Properties

Label 912.3.be.f.145.1
Level $912$
Weight $3$
Character 912.145
Analytic conductor $24.850$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 912.be (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.8502001097\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.92607408.1
Defining polynomial: \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 145.1
Root \(0.500000 + 2.93068i\) of defining polynomial
Character \(\chi\) \(=\) 912.145
Dual form 912.3.be.f.673.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{3} +(-3.20750 - 5.55555i) q^{5} +2.26281 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{3} +(-3.20750 - 5.55555i) q^{5} +2.26281 q^{7} +(1.50000 - 2.59808i) q^{9} +20.0928 q^{11} +(-0.135471 - 0.0782143i) q^{13} +(-9.62250 - 5.55555i) q^{15} +(12.3133 + 21.3272i) q^{17} +(18.9317 + 1.60945i) q^{19} +(3.39422 - 1.95965i) q^{21} +(2.62250 - 4.54230i) q^{23} +(-8.07609 + 13.9882i) q^{25} -5.19615i q^{27} +(-31.4573 - 18.1619i) q^{29} +17.1105i q^{31} +(30.1392 - 17.4009i) q^{33} +(-7.25797 - 12.5712i) q^{35} -42.7124i q^{37} -0.270942 q^{39} +(30.0928 - 17.3741i) q^{41} +(-12.5553 - 21.7464i) q^{43} -19.2450 q^{45} +(14.6778 - 25.4227i) q^{47} -43.8797 q^{49} +(36.9398 + 21.3272i) q^{51} +(48.4176 + 27.9539i) q^{53} +(-64.4476 - 111.627i) q^{55} +(29.7914 - 13.9812i) q^{57} +(29.9269 - 17.2783i) q^{59} +(27.3805 - 47.4244i) q^{61} +(3.39422 - 5.87896i) q^{63} +1.00349i q^{65} +(-66.0698 - 38.1454i) q^{67} -9.08459i q^{69} +(-63.6080 + 36.7241i) q^{71} +(-45.9053 - 79.5103i) q^{73} +27.9764i q^{75} +45.4662 q^{77} +(53.1300 - 30.6746i) q^{79} +(-4.50000 - 7.79423i) q^{81} +148.793 q^{83} +(78.9897 - 136.814i) q^{85} -62.9147 q^{87} +(-62.7829 - 36.2477i) q^{89} +(-0.306546 - 0.176984i) q^{91} +(14.8181 + 25.6657i) q^{93} +(-51.7820 - 110.338i) q^{95} +(-70.0326 + 40.4334i) q^{97} +(30.1392 - 52.2026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 9 q^{3} + 4 q^{5} + 22 q^{7} + 9 q^{9} + 36 q^{11} - 3 q^{13} + 12 q^{15} + 38 q^{17} + 10 q^{19} + 33 q^{21} - 54 q^{23} - 21 q^{25} - 102 q^{29} + 54 q^{33} + 24 q^{35} - 6 q^{39} + 96 q^{41} - 107 q^{43} + 24 q^{45} + 50 q^{47} - 48 q^{49} + 114 q^{51} - 90 q^{53} - 148 q^{55} - 3 q^{57} + 27 q^{61} + 33 q^{63} + 39 q^{67} - 84 q^{71} - 77 q^{73} + 260 q^{77} - 9 q^{79} - 27 q^{81} + 348 q^{83} + 68 q^{85} - 204 q^{87} - 72 q^{89} + 393 q^{91} + 129 q^{93} - 104 q^{95} - 228 q^{97} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 0.866025i 0.500000 0.288675i
\(4\) 0 0
\(5\) −3.20750 5.55555i −0.641500 1.11111i −0.985098 0.171993i \(-0.944979\pi\)
0.343598 0.939117i \(-0.388354\pi\)
\(6\) 0 0
\(7\) 2.26281 0.323259 0.161629 0.986852i \(-0.448325\pi\)
0.161629 + 0.986852i \(0.448325\pi\)
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) 0 0
\(11\) 20.0928 1.82662 0.913309 0.407267i \(-0.133518\pi\)
0.913309 + 0.407267i \(0.133518\pi\)
\(12\) 0 0
\(13\) −0.135471 0.0782143i −0.0104209 0.00601649i 0.494781 0.869018i \(-0.335248\pi\)
−0.505201 + 0.863001i \(0.668582\pi\)
\(14\) 0 0
\(15\) −9.62250 5.55555i −0.641500 0.370370i
\(16\) 0 0
\(17\) 12.3133 + 21.3272i 0.724311 + 1.25454i 0.959257 + 0.282534i \(0.0911752\pi\)
−0.234947 + 0.972008i \(0.575492\pi\)
\(18\) 0 0
\(19\) 18.9317 + 1.60945i 0.996406 + 0.0847081i
\(20\) 0 0
\(21\) 3.39422 1.95965i 0.161629 0.0933168i
\(22\) 0 0
\(23\) 2.62250 4.54230i 0.114022 0.197491i −0.803367 0.595485i \(-0.796960\pi\)
0.917388 + 0.397994i \(0.130293\pi\)
\(24\) 0 0
\(25\) −8.07609 + 13.9882i −0.323044 + 0.559528i
\(26\) 0 0
\(27\) 5.19615i 0.192450i
\(28\) 0 0
\(29\) −31.4573 18.1619i −1.08474 0.626272i −0.152566 0.988293i \(-0.548754\pi\)
−0.932170 + 0.362021i \(0.882087\pi\)
\(30\) 0 0
\(31\) 17.1105i 0.551952i 0.961165 + 0.275976i \(0.0890010\pi\)
−0.961165 + 0.275976i \(0.910999\pi\)
\(32\) 0 0
\(33\) 30.1392 17.4009i 0.913309 0.527299i
\(34\) 0 0
\(35\) −7.25797 12.5712i −0.207370 0.359176i
\(36\) 0 0
\(37\) 42.7124i 1.15439i −0.816607 0.577194i \(-0.804148\pi\)
0.816607 0.577194i \(-0.195852\pi\)
\(38\) 0 0
\(39\) −0.270942 −0.00694724
\(40\) 0 0
\(41\) 30.0928 17.3741i 0.733971 0.423758i −0.0859022 0.996304i \(-0.527377\pi\)
0.819873 + 0.572545i \(0.194044\pi\)
\(42\) 0 0
\(43\) −12.5553 21.7464i −0.291984 0.505731i 0.682295 0.731077i \(-0.260982\pi\)
−0.974279 + 0.225346i \(0.927649\pi\)
\(44\) 0 0
\(45\) −19.2450 −0.427666
\(46\) 0 0
\(47\) 14.6778 25.4227i 0.312294 0.540909i −0.666565 0.745447i \(-0.732236\pi\)
0.978859 + 0.204538i \(0.0655693\pi\)
\(48\) 0 0
\(49\) −43.8797 −0.895504
\(50\) 0 0
\(51\) 36.9398 + 21.3272i 0.724311 + 0.418181i
\(52\) 0 0
\(53\) 48.4176 + 27.9539i 0.913540 + 0.527433i 0.881568 0.472056i \(-0.156488\pi\)
0.0319716 + 0.999489i \(0.489821\pi\)
\(54\) 0 0
\(55\) −64.4476 111.627i −1.17178 2.02957i
\(56\) 0 0
\(57\) 29.7914 13.9812i 0.522656 0.245284i
\(58\) 0 0
\(59\) 29.9269 17.2783i 0.507235 0.292852i −0.224461 0.974483i \(-0.572062\pi\)
0.731696 + 0.681631i \(0.238729\pi\)
\(60\) 0 0
\(61\) 27.3805 47.4244i 0.448860 0.777448i −0.549452 0.835525i \(-0.685164\pi\)
0.998312 + 0.0580769i \(0.0184968\pi\)
\(62\) 0 0
\(63\) 3.39422 5.87896i 0.0538765 0.0933168i
\(64\) 0 0
\(65\) 1.00349i 0.0154383i
\(66\) 0 0
\(67\) −66.0698 38.1454i −0.986117 0.569335i −0.0820054 0.996632i \(-0.526132\pi\)
−0.904111 + 0.427297i \(0.859466\pi\)
\(68\) 0 0
\(69\) 9.08459i 0.131661i
\(70\) 0 0
\(71\) −63.6080 + 36.7241i −0.895887 + 0.517240i −0.875863 0.482559i \(-0.839707\pi\)
−0.0200233 + 0.999800i \(0.506374\pi\)
\(72\) 0 0
\(73\) −45.9053 79.5103i −0.628840 1.08918i −0.987785 0.155824i \(-0.950197\pi\)
0.358945 0.933359i \(-0.383137\pi\)
\(74\) 0 0
\(75\) 27.9764i 0.373019i
\(76\) 0 0
\(77\) 45.4662 0.590471
\(78\) 0 0
\(79\) 53.1300 30.6746i 0.672531 0.388286i −0.124504 0.992219i \(-0.539734\pi\)
0.797035 + 0.603933i \(0.206401\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 148.793 1.79268 0.896342 0.443363i \(-0.146215\pi\)
0.896342 + 0.443363i \(0.146215\pi\)
\(84\) 0 0
\(85\) 78.9897 136.814i 0.929290 1.60958i
\(86\) 0 0
\(87\) −62.9147 −0.723157
\(88\) 0 0
\(89\) −62.7829 36.2477i −0.705426 0.407278i 0.103939 0.994584i \(-0.466855\pi\)
−0.809365 + 0.587306i \(0.800189\pi\)
\(90\) 0 0
\(91\) −0.306546 0.176984i −0.00336864 0.00194488i
\(92\) 0 0
\(93\) 14.8181 + 25.6657i 0.159335 + 0.275976i
\(94\) 0 0
\(95\) −51.7820 110.338i −0.545074 1.16146i
\(96\) 0 0
\(97\) −70.0326 + 40.4334i −0.721986 + 0.416839i −0.815483 0.578781i \(-0.803529\pi\)
0.0934972 + 0.995620i \(0.470195\pi\)
\(98\) 0 0
\(99\) 30.1392 52.2026i 0.304436 0.527299i
\(100\) 0 0
\(101\) −76.6770 + 132.809i −0.759178 + 1.31494i 0.184092 + 0.982909i \(0.441066\pi\)
−0.943270 + 0.332027i \(0.892268\pi\)
\(102\) 0 0
\(103\) 168.948i 1.64027i 0.572169 + 0.820136i \(0.306102\pi\)
−0.572169 + 0.820136i \(0.693898\pi\)
\(104\) 0 0
\(105\) −21.7739 12.5712i −0.207370 0.119725i
\(106\) 0 0
\(107\) 139.060i 1.29963i 0.760093 + 0.649815i \(0.225154\pi\)
−0.760093 + 0.649815i \(0.774846\pi\)
\(108\) 0 0
\(109\) −9.15888 + 5.28788i −0.0840264 + 0.0485127i −0.541424 0.840749i \(-0.682115\pi\)
0.457398 + 0.889262i \(0.348781\pi\)
\(110\) 0 0
\(111\) −36.9900 64.0685i −0.333243 0.577194i
\(112\) 0 0
\(113\) 69.1581i 0.612018i 0.952029 + 0.306009i \(0.0989938\pi\)
−0.952029 + 0.306009i \(0.901006\pi\)
\(114\) 0 0
\(115\) −33.6466 −0.292579
\(116\) 0 0
\(117\) −0.406413 + 0.234643i −0.00347362 + 0.00200550i
\(118\) 0 0
\(119\) 27.8626 + 48.2595i 0.234140 + 0.405542i
\(120\) 0 0
\(121\) 282.721 2.33654
\(122\) 0 0
\(123\) 30.0928 52.1223i 0.244657 0.423758i
\(124\) 0 0
\(125\) −56.7587 −0.454070
\(126\) 0 0
\(127\) 25.6547 + 14.8118i 0.202006 + 0.116628i 0.597591 0.801801i \(-0.296125\pi\)
−0.395585 + 0.918429i \(0.629458\pi\)
\(128\) 0 0
\(129\) −37.6659 21.7464i −0.291984 0.168577i
\(130\) 0 0
\(131\) 28.6526 + 49.6278i 0.218722 + 0.378838i 0.954418 0.298474i \(-0.0964777\pi\)
−0.735695 + 0.677313i \(0.763144\pi\)
\(132\) 0 0
\(133\) 42.8389 + 3.64189i 0.322097 + 0.0273826i
\(134\) 0 0
\(135\) −28.8675 + 16.6667i −0.213833 + 0.123457i
\(136\) 0 0
\(137\) 47.4499 82.1856i 0.346349 0.599895i −0.639249 0.769000i \(-0.720755\pi\)
0.985598 + 0.169105i \(0.0540879\pi\)
\(138\) 0 0
\(139\) 91.2747 158.092i 0.656652 1.13736i −0.324824 0.945774i \(-0.605305\pi\)
0.981477 0.191581i \(-0.0613614\pi\)
\(140\) 0 0
\(141\) 50.8454i 0.360606i
\(142\) 0 0
\(143\) −2.72200 1.57155i −0.0190349 0.0109898i
\(144\) 0 0
\(145\) 233.017i 1.60701i
\(146\) 0 0
\(147\) −65.8195 + 38.0009i −0.447752 + 0.258510i
\(148\) 0 0
\(149\) −5.50439 9.53389i −0.0369422 0.0639858i 0.846963 0.531652i \(-0.178428\pi\)
−0.883905 + 0.467666i \(0.845095\pi\)
\(150\) 0 0
\(151\) 238.846i 1.58176i −0.611968 0.790882i \(-0.709622\pi\)
0.611968 0.790882i \(-0.290378\pi\)
\(152\) 0 0
\(153\) 73.8797 0.482874
\(154\) 0 0
\(155\) 95.0582 54.8819i 0.613279 0.354077i
\(156\) 0 0
\(157\) 22.8125 + 39.5124i 0.145303 + 0.251671i 0.929486 0.368858i \(-0.120251\pi\)
−0.784183 + 0.620529i \(0.786918\pi\)
\(158\) 0 0
\(159\) 96.8353 0.609027
\(160\) 0 0
\(161\) 5.93421 10.2784i 0.0368585 0.0638407i
\(162\) 0 0
\(163\) −5.89159 −0.0361447 −0.0180724 0.999837i \(-0.505753\pi\)
−0.0180724 + 0.999837i \(0.505753\pi\)
\(164\) 0 0
\(165\) −193.343 111.627i −1.17178 0.676525i
\(166\) 0 0
\(167\) −142.140 82.0646i −0.851138 0.491405i 0.00989689 0.999951i \(-0.496850\pi\)
−0.861035 + 0.508546i \(0.830183\pi\)
\(168\) 0 0
\(169\) −84.4878 146.337i −0.499928 0.865900i
\(170\) 0 0
\(171\) 32.5790 46.7718i 0.190521 0.273520i
\(172\) 0 0
\(173\) 234.355 135.305i 1.35465 0.782109i 0.365755 0.930711i \(-0.380811\pi\)
0.988897 + 0.148603i \(0.0474775\pi\)
\(174\) 0 0
\(175\) −18.2747 + 31.6527i −0.104427 + 0.180872i
\(176\) 0 0
\(177\) 29.9269 51.8349i 0.169078 0.292852i
\(178\) 0 0
\(179\) 186.439i 1.04156i 0.853691 + 0.520779i \(0.174359\pi\)
−0.853691 + 0.520779i \(0.825641\pi\)
\(180\) 0 0
\(181\) −40.1939 23.2059i −0.222066 0.128210i 0.384841 0.922983i \(-0.374256\pi\)
−0.606906 + 0.794773i \(0.707590\pi\)
\(182\) 0 0
\(183\) 94.8487i 0.518299i
\(184\) 0 0
\(185\) −237.291 + 137.000i −1.28265 + 0.740539i
\(186\) 0 0
\(187\) 247.408 + 428.524i 1.32304 + 2.29157i
\(188\) 0 0
\(189\) 11.7579i 0.0622112i
\(190\) 0 0
\(191\) 36.7222 0.192263 0.0961315 0.995369i \(-0.469353\pi\)
0.0961315 + 0.995369i \(0.469353\pi\)
\(192\) 0 0
\(193\) −173.472 + 100.154i −0.898817 + 0.518932i −0.876816 0.480826i \(-0.840337\pi\)
−0.0220009 + 0.999758i \(0.507004\pi\)
\(194\) 0 0
\(195\) 0.869047 + 1.50523i 0.00445665 + 0.00771915i
\(196\) 0 0
\(197\) −171.512 −0.870620 −0.435310 0.900281i \(-0.643361\pi\)
−0.435310 + 0.900281i \(0.643361\pi\)
\(198\) 0 0
\(199\) 43.7500 75.7772i 0.219849 0.380790i −0.734913 0.678162i \(-0.762777\pi\)
0.954762 + 0.297372i \(0.0961102\pi\)
\(200\) 0 0
\(201\) −132.140 −0.657411
\(202\) 0 0
\(203\) −71.1820 41.0970i −0.350650 0.202448i
\(204\) 0 0
\(205\) −193.045 111.455i −0.941684 0.543682i
\(206\) 0 0
\(207\) −7.86749 13.6269i −0.0380072 0.0658304i
\(208\) 0 0
\(209\) 380.391 + 32.3384i 1.82005 + 0.154729i
\(210\) 0 0
\(211\) −16.3950 + 9.46566i −0.0777014 + 0.0448609i −0.538347 0.842723i \(-0.680951\pi\)
0.460646 + 0.887584i \(0.347618\pi\)
\(212\) 0 0
\(213\) −63.6080 + 110.172i −0.298629 + 0.517240i
\(214\) 0 0
\(215\) −80.5423 + 139.503i −0.374615 + 0.648853i
\(216\) 0 0
\(217\) 38.7178i 0.178423i
\(218\) 0 0
\(219\) −137.716 79.5103i −0.628840 0.363061i
\(220\) 0 0
\(221\) 3.85230i 0.0174312i
\(222\) 0 0
\(223\) 224.162 129.420i 1.00521 0.580358i 0.0954244 0.995437i \(-0.469579\pi\)
0.909786 + 0.415078i \(0.136246\pi\)
\(224\) 0 0
\(225\) 24.2283 + 41.9646i 0.107681 + 0.186509i
\(226\) 0 0
\(227\) 129.054i 0.568522i 0.958747 + 0.284261i \(0.0917482\pi\)
−0.958747 + 0.284261i \(0.908252\pi\)
\(228\) 0 0
\(229\) −98.8946 −0.431854 −0.215927 0.976409i \(-0.569277\pi\)
−0.215927 + 0.976409i \(0.569277\pi\)
\(230\) 0 0
\(231\) 68.1994 39.3749i 0.295235 0.170454i
\(232\) 0 0
\(233\) 174.731 + 302.644i 0.749920 + 1.29890i 0.947861 + 0.318685i \(0.103241\pi\)
−0.197941 + 0.980214i \(0.563425\pi\)
\(234\) 0 0
\(235\) −188.316 −0.801346
\(236\) 0 0
\(237\) 53.1300 92.0238i 0.224177 0.388286i
\(238\) 0 0
\(239\) −301.091 −1.25979 −0.629897 0.776679i \(-0.716903\pi\)
−0.629897 + 0.776679i \(0.716903\pi\)
\(240\) 0 0
\(241\) 110.242 + 63.6485i 0.457438 + 0.264102i 0.710966 0.703226i \(-0.248258\pi\)
−0.253529 + 0.967328i \(0.581591\pi\)
\(242\) 0 0
\(243\) −13.5000 7.79423i −0.0555556 0.0320750i
\(244\) 0 0
\(245\) 140.744 + 243.776i 0.574465 + 0.995003i
\(246\) 0 0
\(247\) −2.43882 1.69877i −0.00987376 0.00687759i
\(248\) 0 0
\(249\) 223.189 128.858i 0.896342 0.517503i
\(250\) 0 0
\(251\) −177.023 + 306.613i −0.705271 + 1.22157i 0.261322 + 0.965252i \(0.415841\pi\)
−0.966594 + 0.256314i \(0.917492\pi\)
\(252\) 0 0
\(253\) 52.6933 91.2675i 0.208274 0.360741i
\(254\) 0 0
\(255\) 273.628i 1.07305i
\(256\) 0 0
\(257\) −236.669 136.641i −0.920889 0.531676i −0.0369706 0.999316i \(-0.511771\pi\)
−0.883919 + 0.467641i \(0.845104\pi\)
\(258\) 0 0
\(259\) 96.6500i 0.373166i
\(260\) 0 0
\(261\) −94.3720 + 54.4857i −0.361579 + 0.208757i
\(262\) 0 0
\(263\) 75.5642 + 130.881i 0.287316 + 0.497646i 0.973168 0.230095i \(-0.0739036\pi\)
−0.685852 + 0.727741i \(0.740570\pi\)
\(264\) 0 0
\(265\) 358.649i 1.35339i
\(266\) 0 0
\(267\) −125.566 −0.470284
\(268\) 0 0
\(269\) 58.9364 34.0269i 0.219094 0.126494i −0.386437 0.922316i \(-0.626294\pi\)
0.605531 + 0.795822i \(0.292961\pi\)
\(270\) 0 0
\(271\) −56.8991 98.5521i −0.209960 0.363661i 0.741742 0.670685i \(-0.234000\pi\)
−0.951702 + 0.307025i \(0.900667\pi\)
\(272\) 0 0
\(273\) −0.613092 −0.00224576
\(274\) 0 0
\(275\) −162.271 + 281.062i −0.590078 + 1.02204i
\(276\) 0 0
\(277\) 440.910 1.59173 0.795867 0.605472i \(-0.207016\pi\)
0.795867 + 0.605472i \(0.207016\pi\)
\(278\) 0 0
\(279\) 44.4544 + 25.6657i 0.159335 + 0.0919919i
\(280\) 0 0
\(281\) 78.0928 + 45.0869i 0.277910 + 0.160452i 0.632477 0.774579i \(-0.282038\pi\)
−0.354567 + 0.935031i \(0.615372\pi\)
\(282\) 0 0
\(283\) −34.5331 59.8131i −0.122025 0.211354i 0.798541 0.601940i \(-0.205606\pi\)
−0.920566 + 0.390587i \(0.872272\pi\)
\(284\) 0 0
\(285\) −173.229 120.663i −0.607821 0.423379i
\(286\) 0 0
\(287\) 68.0944 39.3143i 0.237263 0.136984i
\(288\) 0 0
\(289\) −158.734 + 274.935i −0.549252 + 0.951332i
\(290\) 0 0
\(291\) −70.0326 + 121.300i −0.240662 + 0.416839i
\(292\) 0 0
\(293\) 410.238i 1.40013i 0.714079 + 0.700065i \(0.246846\pi\)
−0.714079 + 0.700065i \(0.753154\pi\)
\(294\) 0 0
\(295\) −191.981 110.840i −0.650782 0.375729i
\(296\) 0 0
\(297\) 104.405i 0.351533i
\(298\) 0 0
\(299\) −0.710545 + 0.410233i −0.00237640 + 0.00137202i
\(300\) 0 0
\(301\) −28.4103 49.2081i −0.0943864 0.163482i
\(302\) 0 0
\(303\) 265.617i 0.876624i
\(304\) 0 0
\(305\) −351.291 −1.15177
\(306\) 0 0
\(307\) 201.882 116.556i 0.657595 0.379663i −0.133765 0.991013i \(-0.542707\pi\)
0.791360 + 0.611350i \(0.209373\pi\)
\(308\) 0 0
\(309\) 146.313 + 253.422i 0.473506 + 0.820136i
\(310\) 0 0
\(311\) 441.280 1.41891 0.709454 0.704752i \(-0.248942\pi\)
0.709454 + 0.704752i \(0.248942\pi\)
\(312\) 0 0
\(313\) −60.6339 + 105.021i −0.193719 + 0.335530i −0.946480 0.322763i \(-0.895388\pi\)
0.752761 + 0.658294i \(0.228722\pi\)
\(314\) 0 0
\(315\) −43.5478 −0.138247
\(316\) 0 0
\(317\) 286.409 + 165.358i 0.903499 + 0.521635i 0.878334 0.478048i \(-0.158656\pi\)
0.0251649 + 0.999683i \(0.491989\pi\)
\(318\) 0 0
\(319\) −632.066 364.924i −1.98140 1.14396i
\(320\) 0 0
\(321\) 120.430 + 208.591i 0.375171 + 0.649815i
\(322\) 0 0
\(323\) 198.786 + 423.579i 0.615437 + 1.31139i
\(324\) 0 0
\(325\) 2.18816 1.26333i 0.00673279 0.00388718i
\(326\) 0 0
\(327\) −9.15888 + 15.8636i −0.0280088 + 0.0485127i
\(328\) 0 0
\(329\) 33.2131 57.5268i 0.100952 0.174854i
\(330\) 0 0
\(331\) 436.308i 1.31815i 0.752077 + 0.659075i \(0.229052\pi\)
−0.752077 + 0.659075i \(0.770948\pi\)
\(332\) 0 0
\(333\) −110.970 64.0685i −0.333243 0.192398i
\(334\) 0 0
\(335\) 489.406i 1.46091i
\(336\) 0 0
\(337\) −217.027 + 125.301i −0.643997 + 0.371812i −0.786153 0.618033i \(-0.787930\pi\)
0.142156 + 0.989844i \(0.454597\pi\)
\(338\) 0 0
\(339\) 59.8927 + 103.737i 0.176675 + 0.306009i
\(340\) 0 0
\(341\) 343.798i 1.00821i
\(342\) 0 0
\(343\) −210.169 −0.612738
\(344\) 0 0
\(345\) −50.4699 + 29.1388i −0.146290 + 0.0844603i
\(346\) 0 0
\(347\) 83.6670 + 144.915i 0.241115 + 0.417624i 0.961032 0.276436i \(-0.0891535\pi\)
−0.719917 + 0.694060i \(0.755820\pi\)
\(348\) 0 0
\(349\) −486.776 −1.39477 −0.697387 0.716695i \(-0.745654\pi\)
−0.697387 + 0.716695i \(0.745654\pi\)
\(350\) 0 0
\(351\) −0.406413 + 0.703929i −0.00115787 + 0.00200550i
\(352\) 0 0
\(353\) 30.1507 0.0854128 0.0427064 0.999088i \(-0.486402\pi\)
0.0427064 + 0.999088i \(0.486402\pi\)
\(354\) 0 0
\(355\) 408.045 + 235.585i 1.14942 + 0.663619i
\(356\) 0 0
\(357\) 83.5879 + 48.2595i 0.234140 + 0.135181i
\(358\) 0 0
\(359\) 75.0088 + 129.919i 0.208938 + 0.361891i 0.951380 0.308019i \(-0.0996659\pi\)
−0.742442 + 0.669910i \(0.766333\pi\)
\(360\) 0 0
\(361\) 355.819 + 60.9394i 0.985649 + 0.168807i
\(362\) 0 0
\(363\) 424.081 244.843i 1.16827 0.674500i
\(364\) 0 0
\(365\) −294.482 + 510.058i −0.806801 + 1.39742i
\(366\) 0 0
\(367\) −248.090 + 429.704i −0.675994 + 1.17086i 0.300183 + 0.953882i \(0.402952\pi\)
−0.976177 + 0.216975i \(0.930381\pi\)
\(368\) 0 0
\(369\) 104.245i 0.282506i
\(370\) 0 0
\(371\) 109.560 + 63.2545i 0.295310 + 0.170497i
\(372\) 0 0
\(373\) 449.613i 1.20540i 0.797969 + 0.602698i \(0.205908\pi\)
−0.797969 + 0.602698i \(0.794092\pi\)
\(374\) 0 0
\(375\) −85.1381 + 49.1545i −0.227035 + 0.131079i
\(376\) 0 0
\(377\) 2.84104 + 4.92083i 0.00753592 + 0.0130526i
\(378\) 0 0
\(379\) 471.336i 1.24363i 0.783163 + 0.621816i \(0.213605\pi\)
−0.783163 + 0.621816i \(0.786395\pi\)
\(380\) 0 0
\(381\) 51.3095 0.134670
\(382\) 0 0
\(383\) 23.4258 13.5249i 0.0611641 0.0353131i −0.469106 0.883142i \(-0.655424\pi\)
0.530270 + 0.847829i \(0.322090\pi\)
\(384\) 0 0
\(385\) −145.833 252.590i −0.378787 0.656078i
\(386\) 0 0
\(387\) −75.3319 −0.194656
\(388\) 0 0
\(389\) 177.144 306.822i 0.455382 0.788745i −0.543328 0.839520i \(-0.682836\pi\)
0.998710 + 0.0507758i \(0.0161694\pi\)
\(390\) 0 0
\(391\) 129.166 0.330348
\(392\) 0 0
\(393\) 85.9579 + 49.6278i 0.218722 + 0.126279i
\(394\) 0 0
\(395\) −340.829 196.777i −0.862857 0.498171i
\(396\) 0 0
\(397\) −79.5105 137.716i −0.200278 0.346892i 0.748340 0.663316i \(-0.230851\pi\)
−0.948618 + 0.316423i \(0.897518\pi\)
\(398\) 0 0
\(399\) 67.4123 31.6367i 0.168953 0.0792901i
\(400\) 0 0
\(401\) −277.534 + 160.234i −0.692105 + 0.399587i −0.804400 0.594088i \(-0.797513\pi\)
0.112295 + 0.993675i \(0.464180\pi\)
\(402\) 0 0
\(403\) 1.33829 2.31798i 0.00332081 0.00575181i
\(404\) 0 0
\(405\) −28.8675 + 50.0000i −0.0712777 + 0.123457i
\(406\) 0 0
\(407\) 858.211i 2.10863i
\(408\) 0 0
\(409\) −251.776 145.363i −0.615590 0.355411i 0.159560 0.987188i \(-0.448992\pi\)
−0.775150 + 0.631777i \(0.782326\pi\)
\(410\) 0 0
\(411\) 164.371i 0.399930i
\(412\) 0 0
\(413\) 67.7189 39.0975i 0.163968 0.0946671i
\(414\) 0 0
\(415\) −477.253 826.626i −1.15001 1.99187i
\(416\) 0 0
\(417\) 316.185i 0.758237i
\(418\) 0 0
\(419\) 141.846 0.338535 0.169267 0.985570i \(-0.445860\pi\)
0.169267 + 0.985570i \(0.445860\pi\)
\(420\) 0 0
\(421\) 98.6666 56.9652i 0.234362 0.135309i −0.378220 0.925716i \(-0.623464\pi\)
0.612583 + 0.790406i \(0.290131\pi\)
\(422\) 0 0
\(423\) −44.0334 76.2681i −0.104098 0.180303i
\(424\) 0 0
\(425\) −397.773 −0.935936
\(426\) 0 0
\(427\) 61.9568 107.312i 0.145098 0.251317i
\(428\) 0 0
\(429\) −5.44399 −0.0126900
\(430\) 0 0
\(431\) −229.263 132.365i −0.531932 0.307111i 0.209871 0.977729i \(-0.432696\pi\)
−0.741803 + 0.670618i \(0.766029\pi\)
\(432\) 0 0
\(433\) −631.333 364.500i −1.45804 0.841802i −0.459129 0.888369i \(-0.651839\pi\)
−0.998915 + 0.0465669i \(0.985172\pi\)
\(434\) 0 0
\(435\) 201.799 + 349.526i 0.463905 + 0.803507i
\(436\) 0 0
\(437\) 56.9589 81.7726i 0.130341 0.187123i
\(438\) 0 0
\(439\) −319.591 + 184.516i −0.727998 + 0.420310i −0.817689 0.575660i \(-0.804745\pi\)
0.0896911 + 0.995970i \(0.471412\pi\)
\(440\) 0 0
\(441\) −65.8195 + 114.003i −0.149251 + 0.258510i
\(442\) 0 0
\(443\) 291.547 504.975i 0.658120 1.13990i −0.322982 0.946405i \(-0.604685\pi\)
0.981102 0.193492i \(-0.0619815\pi\)
\(444\) 0 0
\(445\) 465.058i 1.04507i
\(446\) 0 0
\(447\) −16.5132 9.53389i −0.0369422 0.0213286i
\(448\) 0 0
\(449\) 314.423i 0.700273i −0.936699 0.350137i \(-0.886135\pi\)
0.936699 0.350137i \(-0.113865\pi\)
\(450\) 0 0
\(451\) 604.649 349.094i 1.34068 0.774045i
\(452\) 0 0
\(453\) −206.847 358.270i −0.456616 0.790882i
\(454\) 0 0
\(455\) 2.27071i 0.00499057i
\(456\) 0 0
\(457\) 505.253 1.10559 0.552793 0.833319i \(-0.313562\pi\)
0.552793 + 0.833319i \(0.313562\pi\)
\(458\) 0 0
\(459\) 110.820 63.9817i 0.241437 0.139394i
\(460\) 0 0
\(461\) 136.902 + 237.122i 0.296968 + 0.514364i 0.975441 0.220262i \(-0.0706912\pi\)
−0.678473 + 0.734626i \(0.737358\pi\)
\(462\) 0 0
\(463\) −319.780 −0.690669 −0.345334 0.938480i \(-0.612235\pi\)
−0.345334 + 0.938480i \(0.612235\pi\)
\(464\) 0 0
\(465\) 95.0582 164.646i 0.204426 0.354077i
\(466\) 0 0
\(467\) 295.510 0.632785 0.316392 0.948628i \(-0.397528\pi\)
0.316392 + 0.948628i \(0.397528\pi\)
\(468\) 0 0
\(469\) −149.504 86.3159i −0.318771 0.184042i
\(470\) 0 0
\(471\) 68.4375 + 39.5124i 0.145303 + 0.0838905i
\(472\) 0 0
\(473\) −252.271 436.947i −0.533344 0.923778i
\(474\) 0 0
\(475\) −175.408 + 251.822i −0.369279 + 0.530153i
\(476\) 0 0
\(477\) 145.253 83.8618i 0.304513 0.175811i
\(478\) 0 0
\(479\) −204.559 + 354.306i −0.427054 + 0.739679i −0.996610 0.0822735i \(-0.973782\pi\)
0.569556 + 0.821953i \(0.307115\pi\)
\(480\) 0 0
\(481\) −3.34072 + 5.78629i −0.00694536 + 0.0120297i
\(482\) 0 0
\(483\) 20.5567i 0.0425605i
\(484\) 0 0
\(485\) 449.259 + 259.380i 0.926308 + 0.534804i
\(486\) 0 0
\(487\) 638.208i 1.31049i 0.755417 + 0.655244i \(0.227434\pi\)
−0.755417 + 0.655244i \(0.772566\pi\)
\(488\) 0 0
\(489\) −8.83738 + 5.10227i −0.0180724 + 0.0104341i
\(490\) 0 0
\(491\) 173.278 + 300.126i 0.352908 + 0.611255i 0.986758 0.162202i \(-0.0518595\pi\)
−0.633850 + 0.773456i \(0.718526\pi\)
\(492\) 0 0
\(493\) 894.530i 1.81446i
\(494\) 0 0
\(495\) −386.686 −0.781184
\(496\) 0 0
\(497\) −143.933 + 83.0997i −0.289603 + 0.167203i
\(498\) 0 0
\(499\) 40.3510 + 69.8900i 0.0808638 + 0.140060i 0.903621 0.428333i \(-0.140899\pi\)
−0.822757 + 0.568393i \(0.807565\pi\)
\(500\) 0 0
\(501\) −284.280 −0.567425
\(502\) 0 0
\(503\) 247.050 427.903i 0.491153 0.850701i −0.508796 0.860887i \(-0.669909\pi\)
0.999948 + 0.0101862i \(0.00324242\pi\)
\(504\) 0 0
\(505\) 983.766 1.94805
\(506\) 0 0
\(507\) −253.463 146.337i −0.499928 0.288633i
\(508\) 0 0
\(509\) 63.9084 + 36.8975i 0.125557 + 0.0724902i 0.561463 0.827502i \(-0.310239\pi\)
−0.435906 + 0.899992i \(0.643572\pi\)
\(510\) 0 0
\(511\) −103.875 179.917i −0.203278 0.352088i
\(512\) 0 0
\(513\) 8.36297 98.3721i 0.0163021 0.191758i
\(514\) 0 0
\(515\) 938.599 541.900i 1.82252 1.05223i
\(516\) 0 0
\(517\) 294.918 510.814i 0.570442 0.988034i
\(518\) 0 0
\(519\) 234.355 405.914i 0.451551 0.782109i
\(520\) 0 0
\(521\) 357.582i 0.686337i −0.939274 0.343169i \(-0.888500\pi\)
0.939274 0.343169i \(-0.111500\pi\)
\(522\) 0 0
\(523\) −382.935 221.088i −0.732190 0.422730i 0.0870328 0.996205i \(-0.472261\pi\)
−0.819223 + 0.573475i \(0.805595\pi\)
\(524\) 0 0
\(525\) 63.3053i 0.120582i
\(526\) 0 0
\(527\) −364.919 + 210.686i −0.692447 + 0.399784i
\(528\) 0 0
\(529\) 250.745 + 434.303i 0.473998 + 0.820989i
\(530\) 0 0
\(531\) 103.670i 0.195235i
\(532\) 0 0
\(533\) −5.43561 −0.0101981
\(534\) 0 0
\(535\) 772.557 446.036i 1.44403 0.833712i
\(536\) 0 0
\(537\) 161.461 + 279.658i 0.300672 + 0.520779i
\(538\) 0 0
\(539\) −881.666 −1.63574
\(540\) 0 0
\(541\) −487.737 + 844.785i −0.901547 + 1.56152i −0.0760596 + 0.997103i \(0.524234\pi\)
−0.825487 + 0.564421i \(0.809099\pi\)
\(542\) 0 0
\(543\) −80.3877 −0.148044
\(544\) 0 0
\(545\) 58.7542 + 33.9217i 0.107806 + 0.0622417i
\(546\) 0 0
\(547\) −350.050 202.102i −0.639945 0.369473i 0.144648 0.989483i \(-0.453795\pi\)
−0.784594 + 0.620010i \(0.787128\pi\)
\(548\) 0 0
\(549\) −82.1414 142.273i −0.149620 0.259149i
\(550\) 0 0
\(551\) −566.310 394.465i −1.02779 0.715907i
\(552\) 0 0
\(553\) 120.223 69.4109i 0.217402 0.125517i
\(554\) 0 0
\(555\) −237.291 + 410.999i −0.427551 + 0.740539i
\(556\) 0 0
\(557\) −29.9352 + 51.8492i −0.0537435 + 0.0930866i −0.891646 0.452734i \(-0.850449\pi\)
0.837902 + 0.545821i \(0.183782\pi\)
\(558\) 0 0
\(559\) 3.92802i 0.00702687i
\(560\) 0 0
\(561\) 742.225 + 428.524i 1.32304 + 0.763857i
\(562\) 0 0
\(563\) 247.579i 0.439749i −0.975528 0.219874i \(-0.929435\pi\)
0.975528 0.219874i \(-0.0705648\pi\)
\(564\) 0 0
\(565\) 384.211 221.824i 0.680020 0.392610i
\(566\) 0 0
\(567\) −10.1827 17.6369i −0.0179588 0.0311056i
\(568\) 0 0
\(569\) 76.4991i 0.134445i −0.997738 0.0672224i \(-0.978586\pi\)
0.997738 0.0672224i \(-0.0214137\pi\)
\(570\) 0 0
\(571\) 624.523 1.09373 0.546867 0.837219i \(-0.315820\pi\)
0.546867 + 0.837219i \(0.315820\pi\)
\(572\) 0 0
\(573\) 55.0834 31.8024i 0.0961315 0.0555016i
\(574\) 0 0
\(575\) 42.3590 + 73.3680i 0.0736679 + 0.127597i
\(576\) 0 0
\(577\) 185.550 0.321577 0.160789 0.986989i \(-0.448596\pi\)
0.160789 + 0.986989i \(0.448596\pi\)
\(578\) 0 0
\(579\) −173.472 + 300.462i −0.299606 + 0.518932i
\(580\) 0 0
\(581\) 336.690 0.579501
\(582\) 0 0
\(583\) 972.846 + 561.673i 1.66869 + 0.963418i
\(584\) 0 0
\(585\) 2.60714 + 1.50523i 0.00445665 + 0.00257305i
\(586\) 0 0
\(587\) 130.891 + 226.710i 0.222983 + 0.386218i 0.955712 0.294302i \(-0.0950872\pi\)
−0.732729 + 0.680520i \(0.761754\pi\)
\(588\) 0 0
\(589\) −27.5386 + 323.931i −0.0467548 + 0.549968i
\(590\) 0 0
\(591\) −257.268 + 148.534i −0.435310 + 0.251326i
\(592\) 0 0
\(593\) −124.254 + 215.215i −0.209535 + 0.362925i −0.951568 0.307438i \(-0.900528\pi\)
0.742033 + 0.670363i \(0.233862\pi\)
\(594\) 0 0
\(595\) 178.739 309.585i 0.300401 0.520310i
\(596\) 0 0
\(597\) 151.554i 0.253860i
\(598\) 0 0
\(599\) 167.646 + 96.7905i 0.279877 + 0.161587i 0.633368 0.773851i \(-0.281672\pi\)
−0.353491 + 0.935438i \(0.615005\pi\)
\(600\) 0 0
\(601\) 675.975i 1.12475i −0.826882 0.562375i \(-0.809888\pi\)
0.826882 0.562375i \(-0.190112\pi\)
\(602\) 0 0
\(603\) −198.209 + 114.436i −0.328706 + 0.189778i
\(604\) 0 0
\(605\) −906.827 1570.67i −1.49889 2.59615i
\(606\) 0 0
\(607\) 383.052i 0.631057i −0.948916 0.315528i \(-0.897818\pi\)
0.948916 0.315528i \(-0.102182\pi\)
\(608\) 0 0
\(609\) −142.364 −0.233767
\(610\) 0 0
\(611\) −3.97684 + 2.29603i −0.00650874 + 0.00375782i
\(612\) 0 0
\(613\) −27.5410 47.7025i −0.0449283 0.0778180i 0.842687 0.538404i \(-0.180973\pi\)
−0.887615 + 0.460586i \(0.847639\pi\)
\(614\) 0 0
\(615\) −386.091 −0.627789
\(616\) 0 0
\(617\) −51.7851 + 89.6944i −0.0839305 + 0.145372i −0.904935 0.425550i \(-0.860081\pi\)
0.821004 + 0.570922i \(0.193414\pi\)
\(618\) 0 0
\(619\) 263.102 0.425043 0.212521 0.977156i \(-0.431832\pi\)
0.212521 + 0.977156i \(0.431832\pi\)
\(620\) 0 0
\(621\) −23.6025 13.6269i −0.0380072 0.0219435i
\(622\) 0 0
\(623\) −142.066 82.0218i −0.228035 0.131656i
\(624\) 0 0
\(625\) 383.956 + 665.031i 0.614329 + 1.06405i
\(626\) 0 0
\(627\) 598.593 280.921i 0.954693 0.448039i
\(628\) 0 0
\(629\) 910.936 525.929i 1.44823 0.836135i
\(630\) 0 0
\(631\) −72.5474 + 125.656i −0.114972 + 0.199137i −0.917769 0.397116i \(-0.870011\pi\)
0.802797 + 0.596253i \(0.203345\pi\)
\(632\) 0 0
\(633\) −16.3950 + 28.3970i −0.0259005 + 0.0448609i
\(634\) 0 0
\(635\) 190.035i 0.299267i
\(636\) 0 0
\(637\) 5.94443 + 3.43202i 0.00933192 + 0.00538779i
\(638\) 0 0
\(639\) 220.344i 0.344827i
\(640\) 0 0
\(641\) −583.796 + 337.055i −0.910758 + 0.525826i −0.880675 0.473721i \(-0.842911\pi\)
−0.0300832 + 0.999547i \(0.509577\pi\)
\(642\) 0 0
\(643\) −0.719856 1.24683i −0.00111953 0.00193908i 0.865465 0.500969i \(-0.167023\pi\)
−0.866585 + 0.499030i \(0.833690\pi\)
\(644\) 0 0
\(645\) 279.007i 0.432569i
\(646\) 0 0
\(647\) 614.044 0.949063 0.474532 0.880239i \(-0.342617\pi\)
0.474532 + 0.880239i \(0.342617\pi\)
\(648\) 0 0
\(649\) 601.315 347.169i 0.926525 0.534929i
\(650\) 0 0
\(651\) 33.5306 + 58.0768i 0.0515064 + 0.0892116i
\(652\) 0 0
\(653\) 822.374 1.25938 0.629689 0.776847i \(-0.283182\pi\)
0.629689 + 0.776847i \(0.283182\pi\)
\(654\) 0 0
\(655\) 183.807 318.362i 0.280621 0.486049i
\(656\) 0 0
\(657\) −275.432 −0.419227
\(658\) 0 0
\(659\) 549.386 + 317.188i 0.833666 + 0.481317i 0.855106 0.518453i \(-0.173492\pi\)
−0.0214404 + 0.999770i \(0.506825\pi\)
\(660\) 0 0
\(661\) −818.470 472.544i −1.23823 0.714893i −0.269498 0.963001i \(-0.586858\pi\)
−0.968732 + 0.248108i \(0.920191\pi\)
\(662\) 0 0
\(663\) −3.33619 5.77845i −0.00503196 0.00871561i
\(664\) 0 0
\(665\) −117.173 249.675i −0.176200 0.375451i
\(666\) 0 0
\(667\) −164.993 + 95.2590i −0.247366 + 0.142817i
\(668\) 0 0
\(669\) 224.162 388.260i 0.335070 0.580358i
\(670\) 0 0
\(671\) 550.150 952.888i 0.819896 1.42010i
\(672\) 0 0
\(673\) 570.803i 0.848147i −0.905628 0.424074i \(-0.860600\pi\)
0.905628 0.424074i \(-0.139400\pi\)
\(674\) 0 0
\(675\) 72.6848 + 41.9646i 0.107681 + 0.0621698i
\(676\) 0 0
\(677\) 275.976i 0.407646i −0.979008 0.203823i \(-0.934663\pi\)
0.979008 0.203823i \(-0.0653367\pi\)
\(678\) 0 0
\(679\) −158.471 + 91.4931i −0.233388 + 0.134747i
\(680\) 0 0
\(681\) 111.764 + 193.582i 0.164118 + 0.284261i
\(682\) 0 0
\(683\) 106.224i 0.155525i −0.996972 0.0777627i \(-0.975222\pi\)
0.996972 0.0777627i \(-0.0247776\pi\)
\(684\) 0 0
\(685\) −608.781 −0.888732
\(686\) 0 0
\(687\) −148.342 + 85.6453i −0.215927 + 0.124666i
\(688\) 0 0
\(689\) −4.37279 7.57390i −0.00634658 0.0109926i
\(690\) 0 0
\(691\) −244.177 −0.353367 −0.176684 0.984268i \(-0.556537\pi\)
−0.176684 + 0.984268i \(0.556537\pi\)
\(692\) 0 0
\(693\) 68.1994 118.125i 0.0984118 0.170454i
\(694\) 0 0
\(695\) −1171.05 −1.68497
\(696\) 0 0
\(697\) 741.082 + 427.864i 1.06325 + 0.613865i
\(698\) 0 0
\(699\) 524.194 + 302.644i 0.749920 + 0.432966i
\(700\) 0 0
\(701\) 143.276 + 248.161i 0.204388 + 0.354010i 0.949938 0.312440i \(-0.101146\pi\)
−0.745550 + 0.666450i \(0.767813\pi\)
\(702\) 0 0
\(703\) 68.7436 808.618i 0.0977860 1.15024i
\(704\) 0 0
\(705\) −282.474 + 163.087i −0.400673 + 0.231329i
\(706\) 0 0
\(707\) −173.506 + 300.521i −0.245411 + 0.425065i
\(708\) 0 0
\(709\) −5.70585 + 9.88282i −0.00804774 + 0.0139391i −0.870021 0.493014i \(-0.835895\pi\)
0.861973 + 0.506953i \(0.169228\pi\)
\(710\) 0 0
\(711\) 184.048i 0.258857i
\(712\) 0 0
\(713\) 77.7209 + 44.8722i 0.109006 + 0.0629344i
\(714\) 0 0
\(715\) 20.1629i 0.0281999i
\(716\) 0 0
\(717\) −451.636 + 260.752i −0.629897 + 0.363671i
\(718\) 0 0
\(719\) −438.491 759.488i −0.609862 1.05631i −0.991263 0.131902i \(-0.957892\pi\)
0.381401 0.924410i \(-0.375442\pi\)
\(720\) 0 0
\(721\) 382.298i 0.530232i
\(722\) 0 0
\(723\) 220.485 0.304958
\(724\) 0 0
\(725\) 508.105 293.354i 0.700834 0.404627i
\(726\) 0 0
\(727\) 360.167 + 623.827i 0.495415 + 0.858084i 0.999986 0.00528653i \(-0.00168276\pi\)
−0.504571 + 0.863370i \(0.668349\pi\)
\(728\) 0 0
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 309.194 535.540i 0.422974 0.732613i
\(732\) 0 0
\(733\) −170.651 −0.232812 −0.116406 0.993202i \(-0.537137\pi\)
−0.116406 + 0.993202i \(0.537137\pi\)
\(734\) 0 0
\(735\) 422.232 + 243.776i 0.574465 + 0.331668i
\(736\) 0 0
\(737\) −1327.53 766.449i −1.80126 1.03996i
\(738\) 0 0
\(739\) −530.334 918.566i −0.717637 1.24298i −0.961933 0.273284i \(-0.911890\pi\)
0.244296 0.969701i \(-0.421443\pi\)
\(740\) 0 0
\(741\) −5.12940 0.436069i −0.00692227 0.000588487i
\(742\) 0 0
\(743\) −290.537 + 167.742i −0.391033 + 0.225763i −0.682607 0.730785i \(-0.739154\pi\)
0.291575 + 0.956548i \(0.405821\pi\)
\(744\) 0 0
\(745\) −35.3107 + 61.1599i −0.0473969 + 0.0820938i
\(746\) 0 0
\(747\) 223.189 386.575i 0.298781 0.517503i
\(748\) 0 0
\(749\) 314.668i 0.420117i
\(750\) 0 0
\(751\) 1128.41 + 651.490i 1.50255 + 0.867497i 0.999996 + 0.00295120i \(0.000939399\pi\)
0.502554 + 0.864546i \(0.332394\pi\)
\(752\) 0 0
\(753\) 613.226i 0.814377i
\(754\) 0 0
\(755\) −1326.92 + 766.100i −1.75751 + 1.01470i
\(756\) 0 0
\(757\) −60.1511 104.185i −0.0794598 0.137628i 0.823557 0.567233i \(-0.191986\pi\)
−0.903017 + 0.429605i \(0.858653\pi\)
\(758\) 0 0
\(759\) 182.535i 0.240494i
\(760\) 0 0
\(761\) 1346.45 1.76932 0.884658 0.466240i \(-0.154392\pi\)
0.884658 + 0.466240i \(0.154392\pi\)
\(762\) 0 0
\(763\) −20.7248 + 11.9655i −0.0271623 + 0.0156822i
\(764\) 0 0
\(765\) −236.969 410.442i −0.309763 0.536526i
\(766\) 0 0
\(767\) −5.40564 −0.00704777
\(768\) 0 0
\(769\) 109.016 188.821i 0.141763 0.245541i −0.786398 0.617721i \(-0.788056\pi\)
0.928161 + 0.372180i \(0.121390\pi\)
\(770\) 0 0
\(771\) −473.337 −0.613926
\(772\) 0 0
\(773\) −48.6422 28.0836i −0.0629266 0.0363307i 0.468207 0.883619i \(-0.344900\pi\)
−0.531133 + 0.847288i \(0.678234\pi\)
\(774\) 0 0
\(775\) −239.345 138.186i −0.308832 0.178304i
\(776\) 0 0
\(777\) −83.7014 144.975i −0.107724 0.186583i
\(778\) 0 0
\(779\) 597.671 280.488i 0.767229 0.360062i
\(780\) 0 0
\(781\) −1278.06 + 737.890i −1.63644 + 0.944801i
\(782\) 0 0
\(783\) −94.3720 + 163.457i −0.120526 + 0.208757i
\(784\) 0 0
\(785\) 146.342 253.472i 0.186423 0.322894i
\(786\) 0 0
\(787\) 170.104i 0.216142i 0.994143 + 0.108071i \(0.0344674\pi\)
−0.994143 + 0.108071i \(0.965533\pi\)
\(788\) 0 0
\(789\) 226.693 + 130.881i 0.287316 + 0.165882i
\(790\) 0 0
\(791\) 156.492i 0.197840i
\(792\) 0 0