Properties

Label 403.2.f.a.373.1
Level 403
Weight 2
Character 403.373
Analytic conductor 3.218
Analytic rank 1
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 403.373
Dual form 403.2.f.a.94.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-2.50000 - 2.59808i) q^{13} +2.00000 q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} -3.00000 q^{18} +(-2.00000 - 3.46410i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(-2.00000 + 3.46410i) q^{23} +4.00000 q^{25} +(3.50000 - 0.866025i) q^{26} +(1.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} -1.00000 q^{31} +(-2.50000 - 4.33013i) q^{32} +5.00000 q^{34} +(3.00000 + 5.19615i) q^{35} +(-1.50000 + 2.59808i) q^{36} +(2.50000 - 4.33013i) q^{37} +4.00000 q^{38} +9.00000 q^{40} +(-3.50000 + 6.06218i) q^{41} +(1.00000 + 1.73205i) q^{43} +(-4.50000 - 7.79423i) q^{45} +(-2.00000 - 3.46410i) q^{46} -6.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(1.00000 - 3.46410i) q^{52} -9.00000 q^{53} +(3.00000 + 5.19615i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{61} +(0.500000 - 0.866025i) q^{62} +(3.00000 - 5.19615i) q^{63} +7.00000 q^{64} +(7.50000 + 7.79423i) q^{65} +(-5.00000 + 8.66025i) q^{67} +(2.50000 - 4.33013i) q^{68} -6.00000 q^{70} +(2.00000 + 3.46410i) q^{71} +(-4.50000 - 7.79423i) q^{72} -3.00000 q^{73} +(2.50000 + 4.33013i) q^{74} +(2.00000 - 3.46410i) q^{76} +2.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.50000 - 6.06218i) q^{82} -2.00000 q^{83} +(7.50000 + 12.9904i) q^{85} -2.00000 q^{86} +(3.00000 - 5.19615i) q^{89} +9.00000 q^{90} +(-2.00000 + 6.92820i) q^{91} -4.00000 q^{92} +(3.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +(9.00000 + 15.5885i) q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{4} - 6q^{5} - 2q^{7} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{4} - 6q^{5} - 2q^{7} - 6q^{8} + 3q^{9} + 3q^{10} - 5q^{13} + 4q^{14} + q^{16} - 5q^{17} - 6q^{18} - 4q^{19} - 3q^{20} - 4q^{23} + 8q^{25} + 7q^{26} + 2q^{28} - 3q^{29} - 2q^{31} - 5q^{32} + 10q^{34} + 6q^{35} - 3q^{36} + 5q^{37} + 8q^{38} + 18q^{40} - 7q^{41} + 2q^{43} - 9q^{45} - 4q^{46} - 12q^{47} + 3q^{49} - 4q^{50} + 2q^{52} - 18q^{53} + 6q^{56} - 3q^{58} + 6q^{59} + q^{61} + q^{62} + 6q^{63} + 14q^{64} + 15q^{65} - 10q^{67} + 5q^{68} - 12q^{70} + 4q^{71} - 9q^{72} - 6q^{73} + 5q^{74} + 4q^{76} + 4q^{79} - 3q^{80} - 9q^{81} - 7q^{82} - 4q^{83} + 15q^{85} - 4q^{86} + 6q^{89} + 18q^{90} - 4q^{91} - 8q^{92} + 6q^{94} + 12q^{95} + 18q^{97} + 3q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i −0.986869 0.161521i \(-0.948360\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 0 0
\(7\) −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) −3.00000 −1.06066
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 0 0
\(13\) −2.50000 2.59808i −0.693375 0.720577i
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −2.50000 4.33013i −0.606339 1.05021i −0.991838 0.127502i \(-0.959304\pi\)
0.385499 0.922708i \(-0.374029\pi\)
\(18\) −3.00000 −0.707107
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) −1.50000 2.59808i −0.335410 0.580948i
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 3.50000 0.866025i 0.686406 0.169842i
\(27\) 0 0
\(28\) 1.00000 1.73205i 0.188982 0.327327i
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605
\(32\) −2.50000 4.33013i −0.441942 0.765466i
\(33\) 0 0
\(34\) 5.00000 0.857493
\(35\) 3.00000 + 5.19615i 0.507093 + 0.878310i
\(36\) −1.50000 + 2.59808i −0.250000 + 0.433013i
\(37\) 2.50000 4.33013i 0.410997 0.711868i −0.584002 0.811752i \(-0.698514\pi\)
0.994999 + 0.0998840i \(0.0318472\pi\)
\(38\) 4.00000 0.648886
\(39\) 0 0
\(40\) 9.00000 1.42302
\(41\) −3.50000 + 6.06218i −0.546608 + 0.946753i 0.451896 + 0.892071i \(0.350748\pi\)
−0.998504 + 0.0546823i \(0.982585\pi\)
\(42\) 0 0
\(43\) 1.00000 + 1.73205i 0.152499 + 0.264135i 0.932145 0.362084i \(-0.117935\pi\)
−0.779647 + 0.626219i \(0.784601\pi\)
\(44\) 0 0
\(45\) −4.50000 7.79423i −0.670820 1.16190i
\(46\) −2.00000 3.46410i −0.294884 0.510754i
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) −2.00000 + 3.46410i −0.282843 + 0.489898i
\(51\) 0 0
\(52\) 1.00000 3.46410i 0.138675 0.480384i
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 3.00000 + 5.19615i 0.400892 + 0.694365i
\(57\) 0 0
\(58\) −1.50000 2.59808i −0.196960 0.341144i
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 0.500000 0.866025i 0.0635001 0.109985i
\(63\) 3.00000 5.19615i 0.377964 0.654654i
\(64\) 7.00000 0.875000
\(65\) 7.50000 + 7.79423i 0.930261 + 0.966755i
\(66\) 0 0
\(67\) −5.00000 + 8.66025i −0.610847 + 1.05802i 0.380251 + 0.924883i \(0.375838\pi\)
−0.991098 + 0.133135i \(0.957496\pi\)
\(68\) 2.50000 4.33013i 0.303170 0.525105i
\(69\) 0 0
\(70\) −6.00000 −0.717137
\(71\) 2.00000 + 3.46410i 0.237356 + 0.411113i 0.959955 0.280155i \(-0.0903858\pi\)
−0.722599 + 0.691268i \(0.757052\pi\)
\(72\) −4.50000 7.79423i −0.530330 0.918559i
\(73\) −3.00000 −0.351123 −0.175562 0.984468i \(-0.556174\pi\)
−0.175562 + 0.984468i \(0.556174\pi\)
\(74\) 2.50000 + 4.33013i 0.290619 + 0.503367i
\(75\) 0 0
\(76\) 2.00000 3.46410i 0.229416 0.397360i
\(77\) 0 0
\(78\) 0 0
\(79\) 2.00000 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −3.50000 6.06218i −0.386510 0.669456i
\(83\) −2.00000 −0.219529 −0.109764 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) 0 0
\(85\) 7.50000 + 12.9904i 0.813489 + 1.40900i
\(86\) −2.00000 −0.215666
\(87\) 0 0
\(88\) 0 0
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 9.00000 0.948683
\(91\) −2.00000 + 6.92820i −0.209657 + 0.726273i
\(92\) −4.00000 −0.417029
\(93\) 0 0
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 6.00000 + 10.3923i 0.615587 + 1.06623i
\(96\) 0 0
\(97\) 9.00000 + 15.5885i 0.913812 + 1.58277i 0.808632 + 0.588315i \(0.200208\pi\)
0.105180 + 0.994453i \(0.466458\pi\)
\(98\) 1.50000 + 2.59808i 0.151523 + 0.262445i
\(99\) 0 0
\(100\) 2.00000 + 3.46410i 0.200000 + 0.346410i
\(101\) 3.50000 6.06218i 0.348263 0.603209i −0.637678 0.770303i \(-0.720105\pi\)
0.985941 + 0.167094i \(0.0534383\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 7.50000 + 7.79423i 0.735436 + 0.764287i
\(105\) 0 0
\(106\) 4.50000 7.79423i 0.437079 0.757042i
\(107\) −5.00000 + 8.66025i −0.483368 + 0.837218i −0.999818 0.0190994i \(-0.993920\pi\)
0.516449 + 0.856318i \(0.327253\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.00000 −0.188982
\(113\) 0.500000 + 0.866025i 0.0470360 + 0.0814688i 0.888585 0.458712i \(-0.151689\pi\)
−0.841549 + 0.540181i \(0.818356\pi\)
\(114\) 0 0
\(115\) 6.00000 10.3923i 0.559503 0.969087i
\(116\) −3.00000 −0.278543
\(117\) 3.00000 10.3923i 0.277350 0.960769i
\(118\) −6.00000 −0.552345
\(119\) −5.00000 + 8.66025i −0.458349 + 0.793884i
\(120\) 0 0
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) −1.00000 −0.0905357
\(123\) 0 0
\(124\) −0.500000 0.866025i −0.0449013 0.0777714i
\(125\) 3.00000 0.268328
\(126\) 3.00000 + 5.19615i 0.267261 + 0.462910i
\(127\) −1.00000 + 1.73205i −0.0887357 + 0.153695i −0.906977 0.421180i \(-0.861616\pi\)
0.818241 + 0.574875i \(0.194949\pi\)
\(128\) 1.50000 2.59808i 0.132583 0.229640i
\(129\) 0 0
\(130\) −10.5000 + 2.59808i −0.920911 + 0.227866i
\(131\) −20.0000 −1.74741 −0.873704 0.486458i \(-0.838289\pi\)
−0.873704 + 0.486458i \(0.838289\pi\)
\(132\) 0 0
\(133\) −4.00000 + 6.92820i −0.346844 + 0.600751i
\(134\) −5.00000 8.66025i −0.431934 0.748132i
\(135\) 0 0
\(136\) 7.50000 + 12.9904i 0.643120 + 1.11392i
\(137\) 3.50000 + 6.06218i 0.299025 + 0.517927i 0.975913 0.218159i \(-0.0700052\pi\)
−0.676888 + 0.736086i \(0.736672\pi\)
\(138\) 0 0
\(139\) −5.00000 8.66025i −0.424094 0.734553i 0.572241 0.820086i \(-0.306074\pi\)
−0.996335 + 0.0855324i \(0.972741\pi\)
\(140\) −3.00000 + 5.19615i −0.253546 + 0.439155i
\(141\) 0 0
\(142\) −4.00000 −0.335673
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) 4.50000 7.79423i 0.373705 0.647275i
\(146\) 1.50000 2.59808i 0.124141 0.215018i
\(147\) 0 0
\(148\) 5.00000 0.410997
\(149\) −6.50000 11.2583i −0.532501 0.922318i −0.999280 0.0379444i \(-0.987919\pi\)
0.466779 0.884374i \(-0.345414\pi\)
\(150\) 0 0
\(151\) −14.0000 −1.13930 −0.569652 0.821886i \(-0.692922\pi\)
−0.569652 + 0.821886i \(0.692922\pi\)
\(152\) 6.00000 + 10.3923i 0.486664 + 0.842927i
\(153\) 7.50000 12.9904i 0.606339 1.05021i
\(154\) 0 0
\(155\) 3.00000 0.240966
\(156\) 0 0
\(157\) 9.00000 0.718278 0.359139 0.933284i \(-0.383070\pi\)
0.359139 + 0.933284i \(0.383070\pi\)
\(158\) −1.00000 + 1.73205i −0.0795557 + 0.137795i
\(159\) 0 0
\(160\) 7.50000 + 12.9904i 0.592927 + 1.02698i
\(161\) 8.00000 0.630488
\(162\) −4.50000 7.79423i −0.353553 0.612372i
\(163\) −3.00000 5.19615i −0.234978 0.406994i 0.724288 0.689497i \(-0.242169\pi\)
−0.959266 + 0.282503i \(0.908835\pi\)
\(164\) −7.00000 −0.546608
\(165\) 0 0
\(166\) 1.00000 1.73205i 0.0776151 0.134433i
\(167\) 11.0000 19.0526i 0.851206 1.47433i −0.0289155 0.999582i \(-0.509205\pi\)
0.880121 0.474749i \(-0.157461\pi\)
\(168\) 0 0
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) −15.0000 −1.15045
\(171\) 6.00000 10.3923i 0.458831 0.794719i
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −7.00000 12.1244i −0.532200 0.921798i −0.999293 0.0375896i \(-0.988032\pi\)
0.467093 0.884208i \(-0.345301\pi\)
\(174\) 0 0
\(175\) −4.00000 6.92820i −0.302372 0.523723i
\(176\) 0 0
\(177\) 0 0
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) 10.0000 17.3205i 0.747435 1.29460i −0.201613 0.979465i \(-0.564618\pi\)
0.949048 0.315130i \(-0.102048\pi\)
\(180\) 4.50000 7.79423i 0.335410 0.580948i
\(181\) −1.00000 −0.0743294 −0.0371647 0.999309i \(-0.511833\pi\)
−0.0371647 + 0.999309i \(0.511833\pi\)
\(182\) −5.00000 5.19615i −0.370625 0.385164i
\(183\) 0 0
\(184\) 6.00000 10.3923i 0.442326 0.766131i
\(185\) −7.50000 + 12.9904i −0.551411 + 0.955072i
\(186\) 0 0
\(187\) 0 0
\(188\) −3.00000 5.19615i −0.218797 0.378968i
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) 4.00000 + 6.92820i 0.289430 + 0.501307i 0.973674 0.227946i \(-0.0732010\pi\)
−0.684244 + 0.729253i \(0.739868\pi\)
\(192\) 0 0
\(193\) 12.5000 21.6506i 0.899770 1.55845i 0.0719816 0.997406i \(-0.477068\pi\)
0.827788 0.561041i \(-0.189599\pi\)
\(194\) −18.0000 −1.29232
\(195\) 0 0
\(196\) 3.00000 0.214286
\(197\) 3.00000 5.19615i 0.213741 0.370211i −0.739141 0.673550i \(-0.764768\pi\)
0.952882 + 0.303340i \(0.0981018\pi\)
\(198\) 0 0
\(199\) −13.0000 22.5167i −0.921546 1.59616i −0.797025 0.603947i \(-0.793594\pi\)
−0.124521 0.992217i \(-0.539739\pi\)
\(200\) −12.0000 −0.848528
\(201\) 0 0
\(202\) 3.50000 + 6.06218i 0.246259 + 0.426533i
\(203\) 6.00000 0.421117
\(204\) 0 0
\(205\) 10.5000 18.1865i 0.733352 1.27020i
\(206\) 0 0
\(207\) −12.0000 −0.834058
\(208\) −3.50000 + 0.866025i −0.242681 + 0.0600481i
\(209\) 0 0
\(210\) 0 0
\(211\) 5.00000 8.66025i 0.344214 0.596196i −0.640996 0.767544i \(-0.721479\pi\)
0.985211 + 0.171347i \(0.0548120\pi\)
\(212\) −4.50000 7.79423i −0.309061 0.535310i
\(213\) 0 0
\(214\) −5.00000 8.66025i −0.341793 0.592003i
\(215\) −3.00000 5.19615i −0.204598 0.354375i
\(216\) 0 0
\(217\) 1.00000 + 1.73205i 0.0678844 + 0.117579i
\(218\) 5.00000 8.66025i 0.338643 0.586546i
\(219\) 0 0
\(220\) 0 0
\(221\) −5.00000 + 17.3205i −0.336336 + 1.16510i
\(222\) 0 0
\(223\) −7.00000 + 12.1244i −0.468755 + 0.811907i −0.999362 0.0357107i \(-0.988630\pi\)
0.530607 + 0.847618i \(0.321964\pi\)
\(224\) −5.00000 + 8.66025i −0.334077 + 0.578638i
\(225\) 6.00000 + 10.3923i 0.400000 + 0.692820i
\(226\) −1.00000 −0.0665190
\(227\) −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 6.00000 + 10.3923i 0.395628 + 0.685248i
\(231\) 0 0
\(232\) 4.50000 7.79423i 0.295439 0.511716i
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 7.50000 + 7.79423i 0.490290 + 0.509525i
\(235\) 18.0000 1.17419
\(236\) −3.00000 + 5.19615i −0.195283 + 0.338241i
\(237\) 0 0
\(238\) −5.00000 8.66025i −0.324102 0.561361i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) 9.50000 + 16.4545i 0.611949 + 1.05993i 0.990912 + 0.134515i \(0.0429475\pi\)
−0.378963 + 0.925412i \(0.623719\pi\)
\(242\) −11.0000 −0.707107
\(243\) 0 0
\(244\) −0.500000 + 0.866025i −0.0320092 + 0.0554416i
\(245\) −4.50000 + 7.79423i −0.287494 + 0.497955i
\(246\) 0 0
\(247\) −4.00000 + 13.8564i −0.254514 + 0.881662i
\(248\) 3.00000 0.190500
\(249\) 0 0
\(250\) −1.50000 + 2.59808i −0.0948683 + 0.164317i
\(251\) 6.00000 + 10.3923i 0.378717 + 0.655956i 0.990876 0.134778i \(-0.0430322\pi\)
−0.612159 + 0.790735i \(0.709699\pi\)
\(252\) 6.00000 0.377964
\(253\) 0 0
\(254\) −1.00000 1.73205i −0.0627456 0.108679i
\(255\) 0 0
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) −7.50000 + 12.9904i −0.467837 + 0.810318i −0.999325 0.0367485i \(-0.988300\pi\)
0.531487 + 0.847066i \(0.321633\pi\)
\(258\) 0 0
\(259\) −10.0000 −0.621370
\(260\) −3.00000 + 10.3923i −0.186052 + 0.644503i
\(261\) −9.00000 −0.557086
\(262\) 10.0000 17.3205i 0.617802 1.07006i
\(263\) 3.00000 5.19615i 0.184988 0.320408i −0.758585 0.651575i \(-0.774109\pi\)
0.943572 + 0.331166i \(0.107442\pi\)
\(264\) 0 0
\(265\) 27.0000 1.65860
\(266\) −4.00000 6.92820i −0.245256 0.424795i
\(267\) 0 0
\(268\) −10.0000 −0.610847
\(269\) −9.00000 15.5885i −0.548740 0.950445i −0.998361 0.0572259i \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) 0 0
\(271\) −12.0000 + 20.7846i −0.728948 + 1.26258i 0.228380 + 0.973572i \(0.426657\pi\)
−0.957328 + 0.289003i \(0.906676\pi\)
\(272\) −5.00000 −0.303170
\(273\) 0 0
\(274\) −7.00000 −0.422885
\(275\) 0 0
\(276\) 0 0
\(277\) −15.5000 26.8468i −0.931305 1.61307i −0.781094 0.624413i \(-0.785338\pi\)
−0.150210 0.988654i \(-0.547995\pi\)
\(278\) 10.0000 0.599760
\(279\) −1.50000 2.59808i −0.0898027 0.155543i
\(280\) −9.00000 15.5885i −0.537853 0.931589i
\(281\) 15.0000 0.894825 0.447412 0.894328i \(-0.352346\pi\)
0.447412 + 0.894328i \(0.352346\pi\)
\(282\) 0 0
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −2.00000 + 3.46410i −0.118678 + 0.205557i
\(285\) 0 0
\(286\) 0 0
\(287\) 14.0000 0.826394
\(288\) 7.50000 12.9904i 0.441942 0.765466i
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 4.50000 + 7.79423i 0.264249 + 0.457693i
\(291\) 0 0
\(292\) −1.50000 2.59808i −0.0877809 0.152041i
\(293\) 9.50000 + 16.4545i 0.554996 + 0.961281i 0.997904 + 0.0647140i \(0.0206135\pi\)
−0.442908 + 0.896567i \(0.646053\pi\)
\(294\) 0 0
\(295\) −9.00000 15.5885i −0.524000 0.907595i
\(296\) −7.50000 + 12.9904i −0.435929 + 0.755051i
\(297\) 0 0
\(298\) 13.0000 0.753070
\(299\) 14.0000 3.46410i 0.809641 0.200334i
\(300\) 0 0
\(301\) 2.00000 3.46410i 0.115278 0.199667i
\(302\) 7.00000 12.1244i 0.402805 0.697678i
\(303\) 0 0
\(304\) −4.00000 −0.229416
\(305\) −1.50000 2.59808i −0.0858898 0.148765i
\(306\) 7.50000 + 12.9904i 0.428746 + 0.742611i
\(307\) −32.0000 −1.82634 −0.913168 0.407583i \(-0.866372\pi\)
−0.913168 + 0.407583i \(0.866372\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1.50000 + 2.59808i −0.0851943 + 0.147561i
\(311\) −26.0000 −1.47432 −0.737162 0.675716i \(-0.763835\pi\)
−0.737162 + 0.675716i \(0.763835\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) −4.50000 + 7.79423i −0.253950 + 0.439854i
\(315\) −9.00000 + 15.5885i −0.507093 + 0.878310i
\(316\) 1.00000 + 1.73205i 0.0562544 + 0.0974355i
\(317\) −7.00000 −0.393159 −0.196580 0.980488i \(-0.562983\pi\)
−0.196580 + 0.980488i \(0.562983\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −21.0000 −1.17394
\(321\) 0 0
\(322\) −4.00000 + 6.92820i −0.222911 + 0.386094i
\(323\) −10.0000 + 17.3205i −0.556415 + 0.963739i
\(324\) −9.00000 −0.500000
\(325\) −10.0000 10.3923i −0.554700 0.576461i
\(326\) 6.00000 0.332309
\(327\) 0 0
\(328\) 10.5000 18.1865i 0.579766 1.00418i
\(329\) 6.00000 + 10.3923i 0.330791 + 0.572946i
\(330\) 0 0
\(331\) −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i \(-0.255287\pi\)
−0.970091 + 0.242742i \(0.921953\pi\)
\(332\) −1.00000 1.73205i −0.0548821 0.0950586i
\(333\) 15.0000 0.821995
\(334\) 11.0000 + 19.0526i 0.601893 + 1.04251i
\(335\) 15.0000 25.9808i 0.819538 1.41948i
\(336\) 0 0
\(337\) 29.0000 1.57973 0.789865 0.613280i \(-0.210150\pi\)
0.789865 + 0.613280i \(0.210150\pi\)
\(338\) −11.0000 6.92820i −0.598321 0.376845i
\(339\) 0 0
\(340\) −7.50000 + 12.9904i −0.406745 + 0.704502i
\(341\) 0 0
\(342\) 6.00000 + 10.3923i 0.324443 + 0.561951i
\(343\) −20.0000 −1.07990
\(344\) −3.00000 5.19615i −0.161749 0.280158i
\(345\) 0 0
\(346\) 14.0000 0.752645
\(347\) 15.0000 + 25.9808i 0.805242 + 1.39472i 0.916127 + 0.400887i \(0.131298\pi\)
−0.110885 + 0.993833i \(0.535369\pi\)
\(348\) 0 0
\(349\) −7.00000 + 12.1244i −0.374701 + 0.649002i −0.990282 0.139072i \(-0.955588\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(350\) 8.00000 0.427618
\(351\) 0 0
\(352\) 0 0
\(353\) 9.50000 16.4545i 0.505634 0.875784i −0.494345 0.869266i \(-0.664592\pi\)
0.999979 0.00651782i \(-0.00207470\pi\)
\(354\) 0 0
\(355\) −6.00000 10.3923i −0.318447 0.551566i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 10.0000 + 17.3205i 0.528516 + 0.915417i
\(359\) −30.0000 −1.58334 −0.791670 0.610949i \(-0.790788\pi\)
−0.791670 + 0.610949i \(0.790788\pi\)
\(360\) 13.5000 + 23.3827i 0.711512 + 1.23238i
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 0.500000 0.866025i 0.0262794 0.0455173i
\(363\) 0 0
\(364\) −7.00000 + 1.73205i −0.366900 + 0.0907841i
\(365\) 9.00000 0.471082
\(366\) 0 0
\(367\) −15.0000 + 25.9808i −0.782994 + 1.35618i 0.147197 + 0.989107i \(0.452975\pi\)
−0.930190 + 0.367078i \(0.880358\pi\)
\(368\) 2.00000 + 3.46410i 0.104257 + 0.180579i
\(369\) −21.0000 −1.09322
\(370\) −7.50000 12.9904i −0.389906 0.675338i
\(371\) 9.00000 + 15.5885i 0.467257 + 0.809312i
\(372\) 0 0
\(373\) −6.50000 11.2583i −0.336557 0.582934i 0.647225 0.762299i \(-0.275929\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 18.0000 0.928279
\(377\) 10.5000 2.59808i 0.540778 0.133808i
\(378\) 0 0
\(379\) −3.00000 + 5.19615i −0.154100 + 0.266908i −0.932731 0.360573i \(-0.882581\pi\)
0.778631 + 0.627482i \(0.215914\pi\)
\(380\) −6.00000 + 10.3923i −0.307794 + 0.533114i
\(381\) 0 0
\(382\) −8.00000 −0.409316
\(383\) 13.0000 + 22.5167i 0.664269 + 1.15055i 0.979483 + 0.201527i \(0.0645904\pi\)
−0.315214 + 0.949021i \(0.602076\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 12.5000 + 21.6506i 0.636233 + 1.10199i
\(387\) −3.00000 + 5.19615i −0.152499 + 0.264135i
\(388\) −9.00000 + 15.5885i −0.456906 + 0.791384i
\(389\) 39.0000 1.97738 0.988689 0.149979i \(-0.0479205\pi\)
0.988689 + 0.149979i \(0.0479205\pi\)
\(390\) 0 0
\(391\) 20.0000 1.01144
\(392\) −4.50000 + 7.79423i −0.227284 + 0.393668i
\(393\) 0 0
\(394\) 3.00000 + 5.19615i 0.151138 + 0.261778i
\(395\) −6.00000 −0.301893
\(396\) 0 0
\(397\) −7.00000 12.1244i −0.351320 0.608504i 0.635161 0.772380i \(-0.280934\pi\)
−0.986481 + 0.163876i \(0.947600\pi\)
\(398\) 26.0000 1.30326
\(399\) 0 0
\(400\) 2.00000 3.46410i 0.100000 0.173205i
\(401\) 15.5000 26.8468i 0.774033 1.34066i −0.161303 0.986905i \(-0.551570\pi\)
0.935336 0.353760i \(-0.115097\pi\)
\(402\) 0 0
\(403\) 2.50000 + 2.59808i 0.124534 + 0.129419i
\(404\) 7.00000 0.348263
\(405\) 13.5000 23.3827i 0.670820 1.16190i
\(406\) −3.00000 + 5.19615i −0.148888 + 0.257881i
\(407\) 0 0
\(408\) 0 0
\(409\) 15.5000 + 26.8468i 0.766426 + 1.32749i 0.939490 + 0.342578i \(0.111300\pi\)
−0.173064 + 0.984911i \(0.555367\pi\)
\(410\) 10.5000 + 18.1865i 0.518558 + 0.898169i
\(411\) 0 0
\(412\) 0 0
\(413\) 6.00000 10.3923i 0.295241 0.511372i
\(414\) 6.00000 10.3923i 0.294884 0.510754i
\(415\) 6.00000 0.294528
\(416\) −5.00000 + 17.3205i −0.245145 + 0.849208i
\(417\) 0 0
\(418\) 0 0
\(419\) 18.0000 31.1769i 0.879358 1.52309i 0.0273103 0.999627i \(-0.491306\pi\)
0.852047 0.523465i \(-0.175361\pi\)
\(420\) 0 0
\(421\) 1.00000 0.0487370 0.0243685 0.999703i \(-0.492242\pi\)
0.0243685 + 0.999703i \(0.492242\pi\)
\(422\) 5.00000 + 8.66025i 0.243396 + 0.421575i
\(423\) −9.00000 15.5885i −0.437595 0.757937i
\(424\) 27.0000 1.31124
\(425\) −10.0000 17.3205i −0.485071 0.840168i
\(426\) 0 0
\(427\) 1.00000 1.73205i 0.0483934 0.0838198i
\(428\) −10.0000 −0.483368
\(429\) 0 0
\(430\) 6.00000 0.289346
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 0 0
\(433\) 5.50000 + 9.52628i 0.264313 + 0.457804i 0.967383 0.253317i \(-0.0815214\pi\)
−0.703070 + 0.711120i \(0.748188\pi\)
\(434\) −2.00000 −0.0960031
\(435\) 0 0
\(436\) −5.00000 8.66025i −0.239457 0.414751i
\(437\) 16.0000 0.765384
\(438\) 0 0
\(439\) 5.00000 8.66025i 0.238637 0.413331i −0.721686 0.692220i \(-0.756633\pi\)
0.960323 + 0.278889i \(0.0899661\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) −12.5000 12.9904i −0.594564 0.617889i
\(443\) −22.0000 −1.04525 −0.522626 0.852562i \(-0.675047\pi\)
−0.522626 + 0.852562i \(0.675047\pi\)
\(444\) 0 0
\(445\) −9.00000 + 15.5885i −0.426641 + 0.738964i
\(446\) −7.00000 12.1244i −0.331460 0.574105i
\(447\) 0 0
\(448\) −7.00000 12.1244i −0.330719 0.572822i
\(449\) −7.00000 12.1244i −0.330350 0.572184i 0.652230 0.758021i \(-0.273834\pi\)
−0.982581 + 0.185837i \(0.940500\pi\)
\(450\) −12.0000 −0.565685
\(451\) 0 0
\(452\) −0.500000 + 0.866025i −0.0235180 + 0.0407344i
\(453\) 0 0
\(454\) 12.0000 0.563188
\(455\) 6.00000 20.7846i 0.281284 0.974398i
\(456\) 0 0
\(457\) −2.50000 + 4.33013i −0.116945 + 0.202555i −0.918556 0.395292i \(-0.870643\pi\)
0.801611 + 0.597847i \(0.203977\pi\)
\(458\) −1.00000 + 1.73205i −0.0467269 + 0.0809334i
\(459\) 0 0
\(460\) 12.0000 0.559503
\(461\) 16.5000 + 28.5788i 0.768482 + 1.33105i 0.938386 + 0.345589i \(0.112321\pi\)
−0.169904 + 0.985461i \(0.554346\pi\)
\(462\) 0 0
\(463\) −42.0000 −1.95191 −0.975953 0.217982i \(-0.930053\pi\)
−0.975953 + 0.217982i \(0.930053\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) 0 0
\(466\) −7.00000 + 12.1244i −0.324269 + 0.561650i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 10.5000 2.59808i 0.485363 0.120096i
\(469\) 20.0000 0.923514
\(470\) −9.00000 + 15.5885i −0.415139 + 0.719042i
\(471\) 0 0
\(472\) −9.00000 15.5885i −0.414259 0.717517i
\(473\) 0 0
\(474\) 0 0
\(475\) −8.00000 13.8564i −0.367065 0.635776i
\(476\) −10.0000 −0.458349
\(477\) −13.5000 23.3827i −0.618123 1.07062i
\(478\) 3.00000 5.19615i 0.137217 0.237666i
\(479\) 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i \(-0.648611\pi\)
0.998392 0.0566937i \(-0.0180558\pi\)
\(480\) 0 0
\(481\) −17.5000 + 4.33013i −0.797931 + 0.197437i
\(482\) −19.0000 −0.865426
\(483\) 0 0
\(484\) −5.50000 + 9.52628i −0.250000 + 0.433013i
\(485\) −27.0000 46.7654i −1.22601 2.12351i
\(486\) 0 0
\(487\) 13.0000 + 22.5167i 0.589086 + 1.02033i 0.994352 + 0.106129i \(0.0338455\pi\)
−0.405266 + 0.914199i \(0.632821\pi\)
\(488\) −1.50000 2.59808i −0.0679018 0.117609i
\(489\) 0 0
\(490\) −4.50000 7.79423i −0.203289 0.352107i
\(491\) −12.0000 + 20.7846i −0.541552 + 0.937996i 0.457263 + 0.889332i \(0.348830\pi\)
−0.998815 + 0.0486647i \(0.984503\pi\)
\(492\) 0 0
\(493\) 15.0000 0.675566
\(494\) −10.0000 10.3923i −0.449921 0.467572i
\(495\) 0 0
\(496\) −0.500000 + 0.866025i −0.0224507 + 0.0388857i
\(497\) 4.00000 6.92820i 0.179425 0.310772i
\(498\) 0 0
\(499\) −6.00000 −0.268597 −0.134298 0.990941i \(-0.542878\pi\)
−0.134298 + 0.990941i \(0.542878\pi\)
\(500\) 1.50000 + 2.59808i 0.0670820 + 0.116190i
\(501\) 0 0
\(502\) −12.0000 −0.535586
\(503\) 21.0000 + 36.3731i 0.936344 + 1.62179i 0.772220 + 0.635355i \(0.219146\pi\)
0.164124 + 0.986440i \(0.447520\pi\)
\(504\) −9.00000 + 15.5885i −0.400892 + 0.694365i
\(505\) −10.5000 + 18.1865i −0.467244 + 0.809290i
\(506\) 0 0
\(507\) 0 0
\(508\) −2.00000 −0.0887357
\(509\) 2.50000 4.33013i 0.110811 0.191930i −0.805287 0.592886i \(-0.797989\pi\)
0.916097 + 0.400956i \(0.131322\pi\)
\(510\) 0 0
\(511\) 3.00000 + 5.19615i 0.132712 + 0.229864i
\(512\) −11.0000 −0.486136
\(513\) 0 0
\(514\) −7.50000 12.9904i −0.330811 0.572981i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 5.00000 8.66025i 0.219687 0.380510i
\(519\) 0 0
\(520\) −22.5000 23.3827i −0.986690 1.02540i
\(521\) −25.0000 −1.09527 −0.547635 0.836717i \(-0.684472\pi\)
−0.547635 + 0.836717i \(0.684472\pi\)
\(522\) 4.50000 7.79423i 0.196960 0.341144i
\(523\) 12.0000 20.7846i 0.524723 0.908848i −0.474862 0.880060i \(-0.657502\pi\)
0.999586 0.0287874i \(-0.00916457\pi\)
\(524\) −10.0000 17.3205i −0.436852 0.756650i
\(525\) 0 0
\(526\) 3.00000 + 5.19615i 0.130806 + 0.226563i
\(527\) 2.50000 + 4.33013i 0.108902 + 0.188623i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) −13.5000 + 23.3827i −0.586403 + 1.01568i
\(531\) −9.00000 + 15.5885i −0.390567 + 0.676481i
\(532\) −8.00000 −0.346844
\(533\) 24.5000 6.06218i 1.06121 0.262582i
\(534\) 0 0
\(535\) 15.0000 25.9808i 0.648507 1.12325i
\(536\) 15.0000 25.9808i 0.647901 1.12220i
\(537\) 0 0
\(538\) 18.0000 0.776035
\(539\) 0 0
\(540\) 0 0
\(541\) −3.00000 −0.128980 −0.0644900 0.997918i \(-0.520542\pi\)
−0.0644900 + 0.997918i \(0.520542\pi\)
\(542\) −12.0000 20.7846i −0.515444 0.892775i
\(543\) 0 0
\(544\) −12.5000 + 21.6506i −0.535933 + 0.928263i
\(545\) 30.0000 1.28506
\(546\) 0 0
\(547\) −22.0000 −0.940652 −0.470326 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) −3.50000 + 6.06218i −0.149513 + 0.258963i
\(549\) −1.50000 + 2.59808i −0.0640184 + 0.110883i
\(550\) 0 0
\(551\) 12.0000 0.511217
\(552\) 0 0
\(553\) −2.00000 3.46410i −0.0850487 0.147309i
\(554\) 31.0000 1.31706
\(555\) 0 0
\(556\) 5.00000 8.66025i 0.212047 0.367277i
\(557\) 18.5000 32.0429i 0.783870 1.35770i −0.145802 0.989314i \(-0.546576\pi\)
0.929672 0.368389i \(-0.120091\pi\)
\(558\) 3.00000 0.127000
\(559\) 2.00000 6.92820i 0.0845910 0.293032i
\(560\) 6.00000 0.253546
\(561\) 0 0
\(562\) −7.50000 + 12.9904i −0.316368 + 0.547966i
\(563\) 3.00000 + 5.19615i 0.126435 + 0.218992i 0.922293 0.386492i \(-0.126313\pi\)
−0.795858 + 0.605483i \(0.792980\pi\)
\(564\) 0 0
\(565\) −1.50000 2.59808i −0.0631055 0.109302i
\(566\) 2.00000 + 3.46410i 0.0840663 + 0.145607i
\(567\) 18.0000 0.755929
\(568\) −6.00000 10.3923i −0.251754 0.436051i
\(569\) −21.0000 + 36.3731i −0.880366 + 1.52484i −0.0294311 + 0.999567i \(0.509370\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(570\) 0 0
\(571\) 34.0000 1.42286 0.711428 0.702759i \(-0.248049\pi\)
0.711428 + 0.702759i \(0.248049\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −7.00000 + 12.1244i −0.292174 + 0.506061i
\(575\) −8.00000 + 13.8564i −0.333623 + 0.577852i
\(576\) 10.5000 + 18.1865i 0.437500 + 0.757772i
\(577\) −21.0000 −0.874241 −0.437121 0.899403i \(-0.644002\pi\)
−0.437121 + 0.899403i \(0.644002\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) 0 0
\(580\) 9.00000 0.373705
\(581\) 2.00000 + 3.46410i 0.0829740 + 0.143715i
\(582\) 0 0
\(583\) 0 0
\(584\) 9.00000 0.372423
\(585\) −9.00000 + 31.1769i −0.372104 + 1.28901i
\(586\) −19.0000 −0.784883
\(587\) 6.00000 10.3923i 0.247647 0.428936i −0.715226 0.698893i \(-0.753676\pi\)
0.962872 + 0.269957i \(0.0870095\pi\)
\(588\) 0 0
\(589\) 2.00000 + 3.46410i 0.0824086 + 0.142736i
\(590\) 18.0000 0.741048
\(591\) 0 0
\(592\) −2.50000 4.33013i −0.102749 0.177967i
\(593\) −45.0000 −1.84793 −0.923964 0.382479i \(-0.875070\pi\)
−0.923964 + 0.382479i \(0.875070\pi\)
\(594\) 0 0
\(595\) 15.0000 25.9808i 0.614940 1.06511i
\(596\) 6.50000 11.2583i 0.266250 0.461159i
\(597\) 0 0
\(598\) −4.00000 + 13.8564i −0.163572 + 0.566631i
\(599\) 6.00000 0.245153 0.122577 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) 0 0
\(601\) −4.50000 + 7.79423i −0.183559 + 0.317933i −0.943090 0.332538i \(-0.892095\pi\)
0.759531 + 0.650471i \(0.225428\pi\)
\(602\) 2.00000 + 3.46410i 0.0815139 + 0.141186i
\(603\) −30.0000 −1.22169
\(604\) −7.00000 12.1244i −0.284826 0.493333i
\(605\) −16.5000 28.5788i −0.670820 1.16190i
\(606\) 0 0
\(607\) −19.0000 32.9090i −0.771186 1.33573i −0.936913 0.349562i \(-0.886330\pi\)
0.165727 0.986172i \(-0.447003\pi\)
\(608\) −10.0000 + 17.3205i −0.405554 + 0.702439i
\(609\) 0 0
\(610\) 3.00000 0.121466
\(611\) 15.0000 + 15.5885i 0.606835 + 0.630641i
\(612\) 15.0000 0.606339
\(613\) −15.5000 + 26.8468i −0.626039 + 1.08433i 0.362300 + 0.932062i \(0.381992\pi\)
−0.988339 + 0.152270i \(0.951342\pi\)
\(614\) 16.0000 27.7128i 0.645707 1.11840i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.50000 2.59808i −0.0603877 0.104595i 0.834251 0.551385i \(-0.185900\pi\)
−0.894639 + 0.446790i \(0.852567\pi\)
\(618\) 0 0
\(619\) −30.0000 −1.20580 −0.602901 0.797816i \(-0.705989\pi\)
−0.602901 + 0.797816i \(0.705989\pi\)
\(620\) 1.50000 + 2.59808i 0.0602414 + 0.104341i
\(621\) 0 0
\(622\) 13.0000 22.5167i 0.521253 0.902836i
\(623\) −12.0000 −0.480770
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) −3.00000 + 5.19615i −0.119904 + 0.207680i
\(627\) 0 0
\(628\) 4.50000 + 7.79423i 0.179570 + 0.311024i
\(629\) −25.0000 −0.996815
\(630\) −9.00000 15.5885i −0.358569 0.621059i
\(631\) 7.00000 + 12.1244i 0.278666 + 0.482663i 0.971053 0.238863i \(-0.0767746\pi\)
−0.692388 + 0.721526i \(0.743441\pi\)
\(632\) −6.00000 −0.238667
\(633\) 0 0
\(634\) 3.50000 6.06218i 0.139003 0.240760i
\(635\) 3.00000 5.19615i 0.119051 0.206203i
\(636\) 0 0
\(637\) −10.5000 + 2.59808i −0.416025 + 0.102940i
\(638\) 0 0
\(639\) −6.00000 + 10.3923i −0.237356 + 0.411113i
\(640\) −4.50000 + 7.79423i −0.177878 + 0.308094i
\(641\) −4.50000 7.79423i −0.177739 0.307854i 0.763367 0.645966i \(-0.223545\pi\)
−0.941106 + 0.338112i \(0.890212\pi\)
\(642\) 0 0
\(643\) 23.0000 + 39.8372i 0.907031 + 1.57102i 0.818167 + 0.574981i \(0.194991\pi\)
0.0888646 + 0.996044i \(0.471676\pi\)
\(644\) 4.00000 + 6.92820i 0.157622 + 0.273009i
\(645\) 0 0
\(646\) −10.0000 17.3205i −0.393445 0.681466i
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) 13.5000 23.3827i 0.530330 0.918559i
\(649\) 0 0
\(650\) 14.0000 3.46410i 0.549125 0.135873i
\(651\) 0 0
\(652\) 3.00000 5.19615i 0.117489 0.203497i
\(653\) −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) 0 0
\(655\) 60.0000 2.34439
\(656\) 3.50000 + 6.06218i 0.136652 + 0.236688i
\(657\) −4.50000 7.79423i −0.175562 0.304082i
\(658\) −12.0000 −0.467809
\(659\) −14.0000 24.2487i −0.545363 0.944596i −0.998584 0.0531977i \(-0.983059\pi\)
0.453221 0.891398i \(-0.350275\pi\)
\(660\) 0 0
\(661\) −6.50000 + 11.2583i −0.252821 + 0.437898i −0.964301 0.264807i \(-0.914692\pi\)
0.711481 + 0.702706i \(0.248025\pi\)
\(662\) 10.0000 0.388661
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 12.0000 20.7846i 0.465340 0.805993i
\(666\) −7.50000 + 12.9904i −0.290619 + 0.503367i
\(667\) −6.00000 10.3923i −0.232321 0.402392i
\(668\) 22.0000 0.851206
\(669\) 0 0
\(670\) 15.0000 + 25.9808i 0.579501 + 1.00372i
\(671\) 0 0
\(672\) 0 0
\(673\) −20.5000 + 35.5070i −0.790217 + 1.36870i 0.135615 + 0.990762i \(0.456699\pi\)
−0.925832 + 0.377934i \(0.876635\pi\)
\(674\) −14.5000 + 25.1147i −0.558519 + 0.967384i
\(675\) 0 0
\(676\) −11.5000 + 6.06218i −0.442308 + 0.233161i
\(677\) 2.00000 0.0768662 0.0384331 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 0 0
\(679\) 18.0000 31.1769i 0.690777 1.19646i
\(680\) −22.5000 38.9711i −0.862836 1.49448i
\(681\) 0 0
\(682\) 0 0
\(683\) −19.0000 32.9090i −0.727015 1.25923i −0.958139 0.286302i \(-0.907574\pi\)
0.231125 0.972924i \(-0.425760\pi\)
\(684\) 12.0000 0.458831
\(685\) −10.5000 18.1865i −0.401184 0.694872i
\(686\) 10.0000 17.3205i 0.381802 0.661300i
\(687\) 0 0
\(688\) 2.00000 0.0762493
\(689\) 22.5000 + 23.3827i 0.857182 + 0.890809i
\(690\) 0 0
\(691\) −10.0000 + 17.3205i −0.380418 + 0.658903i −0.991122 0.132956i \(-0.957553\pi\)
0.610704 + 0.791859i \(0.290887\pi\)
\(692\) 7.00000 12.1244i 0.266100 0.460899i
\(693\) 0 0
\(694\) −30.0000 −1.13878
\(695\) 15.0000 + 25.9808i 0.568982 + 0.985506i
\(696\) 0 0
\(697\) 35.0000 1.32572
\(698\) −7.00000 12.1244i −0.264954 0.458914i
\(699\) 0 0
\(700\) 4.00000 6.92820i 0.151186 0.261861i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) −20.0000 −0.754314
\(704\) 0 0
\(705\) 0 0
\(706\) 9.50000 + 16.4545i 0.357537 + 0.619273i
\(707\) −14.0000 −0.526524
\(708\) 0 0
\(709\) −17.5000 30.3109i −0.657226 1.13835i −0.981331 0.192328i \(-0.938396\pi\)
0.324104 0.946021i \(-0.394937\pi\)
\(710\) 12.0000 0.450352
\(711\) 3.00000 + 5.19615i 0.112509 + 0.194871i
\(712\) −9.00000 + 15.5885i −0.337289 + 0.584202i
\(713\) 2.00000 3.46410i 0.0749006 0.129732i
\(714\) 0 0
\(715\) 0 0
\(716\) 20.0000 0.747435
\(717\) 0 0
\(718\) 15.0000 25.9808i 0.559795 0.969593i
\(719\) −20.0000 34.6410i −0.745874 1.29189i −0.949785 0.312903i \(-0.898699\pi\)
0.203911 0.978989i \(-0.434635\pi\)
\(720\) −9.00000 −0.335410
\(721\) 0 0
\(722\) 1.50000 + 2.59808i 0.0558242 + 0.0966904i
\(723\) 0 0
\(724\) −0.500000 0.866025i −0.0185824 0.0321856i
\(725\) −6.00000 + 10.3923i −0.222834 + 0.385961i
\(726\) 0 0
\(727\) 16.0000 0.593407 0.296704 0.954970i \(-0.404113\pi\)
0.296704 + 0.954970i \(0.404113\pi\)
\(728\) 6.00000 20.7846i 0.222375 0.770329i
\(729\) −27.0000 −1.00000
\(730\) −4.50000 + 7.79423i −0.166552 + 0.288477i
\(731\) 5.00000 8.66025i 0.184932 0.320311i
\(732\) 0 0
\(733\) 41.0000 1.51437 0.757185 0.653201i \(-0.226574\pi\)
0.757185 + 0.653201i \(0.226574\pi\)
\(734\) −15.0000 25.9808i −0.553660 0.958967i
\(735\) 0 0
\(736\) 20.0000 0.737210
\(737\) 0 0
\(738\) 10.5000 18.1865i 0.386510 0.669456i
\(739\) −25.0000 + 43.3013i −0.919640 + 1.59286i −0.119677 + 0.992813i \(0.538186\pi\)
−0.799962 + 0.600050i \(0.795147\pi\)
\(740\) −15.0000 −0.551411
\(741\) 0 0
\(742\) −18.0000 −0.660801
\(743\) 4.00000 6.92820i 0.146746 0.254171i −0.783277 0.621673i \(-0.786453\pi\)
0.930023 + 0.367502i \(0.119787\pi\)
\(744\) 0 0
\(745\) 19.5000 + 33.7750i 0.714425 + 1.23742i
\(746\) 13.0000 0.475964
\(747\) −3.00000 5.19615i −0.109764 0.190117i
\(748\) 0 0
\(749\) 20.0000 0.730784
\(750\) 0 0
\(751\) 10.0000 17.3205i 0.364905 0.632034i −0.623856 0.781540i \(-0.714435\pi\)
0.988761 + 0.149505i \(0.0477681\pi\)
\(752\) −3.00000 + 5.19615i −0.109399 + 0.189484i
\(753\) 0 0
\(754\) −3.00000 + 10.3923i −0.109254 + 0.378465i
\(755\) 42.0000 1.52854
\(756\) 0 0
\(757\) 3.00000 5.19615i 0.109037 0.188857i −0.806343 0.591448i \(-0.798557\pi\)
0.915380 + 0.402590i \(0.131890\pi\)
\(758\) −3.00000 5.19615i −0.108965 0.188733i
\(759\) 0 0
\(760\) −18.0000 31.1769i −0.652929 1.13091i
\(761\) 5.00000 + 8.66025i 0.181250 + 0.313934i 0.942306 0.334752i \(-0.108652\pi\)
−0.761057 + 0.648686i \(0.775319\pi\)
\(762\) 0 0
\(763\) 10.0000 + 17.3205i 0.362024 + 0.627044i
\(764\) −4.00000 + 6.92820i −0.144715 + 0.250654i
\(765\) −22.5000 + 38.9711i −0.813489 + 1.40900i
\(766\) −26.0000 −0.939418
\(767\) 6.00000 20.7846i 0.216647 0.750489i
\(768\) 0 0
\(769\) −15.0000 + 25.9808i −0.540914 + 0.936890i 0.457938 + 0.888984i \(0.348588\pi\)
−0.998852 + 0.0479061i \(0.984745\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 25.0000 0.899770
\(773\) −9.00000 15.5885i −0.323708 0.560678i 0.657542 0.753418i \(-0.271596\pi\)
−0.981250 + 0.192740i \(0.938263\pi\)
\(774\) −3.00000 5.19615i −0.107833 0.186772i
\(775\) −4.00000 −0.143684
\(776\) −27.0000 46.7654i −0.969244 1.67878i
\(777\) 0 0
\(778\) −19.5000 + 33.7750i −0.699109 + 1.21089i
\(779\) 28.0000 1.00320
\(780\) 0 0
\(781\) 0 0
\(782\) −10.0000 + 17.3205i −0.357599 + 0.619380i
\(783\) 0 0
\(784\) −1.50000 2.59808i −0.0535714 0.0927884i
\(785\) −27.0000 −0.963671
\(786\) 0 0
\(787\) −23.0000 39.8372i −0.819861 1.42004i −0.905784 0.423740i \(-0.860717\pi\)
0.0859225 0.996302i \(-0.472616\pi\)
\(788\) 6.00000 0.213741
\(789\) 0 0
\(790\) 3.00000 5.19615i 0.106735 0.184871i
\(791\) 1.00000 1.73205i 0.0355559 0.0615846i
\(792\) 0 0
\(793\) 1.00000 3.46410i 0.0355110 0.123014i
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) 13.0000 22.5167i 0.460773 0.798082i
\(797\) 19.0000 + 32.9090i 0.673015 + 1.16570i 0.977045 + 0.213033i \(0.0683342\pi\)
−0.304030 + 0.952662i \(0.598332\pi\)
\(798\) 0 0
\(799\) 15.0000 + 25.9808i 0.530662 + 0.919133i
\(800\) −10.0000 17.3205i −0.353553 0.612372i
\(801\) 18.0000 0.635999
\(802\) 15.5000 +