Properties

Label 756.2.ba.a.71.10
Level $756$
Weight $2$
Character 756.71
Analytic conductor $6.037$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ba (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.10
Character \(\chi\) \(=\) 756.71
Dual form 756.2.ba.a.575.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.908765 - 1.08358i) q^{2} +(-0.348292 + 1.96944i) q^{4} +(-2.24261 - 1.29477i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.45056 - 1.41236i) q^{8} +O(q^{10})\) \(q+(-0.908765 - 1.08358i) q^{2} +(-0.348292 + 1.96944i) q^{4} +(-2.24261 - 1.29477i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(2.45056 - 1.41236i) q^{8} +(0.635018 + 3.60669i) q^{10} +(0.124825 + 0.216204i) q^{11} +(-0.0646102 + 0.111908i) q^{13} +(1.32880 + 0.484025i) q^{14} +(-3.75739 - 1.37188i) q^{16} -0.554691i q^{17} +3.58986i q^{19} +(3.33106 - 3.96573i) q^{20} +(0.120837 - 0.331737i) q^{22} +(-3.94814 + 6.83839i) q^{23} +(0.852871 + 1.47722i) q^{25} +(0.179977 - 0.0316879i) q^{26} +(-0.683091 - 1.87973i) q^{28} +(5.90477 - 3.40912i) q^{29} +(6.96683 + 4.02230i) q^{31} +(1.92804 + 5.31814i) q^{32} +(-0.601052 + 0.504084i) q^{34} +2.58954 q^{35} +9.96519 q^{37} +(3.88991 - 3.26234i) q^{38} +(-7.32434 - 0.00555133i) q^{40} +(-4.25964 - 2.45930i) q^{41} +(3.78791 - 2.18695i) q^{43} +(-0.469276 + 0.170534i) q^{44} +(10.9979 - 1.93636i) q^{46} +(2.41916 + 4.19011i) q^{47} +(0.500000 - 0.866025i) q^{49} +(0.825622 - 2.26660i) q^{50} +(-0.197893 - 0.166223i) q^{52} +9.00057i q^{53} -0.646482i q^{55} +(-1.41607 + 2.44842i) q^{56} +(-9.06010 - 3.30020i) q^{58} +(-3.71629 + 6.43680i) q^{59} +(6.42524 + 11.1288i) q^{61} +(-1.97273 - 11.2045i) q^{62} +(4.01050 - 6.92213i) q^{64} +(0.289791 - 0.167311i) q^{65} +(5.23554 + 3.02274i) q^{67} +(1.09243 + 0.193194i) q^{68} +(-2.35329 - 2.80598i) q^{70} +15.7820 q^{71} -14.1020 q^{73} +(-9.05602 - 10.7981i) q^{74} +(-7.07002 - 1.25032i) q^{76} +(-0.216204 - 0.124825i) q^{77} +(2.04035 - 1.17800i) q^{79} +(6.65009 + 7.94155i) q^{80} +(1.20616 + 6.85059i) q^{82} +(2.36518 + 4.09661i) q^{83} +(-0.718199 + 1.24396i) q^{85} +(-5.81205 - 2.11708i) q^{86} +(0.611249 + 0.353523i) q^{88} -7.82233i q^{89} -0.129220i q^{91} +(-12.0927 - 10.1574i) q^{92} +(2.34187 - 6.42918i) q^{94} +(4.64806 - 8.05067i) q^{95} +(-5.67078 - 9.82208i) q^{97} +(-1.39279 + 0.245224i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + O(q^{10}) \) \( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.908765 1.08358i −0.642594 0.766207i
\(3\) 0 0
\(4\) −0.348292 + 1.96944i −0.174146 + 0.984720i
\(5\) −2.24261 1.29477i −1.00293 0.579040i −0.0938136 0.995590i \(-0.529906\pi\)
−0.909113 + 0.416550i \(0.863239\pi\)
\(6\) 0 0
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 2.45056 1.41236i 0.866404 0.499343i
\(9\) 0 0
\(10\) 0.635018 + 3.60669i 0.200810 + 1.14054i
\(11\) 0.124825 + 0.216204i 0.0376363 + 0.0651879i 0.884230 0.467052i \(-0.154684\pi\)
−0.846594 + 0.532240i \(0.821351\pi\)
\(12\) 0 0
\(13\) −0.0646102 + 0.111908i −0.0179197 + 0.0310377i −0.874846 0.484401i \(-0.839038\pi\)
0.856927 + 0.515439i \(0.172371\pi\)
\(14\) 1.32880 + 0.484025i 0.355138 + 0.129361i
\(15\) 0 0
\(16\) −3.75739 1.37188i −0.939347 0.342970i
\(17\) 0.554691i 0.134532i −0.997735 0.0672662i \(-0.978572\pi\)
0.997735 0.0672662i \(-0.0214277\pi\)
\(18\) 0 0
\(19\) 3.58986i 0.823571i 0.911281 + 0.411786i \(0.135095\pi\)
−0.911281 + 0.411786i \(0.864905\pi\)
\(20\) 3.33106 3.96573i 0.744847 0.886764i
\(21\) 0 0
\(22\) 0.120837 0.331737i 0.0257626 0.0707265i
\(23\) −3.94814 + 6.83839i −0.823245 + 1.42590i 0.0800083 + 0.996794i \(0.474505\pi\)
−0.903253 + 0.429108i \(0.858828\pi\)
\(24\) 0 0
\(25\) 0.852871 + 1.47722i 0.170574 + 0.295443i
\(26\) 0.179977 0.0316879i 0.0352964 0.00621451i
\(27\) 0 0
\(28\) −0.683091 1.87973i −0.129092 0.355236i
\(29\) 5.90477 3.40912i 1.09649 0.633058i 0.161192 0.986923i \(-0.448466\pi\)
0.935296 + 0.353865i \(0.115133\pi\)
\(30\) 0 0
\(31\) 6.96683 + 4.02230i 1.25128 + 0.722427i 0.971364 0.237597i \(-0.0763598\pi\)
0.279917 + 0.960024i \(0.409693\pi\)
\(32\) 1.92804 + 5.31814i 0.340833 + 0.940124i
\(33\) 0 0
\(34\) −0.601052 + 0.504084i −0.103080 + 0.0864497i
\(35\) 2.58954 0.437713
\(36\) 0 0
\(37\) 9.96519 1.63827 0.819134 0.573603i \(-0.194455\pi\)
0.819134 + 0.573603i \(0.194455\pi\)
\(38\) 3.88991 3.26234i 0.631026 0.529222i
\(39\) 0 0
\(40\) −7.32434 0.00555133i −1.15808 0.000877742i
\(41\) −4.25964 2.45930i −0.665244 0.384079i 0.129028 0.991641i \(-0.458814\pi\)
−0.794272 + 0.607562i \(0.792148\pi\)
\(42\) 0 0
\(43\) 3.78791 2.18695i 0.577651 0.333507i −0.182549 0.983197i \(-0.558435\pi\)
0.760199 + 0.649690i \(0.225101\pi\)
\(44\) −0.469276 + 0.170534i −0.0707460 + 0.0257090i
\(45\) 0 0
\(46\) 10.9979 1.93636i 1.62155 0.285500i
\(47\) 2.41916 + 4.19011i 0.352871 + 0.611190i 0.986751 0.162241i \(-0.0518721\pi\)
−0.633880 + 0.773431i \(0.718539\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 0.825622 2.26660i 0.116761 0.320545i
\(51\) 0 0
\(52\) −0.197893 0.166223i −0.0274429 0.0230509i
\(53\) 9.00057i 1.23632i 0.786051 + 0.618162i \(0.212122\pi\)
−0.786051 + 0.618162i \(0.787878\pi\)
\(54\) 0 0
\(55\) 0.646482i 0.0871715i
\(56\) −1.41607 + 2.44842i −0.189230 + 0.327184i
\(57\) 0 0
\(58\) −9.06010 3.30020i −1.18965 0.433338i
\(59\) −3.71629 + 6.43680i −0.483820 + 0.838001i −0.999827 0.0185836i \(-0.994084\pi\)
0.516007 + 0.856584i \(0.327418\pi\)
\(60\) 0 0
\(61\) 6.42524 + 11.1288i 0.822667 + 1.42490i 0.903689 + 0.428189i \(0.140848\pi\)
−0.0810220 + 0.996712i \(0.525818\pi\)
\(62\) −1.97273 11.2045i −0.250537 1.42297i
\(63\) 0 0
\(64\) 4.01050 6.92213i 0.501312 0.865266i
\(65\) 0.289791 0.167311i 0.0359442 0.0207524i
\(66\) 0 0
\(67\) 5.23554 + 3.02274i 0.639623 + 0.369287i 0.784469 0.620167i \(-0.212935\pi\)
−0.144846 + 0.989454i \(0.546269\pi\)
\(68\) 1.09243 + 0.193194i 0.132477 + 0.0234282i
\(69\) 0 0
\(70\) −2.35329 2.80598i −0.281272 0.335379i
\(71\) 15.7820 1.87298 0.936489 0.350697i \(-0.114055\pi\)
0.936489 + 0.350697i \(0.114055\pi\)
\(72\) 0 0
\(73\) −14.1020 −1.65051 −0.825256 0.564759i \(-0.808969\pi\)
−0.825256 + 0.564759i \(0.808969\pi\)
\(74\) −9.05602 10.7981i −1.05274 1.25525i
\(75\) 0 0
\(76\) −7.07002 1.25032i −0.810987 0.143421i
\(77\) −0.216204 0.124825i −0.0246387 0.0142252i
\(78\) 0 0
\(79\) 2.04035 1.17800i 0.229558 0.132535i −0.380810 0.924653i \(-0.624355\pi\)
0.610368 + 0.792118i \(0.291022\pi\)
\(80\) 6.65009 + 7.94155i 0.743502 + 0.887892i
\(81\) 0 0
\(82\) 1.20616 + 6.85059i 0.133198 + 0.756521i
\(83\) 2.36518 + 4.09661i 0.259612 + 0.449662i 0.966138 0.258026i \(-0.0830719\pi\)
−0.706526 + 0.707687i \(0.749739\pi\)
\(84\) 0 0
\(85\) −0.718199 + 1.24396i −0.0778996 + 0.134926i
\(86\) −5.81205 2.11708i −0.626730 0.228290i
\(87\) 0 0
\(88\) 0.611249 + 0.353523i 0.0651594 + 0.0376856i
\(89\) 7.82233i 0.829165i −0.910012 0.414582i \(-0.863928\pi\)
0.910012 0.414582i \(-0.136072\pi\)
\(90\) 0 0
\(91\) 0.129220i 0.0135460i
\(92\) −12.0927 10.1574i −1.26075 1.05898i
\(93\) 0 0
\(94\) 2.34187 6.42918i 0.241545 0.663119i
\(95\) 4.64806 8.05067i 0.476881 0.825981i
\(96\) 0 0
\(97\) −5.67078 9.82208i −0.575780 0.997281i −0.995956 0.0898382i \(-0.971365\pi\)
0.420176 0.907443i \(-0.361968\pi\)
\(98\) −1.39279 + 0.245224i −0.140693 + 0.0247713i
\(99\) 0 0
\(100\) −3.20634 + 1.16518i −0.320634 + 0.116518i
\(101\) 3.16980 1.83009i 0.315407 0.182100i −0.333936 0.942596i \(-0.608377\pi\)
0.649344 + 0.760495i \(0.275044\pi\)
\(102\) 0 0
\(103\) −5.95960 3.44077i −0.587216 0.339030i 0.176780 0.984250i \(-0.443432\pi\)
−0.763996 + 0.645221i \(0.776765\pi\)
\(104\) −0.000277016 0.365490i −2.71637e−5 0.0358393i
\(105\) 0 0
\(106\) 9.75284 8.17941i 0.947280 0.794454i
\(107\) −7.43669 −0.718932 −0.359466 0.933158i \(-0.617041\pi\)
−0.359466 + 0.933158i \(0.617041\pi\)
\(108\) 0 0
\(109\) −8.23684 −0.788947 −0.394473 0.918907i \(-0.629073\pi\)
−0.394473 + 0.918907i \(0.629073\pi\)
\(110\) −0.700514 + 0.587500i −0.0667914 + 0.0560159i
\(111\) 0 0
\(112\) 3.93993 0.690611i 0.372288 0.0652567i
\(113\) 7.42933 + 4.28933i 0.698893 + 0.403506i 0.806935 0.590640i \(-0.201125\pi\)
−0.108042 + 0.994146i \(0.534458\pi\)
\(114\) 0 0
\(115\) 17.7083 10.2239i 1.65131 0.953383i
\(116\) 4.65748 + 12.8165i 0.432436 + 1.18998i
\(117\) 0 0
\(118\) 10.3520 1.82265i 0.952981 0.167788i
\(119\) 0.277346 + 0.480377i 0.0254242 + 0.0440361i
\(120\) 0 0
\(121\) 5.46884 9.47230i 0.497167 0.861119i
\(122\) 6.21995 17.0758i 0.563128 1.54597i
\(123\) 0 0
\(124\) −10.3482 + 12.3198i −0.929294 + 1.10635i
\(125\) 8.53063i 0.763003i
\(126\) 0 0
\(127\) 4.71023i 0.417965i 0.977919 + 0.208982i \(0.0670152\pi\)
−0.977919 + 0.208982i \(0.932985\pi\)
\(128\) −11.1453 + 1.94490i −0.985113 + 0.171906i
\(129\) 0 0
\(130\) −0.444647 0.161966i −0.0389981 0.0142053i
\(131\) −4.97136 + 8.61065i −0.434350 + 0.752316i −0.997242 0.0742144i \(-0.976355\pi\)
0.562893 + 0.826530i \(0.309688\pi\)
\(132\) 0 0
\(133\) −1.79493 3.10891i −0.155640 0.269577i
\(134\) −1.48250 8.42009i −0.128068 0.727385i
\(135\) 0 0
\(136\) −0.783422 1.35930i −0.0671779 0.116559i
\(137\) −13.1903 + 7.61545i −1.12693 + 0.650632i −0.943160 0.332338i \(-0.892162\pi\)
−0.183767 + 0.982970i \(0.558829\pi\)
\(138\) 0 0
\(139\) −1.53695 0.887356i −0.130362 0.0752645i 0.433401 0.901201i \(-0.357313\pi\)
−0.563763 + 0.825937i \(0.690647\pi\)
\(140\) −0.901917 + 5.09995i −0.0762259 + 0.431025i
\(141\) 0 0
\(142\) −14.3421 17.1011i −1.20356 1.43509i
\(143\) −0.0322600 −0.00269771
\(144\) 0 0
\(145\) −17.6561 −1.46626
\(146\) 12.8154 + 15.2806i 1.06061 + 1.26463i
\(147\) 0 0
\(148\) −3.47079 + 19.6258i −0.285297 + 1.61323i
\(149\) 14.3488 + 8.28427i 1.17550 + 0.678674i 0.954969 0.296706i \(-0.0958882\pi\)
0.220529 + 0.975380i \(0.429222\pi\)
\(150\) 0 0
\(151\) −15.2363 + 8.79668i −1.23991 + 0.715864i −0.969076 0.246761i \(-0.920634\pi\)
−0.270836 + 0.962625i \(0.587300\pi\)
\(152\) 5.07017 + 8.79718i 0.411245 + 0.713546i
\(153\) 0 0
\(154\) 0.0612203 + 0.347711i 0.00493327 + 0.0280194i
\(155\) −10.4159 18.0409i −0.836628 1.44908i
\(156\) 0 0
\(157\) 1.12675 1.95160i 0.0899248 0.155754i −0.817554 0.575851i \(-0.804671\pi\)
0.907479 + 0.420097i \(0.138004\pi\)
\(158\) −3.13066 1.14036i −0.249062 0.0907223i
\(159\) 0 0
\(160\) 2.56194 14.4229i 0.202539 1.14023i
\(161\) 7.89629i 0.622315i
\(162\) 0 0
\(163\) 6.99511i 0.547899i 0.961744 + 0.273950i \(0.0883302\pi\)
−0.961744 + 0.273950i \(0.911670\pi\)
\(164\) 6.32705 7.53255i 0.494060 0.588193i
\(165\) 0 0
\(166\) 2.28961 6.28572i 0.177709 0.487867i
\(167\) −5.40220 + 9.35689i −0.418035 + 0.724058i −0.995742 0.0921866i \(-0.970614\pi\)
0.577707 + 0.816244i \(0.303948\pi\)
\(168\) 0 0
\(169\) 6.49165 + 11.2439i 0.499358 + 0.864913i
\(170\) 2.00060 0.352239i 0.153439 0.0270155i
\(171\) 0 0
\(172\) 2.98777 + 8.22175i 0.227815 + 0.626903i
\(173\) −4.01988 + 2.32088i −0.305626 + 0.176453i −0.644968 0.764210i \(-0.723129\pi\)
0.339341 + 0.940663i \(0.389796\pi\)
\(174\) 0 0
\(175\) −1.47722 0.852871i −0.111667 0.0644710i
\(176\) −0.172412 0.983606i −0.0129960 0.0741421i
\(177\) 0 0
\(178\) −8.47612 + 7.10866i −0.635312 + 0.532816i
\(179\) −6.66668 −0.498291 −0.249145 0.968466i \(-0.580150\pi\)
−0.249145 + 0.968466i \(0.580150\pi\)
\(180\) 0 0
\(181\) −7.61248 −0.565831 −0.282916 0.959145i \(-0.591302\pi\)
−0.282916 + 0.959145i \(0.591302\pi\)
\(182\) −0.140021 + 0.117431i −0.0103790 + 0.00870457i
\(183\) 0 0
\(184\) −0.0169276 + 22.3341i −0.00124792 + 1.64649i
\(185\) −22.3481 12.9027i −1.64306 0.948622i
\(186\) 0 0
\(187\) 0.119926 0.0692395i 0.00876988 0.00506329i
\(188\) −9.09474 + 3.30501i −0.663302 + 0.241043i
\(189\) 0 0
\(190\) −12.9475 + 2.27963i −0.939313 + 0.165382i
\(191\) 2.15506 + 3.73268i 0.155935 + 0.270087i 0.933399 0.358840i \(-0.116828\pi\)
−0.777464 + 0.628927i \(0.783494\pi\)
\(192\) 0 0
\(193\) −0.690908 + 1.19669i −0.0497327 + 0.0861395i −0.889820 0.456312i \(-0.849170\pi\)
0.840087 + 0.542451i \(0.182504\pi\)
\(194\) −5.48960 + 15.0707i −0.394130 + 1.08201i
\(195\) 0 0
\(196\) 1.53144 + 1.28635i 0.109389 + 0.0918821i
\(197\) 9.26481i 0.660091i −0.943965 0.330045i \(-0.892936\pi\)
0.943965 0.330045i \(-0.107064\pi\)
\(198\) 0 0
\(199\) 24.5989i 1.74377i −0.489712 0.871884i \(-0.662898\pi\)
0.489712 0.871884i \(-0.337102\pi\)
\(200\) 4.17637 + 2.41545i 0.295314 + 0.170798i
\(201\) 0 0
\(202\) −4.86365 1.77162i −0.342205 0.124650i
\(203\) −3.40912 + 5.90477i −0.239273 + 0.414434i
\(204\) 0 0
\(205\) 6.36848 + 11.0305i 0.444794 + 0.770406i
\(206\) 1.68752 + 9.58456i 0.117575 + 0.667788i
\(207\) 0 0
\(208\) 0.396290 0.331845i 0.0274778 0.0230093i
\(209\) −0.776142 + 0.448106i −0.0536869 + 0.0309961i
\(210\) 0 0
\(211\) 8.98731 + 5.18882i 0.618712 + 0.357213i 0.776367 0.630281i \(-0.217060\pi\)
−0.157655 + 0.987494i \(0.550394\pi\)
\(212\) −17.7261 3.13482i −1.21743 0.215301i
\(213\) 0 0
\(214\) 6.75820 + 8.05824i 0.461981 + 0.550850i
\(215\) −11.3264 −0.772455
\(216\) 0 0
\(217\) −8.04461 −0.546104
\(218\) 7.48536 + 8.92528i 0.506972 + 0.604496i
\(219\) 0 0
\(220\) 1.27321 + 0.225164i 0.0858396 + 0.0151806i
\(221\) 0.0620745 + 0.0358387i 0.00417558 + 0.00241077i
\(222\) 0 0
\(223\) −22.3502 + 12.9039i −1.49668 + 0.864109i −0.999993 0.00382012i \(-0.998784\pi\)
−0.496688 + 0.867929i \(0.665451\pi\)
\(224\) −4.32881 3.64163i −0.289230 0.243316i
\(225\) 0 0
\(226\) −2.10369 11.9483i −0.139935 0.794787i
\(227\) −6.74196 11.6774i −0.447480 0.775057i 0.550742 0.834676i \(-0.314345\pi\)
−0.998221 + 0.0596183i \(0.981012\pi\)
\(228\) 0 0
\(229\) 6.49974 11.2579i 0.429515 0.743941i −0.567315 0.823501i \(-0.692018\pi\)
0.996830 + 0.0795594i \(0.0253513\pi\)
\(230\) −27.1711 9.89725i −1.79161 0.652605i
\(231\) 0 0
\(232\) 9.65510 16.6939i 0.633889 1.09601i
\(233\) 22.7845i 1.49266i 0.665575 + 0.746331i \(0.268186\pi\)
−0.665575 + 0.746331i \(0.731814\pi\)
\(234\) 0 0
\(235\) 12.5291i 0.817305i
\(236\) −11.3825 9.56089i −0.740941 0.622361i
\(237\) 0 0
\(238\) 0.268485 0.737076i 0.0174033 0.0477775i
\(239\) 10.1962 17.6603i 0.659537 1.14235i −0.321198 0.947012i \(-0.604086\pi\)
0.980736 0.195340i \(-0.0625810\pi\)
\(240\) 0 0
\(241\) 3.27539 + 5.67314i 0.210986 + 0.365439i 0.952024 0.306025i \(-0.0989991\pi\)
−0.741037 + 0.671464i \(0.765666\pi\)
\(242\) −15.2339 + 2.68218i −0.979271 + 0.172417i
\(243\) 0 0
\(244\) −24.1554 + 8.77804i −1.54639 + 0.561956i
\(245\) −2.24261 + 1.29477i −0.143275 + 0.0827200i
\(246\) 0 0
\(247\) −0.401735 0.231942i −0.0255618 0.0147581i
\(248\) 22.7536 + 0.0172456i 1.44485 + 0.00109510i
\(249\) 0 0
\(250\) 9.24362 7.75234i 0.584618 0.490301i
\(251\) 18.3086 1.15563 0.577814 0.816169i \(-0.303906\pi\)
0.577814 + 0.816169i \(0.303906\pi\)
\(252\) 0 0
\(253\) −1.97131 −0.123935
\(254\) 5.10391 4.28049i 0.320248 0.268582i
\(255\) 0 0
\(256\) 12.2359 + 10.3094i 0.764744 + 0.644335i
\(257\) −13.8378 7.98924i −0.863176 0.498355i 0.00189858 0.999998i \(-0.499396\pi\)
−0.865075 + 0.501643i \(0.832729\pi\)
\(258\) 0 0
\(259\) −8.63011 + 4.98260i −0.536249 + 0.309603i
\(260\) 0.228577 + 0.628999i 0.0141758 + 0.0390089i
\(261\) 0 0
\(262\) 13.8481 2.43819i 0.855540 0.150632i
\(263\) 1.92259 + 3.33002i 0.118552 + 0.205338i 0.919194 0.393805i \(-0.128841\pi\)
−0.800642 + 0.599143i \(0.795508\pi\)
\(264\) 0 0
\(265\) 11.6537 20.1848i 0.715881 1.23994i
\(266\) −1.73758 + 4.77022i −0.106538 + 0.292481i
\(267\) 0 0
\(268\) −7.77660 + 9.25829i −0.475032 + 0.565540i
\(269\) 3.59531i 0.219210i 0.993975 + 0.109605i \(0.0349585\pi\)
−0.993975 + 0.109605i \(0.965041\pi\)
\(270\) 0 0
\(271\) 4.24361i 0.257781i 0.991659 + 0.128891i \(0.0411416\pi\)
−0.991659 + 0.128891i \(0.958858\pi\)
\(272\) −0.760969 + 2.08419i −0.0461405 + 0.126373i
\(273\) 0 0
\(274\) 20.2389 + 7.37214i 1.22267 + 0.445367i
\(275\) −0.212920 + 0.368788i −0.0128395 + 0.0222387i
\(276\) 0 0
\(277\) 4.88987 + 8.46950i 0.293804 + 0.508883i 0.974706 0.223491i \(-0.0717454\pi\)
−0.680902 + 0.732374i \(0.738412\pi\)
\(278\) 0.435201 + 2.47180i 0.0261016 + 0.148249i
\(279\) 0 0
\(280\) 6.34584 3.65736i 0.379236 0.218569i
\(281\) −20.3980 + 11.7768i −1.21684 + 0.702544i −0.964241 0.265027i \(-0.914619\pi\)
−0.252600 + 0.967571i \(0.581286\pi\)
\(282\) 0 0
\(283\) 4.19988 + 2.42480i 0.249657 + 0.144139i 0.619607 0.784912i \(-0.287292\pi\)
−0.369950 + 0.929052i \(0.620625\pi\)
\(284\) −5.49673 + 31.0817i −0.326171 + 1.84436i
\(285\) 0 0
\(286\) 0.0293167 + 0.0349563i 0.00173353 + 0.00206701i
\(287\) 4.91861 0.290336
\(288\) 0 0
\(289\) 16.6923 0.981901
\(290\) 16.0453 + 19.1318i 0.942212 + 1.12346i
\(291\) 0 0
\(292\) 4.91160 27.7730i 0.287430 1.62529i
\(293\) 16.8856 + 9.74890i 0.986467 + 0.569537i 0.904216 0.427075i \(-0.140456\pi\)
0.0822504 + 0.996612i \(0.473789\pi\)
\(294\) 0 0
\(295\) 16.6684 9.62350i 0.970471 0.560302i
\(296\) 24.4203 14.0744i 1.41940 0.818058i
\(297\) 0 0
\(298\) −4.06300 23.0765i −0.235363 1.33679i
\(299\) −0.510181 0.883659i −0.0295045 0.0511033i
\(300\) 0 0
\(301\) −2.18695 + 3.78791i −0.126054 + 0.218331i
\(302\) 23.3781 + 8.51563i 1.34526 + 0.490020i
\(303\) 0 0
\(304\) 4.92486 13.4885i 0.282460 0.773619i
\(305\) 33.2769i 1.90543i
\(306\) 0 0
\(307\) 6.21611i 0.354772i −0.984141 0.177386i \(-0.943236\pi\)
0.984141 0.177386i \(-0.0567642\pi\)
\(308\) 0.321138 0.382325i 0.0182985 0.0217850i
\(309\) 0 0
\(310\) −10.0832 + 27.6815i −0.572685 + 1.57220i
\(311\) 11.2742 19.5275i 0.639303 1.10731i −0.346283 0.938130i \(-0.612556\pi\)
0.985586 0.169176i \(-0.0541105\pi\)
\(312\) 0 0
\(313\) −7.53213 13.0460i −0.425741 0.737405i 0.570748 0.821125i \(-0.306653\pi\)
−0.996489 + 0.0837201i \(0.973320\pi\)
\(314\) −3.13867 + 0.552614i −0.177125 + 0.0311858i
\(315\) 0 0
\(316\) 1.60936 + 4.42864i 0.0905335 + 0.249130i
\(317\) 9.34442 5.39500i 0.524835 0.303013i −0.214076 0.976817i \(-0.568674\pi\)
0.738911 + 0.673804i \(0.235341\pi\)
\(318\) 0 0
\(319\) 1.47413 + 0.851089i 0.0825354 + 0.0476518i
\(320\) −17.9566 + 10.3310i −1.00380 + 0.577519i
\(321\) 0 0
\(322\) −8.55626 + 7.17587i −0.476822 + 0.399896i
\(323\) 1.99127 0.110797
\(324\) 0 0
\(325\) −0.220417 −0.0122265
\(326\) 7.57976 6.35691i 0.419804 0.352077i
\(327\) 0 0
\(328\) −13.9119 0.0105443i −0.768158 0.000582209i
\(329\) −4.19011 2.41916i −0.231008 0.133373i
\(330\) 0 0
\(331\) −9.03466 + 5.21616i −0.496590 + 0.286706i −0.727304 0.686315i \(-0.759227\pi\)
0.230714 + 0.973021i \(0.425894\pi\)
\(332\) −8.89181 + 3.23127i −0.488001 + 0.177339i
\(333\) 0 0
\(334\) 15.0483 2.64950i 0.823405 0.144974i
\(335\) −7.82753 13.5577i −0.427663 0.740735i
\(336\) 0 0
\(337\) 15.0986 26.1516i 0.822475 1.42457i −0.0813590 0.996685i \(-0.525926\pi\)
0.903834 0.427883i \(-0.140741\pi\)
\(338\) 6.28425 17.2523i 0.341818 0.938399i
\(339\) 0 0
\(340\) −2.19976 1.84771i −0.119299 0.100206i
\(341\) 2.00834i 0.108758i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 6.19375 10.7091i 0.333944 0.577398i
\(345\) 0 0
\(346\) 6.16799 + 2.24673i 0.331593 + 0.120785i
\(347\) 12.7498 22.0832i 0.684443 1.18549i −0.289169 0.957278i \(-0.593379\pi\)
0.973612 0.228212i \(-0.0732878\pi\)
\(348\) 0 0
\(349\) 15.4421 + 26.7465i 0.826597 + 1.43171i 0.900692 + 0.434457i \(0.143060\pi\)
−0.0740953 + 0.997251i \(0.523607\pi\)
\(350\) 0.418288 + 2.37574i 0.0223585 + 0.126989i
\(351\) 0 0
\(352\) −0.909134 + 1.08069i −0.0484570 + 0.0576009i
\(353\) 30.2542 17.4672i 1.61027 0.929688i 0.620958 0.783843i \(-0.286744\pi\)
0.989308 0.145844i \(-0.0465898\pi\)
\(354\) 0 0
\(355\) −35.3929 20.4341i −1.87846 1.08453i
\(356\) 15.4056 + 2.72445i 0.816495 + 0.144396i
\(357\) 0 0
\(358\) 6.05844 + 7.22388i 0.320199 + 0.381794i
\(359\) −5.92966 −0.312956 −0.156478 0.987681i \(-0.550014\pi\)
−0.156478 + 0.987681i \(0.550014\pi\)
\(360\) 0 0
\(361\) 6.11288 0.321730
\(362\) 6.91796 + 8.24873i 0.363600 + 0.433544i
\(363\) 0 0
\(364\) 0.254492 + 0.0450064i 0.0133390 + 0.00235898i
\(365\) 31.6253 + 18.2589i 1.65534 + 0.955712i
\(366\) 0 0
\(367\) −26.1820 + 15.1162i −1.36669 + 0.789059i −0.990504 0.137485i \(-0.956098\pi\)
−0.376187 + 0.926544i \(0.622765\pi\)
\(368\) 24.2161 20.2781i 1.26235 1.05707i
\(369\) 0 0
\(370\) 6.32807 + 35.9414i 0.328981 + 1.86850i
\(371\) −4.50029 7.79472i −0.233643 0.404682i
\(372\) 0 0
\(373\) 2.54373 4.40588i 0.131710 0.228128i −0.792626 0.609708i \(-0.791287\pi\)
0.924336 + 0.381580i \(0.124620\pi\)
\(374\) −0.184011 0.0670273i −0.00951501 0.00346590i
\(375\) 0 0
\(376\) 11.8462 + 6.85140i 0.610923 + 0.353334i
\(377\) 0.881056i 0.0453767i
\(378\) 0 0
\(379\) 18.6036i 0.955600i 0.878469 + 0.477800i \(0.158566\pi\)
−0.878469 + 0.477800i \(0.841434\pi\)
\(380\) 14.2364 + 11.9580i 0.730314 + 0.613435i
\(381\) 0 0
\(382\) 2.08621 5.72731i 0.106740 0.293035i
\(383\) 5.98305 10.3630i 0.305720 0.529522i −0.671702 0.740822i \(-0.734436\pi\)
0.977421 + 0.211300i \(0.0677696\pi\)
\(384\) 0 0
\(385\) 0.323241 + 0.559869i 0.0164739 + 0.0285336i
\(386\) 1.92458 0.338854i 0.0979586 0.0172472i
\(387\) 0 0
\(388\) 21.3191 7.74731i 1.08231 0.393310i
\(389\) 16.3655 9.44864i 0.829765 0.479065i −0.0240072 0.999712i \(-0.507642\pi\)
0.853772 + 0.520647i \(0.174309\pi\)
\(390\) 0 0
\(391\) 3.79319 + 2.19000i 0.191830 + 0.110753i
\(392\) 0.00214375 2.82843i 0.000108276 0.142857i
\(393\) 0 0
\(394\) −10.0392 + 8.41954i −0.505766 + 0.424170i
\(395\) −6.10096 −0.306973
\(396\) 0 0
\(397\) −26.3234 −1.32113 −0.660566 0.750768i \(-0.729684\pi\)
−0.660566 + 0.750768i \(0.729684\pi\)
\(398\) −26.6549 + 22.3546i −1.33609 + 1.12054i
\(399\) 0 0
\(400\) −1.17801 6.72051i −0.0589003 0.336025i
\(401\) 7.64521 + 4.41396i 0.381783 + 0.220423i 0.678594 0.734514i \(-0.262590\pi\)
−0.296811 + 0.954936i \(0.595923\pi\)
\(402\) 0 0
\(403\) −0.900257 + 0.519764i −0.0448450 + 0.0258913i
\(404\) 2.50023 + 6.88014i 0.124391 + 0.342300i
\(405\) 0 0
\(406\) 9.49638 1.67199i 0.471297 0.0829797i
\(407\) 1.24391 + 2.15451i 0.0616582 + 0.106795i
\(408\) 0 0
\(409\) −11.4524 + 19.8361i −0.566283 + 0.980831i 0.430646 + 0.902521i \(0.358286\pi\)
−0.996929 + 0.0783100i \(0.975048\pi\)
\(410\) 6.16501 16.9249i 0.304468 0.835862i
\(411\) 0 0
\(412\) 8.85207 10.5387i 0.436110 0.519203i
\(413\) 7.43258i 0.365733i
\(414\) 0 0
\(415\) 12.2495i 0.601304i
\(416\) −0.719715 0.127843i −0.0352869 0.00626801i
\(417\) 0 0
\(418\) 1.19089 + 0.433789i 0.0582483 + 0.0212173i
\(419\) −5.10769 + 8.84679i −0.249527 + 0.432194i −0.963395 0.268087i \(-0.913609\pi\)
0.713868 + 0.700281i \(0.246942\pi\)
\(420\) 0 0
\(421\) 5.95328 + 10.3114i 0.290145 + 0.502546i 0.973844 0.227218i \(-0.0729630\pi\)
−0.683699 + 0.729765i \(0.739630\pi\)
\(422\) −2.54485 14.4539i −0.123881 0.703604i
\(423\) 0 0
\(424\) 12.7120 + 22.0565i 0.617350 + 1.07116i
\(425\) 0.819399 0.473080i 0.0397467 0.0229478i
\(426\) 0 0
\(427\) −11.1288 6.42524i −0.538562 0.310939i
\(428\) 2.59013 14.6461i 0.125199 0.707946i
\(429\) 0 0
\(430\) 10.2930 + 12.2731i 0.496375 + 0.591860i
\(431\) −4.26567 −0.205470 −0.102735 0.994709i \(-0.532759\pi\)
−0.102735 + 0.994709i \(0.532759\pi\)
\(432\) 0 0
\(433\) 36.7838 1.76772 0.883858 0.467756i \(-0.154937\pi\)
0.883858 + 0.467756i \(0.154937\pi\)
\(434\) 7.31066 + 8.71698i 0.350923 + 0.418428i
\(435\) 0 0
\(436\) 2.86882 16.2220i 0.137392 0.776891i
\(437\) −24.5489 14.1733i −1.17433 0.678001i
\(438\) 0 0
\(439\) 13.2806 7.66755i 0.633848 0.365952i −0.148393 0.988928i \(-0.547410\pi\)
0.782241 + 0.622976i \(0.214077\pi\)
\(440\) −0.913062 1.58424i −0.0435285 0.0755258i
\(441\) 0 0
\(442\) −0.0175770 0.0998317i −0.000836053 0.00474851i
\(443\) 5.27986 + 9.14498i 0.250854 + 0.434491i 0.963761 0.266767i \(-0.0859554\pi\)
−0.712907 + 0.701258i \(0.752622\pi\)
\(444\) 0 0
\(445\) −10.1281 + 17.5424i −0.480119 + 0.831591i
\(446\) 34.2935 + 12.4916i 1.62384 + 0.591496i
\(447\) 0 0
\(448\) −0.0121269 + 7.99999i −0.000572940 + 0.377964i
\(449\) 16.5280i 0.780006i 0.920813 + 0.390003i \(0.127526\pi\)
−0.920813 + 0.390003i \(0.872474\pi\)
\(450\) 0 0
\(451\) 1.22793i 0.0578212i
\(452\) −11.0351 + 13.1377i −0.519050 + 0.617945i
\(453\) 0 0
\(454\) −6.52656 + 17.9175i −0.306307 + 0.840909i
\(455\) −0.167311 + 0.289791i −0.00784366 + 0.0135856i
\(456\) 0 0
\(457\) −5.27095 9.12955i −0.246564 0.427062i 0.716006 0.698094i \(-0.245968\pi\)
−0.962570 + 0.271032i \(0.912635\pi\)
\(458\) −18.1055 + 3.18778i −0.846016 + 0.148955i
\(459\) 0 0
\(460\) 13.9677 + 38.4363i 0.651247 + 1.79210i
\(461\) 21.5838 12.4614i 1.00526 0.580387i 0.0954593 0.995433i \(-0.469568\pi\)
0.909800 + 0.415046i \(0.136235\pi\)
\(462\) 0 0
\(463\) −27.8446 16.0761i −1.29405 0.747119i −0.314679 0.949198i \(-0.601897\pi\)
−0.979369 + 0.202079i \(0.935230\pi\)
\(464\) −26.8634 + 4.70876i −1.24710 + 0.218598i
\(465\) 0 0
\(466\) 24.6888 20.7058i 1.14369 0.959176i
\(467\) −8.54957 −0.395627 −0.197813 0.980240i \(-0.563384\pi\)
−0.197813 + 0.980240i \(0.563384\pi\)
\(468\) 0 0
\(469\) −6.04548 −0.279155
\(470\) −13.5762 + 11.3860i −0.626225 + 0.525195i
\(471\) 0 0
\(472\) −0.0159336 + 21.0225i −0.000733402 + 0.967639i
\(473\) 0.945654 + 0.545973i 0.0434812 + 0.0251039i
\(474\) 0 0
\(475\) −5.30300 + 3.06169i −0.243319 + 0.140480i
\(476\) −1.04267 + 0.378904i −0.0477907 + 0.0173671i
\(477\) 0 0
\(478\) −28.4023 + 5.00070i −1.29909 + 0.228727i
\(479\) 8.25859 + 14.3043i 0.377345 + 0.653580i 0.990675 0.136247i \(-0.0435039\pi\)
−0.613330 + 0.789826i \(0.710171\pi\)
\(480\) 0 0
\(481\) −0.643853 + 1.11519i −0.0293572 + 0.0508481i
\(482\) 3.17074 8.70470i 0.144423 0.396488i
\(483\) 0 0
\(484\) 16.7504 + 14.0697i 0.761381 + 0.639530i
\(485\) 29.3695i 1.33360i
\(486\) 0 0
\(487\) 7.93519i 0.359578i −0.983705 0.179789i \(-0.942459\pi\)
0.983705 0.179789i \(-0.0575415\pi\)
\(488\) 31.4633 + 18.1972i 1.42428 + 0.823747i
\(489\) 0 0
\(490\) 3.44100 + 1.25341i 0.155448 + 0.0566231i
\(491\) −1.83003 + 3.16970i −0.0825880 + 0.143047i −0.904361 0.426769i \(-0.859652\pi\)
0.821773 + 0.569815i \(0.192985\pi\)
\(492\) 0 0
\(493\) −1.89101 3.27532i −0.0851668 0.147513i
\(494\) 0.113755 + 0.646093i 0.00511809 + 0.0290691i
\(495\) 0 0
\(496\) −20.6590 24.6710i −0.927615 1.10776i
\(497\) −13.6676 + 7.89100i −0.613076 + 0.353960i
\(498\) 0 0
\(499\) −7.46689 4.31101i −0.334264 0.192987i 0.323469 0.946239i \(-0.395151\pi\)
−0.657733 + 0.753252i \(0.728484\pi\)
\(500\) −16.8006 2.97115i −0.751344 0.132874i
\(501\) 0 0
\(502\) −16.6382 19.8388i −0.742599 0.885449i
\(503\) −44.0191 −1.96271 −0.981357 0.192194i \(-0.938440\pi\)
−0.981357 + 0.192194i \(0.938440\pi\)
\(504\) 0 0
\(505\) −9.47818 −0.421773
\(506\) 1.79146 + 2.13608i 0.0796402 + 0.0949602i
\(507\) 0 0
\(508\) −9.27651 1.64053i −0.411578 0.0727868i
\(509\) −9.48279 5.47489i −0.420317 0.242670i 0.274896 0.961474i \(-0.411357\pi\)
−0.695213 + 0.718804i \(0.744690\pi\)
\(510\) 0 0
\(511\) 12.2127 7.05099i 0.540257 0.311917i
\(512\) 0.0514499 22.6274i 0.00227379 0.999997i
\(513\) 0 0
\(514\) 3.91830 + 22.2547i 0.172829 + 0.981611i
\(515\) 8.91004 + 15.4326i 0.392623 + 0.680043i
\(516\) 0 0
\(517\) −0.603945 + 1.04606i −0.0265615 + 0.0460058i
\(518\) 13.2418 + 4.82340i 0.581811 + 0.211928i
\(519\) 0 0
\(520\) 0.473848 0.819295i 0.0207796 0.0359284i
\(521\) 6.26841i 0.274624i −0.990528 0.137312i \(-0.956154\pi\)
0.990528 0.137312i \(-0.0438463\pi\)
\(522\) 0 0
\(523\) 18.7279i 0.818913i 0.912330 + 0.409456i \(0.134282\pi\)
−0.912330 + 0.409456i \(0.865718\pi\)
\(524\) −15.2267 12.7898i −0.665180 0.558725i
\(525\) 0 0
\(526\) 1.86116 5.10948i 0.0811505 0.222784i
\(527\) 2.23114 3.86444i 0.0971898 0.168338i
\(528\) 0 0
\(529\) −19.6757 34.0793i −0.855465 1.48171i
\(530\) −32.4623 + 5.71552i −1.41007 + 0.248267i
\(531\) 0 0
\(532\) 6.74798 2.45220i 0.292562 0.106316i
\(533\) 0.550433 0.317792i 0.0238419 0.0137651i
\(534\) 0 0
\(535\) 16.6776 + 9.62882i 0.721035 + 0.416290i
\(536\) 17.0992 + 0.0129600i 0.738573 + 0.000559786i
\(537\) 0 0
\(538\) 3.89580 3.26729i 0.167960 0.140863i
\(539\) 0.249651 0.0107532
\(540\) 0 0
\(541\) 24.7122 1.06246 0.531230 0.847228i \(-0.321730\pi\)
0.531230 + 0.847228i \(0.321730\pi\)
\(542\) 4.59830 3.85645i 0.197514 0.165649i
\(543\) 0 0
\(544\) 2.94993 1.06947i 0.126477 0.0458531i
\(545\) 18.4720 + 10.6648i 0.791255 + 0.456832i
\(546\) 0 0
\(547\) 23.9787 13.8441i 1.02525 0.591930i 0.109632 0.993972i \(-0.465033\pi\)
0.915621 + 0.402042i \(0.131699\pi\)
\(548\) −10.4041 28.6300i −0.444440 1.22301i
\(549\) 0 0
\(550\) 0.593105 0.104426i 0.0252901 0.00445274i
\(551\) 12.2383 + 21.1973i 0.521368 + 0.903036i
\(552\) 0 0
\(553\) −1.17800 + 2.04035i −0.0500936 + 0.0867646i
\(554\) 4.73364 12.9954i 0.201113 0.552120i
\(555\) 0 0
\(556\) 2.28290 2.71786i 0.0968165 0.115263i
\(557\) 43.5015i 1.84322i −0.388119 0.921609i \(-0.626875\pi\)
0.388119 0.921609i \(-0.373125\pi\)
\(558\) 0 0
\(559\) 0.565197i 0.0239053i
\(560\) −9.72992 3.55254i −0.411164 0.150122i
\(561\) 0 0
\(562\) 31.2981 + 11.4005i 1.32023 + 0.480902i
\(563\) 0.525773 0.910665i 0.0221587 0.0383800i −0.854733 0.519067i \(-0.826279\pi\)
0.876892 + 0.480687i \(0.159613\pi\)
\(564\) 0 0
\(565\) −11.1074 19.2386i −0.467292 0.809374i
\(566\) −1.18924 6.75448i −0.0499874 0.283912i
\(567\) 0 0
\(568\) 38.6747 22.2898i 1.62276 0.935259i
\(569\) 4.94731 2.85633i 0.207402 0.119744i −0.392701 0.919666i \(-0.628459\pi\)
0.600103 + 0.799922i \(0.295126\pi\)
\(570\) 0 0
\(571\) 15.2710 + 8.81671i 0.639071 + 0.368968i 0.784257 0.620436i \(-0.213045\pi\)
−0.145185 + 0.989404i \(0.546378\pi\)
\(572\) 0.0112359 0.0635341i 0.000469795 0.00265649i
\(573\) 0 0
\(574\) −4.46986 5.32971i −0.186568 0.222458i
\(575\) −13.4690 −0.561697
\(576\) 0 0
\(577\) −18.3399 −0.763501 −0.381751 0.924265i \(-0.624679\pi\)
−0.381751 + 0.924265i \(0.624679\pi\)
\(578\) −15.1694 18.0875i −0.630964 0.752339i
\(579\) 0 0
\(580\) 6.14948 34.7727i 0.255343 1.44386i
\(581\) −4.09661 2.36518i −0.169956 0.0981243i
\(582\) 0 0
\(583\) −1.94596 + 1.12350i −0.0805933 + 0.0465306i
\(584\) −34.5578 + 19.9170i −1.43001 + 0.824172i
\(585\) 0 0
\(586\) −4.78132 27.1563i −0.197515 1.12182i
\(587\) 8.18823 + 14.1824i 0.337965 + 0.585372i 0.984050 0.177893i \(-0.0569282\pi\)
−0.646085 + 0.763265i \(0.723595\pi\)
\(588\) 0 0
\(589\) −14.4395 + 25.0100i −0.594970 + 1.03052i
\(590\) −25.5755 9.31603i −1.05293 0.383535i
\(591\) 0 0
\(592\) −37.4431 13.6710i −1.53890 0.561876i
\(593\) 2.86950i 0.117836i −0.998263 0.0589181i \(-0.981235\pi\)
0.998263 0.0589181i \(-0.0187651\pi\)
\(594\) 0 0
\(595\) 1.43640i 0.0588866i
\(596\) −21.3129 + 25.3737i −0.873012 + 1.03935i
\(597\) 0 0
\(598\) −0.493881 + 1.35586i −0.0201963 + 0.0554453i
\(599\) −0.530101 + 0.918163i −0.0216594 + 0.0375151i −0.876652 0.481125i \(-0.840228\pi\)
0.854993 + 0.518640i \(0.173562\pi\)
\(600\) 0 0
\(601\) 6.48648 + 11.2349i 0.264589 + 0.458282i 0.967456 0.253040i \(-0.0814303\pi\)
−0.702867 + 0.711322i \(0.748097\pi\)
\(602\) 6.09192 1.07258i 0.248288 0.0437153i
\(603\) 0 0
\(604\) −12.0179 33.0708i −0.489000 1.34563i
\(605\) −24.5290 + 14.1618i −0.997244 + 0.575759i
\(606\) 0 0
\(607\) 24.3945 + 14.0842i 0.990144 + 0.571660i 0.905317 0.424736i \(-0.139633\pi\)
0.0848266 + 0.996396i \(0.472966\pi\)
\(608\) −19.0914 + 6.92141i −0.774259 + 0.280700i
\(609\) 0 0
\(610\) −36.0582 + 30.2409i −1.45995 + 1.22442i
\(611\) −0.625210 −0.0252933
\(612\) 0 0
\(613\) −22.1934 −0.896381 −0.448191 0.893938i \(-0.647931\pi\)
−0.448191 + 0.893938i \(0.647931\pi\)
\(614\) −6.73566 + 5.64899i −0.271829 + 0.227975i
\(615\) 0 0
\(616\) −0.706118 0.000535188i −0.0284503 2.15633e-5i
\(617\) −12.7221 7.34512i −0.512173 0.295703i 0.221553 0.975148i \(-0.428887\pi\)
−0.733726 + 0.679445i \(0.762221\pi\)
\(618\) 0 0
\(619\) −14.2161 + 8.20765i −0.571392 + 0.329893i −0.757705 0.652597i \(-0.773679\pi\)
0.186313 + 0.982490i \(0.440346\pi\)
\(620\) 39.1583 14.2301i 1.57264 0.571493i
\(621\) 0 0
\(622\) −31.4053 + 5.52942i −1.25924 + 0.221710i
\(623\) 3.91116 + 6.77433i 0.156697 + 0.271408i
\(624\) 0 0
\(625\) 15.3096 26.5170i 0.612383 1.06068i
\(626\) −7.29148 + 20.0174i −0.291426 + 0.800058i
\(627\) 0 0
\(628\) 3.45111 + 2.89880i 0.137714 + 0.115675i
\(629\) 5.52760i 0.220400i
\(630\) 0 0
\(631\) 12.7711i 0.508411i −0.967150 0.254205i \(-0.918186\pi\)
0.967150 0.254205i \(-0.0818139\pi\)
\(632\) 3.33626 5.76846i 0.132709 0.229457i
\(633\) 0 0
\(634\) −14.3378 5.22263i −0.569427 0.207417i
\(635\) 6.09867 10.5632i 0.242018 0.419188i
\(636\) 0 0
\(637\) 0.0646102 + 0.111908i 0.00255995 + 0.00443396i
\(638\) −0.417414 2.37078i −0.0165256 0.0938600i
\(639\) 0 0
\(640\) 27.5127 + 10.0690i 1.08754 + 0.398010i
\(641\) −13.2162 + 7.63040i −0.522010 + 0.301383i −0.737757 0.675067i \(-0.764115\pi\)
0.215746 + 0.976449i \(0.430782\pi\)
\(642\) 0 0
\(643\) 33.5137 + 19.3492i 1.32165 + 0.763057i 0.983992 0.178211i \(-0.0570311\pi\)
0.337661 + 0.941268i \(0.390364\pi\)
\(644\) 15.5513 + 2.75021i 0.612806 + 0.108373i
\(645\) 0 0
\(646\) −1.80959 2.15770i −0.0711975 0.0848934i
\(647\) 0.564326 0.0221860 0.0110930 0.999938i \(-0.496469\pi\)
0.0110930 + 0.999938i \(0.496469\pi\)
\(648\) 0 0
\(649\) −1.85555 −0.0728367
\(650\) 0.200307 + 0.238839i 0.00785669 + 0.00936804i
\(651\) 0 0
\(652\) −13.7765 2.43634i −0.539527 0.0954144i
\(653\) 3.90030 + 2.25184i 0.152631 + 0.0881214i 0.574370 0.818596i \(-0.305247\pi\)
−0.421740 + 0.906717i \(0.638580\pi\)
\(654\) 0 0
\(655\) 22.2977 12.8736i 0.871241 0.503011i
\(656\) 12.6312 + 15.0843i 0.493167 + 0.588942i
\(657\) 0 0
\(658\) 1.18647 + 6.73877i 0.0462535 + 0.262705i
\(659\) −7.02737 12.1718i −0.273747 0.474144i 0.696071 0.717973i \(-0.254930\pi\)
−0.969818 + 0.243829i \(0.921597\pi\)
\(660\) 0 0
\(661\) −17.4242 + 30.1797i −0.677724 + 1.17385i 0.297940 + 0.954585i \(0.403700\pi\)
−0.975665 + 0.219269i \(0.929633\pi\)
\(662\) 13.8625 + 5.04951i 0.538782 + 0.196255i
\(663\) 0 0
\(664\) 11.5819 + 6.69852i 0.449465 + 0.259953i
\(665\) 9.29611i 0.360488i
\(666\) 0 0
\(667\) 53.8388i 2.08465i
\(668\) −16.5463 13.8982i −0.640195 0.537739i
\(669\) 0 0
\(670\) −7.57744 + 20.8025i −0.292742 + 0.803670i
\(671\) −1.60406 + 2.77832i −0.0619242 + 0.107256i
\(672\) 0 0
\(673\) −9.76133 16.9071i −0.376272 0.651722i 0.614245 0.789115i \(-0.289461\pi\)
−0.990516 + 0.137394i \(0.956127\pi\)
\(674\) −42.0585 + 7.40509i −1.62003 + 0.285233i
\(675\) 0 0
\(676\) −24.4051 + 8.86877i −0.938658 + 0.341107i
\(677\) −7.35277 + 4.24512i −0.282590 + 0.163153i −0.634595 0.772845i \(-0.718833\pi\)
0.352005 + 0.935998i \(0.385500\pi\)
\(678\) 0 0
\(679\) 9.82208 + 5.67078i 0.376937 + 0.217625i
\(680\) −0.00307927 + 4.06275i −0.000118085 + 0.155799i
\(681\) 0 0
\(682\) 2.17620 1.82511i 0.0833310 0.0698871i
\(683\) 16.0399 0.613751 0.306876 0.951750i \(-0.400716\pi\)
0.306876 + 0.951750i \(0.400716\pi\)
\(684\) 0 0
\(685\) 39.4411 1.50697
\(686\) 1.08358 0.908765i 0.0413713 0.0346968i
\(687\) 0 0
\(688\) −17.2329 + 3.02066i −0.656997 + 0.115162i
\(689\) −1.00724 0.581529i −0.0383727 0.0221545i
\(690\) 0 0
\(691\) 17.7036 10.2212i 0.673476 0.388831i −0.123917 0.992293i \(-0.539546\pi\)
0.797392 + 0.603461i \(0.206212\pi\)
\(692\) −3.17074 8.72526i −0.120534 0.331685i
\(693\) 0 0
\(694\) −35.5155 + 6.25309i −1.34815 + 0.237364i
\(695\) 2.29785 + 3.97999i 0.0871623 + 0.150970i
\(696\) 0 0
\(697\) −1.36415 + 2.36279i −0.0516710 + 0.0894969i
\(698\) 14.9487 41.0391i 0.565818 1.55335i
\(699\) 0 0
\(700\) 2.19418 2.61224i 0.0829322 0.0987334i
\(701\) 11.4242i 0.431488i 0.976450 + 0.215744i \(0.0692176\pi\)
−0.976450 + 0.215744i \(0.930782\pi\)
\(702\) 0 0
\(703\) 35.7737i 1.34923i
\(704\) 1.99720 + 0.00302748i 0.0752724 + 0.000114102i
\(705\) 0 0
\(706\) −46.4211 16.9092i −1.74708 0.636385i
\(707\) −1.83009 + 3.16980i −0.0688275 + 0.119213i
\(708\) 0 0
\(709\) 5.08955 + 8.81537i 0.191142 + 0.331068i 0.945629 0.325247i \(-0.105447\pi\)
−0.754487 + 0.656315i \(0.772114\pi\)
\(710\) 10.0218 + 56.9208i 0.376113 + 2.13620i
\(711\) 0 0
\(712\) −11.0479 19.1691i −0.414038 0.718392i
\(713\) −55.0121 + 31.7613i −2.06022 + 1.18947i
\(714\) 0 0
\(715\) 0.0723466 + 0.0417693i 0.00270561 + 0.00156208i
\(716\) 2.32195 13.1296i 0.0867752 0.490677i
\(717\) 0 0
\(718\) 5.38867 + 6.42526i 0.201103 + 0.239789i
\(719\) 25.4397 0.948741 0.474370 0.880325i \(-0.342676\pi\)
0.474370 + 0.880325i \(0.342676\pi\)
\(720\) 0 0
\(721\) 6.88155 0.256282
\(722\) −5.55517 6.62379i −0.206742 0.246512i
\(723\) 0 0
\(724\) 2.65136 14.9923i 0.0985371 0.557185i
\(725\) 10.0720 + 5.81508i 0.374065 + 0.215967i
\(726\) 0 0
\(727\) −14.2142 + 8.20655i −0.527174 + 0.304364i −0.739865 0.672756i \(-0.765111\pi\)
0.212691 + 0.977120i \(0.431777\pi\)
\(728\) −0.182505 0.316663i −0.00676410 0.0117363i
\(729\) 0 0
\(730\) −8.95501 50.8615i −0.331440 1.88247i
\(731\) −1.21308 2.10112i −0.0448674 0.0777127i
\(732\) 0 0
\(733\) −18.2362 + 31.5859i −0.673568 + 1.16665i 0.303318 + 0.952889i \(0.401906\pi\)
−0.976885 + 0.213764i \(0.931428\pi\)
\(734\) 40.1729 + 14.6332i 1.48281 + 0.540123i
\(735\) 0 0
\(736\) −43.9797 7.81211i −1.62111 0.287958i
\(737\) 1.50926i 0.0555943i
\(738\) 0 0
\(739\) 43.0747i 1.58453i −0.610177 0.792265i \(-0.708902\pi\)
0.610177 0.792265i \(-0.291098\pi\)
\(740\) 33.1946 39.5193i 1.22026 1.45276i
\(741\) 0 0
\(742\) −4.35650 + 11.9600i −0.159932 + 0.439065i
\(743\) −21.0352 + 36.4340i −0.771705 + 1.33663i 0.164922 + 0.986307i \(0.447263\pi\)
−0.936628 + 0.350326i \(0.886071\pi\)
\(744\) 0 0
\(745\) −21.4525 37.1568i −0.785959 1.36132i
\(746\) −7.08578 + 1.24757i −0.259429 + 0.0456767i
\(747\) 0 0
\(748\) 0.0945937 + 0.260303i 0.00345869 + 0.00951763i
\(749\) 6.44036 3.71834i 0.235326 0.135865i
\(750\) 0 0
\(751\) −3.20236 1.84888i −0.116856 0.0674667i 0.440433 0.897786i \(-0.354825\pi\)
−0.557289 + 0.830319i \(0.688158\pi\)
\(752\) −3.34140 19.0627i −0.121848 0.695144i
\(753\) 0 0
\(754\) 0.954695 0.800673i 0.0347679 0.0291588i
\(755\) 45.5588 1.65805
\(756\) 0 0
\(757\) 12.8240 0.466097 0.233048 0.972465i \(-0.425130\pi\)
0.233048 + 0.972465i \(0.425130\pi\)
\(758\) 20.1584 16.9063i 0.732188 0.614063i
\(759\) 0 0
\(760\) 0.0199285 26.2934i 0.000722883 0.953761i
\(761\) −30.7741 17.7674i −1.11556 0.644069i −0.175296 0.984516i \(-0.556088\pi\)
−0.940264 + 0.340447i \(0.889422\pi\)
\(762\) 0 0
\(763\) 7.13332 4.11842i 0.258243 0.149097i
\(764\) −8.10188 + 2.94421i −0.293116 + 0.106518i
\(765\) 0 0
\(766\) −16.6663 + 2.93437i −0.602177 + 0.106023i
\(767\) −0.480221 0.831767i −0.0173398 0.0300334i
\(768\) 0 0
\(769\) −3.57085 + 6.18489i −0.128768 + 0.223033i −0.923200 0.384321i \(-0.874436\pi\)
0.794431 + 0.607354i \(0.207769\pi\)
\(770\) 0.312913 0.859047i 0.0112766 0.0309579i
\(771\) 0 0
\(772\) −2.11617 1.77750i −0.0761626 0.0639736i
\(773\) 39.5269i 1.42168i 0.703351 + 0.710842i \(0.251686\pi\)
−0.703351 + 0.710842i \(0.748314\pi\)
\(774\) 0 0
\(775\) 13.7220i 0.492910i
\(776\) −27.7689 16.0604i −0.996844 0.576536i
\(777\) 0 0
\(778\) −25.1108 9.14676i −0.900265 0.327927i
\(779\) 8.82857 15.2915i 0.316316 0.547876i
\(780\) 0 0
\(781\) 1.96999 + 3.41213i 0.0704919 + 0.122095i
\(782\) −1.07408 6.10042i −0.0384090 0.218151i
\(783\) 0 0
\(784\) −3.06677 + 2.56805i −0.109528 + 0.0917162i
\(785\) −5.05375 + 2.91778i −0.180376 + 0.104140i
\(786\) 0 0
\(787\) −37.4865 21.6428i −1.33625 0.771484i −0.350000 0.936750i \(-0.613818\pi\)
−0.986249 + 0.165266i \(0.947152\pi\)
\(788\) 18.2465 + 3.22686i 0.650004 + 0.114952i
\(789\) 0 0