Properties

Label 1950.2.i.d.451.1
Level $1950$
Weight $2$
Character 1950.451
Analytic conductor $15.571$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
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: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1950.451
Dual form 1950.2.i.d.601.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.50000 - 4.33013i) q^{11} +1.00000 q^{12} +(1.00000 + 3.46410i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +1.00000 q^{18} +(1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(2.50000 + 4.33013i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.50000 - 0.866025i) q^{26} +1.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(-2.50000 + 4.33013i) q^{29} -11.0000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.50000 + 4.33013i) q^{33} +2.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(1.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(-3.50000 - 0.866025i) q^{39} +(1.00000 - 1.73205i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(-5.50000 - 9.52628i) q^{43} -5.00000 q^{44} +(-0.500000 - 0.866025i) q^{46} -9.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +2.00000 q^{51} +(2.50000 - 2.59808i) q^{52} -6.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.00000 - 1.73205i) q^{56} -2.00000 q^{57} +(-2.50000 - 4.33013i) q^{58} +(7.50000 + 12.9904i) q^{59} +(-5.00000 - 8.66025i) q^{61} +(5.50000 - 9.52628i) q^{62} +(-1.00000 + 1.73205i) q^{63} +1.00000 q^{64} -5.00000 q^{66} +(8.00000 - 13.8564i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(-0.500000 - 0.866025i) q^{69} +(-0.500000 - 0.866025i) q^{72} +6.00000 q^{73} +(1.50000 + 2.59808i) q^{74} +(1.00000 - 1.73205i) q^{76} -10.0000 q^{77} +(2.50000 - 2.59808i) q^{78} -11.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{82} -6.00000 q^{83} +(-1.00000 - 1.73205i) q^{84} +11.0000 q^{86} +(-2.50000 - 4.33013i) q^{87} +(2.50000 - 4.33013i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(5.00000 - 5.19615i) q^{91} +1.00000 q^{92} +(5.50000 - 9.52628i) q^{93} +(4.50000 - 7.79423i) q^{94} +1.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(1.50000 + 2.59808i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{3} - q^{4} - q^{6} - 2q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{3} - q^{4} - q^{6} - 2q^{7} + 2q^{8} - q^{9} + 5q^{11} + 2q^{12} + 2q^{13} + 4q^{14} - q^{16} - 2q^{17} + 2q^{18} + 2q^{19} + 4q^{21} + 5q^{22} - q^{23} - q^{24} - 7q^{26} + 2q^{27} - 2q^{28} - 5q^{29} - 22q^{31} - q^{32} + 5q^{33} + 4q^{34} - q^{36} + 3q^{37} - 4q^{38} - 7q^{39} + 2q^{41} - 2q^{42} - 11q^{43} - 10q^{44} - q^{46} - 18q^{47} - q^{48} + 3q^{49} + 4q^{51} + 5q^{52} - 12q^{53} - q^{54} - 2q^{56} - 4q^{57} - 5q^{58} + 15q^{59} - 10q^{61} + 11q^{62} - 2q^{63} + 2q^{64} - 10q^{66} + 16q^{67} - 2q^{68} - q^{69} - q^{72} + 12q^{73} + 3q^{74} + 2q^{76} - 20q^{77} + 5q^{78} - 22q^{79} - q^{81} + 2q^{82} - 12q^{83} - 2q^{84} + 22q^{86} - 5q^{87} + 5q^{88} - 2q^{89} + 10q^{91} + 2q^{92} + 11q^{93} + 9q^{94} + 2q^{96} - 2q^{97} + 3q^{98} - 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000 + 3.46410i 0.277350 + 0.960769i
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i \(-0.0929851\pi\)
−0.728219 + 0.685344i \(0.759652\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) 2.50000 + 4.33013i 0.533002 + 0.923186i
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) −3.50000 0.866025i −0.686406 0.169842i
\(27\) 1.00000 0.192450
\(28\) −1.00000 + 1.73205i −0.188982 + 0.327327i
\(29\) −2.50000 + 4.33013i −0.464238 + 0.804084i −0.999167 0.0408130i \(-0.987005\pi\)
0.534928 + 0.844897i \(0.320339\pi\)
\(30\) 0 0
\(31\) −11.0000 −1.97566 −0.987829 0.155543i \(-0.950287\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 2.50000 + 4.33013i 0.435194 + 0.753778i
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 1.50000 2.59808i 0.246598 0.427121i −0.715981 0.698119i \(-0.754020\pi\)
0.962580 + 0.270998i \(0.0873538\pi\)
\(38\) −2.00000 −0.324443
\(39\) −3.50000 0.866025i −0.560449 0.138675i
\(40\) 0 0
\(41\) 1.00000 1.73205i 0.156174 0.270501i −0.777312 0.629115i \(-0.783417\pi\)
0.933486 + 0.358614i \(0.116751\pi\)
\(42\) −1.00000 + 1.73205i −0.154303 + 0.267261i
\(43\) −5.50000 9.52628i −0.838742 1.45274i −0.890947 0.454108i \(-0.849958\pi\)
0.0522047 0.998636i \(-0.483375\pi\)
\(44\) −5.00000 −0.753778
\(45\) 0 0
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) −9.00000 −1.31278 −0.656392 0.754420i \(-0.727918\pi\)
−0.656392 + 0.754420i \(0.727918\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0 0
\(51\) 2.00000 0.280056
\(52\) 2.50000 2.59808i 0.346688 0.360288i
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −1.00000 1.73205i −0.133631 0.231455i
\(57\) −2.00000 −0.264906
\(58\) −2.50000 4.33013i −0.328266 0.568574i
\(59\) 7.50000 + 12.9904i 0.976417 + 1.69120i 0.675178 + 0.737655i \(0.264067\pi\)
0.301239 + 0.953549i \(0.402600\pi\)
\(60\) 0 0
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) 5.50000 9.52628i 0.698501 1.20984i
\(63\) −1.00000 + 1.73205i −0.125988 + 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −5.00000 −0.615457
\(67\) 8.00000 13.8564i 0.977356 1.69283i 0.305424 0.952217i \(-0.401202\pi\)
0.671932 0.740613i \(-0.265465\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) −0.500000 0.866025i −0.0601929 0.104257i
\(70\) 0 0
\(71\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 1.50000 + 2.59808i 0.174371 + 0.302020i
\(75\) 0 0
\(76\) 1.00000 1.73205i 0.114708 0.198680i
\(77\) −10.0000 −1.13961
\(78\) 2.50000 2.59808i 0.283069 0.294174i
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.00000 + 1.73205i 0.110432 + 0.191273i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −1.00000 1.73205i −0.109109 0.188982i
\(85\) 0 0
\(86\) 11.0000 1.18616
\(87\) −2.50000 4.33013i −0.268028 0.464238i
\(88\) 2.50000 4.33013i 0.266501 0.461593i
\(89\) −1.00000 + 1.73205i −0.106000 + 0.183597i −0.914146 0.405385i \(-0.867138\pi\)
0.808146 + 0.588982i \(0.200471\pi\)
\(90\) 0 0
\(91\) 5.00000 5.19615i 0.524142 0.544705i
\(92\) 1.00000 0.104257
\(93\) 5.50000 9.52628i 0.570323 0.987829i
\(94\) 4.50000 7.79423i 0.464140 0.803913i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 1.50000 + 2.59808i 0.151523 + 0.262445i
\(99\) −5.00000 −0.502519
\(100\) 0 0
\(101\) −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i \(-0.865059\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) −1.00000 + 1.73205i −0.0990148 + 0.171499i
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) 1.00000 + 3.46410i 0.0980581 + 0.339683i
\(105\) 0 0
\(106\) 3.00000 5.19615i 0.291386 0.504695i
\(107\) 5.00000 8.66025i 0.483368 0.837218i −0.516449 0.856318i \(-0.672747\pi\)
0.999818 + 0.0190994i \(0.00607989\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 0 0
\(111\) 1.50000 + 2.59808i 0.142374 + 0.246598i
\(112\) 2.00000 0.188982
\(113\) 5.50000 + 9.52628i 0.517396 + 0.896157i 0.999796 + 0.0202056i \(0.00643208\pi\)
−0.482399 + 0.875951i \(0.660235\pi\)
\(114\) 1.00000 1.73205i 0.0936586 0.162221i
\(115\) 0 0
\(116\) 5.00000 0.464238
\(117\) 2.50000 2.59808i 0.231125 0.240192i
\(118\) −15.0000 −1.38086
\(119\) −2.00000 + 3.46410i −0.183340 + 0.317554i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 10.0000 0.905357
\(123\) 1.00000 + 1.73205i 0.0901670 + 0.156174i
\(124\) 5.50000 + 9.52628i 0.493915 + 0.855485i
\(125\) 0 0
\(126\) −1.00000 1.73205i −0.0890871 0.154303i
\(127\) 1.00000 1.73205i 0.0887357 0.153695i −0.818241 0.574875i \(-0.805051\pi\)
0.906977 + 0.421180i \(0.138384\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 11.0000 0.968496
\(130\) 0 0
\(131\) −1.00000 −0.0873704 −0.0436852 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) 2.50000 4.33013i 0.217597 0.376889i
\(133\) 2.00000 3.46410i 0.173422 0.300376i
\(134\) 8.00000 + 13.8564i 0.691095 + 1.19701i
\(135\) 0 0
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) −5.50000 9.52628i −0.469897 0.813885i 0.529511 0.848303i \(-0.322376\pi\)
−0.999408 + 0.0344182i \(0.989042\pi\)
\(138\) 1.00000 0.0851257
\(139\) −1.00000 1.73205i −0.0848189 0.146911i 0.820495 0.571654i \(-0.193698\pi\)
−0.905314 + 0.424743i \(0.860365\pi\)
\(140\) 0 0
\(141\) 4.50000 7.79423i 0.378968 0.656392i
\(142\) 0 0
\(143\) 17.5000 + 4.33013i 1.46342 + 0.362103i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −3.00000 + 5.19615i −0.248282 + 0.430037i
\(147\) 1.50000 + 2.59808i 0.123718 + 0.214286i
\(148\) −3.00000 −0.246598
\(149\) −8.50000 14.7224i −0.696347 1.20611i −0.969724 0.244202i \(-0.921474\pi\)
0.273377 0.961907i \(-0.411859\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) −1.00000 + 1.73205i −0.0808452 + 0.140028i
\(154\) 5.00000 8.66025i 0.402911 0.697863i
\(155\) 0 0
\(156\) 1.00000 + 3.46410i 0.0800641 + 0.277350i
\(157\) 7.00000 0.558661 0.279330 0.960195i \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(158\) 5.50000 9.52628i 0.437557 0.757870i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 0 0
\(161\) 2.00000 0.157622
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −7.50000 12.9904i −0.587445 1.01749i −0.994566 0.104111i \(-0.966800\pi\)
0.407120 0.913375i \(-0.366533\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) 1.50000 2.59808i 0.116073 0.201045i −0.802135 0.597143i \(-0.796303\pi\)
0.918208 + 0.396098i \(0.129636\pi\)
\(168\) 2.00000 0.154303
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 0 0
\(171\) 1.00000 1.73205i 0.0764719 0.132453i
\(172\) −5.50000 + 9.52628i −0.419371 + 0.726372i
\(173\) 10.0000 + 17.3205i 0.760286 + 1.31685i 0.942703 + 0.333633i \(0.108275\pi\)
−0.182417 + 0.983221i \(0.558392\pi\)
\(174\) 5.00000 0.379049
\(175\) 0 0
\(176\) 2.50000 + 4.33013i 0.188445 + 0.326396i
\(177\) −15.0000 −1.12747
\(178\) −1.00000 1.73205i −0.0749532 0.129823i
\(179\) 6.50000 11.2583i 0.485833 0.841487i −0.514035 0.857769i \(-0.671850\pi\)
0.999867 + 0.0162823i \(0.00518305\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 2.00000 + 6.92820i 0.148250 + 0.513553i
\(183\) 10.0000 0.739221
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 0 0
\(186\) 5.50000 + 9.52628i 0.403280 + 0.698501i
\(187\) −10.0000 −0.731272
\(188\) 4.50000 + 7.79423i 0.328196 + 0.568453i
\(189\) −1.00000 1.73205i −0.0727393 0.125988i
\(190\) 0 0
\(191\) −2.00000 3.46410i −0.144715 0.250654i 0.784552 0.620063i \(-0.212893\pi\)
−0.929267 + 0.369410i \(0.879560\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −12.0000 + 20.7846i −0.863779 + 1.49611i 0.00447566 + 0.999990i \(0.498575\pi\)
−0.868255 + 0.496119i \(0.834758\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −4.00000 + 6.92820i −0.284988 + 0.493614i −0.972606 0.232458i \(-0.925323\pi\)
0.687618 + 0.726073i \(0.258656\pi\)
\(198\) 2.50000 4.33013i 0.177667 0.307729i
\(199\) −12.0000 20.7846i −0.850657 1.47338i −0.880616 0.473831i \(-0.842871\pi\)
0.0299585 0.999551i \(-0.490462\pi\)
\(200\) 0 0
\(201\) 8.00000 + 13.8564i 0.564276 + 0.977356i
\(202\) −1.00000 1.73205i −0.0703598 0.121867i
\(203\) 10.0000 0.701862
\(204\) −1.00000 1.73205i −0.0700140 0.121268i
\(205\) 0 0
\(206\) 5.00000 8.66025i 0.348367 0.603388i
\(207\) 1.00000 0.0695048
\(208\) −3.50000 0.866025i −0.242681 0.0600481i
\(209\) 10.0000 0.691714
\(210\) 0 0
\(211\) 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i \(-0.789367\pi\)
0.926620 + 0.375999i \(0.122700\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 0 0
\(214\) 5.00000 + 8.66025i 0.341793 + 0.592003i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 11.0000 + 19.0526i 0.746729 + 1.29337i
\(218\) 1.00000 1.73205i 0.0677285 0.117309i
\(219\) −3.00000 + 5.19615i −0.202721 + 0.351123i
\(220\) 0 0
\(221\) 5.00000 5.19615i 0.336336 0.349531i
\(222\) −3.00000 −0.201347
\(223\) 13.0000 22.5167i 0.870544 1.50783i 0.00910984 0.999959i \(-0.497100\pi\)
0.861435 0.507869i \(-0.169566\pi\)
\(224\) −1.00000 + 1.73205i −0.0668153 + 0.115728i
\(225\) 0 0
\(226\) −11.0000 −0.731709
\(227\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(228\) 1.00000 + 1.73205i 0.0662266 + 0.114708i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) 5.00000 8.66025i 0.328976 0.569803i
\(232\) −2.50000 + 4.33013i −0.164133 + 0.284287i
\(233\) −1.00000 −0.0655122 −0.0327561 0.999463i \(-0.510428\pi\)
−0.0327561 + 0.999463i \(0.510428\pi\)
\(234\) 1.00000 + 3.46410i 0.0653720 + 0.226455i
\(235\) 0 0
\(236\) 7.50000 12.9904i 0.488208 0.845602i
\(237\) 5.50000 9.52628i 0.357263 0.618798i
\(238\) −2.00000 3.46410i −0.129641 0.224544i
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 0 0
\(241\) 3.50000 + 6.06218i 0.225455 + 0.390499i 0.956456 0.291877i \(-0.0942799\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) 14.0000 0.899954
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −5.00000 + 8.66025i −0.320092 + 0.554416i
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) −5.00000 + 5.19615i −0.318142 + 0.330623i
\(248\) −11.0000 −0.698501
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) 0 0
\(251\) −12.5000 21.6506i −0.788993 1.36658i −0.926584 0.376087i \(-0.877269\pi\)
0.137591 0.990489i \(-0.456064\pi\)
\(252\) 2.00000 0.125988
\(253\) 2.50000 + 4.33013i 0.157174 + 0.272233i
\(254\) 1.00000 + 1.73205i 0.0627456 + 0.108679i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −8.50000 + 14.7224i −0.530215 + 0.918360i 0.469163 + 0.883112i \(0.344556\pi\)
−0.999379 + 0.0352486i \(0.988778\pi\)
\(258\) −5.50000 + 9.52628i −0.342415 + 0.593080i
\(259\) −6.00000 −0.372822
\(260\) 0 0
\(261\) 5.00000 0.309492
\(262\) 0.500000 0.866025i 0.0308901 0.0535032i
\(263\) 10.5000 18.1865i 0.647458 1.12143i −0.336270 0.941766i \(-0.609166\pi\)
0.983728 0.179664i \(-0.0575011\pi\)
\(264\) 2.50000 + 4.33013i 0.153864 + 0.266501i
\(265\) 0 0
\(266\) 2.00000 + 3.46410i 0.122628 + 0.212398i
\(267\) −1.00000 1.73205i −0.0611990 0.106000i
\(268\) −16.0000 −0.977356
\(269\) −7.00000 12.1244i −0.426798 0.739235i 0.569789 0.821791i \(-0.307025\pi\)
−0.996586 + 0.0825561i \(0.973692\pi\)
\(270\) 0 0
\(271\) 6.50000 11.2583i 0.394847 0.683895i −0.598235 0.801321i \(-0.704131\pi\)
0.993082 + 0.117426i \(0.0374643\pi\)
\(272\) 2.00000 0.121268
\(273\) 2.00000 + 6.92820i 0.121046 + 0.419314i
\(274\) 11.0000 0.664534
\(275\) 0 0
\(276\) −0.500000 + 0.866025i −0.0300965 + 0.0521286i
\(277\) −5.50000 9.52628i −0.330463 0.572379i 0.652140 0.758099i \(-0.273872\pi\)
−0.982603 + 0.185720i \(0.940538\pi\)
\(278\) 2.00000 0.119952
\(279\) 5.50000 + 9.52628i 0.329276 + 0.570323i
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 4.50000 + 7.79423i 0.267971 + 0.464140i
\(283\) 9.50000 16.4545i 0.564716 0.978117i −0.432360 0.901701i \(-0.642319\pi\)
0.997076 0.0764162i \(-0.0243478\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −12.5000 + 12.9904i −0.739140 + 0.768137i
\(287\) −4.00000 −0.236113
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) 2.00000 0.117242
\(292\) −3.00000 5.19615i −0.175562 0.304082i
\(293\) 3.00000 + 5.19615i 0.175262 + 0.303562i 0.940252 0.340480i \(-0.110589\pi\)
−0.764990 + 0.644042i \(0.777256\pi\)
\(294\) −3.00000 −0.174964
\(295\) 0 0
\(296\) 1.50000 2.59808i 0.0871857 0.151010i
\(297\) 2.50000 4.33013i 0.145065 0.251259i
\(298\) 17.0000 0.984784
\(299\) −3.50000 0.866025i −0.202410 0.0500835i
\(300\) 0 0
\(301\) −11.0000 + 19.0526i −0.634029 + 1.09817i
\(302\) −4.00000 + 6.92820i −0.230174 + 0.398673i
\(303\) −1.00000 1.73205i −0.0574485 0.0995037i
\(304\) −2.00000 −0.114708
\(305\) 0 0
\(306\) −1.00000 1.73205i −0.0571662 0.0990148i
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 5.00000 + 8.66025i 0.284901 + 0.493464i
\(309\) 5.00000 8.66025i 0.284440 0.492665i
\(310\) 0 0
\(311\) 20.0000 1.13410 0.567048 0.823685i \(-0.308085\pi\)
0.567048 + 0.823685i \(0.308085\pi\)
\(312\) −3.50000 0.866025i −0.198148 0.0490290i
\(313\) −20.0000 −1.13047 −0.565233 0.824931i \(-0.691214\pi\)
−0.565233 + 0.824931i \(0.691214\pi\)
\(314\) −3.50000 + 6.06218i −0.197516 + 0.342108i
\(315\) 0 0
\(316\) 5.50000 + 9.52628i 0.309399 + 0.535895i
\(317\) −16.0000 −0.898650 −0.449325 0.893368i \(-0.648335\pi\)
−0.449325 + 0.893368i \(0.648335\pi\)
\(318\) 3.00000 + 5.19615i 0.168232 + 0.291386i
\(319\) 12.5000 + 21.6506i 0.699866 + 1.21220i
\(320\) 0 0
\(321\) 5.00000 + 8.66025i 0.279073 + 0.483368i
\(322\) −1.00000 + 1.73205i −0.0557278 + 0.0965234i
\(323\) 2.00000 3.46410i 0.111283 0.192748i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 15.0000 0.830773
\(327\) 1.00000 1.73205i 0.0553001 0.0957826i
\(328\) 1.00000 1.73205i 0.0552158 0.0956365i
\(329\) 9.00000 + 15.5885i 0.496186 + 0.859419i
\(330\) 0 0
\(331\) 14.0000 + 24.2487i 0.769510 + 1.33283i 0.937829 + 0.347097i \(0.112833\pi\)
−0.168320 + 0.985732i \(0.553834\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) −3.00000 −0.164399
\(334\) 1.50000 + 2.59808i 0.0820763 + 0.142160i
\(335\) 0 0
\(336\) −1.00000 + 1.73205i −0.0545545 + 0.0944911i
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) −0.500000 12.9904i −0.0271964 0.706584i
\(339\) −11.0000 −0.597438
\(340\) 0 0
\(341\) −27.5000 + 47.6314i −1.48921 + 2.57938i
\(342\) 1.00000 + 1.73205i 0.0540738 + 0.0936586i
\(343\) −20.0000 −1.07990
\(344\) −5.50000 9.52628i −0.296540 0.513623i
\(345\) 0 0
\(346\) −20.0000 −1.07521
\(347\) 17.0000 + 29.4449i 0.912608 + 1.58068i 0.810366 + 0.585923i \(0.199268\pi\)
0.102241 + 0.994760i \(0.467399\pi\)
\(348\) −2.50000 + 4.33013i −0.134014 + 0.232119i
\(349\) −10.0000 + 17.3205i −0.535288 + 0.927146i 0.463862 + 0.885908i \(0.346463\pi\)
−0.999149 + 0.0412379i \(0.986870\pi\)
\(350\) 0 0
\(351\) 1.00000 + 3.46410i 0.0533761 + 0.184900i
\(352\) −5.00000 −0.266501
\(353\) −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i \(-0.992342\pi\)
0.520689 + 0.853746i \(0.325675\pi\)
\(354\) 7.50000 12.9904i 0.398621 0.690431i
\(355\) 0 0
\(356\) 2.00000 0.106000
\(357\) −2.00000 3.46410i −0.105851 0.183340i
\(358\) 6.50000 + 11.2583i 0.343536 + 0.595021i
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 8.00000 13.8564i 0.420471 0.728277i
\(363\) 14.0000 0.734809
\(364\) −7.00000 1.73205i −0.366900 0.0907841i
\(365\) 0 0
\(366\) −5.00000 + 8.66025i −0.261354 + 0.452679i
\(367\) −8.00000 + 13.8564i −0.417597 + 0.723299i −0.995697 0.0926670i \(-0.970461\pi\)
0.578101 + 0.815966i \(0.303794\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) −2.00000 −0.104116
\(370\) 0 0
\(371\) 6.00000 + 10.3923i 0.311504 + 0.539542i
\(372\) −11.0000 −0.570323
\(373\) −9.50000 16.4545i −0.491891 0.851981i 0.508065 0.861319i \(-0.330361\pi\)
−0.999956 + 0.00933789i \(0.997028\pi\)
\(374\) 5.00000 8.66025i 0.258544 0.447811i
\(375\) 0 0
\(376\) −9.00000 −0.464140
\(377\) −17.5000 4.33013i −0.901296 0.223013i
\(378\) 2.00000 0.102869
\(379\) 1.00000 1.73205i 0.0513665 0.0889695i −0.839199 0.543825i \(-0.816976\pi\)
0.890565 + 0.454855i \(0.150309\pi\)
\(380\) 0 0
\(381\) 1.00000 + 1.73205i 0.0512316 + 0.0887357i
\(382\) 4.00000 0.204658
\(383\) 15.5000 + 26.8468i 0.792013 + 1.37181i 0.924719 + 0.380651i \(0.124300\pi\)
−0.132706 + 0.991155i \(0.542367\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) −12.0000 20.7846i −0.610784 1.05791i
\(387\) −5.50000 + 9.52628i −0.279581 + 0.484248i
\(388\) −1.00000 + 1.73205i −0.0507673 + 0.0879316i
\(389\) 5.00000 0.253510 0.126755 0.991934i \(-0.459544\pi\)
0.126755 + 0.991934i \(0.459544\pi\)
\(390\) 0 0
\(391\) 2.00000 0.101144
\(392\) 1.50000 2.59808i 0.0757614 0.131223i
\(393\) 0.500000 0.866025i 0.0252217 0.0436852i
\(394\) −4.00000 6.92820i −0.201517 0.349038i
\(395\) 0 0
\(396\) 2.50000 + 4.33013i 0.125630 + 0.217597i
\(397\) 1.50000 + 2.59808i 0.0752828 + 0.130394i 0.901209 0.433384i \(-0.142681\pi\)
−0.825926 + 0.563778i \(0.809347\pi\)
\(398\) 24.0000 1.20301
\(399\) 2.00000 + 3.46410i 0.100125 + 0.173422i
\(400\) 0 0
\(401\) −18.0000 + 31.1769i −0.898877 + 1.55690i −0.0699455 + 0.997551i \(0.522283\pi\)
−0.828932 + 0.559350i \(0.811051\pi\)
\(402\) −16.0000 −0.798007
\(403\) −11.0000 38.1051i −0.547949 1.89815i
\(404\) 2.00000 0.0995037
\(405\) 0 0
\(406\) −5.00000 + 8.66025i −0.248146 + 0.429801i
\(407\) −7.50000 12.9904i −0.371761 0.643909i
\(408\) 2.00000 0.0990148
\(409\) −15.0000 25.9808i −0.741702 1.28467i −0.951720 0.306968i \(-0.900685\pi\)
0.210017 0.977698i \(-0.432648\pi\)
\(410\) 0 0
\(411\) 11.0000 0.542590
\(412\) 5.00000 + 8.66025i 0.246332 + 0.426660i
\(413\) 15.0000 25.9808i 0.738102 1.27843i
\(414\) −0.500000 + 0.866025i −0.0245737 + 0.0425628i
\(415\) 0 0
\(416\) 2.50000 2.59808i 0.122573 0.127381i
\(417\) 2.00000 0.0979404
\(418\) −5.00000 + 8.66025i −0.244558 + 0.423587i
\(419\) 2.00000 3.46410i 0.0977064 0.169232i −0.813029 0.582224i \(-0.802183\pi\)
0.910735 + 0.412991i \(0.135516\pi\)
\(420\) 0 0
\(421\) −16.0000 −0.779792 −0.389896 0.920859i \(-0.627489\pi\)
−0.389896 + 0.920859i \(0.627489\pi\)
\(422\) 2.00000 + 3.46410i 0.0973585 + 0.168630i
\(423\) 4.50000 + 7.79423i 0.218797 + 0.378968i
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) −10.0000 + 17.3205i −0.483934 + 0.838198i
\(428\) −10.0000 −0.483368
\(429\) −12.5000 + 12.9904i −0.603506 + 0.627182i
\(430\) 0 0
\(431\) −20.0000 + 34.6410i −0.963366 + 1.66860i −0.249424 + 0.968394i \(0.580241\pi\)
−0.713942 + 0.700205i \(0.753092\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 14.0000 + 24.2487i 0.672797 + 1.16532i 0.977108 + 0.212746i \(0.0682406\pi\)
−0.304311 + 0.952573i \(0.598426\pi\)
\(434\) −22.0000 −1.05603
\(435\) 0 0
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) −2.00000 −0.0956730
\(438\) −3.00000 5.19615i −0.143346 0.248282i
\(439\) 2.00000 3.46410i 0.0954548 0.165333i −0.814344 0.580383i \(-0.802903\pi\)
0.909798 + 0.415051i \(0.136236\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 2.00000 + 6.92820i 0.0951303 + 0.329541i
\(443\) −20.0000 −0.950229 −0.475114 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 1.50000 2.59808i 0.0711868 0.123299i
\(445\) 0 0
\(446\) 13.0000 + 22.5167i 0.615568 + 1.06619i
\(447\) 17.0000 0.804072
\(448\) −1.00000 1.73205i −0.0472456 0.0818317i
\(449\) −6.00000 10.3923i −0.283158 0.490443i 0.689003 0.724758i \(-0.258049\pi\)
−0.972161 + 0.234315i \(0.924715\pi\)
\(450\) 0 0
\(451\) −5.00000 8.66025i −0.235441 0.407795i
\(452\) 5.50000 9.52628i 0.258698 0.448078i
\(453\) −4.00000 + 6.92820i −0.187936 + 0.325515i
\(454\) 0 0
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 19.0000 32.9090i 0.888783 1.53942i 0.0474665 0.998873i \(-0.484885\pi\)
0.841316 0.540544i \(-0.181781\pi\)
\(458\) −5.00000 + 8.66025i −0.233635 + 0.404667i
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) 0 0
\(461\) 19.5000 + 33.7750i 0.908206 + 1.57306i 0.816556 + 0.577267i \(0.195881\pi\)
0.0916500 + 0.995791i \(0.470786\pi\)
\(462\) 5.00000 + 8.66025i 0.232621 + 0.402911i
\(463\) −14.0000 −0.650635 −0.325318 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) −2.50000 4.33013i −0.116060 0.201021i
\(465\) 0 0
\(466\) 0.500000 0.866025i 0.0231621 0.0401179i
\(467\) −6.00000 −0.277647 −0.138823 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) −3.50000 0.866025i −0.161788 0.0400320i
\(469\) −32.0000 −1.47762
\(470\) 0 0
\(471\) −3.50000 + 6.06218i −0.161271 + 0.279330i
\(472\) 7.50000 + 12.9904i 0.345215 + 0.597931i
\(473\) −55.0000 −2.52890
\(474\) 5.50000 + 9.52628i 0.252623 + 0.437557i
\(475\) 0 0
\(476\) 4.00000 0.183340
\(477\) 3.00000 + 5.19615i 0.137361 + 0.237915i
\(478\) 10.0000 17.3205i 0.457389 0.792222i
\(479\) 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
\(481\) 10.5000 + 2.59808i 0.478759 + 0.118462i
\(482\) −7.00000 −0.318841
\(483\) −1.00000 + 1.73205i −0.0455016 + 0.0788110i
\(484\) −7.00000 + 12.1244i −0.318182 + 0.551107i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 1.00000 + 1.73205i 0.0453143 + 0.0784867i 0.887793 0.460243i \(-0.152238\pi\)
−0.842479 + 0.538730i \(0.818904\pi\)
\(488\) −5.00000 8.66025i −0.226339 0.392031i
\(489\) 15.0000 0.678323
\(490\) 0 0
\(491\) 8.00000 13.8564i 0.361035 0.625331i −0.627096 0.778942i \(-0.715757\pi\)
0.988131 + 0.153611i \(0.0490902\pi\)
\(492\) 1.00000 1.73205i 0.0450835 0.0780869i
\(493\) 10.0000 0.450377
\(494\) −2.00000 6.92820i −0.0899843 0.311715i
\(495\) 0 0
\(496\) 5.50000 9.52628i 0.246957 0.427743i
\(497\) 0 0
\(498\) 3.00000 + 5.19615i 0.134433 + 0.232845i
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) 0 0
\(501\) 1.50000 + 2.59808i 0.0670151 + 0.116073i
\(502\) 25.0000 1.11580
\(503\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(504\) −1.00000 + 1.73205i −0.0445435 + 0.0771517i
\(505\) 0 0
\(506\) −5.00000 −0.222277
\(507\) −0.500000 12.9904i −0.0222058 0.576923i
\(508\) −2.00000 −0.0887357
\(509\) −14.5000 + 25.1147i −0.642701 + 1.11319i 0.342126 + 0.939654i \(0.388853\pi\)
−0.984827 + 0.173537i \(0.944480\pi\)
\(510\) 0 0
\(511\) −6.00000 10.3923i −0.265424 0.459728i
\(512\) 1.00000 0.0441942
\(513\) 1.00000 + 1.73205i 0.0441511 + 0.0764719i
\(514\) −8.50000 14.7224i −0.374919 0.649379i
\(515\) 0 0
\(516\) −5.50000 9.52628i −0.242124 0.419371i
\(517\) −22.5000 + 38.9711i −0.989549 + 1.71395i
\(518\) 3.00000 5.19615i 0.131812 0.228306i
\(519\) −20.0000 −0.877903
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) −2.50000 + 4.33013i −0.109422 + 0.189525i
\(523\) −15.5000 + 26.8468i −0.677768 + 1.17393i 0.297884 + 0.954602i \(0.403719\pi\)
−0.975652 + 0.219326i \(0.929614\pi\)
\(524\) 0.500000 + 0.866025i 0.0218426 + 0.0378325i
\(525\) 0 0
\(526\) 10.5000 + 18.1865i 0.457822 + 0.792971i
\(527\) 11.0000 + 19.0526i 0.479168 + 0.829943i
\(528\) −5.00000 −0.217597
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) 7.50000 12.9904i 0.325472 0.563735i
\(532\) −4.00000 −0.173422
\(533\) 7.00000 + 1.73205i 0.303204 + 0.0750234i
\(534\) 2.00000 0.0865485
\(535\) 0 0
\(536\) 8.00000 13.8564i 0.345547 0.598506i
\(537\) 6.50000 + 11.2583i 0.280496 + 0.485833i
\(538\) 14.0000 0.603583
\(539\) −7.50000 12.9904i −0.323048 0.559535i
\(540\) 0 0
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 6.50000 + 11.2583i 0.279199 + 0.483587i
\(543\) 8.00000 13.8564i 0.343313 0.594635i
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) 0 0
\(546\) −7.00000 1.73205i −0.299572 0.0741249i
\(547\) 12.0000 0.513083 0.256541 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) −5.50000 + 9.52628i −0.234948 + 0.406942i
\(549\) −5.00000 + 8.66025i −0.213395 + 0.369611i
\(550\) 0 0
\(551\) −10.0000 −0.426014
\(552\) −0.500000 0.866025i −0.0212814 0.0368605i
\(553\) 11.0000 + 19.0526i 0.467768 + 0.810197i
\(554\) 11.0000 0.467345
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) 13.0000 22.5167i 0.550828 0.954062i −0.447387 0.894340i \(-0.647645\pi\)
0.998215 0.0597213i \(-0.0190212\pi\)
\(558\) −11.0000 −0.465667
\(559\) 27.5000 28.5788i 1.16313 1.20876i
\(560\) 0 0
\(561\) 5.00000 8.66025i 0.211100 0.365636i
\(562\) 5.00000 8.66025i 0.210912 0.365311i
\(563\) 6.00000 + 10.3923i 0.252870 + 0.437983i 0.964315 0.264758i \(-0.0852922\pi\)
−0.711445 + 0.702742i \(0.751959\pi\)
\(564\) −9.00000 −0.378968
\(565\) 0 0
\(566\) 9.50000 + 16.4545i 0.399315 + 0.691633i
\(567\) 2.00000 0.0839921
\(568\) 0 0
\(569\) 11.0000 19.0526i 0.461144 0.798725i −0.537874 0.843025i \(-0.680772\pi\)
0.999018 + 0.0443003i \(0.0141058\pi\)
\(570\) 0 0
\(571\) −16.0000 −0.669579 −0.334790 0.942293i \(-0.608665\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) −5.00000 17.3205i −0.209061 0.724207i
\(573\) 4.00000 0.167102
\(574\) 2.00000 3.46410i 0.0834784 0.144589i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 22.0000 0.915872 0.457936 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) −12.0000 20.7846i −0.498703 0.863779i
\(580\) 0 0
\(581\) 6.00000 + 10.3923i 0.248922 + 0.431145i
\(582\) −1.00000 + 1.73205i −0.0414513 + 0.0717958i
\(583\) −15.0000 + 25.9808i −0.621237 + 1.07601i
\(584\) 6.00000 0.248282
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) −9.00000 + 15.5885i −0.371470 + 0.643404i −0.989792 0.142520i \(-0.954479\pi\)
0.618322 + 0.785925i \(0.287813\pi\)
\(588\) 1.50000 2.59808i 0.0618590 0.107143i
\(589\) −11.0000 19.0526i −0.453247 0.785047i
\(590\) 0 0
\(591\) −4.00000 6.92820i −0.164538 0.284988i
\(592\) 1.50000 + 2.59808i 0.0616496 + 0.106780i
\(593\) −31.0000 −1.27302 −0.636509 0.771270i \(-0.719622\pi\)
−0.636509 + 0.771270i \(0.719622\pi\)
\(594\) 2.50000 + 4.33013i 0.102576 + 0.177667i
\(595\) 0 0
\(596\) −8.50000 + 14.7224i −0.348174 + 0.603054i
\(597\) 24.0000 0.982255
\(598\) 2.50000 2.59808i 0.102233 0.106243i
\(599\) 42.0000 1.71607 0.858037 0.513588i \(-0.171684\pi\)
0.858037 + 0.513588i \(0.171684\pi\)
\(600\) 0 0
\(601\) 1.50000 2.59808i 0.0611863 0.105978i −0.833810 0.552052i \(-0.813845\pi\)
0.894996 + 0.446074i \(0.147178\pi\)
\(602\) −11.0000 19.0526i −0.448327 0.776524i
\(603\) −16.0000 −0.651570
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) 0 0
\(606\) 2.00000 0.0812444
\(607\) 9.00000 + 15.5885i 0.365299 + 0.632716i 0.988824 0.149087i \(-0.0476335\pi\)
−0.623525 + 0.781803i \(0.714300\pi\)
\(608\) 1.00000 1.73205i 0.0405554 0.0702439i
\(609\) −5.00000 + 8.66025i −0.202610 + 0.350931i
\(610\) 0 0
\(611\) −9.00000 31.1769i −0.364101 1.26128i
\(612\) 2.00000 0.0808452
\(613\) −14.5000 + 25.1147i −0.585649 + 1.01437i 0.409145 + 0.912470i \(0.365827\pi\)
−0.994794 + 0.101905i \(0.967506\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −10.0000 −0.402911
\(617\) 20.5000 + 35.5070i 0.825299 + 1.42946i 0.901691 + 0.432382i \(0.142327\pi\)
−0.0763917 + 0.997078i \(0.524340\pi\)
\(618\) 5.00000 + 8.66025i 0.201129 + 0.348367i
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 0 0
\(621\) −0.500000 + 0.866025i −0.0200643 + 0.0347524i
\(622\) −10.0000 + 17.3205i −0.400963 + 0.694489i
\(623\) 4.00000 0.160257
\(624\) 2.50000 2.59808i 0.100080 0.104006i
\(625\) 0 0
\(626\) 10.0000 17.3205i 0.399680 0.692267i
\(627\) −5.00000 + 8.66025i −0.199681 + 0.345857i
\(628\) −3.50000 6.06218i −0.139665 0.241907i
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) −20.0000 34.6410i −0.796187 1.37904i −0.922082 0.386994i \(-0.873514\pi\)
0.125895 0.992044i \(-0.459820\pi\)
\(632\) −11.0000 −0.437557
\(633\) 2.00000 + 3.46410i 0.0794929 + 0.137686i
\(634\) 8.00000 13.8564i 0.317721 0.550308i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) 10.5000 + 2.59808i 0.416025 + 0.102940i
\(638\) −25.0000 −0.989759
\(639\) 0 0
\(640\) 0 0
\(641\) 15.0000 + 25.9808i 0.592464 + 1.02618i 0.993899 + 0.110291i \(0.0351782\pi\)
−0.401435 + 0.915888i \(0.631488\pi\)
\(642\) −10.0000 −0.394669
\(643\) 4.00000 + 6.92820i 0.157745 + 0.273222i 0.934055 0.357129i \(-0.116244\pi\)
−0.776310 + 0.630351i \(0.782911\pi\)
\(644\) −1.00000 1.73205i −0.0394055 0.0682524i
\(645\) 0 0
\(646\) 2.00000 + 3.46410i 0.0786889 + 0.136293i
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 75.0000 2.94401
\(650\) 0 0
\(651\) −22.0000 −0.862248
\(652\) −7.50000 + 12.9904i −0.293723 + 0.508743i
\(653\) 17.0000 29.4449i 0.665261 1.15227i −0.313953 0.949439i \(-0.601653\pi\)
0.979214 0.202828i \(-0.0650132\pi\)
\(654\) 1.00000 + 1.73205i 0.0391031 + 0.0677285i
\(655\) 0 0
\(656\) 1.00000 + 1.73205i 0.0390434 + 0.0676252i
\(657\) −3.00000 5.19615i −0.117041 0.202721i
\(658\) −18.0000 −0.701713
\(659\) 19.5000 + 33.7750i 0.759612 + 1.31569i 0.943049 + 0.332655i \(0.107945\pi\)
−0.183436 + 0.983032i \(0.558722\pi\)
\(660\) 0 0
\(661\) −16.0000 + 27.7128i −0.622328 + 1.07790i 0.366723 + 0.930330i \(0.380480\pi\)
−0.989051 + 0.147573i \(0.952854\pi\)
\(662\) −28.0000 −1.08825
\(663\) 2.00000 + 6.92820i 0.0776736 + 0.269069i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 1.50000 2.59808i 0.0581238 0.100673i
\(667\) −2.50000 4.33013i −0.0968004 0.167663i
\(668\) −3.00000 −0.116073
\(669\) 13.0000 + 22.5167i 0.502609 + 0.870544i
\(670\) 0 0
\(671\) −50.0000 −1.93023
\(672\) −1.00000 1.73205i −0.0385758 0.0668153i
\(673\) 4.00000 6.92820i 0.154189 0.267063i −0.778575 0.627552i \(-0.784057\pi\)
0.932763 + 0.360489i \(0.117390\pi\)
\(674\) −1.00000 + 1.73205i −0.0385186 + 0.0667161i
\(675\) 0 0
\(676\) 11.5000 + 6.06218i 0.442308 + 0.233161i
\(677\) 4.00000 0.153732 0.0768662 0.997041i \(-0.475509\pi\)
0.0768662 + 0.997041i \(0.475509\pi\)
\(678\) 5.50000 9.52628i 0.211226 0.365855i
\(679\) −2.00000 + 3.46410i −0.0767530 + 0.132940i
\(680\) 0 0
\(681\) 0 0
\(682\) −27.5000 47.6314i −1.05303 1.82390i
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 0 0
\(686\) 10.0000 17.3205i 0.381802 0.661300i
\(687\) −5.00000 + 8.66025i −0.190762 + 0.330409i
\(688\) 11.0000 0.419371
\(689\) −6.00000 20.7846i −0.228582 0.791831i
\(690\) 0 0
\(691\) 15.0000 25.9808i 0.570627 0.988355i −0.425875 0.904782i \(-0.640034\pi\)
0.996502 0.0835727i \(-0.0266331\pi\)
\(692\) 10.0000 17.3205i 0.380143 0.658427i
\(693\) 5.00000 + 8.66025i 0.189934 + 0.328976i
\(694\) −34.0000 −1.29062
\(695\) 0 0
\(696\) −2.50000 4.33013i −0.0947623 0.164133i
\(697\) −4.00000 −0.151511
\(698\) −10.0000 17.3205i −0.378506 0.655591i
\(699\) 0.500000 0.866025i 0.0189117 0.0327561i
\(700\) 0 0
\(701\) 13.0000 0.491003 0.245502 0.969396i \(-0.421047\pi\)
0.245502 + 0.969396i \(0.421047\pi\)
\(702\) −3.50000 0.866025i −0.132099 0.0326860i
\(703\) 6.00000 0.226294
\(704\) 2.50000 4.33013i 0.0942223 0.163198i
\(705\) 0 0
\(706\) −9.00000 15.5885i −0.338719 0.586679i
\(707\) 4.00000 0.150435
\(708\) 7.50000 + 12.9904i 0.281867 + 0.488208i
\(709\) 4.00000 + 6.92820i 0.150223 + 0.260194i 0.931309 0.364229i \(-0.118667\pi\)
−0.781086 + 0.624423i \(0.785334\pi\)
\(710\) 0 0
\(711\) 5.50000 + 9.52628i 0.206266 + 0.357263i
\(712\) −1.00000 + 1.73205i −0.0374766 + 0.0649113i
\(713\) 5.50000 9.52628i 0.205977 0.356762i
\(714\) 4.00000 0.149696
\(715\) 0 0
\(716\) −13.0000 −0.485833
\(717\) 10.0000 17.3205i 0.373457 0.646846i
\(718\) −6.00000 + 10.3923i −0.223918 + 0.387837i
\(719\) −12.0000 20.7846i −0.447524 0.775135i 0.550700 0.834703i \(-0.314361\pi\)
−0.998224 + 0.0595683i \(0.981028\pi\)
\(720\) 0 0
\(721\) 10.0000 + 17.3205i 0.372419 + 0.645049i
\(722\) 7.50000 + 12.9904i 0.279121 + 0.483452i
\(723\) −7.00000 −0.260333
\(724\) 8.00000 + 13.8564i 0.297318 + 0.514969i
\(725\) 0 0
\(726\) −7.00000 + 12.1244i −0.259794 + 0.449977i
\(727\) 40.0000 1.48352 0.741759 0.670667i \(-0.233992\pi\)
0.741759 + 0.670667i \(0.233992\pi\)
\(728\) 5.00000 5.19615i 0.185312 0.192582i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −11.0000 + 19.0526i −0.406850 + 0.704684i
\(732\) −5.00000 8.66025i −0.184805 0.320092i
\(733\) −6.00000 −0.221615 −0.110808 0.993842i \(-0.535344\pi\)
−0.110808 + 0.993842i \(0.535344\pi\)
\(734\) −8.00000 13.8564i −0.295285 0.511449i
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −40.0000 69.2820i −1.47342 2.55204i
\(738\) 1.00000 1.73205i 0.0368105 0.0637577i
\(739\) −22.0000 + 38.1051i −0.809283 + 1.40172i 0.104078 + 0.994569i \(0.466811\pi\)
−0.913361 + 0.407150i \(0.866523\pi\)
\(740\) 0 0
\(741\) −2.00000 6.92820i −0.0734718 0.254514i
\(742\) −12.0000 −0.440534
\(743\) 25.5000 44.1673i 0.935504 1.62034i 0.161772 0.986828i \(-0.448279\pi\)
0.773732 0.633513i \(-0.218388\pi\)
\(744\) 5.50000 9.52628i 0.201640 0.349250i
\(745\) 0 0
\(746\) 19.0000 0.695639
\(747\) 3.00000 + 5.19615i 0.109764 + 0.190117i
\(748\) 5.00000 + 8.66025i 0.182818 + 0.316650i
\(749\) −20.0000 −0.730784
\(750\) 0 0
\(751\) 11.5000 19.9186i 0.419641 0.726839i −0.576262 0.817265i \(-0.695489\pi\)
0.995903 + 0.0904254i \(0.0288227\pi\)
\(752\) 4.50000 7.79423i 0.164098 0.284226i
\(753\) 25.0000 0.911051
\(754\) 12.5000 12.9904i 0.455223 0.473082i
\(755\) 0 0
\(756\) −1.00000 + 1.73205i −0.0363696 + 0.0629941i
\(757\) 5.00000 8.66025i 0.181728 0.314762i −0.760741 0.649056i \(-0.775164\pi\)
0.942469 + 0.334293i \(0.108498\pi\)
\(758\) 1.00000 + 1.73205i 0.0363216 + 0.0629109i
\(759\) −5.00000 −0.181489
\(760\) 0 0
\(761\) −10.0000 17.3205i −0.362500 0.627868i 0.625872 0.779926i \(-0.284743\pi\)
−0.988372 + 0.152058i \(0.951410\pi\)
\(762\) −2.00000 −0.0724524
\(763\) 2.00000 + 3.46410i 0.0724049 + 0.125409i
\(764\) −2.00000 + 3.46410i −0.0723575 + 0.125327i
\(765\) 0 0
\(766\) −31.0000 −1.12008
\(767\) −37.5000 + 38.9711i −1.35405 + 1.40717i
\(768\) 1.00000 0.0360844
\(769\) −21.5000 + 37.2391i −0.775310 + 1.34288i 0.159310 + 0.987229i \(0.449073\pi\)
−0.934620 + 0.355647i \(0.884260\pi\)
\(770\) 0 0
\(771\) −8.50000 14.7224i −0.306120 0.530215i
\(772\) 24.0000 0.863779
\(773\) 16.0000 + 27.7128i 0.575480 + 0.996761i 0.995989 + 0.0894724i \(0.0285181\pi\)
−0.420509 + 0.907288i \(0.638149\pi\)
\(774\) −5.50000 9.52628i −0.197693 0.342415i
\(775\) 0 0
\(776\) −1.00000 1.73205i −0.0358979 0.0621770i
\(777\) 3.00000 5.19615i 0.107624 0.186411i
\(778\) −2.50000 + 4.33013i −0.0896293 + 0.155243i
\(779\) 4.00000 0.143315
\(780\) 0 0
\(781\) 0 0
\(782\) −1.00000 + 1.73205i −0.0357599 + 0.0619380i
\(783\) −2.50000 + 4.33013i −0.0893427 + 0.154746i
\(784\) 1.50000 + 2.59808i 0.0535714 + 0.0927884i
\(785\) 0 0
\(786\) 0.500000 +