Properties

Label 15.4.b.a.4.1
Level $15$
Weight $4$
Character 15.4
Analytic conductor $0.885$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 15.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.885028650086\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{41})\)
Defining polynomial: \( x^{4} + 21x^{2} + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.1
Root \(-3.70156i\) of defining polynomial
Character \(\chi\) \(=\) 15.4
Dual form 15.4.b.a.4.4

$q$-expansion

\(f(q)\) \(=\) \(q-4.70156i q^{2} +3.00000i q^{3} -14.1047 q^{4} +(11.1047 - 1.29844i) q^{5} +14.1047 q^{6} +16.2094i q^{7} +28.7016i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q-4.70156i q^{2} +3.00000i q^{3} -14.1047 q^{4} +(11.1047 - 1.29844i) q^{5} +14.1047 q^{6} +16.2094i q^{7} +28.7016i q^{8} -9.00000 q^{9} +(-6.10469 - 52.2094i) q^{10} -40.2094 q^{11} -42.3141i q^{12} +19.7906i q^{13} +76.2094 q^{14} +(3.89531 + 33.3141i) q^{15} +22.1047 q^{16} -83.0156i q^{17} +42.3141i q^{18} +48.8375 q^{19} +(-156.628 + 18.3141i) q^{20} -48.6281 q^{21} +189.047i q^{22} +1.61250i q^{23} -86.1047 q^{24} +(121.628 - 28.8375i) q^{25} +93.0469 q^{26} -27.0000i q^{27} -228.628i q^{28} +24.5344 q^{29} +(156.628 - 18.3141i) q^{30} -12.4187 q^{31} +125.686i q^{32} -120.628i q^{33} -390.303 q^{34} +(21.0469 + 180.000i) q^{35} +126.942 q^{36} -325.884i q^{37} -229.612i q^{38} -59.3719 q^{39} +(37.2672 + 318.722i) q^{40} -242.419 q^{41} +228.628i q^{42} +367.350i q^{43} +567.141 q^{44} +(-99.9422 + 11.6859i) q^{45} +7.58125 q^{46} +204.544i q^{47} +66.3141i q^{48} +80.2562 q^{49} +(-135.581 - 571.842i) q^{50} +249.047 q^{51} -279.141i q^{52} -61.5281i q^{53} -126.942 q^{54} +(-446.512 + 52.2094i) q^{55} -465.234 q^{56} +146.512i q^{57} -115.350i q^{58} +112.209 q^{59} +(-54.9422 - 469.884i) q^{60} +477.350 q^{61} +58.3875i q^{62} -145.884i q^{63} +767.758 q^{64} +(25.6969 + 219.769i) q^{65} -567.141 q^{66} -558.094i q^{67} +1170.91i q^{68} -4.83749 q^{69} +(846.281 - 98.9531i) q^{70} +558.281 q^{71} -258.314i q^{72} +1011.77i q^{73} -1532.17 q^{74} +(86.5125 + 364.884i) q^{75} -688.837 q^{76} -651.769i q^{77} +279.141i q^{78} -1150.47 q^{79} +(245.466 - 28.7016i) q^{80} +81.0000 q^{81} +1139.75i q^{82} -1157.92i q^{83} +685.884 q^{84} +(-107.791 - 921.862i) q^{85} +1727.12 q^{86} +73.6032i q^{87} -1154.07i q^{88} -96.9751 q^{89} +(54.9422 + 469.884i) q^{90} -320.794 q^{91} -22.7438i q^{92} -37.2562i q^{93} +961.675 q^{94} +(542.325 - 63.4124i) q^{95} -377.058 q^{96} +1152.37i q^{97} -377.330i q^{98} +361.884 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{4} + 6 q^{5} + 18 q^{6} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 18 q^{4} + 6 q^{5} + 18 q^{6} - 36 q^{9} + 14 q^{10} - 84 q^{11} + 228 q^{14} + 54 q^{15} + 50 q^{16} - 112 q^{19} - 396 q^{20} + 36 q^{21} - 306 q^{24} + 256 q^{25} - 12 q^{26} + 636 q^{29} + 396 q^{30} + 104 q^{31} - 716 q^{34} - 300 q^{35} + 162 q^{36} - 468 q^{39} + 418 q^{40} - 816 q^{41} + 1116 q^{44} - 54 q^{45} + 184 q^{46} - 140 q^{49} - 696 q^{50} + 612 q^{51} - 162 q^{54} - 864 q^{55} + 60 q^{56} + 372 q^{59} + 126 q^{60} + 680 q^{61} + 958 q^{64} + 948 q^{65} - 1116 q^{66} + 288 q^{69} + 1080 q^{70} - 72 q^{71} - 3132 q^{74} - 576 q^{75} - 2448 q^{76} - 760 q^{79} + 444 q^{80} + 324 q^{81} + 2052 q^{84} - 508 q^{85} + 4296 q^{86} - 2232 q^{89} - 126 q^{90} + 1944 q^{91} + 3232 q^{94} + 2784 q^{95} - 1854 q^{96} + 756 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.70156i 1.66225i −0.556083 0.831127i \(-0.687696\pi\)
0.556083 0.831127i \(-0.312304\pi\)
\(3\) 3.00000i 0.577350i
\(4\) −14.1047 −1.76309
\(5\) 11.1047 1.29844i 0.993233 0.116136i
\(6\) 14.1047 0.959702
\(7\) 16.2094i 0.875224i 0.899164 + 0.437612i \(0.144176\pi\)
−0.899164 + 0.437612i \(0.855824\pi\)
\(8\) 28.7016i 1.26844i
\(9\) −9.00000 −0.333333
\(10\) −6.10469 52.2094i −0.193047 1.65101i
\(11\) −40.2094 −1.10214 −0.551072 0.834458i \(-0.685781\pi\)
−0.551072 + 0.834458i \(0.685781\pi\)
\(12\) 42.3141i 1.01792i
\(13\) 19.7906i 0.422226i 0.977462 + 0.211113i \(0.0677087\pi\)
−0.977462 + 0.211113i \(0.932291\pi\)
\(14\) 76.2094 1.45484
\(15\) 3.89531 + 33.3141i 0.0670510 + 0.573444i
\(16\) 22.1047 0.345386
\(17\) 83.0156i 1.18437i −0.805803 0.592184i \(-0.798266\pi\)
0.805803 0.592184i \(-0.201734\pi\)
\(18\) 42.3141i 0.554084i
\(19\) 48.8375 0.589689 0.294844 0.955545i \(-0.404732\pi\)
0.294844 + 0.955545i \(0.404732\pi\)
\(20\) −156.628 + 18.3141i −1.75116 + 0.204757i
\(21\) −48.6281 −0.505311
\(22\) 189.047i 1.83204i
\(23\) 1.61250i 0.0146186i 0.999973 + 0.00730932i \(0.00232665\pi\)
−0.999973 + 0.00730932i \(0.997673\pi\)
\(24\) −86.1047 −0.732335
\(25\) 121.628 28.8375i 0.973025 0.230700i
\(26\) 93.0469 0.701846
\(27\) 27.0000i 0.192450i
\(28\) 228.628i 1.54309i
\(29\) 24.5344 0.157101 0.0785504 0.996910i \(-0.474971\pi\)
0.0785504 + 0.996910i \(0.474971\pi\)
\(30\) 156.628 18.3141i 0.953208 0.111456i
\(31\) −12.4187 −0.0719507 −0.0359754 0.999353i \(-0.511454\pi\)
−0.0359754 + 0.999353i \(0.511454\pi\)
\(32\) 125.686i 0.694323i
\(33\) 120.628i 0.636323i
\(34\) −390.303 −1.96872
\(35\) 21.0469 + 180.000i 0.101645 + 0.869302i
\(36\) 126.942 0.587695
\(37\) 325.884i 1.44797i −0.689813 0.723987i \(-0.742307\pi\)
0.689813 0.723987i \(-0.257693\pi\)
\(38\) 229.612i 0.980212i
\(39\) −59.3719 −0.243772
\(40\) 37.2672 + 318.722i 0.147312 + 1.25986i
\(41\) −242.419 −0.923401 −0.461701 0.887036i \(-0.652761\pi\)
−0.461701 + 0.887036i \(0.652761\pi\)
\(42\) 228.628i 0.839954i
\(43\) 367.350i 1.30280i 0.758735 + 0.651399i \(0.225818\pi\)
−0.758735 + 0.651399i \(0.774182\pi\)
\(44\) 567.141 1.94317
\(45\) −99.9422 + 11.6859i −0.331078 + 0.0387119i
\(46\) 7.58125 0.0242999
\(47\) 204.544i 0.634804i 0.948291 + 0.317402i \(0.102810\pi\)
−0.948291 + 0.317402i \(0.897190\pi\)
\(48\) 66.3141i 0.199409i
\(49\) 80.2562 0.233983
\(50\) −135.581 571.842i −0.383482 1.61741i
\(51\) 249.047 0.683795
\(52\) 279.141i 0.744420i
\(53\) 61.5281i 0.159463i −0.996816 0.0797314i \(-0.974594\pi\)
0.996816 0.0797314i \(-0.0254063\pi\)
\(54\) −126.942 −0.319901
\(55\) −446.512 + 52.2094i −1.09469 + 0.127998i
\(56\) −465.234 −1.11017
\(57\) 146.512i 0.340457i
\(58\) 115.350i 0.261141i
\(59\) 112.209 0.247600 0.123800 0.992307i \(-0.460492\pi\)
0.123800 + 0.992307i \(0.460492\pi\)
\(60\) −54.9422 469.884i −0.118217 1.01103i
\(61\) 477.350 1.00194 0.500970 0.865464i \(-0.332977\pi\)
0.500970 + 0.865464i \(0.332977\pi\)
\(62\) 58.3875i 0.119600i
\(63\) 145.884i 0.291741i
\(64\) 767.758 1.49953
\(65\) 25.6969 + 219.769i 0.0490355 + 0.419369i
\(66\) −567.141 −1.05773
\(67\) 558.094i 1.01764i −0.860872 0.508821i \(-0.830082\pi\)
0.860872 0.508821i \(-0.169918\pi\)
\(68\) 1170.91i 2.08814i
\(69\) −4.83749 −0.00844008
\(70\) 846.281 98.9531i 1.44500 0.168959i
\(71\) 558.281 0.933180 0.466590 0.884474i \(-0.345482\pi\)
0.466590 + 0.884474i \(0.345482\pi\)
\(72\) 258.314i 0.422814i
\(73\) 1011.77i 1.62217i 0.584927 + 0.811086i \(0.301123\pi\)
−0.584927 + 0.811086i \(0.698877\pi\)
\(74\) −1532.17 −2.40690
\(75\) 86.5125 + 364.884i 0.133195 + 0.561776i
\(76\) −688.837 −1.03967
\(77\) 651.769i 0.964623i
\(78\) 279.141i 0.405211i
\(79\) −1150.47 −1.63845 −0.819227 0.573470i \(-0.805597\pi\)
−0.819227 + 0.573470i \(0.805597\pi\)
\(80\) 245.466 28.7016i 0.343049 0.0401117i
\(81\) 81.0000 0.111111
\(82\) 1139.75i 1.53493i
\(83\) 1157.92i 1.53131i −0.643251 0.765655i \(-0.722415\pi\)
0.643251 0.765655i \(-0.277585\pi\)
\(84\) 685.884 0.890906
\(85\) −107.791 921.862i −0.137547 1.17635i
\(86\) 1727.12 2.16558
\(87\) 73.6032i 0.0907022i
\(88\) 1154.07i 1.39801i
\(89\) −96.9751 −0.115498 −0.0577491 0.998331i \(-0.518392\pi\)
−0.0577491 + 0.998331i \(0.518392\pi\)
\(90\) 54.9422 + 469.884i 0.0643490 + 0.550335i
\(91\) −320.794 −0.369542
\(92\) 22.7438i 0.0257739i
\(93\) 37.2562i 0.0415408i
\(94\) 961.675 1.05520
\(95\) 542.325 63.4124i 0.585699 0.0684840i
\(96\) −377.058 −0.400868
\(97\) 1152.37i 1.20625i 0.797648 + 0.603123i \(0.206077\pi\)
−0.797648 + 0.603123i \(0.793923\pi\)
\(98\) 377.330i 0.388939i
\(99\) 361.884 0.367381
\(100\) −1715.53 + 406.744i −1.71553 + 0.406744i
\(101\) −1156.49 −1.13936 −0.569679 0.821867i \(-0.692932\pi\)
−0.569679 + 0.821867i \(0.692932\pi\)
\(102\) 1170.91i 1.13664i
\(103\) 1333.70i 1.27585i −0.770096 0.637927i \(-0.779792\pi\)
0.770096 0.637927i \(-0.220208\pi\)
\(104\) −568.022 −0.535569
\(105\) −540.000 + 63.1406i −0.501891 + 0.0586847i
\(106\) −289.278 −0.265068
\(107\) 798.263i 0.721224i 0.932716 + 0.360612i \(0.117432\pi\)
−0.932716 + 0.360612i \(0.882568\pi\)
\(108\) 380.827i 0.339306i
\(109\) 985.119 0.865663 0.432831 0.901475i \(-0.357515\pi\)
0.432831 + 0.901475i \(0.357515\pi\)
\(110\) 245.466 + 2099.31i 0.212766 + 1.81965i
\(111\) 977.653 0.835988
\(112\) 358.303i 0.302290i
\(113\) 1888.25i 1.57196i 0.618253 + 0.785979i \(0.287841\pi\)
−0.618253 + 0.785979i \(0.712159\pi\)
\(114\) 688.837 0.565926
\(115\) 2.09373 + 17.9063i 0.00169775 + 0.0145197i
\(116\) −346.050 −0.276982
\(117\) 178.116i 0.140742i
\(118\) 527.559i 0.411574i
\(119\) 1345.63 1.03659
\(120\) −956.166 + 111.802i −0.727380 + 0.0850503i
\(121\) 285.794 0.214721
\(122\) 2244.29i 1.66548i
\(123\) 727.256i 0.533126i
\(124\) 175.163 0.126855
\(125\) 1313.20 478.158i 0.939648 0.342142i
\(126\) −685.884 −0.484948
\(127\) 620.859i 0.433798i 0.976194 + 0.216899i \(0.0695943\pi\)
−0.976194 + 0.216899i \(0.930406\pi\)
\(128\) 2604.17i 1.79827i
\(129\) −1102.05 −0.752171
\(130\) 1033.26 120.816i 0.697097 0.0815094i
\(131\) −2588.35 −1.72630 −0.863151 0.504947i \(-0.831512\pi\)
−0.863151 + 0.504947i \(0.831512\pi\)
\(132\) 1701.42i 1.12189i
\(133\) 791.625i 0.516110i
\(134\) −2623.91 −1.69158
\(135\) −35.0578 299.827i −0.0223503 0.191148i
\(136\) 2382.68 1.50230
\(137\) 1656.29i 1.03289i 0.856319 + 0.516447i \(0.172746\pi\)
−0.856319 + 0.516447i \(0.827254\pi\)
\(138\) 22.7438i 0.0140295i
\(139\) 153.256 0.0935182 0.0467591 0.998906i \(-0.485111\pi\)
0.0467591 + 0.998906i \(0.485111\pi\)
\(140\) −296.859 2538.84i −0.179209 1.53265i
\(141\) −613.631 −0.366504
\(142\) 2624.79i 1.55118i
\(143\) 795.769i 0.465353i
\(144\) −198.942 −0.115129
\(145\) 272.447 31.8564i 0.156038 0.0182450i
\(146\) 4756.89 2.69646
\(147\) 240.769i 0.135090i
\(148\) 4596.50i 2.55290i
\(149\) −1483.38 −0.815591 −0.407795 0.913073i \(-0.633702\pi\)
−0.407795 + 0.913073i \(0.633702\pi\)
\(150\) 1715.53 406.744i 0.933814 0.221403i
\(151\) −394.281 −0.212491 −0.106246 0.994340i \(-0.533883\pi\)
−0.106246 + 0.994340i \(0.533883\pi\)
\(152\) 1401.71i 0.747986i
\(153\) 747.141i 0.394789i
\(154\) −3064.33 −1.60345
\(155\) −137.906 + 16.1250i −0.0714639 + 0.00835606i
\(156\) 837.422 0.429791
\(157\) 1727.05i 0.877922i −0.898506 0.438961i \(-0.855347\pi\)
0.898506 0.438961i \(-0.144653\pi\)
\(158\) 5409.00i 2.72352i
\(159\) 184.584 0.0920659
\(160\) 163.195 + 1395.70i 0.0806358 + 0.689625i
\(161\) −26.1376 −0.0127946
\(162\) 380.827i 0.184695i
\(163\) 2034.28i 0.977529i −0.872416 0.488764i \(-0.837448\pi\)
0.872416 0.488764i \(-0.162552\pi\)
\(164\) 3419.24 1.62804
\(165\) −156.628 1339.54i −0.0738999 0.632017i
\(166\) −5444.06 −2.54543
\(167\) 192.900i 0.0893835i −0.999001 0.0446918i \(-0.985769\pi\)
0.999001 0.0446918i \(-0.0142306\pi\)
\(168\) 1395.70i 0.640957i
\(169\) 1805.33 0.821726
\(170\) −4334.19 + 506.784i −1.95540 + 0.228639i
\(171\) −439.537 −0.196563
\(172\) 5181.36i 2.29695i
\(173\) 1239.91i 0.544905i −0.962169 0.272452i \(-0.912165\pi\)
0.962169 0.272452i \(-0.0878347\pi\)
\(174\) 346.050 0.150770
\(175\) 467.438 + 1971.52i 0.201914 + 0.851615i
\(176\) −888.816 −0.380665
\(177\) 336.628i 0.142952i
\(178\) 455.934i 0.191987i
\(179\) 2636.86 1.10105 0.550525 0.834818i \(-0.314427\pi\)
0.550525 + 0.834818i \(0.314427\pi\)
\(180\) 1409.65 164.827i 0.583719 0.0682525i
\(181\) 3317.58 1.36240 0.681199 0.732099i \(-0.261459\pi\)
0.681199 + 0.732099i \(0.261459\pi\)
\(182\) 1508.23i 0.614272i
\(183\) 1432.05i 0.578471i
\(184\) −46.2812 −0.0185429
\(185\) −423.141 3618.84i −0.168162 1.43818i
\(186\) −175.163 −0.0690513
\(187\) 3338.01i 1.30534i
\(188\) 2885.02i 1.11921i
\(189\) 437.653 0.168437
\(190\) −298.138 2549.77i −0.113838 0.973579i
\(191\) −624.506 −0.236585 −0.118292 0.992979i \(-0.537742\pi\)
−0.118292 + 0.992979i \(0.537742\pi\)
\(192\) 2303.27i 0.865752i
\(193\) 436.144i 0.162665i −0.996687 0.0813324i \(-0.974082\pi\)
0.996687 0.0813324i \(-0.0259175\pi\)
\(194\) 5417.96 2.00509
\(195\) −659.306 + 77.0907i −0.242123 + 0.0283107i
\(196\) −1131.99 −0.412532
\(197\) 3355.81i 1.21366i −0.794831 0.606831i \(-0.792440\pi\)
0.794831 0.606831i \(-0.207560\pi\)
\(198\) 1701.42i 0.610681i
\(199\) −3799.77 −1.35356 −0.676780 0.736185i \(-0.736625\pi\)
−0.676780 + 0.736185i \(0.736625\pi\)
\(200\) 827.681 + 3490.92i 0.292629 + 1.23423i
\(201\) 1674.28 0.587536
\(202\) 5437.31i 1.89390i
\(203\) 397.687i 0.137498i
\(204\) −3512.73 −1.20559
\(205\) −2691.98 + 314.766i −0.917153 + 0.107240i
\(206\) −6270.46 −2.12079
\(207\) 14.5125i 0.00487288i
\(208\) 437.466i 0.145831i
\(209\) −1963.72 −0.649922
\(210\) 296.859 + 2538.84i 0.0975488 + 0.834271i
\(211\) 2365.27 0.771715 0.385857 0.922558i \(-0.373906\pi\)
0.385857 + 0.922558i \(0.373906\pi\)
\(212\) 867.834i 0.281147i
\(213\) 1674.84i 0.538772i
\(214\) 3753.08 1.19886
\(215\) 476.981 + 4079.31i 0.151302 + 1.29398i
\(216\) 774.942 0.244112
\(217\) 201.300i 0.0629730i
\(218\) 4631.60i 1.43895i
\(219\) −3035.31 −0.936562
\(220\) 6297.92 736.397i 1.93003 0.225672i
\(221\) 1642.93 0.500070
\(222\) 4596.50i 1.38962i
\(223\) 3328.58i 0.999545i −0.866157 0.499772i \(-0.833417\pi\)
0.866157 0.499772i \(-0.166583\pi\)
\(224\) −2037.29 −0.607688
\(225\) −1094.65 + 259.537i −0.324342 + 0.0769000i
\(226\) 8877.71 2.61299
\(227\) 527.100i 0.154118i 0.997027 + 0.0770592i \(0.0245530\pi\)
−0.997027 + 0.0770592i \(0.975447\pi\)
\(228\) 2066.51i 0.600255i
\(229\) −2566.06 −0.740479 −0.370240 0.928936i \(-0.620724\pi\)
−0.370240 + 0.928936i \(0.620724\pi\)
\(230\) 84.1875 9.84379i 0.0241355 0.00282209i
\(231\) 1955.31 0.556925
\(232\) 704.175i 0.199273i
\(233\) 5534.99i 1.55626i 0.628101 + 0.778132i \(0.283832\pi\)
−0.628101 + 0.778132i \(0.716168\pi\)
\(234\) −837.422 −0.233949
\(235\) 265.587 + 2271.39i 0.0737234 + 0.630508i
\(236\) −1582.68 −0.436541
\(237\) 3451.41i 0.945962i
\(238\) 6326.57i 1.72307i
\(239\) −1010.01 −0.273355 −0.136678 0.990616i \(-0.543642\pi\)
−0.136678 + 0.990616i \(0.543642\pi\)
\(240\) 86.1047 + 736.397i 0.0231585 + 0.198059i
\(241\) −4074.29 −1.08900 −0.544498 0.838762i \(-0.683280\pi\)
−0.544498 + 0.838762i \(0.683280\pi\)
\(242\) 1343.68i 0.356921i
\(243\) 243.000i 0.0641500i
\(244\) −6732.87 −1.76651
\(245\) 891.220 104.208i 0.232400 0.0271738i
\(246\) −3419.24 −0.886190
\(247\) 966.525i 0.248982i
\(248\) 356.437i 0.0912653i
\(249\) 3473.77 0.884103
\(250\) −2248.09 6174.08i −0.568726 1.56193i
\(251\) 1773.98 0.446107 0.223054 0.974806i \(-0.428398\pi\)
0.223054 + 0.974806i \(0.428398\pi\)
\(252\) 2057.65i 0.514365i
\(253\) 64.8375i 0.0161119i
\(254\) 2919.01 0.721082
\(255\) 2765.59 323.372i 0.679168 0.0794131i
\(256\) −6101.62 −1.48965
\(257\) 662.784i 0.160869i −0.996760 0.0804345i \(-0.974369\pi\)
0.996760 0.0804345i \(-0.0256308\pi\)
\(258\) 5181.36i 1.25030i
\(259\) 5282.38 1.26730
\(260\) −362.447 3099.77i −0.0864538 0.739383i
\(261\) −220.810 −0.0523669
\(262\) 12169.3i 2.86955i
\(263\) 712.312i 0.167008i 0.996507 + 0.0835039i \(0.0266111\pi\)
−0.996507 + 0.0835039i \(0.973389\pi\)
\(264\) 3462.22 0.807139
\(265\) −79.8904 683.250i −0.0185194 0.158384i
\(266\) 3721.87 0.857905
\(267\) 290.925i 0.0666829i
\(268\) 7871.74i 1.79419i
\(269\) 3136.41 0.710894 0.355447 0.934696i \(-0.384329\pi\)
0.355447 + 0.934696i \(0.384329\pi\)
\(270\) −1409.65 + 164.827i −0.317736 + 0.0371519i
\(271\) −2275.69 −0.510105 −0.255053 0.966927i \(-0.582093\pi\)
−0.255053 + 0.966927i \(0.582093\pi\)
\(272\) 1835.03i 0.409064i
\(273\) 962.381i 0.213355i
\(274\) 7787.15 1.71693
\(275\) −4890.59 + 1159.54i −1.07241 + 0.254264i
\(276\) 68.2313 0.0148806
\(277\) 5171.00i 1.12164i −0.827937 0.560821i \(-0.810485\pi\)
0.827937 0.560821i \(-0.189515\pi\)
\(278\) 720.544i 0.155451i
\(279\) 111.769 0.0239836
\(280\) −5166.28 + 604.078i −1.10266 + 0.128931i
\(281\) 2240.14 0.475571 0.237785 0.971318i \(-0.423578\pi\)
0.237785 + 0.971318i \(0.423578\pi\)
\(282\) 2885.02i 0.609222i
\(283\) 225.244i 0.0473123i 0.999720 + 0.0236561i \(0.00753068\pi\)
−0.999720 + 0.0236561i \(0.992469\pi\)
\(284\) −7874.38 −1.64528
\(285\) 190.237 + 1626.98i 0.0395393 + 0.338153i
\(286\) −3741.36 −0.773535
\(287\) 3929.46i 0.808183i
\(288\) 1131.17i 0.231441i
\(289\) −1978.59 −0.402726
\(290\) −149.775 1280.93i −0.0303279 0.259374i
\(291\) −3457.12 −0.696427
\(292\) 14270.7i 2.86003i
\(293\) 1139.86i 0.227274i 0.993522 + 0.113637i \(0.0362501\pi\)
−0.993522 + 0.113637i \(0.963750\pi\)
\(294\) 1131.99 0.224554
\(295\) 1246.05 145.697i 0.245925 0.0287553i
\(296\) 9353.39 1.83667
\(297\) 1085.65i 0.212108i
\(298\) 6974.19i 1.35572i
\(299\) −31.9123 −0.00617237
\(300\) −1220.23 5146.58i −0.234834 0.990460i
\(301\) −5954.51 −1.14024
\(302\) 1853.74i 0.353214i
\(303\) 3469.47i 0.657808i
\(304\) 1079.54 0.203670
\(305\) 5300.82 619.809i 0.995161 0.116361i
\(306\) 3512.73 0.656240
\(307\) 5244.86i 0.975049i −0.873109 0.487525i \(-0.837900\pi\)
0.873109 0.487525i \(-0.162100\pi\)
\(308\) 9192.99i 1.70071i
\(309\) 4001.09 0.736615
\(310\) 75.8125 + 648.375i 0.0138899 + 0.118791i
\(311\) −5188.26 −0.945977 −0.472989 0.881068i \(-0.656825\pi\)
−0.472989 + 0.881068i \(0.656825\pi\)
\(312\) 1704.07i 0.309211i
\(313\) 486.656i 0.0878832i 0.999034 + 0.0439416i \(0.0139915\pi\)
−0.999034 + 0.0439416i \(0.986008\pi\)
\(314\) −8119.85 −1.45933
\(315\) −189.422 1620.00i −0.0338816 0.289767i
\(316\) 16227.0 2.88873
\(317\) 4218.87i 0.747493i 0.927531 + 0.373747i \(0.121927\pi\)
−0.927531 + 0.373747i \(0.878073\pi\)
\(318\) 867.834i 0.153037i
\(319\) −986.512 −0.173148
\(320\) 8525.71 996.886i 1.48938 0.174149i
\(321\) −2394.79 −0.416399
\(322\) 122.887i 0.0212678i
\(323\) 4054.27i 0.698408i
\(324\) −1142.48 −0.195898
\(325\) 570.712 + 2407.10i 0.0974074 + 0.410836i
\(326\) −9564.30 −1.62490
\(327\) 2955.36i 0.499791i
\(328\) 6957.80i 1.17128i
\(329\) −3315.53 −0.555595
\(330\) −6297.92 + 736.397i −1.05057 + 0.122840i
\(331\) 7439.94 1.23546 0.617728 0.786392i \(-0.288053\pi\)
0.617728 + 0.786392i \(0.288053\pi\)
\(332\) 16332.2i 2.69983i
\(333\) 2932.96i 0.482658i
\(334\) −906.931 −0.148578
\(335\) −724.650 6197.46i −0.118185 1.01076i
\(336\) −1074.91 −0.174527
\(337\) 6555.39i 1.05963i 0.848113 + 0.529815i \(0.177739\pi\)
−0.848113 + 0.529815i \(0.822261\pi\)
\(338\) 8487.88i 1.36592i
\(339\) −5664.74 −0.907571
\(340\) 1520.35 + 13002.6i 0.242508 + 2.07401i
\(341\) 499.350 0.0793000
\(342\) 2066.51i 0.326737i
\(343\) 6860.72i 1.08001i
\(344\) −10543.5 −1.65252
\(345\) −53.7188 + 6.28118i −0.00838297 + 0.000980195i
\(346\) −5829.51 −0.905770
\(347\) 1950.56i 0.301763i −0.988552 0.150881i \(-0.951789\pi\)
0.988552 0.150881i \(-0.0482112\pi\)
\(348\) 1038.15i 0.159916i
\(349\) 1426.74 0.218830 0.109415 0.993996i \(-0.465102\pi\)
0.109415 + 0.993996i \(0.465102\pi\)
\(350\) 9269.20 2197.69i 1.41560 0.335632i
\(351\) 534.347 0.0812573
\(352\) 5053.75i 0.765244i
\(353\) 7078.96i 1.06735i −0.845689 0.533676i \(-0.820810\pi\)
0.845689 0.533676i \(-0.179190\pi\)
\(354\) 1582.68 0.237623
\(355\) 6199.54 724.893i 0.926866 0.108376i
\(356\) 1367.80 0.203633
\(357\) 4036.89i 0.598474i
\(358\) 12397.4i 1.83023i
\(359\) 5409.79 0.795314 0.397657 0.917534i \(-0.369823\pi\)
0.397657 + 0.917534i \(0.369823\pi\)
\(360\) −335.405 2868.50i −0.0491038 0.419953i
\(361\) −4473.90 −0.652267
\(362\) 15597.8i 2.26465i
\(363\) 857.381i 0.123969i
\(364\) 4524.69 0.651534
\(365\) 1313.72 + 11235.4i 0.188392 + 1.61120i
\(366\) 6732.87 0.961565
\(367\) 4940.09i 0.702645i −0.936255 0.351322i \(-0.885732\pi\)
0.936255 0.351322i \(-0.114268\pi\)
\(368\) 35.6437i 0.00504907i
\(369\) 2181.77 0.307800
\(370\) −17014.2 + 1989.42i −2.39061 + 0.279527i
\(371\) 997.332 0.139566
\(372\) 525.488i 0.0732399i
\(373\) 12891.9i 1.78959i 0.446473 + 0.894797i \(0.352680\pi\)
−0.446473 + 0.894797i \(0.647320\pi\)
\(374\) 15693.8 2.16981
\(375\) 1434.47 + 3939.60i 0.197536 + 0.542506i
\(376\) −5870.72 −0.805211
\(377\) 485.551i 0.0663320i
\(378\) 2057.65i 0.279985i
\(379\) 9475.15 1.28418 0.642092 0.766627i \(-0.278067\pi\)
0.642092 + 0.766627i \(0.278067\pi\)
\(380\) −7649.32 + 894.413i −1.03264 + 0.120743i
\(381\) −1862.58 −0.250453
\(382\) 2936.16i 0.393264i
\(383\) 5800.97i 0.773931i −0.922094 0.386966i \(-0.873523\pi\)
0.922094 0.386966i \(-0.126477\pi\)
\(384\) 7812.52 1.03823
\(385\) −846.281 7237.69i −0.112027 0.958095i
\(386\) −2050.56 −0.270390
\(387\) 3306.15i 0.434266i
\(388\) 16253.9i 2.12672i
\(389\) −13779.7 −1.79603 −0.898016 0.439962i \(-0.854992\pi\)
−0.898016 + 0.439962i \(0.854992\pi\)
\(390\) 362.447 + 3099.77i 0.0470595 + 0.402469i
\(391\) 133.862 0.0173138
\(392\) 2303.48i 0.296794i
\(393\) 7765.06i 0.996680i
\(394\) −15777.5 −2.01741
\(395\) −12775.6 + 1493.81i −1.62737 + 0.190283i
\(396\) −5104.27 −0.647725
\(397\) 2816.46i 0.356056i 0.984025 + 0.178028i \(0.0569718\pi\)
−0.984025 + 0.178028i \(0.943028\pi\)
\(398\) 17864.8i 2.24996i
\(399\) −2374.88 −0.297976
\(400\) 2688.55 637.444i 0.336069 0.0796805i
\(401\) 11986.4 1.49270 0.746352 0.665551i \(-0.231804\pi\)
0.746352 + 0.665551i \(0.231804\pi\)
\(402\) 7871.74i 0.976633i
\(403\) 245.775i 0.0303794i
\(404\) 16311.9 2.00879
\(405\) 899.480 105.173i 0.110359 0.0129040i
\(406\) 1869.75 0.228557
\(407\) 13103.6i 1.59588i
\(408\) 7148.03i 0.867354i
\(409\) 3339.07 0.403683 0.201841 0.979418i \(-0.435307\pi\)
0.201841 + 0.979418i \(0.435307\pi\)
\(410\) 1479.89 + 12656.5i 0.178260 + 1.52454i
\(411\) −4968.87 −0.596342
\(412\) 18811.4i 2.24944i
\(413\) 1818.84i 0.216706i
\(414\) −68.2313 −0.00809996
\(415\) −1503.49 12858.4i −0.177840 1.52095i
\(416\) −2487.40 −0.293161
\(417\) 459.769i 0.0539927i
\(418\) 9232.57i 1.08033i
\(419\) −1688.52 −0.196873 −0.0984363 0.995143i \(-0.531384\pi\)
−0.0984363 + 0.995143i \(0.531384\pi\)
\(420\) 7616.53 890.578i 0.884878 0.103466i
\(421\) −2664.27 −0.308429 −0.154214 0.988037i \(-0.549285\pi\)
−0.154214 + 0.988037i \(0.549285\pi\)
\(422\) 11120.5i 1.28279i
\(423\) 1840.89i 0.211601i
\(424\) 1765.95 0.202269
\(425\) −2393.96 10097.0i −0.273233 1.15242i
\(426\) 7874.38 0.895575
\(427\) 7737.54i 0.876923i
\(428\) 11259.2i 1.27158i
\(429\) 2387.31 0.268672
\(430\) 19179.1 2242.56i 2.15093 0.251502i
\(431\) 12266.0 1.37084 0.685420 0.728148i \(-0.259619\pi\)
0.685420 + 0.728148i \(0.259619\pi\)
\(432\) 596.827i 0.0664695i
\(433\) 15647.3i 1.73664i −0.496008 0.868318i \(-0.665201\pi\)
0.496008 0.868318i \(-0.334799\pi\)
\(434\) −946.425 −0.104677
\(435\) 95.5691 + 817.340i 0.0105338 + 0.0900884i
\(436\) −13894.8 −1.52624
\(437\) 78.7503i 0.00862045i
\(438\) 14270.7i 1.55680i
\(439\) −16131.0 −1.75373 −0.876867 0.480733i \(-0.840371\pi\)
−0.876867 + 0.480733i \(0.840371\pi\)
\(440\) −1498.49 12815.6i −0.162358 1.38855i
\(441\) −722.306 −0.0779944
\(442\) 7724.34i 0.831243i
\(443\) 10053.7i 1.07825i 0.842225 + 0.539127i \(0.181246\pi\)
−0.842225 + 0.539127i \(0.818754\pi\)
\(444\) −13789.5 −1.47392
\(445\) −1076.88 + 125.916i −0.114717 + 0.0134135i
\(446\) −15649.5 −1.66150
\(447\) 4450.13i 0.470882i
\(448\) 12444.9i 1.31242i
\(449\) −7477.71 −0.785957 −0.392979 0.919548i \(-0.628555\pi\)
−0.392979 + 0.919548i \(0.628555\pi\)
\(450\) 1220.23 + 5146.58i 0.127827 + 0.539138i
\(451\) 9747.51 1.01772
\(452\) 26633.1i 2.77150i
\(453\) 1182.84i 0.122682i
\(454\) 2478.19 0.256184
\(455\) −3562.31 + 416.531i −0.367041 + 0.0429170i
\(456\) −4205.14 −0.431850
\(457\) 1363.46i 0.139562i −0.997562 0.0697812i \(-0.977770\pi\)
0.997562 0.0697812i \(-0.0222301\pi\)
\(458\) 12064.5i 1.23086i
\(459\) −2241.42 −0.227932
\(460\) −29.5314 252.562i −0.00299328 0.0255995i
\(461\) 5276.77 0.533109 0.266555 0.963820i \(-0.414115\pi\)
0.266555 + 0.963820i \(0.414115\pi\)
\(462\) 9192.99i 0.925751i
\(463\) 5740.02i 0.576159i 0.957607 + 0.288079i \(0.0930167\pi\)
−0.957607 + 0.288079i \(0.906983\pi\)
\(464\) 542.325 0.0542604
\(465\) −48.3749 413.719i −0.00482437 0.0412597i
\(466\) 26023.1 2.58690
\(467\) 6233.36i 0.617657i −0.951118 0.308828i \(-0.900063\pi\)
0.951118 0.308828i \(-0.0999368\pi\)
\(468\) 2512.27i 0.248140i
\(469\) 9046.35 0.890664
\(470\) 10679.1 1248.68i 1.04806 0.122547i
\(471\) 5181.16 0.506869
\(472\) 3220.58i 0.314067i
\(473\) 14770.9i 1.43587i
\(474\) −16227.0 −1.57243
\(475\) 5940.01 1408.35i 0.573782 0.136041i
\(476\) −18979.7 −1.82759
\(477\) 553.753i 0.0531543i
\(478\) 4748.61i 0.454385i
\(479\) 19688.2 1.87803 0.939013 0.343881i \(-0.111742\pi\)
0.939013 + 0.343881i \(0.111742\pi\)
\(480\) −4187.11 + 489.586i −0.398155 + 0.0465551i
\(481\) 6449.46 0.611372
\(482\) 19155.5i 1.81019i
\(483\) 78.4127i 0.00738696i
\(484\) −4031.03 −0.378572
\(485\) 1496.29 + 12796.8i 0.140088 + 1.19808i
\(486\) 1142.48 0.106634
\(487\) 3955.08i 0.368012i 0.982925 + 0.184006i \(0.0589065\pi\)
−0.982925 + 0.184006i \(0.941093\pi\)
\(488\) 13700.7i 1.27090i
\(489\) 6102.84 0.564377
\(490\) −489.939 4190.13i −0.0451698 0.386308i
\(491\) −13893.5 −1.27699 −0.638497 0.769624i \(-0.720443\pi\)
−0.638497 + 0.769624i \(0.720443\pi\)
\(492\) 10257.7i 0.939947i
\(493\) 2036.74i 0.186065i
\(494\) 4544.18 0.413871
\(495\) 4018.61 469.884i 0.364895 0.0426661i
\(496\) −274.512 −0.0248508
\(497\) 9049.39i 0.816741i
\(498\) 16332.2i 1.46960i
\(499\) −13523.7 −1.21324 −0.606618 0.794993i \(-0.707474\pi\)
−0.606618 + 0.794993i \(0.707474\pi\)
\(500\) −18522.3 + 6744.27i −1.65668 + 0.603226i
\(501\) 578.700 0.0516056
\(502\) 8340.50i 0.741543i
\(503\) 13135.4i 1.16437i 0.813057 + 0.582184i \(0.197802\pi\)
−0.813057 + 0.582184i \(0.802198\pi\)
\(504\) 4187.11 0.370057
\(505\) −12842.5 + 1501.63i −1.13165 + 0.132320i
\(506\) −304.837 −0.0267820
\(507\) 5415.99i 0.474423i
\(508\) 8757.03i 0.764823i
\(509\) 2222.71 0.193556 0.0967778 0.995306i \(-0.469146\pi\)
0.0967778 + 0.995306i \(0.469146\pi\)
\(510\) −1520.35 13002.6i −0.132005 1.12895i
\(511\) −16400.1 −1.41976
\(512\) 7853.76i 0.677911i
\(513\) 1318.61i 0.113486i
\(514\) −3116.12 −0.267405
\(515\) −1731.72 14810.3i −0.148172 1.26722i
\(516\) 15544.1 1.32614
\(517\) 8224.57i 0.699645i
\(518\) 24835.4i 2.10658i
\(519\) 3719.73 0.314601
\(520\) −6307.71 + 737.541i −0.531945 + 0.0621987i
\(521\) −4916.42 −0.413421 −0.206710 0.978402i \(-0.566276\pi\)
−0.206710 + 0.978402i \(0.566276\pi\)
\(522\) 1038.15i 0.0870471i
\(523\) 17743.4i 1.48349i 0.670681 + 0.741746i \(0.266002\pi\)
−0.670681 + 0.741746i \(0.733998\pi\)
\(524\) 36507.9 3.04362
\(525\) −5914.55 + 1402.31i −0.491680 + 0.116575i
\(526\) 3348.98 0.277609
\(527\) 1030.95i 0.0852161i
\(528\) 2666.45i 0.219777i
\(529\) 12164.4 0.999786
\(530\) −3212.34 + 375.610i −0.263274 + 0.0307839i
\(531\) −1009.88 −0.0825334
\(532\) 11165.6i 0.909946i
\(533\) 4797.62i 0.389884i
\(534\) −1367.80 −0.110844
\(535\) 1036.49 + 8864.46i 0.0837599 + 0.716344i
\(536\) 16018.2 1.29082
\(537\) 7910.58i 0.635692i
\(538\) 14746.0i 1.18169i
\(539\) −3227.05 −0.257883
\(540\) 494.480 + 4228.96i 0.0394056 + 0.337010i
\(541\) −12671.3 −1.00699 −0.503495 0.863998i \(-0.667953\pi\)
−0.503495 + 0.863998i \(0.667953\pi\)
\(542\) 10699.3i 0.847924i
\(543\) 9952.74i 0.786580i
\(544\) 10433.9 0.822334
\(545\) 10939.4 1279.12i 0.859805 0.100534i
\(546\) −4524.69 −0.354650
\(547\) 5250.90i 0.410443i −0.978716 0.205221i \(-0.934209\pi\)
0.978716 0.205221i \(-0.0657915\pi\)
\(548\) 23361.5i 1.82108i
\(549\) −4296.15 −0.333980
\(550\) 5451.64 + 22993.4i 0.422652 + 1.78262i
\(551\) 1198.20 0.0926406
\(552\) 138.844i 0.0107057i
\(553\) 18648.4i 1.43401i
\(554\) −24311.8 −1.86445
\(555\) 10856.5 1269.42i 0.830332 0.0970882i
\(556\) −2161.63 −0.164881
\(557\) 25830.2i 1.96492i −0.186465 0.982462i \(-0.559703\pi\)
0.186465 0.982462i \(-0.440297\pi\)
\(558\) 525.488i 0.0398668i
\(559\) −7270.09 −0.550075
\(560\) 465.234 + 3978.84i 0.0351067 + 0.300244i
\(561\) −10014.0 −0.753640
\(562\) 10532.1i 0.790519i
\(563\) 2021.14i 0.151298i 0.997135 + 0.0756490i \(0.0241029\pi\)
−0.997135 + 0.0756490i \(0.975897\pi\)
\(564\) 8655.07 0.646178
\(565\) 2451.77 + 20968.4i 0.182561 + 1.56132i
\(566\) 1059.00 0.0786450
\(567\) 1312.96i 0.0972471i
\(568\) 16023.5i 1.18368i
\(569\) −8706.51 −0.641469 −0.320734 0.947169i \(-0.603930\pi\)
−0.320734 + 0.947169i \(0.603930\pi\)
\(570\) 7649.32 894.413i 0.562096 0.0657243i
\(571\) −12194.5 −0.893740 −0.446870 0.894599i \(-0.647461\pi\)
−0.446870 + 0.894599i \(0.647461\pi\)
\(572\) 11224.1i 0.820458i
\(573\) 1873.52i 0.136592i
\(574\) −18474.6 −1.34340
\(575\) 46.5004 + 196.125i 0.00337252 + 0.0142243i
\(576\) −6909.82 −0.499842
\(577\) 15264.0i 1.10130i 0.834737 + 0.550649i \(0.185620\pi\)
−0.834737 + 0.550649i \(0.814380\pi\)
\(578\) 9302.48i 0.669433i
\(579\) 1308.43 0.0939146
\(580\) −3842.78 + 449.324i −0.275108 + 0.0321675i
\(581\) 18769.2 1.34024
\(582\) 16253.9i 1.15764i
\(583\) 2474.01i 0.175751i
\(584\) −29039.3 −2.05763
\(585\) −231.272 1977.92i −0.0163452 0.139790i
\(586\) 5359.12 0.377787
\(587\) 8456.89i 0.594639i 0.954778 + 0.297319i \(0.0960926\pi\)
−0.954778 + 0.297319i \(0.903907\pi\)
\(588\) 3395.97i 0.238176i
\(589\) −606.500 −0.0424285
\(590\) −685.003 5858.38i −0.0477985 0.408789i
\(591\) 10067.4 0.700708
\(592\) 7203.57i 0.500110i
\(593\) 1225.23i 0.0848467i −0.999100 0.0424234i \(-0.986492\pi\)
0.999100 0.0424234i \(-0.0135078\pi\)
\(594\) 5104.27 0.352577
\(595\) 14942.8 1747.22i 1.02957 0.120385i
\(596\) 20922.6 1.43796
\(597\) 11399.3i 0.781478i
\(598\) 150.038i 0.0102600i
\(599\) 16060.0 1.09548 0.547741 0.836648i \(-0.315488\pi\)
0.547741 + 0.836648i \(0.315488\pi\)
\(600\) −10472.8 + 2483.04i −0.712580 + 0.168950i
\(601\) 9699.93 0.658350 0.329175 0.944269i \(-0.393229\pi\)
0.329175 + 0.944269i \(0.393229\pi\)
\(602\) 27995.5i 1.89537i
\(603\) 5022.84i 0.339214i
\(604\) 5561.21 0.374640
\(605\) 3173.65 371.085i 0.213268 0.0249368i
\(606\) −16311.9 −1.09344
\(607\) 23661.2i 1.58217i −0.611703 0.791087i \(-0.709515\pi\)
0.611703 0.791087i \(-0.290485\pi\)
\(608\) 6138.19i 0.409435i
\(609\) −1193.06 −0.0793847
\(610\) −2914.07 24922.1i −0.193422 1.65421i
\(611\) −4048.05 −0.268030
\(612\) 10538.2i 0.696047i
\(613\) 8085.63i 0.532749i −0.963870 0.266375i \(-0.914174\pi\)
0.963870 0.266375i \(-0.0858258\pi\)
\(614\) −24659.0 −1.62078
\(615\) −944.297 8075.95i −0.0619150 0.529518i
\(616\) 18706.8 1.22357
\(617\) 11035.1i 0.720029i 0.932947 + 0.360014i \(0.117228\pi\)
−0.932947 + 0.360014i \(0.882772\pi\)
\(618\) 18811.4i 1.22444i
\(619\) 16826.3 1.09258 0.546290 0.837596i \(-0.316040\pi\)
0.546290 + 0.837596i \(0.316040\pi\)
\(620\) 1945.12 227.438i 0.125997 0.0147324i
\(621\) 43.5374 0.00281336
\(622\) 24392.9i 1.57245i
\(623\) 1571.90i 0.101087i
\(624\) −1312.40 −0.0841954
\(625\) 13961.8 7014.90i 0.893555 0.448954i
\(626\) 2288.04 0.146084
\(627\) 5891.17i 0.375233i
\(628\) 24359.5i 1.54785i
\(629\) −27053.5 −1.71493
\(630\) −7616.53 + 890.578i −0.481666 + 0.0563198i
\(631\) −3705.91 −0.233803 −0.116902 0.993144i \(-0.537296\pi\)
−0.116902 + 0.993144i \(0.537296\pi\)
\(632\) 33020.2i 2.07828i
\(633\) 7095.81i 0.445550i
\(634\) 19835.3 1.24252
\(635\) 806.147 + 6894.45i 0.0503795 + 0.430863i
\(636\) −2603.50 −0.162320
\(637\) 1588.32i 0.0987937i
\(638\) 4638.15i 0.287815i
\(639\) −5024.53 −0.311060
\(640\) −3381.36 28918.5i −0.208844 1.78610i
\(641\) −24597.4 −1.51566 −0.757829 0.652453i \(-0.773740\pi\)
−0.757829 + 0.652453i \(0.773740\pi\)
\(642\) 11259.2i 0.692160i
\(643\) 21479.5i 1.31737i −0.752419 0.658685i \(-0.771113\pi\)
0.752419 0.658685i \(-0.228887\pi\)
\(644\) 368.662 0.0225580
\(645\) −12237.9 + 1430.94i −0.747081 + 0.0873540i
\(646\) −19061.4 −1.16093
\(647\) 27119.7i 1.64789i −0.566668 0.823946i \(-0.691768\pi\)
0.566668 0.823946i \(-0.308232\pi\)
\(648\) 2324.83i 0.140938i
\(649\) −4511.87 −0.272891
\(650\) 11317.1 2683.24i 0.682913 0.161916i
\(651\) 603.900 0.0363575
\(652\) 28692.9i 1.72347i
\(653\) 18476.4i 1.10725i 0.832765 + 0.553627i \(0.186757\pi\)
−0.832765 + 0.553627i \(0.813243\pi\)
\(654\) 13894.8 0.830779
\(655\) −28742.8 + 3360.82i −1.71462 + 0.200485i
\(656\) −5358.59 −0.318930
\(657\) 9105.92i 0.540724i
\(658\) 15588.1i 0.923540i
\(659\) 19273.5 1.13928 0.569641 0.821894i \(-0.307082\pi\)
0.569641 + 0.821894i \(0.307082\pi\)
\(660\) 2209.19 + 18893.8i 0.130292 + 1.11430i
\(661\) 25605.3 1.50670 0.753352 0.657618i \(-0.228436\pi\)
0.753352 + 0.657618i \(0.228436\pi\)
\(662\) 34979.3i 2.05364i
\(663\) 4928.79i 0.288716i
\(664\) 33234.3 1.94238
\(665\) 1027.88 + 8790.75i 0.0599388 + 0.512617i
\(666\) 13789.5 0.802300
\(667\) 39.5616i 0.00229660i
\(668\) 2720.79i 0.157591i
\(669\) 9985.75 0.577087
\(670\) −29137.7 + 3406.99i −1.68013 + 0.196453i
\(671\) −19193.9 −1.10428
\(672\) 6111.87i 0.350849i
\(673\) 7855.52i 0.449938i 0.974366 + 0.224969i \(0.0722280\pi\)
−0.974366 + 0.224969i \(0.927772\pi\)
\(674\) 30820.6 1.76137
\(675\) −778.612 3283.96i −0.0443982 0.187259i
\(676\) −25463.6 −1.44877
\(677\) 6763.09i 0.383939i 0.981401 + 0.191970i \(0.0614875\pi\)
−0.981401 + 0.191970i \(0.938512\pi\)
\(678\) 26633.1i 1.50861i
\(679\) −18679.3 −1.05574
\(680\) 26458.9 3093.76i 1.49214 0.174471i
\(681\) −1581.30 −0.0889803
\(682\) 2347.72i 0.131817i
\(683\) 15608.6i 0.874447i 0.899353 + 0.437224i \(0.144038\pi\)
−0.899353 + 0.437224i \(0.855962\pi\)
\(684\) 6199.54 0.346557
\(685\) 2150.59 + 18392.6i 0.119956 + 1.02590i
\(686\) 32256.1 1.79525
\(687\) 7698.17i 0.427516i
\(688\) 8120.16i 0.449968i
\(689\) 1217.68 0.0673293
\(690\) 29.5314 + 252.562i 0.00162933 + 0.0139346i
\(691\) 6203.15 0.341504 0.170752 0.985314i \(-0.445380\pi\)
0.170752 + 0.985314i \(0.445380\pi\)
\(692\) 17488.5i 0.960714i
\(693\) 5865.92i 0.321541i
\(694\) −9170.69 −0.501606
\(695\) 1701.86 198.994i 0.0928854 0.0108608i
\(696\) −2112.53 −0.115050
\(697\) 20124.5i 1.09365i
\(698\) 6707.90i 0.363750i
\(699\) −16605.0 −0.898509
\(700\) −6593.06 27807.6i −0.355992 1.50147i
\(701\) −16507.9 −0.889435 −0.444718 0.895671i \(-0.646696\pi\)
−0.444718 + 0.895671i \(0.646696\pi\)
\(702\) 2512.27i 0.135070i
\(703\) 15915.4i 0.853854i
\(704\) −30871.1 −1.65269
\(705\) −6814.18 + 796.762i −0.364024 + 0.0425642i
\(706\) −33282.2 −1.77421
\(707\) 18746.0i 0.997193i
\(708\) 4748.03i 0.252037i
\(709\) 25539.6 1.35283 0.676416 0.736520i \(-0.263532\pi\)
0.676416 + 0.736520i \(0.263532\pi\)
\(710\) −3408.13 29147.5i −0.180148 1.54069i
\(711\) 10354.2 0.546151
\(712\) 2783.34i 0.146503i
\(713\) 20.0252i 0.00105182i
\(714\) 18979.7 0.994815
\(715\) −1033.26 8836.76i −0.0540442 0.462204i
\(716\) −37192.1 −1.94125
\(717\) 3030.02i 0.157822i
\(718\) 25434.4i 1.32201i
\(719\) 7353.45 0.381415 0.190708 0.981647i \(-0.438922\pi\)
0.190708 + 0.981647i \(0.438922\pi\)
\(720\) −2209.19 + 258.314i −0.114350 + 0.0133706i
\(721\) 21618.4 1.11666
\(722\) 21034.3i 1.08423i
\(723\) 12222.9i 0.628732i
\(724\) −46793.4 −2.40202
\(725\) 2984.07 707.510i 0.152863 0.0362431i
\(726\) 4031.03 0.206068
\(727\) 21696.5i 1.10685i 0.832900 + 0.553424i \(0.186679\pi\)
−0.832900 + 0.553424i \(0.813321\pi\)
\(728\) 9207.28i 0.468742i
\(729\) −729.000 −0.0370370
\(730\) 52823.8 6176.53i 2.67821 0.313156i
\(731\) 30495.8 1.54299
\(732\) 20198.6i 1.01989i
\(733\) 90.2714i 0.00454877i 0.999997 + 0.00227439i \(0.000723960\pi\)
−0.999997 + 0.00227439i \(0.999276\pi\)
\(734\) −23226.1 −1.16797
\(735\) 312.623 + 2673.66i 0.0156888 + 0.134176i
\(736\) −202.668 −0.0101501
\(737\) 22440.6i 1.12159i
\(738\) 10257.7i 0.511642i
\(739\) −14273.1 −0.710479 −0.355239 0.934775i \(-0.615601\pi\)
−0.355239 + 0.934775i \(0.615601\pi\)
\(740\) 5968.27 + 51042.7i 0.296484 + 2.53563i
\(741\) −2899.57 −0.143750
\(742\) 4689.02i 0.231994i
\(743\) 15866.6i 0.783429i 0.920087 + 0.391715i \(0.128118\pi\)
−0.920087 + 0.391715i \(0.871882\pi\)
\(744\) 1069.31 0.0526921
\(745\) −16472.4 + 1926.07i −0.810072 + 0.0947193i
\(746\) 60612.2 2.97476
\(747\) 10421.3i 0.510437i
\(748\) 47081.5i 2.30143i
\(749\) −12939.3 −0.631232
\(750\) 18522.3 6744.27i 0.901783 0.328354i
\(751\) 26776.9 1.30107 0.650534 0.759477i \(-0.274545\pi\)
0.650534 + 0.759477i \(0.274545\pi\)
\(752\) 4521.37i 0.219252i
\(753\) 5321.95i 0.257560i
\(754\) 2282.85 0.110261
\(755\) −4378.37 + 511.950i −0.211053 + 0.0246778i
\(756\) −6172.96 −0.296969
\(757\) 30478.0i 1.46333i −0.681663 0.731666i \(-0.738743\pi\)
0.681663 0.731666i \(-0.261257\pi\)
\(758\) 44548.0i 2.13464i
\(759\) 194.512 0.00930218
\(760\) 1820.04 + 15565.6i 0.0868680 + 0.742925i
\(761\) 29104.7 1.38639 0.693195 0.720750i \(-0.256202\pi\)
0.693195 + 0.720750i \(0.256202\pi\)
\(762\) 8757.03i 0.416317i
\(763\) 15968.2i 0.757649i
\(764\) 8808.47 0.417119
\(765\) 970.116 + 8296.76i 0.0458492 + 0.392118i
\(766\) −27273.6 −1.28647
\(767\) 2220.69i 0.104543i
\(768\) 18304.9i 0.860052i
\(769\) −4170.65 −0.195575 −0.0977876 0.995207i \(-0.531177\pi\)
−0.0977876 + 0.995207i \(0.531177\pi\)
\(770\) −34028.4 + 3978.84i −1.59260 + 0.186218i
\(771\) 1988.35 0.0928778
\(772\) 6151.67i 0.286792i
\(773\) 17738.5i 0.825367i −0.910874 0.412684i \(-0.864591\pi\)
0.910874 0.412684i \(-0.135409\pi\)
\(774\) −15544.1 −0.721860
\(775\) −1510.47 + 358.125i −0.0700099 + 0.0165990i
\(776\) −33075.0 −1.53005
\(777\) 15847.1i 0.731677i
\(778\) 64786.0i 2.98546i
\(779\) −11839.1 −0.544519
\(780\) 9299.31 1087.34i 0.426883 0.0499141i
\(781\) −22448.1 −1.02850
\(782\) 629.363i 0.0287800i