Properties

Label 13.3.d.a.5.1
Level 13
Weight 3
Character 13.5
Analytic conductor 0.354
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 13.d (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.354224343668\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{10})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.1
Root \(-1.58114 + 1.58114i\)
Character \(\chi\) = 13.5
Dual form 13.3.d.a.8.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(-2.58114 + 2.58114i) q^{2}\) \(+2.16228 q^{3}\) \(-9.32456i q^{4}\) \(+(0.418861 - 0.418861i) q^{5}\) \(+(-5.58114 + 5.58114i) q^{6}\) \(+(-1.41886 - 1.41886i) q^{7}\) \(+(13.7434 + 13.7434i) q^{8}\) \(-4.32456 q^{9}\) \(+O(q^{10})\) \(q\)\(+(-2.58114 + 2.58114i) q^{2}\) \(+2.16228 q^{3}\) \(-9.32456i q^{4}\) \(+(0.418861 - 0.418861i) q^{5}\) \(+(-5.58114 + 5.58114i) q^{6}\) \(+(-1.41886 - 1.41886i) q^{7}\) \(+(13.7434 + 13.7434i) q^{8}\) \(-4.32456 q^{9}\) \(+2.16228i q^{10}\) \(+(-7.32456 - 7.32456i) q^{11}\) \(-20.1623i q^{12}\) \(+(9.90569 + 8.41886i) q^{13}\) \(+7.32456 q^{14}\) \(+(0.905694 - 0.905694i) q^{15}\) \(-33.6491 q^{16}\) \(+15.9737i q^{17}\) \(+(11.1623 - 11.1623i) q^{18}\) \(+(-3.16228 + 3.16228i) q^{19}\) \(+(-3.90569 - 3.90569i) q^{20}\) \(+(-3.06797 - 3.06797i) q^{21}\) \(+37.8114 q^{22}\) \(-27.4868i q^{23}\) \(+(29.7171 + 29.7171i) q^{24}\) \(+24.6491i q^{25}\) \(+(-47.2982 + 3.83772i) q^{26}\) \(-28.8114 q^{27}\) \(+(-13.2302 + 13.2302i) q^{28}\) \(+25.8114 q^{29}\) \(+4.67544i q^{30}\) \(+(19.4868 - 19.4868i) q^{31}\) \(+(31.8794 - 31.8794i) q^{32}\) \(+(-15.8377 - 15.8377i) q^{33}\) \(+(-41.2302 - 41.2302i) q^{34}\) \(-1.18861 q^{35}\) \(+40.3246i q^{36}\) \(+(-4.23025 - 4.23025i) q^{37}\) \(-16.3246i q^{38}\) \(+(21.4189 + 18.2039i) q^{39}\) \(+11.5132 q^{40}\) \(+(11.1623 - 11.1623i) q^{41}\) \(+15.8377 q^{42}\) \(+11.5132i q^{43}\) \(+(-68.2982 + 68.2982i) q^{44}\) \(+(-1.81139 + 1.81139i) q^{45}\) \(+(70.9473 + 70.9473i) q^{46}\) \(+(35.3662 + 35.3662i) q^{47}\) \(-72.7587 q^{48}\) \(-44.9737i q^{49}\) \(+(-63.6228 - 63.6228i) q^{50}\) \(+34.5395i q^{51}\) \(+(78.5021 - 92.3662i) q^{52}\) \(-4.18861 q^{53}\) \(+(74.3662 - 74.3662i) q^{54}\) \(-6.13594 q^{55}\) \(-39.0000i q^{56}\) \(+(-6.83772 + 6.83772i) q^{57}\) \(+(-66.6228 + 66.6228i) q^{58}\) \(+(-30.2719 - 30.2719i) q^{59}\) \(+(-8.44520 - 8.44520i) q^{60}\) \(-67.6754 q^{61}\) \(+100.596i q^{62}\) \(+(6.13594 + 6.13594i) q^{63}\) \(+29.9737i q^{64}\) \(+(7.67544 - 0.622777i) q^{65}\) \(+81.7587 q^{66}\) \(+(-81.0833 + 81.0833i) q^{67}\) \(+148.947 q^{68}\) \(-59.4342i q^{69}\) \(+(3.06797 - 3.06797i) q^{70}\) \(+(50.4452 - 50.4452i) q^{71}\) \(+(-59.4342 - 59.4342i) q^{72}\) \(+(-31.6228 - 31.6228i) q^{73}\) \(+21.8377 q^{74}\) \(+53.2982i q^{75}\) \(+(29.4868 + 29.4868i) q^{76}\) \(+20.7851i q^{77}\) \(+(-102.272 + 8.29822i) q^{78}\) \(+50.7851 q^{79}\) \(+(-14.0943 + 14.0943i) q^{80}\) \(-23.3772 q^{81}\) \(+57.6228i q^{82}\) \(+(18.6228 - 18.6228i) q^{83}\) \(+(-28.6075 + 28.6075i) q^{84}\) \(+(6.69075 + 6.69075i) q^{85}\) \(+(-29.7171 - 29.7171i) q^{86}\) \(+55.8114 q^{87}\) \(-201.329i q^{88}\) \(+(91.1096 + 91.1096i) q^{89}\) \(-9.35089i q^{90}\) \(+(-2.10961 - 26.0000i) q^{91}\) \(-256.302 q^{92}\) \(+(42.1359 - 42.1359i) q^{93}\) \(-182.570 q^{94}\) \(+2.64911i q^{95}\) \(+(68.9320 - 68.9320i) q^{96}\) \(+(87.3552 - 87.3552i) q^{97}\) \(+(116.083 + 116.083i) q^{98}\) \(+(31.6754 + 31.6754i) q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 28q^{15} \) \(\mathstrut -\mathstrut 84q^{16} \) \(\mathstrut +\mathstrut 32q^{18} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut +\mathstrut 32q^{21} \) \(\mathstrut +\mathstrut 88q^{22} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut -\mathstrut 88q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 40q^{29} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 20q^{32} \) \(\mathstrut -\mathstrut 76q^{33} \) \(\mathstrut -\mathstrut 108q^{34} \) \(\mathstrut -\mathstrut 68q^{35} \) \(\mathstrut +\mathstrut 40q^{37} \) \(\mathstrut +\mathstrut 92q^{39} \) \(\mathstrut +\mathstrut 84q^{40} \) \(\mathstrut +\mathstrut 32q^{41} \) \(\mathstrut +\mathstrut 76q^{42} \) \(\mathstrut -\mathstrut 172q^{44} \) \(\mathstrut +\mathstrut 56q^{45} \) \(\mathstrut +\mathstrut 132q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 76q^{48} \) \(\mathstrut -\mathstrut 128q^{50} \) \(\mathstrut +\mathstrut 80q^{52} \) \(\mathstrut -\mathstrut 80q^{53} \) \(\mathstrut +\mathstrut 152q^{54} \) \(\mathstrut +\mathstrut 64q^{55} \) \(\mathstrut -\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 140q^{58} \) \(\mathstrut +\mathstrut 56q^{59} \) \(\mathstrut -\mathstrut 116q^{60} \) \(\mathstrut -\mathstrut 296q^{61} \) \(\mathstrut -\mathstrut 64q^{63} \) \(\mathstrut +\mathstrut 56q^{65} \) \(\mathstrut +\mathstrut 112q^{66} \) \(\mathstrut -\mathstrut 84q^{67} \) \(\mathstrut +\mathstrut 444q^{68} \) \(\mathstrut -\mathstrut 32q^{70} \) \(\mathstrut +\mathstrut 284q^{71} \) \(\mathstrut -\mathstrut 48q^{72} \) \(\mathstrut +\mathstrut 100q^{74} \) \(\mathstrut +\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 232q^{78} \) \(\mathstrut +\mathstrut 64q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut -\mathstrut 220q^{81} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 184q^{84} \) \(\mathstrut -\mathstrut 144q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 160q^{87} \) \(\mathstrut +\mathstrut 200q^{89} \) \(\mathstrut +\mathstrut 156q^{91} \) \(\mathstrut -\mathstrut 456q^{92} \) \(\mathstrut +\mathstrut 80q^{93} \) \(\mathstrut -\mathstrut 452q^{94} \) \(\mathstrut +\mathstrut 320q^{96} \) \(\mathstrut -\mathstrut 68q^{97} \) \(\mathstrut +\mathstrut 224q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58114 + 2.58114i −1.29057 + 1.29057i −0.356135 + 0.934435i \(0.615906\pi\)
−0.934435 + 0.356135i \(0.884094\pi\)
\(3\) 2.16228 0.720759 0.360380 0.932806i \(-0.382647\pi\)
0.360380 + 0.932806i \(0.382647\pi\)
\(4\) 9.32456i 2.33114i
\(5\) 0.418861 0.418861i 0.0837722 0.0837722i −0.663979 0.747751i \(-0.731134\pi\)
0.747751 + 0.663979i \(0.231134\pi\)
\(6\) −5.58114 + 5.58114i −0.930190 + 0.930190i
\(7\) −1.41886 1.41886i −0.202694 0.202694i 0.598459 0.801153i \(-0.295780\pi\)
−0.801153 + 0.598459i \(0.795780\pi\)
\(8\) 13.7434 + 13.7434i 1.71793 + 1.71793i
\(9\) −4.32456 −0.480506
\(10\) 2.16228i 0.216228i
\(11\) −7.32456 7.32456i −0.665869 0.665869i 0.290888 0.956757i \(-0.406049\pi\)
−0.956757 + 0.290888i \(0.906049\pi\)
\(12\) 20.1623i 1.68019i
\(13\) 9.90569 + 8.41886i 0.761976 + 0.647605i
\(14\) 7.32456 0.523183
\(15\) 0.905694 0.905694i 0.0603796 0.0603796i
\(16\) −33.6491 −2.10307
\(17\) 15.9737i 0.939627i 0.882766 + 0.469814i \(0.155679\pi\)
−0.882766 + 0.469814i \(0.844321\pi\)
\(18\) 11.1623 11.1623i 0.620127 0.620127i
\(19\) −3.16228 + 3.16228i −0.166436 + 0.166436i −0.785411 0.618975i \(-0.787548\pi\)
0.618975 + 0.785411i \(0.287548\pi\)
\(20\) −3.90569 3.90569i −0.195285 0.195285i
\(21\) −3.06797 3.06797i −0.146094 0.146094i
\(22\) 37.8114 1.71870
\(23\) 27.4868i 1.19508i −0.801839 0.597540i \(-0.796145\pi\)
0.801839 0.597540i \(-0.203855\pi\)
\(24\) 29.7171 + 29.7171i 1.23821 + 1.23821i
\(25\) 24.6491i 0.985964i
\(26\) −47.2982 + 3.83772i −1.81916 + 0.147605i
\(27\) −28.8114 −1.06709
\(28\) −13.2302 + 13.2302i −0.472509 + 0.472509i
\(29\) 25.8114 0.890048 0.445024 0.895519i \(-0.353195\pi\)
0.445024 + 0.895519i \(0.353195\pi\)
\(30\) 4.67544i 0.155848i
\(31\) 19.4868 19.4868i 0.628608 0.628608i −0.319110 0.947718i \(-0.603384\pi\)
0.947718 + 0.319110i \(0.103384\pi\)
\(32\) 31.8794 31.8794i 0.996230 0.996230i
\(33\) −15.8377 15.8377i −0.479931 0.479931i
\(34\) −41.2302 41.2302i −1.21265 1.21265i
\(35\) −1.18861 −0.0339603
\(36\) 40.3246i 1.12013i
\(37\) −4.23025 4.23025i −0.114331 0.114331i 0.647627 0.761958i \(-0.275762\pi\)
−0.761958 + 0.647627i \(0.775762\pi\)
\(38\) 16.3246i 0.429594i
\(39\) 21.4189 + 18.2039i 0.549202 + 0.466767i
\(40\) 11.5132 0.287829
\(41\) 11.1623 11.1623i 0.272251 0.272251i −0.557755 0.830006i \(-0.688337\pi\)
0.830006 + 0.557755i \(0.188337\pi\)
\(42\) 15.8377 0.377089
\(43\) 11.5132i 0.267748i 0.990998 + 0.133874i \(0.0427418\pi\)
−0.990998 + 0.133874i \(0.957258\pi\)
\(44\) −68.2982 + 68.2982i −1.55223 + 1.55223i
\(45\) −1.81139 + 1.81139i −0.0402531 + 0.0402531i
\(46\) 70.9473 + 70.9473i 1.54233 + 1.54233i
\(47\) 35.3662 + 35.3662i 0.752472 + 0.752472i 0.974940 0.222468i \(-0.0714112\pi\)
−0.222468 + 0.974940i \(0.571411\pi\)
\(48\) −72.7587 −1.51581
\(49\) 44.9737i 0.917830i
\(50\) −63.6228 63.6228i −1.27246 1.27246i
\(51\) 34.5395i 0.677245i
\(52\) 78.5021 92.3662i 1.50966 1.77627i
\(53\) −4.18861 −0.0790304 −0.0395152 0.999219i \(-0.512581\pi\)
−0.0395152 + 0.999219i \(0.512581\pi\)
\(54\) 74.3662 74.3662i 1.37715 1.37715i
\(55\) −6.13594 −0.111563
\(56\) 39.0000i 0.696429i
\(57\) −6.83772 + 6.83772i −0.119960 + 0.119960i
\(58\) −66.6228 + 66.6228i −1.14867 + 1.14867i
\(59\) −30.2719 30.2719i −0.513083 0.513083i 0.402387 0.915470i \(-0.368181\pi\)
−0.915470 + 0.402387i \(0.868181\pi\)
\(60\) −8.44520 8.44520i −0.140753 0.140753i
\(61\) −67.6754 −1.10943 −0.554717 0.832039i \(-0.687173\pi\)
−0.554717 + 0.832039i \(0.687173\pi\)
\(62\) 100.596i 1.62252i
\(63\) 6.13594 + 6.13594i 0.0973959 + 0.0973959i
\(64\) 29.9737i 0.468339i
\(65\) 7.67544 0.622777i 0.118084 0.00958118i
\(66\) 81.7587 1.23877
\(67\) −81.0833 + 81.0833i −1.21020 + 1.21020i −0.239237 + 0.970961i \(0.576897\pi\)
−0.970961 + 0.239237i \(0.923103\pi\)
\(68\) 148.947 2.19040
\(69\) 59.4342i 0.861365i
\(70\) 3.06797 3.06797i 0.0438282 0.0438282i
\(71\) 50.4452 50.4452i 0.710496 0.710496i −0.256143 0.966639i \(-0.582452\pi\)
0.966639 + 0.256143i \(0.0824518\pi\)
\(72\) −59.4342 59.4342i −0.825475 0.825475i
\(73\) −31.6228 31.6228i −0.433189 0.433189i 0.456523 0.889712i \(-0.349095\pi\)
−0.889712 + 0.456523i \(0.849095\pi\)
\(74\) 21.8377 0.295104
\(75\) 53.2982i 0.710643i
\(76\) 29.4868 + 29.4868i 0.387985 + 0.387985i
\(77\) 20.7851i 0.269936i
\(78\) −102.272 + 8.29822i −1.31118 + 0.106387i
\(79\) 50.7851 0.642849 0.321424 0.946935i \(-0.395838\pi\)
0.321424 + 0.946935i \(0.395838\pi\)
\(80\) −14.0943 + 14.0943i −0.176179 + 0.176179i
\(81\) −23.3772 −0.288608
\(82\) 57.6228i 0.702717i
\(83\) 18.6228 18.6228i 0.224371 0.224371i −0.585965 0.810336i \(-0.699285\pi\)
0.810336 + 0.585965i \(0.199285\pi\)
\(84\) −28.6075 + 28.6075i −0.340565 + 0.340565i
\(85\) 6.69075 + 6.69075i 0.0787147 + 0.0787147i
\(86\) −29.7171 29.7171i −0.345547 0.345547i
\(87\) 55.8114 0.641510
\(88\) 201.329i 2.28783i
\(89\) 91.1096 + 91.1096i 1.02370 + 1.02370i 0.999712 + 0.0239913i \(0.00763740\pi\)
0.0239913 + 0.999712i \(0.492363\pi\)
\(90\) 9.35089i 0.103899i
\(91\) −2.10961 26.0000i −0.0231825 0.285714i
\(92\) −256.302 −2.78590
\(93\) 42.1359 42.1359i 0.453075 0.453075i
\(94\) −182.570 −1.94224
\(95\) 2.64911i 0.0278854i
\(96\) 68.9320 68.9320i 0.718042 0.718042i
\(97\) 87.3552 87.3552i 0.900569 0.900569i −0.0949165 0.995485i \(-0.530258\pi\)
0.995485 + 0.0949165i \(0.0302584\pi\)
\(98\) 116.083 + 116.083i 1.18452 + 1.18452i
\(99\) 31.6754 + 31.6754i 0.319954 + 0.319954i
\(100\) 229.842 2.29842
\(101\) 8.92100i 0.0883267i 0.999024 + 0.0441634i \(0.0140622\pi\)
−0.999024 + 0.0441634i \(0.985938\pi\)
\(102\) −89.1512 89.1512i −0.874032 0.874032i
\(103\) 59.4342i 0.577031i −0.957475 0.288515i \(-0.906838\pi\)
0.957475 0.288515i \(-0.0931616\pi\)
\(104\) 20.4342 + 251.842i 0.196482 + 2.42156i
\(105\) −2.57011 −0.0244772
\(106\) 10.8114 10.8114i 0.101994 0.101994i
\(107\) −143.570 −1.34178 −0.670888 0.741558i \(-0.734087\pi\)
−0.670888 + 0.741558i \(0.734087\pi\)
\(108\) 268.653i 2.48753i
\(109\) −84.7740 + 84.7740i −0.777743 + 0.777743i −0.979447 0.201703i \(-0.935352\pi\)
0.201703 + 0.979447i \(0.435352\pi\)
\(110\) 15.8377 15.8377i 0.143979 0.143979i
\(111\) −9.14697 9.14697i −0.0824052 0.0824052i
\(112\) 47.7434 + 47.7434i 0.426281 + 0.426281i
\(113\) −108.544 −0.960564 −0.480282 0.877114i \(-0.659466\pi\)
−0.480282 + 0.877114i \(0.659466\pi\)
\(114\) 35.2982i 0.309634i
\(115\) −11.5132 11.5132i −0.100114 0.100114i
\(116\) 240.680i 2.07483i
\(117\) −42.8377 36.4078i −0.366134 0.311178i
\(118\) 156.272 1.32434
\(119\) 22.6644 22.6644i 0.190457 0.190457i
\(120\) 24.8947 0.207456
\(121\) 13.7018i 0.113238i
\(122\) 174.680 174.680i 1.43180 1.43180i
\(123\) 24.1359 24.1359i 0.196227 0.196227i
\(124\) −181.706 181.706i −1.46537 1.46537i
\(125\) 20.7961 + 20.7961i 0.166369 + 0.166369i
\(126\) −31.6754 −0.251392
\(127\) 94.8377i 0.746754i 0.927680 + 0.373377i \(0.121800\pi\)
−0.927680 + 0.373377i \(0.878200\pi\)
\(128\) 50.1512 + 50.1512i 0.391807 + 0.391807i
\(129\) 24.8947i 0.192982i
\(130\) −18.2039 + 21.4189i −0.140030 + 0.164760i
\(131\) −112.268 −0.857005 −0.428502 0.903541i \(-0.640959\pi\)
−0.428502 + 0.903541i \(0.640959\pi\)
\(132\) −147.680 + 147.680i −1.11879 + 1.11879i
\(133\) 8.97367 0.0674712
\(134\) 418.574i 3.12369i
\(135\) −12.0680 + 12.0680i −0.0893924 + 0.0893924i
\(136\) −219.533 + 219.533i −1.61421 + 1.61421i
\(137\) 86.7281 + 86.7281i 0.633052 + 0.633052i 0.948832 0.315780i \(-0.102266\pi\)
−0.315780 + 0.948832i \(0.602266\pi\)
\(138\) 153.408 + 153.408i 1.11165 + 1.11165i
\(139\) 78.5395 0.565032 0.282516 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(140\) 11.0833i 0.0791663i
\(141\) 76.4715 + 76.4715i 0.542351 + 0.542351i
\(142\) 260.412i 1.83389i
\(143\) −10.8904 134.219i −0.0761566 0.938596i
\(144\) 145.517 1.01054
\(145\) 10.8114 10.8114i 0.0745613 0.0745613i
\(146\) 163.246 1.11812
\(147\) 97.2456i 0.661534i
\(148\) −39.4452 + 39.4452i −0.266522 + 0.266522i
\(149\) −128.219 + 128.219i −0.860532 + 0.860532i −0.991400 0.130868i \(-0.958224\pi\)
0.130868 + 0.991400i \(0.458224\pi\)
\(150\) −137.570 137.570i −0.917134 0.917134i
\(151\) 29.1776 + 29.1776i 0.193229 + 0.193229i 0.797090 0.603861i \(-0.206372\pi\)
−0.603861 + 0.797090i \(0.706372\pi\)
\(152\) −86.9210 −0.571849
\(153\) 69.0790i 0.451497i
\(154\) −53.6491 53.6491i −0.348371 0.348371i
\(155\) 16.3246i 0.105320i
\(156\) 169.743 199.721i 1.08810 1.28027i
\(157\) 232.544 1.48117 0.740585 0.671962i \(-0.234548\pi\)
0.740585 + 0.671962i \(0.234548\pi\)
\(158\) −131.083 + 131.083i −0.829641 + 0.829641i
\(159\) −9.05694 −0.0569619
\(160\) 26.7061i 0.166913i
\(161\) −39.0000 + 39.0000i −0.242236 + 0.242236i
\(162\) 60.3399 60.3399i 0.372468 0.372468i
\(163\) 11.4605 + 11.4605i 0.0703098 + 0.0703098i 0.741387 0.671077i \(-0.234168\pi\)
−0.671077 + 0.741387i \(0.734168\pi\)
\(164\) −104.083 104.083i −0.634654 0.634654i
\(165\) −13.2676 −0.0804098
\(166\) 96.1359i 0.579132i
\(167\) −206.785 206.785i −1.23823 1.23823i −0.960722 0.277512i \(-0.910490\pi\)
−0.277512 0.960722i \(-0.589510\pi\)
\(168\) 84.3288i 0.501957i
\(169\) 27.2456 + 166.789i 0.161216 + 0.986919i
\(170\) −34.5395 −0.203174
\(171\) 13.6754 13.6754i 0.0799734 0.0799734i
\(172\) 107.355 0.624158
\(173\) 91.3815i 0.528217i 0.964493 + 0.264108i \(0.0850777\pi\)
−0.964493 + 0.264108i \(0.914922\pi\)
\(174\) −144.057 + 144.057i −0.827913 + 0.827913i
\(175\) 34.9737 34.9737i 0.199850 0.199850i
\(176\) 246.465 + 246.465i 1.40037 + 1.40037i
\(177\) −65.4562 65.4562i −0.369809 0.369809i
\(178\) −470.333 −2.64232
\(179\) 71.6712i 0.400398i 0.979755 + 0.200199i \(0.0641588\pi\)
−0.979755 + 0.200199i \(0.935841\pi\)
\(180\) 16.8904 + 16.8904i 0.0938355 + 0.0938355i
\(181\) 274.144i 1.51461i −0.653061 0.757305i \(-0.726516\pi\)
0.653061 0.757305i \(-0.273484\pi\)
\(182\) 72.5548 + 61.6644i 0.398653 + 0.338815i
\(183\) −146.333 −0.799634
\(184\) 377.763 377.763i 2.05306 2.05306i
\(185\) −3.54377 −0.0191555
\(186\) 217.517i 1.16945i
\(187\) 117.000 117.000i 0.625668 0.625668i
\(188\) 329.774 329.774i 1.75412 1.75412i
\(189\) 40.8794 + 40.8794i 0.216293 + 0.216293i
\(190\) −6.83772 6.83772i −0.0359880 0.0359880i
\(191\) 179.706 0.940869 0.470435 0.882435i \(-0.344097\pi\)
0.470435 + 0.882435i \(0.344097\pi\)
\(192\) 64.8114i 0.337559i
\(193\) −1.13594 1.13594i −0.00588572 0.00588572i 0.704158 0.710044i \(-0.251325\pi\)
−0.710044 + 0.704158i \(0.751325\pi\)
\(194\) 450.952i 2.32449i
\(195\) 16.5964 1.34662i 0.0851100 0.00690572i
\(196\) −419.359 −2.13959
\(197\) 141.906 141.906i 0.720333 0.720333i −0.248340 0.968673i \(-0.579885\pi\)
0.968673 + 0.248340i \(0.0798849\pi\)
\(198\) −163.517 −0.825846
\(199\) 259.759i 1.30532i 0.757651 + 0.652660i \(0.226347\pi\)
−0.757651 + 0.652660i \(0.773653\pi\)
\(200\) −338.763 + 338.763i −1.69381 + 1.69381i
\(201\) −175.325 + 175.325i −0.872261 + 0.872261i
\(202\) −23.0263 23.0263i −0.113992 0.113992i
\(203\) −36.6228 36.6228i −0.180408 0.180408i
\(204\) 322.065 1.57875
\(205\) 9.35089i 0.0456141i
\(206\) 153.408 + 153.408i 0.744698 + 0.744698i
\(207\) 118.868i 0.574243i
\(208\) −333.318 283.287i −1.60249 1.36196i
\(209\) 46.3246 0.221649
\(210\) 6.63381 6.63381i 0.0315896 0.0315896i
\(211\) 325.574 1.54301 0.771503 0.636225i \(-0.219505\pi\)
0.771503 + 0.636225i \(0.219505\pi\)
\(212\) 39.0569i 0.184231i
\(213\) 109.077 109.077i 0.512096 0.512096i
\(214\) 370.574 370.574i 1.73166 1.73166i
\(215\) 4.82242 + 4.82242i 0.0224299 + 0.0224299i
\(216\) −395.967 395.967i −1.83318 1.83318i
\(217\) −55.2982 −0.254831
\(218\) 437.627i 2.00746i
\(219\) −68.3772 68.3772i −0.312225 0.312225i
\(220\) 57.2149i 0.260068i
\(221\) −134.480 + 158.230i −0.608507 + 0.715974i
\(222\) 47.2192 0.212699
\(223\) −243.774 + 243.774i −1.09316 + 1.09316i −0.0979674 + 0.995190i \(0.531234\pi\)
−0.995190 + 0.0979674i \(0.968766\pi\)
\(224\) −90.4648 −0.403861
\(225\) 106.596i 0.473762i
\(226\) 280.167 280.167i 1.23968 1.23968i
\(227\) −100.732 + 100.732i −0.443755 + 0.443755i −0.893272 0.449517i \(-0.851596\pi\)
0.449517 + 0.893272i \(0.351596\pi\)
\(228\) 63.7587 + 63.7587i 0.279644 + 0.279644i
\(229\) −240.366 240.366i −1.04963 1.04963i −0.998702 0.0509319i \(-0.983781\pi\)
−0.0509319 0.998702i \(-0.516219\pi\)
\(230\) 59.4342 0.258409
\(231\) 44.9431i 0.194559i
\(232\) 354.737 + 354.737i 1.52904 + 1.52904i
\(233\) 10.7893i 0.0463061i 0.999732 + 0.0231531i \(0.00737051\pi\)
−0.999732 + 0.0231531i \(0.992629\pi\)
\(234\) 204.544 16.5964i 0.874119 0.0709250i
\(235\) 29.6271 0.126073
\(236\) −282.272 + 282.272i −1.19607 + 1.19607i
\(237\) 109.811 0.463339
\(238\) 117.000i 0.491597i
\(239\) −98.0153 + 98.0153i −0.410106 + 0.410106i −0.881775 0.471670i \(-0.843652\pi\)
0.471670 + 0.881775i \(0.343652\pi\)
\(240\) −30.4758 + 30.4758i −0.126983 + 0.126983i
\(241\) −196.197 196.197i −0.814096 0.814096i 0.171149 0.985245i \(-0.445252\pi\)
−0.985245 + 0.171149i \(0.945252\pi\)
\(242\) 35.3662 + 35.3662i 0.146141 + 0.146141i
\(243\) 208.754 0.859072
\(244\) 631.043i 2.58624i
\(245\) −18.8377 18.8377i −0.0768887 0.0768887i
\(246\) 124.596i 0.506490i
\(247\) −57.9473 + 4.70178i −0.234605 + 0.0190355i
\(248\) 535.631 2.15980
\(249\) 40.2676 40.2676i 0.161717 0.161717i
\(250\) −107.355 −0.429421
\(251\) 95.8420i 0.381841i 0.981606 + 0.190920i \(0.0611472\pi\)
−0.981606 + 0.190920i \(0.938853\pi\)
\(252\) 57.2149 57.2149i 0.227043 0.227043i
\(253\) −201.329 + 201.329i −0.795766 + 0.795766i
\(254\) −244.789 244.789i −0.963738 0.963738i
\(255\) 14.4673 + 14.4673i 0.0567343 + 0.0567343i
\(256\) −378.789 −1.47965
\(257\) 450.579i 1.75322i −0.481198 0.876612i \(-0.659798\pi\)
0.481198 0.876612i \(-0.340202\pi\)
\(258\) −64.2566 64.2566i −0.249057 0.249057i
\(259\) 12.0043i 0.0463485i
\(260\) −5.80711 71.5701i −0.0223351 0.275270i
\(261\) −111.623 −0.427673
\(262\) 289.778 289.778i 1.10602 1.10602i
\(263\) 166.982 0.634913 0.317457 0.948273i \(-0.397171\pi\)
0.317457 + 0.948273i \(0.397171\pi\)
\(264\) 435.329i 1.64897i
\(265\) −1.75445 + 1.75445i −0.00662055 + 0.00662055i
\(266\) −23.1623 + 23.1623i −0.0870762 + 0.0870762i
\(267\) 197.004 + 197.004i 0.737844 + 0.737844i
\(268\) 756.065 + 756.065i 2.82114 + 2.82114i
\(269\) 170.061 0.632198 0.316099 0.948726i \(-0.397627\pi\)
0.316099 + 0.948726i \(0.397627\pi\)
\(270\) 62.2982i 0.230734i
\(271\) −217.072 217.072i −0.801005 0.801005i 0.182248 0.983253i \(-0.441663\pi\)
−0.983253 + 0.182248i \(0.941663\pi\)
\(272\) 537.500i 1.97610i
\(273\) −4.56156 56.2192i −0.0167090 0.205931i
\(274\) −447.715 −1.63399
\(275\) 180.544 180.544i 0.656523 0.656523i
\(276\) −554.197 −2.00796
\(277\) 187.947i 0.678510i −0.940694 0.339255i \(-0.889825\pi\)
0.940694 0.339255i \(-0.110175\pi\)
\(278\) −202.721 + 202.721i −0.729214 + 0.729214i
\(279\) −84.2719 + 84.2719i −0.302050 + 0.302050i
\(280\) −16.3356 16.3356i −0.0583414 0.0583414i
\(281\) 286.846 + 286.846i 1.02081 + 1.02081i 0.999779 + 0.0210263i \(0.00669337\pi\)
0.0210263 + 0.999779i \(0.493307\pi\)
\(282\) −394.767 −1.39988
\(283\) 399.201i 1.41061i 0.708906 + 0.705303i \(0.249189\pi\)
−0.708906 + 0.705303i \(0.750811\pi\)
\(284\) −470.379 470.379i −1.65626 1.65626i
\(285\) 5.72811i 0.0200986i
\(286\) 374.548 + 318.329i 1.30961 + 1.11304i
\(287\) −31.6754 −0.110367
\(288\) −137.864 + 137.864i −0.478695 + 0.478695i
\(289\) 33.8420 0.117100
\(290\) 55.8114i 0.192453i
\(291\) 188.886 188.886i 0.649093 0.649093i
\(292\) −294.868 + 294.868i −1.00982 + 1.00982i
\(293\) 136.156 + 136.156i 0.464695 + 0.464695i 0.900191 0.435496i \(-0.143427\pi\)
−0.435496 + 0.900191i \(0.643427\pi\)
\(294\) 251.004 + 251.004i 0.853756 + 0.853756i
\(295\) −25.3594 −0.0859642
\(296\) 116.276i 0.392825i
\(297\) 211.031 + 211.031i 0.710541 + 0.710541i
\(298\) 661.903i 2.22115i
\(299\) 231.408 272.276i 0.773939 0.910623i
\(300\) 496.982 1.65661
\(301\) 16.3356 16.3356i 0.0542710 0.0542710i
\(302\) −150.623 −0.498751
\(303\) 19.2897i 0.0636623i
\(304\) 106.408 106.408i 0.350026 0.350026i
\(305\) −28.3466 + 28.3466i −0.0929397 + 0.0929397i
\(306\) 178.302 + 178.302i 0.582688 + 0.582688i
\(307\) −235.684 235.684i −0.767700 0.767700i 0.210001 0.977701i \(-0.432653\pi\)
−0.977701 + 0.210001i \(0.932653\pi\)
\(308\) 193.811 0.629258
\(309\) 128.513i 0.415900i
\(310\) 42.1359 + 42.1359i 0.135922 + 0.135922i
\(311\) 113.684i 0.365543i 0.983155 + 0.182772i \(0.0585069\pi\)
−0.983155 + 0.182772i \(0.941493\pi\)
\(312\) 44.1843 + 544.552i 0.141616 + 1.74536i
\(313\) 223.483 0.714002 0.357001 0.934104i \(-0.383799\pi\)
0.357001 + 0.934104i \(0.383799\pi\)
\(314\) −600.228 + 600.228i −1.91155 + 1.91155i
\(315\) 5.14022 0.0163181
\(316\) 473.548i 1.49857i
\(317\) −125.140 + 125.140i −0.394764 + 0.394764i −0.876382 0.481617i \(-0.840049\pi\)
0.481617 + 0.876382i \(0.340049\pi\)
\(318\) 23.3772 23.3772i 0.0735133 0.0735133i
\(319\) −189.057 189.057i −0.592655 0.592655i
\(320\) 12.5548 + 12.5548i 0.0392338 + 0.0392338i
\(321\) −310.438 −0.967098
\(322\) 201.329i 0.625245i
\(323\) −50.5132 50.5132i −0.156388 0.156388i
\(324\) 217.982i 0.672785i
\(325\) −207.517 + 244.167i −0.638515 + 0.751282i
\(326\) −59.1623 −0.181479
\(327\) −183.305 + 183.305i −0.560566 + 0.560566i
\(328\) 306.816 0.935414
\(329\) 100.359i 0.305044i
\(330\) 34.2456 34.2456i 0.103774 0.103774i
\(331\) 309.982 309.982i 0.936502 0.936502i −0.0615988 0.998101i \(-0.519620\pi\)
0.998101 + 0.0615988i \(0.0196199\pi\)
\(332\) −173.649 173.649i −0.523039 0.523039i
\(333\) 18.2939 + 18.2939i 0.0549368 + 0.0549368i
\(334\) 1067.48 3.19605
\(335\) 67.9253i 0.202762i
\(336\) 103.235 + 103.235i 0.307246 + 0.307246i
\(337\) 5.32456i 0.0157999i −0.999969 0.00789993i \(-0.997485\pi\)
0.999969 0.00789993i \(-0.00251465\pi\)
\(338\) −500.831 360.182i −1.48175 1.06563i
\(339\) −234.702 −0.692336
\(340\) 62.3883 62.3883i 0.183495 0.183495i
\(341\) −285.465 −0.837140
\(342\) 70.5964i 0.206422i
\(343\) −133.336 + 133.336i −0.388733 + 0.388733i
\(344\) −158.230 + 158.230i −0.459972 + 0.459972i
\(345\) −24.8947 24.8947i −0.0721584 0.0721584i
\(346\) −235.868 235.868i −0.681700 0.681700i
\(347\) −47.2413 −0.136142 −0.0680710 0.997680i \(-0.521684\pi\)
−0.0680710 + 0.997680i \(0.521684\pi\)
\(348\) 520.416i 1.49545i
\(349\) 223.581 + 223.581i 0.640634 + 0.640634i 0.950711 0.310078i \(-0.100355\pi\)
−0.310078 + 0.950711i \(0.600355\pi\)
\(350\) 180.544i 0.515839i
\(351\) −285.397 242.559i −0.813096 0.691052i
\(352\) −467.004 −1.32672
\(353\) 110.320 110.320i 0.312522 0.312522i −0.533364 0.845886i \(-0.679072\pi\)
0.845886 + 0.533364i \(0.179072\pi\)
\(354\) 337.903 0.954529
\(355\) 42.2591i 0.119040i
\(356\) 849.557 849.557i 2.38639 2.38639i
\(357\) 49.0068 49.0068i 0.137274 0.137274i
\(358\) −184.993 184.993i −0.516741 0.516741i
\(359\) 63.2149 + 63.2149i 0.176086 + 0.176086i 0.789647 0.613561i \(-0.210264\pi\)
−0.613561 + 0.789647i \(0.710264\pi\)
\(360\) −49.7893 −0.138304
\(361\) 341.000i 0.944598i
\(362\) 707.605 + 707.605i 1.95471 + 1.95471i
\(363\) 29.6271i 0.0816172i
\(364\) −242.438 + 19.6712i −0.666040 + 0.0540417i
\(365\) −26.4911 −0.0725784
\(366\) 377.706 377.706i 1.03198 1.03198i
\(367\) −318.416 −0.867620 −0.433810 0.901004i \(-0.642831\pi\)
−0.433810 + 0.901004i \(0.642831\pi\)
\(368\) 924.907i 2.51334i
\(369\) −48.2719 + 48.2719i −0.130818 + 0.130818i
\(370\) 9.14697 9.14697i 0.0247216 0.0247216i
\(371\) 5.94306 + 5.94306i 0.0160190 + 0.0160190i
\(372\) −392.899 392.899i −1.05618 1.05618i
\(373\) 8.87688 0.0237986 0.0118993 0.999929i \(-0.496212\pi\)
0.0118993 + 0.999929i \(0.496212\pi\)
\(374\) 603.986i 1.61494i
\(375\) 44.9669 + 44.9669i 0.119912 + 0.119912i
\(376\) 972.105i 2.58538i
\(377\) 255.680 + 217.302i 0.678196 + 0.576399i
\(378\) −211.031 −0.558282
\(379\) −144.698 + 144.698i −0.381788 + 0.381788i −0.871746 0.489958i \(-0.837012\pi\)
0.489958 + 0.871746i \(0.337012\pi\)
\(380\) 24.7018 0.0650047
\(381\) 205.065i 0.538230i
\(382\) −463.846 + 463.846i −1.21426 + 1.21426i
\(383\) 357.261 357.261i 0.932796 0.932796i −0.0650838 0.997880i \(-0.520731\pi\)
0.997880 + 0.0650838i \(0.0207315\pi\)
\(384\) 108.441 + 108.441i 0.282398 + 0.282398i
\(385\) 8.70605 + 8.70605i 0.0226131 + 0.0226131i
\(386\) 5.86406 0.0151919
\(387\) 49.7893i 0.128655i
\(388\) −814.548 814.548i −2.09935 2.09935i
\(389\) 438.342i 1.12684i −0.826170 0.563421i \(-0.809485\pi\)
0.826170 0.563421i \(-0.190515\pi\)
\(390\) −39.3619 + 46.3135i −0.100928 + 0.118753i
\(391\) 439.065 1.12293
\(392\) 618.092 618.092i 1.57676 1.57676i
\(393\) −242.754 −0.617694
\(394\) 732.557i 1.85928i
\(395\) 21.2719 21.2719i 0.0538529 0.0538529i
\(396\) 295.359 295.359i 0.745857 0.745857i
\(397\) 250.061 + 250.061i 0.629877 + 0.629877i 0.948037 0.318160i \(-0.103065\pi\)
−0.318160 + 0.948037i \(0.603065\pi\)
\(398\) −670.473 670.473i −1.68461 1.68461i
\(399\) 19.4036 0.0486305
\(400\) 829.421i 2.07355i
\(401\) 93.7018 + 93.7018i 0.233670 + 0.233670i 0.814223 0.580553i \(-0.197163\pi\)
−0.580553 + 0.814223i \(0.697163\pi\)
\(402\) 905.074i 2.25143i
\(403\) 357.088 28.9737i 0.886073 0.0718950i
\(404\) 83.1843 0.205902
\(405\) −9.79181 + 9.79181i −0.0241773 + 0.0241773i
\(406\) 189.057 0.465657
\(407\) 61.9694i 0.152259i
\(408\) −474.691 + 474.691i −1.16346 + 1.16346i
\(409\) 370.140 370.140i 0.904988 0.904988i −0.0908741 0.995862i \(-0.528966\pi\)
0.995862 + 0.0908741i \(0.0289661\pi\)
\(410\) 24.1359 + 24.1359i 0.0588682 + 0.0588682i
\(411\) 187.530 + 187.530i 0.456278 + 0.456278i
\(412\) −554.197 −1.34514
\(413\) 85.9032i 0.207998i
\(414\) −306.816 306.816i −0.741101 0.741101i
\(415\) 15.6007i 0.0375921i
\(416\) 584.175 47.3993i 1.40427 0.113941i
\(417\) 169.824 0.407252
\(418\) −119.570 + 119.570i −0.286053 + 0.286053i
\(419\) −658.767 −1.57224 −0.786118 0.618076i \(-0.787912\pi\)
−0.786118 + 0.618076i \(0.787912\pi\)
\(420\) 23.9651i 0.0570598i
\(421\) −80.3135 + 80.3135i −0.190768 + 0.190768i −0.796028 0.605260i \(-0.793069\pi\)
0.605260 + 0.796028i \(0.293069\pi\)
\(422\) −840.353 + 840.353i −1.99136 + 1.99136i
\(423\) −152.943 152.943i −0.361568 0.361568i
\(424\) −57.5658 57.5658i −0.135768 0.135768i
\(425\) −393.737 −0.926439
\(426\) 563.083i 1.32179i
\(427\) 96.0221 + 96.0221i 0.224876 + 0.224876i
\(428\) 1338.73i 3.12787i
\(429\) −23.5480 290.219i −0.0548906 0.676502i
\(430\) −24.8947 −0.0578946
\(431\) 296.037 296.037i 0.686862 0.686862i −0.274675 0.961537i \(-0.588570\pi\)
0.961537 + 0.274675i \(0.0885704\pi\)
\(432\) 969.478 2.24416
\(433\) 156.140i 0.360601i −0.983612 0.180300i \(-0.942293\pi\)
0.983612 0.180300i \(-0.0577070\pi\)
\(434\) 142.732 142.732i 0.328876 0.328876i
\(435\) 23.3772 23.3772i 0.0537407 0.0537407i
\(436\) 790.480 + 790.480i 1.81303 + 1.81303i
\(437\) 86.9210 + 86.9210i 0.198904 + 0.198904i
\(438\) 352.982 0.805895
\(439\) 448.710i 1.02212i −0.859545 0.511060i \(-0.829253\pi\)
0.859545 0.511060i \(-0.170747\pi\)
\(440\) −84.3288 84.3288i −0.191656 0.191656i
\(441\) 194.491i 0.441023i
\(442\) −61.3025 755.526i −0.138693 1.70933i
\(443\) −577.372 −1.30332 −0.651662 0.758510i \(-0.725928\pi\)
−0.651662 + 0.758510i \(0.725928\pi\)
\(444\) −85.2915 + 85.2915i −0.192098 + 0.192098i
\(445\) 76.3246 0.171516
\(446\) 1258.43i 2.82159i
\(447\) −277.246 + 277.246i −0.620236 + 0.620236i
\(448\) 42.5285 42.5285i 0.0949296 0.0949296i
\(449\) −107.127 107.127i −0.238591 0.238591i 0.577675 0.816267i \(-0.303960\pi\)
−0.816267 + 0.577675i \(0.803960\pi\)
\(450\) 275.140 + 275.140i 0.611423 + 0.611423i
\(451\) −163.517 −0.362566
\(452\) 1012.12i 2.23921i
\(453\) 63.0900 + 63.0900i 0.139272 + 0.139272i
\(454\) 520.009i 1.14539i
\(455\) −11.7740 10.0068i −0.0258770 0.0219929i
\(456\) −187.947 −0.412165
\(457\) −356.092 + 356.092i −0.779194 + 0.779194i −0.979694 0.200499i \(-0.935744\pi\)
0.200499 + 0.979694i \(0.435744\pi\)
\(458\) 1240.84 2.70925
\(459\) 460.223i 1.00267i
\(460\) −107.355 + 107.355i −0.233381 + 0.233381i
\(461\) 33.7477 33.7477i 0.0732054 0.0732054i −0.669556 0.742761i \(-0.733516\pi\)
0.742761 + 0.669556i \(0.233516\pi\)
\(462\) −116.004 116.004i −0.251092 0.251092i
\(463\) 336.355 + 336.355i 0.726469 + 0.726469i 0.969915 0.243446i \(-0.0782777\pi\)
−0.243446 + 0.969915i \(0.578278\pi\)
\(464\) −868.530 −1.87183
\(465\) 35.2982i 0.0759102i
\(466\) −27.8488 27.8488i −0.0597613 0.0597613i
\(467\) 308.263i 0.660093i 0.943965 + 0.330046i \(0.107064\pi\)
−0.943965 + 0.330046i \(0.892936\pi\)
\(468\) −339.487 + 399.443i −0.725399 + 0.853510i
\(469\) 230.092 0.490601
\(470\) −76.4715 + 76.4715i −0.162705 + 0.162705i
\(471\) 502.824 1.06757
\(472\) 832.078i 1.76288i
\(473\) 84.3288 84.3288i 0.178285 0.178285i
\(474\) −283.438 + 283.438i −0.597971 + 0.597971i
\(475\) −77.9473 77.9473i −0.164100 0.164100i
\(476\) −211.336 211.336i −0.443982 0.443982i
\(477\) 18.1139 0.0379746
\(478\) 505.982i 1.05854i
\(479\) 76.6424 + 76.6424i 0.160005 + 0.160005i 0.782569 0.622564i \(-0.213909\pi\)
−0.622564 + 0.782569i \(0.713909\pi\)
\(480\) 57.7459i 0.120304i
\(481\) −6.28967 77.5174i −0.0130762 0.161159i
\(482\) 1012.82 2.10130
\(483\) −84.3288 + 84.3288i −0.174594 + 0.174594i
\(484\) −127.763 −0.263973
\(485\) 73.1794i 0.150885i
\(486\) −538.824 + 538.824i −1.10869 + 1.10869i
\(487\) −69.0655 + 69.0655i −0.141818 + 0.141818i −0.774452 0.632633i \(-0.781974\pi\)
0.632633 + 0.774452i \(0.281974\pi\)
\(488\) −930.092 930.092i −1.90593 1.90593i
\(489\) 24.7808 + 24.7808i 0.0506764 + 0.0506764i
\(490\) 97.2456 0.198460
\(491\) 685.302i 1.39573i 0.716230 + 0.697864i \(0.245866\pi\)
−0.716230 + 0.697864i \(0.754134\pi\)
\(492\) −225.057 225.057i −0.457433 0.457433i
\(493\) 412.302i 0.836313i
\(494\) 137.434 161.706i 0.278207 0.327340i
\(495\) 26.5352 0.0536065
\(496\) −655.715 + 655.715i −1.32201 + 1.32201i
\(497\) −143.149 −0.288027
\(498\) 207.873i 0.417415i
\(499\) 349.329 349.329i 0.700058 0.700058i −0.264365 0.964423i \(-0.585162\pi\)
0.964423 + 0.264365i \(0.0851623\pi\)
\(500\) 193.914 193.914i 0.387828 0.387828i
\(501\) −447.127 447.127i −0.892468 0.892468i
\(502\) −247.381 247.381i −0.492792 0.492792i
\(503\) 42.2719 0.0840395 0.0420198 0.999117i \(-0.486621\pi\)
0.0420198 + 0.999117i \(0.486621\pi\)
\(504\) 168.658i 0.334638i
\(505\) 3.73666 + 3.73666i 0.00739933 + 0.00739933i
\(506\) 1039.32i 2.05398i
\(507\) 58.9125 + 360.645i 0.116198 + 0.711331i
\(508\) 884.320 1.74079
\(509\) 184.280 184.280i 0.362044 0.362044i −0.502521 0.864565i \(-0.667594\pi\)
0.864565 + 0.502521i \(0.167594\pi\)
\(510\) −74.6840 −0.146439
\(511\) 89.7367i 0.175610i
\(512\) 777.103 777.103i 1.51778 1.51778i
\(513\) 91.1096 91.1096i 0.177602 0.177602i
\(514\) 1163.01 + 1163.01i 2.26266 + 2.26266i
\(515\) −24.8947 24.8947i −0.0483392 0.0483392i
\(516\) 232.132 0.449868
\(517\) 518.083i 1.00210i
\(518\) −30.9847 30.9847i −0.0598160 0.0598160i
\(519\) 197.592i 0.380717i
\(520\) 114.046 + 96.9278i 0.219319 + 0.186400i
\(521\) −757.122 −1.45321 −0.726605 0.687055i \(-0.758903\pi\)
−0.726605 + 0.687055i \(0.758903\pi\)
\(522\) 288.114 288.114i 0.551942 0.551942i
\(523\) −221.851 −0.424188 −0.212094 0.977249i \(-0.568028\pi\)
−0.212094 + 0.977249i \(0.568028\pi\)
\(524\) 1046.85i 1.99780i
\(525\) 75.6228 75.6228i 0.144043 0.144043i
\(526\) −431.004 + 431.004i −0.819400 + 0.819400i
\(527\) 311.276 + 311.276i 0.590657 + 0.590657i
\(528\) 532.925 + 532.925i 1.00933 + 1.00933i
\(529\) −226.526 −0.428215
\(530\) 9.05694i 0.0170886i
\(531\) 130.912 + 130.912i 0.246539 + 0.246539i
\(532\) 83.6754i 0.157285i
\(533\) 204.544 16.5964i 0.383759 0.0311378i
\(534\) −1016.99 −1.90448
\(535\) −60.1359 + 60.1359i −0.112404 + 0.112404i
\(536\) −2228.72 −4.15806
\(537\) 154.973i 0.288590i
\(538\) −438.952 + 438.952i −0.815895 + 0.815895i
\(539\) −329.412 + 329.412i −0.611154 + 0.611154i
\(540\) 112.528 + 112.528i 0.208386 + 0.208386i
\(541\) −243.379 243.379i −0.449869 0.449869i 0.445442 0.895311i \(-0.353047\pi\)
−0.895311 + 0.445442i \(0.853047\pi\)
\(542\) 1120.59 2.06750
\(543\) 592.777i 1.09167i
\(544\) 509.230 + 509.230i 0.936085 + 0.936085i
\(545\) 71.0171i 0.130307i
\(546\) 156.884 + 133.336i 0.287333 + 0.244204i
\(547\) −317.777 −0.580944 −0.290472 0.956883i \(-0.593812\pi\)
−0.290472 + 0.956883i \(0.593812\pi\)
\(548\) 808.701 808.701i 1.47573 1.47573i
\(549\) 292.666 0.533090
\(550\) 932.017i 1.69458i
\(551\) −81.6228 + 81.6228i −0.148136 + 0.148136i
\(552\) 816.828 816.828i 1.47976 1.47976i
\(553\) −72.0569 72.0569i −0.130302 0.130302i
\(554\) 485.118 + 485.118i 0.875665 + 0.875665i
\(555\) −7.66262 −0.0138065
\(556\) 732.346i 1.31717i
\(557\) −479.423 479.423i −0.860724 0.860724i 0.130698 0.991422i \(-0.458278\pi\)
−0.991422 + 0.130698i \(0.958278\pi\)
\(558\) 435.035i 0.779632i
\(559\) −96.9278 + 114.046i −0.173395 + 0.204018i
\(560\) 39.9957 0.0714209
\(561\) 252.986 252.986i 0.450956 0.450956i
\(562\) −1480.78 −2.63484
\(563\) 461.671i 0.820020i 0.912081 + 0.410010i \(0.134475\pi\)
−0.912081 + 0.410010i \(0.865525\pi\)
\(564\) 713.063 713.063i 1.26430 1.26430i
\(565\) −45.4648 + 45.4648i −0.0804686 + 0.0804686i
\(566\) −1030.39 1030.39i −1.82048 1.82048i
\(567\) 33.1690 + 33.1690i 0.0584992 + 0.0584992i
\(568\) 1386.58 2.44116
\(569\) 523.394i 0.919849i −0.887958 0.459925i \(-0.847876\pi\)
0.887958 0.459925i \(-0.152124\pi\)
\(570\) −14.7851 14.7851i −0.0259387 0.0259387i
\(571\) 115.715i 0.202654i −0.994853 0.101327i \(-0.967691\pi\)
0.994853 0.101327i \(-0.0323088\pi\)
\(572\) −1251.53 + 101.548i −2.18800 + 0.177532i
\(573\) 388.574 0.678140
\(574\) 81.7587 81.7587i 0.142437 0.142437i
\(575\) 677.526 1.17831
\(576\) 129.623i 0.225040i
\(577\) 130.158 130.158i 0.225577 0.225577i −0.585265 0.810842i \(-0.699010\pi\)
0.810842 + 0.585265i \(0.199010\pi\)
\(578\) −87.3509 + 87.3509i −0.151126 + 0.151126i
\(579\) −2.45623 2.45623i −0.00424219 0.00424219i
\(580\) −100.811 100.811i −0.173813 0.173813i
\(581\) −52.8463 −0.0909574
\(582\) 975.083i 1.67540i
\(583\) 30.6797 + 30.6797i 0.0526239 + 0.0526239i
\(584\) 869.210i 1.48837i
\(585\) −33.1929 + 2.69323i −0.0567400 + 0.00460382i
\(586\) −702.873 −1.19944
\(587\) −347.311 + 347.311i −0.591671 + 0.591671i −0.938083 0.346411i \(-0.887400\pi\)
0.346411 + 0.938083i \(0.387400\pi\)
\(588\) −906.772 −1.54213
\(589\) 123.246i 0.209245i
\(590\) 65.4562 65.4562i 0.110943 0.110943i
\(591\) 306.840 306.840i 0.519187 0.519187i
\(592\) 142.344 + 142.344i 0.240446 + 0.240446i
\(593\) −240.285 240.285i −0.405202 0.405202i 0.474860 0.880062i \(-0.342499\pi\)
−0.880062 + 0.474860i \(0.842499\pi\)
\(594\) −1089.40 −1.83400
\(595\) 18.9865i 0.0319101i
\(596\) 1195.59 + 1195.59i 2.00602 + 2.00602i
\(597\) 561.670i 0.940822i
\(598\) 105.487 + 1300.08i 0.176399 + 2.17404i
\(599\) 1044.77 1.74419 0.872096 0.489334i \(-0.162760\pi\)
0.872096 + 0.489334i \(0.162760\pi\)
\(600\) −732.500 + 732.500i −1.22083 + 1.22083i
\(601\) 933.298 1.55291 0.776454 0.630174i \(-0.217016\pi\)
0.776454 + 0.630174i \(0.217016\pi\)
\(602\) 84.3288i 0.140081i
\(603\) 350.649 350.649i 0.581508 0.581508i
\(604\) 272.068 272.068i 0.450444 0.450444i
\(605\) −5.73914 5.73914i −0.00948619 0.00948619i
\(606\) −49.7893 49.7893i −0.0821606 0.0821606i
\(607\) 579.912 0.955374 0.477687 0.878530i \(-0.341475\pi\)
0.477687 + 0.878530i \(0.341475\pi\)
\(608\) 201.623i 0.331616i
\(609\) −79.1886 79.1886i −0.130031 0.130031i
\(610\) 146.333i 0.239890i
\(611\) 52.5836 + 648.070i 0.0860616 + 1.06067i
\(612\) −644.131 −1.05250
\(613\) −288.460 + 288.460i −0.470572 + 0.470572i −0.902100 0.431528i \(-0.857975\pi\)
0.431528 + 0.902100i \(0.357975\pi\)
\(614\) 1216.67 1.98154
\(615\) 20.2192i 0.0328768i
\(616\) −285.658 + 285.658i −0.463730 + 0.463730i
\(617\) 95.4121 95.4121i 0.154639 0.154639i −0.625547 0.780186i \(-0.715124\pi\)
0.780186 + 0.625547i \(0.215124\pi\)
\(618\) 331.710 + 331.710i 0.536748 + 0.536748i
\(619\) −544.952 544.952i −0.880374 0.880374i 0.113198 0.993572i \(-0.463890\pi\)
−0.993572 + 0.113198i \(0.963890\pi\)
\(620\) −152.219 −0.245515
\(621\) 791.934i 1.27526i
\(622\) −293.434 293.434i −0.471759 0.471759i
\(623\) 258.544i 0.414998i
\(624\) −720.726 612.546i −1.15501 0.981644i
\(625\) −598.806 −0.958090
\(626\) −576.840 + 576.840i −0.921469 + 0.921469i
\(627\) 100.167 0.159755
\(628\) 2168.37i 3.45281i
\(629\) 67.5726 67.5726i 0.107429 0.107429i
\(630\) −13.2676 + 13.2676i −0.0210597 + 0.0210597i
\(631\) −642.537 642.537i −1.01828 1.01828i −0.999830 0.0184540i \(-0.994126\pi\)
−0.0184540 0.999830i \(-0.505874\pi\)
\(632\) 697.960 + 697.960i 1.10437 + 1.10437i
\(633\) 703.982 1.11214
\(634\) 646.009i 1.01894i
\(635\) 39.7238 + 39.7238i 0.0625572 + 0.0625572i
\(636\) 84.4520i 0.132786i
\(637\) 378.627 445.495i 0.594391 0.699365i
\(638\) 975.964 1.52972
\(639\) −218.153 + 218.153i −0.341398 + 0.341398i
\(640\) 42.0128 0.0656450
\(641\) 487.290i 0.760202i 0.924945 + 0.380101i \(0.124111\pi\)
−0.924945 + 0.380101i \(0.875889\pi\)
\(642\) 801.285 801.285i 1.24811 1.24811i
\(643\) −797.688 + 797.688i −1.24057 + 1.24057i −0.280809 + 0.959764i \(0.590603\pi\)
−0.959764 + 0.280809i \(0.909397\pi\)
\(644\) 363.658 + 363.658i 0.564686 + 0.564686i
\(645\) 10.4274 + 10.4274i 0.0161665 + 0.0161665i
\(646\) 260.763 0.403658
\(647\) 989.526i 1.52941i −0.644383 0.764703i \(-0.722886\pi\)
0.644383 0.764703i \(-0.277114\pi\)
\(648\) −321.283 321.283i −0.495807 0.495807i
\(649\) 443.456i 0.683292i
\(650\) −94.5964 1165.86i −0.145533 1.79363i
\(651\) −119.570 −0.183671
\(652\) 106.864 106.864i 0.163902 0.163902i
\(653\) −86.3075 −0.132171 −0.0660853 0.997814i \(-0.521051\pi\)
−0.0660853 + 0.997814i \(0.521051\pi\)
\(654\) 946.271i 1.44690i
\(655\) −47.0245 + 47.0245i −0.0717932 + 0.0717932i
\(656\) −375.601 + 375.601i −0.572562 + 0.572562i
\(657\) 136.754 + 136.754i 0.208150 + 0.208150i
\(658\) 259.042 + 259.042i 0.393680 + 0.393680i
\(659\) −1184.99 −1.79817 −0.899083 0.437779i \(-0.855765\pi\)
−0.899083 + 0.437779i \(0.855765\pi\)
\(660\) 123.715i 0.187446i
\(661\) −194.408 194.408i −0.294112 0.294112i 0.544590 0.838702i \(-0.316685\pi\)
−0.838702 + 0.544590i \(0.816685\pi\)
\(662\) 1600.21i 2.41724i
\(663\) −290.783 + 342.138i −0.438587 + 0.516045i
\(664\) 511.881 0.770905
\(665\) 3.75872 3.75872i 0.00565221 0.00565221i
\(666\) −94.4384 −0.141799
\(667\) 709.473i 1.06368i
\(668\) −1928.18 + 1928.18i −2.88650 + 2.88650i
\(669\) −527.107 + 527.107i −0.787903 + 0.787903i
\(670\) −175.325 175.325i −0.261678 0.261678i
\(671\) 495.693 + 495.693i 0.738737 + 0.738737i
\(672\) −195.610 −0.291086
\(673\) 615.500i 0.914561i 0.889322 + 0.457281i \(0.151176\pi\)
−0.889322 + 0.457281i \(0.848824\pi\)
\(674\) 13.7434 + 13.7434i 0.0203908 + 0.0203908i
\(675\) 710.175i 1.05211i
\(676\) 1555.24 254.053i 2.30065 0.375818i
\(677\) −412.031 −0.608612 −0.304306 0.952574i \(-0.598425\pi\)
−0.304306 + 0.952574i \(0.598425\pi\)
\(678\) 605.798 605.798i 0.893507 0.893507i
\(679\) −247.890 −0.365081
\(680\) 183.907i 0.270452i
\(681\) −217.811 + 217.811i −0.319841 + 0.319841i
\(682\) 736.824 736.824i 1.08039 1.08039i
\(683\) 129.044 + 129.044i 0.188937 + 0.188937i 0.795237 0.606299i \(-0.207347\pi\)
−0.606299 + 0.795237i \(0.707347\pi\)
\(684\) −127.517 127.517i −0.186429 0.186429i
\(685\) 72.6541 0.106064
\(686\) 688.315i 1.00338i
\(687\) −519.738 519.738i −0.756533 0.756533i
\(688\) 387.408i 0.563093i
\(689\) −41.4911 35.2633i −0.0602193 0.0511805i
\(690\) 128.513 0.186251
\(691\) 727.105 727.105i 1.05225 1.05225i 0.0536923 0.998558i \(-0.482901\pi\)
0.998558 0.0536923i \(-0.0170990\pi\)
\(692\) 852.092 1.23135
\(693\) 89.8861i 0.129706i
\(694\) 121.936 121.936i 0.175701 0.175701i
\(695\) 32.8971 32.8971i 0.0473340 0.0473340i
\(696\) 767.039 + 767.039i 1.10207 + 1.10207i
\(697\) 178.302 + 178.302i 0.255814 + 0.255814i
\(698\) −1154.19 −1.65356
\(699\) 23.3295i 0.0333756i
\(700\) −326.114 326.114i −0.465877 0.465877i
\(701\) 635.934i 0.907181i −0.891210 0.453590i \(-0.850143\pi\)
0.891210 0.453590i \(-0.149857\pi\)
\(702\) 1362.73 110.570i 1.94121 0.157507i
\(703\) 26.7544 0.0380575
\(704\) 219.544 219.544i 0.311852 0.311852i
\(705\) 64.0619 0.0908680
\(706\) 569.504i 0.806663i
\(707\) 12.6577 12.6577i 0.0179033 0.0179033i
\(708\) −610.350 + 610.350i −0.862077 + 0.862077i
\(709\) 695.315 + 695.315i 0.980699 + 0.980699i 0.999817 0.0191186i \(-0.00608601\pi\)
−0.0191186 + 0.999817i \(0.506086\pi\)
\(710\) 109.077 + 109.077i 0.153629 + 0.153629i
\(711\) −219.623 −0.308893
\(712\) 2504.31i 3.51730i
\(713\) −535.631 535.631i −0.751236 0.751236i
\(714\) 252.986i 0.354323i
\(715\) −60.7808 51.6577i −0.0850081 0.0722485i
\(716\) 668.302 0.933382
\(717\) −211.936 + 211.936i −0.295588 + 0.295588i
\(718\) −326.333 −0.454503
\(719\) 859.565i 1.19550i 0.801682 + 0.597750i \(0.203939\pi\)
−0.801682 + 0.597750i \(0.796061\pi\)
\(720\) 60.9516 60.9516i 0.0846550 0.0846550i
\(721\) −84.3288 + 84.3288i −0.116961 + 0.116961i
\(722\) −880.168 880.168i −1.21907 1.21907i
\(723\) −424.233 424.233i −0.586767 0.586767i
\(724\) −2556.28 −3.53077
\(725\) 636.228i 0.877556i
\(726\) 76.4715 + 76.4715i 0.105333 + 0.105333i
\(727\) 437.337i 0.601564i −0.953693 0.300782i \(-0.902752\pi\)
0.953693 0.300782i \(-0.0972477\pi\)
\(728\) 328.336 386.322i 0.451010 0.530662i
\(729\) 661.780 0.907792
\(730\) 68.3772 68.3772i 0.0936674 0.0936674i
\(731\) −183.907 −0.251583
\(732\) 1364.49i 1.86406i
\(733\) 39.5591 39.5591i 0.0539687 0.0539687i −0.679607 0.733576i \(-0.737850\pi\)
0.733576 + 0.679607i \(0.237850\pi\)
\(734\) 821.877 821.877i 1.11972 1.11972i
\(735\) −40.7324 40.7324i −0.0554182 0.0554182i
\(736\) −876.263 876.263i −1.19057 1.19057i
\(737\) 1187.80 1.61167
\(738\) 249.193i 0.337660i
\(739\) 919.732 + 919.732i 1.24456 + 1.24456i 0.958088 + 0.286475i \(0.0924834\pi\)
0.286475 + 0.958088i \(0.407517\pi\)
\(740\) 33.0441i 0.0446542i
\(741\) −125.298 + 10.1666i −0.169093 + 0.0137200i
\(742\) −30.6797 −0.0413473
\(743\) 730.642 730.642i 0.983368 0.983368i −0.0164960 0.999864i \(-0.505251\pi\)
0.999864 + 0.0164960i \(0.00525109\pi\)
\(744\) 1158.18 1.55670
\(745\) 107.412i 0.144177i
\(746\) −22.9125 + 22.9125i −0.0307137 + 0.0307137i
\(747\) −80.5352 + 80.5352i −0.107812 + 0.107812i
\(748\) −1090.97 1090.97i −1.45852 1.45852i
\(749\) 203.706 + 203.706i 0.271971 + 0.271971i
\(750\) −232.132 −0.309509
\(751\) 199.764i 0.265997i −0.991116 0.132998i \(-0.957539\pi\)
0.991116 0.132998i \(-0.0424605\pi\)
\(752\) −1190.04 1190.04i −1.58250 1.58250i
\(753\) 207.237i 0.275215i
\(754\) −1220.83 + 99.0569i −1.61914 + 0.131375i
\(755\) 24.4427 0.0323745
\(756\) 381.182 381.182i 0.504209 0.504209i
\(757\) 124.549 0.164529 0.0822647 0.996611i \(-0.473785\pi\)
0.0822647 + 0.996611i \(0.473785\pi\)
\(758\) 746.969i 0.985447i
\(759\) −435.329 + 435.329i −0.573556 + 0.573556i
\(760\) −36.4078 + 36.4078i −0.0479050 + 0.0479050i
\(761\) 161.412 + 161.412i 0.212105 + 0.212105i 0.805161 0.593056i \(-0.202079\pi\)
−0.593056 + 0.805161i \(0.702079\pi\)
\(762\) −529.302 529.302i −0.694623 0.694623i
\(763\) 240.565 0.315289
\(764\) 1675.68i 2.19330i
\(765\) −28.9345 28.9345i −0.0378229 0.0378229i
\(766\) 1844.28i 2.40768i
\(767\) −45.0092 554.719i −0.0586822 0.723232i
\(768\) −819.048 −1.06647
\(769\) 137.947 137.947i 0.179385 0.179385i −0.611703 0.791088i \(-0.709515\pi\)
0.791088 + 0.611703i \(0.209515\pi\)
\(770\) −44.9431 −0.0583676
\(771\) 974.276i 1.26365i
\(772\) −10.5922 + 10.5922i −0.0137204 + 0.0137204i
\(773\) 550.813 550.813i 0.712566 0.712566i −0.254506 0.967071i \(-0.581913\pi\)
0.967071 + 0.254506i \(0.0819128\pi\)
\(774\) 128.513 + 128.513i 0.166038 + 0.166038i
\(775\) 480.333 + 480.333i 0.619785 + 0.619785i
\(776\) 2401.12 3.09422
\(777\) 25.9566i 0.0334061i
\(778\) 1131.42 + 1131.42i 1.45427 + 1.45427i
\(779\) 70.5964i 0.0906244i
\(780\) −12.5566 154.754i −0.0160982 0.198403i
\(781\) −738.977 −0.946194
\(782\) −1133.29 + 1133.29i −1.44922 + 1.44922i<