Properties

Label 525.2.j.b.407.2
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 407.2
Character \(\chi\) \(=\) 525.407
Dual form 525.2.j.b.218.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.54414 + 1.54414i) q^{2} +(1.73204 - 0.00622252i) q^{3} -2.76875i q^{4} +(-2.66491 + 2.68412i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.18705 + 1.18705i) q^{8} +(2.99992 - 0.0215553i) q^{9} +O(q^{10})\) \(q+(-1.54414 + 1.54414i) q^{2} +(1.73204 - 0.00622252i) 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} +(-0.0172286 - 4.79558i) q^{12} +(0.206632 - 0.206632i) q^{13} +2.18375 q^{14} +1.87154 q^{16} +(-0.167409 + 0.167409i) q^{17} +(-4.59902 + 4.66559i) 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} +(5.19585 - 0.0560017i) q^{27} +(-1.95780 + 1.95780i) q^{28} -2.84268 q^{29} +9.11776 q^{31} +(-5.26402 + 5.26402i) q^{32} +(0.0210636 + 5.86307i) 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} +(3.78233 - 0.0135884i) q^{42} +(3.76875 - 3.76875i) q^{43} +9.37239 q^{44} -15.6815 q^{46} +(3.56639 - 3.56639i) q^{47} +(3.24158 - 0.0116457i) 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} +(0.0330677 + 9.20439i) q^{57} +(4.38949 - 4.38949i) q^{58} -10.3168 q^{59} -6.80634 q^{61} +(-14.0791 + 14.0791i) q^{62} +(-2.13651 - 2.10602i) 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} +(3.58665 + 3.53548i) q^{72} +(-8.61099 + 8.61099i) q^{73} -16.2757 q^{74} +14.7136 q^{76} +(2.39360 - 2.39360i) q^{77} +(0.00397083 + 1.10528i) 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} +(-4.92363 + 0.0176886i) q^{87} +(-4.01825 + 4.01825i) q^{88} +2.00190 q^{89} -0.292222 q^{91} +(14.0589 - 14.0589i) q^{92} +(15.7923 - 0.0567354i) 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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.54414 + 1.54414i −1.09187 + 1.09187i −0.0965442 + 0.995329i \(0.530779\pi\)
−0.995329 + 0.0965442i \(0.969221\pi\)
\(3\) 1.73204 0.00622252i 0.999994 0.00359257i
\(4\) 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 \(0.829528\pi\)
\(12\) −0.0172286 4.79558i −0.00497346 1.38436i
\(13\) 0.206632 0.206632i 0.0573094 0.0573094i −0.677871 0.735181i \(-0.737097\pi\)
0.735181 + 0.677871i \(0.237097\pi\)
\(14\) 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 \(-0.759140\pi\)
0.686514 + 0.727117i \(0.259140\pi\)
\(18\) −4.59902 + 4.66559i −1.08400 + 1.09969i
\(19\) 5.31419i 1.21916i 0.792725 + 0.609579i \(0.208662\pi\)
−0.792725 + 0.609579i \(0.791338\pi\)
\(20\) 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 0.998161 + 0.0606179i \(0.0193071\pi\)
0.0606179 + 0.998161i \(0.480693\pi\)
\(24\) 2.06341 + 2.04864i 0.421191 + 0.418176i
\(25\) 0 0
\(26\) 0.638138i 0.125149i
\(27\) 5.19585 0.0560017i 0.999942 0.0107775i
\(28\) −1.95780 + 1.95780i −0.369989 + 0.369989i
\(29\) −2.84268 −0.527872 −0.263936 0.964540i \(-0.585021\pi\)
−0.263936 + 0.964540i \(0.585021\pi\)
\(30\) 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
\(33\) 0.0210636 + 5.86307i 0.00366671 + 1.02063i
\(34\) 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 0.992072 0.125668i \(-0.0401075\pi\)
−0.125668 + 0.992072i \(0.540107\pi\)
\(38\) −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 \(0.999217\pi\)
\(42\) 3.78233 0.0135884i 0.583627 0.00209674i
\(43\) 3.76875 3.76875i 0.574728 0.574728i −0.358718 0.933446i \(-0.616786\pi\)
0.933446 + 0.358718i \(0.116786\pi\)
\(44\) 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 \(-0.630096\pi\)
0.917635 + 0.397424i \(0.130096\pi\)
\(48\) 3.24158 0.0116457i 0.467881 0.00168091i
\(49\) 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 \(-0.362151\pi\)
−0.907684 + 0.419654i \(0.862151\pi\)
\(54\) −7.93665 + 8.10960i −1.08004 + 1.10358i
\(55\) 0 0
\(56\) 1.67875i 0.224332i
\(57\) 0.0330677 + 9.20439i 0.00437992 + 1.21915i
\(58\) 4.38949 4.38949i 0.576369 0.576369i
\(59\) −10.3168 −1.34313 −0.671565 0.740946i \(-0.734378\pi\)
−0.671565 + 0.740946i \(0.734378\pi\)
\(60\) 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
\(63\) −2.13651 2.10602i −0.269175 0.265334i
\(64\) 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 0.203530 0.979069i \(-0.434759\pi\)
−0.979069 + 0.203530i \(0.934759\pi\)
\(68\) 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 \(0.924603\pi\)
\(72\) 3.58665 + 3.53548i 0.422691 + 0.416660i
\(73\) −8.61099 + 8.61099i −1.00784 + 1.00784i −0.00787086 + 0.999969i \(0.502505\pi\)
−0.999969 + 0.00787086i \(0.997495\pi\)
\(74\) −16.2757 −1.89201
\(75\) 0 0
\(76\) 14.7136 1.68777
\(77\) 2.39360 2.39360i 0.272776 0.272776i
\(78\) 0.00397083 + 1.10528i 0.000449608 + 0.125148i
\(79\) 11.4449i 1.28766i −0.765170 0.643828i \(-0.777345\pi\)
0.765170 0.643828i \(-0.222655\pi\)
\(80\) 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 \(-0.347385\pi\)
−0.887246 + 0.461296i \(0.847385\pi\)
\(84\) −3.37880 + 3.40317i −0.368658 + 0.371316i
\(85\) 0 0
\(86\) 11.6390i 1.25506i
\(87\) −4.92363 + 0.0176886i −0.527868 + 0.00189642i
\(88\) −4.01825 + 4.01825i −0.428347 + 0.428347i
\(89\) 2.00190 0.212201 0.106100 0.994355i \(-0.466164\pi\)
0.106100 + 0.994355i \(0.466164\pi\)
\(90\) 0 0
\(91\) −0.292222 −0.0306332
\(92\) 14.0589 14.0589i 1.46574 1.46574i
\(93\) 15.7923 0.0567354i 1.63759 0.00588319i
\(94\) 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 0.582553 0.812793i \(-0.302054\pi\)
−0.812793 + 0.582553i \(0.802054\pi\)
\(98\) −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 \(-0.141371\pi\)
\(102\) −0.00321708 0.895474i −0.000318538 0.0886651i
\(103\) −0.964332 + 0.964332i −0.0950185 + 0.0950185i −0.753018 0.658000i \(-0.771403\pi\)
0.658000 + 0.753018i \(0.271403\pi\)
\(104\) 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 \(-0.685179\pi\)
0.835499 + 0.549492i \(0.185179\pi\)
\(108\) −0.155055 14.3860i −0.0149201 1.38429i
\(109\) 2.82182i 0.270281i −0.990826 0.135141i \(-0.956851\pi\)
0.990826 0.135141i \(-0.0431486\pi\)
\(110\) 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 \(-0.292857\pi\)
−0.795625 + 0.605790i \(0.792857\pi\)
\(114\) −14.2639 14.1618i −1.33594 1.32638i
\(115\) 0 0
\(116\) 7.87065i 0.730771i
\(117\) 0.615426 0.624334i 0.0568961 0.0577197i
\(118\) 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
\(123\) 0.000195990 0.0545538i 1.76718e−5 0.00491895i
\(124\) 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 0.999480 + 0.0322583i \(0.0102699\pi\)
0.0322583 + 0.999480i \(0.489730\pi\)
\(128\) 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 \(-0.187228\pi\)
\(132\) 16.2333 0.0583199i 1.41293 0.00507609i
\(133\) 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 \(-0.648394\pi\)
0.893286 + 0.449489i \(0.148394\pi\)
\(138\) −27.1609 + 0.0975782i −2.31209 + 0.00830641i
\(139\) 12.3138i 1.04444i −0.852810 0.522221i \(-0.825103\pi\)
0.852810 0.522221i \(-0.174897\pi\)
\(140\) 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
\(147\) 0.00622252 + 1.73204i 0.000513225 + 0.142856i
\(148\) 14.5917 14.5917i 1.19943 1.19943i
\(149\) 18.9350 1.55121 0.775607 0.631216i \(-0.217444\pi\)
0.775607 + 0.631216i \(0.217444\pi\)
\(150\) 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
\(153\) −0.498604 + 0.505822i −0.0403098 + 0.0408933i
\(154\) 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 0.858077 0.513521i \(-0.171659\pi\)
−0.513521 + 0.858077i \(0.671659\pi\)
\(158\) 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
\(162\) −13.6961 + 14.0955i −1.07607 + 1.10745i
\(163\) −3.57655 + 3.57655i −0.280137 + 0.280137i −0.833164 0.553027i \(-0.813473\pi\)
0.553027 + 0.833164i \(0.313473\pi\)
\(164\) 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 \(-0.636257\pi\)
0.909771 + 0.415111i \(0.136257\pi\)
\(168\) −0.0104460 2.90765i −0.000805929 0.224330i
\(169\) 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 \(-0.317026\pi\)
−0.839285 + 0.543692i \(0.817026\pi\)
\(174\) 7.57546 7.63009i 0.574294 0.578436i
\(175\) 0 0
\(176\) 6.33528i 0.477540i
\(177\) −17.8691 + 0.0641964i −1.34312 + 0.00482529i
\(178\) −3.09121 + 3.09121i −0.231696 + 0.231696i
\(179\) −14.6322 −1.09366 −0.546832 0.837242i \(-0.684166\pi\)
−0.546832 + 0.837242i \(0.684166\pi\)
\(180\) 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
\(183\) −11.7888 + 0.0423526i −0.871456 + 0.00313079i
\(184\) 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 \(-0.0741275\pi\)
\(192\) −0.0778669 21.6743i −0.00561956 1.56421i
\(193\) −7.56336 + 7.56336i −0.544422 + 0.544422i −0.924822 0.380400i \(-0.875786\pi\)
0.380400 + 0.924822i \(0.375786\pi\)
\(194\) 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 \(-0.733718\pi\)
0.742336 + 0.670027i \(0.233718\pi\)
\(198\) −15.7933 15.5680i −1.12238 1.10637i
\(199\) 9.40041i 0.666378i 0.942860 + 0.333189i \(0.108125\pi\)
−0.942860 + 0.333189i \(0.891875\pi\)
\(200\) 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
\(207\) 15.3422 + 15.1233i 1.06636 + 1.05114i
\(208\) 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
\(213\) 0.0246072 + 6.84942i 0.00168606 + 0.469315i
\(214\) 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
\(222\) −28.1901 + 0.101276i −1.89199 + 0.00679717i
\(223\) −3.86020 + 3.86020i −0.258498 + 0.258498i −0.824443 0.565945i \(-0.808511\pi\)
0.565945 + 0.824443i \(0.308511\pi\)
\(224\) 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 \(-0.772538\pi\)
0.655310 + 0.755360i \(0.272538\pi\)
\(228\) 25.4846 0.0915560i 1.68776 0.00606344i
\(229\) 6.26009i 0.413678i −0.978375 0.206839i \(-0.933682\pi\)
0.978375 0.206839i \(-0.0663177\pi\)
\(230\) 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 \(-0.210466\pi\)
−0.614063 + 0.789257i \(0.710466\pi\)
\(234\) 0.0137553 + 1.91436i 0.000899209 + 0.125146i
\(235\) 0 0
\(236\) 28.5645i 1.85939i
\(237\) −0.0712164 19.8231i −0.00462600 1.28765i
\(238\) −0.365578 + 0.365578i −0.0236969 + 0.0236969i
\(239\) 2.08521 0.134881 0.0674406 0.997723i \(-0.478517\pi\)
0.0674406 + 0.997723i \(0.478517\pi\)
\(240\) 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
\(243\) 15.5859 0.279999i 0.999839 0.0179619i
\(244\) 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 \(-0.263614\pi\)
\(252\) −5.83104 + 5.91545i −0.367321 + 0.372638i
\(253\) −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 \(-0.910083\pi\)
0.278740 + 0.960367i \(0.410083\pi\)
\(258\) 0.0724236 + 20.1591i 0.00450890 + 1.25505i
\(259\) 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 −0.991580 0.129497i \(-0.958664\pi\)
−0.129497 0.991580i \(-0.541336\pi\)
\(264\) −6.93477 + 6.98477i −0.426805 + 0.429883i
\(265\) 0 0
\(266\) 11.6048i 0.711539i
\(267\) 3.46737 0.0124569i 0.212199 0.000762347i
\(268\) −17.5762 + 17.5762i −1.07364 + 1.07364i
\(269\) 28.5125 1.73844 0.869219 0.494428i \(-0.164622\pi\)
0.869219 + 0.494428i \(0.164622\pi\)
\(270\) 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
\(273\) −0.506139 + 0.00181836i −0.0306330 + 0.000110052i
\(274\) 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 0.235913 0.971774i \(-0.424192\pi\)
−0.971774 + 0.235913i \(0.924192\pi\)
\(278\) 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 \(0.876148\pi\)
\(282\) 0.0685349 + 19.0767i 0.00408120 + 1.13600i
\(283\) 19.8271 19.8271i 1.17860 1.17860i 0.198495 0.980102i \(-0.436395\pi\)
0.980102 0.198495i \(-0.0636053\pi\)
\(284\) 10.9491 0.649711
\(285\) 0 0
\(286\) −2.16014 −0.127732
\(287\) 0.0222716 0.0222716i 0.00131465 0.00131465i
\(288\) −15.6782 + 15.9051i −0.923847 + 0.937219i
\(289\) 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 \(-0.160346\pi\)
−0.482707 + 0.875782i \(0.660346\pi\)
\(294\) −2.68412 2.66491i −0.156541 0.155420i
\(295\) 0 0
\(296\) 12.5118i 0.727236i
\(297\) 0.189570 + 17.5883i 0.0109999 + 1.02058i
\(298\) −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
\(303\) −0.0537396 14.9584i −0.00308726 0.859339i
\(304\) 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 0.357051 0.934085i \(-0.383782\pi\)
−0.934085 + 0.357051i \(0.883782\pi\)
\(308\) −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 \(-0.00355726\pi\)
\(312\) 0.849680 0.00305256i 0.0481036 0.000172817i
\(313\) 10.3810 10.3810i 0.586767 0.586767i −0.349987 0.936754i \(-0.613814\pi\)
0.936754 + 0.349987i \(0.113814\pi\)
\(314\) −13.3330 −0.752424
\(315\) 0 0
\(316\) −31.6881 −1.78260
\(317\) 19.8075 19.8075i 1.11250 1.11250i 0.119688 0.992812i \(-0.461810\pi\)
0.992812 0.119688i \(-0.0381896\pi\)
\(318\) 19.0046 0.0682759i 1.06573 0.00382872i
\(319\) 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
\(327\) −0.0175588 4.88750i −0.000971005 0.270279i
\(328\) −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
\(333\) 15.9236 + 15.6964i 0.872607 + 0.860157i
\(334\) 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 0.793655 0.608369i \(-0.208176\pi\)
−0.608369 + 0.793655i \(0.708176\pi\)
\(338\) −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
\(342\) −24.7938 24.4401i −1.34070 1.32157i
\(343\) 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 −0.355421 + 0.934706i \(0.615663\pi\)
−0.934706 + 0.355421i \(0.884337\pi\)
\(348\) 0.0489753 + 13.6323i 0.00262535 + 0.730766i
\(349\) 9.37078i 0.501607i 0.968038 + 0.250803i \(0.0806947\pi\)
−0.968038 + 0.250803i \(0.919305\pi\)
\(350\) 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 \(-0.435012\pi\)
−0.979231 + 0.202750i \(0.935012\pi\)
\(354\) 27.4932 27.6915i 1.46125 1.47179i
\(355\) 0 0
\(356\) 5.54275i 0.293765i
\(357\) 0.410063 0.00147319i 0.0217028 7.79696e-5i
\(358\) 22.5942 22.5942i 1.19414 1.19414i
\(359\) 27.2654 1.43901 0.719506 0.694486i \(-0.244368\pi\)
0.719506 + 0.694486i \(0.244368\pi\)
\(360\) 0 0
\(361\) −9.24062 −0.486349
\(362\) 15.1900 15.1900i 0.798369 0.798369i
\(363\) −0.794430 + 0.00285407i −0.0416968 + 0.000149800i
\(364\) 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 0.156465 0.987683i \(-0.449990\pi\)
−0.987683 + 0.156465i \(0.949990\pi\)
\(368\) 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
\(372\) −0.157086 43.7249i −0.00814453 2.26703i
\(373\) −23.3283 + 23.3283i −1.20790 + 1.20790i −0.236189 + 0.971707i \(0.575898\pi\)
−0.971707 + 0.236189i \(0.924102\pi\)
\(374\) 1.75010 0.0904954
\(375\) 0 0
\(376\) 8.46698 0.436651
\(377\) −0.587387 + 0.587387i −0.0302520 + 0.0302520i
\(378\) 11.3464 0.122294i 0.583597 0.00629010i
\(379\) 37.4477i 1.92356i −0.273828 0.961779i \(-0.588290\pi\)
0.273828 0.961779i \(-0.411710\pi\)
\(380\) 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 \(-0.192710\pi\)
−0.569105 + 0.822265i \(0.692710\pi\)
\(384\) 15.2879 + 15.1784i 0.780155 + 0.774570i
\(385\) 0 0
\(386\) 23.3578i 1.18888i
\(387\) 11.2247 11.3872i 0.570584 0.578843i
\(388\) −6.27841 + 6.27841i −0.318738 + 0.318738i
\(389\) 9.20279 0.466600 0.233300 0.972405i \(-0.425048\pi\)
0.233300 + 0.972405i \(0.425048\pi\)
\(390\) 0 0
\(391\) −1.70011 −0.0859783
\(392\) −1.18705 + 1.18705i −0.0599552 + 0.0599552i
\(393\) −0.0790344 21.9992i −0.00398676 1.10971i
\(394\) 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 −0.994369 0.105976i \(-0.966203\pi\)
−0.105976 0.994369i \(-0.533797\pi\)
\(398\) −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 \(0.777697\pi\)
\(402\) 33.9560 0.121990i 1.69357 0.00608431i
\(403\) 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
\(408\) −0.688392 + 0.00247311i −0.0340805 + 0.000122437i
\(409\) 10.9496i 0.541425i −0.962660 0.270712i \(-0.912741\pi\)
0.962660 0.270712i \(-0.0872592\pi\)
\(410\) 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
\(417\) −0.0766229 21.3280i −0.00375224 1.04444i
\(418\) 27.7774 27.7774i 1.35864 1.35864i
\(419\) −5.86958 −0.286748 −0.143374 0.989669i \(-0.545795\pi\)
−0.143374 + 0.989669i \(0.545795\pi\)
\(420\) 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
\(423\) 10.6220 10.7758i 0.516460 0.523936i
\(424\) 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 \(0.967892\pi\)
\(432\) 9.72423 0.104809i 0.467857 0.00504264i
\(433\) 2.20877 2.20877i 0.106146 0.106146i −0.652039 0.758185i \(-0.726086\pi\)
0.758185 + 0.652039i \(0.226086\pi\)
\(434\) 19.9109 0.955752
\(435\) 0 0
\(436\) −7.81290 −0.374170
\(437\) −26.9840 + 26.9840i −1.29082 + 1.29082i
\(438\) −0.165477 46.0604i −0.00790678 2.20085i
\(439\) 27.6028i 1.31741i −0.752401 0.658706i \(-0.771104\pi\)
0.752401 0.658706i \(-0.228896\pi\)
\(440\) 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 \(-0.385646\pi\)
−0.936159 + 0.351577i \(0.885646\pi\)
\(444\) 25.1825 25.3641i 1.19511 1.20373i
\(445\) 0 0
\(446\) 11.9214i 0.564494i
\(447\) 32.7961 0.117823i 1.55120 0.00557285i
\(448\) −8.84854 + 8.84854i −0.418054 + 0.418054i
\(449\) −34.1859 −1.61333 −0.806666 0.591008i \(-0.798730\pi\)
−0.806666 + 0.591008i \(0.798730\pi\)
\(450\) 0 0
\(451\) −0.106619 −0.00502049
\(452\) −5.58726 + 5.58726i −0.262803 + 0.262803i
\(453\) −3.30000 + 0.0118556i −0.155048 + 0.000557024i
\(454\) 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 0.890499 0.454986i \(-0.150356\pi\)
−0.454986 + 0.890499i \(0.650356\pi\)
\(458\) 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 \(0.796159\pi\)
\(462\) 0.0459976 + 12.8034i 0.00214000 + 0.595670i
\(463\) −13.2170 + 13.2170i −0.614248 + 0.614248i −0.944050 0.329802i \(-0.893018\pi\)
0.329802 + 0.944050i \(0.393018\pi\)
\(464\) −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 \(-0.527486\pi\)
0.996274 + 0.0862431i \(0.0274862\pi\)
\(468\) −1.72862 1.70396i −0.0799056 0.0787655i
\(469\) 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
\(477\) −10.7350 10.5819i −0.491524 0.484510i
\(478\) −3.21986 + 3.21986i −0.147273 + 0.147273i
\(479\) −26.9725 −1.23240 −0.616202 0.787588i \(-0.711330\pi\)
−0.616202 + 0.787588i \(0.711330\pi\)
\(480\) 0 0
\(481\) 2.17795 0.0993062
\(482\) 8.39528 8.39528i 0.382395 0.382395i
\(483\) −0.0446838 12.4378i −0.00203319 0.565937i
\(484\) 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 0.929529 + 0.368749i \(0.120214\pi\)
0.368749 + 0.929529i \(0.379786\pi\)
\(488\) −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 \(0.980270\pi\)
\(492\) 0.151046 0.000542646i 0.00680966 2.44644e-5i
\(493\) 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
\(498\) 20.7574 0.0745730i 0.930162 0.00334170i
\(499\) 30.3151i 1.35709i 0.734558 + 0.678546i \(0.237389\pi\)
−0.734558 + 0.678546i \(0.762611\pi\)
\(500\) 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 \(-0.246670\pi\)
−0.699671 + 0.714466i \(0.746670\pi\)
\(504\) −0.0361859 5.03611i −0.00161185 0.224326i
\(505\) 0 0
\(506\) 53.0827i 2.35982i
\(507\) 0.0803614 + 22.3686i 0.00356898 + 0.993425i
\(508\) 32.1925 32.1925i 1.42831 1.42831i
\(509\) 14.6491 0.649311 0.324656 0.945832i \(-0.394752\pi\)
0.324656 + 0.945832i \(0.394752\pi\)
\(510\) 0 0
\(511\) 12.1778 0.538713
\(512\) −14.2950 + 14.2950i −0.631758 + 0.631758i
\(513\) 0.297604 + 27.6117i 0.0131395 + 1.21909i
\(514\) 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 \(-0.181565\pi\)
\(522\) 13.0735 13.2628i 0.572212 0.580495i
\(523\) 23.4069 23.4069i 1.02351 1.02351i 0.0237950 0.999717i \(-0.492425\pi\)
0.999717 0.0237950i \(-0.00757491\pi\)
\(524\) −35.1668 −1.53627
\(525\) 0 0
\(526\) 56.1475 2.44815
\(527\) −1.52639 + 1.52639i −0.0664907 + 0.0664907i
\(528\) 0.0394214 + 10.9730i 0.00171560 + 0.477536i
\(529\) 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
\(537\) −25.3436 + 0.0910493i −1.09366 + 0.00392907i
\(538\) −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
\(543\) −17.0384 + 0.0612121i −0.731187 + 0.00262686i
\(544\) 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 0.780530 0.625119i \(-0.214949\pi\)
−0.625119 + 0.780530i \(0.714949\pi\)
\(548\) −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
\(552\) 0.0750128 + 20.8798i 0.00319276 + 0.888705i
\(553\) −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 \(-0.806735\pi\)
0.570538 + 0.821271i \(0.306735\pi\)
\(558\) −41.9328 + 42.5397i −1.77516 + 1.80085i
\(559\) 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 \(-0.114813\pi\)
−0.352924 + 0.935652i \(0.614813\pi\)
\(564\) −17.1643 17.0414i −0.722749 0.717574i
\(565\) 0 0
\(566\) 61.2316i 2.57376i
\(567\) −6.45475 6.27185i −0.271074 0.263393i
\(568\) −4.69425 + 4.69425i −0.196966 + 0.196966i
\(569\) −6.82232 −0.286007 −0.143003 0.989722i \(-0.545676\pi\)
−0.143003 + 0.989722i \(0.545676\pi\)
\(570\) 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
\(573\) −0.0396926 11.0484i −0.00165818 0.461555i
\(574\) 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 0.683683 0.729779i \(-0.260377\pi\)
−0.729779 + 0.683683i \(0.760377\pi\)
\(578\) −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
\(582\) 12.1295 0.0435762i 0.502782 0.00180629i
\(583\) 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 \(-0.822789\pi\)
0.528408 + 0.848990i \(0.322789\pi\)
\(588\) 4.79558 0.0172286i 0.197766 0.000710495i
\(589\) 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 \(-0.175252\pi\)
−0.523172 + 0.852227i \(0.675252\pi\)
\(594\) −27.4515 26.8661i −1.12635 1.10233i
\(595\) 0 0
\(596\) 52.4261i 2.14746i
\(597\) 0.0584943 + 16.2819i 0.00239401 + 0.666373i
\(598\) −3.24029 + 3.24029i −0.132505 + 0.132505i
\(599\) −20.3742 −0.832467 −0.416233 0.909258i \(-0.636650\pi\)
−0.416233 + 0.909258i \(0.636650\pi\)
\(600\) 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
\(603\) −19.1805 18.9069i −0.781092 0.769947i
\(604\) 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 0.708529 0.705681i \(-0.249359\pi\)
−0.705681 + 0.708529i \(0.749359\pi\)
\(608\) −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
\(612\) 1.40049 + 1.38051i 0.0566115 + 0.0558038i
\(613\) 26.6840 26.6840i 1.07776 1.07776i 0.0810445 0.996710i \(-0.474174\pi\)
0.996710 0.0810445i \(-0.0258256\pi\)
\(614\) 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 \(-0.808069\pi\)
0.567090 + 0.823656i \(0.308069\pi\)
\(618\) −0.0185315 5.15824i −0.000745446 0.207495i
\(619\) 17.7676i 0.714139i −0.934078 0.357070i \(-0.883776\pi\)
0.934078 0.357070i \(-0.116224\pi\)
\(620\) 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
\(627\) −31.1575 + 0.111936i −1.24431 + 0.00447030i
\(628\) 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
\(633\) −14.3613 + 0.0515944i −0.570811 + 0.00205070i
\(634\) 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 \(0.905408\pi\)
\(642\) 0.0568527 + 15.8250i 0.00224380 + 0.624562i
\(643\) 32.7229 32.7229i 1.29047 1.29047i 0.355968 0.934498i \(-0.384151\pi\)
0.934498 0.355968i \(-0.115849\pi\)
\(644\) −19.8823 −0.783474
\(645\) 0 0
\(646\) 2.74747 0.108098
\(647\) 27.0564 27.0564i 1.06370 1.06370i 0.0658674 0.997828i \(-0.479019\pi\)
0.997828 0.0658674i \(-0.0209814\pi\)
\(648\) 10.8359 + 10.5289i 0.425674 + 0.413612i
\(649\) 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 \(-0.214260\pi\)
−0.623426 + 0.781883i \(0.714260\pi\)
\(654\) 7.57410 + 7.51988i 0.296171 + 0.294050i
\(655\) 0 0
\(656\) 0.0589475i 0.00230151i
\(657\) −25.6467 + 26.0179i −1.00057 + 1.01506i
\(658\) 7.78809 7.78809i 0.303611 0.303611i
\(659\) 11.5870 0.451366 0.225683 0.974201i \(-0.427539\pi\)
0.225683 + 0.974201i \(0.427539\pi\)
\(660\) 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
\(663\) 0.000430499 0.119829i 1.67192e−5 0.00465379i
\(664\) 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
\(672\) 12.8941 0.0463233i 0.497400 0.00178696i
\(673\) 13.7667 13.7667i 0.530666 0.530666i −0.390105 0.920770i \(-0.627561\pi\)
0.920770 + 0.390105i \(0.127561\pi\)
\(674\) −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 \(-0.896650\pi\)
0.319009 + 0.947752i \(0.396650\pi\)
\(678\) 10.7942 0.0387793i 0.414549 0.00148931i
\(679\) 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 \(-0.300650\pi\)
−0.810215 + 0.586133i \(0.800650\pi\)
\(684\) 44.1398 0.317157i 1.68773 0.0121268i
\(685\) 0 0
\(686\) 2.18375i 0.0833758i
\(687\) −0.0389535 10.8427i −0.00148617 0.413676i
\(688\) 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
\(693\) 7.12903 7.23222i 0.270809 0.274729i
\(694\) 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 \(0.746017\pi\)
\(702\) 0.0357368 + 3.31567i 0.00134880 + 0.125142i
\(703\) −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
\(708\) 0.177743 + 49.4749i 0.00668001 + 1.85938i
\(709\) 16.6841i 0.626586i −0.949656 0.313293i \(-0.898568\pi\)
0.949656 0.313293i \(-0.101432\pi\)
\(710\) 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
\(717\) 3.61167 0.0129753i 0.134880 0.000484570i
\(718\) −42.1016 + 42.1016i −1.57122 + 1.57122i
\(719\) 13.0709 0.487464 0.243732 0.969843i \(-0.421628\pi\)
0.243732 + 0.969843i \(0.421628\pi\)
\(720\) 0 0
\(721\) 1.36377 0.0507895
\(722\) 14.2688 14.2688i 0.531031 0.531031i
\(723\) −9.41686 + 0.0338310i −0.350217 + 0.00125819i
\(724\) 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 0.246406 0.969167i \(-0.420750\pi\)
−0.969167 + 0.246406i \(0.920750\pi\)
\(728\) −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
\(732\) 0.117264 + 32.6403i 0.00433418 + 1.20642i
\(733\) −24.5624 + 24.5624i −0.907232 + 0.907232i −0.996048 0.0888162i \(-0.971692\pi\)
0.0888162 + 0.996048i \(0.471692\pi\)
\(734\) 49.1774 1.81517
\(735\) 0 0
\(736\) −53.4585 −1.97051
\(737\) 21.4886 21.4886i 0.791543 0.791543i
\(738\) −0.146951 0.144855i −0.00540935 0.00533217i
\(739\) 25.3925i 0.934079i −0.884236 0.467040i \(-0.845321\pi\)
0.884236 0.467040i \(-0.154679\pi\)
\(740\) 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 \(-0.127742\pi\)
−0.390626 + 0.920549i \(0.627742\pi\)
\(744\) 18.8137 + 18.6790i 0.689742 + 0.684804i
\(745\) 0 0
\(746\) 72.0445i 2.63774i
\(747\) −11.7251 11.5578i −0.429000 0.422879i
\(748\) −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
\(753\) −0.145251 40.4307i −0.00529325 1.47338i
\(754\) 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 0.890418 0.455144i \(-0.150412\pi\)
−0.455144 + 0.890418i \(0.650412\pi\)
\(758\) 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 \(-0.268070\pi\)
\(762\) −62.1937 + 0.223437i −2.25304 + 0.00809426i
\(763\) −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
\(768\) −3.69569 + 0.0132771i −0.133357 + 0.000479097i
\(769\) 3.96520i 0.142989i 0.997441 + 0.0714944i \(0.0227768\pi\)
−0.997441 + 0.0714944i \(0.977223\pi\)
\(770\) 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 \(-0.201241\pi\)
−0.590935 + 0.806719i \(0.701241\pi\)
\(774\) 0.250881 + 34.9160i 0.00901774 + 1.25503i
\(775\) 0 0
\(776\) 5.38352i 0.193257i
\(777\) −0.0463770 12.9090i −0.00166377 0.463109i