Properties

Label 13.4.b.a.12.2
Level $13$
Weight $4$
Character 13.12
Analytic conductor $0.767$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 13.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.767024830075\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 12.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 13.12
Dual form 13.4.b.a.12.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -9.00000i q^{5} -3.00000i q^{6} -15.0000i q^{7} +21.0000i q^{8} -26.0000 q^{9} +O(q^{10})\) \(q+3.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -9.00000i q^{5} -3.00000i q^{6} -15.0000i q^{7} +21.0000i q^{8} -26.0000 q^{9} +27.0000 q^{10} +48.0000i q^{11} +1.00000 q^{12} +(26.0000 - 39.0000i) q^{13} +45.0000 q^{14} +9.00000i q^{15} -71.0000 q^{16} -45.0000 q^{17} -78.0000i q^{18} +6.00000i q^{19} +9.00000i q^{20} +15.0000i q^{21} -144.000 q^{22} +162.000 q^{23} -21.0000i q^{24} +44.0000 q^{25} +(117.000 + 78.0000i) q^{26} +53.0000 q^{27} +15.0000i q^{28} -144.000 q^{29} -27.0000 q^{30} +264.000i q^{31} -45.0000i q^{32} -48.0000i q^{33} -135.000i q^{34} -135.000 q^{35} +26.0000 q^{36} -303.000i q^{37} -18.0000 q^{38} +(-26.0000 + 39.0000i) q^{39} +189.000 q^{40} -192.000i q^{41} -45.0000 q^{42} -97.0000 q^{43} -48.0000i q^{44} +234.000i q^{45} +486.000i q^{46} -111.000i q^{47} +71.0000 q^{48} +118.000 q^{49} +132.000i q^{50} +45.0000 q^{51} +(-26.0000 + 39.0000i) q^{52} -414.000 q^{53} +159.000i q^{54} +432.000 q^{55} +315.000 q^{56} -6.00000i q^{57} -432.000i q^{58} -522.000i q^{59} -9.00000i q^{60} +376.000 q^{61} -792.000 q^{62} +390.000i q^{63} -433.000 q^{64} +(-351.000 - 234.000i) q^{65} +144.000 q^{66} -36.0000i q^{67} +45.0000 q^{68} -162.000 q^{69} -405.000i q^{70} +357.000i q^{71} -546.000i q^{72} +1098.00i q^{73} +909.000 q^{74} -44.0000 q^{75} -6.00000i q^{76} +720.000 q^{77} +(-117.000 - 78.0000i) q^{78} -830.000 q^{79} +639.000i q^{80} +649.000 q^{81} +576.000 q^{82} -438.000i q^{83} -15.0000i q^{84} +405.000i q^{85} -291.000i q^{86} +144.000 q^{87} -1008.00 q^{88} +438.000i q^{89} -702.000 q^{90} +(-585.000 - 390.000i) q^{91} -162.000 q^{92} -264.000i q^{93} +333.000 q^{94} +54.0000 q^{95} +45.0000i q^{96} -852.000i q^{97} +354.000i q^{98} -1248.00i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} - 2 q^{4} - 52 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{3} - 2 q^{4} - 52 q^{9} + 54 q^{10} + 2 q^{12} + 52 q^{13} + 90 q^{14} - 142 q^{16} - 90 q^{17} - 288 q^{22} + 324 q^{23} + 88 q^{25} + 234 q^{26} + 106 q^{27} - 288 q^{29} - 54 q^{30} - 270 q^{35} + 52 q^{36} - 36 q^{38} - 52 q^{39} + 378 q^{40} - 90 q^{42} - 194 q^{43} + 142 q^{48} + 236 q^{49} + 90 q^{51} - 52 q^{52} - 828 q^{53} + 864 q^{55} + 630 q^{56} + 752 q^{61} - 1584 q^{62} - 866 q^{64} - 702 q^{65} + 288 q^{66} + 90 q^{68} - 324 q^{69} + 1818 q^{74} - 88 q^{75} + 1440 q^{77} - 234 q^{78} - 1660 q^{79} + 1298 q^{81} + 1152 q^{82} + 288 q^{87} - 2016 q^{88} - 1404 q^{90} - 1170 q^{91} - 324 q^{92} + 666 q^{94} + 108 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.00000i 1.06066i 0.847791 + 0.530330i \(0.177932\pi\)
−0.847791 + 0.530330i \(0.822068\pi\)
\(3\) −1.00000 −0.192450 −0.0962250 0.995360i \(-0.530677\pi\)
−0.0962250 + 0.995360i \(0.530677\pi\)
\(4\) −1.00000 −0.125000
\(5\) 9.00000i 0.804984i −0.915423 0.402492i \(-0.868144\pi\)
0.915423 0.402492i \(-0.131856\pi\)
\(6\) 3.00000i 0.204124i
\(7\) 15.0000i 0.809924i −0.914334 0.404962i \(-0.867285\pi\)
0.914334 0.404962i \(-0.132715\pi\)
\(8\) 21.0000i 0.928078i
\(9\) −26.0000 −0.962963
\(10\) 27.0000 0.853815
\(11\) 48.0000i 1.31569i 0.753155 + 0.657843i \(0.228531\pi\)
−0.753155 + 0.657843i \(0.771469\pi\)
\(12\) 1.00000 0.0240563
\(13\) 26.0000 39.0000i 0.554700 0.832050i
\(14\) 45.0000 0.859054
\(15\) 9.00000i 0.154919i
\(16\) −71.0000 −1.10938
\(17\) −45.0000 −0.642006 −0.321003 0.947078i \(-0.604020\pi\)
−0.321003 + 0.947078i \(0.604020\pi\)
\(18\) 78.0000i 1.02138i
\(19\) 6.00000i 0.0724471i 0.999344 + 0.0362235i \(0.0115328\pi\)
−0.999344 + 0.0362235i \(0.988467\pi\)
\(20\) 9.00000i 0.100623i
\(21\) 15.0000i 0.155870i
\(22\) −144.000 −1.39550
\(23\) 162.000 1.46867 0.734333 0.678789i \(-0.237495\pi\)
0.734333 + 0.678789i \(0.237495\pi\)
\(24\) 21.0000i 0.178609i
\(25\) 44.0000 0.352000
\(26\) 117.000 + 78.0000i 0.882523 + 0.588348i
\(27\) 53.0000 0.377772
\(28\) 15.0000i 0.101240i
\(29\) −144.000 −0.922073 −0.461037 0.887381i \(-0.652522\pi\)
−0.461037 + 0.887381i \(0.652522\pi\)
\(30\) −27.0000 −0.164317
\(31\) 264.000i 1.52954i 0.644302 + 0.764771i \(0.277148\pi\)
−0.644302 + 0.764771i \(0.722852\pi\)
\(32\) 45.0000i 0.248592i
\(33\) 48.0000i 0.253204i
\(34\) 135.000i 0.680950i
\(35\) −135.000 −0.651976
\(36\) 26.0000 0.120370
\(37\) 303.000i 1.34629i −0.739509 0.673147i \(-0.764942\pi\)
0.739509 0.673147i \(-0.235058\pi\)
\(38\) −18.0000 −0.0768417
\(39\) −26.0000 + 39.0000i −0.106752 + 0.160128i
\(40\) 189.000 0.747088
\(41\) 192.000i 0.731350i −0.930743 0.365675i \(-0.880838\pi\)
0.930743 0.365675i \(-0.119162\pi\)
\(42\) −45.0000 −0.165325
\(43\) −97.0000 −0.344008 −0.172004 0.985096i \(-0.555024\pi\)
−0.172004 + 0.985096i \(0.555024\pi\)
\(44\) 48.0000i 0.164461i
\(45\) 234.000i 0.775170i
\(46\) 486.000i 1.55776i
\(47\) 111.000i 0.344490i −0.985054 0.172245i \(-0.944898\pi\)
0.985054 0.172245i \(-0.0551020\pi\)
\(48\) 71.0000 0.213499
\(49\) 118.000 0.344023
\(50\) 132.000i 0.373352i
\(51\) 45.0000 0.123554
\(52\) −26.0000 + 39.0000i −0.0693375 + 0.104006i
\(53\) −414.000 −1.07297 −0.536484 0.843911i \(-0.680248\pi\)
−0.536484 + 0.843911i \(0.680248\pi\)
\(54\) 159.000i 0.400688i
\(55\) 432.000 1.05911
\(56\) 315.000 0.751672
\(57\) 6.00000i 0.0139424i
\(58\) 432.000i 0.978007i
\(59\) 522.000i 1.15184i −0.817506 0.575920i \(-0.804644\pi\)
0.817506 0.575920i \(-0.195356\pi\)
\(60\) 9.00000i 0.0193649i
\(61\) 376.000 0.789211 0.394605 0.918851i \(-0.370881\pi\)
0.394605 + 0.918851i \(0.370881\pi\)
\(62\) −792.000 −1.62232
\(63\) 390.000i 0.779927i
\(64\) −433.000 −0.845703
\(65\) −351.000 234.000i −0.669788 0.446525i
\(66\) 144.000 0.268563
\(67\) 36.0000i 0.0656433i −0.999461 0.0328216i \(-0.989551\pi\)
0.999461 0.0328216i \(-0.0104493\pi\)
\(68\) 45.0000 0.0802508
\(69\) −162.000 −0.282645
\(70\) 405.000i 0.691525i
\(71\) 357.000i 0.596734i 0.954451 + 0.298367i \(0.0964419\pi\)
−0.954451 + 0.298367i \(0.903558\pi\)
\(72\) 546.000i 0.893704i
\(73\) 1098.00i 1.76043i 0.474578 + 0.880214i \(0.342601\pi\)
−0.474578 + 0.880214i \(0.657399\pi\)
\(74\) 909.000 1.42796
\(75\) −44.0000 −0.0677424
\(76\) 6.00000i 0.00905588i
\(77\) 720.000 1.06561
\(78\) −117.000 78.0000i −0.169842 0.113228i
\(79\) −830.000 −1.18205 −0.591027 0.806652i \(-0.701277\pi\)
−0.591027 + 0.806652i \(0.701277\pi\)
\(80\) 639.000i 0.893030i
\(81\) 649.000 0.890261
\(82\) 576.000 0.775714
\(83\) 438.000i 0.579238i −0.957142 0.289619i \(-0.906471\pi\)
0.957142 0.289619i \(-0.0935286\pi\)
\(84\) 15.0000i 0.0194837i
\(85\) 405.000i 0.516805i
\(86\) 291.000i 0.364876i
\(87\) 144.000 0.177453
\(88\) −1008.00 −1.22106
\(89\) 438.000i 0.521662i 0.965384 + 0.260831i \(0.0839965\pi\)
−0.965384 + 0.260831i \(0.916003\pi\)
\(90\) −702.000 −0.822192
\(91\) −585.000 390.000i −0.673897 0.449265i
\(92\) −162.000 −0.183583
\(93\) 264.000i 0.294360i
\(94\) 333.000 0.365386
\(95\) 54.0000 0.0583188
\(96\) 45.0000i 0.0478416i
\(97\) 852.000i 0.891830i −0.895075 0.445915i \(-0.852878\pi\)
0.895075 0.445915i \(-0.147122\pi\)
\(98\) 354.000i 0.364892i
\(99\) 1248.00i 1.26696i
\(100\) −44.0000 −0.0440000
\(101\) 396.000 0.390133 0.195067 0.980790i \(-0.437508\pi\)
0.195067 + 0.980790i \(0.437508\pi\)
\(102\) 135.000i 0.131049i
\(103\) 182.000 0.174107 0.0870534 0.996204i \(-0.472255\pi\)
0.0870534 + 0.996204i \(0.472255\pi\)
\(104\) 819.000 + 546.000i 0.772207 + 0.514805i
\(105\) 135.000 0.125473
\(106\) 1242.00i 1.13805i
\(107\) −612.000 −0.552937 −0.276469 0.961023i \(-0.589164\pi\)
−0.276469 + 0.961023i \(0.589164\pi\)
\(108\) −53.0000 −0.0472215
\(109\) 1083.00i 0.951675i 0.879533 + 0.475838i \(0.157855\pi\)
−0.879533 + 0.475838i \(0.842145\pi\)
\(110\) 1296.00i 1.12335i
\(111\) 303.000i 0.259094i
\(112\) 1065.00i 0.898509i
\(113\) 90.0000 0.0749247 0.0374623 0.999298i \(-0.488073\pi\)
0.0374623 + 0.999298i \(0.488073\pi\)
\(114\) 18.0000 0.0147882
\(115\) 1458.00i 1.18225i
\(116\) 144.000 0.115259
\(117\) −676.000 + 1014.00i −0.534156 + 0.801234i
\(118\) 1566.00 1.22171
\(119\) 675.000i 0.519976i
\(120\) −189.000 −0.143777
\(121\) −973.000 −0.731029
\(122\) 1128.00i 0.837085i
\(123\) 192.000i 0.140748i
\(124\) 264.000i 0.191193i
\(125\) 1521.00i 1.08834i
\(126\) −1170.00 −0.827237
\(127\) 2086.00 1.45750 0.728750 0.684780i \(-0.240102\pi\)
0.728750 + 0.684780i \(0.240102\pi\)
\(128\) 1659.00i 1.14560i
\(129\) 97.0000 0.0662044
\(130\) 702.000 1053.00i 0.473611 0.710417i
\(131\) −1467.00 −0.978415 −0.489208 0.872167i \(-0.662714\pi\)
−0.489208 + 0.872167i \(0.662714\pi\)
\(132\) 48.0000i 0.0316505i
\(133\) 90.0000 0.0586766
\(134\) 108.000 0.0696252
\(135\) 477.000i 0.304101i
\(136\) 945.000i 0.595831i
\(137\) 414.000i 0.258178i 0.991633 + 0.129089i \(0.0412053\pi\)
−0.991633 + 0.129089i \(0.958795\pi\)
\(138\) 486.000i 0.299790i
\(139\) −2419.00 −1.47609 −0.738046 0.674750i \(-0.764251\pi\)
−0.738046 + 0.674750i \(0.764251\pi\)
\(140\) 135.000 0.0814970
\(141\) 111.000i 0.0662971i
\(142\) −1071.00 −0.632932
\(143\) 1872.00 + 1248.00i 1.09472 + 0.729811i
\(144\) 1846.00 1.06829
\(145\) 1296.00i 0.742255i
\(146\) −3294.00 −1.86721
\(147\) −118.000 −0.0662073
\(148\) 303.000i 0.168287i
\(149\) 930.000i 0.511333i −0.966765 0.255666i \(-0.917705\pi\)
0.966765 0.255666i \(-0.0822948\pi\)
\(150\) 132.000i 0.0718517i
\(151\) 1683.00i 0.907024i 0.891250 + 0.453512i \(0.149829\pi\)
−0.891250 + 0.453512i \(0.850171\pi\)
\(152\) −126.000 −0.0672365
\(153\) 1170.00 0.618228
\(154\) 2160.00i 1.13025i
\(155\) 2376.00 1.23126
\(156\) 26.0000 39.0000i 0.0133440 0.0200160i
\(157\) 1874.00 0.952621 0.476310 0.879277i \(-0.341974\pi\)
0.476310 + 0.879277i \(0.341974\pi\)
\(158\) 2490.00i 1.25376i
\(159\) 414.000 0.206493
\(160\) −405.000 −0.200113
\(161\) 2430.00i 1.18951i
\(162\) 1947.00i 0.944264i
\(163\) 1194.00i 0.573750i 0.957968 + 0.286875i \(0.0926165\pi\)
−0.957968 + 0.286875i \(0.907384\pi\)
\(164\) 192.000i 0.0914188i
\(165\) −432.000 −0.203825
\(166\) 1314.00 0.614375
\(167\) 2388.00i 1.10652i 0.833008 + 0.553260i \(0.186617\pi\)
−0.833008 + 0.553260i \(0.813383\pi\)
\(168\) −315.000 −0.144659
\(169\) −845.000 2028.00i −0.384615 0.923077i
\(170\) −1215.00 −0.548154
\(171\) 156.000i 0.0697638i
\(172\) 97.0000 0.0430011
\(173\) −1566.00 −0.688213 −0.344106 0.938931i \(-0.611818\pi\)
−0.344106 + 0.938931i \(0.611818\pi\)
\(174\) 432.000i 0.188217i
\(175\) 660.000i 0.285093i
\(176\) 3408.00i 1.45959i
\(177\) 522.000i 0.221672i
\(178\) −1314.00 −0.553306
\(179\) −657.000 −0.274338 −0.137169 0.990548i \(-0.543800\pi\)
−0.137169 + 0.990548i \(0.543800\pi\)
\(180\) 234.000i 0.0968963i
\(181\) −1222.00 −0.501826 −0.250913 0.968010i \(-0.580731\pi\)
−0.250913 + 0.968010i \(0.580731\pi\)
\(182\) 1170.00 1755.00i 0.476517 0.714776i
\(183\) −376.000 −0.151884
\(184\) 3402.00i 1.36304i
\(185\) −2727.00 −1.08375
\(186\) 792.000 0.312216
\(187\) 2160.00i 0.844678i
\(188\) 111.000i 0.0430612i
\(189\) 795.000i 0.305967i
\(190\) 162.000i 0.0618564i
\(191\) 1260.00 0.477332 0.238666 0.971102i \(-0.423290\pi\)
0.238666 + 0.971102i \(0.423290\pi\)
\(192\) 433.000 0.162756
\(193\) 342.000i 0.127553i −0.997964 0.0637764i \(-0.979686\pi\)
0.997964 0.0637764i \(-0.0203145\pi\)
\(194\) 2556.00 0.945928
\(195\) 351.000 + 234.000i 0.128901 + 0.0859338i
\(196\) −118.000 −0.0430029
\(197\) 81.0000i 0.0292945i 0.999893 + 0.0146472i \(0.00466253\pi\)
−0.999893 + 0.0146472i \(0.995337\pi\)
\(198\) 3744.00 1.34381
\(199\) 1996.00 0.711019 0.355509 0.934673i \(-0.384307\pi\)
0.355509 + 0.934673i \(0.384307\pi\)
\(200\) 924.000i 0.326683i
\(201\) 36.0000i 0.0126331i
\(202\) 1188.00i 0.413799i
\(203\) 2160.00i 0.746809i
\(204\) −45.0000 −0.0154443
\(205\) −1728.00 −0.588726
\(206\) 546.000i 0.184668i
\(207\) −4212.00 −1.41427
\(208\) −1846.00 + 2769.00i −0.615371 + 0.923056i
\(209\) −288.000 −0.0953176
\(210\) 405.000i 0.133084i
\(211\) 2833.00 0.924321 0.462161 0.886796i \(-0.347074\pi\)
0.462161 + 0.886796i \(0.347074\pi\)
\(212\) 414.000 0.134121
\(213\) 357.000i 0.114841i
\(214\) 1836.00i 0.586478i
\(215\) 873.000i 0.276921i
\(216\) 1113.00i 0.350602i
\(217\) 3960.00 1.23881
\(218\) −3249.00 −1.00940
\(219\) 1098.00i 0.338794i
\(220\) −432.000 −0.132388
\(221\) −1170.00 + 1755.00i −0.356121 + 0.534181i
\(222\) −909.000 −0.274811
\(223\) 3507.00i 1.05312i −0.850138 0.526561i \(-0.823481\pi\)
0.850138 0.526561i \(-0.176519\pi\)
\(224\) −675.000 −0.201341
\(225\) −1144.00 −0.338963
\(226\) 270.000i 0.0794696i
\(227\) 228.000i 0.0666647i −0.999444 0.0333324i \(-0.989388\pi\)
0.999444 0.0333324i \(-0.0106120\pi\)
\(228\) 6.00000i 0.00174281i
\(229\) 5493.00i 1.58510i −0.609808 0.792549i \(-0.708753\pi\)
0.609808 0.792549i \(-0.291247\pi\)
\(230\) 4374.00 1.25397
\(231\) −720.000 −0.205076
\(232\) 3024.00i 0.855756i
\(233\) 3627.00 1.01980 0.509898 0.860235i \(-0.329683\pi\)
0.509898 + 0.860235i \(0.329683\pi\)
\(234\) −3042.00 2028.00i −0.849837 0.566558i
\(235\) −999.000 −0.277309
\(236\) 522.000i 0.143980i
\(237\) 830.000 0.227486
\(238\) −2025.00 −0.551518
\(239\) 6075.00i 1.64418i 0.569357 + 0.822090i \(0.307192\pi\)
−0.569357 + 0.822090i \(0.692808\pi\)
\(240\) 639.000i 0.171864i
\(241\) 210.000i 0.0561298i −0.999606 0.0280649i \(-0.991065\pi\)
0.999606 0.0280649i \(-0.00893451\pi\)
\(242\) 2919.00i 0.775374i
\(243\) −2080.00 −0.549103
\(244\) −376.000 −0.0986514
\(245\) 1062.00i 0.276933i
\(246\) −576.000 −0.149286
\(247\) 234.000 + 156.000i 0.0602796 + 0.0401864i
\(248\) −5544.00 −1.41953
\(249\) 438.000i 0.111474i
\(250\) 4563.00 1.15436
\(251\) 7092.00 1.78344 0.891719 0.452589i \(-0.149499\pi\)
0.891719 + 0.452589i \(0.149499\pi\)
\(252\) 390.000i 0.0974908i
\(253\) 7776.00i 1.93230i
\(254\) 6258.00i 1.54591i
\(255\) 405.000i 0.0994592i
\(256\) 1513.00 0.369385
\(257\) −5805.00 −1.40897 −0.704486 0.709718i \(-0.748823\pi\)
−0.704486 + 0.709718i \(0.748823\pi\)
\(258\) 291.000i 0.0702204i
\(259\) −4545.00 −1.09040
\(260\) 351.000 + 234.000i 0.0837234 + 0.0558156i
\(261\) 3744.00 0.887923
\(262\) 4401.00i 1.03777i
\(263\) 792.000 0.185691 0.0928457 0.995681i \(-0.470404\pi\)
0.0928457 + 0.995681i \(0.470404\pi\)
\(264\) 1008.00 0.234993
\(265\) 3726.00i 0.863722i
\(266\) 270.000i 0.0622359i
\(267\) 438.000i 0.100394i
\(268\) 36.0000i 0.00820541i
\(269\) 5472.00 1.24027 0.620137 0.784493i \(-0.287077\pi\)
0.620137 + 0.784493i \(0.287077\pi\)
\(270\) 1431.00 0.322548
\(271\) 2331.00i 0.522502i −0.965271 0.261251i \(-0.915865\pi\)
0.965271 0.261251i \(-0.0841351\pi\)
\(272\) 3195.00 0.712225
\(273\) 585.000 + 390.000i 0.129692 + 0.0864611i
\(274\) −1242.00 −0.273839
\(275\) 2112.00i 0.463121i
\(276\) 162.000 0.0353306
\(277\) −1384.00 −0.300204 −0.150102 0.988671i \(-0.547960\pi\)
−0.150102 + 0.988671i \(0.547960\pi\)
\(278\) 7257.00i 1.56563i
\(279\) 6864.00i 1.47289i
\(280\) 2835.00i 0.605084i
\(281\) 4062.00i 0.862344i 0.902270 + 0.431172i \(0.141900\pi\)
−0.902270 + 0.431172i \(0.858100\pi\)
\(282\) −333.000 −0.0703187
\(283\) −3764.00 −0.790624 −0.395312 0.918547i \(-0.629364\pi\)
−0.395312 + 0.918547i \(0.629364\pi\)
\(284\) 357.000i 0.0745917i
\(285\) −54.0000 −0.0112235
\(286\) −3744.00 + 5616.00i −0.774082 + 1.16112i
\(287\) −2880.00 −0.592338
\(288\) 1170.00i 0.239385i
\(289\) −2888.00 −0.587828
\(290\) −3888.00 −0.787280
\(291\) 852.000i 0.171633i
\(292\) 1098.00i 0.220053i
\(293\) 4227.00i 0.842812i −0.906872 0.421406i \(-0.861537\pi\)
0.906872 0.421406i \(-0.138463\pi\)
\(294\) 354.000i 0.0702235i
\(295\) −4698.00 −0.927214
\(296\) 6363.00 1.24947
\(297\) 2544.00i 0.497030i
\(298\) 2790.00 0.542350
\(299\) 4212.00 6318.00i 0.814670 1.22200i
\(300\) 44.0000 0.00846780
\(301\) 1455.00i 0.278621i
\(302\) −5049.00 −0.962044
\(303\) −396.000 −0.0750812
\(304\) 426.000i 0.0803710i
\(305\) 3384.00i 0.635303i
\(306\) 3510.00i 0.655730i
\(307\) 306.000i 0.0568871i −0.999595 0.0284436i \(-0.990945\pi\)
0.999595 0.0284436i \(-0.00905509\pi\)
\(308\) −720.000 −0.133201
\(309\) −182.000 −0.0335069
\(310\) 7128.00i 1.30595i
\(311\) −2106.00 −0.383988 −0.191994 0.981396i \(-0.561495\pi\)
−0.191994 + 0.981396i \(0.561495\pi\)
\(312\) −819.000 546.000i −0.148611 0.0990742i
\(313\) 10051.0 1.81507 0.907534 0.419979i \(-0.137963\pi\)
0.907534 + 0.419979i \(0.137963\pi\)
\(314\) 5622.00i 1.01041i
\(315\) 3510.00 0.627829
\(316\) 830.000 0.147757
\(317\) 2154.00i 0.381643i −0.981625 0.190821i \(-0.938885\pi\)
0.981625 0.190821i \(-0.0611151\pi\)
\(318\) 1242.00i 0.219019i
\(319\) 6912.00i 1.21316i
\(320\) 3897.00i 0.680778i
\(321\) 612.000 0.106413
\(322\) 7290.00 1.26166
\(323\) 270.000i 0.0465115i
\(324\) −649.000 −0.111283
\(325\) 1144.00 1716.00i 0.195254 0.292882i
\(326\) −3582.00 −0.608554
\(327\) 1083.00i 0.183150i
\(328\) 4032.00 0.678750
\(329\) −1665.00 −0.279010
\(330\) 1296.00i 0.216189i
\(331\) 10770.0i 1.78844i 0.447630 + 0.894219i \(0.352268\pi\)
−0.447630 + 0.894219i \(0.647732\pi\)
\(332\) 438.000i 0.0724047i
\(333\) 7878.00i 1.29643i
\(334\) −7164.00 −1.17364
\(335\) −324.000 −0.0528418
\(336\) 1065.00i 0.172918i
\(337\) −2171.00 −0.350926 −0.175463 0.984486i \(-0.556142\pi\)
−0.175463 + 0.984486i \(0.556142\pi\)
\(338\) 6084.00 2535.00i 0.979071 0.407946i
\(339\) −90.0000 −0.0144193
\(340\) 405.000i 0.0646006i
\(341\) −12672.0 −2.01240
\(342\) 468.000 0.0739957
\(343\) 6915.00i 1.08856i
\(344\) 2037.00i 0.319267i
\(345\) 1458.00i 0.227525i
\(346\) 4698.00i 0.729960i
\(347\) −7047.00 −1.09021 −0.545105 0.838368i \(-0.683510\pi\)
−0.545105 + 0.838368i \(0.683510\pi\)
\(348\) −144.000 −0.0221816
\(349\) 6873.00i 1.05416i 0.849814 + 0.527082i \(0.176714\pi\)
−0.849814 + 0.527082i \(0.823286\pi\)
\(350\) 1980.00 0.302387
\(351\) 1378.00 2067.00i 0.209550 0.314326i
\(352\) 2160.00 0.327069
\(353\) 9318.00i 1.40495i −0.711709 0.702475i \(-0.752078\pi\)
0.711709 0.702475i \(-0.247922\pi\)
\(354\) −1566.00 −0.235119
\(355\) 3213.00 0.480362
\(356\) 438.000i 0.0652077i
\(357\) 675.000i 0.100069i
\(358\) 1971.00i 0.290979i
\(359\) 4128.00i 0.606873i −0.952852 0.303437i \(-0.901866\pi\)
0.952852 0.303437i \(-0.0981341\pi\)
\(360\) −4914.00 −0.719418
\(361\) 6823.00 0.994751
\(362\) 3666.00i 0.532267i
\(363\) 973.000 0.140687
\(364\) 585.000 + 390.000i 0.0842372 + 0.0561581i
\(365\) 9882.00 1.41712
\(366\) 1128.00i 0.161097i
\(367\) −2536.00 −0.360703 −0.180352 0.983602i \(-0.557724\pi\)
−0.180352 + 0.983602i \(0.557724\pi\)
\(368\) −11502.0 −1.62930
\(369\) 4992.00i 0.704263i
\(370\) 8181.00i 1.14949i
\(371\) 6210.00i 0.869022i
\(372\) 264.000i 0.0367951i
\(373\) −92.0000 −0.0127710 −0.00638550 0.999980i \(-0.502033\pi\)
−0.00638550 + 0.999980i \(0.502033\pi\)
\(374\) 6480.00 0.895917
\(375\) 1521.00i 0.209451i
\(376\) 2331.00 0.319713
\(377\) −3744.00 + 5616.00i −0.511474 + 0.767211i
\(378\) 2385.00 0.324527
\(379\) 10182.0i 1.37998i 0.723817 + 0.689992i \(0.242386\pi\)
−0.723817 + 0.689992i \(0.757614\pi\)
\(380\) −54.0000 −0.00728985
\(381\) −2086.00 −0.280496
\(382\) 3780.00i 0.506287i
\(383\) 579.000i 0.0772468i −0.999254 0.0386234i \(-0.987703\pi\)
0.999254 0.0386234i \(-0.0122973\pi\)
\(384\) 1659.00i 0.220470i
\(385\) 6480.00i 0.857796i
\(386\) 1026.00 0.135290
\(387\) 2522.00 0.331267
\(388\) 852.000i 0.111479i
\(389\) 2106.00 0.274495 0.137247 0.990537i \(-0.456174\pi\)
0.137247 + 0.990537i \(0.456174\pi\)
\(390\) −702.000 + 1053.00i −0.0911465 + 0.136720i
\(391\) −7290.00 −0.942893
\(392\) 2478.00i 0.319280i
\(393\) 1467.00 0.188296
\(394\) −243.000 −0.0310715
\(395\) 7470.00i 0.951535i
\(396\) 1248.00i 0.158370i
\(397\) 1974.00i 0.249552i 0.992185 + 0.124776i \(0.0398213\pi\)
−0.992185 + 0.124776i \(0.960179\pi\)
\(398\) 5988.00i 0.754149i
\(399\) −90.0000 −0.0112923
\(400\) −3124.00 −0.390500
\(401\) 11886.0i 1.48020i −0.672499 0.740098i \(-0.734779\pi\)
0.672499 0.740098i \(-0.265221\pi\)
\(402\) −108.000 −0.0133994
\(403\) 10296.0 + 6864.00i 1.27266 + 0.848437i
\(404\) −396.000 −0.0487667
\(405\) 5841.00i 0.716646i
\(406\) −6480.00 −0.792111
\(407\) 14544.0 1.77130
\(408\) 945.000i 0.114668i
\(409\) 1254.00i 0.151605i 0.997123 + 0.0758023i \(0.0241518\pi\)
−0.997123 + 0.0758023i \(0.975848\pi\)
\(410\) 5184.00i 0.624438i
\(411\) 414.000i 0.0496864i
\(412\) −182.000 −0.0217633
\(413\) −7830.00 −0.932903
\(414\) 12636.0i 1.50006i
\(415\) −3942.00 −0.466278
\(416\) −1755.00 1170.00i −0.206841 0.137894i
\(417\) 2419.00 0.284074
\(418\) 864.000i 0.101100i
\(419\) 5823.00 0.678931 0.339466 0.940618i \(-0.389754\pi\)
0.339466 + 0.940618i \(0.389754\pi\)
\(420\) −135.000 −0.0156841
\(421\) 7341.00i 0.849830i −0.905233 0.424915i \(-0.860304\pi\)
0.905233 0.424915i \(-0.139696\pi\)
\(422\) 8499.00i 0.980391i
\(423\) 2886.00i 0.331731i
\(424\) 8694.00i 0.995797i
\(425\) −1980.00 −0.225986
\(426\) 1071.00 0.121808
\(427\) 5640.00i 0.639201i
\(428\) 612.000 0.0691171
\(429\) −1872.00 1248.00i −0.210678 0.140452i
\(430\) −2619.00 −0.293720
\(431\) 7485.00i 0.836519i −0.908328 0.418260i \(-0.862640\pi\)
0.908328 0.418260i \(-0.137360\pi\)
\(432\) −3763.00 −0.419091
\(433\) −15203.0 −1.68732 −0.843660 0.536878i \(-0.819604\pi\)
−0.843660 + 0.536878i \(0.819604\pi\)
\(434\) 11880.0i 1.31396i
\(435\) 1296.00i 0.142847i
\(436\) 1083.00i 0.118959i
\(437\) 972.000i 0.106401i
\(438\) 3294.00 0.359346
\(439\) −1762.00 −0.191562 −0.0957809 0.995402i \(-0.530535\pi\)
−0.0957809 + 0.995402i \(0.530535\pi\)
\(440\) 9072.00i 0.982933i
\(441\) −3068.00 −0.331282
\(442\) −5265.00 3510.00i −0.566585 0.377723i
\(443\) −7317.00 −0.784743 −0.392372 0.919807i \(-0.628345\pi\)
−0.392372 + 0.919807i \(0.628345\pi\)
\(444\) 303.000i 0.0323868i
\(445\) 3942.00 0.419930
\(446\) 10521.0 1.11700
\(447\) 930.000i 0.0984060i
\(448\) 6495.00i 0.684955i
\(449\) 5016.00i 0.527215i 0.964630 + 0.263608i \(0.0849124\pi\)
−0.964630 + 0.263608i \(0.915088\pi\)
\(450\) 3432.00i 0.359525i
\(451\) 9216.00 0.962227
\(452\) −90.0000 −0.00936558
\(453\) 1683.00i 0.174557i
\(454\) 684.000 0.0707086
\(455\) −3510.00 + 5265.00i −0.361651 + 0.542477i
\(456\) 126.000 0.0129397
\(457\) 9870.00i 1.01028i 0.863037 + 0.505141i \(0.168560\pi\)
−0.863037 + 0.505141i \(0.831440\pi\)
\(458\) 16479.0 1.68125
\(459\) −2385.00 −0.242532
\(460\) 1458.00i 0.147782i
\(461\) 14541.0i 1.46907i −0.678570 0.734536i \(-0.737400\pi\)
0.678570 0.734536i \(-0.262600\pi\)
\(462\) 2160.00i 0.217516i
\(463\) 2112.00i 0.211993i 0.994366 + 0.105997i \(0.0338033\pi\)
−0.994366 + 0.105997i \(0.966197\pi\)
\(464\) 10224.0 1.02293
\(465\) −2376.00 −0.236956
\(466\) 10881.0i 1.08166i
\(467\) 3276.00 0.324615 0.162307 0.986740i \(-0.448106\pi\)
0.162307 + 0.986740i \(0.448106\pi\)
\(468\) 676.000 1014.00i 0.0667695 0.100154i
\(469\) −540.000 −0.0531661
\(470\) 2997.00i 0.294130i
\(471\) −1874.00 −0.183332
\(472\) 10962.0 1.06900
\(473\) 4656.00i 0.452607i
\(474\) 2490.00i 0.241286i
\(475\) 264.000i 0.0255014i
\(476\) 675.000i 0.0649970i
\(477\) 10764.0 1.03323
\(478\) −18225.0 −1.74392
\(479\) 15453.0i 1.47404i 0.675870 + 0.737020i \(0.263768\pi\)
−0.675870 + 0.737020i \(0.736232\pi\)
\(480\) 405.000 0.0385117
\(481\) −11817.0 7878.00i −1.12018 0.746790i
\(482\) 630.000 0.0595347
\(483\) 2430.00i 0.228921i
\(484\) 973.000 0.0913787
\(485\) −7668.00 −0.717909
\(486\) 6240.00i 0.582412i
\(487\) 3660.00i 0.340555i −0.985396 0.170278i \(-0.945534\pi\)
0.985396 0.170278i \(-0.0544665\pi\)
\(488\) 7896.00i 0.732449i
\(489\) 1194.00i 0.110418i
\(490\) 3186.00 0.293732
\(491\) 747.000 0.0686591 0.0343296 0.999411i \(-0.489070\pi\)
0.0343296 + 0.999411i \(0.489070\pi\)
\(492\) 192.000i 0.0175936i
\(493\) 6480.00 0.591977
\(494\) −468.000 + 702.000i −0.0426241 + 0.0639362i
\(495\) −11232.0 −1.01988
\(496\) 18744.0i 1.69684i
\(497\) 5355.00 0.483309
\(498\) −1314.00 −0.118236
\(499\) 15804.0i 1.41780i −0.705307 0.708902i \(-0.749191\pi\)
0.705307 0.708902i \(-0.250809\pi\)
\(500\) 1521.00i 0.136042i
\(501\) 2388.00i 0.212950i
\(502\) 21276.0i 1.89162i
\(503\) −12078.0 −1.07064 −0.535319 0.844650i \(-0.679809\pi\)
−0.535319 + 0.844650i \(0.679809\pi\)
\(504\) −8190.00 −0.723833
\(505\) 3564.00i 0.314051i
\(506\) −23328.0 −2.04952
\(507\) 845.000 + 2028.00i 0.0740193 + 0.177646i
\(508\) −2086.00 −0.182188
\(509\) 16110.0i 1.40287i 0.712731 + 0.701437i \(0.247458\pi\)
−0.712731 + 0.701437i \(0.752542\pi\)
\(510\) 1215.00 0.105492
\(511\) 16470.0 1.42581
\(512\) 8733.00i 0.753804i
\(513\) 318.000i 0.0273685i
\(514\) 17415.0i 1.49444i
\(515\) 1638.00i 0.140153i
\(516\) −97.0000 −0.00827556
\(517\) 5328.00 0.453240
\(518\) 13635.0i 1.15654i
\(519\) 1566.00 0.132447
\(520\) 4914.00 7371.00i 0.414410 0.621615i
\(521\) 3915.00 0.329212 0.164606 0.986359i \(-0.447365\pi\)
0.164606 + 0.986359i \(0.447365\pi\)
\(522\) 11232.0i 0.941784i
\(523\) 16184.0 1.35311 0.676555 0.736392i \(-0.263472\pi\)
0.676555 + 0.736392i \(0.263472\pi\)
\(524\) 1467.00 0.122302
\(525\) 660.000i 0.0548662i
\(526\) 2376.00i 0.196955i
\(527\) 11880.0i 0.981975i
\(528\) 3408.00i 0.280898i
\(529\) 14077.0 1.15698
\(530\) −11178.0 −0.916116
\(531\) 13572.0i 1.10918i
\(532\) −90.0000 −0.00733458
\(533\) −7488.00 4992.00i −0.608520 0.405680i
\(534\) 1314.00 0.106484
\(535\) 5508.00i 0.445106i
\(536\) 756.000 0.0609221
\(537\) 657.000 0.0527964
\(538\) 16416.0i 1.31551i
\(539\) 5664.00i 0.452627i
\(540\) 477.000i 0.0380126i
\(541\) 7923.00i 0.629642i 0.949151 + 0.314821i \(0.101945\pi\)
−0.949151 + 0.314821i \(0.898055\pi\)
\(542\) 6993.00 0.554198
\(543\) 1222.00 0.0965765
\(544\) 2025.00i 0.159598i
\(545\) 9747.00 0.766084
\(546\) −1170.00 + 1755.00i −0.0917058 + 0.137559i
\(547\) −14389.0 −1.12473 −0.562367 0.826888i \(-0.690109\pi\)
−0.562367 + 0.826888i \(0.690109\pi\)
\(548\) 414.000i 0.0322723i
\(549\) −9776.00 −0.759981
\(550\) −6336.00 −0.491214
\(551\) 864.000i 0.0668015i
\(552\) 3402.00i 0.262317i
\(553\) 12450.0i 0.957374i
\(554\) 4152.00i 0.318414i
\(555\) 2727.00 0.208567
\(556\) 2419.00 0.184512
\(557\) 10383.0i 0.789842i 0.918715 + 0.394921i \(0.129228\pi\)
−0.918715 + 0.394921i \(0.870772\pi\)
\(558\) 20592.0 1.56224
\(559\) −2522.00 + 3783.00i −0.190822 + 0.286232i
\(560\) 9585.00 0.723286
\(561\) 2160.00i 0.162558i
\(562\) −12186.0 −0.914654
\(563\) −16425.0 −1.22954 −0.614770 0.788706i \(-0.710751\pi\)
−0.614770 + 0.788706i \(0.710751\pi\)
\(564\) 111.000i 0.00828713i
\(565\) 810.000i 0.0603132i
\(566\) 11292.0i 0.838583i
\(567\) 9735.00i 0.721043i
\(568\) −7497.00 −0.553815
\(569\) 12213.0 0.899817 0.449908 0.893075i \(-0.351457\pi\)
0.449908 + 0.893075i \(0.351457\pi\)
\(570\) 162.000i 0.0119043i
\(571\) −6383.00 −0.467811 −0.233906 0.972259i \(-0.575151\pi\)
−0.233906 + 0.972259i \(0.575151\pi\)
\(572\) −1872.00 1248.00i −0.136840 0.0912264i
\(573\) −1260.00 −0.0918626
\(574\) 8640.00i 0.628269i
\(575\) 7128.00 0.516971
\(576\) 11258.0 0.814381
\(577\) 6426.00i 0.463636i 0.972759 + 0.231818i \(0.0744674\pi\)
−0.972759 + 0.231818i \(0.925533\pi\)
\(578\) 8664.00i 0.623486i
\(579\) 342.000i 0.0245476i
\(580\) 1296.00i 0.0927818i
\(581\) −6570.00 −0.469139
\(582\) −2556.00 −0.182044
\(583\) 19872.0i 1.41169i
\(584\) −23058.0 −1.63381
\(585\) 9126.00 + 6084.00i 0.644981 + 0.429987i
\(586\) 12681.0 0.893937
\(587\) 21330.0i 1.49980i −0.661551 0.749901i \(-0.730101\pi\)
0.661551 0.749901i \(-0.269899\pi\)
\(588\) 118.000 0.00827591
\(589\) −1584.00 −0.110811
\(590\) 14094.0i 0.983459i
\(591\) 81.0000i 0.00563772i
\(592\) 21513.0i 1.49355i
\(593\) 12084.0i 0.836813i −0.908260 0.418407i \(-0.862589\pi\)
0.908260 0.418407i \(-0.137411\pi\)
\(594\) −7632.00 −0.527180
\(595\) 6075.00 0.418573
\(596\) 930.000i 0.0639166i
\(597\) −1996.00 −0.136836
\(598\) 18954.0 + 12636.0i 1.29613 + 0.864088i
\(599\) 2394.00 0.163299 0.0816496 0.996661i \(-0.473981\pi\)
0.0816496 + 0.996661i \(0.473981\pi\)
\(600\) 924.000i 0.0628702i
\(601\) −21971.0 −1.49121 −0.745604 0.666389i \(-0.767839\pi\)
−0.745604 + 0.666389i \(0.767839\pi\)
\(602\) −4365.00 −0.295522
\(603\) 936.000i 0.0632121i
\(604\) 1683.00i 0.113378i
\(605\) 8757.00i 0.588467i
\(606\) 1188.00i 0.0796356i
\(607\) −15406.0 −1.03017 −0.515083 0.857141i \(-0.672239\pi\)
−0.515083 + 0.857141i \(0.672239\pi\)
\(608\) 270.000 0.0180098
\(609\) 2160.00i 0.143724i
\(610\) 10152.0 0.673840
\(611\) −4329.00 2886.00i −0.286633 0.191088i
\(612\) −1170.00 −0.0772785
\(613\) 9630.00i 0.634506i −0.948341 0.317253i \(-0.897240\pi\)
0.948341 0.317253i \(-0.102760\pi\)
\(614\) 918.000 0.0603379
\(615\) 1728.00 0.113300
\(616\) 15120.0i 0.988965i
\(617\) 14748.0i 0.962289i 0.876641 + 0.481144i \(0.159779\pi\)
−0.876641 + 0.481144i \(0.840221\pi\)
\(618\) 546.000i 0.0355394i
\(619\) 3672.00i 0.238433i 0.992868 + 0.119217i \(0.0380383\pi\)
−0.992868 + 0.119217i \(0.961962\pi\)
\(620\) −2376.00 −0.153907
\(621\) 8586.00 0.554822
\(622\) 6318.00i 0.407281i
\(623\) 6570.00 0.422506
\(624\) 1846.00 2769.00i 0.118428 0.177642i
\(625\) −8189.00 −0.524096
\(626\) 30153.0i 1.92517i
\(627\) 288.000 0.0183439
\(628\) −1874.00 −0.119078
\(629\) 13635.0i 0.864329i
\(630\) 10530.0i 0.665913i
\(631\) 19875.0i 1.25390i 0.779059 + 0.626950i \(0.215697\pi\)
−0.779059 + 0.626950i \(0.784303\pi\)
\(632\) 17430.0i 1.09704i
\(633\) −2833.00 −0.177886
\(634\) 6462.00 0.404793
\(635\) 18774.0i 1.17327i
\(636\) −414.000 −0.0258116
\(637\) 3068.00 4602.00i 0.190830 0.286245i
\(638\) 20736.0 1.28675
\(639\) 9282.00i 0.574633i
\(640\) −14931.0 −0.922187
\(641\) 1710.00 0.105368 0.0526840 0.998611i \(-0.483222\pi\)
0.0526840 + 0.998611i \(0.483222\pi\)
\(642\) 1836.00i 0.112868i
\(643\) 16452.0i 1.00903i −0.863404 0.504513i \(-0.831672\pi\)
0.863404 0.504513i \(-0.168328\pi\)
\(644\) 2430.00i 0.148689i
\(645\) 873.000i 0.0532936i
\(646\) 810.000 0.0493329
\(647\) 25902.0 1.57390 0.786950 0.617017i \(-0.211659\pi\)
0.786950 + 0.617017i \(0.211659\pi\)
\(648\) 13629.0i 0.826231i
\(649\) 25056.0 1.51546
\(650\) 5148.00 + 3432.00i 0.310648 + 0.207099i
\(651\) −3960.00 −0.238410
\(652\) 1194.00i 0.0717188i
\(653\) 18108.0 1.08518 0.542589 0.839999i \(-0.317444\pi\)
0.542589 + 0.839999i \(0.317444\pi\)
\(654\) 3249.00 0.194260
\(655\) 13203.0i 0.787609i
\(656\) 13632.0i 0.811342i
\(657\) 28548.0i 1.69523i
\(658\) 4995.00i 0.295935i
\(659\) −32904.0 −1.94500 −0.972502 0.232894i \(-0.925181\pi\)
−0.972502 + 0.232894i \(0.925181\pi\)
\(660\) 432.000 0.0254781
\(661\) 15318.0i 0.901363i −0.892685 0.450682i \(-0.851181\pi\)
0.892685 0.450682i \(-0.148819\pi\)
\(662\) −32310.0 −1.89692
\(663\) 1170.00 1755.00i 0.0685355 0.102803i
\(664\) 9198.00 0.537578
\(665\) 810.000i 0.0472338i
\(666\) −23634.0 −1.37507
\(667\) −23328.0 −1.35422
\(668\) 2388.00i 0.138315i
\(669\) 3507.00i 0.202673i
\(670\) 972.000i 0.0560472i
\(671\) 18048.0i 1.03835i
\(672\) 675.000 0.0387481
\(673\) −7729.00 −0.442691 −0.221346 0.975195i \(-0.571045\pi\)
−0.221346 + 0.975195i \(0.571045\pi\)
\(674\) 6513.00i 0.372213i
\(675\) 2332.00 0.132976
\(676\) 845.000 + 2028.00i 0.0480769 + 0.115385i
\(677\) 19242.0 1.09236 0.546182 0.837667i \(-0.316081\pi\)
0.546182 + 0.837667i \(0.316081\pi\)
\(678\) 270.000i 0.0152939i
\(679\) −12780.0 −0.722314
\(680\) −8505.00 −0.479635
\(681\) 228.000i 0.0128296i
\(682\) 38016.0i 2.13447i
\(683\) 22518.0i 1.26153i −0.775973 0.630767i \(-0.782740\pi\)
0.775973 0.630767i \(-0.217260\pi\)
\(684\) 156.000i 0.00872048i
\(685\) 3726.00 0.207829
\(686\) 20745.0 1.15459
\(687\) 5493.00i 0.305052i
\(688\) 6887.00 0.381634
\(689\) −10764.0 + 16146.0i −0.595175 + 0.892763i
\(690\) −4374.00 −0.241327
\(691\) 9168.00i 0.504728i 0.967632 + 0.252364i \(0.0812081\pi\)
−0.967632 + 0.252364i \(0.918792\pi\)
\(692\) 1566.00 0.0860266
\(693\) −18720.0 −1.02614
\(694\) 21141.0i 1.15634i
\(695\) 21771.0i 1.18823i
\(696\) 3024.00i 0.164690i
\(697\) 8640.00i 0.469531i
\(698\) −20619.0 −1.11811
\(699\) −3627.00 −0.196260
\(700\) 660.000i 0.0356367i
\(701\) 1170.00 0.0630389 0.0315195 0.999503i \(-0.489965\pi\)
0.0315195 + 0.999503i \(0.489965\pi\)
\(702\) 6201.00 + 4134.00i 0.333393 + 0.222262i
\(703\) 1818.00 0.0975351
\(704\) 20784.0i 1.11268i
\(705\) 999.000 0.0533681
\(706\) 27954.0 1.49017
\(707\) 5940.00i 0.315978i
\(708\) 522.000i 0.0277090i
\(709\) 1662.00i 0.0880363i 0.999031 + 0.0440181i \(0.0140159\pi\)
−0.999031 + 0.0440181i \(0.985984\pi\)
\(710\) 9639.00i 0.509500i
\(711\) 21580.0 1.13827
\(712\) −9198.00 −0.484143
\(713\) 42768.0i 2.24639i
\(714\) 2025.00 0.106140
\(715\) 11232.0 16848.0i 0.587487 0.881230i
\(716\) 657.000 0.0342922
\(717\) 6075.00i 0.316423i
\(718\) 12384.0 0.643686
\(719\) 30960.0 1.60586 0.802930 0.596073i \(-0.203273\pi\)
0.802930 + 0.596073i \(0.203273\pi\)
\(720\) 16614.0i 0.859954i
\(721\) 2730.00i 0.141013i
\(722\) 20469.0i 1.05509i
\(723\) 210.000i 0.0108022i
\(724\) 1222.00 0.0627283
\(725\) −6336.00 −0.324570
\(726\) 2919.00i 0.149221i
\(727\) −8372.00 −0.427098 −0.213549 0.976932i \(-0.568502\pi\)
−0.213549 + 0.976932i \(0.568502\pi\)
\(728\) 8190.00 12285.0i 0.416953 0.625429i
\(729\) −15443.0 −0.784586
\(730\) 29646.0i 1.50308i
\(731\) 4365.00 0.220855
\(732\) 376.000 0.0189855
\(733\) 2739.00i 0.138018i −0.997616 0.0690091i \(-0.978016\pi\)
0.997616 0.0690091i \(-0.0219837\pi\)
\(734\) 7608.00i 0.382584i
\(735\) 1062.00i 0.0532959i
\(736\) 7290.00i 0.365099i
\(737\) 1728.00 0.0863659
\(738\) −14976.0 −0.746984
\(739\) 6756.00i 0.336297i 0.985762 + 0.168148i \(0.0537788\pi\)
−0.985762 + 0.168148i \(0.946221\pi\)
\(740\) 2727.00 0.135468
\(741\) −234.000 156.000i −0.0116008 0.00773388i
\(742\) −18630.0 −0.921737
\(743\) 29643.0i 1.46366i 0.681490 + 0.731828i \(0.261332\pi\)
−0.681490 + 0.731828i \(0.738668\pi\)
\(744\) 5544.00 0.273189
\(745\) −8370.00 −0.411615
\(746\) 276.000i 0.0135457i
\(747\) 11388.0i 0.557785i
\(748\) 2160.00i 0.105585i
\(749\) 9180.00i 0.447837i
\(750\) −4563.00 −0.222156
\(751\) 18128.0 0.880826 0.440413 0.897795i \(-0.354832\pi\)
0.440413 + 0.897795i \(0.354832\pi\)
\(752\) 7881.00i 0.382168i
\(753\) −7092.00 −0.343223
\(754\) −16848.0 11232.0i −0.813751 0.542500i
\(755\) 15147.0 0.730140
\(756\) 795.000i 0.0382459i
\(757\) −6410.00 −0.307761 −0.153881 0.988089i \(-0.549177\pi\)
−0.153881 + 0.988089i \(0.549177\pi\)
\(758\) −30546.0 −1.46369
\(759\) 7776.00i 0.371872i
\(760\) 1134.00i 0.0541243i
\(761\) 28290.0i 1.34758i −0.738921 0.673792i \(-0.764664\pi\)
0.738921 0.673792i \(-0.235336\pi\)
\(762\) 6258.00i 0.297511i
\(763\) 16245.0 0.770784
\(764\) −1260.00 −0.0596665
\(765\) 10530.0i 0.497664i
\(766\) 1737.00 0.0819326
\(767\) −20358.0 13572.0i −0.958390 0.638926i
\(768\) −1513.00 −0.0710881
\(769\) 27960.0i 1.31114i −0.755136 0.655568i \(-0.772429\pi\)
0.755136 0.655568i \(-0.227571\pi\)
\(770\) 19440.0 0.909830
\(771\) 5805.00 0.271157
\(772\) 342.000i 0.0159441i
\(773\) 5649.00i 0.262847i −0.991326 0.131423i \(-0.958045\pi\)
0.991326 0.131423i \(-0.0419547\pi\)
\(774\) 7566.00i 0.351362i
\(775\) 11616.0i 0.538399i
\(776\) 17892.0 0.827687
\(777\) 4545.00 0.209847
\(778\) 6318.00i 0.291146i
\(779\) 1152.00 0.0529842
\(780\) −351.000 234.000i −0.0161126 0.0107417i
\(781\) −17136.0 −0.785114
\(782\) 21870.0i 1.00009i
\(783\) −7632.00 −0.348334
\(784\) −8378.00 −0.381651
\(785\) 16866.0i 0.766845i
\(786\) 4401.00i 0.199718i