Properties

Label 637.2.c.g.246.10
Level $637$
Weight $2$
Character 637.246
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 10 x^{14} + 121 x^{12} + 296 x^{10} + 3468 x^{8} - 1748 x^{6} + 40192 x^{4} - 65056 x^{2} + 228484\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 246.10
Root \(-1.41421 + 0.680196i\) of defining polynomial
Character \(\chi\) \(=\) 637.246
Dual form 637.2.c.g.246.8

$q$-expansion

\(f(q)\) \(=\) \(q+0.680196i q^{2} +2.33413 q^{3} +1.53733 q^{4} +3.24613i q^{5} +1.58766i q^{6} +2.40608i q^{8} +2.44815 q^{9} +O(q^{10})\) \(q+0.680196i q^{2} +2.33413 q^{3} +1.53733 q^{4} +3.24613i q^{5} +1.58766i q^{6} +2.40608i q^{8} +2.44815 q^{9} -2.20800 q^{10} -5.33157i q^{11} +3.58833 q^{12} +(1.47728 - 3.28902i) q^{13} +7.57687i q^{15} +1.43806 q^{16} +2.66842 q^{17} +1.66522i q^{18} +0.696519i q^{19} +4.99038i q^{20} +3.62652 q^{22} -8.96087 q^{23} +5.61610i q^{24} -5.53733 q^{25} +(2.23718 + 1.00484i) q^{26} -1.28809 q^{27} -5.28644 q^{29} -5.15376 q^{30} +5.45951i q^{31} +5.79032i q^{32} -12.4446i q^{33} +1.81505i q^{34} +3.76362 q^{36} -6.69197i q^{37} -0.473769 q^{38} +(3.44815 - 7.67699i) q^{39} -7.81044 q^{40} +2.21339i q^{41} +2.39014 q^{43} -8.19640i q^{44} +7.94700i q^{45} -6.09515i q^{46} +5.79573i q^{47} +3.35661 q^{48} -3.76647i q^{50} +6.22843 q^{51} +(2.27106 - 5.05632i) q^{52} -4.71570 q^{53} -0.876153i q^{54} +17.3070 q^{55} +1.62576i q^{57} -3.59581i q^{58} -2.98070i q^{59} +11.6482i q^{60} -2.19465 q^{61} -3.71354 q^{62} -1.06244 q^{64} +(10.6766 + 4.79542i) q^{65} +8.46475 q^{66} -8.70594i q^{67} +4.10225 q^{68} -20.9158 q^{69} -8.56190i q^{71} +5.89045i q^{72} -5.88152i q^{73} +4.55185 q^{74} -12.9248 q^{75} +1.07078i q^{76} +(5.22186 + 2.34542i) q^{78} +0.910817 q^{79} +4.66812i q^{80} -10.3510 q^{81} -1.50554 q^{82} +11.7481i q^{83} +8.66202i q^{85} +1.62576i q^{86} -12.3392 q^{87} +12.8282 q^{88} -0.986019i q^{89} -5.40552 q^{90} -13.7758 q^{92} +12.7432i q^{93} -3.94224 q^{94} -2.26099 q^{95} +13.5154i q^{96} -15.3454i q^{97} -13.0525i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 20 q^{4} + 16 q^{9} + O(q^{10}) \) \( 16 q - 20 q^{4} + 16 q^{9} + 28 q^{16} - 8 q^{22} - 36 q^{23} - 44 q^{25} + 36 q^{29} + 52 q^{36} + 32 q^{39} - 36 q^{43} - 72 q^{51} + 12 q^{53} - 164 q^{64} - 24 q^{65} + 96 q^{74} + 24 q^{78} + 36 q^{79} + 16 q^{81} + 136 q^{88} + 24 q^{92} - 84 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.680196i 0.480971i 0.970653 + 0.240486i \(0.0773067\pi\)
−0.970653 + 0.240486i \(0.922693\pi\)
\(3\) 2.33413 1.34761 0.673804 0.738910i \(-0.264659\pi\)
0.673804 + 0.738910i \(0.264659\pi\)
\(4\) 1.53733 0.768667
\(5\) 3.24613i 1.45171i 0.687847 + 0.725856i \(0.258556\pi\)
−0.687847 + 0.725856i \(0.741444\pi\)
\(6\) 1.58766i 0.648161i
\(7\) 0 0
\(8\) 2.40608i 0.850678i
\(9\) 2.44815 0.816050
\(10\) −2.20800 −0.698232
\(11\) 5.33157i 1.60753i −0.594947 0.803765i \(-0.702827\pi\)
0.594947 0.803765i \(-0.297173\pi\)
\(12\) 3.58833 1.03586
\(13\) 1.47728 3.28902i 0.409723 0.912210i
\(14\) 0 0
\(15\) 7.57687i 1.95634i
\(16\) 1.43806 0.359515
\(17\) 2.66842 0.647186 0.323593 0.946196i \(-0.395109\pi\)
0.323593 + 0.946196i \(0.395109\pi\)
\(18\) 1.66522i 0.392497i
\(19\) 0.696519i 0.159792i 0.996803 + 0.0798962i \(0.0254589\pi\)
−0.996803 + 0.0798962i \(0.974541\pi\)
\(20\) 4.99038i 1.11588i
\(21\) 0 0
\(22\) 3.62652 0.773176
\(23\) −8.96087 −1.86847 −0.934236 0.356656i \(-0.883917\pi\)
−0.934236 + 0.356656i \(0.883917\pi\)
\(24\) 5.61610i 1.14638i
\(25\) −5.53733 −1.10747
\(26\) 2.23718 + 1.00484i 0.438747 + 0.197065i
\(27\) −1.28809 −0.247893
\(28\) 0 0
\(29\) −5.28644 −0.981667 −0.490833 0.871253i \(-0.663308\pi\)
−0.490833 + 0.871253i \(0.663308\pi\)
\(30\) −5.15376 −0.940943
\(31\) 5.45951i 0.980557i 0.871566 + 0.490279i \(0.163105\pi\)
−0.871566 + 0.490279i \(0.836895\pi\)
\(32\) 5.79032i 1.02359i
\(33\) 12.4446i 2.16632i
\(34\) 1.81505i 0.311278i
\(35\) 0 0
\(36\) 3.76362 0.627270
\(37\) 6.69197i 1.10015i −0.835114 0.550076i \(-0.814599\pi\)
0.835114 0.550076i \(-0.185401\pi\)
\(38\) −0.473769 −0.0768555
\(39\) 3.44815 7.67699i 0.552146 1.22930i
\(40\) −7.81044 −1.23494
\(41\) 2.21339i 0.345673i 0.984951 + 0.172836i \(0.0552932\pi\)
−0.984951 + 0.172836i \(0.944707\pi\)
\(42\) 0 0
\(43\) 2.39014 0.364493 0.182246 0.983253i \(-0.441663\pi\)
0.182246 + 0.983253i \(0.441663\pi\)
\(44\) 8.19640i 1.23565i
\(45\) 7.94700i 1.18467i
\(46\) 6.09515i 0.898681i
\(47\) 5.79573i 0.845395i 0.906271 + 0.422697i \(0.138917\pi\)
−0.906271 + 0.422697i \(0.861083\pi\)
\(48\) 3.35661 0.484485
\(49\) 0 0
\(50\) 3.76647i 0.532660i
\(51\) 6.22843 0.872154
\(52\) 2.27106 5.05632i 0.314940 0.701185i
\(53\) −4.71570 −0.647751 −0.323876 0.946100i \(-0.604986\pi\)
−0.323876 + 0.946100i \(0.604986\pi\)
\(54\) 0.876153i 0.119229i
\(55\) 17.3070 2.33367
\(56\) 0 0
\(57\) 1.62576i 0.215338i
\(58\) 3.59581i 0.472154i
\(59\) 2.98070i 0.388054i −0.980996 0.194027i \(-0.937845\pi\)
0.980996 0.194027i \(-0.0621550\pi\)
\(60\) 11.6482i 1.50377i
\(61\) −2.19465 −0.280996 −0.140498 0.990081i \(-0.544870\pi\)
−0.140498 + 0.990081i \(0.544870\pi\)
\(62\) −3.71354 −0.471620
\(63\) 0 0
\(64\) −1.06244 −0.132805
\(65\) 10.6766 + 4.79542i 1.32427 + 0.594799i
\(66\) 8.46475 1.04194
\(67\) 8.70594i 1.06360i −0.846870 0.531800i \(-0.821516\pi\)
0.846870 0.531800i \(-0.178484\pi\)
\(68\) 4.10225 0.497470
\(69\) −20.9158 −2.51797
\(70\) 0 0
\(71\) 8.56190i 1.01611i −0.861325 0.508055i \(-0.830365\pi\)
0.861325 0.508055i \(-0.169635\pi\)
\(72\) 5.89045i 0.694196i
\(73\) 5.88152i 0.688380i −0.938900 0.344190i \(-0.888154\pi\)
0.938900 0.344190i \(-0.111846\pi\)
\(74\) 4.55185 0.529142
\(75\) −12.9248 −1.49243
\(76\) 1.07078i 0.122827i
\(77\) 0 0
\(78\) 5.22186 + 2.34542i 0.591259 + 0.265566i
\(79\) 0.910817 0.102475 0.0512374 0.998687i \(-0.483683\pi\)
0.0512374 + 0.998687i \(0.483683\pi\)
\(80\) 4.66812i 0.521912i
\(81\) −10.3510 −1.15011
\(82\) −1.50554 −0.166259
\(83\) 11.7481i 1.28952i 0.764387 + 0.644758i \(0.223042\pi\)
−0.764387 + 0.644758i \(0.776958\pi\)
\(84\) 0 0
\(85\) 8.66202i 0.939528i
\(86\) 1.62576i 0.175311i
\(87\) −12.3392 −1.32290
\(88\) 12.8282 1.36749
\(89\) 0.986019i 0.104518i −0.998634 0.0522589i \(-0.983358\pi\)
0.998634 0.0522589i \(-0.0166421\pi\)
\(90\) −5.40552 −0.569792
\(91\) 0 0
\(92\) −13.7758 −1.43623
\(93\) 12.7432i 1.32141i
\(94\) −3.94224 −0.406611
\(95\) −2.26099 −0.231972
\(96\) 13.5154i 1.37940i
\(97\) 15.3454i 1.55809i −0.626969 0.779044i \(-0.715705\pi\)
0.626969 0.779044i \(-0.284295\pi\)
\(98\) 0 0
\(99\) 13.0525i 1.31182i
\(100\) −8.51273 −0.851273
\(101\) −3.90927 −0.388987 −0.194493 0.980904i \(-0.562306\pi\)
−0.194493 + 0.980904i \(0.562306\pi\)
\(102\) 4.23655i 0.419481i
\(103\) 18.5612 1.82889 0.914443 0.404715i \(-0.132629\pi\)
0.914443 + 0.404715i \(0.132629\pi\)
\(104\) 7.91365 + 3.55444i 0.775997 + 0.348542i
\(105\) 0 0
\(106\) 3.20760i 0.311550i
\(107\) 13.1058 1.26699 0.633495 0.773747i \(-0.281620\pi\)
0.633495 + 0.773747i \(0.281620\pi\)
\(108\) −1.98022 −0.190547
\(109\) 15.3979i 1.47485i 0.675428 + 0.737426i \(0.263959\pi\)
−0.675428 + 0.737426i \(0.736041\pi\)
\(110\) 11.7721i 1.12243i
\(111\) 15.6199i 1.48258i
\(112\) 0 0
\(113\) 12.7346 1.19797 0.598985 0.800761i \(-0.295571\pi\)
0.598985 + 0.800761i \(0.295571\pi\)
\(114\) −1.10584 −0.103571
\(115\) 29.0881i 2.71248i
\(116\) −8.12701 −0.754574
\(117\) 3.61659 8.05201i 0.334354 0.744409i
\(118\) 2.02746 0.186643
\(119\) 0 0
\(120\) −18.2306 −1.66422
\(121\) −17.4257 −1.58415
\(122\) 1.49279i 0.135151i
\(123\) 5.16633i 0.465832i
\(124\) 8.39309i 0.753722i
\(125\) 1.74425i 0.156011i
\(126\) 0 0
\(127\) 10.2763 0.911878 0.455939 0.890011i \(-0.349303\pi\)
0.455939 + 0.890011i \(0.349303\pi\)
\(128\) 10.8580i 0.959719i
\(129\) 5.57889 0.491193
\(130\) −3.26183 + 7.26217i −0.286081 + 0.636934i
\(131\) 12.5813 1.09923 0.549615 0.835418i \(-0.314774\pi\)
0.549615 + 0.835418i \(0.314774\pi\)
\(132\) 19.1315i 1.66518i
\(133\) 0 0
\(134\) 5.92175 0.511561
\(135\) 4.18130i 0.359869i
\(136\) 6.42043i 0.550547i
\(137\) 1.72588i 0.147452i −0.997279 0.0737261i \(-0.976511\pi\)
0.997279 0.0737261i \(-0.0234891\pi\)
\(138\) 14.2269i 1.21107i
\(139\) −2.93311 −0.248783 −0.124391 0.992233i \(-0.539698\pi\)
−0.124391 + 0.992233i \(0.539698\pi\)
\(140\) 0 0
\(141\) 13.5280i 1.13926i
\(142\) 5.82377 0.488720
\(143\) −17.5357 7.87620i −1.46641 0.658641i
\(144\) 3.52058 0.293382
\(145\) 17.1604i 1.42510i
\(146\) 4.00059 0.331091
\(147\) 0 0
\(148\) 10.2878i 0.845650i
\(149\) 13.2399i 1.08465i 0.840168 + 0.542327i \(0.182457\pi\)
−0.840168 + 0.542327i \(0.817543\pi\)
\(150\) 8.79143i 0.717817i
\(151\) 9.25883i 0.753473i −0.926320 0.376736i \(-0.877046\pi\)
0.926320 0.376736i \(-0.122954\pi\)
\(152\) −1.67588 −0.135932
\(153\) 6.53268 0.528136
\(154\) 0 0
\(155\) −17.7223 −1.42349
\(156\) 5.30095 11.8021i 0.424416 0.944924i
\(157\) −1.65626 −0.132184 −0.0660922 0.997814i \(-0.521053\pi\)
−0.0660922 + 0.997814i \(0.521053\pi\)
\(158\) 0.619534i 0.0492875i
\(159\) −11.0070 −0.872915
\(160\) −18.7961 −1.48596
\(161\) 0 0
\(162\) 7.04072i 0.553171i
\(163\) 9.89957i 0.775394i 0.921787 + 0.387697i \(0.126729\pi\)
−0.921787 + 0.387697i \(0.873271\pi\)
\(164\) 3.40271i 0.265707i
\(165\) 40.3966 3.14487
\(166\) −7.99098 −0.620220
\(167\) 6.10891i 0.472721i 0.971665 + 0.236361i \(0.0759547\pi\)
−0.971665 + 0.236361i \(0.924045\pi\)
\(168\) 0 0
\(169\) −8.63531 9.71758i −0.664255 0.747506i
\(170\) −5.89187 −0.451886
\(171\) 1.70518i 0.130398i
\(172\) 3.67444 0.280173
\(173\) −18.7212 −1.42334 −0.711672 0.702512i \(-0.752062\pi\)
−0.711672 + 0.702512i \(0.752062\pi\)
\(174\) 8.39309i 0.636278i
\(175\) 0 0
\(176\) 7.66712i 0.577931i
\(177\) 6.95734i 0.522945i
\(178\) 0.670687 0.0502701
\(179\) 9.93756 0.742768 0.371384 0.928479i \(-0.378883\pi\)
0.371384 + 0.928479i \(0.378883\pi\)
\(180\) 12.2172i 0.910615i
\(181\) −22.6991 −1.68721 −0.843606 0.536962i \(-0.819572\pi\)
−0.843606 + 0.536962i \(0.819572\pi\)
\(182\) 0 0
\(183\) −5.12259 −0.378673
\(184\) 21.5606i 1.58947i
\(185\) 21.7230 1.59710
\(186\) −8.66787 −0.635559
\(187\) 14.2269i 1.04037i
\(188\) 8.90997i 0.649827i
\(189\) 0 0
\(190\) 1.53791i 0.111572i
\(191\) 5.42926 0.392848 0.196424 0.980519i \(-0.437067\pi\)
0.196424 + 0.980519i \(0.437067\pi\)
\(192\) −2.47987 −0.178969
\(193\) 1.97005i 0.141807i 0.997483 + 0.0709037i \(0.0225883\pi\)
−0.997483 + 0.0709037i \(0.977412\pi\)
\(194\) 10.4379 0.749396
\(195\) 24.9205 + 11.1931i 1.78459 + 0.801557i
\(196\) 0 0
\(197\) 19.1476i 1.36421i −0.731253 0.682107i \(-0.761064\pi\)
0.731253 0.682107i \(-0.238936\pi\)
\(198\) 8.87825 0.630950
\(199\) 0.194811 0.0138098 0.00690489 0.999976i \(-0.497802\pi\)
0.00690489 + 0.999976i \(0.497802\pi\)
\(200\) 13.3233i 0.942097i
\(201\) 20.3208i 1.43332i
\(202\) 2.65907i 0.187091i
\(203\) 0 0
\(204\) 9.57516 0.670396
\(205\) −7.18493 −0.501817
\(206\) 12.6252i 0.879642i
\(207\) −21.9376 −1.52477
\(208\) 2.12441 4.72981i 0.147301 0.327953i
\(209\) 3.71354 0.256871
\(210\) 0 0
\(211\) 12.2618 0.844139 0.422070 0.906563i \(-0.361304\pi\)
0.422070 + 0.906563i \(0.361304\pi\)
\(212\) −7.24960 −0.497905
\(213\) 19.9846i 1.36932i
\(214\) 8.91454i 0.609386i
\(215\) 7.75869i 0.529138i
\(216\) 3.09925i 0.210877i
\(217\) 0 0
\(218\) −10.4736 −0.709362
\(219\) 13.7282i 0.927667i
\(220\) 26.6066 1.79381
\(221\) 3.94199 8.77648i 0.265167 0.590370i
\(222\) 10.6246 0.713076
\(223\) 27.1733i 1.81966i 0.414981 + 0.909830i \(0.363788\pi\)
−0.414981 + 0.909830i \(0.636212\pi\)
\(224\) 0 0
\(225\) −13.5562 −0.903748
\(226\) 8.66202i 0.576189i
\(227\) 7.21285i 0.478733i −0.970929 0.239367i \(-0.923060\pi\)
0.970929 0.239367i \(-0.0769398\pi\)
\(228\) 2.49934i 0.165523i
\(229\) 17.1127i 1.13084i 0.824804 + 0.565419i \(0.191286\pi\)
−0.824804 + 0.565419i \(0.808714\pi\)
\(230\) 19.7856 1.30463
\(231\) 0 0
\(232\) 12.7196i 0.835082i
\(233\) 12.6353 0.827767 0.413883 0.910330i \(-0.364172\pi\)
0.413883 + 0.910330i \(0.364172\pi\)
\(234\) 5.47695 + 2.45999i 0.358039 + 0.160815i
\(235\) −18.8137 −1.22727
\(236\) 4.58233i 0.298284i
\(237\) 2.12596 0.138096
\(238\) 0 0
\(239\) 7.70807i 0.498594i −0.968427 0.249297i \(-0.919801\pi\)
0.968427 0.249297i \(-0.0801995\pi\)
\(240\) 10.8960i 0.703333i
\(241\) 19.2022i 1.23693i 0.785814 + 0.618463i \(0.212244\pi\)
−0.785814 + 0.618463i \(0.787756\pi\)
\(242\) 11.8529i 0.761932i
\(243\) −20.2963 −1.30201
\(244\) −3.37390 −0.215992
\(245\) 0 0
\(246\) −3.51412 −0.224052
\(247\) 2.29086 + 1.02895i 0.145764 + 0.0654705i
\(248\) −13.1360 −0.834139
\(249\) 27.4214i 1.73776i
\(250\) 1.18643 0.0750366
\(251\) −17.6761 −1.11570 −0.557851 0.829941i \(-0.688374\pi\)
−0.557851 + 0.829941i \(0.688374\pi\)
\(252\) 0 0
\(253\) 47.7756i 3.00362i
\(254\) 6.98993i 0.438587i
\(255\) 20.2183i 1.26612i
\(256\) −9.51044 −0.594402
\(257\) 2.61935 0.163390 0.0816952 0.996657i \(-0.473967\pi\)
0.0816952 + 0.996657i \(0.473967\pi\)
\(258\) 3.79474i 0.236250i
\(259\) 0 0
\(260\) 16.4135 + 7.37216i 1.01792 + 0.457202i
\(261\) −12.9420 −0.801089
\(262\) 8.55773i 0.528698i
\(263\) 5.62875 0.347084 0.173542 0.984827i \(-0.444479\pi\)
0.173542 + 0.984827i \(0.444479\pi\)
\(264\) 29.9426 1.84284
\(265\) 15.3078i 0.940348i
\(266\) 0 0
\(267\) 2.30149i 0.140849i
\(268\) 13.3839i 0.817554i
\(269\) −13.8581 −0.844944 −0.422472 0.906376i \(-0.638837\pi\)
−0.422472 + 0.906376i \(0.638837\pi\)
\(270\) 2.84410 0.173087
\(271\) 8.00871i 0.486495i 0.969964 + 0.243247i \(0.0782127\pi\)
−0.969964 + 0.243247i \(0.921787\pi\)
\(272\) 3.83734 0.232673
\(273\) 0 0
\(274\) 1.17394 0.0709203
\(275\) 29.5227i 1.78029i
\(276\) −32.1546 −1.93548
\(277\) −18.2930 −1.09912 −0.549560 0.835454i \(-0.685205\pi\)
−0.549560 + 0.835454i \(0.685205\pi\)
\(278\) 1.99509i 0.119657i
\(279\) 13.3657i 0.800184i
\(280\) 0 0
\(281\) 19.3790i 1.15605i 0.816018 + 0.578026i \(0.196177\pi\)
−0.816018 + 0.578026i \(0.803823\pi\)
\(282\) −9.20168 −0.547952
\(283\) −6.43729 −0.382657 −0.191329 0.981526i \(-0.561280\pi\)
−0.191329 + 0.981526i \(0.561280\pi\)
\(284\) 13.1625i 0.781050i
\(285\) −5.27743 −0.312608
\(286\) 5.35737 11.9277i 0.316788 0.705299i
\(287\) 0 0
\(288\) 14.1756i 0.835304i
\(289\) −9.87955 −0.581150
\(290\) 11.6725 0.685431
\(291\) 35.8181i 2.09969i
\(292\) 9.04186i 0.529135i
\(293\) 7.66381i 0.447725i 0.974621 + 0.223862i \(0.0718666\pi\)
−0.974621 + 0.223862i \(0.928133\pi\)
\(294\) 0 0
\(295\) 9.67573 0.563343
\(296\) 16.1014 0.935876
\(297\) 6.86754i 0.398495i
\(298\) −9.00572 −0.521687
\(299\) −13.2377 + 29.4725i −0.765555 + 1.70444i
\(300\) −19.8698 −1.14718
\(301\) 0 0
\(302\) 6.29782 0.362399
\(303\) −9.12472 −0.524202
\(304\) 1.00163i 0.0574477i
\(305\) 7.12410i 0.407925i
\(306\) 4.44351i 0.254018i
\(307\) 0.312144i 0.0178150i −0.999960 0.00890751i \(-0.997165\pi\)
0.999960 0.00890751i \(-0.00283539\pi\)
\(308\) 0 0
\(309\) 43.3241 2.46462
\(310\) 12.0546i 0.684656i
\(311\) 2.81507 0.159628 0.0798141 0.996810i \(-0.474567\pi\)
0.0798141 + 0.996810i \(0.474567\pi\)
\(312\) 18.4715 + 8.29653i 1.04574 + 0.469698i
\(313\) −13.2930 −0.751366 −0.375683 0.926748i \(-0.622592\pi\)
−0.375683 + 0.926748i \(0.622592\pi\)
\(314\) 1.12658i 0.0635769i
\(315\) 0 0
\(316\) 1.40023 0.0787690
\(317\) 0.972179i 0.0546030i −0.999627 0.0273015i \(-0.991309\pi\)
0.999627 0.0273015i \(-0.00869142\pi\)
\(318\) 7.48695i 0.419847i
\(319\) 28.1850i 1.57806i
\(320\) 3.44881i 0.192794i
\(321\) 30.5907 1.70741
\(322\) 0 0
\(323\) 1.85860i 0.103415i
\(324\) −15.9130 −0.884053
\(325\) −8.18017 + 18.2124i −0.453754 + 1.01024i
\(326\) −6.73365 −0.372942
\(327\) 35.9407i 1.98752i
\(328\) −5.32559 −0.294056
\(329\) 0 0
\(330\) 27.4776i 1.51259i
\(331\) 7.72092i 0.424380i −0.977228 0.212190i \(-0.931940\pi\)
0.977228 0.212190i \(-0.0680596\pi\)
\(332\) 18.0607i 0.991208i
\(333\) 16.3829i 0.897779i
\(334\) −4.15525 −0.227365
\(335\) 28.2606 1.54404
\(336\) 0 0
\(337\) −27.4858 −1.49725 −0.748624 0.662995i \(-0.769285\pi\)
−0.748624 + 0.662995i \(0.769285\pi\)
\(338\) 6.60986 5.87371i 0.359529 0.319488i
\(339\) 29.7241 1.61439
\(340\) 13.3164i 0.722184i
\(341\) 29.1078 1.57628
\(342\) −1.15986 −0.0627179
\(343\) 0 0
\(344\) 5.75086i 0.310066i
\(345\) 67.8954i 3.65536i
\(346\) 12.7341i 0.684588i
\(347\) −3.69546 −0.198383 −0.0991914 0.995068i \(-0.531626\pi\)
−0.0991914 + 0.995068i \(0.531626\pi\)
\(348\) −18.9695 −1.01687
\(349\) 26.7513i 1.43197i −0.698118 0.715983i \(-0.745979\pi\)
0.698118 0.715983i \(-0.254021\pi\)
\(350\) 0 0
\(351\) −1.90286 + 4.23655i −0.101567 + 0.226130i
\(352\) 30.8715 1.64546
\(353\) 2.75332i 0.146544i −0.997312 0.0732722i \(-0.976656\pi\)
0.997312 0.0732722i \(-0.0233442\pi\)
\(354\) 4.73235 0.251522
\(355\) 27.7930 1.47510
\(356\) 1.51584i 0.0803394i
\(357\) 0 0
\(358\) 6.75949i 0.357250i
\(359\) 35.0545i 1.85011i 0.379837 + 0.925053i \(0.375980\pi\)
−0.379837 + 0.925053i \(0.624020\pi\)
\(360\) −19.1211 −1.00777
\(361\) 18.5149 0.974466
\(362\) 15.4399i 0.811501i
\(363\) −40.6737 −2.13482
\(364\) 0 0
\(365\) 19.0922 0.999329
\(366\) 3.48436i 0.182131i
\(367\) 15.0005 0.783022 0.391511 0.920173i \(-0.371953\pi\)
0.391511 + 0.920173i \(0.371953\pi\)
\(368\) −12.8863 −0.671743
\(369\) 5.41870i 0.282086i
\(370\) 14.7759i 0.768161i
\(371\) 0 0
\(372\) 19.5905i 1.01572i
\(373\) 20.9943 1.08704 0.543521 0.839395i \(-0.317091\pi\)
0.543521 + 0.839395i \(0.317091\pi\)
\(374\) 9.67706 0.500389
\(375\) 4.07130i 0.210241i
\(376\) −13.9450 −0.719159
\(377\) −7.80953 + 17.3872i −0.402211 + 0.895486i
\(378\) 0 0
\(379\) 15.2425i 0.782956i 0.920187 + 0.391478i \(0.128036\pi\)
−0.920187 + 0.391478i \(0.871964\pi\)
\(380\) −3.47589 −0.178309
\(381\) 23.9863 1.22886
\(382\) 3.69296i 0.188948i
\(383\) 24.5760i 1.25577i −0.778305 0.627887i \(-0.783920\pi\)
0.778305 0.627887i \(-0.216080\pi\)
\(384\) 25.3439i 1.29333i
\(385\) 0 0
\(386\) −1.34002 −0.0682053
\(387\) 5.85141 0.297444
\(388\) 23.5910i 1.19765i
\(389\) −19.2407 −0.975545 −0.487772 0.872971i \(-0.662190\pi\)
−0.487772 + 0.872971i \(0.662190\pi\)
\(390\) −7.61352 + 16.9508i −0.385526 + 0.858338i
\(391\) −23.9114 −1.20925
\(392\) 0 0
\(393\) 29.3663 1.48133
\(394\) 13.0242 0.656147
\(395\) 2.95663i 0.148764i
\(396\) 20.0660i 1.00836i
\(397\) 0.596764i 0.0299507i 0.999888 + 0.0149754i \(0.00476699\pi\)
−0.999888 + 0.0149754i \(0.995233\pi\)
\(398\) 0.132510i 0.00664211i
\(399\) 0 0
\(400\) −7.96301 −0.398151
\(401\) 1.59469i 0.0796348i −0.999207 0.0398174i \(-0.987322\pi\)
0.999207 0.0398174i \(-0.0126776\pi\)
\(402\) 13.8221 0.689384
\(403\) 17.9564 + 8.06521i 0.894474 + 0.401756i
\(404\) −6.00984 −0.299001
\(405\) 33.6007i 1.66963i
\(406\) 0 0
\(407\) −35.6787 −1.76853
\(408\) 14.9861i 0.741922i
\(409\) 28.9884i 1.43338i 0.697390 + 0.716691i \(0.254344\pi\)
−0.697390 + 0.716691i \(0.745656\pi\)
\(410\) 4.88716i 0.241360i
\(411\) 4.02843i 0.198708i
\(412\) 28.5347 1.40580
\(413\) 0 0
\(414\) 14.9218i 0.733369i
\(415\) −38.1357 −1.87201
\(416\) 19.0445 + 8.55391i 0.933733 + 0.419390i
\(417\) −6.84624 −0.335262
\(418\) 2.52594i 0.123548i
\(419\) −5.18611 −0.253358 −0.126679 0.991944i \(-0.540432\pi\)
−0.126679 + 0.991944i \(0.540432\pi\)
\(420\) 0 0
\(421\) 2.84363i 0.138590i −0.997596 0.0692950i \(-0.977925\pi\)
0.997596 0.0692950i \(-0.0220750\pi\)
\(422\) 8.34045i 0.406007i
\(423\) 14.1888i 0.689884i
\(424\) 11.3464i 0.551028i
\(425\) −14.7759 −0.716737
\(426\) 13.5934 0.658603
\(427\) 0 0
\(428\) 20.1480 0.973892
\(429\) −40.9304 18.3841i −1.97614 0.887591i
\(430\) −5.27743 −0.254500
\(431\) 3.98106i 0.191761i −0.995393 0.0958804i \(-0.969433\pi\)
0.995393 0.0958804i \(-0.0305666\pi\)
\(432\) −1.85235 −0.0891211
\(433\) 7.42082 0.356622 0.178311 0.983974i \(-0.442937\pi\)
0.178311 + 0.983974i \(0.442937\pi\)
\(434\) 0 0
\(435\) 40.0546i 1.92047i
\(436\) 23.6717i 1.13367i
\(437\) 6.24142i 0.298567i
\(438\) 9.33789 0.446181
\(439\) 30.5670 1.45888 0.729442 0.684043i \(-0.239780\pi\)
0.729442 + 0.684043i \(0.239780\pi\)
\(440\) 41.6419i 1.98520i
\(441\) 0 0
\(442\) 5.96973 + 2.68133i 0.283951 + 0.127538i
\(443\) −4.30975 −0.204762 −0.102381 0.994745i \(-0.532646\pi\)
−0.102381 + 0.994745i \(0.532646\pi\)
\(444\) 24.0130i 1.13961i
\(445\) 3.20074 0.151730
\(446\) −18.4832 −0.875205
\(447\) 30.9036i 1.46169i
\(448\) 0 0
\(449\) 30.7830i 1.45274i −0.687305 0.726369i \(-0.741206\pi\)
0.687305 0.726369i \(-0.258794\pi\)
\(450\) 9.22089i 0.434677i
\(451\) 11.8008 0.555680
\(452\) 19.5773 0.920839
\(453\) 21.6113i 1.01539i
\(454\) 4.90615 0.230257
\(455\) 0 0
\(456\) −3.91172 −0.183183
\(457\) 13.4954i 0.631287i −0.948878 0.315644i \(-0.897780\pi\)
0.948878 0.315644i \(-0.102220\pi\)
\(458\) −11.6400 −0.543901
\(459\) −3.43716 −0.160433
\(460\) 44.7181i 2.08499i
\(461\) 27.4778i 1.27977i −0.768471 0.639885i \(-0.778982\pi\)
0.768471 0.639885i \(-0.221018\pi\)
\(462\) 0 0
\(463\) 8.06521i 0.374822i −0.982282 0.187411i \(-0.939990\pi\)
0.982282 0.187411i \(-0.0600096\pi\)
\(464\) −7.60221 −0.352924
\(465\) −41.3660 −1.91830
\(466\) 8.59449i 0.398132i
\(467\) 12.6325 0.584564 0.292282 0.956332i \(-0.405585\pi\)
0.292282 + 0.956332i \(0.405585\pi\)
\(468\) 5.55991 12.3786i 0.257007 0.572202i
\(469\) 0 0
\(470\) 12.7970i 0.590281i
\(471\) −3.86593 −0.178133
\(472\) 7.17181 0.330109
\(473\) 12.7432i 0.585933i
\(474\) 1.44607i 0.0664202i
\(475\) 3.85685i 0.176965i
\(476\) 0 0
\(477\) −11.5447 −0.528597
\(478\) 5.24300 0.239809
\(479\) 31.5380i 1.44101i 0.693451 + 0.720504i \(0.256089\pi\)
−0.693451 + 0.720504i \(0.743911\pi\)
\(480\) −43.8725 −2.00250
\(481\) −22.0100 9.88588i −1.00357 0.450757i
\(482\) −13.0613 −0.594926
\(483\) 0 0
\(484\) −26.7891 −1.21769
\(485\) 49.8131 2.26190
\(486\) 13.8055i 0.626229i
\(487\) 42.1218i 1.90872i −0.298654 0.954362i \(-0.596538\pi\)
0.298654 0.954362i \(-0.403462\pi\)
\(488\) 5.28050i 0.239037i
\(489\) 23.1068i 1.04493i
\(490\) 0 0
\(491\) −30.2284 −1.36419 −0.682095 0.731264i \(-0.738931\pi\)
−0.682095 + 0.731264i \(0.738931\pi\)
\(492\) 7.94236i 0.358069i
\(493\) −14.1064 −0.635321
\(494\) −0.699888 + 1.55824i −0.0314894 + 0.0701084i
\(495\) 42.3700 1.90439
\(496\) 7.85110i 0.352525i
\(497\) 0 0
\(498\) −18.6520 −0.835815
\(499\) 3.50797i 0.157038i 0.996913 + 0.0785191i \(0.0250192\pi\)
−0.996913 + 0.0785191i \(0.974981\pi\)
\(500\) 2.68149i 0.119920i
\(501\) 14.2590i 0.637043i
\(502\) 12.0232i 0.536621i
\(503\) 22.8622 1.01937 0.509687 0.860360i \(-0.329761\pi\)
0.509687 + 0.860360i \(0.329761\pi\)
\(504\) 0 0
\(505\) 12.6900i 0.564696i
\(506\) −32.4968 −1.44466
\(507\) −20.1559 22.6821i −0.895156 1.00735i
\(508\) 15.7982 0.700930
\(509\) 21.7755i 0.965183i 0.875846 + 0.482592i \(0.160304\pi\)
−0.875846 + 0.482592i \(0.839696\pi\)
\(510\) −13.7524 −0.608966
\(511\) 0 0
\(512\) 15.2470i 0.673829i
\(513\) 0.897178i 0.0396114i
\(514\) 1.78167i 0.0785861i
\(515\) 60.2519i 2.65501i
\(516\) 8.57660 0.377564
\(517\) 30.9004 1.35900
\(518\) 0 0
\(519\) −43.6976 −1.91811
\(520\) −11.5382 + 25.6887i −0.505982 + 1.12652i
\(521\) −14.5235 −0.636287 −0.318144 0.948042i \(-0.603059\pi\)
−0.318144 + 0.948042i \(0.603059\pi\)
\(522\) 8.80309i 0.385301i
\(523\) −16.4188 −0.717945 −0.358973 0.933348i \(-0.616873\pi\)
−0.358973 + 0.933348i \(0.616873\pi\)
\(524\) 19.3416 0.844942
\(525\) 0 0
\(526\) 3.82865i 0.166937i
\(527\) 14.5683i 0.634603i
\(528\) 17.8960i 0.778825i
\(529\) 57.2973 2.49119
\(530\) 10.4123 0.452280
\(531\) 7.29720i 0.316672i
\(532\) 0 0
\(533\) 7.27987 + 3.26978i 0.315326 + 0.141630i
\(534\) 1.56547 0.0677444
\(535\) 42.5432i 1.83930i
\(536\) 20.9472 0.904781
\(537\) 23.1955 1.00096
\(538\) 9.42623i 0.406394i
\(539\) 0 0
\(540\) 6.42805i 0.276619i
\(541\) 13.4954i 0.580212i −0.956995 0.290106i \(-0.906309\pi\)
0.956995 0.290106i \(-0.0936905\pi\)
\(542\) −5.44750 −0.233990
\(543\) −52.9826 −2.27370
\(544\) 15.4510i 0.662456i
\(545\) −49.9835 −2.14106
\(546\) 0 0
\(547\) 13.5615 0.579847 0.289924 0.957050i \(-0.406370\pi\)
0.289924 + 0.957050i \(0.406370\pi\)
\(548\) 2.65326i 0.113342i
\(549\) −5.37283 −0.229307
\(550\) −20.0812 −0.856267
\(551\) 3.68210i 0.156863i
\(552\) 50.3252i 2.14198i
\(553\) 0 0
\(554\) 12.4428i 0.528645i
\(555\) 50.7042 2.15227
\(556\) −4.50916 −0.191231
\(557\) 35.2736i 1.49459i 0.664493 + 0.747294i \(0.268648\pi\)
−0.664493 + 0.747294i \(0.731352\pi\)
\(558\) −9.09130 −0.384865
\(559\) 3.53089 7.86121i 0.149341 0.332494i
\(560\) 0 0
\(561\) 33.2073i 1.40201i
\(562\) −13.1815 −0.556028
\(563\) 36.1102 1.52186 0.760931 0.648833i \(-0.224742\pi\)
0.760931 + 0.648833i \(0.224742\pi\)
\(564\) 20.7970i 0.875712i
\(565\) 41.3381i 1.73911i
\(566\) 4.37862i 0.184047i
\(567\) 0 0
\(568\) 20.6006 0.864383
\(569\) −11.8362 −0.496197 −0.248099 0.968735i \(-0.579806\pi\)
−0.248099 + 0.968735i \(0.579806\pi\)
\(570\) 3.58969i 0.150356i
\(571\) 45.9414 1.92259 0.961294 0.275526i \(-0.0888521\pi\)
0.961294 + 0.275526i \(0.0888521\pi\)
\(572\) −26.9581 12.1084i −1.12718 0.506276i
\(573\) 12.6726 0.529405
\(574\) 0 0
\(575\) 49.6193 2.06927
\(576\) −2.60101 −0.108375
\(577\) 29.7470i 1.23838i −0.785240 0.619192i \(-0.787460\pi\)
0.785240 0.619192i \(-0.212540\pi\)
\(578\) 6.72003i 0.279517i
\(579\) 4.59835i 0.191101i
\(580\) 26.3813i 1.09542i
\(581\) 0 0
\(582\) 24.3633 1.00989
\(583\) 25.1421i 1.04128i
\(584\) 14.1514 0.585590
\(585\) 26.1379 + 11.7399i 1.08067 + 0.485386i
\(586\) −5.21290 −0.215343
\(587\) 11.3406i 0.468078i −0.972227 0.234039i \(-0.924806\pi\)
0.972227 0.234039i \(-0.0751943\pi\)
\(588\) 0 0
\(589\) −3.80265 −0.156686
\(590\) 6.58140i 0.270952i
\(591\) 44.6930i 1.83843i
\(592\) 9.62344i 0.395521i
\(593\) 2.87084i 0.117891i 0.998261 + 0.0589455i \(0.0187738\pi\)
−0.998261 + 0.0589455i \(0.981226\pi\)
\(594\) −4.67128 −0.191665
\(595\) 0 0
\(596\) 20.3541i 0.833737i
\(597\) 0.454713 0.0186102
\(598\) −20.0471 9.00422i −0.819786 0.368210i
\(599\) −5.41559 −0.221275 −0.110637 0.993861i \(-0.535289\pi\)
−0.110637 + 0.993861i \(0.535289\pi\)
\(600\) 31.0982i 1.26958i
\(601\) −34.1648 −1.39361 −0.696805 0.717261i \(-0.745396\pi\)
−0.696805 + 0.717261i \(0.745396\pi\)
\(602\) 0 0
\(603\) 21.3134i 0.867951i
\(604\) 14.2339i 0.579169i
\(605\) 56.5659i 2.29973i
\(606\) 6.20660i 0.252126i
\(607\) −22.0430 −0.894697 −0.447349 0.894360i \(-0.647632\pi\)
−0.447349 + 0.894360i \(0.647632\pi\)
\(608\) −4.03307 −0.163562
\(609\) 0 0
\(610\) 4.84579 0.196200
\(611\) 19.0623 + 8.56190i 0.771178 + 0.346377i
\(612\) 10.0429 0.405961
\(613\) 24.7446i 0.999424i −0.866191 0.499712i \(-0.833439\pi\)
0.866191 0.499712i \(-0.166561\pi\)
\(614\) 0.212320 0.00856852
\(615\) −16.7705 −0.676254
\(616\) 0 0
\(617\) 19.9659i 0.803797i −0.915684 0.401898i \(-0.868350\pi\)
0.915684 0.401898i \(-0.131650\pi\)
\(618\) 29.4689i 1.18541i
\(619\) 10.0750i 0.404949i −0.979288 0.202474i \(-0.935102\pi\)
0.979288 0.202474i \(-0.0648983\pi\)
\(620\) −27.2450 −1.09419
\(621\) 11.5424 0.463181
\(622\) 1.91480i 0.0767766i
\(623\) 0 0
\(624\) 4.95864 11.0400i 0.198505 0.441952i
\(625\) −22.0246 −0.880984
\(626\) 9.04186i 0.361385i
\(627\) 8.66787 0.346162
\(628\) −2.54623 −0.101606
\(629\) 17.8570i 0.712004i
\(630\) 0 0
\(631\) 26.2386i 1.04454i 0.852780 + 0.522271i \(0.174915\pi\)
−0.852780 + 0.522271i \(0.825085\pi\)
\(632\) 2.19150i 0.0871731i
\(633\) 28.6207 1.13757
\(634\) 0.661273 0.0262625
\(635\) 33.3583i 1.32378i
\(636\) −16.9215 −0.670981
\(637\) 0 0
\(638\) −19.1714 −0.759001
\(639\) 20.9608i 0.829197i
\(640\) −35.2464 −1.39324
\(641\) −37.2213 −1.47015 −0.735077 0.677984i \(-0.762854\pi\)
−0.735077 + 0.677984i \(0.762854\pi\)
\(642\) 20.8077i 0.821213i
\(643\) 10.8569i 0.428155i 0.976817 + 0.214077i \(0.0686744\pi\)
−0.976817 + 0.214077i \(0.931326\pi\)
\(644\) 0 0
\(645\) 18.1098i 0.713071i
\(646\) −1.26421 −0.0497398
\(647\) 11.2388 0.441841 0.220921 0.975292i \(-0.429094\pi\)
0.220921 + 0.975292i \(0.429094\pi\)
\(648\) 24.9054i 0.978375i
\(649\) −15.8918 −0.623809
\(650\) −12.3880 5.56412i −0.485898 0.218243i
\(651\) 0 0
\(652\) 15.2189i 0.596019i
\(653\) −15.8246 −0.619265 −0.309632 0.950856i \(-0.600206\pi\)
−0.309632 + 0.950856i \(0.600206\pi\)
\(654\) −24.4467 −0.955942
\(655\) 40.8404i 1.59577i
\(656\) 3.18298i 0.124274i
\(657\) 14.3988i 0.561753i
\(658\) 0 0
\(659\) −27.8237 −1.08386 −0.541928 0.840425i \(-0.682306\pi\)
−0.541928 + 0.840425i \(0.682306\pi\)
\(660\) 62.1031 2.41736
\(661\) 17.4521i 0.678808i −0.940641 0.339404i \(-0.889775\pi\)
0.940641 0.339404i \(-0.110225\pi\)
\(662\) 5.25174 0.204115
\(663\) 9.20110 20.4854i 0.357341 0.795588i
\(664\) −28.2668 −1.09696
\(665\) 0 0
\(666\) 11.1436 0.431806
\(667\) 47.3711 1.83422
\(668\) 9.39142i 0.363365i
\(669\) 63.4260i 2.45219i
\(670\) 19.2227i 0.742639i
\(671\) 11.7009i 0.451709i
\(672\) 0 0
\(673\) −30.6883 −1.18295 −0.591474 0.806324i \(-0.701454\pi\)
−0.591474 + 0.806324i \(0.701454\pi\)
\(674\) 18.6958i 0.720134i
\(675\) 7.13258 0.274533
\(676\) −13.2754 14.9392i −0.510590 0.574583i
\(677\) 3.47556 0.133577 0.0667883 0.997767i \(-0.478725\pi\)
0.0667883 + 0.997767i \(0.478725\pi\)
\(678\) 20.2183i 0.776477i
\(679\) 0 0
\(680\) −20.8415 −0.799236
\(681\) 16.8357i 0.645145i
\(682\) 19.7990i 0.758143i
\(683\) 2.98767i 0.114320i −0.998365 0.0571601i \(-0.981795\pi\)
0.998365 0.0571601i \(-0.0182045\pi\)
\(684\) 2.62143i 0.100233i
\(685\) 5.60244 0.214058
\(686\) 0 0
\(687\) 39.9432i 1.52393i
\(688\) 3.43716 0.131040
\(689\) −6.96639 + 15.5100i −0.265398 + 0.590885i
\(690\) 46.1822 1.75813
\(691\) 11.4913i 0.437150i −0.975820 0.218575i \(-0.929859\pi\)
0.975820 0.218575i \(-0.0701408\pi\)
\(692\) −28.7807 −1.09408
\(693\) 0 0
\(694\) 2.51364i 0.0954164i
\(695\) 9.52123i 0.361161i
\(696\) 29.6891i 1.12536i
\(697\) 5.90624i 0.223715i
\(698\) 18.1961 0.688734
\(699\) 29.4924 1.11551
\(700\) 0 0
\(701\) −0.977624 −0.0369244 −0.0184622 0.999830i \(-0.505877\pi\)
−0.0184622 + 0.999830i \(0.505877\pi\)
\(702\) −2.88169 1.29432i −0.108762 0.0488510i
\(703\) 4.66108 0.175796
\(704\) 5.66447i 0.213488i
\(705\) −43.9135 −1.65388
\(706\) 1.87280 0.0704836
\(707\) 0 0
\(708\) 10.6957i 0.401971i
\(709\) 9.85564i 0.370136i −0.982726 0.185068i \(-0.940749\pi\)
0.982726 0.185068i \(-0.0592506\pi\)
\(710\) 18.9047i 0.709480i
\(711\) 2.22982 0.0836246
\(712\) 2.37244 0.0889110
\(713\) 48.9220i 1.83214i
\(714\) 0 0
\(715\) 25.5672 56.9229i 0.956157 2.12880i
\(716\) 15.2773 0.570941
\(717\) 17.9916i 0.671909i
\(718\) −23.8440 −0.889848
\(719\) 19.5346 0.728517 0.364258 0.931298i \(-0.381322\pi\)
0.364258 + 0.931298i \(0.381322\pi\)
\(720\) 11.4283i 0.425906i
\(721\) 0 0
\(722\) 12.5937i 0.468690i
\(723\) 44.8205i 1.66689i
\(724\) −34.8961 −1.29690
\(725\) 29.2728 1.08716
\(726\) 27.6661i 1.02679i
\(727\) 24.4958 0.908498 0.454249 0.890875i \(-0.349908\pi\)
0.454249 + 0.890875i \(0.349908\pi\)
\(728\) 0 0
\(729\) −16.3211 −0.604486
\(730\) 12.9864i 0.480649i
\(731\) 6.37788 0.235895
\(732\) −7.87512 −0.291073
\(733\) 30.8279i 1.13865i 0.822111 + 0.569327i \(0.192796\pi\)
−0.822111 + 0.569327i \(0.807204\pi\)
\(734\) 10.2033i 0.376611i
\(735\) 0 0
\(736\) 51.8864i 1.91256i
\(737\) −46.4164 −1.70977
\(738\) −3.68578 −0.135675
\(739\) 2.69864i 0.0992710i −0.998767 0.0496355i \(-0.984194\pi\)
0.998767 0.0496355i \(-0.0158060\pi\)
\(740\) 33.3954 1.22764
\(741\) 5.34717 + 2.40170i 0.196433 + 0.0882287i
\(742\) 0 0
\(743\) 15.2204i 0.558382i 0.960236 + 0.279191i \(0.0900662\pi\)
−0.960236 + 0.279191i \(0.909934\pi\)
\(744\) −30.6612 −1.12409
\(745\) −42.9783 −1.57460
\(746\) 14.2802i 0.522836i
\(747\) 28.7610i 1.05231i
\(748\) 21.8714i 0.799699i
\(749\) 0 0
\(750\) 2.76929 0.101120
\(751\) 24.5482 0.895777 0.447888 0.894089i \(-0.352176\pi\)
0.447888 + 0.894089i \(0.352176\pi\)
\(752\) 8.33461i 0.303932i
\(753\) −41.2581 −1.50353
\(754\) −11.8267 5.31201i −0.430703 0.193452i
\(755\) 30.0553 1.09383
\(756\) 0 0
\(757\) 11.0892 0.403043 0.201522 0.979484i \(-0.435411\pi\)
0.201522 + 0.979484i \(0.435411\pi\)
\(758\) −10.3679 −0.376580
\(759\) 111.514i 4.04771i
\(760\) 5.44012i 0.197334i
\(761\) 16.9512i 0.614481i −0.951632 0.307241i \(-0.900594\pi\)
0.951632 0.307241i \(-0.0994057\pi\)
\(762\) 16.3154i 0.591044i
\(763\) 0 0
\(764\) 8.34659 0.301969
\(765\) 21.2059i 0.766702i
\(766\) 16.7165 0.603991
\(767\) −9.80359 4.40332i −0.353987 0.158995i
\(768\) −22.1986 −0.801022
\(769\) 50.7371i 1.82962i 0.403879 + 0.914812i \(0.367662\pi\)
−0.403879 + 0.914812i \(0.632338\pi\)
\(770\) 0 0
\(771\) 6.11389 0.220186
\(772\) 3.02863i 0.109003i
\(773\) 30.8560i 1.10981i −0.831912 0.554907i \(-0.812754\pi\)
0.831912 0.554907i \(-0.187246\pi\)
\(774\) 3.98011i 0.143062i
\(775\) 30.2311i 1.08593i
\(776\) 36.9223 1.32543
\(777\) 0 0
\(778\) 13.0875i 0.469209i
\(779\) −1.54166 −0.0552359
\(780\) 38.3111 + 17.2076i 1.37176 + 0.616130i
\(781\) −45.6484 −1.63343
\(782\) 16.2644i 0.581614i
\(783\) 6.80940 0.243348
\(784\) 0 0
\(785\) 5.37644i 0.191893i
\(786\) 19.9748i 0.712479i
\(787\) 4.00436i 0.142740i 0.997450 + 0.0713700i \(0.0227371\pi\)
−0.997450 + 0.0713700i \(0.977263\pi\)
\(788\) 29.4363i 1.04862i
\(789\) 13.1382 0.467733
\(790\) −2.01109 −0.0715512
\(791\) 0 0
\(792\) 31.4053 1.11594
\(793\) −3.24210 + 7.21824i −0.115130 + 0.256327i
\(794\) −0.405917 −0.0144054
\(795\)