Properties

Label 1050.3.f.e.601.8
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 601.8
Root \(-0.207107 - 1.12945i\) of defining polynomial
Character \(\chi\) \(=\) 1050.601
Dual form 1050.3.f.e.601.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(6.73333 + 1.91369i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(6.73333 + 1.91369i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +17.5116 q^{11} +3.46410i q^{12} +4.83531i q^{13} +(-9.52237 - 2.70636i) q^{14} +4.00000 q^{16} +18.0284i q^{17} +4.24264 q^{18} +9.13350i q^{19} +(-3.31461 + 11.6625i) q^{21} -24.7651 q^{22} -3.72515 q^{23} -4.89898i q^{24} -6.83816i q^{26} -5.19615i q^{27} +(13.4667 + 3.82738i) q^{28} -1.12582 q^{29} -57.0859i q^{31} -5.65685 q^{32} +30.3310i q^{33} -25.4960i q^{34} -6.00000 q^{36} +41.3624 q^{37} -12.9167i q^{38} -8.37500 q^{39} -11.7156i q^{41} +(4.68756 - 16.4932i) q^{42} +64.4171 q^{43} +35.0232 q^{44} +5.26816 q^{46} +77.6614i q^{47} +6.92820i q^{48} +(41.6756 + 25.7710i) q^{49} -31.2261 q^{51} +9.67062i q^{52} -77.5383 q^{53} +7.34847i q^{54} +(-19.0447 - 5.41273i) q^{56} -15.8197 q^{57} +1.59215 q^{58} -87.0651i q^{59} -5.36957i q^{61} +80.7317i q^{62} +(-20.2000 - 5.74106i) q^{63} +8.00000 q^{64} -42.8945i q^{66} +47.1879 q^{67} +36.0568i q^{68} -6.45216i q^{69} -58.3047 q^{71} +8.48528 q^{72} +53.4082i q^{73} -58.4953 q^{74} +18.2670i q^{76} +(117.911 + 33.5117i) q^{77} +11.8440 q^{78} +74.9637 q^{79} +9.00000 q^{81} +16.5683i q^{82} -28.7890i q^{83} +(-6.62921 + 23.3250i) q^{84} -91.0996 q^{86} -1.94997i q^{87} -49.5303 q^{88} +101.499i q^{89} +(-9.25327 + 32.5578i) q^{91} -7.45031 q^{92} +98.8757 q^{93} -109.830i q^{94} -9.79796i q^{96} +107.830i q^{97} +(-58.9382 - 36.4457i) q^{98} -52.5348 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) 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
\(7\) 6.73333 + 1.91369i 0.961905 + 0.273384i
\(8\) −2.82843 −0.353553
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 17.5116 1.59196 0.795982 0.605321i \(-0.206955\pi\)
0.795982 + 0.605321i \(0.206955\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 4.83531i 0.371947i 0.982555 + 0.185973i \(0.0595438\pi\)
−0.982555 + 0.185973i \(0.940456\pi\)
\(14\) −9.52237 2.70636i −0.680170 0.193312i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 18.0284i 1.06049i 0.847843 + 0.530247i \(0.177901\pi\)
−0.847843 + 0.530247i \(0.822099\pi\)
\(18\) 4.24264 0.235702
\(19\) 9.13350i 0.480711i 0.970685 + 0.240355i \(0.0772640\pi\)
−0.970685 + 0.240355i \(0.922736\pi\)
\(20\) 0 0
\(21\) −3.31461 + 11.6625i −0.157838 + 0.555356i
\(22\) −24.7651 −1.12569
\(23\) −3.72515 −0.161963 −0.0809816 0.996716i \(-0.525806\pi\)
−0.0809816 + 0.996716i \(0.525806\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 0 0
\(26\) 6.83816i 0.263006i
\(27\) 5.19615i 0.192450i
\(28\) 13.4667 + 3.82738i 0.480952 + 0.136692i
\(29\) −1.12582 −0.0388213 −0.0194107 0.999812i \(-0.506179\pi\)
−0.0194107 + 0.999812i \(0.506179\pi\)
\(30\) 0 0
\(31\) 57.0859i 1.84148i −0.390175 0.920741i \(-0.627585\pi\)
0.390175 0.920741i \(-0.372415\pi\)
\(32\) −5.65685 −0.176777
\(33\) 30.3310i 0.919120i
\(34\) 25.4960i 0.749882i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 41.3624 1.11790 0.558952 0.829200i \(-0.311204\pi\)
0.558952 + 0.829200i \(0.311204\pi\)
\(38\) 12.9167i 0.339914i
\(39\) −8.37500 −0.214744
\(40\) 0 0
\(41\) 11.7156i 0.285745i −0.989741 0.142873i \(-0.954366\pi\)
0.989741 0.142873i \(-0.0456340\pi\)
\(42\) 4.68756 16.4932i 0.111609 0.392696i
\(43\) 64.4171 1.49807 0.749036 0.662529i \(-0.230517\pi\)
0.749036 + 0.662529i \(0.230517\pi\)
\(44\) 35.0232 0.795982
\(45\) 0 0
\(46\) 5.26816 0.114525
\(47\) 77.6614i 1.65237i 0.563399 + 0.826185i \(0.309493\pi\)
−0.563399 + 0.826185i \(0.690507\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 41.6756 + 25.7710i 0.850522 + 0.525939i
\(50\) 0 0
\(51\) −31.2261 −0.612276
\(52\) 9.67062i 0.185973i
\(53\) −77.5383 −1.46299 −0.731493 0.681849i \(-0.761176\pi\)
−0.731493 + 0.681849i \(0.761176\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 0 0
\(56\) −19.0447 5.41273i −0.340085 0.0966559i
\(57\) −15.8197 −0.277539
\(58\) 1.59215 0.0274508
\(59\) 87.0651i 1.47568i −0.674976 0.737839i \(-0.735846\pi\)
0.674976 0.737839i \(-0.264154\pi\)
\(60\) 0 0
\(61\) 5.36957i 0.0880258i −0.999031 0.0440129i \(-0.985986\pi\)
0.999031 0.0440129i \(-0.0140143\pi\)
\(62\) 80.7317i 1.30212i
\(63\) −20.2000 5.74106i −0.320635 0.0911280i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) 42.8945i 0.649916i
\(67\) 47.1879 0.704297 0.352149 0.935944i \(-0.385451\pi\)
0.352149 + 0.935944i \(0.385451\pi\)
\(68\) 36.0568i 0.530247i
\(69\) 6.45216i 0.0935095i
\(70\) 0 0
\(71\) −58.3047 −0.821193 −0.410597 0.911817i \(-0.634680\pi\)
−0.410597 + 0.911817i \(0.634680\pi\)
\(72\) 8.48528 0.117851
\(73\) 53.4082i 0.731619i 0.930690 + 0.365810i \(0.119208\pi\)
−0.930690 + 0.365810i \(0.880792\pi\)
\(74\) −58.4953 −0.790477
\(75\) 0 0
\(76\) 18.2670i 0.240355i
\(77\) 117.911 + 33.5117i 1.53132 + 0.435217i
\(78\) 11.8440 0.151847
\(79\) 74.9637 0.948907 0.474454 0.880280i \(-0.342646\pi\)
0.474454 + 0.880280i \(0.342646\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 16.5683i 0.202053i
\(83\) 28.7890i 0.346855i −0.984847 0.173428i \(-0.944516\pi\)
0.984847 0.173428i \(-0.0554843\pi\)
\(84\) −6.62921 + 23.3250i −0.0789192 + 0.277678i
\(85\) 0 0
\(86\) −91.0996 −1.05930
\(87\) 1.94997i 0.0224135i
\(88\) −49.5303 −0.562844
\(89\) 101.499i 1.14043i 0.821494 + 0.570217i \(0.193141\pi\)
−0.821494 + 0.570217i \(0.806859\pi\)
\(90\) 0 0
\(91\) −9.25327 + 32.5578i −0.101684 + 0.357778i
\(92\) −7.45031 −0.0809816
\(93\) 98.8757 1.06318
\(94\) 109.830i 1.16840i
\(95\) 0 0
\(96\) 9.79796i 0.102062i
\(97\) 107.830i 1.11165i 0.831298 + 0.555827i \(0.187598\pi\)
−0.831298 + 0.555827i \(0.812402\pi\)
\(98\) −58.9382 36.4457i −0.601410 0.371895i
\(99\) −52.5348 −0.530654
\(100\) 0 0
\(101\) 52.6151i 0.520941i 0.965482 + 0.260471i \(0.0838777\pi\)
−0.965482 + 0.260471i \(0.916122\pi\)
\(102\) 44.1604 0.432945
\(103\) 72.4002i 0.702915i −0.936204 0.351457i \(-0.885686\pi\)
0.936204 0.351457i \(-0.114314\pi\)
\(104\) 13.6763i 0.131503i
\(105\) 0 0
\(106\) 109.656 1.03449
\(107\) −173.562 −1.62207 −0.811037 0.584994i \(-0.801097\pi\)
−0.811037 + 0.584994i \(0.801097\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) −49.9966 −0.458684 −0.229342 0.973346i \(-0.573658\pi\)
−0.229342 + 0.973346i \(0.573658\pi\)
\(110\) 0 0
\(111\) 71.6418i 0.645422i
\(112\) 26.9333 + 7.65475i 0.240476 + 0.0683460i
\(113\) 70.1536 0.620828 0.310414 0.950601i \(-0.399532\pi\)
0.310414 + 0.950601i \(0.399532\pi\)
\(114\) 22.3724 0.196249
\(115\) 0 0
\(116\) −2.25164 −0.0194107
\(117\) 14.5059i 0.123982i
\(118\) 123.129i 1.04346i
\(119\) −34.5007 + 121.391i −0.289922 + 1.02009i
\(120\) 0 0
\(121\) 185.656 1.53435
\(122\) 7.59373i 0.0622436i
\(123\) 20.2919 0.164975
\(124\) 114.172i 0.920741i
\(125\) 0 0
\(126\) 28.5671 + 8.11909i 0.226723 + 0.0644372i
\(127\) −197.945 −1.55863 −0.779313 0.626635i \(-0.784432\pi\)
−0.779313 + 0.626635i \(0.784432\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 111.574i 0.864912i
\(130\) 0 0
\(131\) 114.901i 0.877105i 0.898706 + 0.438552i \(0.144509\pi\)
−0.898706 + 0.438552i \(0.855491\pi\)
\(132\) 60.6619i 0.459560i
\(133\) −17.4787 + 61.4989i −0.131419 + 0.462398i
\(134\) −66.7338 −0.498013
\(135\) 0 0
\(136\) 50.9920i 0.374941i
\(137\) 95.3358 0.695882 0.347941 0.937516i \(-0.386881\pi\)
0.347941 + 0.937516i \(0.386881\pi\)
\(138\) 9.12473i 0.0661212i
\(139\) 237.587i 1.70926i 0.519237 + 0.854630i \(0.326216\pi\)
−0.519237 + 0.854630i \(0.673784\pi\)
\(140\) 0 0
\(141\) −134.513 −0.953996
\(142\) 82.4553 0.580671
\(143\) 84.6740i 0.592126i
\(144\) −12.0000 −0.0833333
\(145\) 0 0
\(146\) 75.5306i 0.517333i
\(147\) −44.6367 + 72.1842i −0.303651 + 0.491049i
\(148\) 82.7248 0.558952
\(149\) −133.844 −0.898285 −0.449142 0.893460i \(-0.648270\pi\)
−0.449142 + 0.893460i \(0.648270\pi\)
\(150\) 0 0
\(151\) 155.064 1.02691 0.513456 0.858116i \(-0.328365\pi\)
0.513456 + 0.858116i \(0.328365\pi\)
\(152\) 25.8335i 0.169957i
\(153\) 54.0852i 0.353498i
\(154\) −166.752 47.3928i −1.08280 0.307745i
\(155\) 0 0
\(156\) −16.7500 −0.107372
\(157\) 104.634i 0.666459i 0.942846 + 0.333230i \(0.108138\pi\)
−0.942846 + 0.333230i \(0.891862\pi\)
\(158\) −106.015 −0.670979
\(159\) 134.300i 0.844656i
\(160\) 0 0
\(161\) −25.0827 7.12878i −0.155793 0.0442782i
\(162\) −12.7279 −0.0785674
\(163\) 130.909 0.803120 0.401560 0.915833i \(-0.368468\pi\)
0.401560 + 0.915833i \(0.368468\pi\)
\(164\) 23.4311i 0.142873i
\(165\) 0 0
\(166\) 40.7138i 0.245264i
\(167\) 102.845i 0.615838i 0.951413 + 0.307919i \(0.0996325\pi\)
−0.951413 + 0.307919i \(0.900367\pi\)
\(168\) 9.37512 32.9865i 0.0558043 0.196348i
\(169\) 145.620 0.861656
\(170\) 0 0
\(171\) 27.4005i 0.160237i
\(172\) 128.834 0.749036
\(173\) 197.432i 1.14122i 0.821220 + 0.570612i \(0.193294\pi\)
−0.821220 + 0.570612i \(0.806706\pi\)
\(174\) 2.75768i 0.0158487i
\(175\) 0 0
\(176\) 70.0464 0.397991
\(177\) 150.801 0.851984
\(178\) 143.541i 0.806409i
\(179\) 118.822 0.663809 0.331904 0.943313i \(-0.392309\pi\)
0.331904 + 0.943313i \(0.392309\pi\)
\(180\) 0 0
\(181\) 14.4148i 0.0796399i −0.999207 0.0398199i \(-0.987322\pi\)
0.999207 0.0398199i \(-0.0126784\pi\)
\(182\) 13.0861 46.0436i 0.0719017 0.252987i
\(183\) 9.30038 0.0508217
\(184\) 10.5363 0.0572626
\(185\) 0 0
\(186\) −139.831 −0.751782
\(187\) 315.706i 1.68827i
\(188\) 155.323i 0.826185i
\(189\) 9.94382 34.9874i 0.0526128 0.185119i
\(190\) 0 0
\(191\) 59.9375 0.313809 0.156904 0.987614i \(-0.449849\pi\)
0.156904 + 0.987614i \(0.449849\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) −245.948 −1.27434 −0.637171 0.770723i \(-0.719895\pi\)
−0.637171 + 0.770723i \(0.719895\pi\)
\(194\) 152.495i 0.786058i
\(195\) 0 0
\(196\) 83.3512 + 51.5420i 0.425261 + 0.262969i
\(197\) 82.0594 0.416545 0.208273 0.978071i \(-0.433216\pi\)
0.208273 + 0.978071i \(0.433216\pi\)
\(198\) 74.2954 0.375229
\(199\) 289.338i 1.45396i 0.686658 + 0.726981i \(0.259077\pi\)
−0.686658 + 0.726981i \(0.740923\pi\)
\(200\) 0 0
\(201\) 81.7319i 0.406626i
\(202\) 74.4089i 0.368361i
\(203\) −7.58051 2.15447i −0.0373424 0.0106131i
\(204\) −62.4522 −0.306138
\(205\) 0 0
\(206\) 102.389i 0.497036i
\(207\) 11.1755 0.0539877
\(208\) 19.3412i 0.0929867i
\(209\) 159.942i 0.765274i
\(210\) 0 0
\(211\) 33.6995 0.159713 0.0798567 0.996806i \(-0.474554\pi\)
0.0798567 + 0.996806i \(0.474554\pi\)
\(212\) −155.077 −0.731493
\(213\) 100.987i 0.474116i
\(214\) 245.454 1.14698
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 109.245 384.379i 0.503432 1.77133i
\(218\) 70.7059 0.324339
\(219\) −92.5057 −0.422401
\(220\) 0 0
\(221\) −87.1728 −0.394447
\(222\) 101.317i 0.456382i
\(223\) 10.7556i 0.0482313i −0.999709 0.0241156i \(-0.992323\pi\)
0.999709 0.0241156i \(-0.00767699\pi\)
\(224\) −38.0895 10.8255i −0.170042 0.0483279i
\(225\) 0 0
\(226\) −99.2121 −0.438992
\(227\) 416.450i 1.83458i −0.398219 0.917290i \(-0.630372\pi\)
0.398219 0.917290i \(-0.369628\pi\)
\(228\) −31.6394 −0.138769
\(229\) 388.469i 1.69637i −0.529700 0.848185i \(-0.677695\pi\)
0.529700 0.848185i \(-0.322305\pi\)
\(230\) 0 0
\(231\) −58.0440 + 204.229i −0.251273 + 0.884107i
\(232\) 3.18429 0.0137254
\(233\) 70.4036 0.302162 0.151081 0.988521i \(-0.451725\pi\)
0.151081 + 0.988521i \(0.451725\pi\)
\(234\) 20.5145i 0.0876687i
\(235\) 0 0
\(236\) 174.130i 0.737839i
\(237\) 129.841i 0.547852i
\(238\) 48.7914 171.673i 0.205006 0.721315i
\(239\) 313.133 1.31018 0.655091 0.755550i \(-0.272630\pi\)
0.655091 + 0.755550i \(0.272630\pi\)
\(240\) 0 0
\(241\) 198.727i 0.824595i −0.911049 0.412297i \(-0.864726\pi\)
0.911049 0.412297i \(-0.135274\pi\)
\(242\) −262.557 −1.08495
\(243\) 15.5885i 0.0641500i
\(244\) 10.7391i 0.0440129i
\(245\) 0 0
\(246\) −28.6971 −0.116655
\(247\) −44.1633 −0.178799
\(248\) 161.463i 0.651062i
\(249\) 49.8640 0.200257
\(250\) 0 0
\(251\) 300.878i 1.19872i 0.800480 + 0.599359i \(0.204578\pi\)
−0.800480 + 0.599359i \(0.795422\pi\)
\(252\) −40.4000 11.4821i −0.160317 0.0455640i
\(253\) −65.2334 −0.257839
\(254\) 279.937 1.10211
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 306.052i 1.19087i −0.803405 0.595433i \(-0.796981\pi\)
0.803405 0.595433i \(-0.203019\pi\)
\(258\) 157.789i 0.611585i
\(259\) 278.507 + 79.1548i 1.07532 + 0.305617i
\(260\) 0 0
\(261\) 3.37745 0.0129404
\(262\) 162.494i 0.620207i
\(263\) −286.135 −1.08797 −0.543984 0.839096i \(-0.683085\pi\)
−0.543984 + 0.839096i \(0.683085\pi\)
\(264\) 85.7889i 0.324958i
\(265\) 0 0
\(266\) 24.7186 86.9726i 0.0929270 0.326965i
\(267\) −175.801 −0.658430
\(268\) 94.3758 0.352149
\(269\) 188.412i 0.700415i −0.936672 0.350208i \(-0.886111\pi\)
0.936672 0.350208i \(-0.113889\pi\)
\(270\) 0 0
\(271\) 9.59288i 0.0353981i −0.999843 0.0176990i \(-0.994366\pi\)
0.999843 0.0176990i \(-0.00563408\pi\)
\(272\) 72.1136i 0.265123i
\(273\) −56.3917 16.0271i −0.206563 0.0587075i
\(274\) −134.825 −0.492063
\(275\) 0 0
\(276\) 12.9043i 0.0467548i
\(277\) −161.066 −0.581464 −0.290732 0.956804i \(-0.593899\pi\)
−0.290732 + 0.956804i \(0.593899\pi\)
\(278\) 335.999i 1.20863i
\(279\) 171.258i 0.613827i
\(280\) 0 0
\(281\) −343.107 −1.22102 −0.610510 0.792008i \(-0.709036\pi\)
−0.610510 + 0.792008i \(0.709036\pi\)
\(282\) 190.231 0.674577
\(283\) 324.748i 1.14752i −0.819024 0.573759i \(-0.805484\pi\)
0.819024 0.573759i \(-0.194516\pi\)
\(284\) −116.609 −0.410597
\(285\) 0 0
\(286\) 119.747i 0.418696i
\(287\) 22.4199 78.8848i 0.0781182 0.274860i
\(288\) 16.9706 0.0589256
\(289\) −36.0229 −0.124647
\(290\) 0 0
\(291\) −186.768 −0.641813
\(292\) 106.816i 0.365810i
\(293\) 100.918i 0.344429i 0.985059 + 0.172215i \(0.0550923\pi\)
−0.985059 + 0.172215i \(0.944908\pi\)
\(294\) 63.1258 102.084i 0.214714 0.347224i
\(295\) 0 0
\(296\) −116.991 −0.395238
\(297\) 90.9929i 0.306373i
\(298\) 189.285 0.635183
\(299\) 18.0123i 0.0602417i
\(300\) 0 0
\(301\) 433.742 + 123.274i 1.44100 + 0.409549i
\(302\) −219.293 −0.726136
\(303\) −91.1320 −0.300766
\(304\) 36.5340i 0.120178i
\(305\) 0 0
\(306\) 76.4880i 0.249961i
\(307\) 41.3057i 0.134546i −0.997735 0.0672732i \(-0.978570\pi\)
0.997735 0.0672732i \(-0.0214299\pi\)
\(308\) 235.823 + 67.0235i 0.765659 + 0.217609i
\(309\) 125.401 0.405828
\(310\) 0 0
\(311\) 470.341i 1.51235i 0.654369 + 0.756176i \(0.272934\pi\)
−0.654369 + 0.756176i \(0.727066\pi\)
\(312\) 23.6881 0.0759233
\(313\) 160.220i 0.511884i −0.966692 0.255942i \(-0.917614\pi\)
0.966692 0.255942i \(-0.0823855\pi\)
\(314\) 147.975i 0.471258i
\(315\) 0 0
\(316\) 149.927 0.474454
\(317\) 268.766 0.847843 0.423922 0.905699i \(-0.360653\pi\)
0.423922 + 0.905699i \(0.360653\pi\)
\(318\) 189.929i 0.597262i
\(319\) −19.7149 −0.0618021
\(320\) 0 0
\(321\) 300.618i 0.936505i
\(322\) 35.4723 + 10.0816i 0.110162 + 0.0313094i
\(323\) −164.662 −0.509791
\(324\) 18.0000 0.0555556
\(325\) 0 0
\(326\) −185.133 −0.567891
\(327\) 86.5967i 0.264822i
\(328\) 33.1366i 0.101026i
\(329\) −148.620 + 522.920i −0.451732 + 1.58942i
\(330\) 0 0
\(331\) 555.018 1.67679 0.838395 0.545063i \(-0.183494\pi\)
0.838395 + 0.545063i \(0.183494\pi\)
\(332\) 57.5780i 0.173428i
\(333\) −124.087 −0.372634
\(334\) 145.445i 0.435463i
\(335\) 0 0
\(336\) −13.2584 + 46.6499i −0.0394596 + 0.138839i
\(337\) 47.7972 0.141831 0.0709157 0.997482i \(-0.477408\pi\)
0.0709157 + 0.997482i \(0.477408\pi\)
\(338\) −205.937 −0.609282
\(339\) 121.510i 0.358435i
\(340\) 0 0
\(341\) 999.666i 2.93157i
\(342\) 38.7502i 0.113305i
\(343\) 231.298 + 253.279i 0.674338 + 0.738422i
\(344\) −182.199 −0.529649
\(345\) 0 0
\(346\) 279.211i 0.806967i
\(347\) −283.766 −0.817771 −0.408885 0.912586i \(-0.634082\pi\)
−0.408885 + 0.912586i \(0.634082\pi\)
\(348\) 3.89995i 0.0112067i
\(349\) 20.0321i 0.0573987i 0.999588 + 0.0286993i \(0.00913653\pi\)
−0.999588 + 0.0286993i \(0.990863\pi\)
\(350\) 0 0
\(351\) 25.1250 0.0715812
\(352\) −99.0605 −0.281422
\(353\) 595.015i 1.68559i −0.538231 0.842797i \(-0.680907\pi\)
0.538231 0.842797i \(-0.319093\pi\)
\(354\) −213.265 −0.602443
\(355\) 0 0
\(356\) 202.997i 0.570217i
\(357\) −210.256 59.7570i −0.588952 0.167387i
\(358\) −168.039 −0.469384
\(359\) −588.390 −1.63897 −0.819485 0.573101i \(-0.805740\pi\)
−0.819485 + 0.573101i \(0.805740\pi\)
\(360\) 0 0
\(361\) 277.579 0.768917
\(362\) 20.3856i 0.0563139i
\(363\) 321.566i 0.885856i
\(364\) −18.5065 + 65.1155i −0.0508422 + 0.178889i
\(365\) 0 0
\(366\) −13.1527 −0.0359364
\(367\) 662.601i 1.80545i −0.430215 0.902726i \(-0.641562\pi\)
0.430215 0.902726i \(-0.358438\pi\)
\(368\) −14.9006 −0.0404908
\(369\) 35.1467i 0.0952485i
\(370\) 0 0
\(371\) −522.091 148.384i −1.40725 0.399957i
\(372\) 197.751 0.531590
\(373\) −236.349 −0.633644 −0.316822 0.948485i \(-0.602616\pi\)
−0.316822 + 0.948485i \(0.602616\pi\)
\(374\) 446.476i 1.19378i
\(375\) 0 0
\(376\) 219.660i 0.584201i
\(377\) 5.44368i 0.0144395i
\(378\) −14.0627 + 49.4797i −0.0372029 + 0.130899i
\(379\) −344.235 −0.908272 −0.454136 0.890932i \(-0.650052\pi\)
−0.454136 + 0.890932i \(0.650052\pi\)
\(380\) 0 0
\(381\) 342.852i 0.899873i
\(382\) −84.7644 −0.221896
\(383\) 65.7097i 0.171566i −0.996314 0.0857828i \(-0.972661\pi\)
0.996314 0.0857828i \(-0.0273391\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 347.823 0.901095
\(387\) −193.251 −0.499357
\(388\) 215.661i 0.555827i
\(389\) −161.296 −0.414642 −0.207321 0.978273i \(-0.566474\pi\)
−0.207321 + 0.978273i \(0.566474\pi\)
\(390\) 0 0
\(391\) 67.1585i 0.171761i
\(392\) −117.876 72.8914i −0.300705 0.185947i
\(393\) −199.014 −0.506397
\(394\) −116.050 −0.294542
\(395\) 0 0
\(396\) −105.070 −0.265327
\(397\) 667.752i 1.68200i −0.541039 0.840998i \(-0.681969\pi\)
0.541039 0.840998i \(-0.318031\pi\)
\(398\) 409.186i 1.02811i
\(399\) −106.519 30.2740i −0.266966 0.0758746i
\(400\) 0 0
\(401\) −593.826 −1.48086 −0.740431 0.672132i \(-0.765379\pi\)
−0.740431 + 0.672132i \(0.765379\pi\)
\(402\) 115.586i 0.287528i
\(403\) 276.028 0.684933
\(404\) 105.230i 0.260471i
\(405\) 0 0
\(406\) 10.7205 + 3.04687i 0.0264051 + 0.00750461i
\(407\) 724.322 1.77966
\(408\) 88.3207 0.216472
\(409\) 569.625i 1.39273i −0.717690 0.696363i \(-0.754800\pi\)
0.717690 0.696363i \(-0.245200\pi\)
\(410\) 0 0
\(411\) 165.127i 0.401768i
\(412\) 144.800i 0.351457i
\(413\) 166.615 586.238i 0.403427 1.41946i
\(414\) −15.8045 −0.0381751
\(415\) 0 0
\(416\) 27.3526i 0.0657515i
\(417\) −411.513 −0.986842
\(418\) 226.192i 0.541130i
\(419\) 209.456i 0.499894i 0.968260 + 0.249947i \(0.0804132\pi\)
−0.968260 + 0.249947i \(0.919587\pi\)
\(420\) 0 0
\(421\) −169.713 −0.403119 −0.201560 0.979476i \(-0.564601\pi\)
−0.201560 + 0.979476i \(0.564601\pi\)
\(422\) −47.6583 −0.112934
\(423\) 232.984i 0.550790i
\(424\) 219.311 0.517244
\(425\) 0 0
\(426\) 142.817i 0.335251i
\(427\) 10.2757 36.1551i 0.0240649 0.0846725i
\(428\) −347.124 −0.811037
\(429\) −146.660 −0.341864
\(430\) 0 0
\(431\) 538.427 1.24925 0.624625 0.780925i \(-0.285252\pi\)
0.624625 + 0.780925i \(0.285252\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) 118.314i 0.273243i 0.990623 + 0.136622i \(0.0436244\pi\)
−0.990623 + 0.136622i \(0.956376\pi\)
\(434\) −154.495 + 543.593i −0.355980 + 1.25252i
\(435\) 0 0
\(436\) −99.9932 −0.229342
\(437\) 34.0237i 0.0778575i
\(438\) 130.823 0.298682
\(439\) 434.834i 0.990510i −0.868748 0.495255i \(-0.835075\pi\)
0.868748 0.495255i \(-0.164925\pi\)
\(440\) 0 0
\(441\) −125.027 77.3130i −0.283507 0.175313i
\(442\) 123.281 0.278916
\(443\) 555.005 1.25283 0.626417 0.779488i \(-0.284521\pi\)
0.626417 + 0.779488i \(0.284521\pi\)
\(444\) 143.284i 0.322711i
\(445\) 0 0
\(446\) 15.2107i 0.0341047i
\(447\) 231.825i 0.518625i
\(448\) 53.8667 + 15.3095i 0.120238 + 0.0341730i
\(449\) 66.8926 0.148981 0.0744906 0.997222i \(-0.476267\pi\)
0.0744906 + 0.997222i \(0.476267\pi\)
\(450\) 0 0
\(451\) 205.158i 0.454896i
\(452\) 140.307 0.310414
\(453\) 268.578i 0.592888i
\(454\) 588.949i 1.29724i
\(455\) 0 0
\(456\) 44.7449 0.0981247
\(457\) −750.939 −1.64319 −0.821596 0.570070i \(-0.806916\pi\)
−0.821596 + 0.570070i \(0.806916\pi\)
\(458\) 549.378i 1.19951i
\(459\) 93.6783 0.204092
\(460\) 0 0
\(461\) 395.377i 0.857651i 0.903387 + 0.428826i \(0.141072\pi\)
−0.903387 + 0.428826i \(0.858928\pi\)
\(462\) 82.0867 288.823i 0.177677 0.625158i
\(463\) −423.981 −0.915726 −0.457863 0.889023i \(-0.651385\pi\)
−0.457863 + 0.889023i \(0.651385\pi\)
\(464\) −4.50327 −0.00970533
\(465\) 0 0
\(466\) −99.5658 −0.213660
\(467\) 584.408i 1.25141i 0.780060 + 0.625705i \(0.215188\pi\)
−0.780060 + 0.625705i \(0.784812\pi\)
\(468\) 29.0119i 0.0619911i
\(469\) 317.732 + 90.3030i 0.677467 + 0.192544i
\(470\) 0 0
\(471\) −181.232 −0.384780
\(472\) 246.257i 0.521731i
\(473\) 1128.05 2.38488
\(474\) 183.623i 0.387390i
\(475\) 0 0
\(476\) −69.0014 + 242.782i −0.144961 + 0.510047i
\(477\) 232.615 0.487662
\(478\) −442.837 −0.926438
\(479\) 734.511i 1.53343i −0.641990 0.766713i \(-0.721891\pi\)
0.641990 0.766713i \(-0.278109\pi\)
\(480\) 0 0
\(481\) 200.000i 0.415801i
\(482\) 281.043i 0.583077i
\(483\) 12.3474 43.4445i 0.0255640 0.0899473i
\(484\) 371.312 0.767174
\(485\) 0 0
\(486\) 22.0454i 0.0453609i
\(487\) 91.6643 0.188222 0.0941111 0.995562i \(-0.469999\pi\)
0.0941111 + 0.995562i \(0.469999\pi\)
\(488\) 15.1875i 0.0311218i
\(489\) 226.740i 0.463681i
\(490\) 0 0
\(491\) 460.086 0.937038 0.468519 0.883453i \(-0.344788\pi\)
0.468519 + 0.883453i \(0.344788\pi\)
\(492\) 40.5839 0.0824876
\(493\) 20.2967i 0.0411698i
\(494\) 62.4564 0.126430
\(495\) 0 0
\(496\) 228.344i 0.460370i
\(497\) −392.585 111.577i −0.789910 0.224501i
\(498\) −70.5184 −0.141603
\(499\) 487.126 0.976204 0.488102 0.872786i \(-0.337689\pi\)
0.488102 + 0.872786i \(0.337689\pi\)
\(500\) 0 0
\(501\) −178.133 −0.355554
\(502\) 425.506i 0.847622i
\(503\) 305.145i 0.606650i 0.952887 + 0.303325i \(0.0980967\pi\)
−0.952887 + 0.303325i \(0.901903\pi\)
\(504\) 57.1342 + 16.2382i 0.113362 + 0.0322186i
\(505\) 0 0
\(506\) 92.2539 0.182320
\(507\) 252.221i 0.497477i
\(508\) −395.891 −0.779313
\(509\) 800.434i 1.57256i −0.617869 0.786281i \(-0.712004\pi\)
0.617869 0.786281i \(-0.287996\pi\)
\(510\) 0 0
\(511\) −102.207 + 359.615i −0.200013 + 0.703748i
\(512\) −22.6274 −0.0441942
\(513\) 47.4591 0.0925128
\(514\) 432.824i 0.842069i
\(515\) 0 0
\(516\) 223.147i 0.432456i
\(517\) 1359.97i 2.63051i
\(518\) −393.868 111.942i −0.760364 0.216104i
\(519\) −341.962 −0.658886
\(520\) 0 0
\(521\) 21.4194i 0.0411121i −0.999789 0.0205560i \(-0.993456\pi\)
0.999789 0.0205560i \(-0.00654365\pi\)
\(522\) −4.77644 −0.00915027
\(523\) 842.290i 1.61050i 0.592937 + 0.805249i \(0.297968\pi\)
−0.592937 + 0.805249i \(0.702032\pi\)
\(524\) 229.801i 0.438552i
\(525\) 0 0
\(526\) 404.657 0.769309
\(527\) 1029.17 1.95288
\(528\) 121.324i 0.229780i
\(529\) −515.123 −0.973768
\(530\) 0 0
\(531\) 261.195i 0.491893i
\(532\) −34.9574 + 122.998i −0.0657093 + 0.231199i
\(533\) 56.6484 0.106282
\(534\) 248.620 0.465580
\(535\) 0 0
\(536\) −133.468 −0.249007
\(537\) 205.805i 0.383250i
\(538\) 266.454i 0.495268i
\(539\) 729.806 + 451.291i 1.35400 + 0.837275i
\(540\) 0 0
\(541\) −15.6795 −0.0289824 −0.0144912 0.999895i \(-0.504613\pi\)
−0.0144912 + 0.999895i \(0.504613\pi\)
\(542\) 13.5664i 0.0250302i
\(543\) 24.9672 0.0459801
\(544\) 101.984i 0.187471i
\(545\) 0 0
\(546\) 79.7499 + 22.6658i 0.146062 + 0.0415125i
\(547\) −315.792 −0.577317 −0.288659 0.957432i \(-0.593209\pi\)
−0.288659 + 0.957432i \(0.593209\pi\)
\(548\) 190.672 0.347941
\(549\) 16.1087i 0.0293419i
\(550\) 0 0
\(551\) 10.2827i 0.0186618i
\(552\) 18.2495i 0.0330606i
\(553\) 504.756 + 143.457i 0.912759 + 0.259416i
\(554\) 227.781 0.411157
\(555\) 0 0
\(556\) 475.174i 0.854630i
\(557\) 358.421 0.643484 0.321742 0.946827i \(-0.395732\pi\)
0.321742 + 0.946827i \(0.395732\pi\)
\(558\) 242.195i 0.434041i
\(559\) 311.477i 0.557203i
\(560\) 0 0
\(561\) −546.819 −0.974721
\(562\) 485.226 0.863392
\(563\) 622.834i 1.10628i −0.833089 0.553138i \(-0.813430\pi\)
0.833089 0.553138i \(-0.186570\pi\)
\(564\) −269.027 −0.476998
\(565\) 0 0
\(566\) 459.263i 0.811418i
\(567\) 60.6000 + 17.2232i 0.106878 + 0.0303760i
\(568\) 164.911 0.290336
\(569\) 185.789 0.326518 0.163259 0.986583i \(-0.447799\pi\)
0.163259 + 0.986583i \(0.447799\pi\)
\(570\) 0 0
\(571\) −486.258 −0.851589 −0.425795 0.904820i \(-0.640005\pi\)
−0.425795 + 0.904820i \(0.640005\pi\)
\(572\) 169.348i 0.296063i
\(573\) 103.815i 0.181178i
\(574\) −31.7066 + 111.560i −0.0552379 + 0.194355i
\(575\) 0 0
\(576\) −24.0000 −0.0416667
\(577\) 270.057i 0.468037i −0.972232 0.234018i \(-0.924812\pi\)
0.972232 0.234018i \(-0.0751876\pi\)
\(578\) 50.9440 0.0881385
\(579\) 425.994i 0.735741i
\(580\) 0 0
\(581\) 55.0932 193.846i 0.0948247 0.333642i
\(582\) 264.129 0.453831
\(583\) −1357.82 −2.32902
\(584\) 151.061i 0.258666i
\(585\) 0 0
\(586\) 142.719i 0.243548i
\(587\) 400.613i 0.682476i −0.939977 0.341238i \(-0.889154\pi\)
0.939977 0.341238i \(-0.110846\pi\)
\(588\) −89.2734 + 144.368i −0.151825 + 0.245525i
\(589\) 521.395 0.885220
\(590\) 0 0
\(591\) 142.131i 0.240493i
\(592\) 165.450 0.279476
\(593\) 157.686i 0.265912i −0.991122 0.132956i \(-0.957553\pi\)
0.991122 0.132956i \(-0.0424469\pi\)
\(594\) 128.683i 0.216639i
\(595\) 0 0
\(596\) −267.689 −0.449142
\(597\) −501.149 −0.839445
\(598\) 25.4732i 0.0425973i
\(599\) 468.940 0.782872 0.391436 0.920205i \(-0.371978\pi\)
0.391436 + 0.920205i \(0.371978\pi\)
\(600\) 0 0
\(601\) 255.932i 0.425844i 0.977069 + 0.212922i \(0.0682980\pi\)
−0.977069 + 0.212922i \(0.931702\pi\)
\(602\) −613.404 174.336i −1.01894 0.289595i
\(603\) −141.564 −0.234766
\(604\) 310.127 0.513456
\(605\) 0 0
\(606\) 128.880 0.212673
\(607\) 773.553i 1.27439i 0.770704 + 0.637194i \(0.219905\pi\)
−0.770704 + 0.637194i \(0.780095\pi\)
\(608\) 51.6669i 0.0849785i
\(609\) 3.73164 13.1298i 0.00612749 0.0215597i
\(610\) 0 0
\(611\) −375.517 −0.614594
\(612\) 108.170i 0.176749i
\(613\) 443.208 0.723015 0.361507 0.932369i \(-0.382262\pi\)
0.361507 + 0.932369i \(0.382262\pi\)
\(614\) 58.4151i 0.0951386i
\(615\) 0 0
\(616\) −333.504 94.7855i −0.541402 0.153873i
\(617\) 363.298 0.588813 0.294407 0.955680i \(-0.404878\pi\)
0.294407 + 0.955680i \(0.404878\pi\)
\(618\) −177.344 −0.286964
\(619\) 292.211i 0.472069i 0.971745 + 0.236035i \(0.0758479\pi\)
−0.971745 + 0.236035i \(0.924152\pi\)
\(620\) 0 0
\(621\) 19.3565i 0.0311698i
\(622\) 665.163i 1.06939i
\(623\) −194.237 + 683.425i −0.311777 + 1.09699i
\(624\) −33.5000 −0.0536859
\(625\) 0 0
\(626\) 226.585i 0.361956i
\(627\) −277.028 −0.441831
\(628\) 209.268i 0.333230i
\(629\) 745.698i 1.18553i
\(630\) 0 0
\(631\) 189.221 0.299874 0.149937 0.988696i \(-0.452093\pi\)
0.149937 + 0.988696i \(0.452093\pi\)
\(632\) −212.029 −0.335489
\(633\) 58.3693i 0.0922106i
\(634\) −380.093 −0.599516
\(635\) 0 0
\(636\) 268.600i 0.422328i
\(637\) −124.611 + 201.514i −0.195621 + 0.316349i
\(638\) 27.8810 0.0437007
\(639\) 174.914 0.273731
\(640\) 0 0
\(641\) 1162.94 1.81425 0.907127 0.420857i \(-0.138271\pi\)
0.907127 + 0.420857i \(0.138271\pi\)
\(642\) 425.138i 0.662209i
\(643\) 1096.08i 1.70464i −0.523021 0.852320i \(-0.675195\pi\)
0.523021 0.852320i \(-0.324805\pi\)
\(644\) −50.1654 14.2576i −0.0778966 0.0221391i
\(645\) 0 0
\(646\) 232.868 0.360476
\(647\) 262.877i 0.406302i −0.979147 0.203151i \(-0.934882\pi\)
0.979147 0.203151i \(-0.0651182\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 1524.65i 2.34923i
\(650\) 0 0
\(651\) 665.763 + 189.217i 1.02268 + 0.290656i
\(652\) 261.817 0.401560
\(653\) 242.905 0.371983 0.185992 0.982551i \(-0.440450\pi\)
0.185992 + 0.982551i \(0.440450\pi\)
\(654\) 122.466i 0.187257i
\(655\) 0 0
\(656\) 46.8622i 0.0714364i
\(657\) 160.225i 0.243873i
\(658\) 210.180 739.521i 0.319422 1.12389i
\(659\) −1176.49 −1.78527 −0.892634 0.450783i \(-0.851145\pi\)
−0.892634 + 0.450783i \(0.851145\pi\)
\(660\) 0 0
\(661\) 246.444i 0.372835i −0.982471 0.186418i \(-0.940312\pi\)
0.982471 0.186418i \(-0.0596877\pi\)
\(662\) −784.914 −1.18567
\(663\) 150.988i 0.227734i
\(664\) 81.4276i 0.122632i
\(665\) 0 0
\(666\) 175.486 0.263492
\(667\) 4.19385 0.00628763
\(668\) 205.690i 0.307919i
\(669\) 18.6292 0.0278464
\(670\) 0 0
\(671\) 94.0298i 0.140134i
\(672\) 18.7502 65.9729i 0.0279021 0.0981740i
\(673\) −76.3328 −0.113422 −0.0567109 0.998391i \(-0.518061\pi\)
−0.0567109 + 0.998391i \(0.518061\pi\)
\(674\) −67.5954 −0.100290
\(675\) 0 0
\(676\) 291.240 0.430828
\(677\) 310.277i 0.458312i 0.973390 + 0.229156i \(0.0735965\pi\)
−0.973390 + 0.229156i \(0.926403\pi\)
\(678\) 171.840i 0.253452i
\(679\) −206.354 + 726.058i −0.303908 + 1.06930i
\(680\) 0 0
\(681\) 721.312 1.05920
\(682\) 1413.74i 2.07293i
\(683\) 157.333 0.230356 0.115178 0.993345i \(-0.463256\pi\)
0.115178 + 0.993345i \(0.463256\pi\)
\(684\) 54.8010i 0.0801185i
\(685\) 0 0
\(686\) −327.105 358.190i −0.476829 0.522144i
\(687\) 672.848 0.979400
\(688\) 257.668 0.374518
\(689\) 374.921i 0.544153i
\(690\) 0 0
\(691\) 683.565i 0.989240i −0.869109 0.494620i \(-0.835307\pi\)
0.869109 0.494620i \(-0.164693\pi\)
\(692\) 394.863i 0.570612i
\(693\) −353.734 100.535i −0.510439 0.145072i
\(694\) 401.306 0.578251
\(695\) 0 0
\(696\) 5.51536i 0.00792437i
\(697\) 211.213 0.303031
\(698\) 28.3297i 0.0405870i
\(699\) 121.943i 0.174453i
\(700\) 0 0
\(701\) −306.153 −0.436738 −0.218369 0.975866i \(-0.570074\pi\)
−0.218369 + 0.975866i \(0.570074\pi\)
\(702\) −35.5321 −0.0506156
\(703\) 377.784i 0.537388i
\(704\) 140.093 0.198995
\(705\) 0 0
\(706\) 841.478i 1.19190i
\(707\) −100.689 + 354.275i −0.142417 + 0.501096i
\(708\) 301.602 0.425992
\(709\) −444.082 −0.626350 −0.313175 0.949695i \(-0.601393\pi\)
−0.313175 + 0.949695i \(0.601393\pi\)
\(710\) 0 0
\(711\) −224.891 −0.316302
\(712\) 287.082i 0.403205i
\(713\) 212.654i 0.298252i
\(714\) 297.346 + 84.5092i 0.416452 + 0.118360i
\(715\) 0 0
\(716\) 237.643 0.331904
\(717\) 542.363i 0.756434i
\(718\) 832.109 1.15893
\(719\) 672.926i 0.935919i −0.883750 0.467960i \(-0.844989\pi\)
0.883750 0.467960i \(-0.155011\pi\)
\(720\) 0 0
\(721\) 138.551 487.495i 0.192166 0.676137i
\(722\) −392.556 −0.543707
\(723\) 344.206 0.476080
\(724\) 28.8296i 0.0398199i
\(725\) 0 0
\(726\) 454.762i 0.626395i
\(727\) 675.927i 0.929748i 0.885377 + 0.464874i \(0.153900\pi\)
−0.885377 + 0.464874i \(0.846100\pi\)
\(728\) 26.1722 92.0872i 0.0359508 0.126493i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 1161.34i 1.58870i
\(732\) 18.6008 0.0254109
\(733\) 387.908i 0.529206i 0.964357 + 0.264603i \(0.0852409\pi\)
−0.964357 + 0.264603i \(0.914759\pi\)
\(734\) 937.059i 1.27665i
\(735\) 0 0
\(736\) 21.0727 0.0286313
\(737\) 826.336 1.12122
\(738\) 49.7049i 0.0673508i
\(739\) 394.643 0.534024 0.267012 0.963693i \(-0.413964\pi\)
0.267012 + 0.963693i \(0.413964\pi\)
\(740\) 0 0
\(741\) 76.4931i 0.103230i
\(742\) 738.348 + 209.847i 0.995079 + 0.282812i
\(743\) 147.027 0.197883 0.0989414 0.995093i \(-0.468454\pi\)
0.0989414 + 0.995093i \(0.468454\pi\)
\(744\) −279.663 −0.375891
\(745\) 0 0
\(746\) 334.248 0.448054
\(747\) 86.3670i 0.115618i
\(748\) 631.412i 0.844133i
\(749\) −1168.65 332.144i −1.56028 0.443449i
\(750\) 0 0
\(751\) 103.003 0.137154 0.0685771 0.997646i \(-0.478154\pi\)
0.0685771 + 0.997646i \(0.478154\pi\)
\(752\) 310.646i 0.413092i
\(753\) −521.136 −0.692080
\(754\) 7.69852i 0.0102102i
\(755\) 0 0
\(756\) 19.8876 69.9749i 0.0263064 0.0925593i
\(757\) −547.747 −0.723575 −0.361788 0.932261i \(-0.617833\pi\)
−0.361788 + 0.932261i \(0.617833\pi\)
\(758\) 486.822 0.642246
\(759\) 112.988i 0.148864i
\(760\) 0 0
\(761\) 1223.78i 1.60813i −0.594544 0.804063i \(-0.702668\pi\)
0.594544 0.804063i \(-0.297332\pi\)
\(762\) 484.865i 0.636306i
\(763\) −336.644 95.6779i −0.441211 0.125397i
\(764\) 119.875 0.156904
\(765\) 0 0
\(766\) 92.9275i 0.121315i
\(767\) 420.986 0.548874
\(768\) 27.7128i 0.0360844i
\(769\) 194.874i 0.253413i −0.991940 0.126706i \(-0.959559\pi\)
0.991940 0.126706i \(-0.0404406\pi\)
\(770\) 0 0
\(771\) 530.098 0.687547
\(772\) −491.896 −0.637171
\(773\) 1017.59i 1.31642i 0.752835 + 0.658209i \(0.228686\pi\)
−0.752835 + 0.658209i \(0.771314\pi\)
\(774\) 273.299 0.353099
\(775\) 0 0
\(776\) 304.990i 0.393029i
\(777\) −137.100 + 482.388i −0.176448 + 0.620834i
\(778\) 228.107 0.293196
\(779\) 107.004 0.137361
\(780\) 0 0
\(781\) −1021.01 −1.30731
\(782\) 94.9765i 0.121453i
\(783\) 5.84992i 0.00747117i
\(784\) 166.702 + 103.084i 0.212631 + 0.131485i
\(785\) 0 0
\(786\) 281.448 0.358076
\(787\) 222.094i 0.282203i −0.989995 0.141101i \(-0.954936\pi\)
0.989995 0.141101i \(-0.0450644\pi\)
\(788\) 164.119 0.208273
\(789\) 495.601i 0.628138i
\(790\) 0 0