497577 + 0.867420i \(0.334223\pi\)
\(270\) 0 0
\(271\) −27.3911 −1.66389 −0.831944 0.554859i \(-0.812772\pi\)
−0.831944 + 0.554859i \(0.812772\pi\)
\(272\) 1.54258 1.54258i 0.0935328 0.0935328i
\(273\) 0 0
\(274\) 17.2913i 1.04460i
\(275\) 0 0
\(276\) 0 0
\(277\) −0.564607 0.564607i −0.0339239 0.0339239i 0.689941 0.723865i \(-0.257636\pi\)
−0.723865 + 0.689941i \(0.757636\pi\)
\(278\) 10.7919 + 10.7919i 0.647256 + 0.647256i
\(279\) 0 0
\(280\) 0 0
\(281\) 6.14214i 0.366409i −0.983075 0.183205i \(-0.941353\pi\)
0.983075 0.183205i \(-0.0586471\pi\)
\(282\) 0 0
\(283\) −10.9959 + 10.9959i −0.653637 + 0.653637i −0.953867 0.300230i \(-0.902937\pi\)
0.300230 + 0.953867i \(0.402937\pi\)
\(284\) −2.92820 −0.173757
\(285\) 0 0
\(286\) −6.94887 −0.410895
\(287\) −5.62070 + 5.62070i −0.331779 + 0.331779i
\(288\) 0 0
\(289\) 12.2409i 0.720052i
\(290\) 0 0
\(291\) 0 0
\(292\) −5.97469 5.97469i −0.349642 0.349642i
\(293\) 17.4135 + 17.4135i 1.01731 + 1.01731i 0.999848 + 0.0174591i \(0.00555767\pi\)
0.0174591 + 0.999848i \(0.494442\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.0705524i 0.00410077i
\(297\) 0 0
\(298\) 4.25397 4.25397i 0.246426 0.246426i
\(299\) −3.32905 −0.192524
\(300\) 0 0
\(301\) 6.58114 0.379331
\(302\) 3.62106 3.62106i 0.208369 0.208369i
\(303\) 0 0
\(304\) 2.04989i 0.117569i
\(305\) 0 0
\(306\) 0 0
\(307\) 17.2979 + 17.2979i 0.987241 + 0.987241i 0.999920 0.0126790i \(-0.00403597\pi\)
−0.0126790 + 0.999920i \(0.504036\pi\)
\(308\) 2.41421 + 2.41421i 0.137563 + 0.137563i
\(309\) 0 0
\(310\) 0 0
\(311\) 12.3046i 0.697732i −0.937173 0.348866i \(-0.886567\pi\)
0.937173 0.348866i \(-0.113433\pi\)
\(312\) 0 0
\(313\) 16.8031 16.8031i 0.949768 0.949768i −0.0490289 0.998797i \(-0.515613\pi\)
0.998797 + 0.0490289i \(0.0156127\pi\)
\(314\) −12.4440 −0.702253
\(315\) 0 0
\(316\) 11.6410 0.654857
\(317\) 3.16781 3.16781i 0.177922 0.177922i −0.612527 0.790449i \(-0.709847\pi\)
0.790449 + 0.612527i \(0.209847\pi\)
\(318\) 0 0
\(319\) 27.4682i 1.53792i
\(320\) 0 0
\(321\) 0 0
\(322\) 1.15660 + 1.15660i 0.0644546 + 0.0644546i
\(323\) −3.16212 3.16212i −0.175945 0.175945i
\(324\) 0 0
\(325\) 0 0
\(326\) 3.87492i 0.214612i
\(327\) 0 0
\(328\) −5.62070 + 5.62070i −0.310351 + 0.310351i
\(329\) −1.97934 −0.109124
\(330\) 0 0
\(331\) −13.4986 −0.741953 −0.370976 0.928642i \(-0.620977\pi\)
−0.370976 + 0.928642i \(0.620977\pi\)
\(332\) −1.52797 + 1.52797i −0.0838583 + 0.0838583i
\(333\) 0 0
\(334\) 9.17084i 0.501806i
\(335\) 0 0
\(336\) 0 0
\(337\) −18.1303 18.1303i −0.987620 0.987620i 0.0123043 0.999924i \(-0.496083\pi\)
−0.999924 + 0.0123043i \(0.996083\pi\)
\(338\) −6.26330 6.26330i −0.340679 0.340679i
\(339\) 0 0
\(340\) 0 0
\(341\) 21.7632i 1.17854i
\(342\) 0 0
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 6.58114 0.354831
\(345\) 0 0
\(346\) −1.57774 −0.0848200
\(347\) −18.2259 + 18.2259i −0.978417 + 0.978417i −0.999772 0.0213548i \(-0.993202\pi\)
0.0213548 + 0.999772i \(0.493202\pi\)
\(348\) 0 0
\(349\) 0.538551i 0.0288280i −0.999896 0.0144140i \(-0.995412\pi\)
0.999896 0.0144140i \(-0.00458827\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.41421 + 2.41421i 0.128678 + 0.128678i
\(353\) −16.3830 16.3830i −0.871980 0.871980i 0.120708 0.992688i \(-0.461484\pi\)
−0.992688 + 0.120708i \(0.961484\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 5.72741i 0.303552i
\(357\) 0 0
\(358\) −0.707987 + 0.707987i −0.0374183 + 0.0374183i
\(359\) 31.9223 1.68480 0.842398 0.538856i \(-0.181143\pi\)
0.842398 + 0.538856i \(0.181143\pi\)
\(360\) 0 0
\(361\) 14.7980 0.778840
\(362\) 16.2925 16.2925i 0.856316 0.856316i
\(363\) 0 0
\(364\) 2.03528i 0.106677i
\(365\) 0 0
\(366\) 0 0
\(367\) 24.5854 + 24.5854i 1.28335 + 1.28335i 0.938750 + 0.344598i \(0.111985\pi\)
0.344598 + 0.938750i \(0.388015\pi\)
\(368\) 1.15660 + 1.15660i 0.0602918 + 0.0602918i
\(369\) 0 0
\(370\) 0 0
\(371\) 4.20736i 0.218435i
\(372\) 0 0
\(373\) −2.79796 + 2.79796i −0.144873 + 0.144873i −0.775823 0.630950i \(-0.782665\pi\)
0.630950 + 0.775823i \(0.282665\pi\)
\(374\) 7.44825 0.385140
\(375\) 0 0
\(376\) −1.97934 −0.102076
\(377\) −11.5784 + 11.5784i −0.596317 + 0.596317i
\(378\) 0 0
\(379\) 26.4390i 1.35808i −0.734102 0.679039i \(-0.762397\pi\)
0.734102 0.679039i \(-0.237603\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −2.53918 2.53918i −0.129916 0.129916i
\(383\) −17.2280 17.2280i −0.880311 0.880311i 0.113255 0.993566i \(-0.463872\pi\)
−0.993566 + 0.113255i \(0.963872\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 7.05040i 0.358856i
\(387\) 0 0
\(388\) −9.64564 + 9.64564i −0.489683 + 0.489683i
\(389\) −32.8766 −1.66691 −0.833454 0.552589i \(-0.813640\pi\)
−0.833454 + 0.552589i \(0.813640\pi\)
\(390\) 0 0
\(391\) 3.56829 0.180456
\(392\) −0.707107 + 0.707107i −0.0357143 + 0.0357143i
\(393\) 0 0
\(394\) 14.1660i 0.713675i
\(395\) 0 0
\(396\) 0 0
\(397\) 5.39783 + 5.39783i 0.270909 + 0.270909i 0.829466 0.558557i \(-0.188645\pi\)
−0.558557 + 0.829466i \(0.688645\pi\)
\(398\) −19.2913 19.2913i −0.966985 0.966985i
\(399\) 0 0
\(400\) 0 0
\(401\) 14.4760i 0.722897i 0.932392 + 0.361448i \(0.117718\pi\)
−0.932392 + 0.361448i \(0.882282\pi\)
\(402\) 0 0
\(403\) −9.17361 + 9.17361i −0.456970 + 0.456970i
\(404\) 16.7420 0.832947
\(405\) 0 0
\(406\) 8.04524 0.399279
\(407\) 0.170328 0.170328i 0.00844287 0.00844287i
\(408\) 0 0
\(409\) 16.5156i 0.816642i 0.912838 + 0.408321i \(0.133886\pi\)
−0.912838 + 0.408321i \(0.866114\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −8.65597 8.65597i −0.426449 0.426449i
\(413\) 3.01033 + 3.01033i 0.148129 + 0.148129i
\(414\) 0 0
\(415\) 0 0
\(416\) 2.03528i 0.0997876i
\(417\) 0 0
\(418\) 4.94887 4.94887i 0.242057 0.242057i
\(419\) −12.0421 −0.588294 −0.294147 0.955760i \(-0.595036\pi\)
−0.294147 + 0.955760i \(0.595036\pi\)
\(420\) 0 0
\(421\) 32.4894 1.58343 0.791717 0.610888i \(-0.209187\pi\)
0.791717 + 0.610888i \(0.209187\pi\)
\(422\) 6.15320 6.15320i 0.299533 0.299533i
\(423\) 0 0
\(424\) 4.20736i 0.204328i
\(425\) 0 0
\(426\) 0 0
\(427\) −4.87163 4.87163i −0.235755 0.235755i
\(428\) 10.9489 + 10.9489i 0.529233 + 0.529233i
\(429\) 0 0
\(430\) 0 0
\(431\) 8.50883i 0.409856i −0.978777 0.204928i \(-0.934304\pi\)
0.978777 0.204928i \(-0.0656960\pi\)
\(432\) 0 0
\(433\) 3.55532 3.55532i 0.170858 0.170858i −0.616498 0.787356i \(-0.711449\pi\)
0.787356 + 0.616498i \(0.211449\pi\)
\(434\) 6.37429 0.305976
\(435\) 0 0
\(436\) 5.23659 0.250787
\(437\) 2.37089 2.37089i 0.113415 0.113415i
\(438\) 0 0
\(439\) 13.2309i 0.631477i 0.948846 + 0.315739i \(0.102252\pi\)
−0.948846 + 0.315739i \(0.897748\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −3.13958 3.13958i −0.149335 0.149335i
\(443\) −23.9223 23.9223i −1.13658 1.13658i −0.989058 0.147525i \(-0.952869\pi\)
−0.147525 0.989058i \(-0.547131\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 3.97129i 0.188046i
\(447\) 0 0
\(448\) −0.707107 + 0.707107i −0.0334077 + 0.0334077i
\(449\) −4.09905 −0.193446 −0.0967230 0.995311i \(-0.530836\pi\)
−0.0967230 + 0.995311i \(0.530836\pi\)
\(450\) 0 0
\(451\) −27.1391 −1.27793
\(452\) −1.59575 + 1.59575i −0.0750580 + 0.0750580i
\(453\) 0 0
\(454\) 4.08104i 0.191532i
\(455\) 0 0
\(456\) 0 0
\(457\) 23.4150 + 23.4150i 1.09531 + 1.09531i 0.994952 + 0.100356i \(0.0319983\pi\)
0.100356 + 0.994952i \(0.468002\pi\)
\(458\) −6.47871 6.47871i −0.302730 0.302730i
\(459\) 0 0
\(460\) 0 0
\(461\) 19.4974i 0.908085i −0.890980 0.454042i \(-0.849981\pi\)
0.890980 0.454042i \(-0.150019\pi\)
\(462\) 0 0
\(463\) −9.62033 + 9.62033i −0.447095 + 0.447095i −0.894388 0.447293i \(-0.852388\pi\)
0.447293 + 0.894388i \(0.352388\pi\)
\(464\) 8.04524 0.373491
\(465\) 0 0
\(466\) 6.61302 0.306342
\(467\) 14.8643 14.8643i 0.687839 0.687839i −0.273915 0.961754i \(-0.588319\pi\)
0.961754 + 0.273915i \(0.0883186\pi\)
\(468\) 0 0
\(469\) 8.26330i 0.381564i
\(470\) 0 0
\(471\) 0 0
\(472\) 3.01033 + 3.01033i 0.138562 + 0.138562i
\(473\) 15.8883 + 15.8883i 0.730544 + 0.730544i
\(474\) 0 0
\(475\) 0 0
\(476\) 2.18154i 0.0999907i
\(477\) 0 0
\(478\) 11.6569 11.6569i 0.533172 0.533172i
\(479\) 11.6065 0.530313 0.265157 0.964205i \(-0.414576\pi\)
0.265157 + 0.964205i \(0.414576\pi\)
\(480\) 0 0
\(481\) −0.143594 −0.00654730
\(482\) 6.01337 6.01337i 0.273901 0.273901i
\(483\) 0 0
\(484\) 0.656854i 0.0298570i
\(485\) 0 0
\(486\) 0 0
\(487\) 26.5745 + 26.5745i 1.20421 + 1.20421i 0.972875 + 0.231332i \(0.0743083\pi\)
0.231332 + 0.972875i \(0.425692\pi\)
\(488\) −4.87163 4.87163i −0.220528 0.220528i
\(489\) 0 0
\(490\) 0 0
\(491\) 33.5029i 1.51197i −0.654591 0.755983i \(-0.727159\pi\)
0.654591 0.755983i \(-0.272841\pi\)
\(492\) 0 0
\(493\) 12.4104 12.4104i 0.558939 0.558939i
\(494\) −4.17209 −0.187711
\(495\) 0 0
\(496\) 6.37429 0.286214
\(497\) 2.07055 2.07055i 0.0928770 0.0928770i
\(498\) 0 0
\(499\) 6.58504i 0.294787i 0.989078 + 0.147393i \(0.0470883\pi\)
−0.989078 + 0.147393i \(0.952912\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 13.3820 + 13.3820i 0.597267 + 0.597267i
\(503\) 26.4682 + 26.4682i 1.18016 + 1.18016i 0.979703 + 0.200455i \(0.0642420\pi\)
0.200455 + 0.979703i \(0.435758\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 5.58454i 0.248263i
\(507\) 0 0
\(508\) −7.72084 + 7.72084i −0.342557 + 0.342557i
\(509\) −11.6050 −0.514381 −0.257191 0.966361i \(-0.582797\pi\)
−0.257191 + 0.966361i \(0.582797\pi\)
\(510\) 0 0
\(511\) 8.44949 0.373783
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 23.8573i 1.05230i
\(515\) 0 0
\(516\) 0 0
\(517\) −4.77854 4.77854i −0.210160 0.210160i
\(518\) 0.0498881 + 0.0498881i 0.00219196 + 0.00219196i
\(519\) 0 0
\(520\) 0 0
\(521\) 27.9474i 1.22440i 0.790704 + 0.612199i \(0.209715\pi\)
−0.790704 + 0.612199i \(0.790285\pi\)
\(522\) 0 0
\(523\) −21.4247 + 21.4247i −0.936837 + 0.936837i −0.998120 0.0612838i \(-0.980481\pi\)
0.0612838 + 0.998120i \(0.480481\pi\)
\(524\) −7.38426 −0.322583
\(525\) 0 0
\(526\) 11.7778 0.513537
\(527\) 9.83287 9.83287i 0.428327 0.428327i
\(528\) 0 0
\(529\) 20.3246i 0.883677i
\(530\) 0 0
\(531\) 0 0
\(532\) 1.44949 + 1.44949i 0.0628434 + 0.0628434i
\(533\) 11.4397 + 11.4397i 0.495507 + 0.495507i
\(534\) 0 0
\(535\) 0 0
\(536\) 8.26330i 0.356920i
\(537\) 0 0
\(538\) −11.5412 + 11.5412i −0.497577 + 0.497577i
\(539\) −3.41421 −0.147061
\(540\) 0 0
\(541\) 32.4705 1.39601 0.698007 0.716091i \(-0.254070\pi\)
0.698007 + 0.716091i \(0.254070\pi\)
\(542\) 19.3684 19.3684i 0.831944 0.831944i
\(543\) 0 0
\(544\) 2.18154i 0.0935328i
\(545\) 0 0
\(546\) 0 0
\(547\) −6.60441 6.60441i −0.282384 0.282384i 0.551675 0.834059i \(-0.313989\pi\)
−0.834059 + 0.551675i \(0.813989\pi\)
\(548\) 12.2268 + 12.2268i 0.522302 + 0.522302i
\(549\) 0 0
\(550\) 0 0
\(551\) 16.4918i 0.702576i
\(552\) 0 0
\(553\) −8.23143 + 8.23143i −0.350036 + 0.350036i
\(554\) 0.798474 0.0339239
\(555\) 0 0
\(556\) −15.2621 −0.647256
\(557\) −25.2207 + 25.2207i −1.06864 + 1.06864i −0.0711727 + 0.997464i \(0.522674\pi\)
−0.997464 + 0.0711727i \(0.977326\pi\)
\(558\) 0 0
\(559\) 13.3944i 0.566525i
\(560\) 0 0
\(561\) 0 0
\(562\) 4.34315 + 4.34315i 0.183205 + 0.183205i
\(563\) −0.0225400 0.0225400i −0.000949948 0.000949948i 0.706632 0.707582i \(-0.250214\pi\)
−0.707582 + 0.706632i \(0.750214\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 15.5505i 0.653637i
\(567\) 0 0
\(568\) 2.07055 2.07055i 0.0868784 0.0868784i
\(569\) −16.4767 −0.690740 −0.345370 0.938467i \(-0.612247\pi\)
−0.345370 + 0.938467i \(0.612247\pi\)
\(570\) 0 0
\(571\) 28.9560 1.21177 0.605884 0.795553i \(-0.292819\pi\)
0.605884 + 0.795553i \(0.292819\pi\)
\(572\) 4.91359 4.91359i 0.205448 0.205448i
\(573\) 0 0
\(574\) 7.94887i 0.331779i
\(575\) 0 0
\(576\) 0 0
\(577\) 30.3424 + 30.3424i 1.26317 + 1.26317i 0.949547 + 0.313624i \(0.101543\pi\)
0.313624 + 0.949547i \(0.398457\pi\)
\(578\) −8.65561 8.65561i −0.360026 0.360026i
\(579\) 0 0
\(580\) 0 0
\(581\) 2.16088i 0.0896483i
\(582\) 0 0
\(583\) −10.1575 + 10.1575i −0.420680 + 0.420680i
\(584\) 8.44949 0.349642
\(585\) 0 0
\(586\) −24.6264 −1.01731
\(587\) −5.98778 + 5.98778i −0.247142 + 0.247142i −0.819797 0.572655i \(-0.805914\pi\)
0.572655 + 0.819797i \(0.305914\pi\)
\(588\) 0 0
\(589\) 13.0666i 0.538399i
\(590\) 0 0
\(591\) 0 0
\(592\) 0.0498881 + 0.0498881i 0.00205039 + 0.00205039i
\(593\) 33.1306 + 33.1306i 1.36051 + 1.36051i 0.873266 + 0.487243i \(0.161997\pi\)
0.487243 + 0.873266i \(0.338003\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.01602i 0.246426i
\(597\) 0 0
\(598\) 2.35399 2.35399i 0.0962619 0.0962619i
\(599\) −0.303973 −0.0124200 −0.00620999 0.999981i \(-0.501977\pi\)
−0.00620999 + 0.999981i \(0.501977\pi\)
\(600\) 0 0
\(601\) 17.2813 0.704918 0.352459 0.935827i \(-0.385346\pi\)
0.352459 + 0.935827i \(0.385346\pi\)
\(602\) −4.65357 + 4.65357i −0.189665 + 0.189665i
\(603\) 0 0
\(604\) 5.12096i 0.208369i
\(605\) 0 0
\(606\) 0 0
\(607\) −16.4243 16.4243i −0.666644 0.666644i 0.290294 0.956938i \(-0.406247\pi\)
−0.956938 + 0.290294i \(0.906247\pi\)
\(608\) 1.44949 + 1.44949i 0.0587846 + 0.0587846i
\(609\) 0 0
\(610\) 0 0
\(611\) 4.02849i 0.162975i
\(612\) 0 0
\(613\) 14.6330 14.6330i 0.591019 0.591019i −0.346887 0.937907i \(-0.612761\pi\)
0.937907 + 0.346887i \(0.112761\pi\)
\(614\) −24.4629 −0.987241
\(615\) 0 0
\(616\) −3.41421 −0.137563
\(617\) 32.8831 32.8831i 1.32382 1.32382i 0.413171 0.910653i \(-0.364421\pi\)
0.910653 0.413171i \(-0.135579\pi\)
\(618\) 0 0
\(619\) 28.1001i 1.12944i 0.825283 + 0.564719i \(0.191016\pi\)
−0.825283 + 0.564719i \(0.808984\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 8.70069 + 8.70069i 0.348866 + 0.348866i
\(623\) −4.04989 4.04989i −0.162255 0.162255i
\(624\) 0 0
\(625\) 0 0
\(626\) 23.7632i 0.949768i
\(627\) 0 0
\(628\) 8.79920 8.79920i 0.351126 0.351126i
\(629\) 0.153913 0.00613691
\(630\) 0 0
\(631\) −16.9867 −0.676228 −0.338114 0.941105i \(-0.609789\pi\)
−0.338114 + 0.941105i \(0.609789\pi\)
\(632\) −8.23143 + 8.23143i −0.327429 + 0.327429i
\(633\) 0 0
\(634\) 4.47996i 0.177922i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.43916 + 1.43916i 0.0570215 + 0.0570215i
\(638\) 19.4229 + 19.4229i 0.768961 + 0.768961i
\(639\) 0 0
\(640\) 0 0
\(641\) 12.1607i 0.480319i −0.970733 0.240160i \(-0.922800\pi\)
0.970733 0.240160i \(-0.0771998\pi\)
\(642\) 0 0
\(643\) −2.93285 + 2.93285i −0.115660 + 0.115660i −0.762568 0.646908i \(-0.776062\pi\)
0.646908 + 0.762568i \(0.276062\pi\)
\(644\) −1.63567 −0.0644546
\(645\) 0 0
\(646\) 4.47191 0.175945
\(647\) 29.4705 29.4705i 1.15860 1.15860i 0.173827 0.984776i \(-0.444387\pi\)
0.984776 0.173827i \(-0.0556133\pi\)
\(648\) 0 0
\(649\) 14.5352i 0.570555i
\(650\) 0 0
\(651\) 0 0
\(652\) −2.73998 2.73998i −0.107306 0.107306i
\(653\) −7.46337 7.46337i −0.292064 0.292064i 0.545831 0.837895i \(-0.316214\pi\)
−0.837895 + 0.545831i \(0.816214\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 7.94887i 0.310351i
\(657\) 0 0
\(658\) 1.39960 1.39960i 0.0545622 0.0545622i
\(659\) −24.7639 −0.964666 −0.482333 0.875988i \(-0.660211\pi\)
−0.482333 + 0.875988i \(0.660211\pi\)
\(660\) 0 0
\(661\) 10.3827 0.403840 0.201920 0.979402i \(-0.435282\pi\)
0.201920 + 0.979402i \(0.435282\pi\)
\(662\) 9.54499 9.54499i 0.370976 0.370976i
\(663\) 0 0
\(664\) 2.16088i 0.0838583i
\(665\) 0 0
\(666\) 0 0
\(667\) 9.30510 + 9.30510i 0.360295 + 0.360295i
\(668\) 6.48477 + 6.48477i 0.250903 + 0.250903i
\(669\) 0 0
\(670\) 0 0
\(671\) 23.5223i 0.908069i
\(672\) 0 0
\(673\) −11.8380 + 11.8380i −0.456321 + 0.456321i −0.897446 0.441125i \(-0.854580\pi\)
0.441125 + 0.897446i \(0.354580\pi\)
\(674\) 25.6401 0.987620
\(675\) 0 0
\(676\) 8.85765 0.340679
\(677\) 12.7408 12.7408i 0.489668 0.489668i −0.418534 0.908201i \(-0.637456\pi\)
0.908201 + 0.418534i \(0.137456\pi\)
\(678\) 0 0
\(679\) 13.6410i 0.523493i
\(680\) 0 0
\(681\) 0 0
\(682\) 15.3889 + 15.3889i 0.589272 + 0.589272i
\(683\) 5.61177 + 5.61177i 0.214729 + 0.214729i 0.806273 0.591544i \(-0.201481\pi\)
−0.591544 + 0.806273i \(0.701481\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) −4.65357 + 4.65357i −0.177416 + 0.177416i
\(689\) 8.56315 0.326230
\(690\) 0 0
\(691\) 31.6347 1.20344 0.601721 0.798706i \(-0.294482\pi\)
0.601721 + 0.798706i \(0.294482\pi\)
\(692\) 1.11563 1.11563i 0.0424100 0.0424100i
\(693\) 0 0
\(694\) 25.7753i 0.978417i
\(695\) 0 0
\(696\) 0 0
\(697\) −12.2618 12.2618i −0.464448 0.464448i
\(698\) 0.380813 + 0.380813i 0.0144140 + 0.0144140i
\(699\) 0 0
\(700\) 0 0
\(701\) 32.7205i 1.23583i −0.786243 0.617917i \(-0.787977\pi\)
0.786243 0.617917i \(-0.212023\pi\)
\(702\) 0 0
\(703\) 0.102265 0.102265i 0.00385699 0.00385699i
\(704\) −3.41421 −0.128678
\(705\) 0 0
\(706\) 23.1691 0.871980
\(707\) −11.8384 + 11.8384i −0.445229 + 0.445229i
\(708\) 0 0
\(709\) 47.0878i 1.76842i 0.467091 + 0.884209i \(0.345302\pi\)
−0.467091 + 0.884209i \(0.654698\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −4.04989 4.04989i −0.151776 0.151776i
\(713\) 7.37249 + 7.37249i 0.276102 + 0.276102i
\(714\) 0 0
\(715\) 0 0
\(716\) 1.00124i 0.0374183i
\(717\) 0 0
\(718\) −22.5725 + 22.5725i −0.842398 + 0.842398i
\(719\) 13.9350 0.519687 0.259844 0.965651i \(-0.416329\pi\)
0.259844 + 0.965651i \(0.416329\pi\)
\(720\) 0 0
\(721\) 12.2414 0.455893
\(722\) −10.4637 + 10.4637i −0.389420 + 0.389420i
\(723\) 0 0
\(724\) 23.0411i 0.856316i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.199188 + 0.199188i 0.00738746 + 0.00738746i 0.710791 0.703403i \(-0.248337\pi\)
−0.703403 + 0.710791i \(0.748337\pi\)
\(728\) 1.43916 + 1.43916i 0.0533387 + 0.0533387i
\(729\) 0 0
\(730\) 0 0
\(731\) 14.3570i 0.531014i
\(732\) 0 0
\(733\) −10.2245 + 10.2245i −0.377650 + 0.377650i −0.870254 0.492603i \(-0.836045\pi\)
0.492603 + 0.870254i \(0.336045\pi\)
\(734\) −34.7690 −1.28335
\(735\) 0 0
\(736\) −1.63567 −0.0602918
\(737\) 19.9494 19.9494i 0.734845 0.734845i
\(738\) 0 0
\(739\) 35.1993i 1.29483i −0.762139 0.647414i \(-0.775851\pi\)
0.762139 0.647414i \(-0.224149\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −2.97506 2.97506i −0.109218 0.109218i
\(743\) −12.2052 12.2052i −0.447767 0.447767i 0.446845 0.894612i \(-0.352548\pi\)
−0.894612 + 0.446845i \(0.852548\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 3.95691i 0.144873i
\(747\) 0 0
\(748\) −5.26670 + 5.26670i −0.192570 + 0.192570i
\(749\) −15.4840 −0.565774
\(750\) 0 0
\(751\) −3.73294 −0.136217 −0.0681085 0.997678i \(-0.521696\pi\)
−0.0681085 + 0.997678i \(0.521696\pi\)
\(752\) 1.39960 1.39960i 0.0510382 0.0510382i
\(753\) 0 0
\(754\) 16.3743i 0.596317i
\(755\) 0 0
\(756\) 0 0
\(757\) 0.363597 + 0.363597i 0.0132151 + 0.0132151i 0.713683 0.700468i \(-0.247026\pi\)
−0.700468 + 0.713683i \(0.747026\pi\)
\(758\) 18.6952 + 18.6952i 0.679039 + 0.679039i
\(759\) 0 0
\(760\) 0 0
\(761\) 26.1799i 0.949022i 0.880250 + 0.474511i \(0.157375\pi\)
−0.880250 + 0.474511i \(0.842625\pi\)
\(762\) 0 0
\(763\) −3.70283 + 3.70283i −0.134051 + 0.134051i
\(764\) 3.59095 0.129916
\(765\) 0 0
\(766\) 24.3641 0.880311
\(767\) 6.12686 6.12686i 0.221228 0.221228i
\(768\) 0 0
\(769\) 28.9756i 1.04489i −0.852674 0.522443i \(-0.825021\pi\)
0.852674 0.522443i \(-0.174979\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4.98539 + 4.98539i 0.179428 + 0.179428i
\(773\) 27.3745 + 27.3745i 0.984591 + 0.984591i 0.999883 0.0152923i \(-0.00486787\pi\)
−0.0152923 + 0.999883i \(0.504868\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 13.6410i 0.489683i
\(777\) 0 0
\(778\) 23.2472 23.2472i 0.833454 0.833454i
\(779\) −16.2943 −0.583803
\(780\) 0 0
\(781\) 9.99751 0.357739
\(782\) −2.52316 + 2.52316i −0.0902281 + 0.0902281i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) 26.8559 + 26.8559i 0.957309 + 0.957309i 0.999125 0.0418162i \(-0.0133144\pi\)
−0.0418162 + 0.999125i \(0.513314\pi\)
\(788\) 10.0169 + 10.0169i 0.356837 + 0.356837i
\(789\) 0 0
\(790\) 0 0
\(791\) 2.25674i 0.0802403i
\(792\) 0 0
\(793\) −9.91512 + 9.91512i −0.352096 + 0.352096i
\(794\) −7.63368 −0.270909
\(795\) 0 0
\(796\) 27.2820 0.966985
\(797\) −5.58506 + 5.58506i −0.197833 + 0.197833i −0.799070 0.601237i \(-0.794675\pi\)
0.601237 + 0.799070i \(0.294675\pi\)
\(798\) 0 0