Properties

Label 819.2.do.e.361.2
Level $819$
Weight $2$
Character 819.361
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.do (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.2
Root \(0.874681 + 1.11128i\) of defining polynomial
Character \(\chi\) \(=\) 819.361
Dual form 819.2.do.e.667.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.16500 - 0.672613i) q^{2} +(-0.0951832 - 0.164862i) q^{4} +(3.08979 - 1.78389i) q^{5} +(-2.09638 - 1.61406i) q^{7} +2.94654i q^{8} +O(q^{10})\) \(q+(-1.16500 - 0.672613i) q^{2} +(-0.0951832 - 0.164862i) q^{4} +(3.08979 - 1.78389i) q^{5} +(-2.09638 - 1.61406i) q^{7} +2.94654i q^{8} -4.79947 q^{10} -1.27867i q^{11} +(3.57420 - 0.474474i) q^{13} +(1.35664 + 3.29043i) q^{14} +(1.79151 - 3.10299i) q^{16} +(-3.86960 - 6.70234i) q^{17} +0.943878i q^{19} +(-0.588191 - 0.339592i) q^{20} +(-0.860052 + 1.48965i) q^{22} +(-0.823637 + 1.42658i) q^{23} +(3.86451 - 6.69354i) q^{25} +(-4.48308 - 1.85129i) q^{26} +(-0.0665578 + 0.499245i) q^{28} +(2.02242 + 3.50293i) q^{29} +(-4.46193 - 2.57610i) q^{31} +(0.929326 - 0.536547i) q^{32} +10.4110i q^{34} +(-9.35667 - 1.24740i) q^{35} +(0.914594 + 0.528041i) q^{37} +(0.634865 - 1.09962i) q^{38} +(5.25629 + 9.10417i) q^{40} +(3.63629 - 2.09941i) q^{41} +(1.91532 - 3.31744i) q^{43} +(-0.210805 + 0.121708i) q^{44} +(1.91908 - 1.10798i) q^{46} +(0.774415 - 0.447109i) q^{47} +(1.78961 + 6.76737i) q^{49} +(-9.00432 + 5.19865i) q^{50} +(-0.418426 - 0.544088i) q^{52} +(-0.0399961 + 0.0692754i) q^{53} +(-2.28101 - 3.95082i) q^{55} +(4.75590 - 6.17706i) q^{56} -5.44122i q^{58} +(-9.68627 + 5.59237i) q^{59} -7.62392 q^{61} +(3.46543 + 6.00231i) q^{62} -8.60961 q^{64} +(10.1971 - 7.84199i) q^{65} -6.32103i q^{67} +(-0.736641 + 1.27590i) q^{68} +(10.0615 + 7.74664i) q^{70} +(-9.89346 - 5.71199i) q^{71} +(-0.658617 - 0.380253i) q^{73} +(-0.710335 - 1.23034i) q^{74} +(0.155610 - 0.0898413i) q^{76} +(-2.06386 + 2.68058i) q^{77} +(1.42765 + 2.47277i) q^{79} -12.7834i q^{80} -5.64837 q^{82} -2.32483i q^{83} +(-23.9125 - 13.8059i) q^{85} +(-4.46270 + 2.57654i) q^{86} +3.76766 q^{88} +(-6.56124 - 3.78813i) q^{89} +(-8.25870 - 4.77430i) q^{91} +0.313586 q^{92} -1.20292 q^{94} +(1.68377 + 2.91638i) q^{95} +(-0.414443 - 0.239279i) q^{97} +(2.46693 - 9.08770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{4} - 3q^{5} + 3q^{7} + O(q^{10}) \) \( 12q + 4q^{4} - 3q^{5} + 3q^{7} - 24q^{10} - 2q^{13} - 4q^{14} - 8q^{16} - 17q^{17} + 3q^{20} - 15q^{22} - 3q^{23} - 5q^{25} + 9q^{26} + 27q^{28} + q^{29} - 18q^{31} - 18q^{32} - 18q^{35} + 15q^{37} - 19q^{38} - q^{40} + 6q^{41} + 11q^{43} - 33q^{44} - 30q^{46} - 15q^{47} + 9q^{49} - 18q^{50} + 47q^{52} + 8q^{53} - 15q^{55} - 27q^{59} - 10q^{61} - 41q^{62} + 2q^{64} + 3q^{65} + 11q^{68} - 3q^{70} - 30q^{71} - 42q^{73} + 33q^{74} - 45q^{76} + 19q^{77} - 35q^{79} - 10q^{82} - 21q^{85} - 57q^{86} + 28q^{88} - 48q^{89} - 16q^{91} + 66q^{92} - 2q^{94} - 2q^{95} - 3q^{97} + 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16500 0.672613i −0.823779 0.475609i 0.0279386 0.999610i \(-0.491106\pi\)
−0.851718 + 0.524000i \(0.824439\pi\)
\(3\) 0 0
\(4\) −0.0951832 0.164862i −0.0475916 0.0824311i
\(5\) 3.08979 1.78389i 1.38179 0.797779i 0.389422 0.921059i \(-0.372675\pi\)
0.992372 + 0.123280i \(0.0393415\pi\)
\(6\) 0 0
\(7\) −2.09638 1.61406i −0.792357 0.610058i
\(8\) 2.94654i 1.04176i
\(9\) 0 0
\(10\) −4.79947 −1.51772
\(11\) 1.27867i 0.385534i −0.981245 0.192767i \(-0.938254\pi\)
0.981245 0.192767i \(-0.0617462\pi\)
\(12\) 0 0
\(13\) 3.57420 0.474474i 0.991304 0.131595i
\(14\) 1.35664 + 3.29043i 0.362578 + 0.879406i
\(15\) 0 0
\(16\) 1.79151 3.10299i 0.447878 0.775748i
\(17\) −3.86960 6.70234i −0.938515 1.62556i −0.768242 0.640159i \(-0.778868\pi\)
−0.170273 0.985397i \(-0.554465\pi\)
\(18\) 0 0
\(19\) 0.943878i 0.216540i 0.994121 + 0.108270i \(0.0345312\pi\)
−0.994121 + 0.108270i \(0.965469\pi\)
\(20\) −0.588191 0.339592i −0.131524 0.0759352i
\(21\) 0 0
\(22\) −0.860052 + 1.48965i −0.183364 + 0.317595i
\(23\) −0.823637 + 1.42658i −0.171740 + 0.297463i −0.939028 0.343840i \(-0.888272\pi\)
0.767288 + 0.641303i \(0.221606\pi\)
\(24\) 0 0
\(25\) 3.86451 6.69354i 0.772903 1.33871i
\(26\) −4.48308 1.85129i −0.879203 0.363068i
\(27\) 0 0
\(28\) −0.0665578 + 0.499245i −0.0125782 + 0.0943485i
\(29\) 2.02242 + 3.50293i 0.375554 + 0.650478i 0.990410 0.138161i \(-0.0441192\pi\)
−0.614856 + 0.788639i \(0.710786\pi\)
\(30\) 0 0
\(31\) −4.46193 2.57610i −0.801387 0.462681i 0.0425691 0.999094i \(-0.486446\pi\)
−0.843956 + 0.536413i \(0.819779\pi\)
\(32\) 0.929326 0.536547i 0.164283 0.0948490i
\(33\) 0 0
\(34\) 10.4110i 1.78547i
\(35\) −9.35667 1.24740i −1.58157 0.210849i
\(36\) 0 0
\(37\) 0.914594 + 0.528041i 0.150358 + 0.0868094i 0.573292 0.819351i \(-0.305666\pi\)
−0.422933 + 0.906161i \(0.639000\pi\)
\(38\) 0.634865 1.09962i 0.102989 0.178382i
\(39\) 0 0
\(40\) 5.25629 + 9.10417i 0.831093 + 1.43950i
\(41\) 3.63629 2.09941i 0.567893 0.327873i −0.188415 0.982090i \(-0.560335\pi\)
0.756307 + 0.654217i \(0.227002\pi\)
\(42\) 0 0
\(43\) 1.91532 3.31744i 0.292084 0.505904i −0.682218 0.731148i \(-0.738985\pi\)
0.974302 + 0.225244i \(0.0723180\pi\)
\(44\) −0.210805 + 0.121708i −0.0317800 + 0.0183482i
\(45\) 0 0
\(46\) 1.91908 1.10798i 0.282952 0.163363i
\(47\) 0.774415 0.447109i 0.112960 0.0652175i −0.442456 0.896790i \(-0.645893\pi\)
0.555416 + 0.831573i \(0.312559\pi\)
\(48\) 0 0
\(49\) 1.78961 + 6.76737i 0.255658 + 0.966767i
\(50\) −9.00432 + 5.19865i −1.27340 + 0.735200i
\(51\) 0 0
\(52\) −0.418426 0.544088i −0.0580253 0.0754514i
\(53\) −0.0399961 + 0.0692754i −0.00549389 + 0.00951570i −0.868759 0.495235i \(-0.835082\pi\)
0.863265 + 0.504750i \(0.168415\pi\)
\(54\) 0 0
\(55\) −2.28101 3.95082i −0.307571 0.532729i
\(56\) 4.75590 6.17706i 0.635533 0.825444i
\(57\) 0 0
\(58\) 5.44122i 0.714467i
\(59\) −9.68627 + 5.59237i −1.26104 + 0.728064i −0.973277 0.229636i \(-0.926246\pi\)
−0.287768 + 0.957700i \(0.592913\pi\)
\(60\) 0 0
\(61\) −7.62392 −0.976143 −0.488072 0.872804i \(-0.662299\pi\)
−0.488072 + 0.872804i \(0.662299\pi\)
\(62\) 3.46543 + 6.00231i 0.440111 + 0.762294i
\(63\) 0 0
\(64\) −8.60961 −1.07620
\(65\) 10.1971 7.84199i 1.26479 0.972679i
\(66\) 0 0
\(67\) 6.32103i 0.772237i −0.922449 0.386119i \(-0.873816\pi\)
0.922449 0.386119i \(-0.126184\pi\)
\(68\) −0.736641 + 1.27590i −0.0893309 + 0.154726i
\(69\) 0 0
\(70\) 10.0615 + 7.74664i 1.20258 + 0.925900i
\(71\) −9.89346 5.71199i −1.17414 0.677889i −0.219487 0.975616i \(-0.570438\pi\)
−0.954651 + 0.297727i \(0.903772\pi\)
\(72\) 0 0
\(73\) −0.658617 0.380253i −0.0770853 0.0445052i 0.460962 0.887420i \(-0.347504\pi\)
−0.538047 + 0.842915i \(0.680838\pi\)
\(74\) −0.710335 1.23034i −0.0825747 0.143024i
\(75\) 0 0
\(76\) 0.155610 0.0898413i 0.0178497 0.0103055i
\(77\) −2.06386 + 2.68058i −0.235198 + 0.305481i
\(78\) 0 0
\(79\) 1.42765 + 2.47277i 0.160624 + 0.278208i 0.935093 0.354404i \(-0.115316\pi\)
−0.774469 + 0.632612i \(0.781983\pi\)
\(80\) 12.7834i 1.42923i
\(81\) 0 0
\(82\) −5.64837 −0.623758
\(83\) 2.32483i 0.255183i −0.991827 0.127591i \(-0.959275\pi\)
0.991827 0.127591i \(-0.0407246\pi\)
\(84\) 0 0
\(85\) −23.9125 13.8059i −2.59367 1.49746i
\(86\) −4.46270 + 2.57654i −0.481226 + 0.277836i
\(87\) 0 0
\(88\) 3.76766 0.401634
\(89\) −6.56124 3.78813i −0.695490 0.401541i 0.110176 0.993912i \(-0.464859\pi\)
−0.805665 + 0.592371i \(0.798192\pi\)
\(90\) 0 0
\(91\) −8.25870 4.77430i −0.865747 0.500482i
\(92\) 0.313586 0.0326936
\(93\) 0 0
\(94\) −1.20292 −0.124072
\(95\) 1.68377 + 2.91638i 0.172751 + 0.299214i
\(96\) 0 0
\(97\) −0.414443 0.239279i −0.0420803 0.0242951i 0.478812 0.877917i \(-0.341067\pi\)
−0.520893 + 0.853622i \(0.674401\pi\)
\(98\) 2.46693 9.08770i 0.249198 0.917996i
\(99\) 0 0
\(100\) −1.47135 −0.147135
\(101\) 2.87836 0.286407 0.143204 0.989693i \(-0.454260\pi\)
0.143204 + 0.989693i \(0.454260\pi\)
\(102\) 0 0
\(103\) −5.66755 9.81649i −0.558441 0.967248i −0.997627 0.0688516i \(-0.978066\pi\)
0.439186 0.898396i \(-0.355267\pi\)
\(104\) 1.39806 + 10.5315i 0.137091 + 1.03270i
\(105\) 0 0
\(106\) 0.0931910 0.0538039i 0.00905151 0.00522589i
\(107\) −3.28603 + 5.69157i −0.317673 + 0.550225i −0.980002 0.198988i \(-0.936235\pi\)
0.662329 + 0.749213i \(0.269568\pi\)
\(108\) 0 0
\(109\) 5.05684 + 2.91957i 0.484358 + 0.279644i 0.722231 0.691652i \(-0.243117\pi\)
−0.237873 + 0.971296i \(0.576450\pi\)
\(110\) 6.13694i 0.585135i
\(111\) 0 0
\(112\) −8.76412 + 3.61343i −0.828131 + 0.341437i
\(113\) 3.26617 5.65717i 0.307255 0.532181i −0.670506 0.741904i \(-0.733923\pi\)
0.977761 + 0.209723i \(0.0672562\pi\)
\(114\) 0 0
\(115\) 5.87711i 0.548043i
\(116\) 0.385001 0.666841i 0.0357464 0.0619146i
\(117\) 0 0
\(118\) 15.0460 1.38510
\(119\) −2.70585 + 20.2964i −0.248045 + 1.86057i
\(120\) 0 0
\(121\) 9.36500 0.851363
\(122\) 8.88187 + 5.12795i 0.804127 + 0.464263i
\(123\) 0 0
\(124\) 0.980805i 0.0880789i
\(125\) 9.73656i 0.870865i
\(126\) 0 0
\(127\) 7.35818 + 12.7447i 0.652932 + 1.13091i 0.982408 + 0.186748i \(0.0597948\pi\)
−0.329475 + 0.944164i \(0.606872\pi\)
\(128\) 8.17154 + 4.71784i 0.722269 + 0.417002i
\(129\) 0 0
\(130\) −17.1542 + 2.27722i −1.50453 + 0.199726i
\(131\) 5.59335 + 9.68796i 0.488693 + 0.846441i 0.999915 0.0130074i \(-0.00414049\pi\)
−0.511222 + 0.859448i \(0.670807\pi\)
\(132\) 0 0
\(133\) 1.52348 1.97873i 0.132102 0.171577i
\(134\) −4.25161 + 7.36400i −0.367283 + 0.636153i
\(135\) 0 0
\(136\) 19.7487 11.4019i 1.69344 0.977706i
\(137\) 15.2687 8.81541i 1.30450 0.753151i 0.323324 0.946288i \(-0.395200\pi\)
0.981172 + 0.193137i \(0.0618662\pi\)
\(138\) 0 0
\(139\) 2.92855 5.07240i 0.248396 0.430235i −0.714685 0.699447i \(-0.753430\pi\)
0.963081 + 0.269212i \(0.0867631\pi\)
\(140\) 0.684948 + 1.66129i 0.0578887 + 0.140405i
\(141\) 0 0
\(142\) 7.68392 + 13.3089i 0.644820 + 1.11686i
\(143\) −0.606697 4.57022i −0.0507345 0.382181i
\(144\) 0 0
\(145\) 12.4977 + 7.21554i 1.03788 + 0.599218i
\(146\) 0.511526 + 0.885989i 0.0423342 + 0.0733250i
\(147\) 0 0
\(148\) 0.201043i 0.0165256i
\(149\) 10.4790i 0.858470i −0.903193 0.429235i \(-0.858783\pi\)
0.903193 0.429235i \(-0.141217\pi\)
\(150\) 0 0
\(151\) 4.08249 + 2.35703i 0.332229 + 0.191812i 0.656830 0.754039i \(-0.271897\pi\)
−0.324602 + 0.945851i \(0.605230\pi\)
\(152\) −2.78117 −0.225583
\(153\) 0 0
\(154\) 4.20739 1.73470i 0.339041 0.139786i
\(155\) −18.3819 −1.47647
\(156\) 0 0
\(157\) −4.50105 + 7.79604i −0.359223 + 0.622192i −0.987831 0.155530i \(-0.950291\pi\)
0.628608 + 0.777722i \(0.283625\pi\)
\(158\) 3.84103i 0.305576i
\(159\) 0 0
\(160\) 1.91428 3.31563i 0.151337 0.262123i
\(161\) 4.02925 1.66125i 0.317549 0.130925i
\(162\) 0 0
\(163\) 12.0324i 0.942449i 0.882013 + 0.471224i \(0.156188\pi\)
−0.882013 + 0.471224i \(0.843812\pi\)
\(164\) −0.692227 0.399657i −0.0540538 0.0312080i
\(165\) 0 0
\(166\) −1.56371 + 2.70842i −0.121367 + 0.210214i
\(167\) 16.8199 9.71099i 1.30157 0.751459i 0.320893 0.947116i \(-0.396017\pi\)
0.980672 + 0.195657i \(0.0626838\pi\)
\(168\) 0 0
\(169\) 12.5497 3.39173i 0.965365 0.260902i
\(170\) 18.5720 + 32.1677i 1.42441 + 2.46715i
\(171\) 0 0
\(172\) −0.729226 −0.0556030
\(173\) 14.3795 1.09325 0.546627 0.837376i \(-0.315912\pi\)
0.546627 + 0.837376i \(0.315912\pi\)
\(174\) 0 0
\(175\) −18.9053 + 7.79462i −1.42910 + 0.589218i
\(176\) −3.96771 2.29076i −0.299077 0.172672i
\(177\) 0 0
\(178\) 5.09589 + 8.82635i 0.381953 + 0.661563i
\(179\) 5.42606 0.405563 0.202781 0.979224i \(-0.435002\pi\)
0.202781 + 0.979224i \(0.435002\pi\)
\(180\) 0 0
\(181\) −15.4902 −1.15138 −0.575688 0.817669i \(-0.695266\pi\)
−0.575688 + 0.817669i \(0.695266\pi\)
\(182\) 6.41013 + 11.1170i 0.475150 + 0.824044i
\(183\) 0 0
\(184\) −4.20348 2.42688i −0.309885 0.178912i
\(185\) 3.76786 0.277019
\(186\) 0 0
\(187\) −8.57010 + 4.94795i −0.626707 + 0.361830i
\(188\) −0.147423 0.0851144i −0.0107519 0.00620761i
\(189\) 0 0
\(190\) 4.53011i 0.328649i
\(191\) −4.74622 −0.343425 −0.171712 0.985147i \(-0.554930\pi\)
−0.171712 + 0.985147i \(0.554930\pi\)
\(192\) 0 0
\(193\) 21.0391i 1.51443i −0.653166 0.757215i \(-0.726559\pi\)
0.653166 0.757215i \(-0.273441\pi\)
\(194\) 0.321884 + 0.557519i 0.0231099 + 0.0400276i
\(195\) 0 0
\(196\) 0.945343 0.939178i 0.0675245 0.0670842i
\(197\) −5.03342 + 2.90604i −0.358616 + 0.207047i −0.668474 0.743736i \(-0.733052\pi\)
0.309857 + 0.950783i \(0.399719\pi\)
\(198\) 0 0
\(199\) 5.30909 + 9.19562i 0.376352 + 0.651860i 0.990528 0.137309i \(-0.0438452\pi\)
−0.614177 + 0.789168i \(0.710512\pi\)
\(200\) 19.7228 + 11.3869i 1.39461 + 0.805178i
\(201\) 0 0
\(202\) −3.35329 1.93602i −0.235936 0.136218i
\(203\) 1.41420 10.6078i 0.0992571 0.744520i
\(204\) 0 0
\(205\) 7.49023 12.9735i 0.523140 0.906106i
\(206\) 15.2483i 1.06240i
\(207\) 0 0
\(208\) 4.93093 11.9407i 0.341899 0.827941i
\(209\) 1.20691 0.0834837
\(210\) 0 0
\(211\) 2.33275 + 4.04043i 0.160593 + 0.278155i 0.935081 0.354433i \(-0.115326\pi\)
−0.774489 + 0.632588i \(0.781993\pi\)
\(212\) 0.0152278 0.00104585
\(213\) 0 0
\(214\) 7.65645 4.42046i 0.523384 0.302176i
\(215\) 13.6669i 0.932074i
\(216\) 0 0
\(217\) 5.19592 + 12.6023i 0.352722 + 0.855501i
\(218\) −3.92748 6.80260i −0.266003 0.460730i
\(219\) 0 0
\(220\) −0.434227 + 0.752104i −0.0292756 + 0.0507068i
\(221\) −17.0108 22.1195i −1.14427 1.48792i
\(222\) 0 0
\(223\) 20.9798 12.1127i 1.40491 0.811126i 0.410020 0.912076i \(-0.365522\pi\)
0.994891 + 0.100950i \(0.0321883\pi\)
\(224\) −2.81424 0.375185i −0.188034 0.0250681i
\(225\) 0 0
\(226\) −7.61017 + 4.39373i −0.506221 + 0.292267i
\(227\) 13.3154 7.68764i 0.883773 0.510247i 0.0118726 0.999930i \(-0.496221\pi\)
0.871901 + 0.489683i \(0.162887\pi\)
\(228\) 0 0
\(229\) 14.1608 8.17573i 0.935771 0.540268i 0.0471389 0.998888i \(-0.484990\pi\)
0.888632 + 0.458621i \(0.151656\pi\)
\(230\) 3.95302 6.84683i 0.260654 0.451467i
\(231\) 0 0
\(232\) −10.3215 + 5.95913i −0.677641 + 0.391236i
\(233\) 14.5554 + 25.2106i 0.953554 + 1.65160i 0.737643 + 0.675191i \(0.235939\pi\)
0.215911 + 0.976413i \(0.430728\pi\)
\(234\) 0 0
\(235\) 1.59518 2.76294i 0.104058 0.180234i
\(236\) 1.84394 + 1.06460i 0.120030 + 0.0692995i
\(237\) 0 0
\(238\) 16.8040 21.8253i 1.08924 1.41473i
\(239\) 8.65409i 0.559787i 0.960031 + 0.279893i \(0.0902991\pi\)
−0.960031 + 0.279893i \(0.909701\pi\)
\(240\) 0 0
\(241\) 15.7601 9.09909i 1.01520 0.586124i 0.102487 0.994734i \(-0.467320\pi\)
0.912709 + 0.408611i \(0.133987\pi\)
\(242\) −10.9102 6.29902i −0.701336 0.404916i
\(243\) 0 0
\(244\) 0.725669 + 1.25690i 0.0464562 + 0.0804645i
\(245\) 17.6017 + 17.7173i 1.12453 + 1.13191i
\(246\) 0 0
\(247\) 0.447846 + 3.37360i 0.0284957 + 0.214657i
\(248\) 7.59057 13.1473i 0.482002 0.834851i
\(249\) 0 0
\(250\) −6.54894 + 11.3431i −0.414191 + 0.717400i
\(251\) −7.93598 + 13.7455i −0.500915 + 0.867610i 0.499085 + 0.866553i \(0.333670\pi\)
−0.999999 + 0.00105678i \(0.999664\pi\)
\(252\) 0 0
\(253\) 1.82413 + 1.05316i 0.114682 + 0.0662117i
\(254\) 19.7968i 1.24216i
\(255\) 0 0
\(256\) 2.26304 + 3.91971i 0.141440 + 0.244982i
\(257\) 12.1634 21.0676i 0.758730 1.31416i −0.184769 0.982782i \(-0.559154\pi\)
0.943499 0.331376i \(-0.107513\pi\)
\(258\) 0 0
\(259\) −1.06504 2.58319i −0.0661786 0.160511i
\(260\) −2.26344 0.934688i −0.140372 0.0579669i
\(261\) 0 0
\(262\) 15.0486i 0.929708i
\(263\) −15.4345 −0.951734 −0.475867 0.879517i \(-0.657866\pi\)
−0.475867 + 0.879517i \(0.657866\pi\)
\(264\) 0 0
\(265\) 0.285395i 0.0175317i
\(266\) −3.10577 + 1.28050i −0.190427 + 0.0785128i
\(267\) 0 0
\(268\) −1.04210 + 0.601656i −0.0636563 + 0.0367520i
\(269\) −6.52035 11.2936i −0.397553 0.688582i 0.595870 0.803081i \(-0.296807\pi\)
−0.993423 + 0.114499i \(0.963474\pi\)
\(270\) 0 0
\(271\) 23.3572 + 13.4853i 1.41885 + 0.819174i 0.996198 0.0871168i \(-0.0277653\pi\)
0.422654 + 0.906291i \(0.361099\pi\)
\(272\) −27.7298 −1.68136
\(273\) 0 0
\(274\) −23.7174 −1.43282
\(275\) −8.55884 4.94145i −0.516117 0.297980i
\(276\) 0 0
\(277\) 6.35073 + 10.9998i 0.381578 + 0.660913i 0.991288 0.131712i \(-0.0420474\pi\)
−0.609710 + 0.792625i \(0.708714\pi\)
\(278\) −6.82352 + 3.93956i −0.409248 + 0.236279i
\(279\) 0 0
\(280\) 3.67551 27.5698i 0.219654 1.64761i
\(281\) 26.7216i 1.59408i 0.603930 + 0.797038i \(0.293601\pi\)
−0.603930 + 0.797038i \(0.706399\pi\)
\(282\) 0 0
\(283\) −14.7423 −0.876336 −0.438168 0.898893i \(-0.644373\pi\)
−0.438168 + 0.898893i \(0.644373\pi\)
\(284\) 2.17474i 0.129047i
\(285\) 0 0
\(286\) −2.36719 + 5.73238i −0.139975 + 0.338963i
\(287\) −11.0116 1.46803i −0.649995 0.0866553i
\(288\) 0 0
\(289\) −21.4476 + 37.1483i −1.26162 + 2.18519i
\(290\) −9.70653 16.8122i −0.569987 0.987247i
\(291\) 0 0
\(292\) 0.144775i 0.00847230i
\(293\) 10.0312 + 5.79153i 0.586030 + 0.338345i 0.763526 0.645777i \(-0.223466\pi\)
−0.177496 + 0.984121i \(0.556800\pi\)
\(294\) 0 0
\(295\) −19.9523 + 34.5584i −1.16167 + 2.01207i
\(296\) −1.55589 + 2.69489i −0.0904344 + 0.156637i
\(297\) 0 0
\(298\) −7.04829 + 12.2080i −0.408297 + 0.707190i
\(299\) −2.26697 + 5.48968i −0.131102 + 0.317476i
\(300\) 0 0
\(301\) −9.36979 + 3.86315i −0.540066 + 0.222668i
\(302\) −3.17074 5.49188i −0.182455 0.316022i
\(303\) 0 0
\(304\) 2.92885 + 1.69097i 0.167981 + 0.0969838i
\(305\) −23.5563 + 13.6002i −1.34883 + 0.778746i
\(306\) 0 0
\(307\) 29.3335i 1.67415i −0.547086 0.837076i \(-0.684263\pi\)
0.547086 0.837076i \(-0.315737\pi\)
\(308\) 0.638371 + 0.0851055i 0.0363746 + 0.00484934i
\(309\) 0 0
\(310\) 21.4149 + 12.3639i 1.21628 + 0.702222i
\(311\) 0.0753271 0.130470i 0.00427141 0.00739830i −0.863882 0.503695i \(-0.831974\pi\)
0.868153 + 0.496296i \(0.165307\pi\)
\(312\) 0 0
\(313\) 5.26057 + 9.11157i 0.297345 + 0.515016i 0.975528 0.219877i \(-0.0705656\pi\)
−0.678183 + 0.734893i \(0.737232\pi\)
\(314\) 10.4874 6.05493i 0.591841 0.341699i
\(315\) 0 0
\(316\) 0.271777 0.470732i 0.0152887 0.0264808i
\(317\) 1.30489 0.753380i 0.0732901 0.0423140i −0.462907 0.886407i \(-0.653194\pi\)
0.536197 + 0.844093i \(0.319860\pi\)
\(318\) 0 0
\(319\) 4.47910 2.58601i 0.250782 0.144789i
\(320\) −26.6018 + 15.3586i −1.48709 + 0.858571i
\(321\) 0 0
\(322\) −5.81145 0.774765i −0.323860 0.0431759i
\(323\) 6.32619 3.65243i 0.351999 0.203227i
\(324\) 0 0
\(325\) 10.6366 25.7576i 0.590014 1.42878i
\(326\) 8.09314 14.0177i 0.448237 0.776370i
\(327\) 0 0
\(328\) 6.18600 + 10.7145i 0.341565 + 0.591607i
\(329\) −2.34513 0.312645i −0.129291 0.0172367i
\(330\) 0 0
\(331\) 25.2509i 1.38791i −0.720017 0.693957i \(-0.755866\pi\)
0.720017 0.693957i \(-0.244134\pi\)
\(332\) −0.383276 + 0.221284i −0.0210350 + 0.0121446i
\(333\) 0 0
\(334\) −26.1270 −1.42960
\(335\) −11.2760 19.5306i −0.616075 1.06707i
\(336\) 0 0
\(337\) 32.1811 1.75302 0.876509 0.481386i \(-0.159866\pi\)
0.876509 + 0.481386i \(0.159866\pi\)
\(338\) −16.9018 4.48977i −0.919335 0.244211i
\(339\) 0 0
\(340\) 5.25634i 0.285065i
\(341\) −3.29398 + 5.70535i −0.178379 + 0.308962i
\(342\) 0 0
\(343\) 7.17127 17.0755i 0.387212 0.921991i
\(344\) 9.77495 + 5.64357i 0.527030 + 0.304281i
\(345\) 0 0
\(346\) −16.7521 9.67185i −0.900600 0.519962i
\(347\) 12.3819 + 21.4461i 0.664695 + 1.15128i 0.979368 + 0.202085i \(0.0647717\pi\)
−0.314673 + 0.949200i \(0.601895\pi\)
\(348\) 0 0
\(349\) −10.0075 + 5.77782i −0.535688 + 0.309280i −0.743330 0.668925i \(-0.766755\pi\)
0.207642 + 0.978205i \(0.433421\pi\)
\(350\) 27.2674 + 3.63520i 1.45750 + 0.194310i
\(351\) 0 0
\(352\) −0.686067 1.18830i −0.0365675 0.0633368i
\(353\) 20.0884i 1.06920i −0.845106 0.534599i \(-0.820463\pi\)
0.845106 0.534599i \(-0.179537\pi\)
\(354\) 0 0
\(355\) −40.7582 −2.16322
\(356\) 1.44227i 0.0764399i
\(357\) 0 0
\(358\) −6.32136 3.64964i −0.334094 0.192890i
\(359\) 13.0346 7.52551i 0.687938 0.397181i −0.114901 0.993377i \(-0.536655\pi\)
0.802839 + 0.596196i \(0.203322\pi\)
\(360\) 0 0
\(361\) 18.1091 0.953110
\(362\) 18.0461 + 10.4189i 0.948481 + 0.547606i
\(363\) 0 0
\(364\) −0.00101167 + 1.81598i −5.30260e−5 + 0.0951832i
\(365\) −2.71331 −0.142021
\(366\) 0 0
\(367\) 9.00355 0.469982 0.234991 0.971998i \(-0.424494\pi\)
0.234991 + 0.971998i \(0.424494\pi\)
\(368\) 2.95112 + 5.11148i 0.153838 + 0.266454i
\(369\) 0 0
\(370\) −4.38956 2.53431i −0.228202 0.131753i
\(371\) 0.195662 0.0806711i 0.0101583 0.00418823i
\(372\) 0 0
\(373\) −16.1391 −0.835649 −0.417824 0.908528i \(-0.637207\pi\)
−0.417824 + 0.908528i \(0.637207\pi\)
\(374\) 13.3122 0.688358
\(375\) 0 0
\(376\) 1.31742 + 2.28184i 0.0679409 + 0.117677i
\(377\) 8.89057 + 11.5606i 0.457888 + 0.595400i
\(378\) 0 0
\(379\) −13.5668 + 7.83277i −0.696878 + 0.402342i −0.806183 0.591666i \(-0.798471\pi\)
0.109306 + 0.994008i \(0.465137\pi\)
\(380\) 0.320534 0.555181i 0.0164430 0.0284802i
\(381\) 0 0
\(382\) 5.52935 + 3.19237i 0.282906 + 0.163336i
\(383\) 24.6328i 1.25868i −0.777131 0.629339i \(-0.783326\pi\)
0.777131 0.629339i \(-0.216674\pi\)
\(384\) 0 0
\(385\) −1.59502 + 11.9641i −0.0812896 + 0.609747i
\(386\) −14.1512 + 24.5106i −0.720277 + 1.24756i
\(387\) 0 0
\(388\) 0.0911013i 0.00462497i
\(389\) 9.42834 16.3304i 0.478036 0.827982i −0.521647 0.853161i \(-0.674682\pi\)
0.999683 + 0.0251791i \(0.00801560\pi\)
\(390\) 0 0
\(391\) 12.7486 0.644724
\(392\) −19.9403 + 5.27314i −1.00714 + 0.266334i
\(393\) 0 0
\(394\) 7.81857 0.393894
\(395\) 8.82229 + 5.09355i 0.443897 + 0.256284i
\(396\) 0 0
\(397\) 14.5030i 0.727884i −0.931422 0.363942i \(-0.881431\pi\)
0.931422 0.363942i \(-0.118569\pi\)
\(398\) 14.2839i 0.715985i
\(399\) 0 0
\(400\) −13.8467 23.9831i −0.692333 1.19916i
\(401\) −18.1770 10.4945i −0.907714 0.524069i −0.0280189 0.999607i \(-0.508920\pi\)
−0.879695 + 0.475539i \(0.842253\pi\)
\(402\) 0 0
\(403\) −17.1701 7.09041i −0.855304 0.353198i
\(404\) −0.273971 0.474532i −0.0136306 0.0236089i
\(405\) 0 0
\(406\) −8.78247 + 11.4069i −0.435867 + 0.566113i
\(407\) 0.675191 1.16947i 0.0334680 0.0579683i
\(408\) 0 0
\(409\) −18.5568 + 10.7138i −0.917576 + 0.529763i −0.882861 0.469635i \(-0.844386\pi\)
−0.0347148 + 0.999397i \(0.511052\pi\)
\(410\) −17.4522 + 10.0761i −0.861905 + 0.497621i
\(411\) 0 0
\(412\) −1.07891 + 1.86873i −0.0531542 + 0.0920657i
\(413\) 29.3325 + 3.91052i 1.44336 + 0.192424i
\(414\) 0 0
\(415\) −4.14723 7.18321i −0.203580 0.352610i
\(416\) 3.06702 2.35866i 0.150373 0.115643i
\(417\) 0 0
\(418\) −1.40605 0.811784i −0.0687722 0.0397056i
\(419\) 3.98203 + 6.89708i 0.194535 + 0.336944i 0.946748 0.321976i \(-0.104347\pi\)
−0.752213 + 0.658920i \(0.771014\pi\)
\(420\) 0 0
\(421\) 2.81786i 0.137334i 0.997640 + 0.0686670i \(0.0218746\pi\)
−0.997640 + 0.0686670i \(0.978125\pi\)
\(422\) 6.27614i 0.305518i
\(423\) 0 0
\(424\) −0.204122 0.117850i −0.00991306 0.00572331i
\(425\) −59.8165 −2.90152
\(426\) 0 0
\(427\) 15.9826 + 12.3055i 0.773453 + 0.595504i
\(428\) 1.25110 0.0604742
\(429\) 0 0
\(430\) −9.19253 + 15.9219i −0.443303 + 0.767823i
\(431\) 5.73626i 0.276306i 0.990411 + 0.138153i \(0.0441166\pi\)
−0.990411 + 0.138153i \(0.955883\pi\)
\(432\) 0 0
\(433\) −12.2628 + 21.2398i −0.589314 + 1.02072i 0.405009 + 0.914313i \(0.367268\pi\)
−0.994322 + 0.106409i \(0.966065\pi\)
\(434\) 2.42324 18.1765i 0.116319 0.872502i
\(435\) 0 0
\(436\) 1.11158i 0.0532349i
\(437\) −1.34652 0.777413i −0.0644128 0.0371887i
\(438\) 0 0
\(439\) 18.3211 31.7332i 0.874420 1.51454i 0.0170416 0.999855i \(-0.494575\pi\)
0.857379 0.514686i \(-0.172091\pi\)
\(440\) 11.6412 6.72108i 0.554975 0.320415i
\(441\) 0 0
\(442\) 4.93973 + 37.2108i 0.234959 + 1.76994i
\(443\) 13.5467 + 23.4635i 0.643622 + 1.11479i 0.984618 + 0.174721i \(0.0559022\pi\)
−0.340996 + 0.940065i \(0.610764\pi\)
\(444\) 0 0
\(445\) −27.0304 −1.28136
\(446\) −32.5886 −1.54312
\(447\) 0 0
\(448\) 18.0490 + 13.8964i 0.852735 + 0.656545i
\(449\) −23.7571 13.7162i −1.12117 0.647307i −0.179470 0.983764i \(-0.557438\pi\)
−0.941699 + 0.336456i \(0.890772\pi\)
\(450\) 0 0
\(451\) −2.68446 4.64962i −0.126406 0.218942i
\(452\) −1.24354 −0.0584911
\(453\) 0 0
\(454\) −20.6832 −0.970712
\(455\) −34.0344 0.0189604i −1.59556 0.000888877i
\(456\) 0 0
\(457\) −34.3500 19.8320i −1.60682 0.927700i −0.990075 0.140539i \(-0.955116\pi\)
−0.616748 0.787161i \(-0.711550\pi\)
\(458\) −21.9964 −1.02783
\(459\) 0 0
\(460\) 0.968913 0.559402i 0.0451758 0.0260823i
\(461\) 4.23988 + 2.44790i 0.197471 + 0.114010i 0.595475 0.803374i \(-0.296964\pi\)
−0.398004 + 0.917384i \(0.630297\pi\)
\(462\) 0 0
\(463\) 4.71193i 0.218982i −0.993988 0.109491i \(-0.965078\pi\)
0.993988 0.109491i \(-0.0349221\pi\)
\(464\) 14.4928 0.672810
\(465\) 0 0
\(466\) 39.1605i 1.81408i
\(467\) −16.0081 27.7268i −0.740765 1.28304i −0.952147 0.305639i \(-0.901130\pi\)
0.211383 0.977403i \(-0.432203\pi\)
\(468\) 0 0
\(469\) −10.2025 + 13.2513i −0.471110 + 0.611887i
\(470\) −3.71678 + 2.14588i −0.171442 + 0.0989822i
\(471\) 0 0
\(472\) −16.4781 28.5410i −0.758467 1.31370i
\(473\) −4.24191 2.44907i −0.195043 0.112608i
\(474\) 0 0
\(475\) 6.31788 + 3.64763i 0.289884 + 0.167365i
\(476\) 3.60366 1.48578i 0.165174 0.0681008i
\(477\) 0 0
\(478\) 5.82086 10.0820i 0.266240 0.461141i
\(479\) 18.0245i 0.823560i 0.911283 + 0.411780i \(0.135093\pi\)
−0.911283 + 0.411780i \(0.864907\pi\)
\(480\) 0 0
\(481\) 3.51948 + 1.45337i 0.160474 + 0.0662680i
\(482\) −24.4807 −1.11506
\(483\) 0 0
\(484\) −0.891390 1.54393i −0.0405177 0.0701788i
\(485\) −1.70739 −0.0775284
\(486\) 0 0
\(487\) −15.2424 + 8.80020i −0.690699 + 0.398775i −0.803874 0.594800i \(-0.797231\pi\)
0.113175 + 0.993575i \(0.463898\pi\)
\(488\) 22.4642i 1.01691i
\(489\) 0 0
\(490\) −8.58915 32.4798i −0.388018 1.46729i
\(491\) −1.93180 3.34598i −0.0871810 0.151002i 0.819138 0.573597i \(-0.194453\pi\)
−0.906318 + 0.422595i \(0.861119\pi\)
\(492\) 0 0
\(493\) 15.6519 27.1099i 0.704926 1.22097i
\(494\) 1.74739 4.23148i 0.0786188 0.190383i
\(495\) 0 0
\(496\) −15.9872 + 9.23023i −0.717848 + 0.414450i
\(497\) 11.5209 + 27.9432i 0.516784 + 1.25342i
\(498\) 0 0
\(499\) 10.9528 6.32363i 0.490317 0.283084i −0.234389 0.972143i \(-0.575309\pi\)
0.724706 + 0.689058i \(0.241976\pi\)
\(500\) −1.60519 + 0.926757i −0.0717863 + 0.0414458i
\(501\) 0 0
\(502\) 18.4908 10.6757i 0.825287 0.476480i
\(503\) 11.0180 19.0837i 0.491268 0.850902i −0.508681 0.860955i \(-0.669867\pi\)
0.999949 + 0.0100533i \(0.00320011\pi\)
\(504\) 0 0
\(505\) 8.89351 5.13467i 0.395756 0.228490i
\(506\) −1.41674 2.45387i −0.0629818 0.109088i
\(507\) 0 0
\(508\) 1.40075 2.42617i 0.0621482 0.107644i
\(509\) 13.5708 + 7.83509i 0.601514 + 0.347284i 0.769637 0.638482i \(-0.220437\pi\)
−0.168123 + 0.985766i \(0.553771\pi\)
\(510\) 0 0
\(511\) 0.766959 + 1.86020i 0.0339283 + 0.0822906i
\(512\) 24.9600i 1.10309i
\(513\) 0 0
\(514\) −28.3406 + 16.3625i −1.25005 + 0.721718i
\(515\) −35.0230 20.2206i −1.54330 0.891025i
\(516\) 0 0
\(517\) −0.571705 0.990222i −0.0251436 0.0435499i
\(518\) −0.496708 + 3.72577i −0.0218241 + 0.163701i
\(519\) 0 0
\(520\) 23.1067 + 30.0461i 1.01330 + 1.31761i
\(521\) −12.6207 + 21.8598i −0.552925 + 0.957694i 0.445137 + 0.895463i \(0.353155\pi\)
−0.998062 + 0.0622317i \(0.980178\pi\)
\(522\) 0 0
\(523\) 6.62383 11.4728i 0.289640 0.501671i −0.684084 0.729403i \(-0.739798\pi\)
0.973724 + 0.227733i \(0.0731312\pi\)
\(524\) 1.06479 1.84426i 0.0465154 0.0805670i
\(525\) 0 0
\(526\) 17.9812 + 10.3815i 0.784019 + 0.452654i
\(527\) 39.8738i 1.73693i
\(528\) 0 0
\(529\) 10.1432 + 17.5686i 0.441011 + 0.763853i
\(530\) 0.191960 0.332485i 0.00833822 0.0144422i
\(531\) 0 0
\(532\) −0.471226 0.0628224i −0.0204303 0.00272370i
\(533\) 12.0007 9.22903i 0.519807 0.399754i
\(534\) 0 0
\(535\) 23.4477i 1.01373i
\(536\) 18.6252 0.804485
\(537\) 0 0
\(538\) 17.5427i 0.756320i
\(539\) 8.65325 2.28832i 0.372722 0.0985649i
\(540\) 0 0
\(541\) 12.4737 7.20170i 0.536287 0.309625i −0.207286 0.978280i \(-0.566463\pi\)
0.743573 + 0.668655i \(0.233130\pi\)
\(542\) −18.1408 31.4208i −0.779214 1.34964i
\(543\) 0 0
\(544\) −7.19224 4.15244i −0.308365 0.178034i
\(545\) 20.8328 0.892377
\(546\) 0 0
\(547\) 2.00679 0.0858042 0.0429021 0.999079i \(-0.486340\pi\)
0.0429021 + 0.999079i \(0.486340\pi\)
\(548\) −2.90665 1.67816i −0.124166 0.0716873i
\(549\) 0 0
\(550\) 6.64736 + 11.5136i 0.283445 + 0.490940i
\(551\) −3.30634 + 1.90892i −0.140855 + 0.0813226i
\(552\) 0 0
\(553\) 0.998300 7.48818i 0.0424521 0.318430i
\(554\) 17.0863i 0.725928i
\(555\) 0 0
\(556\) −1.11499 −0.0472863
\(557\) 8.57916i 0.363511i −0.983344 0.181755i \(-0.941822\pi\)
0.983344 0.181755i \(-0.0581779\pi\)
\(558\) 0 0
\(559\) 5.27170 12.7659i 0.222969 0.539942i
\(560\) −20.6333 + 26.7989i −0.871915 + 1.13246i
\(561\) 0 0
\(562\) 17.9733 31.1306i 0.758157 1.31317i
\(563\) 6.38718 + 11.0629i 0.269188 + 0.466247i 0.968652 0.248421i \(-0.0799115\pi\)
−0.699465 + 0.714667i \(0.746578\pi\)
\(564\) 0 0
\(565\) 23.3059i 0.980487i
\(566\) 17.1747 + 9.91583i 0.721908 + 0.416794i
\(567\) 0 0
\(568\) 16.8306 29.1515i 0.706196 1.22317i
\(569\) 2.89558 5.01530i 0.121389 0.210252i −0.798927 0.601429i \(-0.794598\pi\)
0.920316 + 0.391176i \(0.127932\pi\)
\(570\) 0 0
\(571\) −22.0666 + 38.2204i −0.923458 + 1.59948i −0.129435 + 0.991588i \(0.541316\pi\)
−0.794023 + 0.607888i \(0.792017\pi\)
\(572\) −0.695710 + 0.535030i −0.0290891 + 0.0223707i
\(573\) 0 0
\(574\) 11.8411 + 9.11682i 0.494239 + 0.380529i
\(575\) 6.36592 + 11.0261i 0.265477 + 0.459820i
\(576\) 0 0
\(577\) −10.3343 5.96649i −0.430221 0.248388i 0.269220 0.963079i \(-0.413234\pi\)
−0.699441 + 0.714691i \(0.746568\pi\)
\(578\) 49.9729 28.8518i 2.07860 1.20008i
\(579\) 0 0
\(580\) 2.74719i 0.114071i
\(581\) −3.75242 + 4.87372i −0.155676 + 0.202196i
\(582\) 0 0
\(583\) 0.0885805 + 0.0511420i 0.00366863 + 0.00211808i
\(584\) 1.12043 1.94064i 0.0463637 0.0803043i
\(585\) 0 0
\(586\) −7.79091 13.4943i −0.321840 0.557443i
\(587\) −17.6250 + 10.1758i −0.727462 + 0.420000i −0.817493 0.575939i \(-0.804637\pi\)
0.0900312 + 0.995939i \(0.471303\pi\)
\(588\) 0 0
\(589\) 2.43152 4.21152i 0.100189 0.173533i
\(590\) 46.4889 26.8404i 1.91392 1.10500i
\(591\) 0 0
\(592\) 3.27701 1.89199i 0.134684 0.0777601i
\(593\) 15.7443 9.09000i 0.646543 0.373282i −0.140588 0.990068i \(-0.544899\pi\)
0.787130 + 0.616787i \(0.211566\pi\)
\(594\) 0 0
\(595\) 27.8460 + 67.5385i 1.14158 + 2.76881i
\(596\) −1.72759 + 0.997422i −0.0707646 + 0.0408560i
\(597\) 0 0
\(598\) 6.33344 4.87068i 0.258994 0.199177i
\(599\) −19.1341 + 33.1412i −0.781797 + 1.35411i 0.149096 + 0.988823i \(0.452364\pi\)
−0.930894 + 0.365290i \(0.880970\pi\)
\(600\) 0 0
\(601\) 13.4360 + 23.2718i 0.548064 + 0.949275i 0.998407 + 0.0564195i \(0.0179684\pi\)
−0.450343 + 0.892856i \(0.648698\pi\)
\(602\) 13.5142 + 1.80167i 0.550798 + 0.0734306i
\(603\) 0 0
\(604\) 0.897398i 0.0365146i
\(605\) 28.9358 16.7061i 1.17641 0.679200i
\(606\) 0 0
\(607\) −9.40209 −0.381619 −0.190810 0.981627i \(-0.561111\pi\)
−0.190810 + 0.981627i \(0.561111\pi\)
\(608\) 0.506435 + 0.877171i 0.0205386 + 0.0355740i
\(609\) 0 0
\(610\) 36.5908 1.48152
\(611\) 2.55577 1.96549i 0.103395 0.0795153i
\(612\) 0 0
\(613\) 13.2894i 0.536753i −0.963314 0.268376i \(-0.913513\pi\)
0.963314 0.268376i \(-0.0864871\pi\)
\(614\) −19.7301 + 34.1735i −0.796242 + 1.37913i
\(615\) 0 0
\(616\) −7.89843 6.08123i −0.318237 0.245020i
\(617\) 9.72211 + 5.61306i 0.391397 + 0.225973i 0.682765 0.730638i \(-0.260777\pi\)
−0.291368 + 0.956611i \(0.594110\pi\)
\(618\) 0 0
\(619\) 8.04109 + 4.64253i 0.323199 + 0.186599i 0.652817 0.757515i \(-0.273587\pi\)
−0.329619 + 0.944114i \(0.606920\pi\)
\(620\) 1.74965 + 3.03048i 0.0702675 + 0.121707i
\(621\) 0 0
\(622\) −0.175512 + 0.101332i −0.00703740 + 0.00406304i
\(623\) 7.64055 + 18.5316i 0.306112 + 0.742453i
\(624\) 0 0
\(625\) 1.95363 + 3.38379i 0.0781452 + 0.135351i
\(626\) 14.1533i 0.565680i
\(627\) 0 0
\(628\) 1.71370 0.0683839
\(629\) 8.17322i 0.325888i
\(630\) 0 0
\(631\) 9.00894 + 5.20132i 0.358640 + 0.207061i 0.668484 0.743726i \(-0.266943\pi\)
−0.309844 + 0.950787i \(0.600277\pi\)
\(632\) −7.28611 + 4.20664i −0.289826 + 0.167331i
\(633\) 0 0
\(634\) −2.02693 −0.0804998
\(635\) 45.4704 + 26.2523i 1.80444 + 1.04179i
\(636\) 0 0
\(637\) 9.60734 + 23.3388i 0.380657 + 0.924716i
\(638\) −6.95754 −0.275452
\(639\) 0 0
\(640\) 33.6644 1.33070
\(641\) −7.42955 12.8684i −0.293449 0.508269i 0.681174 0.732122i \(-0.261470\pi\)
−0.974623 + 0.223853i \(0.928137\pi\)
\(642\) 0 0
\(643\) 1.98945 + 1.14861i 0.0784563 + 0.0452968i 0.538715 0.842488i \(-0.318910\pi\)
−0.460259 + 0.887785i \(0.652243\pi\)
\(644\) −0.657395 0.506147i −0.0259050 0.0199450i
\(645\) 0 0
\(646\) −9.82669 −0.386626
\(647\) 7.99865 0.314459 0.157230 0.987562i \(-0.449744\pi\)
0.157230 + 0.987562i \(0.449744\pi\)
\(648\) 0 0
\(649\) 7.15081 + 12.3856i 0.280694 + 0.486176i
\(650\) −29.7166 + 22.8533i −1.16558 + 0.896380i
\(651\) 0 0
\(652\) 1.98368 1.14528i 0.0776871 0.0448526i
\(653\) 1.99222 3.45062i 0.0779615 0.135033i −0.824409 0.565995i \(-0.808492\pi\)
0.902370 + 0.430962i \(0.141826\pi\)
\(654\) 0 0
\(655\) 34.5645 + 19.9558i 1.35055 + 0.779738i
\(656\) 15.0445i 0.587389i
\(657\) 0 0
\(658\) 2.52178 + 1.94159i 0.0983094 + 0.0756912i
\(659\) −13.7501 + 23.8159i −0.535629 + 0.927737i 0.463504 + 0.886095i \(0.346592\pi\)
−0.999133 + 0.0416417i \(0.986741\pi\)
\(660\) 0 0
\(661\) 6.98621i 0.271732i −0.990727 0.135866i \(-0.956618\pi\)
0.990727 0.135866i \(-0.0433817\pi\)
\(662\) −16.9841 + 29.4173i −0.660105 + 1.14333i
\(663\) 0 0
\(664\) 6.85019 0.265839
\(665\) 1.17739 8.83155i 0.0456574 0.342473i
\(666\) 0 0
\(667\) −6.66296 −0.257991
\(668\) −3.20195 1.84865i −0.123887 0.0715263i
\(669\) 0 0
\(670\) 30.3376i 1.17204i
\(671\) 9.74849i 0.376336i
\(672\) 0 0
\(673\) 2.72783 + 4.72474i 0.105150 + 0.182125i 0.913800 0.406166i \(-0.133134\pi\)
−0.808649 + 0.588291i \(0.799801\pi\)
\(674\) −37.4910 21.6455i −1.44410 0.833752i
\(675\) 0 0
\(676\) −1.75369 1.74614i −0.0674497 0.0671594i
\(677\) 16.8961 + 29.2649i 0.649371 + 1.12474i 0.983273 + 0.182135i \(0.0583009\pi\)
−0.333903 + 0.942607i \(0.608366\pi\)
\(678\) 0 0
\(679\) 0.482618 + 1.17056i 0.0185212 + 0.0449218i
\(680\) 40.6795 70.4590i 1.55999 2.70198i
\(681\) 0 0
\(682\) 7.67498 4.43115i 0.293890 0.169678i
\(683\) 10.6511 6.14942i 0.407553 0.235301i −0.282185 0.959360i \(-0.591059\pi\)
0.689738 + 0.724059i \(0.257726\pi\)
\(684\) 0 0
\(685\) 31.4514 54.4754i 1.20170 2.08140i
\(686\) −19.8397 + 15.0695i −0.757485 + 0.575355i
\(687\) 0 0
\(688\) −6.86265 11.8865i −0.261636 0.453167i
\(689\) −0.110085 + 0.266581i −0.00419389 + 0.0101559i
\(690\) 0 0
\(691\) 9.60393 + 5.54483i 0.365351 + 0.210935i 0.671425 0.741072i \(-0.265682\pi\)
−0.306075 + 0.952008i \(0.599016\pi\)
\(692\) −1.36869 2.37064i −0.0520297 0.0901181i
\(693\) 0 0
\(694\) 33.3129i 1.26454i
\(695\) 20.8968i 0.792662i
\(696\) 0 0
\(697\) −28.1419 16.2478i −1.06595 0.615428i
\(698\) 15.5449 0.588385
\(699\) 0 0
\(700\) 3.08450 + 2.37485i 0.116583 + 0.0897608i
\(701\) −10.6470 −0.402133 −0.201066 0.979578i \(-0.564441\pi\)
−0.201066 + 0.979578i \(0.564441\pi\)
\(702\) 0 0
\(703\) −0.498406 + 0.863265i −0.0187977 + 0.0325587i
\(704\) 11.0089i 0.414912i
\(705\) 0 0
\(706\) −13.5117 + 23.4030i −0.508521 + 0.880784i
\(707\) −6.03413 4.64585i −0.226937 0.174725i
\(708\) 0 0
\(709\) 40.7069i 1.52878i 0.644754 + 0.764391i \(0.276960\pi\)
−0.644754 + 0.764391i \(0.723040\pi\)
\(710\) 47.4833 + 27.4145i 1.78202 + 1.02885i
\(711\) 0 0
\(712\) 11.1619 19.3329i 0.418309 0.724532i
\(713\) 7.35003 4.24354i 0.275261 0.158922i
\(714\) 0 0
\(715\) −10.0273 13.0387i −0.375001 0.487621i
\(716\) −0.516470 0.894552i −0.0193014 0.0334310i
\(717\) 0 0
\(718\) −20.2470 −0.755612
\(719\) −9.77537 −0.364560 −0.182280 0.983247i \(-0.558348\pi\)
−0.182280 + 0.983247i \(0.558348\pi\)
\(720\) 0 0
\(721\) −3.96309 + 29.7269i −0.147593 + 1.10709i
\(722\) −21.0971 12.1804i −0.785153 0.453308i
\(723\) 0 0
\(724\) 1.47441 + 2.55375i 0.0547959 + 0.0949092i
\(725\) 31.2627 1.16107
\(726\) 0 0
\(727\) −12.2091 −0.452811 −0.226406 0.974033i \(-0.572697\pi\)
−0.226406 + 0.974033i \(0.572697\pi\)
\(728\) 14.0677 24.3346i 0.521382 0.901899i
\(729\) 0 0
\(730\) 3.16101 + 1.82501i 0.116994 + 0.0675467i
\(731\) −29.6461 −1.09650
\(732\) 0 0
\(733\) 19.3256 11.1577i 0.713809 0.412118i −0.0986608 0.995121i \(-0.531456\pi\)
0.812470 + 0.583003i \(0.198123\pi\)
\(734\) −10.4891 6.05591i −0.387161 0.223528i
\(735\) 0 0
\(736\) 1.76768i 0.0651576i
\(737\) −8.08253 −0.297724
\(738\) 0 0
\(739\) 42.3729i 1.55871i 0.626580 + 0.779357i \(0.284454\pi\)
−0.626580 + 0.779357i \(0.715546\pi\)
\(740\) −0.358637 0.621178i −0.0131838 0.0228350i
\(741\) 0 0
\(742\) −0.282206 0.0376229i −0.0103601 0.00138118i
\(743\) 26.8296 15.4901i 0.984282 0.568276i 0.0807220 0.996737i \(-0.474277\pi\)
0.903560 + 0.428461i \(0.140944\pi\)
\(744\) 0 0
\(745\) −18.6933 32.3778i −0.684870 1.18623i
\(746\) 18.8020 + 10.8553i 0.688390 + 0.397442i
\(747\) 0 0
\(748\) 1.63146 + 0.941923i 0.0596520 + 0.0344401i
\(749\) 16.0753 6.62783i 0.587379 0.242176i
\(750\) 0 0
\(751\) 11.2830 19.5427i 0.411722 0.713123i −0.583356 0.812216i \(-0.698261\pi\)
0.995078 + 0.0990930i \(0.0315941\pi\)
\(752\) 3.20400i 0.116838i
\(753\) 0 0
\(754\) −2.58172 19.4480i −0.0940206 0.708254i
\(755\) 16.8187 0.612095
\(756\) 0 0
\(757\) −16.1404 27.9560i −0.586633 1.01608i −0.994670 0.103112i \(-0.967120\pi\)
0.408037 0.912965i \(-0.366213\pi\)
\(758\) 21.0737 0.765431
\(759\) 0 0
\(760\) −8.59323 + 4.96130i −0.311709 + 0.179965i
\(761\) 29.7517i 1.07850i 0.842147 + 0.539249i \(0.181292\pi\)
−0.842147 + 0.539249i \(0.818708\pi\)
\(762\) 0 0
\(763\) −5.88869 14.2826i −0.213185 0.517064i
\(764\) 0.451761 + 0.782473i 0.0163441 + 0.0283089i
\(765\) 0 0
\(766\) −16.5684 + 28.6972i −0.598639 + 1.03687i
\(767\) −31.9672 + 24.5841i −1.15427 + 0.887680i
\(768\) 0 0
\(769\) −36.2090 + 20.9053i −1.30573 + 0.753863i −0.981380 0.192075i \(-0.938478\pi\)
−0.324349 + 0.945938i \(0.605145\pi\)
\(770\) 9.90541 12.8654i 0.356966 0.463635i
\(771\) 0 0
\(772\) −3.46856 + 2.00257i −0.124836 + 0.0720742i
\(773\) −35.8826 + 20.7168i −1.29061 + 0.745132i −0.978762 0.205001i \(-0.934280\pi\)
−0.311845 + 0.950133i \(0.600947\pi\)
\(774\) 0 0
\(775\) −34.4864 + 19.9107i −1.23879 + 0.715215i
\(776\) 0.705044 1.22117i 0.0253096 0.0438375i
\(777\) 0 0
\(778\) −21.9680 + 12.6832i −0.787592 + 0.454716i
\(779\) 1.98159 + 3.43221i 0.0709978 + 0.122972i
\(780\) 0 0
\(781\) −7.30376 + 12.6505i −0.261349 + 0.452670i
\(782\) −14.8521 8.57486i −0.531110 0.306637i
\(783\) 0 0
\(784\) 24.2052 + 6.57071i 0.864472 + 0.234668i
\(785\) 32.1175i 1.14632i
\(786\) 0 0
\(787\) 20.6657 11.9313i 0.736651 0.425306i −0.0841992 0.996449i \(-0.526833\pi\)
0.820851 + 0.571143i \(0.193500\pi\)
\(788\) 0.958193 + 0.553213i 0.0341342