Properties

Label 525.2.m.b.307.4
Level 525
Weight 2
Character 525.307
Analytic conductor 4.192
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
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: \( 2^{8} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.4
Root \(1.36166 - 0.381939i\) of \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Character \(\chi\) \(=\) 525.307
Dual form 525.2.m.b.118.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.540143 - 0.540143i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.41649i q^{4} -0.763878i q^{6} +(-0.614060 - 2.57351i) q^{7} +(-1.84539 + 1.84539i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.540143 - 0.540143i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.41649i q^{4} -0.763878i q^{6} +(-0.614060 - 2.57351i) q^{7} +(-1.84539 + 1.84539i) q^{8} +1.00000i q^{9} -3.85136 q^{11} +(1.00161 - 1.00161i) q^{12} +(-3.66816 - 3.66816i) q^{13} +(-1.05838 + 1.72174i) q^{14} -0.839427 q^{16} +(1.49007 - 1.49007i) q^{17} +(0.540143 - 0.540143i) q^{18} -0.0697674 q^{19} +(1.38554 - 2.25395i) q^{21} +(2.08029 + 2.08029i) q^{22} +(0.534176 - 0.534176i) q^{23} -2.60978 q^{24} +3.96267i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-3.64535 + 0.869810i) q^{28} +2.77107i q^{29} +2.39674i q^{31} +(4.14420 + 4.14420i) q^{32} +(-2.72332 - 2.72332i) q^{33} -1.60970 q^{34} +1.41649 q^{36} +(-6.18757 - 6.18757i) q^{37} +(0.0376844 + 0.0376844i) q^{38} -5.18757i q^{39} -8.68077i q^{41} +(-1.96584 + 0.469067i) q^{42} +(2.77107 - 2.77107i) q^{43} +5.45542i q^{44} -0.577063 q^{46} +(5.49042 - 5.49042i) q^{47} +(-0.593565 - 0.593565i) q^{48} +(-6.24586 + 3.16057i) q^{49} +2.10728 q^{51} +(-5.19592 + 5.19592i) q^{52} +(-6.13823 + 6.13823i) q^{53} +0.763878 q^{54} +(5.88231 + 3.61595i) q^{56} +(-0.0493330 - 0.0493330i) q^{57} +(1.49678 - 1.49678i) q^{58} +6.97440 q^{59} -14.3107i q^{61} +(1.29458 - 1.29458i) q^{62} +(2.57351 - 0.614060i) q^{63} -2.79807i q^{64} +2.94197i q^{66} +(-0.416491 - 0.416491i) q^{67} +(-2.11067 - 2.11067i) q^{68} +0.755439 q^{69} -8.12783 q^{71} +(-1.84539 - 1.84539i) q^{72} +(9.55210 + 9.55210i) q^{73} +6.68434i q^{74} +0.0988248i q^{76} +(2.36497 + 9.91150i) q^{77} +(-2.80203 + 2.80203i) q^{78} -9.86329i q^{79} -1.00000 q^{81} +(-4.68886 + 4.68886i) q^{82} +(1.63570 + 1.63570i) q^{83} +(-3.19270 - 1.96260i) q^{84} -2.99355 q^{86} +(-1.95945 + 1.95945i) q^{87} +(7.10728 - 7.10728i) q^{88} +5.05313 q^{89} +(-7.18757 + 11.6925i) q^{91} +(-0.756656 - 0.756656i) q^{92} +(-1.69475 + 1.69475i) q^{93} -5.93123 q^{94} +5.86078i q^{96} +(6.85851 - 6.85851i) q^{97} +(5.08082 + 1.66650i) q^{98} -3.85136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} - 24q^{8} + O(q^{10}) \) \( 16q + 8q^{7} - 24q^{8} - 16q^{11} - 48q^{16} + 8q^{21} + 16q^{22} + 40q^{23} - 24q^{28} - 48q^{32} - 16q^{36} - 32q^{37} + 16q^{42} + 16q^{43} + 64q^{46} - 16q^{51} - 24q^{53} + 24q^{56} - 8q^{57} - 32q^{58} - 8q^{63} + 32q^{67} + 64q^{71} - 24q^{72} + 24q^{77} + 8q^{78} - 16q^{81} + 64q^{86} + 64q^{88} - 48q^{91} + 40q^{92} - 24q^{93} + 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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 0.489861 0.871800i \(-0.337047\pi\)
−0.871800 + 0.489861i \(0.837047\pi\)
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.41649i 0.708245i
\(5\) 0 0
\(6\) 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
\(10\) 0 0
\(11\) −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
\(15\) 0 0
\(16\) −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 \(-0.502547\pi\)
−0.00800286 + 0.999968i \(0.502547\pi\)
\(20\) 0 0
\(21\) 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 \(-0.724904\pi\)
0.760602 + 0.649218i \(0.224904\pi\)
\(24\) −2.60978 −0.532719
\(25\) 0 0
\(26\) 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 \(0.0828288\pi\)
−0.966335 + 0.257288i \(0.917171\pi\)
\(30\) 0 0
\(31\) 2.39674i 0.430467i 0.976563 + 0.215233i \(0.0690512\pi\)
−0.976563 + 0.215233i \(0.930949\pi\)
\(32\) 4.14420 + 4.14420i 0.732598 + 0.732598i
\(33\) −2.72332 2.72332i −0.474070 0.474070i
\(34\) −1.60970 −0.276062
\(35\) 0 0
\(36\) 1.41649 0.236082
\(37\) −6.18757 6.18757i −1.01723 1.01723i −0.999849 0.0173805i \(-0.994467\pi\)
−0.0173805 0.999849i \(-0.505533\pi\)
\(38\) 0.0376844 + 0.0376844i 0.00611321 + 0.00611321i
\(39\) 5.18757i 0.830675i
\(40\) 0 0
\(41\) 8.68077i 1.35571i −0.735196 0.677854i \(-0.762910\pi\)
0.735196 0.677854i \(-0.237090\pi\)
\(42\) −1.96584 + 0.469067i −0.303336 + 0.0723786i
\(43\) 2.77107 2.77107i 0.422585 0.422585i −0.463508 0.886093i \(-0.653409\pi\)
0.886093 + 0.463508i \(0.153409\pi\)
\(44\) 5.45542i 0.822435i
\(45\) 0 0
\(46\) −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 0
\(51\) 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 \(-0.953323\pi\)
0.146116 + 0.989267i \(0.453323\pi\)
\(54\) 0.763878 0.103951
\(55\) 0 0
\(56\) 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 0
\(61\) 14.3107i 1.83230i −0.400835 0.916150i \(-0.631280\pi\)
0.400835 0.916150i \(-0.368720\pi\)
\(62\) 1.29458 1.29458i 0.164412 0.164412i
\(63\) 2.57351 0.614060i 0.324231 0.0773643i
\(64\) 2.79807i 0.349758i
\(65\) 0 0
\(66\) 2.94197i 0.362131i
\(67\) −0.416491 0.416491i −0.0508824 0.0508824i 0.681208 0.732090i \(-0.261455\pi\)
−0.732090 + 0.681208i \(0.761455\pi\)
\(68\) −2.11067 2.11067i −0.255957 0.255957i
\(69\) 0.755439 0.0909442
\(70\) 0 0
\(71\) −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 0
\(76\) 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 \(-0.812774\pi\)
0.831948 0.554854i \(-0.187226\pi\)
\(80\) 0 0
\(81\) −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
\(85\) 0 0
\(86\) −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 0
\(91\) −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 0
\(96\) 5.86078i 0.598164i
\(97\) 6.85851 6.85851i 0.696376 0.696376i −0.267251 0.963627i \(-0.586115\pi\)
0.963627 + 0.267251i \(0.0861152\pi\)
\(98\) 5.08082 + 1.66650i 0.513240 + 0.168342i
\(99\) 3.85136i 0.387076i
\(100\) 0 0
\(101\) 19.1953i 1.91000i 0.296605 + 0.955000i \(0.404145\pi\)
−0.296605 + 0.955000i \(0.595855\pi\)
\(102\) −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
\(105\) 0 0
\(106\) 6.63105 0.644064
\(107\) 6.39747 + 6.39747i 0.618467 + 0.618467i 0.945138 0.326671i \(-0.105927\pi\)
−0.326671 + 0.945138i \(0.605927\pi\)
\(108\) 1.00161 + 1.00161i 0.0963800 + 0.0963800i
\(109\) 2.16057i 0.206945i −0.994632 0.103473i \(-0.967005\pi\)
0.994632 0.103473i \(-0.0329954\pi\)
\(110\) 0 0
\(111\) 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 \(-0.661232\pi\)
0.874435 + 0.485143i \(0.161232\pi\)
\(114\) 0.0532937i 0.00499142i
\(115\) 0 0
\(116\) 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
\(120\) 0 0
\(121\) 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
\(125\) 0 0
\(126\) −1.72174 1.05838i −0.153385 0.0942881i
\(127\) 4.83298 + 4.83298i 0.428858 + 0.428858i 0.888239 0.459381i \(-0.151929\pi\)
−0.459381 + 0.888239i \(0.651929\pi\)
\(128\) 6.77704 6.77704i 0.599011 0.599011i
\(129\) 3.91889 0.345039
\(130\) 0 0
\(131\) 0.647499i 0.0565722i −0.999600 0.0282861i \(-0.990995\pi\)
0.999600 0.0282861i \(-0.00900495\pi\)
\(132\) −3.85756 + 3.85756i −0.335758 + 0.335758i
\(133\) 0.0428413 + 0.179547i 0.00371481 + 0.0155687i
\(134\) 0.449929i 0.0388680i
\(135\) 0 0
\(136\) 5.49954i 0.471581i
\(137\) −10.2369 10.2369i −0.874597 0.874597i 0.118372 0.992969i \(-0.462232\pi\)
−0.992969 + 0.118372i \(0.962232\pi\)
\(138\) −0.408045 0.408045i −0.0347351 0.0347351i
\(139\) 22.1663 1.88012 0.940060 0.341009i \(-0.110769\pi\)
0.940060 + 0.341009i \(0.110769\pi\)
\(140\) 0 0
\(141\) 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
\(145\) 0 0
\(146\) 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 \(-0.850523\pi\)
0.891752 0.452525i \(-0.149477\pi\)
\(150\) 0 0
\(151\) 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
\(155\) 0 0
\(156\) −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
\(160\) 0 0
\(161\) −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 \(-0.848628\pi\)
0.457826 + 0.889042i \(0.348628\pi\)
\(164\) −12.2962 −0.960174
\(165\) 0 0
\(166\) 1.76702i 0.137147i
\(167\) 1.88968 1.88968i 0.146228 0.146228i −0.630203 0.776431i \(-0.717028\pi\)
0.776431 + 0.630203i \(0.217028\pi\)
\(168\) 1.60256 + 6.71629i 0.123640 + 0.518173i
\(169\) 13.9108i 1.07006i
\(170\) 0 0
\(171\) 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
\(175\) 0 0
\(176\) 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 \(0.755591\pi\)
\(180\) 0 0
\(181\) 8.48528i 0.630706i −0.948974 0.315353i \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) 10.1979 2.43331i 0.755922 0.180369i
\(183\) 10.1192 10.1192i 0.748034 0.748034i
\(184\) 1.97153i 0.145343i
\(185\) 0 0
\(186\) 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 0
\(191\) −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 \(-0.671337\pi\)
0.858596 + 0.512653i \(0.171337\pi\)
\(194\) −7.40916 −0.531946
\(195\) 0 0
\(196\) 4.47692 + 8.84720i 0.319780 + 0.631943i
\(197\) −12.6739 12.6739i −0.902981 0.902981i 0.0927124 0.995693i \(-0.470446\pi\)
−0.995693 + 0.0927124i \(0.970446\pi\)
\(198\) −2.08029 + 2.08029i −0.147840 + 0.147840i
\(199\) 2.67111 0.189350 0.0946750 0.995508i \(-0.469819\pi\)
0.0946750 + 0.995508i \(0.469819\pi\)
\(200\) 0 0
\(201\) 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
\(205\) 0 0
\(206\) 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
\(210\) 0 0
\(211\) −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
\(215\) 0 0
\(216\) 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
\(220\) 0 0
\(221\) −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
\(225\) 0 0
\(226\) −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 \(-0.583331\pi\)
−0.258812 + 0.965928i \(0.583331\pi\)
\(230\) 0 0
\(231\) −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 \(-0.764868\pi\)
0.673318 + 0.739353i \(0.264868\pi\)
\(234\) −3.96267 −0.259048
\(235\) 0 0
\(236\) 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 \(-0.772282\pi\)
0.754833 0.655917i \(-0.227718\pi\)
\(240\) 0 0
\(241\) 2.76994i 0.178427i −0.996013 0.0892136i \(-0.971565\pi\)
0.996013 0.0892136i \(-0.0284354\pi\)
\(242\) −2.07036 2.07036i −0.133088 0.133088i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −20.2710 −1.29772
\(245\) 0 0
\(246\) −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
\(250\) 0 0
\(251\) 6.09982i 0.385017i 0.981295 + 0.192509i \(0.0616623\pi\)
−0.981295 + 0.192509i \(0.938338\pi\)
\(252\) −0.869810 3.64535i −0.0547929 0.229635i
\(253\) −2.05731 + 2.05731i −0.129342 + 0.129342i
\(254\) 5.22100i 0.327595i
\(255\) 0 0
\(256\) −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
\(260\) 0 0
\(261\) −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 \(0.511014\pi\)
−0.999401 + 0.0345941i \(0.988986\pi\)
\(264\) 10.0512 0.618609
\(265\) 0 0
\(266\) 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 0
\(271\) 4.13470i 0.251165i −0.992083 0.125583i \(-0.959920\pi\)
0.992083 0.125583i \(-0.0400800\pi\)
\(272\) −1.25081 + 1.25081i −0.0758413 + 0.0758413i
\(273\) −13.3502 + 3.18548i −0.807993 + 0.192794i
\(274\) 11.0588i 0.668085i
\(275\) 0 0
\(276\) 1.07007i 0.0644108i
\(277\) 12.1128 + 12.1128i 0.727786 + 0.727786i 0.970178 0.242393i \(-0.0779322\pi\)
−0.242393 + 0.970178i \(0.577932\pi\)
\(278\) −11.9730 11.9730i −0.718091 0.718091i
\(279\) −2.39674 −0.143489
\(280\) 0 0
\(281\) 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 0
\(286\) 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
\(290\) 0 0
\(291\) 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
\(295\) 0 0
\(296\) 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
\(300\) 0 0
\(301\) −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
\(305\) 0 0
\(306\) 1.60970i 0.0920206i
\(307\) −14.6198 + 14.6198i −0.834394 + 0.834394i −0.988114 0.153721i \(-0.950874\pi\)
0.153721 + 0.988114i \(0.450874\pi\)
\(308\) 14.0395 3.34995i 0.799977 0.190881i
\(309\) 3.30678i 0.188116i
\(310\) 0 0
\(311\) 2.86218i 0.162299i −0.996702 0.0811497i \(-0.974141\pi\)
0.996702 0.0811497i \(-0.0258592\pi\)
\(312\) 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
\(315\) 0 0
\(316\) −13.9713 −0.785945
\(317\) −7.38310 7.38310i −0.414676 0.414676i 0.468688 0.883364i \(-0.344727\pi\)
−0.883364 + 0.468688i \(0.844727\pi\)
\(318\) 4.68886 + 4.68886i 0.262938 + 0.262938i
\(319\) 10.6724i 0.597540i
\(320\) 0 0
\(321\) 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
\(325\) 0 0
\(326\) 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
\(330\) 0 0
\(331\) 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
\(335\) 0 0
\(336\) −1.16306 + 1.89203i −0.0634500 + 0.103219i
\(337\) 4.93809 + 4.93809i 0.268995 + 0.268995i 0.828695 0.559700i \(-0.189084\pi\)
−0.559700 + 0.828695i \(0.689084\pi\)
\(338\) 7.51384 7.51384i 0.408699 0.408699i
\(339\) 5.85234 0.317856
\(340\) 0 0
\(341\) 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 0
\(346\) 5.30151i 0.285011i
\(347\) −5.83694 5.83694i −0.313343 0.313343i 0.532860 0.846203i \(-0.321117\pi\)
−0.846203 + 0.532860i \(0.821117\pi\)
\(348\) 2.77554 + 2.77554i 0.148784 + 0.148784i
\(349\) 16.9121 0.905282 0.452641 0.891693i \(-0.350482\pi\)
0.452641 + 0.891693i \(0.350482\pi\)
\(350\) 0 0
\(351\) 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
\(355\) 0 0
\(356\) 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 \(-0.931014\pi\)
0.976606 0.215034i \(-0.0689864\pi\)
\(360\) 0 0
\(361\) −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
\(365\) 0 0
\(366\) −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
\(370\) 0 0
\(371\) 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 \(-0.767427\pi\)
0.667353 + 0.744741i \(0.267427\pi\)
\(374\) 6.19955 0.320571
\(375\) 0 0
\(376\) 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 \(-0.840410\pi\)
0.876927 0.480624i \(-0.159590\pi\)
\(380\) 0 0
\(381\) 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
\(385\) 0 0
\(386\) −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 \(-0.225455\pi\)
\(390\) 0 0
\(391\) 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
\(395\) 0 0
\(396\) −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
\(400\) 0 0
\(401\) 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
\(405\) 0 0
\(406\) −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 \(0.584082\pi\)
\(410\) 0 0
\(411\) 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
\(415\) 0 0
\(416\) 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 \(0.623996\pi\)
\(420\) 0 0
\(421\) 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
\(425\) 0 0
\(426\) 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
\(430\) 0 0
\(431\) −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
\(435\) 0 0
\(436\) −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 \(0.275975\pi\)
\(440\) 0 0
\(441\) −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 \(-0.448738\pi\)
0.987060 0.160349i \(-0.0512618\pi\)
\(444\) −12.3951 −0.588243
\(445\) 0 0
\(446\) 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 \(0.0743006\pi\)
−0.972881 + 0.231308i \(0.925699\pi\)
\(450\) 0 0
\(451\) 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
\(455\) 0 0
\(456\) 0.182078 0.00852656
\(457\) −0.550071 0.550071i −0.0257312 0.0257312i 0.694124 0.719855i \(-0.255792\pi\)
−0.719855 + 0.694124i \(0.755792\pi\)
\(458\) 4.23099 + 4.23099i 0.197701 + 0.197701i
\(459\) 2.10728i 0.0983594i
\(460\) 0 0
\(461\) 0.831786i 0.0387401i −0.999812 0.0193701i \(-0.993834\pi\)
0.999812 0.0193701i \(-0.00616607\pi\)
\(462\) 7.57117 1.80655i 0.352243 0.0840481i
\(463\) −5.45140 + 5.45140i −0.253348 + 0.253348i −0.822342 0.568994i \(-0.807333\pi\)
0.568994 + 0.822342i \(0.307333\pi\)
\(464\) 2.32612i 0.107987i
\(465\) 0 0
\(466\) 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
\(470\) 0 0
\(471\) −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 0
\(476\) −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 \(0.125157\pi\)
\(480\) 0 0
\(481\) 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
\(485\) 0 0
\(486\) 0.763878i 0.0346502i
\(487\) 7.22893 + 7.22893i 0.327574 + 0.327574i 0.851663 0.524089i \(-0.175594\pi\)
−0.524089 + 0.851663i \(0.675594\pi\)
\(488\) 26.4089 + 26.4089i 1.19548 + 1.19548i
\(489\) −7.78580 −0.352086
\(490\) 0 0
\(491\) 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
\(495\) 0 0
\(496\) 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 \(-0.887809\pi\)
0.938527 0.345207i \(-0.112191\pi\)
\(500\) 0 0
\(501\) 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
\(505\) 0 0
\(506\) 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 \(0.807598\pi\)
\(510\) 0 0
\(511\) 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
\(515\) 0 0
\(516\) 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
\(520\) 0 0
\(521\) 2.59132i 0.113528i 0.998388 + 0.0567639i \(0.0180782\pi\)
−0.998388 + 0.0567639i \(0.981922\pi\)
\(522\) 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
\(525\) 0 0
\(526\) 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
\(530\) 0 0
\(531\) 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
\(535\) 0 0
\(536\) 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
\(540\) 0 0
\(541\) −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
\(545\) 0 0
\(546\) 8.93165 + 5.49042i 0.382239 + 0.234968i
\(547\) 0.828381 + 0.828381i 0.0354190 + 0.0354190i 0.724594 0.689175i \(-0.242027\pi\)
−0.689175 + 0.724594i \(0.742027\pi\)
\(548\) −14.5005 + 14.5005i −0.619429 + 0.619429i
\(549\) 14.3107 0.610767
\(550\) 0 0
\(551\) 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
\(555\) 0 0
\(556\) 31.3983i 1.33159i
\(557\) −14.7120 14.7120i −0.623366 0.623366i 0.323024 0.946391i \(-0.395300\pi\)
−0.946391 + 0.323024i \(0.895300\pi\)
\(558\) 1.29458 + 1.29458i 0.0548040 + 0.0548040i
\(559\) −20.3295 −0.859846
\(560\) 0 0
\(561\) −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
\(565\) 0 0
\(566\) 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 \(-0.893499\pi\)
0.944547 0.328376i \(-0.106501\pi\)
\(570\) 0 0
\(571\) 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
\(575\) 0 0
\(576\) 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
\(580\) 0 0
\(581\) 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
\(585\) 0 0
\(586\) 16.4804i 0.680798i
\(587\) −15.7111 + 15.7111i −0.648468 + 0.648468i −0.952623 0.304155i \(-0.901626\pi\)
0.304155 + 0.952623i \(0.401626\pi\)
\(588\) −3.09026 + 9.42158i −0.127440 + 0.388539i
\(589\) 0.167214i 0.00688993i
\(590\) 0 0
\(591\) 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 0
\(596\) −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 \(0.582473\pi\)
\(600\) 0 0
\(601\) 11.0819i 0.452041i 0.974123 + 0.226021i \(0.0725717\pi\)
−0.974123 + 0.226021i \(0.927428\pi\)
\(602\) 1.83822 + 7.70393i 0.0749203 + 0.313989i
\(603\) 0.416491 0.416491i 0.0169608 0.0169608i
\(604\) 26.0620i 1.06045i
\(605\) 0 0
\(606\) 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
\(610\) 0 0
\(611\) −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 \(-0.726115\pi\)
0.758126 + 0.652108i \(0.226115\pi\)
\(614\) 15.7935 0.637375
\(615\) 0 0
\(616\) −22.6549 13.9263i −0.912793 0.561108i
\(617\) −11.3212 11.3212i −0.455774 0.455774i 0.441491 0.897266i \(-0.354450\pi\)
−0.897266 + 0.441491i \(0.854450\pi\)
\(618\) 1.78613 1.78613i 0.0718488 0.0718488i
\(619\) 9.06771 0.364462 0.182231 0.983256i \(-0.441668\pi\)
0.182231 + 0.983256i \(0.441668\pi\)
\(620\) 0 0
\(621\) 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
\(625\) 0 0
\(626\) 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 0
\(631\) −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
\(635\) 0 0
\(636\) 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
\(640\) 0 0
\(641\) −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
\(645\) 0 0
\(646\) 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
\(650\) 0 0
\(651\) 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 \(-0.530463\pi\)
0.995424 + 0.0955569i \(0.0304632\pi\)
\(654\) −1.65041 −0.0645363
\(655\) 0 0
\(656\) 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 \(0.220223\pi\)
−0.770067 + 0.637963i \(0.779777\pi\)
\(660\) 0 0
\(661\) 32.5174i 1.26478i −0.774650 0.632391i \(-0.782074\pi\)
0.774650 0.632391i \(-0.217926\pi\)
\(662\) −12.7582 12.7582i −0.495861 0.495861i
\(663\) −7.72984 7.72984i −0.300202 0.300202i
\(664\) −6.03701 −0.234281
\(665\) 0 0
\(666\) −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 0
\(671\) 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 \(-0.599050\pi\)
0.951974 + 0.306179i \(0.0990504\pi\)
\(674\) 5.33455i 0.205479i
\(675\) 0 0
\(676\) 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
\(680\) 0 0
\(681\) 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 \(-0.966391\pi\)
0.105389 + 0.994431i \(0.466391\pi\)
\(684\) −0.0988248 −0.00377866
\(685\) 0 0
\(686\) 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
\(690\) 0 0
\(691\) 42.4714i 1.61569i −0.589395 0.807845i \(-0.700634\pi\)
0.589395 0.807845i \(-0.299366\pi\)
\(692\) −6.95144 + 6.95144i −0.264254 + 0.264254i
\(693\) −9.91150 + 2.36497i −0.376507 + 0.0898376i
\(694\) 6.30557i 0.239356i
\(695\) 0 0
\(696\) 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
\(700\) 0 0
\(701\) 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
\(705\) 0 0
\(706\) 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 \(0.210260\pi\)
−0.789654 + 0.613552i \(0.789740\pi\)
\(710\) 0 0
\(711\) 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
\(715\) 0 0
\(716\) 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 \(0.382659\pi\)
\(720\) 0 0
\(721\) 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
\(725\) 0 0
\(726\) 2.92793i 0.108666i
\(727\) 2.71795 2.71795i 0.100803 0.100803i −0.654907 0.755710i \(-0.727292\pi\)
0.755710 + 0.654907i \(0.227292\pi\)
\(728\) −8.31339 34.8412i −0.308115 1.29130i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 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
\(735\) 0 0
\(736\) 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 \(0.970940\pi\)
\(740\) 0 0
\(741\) 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 \(-0.883120\pi\)
0.358993 + 0.933340i \(0.383120\pi\)
\(744\) 6.25496i 0.229318i
\(745\) 0 0
\(746\) 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
\(750\) 0 0
\(751\) −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
\(755\) 0 0
\(756\) 1.96260 3.19270i 0.0713791 0.116117i
\(757\) −29.4977 29.4977i −1.07211 1.07211i −0.997189 0.0749214i \(-0.976129\pi\)
−0.0749214 0.997189i \(-0.523871\pi\)
\(758\) −10.1080 + 10.1080i −0.367138 + 0.367138i
\(759\) −2.90947 −0.105607
\(760\) 0 0
\(761\) 28.1175i 1.01926i −0.860395 0.509629i \(-0.829783\pi\)
0.860395 0.509629i \(-0.170217\pi\)
\(762\) 3.69181 3.69181i 0.133740 0.133740i
\(763\) −5.56025 + 1.32672i −0.201294 + 0.0480305i
\(764\) 7.63986i 0.276400i
\(765\) 0 0
\(766\) 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 \(0.538041\pi\)
\(770\) 0 0
\(771\) −2.85449 −0.102802
\(772\) −6.80764 6.80764i −0.245012 0.245012i
\(773\) 31.7247 + 31.7247i 1.14106 + 1.14106i 0.988257 + 0.152800i \(0.0488290\pi\)
0.152800 + 0.988257i \(0.451171\pi\)
\(774\) 2.99355i 0.107601i
\(775\) 0 0
\(776\) 25.3133i 0.908695i
\(777\) −22.5196 + 5.37335i −0.807885 + 0.192768i
\(778\) −13.8607 + 13.8607i −0.496929 + 0.496929i
\(779\) 0.605634i 0.0216991i
\(780\) 0 0
\(781\) 31.3032 1.12012