Properties

Label 324.3.f.i.271.1
Level $324$
Weight $3$
Character 324.271
Analytic conductor $8.828$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 324.271
Dual form 324.3.f.i.55.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +4.00000 q^{4} +(-3.50000 + 6.06218i) q^{5} +(-7.50000 + 4.33013i) q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+2.00000 q^{2} +4.00000 q^{4} +(-3.50000 + 6.06218i) q^{5} +(-7.50000 + 4.33013i) q^{7} +8.00000 q^{8} +(-7.00000 + 12.1244i) q^{10} +(7.50000 - 4.33013i) q^{11} +(-10.0000 + 17.3205i) q^{13} +(-15.0000 + 8.66025i) q^{14} +16.0000 q^{16} -8.00000 q^{17} +10.3923i q^{19} +(-14.0000 + 24.2487i) q^{20} +(15.0000 - 8.66025i) q^{22} +(3.00000 + 1.73205i) q^{23} +(-12.0000 - 20.7846i) q^{25} +(-20.0000 + 34.6410i) q^{26} +(-30.0000 + 17.3205i) q^{28} +(-5.00000 - 8.66025i) q^{29} +(46.5000 + 26.8468i) q^{31} +32.0000 q^{32} -16.0000 q^{34} -60.6218i q^{35} -10.0000 q^{37} +20.7846i q^{38} +(-28.0000 + 48.4974i) q^{40} +(25.0000 - 43.3013i) q^{41} +(15.0000 - 8.66025i) q^{43} +(30.0000 - 17.3205i) q^{44} +(6.00000 + 3.46410i) q^{46} +(75.0000 - 43.3013i) q^{47} +(13.0000 - 22.5167i) q^{49} +(-24.0000 - 41.5692i) q^{50} +(-40.0000 + 69.2820i) q^{52} -47.0000 q^{53} +60.6218i q^{55} +(-60.0000 + 34.6410i) q^{56} +(-10.0000 - 17.3205i) q^{58} +(30.0000 + 17.3205i) q^{59} +(32.0000 + 55.4256i) q^{61} +(93.0000 + 53.6936i) q^{62} +64.0000 q^{64} +(-70.0000 - 121.244i) q^{65} +(-75.0000 - 43.3013i) q^{67} -32.0000 q^{68} -121.244i q^{70} -55.0000 q^{73} -20.0000 q^{74} +41.5692i q^{76} +(-37.5000 + 64.9519i) q^{77} +(6.00000 - 3.46410i) q^{79} +(-56.0000 + 96.9948i) q^{80} +(50.0000 - 86.6025i) q^{82} +(25.5000 - 14.7224i) q^{83} +(28.0000 - 48.4974i) q^{85} +(30.0000 - 17.3205i) q^{86} +(60.0000 - 34.6410i) q^{88} +10.0000 q^{89} -173.205i q^{91} +(12.0000 + 6.92820i) q^{92} +(150.000 - 86.6025i) q^{94} +(-63.0000 - 36.3731i) q^{95} +(12.5000 + 21.6506i) q^{97} +(26.0000 - 45.0333i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} + 8 q^{4} - 7 q^{5} - 15 q^{7} + 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 4 q^{2} + 8 q^{4} - 7 q^{5} - 15 q^{7} + 16 q^{8} - 14 q^{10} + 15 q^{11} - 20 q^{13} - 30 q^{14} + 32 q^{16} - 16 q^{17} - 28 q^{20} + 30 q^{22} + 6 q^{23} - 24 q^{25} - 40 q^{26} - 60 q^{28} - 10 q^{29} + 93 q^{31} + 64 q^{32} - 32 q^{34} - 20 q^{37} - 56 q^{40} + 50 q^{41} + 30 q^{43} + 60 q^{44} + 12 q^{46} + 150 q^{47} + 26 q^{49} - 48 q^{50} - 80 q^{52} - 94 q^{53} - 120 q^{56} - 20 q^{58} + 60 q^{59} + 64 q^{61} + 186 q^{62} + 128 q^{64} - 140 q^{65} - 150 q^{67} - 64 q^{68} - 110 q^{73} - 40 q^{74} - 75 q^{77} + 12 q^{79} - 112 q^{80} + 100 q^{82} + 51 q^{83} + 56 q^{85} + 60 q^{86} + 120 q^{88} + 20 q^{89} + 24 q^{92} + 300 q^{94} - 126 q^{95} + 25 q^{97} + 52 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.00000
\(3\) 0 0
\(4\) 4.00000 1.00000
\(5\) −3.50000 + 6.06218i −0.700000 + 1.21244i 0.268466 + 0.963289i \(0.413483\pi\)
−0.968466 + 0.249146i \(0.919850\pi\)
\(6\) 0 0
\(7\) −7.50000 + 4.33013i −1.07143 + 0.618590i −0.928571 0.371154i \(-0.878962\pi\)
−0.142857 + 0.989743i \(0.545629\pi\)
\(8\) 8.00000 1.00000
\(9\) 0 0
\(10\) −7.00000 + 12.1244i −0.700000 + 1.21244i
\(11\) 7.50000 4.33013i 0.681818 0.393648i −0.118722 0.992928i \(-0.537880\pi\)
0.800540 + 0.599280i \(0.204546\pi\)
\(12\) 0 0
\(13\) −10.0000 + 17.3205i −0.769231 + 1.33235i 0.168750 + 0.985659i \(0.446027\pi\)
−0.937981 + 0.346688i \(0.887306\pi\)
\(14\) −15.0000 + 8.66025i −1.07143 + 0.618590i
\(15\) 0 0
\(16\) 16.0000 1.00000
\(17\) −8.00000 −0.470588 −0.235294 0.971924i \(-0.575605\pi\)
−0.235294 + 0.971924i \(0.575605\pi\)
\(18\) 0 0
\(19\) 10.3923i 0.546963i 0.961877 + 0.273482i \(0.0881753\pi\)
−0.961877 + 0.273482i \(0.911825\pi\)
\(20\) −14.0000 + 24.2487i −0.700000 + 1.21244i
\(21\) 0 0
\(22\) 15.0000 8.66025i 0.681818 0.393648i
\(23\) 3.00000 + 1.73205i 0.130435 + 0.0753066i 0.563798 0.825913i \(-0.309340\pi\)
−0.433363 + 0.901220i \(0.642673\pi\)
\(24\) 0 0
\(25\) −12.0000 20.7846i −0.480000 0.831384i
\(26\) −20.0000 + 34.6410i −0.769231 + 1.33235i
\(27\) 0 0
\(28\) −30.0000 + 17.3205i −1.07143 + 0.618590i
\(29\) −5.00000 8.66025i −0.172414 0.298629i 0.766849 0.641827i \(-0.221823\pi\)
−0.939263 + 0.343198i \(0.888490\pi\)
\(30\) 0 0
\(31\) 46.5000 + 26.8468i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(32\) 32.0000 1.00000
\(33\) 0 0
\(34\) −16.0000 −0.470588
\(35\) 60.6218i 1.73205i
\(36\) 0 0
\(37\) −10.0000 −0.270270 −0.135135 0.990827i \(-0.543147\pi\)
−0.135135 + 0.990827i \(0.543147\pi\)
\(38\) 20.7846i 0.546963i
\(39\) 0 0
\(40\) −28.0000 + 48.4974i −0.700000 + 1.21244i
\(41\) 25.0000 43.3013i 0.609756 1.05613i −0.381524 0.924359i \(-0.624601\pi\)
0.991280 0.131770i \(-0.0420659\pi\)
\(42\) 0 0
\(43\) 15.0000 8.66025i 0.348837 0.201401i −0.315336 0.948980i \(-0.602117\pi\)
0.664173 + 0.747579i \(0.268784\pi\)
\(44\) 30.0000 17.3205i 0.681818 0.393648i
\(45\) 0 0
\(46\) 6.00000 + 3.46410i 0.130435 + 0.0753066i
\(47\) 75.0000 43.3013i 1.59574 0.921304i 0.603450 0.797401i \(-0.293792\pi\)
0.992294 0.123903i \(-0.0395412\pi\)
\(48\) 0 0
\(49\) 13.0000 22.5167i 0.265306 0.459524i
\(50\) −24.0000 41.5692i −0.480000 0.831384i
\(51\) 0 0
\(52\) −40.0000 + 69.2820i −0.769231 + 1.33235i
\(53\) −47.0000 −0.886792 −0.443396 0.896326i \(-0.646227\pi\)
−0.443396 + 0.896326i \(0.646227\pi\)
\(54\) 0 0
\(55\) 60.6218i 1.10221i
\(56\) −60.0000 + 34.6410i −1.07143 + 0.618590i
\(57\) 0 0
\(58\) −10.0000 17.3205i −0.172414 0.298629i
\(59\) 30.0000 + 17.3205i 0.508475 + 0.293568i 0.732206 0.681083i \(-0.238491\pi\)
−0.223732 + 0.974651i \(0.571824\pi\)
\(60\) 0 0
\(61\) 32.0000 + 55.4256i 0.524590 + 0.908617i 0.999590 + 0.0286310i \(0.00911476\pi\)
−0.475000 + 0.879986i \(0.657552\pi\)
\(62\) 93.0000 + 53.6936i 1.50000 + 0.866025i
\(63\) 0 0
\(64\) 64.0000 1.00000
\(65\) −70.0000 121.244i −1.07692 1.86529i
\(66\) 0 0
\(67\) −75.0000 43.3013i −1.11940 0.646288i −0.178155 0.984003i \(-0.557013\pi\)
−0.941248 + 0.337715i \(0.890346\pi\)
\(68\) −32.0000 −0.470588
\(69\) 0 0
\(70\) 121.244i 1.73205i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −55.0000 −0.753425 −0.376712 0.926330i \(-0.622945\pi\)
−0.376712 + 0.926330i \(0.622945\pi\)
\(74\) −20.0000 −0.270270
\(75\) 0 0
\(76\) 41.5692i 0.546963i
\(77\) −37.5000 + 64.9519i −0.487013 + 0.843531i
\(78\) 0 0
\(79\) 6.00000 3.46410i 0.0759494 0.0438494i −0.461544 0.887117i \(-0.652704\pi\)
0.537494 + 0.843268i \(0.319371\pi\)
\(80\) −56.0000 + 96.9948i −0.700000 + 1.21244i
\(81\) 0 0
\(82\) 50.0000 86.6025i 0.609756 1.05613i
\(83\) 25.5000 14.7224i 0.307229 0.177379i −0.338457 0.940982i \(-0.609905\pi\)
0.645686 + 0.763603i \(0.276572\pi\)
\(84\) 0 0
\(85\) 28.0000 48.4974i 0.329412 0.570558i
\(86\) 30.0000 17.3205i 0.348837 0.201401i
\(87\) 0 0
\(88\) 60.0000 34.6410i 0.681818 0.393648i
\(89\) 10.0000 0.112360 0.0561798 0.998421i \(-0.482108\pi\)
0.0561798 + 0.998421i \(0.482108\pi\)
\(90\) 0 0
\(91\) 173.205i 1.90335i
\(92\) 12.0000 + 6.92820i 0.130435 + 0.0753066i
\(93\) 0 0
\(94\) 150.000 86.6025i 1.59574 0.921304i
\(95\) −63.0000 36.3731i −0.663158 0.382874i
\(96\) 0 0
\(97\) 12.5000 + 21.6506i 0.128866 + 0.223202i 0.923237 0.384230i \(-0.125533\pi\)
−0.794372 + 0.607432i \(0.792200\pi\)
\(98\) 26.0000 45.0333i 0.265306 0.459524i
\(99\) 0 0
\(100\) −48.0000 83.1384i −0.480000 0.831384i
\(101\) 77.5000 + 134.234i 0.767327 + 1.32905i 0.939008 + 0.343896i \(0.111747\pi\)
−0.171681 + 0.985153i \(0.554920\pi\)
\(102\) 0 0
\(103\) −120.000 69.2820i −1.16505 0.672641i −0.212540 0.977152i \(-0.568174\pi\)
−0.952509 + 0.304511i \(0.901507\pi\)
\(104\) −80.0000 + 138.564i −0.769231 + 1.33235i
\(105\) 0 0
\(106\) −94.0000 −0.886792
\(107\) 129.904i 1.21405i −0.794681 0.607027i \(-0.792362\pi\)
0.794681 0.607027i \(-0.207638\pi\)
\(108\) 0 0
\(109\) 134.000 1.22936 0.614679 0.788777i \(-0.289286\pi\)
0.614679 + 0.788777i \(0.289286\pi\)
\(110\) 121.244i 1.10221i
\(111\) 0 0
\(112\) −120.000 + 69.2820i −1.07143 + 0.618590i
\(113\) 37.0000 64.0859i 0.327434 0.567132i −0.654568 0.756003i \(-0.727150\pi\)
0.982002 + 0.188871i \(0.0604829\pi\)
\(114\) 0 0
\(115\) −21.0000 + 12.1244i −0.182609 + 0.105429i
\(116\) −20.0000 34.6410i −0.172414 0.298629i
\(117\) 0 0
\(118\) 60.0000 + 34.6410i 0.508475 + 0.293568i
\(119\) 60.0000 34.6410i 0.504202 0.291101i
\(120\) 0 0
\(121\) −23.0000 + 39.8372i −0.190083 + 0.329233i
\(122\) 64.0000 + 110.851i 0.524590 + 0.908617i
\(123\) 0 0
\(124\) 186.000 + 107.387i 1.50000 + 0.866025i
\(125\) −7.00000 −0.0560000
\(126\) 0 0
\(127\) 25.9808i 0.204573i −0.994755 0.102286i \(-0.967384\pi\)
0.994755 0.102286i \(-0.0326158\pi\)
\(128\) 128.000 1.00000
\(129\) 0 0
\(130\) −140.000 242.487i −1.07692 1.86529i
\(131\) 142.500 + 82.2724i 1.08779 + 0.628034i 0.932986 0.359912i \(-0.117193\pi\)
0.154800 + 0.987946i \(0.450527\pi\)
\(132\) 0 0
\(133\) −45.0000 77.9423i −0.338346 0.586032i
\(134\) −150.000 86.6025i −1.11940 0.646288i
\(135\) 0 0
\(136\) −64.0000 −0.470588
\(137\) 31.0000 + 53.6936i 0.226277 + 0.391924i 0.956702 0.291070i \(-0.0940111\pi\)
−0.730425 + 0.682993i \(0.760678\pi\)
\(138\) 0 0
\(139\) 150.000 + 86.6025i 1.07914 + 0.623040i 0.930663 0.365877i \(-0.119231\pi\)
0.148473 + 0.988916i \(0.452564\pi\)
\(140\) 242.487i 1.73205i
\(141\) 0 0
\(142\) 0 0
\(143\) 173.205i 1.21122i
\(144\) 0 0
\(145\) 70.0000 0.482759
\(146\) −110.000 −0.753425
\(147\) 0 0
\(148\) −40.0000 −0.270270
\(149\) −57.5000 + 99.5929i −0.385906 + 0.668409i −0.991894 0.127065i \(-0.959444\pi\)
0.605988 + 0.795473i \(0.292778\pi\)
\(150\) 0 0
\(151\) 37.5000 21.6506i 0.248344 0.143382i −0.370662 0.928768i \(-0.620869\pi\)
0.619006 + 0.785386i \(0.287536\pi\)
\(152\) 83.1384i 0.546963i
\(153\) 0 0
\(154\) −75.0000 + 129.904i −0.487013 + 0.843531i
\(155\) −325.500 + 187.928i −2.10000 + 1.21244i
\(156\) 0 0
\(157\) −10.0000 + 17.3205i −0.0636943 + 0.110322i −0.896114 0.443824i \(-0.853622\pi\)
0.832420 + 0.554146i \(0.186955\pi\)
\(158\) 12.0000 6.92820i 0.0759494 0.0438494i
\(159\) 0 0
\(160\) −112.000 + 193.990i −0.700000 + 1.21244i
\(161\) −30.0000 −0.186335
\(162\) 0 0
\(163\) 103.923i 0.637565i 0.947828 + 0.318782i \(0.103274\pi\)
−0.947828 + 0.318782i \(0.896726\pi\)
\(164\) 100.000 173.205i 0.609756 1.05613i
\(165\) 0 0
\(166\) 51.0000 29.4449i 0.307229 0.177379i
\(167\) −213.000 122.976i −1.27545 0.736381i −0.299441 0.954115i \(-0.596800\pi\)
−0.976008 + 0.217734i \(0.930133\pi\)
\(168\) 0 0
\(169\) −115.500 200.052i −0.683432 1.18374i
\(170\) 56.0000 96.9948i 0.329412 0.570558i
\(171\) 0 0
\(172\) 60.0000 34.6410i 0.348837 0.201401i
\(173\) −63.5000 109.985i −0.367052 0.635753i 0.622051 0.782977i \(-0.286300\pi\)
−0.989103 + 0.147224i \(0.952966\pi\)
\(174\) 0 0
\(175\) 180.000 + 103.923i 1.02857 + 0.593846i
\(176\) 120.000 69.2820i 0.681818 0.393648i
\(177\) 0 0
\(178\) 20.0000 0.112360
\(179\) 233.827i 1.30630i 0.757231 + 0.653148i \(0.226552\pi\)
−0.757231 + 0.653148i \(0.773448\pi\)
\(180\) 0 0
\(181\) 56.0000 0.309392 0.154696 0.987962i \(-0.450560\pi\)
0.154696 + 0.987962i \(0.450560\pi\)
\(182\) 346.410i 1.90335i
\(183\) 0 0
\(184\) 24.0000 + 13.8564i 0.130435 + 0.0753066i
\(185\) 35.0000 60.6218i 0.189189 0.327685i
\(186\) 0 0
\(187\) −60.0000 + 34.6410i −0.320856 + 0.185246i
\(188\) 300.000 173.205i 1.59574 0.921304i
\(189\) 0 0
\(190\) −126.000 72.7461i −0.663158 0.382874i
\(191\) 30.0000 17.3205i 0.157068 0.0906833i −0.419406 0.907799i \(-0.637762\pi\)
0.576474 + 0.817116i \(0.304428\pi\)
\(192\) 0 0
\(193\) −32.5000 + 56.2917i −0.168394 + 0.291667i −0.937855 0.347027i \(-0.887191\pi\)
0.769462 + 0.638693i \(0.220525\pi\)
\(194\) 25.0000 + 43.3013i 0.128866 + 0.223202i
\(195\) 0 0
\(196\) 52.0000 90.0666i 0.265306 0.459524i
\(197\) 253.000 1.28426 0.642132 0.766594i \(-0.278050\pi\)
0.642132 + 0.766594i \(0.278050\pi\)
\(198\) 0 0
\(199\) 129.904i 0.652783i −0.945235 0.326391i \(-0.894167\pi\)
0.945235 0.326391i \(-0.105833\pi\)
\(200\) −96.0000 166.277i −0.480000 0.831384i
\(201\) 0 0
\(202\) 155.000 + 268.468i 0.767327 + 1.32905i
\(203\) 75.0000 + 43.3013i 0.369458 + 0.213307i
\(204\) 0 0
\(205\) 175.000 + 303.109i 0.853659 + 1.47858i
\(206\) −240.000 138.564i −1.16505 0.672641i
\(207\) 0 0
\(208\) −160.000 + 277.128i −0.769231 + 1.33235i
\(209\) 45.0000 + 77.9423i 0.215311 + 0.372930i
\(210\) 0 0
\(211\) −129.000 74.4782i −0.611374 0.352977i 0.162129 0.986770i \(-0.448164\pi\)
−0.773503 + 0.633792i \(0.781497\pi\)
\(212\) −188.000 −0.886792
\(213\) 0 0
\(214\) 259.808i 1.21405i
\(215\) 121.244i 0.563924i
\(216\) 0 0
\(217\) −465.000 −2.14286
\(218\) 268.000 1.22936
\(219\) 0 0
\(220\) 242.487i 1.10221i
\(221\) 80.0000 138.564i 0.361991 0.626987i
\(222\) 0 0
\(223\) −30.0000 + 17.3205i −0.134529 + 0.0776704i −0.565754 0.824574i \(-0.691415\pi\)
0.431225 + 0.902244i \(0.358082\pi\)
\(224\) −240.000 + 138.564i −1.07143 + 0.618590i
\(225\) 0 0
\(226\) 74.0000 128.172i 0.327434 0.567132i
\(227\) −78.0000 + 45.0333i −0.343612 + 0.198385i −0.661868 0.749620i \(-0.730236\pi\)
0.318256 + 0.948005i \(0.396903\pi\)
\(228\) 0 0
\(229\) −73.0000 + 126.440i −0.318777 + 0.552138i −0.980233 0.197846i \(-0.936606\pi\)
0.661456 + 0.749984i \(0.269939\pi\)
\(230\) −42.0000 + 24.2487i −0.182609 + 0.105429i
\(231\) 0 0
\(232\) −40.0000 69.2820i −0.172414 0.298629i
\(233\) 334.000 1.43348 0.716738 0.697342i \(-0.245634\pi\)
0.716738 + 0.697342i \(0.245634\pi\)
\(234\) 0 0
\(235\) 606.218i 2.57965i
\(236\) 120.000 + 69.2820i 0.508475 + 0.293568i
\(237\) 0 0
\(238\) 120.000 69.2820i 0.504202 0.291101i
\(239\) −15.0000 8.66025i −0.0627615 0.0362354i 0.468291 0.883574i \(-0.344870\pi\)
−0.531052 + 0.847339i \(0.678203\pi\)
\(240\) 0 0
\(241\) −67.0000 116.047i −0.278008 0.481524i 0.692881 0.721052i \(-0.256341\pi\)
−0.970890 + 0.239527i \(0.923008\pi\)
\(242\) −46.0000 + 79.6743i −0.190083 + 0.329233i
\(243\) 0 0
\(244\) 128.000 + 221.703i 0.524590 + 0.908617i
\(245\) 91.0000 + 157.617i 0.371429 + 0.643333i
\(246\) 0 0
\(247\) −180.000 103.923i −0.728745 0.420741i
\(248\) 372.000 + 214.774i 1.50000 + 0.866025i
\(249\) 0 0
\(250\) −14.0000 −0.0560000
\(251\) 207.846i 0.828072i −0.910260 0.414036i \(-0.864119\pi\)
0.910260 0.414036i \(-0.135881\pi\)
\(252\) 0 0
\(253\) 30.0000 0.118577
\(254\) 51.9615i 0.204573i
\(255\) 0 0
\(256\) 256.000 1.00000
\(257\) −134.000 + 232.095i −0.521401 + 0.903093i 0.478289 + 0.878202i \(0.341257\pi\)
−0.999690 + 0.0248904i \(0.992076\pi\)
\(258\) 0 0
\(259\) 75.0000 43.3013i 0.289575 0.167186i
\(260\) −280.000 484.974i −1.07692 1.86529i
\(261\) 0 0
\(262\) 285.000 + 164.545i 1.08779 + 0.628034i
\(263\) −375.000 + 216.506i −1.42586 + 0.823218i −0.996790 0.0800555i \(-0.974490\pi\)
−0.429065 + 0.903274i \(0.641157\pi\)
\(264\) 0 0
\(265\) 164.500 284.922i 0.620755 1.07518i
\(266\) −90.0000 155.885i −0.338346 0.586032i
\(267\) 0 0
\(268\) −300.000 173.205i −1.11940 0.646288i
\(269\) −350.000 −1.30112 −0.650558 0.759457i \(-0.725465\pi\)
−0.650558 + 0.759457i \(0.725465\pi\)
\(270\) 0 0
\(271\) 36.3731i 0.134218i −0.997746 0.0671090i \(-0.978622\pi\)
0.997746 0.0671090i \(-0.0213775\pi\)
\(272\) −128.000 −0.470588
\(273\) 0 0
\(274\) 62.0000 + 107.387i 0.226277 + 0.391924i
\(275\) −180.000 103.923i −0.654545 0.377902i
\(276\) 0 0
\(277\) 260.000 + 450.333i 0.938628 + 1.62575i 0.768033 + 0.640410i \(0.221236\pi\)
0.170595 + 0.985341i \(0.445431\pi\)
\(278\) 300.000 + 173.205i 1.07914 + 0.623040i
\(279\) 0 0
\(280\) 484.974i 1.73205i
\(281\) 220.000 + 381.051i 0.782918 + 1.35605i 0.930235 + 0.366965i \(0.119603\pi\)
−0.147317 + 0.989089i \(0.547064\pi\)
\(282\) 0 0
\(283\) 285.000 + 164.545i 1.00707 + 0.581430i 0.910332 0.413880i \(-0.135827\pi\)
0.0967355 + 0.995310i \(0.469160\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 346.410i 1.21122i
\(287\) 433.013i 1.50876i
\(288\) 0 0
\(289\) −225.000 −0.778547
\(290\) 140.000 0.482759
\(291\) 0 0
\(292\) −220.000 −0.753425
\(293\) 109.000 188.794i 0.372014 0.644347i −0.617862 0.786287i \(-0.712001\pi\)
0.989875 + 0.141940i \(0.0453341\pi\)
\(294\) 0 0
\(295\) −210.000 + 121.244i −0.711864 + 0.410995i
\(296\) −80.0000 −0.270270
\(297\) 0 0
\(298\) −115.000 + 199.186i −0.385906 + 0.668409i
\(299\) −60.0000 + 34.6410i −0.200669 + 0.115856i
\(300\) 0 0
\(301\) −75.0000 + 129.904i −0.249169 + 0.431574i
\(302\) 75.0000 43.3013i 0.248344 0.143382i
\(303\) 0 0
\(304\) 166.277i 0.546963i
\(305\) −448.000 −1.46885
\(306\) 0 0
\(307\) 207.846i 0.677023i −0.940962 0.338512i \(-0.890077\pi\)
0.940962 0.338512i \(-0.109923\pi\)
\(308\) −150.000 + 259.808i −0.487013 + 0.843531i
\(309\) 0 0
\(310\) −651.000 + 375.855i −2.10000 + 1.21244i
\(311\) 255.000 + 147.224i 0.819936 + 0.473390i 0.850394 0.526146i \(-0.176363\pi\)
−0.0304586 + 0.999536i \(0.509697\pi\)
\(312\) 0 0
\(313\) −242.500 420.022i −0.774760 1.34192i −0.934929 0.354835i \(-0.884537\pi\)
0.160169 0.987090i \(-0.448796\pi\)
\(314\) −20.0000 + 34.6410i −0.0636943 + 0.110322i
\(315\) 0 0
\(316\) 24.0000 13.8564i 0.0759494 0.0438494i
\(317\) −108.500 187.928i −0.342271 0.592831i 0.642583 0.766216i \(-0.277863\pi\)
−0.984854 + 0.173385i \(0.944530\pi\)
\(318\) 0 0
\(319\) −75.0000 43.3013i −0.235110 0.135741i
\(320\) −224.000 + 387.979i −0.700000 + 1.21244i
\(321\) 0 0
\(322\) −60.0000 −0.186335
\(323\) 83.1384i 0.257395i
\(324\) 0 0
\(325\) 480.000 1.47692
\(326\) 207.846i 0.637565i
\(327\) 0 0
\(328\) 200.000 346.410i 0.609756 1.05613i
\(329\) −375.000 + 649.519i −1.13982 + 1.97422i
\(330\) 0 0
\(331\) 375.000 216.506i 1.13293 0.654098i 0.188260 0.982119i \(-0.439715\pi\)
0.944670 + 0.328021i \(0.106382\pi\)
\(332\) 102.000 58.8897i 0.307229 0.177379i
\(333\) 0 0
\(334\) −426.000 245.951i −1.27545 0.736381i
\(335\) 525.000 303.109i 1.56716 0.904803i
\(336\) 0 0
\(337\) 155.000 268.468i 0.459941 0.796641i −0.539017 0.842295i \(-0.681204\pi\)
0.998957 + 0.0456545i \(0.0145373\pi\)
\(338\) −231.000 400.104i −0.683432 1.18374i
\(339\) 0 0
\(340\) 112.000 193.990i 0.329412 0.570558i
\(341\) 465.000 1.36364
\(342\) 0 0
\(343\) 199.186i 0.580717i
\(344\) 120.000 69.2820i 0.348837 0.201401i
\(345\) 0 0
\(346\) −127.000 219.970i −0.367052 0.635753i
\(347\) 187.500 + 108.253i 0.540346 + 0.311969i 0.745219 0.666820i \(-0.232345\pi\)
−0.204873 + 0.978789i \(0.565678\pi\)
\(348\) 0 0
\(349\) −37.0000 64.0859i −0.106017 0.183627i 0.808136 0.588996i \(-0.200477\pi\)
−0.914153 + 0.405369i \(0.867143\pi\)
\(350\) 360.000 + 207.846i 1.02857 + 0.593846i
\(351\) 0 0
\(352\) 240.000 138.564i 0.681818 0.393648i
\(353\) −197.000 341.214i −0.558074 0.966612i −0.997657 0.0684103i \(-0.978207\pi\)
0.439584 0.898202i \(-0.355126\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 40.0000 0.112360
\(357\) 0 0
\(358\) 467.654i 1.30630i
\(359\) 571.577i 1.59214i −0.605207 0.796068i \(-0.706910\pi\)
0.605207 0.796068i \(-0.293090\pi\)
\(360\) 0 0
\(361\) 253.000 0.700831
\(362\) 112.000 0.309392
\(363\) 0 0
\(364\) 692.820i 1.90335i
\(365\) 192.500 333.420i 0.527397 0.913479i
\(366\) 0 0
\(367\) 487.500 281.458i 1.32834 0.766916i 0.343295 0.939228i \(-0.388457\pi\)
0.985043 + 0.172311i \(0.0551235\pi\)
\(368\) 48.0000 + 27.7128i 0.130435 + 0.0753066i
\(369\) 0 0
\(370\) 70.0000 121.244i 0.189189 0.327685i
\(371\) 352.500 203.516i 0.950135 0.548561i
\(372\) 0 0
\(373\) 20.0000 34.6410i 0.0536193 0.0928714i −0.837970 0.545716i \(-0.816258\pi\)
0.891589 + 0.452845i \(0.149591\pi\)
\(374\) −120.000 + 69.2820i −0.320856 + 0.185246i
\(375\) 0 0
\(376\) 600.000 346.410i 1.59574 0.921304i
\(377\) 200.000 0.530504
\(378\) 0 0
\(379\) 685.892i 1.80974i −0.425686 0.904871i \(-0.639967\pi\)
0.425686 0.904871i \(-0.360033\pi\)
\(380\) −252.000 145.492i −0.663158 0.382874i
\(381\) 0 0
\(382\) 60.0000 34.6410i 0.157068 0.0906833i
\(383\) −312.000 180.133i −0.814621 0.470322i 0.0339368 0.999424i \(-0.489196\pi\)
−0.848558 + 0.529102i \(0.822529\pi\)
\(384\) 0 0
\(385\) −262.500 454.663i −0.681818 1.18094i
\(386\) −65.0000 + 112.583i −0.168394 + 0.291667i
\(387\) 0 0
\(388\) 50.0000 + 86.6025i 0.128866 + 0.223202i
\(389\) −237.500 411.362i −0.610540 1.05749i −0.991150 0.132750i \(-0.957619\pi\)
0.380610 0.924736i \(-0.375714\pi\)
\(390\) 0 0
\(391\) −24.0000 13.8564i −0.0613811 0.0354384i
\(392\) 104.000 180.133i 0.265306 0.459524i
\(393\) 0 0
\(394\) 506.000 1.28426
\(395\) 48.4974i 0.122778i
\(396\) 0 0
\(397\) 260.000 0.654912 0.327456 0.944866i \(-0.393809\pi\)
0.327456 + 0.944866i \(0.393809\pi\)
\(398\) 259.808i 0.652783i
\(399\) 0 0
\(400\) −192.000 332.554i −0.480000 0.831384i
\(401\) 370.000 640.859i 0.922693 1.59815i 0.127464 0.991843i \(-0.459316\pi\)
0.795230 0.606308i \(-0.207350\pi\)
\(402\) 0 0
\(403\) −930.000 + 536.936i −2.30769 + 1.33235i
\(404\) 310.000 + 536.936i 0.767327 + 1.32905i
\(405\) 0 0
\(406\) 150.000 + 86.6025i 0.369458 + 0.213307i
\(407\) −75.0000 + 43.3013i −0.184275 + 0.106391i
\(408\) 0 0
\(409\) −329.500 + 570.711i −0.805623 + 1.39538i 0.110246 + 0.993904i \(0.464836\pi\)
−0.915869 + 0.401476i \(0.868497\pi\)
\(410\) 350.000 + 606.218i 0.853659 + 1.47858i
\(411\) 0 0
\(412\) −480.000 277.128i −1.16505 0.672641i
\(413\) −300.000 −0.726392
\(414\) 0 0
\(415\) 206.114i 0.496660i
\(416\) −320.000 + 554.256i −0.769231 + 1.33235i
\(417\) 0 0
\(418\) 90.0000 + 155.885i 0.215311 + 0.372930i
\(419\) −510.000 294.449i −1.21718 0.702741i −0.252869 0.967500i \(-0.581374\pi\)
−0.964315 + 0.264759i \(0.914708\pi\)
\(420\) 0 0
\(421\) 248.000 + 429.549i 0.589074 + 1.02031i 0.994354 + 0.106113i \(0.0338405\pi\)
−0.405280 + 0.914192i \(0.632826\pi\)
\(422\) −258.000 148.956i −0.611374 0.352977i
\(423\) 0 0
\(424\) −376.000 −0.886792
\(425\) 96.0000 + 166.277i 0.225882 + 0.391240i
\(426\) 0 0
\(427\) −480.000 277.128i −1.12412 0.649012i
\(428\) 519.615i 1.21405i
\(429\) 0 0
\(430\) 242.487i 0.563924i
\(431\) 571.577i 1.32616i −0.748547 0.663082i \(-0.769248\pi\)
0.748547 0.663082i \(-0.230752\pi\)
\(432\) 0 0
\(433\) −235.000 −0.542725 −0.271363 0.962477i \(-0.587474\pi\)
−0.271363 + 0.962477i \(0.587474\pi\)
\(434\) −930.000 −2.14286
\(435\) 0 0
\(436\) 536.000 1.22936
\(437\) −18.0000 + 31.1769i −0.0411899 + 0.0713431i
\(438\) 0 0
\(439\) −358.500 + 206.980i −0.816629 + 0.471481i −0.849253 0.527987i \(-0.822947\pi\)
0.0326238 + 0.999468i \(0.489614\pi\)
\(440\) 484.974i 1.10221i
\(441\) 0 0
\(442\) 160.000 277.128i 0.361991 0.626987i
\(443\) 498.000 287.520i 1.12415 0.649030i 0.181695 0.983355i \(-0.441841\pi\)
0.942458 + 0.334325i \(0.108508\pi\)
\(444\) 0 0
\(445\) −35.0000 + 60.6218i −0.0786517 + 0.136229i
\(446\) −60.0000 + 34.6410i −0.134529 + 0.0776704i
\(447\) 0 0
\(448\) −480.000 + 277.128i −1.07143 + 0.618590i
\(449\) −470.000 −1.04677 −0.523385 0.852096i \(-0.675331\pi\)
−0.523385 + 0.852096i \(0.675331\pi\)
\(450\) 0 0
\(451\) 433.013i 0.960117i
\(452\) 148.000 256.344i 0.327434 0.567132i
\(453\) 0 0
\(454\) −156.000 + 90.0666i −0.343612 + 0.198385i
\(455\) 1050.00 + 606.218i 2.30769 + 1.33235i
\(456\) 0 0
\(457\) 162.500 + 281.458i 0.355580 + 0.615882i 0.987217 0.159382i \(-0.0509501\pi\)
−0.631637 + 0.775264i \(0.717617\pi\)
\(458\) −146.000 + 252.879i −0.318777 + 0.552138i
\(459\) 0 0
\(460\) −84.0000 + 48.4974i −0.182609 + 0.105429i
\(461\) −327.500 567.247i −0.710412 1.23047i −0.964703 0.263342i \(-0.915175\pi\)
0.254290 0.967128i \(-0.418158\pi\)
\(462\) 0 0
\(463\) −142.500 82.2724i −0.307775 0.177694i 0.338155 0.941090i \(-0.390197\pi\)
−0.645931 + 0.763396i \(0.723530\pi\)
\(464\) −80.0000 138.564i −0.172414 0.298629i
\(465\) 0 0
\(466\) 668.000 1.43348
\(467\) 57.1577i 0.122393i 0.998126 + 0.0611967i \(0.0194917\pi\)
−0.998126 + 0.0611967i \(0.980508\pi\)
\(468\) 0 0
\(469\) 750.000 1.59915
\(470\) 1212.44i 2.57965i
\(471\) 0 0
\(472\) 240.000 + 138.564i 0.508475 + 0.293568i
\(473\) 75.0000 129.904i 0.158562 0.274638i
\(474\) 0 0
\(475\) 216.000 124.708i 0.454737 0.262542i
\(476\) 240.000 138.564i 0.504202 0.291101i
\(477\) 0 0
\(478\) −30.0000 17.3205i −0.0627615 0.0362354i
\(479\) −285.000 + 164.545i −0.594990 + 0.343517i −0.767068 0.641566i \(-0.778285\pi\)
0.172078 + 0.985083i \(0.444952\pi\)
\(480\) 0 0
\(481\) 100.000 173.205i 0.207900 0.360094i
\(482\) −134.000 232.095i −0.278008 0.481524i
\(483\) 0 0
\(484\) −92.0000 + 159.349i −0.190083 + 0.329233i
\(485\) −175.000 −0.360825
\(486\) 0 0
\(487\) 519.615i 1.06697i 0.845809 + 0.533486i \(0.179118\pi\)
−0.845809 + 0.533486i \(0.820882\pi\)
\(488\) 256.000 + 443.405i 0.524590 + 0.908617i
\(489\) 0 0
\(490\) 182.000 + 315.233i 0.371429 + 0.643333i
\(491\) 187.500 + 108.253i 0.381874 + 0.220475i 0.678633 0.734477i \(-0.262573\pi\)
−0.296759 + 0.954952i \(0.595906\pi\)
\(492\) 0 0
\(493\) 40.0000 + 69.2820i 0.0811359 + 0.140532i
\(494\) −360.000 207.846i −0.728745 0.420741i
\(495\) 0 0
\(496\) 744.000 + 429.549i 1.50000 + 0.866025i
\(497\) 0 0
\(498\) 0 0
\(499\) −39.0000 22.5167i −0.0781563 0.0451236i 0.460413 0.887705i \(-0.347701\pi\)
−0.538569 + 0.842581i \(0.681035\pi\)
\(500\) −28.0000 −0.0560000
\(501\) 0 0
\(502\) 415.692i 0.828072i
\(503\) 384.515i 0.764444i −0.924071 0.382222i \(-0.875159\pi\)
0.924071 0.382222i \(-0.124841\pi\)
\(504\) 0 0
\(505\) −1085.00 −2.14851
\(506\) 60.0000 0.118577
\(507\) 0 0
\(508\) 103.923i 0.204573i
\(509\) −132.500 + 229.497i −0.260314 + 0.450878i −0.966325 0.257323i \(-0.917160\pi\)
0.706011 + 0.708201i \(0.250493\pi\)
\(510\) 0 0
\(511\) 412.500 238.157i 0.807241 0.466061i
\(512\) 512.000 1.00000
\(513\) 0 0
\(514\) −268.000 + 464.190i −0.521401 + 0.903093i
\(515\) 840.000 484.974i 1.63107 0.941698i
\(516\) 0 0
\(517\) 375.000 649.519i 0.725338 1.25632i
\(518\) 150.000 86.6025i 0.289575 0.167186i
\(519\) 0 0
\(520\) −560.000 969.948i −1.07692 1.86529i
\(521\) −380.000 −0.729367 −0.364683 0.931132i \(-0.618823\pi\)
−0.364683 + 0.931132i \(0.618823\pi\)
\(522\) 0 0
\(523\) 623.538i 1.19223i 0.802898 + 0.596117i \(0.203291\pi\)
−0.802898 + 0.596117i \(0.796709\pi\)
\(524\) 570.000 + 329.090i 1.08779 + 0.628034i
\(525\) 0 0
\(526\) −750.000 + 433.013i −1.42586 + 0.823218i
\(527\) −372.000 214.774i −0.705882 0.407541i
\(528\) 0 0
\(529\) −258.500 447.735i −0.488658 0.846380i
\(530\) 329.000 569.845i 0.620755 1.07518i
\(531\) 0 0
\(532\) −180.000 311.769i −0.338346 0.586032i
\(533\) 500.000 + 866.025i 0.938086 + 1.62481i
\(534\) 0 0
\(535\) 787.500 + 454.663i 1.47196 + 0.849838i
\(536\) −600.000 346.410i −1.11940 0.646288i
\(537\) 0 0
\(538\) −700.000 −1.30112
\(539\) 225.167i 0.417749i
\(540\) 0 0
\(541\) −532.000 −0.983364 −0.491682 0.870775i \(-0.663618\pi\)
−0.491682 + 0.870775i \(0.663618\pi\)
\(542\) 72.7461i 0.134218i
\(543\) 0 0
\(544\) −256.000 −0.470588
\(545\) −469.000 + 812.332i −0.860550 + 1.49052i
\(546\) 0 0
\(547\) 780.000 450.333i 1.42596 0.823278i 0.429161 0.903228i \(-0.358809\pi\)
0.996799 + 0.0799498i \(0.0254760\pi\)
\(548\) 124.000 + 214.774i 0.226277 + 0.391924i
\(549\) 0 0
\(550\) −360.000 207.846i −0.654545 0.377902i
\(551\) 90.0000 51.9615i 0.163339 0.0943040i
\(552\) 0 0
\(553\) −30.0000 + 51.9615i −0.0542495 + 0.0939630i
\(554\) 520.000 + 900.666i 0.938628 + 1.62575i
\(555\) 0 0
\(556\) 600.000 + 346.410i 1.07914 + 0.623040i
\(557\) −89.0000 −0.159785 −0.0798923 0.996804i \(-0.525458\pi\)
−0.0798923 + 0.996804i \(0.525458\pi\)
\(558\) 0 0
\(559\) 346.410i 0.619696i
\(560\) 969.948i 1.73205i
\(561\) 0 0
\(562\) 440.000 + 762.102i 0.782918 + 1.35605i
\(563\) −262.500 151.554i −0.466252 0.269191i 0.248417 0.968653i \(-0.420090\pi\)
−0.714670 + 0.699462i \(0.753423\pi\)
\(564\) 0 0
\(565\) 259.000 + 448.601i 0.458407 + 0.793984i
\(566\) 570.000 + 329.090i 1.00707 + 0.581430i
\(567\) 0 0
\(568\) 0 0
\(569\) −50.0000 86.6025i −0.0878735 0.152201i 0.818739 0.574166i \(-0.194674\pi\)
−0.906612 + 0.421965i \(0.861340\pi\)
\(570\) 0 0
\(571\) 294.000 + 169.741i 0.514886 + 0.297270i 0.734840 0.678241i \(-0.237257\pi\)
−0.219954 + 0.975510i \(0.570591\pi\)
\(572\) 692.820i 1.21122i
\(573\) 0 0
\(574\) 866.025i 1.50876i
\(575\) 83.1384i 0.144589i
\(576\) 0 0
\(577\) −730.000 −1.26516 −0.632582 0.774493i \(-0.718005\pi\)
−0.632582 + 0.774493i \(0.718005\pi\)
\(578\) −450.000 −0.778547
\(579\) 0 0
\(580\) 280.000 0.482759
\(581\) −127.500 + 220.836i −0.219449 + 0.380097i
\(582\) 0 0
\(583\) −352.500 + 203.516i −0.604631 + 0.349084i
\(584\) −440.000 −0.753425
\(585\) 0 0
\(586\) 218.000 377.587i 0.372014 0.644347i
\(587\) −694.500 + 400.970i −1.18313 + 0.683083i −0.956738 0.290952i \(-0.906028\pi\)
−0.226397 + 0.974035i \(0.572695\pi\)
\(588\) 0 0
\(589\) −279.000 + 483.242i −0.473684 + 0.820445i
\(590\) −420.000 + 242.487i −0.711864 + 0.410995i
\(591\) 0 0
\(592\) −160.000 −0.270270
\(593\) 982.000 1.65599 0.827993 0.560738i \(-0.189483\pi\)
0.827993 + 0.560738i \(0.189483\pi\)
\(594\) 0 0
\(595\) 484.974i 0.815083i
\(596\) −230.000 + 398.372i −0.385906 + 0.668409i
\(597\) 0 0
\(598\) −120.000 + 69.2820i −0.200669 + 0.115856i
\(599\) −195.000 112.583i −0.325543 0.187952i 0.328318 0.944567i \(-0.393518\pi\)
−0.653860 + 0.756615i \(0.726852\pi\)
\(600\) 0 0
\(601\) −125.500 217.372i −0.208819 0.361684i 0.742524 0.669819i \(-0.233629\pi\)
−0.951343 + 0.308135i \(0.900295\pi\)
\(602\) −150.000 + 259.808i −0.249169 + 0.431574i
\(603\) 0 0
\(604\) 150.000 86.6025i 0.248344 0.143382i
\(605\) −161.000 278.860i −0.266116 0.460926i
\(606\) 0 0
\(607\) 330.000 + 190.526i 0.543657 + 0.313881i 0.746560 0.665318i \(-0.231704\pi\)
−0.202903 + 0.979199i \(0.565037\pi\)
\(608\) 332.554i 0.546963i
\(609\) 0 0
\(610\) −896.000 −1.46885
\(611\) 1732.05i 2.83478i
\(612\) 0 0
\(613\) 650.000 1.06036 0.530179 0.847885i \(-0.322125\pi\)
0.530179 + 0.847885i \(0.322125\pi\)
\(614\) 415.692i 0.677023i
\(615\) 0 0
\(616\) −300.000 + 519.615i −0.487013 + 0.843531i
\(617\) 379.000 656.447i 0.614263 1.06393i −0.376251 0.926518i \(-0.622787\pi\)
0.990513 0.137416i \(-0.0438798\pi\)
\(618\) 0 0
\(619\) 150.000 86.6025i 0.242326 0.139907i −0.373919 0.927461i \(-0.621986\pi\)
0.616245 + 0.787554i \(0.288653\pi\)
\(620\) −1302.00 + 751.710i −2.10000 + 1.21244i
\(621\) 0 0
\(622\) 510.000 + 294.449i 0.819936 + 0.473390i
\(623\) −75.0000 + 43.3013i −0.120385 + 0.0695044i
\(624\) 0 0
\(625\) 324.500 562.050i 0.519200 0.899281i
\(626\) −485.000 840.045i −0.774760 1.34192i
\(627\) 0 0
\(628\) −40.0000 + 69.2820i −0.0636943 + 0.110322i
\(629\) 80.0000 0.127186
\(630\) 0 0
\(631\) 119.512i 0.189400i −0.995506 0.0947001i \(-0.969811\pi\)
0.995506 0.0947001i \(-0.0301892\pi\)
\(632\) 48.0000 27.7128i 0.0759494 0.0438494i
\(633\) 0 0
\(634\) −217.000 375.855i −0.342271 0.592831i
\(635\) 157.500 + 90.9327i 0.248031 + 0.143201i
\(636\) 0 0
\(637\) 260.000 + 450.333i 0.408163 + 0.706960i
\(638\) −150.000 86.6025i −0.235110 0.135741i
\(639\) 0 0
\(640\) −448.000 + 775.959i −0.700000 + 1.21244i
\(641\) −455.000 788.083i −0.709828 1.22946i −0.964921 0.262542i \(-0.915439\pi\)
0.255092 0.966917i \(-0.417894\pi\)
\(642\) 0 0
\(643\) −30.0000 17.3205i −0.0466563 0.0269370i 0.476490 0.879180i \(-0.341909\pi\)
−0.523147 + 0.852243i \(0.675242\pi\)
\(644\) −120.000 −0.186335
\(645\) 0 0
\(646\) 166.277i 0.257395i
\(647\) 914.523i 1.41348i −0.707472 0.706741i \(-0.750165\pi\)
0.707472 0.706741i \(-0.249835\pi\)
\(648\) 0 0
\(649\) 300.000 0.462250
\(650\) 960.000 1.47692
\(651\) 0 0
\(652\) 415.692i 0.637565i
\(653\) −51.5000 + 89.2006i −0.0788668 + 0.136601i −0.902761 0.430142i \(-0.858464\pi\)
0.823894 + 0.566743i \(0.191797\pi\)
\(654\) 0 0
\(655\) −997.500 + 575.907i −1.52290 + 0.879247i
\(656\) 400.000 692.820i 0.609756 1.05613i
\(657\) 0 0
\(658\) −750.000 + 1299.04i −1.13982 + 1.97422i
\(659\) 52.5000 30.3109i 0.0796662 0.0459953i −0.459638 0.888106i \(-0.652021\pi\)
0.539304 + 0.842111i \(0.318687\pi\)
\(660\) 0 0
\(661\) −289.000 + 500.563i −0.437216 + 0.757281i −0.997474 0.0710377i \(-0.977369\pi\)
0.560257 + 0.828319i \(0.310702\pi\)
\(662\) 750.000 433.013i 1.13293 0.654098i
\(663\) 0 0
\(664\) 204.000 117.779i 0.307229 0.177379i
\(665\) 630.000 0.947368
\(666\) 0 0
\(667\) 34.6410i 0.0519356i
\(668\) −852.000 491.902i −1.27545 0.736381i
\(669\) 0 0
\(670\) 1050.00 606.218i 1.56716 0.904803i
\(671\) 480.000 + 277.128i 0.715350 + 0.413008i
\(672\) 0 0
\(673\) −422.500 731.791i −0.627786 1.08736i −0.987995 0.154486i \(-0.950628\pi\)
0.360209 0.932872i \(-0.382705\pi\)
\(674\) 310.000 536.936i 0.459941 0.796641i
\(675\) 0 0
\(676\) −462.000 800.207i −0.683432 1.18374i
\(677\) 577.000 + 999.393i 0.852290 + 1.47621i 0.879137 + 0.476569i \(0.158120\pi\)
−0.0268475 + 0.999640i \(0.508547\pi\)
\(678\) 0 0
\(679\) −187.500 108.253i −0.276141 0.159430i
\(680\) 224.000 387.979i 0.329412 0.570558i
\(681\) 0 0
\(682\) 930.000 1.36364
\(683\) 187.061i 0.273882i −0.990579 0.136941i \(-0.956273\pi\)
0.990579 0.136941i \(-0.0437271\pi\)
\(684\) 0 0
\(685\) −434.000 −0.633577
\(686\) 398.372i 0.580717i
\(687\) 0 0
\(688\) 240.000 138.564i 0.348837 0.201401i
\(689\) 470.000 814.064i 0.682148 1.18152i
\(690\) 0 0
\(691\) −426.000 + 245.951i −0.616498 + 0.355935i −0.775504 0.631342i \(-0.782504\pi\)
0.159006 + 0.987278i \(0.449171\pi\)
\(692\) −254.000 439.941i −0.367052 0.635753i
\(693\) 0 0
\(694\) 375.000 + 216.506i 0.540346 + 0.311969i
\(695\) −1050.00 + 606.218i −1.51079 + 0.872256i
\(696\) 0 0
\(697\) −200.000 + 346.410i −0.286944 + 0.497002i
\(698\) −74.0000 128.172i −0.106017 0.183627i
\(699\) 0 0
\(700\) 720.000 + 415.692i 1.02857 + 0.593846i
\(701\) −215.000 −0.306705 −0.153352 0.988172i \(-0.549007\pi\)
−0.153352 + 0.988172i \(0.549007\pi\)
\(702\) 0 0
\(703\) 103.923i 0.147828i
\(704\) 480.000 277.128i 0.681818 0.393648i
\(705\) 0 0
\(706\) −394.000 682.428i −0.558074 0.966612i
\(707\) −1162.50 671.170i −1.64427 0.949321i
\(708\) 0 0
\(709\) 266.000 + 460.726i 0.375176 + 0.649824i 0.990353 0.138565i \(-0.0442488\pi\)
−0.615177 + 0.788389i \(0.710916\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 80.0000 0.112360
\(713\) 93.0000 + 161.081i 0.130435 + 0.225920i
\(714\) 0 0
\(715\) −1050.00 606.218i −1.46853 0.847857i
\(716\) 935.307i 1.30630i
\(717\) 0 0
\(718\) 1143.15i 1.59214i
\(719\) 1143.15i 1.58992i 0.606661 + 0.794961i \(0.292509\pi\)
−0.606661 + 0.794961i \(0.707491\pi\)
\(720\) 0 0
\(721\) 1200.00 1.66436
\(722\) 506.000 0.700831
\(723\) 0 0
\(724\) 224.000 0.309392
\(725\) −120.000 + 207.846i −0.165517 + 0.286684i
\(726\) 0 0
\(727\) 1072.50 619.208i 1.47524 0.851731i 0.475630 0.879645i \(-0.342220\pi\)
0.999610 + 0.0279146i \(0.00888665\pi\)
\(728\) 1385.64i 1.90335i
\(729\) 0 0
\(730\) 385.000 666.840i 0.527397 0.913479i
\(731\) −120.000 + 69.2820i −0.164159 + 0.0947771i
\(732\) 0 0
\(733\) −475.000 + 822.724i −0.648022 + 1.12241i 0.335573 + 0.942014i \(0.391070\pi\)
−0.983595 + 0.180392i \(0.942263\pi\)
\(734\) 975.000 562.917i 1.32834 0.766916i
\(735\) 0 0
\(736\) 96.0000 + 55.4256i 0.130435 + 0.0753066i
\(737\) −750.000 −1.01764
\(738\) 0 0
\(739\) 581.969i 0.787509i −0.919216 0.393754i \(-0.871176\pi\)
0.919216 0.393754i \(-0.128824\pi\)
\(740\) 140.000 242.487i 0.189189 0.327685i
\(741\) 0 0
\(742\) 705.000 407.032i 0.950135 0.548561i
\(743\) 750.000 + 433.013i 1.00942 + 0.582790i 0.911022 0.412357i \(-0.135294\pi\)
0.0983991 + 0.995147i \(0.468628\pi\)
\(744\) 0 0
\(745\) −402.500 697.150i −0.540268 0.935772i
\(746\) 40.0000 69.2820i 0.0536193 0.0928714i
\(747\) 0 0
\(748\) −240.000 + 138.564i −0.320856 + 0.185246i
\(749\) 562.500 + 974.279i 0.751001 + 1.30077i
\(750\) 0 0
\(751\) −151.500 87.4686i −0.201731 0.116469i 0.395732 0.918366i \(-0.370491\pi\)
−0.597463 + 0.801897i \(0.703824\pi\)
\(752\) 1200.00 692.820i 1.59574 0.921304i
\(753\) 0 0
\(754\) 400.000 0.530504
\(755\) 303.109i 0.401469i
\(756\) 0 0
\(757\) 830.000 1.09643 0.548217 0.836336i \(-0.315307\pi\)
0.548217 + 0.836336i \(0.315307\pi\)
\(758\) 1371.78i 1.80974i
\(759\) 0 0
\(760\) −504.000 290.985i −0.663158 0.382874i
\(761\) 280.000 484.974i 0.367937 0.637285i −0.621306 0.783568i \(-0.713398\pi\)
0.989243 + 0.146283i \(0.0467309\pi\)
\(762\) 0 0
\(763\) −1005.00 + 580.237i −1.31717 + 0.760468i
\(764\) 120.000 69.2820i 0.157068 0.0906833i
\(765\) 0 0
\(766\) −624.000 360.267i −0.814621 0.470322i
\(767\) −600.000 + 346.410i −0.782269 + 0.451643i
\(768\) 0 0
\(769\) 165.500 286.654i 0.215215 0.372763i −0.738124 0.674665i \(-0.764288\pi\)
0.953339 + 0.301902i \(0.0976216\pi\)
\(770\) −525.000 909.327i −0.681818 1.18094i
\(771\) 0 0
\(772\) −130.000 + 225.167i −0.168394 + 0.291667i
\(773\) 298.000 0.385511 0.192755 0.981247i \(-0.438258\pi\)
0.192755 + 0.981247i \(0.438258\pi\)
\(774\) 0 0
\(775\) 1288.65i 1.66277i
\(776\) 100.000 + 173.205i 0.128866 + 0.223202i
\(777\) 0 0
\(778\) −475.000 822.724i −0.610540 1.05749i
\(779\) 450.000 + 259.808i 0.577664 + 0.333514i
\(780\) 0 0
\(781\) 0 0
\(782\) −48.0000 27.7128i −0.0613811 0.0354384i
\(783\) 0 0
\(784\) 208.000 360.267i 0.265306 0.459524i
\(785\) −70.0000