Properties

Label 370.2.c.a.369.7
Level $370$
Weight $2$
Character 370.369
Analytic conductor $2.954$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 19 x^{8} + 103 x^{6} + 210 x^{4} + 140 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.7
Root \(0.987983i\) of defining polynomial
Character \(\chi\) \(=\) 370.369
Dual form 370.2.c.a.369.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.987983i q^{3} +1.00000 q^{4} +(-1.85396 + 1.25013i) q^{5} -0.987983i q^{6} -4.78937i q^{7} -1.00000 q^{8} +2.02389 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.987983i q^{3} +1.00000 q^{4} +(-1.85396 + 1.25013i) q^{5} -0.987983i q^{6} -4.78937i q^{7} -1.00000 q^{8} +2.02389 q^{9} +(1.85396 - 1.25013i) q^{10} -5.98732 q^{11} +0.987983i q^{12} -3.49410 q^{13} +4.78937i q^{14} +(-1.23510 - 1.83168i) q^{15} +1.00000 q^{16} +4.96343 q^{17} -2.02389 q^{18} -7.33092i q^{19} +(-1.85396 + 1.25013i) q^{20} +4.73182 q^{21} +5.98732 q^{22} -1.74873 q^{23} -0.987983i q^{24} +(1.87436 - 4.63538i) q^{25} +3.49410 q^{26} +4.96352i q^{27} -4.78937i q^{28} -7.85004i q^{29} +(1.23510 + 1.83168i) q^{30} -3.24097i q^{31} -1.00000 q^{32} -5.91537i q^{33} -4.96343 q^{34} +(5.98732 + 8.87932i) q^{35} +2.02389 q^{36} +(-3.96343 + 4.61424i) q^{37} +7.33092i q^{38} -3.45211i q^{39} +(1.85396 - 1.25013i) q^{40} -0.530665 q^{41} -4.73182 q^{42} +1.76838 q^{43} -5.98732 q^{44} +(-3.75222 + 2.53012i) q^{45} +1.74873 q^{46} -4.30638i q^{47} +0.987983i q^{48} -15.9381 q^{49} +(-1.87436 + 4.63538i) q^{50} +4.90379i q^{51} -3.49410 q^{52} -3.66238i q^{53} -4.96352i q^{54} +(11.1003 - 7.48491i) q^{55} +4.78937i q^{56} +7.24283 q^{57} +7.85004i q^{58} +2.15110i q^{59} +(-1.23510 - 1.83168i) q^{60} +3.06584i q^{61} +3.24097i q^{62} -9.69316i q^{63} +1.00000 q^{64} +(6.47793 - 4.36807i) q^{65} +5.91537i q^{66} -3.79622i q^{67} +4.96343 q^{68} -1.72772i q^{69} +(-5.98732 - 8.87932i) q^{70} -8.47719 q^{71} -2.02389 q^{72} +9.05445i q^{73} +(3.96343 - 4.61424i) q^{74} +(4.57968 + 1.85184i) q^{75} -7.33092i q^{76} +28.6755i q^{77} +3.45211i q^{78} +5.56622i q^{79} +(-1.85396 + 1.25013i) q^{80} +1.16780 q^{81} +0.530665 q^{82} -3.77680i q^{83} +4.73182 q^{84} +(-9.20203 + 6.20492i) q^{85} -1.76838 q^{86} +7.75571 q^{87} +5.98732 q^{88} +8.45791i q^{89} +(3.75222 - 2.53012i) q^{90} +16.7345i q^{91} -1.74873 q^{92} +3.20203 q^{93} +4.30638i q^{94} +(9.16459 + 13.5913i) q^{95} -0.987983i q^{96} +3.64747 q^{97} +15.9381 q^{98} -12.1177 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + 3q^{10} - 2q^{13} - 10q^{15} + 10q^{16} + 18q^{17} + 8q^{18} - 3q^{20} - 12q^{21} + 10q^{23} + 5q^{25} + 2q^{26} + 10q^{30} - 10q^{32} - 18q^{34} - 8q^{36} - 8q^{37} + 3q^{40} - 4q^{41} + 12q^{42} - 10q^{43} + 20q^{45} - 10q^{46} - 8q^{49} - 5q^{50} - 2q^{52} + 5q^{55} + 12q^{57} - 10q^{60} + 10q^{64} + 2q^{65} + 18q^{68} - 20q^{71} + 8q^{72} + 8q^{74} + 25q^{75} - 3q^{80} + 58q^{81} + 4q^{82} - 12q^{84} - 28q^{85} + 10q^{86} - 10q^{87} - 20q^{90} + 10q^{92} - 32q^{93} + 2q^{95} + 2q^{97} + 8q^{98} - 82q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.987983i 0.570412i 0.958466 + 0.285206i \(0.0920621\pi\)
−0.958466 + 0.285206i \(0.907938\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.85396 + 1.25013i −0.829118 + 0.559074i
\(6\) 0.987983i 0.403342i
\(7\) 4.78937i 1.81021i −0.425186 0.905106i \(-0.639791\pi\)
0.425186 0.905106i \(-0.360209\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.02389 0.674630
\(10\) 1.85396 1.25013i 0.586275 0.395325i
\(11\) −5.98732 −1.80525 −0.902623 0.430432i \(-0.858361\pi\)
−0.902623 + 0.430432i \(0.858361\pi\)
\(12\) 0.987983i 0.285206i
\(13\) −3.49410 −0.969088 −0.484544 0.874767i \(-0.661015\pi\)
−0.484544 + 0.874767i \(0.661015\pi\)
\(14\) 4.78937i 1.28001i
\(15\) −1.23510 1.83168i −0.318903 0.472939i
\(16\) 1.00000 0.250000
\(17\) 4.96343 1.20381 0.601905 0.798568i \(-0.294409\pi\)
0.601905 + 0.798568i \(0.294409\pi\)
\(18\) −2.02389 −0.477035
\(19\) 7.33092i 1.68183i −0.541168 0.840915i \(-0.682018\pi\)
0.541168 0.840915i \(-0.317982\pi\)
\(20\) −1.85396 + 1.25013i −0.414559 + 0.279537i
\(21\) 4.73182 1.03257
\(22\) 5.98732 1.27650
\(23\) −1.74873 −0.364635 −0.182318 0.983240i \(-0.558360\pi\)
−0.182318 + 0.983240i \(0.558360\pi\)
\(24\) 0.987983i 0.201671i
\(25\) 1.87436 4.63538i 0.374873 0.927076i
\(26\) 3.49410 0.685249
\(27\) 4.96352i 0.955229i
\(28\) 4.78937i 0.905106i
\(29\) 7.85004i 1.45772i −0.684665 0.728858i \(-0.740051\pi\)
0.684665 0.728858i \(-0.259949\pi\)
\(30\) 1.23510 + 1.83168i 0.225498 + 0.334418i
\(31\) 3.24097i 0.582096i −0.956708 0.291048i \(-0.905996\pi\)
0.956708 0.291048i \(-0.0940039\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.91537i 1.02973i
\(34\) −4.96343 −0.851222
\(35\) 5.98732 + 8.87932i 1.01204 + 1.50088i
\(36\) 2.02389 0.337315
\(37\) −3.96343 + 4.61424i −0.651584 + 0.758576i
\(38\) 7.33092i 1.18923i
\(39\) 3.45211i 0.552780i
\(40\) 1.85396 1.25013i 0.293137 0.197662i
\(41\) −0.530665 −0.0828760 −0.0414380 0.999141i \(-0.513194\pi\)
−0.0414380 + 0.999141i \(0.513194\pi\)
\(42\) −4.73182 −0.730135
\(43\) 1.76838 0.269676 0.134838 0.990868i \(-0.456949\pi\)
0.134838 + 0.990868i \(0.456949\pi\)
\(44\) −5.98732 −0.902623
\(45\) −3.75222 + 2.53012i −0.559348 + 0.377168i
\(46\) 1.74873 0.257836
\(47\) 4.30638i 0.628150i −0.949398 0.314075i \(-0.898306\pi\)
0.949398 0.314075i \(-0.101694\pi\)
\(48\) 0.987983i 0.142603i
\(49\) −15.9381 −2.27687
\(50\) −1.87436 + 4.63538i −0.265075 + 0.655542i
\(51\) 4.90379i 0.686668i
\(52\) −3.49410 −0.484544
\(53\) 3.66238i 0.503067i −0.967849 0.251534i \(-0.919065\pi\)
0.967849 0.251534i \(-0.0809349\pi\)
\(54\) 4.96352i 0.675449i
\(55\) 11.1003 7.48491i 1.49676 1.00927i
\(56\) 4.78937i 0.640007i
\(57\) 7.24283 0.959336
\(58\) 7.85004i 1.03076i
\(59\) 2.15110i 0.280049i 0.990148 + 0.140025i \(0.0447182\pi\)
−0.990148 + 0.140025i \(0.955282\pi\)
\(60\) −1.23510 1.83168i −0.159451 0.236470i
\(61\) 3.06584i 0.392541i 0.980550 + 0.196270i \(0.0628830\pi\)
−0.980550 + 0.196270i \(0.937117\pi\)
\(62\) 3.24097i 0.411604i
\(63\) 9.69316i 1.22122i
\(64\) 1.00000 0.125000
\(65\) 6.47793 4.36807i 0.803489 0.541792i
\(66\) 5.91537i 0.728132i
\(67\) 3.79622i 0.463782i −0.972742 0.231891i \(-0.925509\pi\)
0.972742 0.231891i \(-0.0744912\pi\)
\(68\) 4.96343 0.601905
\(69\) 1.72772i 0.207992i
\(70\) −5.98732 8.87932i −0.715622 1.06128i
\(71\) −8.47719 −1.00606 −0.503028 0.864270i \(-0.667781\pi\)
−0.503028 + 0.864270i \(0.667781\pi\)
\(72\) −2.02389 −0.238518
\(73\) 9.05445i 1.05974i 0.848078 + 0.529872i \(0.177760\pi\)
−0.848078 + 0.529872i \(0.822240\pi\)
\(74\) 3.96343 4.61424i 0.460740 0.536394i
\(75\) 4.57968 + 1.85184i 0.528816 + 0.213832i
\(76\) 7.33092i 0.840915i
\(77\) 28.6755i 3.26788i
\(78\) 3.45211i 0.390874i
\(79\) 5.56622i 0.626248i 0.949712 + 0.313124i \(0.101376\pi\)
−0.949712 + 0.313124i \(0.898624\pi\)
\(80\) −1.85396 + 1.25013i −0.207279 + 0.139768i
\(81\) 1.16780 0.129755
\(82\) 0.530665 0.0586022
\(83\) 3.77680i 0.414558i −0.978282 0.207279i \(-0.933539\pi\)
0.978282 0.207279i \(-0.0664607\pi\)
\(84\) 4.73182 0.516284
\(85\) −9.20203 + 6.20492i −0.998100 + 0.673018i
\(86\) −1.76838 −0.190690
\(87\) 7.75571 0.831499
\(88\) 5.98732 0.638251
\(89\) 8.45791i 0.896537i 0.893899 + 0.448268i \(0.147959\pi\)
−0.893899 + 0.448268i \(0.852041\pi\)
\(90\) 3.75222 2.53012i 0.395519 0.266698i
\(91\) 16.7345i 1.75426i
\(92\) −1.74873 −0.182318
\(93\) 3.20203 0.332035
\(94\) 4.30638i 0.444169i
\(95\) 9.16459 + 13.5913i 0.940267 + 1.39443i
\(96\) 0.987983i 0.100836i
\(97\) 3.64747 0.370345 0.185172 0.982706i \(-0.440716\pi\)
0.185172 + 0.982706i \(0.440716\pi\)
\(98\) 15.9381 1.60999
\(99\) −12.1177 −1.21787
\(100\) 1.87436 4.63538i 0.187436 0.463538i
\(101\) 2.30416 0.229272 0.114636 0.993408i \(-0.463430\pi\)
0.114636 + 0.993408i \(0.463430\pi\)
\(102\) 4.90379i 0.485547i
\(103\) −11.1716 −1.10077 −0.550383 0.834912i \(-0.685518\pi\)
−0.550383 + 0.834912i \(0.685518\pi\)
\(104\) 3.49410 0.342625
\(105\) −8.77262 + 5.91537i −0.856120 + 0.577281i
\(106\) 3.66238i 0.355722i
\(107\) 6.51807i 0.630126i 0.949071 + 0.315063i \(0.102026\pi\)
−0.949071 + 0.315063i \(0.897974\pi\)
\(108\) 4.96352i 0.477615i
\(109\) 1.33812i 0.128169i 0.997944 + 0.0640846i \(0.0204127\pi\)
−0.997944 + 0.0640846i \(0.979587\pi\)
\(110\) −11.1003 + 7.48491i −1.05837 + 0.713659i
\(111\) −4.55879 3.91580i −0.432701 0.371672i
\(112\) 4.78937i 0.452553i
\(113\) −1.39109 −0.130863 −0.0654315 0.997857i \(-0.520842\pi\)
−0.0654315 + 0.997857i \(0.520842\pi\)
\(114\) −7.24283 −0.678353
\(115\) 3.24208 2.18613i 0.302326 0.203858i
\(116\) 7.85004i 0.728858i
\(117\) −7.07167 −0.653776
\(118\) 2.15110i 0.198025i
\(119\) 23.7717i 2.17915i
\(120\) 1.23510 + 1.83168i 0.112749 + 0.167209i
\(121\) 24.8480 2.25891
\(122\) 3.06584i 0.277568i
\(123\) 0.524288i 0.0472735i
\(124\) 3.24097i 0.291048i
\(125\) 2.31981 + 10.9370i 0.207490 + 0.978237i
\(126\) 9.69316i 0.863535i
\(127\) 7.51024i 0.666426i −0.942852 0.333213i \(-0.891867\pi\)
0.942852 0.333213i \(-0.108133\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.74713i 0.153827i
\(130\) −6.47793 + 4.36807i −0.568152 + 0.383105i
\(131\) 6.19975i 0.541675i −0.962625 0.270837i \(-0.912699\pi\)
0.962625 0.270837i \(-0.0873006\pi\)
\(132\) 5.91537i 0.514867i
\(133\) −35.1105 −3.04447
\(134\) 3.79622i 0.327943i
\(135\) −6.20503 9.20218i −0.534044 0.791998i
\(136\) −4.96343 −0.425611
\(137\) 8.97186i 0.766518i −0.923641 0.383259i \(-0.874802\pi\)
0.923641 0.383259i \(-0.125198\pi\)
\(138\) 1.72772i 0.147073i
\(139\) 5.04168 0.427629 0.213815 0.976874i \(-0.431411\pi\)
0.213815 + 0.976874i \(0.431411\pi\)
\(140\) 5.98732 + 8.87932i 0.506021 + 0.750440i
\(141\) 4.25463 0.358305
\(142\) 8.47719 0.711390
\(143\) 20.9203 1.74944
\(144\) 2.02389 0.168657
\(145\) 9.81355 + 14.5537i 0.814971 + 1.20862i
\(146\) 9.05445i 0.749352i
\(147\) 15.7466i 1.29875i
\(148\) −3.96343 + 4.61424i −0.325792 + 0.379288i
\(149\) −21.6451 −1.77324 −0.886619 0.462500i \(-0.846952\pi\)
−0.886619 + 0.462500i \(0.846952\pi\)
\(150\) −4.57968 1.85184i −0.373929 0.151202i
\(151\) 6.47544 0.526964 0.263482 0.964664i \(-0.415129\pi\)
0.263482 + 0.964664i \(0.415129\pi\)
\(152\) 7.33092i 0.594616i
\(153\) 10.0454 0.812126
\(154\) 28.6755i 2.31074i
\(155\) 4.05163 + 6.00865i 0.325435 + 0.482626i
\(156\) 3.45211i 0.276390i
\(157\) 13.1689i 1.05099i −0.850797 0.525495i \(-0.823880\pi\)
0.850797 0.525495i \(-0.176120\pi\)
\(158\) 5.56622i 0.442825i
\(159\) 3.61837 0.286956
\(160\) 1.85396 1.25013i 0.146569 0.0988312i
\(161\) 8.37532i 0.660067i
\(162\) −1.16780 −0.0917509
\(163\) 18.7651 1.46979 0.734896 0.678180i \(-0.237231\pi\)
0.734896 + 0.678180i \(0.237231\pi\)
\(164\) −0.530665 −0.0414380
\(165\) 7.39497 + 10.9669i 0.575697 + 0.853771i
\(166\) 3.77680i 0.293136i
\(167\) 7.19692 0.556914 0.278457 0.960449i \(-0.410177\pi\)
0.278457 + 0.960449i \(0.410177\pi\)
\(168\) −4.73182 −0.365068
\(169\) −0.791278 −0.0608676
\(170\) 9.20203 6.20492i 0.705763 0.475896i
\(171\) 14.8370i 1.13461i
\(172\) 1.76838 0.134838
\(173\) 9.79406i 0.744629i −0.928107 0.372314i \(-0.878564\pi\)
0.928107 0.372314i \(-0.121436\pi\)
\(174\) −7.75571 −0.587959
\(175\) −22.2006 8.97703i −1.67820 0.678600i
\(176\) −5.98732 −0.451311
\(177\) −2.12525 −0.159743
\(178\) 8.45791i 0.633947i
\(179\) 11.2829i 0.843320i −0.906754 0.421660i \(-0.861448\pi\)
0.906754 0.421660i \(-0.138552\pi\)
\(180\) −3.75222 + 2.53012i −0.279674 + 0.188584i
\(181\) 1.82697 0.135798 0.0678989 0.997692i \(-0.478370\pi\)
0.0678989 + 0.997692i \(0.478370\pi\)
\(182\) 16.7345i 1.24045i
\(183\) −3.02900 −0.223910
\(184\) 1.74873 0.128918
\(185\) 1.57968 13.5094i 0.116140 0.993233i
\(186\) −3.20203 −0.234784
\(187\) −29.7177 −2.17317
\(188\) 4.30638i 0.314075i
\(189\) 23.7721 1.72917
\(190\) −9.16459 13.5913i −0.664869 0.986014i
\(191\) 23.8204i 1.72358i 0.507264 + 0.861791i \(0.330657\pi\)
−0.507264 + 0.861791i \(0.669343\pi\)
\(192\) 0.987983i 0.0713015i
\(193\) 8.40405 0.604937 0.302468 0.953159i \(-0.402189\pi\)
0.302468 + 0.953159i \(0.402189\pi\)
\(194\) −3.64747 −0.261873
\(195\) 4.31558 + 6.40009i 0.309045 + 0.458320i
\(196\) −15.9381 −1.13843
\(197\) 4.22797i 0.301230i 0.988592 + 0.150615i \(0.0481254\pi\)
−0.988592 + 0.150615i \(0.951875\pi\)
\(198\) 12.1177 0.861166
\(199\) 17.7545i 1.25858i −0.777170 0.629290i \(-0.783346\pi\)
0.777170 0.629290i \(-0.216654\pi\)
\(200\) −1.87436 + 4.63538i −0.132538 + 0.327771i
\(201\) 3.75060 0.264547
\(202\) −2.30416 −0.162120
\(203\) −37.5968 −2.63878
\(204\) 4.90379i 0.343334i
\(205\) 0.983834 0.663399i 0.0687139 0.0463338i
\(206\) 11.1716 0.778360
\(207\) −3.53924 −0.245994
\(208\) −3.49410 −0.242272
\(209\) 43.8926i 3.03611i
\(210\) 8.77262 5.91537i 0.605368 0.408200i
\(211\) 4.57321 0.314833 0.157417 0.987532i \(-0.449683\pi\)
0.157417 + 0.987532i \(0.449683\pi\)
\(212\) 3.66238i 0.251534i
\(213\) 8.37532i 0.573867i
\(214\) 6.51807i 0.445566i
\(215\) −3.27852 + 2.21071i −0.223593 + 0.150769i
\(216\) 4.96352i 0.337725i
\(217\) −15.5222 −1.05372
\(218\) 1.33812i 0.0906293i
\(219\) −8.94565 −0.604491
\(220\) 11.1003 7.48491i 0.748381 0.504633i
\(221\) −17.3427 −1.16660
\(222\) 4.55879 + 3.91580i 0.305966 + 0.262812i
\(223\) 20.3205i 1.36076i −0.732860 0.680380i \(-0.761815\pi\)
0.732860 0.680380i \(-0.238185\pi\)
\(224\) 4.78937i 0.320003i
\(225\) 3.79351 9.38150i 0.252900 0.625433i
\(226\) 1.39109 0.0925341
\(227\) −5.74303 −0.381178 −0.190589 0.981670i \(-0.561040\pi\)
−0.190589 + 0.981670i \(0.561040\pi\)
\(228\) 7.24283 0.479668
\(229\) 23.4383 1.54885 0.774423 0.632669i \(-0.218040\pi\)
0.774423 + 0.632669i \(0.218040\pi\)
\(230\) −3.24208 + 2.18613i −0.213777 + 0.144149i
\(231\) −28.3309 −1.86404
\(232\) 7.85004i 0.515380i
\(233\) 17.2961i 1.13310i 0.824027 + 0.566551i \(0.191723\pi\)
−0.824027 + 0.566551i \(0.808277\pi\)
\(234\) 7.07167 0.462289
\(235\) 5.38352 + 7.98388i 0.351182 + 0.520811i
\(236\) 2.15110i 0.140025i
\(237\) −5.49933 −0.357220
\(238\) 23.7717i 1.54089i
\(239\) 3.68796i 0.238554i −0.992861 0.119277i \(-0.961942\pi\)
0.992861 0.119277i \(-0.0380577\pi\)
\(240\) −1.23510 1.83168i −0.0797256 0.118235i
\(241\) 11.3613i 0.731844i −0.930646 0.365922i \(-0.880754\pi\)
0.930646 0.365922i \(-0.119246\pi\)
\(242\) −24.8480 −1.59729
\(243\) 16.0443i 1.02924i
\(244\) 3.06584i 0.196270i
\(245\) 29.5486 19.9246i 1.88779 1.27294i
\(246\) 0.524288i 0.0334274i
\(247\) 25.6150i 1.62984i
\(248\) 3.24097i 0.205802i
\(249\) 3.73141 0.236469
\(250\) −2.31981 10.9370i −0.146718 0.691718i
\(251\) 12.8260i 0.809567i −0.914412 0.404784i \(-0.867347\pi\)
0.914412 0.404784i \(-0.132653\pi\)
\(252\) 9.69316i 0.610612i
\(253\) 10.4702 0.658256
\(254\) 7.51024i 0.471234i
\(255\) −6.13036 9.09145i −0.383898 0.569328i
\(256\) 1.00000 0.0625000
\(257\) 14.0268 0.874965 0.437483 0.899227i \(-0.355870\pi\)
0.437483 + 0.899227i \(0.355870\pi\)
\(258\) 1.74713i 0.108772i
\(259\) 22.0993 + 18.9824i 1.37318 + 1.17951i
\(260\) 6.47793 4.36807i 0.401744 0.270896i
\(261\) 15.8876i 0.983419i
\(262\) 6.19975i 0.383022i
\(263\) 3.57182i 0.220248i −0.993918 0.110124i \(-0.964875\pi\)
0.993918 0.110124i \(-0.0351248\pi\)
\(264\) 5.91537i 0.364066i
\(265\) 4.57844 + 6.78993i 0.281252 + 0.417102i
\(266\) 35.1105 2.15276
\(267\) −8.35627 −0.511396
\(268\) 3.79622i 0.231891i
\(269\) −0.458895 −0.0279793 −0.0139897 0.999902i \(-0.504453\pi\)
−0.0139897 + 0.999902i \(0.504453\pi\)
\(270\) 6.20503 + 9.20218i 0.377626 + 0.560027i
\(271\) 28.8897 1.75492 0.877462 0.479645i \(-0.159235\pi\)
0.877462 + 0.479645i \(0.159235\pi\)
\(272\) 4.96343 0.300952
\(273\) −16.5334 −1.00065
\(274\) 8.97186i 0.542010i
\(275\) −11.2224 + 27.7535i −0.676738 + 1.67360i
\(276\) 1.72772i 0.103996i
\(277\) 22.4482 1.34878 0.674391 0.738374i \(-0.264406\pi\)
0.674391 + 0.738374i \(0.264406\pi\)
\(278\) −5.04168 −0.302380
\(279\) 6.55937i 0.392699i
\(280\) −5.98732 8.87932i −0.357811 0.530641i
\(281\) 6.04908i 0.360858i −0.983588 0.180429i \(-0.942251\pi\)
0.983588 0.180429i \(-0.0577486\pi\)
\(282\) −4.25463 −0.253360
\(283\) 10.8317 0.643878 0.321939 0.946760i \(-0.395665\pi\)
0.321939 + 0.946760i \(0.395665\pi\)
\(284\) −8.47719 −0.503028
\(285\) −13.4279 + 9.05445i −0.795403 + 0.536340i
\(286\) −20.9203 −1.23704
\(287\) 2.54155i 0.150023i
\(288\) −2.02389 −0.119259
\(289\) 7.63567 0.449157
\(290\) −9.81355 14.5537i −0.576271 0.854622i
\(291\) 3.60364i 0.211249i
\(292\) 9.05445i 0.529872i
\(293\) 23.3144i 1.36204i −0.732264 0.681021i \(-0.761536\pi\)
0.732264 0.681021i \(-0.238464\pi\)
\(294\) 15.7466i 0.918357i
\(295\) −2.68915 3.98806i −0.156568 0.232194i
\(296\) 3.96343 4.61424i 0.230370 0.268197i
\(297\) 29.7182i 1.72442i
\(298\) 21.6451 1.25387
\(299\) 6.11023 0.353364
\(300\) 4.57968 + 1.85184i 0.264408 + 0.106916i
\(301\) 8.46945i 0.488171i
\(302\) −6.47544 −0.372620
\(303\) 2.27647i 0.130780i
\(304\) 7.33092i 0.420457i
\(305\) −3.83269 5.68396i −0.219459 0.325462i
\(306\) −10.0454 −0.574260
\(307\) 14.2651i 0.814153i −0.913394 0.407077i \(-0.866548\pi\)
0.913394 0.407077i \(-0.133452\pi\)
\(308\) 28.6755i 1.63394i
\(309\) 11.0373i 0.627891i
\(310\) −4.05163 6.00865i −0.230117 0.341268i
\(311\) 22.5322i 1.27768i −0.769339 0.638841i \(-0.779414\pi\)
0.769339 0.638841i \(-0.220586\pi\)
\(312\) 3.45211i 0.195437i
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 13.1689i 0.743162i
\(315\) 12.1177 + 17.9708i 0.682754 + 1.01254i
\(316\) 5.56622i 0.313124i
\(317\) 12.3877i 0.695764i 0.937538 + 0.347882i \(0.113099\pi\)
−0.937538 + 0.347882i \(0.886901\pi\)
\(318\) −3.61837 −0.202908
\(319\) 47.0007i 2.63154i
\(320\) −1.85396 + 1.25013i −0.103640 + 0.0698842i
\(321\) −6.43975 −0.359432
\(322\) 8.37532i 0.466738i
\(323\) 36.3865i 2.02460i
\(324\) 1.16780 0.0648777
\(325\) −6.54921 + 16.1965i −0.363285 + 0.898419i
\(326\) −18.7651 −1.03930
\(327\) −1.32204 −0.0731092
\(328\) 0.530665 0.0293011
\(329\) −20.6249 −1.13709
\(330\) −7.39497 10.9669i −0.407080 0.603707i
\(331\) 19.0068i 1.04471i 0.852728 + 0.522355i \(0.174946\pi\)
−0.852728 + 0.522355i \(0.825054\pi\)
\(332\) 3.77680i 0.207279i
\(333\) −8.02155 + 9.33871i −0.439578 + 0.511758i
\(334\) −7.19692 −0.393798
\(335\) 4.74575 + 7.03805i 0.259288 + 0.384530i
\(336\) 4.73182 0.258142
\(337\) 25.1046i 1.36753i 0.729701 + 0.683766i \(0.239659\pi\)
−0.729701 + 0.683766i \(0.760341\pi\)
\(338\) 0.791278 0.0430399
\(339\) 1.37438i 0.0746459i
\(340\) −9.20203 + 6.20492i −0.499050 + 0.336509i
\(341\) 19.4047i 1.05083i
\(342\) 14.8370i 0.802292i
\(343\) 42.8078i 2.31140i
\(344\) −1.76838 −0.0953449
\(345\) 2.15986 + 3.20312i 0.116283 + 0.172450i
\(346\) 9.79406i 0.526532i
\(347\) 30.4282 1.63347 0.816736 0.577011i \(-0.195781\pi\)
0.816736 + 0.577011i \(0.195781\pi\)
\(348\) 7.75571 0.415750
\(349\) 15.1341 0.810111 0.405056 0.914292i \(-0.367252\pi\)
0.405056 + 0.914292i \(0.367252\pi\)
\(350\) 22.2006 + 8.97703i 1.18667 + 0.479842i
\(351\) 17.3430i 0.925702i
\(352\) 5.98732 0.319125
\(353\) −10.1331 −0.539332 −0.269666 0.962954i \(-0.586913\pi\)
−0.269666 + 0.962954i \(0.586913\pi\)
\(354\) 2.12525 0.112956
\(355\) 15.7164 10.5976i 0.834140 0.562460i
\(356\) 8.45791i 0.448268i
\(357\) 23.4861 1.24301
\(358\) 11.2829i 0.596317i
\(359\) −26.3685 −1.39168 −0.695838 0.718199i \(-0.744967\pi\)
−0.695838 + 0.718199i \(0.744967\pi\)
\(360\) 3.75222 2.53012i 0.197759 0.133349i
\(361\) −34.7424 −1.82855
\(362\) −1.82697 −0.0960235
\(363\) 24.5494i 1.28851i
\(364\) 16.7345i 0.877128i
\(365\) −11.3192 16.7866i −0.592475 0.878653i
\(366\) 3.02900 0.158328
\(367\) 2.21157i 0.115443i −0.998333 0.0577215i \(-0.981616\pi\)
0.998333 0.0577215i \(-0.0183835\pi\)
\(368\) −1.74873 −0.0911588
\(369\) −1.07401 −0.0559106
\(370\) −1.57968 + 13.5094i −0.0821235 + 0.702322i
\(371\) −17.5405 −0.910658
\(372\) 3.20203 0.166017
\(373\) 6.08275i 0.314953i −0.987523 0.157476i \(-0.949664\pi\)
0.987523 0.157476i \(-0.0503358\pi\)
\(374\) 29.7177 1.53666
\(375\) −10.8056 + 2.29193i −0.557998 + 0.118355i
\(376\) 4.30638i 0.222085i
\(377\) 27.4288i 1.41266i
\(378\) −23.7721 −1.22271
\(379\) −20.0919 −1.03205 −0.516025 0.856574i \(-0.672589\pi\)
−0.516025 + 0.856574i \(0.672589\pi\)
\(380\) 9.16459 + 13.5913i 0.470133 + 0.697217i
\(381\) 7.41999 0.380138
\(382\) 23.8204i 1.21876i
\(383\) 11.5368 0.589501 0.294751 0.955574i \(-0.404763\pi\)
0.294751 + 0.955574i \(0.404763\pi\)
\(384\) 0.987983i 0.0504178i
\(385\) −35.8480 53.1634i −1.82698 2.70946i
\(386\) −8.40405 −0.427755
\(387\) 3.57901 0.181932
\(388\) 3.64747 0.185172
\(389\) 8.55057i 0.433531i −0.976224 0.216766i \(-0.930449\pi\)
0.976224 0.216766i \(-0.0695507\pi\)
\(390\) −4.31558 6.40009i −0.218528 0.324081i
\(391\) −8.67970 −0.438951
\(392\) 15.9381 0.804995
\(393\) 6.12525 0.308978
\(394\) 4.22797i 0.213002i
\(395\) −6.95848 10.3196i −0.350119 0.519234i
\(396\) −12.1177 −0.608936
\(397\) 9.84444i 0.494078i −0.969006 0.247039i \(-0.920542\pi\)
0.969006 0.247039i \(-0.0794576\pi\)
\(398\) 17.7545i 0.889951i
\(399\) 34.6886i 1.73660i
\(400\) 1.87436 4.63538i 0.0937182 0.231769i
\(401\) 31.0959i 1.55285i 0.630207 + 0.776427i \(0.282970\pi\)
−0.630207 + 0.776427i \(0.717030\pi\)
\(402\) −3.75060 −0.187063
\(403\) 11.3243i 0.564102i
\(404\) 2.30416 0.114636
\(405\) −2.16506 + 1.45990i −0.107582 + 0.0725428i
\(406\) 37.5968 1.86590
\(407\) 23.7304 27.6269i 1.17627 1.36942i
\(408\) 4.90379i 0.242774i
\(409\) 38.3150i 1.89455i −0.320417 0.947277i \(-0.603823\pi\)
0.320417 0.947277i \(-0.396177\pi\)
\(410\) −0.983834 + 0.663399i −0.0485881 + 0.0327629i
\(411\) 8.86404 0.437231
\(412\) −11.1716 −0.550383
\(413\) 10.3024 0.506948
\(414\) 3.53924 0.173944
\(415\) 4.72148 + 7.00205i 0.231768 + 0.343717i
\(416\) 3.49410 0.171312
\(417\) 4.98109i 0.243925i
\(418\) 43.8926i 2.14686i
\(419\) 29.0183 1.41764 0.708819 0.705391i \(-0.249228\pi\)
0.708819 + 0.705391i \(0.249228\pi\)
\(420\) −8.77262 + 5.91537i −0.428060 + 0.288641i
\(421\) 23.6443i 1.15235i 0.817326 + 0.576175i \(0.195455\pi\)
−0.817326 + 0.576175i \(0.804545\pi\)
\(422\) −4.57321 −0.222621
\(423\) 8.71564i 0.423769i
\(424\) 3.66238i 0.177861i
\(425\) 9.30328 23.0074i 0.451276 1.11602i
\(426\) 8.37532i 0.405785i
\(427\) 14.6834 0.710582
\(428\) 6.51807i 0.315063i
\(429\) 20.6689i 0.997904i
\(430\) 3.27852 2.21071i 0.158104 0.106610i
\(431\) 32.1126i 1.54681i −0.633912 0.773406i \(-0.718552\pi\)
0.633912 0.773406i \(-0.281448\pi\)
\(432\) 4.96352i 0.238807i
\(433\) 13.0575i 0.627504i −0.949505 0.313752i \(-0.898414\pi\)
0.949505 0.313752i \(-0.101586\pi\)
\(434\) 15.5222 0.745091
\(435\) −14.3788 + 9.69562i −0.689411 + 0.464869i
\(436\) 1.33812i 0.0640846i
\(437\) 12.8198i 0.613254i
\(438\) 8.94565 0.427440
\(439\) 28.0499i 1.33875i 0.742924 + 0.669375i \(0.233438\pi\)
−0.742924 + 0.669375i \(0.766562\pi\)
\(440\) −11.1003 + 7.48491i −0.529185 + 0.356829i
\(441\) −32.2569 −1.53604
\(442\) 17.3427 0.824909
\(443\) 6.79629i 0.322902i 0.986881 + 0.161451i \(0.0516173\pi\)
−0.986881 + 0.161451i \(0.948383\pi\)
\(444\) −4.55879 3.91580i −0.216351 0.185836i
\(445\) −10.5735 15.6807i −0.501230 0.743335i
\(446\) 20.3205i 0.962203i
\(447\) 21.3850i 1.01148i
\(448\) 4.78937i 0.226277i
\(449\) 17.3278i 0.817747i 0.912591 + 0.408874i \(0.134078\pi\)
−0.912591 + 0.408874i \(0.865922\pi\)
\(450\) −3.79351 + 9.38150i −0.178828 + 0.442248i
\(451\) 3.17726 0.149611
\(452\) −1.39109 −0.0654315
\(453\) 6.39762i 0.300587i
\(454\) 5.74303 0.269534
\(455\) −20.9203 31.0252i −0.980758 1.45448i
\(456\) −7.24283 −0.339176
\(457\) 3.20960 0.150139 0.0750693 0.997178i \(-0.476082\pi\)
0.0750693 + 0.997178i \(0.476082\pi\)
\(458\) −23.4383 −1.09520
\(459\) 24.6361i 1.14991i
\(460\) 3.24208 2.18613i 0.151163 0.101929i
\(461\) 34.0347i 1.58515i −0.609773 0.792576i \(-0.708739\pi\)
0.609773 0.792576i \(-0.291261\pi\)
\(462\) 28.3309 1.31807
\(463\) 26.0543 1.21085 0.605423 0.795904i \(-0.293004\pi\)
0.605423 + 0.795904i \(0.293004\pi\)
\(464\) 7.85004i 0.364429i
\(465\) −5.93644 + 4.00294i −0.275296 + 0.185632i
\(466\) 17.2961i 0.801224i
\(467\) −20.3289 −0.940710 −0.470355 0.882477i \(-0.655874\pi\)
−0.470355 + 0.882477i \(0.655874\pi\)
\(468\) −7.07167 −0.326888
\(469\) −18.1815 −0.839544
\(470\) −5.38352 7.98388i −0.248323 0.368269i
\(471\) 13.0106 0.599498
\(472\) 2.15110i 0.0990123i
\(473\) −10.5879 −0.486832
\(474\) 5.49933 0.252593
\(475\) −33.9816 13.7408i −1.55918 0.630472i
\(476\) 23.7717i 1.08958i
\(477\) 7.41226i 0.339384i
\(478\) 3.68796i 0.168683i
\(479\) 6.22972i 0.284643i 0.989820 + 0.142322i \(0.0454567\pi\)
−0.989820 + 0.142322i \(0.954543\pi\)
\(480\) 1.23510 + 1.83168i 0.0563745 + 0.0836046i
\(481\) 13.8486 16.1226i 0.631443 0.735127i
\(482\) 11.3613i 0.517492i
\(483\) −8.27467 −0.376511
\(484\) 24.8480 1.12946
\(485\) −6.76228 + 4.55980i −0.307059 + 0.207050i
\(486\) 16.0443i 0.727785i
\(487\) −30.5352 −1.38368 −0.691841 0.722050i \(-0.743200\pi\)
−0.691841 + 0.722050i \(0.743200\pi\)
\(488\) 3.06584i 0.138784i
\(489\) 18.5396i 0.838387i
\(490\) −29.5486 + 19.9246i −1.33487 + 0.900103i
\(491\) 24.5944 1.10993 0.554965 0.831874i \(-0.312732\pi\)
0.554965 + 0.831874i \(0.312732\pi\)
\(492\) 0.524288i 0.0236367i
\(493\) 38.9632i 1.75481i
\(494\) 25.6150i 1.15247i
\(495\) 22.4657 15.1486i 1.00976 0.680881i
\(496\) 3.24097i 0.145524i
\(497\) 40.6004i 1.82118i
\(498\) −3.73141 −0.167209
\(499\) 33.5739i 1.50297i 0.659747 + 0.751487i \(0.270663\pi\)
−0.659747 + 0.751487i \(0.729337\pi\)
\(500\) 2.31981 + 10.9370i 0.103745 + 0.489119i
\(501\) 7.11043i 0.317671i
\(502\) 12.8260i 0.572451i
\(503\) −1.77931 −0.0793357 −0.0396679 0.999213i \(-0.512630\pi\)
−0.0396679 + 0.999213i \(0.512630\pi\)
\(504\) 9.69316i 0.431768i
\(505\) −4.27183 + 2.88049i −0.190094 + 0.128180i
\(506\) −10.4702 −0.465458
\(507\) 0.781770i 0.0347196i
\(508\) 7.51024i 0.333213i
\(509\) 29.5114 1.30807 0.654035 0.756464i \(-0.273075\pi\)
0.654035 + 0.756464i \(0.273075\pi\)
\(510\) 6.13036 + 9.09145i 0.271457 + 0.402576i
\(511\) 43.3651 1.91836
\(512\) −1.00000 −0.0441942
\(513\) 36.3872 1.60653
\(514\) −14.0268 −0.618694
\(515\) 20.7117 13.9659i 0.912665 0.615410i
\(516\) 1.74713i 0.0769133i
\(517\) 25.7837i 1.13397i
\(518\) −22.0993 18.9824i −0.970988 0.834037i
\(519\) 9.67637 0.424745
\(520\) −6.47793 + 4.36807i −0.284076 + 0.191552i
\(521\) 29.2841 1.28296 0.641481 0.767139i \(-0.278320\pi\)
0.641481 + 0.767139i \(0.278320\pi\)
\(522\) 15.8876i 0.695382i
\(523\) −29.9729 −1.31062 −0.655312 0.755359i \(-0.727463\pi\)
−0.655312 + 0.755359i \(0.727463\pi\)
\(524\) 6.19975i 0.270837i
\(525\) 8.86915 21.9338i 0.387082 0.957269i
\(526\) 3.57182i 0.155739i
\(527\) 16.0864i 0.700732i
\(528\) 5.91537i 0.257434i
\(529\) −19.9419 −0.867041
\(530\) −4.57844 6.78993i −0.198875 0.294936i
\(531\) 4.35359i 0.188930i
\(532\) −35.1105 −1.52223
\(533\) 1.85420 0.0803141
\(534\) 8.35627 0.361611
\(535\) −8.14842 12.0843i −0.352287 0.522449i
\(536\) 3.79622i 0.163972i
\(537\) 11.1473 0.481040
\(538\) 0.458895 0.0197844
\(539\) 95.4264 4.11031
\(540\) −6.20503 9.20218i −0.267022 0.395999i
\(541\) 18.7155i 0.804644i 0.915498 + 0.402322i \(0.131797\pi\)
−0.915498 + 0.402322i \(0.868203\pi\)
\(542\) −28.8897 −1.24092
\(543\) 1.80502i 0.0774607i
\(544\) −4.96343 −0.212805
\(545\) −1.67283 2.48084i −0.0716560 0.106267i
\(546\) 16.5334 0.707566
\(547\) −32.4792 −1.38871 −0.694355 0.719633i \(-0.744310\pi\)
−0.694355 + 0.719633i \(0.744310\pi\)
\(548\) 8.97186i 0.383259i
\(549\) 6.20492i 0.264820i
\(550\) 11.2224 27.7535i 0.478526 1.18341i
\(551\) −57.5480 −2.45163
\(552\) 1.72772i 0.0735364i
\(553\) 26.6587 1.13364
\(554\) −22.4482 −0.953733
\(555\) 13.3471 + 1.56069i 0.566552 + 0.0662478i
\(556\) 5.04168 0.213815
\(557\) −16.0158 −0.678612 −0.339306 0.940676i \(-0.610192\pi\)
−0.339306 + 0.940676i \(0.610192\pi\)
\(558\) 6.55937i 0.277680i
\(559\) −6.17891 −0.261340
\(560\) 5.98732 + 8.87932i 0.253011 + 0.375220i
\(561\) 29.3606i 1.23960i
\(562\) 6.04908i 0.255165i
\(563\) −15.3069 −0.645109 −0.322554 0.946551i \(-0.604542\pi\)
−0.322554 + 0.946551i \(0.604542\pi\)
\(564\) 4.25463 0.179152
\(565\) 2.57904 1.73904i 0.108501 0.0731621i
\(566\) −10.8317 −0.455291
\(567\) 5.59302i 0.234885i
\(568\) 8.47719 0.355695
\(569\) 26.6494i 1.11720i −0.829437 0.558601i \(-0.811338\pi\)
0.829437 0.558601i \(-0.188662\pi\)
\(570\) 13.4279 9.05445i 0.562435 0.379249i
\(571\) 23.1683 0.969564 0.484782 0.874635i \(-0.338899\pi\)
0.484782 + 0.874635i \(0.338899\pi\)
\(572\) 20.9203 0.874721
\(573\) −23.5341 −0.983152
\(574\) 2.54155i 0.106082i
\(575\) −3.27776 + 8.10603i −0.136692 + 0.338045i
\(576\) 2.02389 0.0843287
\(577\) −3.54110 −0.147418 −0.0737091 0.997280i \(-0.523484\pi\)
−0.0737091 + 0.997280i \(0.523484\pi\)
\(578\) −7.63567 −0.317602
\(579\) 8.30306i 0.345063i
\(580\) 9.81355 + 14.5537i 0.407485 + 0.604309i
\(581\) −18.0885 −0.750437
\(582\) 3.60364i 0.149376i
\(583\) 21.9279i 0.908160i
\(584\) 9.05445i 0.374676i
\(585\) 13.1106 8.84048i 0.542057 0.365509i
\(586\) 23.3144i 0.963109i
\(587\) 12.0976 0.499320 0.249660 0.968334i \(-0.419681\pi\)
0.249660 + 0.968334i \(0.419681\pi\)
\(588\) 15.7466i 0.649377i
\(589\) −23.7593 −0.978986
\(590\) 2.68915 + 3.98806i 0.110710 + 0.164186i
\(591\) −4.17716 −0.171825
\(592\) −3.96343 + 4.61424i −0.162896 + 0.189644i
\(593\) 17.2007i 0.706348i −0.935558 0.353174i \(-0.885102\pi\)
0.935558 0.353174i \(-0.114898\pi\)
\(594\) 29.7182i 1.21935i
\(595\) 29.7177 + 44.0719i 1.21831 + 1.80677i
\(596\) −21.6451 −0.886619
\(597\) 17.5411 0.717910
\(598\) −6.11023 −0.249866
\(599\) 2.41919 0.0988454 0.0494227 0.998778i \(-0.484262\pi\)
0.0494227 + 0.998778i \(0.484262\pi\)
\(600\) −4.57968 1.85184i −0.186965 0.0756011i
\(601\) −39.0483 −1.59281 −0.796407 0.604761i \(-0.793269\pi\)
−0.796407 + 0.604761i \(0.793269\pi\)
\(602\) 8.46945i 0.345189i
\(603\) 7.68313i 0.312881i
\(604\) 6.47544 0.263482
\(605\) −46.0674 + 31.0632i −1.87290 + 1.26290i
\(606\) 2.27647i 0.0924752i
\(607\) −38.0508 −1.54443 −0.772217 0.635359i \(-0.780852\pi\)
−0.772217 + 0.635359i \(0.780852\pi\)
\(608\) 7.33092i 0.297308i
\(609\) 37.1450i 1.50519i
\(610\) 3.83269 + 5.68396i 0.155181 + 0.230137i
\(611\) 15.0469i 0.608733i
\(612\) 10.0454 0.406063
\(613\) 7.12176i 0.287645i −0.989603 0.143823i \(-0.954061\pi\)
0.989603 0.143823i \(-0.0459395\pi\)
\(614\) 14.2651i 0.575693i
\(615\) 0.655427 + 0.972011i 0.0264294 + 0.0391953i
\(616\) 28.6755i 1.15537i
\(617\) 42.6678i 1.71774i −0.512192 0.858871i \(-0.671166\pi\)
0.512192 0.858871i \(-0.328834\pi\)
\(618\) 11.0373i 0.443986i
\(619\) −6.30429 −0.253391 −0.126695 0.991942i \(-0.540437\pi\)
−0.126695 + 0.991942i \(0.540437\pi\)
\(620\) 4.05163 + 6.00865i 0.162717 + 0.241313i
\(621\) 8.67985i 0.348310i
\(622\) 22.5322i 0.903458i
\(623\) 40.5081 1.62292
\(624\) 3.45211i 0.138195i
\(625\) −17.9735 17.3768i −0.718941 0.695072i
\(626\) 10.0000 0.399680
\(627\) −43.3651 −1.73184
\(628\) 13.1689i 0.525495i
\(629\) −19.6722 + 22.9025i −0.784383 + 0.913181i
\(630\) −12.1177 17.9708i −0.482780 0.715973i
\(631\) 32.6385i 1.29932i 0.760225 + 0.649660i \(0.225089\pi\)
−0.760225 + 0.649660i \(0.774911\pi\)
\(632\) 5.56622i 0.221412i
\(633\) 4.51826i 0.179585i
\(634\) 12.3877i 0.491979i
\(635\) 9.38875 + 13.9237i 0.372581 + 0.552546i
\(636\) 3.61837 0.143478
\(637\) 55.6892 2.20649
\(638\) 47.0007i 1.86078i
\(639\) −17.1569 −0.678716
\(640\) 1.85396 1.25013i 0.0732844 0.0494156i
\(641\) −12.1721 −0.480767 −0.240384 0.970678i \(-0.577273\pi\)
−0.240384 + 0.970678i \(0.577273\pi\)
\(642\) 6.43975 0.254156
\(643\) 10.0853 0.397727 0.198864 0.980027i \(-0.436275\pi\)
0.198864 + 0.980027i \(0.436275\pi\)
\(644\) 8.37532i 0.330034i
\(645\) −2.18414 3.23912i −0.0860004 0.127540i
\(646\) 36.3865i 1.43161i
\(647\) −38.5061 −1.51383 −0.756916 0.653512i \(-0.773295\pi\)
−0.756916 + 0.653512i \(0.773295\pi\)
\(648\) −1.16780 −0.0458754
\(649\) 12.8793i 0.505558i
\(650\) 6.54921 16.1965i 0.256881 0.635278i
\(651\) 15.3357i 0.601053i
\(652\) 18.7651 0.734896
\(653\) −2.20349 −0.0862293 −0.0431146 0.999070i \(-0.513728\pi\)
−0.0431146 + 0.999070i \(0.513728\pi\)
\(654\) 1.32204 0.0516960
\(655\) 7.75048 + 11.4941i 0.302836 + 0.449112i
\(656\) −0.530665 −0.0207190
\(657\) 18.3252i 0.714935i
\(658\) 20.6249 0.804041
\(659\) −20.4048 −0.794859 −0.397430 0.917633i \(-0.630098\pi\)
−0.397430 + 0.917633i \(0.630098\pi\)
\(660\) 7.39497 + 10.9669i 0.287849 + 0.426886i
\(661\) 27.0306i 1.05137i 0.850680 + 0.525684i \(0.176191\pi\)
−0.850680 + 0.525684i \(0.823809\pi\)
\(662\) 19.0068i 0.738721i
\(663\) 17.1343i 0.665442i
\(664\) 3.77680i 0.146568i
\(665\) 65.0936 43.8926i 2.52422 1.70208i
\(666\) 8.02155 9.33871i 0.310829 0.361868i
\(667\) 13.7276i 0.531535i
\(668\) 7.19692 0.278457
\(669\) 20.0763 0.776194
\(670\) −4.74575 7.03805i −0.183344 0.271904i
\(671\) 18.3562i 0.708632i
\(672\) −4.73182 −0.182534
\(673\) 11.6776i 0.450139i −0.974343 0.225070i \(-0.927739\pi\)
0.974343 0.225070i \(-0.0722609\pi\)
\(674\) 25.1046i 0.966991i
\(675\) 23.0078 + 9.30344i 0.885570 + 0.358090i
\(676\) −0.791278 −0.0304338
\(677\) 37.2578i 1.43193i −0.698135 0.715966i \(-0.745986\pi\)
0.698135 0.715966i \(-0.254014\pi\)
\(678\) 1.37438i 0.0527826i
\(679\) 17.4691i 0.670402i
\(680\) 9.20203 6.20492i 0.352882 0.237948i
\(681\) 5.67402i 0.217429i
\(682\) 19.4047i 0.743046i
\(683\) −46.3018 −1.77169 −0.885845 0.463981i \(-0.846420\pi\)
−0.885845 + 0.463981i \(0.846420\pi\)
\(684\) 14.8370i 0.567306i
\(685\) 11.2160 + 16.6335i 0.428540 + 0.635533i
\(686\) 42.8078i 1.63441i
\(687\) 23.1566i 0.883480i
\(688\) 1.76838 0.0674190
\(689\) 12.7967i 0.487516i
\(690\) −2.15986 3.20312i −0.0822246 0.121941i
\(691\) 29.7037 1.12998 0.564991 0.825097i \(-0.308879\pi\)
0.564991 + 0.825097i \(0.308879\pi\)
\(692\) 9.79406i 0.372314i
\(693\) 58.0361i 2.20461i
\(694\) −30.4282 −1.15504
\(695\) −9.34708 + 6.30273i −0.354555 + 0.239076i
\(696\) −7.75571 −0.293979
\(697\) −2.63392 −0.0997669
\(698\) −15.1341 −0.572835
\(699\) −17.0882 −0.646336
\(700\) −22.2006 8.97703i −0.839102 0.339300i
\(701\) 45.9214i 1.73443i −0.497936 0.867214i \(-0.665909\pi\)
0.497936 0.867214i \(-0.334091\pi\)
\(702\) 17.3430i 0.654570i
\(703\) 33.8266 + 29.0556i 1.27580 + 1.09585i
\(704\) −5.98732 −0.225656
\(705\) −7.88793 + 5.31883i −0.297077 + 0.200319i
\(706\) 10.1331 0.381365
\(707\) 11.0355i 0.415031i
\(708\) −2.12525 −0.0798717
\(709\) 52.6575i 1.97759i −0.149266 0.988797i \(-0.547691\pi\)
0.149266 0.988797i \(-0.452309\pi\)
\(710\) −15.7164 + 10.5976i −0.589826 + 0.397719i
\(711\) 11.2654i 0.422486i
\(712\) 8.45791i 0.316974i
\(713\) 5.66759i 0.212253i
\(714\) −23.4861 −0.878944
\(715\) −38.7855 + 26.1530i −1.45049 + 0.978068i
\(716\) 11.2829i 0.421660i
\(717\) 3.64364 0.136074
\(718\) 26.3685 0.984063
\(719\) −13.3494 −0.497850 −0.248925 0.968523i \(-0.580077\pi\)
−0.248925 + 0.968523i \(0.580077\pi\)
\(720\) −3.75222 + 2.53012i −0.139837 + 0.0942920i
\(721\) 53.5048i 1.99262i
\(722\) 34.7424 1.29298
\(723\) 11.2247 0.417453
\(724\) 1.82697 0.0678989
\(725\) −36.3879 14.7138i −1.35141 0.546458i
\(726\) 24.5494i 0.911115i
\(727\) 13.1733 0.488571 0.244286 0.969703i \(-0.421447\pi\)
0.244286 + 0.969703i \(0.421447\pi\)
\(728\) 16.7345i 0.620223i
\(729\) −12.3481 −0.457338
\(730\) 11.3192 + 16.7866i 0.418943 + 0.621301i
\(731\) 8.77726 0.324639
\(732\) −3.02900 −0.111955
\(733\) 32.3264i 1.19400i 0.802241 + 0.597001i \(0.203641\pi\)
−0.802241 + 0.597001i \(0.796359\pi\)
\(734\) 2.21157i 0.0816305i
\(735\) 19.6852 + 29.1935i 0.726099 + 1.07682i
\(736\) 1.74873 0.0644590
\(737\) 22.7292i 0.837240i
\(738\) 1.07401 0.0395348
\(739\) 6.94169 0.255354 0.127677 0.991816i \(-0.459248\pi\)
0.127677 + 0.991816i \(0.459248\pi\)
\(740\) 1.57968 13.5094i 0.0580701 0.496616i
\(741\) −25.3072 −0.929681
\(742\) 17.5405 0.643933
\(743\) 36.0784i 1.32359i 0.749685 + 0.661795i \(0.230205\pi\)
−0.749685 + 0.661795i \(0.769795\pi\)
\(744\) −3.20203 −0.117392
\(745\) 40.1293 27.0592i 1.47022 0.991371i
\(746\) 6.08275i 0.222705i
\(747\) 7.64382i 0.279673i
\(748\) −29.7177 −1.08659
\(749\) 31.2175 1.14066
\(750\) 10.8056 2.29193i 0.394564 0.0836896i
\(751\) −29.9052 −1.09126 −0.545629 0.838027i \(-0.683709\pi\)
−0.545629 + 0.838027i \(0.683709\pi\)
\(752\) 4.30638i 0.157038i
\(753\) 12.6718 0.461787
\(754\) 27.4288i 0.998898i
\(755\) −12.0052 + 8.09512i −0.436915 + 0.294612i
\(756\) 23.7721 0.864584
\(757\) 24.9464 0.906693 0.453347 0.891334i \(-0.350230\pi\)
0.453347 + 0.891334i \(0.350230\pi\)
\(758\) 20.0919 0.729769
\(759\) 10.3444i 0.375477i
\(760\) −9.16459 13.5913i −0.332434 0.493007i
\(761\) 11.7647 0.426469 0.213235 0.977001i \(-0.431600\pi\)
0.213235 + 0.977001i \(0.431600\pi\)
\(762\) −7.41999 −0.268798
\(763\) 6.40878 0.232013
\(764\) 23.8204i 0.861791i
\(765\) −18.6239 + 12.5581i −0.673348 + 0.454038i
\(766\) −11.5368 −0.416840
\(767\) 7.51615i 0.271392i
\(768\) 0.987983i 0.0356508i
\(769\) 26.7939i 0.966214i 0.875561 + 0.483107i \(0.160492\pi\)
−0.875561 + 0.483107i \(0.839508\pi\)
\(770\) 35.8480 + 53.1634i 1.29187 + 1.91587i
\(771\) 13.8582i 0.499091i
\(772\) 8.40405 0.302468
\(773\) 2.77358i 0.0997589i −0.998755 0.0498794i \(-0.984116\pi\)
0.998755 0.0498794i \(-0.0158837\pi\)
\(774\) −3.57901 −0.128645
\(775\) −15.0231 6.07477i −0.539647 0.218212i
\(776\) −3.64747 −0.130937
\(777\) −18.7542 + 21.8337i −0.672805 + 0.783281i
\(778\) 8.55057i 0.306553i
\(779\) 3.89026i 0.139383i
\(780\) 4.31558 + 6.40009i 0.154522 + 0.229160i
\(781\) 50.7556 1.81618
\(782\) 8.67970 0.310386
\(783\) 38.9638 1.39245
\(784\) −15.9381 −0.569217
\(785\) 16.4628 + 24.4146i 0.587581 + 0.871395i
\(786\) −6.12525 −0.218480
\(787\) 28.0910i 1.00134i 0.865639 + 0.500669i \(0.166912\pi\)
−0.865639 + 0.500669i \(0.833088\pi\)