Properties

Label 224.3.o.d.207.5
Level 224
Weight 3
Character 224.207
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 207.5
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 \(\chi\) \(=\) 224.207
Dual form 224.3.o.d.79.5

$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 0.0473064 0.998880i \(-0.484936\pi\)
0.841403 0.540409i \(-0.181730\pi\)
\(4\) 0 0
\(5\) −1.86796 + 1.07847i −0.373592 + 0.215693i −0.675026 0.737794i \(-0.735868\pi\)
0.301435 + 0.953487i \(0.402534\pi\)
\(6\) 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 −0.721392 0.692527i \(-0.756497\pi\)
0.960442 + 0.278480i \(0.0898305\pi\)
\(12\) 0 0
\(13\) 21.4116i 1.64704i −0.567285 0.823522i \(-0.692006\pi\)
0.567285 0.823522i \(-0.307994\pi\)
\(14\) 0 0
\(15\) 11.5013i 0.766754i
\(16\) 0 0
\(17\) −0.463429 + 0.802683i −0.0272606 + 0.0472167i −0.879334 0.476206i \(-0.842012\pi\)
0.852073 + 0.523423i \(0.175345\pi\)
\(18\) 0 0
\(19\) −2.96505 5.13561i −0.156055 0.270295i 0.777388 0.629022i \(-0.216544\pi\)
−0.933443 + 0.358726i \(0.883211\pi\)
\(20\) 0 0
\(21\) −13.5310 + 34.7869i −0.644332 + 1.65652i
\(22\) 0 0
\(23\) 7.52507 4.34460i 0.327177 0.188896i −0.327410 0.944882i \(-0.606176\pi\)
0.654587 + 0.755987i \(0.272843\pi\)
\(24\) 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 \(0.0519403\pi\)
−0.986716 + 0.162452i \(0.948060\pi\)
\(30\) 0 0
\(31\) 29.8813 + 17.2520i 0.963912 + 0.556515i 0.897375 0.441269i \(-0.145471\pi\)
0.0665375 + 0.997784i \(0.478805\pi\)
\(32\) 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 −0.342662 0.939459i \(-0.611328\pi\)
0.642265 + 0.766483i \(0.277995\pi\)
\(38\) 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 −0.0122620 0.999925i \(-0.503903\pi\)
0.859829 + 0.510582i \(0.170570\pi\)
\(48\) 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 −0.252756 0.967530i \(-0.581337\pi\)
−0.964284 + 0.264872i \(0.914670\pi\)
\(54\) 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 −0.543821 0.839201i \(-0.683023\pi\)
0.998680 + 0.0513617i \(0.0163561\pi\)
\(60\) 0 0
\(61\) 24.0893 13.9080i 0.394907 0.228000i −0.289377 0.957215i \(-0.593448\pi\)
0.684284 + 0.729215i \(0.260115\pi\)
\(62\) 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 0.409030 + 0.912521i \(0.365867\pi\)
−0.994781 + 0.102030i \(0.967466\pi\)
\(68\) 0 0
\(69\) 46.3330i 0.671493i
\(70\) 0 0
\(71\) 74.5100i 1.04944i −0.851276 0.524719i \(-0.824171\pi\)
0.851276 0.524719i \(-0.175829\pi\)
\(72\) 0 0
\(73\) −16.8020 + 29.1020i −0.230165 + 0.398657i −0.957857 0.287247i \(-0.907260\pi\)
0.727692 + 0.685904i \(0.240593\pi\)
\(74\) 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 −0.656370 0.754439i \(-0.727909\pi\)
0.325178 + 0.945653i \(0.394576\pi\)
\(80\) 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 0.977944 0.208867i \(-0.0669776\pi\)
−0.669856 + 0.742491i \(0.733644\pi\)
\(90\) 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 0.834404 0.551153i \(-0.185812\pi\)
−0.0601103 + 0.998192i \(0.519145\pi\)
\(102\) 0 0
\(103\) −97.6980 + 56.4060i −0.948525 + 0.547631i −0.892622 0.450805i \(-0.851137\pi\)
−0.0559023 + 0.998436i \(0.517804\pi\)
\(104\) 0 0
\(105\) −12.2412 79.5731i −0.116583 0.757839i
\(106\) 0 0
\(107\) −71.9950 124.699i −0.672851 1.16541i −0.977092 0.212817i \(-0.931736\pi\)
0.304241 0.952595i \(-0.401597\pi\)
\(108\) 0 0
\(109\) 57.7477 + 33.3406i 0.529795 + 0.305877i 0.740933 0.671579i \(-0.234384\pi\)
−0.211138 + 0.977456i \(0.567717\pi\)
\(110\) 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 \(-0.826794\pi\)
0.855572 0.517684i \(-0.173206\pi\)
\(128\) 0 0
\(129\) 111.279 192.742i 0.862631 1.49412i
\(130\) 0 0
\(131\) −4.38060 7.58742i −0.0334397 0.0579193i 0.848821 0.528680i \(-0.177313\pi\)
−0.882261 + 0.470761i \(0.843980\pi\)
\(132\) 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 −0.00327850 0.999995i \(-0.501044\pi\)
0.867660 0.497158i \(-0.165623\pi\)
\(138\) 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 −0.986944 0.161066i \(-0.948507\pi\)
−0.353985 + 0.935251i \(0.615174\pi\)
\(150\) 0 0
\(151\) 128.077 + 73.9452i 0.848190 + 0.489703i 0.860040 0.510227i \(-0.170439\pi\)
−0.0118494 + 0.999930i \(0.503772\pi\)
\(152\) 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 0.782070 0.623190i \(-0.214164\pi\)
−0.148663 + 0.988888i \(0.547497\pi\)
\(158\) 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 0.931689 0.363257i \(-0.118335\pi\)
−0.780434 + 0.625238i \(0.785002\pi\)
\(164\) 0 0
\(165\) 52.3830 + 30.2433i 0.317473 + 0.183293i
\(166\) 0 0
\(167\) 241.457i 1.44585i 0.690926 + 0.722926i \(0.257203\pi\)
−0.690926 + 0.722926i \(0.742797\pi\)
\(168\) 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 −0.629990 0.776603i \(-0.716941\pi\)
0.357563 + 0.933889i \(0.383608\pi\)
\(174\) 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 −0.987084 0.160200i \(-0.948786\pi\)
0.632280 + 0.774740i \(0.282119\pi\)
\(180\) 0 0
\(181\) 212.704i 1.17516i 0.809165 + 0.587581i \(0.199920\pi\)
−0.809165 + 0.587581i \(0.800080\pi\)
\(182\) 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 −0.405282 0.914192i \(-0.632826\pi\)
0.589073 + 0.808080i \(0.299493\pi\)
\(192\) 0 0
\(193\) −141.153 + 244.485i −0.731364 + 1.26676i 0.224936 + 0.974374i \(0.427783\pi\)
−0.956300 + 0.292387i \(0.905551\pi\)
\(194\) 0 0
\(195\) 246.261 1.26288
\(196\) 0 0
\(197\) 261.806i 1.32896i −0.747304 0.664482i \(-0.768652\pi\)
0.747304 0.664482i \(-0.231348\pi\)
\(198\) 0 0
\(199\) 278.968 + 161.062i 1.40185 + 0.809357i 0.994582 0.103953i \(-0.0331492\pi\)
0.407265 + 0.913310i \(0.366482\pi\)
\(200\) 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 \(-0.967497\pi\)
0.994791 0.101934i \(-0.0325031\pi\)
\(224\) 0 0
\(225\) 395.414 1.75740
\(226\) 0 0
\(227\) 92.5653 160.328i 0.407777 0.706290i −0.586864 0.809686i \(-0.699637\pi\)
0.994640 + 0.103396i \(0.0329708\pi\)
\(228\) 0 0
\(229\) 160.173 92.4759i 0.699445 0.403825i −0.107695 0.994184i \(-0.534347\pi\)
0.807141 + 0.590359i \(0.201014\pi\)
\(230\) 0 0
\(231\) 122.857 + 153.101i 0.531849 + 0.662776i
\(232\) 0 0
\(233\) −48.3504 83.7453i −0.207512 0.359422i 0.743418 0.668827i \(-0.233203\pi\)
−0.950930 + 0.309405i \(0.899870\pi\)
\(234\) 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 \(-0.889102\pi\)
0.939921 0.341391i \(-0.110898\pi\)
\(240\) 0 0
\(241\) −102.745 + 177.960i −0.426330 + 0.738424i −0.996544 0.0830718i \(-0.973527\pi\)
0.570214 + 0.821496i \(0.306860\pi\)
\(242\) 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 0.576119 0.817366i \(-0.304566\pi\)
−0.995919 + 0.0902512i \(0.971233\pi\)
\(258\) 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 0.931939 0.362616i \(-0.118116\pi\)
0.151935 + 0.988391i \(0.451450\pi\)
\(264\) 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 0.891058 0.453889i \(-0.149964\pi\)
0.0524492 + 0.998624i \(0.483297\pi\)
\(270\) 0 0
\(271\) −23.2529 + 13.4251i −0.0858042 + 0.0495391i −0.542288 0.840193i \(-0.682442\pi\)
0.456484 + 0.889732i \(0.349109\pi\)
\(272\) 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 −0.124949 0.992163i \(-0.539877\pi\)
−0.921713 + 0.387872i \(0.873210\pi\)
\(278\) 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 −0.866572 0.499053i \(-0.833681\pi\)
0.865478 + 0.500947i \(0.167015\pi\)
\(284\) 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 \(0.0153671\pi\)
−0.998835 + 0.0482584i \(0.984633\pi\)
\(294\) 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 0.256823 0.966459i \(-0.417324\pi\)
−0.708566 + 0.705644i \(0.750658\pi\)
\(312\) 0 0
\(313\) 133.123 + 230.576i 0.425313 + 0.736664i 0.996450 0.0841913i \(-0.0268307\pi\)
−0.571137 + 0.820855i \(0.693497\pi\)
\(314\) 0 0
\(315\) −273.451 106.364i −0.868098 0.337662i
\(316\) 0 0
\(317\) 374.864 216.428i 1.18254 0.682737i 0.225936 0.974142i \(-0.427456\pi\)
0.956600 + 0.291405i \(0.0941228\pi\)
\(318\) 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 0.920847 0.389925i \(-0.127499\pi\)
−0.798108 + 0.602514i \(0.794166\pi\)
\(332\) 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 0.496601 + 0.867979i \(0.334581\pi\)
−0.999992 + 0.00392020i \(0.998752\pi\)
\(348\) 0 0
\(349\) 165.836i 0.475174i −0.971366 0.237587i \(-0.923643\pi\)
0.971366 0.237587i \(-0.0763566\pi\)
\(350\) 0 0
\(351\) 1191.15i 3.39358i
\(352\) 0 0
\(353\) 235.858 408.519i 0.668154 1.15728i −0.310266 0.950650i \(-0.600418\pi\)
0.978420 0.206627i \(-0.0662486\pi\)
\(354\) 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 −0.590731 + 0.806869i \(0.701161\pi\)
−0.994134 + 0.108154i \(0.965506\pi\)
\(360\) 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 0.856866 0.515539i \(-0.172408\pi\)
−0.0180371 + 0.999837i \(0.505742\pi\)
\(368\) 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 −0.819767 0.572698i \(-0.805897\pi\)
0.0860872 + 0.996288i \(0.472564\pi\)
\(374\) 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 0.584225 0.811591i \(-0.301398\pi\)
0.994972 0.100158i \(-0.0319349\pi\)
\(384\) 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 0.291935 0.956438i \(-0.405701\pi\)
−0.682332 + 0.731042i \(0.739034\pi\)
\(390\) 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 −0.0163447 0.999866i \(-0.505203\pi\)
0.857737 + 0.514088i \(0.171870\pi\)
\(398\) 0 0
\(399\) 218.772 33.6549i 0.548301 0.0843481i
\(400\) 0 0
\(401\) −263.548 456.479i −0.657228 1.13835i −0.981330 0.192330i \(-0.938396\pi\)
0.324103 0.946022i \(-0.394938\pi\)
\(402\) 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 −0.481756 0.876305i \(-0.660001\pi\)
0.999781 0.0209399i \(-0.00666585\pi\)
\(410\) 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 \(0.0479119\pi\)
−0.988693 + 0.149952i \(0.952088\pi\)
\(422\) 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 0.222303 0.974978i \(-0.428642\pi\)
−0.733204 + 0.680009i \(0.761976\pi\)
\(432\) 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 −0.205546 0.978647i \(-0.565897\pi\)
0.744760 + 0.667332i \(0.232564\pi\)
\(440\) 0 0
\(441\) −701.946 643.415i −1.59171 1.45899i
\(442\) 0 0
\(443\) 237.385 + 411.163i 0.535858 + 0.928133i 0.999121 + 0.0419124i \(0.0133450\pi\)
−0.463263 + 0.886221i \(0.653322\pi\)
\(444\) 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 0.950893 0.309520i \(-0.100168\pi\)
−0.743498 + 0.668738i \(0.766835\pi\)
\(458\) 0 0
\(459\) 25.7811 44.6541i 0.0561679 0.0972857i
\(460\) 0 0
\(461\) 202.533i 0.439335i 0.975575 + 0.219667i \(0.0704972\pi\)
−0.975575 + 0.219667i \(0.929503\pi\)
\(462\) 0 0
\(463\) 652.927i 1.41021i −0.709103 0.705105i \(-0.750900\pi\)
0.709103 0.705105i \(-0.249100\pi\)
\(464\) 0 0
\(465\) −198.420 + 343.674i −0.426710 + 0.739084i
\(466\) 0 0
\(467\) 272.725 + 472.373i 0.583993 + 1.01150i 0.995000 + 0.0998730i \(0.0318437\pi\)
−0.411008 + 0.911632i \(0.634823\pi\)
\(468\) 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 0.595202 0.803576i \(-0.297072\pi\)
−0.398317 + 0.917248i \(0.630405\pi\)
\(480\) 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 0.0670428 0.997750i \(-0.478644\pi\)
−0.830556 + 0.556936i \(0.811977\pi\)
\(488\) 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 0.983305 0.181967i \(-0.0582463\pi\)
−0.649240 + 0.760583i \(0.724913\pi\)
\(500\) 0 0
\(501\) 1115.02 + 643.755i 2.22558 + 1.28494i
\(502\) 0 0
\(503\) 580.170i 1.15342i 0.816949 + 0.576710i \(0.195664\pi\)
−0.816949 + 0.576710i \(0.804336\pi\)
\(504\) 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 −0.738213 0.674568i \(-0.764330\pi\)
0.215087 + 0.976595i \(0.430997\pi\)
\(510\) 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 0.279316 + 0.960199i \(0.409892\pi\)
−0.971215 + 0.238205i \(0.923441\pi\)
\(522\) 0 0
\(523\) −134.988 233.807i −0.258104 0.447049i 0.707630 0.706583i \(-0.249764\pi\)
−0.965734 + 0.259534i \(0.916431\pi\)
\(524\) 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 −0.998612 0.0526734i \(-0.983226\pi\)
−0.453689 + 0.891160i \(0.649892\pi\)
\(542\) 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 0.985598 0.169103i \(-0.0540869\pi\)
0.346352 + 0.938105i \(0.387420\pi\)
\(558\) 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 −0.859883 0.510491i \(-0.829464\pi\)
0.872040 + 0.489435i \(0.162797\pi\)
\(564\) 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 0.723563 + 0.690258i \(0.242503\pi\)
0.235999 + 0.971753i \(0.424164\pi\)
\(570\) 0 0
\(571\) 359.549 622.757i 0.629683 1.09064i −0.357932 0.933747i \(-0.616518\pi\)
0.987615 0.156895i \(-0.0501485\pi\)
\(572\) 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 0.0578905 0.998323i \(-0.481563\pi\)
0.835628 0.549296i \(-0.185104\pi\)
\(578\) 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 0.677308 0.735700i \(-0.263147\pi\)
−0.975789 + 0.218716i \(0.929813\pi\)
\(594\) 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 0.979901 + 0.199484i \(0.0639265\pi\)
0.662708 + 0.748878i \(0.269407\pi\)
\(600\) 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 −0.783438 0.621470i \(-0.786536\pi\)
0.146490 + 0.989212i \(0.453202\pi\)
\(608\) 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 0.879285 0.476296i \(-0.158021\pi\)
0.0271583 + 0.999631i \(0.491354\pi\)
\(614\) 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 −0.636456 0.771313i \(-0.719600\pi\)
0.986205 + 0.165530i \(0.0529336\pi\)
\(620\) 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 \(0.0606373\pi\)
−0.981910 + 0.189348i \(0.939363\pi\)
\(632\) 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 −0.862904 0.505368i \(-0.831357\pi\)
0.869114 + 0.494612i \(0.164690\pi\)
\(642\) 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 0.707541 0.706672i \(-0.249804\pi\)
−0.258225 + 0.966085i \(0.583138\pi\)
\(648\) 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 −0.467476 0.884006i \(-0.654837\pi\)
0.531833 + 0.846849i \(0.321503\pi\)
\(654\) 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 0.935690 0.352823i \(-0.114778\pi\)
0.162291 + 0.986743i \(0.448112\pi\)
\(662\) 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 −0.928437 0.371490i \(-0.878847\pi\)
−0.142499 + 0.989795i \(0.545514\pi\)
\(678\) 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 −0.888648 0.458591i \(-0.848354\pi\)
0.841475 + 0.540296i \(0.181688\pi\)
\(684\) 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 0.610078 0.792341i \(-0.291138\pi\)
−0.991227 + 0.132172i \(0.957805\pi\)
\(692\) 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 \(-0.834777\pi\)
0.868284 0.496067i \(-0.165223\pi\)
\(702\) 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 −0.944640 0.328110i \(-0.893588\pi\)
−0.188168 + 0.982137i \(0.560255\pi\)
\(710\) 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 0.608471 0.793576i \(-0.291783\pi\)
0.991493 0.130163i \(-0.0415501\pi\)
\(720\) 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 \(0.120977\pi\)
−0.928642 + 0.370977i \(0.879023\pi\)
\(728\) 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 −0.737883 0.674929i \(-0.764174\pi\)
0.215564 + 0.976490i \(0.430841\pi\)
\(734\) 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 0.156848 + 0.987623i \(0.449867\pi\)
−0.933730 + 0.357977i \(0.883467\pi\)
\(740\) 0 0
\(741\) 677.050i 0.913698i
\(742\) 0 0
\(743\) 588.688i 0.792313i 0.918183 + 0.396156i \(0.129656\pi\)
−0.918183 + 0.396156i \(0.870344\pi\)
\(744\) 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 −0.891133 0.453742i \(-0.850089\pi\)
−0.0526140 + 0.998615i \(0.516755\pi\)
\(752\) 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 \(0.0221146\pi\)
−0.997588 + 0.0694192i \(0.977885\pi\)
\(758\) 0 0
\(759\) −211.025 121.835i −0.278030 0.160521i
\(760\) 0 0
\(761\) −507.117 878.352i −0.666382 1.15421i −0.978909 0.204299i \(-0.934509\pi\)
0.312527 0.949909i \(-0.398825\pi\)
\(762\) 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 0.307205 0.951643i \(-0.400606\pi\)
−0.670545 + 0.741869i \(0.733940\pi\)
\(774\) 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 −0.768025 0.640420i \(-0.778760\pi\)
0.938632 + 0.344919i \(0.112094\pi\)
\(788\) 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