Properties

Label 252.4.x.a.41.3
Level $252$
Weight $4$
Character 252.41
Analytic conductor $14.868$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.3
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.81916 + 1.94311i) q^{3} +(9.12012 - 15.7965i) q^{5} +(-9.48165 - 15.9091i) q^{7} +(19.4487 - 18.7283i) q^{9} +O(q^{10})\) \(q+(-4.81916 + 1.94311i) q^{3} +(9.12012 - 15.7965i) q^{5} +(-9.48165 - 15.9091i) q^{7} +(19.4487 - 18.7283i) q^{9} +(-49.3053 + 28.4664i) q^{11} +(9.36748 + 5.40831i) q^{13} +(-13.2570 + 93.8474i) q^{15} +65.2579 q^{17} +36.6039i q^{19} +(76.6067 + 58.2445i) q^{21} +(-70.2538 - 40.5611i) q^{23} +(-103.853 - 179.879i) q^{25} +(-57.3350 + 128.046i) q^{27} +(-233.584 + 134.860i) q^{29} +(-117.775 - 67.9976i) q^{31} +(182.297 - 232.990i) q^{33} +(-337.782 + 4.68434i) q^{35} -125.675 q^{37} +(-55.6523 - 7.86151i) q^{39} +(-117.524 + 203.557i) q^{41} +(22.6360 + 39.2067i) q^{43} +(-118.468 - 478.026i) q^{45} +(-241.097 - 417.592i) q^{47} +(-163.197 + 301.688i) q^{49} +(-314.488 + 126.803i) q^{51} -70.1770i q^{53} +1038.47i q^{55} +(-71.1255 - 176.400i) q^{57} +(176.673 - 306.007i) q^{59} +(512.605 - 295.953i) q^{61} +(-482.355 - 131.835i) q^{63} +(170.865 - 98.6490i) q^{65} +(-261.925 + 453.667i) q^{67} +(417.379 + 58.9595i) q^{69} -895.977i q^{71} +982.681i q^{73} +(850.011 + 665.069i) q^{75} +(920.369 + 514.492i) q^{77} +(510.195 + 883.684i) q^{79} +(27.5000 - 728.481i) q^{81} +(152.345 + 263.869i) q^{83} +(595.160 - 1030.85i) q^{85} +(863.632 - 1103.79i) q^{87} -1022.58 q^{89} +(-2.77785 - 200.308i) q^{91} +(699.705 + 98.8412i) q^{93} +(578.215 + 333.833i) q^{95} +(-677.719 + 391.281i) q^{97} +(-425.793 + 1477.04i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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
\(3\) −4.81916 + 1.94311i −0.927448 + 0.373952i
\(4\) 0 0
\(5\) 9.12012 15.7965i 0.815729 1.41288i −0.0930747 0.995659i \(-0.529670\pi\)
0.908803 0.417225i \(-0.136997\pi\)
\(6\) 0 0
\(7\) −9.48165 15.9091i −0.511961 0.859009i
\(8\) 0 0
\(9\) 19.4487 18.7283i 0.720320 0.693642i
\(10\) 0 0
\(11\) −49.3053 + 28.4664i −1.35146 + 0.780268i −0.988455 0.151518i \(-0.951584\pi\)
−0.363009 + 0.931786i \(0.618251\pi\)
\(12\) 0 0
\(13\) 9.36748 + 5.40831i 0.199852 + 0.115384i 0.596586 0.802549i \(-0.296523\pi\)
−0.396735 + 0.917933i \(0.629857\pi\)
\(14\) 0 0
\(15\) −13.2570 + 93.8474i −0.228196 + 1.61542i
\(16\) 0 0
\(17\) 65.2579 0.931021 0.465511 0.885042i \(-0.345871\pi\)
0.465511 + 0.885042i \(0.345871\pi\)
\(18\) 0 0
\(19\) 36.6039i 0.441975i 0.975277 + 0.220987i \(0.0709280\pi\)
−0.975277 + 0.220987i \(0.929072\pi\)
\(20\) 0 0
\(21\) 76.6067 + 58.2445i 0.796045 + 0.605238i
\(22\) 0 0
\(23\) −70.2538 40.5611i −0.636910 0.367720i 0.146513 0.989209i \(-0.453195\pi\)
−0.783423 + 0.621489i \(0.786528\pi\)
\(24\) 0 0
\(25\) −103.853 179.879i −0.830827 1.43903i
\(26\) 0 0
\(27\) −57.3350 + 128.046i −0.408671 + 0.912682i
\(28\) 0 0
\(29\) −233.584 + 134.860i −1.49571 + 0.863546i −0.999988 0.00493734i \(-0.998428\pi\)
−0.495718 + 0.868484i \(0.665095\pi\)
\(30\) 0 0
\(31\) −117.775 67.9976i −0.682357 0.393959i 0.118385 0.992968i \(-0.462228\pi\)
−0.800743 + 0.599009i \(0.795562\pi\)
\(32\) 0 0
\(33\) 182.297 232.990i 0.961630 1.22904i
\(34\) 0 0
\(35\) −337.782 + 4.68434i −1.63130 + 0.0226228i
\(36\) 0 0
\(37\) −125.675 −0.558400 −0.279200 0.960233i \(-0.590069\pi\)
−0.279200 + 0.960233i \(0.590069\pi\)
\(38\) 0 0
\(39\) −55.6523 7.86151i −0.228500 0.0322782i
\(40\) 0 0
\(41\) −117.524 + 203.557i −0.447662 + 0.775374i −0.998233 0.0594145i \(-0.981077\pi\)
0.550571 + 0.834788i \(0.314410\pi\)
\(42\) 0 0
\(43\) 22.6360 + 39.2067i 0.0802780 + 0.139046i 0.903369 0.428863i \(-0.141086\pi\)
−0.823091 + 0.567909i \(0.807753\pi\)
\(44\) 0 0
\(45\) −118.468 478.026i −0.392449 1.58355i
\(46\) 0 0
\(47\) −241.097 417.592i −0.748246 1.29600i −0.948663 0.316290i \(-0.897563\pi\)
0.200416 0.979711i \(-0.435771\pi\)
\(48\) 0 0
\(49\) −163.197 + 301.688i −0.475792 + 0.879558i
\(50\) 0 0
\(51\) −314.488 + 126.803i −0.863474 + 0.348157i
\(52\) 0 0
\(53\) 70.1770i 0.181878i −0.995856 0.0909392i \(-0.971013\pi\)
0.995856 0.0909392i \(-0.0289869\pi\)
\(54\) 0 0
\(55\) 1038.47i 2.54595i
\(56\) 0 0
\(57\) −71.1255 176.400i −0.165277 0.409909i
\(58\) 0 0
\(59\) 176.673 306.007i 0.389845 0.675232i −0.602583 0.798056i \(-0.705862\pi\)
0.992428 + 0.122824i \(0.0391952\pi\)
\(60\) 0 0
\(61\) 512.605 295.953i 1.07594 0.621194i 0.146142 0.989264i \(-0.453314\pi\)
0.929798 + 0.368069i \(0.119981\pi\)
\(62\) 0 0
\(63\) −482.355 131.835i −0.964620 0.263644i
\(64\) 0 0
\(65\) 170.865 98.6490i 0.326049 0.188245i
\(66\) 0 0
\(67\) −261.925 + 453.667i −0.477600 + 0.827228i −0.999670 0.0256746i \(-0.991827\pi\)
0.522070 + 0.852903i \(0.325160\pi\)
\(68\) 0 0
\(69\) 417.379 + 58.9595i 0.728211 + 0.102868i
\(70\) 0 0
\(71\) 895.977i 1.49765i −0.662770 0.748823i \(-0.730619\pi\)
0.662770 0.748823i \(-0.269381\pi\)
\(72\) 0 0
\(73\) 982.681i 1.57554i 0.615972 + 0.787768i \(0.288763\pi\)
−0.615972 + 0.787768i \(0.711237\pi\)
\(74\) 0 0
\(75\) 850.011 + 665.069i 1.30868 + 1.02394i
\(76\) 0 0
\(77\) 920.369 + 514.492i 1.36215 + 0.761453i
\(78\) 0 0
\(79\) 510.195 + 883.684i 0.726601 + 1.25851i 0.958312 + 0.285725i \(0.0922343\pi\)
−0.231711 + 0.972785i \(0.574432\pi\)
\(80\) 0 0
\(81\) 27.5000 728.481i 0.0377229 0.999288i
\(82\) 0 0
\(83\) 152.345 + 263.869i 0.201470 + 0.348957i 0.949002 0.315269i \(-0.102095\pi\)
−0.747532 + 0.664226i \(0.768761\pi\)
\(84\) 0 0
\(85\) 595.160 1030.85i 0.759461 1.31542i
\(86\) 0 0
\(87\) 863.632 1103.79i 1.06427 1.36022i
\(88\) 0 0
\(89\) −1022.58 −1.21791 −0.608953 0.793206i \(-0.708410\pi\)
−0.608953 + 0.793206i \(0.708410\pi\)
\(90\) 0 0
\(91\) −2.77785 200.308i −0.00319998 0.230747i
\(92\) 0 0
\(93\) 699.705 + 98.8412i 0.780173 + 0.110208i
\(94\) 0 0
\(95\) 578.215 + 333.833i 0.624459 + 0.360532i
\(96\) 0 0
\(97\) −677.719 + 391.281i −0.709402 + 0.409573i −0.810839 0.585269i \(-0.800989\pi\)
0.101438 + 0.994842i \(0.467656\pi\)
\(98\) 0 0
\(99\) −425.793 + 1477.04i −0.432261 + 1.49947i
\(100\) 0 0
\(101\) −786.668 1362.55i −0.775014 1.34236i −0.934787 0.355209i \(-0.884410\pi\)
0.159773 0.987154i \(-0.448924\pi\)
\(102\) 0 0
\(103\) −597.068 344.717i −0.571174 0.329767i 0.186444 0.982466i \(-0.440304\pi\)
−0.757618 + 0.652698i \(0.773637\pi\)
\(104\) 0 0
\(105\) 1618.72 678.921i 1.50449 0.631009i
\(106\) 0 0
\(107\) 627.635i 0.567063i 0.958963 + 0.283532i \(0.0915061\pi\)
−0.958963 + 0.283532i \(0.908494\pi\)
\(108\) 0 0
\(109\) −1110.51 −0.975851 −0.487925 0.872885i \(-0.662246\pi\)
−0.487925 + 0.872885i \(0.662246\pi\)
\(110\) 0 0
\(111\) 605.647 244.200i 0.517887 0.208814i
\(112\) 0 0
\(113\) −1047.17 604.581i −0.871762 0.503312i −0.00382837 0.999993i \(-0.501219\pi\)
−0.867933 + 0.496681i \(0.834552\pi\)
\(114\) 0 0
\(115\) −1281.45 + 739.844i −1.03909 + 0.599920i
\(116\) 0 0
\(117\) 283.473 70.2527i 0.223993 0.0555116i
\(118\) 0 0
\(119\) −618.752 1038.19i −0.476646 0.799755i
\(120\) 0 0
\(121\) 955.174 1654.41i 0.717636 1.24298i
\(122\) 0 0
\(123\) 170.832 1209.34i 0.125231 0.886523i
\(124\) 0 0
\(125\) −1508.59 −1.07946
\(126\) 0 0
\(127\) 2687.40 1.87770 0.938850 0.344327i \(-0.111893\pi\)
0.938850 + 0.344327i \(0.111893\pi\)
\(128\) 0 0
\(129\) −185.269 144.959i −0.126450 0.0989375i
\(130\) 0 0
\(131\) −74.0557 + 128.268i −0.0493914 + 0.0855484i −0.889664 0.456616i \(-0.849062\pi\)
0.840273 + 0.542164i \(0.182395\pi\)
\(132\) 0 0
\(133\) 582.335 347.066i 0.379660 0.226274i
\(134\) 0 0
\(135\) 1499.77 + 2073.49i 0.956148 + 1.32191i
\(136\) 0 0
\(137\) 880.674 508.458i 0.549205 0.317084i −0.199596 0.979878i \(-0.563963\pi\)
0.748801 + 0.662795i \(0.230630\pi\)
\(138\) 0 0
\(139\) 2221.28 + 1282.46i 1.35544 + 0.782566i 0.989006 0.147877i \(-0.0472440\pi\)
0.366438 + 0.930443i \(0.380577\pi\)
\(140\) 0 0
\(141\) 1973.31 + 1543.97i 1.17860 + 0.922166i
\(142\) 0 0
\(143\) −615.821 −0.360123
\(144\) 0 0
\(145\) 4919.75i 2.81768i
\(146\) 0 0
\(147\) 200.258 1770.99i 0.112361 0.993667i
\(148\) 0 0
\(149\) 358.972 + 207.253i 0.197370 + 0.113952i 0.595428 0.803409i \(-0.296982\pi\)
−0.398058 + 0.917360i \(0.630316\pi\)
\(150\) 0 0
\(151\) −949.812 1645.12i −0.511885 0.886610i −0.999905 0.0137779i \(-0.995614\pi\)
0.488021 0.872832i \(-0.337719\pi\)
\(152\) 0 0
\(153\) 1269.18 1222.17i 0.670634 0.645795i
\(154\) 0 0
\(155\) −2148.25 + 1240.29i −1.11324 + 0.642728i
\(156\) 0 0
\(157\) 1833.97 + 1058.84i 0.932271 + 0.538247i 0.887529 0.460751i \(-0.152420\pi\)
0.0447422 + 0.998999i \(0.485753\pi\)
\(158\) 0 0
\(159\) 136.362 + 338.194i 0.0680137 + 0.168683i
\(160\) 0 0
\(161\) 20.8332 + 1502.26i 0.0101981 + 0.735370i
\(162\) 0 0
\(163\) −62.3148 −0.0299440 −0.0149720 0.999888i \(-0.504766\pi\)
−0.0149720 + 0.999888i \(0.504766\pi\)
\(164\) 0 0
\(165\) −2017.86 5004.55i −0.952061 2.36123i
\(166\) 0 0
\(167\) 504.850 874.426i 0.233931 0.405180i −0.725031 0.688717i \(-0.758174\pi\)
0.958961 + 0.283536i \(0.0915077\pi\)
\(168\) 0 0
\(169\) −1040.00 1801.33i −0.473373 0.819906i
\(170\) 0 0
\(171\) 685.530 + 711.897i 0.306572 + 0.318363i
\(172\) 0 0
\(173\) −234.008 405.315i −0.102840 0.178124i 0.810014 0.586411i \(-0.199460\pi\)
−0.912854 + 0.408287i \(0.866126\pi\)
\(174\) 0 0
\(175\) −1877.01 + 3357.76i −0.810792 + 1.45042i
\(176\) 0 0
\(177\) −256.811 + 1817.99i −0.109057 + 0.772025i
\(178\) 0 0
\(179\) 2028.76i 0.847131i −0.905866 0.423565i \(-0.860778\pi\)
0.905866 0.423565i \(-0.139222\pi\)
\(180\) 0 0
\(181\) 3998.62i 1.64207i −0.570876 0.821036i \(-0.693396\pi\)
0.570876 0.821036i \(-0.306604\pi\)
\(182\) 0 0
\(183\) −1895.26 + 2422.29i −0.765582 + 0.978475i
\(184\) 0 0
\(185\) −1146.17 + 1985.22i −0.455503 + 0.788954i
\(186\) 0 0
\(187\) −3217.56 + 1857.66i −1.25824 + 0.726446i
\(188\) 0 0
\(189\) 2580.72 301.937i 0.993225 0.116205i
\(190\) 0 0
\(191\) −1746.98 + 1008.62i −0.661817 + 0.382100i −0.792969 0.609262i \(-0.791466\pi\)
0.131152 + 0.991362i \(0.458132\pi\)
\(192\) 0 0
\(193\) −582.965 + 1009.72i −0.217423 + 0.376588i −0.954020 0.299745i \(-0.903099\pi\)
0.736596 + 0.676333i \(0.236432\pi\)
\(194\) 0 0
\(195\) −631.741 + 807.415i −0.231999 + 0.296514i
\(196\) 0 0
\(197\) 4449.56i 1.60923i −0.593799 0.804613i \(-0.702373\pi\)
0.593799 0.804613i \(-0.297627\pi\)
\(198\) 0 0
\(199\) 5156.28i 1.83678i −0.395677 0.918390i \(-0.629490\pi\)
0.395677 0.918390i \(-0.370510\pi\)
\(200\) 0 0
\(201\) 380.733 2695.25i 0.133606 0.945811i
\(202\) 0 0
\(203\) 4360.26 + 2437.41i 1.50754 + 0.842723i
\(204\) 0 0
\(205\) 2143.67 + 3712.94i 0.730342 + 1.26499i
\(206\) 0 0
\(207\) −2125.98 + 526.878i −0.713845 + 0.176911i
\(208\) 0 0
\(209\) −1041.98 1804.77i −0.344859 0.597313i
\(210\) 0 0
\(211\) −354.558 + 614.113i −0.115682 + 0.200366i −0.918052 0.396460i \(-0.870239\pi\)
0.802370 + 0.596826i \(0.203572\pi\)
\(212\) 0 0
\(213\) 1740.98 + 4317.86i 0.560047 + 1.38899i
\(214\) 0 0
\(215\) 825.771 0.261940
\(216\) 0 0
\(217\) 34.9254 + 2518.42i 0.0109258 + 0.787842i
\(218\) 0 0
\(219\) −1909.46 4735.70i −0.589174 1.46123i
\(220\) 0 0
\(221\) 611.302 + 352.935i 0.186066 + 0.107425i
\(222\) 0 0
\(223\) 270.455 156.147i 0.0812153 0.0468897i −0.458842 0.888518i \(-0.651736\pi\)
0.540058 + 0.841628i \(0.318402\pi\)
\(224\) 0 0
\(225\) −5388.64 1553.41i −1.59664 0.460270i
\(226\) 0 0
\(227\) 364.722 + 631.717i 0.106641 + 0.184707i 0.914407 0.404795i \(-0.132657\pi\)
−0.807767 + 0.589502i \(0.799324\pi\)
\(228\) 0 0
\(229\) −1400.43 808.539i −0.404118 0.233318i 0.284141 0.958782i \(-0.408292\pi\)
−0.688259 + 0.725465i \(0.741625\pi\)
\(230\) 0 0
\(231\) −5435.12 691.044i −1.54807 0.196828i
\(232\) 0 0
\(233\) 2237.18i 0.629023i −0.949254 0.314511i \(-0.898159\pi\)
0.949254 0.314511i \(-0.101841\pi\)
\(234\) 0 0
\(235\) −8795.33 −2.44146
\(236\) 0 0
\(237\) −4175.81 3267.25i −1.14451 0.895489i
\(238\) 0 0
\(239\) −4456.87 2573.17i −1.20624 0.696422i −0.244302 0.969699i \(-0.578559\pi\)
−0.961935 + 0.273278i \(0.911892\pi\)
\(240\) 0 0
\(241\) −933.854 + 539.161i −0.249605 + 0.144110i −0.619583 0.784931i \(-0.712698\pi\)
0.369978 + 0.929040i \(0.379365\pi\)
\(242\) 0 0
\(243\) 1282.99 + 3564.10i 0.338699 + 0.940895i
\(244\) 0 0
\(245\) 3277.25 + 5329.38i 0.854595 + 1.38972i
\(246\) 0 0
\(247\) −197.966 + 342.887i −0.0509970 + 0.0883294i
\(248\) 0 0
\(249\) −1246.90 975.605i −0.317346 0.248299i
\(250\) 0 0
\(251\) 3429.17 0.862340 0.431170 0.902271i \(-0.358101\pi\)
0.431170 + 0.902271i \(0.358101\pi\)
\(252\) 0 0
\(253\) 4618.51 1.14768
\(254\) 0 0
\(255\) −865.123 + 6124.28i −0.212455 + 1.50399i
\(256\) 0 0
\(257\) 3394.82 5880.00i 0.823981 1.42718i −0.0787143 0.996897i \(-0.525081\pi\)
0.902695 0.430280i \(-0.141585\pi\)
\(258\) 0 0
\(259\) 1191.60 + 1999.37i 0.285879 + 0.479670i
\(260\) 0 0
\(261\) −2017.20 + 6997.48i −0.478396 + 1.65951i
\(262\) 0 0
\(263\) −6692.65 + 3864.00i −1.56915 + 0.905949i −0.572881 + 0.819638i \(0.694174\pi\)
−0.996268 + 0.0863104i \(0.972492\pi\)
\(264\) 0 0
\(265\) −1108.55 640.023i −0.256973 0.148363i
\(266\) 0 0
\(267\) 4928.00 1986.99i 1.12955 0.455438i
\(268\) 0 0
\(269\) −2457.17 −0.556938 −0.278469 0.960445i \(-0.589827\pi\)
−0.278469 + 0.960445i \(0.589827\pi\)
\(270\) 0 0
\(271\) 6080.16i 1.36289i −0.731869 0.681446i \(-0.761352\pi\)
0.731869 0.681446i \(-0.238648\pi\)
\(272\) 0 0
\(273\) 402.606 + 959.917i 0.0892559 + 0.212809i
\(274\) 0 0
\(275\) 10241.0 + 5912.67i 2.24566 + 1.29654i
\(276\) 0 0
\(277\) −1092.78 1892.75i −0.237036 0.410558i 0.722827 0.691029i \(-0.242843\pi\)
−0.959862 + 0.280471i \(0.909509\pi\)
\(278\) 0 0
\(279\) −3564.05 + 883.272i −0.764782 + 0.189535i
\(280\) 0 0
\(281\) −2196.63 + 1268.23i −0.466335 + 0.269239i −0.714704 0.699427i \(-0.753439\pi\)
0.248369 + 0.968665i \(0.420105\pi\)
\(282\) 0 0
\(283\) 3627.22 + 2094.17i 0.761893 + 0.439879i 0.829975 0.557801i \(-0.188355\pi\)
−0.0680823 + 0.997680i \(0.521688\pi\)
\(284\) 0 0
\(285\) −3435.19 485.258i −0.713975 0.100857i
\(286\) 0 0
\(287\) 4352.73 60.3634i 0.895238 0.0124151i
\(288\) 0 0
\(289\) −654.409 −0.133199
\(290\) 0 0
\(291\) 2505.74 3202.53i 0.504773 0.645140i
\(292\) 0 0
\(293\) −3751.85 + 6498.40i −0.748074 + 1.29570i 0.200671 + 0.979659i \(0.435688\pi\)
−0.948745 + 0.316043i \(0.897646\pi\)
\(294\) 0 0
\(295\) −3222.56 5581.64i −0.636016 1.10161i
\(296\) 0 0
\(297\) −818.082 7945.45i −0.159831 1.55233i
\(298\) 0 0
\(299\) −438.734 759.909i −0.0848583 0.146979i
\(300\) 0 0
\(301\) 409.115 731.861i 0.0783422 0.140145i
\(302\) 0 0
\(303\) 6438.66 + 5037.76i 1.22076 + 0.955155i
\(304\) 0 0
\(305\) 10796.5i 2.02690i
\(306\) 0 0
\(307\) 4315.01i 0.802184i −0.916038 0.401092i \(-0.868631\pi\)
0.916038 0.401092i \(-0.131369\pi\)
\(308\) 0 0
\(309\) 3547.19 + 501.081i 0.653051 + 0.0922507i
\(310\) 0 0
\(311\) 2224.42 3852.80i 0.405579 0.702483i −0.588810 0.808272i \(-0.700403\pi\)
0.994389 + 0.105788i \(0.0337366\pi\)
\(312\) 0 0
\(313\) 6535.19 3773.10i 1.18016 0.681367i 0.224111 0.974564i \(-0.428052\pi\)
0.956052 + 0.293196i \(0.0947190\pi\)
\(314\) 0 0
\(315\) −6481.67 + 6417.19i −1.15937 + 1.14783i
\(316\) 0 0
\(317\) −7839.87 + 4526.35i −1.38906 + 0.801973i −0.993209 0.116343i \(-0.962883\pi\)
−0.395848 + 0.918316i \(0.629549\pi\)
\(318\) 0 0
\(319\) 7677.95 13298.6i 1.34759 2.33410i
\(320\) 0 0
\(321\) −1219.56 3024.67i −0.212054 0.525922i
\(322\) 0 0
\(323\) 2388.70i 0.411488i
\(324\) 0 0
\(325\) 2246.69i 0.383458i
\(326\) 0 0
\(327\) 5351.74 2157.85i 0.905051 0.364921i
\(328\) 0 0
\(329\) −4357.50 + 7795.08i −0.730203 + 1.30625i
\(330\) 0 0
\(331\) 3366.69 + 5831.27i 0.559063 + 0.968326i 0.997575 + 0.0696003i \(0.0221724\pi\)
−0.438512 + 0.898725i \(0.644494\pi\)
\(332\) 0 0
\(333\) −2444.20 + 2353.68i −0.402227 + 0.387329i
\(334\) 0 0
\(335\) 4777.58 + 8275.00i 0.779185 + 1.34959i
\(336\) 0 0
\(337\) −1414.64 + 2450.22i −0.228665 + 0.396060i −0.957413 0.288723i \(-0.906769\pi\)
0.728747 + 0.684783i \(0.240103\pi\)
\(338\) 0 0
\(339\) 6221.23 + 878.818i 0.996728 + 0.140799i
\(340\) 0 0
\(341\) 7742.59 1.22957
\(342\) 0 0
\(343\) 6346.95 264.193i 0.999135 0.0415892i
\(344\) 0 0
\(345\) 4737.90 6055.42i 0.739363 0.944965i
\(346\) 0 0
\(347\) −1635.49 944.250i −0.253019 0.146081i 0.368127 0.929776i \(-0.379999\pi\)
−0.621146 + 0.783695i \(0.713333\pi\)
\(348\) 0 0
\(349\) 8771.88 5064.44i 1.34541 0.776772i 0.357814 0.933793i \(-0.383522\pi\)
0.987595 + 0.157021i \(0.0501890\pi\)
\(350\) 0 0
\(351\) −1229.60 + 889.379i −0.186983 + 0.135247i
\(352\) 0 0
\(353\) 2939.16 + 5090.78i 0.443161 + 0.767577i 0.997922 0.0644323i \(-0.0205237\pi\)
−0.554761 + 0.832010i \(0.687190\pi\)
\(354\) 0 0
\(355\) −14153.3 8171.42i −2.11600 1.22167i
\(356\) 0 0
\(357\) 4999.19 + 3800.91i 0.741135 + 0.563489i
\(358\) 0 0
\(359\) 5020.49i 0.738081i −0.929413 0.369041i \(-0.879686\pi\)
0.929413 0.369041i \(-0.120314\pi\)
\(360\) 0 0
\(361\) 5519.15 0.804658
\(362\) 0 0
\(363\) −1388.44 + 9828.87i −0.200755 + 1.42116i
\(364\) 0 0
\(365\) 15522.9 + 8962.17i 2.22605 + 1.28521i
\(366\) 0 0
\(367\) −8074.26 + 4661.68i −1.14843 + 0.663045i −0.948504 0.316766i \(-0.897403\pi\)
−0.199924 + 0.979811i \(0.564070\pi\)
\(368\) 0 0
\(369\) 1526.61 + 6159.94i 0.215371 + 0.869035i
\(370\) 0 0
\(371\) −1116.45 + 665.394i −0.156235 + 0.0931146i
\(372\) 0 0
\(373\) −510.522 + 884.250i −0.0708682 + 0.122747i −0.899282 0.437369i \(-0.855910\pi\)
0.828414 + 0.560116i \(0.189244\pi\)
\(374\) 0 0
\(375\) 7270.14 2931.36i 1.00114 0.403666i
\(376\) 0 0
\(377\) −2917.46 −0.398559
\(378\) 0 0
\(379\) −8222.23 −1.11437 −0.557187 0.830387i \(-0.688119\pi\)
−0.557187 + 0.830387i \(0.688119\pi\)
\(380\) 0 0
\(381\) −12951.0 + 5221.90i −1.74147 + 0.702169i
\(382\) 0 0
\(383\) 1833.55 3175.80i 0.244621 0.423697i −0.717404 0.696658i \(-0.754670\pi\)
0.962025 + 0.272961i \(0.0880030\pi\)
\(384\) 0 0
\(385\) 16521.1 9846.40i 2.18699 1.30343i
\(386\) 0 0
\(387\) 1174.51 + 338.583i 0.154274 + 0.0444732i
\(388\) 0 0
\(389\) −1487.93 + 859.056i −0.193936 + 0.111969i −0.593824 0.804595i \(-0.702382\pi\)
0.399888 + 0.916564i \(0.369049\pi\)
\(390\) 0 0
\(391\) −4584.61 2646.93i −0.592977 0.342355i
\(392\) 0 0
\(393\) 107.647 762.043i 0.0138170 0.0978117i
\(394\) 0 0
\(395\) 18612.2 2.37084
\(396\) 0 0
\(397\) 11666.0i 1.47481i 0.675448 + 0.737407i \(0.263950\pi\)
−0.675448 + 0.737407i \(0.736050\pi\)
\(398\) 0 0
\(399\) −2131.98 + 2804.11i −0.267500 + 0.351832i
\(400\) 0 0
\(401\) 2312.57 + 1335.16i 0.287990 + 0.166271i 0.637035 0.770835i \(-0.280161\pi\)
−0.349045 + 0.937106i \(0.613494\pi\)
\(402\) 0 0
\(403\) −735.505 1273.93i −0.0909134 0.157467i
\(404\) 0 0
\(405\) −11256.7 7078.24i −1.38111 0.868446i
\(406\) 0 0
\(407\) 6196.42 3577.51i 0.754657 0.435701i
\(408\) 0 0
\(409\) −375.615 216.862i −0.0454107 0.0262179i 0.477123 0.878837i \(-0.341680\pi\)
−0.522533 + 0.852619i \(0.675013\pi\)
\(410\) 0 0
\(411\) −3256.12 + 4161.59i −0.390785 + 0.499455i
\(412\) 0 0
\(413\) −6543.43 + 90.7439i −0.779615 + 0.0108117i
\(414\) 0 0
\(415\) 5557.62 0.657380
\(416\) 0 0
\(417\) −13196.7 1864.18i −1.54975 0.218919i
\(418\) 0 0
\(419\) 2916.15 5050.92i 0.340008 0.588911i −0.644426 0.764667i \(-0.722904\pi\)
0.984434 + 0.175756i \(0.0562369\pi\)
\(420\) 0 0
\(421\) 5481.42 + 9494.10i 0.634556 + 1.09908i 0.986609 + 0.163104i \(0.0521505\pi\)
−0.352053 + 0.935980i \(0.614516\pi\)
\(422\) 0 0
\(423\) −12509.8 3606.26i −1.43794 0.414521i
\(424\) 0 0
\(425\) −6777.25 11738.5i −0.773517 1.33977i
\(426\) 0 0
\(427\) −9568.67 5348.95i −1.08445 0.606215i
\(428\) 0 0
\(429\) 2967.74 1196.61i 0.333995 0.134669i
\(430\) 0 0
\(431\) 9711.53i 1.08536i −0.839941 0.542678i \(-0.817411\pi\)
0.839941 0.542678i \(-0.182589\pi\)
\(432\) 0 0
\(433\) 28.2134i 0.00313129i −0.999999 0.00156564i \(-0.999502\pi\)
0.999999 0.00156564i \(-0.000498360\pi\)
\(434\) 0 0
\(435\) −9559.62 23709.1i −1.05368 2.61325i
\(436\) 0 0
\(437\) 1484.69 2571.57i 0.162523 0.281498i
\(438\) 0 0
\(439\) −5470.43 + 3158.35i −0.594736 + 0.343371i −0.766968 0.641685i \(-0.778236\pi\)
0.172232 + 0.985056i \(0.444902\pi\)
\(440\) 0 0
\(441\) 2476.16 + 8923.83i 0.267375 + 0.963593i
\(442\) 0 0
\(443\) 13946.4 8051.96i 1.49574 0.863567i 0.495754 0.868463i \(-0.334892\pi\)
0.999988 + 0.00489651i \(0.00155861\pi\)
\(444\) 0 0
\(445\) −9326.09 + 16153.3i −0.993481 + 1.72076i
\(446\) 0 0
\(447\) −2132.66 301.262i −0.225663 0.0318774i
\(448\) 0 0
\(449\) 2392.17i 0.251433i −0.992066 0.125717i \(-0.959877\pi\)
0.992066 0.125717i \(-0.0401230\pi\)
\(450\) 0 0
\(451\) 13381.9i 1.39719i
\(452\) 0 0
\(453\) 7773.95 + 6082.52i 0.806296 + 0.630865i
\(454\) 0 0
\(455\) −3189.50 1782.95i −0.328628 0.183705i
\(456\) 0 0
\(457\) −6222.62 10777.9i −0.636940 1.10321i −0.986100 0.166150i \(-0.946866\pi\)
0.349160 0.937063i \(-0.386467\pi\)
\(458\) 0 0
\(459\) −3741.56 + 8355.99i −0.380482 + 0.849726i
\(460\) 0 0
\(461\) 9386.24 + 16257.4i 0.948288 + 1.64248i 0.749031 + 0.662535i \(0.230519\pi\)
0.199257 + 0.979947i \(0.436147\pi\)
\(462\) 0 0
\(463\) −3011.11 + 5215.40i −0.302243 + 0.523499i −0.976644 0.214866i \(-0.931069\pi\)
0.674401 + 0.738365i \(0.264402\pi\)
\(464\) 0 0
\(465\) 7942.75 10151.5i 0.792120 1.01239i
\(466\) 0 0
\(467\) −8896.12 −0.881506 −0.440753 0.897628i \(-0.645289\pi\)
−0.440753 + 0.897628i \(0.645289\pi\)
\(468\) 0 0
\(469\) 9700.90 134.532i 0.955109 0.0132454i
\(470\) 0 0
\(471\) −10895.6 1539.13i −1.06591 0.150572i
\(472\) 0 0
\(473\) −2232.15 1288.73i −0.216986 0.125277i
\(474\) 0 0
\(475\) 6584.29 3801.44i 0.636017 0.367205i
\(476\) 0 0
\(477\) −1314.30 1364.85i −0.126158 0.131011i
\(478\) 0 0
\(479\) −6.85714 11.8769i −0.000654094 0.00113292i 0.865698 0.500566i \(-0.166875\pi\)
−0.866352 + 0.499433i \(0.833542\pi\)
\(480\) 0 0
\(481\) −1177.25 679.688i −0.111597 0.0644306i
\(482\) 0 0
\(483\) −3019.45 7199.14i −0.284451 0.678204i
\(484\) 0 0
\(485\) 14274.1i 1.33640i
\(486\) 0 0
\(487\) 14175.4 1.31899 0.659497 0.751708i \(-0.270770\pi\)
0.659497 + 0.751708i \(0.270770\pi\)
\(488\) 0 0
\(489\) 300.305 121.084i 0.0277715 0.0111976i
\(490\) 0 0
\(491\) 1949.66 + 1125.63i 0.179199 + 0.103461i 0.586916 0.809648i \(-0.300342\pi\)
−0.407717 + 0.913108i \(0.633675\pi\)
\(492\) 0 0
\(493\) −15243.2 + 8800.67i −1.39253 + 0.803980i
\(494\) 0 0
\(495\) 19448.8 + 20196.8i 1.76598 + 1.83390i
\(496\) 0 0
\(497\) −14254.2 + 8495.34i −1.28649 + 0.766736i
\(498\) 0 0
\(499\) −3676.93 + 6368.63i −0.329864 + 0.571340i −0.982485 0.186344i \(-0.940336\pi\)
0.652621 + 0.757685i \(0.273669\pi\)
\(500\) 0 0
\(501\) −733.849 + 5194.98i −0.0654410 + 0.463263i
\(502\) 0 0
\(503\) 9876.83 0.875519 0.437759 0.899092i \(-0.355772\pi\)
0.437759 + 0.899092i \(0.355772\pi\)
\(504\) 0 0
\(505\) −28698.0 −2.52880
\(506\) 0 0
\(507\) 8512.12 + 6660.08i 0.745634 + 0.583402i
\(508\) 0 0
\(509\) −3653.69 + 6328.37i −0.318167 + 0.551081i −0.980106 0.198477i \(-0.936401\pi\)
0.661939 + 0.749558i \(0.269734\pi\)
\(510\) 0 0
\(511\) 15633.5 9317.43i 1.35340 0.806612i
\(512\) 0 0
\(513\) −4686.98 2098.69i −0.403382 0.180623i
\(514\) 0 0
\(515\) −10890.7 + 6287.73i −0.931845 + 0.538001i
\(516\) 0 0
\(517\) 23774.7 + 13726.3i 2.02246 + 1.16767i
\(518\) 0 0
\(519\) 1915.30 + 1498.57i 0.161989 + 0.126744i
\(520\) 0 0
\(521\) −16702.5 −1.40451 −0.702256 0.711924i \(-0.747824\pi\)
−0.702256 + 0.711924i \(0.747824\pi\)
\(522\) 0 0
\(523\) 17735.9i 1.48286i 0.671028 + 0.741432i \(0.265853\pi\)
−0.671028 + 0.741432i \(0.734147\pi\)
\(524\) 0 0
\(525\) 2521.12 19828.8i 0.209582 1.64838i
\(526\) 0 0
\(527\) −7685.77 4437.38i −0.635289 0.366784i
\(528\) 0 0
\(529\) −2793.10 4837.79i −0.229564 0.397616i
\(530\) 0 0
\(531\) −2294.94 9260.20i −0.187555 0.756796i
\(532\) 0 0
\(533\) −2201.80 + 1271.21i −0.178932 + 0.103306i
\(534\) 0 0
\(535\) 9914.45 + 5724.11i 0.801194 + 0.462570i
\(536\) 0 0
\(537\) 3942.10 + 9776.91i 0.316786 + 0.785670i
\(538\) 0 0
\(539\) −541.521 19520.5i −0.0432745 1.55994i
\(540\) 0 0
\(541\) −14759.1 −1.17291 −0.586454 0.809983i \(-0.699476\pi\)
−0.586454 + 0.809983i \(0.699476\pi\)
\(542\) 0 0
\(543\) 7769.76 + 19270.0i 0.614056 + 1.52294i
\(544\) 0 0
\(545\) −10128.0 + 17542.2i −0.796030 + 1.37876i
\(546\) 0 0
\(547\) −1188.36 2058.30i −0.0928897 0.160890i 0.815836 0.578283i \(-0.196277\pi\)
−0.908726 + 0.417393i \(0.862944\pi\)
\(548\) 0 0
\(549\) 4426.78 15356.1i 0.344136 1.19378i
\(550\) 0 0
\(551\) −4936.40 8550.10i −0.381666 0.661064i
\(552\) 0 0
\(553\) 9221.10 16495.5i 0.709080 1.26846i
\(554\) 0 0
\(555\) 1666.07 11794.2i 0.127425 0.902050i
\(556\) 0 0
\(557\) 15.7702i 0.00119965i −1.00000 0.000599827i \(-0.999809\pi\)
1.00000 0.000599827i \(-0.000190931\pi\)
\(558\) 0 0
\(559\) 489.690i 0.0370513i
\(560\) 0 0
\(561\) 11896.3 15204.4i 0.895298 1.14426i
\(562\) 0 0
\(563\) 3299.49 5714.88i 0.246993 0.427804i −0.715697 0.698411i \(-0.753891\pi\)
0.962690 + 0.270607i \(0.0872243\pi\)
\(564\) 0 0
\(565\) −19100.6 + 11027.7i −1.42224 + 0.821132i
\(566\) 0 0
\(567\) −11850.2 + 6469.70i −0.877710 + 0.479192i
\(568\) 0 0
\(569\) −22038.3 + 12723.8i −1.62371 + 0.937450i −0.637796 + 0.770205i \(0.720154\pi\)
−0.985915 + 0.167245i \(0.946513\pi\)
\(570\) 0 0
\(571\) 10540.7 18257.0i 0.772527 1.33806i −0.163646 0.986519i \(-0.552326\pi\)
0.936174 0.351538i \(-0.114341\pi\)
\(572\) 0 0
\(573\) 6459.12 8255.27i 0.470914 0.601865i
\(574\) 0 0
\(575\) 16849.6i 1.22205i
\(576\) 0 0
\(577\) 847.126i 0.0611201i −0.999533 0.0305601i \(-0.990271\pi\)
0.999533 0.0305601i \(-0.00972908\pi\)
\(578\) 0 0
\(579\) 847.396 5998.79i 0.0608231 0.430572i
\(580\) 0 0
\(581\) 2753.43 4925.58i 0.196612 0.351717i
\(582\) 0 0
\(583\) 1997.69 + 3460.10i 0.141914 + 0.245802i
\(584\) 0 0
\(585\) 1475.57 5118.61i 0.104286 0.361758i
\(586\) 0 0
\(587\) −9171.88 15886.2i −0.644913 1.11702i −0.984322 0.176383i \(-0.943560\pi\)
0.339408 0.940639i \(-0.389773\pi\)
\(588\) 0 0
\(589\) 2488.98 4311.04i 0.174120 0.301585i
\(590\) 0 0
\(591\) 8645.97 + 21443.1i 0.601773 + 1.49247i
\(592\) 0 0
\(593\) −5722.96 −0.396314 −0.198157 0.980170i \(-0.563496\pi\)
−0.198157 + 0.980170i \(0.563496\pi\)
\(594\) 0 0
\(595\) −22042.9 + 305.690i −1.51878 + 0.0210623i
\(596\) 0 0
\(597\) 10019.2 + 24849.0i 0.686867 + 1.70352i
\(598\) 0 0
\(599\) −8776.18 5066.93i −0.598639 0.345625i 0.169867 0.985467i \(-0.445666\pi\)
−0.768506 + 0.639842i \(0.779000\pi\)
\(600\) 0 0
\(601\) −6127.51 + 3537.72i −0.415884 + 0.240111i −0.693315 0.720635i \(-0.743850\pi\)
0.277431 + 0.960746i \(0.410517\pi\)
\(602\) 0 0
\(603\) 3402.34 + 13728.6i 0.229774 + 0.927153i
\(604\) 0 0
\(605\) −17422.6 30176.8i −1.17079 2.02787i
\(606\) 0 0
\(607\) −11291.3 6519.01i −0.755021 0.435912i 0.0724839 0.997370i \(-0.476907\pi\)
−0.827505 + 0.561458i \(0.810241\pi\)
\(608\) 0 0
\(609\) −25748.9 3273.83i −1.71330 0.217836i
\(610\) 0 0
\(611\) 5215.71i 0.345344i
\(612\) 0 0
\(613\) 5876.91 0.387220 0.193610 0.981079i \(-0.437980\pi\)
0.193610 + 0.981079i \(0.437980\pi\)
\(614\) 0 0
\(615\) −17545.3 13727.9i −1.15040 0.900099i
\(616\) 0 0
\(617\) 9655.60 + 5574.66i 0.630016 + 0.363740i 0.780758 0.624833i \(-0.214833\pi\)
−0.150742 + 0.988573i \(0.548166\pi\)
\(618\) 0 0
\(619\) −15732.2 + 9083.00i −1.02154 + 0.589785i −0.914549 0.404476i \(-0.867454\pi\)
−0.106988 + 0.994260i \(0.534121\pi\)
\(620\) 0 0
\(621\) 9221.67 6670.13i 0.595898 0.431019i
\(622\) 0 0
\(623\) 9695.78 + 16268.4i 0.623520 + 1.04619i
\(624\) 0 0
\(625\) −776.867 + 1345.57i −0.0497195 + 0.0861167i
\(626\) 0 0
\(627\) 8528.35 + 6672.78i 0.543205 + 0.425016i
\(628\) 0 0
\(629\) −8201.26 −0.519882
\(630\) 0 0
\(631\) 6044.76 0.381360 0.190680 0.981652i \(-0.438931\pi\)
0.190680 + 0.981652i \(0.438931\pi\)
\(632\) 0 0
\(633\) 515.385 3648.46i 0.0323613 0.229089i
\(634\) 0 0
\(635\) 24509.4 42451.5i 1.53169 2.65297i
\(636\) 0 0
\(637\) −3160.37 + 1943.44i −0.196575 + 0.120882i
\(638\) 0 0
\(639\) −16780.1 17425.5i −1.03883 1.07879i
\(640\) 0 0
\(641\) 3969.31 2291.68i 0.244584 0.141211i −0.372698 0.927953i \(-0.621567\pi\)
0.617282 + 0.786742i \(0.288234\pi\)
\(642\) 0 0
\(643\) 6413.00 + 3702.55i 0.393319 + 0.227083i 0.683597 0.729860i \(-0.260415\pi\)
−0.290278 + 0.956942i \(0.593748\pi\)
\(644\) 0 0
\(645\) −3979.53 + 1604.56i −0.242936 + 0.0979530i
\(646\) 0 0
\(647\) −21755.4 −1.32193 −0.660967 0.750415i \(-0.729854\pi\)
−0.660967 + 0.750415i \(0.729854\pi\)
\(648\) 0 0
\(649\) 20117.0i 1.21673i
\(650\) 0 0
\(651\) −5061.89 12068.8i −0.304748 0.726597i
\(652\) 0 0
\(653\) −1656.32 956.276i −0.0992599 0.0573078i 0.449548 0.893256i \(-0.351585\pi\)
−0.548808 + 0.835948i \(0.684918\pi\)
\(654\) 0 0
\(655\) 1350.79 + 2339.64i 0.0805800 + 0.139569i
\(656\) 0 0
\(657\) 18404.0 + 19111.8i 1.09286 + 1.13489i
\(658\) 0 0
\(659\) −1009.42 + 582.787i −0.0596681 + 0.0344494i −0.529537 0.848287i \(-0.677634\pi\)
0.469869 + 0.882736i \(0.344301\pi\)
\(660\) 0 0
\(661\) 20327.5 + 11736.1i 1.19614 + 0.690593i 0.959693 0.281051i \(-0.0906830\pi\)
0.236449 + 0.971644i \(0.424016\pi\)
\(662\) 0 0
\(663\) −3631.75 513.026i −0.212738 0.0300517i
\(664\) 0 0
\(665\) −171.465 12364.1i −0.00999870 0.720994i
\(666\) 0 0
\(667\) 21880.2 1.27017
\(668\) 0 0
\(669\) −999.956 + 1278.02i −0.0577885 + 0.0738584i
\(670\) 0 0
\(671\) −16849.4 + 29184.1i −0.969396 + 1.67904i
\(672\) 0 0
\(673\) 12009.3 + 20800.7i 0.687850 + 1.19139i 0.972532 + 0.232770i \(0.0747788\pi\)
−0.284682 + 0.958622i \(0.591888\pi\)
\(674\) 0 0
\(675\) 28987.2 2984.59i 1.65292 0.170188i
\(676\) 0 0
\(677\) −8076.04 13988.1i −0.458475 0.794102i 0.540406 0.841405i \(-0.318271\pi\)
−0.998881 + 0.0473029i \(0.984937\pi\)
\(678\) 0 0
\(679\) 12650.8 + 7071.89i 0.715013 + 0.399697i
\(680\) 0 0
\(681\) −2985.15 2335.65i −0.167975 0.131428i
\(682\) 0 0
\(683\) 28554.3i 1.59970i 0.600197 + 0.799852i \(0.295089\pi\)
−0.600197 + 0.799852i \(0.704911\pi\)
\(684\) 0 0
\(685\) 18548.8i 1.03462i
\(686\) 0 0
\(687\) 8319.98 + 1175.29i 0.462048 + 0.0652695i
\(688\) 0 0
\(689\) 379.539 657.381i 0.0209859 0.0363487i
\(690\) 0 0
\(691\) −29465.7 + 17012.0i −1.62218 + 0.936567i −0.635848 + 0.771815i \(0.719349\pi\)
−0.986335 + 0.164753i \(0.947317\pi\)
\(692\) 0 0
\(693\) 27535.5 7230.79i 1.50936 0.396356i
\(694\) 0 0
\(695\) 40516.7 23392.3i 2.21135 1.27672i
\(696\) 0 0
\(697\) −7669.36 + 13283.7i −0.416783 + 0.721889i
\(698\) 0 0
\(699\) 4347.08 + 10781.3i 0.235224 + 0.583386i
\(700\) 0 0
\(701\) 9879.92i 0.532325i −0.963928 0.266162i \(-0.914244\pi\)
0.963928 0.266162i \(-0.0857557\pi\)
\(702\) 0 0
\(703\) 4600.19i 0.246799i
\(704\) 0 0
\(705\) 42386.1 17090.3i 2.26433 0.912990i
\(706\) 0 0
\(707\) −14218.0 + 25434.4i −0.756325 + 1.35298i
\(708\) 0 0
\(709\) −16309.1 28248.1i −0.863893 1.49631i −0.868142 0.496315i \(-0.834686\pi\)
0.00424980 0.999991i \(-0.498647\pi\)
\(710\) 0 0
\(711\) 26472.5 + 7631.36i 1.39634 + 0.402529i
\(712\) 0 0
\(713\) 5516.11 + 9554.18i 0.289733 + 0.501833i
\(714\) 0 0
\(715\) −5616.37 + 9727.83i −0.293763 + 0.508812i
\(716\) 0 0
\(717\) 26478.3 + 3740.36i 1.37915 + 0.194820i
\(718\) 0 0
\(719\) 22467.8 1.16538 0.582689 0.812695i \(-0.302000\pi\)
0.582689 + 0.812695i \(0.302000\pi\)
\(720\) 0 0
\(721\) 177.056 + 12767.3i 0.00914550 + 0.659471i
\(722\) 0 0
\(723\) 3452.74 4412.88i 0.177606 0.226994i
\(724\) 0 0
\(725\) 48517.0 + 28011.3i 2.48534 + 1.43491i
\(726\) 0 0
\(727\) 9455.61 5459.20i 0.482378 0.278501i −0.239029 0.971013i \(-0.576829\pi\)
0.721407 + 0.692511i \(0.243496\pi\)
\(728\) 0 0
\(729\) −13108.4 14683.0i −0.665975 0.745974i
\(730\) 0 0
\(731\) 1477.18 + 2558.54i 0.0747405 + 0.129454i
\(732\) 0 0
\(733\) −10792.3 6230.94i −0.543824 0.313977i 0.202803 0.979219i \(-0.434995\pi\)
−0.746627 + 0.665243i \(0.768328\pi\)
\(734\) 0 0
\(735\) −26149.2 19315.1i −1.31228 0.969316i
\(736\) 0 0
\(737\) 29824.3i 1.49062i
\(738\) 0 0
\(739\) 8019.93 0.399212 0.199606 0.979876i \(-0.436034\pi\)
0.199606 + 0.979876i \(0.436034\pi\)
\(740\) 0 0
\(741\) 287.762 2037.10i 0.0142662 0.100991i
\(742\) 0 0
\(743\) −17310.5 9994.23i −0.854725 0.493476i 0.00751697 0.999972i \(-0.497607\pi\)
−0.862242 + 0.506496i \(0.830941\pi\)
\(744\) 0 0
\(745\) 6547.74 3780.34i 0.322001 0.185907i
\(746\) 0 0
\(747\) 7904.73 + 2278.73i 0.387174 + 0.111612i
\(748\) 0 0
\(749\) 9985.09 5951.01i 0.487112 0.290314i
\(750\) 0 0
\(751\) −5462.66 + 9461.60i −0.265426 + 0.459732i −0.967675 0.252200i \(-0.918846\pi\)
0.702249 + 0.711931i \(0.252179\pi\)
\(752\) 0 0
\(753\) −16525.7 + 6663.26i −0.799776 + 0.322473i
\(754\) 0 0
\(755\) −34649.6 −1.67024
\(756\) 0 0
\(757\) 32902.1 1.57972 0.789859 0.613288i \(-0.210153\pi\)
0.789859 + 0.613288i \(0.210153\pi\)
\(758\) 0 0
\(759\) −22257.4 + 8974.27i −1.06441 + 0.429177i
\(760\) 0 0
\(761\) 13873.1 24028.9i 0.660839 1.14461i −0.319556 0.947567i \(-0.603534\pi\)
0.980395 0.197040i \(-0.0631329\pi\)
\(762\) 0 0
\(763\) 10529.5 + 17667.2i 0.499597 + 0.838264i
\(764\) 0 0
\(765\) −7730.98 31194.9i −0.365378 1.47432i
\(766\) 0 0
\(767\) 3309.96 1911.01i 0.155822 0.0899641i
\(768\) 0 0
\(769\) 22748.3 + 13133.8i 1.06674 + 0.615885i 0.927290 0.374344i \(-0.122132\pi\)
0.139454 + 0.990229i \(0.455465\pi\)
\(770\) 0 0
\(771\) −4934.71 + 34933.2i −0.230505 + 1.63176i
\(772\) 0 0
\(773\) −1419.67 −0.0660570 −0.0330285 0.999454i \(-0.510515\pi\)
−0.0330285 + 0.999454i \(0.510515\pi\)
\(774\) 0 0
\(775\) 28247.1i 1.30925i
\(776\) 0 0
\(777\) −9627.52 7319.86i −0.444511 0.337965i
\(778\) 0 0
\(779\) −7451.00 4301.84i −0.342696 0.197855i
\(780\) 0 0
\(781\) 25505.3 + 44176.4i 1.16857 + 2.02402i
\(782\) 0 0
\(783\) −3875.67 37641.6i −0.176890 1.71801i
\(784\) 0 0
\(785\) 33452.0 19313.5i 1.52096 0.878127i
\(786\) 0 0
\(787\) −11207.6 6470.69i −0.507632 0.293082i 0.224227 0.974537i \(-0.428014\pi\)
−0.731860 + 0.681455i \(0.761347\pi\)
\(788\) 0 0
\(789\) 24744.8 31625.8i 1.11652 1.42701i
\(790\) 0 0
\(791\) 310.529 + 22391.9i 0.0139585 + 1.00653i
\(792\) 0 0
\(793\) 6402.42 0.286705
\(794\) 0 0
\(795\) 6585.93 + 930.336i 0.293810 + 0.0415039i