Properties

Label 324.3.o.a.5.3
Level $324$
Weight $3$
Character 324.5
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
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.o (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 5.3
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.78702 + 1.11018i) q^{3} +(2.99904 - 2.23270i) q^{5} +(-3.97531 + 2.61460i) q^{7} +(6.53498 - 6.18822i) q^{9} +O(q^{10})\) \(q+(-2.78702 + 1.11018i) q^{3} +(2.99904 - 2.23270i) q^{5} +(-3.97531 + 2.61460i) q^{7} +(6.53498 - 6.18822i) q^{9} +(-1.24265 + 10.6316i) q^{11} +(-1.49763 - 5.00242i) q^{13} +(-5.87968 + 9.55208i) q^{15} +(5.51128 + 0.971787i) q^{17} +(1.82736 + 10.3635i) q^{19} +(8.17659 - 11.7003i) q^{21} +(-8.74216 + 13.2918i) q^{23} +(-3.16080 + 10.5578i) q^{25} +(-11.3431 + 24.5017i) q^{27} +(-38.1193 + 35.9637i) q^{29} +(-0.509041 + 8.73990i) q^{31} +(-8.33971 - 31.0100i) q^{33} +(-6.08449 + 16.7170i) q^{35} +(-4.52480 + 1.64689i) q^{37} +(9.72752 + 12.2792i) q^{39} +(-3.69981 + 15.6107i) q^{41} +(21.9847 + 50.9663i) q^{43} +(5.78222 - 33.1494i) q^{45} +(-52.3473 + 3.04888i) q^{47} +(-10.4410 + 24.2049i) q^{49} +(-16.4389 + 3.41014i) q^{51} +(-34.3012 - 19.8038i) q^{53} +(20.0104 + 34.6590i) q^{55} +(-16.5983 - 26.8546i) q^{57} +(-3.82736 - 32.7451i) q^{59} +(85.7037 + 43.0420i) q^{61} +(-9.79885 + 41.6865i) q^{63} +(-15.6604 - 11.6587i) q^{65} +(51.3313 - 54.4080i) q^{67} +(9.60823 - 46.7500i) q^{69} +(20.4870 - 24.4154i) q^{71} +(43.6333 - 36.6127i) q^{73} +(-2.91189 - 32.9339i) q^{75} +(-22.8574 - 45.5129i) q^{77} +(31.4164 - 7.44583i) q^{79} +(4.41193 - 80.8798i) q^{81} +(2.97712 + 12.5614i) q^{83} +(18.6983 - 9.39062i) q^{85} +(66.3129 - 142.551i) q^{87} +(45.6637 + 54.4198i) q^{89} +(19.0329 + 15.9705i) q^{91} +(-8.28419 - 24.9234i) q^{93} +(28.6190 + 27.0006i) q^{95} +(113.983 - 153.105i) q^{97} +(57.6698 + 77.1670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q + O(q^{10}) \) \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{54}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.78702 + 1.11018i −0.929007 + 0.370062i
\(4\) 0 0
\(5\) 2.99904 2.23270i 0.599808 0.446541i −0.253945 0.967219i \(-0.581728\pi\)
0.853753 + 0.520678i \(0.174321\pi\)
\(6\) 0 0
\(7\) −3.97531 + 2.61460i −0.567902 + 0.373515i −0.800750 0.598998i \(-0.795566\pi\)
0.232849 + 0.972513i \(0.425195\pi\)
\(8\) 0 0
\(9\) 6.53498 6.18822i 0.726109 0.687580i
\(10\) 0 0
\(11\) −1.24265 + 10.6316i −0.112968 + 0.966507i 0.811265 + 0.584679i \(0.198779\pi\)
−0.924233 + 0.381828i \(0.875295\pi\)
\(12\) 0 0
\(13\) −1.49763 5.00242i −0.115202 0.384801i 0.880869 0.473360i \(-0.156959\pi\)
−0.996071 + 0.0885588i \(0.971774\pi\)
\(14\) 0 0
\(15\) −5.87968 + 9.55208i −0.391979 + 0.636806i
\(16\) 0 0
\(17\) 5.51128 + 0.971787i 0.324193 + 0.0571639i 0.333376 0.942794i \(-0.391812\pi\)
−0.00918342 + 0.999958i \(0.502923\pi\)
\(18\) 0 0
\(19\) 1.82736 + 10.3635i 0.0961771 + 0.545447i 0.994380 + 0.105867i \(0.0337617\pi\)
−0.898203 + 0.439580i \(0.855127\pi\)
\(20\) 0 0
\(21\) 8.17659 11.7003i 0.389361 0.557157i
\(22\) 0 0
\(23\) −8.74216 + 13.2918i −0.380094 + 0.577905i −0.973977 0.226646i \(-0.927224\pi\)
0.593883 + 0.804551i \(0.297594\pi\)
\(24\) 0 0
\(25\) −3.16080 + 10.5578i −0.126432 + 0.422312i
\(26\) 0 0
\(27\) −11.3431 + 24.5017i −0.420114 + 0.907472i
\(28\) 0 0
\(29\) −38.1193 + 35.9637i −1.31446 + 1.24013i −0.363208 + 0.931708i \(0.618318\pi\)
−0.951251 + 0.308419i \(0.900200\pi\)
\(30\) 0 0
\(31\) −0.509041 + 8.73990i −0.0164207 + 0.281932i 0.980095 + 0.198528i \(0.0636162\pi\)
−0.996516 + 0.0834038i \(0.973421\pi\)
\(32\) 0 0
\(33\) −8.33971 31.0100i −0.252719 0.939697i
\(34\) 0 0
\(35\) −6.08449 + 16.7170i −0.173843 + 0.477629i
\(36\) 0 0
\(37\) −4.52480 + 1.64689i −0.122292 + 0.0445106i −0.402441 0.915446i \(-0.631838\pi\)
0.280149 + 0.959956i \(0.409616\pi\)
\(38\) 0 0
\(39\) 9.72752 + 12.2792i 0.249424 + 0.314851i
\(40\) 0 0
\(41\) −3.69981 + 15.6107i −0.0902392 + 0.380749i −0.999360 0.0357845i \(-0.988607\pi\)
0.909120 + 0.416534i \(0.136755\pi\)
\(42\) 0 0
\(43\) 21.9847 + 50.9663i 0.511273 + 1.18526i 0.956998 + 0.290094i \(0.0936865\pi\)
−0.445726 + 0.895170i \(0.647054\pi\)
\(44\) 0 0
\(45\) 5.78222 33.1494i 0.128494 0.736653i
\(46\) 0 0
\(47\) −52.3473 + 3.04888i −1.11377 + 0.0648699i −0.605144 0.796116i \(-0.706885\pi\)
−0.508629 + 0.860986i \(0.669847\pi\)
\(48\) 0 0
\(49\) −10.4410 + 24.2049i −0.213081 + 0.493977i
\(50\) 0 0
\(51\) −16.4389 + 3.41014i −0.322332 + 0.0668656i
\(52\) 0 0
\(53\) −34.3012 19.8038i −0.647192 0.373656i 0.140188 0.990125i \(-0.455229\pi\)
−0.787379 + 0.616469i \(0.788563\pi\)
\(54\) 0 0
\(55\) 20.0104 + 34.6590i 0.363825 + 0.630164i
\(56\) 0 0
\(57\) −16.5983 26.8546i −0.291198 0.471133i
\(58\) 0 0
\(59\) −3.82736 32.7451i −0.0648704 0.555002i −0.986120 0.166031i \(-0.946905\pi\)
0.921250 0.388971i \(-0.127169\pi\)
\(60\) 0 0
\(61\) 85.7037 + 43.0420i 1.40498 + 0.705606i 0.979889 0.199545i \(-0.0639464\pi\)
0.425089 + 0.905151i \(0.360243\pi\)
\(62\) 0 0
\(63\) −9.79885 + 41.6865i −0.155537 + 0.661690i
\(64\) 0 0
\(65\) −15.6604 11.6587i −0.240929 0.179365i
\(66\) 0 0
\(67\) 51.3313 54.4080i 0.766139 0.812059i −0.220431 0.975403i \(-0.570746\pi\)
0.986569 + 0.163343i \(0.0522278\pi\)
\(68\) 0 0
\(69\) 9.60823 46.7500i 0.139250 0.677536i
\(70\) 0 0
\(71\) 20.4870 24.4154i 0.288549 0.343879i −0.602224 0.798327i \(-0.705719\pi\)
0.890774 + 0.454447i \(0.150163\pi\)
\(72\) 0 0
\(73\) 43.6333 36.6127i 0.597716 0.501544i −0.292994 0.956114i \(-0.594652\pi\)
0.890711 + 0.454571i \(0.150207\pi\)
\(74\) 0 0
\(75\) −2.91189 32.9339i −0.0388253 0.439118i
\(76\) 0 0
\(77\) −22.8574 45.5129i −0.296850 0.591077i
\(78\) 0 0
\(79\) 31.4164 7.44583i 0.397677 0.0942511i −0.0269113 0.999638i \(-0.508567\pi\)
0.424588 + 0.905387i \(0.360419\pi\)
\(80\) 0 0
\(81\) 4.41193 80.8798i 0.0544683 0.998516i
\(82\) 0 0
\(83\) 2.97712 + 12.5614i 0.0358689 + 0.151343i 0.988032 0.154246i \(-0.0492949\pi\)
−0.952164 + 0.305589i \(0.901147\pi\)
\(84\) 0 0
\(85\) 18.6983 9.39062i 0.219979 0.110478i
\(86\) 0 0
\(87\) 66.3129 142.551i 0.762218 1.63852i
\(88\) 0 0
\(89\) 45.6637 + 54.4198i 0.513075 + 0.611459i 0.958929 0.283647i \(-0.0915443\pi\)
−0.445854 + 0.895106i \(0.647100\pi\)
\(90\) 0 0
\(91\) 19.0329 + 15.9705i 0.209152 + 0.175500i
\(92\) 0 0
\(93\) −8.28419 24.9234i −0.0890773 0.267994i
\(94\) 0 0
\(95\) 28.6190 + 27.0006i 0.301252 + 0.284217i
\(96\) 0 0
\(97\) 113.983 153.105i 1.17508 1.57840i 0.444146 0.895954i \(-0.353507\pi\)
0.730932 0.682450i \(-0.239086\pi\)
\(98\) 0 0
\(99\) 57.6698 + 77.1670i 0.582523 + 0.779464i
\(100\) 0 0
\(101\) −8.04628 + 16.0215i −0.0796661 + 0.158628i −0.929939 0.367714i \(-0.880141\pi\)
0.850273 + 0.526342i \(0.176437\pi\)
\(102\) 0 0
\(103\) −105.477 + 12.3285i −1.02405 + 0.119694i −0.611503 0.791242i \(-0.709435\pi\)
−0.412547 + 0.910936i \(0.635361\pi\)
\(104\) 0 0
\(105\) −1.60135 53.3456i −0.0152510 0.508053i
\(106\) 0 0
\(107\) −65.0364 + 37.5488i −0.607817 + 0.350923i −0.772111 0.635488i \(-0.780799\pi\)
0.164294 + 0.986411i \(0.447466\pi\)
\(108\) 0 0
\(109\) −33.1628 + 57.4397i −0.304246 + 0.526970i −0.977093 0.212812i \(-0.931738\pi\)
0.672847 + 0.739782i \(0.265071\pi\)
\(110\) 0 0
\(111\) 10.7824 9.61328i 0.0971383 0.0866062i
\(112\) 0 0
\(113\) −120.171 51.8369i −1.06346 0.458734i −0.208823 0.977953i \(-0.566963\pi\)
−0.854641 + 0.519220i \(0.826223\pi\)
\(114\) 0 0
\(115\) 3.45857 + 59.3814i 0.0300745 + 0.516360i
\(116\) 0 0
\(117\) −40.7430 23.4231i −0.348231 0.200197i
\(118\) 0 0
\(119\) −24.4499 + 10.5466i −0.205461 + 0.0886273i
\(120\) 0 0
\(121\) 6.25217 + 1.48179i 0.0516708 + 0.0122462i
\(122\) 0 0
\(123\) −7.01933 47.6149i −0.0570677 0.387113i
\(124\) 0 0
\(125\) 46.0624 + 126.555i 0.368499 + 1.01244i
\(126\) 0 0
\(127\) −19.7693 7.19543i −0.155664 0.0566569i 0.263013 0.964792i \(-0.415284\pi\)
−0.418677 + 0.908135i \(0.637506\pi\)
\(128\) 0 0
\(129\) −117.854 117.637i −0.913596 0.911916i
\(130\) 0 0
\(131\) −72.3880 4.21612i −0.552580 0.0321841i −0.220416 0.975406i \(-0.570742\pi\)
−0.332164 + 0.943222i \(0.607779\pi\)
\(132\) 0 0
\(133\) −34.3608 36.4203i −0.258352 0.273837i
\(134\) 0 0
\(135\) 20.6868 + 98.8074i 0.153235 + 0.731907i
\(136\) 0 0
\(137\) −127.080 38.0453i −0.927592 0.277703i −0.212845 0.977086i \(-0.568273\pi\)
−0.714747 + 0.699383i \(0.753458\pi\)
\(138\) 0 0
\(139\) −18.1233 11.9199i −0.130383 0.0857545i 0.482642 0.875818i \(-0.339677\pi\)
−0.613025 + 0.790063i \(0.710048\pi\)
\(140\) 0 0
\(141\) 142.508 66.6125i 1.01070 0.472429i
\(142\) 0 0
\(143\) 55.0446 9.70585i 0.384927 0.0678731i
\(144\) 0 0
\(145\) −34.0251 + 192.966i −0.234656 + 1.33080i
\(146\) 0 0
\(147\) 2.22731 79.0508i 0.0151518 0.537761i
\(148\) 0 0
\(149\) 103.319 30.9317i 0.693417 0.207595i 0.0793469 0.996847i \(-0.474717\pi\)
0.614070 + 0.789252i \(0.289531\pi\)
\(150\) 0 0
\(151\) 42.6597 + 4.98621i 0.282515 + 0.0330212i 0.256170 0.966632i \(-0.417539\pi\)
0.0263445 + 0.999653i \(0.491613\pi\)
\(152\) 0 0
\(153\) 42.0297 27.7544i 0.274704 0.181401i
\(154\) 0 0
\(155\) 17.9870 + 27.3478i 0.116045 + 0.176438i
\(156\) 0 0
\(157\) −2.82333 3.79238i −0.0179830 0.0241553i 0.793041 0.609169i \(-0.208497\pi\)
−0.811024 + 0.585013i \(0.801089\pi\)
\(158\) 0 0
\(159\) 117.584 + 17.1130i 0.739522 + 0.107629i
\(160\) 0 0
\(161\) 75.6964i 0.470164i
\(162\) 0 0
\(163\) 215.812 1.32400 0.662001 0.749503i \(-0.269707\pi\)
0.662001 + 0.749503i \(0.269707\pi\)
\(164\) 0 0
\(165\) −94.2473 74.3802i −0.571196 0.450789i
\(166\) 0 0
\(167\) 68.4444 50.9550i 0.409847 0.305120i −0.372419 0.928065i \(-0.621471\pi\)
0.782266 + 0.622945i \(0.214064\pi\)
\(168\) 0 0
\(169\) 118.416 77.8835i 0.700687 0.460849i
\(170\) 0 0
\(171\) 76.0734 + 56.4171i 0.444873 + 0.329925i
\(172\) 0 0
\(173\) −5.63109 + 48.1771i −0.0325497 + 0.278480i 0.967155 + 0.254187i \(0.0818077\pi\)
−0.999705 + 0.0242937i \(0.992266\pi\)
\(174\) 0 0
\(175\) −15.0393 50.2348i −0.0859389 0.287056i
\(176\) 0 0
\(177\) 47.0201 + 87.0123i 0.265650 + 0.491595i
\(178\) 0 0
\(179\) 29.9680 + 5.28417i 0.167419 + 0.0295205i 0.256729 0.966483i \(-0.417355\pi\)
−0.0893101 + 0.996004i \(0.528466\pi\)
\(180\) 0 0
\(181\) 40.4209 + 229.238i 0.223320 + 1.26651i 0.865871 + 0.500267i \(0.166765\pi\)
−0.642552 + 0.766242i \(0.722124\pi\)
\(182\) 0 0
\(183\) −286.643 24.8121i −1.56635 0.135585i
\(184\) 0 0
\(185\) −9.89303 + 15.0416i −0.0534759 + 0.0813061i
\(186\) 0 0
\(187\) −17.1802 + 57.3860i −0.0918729 + 0.306877i
\(188\) 0 0
\(189\) −18.9701 127.060i −0.100371 0.672273i
\(190\) 0 0
\(191\) −153.174 + 144.512i −0.801958 + 0.756608i −0.973529 0.228564i \(-0.926597\pi\)
0.171571 + 0.985172i \(0.445116\pi\)
\(192\) 0 0
\(193\) 18.1666 311.908i 0.0941274 1.61611i −0.539170 0.842197i \(-0.681262\pi\)
0.633297 0.773908i \(-0.281701\pi\)
\(194\) 0 0
\(195\) 56.5891 + 15.1072i 0.290200 + 0.0774727i
\(196\) 0 0
\(197\) −43.7492 + 120.200i −0.222077 + 0.610152i −0.999830 0.0184177i \(-0.994137\pi\)
0.777753 + 0.628570i \(0.216359\pi\)
\(198\) 0 0
\(199\) −359.858 + 130.978i −1.80833 + 0.658179i −0.811010 + 0.585033i \(0.801082\pi\)
−0.997321 + 0.0731461i \(0.976696\pi\)
\(200\) 0 0
\(201\) −82.6585 + 208.623i −0.411236 + 1.03793i
\(202\) 0 0
\(203\) 57.5053 242.634i 0.283277 1.19524i
\(204\) 0 0
\(205\) 23.7582 + 55.0777i 0.115894 + 0.268672i
\(206\) 0 0
\(207\) 25.1228 + 140.960i 0.121366 + 0.680967i
\(208\) 0 0
\(209\) −112.451 + 6.54953i −0.538044 + 0.0313375i
\(210\) 0 0
\(211\) −23.0672 + 53.4759i −0.109323 + 0.253440i −0.964092 0.265570i \(-0.914440\pi\)
0.854768 + 0.519010i \(0.173699\pi\)
\(212\) 0 0
\(213\) −29.9920 + 90.7907i −0.140808 + 0.426247i
\(214\) 0 0
\(215\) 179.726 + 103.765i 0.835934 + 0.482627i
\(216\) 0 0
\(217\) −20.8278 36.0748i −0.0959805 0.166243i
\(218\) 0 0
\(219\) −80.9601 + 150.481i −0.369681 + 0.687130i
\(220\) 0 0
\(221\) −3.39254 29.0251i −0.0153509 0.131335i
\(222\) 0 0
\(223\) −244.819 122.953i −1.09785 0.551359i −0.194773 0.980848i \(-0.562397\pi\)
−0.903072 + 0.429490i \(0.858693\pi\)
\(224\) 0 0
\(225\) 44.6782 + 88.5547i 0.198570 + 0.393576i
\(226\) 0 0
\(227\) 66.7550 + 49.6973i 0.294075 + 0.218931i 0.734077 0.679066i \(-0.237615\pi\)
−0.440002 + 0.897997i \(0.645022\pi\)
\(228\) 0 0
\(229\) −33.2348 + 35.2269i −0.145130 + 0.153829i −0.795861 0.605480i \(-0.792981\pi\)
0.650730 + 0.759309i \(0.274463\pi\)
\(230\) 0 0
\(231\) 114.232 + 101.469i 0.494510 + 0.439262i
\(232\) 0 0
\(233\) −33.2461 + 39.6212i −0.142687 + 0.170048i −0.832655 0.553792i \(-0.813180\pi\)
0.689968 + 0.723840i \(0.257625\pi\)
\(234\) 0 0
\(235\) −150.185 + 126.020i −0.639083 + 0.536255i
\(236\) 0 0
\(237\) −79.2921 + 55.6298i −0.334566 + 0.234725i
\(238\) 0 0
\(239\) −117.132 233.229i −0.490092 0.975854i −0.993716 0.111931i \(-0.964297\pi\)
0.503624 0.863923i \(-0.332000\pi\)
\(240\) 0 0
\(241\) 378.122 89.6165i 1.56897 0.371853i 0.648048 0.761599i \(-0.275585\pi\)
0.920922 + 0.389746i \(0.127437\pi\)
\(242\) 0 0
\(243\) 77.4953 + 230.312i 0.318911 + 0.947785i
\(244\) 0 0
\(245\) 22.7294 + 95.9029i 0.0927731 + 0.391440i
\(246\) 0 0
\(247\) 49.1058 24.6619i 0.198809 0.0998457i
\(248\) 0 0
\(249\) −22.2428 31.7039i −0.0893285 0.127325i
\(250\) 0 0
\(251\) 283.465 + 337.821i 1.12934 + 1.34590i 0.930681 + 0.365831i \(0.119215\pi\)
0.198662 + 0.980068i \(0.436340\pi\)
\(252\) 0 0
\(253\) −130.449 109.460i −0.515611 0.432649i
\(254\) 0 0
\(255\) −41.6871 + 46.9304i −0.163479 + 0.184041i
\(256\) 0 0
\(257\) −5.62529 5.30719i −0.0218883 0.0206505i 0.675220 0.737617i \(-0.264049\pi\)
−0.697108 + 0.716966i \(0.745530\pi\)
\(258\) 0 0
\(259\) 13.6815 18.3775i 0.0528244 0.0709555i
\(260\) 0 0
\(261\) −26.5576 + 470.912i −0.101753 + 1.80426i
\(262\) 0 0
\(263\) 190.163 378.647i 0.723055 1.43972i −0.167982 0.985790i \(-0.553725\pi\)
0.891037 0.453931i \(-0.149979\pi\)
\(264\) 0 0
\(265\) −147.087 + 17.1920i −0.555044 + 0.0648753i
\(266\) 0 0
\(267\) −187.682 100.974i −0.702928 0.378180i
\(268\) 0 0
\(269\) 339.417 195.963i 1.26177 0.728486i 0.288357 0.957523i \(-0.406891\pi\)
0.973418 + 0.229037i \(0.0735578\pi\)
\(270\) 0 0
\(271\) −57.5950 + 99.7574i −0.212528 + 0.368109i −0.952505 0.304523i \(-0.901503\pi\)
0.739977 + 0.672632i \(0.234836\pi\)
\(272\) 0 0
\(273\) −70.7752 23.3801i −0.259250 0.0856412i
\(274\) 0 0
\(275\) −108.318 46.7239i −0.393885 0.169905i
\(276\) 0 0
\(277\) 3.24902 + 55.7835i 0.0117293 + 0.201385i 0.999082 + 0.0428440i \(0.0136418\pi\)
−0.987352 + 0.158541i \(0.949321\pi\)
\(278\) 0 0
\(279\) 50.7578 + 60.2651i 0.181928 + 0.216004i
\(280\) 0 0
\(281\) −392.022 + 169.102i −1.39510 + 0.601786i −0.955119 0.296223i \(-0.904273\pi\)
−0.439977 + 0.898009i \(0.645013\pi\)
\(282\) 0 0
\(283\) −204.478 48.4623i −0.722539 0.171245i −0.147138 0.989116i \(-0.547006\pi\)
−0.575401 + 0.817871i \(0.695154\pi\)
\(284\) 0 0
\(285\) −109.737 43.4789i −0.385043 0.152558i
\(286\) 0 0
\(287\) −26.1079 71.7310i −0.0909684 0.249934i
\(288\) 0 0
\(289\) −242.141 88.1323i −0.837859 0.304956i
\(290\) 0 0
\(291\) −147.697 + 553.249i −0.507550 + 1.90120i
\(292\) 0 0
\(293\) −179.433 10.4508i −0.612398 0.0356681i −0.250857 0.968024i \(-0.580712\pi\)
−0.361541 + 0.932356i \(0.617749\pi\)
\(294\) 0 0
\(295\) −84.5886 89.6586i −0.286741 0.303928i
\(296\) 0 0
\(297\) −246.397 151.042i −0.829618 0.508558i
\(298\) 0 0
\(299\) 79.5837 + 23.8258i 0.266166 + 0.0796849i
\(300\) 0 0
\(301\) −220.653 145.126i −0.733066 0.482145i
\(302\) 0 0
\(303\) 4.63838 53.5850i 0.0153082 0.176848i
\(304\) 0 0
\(305\) 353.129 62.2661i 1.15780 0.204151i
\(306\) 0 0
\(307\) −58.8444 + 333.723i −0.191676 + 1.08705i 0.725398 + 0.688329i \(0.241656\pi\)
−0.917074 + 0.398717i \(0.869455\pi\)
\(308\) 0 0
\(309\) 280.280 151.459i 0.907056 0.490159i
\(310\) 0 0
\(311\) 391.993 117.355i 1.26043 0.377347i 0.414208 0.910182i \(-0.364058\pi\)
0.846219 + 0.532835i \(0.178873\pi\)
\(312\) 0 0
\(313\) 536.791 + 62.7418i 1.71499 + 0.200453i 0.916078 0.401000i \(-0.131337\pi\)
0.798908 + 0.601453i \(0.205411\pi\)
\(314\) 0 0
\(315\) 63.6864 + 146.897i 0.202179 + 0.466341i
\(316\) 0 0
\(317\) 228.446 + 347.335i 0.720649 + 1.09569i 0.991121 + 0.132965i \(0.0424499\pi\)
−0.270472 + 0.962728i \(0.587180\pi\)
\(318\) 0 0
\(319\) −334.982 449.959i −1.05010 1.41053i
\(320\) 0 0
\(321\) 139.572 176.852i 0.434803 0.550940i
\(322\) 0 0
\(323\) 58.8919i 0.182328i
\(324\) 0 0
\(325\) 57.5482 0.177071
\(326\) 0 0
\(327\) 28.6568 196.903i 0.0876356 0.602148i
\(328\) 0 0
\(329\) 200.125 148.988i 0.608284 0.452851i
\(330\) 0 0
\(331\) −24.3183 + 15.9944i −0.0734692 + 0.0483215i −0.585712 0.810519i \(-0.699185\pi\)
0.512243 + 0.858841i \(0.328815\pi\)
\(332\) 0 0
\(333\) −19.3781 + 38.7628i −0.0581926 + 0.116405i
\(334\) 0 0
\(335\) 32.4677 277.779i 0.0969186 0.829192i
\(336\) 0 0
\(337\) −31.2668 104.438i −0.0927798 0.309906i 0.898985 0.437980i \(-0.144306\pi\)
−0.991765 + 0.128074i \(0.959121\pi\)
\(338\) 0 0
\(339\) 392.469 + 11.0581i 1.15773 + 0.0326197i
\(340\) 0 0
\(341\) −92.2863 16.2726i −0.270634 0.0477201i
\(342\) 0 0
\(343\) −62.2654 353.124i −0.181532 1.02952i
\(344\) 0 0
\(345\) −75.5634 161.657i −0.219024 0.468572i
\(346\) 0 0
\(347\) 177.792 270.320i 0.512369 0.779019i −0.482952 0.875647i \(-0.660435\pi\)
0.995321 + 0.0966281i \(0.0308058\pi\)
\(348\) 0 0
\(349\) −130.884 + 437.183i −0.375026 + 1.25267i 0.537364 + 0.843351i \(0.319420\pi\)
−0.912390 + 0.409323i \(0.865765\pi\)
\(350\) 0 0
\(351\) 139.556 + 20.0483i 0.397594 + 0.0571178i
\(352\) 0 0
\(353\) −285.540 + 269.393i −0.808895 + 0.763153i −0.974822 0.222985i \(-0.928420\pi\)
0.165927 + 0.986138i \(0.446938\pi\)
\(354\) 0 0
\(355\) 6.92888 118.964i 0.0195180 0.335111i
\(356\) 0 0
\(357\) 56.4336 56.5376i 0.158077 0.158369i
\(358\) 0 0
\(359\) 56.7575 155.940i 0.158099 0.434373i −0.835200 0.549946i \(-0.814648\pi\)
0.993299 + 0.115573i \(0.0368704\pi\)
\(360\) 0 0
\(361\) 235.166 85.5935i 0.651430 0.237101i
\(362\) 0 0
\(363\) −19.0700 + 2.81128i −0.0525344 + 0.00774457i
\(364\) 0 0
\(365\) 49.1128 207.223i 0.134556 0.567735i
\(366\) 0 0
\(367\) −153.014 354.727i −0.416933 0.966559i −0.989211 0.146499i \(-0.953199\pi\)
0.572278 0.820060i \(-0.306060\pi\)
\(368\) 0 0
\(369\) 72.4243 + 124.911i 0.196272 + 0.338512i
\(370\) 0 0
\(371\) 188.137 10.9577i 0.507108 0.0295356i
\(372\) 0 0
\(373\) 37.3278 86.5355i 0.100074 0.231999i −0.860822 0.508906i \(-0.830050\pi\)
0.960897 + 0.276907i \(0.0893094\pi\)
\(374\) 0 0
\(375\) −268.877 301.575i −0.717004 0.804199i
\(376\) 0 0
\(377\) 236.994 + 136.828i 0.628631 + 0.362940i
\(378\) 0 0
\(379\) −200.722 347.660i −0.529609 0.917309i −0.999404 0.0345335i \(-0.989005\pi\)
0.469795 0.882776i \(-0.344328\pi\)
\(380\) 0 0
\(381\) 63.0856 1.89373i 0.165579 0.00497043i
\(382\) 0 0
\(383\) −61.1247 522.955i −0.159594 1.36542i −0.801206 0.598388i \(-0.795808\pi\)
0.641612 0.767029i \(-0.278266\pi\)
\(384\) 0 0
\(385\) −170.167 85.4612i −0.441993 0.221977i
\(386\) 0 0
\(387\) 459.060 + 197.018i 1.18620 + 0.509089i
\(388\) 0 0
\(389\) −444.345 330.802i −1.14227 0.850392i −0.151844 0.988404i \(-0.548521\pi\)
−0.990431 + 0.138012i \(0.955929\pi\)
\(390\) 0 0
\(391\) −61.0973 + 64.7593i −0.156259 + 0.165625i
\(392\) 0 0
\(393\) 206.427 68.6136i 0.525261 0.174589i
\(394\) 0 0
\(395\) 77.5949 92.4740i 0.196443 0.234111i
\(396\) 0 0
\(397\) 76.8496 64.4845i 0.193576 0.162429i −0.540848 0.841120i \(-0.681897\pi\)
0.734424 + 0.678691i \(0.237452\pi\)
\(398\) 0 0
\(399\) 136.198 + 63.3574i 0.341347 + 0.158790i
\(400\) 0 0
\(401\) 188.161 + 374.660i 0.469230 + 0.934314i 0.996418 + 0.0845650i \(0.0269501\pi\)
−0.527188 + 0.849749i \(0.676754\pi\)
\(402\) 0 0
\(403\) 44.4830 10.5427i 0.110380 0.0261604i
\(404\) 0 0
\(405\) −167.349 252.412i −0.413207 0.623240i
\(406\) 0 0
\(407\) −11.8863 50.1523i −0.0292047 0.123224i
\(408\) 0 0
\(409\) 135.074 67.8368i 0.330255 0.165860i −0.275943 0.961174i \(-0.588990\pi\)
0.606198 + 0.795314i \(0.292694\pi\)
\(410\) 0 0
\(411\) 396.412 35.0493i 0.964506 0.0852782i
\(412\) 0 0
\(413\) 100.830 + 120.165i 0.244142 + 0.290957i
\(414\) 0 0
\(415\) 36.9745 + 31.0253i 0.0890951 + 0.0747597i
\(416\) 0 0
\(417\) 63.7433 + 13.1008i 0.152862 + 0.0314167i
\(418\) 0 0
\(419\) 367.334 + 346.562i 0.876693 + 0.827117i 0.985975 0.166894i \(-0.0533736\pi\)
−0.109282 + 0.994011i \(0.534855\pi\)
\(420\) 0 0
\(421\) 295.389 396.776i 0.701636 0.942461i −0.298292 0.954475i \(-0.596417\pi\)
0.999928 + 0.0120140i \(0.00382426\pi\)
\(422\) 0 0
\(423\) −323.222 + 343.861i −0.764117 + 0.812910i
\(424\) 0 0
\(425\) −27.6800 + 55.1153i −0.0651293 + 0.129683i
\(426\) 0 0
\(427\) −453.237 + 52.9758i −1.06144 + 0.124065i
\(428\) 0 0
\(429\) −142.635 + 88.1601i −0.332483 + 0.205501i
\(430\) 0 0
\(431\) 335.198 193.527i 0.777721 0.449017i −0.0579010 0.998322i \(-0.518441\pi\)
0.835622 + 0.549305i \(0.185107\pi\)
\(432\) 0 0
\(433\) −224.531 + 388.900i −0.518548 + 0.898152i 0.481220 + 0.876600i \(0.340194\pi\)
−0.999768 + 0.0215515i \(0.993139\pi\)
\(434\) 0 0
\(435\) −119.399 575.574i −0.274480 1.32316i
\(436\) 0 0
\(437\) −153.725 66.3104i −0.351773 0.151740i
\(438\) 0 0
\(439\) −34.2243 587.609i −0.0779597 1.33852i −0.779731 0.626115i \(-0.784644\pi\)
0.701771 0.712402i \(-0.252393\pi\)
\(440\) 0 0
\(441\) 81.5535 + 222.789i 0.184928 + 0.505191i
\(442\) 0 0
\(443\) −258.524 + 111.516i −0.583576 + 0.251730i −0.667337 0.744756i \(-0.732566\pi\)
0.0837614 + 0.996486i \(0.473307\pi\)
\(444\) 0 0
\(445\) 258.451 + 61.2539i 0.580788 + 0.137649i
\(446\) 0 0
\(447\) −253.613 + 200.911i −0.567366 + 0.449464i
\(448\) 0 0
\(449\) −50.6783 139.238i −0.112869 0.310106i 0.870377 0.492385i \(-0.163875\pi\)
−0.983247 + 0.182279i \(0.941653\pi\)
\(450\) 0 0
\(451\) −161.369 58.7335i −0.357802 0.130229i
\(452\) 0 0
\(453\) −124.429 + 33.4635i −0.274678 + 0.0738709i
\(454\) 0 0
\(455\) 92.7377 + 5.40136i 0.203819 + 0.0118711i
\(456\) 0 0
\(457\) 558.475 + 591.948i 1.22204 + 1.29529i 0.942122 + 0.335269i \(0.108827\pi\)
0.279923 + 0.960023i \(0.409691\pi\)
\(458\) 0 0
\(459\) −86.3252 + 124.013i −0.188072 + 0.270180i
\(460\) 0 0
\(461\) 668.129 + 200.025i 1.44930 + 0.433893i 0.912243 0.409650i \(-0.134349\pi\)
0.537062 + 0.843543i \(0.319534\pi\)
\(462\) 0 0
\(463\) −313.179 205.981i −0.676412 0.444883i 0.164268 0.986416i \(-0.447474\pi\)
−0.840680 + 0.541533i \(0.817844\pi\)
\(464\) 0 0
\(465\) −80.4912 56.2502i −0.173099 0.120968i
\(466\) 0 0
\(467\) −180.965 + 31.9091i −0.387506 + 0.0683278i −0.364007 0.931396i \(-0.618592\pi\)
−0.0234987 + 0.999724i \(0.507481\pi\)
\(468\) 0 0
\(469\) −61.8026 + 350.500i −0.131775 + 0.747334i
\(470\) 0 0
\(471\) 12.0789 + 7.43504i 0.0256453 + 0.0157857i
\(472\) 0 0
\(473\) −569.172 + 170.399i −1.20332 + 0.360251i
\(474\) 0 0
\(475\) −115.192 13.4640i −0.242509 0.0283452i
\(476\) 0 0
\(477\) −346.708 + 82.8457i −0.726850 + 0.173681i
\(478\) 0 0
\(479\) −287.426 437.010i −0.600054 0.912338i 0.399937 0.916543i \(-0.369032\pi\)
−0.999991 + 0.00420485i \(0.998662\pi\)
\(480\) 0 0
\(481\) 15.0149 + 20.1685i 0.0312160 + 0.0419304i
\(482\) 0 0
\(483\) 84.0370 + 210.968i 0.173990 + 0.436786i
\(484\) 0 0
\(485\) 713.658i 1.47146i
\(486\) 0 0
\(487\) 868.356 1.78307 0.891536 0.452949i \(-0.149628\pi\)
0.891536 + 0.452949i \(0.149628\pi\)
\(488\) 0 0
\(489\) −601.474 + 239.592i −1.23001 + 0.489962i
\(490\) 0 0
\(491\) 584.290 434.987i 1.19000 0.885922i 0.194520 0.980899i \(-0.437685\pi\)
0.995479 + 0.0949771i \(0.0302778\pi\)
\(492\) 0 0
\(493\) −245.035 + 161.162i −0.497028 + 0.326901i
\(494\) 0 0
\(495\) 345.245 + 102.667i 0.697465 + 0.207409i
\(496\) 0 0
\(497\) −17.6055 + 150.624i −0.0354235 + 0.303067i
\(498\) 0 0
\(499\) 168.979 + 564.429i 0.338635 + 1.13112i 0.942548 + 0.334070i \(0.108422\pi\)
−0.603913 + 0.797050i \(0.706393\pi\)
\(500\) 0 0
\(501\) −134.187 + 217.999i −0.267838 + 0.435127i
\(502\) 0 0
\(503\) −461.070 81.2990i −0.916640 0.161628i −0.304623 0.952473i \(-0.598530\pi\)
−0.612017 + 0.790845i \(0.709642\pi\)
\(504\) 0 0
\(505\) 11.6400 + 66.0140i 0.0230496 + 0.130721i
\(506\) 0 0
\(507\) −243.563 + 348.527i −0.480401 + 0.687430i
\(508\) 0 0
\(509\) −216.585 + 329.301i −0.425510 + 0.646956i −0.983081 0.183173i \(-0.941363\pi\)
0.557571 + 0.830129i \(0.311734\pi\)
\(510\) 0 0
\(511\) −77.7283 + 259.631i −0.152110 + 0.508084i
\(512\) 0 0
\(513\) −274.652 72.7803i −0.535383 0.141872i
\(514\) 0 0
\(515\) −288.805 + 272.473i −0.560786 + 0.529074i
\(516\) 0 0
\(517\) 32.6351 560.323i 0.0631240 1.08380i
\(518\) 0 0
\(519\) −37.7915 140.522i −0.0728160 0.270756i
\(520\) 0 0
\(521\) −220.120 + 604.775i −0.422496 + 1.16080i 0.527778 + 0.849382i \(0.323025\pi\)
−0.950274 + 0.311415i \(0.899197\pi\)
\(522\) 0 0
\(523\) 129.725 47.2159i 0.248040 0.0902790i −0.215009 0.976612i \(-0.568978\pi\)
0.463048 + 0.886333i \(0.346756\pi\)
\(524\) 0 0
\(525\) 97.6847 + 123.309i 0.186066 + 0.234874i
\(526\) 0 0
\(527\) −11.2988 + 47.6733i −0.0214398 + 0.0904617i
\(528\) 0 0
\(529\) 109.279 + 253.338i 0.206577 + 0.478900i
\(530\) 0 0
\(531\) −227.646 190.304i −0.428711 0.358388i
\(532\) 0 0
\(533\) 83.6322 4.87102i 0.156908 0.00913888i
\(534\) 0 0
\(535\) −111.212 + 257.817i −0.207872 + 0.481902i
\(536\) 0 0
\(537\) −89.3880 + 18.5430i −0.166458 + 0.0345306i
\(538\) 0 0
\(539\) −244.361 141.082i −0.453360 0.261748i
\(540\) 0 0
\(541\) 290.221 + 502.678i 0.536453 + 0.929164i 0.999091 + 0.0426171i \(0.0135695\pi\)
−0.462638 + 0.886547i \(0.653097\pi\)
\(542\) 0 0
\(543\) −367.150 594.017i −0.676152 1.09395i
\(544\) 0 0
\(545\) 28.7891 + 246.307i 0.0528241 + 0.451939i
\(546\) 0 0
\(547\) −230.863 115.944i −0.422054 0.211963i 0.225079 0.974340i \(-0.427736\pi\)
−0.647133 + 0.762377i \(0.724032\pi\)
\(548\) 0 0
\(549\) 826.425 249.074i 1.50533 0.453687i
\(550\) 0 0
\(551\) −442.367 329.330i −0.802845 0.597696i
\(552\) 0 0
\(553\) −105.422 + 111.741i −0.190637 + 0.202063i
\(554\) 0 0
\(555\) 10.8731 52.9044i 0.0195912 0.0953233i
\(556\) 0 0
\(557\) −530.543 + 632.276i −0.952501 + 1.13515i 0.0382252 + 0.999269i \(0.487830\pi\)
−0.990726 + 0.135877i \(0.956615\pi\)
\(558\) 0 0
\(559\) 222.030 186.305i 0.397191 0.333283i
\(560\) 0 0
\(561\) −15.8273 179.009i −0.0282127 0.319089i
\(562\) 0 0
\(563\) 400.146 + 796.756i 0.710739 + 1.41520i 0.901156 + 0.433494i \(0.142720\pi\)
−0.190417 + 0.981703i \(0.560984\pi\)
\(564\) 0 0
\(565\) −476.135 + 112.846i −0.842718 + 0.199728i
\(566\) 0 0
\(567\) 193.930 + 333.058i 0.342028 + 0.587403i
\(568\) 0 0
\(569\) 226.456 + 955.491i 0.397989 + 1.67925i 0.690776 + 0.723069i \(0.257269\pi\)
−0.292787 + 0.956178i \(0.594583\pi\)
\(570\) 0 0
\(571\) 64.1225 32.2035i 0.112299 0.0563985i −0.391763 0.920066i \(-0.628135\pi\)
0.504062 + 0.863668i \(0.331838\pi\)
\(572\) 0 0
\(573\) 266.464 572.810i 0.465033 0.999668i
\(574\) 0 0
\(575\) −112.700 134.311i −0.196000 0.233584i
\(576\) 0 0
\(577\) 303.996 + 255.083i 0.526856 + 0.442085i 0.867014 0.498283i \(-0.166036\pi\)
−0.340158 + 0.940368i \(0.610481\pi\)
\(578\) 0 0
\(579\) 295.645 + 889.464i 0.510613 + 1.53621i
\(580\) 0 0
\(581\) −44.6782 42.1517i −0.0768987 0.0725502i
\(582\) 0 0
\(583\) 253.170 340.066i 0.434254 0.583304i
\(584\) 0 0
\(585\) −174.487 + 20.7203i −0.298268 + 0.0354193i
\(586\) 0 0
\(587\) 184.790 367.947i 0.314804 0.626827i −0.679468 0.733705i \(-0.737789\pi\)
0.994272 + 0.106878i \(0.0340856\pi\)
\(588\) 0 0
\(589\) −91.5061 + 10.6955i −0.155358 + 0.0181588i
\(590\) 0 0
\(591\) −11.5142 383.570i −0.0194825 0.649018i
\(592\) 0 0
\(593\) 98.1896 56.6898i 0.165581 0.0955983i −0.414919 0.909858i \(-0.636190\pi\)
0.580501 + 0.814260i \(0.302857\pi\)
\(594\) 0 0
\(595\) −49.7787 + 86.2192i −0.0836616 + 0.144906i
\(596\) 0 0
\(597\) 857.522 764.546i 1.43639 1.28065i
\(598\) 0 0
\(599\) −767.126 330.906i −1.28068 0.552430i −0.356465 0.934309i \(-0.616018\pi\)
−0.924213 + 0.381878i \(0.875277\pi\)
\(600\) 0 0
\(601\) −5.42209 93.0937i −0.00902178 0.154898i −0.999810 0.0194794i \(-0.993799\pi\)
0.990788 0.135419i \(-0.0432379\pi\)
\(602\) 0 0
\(603\) −1.23951 673.204i −0.00205557 1.11642i
\(604\) 0 0
\(605\) 22.0589 9.51529i 0.0364610 0.0157278i
\(606\) 0 0
\(607\) 1072.66 + 254.225i 1.76715 + 0.418822i 0.980170 0.198160i \(-0.0634966\pi\)
0.786978 + 0.616982i \(0.211645\pi\)
\(608\) 0 0
\(609\) 109.100 + 740.067i 0.179146 + 1.21522i
\(610\) 0 0
\(611\) 93.6485 + 257.297i 0.153271 + 0.421108i
\(612\) 0 0
\(613\) −1040.43 378.687i −1.69728 0.617760i −0.701770 0.712404i \(-0.747606\pi\)
−0.995511 + 0.0946443i \(0.969829\pi\)
\(614\) 0 0
\(615\) −127.361 127.127i −0.207091 0.206710i
\(616\) 0 0
\(617\) −963.879 56.1395i −1.56220 0.0909879i −0.744892 0.667185i \(-0.767499\pi\)
−0.817311 + 0.576197i \(0.804536\pi\)
\(618\) 0 0
\(619\) 620.422 + 657.609i 1.00230 + 1.06237i 0.998052 + 0.0623821i \(0.0198697\pi\)
0.00424496 + 0.999991i \(0.498649\pi\)
\(620\) 0 0
\(621\) −226.509 364.968i −0.364750 0.587710i
\(622\) 0 0
\(623\) −323.814 96.9435i −0.519765 0.155607i
\(624\) 0 0
\(625\) 190.510 + 125.300i 0.304816 + 0.200481i
\(626\) 0 0
\(627\) 306.132 143.095i 0.488250 0.228222i
\(628\) 0 0
\(629\) −26.5378 + 4.67934i −0.0421905 + 0.00743933i
\(630\) 0 0
\(631\) −86.6647 + 491.500i −0.137345 + 0.778922i 0.835853 + 0.548953i \(0.184974\pi\)
−0.973198 + 0.229969i \(0.926138\pi\)
\(632\) 0 0
\(633\) 4.92080 174.647i 0.00777378 0.275904i
\(634\) 0 0
\(635\) −75.3541 + 22.5595i −0.118668 + 0.0355268i
\(636\) 0 0
\(637\) 136.719 + 15.9802i 0.214630 + 0.0250867i
\(638\) 0 0
\(639\) −17.2060 286.332i −0.0269265 0.448094i
\(640\) 0 0
\(641\) 458.241 + 696.721i 0.714884 + 1.08693i 0.992018 + 0.126097i \(0.0402451\pi\)
−0.277134 + 0.960831i \(0.589384\pi\)
\(642\) 0 0
\(643\) 206.304 + 277.114i 0.320846 + 0.430971i 0.933060 0.359721i \(-0.117128\pi\)
−0.612214 + 0.790692i \(0.709721\pi\)
\(644\) 0 0
\(645\) −616.098 89.6658i −0.955190 0.139017i
\(646\) 0 0
\(647\) 564.348i 0.872253i 0.899885 + 0.436127i \(0.143650\pi\)
−0.899885 + 0.436127i \(0.856350\pi\)
\(648\) 0 0
\(649\) 352.888 0.543742
\(650\) 0 0
\(651\) 98.0971 + 77.4185i 0.150687 + 0.118922i
\(652\) 0 0
\(653\) −43.5742 + 32.4398i −0.0667292 + 0.0496780i −0.630006 0.776590i \(-0.716948\pi\)
0.563277 + 0.826268i \(0.309540\pi\)
\(654\) 0 0
\(655\) −226.508 + 148.977i −0.345814 + 0.227445i
\(656\) 0 0
\(657\) 58.5755 509.276i 0.0891560 0.775153i
\(658\) 0 0
\(659\) 110.969 949.397i 0.168389 1.44066i −0.599651 0.800262i \(-0.704694\pi\)
0.768040 0.640401i \(-0.221232\pi\)
\(660\) 0 0
\(661\) 178.937 + 597.692i 0.270707 + 0.904223i 0.979947 + 0.199257i \(0.0638528\pi\)
−0.709241 + 0.704966i \(0.750962\pi\)
\(662\) 0 0
\(663\) 41.6783 + 77.1272i 0.0628632 + 0.116331i
\(664\) 0 0
\(665\) −184.365 32.5086i −0.277241 0.0488850i
\(666\) 0 0
\(667\) −144.778 821.075i −0.217058 1.23100i
\(668\) 0 0
\(669\) 818.818 + 70.8778i 1.22394 + 0.105946i
\(670\) 0 0
\(671\) −564.104 + 857.679i −0.840692 + 1.27821i
\(672\) 0 0
\(673\) 39.4371 131.729i 0.0585989 0.195734i −0.923678 0.383170i \(-0.874832\pi\)
0.982277 + 0.187436i \(0.0600176\pi\)
\(674\) 0 0
\(675\) −222.831 197.203i −0.330120 0.292152i
\(676\) 0 0
\(677\) 435.742 411.101i 0.643637 0.607240i −0.293602 0.955928i \(-0.594854\pi\)
0.937239 + 0.348688i \(0.113373\pi\)
\(678\) 0 0
\(679\) −52.8070 + 906.661i −0.0777717 + 1.33529i
\(680\) 0 0
\(681\) −241.221 64.3970i −0.354216 0.0945623i
\(682\) 0 0
\(683\) −164.403 + 451.692i −0.240706 + 0.661336i 0.759238 + 0.650813i \(0.225572\pi\)
−0.999945 + 0.0105227i \(0.996650\pi\)
\(684\) 0 0
\(685\) −466.062 + 169.633i −0.680383 + 0.247639i
\(686\) 0 0
\(687\) 53.5179 135.075i 0.0779009 0.196616i
\(688\) 0 0
\(689\) −47.6965 + 201.247i −0.0692257 + 0.292086i
\(690\) 0 0
\(691\) 63.6440 + 147.543i 0.0921041 + 0.213521i 0.958041 0.286633i \(-0.0925359\pi\)
−0.865936 + 0.500154i \(0.833277\pi\)
\(692\) 0 0
\(693\) −431.017 155.979i −0.621957 0.225078i
\(694\) 0 0
\(695\) −80.9660 + 4.71573i −0.116498 + 0.00678523i
\(696\) 0 0
\(697\) −35.5609 + 82.4395i −0.0510200 + 0.118278i
\(698\) 0 0
\(699\) 48.6708 147.334i 0.0696292 0.210779i
\(700\) 0 0
\(701\) −214.085 123.602i −0.305400 0.176323i 0.339466 0.940618i \(-0.389754\pi\)
−0.644866 + 0.764295i \(0.723087\pi\)
\(702\) 0 0
\(703\) −25.3360 43.8833i −0.0360398 0.0624228i
\(704\) 0 0
\(705\) 278.662 517.953i 0.395266 0.734684i
\(706\) 0 0
\(707\) −9.90330 84.7281i −0.0140075 0.119842i
\(708\) 0 0
\(709\) −140.524 70.5738i −0.198200 0.0995399i 0.346931 0.937891i \(-0.387224\pi\)
−0.545131 + 0.838351i \(0.683520\pi\)
\(710\) 0 0
\(711\) 159.229 243.070i 0.223951 0.341871i
\(712\) 0 0
\(713\) −111.719 83.1717i −0.156689 0.116650i
\(714\) 0 0
\(715\) 143.411 152.007i 0.200575 0.212597i
\(716\) 0 0
\(717\) 585.377 + 519.976i 0.816425 + 0.725211i
\(718\) 0 0
\(719\) −660.354 + 786.979i −0.918434 + 1.09455i 0.0768017 + 0.997046i \(0.475529\pi\)
−0.995235 + 0.0975004i \(0.968915\pi\)
\(720\) 0 0
\(721\) 387.071 324.791i 0.536852 0.450473i
\(722\) 0 0
\(723\) −954.343 + 669.548i −1.31998 + 0.926070i
\(724\) 0 0
\(725\) −259.210 516.130i −0.357531 0.711903i
\(726\) 0 0
\(727\) −794.499 + 188.300i −1.09285 + 0.259009i −0.737243 0.675628i \(-0.763873\pi\)
−0.355603 + 0.934637i \(0.615724\pi\)
\(728\) 0 0
\(729\) −471.670 555.850i −0.647009 0.762482i
\(730\) 0 0
\(731\) 71.6355 + 302.254i 0.0979966 + 0.413480i
\(732\) 0 0
\(733\) 644.074 323.466i 0.878682 0.441291i 0.0485263 0.998822i \(-0.484548\pi\)
0.830156 + 0.557531i \(0.188251\pi\)
\(734\) 0 0
\(735\) −169.817 242.050i −0.231044 0.329319i
\(736\) 0 0
\(737\) 514.656 + 613.343i 0.698312 + 0.832215i
\(738\) 0 0
\(739\) −1.82552 1.53179i −0.00247025 0.00207279i 0.641552 0.767080i \(-0.278291\pi\)
−0.644022 + 0.765007i \(0.722735\pi\)
\(740\) 0 0
\(741\) −109.480 + 123.250i −0.147746 + 0.166329i
\(742\) 0 0
\(743\) 905.837 + 854.613i 1.21916 + 1.15022i 0.983982 + 0.178267i \(0.0570490\pi\)
0.235179 + 0.971952i \(0.424432\pi\)
\(744\) 0 0
\(745\) 240.797 323.446i 0.323217 0.434156i
\(746\) 0 0
\(747\) 97.1883 + 63.6657i 0.130105 + 0.0852286i
\(748\) 0 0
\(749\) 160.365 319.313i 0.214105 0.426319i
\(750\) 0 0
\(751\) 22.2978 2.60624i 0.0296909 0.00347037i −0.101235 0.994863i \(-0.532279\pi\)
0.130925 + 0.991392i \(0.458205\pi\)
\(752\) 0 0
\(753\) −1165.07 626.815i −1.54723 0.832423i
\(754\) 0 0
\(755\) 139.071 80.2927i 0.184200 0.106348i
\(756\) 0 0
\(757\) 100.399 173.896i 0.132627 0.229717i −0.792061 0.610441i \(-0.790992\pi\)
0.924688 + 0.380725i \(0.124325\pi\)
\(758\) 0 0
\(759\) 485.086 + 160.245i 0.639113 + 0.211126i
\(760\) 0 0
\(761\) −1163.54 501.904i −1.52897 0.659532i −0.545090 0.838378i \(-0.683505\pi\)
−0.983877 + 0.178846i \(0.942764\pi\)
\(762\) 0 0
\(763\) −18.3495 315.048i −0.0240491 0.412908i
\(764\) 0 0
\(765\) 64.0816 177.076i 0.0837667 0.231472i
\(766\) 0 0
\(767\) −158.073 + 68.1860i −0.206092 + 0.0888996i
\(768\) 0 0
\(769\) 1010.19 + 239.420i 1.31365 + 0.311340i 0.826971 0.562244i \(-0.190062\pi\)
0.486674 + 0.873584i \(0.338210\pi\)
\(770\) 0 0
\(771\) 21.5698 + 8.54614i 0.0279764 + 0.0110845i
\(772\) 0 0
\(773\) −443.535 1218.60i −0.573785 1.57646i −0.798474 0.602030i \(-0.794359\pi\)
0.224689 0.974430i \(-0.427863\pi\)
\(774\) 0 0
\(775\) −90.6651 32.9994i −0.116987 0.0425799i
\(776\) 0 0
\(777\) −17.7283 + 66.4074i −0.0228163 + 0.0854664i
\(778\) 0 0
\(779\) −168.542 9.81648i −0.216357 0.0126014i
\(780\) 0 0
\(781\) 234.116 + 248.149i 0.299765 + 0.317732i
\(782\) 0 0
\(783\) −448.783 1341.93i −0.573158 1.71383i
\(784\) 0 0
\(785\) −16.9345 5.06987i −0.0215727 0.00645843i
\(786\) 0 0
\(787\) 318.724 + 209.628i 0.404986 + 0.266363i 0.735618 0.677396i \(-0.236892\pi\)
−0.330633 + 0.943760i \(0.607262\pi\)
\(788\) 0 0
\(789\) −109.622 + 1266.41i −0.138938 + 1.60509i
\(790\) 0 0
\(791\) 613.252 108.133i 0.775287 0.136704i
\(792\) 0 0
\(793\) 86.9620 493.186i 0.109662 0.621925i
\(794\) 0 0
\(795\) 390.847 211.208i 0.491632 0.265670i