Properties

Label 380.2.i.a.201.1
Level $380$
Weight $2$
Character 380.201
Analytic conductor $3.034$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 380.201
Dual form 380.2.i.a.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} -4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} -4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} -3.00000 q^{11} +(-3.00000 - 5.19615i) q^{13} +(1.00000 + 1.73205i) q^{15} +(-1.00000 + 1.73205i) q^{17} +(3.50000 + 2.59808i) q^{19} +(4.00000 - 6.92820i) q^{21} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{27} +(-0.500000 - 0.866025i) q^{29} -5.00000 q^{31} +(3.00000 - 5.19615i) q^{33} +(-2.00000 + 3.46410i) q^{35} -4.00000 q^{37} +12.0000 q^{39} +(-1.00000 + 1.73205i) q^{41} -1.00000 q^{45} +(-3.00000 - 5.19615i) q^{47} +9.00000 q^{49} +(-2.00000 - 3.46410i) q^{51} +(3.00000 + 5.19615i) q^{53} +(-1.50000 + 2.59808i) q^{55} +(-8.00000 + 3.46410i) q^{57} +(0.500000 - 0.866025i) q^{59} +(3.50000 + 6.06218i) q^{61} +(2.00000 + 3.46410i) q^{63} -6.00000 q^{65} +(7.00000 + 12.1244i) q^{67} +8.00000 q^{69} +(-7.50000 + 12.9904i) q^{71} +(-6.00000 + 10.3923i) q^{73} +2.00000 q^{75} +12.0000 q^{77} +(0.500000 - 0.866025i) q^{79} +(5.50000 - 9.52628i) q^{81} +16.0000 q^{83} +(1.00000 + 1.73205i) q^{85} +2.00000 q^{87} +(-8.50000 - 14.7224i) q^{89} +(12.0000 + 20.7846i) q^{91} +(5.00000 - 8.66025i) q^{93} +(4.00000 - 1.73205i) q^{95} +(-6.00000 + 10.3923i) q^{97} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} + q^{5} - 8 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} + q^{5} - 8 q^{7} - q^{9} - 6 q^{11} - 6 q^{13} + 2 q^{15} - 2 q^{17} + 7 q^{19} + 8 q^{21} - 4 q^{23} - q^{25} - 8 q^{27} - q^{29} - 10 q^{31} + 6 q^{33} - 4 q^{35} - 8 q^{37} + 24 q^{39} - 2 q^{41} - 2 q^{45} - 6 q^{47} + 18 q^{49} - 4 q^{51} + 6 q^{53} - 3 q^{55} - 16 q^{57} + q^{59} + 7 q^{61} + 4 q^{63} - 12 q^{65} + 14 q^{67} + 16 q^{69} - 15 q^{71} - 12 q^{73} + 4 q^{75} + 24 q^{77} + q^{79} + 11 q^{81} + 32 q^{83} + 2 q^{85} + 4 q^{87} - 17 q^{89} + 24 q^{91} + 10 q^{93} + 8 q^{95} - 12 q^{97} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 0
\(3\) −1.00000 + 1.73205i −0.577350 + 1.00000i 0.418432 + 0.908248i \(0.362580\pi\)
−0.995782 + 0.0917517i \(0.970753\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) −3.00000 5.19615i −0.832050 1.44115i −0.896410 0.443227i \(-0.853834\pi\)
0.0643593 0.997927i \(-0.479500\pi\)
\(14\) 0 0
\(15\) 1.00000 + 1.73205i 0.258199 + 0.447214i
\(16\) 0 0
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 0 0
\(19\) 3.50000 + 2.59808i 0.802955 + 0.596040i
\(20\) 0 0
\(21\) 4.00000 6.92820i 0.872872 1.51186i
\(22\) 0 0
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) −0.500000 0.866025i −0.0928477 0.160817i 0.815861 0.578249i \(-0.196264\pi\)
−0.908708 + 0.417432i \(0.862930\pi\)
\(30\) 0 0
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) 0 0
\(33\) 3.00000 5.19615i 0.522233 0.904534i
\(34\) 0 0
\(35\) −2.00000 + 3.46410i −0.338062 + 0.585540i
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) 12.0000 1.92154
\(40\) 0 0
\(41\) −1.00000 + 1.73205i −0.156174 + 0.270501i −0.933486 0.358614i \(-0.883249\pi\)
0.777312 + 0.629115i \(0.216583\pi\)
\(42\) 0 0
\(43\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) 0 0
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 0 0
\(55\) −1.50000 + 2.59808i −0.202260 + 0.350325i
\(56\) 0 0
\(57\) −8.00000 + 3.46410i −1.05963 + 0.458831i
\(58\) 0 0
\(59\) 0.500000 0.866025i 0.0650945 0.112747i −0.831641 0.555313i \(-0.812598\pi\)
0.896736 + 0.442566i \(0.145932\pi\)
\(60\) 0 0
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) 0 0
\(63\) 2.00000 + 3.46410i 0.251976 + 0.436436i
\(64\) 0 0
\(65\) −6.00000 −0.744208
\(66\) 0 0
\(67\) 7.00000 + 12.1244i 0.855186 + 1.48123i 0.876472 + 0.481452i \(0.159891\pi\)
−0.0212861 + 0.999773i \(0.506776\pi\)
\(68\) 0 0
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) −7.50000 + 12.9904i −0.890086 + 1.54167i −0.0503155 + 0.998733i \(0.516023\pi\)
−0.839771 + 0.542941i \(0.817311\pi\)
\(72\) 0 0
\(73\) −6.00000 + 10.3923i −0.702247 + 1.21633i 0.265429 + 0.964130i \(0.414486\pi\)
−0.967676 + 0.252197i \(0.918847\pi\)
\(74\) 0 0
\(75\) 2.00000 0.230940
\(76\) 0 0
\(77\) 12.0000 1.36753
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 0 0
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 0 0
\(83\) 16.0000 1.75623 0.878114 0.478451i \(-0.158802\pi\)
0.878114 + 0.478451i \(0.158802\pi\)
\(84\) 0 0
\(85\) 1.00000 + 1.73205i 0.108465 + 0.187867i
\(86\) 0 0
\(87\) 2.00000 0.214423
\(88\) 0 0
\(89\) −8.50000 14.7224i −0.900998 1.56057i −0.826201 0.563376i \(-0.809502\pi\)
−0.0747975 0.997199i \(-0.523831\pi\)
\(90\) 0 0
\(91\) 12.0000 + 20.7846i 1.25794 + 2.17882i
\(92\) 0 0
\(93\) 5.00000 8.66025i 0.518476 0.898027i
\(94\) 0 0
\(95\) 4.00000 1.73205i 0.410391 0.177705i
\(96\) 0 0
\(97\) −6.00000 + 10.3923i −0.609208 + 1.05518i 0.382164 + 0.924095i \(0.375179\pi\)
−0.991371 + 0.131084i \(0.958154\pi\)
\(98\) 0 0
\(99\) 1.50000 + 2.59808i 0.150756 + 0.261116i
\(100\) 0 0
\(101\) −5.50000 9.52628i −0.547270 0.947900i −0.998460 0.0554722i \(-0.982334\pi\)
0.451190 0.892428i \(-0.351000\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) −4.00000 6.92820i −0.390360 0.676123i
\(106\) 0 0
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) −3.50000 + 6.06218i −0.335239 + 0.580651i −0.983531 0.180741i \(-0.942150\pi\)
0.648292 + 0.761392i \(0.275484\pi\)
\(110\) 0 0
\(111\) 4.00000 6.92820i 0.379663 0.657596i
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) −4.00000 −0.373002
\(116\) 0 0
\(117\) −3.00000 + 5.19615i −0.277350 + 0.480384i
\(118\) 0 0
\(119\) 4.00000 6.92820i 0.366679 0.635107i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) −2.00000 3.46410i −0.180334 0.312348i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −9.00000 15.5885i −0.798621 1.38325i −0.920514 0.390709i \(-0.872230\pi\)
0.121894 0.992543i \(-0.461103\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.0000 17.3205i 0.873704 1.51330i 0.0155672 0.999879i \(-0.495045\pi\)
0.858137 0.513421i \(-0.171622\pi\)
\(132\) 0 0
\(133\) −14.0000 10.3923i −1.21395 0.901127i
\(134\) 0 0
\(135\) −2.00000 + 3.46410i −0.172133 + 0.298142i
\(136\) 0 0
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 0 0
\(139\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) 0 0
\(143\) 9.00000 + 15.5885i 0.752618 + 1.30357i
\(144\) 0 0
\(145\) −1.00000 −0.0830455
\(146\) 0 0
\(147\) −9.00000 + 15.5885i −0.742307 + 1.28571i
\(148\) 0 0
\(149\) 8.50000 14.7224i 0.696347 1.20611i −0.273377 0.961907i \(-0.588141\pi\)
0.969724 0.244202i \(-0.0785259\pi\)
\(150\) 0 0
\(151\) 3.00000 0.244137 0.122068 0.992522i \(-0.461047\pi\)
0.122068 + 0.992522i \(0.461047\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) −2.50000 + 4.33013i −0.200805 + 0.347804i
\(156\) 0 0
\(157\) −9.00000 + 15.5885i −0.718278 + 1.24409i 0.243403 + 0.969925i \(0.421736\pi\)
−0.961681 + 0.274169i \(0.911597\pi\)
\(158\) 0 0
\(159\) −12.0000 −0.951662
\(160\) 0 0
\(161\) 8.00000 + 13.8564i 0.630488 + 1.09204i
\(162\) 0 0
\(163\) 18.0000 1.40987 0.704934 0.709273i \(-0.250976\pi\)
0.704934 + 0.709273i \(0.250976\pi\)
\(164\) 0 0
\(165\) −3.00000 5.19615i −0.233550 0.404520i
\(166\) 0 0
\(167\) −4.00000 6.92820i −0.309529 0.536120i 0.668730 0.743505i \(-0.266838\pi\)
−0.978259 + 0.207385i \(0.933505\pi\)
\(168\) 0 0
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) 0 0
\(171\) 0.500000 4.33013i 0.0382360 0.331133i
\(172\) 0 0
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 2.00000 + 3.46410i 0.151186 + 0.261861i
\(176\) 0 0
\(177\) 1.00000 + 1.73205i 0.0751646 + 0.130189i
\(178\) 0 0
\(179\) −15.0000 −1.12115 −0.560576 0.828103i \(-0.689420\pi\)
−0.560576 + 0.828103i \(0.689420\pi\)
\(180\) 0 0
\(181\) −1.00000 1.73205i −0.0743294 0.128742i 0.826465 0.562988i \(-0.190348\pi\)
−0.900794 + 0.434246i \(0.857015\pi\)
\(182\) 0 0
\(183\) −14.0000 −1.03491
\(184\) 0 0
\(185\) −2.00000 + 3.46410i −0.147043 + 0.254686i
\(186\) 0 0
\(187\) 3.00000 5.19615i 0.219382 0.379980i
\(188\) 0 0
\(189\) 16.0000 1.16383
\(190\) 0 0
\(191\) −13.0000 −0.940647 −0.470323 0.882494i \(-0.655863\pi\)
−0.470323 + 0.882494i \(0.655863\pi\)
\(192\) 0 0
\(193\) −8.00000 + 13.8564i −0.575853 + 0.997406i 0.420096 + 0.907480i \(0.361996\pi\)
−0.995948 + 0.0899262i \(0.971337\pi\)
\(194\) 0 0
\(195\) 6.00000 10.3923i 0.429669 0.744208i
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) −11.5000 19.9186i −0.815213 1.41199i −0.909175 0.416415i \(-0.863286\pi\)
0.0939612 0.995576i \(-0.470047\pi\)
\(200\) 0 0
\(201\) −28.0000 −1.97497
\(202\) 0 0
\(203\) 2.00000 + 3.46410i 0.140372 + 0.243132i
\(204\) 0 0
\(205\) 1.00000 + 1.73205i 0.0698430 + 0.120972i
\(206\) 0 0
\(207\) −2.00000 + 3.46410i −0.139010 + 0.240772i
\(208\) 0 0
\(209\) −10.5000 7.79423i −0.726300 0.539138i
\(210\) 0 0
\(211\) 0.500000 0.866025i 0.0344214 0.0596196i −0.848301 0.529514i \(-0.822374\pi\)
0.882723 + 0.469894i \(0.155708\pi\)
\(212\) 0 0
\(213\) −15.0000 25.9808i −1.02778 1.78017i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 20.0000 1.35769
\(218\) 0 0
\(219\) −12.0000 20.7846i −0.810885 1.40449i
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i \(-0.919650\pi\)
0.700449 + 0.713702i \(0.252983\pi\)
\(224\) 0 0
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) 0 0
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 0 0
\(229\) 21.0000 1.38772 0.693860 0.720110i \(-0.255909\pi\)
0.693860 + 0.720110i \(0.255909\pi\)
\(230\) 0 0
\(231\) −12.0000 + 20.7846i −0.789542 + 1.36753i
\(232\) 0 0
\(233\) 5.00000 8.66025i 0.327561 0.567352i −0.654466 0.756091i \(-0.727107\pi\)
0.982027 + 0.188739i \(0.0604400\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) 0 0
\(237\) 1.00000 + 1.73205i 0.0649570 + 0.112509i
\(238\) 0 0
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) 0 0
\(241\) −2.50000 4.33013i −0.161039 0.278928i 0.774202 0.632938i \(-0.218151\pi\)
−0.935242 + 0.354010i \(0.884818\pi\)
\(242\) 0 0
\(243\) 5.00000 + 8.66025i 0.320750 + 0.555556i
\(244\) 0 0
\(245\) 4.50000 7.79423i 0.287494 0.497955i
\(246\) 0 0
\(247\) 3.00000 25.9808i 0.190885 1.65312i
\(248\) 0 0
\(249\) −16.0000 + 27.7128i −1.01396 + 1.75623i
\(250\) 0 0
\(251\) −15.5000 26.8468i −0.978351 1.69455i −0.668400 0.743802i \(-0.733021\pi\)
−0.309951 0.950753i \(-0.600313\pi\)
\(252\) 0 0
\(253\) 6.00000 + 10.3923i 0.377217 + 0.653359i
\(254\) 0 0
\(255\) −4.00000 −0.250490
\(256\) 0 0
\(257\) −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) 0 0
\(259\) 16.0000 0.994192
\(260\) 0 0
\(261\) −0.500000 + 0.866025i −0.0309492 + 0.0536056i
\(262\) 0 0
\(263\) −5.00000 + 8.66025i −0.308313 + 0.534014i −0.977993 0.208635i \(-0.933098\pi\)
0.669680 + 0.742650i \(0.266431\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 34.0000 2.08077
\(268\) 0 0
\(269\) 0.500000 0.866025i 0.0304855 0.0528025i −0.850380 0.526169i \(-0.823628\pi\)
0.880866 + 0.473366i \(0.156961\pi\)
\(270\) 0 0
\(271\) −8.50000 + 14.7224i −0.516338 + 0.894324i 0.483482 + 0.875354i \(0.339372\pi\)
−0.999820 + 0.0189696i \(0.993961\pi\)
\(272\) 0 0
\(273\) −48.0000 −2.90509
\(274\) 0 0
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) 0 0
\(277\) 16.0000 0.961347 0.480673 0.876900i \(-0.340392\pi\)
0.480673 + 0.876900i \(0.340392\pi\)
\(278\) 0 0
\(279\) 2.50000 + 4.33013i 0.149671 + 0.259238i
\(280\) 0 0
\(281\) 13.0000 + 22.5167i 0.775515 + 1.34323i 0.934505 + 0.355951i \(0.115843\pi\)
−0.158990 + 0.987280i \(0.550824\pi\)
\(282\) 0 0
\(283\) 13.0000 22.5167i 0.772770 1.33848i −0.163270 0.986581i \(-0.552204\pi\)
0.936039 0.351895i \(-0.114463\pi\)
\(284\) 0 0
\(285\) −1.00000 + 8.66025i −0.0592349 + 0.512989i
\(286\) 0 0
\(287\) 4.00000 6.92820i 0.236113 0.408959i
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) −12.0000 20.7846i −0.703452 1.21842i
\(292\) 0 0
\(293\) 16.0000 0.934730 0.467365 0.884064i \(-0.345203\pi\)
0.467365 + 0.884064i \(0.345203\pi\)
\(294\) 0 0
\(295\) −0.500000 0.866025i −0.0291111 0.0504219i
\(296\) 0 0
\(297\) 12.0000 0.696311
\(298\) 0 0
\(299\) −12.0000 + 20.7846i −0.693978 + 1.20201i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 22.0000 1.26387
\(304\) 0 0
\(305\) 7.00000 0.400819
\(306\) 0 0
\(307\) 7.00000 12.1244i 0.399511 0.691974i −0.594154 0.804351i \(-0.702513\pi\)
0.993666 + 0.112377i \(0.0358466\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −17.0000 29.4449i −0.960897 1.66432i −0.720257 0.693708i \(-0.755976\pi\)
−0.240640 0.970614i \(-0.577357\pi\)
\(314\) 0 0
\(315\) 4.00000 0.225374
\(316\) 0 0
\(317\) 6.00000 + 10.3923i 0.336994 + 0.583690i 0.983866 0.178908i \(-0.0572566\pi\)
−0.646872 + 0.762598i \(0.723923\pi\)
\(318\) 0 0
\(319\) 1.50000 + 2.59808i 0.0839839 + 0.145464i
\(320\) 0 0
\(321\) 12.0000 20.7846i 0.669775 1.16008i
\(322\) 0 0
\(323\) −8.00000 + 3.46410i −0.445132 + 0.192748i
\(324\) 0 0
\(325\) −3.00000 + 5.19615i −0.166410 + 0.288231i
\(326\) 0 0
\(327\) −7.00000 12.1244i −0.387101 0.670478i
\(328\) 0 0
\(329\) 12.0000 + 20.7846i 0.661581 + 1.14589i
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 0 0
\(333\) 2.00000 + 3.46410i 0.109599 + 0.189832i
\(334\) 0 0
\(335\) 14.0000 0.764902
\(336\) 0 0
\(337\) −2.00000 + 3.46410i −0.108947 + 0.188702i −0.915344 0.402673i \(-0.868081\pi\)
0.806397 + 0.591375i \(0.201415\pi\)
\(338\) 0 0
\(339\) −14.0000 + 24.2487i −0.760376 + 1.31701i
\(340\) 0 0
\(341\) 15.0000 0.812296
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 4.00000 6.92820i 0.215353 0.373002i
\(346\) 0 0
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) 12.0000 + 20.7846i 0.640513 + 1.10940i
\(352\) 0 0
\(353\) −36.0000 −1.91609 −0.958043 0.286623i \(-0.907467\pi\)
−0.958043 + 0.286623i \(0.907467\pi\)
\(354\) 0 0
\(355\) 7.50000 + 12.9904i 0.398059 + 0.689458i
\(356\) 0 0
\(357\) 8.00000 + 13.8564i 0.423405 + 0.733359i
\(358\) 0 0
\(359\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(360\) 0 0
\(361\) 5.50000 + 18.1865i 0.289474 + 0.957186i
\(362\) 0 0
\(363\) 2.00000 3.46410i 0.104973 0.181818i
\(364\) 0 0
\(365\) 6.00000 + 10.3923i 0.314054 + 0.543958i
\(366\) 0 0
\(367\) 14.0000 + 24.2487i 0.730794 + 1.26577i 0.956544 + 0.291587i \(0.0941834\pi\)
−0.225750 + 0.974185i \(0.572483\pi\)
\(368\) 0 0
\(369\) 2.00000 0.104116
\(370\) 0 0
\(371\) −12.0000 20.7846i −0.623009 1.07908i
\(372\) 0 0
\(373\) −12.0000 −0.621336 −0.310668 0.950518i \(-0.600553\pi\)
−0.310668 + 0.950518i \(0.600553\pi\)
\(374\) 0 0
\(375\) 1.00000 1.73205i 0.0516398 0.0894427i
\(376\) 0 0
\(377\) −3.00000 + 5.19615i −0.154508 + 0.267615i
\(378\) 0 0
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) 0 0
\(381\) 36.0000 1.84434
\(382\) 0 0
\(383\) 9.00000 15.5885i 0.459879 0.796533i −0.539076 0.842257i \(-0.681226\pi\)
0.998954 + 0.0457244i \(0.0145596\pi\)
\(384\) 0 0
\(385\) 6.00000 10.3923i 0.305788 0.529641i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 10.5000 + 18.1865i 0.532371 + 0.922094i 0.999286 + 0.0377914i \(0.0120322\pi\)
−0.466915 + 0.884302i \(0.654634\pi\)
\(390\) 0 0
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) 20.0000 + 34.6410i 1.00887 + 1.74741i
\(394\) 0 0
\(395\) −0.500000 0.866025i −0.0251577 0.0435745i
\(396\) 0 0
\(397\) 4.00000 6.92820i 0.200754 0.347717i −0.748017 0.663679i \(-0.768994\pi\)
0.948772 + 0.315963i \(0.102327\pi\)
\(398\) 0 0
\(399\) 32.0000 13.8564i 1.60200 0.693688i
\(400\) 0 0
\(401\) −7.50000 + 12.9904i −0.374532 + 0.648709i −0.990257 0.139253i \(-0.955530\pi\)
0.615725 + 0.787961i \(0.288863\pi\)
\(402\) 0 0
\(403\) 15.0000 + 25.9808i 0.747203 + 1.29419i
\(404\) 0 0
\(405\) −5.50000 9.52628i −0.273297 0.473365i
\(406\) 0 0
\(407\) 12.0000 0.594818
\(408\) 0 0
\(409\) 0.500000 + 0.866025i 0.0247234 + 0.0428222i 0.878122 0.478436i \(-0.158796\pi\)
−0.853399 + 0.521258i \(0.825463\pi\)
\(410\) 0 0
\(411\) 24.0000 1.18383
\(412\) 0 0
\(413\) −2.00000 + 3.46410i −0.0984136 + 0.170457i
\(414\) 0 0
\(415\) 8.00000 13.8564i 0.392705 0.680184i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.00000 −0.244266 −0.122133 0.992514i \(-0.538973\pi\)
−0.122133 + 0.992514i \(0.538973\pi\)
\(420\) 0 0
\(421\) −12.5000 + 21.6506i −0.609213 + 1.05519i 0.382158 + 0.924097i \(0.375181\pi\)
−0.991370 + 0.131090i \(0.958152\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 2.00000 0.0970143
\(426\) 0 0
\(427\) −14.0000 24.2487i −0.677507 1.17348i
\(428\) 0 0
\(429\) −36.0000 −1.73810
\(430\) 0 0
\(431\) −13.5000 23.3827i −0.650272 1.12630i −0.983057 0.183301i \(-0.941322\pi\)
0.332785 0.943003i \(-0.392012\pi\)
\(432\) 0 0
\(433\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(434\) 0 0
\(435\) 1.00000 1.73205i 0.0479463 0.0830455i
\(436\) 0 0
\(437\) 2.00000 17.3205i 0.0956730 0.828552i
\(438\) 0 0
\(439\) −0.500000 + 0.866025i −0.0238637 + 0.0413331i −0.877711 0.479191i \(-0.840930\pi\)
0.853847 + 0.520524i \(0.174263\pi\)
\(440\) 0 0
\(441\) −4.50000 7.79423i −0.214286 0.371154i
\(442\) 0 0
\(443\) 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i \(-0.0746503\pi\)
−0.687557 + 0.726130i \(0.741317\pi\)
\(444\) 0 0
\(445\) −17.0000 −0.805877
\(446\) 0 0
\(447\) 17.0000 + 29.4449i 0.804072 + 1.39269i
\(448\) 0 0
\(449\) −1.00000 −0.0471929 −0.0235965 0.999722i \(-0.507512\pi\)
−0.0235965 + 0.999722i \(0.507512\pi\)
\(450\) 0 0
\(451\) 3.00000 5.19615i 0.141264 0.244677i
\(452\) 0 0
\(453\) −3.00000 + 5.19615i −0.140952 + 0.244137i
\(454\) 0 0
\(455\) 24.0000 1.12514
\(456\) 0 0
\(457\) −2.00000 −0.0935561 −0.0467780 0.998905i \(-0.514895\pi\)
−0.0467780 + 0.998905i \(0.514895\pi\)
\(458\) 0 0
\(459\) 4.00000 6.92820i 0.186704 0.323381i
\(460\) 0 0
\(461\) −17.5000 + 30.3109i −0.815056 + 1.41172i 0.0942312 + 0.995550i \(0.469961\pi\)
−0.909288 + 0.416169i \(0.863373\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 0 0
\(465\) −5.00000 8.66025i −0.231869 0.401610i
\(466\) 0 0
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 0 0
\(469\) −28.0000 48.4974i −1.29292 2.23940i
\(470\) 0 0
\(471\) −18.0000 31.1769i −0.829396 1.43656i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.500000 4.33013i 0.0229416 0.198680i
\(476\) 0 0
\(477\) 3.00000 5.19615i 0.137361 0.237915i
\(478\) 0 0
\(479\) 1.50000 + 2.59808i 0.0685367 + 0.118709i 0.898257 0.439470i \(-0.144834\pi\)
−0.829721 + 0.558179i \(0.811500\pi\)
\(480\) 0 0
\(481\) 12.0000 + 20.7846i 0.547153 + 0.947697i
\(482\) 0 0
\(483\) −32.0000 −1.45605
\(484\) 0 0
\(485\) 6.00000 + 10.3923i 0.272446 + 0.471890i
\(486\) 0 0
\(487\) 34.0000 1.54069 0.770344 0.637629i \(-0.220085\pi\)
0.770344 + 0.637629i \(0.220085\pi\)
\(488\) 0 0
\(489\) −18.0000 + 31.1769i −0.813988 + 1.40987i
\(490\) 0 0
\(491\) 12.5000 21.6506i 0.564117 0.977079i −0.433014 0.901387i \(-0.642550\pi\)
0.997131 0.0756923i \(-0.0241167\pi\)
\(492\) 0 0
\(493\) 2.00000 0.0900755
\(494\) 0 0
\(495\) 3.00000 0.134840
\(496\) 0 0
\(497\) 30.0000 51.9615i 1.34568 2.33079i
\(498\) 0 0
\(499\) −18.0000 + 31.1769i −0.805791 + 1.39567i 0.109965 + 0.993935i \(0.464926\pi\)
−0.915756 + 0.401735i \(0.868407\pi\)
\(500\) 0 0
\(501\) 16.0000 0.714827
\(502\) 0 0
\(503\) −11.0000 19.0526i −0.490466 0.849512i 0.509474 0.860486i \(-0.329840\pi\)
−0.999940 + 0.0109744i \(0.996507\pi\)
\(504\) 0 0
\(505\) −11.0000 −0.489494
\(506\) 0 0
\(507\) −23.0000 39.8372i −1.02147 1.76923i
\(508\) 0 0
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 0 0
\(511\) 24.0000 41.5692i 1.06170 1.83891i
\(512\) 0 0
\(513\) −14.0000 10.3923i −0.618115 0.458831i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 9.00000 + 15.5885i 0.395820 + 0.685580i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −45.0000 −1.97149 −0.985743 0.168259i \(-0.946186\pi\)
−0.985743 + 0.168259i \(0.946186\pi\)
\(522\) 0 0
\(523\) 5.00000 + 8.66025i 0.218635 + 0.378686i 0.954391 0.298560i \(-0.0965063\pi\)
−0.735756 + 0.677247i \(0.763173\pi\)
\(524\) 0 0
\(525\) −8.00000 −0.349149
\(526\) 0 0
\(527\) 5.00000 8.66025i 0.217803 0.377247i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) −1.00000 −0.0433963
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) −6.00000 + 10.3923i −0.259403 + 0.449299i
\(536\) 0 0
\(537\) 15.0000 25.9808i 0.647298 1.12115i
\(538\) 0 0
\(539\) −27.0000 −1.16297
\(540\) 0 0
\(541\) 12.5000 + 21.6506i 0.537417 + 0.930834i 0.999042 + 0.0437584i \(0.0139332\pi\)
−0.461625 + 0.887075i \(0.652733\pi\)
\(542\) 0 0
\(543\) 4.00000 0.171656
\(544\) 0 0
\(545\) 3.50000 + 6.06218i 0.149924 + 0.259675i
\(546\) 0 0
\(547\) 4.00000 + 6.92820i 0.171028 + 0.296229i 0.938779 0.344519i \(-0.111958\pi\)
−0.767752 + 0.640747i \(0.778625\pi\)
\(548\) 0 0
\(549\) 3.50000 6.06218i 0.149376 0.258727i
\(550\) 0 0
\(551\) 0.500000 4.33013i 0.0213007 0.184470i
\(552\) 0 0
\(553\) −2.00000 + 3.46410i −0.0850487 + 0.147309i
\(554\) 0 0
\(555\) −4.00000 6.92820i −0.169791 0.294086i
\(556\) 0 0
\(557\) 20.0000 + 34.6410i 0.847427 + 1.46779i 0.883497 + 0.468438i \(0.155183\pi\)
−0.0360693 + 0.999349i \(0.511484\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 6.00000 + 10.3923i 0.253320 + 0.438763i
\(562\) 0 0
\(563\) 10.0000 0.421450 0.210725 0.977545i \(-0.432418\pi\)
0.210725 + 0.977545i \(0.432418\pi\)
\(564\) 0 0
\(565\) 7.00000 12.1244i 0.294492 0.510075i
\(566\) 0 0
\(567\) −22.0000 + 38.1051i −0.923913 + 1.60026i
\(568\) 0 0
\(569\) −17.0000 −0.712677 −0.356339 0.934357i \(-0.615975\pi\)
−0.356339 + 0.934357i \(0.615975\pi\)
\(570\) 0 0
\(571\) −17.0000 −0.711428 −0.355714 0.934595i \(-0.615762\pi\)
−0.355714 + 0.934595i \(0.615762\pi\)
\(572\) 0 0
\(573\) 13.0000 22.5167i 0.543083 0.940647i
\(574\) 0 0
\(575\) −2.00000 + 3.46410i −0.0834058 + 0.144463i
\(576\) 0 0
\(577\) −20.0000 −0.832611 −0.416305 0.909225i \(-0.636675\pi\)
−0.416305 + 0.909225i \(0.636675\pi\)
\(578\) 0 0
\(579\) −16.0000 27.7128i −0.664937 1.15171i
\(580\) 0 0
\(581\) −64.0000 −2.65517
\(582\) 0 0
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) 0 0
\(585\) 3.00000 + 5.19615i 0.124035 + 0.214834i
\(586\) 0 0
\(587\) 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
\(589\) −17.5000 12.9904i −0.721075 0.535259i
\(590\) 0 0
\(591\) −2.00000 + 3.46410i −0.0822690 + 0.142494i
\(592\) 0 0
\(593\) 2.00000 + 3.46410i 0.0821302 + 0.142254i 0.904165 0.427184i \(-0.140494\pi\)
−0.822035 + 0.569438i \(0.807161\pi\)
\(594\) 0 0
\(595\) −4.00000 6.92820i −0.163984 0.284029i
\(596\) 0 0
\(597\) 46.0000 1.88265
\(598\) 0 0
\(599\) 12.0000 + 20.7846i 0.490307 + 0.849236i 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) 0 0
\(601\) 17.0000 0.693444 0.346722 0.937968i \(-0.387295\pi\)
0.346722 + 0.937968i \(0.387295\pi\)
\(602\) 0 0
\(603\) 7.00000 12.1244i 0.285062 0.493742i
\(604\) 0 0
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) −14.0000 −0.568242 −0.284121 0.958788i \(-0.591702\pi\)
−0.284121 + 0.958788i \(0.591702\pi\)
\(608\) 0 0
\(609\) −8.00000 −0.324176
\(610\) 0 0
\(611\) −18.0000 + 31.1769i −0.728202 + 1.26128i
\(612\) 0 0
\(613\) 11.0000 19.0526i 0.444286 0.769526i −0.553716 0.832705i \(-0.686791\pi\)
0.998002 + 0.0631797i \(0.0201241\pi\)
\(614\) 0 0
\(615\) −4.00000 −0.161296
\(616\) 0 0
\(617\) 4.00000 + 6.92820i 0.161034 + 0.278919i 0.935240 0.354015i \(-0.115184\pi\)
−0.774206 + 0.632934i \(0.781850\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 0 0
\(621\) 8.00000 + 13.8564i 0.321029 + 0.556038i
\(622\) 0 0
\(623\) 34.0000 + 58.8897i 1.36218 + 2.35937i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 24.0000 10.3923i 0.958468 0.415029i
\(628\) 0 0
\(629\) 4.00000 6.92820i 0.159490 0.276246i
\(630\) 0 0
\(631\) 16.5000 + 28.5788i 0.656855 + 1.13771i 0.981425 + 0.191844i \(0.0614468\pi\)
−0.324571 + 0.945861i \(0.605220\pi\)
\(632\) 0 0
\(633\) 1.00000 + 1.73205i 0.0397464 + 0.0688428i
\(634\) 0 0
\(635\) −18.0000 −0.714308
\(636\) 0 0
\(637\) −27.0000 46.7654i −1.06978 1.85291i
\(638\) 0 0
\(639\) 15.0000 0.593391
\(640\) 0 0
\(641\) −4.50000 + 7.79423i −0.177739 + 0.307854i −0.941106 0.338112i \(-0.890212\pi\)
0.763367 + 0.645966i \(0.223545\pi\)
\(642\) 0 0
\(643\) 1.00000 1.73205i 0.0394362 0.0683054i −0.845634 0.533764i \(-0.820777\pi\)
0.885070 + 0.465458i \(0.154110\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.0000 −1.17942 −0.589711 0.807614i \(-0.700758\pi\)
−0.589711 + 0.807614i \(0.700758\pi\)
\(648\) 0 0
\(649\) −1.50000 + 2.59808i −0.0588802 + 0.101983i
\(650\) 0 0
\(651\) −20.0000 + 34.6410i −0.783862 + 1.35769i
\(652\) 0 0
\(653\) 12.0000 0.469596 0.234798 0.972044i \(-0.424557\pi\)
0.234798 + 0.972044i \(0.424557\pi\)
\(654\) 0 0
\(655\) −10.0000 17.3205i −0.390732 0.676768i
\(656\) 0 0
\(657\) 12.0000 0.468165
\(658\) 0 0
\(659\) 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i \(0.0806766\pi\)
−0.266872 + 0.963732i \(0.585990\pi\)
\(660\) 0 0
\(661\) −20.5000 35.5070i −0.797358 1.38106i −0.921331 0.388778i \(-0.872897\pi\)
0.123974 0.992286i \(-0.460436\pi\)
\(662\) 0 0
\(663\) −12.0000 + 20.7846i −0.466041 + 0.807207i
\(664\) 0 0
\(665\) −16.0000 + 6.92820i −0.620453 + 0.268664i
\(666\) 0 0
\(667\) −2.00000 + 3.46410i −0.0774403 + 0.134131i
\(668\) 0 0
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) 0 0
\(671\) −10.5000 18.1865i −0.405348 0.702083i
\(672\) 0 0
\(673\) −28.0000 −1.07932 −0.539660 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) 0 0
\(675\) 2.00000 + 3.46410i 0.0769800 + 0.133333i
\(676\) 0 0
\(677\) −32.0000 −1.22986 −0.614930 0.788582i \(-0.710816\pi\)
−0.614930 + 0.788582i \(0.710816\pi\)
\(678\) 0 0
\(679\) 24.0000 41.5692i 0.921035 1.59528i
\(680\) 0 0
\(681\) 4.00000 6.92820i 0.153280 0.265489i
\(682\) 0 0
\(683\) 6.00000 0.229584 0.114792 0.993390i \(-0.463380\pi\)
0.114792 + 0.993390i \(0.463380\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) −21.0000 + 36.3731i −0.801200 + 1.38772i
\(688\) 0 0
\(689\) 18.0000 31.1769i 0.685745 1.18775i
\(690\) 0 0
\(691\) 37.0000 1.40755 0.703773 0.710425i \(-0.251497\pi\)
0.703773 + 0.710425i \(0.251497\pi\)
\(692\) 0 0
\(693\) −6.00000 10.3923i −0.227921 0.394771i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −2.00000 3.46410i −0.0757554 0.131212i
\(698\) 0 0
\(699\) 10.0000 + 17.3205i 0.378235 + 0.655122i
\(700\) 0 0
\(701\) 21.0000 36.3731i 0.793159 1.37379i −0.130843 0.991403i \(-0.541768\pi\)
0.924002 0.382389i \(-0.124898\pi\)
\(702\) 0 0
\(703\) −14.0000 10.3923i −0.528020 0.391953i
\(704\) 0 0
\(705\) 6.00000 10.3923i 0.225973 0.391397i
\(706\) 0 0
\(707\) 22.0000 + 38.1051i 0.827395 + 1.43309i
\(708\) 0 0
\(709\) −2.50000 4.33013i −0.0938895 0.162621i 0.815255 0.579102i \(-0.196597\pi\)
−0.909145 + 0.416481i \(0.863263\pi\)
\(710\) 0 0
\(711\) −1.00000 −0.0375029
\(712\) 0 0
\(713\) 10.0000 + 17.3205i 0.374503 + 0.648658i
\(714\) 0 0
\(715\) 18.0000 0.673162
\(716\) 0 0
\(717\) −15.0000 + 25.9808i −0.560185 + 0.970269i
\(718\) 0 0
\(719\) −14.5000 + 25.1147i −0.540759 + 0.936622i 0.458102 + 0.888900i \(0.348529\pi\)
−0.998861 + 0.0477220i \(0.984804\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 10.0000 0.371904
\(724\) 0 0
\(725\) −0.500000 + 0.866025i −0.0185695 + 0.0321634i
\(726\) 0 0
\(727\) −13.0000 + 22.5167i −0.482143 + 0.835097i −0.999790 0.0204978i \(-0.993475\pi\)
0.517647 + 0.855595i \(0.326808\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −12.0000 −0.443230 −0.221615 0.975134i \(-0.571133\pi\)
−0.221615 + 0.975134i \(0.571133\pi\)
\(734\) 0 0
\(735\) 9.00000 + 15.5885i 0.331970 + 0.574989i
\(736\) 0 0
\(737\) −21.0000 36.3731i −0.773545 1.33982i
\(738\) 0 0
\(739\) 9.50000 16.4545i 0.349463 0.605288i −0.636691 0.771119i \(-0.719697\pi\)
0.986154 + 0.165831i \(0.0530307\pi\)
\(740\) 0 0
\(741\) 42.0000 + 31.1769i 1.54291 + 1.14531i
\(742\) 0 0
\(743\) −26.0000 + 45.0333i −0.953847 + 1.65211i −0.216864 + 0.976202i \(0.569583\pi\)
−0.736984 + 0.675910i \(0.763751\pi\)
\(744\) 0 0
\(745\) −8.50000 14.7224i −0.311416 0.539388i
\(746\) 0 0
\(747\) −8.00000 13.8564i −0.292705 0.506979i
\(748\) 0 0
\(749\) 48.0000 1.75388
\(750\) 0 0
\(751\) −9.50000 16.4545i −0.346660 0.600433i 0.638994 0.769212i \(-0.279351\pi\)
−0.985654 + 0.168779i \(0.946018\pi\)
\(752\) 0 0
\(753\) 62.0000 2.25941
\(754\) 0 0
\(755\) 1.50000 2.59808i 0.0545906 0.0945537i
\(756\) 0 0
\(757\) 7.00000 12.1244i 0.254419 0.440667i −0.710318 0.703881i \(-0.751449\pi\)
0.964738 + 0.263213i \(0.0847823\pi\)
\(758\) 0 0
\(759\) −24.0000 −0.871145
\(760\) 0 0
\(761\) 54.0000 1.95750 0.978749 0.205061i \(-0.0657392\pi\)
0.978749 + 0.205061i \(0.0657392\pi\)
\(762\) 0 0
\(763\) 14.0000 24.2487i 0.506834 0.877862i
\(764\) 0 0
\(765\) 1.00000 1.73205i 0.0361551 0.0626224i
\(766\) 0 0
\(767\) −6.00000 −0.216647
\(768\) 0 0
\(769\) −6.50000 11.2583i −0.234396 0.405986i 0.724701 0.689063i \(-0.241978\pi\)
−0.959097 + 0.283078i \(0.908645\pi\)
\(770\) 0 0
\(771\) 36.0000 1.29651
\(772\) 0 0
\(773\) 27.0000 + 46.7654i 0.971123 + 1.68203i 0.692179 + 0.721726i \(0.256651\pi\)
0.278944 + 0.960307i \(0.410016\pi\)
\(774\) 0 0
\(775\) 2.50000 + 4.33013i 0.0898027 + 0.155543i
\(776\) 0 0
\(777\) −16.0000 + 27.7128i −0.573997 + 0.994192i
\(778\) 0 0
\(779\) −8.00000 + 3.46410i −0.286630 + 0.124114i
\(780\) 0 0
\(781\) 22.5000 38.9711i 0.805113 1.39450i
\(782\) 0 0
\(783\) 2.00000 + 3.46410i 0.0714742 + 0.123797i
\(784\) 0 0
\(785\) 9.00000 + 15.5885i 0.321224 + 0.556376i
\(786\) 0 0
\(787\) 38.0000 1.35455 0.677277 0.735728i \(-0.263160\pi\)
0.677277 + 0.735728i \(0.263160\pi\)
\(788\) 0 0
\(789\) −10.0000 17.3205i −0.356009 0.616626i
\(790\) 0 0
\(791\) −56.0000 −1.99113
\(792\) 0 0
\(793\) 21.0000 36.3731i 0.745732 1.29165i
\(794\) 0 0
\(795\)