Properties

Label 105.4.d.b.64.1
Level $105$
Weight $4$
Character 105.64
Analytic conductor $6.195$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 37 x^{8} + 398 x^{6} + 1149 x^{4} + 1040 x^{2} + 100\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9}\cdot 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.1
Root \(3.71490i\) of defining polynomial
Character \(\chi\) \(=\) 105.64
Dual form 105.4.d.b.64.10

$q$-expansion

\(f(q)\) \(=\) \(q-5.18660i q^{2} -3.00000i q^{3} -18.9008 q^{4} +(-4.24321 + 10.3438i) q^{5} -15.5598 q^{6} -7.00000i q^{7} +56.5383i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q-5.18660i q^{2} -3.00000i q^{3} -18.9008 q^{4} +(-4.24321 + 10.3438i) q^{5} -15.5598 q^{6} -7.00000i q^{7} +56.5383i q^{8} -9.00000 q^{9} +(53.6494 + 22.0078i) q^{10} -35.9555 q^{11} +56.7025i q^{12} +45.2622i q^{13} -36.3062 q^{14} +(31.0315 + 12.7296i) q^{15} +142.035 q^{16} -113.154i q^{17} +46.6794i q^{18} -61.5906 q^{19} +(80.2001 - 195.507i) q^{20} -21.0000 q^{21} +186.487i q^{22} -30.6108i q^{23} +169.615 q^{24} +(-88.9904 - 87.7822i) q^{25} +234.757 q^{26} +27.0000i q^{27} +132.306i q^{28} -214.989 q^{29} +(66.0235 - 160.948i) q^{30} +164.206 q^{31} -284.372i q^{32} +107.866i q^{33} -586.882 q^{34} +(72.4069 + 29.7024i) q^{35} +170.107 q^{36} +410.533i q^{37} +319.446i q^{38} +135.787 q^{39} +(-584.823 - 239.904i) q^{40} -309.310 q^{41} +108.919i q^{42} -29.9519i q^{43} +679.589 q^{44} +(38.1889 - 93.0946i) q^{45} -158.766 q^{46} -483.790i q^{47} -426.104i q^{48} -49.0000 q^{49} +(-455.291 + 461.558i) q^{50} -339.461 q^{51} -855.493i q^{52} -295.582i q^{53} +140.038 q^{54} +(152.567 - 371.918i) q^{55} +395.768 q^{56} +184.772i q^{57} +1115.06i q^{58} -416.191 q^{59} +(-586.522 - 240.600i) q^{60} -151.196 q^{61} -851.670i q^{62} +63.0000i q^{63} -338.644 q^{64} +(-468.185 - 192.057i) q^{65} +559.460 q^{66} -89.5253i q^{67} +2138.70i q^{68} -91.8324 q^{69} +(154.055 - 375.546i) q^{70} +714.265 q^{71} -508.844i q^{72} -1135.58i q^{73} +2129.27 q^{74} +(-263.347 + 266.971i) q^{75} +1164.11 q^{76} +251.688i q^{77} -704.271i q^{78} +323.347 q^{79} +(-602.683 + 1469.19i) q^{80} +81.0000 q^{81} +1604.27i q^{82} +297.898i q^{83} +396.917 q^{84} +(1170.44 + 480.134i) q^{85} -155.348 q^{86} +644.966i q^{87} -2032.86i q^{88} +90.2097 q^{89} +(-482.845 - 198.070i) q^{90} +316.835 q^{91} +578.570i q^{92} -492.617i q^{93} -2509.23 q^{94} +(261.342 - 637.084i) q^{95} -853.115 q^{96} +492.101i q^{97} +254.143i q^{98} +323.599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + O(q^{10}) \) \( 10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + 92q^{10} + 132q^{11} - 14q^{14} + 310q^{16} - 348q^{19} + 366q^{20} - 210q^{21} + 198q^{24} - 374q^{25} + 892q^{26} - 740q^{29} - 378q^{30} + 684q^{31} - 224q^{34} + 486q^{36} - 12q^{39} - 2156q^{40} + 1604q^{41} - 580q^{44} + 126q^{45} + 1280q^{46} - 490q^{49} - 2504q^{50} - 648q^{51} + 54q^{54} - 452q^{55} + 462q^{56} - 1408q^{59} - 852q^{60} + 1300q^{61} - 150q^{64} - 3296q^{65} + 3036q^{66} - 696q^{69} - 882q^{70} + 2940q^{71} + 2624q^{74} - 408q^{75} + 8740q^{76} + 1640q^{79} - 4126q^{80} + 810q^{81} + 1134q^{84} - 1704q^{85} + 1664q^{86} - 572q^{89} - 828q^{90} - 28q^{91} - 5080q^{94} + 1268q^{95} + 330q^{96} - 1188q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.18660i 1.83374i −0.399185 0.916870i \(-0.630707\pi\)
0.399185 0.916870i \(-0.369293\pi\)
\(3\) 3.00000i 0.577350i
\(4\) −18.9008 −2.36260
\(5\) −4.24321 + 10.3438i −0.379524 + 0.925182i
\(6\) −15.5598 −1.05871
\(7\) 7.00000i 0.377964i
\(8\) 56.5383i 2.49866i
\(9\) −9.00000 −0.333333
\(10\) 53.6494 + 22.0078i 1.69654 + 0.695948i
\(11\) −35.9555 −0.985545 −0.492772 0.870158i \(-0.664016\pi\)
−0.492772 + 0.870158i \(0.664016\pi\)
\(12\) 56.7025i 1.36405i
\(13\) 45.2622i 0.965652i 0.875716 + 0.482826i \(0.160390\pi\)
−0.875716 + 0.482826i \(0.839610\pi\)
\(14\) −36.3062 −0.693089
\(15\) 31.0315 + 12.7296i 0.534154 + 0.219118i
\(16\) 142.035 2.21929
\(17\) 113.154i 1.61434i −0.590319 0.807170i \(-0.700998\pi\)
0.590319 0.807170i \(-0.299002\pi\)
\(18\) 46.6794i 0.611247i
\(19\) −61.5906 −0.743677 −0.371838 0.928297i \(-0.621272\pi\)
−0.371838 + 0.928297i \(0.621272\pi\)
\(20\) 80.2001 195.507i 0.896665 2.18584i
\(21\) −21.0000 −0.218218
\(22\) 186.487i 1.80723i
\(23\) 30.6108i 0.277513i −0.990327 0.138756i \(-0.955690\pi\)
0.990327 0.138756i \(-0.0443105\pi\)
\(24\) 169.615 1.44260
\(25\) −88.9904 87.7822i −0.711923 0.702257i
\(26\) 234.757 1.77075
\(27\) 27.0000i 0.192450i
\(28\) 132.306i 0.892980i
\(29\) −214.989 −1.37663 −0.688317 0.725410i \(-0.741650\pi\)
−0.688317 + 0.725410i \(0.741650\pi\)
\(30\) 66.0235 160.948i 0.401806 0.979500i
\(31\) 164.206 0.951362 0.475681 0.879618i \(-0.342202\pi\)
0.475681 + 0.879618i \(0.342202\pi\)
\(32\) 284.372i 1.57095i
\(33\) 107.866i 0.569004i
\(34\) −586.882 −2.96028
\(35\) 72.4069 + 29.7024i 0.349686 + 0.143447i
\(36\) 170.107 0.787535
\(37\) 410.533i 1.82409i 0.410095 + 0.912043i \(0.365496\pi\)
−0.410095 + 0.912043i \(0.634504\pi\)
\(38\) 319.446i 1.36371i
\(39\) 135.787 0.557519
\(40\) −584.823 239.904i −2.31172 0.948302i
\(41\) −309.310 −1.17820 −0.589100 0.808060i \(-0.700517\pi\)
−0.589100 + 0.808060i \(0.700517\pi\)
\(42\) 108.919i 0.400155i
\(43\) 29.9519i 0.106224i −0.998589 0.0531118i \(-0.983086\pi\)
0.998589 0.0531118i \(-0.0169140\pi\)
\(44\) 679.589 2.32845
\(45\) 38.1889 93.0946i 0.126508 0.308394i
\(46\) −158.766 −0.508886
\(47\) 483.790i 1.50145i −0.660616 0.750724i \(-0.729705\pi\)
0.660616 0.750724i \(-0.270295\pi\)
\(48\) 426.104i 1.28131i
\(49\) −49.0000 −0.142857
\(50\) −455.291 + 461.558i −1.28776 + 1.30548i
\(51\) −339.461 −0.932039
\(52\) 855.493i 2.28145i
\(53\) 295.582i 0.766063i −0.923735 0.383031i \(-0.874880\pi\)
0.923735 0.383031i \(-0.125120\pi\)
\(54\) 140.038 0.352904
\(55\) 152.567 371.918i 0.374038 0.911808i
\(56\) 395.768 0.944405
\(57\) 184.772i 0.429362i
\(58\) 1115.06i 2.52439i
\(59\) −416.191 −0.918364 −0.459182 0.888342i \(-0.651857\pi\)
−0.459182 + 0.888342i \(0.651857\pi\)
\(60\) −586.522 240.600i −1.26199 0.517690i
\(61\) −151.196 −0.317355 −0.158677 0.987330i \(-0.550723\pi\)
−0.158677 + 0.987330i \(0.550723\pi\)
\(62\) 851.670i 1.74455i
\(63\) 63.0000i 0.125988i
\(64\) −338.644 −0.661415
\(65\) −468.185 192.057i −0.893403 0.366488i
\(66\) 559.460 1.04341
\(67\) 89.5253i 0.163243i −0.996663 0.0816213i \(-0.973990\pi\)
0.996663 0.0816213i \(-0.0260098\pi\)
\(68\) 2138.70i 3.81404i
\(69\) −91.8324 −0.160222
\(70\) 154.055 375.546i 0.263044 0.641233i
\(71\) 714.265 1.19391 0.596955 0.802274i \(-0.296377\pi\)
0.596955 + 0.802274i \(0.296377\pi\)
\(72\) 508.844i 0.832887i
\(73\) 1135.58i 1.82068i −0.413861 0.910340i \(-0.635820\pi\)
0.413861 0.910340i \(-0.364180\pi\)
\(74\) 2129.27 3.34490
\(75\) −263.347 + 266.971i −0.405448 + 0.411029i
\(76\) 1164.11 1.75701
\(77\) 251.688i 0.372501i
\(78\) 704.271i 1.02235i
\(79\) 323.347 0.460498 0.230249 0.973132i \(-0.426046\pi\)
0.230249 + 0.973132i \(0.426046\pi\)
\(80\) −602.683 + 1469.19i −0.842275 + 2.05325i
\(81\) 81.0000 0.111111
\(82\) 1604.27i 2.16051i
\(83\) 297.898i 0.393959i 0.980408 + 0.196979i \(0.0631132\pi\)
−0.980408 + 0.196979i \(0.936887\pi\)
\(84\) 396.917 0.515562
\(85\) 1170.44 + 480.134i 1.49356 + 0.612680i
\(86\) −155.348 −0.194787
\(87\) 644.966i 0.794800i
\(88\) 2032.86i 2.46254i
\(89\) 90.2097 0.107441 0.0537203 0.998556i \(-0.482892\pi\)
0.0537203 + 0.998556i \(0.482892\pi\)
\(90\) −482.845 198.070i −0.565515 0.231983i
\(91\) 316.835 0.364982
\(92\) 578.570i 0.655653i
\(93\) 492.617i 0.549269i
\(94\) −2509.23 −2.75326
\(95\) 261.342 637.084i 0.282243 0.688036i
\(96\) −853.115 −0.906986
\(97\) 492.101i 0.515106i 0.966264 + 0.257553i \(0.0829162\pi\)
−0.966264 + 0.257553i \(0.917084\pi\)
\(98\) 254.143i 0.261963i
\(99\) 323.599 0.328515
\(100\) 1681.99 + 1659.16i 1.68199 + 1.65916i
\(101\) −272.636 −0.268597 −0.134299 0.990941i \(-0.542878\pi\)
−0.134299 + 0.990941i \(0.542878\pi\)
\(102\) 1760.65i 1.70912i
\(103\) 628.179i 0.600936i −0.953792 0.300468i \(-0.902857\pi\)
0.953792 0.300468i \(-0.0971428\pi\)
\(104\) −2559.05 −2.41284
\(105\) 89.1073 217.221i 0.0828189 0.201891i
\(106\) −1533.07 −1.40476
\(107\) 908.469i 0.820794i −0.911907 0.410397i \(-0.865390\pi\)
0.911907 0.410397i \(-0.134610\pi\)
\(108\) 510.322i 0.454683i
\(109\) −984.306 −0.864948 −0.432474 0.901646i \(-0.642359\pi\)
−0.432474 + 0.901646i \(0.642359\pi\)
\(110\) −1928.99 791.302i −1.67202 0.685888i
\(111\) 1231.60 1.05314
\(112\) 994.244i 0.838814i
\(113\) 2228.79i 1.85546i −0.373251 0.927730i \(-0.621757\pi\)
0.373251 0.927730i \(-0.378243\pi\)
\(114\) 958.338 0.787339
\(115\) 316.633 + 129.888i 0.256750 + 0.105323i
\(116\) 4063.47 3.25244
\(117\) 407.360i 0.321884i
\(118\) 2158.62i 1.68404i
\(119\) −792.075 −0.610163
\(120\) −719.711 + 1754.47i −0.547502 + 1.33467i
\(121\) −38.2023 −0.0287019
\(122\) 784.193i 0.581946i
\(123\) 927.931i 0.680234i
\(124\) −3103.63 −2.24769
\(125\) 1285.61 548.025i 0.919908 0.392135i
\(126\) 326.756 0.231030
\(127\) 2860.78i 1.99885i 0.0339770 + 0.999423i \(0.489183\pi\)
−0.0339770 + 0.999423i \(0.510817\pi\)
\(128\) 518.561i 0.358084i
\(129\) −89.8556 −0.0613283
\(130\) −996.122 + 2428.29i −0.672044 + 1.63827i
\(131\) −524.971 −0.350130 −0.175065 0.984557i \(-0.556013\pi\)
−0.175065 + 0.984557i \(0.556013\pi\)
\(132\) 2038.77i 1.34433i
\(133\) 431.134i 0.281083i
\(134\) −464.332 −0.299344
\(135\) −279.284 114.567i −0.178051 0.0730394i
\(136\) 6397.51 4.03369
\(137\) 2149.03i 1.34017i 0.742282 + 0.670087i \(0.233743\pi\)
−0.742282 + 0.670087i \(0.766257\pi\)
\(138\) 476.298i 0.293806i
\(139\) 1507.78 0.920060 0.460030 0.887903i \(-0.347839\pi\)
0.460030 + 0.887903i \(0.347839\pi\)
\(140\) −1368.55 561.401i −0.826169 0.338907i
\(141\) −1451.37 −0.866861
\(142\) 3704.61i 2.18932i
\(143\) 1627.42i 0.951693i
\(144\) −1278.31 −0.739765
\(145\) 912.242 2223.81i 0.522466 1.27364i
\(146\) −5889.80 −3.33865
\(147\) 147.000i 0.0824786i
\(148\) 7759.41i 4.30959i
\(149\) 1013.61 0.557304 0.278652 0.960392i \(-0.410112\pi\)
0.278652 + 0.960392i \(0.410112\pi\)
\(150\) 1384.67 + 1365.87i 0.753721 + 0.743487i
\(151\) 1663.70 0.896623 0.448312 0.893877i \(-0.352025\pi\)
0.448312 + 0.893877i \(0.352025\pi\)
\(152\) 3482.23i 1.85820i
\(153\) 1018.38i 0.538113i
\(154\) 1305.41 0.683070
\(155\) −696.759 + 1698.52i −0.361065 + 0.880183i
\(156\) −2566.48 −1.31720
\(157\) 2399.48i 1.21974i −0.792500 0.609872i \(-0.791221\pi\)
0.792500 0.609872i \(-0.208779\pi\)
\(158\) 1677.07i 0.844434i
\(159\) −886.746 −0.442286
\(160\) 2941.50 + 1206.65i 1.45341 + 0.596212i
\(161\) −214.276 −0.104890
\(162\) 420.115i 0.203749i
\(163\) 1415.81i 0.680337i 0.940365 + 0.340168i \(0.110484\pi\)
−0.940365 + 0.340168i \(0.889516\pi\)
\(164\) 5846.22 2.78362
\(165\) −1115.75 457.700i −0.526433 0.215951i
\(166\) 1545.08 0.722418
\(167\) 3543.86i 1.64211i 0.570850 + 0.821055i \(0.306614\pi\)
−0.570850 + 0.821055i \(0.693386\pi\)
\(168\) 1187.30i 0.545253i
\(169\) 148.335 0.0675170
\(170\) 2490.26 6070.62i 1.12350 2.73880i
\(171\) 554.316 0.247892
\(172\) 566.115i 0.250964i
\(173\) 95.6649i 0.0420420i −0.999779 0.0210210i \(-0.993308\pi\)
0.999779 0.0210210i \(-0.00669169\pi\)
\(174\) 3345.18 1.45746
\(175\) −614.475 + 622.933i −0.265428 + 0.269082i
\(176\) −5106.93 −2.18721
\(177\) 1248.57i 0.530218i
\(178\) 467.882i 0.197018i
\(179\) −2166.13 −0.904491 −0.452245 0.891894i \(-0.649377\pi\)
−0.452245 + 0.891894i \(0.649377\pi\)
\(180\) −721.801 + 1759.57i −0.298888 + 0.728613i
\(181\) −1859.24 −0.763514 −0.381757 0.924263i \(-0.624681\pi\)
−0.381757 + 0.924263i \(0.624681\pi\)
\(182\) 1643.30i 0.669282i
\(183\) 453.588i 0.183225i
\(184\) 1730.68 0.693411
\(185\) −4246.49 1741.98i −1.68761 0.692284i
\(186\) −2555.01 −1.00722
\(187\) 4068.49i 1.59100i
\(188\) 9144.03i 3.54733i
\(189\) 189.000 0.0727393
\(190\) −3304.30 1355.48i −1.26168 0.517561i
\(191\) −2661.60 −1.00831 −0.504154 0.863614i \(-0.668195\pi\)
−0.504154 + 0.863614i \(0.668195\pi\)
\(192\) 1015.93i 0.381868i
\(193\) 1952.03i 0.728033i 0.931393 + 0.364016i \(0.118595\pi\)
−0.931393 + 0.364016i \(0.881405\pi\)
\(194\) 2552.33 0.944570
\(195\) −576.170 + 1404.56i −0.211592 + 0.515807i
\(196\) 926.141 0.337515
\(197\) 3587.80i 1.29757i 0.760974 + 0.648783i \(0.224722\pi\)
−0.760974 + 0.648783i \(0.775278\pi\)
\(198\) 1678.38i 0.602411i
\(199\) 767.691 0.273468 0.136734 0.990608i \(-0.456339\pi\)
0.136734 + 0.990608i \(0.456339\pi\)
\(200\) 4963.05 5031.36i 1.75470 1.77886i
\(201\) −268.576 −0.0942481
\(202\) 1414.06i 0.492538i
\(203\) 1504.92i 0.520319i
\(204\) 6416.09 2.20204
\(205\) 1312.47 3199.46i 0.447155 1.09005i
\(206\) −3258.12 −1.10196
\(207\) 275.497i 0.0925042i
\(208\) 6428.81i 2.14306i
\(209\) 2214.52 0.732927
\(210\) −1126.64 462.164i −0.370216 0.151868i
\(211\) −1199.84 −0.391472 −0.195736 0.980657i \(-0.562710\pi\)
−0.195736 + 0.980657i \(0.562710\pi\)
\(212\) 5586.75i 1.80990i
\(213\) 2142.79i 0.689305i
\(214\) −4711.87 −1.50512
\(215\) 309.818 + 127.092i 0.0982762 + 0.0403144i
\(216\) −1526.53 −0.480868
\(217\) 1149.44i 0.359581i
\(218\) 5105.20i 1.58609i
\(219\) −3406.74 −1.05117
\(220\) −2883.64 + 7029.56i −0.883703 + 2.15424i
\(221\) 5121.58 1.55889
\(222\) 6387.81i 1.93118i
\(223\) 2917.84i 0.876203i −0.898926 0.438101i \(-0.855651\pi\)
0.898926 0.438101i \(-0.144349\pi\)
\(224\) −1990.60 −0.593762
\(225\) 800.914 + 790.040i 0.237308 + 0.234086i
\(226\) −11559.9 −3.40243
\(227\) 612.679i 0.179141i 0.995981 + 0.0895703i \(0.0285494\pi\)
−0.995981 + 0.0895703i \(0.971451\pi\)
\(228\) 3492.34i 1.01441i
\(229\) −2641.51 −0.762253 −0.381126 0.924523i \(-0.624464\pi\)
−0.381126 + 0.924523i \(0.624464\pi\)
\(230\) 673.677 1642.25i 0.193135 0.470812i
\(231\) 755.065 0.215063
\(232\) 12155.1i 3.43974i
\(233\) 2322.87i 0.653117i 0.945177 + 0.326558i \(0.105889\pi\)
−0.945177 + 0.326558i \(0.894111\pi\)
\(234\) −2112.81 −0.590251
\(235\) 5004.25 + 2052.82i 1.38911 + 0.569835i
\(236\) 7866.36 2.16973
\(237\) 970.041i 0.265869i
\(238\) 4108.18i 1.11888i
\(239\) −5372.54 −1.45406 −0.727030 0.686605i \(-0.759100\pi\)
−0.727030 + 0.686605i \(0.759100\pi\)
\(240\) 4407.56 + 1808.05i 1.18544 + 0.486288i
\(241\) −1412.33 −0.377494 −0.188747 0.982026i \(-0.560443\pi\)
−0.188747 + 0.982026i \(0.560443\pi\)
\(242\) 198.140i 0.0526319i
\(243\) 243.000i 0.0641500i
\(244\) 2857.73 0.749784
\(245\) 207.917 506.849i 0.0542177 0.132169i
\(246\) 4812.81 1.24737
\(247\) 2787.73i 0.718133i
\(248\) 9283.91i 2.37713i
\(249\) 893.694 0.227452
\(250\) −2842.39 6667.95i −0.719074 1.68687i
\(251\) 5676.06 1.42737 0.713684 0.700467i \(-0.247025\pi\)
0.713684 + 0.700467i \(0.247025\pi\)
\(252\) 1190.75i 0.297660i
\(253\) 1100.63i 0.273501i
\(254\) 14837.7 3.66536
\(255\) 1440.40 3511.33i 0.353731 0.862306i
\(256\) −5398.72 −1.31805
\(257\) 3939.60i 0.956207i −0.878303 0.478104i \(-0.841324\pi\)
0.878303 0.478104i \(-0.158676\pi\)
\(258\) 466.045i 0.112460i
\(259\) 2873.73 0.689440
\(260\) 8849.09 + 3630.03i 2.11076 + 0.865866i
\(261\) 1934.90 0.458878
\(262\) 2722.82i 0.642047i
\(263\) 5397.68i 1.26553i 0.774343 + 0.632766i \(0.218081\pi\)
−0.774343 + 0.632766i \(0.781919\pi\)
\(264\) −6098.58 −1.42175
\(265\) 3057.46 + 1254.22i 0.708747 + 0.290739i
\(266\) 2236.12 0.515434
\(267\) 270.629i 0.0620308i
\(268\) 1692.10i 0.385678i
\(269\) −4973.60 −1.12731 −0.563654 0.826011i \(-0.690605\pi\)
−0.563654 + 0.826011i \(0.690605\pi\)
\(270\) −594.211 + 1448.53i −0.133935 + 0.326500i
\(271\) 4147.48 0.929672 0.464836 0.885397i \(-0.346113\pi\)
0.464836 + 0.885397i \(0.346113\pi\)
\(272\) 16071.7i 3.58269i
\(273\) 950.506i 0.210722i
\(274\) 11146.2 2.45753
\(275\) 3199.69 + 3156.25i 0.701632 + 0.692106i
\(276\) 1735.71 0.378541
\(277\) 2616.79i 0.567609i −0.958882 0.283805i \(-0.908403\pi\)
0.958882 0.283805i \(-0.0915968\pi\)
\(278\) 7820.26i 1.68715i
\(279\) −1477.85 −0.317121
\(280\) −1679.32 + 4093.76i −0.358424 + 0.873747i
\(281\) 2866.89 0.608628 0.304314 0.952572i \(-0.401573\pi\)
0.304314 + 0.952572i \(0.401573\pi\)
\(282\) 7527.68i 1.58960i
\(283\) 3015.40i 0.633381i −0.948529 0.316691i \(-0.897428\pi\)
0.948529 0.316691i \(-0.102572\pi\)
\(284\) −13500.2 −2.82074
\(285\) −1911.25 784.025i −0.397238 0.162953i
\(286\) −8440.80 −1.74516
\(287\) 2165.17i 0.445318i
\(288\) 2559.35i 0.523649i
\(289\) −7890.73 −1.60609
\(290\) −11534.0 4731.43i −2.33552 0.958067i
\(291\) 1476.30 0.297396
\(292\) 21463.4i 4.30155i
\(293\) 3580.41i 0.713890i −0.934125 0.356945i \(-0.883818\pi\)
0.934125 0.356945i \(-0.116182\pi\)
\(294\) 762.430 0.151244
\(295\) 1765.98 4305.02i 0.348541 0.849653i
\(296\) −23210.8 −4.55777
\(297\) 970.798i 0.189668i
\(298\) 5257.20i 1.02195i
\(299\) 1385.51 0.267981
\(300\) 4977.47 5045.98i 0.957914 0.971099i
\(301\) −209.663 −0.0401488
\(302\) 8628.96i 1.64417i
\(303\) 817.909i 0.155075i
\(304\) −8748.01 −1.65044
\(305\) 641.555 1563.95i 0.120444 0.293611i
\(306\) 5281.94 0.986760
\(307\) 1432.92i 0.266389i −0.991090 0.133194i \(-0.957477\pi\)
0.991090 0.133194i \(-0.0425234\pi\)
\(308\) 4757.12i 0.880072i
\(309\) −1884.54 −0.346950
\(310\) 8809.54 + 3613.81i 1.61403 + 0.662099i
\(311\) 5488.33 1.00069 0.500345 0.865826i \(-0.333206\pi\)
0.500345 + 0.865826i \(0.333206\pi\)
\(312\) 7677.14i 1.39305i
\(313\) 2461.68i 0.444545i −0.974985 0.222272i \(-0.928653\pi\)
0.974985 0.222272i \(-0.0713474\pi\)
\(314\) −12445.2 −2.23669
\(315\) −651.662 267.322i −0.116562 0.0478155i
\(316\) −6111.53 −1.08798
\(317\) 3113.12i 0.551579i −0.961218 0.275789i \(-0.911061\pi\)
0.961218 0.275789i \(-0.0889393\pi\)
\(318\) 4599.20i 0.811038i
\(319\) 7730.03 1.35673
\(320\) 1436.94 3502.88i 0.251023 0.611929i
\(321\) −2725.41 −0.473886
\(322\) 1111.36i 0.192341i
\(323\) 6969.20i 1.20055i
\(324\) −1530.97 −0.262512
\(325\) 3973.21 4027.90i 0.678136 0.687470i
\(326\) 7343.25 1.24756
\(327\) 2952.92i 0.499378i
\(328\) 17487.9i 2.94392i
\(329\) −3386.53 −0.567494
\(330\) −2373.91 + 5786.97i −0.395998 + 0.965341i
\(331\) −6364.21 −1.05682 −0.528411 0.848988i \(-0.677212\pi\)
−0.528411 + 0.848988i \(0.677212\pi\)
\(332\) 5630.52i 0.930768i
\(333\) 3694.79i 0.608029i
\(334\) 18380.6 3.01120
\(335\) 926.036 + 379.874i 0.151029 + 0.0619545i
\(336\) −2982.73 −0.484290
\(337\) 5163.25i 0.834600i 0.908769 + 0.417300i \(0.137024\pi\)
−0.908769 + 0.417300i \(0.862976\pi\)
\(338\) 769.353i 0.123809i
\(339\) −6686.37 −1.07125
\(340\) −22122.4 9074.93i −3.52869 1.44752i
\(341\) −5904.10 −0.937610
\(342\) 2875.01i 0.454570i
\(343\) 343.000i 0.0539949i
\(344\) 1693.43 0.265417
\(345\) 389.664 949.900i 0.0608081 0.148235i
\(346\) −496.176 −0.0770941
\(347\) 305.000i 0.0471851i −0.999722 0.0235926i \(-0.992490\pi\)
0.999722 0.0235926i \(-0.00751044\pi\)
\(348\) 12190.4i 1.87780i
\(349\) 8233.50 1.26283 0.631417 0.775443i \(-0.282474\pi\)
0.631417 + 0.775443i \(0.282474\pi\)
\(350\) 3230.90 + 3187.04i 0.493426 + 0.486727i
\(351\) −1222.08 −0.185840
\(352\) 10224.7i 1.54824i
\(353\) 1064.37i 0.160483i −0.996775 0.0802415i \(-0.974431\pi\)
0.996775 0.0802415i \(-0.0255692\pi\)
\(354\) 6475.85 0.972281
\(355\) −3030.77 + 7388.25i −0.453118 + 1.10458i
\(356\) −1705.04 −0.253839
\(357\) 2376.22i 0.352278i
\(358\) 11234.8i 1.65860i
\(359\) 3915.59 0.575646 0.287823 0.957684i \(-0.407069\pi\)
0.287823 + 0.957684i \(0.407069\pi\)
\(360\) 5263.41 + 2159.13i 0.770572 + 0.316101i
\(361\) −3065.59 −0.446945
\(362\) 9643.13i 1.40009i
\(363\) 114.607i 0.0165711i
\(364\) −5988.45 −0.862308
\(365\) 11746.3 + 4818.50i 1.68446 + 0.690992i
\(366\) 2352.58 0.335987
\(367\) 7430.70i 1.05689i −0.848967 0.528446i \(-0.822775\pi\)
0.848967 0.528446i \(-0.177225\pi\)
\(368\) 4347.80i 0.615882i
\(369\) 2783.79 0.392733
\(370\) −9034.93 + 22024.8i −1.26947 + 3.09464i
\(371\) −2069.07 −0.289544
\(372\) 9310.88i 1.29771i
\(373\) 3275.71i 0.454718i −0.973811 0.227359i \(-0.926991\pi\)
0.973811 0.227359i \(-0.0730090\pi\)
\(374\) 21101.6 2.91749
\(375\) −1644.08 3856.83i −0.226399 0.531109i
\(376\) 27352.7 3.75161
\(377\) 9730.86i 1.32935i
\(378\) 980.268i 0.133385i
\(379\) −5745.18 −0.778655 −0.389327 0.921099i \(-0.627293\pi\)
−0.389327 + 0.921099i \(0.627293\pi\)
\(380\) −4939.58 + 12041.4i −0.666829 + 1.62556i
\(381\) 8582.35 1.15403
\(382\) 13804.7i 1.84897i
\(383\) 101.844i 0.0135874i 0.999977 + 0.00679372i \(0.00216252\pi\)
−0.999977 + 0.00679372i \(0.997837\pi\)
\(384\) −1555.68 −0.206740
\(385\) −2603.43 1067.97i −0.344631 0.141373i
\(386\) 10124.4 1.33502
\(387\) 269.567i 0.0354079i
\(388\) 9301.11i 1.21699i
\(389\) −3047.72 −0.397237 −0.198619 0.980077i \(-0.563646\pi\)
−0.198619 + 0.980077i \(0.563646\pi\)
\(390\) 7284.87 + 2988.37i 0.945856 + 0.388005i
\(391\) −3463.72 −0.448000
\(392\) 2770.38i 0.356952i
\(393\) 1574.91i 0.202147i
\(394\) 18608.5 2.37940
\(395\) −1372.03 + 3344.65i −0.174770 + 0.426045i
\(396\) −6116.30 −0.776151
\(397\) 9830.23i 1.24273i −0.783520 0.621367i \(-0.786578\pi\)
0.783520 0.621367i \(-0.213422\pi\)
\(398\) 3981.71i 0.501470i
\(399\) 1293.40 0.162284
\(400\) −12639.7 12468.1i −1.57997 1.55852i
\(401\) 3693.01 0.459900 0.229950 0.973202i \(-0.426144\pi\)
0.229950 + 0.973202i \(0.426144\pi\)
\(402\) 1393.00i 0.172827i
\(403\) 7432.31i 0.918684i
\(404\) 5153.06 0.634589
\(405\) −343.700 + 837.852i −0.0421693 + 0.102798i
\(406\) 7805.43 0.954130
\(407\) 14760.9i 1.79772i
\(408\) 19192.5i 2.32885i
\(409\) −8815.07 −1.06571 −0.532857 0.846205i \(-0.678882\pi\)
−0.532857 + 0.846205i \(0.678882\pi\)
\(410\) −16594.3 6807.25i −1.99887 0.819966i
\(411\) 6447.09 0.773750
\(412\) 11873.1i 1.41977i
\(413\) 2913.34i 0.347109i
\(414\) 1428.89 0.169629
\(415\) −3081.41 1264.04i −0.364483 0.149517i
\(416\) 12871.3 1.51699
\(417\) 4523.35i 0.531197i
\(418\) 11485.8i 1.34400i
\(419\) −3746.84 −0.436862 −0.218431 0.975852i \(-0.570094\pi\)
−0.218431 + 0.975852i \(0.570094\pi\)
\(420\) −1684.20 + 4105.65i −0.195668 + 0.476989i
\(421\) −10554.5 −1.22184 −0.610922 0.791690i \(-0.709201\pi\)
−0.610922 + 0.791690i \(0.709201\pi\)
\(422\) 6223.10i 0.717858i
\(423\) 4354.11i 0.500482i
\(424\) 16711.7 1.91413
\(425\) −9932.87 + 10069.6i −1.13368 + 1.14929i
\(426\) −11113.8 −1.26401
\(427\) 1058.37i 0.119949i
\(428\) 17170.8i 1.93921i
\(429\) −4882.27 −0.549460
\(430\) 659.175 1606.90i 0.0739262 0.180213i
\(431\) −14029.9 −1.56797 −0.783986 0.620778i \(-0.786817\pi\)
−0.783986 + 0.620778i \(0.786817\pi\)
\(432\) 3834.94i 0.427103i
\(433\) 9639.08i 1.06980i −0.844915 0.534901i \(-0.820349\pi\)
0.844915 0.534901i \(-0.179651\pi\)
\(434\) −5961.69 −0.659378
\(435\) −6671.43 2736.72i −0.735335 0.301646i
\(436\) 18604.2 2.04353
\(437\) 1885.34i 0.206380i
\(438\) 17669.4i 1.92757i
\(439\) −3936.53 −0.427974 −0.213987 0.976837i \(-0.568645\pi\)
−0.213987 + 0.976837i \(0.568645\pi\)
\(440\) 21027.6 + 8625.85i 2.27830 + 0.934594i
\(441\) 441.000 0.0476190
\(442\) 26563.6i 2.85860i
\(443\) 10812.5i 1.15963i −0.814746 0.579817i \(-0.803124\pi\)
0.814746 0.579817i \(-0.196876\pi\)
\(444\) −23278.2 −2.48814
\(445\) −382.778 + 933.115i −0.0407762 + 0.0994020i
\(446\) −15133.7 −1.60673
\(447\) 3040.84i 0.321760i
\(448\) 2370.51i 0.249991i
\(449\) −8154.86 −0.857131 −0.428565 0.903511i \(-0.640981\pi\)
−0.428565 + 0.903511i \(0.640981\pi\)
\(450\) 4097.62 4154.02i 0.429253 0.435161i
\(451\) 11121.4 1.16117
\(452\) 42126.0i 4.38372i
\(453\) 4991.11i 0.517666i
\(454\) 3177.72 0.328497
\(455\) −1344.40 + 3277.30i −0.138519 + 0.337675i
\(456\) −10446.7 −1.07283
\(457\) 17787.5i 1.82071i 0.413833 + 0.910353i \(0.364190\pi\)
−0.413833 + 0.910353i \(0.635810\pi\)
\(458\) 13700.5i 1.39777i
\(459\) 3055.15 0.310680
\(460\) −5984.64 2454.99i −0.606598 0.248836i
\(461\) 13192.1 1.33280 0.666398 0.745596i \(-0.267835\pi\)
0.666398 + 0.745596i \(0.267835\pi\)
\(462\) 3916.22i 0.394371i
\(463\) 542.568i 0.0544607i −0.999629 0.0272303i \(-0.991331\pi\)
0.999629 0.0272303i \(-0.00866876\pi\)
\(464\) −30535.9 −3.05516
\(465\) 5095.56 + 2090.28i 0.508174 + 0.208461i
\(466\) 12047.8 1.19765
\(467\) 5962.51i 0.590818i 0.955371 + 0.295409i \(0.0954559\pi\)
−0.955371 + 0.295409i \(0.904544\pi\)
\(468\) 7699.44i 0.760484i
\(469\) −626.677 −0.0616999
\(470\) 10647.2 25955.1i 1.04493 2.54727i
\(471\) −7198.45 −0.704219
\(472\) 23530.7i 2.29468i
\(473\) 1076.93i 0.104688i
\(474\) −5031.21 −0.487534
\(475\) 5480.98 + 5406.56i 0.529441 + 0.522253i
\(476\) 14970.9 1.44157
\(477\) 2660.24i 0.255354i
\(478\) 27865.2i 2.66637i
\(479\) 1317.66 0.125690 0.0628451 0.998023i \(-0.479983\pi\)
0.0628451 + 0.998023i \(0.479983\pi\)
\(480\) 3619.94 8824.49i 0.344223 0.839127i
\(481\) −18581.6 −1.76143
\(482\) 7325.19i 0.692227i
\(483\) 642.827i 0.0605582i
\(484\) 722.054 0.0678113
\(485\) −5090.22 2088.08i −0.476567 0.195495i
\(486\) −1260.34 −0.117635
\(487\) 5976.21i 0.556074i −0.960570 0.278037i \(-0.910316\pi\)
0.960570 0.278037i \(-0.0896837\pi\)
\(488\) 8548.35i 0.792962i
\(489\) 4247.43 0.392793
\(490\) −2628.82 1078.38i −0.242363 0.0994212i
\(491\) 10338.9 0.950285 0.475143 0.879909i \(-0.342396\pi\)
0.475143 + 0.879909i \(0.342396\pi\)
\(492\) 17538.7i 1.60712i
\(493\) 24326.7i 2.22236i
\(494\) −14458.8 −1.31687
\(495\) −1373.10 + 3347.26i −0.124679 + 0.303936i
\(496\) 23322.9 2.11135
\(497\) 4999.85i 0.451256i
\(498\) 4635.24i 0.417088i
\(499\) 4161.74 0.373357 0.186678 0.982421i \(-0.440228\pi\)
0.186678 + 0.982421i \(0.440228\pi\)
\(500\) −24299.1 + 10358.1i −2.17338 + 0.926460i
\(501\) 10631.6 0.948072
\(502\) 29439.4i 2.61742i
\(503\) 7556.24i 0.669813i 0.942251 + 0.334907i \(0.108705\pi\)
−0.942251 + 0.334907i \(0.891295\pi\)
\(504\) −3561.91 −0.314802
\(505\) 1156.85 2820.11i 0.101939 0.248501i
\(506\) 5708.51 0.501530
\(507\) 445.004i 0.0389809i
\(508\) 54071.2i 4.72248i
\(509\) −7231.12 −0.629693 −0.314847 0.949143i \(-0.601953\pi\)
−0.314847 + 0.949143i \(0.601953\pi\)
\(510\) −18211.9 7470.79i −1.58125 0.648651i
\(511\) −7949.06 −0.688152
\(512\) 23852.5i 2.05887i
\(513\) 1662.95i 0.143121i
\(514\) −20433.1 −1.75344
\(515\) 6497.79 + 2665.50i 0.555975 + 0.228069i
\(516\) 1698.35 0.144894
\(517\) 17394.9i 1.47974i
\(518\) 14904.9i 1.26425i
\(519\) −286.995 −0.0242730
\(520\) 10858.6 26470.4i 0.915729 2.23231i
\(521\) −7378.54 −0.620460 −0.310230 0.950661i \(-0.600406\pi\)
−0.310230 + 0.950661i \(0.600406\pi\)
\(522\) 10035.5i 0.841464i
\(523\) 2200.53i 0.183982i 0.995760 + 0.0919909i \(0.0293231\pi\)
−0.995760 + 0.0919909i \(0.970677\pi\)
\(524\) 9922.40 0.827217
\(525\) 1868.80 + 1843.43i 0.155354 + 0.153245i
\(526\) 27995.6 2.32066
\(527\) 18580.5i 1.53582i
\(528\) 15320.8i 1.26279i
\(529\) 11230.0 0.922987
\(530\) 6505.12 15857.8i 0.533140 1.29966i
\(531\) 3745.72 0.306121
\(532\) 8148.80i 0.664089i
\(533\) 14000.1i 1.13773i
\(534\) −1403.64 −0.113748
\(535\) 9397.06 + 3854.82i 0.759384 + 0.311511i
\(536\) 5061.60 0.407888
\(537\) 6498.38i 0.522208i
\(538\) 25796.1i 2.06719i
\(539\) 1761.82 0.140792
\(540\) 5278.70 + 2165.40i 0.420665 + 0.172563i
\(541\) −23797.3 −1.89118 −0.945588 0.325365i \(-0.894513\pi\)
−0.945588 + 0.325365i \(0.894513\pi\)
\(542\) 21511.3i 1.70478i
\(543\) 5577.72i 0.440815i
\(544\) −32177.7 −2.53604
\(545\) 4176.61 10181.5i 0.328269 0.800235i
\(546\) −4929.89 −0.386410
\(547\) 6586.46i 0.514839i −0.966300 0.257419i \(-0.917128\pi\)
0.966300 0.257419i \(-0.0828721\pi\)
\(548\) 40618.4i 3.16630i
\(549\) 1360.76 0.105785
\(550\) 16370.2 16595.5i 1.26914 1.28661i
\(551\) 13241.3 1.02377
\(552\) 5192.04i 0.400341i
\(553\) 2263.43i 0.174052i
\(554\) −13572.3 −1.04085
\(555\) −5225.93 + 12739.5i −0.399690 + 0.974343i
\(556\) −28498.3 −2.17374
\(557\) 23522.6i 1.78938i −0.446686 0.894691i \(-0.647396\pi\)
0.446686 0.894691i \(-0.352604\pi\)
\(558\) 7665.03i 0.581517i
\(559\) 1355.69 0.102575
\(560\) 10284.3 + 4218.78i 0.776056 + 0.318350i
\(561\) 12205.5 0.918566
\(562\) 14869.4i 1.11607i
\(563\) 17654.3i 1.32156i 0.750578 + 0.660782i \(0.229775\pi\)
−0.750578 + 0.660782i \(0.770225\pi\)
\(564\) 27432.1 2.04805
\(565\) 23054.3 + 9457.22i 1.71664 + 0.704192i
\(566\) −15639.7 −1.16146
\(567\) 567.000i 0.0419961i
\(568\) 40383.3i 2.98318i
\(569\) 13453.6 0.991223 0.495611 0.868544i \(-0.334944\pi\)
0.495611 + 0.868544i \(0.334944\pi\)
\(570\) −4066.43 + 9912.91i −0.298814 + 0.728431i
\(571\) 9019.88 0.661069 0.330534 0.943794i \(-0.392771\pi\)
0.330534 + 0.943794i \(0.392771\pi\)
\(572\) 30759.7i 2.24847i
\(573\) 7984.80i 0.582146i
\(574\) 11229.9 0.816597
\(575\) −2687.08 + 2724.07i −0.194885 + 0.197568i
\(576\) 3047.80 0.220472
\(577\) 1328.73i 0.0958680i −0.998851 0.0479340i \(-0.984736\pi\)
0.998851 0.0479340i \(-0.0152637\pi\)
\(578\) 40926.1i 2.94516i
\(579\) 5856.09 0.420330
\(580\) −17242.1 + 42031.9i −1.23438 + 3.00910i
\(581\) 2085.29 0.148902
\(582\) 7656.99i 0.545348i
\(583\) 10627.8i 0.754989i
\(584\) 64203.8 4.54926
\(585\) 4213.67 + 1728.51i 0.297801 + 0.122163i
\(586\) −18570.2 −1.30909
\(587\) 13927.3i 0.979283i −0.871924 0.489642i \(-0.837128\pi\)
0.871924 0.489642i \(-0.162872\pi\)
\(588\) 2778.42i 0.194864i
\(589\) −10113.5 −0.707506
\(590\) −22328.4 9159.46i −1.55804 0.639134i
\(591\) 10763.4 0.749150
\(592\) 58309.9i 4.04818i
\(593\) 5684.69i 0.393663i −0.980437 0.196831i \(-0.936935\pi\)
0.980437 0.196831i \(-0.0630652\pi\)
\(594\) −5035.14 −0.347802
\(595\) 3360.94 8193.10i 0.231571 0.564512i
\(596\) −19158.1 −1.31669
\(597\) 2303.07i 0.157887i
\(598\) 7186.10i 0.491407i
\(599\) −27961.5 −1.90730 −0.953651 0.300914i \(-0.902708\pi\)
−0.953651 + 0.300914i \(0.902708\pi\)
\(600\) −15094.1 14889.2i −1.02702 1.01308i
\(601\) −12396.7 −0.841386 −0.420693 0.907203i \(-0.638213\pi\)
−0.420693 + 0.907203i \(0.638213\pi\)
\(602\) 1087.44i 0.0736224i
\(603\) 805.727i 0.0544142i
\(604\) −31445.3 −2.11837
\(605\) 162.100 395.158i 0.0108931 0.0265545i
\(606\) 4242.17 0.284367
\(607\) 3124.52i 0.208930i −0.994529 0.104465i \(-0.966687\pi\)
0.994529 0.104465i \(-0.0333130\pi\)
\(608\) 17514.6i 1.16828i
\(609\) 4514.76 0.300406
\(610\) −8111.57 3327.49i −0.538406 0.220863i
\(611\) 21897.4 1.44988
\(612\) 19248.3i 1.27135i
\(613\) 9531.29i 0.628002i −0.949423 0.314001i \(-0.898330\pi\)
0.949423 0.314001i \(-0.101670\pi\)
\(614\) −7432.01 −0.488488
\(615\) −9598.38 3937.40i −0.629340 0.258165i
\(616\) −14230.0 −0.930754
\(617\) 5410.37i 0.353020i 0.984299 + 0.176510i \(0.0564808\pi\)
−0.984299 + 0.176510i \(0.943519\pi\)
\(618\) 9774.35i 0.636217i
\(619\) 10244.9 0.665228 0.332614 0.943063i \(-0.392069\pi\)
0.332614 + 0.943063i \(0.392069\pi\)
\(620\) 13169.3 32103.4i 0.853053 2.07952i
\(621\) 826.492 0.0534074
\(622\) 28465.8i 1.83501i
\(623\) 631.468i 0.0406087i
\(624\) 19286.4 1.23730
\(625\) 213.582 + 15623.5i 0.0136693 + 0.999907i
\(626\) −12767.8 −0.815180
\(627\) 6643.57i 0.423155i
\(628\) 45352.3i 2.88177i
\(629\) 46453.2 2.94469
\(630\) −1386.49 + 3379.91i −0.0876813 + 0.213744i
\(631\) −10342.8 −0.652522 −0.326261 0.945280i \(-0.605789\pi\)
−0.326261 + 0.945280i \(0.605789\pi\)
\(632\) 18281.5i 1.15063i
\(633\) 3599.53i 0.226016i
\(634\) −16146.5 −1.01145
\(635\) −29591.5 12138.9i −1.84930 0.758610i
\(636\) 16760.2 1.04495
\(637\) 2217.85i 0.137950i
\(638\) 40092.6i 2.48790i
\(639\) −6428.38 −0.397970
\(640\) 5363.92 + 2200.36i 0.331293 + 0.135901i
\(641\) −981.309 −0.0604671 −0.0302335 0.999543i \(-0.509625\pi\)
−0.0302335 + 0.999543i \(0.509625\pi\)
\(642\) 14135.6i 0.868984i
\(643\) 16289.5i 0.999062i −0.866296 0.499531i \(-0.833506\pi\)
0.866296 0.499531i \(-0.166494\pi\)
\(644\) 4049.99 0.247813
\(645\) 381.276 929.453i 0.0232755 0.0567398i
\(646\) 36146.5 2.20149
\(647\) 11349.5i 0.689634i 0.938670 + 0.344817i \(0.112059\pi\)
−0.938670 + 0.344817i \(0.887941\pi\)
\(648\) 4579.60i 0.277629i
\(649\) 14964.4 0.905088
\(650\) −20891.1 20607.5i −1.26064 1.24353i
\(651\) −3448.32 −0.207604
\(652\) 26760.0i 1.60737i
\(653\) 20510.7i 1.22917i 0.788852 + 0.614583i \(0.210676\pi\)
−0.788852 + 0.614583i \(0.789324\pi\)
\(654\) 15315.6 0.915730
\(655\) 2227.56 5430.22i 0.132883 0.323934i
\(656\) −43932.8 −2.61477
\(657\) 10220.2i 0.606893i
\(658\) 17564.6i 1.04064i
\(659\) −15480.4 −0.915070 −0.457535 0.889191i \(-0.651268\pi\)
−0.457535 + 0.889191i \(0.651268\pi\)
\(660\) 21088.7 + 8650.91i 1.24375 + 0.510206i
\(661\) 3720.51 0.218928 0.109464 0.993991i \(-0.465087\pi\)
0.109464 + 0.993991i \(0.465087\pi\)
\(662\) 33008.6i 1.93794i
\(663\) 15364.7i 0.900025i
\(664\) −16842.6 −0.984369
\(665\) −4459.59 1829.39i −0.260053 0.106678i
\(666\) −19163.4 −1.11497
\(667\) 6580.98i 0.382034i
\(668\) 66981.9i 3.87965i
\(669\) −8753.53 −0.505876
\(670\) 1970.26 4802.98i 0.113608 0.276948i
\(671\) 5436.32 0.312767
\(672\) 5971.81i 0.342809i
\(673\) 17977.2i 1.02967i 0.857288 + 0.514837i \(0.172147\pi\)
−0.857288 + 0.514837i \(0.827853\pi\)
\(674\) 26779.7 1.53044
\(675\) 2370.12 2402.74i 0.135149 0.137010i
\(676\) −2803.65 −0.159516
\(677\) 13079.2i 0.742505i 0.928532 + 0.371253i \(0.121072\pi\)
−0.928532 + 0.371253i \(0.878928\pi\)
\(678\) 34679.6i 1.96440i
\(679\) 3444.70 0.194692
\(680\) −27145.9 + 66174.8i −1.53088 + 3.73190i
\(681\) 1838.04 0.103427
\(682\) 30622.2i 1.71933i
\(683\) 22608.2i 1.26659i −0.773912 0.633293i \(-0.781703\pi\)
0.773912 0.633293i \(-0.218297\pi\)
\(684\) −10477.0 −0.585671
\(685\) −22229.2 9118.77i −1.23991 0.508628i
\(686\) 1779.00 0.0990127
\(687\) 7924.53i 0.440087i
\(688\) 4254.21i 0.235742i
\(689\) 13378.7 0.739749
\(690\) −4926.75 2021.03i −0.271824 0.111506i
\(691\) 26262.2 1.44582 0.722910 0.690942i \(-0.242804\pi\)
0.722910 + 0.690942i \(0.242804\pi\)
\(692\) 1808.15i 0.0993286i
\(693\) 2265.20i 0.124167i
\(694\) −1581.91 −0.0865253
\(695\) −6397.83 + 15596.3i −0.349185 + 0.851223i
\(696\) −36465.3 −1.98594
\(697\) 34999.6i 1.90201i
\(698\) 42703.9i 2.31571i
\(699\) 6968.61 0.377077
\(700\) 11614.1 11773.9i 0.627102 0.635733i
\(701\) −15831.3 −0.852982 −0.426491 0.904492i \(-0.640250\pi\)
−0.426491 + 0.904492i \(0.640250\pi\)
\(702\) 6338.44i 0.340782i
\(703\) 25285.0i 1.35653i
\(704\) 12176.1 0.651853
\(705\) 6158.46 15012.8i 0.328995 0.802004i
\(706\) −5520.44 −0.294284
\(707\) 1908.46i 0.101520i
\(708\) 23599.1i 1.25269i
\(709\) 874.284 0.0463109 0.0231554 0.999732i \(-0.492629\pi\)
0.0231554 + 0.999732i \(0.492629\pi\)
\(710\) 38319.9 + 15719.4i 2.02552 + 0.830900i
\(711\) −2910.12 −0.153499
\(712\) 5100.30i 0.268458i
\(713\) 5026.47i 0.264015i
\(714\) 12324.5 0.645986
\(715\) 16833.8 + 6905.50i 0.880489 + 0.361190i
\(716\) 40941.6 2.13695
\(717\) 16117.6i 0.839502i
\(718\) 20308.6i 1.05559i
\(719\) −103.934 −0.00539091 −0.00269546 0.999996i \(-0.500858\pi\)
−0.00269546 + 0.999996i \(0.500858\pi\)
\(720\) 5424.15 13222.7i 0.280758 0.684417i
\(721\) −4397.26 −0.227132
\(722\) 15900.0i 0.819580i
\(723\) 4236.99i 0.217946i
\(724\) 35141.2 1.80388
\(725\) 19131.9 + 18872.2i 0.980058 + 0.966752i
\(726\) 594.420 0.0303870
\(727\) 20972.0i 1.06989i −0.844887 0.534945i \(-0.820332\pi\)
0.844887 0.534945i \(-0.179668\pi\)
\(728\) 17913.3i 0.911967i
\(729\) −729.000 −0.0370370
\(730\) 24991.7 60923.2i 1.26710 3.08886i
\(731\) −3389.16 −0.171481
\(732\) 8573.18i 0.432888i
\(733\) 32298.2i 1.62750i 0.581213 + 0.813751i \(0.302578\pi\)
−0.581213 + 0.813751i \(0.697422\pi\)
\(734\) −38540.1 −1.93807
\(735\) −1520.55 623.751i −0.0763077 0.0313026i
\(736\) −8704.85 −0.435958
\(737\) 3218.93i 0.160883i
\(738\) 14438.4i 0.720171i
\(739\) −19402.4 −0.965804 −0.482902 0.875674i \(-0.660417\pi\)
−0.482902 + 0.875674i \(0.660417\pi\)
\(740\) 80262.2 + 32924.8i 3.98716 + 1.63559i
\(741\) −8363.18 −0.414614
\(742\) 10731.5i 0.530949i
\(743\) 28784.0i 1.42124i −0.703575 0.710621i \(-0.748414\pi\)
0.703575 0.710621i \(-0.251586\pi\)
\(744\) 27851.7 1.37244
\(745\) −4300.97 + 10484.7i −0.211510 + 0.515608i
\(746\) −16989.8 −0.833834
\(747\) 2681.08i 0.131320i
\(748\) 76897.9i 3.75891i
\(749\) −6359.28 −0.310231
\(750\) −20003.8 + 8527.17i −0.973916 + 0.415157i
\(751\) 4382.70 0.212952 0.106476 0.994315i \(-0.466043\pi\)
0.106476 + 0.994315i \(0.466043\pi\)
\(752\) 68715.0i 3.33215i
\(753\) 17028.2i 0.824092i
\(754\) −50470.1 −2.43768
\(755\) −7059.43 + 17209.1i −0.340290 + 0.829540i
\(756\) −3572.26 −0.171854
\(757\) 13669.8i 0.656326i −0.944621 0.328163i \(-0.893570\pi\)
0.944621 0.328163i \(-0.106430\pi\)
\(758\) 29798.0i 1.42785i
\(759\) 3301.88 0.157906
\(760\) 36019.6 + 14775.8i 1.71917 + 0.705230i
\(761\) −25216.4 −1.20117 −0.600586 0.799560i \(-0.705066\pi\)
−0.600586 + 0.799560i \(0.705066\pi\)
\(762\) 44513.2i 2.11620i
\(763\) 6890.14i 0.326920i
\(764\) 50306.5 2.38223
\(765\) −10534.0 4321.21i −0.497853 0.204227i
\(766\) 528.225 0.0249158
\(767\) 18837.7i 0.886819i
\(768\) 16196.2i 0.760975i
\(769\) −15930.6 −0.747038 −0.373519 0.927622i \(-0.621849\pi\)
−0.373519 + 0.927622i \(0.621849\pi\)
\(770\) −5539.11 + 13502.9i −0.259241 + 0.631964i
\(771\) −11818.8 −0.552066
\(772\) 36895.0i 1.72005i
\(773\) 28154.5i 1.31002i 0.755618 + 0.655012i \(0.227336\pi\)
−0.755618 + 0.655012i \(0.772664\pi\)
\(774\) 1398.14 0.0649289
\(775\) −14612.7 14414.3i −0.677297 0.668101i
\(776\) −27822.5 −1.28708
\(777\) 8621.19i 0.398048i
\(778\) 15807.3i 0.728430i
\(779\) 19050.6 0.876200
\(780\) 10890.1 26547.3i 0.499908 1.21865i
\(781\) −25681.8 −1.17665
\(782\) 17964.9i 0.821515i
\(783\) 5804.70i 0.264933i
\(784\) −6959.71 −0.317042