Properties

Label 105.2.m.a.97.6
Level 105
Weight 2
Character 105.97
Analytic conductor 0.838
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 97.6
Root \(1.36166 - 0.381939i\)
Character \(\chi\) = 105.97
Dual form 105.2.m.a.13.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.540143 + 0.540143i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.41649i q^{4} +(-1.03649 + 1.98133i) q^{5} +0.763878i q^{6} +(2.57351 + 0.614060i) q^{7} +(1.84539 - 1.84539i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(0.540143 + 0.540143i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.41649i q^{4} +(-1.03649 + 1.98133i) q^{5} +0.763878i q^{6} +(2.57351 + 0.614060i) q^{7} +(1.84539 - 1.84539i) q^{8} +1.00000i q^{9} +(-1.63006 + 0.510348i) q^{10} -3.85136 q^{11} +(1.00161 - 1.00161i) q^{12} +(-3.66816 - 3.66816i) q^{13} +(1.05838 + 1.72174i) q^{14} +(-2.13393 + 0.668102i) q^{15} -0.839427 q^{16} +(1.49007 - 1.49007i) q^{17} +(-0.540143 + 0.540143i) q^{18} +0.0697674 q^{19} +(2.80654 + 1.46818i) q^{20} +(1.38554 + 2.25395i) q^{21} +(-2.08029 - 2.08029i) q^{22} +(-0.534176 + 0.534176i) q^{23} +2.60978 q^{24} +(-2.85136 - 4.10728i) q^{25} -3.96267i q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.869810 - 3.64535i) q^{28} +2.77107i q^{29} +(-1.51350 - 0.791755i) q^{30} -2.39674i q^{31} +(-4.14420 - 4.14420i) q^{32} +(-2.72332 - 2.72332i) q^{33} +1.60970 q^{34} +(-3.88408 + 4.46250i) q^{35} +1.41649 q^{36} +(6.18757 + 6.18757i) q^{37} +(0.0376844 + 0.0376844i) q^{38} -5.18757i q^{39} +(1.74360 + 5.56908i) q^{40} +8.68077i q^{41} +(-0.469067 + 1.96584i) q^{42} +(-2.77107 + 2.77107i) q^{43} +5.45542i q^{44} +(-1.98133 - 1.03649i) q^{45} -0.577063 q^{46} +(5.49042 - 5.49042i) q^{47} +(-0.593565 - 0.593565i) q^{48} +(6.24586 + 3.16057i) q^{49} +(0.678376 - 3.75866i) q^{50} +2.10728 q^{51} +(-5.19592 + 5.19592i) q^{52} +(6.13823 - 6.13823i) q^{53} -0.763878 q^{54} +(3.99191 - 7.63083i) q^{55} +(5.88231 - 3.61595i) q^{56} +(0.0493330 + 0.0493330i) q^{57} +(-1.49678 + 1.49678i) q^{58} -6.97440 q^{59} +(0.946361 + 3.02269i) q^{60} +14.3107i q^{61} +(1.29458 - 1.29458i) q^{62} +(-0.614060 + 2.57351i) q^{63} -2.79807i q^{64} +(11.0699 - 3.46582i) q^{65} -2.94197i q^{66} +(0.416491 + 0.416491i) q^{67} +(-2.11067 - 2.11067i) q^{68} -0.755439 q^{69} +(-4.50835 + 0.312431i) q^{70} -8.12783 q^{71} +(1.84539 + 1.84539i) q^{72} +(9.55210 + 9.55210i) q^{73} +6.68434i q^{74} +(0.888068 - 4.92050i) q^{75} -0.0988248i q^{76} +(-9.91150 - 2.36497i) q^{77} +(2.80203 - 2.80203i) q^{78} -9.86329i q^{79} +(0.870061 - 1.66319i) q^{80} -1.00000 q^{81} +(-4.68886 + 4.68886i) q^{82} +(1.63570 + 1.63570i) q^{83} +(3.19270 - 1.96260i) q^{84} +(1.40788 + 4.49678i) q^{85} -2.99355 q^{86} +(-1.95945 + 1.95945i) q^{87} +(-7.10728 + 7.10728i) q^{88} -5.05313 q^{89} +(-0.510348 - 1.63006i) q^{90} +(-7.18757 - 11.6925i) q^{91} +(0.756656 + 0.756656i) q^{92} +(1.69475 - 1.69475i) q^{93} +5.93123 q^{94} +(-0.0723134 + 0.138232i) q^{95} -5.86078i q^{96} +(6.85851 - 6.85851i) q^{97} +(1.66650 + 5.08082i) q^{98} -3.85136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} + 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} + 24q^{8} - 16q^{11} + 8q^{15} - 48q^{16} + 8q^{21} - 16q^{22} - 40q^{23} + 24q^{28} - 8q^{30} + 48q^{32} - 8q^{35} - 16q^{36} + 32q^{37} - 16q^{42} - 16q^{43} + 64q^{46} - 72q^{50} - 16q^{51} + 24q^{53} + 24q^{56} + 8q^{57} + 32q^{58} + 40q^{60} + 8q^{63} + 40q^{65} - 32q^{67} - 40q^{70} + 64q^{71} + 24q^{72} - 24q^{77} - 8q^{78} - 16q^{81} + 48q^{85} + 64q^{86} - 64q^{88} - 48q^{91} - 40q^{92} + 24q^{93} - 72q^{95} - 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.540143 + 0.540143i 0.381939 + 0.381939i 0.871800 0.489861i \(-0.162953\pi\)
−0.489861 + 0.871800i \(0.662953\pi\)
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.41649i 0.708245i
\(5\) −1.03649 + 1.98133i −0.463534 + 0.886079i
\(6\) 0.763878i 0.311852i
\(7\) 2.57351 + 0.614060i 0.972694 + 0.232093i
\(8\) 1.84539 1.84539i 0.652445 0.652445i
\(9\) 1.00000i 0.333333i
\(10\) −1.63006 + 0.510348i −0.515470 + 0.161386i
\(11\) −3.85136 −1.16123 −0.580615 0.814179i \(-0.697188\pi\)
−0.580615 + 0.814179i \(0.697188\pi\)
\(12\) 1.00161 1.00161i 0.289140 0.289140i
\(13\) −3.66816 3.66816i −1.01737 1.01737i −0.999847 0.0175187i \(-0.994423\pi\)
−0.0175187 0.999847i \(-0.505577\pi\)
\(14\) 1.05838 + 1.72174i 0.282864 + 0.460155i
\(15\) −2.13393 + 0.668102i −0.550977 + 0.172503i
\(16\) −0.839427 −0.209857
\(17\) 1.49007 1.49007i 0.361395 0.361395i −0.502931 0.864326i \(-0.667745\pi\)
0.864326 + 0.502931i \(0.167745\pi\)
\(18\) −0.540143 + 0.540143i −0.127313 + 0.127313i
\(19\) 0.0697674 0.0160057 0.00800286 0.999968i \(-0.497453\pi\)
0.00800286 + 0.999968i \(0.497453\pi\)
\(20\) 2.80654 + 1.46818i 0.627561 + 0.328296i
\(21\) 1.38554 + 2.25395i 0.302349 + 0.491852i
\(22\) −2.08029 2.08029i −0.443519 0.443519i
\(23\) −0.534176 + 0.534176i −0.111383 + 0.111383i −0.760602 0.649218i \(-0.775096\pi\)
0.649218 + 0.760602i \(0.275096\pi\)
\(24\) 2.60978 0.532719
\(25\) −2.85136 4.10728i −0.570272 0.821456i
\(26\) 3.96267i 0.777143i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 0.869810 3.64535i 0.164379 0.688906i
\(29\) 2.77107i 0.514576i 0.966335 + 0.257288i \(0.0828288\pi\)
−0.966335 + 0.257288i \(0.917171\pi\)
\(30\) −1.51350 0.791755i −0.276325 0.144554i
\(31\) 2.39674i 0.430467i −0.976563 0.215233i \(-0.930949\pi\)
0.976563 0.215233i \(-0.0690512\pi\)
\(32\) −4.14420 4.14420i −0.732598 0.732598i
\(33\) −2.72332 2.72332i −0.474070 0.474070i
\(34\) 1.60970 0.276062
\(35\) −3.88408 + 4.46250i −0.656529 + 0.754301i
\(36\) 1.41649 0.236082
\(37\) 6.18757 + 6.18757i 1.01723 + 1.01723i 0.999849 + 0.0173805i \(0.00553267\pi\)
0.0173805 + 0.999849i \(0.494467\pi\)
\(38\) 0.0376844 + 0.0376844i 0.00611321 + 0.00611321i
\(39\) 5.18757i 0.830675i
\(40\) 1.74360 + 5.56908i 0.275687 + 0.880549i
\(41\) 8.68077i 1.35571i 0.735196 + 0.677854i \(0.237090\pi\)
−0.735196 + 0.677854i \(0.762910\pi\)
\(42\) −0.469067 + 1.96584i −0.0723786 + 0.303336i
\(43\) −2.77107 + 2.77107i −0.422585 + 0.422585i −0.886093 0.463508i \(-0.846591\pi\)
0.463508 + 0.886093i \(0.346591\pi\)
\(44\) 5.45542i 0.822435i
\(45\) −1.98133 1.03649i −0.295360 0.154511i
\(46\) −0.577063 −0.0850834
\(47\) 5.49042 5.49042i 0.800860 0.800860i −0.182370 0.983230i \(-0.558377\pi\)
0.983230 + 0.182370i \(0.0583768\pi\)
\(48\) −0.593565 0.593565i −0.0856737 0.0856737i
\(49\) 6.24586 + 3.16057i 0.892266 + 0.451510i
\(50\) 0.678376 3.75866i 0.0959368 0.531555i
\(51\) 2.10728 0.295078
\(52\) −5.19592 + 5.19592i −0.720544 + 0.720544i
\(53\) 6.13823 6.13823i 0.843151 0.843151i −0.146116 0.989267i \(-0.546677\pi\)
0.989267 + 0.146116i \(0.0466774\pi\)
\(54\) −0.763878 −0.103951
\(55\) 3.99191 7.63083i 0.538269 1.02894i
\(56\) 5.88231 3.61595i 0.786057 0.483202i
\(57\) 0.0493330 + 0.0493330i 0.00653431 + 0.00653431i
\(58\) −1.49678 + 1.49678i −0.196536 + 0.196536i
\(59\) −6.97440 −0.907990 −0.453995 0.891004i \(-0.650002\pi\)
−0.453995 + 0.891004i \(0.650002\pi\)
\(60\) 0.946361 + 3.02269i 0.122175 + 0.390227i
\(61\) 14.3107i 1.83230i 0.400835 + 0.916150i \(0.368720\pi\)
−0.400835 + 0.916150i \(0.631280\pi\)
\(62\) 1.29458 1.29458i 0.164412 0.164412i
\(63\) −0.614060 + 2.57351i −0.0773643 + 0.324231i
\(64\) 2.79807i 0.349758i
\(65\) 11.0699 3.46582i 1.37305 0.429883i
\(66\) 2.94197i 0.362131i
\(67\) 0.416491 + 0.416491i 0.0508824 + 0.0508824i 0.732090 0.681208i \(-0.238545\pi\)
−0.681208 + 0.732090i \(0.738545\pi\)
\(68\) −2.11067 2.11067i −0.255957 0.255957i
\(69\) −0.755439 −0.0909442
\(70\) −4.50835 + 0.312431i −0.538851 + 0.0373426i
\(71\) −8.12783 −0.964595 −0.482298 0.876007i \(-0.660198\pi\)
−0.482298 + 0.876007i \(0.660198\pi\)
\(72\) 1.84539 + 1.84539i 0.217482 + 0.217482i
\(73\) 9.55210 + 9.55210i 1.11799 + 1.11799i 0.992036 + 0.125953i \(0.0401987\pi\)
0.125953 + 0.992036i \(0.459801\pi\)
\(74\) 6.68434i 0.777039i
\(75\) 0.888068 4.92050i 0.102545 0.568171i
\(76\) 0.0988248i 0.0113360i
\(77\) −9.91150 2.36497i −1.12952 0.269513i
\(78\) 2.80203 2.80203i 0.317267 0.317267i
\(79\) 9.86329i 1.10971i −0.831948 0.554854i \(-0.812774\pi\)
0.831948 0.554854i \(-0.187226\pi\)
\(80\) 0.870061 1.66319i 0.0972758 0.185950i
\(81\) −1.00000 −0.111111
\(82\) −4.68886 + 4.68886i −0.517798 + 0.517798i
\(83\) 1.63570 + 1.63570i 0.179541 + 0.179541i 0.791156 0.611615i \(-0.209480\pi\)
−0.611615 + 0.791156i \(0.709480\pi\)
\(84\) 3.19270 1.96260i 0.348352 0.214137i
\(85\) 1.40788 + 4.49678i 0.152706 + 0.487744i
\(86\) −2.99355 −0.322803
\(87\) −1.95945 + 1.95945i −0.210075 + 0.210075i
\(88\) −7.10728 + 7.10728i −0.757638 + 0.757638i
\(89\) −5.05313 −0.535631 −0.267815 0.963470i \(-0.586302\pi\)
−0.267815 + 0.963470i \(0.586302\pi\)
\(90\) −0.510348 1.63006i −0.0537954 0.171823i
\(91\) −7.18757 11.6925i −0.753462 1.22571i
\(92\) 0.756656 + 0.756656i 0.0788868 + 0.0788868i
\(93\) 1.69475 1.69475i 0.175737 0.175737i
\(94\) 5.93123 0.611759
\(95\) −0.0723134 + 0.138232i −0.00741920 + 0.0141823i
\(96\) 5.86078i 0.598164i
\(97\) 6.85851 6.85851i 0.696376 0.696376i −0.267251 0.963627i \(-0.586115\pi\)
0.963627 + 0.267251i \(0.0861152\pi\)
\(98\) 1.66650 + 5.08082i 0.168342 + 0.513240i
\(99\) 3.85136i 0.387076i
\(100\) −5.81792 + 4.03893i −0.581792 + 0.403893i
\(101\) 19.1953i 1.91000i −0.296605 0.955000i \(-0.595855\pi\)
0.296605 0.955000i \(-0.404145\pi\)
\(102\) 1.13823 + 1.13823i 0.112702 + 0.112702i
\(103\) 2.33825 + 2.33825i 0.230394 + 0.230394i 0.812857 0.582463i \(-0.197911\pi\)
−0.582463 + 0.812857i \(0.697911\pi\)
\(104\) −13.5384 −1.32755
\(105\) −5.90192 + 0.409006i −0.575969 + 0.0399149i
\(106\) 6.63105 0.644064
\(107\) −6.39747 6.39747i −0.618467 0.618467i 0.326671 0.945138i \(-0.394073\pi\)
−0.945138 + 0.326671i \(0.894073\pi\)
\(108\) 1.00161 + 1.00161i 0.0963800 + 0.0963800i
\(109\) 2.16057i 0.206945i −0.994632 0.103473i \(-0.967005\pi\)
0.994632 0.103473i \(-0.0329954\pi\)
\(110\) 6.27794 1.96554i 0.598578 0.187407i
\(111\) 8.75054i 0.830564i
\(112\) −2.16027 0.515459i −0.204126 0.0487063i
\(113\) −4.13823 + 4.13823i −0.389292 + 0.389292i −0.874435 0.485143i \(-0.838768\pi\)
0.485143 + 0.874435i \(0.338768\pi\)
\(114\) 0.0532937i 0.00499142i
\(115\) −0.504711 1.61205i −0.0470645 0.150325i
\(116\) 3.92520 0.364446
\(117\) 3.66816 3.66816i 0.339122 0.339122i
\(118\) −3.76718 3.76718i −0.346797 0.346797i
\(119\) 4.74970 2.91971i 0.435404 0.267650i
\(120\) −2.70502 + 5.17085i −0.246934 + 0.472032i
\(121\) 3.83298 0.348453
\(122\) −7.72984 + 7.72984i −0.699827 + 0.699827i
\(123\) −6.13823 + 6.13823i −0.553466 + 0.553466i
\(124\) −3.39496 −0.304876
\(125\) 11.0933 1.39233i 0.992215 0.124533i
\(126\) −1.72174 + 1.05838i −0.153385 + 0.0942881i
\(127\) −4.83298 4.83298i −0.428858 0.428858i 0.459381 0.888239i \(-0.348071\pi\)
−0.888239 + 0.459381i \(0.848071\pi\)
\(128\) −6.77704 + 6.77704i −0.599011 + 0.599011i
\(129\) −3.91889 −0.345039
\(130\) 7.85136 + 4.10728i 0.688610 + 0.360232i
\(131\) 0.647499i 0.0565722i 0.999600 + 0.0282861i \(0.00900495\pi\)
−0.999600 + 0.0282861i \(0.990995\pi\)
\(132\) −3.85756 + 3.85756i −0.335758 + 0.335758i
\(133\) 0.179547 + 0.0428413i 0.0155687 + 0.00371481i
\(134\) 0.449929i 0.0388680i
\(135\) −0.668102 2.13393i −0.0575011 0.183659i
\(136\) 5.49954i 0.471581i
\(137\) 10.2369 + 10.2369i 0.874597 + 0.874597i 0.992969 0.118372i \(-0.0377676\pi\)
−0.118372 + 0.992969i \(0.537768\pi\)
\(138\) −0.408045 0.408045i −0.0347351 0.0347351i
\(139\) −22.1663 −1.88012 −0.940060 0.341009i \(-0.889231\pi\)
−0.940060 + 0.341009i \(0.889231\pi\)
\(140\) 6.32109 + 5.50176i 0.534230 + 0.464984i
\(141\) 7.76463 0.653900
\(142\) −4.39019 4.39019i −0.368417 0.368417i
\(143\) 14.1274 + 14.1274i 1.18139 + 1.18139i
\(144\) 0.839427i 0.0699523i
\(145\) −5.49042 2.87220i −0.455955 0.238523i
\(146\) 10.3190i 0.854007i
\(147\) 2.18163 + 6.65135i 0.179938 + 0.548594i
\(148\) 8.76463 8.76463i 0.720448 0.720448i
\(149\) 11.0475i 0.905050i −0.891752 0.452525i \(-0.850523\pi\)
0.891752 0.452525i \(-0.149477\pi\)
\(150\) 3.13746 2.17809i 0.256172 0.177840i
\(151\) 18.3990 1.49729 0.748645 0.662972i \(-0.230705\pi\)
0.748645 + 0.662972i \(0.230705\pi\)
\(152\) 0.128748 0.128748i 0.0104429 0.0104429i
\(153\) 1.49007 + 1.49007i 0.120465 + 0.120465i
\(154\) −4.07621 6.63105i −0.328470 0.534345i
\(155\) 4.74873 + 2.48420i 0.381428 + 0.199536i
\(156\) −7.34814 −0.588322
\(157\) −1.04994 + 1.04994i −0.0837946 + 0.0837946i −0.747762 0.663967i \(-0.768871\pi\)
0.663967 + 0.747762i \(0.268871\pi\)
\(158\) 5.32759 5.32759i 0.423840 0.423840i
\(159\) 8.68077 0.688430
\(160\) 12.5065 3.91560i 0.988724 0.309555i
\(161\) −1.70272 + 1.04669i −0.134193 + 0.0824907i
\(162\) −0.540143 0.540143i −0.0424377 0.0424377i
\(163\) 5.50539 5.50539i 0.431215 0.431215i −0.457826 0.889042i \(-0.651372\pi\)
0.889042 + 0.457826i \(0.151372\pi\)
\(164\) 12.2962 0.960174
\(165\) 8.21852 2.57310i 0.639811 0.200316i
\(166\) 1.76702i 0.137147i
\(167\) 1.88968 1.88968i 0.146228 0.146228i −0.630203 0.776431i \(-0.717028\pi\)
0.776431 + 0.630203i \(0.217028\pi\)
\(168\) 6.71629 + 1.60256i 0.518173 + 0.123640i
\(169\) 13.9108i 1.07006i
\(170\) −1.66845 + 3.18936i −0.127964 + 0.244613i
\(171\) 0.0697674i 0.00533524i
\(172\) 3.92520 + 3.92520i 0.299294 + 0.299294i
\(173\) −4.90751 4.90751i −0.373111 0.373111i 0.495498 0.868609i \(-0.334986\pi\)
−0.868609 + 0.495498i \(0.834986\pi\)
\(174\) −2.11676 −0.160471
\(175\) −4.81588 12.3210i −0.364046 0.931381i
\(176\) 3.23294 0.243692
\(177\) −4.93165 4.93165i −0.370685 0.370685i
\(178\) −2.72941 2.72941i −0.204578 0.204578i
\(179\) 18.5857i 1.38916i 0.719416 + 0.694579i \(0.244409\pi\)
−0.719416 + 0.694579i \(0.755591\pi\)
\(180\) −1.46818 + 2.80654i −0.109432 + 0.209187i
\(181\) 8.48528i 0.630706i 0.948974 + 0.315353i \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) 2.43331 10.1979i 0.180369 0.755922i
\(183\) −10.1192 + 10.1192i −0.748034 + 0.748034i
\(184\) 1.97153i 0.145343i
\(185\) −18.6730 + 5.84625i −1.37287 + 0.429825i
\(186\) 1.83081 0.134242
\(187\) −5.73880 + 5.73880i −0.419663 + 0.419663i
\(188\) −7.77713 7.77713i −0.567206 0.567206i
\(189\) −2.25395 + 1.38554i −0.163951 + 0.100783i
\(190\) −0.113725 + 0.0356057i −0.00825047 + 0.00258311i
\(191\) −5.39351 −0.390261 −0.195130 0.980777i \(-0.562513\pi\)
−0.195130 + 0.980777i \(0.562513\pi\)
\(192\) 1.97853 1.97853i 0.142788 0.142788i
\(193\) −4.80599 + 4.80599i −0.345943 + 0.345943i −0.858596 0.512653i \(-0.828663\pi\)
0.512653 + 0.858596i \(0.328663\pi\)
\(194\) 7.40916 0.531946
\(195\) 10.2783 + 5.37688i 0.736044 + 0.385046i
\(196\) 4.47692 8.84720i 0.319780 0.631943i
\(197\) 12.6739 + 12.6739i 0.902981 + 0.902981i 0.995693 0.0927124i \(-0.0295537\pi\)
−0.0927124 + 0.995693i \(0.529554\pi\)
\(198\) 2.08029 2.08029i 0.147840 0.147840i
\(199\) −2.67111 −0.189350 −0.0946750 0.995508i \(-0.530181\pi\)
−0.0946750 + 0.995508i \(0.530181\pi\)
\(200\) −12.8414 2.31766i −0.908026 0.163884i
\(201\) 0.589007i 0.0415453i
\(202\) 10.3682 10.3682i 0.729503 0.729503i
\(203\) −1.70161 + 7.13138i −0.119429 + 0.500524i
\(204\) 2.98494i 0.208988i
\(205\) −17.1995 8.99757i −1.20127 0.628417i
\(206\) 2.52597i 0.175993i
\(207\) −0.534176 0.534176i −0.0371278 0.0371278i
\(208\) 3.07916 + 3.07916i 0.213501 + 0.213501i
\(209\) −0.268699 −0.0185863
\(210\) −3.40881 2.96696i −0.235230 0.204740i
\(211\) −12.0239 −0.827757 −0.413879 0.910332i \(-0.635826\pi\)
−0.413879 + 0.910332i \(0.635826\pi\)
\(212\) −8.69475 8.69475i −0.597158 0.597158i
\(213\) −5.74724 5.74724i −0.393794 0.393794i
\(214\) 6.91110i 0.472433i
\(215\) −2.61822 8.36262i −0.178561 0.570326i
\(216\) 2.60978i 0.177573i
\(217\) 1.47174 6.16802i 0.0999082 0.418712i
\(218\) 1.16702 1.16702i 0.0790405 0.0790405i
\(219\) 13.5087i 0.912834i
\(220\) −10.8090 5.65451i −0.728742 0.381227i
\(221\) −10.9316 −0.735342
\(222\) −4.72654 + 4.72654i −0.317225 + 0.317225i
\(223\) −11.6925 11.6925i −0.782988 0.782988i 0.197346 0.980334i \(-0.436768\pi\)
−0.980334 + 0.197346i \(0.936768\pi\)
\(224\) −8.12033 13.2099i −0.542563 0.882624i
\(225\) 4.10728 2.85136i 0.273819 0.190091i
\(226\) −4.47048 −0.297372
\(227\) 1.10518 1.10518i 0.0733535 0.0733535i −0.669478 0.742832i \(-0.733482\pi\)
0.742832 + 0.669478i \(0.233482\pi\)
\(228\) 0.0698797 0.0698797i 0.00462790 0.00462790i
\(229\) 7.83309 0.517625 0.258812 0.965928i \(-0.416669\pi\)
0.258812 + 0.965928i \(0.416669\pi\)
\(230\) 0.598123 1.14335i 0.0394390 0.0753906i
\(231\) −5.33620 8.68077i −0.351096 0.571153i
\(232\) 5.11372 + 5.11372i 0.335732 + 0.335732i
\(233\) 1.00797 1.00797i 0.0660345 0.0660345i −0.673318 0.739353i \(-0.735132\pi\)
0.739353 + 0.673318i \(0.235132\pi\)
\(234\) 3.96267 0.259048
\(235\) 5.18757 + 16.5691i 0.338399 + 1.08085i
\(236\) 9.87918i 0.643080i
\(237\) 6.97440 6.97440i 0.453036 0.453036i
\(238\) 4.14258 + 0.988454i 0.268524 + 0.0640720i
\(239\) 20.2805i 1.31183i −0.754833 0.655917i \(-0.772282\pi\)
0.754833 0.655917i \(-0.227718\pi\)
\(240\) 1.79128 0.560823i 0.115626 0.0362010i
\(241\) 2.76994i 0.178427i 0.996013 + 0.0892136i \(0.0284354\pi\)
−0.996013 + 0.0892136i \(0.971565\pi\)
\(242\) 2.07036 + 2.07036i 0.133088 + 0.133088i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 20.2710 1.29772
\(245\) −12.7359 + 9.09922i −0.813670 + 0.581328i
\(246\) −6.63105 −0.422780
\(247\) −0.255918 0.255918i −0.0162837 0.0162837i
\(248\) −4.42292 4.42292i −0.280856 0.280856i
\(249\) 2.31322i 0.146595i
\(250\) 6.74403 + 5.23992i 0.426530 + 0.331401i
\(251\) 6.09982i 0.385017i −0.981295 0.192509i \(-0.938338\pi\)
0.981295 0.192509i \(-0.0616623\pi\)
\(252\) 3.64535 + 0.869810i 0.229635 + 0.0547929i
\(253\) 2.05731 2.05731i 0.129342 0.129342i
\(254\) 5.22100i 0.327595i
\(255\) −2.18418 + 4.17522i −0.136779 + 0.261463i
\(256\) −12.9173 −0.807330
\(257\) −2.01843 + 2.01843i −0.125906 + 0.125906i −0.767252 0.641346i \(-0.778376\pi\)
0.641346 + 0.767252i \(0.278376\pi\)
\(258\) −2.11676 2.11676i −0.131784 0.131784i
\(259\) 12.1242 + 19.7233i 0.753361 + 1.22554i
\(260\) −4.90931 15.6804i −0.304462 0.972456i
\(261\) −2.77107 −0.171525
\(262\) −0.349742 + 0.349742i −0.0216071 + 0.0216071i
\(263\) 16.7686 16.7686i 1.03400 1.03400i 0.0345941 0.999401i \(-0.488986\pi\)
0.999401 0.0345941i \(-0.0110138\pi\)
\(264\) −10.0512 −0.618609
\(265\) 5.79964 + 18.5241i 0.356269 + 1.13793i
\(266\) 0.0738405 + 0.120121i 0.00452745 + 0.00736511i
\(267\) −3.57310 3.57310i −0.218670 0.218670i
\(268\) 0.589955 0.589955i 0.0360372 0.0360372i
\(269\) 24.7351 1.50813 0.754064 0.656801i \(-0.228091\pi\)
0.754064 + 0.656801i \(0.228091\pi\)
\(270\) 0.791755 1.51350i 0.0481847 0.0921085i
\(271\) 4.13470i 0.251165i 0.992083 + 0.125583i \(0.0400800\pi\)
−0.992083 + 0.125583i \(0.959920\pi\)
\(272\) −1.25081 + 1.25081i −0.0758413 + 0.0758413i
\(273\) 3.18548 13.3502i 0.192794 0.807993i
\(274\) 11.0588i 0.668085i
\(275\) 10.9816 + 15.8186i 0.662217 + 0.953898i
\(276\) 1.07007i 0.0644108i
\(277\) −12.1128 12.1128i −0.727786 0.727786i 0.242393 0.970178i \(-0.422068\pi\)
−0.970178 + 0.242393i \(0.922068\pi\)
\(278\) −11.9730 11.9730i −0.718091 0.718091i
\(279\) 2.39674 0.143489
\(280\) 1.06742 + 15.4027i 0.0637904 + 0.920489i
\(281\) 5.25279 0.313355 0.156678 0.987650i \(-0.449922\pi\)
0.156678 + 0.987650i \(0.449922\pi\)
\(282\) 4.19401 + 4.19401i 0.249750 + 0.249750i
\(283\) −1.66729 1.66729i −0.0991101 0.0991101i 0.655813 0.754923i \(-0.272326\pi\)
−0.754923 + 0.655813i \(0.772326\pi\)
\(284\) 11.5130i 0.683170i
\(285\) −0.148878 + 0.0466117i −0.00881879 + 0.00276104i
\(286\) 15.2617i 0.902441i
\(287\) −5.33051 + 22.3400i −0.314650 + 1.31869i
\(288\) 4.14420 4.14420i 0.244199 0.244199i
\(289\) 12.5594i 0.738787i
\(290\) −1.41421 4.51701i −0.0830455 0.265248i
\(291\) 9.69940 0.568589
\(292\) 13.5305 13.5305i 0.791810 0.791810i
\(293\) −15.2556 15.2556i −0.891240 0.891240i 0.103400 0.994640i \(-0.467028\pi\)
−0.994640 + 0.103400i \(0.967028\pi\)
\(294\) −2.41429 + 4.77107i −0.140804 + 0.278255i
\(295\) 7.22893 13.8186i 0.420884 0.804551i
\(296\) 22.8370 1.32737
\(297\) 2.72332 2.72332i 0.158023 0.158023i
\(298\) 5.96725 5.96725i 0.345674 0.345674i
\(299\) 3.91889 0.226635
\(300\) −6.96984 1.25794i −0.402404 0.0726272i
\(301\) −8.83298 + 5.42977i −0.509125 + 0.312967i
\(302\) 9.93809 + 9.93809i 0.571873 + 0.571873i
\(303\) 13.5731 13.5731i 0.779754 0.779754i
\(304\) −0.0585646 −0.00335891
\(305\) −28.3543 14.8330i −1.62356 0.849334i
\(306\) 1.60970i 0.0920206i
\(307\) −14.6198 + 14.6198i −0.834394 + 0.834394i −0.988114 0.153721i \(-0.950874\pi\)
0.153721 + 0.988114i \(0.450874\pi\)
\(308\) −3.34995 + 14.0395i −0.190881 + 0.799977i
\(309\) 3.30678i 0.188116i
\(310\) 1.22317 + 3.90682i 0.0694714 + 0.221893i
\(311\) 2.86218i 0.162299i 0.996702 + 0.0811497i \(0.0258592\pi\)
−0.996702 + 0.0811497i \(0.974141\pi\)
\(312\) −9.57310 9.57310i −0.541970 0.541970i
\(313\) −9.41824 9.41824i −0.532350 0.532350i 0.388921 0.921271i \(-0.372848\pi\)
−0.921271 + 0.388921i \(0.872848\pi\)
\(314\) −1.13424 −0.0640088
\(315\) −4.46250 3.88408i −0.251434 0.218843i
\(316\) −13.9713 −0.785945
\(317\) 7.38310 + 7.38310i 0.414676 + 0.414676i 0.883364 0.468688i \(-0.155273\pi\)
−0.468688 + 0.883364i \(0.655273\pi\)
\(318\) 4.68886 + 4.68886i 0.262938 + 0.262938i
\(319\) 10.6724i 0.597540i
\(320\) 5.54390 + 2.90018i 0.309914 + 0.162125i
\(321\) 9.04739i 0.504976i
\(322\) −1.48508 0.354351i −0.0827600 0.0197472i
\(323\) 0.103958 0.103958i 0.00578440 0.00578440i
\(324\) 1.41649i 0.0786939i
\(325\) −4.60691 + 25.5254i −0.255545 + 1.41590i
\(326\) 5.94740 0.329396
\(327\) 1.52776 1.52776i 0.0844851 0.0844851i
\(328\) 16.0194 + 16.0194i 0.884526 + 0.884526i
\(329\) 17.5011 10.7582i 0.964866 0.593118i
\(330\) 5.82902 + 3.04933i 0.320877 + 0.167860i
\(331\) 23.6200 1.29827 0.649136 0.760672i \(-0.275130\pi\)
0.649136 + 0.760672i \(0.275130\pi\)
\(332\) 2.31695 2.31695i 0.127159 0.127159i
\(333\) −6.18757 + 6.18757i −0.339076 + 0.339076i
\(334\) 2.04139 0.111700
\(335\) −1.25690 + 0.393517i −0.0686716 + 0.0215001i
\(336\) −1.16306 1.89203i −0.0634500 0.103219i
\(337\) −4.93809 4.93809i −0.268995 0.268995i 0.559700 0.828695i \(-0.310916\pi\)
−0.828695 + 0.559700i \(0.810916\pi\)
\(338\) −7.51384 + 7.51384i −0.408699 + 0.408699i
\(339\) −5.85234 −0.317856
\(340\) 6.36964 1.99425i 0.345442 0.108153i
\(341\) 9.23070i 0.499870i
\(342\) −0.0376844 + 0.0376844i −0.00203774 + 0.00203774i
\(343\) 14.1330 + 11.9691i 0.763109 + 0.646270i
\(344\) 10.2274i 0.551427i
\(345\) 0.783008 1.49678i 0.0421558 0.0805838i
\(346\) 5.30151i 0.285011i
\(347\) 5.83694 + 5.83694i 0.313343 + 0.313343i 0.846203 0.532860i \(-0.178883\pi\)
−0.532860 + 0.846203i \(0.678883\pi\)
\(348\) 2.77554 + 2.77554i 0.148784 + 0.148784i
\(349\) −16.9121 −0.905282 −0.452641 0.891693i \(-0.649518\pi\)
−0.452641 + 0.891693i \(0.649518\pi\)
\(350\) 4.05385 9.25637i 0.216687 0.494774i
\(351\) 5.18757 0.276892
\(352\) 15.9608 + 15.9608i 0.850714 + 0.850714i
\(353\) −11.1265 11.1265i −0.592202 0.592202i 0.346024 0.938226i \(-0.387532\pi\)
−0.938226 + 0.346024i \(0.887532\pi\)
\(354\) 5.32759i 0.283158i
\(355\) 8.42444 16.1039i 0.447123 0.854708i
\(356\) 7.15771i 0.379358i
\(357\) 5.42309 + 1.29400i 0.287021 + 0.0684855i
\(358\) −10.0389 + 10.0389i −0.530574 + 0.530574i
\(359\) 8.14864i 0.430069i −0.976606 0.215034i \(-0.931014\pi\)
0.976606 0.215034i \(-0.0689864\pi\)
\(360\) −5.56908 + 1.74360i −0.293516 + 0.0918958i
\(361\) −18.9951 −0.999744
\(362\) −4.58327 + 4.58327i −0.240891 + 0.240891i
\(363\) 2.71033 + 2.71033i 0.142255 + 0.142255i
\(364\) −16.5623 + 10.1811i −0.868102 + 0.533636i
\(365\) −28.8266 + 9.02520i −1.50885 + 0.472401i
\(366\) −10.9316 −0.571406
\(367\) 14.7480 14.7480i 0.769840 0.769840i −0.208238 0.978078i \(-0.566773\pi\)
0.978078 + 0.208238i \(0.0667728\pi\)
\(368\) 0.448402 0.448402i 0.0233746 0.0233746i
\(369\) −8.68077 −0.451903
\(370\) −13.2439 6.92828i −0.688518 0.360184i
\(371\) 19.5660 12.0275i 1.01582 0.624438i
\(372\) −2.40060 2.40060i −0.124465 0.124465i
\(373\) 1.49461 1.49461i 0.0773880 0.0773880i −0.667353 0.744741i \(-0.732573\pi\)
0.744741 + 0.667353i \(0.232573\pi\)
\(374\) −6.19955 −0.320571
\(375\) 8.82867 + 6.85963i 0.455911 + 0.354230i
\(376\) 20.2640i 1.04504i
\(377\) 10.1648 10.1648i 0.523511 0.523511i
\(378\) −1.96584 0.469067i −0.101112 0.0241262i
\(379\) 18.7135i 0.961248i −0.876927 0.480624i \(-0.840410\pi\)
0.876927 0.480624i \(-0.159590\pi\)
\(380\) 0.195805 + 0.102431i 0.0100446 + 0.00525461i
\(381\) 6.83487i 0.350161i
\(382\) −2.91327 2.91327i −0.149056 0.149056i
\(383\) 20.9354 + 20.9354i 1.06975 + 1.06975i 0.997378 + 0.0723706i \(0.0230564\pi\)
0.0723706 + 0.997378i \(0.476944\pi\)
\(384\) −9.58418 −0.489091
\(385\) 14.9590 17.1867i 0.762381 0.875916i
\(386\) −5.19184 −0.264258
\(387\) −2.77107 2.77107i −0.140862 0.140862i
\(388\) −9.71502 9.71502i −0.493205 0.493205i
\(389\) 25.6611i 1.30107i −0.759477 0.650535i \(-0.774545\pi\)
0.759477 0.650535i \(-0.225455\pi\)
\(390\) 2.64747 + 8.45604i 0.134060 + 0.428188i
\(391\) 1.59192i 0.0805069i
\(392\) 17.3586 5.69357i 0.876741 0.287569i
\(393\) −0.457851 + 0.457851i −0.0230955 + 0.0230955i
\(394\) 13.6915i 0.689767i
\(395\) 19.5425 + 10.2232i 0.983288 + 0.514387i
\(396\) −5.45542 −0.274145
\(397\) 6.73585 6.73585i 0.338063 0.338063i −0.517575 0.855638i \(-0.673165\pi\)
0.855638 + 0.517575i \(0.173165\pi\)
\(398\) −1.44278 1.44278i −0.0723201 0.0723201i
\(399\) 0.0966653 + 0.157252i 0.00483932 + 0.00787245i
\(400\) 2.39351 + 3.44776i 0.119676 + 0.172388i
\(401\) 14.7503 0.736593 0.368296 0.929708i \(-0.379941\pi\)
0.368296 + 0.929708i \(0.379941\pi\)
\(402\) −0.318148 + 0.318148i −0.0158678 + 0.0158678i
\(403\) −8.79162 + 8.79162i −0.437942 + 0.437942i
\(404\) −27.1899 −1.35275
\(405\) 1.03649 1.98133i 0.0515038 0.0984532i
\(406\) −4.77107 + 2.93285i −0.236784 + 0.145555i
\(407\) −23.8305 23.8305i −1.18124 1.18124i
\(408\) 3.88876 3.88876i 0.192522 0.192522i
\(409\) 10.5604 0.522180 0.261090 0.965315i \(-0.415918\pi\)
0.261090 + 0.965315i \(0.415918\pi\)
\(410\) −4.43022 14.1502i −0.218793 0.698827i
\(411\) 14.4772i 0.714106i
\(412\) 3.31210 3.31210i 0.163176 0.163176i
\(413\) −17.9487 4.28270i −0.883196 0.210738i
\(414\) 0.577063i 0.0283611i
\(415\) −4.93625 + 1.54547i −0.242311 + 0.0758641i
\(416\) 30.4032i 1.49064i
\(417\) −15.6739 15.6739i −0.767556 0.767556i
\(418\) −0.145136 0.145136i −0.00709884 0.00709884i
\(419\) 15.5472 0.759532 0.379766 0.925083i \(-0.376004\pi\)
0.379766 + 0.925083i \(0.376004\pi\)
\(420\) 0.579354 + 8.36002i 0.0282696 + 0.407927i
\(421\) 3.29886 0.160776 0.0803882 0.996764i \(-0.474384\pi\)
0.0803882 + 0.996764i \(0.474384\pi\)
\(422\) −6.49461 6.49461i −0.316153 0.316153i
\(423\) 5.49042 + 5.49042i 0.266953 + 0.266953i
\(424\) 22.6549i 1.10022i
\(425\) −10.3689 1.87141i −0.502964 0.0907766i
\(426\) 6.20867i 0.300811i
\(427\) −8.78764 + 36.8287i −0.425264 + 1.78227i
\(428\) −9.06196 + 9.06196i −0.438026 + 0.438026i
\(429\) 19.9792i 0.964604i
\(430\) 3.10280 5.93123i 0.149630 0.286029i
\(431\) −14.0911 −0.678743 −0.339371 0.940652i \(-0.610214\pi\)
−0.339371 + 0.940652i \(0.610214\pi\)
\(432\) 0.593565 0.593565i 0.0285579 0.0285579i
\(433\) −1.72650 1.72650i −0.0829702 0.0829702i 0.664404 0.747374i \(-0.268686\pi\)
−0.747374 + 0.664404i \(0.768686\pi\)
\(434\) 4.12656 2.53666i 0.198081 0.121764i
\(435\) −1.85136 5.91327i −0.0887660 0.283519i
\(436\) −3.06043 −0.146568
\(437\) −0.0372681 + 0.0372681i −0.00178277 + 0.00178277i
\(438\) −7.29664 + 7.29664i −0.348647 + 0.348647i
\(439\) −27.1172 −1.29423 −0.647116 0.762392i \(-0.724025\pi\)
−0.647116 + 0.762392i \(0.724025\pi\)
\(440\) −6.71524 21.4485i −0.320136 1.02252i
\(441\) −3.16057 + 6.24586i −0.150503 + 0.297422i
\(442\) −5.90465 5.90465i −0.280856 0.280856i
\(443\) −24.1502 + 24.1502i −1.14741 + 1.14741i −0.160349 + 0.987060i \(0.551262\pi\)
−0.987060 + 0.160349i \(0.948738\pi\)
\(444\) 12.3951 0.588243
\(445\) 5.23754 10.0119i 0.248283 0.474611i
\(446\) 12.6313i 0.598107i
\(447\) 7.81179 7.81179i 0.369485 0.369485i
\(448\) 1.71818 7.20084i 0.0811764 0.340208i
\(449\) 9.80267i 0.462617i 0.972881 + 0.231308i \(0.0743006\pi\)
−0.972881 + 0.231308i \(0.925699\pi\)
\(450\) 3.75866 + 0.678376i 0.177185 + 0.0319789i
\(451\) 33.4328i 1.57429i
\(452\) 5.86177 + 5.86177i 0.275714 + 0.275714i
\(453\) 13.0101 + 13.0101i 0.611266 + 0.611266i
\(454\) 1.19391 0.0560331
\(455\) 30.6166 2.12175i 1.43533 0.0994691i
\(456\) 0.182078 0.00852656
\(457\) 0.550071 + 0.550071i 0.0257312 + 0.0257312i 0.719855 0.694124i \(-0.244208\pi\)
−0.694124 + 0.719855i \(0.744208\pi\)
\(458\) 4.23099 + 4.23099i 0.197701 + 0.197701i
\(459\) 2.10728i 0.0983594i
\(460\) −2.28346 + 0.714918i −0.106467 + 0.0333332i
\(461\) 0.831786i 0.0387401i 0.999812 + 0.0193701i \(0.00616607\pi\)
−0.999812 + 0.0193701i \(0.993834\pi\)
\(462\) 1.80655 7.57117i 0.0840481 0.352243i
\(463\) 5.45140 5.45140i 0.253348 0.253348i −0.568994 0.822342i \(-0.692667\pi\)
0.822342 + 0.568994i \(0.192667\pi\)
\(464\) 2.32612i 0.107987i
\(465\) 1.60127 + 5.11446i 0.0742569 + 0.237177i
\(466\) 1.08890 0.0504423
\(467\) −23.2827 + 23.2827i −1.07740 + 1.07740i −0.0806551 + 0.996742i \(0.525701\pi\)
−0.996742 + 0.0806551i \(0.974299\pi\)
\(468\) −5.19592 5.19592i −0.240181 0.240181i
\(469\) 0.816091 + 1.32759i 0.0376836 + 0.0613025i
\(470\) −6.14768 + 11.7517i −0.283571 + 0.542067i
\(471\) −1.48484 −0.0684180
\(472\) −12.8705 + 12.8705i −0.592414 + 0.592414i
\(473\) 10.6724 10.6724i 0.490718 0.490718i
\(474\) 7.53435 0.346064
\(475\) −0.198932 0.286554i −0.00912762 0.0131480i
\(476\) −4.13575 6.72791i −0.189562 0.308373i
\(477\) 6.13823 + 6.13823i 0.281050 + 0.281050i
\(478\) 10.9544 10.9544i 0.501041 0.501041i
\(479\) −40.4319 −1.84738 −0.923691 0.383138i \(-0.874843\pi\)
−0.923691 + 0.383138i \(0.874843\pi\)
\(480\) 11.6122 + 6.07467i 0.530020 + 0.277269i
\(481\) 45.3940i 2.06979i
\(482\) −1.49616 + 1.49616i −0.0681483 + 0.0681483i
\(483\) −1.94413 0.463885i −0.0884609 0.0211075i
\(484\) 5.42938i 0.246790i
\(485\) 6.48019 + 20.6978i 0.294250 + 0.939839i
\(486\) 0.763878i 0.0346502i
\(487\) −7.22893 7.22893i −0.327574 0.327574i 0.524089 0.851663i \(-0.324406\pi\)
−0.851663 + 0.524089i \(0.824406\pi\)
\(488\) 26.4089 + 26.4089i 1.19548 + 1.19548i
\(489\) 7.78580 0.352086
\(490\) −11.7941 1.96435i −0.532804 0.0887404i
\(491\) 20.1040 0.907279 0.453639 0.891185i \(-0.350125\pi\)
0.453639 + 0.891185i \(0.350125\pi\)
\(492\) 8.69475 + 8.69475i 0.391990 + 0.391990i
\(493\) 4.12910 + 4.12910i 0.185965 + 0.185965i
\(494\) 0.276465i 0.0124387i
\(495\) 7.63083 + 3.99191i 0.342980 + 0.179423i
\(496\) 2.01189i 0.0903364i
\(497\) −20.9170 4.99097i −0.938256 0.223876i
\(498\) −1.24947 + 1.24947i −0.0559902 + 0.0559902i
\(499\) 15.4227i 0.690414i −0.938527 0.345207i \(-0.887809\pi\)
0.938527 0.345207i \(-0.112191\pi\)
\(500\) −1.97222 15.7136i −0.0882002 0.702732i
\(501\) 2.67241 0.119394
\(502\) 3.29478 3.29478i 0.147053 0.147053i
\(503\) 25.9985 + 25.9985i 1.15922 + 1.15922i 0.984644 + 0.174573i \(0.0558546\pi\)
0.174573 + 0.984644i \(0.444145\pi\)
\(504\) 3.61595 + 5.88231i 0.161067 + 0.262019i
\(505\) 38.0322 + 19.8958i 1.69241 + 0.885350i
\(506\) 2.22248 0.0988013
\(507\) −9.83645 + 9.83645i −0.436852 + 0.436852i
\(508\) −6.84587 + 6.84587i −0.303737 + 0.303737i
\(509\) 37.1271 1.64563 0.822816 0.568309i \(-0.192402\pi\)
0.822816 + 0.568309i \(0.192402\pi\)
\(510\) −3.43499 + 1.07545i −0.152104 + 0.0476216i
\(511\) 18.7168 + 30.4479i 0.827983 + 1.34694i
\(512\) 6.57690 + 6.57690i 0.290661 + 0.290661i
\(513\) −0.0493330 + 0.0493330i −0.00217810 + 0.00217810i
\(514\) −2.18048 −0.0961768
\(515\) −7.05642 + 2.20927i −0.310943 + 0.0973519i
\(516\) 5.55107i 0.244372i
\(517\) −21.1456 + 21.1456i −0.929982 + 0.929982i
\(518\) −4.10459 + 17.2022i −0.180345 + 0.755821i
\(519\) 6.94026i 0.304644i
\(520\) 14.0325 26.8241i 0.615365 1.17631i
\(521\) 2.59132i 0.113528i −0.998388 0.0567639i \(-0.981922\pi\)
0.998388 0.0567639i \(-0.0180782\pi\)
\(522\) −1.49678 1.49678i −0.0655122 0.0655122i
\(523\) −6.08854 6.08854i −0.266233 0.266233i 0.561347 0.827581i \(-0.310283\pi\)
−0.827581 + 0.561347i \(0.810283\pi\)
\(524\) 0.917176 0.0400670
\(525\) 5.30693 12.1176i 0.231613 0.528856i
\(526\) 18.1149 0.789846
\(527\) −3.57131 3.57131i −0.155569 0.155569i
\(528\) 2.28603 + 2.28603i 0.0994868 + 0.0994868i
\(529\) 22.4293i 0.975187i
\(530\) −6.87304 + 13.1383i −0.298546 + 0.570692i
\(531\) 6.97440i 0.302663i
\(532\) 0.0606843 0.254326i 0.00263100 0.0110264i
\(533\) 31.8425 31.8425i 1.37925 1.37925i
\(534\) 3.85997i 0.167037i
\(535\) 19.3065 6.04458i 0.834691 0.261330i
\(536\) 1.53718 0.0663960
\(537\) −13.1421 + 13.1421i −0.567122 + 0.567122i
\(538\) 13.3605 + 13.3605i 0.576013 + 0.576013i
\(539\) −24.0551 12.1725i −1.03613 0.524307i
\(540\) −3.02269 + 0.946361i −0.130076 + 0.0407249i
\(541\) −33.4638 −1.43872 −0.719360 0.694638i \(-0.755565\pi\)
−0.719360 + 0.694638i \(0.755565\pi\)
\(542\) −2.23333 + 2.23333i −0.0959297 + 0.0959297i
\(543\) −6.00000 + 6.00000i −0.257485 + 0.257485i
\(544\) −12.3503 −0.529515
\(545\) 4.28081 + 2.23942i 0.183370 + 0.0959262i
\(546\) 8.93165 5.49042i 0.382239 0.234968i
\(547\) −0.828381 0.828381i −0.0354190 0.0354190i 0.689175 0.724594i \(-0.257973\pi\)
−0.724594 + 0.689175i \(0.757973\pi\)
\(548\) 14.5005 14.5005i 0.619429 0.619429i
\(549\) −14.3107 −0.610767
\(550\) −2.61267 + 14.4760i −0.111405 + 0.617257i
\(551\) 0.193331i 0.00823616i
\(552\) −1.39408 + 1.39408i −0.0593361 + 0.0593361i
\(553\) 6.05665 25.3832i 0.257555 1.07941i
\(554\) 13.0853i 0.555939i
\(555\) −17.3377 9.06988i −0.735946 0.384995i
\(556\) 31.3983i 1.33159i
\(557\) 14.7120 + 14.7120i 0.623366 + 0.623366i 0.946391 0.323024i \(-0.104700\pi\)
−0.323024 + 0.946391i \(0.604700\pi\)
\(558\) 1.29458 + 1.29458i 0.0548040 + 0.0548040i
\(559\) 20.3295 0.859846
\(560\) 3.26040 3.74595i 0.137777 0.158295i
\(561\) −8.11589 −0.342653
\(562\) 2.83726 + 2.83726i 0.119683 + 0.119683i
\(563\) −23.9693 23.9693i −1.01019 1.01019i −0.999948 0.0102391i \(-0.996741\pi\)
−0.0102391 0.999948i \(-0.503259\pi\)
\(564\) 10.9985i 0.463121i
\(565\) −3.90996 12.4885i −0.164493 0.525394i
\(566\) 1.80115i 0.0757080i
\(567\) −2.57351 0.614060i −0.108077 0.0257881i
\(568\) −14.9990 + 14.9990i −0.629346 + 0.629346i
\(569\) 15.6660i 0.656751i −0.944547 0.328376i \(-0.893499\pi\)
0.944547 0.328376i \(-0.106501\pi\)
\(570\) −0.105593 0.0552386i −0.00442279 0.00231369i
\(571\) 36.9887 1.54793 0.773964 0.633229i \(-0.218271\pi\)
0.773964 + 0.633229i \(0.218271\pi\)
\(572\) 20.0114 20.0114i 0.836717 0.836717i
\(573\) −3.81379 3.81379i −0.159323 0.159323i
\(574\) −14.9460 + 9.18757i −0.623836 + 0.383482i
\(575\) 3.71714 + 0.670882i 0.155015 + 0.0279777i
\(576\) 2.79807 0.116586
\(577\) 15.5587 15.5587i 0.647717 0.647717i −0.304724 0.952441i \(-0.598564\pi\)
0.952441 + 0.304724i \(0.0985641\pi\)
\(578\) −6.78386 + 6.78386i −0.282171 + 0.282171i
\(579\) −6.79669 −0.282461
\(580\) −4.06845 + 7.77713i −0.168933 + 0.322928i
\(581\) 3.20506 + 5.21389i 0.132968 + 0.216309i
\(582\) 5.23907 + 5.23907i 0.217166 + 0.217166i
\(583\) −23.6405 + 23.6405i −0.979091 + 0.979091i
\(584\) 35.2548 1.45885
\(585\) 3.46582 + 11.0699i 0.143294 + 0.457683i
\(586\) 16.4804i 0.680798i
\(587\) −15.7111 + 15.7111i −0.648468 + 0.648468i −0.952623 0.304155i \(-0.901626\pi\)
0.304155 + 0.952623i \(0.401626\pi\)
\(588\) 9.42158 3.09026i 0.388539 0.127440i
\(589\) 0.167214i 0.00688993i
\(590\) 11.3687 3.55938i 0.468041 0.146537i
\(591\) 17.9237i 0.737281i
\(592\) −5.19401 5.19401i −0.213473 0.213473i
\(593\) −1.85199 1.85199i −0.0760523 0.0760523i 0.668057 0.744110i \(-0.267126\pi\)
−0.744110 + 0.668057i \(0.767126\pi\)
\(594\) 2.94197 0.120710
\(595\) 0.861891 + 12.4370i 0.0353341 + 0.509867i
\(596\) −15.6487 −0.640997
\(597\) −1.88876 1.88876i −0.0773018 0.0773018i
\(598\) 2.11676 + 2.11676i 0.0865609 + 0.0865609i
\(599\) 47.3151i 1.93324i 0.256208 + 0.966622i \(0.417527\pi\)
−0.256208 + 0.966622i \(0.582473\pi\)
\(600\) −7.44143 10.7191i −0.303795 0.437605i
\(601\) 11.0819i 0.452041i −0.974123 0.226021i \(-0.927428\pi\)
0.974123 0.226021i \(-0.0725717\pi\)
\(602\) −7.70393 1.83822i −0.313989 0.0749203i
\(603\) −0.416491 + 0.416491i −0.0169608 + 0.0169608i
\(604\) 26.0620i 1.06045i
\(605\) −3.97286 + 7.59441i −0.161520 + 0.308757i
\(606\) 14.6628 0.595637
\(607\) 7.54653 7.54653i 0.306304 0.306304i −0.537170 0.843474i \(-0.680507\pi\)
0.843474 + 0.537170i \(0.180507\pi\)
\(608\) −0.289130 0.289130i −0.0117258 0.0117258i
\(609\) −6.24586 + 3.83943i −0.253095 + 0.155581i
\(610\) −7.30346 23.3273i −0.295708 0.944496i
\(611\) −40.2795 −1.62953
\(612\) 2.11067 2.11067i 0.0853189 0.0853189i
\(613\) −2.62487 + 2.62487i −0.106017 + 0.106017i −0.758126 0.652108i \(-0.773885\pi\)
0.652108 + 0.758126i \(0.273885\pi\)
\(614\) −15.7935 −0.637375
\(615\) −5.79964 18.5241i −0.233864 0.746965i
\(616\) −22.6549 + 13.9263i −0.912793 + 0.561108i
\(617\) 11.3212 + 11.3212i 0.455774 + 0.455774i 0.897266 0.441491i \(-0.145550\pi\)
−0.441491 + 0.897266i \(0.645550\pi\)
\(618\) −1.78613 + 1.78613i −0.0718488 + 0.0718488i
\(619\) −9.06771 −0.364462 −0.182231 0.983256i \(-0.558332\pi\)
−0.182231 + 0.983256i \(0.558332\pi\)
\(620\) 3.51885 6.72654i 0.141320 0.270144i
\(621\) 0.755439i 0.0303147i
\(622\) −1.54599 + 1.54599i −0.0619884 + 0.0619884i
\(623\) −13.0043 3.10292i −0.521005 0.124316i
\(624\) 4.35458i 0.174323i
\(625\) −8.73948 + 23.4227i −0.349579 + 0.936907i
\(626\) 10.1744i 0.406651i
\(627\) −0.189999 0.189999i −0.00758783 0.00758783i
\(628\) 1.48723 + 1.48723i 0.0593471 + 0.0593471i
\(629\) 18.4398 0.735244
\(630\) −0.312431 4.50835i −0.0124475 0.179617i
\(631\) −9.67260 −0.385060 −0.192530 0.981291i \(-0.561669\pi\)
−0.192530 + 0.981291i \(0.561669\pi\)
\(632\) −18.2017 18.2017i −0.724023 0.724023i
\(633\) −8.50216 8.50216i −0.337930 0.337930i
\(634\) 7.97587i 0.316762i
\(635\) 14.5851 4.56639i 0.578792 0.181212i
\(636\) 12.2962i 0.487577i
\(637\) −11.3173 34.5043i −0.448409 1.36711i
\(638\) 5.76463 5.76463i 0.228224 0.228224i
\(639\) 8.12783i 0.321532i
\(640\) −6.40321 20.4519i −0.253109 0.808434i
\(641\) −40.5847 −1.60300 −0.801500 0.597995i \(-0.795964\pi\)
−0.801500 + 0.597995i \(0.795964\pi\)
\(642\) 4.88689 4.88689i 0.192870 0.192870i
\(643\) 3.89544 + 3.89544i 0.153621 + 0.153621i 0.779733 0.626112i \(-0.215355\pi\)
−0.626112 + 0.779733i \(0.715355\pi\)
\(644\) 1.48263 + 2.41189i 0.0584236 + 0.0950418i
\(645\) 4.06191 7.76463i 0.159937 0.305732i
\(646\) 0.112305 0.00441857
\(647\) 16.8414 16.8414i 0.662104 0.662104i −0.293772 0.955876i \(-0.594911\pi\)
0.955876 + 0.293772i \(0.0949106\pi\)
\(648\) −1.84539 + 1.84539i −0.0724939 + 0.0724939i
\(649\) 26.8609 1.05438
\(650\) −16.2758 + 11.2990i −0.638388 + 0.443183i
\(651\) 5.40212 3.32077i 0.211726 0.130151i
\(652\) −7.79833 7.79833i −0.305406 0.305406i
\(653\) −22.9951 + 22.9951i −0.899867 + 0.899867i −0.995424 0.0955569i \(-0.969537\pi\)
0.0955569 + 0.995424i \(0.469537\pi\)
\(654\) 1.65041 0.0645363
\(655\) −1.28291 0.671128i −0.0501275 0.0262232i
\(656\) 7.28688i 0.284505i
\(657\) −9.55210 + 9.55210i −0.372663 + 0.372663i
\(658\) 15.2640 + 3.64213i 0.595054 + 0.141985i
\(659\) 32.7543i 1.27593i 0.770067 + 0.637963i \(0.220223\pi\)
−0.770067 + 0.637963i \(0.779777\pi\)
\(660\) −3.64478 11.6415i −0.141873 0.453143i
\(661\) 32.5174i 1.26478i 0.774650 + 0.632391i \(0.217926\pi\)
−0.774650 + 0.632391i \(0.782074\pi\)
\(662\) 12.7582 + 12.7582i 0.495861 + 0.495861i
\(663\) −7.72984 7.72984i −0.300202 0.300202i
\(664\) 6.03701 0.234281
\(665\) −0.270982 + 0.311337i −0.0105082 + 0.0120731i
\(666\) −6.68434 −0.259013
\(667\) −1.48024 1.48024i −0.0573152 0.0573152i
\(668\) −2.67671 2.67671i −0.103565 0.103565i
\(669\) 16.5357i 0.639307i
\(670\) −0.891460 0.466349i −0.0344401 0.0180166i
\(671\) 55.1158i 2.12772i
\(672\) 3.59887 15.0828i 0.138829 0.581830i
\(673\) −16.7534 + 16.7534i −0.645796 + 0.645796i −0.951974 0.306179i \(-0.900950\pi\)
0.306179 + 0.951974i \(0.400950\pi\)
\(674\) 5.33455i 0.205479i
\(675\) 4.92050 + 0.888068i 0.189390 + 0.0341818i
\(676\) 19.7046 0.757868
\(677\) −6.85568 + 6.85568i −0.263485 + 0.263485i −0.826468 0.562983i \(-0.809654\pi\)
0.562983 + 0.826468i \(0.309654\pi\)
\(678\) −3.16110 3.16110i −0.121401 0.121401i
\(679\) 21.8620 13.4389i 0.838985 0.515737i
\(680\) 10.8964 + 5.70024i 0.417858 + 0.218594i
\(681\) 1.56296 0.0598929
\(682\) −4.98590 + 4.98590i −0.190920 + 0.190920i
\(683\) 23.2345 23.2345i 0.889042 0.889042i −0.105389 0.994431i \(-0.533609\pi\)
0.994431 + 0.105389i \(0.0336088\pi\)
\(684\) 0.0988248 0.00377866
\(685\) −30.8932 + 9.67222i −1.18037 + 0.369557i
\(686\) 1.16881 + 14.0988i 0.0446255 + 0.538297i
\(687\) 5.53883 + 5.53883i 0.211319 + 0.211319i
\(688\) 2.32612 2.32612i 0.0886823 0.0886823i
\(689\) −45.0321 −1.71559
\(690\) 1.23141 0.385537i 0.0468790 0.0146772i
\(691\) 42.4714i 1.61569i 0.589395 + 0.807845i \(0.299366\pi\)
−0.589395 + 0.807845i \(0.700634\pi\)
\(692\) −6.95144 + 6.95144i −0.264254 + 0.264254i
\(693\) 2.36497 9.91150i 0.0898376 0.376507i
\(694\) 6.30557i 0.239356i
\(695\) 22.9752 43.9188i 0.871500 1.66594i
\(696\) 7.23190i 0.274124i
\(697\) 12.9350 + 12.9350i 0.489947 + 0.489947i
\(698\) −9.13494 9.13494i −0.345763 0.345763i
\(699\) 1.42549 0.0539169
\(700\) −17.4526 + 6.82165i −0.659646 + 0.257834i
\(701\) 17.0793 0.645077 0.322539 0.946556i \(-0.395464\pi\)
0.322539 + 0.946556i \(0.395464\pi\)
\(702\) 2.80203 + 2.80203i 0.105756 + 0.105756i
\(703\) 0.431690 + 0.431690i 0.0162815 + 0.0162815i
\(704\) 10.7764i 0.406150i
\(705\) −8.04799 + 15.3843i −0.303105 + 0.579407i
\(706\) 12.0198i 0.452370i
\(707\) 11.7870 49.3991i 0.443297 1.85785i
\(708\) −6.98563 + 6.98563i −0.262536 + 0.262536i
\(709\) 32.6742i 1.22710i 0.789654 + 0.613552i \(0.210260\pi\)
−0.789654 + 0.613552i \(0.789740\pi\)
\(710\) 13.2488 4.14802i 0.497220 0.155673i
\(711\) 9.86329 0.369902
\(712\) −9.32502 + 9.32502i −0.349470 + 0.349470i
\(713\) 1.28028 + 1.28028i 0.0479469 + 0.0479469i
\(714\) 2.23030 + 3.62819i 0.0834670 + 0.135782i
\(715\) −42.6341 + 13.3481i −1.59443 + 0.499192i
\(716\) 26.3264 0.983865
\(717\) 14.3405 14.3405i 0.535554 0.535554i
\(718\) 4.40143 4.40143i 0.164260 0.164260i
\(719\) −19.3248 −0.720693 −0.360346 0.932819i \(-0.617341\pi\)
−0.360346 + 0.932819i \(0.617341\pi\)
\(720\) 1.66319 + 0.870061i 0.0619832 + 0.0324253i
\(721\) 4.58166 + 7.45331i 0.170630 + 0.277576i
\(722\) −10.2601 10.2601i −0.381841 0.381841i
\(723\) −1.95864 + 1.95864i −0.0728426 + 0.0728426i
\(724\) 12.0193 0.446695
\(725\) 11.3816 7.90133i 0.422701 0.293448i
\(726\) 2.92793i 0.108666i
\(727\) 2.71795 2.71795i 0.100803 0.100803i −0.654907 0.755710i \(-0.727292\pi\)
0.755710 + 0.654907i \(0.227292\pi\)
\(728\) −34.8412 8.31339i −1.29130 0.308115i
\(729\) 1.00000i 0.0370370i
\(730\) −20.4454 10.6956i −0.756718 0.395861i
\(731\) 8.25820i 0.305440i
\(732\) 14.3338 + 14.3338i 0.529791 + 0.529791i
\(733\) −2.38437 2.38437i −0.0880686 0.0880686i 0.661700 0.749769i \(-0.269835\pi\)
−0.749769 + 0.661700i \(0.769835\pi\)
\(734\) 15.9321 0.588064
\(735\) −15.4398 2.57155i −0.569505 0.0948532i
\(736\) 4.42747 0.163199
\(737\) −1.60406 1.60406i −0.0590862 0.0590862i
\(738\) −4.68886 4.68886i −0.172599 0.172599i
\(739\) 4.95679i 0.182339i 0.995835 + 0.0911693i \(0.0290605\pi\)
−0.995835 + 0.0911693i \(0.970940\pi\)
\(740\) 8.28116 + 26.4501i 0.304422 + 0.972326i
\(741\) 0.361923i 0.0132956i
\(742\) 17.0650 + 4.07186i 0.626477 + 0.149483i
\(743\) 15.6556 15.6556i 0.574347 0.574347i −0.358993 0.933340i \(-0.616880\pi\)
0.933340 + 0.358993i \(0.116880\pi\)
\(744\) 6.25496i 0.229318i
\(745\) 21.8889 + 11.4507i 0.801946 + 0.419521i
\(746\) 1.61461 0.0591150
\(747\) −1.63570 + 1.63570i −0.0598470 + 0.0598470i
\(748\) 8.12896 + 8.12896i 0.297224 + 0.297224i
\(749\) −12.5355 20.3924i −0.458037 0.745120i
\(750\) 1.06357 + 8.47393i 0.0388360 + 0.309424i
\(751\) −11.1909 −0.408361 −0.204181 0.978933i \(-0.565453\pi\)
−0.204181 + 0.978933i \(0.565453\pi\)
\(752\) −4.60881 + 4.60881i −0.168066 + 0.168066i
\(753\) 4.31322 4.31322i 0.157183 0.157183i
\(754\) 10.9808 0.399899
\(755\) −19.0704 + 36.4545i −0.694045 + 1.32672i
\(756\) 1.96260 + 3.19270i 0.0713791 + 0.116117i
\(757\) 29.4977 + 29.4977i 1.07211 + 1.07211i 0.997189 + 0.0749214i \(0.0238706\pi\)
0.0749214 + 0.997189i \(0.476129\pi\)
\(758\) 10.1080 10.1080i 0.367138 0.367138i
\(759\) 2.90947 0.105607
\(760\) 0.121646 + 0.388540i 0.00441258 + 0.0140938i
\(761\) 28.1175i 1.01926i 0.860395 + 0.509629i \(0.170217\pi\)
−0.860395 + 0.509629i \(0.829783\pi\)
\(762\) 3.69181 3.69181i 0.133740 0.133740i
\(763\) 1.32672 5.56025i 0.0480305 0.201294i
\(764\) 7.63986i 0.276400i
\(765\) −4.49678 + 1.40788i −0.162581 + 0.0509019i
\(766\) 22.6162i 0.817157i
\(767\) 25.5832 + 25.5832i 0.923757 + 0.923757i
\(768\) −9.13390 9.13390i −0.329591 0.329591i
\(769\) 6.61248 0.238452 0.119226 0.992867i \(-0.461959\pi\)
0.119226 + 0.992867i \(0.461959\pi\)
\(770\) 17.3633 1.20328i 0.625729 0.0433634i
\(771\) −2.85449 −0.102802
\(772\) 6.80764 + 6.80764i 0.245012 + 0.245012i
\(773\) 31.7247 + 31.7247i<