Properties

Label 1050.2.bc.c.607.2
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 607.2
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.c.493.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(1.48356 - 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(1.48356 - 2.19067i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(3.86370 + 3.86370i) q^{13} +(0.866025 - 2.50000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-5.53674 - 1.48356i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(3.09808 - 5.36603i) q^{19} +(-1.73205 - 2.00000i) q^{21} +(-1.93185 - 1.93185i) q^{22} +(0.0693504 + 0.258819i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.73205 + 2.73205i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.189469 - 2.63896i) q^{28} +2.19615i q^{29} +(5.13397 - 2.96410i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-2.63896 + 0.707107i) q^{33} -5.73205 q^{34} -1.00000 q^{36} +(-1.22474 + 0.328169i) q^{37} +(1.60368 - 5.98502i) q^{38} +(4.73205 - 2.73205i) q^{39} +4.46410i q^{41} +(-2.19067 - 1.48356i) q^{42} +(-7.20977 + 7.20977i) q^{43} +(-2.36603 - 1.36603i) q^{44} +(0.133975 + 0.232051i) q^{46} +(-2.84701 - 10.6252i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-2.59808 - 6.50000i) q^{49} +(-2.86603 + 4.96410i) q^{51} +(5.27792 + 1.41421i) q^{52} +(8.43451 + 2.26002i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.500000 - 2.59808i) q^{56} +(-4.38134 - 4.38134i) q^{57} +(0.568406 + 2.12132i) q^{58} +(-3.73205 - 6.46410i) q^{59} +(-1.56218 - 0.901924i) q^{61} +(4.19187 - 4.19187i) q^{62} +(-2.38014 + 1.15539i) q^{63} -1.00000i q^{64} +(-2.36603 + 1.36603i) q^{66} +(-1.03528 + 3.86370i) q^{67} +(-5.53674 + 1.48356i) q^{68} +0.267949 q^{69} +14.8564 q^{71} +(-0.965926 + 0.258819i) q^{72} +(-2.07055 + 7.72741i) q^{73} +(-1.09808 + 0.633975i) q^{74} -6.19615i q^{76} +(-7.20977 - 0.517638i) q^{77} +(3.86370 - 3.86370i) q^{78} +(13.9641 + 8.06218i) q^{79} +(0.500000 + 0.866025i) q^{81} +(1.15539 + 4.31199i) q^{82} +(4.00240 + 4.00240i) q^{83} +(-2.50000 - 0.866025i) q^{84} +(-5.09808 + 8.83013i) q^{86} +(2.12132 + 0.568406i) q^{87} +(-2.63896 - 0.707107i) q^{88} +(0.232051 - 0.401924i) q^{89} +(14.1962 - 2.73205i) q^{91} +(0.189469 + 0.189469i) q^{92} +(-1.53433 - 5.72620i) q^{93} +(-5.50000 - 9.52628i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(4.94975 - 4.94975i) q^{97} +(-4.19187 - 5.60609i) q^{98} +2.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 4q^{11} + 4q^{16} + 4q^{19} - 4q^{24} + 24q^{26} + 48q^{31} - 32q^{34} - 8q^{36} + 24q^{39} - 12q^{44} + 8q^{46} - 16q^{51} - 4q^{54} - 4q^{56} - 16q^{59} + 36q^{61} - 12q^{66} + 16q^{69} + 8q^{71} + 12q^{74} + 84q^{79} + 4q^{81} - 20q^{84} - 20q^{86} - 12q^{89} + 72q^{91} - 44q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 0.258819 0.965926i 0.149429 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 1.48356 2.19067i 0.560734 0.827996i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) −1.36603 2.36603i −0.411872 0.713384i 0.583222 0.812313i \(-0.301792\pi\)
−0.995094 + 0.0989291i \(0.968458\pi\)
\(12\) −0.258819 0.965926i −0.0747146 0.278839i
\(13\) 3.86370 + 3.86370i 1.07160 + 1.07160i 0.997231 + 0.0743676i \(0.0236938\pi\)
0.0743676 + 0.997231i \(0.476306\pi\)
\(14\) 0.866025 2.50000i 0.231455 0.668153i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −5.53674 1.48356i −1.34286 0.359817i −0.485363 0.874313i \(-0.661312\pi\)
−0.857493 + 0.514496i \(0.827979\pi\)
\(18\) −0.965926 0.258819i −0.227671 0.0610042i
\(19\) 3.09808 5.36603i 0.710747 1.23105i −0.253830 0.967249i \(-0.581690\pi\)
0.964577 0.263802i \(-0.0849764\pi\)
\(20\) 0 0
\(21\) −1.73205 2.00000i −0.377964 0.436436i
\(22\) −1.93185 1.93185i −0.411872 0.411872i
\(23\) 0.0693504 + 0.258819i 0.0144605 + 0.0539675i 0.972779 0.231734i \(-0.0744400\pi\)
−0.958319 + 0.285702i \(0.907773\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) 4.73205 + 2.73205i 0.928032 + 0.535799i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 0.189469 2.63896i 0.0358062 0.498716i
\(29\) 2.19615i 0.407815i 0.978990 + 0.203908i \(0.0653642\pi\)
−0.978990 + 0.203908i \(0.934636\pi\)
\(30\) 0 0
\(31\) 5.13397 2.96410i 0.922089 0.532368i 0.0377881 0.999286i \(-0.487969\pi\)
0.884301 + 0.466917i \(0.154635\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) −2.63896 + 0.707107i −0.459384 + 0.123091i
\(34\) −5.73205 −0.983039
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −1.22474 + 0.328169i −0.201347 + 0.0539507i −0.358083 0.933690i \(-0.616569\pi\)
0.156736 + 0.987641i \(0.449903\pi\)
\(38\) 1.60368 5.98502i 0.260152 0.970899i
\(39\) 4.73205 2.73205i 0.757735 0.437478i
\(40\) 0 0
\(41\) 4.46410i 0.697176i 0.937276 + 0.348588i \(0.113339\pi\)
−0.937276 + 0.348588i \(0.886661\pi\)
\(42\) −2.19067 1.48356i −0.338028 0.228919i
\(43\) −7.20977 + 7.20977i −1.09948 + 1.09948i −0.105008 + 0.994471i \(0.533487\pi\)
−0.994471 + 0.105008i \(0.966513\pi\)
\(44\) −2.36603 1.36603i −0.356692 0.205936i
\(45\) 0 0
\(46\) 0.133975 + 0.232051i 0.0197535 + 0.0342140i
\(47\) −2.84701 10.6252i −0.415279 1.54984i −0.784276 0.620412i \(-0.786965\pi\)
0.368997 0.929431i \(-0.379701\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) −2.59808 6.50000i −0.371154 0.928571i
\(50\) 0 0
\(51\) −2.86603 + 4.96410i −0.401324 + 0.695113i
\(52\) 5.27792 + 1.41421i 0.731915 + 0.196116i
\(53\) 8.43451 + 2.26002i 1.15857 + 0.310438i 0.786394 0.617725i \(-0.211945\pi\)
0.372175 + 0.928163i \(0.378612\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −0.500000 2.59808i −0.0668153 0.347183i
\(57\) −4.38134 4.38134i −0.580323 0.580323i
\(58\) 0.568406 + 2.12132i 0.0746354 + 0.278543i
\(59\) −3.73205 6.46410i −0.485872 0.841554i 0.513997 0.857792i \(-0.328164\pi\)
−0.999868 + 0.0162379i \(0.994831\pi\)
\(60\) 0 0
\(61\) −1.56218 0.901924i −0.200016 0.115480i 0.396647 0.917971i \(-0.370174\pi\)
−0.596663 + 0.802492i \(0.703507\pi\)
\(62\) 4.19187 4.19187i 0.532368 0.532368i
\(63\) −2.38014 + 1.15539i −0.299869 + 0.145566i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −2.36603 + 1.36603i −0.291238 + 0.168146i
\(67\) −1.03528 + 3.86370i −0.126479 + 0.472026i −0.999888 0.0149610i \(-0.995238\pi\)
0.873409 + 0.486987i \(0.161904\pi\)
\(68\) −5.53674 + 1.48356i −0.671428 + 0.179909i
\(69\) 0.267949 0.0322573
\(70\) 0 0
\(71\) 14.8564 1.76313 0.881566 0.472062i \(-0.156490\pi\)
0.881566 + 0.472062i \(0.156490\pi\)
\(72\) −0.965926 + 0.258819i −0.113835 + 0.0305021i
\(73\) −2.07055 + 7.72741i −0.242340 + 0.904425i 0.732362 + 0.680915i \(0.238418\pi\)
−0.974702 + 0.223509i \(0.928249\pi\)
\(74\) −1.09808 + 0.633975i −0.127649 + 0.0736980i
\(75\) 0 0
\(76\) 6.19615i 0.710747i
\(77\) −7.20977 0.517638i −0.821629 0.0589903i
\(78\) 3.86370 3.86370i 0.437478 0.437478i
\(79\) 13.9641 + 8.06218i 1.57108 + 0.907066i 0.996036 + 0.0889460i \(0.0283499\pi\)
0.575048 + 0.818120i \(0.304983\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 1.15539 + 4.31199i 0.127592 + 0.476180i
\(83\) 4.00240 + 4.00240i 0.439321 + 0.439321i 0.891783 0.452463i \(-0.149454\pi\)
−0.452463 + 0.891783i \(0.649454\pi\)
\(84\) −2.50000 0.866025i −0.272772 0.0944911i
\(85\) 0 0
\(86\) −5.09808 + 8.83013i −0.549740 + 0.952177i
\(87\) 2.12132 + 0.568406i 0.227429 + 0.0609395i
\(88\) −2.63896 0.707107i −0.281314 0.0753778i
\(89\) 0.232051 0.401924i 0.0245973 0.0426038i −0.853465 0.521151i \(-0.825503\pi\)
0.878062 + 0.478547i \(0.158836\pi\)
\(90\) 0 0
\(91\) 14.1962 2.73205i 1.48816 0.286397i
\(92\) 0.189469 + 0.189469i 0.0197535 + 0.0197535i
\(93\) −1.53433 5.72620i −0.159103 0.593780i
\(94\) −5.50000 9.52628i −0.567282 0.982561i
\(95\) 0 0
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) 4.94975 4.94975i 0.502571 0.502571i −0.409665 0.912236i \(-0.634354\pi\)
0.912236 + 0.409665i \(0.134354\pi\)
\(98\) −4.19187 5.60609i −0.423443 0.566300i
\(99\) 2.73205i 0.274581i
\(100\) 0 0
\(101\) −8.83013 + 5.09808i −0.878630 + 0.507278i −0.870207 0.492687i \(-0.836015\pi\)
−0.00842387 + 0.999965i \(0.502681\pi\)
\(102\) −1.48356 + 5.53674i −0.146895 + 0.548219i
\(103\) −10.2970 + 2.75908i −1.01460 + 0.271860i −0.727548 0.686057i \(-0.759340\pi\)
−0.287047 + 0.957917i \(0.592674\pi\)
\(104\) 5.46410 0.535799
\(105\) 0 0
\(106\) 8.73205 0.848132
\(107\) −9.65926 + 2.58819i −0.933796 + 0.250210i −0.693472 0.720483i \(-0.743920\pi\)
−0.240323 + 0.970693i \(0.577253\pi\)
\(108\) −0.258819 + 0.965926i −0.0249049 + 0.0929463i
\(109\) 3.16987 1.83013i 0.303619 0.175294i −0.340449 0.940263i \(-0.610579\pi\)
0.644067 + 0.764969i \(0.277246\pi\)
\(110\) 0 0
\(111\) 1.26795i 0.120348i
\(112\) −1.15539 2.38014i −0.109175 0.224902i
\(113\) −2.12132 + 2.12132i −0.199557 + 0.199557i −0.799810 0.600253i \(-0.795067\pi\)
0.600253 + 0.799810i \(0.295067\pi\)
\(114\) −5.36603 3.09808i −0.502574 0.290161i
\(115\) 0 0
\(116\) 1.09808 + 1.90192i 0.101954 + 0.176589i
\(117\) −1.41421 5.27792i −0.130744 0.487944i
\(118\) −5.27792 5.27792i −0.485872 0.485872i
\(119\) −11.4641 + 9.92820i −1.05091 + 0.910117i
\(120\) 0 0
\(121\) 1.76795 3.06218i 0.160723 0.278380i
\(122\) −1.74238 0.466870i −0.157748 0.0422684i
\(123\) 4.31199 + 1.15539i 0.388799 + 0.104178i
\(124\) 2.96410 5.13397i 0.266184 0.461045i
\(125\) 0 0
\(126\) −2.00000 + 1.73205i −0.178174 + 0.154303i
\(127\) 8.38375 + 8.38375i 0.743937 + 0.743937i 0.973333 0.229396i \(-0.0736751\pi\)
−0.229396 + 0.973333i \(0.573675\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) 5.09808 + 8.83013i 0.448861 + 0.777449i
\(130\) 0 0
\(131\) −3.16987 1.83013i −0.276953 0.159899i 0.355090 0.934832i \(-0.384450\pi\)
−0.632043 + 0.774933i \(0.717784\pi\)
\(132\) −1.93185 + 1.93185i −0.168146 + 0.168146i
\(133\) −7.15900 14.7477i −0.620764 1.27879i
\(134\) 4.00000i 0.345547i
\(135\) 0 0
\(136\) −4.96410 + 2.86603i −0.425668 + 0.245760i
\(137\) −5.67544 + 21.1810i −0.484885 + 1.80962i 0.0956916 + 0.995411i \(0.469494\pi\)
−0.580577 + 0.814205i \(0.697173\pi\)
\(138\) 0.258819 0.0693504i 0.0220321 0.00590349i
\(139\) −0.928203 −0.0787292 −0.0393646 0.999225i \(-0.512533\pi\)
−0.0393646 + 0.999225i \(0.512533\pi\)
\(140\) 0 0
\(141\) −11.0000 −0.926367
\(142\) 14.3502 3.84512i 1.20424 0.322675i
\(143\) 3.86370 14.4195i 0.323099 1.20582i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 8.00000i 0.662085i
\(147\) −6.95095 + 0.827225i −0.573305 + 0.0682284i
\(148\) −0.896575 + 0.896575i −0.0736980 + 0.0736980i
\(149\) 15.5885 + 9.00000i 1.27706 + 0.737309i 0.976306 0.216394i \(-0.0694297\pi\)
0.300750 + 0.953703i \(0.402763\pi\)
\(150\) 0 0
\(151\) 1.46410 + 2.53590i 0.119147 + 0.206368i 0.919430 0.393254i \(-0.128651\pi\)
−0.800283 + 0.599623i \(0.795317\pi\)
\(152\) −1.60368 5.98502i −0.130076 0.485450i
\(153\) 4.05317 + 4.05317i 0.327680 + 0.327680i
\(154\) −7.09808 + 1.36603i −0.571979 + 0.110077i
\(155\) 0 0
\(156\) 2.73205 4.73205i 0.218739 0.378867i
\(157\) 16.6796 + 4.46927i 1.33117 + 0.356687i 0.853153 0.521661i \(-0.174688\pi\)
0.478021 + 0.878348i \(0.341354\pi\)
\(158\) 15.5749 + 4.17329i 1.23908 + 0.332009i
\(159\) 4.36603 7.56218i 0.346248 0.599720i
\(160\) 0 0
\(161\) 0.669873 + 0.232051i 0.0527934 + 0.0182882i
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) 3.10583 + 11.5911i 0.243267 + 0.907886i 0.974246 + 0.225486i \(0.0723970\pi\)
−0.730979 + 0.682400i \(0.760936\pi\)
\(164\) 2.23205 + 3.86603i 0.174294 + 0.301886i
\(165\) 0 0
\(166\) 4.90192 + 2.83013i 0.380463 + 0.219660i
\(167\) −13.3843 + 13.3843i −1.03571 + 1.03571i −0.0363667 + 0.999339i \(0.511578\pi\)
−0.999339 + 0.0363667i \(0.988422\pi\)
\(168\) −2.63896 0.189469i −0.203600 0.0146178i
\(169\) 16.8564i 1.29665i
\(170\) 0 0
\(171\) −5.36603 + 3.09808i −0.410350 + 0.236916i
\(172\) −2.63896 + 9.84873i −0.201219 + 0.750958i
\(173\) 0.517638 0.138701i 0.0393553 0.0105452i −0.239088 0.970998i \(-0.576848\pi\)
0.278443 + 0.960453i \(0.410182\pi\)
\(174\) 2.19615 0.166490
\(175\) 0 0
\(176\) −2.73205 −0.205936
\(177\) −7.20977 + 1.93185i −0.541919 + 0.145207i
\(178\) 0.120118 0.448288i 0.00900325 0.0336006i
\(179\) 6.80385 3.92820i 0.508543 0.293608i −0.223691 0.974660i \(-0.571811\pi\)
0.732235 + 0.681052i \(0.238477\pi\)
\(180\) 0 0
\(181\) 10.1962i 0.757874i −0.925422 0.378937i \(-0.876290\pi\)
0.925422 0.378937i \(-0.123710\pi\)
\(182\) 13.0053 6.31319i 0.964019 0.467965i
\(183\) −1.27551 + 1.27551i −0.0942886 + 0.0942886i
\(184\) 0.232051 + 0.133975i 0.0171070 + 0.00987674i
\(185\) 0 0
\(186\) −2.96410 5.13397i −0.217338 0.376441i
\(187\) 4.05317 + 15.1266i 0.296397 + 1.10617i
\(188\) −7.77817 7.77817i −0.567282 0.567282i
\(189\) 0.500000 + 2.59808i 0.0363696 + 0.188982i
\(190\) 0 0
\(191\) 1.42820 2.47372i 0.103341 0.178992i −0.809718 0.586819i \(-0.800380\pi\)
0.913059 + 0.407827i \(0.133713\pi\)
\(192\) −0.965926 0.258819i −0.0697097 0.0186787i
\(193\) 19.5773 + 5.24573i 1.40921 + 0.377596i 0.881642 0.471919i \(-0.156438\pi\)
0.527565 + 0.849514i \(0.323105\pi\)
\(194\) 3.50000 6.06218i 0.251285 0.435239i
\(195\) 0 0
\(196\) −5.50000 4.33013i −0.392857 0.309295i
\(197\) 1.31268 + 1.31268i 0.0935244 + 0.0935244i 0.752321 0.658797i \(-0.228934\pi\)
−0.658797 + 0.752321i \(0.728934\pi\)
\(198\) 0.707107 + 2.63896i 0.0502519 + 0.187543i
\(199\) −9.76795 16.9186i −0.692432 1.19933i −0.971039 0.238922i \(-0.923206\pi\)
0.278607 0.960405i \(-0.410127\pi\)
\(200\) 0 0
\(201\) 3.46410 + 2.00000i 0.244339 + 0.141069i
\(202\) −7.20977 + 7.20977i −0.507278 + 0.507278i
\(203\) 4.81105 + 3.25813i 0.337669 + 0.228676i
\(204\) 5.73205i 0.401324i
\(205\) 0 0
\(206\) −9.23205 + 5.33013i −0.643227 + 0.371368i
\(207\) 0.0693504 0.258819i 0.00482018 0.0179892i
\(208\) 5.27792 1.41421i 0.365958 0.0980581i
\(209\) −16.9282 −1.17095
\(210\) 0 0
\(211\) −2.33975 −0.161075 −0.0805374 0.996752i \(-0.525664\pi\)
−0.0805374 + 0.996752i \(0.525664\pi\)
\(212\) 8.43451 2.26002i 0.579285 0.155219i
\(213\) 3.84512 14.3502i 0.263463 0.983259i
\(214\) −8.66025 + 5.00000i −0.592003 + 0.341793i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 1.12321 15.6443i 0.0762484 1.06200i
\(218\) 2.58819 2.58819i 0.175294 0.175294i
\(219\) 6.92820 + 4.00000i 0.468165 + 0.270295i
\(220\) 0 0
\(221\) −15.6603 27.1244i −1.05342 1.82458i
\(222\) 0.328169 + 1.22474i 0.0220253 + 0.0821995i
\(223\) 11.1242 + 11.1242i 0.744934 + 0.744934i 0.973523 0.228589i \(-0.0734111\pi\)
−0.228589 + 0.973523i \(0.573411\pi\)
\(224\) −1.73205 2.00000i −0.115728 0.133631i
\(225\) 0 0
\(226\) −1.50000 + 2.59808i −0.0997785 + 0.172821i
\(227\) 28.3214 + 7.58871i 1.87976 + 0.503680i 0.999578 + 0.0290430i \(0.00924596\pi\)
0.880182 + 0.474637i \(0.157421\pi\)
\(228\) −5.98502 1.60368i −0.396368 0.106206i
\(229\) −11.0981 + 19.2224i −0.733382 + 1.27025i 0.222048 + 0.975036i \(0.428726\pi\)
−0.955430 + 0.295218i \(0.904608\pi\)
\(230\) 0 0
\(231\) −2.36603 + 6.83013i −0.155673 + 0.449389i
\(232\) 1.55291 + 1.55291i 0.101954 + 0.101954i
\(233\) 1.31268 + 4.89898i 0.0859964 + 0.320943i 0.995501 0.0947510i \(-0.0302055\pi\)
−0.909505 + 0.415694i \(0.863539\pi\)
\(234\) −2.73205 4.73205i −0.178600 0.309344i
\(235\) 0 0
\(236\) −6.46410 3.73205i −0.420777 0.242936i
\(237\) 11.4016 11.4016i 0.740616 0.740616i
\(238\) −8.50386 + 12.5570i −0.551224 + 0.813952i
\(239\) 22.8564i 1.47846i 0.673454 + 0.739229i \(0.264810\pi\)
−0.673454 + 0.739229i \(0.735190\pi\)
\(240\) 0 0
\(241\) 0.803848 0.464102i 0.0517804 0.0298954i −0.473886 0.880586i \(-0.657149\pi\)
0.525667 + 0.850691i \(0.323816\pi\)
\(242\) 0.915158 3.41542i 0.0588286 0.219551i
\(243\) 0.965926 0.258819i 0.0619642 0.0166032i
\(244\) −1.80385 −0.115480
\(245\) 0 0
\(246\) 4.46410 0.284621
\(247\) 32.7028 8.76268i 2.08083 0.557556i
\(248\) 1.53433 5.72620i 0.0974302 0.363614i
\(249\) 4.90192 2.83013i 0.310647 0.179352i
\(250\) 0 0
\(251\) 9.85641i 0.622131i 0.950388 + 0.311065i \(0.100686\pi\)
−0.950388 + 0.311065i \(0.899314\pi\)
\(252\) −1.48356 + 2.19067i −0.0934557 + 0.137999i
\(253\) 0.517638 0.517638i 0.0325436 0.0325436i
\(254\) 10.2679 + 5.92820i 0.644268 + 0.371969i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.17449 23.0435i −0.385154 1.43742i −0.837924 0.545788i \(-0.816231\pi\)
0.452769 0.891628i \(-0.350436\pi\)
\(258\) 7.20977 + 7.20977i 0.448861 + 0.448861i
\(259\) −1.09808 + 3.16987i −0.0682311 + 0.196966i
\(260\) 0 0
\(261\) 1.09808 1.90192i 0.0679692 0.117726i
\(262\) −3.53553 0.947343i −0.218426 0.0585271i
\(263\) −25.6131 6.86302i −1.57937 0.423192i −0.640641 0.767840i \(-0.721331\pi\)
−0.938732 + 0.344649i \(0.887998\pi\)
\(264\) −1.36603 + 2.36603i −0.0840731 + 0.145619i
\(265\) 0 0
\(266\) −10.7321 12.3923i −0.658024 0.759821i
\(267\) −0.328169 0.328169i −0.0200836 0.0200836i
\(268\) 1.03528 + 3.86370i 0.0632396 + 0.236013i
\(269\) −4.16987 7.22243i −0.254242 0.440359i 0.710448 0.703750i \(-0.248493\pi\)
−0.964689 + 0.263391i \(0.915159\pi\)
\(270\) 0 0
\(271\) 3.86603 + 2.23205i 0.234844 + 0.135587i 0.612805 0.790234i \(-0.290041\pi\)
−0.377961 + 0.925822i \(0.623375\pi\)
\(272\) −4.05317 + 4.05317i −0.245760 + 0.245760i
\(273\) 1.03528 14.4195i 0.0626578 0.872710i
\(274\) 21.9282i 1.32473i
\(275\) 0 0
\(276\) 0.232051 0.133975i 0.0139678 0.00806432i
\(277\) −3.77577 + 14.0914i −0.226864 + 0.846668i 0.754785 + 0.655972i \(0.227741\pi\)
−0.981649 + 0.190696i \(0.938926\pi\)
\(278\) −0.896575 + 0.240237i −0.0537730 + 0.0144084i
\(279\) −5.92820 −0.354912
\(280\) 0 0
\(281\) −31.9808 −1.90781 −0.953906 0.300105i \(-0.902978\pi\)
−0.953906 + 0.300105i \(0.902978\pi\)
\(282\) −10.6252 + 2.84701i −0.632721 + 0.169537i
\(283\) 4.43211 16.5409i 0.263462 0.983252i −0.699724 0.714414i \(-0.746694\pi\)
0.963185 0.268838i \(-0.0866398\pi\)
\(284\) 12.8660 7.42820i 0.763458 0.440783i
\(285\) 0 0
\(286\) 14.9282i 0.882723i
\(287\) 9.77938 + 6.62278i 0.577258 + 0.390930i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 13.7321 + 7.92820i 0.807768 + 0.466365i
\(290\) 0 0
\(291\) −3.50000 6.06218i −0.205174 0.355371i
\(292\) 2.07055 + 7.72741i 0.121170 + 0.452212i
\(293\) 11.8313 + 11.8313i 0.691195 + 0.691195i 0.962495 0.271300i \(-0.0874536\pi\)
−0.271300 + 0.962495i \(0.587454\pi\)
\(294\) −6.50000 + 2.59808i −0.379088 + 0.151523i
\(295\) 0 0
\(296\) −0.633975 + 1.09808i −0.0368490 + 0.0638244i
\(297\) 2.63896 + 0.707107i 0.153128 + 0.0410305i
\(298\) 17.3867 + 4.65874i 1.00718 + 0.269874i
\(299\) −0.732051 + 1.26795i −0.0423356 + 0.0733274i
\(300\) 0 0
\(301\) 5.09808 + 26.4904i 0.293848 + 1.52688i
\(302\) 2.07055 + 2.07055i 0.119147 + 0.119147i
\(303\) 2.63896 + 9.84873i 0.151604 + 0.565795i
\(304\) −3.09808 5.36603i −0.177687 0.307763i
\(305\) 0 0
\(306\) 4.96410 + 2.86603i 0.283779 + 0.163840i
\(307\) 3.58630 3.58630i 0.204681 0.204681i −0.597321 0.802002i \(-0.703768\pi\)
0.802002 + 0.597321i \(0.203768\pi\)
\(308\) −6.50266 + 3.15660i −0.370524 + 0.179864i
\(309\) 10.6603i 0.606441i
\(310\) 0 0
\(311\) 8.89230 5.13397i 0.504236 0.291121i −0.226225 0.974075i \(-0.572638\pi\)
0.730461 + 0.682954i \(0.239305\pi\)
\(312\) 1.41421 5.27792i 0.0800641 0.298803i
\(313\) −11.1428 + 2.98571i −0.629830 + 0.168762i −0.559592 0.828768i \(-0.689042\pi\)
−0.0702372 + 0.997530i \(0.522376\pi\)
\(314\) 17.2679 0.974487
\(315\) 0 0
\(316\) 16.1244 0.907066
\(317\) −21.4398 + 5.74479i −1.20418 + 0.322659i −0.804476 0.593985i \(-0.797554\pi\)
−0.399705 + 0.916644i \(0.630887\pi\)
\(318\) 2.26002 8.43451i 0.126736 0.472984i
\(319\) 5.19615 3.00000i 0.290929 0.167968i
\(320\) 0 0
\(321\) 10.0000i 0.558146i
\(322\) 0.707107 + 0.0507680i 0.0394055 + 0.00282919i
\(323\) −25.1141 + 25.1141i −1.39738 + 1.39738i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) 6.00000 + 10.3923i 0.332309 + 0.575577i
\(327\) −0.947343 3.53553i −0.0523882 0.195515i
\(328\) 3.15660 + 3.15660i 0.174294 + 0.174294i
\(329\) −27.5000 9.52628i −1.51612 0.525201i
\(330\) 0 0
\(331\) −7.92820 + 13.7321i −0.435773 + 0.754782i −0.997358 0.0726373i \(-0.976858\pi\)
0.561585 + 0.827419i \(0.310192\pi\)
\(332\) 5.46739 + 1.46498i 0.300062 + 0.0804013i
\(333\) 1.22474 + 0.328169i 0.0671156 + 0.0179836i
\(334\) −9.46410 + 16.3923i −0.517853 + 0.896947i
\(335\) 0 0
\(336\) −2.59808 + 0.500000i −0.141737 + 0.0272772i
\(337\) −20.6448 20.6448i −1.12459 1.12459i −0.991042 0.133552i \(-0.957362\pi\)
−0.133552 0.991042i \(-0.542638\pi\)
\(338\) 4.36276 + 16.2820i 0.237303 + 0.885626i
\(339\) 1.50000 + 2.59808i 0.0814688 + 0.141108i
\(340\) 0 0
\(341\) −14.0263 8.09808i −0.759566 0.438535i
\(342\) −4.38134 + 4.38134i −0.236916 + 0.236916i
\(343\) −18.0938 3.95164i −0.976972 0.213368i
\(344\) 10.1962i 0.549740i
\(345\) 0 0
\(346\) 0.464102 0.267949i 0.0249503 0.0144050i
\(347\) 0.669942 2.50026i 0.0359644 0.134221i −0.945609 0.325304i \(-0.894533\pi\)
0.981574 + 0.191083i \(0.0612000\pi\)
\(348\) 2.12132 0.568406i 0.113715 0.0304698i
\(349\) 10.7321 0.574474 0.287237 0.957860i \(-0.407263\pi\)
0.287237 + 0.957860i \(0.407263\pi\)
\(350\) 0 0
\(351\) −5.46410 −0.291652
\(352\) −2.63896 + 0.707107i −0.140657 + 0.0376889i
\(353\) 7.14042 26.6484i 0.380046 1.41835i −0.465784 0.884899i \(-0.654228\pi\)
0.845830 0.533453i \(-0.179106\pi\)
\(354\) −6.46410 + 3.73205i −0.343563 + 0.198356i
\(355\) 0 0
\(356\) 0.464102i 0.0245973i
\(357\) 6.62278 + 13.6431i 0.350515 + 0.722068i
\(358\) 5.55532 5.55532i 0.293608 0.293608i
\(359\) −18.0000 10.3923i −0.950004 0.548485i −0.0569216 0.998379i \(-0.518129\pi\)
−0.893082 + 0.449894i \(0.851462\pi\)
\(360\) 0 0
\(361\) −9.69615 16.7942i −0.510324 0.883907i
\(362\) −2.63896 9.84873i −0.138701 0.517638i
\(363\) −2.50026 2.50026i −0.131229 0.131229i
\(364\) 10.9282 9.46410i 0.572793 0.496054i
\(365\) 0 0
\(366\) −0.901924 + 1.56218i −0.0471443 + 0.0816563i
\(367\) 3.20736 + 0.859411i 0.167423 + 0.0448609i 0.341557 0.939861i \(-0.389046\pi\)
−0.174134 + 0.984722i \(0.555712\pi\)
\(368\) 0.258819 + 0.0693504i 0.0134919 + 0.00361514i
\(369\) 2.23205 3.86603i 0.116196 0.201257i
\(370\) 0 0
\(371\) 17.4641 15.1244i 0.906691 0.785217i
\(372\) −4.19187 4.19187i −0.217338 0.217338i
\(373\) −8.76268 32.7028i −0.453715 1.69329i −0.691840 0.722051i \(-0.743200\pi\)
0.238125 0.971234i \(-0.423467\pi\)
\(374\) 7.83013 + 13.5622i 0.404886 + 0.701284i
\(375\) 0 0
\(376\) −9.52628 5.50000i −0.491280 0.283641i
\(377\) −8.48528 + 8.48528i −0.437014 + 0.437014i
\(378\) 1.15539 + 2.38014i 0.0594271 + 0.122421i
\(379\) 28.0526i 1.44096i −0.693474 0.720482i \(-0.743921\pi\)
0.693474 0.720482i \(-0.256079\pi\)
\(380\) 0 0
\(381\) 10.2679 5.92820i 0.526043 0.303711i
\(382\) 0.739292 2.75908i 0.0378255 0.141167i
\(383\) 18.8702 5.05626i 0.964224 0.258363i 0.257836 0.966189i \(-0.416990\pi\)
0.706387 + 0.707826i \(0.250324\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 20.2679 1.03161
\(387\) 9.84873 2.63896i 0.500639 0.134146i
\(388\) 1.81173 6.76148i 0.0919768 0.343262i
\(389\) −8.95448 + 5.16987i −0.454010 + 0.262123i −0.709522 0.704683i \(-0.751089\pi\)
0.255512 + 0.966806i \(0.417756\pi\)
\(390\) 0 0
\(391\) 1.53590i 0.0776737i
\(392\) −6.43331 2.75908i −0.324931 0.139354i
\(393\) −2.58819 + 2.58819i −0.130557 + 0.130557i
\(394\) 1.60770 + 0.928203i 0.0809945 + 0.0467622i
\(395\) 0 0
\(396\) 1.36603 + 2.36603i 0.0686454 + 0.118897i
\(397\) −3.24453 12.1087i −0.162838 0.607721i −0.998306 0.0581812i \(-0.981470\pi\)
0.835468 0.549539i \(-0.185197\pi\)
\(398\) −13.8140 13.8140i −0.692432 0.692432i
\(399\) −16.0981 + 3.09808i −0.805912 + 0.155098i
\(400\) 0 0
\(401\) 3.53590 6.12436i 0.176574 0.305836i −0.764131 0.645062i \(-0.776832\pi\)
0.940705 + 0.339226i \(0.110165\pi\)
\(402\) 3.86370 + 1.03528i 0.192704 + 0.0516349i
\(403\) 31.2886 + 8.38375i 1.55859 + 0.417624i
\(404\) −5.09808 + 8.83013i −0.253639 + 0.439315i
\(405\) 0 0
\(406\) 5.49038 + 1.90192i 0.272483 + 0.0943909i
\(407\) 2.44949 + 2.44949i 0.121417 + 0.121417i
\(408\) 1.48356 + 5.53674i 0.0734474 + 0.274109i
\(409\) −11.4019 19.7487i −0.563789 0.976511i −0.997161 0.0752960i \(-0.976010\pi\)
0.433372 0.901215i \(-0.357323\pi\)
\(410\) 0 0
\(411\) 18.9904 + 10.9641i 0.936726 + 0.540819i
\(412\) −7.53794 + 7.53794i −0.371368 + 0.371368i
\(413\) −19.6975 1.41421i −0.969248 0.0695889i
\(414\) 0.267949i 0.0131690i
\(415\) 0 0
\(416\) 4.73205 2.73205i 0.232008 0.133950i
\(417\) −0.240237 + 0.896575i −0.0117644 + 0.0439055i
\(418\) −16.3514 + 4.38134i −0.799773 + 0.214298i
\(419\) 20.5885 1.00581 0.502906 0.864341i \(-0.332264\pi\)
0.502906 + 0.864341i \(0.332264\pi\)
\(420\) 0 0
\(421\) −9.46410 −0.461252 −0.230626 0.973042i \(-0.574077\pi\)
−0.230626 + 0.973042i \(0.574077\pi\)
\(422\) −2.26002 + 0.605571i −0.110016 + 0.0294787i
\(423\) −2.84701 + 10.6252i −0.138426 + 0.516614i
\(424\) 7.56218 4.36603i 0.367252 0.212033i
\(425\) 0 0
\(426\) 14.8564i 0.719795i
\(427\) −4.29341 + 2.08416i −0.207773 + 0.100859i
\(428\) −7.07107 + 7.07107i −0.341793 + 0.341793i
\(429\) −12.9282 7.46410i −0.624180 0.360370i
\(430\) 0 0
\(431\) 3.23205 + 5.59808i 0.155682 + 0.269650i 0.933307 0.359079i \(-0.116909\pi\)
−0.777625 + 0.628729i \(0.783576\pi\)
\(432\) 0.258819 + 0.965926i 0.0124524 + 0.0464731i
\(433\) −4.46927 4.46927i −0.214780 0.214780i 0.591515 0.806294i \(-0.298530\pi\)
−0.806294 + 0.591515i \(0.798530\pi\)
\(434\) −2.96410 15.4019i −0.142281 0.739316i
\(435\) 0 0
\(436\) 1.83013 3.16987i 0.0876472 0.151809i
\(437\) 1.60368 + 0.429705i 0.0767145 + 0.0205556i
\(438\) 7.72741 + 2.07055i 0.369230 + 0.0989348i
\(439\) −9.30385 + 16.1147i −0.444048 + 0.769114i −0.997985 0.0634442i \(-0.979792\pi\)
0.553937 + 0.832559i \(0.313125\pi\)
\(440\) 0 0
\(441\) −1.00000 + 6.92820i −0.0476190 + 0.329914i
\(442\) −22.1469 22.1469i −1.05342 1.05342i
\(443\) −6.08656 22.7153i −0.289181 1.07924i −0.945730 0.324955i \(-0.894651\pi\)
0.656548 0.754284i \(-0.272016\pi\)
\(444\) 0.633975 + 1.09808i 0.0300871 + 0.0521124i
\(445\) 0 0
\(446\) 13.6244 + 7.86603i 0.645132 + 0.372467i
\(447\) 12.7279 12.7279i 0.602010 0.602010i
\(448\) −2.19067 1.48356i −0.103499 0.0700918i
\(449\) 26.2679i 1.23966i −0.784736 0.619831i \(-0.787201\pi\)
0.784736 0.619831i \(-0.212799\pi\)
\(450\) 0 0
\(451\) 10.5622 6.09808i 0.497354 0.287147i
\(452\) −0.776457 + 2.89778i −0.0365215 + 0.136300i
\(453\) 2.82843 0.757875i 0.132891 0.0356081i
\(454\) 29.3205 1.37608
\(455\) 0 0
\(456\) −6.19615 −0.290161
\(457\) 5.93426 1.59008i 0.277593 0.0743808i −0.117337 0.993092i \(-0.537436\pi\)
0.394930 + 0.918711i \(0.370769\pi\)
\(458\) −5.74479 + 21.4398i −0.268436 + 1.00182i
\(459\) 4.96410 2.86603i 0.231704 0.133775i
\(460\) 0 0
\(461\) 15.3205i 0.713547i 0.934191 + 0.356774i \(0.116123\pi\)
−0.934191 + 0.356774i \(0.883877\pi\)
\(462\) −0.517638 + 7.20977i −0.0240827 + 0.335429i
\(463\) −25.0261 + 25.0261i −1.16306 + 1.16306i −0.179262 + 0.983801i \(0.557371\pi\)
−0.983801 + 0.179262i \(0.942629\pi\)
\(464\) 1.90192 + 1.09808i 0.0882946 + 0.0509769i
\(465\) 0 0
\(466\) 2.53590 + 4.39230i 0.117473 + 0.203470i
\(467\) 7.77817 + 29.0285i 0.359931 + 1.34328i 0.874164 + 0.485630i \(0.161410\pi\)
−0.514233 + 0.857650i \(0.671923\pi\)
\(468\) −3.86370 3.86370i −0.178600 0.178600i
\(469\) 6.92820 + 8.00000i 0.319915 + 0.369406i
\(470\) 0 0
\(471\) 8.63397 14.9545i 0.397833 0.689066i
\(472\) −7.20977 1.93185i −0.331856 0.0889207i
\(473\) 26.9072 + 7.20977i 1.23720 + 0.331506i
\(474\) 8.06218 13.9641i 0.370308 0.641392i
\(475\) 0 0
\(476\) −4.96410 + 14.3301i −0.227529 + 0.656820i
\(477\) −6.17449 6.17449i −0.282711 0.282711i
\(478\) 5.91567 + 22.0776i 0.270577 + 1.00981i
\(479\) −15.9904 27.6962i −0.730619 1.26547i −0.956619 0.291342i \(-0.905898\pi\)
0.226000 0.974127i \(-0.427435\pi\)
\(480\) 0 0
\(481\) −6.00000 3.46410i −0.273576 0.157949i
\(482\) 0.656339 0.656339i 0.0298954 0.0298954i
\(483\) 0.397520 0.586988i 0.0180878 0.0267089i
\(484\) 3.53590i 0.160723i
\(485\) 0 0
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) −5.29650 + 19.7668i −0.240007 + 0.895719i 0.735820 + 0.677177i \(0.236797\pi\)
−0.975827 + 0.218542i \(0.929870\pi\)
\(488\) −1.74238 + 0.466870i −0.0788740 + 0.0211342i
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) 15.6603 0.706737 0.353369 0.935484i \(-0.385036\pi\)
0.353369 + 0.935484i \(0.385036\pi\)
\(492\) 4.31199 1.15539i 0.194400 0.0520892i
\(493\) 3.25813 12.1595i 0.146739 0.547637i
\(494\) 29.3205 16.9282i 1.31919 0.761636i
\(495\) 0 0
\(496\) 5.92820i 0.266184i
\(497\) 22.0404 32.5455i 0.988648 1.45986i
\(498\) 4.00240 4.00240i 0.179352 0.179352i
\(499\) 26.8301 + 15.4904i 1.20108 + 0.693445i 0.960796 0.277257i \(-0.0894255\pi\)
0.240286 + 0.970702i \(0.422759\pi\)
\(500\) 0 0
\(501\) 9.46410 + 16.3923i 0.422825 + 0.732354i
\(502\) 2.55103 + 9.52056i 0.113858 + 0.424923i
\(503\) −13.5601 13.5601i −0.604616 0.604616i 0.336918 0.941534i \(-0.390616\pi\)
−0.941534 + 0.336918i \(0.890616\pi\)
\(504\) −0.866025 + 2.50000i −0.0385758 + 0.111359i
\(505\) 0 0
\(506\) 0.366025 0.633975i 0.0162718 0.0281836i
\(507\) 16.2820 + 4.36276i 0.723111 + 0.193757i
\(508\) 11.4524 + 3.06866i 0.508118 + 0.136150i
\(509\) 17.0263 29.4904i 0.754677 1.30714i −0.190858 0.981618i \(-0.561127\pi\)
0.945535 0.325521i \(-0.105540\pi\)
\(510\) 0 0
\(511\) 13.8564 + 16.0000i 0.612971 + 0.707798i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 1.60368 + 5.98502i 0.0708043 + 0.264245i
\(514\) −11.9282 20.6603i −0.526130 0.911285i
\(515\) 0 0
\(516\) 8.83013 + 5.09808i 0.388725 + 0.224430i
\(517\) −21.2504 + 21.2504i −0.934590 + 0.934590i
\(518\) −0.240237 + 3.34607i −0.0105554 + 0.147018i
\(519\) 0.535898i 0.0235233i
\(520\) 0 0
\(521\) −33.3109 + 19.2321i −1.45938 + 0.842571i −0.998981 0.0451422i \(-0.985626\pi\)
−0.460396 + 0.887714i \(0.652293\pi\)
\(522\) 0.568406 2.12132i 0.0248785 0.0928477i
\(523\) 3.15660 0.845807i 0.138028 0.0369846i −0.189143 0.981949i \(-0.560571\pi\)
0.327172 + 0.944965i \(0.393904\pi\)
\(524\) −3.66025 −0.159899
\(525\) 0 0
\(526\) −26.5167 −1.15618
\(527\) −32.8229 + 8.79487i −1.42979 + 0.383110i
\(528\) −0.707107 + 2.63896i −0.0307729 + 0.114846i
\(529\) 19.8564 11.4641i 0.863322 0.498439i
\(530\) 0 0
\(531\) 7.46410i 0.323914i
\(532\) −13.5737 9.19239i −0.588496 0.398541i
\(533\) −17.2480 + 17.2480i −0.747092 + 0.747092i
\(534\) −0.401924 0.232051i −0.0173929 0.0100418i
\(535\) 0 0
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) −2.03339 7.58871i −0.0877472 0.327477i
\(538\) −5.89709 5.89709i −0.254242 0.254242i
\(539\) −11.8301 + 15.0263i −0.509560 + 0.647228i
\(540\) 0 0
\(541\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(542\) 4.31199 + 1.15539i 0.185216 + 0.0496284i
\(543\) −9.84873 2.63896i −0.422649 0.113249i
\(544\) −2.86603 + 4.96410i −0.122880 + 0.212834i
\(545\) 0 0
\(546\) −2.73205 14.1962i −0.116921 0.607539i
\(547\) −15.4920 15.4920i −0.662389 0.662389i 0.293554 0.955943i \(-0.405162\pi\)
−0.955943 + 0.293554i \(0.905162\pi\)
\(548\) 5.67544 + 21.1810i 0.242443 + 0.904808i
\(549\) 0.901924 + 1.56218i 0.0384932 + 0.0666721i
\(550\) 0 0
\(551\) 11.7846 + 6.80385i 0.502041 + 0.289854i
\(552\) 0.189469 0.189469i 0.00806432 0.00806432i
\(553\) 38.3782 18.6300i 1.63201 0.792228i
\(554\) 14.5885i 0.619804i
\(555\) 0 0
\(556\) −0.803848 + 0.464102i −0.0340907 + 0.0196823i
\(557\) 9.38186 35.0136i 0.397522 1.48357i −0.419920 0.907561i \(-0.637942\pi\)
0.817442 0.576011i \(-0.195392\pi\)
\(558\) −5.72620 + 1.53433i −0.242410 + 0.0649534i
\(559\) −55.7128 −2.35640
\(560\) 0 0
\(561\) 15.6603 0.661176
\(562\) −30.8910 + 8.27723i −1.30306 + 0.349154i
\(563\) 6.70573 25.0261i 0.282613 1.05473i −0.667953 0.744203i \(-0.732829\pi\)
0.950566 0.310523i \(-0.100504\pi\)
\(564\) −9.52628 + 5.50000i −0.401129 + 0.231592i
\(565\) 0 0
\(566\) 17.1244i 0.719790i
\(567\) 2.63896 + 0.189469i 0.110826 + 0.00795694i
\(568\) 10.5051 10.5051i 0.440783 0.440783i
\(569\) −32.5526 18.7942i −1.36467 0.787895i −0.374432 0.927254i \(-0.622162\pi\)
−0.990242 + 0.139359i \(0.955496\pi\)
\(570\) 0 0
\(571\) 14.1962 + 24.5885i 0.594090 + 1.02899i 0.993675 + 0.112298i \(0.0358212\pi\)
−0.399584 + 0.916697i \(0.630845\pi\)
\(572\) −3.86370 14.4195i −0.161550 0.602911i
\(573\) −2.01978 2.01978i −0.0843777 0.0843777i
\(574\) 11.1603 + 3.86603i 0.465820 + 0.161365i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −44.6728 11.9700i −1.85975 0.498320i −0.859829 0.510582i \(-0.829430\pi\)
−0.999925 + 0.0122622i \(0.996097\pi\)
\(578\) 15.3161 + 4.10394i 0.637066 + 0.170701i
\(579\) 10.1340 17.5526i 0.421154 0.729459i
\(580\) 0 0
\(581\) 14.7058 2.83013i 0.610098 0.117413i
\(582\) −4.94975 4.94975i −0.205174 0.205174i
\(583\) −6.17449 23.0435i −0.255721 0.954365i
\(584\) 4.00000 + 6.92820i 0.165521 + 0.286691i
\(585\) 0 0
\(586\) 14.4904 + 8.36603i 0.598592 + 0.345597i
\(587\) −1.69161 + 1.69161i −0.0698204 + 0.0698204i −0.741155 0.671334i \(-0.765722\pi\)
0.671334 + 0.741155i \(0.265722\pi\)
\(588\) −5.60609 + 4.19187i −0.231191 + 0.172870i
\(589\) 36.7321i 1.51352i
\(590\) 0 0
\(591\) 1.60770 0.928203i 0.0661317 0.0381812i
\(592\) −0.328169 + 1.22474i −0.0134877 + 0.0503367i
\(593\) −26.2695 + 7.03888i −1.07876 + 0.289052i −0.754087 0.656775i \(-0.771920\pi\)
−0.324671 + 0.945827i \(0.605254\pi\)
\(594\) 2.73205 0.112097
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) −18.8702 + 5.05626i −0.772307 + 0.206939i
\(598\) −0.378937 + 1.41421i −0.0154959 + 0.0578315i
\(599\) 26.0429 15.0359i 1.06409 0.614350i 0.137526 0.990498i \(-0.456085\pi\)
0.926560 + 0.376148i \(0.122752\pi\)
\(600\) 0 0
\(601\) 28.2487i 1.15229i 0.817348 + 0.576144i \(0.195443\pi\)
−0.817348 + 0.576144i \(0.804557\pi\)
\(602\) 11.7806 + 24.2683i 0.480141 + 0.989101i
\(603\) 2.82843 2.82843i 0.115182 0.115182i
\(604\) 2.53590 + 1.46410i 0.103184 + 0.0595734i
\(605\) 0 0
\(606\) 5.09808 + 8.83013i 0.207095 + 0.358699i
\(607\) 0.0321856 + 0.120118i 0.00130637 + 0.00487545i 0.966576 0.256380i \(-0.0825300\pi\)
−0.965270 + 0.261256i \(0.915863\pi\)
\(608\) −4.38134 4.38134i −0.177687 0.177687i
\(609\) 4.39230 3.80385i 0.177985 0.154140i
\(610\) 0 0
\(611\) 30.0526 52.0526i 1.21580 2.10582i
\(612\) 5.53674 + 1.48356i 0.223809 + 0.0599695i
\(613\) −25.6825 6.88160i −1.03731 0.277945i −0.300309 0.953842i \(-0.597090\pi\)
−0.736996 + 0.675897i \(0.763757\pi\)
\(614\) 2.53590 4.39230i 0.102341 0.177259i
\(615\) 0 0
\(616\) −5.46410 + 4.73205i −0.220155 + 0.190660i
\(617\) 21.4398 + 21.4398i 0.863135 + 0.863135i 0.991701 0.128566i \(-0.0410373\pi\)
−0.128566 + 0.991701i \(0.541037\pi\)
\(618\) 2.75908 + 10.2970i 0.110986 + 0.414207i
\(619\) −12.0981 20.9545i −0.486263 0.842232i 0.513613 0.858022i \(-0.328307\pi\)
−0.999875 + 0.0157904i \(0.994974\pi\)
\(620\) 0 0
\(621\) −0.232051 0.133975i −0.00931188 0.00537622i
\(622\) 7.26054 7.26054i 0.291121 0.291121i
\(623\) −0.536220 1.10463i −0.0214832 0.0442559i
\(624\) 5.46410i 0.218739i
\(625\) 0 0
\(626\) −9.99038 + 5.76795i −0.399296 + 0.230534i
\(627\) −4.38134 + 16.3514i −0.174974 + 0.653012i
\(628\) 16.6796 4.46927i 0.665587 0.178343i
\(629\) 7.26795 0.289792
\(630\) 0 0
\(631\) −47.5885 −1.89447 −0.947233 0.320545i \(-0.896134\pi\)
−0.947233 + 0.320545i \(0.896134\pi\)
\(632\) 15.5749 4.17329i 0.619538 0.166005i
\(633\) −0.605571 + 2.26002i −0.0240693 + 0.0898278i
\(634\) −19.2224 + 11.0981i −0.763420 + 0.440761i
\(635\) 0 0
\(636\) 8.73205i 0.346248i
\(637\) 15.0759 35.1523i 0.597328 1.39278i
\(638\) 4.24264 4.24264i 0.167968 0.167968i
\(639\) −12.8660 7.42820i −0.508972 0.293855i
\(640\) 0 0
\(641\) 8.33013 + 14.4282i 0.329020 + 0.569880i 0.982318 0.187222i \(-0.0599482\pi\)
−0.653297 + 0.757101i \(0.726615\pi\)
\(642\) 2.58819 + 9.65926i 0.102148 + 0.381221i
\(643\) −9.62209 9.62209i −0.379458 0.379458i 0.491448 0.870907i \(-0.336468\pi\)
−0.870907 + 0.491448i \(0.836468\pi\)
\(644\) 0.696152 0.133975i 0.0274322 0.00527934i
\(645\) 0 0
\(646\) −17.7583 + 30.7583i −0.698692 + 1.21017i
\(647\) −12.1087 3.24453i −0.476044 0.127556i 0.0128160 0.999918i \(-0.495920\pi\)
−0.488860 + 0.872362i \(0.662587\pi\)
\(648\) 0.965926 + 0.258819i 0.0379452 + 0.0101674i
\(649\) −10.1962 + 17.6603i −0.400234 + 0.693226i
\(650\) 0 0
\(651\) −14.8205 5.13397i −0.580862 0.201216i
\(652\) 8.48528 + 8.48528i 0.332309 + 0.332309i
\(653\) 12.0716 + 45.0518i 0.472398 + 1.76301i 0.631117 + 0.775688i \(0.282597\pi\)
−0.158719 + 0.987324i \(0.550736\pi\)
\(654\) −1.83013 3.16987i −0.0715636 0.123952i
\(655\) 0 0
\(656\) 3.86603 + 2.23205i 0.150943 + 0.0871469i
\(657\) 5.65685 5.65685i 0.220695 0.220695i
\(658\) −29.0285 2.08416i −1.13165 0.0812488i
\(659\) 3.80385i 0.148177i −0.997252 0.0740884i \(-0.976395\pi\)
0.997252 0.0740884i \(-0.0236047\pi\)
\(660\) 0 0
\(661\) 10.5167 6.07180i 0.409051 0.236166i −0.281331 0.959611i \(-0.590776\pi\)
0.690382 + 0.723445i \(0.257443\pi\)
\(662\) −4.10394 + 15.3161i −0.159504 + 0.595278i
\(663\) −30.2533 + 8.10634i −1.17494 + 0.314824i
\(664\) 5.66025 0.219660
\(665\) 0 0
\(666\) 1.26795 0.0491320
\(667\) −0.568406 + 0.152304i −0.0220088 + 0.00589723i
\(668\) −4.89898 + 18.2832i −0.189547 + 0.707400i
\(669\) 13.6244 7.86603i 0.526748 0.304118i
\(670\) 0 0
\(671\) 4.92820i 0.190251i
\(672\) −2.38014 + 1.15539i −0.0918159 + 0.0445703i
\(673\) 4.05317 4.05317i 0.156238 0.156238i −0.624659 0.780897i \(-0.714762\pi\)
0.780897 + 0.624659i \(0.214762\pi\)
\(674\) −25.2846 14.5981i −0.973927 0.562297i
\(675\) 0 0
\(676\) 8.42820 + 14.5981i 0.324162 + 0.561464i
\(677\) −9.53416 35.5820i −0.366428 1.36753i −0.865475 0.500952i \(-0.832983\pi\)
0.499048 0.866575i \(-0.333683\pi\)
\(678\) 2.12132 + 2.12132i 0.0814688 + 0.0814688i
\(679\) −3.50000 18.1865i −0.134318 0.697935i
\(680\) 0 0
\(681\) 14.6603 25.3923i 0.561782 0.973035i
\(682\) −15.6443 4.19187i −0.599051 0.160515i
\(683\) 36.7052 + 9.83512i 1.40448 + 0.376331i 0.879953 0.475060i \(-0.157574\pi\)
0.524532 + 0.851391i \(0.324240\pi\)
\(684\) −3.09808 + 5.36603i −0.118458 + 0.205175i
\(685\) 0 0
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 15.6950 + 15.6950i 0.598804 + 0.598804i
\(688\) 2.63896 + 9.84873i 0.100609 + 0.375479i
\(689\) 23.8564 + 41.3205i 0.908857 + 1.57419i
\(690\) 0 0
\(691\) −32.6147 18.8301i −1.24072 0.716332i −0.271482 0.962444i \(-0.587514\pi\)
−0.969241 + 0.246112i \(0.920847\pi\)
\(692\) 0.378937 0.378937i 0.0144050 0.0144050i
\(693\) 5.98502 + 4.05317i 0.227352 + 0.153967i
\(694\) 2.58846i 0.0982565i
\(695\) 0 0
\(696\) 1.90192 1.09808i 0.0720922 0.0416225i
\(697\) 6.62278 24.7166i 0.250856 0.936206i
\(698\) 10.3664 2.77766i 0.392373 0.105136i
\(699\) 5.07180 0.191833
\(700\) 0 0
\(701\) 14.5359 0.549013 0.274507 0.961585i \(-0.411485\pi\)
0.274507 + 0.961585i \(0.411485\pi\)
\(702\) −5.27792 + 1.41421i −0.199202 + 0.0533761i
\(703\) −2.03339 + 7.58871i −0.0766907 + 0.286213i
\(704\) −2.36603 + 1.36603i −0.0891729 + 0.0514840i
\(705\) 0 0
\(706\) 27.5885i 1.03831i
\(707\) −1.93185 + 26.9072i −0.0726548 + 1.01195i
\(708\) −5.27792 + 5.27792i −0.198356 + 0.198356i
\(709\) 20.0718 + 11.5885i 0.753812 + 0.435214i 0.827070 0.562099i \(-0.190006\pi\)
−0.0732575 + 0.997313i \(0.523340\pi\)
\(710\) 0 0
\(711\) −8.06218 13.9641i −0.302355 0.523695i
\(712\) −0.120118 0.448288i −0.00450162 0.0168003i
\(713\) 1.12321 + 1.12321i 0.0420645 + 0.0420645i
\(714\) 9.92820 + 11.4641i 0.371554 + 0.429033i
\(715\) 0 0
\(716\) 3.92820 6.80385i 0.146804 0.254272i
\(717\) 22.0776 + 5.91567i 0.824503 + 0.220925i
\(718\) −20.0764 5.37945i −0.749244 0.200759i
\(719\) −15.3301 + 26.5526i −0.571717 + 0.990243i 0.424673 + 0.905347i \(0.360389\pi\)
−0.996390 + 0.0848963i \(0.972944\pi\)
\(720\) 0 0
\(721\) −9.23205 + 26.6506i −0.343820 + 0.992522i
\(722\) −13.7124 13.7124i −0.510324 0.510324i
\(723\) −0.240237 0.896575i −0.00893450 0.0333440i
\(724\) −5.09808 8.83013i −0.189469 0.328169i
\(725\) 0 0
\(726\) −3.06218 1.76795i −0.113648 0.0656147i
\(727\) 17.0585 17.0585i 0.632665 0.632665i −0.316071 0.948736i \(-0.602364\pi\)
0.948736 + 0.316071i \(0.102364\pi\)
\(728\) 8.10634 11.9700i 0.300441 0.443639i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 50.6147 29.2224i 1.87205 1.08083i
\(732\) −0.466870 + 1.74238i −0.0172560 + 0.0644003i
\(733\) 33.9783 9.10446i 1.25502 0.336281i 0.430744 0.902474i \(-0.358251\pi\)
0.824273 + 0.566193i \(0.191584\pi\)
\(734\) 3.32051 0.122562
\(735\) 0 0
\(736\) 0.267949 0.00987674
\(737\) 10.5558 2.82843i 0.388829 0.104186i
\(738\) 1.15539 4.31199i 0.0425307 0.158727i
\(739\) 38.6147 22.2942i 1.42047 0.820106i 0.424128 0.905602i \(-0.360581\pi\)
0.996339 + 0.0854960i \(0.0272475\pi\)
\(740\) 0 0
\(741\) 33.8564i 1.24375i
\(742\) 12.9546 19.1290i 0.475577 0.702249i
\(743\) −4.60797 + 4.60797i −0.169050 + 0.169050i −0.786562 0.617512i \(-0.788141\pi\)
0.617512 + 0.786562i \(0.288141\pi\)
\(744\) −5.13397 2.96410i −0.188221 0.108669i
\(745\) 0 0
\(746\) −16.9282 29.3205i −0.619786 1.07350i
\(747\) −1.46498 5.46739i −0.0536009 0.200041i
\(748\) 11.0735 + 11.0735i 0.404886 + 0.404886i
\(749\) −8.66025 + 25.0000i −0.316439 + 0.913480i
\(750\) 0 0
\(751\) −0.928203 + 1.60770i −0.0338706 + 0.0586656i −0.882464 0.470380i \(-0.844117\pi\)
0.848593 + 0.529046i \(0.177450\pi\)
\(752\) −10.6252 2.84701i −0.387461 0.103820i
\(753\) 9.52056 + 2.55103i 0.346948 + 0.0929645i
\(754\) −6.00000 + 10.3923i −0.218507 + 0.378465i
\(755\) 0 0
\(756\) 1.73205 + 2.00000i 0.0629941 + 0.0727393i
\(757\) −29.1165 29.1165i −1.05826 1.05826i −0.998195 0.0600616i \(-0.980870\pi\)
−0.0600616 0.998195i \(-0.519130\pi\)
\(758\) −7.26054 27.0967i −0.263715 0.984196i
\(759\) −0.366025 0.633975i −0.0132859 0.0230118i
\(760\) 0 0
\(761\) 4.79423 + 2.76795i 0.173791 + 0.100338i 0.584372 0.811486i \(-0.301341\pi\)
−0.410581 + 0.911824i \(0.634674\pi\)
\(762\) 8.38375 8.38375i 0.303711 0.303711i
\(763\) 0.693504 9.65926i 0.0251065 0.349689i
\(764\) 2.85641i 0.103341i
\(765\) 0 0
\(766\) 16.9186 9.76795i 0.611293 0.352930i
\(767\) 10.5558 39.3949i 0.381149 1.42247i
\(768\) −0.965926 + 0.258819i −0.0348548 + 0.00933933i
\(769\) −22.9282 −0.826812 −0.413406 0.910547i \(-0.635661\pi\)
−0.413406 + 0.910547i \(0.635661\pi\)
\(770\) 0 0
\(771\) −23.8564 −0.859167
\(772\) 19.5773 5.24573i 0.704604 0.188798i
\(773\) 7.19617 26.8565i 0.258828 0.965960i −0.707093 0.707121i \(-0.749994\pi\)
0.965921 0.258839i \(-0.0833397\pi\)
\(774\) 8.83013 5.09808i 0.317392 0.183247i
\(775\) 0 0
\(776\) 7.00000i 0.251285i
\(777\) 2.77766 + 1.88108i 0.0996480 + 0.0674835i
\(778\) −7.31130 + 7.31130i −0.262123 + 0.262123i
\(779\) 23.9545 + 13.8301i 0.858258 + 0.495516i
\(780\) 0 0
\(781\) −20.2942 35.1506i −0.726185 1.25779i
\(782\) −0.397520 1.48356i −0.0142153