Properties

Label 105.2.m.a.13.5
Level 105
Weight 2
Character 105.13
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 13.5
Root \(-1.36166 - 0.381939i\)
Character \(\chi\) = 105.13
Dual form 105.2.m.a.97.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.540143 - 0.540143i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.41649i q^{4} +(1.03649 + 1.98133i) q^{5} +0.763878i q^{6} +(0.614060 - 2.57351i) q^{7} +(1.84539 + 1.84539i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(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} +(0.614060 - 2.57351i) 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} +(3.64535 + 0.869810i) 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} +(5.73544 - 1.45077i) 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} +(1.96584 + 0.469067i) 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} +(-2.57351 - 0.614060i) 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} +(2.31434 - 3.88158i) 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} +(-2.36497 + 9.91150i) 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} +(-5.08082 + 1.66650i) 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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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 −0.489861 0.871800i \(-0.662953\pi\)
0.871800 + 0.489861i \(0.162953\pi\)
\(3\) −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
\(7\) 0.614060 2.57351i 0.232093 0.972694i
\(8\) 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 0.0175187 0.999847i \(-0.494423\pi\)
0.999847 0.0175187i \(-0.00557667\pi\)
\(14\) −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 \(-0.332255\pi\)
−0.864326 + 0.502931i \(0.832255\pi\)
\(18\) −0.540143 0.540143i −0.127313 0.127313i
\(19\) −0.0697674 −0.0160057 −0.00800286 0.999968i \(-0.502547\pi\)
−0.00800286 + 0.999968i \(0.502547\pi\)
\(20\) −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 0.649218 0.760602i \(-0.275096\pi\)
−0.760602 + 0.649218i \(0.775096\pi\)
\(24\) −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
\(28\) 3.64535 + 0.869810i 0.688906 + 0.164379i
\(29\) 2.77107i 0.514576i −0.966335 0.257288i \(-0.917171\pi\)
0.966335 0.257288i \(-0.0828288\pi\)
\(30\) −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
\(35\) 5.73544 1.45077i 0.969466 0.245224i
\(36\) 1.41649 0.236082
\(37\) 6.18757 6.18757i 1.01723 1.01723i 0.0173805 0.999849i \(-0.494467\pi\)
0.999849 0.0173805i \(-0.00553267\pi\)
\(38\) −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 \(0.762910\pi\)
\(42\) 1.96584 + 0.469067i 0.303336 + 0.0723786i
\(43\) −2.77107 2.77107i −0.422585 0.422585i 0.463508 0.886093i \(-0.346591\pi\)
−0.886093 + 0.463508i \(0.846591\pi\)
\(44\) 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 \(-0.441623\pi\)
−0.983230 + 0.182370i \(0.941623\pi\)
\(48\) 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 0.989267 0.146116i \(-0.0466774\pi\)
−0.146116 + 0.989267i \(0.546677\pi\)
\(54\) 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 \(-0.349998\pi\)
0.453995 + 0.891004i \(0.349998\pi\)
\(60\) 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
\(63\) −2.57351 0.614060i −0.324231 0.0773643i
\(64\) 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 −0.681208 0.732090i \(-0.738545\pi\)
0.732090 + 0.681208i \(0.238545\pi\)
\(68\) 2.11067 2.11067i 0.255957 0.255957i
\(69\) 0.755439 0.0909442
\(70\) 2.31434 3.88158i 0.276616 0.463938i
\(71\) −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 −0.125953 + 0.992036i \(0.540199\pi\)
−0.992036 + 0.125953i \(0.959801\pi\)
\(74\) 6.68434i 0.777039i
\(75\) −0.888068 4.92050i −0.102545 0.568171i
\(76\) 0.0988248i 0.0113360i
\(77\) −2.36497 + 9.91150i −0.269513 + 1.12952i
\(78\) 2.80203 + 2.80203i 0.317267 + 0.317267i
\(79\) 9.86329i 1.10971i 0.831948 + 0.554854i \(0.187226\pi\)
−0.831948 + 0.554854i \(0.812774\pi\)
\(80\) −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 \(-0.790520\pi\)
0.611615 + 0.791156i \(0.290520\pi\)
\(84\) −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 \(-0.413698\pi\)
0.267815 + 0.963470i \(0.413698\pi\)
\(90\) 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 \(-0.413885\pi\)
−0.963627 + 0.267251i \(0.913885\pi\)
\(98\) −5.08082 + 1.66650i −0.513240 + 0.168342i
\(99\) 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 \(-0.802089\pi\)
0.582463 + 0.812857i \(0.302089\pi\)
\(104\) 13.5384 1.32755
\(105\) −3.02972 + 5.08142i −0.295671 + 0.495895i
\(106\) 6.63105 0.644064
\(107\) −6.39747 + 6.39747i −0.618467 + 0.618467i −0.945138 0.326671i \(-0.894073\pi\)
0.326671 + 0.945138i \(0.394073\pi\)
\(108\) −1.00161 + 1.00161i −0.0963800 + 0.0963800i
\(109\) 2.16057i 0.206945i 0.994632 + 0.103473i \(0.0329954\pi\)
−0.994632 + 0.103473i \(0.967005\pi\)
\(110\) −6.27794 1.96554i −0.598578 0.187407i
\(111\) 8.75054i 0.830564i
\(112\) −0.515459 + 2.16027i −0.0487063 + 0.204126i
\(113\) −4.13823 4.13823i −0.389292 0.389292i 0.485143 0.874435i \(-0.338768\pi\)
−0.874435 + 0.485143i \(0.838768\pi\)
\(114\) 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 −0.888239 0.459381i \(-0.848071\pi\)
0.459381 + 0.888239i \(0.348071\pi\)
\(128\) −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
\(133\) −0.0428413 + 0.179547i −0.00371481 + 0.0155687i
\(134\) 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 −0.118372 0.992969i \(-0.537768\pi\)
0.992969 + 0.118372i \(0.0377676\pi\)
\(138\) 0.408045 0.408045i 0.0347351 0.0347351i
\(139\) 22.1663 1.88012 0.940060 0.341009i \(-0.110769\pi\)
0.940060 + 0.341009i \(0.110769\pi\)
\(140\) 2.05500 + 8.12420i 0.173679 + 0.686620i
\(141\) 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
\(147\) 6.65135 2.18163i 0.548594 0.179938i
\(148\) 8.76463 + 8.76463i 0.720448 + 0.720448i
\(149\) 11.0475i 0.905050i 0.891752 + 0.452525i \(0.149477\pi\)
−0.891752 + 0.452525i \(0.850523\pi\)
\(150\) −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 \(-0.231129\pi\)
−0.663967 + 0.747762i \(0.731129\pi\)
\(158\) 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 0.889042 0.457826i \(-0.151372\pi\)
−0.457826 + 0.889042i \(0.651372\pi\)
\(164\) −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 \(-0.282972\pi\)
−0.776431 + 0.630203i \(0.782972\pi\)
\(168\) −1.60256 + 6.71629i −0.123640 + 0.518173i
\(169\) 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 \(-0.665014\pi\)
0.868609 + 0.495498i \(0.165014\pi\)
\(174\) 2.11676 0.160471
\(175\) 8.81920 + 9.86011i 0.666669 + 0.745354i
\(176\) 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 \(-0.755591\pi\)
0.719416 0.694579i \(-0.244409\pi\)
\(180\) 1.46818 + 2.80654i 0.109432 + 0.209187i
\(181\) 8.48528i 0.630706i 0.948974 + 0.315353i \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) −10.1979 2.43331i −0.755922 0.180369i
\(183\) −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 0.512653 0.858596i \(-0.328663\pi\)
−0.858596 + 0.512653i \(0.828663\pi\)
\(194\) −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 −0.0927124 0.995693i \(-0.529554\pi\)
0.995693 + 0.0927124i \(0.0295537\pi\)
\(198\) 2.08029 + 2.08029i 0.147840 + 0.147840i
\(199\) 2.67111 0.189350 0.0946750 0.995508i \(-0.469819\pi\)
0.0946750 + 0.995508i \(0.469819\pi\)
\(200\) −12.8414 + 2.31766i −0.908026 + 0.163884i
\(201\) 0.589007i 0.0415453i
\(202\) −10.3682 10.3682i −0.729503 0.729503i
\(203\) −7.13138 1.70161i −0.500524 0.119429i
\(204\) 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
\(210\) 1.10821 + 4.38118i 0.0764736 + 0.302330i
\(211\) −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
\(217\) −6.16802 1.47174i −0.418712 0.0999082i
\(218\) 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 \(-0.563232\pi\)
0.980334 + 0.197346i \(0.0632321\pi\)
\(224\) 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 \(-0.266518\pi\)
−0.742832 + 0.669478i \(0.766518\pi\)
\(228\) 0.0698797 + 0.0698797i 0.00462790 + 0.00462790i
\(229\) −7.83309 −0.517625 −0.258812 0.965928i \(-0.583331\pi\)
−0.258812 + 0.965928i \(0.583331\pi\)
\(230\) −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 0.739353 0.673318i \(-0.235132\pi\)
−0.673318 + 0.739353i \(0.735132\pi\)
\(234\) −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
\(238\) −0.988454 + 4.14258i −0.0640720 + 0.268524i
\(239\) 20.2805i 1.31183i 0.754833 + 0.655917i \(0.227718\pi\)
−0.754833 + 0.655917i \(0.772282\pi\)
\(240\) 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
\(245\) −0.211650 15.6510i −0.0135218 0.999909i
\(246\) −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 \(-0.0616623\pi\)
\(252\) 0.869810 3.64535i 0.0547929 0.229635i
\(253\) 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 \(-0.221624\pi\)
−0.641346 + 0.767252i \(0.721624\pi\)
\(258\) 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 0.999401 + 0.0345941i \(0.0110138\pi\)
0.0345941 + 0.999401i \(0.488986\pi\)
\(264\) 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 \(-0.771909\pi\)
−0.754064 + 0.656801i \(0.771909\pi\)
\(270\) 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
\(273\) 13.3502 + 3.18548i 0.807993 + 0.192794i
\(274\) 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 −0.970178 0.242393i \(-0.922068\pi\)
0.242393 + 0.970178i \(0.422068\pi\)
\(278\) 11.9730 11.9730i 0.718091 0.718091i
\(279\) −2.39674 −0.143489
\(280\) 13.2614 + 7.90691i 0.792519 + 0.472528i
\(281\) 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 \(-0.727674\pi\)
0.754923 + 0.655813i \(0.227674\pi\)
\(284\) 11.5130i 0.683170i
\(285\) 0.148878 + 0.0466117i 0.00881879 + 0.00276104i
\(286\) 15.2617i 0.902441i
\(287\) 22.3400 + 5.33051i 1.31869 + 0.314650i
\(288\) 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 \(-0.532972\pi\)
0.994640 + 0.103400i \(0.0329722\pi\)
\(294\) 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 \(-0.0491256\pi\)
−0.153721 + 0.988114i \(0.549126\pi\)
\(308\) −14.0395 3.34995i −0.799977 0.190881i
\(309\) 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 \(-0.627152\pi\)
0.921271 + 0.388921i \(0.127152\pi\)
\(314\) 1.13424 0.0640088
\(315\) −1.45077 5.73544i −0.0817414 0.323155i
\(316\) −13.9713 −0.785945
\(317\) 7.38310 7.38310i 0.414676 0.414676i −0.468688 0.883364i \(-0.655273\pi\)
0.883364 + 0.468688i \(0.155273\pi\)
\(318\) −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
\(322\) −0.354351 + 1.48508i −0.0197472 + 0.0827600i
\(323\) 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 −0.828695 0.559700i \(-0.810916\pi\)
0.559700 + 0.828695i \(0.310916\pi\)
\(338\) −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
\(343\) −11.9691 + 14.1330i −0.646270 + 0.763109i
\(344\) 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 −0.532860 0.846203i \(-0.678883\pi\)
0.846203 + 0.532860i \(0.178883\pi\)
\(348\) −2.77554 + 2.77554i −0.148784 + 0.148784i
\(349\) 16.9121 0.905282 0.452641 0.891693i \(-0.350482\pi\)
0.452641 + 0.891693i \(0.350482\pi\)
\(350\) 10.0895 + 0.562240i 0.539306 + 0.0300530i
\(351\) 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 \(-0.612468\pi\)
0.938226 + 0.346024i \(0.112468\pi\)
\(354\) 5.32759i 0.283158i
\(355\) −8.42444 16.1039i −0.447123 0.854708i
\(356\) 7.15771i 0.379358i
\(357\) 1.29400 5.42309i 0.0684855 0.287021i
\(358\) −10.0389 10.0389i −0.530574 0.530574i
\(359\) 8.14864i 0.430069i 0.976606 + 0.215034i \(0.0689864\pi\)
−0.976606 + 0.215034i \(0.931014\pi\)
\(360\) 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 \(-0.433227\pi\)
−0.978078 + 0.208238i \(0.933227\pi\)
\(368\) 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 0.744741 0.667353i \(-0.232573\pi\)
−0.667353 + 0.744741i \(0.732573\pi\)
\(374\) 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
\(378\) 0.469067 1.96584i 0.0241262 0.101112i
\(379\) 18.7135i 0.961248i 0.876927 + 0.480624i \(0.159590\pi\)
−0.876927 + 0.480624i \(0.840410\pi\)
\(380\) 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 −0.0723706 + 0.997378i \(0.523056\pi\)
−0.997378 + 0.0723706i \(0.976944\pi\)
\(384\) 9.58418 0.489091
\(385\) −22.0893 + 5.58742i −1.12577 + 0.284761i
\(386\) −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 \(0.225455\pi\)
−0.759477 + 0.650535i \(0.774545\pi\)
\(390\) −2.64747 + 8.45604i −0.134060 + 0.428188i
\(391\) 1.59192i 0.0805069i
\(392\) −5.69357 17.3586i −0.287569 0.876741i
\(393\) −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 \(-0.326835\pi\)
−0.855638 + 0.517575i \(0.826835\pi\)
\(398\) 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 \(-0.584082\pi\)
−0.261090 + 0.965315i \(0.584082\pi\)
\(410\) −4.43022 + 14.1502i −0.218793 + 0.698827i
\(411\) 14.4772i 0.714106i
\(412\) −3.31210 3.31210i −0.163176 0.163176i
\(413\) 4.28270 17.9487i 0.210738 0.883196i
\(414\) 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 \(-0.623996\pi\)
−0.379766 + 0.925083i \(0.623996\pi\)
\(420\) −7.19778 4.29157i −0.351216 0.209407i
\(421\) 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
\(427\) 36.8287 + 8.78764i 1.78227 + 0.425264i
\(428\) −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 \(-0.731314\pi\)
0.747374 + 0.664404i \(0.231314\pi\)
\(434\) −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 \(-0.275975\pi\)
0.647116 + 0.762392i \(0.275975\pi\)
\(440\) 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 −0.987060 0.160349i \(-0.948738\pi\)
−0.160349 0.987060i \(-0.551262\pi\)
\(444\) −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
\(448\) 7.20084 + 1.71818i 0.340208 + 0.0811764i
\(449\) 9.80267i 0.462617i −0.972881 0.231308i \(-0.925699\pi\)
0.972881 0.231308i \(-0.0743006\pi\)
\(450\) 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
\(455\) 15.7169 26.3602i 0.736819 1.23578i
\(456\) 0.182078 0.00852656
\(457\) 0.550071 0.550071i 0.0257312 0.0257312i −0.694124 0.719855i \(-0.744208\pi\)
0.719855 + 0.694124i \(0.244208\pi\)
\(458\) −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 \(0.993834\pi\)
\(462\) −7.57117 1.80655i −0.352243 0.0840481i
\(463\) 5.45140 + 5.45140i 0.253348 + 0.253348i 0.822342 0.568994i \(-0.192667\pi\)
−0.568994 + 0.822342i \(0.692667\pi\)
\(464\) 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 0.996742 + 0.0806551i \(0.0257012\pi\)
0.0806551 + 0.996742i \(0.474299\pi\)
\(468\) 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 \(-0.125157\pi\)
0.923691 + 0.383138i \(0.125157\pi\)
\(480\) 11.6122 6.07467i 0.530020 0.277269i
\(481\) 45.3940i 2.06979i
\(482\) 1.49616 + 1.49616i 0.0681483 + 0.0681483i
\(483\) 0.463885 1.94413i 0.0211075 0.0884609i
\(484\) 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 −0.851663 0.524089i \(-0.824406\pi\)
0.524089 + 0.851663i \(0.324406\pi\)
\(488\) −26.4089 + 26.4089i −1.19548 + 1.19548i
\(489\) −7.78580 −0.352086
\(490\) −8.56813 8.33948i −0.387068 0.376739i
\(491\) 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
\(497\) −4.99097 + 20.9170i −0.223876 + 0.938256i
\(498\) −1.24947 1.24947i −0.0559902 0.0559902i
\(499\) 15.4227i 0.690414i 0.938527 + 0.345207i \(0.112191\pi\)
−0.938527 + 0.345207i \(0.887809\pi\)
\(500\) 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 −0.174573 + 0.984644i \(0.555855\pi\)
−0.984644 + 0.174573i \(0.944145\pi\)
\(504\) −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 \(-0.807598\pi\)
−0.822816 + 0.568309i \(0.807598\pi\)
\(510\) 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
\(518\) −17.2022 4.10459i −0.755821 0.180345i
\(519\) 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 \(-0.689717\pi\)
0.827581 + 0.561347i \(0.189717\pi\)
\(524\) −0.917176 −0.0400670
\(525\) −13.2083 0.736034i −0.576456 0.0321232i
\(526\) 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
\(532\) −0.254326 0.0606843i −0.0110264 0.00263100i
\(533\) 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 −0.724594 0.689175i \(-0.757973\pi\)
0.689175 + 0.724594i \(0.257973\pi\)
\(548\) 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
\(553\) 25.3832 + 6.05665i 1.07941 + 0.257555i
\(554\) 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 −0.323024 0.946391i \(-0.604700\pi\)
0.946391 + 0.323024i \(0.104700\pi\)
\(558\) −1.29458 + 1.29458i −0.0548040 + 0.0548040i
\(559\) −20.3295 −0.859846
\(560\) −4.81449 + 1.21781i −0.203449 + 0.0514620i
\(561\) −8.11589 −0.342653
\(562\) 2.83726 2.83726i 0.119683 0.119683i
\(563\) 23.9693 23.9693i 1.01019 1.01019i 0.0102391 0.999948i \(-0.496741\pi\)
0.999948 0.0102391i \(-0.00325926\pi\)
\(564\) 10.9985i 0.463121i
\(565\) 3.90996 12.4885i 0.164493 0.525394i
\(566\) 1.80115i 0.0757080i
\(567\) −0.614060 + 2.57351i −0.0257881 + 0.108077i
\(568\) −14.9990 14.9990i −0.629346 0.629346i
\(569\) 15.6660i 0.656751i 0.944547 + 0.328376i \(0.106501\pi\)
−0.944547 + 0.328376i \(0.893499\pi\)
\(570\) 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 \(-0.401436\pi\)
−0.952441 + 0.304724i \(0.901436\pi\)
\(578\) −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 \(-0.0983740\pi\)
−0.304155 + 0.952623i \(0.598374\pi\)
\(588\) 3.09026 + 9.42158i 0.127440 + 0.388539i
\(589\) 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 \(-0.732874\pi\)
0.744110 + 0.668057i \(0.232874\pi\)
\(594\) −2.94197 −0.120710
\(595\) −10.7080 6.38447i −0.438984 0.261738i
\(596\) −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 \(-0.582473\pi\)
0.256208 0.966622i \(-0.417527\pi\)
\(600\) 7.44143 10.7191i 0.303795 0.437605i
\(601\) 11.0819i 0.452041i −0.974123 0.226021i \(-0.927428\pi\)
0.974123 0.226021i \(-0.0725717\pi\)
\(602\) −1.83822 + 7.70393i −0.0749203 + 0.313989i
\(603\) −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 \(-0.319493\pi\)
−0.843474 + 0.537170i \(0.819493\pi\)
\(608\) 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 0.652108 0.758126i \(-0.273885\pi\)
−0.758126 + 0.652108i \(0.773885\pi\)
\(614\) 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 −0.441491 0.897266i \(-0.645550\pi\)
0.897266 + 0.441491i \(0.145550\pi\)
\(618\) −1.78613 1.78613i −0.0718488 0.0718488i
\(619\) 9.06771 0.364462 0.182231 0.983256i \(-0.441668\pi\)
0.182231 + 0.983256i \(0.441668\pi\)
\(620\) 3.51885 + 6.72654i 0.141320 + 0.270144i
\(621\) 0.755439i 0.0303147i
\(622\) 1.54599 + 1.54599i 0.0619884 + 0.0619884i
\(623\) 3.10292 13.0043i 0.124316 0.521005i
\(624\) 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
\(630\) −3.88158 2.31434i −0.154646 0.0922054i
\(631\) −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
\(637\) −34.5043 + 11.3173i −1.36711 + 0.448409i
\(638\) 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 \(-0.784645\pi\)
0.626112 + 0.779733i \(0.284645\pi\)
\(644\) −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 \(-0.405089\pi\)
−0.955876 + 0.293772i \(0.905089\pi\)
\(648\) −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 0.0955569 0.995424i \(-0.469537\pi\)
−0.995424 + 0.0955569i \(0.969537\pi\)
\(654\) −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
\(658\) −3.64213 + 15.2640i −0.141985 + 0.595054i
\(659\) 32.7543i 1.27593i −0.770067 0.637963i \(-0.779777\pi\)
0.770067 0.637963i \(-0.220223\pi\)
\(660\) −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
\(665\) −0.400147 + 0.101216i −0.0155170 + 0.00392499i
\(666\) −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
\(672\) −15.0828 3.59887i −0.581830 0.138829i
\(673\) −16.7534 16.7534i −0.645796 0.645796i 0.306179 0.951974i \(-0.400950\pi\)
−0.951974 + 0.306179i \(0.900950\pi\)
\(674\) 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 \(-0.190346\pi\)
−0.562983 + 0.826468i \(0.690346\pi\)
\(678\) 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 0.994431 0.105389i \(-0.0336088\pi\)
−0.105389 + 0.994431i \(0.533609\pi\)
\(684\) −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
\(693\) 9.91150 + 2.36497i 0.376507 + 0.0898376i
\(694\) 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
\(700\) −13.9668 + 12.4923i −0.527894 + 0.472165i
\(701\) 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
\(707\) −49.3991 11.7870i −1.85785 0.443297i
\(708\) −6.98563 6.98563i −0.262536 0.262536i
\(709\) 32.6742i 1.22710i −0.789654 0.613552i \(-0.789740\pi\)
0.789654 0.613552i \(-0.210260\pi\)
\(710\) −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 \(-0.382659\pi\)
0.360346 + 0.932819i \(0.382659\pi\)
\(720\) −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 \(-0.272708\pi\)
−0.755710 + 0.654907i \(0.772708\pi\)
\(728\) 8.31339 34.8412i 0.308115 1.29130i
\(729\) 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 \(-0.730165\pi\)
0.749769 + 0.661700i \(0.230165\pi\)
\(734\) −15.9321 −0.588064
\(735\) 11.2166 + 10.9173i 0.413731 + 0.402691i
\(736\) 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 \(-0.970940\pi\)
0.995835 0.0911693i \(-0.0290605\pi\)
\(740\) −8.28116 + 26.4501i −0.304422 + 0.972326i
\(741\) 0.361923i 0.0132956i
\(742\) 4.07186 17.0650i 0.149483 0.626477i
\(743\) 15.6556 + 15.6556i 0.574347 + 0.574347i 0.933340 0.358993i \(-0.116880\pi\)
−0.358993 + 0.933340i \(0.616880\pi\)
\(744\) 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 0.0749214 0.997189i \(-0.476129\pi\)
0.997189 0.0749214i \(-0.0238706\pi\)
\(758\) 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
\(763\) 5.56025 + 1.32672i 0.201294 + 0.0480305i
\(764\) 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 \(-0.538041\pi\)
−0.119226 + 0.992867i \(0.538041\pi\)
\(770\) −8.91335 + 14.9494i −0.321215 + 0.538738i
\(771\) −2.85449 −0.102802
\(772\) 6.80764 6.80764i 0.245012 0.245012i
\(773\) −31.7247 + 31.7247i −1.14106