Properties

Label 75.3.d.c.74.3
Level $75$
Weight $3$
Character 75.74
Analytic conductor $2.044$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.04360198270\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{11})\)
Defining polynomial: \(x^{4} - 5 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 74.3
Root \(1.65831 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 75.74
Dual form 75.3.d.c.74.4

$q$-expansion

\(f(q)\) \(=\) \(q+3.31662 q^{2} +(-1.65831 - 2.50000i) q^{3} +7.00000 q^{4} +(-5.50000 - 8.29156i) q^{6} +9.94987 q^{8} +(-3.50000 + 8.29156i) q^{9} +O(q^{10})\) \(q+3.31662 q^{2} +(-1.65831 - 2.50000i) q^{3} +7.00000 q^{4} +(-5.50000 - 8.29156i) q^{6} +9.94987 q^{8} +(-3.50000 + 8.29156i) q^{9} +16.5831i q^{11} +(-11.6082 - 17.5000i) q^{12} -10.0000i q^{13} +5.00000 q^{16} +3.31662 q^{17} +(-11.6082 + 27.5000i) q^{18} -7.00000 q^{19} +55.0000i q^{22} -19.8997 q^{23} +(-16.5000 - 24.8747i) q^{24} -33.1662i q^{26} +(26.5330 - 5.00000i) q^{27} -33.1662i q^{29} +42.0000 q^{31} -23.2164 q^{32} +(41.4578 - 27.5000i) q^{33} +11.0000 q^{34} +(-24.5000 + 58.0409i) q^{36} -40.0000i q^{37} -23.2164 q^{38} +(-25.0000 + 16.5831i) q^{39} -16.5831i q^{41} +50.0000i q^{43} +116.082i q^{44} -66.0000 q^{46} -46.4327 q^{47} +(-8.29156 - 12.5000i) q^{48} +49.0000 q^{49} +(-5.50000 - 8.29156i) q^{51} -70.0000i q^{52} +46.4327 q^{53} +(88.0000 - 16.5831i) q^{54} +(11.6082 + 17.5000i) q^{57} -110.000i q^{58} -66.3325i q^{59} -8.00000 q^{61} +139.298 q^{62} -97.0000 q^{64} +(137.500 - 91.2072i) q^{66} +45.0000i q^{67} +23.2164 q^{68} +(33.0000 + 49.7494i) q^{69} +33.1662i q^{71} +(-34.8246 + 82.5000i) q^{72} +35.0000i q^{73} -132.665i q^{74} -49.0000 q^{76} +(-82.9156 + 55.0000i) q^{78} -12.0000 q^{79} +(-56.5000 - 58.0409i) q^{81} -55.0000i q^{82} -69.6491 q^{83} +165.831i q^{86} +(-82.9156 + 55.0000i) q^{87} +165.000i q^{88} +149.248i q^{89} -139.298 q^{92} +(-69.6491 - 105.000i) q^{93} -154.000 q^{94} +(38.5000 + 58.0409i) q^{96} -70.0000i q^{97} +162.515 q^{98} +(-137.500 - 58.0409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 28q^{4} - 22q^{6} - 14q^{9} + O(q^{10}) \) \( 4q + 28q^{4} - 22q^{6} - 14q^{9} + 20q^{16} - 28q^{19} - 66q^{24} + 168q^{31} + 44q^{34} - 98q^{36} - 100q^{39} - 264q^{46} + 196q^{49} - 22q^{51} + 352q^{54} - 32q^{61} - 388q^{64} + 550q^{66} + 132q^{69} - 196q^{76} - 48q^{79} - 226q^{81} - 616q^{94} + 154q^{96} - 550q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.31662 1.65831 0.829156 0.559017i \(-0.188821\pi\)
0.829156 + 0.559017i \(0.188821\pi\)
\(3\) −1.65831 2.50000i −0.552771 0.833333i
\(4\) 7.00000 1.75000
\(5\) 0 0
\(6\) −5.50000 8.29156i −0.916667 1.38193i
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 9.94987 1.24373
\(9\) −3.50000 + 8.29156i −0.388889 + 0.921285i
\(10\) 0 0
\(11\) 16.5831i 1.50756i 0.657129 + 0.753778i \(0.271771\pi\)
−0.657129 + 0.753778i \(0.728229\pi\)
\(12\) −11.6082 17.5000i −0.967349 1.45833i
\(13\) 10.0000i 0.769231i −0.923077 0.384615i \(-0.874334\pi\)
0.923077 0.384615i \(-0.125666\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 5.00000 0.312500
\(17\) 3.31662 0.195096 0.0975478 0.995231i \(-0.468900\pi\)
0.0975478 + 0.995231i \(0.468900\pi\)
\(18\) −11.6082 + 27.5000i −0.644899 + 1.52778i
\(19\) −7.00000 −0.368421 −0.184211 0.982887i \(-0.558973\pi\)
−0.184211 + 0.982887i \(0.558973\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 55.0000i 2.50000i
\(23\) −19.8997 −0.865206 −0.432603 0.901584i \(-0.642405\pi\)
−0.432603 + 0.901584i \(0.642405\pi\)
\(24\) −16.5000 24.8747i −0.687500 1.03645i
\(25\) 0 0
\(26\) 33.1662i 1.27562i
\(27\) 26.5330 5.00000i 0.982704 0.185185i
\(28\) 0 0
\(29\) 33.1662i 1.14366i −0.820371 0.571832i \(-0.806233\pi\)
0.820371 0.571832i \(-0.193767\pi\)
\(30\) 0 0
\(31\) 42.0000 1.35484 0.677419 0.735597i \(-0.263098\pi\)
0.677419 + 0.735597i \(0.263098\pi\)
\(32\) −23.2164 −0.725512
\(33\) 41.4578 27.5000i 1.25630 0.833333i
\(34\) 11.0000 0.323529
\(35\) 0 0
\(36\) −24.5000 + 58.0409i −0.680556 + 1.61225i
\(37\) 40.0000i 1.08108i −0.841318 0.540541i \(-0.818220\pi\)
0.841318 0.540541i \(-0.181780\pi\)
\(38\) −23.2164 −0.610957
\(39\) −25.0000 + 16.5831i −0.641026 + 0.425208i
\(40\) 0 0
\(41\) 16.5831i 0.404466i −0.979337 0.202233i \(-0.935180\pi\)
0.979337 0.202233i \(-0.0648199\pi\)
\(42\) 0 0
\(43\) 50.0000i 1.16279i 0.813621 + 0.581395i \(0.197493\pi\)
−0.813621 + 0.581395i \(0.802507\pi\)
\(44\) 116.082i 2.63822i
\(45\) 0 0
\(46\) −66.0000 −1.43478
\(47\) −46.4327 −0.987931 −0.493965 0.869482i \(-0.664453\pi\)
−0.493965 + 0.869482i \(0.664453\pi\)
\(48\) −8.29156 12.5000i −0.172741 0.260417i
\(49\) 49.0000 1.00000
\(50\) 0 0
\(51\) −5.50000 8.29156i −0.107843 0.162580i
\(52\) 70.0000i 1.34615i
\(53\) 46.4327 0.876090 0.438045 0.898953i \(-0.355671\pi\)
0.438045 + 0.898953i \(0.355671\pi\)
\(54\) 88.0000 16.5831i 1.62963 0.307095i
\(55\) 0 0
\(56\) 0 0
\(57\) 11.6082 + 17.5000i 0.203652 + 0.307018i
\(58\) 110.000i 1.89655i
\(59\) 66.3325i 1.12428i −0.827042 0.562140i \(-0.809978\pi\)
0.827042 0.562140i \(-0.190022\pi\)
\(60\) 0 0
\(61\) −8.00000 −0.131148 −0.0655738 0.997848i \(-0.520888\pi\)
−0.0655738 + 0.997848i \(0.520888\pi\)
\(62\) 139.298 2.24675
\(63\) 0 0
\(64\) −97.0000 −1.51562
\(65\) 0 0
\(66\) 137.500 91.2072i 2.08333 1.38193i
\(67\) 45.0000i 0.671642i 0.941926 + 0.335821i \(0.109014\pi\)
−0.941926 + 0.335821i \(0.890986\pi\)
\(68\) 23.2164 0.341417
\(69\) 33.0000 + 49.7494i 0.478261 + 0.721005i
\(70\) 0 0
\(71\) 33.1662i 0.467130i 0.972341 + 0.233565i \(0.0750392\pi\)
−0.972341 + 0.233565i \(0.924961\pi\)
\(72\) −34.8246 + 82.5000i −0.483674 + 1.14583i
\(73\) 35.0000i 0.479452i 0.970841 + 0.239726i \(0.0770576\pi\)
−0.970841 + 0.239726i \(0.922942\pi\)
\(74\) 132.665i 1.79277i
\(75\) 0 0
\(76\) −49.0000 −0.644737
\(77\) 0 0
\(78\) −82.9156 + 55.0000i −1.06302 + 0.705128i
\(79\) −12.0000 −0.151899 −0.0759494 0.997112i \(-0.524199\pi\)
−0.0759494 + 0.997112i \(0.524199\pi\)
\(80\) 0 0
\(81\) −56.5000 58.0409i −0.697531 0.716555i
\(82\) 55.0000i 0.670732i
\(83\) −69.6491 −0.839146 −0.419573 0.907722i \(-0.637820\pi\)
−0.419573 + 0.907722i \(0.637820\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 165.831i 1.92827i
\(87\) −82.9156 + 55.0000i −0.953053 + 0.632184i
\(88\) 165.000i 1.87500i
\(89\) 149.248i 1.67695i 0.544944 + 0.838473i \(0.316551\pi\)
−0.544944 + 0.838473i \(0.683449\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −139.298 −1.51411
\(93\) −69.6491 105.000i −0.748915 1.12903i
\(94\) −154.000 −1.63830
\(95\) 0 0
\(96\) 38.5000 + 58.0409i 0.401042 + 0.604593i
\(97\) 70.0000i 0.721649i −0.932634 0.360825i \(-0.882495\pi\)
0.932634 0.360825i \(-0.117505\pi\)
\(98\) 162.515 1.65831
\(99\) −137.500 58.0409i −1.38889 0.586272i
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) −18.2414 27.5000i −0.178838 0.269608i
\(103\) 70.0000i 0.679612i 0.940496 + 0.339806i \(0.110361\pi\)
−0.940496 + 0.339806i \(0.889639\pi\)
\(104\) 99.4987i 0.956719i
\(105\) 0 0
\(106\) 154.000 1.45283
\(107\) 69.6491 0.650926 0.325463 0.945555i \(-0.394480\pi\)
0.325463 + 0.945555i \(0.394480\pi\)
\(108\) 185.731 35.0000i 1.71973 0.324074i
\(109\) 88.0000 0.807339 0.403670 0.914905i \(-0.367734\pi\)
0.403670 + 0.914905i \(0.367734\pi\)
\(110\) 0 0
\(111\) −100.000 + 66.3325i −0.900901 + 0.597590i
\(112\) 0 0
\(113\) −102.815 −0.909871 −0.454935 0.890525i \(-0.650338\pi\)
−0.454935 + 0.890525i \(0.650338\pi\)
\(114\) 38.5000 + 58.0409i 0.337719 + 0.509131i
\(115\) 0 0
\(116\) 232.164i 2.00141i
\(117\) 82.9156 + 35.0000i 0.708681 + 0.299145i
\(118\) 220.000i 1.86441i
\(119\) 0 0
\(120\) 0 0
\(121\) −154.000 −1.27273
\(122\) −26.5330 −0.217484
\(123\) −41.4578 + 27.5000i −0.337055 + 0.223577i
\(124\) 294.000 2.37097
\(125\) 0 0
\(126\) 0 0
\(127\) 190.000i 1.49606i 0.663663 + 0.748031i \(0.269001\pi\)
−0.663663 + 0.748031i \(0.730999\pi\)
\(128\) −228.847 −1.78787
\(129\) 125.000 82.9156i 0.968992 0.642757i
\(130\) 0 0
\(131\) 198.997i 1.51906i −0.650469 0.759532i \(-0.725428\pi\)
0.650469 0.759532i \(-0.274572\pi\)
\(132\) 290.205 192.500i 2.19852 1.45833i
\(133\) 0 0
\(134\) 149.248i 1.11379i
\(135\) 0 0
\(136\) 33.0000 0.242647
\(137\) 69.6491 0.508388 0.254194 0.967153i \(-0.418190\pi\)
0.254194 + 0.967153i \(0.418190\pi\)
\(138\) 109.449 + 165.000i 0.793106 + 1.19565i
\(139\) −77.0000 −0.553957 −0.276978 0.960876i \(-0.589333\pi\)
−0.276978 + 0.960876i \(0.589333\pi\)
\(140\) 0 0
\(141\) 77.0000 + 116.082i 0.546099 + 0.823276i
\(142\) 110.000i 0.774648i
\(143\) 165.831 1.15966
\(144\) −17.5000 + 41.4578i −0.121528 + 0.287901i
\(145\) 0 0
\(146\) 116.082i 0.795081i
\(147\) −81.2573 122.500i −0.552771 0.833333i
\(148\) 280.000i 1.89189i
\(149\) 165.831i 1.11296i 0.830861 + 0.556481i \(0.187849\pi\)
−0.830861 + 0.556481i \(0.812151\pi\)
\(150\) 0 0
\(151\) 172.000 1.13907 0.569536 0.821966i \(-0.307123\pi\)
0.569536 + 0.821966i \(0.307123\pi\)
\(152\) −69.6491 −0.458218
\(153\) −11.6082 + 27.5000i −0.0758705 + 0.179739i
\(154\) 0 0
\(155\) 0 0
\(156\) −175.000 + 116.082i −1.12179 + 0.744115i
\(157\) 250.000i 1.59236i −0.605062 0.796178i \(-0.706852\pi\)
0.605062 0.796178i \(-0.293148\pi\)
\(158\) −39.7995 −0.251896
\(159\) −77.0000 116.082i −0.484277 0.730075i
\(160\) 0 0
\(161\) 0 0
\(162\) −187.389 192.500i −1.15672 1.18827i
\(163\) 35.0000i 0.214724i −0.994220 0.107362i \(-0.965760\pi\)
0.994220 0.107362i \(-0.0342404\pi\)
\(164\) 116.082i 0.707816i
\(165\) 0 0
\(166\) −231.000 −1.39157
\(167\) −179.098 −1.07244 −0.536221 0.844078i \(-0.680149\pi\)
−0.536221 + 0.844078i \(0.680149\pi\)
\(168\) 0 0
\(169\) 69.0000 0.408284
\(170\) 0 0
\(171\) 24.5000 58.0409i 0.143275 0.339421i
\(172\) 350.000i 2.03488i
\(173\) 278.596 1.61038 0.805192 0.593014i \(-0.202062\pi\)
0.805192 + 0.593014i \(0.202062\pi\)
\(174\) −275.000 + 182.414i −1.58046 + 1.04836i
\(175\) 0 0
\(176\) 82.9156i 0.471111i
\(177\) −165.831 + 110.000i −0.936900 + 0.621469i
\(178\) 495.000i 2.78090i
\(179\) 116.082i 0.648502i −0.945971 0.324251i \(-0.894888\pi\)
0.945971 0.324251i \(-0.105112\pi\)
\(180\) 0 0
\(181\) 182.000 1.00552 0.502762 0.864425i \(-0.332317\pi\)
0.502762 + 0.864425i \(0.332317\pi\)
\(182\) 0 0
\(183\) 13.2665 + 20.0000i 0.0724945 + 0.109290i
\(184\) −198.000 −1.07609
\(185\) 0 0
\(186\) −231.000 348.246i −1.24194 1.87229i
\(187\) 55.0000i 0.294118i
\(188\) −325.029 −1.72888
\(189\) 0 0
\(190\) 0 0
\(191\) 232.164i 1.21552i 0.794122 + 0.607758i \(0.207931\pi\)
−0.794122 + 0.607758i \(0.792069\pi\)
\(192\) 160.856 + 242.500i 0.837793 + 1.26302i
\(193\) 25.0000i 0.129534i 0.997900 + 0.0647668i \(0.0206304\pi\)
−0.997900 + 0.0647668i \(0.979370\pi\)
\(194\) 232.164i 1.19672i
\(195\) 0 0
\(196\) 343.000 1.75000
\(197\) 218.897 1.11115 0.555577 0.831465i \(-0.312498\pi\)
0.555577 + 0.831465i \(0.312498\pi\)
\(198\) −456.036 192.500i −2.30321 0.972222i
\(199\) 68.0000 0.341709 0.170854 0.985296i \(-0.445347\pi\)
0.170854 + 0.985296i \(0.445347\pi\)
\(200\) 0 0
\(201\) 112.500 74.6241i 0.559701 0.371264i
\(202\) 0 0
\(203\) 0 0
\(204\) −38.5000 58.0409i −0.188725 0.284514i
\(205\) 0 0
\(206\) 232.164i 1.12701i
\(207\) 69.6491 165.000i 0.336469 0.797101i
\(208\) 50.0000i 0.240385i
\(209\) 116.082i 0.555416i
\(210\) 0 0
\(211\) 77.0000 0.364929 0.182464 0.983212i \(-0.441593\pi\)
0.182464 + 0.983212i \(0.441593\pi\)
\(212\) 325.029 1.53316
\(213\) 82.9156 55.0000i 0.389275 0.258216i
\(214\) 231.000 1.07944
\(215\) 0 0
\(216\) 264.000 49.7494i 1.22222 0.230321i
\(217\) 0 0
\(218\) 291.863 1.33882
\(219\) 87.5000 58.0409i 0.399543 0.265027i
\(220\) 0 0
\(221\) 33.1662i 0.150074i
\(222\) −331.662 + 220.000i −1.49398 + 0.990991i
\(223\) 140.000i 0.627803i −0.949456 0.313901i \(-0.898364\pi\)
0.949456 0.313901i \(-0.101636\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −341.000 −1.50885
\(227\) 185.731 0.818198 0.409099 0.912490i \(-0.365843\pi\)
0.409099 + 0.912490i \(0.365843\pi\)
\(228\) 81.2573 + 122.500i 0.356392 + 0.537281i
\(229\) −372.000 −1.62445 −0.812227 0.583341i \(-0.801745\pi\)
−0.812227 + 0.583341i \(0.801745\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 330.000i 1.42241i
\(233\) −119.398 −0.512440 −0.256220 0.966619i \(-0.582477\pi\)
−0.256220 + 0.966619i \(0.582477\pi\)
\(234\) 275.000 + 116.082i 1.17521 + 0.496076i
\(235\) 0 0
\(236\) 464.327i 1.96749i
\(237\) 19.8997 + 30.0000i 0.0839652 + 0.126582i
\(238\) 0 0
\(239\) 232.164i 0.971396i 0.874127 + 0.485698i \(0.161435\pi\)
−0.874127 + 0.485698i \(0.838565\pi\)
\(240\) 0 0
\(241\) −413.000 −1.71369 −0.856846 0.515572i \(-0.827580\pi\)
−0.856846 + 0.515572i \(0.827580\pi\)
\(242\) −510.760 −2.11058
\(243\) −51.4077 + 237.500i −0.211554 + 0.977366i
\(244\) −56.0000 −0.229508
\(245\) 0 0
\(246\) −137.500 + 91.2072i −0.558943 + 0.370761i
\(247\) 70.0000i 0.283401i
\(248\) 417.895 1.68506
\(249\) 115.500 + 174.123i 0.463855 + 0.699288i
\(250\) 0 0
\(251\) 248.747i 0.991023i 0.868601 + 0.495512i \(0.165019\pi\)
−0.868601 + 0.495512i \(0.834981\pi\)
\(252\) 0 0
\(253\) 330.000i 1.30435i
\(254\) 630.159i 2.48094i
\(255\) 0 0
\(256\) −371.000 −1.44922
\(257\) −278.596 −1.08403 −0.542017 0.840368i \(-0.682339\pi\)
−0.542017 + 0.840368i \(0.682339\pi\)
\(258\) 414.578 275.000i 1.60689 1.06589i
\(259\) 0 0
\(260\) 0 0
\(261\) 275.000 + 116.082i 1.05364 + 0.444758i
\(262\) 660.000i 2.51908i
\(263\) −285.230 −1.08452 −0.542262 0.840210i \(-0.682432\pi\)
−0.542262 + 0.840210i \(0.682432\pi\)
\(264\) 412.500 273.622i 1.56250 1.03645i
\(265\) 0 0
\(266\) 0 0
\(267\) 373.120 247.500i 1.39745 0.926966i
\(268\) 315.000i 1.17537i
\(269\) 464.327i 1.72612i −0.505098 0.863062i \(-0.668544\pi\)
0.505098 0.863062i \(-0.331456\pi\)
\(270\) 0 0
\(271\) 22.0000 0.0811808 0.0405904 0.999176i \(-0.487076\pi\)
0.0405904 + 0.999176i \(0.487076\pi\)
\(272\) 16.5831 0.0609674
\(273\) 0 0
\(274\) 231.000 0.843066
\(275\) 0 0
\(276\) 231.000 + 348.246i 0.836957 + 1.26176i
\(277\) 210.000i 0.758123i −0.925372 0.379061i \(-0.876247\pi\)
0.925372 0.379061i \(-0.123753\pi\)
\(278\) −255.380 −0.918633
\(279\) −147.000 + 348.246i −0.526882 + 1.24819i
\(280\) 0 0
\(281\) 198.997i 0.708176i −0.935212 0.354088i \(-0.884791\pi\)
0.935212 0.354088i \(-0.115209\pi\)
\(282\) 255.380 + 385.000i 0.905603 + 1.36525i
\(283\) 345.000i 1.21908i −0.792755 0.609541i \(-0.791354\pi\)
0.792755 0.609541i \(-0.208646\pi\)
\(284\) 232.164i 0.817478i
\(285\) 0 0
\(286\) 550.000 1.92308
\(287\) 0 0
\(288\) 81.2573 192.500i 0.282143 0.668403i
\(289\) −278.000 −0.961938
\(290\) 0 0
\(291\) −175.000 + 116.082i −0.601375 + 0.398907i
\(292\) 245.000i 0.839041i
\(293\) −318.396 −1.08668 −0.543338 0.839514i \(-0.682840\pi\)
−0.543338 + 0.839514i \(0.682840\pi\)
\(294\) −269.500 406.287i −0.916667 1.38193i
\(295\) 0 0
\(296\) 397.995i 1.34458i
\(297\) 82.9156 + 440.000i 0.279177 + 1.48148i
\(298\) 550.000i 1.84564i
\(299\) 198.997i 0.665543i
\(300\) 0 0
\(301\) 0 0
\(302\) 570.459 1.88894
\(303\) 0 0
\(304\) −35.0000 −0.115132
\(305\) 0 0
\(306\) −38.5000 + 91.2072i −0.125817 + 0.298063i
\(307\) 325.000i 1.05863i 0.848425 + 0.529316i \(0.177551\pi\)
−0.848425 + 0.529316i \(0.822449\pi\)
\(308\) 0 0
\(309\) 175.000 116.082i 0.566343 0.375669i
\(310\) 0 0
\(311\) 397.995i 1.27973i −0.768489 0.639863i \(-0.778991\pi\)
0.768489 0.639863i \(-0.221009\pi\)
\(312\) −248.747 + 165.000i −0.797266 + 0.528846i
\(313\) 490.000i 1.56550i 0.622339 + 0.782748i \(0.286182\pi\)
−0.622339 + 0.782748i \(0.713818\pi\)
\(314\) 829.156i 2.64062i
\(315\) 0 0
\(316\) −84.0000 −0.265823
\(317\) −212.264 −0.669602 −0.334801 0.942289i \(-0.608669\pi\)
−0.334801 + 0.942289i \(0.608669\pi\)
\(318\) −255.380 385.000i −0.803082 1.21069i
\(319\) 550.000 1.72414
\(320\) 0 0
\(321\) −115.500 174.123i −0.359813 0.542439i
\(322\) 0 0
\(323\) −23.2164 −0.0718773
\(324\) −395.500 406.287i −1.22068 1.25397i
\(325\) 0 0
\(326\) 116.082i 0.356079i
\(327\) −145.931 220.000i −0.446274 0.672783i
\(328\) 165.000i 0.503049i
\(329\) 0 0
\(330\) 0 0
\(331\) −243.000 −0.734139 −0.367069 0.930194i \(-0.619639\pi\)
−0.367069 + 0.930194i \(0.619639\pi\)
\(332\) −487.544 −1.46851
\(333\) 331.662 + 140.000i 0.995983 + 0.420420i
\(334\) −594.000 −1.77844
\(335\) 0 0
\(336\) 0 0
\(337\) 385.000i 1.14243i 0.820799 + 0.571217i \(0.193528\pi\)
−0.820799 + 0.571217i \(0.806472\pi\)
\(338\) 228.847 0.677062
\(339\) 170.500 + 257.038i 0.502950 + 0.758225i
\(340\) 0 0
\(341\) 696.491i 2.04250i
\(342\) 81.2573 192.500i 0.237594 0.562865i
\(343\) 0 0
\(344\) 497.494i 1.44620i
\(345\) 0 0
\(346\) 924.000 2.67052
\(347\) −295.180 −0.850662 −0.425331 0.905038i \(-0.639842\pi\)
−0.425331 + 0.905038i \(0.639842\pi\)
\(348\) −580.409 + 385.000i −1.66784 + 1.10632i
\(349\) −532.000 −1.52436 −0.762178 0.647368i \(-0.775870\pi\)
−0.762178 + 0.647368i \(0.775870\pi\)
\(350\) 0 0
\(351\) −50.0000 265.330i −0.142450 0.755926i
\(352\) 385.000i 1.09375i
\(353\) 278.596 0.789225 0.394613 0.918848i \(-0.370879\pi\)
0.394613 + 0.918848i \(0.370879\pi\)
\(354\) −550.000 + 364.829i −1.55367 + 1.03059i
\(355\) 0 0
\(356\) 1044.74i 2.93465i
\(357\) 0 0
\(358\) 385.000i 1.07542i
\(359\) 397.995i 1.10862i −0.832310 0.554311i \(-0.812982\pi\)
0.832310 0.554311i \(-0.187018\pi\)
\(360\) 0 0
\(361\) −312.000 −0.864266
\(362\) 603.626 1.66747
\(363\) 255.380 + 385.000i 0.703526 + 1.06061i
\(364\) 0 0
\(365\) 0 0
\(366\) 44.0000 + 66.3325i 0.120219 + 0.181236i
\(367\) 180.000i 0.490463i −0.969465 0.245232i \(-0.921136\pi\)
0.969465 0.245232i \(-0.0788640\pi\)
\(368\) −99.4987 −0.270377
\(369\) 137.500 + 58.0409i 0.372629 + 0.157293i
\(370\) 0 0
\(371\) 0 0
\(372\) −487.544 735.000i −1.31060 1.97581i
\(373\) 110.000i 0.294906i 0.989069 + 0.147453i \(0.0471075\pi\)
−0.989069 + 0.147453i \(0.952892\pi\)
\(374\) 182.414i 0.487739i
\(375\) 0 0
\(376\) −462.000 −1.22872
\(377\) −331.662 −0.879741
\(378\) 0 0
\(379\) 533.000 1.40633 0.703166 0.711025i \(-0.251769\pi\)
0.703166 + 0.711025i \(0.251769\pi\)
\(380\) 0 0
\(381\) 475.000 315.079i 1.24672 0.826980i
\(382\) 770.000i 2.01571i
\(383\) 79.5990 0.207830 0.103915 0.994586i \(-0.466863\pi\)
0.103915 + 0.994586i \(0.466863\pi\)
\(384\) 379.500 + 572.118i 0.988281 + 1.48989i
\(385\) 0 0
\(386\) 82.9156i 0.214807i
\(387\) −414.578 175.000i −1.07126 0.452196i
\(388\) 490.000i 1.26289i
\(389\) 99.4987i 0.255781i −0.991788 0.127890i \(-0.959179\pi\)
0.991788 0.127890i \(-0.0408206\pi\)
\(390\) 0 0
\(391\) −66.0000 −0.168798
\(392\) 487.544 1.24373
\(393\) −497.494 + 330.000i −1.26589 + 0.839695i
\(394\) 726.000 1.84264
\(395\) 0 0
\(396\) −962.500 406.287i −2.43056 1.02598i
\(397\) 20.0000i 0.0503778i −0.999683 0.0251889i \(-0.991981\pi\)
0.999683 0.0251889i \(-0.00801873\pi\)
\(398\) 225.530 0.566660
\(399\) 0 0
\(400\) 0 0
\(401\) 746.241i 1.86095i −0.366357 0.930475i \(-0.619395\pi\)
0.366357 0.930475i \(-0.380605\pi\)
\(402\) 373.120 247.500i 0.928160 0.615672i
\(403\) 420.000i 1.04218i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 663.325 1.62979
\(408\) −54.7243 82.5000i −0.134128 0.202206i
\(409\) −77.0000 −0.188264 −0.0941320 0.995560i \(-0.530008\pi\)
−0.0941320 + 0.995560i \(0.530008\pi\)
\(410\) 0 0
\(411\) −115.500 174.123i −0.281022 0.423656i
\(412\) 490.000i 1.18932i
\(413\) 0 0
\(414\) 231.000 547.243i 0.557971 1.32184i
\(415\) 0 0
\(416\) 232.164i 0.558086i
\(417\) 127.690 + 192.500i 0.306211 + 0.461631i
\(418\) 385.000i 0.921053i
\(419\) 116.082i 0.277045i 0.990359 + 0.138523i \(0.0442353\pi\)
−0.990359 + 0.138523i \(0.955765\pi\)
\(420\) 0 0
\(421\) 412.000 0.978622 0.489311 0.872109i \(-0.337248\pi\)
0.489311 + 0.872109i \(0.337248\pi\)
\(422\) 255.380 0.605166
\(423\) 162.515 385.000i 0.384195 0.910165i
\(424\) 462.000 1.08962
\(425\) 0 0
\(426\) 275.000 182.414i 0.645540 0.428203i
\(427\) 0 0
\(428\) 487.544 1.13912
\(429\) −275.000 414.578i −0.641026 0.966383i
\(430\) 0 0
\(431\) 198.997i 0.461711i −0.972988 0.230856i \(-0.925848\pi\)
0.972988 0.230856i \(-0.0741525\pi\)
\(432\) 132.665 25.0000i 0.307095 0.0578704i
\(433\) 455.000i 1.05081i 0.850853 + 0.525404i \(0.176086\pi\)
−0.850853 + 0.525404i \(0.823914\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 616.000 1.41284
\(437\) 139.298 0.318760
\(438\) 290.205 192.500i 0.662568 0.439498i
\(439\) −22.0000 −0.0501139 −0.0250569 0.999686i \(-0.507977\pi\)
−0.0250569 + 0.999686i \(0.507977\pi\)
\(440\) 0 0
\(441\) −171.500 + 406.287i −0.388889 + 0.921285i
\(442\) 110.000i 0.248869i
\(443\) 527.343 1.19039 0.595196 0.803581i \(-0.297075\pi\)
0.595196 + 0.803581i \(0.297075\pi\)
\(444\) −700.000 + 464.327i −1.57658 + 1.04578i
\(445\) 0 0
\(446\) 464.327i 1.04109i
\(447\) 414.578 275.000i 0.927468 0.615213i
\(448\) 0 0
\(449\) 82.9156i 0.184667i 0.995728 + 0.0923337i \(0.0294326\pi\)
−0.995728 + 0.0923337i \(0.970567\pi\)
\(450\) 0 0
\(451\) 275.000 0.609756
\(452\) −719.708 −1.59227
\(453\) −285.230 430.000i −0.629646 0.949227i
\(454\) 616.000 1.35683
\(455\) 0 0
\(456\) 115.500 + 174.123i 0.253289 + 0.381848i
\(457\) 275.000i 0.601751i −0.953663 0.300875i \(-0.902721\pi\)
0.953663 0.300875i \(-0.0972788\pi\)
\(458\) −1233.78 −2.69385
\(459\) 88.0000 16.5831i 0.191721 0.0361288i
\(460\) 0 0
\(461\) 596.992i 1.29499i 0.762068 + 0.647497i \(0.224184\pi\)
−0.762068 + 0.647497i \(0.775816\pi\)
\(462\) 0 0
\(463\) 240.000i 0.518359i 0.965829 + 0.259179i \(0.0834520\pi\)
−0.965829 + 0.259179i \(0.916548\pi\)
\(464\) 165.831i 0.357395i
\(465\) 0 0
\(466\) −396.000 −0.849785
\(467\) −13.2665 −0.0284079 −0.0142040 0.999899i \(-0.504521\pi\)
−0.0142040 + 0.999899i \(0.504521\pi\)
\(468\) 580.409 + 245.000i 1.24019 + 0.523504i
\(469\) 0 0
\(470\) 0 0
\(471\) −625.000 + 414.578i −1.32696 + 0.880208i
\(472\) 660.000i 1.39831i
\(473\) −829.156 −1.75297
\(474\) 66.0000 + 99.4987i 0.139241 + 0.209913i
\(475\) 0 0
\(476\) 0 0
\(477\) −162.515 + 385.000i −0.340701 + 0.807128i
\(478\) 770.000i 1.61088i
\(479\) 298.496i 0.623165i 0.950219 + 0.311583i \(0.100859\pi\)
−0.950219 + 0.311583i \(0.899141\pi\)
\(480\) 0 0
\(481\) −400.000 −0.831601
\(482\) −1369.77 −2.84184
\(483\) 0 0
\(484\) −1078.00 −2.22727
\(485\) 0 0
\(486\) −170.500 + 787.698i −0.350823 + 1.62078i
\(487\) 410.000i 0.841889i 0.907086 + 0.420945i \(0.138301\pi\)
−0.907086 + 0.420945i \(0.861699\pi\)
\(488\) −79.5990 −0.163113
\(489\) −87.5000 + 58.0409i −0.178937 + 0.118693i
\(490\) 0 0
\(491\) 265.330i 0.540387i −0.962806 0.270193i \(-0.912912\pi\)
0.962806 0.270193i \(-0.0870877\pi\)
\(492\) −290.205 + 192.500i −0.589847 + 0.391260i
\(493\) 110.000i 0.223124i
\(494\) 232.164i 0.469967i
\(495\) 0 0
\(496\) 210.000 0.423387
\(497\) 0 0
\(498\) 383.070 + 577.500i 0.769217 + 1.15964i
\(499\) −322.000 −0.645291 −0.322645 0.946520i \(-0.604572\pi\)
−0.322645 + 0.946520i \(0.604572\pi\)
\(500\) 0 0
\(501\) 297.000 + 447.744i 0.592814 + 0.893701i
\(502\) 825.000i 1.64343i
\(503\) 411.261 0.817617 0.408809 0.912620i \(-0.365944\pi\)
0.408809 + 0.912620i \(0.365944\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 1094.49i 2.16302i
\(507\) −114.424 172.500i −0.225687 0.340237i
\(508\) 1330.00i 2.61811i
\(509\) 431.161i 0.847075i 0.905879 + 0.423538i \(0.139212\pi\)
−0.905879 + 0.423538i \(0.860788\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −315.079 −0.615389
\(513\) −185.731 + 35.0000i −0.362049 + 0.0682261i
\(514\) −924.000 −1.79767
\(515\) 0 0
\(516\) 875.000 580.409i 1.69574 1.12482i
\(517\) 770.000i 1.48936i
\(518\) 0 0
\(519\) −462.000 696.491i −0.890173 1.34199i
\(520\) 0 0
\(521\) 281.913i 0.541100i 0.962706 + 0.270550i \(0.0872055\pi\)
−0.962706 + 0.270550i \(0.912794\pi\)
\(522\) 912.072 + 385.000i 1.74726 + 0.737548i
\(523\) 1015.00i 1.94073i −0.241651 0.970363i \(-0.577689\pi\)
0.241651 0.970363i \(-0.422311\pi\)
\(524\) 1392.98i 2.65836i
\(525\) 0 0
\(526\) −946.000 −1.79848
\(527\) 139.298 0.264323
\(528\) 207.289 137.500i 0.392593 0.260417i
\(529\) −133.000 −0.251418
\(530\) 0 0
\(531\) 550.000 + 232.164i 1.03578 + 0.437220i
\(532\) 0 0
\(533\) −165.831 −0.311128
\(534\) 1237.50 820.865i 2.31742 1.53720i
\(535\) 0 0
\(536\) 447.744i 0.835344i
\(537\) −290.205 + 192.500i −0.540418 + 0.358473i
\(538\) 1540.00i 2.86245i
\(539\) 812.573i 1.50756i
\(540\) 0 0
\(541\) 912.000 1.68577 0.842884 0.538096i \(-0.180856\pi\)
0.842884 + 0.538096i \(0.180856\pi\)
\(542\) 72.9657 0.134623
\(543\) −301.813 455.000i −0.555825 0.837937i
\(544\) −77.0000 −0.141544
\(545\) 0 0
\(546\) 0 0
\(547\) 55.0000i 0.100548i 0.998735 + 0.0502742i \(0.0160095\pi\)
−0.998735 + 0.0502742i \(0.983990\pi\)
\(548\) 487.544 0.889679
\(549\) 28.0000 66.3325i 0.0510018 0.120824i
\(550\) 0 0
\(551\) 232.164i 0.421350i
\(552\) 328.346 + 495.000i 0.594829 + 0.896739i
\(553\) 0 0
\(554\) 696.491i 1.25720i
\(555\) 0 0
\(556\) −539.000 −0.969424
\(557\) 1014.89 1.82206 0.911030 0.412341i \(-0.135289\pi\)
0.911030 + 0.412341i \(0.135289\pi\)
\(558\) −487.544 + 1155.00i −0.873734 + 2.06989i
\(559\) 500.000 0.894454
\(560\) 0 0
\(561\) 137.500 91.2072i 0.245098 0.162580i
\(562\) 660.000i 1.17438i
\(563\) −119.398 −0.212075 −0.106038 0.994362i \(-0.533816\pi\)
−0.106038 + 0.994362i \(0.533816\pi\)
\(564\) 539.000 + 812.573i 0.955674 + 1.44073i
\(565\) 0 0
\(566\) 1144.24i 2.02162i
\(567\) 0 0
\(568\) 330.000i 0.580986i
\(569\) 49.7494i 0.0874330i −0.999044 0.0437165i \(-0.986080\pi\)
0.999044 0.0437165i \(-0.0139198\pi\)
\(570\) 0 0
\(571\) 242.000 0.423818 0.211909 0.977289i \(-0.432032\pi\)
0.211909 + 0.977289i \(0.432032\pi\)
\(572\) 1160.82 2.02940
\(573\) 580.409 385.000i 1.01293 0.671902i
\(574\) 0 0
\(575\) 0 0
\(576\) 339.500 804.282i 0.589410 1.39632i
\(577\) 665.000i 1.15251i 0.817269 + 0.576256i \(0.195487\pi\)
−0.817269 + 0.576256i \(0.804513\pi\)
\(578\) −922.022 −1.59519
\(579\) 62.5000 41.4578i 0.107945 0.0716024i
\(580\) 0 0
\(581\) 0 0
\(582\) −580.409 + 385.000i −0.997267 + 0.661512i
\(583\) 770.000i 1.32075i
\(584\) 348.246i 0.596311i
\(585\) 0 0
\(586\) −1056.00 −1.80205
\(587\) −626.842 −1.06787 −0.533937 0.845524i \(-0.679288\pi\)
−0.533937 + 0.845524i \(0.679288\pi\)
\(588\) −568.801 857.500i −0.967349 1.45833i
\(589\) −294.000 −0.499151
\(590\) 0 0
\(591\) −363.000 547.243i −0.614213 0.925961i
\(592\) 200.000i 0.337838i
\(593\) 859.006 1.44858 0.724288 0.689497i \(-0.242169\pi\)
0.724288 + 0.689497i \(0.242169\pi\)
\(594\) 275.000 + 1459.31i 0.462963 + 2.45676i
\(595\) 0 0
\(596\) 1160.82i 1.94768i
\(597\) −112.765 170.000i −0.188887 0.284757i
\(598\) 660.000i 1.10368i
\(599\) 331.662i 0.553694i −0.960914 0.276847i \(-0.910711\pi\)
0.960914 0.276847i \(-0.0892895\pi\)
\(600\) 0 0
\(601\) −343.000 −0.570715 −0.285358 0.958421i \(-0.592112\pi\)
−0.285358 + 0.958421i \(0.592112\pi\)
\(602\) 0 0
\(603\) −373.120 157.500i −0.618773 0.261194i
\(604\) 1204.00 1.99338
\(605\) 0 0
\(606\) 0 0
\(607\) 1100.00i 1.81219i −0.423073 0.906096i \(-0.639049\pi\)
0.423073 0.906096i \(-0.360951\pi\)
\(608\) 162.515 0.267294
\(609\) 0 0
\(610\) 0 0
\(611\) 464.327i 0.759947i
\(612\) −81.2573 + 192.500i −0.132773 + 0.314542i
\(613\) 290.000i 0.473083i 0.971621 + 0.236542i \(0.0760140\pi\)
−0.971621 + 0.236542i \(0.923986\pi\)
\(614\) 1077.90i 1.75554i
\(615\) 0 0
\(616\) 0 0
\(617\) −79.5990 −0.129010 −0.0645049 0.997917i \(-0.520547\pi\)
−0.0645049 + 0.997917i \(0.520547\pi\)
\(618\) 580.409 385.000i 0.939174 0.622977i
\(619\) 58.0000 0.0936995 0.0468498 0.998902i \(-0.485082\pi\)
0.0468498 + 0.998902i \(0.485082\pi\)
\(620\) 0 0
\(621\) −528.000 + 99.4987i −0.850242 + 0.160223i
\(622\) 1320.00i 2.12219i
\(623\) 0 0
\(624\) −125.000 + 82.9156i −0.200321 + 0.132878i
\(625\) 0 0
\(626\) 1625.15i 2.59608i
\(627\) −290.205 + 192.500i −0.462846 + 0.307018i
\(628\) 1750.00i 2.78662i
\(629\) 132.665i 0.210914i
\(630\) 0 0
\(631\) 862.000 1.36609 0.683043 0.730378i \(-0.260656\pi\)
0.683043 + 0.730378i \(0.260656\pi\)
\(632\) −119.398 −0.188922
\(633\) −127.690 192.500i −0.201722 0.304107i
\(634\) −704.000 −1.11041
\(635\) 0 0
\(636\) −539.000 812.573i −0.847484 1.27763i
\(637\) 490.000i 0.769231i
\(638\) 1824.14 2.85916
\(639\) −275.000 116.082i −0.430360 0.181662i
\(640\) 0 0
\(641\) 596.992i 0.931345i −0.884957 0.465673i \(-0.845812\pi\)
0.884957 0.465673i \(-0.154188\pi\)
\(642\) −383.070 577.500i −0.596682 0.899533i
\(643\) 1050.00i 1.63297i 0.577366 + 0.816485i \(0.304080\pi\)
−0.577366 + 0.816485i \(0.695920\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −77.0000 −0.119195
\(647\) 252.063 0.389588 0.194794 0.980844i \(-0.437596\pi\)
0.194794 + 0.980844i \(0.437596\pi\)
\(648\) −562.168 577.500i −0.867543 0.891204i
\(649\) 1100.00 1.69492
\(650\) 0 0
\(651\) 0 0
\(652\) 245.000i 0.375767i
\(653\) 1207.25 1.84878 0.924389 0.381452i \(-0.124576\pi\)
0.924389 + 0.381452i \(0.124576\pi\)
\(654\) −484.000 729.657i −0.740061 1.11568i
\(655\) 0 0
\(656\) 82.9156i 0.126396i
\(657\) −290.205 122.500i −0.441712 0.186454i
\(658\) 0 0
\(659\) 812.573i 1.23304i −0.787339 0.616520i \(-0.788542\pi\)
0.787339 0.616520i \(-0.211458\pi\)
\(660\) 0 0
\(661\) −98.0000 −0.148260 −0.0741301 0.997249i \(-0.523618\pi\)
−0.0741301 + 0.997249i \(0.523618\pi\)
\(662\) −805.940 −1.21743
\(663\) −82.9156 + 55.0000i −0.125061 + 0.0829563i
\(664\) −693.000 −1.04367
\(665\) 0 0
\(666\) 1100.00 + 464.327i 1.65165 + 0.697188i
\(667\) 660.000i 0.989505i
\(668\) −1253.68 −1.87677
\(669\) −350.000 + 232.164i −0.523169 + 0.347031i
\(670\) 0 0
\(671\) 132.665i 0.197712i
\(672\) 0 0
\(673\) 210.000i 0.312036i 0.987754 + 0.156018i \(0.0498657\pi\)
−0.987754 + 0.156018i \(0.950134\pi\)
\(674\) 1276.90i 1.89451i
\(675\) 0 0
\(676\) 483.000 0.714497
\(677\) −79.5990 −0.117576 −0.0587880 0.998270i \(-0.518724\pi\)
−0.0587880 + 0.998270i \(0.518724\pi\)
\(678\) 565.485 + 852.500i 0.834048 + 1.25737i
\(679\) 0 0
\(680\) 0 0
\(681\) −308.000 464.327i −0.452276 0.681832i
\(682\) 2310.00i 3.38710i
\(683\) −169.148 −0.247654 −0.123827 0.992304i \(-0.539517\pi\)
−0.123827 + 0.992304i \(0.539517\pi\)
\(684\) 171.500 406.287i 0.250731 0.593986i
\(685\) 0 0
\(686\) 0 0
\(687\) 616.892 + 930.000i 0.897951 + 1.35371i
\(688\) 250.000i 0.363372i
\(689\) 464.327i 0.673915i
\(690\) 0 0
\(691\) −713.000 −1.03184 −0.515919 0.856637i \(-0.672549\pi\)
−0.515919 + 0.856637i \(0.672549\pi\)
\(692\) 1950.18 2.81817
\(693\) 0 0
\(694\) −979.000 −1.41066
\(695\) 0 0
\(696\) −825.000 + 547.243i −1.18534 + 0.786269i
\(697\) 55.0000i 0.0789096i
\(698\) −1764.44 −2.52786
\(699\) 198.000 + 298.496i 0.283262 + 0.427033i
\(700\) 0 0
\(701\) 1160.82i 1.65595i −0.560767 0.827973i \(-0.689494\pi\)
0.560767 0.827973i \(-0.310506\pi\)
\(702\) −165.831 880.000i −0.236227 1.25356i
\(703\) 280.000i 0.398293i
\(704\) 1608.56i 2.28489i
\(705\) 0 0
\(706\) 924.000 1.30878
\(707\) 0 0
\(708\) −1160.82 + 770.000i −1.63957 + 1.08757i
\(709\) 248.000 0.349788 0.174894 0.984587i \(-0.444042\pi\)
0.174894 + 0.984587i \(0.444042\pi\)
\(710\) 0 0
\(711\) 42.0000 99.4987i 0.0590717 0.139942i
\(712\) 1485.00i 2.08567i
\(713\) −835.789 −1.17222
\(714\) 0 0
\(715\) 0 0
\(716\) 812.573i 1.13488i
\(717\) 580.409 385.000i 0.809497 0.536960i
\(718\) 1320.00i 1.83844i
\(719\) 198.997i 0.276770i 0.990379 + 0.138385i \(0.0441911\pi\)
−0.990379 + 0.138385i \(0.955809\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1034.79 −1.43322
\(723\) 684.883 + 1032.50i 0.947279 + 1.42808i
\(724\) 1274.00 1.75967
\(725\) 0 0
\(726\) 847.000 + 1276.90i 1.16667 + 1.75882i
\(727\) 10.0000i 0.0137552i −0.999976 0.00687758i \(-0.997811\pi\)
0.999976 0.00687758i \(-0.00218922\pi\)
\(728\) 0 0
\(729\) 679.000 265.330i 0.931413 0.363964i
\(730\) 0 0
\(731\) 165.831i 0.226855i
\(732\) 92.8655 + 140.000i 0.126865 + 0.191257i
\(733\) 770.000i 1.05048i −0.850955 0.525239i \(-0.823976\pi\)
0.850955 0.525239i \(-0.176024\pi\)
\(734\) 596.992i 0.813341i
\(735\) 0 0
\(736\) 462.000 0.627717
\(737\) −746.241 −1.01254
\(738\) 456.036 + 192.500i 0.617935 + 0.260840i
\(739\) −802.000 −1.08525 −0.542625 0.839975i \(-0.682570\pi\)
−0.542625 + 0.839975i \(0.682570\pi\)
\(740\) 0 0
\(741\) 175.000 116.082i 0.236167 0.156656i
\(742\) 0 0
\(743\) −1346.55 −1.81231 −0.906157 0.422941i \(-0.860998\pi\)
−0.906157 + 0.422941i \(0.860998\pi\)
\(744\) −693.000 1044.74i −0.931452 1.40422i
\(745\) 0 0
\(746\) 364.829i 0.489047i
\(747\) 243.772 577.500i 0.326335 0.773092i
\(748\) 385.000i 0.514706i
\(749\) 0 0
\(750\) 0 0
\(751\) 322.000 0.428762 0.214381 0.976750i \(-0.431227\pi\)
0.214381 + 0.976750i \(0.431227\pi\)
\(752\) −232.164 −0.308728
\(753\) 621.867 412.500i 0.825853 0.547809i
\(754\) −1100.00 −1.45889
\(755\) 0 0
\(756\) 0 0
\(757\) 400.000i 0.528402i 0.964468 + 0.264201i \(0.0851082\pi\)
−0.964468 + 0.264201i \(0.914892\pi\)
\(758\) 1767.76 2.33214
\(759\) −825.000 + 547.243i −1.08696 + 0.721005i
\(760\) 0 0
\(761\) 348.246i 0.457616i 0.973472 + 0.228808i \(0.0734828\pi\)
−0.973472 + 0.228808i \(0.926517\pi\)
\(762\) 1575.40 1045.00i 2.06745 1.37139i
\(763\) 0 0
\(764\) 1625.15i 2.12715i
\(765\) 0 0
\(766\) 264.000 0.344648
\(767\) −663.325 −0.864830
\(768\) 615.234 + 927.500i 0.801086 + 1.20768i
\(769\) 193.000 0.250975 0.125488 0.992095i \(-0.459950\pi\)
0.125488 + 0.992095i \(0.459950\pi\)
\(770\) 0 0
\(771\) 462.000 + 696.491i 0.599222 + 0.903361i
\(772\) 175.000i 0.226684i
\(773\) −417.895 −0.540614 −0.270307 0.962774i \(-0.587125\pi\)
−0.270307 + 0.962774i \(0.587125\pi\)
\(774\) −1375.00 580.409i −1.77649 0.749883i
\(775\) 0 0
\(776\) 696.491i 0.897540i
\(777\) 0 0
\(778\) 330.000i 0.424165i
\(779\) 116.082i 0.149014i
\(780\) 0 0
\(781\) −550.000 −0.704225
\(782\) −218.897 −0.279920
\(783\) −165.831 880.000i −0.211790 1.12388i
\(784\) 245.000 0.312500
\(785\) 0 0
\(786\) −1650.00 + 1094.49i −2.09924 + 1.39248i
\(787\) 910.000i 1.15629i 0.815934 + 0.578145i \(0.196223\pi\)
−0.815934 + 0.578145i \(0.803777\pi\)
\(788\) 1532.28 1.94452
\(789\) 473.000 + 713.074i 0.599493 + 0.903770i
\(790\) 0 0
\(791\) 0 0
\(792\) −1368.11 577.500i