Properties

Label 504.2.r.a.169.1
Level $504$
Weight $2$
Character 504.169
Analytic conductor $4.024$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.r (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
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 169.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 504.169
Dual form 504.2.r.a.337.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205i q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{7} -3.00000 q^{9} +O(q^{10})\) \(q-1.73205i q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{7} -3.00000 q^{9} +(3.00000 - 5.19615i) q^{11} +(-3.00000 - 5.19615i) q^{13} +(1.50000 - 0.866025i) q^{15} -2.00000 q^{17} +7.00000 q^{19} +(1.50000 + 0.866025i) q^{21} +(0.500000 + 0.866025i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.19615i q^{27} +(-1.00000 + 1.73205i) q^{29} +(-5.00000 - 8.66025i) q^{31} +(-9.00000 - 5.19615i) q^{33} -1.00000 q^{35} -6.00000 q^{37} +(-9.00000 + 5.19615i) q^{39} +(4.00000 + 6.92820i) q^{41} +(5.00000 - 8.66025i) q^{43} +(-1.50000 - 2.59808i) q^{45} +(-4.00000 + 6.92820i) q^{47} +(-0.500000 - 0.866025i) q^{49} +3.46410i q^{51} +2.00000 q^{53} +6.00000 q^{55} -12.1244i q^{57} +(-3.50000 + 6.06218i) q^{61} +(1.50000 - 2.59808i) q^{63} +(3.00000 - 5.19615i) q^{65} +(6.00000 + 10.3923i) q^{67} +(1.50000 - 0.866025i) q^{69} +15.0000 q^{71} -2.00000 q^{73} +(-6.00000 - 3.46410i) q^{75} +(3.00000 + 5.19615i) q^{77} +(-0.500000 + 0.866025i) q^{79} +9.00000 q^{81} +(-6.00000 + 10.3923i) q^{83} +(-1.00000 - 1.73205i) q^{85} +(3.00000 + 1.73205i) q^{87} +4.00000 q^{89} +6.00000 q^{91} +(-15.0000 + 8.66025i) q^{93} +(3.50000 + 6.06218i) q^{95} +(1.00000 - 1.73205i) q^{97} +(-9.00000 + 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{5} - q^{7} - 6q^{9} + O(q^{10}) \) \( 2q + q^{5} - q^{7} - 6q^{9} + 6q^{11} - 6q^{13} + 3q^{15} - 4q^{17} + 14q^{19} + 3q^{21} + q^{23} + 4q^{25} - 2q^{29} - 10q^{31} - 18q^{33} - 2q^{35} - 12q^{37} - 18q^{39} + 8q^{41} + 10q^{43} - 3q^{45} - 8q^{47} - q^{49} + 4q^{53} + 12q^{55} - 7q^{61} + 3q^{63} + 6q^{65} + 12q^{67} + 3q^{69} + 30q^{71} - 4q^{73} - 12q^{75} + 6q^{77} - q^{79} + 18q^{81} - 12q^{83} - 2q^{85} + 6q^{87} + 8q^{89} + 12q^{91} - 30q^{93} + 7q^{95} + 2q^{97} - 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.73205i 1.00000i
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i \(-0.0948835\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 3.00000 5.19615i 0.904534 1.56670i 0.0829925 0.996550i \(-0.473552\pi\)
0.821541 0.570149i \(-0.193114\pi\)
\(12\) 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
\(15\) 1.50000 0.866025i 0.387298 0.223607i
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 1.50000 + 0.866025i 0.327327 + 0.188982i
\(22\) 0 0
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −1.00000 + 1.73205i −0.185695 + 0.321634i −0.943811 0.330487i \(-0.892787\pi\)
0.758115 + 0.652121i \(0.226120\pi\)
\(30\) 0 0
\(31\) −5.00000 8.66025i −0.898027 1.55543i −0.830014 0.557743i \(-0.811667\pi\)
−0.0680129 0.997684i \(-0.521666\pi\)
\(32\) 0 0
\(33\) −9.00000 5.19615i −1.56670 0.904534i
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) −9.00000 + 5.19615i −1.44115 + 0.832050i
\(40\) 0 0
\(41\) 4.00000 + 6.92820i 0.624695 + 1.08200i 0.988600 + 0.150567i \(0.0481100\pi\)
−0.363905 + 0.931436i \(0.618557\pi\)
\(42\) 0 0
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) 0 0
\(45\) −1.50000 2.59808i −0.223607 0.387298i
\(46\) 0 0
\(47\) −4.00000 + 6.92820i −0.583460 + 1.01058i 0.411606 + 0.911362i \(0.364968\pi\)
−0.995066 + 0.0992202i \(0.968365\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) 3.46410i 0.485071i
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 6.00000 0.809040
\(56\) 0 0
\(57\) 12.1244i 1.60591i
\(58\) 0 0
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i \(-0.981243\pi\)
0.550135 + 0.835076i \(0.314576\pi\)
\(62\) 0 0
\(63\) 1.50000 2.59808i 0.188982 0.327327i
\(64\) 0 0
\(65\) 3.00000 5.19615i 0.372104 0.644503i
\(66\) 0 0
\(67\) 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) 0 0
\(69\) 1.50000 0.866025i 0.180579 0.104257i
\(70\) 0 0
\(71\) 15.0000 1.78017 0.890086 0.455792i \(-0.150644\pi\)
0.890086 + 0.455792i \(0.150644\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) −6.00000 3.46410i −0.692820 0.400000i
\(76\) 0 0
\(77\) 3.00000 + 5.19615i 0.341882 + 0.592157i
\(78\) 0 0
\(79\) −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i \(-0.851249\pi\)
0.836527 + 0.547926i \(0.184582\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) 0 0
\(85\) −1.00000 1.73205i −0.108465 0.187867i
\(86\) 0 0
\(87\) 3.00000 + 1.73205i 0.321634 + 0.185695i
\(88\) 0 0
\(89\) 4.00000 0.423999 0.212000 0.977270i \(-0.432002\pi\)
0.212000 + 0.977270i \(0.432002\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) 0 0
\(93\) −15.0000 + 8.66025i −1.55543 + 0.898027i
\(94\) 0 0
\(95\) 3.50000 + 6.06218i 0.359092 + 0.621966i
\(96\) 0 0
\(97\) 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) 0 0
\(99\) −9.00000 + 15.5885i −0.904534 + 1.56670i
\(100\) 0 0
\(101\) −1.50000 + 2.59808i −0.149256 + 0.258518i −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) 0 0
\(103\) −3.00000 5.19615i −0.295599 0.511992i 0.679525 0.733652i \(-0.262186\pi\)
−0.975124 + 0.221660i \(0.928852\pi\)
\(104\) 0 0
\(105\) 1.73205i 0.169031i
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 10.3923i 0.986394i
\(112\) 0 0
\(113\) 4.50000 + 7.79423i 0.423324 + 0.733219i 0.996262 0.0863794i \(-0.0275297\pi\)
−0.572938 + 0.819599i \(0.694196\pi\)
\(114\) 0 0
\(115\) −0.500000 + 0.866025i −0.0466252 + 0.0807573i
\(116\) 0 0
\(117\) 9.00000 + 15.5885i 0.832050 + 1.44115i
\(118\) 0 0
\(119\) 1.00000 1.73205i 0.0916698 0.158777i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) 0 0
\(123\) 12.0000 6.92820i 1.08200 0.624695i
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 0 0
\(129\) −15.0000 8.66025i −1.32068 0.762493i
\(130\) 0 0
\(131\) −8.50000 14.7224i −0.742648 1.28630i −0.951285 0.308312i \(-0.900236\pi\)
0.208637 0.977993i \(-0.433097\pi\)
\(132\) 0 0
\(133\) −3.50000 + 6.06218i −0.303488 + 0.525657i
\(134\) 0 0
\(135\) −4.50000 + 2.59808i −0.387298 + 0.223607i
\(136\) 0 0
\(137\) −7.00000 + 12.1244i −0.598050 + 1.03585i 0.395058 + 0.918656i \(0.370724\pi\)
−0.993109 + 0.117198i \(0.962609\pi\)
\(138\) 0 0
\(139\) −1.50000 2.59808i −0.127228 0.220366i 0.795373 0.606120i \(-0.207275\pi\)
−0.922602 + 0.385754i \(0.873941\pi\)
\(140\) 0 0
\(141\) 12.0000 + 6.92820i 1.01058 + 0.583460i
\(142\) 0 0
\(143\) −36.0000 −3.01047
\(144\) 0 0
\(145\) −2.00000 −0.166091
\(146\) 0 0
\(147\) −1.50000 + 0.866025i −0.123718 + 0.0714286i
\(148\) 0 0
\(149\) 7.00000 + 12.1244i 0.573462 + 0.993266i 0.996207 + 0.0870170i \(0.0277334\pi\)
−0.422744 + 0.906249i \(0.638933\pi\)
\(150\) 0 0
\(151\) 2.50000 4.33013i 0.203447 0.352381i −0.746190 0.665733i \(-0.768119\pi\)
0.949637 + 0.313353i \(0.101452\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 5.00000 8.66025i 0.401610 0.695608i
\(156\) 0 0
\(157\) 7.50000 + 12.9904i 0.598565 + 1.03675i 0.993033 + 0.117836i \(0.0375956\pi\)
−0.394468 + 0.918910i \(0.629071\pi\)
\(158\) 0 0
\(159\) 3.46410i 0.274721i
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) 10.0000 0.783260 0.391630 0.920123i \(-0.371911\pi\)
0.391630 + 0.920123i \(0.371911\pi\)
\(164\) 0 0
\(165\) 10.3923i 0.809040i
\(166\) 0 0
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 0 0
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) 0 0
\(171\) −21.0000 −1.60591
\(172\) 0 0
\(173\) −7.00000 + 12.1244i −0.532200 + 0.921798i 0.467093 + 0.884208i \(0.345301\pi\)
−0.999293 + 0.0375896i \(0.988032\pi\)
\(174\) 0 0
\(175\) 2.00000 + 3.46410i 0.151186 + 0.261861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 10.5000 + 6.06218i 0.776182 + 0.448129i
\(184\) 0 0
\(185\) −3.00000 5.19615i −0.220564 0.382029i
\(186\) 0 0
\(187\) −6.00000 + 10.3923i −0.438763 + 0.759961i
\(188\) 0 0
\(189\) −4.50000 2.59808i −0.327327 0.188982i
\(190\) 0 0
\(191\) 2.50000 4.33013i 0.180894 0.313317i −0.761291 0.648410i \(-0.775434\pi\)
0.942185 + 0.335093i \(0.108768\pi\)
\(192\) 0 0
\(193\) −4.50000 7.79423i −0.323917 0.561041i 0.657376 0.753563i \(-0.271667\pi\)
−0.981293 + 0.192522i \(0.938333\pi\)
\(194\) 0 0
\(195\) −9.00000 5.19615i −0.644503 0.372104i
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) 0 0
\(201\) 18.0000 10.3923i 1.26962 0.733017i
\(202\) 0 0
\(203\) −1.00000 1.73205i −0.0701862 0.121566i
\(204\) 0 0
\(205\) −4.00000 + 6.92820i −0.279372 + 0.483887i
\(206\) 0 0
\(207\) −1.50000 2.59808i −0.104257 0.180579i
\(208\) 0 0
\(209\) 21.0000 36.3731i 1.45260 2.51598i
\(210\) 0 0
\(211\) 2.00000 + 3.46410i 0.137686 + 0.238479i 0.926620 0.375999i \(-0.122700\pi\)
−0.788935 + 0.614477i \(0.789367\pi\)
\(212\) 0 0
\(213\) 25.9808i 1.78017i
\(214\) 0 0
\(215\) 10.0000 0.681994
\(216\) 0 0
\(217\) 10.0000 0.678844
\(218\) 0 0
\(219\) 3.46410i 0.234082i
\(220\) 0 0
\(221\) 6.00000 + 10.3923i 0.403604 + 0.699062i
\(222\) 0 0
\(223\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(224\) 0 0
\(225\) −6.00000 + 10.3923i −0.400000 + 0.692820i
\(226\) 0 0
\(227\) 0.500000 0.866025i 0.0331862 0.0574801i −0.848955 0.528465i \(-0.822768\pi\)
0.882141 + 0.470985i \(0.156101\pi\)
\(228\) 0 0
\(229\) −2.50000 4.33013i −0.165205 0.286143i 0.771523 0.636201i \(-0.219495\pi\)
−0.936728 + 0.350058i \(0.886162\pi\)
\(230\) 0 0
\(231\) 9.00000 5.19615i 0.592157 0.341882i
\(232\) 0 0
\(233\) −7.00000 −0.458585 −0.229293 0.973358i \(-0.573641\pi\)
−0.229293 + 0.973358i \(0.573641\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) 0 0
\(237\) 1.50000 + 0.866025i 0.0974355 + 0.0562544i
\(238\) 0 0
\(239\) −2.50000 4.33013i −0.161712 0.280093i 0.773771 0.633465i \(-0.218368\pi\)
−0.935483 + 0.353373i \(0.885035\pi\)
\(240\) 0 0
\(241\) −2.00000 + 3.46410i −0.128831 + 0.223142i −0.923224 0.384262i \(-0.874456\pi\)
0.794393 + 0.607404i \(0.207789\pi\)
\(242\) 0 0
\(243\) 15.5885i 1.00000i
\(244\) 0 0
\(245\) 0.500000 0.866025i 0.0319438 0.0553283i
\(246\) 0 0
\(247\) −21.0000 36.3731i −1.33620 2.31436i
\(248\) 0 0
\(249\) 18.0000 + 10.3923i 1.14070 + 0.658586i
\(250\) 0 0
\(251\) 13.0000 0.820553 0.410276 0.911961i \(-0.365432\pi\)
0.410276 + 0.911961i \(0.365432\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 0 0
\(255\) −3.00000 + 1.73205i −0.187867 + 0.108465i
\(256\) 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
\(259\) 3.00000 5.19615i 0.186411 0.322873i
\(260\) 0 0
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) 0 0
\(263\) −7.50000 + 12.9904i −0.462470 + 0.801021i −0.999083 0.0428069i \(-0.986370\pi\)
0.536614 + 0.843828i \(0.319703\pi\)
\(264\) 0 0
\(265\) 1.00000 + 1.73205i 0.0614295 + 0.106399i
\(266\) 0 0
\(267\) 6.92820i 0.423999i
\(268\) 0 0
\(269\) −3.00000 −0.182913 −0.0914566 0.995809i \(-0.529152\pi\)
−0.0914566 + 0.995809i \(0.529152\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 0 0
\(273\) 10.3923i 0.628971i
\(274\) 0 0
\(275\) −12.0000 20.7846i −0.723627 1.25336i
\(276\) 0 0
\(277\) −2.00000 + 3.46410i −0.120168 + 0.208138i −0.919834 0.392308i \(-0.871677\pi\)
0.799666 + 0.600446i \(0.205010\pi\)
\(278\) 0 0
\(279\) 15.0000 + 25.9808i 0.898027 + 1.55543i
\(280\) 0 0
\(281\) 1.50000 2.59808i 0.0894825 0.154988i −0.817810 0.575488i \(-0.804812\pi\)
0.907293 + 0.420500i \(0.138145\pi\)
\(282\) 0 0
\(283\) 6.50000 + 11.2583i 0.386385 + 0.669238i 0.991960 0.126550i \(-0.0403903\pi\)
−0.605575 + 0.795788i \(0.707057\pi\)
\(284\) 0 0
\(285\) 10.5000 6.06218i 0.621966 0.359092i
\(286\) 0 0
\(287\) −8.00000 −0.472225
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −3.00000 1.73205i −0.175863 0.101535i
\(292\) 0 0
\(293\) 4.50000 + 7.79423i 0.262893 + 0.455344i 0.967009 0.254741i \(-0.0819901\pi\)
−0.704117 + 0.710084i \(0.748657\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 27.0000 + 15.5885i 1.56670 + 0.904534i
\(298\) 0 0
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) 5.00000 + 8.66025i 0.288195 + 0.499169i
\(302\) 0 0
\(303\) 4.50000 + 2.59808i 0.258518 + 0.149256i
\(304\) 0 0
\(305\) −7.00000 −0.400819
\(306\) 0 0
\(307\) −23.0000 −1.31268 −0.656340 0.754466i \(-0.727896\pi\)
−0.656340 + 0.754466i \(0.727896\pi\)
\(308\) 0 0
\(309\) −9.00000 + 5.19615i −0.511992 + 0.295599i
\(310\) 0 0
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 0 0
\(313\) −1.00000 + 1.73205i −0.0565233 + 0.0979013i −0.892903 0.450250i \(-0.851335\pi\)
0.836379 + 0.548151i \(0.184668\pi\)
\(314\) 0 0
\(315\) 3.00000 0.169031
\(316\) 0 0
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 0 0
\(319\) 6.00000 + 10.3923i 0.335936 + 0.581857i
\(320\) 0 0
\(321\) 20.7846i 1.16008i
\(322\) 0 0
\(323\) −14.0000 −0.778981
\(324\) 0 0
\(325\) −24.0000 −1.33128
\(326\) 0 0
\(327\) 17.3205i 0.957826i
\(328\) 0 0
\(329\) −4.00000 6.92820i −0.220527 0.381964i
\(330\) 0 0
\(331\) −7.00000 + 12.1244i −0.384755 + 0.666415i −0.991735 0.128302i \(-0.959047\pi\)
0.606980 + 0.794717i \(0.292381\pi\)
\(332\) 0 0
\(333\) 18.0000 0.986394
\(334\) 0 0
\(335\) −6.00000 + 10.3923i −0.327815 + 0.567792i
\(336\) 0 0
\(337\) −1.00000 1.73205i −0.0544735 0.0943508i 0.837503 0.546433i \(-0.184015\pi\)
−0.891976 + 0.452082i \(0.850681\pi\)
\(338\) 0 0
\(339\) 13.5000 7.79423i 0.733219 0.423324i
\(340\) 0 0
\(341\) −60.0000 −3.24918
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 1.50000 + 0.866025i 0.0807573 + 0.0466252i
\(346\) 0 0
\(347\) −12.0000 20.7846i −0.644194 1.11578i −0.984487 0.175457i \(-0.943860\pi\)
0.340293 0.940319i \(-0.389474\pi\)
\(348\) 0 0
\(349\) 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i \(-0.747088\pi\)
0.968253 + 0.249973i \(0.0804216\pi\)
\(350\) 0 0
\(351\) 27.0000 15.5885i 1.44115 0.832050i
\(352\) 0 0
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 0 0
\(355\) 7.50000 + 12.9904i 0.398059 + 0.689458i
\(356\) 0 0
\(357\) −3.00000 1.73205i −0.158777 0.0916698i
\(358\) 0 0
\(359\) 33.0000 1.74167 0.870837 0.491572i \(-0.163578\pi\)
0.870837 + 0.491572i \(0.163578\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) 0 0
\(363\) −37.5000 + 21.6506i −1.96824 + 1.13636i
\(364\) 0 0
\(365\) −1.00000 1.73205i −0.0523424 0.0906597i
\(366\) 0 0
\(367\) −16.0000 + 27.7128i −0.835193 + 1.44660i 0.0586798 + 0.998277i \(0.481311\pi\)
−0.893873 + 0.448320i \(0.852022\pi\)
\(368\) 0 0
\(369\) −12.0000 20.7846i −0.624695 1.08200i
\(370\) 0 0
\(371\) −1.00000 + 1.73205i −0.0519174 + 0.0899236i
\(372\) 0 0
\(373\) −1.00000 1.73205i −0.0517780 0.0896822i 0.838975 0.544170i \(-0.183156\pi\)
−0.890753 + 0.454488i \(0.849822\pi\)
\(374\) 0 0
\(375\) 15.5885i 0.804984i
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 6.00000 0.308199 0.154100 0.988055i \(-0.450752\pi\)
0.154100 + 0.988055i \(0.450752\pi\)
\(380\) 0 0
\(381\) 8.66025i 0.443678i
\(382\) 0 0
\(383\) 3.00000 + 5.19615i 0.153293 + 0.265511i 0.932436 0.361335i \(-0.117679\pi\)
−0.779143 + 0.626846i \(0.784346\pi\)
\(384\) 0 0
\(385\) −3.00000 + 5.19615i −0.152894 + 0.264820i
\(386\) 0 0
\(387\) −15.0000 + 25.9808i −0.762493 + 1.32068i
\(388\) 0 0
\(389\) 10.0000 17.3205i 0.507020 0.878185i −0.492947 0.870059i \(-0.664080\pi\)
0.999967 0.00812520i \(-0.00258636\pi\)
\(390\) 0 0
\(391\) −1.00000 1.73205i −0.0505722 0.0875936i
\(392\) 0 0
\(393\) −25.5000 + 14.7224i −1.28630 + 0.742648i
\(394\) 0 0
\(395\) −1.00000 −0.0503155
\(396\) 0 0
\(397\) 22.0000 1.10415 0.552074 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 0 0
\(399\) 10.5000 + 6.06218i 0.525657 + 0.303488i
\(400\) 0 0
\(401\) 10.5000 + 18.1865i 0.524345 + 0.908192i 0.999598 + 0.0283431i \(0.00902310\pi\)
−0.475253 + 0.879849i \(0.657644\pi\)
\(402\) 0 0
\(403\) −30.0000 + 51.9615i −1.49441 + 2.58839i
\(404\) 0 0
\(405\) 4.50000 + 7.79423i 0.223607 + 0.387298i
\(406\) 0 0
\(407\) −18.0000 + 31.1769i −0.892227 + 1.54538i
\(408\) 0 0
\(409\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(410\) 0 0
\(411\) 21.0000 + 12.1244i 1.03585 + 0.598050i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) −4.50000 + 2.59808i −0.220366 + 0.127228i
\(418\) 0 0
\(419\) 3.50000 + 6.06218i 0.170986 + 0.296157i 0.938765 0.344558i \(-0.111971\pi\)
−0.767779 + 0.640715i \(0.778638\pi\)
\(420\) 0 0
\(421\) −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i \(-0.911690\pi\)
0.718076 + 0.695965i \(0.245023\pi\)
\(422\) 0 0
\(423\) 12.0000 20.7846i 0.583460 1.01058i
\(424\) 0 0
\(425\) −4.00000 + 6.92820i −0.194029 + 0.336067i
\(426\) 0 0
\(427\) −3.50000 6.06218i −0.169377 0.293369i
\(428\) 0 0
\(429\) 62.3538i 3.01047i
\(430\) 0 0
\(431\) 36.0000 1.73406 0.867029 0.498257i \(-0.166026\pi\)
0.867029 + 0.498257i \(0.166026\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 3.46410i 0.166091i
\(436\) 0 0
\(437\) 3.50000 + 6.06218i 0.167428 + 0.289993i
\(438\) 0 0
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 1.50000 + 2.59808i 0.0714286 + 0.123718i
\(442\) 0 0
\(443\) 17.0000 29.4449i 0.807694 1.39897i −0.106763 0.994285i \(-0.534048\pi\)
0.914457 0.404683i \(-0.132618\pi\)
\(444\) 0 0
\(445\) 2.00000 + 3.46410i 0.0948091 + 0.164214i
\(446\) 0 0
\(447\) 21.0000 12.1244i 0.993266 0.573462i
\(448\) 0 0
\(449\) 1.00000 0.0471929 0.0235965 0.999722i \(-0.492488\pi\)
0.0235965 + 0.999722i \(0.492488\pi\)
\(450\) 0 0
\(451\) 48.0000 2.26023
\(452\) 0 0
\(453\) −7.50000 4.33013i −0.352381 0.203447i
\(454\) 0 0
\(455\) 3.00000 + 5.19615i 0.140642 + 0.243599i
\(456\) 0 0
\(457\) 5.50000 9.52628i 0.257279 0.445621i −0.708233 0.705979i \(-0.750507\pi\)
0.965512 + 0.260358i \(0.0838407\pi\)
\(458\) 0 0
\(459\) 10.3923i 0.485071i
\(460\) 0 0
\(461\) 1.50000 2.59808i 0.0698620 0.121004i −0.828978 0.559281i \(-0.811077\pi\)
0.898840 + 0.438276i \(0.144411\pi\)
\(462\) 0 0
\(463\) −11.5000 19.9186i −0.534450 0.925695i −0.999190 0.0402476i \(-0.987185\pi\)
0.464739 0.885448i \(-0.346148\pi\)
\(464\) 0 0
\(465\) −15.0000 8.66025i −0.695608 0.401610i
\(466\) 0 0
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) −12.0000 −0.554109
\(470\) 0 0
\(471\) 22.5000 12.9904i 1.03675 0.598565i
\(472\) 0 0
\(473\) −30.0000 51.9615i −1.37940 2.38919i
\(474\) 0 0
\(475\) 14.0000 24.2487i 0.642364 1.11261i
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) −17.0000 + 29.4449i −0.776750 + 1.34537i 0.157056 + 0.987590i \(0.449800\pi\)
−0.933806 + 0.357780i \(0.883534\pi\)
\(480\) 0 0
\(481\) 18.0000 + 31.1769i 0.820729 + 1.42154i
\(482\) 0 0
\(483\) 1.73205i 0.0788110i
\(484\) 0 0
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) 1.00000 0.0453143 0.0226572 0.999743i \(-0.492787\pi\)
0.0226572 + 0.999743i \(0.492787\pi\)
\(488\) 0 0
\(489\) 17.3205i 0.783260i
\(490\) 0 0
\(491\) 3.00000 + 5.19615i 0.135388 + 0.234499i 0.925746 0.378147i \(-0.123439\pi\)
−0.790358 + 0.612646i \(0.790105\pi\)
\(492\) 0 0
\(493\) 2.00000 3.46410i 0.0900755 0.156015i
\(494\) 0 0
\(495\) −18.0000 −0.809040
\(496\) 0 0
\(497\) −7.50000 + 12.9904i −0.336421 + 0.582698i
\(498\) 0 0
\(499\) −8.00000 13.8564i −0.358129 0.620298i 0.629519 0.776985i \(-0.283252\pi\)
−0.987648 + 0.156687i \(0.949919\pi\)
\(500\) 0 0
\(501\) −18.0000 + 10.3923i −0.804181 + 0.464294i
\(502\) 0 0
\(503\) −32.0000 −1.42681 −0.713405 0.700752i \(-0.752848\pi\)
−0.713405 + 0.700752i \(0.752848\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) 0 0
\(507\) 34.5000 + 19.9186i 1.53220 + 0.884615i
\(508\) 0 0
\(509\) 15.0000 + 25.9808i 0.664863 + 1.15158i 0.979322 + 0.202306i \(0.0648436\pi\)
−0.314459 + 0.949271i \(0.601823\pi\)
\(510\) 0 0
\(511\) 1.00000 1.73205i 0.0442374 0.0766214i
\(512\) 0 0
\(513\) 36.3731i 1.60591i
\(514\) 0 0
\(515\) 3.00000 5.19615i 0.132196 0.228970i
\(516\) 0 0
\(517\) 24.0000 + 41.5692i 1.05552 + 1.82821i
\(518\) 0 0
\(519\) 21.0000 + 12.1244i 0.921798 + 0.532200i
\(520\) 0 0
\(521\) −12.0000 −0.525730 −0.262865 0.964833i \(-0.584667\pi\)
−0.262865 + 0.964833i \(0.584667\pi\)
\(522\) 0 0
\(523\) 29.0000 1.26808 0.634041 0.773300i \(-0.281395\pi\)
0.634041 + 0.773300i \(0.281395\pi\)
\(524\) 0 0
\(525\) 6.00000 3.46410i 0.261861 0.151186i
\(526\) 0 0
\(527\) 10.0000 + 17.3205i 0.435607 + 0.754493i
\(528\) 0 0
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 24.0000 41.5692i 1.03956 1.80056i
\(534\) 0 0
\(535\) 6.00000 + 10.3923i 0.259403 + 0.449299i
\(536\) 0 0
\(537\) 17.3205i 0.747435i
\(538\) 0 0
\(539\) −6.00000 −0.258438
\(540\) 0 0
\(541\) −14.0000 −0.601907 −0.300954 0.953639i \(-0.597305\pi\)
−0.300954 + 0.953639i \(0.597305\pi\)
\(542\) 0 0
\(543\) 8.66025i 0.371647i
\(544\) 0 0
\(545\) 5.00000 + 8.66025i 0.214176 + 0.370965i
\(546\) 0 0
\(547\) 4.00000 6.92820i 0.171028 0.296229i −0.767752 0.640747i \(-0.778625\pi\)
0.938779 + 0.344519i \(0.111958\pi\)
\(548\) 0 0
\(549\) 10.5000 18.1865i 0.448129 0.776182i
\(550\) 0 0
\(551\) −7.00000 + 12.1244i −0.298210 + 0.516515i
\(552\) 0 0
\(553\) −0.500000 0.866025i −0.0212622 0.0368271i
\(554\) 0 0
\(555\) −9.00000 + 5.19615i −0.382029 + 0.220564i
\(556\) 0 0
\(557\) −44.0000 −1.86434 −0.932170 0.362021i \(-0.882087\pi\)
−0.932170 + 0.362021i \(0.882087\pi\)
\(558\) 0 0
\(559\) −60.0000 −2.53773
\(560\) 0 0
\(561\) 18.0000 + 10.3923i 0.759961 + 0.438763i
\(562\) 0 0
\(563\) 11.5000 + 19.9186i 0.484667 + 0.839468i 0.999845 0.0176152i \(-0.00560738\pi\)
−0.515178 + 0.857083i \(0.672274\pi\)
\(564\) 0 0
\(565\) −4.50000 + 7.79423i −0.189316 + 0.327906i
\(566\) 0 0
\(567\) −4.50000 + 7.79423i −0.188982 + 0.327327i
\(568\) 0 0
\(569\) −15.0000 + 25.9808i −0.628833 + 1.08917i 0.358954 + 0.933355i \(0.383134\pi\)
−0.987786 + 0.155815i \(0.950200\pi\)
\(570\) 0 0
\(571\) 20.0000 + 34.6410i 0.836974 + 1.44968i 0.892413 + 0.451219i \(0.149011\pi\)
−0.0554391 + 0.998462i \(0.517656\pi\)
\(572\) 0 0
\(573\) −7.50000 4.33013i −0.313317 0.180894i
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) 36.0000 1.49870 0.749350 0.662174i \(-0.230366\pi\)
0.749350 + 0.662174i \(0.230366\pi\)
\(578\) 0 0
\(579\) −13.5000 + 7.79423i −0.561041 + 0.323917i
\(580\) 0 0
\(581\) −6.00000 10.3923i −0.248922 0.431145i
\(582\) 0 0
\(583\) 6.00000 10.3923i 0.248495 0.430405i
\(584\) 0 0
\(585\) −9.00000 + 15.5885i −0.372104 + 0.644503i
\(586\) 0 0
\(587\) 2.50000 4.33013i 0.103186 0.178723i −0.809810 0.586693i \(-0.800430\pi\)
0.912996 + 0.407969i \(0.133763\pi\)
\(588\) 0 0
\(589\) −35.0000 60.6218i −1.44215 2.49788i
\(590\) 0 0
\(591\) 10.3923i 0.427482i
\(592\) 0 0
\(593\) −12.0000 −0.492781 −0.246390 0.969171i \(-0.579245\pi\)
−0.246390 + 0.969171i \(0.579245\pi\)
\(594\) 0 0
\(595\) 2.00000 0.0819920
\(596\) 0 0
\(597\) 3.46410i 0.141776i
\(598\) 0 0
\(599\) 16.0000 + 27.7128i 0.653742 + 1.13231i 0.982208 + 0.187799i \(0.0601353\pi\)
−0.328465 + 0.944516i \(0.606531\pi\)
\(600\) 0 0
\(601\) 7.00000 12.1244i 0.285536 0.494563i −0.687203 0.726465i \(-0.741162\pi\)
0.972739 + 0.231903i \(0.0744951\pi\)
\(602\) 0 0
\(603\) −18.0000 31.1769i −0.733017 1.26962i
\(604\) 0 0
\(605\) 12.5000 21.6506i 0.508197 0.880223i
\(606\) 0 0
\(607\) 1.00000 + 1.73205i 0.0405887 + 0.0703018i 0.885606 0.464437i \(-0.153743\pi\)
−0.845017 + 0.534739i \(0.820410\pi\)
\(608\) 0 0
\(609\) −3.00000 + 1.73205i −0.121566 + 0.0701862i
\(610\) 0 0
\(611\) 48.0000 1.94187
\(612\) 0 0
\(613\) −20.0000 −0.807792 −0.403896 0.914805i \(-0.632344\pi\)
−0.403896 + 0.914805i \(0.632344\pi\)
\(614\) 0 0
\(615\) 12.0000 + 6.92820i 0.483887 + 0.279372i
\(616\) 0 0
\(617\) 15.0000 + 25.9808i 0.603877 + 1.04595i 0.992228 + 0.124434i \(0.0397116\pi\)
−0.388351 + 0.921512i \(0.626955\pi\)
\(618\) 0 0
\(619\) 16.5000 28.5788i 0.663191 1.14868i −0.316581 0.948565i \(-0.602535\pi\)
0.979772 0.200115i \(-0.0641316\pi\)
\(620\) 0 0
\(621\) −4.50000 + 2.59808i −0.180579 + 0.104257i
\(622\) 0 0
\(623\) −2.00000 + 3.46410i −0.0801283 + 0.138786i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) −63.0000 36.3731i −2.51598 1.45260i
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 5.00000 0.199047 0.0995234 0.995035i \(-0.468268\pi\)
0.0995234 + 0.995035i \(0.468268\pi\)
\(632\) 0 0
\(633\) 6.00000 3.46410i 0.238479 0.137686i
\(634\) 0 0
\(635\) 2.50000 + 4.33013i 0.0992095 + 0.171836i
\(636\) 0 0
\(637\) −3.00000 + 5.19615i −0.118864 + 0.205879i
\(638\) 0 0
\(639\) −45.0000 −1.78017
\(640\) 0 0
\(641\) −21.5000 + 37.2391i −0.849199 + 1.47086i 0.0327252 + 0.999464i \(0.489581\pi\)
−0.881924 + 0.471391i \(0.843752\pi\)
\(642\) 0 0
\(643\) −2.00000 3.46410i −0.0788723 0.136611i 0.823891 0.566748i \(-0.191799\pi\)
−0.902764 + 0.430137i \(0.858465\pi\)
\(644\) 0 0
\(645\) 17.3205i 0.681994i
\(646\) 0 0
\(647\) 12.0000 0.471769 0.235884 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 17.3205i 0.678844i
\(652\) 0 0
\(653\) −22.0000 38.1051i −0.860927 1.49117i −0.871036 0.491220i \(-0.836551\pi\)
0.0101092 0.999949i \(-0.496782\pi\)
\(654\) 0 0
\(655\) 8.50000 14.7224i 0.332122 0.575253i
\(656\) 0 0
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) 17.0000 29.4449i 0.662226 1.14701i −0.317803 0.948157i \(-0.602945\pi\)
0.980029 0.198852i \(-0.0637214\pi\)
\(660\) 0 0
\(661\) 12.5000 + 21.6506i 0.486194 + 0.842112i 0.999874 0.0158695i \(-0.00505163\pi\)
−0.513680 + 0.857982i \(0.671718\pi\)
\(662\) 0 0
\(663\) 18.0000 10.3923i 0.699062 0.403604i
\(664\) 0 0
\(665\) −7.00000 −0.271448
\(666\) 0 0
\(667\) −2.00000 −0.0774403
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 21.0000 + 36.3731i 0.810696 + 1.40417i
\(672\) 0 0
\(673\) −9.50000 + 16.4545i −0.366198 + 0.634274i −0.988968 0.148132i \(-0.952674\pi\)
0.622770 + 0.782405i \(0.286007\pi\)
\(674\) 0 0
\(675\) 18.0000 + 10.3923i 0.692820 + 0.400000i
\(676\) 0 0
\(677\) 21.0000 36.3731i 0.807096 1.39793i −0.107772 0.994176i \(-0.534372\pi\)
0.914867 0.403755i \(-0.132295\pi\)
\(678\) 0 0
\(679\) 1.00000 + 1.73205i 0.0383765 + 0.0664700i
\(680\) 0 0
\(681\) −1.50000 0.866025i −0.0574801 0.0331862i
\(682\) 0 0
\(683\) 18.0000 0.688751 0.344375 0.938832i \(-0.388091\pi\)
0.344375 + 0.938832i \(0.388091\pi\)
\(684\) 0 0
\(685\) −14.0000 −0.534913
\(686\) 0 0
\(687\) −7.50000 + 4.33013i −0.286143 + 0.165205i
\(688\) 0 0
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) −20.5000 + 35.5070i −0.779857 + 1.35075i 0.152167 + 0.988355i \(0.451375\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 0 0
\(693\) −9.00000 15.5885i −0.341882 0.592157i
\(694\) 0 0
\(695\) 1.50000 2.59808i 0.0568982 0.0985506i
\(696\) 0 0
\(697\) −8.00000 13.8564i −0.303022 0.524849i
\(698\) 0 0
\(699\) 12.1244i 0.458585i
\(700\) 0 0
\(701\) −26.0000 −0.982006 −0.491003 0.871158i \(-0.663370\pi\)
−0.491003 + 0.871158i \(0.663370\pi\)
\(702\) 0 0
\(703\) −42.0000 −1.58406
\(704\) 0 0
\(705\) 13.8564i 0.521862i
\(706\) 0 0
\(707\) −1.50000 2.59808i −0.0564133 0.0977107i
\(708\) 0 0
\(709\) 22.0000 38.1051i 0.826227 1.43107i −0.0747503 0.997202i \(-0.523816\pi\)
0.900978 0.433865i \(-0.142851\pi\)
\(710\) 0 0
\(711\) 1.50000 2.59808i 0.0562544 0.0974355i
\(712\) 0 0
\(713\) 5.00000 8.66025i 0.187251 0.324329i
\(714\) 0 0
\(715\) −18.0000 31.1769i −0.673162 1.16595i
\(716\) 0 0
\(717\) −7.50000 + 4.33013i −0.280093 + 0.161712i
\(718\) 0 0
\(719\) −12.0000 −0.447524 −0.223762 0.974644i \(-0.571834\pi\)
−0.223762 + 0.974644i \(0.571834\pi\)
\(720\) 0 0
\(721\) 6.00000 0.223452
\(722\) 0 0
\(723\) 6.00000 + 3.46410i 0.223142 + 0.128831i
\(724\) 0 0
\(725\) 4.00000 + 6.92820i 0.148556 + 0.257307i
\(726\) 0 0
\(727\) 14.0000 24.2487i 0.519231 0.899335i −0.480519 0.876984i \(-0.659552\pi\)
0.999750 0.0223506i \(-0.00711500\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −10.0000 + 17.3205i −0.369863 + 0.640622i
\(732\) 0 0
\(733\) −15.5000 26.8468i −0.572506 0.991609i −0.996308 0.0858539i \(-0.972638\pi\)
0.423802 0.905755i \(-0.360695\pi\)
\(734\) 0 0
\(735\) −1.50000 0.866025i −0.0553283 0.0319438i
\(736\) 0 0
\(737\) 72.0000 2.65215
\(738\) 0 0
\(739\) −38.0000 −1.39785 −0.698926 0.715194i \(-0.746338\pi\)
−0.698926 + 0.715194i \(0.746338\pi\)
\(740\) 0 0
\(741\) −63.0000 + 36.3731i −2.31436 + 1.33620i
\(742\) 0 0
\(743\) −22.0000 38.1051i −0.807102 1.39794i −0.914863 0.403764i \(-0.867702\pi\)
0.107761 0.994177i \(-0.465632\pi\)
\(744\) 0 0
\(745\) −7.00000 + 12.1244i −0.256460 + 0.444202i
\(746\) 0 0
\(747\) 18.0000 31.1769i 0.658586 1.14070i
\(748\) 0 0
\(749\) −6.00000 + 10.3923i −0.219235 + 0.379727i
\(750\) 0 0
\(751\) −2.50000 4.33013i −0.0912263 0.158009i 0.816801 0.576919i \(-0.195745\pi\)
−0.908027 + 0.418911i \(0.862412\pi\)
\(752\) 0 0
\(753\) 22.5167i 0.820553i
\(754\) 0 0
\(755\) 5.00000 0.181969
\(756\) 0 0
\(757\) 34.0000 1.23575 0.617876 0.786276i \(-0.287994\pi\)
0.617876 + 0.786276i \(0.287994\pi\)
\(758\) 0 0
\(759\) 10.3923i 0.377217i
\(760\) 0 0
\(761\) −3.00000 5.19615i −0.108750 0.188360i 0.806514 0.591215i \(-0.201351\pi\)
−0.915264 + 0.402854i \(0.868018\pi\)
\(762\) 0 0
\(763\) −5.00000 + 8.66025i −0.181012 + 0.313522i
\(764\) 0 0
\(765\) 3.00000 + 5.19615i 0.108465 + 0.187867i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −5.00000 8.66025i −0.180305 0.312297i 0.761680 0.647954i \(-0.224375\pi\)
−0.941984 + 0.335657i \(0.891042\pi\)
\(770\) 0 0
\(771\) −27.0000 + 15.5885i −0.972381 + 0.561405i
\(772\) 0 0
\(773\) 31.0000 1.11499 0.557496 0.830179i \(-0.311762\pi\)
0.557496 + 0.830179i \(0.311762\pi\)
\(774\) 0 0
\(775\) −40.0000 −1.43684
\(776\) 0 0
\(777\) −9.00000 5.19615i −0.322873 0.186411i
\(778\) 0 0
\(779\) 28.0000 + 48.4974i 1.00320 + 1.73760i
\(780\) 0 0
\(781\) 45.0000 77.9423i 1.61023 2.78899i
\(782\) 0 0
\(783\) −9.00000 5.19615i −0.321634 0.185695i
\(784\) 0 0
\(785\) −7.50000 + 12.9904i −0.267686 + 0.463647i
\(786\) 0 0
\(787\) 10.0000 + 17.3205i 0.356462 + 0.617409i 0.987367 0.158450i \(-0.0506498\pi\)
−0.630905 + 0.775860i \(0.717316\pi\)
\(788\) 0 0
\(789\) 22.5000 + 12.9904i 0.801021 + 0.462470i
\(790\) 0 0
\(791\) −9.00000 −0.320003
\(792\) 0 0
\(793\) 42.0000 1.49146
\(794\) 0 0
\(795\) 3.00000 1.73205i 0.106399 0.0614295i
\(796\) 0 0
\(797\) −4.50000 7.79423i −0.159398 0.276086i 0.775254 0.631650i