Properties

Label 525.2.j.b.218.11
Level 525
Weight 2
Character 525.218
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 218.11
Character \(\chi\) \(=\) 525.218
Dual form 525.2.j.b.407.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.54414 + 1.54414i) q^{2} +(0.00622252 + 1.73204i) q^{3} +2.76875i q^{4} +(-2.66491 + 2.68412i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.18705 + 1.18705i) q^{8} +(-2.99992 + 0.0215553i) q^{9} +O(q^{10})\) \(q+(1.54414 + 1.54414i) q^{2} +(0.00622252 + 1.73204i) q^{3} +2.76875i q^{4} +(-2.66491 + 2.68412i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.18705 + 1.18705i) q^{8} +(-2.99992 + 0.0215553i) q^{9} +3.38507i q^{11} +(-4.79558 + 0.0172286i) q^{12} +(0.206632 + 0.206632i) q^{13} -2.18375 q^{14} +1.87154 q^{16} +(0.167409 + 0.167409i) q^{17} +(-4.66559 - 4.59902i) q^{18} -5.31419i q^{19} +(-1.22914 - 1.22034i) q^{21} +(-5.22702 + 5.22702i) q^{22} +(-5.07773 + 5.07773i) q^{23} +(-2.06341 - 2.04864i) q^{24} +0.638138i q^{26} +(-0.0560017 - 5.19585i) q^{27} +(-1.95780 - 1.95780i) q^{28} +2.84268 q^{29} +9.11776 q^{31} +(5.26402 + 5.26402i) q^{32} +(-5.86307 + 0.0210636i) q^{33} +0.517005i q^{34} +(-0.0596812 - 8.30602i) q^{36} +(5.27013 - 5.27013i) q^{37} +(8.20586 - 8.20586i) q^{38} +(-0.356609 + 0.359180i) q^{39} +0.0314968i q^{41} +(-0.0135884 - 3.78233i) q^{42} +(3.76875 + 3.76875i) q^{43} -9.37239 q^{44} -15.6815 q^{46} +(-3.56639 - 3.56639i) q^{47} +(0.0116457 + 3.24158i) q^{48} -1.00000i q^{49} +(-0.288917 + 0.291000i) q^{51} +(-0.572111 + 0.572111i) q^{52} +(3.55291 - 3.55291i) q^{53} +(7.93665 - 8.10960i) q^{54} -1.67875i q^{56} +(9.20439 - 0.0330677i) q^{57} +(4.38949 + 4.38949i) q^{58} +10.3168 q^{59} -6.80634 q^{61} +(14.0791 + 14.0791i) q^{62} +(2.10602 - 2.13651i) q^{63} +12.5137i q^{64} +(-9.08593 - 9.02088i) q^{66} +(-6.34806 + 6.34806i) q^{67} +(-0.463512 + 0.463512i) q^{68} +(-8.82642 - 8.76323i) q^{69} +3.95454i q^{71} +(3.53548 - 3.58665i) q^{72} +(-8.61099 - 8.61099i) q^{73} +16.2757 q^{74} +14.7136 q^{76} +(-2.39360 - 2.39360i) q^{77} +(-1.10528 + 0.00397083i) q^{78} +11.4449i q^{79} +(8.99907 - 0.129328i) q^{81} +(-0.0486356 + 0.0486356i) q^{82} +(3.88059 - 3.88059i) q^{83} +(3.37880 - 3.40317i) q^{84} +11.6390i q^{86} +(0.0176886 + 4.92363i) q^{87} +(-4.01825 - 4.01825i) q^{88} -2.00190 q^{89} -0.292222 q^{91} +(-14.0589 - 14.0589i) q^{92} +(0.0567354 + 15.7923i) q^{93} -11.0140i q^{94} +(-9.08474 + 9.15025i) q^{96} +(-2.26760 + 2.26760i) q^{97} +(1.54414 - 1.54414i) q^{98} +(-0.0729661 - 10.1549i) 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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.54414 + 1.54414i 1.09187 + 1.09187i 0.995329 + 0.0965442i \(0.0307789\pi\)
0.0965442 + 0.995329i \(0.469221\pi\)
\(3\) 0.00622252 + 1.73204i 0.00359257 + 0.999994i
\(4\) 2.76875i 1.38437i
\(5\) 0 0
\(6\) −2.66491 + 2.68412i −1.08794 + 1.09579i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −1.18705 + 1.18705i −0.419686 + 0.419686i
\(9\) −2.99992 + 0.0215553i −0.999974 + 0.00718510i
\(10\) 0 0
\(11\) 3.38507i 1.02064i 0.859986 + 0.510318i \(0.170472\pi\)
−0.859986 + 0.510318i \(0.829528\pi\)
\(12\) −4.79558 + 0.0172286i −1.38436 + 0.00497346i
\(13\) 0.206632 + 0.206632i 0.0573094 + 0.0573094i 0.735181 0.677871i \(-0.237097\pi\)
−0.677871 + 0.735181i \(0.737097\pi\)
\(14\) −2.18375 −0.583631
\(15\) 0 0
\(16\) 1.87154 0.467884
\(17\) 0.167409 + 0.167409i 0.0406026 + 0.0406026i 0.727117 0.686514i \(-0.240860\pi\)
−0.686514 + 0.727117i \(0.740860\pi\)
\(18\) −4.66559 4.59902i −1.09969 1.08400i
\(19\) 5.31419i 1.21916i −0.792725 0.609579i \(-0.791338\pi\)
0.792725 0.609579i \(-0.208662\pi\)
\(20\) 0 0
\(21\) −1.22914 1.22034i −0.268220 0.266299i
\(22\) −5.22702 + 5.22702i −1.11440 + 1.11440i
\(23\) −5.07773 + 5.07773i −1.05878 + 1.05878i −0.0606179 + 0.998161i \(0.519307\pi\)
−0.998161 + 0.0606179i \(0.980693\pi\)
\(24\) −2.06341 2.04864i −0.421191 0.418176i
\(25\) 0 0
\(26\) 0.638138i 0.125149i
\(27\) −0.0560017 5.19585i −0.0107775 0.999942i
\(28\) −1.95780 1.95780i −0.369989 0.369989i
\(29\) 2.84268 0.527872 0.263936 0.964540i \(-0.414979\pi\)
0.263936 + 0.964540i \(0.414979\pi\)
\(30\) 0 0
\(31\) 9.11776 1.63760 0.818799 0.574081i \(-0.194640\pi\)
0.818799 + 0.574081i \(0.194640\pi\)
\(32\) 5.26402 + 5.26402i 0.930557 + 0.930557i
\(33\) −5.86307 + 0.0210636i −1.02063 + 0.00366671i
\(34\) 0.517005i 0.0886657i
\(35\) 0 0
\(36\) −0.0596812 8.30602i −0.00994686 1.38434i
\(37\) 5.27013 5.27013i 0.866404 0.866404i −0.125668 0.992072i \(-0.540107\pi\)
0.992072 + 0.125668i \(0.0401075\pi\)
\(38\) 8.20586 8.20586i 1.33117 1.33117i
\(39\) −0.356609 + 0.359180i −0.0571031 + 0.0575149i
\(40\) 0 0
\(41\) 0.0314968i 0.00491898i 0.999997 + 0.00245949i \(0.000782881\pi\)
−0.999997 + 0.00245949i \(0.999217\pi\)
\(42\) −0.0135884 3.78233i −0.00209674 0.583627i
\(43\) 3.76875 + 3.76875i 0.574728 + 0.574728i 0.933446 0.358718i \(-0.116786\pi\)
−0.358718 + 0.933446i \(0.616786\pi\)
\(44\) −9.37239 −1.41294
\(45\) 0 0
\(46\) −15.6815 −2.31210
\(47\) −3.56639 3.56639i −0.520211 0.520211i 0.397424 0.917635i \(-0.369904\pi\)
−0.917635 + 0.397424i \(0.869904\pi\)
\(48\) 0.0116457 + 3.24158i 0.00168091 + 0.467881i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −0.288917 + 0.291000i −0.0404564 + 0.0407482i
\(52\) −0.572111 + 0.572111i −0.0793376 + 0.0793376i
\(53\) 3.55291 3.55291i 0.488030 0.488030i −0.419654 0.907684i \(-0.637849\pi\)
0.907684 + 0.419654i \(0.137849\pi\)
\(54\) 7.93665 8.10960i 1.08004 1.10358i
\(55\) 0 0
\(56\) 1.67875i 0.224332i
\(57\) 9.20439 0.0330677i 1.21915 0.00437992i
\(58\) 4.38949 + 4.38949i 0.576369 + 0.576369i
\(59\) 10.3168 1.34313 0.671565 0.740946i \(-0.265622\pi\)
0.671565 + 0.740946i \(0.265622\pi\)
\(60\) 0 0
\(61\) −6.80634 −0.871462 −0.435731 0.900077i \(-0.643510\pi\)
−0.435731 + 0.900077i \(0.643510\pi\)
\(62\) 14.0791 + 14.0791i 1.78805 + 1.78805i
\(63\) 2.10602 2.13651i 0.265334 0.269175i
\(64\) 12.5137i 1.56422i
\(65\) 0 0
\(66\) −9.08593 9.02088i −1.11840 1.11039i
\(67\) −6.34806 + 6.34806i −0.775539 + 0.775539i −0.979069 0.203530i \(-0.934759\pi\)
0.203530 + 0.979069i \(0.434759\pi\)
\(68\) −0.463512 + 0.463512i −0.0562091 + 0.0562091i
\(69\) −8.82642 8.76323i −1.06258 1.05497i
\(70\) 0 0
\(71\) 3.95454i 0.469318i 0.972078 + 0.234659i \(0.0753973\pi\)
−0.972078 + 0.234659i \(0.924603\pi\)
\(72\) 3.53548 3.58665i 0.416660 0.422691i
\(73\) −8.61099 8.61099i −1.00784 1.00784i −0.999969 0.00787086i \(-0.997495\pi\)
−0.00787086 0.999969i \(-0.502505\pi\)
\(74\) 16.2757 1.89201
\(75\) 0 0
\(76\) 14.7136 1.68777
\(77\) −2.39360 2.39360i −0.272776 0.272776i
\(78\) −1.10528 + 0.00397083i −0.125148 + 0.000449608i
\(79\) 11.4449i 1.28766i 0.765170 + 0.643828i \(0.222655\pi\)
−0.765170 + 0.643828i \(0.777345\pi\)
\(80\) 0 0
\(81\) 8.99907 0.129328i 0.999897 0.0143698i
\(82\) −0.0486356 + 0.0486356i −0.00537090 + 0.00537090i
\(83\) 3.88059 3.88059i 0.425951 0.425951i −0.461296 0.887246i \(-0.652615\pi\)
0.887246 + 0.461296i \(0.152615\pi\)
\(84\) 3.37880 3.40317i 0.368658 0.371316i
\(85\) 0 0
\(86\) 11.6390i 1.25506i
\(87\) 0.0176886 + 4.92363i 0.00189642 + 0.527868i
\(88\) −4.01825 4.01825i −0.428347 0.428347i
\(89\) −2.00190 −0.212201 −0.106100 0.994355i \(-0.533836\pi\)
−0.106100 + 0.994355i \(0.533836\pi\)
\(90\) 0 0
\(91\) −0.292222 −0.0306332
\(92\) −14.0589 14.0589i −1.46574 1.46574i
\(93\) 0.0567354 + 15.7923i 0.00588319 + 1.63759i
\(94\) 11.0140i 1.13601i
\(95\) 0 0
\(96\) −9.08474 + 9.15025i −0.927208 + 0.933894i
\(97\) −2.26760 + 2.26760i −0.230240 + 0.230240i −0.812793 0.582553i \(-0.802054\pi\)
0.582553 + 0.812793i \(0.302054\pi\)
\(98\) 1.54414 1.54414i 0.155982 0.155982i
\(99\) −0.0729661 10.1549i −0.00733337 1.02061i
\(100\) 0 0
\(101\) 8.63630i 0.859344i −0.902985 0.429672i \(-0.858629\pi\)
0.902985 0.429672i \(-0.141371\pi\)
\(102\) −0.895474 + 0.00321708i −0.0886651 + 0.000318538i
\(103\) −0.964332 0.964332i −0.0950185 0.0950185i 0.658000 0.753018i \(-0.271403\pi\)
−0.753018 + 0.658000i \(0.771403\pi\)
\(104\) −0.490566 −0.0481039
\(105\) 0 0
\(106\) 10.9724 1.06573
\(107\) −2.95847 2.95847i −0.286007 0.286007i 0.549492 0.835499i \(-0.314821\pi\)
−0.835499 + 0.549492i \(0.814821\pi\)
\(108\) 14.3860 0.155055i 1.38429 0.0149201i
\(109\) 2.82182i 0.270281i 0.990826 + 0.135141i \(0.0431486\pi\)
−0.990826 + 0.135141i \(0.956851\pi\)
\(110\) 0 0
\(111\) 9.16087 + 9.09528i 0.869511 + 0.863286i
\(112\) −1.32338 + 1.32338i −0.125047 + 0.125047i
\(113\) 2.01798 2.01798i 0.189835 0.189835i −0.605790 0.795625i \(-0.707143\pi\)
0.795625 + 0.605790i \(0.207143\pi\)
\(114\) 14.2639 + 14.1618i 1.33594 + 1.32638i
\(115\) 0 0
\(116\) 7.87065i 0.730771i
\(117\) −0.624334 0.615426i −0.0577197 0.0568961i
\(118\) 15.9306 + 15.9306i 1.46653 + 1.46653i
\(119\) −0.236752 −0.0217030
\(120\) 0 0
\(121\) −0.458667 −0.0416970
\(122\) −10.5099 10.5099i −0.951526 0.951526i
\(123\) −0.0545538 0.000195990i −0.00491895 1.76718e-5i
\(124\) 25.2448i 2.26705i
\(125\) 0 0
\(126\) 6.55107 0.0470713i 0.583616 0.00419345i
\(127\) 11.6271 11.6271i 1.03174 1.03174i 0.0322583 0.999480i \(-0.489730\pi\)
0.999480 0.0322583i \(-0.0102699\pi\)
\(128\) −8.79491 + 8.79491i −0.777367 + 0.777367i
\(129\) −6.50417 + 6.55107i −0.572660 + 0.576789i
\(130\) 0 0
\(131\) 12.7013i 1.10972i −0.831943 0.554861i \(-0.812772\pi\)
0.831943 0.554861i \(-0.187228\pi\)
\(132\) −0.0583199 16.2333i −0.00507609 1.41293i
\(133\) 3.75770 + 3.75770i 0.325834 + 0.325834i
\(134\) −19.6046 −1.69358
\(135\) 0 0
\(136\) −0.397446 −0.0340807
\(137\) −5.19451 5.19451i −0.443797 0.443797i 0.449489 0.893286i \(-0.351606\pi\)
−0.893286 + 0.449489i \(0.851606\pi\)
\(138\) −0.0975782 27.1609i −0.00830641 2.31209i
\(139\) 12.3138i 1.04444i 0.852810 + 0.522221i \(0.174897\pi\)
−0.852810 + 0.522221i \(0.825103\pi\)
\(140\) 0 0
\(141\) 6.15493 6.19932i 0.518339 0.522077i
\(142\) −6.10637 + 6.10637i −0.512435 + 0.512435i
\(143\) −0.699463 + 0.699463i −0.0584920 + 0.0584920i
\(144\) −5.61447 + 0.0403416i −0.467872 + 0.00336180i
\(145\) 0 0
\(146\) 26.5932i 2.20087i
\(147\) 1.73204 0.00622252i 0.142856 0.000513225i
\(148\) 14.5917 + 14.5917i 1.19943 + 1.19943i
\(149\) −18.9350 −1.55121 −0.775607 0.631216i \(-0.782556\pi\)
−0.775607 + 0.631216i \(0.782556\pi\)
\(150\) 0 0
\(151\) −1.90527 −0.155049 −0.0775243 0.996990i \(-0.524702\pi\)
−0.0775243 + 0.996990i \(0.524702\pi\)
\(152\) 6.30822 + 6.30822i 0.511665 + 0.511665i
\(153\) −0.505822 0.498604i −0.0408933 0.0403098i
\(154\) 7.39212i 0.595674i
\(155\) 0 0
\(156\) −0.994479 0.987359i −0.0796221 0.0790520i
\(157\) 4.31728 4.31728i 0.344557 0.344557i −0.513521 0.858077i \(-0.671659\pi\)
0.858077 + 0.513521i \(0.171659\pi\)
\(158\) −17.6726 + 17.6726i −1.40596 + 1.40596i
\(159\) 6.17589 + 6.13167i 0.489780 + 0.486273i
\(160\) 0 0
\(161\) 7.18099i 0.565941i
\(162\) 14.0955 + 13.6961i 1.10745 + 1.07607i
\(163\) −3.57655 3.57655i −0.280137 0.280137i 0.553027 0.833164i \(-0.313473\pi\)
−0.833164 + 0.553027i \(0.813473\pi\)
\(164\) −0.0872068 −0.00680970
\(165\) 0 0
\(166\) 11.9844 0.930168
\(167\) −6.39241 6.39241i −0.494659 0.494659i 0.415111 0.909771i \(-0.363743\pi\)
−0.909771 + 0.415111i \(0.863743\pi\)
\(168\) 2.90765 0.0104460i 0.224330 0.000805929i
\(169\) 12.9146i 0.993431i
\(170\) 0 0
\(171\) 0.114549 + 15.9422i 0.00875978 + 1.21913i
\(172\) −10.4347 + 10.4347i −0.795638 + 0.795638i
\(173\) 3.88791 3.88791i 0.295592 0.295592i −0.543692 0.839285i \(-0.682974\pi\)
0.839285 + 0.543692i \(0.182974\pi\)
\(174\) −7.57546 + 7.63009i −0.574294 + 0.578436i
\(175\) 0 0
\(176\) 6.33528i 0.477540i
\(177\) 0.0641964 + 17.8691i 0.00482529 + 1.34312i
\(178\) −3.09121 3.09121i −0.231696 0.231696i
\(179\) 14.6322 1.09366 0.546832 0.837242i \(-0.315834\pi\)
0.546832 + 0.837242i \(0.315834\pi\)
\(180\) 0 0
\(181\) −9.83718 −0.731192 −0.365596 0.930774i \(-0.619135\pi\)
−0.365596 + 0.930774i \(0.619135\pi\)
\(182\) −0.451232 0.451232i −0.0334475 0.0334475i
\(183\) −0.0423526 11.7888i −0.00313079 0.871456i
\(184\) 12.0551i 0.888710i
\(185\) 0 0
\(186\) −24.2980 + 24.4732i −1.78161 + 1.79446i
\(187\) −0.566689 + 0.566689i −0.0414404 + 0.0414404i
\(188\) 9.87442 9.87442i 0.720166 0.720166i
\(189\) 3.71362 + 3.63442i 0.270126 + 0.264365i
\(190\) 0 0
\(191\) 6.37886i 0.461558i −0.973006 0.230779i \(-0.925873\pi\)
0.973006 0.230779i \(-0.0741275\pi\)
\(192\) −21.6743 + 0.0778669i −1.56421 + 0.00561956i
\(193\) −7.56336 7.56336i −0.544422 0.544422i 0.380400 0.924822i \(-0.375786\pi\)
−0.924822 + 0.380400i \(0.875786\pi\)
\(194\) −7.00299 −0.502785
\(195\) 0 0
\(196\) 2.76875 0.197768
\(197\) −1.01490 1.01490i −0.0723090 0.0723090i 0.670027 0.742336i \(-0.266282\pi\)
−0.742336 + 0.670027i \(0.766282\pi\)
\(198\) 15.5680 15.7933i 1.10637 1.12238i
\(199\) 9.40041i 0.666378i −0.942860 0.333189i \(-0.891875\pi\)
0.942860 0.333189i \(-0.108125\pi\)
\(200\) 0 0
\(201\) −11.0346 10.9556i −0.778320 0.772748i
\(202\) 13.3357 13.3357i 0.938295 0.938295i
\(203\) −2.01007 + 2.01007i −0.141080 + 0.141080i
\(204\) −0.805705 0.799937i −0.0564107 0.0560068i
\(205\) 0 0
\(206\) 2.97813i 0.207496i
\(207\) 15.1233 15.3422i 1.05114 1.06636i
\(208\) 0.386719 + 0.386719i 0.0268142 + 0.0268142i
\(209\) 17.9889 1.24432
\(210\) 0 0
\(211\) −8.29157 −0.570815 −0.285407 0.958406i \(-0.592129\pi\)
−0.285407 + 0.958406i \(0.592129\pi\)
\(212\) 9.83710 + 9.83710i 0.675615 + 0.675615i
\(213\) −6.84942 + 0.0246072i −0.469315 + 0.00168606i
\(214\) 9.13661i 0.624566i
\(215\) 0 0
\(216\) 6.23422 + 6.10127i 0.424185 + 0.415139i
\(217\) −6.44723 + 6.44723i −0.437666 + 0.437666i
\(218\) −4.35729 + 4.35729i −0.295113 + 0.295113i
\(219\) 14.8610 14.9682i 1.00421 1.01145i
\(220\) 0 0
\(221\) 0.0691839i 0.00465382i
\(222\) 0.101276 + 28.1901i 0.00679717 + 1.89199i
\(223\) −3.86020 3.86020i −0.258498 0.258498i 0.565945 0.824443i \(-0.308511\pi\)
−0.824443 + 0.565945i \(0.808511\pi\)
\(224\) −7.44445 −0.497404
\(225\) 0 0
\(226\) 6.23208 0.414552
\(227\) 1.50739 + 1.50739i 0.100049 + 0.100049i 0.755360 0.655310i \(-0.227462\pi\)
−0.655310 + 0.755360i \(0.727462\pi\)
\(228\) 0.0915560 + 25.4846i 0.00606344 + 1.68776i
\(229\) 6.26009i 0.413678i 0.978375 + 0.206839i \(0.0663177\pi\)
−0.978375 + 0.206839i \(0.933682\pi\)
\(230\) 0 0
\(231\) 4.13092 4.16071i 0.271795 0.273755i
\(232\) −3.37440 + 3.37440i −0.221541 + 0.221541i
\(233\) −2.67422 + 2.67422i −0.175194 + 0.175194i −0.789257 0.614063i \(-0.789534\pi\)
0.614063 + 0.789257i \(0.289534\pi\)
\(234\) −0.0137553 1.91436i −0.000899209 0.125146i
\(235\) 0 0
\(236\) 28.5645i 1.85939i
\(237\) −19.8231 + 0.0712164i −1.28765 + 0.00462600i
\(238\) −0.365578 0.365578i −0.0236969 0.0236969i
\(239\) −2.08521 −0.134881 −0.0674406 0.997723i \(-0.521483\pi\)
−0.0674406 + 0.997723i \(0.521483\pi\)
\(240\) 0 0
\(241\) −5.43686 −0.350219 −0.175110 0.984549i \(-0.556028\pi\)
−0.175110 + 0.984549i \(0.556028\pi\)
\(242\) −0.708247 0.708247i −0.0455279 0.0455279i
\(243\) 0.279999 + 15.5859i 0.0179619 + 0.999839i
\(244\) 18.8450i 1.20643i
\(245\) 0 0
\(246\) −0.0845414 0.0839361i −0.00539016 0.00535157i
\(247\) 1.09808 1.09808i 0.0698692 0.0698692i
\(248\) −10.8233 + 10.8233i −0.687278 + 0.687278i
\(249\) 6.74549 + 6.69720i 0.427478 + 0.424418i
\(250\) 0 0
\(251\) 23.3428i 1.47339i −0.676227 0.736693i \(-0.736386\pi\)
0.676227 0.736693i \(-0.263614\pi\)
\(252\) 5.91545 + 5.83104i 0.372638 + 0.367321i
\(253\) −17.1884 17.1884i −1.08063 1.08063i
\(254\) 35.9078 2.25305
\(255\) 0 0
\(256\) −2.13372 −0.133358
\(257\) 10.9273 + 10.9273i 0.681627 + 0.681627i 0.960367 0.278740i \(-0.0899167\pi\)
−0.278740 + 0.960367i \(0.589917\pi\)
\(258\) −20.1591 + 0.0724236i −1.25505 + 0.00450890i
\(259\) 7.45309i 0.463112i
\(260\) 0 0
\(261\) −8.52781 + 0.0612747i −0.527858 + 0.00379281i
\(262\) 19.6127 19.6127i 1.21167 1.21167i
\(263\) 18.1808 18.1808i 1.12108 1.12108i 0.129497 0.991580i \(-0.458664\pi\)
0.991580 0.129497i \(-0.0413364\pi\)
\(264\) 6.93477 6.98477i 0.426805 0.429883i
\(265\) 0 0
\(266\) 11.6048i 0.711539i
\(267\) −0.0124569 3.46737i −0.000762347 0.212199i
\(268\) −17.5762 17.5762i −1.07364 1.07364i
\(269\) −28.5125 −1.73844 −0.869219 0.494428i \(-0.835378\pi\)
−0.869219 + 0.494428i \(0.835378\pi\)
\(270\) 0 0
\(271\) 3.12214 0.189656 0.0948282 0.995494i \(-0.469770\pi\)
0.0948282 + 0.995494i \(0.469770\pi\)
\(272\) 0.313312 + 0.313312i 0.0189973 + 0.0189973i
\(273\) −0.00181836 0.506139i −0.000110052 0.0306330i
\(274\) 16.0421i 0.969139i
\(275\) 0 0
\(276\) 24.2631 24.4381i 1.46047 1.47100i
\(277\) −12.2472 + 12.2472i −0.735861 + 0.735861i −0.971774 0.235913i \(-0.924192\pi\)
0.235913 + 0.971774i \(0.424192\pi\)
\(278\) −19.0142 + 19.0142i −1.14040 + 1.14040i
\(279\) −27.3526 + 0.196536i −1.63756 + 0.0117663i
\(280\) 0 0
\(281\) 12.7181i 0.758698i 0.925254 + 0.379349i \(0.123852\pi\)
−0.925254 + 0.379349i \(0.876148\pi\)
\(282\) 19.0767 0.0685349i 1.13600 0.00408120i
\(283\) 19.8271 + 19.8271i 1.17860 + 1.17860i 0.980102 + 0.198495i \(0.0636053\pi\)
0.198495 + 0.980102i \(0.436395\pi\)
\(284\) −10.9491 −0.649711
\(285\) 0 0
\(286\) −2.16014 −0.127732
\(287\) −0.0222716 0.0222716i −0.00131465 0.00131465i
\(288\) −15.9051 15.6782i −0.937219 0.923847i
\(289\) 16.9439i 0.996703i
\(290\) 0 0
\(291\) −3.94168 3.91346i −0.231066 0.229411i
\(292\) 23.8416 23.8416i 1.39523 1.39523i
\(293\) −6.72836 + 6.72836i −0.393075 + 0.393075i −0.875782 0.482707i \(-0.839654\pi\)
0.482707 + 0.875782i \(0.339654\pi\)
\(294\) 2.68412 + 2.66491i 0.156541 + 0.155420i
\(295\) 0 0
\(296\) 12.5118i 0.727236i
\(297\) 17.5883 0.189570i 1.02058 0.0109999i
\(298\) −29.2383 29.2383i −1.69373 1.69373i
\(299\) −2.09844 −0.121356
\(300\) 0 0
\(301\) −5.32981 −0.307205
\(302\) −2.94201 2.94201i −0.169293 0.169293i
\(303\) 14.9584 0.0537396i 0.859339 0.00308726i
\(304\) 9.94571i 0.570426i
\(305\) 0 0
\(306\) −0.0111442 1.55098i −0.000637072 0.0886634i
\(307\) −10.1105 + 10.1105i −0.577034 + 0.577034i −0.934085 0.357051i \(-0.883782\pi\)
0.357051 + 0.934085i \(0.383782\pi\)
\(308\) 6.62728 6.62728i 0.377624 0.377624i
\(309\) 1.66426 1.67626i 0.0946765 0.0953592i
\(310\) 0 0
\(311\) 0.394155i 0.0223505i −0.999938 0.0111752i \(-0.996443\pi\)
0.999938 0.0111752i \(-0.00355726\pi\)
\(312\) −0.00305256 0.849680i −0.000172817 0.0481036i
\(313\) 10.3810 + 10.3810i 0.586767 + 0.586767i 0.936754 0.349987i \(-0.113814\pi\)
−0.349987 + 0.936754i \(0.613814\pi\)
\(314\) 13.3330 0.752424
\(315\) 0 0
\(316\) −31.6881 −1.78260
\(317\) −19.8075 19.8075i −1.11250 1.11250i −0.992812 0.119688i \(-0.961810\pi\)
−0.119688 0.992812i \(-0.538190\pi\)
\(318\) 0.0682759 + 19.0046i 0.00382872 + 1.06573i
\(319\) 9.62264i 0.538764i
\(320\) 0 0
\(321\) 5.10579 5.14260i 0.284977 0.287032i
\(322\) 11.0885 11.0885i 0.617936 0.617936i
\(323\) 0.889642 0.889642i 0.0495010 0.0495010i
\(324\) 0.358078 + 24.9161i 0.0198932 + 1.38423i
\(325\) 0 0
\(326\) 11.0454i 0.611748i
\(327\) −4.88750 + 0.0175588i −0.270279 + 0.000971005i
\(328\) −0.0373884 0.0373884i −0.00206443 0.00206443i
\(329\) 5.04363 0.278065
\(330\) 0 0
\(331\) −24.7348 −1.35955 −0.679774 0.733422i \(-0.737922\pi\)
−0.679774 + 0.733422i \(0.737922\pi\)
\(332\) 10.7444 + 10.7444i 0.589674 + 0.589674i
\(333\) −15.6964 + 15.9236i −0.860157 + 0.872607i
\(334\) 19.7416i 1.08021i
\(335\) 0 0
\(336\) −2.30038 2.28391i −0.125496 0.124597i
\(337\) 3.40139 3.40139i 0.185286 0.185286i −0.608369 0.793655i \(-0.708176\pi\)
0.793655 + 0.608369i \(0.208176\pi\)
\(338\) 19.9420 19.9420i 1.08470 1.08470i
\(339\) 3.50777 + 3.48266i 0.190516 + 0.189152i
\(340\) 0 0
\(341\) 30.8642i 1.67139i
\(342\) −24.4401 + 24.7938i −1.32157 + 1.34070i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −8.94740 −0.482411
\(345\) 0 0
\(346\) 12.0070 0.645498
\(347\) 24.0324 + 24.0324i 1.29013 + 1.29013i 0.934706 + 0.355421i \(0.115663\pi\)
0.355421 + 0.934706i \(0.384337\pi\)
\(348\) −13.6323 + 0.0489753i −0.730766 + 0.00262535i
\(349\) 9.37078i 0.501607i −0.968038 0.250803i \(-0.919305\pi\)
0.968038 0.250803i \(-0.0806947\pi\)
\(350\) 0 0
\(351\) 1.06206 1.08520i 0.0566884 0.0579237i
\(352\) −17.8191 + 17.8191i −0.949759 + 0.949759i
\(353\) 14.5888 14.5888i 0.776481 0.776481i −0.202750 0.979231i \(-0.564988\pi\)
0.979231 + 0.202750i \(0.0649878\pi\)
\(354\) −27.4932 + 27.6915i −1.46125 + 1.47179i
\(355\) 0 0
\(356\) 5.54275i 0.293765i
\(357\) −0.00147319 0.410063i −7.79696e−5 0.0217028i
\(358\) 22.5942 + 22.5942i 1.19414 + 1.19414i
\(359\) −27.2654 −1.43901 −0.719506 0.694486i \(-0.755632\pi\)
−0.719506 + 0.694486i \(0.755632\pi\)
\(360\) 0 0
\(361\) −9.24062 −0.486349
\(362\) −15.1900 15.1900i −0.798369 0.798369i
\(363\) −0.00285407 0.794430i −0.000149800 0.0416968i
\(364\) 0.809088i 0.0424077i
\(365\) 0 0
\(366\) 18.1382 18.2690i 0.948101 0.954938i
\(367\) −15.9239 + 15.9239i −0.831218 + 0.831218i −0.987683 0.156465i \(-0.949990\pi\)
0.156465 + 0.987683i \(0.449990\pi\)
\(368\) −9.50315 + 9.50315i −0.495386 + 0.495386i
\(369\) −0.000678924 0.0944881i −3.53434e−5 0.00491885i
\(370\) 0 0
\(371\) 5.02457i 0.260863i
\(372\) −43.7249 + 0.157086i −2.26703 + 0.00814453i
\(373\) −23.3283 23.3283i −1.20790 1.20790i −0.971707 0.236189i \(-0.924102\pi\)
−0.236189 0.971707i \(-0.575898\pi\)
\(374\) −1.75010 −0.0904954
\(375\) 0 0
\(376\) 8.46698 0.436651
\(377\) 0.587387 + 0.587387i 0.0302520 + 0.0302520i
\(378\) 0.122294 + 11.3464i 0.00629010 + 0.583597i
\(379\) 37.4477i 1.92356i 0.273828 + 0.961779i \(0.411710\pi\)
−0.273828 + 0.961779i \(0.588290\pi\)
\(380\) 0 0
\(381\) 20.2109 + 20.0662i 1.03544 + 1.02802i
\(382\) 9.84986 9.84986i 0.503963 0.503963i
\(383\) −4.95443 + 4.95443i −0.253159 + 0.253159i −0.822265 0.569105i \(-0.807290\pi\)
0.569105 + 0.822265i \(0.307290\pi\)
\(384\) −15.2879 15.1784i −0.780155 0.774570i
\(385\) 0 0
\(386\) 23.3578i 1.18888i
\(387\) −11.3872 11.2247i −0.578843 0.570584i
\(388\) −6.27841 6.27841i −0.318738 0.318738i
\(389\) −9.20279 −0.466600 −0.233300 0.972405i \(-0.574952\pi\)
−0.233300 + 0.972405i \(0.574952\pi\)
\(390\) 0 0
\(391\) −1.70011 −0.0859783
\(392\) 1.18705 + 1.18705i 0.0599552 + 0.0599552i
\(393\) 21.9992 0.0790344i 1.10971 0.00398676i
\(394\) 3.13431i 0.157904i
\(395\) 0 0
\(396\) 28.1164 0.202025i 1.41290 0.0101521i
\(397\) −21.9242 + 21.9242i −1.10034 + 1.10034i −0.105976 + 0.994369i \(0.533797\pi\)
−0.994369 + 0.105976i \(0.966203\pi\)
\(398\) 14.5156 14.5156i 0.727600 0.727600i
\(399\) −6.48510 + 6.53187i −0.324661 + 0.327002i
\(400\) 0 0
\(401\) 25.7514i 1.28596i 0.765882 + 0.642982i \(0.222303\pi\)
−0.765882 + 0.642982i \(0.777697\pi\)
\(402\) −0.121990 33.9560i −0.00608431 1.69357i
\(403\) 1.88402 + 1.88402i 0.0938497 + 0.0938497i
\(404\) 23.9117 1.18965
\(405\) 0 0
\(406\) −6.20768 −0.308082
\(407\) 17.8397 + 17.8397i 0.884283 + 0.884283i
\(408\) −0.00247311 0.688392i −0.000122437 0.0340805i
\(409\) 10.9496i 0.541425i 0.962660 + 0.270712i \(0.0872592\pi\)
−0.962660 + 0.270712i \(0.912741\pi\)
\(410\) 0 0
\(411\) 8.96477 9.02942i 0.442200 0.445388i
\(412\) 2.66999 2.66999i 0.131541 0.131541i
\(413\) −7.29506 + 7.29506i −0.358967 + 0.358967i
\(414\) 47.0431 0.338019i 2.31204 0.0166127i
\(415\) 0 0
\(416\) 2.17543i 0.106659i
\(417\) −21.3280 + 0.0766229i −1.04444 + 0.00375224i
\(418\) 27.7774 + 27.7774i 1.35864 + 1.35864i
\(419\) 5.86958 0.286748 0.143374 0.989669i \(-0.454205\pi\)
0.143374 + 0.989669i \(0.454205\pi\)
\(420\) 0 0
\(421\) 26.8842 1.31026 0.655129 0.755517i \(-0.272614\pi\)
0.655129 + 0.755517i \(0.272614\pi\)
\(422\) −12.8034 12.8034i −0.623257 0.623257i
\(423\) 10.7758 + 10.6220i 0.523936 + 0.516460i
\(424\) 8.43498i 0.409639i
\(425\) 0 0
\(426\) −10.6145 10.5385i −0.514273 0.510591i
\(427\) 4.81281 4.81281i 0.232908 0.232908i
\(428\) 8.19126 8.19126i 0.395940 0.395940i
\(429\) −1.21585 1.20714i −0.0587018 0.0582815i
\(430\) 0 0
\(431\) 4.18118i 0.201400i 0.994917 + 0.100700i \(0.0321083\pi\)
−0.994917 + 0.100700i \(0.967892\pi\)
\(432\) −0.104809 9.72423i −0.00504264 0.467857i
\(433\) 2.20877 + 2.20877i 0.106146 + 0.106146i 0.758185 0.652039i \(-0.226086\pi\)
−0.652039 + 0.758185i \(0.726086\pi\)
\(434\) −19.9109 −0.955752
\(435\) 0 0
\(436\) −7.81290 −0.374170
\(437\) 26.9840 + 26.9840i 1.29082 + 1.29082i
\(438\) 46.0604 0.165477i 2.20085 0.00790678i
\(439\) 27.6028i 1.31741i 0.752401 + 0.658706i \(0.228896\pi\)
−0.752401 + 0.658706i \(0.771104\pi\)
\(440\) 0 0
\(441\) 0.0215553 + 2.99992i 0.00102644 + 0.142853i
\(442\) −0.106830 + 0.106830i −0.00508138 + 0.00508138i
\(443\) 12.3040 12.3040i 0.584582 0.584582i −0.351577 0.936159i \(-0.614354\pi\)
0.936159 + 0.351577i \(0.114354\pi\)
\(444\) −25.1825 + 25.3641i −1.19511 + 1.20373i
\(445\) 0 0
\(446\) 11.9214i 0.564494i
\(447\) −0.117823 32.7961i −0.00557285 1.55120i
\(448\) −8.84854 8.84854i −0.418054 0.418054i
\(449\) 34.1859 1.61333 0.806666 0.591008i \(-0.201270\pi\)
0.806666 + 0.591008i \(0.201270\pi\)
\(450\) 0 0
\(451\) −0.106619 −0.00502049
\(452\) 5.58726 + 5.58726i 0.262803 + 0.262803i
\(453\) −0.0118556 3.30000i −0.000557024 0.155048i
\(454\) 4.65526i 0.218482i
\(455\) 0 0
\(456\) −10.8868 + 10.9653i −0.509823 + 0.513499i
\(457\) 9.31021 9.31021i 0.435513 0.435513i −0.454986 0.890499i \(-0.650356\pi\)
0.890499 + 0.454986i \(0.150356\pi\)
\(458\) −9.66646 + 9.66646i −0.451684 + 0.451684i
\(459\) 0.860455 0.879206i 0.0401626 0.0410378i
\(460\) 0 0
\(461\) 25.6579i 1.19501i 0.801865 + 0.597505i \(0.203841\pi\)
−0.801865 + 0.597505i \(0.796159\pi\)
\(462\) 12.8034 0.0459976i 0.595670 0.00214000i
\(463\) −13.2170 13.2170i −0.614248 0.614248i 0.329802 0.944050i \(-0.393018\pi\)
−0.944050 + 0.329802i \(0.893018\pi\)
\(464\) 5.32017 0.246983
\(465\) 0 0
\(466\) −8.25874 −0.382579
\(467\) −19.6659 19.6659i −0.910031 0.910031i 0.0862431 0.996274i \(-0.472514\pi\)
−0.996274 + 0.0862431i \(0.972514\pi\)
\(468\) 1.70396 1.72862i 0.0787655 0.0799056i
\(469\) 8.97752i 0.414543i
\(470\) 0 0
\(471\) 7.50457 + 7.45084i 0.345792 + 0.343317i
\(472\) −12.2466 + 12.2466i −0.563693 + 0.563693i
\(473\) −12.7575 + 12.7575i −0.586588 + 0.586588i
\(474\) −30.7196 30.4997i −1.41100 1.40090i
\(475\) 0 0
\(476\) 0.655505i 0.0300450i
\(477\) −10.5819 + 10.7350i −0.484510 + 0.491524i
\(478\) −3.21986 3.21986i −0.147273 0.147273i
\(479\) 26.9725 1.23240 0.616202 0.787588i \(-0.288670\pi\)
0.616202 + 0.787588i \(0.288670\pi\)
\(480\) 0 0
\(481\) 2.17795 0.0993062
\(482\) −8.39528 8.39528i −0.382395 0.382395i
\(483\) 12.4378 0.0446838i 0.565937 0.00203319i
\(484\) 1.26993i 0.0577242i
\(485\) 0 0
\(486\) −23.6345 + 24.4993i −1.07208 + 1.11131i
\(487\) 28.6505 28.6505i 1.29828 1.29828i 0.368749 0.929529i \(-0.379786\pi\)
0.929529 0.368749i \(-0.120214\pi\)
\(488\) 8.07948 8.07948i 0.365741 0.365741i
\(489\) 6.17247 6.21698i 0.279129 0.281141i
\(490\) 0 0
\(491\) 2.74522i 0.123890i 0.998080 + 0.0619450i \(0.0197303\pi\)
−0.998080 + 0.0619450i \(0.980270\pi\)
\(492\) −0.000542646 0.151046i −2.44644e−5 0.00680966i
\(493\) 0.475888 + 0.475888i 0.0214329 + 0.0214329i
\(494\) 3.39119 0.152577
\(495\) 0 0
\(496\) 17.0642 0.766206
\(497\) −2.79628 2.79628i −0.125430 0.125430i
\(498\) 0.0745730 + 20.7574i 0.00334170 + 0.930162i
\(499\) 30.3151i 1.35709i −0.734558 0.678546i \(-0.762611\pi\)
0.734558 0.678546i \(-0.237389\pi\)
\(500\) 0 0
\(501\) 11.0321 11.1117i 0.492879 0.496433i
\(502\) 36.0446 36.0446i 1.60875 1.60875i
\(503\) −0.331820 + 0.331820i −0.0147951 + 0.0147951i −0.714466 0.699671i \(-0.753330\pi\)
0.699671 + 0.714466i \(0.253330\pi\)
\(504\) 0.0361859 + 5.03611i 0.00161185 + 0.224326i
\(505\) 0 0
\(506\) 53.0827i 2.35982i
\(507\) 22.3686 0.0803614i 0.993425 0.00356898i
\(508\) 32.1925 + 32.1925i 1.42831 + 1.42831i
\(509\) −14.6491 −0.649311 −0.324656 0.945832i \(-0.605248\pi\)
−0.324656 + 0.945832i \(0.605248\pi\)
\(510\) 0 0
\(511\) 12.1778 0.538713
\(512\) 14.2950 + 14.2950i 0.631758 + 0.631758i
\(513\) −27.6117 + 0.297604i −1.21909 + 0.0131395i
\(514\) 33.7466i 1.48850i
\(515\) 0 0
\(516\) −18.1382 18.0084i −0.798492 0.792775i
\(517\) 12.0725 12.0725i 0.530946 0.530946i
\(518\) −11.5086 + 11.5086i −0.505660 + 0.505660i
\(519\) 6.75820 + 6.70982i 0.296652 + 0.294528i
\(520\) 0 0
\(521\) 24.6501i 1.07994i −0.841683 0.539971i \(-0.818435\pi\)
0.841683 0.539971i \(-0.181565\pi\)
\(522\) −13.2628 13.0735i −0.580495 0.572212i
\(523\) 23.4069 + 23.4069i 1.02351 + 1.02351i 0.999717 + 0.0237950i \(0.00757491\pi\)
0.0237950 + 0.999717i \(0.492425\pi\)
\(524\) 35.1668 1.53627
\(525\) 0 0
\(526\) 56.1475 2.44815
\(527\) 1.52639 + 1.52639i 0.0664907 + 0.0664907i
\(528\) −10.9730 + 0.0394214i −0.477536 + 0.00171560i
\(529\) 28.5666i 1.24203i
\(530\) 0 0
\(531\) −30.9495 + 0.222381i −1.34310 + 0.00965053i
\(532\) −10.4041 + 10.4041i −0.451076 + 0.451076i
\(533\) −0.00650825 + 0.00650825i −0.000281904 + 0.000281904i
\(534\) 5.33487 5.37334i 0.230862 0.232527i
\(535\) 0 0
\(536\) 15.0710i 0.650967i
\(537\) 0.0910493 + 25.3436i 0.00392907 + 1.09366i
\(538\) −44.0273 44.0273i −1.89815 1.89815i
\(539\) 3.38507 0.145805
\(540\) 0 0
\(541\) −27.2143 −1.17003 −0.585017 0.811021i \(-0.698912\pi\)
−0.585017 + 0.811021i \(0.698912\pi\)
\(542\) 4.82102 + 4.82102i 0.207081 + 0.207081i
\(543\) −0.0612121 17.0384i −0.00262686 0.731187i
\(544\) 1.76249i 0.0755660i
\(545\) 0 0
\(546\) 0.778743 0.784359i 0.0333271 0.0335675i
\(547\) 3.63475 3.63475i 0.155411 0.155411i −0.625119 0.780530i \(-0.714949\pi\)
0.780530 + 0.625119i \(0.214949\pi\)
\(548\) 14.3823 14.3823i 0.614380 0.614380i
\(549\) 20.4185 0.146713i 0.871440 0.00626154i
\(550\) 0 0
\(551\) 15.1065i 0.643559i
\(552\) 20.8798 0.0750128i 0.888705 0.00319276i
\(553\) −8.09279 8.09279i −0.344141 0.344141i
\(554\) −37.8227 −1.60693
\(555\) 0 0
\(556\) −34.0938 −1.44590
\(557\) 5.91751 + 5.91751i 0.250733 + 0.250733i 0.821271 0.570538i \(-0.193265\pi\)
−0.570538 + 0.821271i \(0.693265\pi\)
\(558\) −42.5397 41.9328i −1.80085 1.77516i
\(559\) 1.55749i 0.0658747i
\(560\) 0 0
\(561\) −0.985055 0.978002i −0.0415890 0.0412913i
\(562\) −19.6385 + 19.6385i −0.828402 + 0.828402i
\(563\) −13.8267 + 13.8267i −0.582728 + 0.582728i −0.935652 0.352924i \(-0.885187\pi\)
0.352924 + 0.935652i \(0.385187\pi\)
\(564\) 17.1643 + 17.0414i 0.722749 + 0.717574i
\(565\) 0 0
\(566\) 61.2316i 2.57376i
\(567\) −6.27185 + 6.45475i −0.263393 + 0.271074i
\(568\) −4.69425 4.69425i −0.196966 0.196966i
\(569\) 6.82232 0.286007 0.143003 0.989722i \(-0.454324\pi\)
0.143003 + 0.989722i \(0.454324\pi\)
\(570\) 0 0
\(571\) 19.7545 0.826701 0.413351 0.910572i \(-0.364358\pi\)
0.413351 + 0.910572i \(0.364358\pi\)
\(572\) −1.93663 1.93663i −0.0809747 0.0809747i
\(573\) 11.0484 0.0396926i 0.461555 0.00165818i
\(574\) 0.0687811i 0.00287087i
\(575\) 0 0
\(576\) −0.269737 37.5402i −0.0112390 1.56417i
\(577\) −1.10727 + 1.10727i −0.0460964 + 0.0460964i −0.729779 0.683683i \(-0.760377\pi\)
0.683683 + 0.729779i \(0.260377\pi\)
\(578\) 26.1639 26.1639i 1.08827 1.08827i
\(579\) 13.0530 13.1471i 0.542463 0.546375i
\(580\) 0 0
\(581\) 5.48799i 0.227680i
\(582\) −0.0435762 12.1295i −0.00180629 0.502782i
\(583\) 12.0268 + 12.0268i 0.498100 + 0.498100i
\(584\) 20.4434 0.845953
\(585\) 0 0
\(586\) −20.7791 −0.858376
\(587\) 7.76708 + 7.76708i 0.320582 + 0.320582i 0.848990 0.528408i \(-0.177211\pi\)
−0.528408 + 0.848990i \(0.677211\pi\)
\(588\) 0.0172286 + 4.79558i 0.000710495 + 0.197766i
\(589\) 48.4535i 1.99649i
\(590\) 0 0
\(591\) 1.75154 1.76417i 0.0720487 0.0725683i
\(592\) 9.86325 9.86325i 0.405377 0.405377i
\(593\) −8.01301 + 8.01301i −0.329055 + 0.329055i −0.852227 0.523172i \(-0.824748\pi\)
0.523172 + 0.852227i \(0.324748\pi\)
\(594\) 27.4515 + 26.8661i 1.12635 + 1.10233i
\(595\) 0 0
\(596\) 52.4261i 2.14746i
\(597\) 16.2819 0.0584943i 0.666373 0.00239401i
\(598\) −3.24029 3.24029i −0.132505 0.132505i
\(599\) 20.3742 0.832467 0.416233 0.909258i \(-0.363350\pi\)
0.416233 + 0.909258i \(0.363350\pi\)
\(600\) 0 0
\(601\) −32.4833 −1.32502 −0.662511 0.749052i \(-0.730509\pi\)
−0.662511 + 0.749052i \(0.730509\pi\)
\(602\) −8.22998 8.22998i −0.335429 0.335429i
\(603\) 18.9069 19.1805i 0.769947 0.781092i
\(604\) 5.27521i 0.214645i
\(605\) 0 0
\(606\) 23.1809 + 23.0149i 0.941660 + 0.934918i
\(607\) 0.0701607 0.0701607i 0.00284774 0.00284774i −0.705681 0.708529i \(-0.749359\pi\)
0.708529 + 0.705681i \(0.249359\pi\)
\(608\) 27.9740 27.9740i 1.13450 1.13450i
\(609\) −3.49404 3.46902i −0.141586 0.140572i
\(610\) 0 0
\(611\) 1.47386i 0.0596260i
\(612\) 1.38051 1.40049i 0.0558038 0.0566115i
\(613\) 26.6840 + 26.6840i 1.07776 + 1.07776i 0.996710 + 0.0810445i \(0.0258256\pi\)
0.0810445 + 0.996710i \(0.474174\pi\)
\(614\) −31.2239 −1.26010
\(615\) 0 0
\(616\) 5.68266 0.228961
\(617\) 6.37294 + 6.37294i 0.256565 + 0.256565i 0.823656 0.567090i \(-0.191931\pi\)
−0.567090 + 0.823656i \(0.691931\pi\)
\(618\) 5.15824 0.0185315i 0.207495 0.000745446i
\(619\) 17.7676i 0.714139i 0.934078 + 0.357070i \(0.116224\pi\)
−0.934078 + 0.357070i \(0.883776\pi\)
\(620\) 0 0
\(621\) 26.6675 + 26.0987i 1.07013 + 1.04731i
\(622\) 0.608631 0.608631i 0.0244039 0.0244039i
\(623\) 1.41556 1.41556i 0.0567130 0.0567130i
\(624\) −0.667407 + 0.672220i −0.0267177 + 0.0269103i
\(625\) 0 0
\(626\) 32.0594i 1.28135i
\(627\) 0.111936 + 31.1575i 0.00447030 + 1.24431i
\(628\) 11.9535 + 11.9535i 0.476995 + 0.476995i
\(629\) 1.76453 0.0703565
\(630\) 0 0
\(631\) 17.8248 0.709592 0.354796 0.934944i \(-0.384550\pi\)
0.354796 + 0.934944i \(0.384550\pi\)
\(632\) −13.5857 13.5857i −0.540412 0.540412i
\(633\) −0.0515944 14.3613i −0.00205070 0.570811i
\(634\) 61.1712i 2.42942i
\(635\) 0 0
\(636\) −16.9770 + 17.0995i −0.673183 + 0.678038i
\(637\) 0.206632 0.206632i 0.00818705 0.00818705i
\(638\) −14.8587 + 14.8587i −0.588262 + 0.588262i
\(639\) −0.0852413 11.8633i −0.00337210 0.469306i
\(640\) 0 0
\(641\) 14.8270i 0.585630i 0.956169 + 0.292815i \(0.0945920\pi\)
−0.956169 + 0.292815i \(0.905408\pi\)
\(642\) 15.8250 0.0568527i 0.624562 0.00224380i
\(643\) 32.7229 + 32.7229i 1.29047 + 1.29047i 0.934498 + 0.355968i \(0.115849\pi\)
0.355968 + 0.934498i \(0.384151\pi\)
\(644\) 19.8823 0.783474
\(645\) 0 0
\(646\) 2.74747 0.108098
\(647\) −27.0564 27.0564i −1.06370 1.06370i −0.997828 0.0658674i \(-0.979019\pi\)
−0.0658674 0.997828i \(-0.520981\pi\)
\(648\) −10.5289 + 10.8359i −0.413612 + 0.425674i
\(649\) 34.9230i 1.37085i
\(650\) 0 0
\(651\) −11.2070 11.1267i −0.439236 0.436091i
\(652\) 9.90255 9.90255i 0.387814 0.387814i
\(653\) −4.04918 + 4.04918i −0.158457 + 0.158457i −0.781883 0.623426i \(-0.785740\pi\)
0.623426 + 0.781883i \(0.285740\pi\)
\(654\) −7.57410 7.51988i −0.296171 0.294050i
\(655\) 0 0
\(656\) 0.0589475i 0.00230151i
\(657\) 26.0179 + 25.6467i 1.01506 + 1.00057i
\(658\) 7.78809 + 7.78809i 0.303611 + 0.303611i
\(659\) −11.5870 −0.451366 −0.225683 0.974201i \(-0.572461\pi\)
−0.225683 + 0.974201i \(0.572461\pi\)
\(660\) 0 0
\(661\) −15.1550 −0.589462 −0.294731 0.955580i \(-0.595230\pi\)
−0.294731 + 0.955580i \(0.595230\pi\)
\(662\) −38.1940 38.1940i −1.48445 1.48445i
\(663\) −0.119829 0.000430499i −0.00465379 1.67192e-5i
\(664\) 9.21294i 0.357531i
\(665\) 0 0
\(666\) −48.8257 + 0.350827i −1.89196 + 0.0135943i
\(667\) −14.4343 + 14.4343i −0.558899 + 0.558899i
\(668\) 17.6990 17.6990i 0.684793 0.684793i
\(669\) 6.66199 6.71003i 0.257568 0.259425i
\(670\) 0 0
\(671\) 23.0399i 0.889445i
\(672\) −0.0463233 12.8941i −0.00178696 0.497400i
\(673\) 13.7667 + 13.7667i 0.530666 + 0.530666i 0.920770 0.390105i \(-0.127561\pi\)
−0.390105 + 0.920770i \(0.627561\pi\)
\(674\) 10.5045 0.404617
\(675\) 0 0
\(676\) 35.7573 1.37528
\(677\) 16.3594 + 16.3594i 0.628742 + 0.628742i 0.947752 0.319009i \(-0.103350\pi\)
−0.319009 + 0.947752i \(0.603350\pi\)
\(678\) 0.0387793 + 10.7942i 0.00148931 + 0.414549i
\(679\) 3.20687i 0.123068i
\(680\) 0 0
\(681\) −2.60148 + 2.62024i −0.0996891 + 0.100408i
\(682\) −47.6587 + 47.6587i −1.82495 + 1.82495i
\(683\) 5.85622 5.85622i 0.224082 0.224082i −0.586133 0.810215i \(-0.699350\pi\)
0.810215 + 0.586133i \(0.199350\pi\)
\(684\) −44.1398 + 0.317157i −1.68773 + 0.0121268i
\(685\) 0 0
\(686\) 2.18375i 0.0833758i
\(687\) −10.8427 + 0.0389535i −0.413676 + 0.00148617i
\(688\) 7.05335 + 7.05335i 0.268906 + 0.268906i
\(689\) 1.46829 0.0559373
\(690\) 0 0
\(691\) 25.9095 0.985642 0.492821 0.870131i \(-0.335966\pi\)
0.492821 + 0.870131i \(0.335966\pi\)
\(692\) 10.7646 + 10.7646i 0.409210 + 0.409210i
\(693\) 7.23222 + 7.12903i 0.274729 + 0.270809i
\(694\) 74.2189i 2.81731i
\(695\) 0 0
\(696\) −5.86560 5.82361i −0.222335 0.220743i
\(697\) −0.00527284 + 0.00527284i −0.000199723 + 0.000199723i
\(698\) 14.4698 14.4698i 0.547691 0.547691i
\(699\) −4.64849 4.61521i −0.175822 0.174563i
\(700\) 0 0
\(701\) 37.9089i 1.43180i 0.698204 + 0.715899i \(0.253983\pi\)
−0.698204 + 0.715899i \(0.746017\pi\)
\(702\) 3.31567 0.0357368i 0.125142 0.00134880i
\(703\) −28.0065 28.0065i −1.05628 1.05628i
\(704\) −42.3598 −1.59649
\(705\) 0 0
\(706\) 45.0542 1.69564
\(707\) 6.10679 + 6.10679i 0.229669 + 0.229669i
\(708\) −49.4749 + 0.177743i −1.85938 + 0.00668001i
\(709\) 16.6841i 0.626586i 0.949656 + 0.313293i \(0.101432\pi\)
−0.949656 + 0.313293i \(0.898568\pi\)
\(710\) 0 0
\(711\) −0.246699 34.3339i −0.00925194 1.28762i
\(712\) 2.37636 2.37636i 0.0890578 0.0890578i
\(713\) −46.2975 + 46.2975i −1.73385 + 1.73385i
\(714\) 0.630921 0.635470i 0.0236116 0.0237819i
\(715\) 0 0
\(716\) 40.5129i 1.51404i
\(717\) −0.0129753 3.61167i −0.000484570 0.134880i
\(718\) −42.1016 42.1016i −1.57122 1.57122i
\(719\) −13.0709 −0.487464 −0.243732 0.969843i \(-0.578372\pi\)
−0.243732 + 0.969843i \(0.578372\pi\)
\(720\) 0 0
\(721\) 1.36377 0.0507895
\(722\) −14.2688 14.2688i −0.531031 0.531031i
\(723\) −0.0338310 9.41686i −0.00125819 0.350217i
\(724\) 27.2367i 1.01224i
\(725\) 0 0
\(726\) 1.22231 1.23112i 0.0453640 0.0456911i
\(727\) −19.4878 + 19.4878i −0.722761 + 0.722761i −0.969167 0.246406i \(-0.920750\pi\)
0.246406 + 0.969167i \(0.420750\pi\)
\(728\) 0.346882 0.346882i 0.0128563 0.0128563i
\(729\) −26.9937 + 0.581953i −0.999768 + 0.0215538i
\(730\) 0 0
\(731\) 1.26184i 0.0466709i
\(732\) 32.6403 0.117264i 1.20642 0.00433418i
\(733\) −24.5624 24.5624i −0.907232 0.907232i 0.0888162 0.996048i \(-0.471692\pi\)
−0.996048 + 0.0888162i \(0.971692\pi\)
\(734\) −49.1774 −1.81517
\(735\) 0 0
\(736\) −53.4585 −1.97051
\(737\) −21.4886 21.4886i −0.791543 0.791543i
\(738\) 0.144855 0.146951i 0.00533217 0.00540935i
\(739\) 25.3925i 0.934079i 0.884236 + 0.467040i \(0.154679\pi\)
−0.884236 + 0.467040i \(0.845321\pi\)
\(740\) 0 0
\(741\) 1.90875 + 1.89509i 0.0701198 + 0.0696178i
\(742\) −7.75865 + 7.75865i −0.284829 + 0.284829i
\(743\) −14.4447 + 14.4447i −0.529923 + 0.529923i −0.920549 0.390626i \(-0.872258\pi\)
0.390626 + 0.920549i \(0.372258\pi\)
\(744\) −18.8137 18.6790i −0.689742 0.684804i
\(745\) 0 0
\(746\) 72.0445i 2.63774i
\(747\) −11.5578 + 11.7251i −0.422879 + 0.429000i
\(748\) −1.56902 1.56902i −0.0573690 0.0573690i
\(749\) 4.18391 0.152877
\(750\) 0 0
\(751\) 27.4358 1.00115 0.500573 0.865694i \(-0.333123\pi\)
0.500573 + 0.865694i \(0.333123\pi\)
\(752\) −6.67463 6.67463i −0.243399 0.243399i
\(753\) 40.4307 0.145251i 1.47338 0.00529325i
\(754\) 1.81402i 0.0660627i
\(755\) 0 0
\(756\) −10.0628 + 10.2821i −0.365980 + 0.373955i
\(757\) 11.9760 11.9760i 0.435274 0.435274i −0.455144 0.890418i \(-0.650412\pi\)
0.890418 + 0.455144i \(0.150412\pi\)
\(758\) −57.8245 + 57.8245i −2.10028 + 2.10028i
\(759\) 29.6641 29.8780i 1.07674 1.08450i
\(760\) 0 0
\(761\) 41.1635i 1.49217i −0.665848 0.746087i \(-0.731930\pi\)
0.665848 0.746087i \(-0.268070\pi\)
\(762\) 0.223437 + 62.1937i 0.00809426 + 2.25304i
\(763\) −1.99533 1.99533i −0.0722357 0.0722357i
\(764\) 17.6614 0.638969
\(765\) 0 0
\(766\) −15.3007 −0.552836
\(767\) 2.13178 + 2.13178i 0.0769740 + 0.0769740i
\(768\) −0.0132771 3.69569i −0.000479097 0.133357i
\(769\) 3.96520i 0.142989i −0.997441 0.0714944i \(-0.977223\pi\)
0.997441 0.0714944i \(-0.0227768\pi\)
\(770\) 0 0
\(771\) −18.8585 + 18.9945i −0.679174 + 0.684071i
\(772\) 20.9410 20.9410i 0.753684 0.753684i
\(773\) −5.99943 + 5.99943i −0.215785 + 0.215785i −0.806719 0.590935i \(-0.798759\pi\)
0.590935 + 0.806719i \(0.298759\pi\)
\(774\) −0.250881 34.9160i −0.00901774 1.25503i
\(775\) 0 0
\(776\) 5.38352i 0.193257i
\(777\) −12.9090 + 0.0463770i −0.463109 + 0.00166377i