Properties

Label 336.4.h.a.239.8
Level $336$
Weight $4$
Character 336.239
Analytic conductor $19.825$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 152 x^{10} + 8222 x^{8} + 194132 x^{6} + 1882697 x^{4} + 5152508 x^{2} + 4008004\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7}\cdot 3^{2}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 239.8
Root \(5.90052i\) of defining polynomial
Character \(\chi\) \(=\) 336.239
Dual form 336.4.h.a.239.7

$q$-expansion

\(f(q)\) \(=\) \(q+(2.18705 + 4.71347i) q^{3} +14.5852i q^{5} -7.00000i q^{7} +(-17.4336 + 20.6172i) q^{9} +O(q^{10})\) \(q+(2.18705 + 4.71347i) q^{3} +14.5852i q^{5} -7.00000i q^{7} +(-17.4336 + 20.6172i) q^{9} -31.0233 q^{11} -55.7458 q^{13} +(-68.7469 + 31.8986i) q^{15} -86.4384i q^{17} +96.8558i q^{19} +(32.9943 - 15.3094i) q^{21} +115.219 q^{23} -87.7283 q^{25} +(-135.307 - 37.0818i) q^{27} -49.1735i q^{29} -12.5750i q^{31} +(-67.8496 - 146.228i) q^{33} +102.096 q^{35} -296.822 q^{37} +(-121.919 - 262.756i) q^{39} -213.956i q^{41} +165.680i q^{43} +(-300.706 - 254.273i) q^{45} +426.135 q^{47} -49.0000 q^{49} +(407.425 - 189.045i) q^{51} +460.767i q^{53} -452.482i q^{55} +(-456.527 + 211.829i) q^{57} -686.382 q^{59} -583.424 q^{61} +(144.320 + 122.035i) q^{63} -813.064i q^{65} +589.155i q^{67} +(251.989 + 543.080i) q^{69} +766.330 q^{71} -904.778 q^{73} +(-191.866 - 413.505i) q^{75} +217.163i q^{77} +459.440i q^{79} +(-121.139 - 718.865i) q^{81} -1115.25 q^{83} +1260.72 q^{85} +(231.778 - 107.545i) q^{87} +119.900i q^{89} +390.221i q^{91} +(59.2717 - 27.5021i) q^{93} -1412.66 q^{95} -331.017 q^{97} +(540.848 - 639.614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 76q^{9} + O(q^{10}) \) \( 12q + 76q^{9} - 96q^{13} + 112q^{21} - 1068q^{25} - 832q^{33} - 720q^{37} + 392q^{45} - 588q^{49} - 2336q^{57} + 432q^{61} - 424q^{69} + 1656q^{73} - 868q^{81} - 1464q^{85} + 696q^{93} - 6264q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.18705 + 4.71347i 0.420898 + 0.907108i
\(4\) 0 0
\(5\) 14.5852i 1.30454i 0.757986 + 0.652270i \(0.226183\pi\)
−0.757986 + 0.652270i \(0.773817\pi\)
\(6\) 0 0
\(7\) 7.00000i 0.377964i
\(8\) 0 0
\(9\) −17.4336 + 20.6172i −0.645689 + 0.763600i
\(10\) 0 0
\(11\) −31.0233 −0.850353 −0.425177 0.905110i \(-0.639788\pi\)
−0.425177 + 0.905110i \(0.639788\pi\)
\(12\) 0 0
\(13\) −55.7458 −1.18932 −0.594658 0.803979i \(-0.702713\pi\)
−0.594658 + 0.803979i \(0.702713\pi\)
\(14\) 0 0
\(15\) −68.7469 + 31.8986i −1.18336 + 0.549079i
\(16\) 0 0
\(17\) 86.4384i 1.23320i −0.787277 0.616600i \(-0.788510\pi\)
0.787277 0.616600i \(-0.211490\pi\)
\(18\) 0 0
\(19\) 96.8558i 1.16949i 0.811218 + 0.584743i \(0.198805\pi\)
−0.811218 + 0.584743i \(0.801195\pi\)
\(20\) 0 0
\(21\) 32.9943 15.3094i 0.342855 0.159085i
\(22\) 0 0
\(23\) 115.219 1.04456 0.522278 0.852775i \(-0.325082\pi\)
0.522278 + 0.852775i \(0.325082\pi\)
\(24\) 0 0
\(25\) −87.7283 −0.701826
\(26\) 0 0
\(27\) −135.307 37.0818i −0.964437 0.264311i
\(28\) 0 0
\(29\) 49.1735i 0.314872i −0.987529 0.157436i \(-0.949677\pi\)
0.987529 0.157436i \(-0.0503228\pi\)
\(30\) 0 0
\(31\) 12.5750i 0.0728558i −0.999336 0.0364279i \(-0.988402\pi\)
0.999336 0.0364279i \(-0.0115979\pi\)
\(32\) 0 0
\(33\) −67.8496 146.228i −0.357912 0.771362i
\(34\) 0 0
\(35\) 102.096 0.493070
\(36\) 0 0
\(37\) −296.822 −1.31884 −0.659421 0.751774i \(-0.729199\pi\)
−0.659421 + 0.751774i \(0.729199\pi\)
\(38\) 0 0
\(39\) −121.919 262.756i −0.500581 1.07884i
\(40\) 0 0
\(41\) 213.956i 0.814982i −0.913209 0.407491i \(-0.866404\pi\)
0.913209 0.407491i \(-0.133596\pi\)
\(42\) 0 0
\(43\) 165.680i 0.587581i 0.955870 + 0.293790i \(0.0949168\pi\)
−0.955870 + 0.293790i \(0.905083\pi\)
\(44\) 0 0
\(45\) −300.706 254.273i −0.996148 0.842328i
\(46\) 0 0
\(47\) 426.135 1.32251 0.661257 0.750159i \(-0.270023\pi\)
0.661257 + 0.750159i \(0.270023\pi\)
\(48\) 0 0
\(49\) −49.0000 −0.142857
\(50\) 0 0
\(51\) 407.425 189.045i 1.11864 0.519052i
\(52\) 0 0
\(53\) 460.767i 1.19417i 0.802177 + 0.597087i \(0.203675\pi\)
−0.802177 + 0.597087i \(0.796325\pi\)
\(54\) 0 0
\(55\) 452.482i 1.10932i
\(56\) 0 0
\(57\) −456.527 + 211.829i −1.06085 + 0.492235i
\(58\) 0 0
\(59\) −686.382 −1.51456 −0.757282 0.653088i \(-0.773473\pi\)
−0.757282 + 0.653088i \(0.773473\pi\)
\(60\) 0 0
\(61\) −583.424 −1.22459 −0.612293 0.790631i \(-0.709753\pi\)
−0.612293 + 0.790631i \(0.709753\pi\)
\(62\) 0 0
\(63\) 144.320 + 122.035i 0.288614 + 0.244048i
\(64\) 0 0
\(65\) 813.064i 1.55151i
\(66\) 0 0
\(67\) 589.155i 1.07428i 0.843493 + 0.537140i \(0.180495\pi\)
−0.843493 + 0.537140i \(0.819505\pi\)
\(68\) 0 0
\(69\) 251.989 + 543.080i 0.439652 + 0.947524i
\(70\) 0 0
\(71\) 766.330 1.28094 0.640469 0.767984i \(-0.278740\pi\)
0.640469 + 0.767984i \(0.278740\pi\)
\(72\) 0 0
\(73\) −904.778 −1.45063 −0.725317 0.688415i \(-0.758307\pi\)
−0.725317 + 0.688415i \(0.758307\pi\)
\(74\) 0 0
\(75\) −191.866 413.505i −0.295397 0.636632i
\(76\) 0 0
\(77\) 217.163i 0.321403i
\(78\) 0 0
\(79\) 459.440i 0.654317i 0.944969 + 0.327159i \(0.106091\pi\)
−0.944969 + 0.327159i \(0.893909\pi\)
\(80\) 0 0
\(81\) −121.139 718.865i −0.166171 0.986097i
\(82\) 0 0
\(83\) −1115.25 −1.47487 −0.737436 0.675417i \(-0.763964\pi\)
−0.737436 + 0.675417i \(0.763964\pi\)
\(84\) 0 0
\(85\) 1260.72 1.60876
\(86\) 0 0
\(87\) 231.778 107.545i 0.285623 0.132529i
\(88\) 0 0
\(89\) 119.900i 0.142802i 0.997448 + 0.0714011i \(0.0227470\pi\)
−0.997448 + 0.0714011i \(0.977253\pi\)
\(90\) 0 0
\(91\) 390.221i 0.449519i
\(92\) 0 0
\(93\) 59.2717 27.5021i 0.0660881 0.0306649i
\(94\) 0 0
\(95\) −1412.66 −1.52564
\(96\) 0 0
\(97\) −331.017 −0.346491 −0.173246 0.984879i \(-0.555425\pi\)
−0.173246 + 0.984879i \(0.555425\pi\)
\(98\) 0 0
\(99\) 540.848 639.614i 0.549064 0.649330i
\(100\) 0 0
\(101\) 1609.16i 1.58532i −0.609662 0.792661i \(-0.708695\pi\)
0.609662 0.792661i \(-0.291305\pi\)
\(102\) 0 0
\(103\) 1388.96i 1.32872i 0.747411 + 0.664362i \(0.231297\pi\)
−0.747411 + 0.664362i \(0.768703\pi\)
\(104\) 0 0
\(105\) 223.290 + 481.229i 0.207532 + 0.447268i
\(106\) 0 0
\(107\) 502.365 0.453883 0.226941 0.973908i \(-0.427127\pi\)
0.226941 + 0.973908i \(0.427127\pi\)
\(108\) 0 0
\(109\) 1599.88 1.40588 0.702938 0.711251i \(-0.251871\pi\)
0.702938 + 0.711251i \(0.251871\pi\)
\(110\) 0 0
\(111\) −649.164 1399.06i −0.555099 1.19633i
\(112\) 0 0
\(113\) 934.016i 0.777565i 0.921330 + 0.388782i \(0.127104\pi\)
−0.921330 + 0.388782i \(0.872896\pi\)
\(114\) 0 0
\(115\) 1680.49i 1.36266i
\(116\) 0 0
\(117\) 971.851 1149.32i 0.767928 0.908162i
\(118\) 0 0
\(119\) −605.069 −0.466105
\(120\) 0 0
\(121\) −368.553 −0.276900
\(122\) 0 0
\(123\) 1008.47 467.932i 0.739277 0.343025i
\(124\) 0 0
\(125\) 543.616i 0.388980i
\(126\) 0 0
\(127\) 301.355i 0.210558i 0.994443 + 0.105279i \(0.0335736\pi\)
−0.994443 + 0.105279i \(0.966426\pi\)
\(128\) 0 0
\(129\) −780.928 + 362.351i −0.532999 + 0.247312i
\(130\) 0 0
\(131\) −389.347 −0.259675 −0.129837 0.991535i \(-0.541445\pi\)
−0.129837 + 0.991535i \(0.541445\pi\)
\(132\) 0 0
\(133\) 677.991 0.442024
\(134\) 0 0
\(135\) 540.846 1973.48i 0.344805 1.25815i
\(136\) 0 0
\(137\) 3037.04i 1.89395i 0.321302 + 0.946977i \(0.395880\pi\)
−0.321302 + 0.946977i \(0.604120\pi\)
\(138\) 0 0
\(139\) 1287.18i 0.785445i 0.919657 + 0.392723i \(0.128467\pi\)
−0.919657 + 0.392723i \(0.871533\pi\)
\(140\) 0 0
\(141\) 931.979 + 2008.57i 0.556644 + 1.19966i
\(142\) 0 0
\(143\) 1729.42 1.01134
\(144\) 0 0
\(145\) 717.205 0.410763
\(146\) 0 0
\(147\) −107.166 230.960i −0.0601283 0.129587i
\(148\) 0 0
\(149\) 2051.44i 1.12792i 0.825801 + 0.563961i \(0.190723\pi\)
−0.825801 + 0.563961i \(0.809277\pi\)
\(150\) 0 0
\(151\) 473.535i 0.255204i 0.991825 + 0.127602i \(0.0407280\pi\)
−0.991825 + 0.127602i \(0.959272\pi\)
\(152\) 0 0
\(153\) 1782.12 + 1506.93i 0.941671 + 0.796263i
\(154\) 0 0
\(155\) 183.409 0.0950434
\(156\) 0 0
\(157\) 1184.81 0.602280 0.301140 0.953580i \(-0.402633\pi\)
0.301140 + 0.953580i \(0.402633\pi\)
\(158\) 0 0
\(159\) −2171.81 + 1007.72i −1.08324 + 0.502626i
\(160\) 0 0
\(161\) 806.531i 0.394805i
\(162\) 0 0
\(163\) 4055.24i 1.94866i −0.225132 0.974328i \(-0.572281\pi\)
0.225132 0.974328i \(-0.427719\pi\)
\(164\) 0 0
\(165\) 2132.76 989.601i 1.00627 0.466911i
\(166\) 0 0
\(167\) 3681.23 1.70576 0.852881 0.522105i \(-0.174853\pi\)
0.852881 + 0.522105i \(0.174853\pi\)
\(168\) 0 0
\(169\) 910.598 0.414473
\(170\) 0 0
\(171\) −1996.90 1688.55i −0.893020 0.755125i
\(172\) 0 0
\(173\) 1069.27i 0.469914i 0.972006 + 0.234957i \(0.0754949\pi\)
−0.972006 + 0.234957i \(0.924505\pi\)
\(174\) 0 0
\(175\) 614.098i 0.265265i
\(176\) 0 0
\(177\) −1501.15 3235.24i −0.637478 1.37387i
\(178\) 0 0
\(179\) 2666.57 1.11346 0.556728 0.830695i \(-0.312056\pi\)
0.556728 + 0.830695i \(0.312056\pi\)
\(180\) 0 0
\(181\) 2648.47 1.08762 0.543810 0.839208i \(-0.316981\pi\)
0.543810 + 0.839208i \(0.316981\pi\)
\(182\) 0 0
\(183\) −1275.98 2749.95i −0.515427 1.11083i
\(184\) 0 0
\(185\) 4329.20i 1.72048i
\(186\) 0 0
\(187\) 2681.61i 1.04865i
\(188\) 0 0
\(189\) −259.573 + 947.148i −0.0999003 + 0.364523i
\(190\) 0 0
\(191\) 864.174 0.327379 0.163690 0.986512i \(-0.447660\pi\)
0.163690 + 0.986512i \(0.447660\pi\)
\(192\) 0 0
\(193\) −1133.69 −0.422822 −0.211411 0.977397i \(-0.567806\pi\)
−0.211411 + 0.977397i \(0.567806\pi\)
\(194\) 0 0
\(195\) 3832.36 1778.21i 1.40739 0.653029i
\(196\) 0 0
\(197\) 1642.58i 0.594056i −0.954869 0.297028i \(-0.904004\pi\)
0.954869 0.297028i \(-0.0959955\pi\)
\(198\) 0 0
\(199\) 4912.39i 1.74990i 0.484213 + 0.874950i \(0.339106\pi\)
−0.484213 + 0.874950i \(0.660894\pi\)
\(200\) 0 0
\(201\) −2776.96 + 1288.51i −0.974487 + 0.452162i
\(202\) 0 0
\(203\) −344.214 −0.119010
\(204\) 0 0
\(205\) 3120.59 1.06318
\(206\) 0 0
\(207\) −2008.68 + 2375.49i −0.674458 + 0.797623i
\(208\) 0 0
\(209\) 3004.79i 0.994476i
\(210\) 0 0
\(211\) 928.566i 0.302963i 0.988460 + 0.151481i \(0.0484043\pi\)
−0.988460 + 0.151481i \(0.951596\pi\)
\(212\) 0 0
\(213\) 1676.00 + 3612.07i 0.539145 + 1.16195i
\(214\) 0 0
\(215\) −2416.48 −0.766523
\(216\) 0 0
\(217\) −88.0248 −0.0275369
\(218\) 0 0
\(219\) −1978.80 4264.64i −0.610569 1.31588i
\(220\) 0 0
\(221\) 4818.58i 1.46666i
\(222\) 0 0
\(223\) 208.318i 0.0625561i −0.999511 0.0312781i \(-0.990042\pi\)
0.999511 0.0312781i \(-0.00995774\pi\)
\(224\) 0 0
\(225\) 1529.42 1808.71i 0.453161 0.535915i
\(226\) 0 0
\(227\) −6151.95 −1.79876 −0.899382 0.437165i \(-0.855983\pi\)
−0.899382 + 0.437165i \(0.855983\pi\)
\(228\) 0 0
\(229\) 1493.71 0.431035 0.215518 0.976500i \(-0.430856\pi\)
0.215518 + 0.976500i \(0.430856\pi\)
\(230\) 0 0
\(231\) −1023.59 + 474.947i −0.291547 + 0.135278i
\(232\) 0 0
\(233\) 1003.48i 0.282146i 0.989999 + 0.141073i \(0.0450552\pi\)
−0.989999 + 0.141073i \(0.954945\pi\)
\(234\) 0 0
\(235\) 6215.27i 1.72527i
\(236\) 0 0
\(237\) −2165.56 + 1004.82i −0.593536 + 0.275401i
\(238\) 0 0
\(239\) −6048.49 −1.63701 −0.818503 0.574502i \(-0.805196\pi\)
−0.818503 + 0.574502i \(0.805196\pi\)
\(240\) 0 0
\(241\) −5619.61 −1.50204 −0.751018 0.660282i \(-0.770437\pi\)
−0.751018 + 0.660282i \(0.770437\pi\)
\(242\) 0 0
\(243\) 3123.41 2143.18i 0.824555 0.565782i
\(244\) 0 0
\(245\) 714.675i 0.186363i
\(246\) 0 0
\(247\) 5399.31i 1.39089i
\(248\) 0 0
\(249\) −2439.11 5256.69i −0.620771 1.33787i
\(250\) 0 0
\(251\) 6402.41 1.61003 0.805013 0.593257i \(-0.202158\pi\)
0.805013 + 0.593257i \(0.202158\pi\)
\(252\) 0 0
\(253\) −3574.47 −0.888241
\(254\) 0 0
\(255\) 2757.26 + 5942.37i 0.677124 + 1.45932i
\(256\) 0 0
\(257\) 1609.20i 0.390580i 0.980746 + 0.195290i \(0.0625648\pi\)
−0.980746 + 0.195290i \(0.937435\pi\)
\(258\) 0 0
\(259\) 2077.75i 0.498475i
\(260\) 0 0
\(261\) 1013.82 + 857.271i 0.240436 + 0.203309i
\(262\) 0 0
\(263\) −1897.73 −0.444940 −0.222470 0.974940i \(-0.571412\pi\)
−0.222470 + 0.974940i \(0.571412\pi\)
\(264\) 0 0
\(265\) −6720.38 −1.55785
\(266\) 0 0
\(267\) −565.146 + 262.228i −0.129537 + 0.0601053i
\(268\) 0 0
\(269\) 3874.72i 0.878238i 0.898429 + 0.439119i \(0.144709\pi\)
−0.898429 + 0.439119i \(0.855291\pi\)
\(270\) 0 0
\(271\) 1292.92i 0.289813i 0.989445 + 0.144906i \(0.0462881\pi\)
−0.989445 + 0.144906i \(0.953712\pi\)
\(272\) 0 0
\(273\) −1839.29 + 853.433i −0.407762 + 0.189202i
\(274\) 0 0
\(275\) 2721.62 0.596800
\(276\) 0 0
\(277\) −5644.74 −1.22440 −0.612202 0.790702i \(-0.709716\pi\)
−0.612202 + 0.790702i \(0.709716\pi\)
\(278\) 0 0
\(279\) 259.261 + 219.227i 0.0556328 + 0.0470422i
\(280\) 0 0
\(281\) 1146.55i 0.243407i −0.992566 0.121704i \(-0.961164\pi\)
0.992566 0.121704i \(-0.0388357\pi\)
\(282\) 0 0
\(283\) 5222.40i 1.09696i 0.836164 + 0.548479i \(0.184793\pi\)
−0.836164 + 0.548479i \(0.815207\pi\)
\(284\) 0 0
\(285\) −3089.57 6658.54i −0.642141 1.38392i
\(286\) 0 0
\(287\) −1497.69 −0.308034
\(288\) 0 0
\(289\) −2558.59 −0.520780
\(290\) 0 0
\(291\) −723.951 1560.24i −0.145838 0.314305i
\(292\) 0 0
\(293\) 4783.47i 0.953765i −0.878967 0.476883i \(-0.841767\pi\)
0.878967 0.476883i \(-0.158233\pi\)
\(294\) 0 0
\(295\) 10011.0i 1.97581i
\(296\) 0 0
\(297\) 4197.67 + 1150.40i 0.820112 + 0.224758i
\(298\) 0 0
\(299\) −6422.97 −1.24231
\(300\) 0 0
\(301\) 1159.76 0.222085
\(302\) 0 0
\(303\) 7584.74 3519.32i 1.43806 0.667260i
\(304\) 0 0
\(305\) 8509.36i 1.59752i
\(306\) 0 0
\(307\) 9710.23i 1.80519i −0.430494 0.902593i \(-0.641661\pi\)
0.430494 0.902593i \(-0.358339\pi\)
\(308\) 0 0
\(309\) −6546.84 + 3037.74i −1.20530 + 0.559258i
\(310\) 0 0
\(311\) 3463.09 0.631427 0.315713 0.948855i \(-0.397756\pi\)
0.315713 + 0.948855i \(0.397756\pi\)
\(312\) 0 0
\(313\) 2972.44 0.536780 0.268390 0.963310i \(-0.413508\pi\)
0.268390 + 0.963310i \(0.413508\pi\)
\(314\) 0 0
\(315\) −1779.91 + 2104.94i −0.318370 + 0.376508i
\(316\) 0 0
\(317\) 1056.65i 0.187217i −0.995609 0.0936083i \(-0.970160\pi\)
0.995609 0.0936083i \(-0.0298401\pi\)
\(318\) 0 0
\(319\) 1525.52i 0.267752i
\(320\) 0 0
\(321\) 1098.70 + 2367.88i 0.191038 + 0.411720i
\(322\) 0 0
\(323\) 8372.06 1.44221
\(324\) 0 0
\(325\) 4890.48 0.834693
\(326\) 0 0
\(327\) 3499.02 + 7540.97i 0.591731 + 1.27528i
\(328\) 0 0
\(329\) 2982.94i 0.499863i
\(330\) 0 0
\(331\) 11409.6i 1.89465i −0.320279 0.947323i \(-0.603777\pi\)
0.320279 0.947323i \(-0.396223\pi\)
\(332\) 0 0
\(333\) 5174.67 6119.63i 0.851562 1.00707i
\(334\) 0 0
\(335\) −8592.94 −1.40144
\(336\) 0 0
\(337\) −6052.69 −0.978371 −0.489185 0.872180i \(-0.662706\pi\)
−0.489185 + 0.872180i \(0.662706\pi\)
\(338\) 0 0
\(339\) −4402.45 + 2042.74i −0.705335 + 0.327276i
\(340\) 0 0
\(341\) 390.117i 0.0619532i
\(342\) 0 0
\(343\) 343.000i 0.0539949i
\(344\) 0 0
\(345\) −7920.94 + 3675.32i −1.23608 + 0.573543i
\(346\) 0 0
\(347\) −1661.68 −0.257071 −0.128535 0.991705i \(-0.541028\pi\)
−0.128535 + 0.991705i \(0.541028\pi\)
\(348\) 0 0
\(349\) −5890.92 −0.903535 −0.451768 0.892136i \(-0.649206\pi\)
−0.451768 + 0.892136i \(0.649206\pi\)
\(350\) 0 0
\(351\) 7542.79 + 2067.16i 1.14702 + 0.314350i
\(352\) 0 0
\(353\) 4847.63i 0.730916i 0.930828 + 0.365458i \(0.119088\pi\)
−0.930828 + 0.365458i \(0.880912\pi\)
\(354\) 0 0
\(355\) 11177.1i 1.67104i
\(356\) 0 0
\(357\) −1323.32 2851.97i −0.196183 0.422808i
\(358\) 0 0
\(359\) 9508.69 1.39791 0.698954 0.715166i \(-0.253649\pi\)
0.698954 + 0.715166i \(0.253649\pi\)
\(360\) 0 0
\(361\) −2522.04 −0.367699
\(362\) 0 0
\(363\) −806.046 1737.17i −0.116547 0.251178i
\(364\) 0 0
\(365\) 13196.4i 1.89241i
\(366\) 0 0
\(367\) 3663.26i 0.521037i −0.965469 0.260518i \(-0.916106\pi\)
0.965469 0.260518i \(-0.0838935\pi\)
\(368\) 0 0
\(369\) 4411.17 + 3730.02i 0.622321 + 0.526225i
\(370\) 0 0
\(371\) 3225.37 0.451355
\(372\) 0 0
\(373\) 6227.72 0.864502 0.432251 0.901753i \(-0.357720\pi\)
0.432251 + 0.901753i \(0.357720\pi\)
\(374\) 0 0
\(375\) −2562.32 + 1188.92i −0.352847 + 0.163721i
\(376\) 0 0
\(377\) 2741.22i 0.374482i
\(378\) 0 0
\(379\) 5881.91i 0.797186i 0.917128 + 0.398593i \(0.130501\pi\)
−0.917128 + 0.398593i \(0.869499\pi\)
\(380\) 0 0
\(381\) −1420.43 + 659.079i −0.190999 + 0.0886237i
\(382\) 0 0
\(383\) −3238.56 −0.432069 −0.216035 0.976386i \(-0.569312\pi\)
−0.216035 + 0.976386i \(0.569312\pi\)
\(384\) 0 0
\(385\) −3167.37 −0.419284
\(386\) 0 0
\(387\) −3415.86 2888.40i −0.448677 0.379395i
\(388\) 0 0
\(389\) 7962.71i 1.03785i 0.854818 + 0.518927i \(0.173668\pi\)
−0.854818 + 0.518927i \(0.826332\pi\)
\(390\) 0 0
\(391\) 9959.32i 1.28814i
\(392\) 0 0
\(393\) −851.521 1835.17i −0.109297 0.235553i
\(394\) 0 0
\(395\) −6701.03 −0.853583
\(396\) 0 0
\(397\) −5784.53 −0.731277 −0.365639 0.930757i \(-0.619149\pi\)
−0.365639 + 0.930757i \(0.619149\pi\)
\(398\) 0 0
\(399\) 1482.80 + 3195.69i 0.186047 + 0.400964i
\(400\) 0 0
\(401\) 2460.74i 0.306443i 0.988192 + 0.153221i \(0.0489647\pi\)
−0.988192 + 0.153221i \(0.951035\pi\)
\(402\) 0 0
\(403\) 701.002i 0.0866486i
\(404\) 0 0
\(405\) 10484.8 1766.84i 1.28640 0.216777i
\(406\) 0 0
\(407\) 9208.39 1.12148
\(408\) 0 0
\(409\) 12763.1 1.54301 0.771507 0.636221i \(-0.219503\pi\)
0.771507 + 0.636221i \(0.219503\pi\)
\(410\) 0 0
\(411\) −14315.0 + 6642.16i −1.71802 + 0.797162i
\(412\) 0 0
\(413\) 4804.67i 0.572452i
\(414\) 0 0
\(415\) 16266.1i 1.92403i
\(416\) 0 0
\(417\) −6067.07 + 2815.12i −0.712483 + 0.330593i
\(418\) 0 0
\(419\) −7332.36 −0.854915 −0.427457 0.904035i \(-0.640591\pi\)
−0.427457 + 0.904035i \(0.640591\pi\)
\(420\) 0 0
\(421\) 11584.3 1.34106 0.670528 0.741885i \(-0.266068\pi\)
0.670528 + 0.741885i \(0.266068\pi\)
\(422\) 0 0
\(423\) −7429.07 + 8785.71i −0.853933 + 1.00987i
\(424\) 0 0
\(425\) 7583.09i 0.865491i
\(426\) 0 0
\(427\) 4083.97i 0.462850i
\(428\) 0 0
\(429\) 3782.33 + 8151.57i 0.425671 + 0.917393i
\(430\) 0 0
\(431\) −973.251 −0.108770 −0.0543850 0.998520i \(-0.517320\pi\)
−0.0543850 + 0.998520i \(0.517320\pi\)
\(432\) 0 0
\(433\) −6021.08 −0.668256 −0.334128 0.942528i \(-0.608442\pi\)
−0.334128 + 0.942528i \(0.608442\pi\)
\(434\) 0 0
\(435\) 1568.56 + 3380.52i 0.172890 + 0.372606i
\(436\) 0 0
\(437\) 11159.6i 1.22159i
\(438\) 0 0
\(439\) 4643.72i 0.504858i 0.967615 + 0.252429i \(0.0812295\pi\)
−0.967615 + 0.252429i \(0.918771\pi\)
\(440\) 0 0
\(441\) 854.247 1010.24i 0.0922413 0.109086i
\(442\) 0 0
\(443\) 14381.2 1.54238 0.771189 0.636606i \(-0.219662\pi\)
0.771189 + 0.636606i \(0.219662\pi\)
\(444\) 0 0
\(445\) −1748.77 −0.186291
\(446\) 0 0
\(447\) −9669.40 + 4486.61i −1.02315 + 0.474741i
\(448\) 0 0
\(449\) 10241.0i 1.07639i 0.842819 + 0.538197i \(0.180894\pi\)
−0.842819 + 0.538197i \(0.819106\pi\)
\(450\) 0 0
\(451\) 6637.62i 0.693023i
\(452\) 0 0
\(453\) −2231.99 + 1035.65i −0.231497 + 0.107415i
\(454\) 0 0
\(455\) −5691.45 −0.586416
\(456\) 0 0
\(457\) 18144.7 1.85728 0.928638 0.370988i \(-0.120981\pi\)
0.928638 + 0.370988i \(0.120981\pi\)
\(458\) 0 0
\(459\) −3205.29 + 11695.7i −0.325948 + 1.18934i
\(460\) 0 0
\(461\) 10005.2i 1.01083i −0.862877 0.505413i \(-0.831340\pi\)
0.862877 0.505413i \(-0.168660\pi\)
\(462\) 0 0
\(463\) 13659.6i 1.37109i −0.728031 0.685544i \(-0.759564\pi\)
0.728031 0.685544i \(-0.240436\pi\)
\(464\) 0 0
\(465\) 401.124 + 864.491i 0.0400036 + 0.0862146i
\(466\) 0 0
\(467\) 11500.9 1.13961 0.569804 0.821781i \(-0.307019\pi\)
0.569804 + 0.821781i \(0.307019\pi\)
\(468\) 0 0
\(469\) 4124.08 0.406039
\(470\) 0 0
\(471\) 2591.24 + 5584.56i 0.253499 + 0.546333i
\(472\) 0 0
\(473\) 5139.95i 0.499651i
\(474\) 0 0
\(475\) 8496.99i 0.820776i
\(476\) 0 0
\(477\) −9499.73 8032.83i −0.911871 0.771065i
\(478\) 0 0
\(479\) −3223.54 −0.307489 −0.153745 0.988111i \(-0.549133\pi\)
−0.153745 + 0.988111i \(0.549133\pi\)
\(480\) 0 0
\(481\) 16546.6 1.56852
\(482\) 0 0
\(483\) 3801.56 1763.93i 0.358131 0.166173i
\(484\) 0 0
\(485\) 4827.95i 0.452012i
\(486\) 0 0
\(487\) 13316.6i 1.23908i −0.784964 0.619542i \(-0.787318\pi\)
0.784964 0.619542i \(-0.212682\pi\)
\(488\) 0 0
\(489\) 19114.3 8869.03i 1.76764 0.820187i
\(490\) 0 0
\(491\) −4229.41 −0.388739 −0.194369 0.980928i \(-0.562266\pi\)
−0.194369 + 0.980928i \(0.562266\pi\)
\(492\) 0 0
\(493\) −4250.47 −0.388300
\(494\) 0 0
\(495\) 9328.91 + 7888.38i 0.847077 + 0.716276i
\(496\) 0 0
\(497\) 5364.31i 0.484149i
\(498\) 0 0
\(499\) 2412.58i 0.216437i −0.994127 0.108219i \(-0.965485\pi\)
0.994127 0.108219i \(-0.0345146\pi\)
\(500\) 0 0
\(501\) 8051.05 + 17351.4i 0.717953 + 1.54731i
\(502\) 0 0
\(503\) 6942.70 0.615427 0.307714 0.951479i \(-0.400436\pi\)
0.307714 + 0.951479i \(0.400436\pi\)
\(504\) 0 0
\(505\) 23470.0 2.06812
\(506\) 0 0
\(507\) 1991.52 + 4292.07i 0.174451 + 0.375972i
\(508\) 0 0
\(509\) 5335.45i 0.464616i −0.972642 0.232308i \(-0.925372\pi\)
0.972642 0.232308i \(-0.0746278\pi\)
\(510\) 0 0
\(511\) 6333.44i 0.548288i
\(512\) 0 0
\(513\) 3591.59 13105.2i 0.309108 1.12790i
\(514\) 0 0
\(515\) −20258.3 −1.73337
\(516\) 0 0
\(517\) −13220.1 −1.12460
\(518\) 0 0
\(519\) −5039.97 + 2338.55i −0.426262 + 0.197786i
\(520\) 0 0
\(521\) 4804.38i 0.404000i −0.979386 0.202000i \(-0.935256\pi\)
0.979386 0.202000i \(-0.0647440\pi\)
\(522\) 0 0
\(523\) 20692.5i 1.73006i −0.501722 0.865029i \(-0.667300\pi\)
0.501722 0.865029i \(-0.332700\pi\)
\(524\) 0 0
\(525\) −2894.53 + 1343.06i −0.240624 + 0.111650i
\(526\) 0 0
\(527\) −1086.96 −0.0898458
\(528\) 0 0
\(529\) 1108.36 0.0910959
\(530\) 0 0
\(531\) 11966.1 14151.3i 0.977938 1.15652i
\(532\) 0 0
\(533\) 11927.1i 0.969271i
\(534\) 0 0
\(535\) 7327.09i 0.592108i
\(536\) 0 0
\(537\) 5831.93 + 12568.8i 0.468652 + 1.01003i
\(538\) 0 0
\(539\) 1520.14 0.121479
\(540\) 0 0
\(541\) −5176.25 −0.411357 −0.205679 0.978620i \(-0.565940\pi\)
−0.205679 + 0.978620i \(0.565940\pi\)
\(542\) 0 0
\(543\) 5792.34 + 12483.5i 0.457777 + 0.986588i
\(544\) 0 0
\(545\) 23334.5i 1.83402i
\(546\) 0 0
\(547\) 439.585i 0.0343607i 0.999852 + 0.0171804i \(0.00546895\pi\)
−0.999852 + 0.0171804i \(0.994531\pi\)
\(548\) 0 0
\(549\) 10171.2 12028.6i 0.790702 0.935095i
\(550\) 0 0
\(551\) 4762.73 0.368238
\(552\) 0 0
\(553\) 3216.08 0.247309
\(554\) 0 0
\(555\) 20405.6 9468.20i 1.56066 0.724149i
\(556\) 0 0
\(557\) 19663.7i 1.49583i −0.663795 0.747914i \(-0.731055\pi\)
0.663795 0.747914i \(-0.268945\pi\)
\(558\) 0 0
\(559\) 9235.97i 0.698819i
\(560\) 0 0
\(561\) −12639.7 + 5864.81i −0.951243 + 0.441377i
\(562\) 0 0
\(563\) 3268.52 0.244675 0.122337 0.992489i \(-0.460961\pi\)
0.122337 + 0.992489i \(0.460961\pi\)
\(564\) 0 0
\(565\) −13622.8 −1.01436
\(566\) 0 0
\(567\) −5032.05 + 847.973i −0.372710 + 0.0628069i
\(568\) 0 0
\(569\) 12364.5i 0.910980i 0.890241 + 0.455490i \(0.150536\pi\)
−0.890241 + 0.455490i \(0.849464\pi\)
\(570\) 0 0
\(571\) 12593.6i 0.922990i 0.887143 + 0.461495i \(0.152687\pi\)
−0.887143 + 0.461495i \(0.847313\pi\)
\(572\) 0 0
\(573\) 1889.99 + 4073.26i 0.137793 + 0.296968i
\(574\) 0 0
\(575\) −10107.9 −0.733096
\(576\) 0 0
\(577\) −13016.7 −0.939156 −0.469578 0.882891i \(-0.655594\pi\)
−0.469578 + 0.882891i \(0.655594\pi\)
\(578\) 0 0
\(579\) −2479.43 5343.60i −0.177965 0.383545i
\(580\) 0 0
\(581\) 7806.74i 0.557449i
\(582\) 0 0
\(583\) 14294.5i 1.01547i
\(584\) 0 0
\(585\) 16763.1 + 14174.6i 1.18473 + 1.00179i
\(586\) 0 0
\(587\) 16247.0 1.14240 0.571199 0.820812i \(-0.306479\pi\)
0.571199 + 0.820812i \(0.306479\pi\)
\(588\) 0 0
\(589\) 1217.96 0.0852039
\(590\) 0 0
\(591\) 7742.26 3592.41i 0.538873 0.250037i
\(592\) 0 0
\(593\) 17711.4i 1.22651i −0.789885 0.613256i \(-0.789860\pi\)
0.789885 0.613256i \(-0.210140\pi\)
\(594\) 0 0
\(595\) 8825.05i 0.608053i
\(596\) 0 0
\(597\) −23154.4 + 10743.7i −1.58735 + 0.736530i
\(598\) 0 0
\(599\) 8240.46 0.562097 0.281048 0.959694i \(-0.409318\pi\)
0.281048 + 0.959694i \(0.409318\pi\)
\(600\) 0 0
\(601\) 5366.47 0.364231 0.182116 0.983277i \(-0.441706\pi\)
0.182116 + 0.983277i \(0.441706\pi\)
\(602\) 0 0
\(603\) −12146.7 10271.1i −0.820320 0.693650i
\(604\) 0 0
\(605\) 5375.43i 0.361227i
\(606\) 0 0
\(607\) 7742.72i 0.517739i 0.965912 + 0.258869i \(0.0833499\pi\)
−0.965912 + 0.258869i \(0.916650\pi\)
\(608\) 0 0
\(609\) −752.814 1622.44i −0.0500913 0.107955i
\(610\) 0 0
\(611\) −23755.2 −1.57289
\(612\) 0 0
\(613\) 2581.09 0.170064 0.0850320 0.996378i \(-0.472901\pi\)
0.0850320 + 0.996378i \(0.472901\pi\)
\(614\) 0 0
\(615\) 6824.89 + 14708.8i 0.447490 + 0.964416i
\(616\) 0 0
\(617\) 5974.41i 0.389823i 0.980821 + 0.194911i \(0.0624419\pi\)
−0.980821 + 0.194911i \(0.937558\pi\)
\(618\) 0 0
\(619\) 6142.33i 0.398839i 0.979914 + 0.199419i \(0.0639056\pi\)
−0.979914 + 0.199419i \(0.936094\pi\)
\(620\) 0 0
\(621\) −15589.9 4272.52i −1.00741 0.276088i
\(622\) 0 0
\(623\) 839.302 0.0539742
\(624\) 0 0
\(625\) −18894.8 −1.20927
\(626\) 0 0
\(627\) 14163.0 6571.63i 0.902097 0.418574i
\(628\) 0 0
\(629\) 25656.8i 1.62639i
\(630\) 0 0
\(631\) 4185.65i 0.264070i −0.991245 0.132035i \(-0.957849\pi\)
0.991245 0.132035i \(-0.0421511\pi\)
\(632\) 0 0
\(633\) −4376.77 + 2030.82i −0.274820 + 0.127517i
\(634\) 0 0
\(635\) −4395.32 −0.274682
\(636\) 0 0
\(637\) 2731.55 0.169902
\(638\) 0 0
\(639\) −13359.9 + 15799.6i −0.827088 + 0.978125i
\(640\) 0 0
\(641\) 11627.2i 0.716452i −0.933635 0.358226i \(-0.883382\pi\)
0.933635 0.358226i \(-0.116618\pi\)
\(642\) 0 0
\(643\) 30093.1i 1.84565i 0.385215 + 0.922827i \(0.374127\pi\)
−0.385215 + 0.922827i \(0.625873\pi\)
\(644\) 0 0
\(645\) −5284.96 11390.0i −0.322628 0.695319i
\(646\) 0 0
\(647\) −23676.7 −1.43868 −0.719340 0.694659i \(-0.755555\pi\)
−0.719340 + 0.694659i \(0.755555\pi\)
\(648\) 0 0
\(649\) 21293.8 1.28791
\(650\) 0 0
\(651\) −192.515 414.902i −0.0115902 0.0249790i
\(652\) 0 0
\(653\) 13535.0i 0.811126i −0.914067 0.405563i \(-0.867076\pi\)
0.914067 0.405563i \(-0.132924\pi\)
\(654\) 0 0
\(655\) 5678.70i 0.338756i
\(656\) 0 0
\(657\) 15773.5 18654.0i 0.936658 1.10770i
\(658\) 0 0
\(659\) −4587.12 −0.271152 −0.135576 0.990767i \(-0.543288\pi\)
−0.135576 + 0.990767i \(0.543288\pi\)
\(660\) 0 0
\(661\) −22014.3 −1.29540 −0.647698 0.761897i \(-0.724268\pi\)
−0.647698 + 0.761897i \(0.724268\pi\)
\(662\) 0 0
\(663\) −22712.2 + 10538.5i −1.33042 + 0.617316i
\(664\) 0 0
\(665\) 9888.63i 0.576639i
\(666\) 0 0
\(667\) 5665.70i 0.328901i
\(668\) 0 0
\(669\) 981.902 455.603i 0.0567452 0.0263298i
\(670\) 0 0
\(671\) 18099.8 1.04133
\(672\) 0 0
\(673\) 5312.83 0.304301 0.152150 0.988357i \(-0.451380\pi\)
0.152150 + 0.988357i \(0.451380\pi\)
\(674\) 0 0
\(675\) 11870.2 + 3253.13i 0.676867 + 0.185501i
\(676\) 0 0
\(677\) 31630.1i 1.79563i −0.440372 0.897815i \(-0.645154\pi\)
0.440372 0.897815i \(-0.354846\pi\)
\(678\) 0 0
\(679\) 2317.12i 0.130961i
\(680\) 0 0
\(681\) −13454.6 28997.0i −0.757097 1.63167i
\(682\) 0 0
\(683\) 16304.5 0.913435 0.456718 0.889612i \(-0.349025\pi\)
0.456718 + 0.889612i \(0.349025\pi\)
\(684\) 0 0
\(685\) −44295.8 −2.47074
\(686\) 0 0
\(687\) 3266.82 + 7040.55i 0.181422 + 0.390995i
\(688\) 0 0
\(689\) 25685.8i 1.42025i
\(690\) 0 0
\(691\) 9225.62i 0.507900i 0.967217 + 0.253950i \(0.0817299\pi\)
−0.967217 + 0.253950i \(0.918270\pi\)
\(692\) 0 0
\(693\) −4477.30 3785.94i −0.245424 0.207527i
\(694\) 0 0
\(695\) −18773.7 −1.02464
\(696\) 0 0
\(697\) −18494.0 −1.00504
\(698\) 0 0
\(699\) −4729.86 + 2194.66i −0.255937 + 0.118755i
\(700\) 0 0
\(701\) 4759.97i 0.256464i 0.991744 + 0.128232i \(0.0409303\pi\)
−0.991744 + 0.128232i \(0.959070\pi\)
\(702\) 0 0
\(703\) 28748.9i 1.54237i
\(704\) 0 0
\(705\) −29295.5 + 13593.1i −1.56501 + 0.726165i
\(706\) 0 0
\(707\) −11264.1 −0.599196
\(708\) 0 0
\(709\) 29605.9 1.56823 0.784114 0.620617i \(-0.213118\pi\)
0.784114 + 0.620617i \(0.213118\pi\)
\(710\) 0 0
\(711\) −9472.38 8009.70i −0.499637 0.422485i
\(712\) 0 0
\(713\) 1448.87i 0.0761020i
\(714\) 0 0
\(715\) 25224.0i 1.31933i
\(716\) 0 0
\(717\) −13228.4 28509.4i −0.689013 1.48494i
\(718\) 0 0
\(719\) −34086.2 −1.76801 −0.884007 0.467474i \(-0.845164\pi\)
−0.884007 + 0.467474i \(0.845164\pi\)
\(720\) 0 0
\(721\) 9722.74 0.502211
\(722\) 0 0
\(723\) −12290.4 26487.8i −0.632204 1.36251i
\(724\) 0 0
\(725\) 4313.90i 0.220985i
\(726\) 0 0
\(727\) 15552.2i 0.793396i 0.917949 + 0.396698i \(0.129844\pi\)
−0.917949 + 0.396698i \(0.870156\pi\)
\(728\) 0 0
\(729\) 16932.9 + 10034.9i 0.860279 + 0.509823i
\(730\) 0 0
\(731\) 14321.1 0.724604
\(732\) 0 0
\(733\) −1511.48 −0.0761636 −0.0380818 0.999275i \(-0.512125\pi\)
−0.0380818 + 0.999275i \(0.512125\pi\)
\(734\) 0 0
\(735\) 3368.60 1563.03i 0.169051 0.0784399i
\(736\) 0 0
\(737\) 18277.5i 0.913517i
\(738\) 0 0
\(739\) 6749.94i 0.335995i 0.985787 + 0.167998i \(0.0537301\pi\)
−0.985787 + 0.167998i \(0.946270\pi\)
\(740\) 0 0
\(741\) 25449.5 11808.6i 1.26169 0.585423i
\(742\) 0 0
\(743\) 24008.4 1.18544 0.592719 0.805409i \(-0.298054\pi\)
0.592719 + 0.805409i \(0.298054\pi\)
\(744\) 0 0
\(745\) −29920.7 −1.47142
\(746\) 0 0
\(747\) 19442.8 22993.3i 0.952309 1.12621i
\(748\) 0 0
\(749\) 3516.55i 0.171552i
\(750\) 0 0
\(751\) 35758.5i 1.73748i 0.495272 + 0.868738i \(0.335069\pi\)
−0.495272 + 0.868738i \(0.664931\pi\)
\(752\) 0 0
\(753\) 14002.4 + 30177.6i 0.677658 + 1.46047i
\(754\) 0 0
\(755\) −6906.61 −0.332924
\(756\) 0 0
\(757\) −12640.7 −0.606916 −0.303458 0.952845i \(-0.598141\pi\)
−0.303458 + 0.952845i \(0.598141\pi\)
\(758\) 0 0
\(759\) −7817.55 16848.2i −0.373859 0.805730i
\(760\) 0 0
\(761\) 28346.1i 1.35026i 0.737699 + 0.675129i \(0.235912\pi\)
−0.737699 + 0.675129i \(0.764088\pi\)
\(762\) 0 0
\(763\) 11199.1i 0.531371i
\(764\) 0 0
\(765\) −21978.9 + 25992.6i −1.03876 + 1.22845i
\(766\) 0 0
\(767\) 38262.9 1.80130
\(768\) 0 0
\(769\) −15226.0 −0.713999 −0.356999 0.934105i \(-0.616200\pi\)
−0.356999 + 0.934105i \(0.616200\pi\)
\(770\) 0 0
\(771\) −7584.91 + 3519.40i −0.354298 + 0.164395i
\(772\) 0 0
\(773\) 20084.4i 0.934522i 0.884119 + 0.467261i \(0.154759\pi\)
−0.884119 + 0.467261i \(0.845241\pi\)
\(774\) 0 0
\(775\) 1103.18i 0.0511321i
\(776\) 0 0
\(777\) −9793.42 + 4544.15i −0.452171 + 0.209808i
\(778\) 0 0
\(779\) 20722.8 0.953110
\(780\) 0 0
\(781\) −23774.1 −1.08925
\(782\) 0 0
\(783\) −1823.44 + 6653.50i −0.0832242 + 0.303674i
\(784\) 0 0
\(785\) 17280.7i 0.785699i
\(786\) 0 0
\(787\) 18800.0i 0.851522i 0.904836 + 0.425761i \(0.139994\pi\)
−0.904836 + 0.425761i \(0.860006\pi\)
\(788\) 0 0
\(789\) −4150.44 8944.91i −0.187275 0.403609i
\(790\) 0 0
\(791\) 6538.11 0.293892
\(792\) 0 0
\(793\) 32523.5 1.45642
\(794\) 0 0
\(795\) −14697.8 31676.3i −0.655696 1.41314i
\(796\) 0 0
\(797\) 28103.9i 1.24905i −0.781005 0.624524i \(-0.785293\pi\)
0.781005 0.624524i \(-0.214707\pi\)
\(798\)