Properties

Label 403.2.c.b.311.17
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.17
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.16

$q$-expansion

\(f(q)\) \(=\) \(q+0.327248i q^{2} -1.21221 q^{3} +1.89291 q^{4} +2.01769i q^{5} -0.396693i q^{6} -0.699230i q^{7} +1.27395i q^{8} -1.53055 q^{9} +O(q^{10})\) \(q+0.327248i q^{2} -1.21221 q^{3} +1.89291 q^{4} +2.01769i q^{5} -0.396693i q^{6} -0.699230i q^{7} +1.27395i q^{8} -1.53055 q^{9} -0.660284 q^{10} +4.61697i q^{11} -2.29460 q^{12} +(3.60514 - 0.0546339i) q^{13} +0.228822 q^{14} -2.44585i q^{15} +3.36892 q^{16} -4.66988 q^{17} -0.500871i q^{18} +2.12056i q^{19} +3.81929i q^{20} +0.847613i q^{21} -1.51089 q^{22} -0.894850 q^{23} -1.54429i q^{24} +0.928944 q^{25} +(0.0178789 + 1.17977i) q^{26} +5.49197 q^{27} -1.32358i q^{28} -3.00018 q^{29} +0.800402 q^{30} +1.00000i q^{31} +3.65037i q^{32} -5.59672i q^{33} -1.52821i q^{34} +1.41083 q^{35} -2.89720 q^{36} +9.14616i q^{37} -0.693950 q^{38} +(-4.37018 + 0.0662277i) q^{39} -2.57043 q^{40} +8.88294i q^{41} -0.277380 q^{42} -0.0731027 q^{43} +8.73949i q^{44} -3.08817i q^{45} -0.292838i q^{46} -10.2247i q^{47} -4.08383 q^{48} +6.51108 q^{49} +0.303995i q^{50} +5.66086 q^{51} +(6.82420 - 0.103417i) q^{52} +6.80879 q^{53} +1.79724i q^{54} -9.31559 q^{55} +0.890783 q^{56} -2.57056i q^{57} -0.981804i q^{58} -10.8578i q^{59} -4.62978i q^{60} -1.63534 q^{61} -0.327248 q^{62} +1.07021i q^{63} +5.54326 q^{64} +(0.110234 + 7.27403i) q^{65} +1.83152 q^{66} -12.8524i q^{67} -8.83965 q^{68} +1.08474 q^{69} +0.461691i q^{70} -7.88186i q^{71} -1.94984i q^{72} -12.0989i q^{73} -2.99307 q^{74} -1.12607 q^{75} +4.01403i q^{76} +3.22832 q^{77} +(-0.0216729 - 1.43013i) q^{78} -13.7040 q^{79} +6.79742i q^{80} -2.06575 q^{81} -2.90693 q^{82} -4.48027i q^{83} +1.60445i q^{84} -9.42235i q^{85} -0.0239227i q^{86} +3.63684 q^{87} -5.88177 q^{88} +5.02369i q^{89} +1.01060 q^{90} +(-0.0382017 - 2.52082i) q^{91} -1.69387 q^{92} -1.21221i q^{93} +3.34601 q^{94} -4.27863 q^{95} -4.42501i q^{96} -17.0411i q^{97} +2.13074i q^{98} -7.06651i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

Character Values

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

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.327248i 0.231399i 0.993284 + 0.115700i \(0.0369110\pi\)
−0.993284 + 0.115700i \(0.963089\pi\)
\(3\) −1.21221 −0.699869 −0.349934 0.936774i \(-0.613796\pi\)
−0.349934 + 0.936774i \(0.613796\pi\)
\(4\) 1.89291 0.946454
\(5\) 2.01769i 0.902337i 0.892439 + 0.451168i \(0.148993\pi\)
−0.892439 + 0.451168i \(0.851007\pi\)
\(6\) 0.396693i 0.161949i
\(7\) 0.699230i 0.264284i −0.991231 0.132142i \(-0.957814\pi\)
0.991231 0.132142i \(-0.0421855\pi\)
\(8\) 1.27395i 0.450408i
\(9\) −1.53055 −0.510184
\(10\) −0.660284 −0.208800
\(11\) 4.61697i 1.39207i 0.718009 + 0.696034i \(0.245054\pi\)
−0.718009 + 0.696034i \(0.754946\pi\)
\(12\) −2.29460 −0.662394
\(13\) 3.60514 0.0546339i 0.999885 0.0151527i
\(14\) 0.228822 0.0611552
\(15\) 2.44585i 0.631517i
\(16\) 3.36892 0.842230
\(17\) −4.66988 −1.13261 −0.566306 0.824195i \(-0.691628\pi\)
−0.566306 + 0.824195i \(0.691628\pi\)
\(18\) 0.500871i 0.118056i
\(19\) 2.12056i 0.486490i 0.969965 + 0.243245i \(0.0782119\pi\)
−0.969965 + 0.243245i \(0.921788\pi\)
\(20\) 3.81929i 0.854020i
\(21\) 0.847613i 0.184964i
\(22\) −1.51089 −0.322124
\(23\) −0.894850 −0.186589 −0.0932945 0.995639i \(-0.529740\pi\)
−0.0932945 + 0.995639i \(0.529740\pi\)
\(24\) 1.54429i 0.315227i
\(25\) 0.928944 0.185789
\(26\) 0.0178789 + 1.17977i 0.00350633 + 0.231373i
\(27\) 5.49197 1.05693
\(28\) 1.32358i 0.250133i
\(29\) −3.00018 −0.557120 −0.278560 0.960419i \(-0.589857\pi\)
−0.278560 + 0.960419i \(0.589857\pi\)
\(30\) 0.800402 0.146133
\(31\) 1.00000i 0.179605i
\(32\) 3.65037i 0.645300i
\(33\) 5.59672i 0.974264i
\(34\) 1.52821i 0.262086i
\(35\) 1.41083 0.238473
\(36\) −2.89720 −0.482866
\(37\) 9.14616i 1.50362i 0.659380 + 0.751810i \(0.270819\pi\)
−0.659380 + 0.751810i \(0.729181\pi\)
\(38\) −0.693950 −0.112574
\(39\) −4.37018 + 0.0662277i −0.699788 + 0.0106049i
\(40\) −2.57043 −0.406420
\(41\) 8.88294i 1.38728i 0.720321 + 0.693641i \(0.243995\pi\)
−0.720321 + 0.693641i \(0.756005\pi\)
\(42\) −0.277380 −0.0428006
\(43\) −0.0731027 −0.0111481 −0.00557403 0.999984i \(-0.501774\pi\)
−0.00557403 + 0.999984i \(0.501774\pi\)
\(44\) 8.73949i 1.31753i
\(45\) 3.08817i 0.460358i
\(46\) 0.292838i 0.0431766i
\(47\) 10.2247i 1.49142i −0.666270 0.745711i \(-0.732110\pi\)
0.666270 0.745711i \(-0.267890\pi\)
\(48\) −4.08383 −0.589450
\(49\) 6.51108 0.930154
\(50\) 0.303995i 0.0429914i
\(51\) 5.66086 0.792680
\(52\) 6.82420 0.103417i 0.946346 0.0143414i
\(53\) 6.80879 0.935259 0.467630 0.883924i \(-0.345108\pi\)
0.467630 + 0.883924i \(0.345108\pi\)
\(54\) 1.79724i 0.244573i
\(55\) −9.31559 −1.25611
\(56\) 0.890783 0.119036
\(57\) 2.57056i 0.340479i
\(58\) 0.981804i 0.128917i
\(59\) 10.8578i 1.41357i −0.707429 0.706785i \(-0.750145\pi\)
0.707429 0.706785i \(-0.249855\pi\)
\(60\) 4.62978i 0.597702i
\(61\) −1.63534 −0.209384 −0.104692 0.994505i \(-0.533386\pi\)
−0.104692 + 0.994505i \(0.533386\pi\)
\(62\) −0.327248 −0.0415606
\(63\) 1.07021i 0.134834i
\(64\) 5.54326 0.692908
\(65\) 0.110234 + 7.27403i 0.0136729 + 0.902233i
\(66\) 1.83152 0.225444
\(67\) 12.8524i 1.57016i −0.619391 0.785082i \(-0.712621\pi\)
0.619391 0.785082i \(-0.287379\pi\)
\(68\) −8.83965 −1.07197
\(69\) 1.08474 0.130588
\(70\) 0.461691i 0.0551826i
\(71\) 7.88186i 0.935405i −0.883886 0.467703i \(-0.845082\pi\)
0.883886 0.467703i \(-0.154918\pi\)
\(72\) 1.94984i 0.229791i
\(73\) 12.0989i 1.41606i −0.706180 0.708032i \(-0.749583\pi\)
0.706180 0.708032i \(-0.250417\pi\)
\(74\) −2.99307 −0.347937
\(75\) −1.12607 −0.130028
\(76\) 4.01403i 0.460441i
\(77\) 3.22832 0.367902
\(78\) −0.0216729 1.43013i −0.00245397 0.161931i
\(79\) −13.7040 −1.54182 −0.770912 0.636942i \(-0.780199\pi\)
−0.770912 + 0.636942i \(0.780199\pi\)
\(80\) 6.79742i 0.759975i
\(81\) −2.06575 −0.229528
\(82\) −2.90693 −0.321016
\(83\) 4.48027i 0.491774i −0.969298 0.245887i \(-0.920921\pi\)
0.969298 0.245887i \(-0.0790792\pi\)
\(84\) 1.60445i 0.175060i
\(85\) 9.42235i 1.02200i
\(86\) 0.0239227i 0.00257965i
\(87\) 3.63684 0.389911
\(88\) −5.88177 −0.626999
\(89\) 5.02369i 0.532510i 0.963903 + 0.266255i \(0.0857863\pi\)
−0.963903 + 0.266255i \(0.914214\pi\)
\(90\) 1.01060 0.106527
\(91\) −0.0382017 2.52082i −0.00400463 0.264254i
\(92\) −1.69387 −0.176598
\(93\) 1.21221i 0.125700i
\(94\) 3.34601 0.345114
\(95\) −4.27863 −0.438978
\(96\) 4.42501i 0.451625i
\(97\) 17.0411i 1.73026i −0.501547 0.865131i \(-0.667235\pi\)
0.501547 0.865131i \(-0.332765\pi\)
\(98\) 2.13074i 0.215237i
\(99\) 7.06651i 0.710211i
\(100\) 1.75841 0.175841
\(101\) 18.1294 1.80394 0.901970 0.431799i \(-0.142121\pi\)
0.901970 + 0.431799i \(0.142121\pi\)
\(102\) 1.85251i 0.183426i
\(103\) 2.39529 0.236015 0.118007 0.993013i \(-0.462349\pi\)
0.118007 + 0.993013i \(0.462349\pi\)
\(104\) 0.0696008 + 4.59276i 0.00682492 + 0.450357i
\(105\) −1.71022 −0.166900
\(106\) 2.22817i 0.216419i
\(107\) 15.3468 1.48363 0.741814 0.670605i \(-0.233966\pi\)
0.741814 + 0.670605i \(0.233966\pi\)
\(108\) 10.3958 1.00034
\(109\) 11.2306i 1.07569i 0.843043 + 0.537846i \(0.180762\pi\)
−0.843043 + 0.537846i \(0.819238\pi\)
\(110\) 3.04851i 0.290664i
\(111\) 11.0870i 1.05234i
\(112\) 2.35565i 0.222588i
\(113\) −3.45258 −0.324791 −0.162396 0.986726i \(-0.551922\pi\)
−0.162396 + 0.986726i \(0.551922\pi\)
\(114\) 0.841212 0.0787867
\(115\) 1.80553i 0.168366i
\(116\) −5.67907 −0.527288
\(117\) −5.51785 + 0.0836201i −0.510125 + 0.00773068i
\(118\) 3.55321 0.327099
\(119\) 3.26532i 0.299332i
\(120\) 3.11589 0.284441
\(121\) −10.3164 −0.937852
\(122\) 0.535162i 0.0484513i
\(123\) 10.7680i 0.970915i
\(124\) 1.89291i 0.169988i
\(125\) 11.9627i 1.06998i
\(126\) −0.350224 −0.0312004
\(127\) 2.00484 0.177901 0.0889503 0.996036i \(-0.471649\pi\)
0.0889503 + 0.996036i \(0.471649\pi\)
\(128\) 9.11476i 0.805639i
\(129\) 0.0886157 0.00780218
\(130\) −2.38042 + 0.0360739i −0.208776 + 0.00316389i
\(131\) −10.2051 −0.891620 −0.445810 0.895128i \(-0.647084\pi\)
−0.445810 + 0.895128i \(0.647084\pi\)
\(132\) 10.5941i 0.922097i
\(133\) 1.48276 0.128572
\(134\) 4.20591 0.363335
\(135\) 11.0811i 0.953707i
\(136\) 5.94918i 0.510138i
\(137\) 2.21909i 0.189589i 0.995497 + 0.0947947i \(0.0302195\pi\)
−0.995497 + 0.0947947i \(0.969781\pi\)
\(138\) 0.354981i 0.0302180i
\(139\) 16.0205 1.35884 0.679422 0.733747i \(-0.262230\pi\)
0.679422 + 0.733747i \(0.262230\pi\)
\(140\) 2.67057 0.225704
\(141\) 12.3944i 1.04380i
\(142\) 2.57933 0.216452
\(143\) 0.252243 + 16.6448i 0.0210936 + 1.39191i
\(144\) −5.15631 −0.429692
\(145\) 6.05342i 0.502710i
\(146\) 3.95933 0.327677
\(147\) −7.89278 −0.650985
\(148\) 17.3128i 1.42311i
\(149\) 1.88611i 0.154516i 0.997011 + 0.0772579i \(0.0246165\pi\)
−0.997011 + 0.0772579i \(0.975384\pi\)
\(150\) 0.368505i 0.0300883i
\(151\) 1.17038i 0.0952439i −0.998865 0.0476220i \(-0.984836\pi\)
0.998865 0.0476220i \(-0.0151643\pi\)
\(152\) −2.70148 −0.219119
\(153\) 7.14749 0.577841
\(154\) 1.05646i 0.0851322i
\(155\) −2.01769 −0.162064
\(156\) −8.27234 + 0.125363i −0.662318 + 0.0100371i
\(157\) −11.3089 −0.902546 −0.451273 0.892386i \(-0.649030\pi\)
−0.451273 + 0.892386i \(0.649030\pi\)
\(158\) 4.48462i 0.356777i
\(159\) −8.25367 −0.654559
\(160\) −7.36530 −0.582278
\(161\) 0.625706i 0.0493126i
\(162\) 0.676015i 0.0531127i
\(163\) 13.5178i 1.05880i 0.848373 + 0.529400i \(0.177583\pi\)
−0.848373 + 0.529400i \(0.822417\pi\)
\(164\) 16.8146i 1.31300i
\(165\) 11.2924 0.879114
\(166\) 1.46616 0.113796
\(167\) 16.8398i 1.30310i −0.758604 0.651552i \(-0.774118\pi\)
0.758604 0.651552i \(-0.225882\pi\)
\(168\) −1.07981 −0.0833095
\(169\) 12.9940 0.393926i 0.999541 0.0303020i
\(170\) 3.08345 0.236490
\(171\) 3.24563i 0.248199i
\(172\) −0.138377 −0.0105511
\(173\) 15.0900 1.14727 0.573636 0.819110i \(-0.305532\pi\)
0.573636 + 0.819110i \(0.305532\pi\)
\(174\) 1.19015i 0.0902251i
\(175\) 0.649546i 0.0491010i
\(176\) 15.5542i 1.17244i
\(177\) 13.1619i 0.989313i
\(178\) −1.64399 −0.123223
\(179\) −15.7065 −1.17396 −0.586979 0.809602i \(-0.699683\pi\)
−0.586979 + 0.809602i \(0.699683\pi\)
\(180\) 5.84563i 0.435708i
\(181\) −22.0513 −1.63906 −0.819531 0.573034i \(-0.805766\pi\)
−0.819531 + 0.573034i \(0.805766\pi\)
\(182\) 0.824935 0.0125014i 0.0611482 0.000926669i
\(183\) 1.98237 0.146541
\(184\) 1.13999i 0.0840413i
\(185\) −18.4541 −1.35677
\(186\) 0.396693 0.0290869
\(187\) 21.5607i 1.57667i
\(188\) 19.3544i 1.41156i
\(189\) 3.84015i 0.279330i
\(190\) 1.40017i 0.101579i
\(191\) −4.94588 −0.357871 −0.178936 0.983861i \(-0.557265\pi\)
−0.178936 + 0.983861i \(0.557265\pi\)
\(192\) −6.71959 −0.484944
\(193\) 19.2814i 1.38791i 0.720020 + 0.693954i \(0.244133\pi\)
−0.720020 + 0.693954i \(0.755867\pi\)
\(194\) 5.57667 0.400382
\(195\) −0.133627 8.81764i −0.00956921 0.631444i
\(196\) 12.3249 0.880348
\(197\) 4.28606i 0.305369i −0.988275 0.152685i \(-0.951208\pi\)
0.988275 0.152685i \(-0.0487919\pi\)
\(198\) 2.31250 0.164342
\(199\) 4.86238 0.344685 0.172343 0.985037i \(-0.444866\pi\)
0.172343 + 0.985037i \(0.444866\pi\)
\(200\) 1.18343i 0.0836808i
\(201\) 15.5797i 1.09891i
\(202\) 5.93280i 0.417431i
\(203\) 2.09782i 0.147238i
\(204\) 10.7155 0.750235
\(205\) −17.9230 −1.25180
\(206\) 0.783854i 0.0546137i
\(207\) 1.36961 0.0951948
\(208\) 12.1454 0.184057i 0.842133 0.0127621i
\(209\) −9.79056 −0.677227
\(210\) 0.559665i 0.0386206i
\(211\) 4.12075 0.283684 0.141842 0.989889i \(-0.454698\pi\)
0.141842 + 0.989889i \(0.454698\pi\)
\(212\) 12.8884 0.885180
\(213\) 9.55446i 0.654661i
\(214\) 5.02221i 0.343311i
\(215\) 0.147498i 0.0100593i
\(216\) 6.99648i 0.476050i
\(217\) 0.699230 0.0474669
\(218\) −3.67518 −0.248915
\(219\) 14.6663i 0.991059i
\(220\) −17.6336 −1.18885
\(221\) −16.8356 + 0.255134i −1.13248 + 0.0171622i
\(222\) 3.62822 0.243510
\(223\) 8.03216i 0.537873i −0.963158 0.268936i \(-0.913328\pi\)
0.963158 0.268936i \(-0.0866722\pi\)
\(224\) 2.55245 0.170543
\(225\) −1.42180 −0.0947864
\(226\) 1.12985i 0.0751565i
\(227\) 19.5451i 1.29725i −0.761108 0.648626i \(-0.775344\pi\)
0.761108 0.648626i \(-0.224656\pi\)
\(228\) 4.86584i 0.322248i
\(229\) 2.50838i 0.165758i 0.996560 + 0.0828791i \(0.0264115\pi\)
−0.996560 + 0.0828791i \(0.973588\pi\)
\(230\) 0.590855 0.0389598
\(231\) −3.91340 −0.257483
\(232\) 3.82207i 0.250931i
\(233\) 14.3889 0.942646 0.471323 0.881961i \(-0.343777\pi\)
0.471323 + 0.881961i \(0.343777\pi\)
\(234\) −0.0273645 1.80571i −0.00178888 0.118043i
\(235\) 20.6302 1.34576
\(236\) 20.5529i 1.33788i
\(237\) 16.6121 1.07907
\(238\) −1.06857 −0.0692652
\(239\) 6.28434i 0.406500i 0.979127 + 0.203250i \(0.0651504\pi\)
−0.979127 + 0.203250i \(0.934850\pi\)
\(240\) 8.23989i 0.531883i
\(241\) 4.56420i 0.294006i 0.989136 + 0.147003i \(0.0469626\pi\)
−0.989136 + 0.147003i \(0.953037\pi\)
\(242\) 3.37602i 0.217018i
\(243\) −13.9718 −0.896291
\(244\) −3.09555 −0.198172
\(245\) 13.1373i 0.839312i
\(246\) 3.52380 0.224669
\(247\) 0.115855 + 7.64491i 0.00737165 + 0.486434i
\(248\) −1.27395 −0.0808958
\(249\) 5.43102i 0.344177i
\(250\) −3.91479 −0.247593
\(251\) 11.3881 0.718809 0.359404 0.933182i \(-0.382980\pi\)
0.359404 + 0.933182i \(0.382980\pi\)
\(252\) 2.02581i 0.127614i
\(253\) 4.13149i 0.259745i
\(254\) 0.656080i 0.0411661i
\(255\) 11.4218i 0.715264i
\(256\) 8.10374 0.506484
\(257\) −3.40809 −0.212591 −0.106295 0.994335i \(-0.533899\pi\)
−0.106295 + 0.994335i \(0.533899\pi\)
\(258\) 0.0289993i 0.00180542i
\(259\) 6.39527 0.397383
\(260\) 0.208663 + 13.7691i 0.0129407 + 0.853922i
\(261\) 4.59193 0.284234
\(262\) 3.33959i 0.206320i
\(263\) 9.90035 0.610482 0.305241 0.952275i \(-0.401263\pi\)
0.305241 + 0.952275i \(0.401263\pi\)
\(264\) 7.12993 0.438817
\(265\) 13.7380i 0.843919i
\(266\) 0.485231i 0.0297514i
\(267\) 6.08976i 0.372687i
\(268\) 24.3283i 1.48609i
\(269\) −5.96941 −0.363961 −0.181981 0.983302i \(-0.558251\pi\)
−0.181981 + 0.983302i \(0.558251\pi\)
\(270\) −3.62626 −0.220687
\(271\) 26.2814i 1.59648i 0.602338 + 0.798241i \(0.294236\pi\)
−0.602338 + 0.798241i \(0.705764\pi\)
\(272\) −15.7324 −0.953920
\(273\) 0.0463084 + 3.05576i 0.00280271 + 0.184943i
\(274\) −0.726192 −0.0438709
\(275\) 4.28890i 0.258630i
\(276\) 2.05332 0.123595
\(277\) 14.3088 0.859735 0.429867 0.902892i \(-0.358560\pi\)
0.429867 + 0.902892i \(0.358560\pi\)
\(278\) 5.24270i 0.314436i
\(279\) 1.53055i 0.0916318i
\(280\) 1.79732i 0.107410i
\(281\) 31.8409i 1.89947i 0.313054 + 0.949735i \(0.398648\pi\)
−0.313054 + 0.949735i \(0.601352\pi\)
\(282\) −4.05605 −0.241535
\(283\) −10.4060 −0.618573 −0.309287 0.950969i \(-0.600090\pi\)
−0.309287 + 0.950969i \(0.600090\pi\)
\(284\) 14.9196i 0.885318i
\(285\) 5.18658 0.307227
\(286\) −5.44698 + 0.0825461i −0.322087 + 0.00488105i
\(287\) 6.21122 0.366637
\(288\) 5.58708i 0.329222i
\(289\) 4.80777 0.282810
\(290\) 1.98097 0.116327
\(291\) 20.6574i 1.21096i
\(292\) 22.9020i 1.34024i
\(293\) 6.03440i 0.352533i −0.984342 0.176267i \(-0.943598\pi\)
0.984342 0.176267i \(-0.0564021\pi\)
\(294\) 2.58290i 0.150638i
\(295\) 21.9077 1.27552
\(296\) −11.6517 −0.677243
\(297\) 25.3562i 1.47132i
\(298\) −0.617225 −0.0357549
\(299\) −3.22606 + 0.0488892i −0.186568 + 0.00282733i
\(300\) −2.13155 −0.123065
\(301\) 0.0511156i 0.00294626i
\(302\) 0.383004 0.0220394
\(303\) −21.9766 −1.26252
\(304\) 7.14400i 0.409737i
\(305\) 3.29960i 0.188935i
\(306\) 2.33900i 0.133712i
\(307\) 3.95437i 0.225688i 0.993613 + 0.112844i \(0.0359960\pi\)
−0.993613 + 0.112844i \(0.964004\pi\)
\(308\) 6.11092 0.348202
\(309\) −2.90359 −0.165179
\(310\) 0.660284i 0.0375016i
\(311\) 22.0723 1.25161 0.625803 0.779981i \(-0.284771\pi\)
0.625803 + 0.779981i \(0.284771\pi\)
\(312\) −0.0843706 5.56738i −0.00477655 0.315191i
\(313\) −30.6318 −1.73141 −0.865706 0.500552i \(-0.833130\pi\)
−0.865706 + 0.500552i \(0.833130\pi\)
\(314\) 3.70081i 0.208849i
\(315\) −2.15934 −0.121665
\(316\) −25.9405 −1.45927
\(317\) 7.53657i 0.423296i −0.977346 0.211648i \(-0.932117\pi\)
0.977346 0.211648i \(-0.0678830\pi\)
\(318\) 2.70100i 0.151465i
\(319\) 13.8517i 0.775548i
\(320\) 11.1846i 0.625236i
\(321\) −18.6035 −1.03835
\(322\) −0.204761 −0.0114109
\(323\) 9.90276i 0.551005i
\(324\) −3.91028 −0.217238
\(325\) 3.34897 0.0507518i 0.185767 0.00281521i
\(326\) −4.42369 −0.245006
\(327\) 13.6138i 0.752843i
\(328\) −11.3164 −0.624843
\(329\) −7.14940 −0.394159
\(330\) 3.69543i 0.203427i
\(331\) 10.6709i 0.586525i 0.956032 + 0.293263i \(0.0947410\pi\)
−0.956032 + 0.293263i \(0.905259\pi\)
\(332\) 8.48075i 0.465442i
\(333\) 13.9987i 0.767123i
\(334\) 5.51080 0.301538
\(335\) 25.9320 1.41682
\(336\) 2.85554i 0.155782i
\(337\) −7.59648 −0.413806 −0.206903 0.978361i \(-0.566339\pi\)
−0.206903 + 0.978361i \(0.566339\pi\)
\(338\) 0.128912 + 4.25227i 0.00701186 + 0.231293i
\(339\) 4.18524 0.227311
\(340\) 17.8356i 0.967274i
\(341\) −4.61697 −0.250023
\(342\) 1.06213 0.0574332
\(343\) 9.44736i 0.510109i
\(344\) 0.0931290i 0.00502118i
\(345\) 2.18867i 0.117834i
\(346\) 4.93818i 0.265478i
\(347\) −2.98264 −0.160116 −0.0800582 0.996790i \(-0.525511\pi\)
−0.0800582 + 0.996790i \(0.525511\pi\)
\(348\) 6.88421 0.369033
\(349\) 22.5564i 1.20742i −0.797204 0.603709i \(-0.793689\pi\)
0.797204 0.603709i \(-0.206311\pi\)
\(350\) 0.212563 0.0113620
\(351\) 19.7993 0.300048i 1.05681 0.0160154i
\(352\) −16.8536 −0.898301
\(353\) 3.59914i 0.191563i −0.995402 0.0957815i \(-0.969465\pi\)
0.995402 0.0957815i \(-0.0305350\pi\)
\(354\) −4.30723 −0.228926
\(355\) 15.9031 0.844050
\(356\) 9.50939i 0.503996i
\(357\) 3.95825i 0.209493i
\(358\) 5.13992i 0.271653i
\(359\) 9.02624i 0.476387i 0.971218 + 0.238193i \(0.0765552\pi\)
−0.971218 + 0.238193i \(0.923445\pi\)
\(360\) 3.93417 0.207349
\(361\) 14.5032 0.763327
\(362\) 7.21626i 0.379278i
\(363\) 12.5056 0.656373
\(364\) −0.0723124 4.77169i −0.00379020 0.250104i
\(365\) 24.4117 1.27777
\(366\) 0.648727i 0.0339095i
\(367\) −5.62283 −0.293509 −0.146755 0.989173i \(-0.546883\pi\)
−0.146755 + 0.989173i \(0.546883\pi\)
\(368\) −3.01468 −0.157151
\(369\) 13.5958i 0.707769i
\(370\) 6.03907i 0.313956i
\(371\) 4.76091i 0.247174i
\(372\) 2.29460i 0.118969i
\(373\) 18.2843 0.946723 0.473362 0.880868i \(-0.343040\pi\)
0.473362 + 0.880868i \(0.343040\pi\)
\(374\) 7.05569 0.364841
\(375\) 14.5013i 0.748846i
\(376\) 13.0257 0.671749
\(377\) −10.8161 + 0.163912i −0.557056 + 0.00844188i
\(378\) 1.25668 0.0646368
\(379\) 29.7452i 1.52791i −0.645271 0.763953i \(-0.723256\pi\)
0.645271 0.763953i \(-0.276744\pi\)
\(380\) −8.09905 −0.415472
\(381\) −2.43028 −0.124507
\(382\) 1.61853i 0.0828112i
\(383\) 0.0171338i 0.000875497i −1.00000 0.000437748i \(-0.999861\pi\)
1.00000 0.000437748i \(-0.000139340\pi\)
\(384\) 11.0490i 0.563841i
\(385\) 6.51374i 0.331971i
\(386\) −6.30981 −0.321161
\(387\) 0.111888 0.00568756
\(388\) 32.2572i 1.63761i
\(389\) −30.7615 −1.55967 −0.779836 0.625984i \(-0.784698\pi\)
−0.779836 + 0.625984i \(0.784698\pi\)
\(390\) 2.88556 0.0437291i 0.146116 0.00221431i
\(391\) 4.17884 0.211333
\(392\) 8.29477i 0.418949i
\(393\) 12.3707 0.624017
\(394\) 1.40261 0.0706623
\(395\) 27.6504i 1.39124i
\(396\) 13.3763i 0.672182i
\(397\) 3.19453i 0.160329i −0.996782 0.0801644i \(-0.974455\pi\)
0.996782 0.0801644i \(-0.0255445\pi\)
\(398\) 1.59121i 0.0797600i
\(399\) −1.79741 −0.0899833
\(400\) 3.12954 0.156477
\(401\) 25.9036i 1.29357i 0.762674 + 0.646783i \(0.223886\pi\)
−0.762674 + 0.646783i \(0.776114\pi\)
\(402\) −5.09844 −0.254287
\(403\) 0.0546339 + 3.60514i 0.00272151 + 0.179585i
\(404\) 34.3172 1.70735
\(405\) 4.16804i 0.207112i
\(406\) −0.686507 −0.0340708
\(407\) −42.2275 −2.09314
\(408\) 7.21164i 0.357030i
\(409\) 16.1309i 0.797624i −0.917033 0.398812i \(-0.869423\pi\)
0.917033 0.398812i \(-0.130577\pi\)
\(410\) 5.86526i 0.289665i
\(411\) 2.68999i 0.132688i
\(412\) 4.53406 0.223377
\(413\) −7.59213 −0.373584
\(414\) 0.448204i 0.0220280i
\(415\) 9.03979 0.443746
\(416\) 0.199434 + 13.1601i 0.00977806 + 0.645226i
\(417\) −19.4202 −0.951013
\(418\) 3.20394i 0.156710i
\(419\) 23.6032 1.15309 0.576545 0.817065i \(-0.304400\pi\)
0.576545 + 0.817065i \(0.304400\pi\)
\(420\) −3.23728 −0.157963
\(421\) 25.8384i 1.25928i −0.776885 0.629642i \(-0.783202\pi\)
0.776885 0.629642i \(-0.216798\pi\)
\(422\) 1.34851i 0.0656443i
\(423\) 15.6494i 0.760899i
\(424\) 8.67404i 0.421249i
\(425\) −4.33805 −0.210427
\(426\) −3.12668 −0.151488
\(427\) 1.14348i 0.0553368i
\(428\) 29.0500 1.40419
\(429\) −0.305771 20.1770i −0.0147628 0.974152i
\(430\) 0.0482686 0.00232772
\(431\) 7.48330i 0.360458i −0.983625 0.180229i \(-0.942316\pi\)
0.983625 0.180229i \(-0.0576839\pi\)
\(432\) 18.5020 0.890178
\(433\) 31.5403 1.51573 0.757865 0.652412i \(-0.226243\pi\)
0.757865 + 0.652412i \(0.226243\pi\)
\(434\) 0.228822i 0.0109838i
\(435\) 7.33801i 0.351831i
\(436\) 21.2584i 1.01809i
\(437\) 1.89758i 0.0907737i
\(438\) −4.79953 −0.229331
\(439\) −15.0348 −0.717571 −0.358786 0.933420i \(-0.616809\pi\)
−0.358786 + 0.933420i \(0.616809\pi\)
\(440\) 11.8676i 0.565764i
\(441\) −9.96554 −0.474550
\(442\) −0.0834921 5.50941i −0.00397132 0.262056i
\(443\) −39.0334 −1.85453 −0.927267 0.374402i \(-0.877848\pi\)
−0.927267 + 0.374402i \(0.877848\pi\)
\(444\) 20.9868i 0.995988i
\(445\) −10.1362 −0.480503
\(446\) 2.62851 0.124464
\(447\) 2.28635i 0.108141i
\(448\) 3.87602i 0.183125i
\(449\) 12.3994i 0.585162i −0.956241 0.292581i \(-0.905486\pi\)
0.956241 0.292581i \(-0.0945141\pi\)
\(450\) 0.465280i 0.0219335i
\(451\) −41.0122 −1.93119
\(452\) −6.53542 −0.307400
\(453\) 1.41874i 0.0666582i
\(454\) 6.39609 0.300183
\(455\) 5.08623 0.0770791i 0.238446 0.00361352i
\(456\) 3.27476 0.153355
\(457\) 34.8908i 1.63212i 0.577964 + 0.816062i \(0.303847\pi\)
−0.577964 + 0.816062i \(0.696153\pi\)
\(458\) −0.820862 −0.0383564
\(459\) −25.6468 −1.19709
\(460\) 3.41769i 0.159351i
\(461\) 14.2242i 0.662489i −0.943545 0.331244i \(-0.892532\pi\)
0.943545 0.331244i \(-0.107468\pi\)
\(462\) 1.28065i 0.0595814i
\(463\) 37.6491i 1.74970i 0.484394 + 0.874850i \(0.339040\pi\)
−0.484394 + 0.874850i \(0.660960\pi\)
\(464\) −10.1074 −0.469223
\(465\) 2.44585 0.113424
\(466\) 4.70873i 0.218128i
\(467\) −15.2210 −0.704342 −0.352171 0.935936i \(-0.614556\pi\)
−0.352171 + 0.935936i \(0.614556\pi\)
\(468\) −10.4448 + 0.158285i −0.482810 + 0.00731674i
\(469\) −8.98676 −0.414970
\(470\) 6.75119i 0.311409i
\(471\) 13.7087 0.631664
\(472\) 13.8323 0.636684
\(473\) 0.337513i 0.0155189i
\(474\) 5.43629i 0.249697i
\(475\) 1.96988i 0.0903844i
\(476\) 6.18096i 0.283304i
\(477\) −10.4212 −0.477154
\(478\) −2.05654 −0.0940639
\(479\) 4.97318i 0.227230i −0.993525 0.113615i \(-0.963757\pi\)
0.993525 0.113615i \(-0.0362431\pi\)
\(480\) 8.92827 0.407518
\(481\) 0.499691 + 32.9732i 0.0227839 + 1.50345i
\(482\) −1.49363 −0.0680328
\(483\) 0.758486i 0.0345123i
\(484\) −19.5279 −0.887634
\(485\) 34.3836 1.56128
\(486\) 4.57224i 0.207401i
\(487\) 12.7955i 0.579817i −0.957054 0.289909i \(-0.906375\pi\)
0.957054 0.289909i \(-0.0936249\pi\)
\(488\) 2.08334i 0.0943082i
\(489\) 16.3864i 0.741020i
\(490\) −4.29916 −0.194216
\(491\) 17.6587 0.796925 0.398462 0.917185i \(-0.369544\pi\)
0.398462 + 0.917185i \(0.369544\pi\)
\(492\) 20.3828i 0.918927i
\(493\) 14.0105 0.631001
\(494\) −2.50178 + 0.0379132i −0.112561 + 0.00170580i
\(495\) 14.2580 0.640849
\(496\) 3.36892i 0.151269i
\(497\) −5.51124 −0.247213
\(498\) −1.77729 −0.0796424
\(499\) 19.2207i 0.860435i 0.902725 + 0.430217i \(0.141563\pi\)
−0.902725 + 0.430217i \(0.858437\pi\)
\(500\) 22.6444i 1.01269i
\(501\) 20.4134i 0.912002i
\(502\) 3.72673i 0.166332i
\(503\) 8.98709 0.400714 0.200357 0.979723i \(-0.435790\pi\)
0.200357 + 0.979723i \(0.435790\pi\)
\(504\) −1.36339 −0.0607302
\(505\) 36.5794i 1.62776i
\(506\) 1.35202 0.0601048
\(507\) −15.7515 + 0.477520i −0.699547 + 0.0212074i
\(508\) 3.79498 0.168375
\(509\) 43.5846i 1.93186i −0.258813 0.965928i \(-0.583331\pi\)
0.258813 0.965928i \(-0.416669\pi\)
\(510\) −3.73778 −0.165512
\(511\) −8.45989 −0.374244
\(512\) 20.8815i 0.922839i
\(513\) 11.6461i 0.514186i
\(514\) 1.11529i 0.0491934i
\(515\) 4.83294i 0.212965i
\(516\) 0.167741 0.00738440
\(517\) 47.2070 2.07616
\(518\) 2.09284i 0.0919542i
\(519\) −18.2922 −0.802940
\(520\) −9.26674 + 0.140433i −0.406373 + 0.00615837i
\(521\) 20.4202 0.894626 0.447313 0.894378i \(-0.352381\pi\)
0.447313 + 0.894378i \(0.352381\pi\)
\(522\) 1.50270i 0.0657715i
\(523\) −13.3544 −0.583949 −0.291974 0.956426i \(-0.594312\pi\)
−0.291974 + 0.956426i \(0.594312\pi\)
\(524\) −19.3172 −0.843878
\(525\) 0.787384i 0.0343643i
\(526\) 3.23987i 0.141265i
\(527\) 4.66988i 0.203423i
\(528\) 18.8549i 0.820555i
\(529\) −22.1992 −0.965185
\(530\) −4.49574 −0.195282
\(531\) 16.6185i 0.721180i
\(532\) 2.80673 0.121687
\(533\) 0.485310 + 32.0242i 0.0210211 + 1.38712i
\(534\) 1.99286 0.0862396
\(535\) 30.9650i 1.33873i
\(536\) 16.3732 0.707216
\(537\) 19.0395 0.821617
\(538\) 1.95348i 0.0842205i
\(539\) 30.0614i 1.29484i
\(540\) 20.9755i 0.902640i
\(541\) 12.8644i 0.553086i −0.961002 0.276543i \(-0.910811\pi\)
0.961002 0.276543i \(-0.0891888\pi\)
\(542\) −8.60054 −0.369425
\(543\) 26.7308 1.14713
\(544\) 17.0468i 0.730875i
\(545\) −22.6597 −0.970637
\(546\) −0.999992 + 0.0151544i −0.0427957 + 0.000648546i
\(547\) 8.34081 0.356627 0.178314 0.983974i \(-0.442936\pi\)
0.178314 + 0.983974i \(0.442936\pi\)
\(548\) 4.20053i 0.179438i
\(549\) 2.50297 0.106824
\(550\) −1.40354 −0.0598469
\(551\) 6.36207i 0.271033i
\(552\) 1.38191i 0.0588179i
\(553\) 9.58227i 0.407480i
\(554\) 4.68254i 0.198942i
\(555\) 22.3702 0.949561
\(556\) 30.3254 1.28608
\(557\) 4.36612i 0.184999i −0.995713 0.0924993i \(-0.970514\pi\)
0.995713 0.0924993i \(-0.0294856\pi\)
\(558\) 0.500871 0.0212035
\(559\) −0.263545 + 0.00399389i −0.0111468 + 0.000168924i
\(560\) 4.75296 0.200849
\(561\) 26.1360i 1.10346i
\(562\) −10.4199 −0.439536
\(563\) −41.3744 −1.74372 −0.871862 0.489751i \(-0.837088\pi\)
−0.871862 + 0.489751i \(0.837088\pi\)
\(564\) 23.4615i 0.987908i
\(565\) 6.96622i 0.293071i
\(566\) 3.40535i 0.143138i
\(567\) 1.44444i 0.0606607i
\(568\) 10.0411 0.421314
\(569\) 12.2313 0.512761 0.256380 0.966576i \(-0.417470\pi\)
0.256380 + 0.966576i \(0.417470\pi\)
\(570\) 1.69730i 0.0710921i
\(571\) −16.7386 −0.700488 −0.350244 0.936659i \(-0.613901\pi\)
−0.350244 + 0.936659i \(0.613901\pi\)
\(572\) 0.477473 + 31.5071i 0.0199641 + 1.31738i
\(573\) 5.99543 0.250463
\(574\) 2.03261i 0.0848395i
\(575\) −0.831265 −0.0346661
\(576\) −8.48425 −0.353511
\(577\) 22.9801i 0.956675i −0.878176 0.478338i \(-0.841240\pi\)
0.878176 0.478338i \(-0.158760\pi\)
\(578\) 1.57333i 0.0654421i
\(579\) 23.3731i 0.971353i
\(580\) 11.4586i 0.475792i
\(581\) −3.13274 −0.129968
\(582\) −6.76008 −0.280214
\(583\) 31.4360i 1.30194i
\(584\) 15.4133 0.637808
\(585\) −0.168719 11.1333i −0.00697568 0.460305i
\(586\) 1.97475 0.0815760
\(587\) 19.9101i 0.821778i −0.911685 0.410889i \(-0.865218\pi\)
0.911685 0.410889i \(-0.134782\pi\)
\(588\) −14.9403 −0.616128
\(589\) −2.12056 −0.0873762
\(590\) 7.16926i 0.295154i
\(591\) 5.19560i 0.213718i
\(592\) 30.8127i 1.26639i
\(593\) 23.6656i 0.971828i 0.874007 + 0.485914i \(0.161513\pi\)
−0.874007 + 0.485914i \(0.838487\pi\)
\(594\) −8.29779 −0.340462
\(595\) −6.58839 −0.270098
\(596\) 3.57022i 0.146242i
\(597\) −5.89422 −0.241234
\(598\) −0.0159989 1.05572i −0.000654243 0.0431717i
\(599\) 30.9359 1.26401 0.632004 0.774965i \(-0.282233\pi\)
0.632004 + 0.774965i \(0.282233\pi\)
\(600\) 1.43456i 0.0585656i
\(601\) 7.06072 0.288013 0.144006 0.989577i \(-0.454001\pi\)
0.144006 + 0.989577i \(0.454001\pi\)
\(602\) −0.0167275 −0.000681762
\(603\) 19.6712i 0.801073i
\(604\) 2.21542i 0.0901440i
\(605\) 20.8152i 0.846258i
\(606\) 7.19179i 0.292147i
\(607\) −6.08348 −0.246921 −0.123460 0.992350i \(-0.539399\pi\)
−0.123460 + 0.992350i \(0.539399\pi\)
\(608\) −7.74083 −0.313932
\(609\) 2.54299i 0.103047i
\(610\) 1.07979 0.0437193
\(611\) −0.558614 36.8613i −0.0225991 1.49125i
\(612\) 13.5296 0.546900
\(613\) 8.79807i 0.355351i −0.984089 0.177675i \(-0.943142\pi\)
0.984089 0.177675i \(-0.0568577\pi\)
\(614\) −1.29406 −0.0522240
\(615\) 21.7264 0.876092
\(616\) 4.11271i 0.165706i
\(617\) 18.8381i 0.758394i −0.925316 0.379197i \(-0.876200\pi\)
0.925316 0.379197i \(-0.123800\pi\)
\(618\) 0.950195i 0.0382224i
\(619\) 35.9128i 1.44346i −0.692177 0.721728i \(-0.743348\pi\)
0.692177 0.721728i \(-0.256652\pi\)
\(620\) −3.81929 −0.153387
\(621\) −4.91449 −0.197212
\(622\) 7.22313i 0.289621i
\(623\) 3.51272 0.140734
\(624\) −14.7228 + 0.223116i −0.589383 + 0.00893178i
\(625\) −19.4923 −0.779694
\(626\) 10.0242i 0.400648i
\(627\) 11.8682 0.473970
\(628\) −21.4067 −0.854219
\(629\) 42.7115i 1.70302i
\(630\) 0.706642i 0.0281533i
\(631\) 32.0555i 1.27611i −0.769990 0.638056i \(-0.779739\pi\)
0.769990 0.638056i \(-0.220261\pi\)
\(632\) 17.4582i 0.694450i
\(633\) −4.99520 −0.198542
\(634\) 2.46633 0.0979505
\(635\) 4.04513i 0.160526i
\(636\) −15.6234 −0.619510
\(637\) 23.4733 0.355726i 0.930047 0.0140944i
\(638\) 4.53296 0.179461
\(639\) 12.0636i 0.477229i
\(640\) −18.3907 −0.726957
\(641\) 41.4629 1.63769 0.818843 0.574018i \(-0.194616\pi\)
0.818843 + 0.574018i \(0.194616\pi\)
\(642\) 6.08796i 0.240272i
\(643\) 39.4717i 1.55661i 0.627884 + 0.778307i \(0.283921\pi\)
−0.627884 + 0.778307i \(0.716079\pi\)
\(644\) 1.18440i 0.0466721i
\(645\) 0.178799i 0.00704019i
\(646\) 3.24066 0.127502
\(647\) −23.3211 −0.916847 −0.458423 0.888734i \(-0.651586\pi\)
−0.458423 + 0.888734i \(0.651586\pi\)
\(648\) 2.63166i 0.103381i
\(649\) 50.1302 1.96778
\(650\) 0.0166085 + 1.09594i 0.000651437 + 0.0429865i
\(651\) −0.847613 −0.0332206
\(652\) 25.5880i 1.00210i
\(653\) −24.5064 −0.959011 −0.479506 0.877539i \(-0.659184\pi\)
−0.479506 + 0.877539i \(0.659184\pi\)
\(654\) 4.45508 0.174208
\(655\) 20.5906i 0.804542i
\(656\) 29.9259i 1.16841i
\(657\) 18.5179i 0.722454i
\(658\) 2.33963i 0.0912082i
\(659\) 11.9514 0.465560 0.232780 0.972529i \(-0.425218\pi\)
0.232780 + 0.972529i \(0.425218\pi\)
\(660\) 21.3755 0.832041
\(661\) 38.7978i 1.50906i 0.656266 + 0.754529i \(0.272135\pi\)
−0.656266 + 0.754529i \(0.727865\pi\)
\(662\) −3.49203 −0.135722
\(663\) 20.4082 0.309275i 0.792589 0.0120113i
\(664\) 5.70764 0.221499
\(665\) 2.99175i 0.116015i
\(666\) 4.58104 0.177512
\(667\) 2.68471 0.103952
\(668\) 31.8762i 1.23333i
\(669\) 9.73664i 0.376440i
\(670\) 8.48621i 0.327851i
\(671\) 7.55030i 0.291476i
\(672\) −3.09410 −0.119357
\(673\) −40.0398 −1.54342 −0.771711 0.635974i \(-0.780599\pi\)
−0.771711 + 0.635974i \(0.780599\pi\)
\(674\) 2.48593i 0.0957546i
\(675\) 5.10173 0.196366
\(676\) 24.5965 0.745665i 0.946020 0.0286794i
\(677\) 7.21788 0.277406 0.138703 0.990334i \(-0.455707\pi\)
0.138703 + 0.990334i \(0.455707\pi\)
\(678\) 1.36961i 0.0525997i
\(679\) −11.9157 −0.457281
\(680\) 12.0036 0.460316
\(681\) 23.6927i 0.907905i
\(682\) 1.51089i 0.0578551i
\(683\) 14.1103i 0.539916i −0.962872 0.269958i \(-0.912990\pi\)
0.962872 0.269958i \(-0.0870099\pi\)
\(684\) 6.14368i 0.234909i
\(685\) −4.47742 −0.171073
\(686\) 3.09163 0.118039
\(687\) 3.04068i 0.116009i
\(688\) −0.246277 −0.00938923
\(689\) 24.5466 0.371991i 0.935152 0.0141717i
\(690\) −0.716239 −0.0272668
\(691\) 37.5902i 1.43000i 0.699126 + 0.714998i \(0.253573\pi\)
−0.699126 + 0.714998i \(0.746427\pi\)
\(692\) 28.5640 1.08584
\(693\) −4.94112 −0.187697
\(694\) 0.976063i 0.0370508i
\(695\) 32.3244i 1.22614i
\(696\) 4.63315i 0.175619i
\(697\) 41.4822i 1.57125i
\(698\) 7.38156 0.279396
\(699\) −17.4423 −0.659729
\(700\) 1.22953i 0.0464719i
\(701\) −46.6987 −1.76378 −0.881892 0.471451i \(-0.843730\pi\)
−0.881892 + 0.471451i \(0.843730\pi\)
\(702\) 0.0981902 + 6.47929i 0.00370595 + 0.244545i
\(703\) −19.3950 −0.731496
\(704\) 25.5931i 0.964575i
\(705\) −25.0081 −0.941858
\(706\) 1.17781 0.0443276
\(707\) 12.6766i 0.476753i
\(708\) 24.9144i 0.936339i
\(709\) 1.41589i 0.0531749i 0.999646 + 0.0265874i \(0.00846404\pi\)
−0.999646 + 0.0265874i \(0.991536\pi\)
\(710\) 5.20427i 0.195313i
\(711\) 20.9747 0.786614
\(712\) −6.39992 −0.239847
\(713\) 0.894850i 0.0335124i
\(714\) 1.29533 0.0484765
\(715\) −33.5840 + 0.508947i −1.25597 + 0.0190335i
\(716\) −29.7310 −1.11110
\(717\) 7.61793i 0.284497i
\(718\) −2.95382 −0.110236
\(719\) −23.6465 −0.881864 −0.440932 0.897541i \(-0.645352\pi\)
−0.440932 + 0.897541i \(0.645352\pi\)
\(720\) 10.4038i 0.387727i
\(721\) 1.67486i 0.0623750i
\(722\) 4.74615i 0.176634i
\(723\) 5.53275i 0.205765i
\(724\) −41.7412 −1.55130
\(725\) −2.78700 −0.103507
\(726\) 4.09243i 0.151884i
\(727\) −9.85004 −0.365318 −0.182659 0.983176i \(-0.558470\pi\)
−0.182659 + 0.983176i \(0.558470\pi\)
\(728\) 3.21139 0.0486670i 0.119022 0.00180372i
\(729\) 23.1340 0.856814
\(730\) 7.98869i 0.295675i
\(731\) 0.341381 0.0126264
\(732\) 3.75245 0.138694
\(733\) 39.7533i 1.46832i 0.678977 + 0.734160i \(0.262424\pi\)
−0.678977 + 0.734160i \(0.737576\pi\)
\(734\) 1.84006i 0.0679179i
\(735\) 15.9251i 0.587408i
\(736\) 3.26653i 0.120406i
\(737\) 59.3389 2.18578
\(738\) 4.44920 0.163777
\(739\) 20.1976i 0.742979i −0.928437 0.371490i \(-0.878847\pi\)
0.928437 0.371490i \(-0.121153\pi\)
\(740\) −34.9319 −1.28412
\(741\) −0.140440 9.26723i −0.00515919 0.340440i
\(742\) 1.55800 0.0571960
\(743\) 11.4479i 0.419984i 0.977703 + 0.209992i \(0.0673438\pi\)
−0.977703 + 0.209992i \(0.932656\pi\)
\(744\) 1.54429 0.0566164
\(745\) −3.80557 −0.139425
\(746\) 5.98349i 0.219071i
\(747\) 6.85729i 0.250895i
\(748\) 40.8124i 1.49225i
\(749\) 10.7309i 0.392100i
\(750\) 4.74554 0.173283
\(751\) −47.6401 −1.73841 −0.869206 0.494451i \(-0.835369\pi\)
−0.869206 + 0.494451i \(0.835369\pi\)
\(752\) 34.4461i 1.25612i
\(753\) −13.8047 −0.503072
\(754\) −0.0536398 3.53954i −0.00195345 0.128902i
\(755\) 2.36145 0.0859421
\(756\) 7.26906i 0.264373i
\(757\) 7.16086 0.260266 0.130133 0.991497i \(-0.458460\pi\)
0.130133 + 0.991497i \(0.458460\pi\)
\(758\) 9.73406 0.353557
\(759\) 5.00822i 0.181787i
\(760\) 5.45075i 0.197719i
\(761\) 20.6576i 0.748839i 0.927259 + 0.374420i \(0.122158\pi\)
−0.927259 + 0.374420i \(0.877842\pi\)
\(762\) 0.795305i 0.0288109i
\(763\) 7.85275 0.284289
\(764\) −9.36209 −0.338709
\(765\) 14.4214i 0.521407i
\(766\) 0.00560701 0.000202589
\(767\) −0.593206 39.1440i −0.0214194 1.41341i
\(768\) −9.82341 −0.354472
\(769\) 7.53702i 0.271792i 0.990723 + 0.135896i \(0.0433913\pi\)
−0.990723 + 0.135896i \(0.956609\pi\)
\(770\) −2.13161 −0.0768179
\(771\) 4.13131 0.148786
\(772\) 36.4980i 1.31359i
\(773\) 43.9283i 1.57999i −0.613113 0.789995i \(-0.710083\pi\)
0.613113 0.789995i \(-0.289917\pi\)
\(774\) 0.0366150i 0.00131610i
\(775\) 0.928944i 0.0333686i
\(776\) 21.7095 0.779324
\(777\) −7.75240 −0.278116
\(778\) 10.0667i 0.360907i
\(779\) −18.8368 −0.674899
\(780\) −0.252943 16.6910i −0.00905682 0.597633i
\(781\) 36.3903 1.30215
\(782\) 1.36752i 0.0489023i