Properties

Label 336.4.q.m.193.1
Level $336$
Weight $4$
Character 336.193
Analytic conductor $19.825$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 173 x^{6} + 9457 x^{4} + 168048 x^{2} + 746496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 7 \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.1
Root \(8.67551i\) of defining polynomial
Character \(\chi\) \(=\) 336.193
Dual form 336.4.q.m.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{3} +(-9.47901 - 16.4181i) q^{5} +(-12.8033 - 13.3819i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{3} +(-9.47901 - 16.4181i) q^{5} +(-12.8033 - 13.3819i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(27.3654 - 47.3983i) q^{11} +62.0173 q^{13} -56.8741 q^{15} +(-61.2195 + 106.035i) q^{17} +(-6.25288 - 10.8303i) q^{19} +(-53.9722 + 13.1910i) q^{21} +(-37.2195 - 64.4661i) q^{23} +(-117.203 + 203.002i) q^{25} -27.0000 q^{27} -232.572 q^{29} +(5.18387 - 8.97872i) q^{31} +(-82.0962 - 142.195i) q^{33} +(-98.3438 + 337.053i) q^{35} +(122.993 + 213.031i) q^{37} +(93.0260 - 161.126i) q^{39} +238.653 q^{41} +92.9718 q^{43} +(-85.3111 + 147.763i) q^{45} +(-242.822 - 420.580i) q^{47} +(-15.1521 + 342.665i) q^{49} +(183.659 + 318.106i) q^{51} +(189.278 - 327.840i) q^{53} -1037.59 q^{55} -37.5173 q^{57} +(-91.3918 + 158.295i) q^{59} +(-198.235 - 343.353i) q^{61} +(-46.6871 + 160.010i) q^{63} +(-587.863 - 1018.21i) q^{65} +(-130.620 + 226.240i) q^{67} -223.317 q^{69} +874.523 q^{71} +(-76.2032 + 131.988i) q^{73} +(351.610 + 609.006i) q^{75} +(-984.647 + 240.651i) q^{77} +(286.679 + 496.542i) q^{79} +(-40.5000 + 70.1481i) q^{81} -317.754 q^{83} +2321.20 q^{85} +(-348.858 + 604.240i) q^{87} +(47.5080 + 82.2863i) q^{89} +(-794.025 - 829.911i) q^{91} +(-15.5516 - 26.9362i) q^{93} +(-118.542 + 205.321i) q^{95} -1608.78 q^{97} -492.577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 12q^{3} - 4q^{5} - 18q^{7} - 36q^{9} + O(q^{10}) \) \( 8q + 12q^{3} - 4q^{5} - 18q^{7} - 36q^{9} + 14q^{11} + 44q^{13} - 24q^{15} - 96q^{17} - 26q^{19} - 36q^{21} + 96q^{23} - 110q^{25} - 216q^{27} - 152q^{29} + 238q^{31} - 42q^{33} - 152q^{35} - 562q^{37} + 66q^{39} + 856q^{41} + 516q^{43} - 36q^{45} - 80q^{47} + 156q^{49} + 288q^{51} - 2952q^{55} - 156q^{57} + 262q^{59} + 276q^{61} + 54q^{63} - 2196q^{65} + 150q^{67} + 576q^{69} + 1696q^{71} + 218q^{73} + 330q^{75} - 764q^{77} + 1762q^{79} - 324q^{81} - 6900q^{83} + 2904q^{85} - 228q^{87} + 344q^{89} + 2806q^{91} - 714q^{93} + 2004q^{95} - 1244q^{97} - 252q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) 0 0
\(5\) −9.47901 16.4181i −0.847828 1.46848i −0.883142 0.469106i \(-0.844576\pi\)
0.0353138 0.999376i \(-0.488757\pi\)
\(6\) 0 0
\(7\) −12.8033 13.3819i −0.691312 0.722556i
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) 27.3654 47.3983i 0.750089 1.29919i −0.197690 0.980265i \(-0.563344\pi\)
0.947779 0.318928i \(-0.103323\pi\)
\(12\) 0 0
\(13\) 62.0173 1.32312 0.661558 0.749894i \(-0.269896\pi\)
0.661558 + 0.749894i \(0.269896\pi\)
\(14\) 0 0
\(15\) −56.8741 −0.978988
\(16\) 0 0
\(17\) −61.2195 + 106.035i −0.873407 + 1.51279i −0.0149571 + 0.999888i \(0.504761\pi\)
−0.858450 + 0.512897i \(0.828572\pi\)
\(18\) 0 0
\(19\) −6.25288 10.8303i −0.0755004 0.130771i 0.825803 0.563958i \(-0.190722\pi\)
−0.901304 + 0.433188i \(0.857389\pi\)
\(20\) 0 0
\(21\) −53.9722 + 13.1910i −0.560843 + 0.137072i
\(22\) 0 0
\(23\) −37.2195 64.4661i −0.337427 0.584440i 0.646521 0.762896i \(-0.276223\pi\)
−0.983948 + 0.178456i \(0.942890\pi\)
\(24\) 0 0
\(25\) −117.203 + 203.002i −0.937626 + 1.62402i
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −232.572 −1.48923 −0.744613 0.667496i \(-0.767366\pi\)
−0.744613 + 0.667496i \(0.767366\pi\)
\(30\) 0 0
\(31\) 5.18387 8.97872i 0.0300339 0.0520202i −0.850618 0.525785i \(-0.823772\pi\)
0.880652 + 0.473764i \(0.157105\pi\)
\(32\) 0 0
\(33\) −82.0962 142.195i −0.433064 0.750089i
\(34\) 0 0
\(35\) −98.3438 + 337.053i −0.474947 + 1.62778i
\(36\) 0 0
\(37\) 122.993 + 213.031i 0.546486 + 0.946541i 0.998512 + 0.0545365i \(0.0173681\pi\)
−0.452026 + 0.892005i \(0.649299\pi\)
\(38\) 0 0
\(39\) 93.0260 161.126i 0.381951 0.661558i
\(40\) 0 0
\(41\) 238.653 0.909056 0.454528 0.890733i \(-0.349808\pi\)
0.454528 + 0.890733i \(0.349808\pi\)
\(42\) 0 0
\(43\) 92.9718 0.329722 0.164861 0.986317i \(-0.447282\pi\)
0.164861 + 0.986317i \(0.447282\pi\)
\(44\) 0 0
\(45\) −85.3111 + 147.763i −0.282609 + 0.489494i
\(46\) 0 0
\(47\) −242.822 420.580i −0.753601 1.30528i −0.946067 0.323972i \(-0.894982\pi\)
0.192465 0.981304i \(-0.438352\pi\)
\(48\) 0 0
\(49\) −15.1521 + 342.665i −0.0441751 + 0.999024i
\(50\) 0 0
\(51\) 183.659 + 318.106i 0.504262 + 0.873407i
\(52\) 0 0
\(53\) 189.278 327.840i 0.490555 0.849666i −0.509386 0.860538i \(-0.670128\pi\)
0.999941 + 0.0108725i \(0.00346088\pi\)
\(54\) 0 0
\(55\) −1037.59 −2.54379
\(56\) 0 0
\(57\) −37.5173 −0.0871804
\(58\) 0 0
\(59\) −91.3918 + 158.295i −0.201664 + 0.349293i −0.949065 0.315081i \(-0.897968\pi\)
0.747400 + 0.664374i \(0.231302\pi\)
\(60\) 0 0
\(61\) −198.235 343.353i −0.416088 0.720686i 0.579454 0.815005i \(-0.303266\pi\)
−0.995542 + 0.0943190i \(0.969933\pi\)
\(62\) 0 0
\(63\) −46.6871 + 160.010i −0.0933653 + 0.319991i
\(64\) 0 0
\(65\) −587.863 1018.21i −1.12178 1.94297i
\(66\) 0 0
\(67\) −130.620 + 226.240i −0.238175 + 0.412531i −0.960191 0.279346i \(-0.909882\pi\)
0.722016 + 0.691877i \(0.243216\pi\)
\(68\) 0 0
\(69\) −223.317 −0.389627
\(70\) 0 0
\(71\) 874.523 1.46179 0.730893 0.682492i \(-0.239104\pi\)
0.730893 + 0.682492i \(0.239104\pi\)
\(72\) 0 0
\(73\) −76.2032 + 131.988i −0.122177 + 0.211617i −0.920626 0.390446i \(-0.872321\pi\)
0.798449 + 0.602062i \(0.205654\pi\)
\(74\) 0 0
\(75\) 351.610 + 609.006i 0.541339 + 0.937626i
\(76\) 0 0
\(77\) −984.647 + 240.651i −1.45729 + 0.356166i
\(78\) 0 0
\(79\) 286.679 + 496.542i 0.408277 + 0.707156i 0.994697 0.102851i \(-0.0327965\pi\)
−0.586420 + 0.810007i \(0.699463\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −317.754 −0.420217 −0.210108 0.977678i \(-0.567382\pi\)
−0.210108 + 0.977678i \(0.567382\pi\)
\(84\) 0 0
\(85\) 2321.20 2.96200
\(86\) 0 0
\(87\) −348.858 + 604.240i −0.429903 + 0.744613i
\(88\) 0 0
\(89\) 47.5080 + 82.2863i 0.0565824 + 0.0980037i 0.892929 0.450197i \(-0.148646\pi\)
−0.836347 + 0.548201i \(0.815313\pi\)
\(90\) 0 0
\(91\) −794.025 829.911i −0.914686 0.956026i
\(92\) 0 0
\(93\) −15.5516 26.9362i −0.0173401 0.0300339i
\(94\) 0 0
\(95\) −118.542 + 205.321i −0.128023 + 0.221742i
\(96\) 0 0
\(97\) −1608.78 −1.68398 −0.841992 0.539490i \(-0.818617\pi\)
−0.841992 + 0.539490i \(0.818617\pi\)
\(98\) 0 0
\(99\) −492.577 −0.500059
\(100\) 0 0
\(101\) 391.521 678.135i 0.385721 0.668089i −0.606148 0.795352i \(-0.707286\pi\)
0.991869 + 0.127263i \(0.0406194\pi\)
\(102\) 0 0
\(103\) −744.805 1290.04i −0.712503 1.23409i −0.963915 0.266211i \(-0.914228\pi\)
0.251412 0.967880i \(-0.419105\pi\)
\(104\) 0 0
\(105\) 728.174 + 761.085i 0.676786 + 0.707374i
\(106\) 0 0
\(107\) 356.385 + 617.276i 0.321991 + 0.557704i 0.980899 0.194519i \(-0.0623147\pi\)
−0.658908 + 0.752223i \(0.728981\pi\)
\(108\) 0 0
\(109\) −520.924 + 902.267i −0.457757 + 0.792858i −0.998842 0.0481100i \(-0.984680\pi\)
0.541085 + 0.840968i \(0.318014\pi\)
\(110\) 0 0
\(111\) 737.960 0.631028
\(112\) 0 0
\(113\) 352.093 0.293116 0.146558 0.989202i \(-0.453181\pi\)
0.146558 + 0.989202i \(0.453181\pi\)
\(114\) 0 0
\(115\) −705.609 + 1222.15i −0.572160 + 0.991010i
\(116\) 0 0
\(117\) −279.078 483.377i −0.220519 0.381951i
\(118\) 0 0
\(119\) 2202.77 538.365i 1.69687 0.414721i
\(120\) 0 0
\(121\) −832.231 1441.47i −0.625267 1.08299i
\(122\) 0 0
\(123\) 357.979 620.038i 0.262422 0.454528i
\(124\) 0 0
\(125\) 2074.13 1.48413
\(126\) 0 0
\(127\) 1093.73 0.764194 0.382097 0.924122i \(-0.375202\pi\)
0.382097 + 0.924122i \(0.375202\pi\)
\(128\) 0 0
\(129\) 139.458 241.548i 0.0951826 0.164861i
\(130\) 0 0
\(131\) −1083.19 1876.13i −0.722430 1.25129i −0.960023 0.279921i \(-0.909692\pi\)
0.237593 0.971365i \(-0.423642\pi\)
\(132\) 0 0
\(133\) −64.8730 + 222.339i −0.0422947 + 0.144957i
\(134\) 0 0
\(135\) 255.933 + 443.289i 0.163165 + 0.282609i
\(136\) 0 0
\(137\) 982.461 1701.67i 0.612681 1.06119i −0.378105 0.925763i \(-0.623424\pi\)
0.990787 0.135432i \(-0.0432424\pi\)
\(138\) 0 0
\(139\) 136.976 0.0835840 0.0417920 0.999126i \(-0.486693\pi\)
0.0417920 + 0.999126i \(0.486693\pi\)
\(140\) 0 0
\(141\) −1456.93 −0.870184
\(142\) 0 0
\(143\) 1697.13 2939.51i 0.992455 1.71898i
\(144\) 0 0
\(145\) 2204.55 + 3818.40i 1.26261 + 2.18690i
\(146\) 0 0
\(147\) 867.542 + 553.364i 0.486760 + 0.310481i
\(148\) 0 0
\(149\) 140.053 + 242.578i 0.0770037 + 0.133374i 0.901956 0.431828i \(-0.142131\pi\)
−0.824952 + 0.565203i \(0.808798\pi\)
\(150\) 0 0
\(151\) 1097.07 1900.17i 0.591245 1.02407i −0.402820 0.915279i \(-0.631970\pi\)
0.994065 0.108787i \(-0.0346967\pi\)
\(152\) 0 0
\(153\) 1101.95 0.582271
\(154\) 0 0
\(155\) −196.552 −0.101854
\(156\) 0 0
\(157\) 110.409 191.234i 0.0561248 0.0972111i −0.836598 0.547817i \(-0.815459\pi\)
0.892723 + 0.450606i \(0.148792\pi\)
\(158\) 0 0
\(159\) −567.835 983.520i −0.283222 0.490555i
\(160\) 0 0
\(161\) −386.149 + 1323.45i −0.189024 + 0.647840i
\(162\) 0 0
\(163\) 738.431 + 1279.00i 0.354837 + 0.614596i 0.987090 0.160166i \(-0.0512031\pi\)
−0.632253 + 0.774762i \(0.717870\pi\)
\(164\) 0 0
\(165\) −1556.38 + 2695.73i −0.734328 + 1.27189i
\(166\) 0 0
\(167\) −2197.66 −1.01832 −0.509162 0.860671i \(-0.670045\pi\)
−0.509162 + 0.860671i \(0.670045\pi\)
\(168\) 0 0
\(169\) 1649.15 0.750635
\(170\) 0 0
\(171\) −56.2759 + 97.4727i −0.0251668 + 0.0435902i
\(172\) 0 0
\(173\) −1045.80 1811.38i −0.459601 0.796052i 0.539339 0.842089i \(-0.318674\pi\)
−0.998940 + 0.0460370i \(0.985341\pi\)
\(174\) 0 0
\(175\) 4217.14 1030.69i 1.82163 0.445214i
\(176\) 0 0
\(177\) 274.175 + 474.886i 0.116431 + 0.201664i
\(178\) 0 0
\(179\) 1167.27 2021.77i 0.487406 0.844212i −0.512489 0.858694i \(-0.671276\pi\)
0.999895 + 0.0144814i \(0.00460974\pi\)
\(180\) 0 0
\(181\) 1758.40 0.722105 0.361053 0.932545i \(-0.382417\pi\)
0.361053 + 0.932545i \(0.382417\pi\)
\(182\) 0 0
\(183\) −1189.41 −0.480457
\(184\) 0 0
\(185\) 2331.71 4038.64i 0.926652 1.60501i
\(186\) 0 0
\(187\) 3350.60 + 5803.40i 1.31027 + 2.26945i
\(188\) 0 0
\(189\) 345.689 + 361.312i 0.133043 + 0.139056i
\(190\) 0 0
\(191\) −1850.34 3204.88i −0.700973 1.21412i −0.968125 0.250467i \(-0.919416\pi\)
0.267152 0.963654i \(-0.413917\pi\)
\(192\) 0 0
\(193\) −1354.22 + 2345.58i −0.505073 + 0.874812i 0.494910 + 0.868944i \(0.335201\pi\)
−0.999983 + 0.00586773i \(0.998132\pi\)
\(194\) 0 0
\(195\) −3527.18 −1.29531
\(196\) 0 0
\(197\) −160.686 −0.0581138 −0.0290569 0.999578i \(-0.509250\pi\)
−0.0290569 + 0.999578i \(0.509250\pi\)
\(198\) 0 0
\(199\) −1033.00 + 1789.20i −0.367976 + 0.637353i −0.989249 0.146241i \(-0.953282\pi\)
0.621273 + 0.783594i \(0.286616\pi\)
\(200\) 0 0
\(201\) 391.859 + 678.719i 0.137510 + 0.238175i
\(202\) 0 0
\(203\) 2977.69 + 3112.27i 1.02952 + 1.07605i
\(204\) 0 0
\(205\) −2262.19 3918.23i −0.770723 1.33493i
\(206\) 0 0
\(207\) −334.976 + 580.195i −0.112476 + 0.194813i
\(208\) 0 0
\(209\) −684.450 −0.226528
\(210\) 0 0
\(211\) 1007.12 0.328592 0.164296 0.986411i \(-0.447465\pi\)
0.164296 + 0.986411i \(0.447465\pi\)
\(212\) 0 0
\(213\) 1311.78 2272.08i 0.421981 0.730893i
\(214\) 0 0
\(215\) −881.280 1526.42i −0.279548 0.484191i
\(216\) 0 0
\(217\) −186.523 + 45.5869i −0.0583503 + 0.0142610i
\(218\) 0 0
\(219\) 228.610 + 395.964i 0.0705389 + 0.122177i
\(220\) 0 0
\(221\) −3796.67 + 6576.03i −1.15562 + 2.00159i
\(222\) 0 0
\(223\) −1644.83 −0.493929 −0.246964 0.969025i \(-0.579433\pi\)
−0.246964 + 0.969025i \(0.579433\pi\)
\(224\) 0 0
\(225\) 2109.66 0.625084
\(226\) 0 0
\(227\) 159.437 276.153i 0.0466177 0.0807442i −0.841775 0.539829i \(-0.818489\pi\)
0.888393 + 0.459084i \(0.151822\pi\)
\(228\) 0 0
\(229\) −1268.05 2196.33i −0.365918 0.633789i 0.623005 0.782218i \(-0.285912\pi\)
−0.988923 + 0.148429i \(0.952578\pi\)
\(230\) 0 0
\(231\) −851.740 + 2919.17i −0.242599 + 0.831459i
\(232\) 0 0
\(233\) −1166.41 2020.28i −0.327957 0.568038i 0.654150 0.756365i \(-0.273027\pi\)
−0.982106 + 0.188328i \(0.939693\pi\)
\(234\) 0 0
\(235\) −4603.43 + 7973.37i −1.27785 + 2.21330i
\(236\) 0 0
\(237\) 1720.07 0.471438
\(238\) 0 0
\(239\) −2713.85 −0.734495 −0.367248 0.930123i \(-0.619700\pi\)
−0.367248 + 0.930123i \(0.619700\pi\)
\(240\) 0 0
\(241\) 2087.29 3615.30i 0.557902 0.966315i −0.439769 0.898111i \(-0.644940\pi\)
0.997671 0.0682042i \(-0.0217269\pi\)
\(242\) 0 0
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 5769.55 2999.36i 1.50450 0.782130i
\(246\) 0 0
\(247\) −387.786 671.666i −0.0998958 0.173025i
\(248\) 0 0
\(249\) −476.631 + 825.548i −0.121306 + 0.210108i
\(250\) 0 0
\(251\) −6123.58 −1.53991 −0.769954 0.638099i \(-0.779721\pi\)
−0.769954 + 0.638099i \(0.779721\pi\)
\(252\) 0 0
\(253\) −4074.11 −1.01240
\(254\) 0 0
\(255\) 3481.80 6030.66i 0.855055 1.48100i
\(256\) 0 0
\(257\) −2316.96 4013.09i −0.562365 0.974045i −0.997289 0.0735777i \(-0.976558\pi\)
0.434925 0.900467i \(-0.356775\pi\)
\(258\) 0 0
\(259\) 1276.04 4373.38i 0.306137 1.04922i
\(260\) 0 0
\(261\) 1046.58 + 1812.72i 0.248204 + 0.429903i
\(262\) 0 0
\(263\) 1641.61 2843.36i 0.384891 0.666650i −0.606863 0.794806i \(-0.707572\pi\)
0.991754 + 0.128156i \(0.0409058\pi\)
\(264\) 0 0
\(265\) −7176.69 −1.66362
\(266\) 0 0
\(267\) 285.048 0.0653358
\(268\) 0 0
\(269\) 399.493 691.942i 0.0905483 0.156834i −0.817194 0.576363i \(-0.804471\pi\)
0.907742 + 0.419529i \(0.137805\pi\)
\(270\) 0 0
\(271\) −3353.04 5807.63i −0.751596 1.30180i −0.947049 0.321089i \(-0.895951\pi\)
0.195453 0.980713i \(-0.437382\pi\)
\(272\) 0 0
\(273\) −3347.21 + 818.070i −0.742060 + 0.181362i
\(274\) 0 0
\(275\) 6414.63 + 11110.5i 1.40661 + 2.43631i
\(276\) 0 0
\(277\) −581.135 + 1006.56i −0.126054 + 0.218332i −0.922145 0.386845i \(-0.873565\pi\)
0.796090 + 0.605178i \(0.206898\pi\)
\(278\) 0 0
\(279\) −93.3096 −0.0200226
\(280\) 0 0
\(281\) 2718.17 0.577055 0.288527 0.957472i \(-0.406834\pi\)
0.288527 + 0.957472i \(0.406834\pi\)
\(282\) 0 0
\(283\) −1504.74 + 2606.29i −0.316069 + 0.547448i −0.979664 0.200644i \(-0.935697\pi\)
0.663595 + 0.748092i \(0.269030\pi\)
\(284\) 0 0
\(285\) 355.626 + 615.963i 0.0739140 + 0.128023i
\(286\) 0 0
\(287\) −3055.54 3193.63i −0.628441 0.656844i
\(288\) 0 0
\(289\) −5039.17 8728.09i −1.02568 1.77653i
\(290\) 0 0
\(291\) −2413.16 + 4179.72i −0.486124 + 0.841992i
\(292\) 0 0
\(293\) 4209.15 0.839252 0.419626 0.907697i \(-0.362161\pi\)
0.419626 + 0.907697i \(0.362161\pi\)
\(294\) 0 0
\(295\) 3465.21 0.683907
\(296\) 0 0
\(297\) −738.866 + 1279.75i −0.144355 + 0.250030i
\(298\) 0 0
\(299\) −2308.26 3998.02i −0.446454 0.773282i
\(300\) 0 0
\(301\) −1190.34 1244.14i −0.227941 0.238243i
\(302\) 0 0
\(303\) −1174.56 2034.40i −0.222696 0.385721i
\(304\) 0 0
\(305\) −3758.14 + 6509.29i −0.705543 + 1.22204i
\(306\) 0 0
\(307\) 3114.82 0.579063 0.289531 0.957169i \(-0.406501\pi\)
0.289531 + 0.957169i \(0.406501\pi\)
\(308\) 0 0
\(309\) −4468.83 −0.822727
\(310\) 0 0
\(311\) −4243.62 + 7350.16i −0.773741 + 1.34016i 0.161758 + 0.986831i \(0.448284\pi\)
−0.935499 + 0.353329i \(0.885050\pi\)
\(312\) 0 0
\(313\) 2477.46 + 4291.08i 0.447393 + 0.774908i 0.998215 0.0597148i \(-0.0190191\pi\)
−0.550822 + 0.834623i \(0.685686\pi\)
\(314\) 0 0
\(315\) 3069.62 750.226i 0.549058 0.134192i
\(316\) 0 0
\(317\) 2804.40 + 4857.36i 0.496879 + 0.860619i 0.999994 0.00360042i \(-0.00114605\pi\)
−0.503115 + 0.864220i \(0.667813\pi\)
\(318\) 0 0
\(319\) −6364.43 + 11023.5i −1.11705 + 1.93479i
\(320\) 0 0
\(321\) 2138.31 0.371803
\(322\) 0 0
\(323\) 1531.19 0.263770
\(324\) 0 0
\(325\) −7268.63 + 12589.6i −1.24059 + 2.14876i
\(326\) 0 0
\(327\) 1562.77 + 2706.80i 0.264286 + 0.457757i
\(328\) 0 0
\(329\) −2519.26 + 8634.24i −0.422162 + 1.44687i
\(330\) 0 0
\(331\) −3304.75 5723.99i −0.548777 0.950510i −0.998359 0.0572706i \(-0.981760\pi\)
0.449582 0.893239i \(-0.351573\pi\)
\(332\) 0 0
\(333\) 1106.94 1917.28i 0.182162 0.315514i
\(334\) 0 0
\(335\) 4952.57 0.807725
\(336\) 0 0
\(337\) 11455.5 1.85170 0.925850 0.377891i \(-0.123350\pi\)
0.925850 + 0.377891i \(0.123350\pi\)
\(338\) 0 0
\(339\) 528.139 914.764i 0.0846153 0.146558i
\(340\) 0 0
\(341\) −283.717 491.413i −0.0450562 0.0780395i
\(342\) 0 0
\(343\) 4779.52 4184.47i 0.752390 0.658718i
\(344\) 0 0
\(345\) 2116.83 + 3666.45i 0.330337 + 0.572160i
\(346\) 0 0
\(347\) −3022.08 + 5234.39i −0.467532 + 0.809789i −0.999312 0.0370937i \(-0.988190\pi\)
0.531780 + 0.846883i \(0.321523\pi\)
\(348\) 0 0
\(349\) −5487.93 −0.841726 −0.420863 0.907124i \(-0.638273\pi\)
−0.420863 + 0.907124i \(0.638273\pi\)
\(350\) 0 0
\(351\) −1674.47 −0.254634
\(352\) 0 0
\(353\) −3440.08 + 5958.39i −0.518688 + 0.898394i 0.481076 + 0.876679i \(0.340246\pi\)
−0.999764 + 0.0217151i \(0.993087\pi\)
\(354\) 0 0
\(355\) −8289.61 14358.0i −1.23934 2.14660i
\(356\) 0 0
\(357\) 1905.44 6530.51i 0.282483 0.968154i
\(358\) 0 0
\(359\) −1969.17 3410.70i −0.289495 0.501420i 0.684194 0.729300i \(-0.260154\pi\)
−0.973689 + 0.227880i \(0.926821\pi\)
\(360\) 0 0
\(361\) 3351.30 5804.63i 0.488599 0.846279i
\(362\) 0 0
\(363\) −4993.38 −0.721996
\(364\) 0 0
\(365\) 2889.32 0.414340
\(366\) 0 0
\(367\) 719.814 1246.75i 0.102381 0.177330i −0.810284 0.586038i \(-0.800687\pi\)
0.912665 + 0.408708i \(0.134020\pi\)
\(368\) 0 0
\(369\) −1073.94 1860.11i −0.151509 0.262422i
\(370\) 0 0
\(371\) −6810.52 + 1664.51i −0.953058 + 0.232931i
\(372\) 0 0
\(373\) 1247.05 + 2159.96i 0.173110 + 0.299835i 0.939506 0.342534i \(-0.111285\pi\)
−0.766396 + 0.642369i \(0.777952\pi\)
\(374\) 0 0
\(375\) 3111.19 5388.75i 0.428430 0.742063i
\(376\) 0 0
\(377\) −14423.5 −1.97042
\(378\) 0 0
\(379\) 1309.25 0.177445 0.0887225 0.996056i \(-0.471722\pi\)
0.0887225 + 0.996056i \(0.471722\pi\)
\(380\) 0 0
\(381\) 1640.59 2841.59i 0.220604 0.382097i
\(382\) 0 0
\(383\) 3480.90 + 6029.10i 0.464402 + 0.804367i 0.999174 0.0406289i \(-0.0129361\pi\)
−0.534773 + 0.844996i \(0.679603\pi\)
\(384\) 0 0
\(385\) 13284.5 + 13884.9i 1.75855 + 1.83803i
\(386\) 0 0
\(387\) −418.373 724.643i −0.0549537 0.0951826i
\(388\) 0 0
\(389\) −3176.72 + 5502.25i −0.414052 + 0.717159i −0.995328 0.0965470i \(-0.969220\pi\)
0.581276 + 0.813706i \(0.302554\pi\)
\(390\) 0 0
\(391\) 9114.25 1.17884
\(392\) 0 0
\(393\) −6499.11 −0.834191
\(394\) 0 0
\(395\) 5434.86 9413.45i 0.692297 1.19909i
\(396\) 0 0
\(397\) −5752.70 9963.97i −0.727254 1.25964i −0.958039 0.286637i \(-0.907463\pi\)
0.230785 0.973005i \(-0.425871\pi\)
\(398\) 0 0
\(399\) 480.344 + 502.053i 0.0602689 + 0.0629927i
\(400\) 0 0
\(401\) −826.664 1431.82i −0.102947 0.178309i 0.809951 0.586498i \(-0.199494\pi\)
−0.912897 + 0.408189i \(0.866160\pi\)
\(402\) 0 0
\(403\) 321.489 556.836i 0.0397383 0.0688287i
\(404\) 0 0
\(405\) 1535.60 0.188406
\(406\) 0 0
\(407\) 13463.0 1.63965
\(408\) 0 0
\(409\) 2447.41 4239.04i 0.295885 0.512487i −0.679306 0.733855i \(-0.737719\pi\)
0.975190 + 0.221368i \(0.0710523\pi\)
\(410\) 0 0
\(411\) −2947.38 5105.02i −0.353732 0.612681i
\(412\) 0 0
\(413\) 3288.41 803.699i 0.391797 0.0957566i
\(414\) 0 0
\(415\) 3011.99 + 5216.92i 0.356272 + 0.617081i
\(416\) 0 0
\(417\) 205.464 355.875i 0.0241286 0.0417920i
\(418\) 0 0
\(419\) 265.504 0.0309563 0.0154782 0.999880i \(-0.495073\pi\)
0.0154782 + 0.999880i \(0.495073\pi\)
\(420\) 0 0
\(421\) 11136.8 1.28925 0.644623 0.764500i \(-0.277014\pi\)
0.644623 + 0.764500i \(0.277014\pi\)
\(422\) 0 0
\(423\) −2185.40 + 3785.22i −0.251200 + 0.435092i
\(424\) 0 0
\(425\) −14350.3 24855.4i −1.63786 2.83685i
\(426\) 0 0
\(427\) −2056.67 + 7048.81i −0.233089 + 0.798866i
\(428\) 0 0
\(429\) −5091.39 8818.54i −0.572994 0.992455i
\(430\) 0 0
\(431\) 2596.71 4497.63i 0.290206 0.502652i −0.683652 0.729808i \(-0.739609\pi\)
0.973858 + 0.227156i \(0.0729427\pi\)
\(432\) 0 0
\(433\) 6314.17 0.700785 0.350392 0.936603i \(-0.386048\pi\)
0.350392 + 0.936603i \(0.386048\pi\)
\(434\) 0 0
\(435\) 13227.3 1.45794
\(436\) 0 0
\(437\) −465.458 + 806.198i −0.0509517 + 0.0882509i
\(438\) 0 0
\(439\) −7711.66 13357.0i −0.838399 1.45215i −0.891232 0.453547i \(-0.850158\pi\)
0.0528329 0.998603i \(-0.483175\pi\)
\(440\) 0 0
\(441\) 2738.99 1423.89i 0.295756 0.153752i
\(442\) 0 0
\(443\) −4353.06 7539.72i −0.466862 0.808629i 0.532421 0.846480i \(-0.321282\pi\)
−0.999283 + 0.0378504i \(0.987949\pi\)
\(444\) 0 0
\(445\) 900.657 1559.98i 0.0959444 0.166181i
\(446\) 0 0
\(447\) 840.315 0.0889162
\(448\) 0 0
\(449\) 5495.91 0.577657 0.288829 0.957381i \(-0.406734\pi\)
0.288829 + 0.957381i \(0.406734\pi\)
\(450\) 0 0
\(451\) 6530.83 11311.7i 0.681873 1.18104i
\(452\) 0 0
\(453\) −3291.20 5700.52i −0.341355 0.591245i
\(454\) 0 0
\(455\) −6099.02 + 20903.1i −0.628409 + 2.15375i
\(456\) 0 0
\(457\) 5678.63 + 9835.67i 0.581258 + 1.00677i 0.995331 + 0.0965247i \(0.0307727\pi\)
−0.414072 + 0.910244i \(0.635894\pi\)
\(458\) 0 0
\(459\) 1652.93 2862.95i 0.168087 0.291136i
\(460\) 0 0
\(461\) 14514.2 1.46637 0.733184 0.680030i \(-0.238033\pi\)
0.733184 + 0.680030i \(0.238033\pi\)
\(462\) 0 0
\(463\) −9971.00 −1.00085 −0.500423 0.865781i \(-0.666822\pi\)
−0.500423 + 0.865781i \(0.666822\pi\)
\(464\) 0 0
\(465\) −294.828 + 510.656i −0.0294028 + 0.0509271i
\(466\) 0 0
\(467\) −198.739 344.226i −0.0196928 0.0341089i 0.856011 0.516957i \(-0.172935\pi\)
−0.875704 + 0.482849i \(0.839602\pi\)
\(468\) 0 0
\(469\) 4699.88 1148.67i 0.462730 0.113093i
\(470\) 0 0
\(471\) −331.227 573.702i −0.0324037 0.0561248i
\(472\) 0 0
\(473\) 2544.21 4406.70i 0.247321 0.428373i
\(474\) 0 0
\(475\) 2931.43 0.283165
\(476\) 0 0
\(477\) −3407.01 −0.327036
\(478\) 0 0
\(479\) −7030.20 + 12176.7i −0.670602 + 1.16152i 0.307132 + 0.951667i \(0.400631\pi\)
−0.977734 + 0.209849i \(0.932703\pi\)
\(480\) 0 0
\(481\) 7627.71 + 13211.6i 0.723064 + 1.25238i
\(482\) 0 0
\(483\) 2859.19 + 2988.42i 0.269354 + 0.281527i
\(484\) 0 0
\(485\) 15249.6 + 26413.1i 1.42773 + 2.47290i
\(486\) 0 0
\(487\) −6767.34 + 11721.4i −0.629687 + 1.09065i 0.357927 + 0.933749i \(0.383484\pi\)
−0.987614 + 0.156900i \(0.949850\pi\)
\(488\) 0 0
\(489\) 4430.59 0.409730
\(490\) 0 0
\(491\) 8693.29 0.799028 0.399514 0.916727i \(-0.369179\pi\)
0.399514 + 0.916727i \(0.369179\pi\)
\(492\) 0 0
\(493\) 14238.0 24660.9i 1.30070 2.25288i
\(494\) 0 0
\(495\) 4669.14 + 8087.20i 0.423965 + 0.734328i
\(496\) 0 0
\(497\) −11196.8 11702.8i −1.01055 1.05622i
\(498\) 0 0
\(499\) 2008.97 + 3479.63i 0.180228 + 0.312164i 0.941958 0.335731i \(-0.108983\pi\)
−0.761730 + 0.647894i \(0.775650\pi\)
\(500\) 0 0
\(501\) −3296.49 + 5709.69i −0.293965 + 0.509162i
\(502\) 0 0
\(503\) −52.2455 −0.00463124 −0.00231562 0.999997i \(-0.500737\pi\)
−0.00231562 + 0.999997i \(0.500737\pi\)
\(504\) 0 0
\(505\) −14844.9 −1.30810
\(506\) 0 0
\(507\) 2473.72 4284.61i 0.216690 0.375318i
\(508\) 0 0
\(509\) −4619.55 8001.30i −0.402275 0.696761i 0.591725 0.806140i \(-0.298447\pi\)
−0.994000 + 0.109379i \(0.965114\pi\)
\(510\) 0 0
\(511\) 2741.90 670.131i 0.237367 0.0580134i
\(512\) 0 0
\(513\) 168.828 + 292.418i 0.0145301 + 0.0251668i
\(514\) 0 0
\(515\) −14120.0 + 24456.6i −1.20816 + 2.09259i
\(516\) 0 0
\(517\) −26579.7 −2.26107
\(518\) 0 0
\(519\) −6274.82 −0.530701
\(520\) 0 0
\(521\) −7486.70 + 12967.3i −0.629555 + 1.09042i 0.358086 + 0.933689i \(0.383429\pi\)
−0.987641 + 0.156733i \(0.949904\pi\)
\(522\) 0 0
\(523\) 6801.76 + 11781.0i 0.568681 + 0.984985i 0.996697 + 0.0812134i \(0.0258795\pi\)
−0.428015 + 0.903771i \(0.640787\pi\)
\(524\) 0 0
\(525\) 3647.92 12502.5i 0.303254 1.03934i
\(526\) 0 0
\(527\) 634.708 + 1099.35i 0.0524636 + 0.0908696i
\(528\) 0 0
\(529\) 3312.91 5738.13i 0.272287 0.471614i
\(530\) 0 0
\(531\) 1645.05 0.134443
\(532\) 0 0
\(533\) 14800.6 1.20279
\(534\) 0 0
\(535\) 6756.35 11702.3i 0.545986 0.945675i
\(536\) 0 0
\(537\) −3501.80 6065.30i −0.281404 0.487406i
\(538\) 0 0
\(539\) 15827.1 + 10095.4i 1.26479 + 0.806749i
\(540\) 0 0
\(541\) 8443.19 + 14624.0i 0.670981 + 1.16217i 0.977626 + 0.210350i \(0.0674603\pi\)
−0.306645 + 0.951824i \(0.599206\pi\)
\(542\) 0 0
\(543\) 2637.61 4568.47i 0.208454 0.361053i
\(544\) 0 0
\(545\) 19751.4 1.55240
\(546\) 0 0
\(547\) 5987.25 0.468001 0.234000 0.972237i \(-0.424818\pi\)
0.234000 + 0.972237i \(0.424818\pi\)
\(548\) 0 0
\(549\) −1784.11 + 3090.18i −0.138696 + 0.240229i
\(550\) 0 0
\(551\) 1454.25 + 2518.83i 0.112437 + 0.194747i
\(552\) 0 0
\(553\) 2974.26 10193.7i 0.228713 0.783869i
\(554\) 0 0
\(555\) −6995.13 12115.9i −0.535003 0.926652i
\(556\) 0 0
\(557\) −1119.35 + 1938.78i −0.0851499 + 0.147484i −0.905455 0.424442i \(-0.860470\pi\)
0.820305 + 0.571926i \(0.193804\pi\)
\(558\) 0 0
\(559\) 5765.86 0.436261
\(560\) 0 0
\(561\) 20103.6 1.51297
\(562\) 0 0
\(563\) 4226.42 7320.38i 0.316381 0.547988i −0.663349 0.748310i \(-0.730866\pi\)
0.979730 + 0.200322i \(0.0641989\pi\)
\(564\) 0 0
\(565\) −3337.49 5780.70i −0.248512 0.430435i
\(566\) 0 0
\(567\) 1457.25 356.157i 0.107934 0.0263795i
\(568\) 0 0
\(569\) −7476.78 12950.2i −0.550866 0.954128i −0.998212 0.0597671i \(-0.980964\pi\)
0.447346 0.894361i \(-0.352369\pi\)
\(570\) 0 0
\(571\) 8010.92 13875.3i 0.587122 1.01693i −0.407485 0.913212i \(-0.633594\pi\)
0.994607 0.103713i \(-0.0330725\pi\)
\(572\) 0 0
\(573\) −11102.0 −0.809414
\(574\) 0 0
\(575\) 17449.0 1.26552
\(576\) 0 0
\(577\) 8056.54 13954.3i 0.581279 1.00681i −0.414049 0.910255i \(-0.635886\pi\)
0.995328 0.0965505i \(-0.0307809\pi\)
\(578\) 0 0
\(579\) 4062.67 + 7036.75i 0.291604 + 0.505073i
\(580\) 0 0
\(581\) 4068.29 + 4252.16i 0.290501 + 0.303630i
\(582\) 0 0
\(583\) −10359.4 17942.9i −0.735919 1.27465i
\(584\) 0 0
\(585\) −5290.76 + 9163.87i −0.373925 + 0.647657i
\(586\) 0 0
\(587\) 9552.04 0.671644 0.335822 0.941925i \(-0.390986\pi\)
0.335822 + 0.941925i \(0.390986\pi\)
\(588\) 0 0
\(589\) −129.656 −0.00907028
\(590\) 0 0
\(591\) −241.029 + 417.475i −0.0167760 + 0.0290569i
\(592\) 0 0
\(593\) 12083.9 + 20929.9i 0.836807 + 1.44939i 0.892551 + 0.450947i \(0.148913\pi\)
−0.0557443 + 0.998445i \(0.517753\pi\)
\(594\) 0 0
\(595\) −29719.0 31062.2i −2.04766 2.14021i
\(596\) 0 0
\(597\) 3098.99 + 5367.61i 0.212451 + 0.367976i
\(598\) 0 0
\(599\) 410.665 711.293i 0.0280122 0.0485186i −0.851679 0.524063i \(-0.824416\pi\)
0.879692 + 0.475544i \(0.157749\pi\)
\(600\) 0 0
\(601\) −14674.7 −0.995996 −0.497998 0.867178i \(-0.665931\pi\)
−0.497998 + 0.867178i \(0.665931\pi\)
\(602\) 0 0
\(603\) 2351.15 0.158783
\(604\) 0 0
\(605\) −15777.4 + 27327.3i −1.06024 + 1.83639i
\(606\) 0 0
\(607\) 2541.56 + 4402.11i 0.169949 + 0.294359i 0.938402 0.345547i \(-0.112307\pi\)
−0.768453 + 0.639906i \(0.778973\pi\)
\(608\) 0 0
\(609\) 12552.4 3067.86i 0.835222 0.204131i
\(610\) 0 0
\(611\) −15059.2 26083.3i −0.997102 1.72703i
\(612\) 0 0
\(613\) 11101.0 19227.5i 0.731428 1.26687i −0.224845 0.974395i \(-0.572187\pi\)
0.956273 0.292476i \(-0.0944792\pi\)
\(614\) 0 0
\(615\) −13573.1 −0.889954
\(616\) 0 0
\(617\) −14990.6 −0.978121 −0.489060 0.872250i \(-0.662660\pi\)
−0.489060 + 0.872250i \(0.662660\pi\)
\(618\) 0 0
\(619\) 1536.51 2661.32i 0.0997700 0.172807i −0.811819 0.583909i \(-0.801523\pi\)
0.911589 + 0.411102i \(0.134856\pi\)
\(620\) 0 0
\(621\) 1004.93 + 1740.59i 0.0649378 + 0.112476i
\(622\) 0 0
\(623\) 492.891 1689.28i 0.0316970 0.108635i
\(624\) 0 0
\(625\) −5010.29 8678.08i −0.320659 0.555397i
\(626\) 0 0
\(627\) −1026.67 + 1778.25i −0.0653931 + 0.113264i
\(628\) 0 0
\(629\) −30118.4 −1.90922
\(630\) 0 0
\(631\) −26012.7 −1.64113 −0.820563 0.571556i \(-0.806340\pi\)
−0.820563 + 0.571556i \(0.806340\pi\)
\(632\) 0 0
\(633\) 1510.68 2616.57i 0.0948565 0.164296i
\(634\) 0 0
\(635\) −10367.5 17957.0i −0.647905 1.12220i
\(636\) 0 0
\(637\) −939.691 + 21251.2i −0.0584488 + 1.32182i
\(638\) 0 0
\(639\) −3935.35 6816.23i −0.243631 0.421981i
\(640\) 0 0
\(641\) −4016.12 + 6956.12i −0.247468 + 0.428627i −0.962823 0.270134i \(-0.912932\pi\)
0.715355 + 0.698762i \(0.246265\pi\)
\(642\) 0 0
\(643\) 24887.7 1.52640 0.763200 0.646162i \(-0.223627\pi\)
0.763200 + 0.646162i \(0.223627\pi\)
\(644\) 0 0
\(645\) −5287.68 −0.322794
\(646\) 0 0
\(647\) −10542.2 + 18259.6i −0.640580 + 1.10952i 0.344723 + 0.938704i \(0.387973\pi\)
−0.985303 + 0.170813i \(0.945360\pi\)
\(648\) 0 0
\(649\) 5001.95 + 8663.62i 0.302532 + 0.524002i
\(650\) 0 0
\(651\) −161.346 + 552.982i −0.00971377 + 0.0332919i
\(652\) 0 0
\(653\) −6583.16 11402.4i −0.394516 0.683322i 0.598523 0.801106i \(-0.295754\pi\)
−0.993039 + 0.117783i \(0.962421\pi\)
\(654\) 0 0
\(655\) −20535.1 + 35567.8i −1.22499 + 2.12175i
\(656\) 0 0
\(657\) 1371.66 0.0814513
\(658\) 0 0
\(659\) 13903.4 0.821851 0.410926 0.911669i \(-0.365206\pi\)
0.410926 + 0.911669i \(0.365206\pi\)
\(660\) 0 0
\(661\) −3153.30 + 5461.68i −0.185551 + 0.321384i −0.943762 0.330625i \(-0.892740\pi\)
0.758211 + 0.652009i \(0.226074\pi\)
\(662\) 0 0
\(663\) 11390.0 + 19728.1i 0.667197 + 1.15562i
\(664\) 0 0
\(665\) 4265.32 1042.46i 0.248725 0.0607892i
\(666\) 0 0
\(667\) 8656.23 + 14993.0i 0.502505 + 0.870364i
\(668\) 0 0
\(669\) −2467.25 + 4273.40i −0.142585 + 0.246964i
\(670\) 0 0
\(671\) −21699.1 −1.24841
\(672\) 0 0
\(673\) −24407.6 −1.39798 −0.698992 0.715129i \(-0.746368\pi\)
−0.698992 + 0.715129i \(0.746368\pi\)
\(674\) 0 0
\(675\) 3164.49 5481.05i 0.180446 0.312542i
\(676\) 0 0
\(677\) 15540.1 + 26916.3i 0.882209 + 1.52803i 0.848879 + 0.528587i \(0.177278\pi\)
0.0333299 + 0.999444i \(0.489389\pi\)
\(678\) 0 0
\(679\) 20597.6 + 21528.5i 1.16416 + 1.21677i
\(680\) 0 0
\(681\) −478.312 828.460i −0.0269147 0.0466177i
\(682\) 0 0
\(683\) 14379.7 24906.4i 0.805601 1.39534i −0.110283 0.993900i \(-0.535176\pi\)
0.915885 0.401442i \(-0.131491\pi\)
\(684\) 0 0
\(685\) −37251.0 −2.07779
\(686\) 0 0
\(687\) −7608.32 −0.422526
\(688\) 0 0
\(689\) 11738.5 20331.7i 0.649061 1.12421i
\(690\) 0 0
\(691\) 12447.7 + 21560.1i 0.685287 + 1.18695i 0.973346 + 0.229340i \(0.0736566\pi\)
−0.288059 + 0.957613i \(0.593010\pi\)
\(692\) 0 0
\(693\) 6306.60 + 6591.63i 0.345697 + 0.361321i
\(694\) 0 0
\(695\) −1298.40 2248.89i −0.0708649 0.122742i
\(696\) 0 0
\(697\) −14610.2 + 25305.6i −0.793976 + 1.37521i
\(698\) 0 0
\(699\) −6998.44 −0.378692
\(700\) 0 0
\(701\) −1702.74 −0.0917427 −0.0458714 0.998947i \(-0.514606\pi\)
−0.0458714 + 0.998947i \(0.514606\pi\)
\(702\) 0 0
\(703\) 1538.12 2664.11i 0.0825198 0.142929i
\(704\) 0 0
\(705\) 13810.3 + 23920.1i 0.737767 + 1.27785i
\(706\) 0 0
\(707\) −14087.5 + 3443.04i −0.749385 + 0.183153i
\(708\) 0 0
\(709\) −3261.60 5649.26i −0.172767 0.299242i 0.766619 0.642102i \(-0.221938\pi\)
−0.939386 + 0.342860i \(0.888604\pi\)
\(710\) 0 0
\(711\) 2580.11 4468.88i 0.136092 0.235719i
\(712\) 0 0
\(713\) −771.765 −0.0405369
\(714\) 0 0
\(715\) −64348.4 −3.36572
\(716\) 0 0
\(717\) −4070.77 + 7050.79i −0.212030 + 0.367248i
\(718\) 0 0
\(719\) −12627.2 21871.0i −0.654959 1.13442i −0.981904 0.189379i \(-0.939352\pi\)
0.326945 0.945044i \(-0.393981\pi\)
\(720\) 0 0
\(721\) −7727.27 + 26483.7i −0.399138 + 1.36797i
\(722\) 0 0
\(723\) −6261.88 10845.9i −0.322105 0.557902i
\(724\) 0 0
\(725\) 27258.2 47212.6i 1.39634 2.41853i
\(726\) 0 0
\(727\) 27964.9 1.42663 0.713316 0.700843i \(-0.247192\pi\)
0.713316 + 0.700843i \(0.247192\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −5691.69 + 9858.29i −0.287982 + 0.498799i
\(732\) 0 0
\(733\) 4647.19 + 8049.17i 0.234172 + 0.405597i 0.959032 0.283299i \(-0.0914288\pi\)
−0.724860 + 0.688896i \(0.758096\pi\)
\(734\) 0 0
\(735\) 861.760 19488.8i 0.0432469 0.978032i
\(736\) 0 0
\(737\) 7148.91 + 12382.3i 0.357305 + 0.618870i
\(738\) 0 0
\(739\) 9145.60 15840.6i 0.455245 0.788508i −0.543457 0.839437i \(-0.682885\pi\)
0.998702 + 0.0509292i \(0.0162183\pi\)
\(740\) 0 0
\(741\) −2326.72 −0.115350
\(742\) 0 0
\(743\) −14742.4 −0.727921 −0.363960 0.931414i \(-0.618576\pi\)
−0.363960 + 0.931414i \(0.618576\pi\)
\(744\) 0 0
\(745\) 2655.12 4598.80i 0.130572 0.226157i
\(746\) 0 0
\(747\) 1429.89 + 2476.64i 0.0700361 + 0.121306i
\(748\) 0 0
\(749\) 3697.46 12672.3i 0.180377 0.618204i
\(750\) 0 0
\(751\) 14231.7 + 24650.0i 0.691507 + 1.19773i 0.971344 + 0.237678i \(0.0763863\pi\)
−0.279837 + 0.960048i \(0.590280\pi\)
\(752\) 0 0
\(753\) −9185.37 + 15909.5i −0.444533 + 0.769954i
\(754\) 0 0
\(755\) −41596.4 −2.00510
\(756\) 0 0
\(757\) −20336.7 −0.976422 −0.488211 0.872726i \(-0.662350\pi\)
−0.488211 + 0.872726i \(0.662350\pi\)
\(758\) 0 0
\(759\) −6111.17 + 10584.9i −0.292255 + 0.506200i
\(760\) 0 0
\(761\) −19790.8 34278.7i −0.942728 1.63285i −0.760238 0.649644i \(-0.774918\pi\)
−0.182489 0.983208i \(-0.558415\pi\)
\(762\) 0 0
\(763\) 18743.6 4581.01i 0.889337 0.217357i
\(764\) 0 0
\(765\) −10445.4 18092.0i −0.493666 0.855055i
\(766\) 0 0
\(767\) −5667.87 + 9817.04i −0.266825 + 0.462155i
\(768\) 0 0
\(769\) 10580.3 0.496146 0.248073 0.968741i \(-0.420203\pi\)
0.248073 + 0.968741i \(0.420203\pi\)
\(770\) 0 0
\(771\) −13901.7 −0.649363
\(772\) 0 0
\(773\) −12961.1 + 22449.3i −0.603077 + 1.04456i 0.389275 + 0.921122i \(0.372726\pi\)
−0.992352 + 0.123439i \(0.960608\pi\)
\(774\) 0 0
\(775\) 1215.13 + 2104.67i 0.0563211 + 0.0975509i
\(776\) 0 0
\(777\) −9448.31 9875.33i −0.436237 0.455953i
\(778\) 0 0
\(779\) −1492.27 2584.68i −0.0686341 0.118878i
\(780\) 0 0
\(781\) 23931.7 41450.9i 1.09647 1.89914i
\(782\) 0 0
\(783\) 6279.45 0.286602
\(784\) 0 0
\(785\) −4186.27 −0.190337
\(786\) 0 0
\(787\) 8610.00 14913.0i 0.389979 0.675463i −0.602467 0.798143i \(-0.705816\pi\)
0.992446 + 0.122680i \(0.0391490\pi\)
\(788\) 0 0
\(789\) −4924.84 8530.08i −0.222217 0.384891i
\(790\) 0 0
\(791\) −4507.94 4711.68i −0.202635 0.211793i
\(792\) 0 0
\(793\) −12294.0 21293.8i −0.550533 0.953551i
\(794\) 0 0