Properties

Label 105.2.j.a.8.11
Level 105
Weight 2
Character 105.8
Analytic conductor 0.838
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.11
Character \(\chi\) = 105.8
Dual form 105.2.j.a.92.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.54414 + 1.54414i) q^{2} +(-1.73204 - 0.00622252i) q^{3} +2.76875i q^{4} +(-0.252500 + 2.22177i) q^{5} +(-2.66491 - 2.68412i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.18705 + 1.18705i) q^{8} +(2.99992 + 0.0215553i) q^{9} +O(q^{10})\) \(q+(1.54414 + 1.54414i) q^{2} +(-1.73204 - 0.00622252i) q^{3} +2.76875i q^{4} +(-0.252500 + 2.22177i) q^{5} +(-2.66491 - 2.68412i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.18705 + 1.18705i) q^{8} +(2.99992 + 0.0215553i) q^{9} +(-3.82062 + 3.04083i) q^{10} -3.38507i q^{11} +(0.0172286 - 4.79558i) q^{12} +(-0.206632 - 0.206632i) q^{13} +2.18375 q^{14} +(0.451165 - 3.84662i) q^{15} +1.87154 q^{16} +(0.167409 + 0.167409i) q^{17} +(4.59902 + 4.66559i) q^{18} -5.31419i q^{19} +(-6.15151 - 0.699108i) q^{20} +(-1.22914 + 1.22034i) q^{21} +(5.22702 - 5.22702i) q^{22} +(-5.07773 + 5.07773i) q^{23} +(2.06341 - 2.04864i) q^{24} +(-4.87249 - 1.12199i) q^{25} -0.638138i q^{26} +(-5.19585 - 0.0560017i) q^{27} +(1.95780 + 1.95780i) q^{28} -2.84268 q^{29} +(6.63638 - 5.24306i) q^{30} +9.11776 q^{31} +(5.26402 + 5.26402i) q^{32} +(-0.0210636 + 5.86307i) q^{33} +0.517005i q^{34} +(1.39248 + 1.74957i) q^{35} +(-0.0596812 + 8.30602i) q^{36} +(-5.27013 + 5.27013i) q^{37} +(8.20586 - 8.20586i) q^{38} +(0.356609 + 0.359180i) q^{39} +(-2.33762 - 2.93708i) q^{40} -0.0314968i q^{41} +(-3.78233 - 0.0135884i) q^{42} +(-3.76875 - 3.76875i) q^{43} +9.37239 q^{44} +(-0.805371 + 6.65968i) q^{45} -15.6815 q^{46} +(-3.56639 - 3.56639i) q^{47} +(-3.24158 - 0.0116457i) q^{48} -1.00000i q^{49} +(-5.79130 - 9.25632i) q^{50} +(-0.288917 - 0.291000i) q^{51} +(0.572111 - 0.572111i) q^{52} +(3.55291 - 3.55291i) q^{53} +(-7.93665 - 8.10960i) q^{54} +(7.52082 + 0.854729i) q^{55} +1.67875i q^{56} +(-0.0330677 + 9.20439i) q^{57} +(-4.38949 - 4.38949i) q^{58} -10.3168 q^{59} +(10.6503 + 1.24916i) q^{60} -6.80634 q^{61} +(14.0791 + 14.0791i) q^{62} +(2.13651 - 2.10602i) q^{63} +12.5137i q^{64} +(0.511262 - 0.406913i) q^{65} +(-9.08593 + 9.02088i) q^{66} +(6.34806 - 6.34806i) q^{67} +(-0.463512 + 0.463512i) q^{68} +(8.82642 - 8.76323i) q^{69} +(-0.551396 + 4.85177i) q^{70} -3.95454i q^{71} +(-3.58665 + 3.53548i) q^{72} +(8.61099 + 8.61099i) q^{73} -16.2757 q^{74} +(8.43236 + 1.97365i) q^{75} +14.7136 q^{76} +(-2.39360 - 2.39360i) q^{77} +(-0.00397083 + 1.10528i) q^{78} +11.4449i q^{79} +(-0.472563 + 4.15812i) q^{80} +(8.99907 + 0.129328i) q^{81} +(0.0486356 - 0.0486356i) q^{82} +(3.88059 - 3.88059i) q^{83} +(-3.37880 - 3.40317i) q^{84} +(-0.414214 + 0.329672i) q^{85} -11.6390i q^{86} +(4.92363 + 0.0176886i) q^{87} +(4.01825 + 4.01825i) q^{88} +2.00190 q^{89} +(-11.5271 + 9.03989i) q^{90} -0.292222 q^{91} +(-14.0589 - 14.0589i) q^{92} +(-15.7923 - 0.0567354i) q^{93} -11.0140i q^{94} +(11.8069 + 1.34183i) q^{95} +(-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{3} + O(q^{10}) \) \( 24q - 4q^{3} - 16q^{10} + 16q^{12} - 8q^{13} - 16q^{15} - 16q^{16} - 20q^{18} + 4q^{21} + 8q^{22} - 16q^{25} - 16q^{27} + 20q^{30} + 28q^{33} + 16q^{36} - 16q^{37} + 64q^{40} - 20q^{42} - 40q^{43} + 20q^{45} - 64q^{46} + 16q^{48} - 20q^{51} + 40q^{55} + 4q^{57} + 40q^{58} + 32q^{60} + 32q^{61} - 8q^{63} - 16q^{66} + 24q^{67} - 8q^{70} - 8q^{72} + 32q^{73} - 60q^{75} + 32q^{76} + 60q^{78} + 52q^{81} - 80q^{82} + 24q^{85} + 4q^{87} + 96q^{88} - 24q^{90} - 24q^{91} - 76q^{93} - 96q^{96} + 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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 \(0.469221\pi\)
\(3\) −1.73204 0.00622252i −0.999994 0.00359257i
\(4\) 2.76875i 1.38437i
\(5\) −0.252500 + 2.22177i −0.112921 + 0.993604i
\(6\) −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
\(10\) −3.82062 + 3.04083i −1.20819 + 0.961593i
\(11\) 3.38507i 1.02064i −0.859986 0.510318i \(-0.829528\pi\)
0.859986 0.510318i \(-0.170472\pi\)
\(12\) 0.0172286 4.79558i 0.00497346 1.38436i
\(13\) −0.206632 0.206632i −0.0573094 0.0573094i 0.677871 0.735181i \(-0.262903\pi\)
−0.735181 + 0.677871i \(0.762903\pi\)
\(14\) 2.18375 0.583631
\(15\) 0.451165 3.84662i 0.116490 0.993192i
\(16\) 1.87154 0.467884
\(17\) 0.167409 + 0.167409i 0.0406026 + 0.0406026i 0.727117 0.686514i \(-0.240860\pi\)
−0.686514 + 0.727117i \(0.740860\pi\)
\(18\) 4.59902 + 4.66559i 1.08400 + 1.09969i
\(19\) 5.31419i 1.21916i −0.792725 0.609579i \(-0.791338\pi\)
0.792725 0.609579i \(-0.208662\pi\)
\(20\) −6.15151 0.699108i −1.37552 0.156325i
\(21\) −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
\(25\) −4.87249 1.12199i −0.974497 0.224398i
\(26\) 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 \(0.585021\pi\)
\(30\) 6.63638 5.24306i 1.21163 0.957247i
\(31\) 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
\(35\) 1.39248 + 1.74957i 0.235372 + 0.295731i
\(36\) −0.0596812 + 8.30602i −0.00994686 + 1.38434i
\(37\) −5.27013 + 5.27013i −0.866404 + 0.866404i −0.992072 0.125668i \(-0.959893\pi\)
0.125668 + 0.992072i \(0.459893\pi\)
\(38\) 8.20586 8.20586i 1.33117 1.33117i
\(39\) 0.356609 + 0.359180i 0.0571031 + 0.0575149i
\(40\) −2.33762 2.93708i −0.369611 0.464394i
\(41\) 0.0314968i 0.00491898i −0.999997 0.00245949i \(-0.999217\pi\)
0.999997 0.00245949i \(-0.000782881\pi\)
\(42\) −3.78233 0.0135884i −0.583627 0.00209674i
\(43\) −3.76875 3.76875i −0.574728 0.574728i 0.358718 0.933446i \(-0.383214\pi\)
−0.933446 + 0.358718i \(0.883214\pi\)
\(44\) 9.37239 1.41294
\(45\) −0.805371 + 6.65968i −0.120058 + 0.992767i
\(46\) −15.6815 −2.31210
\(47\) −3.56639 3.56639i −0.520211 0.520211i 0.397424 0.917635i \(-0.369904\pi\)
−0.917635 + 0.397424i \(0.869904\pi\)
\(48\) −3.24158 0.0116457i −0.467881 0.00168091i
\(49\) 1.00000i 0.142857i
\(50\) −5.79130 9.25632i −0.819013 1.30904i
\(51\) −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
\(55\) 7.52082 + 0.854729i 1.01411 + 0.115252i
\(56\) 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 \(0.734378\pi\)
\(60\) 10.6503 + 1.24916i 1.37495 + 0.161266i
\(61\) −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
\(65\) 0.511262 0.406913i 0.0634143 0.0504714i
\(66\) −9.08593 + 9.02088i −1.11840 + 1.11039i
\(67\) 6.34806 6.34806i 0.775539 0.775539i −0.203530 0.979069i \(-0.565241\pi\)
0.979069 + 0.203530i \(0.0652413\pi\)
\(68\) −0.463512 + 0.463512i −0.0562091 + 0.0562091i
\(69\) 8.82642 8.76323i 1.06258 1.05497i
\(70\) −0.551396 + 4.85177i −0.0659044 + 0.579898i
\(71\) 3.95454i 0.469318i −0.972078 0.234659i \(-0.924603\pi\)
0.972078 0.234659i \(-0.0753973\pi\)
\(72\) −3.58665 + 3.53548i −0.422691 + 0.416660i
\(73\) 8.61099 + 8.61099i 1.00784 + 1.00784i 0.999969 + 0.00787086i \(0.00250540\pi\)
0.00787086 + 0.999969i \(0.497495\pi\)
\(74\) −16.2757 −1.89201
\(75\) 8.43236 + 1.97365i 0.973685 + 0.227898i
\(76\) 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 \(0.222655\pi\)
−0.765170 + 0.643828i \(0.777345\pi\)
\(80\) −0.472563 + 4.15812i −0.0528342 + 0.464892i
\(81\) 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
\(85\) −0.414214 + 0.329672i −0.0449278 + 0.0357580i
\(86\) 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 \(0.466164\pi\)
\(90\) −11.5271 + 9.03989i −1.21506 + 0.952888i
\(91\) −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
\(95\) 11.8069 + 1.34183i 1.21136 + 0.137669i
\(96\) −9.08474 9.15025i −0.927208 0.933894i
\(97\) 2.26760 2.26760i 0.230240 0.230240i −0.582553 0.812793i \(-0.697946\pi\)
0.812793 + 0.582553i \(0.197946\pi\)
\(98\) 1.54414 1.54414i 0.155982 0.155982i
\(99\) 0.0729661 10.1549i 0.00733337 1.02061i
\(100\) 3.10651 13.4907i 0.310651 1.34907i
\(101\) 8.63630i 0.859344i 0.902985 + 0.429672i \(0.141371\pi\)
−0.902985 + 0.429672i \(0.858629\pi\)
\(102\) 0.00321708 0.895474i 0.000318538 0.0886651i
\(103\) 0.964332 + 0.964332i 0.0950185 + 0.0950185i 0.753018 0.658000i \(-0.228597\pi\)
−0.658000 + 0.753018i \(0.728597\pi\)
\(104\) 0.490566 0.0481039
\(105\) −2.40095 3.03899i −0.234308 0.296575i
\(106\) 10.9724 1.06573
\(107\) −2.95847 2.95847i −0.286007 0.286007i 0.549492 0.835499i \(-0.314821\pi\)
−0.835499 + 0.549492i \(0.814821\pi\)
\(108\) 0.155055 14.3860i 0.0149201 1.38429i
\(109\) 2.82182i 0.270281i 0.990826 + 0.135141i \(0.0431486\pi\)
−0.990826 + 0.135141i \(0.956851\pi\)
\(110\) 10.2934 + 12.9330i 0.981436 + 1.23312i
\(111\) 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
\(115\) −9.99939 12.5636i −0.932448 1.17157i
\(116\) 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
\(120\) 4.03058 + 5.10169i 0.367940 + 0.465719i
\(121\) −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
\(125\) 3.72311 10.5422i 0.333005 0.942925i
\(126\) 6.55107 + 0.0470713i 0.583616 + 0.00419345i
\(127\) −11.6271 + 11.6271i −1.03174 + 1.03174i −0.0322583 + 0.999480i \(0.510270\pi\)
−0.999480 + 0.0322583i \(0.989730\pi\)
\(128\) −8.79491 + 8.79491i −0.777367 + 0.777367i
\(129\) 6.50417 + 6.55107i 0.572660 + 0.576789i
\(130\) 1.41779 + 0.161130i 0.124349 + 0.0141320i
\(131\) 12.7013i 1.10972i 0.831943 + 0.554861i \(0.187228\pi\)
−0.831943 + 0.554861i \(0.812772\pi\)
\(132\) −16.2333 0.0583199i −1.41293 0.00507609i
\(133\) −3.75770 3.75770i −0.325834 0.325834i
\(134\) 19.6046 1.69358
\(135\) 1.43638 11.5298i 0.123623 0.992329i
\(136\) −0.397446 −0.0340807
\(137\) −5.19451 5.19451i −0.443797 0.443797i 0.449489 0.893286i \(-0.351606\pi\)
−0.893286 + 0.449489i \(0.851606\pi\)
\(138\) 27.1609 + 0.0975782i 2.31209 + 0.00830641i
\(139\) 12.3138i 1.04444i 0.852810 + 0.522221i \(0.174897\pi\)
−0.852810 + 0.522221i \(0.825103\pi\)
\(140\) −4.84412 + 3.85543i −0.409402 + 0.325843i
\(141\) 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
\(145\) 0.717776 6.31576i 0.0596080 0.524495i
\(146\) 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 \(0.217444\pi\)
\(150\) 9.97316 + 16.0684i 0.814305 + 1.31198i
\(151\) −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
\(155\) −2.30223 + 20.2575i −0.184920 + 1.62712i
\(156\) −0.994479 + 0.987359i −0.0796221 + 0.0790520i
\(157\) −4.31728 + 4.31728i −0.344557 + 0.344557i −0.858077 0.513521i \(-0.828341\pi\)
0.513521 + 0.858077i \(0.328341\pi\)
\(158\) −17.6726 + 17.6726i −1.40596 + 1.40596i
\(159\) −6.17589 + 6.13167i −0.489780 + 0.486273i
\(160\) −13.0246 + 10.3663i −1.02968 + 0.819525i
\(161\) 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 \(-0.186527\pi\)
−0.553027 + 0.833164i \(0.686527\pi\)
\(164\) 0.0872068 0.00680970
\(165\) −13.0210 1.52722i −1.01369 0.118894i
\(166\) 11.9844 0.930168
\(167\) −6.39241 6.39241i −0.494659 0.494659i 0.415111 0.909771i \(-0.363743\pi\)
−0.909771 + 0.415111i \(0.863743\pi\)
\(168\) 0.0104460 2.90765i 0.000805929 0.224330i
\(169\) 12.9146i 0.993431i
\(170\) −1.14866 0.130544i −0.0880986 0.0100123i
\(171\) 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
\(175\) −4.23874 + 2.65200i −0.320418 + 0.200472i
\(176\) 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 \(0.684166\pi\)
\(180\) −18.4390 2.22987i −1.37436 0.166205i
\(181\) −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
\(185\) −10.3783 13.0397i −0.763027 0.958698i
\(186\) −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
\(190\) 16.1595 + 20.3035i 1.17234 + 1.47297i
\(191\) 6.37886i 0.461558i 0.973006 + 0.230779i \(0.0741275\pi\)
−0.973006 + 0.230779i \(0.925873\pi\)
\(192\) 0.0778669 21.6743i 0.00561956 1.56421i
\(193\) 7.56336 + 7.56336i 0.544422 + 0.544422i 0.924822 0.380400i \(-0.124214\pi\)
−0.380400 + 0.924822i \(0.624214\pi\)
\(194\) 7.00299 0.502785
\(195\) −0.888059 + 0.701608i −0.0635952 + 0.0502432i
\(196\) 2.76875 0.197768
\(197\) −1.01490 1.01490i −0.0723090 0.0723090i 0.670027 0.742336i \(-0.266282\pi\)
−0.742336 + 0.670027i \(0.766282\pi\)
\(198\) 15.7933 15.5680i 1.12238 1.10637i
\(199\) 9.40041i 0.666378i −0.942860 0.333189i \(-0.891875\pi\)
0.942860 0.333189i \(-0.108125\pi\)
\(200\) 7.11576 4.45204i 0.503160 0.314806i
\(201\) −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
\(205\) 0.0699786 + 0.00795295i 0.00488752 + 0.000555458i
\(206\) 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
\(210\) 0.985230 8.40003i 0.0679873 0.579657i
\(211\) −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
\(215\) 9.32488 7.42166i 0.635952 0.506153i
\(216\) 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
\(220\) −2.36653 + 20.8232i −0.159551 + 1.40390i
\(221\) 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 \(-0.191489\pi\)
−0.565945 + 0.824443i \(0.691489\pi\)
\(224\) 7.44445 0.497404
\(225\) −14.5929 3.47092i −0.972860 0.231394i
\(226\) 6.23208 0.414552
\(227\) 1.50739 + 1.50739i 0.100049 + 0.100049i 0.755360 0.655310i \(-0.227462\pi\)
−0.655310 + 0.755360i \(0.727462\pi\)
\(228\) −25.4846 0.0915560i −1.68776 0.00606344i
\(229\) 6.26009i 0.413678i 0.978375 + 0.206839i \(0.0663177\pi\)
−0.978375 + 0.206839i \(0.933682\pi\)
\(230\) 3.95957 34.8405i 0.261086 2.29732i
\(231\) 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
\(235\) 8.82419 7.02317i 0.575627 0.458141i
\(236\) 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 \(0.478517\pi\)
\(240\) 0.844372 7.19909i 0.0545040 0.464699i
\(241\) −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
\(245\) 2.22177 + 0.252500i 0.141943 + 0.0161316i
\(246\) −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
\(250\) 22.0277 10.5297i 1.39315 0.665956i
\(251\) 23.3428i 1.47339i 0.676227 + 0.736693i \(0.263614\pi\)
−0.676227 + 0.736693i \(0.736386\pi\)
\(252\) 5.83104 + 5.91545i 0.367321 + 0.372638i
\(253\) 17.1884 + 17.1884i 1.08063 + 1.08063i
\(254\) −35.9078 −2.25305
\(255\) 0.719486 0.568428i 0.0450559 0.0355963i
\(256\) −2.13372 −0.133358
\(257\) 10.9273 + 10.9273i 0.681627 + 0.681627i 0.960367 0.278740i \(-0.0899167\pi\)
−0.278740 + 0.960367i \(0.589917\pi\)
\(258\) −0.0724236 + 20.1591i −0.00450890 + 1.25505i
\(259\) 7.45309i 0.463112i
\(260\) 1.12664 + 1.41556i 0.0698712 + 0.0877890i
\(261\) −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
\(265\) 6.99662 + 8.79084i 0.429799 + 0.540017i
\(266\) 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 \(0.164622\pi\)
\(270\) 20.0216 15.5857i 1.21848 0.948516i
\(271\) 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
\(275\) −3.79802 + 16.4937i −0.229029 + 0.994607i
\(276\) 24.2631 + 24.4381i 1.46047 + 1.47100i
\(277\) 12.2472 12.2472i 0.735861 0.735861i −0.235913 0.971774i \(-0.575808\pi\)
0.971774 + 0.235913i \(0.0758081\pi\)
\(278\) −19.0142 + 19.0142i −1.14040 + 1.14040i
\(279\) 27.3526 + 0.196536i 1.63756 + 0.0117663i
\(280\) −3.72978 0.423883i −0.222897 0.0253319i
\(281\) 12.7181i 0.758698i −0.925254 0.379349i \(-0.876148\pi\)
0.925254 0.379349i \(-0.123852\pi\)
\(282\) −0.0685349 + 19.0767i −0.00408120 + 1.13600i
\(283\) −19.8271 19.8271i −1.17860 1.17860i −0.980102 0.198495i \(-0.936395\pi\)
−0.198495 0.980102i \(-0.563605\pi\)
\(284\) 10.9491 0.649711
\(285\) −20.4416 2.39758i −1.21086 0.142020i
\(286\) −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
\(290\) 10.8608 8.64408i 0.637767 0.507598i
\(291\) −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
\(295\) 2.60499 22.9215i 0.151668 1.33454i
\(296\) 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
\(300\) −5.46455 + 23.3471i −0.315496 + 1.34794i
\(301\) −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
\(305\) 1.71860 15.1221i 0.0984068 0.865888i
\(306\) −0.0111442 + 1.55098i −0.000637072 + 0.0886634i
\(307\) 10.1105 10.1105i 0.577034 0.577034i −0.357051 0.934085i \(-0.616218\pi\)
0.934085 + 0.357051i \(0.116218\pi\)
\(308\) 6.62728 6.62728i 0.377624 0.377624i
\(309\) −1.66426 1.67626i −0.0946765 0.0953592i
\(310\) −34.8355 + 27.7255i −1.97852 + 1.57470i
\(311\) 0.394155i 0.0223505i 0.999938 + 0.0111752i \(0.00355726\pi\)
−0.999938 + 0.0111752i \(0.996443\pi\)
\(312\) −0.849680 0.00305256i −0.0481036 0.000172817i
\(313\) −10.3810 10.3810i −0.586767 0.586767i 0.349987 0.936754i \(-0.386186\pi\)
−0.936754 + 0.349987i \(0.886186\pi\)
\(314\) −13.3330 −0.752424
\(315\) 4.13962 + 5.27859i 0.233241 + 0.297415i
\(316\) −31.6881 −1.78260
\(317\) −19.8075 19.8075i −1.11250 1.11250i −0.992812 0.119688i \(-0.961810\pi\)
−0.119688 0.992812i \(-0.538190\pi\)
\(318\) −19.0046 0.0682759i −1.06573 0.00382872i
\(319\) 9.62264i 0.538764i
\(320\) −27.8026 3.15971i −1.55421 0.176633i
\(321\) 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
\(325\) 0.774972 + 1.23865i 0.0429877 + 0.0687080i
\(326\) 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
\(330\) −17.7481 22.4646i −0.977000 1.23663i
\(331\) −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
\(335\) 12.5010 + 15.7068i 0.683004 + 0.858154i
\(336\) −2.30038 + 2.28391i −0.125496 + 0.124597i
\(337\) −3.40139 + 3.40139i −0.185286 + 0.185286i −0.793655 0.608369i \(-0.791824\pi\)
0.608369 + 0.793655i \(0.291824\pi\)
\(338\) 19.9420 19.9420i 1.08470 1.08470i
\(339\) −3.50777 + 3.48266i −0.190516 + 0.189152i
\(340\) −0.912779 1.14685i −0.0495024 0.0621968i
\(341\) 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
\(345\) 17.2412 + 21.8229i 0.928233 + 1.17491i
\(346\) 12.0070 0.645498
\(347\) 24.0324 + 24.0324i 1.29013 + 1.29013i 0.934706 + 0.355421i \(0.115663\pi\)
0.355421 + 0.934706i \(0.384337\pi\)
\(348\) −0.0489753 + 13.6323i −0.00262535 + 0.730766i
\(349\) 9.37078i 0.501607i −0.968038 0.250803i \(-0.919305\pi\)
0.968038 0.250803i \(-0.0806947\pi\)
\(350\) −10.6403 2.45015i −0.568747 0.130966i
\(351\) 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
\(355\) 8.78606 + 0.998522i 0.466316 + 0.0529960i
\(356\) 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 \(0.244368\pi\)
\(360\) −6.94938 8.86141i −0.366264 0.467037i
\(361\) −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
\(365\) −21.3059 + 16.9573i −1.11520 + 0.887587i
\(366\) 18.1382 + 18.2690i 0.948101 + 0.954938i
\(367\) 15.9239 15.9239i 0.831218 0.831218i −0.156465 0.987683i \(-0.550010\pi\)
0.987683 + 0.156465i \(0.0500099\pi\)
\(368\) −9.50315 + 9.50315i −0.495386 + 0.495386i
\(369\) 0.000678924 0.0944881i 3.53434e−5 0.00491885i
\(370\) 4.10960 36.1607i 0.213648 1.87990i
\(371\) 5.02457i 0.260863i
\(372\) 0.157086 43.7249i 0.00814453 2.26703i
\(373\) 23.3283 + 23.3283i 1.20790 + 1.20790i 0.971707 + 0.236189i \(0.0758984\pi\)
0.236189 + 0.971707i \(0.424102\pi\)
\(374\) 1.75010 0.0904954
\(375\) −6.51417 + 18.2364i −0.336390 + 0.941723i
\(376\) 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 \(0.411710\pi\)
−0.273828 + 0.961779i \(0.588290\pi\)
\(380\) −3.71520 + 32.6903i −0.190586 + 1.67698i
\(381\) 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
\(385\) 5.92241 4.71364i 0.301834 0.240229i
\(386\) 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 \(0.425048\pi\)
\(390\) −2.45467 0.287905i −0.124297 0.0145787i
\(391\) −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
\(395\) −25.4280 2.88985i −1.27942 0.145404i
\(396\) 28.1164 + 0.202025i 1.41290 + 0.0101521i
\(397\) 21.9242 21.9242i 1.10034 1.10034i 0.105976 0.994369i \(-0.466203\pi\)
0.994369 0.105976i \(-0.0337966\pi\)
\(398\) 14.5156 14.5156i 0.727600 0.727600i
\(399\) 6.48510 + 6.53187i 0.324661 + 0.327002i
\(400\) −9.11904 2.09985i −0.455952 0.104993i
\(401\) 25.7514i 1.28596i −0.765882 0.642982i \(-0.777697\pi\)
0.765882 0.642982i \(-0.222303\pi\)
\(402\) −33.9560 0.121990i −1.69357 0.00608431i
\(403\) −1.88402 1.88402i −0.0938497 0.0938497i
\(404\) −23.9117 −1.18965
\(405\) −2.55960 + 19.9612i −0.127188 + 0.991879i
\(406\) −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 \(0.0872592\pi\)
−0.962660 + 0.270712i \(0.912741\pi\)
\(410\) 0.0957764 + 0.120337i 0.00473006 + 0.00594304i
\(411\) 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
\(415\) 7.64192 + 9.60162i 0.375127 + 0.471325i
\(416\) 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 \(0.545795\pi\)
\(420\) 8.41419 6.64761i 0.410570 0.324370i
\(421\) 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
\(425\) −0.627865 1.00353i −0.0304559 0.0486782i
\(426\) −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
\(430\) 25.8590 + 2.93884i 1.24703 + 0.141723i
\(431\) 4.18118i 0.201400i −0.994917 0.100700i \(-0.967892\pi\)
0.994917 0.100700i \(-0.0321083\pi\)
\(432\) −9.72423 0.104809i −0.467857 0.00504264i
\(433\) −2.20877 2.20877i −0.106146 0.106146i 0.652039 0.758185i \(-0.273914\pi\)
−0.758185 + 0.652039i \(0.773914\pi\)
\(434\) 19.9109 0.955752
\(435\) −1.28252 + 10.9347i −0.0614919 + 0.524278i
\(436\) −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 \(0.228896\pi\)
−0.752401 + 0.658706i \(0.771104\pi\)
\(440\) −9.94222 + 7.91300i −0.473977 + 0.377238i
\(441\) 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
\(445\) −0.505479 + 4.44775i −0.0239620 + 0.210843i
\(446\) 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 \(0.798730\pi\)
\(450\) −17.1739 27.8931i −0.809586 1.31489i
\(451\) −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
\(455\) 0.0737860 0.649248i 0.00345914 0.0304372i
\(456\) −10.8868 10.9653i −0.509823 0.513499i
\(457\) −9.31021 + 9.31021i −0.435513 + 0.435513i −0.890499 0.454986i \(-0.849644\pi\)
0.454986 + 0.890499i \(0.349644\pi\)
\(458\) −9.66646 + 9.66646i −0.451684 + 0.451684i
\(459\) −0.860455 0.879206i −0.0401626 0.0410378i
\(460\) 34.7855 27.6858i 1.62188 1.29086i
\(461\) 25.6579i 1.19501i −0.801865 0.597505i \(-0.796159\pi\)
0.801865 0.597505i \(-0.203841\pi\)
\(462\) −0.0459976 + 12.8034i −0.00214000 + 0.595670i
\(463\) 13.2170 + 13.2170i 0.614248 + 0.614248i 0.944050 0.329802i \(-0.106982\pi\)
−0.329802 + 0.944050i \(0.606982\pi\)
\(464\) −5.32017 −0.246983
\(465\) 4.11361 35.0725i 0.190764 1.62645i
\(466\) −8.25874 −0.382579
\(467\) −19.6659 19.6659i −0.910031 0.910031i 0.0862431 0.996274i \(-0.472514\pi\)
−0.996274 + 0.0862431i \(0.972514\pi\)
\(468\) 1.72862 1.70396i 0.0799056 0.0787655i
\(469\) 8.97752i 0.414543i
\(470\) 24.4706 + 2.78104i 1.12874 + 0.128280i
\(471\) 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
\(475\) −5.96248 + 25.8933i −0.273577 + 1.18807i
\(476\) 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 \(0.711330\pi\)
\(480\) 22.6236 17.8737i 1.03262 0.815821i
\(481\) 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
\(485\) 4.46551 + 5.61064i 0.202768 + 0.254766i
\(486\) −23.6345 24.4993i −1.07208 1.11131i
\(487\) −28.6505 + 28.6505i −1.29828 + 1.29828i −0.368749 + 0.929529i \(0.620214\pi\)
−0.929529 + 0.368749i \(0.879786\pi\)
\(488\) 8.07948 8.07948i 0.365741 0.365741i
\(489\) −6.17247 6.21698i −0.279129 0.281141i
\(490\) 3.04083 + 3.82062i 0.137370 + 0.172598i
\(491\) 2.74522i 0.123890i −0.998080 0.0619450i \(-0.980270\pi\)
0.998080 0.0619450i \(-0.0197303\pi\)
\(492\) −0.151046 0.000542646i −0.00680966 2.44644e-5i
\(493\) −0.475888 0.475888i −0.0214329 0.0214329i
\(494\) −3.39119 −0.152577
\(495\) 22.5435 + 2.72623i 1.01325 + 0.122535i
\(496\) 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 \(-0.762611\pi\)
0.734558 0.678546i \(-0.237389\pi\)
\(500\) 29.1887 + 10.3083i 1.30536 + 0.461003i
\(501\) 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
\(505\) −19.1878 2.18067i −0.853848 0.0970384i
\(506\) 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 \(0.394752\pi\)
\(510\) 1.98872 + 0.233255i 0.0880620 + 0.0103287i
\(511\) 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
\(515\) −2.38601 + 1.89903i −0.105140 + 0.0836811i
\(516\) −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
\(520\) −0.123868 + 1.08992i −0.00543197 + 0.0477963i
\(521\) 24.6501i 1.07994i 0.841683 + 0.539971i \(0.181565\pi\)
−0.841683 + 0.539971i \(0.818435\pi\)
\(522\) −13.0735 13.2628i −0.572212 0.580495i
\(523\) −23.4069 23.4069i −1.02351 1.02351i −0.999717 0.0237950i \(-0.992425\pi\)
−0.0237950 0.999717i \(-0.507575\pi\)
\(524\) −35.1668 −1.53627
\(525\) 7.35816 4.56699i 0.321137 0.199320i
\(526\) 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
\(530\) −2.77053 + 24.3781i −0.120344 + 1.05892i
\(531\) −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
\(535\) 7.32005 5.82602i 0.316473 0.251881i
\(536\) 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
\(540\) 31.9232 + 3.97696i 1.37375 + 0.171141i
\(541\) −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
\(545\) −6.26942 0.712509i −0.268552 0.0305205i
\(546\) 0.778743 + 0.784359i 0.0333271 + 0.0335675i
\(547\) −3.63475 + 3.63475i −0.155411 + 0.155411i −0.780530 0.625119i \(-0.785051\pi\)
0.625119 + 0.780530i \(0.285051\pi\)
\(548\) 14.3823 14.3823i 0.614380 0.614380i
\(549\) −20.4185 0.146713i −0.871440 0.00626154i
\(550\) −31.3333 + 19.6039i −1.33605 + 0.835914i
\(551\) 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
\(555\) 17.8945 + 22.6499i 0.759578 + 0.961433i
\(556\) −34.0938 −1.44590
\(557\) 5.91751 + 5.91751i 0.250733 + 0.250733i 0.821271 0.570538i \(-0.193265\pi\)
−0.570538 + 0.821271i \(0.693265\pi\)
\(558\) 41.9328 + 42.5397i 1.77516 + 1.80085i
\(559\) 1.55749i 0.0658747i
\(560\) 2.60608 + 3.27439i 0.110127 + 0.138368i
\(561\) −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
\(565\) 3.97393 + 4.99301i 0.167185 + 0.210058i
\(566\) 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 \(0.545676\pi\)
\(570\) −27.8626 35.2670i −1.16704 1.47717i
\(571\) 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
\(575\) 30.4383 19.0440i 1.26937 0.794189i
\(576\) −0.269737 + 37.5402i −0.0112390 + 1.56417i
\(577\) 1.10727 1.10727i 0.0460964 0.0460964i −0.683683 0.729779i \(-0.739623\pi\)
0.729779 + 0.683683i \(0.239623\pi\)
\(578\) 26.1639 26.1639i 1.08827 1.08827i
\(579\) −13.0530 13.1471i −0.542463 0.546375i
\(580\) 17.4867 + 1.98734i 0.726097 + 0.0825197i
\(581\) 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
\(585\) 1.54252 1.20969i 0.0637753 0.0500144i
\(586\) −20.7791 −0.858376
\(587\) 7.76708 + 7.76708i 0.320582 + 0.320582i 0.848990 0.528408i \(-0.177211\pi\)
−0.528408 + 0.848990i \(0.677211\pi\)
\(588\) −4.79558 0.0172286i −0.197766 0.000710495i
\(589\) 48.4535i 1.99649i
\(590\) 39.4165 31.3715i 1.62275 1.29154i
\(591\) 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
\(595\) −0.0597798 + 0.526007i −0.00245073 + 0.0215642i
\(596\) 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 \(0.636650\pi\)
\(600\) −12.3525 + 7.66682i −0.504288 + 0.312997i
\(601\) −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
\(605\) 0.115814 1.01905i 0.00470849 0.0414303i
\(606\) 23.1809 23.0149i 0.941660 0.934918i
\(607\) −0.0701607 + 0.0701607i −0.00284774 + 0.00284774i −0.708529 0.705681i \(-0.750641\pi\)
0.705681 + 0.708529i \(0.250641\pi\)
\(608\) 27.9740 27.9740i 1.13450 1.13450i
\(609\) 3.49404 3.46902i 0.141586 0.140572i
\(610\) 26.0044 20.6969i 1.05289 0.837992i
\(611\) 1.47386i 0.0596260i
\(612\) −1.40049 + 1.38051i −0.0566115 + 0.0558038i
\(613\) −26.6840 26.6840i −1.07776 1.07776i −0.996710 0.0810445i \(-0.974174\pi\)
−0.0810445 0.996710i \(-0.525826\pi\)
\(614\) 31.2239 1.26010
\(615\) −0.121156 0.0142103i −0.00488549 0.000573014i
\(616\) 5.68266 0.228961
\(617\) 6.37294 + 6.37294i 0.256565 + 0.256565i 0.823656 0.567090i \(-0.191931\pi\)
−0.567090 + 0.823656i \(0.691931\pi\)
\(618\) 0.0185315 5.15824i 0.000745446 0.207495i
\(619\) 17.7676i 0.714139i 0.934078 + 0.357070i \(0.116224\pi\)
−0.934078 + 0.357070i \(0.883776\pi\)
\(620\) −56.0879 6.37430i −2.25255 0.255998i
\(621\) 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
\(625\) 22.4823 + 10.9338i 0.899291 + 0.437351i
\(626\) 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
\(630\) −1.75873 + 14.5431i −0.0700693 + 0.579409i
\(631\) 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
\(635\) −22.8968 28.7685i −0.908633 1.14164i
\(636\) −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
\(640\) −17.3195 21.7609i −0.684614 0.860177i
\(641\) 14.8270i 0.585630i −0.956169 0.292815i \(-0.905408\pi\)
0.956169 0.292815i \(-0.0945920\pi\)
\(642\) −0.0568527 + 15.8250i −0.00224380 + 0.624562i
\(643\) −32.7229 32.7229i −1.29047 1.29047i −0.934498 0.355968i \(-0.884151\pi\)
−0.355968 0.934498i \(-0.615849\pi\)
\(644\) −19.8823 −0.783474
\(645\) −16.1972 + 12.7966i −0.637766 + 0.503865i
\(646\) 2.74747 0.108098
\(647\) −27.0564 27.0564i −1.06370 1.06370i −0.997828 0.0658674i \(-0.979019\pi\)
−0.0658674 0.997828i \(-0.520981\pi\)
\(648\) −10.8359 + 10.5289i −0.425674 + 0.413612i
\(649\) 34.9230i 1.37085i
\(650\) −0.715985 + 3.10932i −0.0280833 + 0.121958i
\(651\) −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
\(655\) −28.2194 3.20709i −1.10262 0.125311i
\(656\) 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 \(0.427539\pi\)
\(660\) 4.22849 36.0520i 0.164594 1.40332i
\(661\) −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
\(665\) 9.29755 7.39991i 0.360544 0.286956i
\(666\) −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
\(670\) −4.95017 + 43.5569i −0.191242 + 1.68275i
\(671\) 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 \(-0.372439\pi\)
−0.920770 + 0.390105i \(0.872439\pi\)
\(674\) −10.5045 −0.404617
\(675\) 25.2539 + 6.10257i 0.972022 + 0.234888i
\(676\) 35.7573 1.37528
\(677\) 16.3594 + 16.3594i 0.628742 + 0.628742i 0.947752 0.319009i \(-0.103350\pi\)
−0.319009 + 0.947752i \(0.603350\pi\)
\(678\) −10.7942 0.0387793i −0.414549 0.00148931i
\(679\) 3.20687i 0.123068i
\(680\) 0.100355 0.883031i 0.00384844 0.0338627i
\(681\) −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
\(685\) 12.8526 10.2294i 0.491072 0.390844i
\(686\) 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
\(690\) −7.07492 + 60.3205i −0.269338 + 2.29636i
\(691\) 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
\(695\) −27.3584 3.10923i −1.03776 0.117940i
\(696\) −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
\(700\) −7.34272 11.7360i −0.277529 0.443579i
\(701\) 37.9089i 1.43180i −0.698204 0.715899i \(-0.746017\pi\)
0.698204 0.715899i \(-0.253983\pi\)
\(702\) −0.0357368 + 3.31567i −0.00134880 + 0.125142i
\(703\) 28.0065 + 28.0065i 1.05628 + 1.05628i
\(704\) 42.3598 1.59649
\(705\) −15.3276 + 12.1095i −0.577269 + 0.456070i
\(706\) 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 \(0.101432\pi\)
−0.949656 + 0.313293i \(0.898568\pi\)
\(710\) 12.0251 + 15.1088i 0.451293 + 0.567023i
\(711\) −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
\(715\) −1.37743 1.73066i −0.0515129 0.0647229i
\(716\) 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 \(0.421628\pi\)
\(720\) −1.50728 + 12.4638i −0.0561731 + 0.464500i
\(721\) 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
\(725\) 13.8509 + 3.18946i 0.514409 + 0.118454i
\(726\) 1.22231 + 1.23112i 0.0453640 + 0.0456911i
\(727\) 19.4878 19.4878i 0.722761 0.722761i −0.246406 0.969167i \(-0.579250\pi\)
0.969167 + 0.246406i \(0.0792495\pi\)
\(728\) 0.346882 0.346882i 0.0128563 0.0128563i
\(729\) 26.9937 + 0.581953i 0.999768 + 0.0215538i
\(730\) −59.0838 6.71478i −2.18679 0.248525i
\(731\) 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 \(-0.0283084\pi\)
−0.0888162 + 0.996048i \(0.528308\pi\)
\(734\) 49.1774 1.81517
\(735\) −3.84662 0.451165i −0.141885 0.0166415i
\(736\) −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 \(0.154679\pi\)
−0.884236 + 0.467040i \(0.845321\pi\)
\(740\) 36.1036 28.7348i 1.32720 1.05631i
\(741\) 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
\(745\) −4.78108 + 42.0691i −0.175165 + 1.54129i
\(746\) 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
\(750\) −38.2184 + 18.1008i −1.39554 + 0.660946i
\(751\) 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
\(755\) 0.481081 4.23306i 0.0175083 0.154057i
\(756\) −10.0628 10.2821i −0.365980 0.373955i
\(757\) −11.9760 + 11.9760i −0.435274 + 0.435274i −0.890418 0.455144i \(-0.849588\pi\)
0.455144 + 0.890418i \(0.349588\pi\)
\(758\) −57.8245 + 57.8245i −2.10028 + 2.10028i
\(759\) −29.6641 29.8780i −1.07674 1.08450i
\(760\) −15.6082 + 12.4226i −0.566170 + 0.450614i
\(761\) 41.1635i 1.49217i 0.665848 + 0.746087i \(0.268070\pi\)
−0.665848 + 0.746087i \(0.731930\pi\)
\(762\) 62.1937 + 0.223437i 2.25304 + 0.00809426i
\(763\) 1.99533 + 1.99533i 0.0722357 + 0.0722357i
\(764\) −17.6614 −0.638969
\(765\) −1.24971 + 0.980062i −0.0451835 + 0.0354342i
\(766\) −15.3007 −0.552836
\(767\) 2.13178 + 2.13178i 0.0769740 + 0.0769740i
\(768\) 3.69569 + 0.0132771i 0.133357 + 0.000479097i
\(769\) &