Properties

Label 690.2.e.a.551.5
Level $690$
Weight $2$
Character 690.551
Analytic conductor $5.510$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} - 198 x^{7} + 405 x^{6} - 108 x^{5} + 1215 x^{4} - 2916 x^{3} + 2187 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 551.5
Root \(1.73162 + 0.0386882i\) of defining polynomial
Character \(\chi\) \(=\) 690.551
Dual form 690.2.e.a.551.13

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-0.0386882 + 1.73162i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.73162 + 0.0386882i) q^{6} -2.83902i q^{7} +1.00000i q^{8} +(-2.99701 - 0.133986i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-0.0386882 + 1.73162i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.73162 + 0.0386882i) q^{6} -2.83902i q^{7} +1.00000i q^{8} +(-2.99701 - 0.133986i) q^{9} +1.00000i q^{10} +4.50428 q^{11} +(0.0386882 - 1.73162i) q^{12} -5.89898 q^{13} -2.83902 q^{14} +(0.0386882 - 1.73162i) q^{15} +1.00000 q^{16} -5.40124 q^{17} +(-0.133986 + 2.99701i) q^{18} -2.26797i q^{19} +1.00000 q^{20} +(4.91611 + 0.109837i) q^{21} -4.50428i q^{22} +(3.64088 - 3.12154i) q^{23} +(-1.73162 - 0.0386882i) q^{24} +1.00000 q^{25} +5.89898i q^{26} +(0.347962 - 5.18449i) q^{27} +2.83902i q^{28} -4.81253i q^{29} +(-1.73162 - 0.0386882i) q^{30} -9.92135 q^{31} -1.00000i q^{32} +(-0.174262 + 7.79970i) q^{33} +5.40124i q^{34} +2.83902i q^{35} +(2.99701 + 0.133986i) q^{36} -3.92624i q^{37} -2.26797 q^{38} +(0.228221 - 10.2148i) q^{39} -1.00000i q^{40} -2.24625i q^{41} +(0.109837 - 4.91611i) q^{42} -11.5505i q^{43} -4.50428 q^{44} +(2.99701 + 0.133986i) q^{45} +(-3.12154 - 3.64088i) q^{46} +1.55237i q^{47} +(-0.0386882 + 1.73162i) q^{48} -1.06006 q^{49} -1.00000i q^{50} +(0.208964 - 9.35288i) q^{51} +5.89898 q^{52} -6.08832 q^{53} +(-5.18449 - 0.347962i) q^{54} -4.50428 q^{55} +2.83902 q^{56} +(3.92726 + 0.0877437i) q^{57} -4.81253 q^{58} +10.8538i q^{59} +(-0.0386882 + 1.73162i) q^{60} -11.6821i q^{61} +9.92135i q^{62} +(-0.380390 + 8.50857i) q^{63} -1.00000 q^{64} +5.89898 q^{65} +(7.79970 + 0.174262i) q^{66} +3.47626i q^{67} +5.40124 q^{68} +(5.26445 + 6.42538i) q^{69} +2.83902 q^{70} +9.84805i q^{71} +(0.133986 - 2.99701i) q^{72} +0.323623 q^{73} -3.92624 q^{74} +(-0.0386882 + 1.73162i) q^{75} +2.26797i q^{76} -12.7878i q^{77} +(-10.2148 - 0.228221i) q^{78} -5.69882i q^{79} -1.00000 q^{80} +(8.96410 + 0.803115i) q^{81} -2.24625 q^{82} -4.31060 q^{83} +(-4.91611 - 0.109837i) q^{84} +5.40124 q^{85} -11.5505 q^{86} +(8.33347 + 0.186188i) q^{87} +4.50428i q^{88} +11.6518 q^{89} +(0.133986 - 2.99701i) q^{90} +16.7474i q^{91} +(-3.64088 + 3.12154i) q^{92} +(0.383839 - 17.1800i) q^{93} +1.55237 q^{94} +2.26797i q^{95} +(1.73162 + 0.0386882i) q^{96} +8.21290i q^{97} +1.06006i q^{98} +(-13.4994 - 0.603512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} + O(q^{10}) \) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} - 12q^{11} - 12q^{14} + 16q^{16} + 8q^{18} + 16q^{20} - 4q^{21} + 4q^{23} - 2q^{24} + 16q^{25} + 24q^{27} - 2q^{30} + 4q^{31} - 28q^{33} - 2q^{36} - 16q^{38} - 8q^{39} + 12q^{44} - 2q^{45} - 4q^{46} - 4q^{49} - 2q^{51} - 8q^{53} - 26q^{54} + 12q^{55} + 12q^{56} + 28q^{57} - 8q^{58} - 16q^{64} + 10q^{66} + 30q^{69} + 12q^{70} - 8q^{72} - 16q^{73} - 24q^{74} - 12q^{78} - 16q^{80} + 22q^{81} - 16q^{82} - 40q^{83} + 4q^{84} - 40q^{86} + 20q^{87} + 80q^{89} - 8q^{90} - 4q^{92} - 4q^{93} - 24q^{94} + 2q^{96} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.0386882 + 1.73162i −0.0223366 + 0.999751i
\(4\) −1.00000 −0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.73162 + 0.0386882i 0.706930 + 0.0157944i
\(7\) 2.83902i 1.07305i −0.843884 0.536525i \(-0.819737\pi\)
0.843884 0.536525i \(-0.180263\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −2.99701 0.133986i −0.999002 0.0446621i
\(10\) 1.00000i 0.316228i
\(11\) 4.50428 1.35809 0.679046 0.734096i \(-0.262394\pi\)
0.679046 + 0.734096i \(0.262394\pi\)
\(12\) 0.0386882 1.73162i 0.0111683 0.499875i
\(13\) −5.89898 −1.63608 −0.818042 0.575159i \(-0.804940\pi\)
−0.818042 + 0.575159i \(0.804940\pi\)
\(14\) −2.83902 −0.758761
\(15\) 0.0386882 1.73162i 0.00998924 0.447102i
\(16\) 1.00000 0.250000
\(17\) −5.40124 −1.30999 −0.654996 0.755632i \(-0.727330\pi\)
−0.654996 + 0.755632i \(0.727330\pi\)
\(18\) −0.133986 + 2.99701i −0.0315809 + 0.706401i
\(19\) 2.26797i 0.520309i −0.965567 0.260154i \(-0.916227\pi\)
0.965567 0.260154i \(-0.0837734\pi\)
\(20\) 1.00000 0.223607
\(21\) 4.91611 + 0.109837i 1.07278 + 0.0239683i
\(22\) 4.50428i 0.960316i
\(23\) 3.64088 3.12154i 0.759176 0.650885i
\(24\) −1.73162 0.0386882i −0.353465 0.00789719i
\(25\) 1.00000 0.200000
\(26\) 5.89898i 1.15689i
\(27\) 0.347962 5.18449i 0.0669653 0.997755i
\(28\) 2.83902i 0.536525i
\(29\) 4.81253i 0.893665i −0.894618 0.446832i \(-0.852552\pi\)
0.894618 0.446832i \(-0.147448\pi\)
\(30\) −1.73162 0.0386882i −0.316149 0.00706346i
\(31\) −9.92135 −1.78193 −0.890964 0.454075i \(-0.849970\pi\)
−0.890964 + 0.454075i \(0.849970\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −0.174262 + 7.79970i −0.0303352 + 1.35775i
\(34\) 5.40124i 0.926304i
\(35\) 2.83902i 0.479883i
\(36\) 2.99701 + 0.133986i 0.499501 + 0.0223310i
\(37\) 3.92624i 0.645470i −0.946489 0.322735i \(-0.895398\pi\)
0.946489 0.322735i \(-0.104602\pi\)
\(38\) −2.26797 −0.367914
\(39\) 0.228221 10.2148i 0.0365446 1.63568i
\(40\) 1.00000i 0.158114i
\(41\) 2.24625i 0.350805i −0.984497 0.175402i \(-0.943877\pi\)
0.984497 0.175402i \(-0.0561226\pi\)
\(42\) 0.109837 4.91611i 0.0169482 0.758572i
\(43\) 11.5505i 1.76143i −0.473648 0.880714i \(-0.657063\pi\)
0.473648 0.880714i \(-0.342937\pi\)
\(44\) −4.50428 −0.679046
\(45\) 2.99701 + 0.133986i 0.446767 + 0.0199735i
\(46\) −3.12154 3.64088i −0.460245 0.536819i
\(47\) 1.55237i 0.226437i 0.993570 + 0.113218i \(0.0361160\pi\)
−0.993570 + 0.113218i \(0.963884\pi\)
\(48\) −0.0386882 + 1.73162i −0.00558415 + 0.249938i
\(49\) −1.06006 −0.151437
\(50\) 1.00000i 0.141421i
\(51\) 0.208964 9.35288i 0.0292608 1.30967i
\(52\) 5.89898 0.818042
\(53\) −6.08832 −0.836295 −0.418147 0.908379i \(-0.637320\pi\)
−0.418147 + 0.908379i \(0.637320\pi\)
\(54\) −5.18449 0.347962i −0.705520 0.0473516i
\(55\) −4.50428 −0.607357
\(56\) 2.83902 0.379381
\(57\) 3.92726 + 0.0877437i 0.520179 + 0.0116219i
\(58\) −4.81253 −0.631916
\(59\) 10.8538i 1.41305i 0.707690 + 0.706523i \(0.249737\pi\)
−0.707690 + 0.706523i \(0.750263\pi\)
\(60\) −0.0386882 + 1.73162i −0.00499462 + 0.223551i
\(61\) 11.6821i 1.49574i −0.663843 0.747872i \(-0.731076\pi\)
0.663843 0.747872i \(-0.268924\pi\)
\(62\) 9.92135i 1.26001i
\(63\) −0.380390 + 8.50857i −0.0479247 + 1.07198i
\(64\) −1.00000 −0.125000
\(65\) 5.89898 0.731679
\(66\) 7.79970 + 0.174262i 0.960077 + 0.0214502i
\(67\) 3.47626i 0.424693i 0.977194 + 0.212346i \(0.0681105\pi\)
−0.977194 + 0.212346i \(0.931890\pi\)
\(68\) 5.40124 0.654996
\(69\) 5.26445 + 6.42538i 0.633765 + 0.773525i
\(70\) 2.83902 0.339328
\(71\) 9.84805i 1.16875i 0.811484 + 0.584374i \(0.198660\pi\)
−0.811484 + 0.584374i \(0.801340\pi\)
\(72\) 0.133986 2.99701i 0.0157904 0.353201i
\(73\) 0.323623 0.0378772 0.0189386 0.999821i \(-0.493971\pi\)
0.0189386 + 0.999821i \(0.493971\pi\)
\(74\) −3.92624 −0.456416
\(75\) −0.0386882 + 1.73162i −0.00446732 + 0.199950i
\(76\) 2.26797i 0.260154i
\(77\) 12.7878i 1.45730i
\(78\) −10.2148 0.228221i −1.15660 0.0258409i
\(79\) 5.69882i 0.641168i −0.947220 0.320584i \(-0.896121\pi\)
0.947220 0.320584i \(-0.103879\pi\)
\(80\) −1.00000 −0.111803
\(81\) 8.96410 + 0.803115i 0.996011 + 0.0892350i
\(82\) −2.24625 −0.248056
\(83\) −4.31060 −0.473150 −0.236575 0.971613i \(-0.576025\pi\)
−0.236575 + 0.971613i \(0.576025\pi\)
\(84\) −4.91611 0.109837i −0.536391 0.0119842i
\(85\) 5.40124 0.585846
\(86\) −11.5505 −1.24552
\(87\) 8.33347 + 0.186188i 0.893442 + 0.0199614i
\(88\) 4.50428i 0.480158i
\(89\) 11.6518 1.23509 0.617543 0.786537i \(-0.288128\pi\)
0.617543 + 0.786537i \(0.288128\pi\)
\(90\) 0.133986 2.99701i 0.0141234 0.315912i
\(91\) 16.7474i 1.75560i
\(92\) −3.64088 + 3.12154i −0.379588 + 0.325443i
\(93\) 0.383839 17.1800i 0.0398022 1.78148i
\(94\) 1.55237 0.160115
\(95\) 2.26797i 0.232689i
\(96\) 1.73162 + 0.0386882i 0.176733 + 0.00394859i
\(97\) 8.21290i 0.833893i 0.908931 + 0.416947i \(0.136900\pi\)
−0.908931 + 0.416947i \(0.863100\pi\)
\(98\) 1.06006i 0.107082i
\(99\) −13.4994 0.603512i −1.35674 0.0606552i
\(100\) −1.00000 −0.100000
\(101\) 8.57100i 0.852846i 0.904524 + 0.426423i \(0.140227\pi\)
−0.904524 + 0.426423i \(0.859773\pi\)
\(102\) −9.35288 0.208964i −0.926073 0.0206905i
\(103\) 7.45638i 0.734699i 0.930083 + 0.367350i \(0.119735\pi\)
−0.930083 + 0.367350i \(0.880265\pi\)
\(104\) 5.89898i 0.578443i
\(105\) −4.91611 0.109837i −0.479763 0.0107190i
\(106\) 6.08832i 0.591350i
\(107\) −15.4707 −1.49561 −0.747807 0.663916i \(-0.768893\pi\)
−0.747807 + 0.663916i \(0.768893\pi\)
\(108\) −0.347962 + 5.18449i −0.0334826 + 0.498878i
\(109\) 11.6976i 1.12043i 0.828347 + 0.560215i \(0.189282\pi\)
−0.828347 + 0.560215i \(0.810718\pi\)
\(110\) 4.50428i 0.429466i
\(111\) 6.79875 + 0.151899i 0.645309 + 0.0144176i
\(112\) 2.83902i 0.268263i
\(113\) 8.40341 0.790527 0.395263 0.918568i \(-0.370653\pi\)
0.395263 + 0.918568i \(0.370653\pi\)
\(114\) 0.0877437 3.92726i 0.00821795 0.367822i
\(115\) −3.64088 + 3.12154i −0.339514 + 0.291085i
\(116\) 4.81253i 0.446832i
\(117\) 17.6793 + 0.790383i 1.63445 + 0.0730709i
\(118\) 10.8538 0.999174
\(119\) 15.3342i 1.40569i
\(120\) 1.73162 + 0.0386882i 0.158074 + 0.00353173i
\(121\) 9.28856 0.844414
\(122\) −11.6821 −1.05765
\(123\) 3.88964 + 0.0869031i 0.350717 + 0.00783579i
\(124\) 9.92135 0.890964
\(125\) −1.00000 −0.0894427
\(126\) 8.50857 + 0.380390i 0.758004 + 0.0338879i
\(127\) −13.8803 −1.23168 −0.615839 0.787872i \(-0.711183\pi\)
−0.615839 + 0.787872i \(0.711183\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 20.0010 + 0.446866i 1.76099 + 0.0393444i
\(130\) 5.89898i 0.517375i
\(131\) 7.37577i 0.644424i 0.946667 + 0.322212i \(0.104426\pi\)
−0.946667 + 0.322212i \(0.895574\pi\)
\(132\) 0.174262 7.79970i 0.0151676 0.678877i
\(133\) −6.43883 −0.558317
\(134\) 3.47626 0.300303
\(135\) −0.347962 + 5.18449i −0.0299478 + 0.446210i
\(136\) 5.40124i 0.463152i
\(137\) −1.02064 −0.0871996 −0.0435998 0.999049i \(-0.513883\pi\)
−0.0435998 + 0.999049i \(0.513883\pi\)
\(138\) 6.42538 5.26445i 0.546965 0.448140i
\(139\) −0.625898 −0.0530880 −0.0265440 0.999648i \(-0.508450\pi\)
−0.0265440 + 0.999648i \(0.508450\pi\)
\(140\) 2.83902i 0.239941i
\(141\) −2.68812 0.0600584i −0.226380 0.00505783i
\(142\) 9.84805 0.826430
\(143\) −26.5707 −2.22195
\(144\) −2.99701 0.133986i −0.249751 0.0111655i
\(145\) 4.81253i 0.399659i
\(146\) 0.323623i 0.0267832i
\(147\) 0.0410117 1.83562i 0.00338259 0.151399i
\(148\) 3.92624i 0.322735i
\(149\) −8.47908 −0.694633 −0.347317 0.937748i \(-0.612907\pi\)
−0.347317 + 0.937748i \(0.612907\pi\)
\(150\) 1.73162 + 0.0386882i 0.141386 + 0.00315887i
\(151\) 23.4124 1.90527 0.952637 0.304110i \(-0.0983592\pi\)
0.952637 + 0.304110i \(0.0983592\pi\)
\(152\) 2.26797 0.183957
\(153\) 16.1875 + 0.723691i 1.30868 + 0.0585070i
\(154\) −12.7878 −1.03047
\(155\) 9.92135 0.796902
\(156\) −0.228221 + 10.2148i −0.0182723 + 0.817838i
\(157\) 0.880316i 0.0702569i −0.999383 0.0351284i \(-0.988816\pi\)
0.999383 0.0351284i \(-0.0111840\pi\)
\(158\) −5.69882 −0.453374
\(159\) 0.235546 10.5426i 0.0186800 0.836086i
\(160\) 1.00000i 0.0790569i
\(161\) −8.86211 10.3366i −0.698432 0.814634i
\(162\) 0.803115 8.96410i 0.0630987 0.704286i
\(163\) 12.2560 0.959964 0.479982 0.877278i \(-0.340643\pi\)
0.479982 + 0.877278i \(0.340643\pi\)
\(164\) 2.24625i 0.175402i
\(165\) 0.174262 7.79970i 0.0135663 0.607206i
\(166\) 4.31060i 0.334568i
\(167\) 21.5502i 1.66761i −0.552062 0.833803i \(-0.686159\pi\)
0.552062 0.833803i \(-0.313841\pi\)
\(168\) −0.109837 + 4.91611i −0.00847408 + 0.379286i
\(169\) 21.7980 1.67677
\(170\) 5.40124i 0.414256i
\(171\) −0.303877 + 6.79713i −0.0232381 + 0.519789i
\(172\) 11.5505i 0.880714i
\(173\) 2.77254i 0.210792i 0.994430 + 0.105396i \(0.0336111\pi\)
−0.994430 + 0.105396i \(0.966389\pi\)
\(174\) 0.186188 8.33347i 0.0141149 0.631759i
\(175\) 2.83902i 0.214610i
\(176\) 4.50428 0.339523
\(177\) −18.7947 0.419914i −1.41269 0.0315627i
\(178\) 11.6518i 0.873338i
\(179\) 5.79371i 0.433042i −0.976278 0.216521i \(-0.930529\pi\)
0.976278 0.216521i \(-0.0694710\pi\)
\(180\) −2.99701 0.133986i −0.223384 0.00998675i
\(181\) 19.0813i 1.41830i −0.705058 0.709150i \(-0.749079\pi\)
0.705058 0.709150i \(-0.250921\pi\)
\(182\) 16.7474 1.24140
\(183\) 20.2290 + 0.451960i 1.49537 + 0.0334099i
\(184\) 3.12154 + 3.64088i 0.230123 + 0.268409i
\(185\) 3.92624i 0.288663i
\(186\) −17.1800 0.383839i −1.25970 0.0281444i
\(187\) −24.3287 −1.77909
\(188\) 1.55237i 0.113218i
\(189\) −14.7189 0.987872i −1.07064 0.0718571i
\(190\) 2.26797 0.164536
\(191\) 12.9022 0.933573 0.466787 0.884370i \(-0.345412\pi\)
0.466787 + 0.884370i \(0.345412\pi\)
\(192\) 0.0386882 1.73162i 0.00279208 0.124969i
\(193\) 2.08785 0.150286 0.0751432 0.997173i \(-0.476059\pi\)
0.0751432 + 0.997173i \(0.476059\pi\)
\(194\) 8.21290 0.589652
\(195\) −0.228221 + 10.2148i −0.0163432 + 0.731496i
\(196\) 1.06006 0.0757185
\(197\) 1.94161i 0.138334i −0.997605 0.0691671i \(-0.977966\pi\)
0.997605 0.0691671i \(-0.0220342\pi\)
\(198\) −0.603512 + 13.4994i −0.0428897 + 0.959358i
\(199\) 20.2897i 1.43830i −0.694855 0.719149i \(-0.744532\pi\)
0.694855 0.719149i \(-0.255468\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −6.01955 0.134490i −0.424587 0.00948620i
\(202\) 8.57100 0.603053
\(203\) −13.6629 −0.958947
\(204\) −0.208964 + 9.35288i −0.0146304 + 0.654833i
\(205\) 2.24625i 0.156885i
\(206\) 7.45638 0.519511
\(207\) −11.3300 + 8.86743i −0.787489 + 0.616329i
\(208\) −5.89898 −0.409021
\(209\) 10.2156i 0.706627i
\(210\) −0.109837 + 4.91611i −0.00757945 + 0.339244i
\(211\) −8.99923 −0.619532 −0.309766 0.950813i \(-0.600251\pi\)
−0.309766 + 0.950813i \(0.600251\pi\)
\(212\) 6.08832 0.418147
\(213\) −17.0531 0.381003i −1.16846 0.0261059i
\(214\) 15.4707i 1.05756i
\(215\) 11.5505i 0.787735i
\(216\) 5.18449 + 0.347962i 0.352760 + 0.0236758i
\(217\) 28.1670i 1.91210i
\(218\) 11.6976 0.792264
\(219\) −0.0125204 + 0.560391i −0.000846048 + 0.0378677i
\(220\) 4.50428 0.303679
\(221\) 31.8618 2.14326
\(222\) 0.151899 6.79875i 0.0101948 0.456302i
\(223\) 13.9192 0.932099 0.466049 0.884759i \(-0.345677\pi\)
0.466049 + 0.884759i \(0.345677\pi\)
\(224\) −2.83902 −0.189690
\(225\) −2.99701 0.133986i −0.199800 0.00893242i
\(226\) 8.40341i 0.558987i
\(227\) −11.5024 −0.763442 −0.381721 0.924278i \(-0.624668\pi\)
−0.381721 + 0.924278i \(0.624668\pi\)
\(228\) −3.92726 0.0877437i −0.260089 0.00581097i
\(229\) 14.9027i 0.984797i −0.870370 0.492398i \(-0.836120\pi\)
0.870370 0.492398i \(-0.163880\pi\)
\(230\) 3.12154 + 3.64088i 0.205828 + 0.240073i
\(231\) 22.1435 + 0.494735i 1.45694 + 0.0325512i
\(232\) 4.81253 0.315958
\(233\) 3.74448i 0.245309i −0.992449 0.122655i \(-0.960859\pi\)
0.992449 0.122655i \(-0.0391407\pi\)
\(234\) 0.790383 17.6793i 0.0516689 1.15573i
\(235\) 1.55237i 0.101266i
\(236\) 10.8538i 0.706523i
\(237\) 9.86819 + 0.220477i 0.641008 + 0.0143215i
\(238\) 15.3342 0.993971
\(239\) 23.2940i 1.50676i −0.657585 0.753381i \(-0.728422\pi\)
0.657585 0.753381i \(-0.271578\pi\)
\(240\) 0.0386882 1.73162i 0.00249731 0.111776i
\(241\) 29.3778i 1.89239i 0.323598 + 0.946195i \(0.395107\pi\)
−0.323598 + 0.946195i \(0.604893\pi\)
\(242\) 9.28856i 0.597091i
\(243\) −1.73749 + 15.4913i −0.111460 + 0.993769i
\(244\) 11.6821i 0.747872i
\(245\) 1.06006 0.0677246
\(246\) 0.0869031 3.88964i 0.00554074 0.247995i
\(247\) 13.3787i 0.851268i
\(248\) 9.92135i 0.630006i
\(249\) 0.166769 7.46432i 0.0105686 0.473032i
\(250\) 1.00000i 0.0632456i
\(251\) 28.0442 1.77014 0.885068 0.465462i \(-0.154112\pi\)
0.885068 + 0.465462i \(0.154112\pi\)
\(252\) 0.380390 8.50857i 0.0239623 0.535990i
\(253\) 16.3996 14.0603i 1.03103 0.883962i
\(254\) 13.8803i 0.870928i
\(255\) −0.208964 + 9.35288i −0.0130858 + 0.585700i
\(256\) 1.00000 0.0625000
\(257\) 10.1173i 0.631102i 0.948909 + 0.315551i \(0.102189\pi\)
−0.948909 + 0.315551i \(0.897811\pi\)
\(258\) 0.446866 20.0010i 0.0278207 1.24521i
\(259\) −11.1467 −0.692621
\(260\) −5.89898 −0.365839
\(261\) −0.644813 + 14.4232i −0.0399129 + 0.892773i
\(262\) 7.37577 0.455677
\(263\) −27.9974 −1.72639 −0.863197 0.504867i \(-0.831541\pi\)
−0.863197 + 0.504867i \(0.831541\pi\)
\(264\) −7.79970 0.174262i −0.480038 0.0107251i
\(265\) 6.08832 0.374002
\(266\) 6.43883i 0.394790i
\(267\) −0.450786 + 20.1765i −0.0275877 + 1.23478i
\(268\) 3.47626i 0.212346i
\(269\) 11.8305i 0.721318i 0.932698 + 0.360659i \(0.117448\pi\)
−0.932698 + 0.360659i \(0.882552\pi\)
\(270\) 5.18449 + 0.347962i 0.315518 + 0.0211763i
\(271\) −27.3595 −1.66197 −0.830987 0.556292i \(-0.812224\pi\)
−0.830987 + 0.556292i \(0.812224\pi\)
\(272\) −5.40124 −0.327498
\(273\) −29.0000 0.647924i −1.75516 0.0392142i
\(274\) 1.02064i 0.0616594i
\(275\) 4.50428 0.271618
\(276\) −5.26445 6.42538i −0.316883 0.386763i
\(277\) −17.9484 −1.07842 −0.539208 0.842173i \(-0.681276\pi\)
−0.539208 + 0.842173i \(0.681276\pi\)
\(278\) 0.625898i 0.0375389i
\(279\) 29.7344 + 1.32932i 1.78015 + 0.0795846i
\(280\) −2.83902 −0.169664
\(281\) 0.662441 0.0395179 0.0197590 0.999805i \(-0.493710\pi\)
0.0197590 + 0.999805i \(0.493710\pi\)
\(282\) −0.0600584 + 2.68812i −0.00357643 + 0.160075i
\(283\) 25.7017i 1.52781i −0.645331 0.763903i \(-0.723280\pi\)
0.645331 0.763903i \(-0.276720\pi\)
\(284\) 9.84805i 0.584374i
\(285\) −3.92726 0.0877437i −0.232631 0.00519749i
\(286\) 26.5707i 1.57116i
\(287\) −6.37715 −0.376431
\(288\) −0.133986 + 2.99701i −0.00789522 + 0.176600i
\(289\) 12.1733 0.716079
\(290\) 4.81253 0.282602
\(291\) −14.2216 0.317742i −0.833685 0.0186264i
\(292\) −0.323623 −0.0189386
\(293\) 19.4320 1.13523 0.567614 0.823295i \(-0.307867\pi\)
0.567614 + 0.823295i \(0.307867\pi\)
\(294\) −1.83562 0.0410117i −0.107055 0.00239185i
\(295\) 10.8538i 0.631933i
\(296\) 3.92624 0.228208
\(297\) 1.56732 23.3524i 0.0909450 1.35504i
\(298\) 8.47908i 0.491180i
\(299\) −21.4775 + 18.4139i −1.24208 + 1.06490i
\(300\) 0.0386882 1.73162i 0.00223366 0.0999751i
\(301\) −32.7920 −1.89010
\(302\) 23.4124i 1.34723i
\(303\) −14.8417 0.331596i −0.852633 0.0190497i
\(304\) 2.26797i 0.130077i
\(305\) 11.6821i 0.668917i
\(306\) 0.723691 16.1875i 0.0413707 0.925380i
\(307\) 1.65943 0.0947088 0.0473544 0.998878i \(-0.484921\pi\)
0.0473544 + 0.998878i \(0.484921\pi\)
\(308\) 12.7878i 0.728651i
\(309\) −12.9116 0.288474i −0.734516 0.0164107i
\(310\) 9.92135i 0.563495i
\(311\) 12.5570i 0.712043i 0.934478 + 0.356022i \(0.115867\pi\)
−0.934478 + 0.356022i \(0.884133\pi\)
\(312\) 10.2148 + 0.228221i 0.578299 + 0.0129205i
\(313\) 13.5424i 0.765459i −0.923860 0.382730i \(-0.874984\pi\)
0.923860 0.382730i \(-0.125016\pi\)
\(314\) −0.880316 −0.0496791
\(315\) 0.380390 8.50857i 0.0214326 0.479404i
\(316\) 5.69882i 0.320584i
\(317\) 11.1266i 0.624935i −0.949929 0.312467i \(-0.898845\pi\)
0.949929 0.312467i \(-0.101155\pi\)
\(318\) −10.5426 0.235546i −0.591202 0.0132088i
\(319\) 21.6770i 1.21368i
\(320\) 1.00000 0.0559017
\(321\) 0.598535 26.7894i 0.0334070 1.49524i
\(322\) −10.3366 + 8.86211i −0.576033 + 0.493866i
\(323\) 12.2499i 0.681600i
\(324\) −8.96410 0.803115i −0.498005 0.0446175i
\(325\) −5.89898 −0.327217
\(326\) 12.2560i 0.678797i
\(327\) −20.2558 0.452560i −1.12015 0.0250266i
\(328\) 2.24625 0.124028
\(329\) 4.40722 0.242978
\(330\) −7.79970 0.174262i −0.429359 0.00959283i
\(331\) −5.37160 −0.295250 −0.147625 0.989043i \(-0.547163\pi\)
−0.147625 + 0.989043i \(0.547163\pi\)
\(332\) 4.31060 0.236575
\(333\) −0.526062 + 11.7670i −0.0288280 + 0.644826i
\(334\) −21.5502 −1.17918
\(335\) 3.47626i 0.189928i
\(336\) 4.91611 + 0.109837i 0.268196 + 0.00599208i
\(337\) 17.9318i 0.976809i −0.872617 0.488404i \(-0.837579\pi\)
0.872617 0.488404i \(-0.162421\pi\)
\(338\) 21.7980i 1.18566i
\(339\) −0.325113 + 14.5515i −0.0176577 + 0.790330i
\(340\) −5.40124 −0.292923
\(341\) −44.6886 −2.42002
\(342\) 6.79713 + 0.303877i 0.367547 + 0.0164318i
\(343\) 16.8636i 0.910551i
\(344\) 11.5505 0.622759
\(345\) −5.26445 6.42538i −0.283428 0.345931i
\(346\) 2.77254 0.149053
\(347\) 9.99097i 0.536343i 0.963371 + 0.268172i \(0.0864195\pi\)
−0.963371 + 0.268172i \(0.913581\pi\)
\(348\) −8.33347 0.186188i −0.446721 0.00998072i
\(349\) −15.3124 −0.819657 −0.409828 0.912163i \(-0.634411\pi\)
−0.409828 + 0.912163i \(0.634411\pi\)
\(350\) −2.83902 −0.151752
\(351\) −2.05262 + 30.5832i −0.109561 + 1.63241i
\(352\) 4.50428i 0.240079i
\(353\) 8.49859i 0.452334i −0.974089 0.226167i \(-0.927380\pi\)
0.974089 0.226167i \(-0.0726195\pi\)
\(354\) −0.419914 + 18.7947i −0.0223182 + 0.998925i
\(355\) 9.84805i 0.522680i
\(356\) −11.6518 −0.617543
\(357\) −26.5531 0.593253i −1.40534 0.0313983i
\(358\) −5.79371 −0.306207
\(359\) 23.5828 1.24465 0.622327 0.782758i \(-0.286188\pi\)
0.622327 + 0.782758i \(0.286188\pi\)
\(360\) −0.133986 + 2.99701i −0.00706170 + 0.157956i
\(361\) 13.8563 0.729279
\(362\) −19.0813 −1.00289
\(363\) −0.359357 + 16.0842i −0.0188614 + 0.844204i
\(364\) 16.7474i 0.877800i
\(365\) −0.323623 −0.0169392
\(366\) 0.451960 20.2290i 0.0236243 1.05739i
\(367\) 34.0961i 1.77980i 0.456155 + 0.889900i \(0.349226\pi\)
−0.456155 + 0.889900i \(0.650774\pi\)
\(368\) 3.64088 3.12154i 0.189794 0.162721i
\(369\) −0.300966 + 6.73201i −0.0156677 + 0.350455i
\(370\) 3.92624 0.204115
\(371\) 17.2849i 0.897386i
\(372\) −0.383839 + 17.1800i −0.0199011 + 0.890741i
\(373\) 3.12850i 0.161988i −0.996715 0.0809938i \(-0.974191\pi\)
0.996715 0.0809938i \(-0.0258094\pi\)
\(374\) 24.3287i 1.25801i
\(375\) 0.0386882 1.73162i 0.00199785 0.0894204i
\(376\) −1.55237 −0.0800575
\(377\) 28.3890i 1.46211i
\(378\) −0.987872 + 14.7189i −0.0508106 + 0.757058i
\(379\) 0.796283i 0.0409023i 0.999791 + 0.0204511i \(0.00651026\pi\)
−0.999791 + 0.0204511i \(0.993490\pi\)
\(380\) 2.26797i 0.116345i
\(381\) 0.537004 24.0354i 0.0275115 1.23137i
\(382\) 12.9022i 0.660136i
\(383\) 11.8370 0.604842 0.302421 0.953174i \(-0.402205\pi\)
0.302421 + 0.953174i \(0.402205\pi\)
\(384\) −1.73162 0.0386882i −0.0883663 0.00197430i
\(385\) 12.7878i 0.651725i
\(386\) 2.08785i 0.106269i
\(387\) −1.54760 + 34.6168i −0.0786691 + 1.75967i
\(388\) 8.21290i 0.416947i
\(389\) 0.884618 0.0448519 0.0224260 0.999749i \(-0.492861\pi\)
0.0224260 + 0.999749i \(0.492861\pi\)
\(390\) 10.2148 + 0.228221i 0.517246 + 0.0115564i
\(391\) −19.6653 + 16.8601i −0.994515 + 0.852654i
\(392\) 1.06006i 0.0535410i
\(393\) −12.7720 0.285355i −0.644264 0.0143943i
\(394\) −1.94161 −0.0978170
\(395\) 5.69882i 0.286739i
\(396\) 13.4994 + 0.603512i 0.678369 + 0.0303276i
\(397\) 5.97733 0.299993 0.149997 0.988686i \(-0.452074\pi\)
0.149997 + 0.988686i \(0.452074\pi\)
\(398\) −20.2897 −1.01703
\(399\) 0.249106 11.1496i 0.0124709 0.558178i
\(400\) 1.00000 0.0500000
\(401\) 13.0800 0.653184 0.326592 0.945165i \(-0.394100\pi\)
0.326592 + 0.945165i \(0.394100\pi\)
\(402\) −0.134490 + 6.01955i −0.00670775 + 0.300228i
\(403\) 58.5259 2.91538
\(404\) 8.57100i 0.426423i
\(405\) −8.96410 0.803115i −0.445429 0.0399071i
\(406\) 13.6629i 0.678078i
\(407\) 17.6849i 0.876607i
\(408\) 9.35288 + 0.208964i 0.463037 + 0.0103453i
\(409\) −0.595984 −0.0294695 −0.0147348 0.999891i \(-0.504690\pi\)
−0.0147348 + 0.999891i \(0.504690\pi\)
\(410\) 2.24625 0.110934
\(411\) 0.0394869 1.76737i 0.00194774 0.0871778i
\(412\) 7.45638i 0.367350i
\(413\) 30.8142 1.51627
\(414\) 8.86743 + 11.3300i 0.435811 + 0.556839i
\(415\) 4.31060 0.211599
\(416\) 5.89898i 0.289221i
\(417\) 0.0242148 1.08382i 0.00118581 0.0530747i
\(418\) −10.2156 −0.499661
\(419\) 1.73544 0.0847816 0.0423908 0.999101i \(-0.486503\pi\)
0.0423908 + 0.999101i \(0.486503\pi\)
\(420\) 4.91611 + 0.109837i 0.239881 + 0.00535948i
\(421\) 5.82242i 0.283767i 0.989883 + 0.141884i \(0.0453159\pi\)
−0.989883 + 0.141884i \(0.954684\pi\)
\(422\) 8.99923i 0.438076i
\(423\) 0.207997 4.65247i 0.0101131 0.226211i
\(424\) 6.08832i 0.295675i
\(425\) −5.40124 −0.261998
\(426\) −0.381003 + 17.0531i −0.0184596 + 0.826224i
\(427\) −33.1659 −1.60501
\(428\) 15.4707 0.747807
\(429\) 1.02797 46.0103i 0.0496309 2.22140i
\(430\) 11.5505 0.557013
\(431\) −6.19650 −0.298475 −0.149237 0.988801i \(-0.547682\pi\)
−0.149237 + 0.988801i \(0.547682\pi\)
\(432\) 0.347962 5.18449i 0.0167413 0.249439i
\(433\) 10.6171i 0.510226i −0.966911 0.255113i \(-0.917887\pi\)
0.966911 0.255113i \(-0.0821127\pi\)
\(434\) 28.1670 1.35206
\(435\) −8.33347 0.186188i −0.399559 0.00892703i
\(436\) 11.6976i 0.560215i
\(437\) −7.07956 8.25742i −0.338661 0.395006i
\(438\) 0.560391 + 0.0125204i 0.0267765 + 0.000598246i
\(439\) −24.8996 −1.18839 −0.594197 0.804319i \(-0.702530\pi\)
−0.594197 + 0.804319i \(0.702530\pi\)
\(440\) 4.50428i 0.214733i
\(441\) 3.17700 + 0.142033i 0.151286 + 0.00676349i
\(442\) 31.8618i 1.51551i
\(443\) 8.79242i 0.417741i −0.977943 0.208870i \(-0.933021\pi\)
0.977943 0.208870i \(-0.0669786\pi\)
\(444\) −6.79875 0.151899i −0.322654 0.00720880i
\(445\) −11.6518 −0.552348
\(446\) 13.9192i 0.659093i
\(447\) 0.328040 14.6825i 0.0155158 0.694460i
\(448\) 2.83902i 0.134131i
\(449\) 21.0781i 0.994739i −0.867539 0.497370i \(-0.834299\pi\)
0.867539 0.497370i \(-0.165701\pi\)
\(450\) −0.133986 + 2.99701i −0.00631617 + 0.141280i
\(451\) 10.1177i 0.476425i
\(452\) −8.40341 −0.395263
\(453\) −0.905782 + 40.5413i −0.0425574 + 1.90480i
\(454\) 11.5024i 0.539835i
\(455\) 16.7474i 0.785128i
\(456\) −0.0877437 + 3.92726i −0.00410897 + 0.183911i
\(457\) 7.66411i 0.358512i −0.983802 0.179256i \(-0.942631\pi\)
0.983802 0.179256i \(-0.0573690\pi\)
\(458\) −14.9027 −0.696357
\(459\) −1.87942 + 28.0026i −0.0877240 + 1.30705i
\(460\) 3.64088 3.12154i 0.169757 0.145542i
\(461\) 36.6333i 1.70618i −0.521761 0.853092i \(-0.674725\pi\)
0.521761 0.853092i \(-0.325275\pi\)
\(462\) 0.494735 22.1435i 0.0230172 1.03021i
\(463\) 7.73369 0.359415 0.179708 0.983720i \(-0.442485\pi\)
0.179708 + 0.983720i \(0.442485\pi\)
\(464\) 4.81253i 0.223416i
\(465\) −0.383839 + 17.1800i −0.0178001 + 0.796703i
\(466\) −3.74448 −0.173460
\(467\) −20.9022 −0.967237 −0.483618 0.875279i \(-0.660678\pi\)
−0.483618 + 0.875279i \(0.660678\pi\)
\(468\) −17.6793 0.790383i −0.817226 0.0365355i
\(469\) 9.86918 0.455717
\(470\) −1.55237 −0.0716056
\(471\) 1.52437 + 0.0340578i 0.0702394 + 0.00156930i
\(472\) −10.8538 −0.499587
\(473\) 52.0265i 2.39218i
\(474\) 0.220477 9.86819i 0.0101268 0.453261i
\(475\) 2.26797i 0.104062i
\(476\) 15.3342i 0.702844i
\(477\) 18.2467 + 0.815751i 0.835460 + 0.0373507i
\(478\) −23.2940 −1.06544
\(479\) −33.1326 −1.51387 −0.756933 0.653492i \(-0.773303\pi\)
−0.756933 + 0.653492i \(0.773303\pi\)
\(480\) −1.73162 0.0386882i −0.0790372 0.00176586i
\(481\) 23.1608i 1.05604i
\(482\) 29.3778 1.33812
\(483\) 18.2418 14.9459i 0.830032 0.680062i
\(484\) −9.28856 −0.422207
\(485\) 8.21290i 0.372928i
\(486\) 15.4913 + 1.73749i 0.702701 + 0.0788143i
\(487\) 10.1567 0.460244 0.230122 0.973162i \(-0.426087\pi\)
0.230122 + 0.973162i \(0.426087\pi\)
\(488\) 11.6821 0.528825
\(489\) −0.474162 + 21.2227i −0.0214423 + 0.959724i
\(490\) 1.06006i 0.0478886i
\(491\) 28.9321i 1.30569i 0.757492 + 0.652844i \(0.226424\pi\)
−0.757492 + 0.652844i \(0.773576\pi\)
\(492\) −3.88964 0.0869031i −0.175359 0.00391790i
\(493\) 25.9936i 1.17069i
\(494\) 13.3787 0.601938
\(495\) 13.4994 + 0.603512i 0.606751 + 0.0271258i
\(496\) −9.92135 −0.445482
\(497\) 27.9588 1.25413
\(498\) −7.46432 0.166769i −0.334484 0.00747311i
\(499\) 5.77406 0.258482 0.129241 0.991613i \(-0.458746\pi\)
0.129241 + 0.991613i \(0.458746\pi\)
\(500\) 1.00000 0.0447214
\(501\) 37.3168 + 0.833738i 1.66719 + 0.0372487i
\(502\) 28.0442i 1.25168i
\(503\) 40.2622 1.79520 0.897601 0.440809i \(-0.145308\pi\)
0.897601 + 0.440809i \(0.145308\pi\)
\(504\) −8.50857 0.380390i −0.379002 0.0169439i
\(505\) 8.57100i 0.381404i
\(506\) −14.0603 16.3996i −0.625056 0.729049i
\(507\) −0.843325 + 37.7458i −0.0374534 + 1.67635i
\(508\) 13.8803 0.615839
\(509\) 38.6823i 1.71456i −0.514846 0.857282i \(-0.672151\pi\)
0.514846 0.857282i \(-0.327849\pi\)
\(510\) 9.35288 + 0.208964i 0.414152 + 0.00925307i
\(511\) 0.918773i 0.0406441i
\(512\) 1.00000i 0.0441942i
\(513\) −11.7583 0.789168i −0.519141 0.0348426i
\(514\) 10.1173 0.446256
\(515\) 7.45638i 0.328567i
\(516\) −20.0010 0.446866i −0.880495 0.0196722i
\(517\) 6.99233i 0.307522i
\(518\) 11.1467i 0.489757i
\(519\) −4.80098 0.107264i −0.210740 0.00470839i
\(520\) 5.89898i 0.258688i
\(521\) −18.5534 −0.812838 −0.406419 0.913687i \(-0.633223\pi\)
−0.406419 + 0.913687i \(0.633223\pi\)
\(522\) 14.4232 + 0.644813i 0.631286 + 0.0282227i
\(523\) 30.0881i 1.31566i −0.753166 0.657830i \(-0.771474\pi\)
0.753166 0.657830i \(-0.228526\pi\)
\(524\) 7.37577i 0.322212i
\(525\) 4.91611 + 0.109837i 0.214557 + 0.00479366i
\(526\) 27.9974i 1.22074i
\(527\) 53.5875 2.33431
\(528\) −0.174262 + 7.79970i −0.00758380 + 0.339438i
\(529\) 3.51204 22.7303i 0.152697 0.988273i
\(530\) 6.08832i 0.264460i
\(531\) 1.45426 32.5289i 0.0631096 1.41164i
\(532\) 6.43883 0.279159
\(533\) 13.2506i 0.573946i
\(534\) 20.1765 + 0.450786i 0.873120 + 0.0195074i
\(535\) 15.4707 0.668859
\(536\) −3.47626 −0.150152
\(537\) 10.0325 + 0.224148i 0.432934 + 0.00967270i
\(538\) 11.8305 0.510049
\(539\) −4.77480 −0.205665
\(540\) 0.347962 5.18449i 0.0149739 0.223105i
\(541\) −34.7417 −1.49366 −0.746831 0.665014i \(-0.768425\pi\)
−0.746831 + 0.665014i \(0.768425\pi\)
\(542\) 27.3595i 1.17519i
\(543\) 33.0415 + 0.738219i 1.41795 + 0.0316800i
\(544\) 5.40124i 0.231576i
\(545\) 11.6976i 0.501072i
\(546\) −0.647924 + 29.0000i −0.0277286 + 1.24109i
\(547\) 17.2491 0.737518 0.368759 0.929525i \(-0.379783\pi\)
0.368759 + 0.929525i \(0.379783\pi\)
\(548\) 1.02064 0.0435998
\(549\) −1.56525 + 35.0114i −0.0668031 + 1.49425i
\(550\) 4.50428i 0.192063i
\(551\) −10.9147 −0.464981
\(552\) −6.42538 + 5.26445i −0.273483 + 0.224070i
\(553\) −16.1791 −0.688005
\(554\) 17.9484i 0.762555i
\(555\) −6.79875 0.151899i −0.288591 0.00644775i
\(556\) 0.625898 0.0265440
\(557\) 31.7721 1.34623 0.673114 0.739539i \(-0.264957\pi\)
0.673114 + 0.739539i \(0.264957\pi\)
\(558\) 1.32932 29.7344i 0.0562748 1.25876i
\(559\) 68.1360i 2.88184i
\(560\) 2.83902i 0.119971i
\(561\) 0.941232 42.1280i 0.0397388 1.77865i
\(562\) 0.662441i 0.0279434i
\(563\) −1.96043 −0.0826222 −0.0413111 0.999146i \(-0.513153\pi\)
−0.0413111 + 0.999146i \(0.513153\pi\)
\(564\) 2.68812 + 0.0600584i 0.113190 + 0.00252892i
\(565\) −8.40341 −0.353534
\(566\) −25.7017 −1.08032
\(567\) 2.28006 25.4493i 0.0957537 1.06877i
\(568\) −9.84805 −0.413215
\(569\) 6.75996 0.283392 0.141696 0.989910i \(-0.454744\pi\)
0.141696 + 0.989910i \(0.454744\pi\)
\(570\) −0.0877437 + 3.92726i −0.00367518 + 0.164495i
\(571\) 28.8048i 1.20544i 0.797951 + 0.602722i \(0.205917\pi\)
−0.797951 + 0.602722i \(0.794083\pi\)
\(572\) 26.5707 1.11098
\(573\) −0.499164 + 22.3418i −0.0208529 + 0.933341i
\(574\) 6.37715i 0.266177i
\(575\) 3.64088 3.12154i 0.151835 0.130177i
\(576\) 2.99701 + 0.133986i 0.124875 + 0.00558276i
\(577\) 44.8855 1.86861 0.934303 0.356479i \(-0.116023\pi\)
0.934303 + 0.356479i \(0.116023\pi\)
\(578\) 12.1733i 0.506344i
\(579\) −0.0807749 + 3.61535i −0.00335689 + 0.150249i
\(580\) 4.81253i 0.199829i
\(581\) 12.2379i 0.507714i
\(582\) −0.317742 + 14.2216i −0.0131708 + 0.589505i
\(583\) −27.4235 −1.13577
\(584\) 0.323623i 0.0133916i
\(585\) −17.6793 0.790383i −0.730949 0.0326783i
\(586\) 19.4320i 0.802727i
\(587\) 2.23860i 0.0923968i 0.998932 + 0.0461984i \(0.0147106\pi\)
−0.998932 + 0.0461984i \(0.985289\pi\)
\(588\) −0.0410117 + 1.83562i −0.00169129 + 0.0756996i
\(589\) 22.5013i 0.927152i
\(590\) −10.8538 −0.446844
\(591\) 3.36213 + 0.0751174i 0.138300 + 0.00308992i
\(592\) 3.92624i 0.161367i
\(593\) 22.0150i 0.904048i 0.892006 + 0.452024i \(0.149298\pi\)
−0.892006 + 0.452024i \(0.850702\pi\)
\(594\) −23.3524 1.56732i −0.958161 0.0643078i
\(595\) 15.3342i 0.628642i
\(596\) 8.47908 0.347317
\(597\) 35.1340 + 0.784971i 1.43794 + 0.0321267i
\(598\) 18.4139 + 21.4775i 0.753000 + 0.878280i
\(599\) 5.53313i 0.226078i −0.993591 0.113039i \(-0.963942\pi\)
0.993591 0.113039i \(-0.0360584\pi\)
\(600\) −1.73162 0.0386882i −0.0706930 0.00157944i
\(601\) 10.0314 0.409190 0.204595 0.978847i \(-0.434412\pi\)
0.204595 + 0.978847i \(0.434412\pi\)
\(602\) 32.7920i 1.33650i
\(603\) 0.465771 10.4184i 0.0189677 0.424269i
\(604\) −23.4124 −0.952637
\(605\) −9.28856 −0.377634
\(606\) −0.331596 + 14.8417i −0.0134702 + 0.602903i
\(607\) 13.3385 0.541392 0.270696 0.962665i \(-0.412746\pi\)
0.270696 + 0.962665i \(0.412746\pi\)
\(608\) −2.26797 −0.0919784
\(609\) 0.528592 23.6589i 0.0214196 0.958708i
\(610\) 11.6821 0.472996
\(611\) 9.15742i 0.370470i
\(612\) −16.1875 0.723691i −0.654342 0.0292535i
\(613\) 4.93121i 0.199170i −0.995029 0.0995849i \(-0.968249\pi\)
0.995029 0.0995849i \(-0.0317515\pi\)
\(614\) 1.65943i 0.0669692i
\(615\) −3.88964 0.0869031i −0.156846 0.00350427i
\(616\) 12.7878 0.515234
\(617\) −40.0242 −1.61131 −0.805657 0.592383i \(-0.798187\pi\)
−0.805657 + 0.592383i \(0.798187\pi\)
\(618\) −0.288474 + 12.9116i −0.0116041 + 0.519381i
\(619\) 10.5263i 0.423088i −0.977368 0.211544i \(-0.932151\pi\)
0.977368 0.211544i \(-0.0678492\pi\)
\(620\) −9.92135 −0.398451
\(621\) −14.9167 19.9623i −0.598586 0.801059i
\(622\) 12.5570 0.503491
\(623\) 33.0797i 1.32531i
\(624\) 0.228221 10.2148i 0.00913614 0.408919i
\(625\) 1.00000 0.0400000
\(626\) −13.5424 −0.541261
\(627\) 17.6895 + 0.395222i 0.706451 + 0.0157837i
\(628\) 0.880316i 0.0351284i
\(629\) 21.2065i 0.845560i
\(630\) −8.50857 0.380390i −0.338990 0.0151551i
\(631\) 14.8373i 0.590665i −0.955395 0.295333i \(-0.904570\pi\)
0.955395 0.295333i \(-0.0954304\pi\)
\(632\) 5.69882 0.226687
\(633\) 0.348164 15.5832i 0.0138383 0.619378i
\(634\) −11.1266 −0.441896
\(635\) 13.8803 0.550823
\(636\) −0.235546 + 10.5426i −0.00934000 + 0.418043i
\(637\) 6.25327 0.247763
\(638\) −21.6770 −0.858201
\(639\) 1.31950 29.5147i 0.0521987 1.16758i
\(640\) 1.00000i 0.0395285i
\(641\) 27.3936 1.08198 0.540992 0.841028i \(-0.318049\pi\)
0.540992 + 0.841028i \(0.318049\pi\)
\(642\) −26.7894 0.598535i −1.05729 0.0236223i
\(643\) 9.23957i 0.364373i −0.983264 0.182187i \(-0.941683\pi\)
0.983264 0.182187i \(-0.0583175\pi\)
\(644\) 8.86211 + 10.3366i 0.349216 + 0.407317i
\(645\) −20.0010 0.446866i −0.787538 0.0175953i
\(646\) 12.2499 0.481964
\(647\) 26.5662i 1.04443i 0.852815 + 0.522213i \(0.174893\pi\)
−0.852815 + 0.522213i \(0.825107\pi\)
\(648\) −0.803115 + 8.96410i −0.0315494 + 0.352143i
\(649\) 48.8886i 1.91905i
\(650\) 5.89898i 0.231377i
\(651\) −48.7744 1.08973i −1.91162 0.0427098i
\(652\) −12.2560 −0.479982
\(653\) 40.1114i 1.56968i 0.619699 + 0.784840i \(0.287255\pi\)
−0.619699 + 0.784840i \(0.712745\pi\)
\(654\) −0.452560 + 20.2558i −0.0176965 + 0.792066i
\(655\) 7.37577i 0.288195i
\(656\) 2.24625i 0.0877012i
\(657\) −0.969899 0.0433610i −0.0378394 0.00169167i
\(658\) 4.40722i 0.171811i
\(659\) −18.0278 −0.702263 −0.351132 0.936326i \(-0.614203\pi\)
−0.351132 + 0.936326i \(0.614203\pi\)
\(660\) −0.174262 + 7.79970i −0.00678315 + 0.303603i
\(661\) 44.4660i 1.72953i −0.502179 0.864764i \(-0.667468\pi\)
0.502179 0.864764i \(-0.332532\pi\)
\(662\) 5.37160i 0.208773i
\(663\) −1.23267 + 55.1725i −0.0478731 + 2.14272i
\(664\) 4.31060i 0.167284i
\(665\) 6.43883 0.249687
\(666\) 11.7670 + 0.526062i 0.455961 + 0.0203845i
\(667\) −15.0225 17.5219i −0.581673 0.678449i
\(668\) 21.5502i 0.833803i
\(669\) −0.538508 + 24.1028i −0.0208199 + 0.931866i
\(670\) −3.47626 −0.134300
\(671\) 52.6196i 2.03136i
\(672\) 0.109837 4.91611i 0.00423704 0.189643i
\(673\) −5.30845 −0.204626 −0.102313 0.994752i \(-0.532624\pi\)
−0.102313 + 0.994752i \(0.532624\pi\)
\(674\) −17.9318 −0.690708
\(675\) 0.347962 5.18449i 0.0133931 0.199551i
\(676\) −21.7980 −0.838385
\(677\) −16.8563 −0.647842 −0.323921 0.946084i \(-0.605001\pi\)
−0.323921 + 0.946084i \(0.605001\pi\)
\(678\) 14.5515 + 0.325113i 0.558847 + 0.0124859i
\(679\) 23.3166 0.894810
\(680\) 5.40124i 0.207128i
\(681\) 0.445007 19.9178i 0.0170527 0.763252i
\(682\) 44.6886i 1.71121i
\(683\) 10.9720i 0.419833i −0.977719 0.209916i \(-0.932681\pi\)
0.977719 0.209916i \(-0.0673192\pi\)
\(684\) 0.303877 6.79713i 0.0116190 0.259895i
\(685\) 1.02064 0.0389968
\(686\) −16.8636 −0.643857
\(687\) 25.8058 + 0.576557i 0.984551 + 0.0219970i
\(688\) 11.5505i 0.440357i
\(689\) 35.9149 1.36825
\(690\) −6.42538 + 5.26445i −0.244610 + 0.200414i
\(691\) 10.3095 0.392190 0.196095 0.980585i \(-0.437174\pi\)
0.196095 + 0.980585i \(0.437174\pi\)
\(692\) 2.77254i 0.105396i
\(693\) −1.71339 + 38.3250i −0.0650861 + 1.45585i
\(694\) 9.99097 0.379252
\(695\) 0.625898 0.0237417
\(696\) −0.186188 + 8.33347i −0.00705744 + 0.315879i
\(697\) 12.1325i 0.459551i
\(698\) 15.3124i 0.579585i
\(699\) 6.48402 + 0.144867i 0.245248 + 0.00547938i
\(700\) 2.83902i 0.107305i
\(701\) 10.9168 0.412323 0.206162 0.978518i \(-0.433903\pi\)
0.206162 + 0.978518i \(0.433903\pi\)
\(702\) 30.5832 + 2.05262i 1.15429 + 0.0774712i
\(703\) −8.90460 −0.335843
\(704\) −4.50428 −0.169762
\(705\) 2.68812 + 0.0600584i 0.101240 + 0.00226193i
\(706\) −8.49859 −0.319849
\(707\) 24.3333 0.915147
\(708\) 18.7947 + 0.419914i 0.706347 + 0.0157813i
\(709\) 17.8897i 0.671863i −0.941886 0.335932i \(-0.890949\pi\)
0.941886 0.335932i \(-0.109051\pi\)
\(710\) −9.84805 −0.369591
\(711\) −0.763564 + 17.0794i −0.0286359 + 0.640528i
\(712\) 11.6518i 0.436669i
\(713\) −36.1225 + 30.9698i −1.35280 + 1.15983i
\(714\) −0.593253 + 26.5531i −0.0222019 + 0.993723i
\(715\) 26.5707 0.993687
\(716\) 5.79371i 0.216521i
\(717\) 40.3363 + 0.901201i 1.50639 + 0.0336560i
\(718\) 23.5828i 0.880103i
\(719\) 11.7246i 0.437252i −0.975809 0.218626i \(-0.929843\pi\)
0.975809 0.218626i \(-0.0701575\pi\)
\(720\) 2.99701 + 0.133986i 0.111692 + 0.00499337i
\(721\) 21.1689 0.788369
\(722\) 13.8563i 0.515678i
\(723\) −50.8711 1.13657i −1.89192 0.0422696i
\(724\) 19.0813i 0.709150i
\(725\) 4.81253i 0.178733i
\(726\) 16.0842 + 0.359357i 0.596942 + 0.0133370i
\(727\) 17.9754i 0.666670i −0.942809 0.333335i \(-0.891826\pi\)
0.942809 0.333335i \(-0.108174\pi\)
\(728\) −16.7474 −0.620698
\(729\) −26.7578 3.60801i −0.991031 0.133630i
\(730\) 0.323623i 0.0119778i
\(731\) 62.3867i 2.30746i
\(732\) −20.2290 0.451960i −0.747686 0.0167049i
\(733\) 2.11900i 0.0782669i 0.999234 + 0.0391335i \(0.0124597\pi\)
−0.999234 + 0.0391335i \(0.987540\pi\)
\(734\) 34.0961 1.25851
\(735\) −0.0410117 + 1.83562i −0.00151274 + 0.0677078i
\(736\) −3.12154 3.64088i −0.115061 0.134205i
\(737\) 15.6581i 0.576772i
\(738\) 6.73201 + 0.300966i 0.247809 + 0.0110787i
\(739\) −9.43652 −0.347128 −0.173564 0.984823i \(-0.555528\pi\)
−0.173564 + 0.984823i \(0.555528\pi\)
\(740\) 3.92624i 0.144331i
\(741\) −23.1669 0.517599i −0.851056 0.0190145i
\(742\) 17.2849 0.634548
\(743\) 23.0507 0.845649 0.422825 0.906212i \(-0.361039\pi\)
0.422825 + 0.906212i \(0.361039\pi\)
\(744\) 17.1800 + 0.383839i 0.629849 + 0.0140722i
\(745\) 8.47908 0.310649
\(746\) −3.12850 −0.114543
\(747\) 12.9189 + 0.577562i 0.472678 + 0.0211319i
\(748\) 24.3287 0.889545
\(749\) 43.9218i 1.60487i
\(750\) −1.73162 0.0386882i −0.0632298 0.00141269i
\(751\) 7.57725i 0.276498i 0.990398 + 0.138249i \(0.0441474\pi\)
−0.990398 + 0.138249i \(0.955853\pi\)
\(752\) 1.55237i 0.0566092i
\(753\) −1.08498 + 48.5619i −0.0395389 + 1.76969i
\(754\) 28.3890 1.03387
\(755\) −23.4124 −0.852064
\(756\) 14.7189 + 0.987872i 0.535321 + 0.0359286i
\(757\) 20.5957i 0.748562i 0.927315 + 0.374281i \(0.122110\pi\)
−0.927315 + 0.374281i \(0.877890\pi\)
\(758\) 0.796283 0.0289223
\(759\) 23.7126 + 28.9417i 0.860712 + 1.05052i
\(760\) −2.26797 −0.0822680
\(761\) 34.2533i 1.24168i −0.783937 0.620840i \(-0.786792\pi\)
0.783937 0.620840i \(-0.213208\pi\)
\(762\) −24.0354 0.537004i −0.870711 0.0194536i
\(763\) 33.2099 1.20228
\(764\) −12.9022 −0.466787
\(765\) −16.1875 0.723691i −0.585262 0.0261651i
\(766\) 11.8370i 0.427688i
\(767\) 64.0265i 2.31186i
\(768\) −0.0386882 + 1.73162i −0.00139604 + 0.0624844i
\(769\) 29.2604i 1.05516i −0.849506 0.527579i \(-0.823100\pi\)
0.849506 0.527579i \(-0.176900\pi\)
\(770\) 12.7878 0.460839
\(771\) −17.5194 0.391421i −0.630944 0.0140967i
\(772\) −2.08785 −0.0751432
\(773\) −9.29477 −0.334310 −0.167155 0.985931i \(-0.553458\pi\)
−0.167155 + 0.985931i \(0.553458\pi\)
\(774\) 34.6168 + 1.54760i 1.24428 + 0.0556274i
\(775\) −9.92135 −0.356385
\(776\) −8.21290 −0.294826
\(777\) 0.431245 19.3018i 0.0154708 0.692449i
\(778\) 0.884618i 0.0317151i
\(779\) −5.09443 −0.182527
\(780\) 0.228221 10.2148i 0.00817162 0.365748i
\(781\) 44.3584i 1.58727i
\(782\) 16.8601 + 19.6653i 0.602918 + 0.703228i
\(783\) −24.9505 1.67458i −0.891659 0.0598445i
\(784\) −1.06006