Properties

Label 1050.3.f.e.601.7
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 601.7
Root \(-0.207107 - 3.39361i\) of defining polynomial
Character \(\chi\) \(=\) 1050.601
Dual form 1050.3.f.e.601.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(1.57881 + 6.81963i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(1.57881 + 6.81963i) q^{7} -2.82843 q^{8} -3.00000 q^{9} -8.15965 q^{11} +3.46410i q^{12} -14.6064i q^{13} +(-2.23278 - 9.64441i) q^{14} +4.00000 q^{16} +5.81421i q^{17} +4.24264 q^{18} -33.7736i q^{19} +(-11.8119 + 2.73459i) q^{21} +11.5395 q^{22} +37.2576 q^{23} -4.89898i q^{24} +20.6566i q^{26} -5.19615i q^{27} +(3.15763 + 13.6393i) q^{28} +9.25305 q^{29} -19.2558i q^{31} -5.65685 q^{32} -14.1329i q^{33} -8.22253i q^{34} -6.00000 q^{36} +63.4350 q^{37} +47.7631i q^{38} +25.2990 q^{39} +8.25880i q^{41} +(16.7046 - 3.86729i) q^{42} -42.0893 q^{43} -16.3193 q^{44} -52.6901 q^{46} +23.3380i q^{47} +6.92820i q^{48} +(-44.0147 + 21.5339i) q^{49} -10.0705 q^{51} -29.2128i q^{52} +71.3497 q^{53} +7.34847i q^{54} +(-4.46556 - 19.2888i) q^{56} +58.4976 q^{57} -13.0858 q^{58} +42.9350i q^{59} -34.2864i q^{61} +27.2318i q^{62} +(-4.73644 - 20.4589i) q^{63} +8.00000 q^{64} +19.9870i q^{66} +4.99889 q^{67} +11.6284i q^{68} +64.5320i q^{69} -38.8120 q^{71} +8.48528 q^{72} -124.629i q^{73} -89.7107 q^{74} -67.5472i q^{76} +(-12.8826 - 55.6458i) q^{77} -35.7782 q^{78} +56.1842 q^{79} +9.00000 q^{81} -11.6797i q^{82} +90.3980i q^{83} +(-23.6239 + 5.46917i) q^{84} +59.5233 q^{86} +16.0267i q^{87} +23.0790 q^{88} -16.2289i q^{89} +(99.6102 - 23.0608i) q^{91} +74.5151 q^{92} +33.3520 q^{93} -33.0048i q^{94} -9.79796i q^{96} +82.7605i q^{97} +(62.2462 - 30.4535i) q^{98} +24.4789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) 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
\(7\) 1.57881 + 6.81963i 0.225545 + 0.974233i
\(8\) −2.82843 −0.353553
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) −8.15965 −0.741786 −0.370893 0.928676i \(-0.620948\pi\)
−0.370893 + 0.928676i \(0.620948\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 14.6064i 1.12357i −0.827284 0.561785i \(-0.810115\pi\)
0.827284 0.561785i \(-0.189885\pi\)
\(14\) −2.23278 9.64441i −0.159484 0.688887i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 5.81421i 0.342012i 0.985270 + 0.171006i \(0.0547018\pi\)
−0.985270 + 0.171006i \(0.945298\pi\)
\(18\) 4.24264 0.235702
\(19\) 33.7736i 1.77756i −0.458337 0.888778i \(-0.651555\pi\)
0.458337 0.888778i \(-0.348445\pi\)
\(20\) 0 0
\(21\) −11.8119 + 2.73459i −0.562474 + 0.130218i
\(22\) 11.5395 0.524522
\(23\) 37.2576 1.61989 0.809947 0.586503i \(-0.199496\pi\)
0.809947 + 0.586503i \(0.199496\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 0 0
\(26\) 20.6566i 0.794483i
\(27\) 5.19615i 0.192450i
\(28\) 3.15763 + 13.6393i 0.112772 + 0.487116i
\(29\) 9.25305 0.319071 0.159535 0.987192i \(-0.449000\pi\)
0.159535 + 0.987192i \(0.449000\pi\)
\(30\) 0 0
\(31\) 19.2558i 0.621154i −0.950548 0.310577i \(-0.899478\pi\)
0.950548 0.310577i \(-0.100522\pi\)
\(32\) −5.65685 −0.176777
\(33\) 14.1329i 0.428270i
\(34\) 8.22253i 0.241839i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 63.4350 1.71446 0.857230 0.514933i \(-0.172183\pi\)
0.857230 + 0.514933i \(0.172183\pi\)
\(38\) 47.7631i 1.25692i
\(39\) 25.2990 0.648693
\(40\) 0 0
\(41\) 8.25880i 0.201434i 0.994915 + 0.100717i \(0.0321137\pi\)
−0.994915 + 0.100717i \(0.967886\pi\)
\(42\) 16.7046 3.86729i 0.397729 0.0920783i
\(43\) −42.0893 −0.978822 −0.489411 0.872053i \(-0.662788\pi\)
−0.489411 + 0.872053i \(0.662788\pi\)
\(44\) −16.3193 −0.370893
\(45\) 0 0
\(46\) −52.6901 −1.14544
\(47\) 23.3380i 0.496552i 0.968689 + 0.248276i \(0.0798640\pi\)
−0.968689 + 0.248276i \(0.920136\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −44.0147 + 21.5339i −0.898259 + 0.439466i
\(50\) 0 0
\(51\) −10.0705 −0.197461
\(52\) 29.2128i 0.561785i
\(53\) 71.3497 1.34622 0.673110 0.739542i \(-0.264958\pi\)
0.673110 + 0.739542i \(0.264958\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 0 0
\(56\) −4.46556 19.2888i −0.0797422 0.344443i
\(57\) 58.4976 1.02627
\(58\) −13.0858 −0.225617
\(59\) 42.9350i 0.727712i 0.931455 + 0.363856i \(0.118540\pi\)
−0.931455 + 0.363856i \(0.881460\pi\)
\(60\) 0 0
\(61\) 34.2864i 0.562072i −0.959697 0.281036i \(-0.909322\pi\)
0.959697 0.281036i \(-0.0906781\pi\)
\(62\) 27.2318i 0.439222i
\(63\) −4.73644 20.4589i −0.0751816 0.324744i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) 19.9870i 0.302833i
\(67\) 4.99889 0.0746102 0.0373051 0.999304i \(-0.488123\pi\)
0.0373051 + 0.999304i \(0.488123\pi\)
\(68\) 11.6284i 0.171006i
\(69\) 64.5320i 0.935246i
\(70\) 0 0
\(71\) −38.8120 −0.546648 −0.273324 0.961922i \(-0.588123\pi\)
−0.273324 + 0.961922i \(0.588123\pi\)
\(72\) 8.48528 0.117851
\(73\) 124.629i 1.70725i −0.520886 0.853626i \(-0.674398\pi\)
0.520886 0.853626i \(-0.325602\pi\)
\(74\) −89.7107 −1.21231
\(75\) 0 0
\(76\) 67.5472i 0.888778i
\(77\) −12.8826 55.6458i −0.167306 0.722672i
\(78\) −35.7782 −0.458695
\(79\) 56.1842 0.711192 0.355596 0.934640i \(-0.384278\pi\)
0.355596 + 0.934640i \(0.384278\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 11.6797i 0.142435i
\(83\) 90.3980i 1.08913i 0.838718 + 0.544566i \(0.183306\pi\)
−0.838718 + 0.544566i \(0.816694\pi\)
\(84\) −23.6239 + 5.46917i −0.281237 + 0.0651092i
\(85\) 0 0
\(86\) 59.5233 0.692131
\(87\) 16.0267i 0.184215i
\(88\) 23.0790 0.262261
\(89\) 16.2289i 0.182347i −0.995835 0.0911736i \(-0.970938\pi\)
0.995835 0.0911736i \(-0.0290618\pi\)
\(90\) 0 0
\(91\) 99.6102 23.0608i 1.09462 0.253415i
\(92\) 74.5151 0.809947
\(93\) 33.3520 0.358624
\(94\) 33.0048i 0.351115i
\(95\) 0 0
\(96\) 9.79796i 0.102062i
\(97\) 82.7605i 0.853201i 0.904440 + 0.426601i \(0.140289\pi\)
−0.904440 + 0.426601i \(0.859711\pi\)
\(98\) 62.2462 30.4535i 0.635165 0.310750i
\(99\) 24.4789 0.247262
\(100\) 0 0
\(101\) 87.2055i 0.863420i −0.902012 0.431710i \(-0.857910\pi\)
0.902012 0.431710i \(-0.142090\pi\)
\(102\) 14.2418 0.139626
\(103\) 187.567i 1.82104i 0.413462 + 0.910521i \(0.364319\pi\)
−0.413462 + 0.910521i \(0.635681\pi\)
\(104\) 41.3131i 0.397242i
\(105\) 0 0
\(106\) −100.904 −0.951922
\(107\) 157.858 1.47531 0.737653 0.675180i \(-0.235934\pi\)
0.737653 + 0.675180i \(0.235934\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) 112.073 1.02819 0.514097 0.857732i \(-0.328127\pi\)
0.514097 + 0.857732i \(0.328127\pi\)
\(110\) 0 0
\(111\) 109.873i 0.989844i
\(112\) 6.31526 + 27.2785i 0.0563862 + 0.243558i
\(113\) −141.987 −1.25653 −0.628263 0.778001i \(-0.716234\pi\)
−0.628263 + 0.778001i \(0.716234\pi\)
\(114\) −82.7280 −0.725684
\(115\) 0 0
\(116\) 18.5061 0.159535
\(117\) 43.8192i 0.374523i
\(118\) 60.7192i 0.514570i
\(119\) −39.6507 + 9.17955i −0.333199 + 0.0771391i
\(120\) 0 0
\(121\) −54.4202 −0.449754
\(122\) 48.4883i 0.397445i
\(123\) −14.3047 −0.116298
\(124\) 38.5116i 0.310577i
\(125\) 0 0
\(126\) 6.69834 + 28.9332i 0.0531614 + 0.229629i
\(127\) 202.414 1.59381 0.796905 0.604104i \(-0.206469\pi\)
0.796905 + 0.604104i \(0.206469\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 72.9008i 0.565123i
\(130\) 0 0
\(131\) 141.260i 1.07832i 0.842203 + 0.539160i \(0.181258\pi\)
−0.842203 + 0.539160i \(0.818742\pi\)
\(132\) 28.2658i 0.214135i
\(133\) 230.323 53.3222i 1.73175 0.400919i
\(134\) −7.06949 −0.0527574
\(135\) 0 0
\(136\) 16.4451i 0.120920i
\(137\) −50.6430 −0.369657 −0.184829 0.982771i \(-0.559173\pi\)
−0.184829 + 0.982771i \(0.559173\pi\)
\(138\) 91.2620i 0.661319i
\(139\) 74.0256i 0.532559i −0.963896 0.266279i \(-0.914206\pi\)
0.963896 0.266279i \(-0.0857943\pi\)
\(140\) 0 0
\(141\) −40.4225 −0.286685
\(142\) 54.8885 0.386538
\(143\) 119.183i 0.833448i
\(144\) −12.0000 −0.0833333
\(145\) 0 0
\(146\) 176.253i 1.20721i
\(147\) −37.2977 76.2357i −0.253726 0.518610i
\(148\) 126.870 0.857230
\(149\) 226.979 1.52335 0.761676 0.647958i \(-0.224377\pi\)
0.761676 + 0.647958i \(0.224377\pi\)
\(150\) 0 0
\(151\) 294.426 1.94984 0.974920 0.222558i \(-0.0714406\pi\)
0.974920 + 0.222558i \(0.0714406\pi\)
\(152\) 95.5261i 0.628461i
\(153\) 17.4426i 0.114004i
\(154\) 18.2187 + 78.6950i 0.118303 + 0.511006i
\(155\) 0 0
\(156\) 50.5981 0.324346
\(157\) 65.8596i 0.419488i −0.977756 0.209744i \(-0.932737\pi\)
0.977756 0.209744i \(-0.0672630\pi\)
\(158\) −79.4564 −0.502889
\(159\) 123.581i 0.777241i
\(160\) 0 0
\(161\) 58.8227 + 254.083i 0.365359 + 1.57815i
\(162\) −12.7279 −0.0785674
\(163\) −28.2075 −0.173052 −0.0865260 0.996250i \(-0.527577\pi\)
−0.0865260 + 0.996250i \(0.527577\pi\)
\(164\) 16.5176i 0.100717i
\(165\) 0 0
\(166\) 127.842i 0.770133i
\(167\) 128.461i 0.769227i 0.923078 + 0.384614i \(0.125665\pi\)
−0.923078 + 0.384614i \(0.874335\pi\)
\(168\) 33.4092 7.73458i 0.198864 0.0460392i
\(169\) −44.3469 −0.262408
\(170\) 0 0
\(171\) 101.321i 0.592519i
\(172\) −84.1786 −0.489411
\(173\) 112.446i 0.649976i −0.945718 0.324988i \(-0.894640\pi\)
0.945718 0.324988i \(-0.105360\pi\)
\(174\) 22.6652i 0.130260i
\(175\) 0 0
\(176\) −32.6386 −0.185446
\(177\) −74.3656 −0.420144
\(178\) 22.9511i 0.128939i
\(179\) 68.9019 0.384927 0.192464 0.981304i \(-0.438352\pi\)
0.192464 + 0.981304i \(0.438352\pi\)
\(180\) 0 0
\(181\) 166.537i 0.920094i −0.887895 0.460047i \(-0.847833\pi\)
0.887895 0.460047i \(-0.152167\pi\)
\(182\) −140.870 + 32.6129i −0.774012 + 0.179192i
\(183\) 59.3858 0.324513
\(184\) −105.380 −0.572719
\(185\) 0 0
\(186\) −47.1668 −0.253585
\(187\) 47.4419i 0.253700i
\(188\) 46.6759i 0.248276i
\(189\) 35.4358 8.20376i 0.187491 0.0434061i
\(190\) 0 0
\(191\) −148.289 −0.776382 −0.388191 0.921579i \(-0.626900\pi\)
−0.388191 + 0.921579i \(0.626900\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) 35.1886 0.182324 0.0911622 0.995836i \(-0.470942\pi\)
0.0911622 + 0.995836i \(0.470942\pi\)
\(194\) 117.041i 0.603304i
\(195\) 0 0
\(196\) −88.0294 + 43.0677i −0.449130 + 0.219733i
\(197\) 193.634 0.982915 0.491457 0.870902i \(-0.336464\pi\)
0.491457 + 0.870902i \(0.336464\pi\)
\(198\) −34.6184 −0.174841
\(199\) 181.838i 0.913759i −0.889529 0.456880i \(-0.848967\pi\)
0.889529 0.456880i \(-0.151033\pi\)
\(200\) 0 0
\(201\) 8.65832i 0.0430762i
\(202\) 123.327i 0.610530i
\(203\) 14.6088 + 63.1023i 0.0719647 + 0.310849i
\(204\) −20.1410 −0.0987304
\(205\) 0 0
\(206\) 265.260i 1.28767i
\(207\) −111.773 −0.539965
\(208\) 58.4256i 0.280892i
\(209\) 275.580i 1.31857i
\(210\) 0 0
\(211\) 175.914 0.833717 0.416859 0.908971i \(-0.363131\pi\)
0.416859 + 0.908971i \(0.363131\pi\)
\(212\) 142.699 0.673110
\(213\) 67.2244i 0.315607i
\(214\) −223.244 −1.04320
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 131.317 30.4013i 0.605149 0.140098i
\(218\) −158.495 −0.727042
\(219\) 215.864 0.985683
\(220\) 0 0
\(221\) 84.9246 0.384274
\(222\) 155.384i 0.699926i
\(223\) 20.5675i 0.0922308i −0.998936 0.0461154i \(-0.985316\pi\)
0.998936 0.0461154i \(-0.0146842\pi\)
\(224\) −8.93112 38.5776i −0.0398711 0.172222i
\(225\) 0 0
\(226\) 200.801 0.888498
\(227\) 414.087i 1.82417i −0.410001 0.912085i \(-0.634472\pi\)
0.410001 0.912085i \(-0.365528\pi\)
\(228\) 116.995 0.513136
\(229\) 195.520i 0.853799i −0.904299 0.426899i \(-0.859606\pi\)
0.904299 0.426899i \(-0.140394\pi\)
\(230\) 0 0
\(231\) 96.3813 22.3133i 0.417235 0.0965942i
\(232\) −26.1716 −0.112808
\(233\) 81.3006 0.348930 0.174465 0.984663i \(-0.444180\pi\)
0.174465 + 0.984663i \(0.444180\pi\)
\(234\) 61.9697i 0.264828i
\(235\) 0 0
\(236\) 85.8700i 0.363856i
\(237\) 97.3138i 0.410607i
\(238\) 56.0746 12.9818i 0.235608 0.0545456i
\(239\) 249.265 1.04295 0.521475 0.853267i \(-0.325382\pi\)
0.521475 + 0.853267i \(0.325382\pi\)
\(240\) 0 0
\(241\) 262.343i 1.08856i −0.838904 0.544280i \(-0.816803\pi\)
0.838904 0.544280i \(-0.183197\pi\)
\(242\) 76.9618 0.318024
\(243\) 15.5885i 0.0641500i
\(244\) 68.5728i 0.281036i
\(245\) 0 0
\(246\) 20.2298 0.0822351
\(247\) −493.310 −1.99721
\(248\) 54.4636i 0.219611i
\(249\) −156.574 −0.628811
\(250\) 0 0
\(251\) 141.917i 0.565406i −0.959208 0.282703i \(-0.908769\pi\)
0.959208 0.282703i \(-0.0912310\pi\)
\(252\) −9.47288 40.9178i −0.0375908 0.162372i
\(253\) −304.008 −1.20161
\(254\) −286.257 −1.12699
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 170.843i 0.664757i 0.943146 + 0.332379i \(0.107851\pi\)
−0.943146 + 0.332379i \(0.892149\pi\)
\(258\) 103.097i 0.399602i
\(259\) 100.152 + 432.604i 0.386688 + 1.67028i
\(260\) 0 0
\(261\) −27.7591 −0.106357
\(262\) 199.772i 0.762488i
\(263\) −383.417 −1.45786 −0.728930 0.684588i \(-0.759982\pi\)
−0.728930 + 0.684588i \(0.759982\pi\)
\(264\) 39.9739i 0.151416i
\(265\) 0 0
\(266\) −325.726 + 75.4090i −1.22454 + 0.283492i
\(267\) 28.1093 0.105278
\(268\) 9.99777 0.0373051
\(269\) 154.512i 0.574393i 0.957872 + 0.287196i \(0.0927232\pi\)
−0.957872 + 0.287196i \(0.907277\pi\)
\(270\) 0 0
\(271\) 320.328i 1.18202i −0.806664 0.591010i \(-0.798729\pi\)
0.806664 0.591010i \(-0.201271\pi\)
\(272\) 23.2568i 0.0855030i
\(273\) 39.9425 + 172.530i 0.146309 + 0.631978i
\(274\) 71.6200 0.261387
\(275\) 0 0
\(276\) 129.064i 0.467623i
\(277\) −222.854 −0.804526 −0.402263 0.915524i \(-0.631776\pi\)
−0.402263 + 0.915524i \(0.631776\pi\)
\(278\) 104.688i 0.376576i
\(279\) 57.7673i 0.207051i
\(280\) 0 0
\(281\) 218.973 0.779263 0.389631 0.920971i \(-0.372602\pi\)
0.389631 + 0.920971i \(0.372602\pi\)
\(282\) 57.1661 0.202717
\(283\) 36.3957i 0.128607i −0.997930 0.0643034i \(-0.979517\pi\)
0.997930 0.0643034i \(-0.0204825\pi\)
\(284\) −77.6240 −0.273324
\(285\) 0 0
\(286\) 168.550i 0.589337i
\(287\) −56.3219 + 13.0391i −0.196244 + 0.0454324i
\(288\) 16.9706 0.0589256
\(289\) 255.195 0.883028
\(290\) 0 0
\(291\) −143.345 −0.492596
\(292\) 249.259i 0.853626i
\(293\) 168.440i 0.574882i 0.957798 + 0.287441i \(0.0928045\pi\)
−0.957798 + 0.287441i \(0.907195\pi\)
\(294\) 52.7470 + 107.814i 0.179411 + 0.366713i
\(295\) 0 0
\(296\) −179.421 −0.606153
\(297\) 42.3988i 0.142757i
\(298\) −320.997 −1.07717
\(299\) 544.199i 1.82006i
\(300\) 0 0
\(301\) −66.4512 287.034i −0.220768 0.953600i
\(302\) −416.381 −1.37874
\(303\) 151.044 0.498496
\(304\) 135.094i 0.444389i
\(305\) 0 0
\(306\) 24.6676i 0.0806130i
\(307\) 223.400i 0.727688i 0.931460 + 0.363844i \(0.118536\pi\)
−0.931460 + 0.363844i \(0.881464\pi\)
\(308\) −25.7651 111.292i −0.0836530 0.361336i
\(309\) −324.876 −1.05138
\(310\) 0 0
\(311\) 46.0396i 0.148037i 0.997257 + 0.0740186i \(0.0235824\pi\)
−0.997257 + 0.0740186i \(0.976418\pi\)
\(312\) −71.5565 −0.229348
\(313\) 80.0375i 0.255711i 0.991793 + 0.127855i \(0.0408094\pi\)
−0.991793 + 0.127855i \(0.959191\pi\)
\(314\) 93.1395i 0.296623i
\(315\) 0 0
\(316\) 112.368 0.355596
\(317\) −185.237 −0.584343 −0.292171 0.956366i \(-0.594378\pi\)
−0.292171 + 0.956366i \(0.594378\pi\)
\(318\) 174.770i 0.549592i
\(319\) −75.5016 −0.236682
\(320\) 0 0
\(321\) 273.418i 0.851768i
\(322\) −83.1879 359.327i −0.258348 1.11592i
\(323\) 196.367 0.607946
\(324\) 18.0000 0.0555556
\(325\) 0 0
\(326\) 39.8914 0.122366
\(327\) 194.116i 0.593628i
\(328\) 23.3594i 0.0712177i
\(329\) −159.156 + 36.8463i −0.483757 + 0.111995i
\(330\) 0 0
\(331\) 61.4686 0.185706 0.0928529 0.995680i \(-0.470401\pi\)
0.0928529 + 0.995680i \(0.470401\pi\)
\(332\) 180.796i 0.544566i
\(333\) −190.305 −0.571487
\(334\) 181.671i 0.543926i
\(335\) 0 0
\(336\) −47.2478 + 10.9383i −0.140618 + 0.0325546i
\(337\) −656.501 −1.94807 −0.974037 0.226387i \(-0.927309\pi\)
−0.974037 + 0.226387i \(0.927309\pi\)
\(338\) 62.7160 0.185550
\(339\) 245.929i 0.725456i
\(340\) 0 0
\(341\) 157.120i 0.460764i
\(342\) 143.289i 0.418974i
\(343\) −216.344 266.166i −0.630740 0.775994i
\(344\) 119.047 0.346066
\(345\) 0 0
\(346\) 159.022i 0.459603i
\(347\) −321.323 −0.926002 −0.463001 0.886358i \(-0.653227\pi\)
−0.463001 + 0.886358i \(0.653227\pi\)
\(348\) 32.0535i 0.0921077i
\(349\) 185.135i 0.530474i 0.964183 + 0.265237i \(0.0854501\pi\)
−0.964183 + 0.265237i \(0.914550\pi\)
\(350\) 0 0
\(351\) −75.8971 −0.216231
\(352\) 46.1579 0.131130
\(353\) 597.338i 1.69218i −0.533043 0.846088i \(-0.678952\pi\)
0.533043 0.846088i \(-0.321048\pi\)
\(354\) 105.169 0.297087
\(355\) 0 0
\(356\) 32.4578i 0.0911736i
\(357\) −15.8995 68.6771i −0.0445363 0.192373i
\(358\) −97.4421 −0.272185
\(359\) −239.446 −0.666982 −0.333491 0.942753i \(-0.608227\pi\)
−0.333491 + 0.942753i \(0.608227\pi\)
\(360\) 0 0
\(361\) −779.655 −2.15971
\(362\) 235.519i 0.650604i
\(363\) 94.2585i 0.259665i
\(364\) 199.220 46.1216i 0.547309 0.126708i
\(365\) 0 0
\(366\) −83.9842 −0.229465
\(367\) 398.743i 1.08649i 0.839573 + 0.543246i \(0.182805\pi\)
−0.839573 + 0.543246i \(0.817195\pi\)
\(368\) 149.030 0.404973
\(369\) 24.7764i 0.0671447i
\(370\) 0 0
\(371\) 112.648 + 486.578i 0.303633 + 1.31153i
\(372\) 66.7040 0.179312
\(373\) 34.7064 0.0930466 0.0465233 0.998917i \(-0.485186\pi\)
0.0465233 + 0.998917i \(0.485186\pi\)
\(374\) 67.0929i 0.179393i
\(375\) 0 0
\(376\) 66.0097i 0.175558i
\(377\) 135.154i 0.358498i
\(378\) −50.1138 + 11.6019i −0.132576 + 0.0306928i
\(379\) 109.217 0.288172 0.144086 0.989565i \(-0.453976\pi\)
0.144086 + 0.989565i \(0.453976\pi\)
\(380\) 0 0
\(381\) 350.591i 0.920187i
\(382\) 209.712 0.548985
\(383\) 336.420i 0.878381i −0.898394 0.439191i \(-0.855265\pi\)
0.898394 0.439191i \(-0.144735\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −49.7642 −0.128923
\(387\) 126.268 0.326274
\(388\) 165.521i 0.426601i
\(389\) 311.173 0.799930 0.399965 0.916530i \(-0.369022\pi\)
0.399965 + 0.916530i \(0.369022\pi\)
\(390\) 0 0
\(391\) 216.623i 0.554023i
\(392\) 124.492 60.9069i 0.317583 0.155375i
\(393\) −244.669 −0.622568
\(394\) −273.840 −0.695026
\(395\) 0 0
\(396\) 48.9579 0.123631
\(397\) 41.2679i 0.103949i −0.998648 0.0519747i \(-0.983448\pi\)
0.998648 0.0519747i \(-0.0165515\pi\)
\(398\) 257.158i 0.646125i
\(399\) 92.3568 + 398.932i 0.231471 + 0.999829i
\(400\) 0 0
\(401\) −495.642 −1.23601 −0.618007 0.786173i \(-0.712060\pi\)
−0.618007 + 0.786173i \(0.712060\pi\)
\(402\) 12.2447i 0.0304595i
\(403\) −281.258 −0.697910
\(404\) 174.411i 0.431710i
\(405\) 0 0
\(406\) −20.6600 89.2402i −0.0508867 0.219803i
\(407\) −517.608 −1.27176
\(408\) 28.4837 0.0698129
\(409\) 359.920i 0.880001i −0.897998 0.440000i \(-0.854978\pi\)
0.897998 0.440000i \(-0.145022\pi\)
\(410\) 0 0
\(411\) 87.7163i 0.213422i
\(412\) 375.135i 0.910521i
\(413\) −292.801 + 67.7863i −0.708960 + 0.164132i
\(414\) 158.070 0.381813
\(415\) 0 0
\(416\) 82.6263i 0.198621i
\(417\) 128.216 0.307473
\(418\) 389.730i 0.932367i
\(419\) 482.910i 1.15253i 0.817263 + 0.576265i \(0.195490\pi\)
−0.817263 + 0.576265i \(0.804510\pi\)
\(420\) 0 0
\(421\) −523.520 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(422\) −248.780 −0.589527
\(423\) 70.0139i 0.165517i
\(424\) −201.807 −0.475961
\(425\) 0 0
\(426\) 95.0696i 0.223168i
\(427\) 233.821 54.1319i 0.547589 0.126773i
\(428\) 315.715 0.737653
\(429\) −206.431 −0.481191
\(430\) 0 0
\(431\) 517.027 1.19960 0.599799 0.800150i \(-0.295247\pi\)
0.599799 + 0.800150i \(0.295247\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) 567.712i 1.31111i 0.755146 + 0.655557i \(0.227566\pi\)
−0.755146 + 0.655557i \(0.772434\pi\)
\(434\) −185.711 + 42.9939i −0.427905 + 0.0990644i
\(435\) 0 0
\(436\) 224.146 0.514097
\(437\) 1258.32i 2.87945i
\(438\) −305.279 −0.696983
\(439\) 622.875i 1.41885i −0.704781 0.709425i \(-0.748955\pi\)
0.704781 0.709425i \(-0.251045\pi\)
\(440\) 0 0
\(441\) 132.044 64.6016i 0.299420 0.146489i
\(442\) −120.102 −0.271723
\(443\) 476.699 1.07607 0.538035 0.842923i \(-0.319167\pi\)
0.538035 + 0.842923i \(0.319167\pi\)
\(444\) 219.745i 0.494922i
\(445\) 0 0
\(446\) 29.0868i 0.0652170i
\(447\) 393.140i 0.879507i
\(448\) 12.6305 + 54.5570i 0.0281931 + 0.121779i
\(449\) −861.931 −1.91967 −0.959834 0.280570i \(-0.909477\pi\)
−0.959834 + 0.280570i \(0.909477\pi\)
\(450\) 0 0
\(451\) 67.3889i 0.149421i
\(452\) −283.975 −0.628263
\(453\) 509.960i 1.12574i
\(454\) 585.607i 1.28988i
\(455\) 0 0
\(456\) −165.456 −0.362842
\(457\) 27.5401 0.0602629 0.0301314 0.999546i \(-0.490407\pi\)
0.0301314 + 0.999546i \(0.490407\pi\)
\(458\) 276.507i 0.603727i
\(459\) 30.2115 0.0658203
\(460\) 0 0
\(461\) 378.183i 0.820353i 0.912006 + 0.410176i \(0.134533\pi\)
−0.912006 + 0.410176i \(0.865467\pi\)
\(462\) −136.304 + 31.5557i −0.295030 + 0.0683024i
\(463\) 724.994 1.56586 0.782931 0.622108i \(-0.213724\pi\)
0.782931 + 0.622108i \(0.213724\pi\)
\(464\) 37.0122 0.0797676
\(465\) 0 0
\(466\) −114.976 −0.246731
\(467\) 371.451i 0.795398i −0.917516 0.397699i \(-0.869809\pi\)
0.917516 0.397699i \(-0.130191\pi\)
\(468\) 87.6384i 0.187262i
\(469\) 7.89231 + 34.0905i 0.0168280 + 0.0726877i
\(470\) 0 0
\(471\) 114.072 0.242191
\(472\) 121.438i 0.257285i
\(473\) 343.434 0.726076
\(474\) 137.623i 0.290343i
\(475\) 0 0
\(476\) −79.3015 + 18.3591i −0.166600 + 0.0385695i
\(477\) −214.049 −0.448740
\(478\) −352.514 −0.737477
\(479\) 860.650i 1.79677i 0.439214 + 0.898383i \(0.355257\pi\)
−0.439214 + 0.898383i \(0.644743\pi\)
\(480\) 0 0
\(481\) 926.558i 1.92632i
\(482\) 371.009i 0.769728i
\(483\) −440.084 + 101.884i −0.911147 + 0.210940i
\(484\) −108.840 −0.224877
\(485\) 0 0
\(486\) 22.0454i 0.0453609i
\(487\) 887.173 1.82171 0.910855 0.412726i \(-0.135423\pi\)
0.910855 + 0.412726i \(0.135423\pi\)
\(488\) 96.9766i 0.198723i
\(489\) 48.8568i 0.0999116i
\(490\) 0 0
\(491\) −50.1823 −0.102204 −0.0511021 0.998693i \(-0.516273\pi\)
−0.0511021 + 0.998693i \(0.516273\pi\)
\(492\) −28.6093 −0.0581490
\(493\) 53.7991i 0.109126i
\(494\) 697.646 1.41224
\(495\) 0 0
\(496\) 77.0231i 0.155289i
\(497\) −61.2769 264.683i −0.123294 0.532562i
\(498\) 221.429 0.444636
\(499\) −160.443 −0.321529 −0.160765 0.986993i \(-0.551396\pi\)
−0.160765 + 0.986993i \(0.551396\pi\)
\(500\) 0 0
\(501\) −222.501 −0.444113
\(502\) 200.701i 0.399802i
\(503\) 742.042i 1.47523i −0.675220 0.737616i \(-0.735951\pi\)
0.675220 0.737616i \(-0.264049\pi\)
\(504\) 13.3967 + 57.8665i 0.0265807 + 0.114814i
\(505\) 0 0
\(506\) 429.933 0.849670
\(507\) 76.8111i 0.151501i
\(508\) 404.828 0.796905
\(509\) 978.447i 1.92229i −0.276038 0.961147i \(-0.589021\pi\)
0.276038 0.961147i \(-0.410979\pi\)
\(510\) 0 0
\(511\) 849.927 196.767i 1.66326 0.385062i
\(512\) −22.6274 −0.0441942
\(513\) −175.493 −0.342091
\(514\) 241.608i 0.470054i
\(515\) 0 0
\(516\) 145.802i 0.282561i
\(517\) 190.429i 0.368335i
\(518\) −141.637 611.794i −0.273430 1.18107i
\(519\) 194.762 0.375264
\(520\) 0 0
\(521\) 575.650i 1.10489i −0.833548 0.552447i \(-0.813694\pi\)
0.833548 0.552447i \(-0.186306\pi\)
\(522\) 39.2573 0.0752056
\(523\) 339.090i 0.648355i 0.945996 + 0.324178i \(0.105088\pi\)
−0.945996 + 0.324178i \(0.894912\pi\)
\(524\) 282.520i 0.539160i
\(525\) 0 0
\(526\) 542.234 1.03086
\(527\) 111.957 0.212442
\(528\) 56.5317i 0.107068i
\(529\) 859.125 1.62406
\(530\) 0 0
\(531\) 128.805i 0.242571i
\(532\) 460.647 106.644i 0.865877 0.200459i
\(533\) 120.631 0.226325
\(534\) −39.7525 −0.0744429
\(535\) 0 0
\(536\) −14.1390 −0.0263787
\(537\) 119.342i 0.222238i
\(538\) 218.512i 0.406157i
\(539\) 359.144 175.709i 0.666316 0.325990i
\(540\) 0 0
\(541\) 35.8638 0.0662916 0.0331458 0.999451i \(-0.489447\pi\)
0.0331458 + 0.999451i \(0.489447\pi\)
\(542\) 453.012i 0.835815i
\(543\) 288.450 0.531216
\(544\) 32.8901i 0.0604598i
\(545\) 0 0
\(546\) −56.4872 243.994i −0.103456 0.446876i
\(547\) −700.845 −1.28125 −0.640626 0.767853i \(-0.721325\pi\)
−0.640626 + 0.767853i \(0.721325\pi\)
\(548\) −101.286 −0.184829
\(549\) 102.859i 0.187357i
\(550\) 0 0
\(551\) 312.508i 0.567166i
\(552\) 182.524i 0.330659i
\(553\) 88.7044 + 383.155i 0.160406 + 0.692867i
\(554\) 315.163 0.568886
\(555\) 0 0
\(556\) 148.051i 0.266279i
\(557\) 639.349 1.14784 0.573922 0.818910i \(-0.305421\pi\)
0.573922 + 0.818910i \(0.305421\pi\)
\(558\) 81.6954i 0.146407i
\(559\) 614.773i 1.09977i
\(560\) 0 0
\(561\) 82.1717 0.146474
\(562\) −309.674 −0.551022
\(563\) 227.519i 0.404120i 0.979373 + 0.202060i \(0.0647636\pi\)
−0.979373 + 0.202060i \(0.935236\pi\)
\(564\) −80.8450 −0.143342
\(565\) 0 0
\(566\) 51.4713i 0.0909387i
\(567\) 14.2093 + 61.3767i 0.0250605 + 0.108248i
\(568\) 109.777 0.193269
\(569\) −613.901 −1.07891 −0.539456 0.842014i \(-0.681370\pi\)
−0.539456 + 0.842014i \(0.681370\pi\)
\(570\) 0 0
\(571\) 366.674 0.642161 0.321081 0.947052i \(-0.395954\pi\)
0.321081 + 0.947052i \(0.395954\pi\)
\(572\) 238.366i 0.416724i
\(573\) 256.844i 0.448244i
\(574\) 79.6513 18.4401i 0.138765 0.0321256i
\(575\) 0 0
\(576\) −24.0000 −0.0416667
\(577\) 62.1951i 0.107790i −0.998547 0.0538952i \(-0.982836\pi\)
0.998547 0.0538952i \(-0.0171637\pi\)
\(578\) −360.900 −0.624395
\(579\) 60.9485i 0.105265i
\(580\) 0 0
\(581\) −616.481 + 142.722i −1.06107 + 0.245648i
\(582\) 202.721 0.348318
\(583\) −582.188 −0.998607
\(584\) 352.505i 0.603605i
\(585\) 0 0
\(586\) 238.211i 0.406503i
\(587\) 176.872i 0.301315i −0.988586 0.150658i \(-0.951861\pi\)
0.988586 0.150658i \(-0.0481391\pi\)
\(588\) −74.5955 152.471i −0.126863 0.259305i
\(589\) −650.337 −1.10414
\(590\) 0 0
\(591\) 335.384i 0.567486i
\(592\) 253.740 0.428615
\(593\) 154.878i 0.261176i −0.991437 0.130588i \(-0.958313\pi\)
0.991437 0.130588i \(-0.0416866\pi\)
\(594\) 59.9609i 0.100944i
\(595\) 0 0
\(596\) 453.959 0.761676
\(597\) 314.953 0.527559
\(598\) 769.613i 1.28698i
\(599\) −900.825 −1.50388 −0.751940 0.659231i \(-0.770882\pi\)
−0.751940 + 0.659231i \(0.770882\pi\)
\(600\) 0 0
\(601\) 682.387i 1.13542i 0.823229 + 0.567710i \(0.192170\pi\)
−0.823229 + 0.567710i \(0.807830\pi\)
\(602\) 93.9762 + 405.927i 0.156107 + 0.674297i
\(603\) −14.9967 −0.0248701
\(604\) 588.851 0.974920
\(605\) 0 0
\(606\) −213.609 −0.352490
\(607\) 367.814i 0.605954i 0.952998 + 0.302977i \(0.0979806\pi\)
−0.952998 + 0.302977i \(0.902019\pi\)
\(608\) 191.052i 0.314231i
\(609\) −109.296 + 25.3032i −0.179469 + 0.0415488i
\(610\) 0 0
\(611\) 340.883 0.557911
\(612\) 34.8852i 0.0570020i
\(613\) −117.271 −0.191306 −0.0956532 0.995415i \(-0.530494\pi\)
−0.0956532 + 0.995415i \(0.530494\pi\)
\(614\) 315.936i 0.514553i
\(615\) 0 0
\(616\) 36.4374 + 157.390i 0.0591516 + 0.255503i
\(617\) 1070.18 1.73449 0.867245 0.497881i \(-0.165888\pi\)
0.867245 + 0.497881i \(0.165888\pi\)
\(618\) 459.444 0.743438
\(619\) 532.192i 0.859761i −0.902886 0.429880i \(-0.858556\pi\)
0.902886 0.429880i \(-0.141444\pi\)
\(620\) 0 0
\(621\) 193.596i 0.311749i
\(622\) 65.1098i 0.104678i
\(623\) 110.675 25.6224i 0.177649 0.0411275i
\(624\) 101.196 0.162173
\(625\) 0 0
\(626\) 113.190i 0.180815i
\(627\) −477.319 −0.761275
\(628\) 131.719i 0.209744i
\(629\) 368.825i 0.586366i
\(630\) 0 0
\(631\) 472.933 0.749498 0.374749 0.927126i \(-0.377729\pi\)
0.374749 + 0.927126i \(0.377729\pi\)
\(632\) −158.913 −0.251444
\(633\) 304.693i 0.481347i
\(634\) 261.964 0.413193
\(635\) 0 0
\(636\) 247.163i 0.388620i
\(637\) 314.532 + 642.896i 0.493771 + 1.00926i
\(638\) 106.775 0.167359
\(639\) 116.436 0.182216
\(640\) 0 0
\(641\) −486.990 −0.759734 −0.379867 0.925041i \(-0.624030\pi\)
−0.379867 + 0.925041i \(0.624030\pi\)
\(642\) 386.671i 0.602291i
\(643\) 111.425i 0.173289i 0.996239 + 0.0866447i \(0.0276145\pi\)
−0.996239 + 0.0866447i \(0.972386\pi\)
\(644\) 117.645 + 508.165i 0.182679 + 0.789077i
\(645\) 0 0
\(646\) −277.704 −0.429883
\(647\) 737.696i 1.14018i 0.821583 + 0.570090i \(0.193092\pi\)
−0.821583 + 0.570090i \(0.806908\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 350.334i 0.539806i
\(650\) 0 0
\(651\) 52.6566 + 227.448i 0.0808857 + 0.349383i
\(652\) −56.4149 −0.0865260
\(653\) −193.734 −0.296682 −0.148341 0.988936i \(-0.547393\pi\)
−0.148341 + 0.988936i \(0.547393\pi\)
\(654\) 274.522i 0.419758i
\(655\) 0 0
\(656\) 33.0352i 0.0503585i
\(657\) 373.888i 0.569084i
\(658\) 225.081 52.1085i 0.342068 0.0791923i
\(659\) 823.339 1.24938 0.624688 0.780874i \(-0.285226\pi\)
0.624688 + 0.780874i \(0.285226\pi\)
\(660\) 0 0
\(661\) 657.833i 0.995208i 0.867404 + 0.497604i \(0.165787\pi\)
−0.867404 + 0.497604i \(0.834213\pi\)
\(662\) −86.9298 −0.131314
\(663\) 147.094i 0.221861i
\(664\) 255.684i 0.385066i
\(665\) 0 0
\(666\) 269.132 0.404102
\(667\) 344.746 0.516860
\(668\) 256.922i 0.384614i
\(669\) 35.6239 0.0532495
\(670\) 0 0
\(671\) 279.765i 0.416937i
\(672\) 66.8184 15.4692i 0.0994322 0.0230196i
\(673\) 727.300 1.08068 0.540342 0.841446i \(-0.318295\pi\)
0.540342 + 0.841446i \(0.318295\pi\)
\(674\) 928.433 1.37750
\(675\) 0 0
\(676\) −88.6938 −0.131204
\(677\) 385.964i 0.570110i −0.958511 0.285055i \(-0.907988\pi\)
0.958511 0.285055i \(-0.0920118\pi\)
\(678\) 347.797i 0.512975i
\(679\) −564.396 + 130.663i −0.831217 + 0.192435i
\(680\) 0 0
\(681\) 717.219 1.05319
\(682\) 222.202i 0.325809i
\(683\) −236.488 −0.346249 −0.173124 0.984900i \(-0.555386\pi\)
−0.173124 + 0.984900i \(0.555386\pi\)
\(684\) 202.641i 0.296259i
\(685\) 0 0
\(686\) 305.957 + 376.415i 0.446001 + 0.548711i
\(687\) 338.650 0.492941
\(688\) −168.357 −0.244705
\(689\) 1042.16i 1.51257i
\(690\) 0 0
\(691\) 337.426i 0.488316i 0.969735 + 0.244158i \(0.0785116\pi\)
−0.969735 + 0.244158i \(0.921488\pi\)
\(692\) 224.892i 0.324988i
\(693\) 38.6477 + 166.937i 0.0557687 + 0.240891i
\(694\) 454.419 0.654782
\(695\) 0 0
\(696\) 45.3305i 0.0651300i
\(697\) −48.0184 −0.0688929
\(698\) 261.821i 0.375101i
\(699\) 140.817i 0.201455i
\(700\) 0 0
\(701\) 89.2192 0.127274 0.0636371 0.997973i \(-0.479730\pi\)
0.0636371 + 0.997973i \(0.479730\pi\)
\(702\) 107.335 0.152898
\(703\) 2142.43i 3.04755i
\(704\) −65.2772 −0.0927232
\(705\) 0 0
\(706\) 844.764i 1.19655i
\(707\) 594.709 137.681i 0.841172 0.194740i
\(708\) −148.731 −0.210072
\(709\) −569.646 −0.803450 −0.401725 0.915760i \(-0.631589\pi\)
−0.401725 + 0.915760i \(0.631589\pi\)
\(710\) 0 0
\(711\) −168.552 −0.237064
\(712\) 45.9023i 0.0644695i
\(713\) 717.423i 1.00620i
\(714\) 22.4852 + 97.1241i 0.0314919 + 0.136028i
\(715\) 0 0
\(716\) 137.804 0.192464
\(717\) 431.740i 0.602147i
\(718\) 338.628 0.471627
\(719\) 1261.33i 1.75428i −0.480233 0.877141i \(-0.659448\pi\)
0.480233 0.877141i \(-0.340552\pi\)
\(720\) 0 0
\(721\) −1279.14 + 296.134i −1.77412 + 0.410727i
\(722\) 1102.60 1.52714
\(723\) 454.391 0.628481
\(724\) 333.074i 0.460047i
\(725\) 0 0
\(726\) 133.302i 0.183611i
\(727\) 307.746i 0.423310i −0.977344 0.211655i \(-0.932115\pi\)
0.977344 0.211655i \(-0.0678852\pi\)
\(728\) −281.740 + 65.2258i −0.387006 + 0.0895958i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 244.716i 0.334769i
\(732\) 118.772 0.162256
\(733\) 633.490i 0.864243i 0.901815 + 0.432121i \(0.142235\pi\)
−0.901815 + 0.432121i \(0.857765\pi\)
\(734\) 563.908i 0.768266i
\(735\) 0 0
\(736\) −210.761 −0.286359
\(737\) −40.7891 −0.0553448
\(738\) 35.0391i 0.0474785i
\(739\) −749.557 −1.01428 −0.507142 0.861862i \(-0.669298\pi\)
−0.507142 + 0.861862i \(0.669298\pi\)
\(740\) 0 0
\(741\) 854.439i 1.15309i
\(742\) −159.308 688.126i −0.214701 0.927393i
\(743\) 145.699 0.196095 0.0980476 0.995182i \(-0.468740\pi\)
0.0980476 + 0.995182i \(0.468740\pi\)
\(744\) −94.3337 −0.126793
\(745\) 0 0
\(746\) −49.0822 −0.0657939
\(747\) 271.194i 0.363044i
\(748\) 94.8837i 0.126850i
\(749\) 249.228 + 1076.53i 0.332748 + 1.43729i
\(750\) 0 0
\(751\) 156.811 0.208803 0.104402 0.994535i \(-0.466707\pi\)
0.104402 + 0.994535i \(0.466707\pi\)
\(752\) 93.3518i 0.124138i
\(753\) 245.807 0.326437
\(754\) 191.136i 0.253496i
\(755\) 0 0
\(756\) 70.8717 16.4075i 0.0937456 0.0217031i
\(757\) 296.377 0.391515 0.195758 0.980652i \(-0.437283\pi\)
0.195758 + 0.980652i \(0.437283\pi\)
\(758\) −154.457 −0.203769
\(759\) 526.558i 0.693752i
\(760\) 0 0
\(761\) 312.747i 0.410968i −0.978660 0.205484i \(-0.934123\pi\)
0.978660 0.205484i \(-0.0658769\pi\)
\(762\) 495.811i 0.650670i
\(763\) 176.942 + 764.297i 0.231904 + 1.00170i
\(764\) −296.578 −0.388191
\(765\) 0 0
\(766\) 475.770i 0.621109i
\(767\) 627.125 0.817634
\(768\) 27.7128i 0.0360844i
\(769\) 91.1460i 0.118525i 0.998242 + 0.0592627i \(0.0188750\pi\)
−0.998242 + 0.0592627i \(0.981125\pi\)
\(770\) 0 0
\(771\) −295.908 −0.383798
\(772\) 70.3772 0.0911622
\(773\) 417.539i 0.540154i −0.962839 0.270077i \(-0.912951\pi\)
0.962839 0.270077i \(-0.0870492\pi\)
\(774\) −178.570 −0.230710
\(775\) 0 0
\(776\) 234.082i 0.301652i
\(777\) −749.291 + 173.469i −0.964339 + 0.223254i
\(778\) −440.065 −0.565636
\(779\) 278.929 0.358061
\(780\) 0 0
\(781\) 316.692 0.405496
\(782\) 306.351i 0.391754i
\(783\) 48.0802i 0.0614052i
\(784\) −176.059 + 86.1354i −0.224565 + 0.109867i
\(785\) 0 0
\(786\) 346.015 0.440222
\(787\) 318.111i 0.404207i 0.979364 + 0.202104i \(0.0647778\pi\)
−0.979364 + 0.202104i \(0.935222\pi\)
\(788\) 387.268 0.491457
\(789\) 664.098i 0.841696i
\(790\) 0 0