Properties

Label 960.2.bl.a.529.14
Level $960$
Weight $2$
Character 960.529
Analytic conductor $7.666$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 960.bl (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.66563859404\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 240)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 529.14
Character \(\chi\) \(=\) 960.529
Dual form 960.2.bl.a.49.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{3} +(-2.15195 - 0.607542i) q^{5} -2.25286 q^{7} -1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{3} +(-2.15195 - 0.607542i) q^{5} -2.25286 q^{7} -1.00000i q^{9} +(1.66088 - 1.66088i) q^{11} +(-4.76925 + 4.76925i) q^{13} +(-1.95126 + 1.09206i) q^{15} +6.99777i q^{17} +(2.66634 + 2.66634i) q^{19} +(-1.59301 + 1.59301i) q^{21} +4.41825 q^{23} +(4.26178 + 2.61480i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(2.59286 + 2.59286i) q^{29} +3.93331 q^{31} -2.34884i q^{33} +(4.84805 + 1.36871i) q^{35} +(-2.01181 - 2.01181i) q^{37} +6.74474i q^{39} +4.50104i q^{41} +(-7.14876 - 7.14876i) q^{43} +(-0.607542 + 2.15195i) q^{45} +10.1154i q^{47} -1.92461 q^{49} +(4.94817 + 4.94817i) q^{51} +(0.649299 + 0.649299i) q^{53} +(-4.58319 + 2.56508i) q^{55} +3.77078 q^{57} +(-5.64696 + 5.64696i) q^{59} +(-5.00520 - 5.00520i) q^{61} +2.25286i q^{63} +(13.1607 - 7.36567i) q^{65} +(-4.95274 + 4.95274i) q^{67} +(3.12417 - 3.12417i) q^{69} -2.33178i q^{71} -2.18275 q^{73} +(4.86248 - 1.16459i) q^{75} +(-3.74174 + 3.74174i) q^{77} -6.38450 q^{79} -1.00000 q^{81} +(5.25073 - 5.25073i) q^{83} +(4.25144 - 15.0589i) q^{85} +3.66685 q^{87} +15.7100i q^{89} +(10.7445 - 10.7445i) q^{91} +(2.78127 - 2.78127i) q^{93} +(-4.11792 - 7.35775i) q^{95} -4.61603i q^{97} +(-1.66088 - 1.66088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 8 q^{19} + 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} + 16 q^{61} + 16 q^{65} - 16 q^{69} + 16 q^{75} + 96 q^{79} - 48 q^{81} + 32 q^{91} + 48 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).

\(n\) \(511\) \(577\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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 0
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 0 0
\(5\) −2.15195 0.607542i −0.962382 0.271701i
\(6\) 0 0
\(7\) −2.25286 −0.851502 −0.425751 0.904840i \(-0.639990\pi\)
−0.425751 + 0.904840i \(0.639990\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 1.66088 1.66088i 0.500775 0.500775i −0.410904 0.911679i \(-0.634787\pi\)
0.911679 + 0.410904i \(0.134787\pi\)
\(12\) 0 0
\(13\) −4.76925 + 4.76925i −1.32275 + 1.32275i −0.411212 + 0.911540i \(0.634894\pi\)
−0.911540 + 0.411212i \(0.865106\pi\)
\(14\) 0 0
\(15\) −1.95126 + 1.09206i −0.503812 + 0.281969i
\(16\) 0 0
\(17\) 6.99777i 1.69721i 0.529028 + 0.848604i \(0.322557\pi\)
−0.529028 + 0.848604i \(0.677443\pi\)
\(18\) 0 0
\(19\) 2.66634 + 2.66634i 0.611701 + 0.611701i 0.943389 0.331688i \(-0.107618\pi\)
−0.331688 + 0.943389i \(0.607618\pi\)
\(20\) 0 0
\(21\) −1.59301 + 1.59301i −0.347624 + 0.347624i
\(22\) 0 0
\(23\) 4.41825 0.921269 0.460634 0.887590i \(-0.347622\pi\)
0.460634 + 0.887590i \(0.347622\pi\)
\(24\) 0 0
\(25\) 4.26178 + 2.61480i 0.852357 + 0.522960i
\(26\) 0 0
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 0 0
\(29\) 2.59286 + 2.59286i 0.481481 + 0.481481i 0.905604 0.424123i \(-0.139418\pi\)
−0.424123 + 0.905604i \(0.639418\pi\)
\(30\) 0 0
\(31\) 3.93331 0.706443 0.353221 0.935540i \(-0.385086\pi\)
0.353221 + 0.935540i \(0.385086\pi\)
\(32\) 0 0
\(33\) 2.34884i 0.408881i
\(34\) 0 0
\(35\) 4.84805 + 1.36871i 0.819470 + 0.231354i
\(36\) 0 0
\(37\) −2.01181 2.01181i −0.330739 0.330739i 0.522128 0.852867i \(-0.325138\pi\)
−0.852867 + 0.522128i \(0.825138\pi\)
\(38\) 0 0
\(39\) 6.74474i 1.08002i
\(40\) 0 0
\(41\) 4.50104i 0.702945i 0.936198 + 0.351472i \(0.114319\pi\)
−0.936198 + 0.351472i \(0.885681\pi\)
\(42\) 0 0
\(43\) −7.14876 7.14876i −1.09017 1.09017i −0.995509 0.0946658i \(-0.969822\pi\)
−0.0946658 0.995509i \(-0.530178\pi\)
\(44\) 0 0
\(45\) −0.607542 + 2.15195i −0.0905671 + 0.320794i
\(46\) 0 0
\(47\) 10.1154i 1.47548i 0.675086 + 0.737739i \(0.264107\pi\)
−0.675086 + 0.737739i \(0.735893\pi\)
\(48\) 0 0
\(49\) −1.92461 −0.274945
\(50\) 0 0
\(51\) 4.94817 + 4.94817i 0.692883 + 0.692883i
\(52\) 0 0
\(53\) 0.649299 + 0.649299i 0.0891881 + 0.0891881i 0.750293 0.661105i \(-0.229912\pi\)
−0.661105 + 0.750293i \(0.729912\pi\)
\(54\) 0 0
\(55\) −4.58319 + 2.56508i −0.617997 + 0.345875i
\(56\) 0 0
\(57\) 3.77078 0.499452
\(58\) 0 0
\(59\) −5.64696 + 5.64696i −0.735172 + 0.735172i −0.971639 0.236468i \(-0.924010\pi\)
0.236468 + 0.971639i \(0.424010\pi\)
\(60\) 0 0
\(61\) −5.00520 5.00520i −0.640851 0.640851i 0.309914 0.950765i \(-0.399700\pi\)
−0.950765 + 0.309914i \(0.899700\pi\)
\(62\) 0 0
\(63\) 2.25286i 0.283834i
\(64\) 0 0
\(65\) 13.1607 7.36567i 1.63239 0.913599i
\(66\) 0 0
\(67\) −4.95274 + 4.95274i −0.605074 + 0.605074i −0.941655 0.336581i \(-0.890729\pi\)
0.336581 + 0.941655i \(0.390729\pi\)
\(68\) 0 0
\(69\) 3.12417 3.12417i 0.376106 0.376106i
\(70\) 0 0
\(71\) 2.33178i 0.276732i −0.990381 0.138366i \(-0.955815\pi\)
0.990381 0.138366i \(-0.0441850\pi\)
\(72\) 0 0
\(73\) −2.18275 −0.255472 −0.127736 0.991808i \(-0.540771\pi\)
−0.127736 + 0.991808i \(0.540771\pi\)
\(74\) 0 0
\(75\) 4.86248 1.16459i 0.561471 0.134476i
\(76\) 0 0
\(77\) −3.74174 + 3.74174i −0.426410 + 0.426410i
\(78\) 0 0
\(79\) −6.38450 −0.718312 −0.359156 0.933278i \(-0.616935\pi\)
−0.359156 + 0.933278i \(0.616935\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) 5.25073 5.25073i 0.576342 0.576342i −0.357551 0.933894i \(-0.616388\pi\)
0.933894 + 0.357551i \(0.116388\pi\)
\(84\) 0 0
\(85\) 4.25144 15.0589i 0.461134 1.63336i
\(86\) 0 0
\(87\) 3.66685 0.393128
\(88\) 0 0
\(89\) 15.7100i 1.66525i 0.553833 + 0.832627i \(0.313164\pi\)
−0.553833 + 0.832627i \(0.686836\pi\)
\(90\) 0 0
\(91\) 10.7445 10.7445i 1.12633 1.12633i
\(92\) 0 0
\(93\) 2.78127 2.78127i 0.288404 0.288404i
\(94\) 0 0
\(95\) −4.11792 7.35775i −0.422490 0.754889i
\(96\) 0 0
\(97\) 4.61603i 0.468687i −0.972154 0.234343i \(-0.924706\pi\)
0.972154 0.234343i \(-0.0752940\pi\)
\(98\) 0 0
\(99\) −1.66088 1.66088i −0.166925 0.166925i
\(100\) 0 0
\(101\) −1.13980 + 1.13980i −0.113415 + 0.113415i −0.761537 0.648122i \(-0.775555\pi\)
0.648122 + 0.761537i \(0.275555\pi\)
\(102\) 0 0
\(103\) −4.11257 −0.405224 −0.202612 0.979259i \(-0.564943\pi\)
−0.202612 + 0.979259i \(0.564943\pi\)
\(104\) 0 0
\(105\) 4.39591 2.46026i 0.428997 0.240097i
\(106\) 0 0
\(107\) −4.98634 4.98634i −0.482048 0.482048i 0.423737 0.905785i \(-0.360718\pi\)
−0.905785 + 0.423737i \(0.860718\pi\)
\(108\) 0 0
\(109\) 3.62560 + 3.62560i 0.347269 + 0.347269i 0.859091 0.511822i \(-0.171029\pi\)
−0.511822 + 0.859091i \(0.671029\pi\)
\(110\) 0 0
\(111\) −2.84512 −0.270047
\(112\) 0 0
\(113\) 0.639228i 0.0601335i 0.999548 + 0.0300668i \(0.00957199\pi\)
−0.999548 + 0.0300668i \(0.990428\pi\)
\(114\) 0 0
\(115\) −9.50786 2.68427i −0.886612 0.250310i
\(116\) 0 0
\(117\) 4.76925 + 4.76925i 0.440917 + 0.440917i
\(118\) 0 0
\(119\) 15.7650i 1.44518i
\(120\) 0 0
\(121\) 5.48295i 0.498450i
\(122\) 0 0
\(123\) 3.18272 + 3.18272i 0.286976 + 0.286976i
\(124\) 0 0
\(125\) −7.58255 8.21614i −0.678204 0.734874i
\(126\) 0 0
\(127\) 17.5549i 1.55774i 0.627184 + 0.778871i \(0.284207\pi\)
−0.627184 + 0.778871i \(0.715793\pi\)
\(128\) 0 0
\(129\) −10.1099 −0.890124
\(130\) 0 0
\(131\) −0.826200 0.826200i −0.0721855 0.0721855i 0.670092 0.742278i \(-0.266255\pi\)
−0.742278 + 0.670092i \(0.766255\pi\)
\(132\) 0 0
\(133\) −6.00690 6.00690i −0.520864 0.520864i
\(134\) 0 0
\(135\) 1.09206 + 1.95126i 0.0939897 + 0.167937i
\(136\) 0 0
\(137\) 8.92457 0.762477 0.381239 0.924477i \(-0.375498\pi\)
0.381239 + 0.924477i \(0.375498\pi\)
\(138\) 0 0
\(139\) −4.83668 + 4.83668i −0.410242 + 0.410242i −0.881823 0.471581i \(-0.843683\pi\)
0.471581 + 0.881823i \(0.343683\pi\)
\(140\) 0 0
\(141\) 7.15265 + 7.15265i 0.602361 + 0.602361i
\(142\) 0 0
\(143\) 15.8423i 1.32480i
\(144\) 0 0
\(145\) −4.00443 7.15497i −0.332550 0.594188i
\(146\) 0 0
\(147\) −1.36091 + 1.36091i −0.112246 + 0.112246i
\(148\) 0 0
\(149\) −1.49085 + 1.49085i −0.122135 + 0.122135i −0.765533 0.643397i \(-0.777524\pi\)
0.643397 + 0.765533i \(0.277524\pi\)
\(150\) 0 0
\(151\) 9.61540i 0.782490i 0.920287 + 0.391245i \(0.127956\pi\)
−0.920287 + 0.391245i \(0.872044\pi\)
\(152\) 0 0
\(153\) 6.99777 0.565736
\(154\) 0 0
\(155\) −8.46429 2.38965i −0.679868 0.191941i
\(156\) 0 0
\(157\) −16.0158 + 16.0158i −1.27820 + 1.27820i −0.336521 + 0.941676i \(0.609250\pi\)
−0.941676 + 0.336521i \(0.890750\pi\)
\(158\) 0 0
\(159\) 0.918248 0.0728218
\(160\) 0 0
\(161\) −9.95371 −0.784462
\(162\) 0 0
\(163\) 13.3477 13.3477i 1.04547 1.04547i 0.0465557 0.998916i \(-0.485176\pi\)
0.998916 0.0465557i \(-0.0148245\pi\)
\(164\) 0 0
\(165\) −1.42702 + 5.05459i −0.111093 + 0.393499i
\(166\) 0 0
\(167\) 12.8029 0.990720 0.495360 0.868688i \(-0.335036\pi\)
0.495360 + 0.868688i \(0.335036\pi\)
\(168\) 0 0
\(169\) 32.4915i 2.49934i
\(170\) 0 0
\(171\) 2.66634 2.66634i 0.203900 0.203900i
\(172\) 0 0
\(173\) 12.8300 12.8300i 0.975450 0.975450i −0.0242559 0.999706i \(-0.507722\pi\)
0.999706 + 0.0242559i \(0.00772166\pi\)
\(174\) 0 0
\(175\) −9.60121 5.89079i −0.725784 0.445302i
\(176\) 0 0
\(177\) 7.98601i 0.600265i
\(178\) 0 0
\(179\) −4.61252 4.61252i −0.344756 0.344756i 0.513396 0.858152i \(-0.328387\pi\)
−0.858152 + 0.513396i \(0.828387\pi\)
\(180\) 0 0
\(181\) −4.12071 + 4.12071i −0.306290 + 0.306290i −0.843468 0.537179i \(-0.819490\pi\)
0.537179 + 0.843468i \(0.319490\pi\)
\(182\) 0 0
\(183\) −7.07843 −0.523252
\(184\) 0 0
\(185\) 3.10705 + 5.55156i 0.228435 + 0.408159i
\(186\) 0 0
\(187\) 11.6225 + 11.6225i 0.849919 + 0.849919i
\(188\) 0 0
\(189\) 1.59301 + 1.59301i 0.115875 + 0.115875i
\(190\) 0 0
\(191\) 0.953399 0.0689855 0.0344928 0.999405i \(-0.489018\pi\)
0.0344928 + 0.999405i \(0.489018\pi\)
\(192\) 0 0
\(193\) 4.82186i 0.347085i 0.984826 + 0.173543i \(0.0555214\pi\)
−0.984826 + 0.173543i \(0.944479\pi\)
\(194\) 0 0
\(195\) 4.09771 14.5143i 0.293443 1.03939i
\(196\) 0 0
\(197\) −2.47660 2.47660i −0.176451 0.176451i 0.613356 0.789807i \(-0.289819\pi\)
−0.789807 + 0.613356i \(0.789819\pi\)
\(198\) 0 0
\(199\) 17.4435i 1.23654i −0.785966 0.618270i \(-0.787834\pi\)
0.785966 0.618270i \(-0.212166\pi\)
\(200\) 0 0
\(201\) 7.00424i 0.494041i
\(202\) 0 0
\(203\) −5.84135 5.84135i −0.409982 0.409982i
\(204\) 0 0
\(205\) 2.73457 9.68602i 0.190991 0.676501i
\(206\) 0 0
\(207\) 4.41825i 0.307090i
\(208\) 0 0
\(209\) 8.85695 0.612648
\(210\) 0 0
\(211\) −5.41135 5.41135i −0.372533 0.372533i 0.495866 0.868399i \(-0.334851\pi\)
−0.868399 + 0.495866i \(0.834851\pi\)
\(212\) 0 0
\(213\) −1.64882 1.64882i −0.112975 0.112975i
\(214\) 0 0
\(215\) 11.0406 + 19.7269i 0.752963 + 1.34537i
\(216\) 0 0
\(217\) −8.86120 −0.601538
\(218\) 0 0
\(219\) −1.54344 + 1.54344i −0.104296 + 0.104296i
\(220\) 0 0
\(221\) −33.3741 33.3741i −2.24499 2.24499i
\(222\) 0 0
\(223\) 18.2634i 1.22301i −0.791241 0.611505i \(-0.790564\pi\)
0.791241 0.611505i \(-0.209436\pi\)
\(224\) 0 0
\(225\) 2.61480 4.26178i 0.174320 0.284119i
\(226\) 0 0
\(227\) −2.23773 + 2.23773i −0.148523 + 0.148523i −0.777458 0.628935i \(-0.783491\pi\)
0.628935 + 0.777458i \(0.283491\pi\)
\(228\) 0 0
\(229\) 6.40974 6.40974i 0.423568 0.423568i −0.462862 0.886430i \(-0.653178\pi\)
0.886430 + 0.462862i \(0.153178\pi\)
\(230\) 0 0
\(231\) 5.29162i 0.348163i
\(232\) 0 0
\(233\) 2.67972 0.175555 0.0877773 0.996140i \(-0.472024\pi\)
0.0877773 + 0.996140i \(0.472024\pi\)
\(234\) 0 0
\(235\) 6.14551 21.7678i 0.400889 1.41997i
\(236\) 0 0
\(237\) −4.51452 + 4.51452i −0.293250 + 0.293250i
\(238\) 0 0
\(239\) 26.0323 1.68389 0.841946 0.539562i \(-0.181410\pi\)
0.841946 + 0.539562i \(0.181410\pi\)
\(240\) 0 0
\(241\) 5.87408 0.378383 0.189191 0.981940i \(-0.439413\pi\)
0.189191 + 0.981940i \(0.439413\pi\)
\(242\) 0 0
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 4.14167 + 1.16928i 0.264602 + 0.0747028i
\(246\) 0 0
\(247\) −25.4329 −1.61826
\(248\) 0 0
\(249\) 7.42565i 0.470582i
\(250\) 0 0
\(251\) −8.44080 + 8.44080i −0.532779 + 0.532779i −0.921398 0.388620i \(-0.872952\pi\)
0.388620 + 0.921398i \(0.372952\pi\)
\(252\) 0 0
\(253\) 7.33819 7.33819i 0.461348 0.461348i
\(254\) 0 0
\(255\) −7.64200 13.6544i −0.478561 0.855075i
\(256\) 0 0
\(257\) 22.2011i 1.38487i 0.721480 + 0.692435i \(0.243462\pi\)
−0.721480 + 0.692435i \(0.756538\pi\)
\(258\) 0 0
\(259\) 4.53232 + 4.53232i 0.281625 + 0.281625i
\(260\) 0 0
\(261\) 2.59286 2.59286i 0.160494 0.160494i
\(262\) 0 0
\(263\) 0.464456 0.0286396 0.0143198 0.999897i \(-0.495442\pi\)
0.0143198 + 0.999897i \(0.495442\pi\)
\(264\) 0 0
\(265\) −1.00278 1.79174i −0.0616005 0.110065i
\(266\) 0 0
\(267\) 11.1086 + 11.1086i 0.679837 + 0.679837i
\(268\) 0 0
\(269\) 4.74205 + 4.74205i 0.289128 + 0.289128i 0.836735 0.547608i \(-0.184461\pi\)
−0.547608 + 0.836735i \(0.684461\pi\)
\(270\) 0 0
\(271\) −12.0417 −0.731482 −0.365741 0.930717i \(-0.619184\pi\)
−0.365741 + 0.930717i \(0.619184\pi\)
\(272\) 0 0
\(273\) 15.1950i 0.919641i
\(274\) 0 0
\(275\) 11.4212 2.73544i 0.688724 0.164953i
\(276\) 0 0
\(277\) 17.9760 + 17.9760i 1.08007 + 1.08007i 0.996502 + 0.0835733i \(0.0266333\pi\)
0.0835733 + 0.996502i \(0.473367\pi\)
\(278\) 0 0
\(279\) 3.93331i 0.235481i
\(280\) 0 0
\(281\) 9.58712i 0.571919i −0.958242 0.285960i \(-0.907688\pi\)
0.958242 0.285960i \(-0.0923123\pi\)
\(282\) 0 0
\(283\) −5.09022 5.09022i −0.302582 0.302582i 0.539441 0.842023i \(-0.318636\pi\)
−0.842023 + 0.539441i \(0.818636\pi\)
\(284\) 0 0
\(285\) −8.11453 2.29091i −0.480663 0.135702i
\(286\) 0 0
\(287\) 10.1402i 0.598559i
\(288\) 0 0
\(289\) −31.9688 −1.88052
\(290\) 0 0
\(291\) −3.26403 3.26403i −0.191341 0.191341i
\(292\) 0 0
\(293\) 4.25071 + 4.25071i 0.248329 + 0.248329i 0.820285 0.571955i \(-0.193815\pi\)
−0.571955 + 0.820285i \(0.693815\pi\)
\(294\) 0 0
\(295\) 15.5827 8.72121i 0.907263 0.507769i
\(296\) 0 0
\(297\) −2.34884 −0.136294
\(298\) 0 0
\(299\) −21.0717 + 21.0717i −1.21861 + 1.21861i
\(300\) 0 0
\(301\) 16.1052 + 16.1052i 0.928286 + 0.928286i
\(302\) 0 0
\(303\) 1.61193i 0.0926028i
\(304\) 0 0
\(305\) 7.73008 + 13.8118i 0.442623 + 0.790863i
\(306\) 0 0
\(307\) 0.153856 0.153856i 0.00878103 0.00878103i −0.702703 0.711484i \(-0.748024\pi\)
0.711484 + 0.702703i \(0.248024\pi\)
\(308\) 0 0
\(309\) −2.90803 + 2.90803i −0.165432 + 0.165432i
\(310\) 0 0
\(311\) 34.8210i 1.97452i −0.159115 0.987260i \(-0.550864\pi\)
0.159115 0.987260i \(-0.449136\pi\)
\(312\) 0 0
\(313\) −17.3412 −0.980182 −0.490091 0.871671i \(-0.663036\pi\)
−0.490091 + 0.871671i \(0.663036\pi\)
\(314\) 0 0
\(315\) 1.36871 4.84805i 0.0771180 0.273157i
\(316\) 0 0
\(317\) 10.1485 10.1485i 0.569999 0.569999i −0.362129 0.932128i \(-0.617950\pi\)
0.932128 + 0.362129i \(0.117950\pi\)
\(318\) 0 0
\(319\) 8.61285 0.482227
\(320\) 0 0
\(321\) −7.05175 −0.393591
\(322\) 0 0
\(323\) −18.6584 + 18.6584i −1.03818 + 1.03818i
\(324\) 0 0
\(325\) −32.7962 + 7.85487i −1.81920 + 0.435710i
\(326\) 0 0
\(327\) 5.12737 0.283544
\(328\) 0 0
\(329\) 22.7885i 1.25637i
\(330\) 0 0
\(331\) 9.12552 9.12552i 0.501584 0.501584i −0.410346 0.911930i \(-0.634592\pi\)
0.911930 + 0.410346i \(0.134592\pi\)
\(332\) 0 0
\(333\) −2.01181 + 2.01181i −0.110246 + 0.110246i
\(334\) 0 0
\(335\) 13.6671 7.64906i 0.746711 0.417913i
\(336\) 0 0
\(337\) 4.62620i 0.252005i −0.992030 0.126002i \(-0.959785\pi\)
0.992030 0.126002i \(-0.0402147\pi\)
\(338\) 0 0
\(339\) 0.452002 + 0.452002i 0.0245494 + 0.0245494i
\(340\) 0 0
\(341\) 6.53276 6.53276i 0.353769 0.353769i
\(342\) 0 0
\(343\) 20.1059 1.08562
\(344\) 0 0
\(345\) −8.62114 + 4.82500i −0.464146 + 0.259769i
\(346\) 0 0
\(347\) 16.1909 + 16.1909i 0.869173 + 0.869173i 0.992381 0.123208i \(-0.0393182\pi\)
−0.123208 + 0.992381i \(0.539318\pi\)
\(348\) 0 0
\(349\) 21.6447 + 21.6447i 1.15862 + 1.15862i 0.984774 + 0.173842i \(0.0556182\pi\)
0.173842 + 0.984774i \(0.444382\pi\)
\(350\) 0 0
\(351\) 6.74474 0.360007
\(352\) 0 0
\(353\) 26.1933i 1.39413i −0.717009 0.697064i \(-0.754489\pi\)
0.717009 0.697064i \(-0.245511\pi\)
\(354\) 0 0
\(355\) −1.41666 + 5.01788i −0.0751883 + 0.266322i
\(356\) 0 0
\(357\) −11.1475 11.1475i −0.589991 0.589991i
\(358\) 0 0
\(359\) 5.73157i 0.302501i −0.988495 0.151250i \(-0.951670\pi\)
0.988495 0.151250i \(-0.0483300\pi\)
\(360\) 0 0
\(361\) 4.78125i 0.251645i
\(362\) 0 0
\(363\) 3.87703 + 3.87703i 0.203491 + 0.203491i
\(364\) 0 0
\(365\) 4.69717 + 1.32611i 0.245861 + 0.0694119i
\(366\) 0 0
\(367\) 20.9879i 1.09556i −0.836623 0.547778i \(-0.815474\pi\)
0.836623 0.547778i \(-0.184526\pi\)
\(368\) 0 0
\(369\) 4.50104 0.234315
\(370\) 0 0
\(371\) −1.46278 1.46278i −0.0759438 0.0759438i
\(372\) 0 0
\(373\) 12.9141 + 12.9141i 0.668667 + 0.668667i 0.957407 0.288740i \(-0.0932365\pi\)
−0.288740 + 0.957407i \(0.593236\pi\)
\(374\) 0 0
\(375\) −11.1714 0.448018i −0.576887 0.0231356i
\(376\) 0 0
\(377\) −24.7320 −1.27376
\(378\) 0 0
\(379\) −8.07361 + 8.07361i −0.414713 + 0.414713i −0.883377 0.468663i \(-0.844736\pi\)
0.468663 + 0.883377i \(0.344736\pi\)
\(380\) 0 0
\(381\) 12.4132 + 12.4132i 0.635945 + 0.635945i
\(382\) 0 0
\(383\) 9.23276i 0.471772i −0.971781 0.235886i \(-0.924201\pi\)
0.971781 0.235886i \(-0.0757992\pi\)
\(384\) 0 0
\(385\) 10.3253 5.77877i 0.526226 0.294513i
\(386\) 0 0
\(387\) −7.14876 + 7.14876i −0.363392 + 0.363392i
\(388\) 0 0
\(389\) −6.32362 + 6.32362i −0.320620 + 0.320620i −0.849005 0.528385i \(-0.822798\pi\)
0.528385 + 0.849005i \(0.322798\pi\)
\(390\) 0 0
\(391\) 30.9179i 1.56359i
\(392\) 0 0
\(393\) −1.16842 −0.0589392
\(394\) 0 0
\(395\) 13.7391 + 3.87885i 0.691290 + 0.195166i
\(396\) 0 0
\(397\) 1.07806 1.07806i 0.0541061 0.0541061i −0.679536 0.733642i \(-0.737819\pi\)
0.733642 + 0.679536i \(0.237819\pi\)
\(398\) 0 0
\(399\) −8.49504 −0.425284
\(400\) 0 0
\(401\) 37.0966 1.85252 0.926258 0.376891i \(-0.123007\pi\)
0.926258 + 0.376891i \(0.123007\pi\)
\(402\) 0 0
\(403\) −18.7589 + 18.7589i −0.934449 + 0.934449i
\(404\) 0 0
\(405\) 2.15195 + 0.607542i 0.106931 + 0.0301890i
\(406\) 0 0
\(407\) −6.68274 −0.331251
\(408\) 0 0
\(409\) 17.3422i 0.857518i 0.903419 + 0.428759i \(0.141049\pi\)
−0.903419 + 0.428759i \(0.858951\pi\)
\(410\) 0 0
\(411\) 6.31062 6.31062i 0.311280 0.311280i
\(412\) 0 0
\(413\) 12.7218 12.7218i 0.626000 0.626000i
\(414\) 0 0
\(415\) −14.4894 + 8.10927i −0.711254 + 0.398068i
\(416\) 0 0
\(417\) 6.84010i 0.334961i
\(418\) 0 0
\(419\) 20.4718 + 20.4718i 1.00011 + 1.00011i 1.00000 0.000110566i \(3.51942e-5\pi\)
0.000110566 1.00000i \(0.499965\pi\)
\(420\) 0 0
\(421\) −10.6143 + 10.6143i −0.517308 + 0.517308i −0.916756 0.399448i \(-0.869202\pi\)
0.399448 + 0.916756i \(0.369202\pi\)
\(422\) 0 0
\(423\) 10.1154 0.491826
\(424\) 0 0
\(425\) −18.2978 + 29.8230i −0.887573 + 1.44663i
\(426\) 0 0
\(427\) 11.2760 + 11.2760i 0.545685 + 0.545685i
\(428\) 0 0
\(429\) 11.2022 + 11.2022i 0.540848 + 0.540848i
\(430\) 0 0
\(431\) −17.9747 −0.865812 −0.432906 0.901439i \(-0.642512\pi\)
−0.432906 + 0.901439i \(0.642512\pi\)
\(432\) 0 0
\(433\) 23.1120i 1.11069i 0.831619 + 0.555347i \(0.187414\pi\)
−0.831619 + 0.555347i \(0.812586\pi\)
\(434\) 0 0
\(435\) −7.89089 2.22777i −0.378339 0.106813i
\(436\) 0 0
\(437\) 11.7806 + 11.7806i 0.563541 + 0.563541i
\(438\) 0 0
\(439\) 2.65049i 0.126501i −0.997998 0.0632505i \(-0.979853\pi\)
0.997998 0.0632505i \(-0.0201467\pi\)
\(440\) 0 0
\(441\) 1.92461i 0.0916482i
\(442\) 0 0
\(443\) −0.977227 0.977227i −0.0464294 0.0464294i 0.683511 0.729940i \(-0.260452\pi\)
−0.729940 + 0.683511i \(0.760452\pi\)
\(444\) 0 0
\(445\) 9.54448 33.8071i 0.452452 1.60261i
\(446\) 0 0
\(447\) 2.10838i 0.0997231i
\(448\) 0 0
\(449\) −19.6612 −0.927867 −0.463934 0.885870i \(-0.653562\pi\)
−0.463934 + 0.885870i \(0.653562\pi\)
\(450\) 0 0
\(451\) 7.47570 + 7.47570i 0.352017 + 0.352017i
\(452\) 0 0
\(453\) 6.79911 + 6.79911i 0.319450 + 0.319450i
\(454\) 0 0
\(455\) −29.6493 + 16.5938i −1.38998 + 0.777931i
\(456\) 0 0
\(457\) 25.9752 1.21507 0.607535 0.794293i \(-0.292159\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(458\) 0 0
\(459\) 4.94817 4.94817i 0.230961 0.230961i
\(460\) 0 0
\(461\) −1.94218 1.94218i −0.0904565 0.0904565i 0.660431 0.750887i \(-0.270374\pi\)
−0.750887 + 0.660431i \(0.770374\pi\)
\(462\) 0 0
\(463\) 12.7805i 0.593960i −0.954884 0.296980i \(-0.904021\pi\)
0.954884 0.296980i \(-0.0959795\pi\)
\(464\) 0 0
\(465\) −7.67489 + 4.29541i −0.355915 + 0.199195i
\(466\) 0 0
\(467\) −28.2154 + 28.2154i −1.30565 + 1.30565i −0.381129 + 0.924522i \(0.624465\pi\)
−0.924522 + 0.381129i \(0.875535\pi\)
\(468\) 0 0
\(469\) 11.1578 11.1578i 0.515222 0.515222i
\(470\) 0 0
\(471\) 22.6497i 1.04364i
\(472\) 0 0
\(473\) −23.7465 −1.09186
\(474\) 0 0
\(475\) 4.39142 + 18.3353i 0.201492 + 0.841283i
\(476\) 0 0
\(477\) 0.649299 0.649299i 0.0297294 0.0297294i
\(478\) 0 0
\(479\) 22.6500 1.03490 0.517452 0.855712i \(-0.326881\pi\)
0.517452 + 0.855712i \(0.326881\pi\)
\(480\) 0 0
\(481\) 19.1896 0.874970
\(482\) 0 0
\(483\) −7.03833 + 7.03833i −0.320255 + 0.320255i
\(484\) 0 0
\(485\) −2.80443 + 9.93347i −0.127343 + 0.451056i
\(486\) 0 0
\(487\) −20.1202 −0.911733 −0.455866 0.890048i \(-0.650671\pi\)
−0.455866 + 0.890048i \(0.650671\pi\)
\(488\) 0 0
\(489\) 18.8765i 0.853624i
\(490\) 0 0
\(491\) −20.4434 + 20.4434i −0.922596 + 0.922596i −0.997212 0.0746163i \(-0.976227\pi\)
0.0746163 + 0.997212i \(0.476227\pi\)
\(492\) 0 0
\(493\) −18.1442 + 18.1442i −0.817174 + 0.817174i
\(494\) 0 0
\(495\) 2.56508 + 4.58319i 0.115292 + 0.205999i
\(496\) 0 0
\(497\) 5.25319i 0.235638i
\(498\) 0 0
\(499\) −26.7236 26.7236i −1.19631 1.19631i −0.975262 0.221052i \(-0.929051\pi\)
−0.221052 0.975262i \(-0.570949\pi\)
\(500\) 0 0
\(501\) 9.05304 9.05304i 0.404460 0.404460i
\(502\) 0 0
\(503\) −17.4692 −0.778911 −0.389456 0.921045i \(-0.627337\pi\)
−0.389456 + 0.921045i \(0.627337\pi\)
\(504\) 0 0
\(505\) 3.14528 1.76032i 0.139963 0.0783334i
\(506\) 0 0
\(507\) −22.9749 22.9749i −1.02035 1.02035i
\(508\) 0 0
\(509\) 22.1370 + 22.1370i 0.981205 + 0.981205i 0.999827 0.0186215i \(-0.00592774\pi\)
−0.0186215 + 0.999827i \(0.505928\pi\)
\(510\) 0 0
\(511\) 4.91744 0.217535
\(512\) 0 0
\(513\) 3.77078i 0.166484i
\(514\) 0 0
\(515\) 8.85005 + 2.49856i 0.389980 + 0.110100i
\(516\) 0 0
\(517\) 16.8004 + 16.8004i 0.738882 + 0.738882i
\(518\) 0 0
\(519\) 18.1444i 0.796451i
\(520\) 0 0
\(521\) 20.7634i 0.909663i −0.890577 0.454832i \(-0.849699\pi\)
0.890577 0.454832i \(-0.150301\pi\)
\(522\) 0 0
\(523\) 25.9884 + 25.9884i 1.13640 + 1.13640i 0.989091 + 0.147304i \(0.0470595\pi\)
0.147304 + 0.989091i \(0.452941\pi\)
\(524\) 0 0
\(525\) −10.9545 + 2.62367i −0.478094 + 0.114506i
\(526\) 0 0
\(527\) 27.5244i 1.19898i
\(528\) 0 0
\(529\) −3.47907 −0.151264
\(530\) 0 0
\(531\) 5.64696 + 5.64696i 0.245057 + 0.245057i
\(532\) 0 0
\(533\) −21.4666 21.4666i −0.929821 0.929821i
\(534\) 0 0
\(535\) 7.70095 + 13.7598i 0.332941 + 0.594887i
\(536\) 0 0
\(537\) −6.52309 −0.281492
\(538\) 0 0
\(539\) −3.19655 + 3.19655i −0.137685 + 0.137685i
\(540\) 0 0
\(541\) 4.86704 + 4.86704i 0.209250 + 0.209250i 0.803949 0.594698i \(-0.202729\pi\)
−0.594698 + 0.803949i \(0.702729\pi\)
\(542\) 0 0
\(543\) 5.82756i 0.250085i
\(544\) 0 0
\(545\) −5.59940 10.0048i −0.239852 0.428559i
\(546\) 0 0
\(547\) 16.2487 16.2487i 0.694742 0.694742i −0.268529 0.963272i \(-0.586538\pi\)
0.963272 + 0.268529i \(0.0865376\pi\)
\(548\) 0 0
\(549\) −5.00520 + 5.00520i −0.213617 + 0.213617i
\(550\) 0 0
\(551\) 13.8269i 0.589045i
\(552\) 0 0
\(553\) 14.3834 0.611644
\(554\) 0 0
\(555\) 6.12256 + 1.72853i 0.259888 + 0.0733721i
\(556\) 0 0
\(557\) −0.616853 + 0.616853i −0.0261369 + 0.0261369i −0.720054 0.693918i \(-0.755883\pi\)
0.693918 + 0.720054i \(0.255883\pi\)
\(558\) 0 0
\(559\) 68.1884 2.88406
\(560\) 0 0
\(561\) 16.4367 0.693956
\(562\) 0 0
\(563\) 17.4063 17.4063i 0.733587 0.733587i −0.237742 0.971328i \(-0.576407\pi\)
0.971328 + 0.237742i \(0.0764072\pi\)
\(564\) 0 0
\(565\) 0.388358 1.37559i 0.0163383 0.0578714i
\(566\) 0 0
\(567\) 2.25286 0.0946113
\(568\) 0 0
\(569\) 1.57959i 0.0662197i −0.999452 0.0331098i \(-0.989459\pi\)
0.999452 0.0331098i \(-0.0105411\pi\)
\(570\) 0 0
\(571\) −24.6949 + 24.6949i −1.03345 + 1.03345i −0.0340299 + 0.999421i \(0.510834\pi\)
−0.999421 + 0.0340299i \(0.989166\pi\)
\(572\) 0 0
\(573\) 0.674155 0.674155i 0.0281632 0.0281632i
\(574\) 0 0
\(575\) 18.8296 + 11.5528i 0.785250 + 0.481787i
\(576\) 0 0
\(577\) 33.6673i 1.40159i −0.713363 0.700795i \(-0.752829\pi\)
0.713363 0.700795i \(-0.247171\pi\)
\(578\) 0 0
\(579\) 3.40957 + 3.40957i 0.141697 + 0.141697i
\(580\) 0 0
\(581\) −11.8292 + 11.8292i −0.490757 + 0.490757i
\(582\) 0 0
\(583\) 2.15682 0.0893263
\(584\) 0 0
\(585\) −7.36567 13.1607i −0.304533 0.544128i
\(586\) 0 0
\(587\) −30.6327 30.6327i −1.26435 1.26435i −0.948964 0.315385i \(-0.897866\pi\)
−0.315385 0.948964i \(-0.602134\pi\)
\(588\) 0 0
\(589\) 10.4875 + 10.4875i 0.432132 + 0.432132i
\(590\) 0 0
\(591\) −3.50245 −0.144071
\(592\) 0 0
\(593\) 25.1477i 1.03269i 0.856380 + 0.516347i \(0.172708\pi\)
−0.856380 + 0.516347i \(0.827292\pi\)
\(594\) 0 0
\(595\) −9.57791 + 33.9255i −0.392656 + 1.39081i
\(596\) 0 0
\(597\) −12.3344 12.3344i −0.504815 0.504815i
\(598\) 0 0
\(599\) 18.0767i 0.738594i −0.929311 0.369297i \(-0.879598\pi\)
0.929311 0.369297i \(-0.120402\pi\)
\(600\) 0 0
\(601\) 26.5291i 1.08214i 0.840977 + 0.541072i \(0.181981\pi\)
−0.840977 + 0.541072i \(0.818019\pi\)
\(602\) 0 0
\(603\) 4.95274 + 4.95274i 0.201691 + 0.201691i
\(604\) 0 0
\(605\) 3.33112 11.7990i 0.135429 0.479699i
\(606\) 0 0
\(607\) 28.3496i 1.15068i 0.817916 + 0.575338i \(0.195129\pi\)
−0.817916 + 0.575338i \(0.804871\pi\)
\(608\) 0 0
\(609\) −8.26091 −0.334749
\(610\) 0 0
\(611\) −48.2427 48.2427i −1.95169 1.95169i
\(612\) 0 0
\(613\) −3.24941 3.24941i −0.131243 0.131243i 0.638434 0.769677i \(-0.279583\pi\)
−0.769677 + 0.638434i \(0.779583\pi\)
\(614\) 0 0
\(615\) −4.91542 8.78269i −0.198209 0.354152i
\(616\) 0 0
\(617\) −18.4370 −0.742245 −0.371123 0.928584i \(-0.621027\pi\)
−0.371123 + 0.928584i \(0.621027\pi\)
\(618\) 0 0
\(619\) −9.47769 + 9.47769i −0.380941 + 0.380941i −0.871441 0.490500i \(-0.836814\pi\)
0.490500 + 0.871441i \(0.336814\pi\)
\(620\) 0 0
\(621\) −3.12417 3.12417i −0.125369 0.125369i
\(622\) 0 0
\(623\) 35.3924i 1.41797i
\(624\) 0 0
\(625\) 11.3256 + 22.2874i 0.453025 + 0.891498i
\(626\) 0 0
\(627\) 6.26281 6.26281i 0.250113 0.250113i
\(628\) 0 0
\(629\) 14.0782 14.0782i 0.561333 0.561333i
\(630\) 0 0
\(631\) 10.6343i 0.423346i 0.977341 + 0.211673i \(0.0678912\pi\)
−0.977341 + 0.211673i \(0.932109\pi\)
\(632\) 0 0
\(633\) −7.65281 −0.304172
\(634\) 0 0
\(635\) 10.6653 37.7772i 0.423240 1.49914i
\(636\) 0 0
\(637\) 9.17895 9.17895i 0.363683 0.363683i
\(638\) 0 0
\(639\) −2.33178 −0.0922439
\(640\) 0 0
\(641\) −21.4256 −0.846261 −0.423130 0.906069i \(-0.639069\pi\)
−0.423130 + 0.906069i \(0.639069\pi\)
\(642\) 0 0
\(643\) 28.7046 28.7046i 1.13200 1.13200i 0.142152 0.989845i \(-0.454598\pi\)
0.989845 0.142152i \(-0.0454022\pi\)
\(644\) 0 0
\(645\) 21.7559 + 6.14217i 0.856639 + 0.241848i
\(646\) 0 0
\(647\) 36.8695 1.44949 0.724746 0.689017i \(-0.241957\pi\)
0.724746 + 0.689017i \(0.241957\pi\)
\(648\) 0 0
\(649\) 18.7579i 0.736311i
\(650\) 0 0
\(651\) −6.26582 + 6.26582i −0.245577 + 0.245577i
\(652\) 0 0
\(653\) −27.8096 + 27.8096i −1.08828 + 1.08828i −0.0925688 + 0.995706i \(0.529508\pi\)
−0.995706 + 0.0925688i \(0.970492\pi\)
\(654\) 0 0
\(655\) 1.27599 + 2.27989i 0.0498571 + 0.0890829i
\(656\) 0 0
\(657\) 2.18275i 0.0851572i
\(658\) 0 0
\(659\) 11.6956 + 11.6956i 0.455596 + 0.455596i 0.897207 0.441611i \(-0.145593\pi\)
−0.441611 + 0.897207i \(0.645593\pi\)
\(660\) 0 0
\(661\) 29.7275 29.7275i 1.15627 1.15627i 0.170994 0.985272i \(-0.445302\pi\)
0.985272 0.170994i \(-0.0546979\pi\)
\(662\) 0 0
\(663\) −47.1981 −1.83302
\(664\) 0 0
\(665\) 9.27711 + 16.5760i 0.359751 + 0.642790i
\(666\) 0 0
\(667\) 11.4559 + 11.4559i 0.443574 + 0.443574i
\(668\) 0 0
\(669\) −12.9142 12.9142i −0.499292 0.499292i
\(670\) 0 0
\(671\) −16.6261 −0.641843
\(672\) 0 0
\(673\) 19.4197i 0.748575i 0.927313 + 0.374287i \(0.122113\pi\)
−0.927313 + 0.374287i \(0.877887\pi\)
\(674\) 0 0
\(675\) −1.16459 4.86248i −0.0448252 0.187157i
\(676\) 0 0
\(677\) −22.0550 22.0550i −0.847643 0.847643i 0.142196 0.989839i \(-0.454584\pi\)
−0.989839 + 0.142196i \(0.954584\pi\)
\(678\) 0 0
\(679\) 10.3993i 0.399088i
\(680\) 0 0
\(681\) 3.16462i 0.121269i
\(682\) 0 0
\(683\) 9.95729 + 9.95729i 0.381005 + 0.381005i 0.871464 0.490459i \(-0.163171\pi\)
−0.490459 + 0.871464i \(0.663171\pi\)
\(684\) 0 0
\(685\) −19.2052 5.42205i −0.733794 0.207166i
\(686\) 0 0
\(687\) 9.06474i 0.345842i
\(688\) 0 0
\(689\) −6.19334 −0.235947
\(690\) 0 0
\(691\) 30.1664 + 30.1664i 1.14758 + 1.14758i 0.987027 + 0.160556i \(0.0513288\pi\)
0.160556 + 0.987027i \(0.448671\pi\)
\(692\) 0 0
\(693\) 3.74174 + 3.74174i 0.142137 + 0.142137i
\(694\) 0 0
\(695\) 13.3468 7.46981i 0.506272 0.283346i
\(696\) 0 0
\(697\) −31.4973 −1.19304
\(698\) 0 0
\(699\) 1.89485 1.89485i 0.0716698 0.0716698i
\(700\) 0 0
\(701\) −2.10793 2.10793i −0.0796155 0.0796155i 0.666178 0.745793i \(-0.267929\pi\)
−0.745793 + 0.666178i \(0.767929\pi\)
\(702\) 0 0
\(703\) 10.7283i 0.404626i
\(704\) 0 0
\(705\) −11.0466 19.7377i −0.416039 0.743364i
\(706\) 0 0
\(707\) 2.56782 2.56782i 0.0965729 0.0965729i
\(708\) 0 0
\(709\) −29.5759 + 29.5759i −1.11075 + 1.11075i −0.117697 + 0.993050i \(0.537551\pi\)
−0.993050 + 0.117697i \(0.962449\pi\)
\(710\) 0 0
\(711\) 6.38450i 0.239437i
\(712\) 0 0
\(713\) 17.3783 0.650824
\(714\) 0 0
\(715\) 9.62488 34.0919i 0.359950 1.27496i
\(716\) 0 0
\(717\) 18.4076 18.4076i 0.687446 0.687446i
\(718\) 0 0
\(719\) −15.2528 −0.568833 −0.284417 0.958701i \(-0.591800\pi\)
−0.284417 + 0.958701i \(0.591800\pi\)
\(720\) 0 0
\(721\) 9.26506 0.345049
\(722\) 0 0
\(723\) 4.15360 4.15360i 0.154474 0.154474i
\(724\) 0 0
\(725\) 4.27039 + 17.8300i 0.158598 + 0.662190i
\(726\) 0 0
\(727\) 22.5396 0.835947 0.417973 0.908459i \(-0.362740\pi\)
0.417973 + 0.908459i \(0.362740\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 50.0254 50.0254i 1.85025 1.85025i
\(732\) 0 0
\(733\) 8.88368 8.88368i 0.328126 0.328126i −0.523747 0.851874i \(-0.675466\pi\)
0.851874 + 0.523747i \(0.175466\pi\)
\(734\) 0 0
\(735\) 3.75541 2.10180i 0.138520 0.0775259i
\(736\) 0 0
\(737\) 16.4518i 0.606011i
\(738\) 0 0
\(739\) 3.00557 + 3.00557i 0.110562 + 0.110562i 0.760223 0.649662i \(-0.225089\pi\)
−0.649662 + 0.760223i \(0.725089\pi\)
\(740\) 0 0
\(741\) −17.9838 + 17.9838i −0.660650 + 0.660650i
\(742\) 0 0
\(743\) −14.5808 −0.534919 −0.267459 0.963569i \(-0.586184\pi\)
−0.267459 + 0.963569i \(0.586184\pi\)
\(744\) 0 0
\(745\) 4.11399 2.30248i 0.150725 0.0843565i
\(746\) 0 0
\(747\) −5.25073 5.25073i −0.192114 0.192114i
\(748\) 0 0
\(749\) 11.2335 + 11.2335i 0.410465 + 0.410465i
\(750\) 0 0
\(751\) 1.92675 0.0703083 0.0351541 0.999382i \(-0.488808\pi\)
0.0351541 + 0.999382i \(0.488808\pi\)
\(752\) 0 0
\(753\) 11.9371i 0.435012i
\(754\) 0 0
\(755\) 5.84176 20.6919i 0.212603 0.753054i
\(756\) 0 0
\(757\) 0.389306 + 0.389306i 0.0141496 + 0.0141496i 0.714146 0.699997i \(-0.246815\pi\)
−0.699997 + 0.714146i \(0.746815\pi\)
\(758\) 0 0
\(759\) 10.3778i 0.376689i
\(760\) 0 0
\(761\) 18.0200i 0.653223i 0.945159 + 0.326612i \(0.105907\pi\)
−0.945159 + 0.326612i \(0.894093\pi\)
\(762\) 0 0
\(763\) −8.16797 8.16797i −0.295700 0.295700i
\(764\) 0 0
\(765\) −15.0589 4.25144i −0.544454 0.153711i
\(766\) 0 0
\(767\) 53.8635i 1.94490i
\(768\) 0 0
\(769\) −34.9422 −1.26005 −0.630024 0.776576i \(-0.716955\pi\)
−0.630024 + 0.776576i \(0.716955\pi\)
\(770\) 0 0
\(771\) 15.6986 + 15.6986i 0.565371 + 0.565371i
\(772\) 0 0
\(773\) 9.83112 + 9.83112i 0.353601 + 0.353601i 0.861447 0.507847i \(-0.169558\pi\)
−0.507847 + 0.861447i \(0.669558\pi\)
\(774\) 0 0
\(775\) 16.7629 + 10.2848i 0.602142 + 0.369442i
\(776\) 0 0
\(777\) 6.40967 0.229946
\(778\) 0 0
\(779\) −12.0013 + 12.0013i −0.429992 + 0.429992i
\(780\) 0 0
\(781\) −3.87282 3.87282i −0.138580 0.138580i
\(782\) 0 0
\(783\) 3.66685i 0.131043i
\(784\) 0 0
\(785\) 44.1954 24.7349i 1.57740 0.882826i
\(786\) 0 0
\(787\) 34.3615 34.3615i 1.22486 1.22486i 0.258970 0.965885i \(-0.416617\pi\)
0.965885 0.258970i \(-0.0833831\pi\)
\(788\) 0 0
\(789\) 0.328420 0.328420i 0.0116921 0.0116921i
\(790\) 0 0
\(791\) 1.44009i 0.0512038i
\(792\) 0 0
\(793\) 47.7421 1.69537
\(794\) 0 0
\(795\) −1.97602 0.557874i −0.0700823 0.0197858i
\(796\) 0 0
\(797\) 3.63103 3.63103i 0.128618 0.128618i −0.639868 0.768485i \(-0.721011\pi\)
0.768485 + 0.639868i \(0.221011\pi\)
\(798\) 0 0
\(799\) −70.7850 −2.50419