Properties

Label 525.2.j.b.407.9
Level 525
Weight 2
Character 525.407
Analytic conductor 4.192
Analytic rank 0
Dimension 24
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.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 407.9
Character \(\chi\) \(=\) 525.407
Dual form 525.2.j.b.218.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.800553 - 0.800553i) q^{2} +(1.34285 - 1.09397i) q^{3} +0.718229i q^{4} +(0.199242 - 1.95080i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.17609 + 2.17609i) q^{8} +(0.606476 - 2.93806i) q^{9} +O(q^{10})\) \(q+(0.800553 - 0.800553i) q^{2} +(1.34285 - 1.09397i) q^{3} +0.718229i q^{4} +(0.199242 - 1.95080i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.17609 + 2.17609i) q^{8} +(0.606476 - 2.93806i) q^{9} +5.20191i q^{11} +(0.785718 + 0.964471i) q^{12} +(3.24693 - 3.24693i) q^{13} +1.13215 q^{14} +2.04769 q^{16} +(0.844232 - 0.844232i) q^{17} +(-1.86656 - 2.83759i) q^{18} -1.32025i q^{19} +(1.72309 + 0.175985i) q^{21} +(4.16440 + 4.16440i) q^{22} +(-5.62910 - 5.62910i) q^{23} +(5.30272 + 0.541586i) q^{24} -5.19868i q^{26} +(-2.39973 - 4.60883i) q^{27} +(-0.507864 + 0.507864i) q^{28} -4.38282 q^{29} -1.70499 q^{31} +(-2.71289 + 2.71289i) q^{32} +(5.69071 + 6.98536i) q^{33} -1.35170i q^{34} +(2.11020 + 0.435588i) q^{36} +(1.71171 + 1.71171i) q^{37} +(-1.05693 - 1.05693i) q^{38} +(0.808099 - 7.91217i) q^{39} +1.82176i q^{41} +(1.52031 - 1.23854i) q^{42} +(0.281771 - 0.281771i) q^{43} -3.73616 q^{44} -9.01279 q^{46} +(-3.39588 + 3.39588i) q^{47} +(2.74973 - 2.24010i) q^{48} +1.00000i q^{49} +(0.210113 - 2.05723i) q^{51} +(2.33204 + 2.33204i) q^{52} +(3.51059 + 3.51059i) q^{53} +(-5.61073 - 1.76850i) q^{54} +3.07745i q^{56} +(-1.44431 - 1.77289i) q^{57} +(-3.50868 + 3.50868i) q^{58} -1.81772 q^{59} -2.47514 q^{61} +(-1.36494 + 1.36494i) q^{62} +(2.50636 - 1.64868i) q^{63} +8.43900i q^{64} +(10.1479 + 1.03644i) q^{66} +(-7.92132 - 7.92132i) q^{67} +(0.606352 + 0.606352i) q^{68} +(-13.7171 - 1.40098i) q^{69} -9.06358i q^{71} +(7.71322 - 5.07373i) q^{72} +(1.33856 - 1.33856i) q^{73} +2.74064 q^{74} +0.948239 q^{76} +(-3.67830 + 3.67830i) q^{77} +(-5.68718 - 6.98104i) q^{78} +11.5015i q^{79} +(-8.26437 - 3.56372i) q^{81} +(1.45841 + 1.45841i) q^{82} +(-5.46196 - 5.46196i) q^{83} +(-0.126398 + 1.23757i) q^{84} -0.451146i q^{86} +(-5.88546 + 4.79466i) q^{87} +(-11.3198 + 11.3198i) q^{88} +9.43116 q^{89} +4.59186 q^{91} +(4.04298 - 4.04298i) q^{92} +(-2.28954 + 1.86520i) q^{93} +5.43717i q^{94} +(-0.675186 + 6.61080i) q^{96} +(3.06315 + 3.06315i) q^{97} +(0.800553 + 0.800553i) q^{98} +(15.2835 + 3.15483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{3} + O(q^{10}) \) \( 24q + 4q^{3} - 16q^{12} + 8q^{13} - 16q^{16} + 20q^{18} + 4q^{21} - 8q^{22} + 16q^{27} - 28q^{33} + 16q^{36} + 16q^{37} + 20q^{42} + 40q^{43} - 64q^{46} - 16q^{48} - 20q^{51} - 4q^{57} - 40q^{58} + 32q^{61} + 8q^{63} - 16q^{66} - 24q^{67} + 8q^{72} - 32q^{73} + 32q^{76} - 60q^{78} + 52q^{81} + 80q^{82} - 4q^{87} - 96q^{88} - 24q^{91} + 76q^{93} - 96q^{96} - 24q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.800553 0.800553i 0.566077 0.566077i −0.364950 0.931027i \(-0.618914\pi\)
0.931027 + 0.364950i \(0.118914\pi\)
\(3\) 1.34285 1.09397i 0.775293 0.631602i
\(4\) 0.718229i 0.359114i
\(5\) 0 0
\(6\) 0.199242 1.95080i 0.0813403 0.796410i
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 2.17609 + 2.17609i 0.769363 + 0.769363i
\(9\) 0.606476 2.93806i 0.202159 0.979353i
\(10\) 0 0
\(11\) 5.20191i 1.56843i 0.620487 + 0.784217i \(0.286935\pi\)
−0.620487 + 0.784217i \(0.713065\pi\)
\(12\) 0.785718 + 0.964471i 0.226817 + 0.278419i
\(13\) 3.24693 3.24693i 0.900537 0.900537i −0.0949456 0.995482i \(-0.530268\pi\)
0.995482 + 0.0949456i \(0.0302677\pi\)
\(14\) 1.13215 0.302581
\(15\) 0 0
\(16\) 2.04769 0.511922
\(17\) 0.844232 0.844232i 0.204756 0.204756i −0.597278 0.802034i \(-0.703751\pi\)
0.802034 + 0.597278i \(0.203751\pi\)
\(18\) −1.86656 2.83759i −0.439951 0.668826i
\(19\) 1.32025i 0.302885i −0.988466 0.151443i \(-0.951608\pi\)
0.988466 0.151443i \(-0.0483919\pi\)
\(20\) 0 0
\(21\) 1.72309 + 0.175985i 0.376008 + 0.0384031i
\(22\) 4.16440 + 4.16440i 0.887854 + 0.887854i
\(23\) −5.62910 5.62910i −1.17375 1.17375i −0.981309 0.192440i \(-0.938360\pi\)
−0.192440 0.981309i \(-0.561640\pi\)
\(24\) 5.30272 + 0.541586i 1.08241 + 0.110551i
\(25\) 0 0
\(26\) 5.19868i 1.01955i
\(27\) −2.39973 4.60883i −0.461829 0.886969i
\(28\) −0.507864 + 0.507864i −0.0959774 + 0.0959774i
\(29\) −4.38282 −0.813870 −0.406935 0.913457i \(-0.633402\pi\)
−0.406935 + 0.913457i \(0.633402\pi\)
\(30\) 0 0
\(31\) −1.70499 −0.306225 −0.153113 0.988209i \(-0.548930\pi\)
−0.153113 + 0.988209i \(0.548930\pi\)
\(32\) −2.71289 + 2.71289i −0.479576 + 0.479576i
\(33\) 5.69071 + 6.98536i 0.990625 + 1.21600i
\(34\) 1.35170i 0.231815i
\(35\) 0 0
\(36\) 2.11020 + 0.435588i 0.351700 + 0.0725981i
\(37\) 1.71171 + 1.71171i 0.281404 + 0.281404i 0.833669 0.552265i \(-0.186236\pi\)
−0.552265 + 0.833669i \(0.686236\pi\)
\(38\) −1.05693 1.05693i −0.171456 0.171456i
\(39\) 0.808099 7.91217i 0.129399 1.26696i
\(40\) 0 0
\(41\) 1.82176i 0.284511i 0.989830 + 0.142255i \(0.0454354\pi\)
−0.989830 + 0.142255i \(0.954565\pi\)
\(42\) 1.52031 1.23854i 0.234589 0.191110i
\(43\) 0.281771 0.281771i 0.0429697 0.0429697i −0.685295 0.728265i \(-0.740327\pi\)
0.728265 + 0.685295i \(0.240327\pi\)
\(44\) −3.73616 −0.563247
\(45\) 0 0
\(46\) −9.01279 −1.32886
\(47\) −3.39588 + 3.39588i −0.495340 + 0.495340i −0.909984 0.414644i \(-0.863906\pi\)
0.414644 + 0.909984i \(0.363906\pi\)
\(48\) 2.74973 2.24010i 0.396890 0.323331i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0.210113 2.05723i 0.0294217 0.288071i
\(52\) 2.33204 + 2.33204i 0.323396 + 0.323396i
\(53\) 3.51059 + 3.51059i 0.482216 + 0.482216i 0.905839 0.423623i \(-0.139242\pi\)
−0.423623 + 0.905839i \(0.639242\pi\)
\(54\) −5.61073 1.76850i −0.763523 0.240662i
\(55\) 0 0
\(56\) 3.07745i 0.411242i
\(57\) −1.44431 1.77289i −0.191303 0.234825i
\(58\) −3.50868 + 3.50868i −0.460713 + 0.460713i
\(59\) −1.81772 −0.236647 −0.118323 0.992975i \(-0.537752\pi\)
−0.118323 + 0.992975i \(0.537752\pi\)
\(60\) 0 0
\(61\) −2.47514 −0.316909 −0.158455 0.987366i \(-0.550651\pi\)
−0.158455 + 0.987366i \(0.550651\pi\)
\(62\) −1.36494 + 1.36494i −0.173347 + 0.173347i
\(63\) 2.50636 1.64868i 0.315772 0.207714i
\(64\) 8.43900i 1.05488i
\(65\) 0 0
\(66\) 10.1479 + 1.03644i 1.24912 + 0.127577i
\(67\) −7.92132 7.92132i −0.967743 0.967743i 0.0317530 0.999496i \(-0.489891\pi\)
−0.999496 + 0.0317530i \(0.989891\pi\)
\(68\) 0.606352 + 0.606352i 0.0735309 + 0.0735309i
\(69\) −13.7171 1.40098i −1.65134 0.168658i
\(70\) 0 0
\(71\) 9.06358i 1.07565i −0.843057 0.537825i \(-0.819246\pi\)
0.843057 0.537825i \(-0.180754\pi\)
\(72\) 7.71322 5.07373i 0.909011 0.597944i
\(73\) 1.33856 1.33856i 0.156666 0.156666i −0.624422 0.781088i \(-0.714665\pi\)
0.781088 + 0.624422i \(0.214665\pi\)
\(74\) 2.74064 0.318592
\(75\) 0 0
\(76\) 0.948239 0.108771
\(77\) −3.67830 + 3.67830i −0.419182 + 0.419182i
\(78\) −5.68718 6.98104i −0.643947 0.790447i
\(79\) 11.5015i 1.29402i 0.762481 + 0.647011i \(0.223981\pi\)
−0.762481 + 0.647011i \(0.776019\pi\)
\(80\) 0 0
\(81\) −8.26437 3.56372i −0.918264 0.395969i
\(82\) 1.45841 + 1.45841i 0.161055 + 0.161055i
\(83\) −5.46196 5.46196i −0.599528 0.599528i 0.340659 0.940187i \(-0.389350\pi\)
−0.940187 + 0.340659i \(0.889350\pi\)
\(84\) −0.126398 + 1.23757i −0.0137911 + 0.135030i
\(85\) 0 0
\(86\) 0.451146i 0.0486483i
\(87\) −5.88546 + 4.79466i −0.630988 + 0.514041i
\(88\) −11.3198 + 11.3198i −1.20669 + 1.20669i
\(89\) 9.43116 0.999701 0.499850 0.866112i \(-0.333388\pi\)
0.499850 + 0.866112i \(0.333388\pi\)
\(90\) 0 0
\(91\) 4.59186 0.481357
\(92\) 4.04298 4.04298i 0.421510 0.421510i
\(93\) −2.28954 + 1.86520i −0.237414 + 0.193412i
\(94\) 5.43717i 0.560801i
\(95\) 0 0
\(96\) −0.675186 + 6.61080i −0.0689109 + 0.674712i
\(97\) 3.06315 + 3.06315i 0.311016 + 0.311016i 0.845303 0.534287i \(-0.179420\pi\)
−0.534287 + 0.845303i \(0.679420\pi\)
\(98\) 0.800553 + 0.800553i 0.0808681 + 0.0808681i
\(99\) 15.2835 + 3.15483i 1.53605 + 0.317072i
\(100\) 0 0
\(101\) 3.71640i 0.369796i 0.982758 + 0.184898i \(0.0591954\pi\)
−0.982758 + 0.184898i \(0.940805\pi\)
\(102\) −1.47872 1.81513i −0.146415 0.179725i
\(103\) −1.18049 + 1.18049i −0.116317 + 0.116317i −0.762869 0.646553i \(-0.776210\pi\)
0.646553 + 0.762869i \(0.276210\pi\)
\(104\) 14.1312 1.38568
\(105\) 0 0
\(106\) 5.62082 0.545943
\(107\) −1.38009 + 1.38009i −0.133418 + 0.133418i −0.770662 0.637244i \(-0.780074\pi\)
0.637244 + 0.770662i \(0.280074\pi\)
\(108\) 3.31019 1.72356i 0.318523 0.165849i
\(109\) 5.93506i 0.568475i −0.958754 0.284238i \(-0.908260\pi\)
0.958754 0.284238i \(-0.0917405\pi\)
\(110\) 0 0
\(111\) 4.17113 + 0.426013i 0.395906 + 0.0404353i
\(112\) 1.44794 + 1.44794i 0.136817 + 0.136817i
\(113\) 0.240664 + 0.240664i 0.0226398 + 0.0226398i 0.718336 0.695696i \(-0.244904\pi\)
−0.695696 + 0.718336i \(0.744904\pi\)
\(114\) −2.57554 0.263049i −0.241221 0.0246368i
\(115\) 0 0
\(116\) 3.14787i 0.292272i
\(117\) −7.57049 11.5089i −0.699892 1.06399i
\(118\) −1.45518 + 1.45518i −0.133960 + 0.133960i
\(119\) 1.19392 0.109447
\(120\) 0 0
\(121\) −16.0598 −1.45998
\(122\) −1.98148 + 1.98148i −0.179395 + 0.179395i
\(123\) 1.99294 + 2.44634i 0.179697 + 0.220579i
\(124\) 1.22457i 0.109970i
\(125\) 0 0
\(126\) 0.686624 3.32633i 0.0611693 0.296333i
\(127\) 4.55939 + 4.55939i 0.404581 + 0.404581i 0.879844 0.475263i \(-0.157647\pi\)
−0.475263 + 0.879844i \(0.657647\pi\)
\(128\) 1.33009 + 1.33009i 0.117565 + 0.117565i
\(129\) 0.0701274 0.686624i 0.00617437 0.0604538i
\(130\) 0 0
\(131\) 13.6784i 1.19509i 0.801837 + 0.597543i \(0.203856\pi\)
−0.801837 + 0.597543i \(0.796144\pi\)
\(132\) −5.01709 + 4.08723i −0.436682 + 0.355748i
\(133\) 0.933556 0.933556i 0.0809495 0.0809495i
\(134\) −12.6829 −1.09563
\(135\) 0 0
\(136\) 3.67424 0.315064
\(137\) 10.0232 10.0232i 0.856337 0.856337i −0.134567 0.990904i \(-0.542964\pi\)
0.990904 + 0.134567i \(0.0429643\pi\)
\(138\) −12.1028 + 9.85969i −1.03026 + 0.839313i
\(139\) 15.8262i 1.34236i 0.741292 + 0.671182i \(0.234213\pi\)
−0.741292 + 0.671182i \(0.765787\pi\)
\(140\) 0 0
\(141\) −0.845170 + 8.27513i −0.0711761 + 0.696892i
\(142\) −7.25588 7.25588i −0.608900 0.608900i
\(143\) 16.8902 + 16.8902i 1.41243 + 1.41243i
\(144\) 1.24187 6.01623i 0.103490 0.501353i
\(145\) 0 0
\(146\) 2.14317i 0.177370i
\(147\) 1.09397 + 1.34285i 0.0902288 + 0.110756i
\(148\) −1.22940 + 1.22940i −0.101056 + 0.101056i
\(149\) −9.30594 −0.762373 −0.381186 0.924498i \(-0.624484\pi\)
−0.381186 + 0.924498i \(0.624484\pi\)
\(150\) 0 0
\(151\) −16.8274 −1.36939 −0.684697 0.728827i \(-0.740066\pi\)
−0.684697 + 0.728827i \(0.740066\pi\)
\(152\) 2.87297 2.87297i 0.233029 0.233029i
\(153\) −1.96840 2.99241i −0.159135 0.241922i
\(154\) 5.88936i 0.474578i
\(155\) 0 0
\(156\) 5.68275 + 0.580400i 0.454984 + 0.0464692i
\(157\) −6.80647 6.80647i −0.543216 0.543216i 0.381255 0.924470i \(-0.375492\pi\)
−0.924470 + 0.381255i \(0.875492\pi\)
\(158\) 9.20757 + 9.20757i 0.732515 + 0.732515i
\(159\) 8.55464 + 0.873717i 0.678427 + 0.0692903i
\(160\) 0 0
\(161\) 7.96075i 0.627395i
\(162\) −9.46902 + 3.76312i −0.743957 + 0.295659i
\(163\) −8.77966 + 8.77966i −0.687676 + 0.687676i −0.961718 0.274042i \(-0.911639\pi\)
0.274042 + 0.961718i \(0.411639\pi\)
\(164\) −1.30844 −0.102172
\(165\) 0 0
\(166\) −8.74519 −0.678758
\(167\) 12.4516 12.4516i 0.963532 0.963532i −0.0358258 0.999358i \(-0.511406\pi\)
0.999358 + 0.0358258i \(0.0114062\pi\)
\(168\) 3.36663 + 4.13255i 0.259741 + 0.318833i
\(169\) 8.08513i 0.621933i
\(170\) 0 0
\(171\) −3.87896 0.800698i −0.296632 0.0612309i
\(172\) 0.202376 + 0.202376i 0.0154310 + 0.0154310i
\(173\) −13.7966 13.7966i −1.04894 1.04894i −0.998739 0.0501977i \(-0.984015\pi\)
−0.0501977 0.998739i \(-0.515985\pi\)
\(174\) −0.873244 + 8.55000i −0.0662004 + 0.648174i
\(175\) 0 0
\(176\) 10.6519i 0.802916i
\(177\) −2.44092 + 1.98852i −0.183471 + 0.149466i
\(178\) 7.55015 7.55015i 0.565907 0.565907i
\(179\) −7.03160 −0.525567 −0.262783 0.964855i \(-0.584640\pi\)
−0.262783 + 0.964855i \(0.584640\pi\)
\(180\) 0 0
\(181\) 14.1873 1.05454 0.527268 0.849699i \(-0.323216\pi\)
0.527268 + 0.849699i \(0.323216\pi\)
\(182\) 3.67602 3.67602i 0.272485 0.272485i
\(183\) −3.32374 + 2.70772i −0.245698 + 0.200161i
\(184\) 24.4988i 1.80608i
\(185\) 0 0
\(186\) −0.339706 + 3.32609i −0.0249085 + 0.243881i
\(187\) 4.39161 + 4.39161i 0.321147 + 0.321147i
\(188\) −2.43902 2.43902i −0.177884 0.177884i
\(189\) 1.56207 4.95580i 0.113624 0.360481i
\(190\) 0 0
\(191\) 15.6450i 1.13203i −0.824394 0.566017i \(-0.808484\pi\)
0.824394 0.566017i \(-0.191516\pi\)
\(192\) 9.23199 + 11.3323i 0.666261 + 0.817838i
\(193\) −9.00959 + 9.00959i −0.648525 + 0.648525i −0.952636 0.304112i \(-0.901640\pi\)
0.304112 + 0.952636i \(0.401640\pi\)
\(194\) 4.90443 0.352118
\(195\) 0 0
\(196\) −0.718229 −0.0513021
\(197\) 2.78986 2.78986i 0.198769 0.198769i −0.600703 0.799472i \(-0.705113\pi\)
0.799472 + 0.600703i \(0.205113\pi\)
\(198\) 14.7609 9.70965i 1.04901 0.690035i
\(199\) 14.4320i 1.02306i 0.859266 + 0.511528i \(0.170920\pi\)
−0.859266 + 0.511528i \(0.829080\pi\)
\(200\) 0 0
\(201\) −19.3028 1.97146i −1.36151 0.139056i
\(202\) 2.97518 + 2.97518i 0.209333 + 0.209333i
\(203\) −3.09912 3.09912i −0.217516 0.217516i
\(204\) 1.47757 + 0.150909i 0.103450 + 0.0105658i
\(205\) 0 0
\(206\) 1.89009i 0.131689i
\(207\) −19.9525 + 13.1247i −1.38680 + 0.912231i
\(208\) 6.64871 6.64871i 0.461005 0.461005i
\(209\) 6.86780 0.475056
\(210\) 0 0
\(211\) 11.9845 0.825049 0.412524 0.910947i \(-0.364647\pi\)
0.412524 + 0.910947i \(0.364647\pi\)
\(212\) −2.52140 + 2.52140i −0.173171 + 0.173171i
\(213\) −9.91525 12.1710i −0.679382 0.833943i
\(214\) 2.20967i 0.151050i
\(215\) 0 0
\(216\) 4.80718 15.2512i 0.327087 1.03772i
\(217\) −1.20561 1.20561i −0.0818422 0.0818422i
\(218\) −4.75133 4.75133i −0.321801 0.321801i
\(219\) 0.333141 3.26181i 0.0225116 0.220413i
\(220\) 0 0
\(221\) 5.48233i 0.368781i
\(222\) 3.68025 2.99816i 0.247003 0.201224i
\(223\) 12.1834 12.1834i 0.815858 0.815858i −0.169647 0.985505i \(-0.554263\pi\)
0.985505 + 0.169647i \(0.0542628\pi\)
\(224\) −3.83661 −0.256344
\(225\) 0 0
\(226\) 0.385328 0.0256317
\(227\) 4.17335 4.17335i 0.276995 0.276995i −0.554913 0.831908i \(-0.687249\pi\)
0.831908 + 0.554913i \(0.187249\pi\)
\(228\) 1.27334 1.03734i 0.0843290 0.0686996i
\(229\) 27.2705i 1.80209i −0.433730 0.901043i \(-0.642803\pi\)
0.433730 0.901043i \(-0.357197\pi\)
\(230\) 0 0
\(231\) −0.915459 + 8.96334i −0.0602328 + 0.589744i
\(232\) −9.53740 9.53740i −0.626161 0.626161i
\(233\) 1.96791 + 1.96791i 0.128922 + 0.128922i 0.768624 0.639701i \(-0.220942\pi\)
−0.639701 + 0.768624i \(0.720942\pi\)
\(234\) −15.2740 3.15288i −0.998495 0.206110i
\(235\) 0 0
\(236\) 1.30554i 0.0849832i
\(237\) 12.5823 + 15.4448i 0.817306 + 1.00325i
\(238\) 0.955800 0.955800i 0.0619553 0.0619553i
\(239\) 1.42942 0.0924613 0.0462307 0.998931i \(-0.485279\pi\)
0.0462307 + 0.998931i \(0.485279\pi\)
\(240\) 0 0
\(241\) 29.1319 1.87655 0.938274 0.345893i \(-0.112424\pi\)
0.938274 + 0.345893i \(0.112424\pi\)
\(242\) −12.8567 + 12.8567i −0.826463 + 0.826463i
\(243\) −14.9964 + 4.25541i −0.962018 + 0.272985i
\(244\) 1.77772i 0.113807i
\(245\) 0 0
\(246\) 3.55388 + 0.362971i 0.226587 + 0.0231422i
\(247\) −4.28675 4.28675i −0.272759 0.272759i
\(248\) −3.71021 3.71021i −0.235598 0.235598i
\(249\) −13.3098 1.35938i −0.843473 0.0861470i
\(250\) 0 0
\(251\) 12.3977i 0.782538i 0.920276 + 0.391269i \(0.127964\pi\)
−0.920276 + 0.391269i \(0.872036\pi\)
\(252\) 1.18413 + 1.80014i 0.0745931 + 0.113398i
\(253\) 29.2821 29.2821i 1.84095 1.84095i
\(254\) 7.30007 0.458047
\(255\) 0 0
\(256\) −14.7484 −0.921774
\(257\) −13.8717 + 13.8717i −0.865290 + 0.865290i −0.991947 0.126657i \(-0.959575\pi\)
0.126657 + 0.991947i \(0.459575\pi\)
\(258\) −0.493538 0.605820i −0.0307263 0.0377167i
\(259\) 2.42073i 0.150417i
\(260\) 0 0
\(261\) −2.65808 + 12.8770i −0.164531 + 0.797066i
\(262\) 10.9503 + 10.9503i 0.676511 + 0.676511i
\(263\) −12.2912 12.2912i −0.757909 0.757909i 0.218032 0.975942i \(-0.430036\pi\)
−0.975942 + 0.218032i \(0.930036\pi\)
\(264\) −2.81728 + 27.5842i −0.173392 + 1.69769i
\(265\) 0 0
\(266\) 1.49472i 0.0916473i
\(267\) 12.6646 10.3174i 0.775061 0.631413i
\(268\) 5.68932 5.68932i 0.347530 0.347530i
\(269\) 19.1535 1.16781 0.583906 0.811822i \(-0.301524\pi\)
0.583906 + 0.811822i \(0.301524\pi\)
\(270\) 0 0
\(271\) 18.4629 1.12154 0.560771 0.827971i \(-0.310505\pi\)
0.560771 + 0.827971i \(0.310505\pi\)
\(272\) 1.72872 1.72872i 0.104819 0.104819i
\(273\) 6.16616 5.02333i 0.373193 0.304026i
\(274\) 16.0482i 0.969505i
\(275\) 0 0
\(276\) 1.00622 9.85200i 0.0605674 0.593020i
\(277\) 7.66076 + 7.66076i 0.460290 + 0.460290i 0.898751 0.438460i \(-0.144476\pi\)
−0.438460 + 0.898751i \(0.644476\pi\)
\(278\) 12.6698 + 12.6698i 0.759881 + 0.759881i
\(279\) −1.03404 + 5.00936i −0.0619061 + 0.299903i
\(280\) 0 0
\(281\) 20.4646i 1.22082i −0.792087 0.610408i \(-0.791005\pi\)
0.792087 0.610408i \(-0.208995\pi\)
\(282\) 5.94808 + 7.30129i 0.354203 + 0.434785i
\(283\) −8.24528 + 8.24528i −0.490131 + 0.490131i −0.908347 0.418216i \(-0.862655\pi\)
0.418216 + 0.908347i \(0.362655\pi\)
\(284\) 6.50972 0.386281
\(285\) 0 0
\(286\) 27.0431 1.59909
\(287\) −1.28818 + 1.28818i −0.0760387 + 0.0760387i
\(288\) 6.32533 + 9.61593i 0.372723 + 0.566624i
\(289\) 15.5745i 0.916150i
\(290\) 0 0
\(291\) 7.46433 + 0.762360i 0.437567 + 0.0446903i
\(292\) 0.961389 + 0.961389i 0.0562610 + 0.0562610i
\(293\) 19.7225 + 19.7225i 1.15220 + 1.15220i 0.986111 + 0.166088i \(0.0531135\pi\)
0.166088 + 0.986111i \(0.446886\pi\)
\(294\) 1.95080 + 0.199242i 0.113773 + 0.0116200i
\(295\) 0 0
\(296\) 7.44968i 0.433004i
\(297\) 23.9747 12.4832i 1.39115 0.724348i
\(298\) −7.44990 + 7.44990i −0.431561 + 0.431561i
\(299\) −36.5546 −2.11401
\(300\) 0 0
\(301\) 0.398485 0.0229683
\(302\) −13.4712 + 13.4712i −0.775182 + 0.775182i
\(303\) 4.06562 + 4.99056i 0.233564 + 0.286700i
\(304\) 2.70346i 0.155054i
\(305\) 0 0
\(306\) −3.97139 0.819776i −0.227029 0.0468635i
\(307\) 13.2997 + 13.2997i 0.759057 + 0.759057i 0.976151 0.217094i \(-0.0696578\pi\)
−0.217094 + 0.976151i \(0.569658\pi\)
\(308\) −2.64186 2.64186i −0.150534 0.150534i
\(309\) −0.293801 + 2.87663i −0.0167137 + 0.163646i
\(310\) 0 0
\(311\) 23.8049i 1.34985i −0.737885 0.674926i \(-0.764176\pi\)
0.737885 0.674926i \(-0.235824\pi\)
\(312\) 18.9761 15.4591i 1.07431 0.875197i
\(313\) 18.9352 18.9352i 1.07028 1.07028i 0.0729475 0.997336i \(-0.476759\pi\)
0.997336 0.0729475i \(-0.0232406\pi\)
\(314\) −10.8979 −0.615003
\(315\) 0 0
\(316\) −8.26072 −0.464702
\(317\) −11.6929 + 11.6929i −0.656739 + 0.656739i −0.954607 0.297868i \(-0.903725\pi\)
0.297868 + 0.954607i \(0.403725\pi\)
\(318\) 7.54790 6.14899i 0.423265 0.344818i
\(319\) 22.7990i 1.27650i
\(320\) 0 0
\(321\) −0.343478 + 3.36302i −0.0191711 + 0.187706i
\(322\) −6.37301 6.37301i −0.355154 0.355154i
\(323\) −1.11459 1.11459i −0.0620177 0.0620177i
\(324\) 2.55957 5.93571i 0.142198 0.329762i
\(325\) 0 0
\(326\) 14.0572i 0.778555i
\(327\) −6.49275 7.96987i −0.359050 0.440735i
\(328\) −3.96430 + 3.96430i −0.218892 + 0.218892i
\(329\) −4.80250 −0.264771
\(330\) 0 0
\(331\) −11.5898 −0.637031 −0.318516 0.947918i \(-0.603184\pi\)
−0.318516 + 0.947918i \(0.603184\pi\)
\(332\) 3.92294 3.92294i 0.215299 0.215299i
\(333\) 6.06723 3.99100i 0.332482 0.218706i
\(334\) 19.9363i 1.09087i
\(335\) 0 0
\(336\) 3.52835 + 0.360363i 0.192487 + 0.0196594i
\(337\) 5.46127 + 5.46127i 0.297494 + 0.297494i 0.840032 0.542537i \(-0.182536\pi\)
−0.542537 + 0.840032i \(0.682536\pi\)
\(338\) −6.47258 6.47258i −0.352062 0.352062i
\(339\) 0.586453 + 0.0598966i 0.0318517 + 0.00325314i
\(340\) 0 0
\(341\) 8.86920i 0.480294i
\(342\) −3.74632 + 2.46431i −0.202578 + 0.133255i
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 1.22632 0.0661186
\(345\) 0 0
\(346\) −22.0898 −1.18756
\(347\) 20.1982 20.1982i 1.08430 1.08430i 0.0881938 0.996103i \(-0.471891\pi\)
0.996103 0.0881938i \(-0.0281095\pi\)
\(348\) −3.44366 4.22711i −0.184600 0.226597i
\(349\) 11.9748i 0.640997i −0.947249 0.320498i \(-0.896150\pi\)
0.947249 0.320498i \(-0.103850\pi\)
\(350\) 0 0
\(351\) −22.7563 7.17278i −1.21464 0.382855i
\(352\) −14.1122 14.1122i −0.752183 0.752183i
\(353\) −24.3423 24.3423i −1.29561 1.29561i −0.931264 0.364345i \(-0.881293\pi\)
−0.364345 0.931264i \(-0.618707\pi\)
\(354\) −0.362166 + 3.54600i −0.0192489 + 0.188468i
\(355\) 0 0
\(356\) 6.77373i 0.359007i
\(357\) 1.60326 1.30611i 0.0848534 0.0691268i
\(358\) −5.62917 + 5.62917i −0.297511 + 0.297511i
\(359\) 14.2164 0.750314 0.375157 0.926961i \(-0.377589\pi\)
0.375157 + 0.926961i \(0.377589\pi\)
\(360\) 0 0
\(361\) 17.2569 0.908260
\(362\) 11.3577 11.3577i 0.596948 0.596948i
\(363\) −21.5659 + 17.5689i −1.13192 + 0.922129i
\(364\) 3.29800i 0.172862i
\(365\) 0 0
\(366\) −0.493153 + 4.82850i −0.0257775 + 0.252390i
\(367\) −16.7024 16.7024i −0.871859 0.871859i 0.120816 0.992675i \(-0.461449\pi\)
−0.992675 + 0.120816i \(0.961449\pi\)
\(368\) −11.5267 11.5267i −0.600868 0.600868i
\(369\) 5.35243 + 1.10485i 0.278636 + 0.0575163i
\(370\) 0 0
\(371\) 4.96472i 0.257755i
\(372\) −1.33964 1.64441i −0.0694572 0.0852589i
\(373\) −4.57877 + 4.57877i −0.237080 + 0.237080i −0.815640 0.578560i \(-0.803615\pi\)
0.578560 + 0.815640i \(0.303615\pi\)
\(374\) 7.03144 0.363587
\(375\) 0 0
\(376\) −14.7795 −0.762193
\(377\) −14.2307 + 14.2307i −0.732920 + 0.732920i
\(378\) −2.71686 5.21790i −0.139740 0.268380i
\(379\) 12.6506i 0.649816i 0.945746 + 0.324908i \(0.105333\pi\)
−0.945746 + 0.324908i \(0.894667\pi\)
\(380\) 0 0
\(381\) 11.1104 + 1.13474i 0.569202 + 0.0581347i
\(382\) −12.5247 12.5247i −0.640818 0.640818i
\(383\) 18.0165 + 18.0165i 0.920601 + 0.920601i 0.997072 0.0764705i \(-0.0243651\pi\)
−0.0764705 + 0.997072i \(0.524365\pi\)
\(384\) 3.24119 + 0.331035i 0.165401 + 0.0168930i
\(385\) 0 0
\(386\) 14.4253i 0.734229i
\(387\) −0.656973 0.998748i −0.0333958 0.0507692i
\(388\) −2.20004 + 2.20004i −0.111690 + 0.111690i
\(389\) 17.7215 0.898517 0.449259 0.893402i \(-0.351688\pi\)
0.449259 + 0.893402i \(0.351688\pi\)
\(390\) 0 0
\(391\) −9.50453 −0.480665
\(392\) −2.17609 + 2.17609i −0.109909 + 0.109909i
\(393\) 14.9637 + 18.3680i 0.754819 + 0.926543i
\(394\) 4.46686i 0.225037i
\(395\) 0 0
\(396\) −2.26589 + 10.9771i −0.113865 + 0.551618i
\(397\) −4.43035 4.43035i −0.222353 0.222353i 0.587136 0.809489i \(-0.300255\pi\)
−0.809489 + 0.587136i \(0.800255\pi\)
\(398\) 11.5536 + 11.5536i 0.579128 + 0.579128i
\(399\) 0.232344 2.27490i 0.0116317 0.113887i
\(400\) 0 0
\(401\) 34.4780i 1.72175i 0.508818 + 0.860874i \(0.330082\pi\)
−0.508818 + 0.860874i \(0.669918\pi\)
\(402\) −17.0312 + 13.8746i −0.849437 + 0.692004i
\(403\) −5.53599 + 5.53599i −0.275767 + 0.275767i
\(404\) −2.66923 −0.132799
\(405\) 0 0
\(406\) −4.96203 −0.246261
\(407\) −8.90417 + 8.90417i −0.441364 + 0.441364i
\(408\) 4.93395 4.01950i 0.244267 0.198995i
\(409\) 19.5663i 0.967490i −0.875209 0.483745i \(-0.839276\pi\)
0.875209 0.483745i \(-0.160724\pi\)
\(410\) 0 0
\(411\) 2.49457 24.4246i 0.123048 1.20478i
\(412\) −0.847860 0.847860i −0.0417711 0.0417711i
\(413\) −1.28532 1.28532i −0.0632465 0.0632465i
\(414\) −5.46604 + 26.4801i −0.268641 + 1.30143i
\(415\) 0 0
\(416\) 17.6171i 0.863751i
\(417\) 17.3134 + 21.2522i 0.847840 + 1.04073i
\(418\) 5.49804 5.49804i 0.268918 0.268918i
\(419\) 17.0209 0.831524 0.415762 0.909474i \(-0.363515\pi\)
0.415762 + 0.909474i \(0.363515\pi\)
\(420\) 0 0
\(421\) 21.7474 1.05990 0.529951 0.848028i \(-0.322210\pi\)
0.529951 + 0.848028i \(0.322210\pi\)
\(422\) 9.59425 9.59425i 0.467041 0.467041i
\(423\) 7.91778 + 12.0368i 0.384976 + 0.585250i
\(424\) 15.2787i 0.741998i
\(425\) 0 0
\(426\) −17.6812 1.80585i −0.856658 0.0874936i
\(427\) −1.75019 1.75019i −0.0846976 0.0846976i
\(428\) −0.991221 0.991221i −0.0479125 0.0479125i
\(429\) 41.1583 + 4.20365i 1.98714 + 0.202954i
\(430\) 0 0
\(431\) 10.7912i 0.519796i 0.965636 + 0.259898i \(0.0836889\pi\)
−0.965636 + 0.259898i \(0.916311\pi\)
\(432\) −4.91391 9.43745i −0.236420 0.454059i
\(433\) −0.466927 + 0.466927i −0.0224391 + 0.0224391i −0.718237 0.695798i \(-0.755051\pi\)
0.695798 + 0.718237i \(0.255051\pi\)
\(434\) −1.93031 −0.0926579
\(435\) 0 0
\(436\) 4.26273 0.204148
\(437\) −7.43180 + 7.43180i −0.355511 + 0.355511i
\(438\) −2.34456 2.87795i −0.112027 0.137514i
\(439\) 9.43662i 0.450385i 0.974314 + 0.225193i \(0.0723011\pi\)
−0.974314 + 0.225193i \(0.927699\pi\)
\(440\) 0 0
\(441\) 2.93806 + 0.606476i 0.139908 + 0.0288798i
\(442\) −4.38889 4.38889i −0.208758 0.208758i
\(443\) 16.8956 + 16.8956i 0.802734 + 0.802734i 0.983522 0.180788i \(-0.0578647\pi\)
−0.180788 + 0.983522i \(0.557865\pi\)
\(444\) −0.305975 + 2.99582i −0.0145209 + 0.142175i
\(445\) 0 0
\(446\) 19.5068i 0.923676i
\(447\) −12.4965 + 10.1804i −0.591062 + 0.481516i
\(448\) −5.96728 + 5.96728i −0.281927 + 0.281927i
\(449\) 11.5643 0.545753 0.272876 0.962049i \(-0.412025\pi\)
0.272876 + 0.962049i \(0.412025\pi\)
\(450\) 0 0
\(451\) −9.47661 −0.446236
\(452\) −0.172852 + 0.172852i −0.00813026 + 0.00813026i
\(453\) −22.5966 + 18.4086i −1.06168 + 0.864912i
\(454\) 6.68197i 0.313601i
\(455\) 0 0
\(456\) 0.715027 7.00090i 0.0334842 0.327847i
\(457\) 17.8413 + 17.8413i 0.834580 + 0.834580i 0.988139 0.153560i \(-0.0490737\pi\)
−0.153560 + 0.988139i \(0.549074\pi\)
\(458\) −21.8315 21.8315i −1.02012 1.02012i
\(459\) −5.91685 1.86499i −0.276175 0.0870502i
\(460\) 0 0
\(461\) 13.0571i 0.608129i −0.952651 0.304064i \(-0.901656\pi\)
0.952651 0.304064i \(-0.0983438\pi\)
\(462\) 6.44276 + 7.90850i 0.299744 + 0.367937i
\(463\) −17.3925 + 17.3925i −0.808298 + 0.808298i −0.984376 0.176079i \(-0.943659\pi\)
0.176079 + 0.984376i \(0.443659\pi\)
\(464\) −8.97466 −0.416638
\(465\) 0 0
\(466\) 3.15084 0.145960
\(467\) 9.40605 9.40605i 0.435260 0.435260i −0.455153 0.890413i \(-0.650415\pi\)
0.890413 + 0.455153i \(0.150415\pi\)
\(468\) 8.26600 5.43734i 0.382096 0.251341i
\(469\) 11.2024i 0.517280i
\(470\) 0 0
\(471\) −16.5861 1.69400i −0.764247 0.0780554i
\(472\) −3.95551 3.95551i −0.182067 0.182067i
\(473\) 1.46575 + 1.46575i 0.0673951 + 0.0673951i
\(474\) 22.4371 + 2.29159i 1.03057 + 0.105256i
\(475\) 0 0
\(476\) 0.857511i 0.0393039i
\(477\) 12.4434 8.18522i 0.569744 0.374776i
\(478\) 1.14432 1.14432i 0.0523402 0.0523402i
\(479\) −38.8689 −1.77596 −0.887982 0.459879i \(-0.847893\pi\)
−0.887982 + 0.459879i \(0.847893\pi\)
\(480\) 0 0
\(481\) 11.1156 0.506829
\(482\) 23.3216 23.3216i 1.06227 1.06227i
\(483\) −8.70879 10.6901i −0.396264 0.486415i
\(484\) 11.5346i 0.524301i
\(485\) 0 0
\(486\) −8.59872 + 15.4121i −0.390046 + 0.699106i
\(487\) −23.9549 23.9549i −1.08550 1.08550i −0.995985 0.0895148i \(-0.971468\pi\)
−0.0895148 0.995985i \(-0.528532\pi\)
\(488\) −5.38612 5.38612i −0.243818 0.243818i
\(489\) −2.18509 + 21.3944i −0.0988131 + 0.967488i
\(490\) 0 0
\(491\) 25.6453i 1.15736i 0.815556 + 0.578678i \(0.196431\pi\)
−0.815556 + 0.578678i \(0.803569\pi\)
\(492\) −1.75703 + 1.43139i −0.0792132 + 0.0645319i
\(493\) −3.70012 + 3.70012i −0.166645 + 0.166645i
\(494\) −6.86355 −0.308806
\(495\) 0 0
\(496\) −3.49129 −0.156764
\(497\) 6.40892 6.40892i 0.287479 0.287479i
\(498\) −11.7434 + 9.56694i −0.526236 + 0.428705i
\(499\) 29.1057i 1.30295i 0.758669 + 0.651476i \(0.225850\pi\)
−0.758669 + 0.651476i \(0.774150\pi\)
\(500\) 0 0
\(501\) 3.09896 30.3422i 0.138451 1.35559i
\(502\) 9.92505 + 9.92505i 0.442976 + 0.442976i
\(503\) −10.1763 10.1763i −0.453738 0.453738i 0.442855 0.896593i \(-0.353965\pi\)
−0.896593 + 0.442855i \(0.853965\pi\)
\(504\) 9.04173 + 1.86640i 0.402751 + 0.0831361i
\(505\) 0 0
\(506\) 46.8837i 2.08423i
\(507\) −8.84486 10.8571i −0.392814 0.482181i
\(508\) −3.27469 + 3.27469i −0.145291 + 0.145291i
\(509\) −31.2970 −1.38721 −0.693607 0.720354i \(-0.743979\pi\)
−0.693607 + 0.720354i \(0.743979\pi\)
\(510\) 0 0
\(511\) 1.89300 0.0837415
\(512\) −14.4671 + 14.4671i −0.639360 + 0.639360i
\(513\) −6.08479 + 3.16824i −0.268650 + 0.139881i
\(514\) 22.2100i 0.979641i
\(515\) 0 0
\(516\) 0.493153 + 0.0503675i 0.0217098 + 0.00221731i
\(517\) −17.6651 17.6651i −0.776908 0.776908i
\(518\) 1.93792 + 1.93792i 0.0851474 + 0.0851474i
\(519\) −33.6198 3.43371i −1.47574 0.150723i
\(520\) 0 0
\(521\) 24.4644i 1.07180i 0.844280 + 0.535902i \(0.180028\pi\)
−0.844280 + 0.535902i \(0.819972\pi\)
\(522\) 8.18078 + 12.4366i 0.358063 + 0.544337i
\(523\) −1.82790 + 1.82790i −0.0799284 + 0.0799284i −0.745941 0.666012i \(-0.768000\pi\)
0.666012 + 0.745941i \(0.268000\pi\)
\(524\) −9.82422 −0.429173
\(525\) 0 0
\(526\) −19.6796 −0.858069
\(527\) −1.43941 + 1.43941i −0.0627015 + 0.0627015i
\(528\) 11.6528 + 14.3039i 0.507123 + 0.622495i
\(529\) 40.3736i 1.75537i
\(530\) 0 0
\(531\) −1.10240 + 5.34056i −0.0478402 + 0.231761i
\(532\) 0.670507 + 0.670507i 0.0290701 + 0.0290701i
\(533\) 5.91512 + 5.91512i 0.256212 + 0.256212i
\(534\) 1.87909 18.3983i 0.0813160 0.796172i
\(535\) 0 0
\(536\) 34.4749i 1.48909i
\(537\) −9.44237 + 7.69234i −0.407468 + 0.331949i
\(538\) 15.3334 15.3334i 0.661071 0.661071i
\(539\) −5.20191 −0.224062
\(540\) 0 0
\(541\) 41.8839 1.80073 0.900364 0.435137i \(-0.143300\pi\)
0.900364 + 0.435137i \(0.143300\pi\)
\(542\) 14.7805 14.7805i 0.634879 0.634879i
\(543\) 19.0514 15.5205i 0.817575 0.666047i
\(544\) 4.58061i 0.196392i
\(545\) 0 0
\(546\) 0.914892 8.95779i 0.0391538 0.383358i
\(547\) 21.6813 + 21.6813i 0.927024 + 0.927024i 0.997513 0.0704885i \(-0.0224558\pi\)
−0.0704885 + 0.997513i \(0.522456\pi\)
\(548\) 7.19893 + 7.19893i 0.307523 + 0.307523i
\(549\) −1.50111 + 7.27211i −0.0640660 + 0.310366i
\(550\) 0 0
\(551\) 5.78641i 0.246509i
\(552\) −26.8009 32.8982i −1.14072 1.40024i
\(553\) −8.13280 + 8.13280i −0.345842 + 0.345842i
\(554\) 12.2657 0.521119
\(555\) 0 0
\(556\) −11.3669 −0.482063
\(557\) −13.1204 + 13.1204i −0.555929 + 0.555929i −0.928146 0.372217i \(-0.878598\pi\)
0.372217 + 0.928146i \(0.378598\pi\)
\(558\) 3.18246 + 4.83806i 0.134724 + 0.204811i
\(559\) 1.82978i 0.0773916i
\(560\) 0 0
\(561\) 10.7015 + 1.09299i 0.451819 + 0.0461460i
\(562\) −16.3830 16.3830i −0.691076 0.691076i
\(563\) 15.9166 + 15.9166i 0.670804 + 0.670804i 0.957901 0.287097i \(-0.0926903\pi\)
−0.287097 + 0.957901i \(0.592690\pi\)
\(564\) −5.94344 0.607025i −0.250264 0.0255604i
\(565\) 0 0
\(566\) 13.2016i 0.554903i
\(567\) −3.32386 8.36373i −0.139589 0.351244i
\(568\) 19.7231 19.7231i 0.827565 0.827565i
\(569\) −27.8303 −1.16671 −0.583354 0.812218i \(-0.698260\pi\)
−0.583354 + 0.812218i \(0.698260\pi\)
\(570\) 0 0
\(571\) −4.11555 −0.172230 −0.0861151 0.996285i \(-0.527445\pi\)
−0.0861151 + 0.996285i \(0.527445\pi\)
\(572\) −12.1311 + 12.1311i −0.507225 + 0.507225i
\(573\) −17.1151 21.0089i −0.714994 0.877658i
\(574\) 2.06251i 0.0860874i
\(575\) 0 0
\(576\) 24.7943 + 5.11805i 1.03310 + 0.213252i
\(577\) 15.3143 + 15.3143i 0.637542 + 0.637542i 0.949949 0.312406i \(-0.101135\pi\)
−0.312406 + 0.949949i \(0.601135\pi\)
\(578\) 12.4683 + 12.4683i 0.518611 + 0.518611i
\(579\) −2.24231 + 21.9547i −0.0931874 + 0.912406i
\(580\) 0 0
\(581\) 7.72438i 0.320461i
\(582\) 6.58590 5.36528i 0.272994 0.222398i
\(583\) −18.2617 + 18.2617i −0.756324 + 0.756324i
\(584\) 5.82563 0.241066
\(585\) 0 0
\(586\) 31.5778 1.30447
\(587\) −23.2211 + 23.2211i −0.958439 + 0.958439i −0.999170 0.0407314i \(-0.987031\pi\)
0.0407314 + 0.999170i \(0.487031\pi\)
\(588\) −0.964471 + 0.785718i −0.0397741 + 0.0324025i
\(589\) 2.25101i 0.0927512i
\(590\) 0 0
\(591\) 0.694342 6.79837i 0.0285614 0.279647i
\(592\) 3.50506 + 3.50506i 0.144057 + 0.144057i
\(593\) −24.2941 24.2941i −0.997641 0.997641i 0.00235668 0.999997i \(-0.499250\pi\)
−0.999997 + 0.00235668i \(0.999250\pi\)
\(594\) 9.19956 29.1865i 0.377463 1.19754i
\(595\) 0 0
\(596\) 6.68380i 0.273779i
\(597\) 15.7881 + 19.3799i 0.646164 + 0.793169i
\(598\) −29.2639 + 29.2639i −1.19669 + 1.19669i
\(599\) 22.7865 0.931029 0.465515 0.885040i \(-0.345869\pi\)
0.465515 + 0.885040i \(0.345869\pi\)
\(600\) 0 0
\(601\) −41.7276 −1.70210 −0.851052 0.525082i \(-0.824035\pi\)
−0.851052 + 0.525082i \(0.824035\pi\)
\(602\) 0.319008 0.319008i 0.0130018 0.0130018i
\(603\) −28.0774 + 18.4692i −1.14340 + 0.752124i
\(604\) 12.0859i 0.491769i
\(605\) 0 0
\(606\) 7.24995 + 0.740464i 0.294509 + 0.0300793i
\(607\) 17.5164 + 17.5164i 0.710968 + 0.710968i 0.966738 0.255770i \(-0.0823289\pi\)
−0.255770 + 0.966738i \(0.582329\pi\)
\(608\) 3.58168 + 3.58168i 0.145256 + 0.145256i
\(609\) −7.55198 0.771312i −0.306022 0.0312551i
\(610\) 0 0
\(611\) 22.0524i 0.892144i
\(612\) 2.14923 1.41376i 0.0868776 0.0571478i
\(613\) 25.9860 25.9860i 1.04956 1.04956i 0.0508591 0.998706i \(-0.483804\pi\)
0.998706 0.0508591i \(-0.0161959\pi\)
\(614\) 21.2943 0.859369
\(615\) 0 0
\(616\) −16.0086 −0.645005
\(617\) 8.12737 8.12737i 0.327196 0.327196i −0.524323 0.851519i \(-0.675682\pi\)
0.851519 + 0.524323i \(0.175682\pi\)
\(618\) 2.06769 + 2.53810i 0.0831747 + 0.102097i
\(619\) 7.20599i 0.289633i −0.989459 0.144817i \(-0.953741\pi\)
0.989459 0.144817i \(-0.0462592\pi\)
\(620\) 0 0
\(621\) −12.4352 + 39.4519i −0.499008 + 1.58315i
\(622\) −19.0571 19.0571i −0.764120 0.764120i
\(623\) 6.66884 + 6.66884i 0.267181 + 0.267181i
\(624\) 1.65474 16.2017i 0.0662424 0.648586i
\(625\) 0 0
\(626\) 30.3173i 1.21172i
\(627\) 9.22241 7.51314i 0.368307 0.300046i
\(628\) 4.88860 4.88860i 0.195077 0.195077i
\(629\) 2.89017 0.115238
\(630\) 0 0
\(631\) −29.8770 −1.18938 −0.594692 0.803954i \(-0.702726\pi\)
−0.594692 + 0.803954i \(0.702726\pi\)
\(632\) −25.0283 + 25.0283i −0.995572 + 0.995572i
\(633\) 16.0934 13.1107i 0.639655 0.521102i
\(634\) 18.7216i 0.743530i
\(635\) 0 0
\(636\) −0.627529 + 6.14419i −0.0248831 + 0.243633i
\(637\) 3.24693 + 3.24693i 0.128648 + 0.128648i
\(638\) −18.2518 18.2518i −0.722597 0.722597i
\(639\) −26.6293 5.49684i −1.05344 0.217452i
\(640\) 0 0
\(641\) 19.3661i 0.764917i 0.923973 + 0.382458i \(0.124922\pi\)
−0.923973 + 0.382458i \(0.875078\pi\)
\(642\) 2.41731 + 2.96725i 0.0954035 + 0.117108i
\(643\) −11.6091 + 11.6091i −0.457819 + 0.457819i −0.897939 0.440120i \(-0.854936\pi\)
0.440120 + 0.897939i \(0.354936\pi\)
\(644\) 5.71764 0.225307
\(645\) 0 0
\(646\) −1.78458 −0.0702135
\(647\) −10.6517 + 10.6517i −0.418760 + 0.418760i −0.884776 0.466016i \(-0.845689\pi\)
0.466016 + 0.884776i \(0.345689\pi\)
\(648\) −10.2290 25.7390i −0.401834 1.01112i
\(649\) 9.45560i 0.371165i
\(650\) 0 0
\(651\) −2.93785 0.300053i −0.115143 0.0117600i
\(652\) −6.30580 6.30580i −0.246954 0.246954i
\(653\) −3.67307 3.67307i −0.143738 0.143738i 0.631576 0.775314i \(-0.282408\pi\)
−0.775314 + 0.631576i \(0.782408\pi\)
\(654\) −11.5781 1.18251i −0.452740 0.0462400i
\(655\) 0 0
\(656\) 3.73039i 0.145647i
\(657\) −3.12095 4.74456i −0.121760 0.185103i
\(658\) −3.84466 + 3.84466i −0.149880 + 0.149880i
\(659\) 45.6844 1.77961 0.889807 0.456338i \(-0.150839\pi\)
0.889807 + 0.456338i \(0.150839\pi\)
\(660\) 0 0
\(661\) −21.8518 −0.849935 −0.424968 0.905209i \(-0.639715\pi\)
−0.424968 + 0.905209i \(0.639715\pi\)
\(662\) −9.27823 + 9.27823i −0.360609 + 0.360609i
\(663\) −5.99748 7.36192i −0.232923 0.285913i
\(664\) 23.7714i 0.922510i
\(665\) 0 0
\(666\) 1.66213 8.05215i 0.0644062 0.312014i
\(667\) 24.6714 + 24.6714i 0.955279 + 0.955279i
\(668\) 8.94308 + 8.94308i 0.346018 + 0.346018i
\(669\) 3.03220 29.6886i 0.117232 1.14783i
\(670\) 0 0
\(671\) 12.8755i 0.497051i
\(672\) −5.15197 + 4.19712i −0.198742 + 0.161907i
\(673\) −12.1963 + 12.1963i −0.470132 + 0.470132i −0.901957 0.431825i \(-0.857870\pi\)
0.431825 + 0.901957i \(0.357870\pi\)
\(674\) 8.74408 0.336809
\(675\) 0 0
\(676\) 5.80698 0.223345
\(677\) 30.0858 30.0858i 1.15629 1.15629i 0.171025 0.985267i \(-0.445292\pi\)
0.985267 0.171025i \(-0.0547080\pi\)
\(678\) 0.517437 0.421536i 0.0198721 0.0161890i
\(679\) 4.33195i 0.166245i
\(680\) 0 0
\(681\) 1.03867 10.1697i 0.0398018 0.389703i
\(682\) −7.10027 7.10027i −0.271883 0.271883i
\(683\) −1.48486 1.48486i −0.0568166 0.0568166i 0.678128 0.734944i \(-0.262792\pi\)
−0.734944 + 0.678128i \(0.762792\pi\)
\(684\) 0.575084 2.78598i 0.0219889 0.106525i
\(685\) 0 0
\(686\) 1.13215i 0.0432258i
\(687\) −29.8330 36.6201i −1.13820 1.39714i
\(688\) 0.576980 0.576980i 0.0219972 0.0219972i
\(689\) 22.7973 0.868507
\(690\) 0 0
\(691\) 42.2833 1.60853 0.804267 0.594269i \(-0.202558\pi\)
0.804267 + 0.594269i \(0.202558\pi\)
\(692\) 9.90912 9.90912i 0.376688 0.376688i
\(693\) 8.57627 + 13.0379i 0.325785 + 0.495268i
\(694\) 32.3395i 1.22759i
\(695\) 0 0
\(696\) −23.2409 2.37368i −0.880943 0.0899740i
\(697\) 1.53799 + 1.53799i 0.0582553 + 0.0582553i
\(698\) −9.58647 9.58647i −0.362853 0.362853i
\(699\) 4.79544 + 0.489776i 0.181380 + 0.0185250i
\(700\) 0 0
\(701\) 42.8399i 1.61804i −0.587781 0.809020i \(-0.699998\pi\)
0.587781 0.809020i \(-0.300002\pi\)
\(702\) −23.9598 + 12.4755i −0.904306 + 0.470856i
\(703\) 2.25988 2.25988i 0.0852332 0.0852332i
\(704\) −43.8989 −1.65450
\(705\) 0 0
\(706\) −38.9746 −1.46683
\(707\) −2.62789 + 2.62789i −0.0988320 + 0.0988320i
\(708\) −1.42821 1.75314i −0.0536756 0.0658869i
\(709\) 21.7856i 0.818175i 0.912495 + 0.409087i \(0.134153\pi\)
−0.912495 + 0.409087i \(0.865847\pi\)
\(710\) 0 0
\(711\) 33.7921 + 6.97539i 1.26730 + 0.261598i
\(712\) 20.5230 + 20.5230i 0.769133 + 0.769133i
\(713\) 9.59756 + 9.59756i 0.359432 + 0.359432i
\(714\) 0.237880 2.32911i 0.00890244 0.0871646i
\(715\) 0 0
\(716\) 5.05030i 0.188739i
\(717\) 1.91949 1.56373i 0.0716846 0.0583987i
\(718\) 11.3810 11.3810i 0.424735 0.424735i
\(719\) 45.9617 1.71408 0.857041 0.515249i \(-0.172301\pi\)
0.857041 + 0.515249i \(0.172301\pi\)
\(720\) 0 0
\(721\) −1.66946 −0.0621740
\(722\) 13.8151 13.8151i 0.514145 0.514145i
\(723\) 39.1196 31.8693i 1.45487 1.18523i
\(724\) 10.1898i 0.378699i
\(725\) 0 0
\(726\) −3.19980 + 31.3295i −0.118756 + 1.16275i
\(727\) 4.37251 + 4.37251i 0.162168 + 0.162168i 0.783526 0.621359i \(-0.213419\pi\)
−0.621359 + 0.783526i \(0.713419\pi\)
\(728\) 9.99228 + 9.99228i 0.370338 + 0.370338i
\(729\) −15.4826 + 22.1199i −0.573428 + 0.819256i
\(730\) 0 0
\(731\) 0.475760i 0.0175966i
\(732\) −1.94476 2.38720i −0.0718805 0.0882336i
\(733\) 32.0267 32.0267i 1.18293 1.18293i 0.203952 0.978981i \(-0.434621\pi\)
0.978981 0.203952i \(-0.0653787\pi\)
\(734\) −26.7423 −0.987078
\(735\) 0 0
\(736\) 30.5423 1.12580
\(737\) 41.2059 41.2059i 1.51784 1.51784i
\(738\) 5.16940 3.40041i 0.190288 0.125171i
\(739\) 19.8100i 0.728722i 0.931258 + 0.364361i \(0.118713\pi\)
−0.931258 + 0.364361i \(0.881287\pi\)
\(740\) 0 0
\(741\) −10.4460 1.06689i −0.383744 0.0391932i
\(742\) 3.97452 + 3.97452i 0.145909 + 0.145909i
\(743\) −14.6828 14.6828i −0.538660 0.538660i 0.384475 0.923135i \(-0.374382\pi\)
−0.923135 + 0.384475i \(0.874382\pi\)
\(744\) −9.04108 0.923399i −0.331462 0.0338535i
\(745\) 0 0
\(746\) 7.33110i 0.268411i
\(747\) −19.3601 + 12.7350i −0.708350 + 0.465950i
\(748\) −3.15418 + 3.15418i −0.115328 + 0.115328i
\(749\) −1.95174 −0.0713151
\(750\) 0 0
\(751\) −26.6832 −0.973682 −0.486841 0.873491i \(-0.661851\pi\)
−0.486841 + 0.873491i \(0.661851\pi\)
\(752\) −6.95371 + 6.95371i −0.253576 + 0.253576i
\(753\) 13.5627 + 16.6483i 0.494252 + 0.606696i
\(754\) 22.7849i 0.829777i
\(755\) 0 0
\(756\) 3.55940 + 1.12192i 0.129454 + 0.0408039i
\(757\) 4.11078 + 4.11078i 0.149409 + 0.149409i 0.777854 0.628445i \(-0.216308\pi\)
−0.628445 + 0.777854i \(0.716308\pi\)
\(758\) 10.1275 + 10.1275i 0.367846 + 0.367846i
\(759\) 7.28774 71.3549i 0.264528 2.59002i
\(760\) 0 0
\(761\) 22.2859i 0.807862i 0.914789 + 0.403931i \(0.132356\pi\)
−0.914789 + 0.403931i \(0.867644\pi\)
\(762\) 9.80288 7.98603i 0.355121 0.289303i
\(763\) 4.19672 4.19672i 0.151931 0.151931i
\(764\) 11.2367 0.406530
\(765\) 0 0
\(766\) 28.8464 1.04226
\(767\) −5.90201 + 5.90201i −0.213109 + 0.213109i
\(768\) −19.8048 + 16.1342i −0.714645 + 0.582194i
\(769\) 37.7021i 1.35957i −0.733410 0.679786i \(-0.762073\pi\)
0.733410 0.679786i \(-0.237927\pi\)
\(770\) 0 0
\(771\) −3.45239 + 33.8026i −0.124335 + 1.21737i
\(772\) −6.47095 6.47095i −0.232895 0.232895i
\(773\) 20.5564 + 20.5564i 0.739362 + 0.739362i 0.972455 0.233093i \(-0.0748845\pi\)
−0.233093 + 0.972455i \(0.574884\pi\)
\(774\) −1.32549 0.273609i −0.0476438 0.00983467i
\(775\) 0 0
\(776\) 13.3314i 0.478568i
\(777\) 2.64820 + 3.25067i 0.0950035 + 0.116617i
\(778\) 14.1870 14.1870i 0.508630 0.508630i
\(779\) 2.40517 0.0861741