Properties

Label 403.2.l.c.25.6
Level 403
Weight 2
Character 403.25
Analytic conductor 3.218
Analytic rank 0
Dimension 68
CM No

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.l (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(\zeta_{6})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 25.6
Character \(\chi\) = 403.25
Dual form 403.2.l.c.129.29

$q$-expansion

\(f(q)\) \(=\) \(q-2.06821i q^{2} +(-0.348471 - 0.603570i) q^{3} -2.27750 q^{4} +(1.11091 + 0.641386i) q^{5} +(-1.24831 + 0.720713i) q^{6} +(2.98944 - 1.72596i) q^{7} +0.573935i q^{8} +(1.25714 - 2.17742i) q^{9} +O(q^{10})\) \(q-2.06821i q^{2} +(-0.348471 - 0.603570i) q^{3} -2.27750 q^{4} +(1.11091 + 0.641386i) q^{5} +(-1.24831 + 0.720713i) q^{6} +(2.98944 - 1.72596i) q^{7} +0.573935i q^{8} +(1.25714 - 2.17742i) q^{9} +(1.32652 - 2.29760i) q^{10} +(2.29914 + 1.32741i) q^{11} +(0.793644 + 1.37463i) q^{12} +(1.98762 + 3.00822i) q^{13} +(-3.56964 - 6.18280i) q^{14} -0.894018i q^{15} -3.36799 q^{16} +(-0.311325 - 0.539231i) q^{17} +(-4.50337 - 2.60002i) q^{18} +(-3.82177 + 2.20650i) q^{19} +(-2.53011 - 1.46076i) q^{20} +(-2.08347 - 1.20289i) q^{21} +(2.74536 - 4.75510i) q^{22} -2.13692 q^{23} +(0.346410 - 0.200000i) q^{24} +(-1.67725 - 2.90508i) q^{25} +(6.22163 - 4.11082i) q^{26} -3.84313 q^{27} +(-6.80846 + 3.93087i) q^{28} -4.05259 q^{29} -1.84902 q^{30} +(5.48436 - 0.960081i) q^{31} +8.11358i q^{32} -1.85025i q^{33} +(-1.11524 + 0.643887i) q^{34} +4.42801 q^{35} +(-2.86313 + 4.95909i) q^{36} +(-5.19824 + 3.00121i) q^{37} +(4.56351 + 7.90423i) q^{38} +(1.12304 - 2.24794i) q^{39} +(-0.368114 + 0.637592i) q^{40} +(-0.662206 - 0.382325i) q^{41} +(-2.48784 + 4.30906i) q^{42} +(5.41024 + 9.37081i) q^{43} +(-5.23629 - 3.02317i) q^{44} +(2.79314 - 1.61262i) q^{45} +4.41960i q^{46} -8.87335i q^{47} +(1.17365 + 2.03281i) q^{48} +(2.45784 - 4.25711i) q^{49} +(-6.00832 + 3.46891i) q^{50} +(-0.216976 + 0.375813i) q^{51} +(-4.52681 - 6.85122i) q^{52} +(-5.00538 + 8.66957i) q^{53} +7.94841i q^{54} +(1.70276 + 2.94927i) q^{55} +(0.990586 + 1.71575i) q^{56} +(2.66355 + 1.53780i) q^{57} +8.38163i q^{58} +(5.08142 - 2.93376i) q^{59} +2.03613i q^{60} +4.84999 q^{61} +(-1.98565 - 11.3428i) q^{62} -8.67904i q^{63} +10.0446 q^{64} +(0.278647 + 4.61670i) q^{65} -3.82671 q^{66} +(7.78781 + 4.49629i) q^{67} +(0.709044 + 1.22810i) q^{68} +(0.744655 + 1.28978i) q^{69} -9.15807i q^{70} +(6.12061 + 3.53374i) q^{71} +(1.24970 + 0.721514i) q^{72} +(0.366719 + 0.211725i) q^{73} +(6.20714 + 10.7511i) q^{74} +(-1.16895 + 2.02467i) q^{75} +(8.70409 - 5.02531i) q^{76} +9.16418 q^{77} +(-4.64923 - 2.32268i) q^{78} +(-3.01527 - 5.22259i) q^{79} +(-3.74154 - 2.16018i) q^{80} +(-2.43219 - 4.21267i) q^{81} +(-0.790729 + 1.36958i) q^{82} +(-9.86842 - 5.69753i) q^{83} +(4.74511 + 2.73959i) q^{84} -0.798718i q^{85} +(19.3808 - 11.1895i) q^{86} +(1.41221 + 2.44602i) q^{87} +(-0.761845 + 1.31955i) q^{88} -11.5953i q^{89} +(-3.33524 - 5.77680i) q^{90} +(11.1339 + 5.56234i) q^{91} +4.86684 q^{92} +(-2.49062 - 2.97564i) q^{93} -18.3520 q^{94} -5.66087 q^{95} +(4.89711 - 2.82735i) q^{96} +18.6165i q^{97} +(-8.80461 - 5.08335i) q^{98} +(5.78065 - 3.33746i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68q - 6q^{3} - 76q^{4} - 40q^{9} + O(q^{10}) \) \( 68q - 6q^{3} - 76q^{4} - 40q^{9} + 8q^{10} - 10q^{12} - 3q^{13} + 10q^{14} + 84q^{16} + 6q^{17} + 4q^{22} - 44q^{23} + 30q^{25} - 3q^{26} - 12q^{27} + 48q^{29} - 4q^{30} - 48q^{35} + 40q^{36} + 60q^{38} - 14q^{39} + 20q^{40} - 10q^{42} - 12q^{43} + 32q^{48} + 58q^{49} + 20q^{51} - 27q^{52} + 8q^{53} - 36q^{55} - 50q^{56} - 12q^{61} - 74q^{62} - 15q^{65} + 164q^{66} + 4q^{68} - 34q^{69} - 4q^{74} + 20q^{75} - 200q^{77} - 58q^{78} - 80q^{79} - 82q^{81} - 66q^{82} + 52q^{87} + 16q^{88} - 14q^{90} - 70q^{91} + 108q^{92} - 4q^{94} + 76q^{95} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.06821i 1.46245i −0.682138 0.731224i \(-0.738950\pi\)
0.682138 0.731224i \(-0.261050\pi\)
\(3\) −0.348471 0.603570i −0.201190 0.348471i 0.747722 0.664012i \(-0.231148\pi\)
−0.948912 + 0.315541i \(0.897814\pi\)
\(4\) −2.27750 −1.13875
\(5\) 1.11091 + 0.641386i 0.496815 + 0.286836i 0.727397 0.686216i \(-0.240730\pi\)
−0.230582 + 0.973053i \(0.574063\pi\)
\(6\) −1.24831 + 0.720713i −0.509621 + 0.294230i
\(7\) 2.98944 1.72596i 1.12990 0.652350i 0.185993 0.982551i \(-0.440450\pi\)
0.943911 + 0.330201i \(0.107117\pi\)
\(8\) 0.573935i 0.202917i
\(9\) 1.25714 2.17742i 0.419045 0.725808i
\(10\) 1.32652 2.29760i 0.419483 0.726566i
\(11\) 2.29914 + 1.32741i 0.693216 + 0.400228i 0.804816 0.593525i \(-0.202264\pi\)
−0.111600 + 0.993753i \(0.535598\pi\)
\(12\) 0.793644 + 1.37463i 0.229105 + 0.396822i
\(13\) 1.98762 + 3.00822i 0.551267 + 0.834329i
\(14\) −3.56964 6.18280i −0.954027 1.65242i
\(15\) 0.894018i 0.230834i
\(16\) −3.36799 −0.841997
\(17\) −0.311325 0.539231i −0.0755075 0.130783i 0.825799 0.563964i \(-0.190724\pi\)
−0.901307 + 0.433181i \(0.857391\pi\)
\(18\) −4.50337 2.60002i −1.06146 0.612831i
\(19\) −3.82177 + 2.20650i −0.876773 + 0.506205i −0.869593 0.493769i \(-0.835619\pi\)
−0.00718028 + 0.999974i \(0.502286\pi\)
\(20\) −2.53011 1.46076i −0.565749 0.326635i
\(21\) −2.08347 1.20289i −0.454650 0.262492i
\(22\) 2.74536 4.75510i 0.585313 1.01379i
\(23\) −2.13692 −0.445578 −0.222789 0.974867i \(-0.571516\pi\)
−0.222789 + 0.974867i \(0.571516\pi\)
\(24\) 0.346410 0.200000i 0.0707106 0.0408248i
\(25\) −1.67725 2.90508i −0.335450 0.581016i
\(26\) 6.22163 4.11082i 1.22016 0.806199i
\(27\) −3.84313 −0.739611
\(28\) −6.80846 + 3.93087i −1.28668 + 0.742864i
\(29\) −4.05259 −0.752548 −0.376274 0.926508i \(-0.622795\pi\)
−0.376274 + 0.926508i \(0.622795\pi\)
\(30\) −1.84902 −0.337583
\(31\) 5.48436 0.960081i 0.985021 0.172436i
\(32\) 8.11358i 1.43429i
\(33\) 1.85025i 0.322088i
\(34\) −1.11524 + 0.643887i −0.191263 + 0.110426i
\(35\) 4.42801 0.748471
\(36\) −2.86313 + 4.95909i −0.477188 + 0.826514i
\(37\) −5.19824 + 3.00121i −0.854586 + 0.493396i −0.862196 0.506575i \(-0.830911\pi\)
0.00760943 + 0.999971i \(0.497578\pi\)
\(38\) 4.56351 + 7.90423i 0.740299 + 1.28223i
\(39\) 1.12304 2.24794i 0.179830 0.359959i
\(40\) −0.368114 + 0.637592i −0.0582039 + 0.100812i
\(41\) −0.662206 0.382325i −0.103419 0.0597091i 0.447398 0.894335i \(-0.352351\pi\)
−0.550818 + 0.834626i \(0.685684\pi\)
\(42\) −2.48784 + 4.30906i −0.383881 + 0.664902i
\(43\) 5.41024 + 9.37081i 0.825054 + 1.42904i 0.901878 + 0.431990i \(0.142189\pi\)
−0.0768244 + 0.997045i \(0.524478\pi\)
\(44\) −5.23629 3.02317i −0.789400 0.455760i
\(45\) 2.79314 1.61262i 0.416376 0.240395i
\(46\) 4.41960i 0.651635i
\(47\) 8.87335i 1.29431i −0.762358 0.647156i \(-0.775958\pi\)
0.762358 0.647156i \(-0.224042\pi\)
\(48\) 1.17365 + 2.03281i 0.169401 + 0.293412i
\(49\) 2.45784 4.25711i 0.351121 0.608159i
\(50\) −6.00832 + 3.46891i −0.849705 + 0.490577i
\(51\) −0.216976 + 0.375813i −0.0303827 + 0.0526244i
\(52\) −4.52681 6.85122i −0.627756 0.950093i
\(53\) −5.00538 + 8.66957i −0.687541 + 1.19086i 0.285089 + 0.958501i \(0.407977\pi\)
−0.972631 + 0.232356i \(0.925357\pi\)
\(54\) 7.94841i 1.08164i
\(55\) 1.70276 + 2.94927i 0.229600 + 0.397679i
\(56\) 0.990586 + 1.71575i 0.132373 + 0.229276i
\(57\) 2.66355 + 1.53780i 0.352796 + 0.203687i
\(58\) 8.38163i 1.10056i
\(59\) 5.08142 2.93376i 0.661544 0.381943i −0.131321 0.991340i \(-0.541922\pi\)
0.792865 + 0.609397i \(0.208588\pi\)
\(60\) 2.03613i 0.262863i
\(61\) 4.84999 0.620978 0.310489 0.950577i \(-0.399507\pi\)
0.310489 + 0.950577i \(0.399507\pi\)
\(62\) −1.98565 11.3428i −0.252178 1.44054i
\(63\) 8.67904i 1.09346i
\(64\) 10.0446 1.25558
\(65\) 0.278647 + 4.61670i 0.0345619 + 0.572631i
\(66\) −3.82671 −0.471036
\(67\) 7.78781 + 4.49629i 0.951432 + 0.549310i 0.893526 0.449012i \(-0.148224\pi\)
0.0579067 + 0.998322i \(0.481557\pi\)
\(68\) 0.709044 + 1.22810i 0.0859842 + 0.148929i
\(69\) 0.744655 + 1.28978i 0.0896459 + 0.155271i
\(70\) 9.15807i 1.09460i
\(71\) 6.12061 + 3.53374i 0.726383 + 0.419378i 0.817098 0.576499i \(-0.195582\pi\)
−0.0907143 + 0.995877i \(0.528915\pi\)
\(72\) 1.24970 + 0.721514i 0.147278 + 0.0850312i
\(73\) 0.366719 + 0.211725i 0.0429212 + 0.0247806i 0.521307 0.853369i \(-0.325445\pi\)
−0.478386 + 0.878150i \(0.658778\pi\)
\(74\) 6.20714 + 10.7511i 0.721565 + 1.24979i
\(75\) −1.16895 + 2.02467i −0.134978 + 0.233789i
\(76\) 8.70409 5.02531i 0.998427 0.576442i
\(77\) 9.16418 1.04436
\(78\) −4.64923 2.32268i −0.526421 0.262992i
\(79\) −3.01527 5.22259i −0.339244 0.587588i 0.645047 0.764143i \(-0.276838\pi\)
−0.984291 + 0.176555i \(0.943505\pi\)
\(80\) −3.74154 2.16018i −0.418317 0.241515i
\(81\) −2.43219 4.21267i −0.270243 0.468075i
\(82\) −0.790729 + 1.36958i −0.0873214 + 0.151245i
\(83\) −9.86842 5.69753i −1.08320 0.625386i −0.151442 0.988466i \(-0.548392\pi\)
−0.931758 + 0.363081i \(0.881725\pi\)
\(84\) 4.74511 + 2.73959i 0.517734 + 0.298914i
\(85\) 0.798718i 0.0866332i
\(86\) 19.3808 11.1895i 2.08989 1.20660i
\(87\) 1.41221 + 2.44602i 0.151405 + 0.262241i
\(88\) −0.761845 + 1.31955i −0.0812130 + 0.140665i
\(89\) 11.5953i 1.22910i −0.788879 0.614549i \(-0.789338\pi\)
0.788879 0.614549i \(-0.210662\pi\)
\(90\) −3.33524 5.77680i −0.351565 0.608928i
\(91\) 11.1339 + 5.56234i 1.16715 + 0.583092i
\(92\) 4.86684 0.507403
\(93\) −2.49062 2.97564i −0.258265 0.308559i
\(94\) −18.3520 −1.89286
\(95\) −5.66087 −0.580793
\(96\) 4.89711 2.82735i 0.499810 0.288565i
\(97\) 18.6165i 1.89022i 0.326751 + 0.945110i \(0.394046\pi\)
−0.326751 + 0.945110i \(0.605954\pi\)
\(98\) −8.80461 5.08335i −0.889400 0.513495i
\(99\) 5.78065 3.33746i 0.580977 0.335427i
\(100\) 3.81994 + 6.61633i 0.381994 + 0.661633i
\(101\) −12.9078 −1.28438 −0.642190 0.766546i \(-0.721974\pi\)
−0.642190 + 0.766546i \(0.721974\pi\)
\(102\) 0.777261 + 0.448752i 0.0769603 + 0.0444331i
\(103\) −4.32061 + 7.48352i −0.425723 + 0.737373i −0.996488 0.0837403i \(-0.973313\pi\)
0.570765 + 0.821113i \(0.306647\pi\)
\(104\) −1.72652 + 1.14077i −0.169299 + 0.111861i
\(105\) −1.54304 2.67262i −0.150585 0.260821i
\(106\) 17.9305 + 10.3522i 1.74156 + 1.00549i
\(107\) −2.90223 5.02681i −0.280569 0.485960i 0.690956 0.722897i \(-0.257190\pi\)
−0.971525 + 0.236937i \(0.923857\pi\)
\(108\) 8.75274 0.842233
\(109\) 9.17119i 0.878441i 0.898379 + 0.439220i \(0.144745\pi\)
−0.898379 + 0.439220i \(0.855255\pi\)
\(110\) 6.09971 3.52167i 0.581585 0.335778i
\(111\) 3.62288 + 2.09167i 0.343868 + 0.198532i
\(112\) −10.0684 + 5.81299i −0.951375 + 0.549276i
\(113\) 3.60544 6.24481i 0.339171 0.587462i −0.645106 0.764093i \(-0.723187\pi\)
0.984277 + 0.176631i \(0.0565200\pi\)
\(114\) 3.18050 5.50879i 0.297881 0.515946i
\(115\) −2.37393 1.37059i −0.221370 0.127808i
\(116\) 9.22980 0.856965
\(117\) 9.04887 0.546157i 0.836568 0.0504922i
\(118\) −6.06763 10.5095i −0.558571 0.967473i
\(119\) −1.86138 1.07467i −0.170632 0.0985146i
\(120\) 0.513108 0.0468402
\(121\) −1.97598 3.42250i −0.179635 0.311137i
\(122\) 10.0308i 0.908147i
\(123\) 0.532917i 0.0480515i
\(124\) −12.4907 + 2.18659i −1.12169 + 0.196361i
\(125\) 10.7169i 0.958550i
\(126\) −17.9501 −1.59912
\(127\) 6.26347 + 10.8487i 0.555793 + 0.962662i 0.997841 + 0.0656710i \(0.0209188\pi\)
−0.442048 + 0.896991i \(0.645748\pi\)
\(128\) 4.54728i 0.401927i
\(129\) 3.77063 6.53091i 0.331985 0.575015i
\(130\) 9.54831 0.576301i 0.837442 0.0505450i
\(131\) 7.15699 + 12.3963i 0.625309 + 1.08307i 0.988481 + 0.151344i \(0.0483603\pi\)
−0.363172 + 0.931722i \(0.618306\pi\)
\(132\) 4.21395i 0.366778i
\(133\) −7.61664 + 13.1924i −0.660446 + 1.14393i
\(134\) 9.29929 16.1068i 0.803336 1.39142i
\(135\) −4.26938 2.46493i −0.367450 0.212147i
\(136\) 0.309484 0.178680i 0.0265380 0.0153217i
\(137\) 8.49148 + 4.90256i 0.725476 + 0.418854i 0.816765 0.576971i \(-0.195765\pi\)
−0.0912890 + 0.995824i \(0.529099\pi\)
\(138\) 2.66754 1.54010i 0.227076 0.131102i
\(139\) 17.1513 1.45475 0.727377 0.686238i \(-0.240739\pi\)
0.727377 + 0.686238i \(0.240739\pi\)
\(140\) −10.0848 −0.852322
\(141\) −5.35569 + 3.09211i −0.451030 + 0.260402i
\(142\) 7.30852 12.6587i 0.613317 1.06230i
\(143\) 0.576686 + 9.55468i 0.0482249 + 0.799002i
\(144\) −4.23402 + 7.33353i −0.352835 + 0.611128i
\(145\) −4.50208 2.59928i −0.373877 0.215858i
\(146\) 0.437893 0.758453i 0.0362403 0.0627700i
\(147\) −3.42595 −0.282568
\(148\) 11.8390 6.83526i 0.973161 0.561855i
\(149\) −1.18527 + 0.684314i −0.0971008 + 0.0560611i −0.547764 0.836633i \(-0.684521\pi\)
0.450663 + 0.892694i \(0.351188\pi\)
\(150\) 4.18745 + 2.41763i 0.341904 + 0.197398i
\(151\) 17.3987i 1.41588i 0.706270 + 0.707942i \(0.250376\pi\)
−0.706270 + 0.707942i \(0.749624\pi\)
\(152\) −1.26639 2.19345i −0.102718 0.177912i
\(153\) −1.56551 −0.126564
\(154\) 18.9535i 1.52731i
\(155\) 6.70843 + 2.45103i 0.538834 + 0.196871i
\(156\) −2.55773 + 5.11970i −0.204782 + 0.409904i
\(157\) −15.3718 −1.22681 −0.613403 0.789770i \(-0.710200\pi\)
−0.613403 + 0.789770i \(0.710200\pi\)
\(158\) −10.8014 + 6.23621i −0.859316 + 0.496126i
\(159\) 6.97692 0.553306
\(160\) −5.20394 + 9.01348i −0.411407 + 0.712578i
\(161\) −6.38819 + 3.68823i −0.503460 + 0.290673i
\(162\) −8.71270 + 5.03028i −0.684534 + 0.395216i
\(163\) 3.80971i 0.298400i 0.988807 + 0.149200i \(0.0476698\pi\)
−0.988807 + 0.149200i \(0.952330\pi\)
\(164\) 1.50818 + 0.870746i 0.117769 + 0.0679938i
\(165\) 1.18673 2.05547i 0.0923865 0.160018i
\(166\) −11.7837 + 20.4100i −0.914593 + 1.58412i
\(167\) 12.1600 7.02055i 0.940966 0.543267i 0.0507028 0.998714i \(-0.483854\pi\)
0.890263 + 0.455447i \(0.150521\pi\)
\(168\) 0.690382 1.19578i 0.0532641 0.0922561i
\(169\) −5.09872 + 11.9584i −0.392209 + 0.919876i
\(170\) −1.65192 −0.126696
\(171\) 11.0955i 0.848492i
\(172\) −12.3218 21.3420i −0.939531 1.62732i
\(173\) 5.66149 9.80598i 0.430435 0.745535i −0.566476 0.824078i \(-0.691694\pi\)
0.996911 + 0.0785434i \(0.0250269\pi\)
\(174\) 5.05890 2.92076i 0.383514 0.221422i
\(175\) −10.0281 5.78971i −0.758051 0.437661i
\(176\) −7.74346 4.47069i −0.583685 0.336991i
\(177\) −3.54146 2.04466i −0.266192 0.153686i
\(178\) −23.9815 −1.79749
\(179\) 5.99710 + 10.3873i 0.448245 + 0.776382i 0.998272 0.0587644i \(-0.0187161\pi\)
−0.550027 + 0.835147i \(0.685383\pi\)
\(180\) −6.36138 + 3.67274i −0.474149 + 0.273750i
\(181\) 4.35364 7.54072i 0.323603 0.560497i −0.657625 0.753345i \(-0.728439\pi\)
0.981229 + 0.192848i \(0.0617724\pi\)
\(182\) 11.5041 23.0273i 0.852741 1.70690i
\(183\) −1.69008 2.92731i −0.124935 0.216393i
\(184\) 1.22645i 0.0904153i
\(185\) −7.69973 −0.566095
\(186\) −6.15425 + 5.15113i −0.451251 + 0.377699i
\(187\) 1.65302i 0.120881i
\(188\) 20.2091i 1.47390i
\(189\) −11.4888 + 6.63307i −0.835688 + 0.482485i
\(190\) 11.7079i 0.849379i
\(191\) −0.249217 + 0.431657i −0.0180327 + 0.0312336i −0.874901 0.484302i \(-0.839074\pi\)
0.856868 + 0.515535i \(0.172407\pi\)
\(192\) −3.50027 6.06264i −0.252610 0.437533i
\(193\) 3.56944 2.06082i 0.256934 0.148341i −0.366001 0.930614i \(-0.619273\pi\)
0.622935 + 0.782274i \(0.285940\pi\)
\(194\) 38.5029 2.76435
\(195\) 2.68940 1.77697i 0.192592 0.127251i
\(196\) −5.59775 + 9.69558i −0.399839 + 0.692542i
\(197\) −19.3805 11.1893i −1.38080 0.797206i −0.388546 0.921429i \(-0.627023\pi\)
−0.992254 + 0.124224i \(0.960356\pi\)
\(198\) −6.90258 11.9556i −0.490545 0.849649i
\(199\) 9.89986 17.1471i 0.701782 1.21552i −0.266058 0.963957i \(-0.585721\pi\)
0.967840 0.251565i \(-0.0809454\pi\)
\(200\) 1.66733 0.962631i 0.117898 0.0680683i
\(201\) 6.26731i 0.442062i
\(202\) 26.6962i 1.87834i
\(203\) −12.1150 + 6.99460i −0.850306 + 0.490925i
\(204\) 0.494163 0.855915i 0.0345983 0.0599261i
\(205\) −0.490435 0.849459i −0.0342535 0.0593288i
\(206\) 15.4775 + 8.93594i 1.07837 + 0.622597i
\(207\) −2.68640 + 4.65297i −0.186717 + 0.323404i
\(208\) −6.69428 10.1316i −0.464165 0.702502i
\(209\) −11.7157 −0.810391
\(210\) −5.52754 + 3.19132i −0.381436 + 0.220222i
\(211\) −6.72757 11.6525i −0.463145 0.802191i 0.535971 0.844237i \(-0.319946\pi\)
−0.999116 + 0.0420460i \(0.986612\pi\)
\(212\) 11.3998 19.7450i 0.782939 1.35609i
\(213\) 4.92562i 0.337498i
\(214\) −10.3965 + 6.00243i −0.710691 + 0.410318i
\(215\) 13.8802i 0.946622i
\(216\) 2.20571i 0.150079i
\(217\) 14.7381 12.3359i 1.00049 0.837414i
\(218\) 18.9680 1.28467
\(219\) 0.295121i 0.0199424i
\(220\) −3.87804 6.71696i −0.261457 0.452858i
\(221\) 1.00333 2.00832i 0.0674911 0.135094i
\(222\) 4.32602 7.49288i 0.290343 0.502889i
\(223\) −12.9438 + 7.47308i −0.866778 + 0.500435i −0.866276 0.499565i \(-0.833493\pi\)
−0.000501934 1.00000i \(0.500160\pi\)
\(224\) 14.0037 + 24.2551i 0.935660 + 1.62061i
\(225\) −8.43412 −0.562274
\(226\) −12.9156 7.45682i −0.859132 0.496020i
\(227\) −9.55725 5.51788i −0.634337 0.366234i 0.148093 0.988973i \(-0.452687\pi\)
−0.782430 + 0.622739i \(0.786020\pi\)
\(228\) −6.06625 3.50235i −0.401747 0.231949i
\(229\) 1.53880 0.888428i 0.101687 0.0587090i −0.448294 0.893886i \(-0.647968\pi\)
0.549981 + 0.835177i \(0.314635\pi\)
\(230\) −2.83467 + 4.90979i −0.186913 + 0.323742i
\(231\) −3.19345 5.53122i −0.210114 0.363928i
\(232\) 2.32593i 0.152704i
\(233\) −29.5964 −1.93893 −0.969463 0.245236i \(-0.921135\pi\)
−0.969463 + 0.245236i \(0.921135\pi\)
\(234\) −1.12957 18.7150i −0.0738422 1.22344i
\(235\) 5.69124 9.85752i 0.371256 0.643034i
\(236\) −11.5729 + 6.68164i −0.753334 + 0.434938i
\(237\) −2.10147 + 3.63985i −0.136505 + 0.236434i
\(238\) −2.22264 + 3.84972i −0.144072 + 0.249541i
\(239\) 21.6614 + 12.5062i 1.40116 + 0.808961i 0.994512 0.104624i \(-0.0333639\pi\)
0.406649 + 0.913584i \(0.366697\pi\)
\(240\) 3.01104i 0.194362i
\(241\) 3.34243 1.92975i 0.215305 0.124306i −0.388469 0.921462i \(-0.626996\pi\)
0.603774 + 0.797155i \(0.293663\pi\)
\(242\) −7.07846 + 4.08675i −0.455021 + 0.262706i
\(243\) −7.45979 + 12.9207i −0.478546 + 0.828865i
\(244\) −11.0459 −0.707140
\(245\) 5.46090 3.15285i 0.348884 0.201428i
\(246\) 1.10218 0.0702727
\(247\) −14.2338 7.11102i −0.905678 0.452463i
\(248\) 0.551024 + 3.14767i 0.0349901 + 0.199877i
\(249\) 7.94171i 0.503285i
\(250\) −22.1649 −1.40183
\(251\) 5.31184 + 9.20038i 0.335281 + 0.580723i 0.983539 0.180698i \(-0.0578355\pi\)
−0.648258 + 0.761421i \(0.724502\pi\)
\(252\) 19.7665i 1.24517i
\(253\) −4.91307 2.83656i −0.308882 0.178333i
\(254\) 22.4373 12.9542i 1.40784 0.812818i
\(255\) −0.482082 + 0.278330i −0.0301892 + 0.0174297i
\(256\) 10.6845 0.667783
\(257\) 15.0513 26.0696i 0.938873 1.62618i 0.171296 0.985220i \(-0.445204\pi\)
0.767577 0.640957i \(-0.221462\pi\)
\(258\) −13.5073 7.79845i −0.840929 0.485511i
\(259\) −10.3599 + 17.9439i −0.643733 + 1.11498i
\(260\) −0.634620 10.5145i −0.0393574 0.652084i
\(261\) −5.09466 + 8.82421i −0.315352 + 0.546205i
\(262\) 25.6381 14.8022i 1.58393 0.914481i
\(263\) 1.94425 0.119887 0.0599437 0.998202i \(-0.480908\pi\)
0.0599437 + 0.998202i \(0.480908\pi\)
\(264\) 1.06192 0.0653569
\(265\) −11.1211 + 6.42076i −0.683162 + 0.394424i
\(266\) 27.2847 + 15.7528i 1.67293 + 0.965867i
\(267\) −6.99856 + 4.04062i −0.428305 + 0.247282i
\(268\) −17.7368 10.2403i −1.08344 0.625527i
\(269\) −0.863890 + 1.49630i −0.0526723 + 0.0912311i −0.891159 0.453690i \(-0.850107\pi\)
0.838487 + 0.544921i \(0.183441\pi\)
\(270\) −5.09800 + 8.82999i −0.310254 + 0.537376i
\(271\) 17.1850i 1.04392i −0.852971 0.521959i \(-0.825202\pi\)
0.852971 0.521959i \(-0.174798\pi\)
\(272\) 1.04854 + 1.81612i 0.0635770 + 0.110119i
\(273\) −0.522591 8.65842i −0.0316286 0.524031i
\(274\) 10.1395 17.5622i 0.612551 1.06097i
\(275\) 8.90556i 0.537026i
\(276\) −1.69595 2.93748i −0.102084 0.176815i
\(277\) −19.9631 −1.19947 −0.599735 0.800199i \(-0.704727\pi\)
−0.599735 + 0.800199i \(0.704727\pi\)
\(278\) 35.4725i 2.12750i
\(279\) 4.80409 13.1487i 0.287613 0.787194i
\(280\) 2.54139i 0.151877i
\(281\) 13.1808i 0.786301i 0.919474 + 0.393151i \(0.128615\pi\)
−0.919474 + 0.393151i \(0.871385\pi\)
\(282\) 6.39513 + 11.0767i 0.380825 + 0.659608i
\(283\) −7.22978 −0.429766 −0.214883 0.976640i \(-0.568937\pi\)
−0.214883 + 0.976640i \(0.568937\pi\)
\(284\) −13.9397 8.04810i −0.827170 0.477567i
\(285\) 1.97265 + 3.41673i 0.116850 + 0.202390i
\(286\) 19.7611 1.19271i 1.16850 0.0705263i
\(287\) −2.63950 −0.155805
\(288\) 17.6667 + 10.1999i 1.04102 + 0.601033i
\(289\) 8.30615 14.3867i 0.488597 0.846275i
\(290\) −5.37586 + 9.31126i −0.315681 + 0.546776i
\(291\) 11.2364 6.48732i 0.658688 0.380293i
\(292\) −0.835203 0.482205i −0.0488766 0.0282189i
\(293\) 12.8562 7.42253i 0.751067 0.433629i −0.0750123 0.997183i \(-0.523900\pi\)
0.826079 + 0.563554i \(0.190566\pi\)
\(294\) 7.08560i 0.413240i
\(295\) 7.52668 0.438220
\(296\) −1.72250 2.98345i −0.100118 0.173410i
\(297\) −8.83588 5.10140i −0.512710 0.296013i
\(298\) 1.41531 + 2.45138i 0.0819865 + 0.142005i
\(299\) −4.24738 6.42831i −0.245633 0.371759i
\(300\) 2.66228 4.61120i 0.153707 0.266228i
\(301\) 32.3472 + 18.6757i 1.86446 + 1.07645i
\(302\) 35.9842 2.07066
\(303\) 4.49801 + 7.79079i 0.258404 + 0.447569i
\(304\) 12.8717 7.43146i 0.738240 0.426223i
\(305\) 5.38792 + 3.11072i 0.308511 + 0.178119i
\(306\) 3.23781i 0.185093i
\(307\) 19.0027 10.9712i 1.08454 0.626161i 0.152425 0.988315i \(-0.451292\pi\)
0.932118 + 0.362154i \(0.117958\pi\)
\(308\) −20.8714 −1.18926
\(309\) 6.02244 0.342604
\(310\) 5.06924 13.8745i 0.287914 0.788017i
\(311\) −13.2676 −0.752337 −0.376169 0.926551i \(-0.622759\pi\)
−0.376169 + 0.926551i \(0.622759\pi\)
\(312\) 1.29017 + 0.644552i 0.0730417 + 0.0364905i
\(313\) 1.21832 + 2.11020i 0.0688637 + 0.119275i 0.898401 0.439175i \(-0.144729\pi\)
−0.829538 + 0.558451i \(0.811396\pi\)
\(314\) 31.7922i 1.79414i
\(315\) 5.56661 9.64166i 0.313643 0.543246i
\(316\) 6.86728 + 11.8945i 0.386315 + 0.669116i
\(317\) −13.1774 + 7.60797i −0.740116 + 0.427306i −0.822112 0.569326i \(-0.807204\pi\)
0.0819953 + 0.996633i \(0.473871\pi\)
\(318\) 14.4298i 0.809180i
\(319\) −9.31747 5.37944i −0.521678 0.301191i
\(320\) 11.1587 + 6.44249i 0.623791 + 0.360146i
\(321\) −2.02269 + 3.50340i −0.112895 + 0.195541i
\(322\) 7.62804 + 13.2121i 0.425094 + 0.736284i
\(323\) 2.37963 + 1.37388i 0.132406 + 0.0764446i
\(324\) 5.53931 + 9.59437i 0.307740 + 0.533021i
\(325\) 5.40537 10.8197i 0.299836 0.600170i
\(326\) 7.87930 0.436394
\(327\) 5.53545 3.19590i 0.306111 0.176733i
\(328\) 0.219430 0.380063i 0.0121160 0.0209855i
\(329\) −15.3150 26.5264i −0.844344 1.46245i
\(330\) −4.25115 2.45440i −0.234018 0.135110i
\(331\) −7.48571 4.32187i −0.411452 0.237552i 0.279962 0.960011i \(-0.409678\pi\)
−0.691413 + 0.722459i \(0.743012\pi\)
\(332\) 22.4753 + 12.9761i 1.23349 + 0.712159i
\(333\) 15.0917i 0.827020i
\(334\) −14.5200 25.1494i −0.794499 1.37611i
\(335\) 5.76772 + 9.98998i 0.315124 + 0.545811i
\(336\) 7.01710 + 4.05132i 0.382814 + 0.221018i
\(337\) −0.0583086 −0.00317627 −0.00158814 0.999999i \(-0.500506\pi\)
−0.00158814 + 0.999999i \(0.500506\pi\)
\(338\) 24.7325 + 10.5452i 1.34527 + 0.573586i
\(339\) −5.02557 −0.272952
\(340\) 1.81908i 0.0986536i
\(341\) 13.8837 + 5.07263i 0.751845 + 0.274698i
\(342\) 22.9478 1.24087
\(343\) 7.19485i 0.388486i
\(344\) −5.37824 + 3.10513i −0.289975 + 0.167417i
\(345\) 1.91044i 0.102855i
\(346\) −20.2809 11.7092i −1.09031 0.629488i
\(347\) −10.5059 18.1968i −0.563986 0.976853i −0.997143 0.0755344i \(-0.975934\pi\)
0.433157 0.901319i \(-0.357400\pi\)
\(348\) −3.21632 5.57083i −0.172413 0.298628i
\(349\) 0.151167i 0.00809178i 0.999992 + 0.00404589i \(0.00128785\pi\)
−0.999992 + 0.00404589i \(0.998712\pi\)
\(350\) −11.9744 + 20.7402i −0.640056 + 1.10861i
\(351\) −7.63869 11.5610i −0.407723 0.617079i
\(352\) −10.7700 + 18.6542i −0.574044 + 0.994274i
\(353\) −2.43304 + 1.40472i −0.129498 + 0.0747655i −0.563349 0.826219i \(-0.690487\pi\)
0.433852 + 0.900984i \(0.357154\pi\)
\(354\) −4.22879 + 7.32448i −0.224758 + 0.389292i
\(355\) 4.53298 + 7.85135i 0.240586 + 0.416706i
\(356\) 26.4083i 1.39964i
\(357\) 1.49796i 0.0792806i
\(358\) 21.4831 12.4033i 1.13542 0.655534i
\(359\) 3.52243 + 2.03367i 0.185906 + 0.107333i 0.590065 0.807356i \(-0.299102\pi\)
−0.404158 + 0.914689i \(0.632436\pi\)
\(360\) 0.925538 + 1.60308i 0.0487801 + 0.0844897i
\(361\) 0.237269 0.410962i 0.0124878 0.0216296i
\(362\) −15.5958 9.00424i −0.819697 0.473253i
\(363\) −1.37715 + 2.38529i −0.0722814 + 0.125195i
\(364\) −25.3575 12.6683i −1.32910 0.663997i
\(365\) 0.271595 + 0.470417i 0.0142159 + 0.0246227i
\(366\) −6.05430 + 3.49545i −0.316463 + 0.182710i
\(367\) −15.1851 + 26.3013i −0.792655 + 1.37292i 0.131663 + 0.991295i \(0.457968\pi\)
−0.924318 + 0.381624i \(0.875365\pi\)
\(368\) 7.19711 0.375175
\(369\) −1.66497 + 0.961268i −0.0866746 + 0.0500416i
\(370\) 15.9247i 0.827884i
\(371\) 34.5562i 1.79407i
\(372\) 5.67239 + 6.77702i 0.294100 + 0.351372i
\(373\) 24.7458 1.28129 0.640645 0.767838i \(-0.278667\pi\)
0.640645 + 0.767838i \(0.278667\pi\)
\(374\) −3.41880 −0.176782
\(375\) −6.46840 + 3.73454i −0.334027 + 0.192851i
\(376\) 5.09273 0.262637
\(377\) −8.05502 12.1911i −0.414855 0.627872i
\(378\) 13.7186 + 23.7613i 0.705609 + 1.22215i
\(379\) 15.6277 9.02266i 0.802741 0.463463i −0.0416878 0.999131i \(-0.513273\pi\)
0.844429 + 0.535668i \(0.179940\pi\)
\(380\) 12.8926 0.661379
\(381\) 4.36528 7.56089i 0.223640 0.387356i
\(382\) 0.892758 + 0.515434i 0.0456775 + 0.0263719i
\(383\) 13.1254 + 7.57795i 0.670676 + 0.387215i 0.796333 0.604859i \(-0.206770\pi\)
−0.125657 + 0.992074i \(0.540104\pi\)
\(384\) −2.74460 + 1.58460i −0.140060 + 0.0808636i
\(385\) 10.1806 + 5.87778i 0.518852 + 0.299559i
\(386\) −4.26220 7.38236i −0.216941 0.375752i
\(387\) 27.2056 1.38294
\(388\) 42.3992i 2.15249i
\(389\) −16.5610 28.6845i −0.839675 1.45436i −0.890166 0.455635i \(-0.849412\pi\)
0.0504913 0.998725i \(-0.483921\pi\)
\(390\) −3.67515 5.56225i −0.186098 0.281655i
\(391\) 0.665277 + 1.15229i 0.0336445 + 0.0582740i
\(392\) 2.44331 + 1.41064i 0.123406 + 0.0712482i
\(393\) 4.98801 8.63948i 0.251612 0.435804i
\(394\) −23.1419 + 40.0829i −1.16587 + 2.01935i
\(395\) 7.73580i 0.389230i
\(396\) −13.1655 + 7.60108i −0.661589 + 0.381968i
\(397\) −10.8382 + 6.25743i −0.543953 + 0.314052i −0.746680 0.665184i \(-0.768353\pi\)
0.202726 + 0.979235i \(0.435020\pi\)
\(398\) −35.4638 20.4750i −1.77764 1.02632i
\(399\) 10.6167 0.531500
\(400\) 5.64895 + 9.78427i 0.282447 + 0.489213i
\(401\) 15.2680i 0.762449i −0.924482 0.381225i \(-0.875502\pi\)
0.924482 0.381225i \(-0.124498\pi\)
\(402\) −12.9621 −0.646493
\(403\) 13.7890 + 14.5899i 0.686877 + 0.726773i
\(404\) 29.3977 1.46259
\(405\) 6.23988i 0.310062i
\(406\) 14.4663 + 25.0564i 0.717951 + 1.24353i
\(407\) −15.9353 −0.789883
\(408\) −0.215692 0.124530i −0.0106784 0.00616515i
\(409\) −0.298830 + 0.172530i −0.0147762 + 0.00853104i −0.507370 0.861728i \(-0.669382\pi\)
0.492594 + 0.870259i \(0.336049\pi\)
\(410\) −1.75686 + 1.01432i −0.0867652 + 0.0500939i
\(411\) 6.83360i 0.337077i
\(412\) 9.84021 17.0437i 0.484792 0.839685i
\(413\) 10.1271 17.5406i 0.498321 0.863117i
\(414\) 9.62334 + 5.55604i 0.472961 + 0.273064i
\(415\) −7.30863 12.6589i −0.358767 0.621402i
\(416\) −24.4074 + 16.1267i −1.19667 + 0.790678i
\(417\) −5.97673 10.3520i −0.292682 0.506940i
\(418\) 24.2305i 1.18515i
\(419\) −27.6444 −1.35052 −0.675258 0.737582i \(-0.735968\pi\)
−0.675258 + 0.737582i \(0.735968\pi\)
\(420\) 3.51427 + 6.08689i 0.171479 + 0.297010i
\(421\) −15.4574 8.92435i −0.753349 0.434946i 0.0735539 0.997291i \(-0.476566\pi\)
−0.826903 + 0.562345i \(0.809899\pi\)
\(422\) −24.0998 + 13.9140i −1.17316 + 0.677325i
\(423\) −19.3210 11.1550i −0.939421 0.542375i
\(424\) −4.97577 2.87276i −0.241645 0.139514i
\(425\) −1.04434 + 1.80885i −0.0506579 + 0.0877421i
\(426\) −10.1872 −0.493573
\(427\) 14.4988 8.37087i 0.701645 0.405095i
\(428\) 6.60984 + 11.4486i 0.319499 + 0.553388i
\(429\) 5.56596 3.67760i 0.268727 0.177556i
\(430\) 28.7072 1.38438
\(431\) 8.13460 4.69651i 0.391830 0.226223i −0.291123 0.956686i \(-0.594029\pi\)
0.682953 + 0.730463i \(0.260695\pi\)
\(432\) 12.9436 0.622750
\(433\) −28.9476 −1.39113 −0.695567 0.718461i \(-0.744847\pi\)
−0.695567 + 0.718461i \(0.744847\pi\)
\(434\) −25.5132 30.4816i −1.22467 1.46316i
\(435\) 3.62309i 0.173714i
\(436\) 20.8874i 1.00033i
\(437\) 8.16680 4.71511i 0.390671 0.225554i
\(438\) −0.610372 −0.0291647
\(439\) −7.38765 + 12.7958i −0.352593 + 0.610710i −0.986703 0.162533i \(-0.948033\pi\)
0.634110 + 0.773243i \(0.281367\pi\)
\(440\) −1.69269 + 0.977273i −0.0806957 + 0.0465897i
\(441\) −6.17969 10.7035i −0.294271 0.509692i
\(442\) −4.15363 2.07509i −0.197568 0.0987021i
\(443\) −3.34122 + 5.78716i −0.158746 + 0.274956i −0.934417 0.356182i \(-0.884078\pi\)
0.775671 + 0.631138i \(0.217412\pi\)
\(444\) −8.25111 4.76378i −0.391581 0.226079i
\(445\) 7.43705 12.8814i 0.352550 0.610635i
\(446\) 15.4559 + 26.7704i 0.731859 + 1.26762i
\(447\) 0.826062 + 0.476927i 0.0390714 + 0.0225579i
\(448\) 30.0279 17.3366i 1.41868 0.819077i
\(449\) 18.2760i 0.862498i 0.902233 + 0.431249i \(0.141927\pi\)
−0.902233 + 0.431249i \(0.858073\pi\)
\(450\) 17.4435i 0.822296i
\(451\) −1.01500 1.75803i −0.0477945 0.0827826i
\(452\) −8.21140 + 14.2226i −0.386232 + 0.668973i
\(453\) 10.5013 6.06294i 0.493395 0.284862i
\(454\) −11.4121 + 19.7664i −0.535598 + 0.927684i
\(455\) 8.80121 + 13.3204i 0.412607 + 0.624471i
\(456\) −0.882598 + 1.52871i −0.0413315 + 0.0715882i
\(457\) 6.65501i 0.311308i 0.987812 + 0.155654i \(0.0497485\pi\)
−0.987812 + 0.155654i \(0.950251\pi\)
\(458\) −1.83746 3.18257i −0.0858588 0.148712i
\(459\) 1.19646 + 2.07234i 0.0558461 + 0.0967283i
\(460\) 5.40663 + 3.12152i 0.252086 + 0.145542i
\(461\) 14.2356i 0.663019i 0.943452 + 0.331510i \(0.107558\pi\)
−0.943452 + 0.331510i \(0.892442\pi\)
\(462\) −11.4397 + 6.60474i −0.532225 + 0.307280i
\(463\) 14.8710i 0.691112i −0.938398 0.345556i \(-0.887690\pi\)
0.938398 0.345556i \(-0.112310\pi\)
\(464\) 13.6491 0.633643
\(465\) −0.858330 4.90312i −0.0398041 0.227377i
\(466\) 61.2117i 2.83558i
\(467\) −31.3260 −1.44959 −0.724797 0.688963i \(-0.758066\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(468\) −20.6088 + 1.24387i −0.952643 + 0.0574981i
\(469\) 31.0416 1.43337
\(470\) −20.3874 11.7707i −0.940403 0.542942i
\(471\) 5.35664 + 9.27797i 0.246821 + 0.427506i
\(472\) 1.68379 + 2.91640i 0.0775025 + 0.134238i
\(473\) 28.7264i 1.32084i
\(474\) 7.52798 + 4.34628i 0.345772 + 0.199631i
\(475\) 12.8201 + 7.40169i 0.588227 + 0.339613i
\(476\) 4.23929 + 2.44756i 0.194308 + 0.112184i
\(477\) 12.5849 + 21.7976i 0.576222 + 0.998046i
\(478\) 25.8655 44.8004i 1.18306 2.04912i
\(479\) −1.28492 + 0.741848i −0.0587094 + 0.0338959i −0.529067 0.848580i \(-0.677458\pi\)
0.470358 + 0.882476i \(0.344125\pi\)
\(480\) 7.25369 0.331084
\(481\) −19.3604 9.67218i −0.882759 0.441013i
\(482\) −3.99114 6.91286i −0.181791 0.314872i
\(483\) 4.45220 + 2.57048i 0.202582 + 0.116961i
\(484\) 4.50031 + 7.79476i 0.204559 + 0.354307i
\(485\) −11.9404 + 20.6813i −0.542184 + 0.939091i
\(486\) 26.7228 + 15.4284i 1.21217 + 0.699848i
\(487\) −23.0573 13.3121i −1.04482 0.603229i −0.123628 0.992329i \(-0.539453\pi\)
−0.921196 + 0.389099i \(0.872786\pi\)
\(488\) 2.78358i 0.126007i
\(489\) 2.29943 1.32758i 0.103984 0.0600351i
\(490\) −6.52077 11.2943i −0.294578 0.510225i
\(491\) 1.47636 2.55713i 0.0666271 0.115401i −0.830788 0.556590i \(-0.812110\pi\)
0.897415 + 0.441188i \(0.145443\pi\)
\(492\) 1.21372i 0.0547187i
\(493\) 1.26167 + 2.18529i 0.0568230 + 0.0984203i
\(494\) −14.7071 + 29.4386i −0.661703 + 1.32451i
\(495\) 8.56240 0.384851
\(496\) −18.4713 + 3.23354i −0.829384 + 0.145190i
\(497\) 24.3963 1.09432
\(498\) 16.4251 0.736028
\(499\) 10.3354 5.96714i 0.462676 0.267126i −0.250493 0.968118i \(-0.580593\pi\)
0.713169 + 0.700992i \(0.247259\pi\)
\(500\) 24.4078i 1.09155i
\(501\) −8.47479 4.89292i −0.378626 0.218600i
\(502\) 19.0283 10.9860i 0.849277 0.490330i
\(503\) −0.399467 0.691896i −0.0178113 0.0308501i 0.856982 0.515346i \(-0.172336\pi\)
−0.874794 + 0.484496i \(0.839003\pi\)
\(504\) 4.98120 0.221880
\(505\) −14.3395 8.27891i −0.638099 0.368407i
\(506\) −5.86661 + 10.1613i −0.260803 + 0.451723i
\(507\) 8.99448 1.08972i 0.399459 0.0483961i
\(508\) −14.2651 24.7078i −0.632911 1.09623i
\(509\) −3.60542 2.08159i −0.159807 0.0922648i 0.417964 0.908464i \(-0.362744\pi\)
−0.577771 + 0.816199i \(0.696077\pi\)
\(510\) 0.575646 + 0.997049i 0.0254900 + 0.0441501i
\(511\) 1.46171 0.0646624
\(512\) 31.1924i 1.37852i
\(513\) 14.6875 8.47986i 0.648471 0.374395i
\(514\) −53.9175 31.1293i −2.37820 1.37305i
\(515\) −9.59965 + 5.54236i −0.423011 + 0.244226i
\(516\) −8.58761 + 14.8742i −0.378048 + 0.654799i
\(517\) 11.7785 20.4010i 0.518020 0.897237i
\(518\) 37.1118 + 21.4265i 1.63060 + 0.941426i
\(519\) −7.89146 −0.346397
\(520\) −2.64968 + 0.159925i −0.116196 + 0.00701319i
\(521\) 16.9377 + 29.3369i 0.742053 + 1.28527i 0.951559 + 0.307467i \(0.0994813\pi\)
−0.209505 + 0.977808i \(0.567185\pi\)
\(522\) 18.2503 + 10.5368i 0.798796 + 0.461185i
\(523\) 24.4347 1.06845 0.534227 0.845341i \(-0.320603\pi\)
0.534227 + 0.845341i \(0.320603\pi\)
\(524\) −16.3001 28.2325i −0.712071 1.23334i
\(525\) 8.07019i 0.352212i
\(526\) 4.02112i 0.175329i
\(527\) −2.22513 2.65844i −0.0969280 0.115804i
\(528\) 6.23162i 0.271197i
\(529\) −18.4336 −0.801460
\(530\) 13.2795 + 23.0007i 0.576824 + 0.999089i
\(531\) 14.7525i 0.640205i
\(532\) 17.3469 30.0457i 0.752084 1.30265i
\(533\) −0.166099 2.75198i −0.00719456 0.119201i
\(534\) 8.35687 + 14.4745i 0.361637 + 0.626374i
\(535\) 7.44580i 0.321910i
\(536\) −2.58058 + 4.46970i −0.111464 + 0.193061i
\(537\) 4.17964 7.23934i 0.180365 0.312401i
\(538\) 3.09467 + 1.78671i 0.133421 + 0.0770304i
\(539\) 11.3018 6.52512i 0.486805 0.281057i
\(540\) 9.72353 + 5.61388i 0.418434 + 0.241583i
\(541\) 24.2487 14.0000i 1.04253 0.601906i 0.121983 0.992532i \(-0.461075\pi\)
0.920550 + 0.390626i \(0.127741\pi\)
\(542\) −35.5423 −1.52667
\(543\) −6.06847 −0.260423
\(544\) 4.37510 2.52596i 0.187581 0.108300i
\(545\) −5.88227 + 10.1884i −0.251969 + 0.436423i
\(546\) −17.9074 + 1.08083i −0.766368 + 0.0462552i
\(547\) 21.1582 36.6471i 0.904661 1.56692i 0.0832896 0.996525i \(-0.473457\pi\)
0.821372 0.570394i \(-0.193209\pi\)
\(548\) −19.3394 11.1656i −0.826137 0.476970i
\(549\) 6.09710 10.5605i 0.260218 0.450711i
\(550\) −18.4186 −0.785372
\(551\) 15.4881 8.94204i 0.659814 0.380944i
\(552\) −0.740250 + 0.427383i −0.0315071 + 0.0181906i
\(553\) −18.0279 10.4084i −0.766626 0.442612i
\(554\) 41.2880i 1.75416i
\(555\) 2.68313 + 4.64732i 0.113893 + 0.197268i
\(556\) −39.0621 −1.65660
\(557\) 11.8516i 0.502168i 0.967965 + 0.251084i \(0.0807871\pi\)
−0.967965 + 0.251084i \(0.919213\pi\)
\(558\) −27.1944 9.93587i −1.15123 0.420619i
\(559\) −17.4359 + 34.9008i −0.737460 + 1.47615i
\(560\) −14.9135 −0.630210
\(561\) −0.997714 + 0.576030i −0.0421235 + 0.0243200i
\(562\) 27.2607 1.14992
\(563\) −10.8835 + 18.8508i −0.458685 + 0.794466i −0.998892 0.0470662i \(-0.985013\pi\)
0.540206 + 0.841533i \(0.318346\pi\)
\(564\) 12.1976 7.04228i 0.513611 0.296534i
\(565\) 8.01066 4.62496i 0.337011 0.194573i
\(566\) 14.9527i 0.628510i
\(567\) −14.5418 8.39569i −0.610697 0.352586i
\(568\) −2.02814 + 3.51283i −0.0850987 + 0.147395i
\(569\) −4.98669 + 8.63719i −0.209053 + 0.362090i −0.951416 0.307907i \(-0.900371\pi\)
0.742364 + 0.669997i \(0.233705\pi\)
\(570\) 7.06652 4.07986i 0.295984 0.170886i
\(571\) −4.00159 + 6.93096i −0.167461 + 0.290052i −0.937527 0.347914i \(-0.886890\pi\)
0.770065 + 0.637965i \(0.220224\pi\)
\(572\) −1.31340 21.7608i −0.0549162 0.909865i
\(573\) 0.347380 0.0145120
\(574\) 5.45905i 0.227856i
\(575\) 3.58414 + 6.20792i 0.149469 + 0.258888i
\(576\) 12.6275 21.8714i 0.526145 0.911309i
\(577\) 9.40891 5.43224i 0.391698 0.226147i −0.291198 0.956663i \(-0.594054\pi\)
0.682896 + 0.730516i \(0.260720\pi\)
\(578\) −29.7547 17.1789i −1.23763 0.714548i
\(579\) −2.48769 1.43627i −0.103385 0.0596893i
\(580\) 10.2535 + 5.91986i 0.425753 + 0.245809i
\(581\) −39.3348 −1.63188
\(582\) −13.4172 23.2392i −0.556159 0.963296i
\(583\) −23.0161 + 13.2883i −0.953229 + 0.550347i
\(584\) −0.121517 + 0.210473i −0.00502839 + 0.00870943i
\(585\) 10.4028 + 5.19708i 0.430103 + 0.214873i
\(586\) −15.3514 26.5893i −0.634159 1.09840i
\(587\) 38.3811i 1.58416i −0.610419 0.792079i \(-0.708999\pi\)
0.610419 0.792079i \(-0.291001\pi\)
\(588\) 7.80262 0.321774
\(589\) −18.8415 + 15.7704i −0.776352 + 0.649810i
\(590\) 15.5668i 0.640874i
\(591\) 15.5966i 0.641559i
\(592\) 17.5076 10.1080i 0.719559 0.415437i
\(593\) 44.9193i 1.84461i −0.386457 0.922307i \(-0.626301\pi\)
0.386457 0.922307i \(-0.373699\pi\)
\(594\) −10.5508 + 18.2745i −0.432903 + 0.749811i
\(595\) −1.37855 2.38772i −0.0565151 0.0978871i
\(596\) 2.69945 1.55853i 0.110574 0.0638397i
\(597\) −13.7993 −0.564766
\(598\) −13.2951 + 8.78449i −0.543678 + 0.359225i
\(599\) 18.5605 32.1476i 0.758359 1.31352i −0.185327 0.982677i \(-0.559335\pi\)
0.943687 0.330840i \(-0.107332\pi\)
\(600\) −1.16203 0.670899i −0.0474397 0.0273893i
\(601\) −17.3184 29.9963i −0.706432 1.22358i −0.966172 0.257897i \(-0.916970\pi\)
0.259741 0.965678i \(-0.416363\pi\)
\(602\) 38.6252 66.9009i 1.57425 2.72668i
\(603\) 19.5807 11.3049i 0.797386 0.460371i
\(604\) 39.6255i 1.61234i
\(605\) 5.06947i 0.206103i
\(606\) 16.1130 9.30285i 0.654546 0.377902i
\(607\) 3.14460 5.44661i 0.127635 0.221071i −0.795125 0.606446i \(-0.792595\pi\)
0.922760 + 0.385375i \(0.125928\pi\)
\(608\) −17.9026 31.0082i −0.726046 1.25755i
\(609\) 8.44346 + 4.87483i 0.342146 + 0.197538i
\(610\) 6.43362 11.1434i 0.260490 0.451182i
\(611\) 26.6930 17.6369i 1.07988 0.713511i
\(612\) 3.56546 0.144125
\(613\) −19.8622 + 11.4674i −0.802226 + 0.463165i −0.844249 0.535951i \(-0.819953\pi\)
0.0420229 + 0.999117i \(0.486620\pi\)
\(614\) −22.6908 39.3017i −0.915728 1.58609i
\(615\) −0.341805 + 0.592024i −0.0137829 + 0.0238727i
\(616\) 5.25964i 0.211917i
\(617\) −32.4430 + 18.7310i −1.30611 + 0.754080i −0.981444 0.191750i \(-0.938584\pi\)
−0.324662 + 0.945830i \(0.605250\pi\)
\(618\) 12.4557i 0.501041i
\(619\) 32.2512i 1.29629i −0.761518 0.648143i \(-0.775546\pi\)
0.761518 0.648143i \(-0.224454\pi\)
\(620\) −15.2785 5.58222i −0.613598 0.224187i
\(621\) 8.21245 0.329554
\(622\) 27.4402i 1.10025i
\(623\) −20.0129 34.6634i −0.801802 1.38876i
\(624\) −3.78238 + 7.57105i −0.151416 + 0.303084i
\(625\) −1.51257 + 2.61984i −0.0605027 + 0.104794i
\(626\) 4.36434 2.51975i 0.174434 0.100710i
\(627\) 4.08258 + 7.07123i 0.163042 + 0.282398i
\(628\) 35.0094 1.39703
\(629\) 3.23669 + 1.86870i 0.129055 + 0.0745101i
\(630\) −19.9410 11.5129i −0.794468 0.458687i
\(631\) 12.5595 + 7.25123i 0.499986 + 0.288667i 0.728708 0.684825i \(-0.240121\pi\)
−0.228722 + 0.973492i \(0.573455\pi\)
\(632\) 2.99743 1.73057i 0.119231 0.0688382i
\(633\) −4.68873 + 8.12111i −0.186360 + 0.322785i
\(634\) 15.7349 + 27.2537i 0.624913 + 1.08238i
\(635\) 16.0692i 0.637687i
\(636\) −15.8900 −0.630078
\(637\) 17.6916 1.06780i 0.700966 0.0423077i
\(638\) −11.1258 + 19.2705i −0.440476 + 0.762926i
\(639\) 15.3889 8.88478i 0.608775 0.351476i
\(640\) 2.91656 5.05163i 0.115287 0.199683i
\(641\) −11.1942 + 19.3889i −0.442143 + 0.765814i −0.997848 0.0655651i \(-0.979115\pi\)
0.555705 + 0.831379i \(0.312448\pi\)
\(642\) 7.24577 + 4.18335i 0.285968 + 0.165104i
\(643\) 15.6445i 0.616961i 0.951231 + 0.308480i \(0.0998204\pi\)
−0.951231 + 0.308480i \(0.900180\pi\)
\(644\) 14.5491 8.39995i 0.573316 0.331004i
\(645\) 8.37767 4.83685i 0.329871 0.190451i
\(646\) 2.84147 4.92157i 0.111796 0.193637i
\(647\) −15.6047 −0.613484 −0.306742 0.951793i \(-0.599239\pi\)
−0.306742 + 0.951793i \(0.599239\pi\)
\(648\) 2.41780 1.39592i 0.0949801 0.0548368i
\(649\) 15.5772 0.611457
\(650\) −22.3775 11.1795i −0.877717 0.438494i
\(651\) −12.5814 4.59680i −0.493103 0.180163i
\(652\) 8.67664i 0.339803i
\(653\) 45.3275 1.77380 0.886901 0.461960i \(-0.152854\pi\)
0.886901 + 0.461960i \(0.152854\pi\)
\(654\) −6.60979 11.4485i −0.258463 0.447672i
\(655\) 18.3616i 0.717445i
\(656\) 2.23030 + 1.28766i 0.0870786 + 0.0502749i
\(657\) 0.922031 0.532335i 0.0359719 0.0207684i
\(658\) −54.8622 + 31.6747i −2.13875 + 1.23481i
\(659\) 3.01576 0.117477 0.0587387 0.998273i \(-0.481292\pi\)
0.0587387 + 0.998273i \(0.481292\pi\)
\(660\) −2.70277 + 4.68134i −0.105205 + 0.182221i
\(661\) −15.0536 8.69118i −0.585516 0.338048i 0.177807 0.984065i \(-0.443100\pi\)
−0.763322 + 0.646018i \(0.776433\pi\)
\(662\) −8.93856 + 15.4820i −0.347407 + 0.601726i
\(663\) −1.56179 + 0.0942641i −0.0606550 + 0.00366091i
\(664\) 3.27001 5.66383i 0.126901 0.219799i
\(665\) −16.9228 + 9.77040i −0.656239 + 0.378880i
\(666\) 31.2128 1.20947
\(667\) 8.66006 0.335319
\(668\) −27.6943 + 15.9893i −1.07153 + 0.618646i
\(669\) 9.02105 + 5.20831i 0.348774 + 0.201365i
\(670\) 20.6614 11.9289i 0.798220 0.460852i
\(671\) 11.1508 + 6.43791i 0.430472 + 0.248533i
\(672\) 9.75976 16.9044i 0.376491 0.652101i
\(673\) 3.69020 6.39162i 0.142247 0.246379i −0.786096 0.618105i \(-0.787901\pi\)
0.928342 + 0.371726i \(0.121234\pi\)
\(674\) 0.120595i 0.00464513i
\(675\) 6.44588 + 11.1646i 0.248102 + 0.429726i
\(676\) 11.6124 27.2353i 0.446629 1.04751i
\(677\) −19.0668 + 33.0247i −0.732797 + 1.26924i 0.222887 + 0.974844i \(0.428452\pi\)
−0.955683 + 0.294397i \(0.904881\pi\)
\(678\) 10.3939i 0.399177i
\(679\) 32.1313 + 55.6530i 1.23309 + 2.13577i
\(680\) 0.458412 0.0175793
\(681\) 7.69129i 0.294731i
\(682\) 10.4913 28.7145i 0.401731 1.09953i
\(683\) 2.32957i 0.0891384i 0.999006 + 0.0445692i \(0.0141915\pi\)
−0.999006 + 0.0445692i \(0.985808\pi\)
\(684\) 25.2700i 0.966221i
\(685\) 6.28886 + 10.8926i 0.240285 + 0.416186i
\(686\) 14.8805 0.568140
\(687\) −1.07246 0.619183i −0.0409168 0.0236233i
\(688\) −18.2216 31.5608i −0.694692 1.20324i
\(689\) −36.0287 + 2.17456i −1.37259 + 0.0828442i
\(690\) 3.95120 0.150420
\(691\) −22.2531 12.8478i −0.846548 0.488755i 0.0129363 0.999916i \(-0.495882\pi\)
−0.859485 + 0.511161i \(0.829215\pi\)
\(692\) −12.8941 + 22.3332i −0.490158 + 0.848979i
\(693\) 11.5206 19.9543i 0.437632 0.758001i
\(694\) −37.6348 + 21.7284i −1.42860 + 0.824800i
\(695\) 19.0536 + 11.0006i 0.722744 + 0.417276i
\(696\) −1.40386 + 0.810518i −0.0532131 + 0.0307226i
\(697\) 0.476109i 0.0180339i
\(698\) 0.312645 0.0118338
\(699\) 10.3135 + 17.8635i 0.390093 + 0.675660i
\(700\) 22.8390 + 13.1861i 0.863232 + 0.498387i
\(701\) 10.9402 + 18.9490i 0.413205 + 0.715693i 0.995238 0.0974726i \(-0.0310758\pi\)
−0.582033 + 0.813165i \(0.697743\pi\)
\(702\) −23.9105 + 15.7984i −0.902445 + 0.596273i
\(703\) 13.2443 22.9398i 0.499519 0.865192i
\(704\) 23.0940 + 13.3333i 0.870387 + 0.502518i
\(705\) −7.93293 −0.298772
\(706\) 2.90525 + 5.03204i 0.109341 + 0.189383i
\(707\) −38.5873 + 22.2784i −1.45122 + 0.837864i
\(708\) 8.06568 + 4.65672i 0.303127 + 0.175010i
\(709\) 8.58474i 0.322407i 0.986921 + 0.161203i \(0.0515375\pi\)
−0.986921 + 0.161203i \(0.948463\pi\)
\(710\) 16.2383 9.37516i 0.609411 0.351844i
\(711\) −15.1624 −0.568634
\(712\) 6.65494 0.249404
\(713\) −11.7196 + 2.05161i −0.438904 + 0.0768336i
\(714\) 3.09810 0.115944
\(715\) −5.48759 + 10.9843i −0.205224 + 0.410789i
\(716\) −13.6584 23.6571i −0.510439 0.884106i
\(717\) 17.4322i 0.651019i
\(718\) 4.20607 7.28512i 0.156969 0.271878i
\(719\) −12.7692 22.1169i −0.476210 0.824820i 0.523418 0.852076i \(-0.324657\pi\)
−0.999628 + 0.0272556i \(0.991323\pi\)
\(720\) −9.40724 + 5.43128i −0.350587 + 0.202412i
\(721\) 29.8287i 1.11088i
\(722\) −0.849957 0.490723i −0.0316321 0.0182628i
\(723\) −2.32948 1.34493i −0.0866344 0.0500184i
\(724\) −9.91542 + 17.1740i −0.368504 + 0.638267i
\(725\) 6.79721 + 11.7731i 0.252442 + 0.437242i
\(726\) 4.93328 + 2.84823i 0.183091 + 0.105708i
\(727\) −6.30710 10.9242i −0.233917 0.405157i 0.725040 0.688707i \(-0.241821\pi\)
−0.958958 + 0.283550i \(0.908488\pi\)
\(728\) −3.19242 + 6.39015i −0.118319 + 0.236835i
\(729\) −4.19504 −0.155372
\(730\) 0.972922 0.561717i 0.0360094 0.0207901i
\(731\) 3.36869 5.83474i 0.124595 0.215806i
\(732\) 3.84917 + 6.66696i 0.142269 + 0.246418i
\(733\) 37.3182 + 21.5457i 1.37838 + 0.795808i 0.991964 0.126517i \(-0.0403797\pi\)
0.386416 + 0.922325i \(0.373713\pi\)
\(734\) 54.3968 + 31.4060i 2.00782 + 1.15922i
\(735\) −3.80593 2.19736i −0.140384 0.0810507i
\(736\) 17.3381i 0.639089i
\(737\) 11.9368 + 20.6752i 0.439698 + 0.761580i
\(738\) 1.98811 + 3.44350i 0.0731832 + 0.126757i
\(739\) 10.7108 + 6.18386i 0.394002 + 0.227477i 0.683893 0.729583i \(-0.260286\pi\)
−0.289891 + 0.957060i \(0.593619\pi\)
\(740\) 17.5362 0.644642
\(741\) 0.668091 + 11.0691i 0.0245429 + 0.406634i
\(742\) 71.4696 2.62373
\(743\) 45.8218i 1.68104i 0.541783 + 0.840519i \(0.317750\pi\)
−0.541783 + 0.840519i \(0.682250\pi\)
\(744\) 1.70782 1.42945i 0.0626118 0.0524063i
\(745\) −1.75564 −0.0643215
\(746\) 51.1796i 1.87382i
\(747\) −24.8119 + 14.3251i −0.907819 + 0.524130i
\(748\) 3.76476i 0.137653i
\(749\) −17.3521 10.0182i −0.634032 0.366059i
\(750\) 7.72381 + 13.3780i 0.282034 + 0.488497i
\(751\) 12.3709 + 21.4271i 0.451422 + 0.781885i 0.998475 0.0552127i \(-0.0175837\pi\)
−0.547053 + 0.837098i \(0.684250\pi\)
\(752\) 29.8853i 1.08981i
\(753\) 3.70205 6.41214i 0.134910 0.233671i
\(754\) −25.2137 + 16.6595i −0.918230 + 0.606703i
\(755\) −11.1593 + 19.3284i −0.406127 + 0.703433i
\(756\) 26.1658 15.1068i 0.951641 0.549430i
\(757\) −26.5987 + 46.0703i −0.966746 + 1.67445i −0.261896 + 0.965096i \(0.584348\pi\)
−0.704850 + 0.709357i \(0.748986\pi\)
\(758\) −18.6608 32.3214i −0.677790 1.17397i
\(759\) 3.95384i 0.143515i
\(760\) 3.24897i 0.117853i
\(761\) 17.9406 10.3580i 0.650345 0.375477i −0.138243 0.990398i \(-0.544146\pi\)
0.788588 + 0.614921i \(0.210812\pi\)
\(762\) −15.6375 9.02833i −0.566488 0.327062i
\(763\) 15.8291 + 27.4167i 0.573051 + 0.992553i
\(764\) 0.567593 0.983099i 0.0205348 0.0355673i
\(765\) −1.73915