Properties

Label 224.3.o.d.79.5
Level 224
Weight 3
Character 224.79
Analytic conductor 6.104
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.5
Root \(0.907369 + 0.0534805i\) of \(x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} - 116 x^{3} + 60 x^{2} - 20 x + 4\)
Character \(\chi\) \(=\) 224.79
Dual form 224.3.o.d.207.5

$q$-expansion

\(f(q)\) \(=\) \(q+(2.66613 + 4.61787i) q^{3} +(-1.86796 - 1.07847i) q^{5} +(-6.91861 - 1.06433i) q^{7} +(-9.71647 + 16.8294i) q^{9} +O(q^{10})\) \(q+(2.66613 + 4.61787i) q^{3} +(-1.86796 - 1.07847i) q^{5} +(-6.91861 - 1.06433i) q^{7} +(-9.71647 + 16.8294i) q^{9} +(2.62956 + 4.55453i) q^{11} +21.4116i q^{13} -11.5013i q^{15} +(-0.463429 - 0.802683i) q^{17} +(-2.96505 + 5.13561i) q^{19} +(-13.5310 - 34.7869i) q^{21} +(7.52507 + 4.34460i) q^{23} +(-10.1738 - 17.6216i) q^{25} -55.6311 q^{27} -9.42223i q^{29} +(29.8813 - 17.2520i) q^{31} +(-14.0215 + 24.2859i) q^{33} +(11.7758 + 9.44961i) q^{35} +(11.0853 + 6.40011i) q^{37} +(-98.8758 + 57.0860i) q^{39} +43.1339 q^{41} +41.7382 q^{43} +(36.2999 - 20.9578i) q^{45} +(39.8357 + 22.9991i) q^{47} +(46.7344 + 14.7273i) q^{49} +(2.47112 - 4.28011i) q^{51} +(-64.5031 + 37.2409i) q^{53} -11.3436i q^{55} -31.6208 q^{57} +(26.8367 + 46.4825i) q^{59} +(24.0893 + 13.9080i) q^{61} +(85.1365 - 106.095i) q^{63} +(23.0916 - 39.9959i) q^{65} +(-39.2453 - 67.9749i) q^{67} +46.3330i q^{69} +74.5100i q^{71} +(-16.8020 - 29.1020i) q^{73} +(54.2494 - 93.9627i) q^{75} +(-13.3454 - 34.3097i) q^{77} +(-26.1642 - 15.1059i) q^{79} +(-60.8713 - 105.432i) q^{81} +72.9274 q^{83} +1.99917i q^{85} +(43.5106 - 25.1209i) q^{87} +(27.4198 - 47.4925i) q^{89} +(22.7889 - 148.138i) q^{91} +(159.335 + 91.9919i) q^{93} +(11.0772 - 6.39541i) q^{95} -53.7125 q^{97} -102.200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 6q^{3} - 40q^{9} + O(q^{10}) \) \( 12q + 6q^{3} - 40q^{9} - 30q^{11} + 30q^{17} - 78q^{19} - 92q^{25} - 156q^{27} - 78q^{33} + 222q^{35} - 232q^{41} + 200q^{43} + 372q^{49} - 10q^{51} + 332q^{57} + 110q^{59} - 32q^{65} - 434q^{67} + 102q^{73} + 60q^{75} - 82q^{81} + 536q^{83} + 214q^{89} + 8q^{91} - 152q^{97} - 504q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.66613 + 4.61787i 0.888709 + 1.53929i 0.841403 + 0.540409i \(0.181730\pi\)
0.0473064 + 0.998880i \(0.484936\pi\)
\(4\) 0 0
\(5\) −1.86796 1.07847i −0.373592 0.215693i 0.301435 0.953487i \(-0.402534\pi\)
−0.675026 + 0.737794i \(0.735868\pi\)
\(6\) 0 0
\(7\) −6.91861 1.06433i −0.988373 0.152047i
\(8\) 0 0
\(9\) −9.71647 + 16.8294i −1.07961 + 1.86993i
\(10\) 0 0
\(11\) 2.62956 + 4.55453i 0.239051 + 0.414048i 0.960442 0.278480i \(-0.0898305\pi\)
−0.721392 + 0.692527i \(0.756497\pi\)
\(12\) 0 0
\(13\) 21.4116i 1.64704i 0.567285 + 0.823522i \(0.307994\pi\)
−0.567285 + 0.823522i \(0.692006\pi\)
\(14\) 0 0
\(15\) 11.5013i 0.766754i
\(16\) 0 0
\(17\) −0.463429 0.802683i −0.0272606 0.0472167i 0.852073 0.523423i \(-0.175345\pi\)
−0.879334 + 0.476206i \(0.842012\pi\)
\(18\) 0 0
\(19\) −2.96505 + 5.13561i −0.156055 + 0.270295i −0.933443 0.358726i \(-0.883211\pi\)
0.777388 + 0.629022i \(0.216544\pi\)
\(20\) 0 0
\(21\) −13.5310 34.7869i −0.644332 1.65652i
\(22\) 0 0
\(23\) 7.52507 + 4.34460i 0.327177 + 0.188896i 0.654587 0.755987i \(-0.272843\pi\)
−0.327410 + 0.944882i \(0.606176\pi\)
\(24\) 0 0
\(25\) −10.1738 17.6216i −0.406953 0.704863i
\(26\) 0 0
\(27\) −55.6311 −2.06041
\(28\) 0 0
\(29\) 9.42223i 0.324904i −0.986716 0.162452i \(-0.948060\pi\)
0.986716 0.162452i \(-0.0519403\pi\)
\(30\) 0 0
\(31\) 29.8813 17.2520i 0.963912 0.556515i 0.0665375 0.997784i \(-0.478805\pi\)
0.897375 + 0.441269i \(0.145471\pi\)
\(32\) 0 0
\(33\) −14.0215 + 24.2859i −0.424893 + 0.735936i
\(34\) 0 0
\(35\) 11.7758 + 9.44961i 0.336453 + 0.269989i
\(36\) 0 0
\(37\) 11.0853 + 6.40011i 0.299603 + 0.172976i 0.642265 0.766483i \(-0.277995\pi\)
−0.342662 + 0.939459i \(0.611328\pi\)
\(38\) 0 0
\(39\) −98.8758 + 57.0860i −2.53528 + 1.46374i
\(40\) 0 0
\(41\) 43.1339 1.05205 0.526023 0.850470i \(-0.323683\pi\)
0.526023 + 0.850470i \(0.323683\pi\)
\(42\) 0 0
\(43\) 41.7382 0.970656 0.485328 0.874332i \(-0.338700\pi\)
0.485328 + 0.874332i \(0.338700\pi\)
\(44\) 0 0
\(45\) 36.2999 20.9578i 0.806665 0.465728i
\(46\) 0 0
\(47\) 39.8357 + 22.9991i 0.847567 + 0.489343i 0.859829 0.510582i \(-0.170570\pi\)
−0.0122620 + 0.999925i \(0.503903\pi\)
\(48\) 0 0
\(49\) 46.7344 + 14.7273i 0.953764 + 0.300558i
\(50\) 0 0
\(51\) 2.47112 4.28011i 0.0484534 0.0839238i
\(52\) 0 0
\(53\) −64.5031 + 37.2409i −1.21704 + 0.702658i −0.964284 0.264872i \(-0.914670\pi\)
−0.252756 + 0.967530i \(0.581337\pi\)
\(54\) 0 0
\(55\) 11.3436i 0.206246i
\(56\) 0 0
\(57\) −31.6208 −0.554751
\(58\) 0 0
\(59\) 26.8367 + 46.4825i 0.454860 + 0.787840i 0.998680 0.0513617i \(-0.0163561\pi\)
−0.543821 + 0.839201i \(0.683023\pi\)
\(60\) 0 0
\(61\) 24.0893 + 13.9080i 0.394907 + 0.228000i 0.684284 0.729215i \(-0.260115\pi\)
−0.289377 + 0.957215i \(0.593448\pi\)
\(62\) 0 0
\(63\) 85.1365 106.095i 1.35137 1.68404i
\(64\) 0 0
\(65\) 23.0916 39.9959i 0.355256 0.615322i
\(66\) 0 0
\(67\) −39.2453 67.9749i −0.585751 1.01455i −0.994781 0.102030i \(-0.967466\pi\)
0.409030 0.912521i \(-0.365867\pi\)
\(68\) 0 0
\(69\) 46.3330i 0.671493i
\(70\) 0 0
\(71\) 74.5100i 1.04944i 0.851276 + 0.524719i \(0.175829\pi\)
−0.851276 + 0.524719i \(0.824171\pi\)
\(72\) 0 0
\(73\) −16.8020 29.1020i −0.230165 0.398657i 0.727692 0.685904i \(-0.240593\pi\)
−0.957857 + 0.287247i \(0.907260\pi\)
\(74\) 0 0
\(75\) 54.2494 93.9627i 0.723325 1.25284i
\(76\) 0 0
\(77\) −13.3454 34.3097i −0.173317 0.445581i
\(78\) 0 0
\(79\) −26.1642 15.1059i −0.331192 0.191214i 0.325178 0.945653i \(-0.394576\pi\)
−0.656370 + 0.754439i \(0.727909\pi\)
\(80\) 0 0
\(81\) −60.8713 105.432i −0.751497 1.30163i
\(82\) 0 0
\(83\) 72.9274 0.878644 0.439322 0.898330i \(-0.355219\pi\)
0.439322 + 0.898330i \(0.355219\pi\)
\(84\) 0 0
\(85\) 1.99917i 0.0235197i
\(86\) 0 0
\(87\) 43.5106 25.1209i 0.500122 0.288745i
\(88\) 0 0
\(89\) 27.4198 47.4925i 0.308088 0.533624i −0.669856 0.742491i \(-0.733644\pi\)
0.977944 + 0.208867i \(0.0669776\pi\)
\(90\) 0 0
\(91\) 22.7889 148.138i 0.250428 1.62789i
\(92\) 0 0
\(93\) 159.335 + 91.9919i 1.71328 + 0.989160i
\(94\) 0 0
\(95\) 11.0772 6.39541i 0.116602 0.0673201i
\(96\) 0 0
\(97\) −53.7125 −0.553738 −0.276869 0.960908i \(-0.589297\pi\)
−0.276869 + 0.960908i \(0.589297\pi\)
\(98\) 0 0
\(99\) −102.200 −1.03232
\(100\) 0 0
\(101\) 78.2037 45.1509i 0.774294 0.447039i −0.0601103 0.998192i \(-0.519145\pi\)
0.834404 + 0.551153i \(0.185812\pi\)
\(102\) 0 0
\(103\) −97.6980 56.4060i −0.948525 0.547631i −0.0559023 0.998436i \(-0.517804\pi\)
−0.892622 + 0.450805i \(0.851137\pi\)
\(104\) 0 0
\(105\) −12.2412 + 79.5731i −0.116583 + 0.757839i
\(106\) 0 0
\(107\) −71.9950 + 124.699i −0.672851 + 1.16541i 0.304241 + 0.952595i \(0.401597\pi\)
−0.977092 + 0.212817i \(0.931736\pi\)
\(108\) 0 0
\(109\) 57.7477 33.3406i 0.529795 0.305877i −0.211138 0.977456i \(-0.567717\pi\)
0.740933 + 0.671579i \(0.234384\pi\)
\(110\) 0 0
\(111\) 68.2540i 0.614901i
\(112\) 0 0
\(113\) 7.16467 0.0634042 0.0317021 0.999497i \(-0.489907\pi\)
0.0317021 + 0.999497i \(0.489907\pi\)
\(114\) 0 0
\(115\) −9.37101 16.2311i −0.0814870 0.141140i
\(116\) 0 0
\(117\) −360.344 208.045i −3.07986 1.77816i
\(118\) 0 0
\(119\) 2.35197 + 6.04670i 0.0197645 + 0.0508126i
\(120\) 0 0
\(121\) 46.6709 80.8363i 0.385710 0.668069i
\(122\) 0 0
\(123\) 115.000 + 199.187i 0.934963 + 1.61940i
\(124\) 0 0
\(125\) 97.8118i 0.782494i
\(126\) 0 0
\(127\) 131.492i 1.03537i 0.855572 + 0.517684i \(0.173206\pi\)
−0.855572 + 0.517684i \(0.826794\pi\)
\(128\) 0 0
\(129\) 111.279 + 192.742i 0.862631 + 1.49412i
\(130\) 0 0
\(131\) −4.38060 + 7.58742i −0.0334397 + 0.0579193i −0.882261 0.470761i \(-0.843980\pi\)
0.848821 + 0.528680i \(0.177313\pi\)
\(132\) 0 0
\(133\) 25.9800 32.3755i 0.195338 0.243425i
\(134\) 0 0
\(135\) 103.916 + 59.9962i 0.769752 + 0.444416i
\(136\) 0 0
\(137\) 118.420 + 205.110i 0.864381 + 1.49715i 0.867660 + 0.497158i \(0.165623\pi\)
−0.00327850 + 0.999995i \(0.501044\pi\)
\(138\) 0 0
\(139\) −172.122 −1.23828 −0.619142 0.785279i \(-0.712520\pi\)
−0.619142 + 0.785279i \(0.712520\pi\)
\(140\) 0 0
\(141\) 245.274i 1.73954i
\(142\) 0 0
\(143\) −97.5195 + 56.3029i −0.681955 + 0.393727i
\(144\) 0 0
\(145\) −10.1616 + 17.6003i −0.0700797 + 0.121382i
\(146\) 0 0
\(147\) 56.5909 + 255.078i 0.384972 + 1.73523i
\(148\) 0 0
\(149\) −199.798 115.354i −1.34093 0.774186i −0.353985 0.935251i \(-0.615174\pi\)
−0.986944 + 0.161066i \(0.948507\pi\)
\(150\) 0 0
\(151\) 128.077 73.9452i 0.848190 0.489703i −0.0118494 0.999930i \(-0.503772\pi\)
0.860040 + 0.510227i \(0.170439\pi\)
\(152\) 0 0
\(153\) 18.0116 0.117723
\(154\) 0 0
\(155\) −74.4227 −0.480146
\(156\) 0 0
\(157\) 99.4450 57.4146i 0.633407 0.365698i −0.148663 0.988888i \(-0.547497\pi\)
0.782070 + 0.623190i \(0.214164\pi\)
\(158\) 0 0
\(159\) −343.947 198.578i −2.16319 1.24892i
\(160\) 0 0
\(161\) −47.4389 38.0677i −0.294652 0.236446i
\(162\) 0 0
\(163\) 24.6545 42.7029i 0.151255 0.261981i −0.780434 0.625238i \(-0.785002\pi\)
0.931689 + 0.363257i \(0.118335\pi\)
\(164\) 0 0
\(165\) 52.3830 30.2433i 0.317473 0.183293i
\(166\) 0 0
\(167\) 241.457i 1.44585i −0.690926 0.722926i \(-0.742797\pi\)
0.690926 0.722926i \(-0.257203\pi\)
\(168\) 0 0
\(169\) −289.455 −1.71275
\(170\) 0 0
\(171\) −57.6196 99.8001i −0.336957 0.583626i
\(172\) 0 0
\(173\) −47.1300 27.2105i −0.272428 0.157286i 0.357563 0.933889i \(-0.383608\pi\)
−0.629990 + 0.776603i \(0.716941\pi\)
\(174\) 0 0
\(175\) 51.6336 + 132.745i 0.295049 + 0.758544i
\(176\) 0 0
\(177\) −143.100 + 247.857i −0.808475 + 1.40032i
\(178\) 0 0
\(179\) −63.5100 110.003i −0.354805 0.614540i 0.632280 0.774740i \(-0.282119\pi\)
−0.987084 + 0.160200i \(0.948786\pi\)
\(180\) 0 0
\(181\) 212.704i 1.17516i −0.809165 0.587581i \(-0.800080\pi\)
0.809165 0.587581i \(-0.199920\pi\)
\(182\) 0 0
\(183\) 148.322i 0.810502i
\(184\) 0 0
\(185\) −13.8046 23.9103i −0.0746194 0.129245i
\(186\) 0 0
\(187\) 2.43723 4.22140i 0.0130333 0.0225743i
\(188\) 0 0
\(189\) 384.890 + 59.2097i 2.03645 + 0.313279i
\(190\) 0 0
\(191\) 35.1041 + 20.2674i 0.183791 + 0.106112i 0.589073 0.808080i \(-0.299493\pi\)
−0.405282 + 0.914192i \(0.632826\pi\)
\(192\) 0 0
\(193\) −141.153 244.485i −0.731364 1.26676i −0.956300 0.292387i \(-0.905551\pi\)
0.224936 0.974374i \(-0.427783\pi\)
\(194\) 0 0
\(195\) 246.261 1.26288
\(196\) 0 0
\(197\) 261.806i 1.32896i 0.747304 + 0.664482i \(0.231348\pi\)
−0.747304 + 0.664482i \(0.768652\pi\)
\(198\) 0 0
\(199\) 278.968 161.062i 1.40185 0.809357i 0.407265 0.913310i \(-0.366482\pi\)
0.994582 + 0.103953i \(0.0331492\pi\)
\(200\) 0 0
\(201\) 209.266 362.460i 1.04113 1.80328i
\(202\) 0 0
\(203\) −10.0283 + 65.1887i −0.0494007 + 0.321127i
\(204\) 0 0
\(205\) −80.5723 46.5184i −0.393036 0.226919i
\(206\) 0 0
\(207\) −146.234 + 84.4283i −0.706445 + 0.407866i
\(208\) 0 0
\(209\) −31.1870 −0.149220
\(210\) 0 0
\(211\) −169.792 −0.804702 −0.402351 0.915485i \(-0.631807\pi\)
−0.402351 + 0.915485i \(0.631807\pi\)
\(212\) 0 0
\(213\) −344.077 + 198.653i −1.61539 + 0.932644i
\(214\) 0 0
\(215\) −77.9652 45.0133i −0.362629 0.209364i
\(216\) 0 0
\(217\) −225.099 + 87.5562i −1.03732 + 0.403485i
\(218\) 0 0
\(219\) 89.5927 155.179i 0.409099 0.708581i
\(220\) 0 0
\(221\) 17.1867 9.92275i 0.0777679 0.0448993i
\(222\) 0 0
\(223\) 45.4626i 0.203868i 0.994791 + 0.101934i \(0.0325031\pi\)
−0.994791 + 0.101934i \(0.967497\pi\)
\(224\) 0 0
\(225\) 395.414 1.75740
\(226\) 0 0
\(227\) 92.5653 + 160.328i 0.407777 + 0.706290i 0.994640 0.103396i \(-0.0329708\pi\)
−0.586864 + 0.809686i \(0.699637\pi\)
\(228\) 0 0
\(229\) 160.173 + 92.4759i 0.699445 + 0.403825i 0.807141 0.590359i \(-0.201014\pi\)
−0.107695 + 0.994184i \(0.534347\pi\)
\(230\) 0 0
\(231\) 122.857 153.101i 0.531849 0.662776i
\(232\) 0 0
\(233\) −48.3504 + 83.7453i −0.207512 + 0.359422i −0.950930 0.309405i \(-0.899870\pi\)
0.743418 + 0.668827i \(0.233203\pi\)
\(234\) 0 0
\(235\) −49.6076 85.9228i −0.211096 0.365629i
\(236\) 0 0
\(237\) 161.097i 0.679734i
\(238\) 0 0
\(239\) 163.185i 0.682782i 0.939921 + 0.341391i \(0.110898\pi\)
−0.939921 + 0.341391i \(0.889102\pi\)
\(240\) 0 0
\(241\) −102.745 177.960i −0.426330 0.738424i 0.570214 0.821496i \(-0.306860\pi\)
−0.996544 + 0.0830718i \(0.973527\pi\)
\(242\) 0 0
\(243\) 74.2413 128.590i 0.305520 0.529176i
\(244\) 0 0
\(245\) −71.4150 77.9116i −0.291490 0.318006i
\(246\) 0 0
\(247\) −109.962 63.4863i −0.445188 0.257030i
\(248\) 0 0
\(249\) 194.434 + 336.769i 0.780859 + 1.35249i
\(250\) 0 0
\(251\) 159.299 0.634658 0.317329 0.948316i \(-0.397214\pi\)
0.317329 + 0.948316i \(0.397214\pi\)
\(252\) 0 0
\(253\) 45.6975i 0.180622i
\(254\) 0 0
\(255\) −9.23191 + 5.33005i −0.0362036 + 0.0209021i
\(256\) 0 0
\(257\) −107.889 + 186.868i −0.419800 + 0.727114i −0.995919 0.0902512i \(-0.971233\pi\)
0.576119 + 0.817366i \(0.304566\pi\)
\(258\) 0 0
\(259\) −69.8832 56.0783i −0.269819 0.216518i
\(260\) 0 0
\(261\) 158.571 + 91.5507i 0.607550 + 0.350769i
\(262\) 0 0
\(263\) 285.059 164.579i 1.08387 0.625775i 0.151935 0.988391i \(-0.451450\pi\)
0.931939 + 0.362616i \(0.118116\pi\)
\(264\) 0 0
\(265\) 160.652 0.606234
\(266\) 0 0
\(267\) 292.419 1.09520
\(268\) 0 0
\(269\) 253.803 146.533i 0.943507 0.544734i 0.0524492 0.998624i \(-0.483297\pi\)
0.891058 + 0.453889i \(0.149964\pi\)
\(270\) 0 0
\(271\) −23.2529 13.4251i −0.0858042 0.0495391i 0.456484 0.889732i \(-0.349109\pi\)
−0.542288 + 0.840193i \(0.682442\pi\)
\(272\) 0 0
\(273\) 744.841 289.719i 2.72836 1.06124i
\(274\) 0 0
\(275\) 53.5053 92.6739i 0.194565 0.336996i
\(276\) 0 0
\(277\) −289.925 + 167.389i −1.04666 + 0.604291i −0.921713 0.387872i \(-0.873210\pi\)
−0.124949 + 0.992163i \(0.539877\pi\)
\(278\) 0 0
\(279\) 670.513i 2.40327i
\(280\) 0 0
\(281\) −123.357 −0.438994 −0.219497 0.975613i \(-0.570442\pi\)
−0.219497 + 0.975613i \(0.570442\pi\)
\(282\) 0 0
\(283\) −0.309453 0.535988i −0.00109347 0.00189395i 0.865478 0.500947i \(-0.167015\pi\)
−0.866572 + 0.499053i \(0.833681\pi\)
\(284\) 0 0
\(285\) 59.0663 + 34.1019i 0.207250 + 0.119656i
\(286\) 0 0
\(287\) −298.427 45.9086i −1.03981 0.159960i
\(288\) 0 0
\(289\) 144.070 249.537i 0.498514 0.863451i
\(290\) 0 0
\(291\) −143.204 248.037i −0.492112 0.852362i
\(292\) 0 0
\(293\) 28.2794i 0.0965169i −0.998835 0.0482584i \(-0.984633\pi\)
0.998835 0.0482584i \(-0.0153671\pi\)
\(294\) 0 0
\(295\) 115.770i 0.392440i
\(296\) 0 0
\(297\) −146.285 253.373i −0.492542 0.853108i
\(298\) 0 0
\(299\) −93.0247 + 161.123i −0.311119 + 0.538874i
\(300\) 0 0
\(301\) −288.771 44.4231i −0.959371 0.147585i
\(302\) 0 0
\(303\) 417.002 + 240.756i 1.37624 + 0.794575i
\(304\) 0 0
\(305\) −29.9986 51.9591i −0.0983560 0.170358i
\(306\) 0 0
\(307\) −400.893 −1.30584 −0.652921 0.757426i \(-0.726457\pi\)
−0.652921 + 0.757426i \(0.726457\pi\)
\(308\) 0 0
\(309\) 601.542i 1.94674i
\(310\) 0 0
\(311\) −140.492 + 81.1132i −0.451743 + 0.260814i −0.708566 0.705644i \(-0.750658\pi\)
0.256823 + 0.966459i \(0.417324\pi\)
\(312\) 0 0
\(313\) 133.123 230.576i 0.425313 0.736664i −0.571137 0.820855i \(-0.693497\pi\)
0.996450 + 0.0841913i \(0.0268307\pi\)
\(314\) 0 0
\(315\) −273.451 + 106.364i −0.868098 + 0.337662i
\(316\) 0 0
\(317\) 374.864 + 216.428i 1.18254 + 0.682737i 0.956600 0.291405i \(-0.0941228\pi\)
0.225936 + 0.974142i \(0.427456\pi\)
\(318\) 0 0
\(319\) 42.9138 24.7763i 0.134526 0.0776686i
\(320\) 0 0
\(321\) −767.792 −2.39187
\(322\) 0 0
\(323\) 5.49636 0.0170166
\(324\) 0 0
\(325\) 377.305 217.837i 1.16094 0.670269i
\(326\) 0 0
\(327\) 307.925 + 177.781i 0.941668 + 0.543672i
\(328\) 0 0
\(329\) −251.129 201.520i −0.763310 0.612524i
\(330\) 0 0
\(331\) 40.6264 70.3671i 0.122738 0.212589i −0.798108 0.602514i \(-0.794166\pi\)
0.920847 + 0.389925i \(0.127499\pi\)
\(332\) 0 0
\(333\) −215.420 + 124.373i −0.646907 + 0.373492i
\(334\) 0 0
\(335\) 169.299i 0.505370i
\(336\) 0 0
\(337\) −69.4941 −0.206214 −0.103107 0.994670i \(-0.532878\pi\)
−0.103107 + 0.994670i \(0.532878\pi\)
\(338\) 0 0
\(339\) 19.1019 + 33.0855i 0.0563479 + 0.0975974i
\(340\) 0 0
\(341\) 157.149 + 90.7300i 0.460848 + 0.266071i
\(342\) 0 0
\(343\) −307.663 151.634i −0.896975 0.442080i
\(344\) 0 0
\(345\) 49.9686 86.5481i 0.144836 0.250864i
\(346\) 0 0
\(347\) −174.677 302.549i −0.503391 0.871899i −0.999992 0.00392020i \(-0.998752\pi\)
0.496601 0.867979i \(-0.334581\pi\)
\(348\) 0 0
\(349\) 165.836i 0.475174i 0.971366 + 0.237587i \(0.0763566\pi\)
−0.971366 + 0.237587i \(0.923643\pi\)
\(350\) 0 0
\(351\) 1191.15i 3.39358i
\(352\) 0 0
\(353\) 235.858 + 408.519i 0.668154 + 1.15728i 0.978420 + 0.206627i \(0.0662486\pi\)
−0.310266 + 0.950650i \(0.600418\pi\)
\(354\) 0 0
\(355\) 80.3566 139.182i 0.226356 0.392061i
\(356\) 0 0
\(357\) −21.6522 + 26.9823i −0.0606504 + 0.0755808i
\(358\) 0 0
\(359\) −568.967 328.493i −1.58487 0.915022i −0.994134 0.108154i \(-0.965506\pi\)
−0.590731 0.806869i \(1.29884\pi\)
\(360\) 0 0
\(361\) 162.917 + 282.180i 0.451294 + 0.781663i
\(362\) 0 0
\(363\) 497.722 1.37113
\(364\) 0 0
\(365\) 72.4817i 0.198580i
\(366\) 0 0
\(367\) 307.850 177.737i 0.838829 0.484298i −0.0180371 0.999837i \(-0.505742\pi\)
0.856866 + 0.515539i \(0.172408\pi\)
\(368\) 0 0
\(369\) −419.109 + 725.918i −1.13580 + 1.96726i
\(370\) 0 0
\(371\) 485.908 189.003i 1.30973 0.509441i
\(372\) 0 0
\(373\) −273.662 157.999i −0.733680 0.423590i 0.0860872 0.996288i \(-0.472564\pi\)
−0.819767 + 0.572698i \(0.805897\pi\)
\(374\) 0 0
\(375\) −451.682 + 260.779i −1.20449 + 0.695410i
\(376\) 0 0
\(377\) 201.745 0.535132
\(378\) 0 0
\(379\) 178.404 0.470723 0.235361 0.971908i \(-0.424373\pi\)
0.235361 + 0.971908i \(0.424373\pi\)
\(380\) 0 0
\(381\) −607.211 + 350.574i −1.59373 + 0.920140i
\(382\) 0 0
\(383\) 604.832 + 349.200i 1.57920 + 0.911750i 0.994972 + 0.100158i \(0.0319349\pi\)
0.584225 + 0.811591i \(0.301398\pi\)
\(384\) 0 0
\(385\) −12.0733 + 78.4816i −0.0313591 + 0.203848i
\(386\) 0 0
\(387\) −405.548 + 702.430i −1.04793 + 1.81506i
\(388\) 0 0
\(389\) −151.865 + 87.6790i −0.390397 + 0.225396i −0.682332 0.731042i \(-0.739034\pi\)
0.291935 + 0.956438i \(0.405701\pi\)
\(390\) 0 0
\(391\) 8.05366i 0.0205976i
\(392\) 0 0
\(393\) −46.7170 −0.118873
\(394\) 0 0
\(395\) 32.5824 + 56.4344i 0.0824871 + 0.142872i
\(396\) 0 0
\(397\) 334.033 + 192.854i 0.841393 + 0.485778i 0.857737 0.514088i \(-0.171870\pi\)
−0.0163447 + 0.999866i \(0.505203\pi\)
\(398\) 0 0
\(399\) 218.772 + 33.6549i 0.548301 + 0.0843481i
\(400\) 0 0
\(401\) −263.548 + 456.479i −0.657228 + 1.13835i 0.324103 + 0.946022i \(0.394938\pi\)
−0.981330 + 0.192330i \(0.938396\pi\)
\(402\) 0 0
\(403\) 369.392 + 639.805i 0.916605 + 1.58761i
\(404\) 0 0
\(405\) 262.590i 0.648371i
\(406\) 0 0
\(407\) 67.3178i 0.165400i
\(408\) 0 0
\(409\) 211.872 + 366.973i 0.518025 + 0.897245i 0.999781 + 0.0209399i \(0.00666585\pi\)
−0.481756 + 0.876305i \(0.660001\pi\)
\(410\) 0 0
\(411\) −631.447 + 1093.70i −1.53637 + 2.66107i
\(412\) 0 0
\(413\) −136.200 350.158i −0.329782 0.847840i
\(414\) 0 0
\(415\) −136.225 78.6498i −0.328254 0.189517i
\(416\) 0 0
\(417\) −458.898 794.834i −1.10047 1.90608i
\(418\) 0 0
\(419\) −295.598 −0.705485 −0.352742 0.935721i \(-0.614751\pi\)
−0.352742 + 0.935721i \(0.614751\pi\)
\(420\) 0 0
\(421\) 126.260i 0.299904i −0.988693 0.149952i \(-0.952088\pi\)
0.988693 0.149952i \(-0.0479119\pi\)
\(422\) 0 0
\(423\) −774.124 + 446.941i −1.83008 + 1.05660i
\(424\) 0 0
\(425\) −9.42970 + 16.3327i −0.0221875 + 0.0384299i
\(426\) 0 0
\(427\) −151.862 121.863i −0.355649 0.285393i
\(428\) 0 0
\(429\) −519.999 300.221i −1.21212 0.699817i
\(430\) 0 0
\(431\) −220.198 + 127.131i −0.510900 + 0.294968i −0.733204 0.680009i \(-0.761976\pi\)
0.222303 + 0.974978i \(0.428642\pi\)
\(432\) 0 0
\(433\) 546.301 1.26167 0.630833 0.775919i \(-0.282713\pi\)
0.630833 + 0.775919i \(0.282713\pi\)
\(434\) 0 0
\(435\) −108.368 −0.249122
\(436\) 0 0
\(437\) −44.6244 + 25.7639i −0.102115 + 0.0589563i
\(438\) 0 0
\(439\) 236.715 + 136.667i 0.539214 + 0.311315i 0.744760 0.667332i \(-0.232564\pi\)
−0.205546 + 0.978647i \(0.565897\pi\)
\(440\) 0 0
\(441\) −701.946 + 643.415i −1.59171 + 1.45899i
\(442\) 0 0
\(443\) 237.385 411.163i 0.535858 0.928133i −0.463263 0.886221i \(-0.653322\pi\)
0.999121 0.0419124i \(-0.0133450\pi\)
\(444\) 0 0
\(445\) −102.438 + 59.1427i −0.230198 + 0.132905i
\(446\) 0 0
\(447\) 1230.19i 2.75210i
\(448\) 0 0
\(449\) 782.101 1.74187 0.870936 0.491396i \(-0.163513\pi\)
0.870936 + 0.491396i \(0.163513\pi\)
\(450\) 0 0
\(451\) 113.423 + 196.454i 0.251492 + 0.435597i
\(452\) 0 0
\(453\) 682.938 + 394.294i 1.50759 + 0.870407i
\(454\) 0 0
\(455\) −202.331 + 252.139i −0.444683 + 0.554152i
\(456\) 0 0
\(457\) 94.7793 164.163i 0.207395 0.359218i −0.743498 0.668738i \(-0.766835\pi\)
0.950893 + 0.309520i \(0.100168\pi\)
\(458\) 0 0
\(459\) 25.7811 + 44.6541i 0.0561679 + 0.0972857i
\(460\) 0 0
\(461\) 202.533i 0.439335i −0.975575 0.219667i \(-0.929503\pi\)
0.975575 0.219667i \(-0.0704972\pi\)
\(462\) 0 0
\(463\) 652.927i 1.41021i 0.709103 + 0.705105i \(0.249100\pi\)
−0.709103 + 0.705105i \(0.750900\pi\)
\(464\) 0 0
\(465\) −198.420 343.674i −0.426710 0.739084i
\(466\) 0 0
\(467\) 272.725 472.373i 0.583993 1.01150i −0.411008 0.911632i \(-0.634823\pi\)
0.995000 0.0998730i \(-0.0318437\pi\)
\(468\) 0 0
\(469\) 199.176 + 512.062i 0.424682 + 1.09182i
\(470\) 0 0
\(471\) 530.266 + 306.149i 1.12583 + 0.649998i
\(472\) 0 0
\(473\) 109.753 + 190.098i 0.232036 + 0.401898i
\(474\) 0 0
\(475\) 120.663 0.254028
\(476\) 0 0
\(477\) 1447.40i 3.03438i
\(478\) 0 0
\(479\) 94.3079 54.4487i 0.196885 0.113672i −0.398317 0.917248i \(-0.630405\pi\)
0.595202 + 0.803576i \(0.297072\pi\)
\(480\) 0 0
\(481\) −137.036 + 237.354i −0.284899 + 0.493459i
\(482\) 0 0
\(483\) 49.3135 320.560i 0.102098 0.663686i
\(484\) 0 0
\(485\) 100.333 + 57.9272i 0.206872 + 0.119437i
\(486\) 0 0
\(487\) −371.831 + 214.677i −0.763513 + 0.440814i −0.830556 0.556936i \(-0.811977\pi\)
0.0670428 + 0.997750i \(0.478644\pi\)
\(488\) 0 0
\(489\) 262.929 0.537686
\(490\) 0 0
\(491\) −453.887 −0.924413 −0.462206 0.886772i \(-0.652942\pi\)
−0.462206 + 0.886772i \(0.652942\pi\)
\(492\) 0 0
\(493\) −7.56306 + 4.36654i −0.0153409 + 0.00885707i
\(494\) 0 0
\(495\) 190.905 + 110.219i 0.385667 + 0.222665i
\(496\) 0 0
\(497\) 79.3031 515.506i 0.159564 1.03724i
\(498\) 0 0
\(499\) 166.698 288.730i 0.334064 0.578617i −0.649240 0.760583i \(-0.724913\pi\)
0.983305 + 0.181967i \(0.0582463\pi\)
\(500\) 0 0
\(501\) 1115.02 643.755i 2.22558 1.28494i
\(502\) 0 0
\(503\) 580.170i 1.15342i −0.816949 0.576710i \(-0.804336\pi\)
0.816949 0.576710i \(-0.195664\pi\)
\(504\) 0 0
\(505\) −194.775 −0.385693
\(506\) 0 0
\(507\) −771.724 1336.67i −1.52214 2.63642i
\(508\) 0 0
\(509\) −266.271 153.732i −0.523126 0.302027i 0.215087 0.976595i \(-0.430997\pi\)
−0.738213 + 0.674568i \(0.764330\pi\)
\(510\) 0 0
\(511\) 85.2728 + 219.228i 0.166874 + 0.429018i
\(512\) 0 0
\(513\) 164.949 285.700i 0.321538 0.556919i
\(514\) 0 0
\(515\) 121.664 + 210.728i 0.236241 + 0.409181i
\(516\) 0 0
\(517\) 241.910i 0.467911i
\(518\) 0 0
\(519\) 290.187i 0.559127i
\(520\) 0 0
\(521\) −360.480 624.369i −0.691899 1.19840i −0.971215 0.238205i \(-0.923441\pi\)
0.279316 0.960199i \(-0.409892\pi\)
\(522\) 0 0
\(523\) −134.988 + 233.807i −0.258104 + 0.447049i −0.965734 0.259534i \(-0.916431\pi\)
0.707630 + 0.706583i \(0.249764\pi\)
\(524\) 0 0
\(525\) −475.338 + 592.353i −0.905405 + 1.12829i
\(526\) 0 0
\(527\) −27.6957 15.9901i −0.0525536 0.0303418i
\(528\) 0 0
\(529\) −226.749 392.741i −0.428637 0.742421i
\(530\) 0 0
\(531\) −1043.03 −1.96428
\(532\) 0 0
\(533\) 923.564i 1.73277i
\(534\) 0 0
\(535\) 268.967 155.288i 0.502743 0.290259i
\(536\) 0 0
\(537\) 338.652 586.562i 0.630636 1.09229i
\(538\) 0 0
\(539\) 55.8147 + 251.579i 0.103552 + 0.466752i
\(540\) 0 0
\(541\) −785.695 453.621i −1.45230 0.838486i −0.453689 0.891160i \(-0.649892\pi\)
−0.998612 + 0.0526734i \(0.983226\pi\)
\(542\) 0 0
\(543\) 982.241 567.097i 1.80891 1.04438i
\(544\) 0 0
\(545\) −143.827 −0.263903
\(546\) 0 0
\(547\) 557.327 1.01888 0.509439 0.860506i \(-0.329853\pi\)
0.509439 + 0.860506i \(0.329853\pi\)
\(548\) 0 0
\(549\) −468.127 + 270.273i −0.852690 + 0.492301i
\(550\) 0 0
\(551\) 48.3889 + 27.9374i 0.0878202 + 0.0507030i
\(552\) 0 0
\(553\) 164.942 + 132.359i 0.298268 + 0.239347i
\(554\) 0 0
\(555\) 73.6096 127.496i 0.132630 0.229722i
\(556\) 0 0
\(557\) 741.896 428.334i 1.33195 0.769002i 0.346352 0.938105i \(-0.387420\pi\)
0.985598 + 0.169103i \(0.0540869\pi\)
\(558\) 0 0
\(559\) 893.680i 1.59871i
\(560\) 0 0
\(561\) 25.9918 0.0463313
\(562\) 0 0
\(563\) 6.84436 + 11.8548i 0.0121569 + 0.0210564i 0.872040 0.489435i \(-0.162797\pi\)
−0.859883 + 0.510491i \(0.829464\pi\)
\(564\) 0 0
\(565\) −13.3833 7.72686i −0.0236873 0.0136759i
\(566\) 0 0
\(567\) 308.930 + 794.231i 0.544851 + 1.40076i
\(568\) 0 0
\(569\) 545.991 945.684i 0.959563 1.66201i 0.235999 0.971753i \(-0.424164\pi\)
0.723563 0.690258i \(-0.242503\pi\)
\(570\) 0 0
\(571\) 359.549 + 622.757i 0.629683 + 1.09064i 0.987615 + 0.156895i \(0.0501485\pi\)
−0.357932 + 0.933747i \(0.616518\pi\)
\(572\) 0 0
\(573\) 216.142i 0.377210i
\(574\) 0 0
\(575\) 176.805i 0.307486i
\(576\) 0 0
\(577\) 515.560 + 892.976i 0.893518 + 1.54762i 0.835628 + 0.549296i \(0.185104\pi\)
0.0578905 + 0.998323i \(0.481563\pi\)
\(578\) 0 0
\(579\) 752.665 1303.65i 1.29994 2.25156i
\(580\) 0 0
\(581\) −504.557 77.6187i −0.868428 0.133595i
\(582\) 0 0
\(583\) −339.229 195.854i −0.581868 0.335942i
\(584\) 0 0
\(585\) 448.738 + 777.238i 0.767074 + 1.32861i
\(586\) 0 0
\(587\) 671.907 1.14464 0.572322 0.820029i \(-0.306043\pi\)
0.572322 + 0.820029i \(0.306043\pi\)
\(588\) 0 0
\(589\) 204.612i 0.347388i
\(590\) 0 0
\(591\) −1208.99 + 698.008i −2.04566 + 1.18106i
\(592\) 0 0
\(593\) −176.999 + 306.572i −0.298481 + 0.516984i −0.975789 0.218716i \(-0.929813\pi\)
0.677308 + 0.735700i \(0.263147\pi\)
\(594\) 0 0
\(595\) 2.12777 13.8315i 0.00357609 0.0232462i
\(596\) 0 0
\(597\) 1487.53 + 858.824i 2.49167 + 1.43857i
\(598\) 0 0
\(599\) 983.923 568.068i 1.64261 0.948361i 0.662708 0.748878i \(-0.269407\pi\)
0.979901 0.199484i \(-0.0639265\pi\)
\(600\) 0 0
\(601\) −6.80783 −0.0113275 −0.00566375 0.999984i \(-0.501803\pi\)
−0.00566375 + 0.999984i \(0.501803\pi\)
\(602\) 0 0
\(603\) 1525.30 2.52953
\(604\) 0 0
\(605\) −174.358 + 100.666i −0.288196 + 0.166390i
\(606\) 0 0
\(607\) −386.628 223.220i −0.636948 0.367742i 0.146490 0.989212i \(-0.453202\pi\)
−0.783438 + 0.621470i \(0.786536\pi\)
\(608\) 0 0
\(609\) −327.770 + 127.492i −0.538210 + 0.209346i
\(610\) 0 0
\(611\) −492.447 + 852.944i −0.805970 + 1.39598i
\(612\) 0 0
\(613\) 555.650 320.805i 0.906443 0.523335i 0.0271583 0.999631i \(-0.491354\pi\)
0.879285 + 0.476296i \(0.158021\pi\)
\(614\) 0 0
\(615\) 496.096i 0.806661i
\(616\) 0 0
\(617\) −502.890 −0.815057 −0.407528 0.913193i \(-0.633609\pi\)
−0.407528 + 0.913193i \(0.633609\pi\)
\(618\) 0 0
\(619\) 216.495 + 374.980i 0.349749 + 0.605783i 0.986205 0.165530i \(-0.0529336\pi\)
−0.636456 + 0.771313i \(0.719600\pi\)
\(620\) 0 0
\(621\) −418.627 241.695i −0.674118 0.389202i
\(622\) 0 0
\(623\) −240.255 + 299.399i −0.385642 + 0.480576i
\(624\) 0 0
\(625\) −148.859 + 257.831i −0.238174 + 0.412530i
\(626\) 0 0
\(627\) −83.1486 144.018i −0.132613 0.229693i
\(628\) 0 0
\(629\) 11.8640i 0.0188617i
\(630\) 0 0
\(631\) 238.957i 0.378695i −0.981910 0.189348i \(-0.939363\pi\)
0.981910 0.189348i \(-0.0606373\pi\)
\(632\) 0 0
\(633\) −452.687 784.078i −0.715146 1.23867i
\(634\) 0 0
\(635\) 141.809 245.621i 0.223322 0.386805i
\(636\) 0 0
\(637\) −315.336 + 1000.66i −0.495032 + 1.57089i
\(638\) 0 0
\(639\) −1253.96 723.974i −1.96238 1.13298i
\(640\) 0 0
\(641\) 3.98065 + 6.89469i 0.00621006 + 0.0107561i 0.869114 0.494612i \(-0.164690\pi\)
−0.862904 + 0.505368i \(0.831357\pi\)
\(642\) 0 0
\(643\) 584.919 0.909672 0.454836 0.890575i \(-0.349698\pi\)
0.454836 + 0.890575i \(0.349698\pi\)
\(644\) 0 0
\(645\) 480.044i 0.744255i
\(646\) 0 0
\(647\) 290.707 167.840i 0.449316 0.259413i −0.258225 0.966085i \(-0.583138\pi\)
0.707541 + 0.706672i \(0.249804\pi\)
\(648\) 0 0
\(649\) −141.137 + 244.457i −0.217469 + 0.376667i
\(650\) 0 0
\(651\) −1004.46 806.040i −1.54296 1.23816i
\(652\) 0 0
\(653\) 42.0252 + 24.2632i 0.0643571 + 0.0371566i 0.531833 0.846849i \(-0.321503\pi\)
−0.467476 + 0.884006i \(0.654837\pi\)
\(654\) 0 0
\(655\) 16.3656 9.44866i 0.0249856 0.0144254i
\(656\) 0 0
\(657\) 653.026 0.993951
\(658\) 0 0
\(659\) −1224.65 −1.85835 −0.929176 0.369638i \(-0.879482\pi\)
−0.929176 + 0.369638i \(0.879482\pi\)
\(660\) 0 0
\(661\) 725.765 419.021i 1.09798 0.633919i 0.162291 0.986743i \(-0.448112\pi\)
0.935690 + 0.352823i \(0.114778\pi\)
\(662\) 0 0
\(663\) 91.6439 + 52.9106i 0.138226 + 0.0798049i
\(664\) 0 0
\(665\) −83.4455 + 32.4576i −0.125482 + 0.0488084i
\(666\) 0 0
\(667\) 40.9358 70.9029i 0.0613730 0.106301i
\(668\) 0 0
\(669\) −209.940 + 121.209i −0.313812 + 0.181180i
\(670\) 0 0
\(671\) 146.287i 0.218014i
\(672\) 0 0
\(673\) 147.714 0.219486 0.109743 0.993960i \(-0.464997\pi\)
0.109743 + 0.993960i \(0.464997\pi\)
\(674\) 0 0
\(675\) 565.980 + 980.307i 0.838490 + 1.45231i
\(676\) 0 0
\(677\) −725.024 418.593i −1.07094 0.618305i −0.142499 0.989795i \(-0.545514\pi\)
−0.928437 + 0.371490i \(0.878847\pi\)
\(678\) 0 0
\(679\) 371.616 + 57.1678i 0.547299 + 0.0841941i
\(680\) 0 0
\(681\) −493.582 + 854.909i −0.724790 + 1.25537i
\(682\) 0 0
\(683\) −32.2189 55.8047i −0.0471725 0.0817053i 0.841475 0.540296i \(-0.181688\pi\)
−0.888648 + 0.458591i \(0.848354\pi\)
\(684\) 0 0
\(685\) 510.849i 0.745765i
\(686\) 0 0
\(687\) 986.210i 1.43553i
\(688\) 0 0
\(689\) −797.385 1381.11i −1.15731 2.00452i
\(690\) 0 0
\(691\) −263.374 + 456.177i −0.381149 + 0.660169i −0.991227 0.132172i \(-0.957805\pi\)
0.610078 + 0.792341i \(0.291138\pi\)
\(692\) 0 0
\(693\) 707.082 + 108.774i 1.02032 + 0.156961i
\(694\) 0 0
\(695\) 321.516 + 185.627i 0.462613 + 0.267090i
\(696\) 0 0
\(697\) −19.9895 34.6229i −0.0286794 0.0496741i
\(698\) 0 0
\(699\) −515.633 −0.737672
\(700\) 0 0
\(701\) 695.486i 0.992134i 0.868284 + 0.496067i \(0.165223\pi\)
−0.868284 + 0.496067i \(0.834777\pi\)
\(702\) 0 0
\(703\) −65.7370 + 37.9532i −0.0935092 + 0.0539875i
\(704\) 0 0
\(705\) 264.520 458.162i 0.375206 0.649876i
\(706\) 0 0
\(707\) −589.117 + 229.147i −0.833262 + 0.324112i
\(708\) 0 0
\(709\) −803.161 463.705i −1.13281 0.654027i −0.188168 0.982137i \(-0.560255\pi\)
−0.944640 + 0.328110i \(0.893588\pi\)
\(710\) 0 0
\(711\) 508.447 293.552i 0.715115 0.412872i
\(712\) 0 0
\(713\) 299.812 0.420493
\(714\) 0 0
\(715\) 242.883 0.339697
\(716\) 0 0
\(717\) −753.566 + 435.071i −1.05100 + 0.606794i
\(718\) 0 0
\(719\) 1150.37 + 664.169i 1.59996 + 0.923739i 0.991493 + 0.130163i \(0.0415501\pi\)
0.608471 + 0.793576i \(0.291783\pi\)
\(720\) 0 0
\(721\) 615.900 + 494.234i 0.854231 + 0.685484i
\(722\) 0 0
\(723\) 547.865 948.929i 0.757766 1.31249i
\(724\) 0 0
\(725\) −166.034 + 95.8600i −0.229013 + 0.132221i
\(726\) 0 0
\(727\) 539.401i 0.741954i −0.928642 0.370977i \(-0.879023\pi\)
0.928642 0.370977i \(-0.120977\pi\)
\(728\) 0 0
\(729\) −303.936 −0.416922
\(730\) 0 0
\(731\) −19.3427 33.5026i −0.0264606 0.0458311i
\(732\) 0 0
\(733\) −382.859 221.044i −0.522318 0.301561i 0.215564 0.976490i \(-0.430841\pi\)
−0.737883 + 0.674929i \(0.764174\pi\)
\(734\) 0 0
\(735\) 169.384 537.507i 0.230454 0.731302i
\(736\) 0 0
\(737\) 206.396 357.488i 0.280048 0.485058i
\(738\) 0 0
\(739\) −574.116 994.398i −0.776882 1.34560i −0.933730 0.357977i \(-0.883467\pi\)
0.156848 0.987623i \(-0.449867\pi\)
\(740\) 0 0
\(741\) 677.050i 0.913698i
\(742\) 0 0
\(743\) 588.688i 0.792313i −0.918183 0.396156i \(-0.870344\pi\)
0.918183 0.396156i \(-0.129656\pi\)
\(744\) 0 0
\(745\) 248.810 + 430.952i 0.333973 + 0.578459i
\(746\) 0 0
\(747\) −708.597 + 1227.33i −0.948590 + 1.64301i
\(748\) 0 0
\(749\) 630.826 786.118i 0.842225 1.04956i
\(750\) 0 0
\(751\) −708.754 409.199i −0.943747 0.544873i −0.0526140 0.998615i \(-0.516755\pi\)
−0.891133 + 0.453742i \(0.850089\pi\)
\(752\) 0 0
\(753\) 424.712 + 735.622i 0.564026 + 0.976922i
\(754\) 0 0
\(755\) −318.989 −0.422503
\(756\) 0 0
\(757\) 105.101i 0.138838i −0.997588 0.0694192i \(-0.977885\pi\)
0.997588 0.0694192i \(-0.0221146\pi\)
\(758\) 0 0
\(759\) −211.025 + 121.835i −0.278030 + 0.160521i
\(760\) 0 0
\(761\) −507.117 + 878.352i −0.666382 + 1.15421i 0.312527 + 0.949909i \(0.398825\pi\)
−0.978909 + 0.204299i \(0.934509\pi\)
\(762\) 0 0
\(763\) −435.019 + 169.209i −0.570143 + 0.221767i
\(764\) 0 0
\(765\) −33.6449 19.4249i −0.0439803 0.0253920i
\(766\) 0 0
\(767\) −995.264 + 574.616i −1.29761 + 0.749173i
\(768\) 0 0
\(769\) −1183.99 −1.53964 −0.769822 0.638258i \(-0.779655\pi\)
−0.769822 + 0.638258i \(0.779655\pi\)
\(770\) 0 0
\(771\) −1150.58 −1.49232
\(772\) 0 0
\(773\) −280.862 + 162.156i −0.363340 + 0.209774i −0.670545 0.741869i \(-0.733940\pi\)
0.307205 + 0.951643i \(0.400606\pi\)
\(774\) 0 0
\(775\) −608.014 351.037i −0.784534 0.452951i
\(776\) 0 0
\(777\) 72.6446 472.223i 0.0934937 0.607751i
\(778\) 0 0
\(779\) −127.894 + 221.519i −0.164177 + 0.284363i
\(780\) 0 0
\(781\) −339.358 + 195.928i −0.434517 + 0.250869i
\(782\) 0 0
\(783\) 524.168i 0.669436i
\(784\) 0 0
\(785\) −247.679 −0.315514
\(786\) 0 0
\(787\) 134.268 + 232.559i 0.170607 + 0.295500i 0.938632 0.344919i \(-0.112094\pi\)
−0.768025 + 0.640420i \(0.778760\pi\)
\(788\) 0 0
\(789\) 1520.01 + 877.576i 1.92650 + 1.11226i
\(790\) 0 0
\(791\) −49.5696 7.62556i −0.0626670 0.00964040i
\(792\) 0 0
\(793\) −297.792 + 515.791i −0.375526 + 0.650429i