Properties

Label 280.2.s.a.237.4
Level $280$
Weight $2$
Character 280.237
Analytic conductor $2.236$
Analytic rank $0$
Dimension $8$
CM discriminant -56
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.s (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.40282095616.8
Defining polynomial: \(x^{8} - 4 x^{6} + 8 x^{4} - 36 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{4}]$

Embedding invariants

Embedding label 237.4
Root \(-1.71331 + 0.254137i\) of defining polynomial
Character \(\chi\) \(=\) 280.237
Dual form 280.2.s.a.13.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.96744 - 1.96744i) q^{3} +2.00000i q^{4} +(-0.254137 + 2.22158i) q^{5} -3.93488 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -4.74166i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.96744 - 1.96744i) q^{3} +2.00000i q^{4} +(-0.254137 + 2.22158i) q^{5} -3.93488 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -4.74166i q^{9} +(2.47572 - 1.96744i) q^{10} +(3.93488 + 3.93488i) q^{12} +(4.88578 - 4.88578i) q^{13} -3.74166i q^{14} +(3.87083 + 4.87083i) q^{15} -4.00000 q^{16} +(-4.74166 + 4.74166i) q^{18} -2.41006i q^{19} +(-4.44316 - 0.508274i) q^{20} +7.36149 q^{21} +(-6.74166 + 6.74166i) q^{23} -7.86977i q^{24} +(-4.87083 - 1.12917i) q^{25} -9.77156 q^{26} +(-3.42661 - 3.42661i) q^{27} +(-3.74166 + 3.74166i) q^{28} +(1.00000 - 8.74166i) q^{30} +(4.00000 + 4.00000i) q^{32} +(-4.63164 + 3.68075i) q^{35} +9.48331 q^{36} +(-2.41006 + 2.41006i) q^{38} -19.2250i q^{39} +(3.93488 + 4.95143i) q^{40} +(-7.36149 - 7.36149i) q^{42} +(10.5340 + 1.20503i) q^{45} +13.4833 q^{46} +(-7.86977 + 7.86977i) q^{48} +7.00000i q^{49} +(3.74166 + 6.00000i) q^{50} +(9.77156 + 9.77156i) q^{52} +6.85322i q^{54} +7.48331 q^{56} +(-4.74166 - 4.74166i) q^{57} -10.4111i q^{59} +(-9.74166 + 7.74166i) q^{60} -6.47626 q^{61} +(8.87083 - 8.87083i) q^{63} -8.00000i q^{64} +(9.61249 + 12.0958i) q^{65} +26.5276i q^{69} +(8.31239 + 0.950894i) q^{70} -15.2250 q^{71} +(-9.48331 - 9.48331i) q^{72} +(-11.8047 + 7.36149i) q^{75} +4.82012 q^{76} +(-19.2250 + 19.2250i) q^{78} +8.25834i q^{79} +(1.01655 - 8.88632i) q^{80} +0.741657 q^{81} +(-12.2473 + 12.2473i) q^{83} +14.7230i q^{84} +(-9.32894 - 11.7390i) q^{90} +18.2809 q^{91} +(-13.4833 - 13.4833i) q^{92} +(5.35414 + 0.612486i) q^{95} +15.7395 q^{96} +(7.00000 - 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{2} + 16q^{8} + O(q^{10}) \) \( 8q - 8q^{2} + 16q^{8} + 16q^{15} - 32q^{16} - 8q^{18} - 24q^{23} - 24q^{25} + 8q^{30} + 32q^{32} + 16q^{36} + 48q^{46} - 8q^{57} - 48q^{60} + 56q^{63} + 32q^{65} - 32q^{71} - 16q^{72} - 64q^{78} - 24q^{81} - 48q^{92} - 32q^{95} + 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.707107 0.707107i
\(3\) 1.96744 1.96744i 1.13590 1.13590i 0.146726 0.989177i \(-0.453126\pi\)
0.989177 0.146726i \(-0.0468736\pi\)
\(4\) 2.00000i 1.00000i
\(5\) −0.254137 + 2.22158i −0.113654 + 0.993520i
\(6\) −3.93488 −1.60641
\(7\) 1.87083 + 1.87083i 0.707107 + 0.707107i
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) 4.74166i 1.58055i
\(10\) 2.47572 1.96744i 0.782890 0.622160i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 3.93488 + 3.93488i 1.13590 + 1.13590i
\(13\) 4.88578 4.88578i 1.35507 1.35507i 0.475185 0.879886i \(-0.342381\pi\)
0.879886 0.475185i \(-0.157619\pi\)
\(14\) 3.74166i 1.00000i
\(15\) 3.87083 + 4.87083i 0.999444 + 1.25764i
\(16\) −4.00000 −1.00000
\(17\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) −4.74166 + 4.74166i −1.11762 + 1.11762i
\(19\) 2.41006i 0.552906i −0.961027 0.276453i \(-0.910841\pi\)
0.961027 0.276453i \(-0.0891590\pi\)
\(20\) −4.44316 0.508274i −0.993520 0.113654i
\(21\) 7.36149 1.60641
\(22\) 0 0
\(23\) −6.74166 + 6.74166i −1.40573 + 1.40573i −0.625543 + 0.780189i \(0.715123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 7.86977i 1.60641i
\(25\) −4.87083 1.12917i −0.974166 0.225834i
\(26\) −9.77156 −1.91636
\(27\) −3.42661 3.42661i −0.659451 0.659451i
\(28\) −3.74166 + 3.74166i −0.707107 + 0.707107i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 1.00000 8.74166i 0.182574 1.59600i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 4.00000 + 4.00000i 0.707107 + 0.707107i
\(33\) 0 0
\(34\) 0 0
\(35\) −4.63164 + 3.68075i −0.782890 + 0.622160i
\(36\) 9.48331 1.58055
\(37\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) −2.41006 + 2.41006i −0.390964 + 0.390964i
\(39\) 19.2250i 3.07846i
\(40\) 3.93488 + 4.95143i 0.622160 + 0.782890i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) −7.36149 7.36149i −1.13590 1.13590i
\(43\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) 0 0
\(45\) 10.5340 + 1.20503i 1.57031 + 0.179635i
\(46\) 13.4833 1.98801
\(47\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(48\) −7.86977 + 7.86977i −1.13590 + 1.13590i
\(49\) 7.00000i 1.00000i
\(50\) 3.74166 + 6.00000i 0.529150 + 0.848528i
\(51\) 0 0
\(52\) 9.77156 + 9.77156i 1.35507 + 1.35507i
\(53\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(54\) 6.85322i 0.932605i
\(55\) 0 0
\(56\) 7.48331 1.00000
\(57\) −4.74166 4.74166i −0.628048 0.628048i
\(58\) 0 0
\(59\) 10.4111i 1.35541i −0.735332 0.677707i \(-0.762974\pi\)
0.735332 0.677707i \(-0.237026\pi\)
\(60\) −9.74166 + 7.74166i −1.25764 + 0.999444i
\(61\) −6.47626 −0.829199 −0.414600 0.910004i \(-0.636078\pi\)
−0.414600 + 0.910004i \(0.636078\pi\)
\(62\) 0 0
\(63\) 8.87083 8.87083i 1.11762 1.11762i
\(64\) 8.00000i 1.00000i
\(65\) 9.61249 + 12.0958i 1.19228 + 1.50030i
\(66\) 0 0
\(67\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(68\) 0 0
\(69\) 26.5276i 3.19355i
\(70\) 8.31239 + 0.950894i 0.993520 + 0.113654i
\(71\) −15.2250 −1.80687 −0.903436 0.428723i \(-0.858964\pi\)
−0.903436 + 0.428723i \(0.858964\pi\)
\(72\) −9.48331 9.48331i −1.11762 1.11762i
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) 0 0
\(75\) −11.8047 + 7.36149i −1.36308 + 0.850032i
\(76\) 4.82012 0.552906
\(77\) 0 0
\(78\) −19.2250 + 19.2250i −2.17680 + 2.17680i
\(79\) 8.25834i 0.929136i 0.885537 + 0.464568i \(0.153790\pi\)
−0.885537 + 0.464568i \(0.846210\pi\)
\(80\) 1.01655 8.88632i 0.113654 0.993520i
\(81\) 0.741657 0.0824064
\(82\) 0 0
\(83\) −12.2473 + 12.2473i −1.34431 + 1.34431i −0.452598 + 0.891715i \(0.649503\pi\)
−0.891715 + 0.452598i \(0.850497\pi\)
\(84\) 14.7230i 1.60641i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −9.32894 11.7390i −0.983356 1.23740i
\(91\) 18.2809 1.91636
\(92\) −13.4833 13.4833i −1.40573 1.40573i
\(93\) 0 0
\(94\) 0 0
\(95\) 5.35414 + 0.612486i 0.549324 + 0.0628397i
\(96\) 15.7395 1.60641
\(97\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(98\) 7.00000 7.00000i 0.707107 0.707107i
\(99\) 0 0
\(100\) 2.25834 9.74166i 0.225834 0.974166i
\(101\) −1.39351 −0.138660 −0.0693299 0.997594i \(-0.522086\pi\)
−0.0693299 + 0.997594i \(0.522086\pi\)
\(102\) 0 0
\(103\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) 19.5431i 1.91636i
\(105\) −1.87083 + 16.3541i −0.182574 + 1.59600i
\(106\) 0 0
\(107\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(108\) 6.85322 6.85322i 0.659451 0.659451i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −7.48331 7.48331i −0.707107 0.707107i
\(113\) 11.2250 11.2250i 1.05596 1.05596i 0.0576178 0.998339i \(-0.481650\pi\)
0.998339 0.0576178i \(-0.0183505\pi\)
\(114\) 9.48331i 0.888194i
\(115\) −13.2638 16.6904i −1.23686 1.55639i
\(116\) 0 0
\(117\) −23.1667 23.1667i −2.14176 2.14176i
\(118\) −10.4111 + 10.4111i −0.958423 + 0.958423i
\(119\) 0 0
\(120\) 17.4833 + 2.00000i 1.59600 + 0.182574i
\(121\) 11.0000 1.00000
\(122\) 6.47626 + 6.47626i 0.586333 + 0.586333i
\(123\) 0 0
\(124\) 0 0
\(125\) 3.74640 10.5340i 0.335088 0.942187i
\(126\) −17.7417 −1.58055
\(127\) 10.2250 + 10.2250i 0.907320 + 0.907320i 0.996055 0.0887357i \(-0.0282826\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) −8.00000 + 8.00000i −0.707107 + 0.707107i
\(129\) 0 0
\(130\) 2.48331 21.7083i 0.217801 1.90394i
\(131\) −12.3129 −1.07579 −0.537893 0.843013i \(-0.680779\pi\)
−0.537893 + 0.843013i \(0.680779\pi\)
\(132\) 0 0
\(133\) 4.50881 4.50881i 0.390964 0.390964i
\(134\) 0 0
\(135\) 8.48331 6.74166i 0.730127 0.580229i
\(136\) 0 0
\(137\) 1.51669 + 1.51669i 0.129579 + 0.129579i 0.768922 0.639343i \(-0.220793\pi\)
−0.639343 + 0.768922i \(0.720793\pi\)
\(138\) 26.5276 26.5276i 2.25818 2.25818i
\(139\) 5.32840i 0.451949i −0.974133 0.225974i \(-0.927443\pi\)
0.974133 0.225974i \(-0.0725566\pi\)
\(140\) −7.36149 9.26328i −0.622160 0.782890i
\(141\) 0 0
\(142\) 15.2250 + 15.2250i 1.27765 + 1.27765i
\(143\) 0 0
\(144\) 18.9666i 1.58055i
\(145\) 0 0
\(146\) 0 0
\(147\) 13.7721 + 13.7721i 1.13590 + 1.13590i
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 19.1661 + 4.44316i 1.56491 + 0.362782i
\(151\) −22.4499 −1.82695 −0.913475 0.406894i \(-0.866612\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) −4.82012 4.82012i −0.390964 0.390964i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 38.4499 3.07846
\(157\) 16.3135 + 16.3135i 1.30196 + 1.30196i 0.927071 + 0.374885i \(0.122318\pi\)
0.374885 + 0.927071i \(0.377682\pi\)
\(158\) 8.25834 8.25834i 0.656998 0.656998i
\(159\) 0 0
\(160\) −9.90287 + 7.86977i −0.782890 + 0.622160i
\(161\) −25.2250 −1.98801
\(162\) −0.741657 0.741657i −0.0582701 0.0582701i
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 24.4945 1.90115
\(167\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) 14.7230 14.7230i 1.13590 1.13590i
\(169\) 34.7417i 2.67244i
\(170\) 0 0
\(171\) −11.4277 −0.873897
\(172\) 0 0
\(173\) −0.573929 + 0.573929i −0.0436350 + 0.0436350i −0.728588 0.684953i \(-0.759823\pi\)
0.684953 + 0.728588i \(0.259823\pi\)
\(174\) 0 0
\(175\) −7.00000 11.2250i −0.529150 0.848528i
\(176\) 0 0
\(177\) −20.4833 20.4833i −1.53962 1.53962i
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −2.41006 + 21.0679i −0.179635 + 1.57031i
\(181\) −26.9046 −1.99980 −0.999902 0.0140098i \(-0.995540\pi\)
−0.999902 + 0.0140098i \(0.995540\pi\)
\(182\) −18.2809 18.2809i −1.35507 1.35507i
\(183\) −12.7417 + 12.7417i −0.941890 + 0.941890i
\(184\) 26.9666i 1.98801i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 12.8212i 0.932605i
\(190\) −4.74166 5.96663i −0.343996 0.432865i
\(191\) 4.77503 0.345509 0.172754 0.984965i \(-0.444733\pi\)
0.172754 + 0.984965i \(0.444733\pi\)
\(192\) −15.7395 15.7395i −1.13590 1.13590i
\(193\) −6.00000 + 6.00000i −0.431889 + 0.431889i −0.889271 0.457381i \(-0.848787\pi\)
0.457381 + 0.889271i \(0.348787\pi\)
\(194\) 0 0
\(195\) 42.7098 + 4.88578i 3.05851 + 0.349878i
\(196\) −14.0000 −1.00000
\(197\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −12.0000 + 7.48331i −0.848528 + 0.529150i
\(201\) 0 0
\(202\) 1.39351 + 1.39351i 0.0980473 + 0.0980473i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 31.9666 + 31.9666i 2.22183 + 2.22183i
\(208\) −19.5431 + 19.5431i −1.35507 + 1.35507i
\(209\) 0 0
\(210\) 18.2250 14.4833i 1.25764 0.999444i
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) −29.9543 + 29.9543i −2.05243 + 2.05243i
\(214\) 0 0
\(215\) 0 0
\(216\) −13.7064 −0.932605
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) 14.9666i 1.00000i
\(225\) −5.35414 + 23.0958i −0.356943 + 1.53972i
\(226\) −22.4499 −1.49335
\(227\) 17.0674 + 17.0674i 1.13280 + 1.13280i 0.989709 + 0.143094i \(0.0457050\pi\)
0.143094 + 0.989709i \(0.454295\pi\)
\(228\) 9.48331 9.48331i 0.628048 0.628048i
\(229\) 30.0856i 1.98811i −0.108880 0.994055i \(-0.534726\pi\)
0.108880 0.994055i \(-0.465274\pi\)
\(230\) −3.42661 + 29.9543i −0.225944 + 1.97512i
\(231\) 0 0
\(232\) 0 0
\(233\) 11.9666 11.9666i 0.783960 0.783960i −0.196537 0.980497i \(-0.562969\pi\)
0.980497 + 0.196537i \(0.0629694\pi\)
\(234\) 46.3334i 3.02891i
\(235\) 0 0
\(236\) 20.8223 1.35541
\(237\) 16.2478 + 16.2478i 1.05541 + 1.05541i
\(238\) 0 0
\(239\) 7.48331i 0.484055i −0.970269 0.242028i \(-0.922188\pi\)
0.970269 0.242028i \(-0.0778125\pi\)
\(240\) −15.4833 19.4833i −0.999444 1.25764i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −11.0000 11.0000i −0.707107 0.707107i
\(243\) 11.7390 11.7390i 0.753057 0.753057i
\(244\) 12.9525i 0.829199i
\(245\) −15.5511 1.77896i −0.993520 0.113654i
\(246\) 0 0
\(247\) −11.7750 11.7750i −0.749227 0.749227i
\(248\) 0 0
\(249\) 48.1916i 3.05402i
\(250\) −14.2804 + 6.78757i −0.903170 + 0.429283i
\(251\) 13.1982 0.833061 0.416530 0.909122i \(-0.363246\pi\)
0.416530 + 0.909122i \(0.363246\pi\)
\(252\) 17.7417 + 17.7417i 1.11762 + 1.11762i
\(253\) 0 0
\(254\) 20.4499i 1.28314i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −24.1916 + 19.2250i −1.50030 + 1.19228i
\(261\) 0 0
\(262\) 12.3129 + 12.3129i 0.760695 + 0.760695i
\(263\) 11.2250 11.2250i 0.692161 0.692161i −0.270546 0.962707i \(-0.587204\pi\)
0.962707 + 0.270546i \(0.0872041\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −9.01763 −0.552906
\(267\) 0 0
\(268\) 0 0
\(269\) 17.0017i 1.03661i −0.855194 0.518307i \(-0.826562\pi\)
0.855194 0.518307i \(-0.173438\pi\)
\(270\) −15.2250 1.74166i −0.926562 0.105994i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 35.9666 35.9666i 2.17680 2.17680i
\(274\) 3.03337i 0.183253i
\(275\) 0 0
\(276\) −53.0553 −3.19355
\(277\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(278\) −5.32840 + 5.32840i −0.319576 + 0.319576i
\(279\) 0 0
\(280\) −1.90179 + 16.6248i −0.113654 + 0.993520i
\(281\) 14.9666 0.892834 0.446417 0.894825i \(-0.352700\pi\)
0.446417 + 0.894825i \(0.352700\pi\)
\(282\) 0 0
\(283\) 2.34441 2.34441i 0.139361 0.139361i −0.633985 0.773345i \(-0.718582\pi\)
0.773345 + 0.633985i \(0.218582\pi\)
\(284\) 30.4499i 1.80687i
\(285\) 11.7390 9.32894i 0.695358 0.552599i
\(286\) 0 0
\(287\) 0 0
\(288\) 18.9666 18.9666i 1.11762 1.11762i
\(289\) 17.0000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 24.1832 24.1832i 1.41280 1.41280i 0.674788 0.738011i \(-0.264235\pi\)
0.738011 0.674788i \(-0.235765\pi\)
\(294\) 27.5442i 1.60641i
\(295\) 23.1292 + 2.64586i 1.34663 + 0.154048i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 65.8765i 3.80974i
\(300\) −14.7230 23.6093i −0.850032 1.36308i
\(301\) 0 0
\(302\) 22.4499 + 22.4499i 1.29185 + 1.29185i
\(303\) −2.74166 + 2.74166i −0.157504 + 0.157504i
\(304\) 9.64025i 0.552906i
\(305\) 1.64586 14.3875i 0.0942415 0.823827i
\(306\) 0 0
\(307\) −17.1987 17.1987i −0.981582 0.981582i 0.0182515 0.999833i \(-0.494190\pi\)
−0.999833 + 0.0182515i \(0.994190\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) −38.4499 38.4499i −2.17680 2.17680i
\(313\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(314\) 32.6269i 1.84124i
\(315\) 17.4528 + 21.9617i 0.983356 + 1.23740i
\(316\) −16.5167 −0.929136
\(317\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 17.7726 + 2.03310i 0.993520 + 0.113654i
\(321\) 0 0
\(322\) 25.2250 + 25.2250i 1.40573 + 1.40573i
\(323\) 0 0
\(324\) 1.48331i 0.0824064i
\(325\) −29.3147 + 18.2809i −1.62609 + 1.01404i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −24.4945 24.4945i −1.34431 1.34431i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −29.4460 −1.60641
\(337\) 18.0000 + 18.0000i 0.980522 + 0.980522i 0.999814 0.0192914i \(-0.00614103\pi\)
−0.0192914 + 0.999814i \(0.506141\pi\)
\(338\) −34.7417 + 34.7417i −1.88970 + 1.88970i
\(339\) 44.1690i 2.39893i
\(340\) 0 0
\(341\) 0 0
\(342\) 11.4277 + 11.4277i 0.617939 + 0.617939i
\(343\) −13.0958 + 13.0958i −0.707107 + 0.707107i
\(344\) 0 0
\(345\) −58.9333 6.74166i −3.17286 0.362959i
\(346\) 1.14786 0.0617092
\(347\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(348\) 0 0
\(349\) 17.2644i 0.924140i 0.886843 + 0.462070i \(0.152893\pi\)
−0.886843 + 0.462070i \(0.847107\pi\)
\(350\) −4.22497 + 18.2250i −0.225834 + 0.974166i
\(351\) −33.4833 −1.78721
\(352\) 0 0
\(353\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(354\) 40.9666i 2.17735i
\(355\) 3.86923 33.8235i 0.205357 1.79516i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.00000i 0.316668i −0.987386 0.158334i \(-0.949388\pi\)
0.987386 0.158334i \(-0.0506123\pi\)
\(360\) 23.4780 18.6579i 1.23740 0.983356i
\(361\) 13.1916 0.694295
\(362\) 26.9046 + 26.9046i 1.41407 + 1.41407i
\(363\) 21.6419 21.6419i 1.13590 1.13590i
\(364\) 36.5618i 1.91636i
\(365\) 0 0
\(366\) 25.4833 1.33203
\(367\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(368\) 26.9666 26.9666i 1.40573 1.40573i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(374\) 0 0
\(375\) −13.3541 28.0958i −0.689605 1.45086i
\(376\) 0 0
\(377\) 0 0
\(378\) −12.8212 + 12.8212i −0.659451 + 0.659451i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) −1.22497 + 10.7083i −0.0628397 + 0.549324i
\(381\) 40.2341 2.06125
\(382\) −4.77503 4.77503i −0.244312 0.244312i
\(383\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(384\) 31.4791i 1.60641i
\(385\) 0 0
\(386\) 12.0000 0.610784
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) −37.8240 47.5956i −1.91529 2.41010i
\(391\) 0 0
\(392\) 14.0000 + 14.0000i 0.707107 + 0.707107i
\(393\) −24.2250 + 24.2250i −1.22199 + 1.22199i
\(394\) 0 0
\(395\) −18.3466 2.09875i −0.923116 0.105600i
\(396\) 0 0
\(397\) −28.1181 28.1181i −1.41121 1.41121i −0.751680 0.659528i \(-0.770756\pi\)
−0.659528 0.751680i \(-0.729244\pi\)
\(398\) 0 0
\(399\) 17.7417i 0.888194i
\(400\) 19.4833 + 4.51669i 0.974166 + 0.225834i
\(401\) 14.7750 0.737830 0.368915 0.929463i \(-0.379729\pi\)
0.368915 + 0.929463i \(0.379729\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 2.78703i 0.138660i
\(405\) −0.188483 + 1.64765i −0.00936578 + 0.0818724i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 5.96798 0.294379
\(412\) 0 0
\(413\) 19.4775 19.4775i 0.958423 0.958423i
\(414\) 63.9333i 3.14215i
\(415\) −24.0958 30.3208i −1.18282 1.48839i
\(416\) 39.0862 1.91636
\(417\) −10.4833 10.4833i −0.513370 0.513370i
\(418\) 0 0
\(419\) 26.7733i 1.30796i 0.756511 + 0.653981i \(0.226902\pi\)
−0.756511 + 0.653981i \(0.773098\pi\)
\(420\) −32.7083 3.74166i −1.59600 0.182574i
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 59.9085 2.90258
\(427\) −12.1160 12.1160i −0.586333 0.586333i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −18.0000 −0.867029 −0.433515 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) 13.7064 + 13.7064i 0.659451 + 0.659451i
\(433\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 16.2478 + 16.2478i 0.777238 + 0.777238i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 33.1916 1.58055
\(442\) 0 0
\(443\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 14.9666 14.9666i 0.707107 0.707107i
\(449\) 29.9333i 1.41264i 0.707894 + 0.706319i \(0.249646\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 28.4499 17.7417i 1.34114 0.836350i
\(451\) 0 0
\(452\) 22.4499 + 22.4499i 1.05596 + 1.05596i
\(453\) −44.1690 + 44.1690i −2.07524 + 2.07524i
\(454\) 34.1348i 1.60203i
\(455\) −4.64586 + 40.6125i −0.217801 + 1.90394i
\(456\) −18.9666 −0.888194
\(457\) 3.74166 + 3.74166i 0.175027 + 0.175027i 0.789184 0.614157i \(-0.210504\pi\)
−0.614157 + 0.789184i \(0.710504\pi\)
\(458\) −30.0856 + 30.0856i −1.40581 + 1.40581i
\(459\) 0 0
\(460\) 33.3809 26.5276i 1.55639 1.23686i
\(461\) 41.6276 1.93879 0.969395 0.245505i \(-0.0789539\pi\)
0.969395 + 0.245505i \(0.0789539\pi\)
\(462\) 0 0
\(463\) 24.0000 24.0000i 1.11537 1.11537i 0.122963 0.992411i \(-0.460760\pi\)
0.992411 0.122963i \(-0.0392398\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −23.9333 −1.10869
\(467\) 18.8548 + 18.8548i 0.872498 + 0.872498i 0.992744 0.120246i \(-0.0383684\pi\)
−0.120246 + 0.992744i \(0.538368\pi\)
\(468\) 46.3334 46.3334i 2.14176 2.14176i
\(469\) 0 0
\(470\) 0 0
\(471\) 64.1916 2.95779
\(472\) −20.8223 20.8223i −0.958423 0.958423i
\(473\) 0 0
\(474\) 32.4956i 1.49257i
\(475\) −2.72137 + 11.7390i −0.124865 + 0.538622i
\(476\) 0 0
\(477\) 0 0
\(478\) −7.48331 + 7.48331i −0.342279 + 0.342279i
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) −4.00000 + 34.9666i −0.182574 + 1.59600i
\(481\) 0 0
\(482\) 0 0
\(483\) −49.6287 + 49.6287i −2.25818 + 2.25818i
\(484\) 22.0000i 1.00000i
\(485\) 0 0
\(486\) −23.4780 −1.06498
\(487\) 30.2250 + 30.2250i 1.36962 + 1.36962i 0.860972 + 0.508652i \(0.169856\pi\)
0.508652 + 0.860972i \(0.330144\pi\)
\(488\) −12.9525 + 12.9525i −0.586333 + 0.586333i
\(489\) 0 0
\(490\) 13.7721 + 17.3300i 0.622160 + 0.782890i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 23.5501i 1.05957i
\(495\) 0 0
\(496\) 0 0
\(497\) −28.4833 28.4833i −1.27765 1.27765i
\(498\) 48.1916 48.1916i 2.15952 2.15952i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 21.0679 + 7.49280i 0.942187 + 0.335088i
\(501\) 0 0
\(502\) −13.1982 13.1982i −0.589063 0.589063i
\(503\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) 35.4833i 1.58055i
\(505\) 0.354143 3.09580i 0.0157592 0.137761i
\(506\) 0 0
\(507\) −68.3522 68.3522i −3.03563 3.03563i
\(508\) −20.4499 + 20.4499i −0.907320 + 0.907320i
\(509\) 25.0028i 1.10823i −0.832440 0.554115i \(-0.813057\pi\)
0.832440 0.554115i \(-0.186943\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) −8.25834 + 8.25834i −0.364615 + 0.364615i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 2.25834i 0.0991302i
\(520\) 43.4166 + 4.96663i 1.90394 + 0.217801i
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 26.7246 26.7246i 1.16859 1.16859i 0.186044 0.982541i \(-0.440433\pi\)
0.982541 0.186044i \(-0.0595667\pi\)
\(524\) 24.6259i 1.07579i
\(525\) −35.8566 8.31239i −1.56491 0.362782i
\(526\) −22.4499 −0.978864
\(527\) 0 0
\(528\) 0 0
\(529\) 67.8999i 2.95217i
\(530\) 0 0
\(531\) −49.3661 −2.14230
\(532\) 9.01763 + 9.01763i 0.390964 + 0.390964i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −17.0017 + 17.0017i −0.732997 + 0.732997i
\(539\) 0 0
\(540\) 13.4833 + 16.9666i 0.580229 + 0.730127i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −52.9333 + 52.9333i −2.27158 + 2.27158i
\(544\) 0 0
\(545\) 0 0
\(546\) −71.9333 −3.07846
\(547\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(548\) −3.03337 + 3.03337i −0.129579 + 0.129579i
\(549\) 30.7082i 1.31059i
\(550\) 0 0
\(551\) 0 0
\(552\) 53.0553 + 53.0553i 2.25818 + 2.25818i
\(553\) −15.4499 + 15.4499i −0.656998 + 0.656998i
\(554\) 0 0
\(555\) 0 0
\(556\) 10.6568 0.451949
\(557\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 18.5266 14.7230i 0.782890 0.622160i
\(561\) 0 0
\(562\) −14.9666 14.9666i −0.631329 0.631329i
\(563\) 7.05018 7.05018i 0.297130 0.297130i −0.542759 0.839889i \(-0.682620\pi\)
0.839889 + 0.542759i \(0.182620\pi\)
\(564\) 0 0
\(565\) 22.0845 + 27.7898i 0.929101 + 1.16913i
\(566\) −4.68881 −0.197086
\(567\) 1.38751 + 1.38751i 0.0582701 + 0.0582701i
\(568\) −30.4499 + 30.4499i −1.27765 + 1.27765i
\(569\) 35.6749i 1.49557i 0.663941 + 0.747785i \(0.268883\pi\)
−0.663941 + 0.747785i \(0.731117\pi\)
\(570\) −21.0679 2.41006i −0.882439 0.100946i
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 9.39459 9.39459i 0.392465 0.392465i
\(574\) 0 0
\(575\) 40.4499 25.2250i 1.68688 1.05195i
\(576\) −37.9333 −1.58055
\(577\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(578\) 17.0000 17.0000i 0.707107 0.707107i
\(579\) 23.6093i 0.981169i
\(580\) 0 0
\(581\) −45.8251 −1.90115
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 57.3541 45.5791i 2.37130 1.88446i
\(586\) −48.3665 −1.99800
\(587\) −30.6595 30.6595i −1.26545 1.26545i −0.948412 0.317041i \(-0.897311\pi\)
−0.317041 0.948412i \(-0.602689\pi\)
\(588\) −27.5442 + 27.5442i −1.13590 + 1.13590i
\(589\) 0 0
\(590\) −20.4833 25.7750i −0.843285 1.06114i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 65.8765 65.8765i 2.69389 2.69389i
\(599\) 25.6749i 1.04905i 0.851395 + 0.524524i \(0.175757\pi\)
−0.851395 + 0.524524i \(0.824243\pi\)
\(600\) −8.88632 + 38.3323i −0.362782 + 1.56491i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 44.8999i 1.82695i
\(605\) −2.79551 + 24.4374i −0.113654 + 0.993520i
\(606\) 5.48331 0.222744
\(607\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(608\) 9.64025 9.64025i 0.390964 0.390964i
\(609\) 0 0
\(610\) −16.0334 + 12.7417i −0.649172 + 0.515895i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(614\) 34.3974i 1.38817i
\(615\) 0 0
\(616\) 0 0
\(617\) −33.6749 33.6749i −1.35570 1.35570i −0.879143 0.476558i \(-0.841884\pi\)
−0.476558 0.879143i \(-0.658116\pi\)
\(618\) 0 0
\(619\) 28.9377i 1.16310i 0.813509 + 0.581552i \(0.197554\pi\)
−0.813509 + 0.581552i \(0.802446\pi\)
\(620\) 0 0
\(621\) 46.2021 1.85402
\(622\) 0 0
\(623\) 0 0
\(624\) 76.8999i 3.07846i
\(625\) 22.4499 + 11.0000i 0.897998 + 0.440000i
\(626\) 0 0
\(627\) 0 0
\(628\) −32.6269 + 32.6269i −1.30196 + 1.30196i
\(629\) 0 0
\(630\) 4.50881 39.4145i 0.179635 1.57031i
\(631\) 2.19160 0.0872463 0.0436231 0.999048i \(-0.486110\pi\)
0.0436231 + 0.999048i \(0.486110\pi\)
\(632\) 16.5167 + 16.5167i 0.656998 + 0.656998i
\(633\) 0 0
\(634\) 0 0
\(635\) −25.3141 + 20.1170i −1.00456 + 0.798320i
\(636\) 0 0
\(637\) 34.2004 + 34.2004i 1.35507 + 1.35507i
\(638\) 0 0
\(639\) 72.1916i 2.85586i
\(640\) −15.7395 19.8057i −0.622160 0.782890i
\(641\) −45.2250 −1.78628 −0.893140 0.449780i \(-0.851502\pi\)
−0.893140 + 0.449780i \(0.851502\pi\)
\(642\) 0 0
\(643\) −3.11530 + 3.11530i −0.122855 + 0.122855i −0.765861 0.643006i \(-0.777687\pi\)
0.643006 + 0.765861i \(0.277687\pi\)
\(644\) 50.4499i 1.98801i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(648\) 1.48331 1.48331i 0.0582701 0.0582701i
\(649\) 0 0
\(650\) 47.5956 + 11.0338i 1.86685 + 0.432780i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(654\) 0 0
\(655\) 3.12917 27.3541i 0.122267 1.06881i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 12.4442 0.484025 0.242012 0.970273i \(-0.422193\pi\)
0.242012 + 0.970273i \(0.422193\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 48.9891i 1.90115i
\(665\) 8.87083 + 11.1625i 0.343996 + 0.432865i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 29.4460 + 29.4460i 1.13590 + 1.13590i
\(673\) −35.4499 + 35.4499i −1.36649 + 1.36649i −0.501113 + 0.865382i \(0.667076\pi\)
−0.865382 + 0.501113i \(0.832924\pi\)
\(674\) 36.0000i 1.38667i
\(675\) 12.8212 + 20.5597i 0.493488 + 0.791342i
\(676\) 69.4833 2.67244
\(677\) 35.9879 + 35.9879i 1.38313 + 1.38313i 0.839008 + 0.544119i \(0.183136\pi\)
0.544119 + 0.839008i \(0.316864\pi\)
\(678\) −44.1690 + 44.1690i −1.69630 + 1.69630i
\(679\) 0 0
\(680\) 0 0
\(681\) 67.1582 2.57351
\(682\) 0 0
\(683\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(684\) 22.8554i 0.873897i
\(685\) −3.75488 + 2.98399i −0.143467 + 0.114012i
\(686\) 26.1916 1.00000
\(687\) −59.1916 59.1916i −2.25830 2.25830i
\(688\) 0 0
\(689\) 0 0
\(690\) 52.1916 + 65.6749i 1.98690 + 2.50020i
\(691\) −46.5790 −1.77195 −0.885975 0.463733i \(-0.846510\pi\)
−0.885975 + 0.463733i \(0.846510\pi\)
\(692\) −1.14786 1.14786i −0.0436350 0.0436350i
\(693\) 0 0
\(694\) 0 0
\(695\) 11.8375 + 1.35414i 0.449020 + 0.0513656i
\(696\) 0 0
\(697\) 0 0
\(698\) 17.2644 17.2644i 0.653466 0.653466i
\(699\) 47.0873i 1.78101i
\(700\) 22.4499 14.0000i 0.848528 0.529150i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 33.4833 + 33.4833i 1.26375 + 1.26375i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.60703 2.60703i −0.0980473 0.0980473i
\(708\) 40.9666 40.9666i 1.53962 1.53962i
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) −37.6927 + 29.9543i −1.41458 + 1.12416i
\(711\) 39.1582 1.46855
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −14.7230 14.7230i −0.549840 0.549840i
\(718\) −6.00000 + 6.00000i −0.223918 + 0.223918i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) −42.1359 4.82012i −1.57031 0.179635i
\(721\) 0 0
\(722\) −13.1916 13.1916i −0.490941 0.490941i
\(723\) 0 0
\(724\) 53.8092i 1.99980i
\(725\) 0 0
\(726\) −43.2837 −1.60641
\(727\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(728\) 36.5618 36.5618i 1.35507 1.35507i
\(729\) 43.9666i 1.62839i
\(730\) 0 0
\(731\) 0 0
\(732\) −25.4833 25.4833i −0.941890 0.941890i
\(733\) 19.1005 19.1005i 0.705493 0.705493i −0.260091 0.965584i \(-0.583753\pi\)
0.965584 + 0.260091i \(0.0837526\pi\)
\(734\) 0 0
\(735\) −34.0958 + 27.0958i −1.25764 + 0.999444i
\(736\) −53.9333 −1.98801
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) −46.3334 −1.70210
\(742\) 0 0
\(743\) 23.2583 23.2583i 0.853266 0.853266i −0.137268 0.990534i \(-0.543832\pi\)
0.990534 + 0.137268i \(0.0438322\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 58.0724 + 58.0724i 2.12476 + 2.12476i
\(748\) 0 0
\(749\) 0 0
\(750\) −14.7417 + 41.4499i −0.538289 + 1.51354i
\(751\) −22.4499 −0.819210 −0.409605 0.912263i \(-0.634333\pi\)
−0.409605 + 0.912263i \(0.634333\pi\)
\(752\) 0 0
\(753\) 25.9666 25.9666i 0.946277 0.946277i
\(754\) 0 0
\(755\) 5.70536 49.8743i 0.207639 1.81511i
\(756\) 25.6424 0.932605
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 11.9333 9.48331i 0.432865 0.343996i
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) −40.2341 40.2341i −1.45753 1.45753i
\(763\) 0 0
\(764\) 9.55006i 0.345509i
\(765\) 0 0
\(766\) 0 0
\(767\) −50.8665 50.8665i −1.83668 1.83668i
\(768\) 31.4791 31.4791i 1.13590 1.13590i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −12.0000 12.0000i −0.431889 0.431889i
\(773\) 39.1519 39.1519i 1.40820 1.40820i 0.638932 0.769263i \(-0.279376\pi\)
0.769263 0.638932i \(-0.220624\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −9.77156 + 85.4196i −0.349878 + 3.05851i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 28.0000i 1.00000i
\(785\) −40.3875 + 32.0958i −1.44149 + 1.14555i
\(786\) 48.4499 1.72815
\(787\) 38.5293 + 38.5293i 1.37342 + 1.37342i 0.855321 + 0.518099i \(0.173360\pi\)
0.518099 + 0.855321i \(0.326640\pi\)
\(788\) 0 0
\(789\) 44.1690i 1.57246i
\(790\) 16.2478 + 20.4453i 0.578071 + 0.727412i
\(791\) 42.0000 1.49335
\(792\) 0 0
\(793\) −31.6415 + 31.6415i −1.12362 + 1.12362i
\(794\) 56.2362i 1.99575i
\(795\) 0 0
\(796\) 0 0
\(797\) −34.3318 34.3318i −1.21609 1.21609i