Properties

Label 525.2.j.b.218.6
Level 525
Weight 2
Character 525.218
Analytic conductor 4.192
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 218.6
Character \(\chi\) \(=\) 525.218
Dual form 525.2.j.b.407.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.260263 - 0.260263i) q^{2} +(-0.826909 + 1.52191i) q^{3} -1.86453i q^{4} +(0.611312 - 0.180884i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.00579 + 1.00579i) q^{8} +(-1.63244 - 2.51697i) q^{9} +O(q^{10})\) \(q+(-0.260263 - 0.260263i) q^{2} +(-0.826909 + 1.52191i) q^{3} -1.86453i q^{4} +(0.611312 - 0.180884i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.00579 + 1.00579i) q^{8} +(-1.63244 - 2.51697i) q^{9} +3.38750i q^{11} +(2.83765 + 1.54179i) q^{12} +(-1.59420 - 1.59420i) q^{13} +0.368068 q^{14} -3.20551 q^{16} +(-0.140684 - 0.140684i) q^{17} +(-0.230209 + 1.07994i) q^{18} +7.34691i q^{19} +(-0.491443 - 1.66087i) q^{21} +(0.881641 - 0.881641i) q^{22} +(-2.21444 + 2.21444i) q^{23} +(-0.699032 - 2.36243i) q^{24} +0.829822i q^{26} +(5.18049 - 0.403134i) q^{27} +(1.31842 + 1.31842i) q^{28} -9.49165 q^{29} +0.922582 q^{31} +(2.84586 + 2.84586i) q^{32} +(-5.15548 - 2.80115i) q^{33} +0.0732300i q^{34} +(-4.69295 + 3.04373i) q^{36} +(-5.91558 + 5.91558i) q^{37} +(1.91213 - 1.91213i) q^{38} +(3.74449 - 1.10797i) q^{39} -1.39256i q^{41} +(-0.304359 + 0.560167i) q^{42} +(-0.864526 - 0.864526i) q^{43} +6.31608 q^{44} +1.15267 q^{46} +(-0.651346 - 0.651346i) q^{47} +(2.65066 - 4.87851i) q^{48} -1.00000i q^{49} +(0.330443 - 0.0977764i) q^{51} +(-2.97242 + 2.97242i) q^{52} +(-6.54108 + 6.54108i) q^{53} +(-1.45321 - 1.24337i) q^{54} -1.42241i q^{56} +(-11.1814 - 6.07522i) q^{57} +(2.47033 + 2.47033i) q^{58} -6.25032 q^{59} +1.83261 q^{61} +(-0.240114 - 0.240114i) q^{62} +(2.93408 + 0.625454i) q^{63} +4.92967i q^{64} +(0.612745 + 2.07082i) q^{66} +(0.815500 - 0.815500i) q^{67} +(-0.262310 + 0.262310i) q^{68} +(-1.53904 - 5.20132i) q^{69} -9.77651i q^{71} +(4.17345 + 0.889650i) q^{72} +(4.80768 + 4.80768i) q^{73} +3.07921 q^{74} +13.6985 q^{76} +(-2.39532 - 2.39532i) q^{77} +(-1.26292 - 0.686187i) q^{78} +3.41711i q^{79} +(-3.67026 + 8.21761i) q^{81} +(-0.362432 + 0.362432i) q^{82} +(6.26911 - 6.26911i) q^{83} +(-3.09673 + 0.916307i) q^{84} +0.450009i q^{86} +(7.84873 - 14.4455i) q^{87} +(-3.40712 - 3.40712i) q^{88} +12.3767 q^{89} +2.25454 q^{91} +(4.12888 + 4.12888i) q^{92} +(-0.762891 + 1.40409i) q^{93} +0.339043i q^{94} +(-6.68443 + 1.97789i) q^{96} +(6.71326 - 6.71326i) q^{97} +(-0.260263 + 0.260263i) q^{98} +(8.52622 - 5.52990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{3} + O(q^{10}) \) \( 24q + 4q^{3} - 16q^{12} + 8q^{13} - 16q^{16} + 20q^{18} + 4q^{21} - 8q^{22} + 16q^{27} - 28q^{33} + 16q^{36} + 16q^{37} + 20q^{42} + 40q^{43} - 64q^{46} - 16q^{48} - 20q^{51} - 4q^{57} - 40q^{58} + 32q^{61} + 8q^{63} - 16q^{66} - 24q^{67} + 8q^{72} - 32q^{73} + 32q^{76} - 60q^{78} + 52q^{81} + 80q^{82} - 4q^{87} - 96q^{88} - 24q^{91} + 76q^{93} - 96q^{96} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.260263 0.260263i −0.184034 0.184034i 0.609077 0.793111i \(-0.291540\pi\)
−0.793111 + 0.609077i \(0.791540\pi\)
\(3\) −0.826909 + 1.52191i −0.477416 + 0.878677i
\(4\) 1.86453i 0.932263i
\(5\) 0 0
\(6\) 0.611312 0.180884i 0.249567 0.0738457i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −1.00579 + 1.00579i −0.355602 + 0.355602i
\(9\) −1.63244 2.51697i −0.544148 0.838989i
\(10\) 0 0
\(11\) 3.38750i 1.02137i 0.859768 + 0.510684i \(0.170608\pi\)
−0.859768 + 0.510684i \(0.829392\pi\)
\(12\) 2.83765 + 1.54179i 0.819158 + 0.445077i
\(13\) −1.59420 1.59420i −0.442151 0.442151i 0.450583 0.892734i \(-0.351216\pi\)
−0.892734 + 0.450583i \(0.851216\pi\)
\(14\) 0.368068 0.0983703
\(15\) 0 0
\(16\) −3.20551 −0.801377
\(17\) −0.140684 0.140684i −0.0341210 0.0341210i 0.689840 0.723961i \(-0.257681\pi\)
−0.723961 + 0.689840i \(0.757681\pi\)
\(18\) −0.230209 + 1.07994i −0.0542609 + 0.254544i
\(19\) 7.34691i 1.68550i 0.538308 + 0.842748i \(0.319064\pi\)
−0.538308 + 0.842748i \(0.680936\pi\)
\(20\) 0 0
\(21\) −0.491443 1.66087i −0.107242 0.362431i
\(22\) 0.881641 0.881641i 0.187966 0.187966i
\(23\) −2.21444 + 2.21444i −0.461742 + 0.461742i −0.899226 0.437484i \(-0.855870\pi\)
0.437484 + 0.899226i \(0.355870\pi\)
\(24\) −0.699032 2.36243i −0.142689 0.482229i
\(25\) 0 0
\(26\) 0.829822i 0.162741i
\(27\) 5.18049 0.403134i 0.996986 0.0775831i
\(28\) 1.31842 + 1.31842i 0.249158 + 0.249158i
\(29\) −9.49165 −1.76256 −0.881278 0.472598i \(-0.843316\pi\)
−0.881278 + 0.472598i \(0.843316\pi\)
\(30\) 0 0
\(31\) 0.922582 0.165701 0.0828503 0.996562i \(-0.473598\pi\)
0.0828503 + 0.996562i \(0.473598\pi\)
\(32\) 2.84586 + 2.84586i 0.503083 + 0.503083i
\(33\) −5.15548 2.80115i −0.897454 0.487618i
\(34\) 0.0732300i 0.0125588i
\(35\) 0 0
\(36\) −4.69295 + 3.04373i −0.782159 + 0.507289i
\(37\) −5.91558 + 5.91558i −0.972515 + 0.972515i −0.999632 0.0271173i \(-0.991367\pi\)
0.0271173 + 0.999632i \(0.491367\pi\)
\(38\) 1.91213 1.91213i 0.310188 0.310188i
\(39\) 3.74449 1.10797i 0.599598 0.177418i
\(40\) 0 0
\(41\) 1.39256i 0.217481i −0.994070 0.108741i \(-0.965318\pi\)
0.994070 0.108741i \(-0.0346818\pi\)
\(42\) −0.304359 + 0.560167i −0.0469636 + 0.0864357i
\(43\) −0.864526 0.864526i −0.131839 0.131839i 0.638108 0.769947i \(-0.279717\pi\)
−0.769947 + 0.638108i \(0.779717\pi\)
\(44\) 6.31608 0.952184
\(45\) 0 0
\(46\) 1.15267 0.169952
\(47\) −0.651346 0.651346i −0.0950085 0.0950085i 0.658005 0.753014i \(-0.271401\pi\)
−0.753014 + 0.658005i \(0.771401\pi\)
\(48\) 2.65066 4.87851i 0.382591 0.704152i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0.330443 0.0977764i 0.0462713 0.0136914i
\(52\) −2.97242 + 2.97242i −0.412201 + 0.412201i
\(53\) −6.54108 + 6.54108i −0.898486 + 0.898486i −0.995302 0.0968158i \(-0.969134\pi\)
0.0968158 + 0.995302i \(0.469134\pi\)
\(54\) −1.45321 1.24337i −0.197757 0.169201i
\(55\) 0 0
\(56\) 1.42241i 0.190077i
\(57\) −11.1814 6.07522i −1.48101 0.804683i
\(58\) 2.47033 + 2.47033i 0.324370 + 0.324370i
\(59\) −6.25032 −0.813722 −0.406861 0.913490i \(-0.633377\pi\)
−0.406861 + 0.913490i \(0.633377\pi\)
\(60\) 0 0
\(61\) 1.83261 0.234642 0.117321 0.993094i \(-0.462569\pi\)
0.117321 + 0.993094i \(0.462569\pi\)
\(62\) −0.240114 0.240114i −0.0304945 0.0304945i
\(63\) 2.93408 + 0.625454i 0.369659 + 0.0787998i
\(64\) 4.92967i 0.616209i
\(65\) 0 0
\(66\) 0.612745 + 2.07082i 0.0754237 + 0.254900i
\(67\) 0.815500 0.815500i 0.0996292 0.0996292i −0.655535 0.755165i \(-0.727557\pi\)
0.755165 + 0.655535i \(0.227557\pi\)
\(68\) −0.262310 + 0.262310i −0.0318097 + 0.0318097i
\(69\) −1.53904 5.20132i −0.185279 0.626166i
\(70\) 0 0
\(71\) 9.77651i 1.16026i −0.814524 0.580129i \(-0.803002\pi\)
0.814524 0.580129i \(-0.196998\pi\)
\(72\) 4.17345 + 0.889650i 0.491846 + 0.104846i
\(73\) 4.80768 + 4.80768i 0.562697 + 0.562697i 0.930073 0.367376i \(-0.119744\pi\)
−0.367376 + 0.930073i \(0.619744\pi\)
\(74\) 3.07921 0.357951
\(75\) 0 0
\(76\) 13.6985 1.57133
\(77\) −2.39532 2.39532i −0.272972 0.272972i
\(78\) −1.26292 0.686187i −0.142997 0.0776954i
\(79\) 3.41711i 0.384455i 0.981350 + 0.192228i \(0.0615712\pi\)
−0.981350 + 0.192228i \(0.938429\pi\)
\(80\) 0 0
\(81\) −3.67026 + 8.21761i −0.407807 + 0.913068i
\(82\) −0.362432 + 0.362432i −0.0400239 + 0.0400239i
\(83\) 6.26911 6.26911i 0.688124 0.688124i −0.273693 0.961817i \(-0.588245\pi\)
0.961817 + 0.273693i \(0.0882453\pi\)
\(84\) −3.09673 + 0.916307i −0.337881 + 0.0999773i
\(85\) 0 0
\(86\) 0.450009i 0.0485257i
\(87\) 7.84873 14.4455i 0.841473 1.54872i
\(88\) −3.40712 3.40712i −0.363201 0.363201i
\(89\) 12.3767 1.31192 0.655962 0.754794i \(-0.272263\pi\)
0.655962 + 0.754794i \(0.272263\pi\)
\(90\) 0 0
\(91\) 2.25454 0.236340
\(92\) 4.12888 + 4.12888i 0.430465 + 0.430465i
\(93\) −0.762891 + 1.40409i −0.0791082 + 0.145597i
\(94\) 0.339043i 0.0349696i
\(95\) 0 0
\(96\) −6.68443 + 1.97789i −0.682227 + 0.201867i
\(97\) 6.71326 6.71326i 0.681628 0.681628i −0.278739 0.960367i \(-0.589916\pi\)
0.960367 + 0.278739i \(0.0899164\pi\)
\(98\) −0.260263 + 0.260263i −0.0262906 + 0.0262906i
\(99\) 8.52622 5.52990i 0.856918 0.555775i
\(100\) 0 0
\(101\) 12.4523i 1.23905i −0.784976 0.619526i \(-0.787325\pi\)
0.784976 0.619526i \(-0.212675\pi\)
\(102\) −0.111450 0.0605545i −0.0110352 0.00599579i
\(103\) 9.78924 + 9.78924i 0.964563 + 0.964563i 0.999393 0.0348303i \(-0.0110891\pi\)
−0.0348303 + 0.999393i \(0.511089\pi\)
\(104\) 3.20687 0.314459
\(105\) 0 0
\(106\) 3.40481 0.330704
\(107\) −5.21866 5.21866i −0.504507 0.504507i 0.408328 0.912835i \(-0.366112\pi\)
−0.912835 + 0.408328i \(0.866112\pi\)
\(108\) −0.751653 9.65916i −0.0723279 0.929453i
\(109\) 6.67661i 0.639504i 0.947501 + 0.319752i \(0.103600\pi\)
−0.947501 + 0.319752i \(0.896400\pi\)
\(110\) 0 0
\(111\) −4.11135 13.8946i −0.390233 1.31882i
\(112\) 2.26664 2.26664i 0.214177 0.214177i
\(113\) 8.23451 8.23451i 0.774637 0.774637i −0.204276 0.978913i \(-0.565484\pi\)
0.978913 + 0.204276i \(0.0654841\pi\)
\(114\) 1.32894 + 4.49125i 0.124467 + 0.420644i
\(115\) 0 0
\(116\) 17.6974i 1.64317i
\(117\) −1.41011 + 6.61498i −0.130365 + 0.611555i
\(118\) 1.62673 + 1.62673i 0.149752 + 0.149752i
\(119\) 0.198958 0.0182384
\(120\) 0 0
\(121\) −0.475134 −0.0431940
\(122\) −0.476962 0.476962i −0.0431821 0.0431821i
\(123\) 2.11936 + 1.15152i 0.191096 + 0.103829i
\(124\) 1.72018i 0.154477i
\(125\) 0 0
\(126\) −0.600850 0.926415i −0.0535279 0.0825316i
\(127\) −1.88180 + 1.88180i −0.166983 + 0.166983i −0.785652 0.618669i \(-0.787672\pi\)
0.618669 + 0.785652i \(0.287672\pi\)
\(128\) 6.97474 6.97474i 0.616486 0.616486i
\(129\) 2.03062 0.600850i 0.178786 0.0529019i
\(130\) 0 0
\(131\) 8.97080i 0.783783i 0.920012 + 0.391891i \(0.128179\pi\)
−0.920012 + 0.391891i \(0.871821\pi\)
\(132\) −5.22282 + 9.61252i −0.454588 + 0.836663i
\(133\) −5.19505 5.19505i −0.450468 0.450468i
\(134\) −0.424489 −0.0366703
\(135\) 0 0
\(136\) 0.282999 0.0242670
\(137\) 6.49538 + 6.49538i 0.554938 + 0.554938i 0.927862 0.372924i \(-0.121645\pi\)
−0.372924 + 0.927862i \(0.621645\pi\)
\(138\) −0.953156 + 1.75427i −0.0811380 + 0.149333i
\(139\) 1.83916i 0.155995i −0.996954 0.0779976i \(-0.975147\pi\)
0.996954 0.0779976i \(-0.0248526\pi\)
\(140\) 0 0
\(141\) 1.52990 0.452688i 0.128840 0.0381232i
\(142\) −2.54447 + 2.54447i −0.213527 + 0.213527i
\(143\) 5.40034 5.40034i 0.451599 0.451599i
\(144\) 5.23281 + 8.06817i 0.436068 + 0.672347i
\(145\) 0 0
\(146\) 2.50253i 0.207110i
\(147\) 1.52191 + 0.826909i 0.125525 + 0.0682023i
\(148\) 11.0297 + 11.0297i 0.906640 + 0.906640i
\(149\) −0.987227 −0.0808768 −0.0404384 0.999182i \(-0.512875\pi\)
−0.0404384 + 0.999182i \(0.512875\pi\)
\(150\) 0 0
\(151\) −8.71084 −0.708878 −0.354439 0.935079i \(-0.615328\pi\)
−0.354439 + 0.935079i \(0.615328\pi\)
\(152\) −7.38948 7.38948i −0.599366 0.599366i
\(153\) −0.124439 + 0.583758i −0.0100603 + 0.0471940i
\(154\) 1.24683i 0.100472i
\(155\) 0 0
\(156\) −2.06585 6.98169i −0.165400 0.558983i
\(157\) −5.26306 + 5.26306i −0.420038 + 0.420038i −0.885217 0.465179i \(-0.845990\pi\)
0.465179 + 0.885217i \(0.345990\pi\)
\(158\) 0.889349 0.889349i 0.0707528 0.0707528i
\(159\) −4.54608 15.3638i −0.360528 1.21843i
\(160\) 0 0
\(161\) 3.13169i 0.246812i
\(162\) 3.09398 1.18351i 0.243086 0.0929853i
\(163\) −14.1511 14.1511i −1.10840 1.10840i −0.993361 0.115041i \(-0.963300\pi\)
−0.115041 0.993361i \(-0.536700\pi\)
\(164\) −2.59646 −0.202750
\(165\) 0 0
\(166\) −3.26324 −0.253276
\(167\) −17.4876 17.4876i −1.35323 1.35323i −0.882018 0.471215i \(-0.843816\pi\)
−0.471215 0.882018i \(-0.656184\pi\)
\(168\) 2.16478 + 1.17620i 0.167017 + 0.0907459i
\(169\) 7.91707i 0.609005i
\(170\) 0 0
\(171\) 18.4919 11.9934i 1.41411 0.917159i
\(172\) −1.61193 + 1.61193i −0.122909 + 0.122909i
\(173\) −10.8767 + 10.8767i −0.826942 + 0.826942i −0.987093 0.160150i \(-0.948802\pi\)
0.160150 + 0.987093i \(0.448802\pi\)
\(174\) −5.80236 + 1.71689i −0.439876 + 0.130157i
\(175\) 0 0
\(176\) 10.8587i 0.818502i
\(177\) 5.16844 9.51244i 0.388484 0.714999i
\(178\) −3.22119 3.22119i −0.241439 0.241439i
\(179\) 17.6524 1.31941 0.659703 0.751527i \(-0.270682\pi\)
0.659703 + 0.751527i \(0.270682\pi\)
\(180\) 0 0
\(181\) −11.9237 −0.886282 −0.443141 0.896452i \(-0.646136\pi\)
−0.443141 + 0.896452i \(0.646136\pi\)
\(182\) −0.586773 0.586773i −0.0434945 0.0434945i
\(183\) −1.51541 + 2.78908i −0.112022 + 0.206175i
\(184\) 4.45454i 0.328393i
\(185\) 0 0
\(186\) 0.563986 0.166881i 0.0413534 0.0122363i
\(187\) 0.476568 0.476568i 0.0348501 0.0348501i
\(188\) −1.21445 + 1.21445i −0.0885729 + 0.0885729i
\(189\) −3.37810 + 3.94822i −0.245721 + 0.287191i
\(190\) 0 0
\(191\) 17.7849i 1.28687i 0.765501 + 0.643435i \(0.222491\pi\)
−0.765501 + 0.643435i \(0.777509\pi\)
\(192\) −7.50253 4.07639i −0.541449 0.294188i
\(193\) −14.3394 14.3394i −1.03217 1.03217i −0.999465 0.0327052i \(-0.989588\pi\)
−0.0327052 0.999465i \(-0.510412\pi\)
\(194\) −3.49443 −0.250885
\(195\) 0 0
\(196\) −1.86453 −0.133180
\(197\) 4.10678 + 4.10678i 0.292596 + 0.292596i 0.838105 0.545509i \(-0.183664\pi\)
−0.545509 + 0.838105i \(0.683664\pi\)
\(198\) −3.65829 0.779834i −0.259983 0.0554204i
\(199\) 13.4148i 0.950949i 0.879730 + 0.475474i \(0.157724\pi\)
−0.879730 + 0.475474i \(0.842276\pi\)
\(200\) 0 0
\(201\) 0.566776 + 1.91547i 0.0399773 + 0.135107i
\(202\) −3.24088 + 3.24088i −0.228027 + 0.228027i
\(203\) 6.71161 6.71161i 0.471063 0.471063i
\(204\) −0.182307 0.616119i −0.0127640 0.0431370i
\(205\) 0 0
\(206\) 5.09556i 0.355025i
\(207\) 9.18861 + 1.95873i 0.638653 + 0.136141i
\(208\) 5.11022 + 5.11022i 0.354330 + 0.354330i
\(209\) −24.8876 −1.72151
\(210\) 0 0
\(211\) 8.11525 0.558677 0.279338 0.960193i \(-0.409885\pi\)
0.279338 + 0.960193i \(0.409885\pi\)
\(212\) 12.1960 + 12.1960i 0.837626 + 0.837626i
\(213\) 14.8790 + 8.08429i 1.01949 + 0.553926i
\(214\) 2.71645i 0.185693i
\(215\) 0 0
\(216\) −4.80504 + 5.61598i −0.326941 + 0.382119i
\(217\) −0.652364 + 0.652364i −0.0442854 + 0.0442854i
\(218\) 1.73768 1.73768i 0.117690 0.117690i
\(219\) −11.2924 + 3.34136i −0.763069 + 0.225788i
\(220\) 0 0
\(221\) 0.448558i 0.0301732i
\(222\) −2.54623 + 4.68630i −0.170892 + 0.314524i
\(223\) 11.5431 + 11.5431i 0.772984 + 0.772984i 0.978627 0.205643i \(-0.0659285\pi\)
−0.205643 + 0.978627i \(0.565928\pi\)
\(224\) −4.02466 −0.268909
\(225\) 0 0
\(226\) −4.28628 −0.285119
\(227\) 7.04578 + 7.04578i 0.467645 + 0.467645i 0.901151 0.433506i \(-0.142724\pi\)
−0.433506 + 0.901151i \(0.642724\pi\)
\(228\) −11.3274 + 20.8479i −0.750176 + 1.38069i
\(229\) 4.80117i 0.317270i 0.987337 + 0.158635i \(0.0507093\pi\)
−0.987337 + 0.158635i \(0.949291\pi\)
\(230\) 0 0
\(231\) 5.62619 1.66476i 0.370176 0.109533i
\(232\) 9.54665 9.54665i 0.626768 0.626768i
\(233\) −14.2791 + 14.2791i −0.935455 + 0.935455i −0.998040 0.0625851i \(-0.980066\pi\)
0.0625851 + 0.998040i \(0.480066\pi\)
\(234\) 2.08864 1.35464i 0.136538 0.0885554i
\(235\) 0 0
\(236\) 11.6539i 0.758603i
\(237\) −5.20055 2.82564i −0.337812 0.183545i
\(238\) −0.0517814 0.0517814i −0.00335649 0.00335649i
\(239\) 12.8618 0.831961 0.415981 0.909373i \(-0.363438\pi\)
0.415981 + 0.909373i \(0.363438\pi\)
\(240\) 0 0
\(241\) −16.1856 −1.04261 −0.521304 0.853371i \(-0.674554\pi\)
−0.521304 + 0.853371i \(0.674554\pi\)
\(242\) 0.123660 + 0.123660i 0.00794917 + 0.00794917i
\(243\) −9.47153 12.3810i −0.607599 0.794244i
\(244\) 3.41696i 0.218748i
\(245\) 0 0
\(246\) −0.251892 0.851289i −0.0160601 0.0542762i
\(247\) 11.7124 11.7124i 0.745243 0.745243i
\(248\) −0.927928 + 0.927928i −0.0589235 + 0.0589235i
\(249\) 4.35706 + 14.7250i 0.276117 + 0.933160i
\(250\) 0 0
\(251\) 8.02862i 0.506762i −0.967367 0.253381i \(-0.918457\pi\)
0.967367 0.253381i \(-0.0815426\pi\)
\(252\) 1.16618 5.47066i 0.0734621 0.344619i
\(253\) −7.50140 7.50140i −0.471609 0.471609i
\(254\) 0.979525 0.0614609
\(255\) 0 0
\(256\) 6.22880 0.389300
\(257\) 16.6108 + 16.6108i 1.03615 + 1.03615i 0.999321 + 0.0368323i \(0.0117267\pi\)
0.0368323 + 0.999321i \(0.488273\pi\)
\(258\) −0.684874 0.372116i −0.0426384 0.0231669i
\(259\) 8.36589i 0.519831i
\(260\) 0 0
\(261\) 15.4946 + 23.8902i 0.959091 + 1.47877i
\(262\) 2.33477 2.33477i 0.144243 0.144243i
\(263\) −13.8361 + 13.8361i −0.853173 + 0.853173i −0.990523 0.137350i \(-0.956142\pi\)
0.137350 + 0.990523i \(0.456142\pi\)
\(264\) 8.00273 2.36797i 0.492534 0.145738i
\(265\) 0 0
\(266\) 2.70416i 0.165803i
\(267\) −10.2344 + 18.8362i −0.626334 + 1.15276i
\(268\) −1.52052 1.52052i −0.0928806 0.0928806i
\(269\) −11.4632 −0.698925 −0.349463 0.936950i \(-0.613636\pi\)
−0.349463 + 0.936950i \(0.613636\pi\)
\(270\) 0 0
\(271\) 8.42276 0.511646 0.255823 0.966724i \(-0.417654\pi\)
0.255823 + 0.966724i \(0.417654\pi\)
\(272\) 0.450965 + 0.450965i 0.0273438 + 0.0273438i
\(273\) −1.86430 + 3.43121i −0.112832 + 0.207666i
\(274\) 3.38102i 0.204255i
\(275\) 0 0
\(276\) −9.69800 + 2.86959i −0.583751 + 0.172729i
\(277\) −12.7307 + 12.7307i −0.764914 + 0.764914i −0.977206 0.212293i \(-0.931907\pi\)
0.212293 + 0.977206i \(0.431907\pi\)
\(278\) −0.478665 + 0.478665i −0.0287084 + 0.0287084i
\(279\) −1.50606 2.32211i −0.0901656 0.139021i
\(280\) 0 0
\(281\) 4.41251i 0.263228i 0.991301 + 0.131614i \(0.0420160\pi\)
−0.991301 + 0.131614i \(0.957984\pi\)
\(282\) −0.515994 0.280357i −0.0307270 0.0166950i
\(283\) −2.07246 2.07246i −0.123195 0.123195i 0.642821 0.766016i \(-0.277764\pi\)
−0.766016 + 0.642821i \(0.777764\pi\)
\(284\) −18.2286 −1.08167
\(285\) 0 0
\(286\) −2.81102 −0.166219
\(287\) 0.984688 + 0.984688i 0.0581243 + 0.0581243i
\(288\) 2.51724 11.8087i 0.148330 0.695832i
\(289\) 16.9604i 0.997672i
\(290\) 0 0
\(291\) 4.66575 + 15.7683i 0.273511 + 0.924352i
\(292\) 8.96405 8.96405i 0.524581 0.524581i
\(293\) −7.37595 + 7.37595i −0.430908 + 0.430908i −0.888937 0.458029i \(-0.848555\pi\)
0.458029 + 0.888937i \(0.348555\pi\)
\(294\) −0.180884 0.611312i −0.0105494 0.0356525i
\(295\) 0 0
\(296\) 11.8997i 0.691656i
\(297\) 1.36561 + 17.5489i 0.0792410 + 1.01829i
\(298\) 0.256939 + 0.256939i 0.0148841 + 0.0148841i
\(299\) 7.06050 0.408319
\(300\) 0 0
\(301\) 1.22262 0.0704709
\(302\) 2.26711 + 2.26711i 0.130458 + 0.130458i
\(303\) 18.9513 + 10.2969i 1.08873 + 0.591543i
\(304\) 23.5506i 1.35072i
\(305\) 0 0
\(306\) 0.184318 0.119544i 0.0105367 0.00683386i
\(307\) −11.3608 + 11.3608i −0.648396 + 0.648396i −0.952605 0.304209i \(-0.901608\pi\)
0.304209 + 0.952605i \(0.401608\pi\)
\(308\) −4.46614 + 4.46614i −0.254482 + 0.254482i
\(309\) −22.9932 + 6.80357i −1.30804 + 0.387042i
\(310\) 0 0
\(311\) 8.94291i 0.507106i 0.967322 + 0.253553i \(0.0815992\pi\)
−0.967322 + 0.253553i \(0.918401\pi\)
\(312\) −2.65179 + 4.88058i −0.150128 + 0.276308i
\(313\) −4.52473 4.52473i −0.255753 0.255753i 0.567571 0.823324i \(-0.307883\pi\)
−0.823324 + 0.567571i \(0.807883\pi\)
\(314\) 2.73956 0.154602
\(315\) 0 0
\(316\) 6.37130 0.358414
\(317\) 1.78453 + 1.78453i 0.100229 + 0.100229i 0.755443 0.655214i \(-0.227422\pi\)
−0.655214 + 0.755443i \(0.727422\pi\)
\(318\) −2.81546 + 5.18182i −0.157883 + 0.290582i
\(319\) 32.1529i 1.80022i
\(320\) 0 0
\(321\) 12.2577 3.62699i 0.684158 0.202439i
\(322\) −0.815063 + 0.815063i −0.0454217 + 0.0454217i
\(323\) 1.03360 1.03360i 0.0575108 0.0575108i
\(324\) 15.3220 + 6.84330i 0.851220 + 0.380183i
\(325\) 0 0
\(326\) 7.36604i 0.407967i
\(327\) −10.1612 5.52095i −0.561917 0.305309i
\(328\) 1.40063 + 1.40063i 0.0773368 + 0.0773368i
\(329\) 0.921142 0.0507842
\(330\) 0 0
\(331\) −3.61857 −0.198895 −0.0994474 0.995043i \(-0.531707\pi\)
−0.0994474 + 0.995043i \(0.531707\pi\)
\(332\) −11.6889 11.6889i −0.641512 0.641512i
\(333\) 24.5462 + 5.23248i 1.34512 + 0.286738i
\(334\) 9.10277i 0.498082i
\(335\) 0 0
\(336\) 1.57532 + 5.32393i 0.0859410 + 0.290444i
\(337\) 17.0941 17.0941i 0.931175 0.931175i −0.0666042 0.997779i \(-0.521216\pi\)
0.997779 + 0.0666042i \(0.0212165\pi\)
\(338\) −2.06052 + 2.06052i −0.112078 + 0.112078i
\(339\) 5.72302 + 19.3414i 0.310832 + 1.05048i
\(340\) 0 0
\(341\) 3.12524i 0.169241i
\(342\) −7.93421 1.69133i −0.429033 0.0914565i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 1.73907 0.0937644
\(345\) 0 0
\(346\) 5.66162 0.304371
\(347\) −5.48573 5.48573i −0.294489 0.294489i 0.544361 0.838851i \(-0.316772\pi\)
−0.838851 + 0.544361i \(0.816772\pi\)
\(348\) −26.9340 14.6342i −1.44381 0.784474i
\(349\) 14.8272i 0.793681i 0.917888 + 0.396841i \(0.129893\pi\)
−0.917888 + 0.396841i \(0.870107\pi\)
\(350\) 0 0
\(351\) −8.90140 7.61605i −0.475122 0.406515i
\(352\) −9.64036 + 9.64036i −0.513833 + 0.513833i
\(353\) −7.55570 + 7.55570i −0.402149 + 0.402149i −0.878990 0.476841i \(-0.841782\pi\)
0.476841 + 0.878990i \(0.341782\pi\)
\(354\) −3.82089 + 1.13058i −0.203078 + 0.0600898i
\(355\) 0 0
\(356\) 23.0766i 1.22306i
\(357\) −0.164520 + 0.302797i −0.00870732 + 0.0160257i
\(358\) −4.59428 4.59428i −0.242815 0.242815i
\(359\) −6.09504 −0.321684 −0.160842 0.986980i \(-0.551421\pi\)
−0.160842 + 0.986980i \(0.551421\pi\)
\(360\) 0 0
\(361\) −34.9770 −1.84090
\(362\) 3.10330 + 3.10330i 0.163106 + 0.163106i
\(363\) 0.392893 0.723114i 0.0206215 0.0379536i
\(364\) 4.20364i 0.220331i
\(365\) 0 0
\(366\) 1.12030 0.331491i 0.0585590 0.0173273i
\(367\) −3.52753 + 3.52753i −0.184136 + 0.184136i −0.793155 0.609019i \(-0.791563\pi\)
0.609019 + 0.793155i \(0.291563\pi\)
\(368\) 7.09840 7.09840i 0.370030 0.370030i
\(369\) −3.50503 + 2.27327i −0.182465 + 0.118342i
\(370\) 0 0
\(371\) 9.25048i 0.480261i
\(372\) 2.61796 + 1.42243i 0.135735 + 0.0737496i
\(373\) 7.07089 + 7.07089i 0.366117 + 0.366117i 0.866059 0.499942i \(-0.166645\pi\)
−0.499942 + 0.866059i \(0.666645\pi\)
\(374\) −0.248066 −0.0128272
\(375\) 0 0
\(376\) 1.31024 0.0675704
\(377\) 15.1316 + 15.1316i 0.779315 + 0.779315i
\(378\) 1.90677 0.148381i 0.0980738 0.00763187i
\(379\) 21.4715i 1.10292i 0.834202 + 0.551459i \(0.185929\pi\)
−0.834202 + 0.551459i \(0.814071\pi\)
\(380\) 0 0
\(381\) −1.30786 4.42001i −0.0670036 0.226444i
\(382\) 4.62875 4.62875i 0.236828 0.236828i
\(383\) 14.6559 14.6559i 0.748882 0.748882i −0.225388 0.974269i \(-0.572365\pi\)
0.974269 + 0.225388i \(0.0723648\pi\)
\(384\) 4.84748 + 16.3824i 0.247372 + 0.836012i
\(385\) 0 0
\(386\) 7.46402i 0.379909i
\(387\) −0.764695 + 3.58727i −0.0388716 + 0.182351i
\(388\) −12.5170 12.5170i −0.635457 0.635457i
\(389\) 13.6323 0.691185 0.345592 0.938385i \(-0.387678\pi\)
0.345592 + 0.938385i \(0.387678\pi\)
\(390\) 0 0
\(391\) 0.623074 0.0315102
\(392\) 1.00579 + 1.00579i 0.0508003 + 0.0508003i
\(393\) −13.6528 7.41804i −0.688692 0.374190i
\(394\) 2.13769i 0.107695i
\(395\) 0 0
\(396\) −10.3106 15.8974i −0.518129 0.798873i
\(397\) 24.5632 24.5632i 1.23279 1.23279i 0.269907 0.962886i \(-0.413007\pi\)
0.962886 0.269907i \(-0.0869929\pi\)
\(398\) 3.49137 3.49137i 0.175007 0.175007i
\(399\) 12.2022 3.61058i 0.610876 0.180755i
\(400\) 0 0
\(401\) 15.5011i 0.774088i −0.922061 0.387044i \(-0.873496\pi\)
0.922061 0.387044i \(-0.126504\pi\)
\(402\) 0.351014 0.646036i 0.0175070 0.0322214i
\(403\) −1.47078 1.47078i −0.0732647 0.0732647i
\(404\) −23.2177 −1.15512
\(405\) 0 0
\(406\) −3.49357 −0.173383
\(407\) −20.0390 20.0390i −0.993296 0.993296i
\(408\) −0.234015 + 0.430700i −0.0115854 + 0.0213228i
\(409\) 32.0414i 1.58434i −0.610298 0.792172i \(-0.708950\pi\)
0.610298 0.792172i \(-0.291050\pi\)
\(410\) 0 0
\(411\) −15.2565 + 4.51432i −0.752547 + 0.222675i
\(412\) 18.2523 18.2523i 0.899226 0.899226i
\(413\) 4.41964 4.41964i 0.217476 0.217476i
\(414\) −1.88167 2.90124i −0.0924792 0.142588i
\(415\) 0 0
\(416\) 9.07374i 0.444877i
\(417\) 2.79904 + 1.52081i 0.137069 + 0.0744746i
\(418\) 6.47733 + 6.47733i 0.316817 + 0.316817i
\(419\) −5.95062 −0.290707 −0.145353 0.989380i \(-0.546432\pi\)
−0.145353 + 0.989380i \(0.546432\pi\)
\(420\) 0 0
\(421\) −10.6388 −0.518504 −0.259252 0.965810i \(-0.583476\pi\)
−0.259252 + 0.965810i \(0.583476\pi\)
\(422\) −2.11210 2.11210i −0.102816 0.102816i
\(423\) −0.576132 + 2.70270i −0.0280125 + 0.131410i
\(424\) 13.1580i 0.639007i
\(425\) 0 0
\(426\) −1.76842 5.97650i −0.0856801 0.289563i
\(427\) −1.29585 + 1.29585i −0.0627108 + 0.0627108i
\(428\) −9.73032 + 9.73032i −0.470333 + 0.470333i
\(429\) 3.75326 + 12.6844i 0.181209 + 0.612410i
\(430\) 0 0
\(431\) 11.2739i 0.543045i −0.962432 0.271523i \(-0.912473\pi\)
0.962432 0.271523i \(-0.0875271\pi\)
\(432\) −16.6061 + 1.29225i −0.798962 + 0.0621733i
\(433\) −9.75098 9.75098i −0.468602 0.468602i 0.432859 0.901462i \(-0.357505\pi\)
−0.901462 + 0.432859i \(0.857505\pi\)
\(434\) 0.339573 0.0163000
\(435\) 0 0
\(436\) 12.4487 0.596185
\(437\) −16.2693 16.2693i −0.778265 0.778265i
\(438\) 3.80863 + 2.06936i 0.181983 + 0.0988779i
\(439\) 28.4375i 1.35725i 0.734485 + 0.678625i \(0.237424\pi\)
−0.734485 + 0.678625i \(0.762576\pi\)
\(440\) 0 0
\(441\) −2.51697 + 1.63244i −0.119856 + 0.0777354i
\(442\) 0.116743 0.116743i 0.00555290 0.00555290i
\(443\) 19.2121 19.2121i 0.912796 0.912796i −0.0836955 0.996491i \(-0.526672\pi\)
0.996491 + 0.0836955i \(0.0266723\pi\)
\(444\) −25.9069 + 7.66573i −1.22949 + 0.363799i
\(445\) 0 0
\(446\) 6.00850i 0.284511i
\(447\) 0.816347 1.50247i 0.0386119 0.0710646i
\(448\) −3.48580 3.48580i −0.164689 0.164689i
\(449\) −2.40628 −0.113559 −0.0567796 0.998387i \(-0.518083\pi\)
−0.0567796 + 0.998387i \(0.518083\pi\)
\(450\) 0 0
\(451\) 4.71729 0.222129
\(452\) −15.3534 15.3534i −0.722166 0.722166i
\(453\) 7.20307 13.2572i 0.338430 0.622875i
\(454\) 3.66752i 0.172125i
\(455\) 0 0
\(456\) 17.3566 5.13572i 0.812796 0.240502i
\(457\) −6.21588 + 6.21588i −0.290767 + 0.290767i −0.837383 0.546617i \(-0.815916\pi\)
0.546617 + 0.837383i \(0.315916\pi\)
\(458\) 1.24957 1.24957i 0.0583884 0.0583884i
\(459\) −0.785529 0.672100i −0.0366654 0.0313709i
\(460\) 0 0
\(461\) 35.4227i 1.64980i 0.565278 + 0.824900i \(0.308769\pi\)
−0.565278 + 0.824900i \(0.691231\pi\)
\(462\) −1.89757 1.03101i −0.0882827 0.0479671i
\(463\) 20.0869 + 20.0869i 0.933519 + 0.933519i 0.997924 0.0644045i \(-0.0205148\pi\)
−0.0644045 + 0.997924i \(0.520515\pi\)
\(464\) 30.4256 1.41247
\(465\) 0 0
\(466\) 7.43265 0.344311
\(467\) 5.80567 + 5.80567i 0.268654 + 0.268654i 0.828558 0.559903i \(-0.189162\pi\)
−0.559903 + 0.828558i \(0.689162\pi\)
\(468\) 12.3338 + 2.62918i 0.570130 + 0.121534i
\(469\) 1.15329i 0.0532540i
\(470\) 0 0
\(471\) −3.65785 12.3620i −0.168545 0.569610i
\(472\) 6.28653 6.28653i 0.289361 0.289361i
\(473\) 2.92858 2.92858i 0.134656 0.134656i
\(474\) 0.618102 + 2.08892i 0.0283904 + 0.0959475i
\(475\) 0 0
\(476\) 0.370962i 0.0170030i
\(477\) 27.1416 + 5.78575i 1.24273 + 0.264911i
\(478\) −3.34746 3.34746i −0.153109 0.153109i
\(479\) 40.3829 1.84514 0.922571 0.385828i \(-0.126084\pi\)
0.922571 + 0.385828i \(0.126084\pi\)
\(480\) 0 0
\(481\) 18.8612 0.859997
\(482\) 4.21252 + 4.21252i 0.191875 + 0.191875i
\(483\) 4.76616 + 2.58962i 0.216868 + 0.117832i
\(484\) 0.885900i 0.0402682i
\(485\) 0 0
\(486\) −0.757238 + 5.68742i −0.0343490 + 0.257987i
\(487\) −19.7983 + 19.7983i −0.897147 + 0.897147i −0.995183 0.0980363i \(-0.968744\pi\)
0.0980363 + 0.995183i \(0.468744\pi\)
\(488\) −1.84323 + 1.84323i −0.0834393 + 0.0834393i
\(489\) 33.2385 9.83510i 1.50310 0.444759i
\(490\) 0 0
\(491\) 36.6924i 1.65590i 0.560798 + 0.827952i \(0.310494\pi\)
−0.560798 + 0.827952i \(0.689506\pi\)
\(492\) 2.14704 3.95159i 0.0967960 0.178152i
\(493\) 1.33533 + 1.33533i 0.0601402 + 0.0601402i
\(494\) −6.09662 −0.274300
\(495\) 0 0
\(496\) −2.95735 −0.132789
\(497\) 6.91304 + 6.91304i 0.310092 + 0.310092i
\(498\) 2.69840 4.96636i 0.120918 0.222548i
\(499\) 7.62548i 0.341363i −0.985326 0.170682i \(-0.945403\pi\)
0.985326 0.170682i \(-0.0545970\pi\)
\(500\) 0 0
\(501\) 41.0753 12.1540i 1.83511 0.543000i
\(502\) −2.08955 + 2.08955i −0.0932614 + 0.0932614i
\(503\) 15.7533 15.7533i 0.702406 0.702406i −0.262521 0.964926i \(-0.584554\pi\)
0.964926 + 0.262521i \(0.0845538\pi\)
\(504\) −3.58016 + 2.32200i −0.159473 + 0.103430i
\(505\) 0 0
\(506\) 3.90468i 0.173584i
\(507\) 12.0491 + 6.54670i 0.535119 + 0.290749i
\(508\) 3.50866 + 3.50866i 0.155672 + 0.155672i
\(509\) 14.4091 0.638673 0.319336 0.947641i \(-0.396540\pi\)
0.319336 + 0.947641i \(0.396540\pi\)
\(510\) 0 0
\(511\) −6.79909 −0.300774
\(512\) −15.5706 15.5706i −0.688130 0.688130i
\(513\) 2.96178 + 38.0606i 0.130766 + 1.68042i
\(514\) 8.64637i 0.381375i
\(515\) 0 0
\(516\) −1.12030 3.78614i −0.0493185 0.166676i
\(517\) 2.20643 2.20643i 0.0970387 0.0970387i
\(518\) −2.17733 + 2.17733i −0.0956666 + 0.0956666i
\(519\) −7.55938 25.5475i −0.331820 1.12141i
\(520\) 0 0
\(521\) 25.3850i 1.11214i 0.831136 + 0.556069i \(0.187691\pi\)
−0.831136 + 0.556069i \(0.812309\pi\)
\(522\) 2.18507 10.2504i 0.0956378 0.448648i
\(523\) 16.0464 + 16.0464i 0.701661 + 0.701661i 0.964767 0.263106i \(-0.0847470\pi\)
−0.263106 + 0.964767i \(0.584747\pi\)
\(524\) 16.7263 0.730692
\(525\) 0 0
\(526\) 7.20208 0.314026
\(527\) −0.129793 0.129793i −0.00565387 0.00565387i
\(528\) 16.5259 + 8.97912i 0.719199 + 0.390766i
\(529\) 13.1925i 0.573588i
\(530\) 0 0
\(531\) 10.2033 + 15.7318i 0.442785 + 0.682704i
\(532\) −9.68630 + 9.68630i −0.419954 + 0.419954i
\(533\) −2.22002 + 2.22002i −0.0961595 + 0.0961595i
\(534\) 7.56601 2.23874i 0.327413 0.0968799i
\(535\) 0 0
\(536\) 1.64045i 0.0708567i
\(537\) −14.5970 + 26.8655i −0.629905 + 1.15933i
\(538\) 2.98346 + 2.98346i 0.128626 + 0.128626i
\(539\) 3.38750 0.145910
\(540\) 0 0
\(541\) −26.9427 −1.15836 −0.579178 0.815201i \(-0.696626\pi\)
−0.579178 + 0.815201i \(0.696626\pi\)
\(542\) −2.19213 2.19213i −0.0941602 0.0941602i
\(543\) 9.85981 18.1468i 0.423125 0.778756i
\(544\) 0.800738i 0.0343313i
\(545\) 0 0
\(546\) 1.37823 0.407810i 0.0589826 0.0174527i
\(547\) −17.9286 + 17.9286i −0.766572 + 0.766572i −0.977501 0.210929i \(-0.932351\pi\)
0.210929 + 0.977501i \(0.432351\pi\)
\(548\) 12.1108 12.1108i 0.517348 0.517348i
\(549\) −2.99164 4.61263i −0.127680 0.196862i
\(550\) 0 0
\(551\) 69.7343i 2.97078i
\(552\) 6.77942 + 3.68350i 0.288551 + 0.156780i
\(553\) −2.41627 2.41627i −0.102750 0.102750i
\(554\) 6.62667 0.281540
\(555\) 0 0
\(556\) −3.42915 −0.145428
\(557\) 5.15944 + 5.15944i 0.218613 + 0.218613i 0.807914 0.589301i \(-0.200597\pi\)
−0.589301 + 0.807914i \(0.700597\pi\)
\(558\) −0.212387 + 0.996333i −0.00899106 + 0.0421781i
\(559\) 2.75645i 0.116585i
\(560\) 0 0
\(561\) 0.331217 + 1.11937i 0.0139840 + 0.0472600i
\(562\) 1.14841 1.14841i 0.0484429 0.0484429i
\(563\) 23.2548 23.2548i 0.980072 0.980072i −0.0197332 0.999805i \(-0.506282\pi\)
0.999805 + 0.0197332i \(0.00628169\pi\)
\(564\) −0.844049 2.85253i −0.0355409 0.120113i
\(565\) 0 0
\(566\) 1.07877i 0.0453442i
\(567\) −3.21547 8.40600i −0.135037 0.353019i
\(568\) 9.83316 + 9.83316i 0.412590 + 0.412590i
\(569\) −45.1914 −1.89452 −0.947260 0.320466i \(-0.896161\pi\)
−0.947260 + 0.320466i \(0.896161\pi\)
\(570\) 0 0
\(571\) 15.2468 0.638059 0.319029 0.947745i \(-0.396643\pi\)
0.319029 + 0.947745i \(0.396643\pi\)
\(572\) −10.0691 10.0691i −0.421009 0.421009i
\(573\) −27.0671 14.7065i −1.13074 0.614372i
\(574\) 0.512556i 0.0213937i
\(575\) 0 0
\(576\) 12.4078 8.04741i 0.516993 0.335309i
\(577\) 6.12177 6.12177i 0.254853 0.254853i −0.568104 0.822957i \(-0.692323\pi\)
0.822957 + 0.568104i \(0.192323\pi\)
\(578\) −4.41417 + 4.41417i −0.183605 + 0.183605i
\(579\) 33.6806 9.96593i 1.39972 0.414170i
\(580\) 0 0
\(581\) 8.86586i 0.367818i
\(582\) 2.88958 5.31822i 0.119777 0.220447i
\(583\) −22.1579 22.1579i −0.917686 0.917686i
\(584\) −9.67107 −0.400192
\(585\) 0 0
\(586\) 3.83938 0.158603
\(587\) 3.77086 + 3.77086i 0.155640 + 0.155640i 0.780632 0.624992i \(-0.214898\pi\)
−0.624992 + 0.780632i \(0.714898\pi\)
\(588\) 1.54179 2.83765i 0.0635825 0.117023i
\(589\) 6.77812i 0.279288i
\(590\) 0 0
\(591\) −9.64610 + 2.85423i −0.396787 + 0.117407i
\(592\) 18.9624 18.9624i 0.779352 0.779352i
\(593\) 8.38017 8.38017i 0.344132 0.344132i −0.513786 0.857918i \(-0.671758\pi\)
0.857918 + 0.513786i \(0.171758\pi\)
\(594\) 4.21191 4.92275i 0.172817 0.201983i
\(595\) 0 0
\(596\) 1.84071i 0.0753985i
\(597\) −20.4161 11.0928i −0.835577 0.453998i
\(598\) −1.83759 1.83759i −0.0751446 0.0751446i
\(599\) −6.75588 −0.276038 −0.138019 0.990430i \(-0.544073\pi\)
−0.138019 + 0.990430i \(0.544073\pi\)
\(600\) 0 0
\(601\) 21.2564 0.867068 0.433534 0.901137i \(-0.357266\pi\)
0.433534 + 0.901137i \(0.357266\pi\)
\(602\) −0.318204 0.318204i −0.0129690 0.0129690i
\(603\) −3.38385 0.721331i −0.137801 0.0293749i
\(604\) 16.2416i 0.660861i
\(605\) 0 0
\(606\) −2.25243 7.61225i −0.0914986 0.309227i
\(607\) −2.72491 + 2.72491i −0.110601 + 0.110601i −0.760241 0.649641i \(-0.774919\pi\)
0.649641 + 0.760241i \(0.274919\pi\)
\(608\) −20.9083 + 20.9083i −0.847944 + 0.847944i
\(609\) 4.66460 + 15.7644i 0.189019 + 0.638805i
\(610\) 0 0
\(611\) 2.07675i 0.0840162i
\(612\) 1.08843 + 0.232020i 0.0439972 + 0.00937884i
\(613\) −15.6232 15.6232i −0.631017 0.631017i 0.317306 0.948323i \(-0.397222\pi\)
−0.948323 + 0.317306i \(0.897222\pi\)
\(614\) 5.91361 0.238654
\(615\) 0 0
\(616\) 4.81840 0.194139
\(617\) −5.47009 5.47009i −0.220218 0.220218i 0.588373 0.808590i \(-0.299769\pi\)
−0.808590 + 0.588373i \(0.799769\pi\)
\(618\) 7.75500 + 4.21357i 0.311952 + 0.169494i
\(619\) 42.9951i 1.72812i 0.503389 + 0.864060i \(0.332086\pi\)
−0.503389 + 0.864060i \(0.667914\pi\)
\(620\) 0 0
\(621\) −10.5792 + 12.3646i −0.424527 + 0.496174i
\(622\) 2.32751 2.32751i 0.0933247 0.0933247i
\(623\) −8.75163 + 8.75163i −0.350627 + 0.350627i
\(624\) −12.0030 + 3.55162i −0.480504 + 0.142179i
\(625\) 0 0
\(626\) 2.35524i 0.0941344i
\(627\) 20.5798 37.8768i 0.821878 1.51265i
\(628\) 9.81311 + 9.81311i 0.391586 + 0.391586i
\(629\) 1.66446 0.0663664
\(630\) 0 0
\(631\) −38.0091 −1.51312 −0.756560 0.653925i \(-0.773121\pi\)
−0.756560 + 0.653925i \(0.773121\pi\)
\(632\) −3.43691 3.43691i −0.136713 0.136713i
\(633\) −6.71057 + 12.3507i −0.266721 + 0.490897i
\(634\) 0.928896i 0.0368912i
\(635\) 0 0
\(636\) −28.6463 + 8.47629i −1.13590 + 0.336107i
\(637\) −1.59420 + 1.59420i −0.0631644 + 0.0631644i
\(638\) −8.36823 + 8.36823i −0.331301 + 0.331301i
\(639\) −24.6072 + 15.9596i −0.973445 + 0.631352i
\(640\) 0 0
\(641\) 30.8009i 1.21656i −0.793721 0.608282i \(-0.791859\pi\)
0.793721 0.608282i \(-0.208141\pi\)
\(642\) −4.13420 2.24626i −0.163164 0.0886527i
\(643\) 6.17366 + 6.17366i 0.243465 + 0.243465i 0.818282 0.574817i \(-0.194927\pi\)
−0.574817 + 0.818282i \(0.694927\pi\)
\(644\) −5.83911 −0.230093
\(645\) 0 0
\(646\) −0.538014 −0.0211679
\(647\) 23.4296 + 23.4296i 0.921112 + 0.921112i 0.997108 0.0759964i \(-0.0242137\pi\)
−0.0759964 + 0.997108i \(0.524214\pi\)
\(648\) −4.57370 11.9568i −0.179672 0.469706i
\(649\) 21.1729i 0.831110i
\(650\) 0 0
\(651\) −0.453396 1.53229i −0.0177700 0.0600551i
\(652\) −26.3851 + 26.3851i −1.03332 + 1.03332i
\(653\) −17.1928 + 17.1928i −0.672805 + 0.672805i −0.958362 0.285557i \(-0.907821\pi\)
0.285557 + 0.958362i \(0.407821\pi\)
\(654\) 1.20769 + 4.08150i 0.0472246 + 0.159599i
\(655\) 0 0
\(656\) 4.46386i 0.174285i
\(657\) 4.25252 19.9490i 0.165906 0.778286i
\(658\) −0.239739 0.239739i −0.00934601 0.00934601i
\(659\) 0.0375362 0.00146220 0.000731101 1.00000i \(-0.499767\pi\)
0.000731101 1.00000i \(0.499767\pi\)
\(660\) 0 0
\(661\) 19.6937 0.765995 0.382998 0.923749i \(-0.374892\pi\)
0.382998 + 0.923749i \(0.374892\pi\)
\(662\) 0.941782 + 0.941782i 0.0366034 + 0.0366034i
\(663\) −0.682666 0.370916i −0.0265125 0.0144052i
\(664\) 12.6109i 0.489396i
\(665\) 0 0
\(666\) −5.02664 7.75029i −0.194778 0.300318i
\(667\) 21.0187 21.0187i 0.813846 0.813846i
\(668\) −32.6061 + 32.6061i −1.26157 + 1.26157i
\(669\) −27.1127 + 8.02252i −1.04824 + 0.310169i
\(670\) 0 0
\(671\) 6.20798i 0.239656i
\(672\) 3.32803 6.12519i 0.128381 0.236284i
\(673\) 4.33276 + 4.33276i 0.167016 + 0.167016i 0.785666 0.618651i \(-0.212320\pi\)
−0.618651 + 0.785666i \(0.712320\pi\)
\(674\) −8.89793 −0.342736
\(675\) 0 0
\(676\) −14.7616 −0.567753
\(677\) −3.64637 3.64637i −0.140142 0.140142i 0.633556 0.773697i \(-0.281595\pi\)
−0.773697 + 0.633556i \(0.781595\pi\)
\(678\) 3.54436 6.52335i 0.136120 0.250528i
\(679\) 9.49398i 0.364346i
\(680\) 0 0
\(681\) −16.5493 + 4.89685i −0.634170 + 0.187648i
\(682\) 0.813386 0.813386i 0.0311462 0.0311462i
\(683\) 33.7536 33.7536i 1.29155 1.29155i 0.357718 0.933830i \(-0.383555\pi\)
0.933830 0.357718i \(-0.116445\pi\)
\(684\) −22.3620 34.4787i −0.855033 1.31833i
\(685\) 0 0
\(686\) 0.368068i 0.0140529i
\(687\) −7.30696 3.97013i −0.278778 0.151470i
\(688\) 2.77125 + 2.77125i 0.105653 + 0.105653i
\(689\) 20.8555 0.794533
\(690\) 0 0
\(691\) −12.2184 −0.464812 −0.232406 0.972619i \(-0.574660\pi\)
−0.232406 + 0.972619i \(0.574660\pi\)
\(692\) 20.2799 + 20.2799i 0.770928 + 0.770928i
\(693\) −2.11872 + 9.93918i −0.0804836 + 0.377558i
\(694\) 2.85547i 0.108392i
\(695\) 0 0
\(696\) 6.63497 + 22.4234i 0.251498 + 0.849956i
\(697\) −0.195912 + 0.195912i −0.00742068 + 0.00742068i
\(698\) 3.85897 3.85897i 0.146064 0.146064i
\(699\) −9.92404 33.5391i −0.375362 1.26856i
\(700\) 0 0
\(701\) 21.7907i 0.823024i −0.911404 0.411512i \(-0.865001\pi\)
0.911404 0.411512i \(-0.134999\pi\)
\(702\) 0.334529 + 4.29889i 0.0126260 + 0.162251i
\(703\) −43.4612 43.4612i −1.63917 1.63917i
\(704\) −16.6992 −0.629377
\(705\) 0 0
\(706\) 3.93294 0.148018
\(707\) 8.80511 + 8.80511i 0.331150 + 0.331150i
\(708\) −17.7362 9.63670i −0.666567 0.362169i
\(709\) 14.1622i 0.531874i −0.963990 0.265937i \(-0.914319\pi\)
0.963990 0.265937i \(-0.0856814\pi\)
\(710\) 0 0
\(711\) 8.60077 5.57825i 0.322554 0.209201i
\(712\) −12.4484 + 12.4484i −0.466523 + 0.466523i
\(713\) −2.04300 + 2.04300i −0.0765110 + 0.0765110i
\(714\) 0.121625 0.0359883i 0.00455172 0.00134683i
\(715\) 0 0
\(716\) 32.9134i 1.23003i
\(717\) −10.6355 + 19.5746i −0.397192 + 0.731026i
\(718\) 1.58632 + 1.58632i 0.0592008 + 0.0592008i
\(719\) −39.3153 −1.46621 −0.733106 0.680114i \(-0.761930\pi\)
−0.733106 + 0.680114i \(0.761930\pi\)
\(720\) 0 0
\(721\) −13.8441 −0.515581
\(722\) 9.10324 + 9.10324i 0.338787 + 0.338787i
\(723\) 13.3840 24.6331i 0.497757 0.916115i
\(724\) 22.2320i 0.826248i
\(725\) 0 0
\(726\) −0.290455 + 0.0859443i −0.0107798 + 0.00318969i
\(727\) −10.0141 + 10.0141i −0.371403 + 0.371403i −0.867988 0.496585i \(-0.834587\pi\)
0.496585 + 0.867988i \(0.334587\pi\)
\(728\) −2.26760 + 2.26760i −0.0840428 + 0.0840428i
\(729\) 26.6750 4.17686i 0.987962 0.154699i
\(730\) 0 0
\(731\) 0.243251i 0.00899695i
\(732\) 5.20032 + 2.82551i 0.192209 + 0.104434i
\(733\) 30.5737 + 30.5737i 1.12926 + 1.12926i 0.990297 + 0.138967i \(0.0443783\pi\)
0.138967 + 0.990297i \(0.455622\pi\)
\(734\) 1.83618 0.0677745
\(735\) 0 0
\(736\) −12.6040 −0.464589
\(737\) 2.76250 + 2.76250i 0.101758 + 0.101758i
\(738\) 1.50388 + 0.320580i 0.0553586 + 0.0118007i
\(739\) 16.1095i 0.592598i 0.955095 + 0.296299i \(0.0957525\pi\)
−0.955095 + 0.296299i \(0.904247\pi\)
\(740\) 0 0
\(741\) 8.14019 + 27.5104i 0.299037 + 1.01062i
\(742\) −2.40756 + 2.40756i −0.0883844 + 0.0883844i
\(743\) −23.1679 + 23.1679i −0.849946 + 0.849946i −0.990126 0.140180i \(-0.955232\pi\)
0.140180 + 0.990126i \(0.455232\pi\)
\(744\) −0.644914 2.17954i −0.0236437 0.0799057i
\(745\) 0 0
\(746\) 3.68059i 0.134756i
\(747\) −26.0131 5.54518i −0.951770 0.202888i
\(748\) −0.888574 0.888574i −0.0324895 0.0324895i
\(749\) 7.38030 0.269670
\(750\) 0 0
\(751\) 28.7540 1.04925 0.524625 0.851334i \(-0.324206\pi\)
0.524625 + 0.851334i \(0.324206\pi\)
\(752\) 2.08789 + 2.08789i 0.0761377 + 0.0761377i
\(753\) 12.2189 + 6.63894i 0.445280 + 0.241936i
\(754\) 7.87638i 0.286841i
\(755\) 0 0
\(756\) 7.36156 + 6.29856i 0.267737 + 0.229076i
\(757\) 1.29026 1.29026i 0.0468952 0.0468952i −0.683270 0.730166i \(-0.739443\pi\)
0.730166 + 0.683270i \(0.239443\pi\)
\(758\) 5.58825 5.58825i 0.202974 0.202974i
\(759\) 17.6195 5.21351i 0.639546 0.189238i
\(760\) 0 0
\(761\) 33.9969i 1.23239i 0.787596 + 0.616193i \(0.211326\pi\)
−0.787596 + 0.616193i \(0.788674\pi\)
\(762\) −0.809978 + 1.49075i −0.0293424 + 0.0540043i
\(763\) −4.72108 4.72108i −0.170915 0.170915i
\(764\) 33.1604 1.19970
\(765\) 0 0
\(766\) −7.62879 −0.275639
\(767\) 9.96424 + 9.96424i 0.359788 + 0.359788i
\(768\) −5.15065 + 9.47970i −0.185858 + 0.342069i
\(769\) 21.4206i 0.772448i −0.922405 0.386224i \(-0.873779\pi\)
0.922405 0.386224i \(-0.126221\pi\)
\(770\) 0 0
\(771\) −39.0158 + 11.5446i −1.40512 + 0.415768i
\(772\) −26.7361 + 26.7361i −0.962254 + 0.962254i
\(773\) −9.50533 + 9.50533i −0.341883 + 0.341883i −0.857075 0.515192i \(-0.827721\pi\)
0.515192 + 0.857075i \(0.327721\pi\)
\(774\) 1.13266 0.734614i 0.0407125 0.0264051i
\(775\) 0 0
\(776\) 13.5043i 0.484777i
\(777\) 12.7322 + 6.91783i 0.456764 + 0.248176i