Properties

Label 1050.3.f.e.601.12
Level $1050$
Weight $3$
Character 1050.601
Analytic conductor $28.610$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 8 x^{15} + 88 x^{14} - 476 x^{13} + 2744 x^{12} - 10640 x^{11} + 39126 x^{10} - 108488 x^{9} + 259514 x^{8} - 486436 x^{7} + 690168 x^{6} - 725188 x^{5} + \cdots + 33124 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{20} \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 601.12
Root \(1.20711 + 4.25887i\) of defining polynomial
Character \(\chi\) \(=\) 1050.601
Dual form 1050.3.f.e.601.16

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(4.63050 + 5.24961i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(4.63050 + 5.24961i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +11.7671 q^{11} -3.46410i q^{12} +24.8280i q^{13} +(6.54852 + 7.42407i) q^{14} +4.00000 q^{16} -7.26100i q^{17} -4.24264 q^{18} +23.0050i q^{19} +(9.09260 - 8.02027i) q^{21} +16.6412 q^{22} -26.4223 q^{23} -4.89898i q^{24} +35.1122i q^{26} +5.19615i q^{27} +(9.26101 + 10.4992i) q^{28} -57.0861 q^{29} +10.2222i q^{31} +5.65685 q^{32} -20.3812i q^{33} -10.2686i q^{34} -6.00000 q^{36} +14.2196 q^{37} +32.5340i q^{38} +43.0034 q^{39} +16.2271i q^{41} +(12.8589 - 11.3424i) q^{42} +82.3114 q^{43} +23.5342 q^{44} -37.3668 q^{46} +51.6631i q^{47} -6.92820i q^{48} +(-6.11686 + 48.6167i) q^{49} -12.5764 q^{51} +49.6561i q^{52} +64.8273 q^{53} +7.34847i q^{54} +(13.0970 + 14.8481i) q^{56} +39.8459 q^{57} -80.7320 q^{58} -81.7685i q^{59} -13.1240i q^{61} +14.4564i q^{62} +(-13.8915 - 15.7488i) q^{63} +8.00000 q^{64} -28.8233i q^{66} +22.4035 q^{67} -14.5220i q^{68} +45.7648i q^{69} +91.5022 q^{71} -8.48528 q^{72} -71.9256i q^{73} +20.1096 q^{74} +46.0100i q^{76} +(54.4875 + 61.7726i) q^{77} +60.8160 q^{78} -45.2802 q^{79} +9.00000 q^{81} +22.9486i q^{82} +17.7328i q^{83} +(18.1852 - 16.0405i) q^{84} +116.406 q^{86} +98.8761i q^{87} +33.2823 q^{88} -77.5800i q^{89} +(-130.338 + 114.966i) q^{91} -52.8446 q^{92} +17.7054 q^{93} +73.0627i q^{94} -9.79796i q^{96} +6.15741i q^{97} +(-8.65055 + 68.7544i) q^{98} -35.3012 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 32 q^{4} - 48 q^{9} + 96 q^{11} - 16 q^{14} + 64 q^{16} + 24 q^{21} - 64 q^{29} - 96 q^{36} + 144 q^{39} + 192 q^{44} - 176 q^{46} - 224 q^{49} - 48 q^{51} - 32 q^{56} + 128 q^{64} - 384 q^{71} - 224 q^{74} + 608 q^{79} + 144 q^{81} + 48 q^{84} + 416 q^{86} + 224 q^{91} - 288 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 0.707107
\(3\) 1.73205i 0.577350i
\(4\) 2.00000 0.500000
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) 4.63050 + 5.24961i 0.661501 + 0.749945i
\(8\) 2.82843 0.353553
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 11.7671 1.06973 0.534867 0.844936i \(-0.320362\pi\)
0.534867 + 0.844936i \(0.320362\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 24.8280i 1.90985i 0.296848 + 0.954925i \(0.404065\pi\)
−0.296848 + 0.954925i \(0.595935\pi\)
\(14\) 6.54852 + 7.42407i 0.467752 + 0.530291i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 7.26100i 0.427118i −0.976930 0.213559i \(-0.931494\pi\)
0.976930 0.213559i \(-0.0685055\pi\)
\(18\) −4.24264 −0.235702
\(19\) 23.0050i 1.21079i 0.795925 + 0.605395i \(0.206985\pi\)
−0.795925 + 0.605395i \(0.793015\pi\)
\(20\) 0 0
\(21\) 9.09260 8.02027i 0.432981 0.381918i
\(22\) 16.6412 0.756417
\(23\) −26.4223 −1.14880 −0.574398 0.818576i \(-0.694764\pi\)
−0.574398 + 0.818576i \(0.694764\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 0 0
\(26\) 35.1122i 1.35047i
\(27\) 5.19615i 0.192450i
\(28\) 9.26101 + 10.4992i 0.330750 + 0.374972i
\(29\) −57.0861 −1.96849 −0.984243 0.176819i \(-0.943419\pi\)
−0.984243 + 0.176819i \(0.943419\pi\)
\(30\) 0 0
\(31\) 10.2222i 0.329749i 0.986315 + 0.164874i \(0.0527219\pi\)
−0.986315 + 0.164874i \(0.947278\pi\)
\(32\) 5.65685 0.176777
\(33\) 20.3812i 0.617612i
\(34\) 10.2686i 0.302018i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 14.2196 0.384314 0.192157 0.981364i \(-0.438452\pi\)
0.192157 + 0.981364i \(0.438452\pi\)
\(38\) 32.5340i 0.856158i
\(39\) 43.0034 1.10265
\(40\) 0 0
\(41\) 16.2271i 0.395782i 0.980224 + 0.197891i \(0.0634093\pi\)
−0.980224 + 0.197891i \(0.936591\pi\)
\(42\) 12.8589 11.3424i 0.306164 0.270056i
\(43\) 82.3114 1.91422 0.957110 0.289725i \(-0.0935639\pi\)
0.957110 + 0.289725i \(0.0935639\pi\)
\(44\) 23.5342 0.534867
\(45\) 0 0
\(46\) −37.3668 −0.812321
\(47\) 51.6631i 1.09922i 0.835423 + 0.549608i \(0.185223\pi\)
−0.835423 + 0.549608i \(0.814777\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −6.11686 + 48.6167i −0.124834 + 0.992178i
\(50\) 0 0
\(51\) −12.5764 −0.246597
\(52\) 49.6561i 0.954925i
\(53\) 64.8273 1.22316 0.611579 0.791184i \(-0.290535\pi\)
0.611579 + 0.791184i \(0.290535\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 0 0
\(56\) 13.0970 + 14.8481i 0.233876 + 0.265145i
\(57\) 39.8459 0.699050
\(58\) −80.7320 −1.39193
\(59\) 81.7685i 1.38591i −0.720982 0.692953i \(-0.756309\pi\)
0.720982 0.692953i \(-0.243691\pi\)
\(60\) 0 0
\(61\) 13.1240i 0.215148i −0.994197 0.107574i \(-0.965692\pi\)
0.994197 0.107574i \(-0.0343083\pi\)
\(62\) 14.4564i 0.233168i
\(63\) −13.8915 15.7488i −0.220500 0.249982i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) 28.8233i 0.436717i
\(67\) 22.4035 0.334381 0.167190 0.985925i \(-0.446531\pi\)
0.167190 + 0.985925i \(0.446531\pi\)
\(68\) 14.5220i 0.213559i
\(69\) 45.7648i 0.663257i
\(70\) 0 0
\(71\) 91.5022 1.28876 0.644382 0.764704i \(-0.277115\pi\)
0.644382 + 0.764704i \(0.277115\pi\)
\(72\) −8.48528 −0.117851
\(73\) 71.9256i 0.985282i −0.870233 0.492641i \(-0.836032\pi\)
0.870233 0.492641i \(-0.163968\pi\)
\(74\) 20.1096 0.271751
\(75\) 0 0
\(76\) 46.0100i 0.605395i
\(77\) 54.4875 + 61.7726i 0.707630 + 0.802242i
\(78\) 60.8160 0.779693
\(79\) −45.2802 −0.573167 −0.286584 0.958055i \(-0.592520\pi\)
−0.286584 + 0.958055i \(0.592520\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 22.9486i 0.279860i
\(83\) 17.7328i 0.213648i 0.994278 + 0.106824i \(0.0340681\pi\)
−0.994278 + 0.106824i \(0.965932\pi\)
\(84\) 18.1852 16.0405i 0.216490 0.190959i
\(85\) 0 0
\(86\) 116.406 1.35356
\(87\) 98.8761i 1.13651i
\(88\) 33.2823 0.378208
\(89\) 77.5800i 0.871686i −0.900023 0.435843i \(-0.856450\pi\)
0.900023 0.435843i \(-0.143550\pi\)
\(90\) 0 0
\(91\) −130.338 + 114.966i −1.43228 + 1.26337i
\(92\) −52.8446 −0.574398
\(93\) 17.7054 0.190381
\(94\) 73.0627i 0.777263i
\(95\) 0 0
\(96\) 9.79796i 0.102062i
\(97\) 6.15741i 0.0634785i 0.999496 + 0.0317392i \(0.0101046\pi\)
−0.999496 + 0.0317392i \(0.989895\pi\)
\(98\) −8.65055 + 68.7544i −0.0882709 + 0.701576i
\(99\) −35.3012 −0.356578
\(100\) 0 0
\(101\) 142.983i 1.41568i −0.706374 0.707839i \(-0.749670\pi\)
0.706374 0.707839i \(-0.250330\pi\)
\(102\) −17.7858 −0.174370
\(103\) 14.5292i 0.141060i 0.997510 + 0.0705302i \(0.0224691\pi\)
−0.997510 + 0.0705302i \(0.977531\pi\)
\(104\) 70.2243i 0.675234i
\(105\) 0 0
\(106\) 91.6797 0.864903
\(107\) 78.4228 0.732923 0.366462 0.930433i \(-0.380569\pi\)
0.366462 + 0.930433i \(0.380569\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) 74.7424 0.685710 0.342855 0.939388i \(-0.388606\pi\)
0.342855 + 0.939388i \(0.388606\pi\)
\(110\) 0 0
\(111\) 24.6291i 0.221884i
\(112\) 18.5220 + 20.9985i 0.165375 + 0.187486i
\(113\) −85.2417 −0.754351 −0.377175 0.926142i \(-0.623105\pi\)
−0.377175 + 0.926142i \(0.623105\pi\)
\(114\) 56.3506 0.494303
\(115\) 0 0
\(116\) −114.172 −0.984243
\(117\) 74.4841i 0.636617i
\(118\) 115.638i 0.979984i
\(119\) 38.1175 33.6221i 0.320315 0.282539i
\(120\) 0 0
\(121\) 17.4642 0.144332
\(122\) 18.5602i 0.152133i
\(123\) 28.1061 0.228505
\(124\) 20.4444i 0.164874i
\(125\) 0 0
\(126\) −19.6456 22.2722i −0.155917 0.176764i
\(127\) 66.7734 0.525775 0.262887 0.964827i \(-0.415325\pi\)
0.262887 + 0.964827i \(0.415325\pi\)
\(128\) 11.3137 0.0883883
\(129\) 142.568i 1.10518i
\(130\) 0 0
\(131\) 28.8330i 0.220099i 0.993926 + 0.110049i \(0.0351009\pi\)
−0.993926 + 0.110049i \(0.964899\pi\)
\(132\) 40.7624i 0.308806i
\(133\) −120.767 + 106.525i −0.908026 + 0.800939i
\(134\) 31.6834 0.236443
\(135\) 0 0
\(136\) 20.5372i 0.151009i
\(137\) 119.450 0.871897 0.435948 0.899972i \(-0.356413\pi\)
0.435948 + 0.899972i \(0.356413\pi\)
\(138\) 64.7211i 0.468994i
\(139\) 200.948i 1.44567i −0.691021 0.722834i \(-0.742839\pi\)
0.691021 0.722834i \(-0.257161\pi\)
\(140\) 0 0
\(141\) 89.4832 0.634633
\(142\) 129.404 0.911293
\(143\) 292.154i 2.04303i
\(144\) −12.0000 −0.0833333
\(145\) 0 0
\(146\) 101.718i 0.696700i
\(147\) 84.2066 + 10.5947i 0.572834 + 0.0720729i
\(148\) 28.4392 0.192157
\(149\) 5.70484 0.0382875 0.0191438 0.999817i \(-0.493906\pi\)
0.0191438 + 0.999817i \(0.493906\pi\)
\(150\) 0 0
\(151\) −216.490 −1.43371 −0.716854 0.697223i \(-0.754419\pi\)
−0.716854 + 0.697223i \(0.754419\pi\)
\(152\) 65.0680i 0.428079i
\(153\) 21.7830i 0.142373i
\(154\) 77.0570 + 87.3597i 0.500370 + 0.567271i
\(155\) 0 0
\(156\) 86.0069 0.551326
\(157\) 108.287i 0.689726i 0.938653 + 0.344863i \(0.112075\pi\)
−0.938653 + 0.344863i \(0.887925\pi\)
\(158\) −64.0359 −0.405290
\(159\) 112.284i 0.706190i
\(160\) 0 0
\(161\) −122.349 138.707i −0.759929 0.861533i
\(162\) 12.7279 0.0785674
\(163\) 234.395 1.43800 0.719002 0.695008i \(-0.244599\pi\)
0.719002 + 0.695008i \(0.244599\pi\)
\(164\) 32.4542i 0.197891i
\(165\) 0 0
\(166\) 25.0779i 0.151072i
\(167\) 41.8830i 0.250796i −0.992106 0.125398i \(-0.959979\pi\)
0.992106 0.125398i \(-0.0400209\pi\)
\(168\) 25.7177 22.6847i 0.153082 0.135028i
\(169\) −447.432 −2.64753
\(170\) 0 0
\(171\) 69.0151i 0.403597i
\(172\) 164.623 0.957110
\(173\) 13.0301i 0.0753183i 0.999291 + 0.0376592i \(0.0119901\pi\)
−0.999291 + 0.0376592i \(0.988010\pi\)
\(174\) 139.832i 0.803631i
\(175\) 0 0
\(176\) 47.0683 0.267434
\(177\) −141.627 −0.800154
\(178\) 109.715i 0.616375i
\(179\) 24.1573 0.134957 0.0674786 0.997721i \(-0.478505\pi\)
0.0674786 + 0.997721i \(0.478505\pi\)
\(180\) 0 0
\(181\) 43.5107i 0.240390i 0.992750 + 0.120195i \(0.0383521\pi\)
−0.992750 + 0.120195i \(0.961648\pi\)
\(182\) −184.325 + 162.587i −1.01278 + 0.893335i
\(183\) −22.7315 −0.124216
\(184\) −74.7335 −0.406160
\(185\) 0 0
\(186\) 25.0392 0.134619
\(187\) 85.4408i 0.456903i
\(188\) 103.326i 0.549608i
\(189\) −27.2778 + 24.0608i −0.144327 + 0.127306i
\(190\) 0 0
\(191\) −246.572 −1.29095 −0.645477 0.763780i \(-0.723341\pi\)
−0.645477 + 0.763780i \(0.723341\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) 161.875 0.838733 0.419366 0.907817i \(-0.362252\pi\)
0.419366 + 0.907817i \(0.362252\pi\)
\(194\) 8.70789i 0.0448860i
\(195\) 0 0
\(196\) −12.2337 + 97.2334i −0.0624170 + 0.496089i
\(197\) −44.8380 −0.227604 −0.113802 0.993503i \(-0.536303\pi\)
−0.113802 + 0.993503i \(0.536303\pi\)
\(198\) −49.9235 −0.252139
\(199\) 114.767i 0.576718i 0.957522 + 0.288359i \(0.0931097\pi\)
−0.957522 + 0.288359i \(0.906890\pi\)
\(200\) 0 0
\(201\) 38.8040i 0.193055i
\(202\) 202.209i 1.00104i
\(203\) −264.338 299.680i −1.30216 1.47626i
\(204\) −25.1529 −0.123298
\(205\) 0 0
\(206\) 20.5474i 0.0997448i
\(207\) 79.2669 0.382932
\(208\) 99.3122i 0.477462i
\(209\) 270.702i 1.29522i
\(210\) 0 0
\(211\) −219.602 −1.04077 −0.520384 0.853932i \(-0.674211\pi\)
−0.520384 + 0.853932i \(0.674211\pi\)
\(212\) 129.655 0.611579
\(213\) 158.486i 0.744068i
\(214\) 110.907 0.518255
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −53.6626 + 47.3340i −0.247293 + 0.218129i
\(218\) 105.702 0.484870
\(219\) −124.579 −0.568853
\(220\) 0 0
\(221\) 180.277 0.815731
\(222\) 34.8308i 0.156895i
\(223\) 3.57102i 0.0160136i −0.999968 0.00800678i \(-0.997451\pi\)
0.999968 0.00800678i \(-0.00254866\pi\)
\(224\) 26.1941 + 29.6963i 0.116938 + 0.132573i
\(225\) 0 0
\(226\) −120.550 −0.533407
\(227\) 68.0647i 0.299844i −0.988698 0.149922i \(-0.952098\pi\)
0.988698 0.149922i \(-0.0479023\pi\)
\(228\) 79.6917 0.349525
\(229\) 180.019i 0.786109i −0.919515 0.393054i \(-0.871418\pi\)
0.919515 0.393054i \(-0.128582\pi\)
\(230\) 0 0
\(231\) 106.993 94.3752i 0.463175 0.408550i
\(232\) −161.464 −0.695965
\(233\) 115.207 0.494449 0.247225 0.968958i \(-0.420481\pi\)
0.247225 + 0.968958i \(0.420481\pi\)
\(234\) 105.336i 0.450156i
\(235\) 0 0
\(236\) 163.537i 0.692953i
\(237\) 78.4276i 0.330918i
\(238\) 53.9062 47.5488i 0.226497 0.199785i
\(239\) −15.6873 −0.0656374 −0.0328187 0.999461i \(-0.510448\pi\)
−0.0328187 + 0.999461i \(0.510448\pi\)
\(240\) 0 0
\(241\) 303.442i 1.25909i 0.776962 + 0.629547i \(0.216760\pi\)
−0.776962 + 0.629547i \(0.783240\pi\)
\(242\) 24.6981 0.102058
\(243\) 15.5885i 0.0641500i
\(244\) 26.2481i 0.107574i
\(245\) 0 0
\(246\) 39.7481 0.161578
\(247\) −571.170 −2.31243
\(248\) 28.9128i 0.116584i
\(249\) 30.7141 0.123350
\(250\) 0 0
\(251\) 80.5241i 0.320813i −0.987051 0.160407i \(-0.948719\pi\)
0.987051 0.160407i \(-0.0512805\pi\)
\(252\) −27.7830 31.4977i −0.110250 0.124991i
\(253\) −310.913 −1.22891
\(254\) 94.4318 0.371779
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 39.1012i 0.152145i −0.997102 0.0760723i \(-0.975762\pi\)
0.997102 0.0760723i \(-0.0242380\pi\)
\(258\) 201.621i 0.781477i
\(259\) 65.8439 + 74.6474i 0.254224 + 0.288214i
\(260\) 0 0
\(261\) 171.258 0.656162
\(262\) 40.7760i 0.155633i
\(263\) −79.1644 −0.301005 −0.150503 0.988610i \(-0.548089\pi\)
−0.150503 + 0.988610i \(0.548089\pi\)
\(264\) 57.6467i 0.218359i
\(265\) 0 0
\(266\) −170.791 + 150.649i −0.642071 + 0.566349i
\(267\) −134.373 −0.503268
\(268\) 44.8070 0.167190
\(269\) 53.2775i 0.198058i 0.995085 + 0.0990288i \(0.0315736\pi\)
−0.995085 + 0.0990288i \(0.968426\pi\)
\(270\) 0 0
\(271\) 237.638i 0.876892i −0.898757 0.438446i \(-0.855529\pi\)
0.898757 0.438446i \(-0.144471\pi\)
\(272\) 29.0440i 0.106779i
\(273\) 199.128 + 225.751i 0.729405 + 0.826928i
\(274\) 168.928 0.616524
\(275\) 0 0
\(276\) 91.5295i 0.331629i
\(277\) −168.185 −0.607167 −0.303583 0.952805i \(-0.598183\pi\)
−0.303583 + 0.952805i \(0.598183\pi\)
\(278\) 284.183i 1.02224i
\(279\) 30.6666i 0.109916i
\(280\) 0 0
\(281\) 128.175 0.456140 0.228070 0.973645i \(-0.426758\pi\)
0.228070 + 0.973645i \(0.426758\pi\)
\(282\) 126.548 0.448753
\(283\) 72.7293i 0.256994i 0.991710 + 0.128497i \(0.0410153\pi\)
−0.991710 + 0.128497i \(0.958985\pi\)
\(284\) 183.004 0.644382
\(285\) 0 0
\(286\) 413.168i 1.44464i
\(287\) −85.1859 + 75.1396i −0.296815 + 0.261810i
\(288\) −16.9706 −0.0589256
\(289\) 236.278 0.817570
\(290\) 0 0
\(291\) 10.6649 0.0366493
\(292\) 143.851i 0.492641i
\(293\) 273.216i 0.932477i −0.884659 0.466238i \(-0.845609\pi\)
0.884659 0.466238i \(-0.154391\pi\)
\(294\) 119.086 + 14.9832i 0.405055 + 0.0509632i
\(295\) 0 0
\(296\) 40.2191 0.135875
\(297\) 61.1436i 0.205871i
\(298\) 8.06786 0.0270734
\(299\) 656.014i 2.19403i
\(300\) 0 0
\(301\) 381.143 + 432.103i 1.26626 + 1.43556i
\(302\) −306.163 −1.01379
\(303\) −247.655 −0.817342
\(304\) 92.0201i 0.302698i
\(305\) 0 0
\(306\) 30.8058i 0.100673i
\(307\) 336.086i 1.09474i −0.836889 0.547372i \(-0.815628\pi\)
0.836889 0.547372i \(-0.184372\pi\)
\(308\) 108.975 + 123.545i 0.353815 + 0.401121i
\(309\) 25.1653 0.0814412
\(310\) 0 0
\(311\) 497.276i 1.59896i −0.600693 0.799480i \(-0.705109\pi\)
0.600693 0.799480i \(-0.294891\pi\)
\(312\) 121.632 0.389846
\(313\) 252.024i 0.805188i −0.915379 0.402594i \(-0.868109\pi\)
0.915379 0.402594i \(-0.131891\pi\)
\(314\) 153.141i 0.487710i
\(315\) 0 0
\(316\) −90.5604 −0.286584
\(317\) −270.203 −0.852377 −0.426188 0.904634i \(-0.640144\pi\)
−0.426188 + 0.904634i \(0.640144\pi\)
\(318\) 158.794i 0.499352i
\(319\) −671.737 −2.10576
\(320\) 0 0
\(321\) 135.832i 0.423153i
\(322\) −173.027 196.161i −0.537351 0.609196i
\(323\) 167.040 0.517150
\(324\) 18.0000 0.0555556
\(325\) 0 0
\(326\) 331.484 1.01682
\(327\) 129.458i 0.395895i
\(328\) 45.8971i 0.139930i
\(329\) −271.211 + 239.226i −0.824351 + 0.727132i
\(330\) 0 0
\(331\) −306.813 −0.926926 −0.463463 0.886116i \(-0.653393\pi\)
−0.463463 + 0.886116i \(0.653393\pi\)
\(332\) 35.4656i 0.106824i
\(333\) −42.6588 −0.128105
\(334\) 59.2315i 0.177340i
\(335\) 0 0
\(336\) 36.3704 32.0811i 0.108245 0.0954794i
\(337\) 485.903 1.44185 0.720924 0.693014i \(-0.243718\pi\)
0.720924 + 0.693014i \(0.243718\pi\)
\(338\) −632.764 −1.87208
\(339\) 147.643i 0.435525i
\(340\) 0 0
\(341\) 120.286i 0.352744i
\(342\) 97.6020i 0.285386i
\(343\) −283.543 + 193.009i −0.826656 + 0.562708i
\(344\) 232.812 0.676779
\(345\) 0 0
\(346\) 18.4273i 0.0532581i
\(347\) −8.02712 −0.0231329 −0.0115665 0.999933i \(-0.503682\pi\)
−0.0115665 + 0.999933i \(0.503682\pi\)
\(348\) 197.752i 0.568253i
\(349\) 649.899i 1.86217i 0.364798 + 0.931087i \(0.381138\pi\)
−0.364798 + 0.931087i \(0.618862\pi\)
\(350\) 0 0
\(351\) −129.010 −0.367551
\(352\) 66.5647 0.189104
\(353\) 396.496i 1.12322i 0.827403 + 0.561608i \(0.189817\pi\)
−0.827403 + 0.561608i \(0.810183\pi\)
\(354\) −200.291 −0.565794
\(355\) 0 0
\(356\) 155.160i 0.435843i
\(357\) −58.2352 66.0214i −0.163124 0.184934i
\(358\) 34.1636 0.0954291
\(359\) −398.981 −1.11137 −0.555684 0.831394i \(-0.687543\pi\)
−0.555684 + 0.831394i \(0.687543\pi\)
\(360\) 0 0
\(361\) −168.231 −0.466014
\(362\) 61.5334i 0.169982i
\(363\) 30.2489i 0.0833303i
\(364\) −260.675 + 229.933i −0.716141 + 0.631683i
\(365\) 0 0
\(366\) −32.1472 −0.0878339
\(367\) 506.200i 1.37929i 0.724147 + 0.689646i \(0.242234\pi\)
−0.724147 + 0.689646i \(0.757766\pi\)
\(368\) −105.689 −0.287199
\(369\) 48.6812i 0.131927i
\(370\) 0 0
\(371\) 300.183 + 340.318i 0.809119 + 0.917300i
\(372\) 35.4108 0.0951903
\(373\) −278.751 −0.747322 −0.373661 0.927565i \(-0.621898\pi\)
−0.373661 + 0.927565i \(0.621898\pi\)
\(374\) 120.832i 0.323079i
\(375\) 0 0
\(376\) 146.125i 0.388631i
\(377\) 1417.34i 3.75951i
\(378\) −38.5766 + 34.0271i −0.102055 + 0.0900188i
\(379\) 515.959 1.36137 0.680685 0.732576i \(-0.261682\pi\)
0.680685 + 0.732576i \(0.261682\pi\)
\(380\) 0 0
\(381\) 115.655i 0.303556i
\(382\) −348.706 −0.912842
\(383\) 238.715i 0.623276i −0.950201 0.311638i \(-0.899122\pi\)
0.950201 0.311638i \(-0.100878\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 228.926 0.593073
\(387\) −246.934 −0.638073
\(388\) 12.3148i 0.0317392i
\(389\) 170.748 0.438941 0.219471 0.975619i \(-0.429567\pi\)
0.219471 + 0.975619i \(0.429567\pi\)
\(390\) 0 0
\(391\) 191.852i 0.490671i
\(392\) −17.3011 + 137.509i −0.0441355 + 0.350788i
\(393\) 49.9402 0.127074
\(394\) −63.4105 −0.160940
\(395\) 0 0
\(396\) −70.6025 −0.178289
\(397\) 80.7184i 0.203321i −0.994819 0.101660i \(-0.967584\pi\)
0.994819 0.101660i \(-0.0324155\pi\)
\(398\) 162.305i 0.407801i
\(399\) 184.506 + 209.175i 0.462422 + 0.524249i
\(400\) 0 0
\(401\) 469.375 1.17051 0.585255 0.810849i \(-0.300994\pi\)
0.585255 + 0.810849i \(0.300994\pi\)
\(402\) 54.8772i 0.136510i
\(403\) −253.798 −0.629770
\(404\) 285.967i 0.707839i
\(405\) 0 0
\(406\) −373.830 423.812i −0.920763 1.04387i
\(407\) 167.323 0.411114
\(408\) −35.5715 −0.0871851
\(409\) 671.238i 1.64117i −0.571525 0.820585i \(-0.693648\pi\)
0.571525 0.820585i \(-0.306352\pi\)
\(410\) 0 0
\(411\) 206.893i 0.503390i
\(412\) 29.0584i 0.0705302i
\(413\) 429.253 378.629i 1.03935 0.916778i
\(414\) 112.100 0.270774
\(415\) 0 0
\(416\) 140.449i 0.337617i
\(417\) −348.052 −0.834657
\(418\) 382.830i 0.915862i
\(419\) 16.1628i 0.0385747i −0.999814 0.0192874i \(-0.993860\pi\)
0.999814 0.0192874i \(-0.00613974\pi\)
\(420\) 0 0
\(421\) −463.356 −1.10061 −0.550304 0.834964i \(-0.685488\pi\)
−0.550304 + 0.834964i \(0.685488\pi\)
\(422\) −310.564 −0.735934
\(423\) 154.989i 0.366405i
\(424\) 183.359 0.432451
\(425\) 0 0
\(426\) 224.134i 0.526135i
\(427\) 68.8961 60.7709i 0.161349 0.142321i
\(428\) 156.846 0.366462
\(429\) 506.025 1.17955
\(430\) 0 0
\(431\) 425.457 0.987140 0.493570 0.869706i \(-0.335692\pi\)
0.493570 + 0.869706i \(0.335692\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) 480.947i 1.11073i −0.831606 0.555366i \(-0.812578\pi\)
0.831606 0.555366i \(-0.187422\pi\)
\(434\) −75.8904 + 66.9404i −0.174863 + 0.154240i
\(435\) 0 0
\(436\) 149.485 0.342855
\(437\) 607.845i 1.39095i
\(438\) −176.181 −0.402240
\(439\) 73.3796i 0.167152i −0.996501 0.0835759i \(-0.973366\pi\)
0.996501 0.0835759i \(-0.0266341\pi\)
\(440\) 0 0
\(441\) 18.3506 145.850i 0.0416113 0.330726i
\(442\) 254.950 0.576809
\(443\) −72.4361 −0.163513 −0.0817563 0.996652i \(-0.526053\pi\)
−0.0817563 + 0.996652i \(0.526053\pi\)
\(444\) 49.2582i 0.110942i
\(445\) 0 0
\(446\) 5.05019i 0.0113233i
\(447\) 9.88107i 0.0221053i
\(448\) 37.0440 + 41.9969i 0.0826876 + 0.0937431i
\(449\) 721.760 1.60748 0.803742 0.594978i \(-0.202839\pi\)
0.803742 + 0.594978i \(0.202839\pi\)
\(450\) 0 0
\(451\) 190.945i 0.423382i
\(452\) −170.483 −0.377175
\(453\) 374.972i 0.827752i
\(454\) 96.2580i 0.212022i
\(455\) 0 0
\(456\) 112.701 0.247152
\(457\) 622.396 1.36192 0.680958 0.732322i \(-0.261564\pi\)
0.680958 + 0.732322i \(0.261564\pi\)
\(458\) 254.585i 0.555863i
\(459\) 37.7293 0.0821989
\(460\) 0 0
\(461\) 600.196i 1.30194i 0.759102 + 0.650971i \(0.225638\pi\)
−0.759102 + 0.650971i \(0.774362\pi\)
\(462\) 151.311 133.467i 0.327514 0.288889i
\(463\) 127.513 0.275406 0.137703 0.990474i \(-0.456028\pi\)
0.137703 + 0.990474i \(0.456028\pi\)
\(464\) −228.344 −0.492122
\(465\) 0 0
\(466\) 162.927 0.349628
\(467\) 11.4438i 0.0245048i −0.999925 0.0122524i \(-0.996100\pi\)
0.999925 0.0122524i \(-0.00390016\pi\)
\(468\) 148.968i 0.318308i
\(469\) 103.740 + 117.610i 0.221193 + 0.250767i
\(470\) 0 0
\(471\) 187.559 0.398214
\(472\) 231.276i 0.489992i
\(473\) 968.566 2.04771
\(474\) 110.913i 0.233995i
\(475\) 0 0
\(476\) 76.2349 67.2442i 0.160157 0.141269i
\(477\) −194.482 −0.407719
\(478\) −22.1853 −0.0464127
\(479\) 205.867i 0.429784i −0.976638 0.214892i \(-0.931060\pi\)
0.976638 0.214892i \(-0.0689400\pi\)
\(480\) 0 0
\(481\) 353.045i 0.733981i
\(482\) 429.131i 0.890314i
\(483\) −240.247 + 211.914i −0.497406 + 0.438745i
\(484\) 34.9284 0.0721662
\(485\) 0 0
\(486\) 22.0454i 0.0453609i
\(487\) −603.451 −1.23912 −0.619559 0.784950i \(-0.712689\pi\)
−0.619559 + 0.784950i \(0.712689\pi\)
\(488\) 37.1204i 0.0760664i
\(489\) 405.983i 0.830232i
\(490\) 0 0
\(491\) −522.576 −1.06431 −0.532154 0.846647i \(-0.678617\pi\)
−0.532154 + 0.846647i \(0.678617\pi\)
\(492\) 56.2123 0.114253
\(493\) 414.503i 0.840776i
\(494\) −807.756 −1.63513
\(495\) 0 0
\(496\) 40.8888i 0.0824372i
\(497\) 423.701 + 480.351i 0.852518 + 0.966501i
\(498\) 43.4363 0.0872214
\(499\) −124.569 −0.249636 −0.124818 0.992180i \(-0.539835\pi\)
−0.124818 + 0.992180i \(0.539835\pi\)
\(500\) 0 0
\(501\) −72.5435 −0.144797
\(502\) 113.878i 0.226849i
\(503\) 33.8355i 0.0672673i −0.999434 0.0336337i \(-0.989292\pi\)
0.999434 0.0336337i \(-0.0107079\pi\)
\(504\) −39.2911 44.5444i −0.0779586 0.0883818i
\(505\) 0 0
\(506\) −439.698 −0.868968
\(507\) 774.975i 1.52855i
\(508\) 133.547 0.262887
\(509\) 630.938i 1.23956i −0.784774 0.619782i \(-0.787221\pi\)
0.784774 0.619782i \(-0.212779\pi\)
\(510\) 0 0
\(511\) 377.582 333.052i 0.738907 0.651765i
\(512\) 22.6274 0.0441942
\(513\) −119.538 −0.233017
\(514\) 55.2974i 0.107582i
\(515\) 0 0
\(516\) 285.135i 0.552588i
\(517\) 607.924i 1.17587i
\(518\) 93.1174 + 105.567i 0.179763 + 0.203798i
\(519\) 22.5687 0.0434850
\(520\) 0 0
\(521\) 492.821i 0.945914i 0.881086 + 0.472957i \(0.156813\pi\)
−0.881086 + 0.472957i \(0.843187\pi\)
\(522\) 242.196 0.463977
\(523\) 331.944i 0.634692i −0.948310 0.317346i \(-0.897208\pi\)
0.948310 0.317346i \(-0.102792\pi\)
\(524\) 57.6659i 0.110049i
\(525\) 0 0
\(526\) −111.955 −0.212843
\(527\) 74.2235 0.140842
\(528\) 81.5247i 0.154403i
\(529\) 169.138 0.319731
\(530\) 0 0
\(531\) 245.306i 0.461969i
\(532\) −241.535 + 213.050i −0.454013 + 0.400469i
\(533\) −402.887 −0.755885
\(534\) −190.031 −0.355864
\(535\) 0 0
\(536\) 63.3667 0.118221
\(537\) 41.8417i 0.0779175i
\(538\) 75.3457i 0.140048i
\(539\) −71.9776 + 572.077i −0.133539 + 1.06137i
\(540\) 0 0
\(541\) −96.8104 −0.178947 −0.0894735 0.995989i \(-0.528518\pi\)
−0.0894735 + 0.995989i \(0.528518\pi\)
\(542\) 336.071i 0.620057i
\(543\) 75.3627 0.138789
\(544\) 41.0744i 0.0755045i
\(545\) 0 0
\(546\) 281.609 + 319.261i 0.515767 + 0.584726i
\(547\) −772.034 −1.41140 −0.705699 0.708512i \(-0.749367\pi\)
−0.705699 + 0.708512i \(0.749367\pi\)
\(548\) 238.900 0.435948
\(549\) 39.3721i 0.0717161i
\(550\) 0 0
\(551\) 1313.27i 2.38343i
\(552\) 129.442i 0.234497i
\(553\) −209.670 237.704i −0.379150 0.429844i
\(554\) −237.850 −0.429332
\(555\) 0 0
\(556\) 401.896i 0.722834i
\(557\) −42.3682 −0.0760650 −0.0380325 0.999277i \(-0.512109\pi\)
−0.0380325 + 0.999277i \(0.512109\pi\)
\(558\) 43.3692i 0.0777225i
\(559\) 2043.63i 3.65587i
\(560\) 0 0
\(561\) −147.988 −0.263793
\(562\) 181.267 0.322540
\(563\) 370.393i 0.657891i 0.944349 + 0.328946i \(0.106693\pi\)
−0.944349 + 0.328946i \(0.893307\pi\)
\(564\) 178.966 0.317316
\(565\) 0 0
\(566\) 102.855i 0.181722i
\(567\) 41.6745 + 47.2465i 0.0735001 + 0.0833272i
\(568\) 258.807 0.455647
\(569\) 419.012 0.736401 0.368201 0.929746i \(-0.379974\pi\)
0.368201 + 0.929746i \(0.379974\pi\)
\(570\) 0 0
\(571\) −113.210 −0.198266 −0.0991329 0.995074i \(-0.531607\pi\)
−0.0991329 + 0.995074i \(0.531607\pi\)
\(572\) 584.307i 1.02152i
\(573\) 427.075i 0.745332i
\(574\) −120.471 + 106.263i −0.209880 + 0.185128i
\(575\) 0 0
\(576\) −24.0000 −0.0416667
\(577\) 604.749i 1.04809i 0.851690 + 0.524046i \(0.175578\pi\)
−0.851690 + 0.524046i \(0.824422\pi\)
\(578\) 334.147 0.578109
\(579\) 280.376i 0.484242i
\(580\) 0 0
\(581\) −93.0902 + 82.1117i −0.160224 + 0.141328i
\(582\) 15.0825 0.0259150
\(583\) 762.829 1.30845
\(584\) 203.436i 0.348350i
\(585\) 0 0
\(586\) 386.385i 0.659360i
\(587\) 458.151i 0.780496i 0.920710 + 0.390248i \(0.127611\pi\)
−0.920710 + 0.390248i \(0.872389\pi\)
\(588\) 168.413 + 21.1894i 0.286417 + 0.0360365i
\(589\) −235.162 −0.399257
\(590\) 0 0
\(591\) 77.6616i 0.131407i
\(592\) 56.8784 0.0960784
\(593\) 780.457i 1.31612i −0.752967 0.658059i \(-0.771378\pi\)
0.752967 0.658059i \(-0.228622\pi\)
\(594\) 86.4700i 0.145572i
\(595\) 0 0
\(596\) 11.4097 0.0191438
\(597\) 198.782 0.332968
\(598\) 927.744i 1.55141i
\(599\) 11.7391 0.0195977 0.00979887 0.999952i \(-0.496881\pi\)
0.00979887 + 0.999952i \(0.496881\pi\)
\(600\) 0 0
\(601\) 182.878i 0.304290i 0.988358 + 0.152145i \(0.0486181\pi\)
−0.988358 + 0.152145i \(0.951382\pi\)
\(602\) 539.018 + 611.086i 0.895379 + 1.01509i
\(603\) −67.2106 −0.111460
\(604\) −432.980 −0.716854
\(605\) 0 0
\(606\) −350.236 −0.577948
\(607\) 777.171i 1.28035i −0.768230 0.640174i \(-0.778862\pi\)
0.768230 0.640174i \(-0.221138\pi\)
\(608\) 130.136i 0.214040i
\(609\) −519.061 + 457.846i −0.852317 + 0.751800i
\(610\) 0 0
\(611\) −1282.69 −2.09934
\(612\) 43.5660i 0.0711863i
\(613\) −106.169 −0.173196 −0.0865978 0.996243i \(-0.527600\pi\)
−0.0865978 + 0.996243i \(0.527600\pi\)
\(614\) 475.298i 0.774101i
\(615\) 0 0
\(616\) 154.114 + 174.719i 0.250185 + 0.283635i
\(617\) 680.569 1.10303 0.551515 0.834165i \(-0.314050\pi\)
0.551515 + 0.834165i \(0.314050\pi\)
\(618\) 35.5892 0.0575877
\(619\) 861.054i 1.39104i −0.718507 0.695520i \(-0.755174\pi\)
0.718507 0.695520i \(-0.244826\pi\)
\(620\) 0 0
\(621\) 137.294i 0.221086i
\(622\) 703.255i 1.13063i
\(623\) 407.265 359.235i 0.653716 0.576621i
\(624\) 172.014 0.275663
\(625\) 0 0
\(626\) 356.416i 0.569354i
\(627\) 468.870 0.747798
\(628\) 216.574i 0.344863i
\(629\) 103.249i 0.164147i
\(630\) 0 0
\(631\) −489.247 −0.775352 −0.387676 0.921796i \(-0.626722\pi\)
−0.387676 + 0.921796i \(0.626722\pi\)
\(632\) −128.072 −0.202645
\(633\) 380.362i 0.600888i
\(634\) −382.125 −0.602721
\(635\) 0 0
\(636\) 224.569i 0.353095i
\(637\) −1207.06 151.870i −1.89491 0.238414i
\(638\) −949.980 −1.48900
\(639\) −274.507 −0.429588
\(640\) 0 0
\(641\) 962.813 1.50205 0.751024 0.660275i \(-0.229560\pi\)
0.751024 + 0.660275i \(0.229560\pi\)
\(642\) 192.096i 0.299215i
\(643\) 581.069i 0.903684i 0.892098 + 0.451842i \(0.149233\pi\)
−0.892098 + 0.451842i \(0.850767\pi\)
\(644\) −244.697 277.414i −0.379964 0.430766i
\(645\) 0 0
\(646\) 236.230 0.365681
\(647\) 339.036i 0.524012i −0.965066 0.262006i \(-0.915616\pi\)
0.965066 0.262006i \(-0.0843840\pi\)
\(648\) 25.4558 0.0392837
\(649\) 962.177i 1.48255i
\(650\) 0 0
\(651\) 81.9849 + 92.9464i 0.125937 + 0.142775i
\(652\) 468.789 0.719002
\(653\) 289.383 0.443159 0.221580 0.975142i \(-0.428879\pi\)
0.221580 + 0.975142i \(0.428879\pi\)
\(654\) 183.081i 0.279940i
\(655\) 0 0
\(656\) 64.9083i 0.0989456i
\(657\) 215.777i 0.328427i
\(658\) −383.551 + 338.317i −0.582904 + 0.514160i
\(659\) −62.6627 −0.0950875 −0.0475438 0.998869i \(-0.515139\pi\)
−0.0475438 + 0.998869i \(0.515139\pi\)
\(660\) 0 0
\(661\) 148.826i 0.225153i 0.993643 + 0.112577i \(0.0359104\pi\)
−0.993643 + 0.112577i \(0.964090\pi\)
\(662\) −433.899 −0.655436
\(663\) 312.248i 0.470962i
\(664\) 50.1559i 0.0755360i
\(665\) 0 0
\(666\) −60.3287 −0.0905836
\(667\) 1508.35 2.26139
\(668\) 83.7660i 0.125398i
\(669\) −6.18519 −0.00924543
\(670\) 0 0
\(671\) 154.432i 0.230152i
\(672\) 51.4355 45.3695i 0.0765409 0.0675141i
\(673\) −833.049 −1.23781 −0.618907 0.785464i \(-0.712424\pi\)
−0.618907 + 0.785464i \(0.712424\pi\)
\(674\) 687.170 1.01954
\(675\) 0 0
\(676\) −894.864 −1.32376
\(677\) 391.042i 0.577611i 0.957388 + 0.288805i \(0.0932581\pi\)
−0.957388 + 0.288805i \(0.906742\pi\)
\(678\) 208.799i 0.307962i
\(679\) −32.3240 + 28.5119i −0.0476053 + 0.0419910i
\(680\) 0 0
\(681\) −117.891 −0.173115
\(682\) 170.110i 0.249427i
\(683\) −992.775 −1.45355 −0.726775 0.686875i \(-0.758982\pi\)
−0.726775 + 0.686875i \(0.758982\pi\)
\(684\) 138.030i 0.201798i
\(685\) 0 0
\(686\) −400.990 + 272.956i −0.584534 + 0.397894i
\(687\) −311.802 −0.453860
\(688\) 329.246 0.478555
\(689\) 1609.54i 2.33605i
\(690\) 0 0
\(691\) 697.871i 1.00994i −0.863136 0.504972i \(-0.831503\pi\)
0.863136 0.504972i \(-0.168497\pi\)
\(692\) 26.0601i 0.0376592i
\(693\) −163.463 185.318i −0.235877 0.267414i
\(694\) −11.3521 −0.0163574
\(695\) 0 0
\(696\) 279.664i 0.401816i
\(697\) 117.825 0.169046
\(698\) 919.095i 1.31676i
\(699\) 199.544i 0.285470i
\(700\) 0 0
\(701\) −222.920 −0.318003 −0.159002 0.987278i \(-0.550828\pi\)
−0.159002 + 0.987278i \(0.550828\pi\)
\(702\) −182.448 −0.259898
\(703\) 327.122i 0.465323i
\(704\) 94.1367 0.133717
\(705\) 0 0
\(706\) 560.729i 0.794234i
\(707\) 750.608 662.085i 1.06168 0.936472i
\(708\) −283.254 −0.400077
\(709\) 267.679 0.377544 0.188772 0.982021i \(-0.439549\pi\)
0.188772 + 0.982021i \(0.439549\pi\)
\(710\) 0 0
\(711\) 135.841 0.191056
\(712\) 219.429i 0.308187i
\(713\) 270.094i 0.378814i
\(714\) −82.3570 93.3683i −0.115346 0.130768i
\(715\) 0 0
\(716\) 48.3147 0.0674786
\(717\) 27.1713i 0.0378958i
\(718\) −564.244 −0.785856
\(719\) 217.258i 0.302167i 0.988521 + 0.151083i \(0.0482762\pi\)
−0.988521 + 0.151083i \(0.951724\pi\)
\(720\) 0 0
\(721\) −76.2728 + 67.2776i −0.105787 + 0.0933115i
\(722\) −237.915 −0.329522
\(723\) 525.577 0.726939
\(724\) 87.0213i 0.120195i
\(725\) 0 0
\(726\) 42.7784i 0.0589235i
\(727\) 771.678i 1.06146i 0.847543 + 0.530728i \(0.178081\pi\)
−0.847543 + 0.530728i \(0.821919\pi\)
\(728\) −368.650 + 325.174i −0.506388 + 0.446668i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 597.664i 0.817598i
\(732\) −45.4630 −0.0621080
\(733\) 1103.98i 1.50611i 0.657960 + 0.753053i \(0.271420\pi\)
−0.657960 + 0.753053i \(0.728580\pi\)
\(734\) 715.875i 0.975306i
\(735\) 0 0
\(736\) −149.467 −0.203080
\(737\) 263.624 0.357699
\(738\) 68.8457i 0.0932868i
\(739\) −264.136 −0.357423 −0.178712 0.983901i \(-0.557193\pi\)
−0.178712 + 0.983901i \(0.557193\pi\)
\(740\) 0 0
\(741\) 989.295i 1.33508i
\(742\) 424.523 + 481.283i 0.572134 + 0.648629i
\(743\) 1069.03 1.43880 0.719401 0.694595i \(-0.244417\pi\)
0.719401 + 0.694595i \(0.244417\pi\)
\(744\) 50.0784 0.0673097
\(745\) 0 0
\(746\) −394.213 −0.528436
\(747\) 53.1983i 0.0712160i
\(748\) 170.882i 0.228451i
\(749\) 363.137 + 411.689i 0.484829 + 0.549652i
\(750\) 0 0
\(751\) 987.190 1.31450 0.657250 0.753673i \(-0.271720\pi\)
0.657250 + 0.753673i \(0.271720\pi\)
\(752\) 206.653i 0.274804i
\(753\) −139.472 −0.185222
\(754\) 2004.42i 2.65838i
\(755\) 0 0
\(756\) −54.5556 + 48.1216i −0.0721635 + 0.0636529i
\(757\) 1173.09 1.54966 0.774830 0.632169i \(-0.217835\pi\)
0.774830 + 0.632169i \(0.217835\pi\)
\(758\) 729.677 0.962634
\(759\) 538.518i 0.709509i
\(760\) 0 0
\(761\) 271.712i 0.357045i 0.983936 + 0.178523i \(0.0571318\pi\)
−0.983936 + 0.178523i \(0.942868\pi\)
\(762\) 163.561i 0.214647i
\(763\) 346.095 + 392.369i 0.453598 + 0.514245i
\(764\) −493.144 −0.645477
\(765\) 0 0
\(766\) 337.594i 0.440723i
\(767\) 2030.15 2.64687
\(768\) 27.7128i 0.0360844i
\(769\) 1031.82i 1.34177i 0.741563 + 0.670883i \(0.234085\pi\)
−0.741563 + 0.670883i \(0.765915\pi\)
\(770\) 0 0
\(771\) −67.7252 −0.0878407
\(772\) 323.751 0.419366
\(773\) 877.988i 1.13582i 0.823091 + 0.567910i \(0.192248\pi\)
−0.823091 + 0.567910i \(0.807752\pi\)
\(774\) −349.218 −0.451186
\(775\) 0 0
\(776\) 17.4158i 0.0224430i
\(777\) 129.293 114.045i 0.166400 0.146776i
\(778\) 241.474 0.310378
\(779\) −373.304 −0.479210
\(780\) 0 0
\(781\) 1076.71 1.37863
\(782\) 271.320i 0.346957i
\(783\) 296.628i 0.378835i
\(784\) −24.4675 + 194.467i −0.0312085 + 0.248044i
\(785\) 0 0
\(786\) 70.6260 0.0898550
\(787\) 142.727i 0.181356i 0.995880 + 0.0906780i \(0.0289034\pi\)
−0.995880 + 0.0906780i \(0.971097\pi\)
\(788\) −89.6759 −0.113802
\(789\) 137.117i 0.173786i
\(790\) 0 0
\(791\)