Properties

Label 637.2.c.g.246.5
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 246.5
Root \(-1.41421 - 1.52340i\) of defining polynomial
Character \(\chi\) \(=\) 637.246
Dual form 637.2.c.g.246.11

$q$-expansion

\(f(q)\) \(=\) \(q-1.52340i q^{2} -2.99510 q^{3} -0.320733 q^{4} -2.94606i q^{5} +4.56272i q^{6} -2.55819i q^{8} +5.97063 q^{9} +O(q^{10})\) \(q-1.52340i q^{2} -2.99510 q^{3} -0.320733 q^{4} -2.94606i q^{5} +4.56272i q^{6} -2.55819i q^{8} +5.97063 q^{9} -4.48801 q^{10} -2.37108i q^{11} +0.960628 q^{12} +(-2.32734 - 2.75381i) q^{13} +8.82374i q^{15} -4.53860 q^{16} +5.36994 q^{17} -9.09563i q^{18} -5.35438i q^{19} +0.944899i q^{20} -3.61209 q^{22} -2.79056 q^{23} +7.66203i q^{24} -3.67927 q^{25} +(-4.19514 + 3.54546i) q^{26} -8.89733 q^{27} +0.585818 q^{29} +13.4421 q^{30} +8.33379i q^{31} +1.79770i q^{32} +7.10163i q^{33} -8.18054i q^{34} -1.91498 q^{36} +0.675710i q^{37} -8.15683 q^{38} +(6.97063 + 8.24794i) q^{39} -7.53657 q^{40} +11.2799i q^{41} -10.5271 q^{43} +0.760484i q^{44} -17.5898i q^{45} +4.25113i q^{46} -0.537744i q^{47} +13.5936 q^{48} +5.60498i q^{50} -16.0835 q^{51} +(0.746456 + 0.883239i) q^{52} +7.90345 q^{53} +13.5541i q^{54} -6.98535 q^{55} +16.0369i q^{57} -0.892432i q^{58} +6.14603i q^{59} -2.83007i q^{60} +2.78689 q^{61} +12.6957 q^{62} -6.33858 q^{64} +(-8.11289 + 6.85649i) q^{65} +10.8186 q^{66} -4.21353i q^{67} -1.72232 q^{68} +8.35802 q^{69} -1.25151i q^{71} -15.2740i q^{72} -10.8620i q^{73} +1.02937 q^{74} +11.0198 q^{75} +1.71733i q^{76} +(12.5649 - 10.6190i) q^{78} +6.29136 q^{79} +13.3710i q^{80} +8.73651 q^{81} +17.1837 q^{82} -1.74725i q^{83} -15.8202i q^{85} +16.0369i q^{86} -1.75458 q^{87} -6.06567 q^{88} -10.2343i q^{89} -26.7963 q^{90} +0.895027 q^{92} -24.9605i q^{93} -0.819196 q^{94} -15.7743 q^{95} -5.38430i q^{96} -9.90640i q^{97} -14.1568i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 20q^{4} + 16q^{9} + O(q^{10}) \) \( 16q - 20q^{4} + 16q^{9} + 28q^{16} - 8q^{22} - 36q^{23} - 44q^{25} + 36q^{29} + 52q^{36} + 32q^{39} - 36q^{43} - 72q^{51} + 12q^{53} - 164q^{64} - 24q^{65} + 96q^{74} + 24q^{78} + 36q^{79} + 16q^{81} + 136q^{88} + 24q^{92} - 84q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.52340i 1.07720i −0.842561 0.538602i \(-0.818953\pi\)
0.842561 0.538602i \(-0.181047\pi\)
\(3\) −2.99510 −1.72922 −0.864611 0.502442i \(-0.832435\pi\)
−0.864611 + 0.502442i \(0.832435\pi\)
\(4\) −0.320733 −0.160367
\(5\) 2.94606i 1.31752i −0.752354 0.658759i \(-0.771082\pi\)
0.752354 0.658759i \(-0.228918\pi\)
\(6\) 4.56272i 1.86272i
\(7\) 0 0
\(8\) 2.55819i 0.904456i
\(9\) 5.97063 1.99021
\(10\) −4.48801 −1.41923
\(11\) 2.37108i 0.714908i −0.933931 0.357454i \(-0.883645\pi\)
0.933931 0.357454i \(-0.116355\pi\)
\(12\) 0.960628 0.277309
\(13\) −2.32734 2.75381i −0.645489 0.763770i
\(14\) 0 0
\(15\) 8.82374i 2.27828i
\(16\) −4.53860 −1.13465
\(17\) 5.36994 1.30240 0.651201 0.758905i \(-0.274265\pi\)
0.651201 + 0.758905i \(0.274265\pi\)
\(18\) 9.09563i 2.14386i
\(19\) 5.35438i 1.22838i −0.789159 0.614189i \(-0.789483\pi\)
0.789159 0.614189i \(-0.210517\pi\)
\(20\) 0.944899i 0.211286i
\(21\) 0 0
\(22\) −3.61209 −0.770101
\(23\) −2.79056 −0.581873 −0.290936 0.956742i \(-0.593967\pi\)
−0.290936 + 0.956742i \(0.593967\pi\)
\(24\) 7.66203i 1.56400i
\(25\) −3.67927 −0.735853
\(26\) −4.19514 + 3.54546i −0.822735 + 0.695323i
\(27\) −8.89733 −1.71229
\(28\) 0 0
\(29\) 0.585818 0.108784 0.0543918 0.998520i \(-0.482678\pi\)
0.0543918 + 0.998520i \(0.482678\pi\)
\(30\) 13.4421 2.45417
\(31\) 8.33379i 1.49679i 0.663252 + 0.748397i \(0.269176\pi\)
−0.663252 + 0.748397i \(0.730824\pi\)
\(32\) 1.79770i 0.317792i
\(33\) 7.10163i 1.23623i
\(34\) 8.18054i 1.40295i
\(35\) 0 0
\(36\) −1.91498 −0.319163
\(37\) 0.675710i 0.111086i 0.998456 + 0.0555430i \(0.0176890\pi\)
−0.998456 + 0.0555430i \(0.982311\pi\)
\(38\) −8.15683 −1.32321
\(39\) 6.97063 + 8.24794i 1.11619 + 1.32073i
\(40\) −7.53657 −1.19164
\(41\) 11.2799i 1.76162i 0.473473 + 0.880808i \(0.343000\pi\)
−0.473473 + 0.880808i \(0.657000\pi\)
\(42\) 0 0
\(43\) −10.5271 −1.60536 −0.802682 0.596408i \(-0.796594\pi\)
−0.802682 + 0.596408i \(0.796594\pi\)
\(44\) 0.760484i 0.114647i
\(45\) 17.5898i 2.62214i
\(46\) 4.25113i 0.626795i
\(47\) 0.537744i 0.0784380i −0.999231 0.0392190i \(-0.987513\pi\)
0.999231 0.0392190i \(-0.0124870\pi\)
\(48\) 13.5936 1.96206
\(49\) 0 0
\(50\) 5.60498i 0.792664i
\(51\) −16.0835 −2.25214
\(52\) 0.746456 + 0.883239i 0.103515 + 0.122483i
\(53\) 7.90345 1.08562 0.542811 0.839855i \(-0.317360\pi\)
0.542811 + 0.839855i \(0.317360\pi\)
\(54\) 13.5541i 1.84449i
\(55\) −6.98535 −0.941904
\(56\) 0 0
\(57\) 16.0369i 2.12414i
\(58\) 0.892432i 0.117182i
\(59\) 6.14603i 0.800145i 0.916484 + 0.400072i \(0.131015\pi\)
−0.916484 + 0.400072i \(0.868985\pi\)
\(60\) 2.83007i 0.365360i
\(61\) 2.78689 0.356824 0.178412 0.983956i \(-0.442904\pi\)
0.178412 + 0.983956i \(0.442904\pi\)
\(62\) 12.6957 1.61235
\(63\) 0 0
\(64\) −6.33858 −0.792323
\(65\) −8.11289 + 6.85649i −1.00628 + 0.850443i
\(66\) 10.8186 1.33168
\(67\) 4.21353i 0.514765i −0.966310 0.257382i \(-0.917140\pi\)
0.966310 0.257382i \(-0.0828600\pi\)
\(68\) −1.72232 −0.208862
\(69\) 8.35802 1.00619
\(70\) 0 0
\(71\) 1.25151i 0.148527i −0.997239 0.0742637i \(-0.976339\pi\)
0.997239 0.0742637i \(-0.0236607\pi\)
\(72\) 15.2740i 1.80006i
\(73\) 10.8620i 1.27130i −0.771977 0.635650i \(-0.780732\pi\)
0.771977 0.635650i \(-0.219268\pi\)
\(74\) 1.02937 0.119662
\(75\) 11.0198 1.27245
\(76\) 1.71733i 0.196991i
\(77\) 0 0
\(78\) 12.5649 10.6190i 1.42269 1.20237i
\(79\) 6.29136 0.707833 0.353917 0.935277i \(-0.384850\pi\)
0.353917 + 0.935277i \(0.384850\pi\)
\(80\) 13.3710i 1.49492i
\(81\) 8.73651 0.970723
\(82\) 17.1837 1.89762
\(83\) 1.74725i 0.191786i −0.995392 0.0958928i \(-0.969429\pi\)
0.995392 0.0958928i \(-0.0305706\pi\)
\(84\) 0 0
\(85\) 15.8202i 1.71594i
\(86\) 16.0369i 1.72930i
\(87\) −1.75458 −0.188111
\(88\) −6.06567 −0.646602
\(89\) 10.2343i 1.08483i −0.840110 0.542416i \(-0.817510\pi\)
0.840110 0.542416i \(-0.182490\pi\)
\(90\) −26.7963 −2.82457
\(91\) 0 0
\(92\) 0.895027 0.0933130
\(93\) 24.9605i 2.58829i
\(94\) −0.819196 −0.0844936
\(95\) −15.7743 −1.61841
\(96\) 5.38430i 0.549533i
\(97\) 9.90640i 1.00584i −0.864332 0.502921i \(-0.832259\pi\)
0.864332 0.502921i \(-0.167741\pi\)
\(98\) 0 0
\(99\) 14.1568i 1.42282i
\(100\) 1.18006 0.118006
\(101\) −2.05077 −0.204059 −0.102030 0.994781i \(-0.532534\pi\)
−0.102030 + 0.994781i \(0.532534\pi\)
\(102\) 24.5016i 2.42602i
\(103\) −3.02962 −0.298517 −0.149259 0.988798i \(-0.547689\pi\)
−0.149259 + 0.988798i \(0.547689\pi\)
\(104\) −7.04476 + 5.95378i −0.690796 + 0.583816i
\(105\) 0 0
\(106\) 12.0401i 1.16944i
\(107\) −12.4305 −1.20170 −0.600852 0.799360i \(-0.705172\pi\)
−0.600852 + 0.799360i \(0.705172\pi\)
\(108\) 2.85367 0.274594
\(109\) 3.53782i 0.338862i 0.985542 + 0.169431i \(0.0541929\pi\)
−0.985542 + 0.169431i \(0.945807\pi\)
\(110\) 10.6414i 1.01462i
\(111\) 2.02382i 0.192092i
\(112\) 0 0
\(113\) 10.3848 0.976921 0.488460 0.872586i \(-0.337559\pi\)
0.488460 + 0.872586i \(0.337559\pi\)
\(114\) 24.4305 2.28813
\(115\) 8.22117i 0.766628i
\(116\) −0.187891 −0.0174453
\(117\) −13.8957 16.4420i −1.28466 1.52006i
\(118\) 9.36283 0.861918
\(119\) 0 0
\(120\) 22.5728 2.06060
\(121\) 5.37797 0.488907
\(122\) 4.24553i 0.384372i
\(123\) 33.7843i 3.04623i
\(124\) 2.67292i 0.240036i
\(125\) 3.89096i 0.348018i
\(126\) 0 0
\(127\) −5.09504 −0.452112 −0.226056 0.974114i \(-0.572583\pi\)
−0.226056 + 0.974114i \(0.572583\pi\)
\(128\) 13.2516i 1.17128i
\(129\) 31.5296 2.77603
\(130\) 10.4451 + 12.3591i 0.916100 + 1.08397i
\(131\) 22.5443 1.96971 0.984854 0.173386i \(-0.0554707\pi\)
0.984854 + 0.173386i \(0.0554707\pi\)
\(132\) 2.27773i 0.198251i
\(133\) 0 0
\(134\) −6.41887 −0.554506
\(135\) 26.2121i 2.25597i
\(136\) 13.7373i 1.17797i
\(137\) 1.03479i 0.0884082i 0.999023 + 0.0442041i \(0.0140752\pi\)
−0.999023 + 0.0442041i \(0.985925\pi\)
\(138\) 12.7326i 1.08387i
\(139\) 8.49456 0.720499 0.360249 0.932856i \(-0.382692\pi\)
0.360249 + 0.932856i \(0.382692\pi\)
\(140\) 0 0
\(141\) 1.61060i 0.135637i
\(142\) −1.90655 −0.159994
\(143\) −6.52951 + 5.51832i −0.546025 + 0.461465i
\(144\) −27.0983 −2.25819
\(145\) 1.72585i 0.143324i
\(146\) −16.5471 −1.36945
\(147\) 0 0
\(148\) 0.216723i 0.0178145i
\(149\) 4.31343i 0.353370i −0.984267 0.176685i \(-0.943463\pi\)
0.984267 0.176685i \(-0.0565374\pi\)
\(150\) 16.7875i 1.37069i
\(151\) 12.2447i 0.996463i 0.867044 + 0.498232i \(0.166017\pi\)
−0.867044 + 0.498232i \(0.833983\pi\)
\(152\) −13.6975 −1.11101
\(153\) 32.0619 2.59205
\(154\) 0 0
\(155\) 24.5518 1.97205
\(156\) −2.23571 2.64539i −0.179000 0.211801i
\(157\) −22.2040 −1.77207 −0.886035 0.463619i \(-0.846551\pi\)
−0.886035 + 0.463619i \(0.846551\pi\)
\(158\) 9.58423i 0.762480i
\(159\) −23.6716 −1.87728
\(160\) 5.29614 0.418697
\(161\) 0 0
\(162\) 13.3092i 1.04567i
\(163\) 11.3644i 0.890127i 0.895499 + 0.445063i \(0.146819\pi\)
−0.895499 + 0.445063i \(0.853181\pi\)
\(164\) 3.61782i 0.282505i
\(165\) 20.9218 1.62876
\(166\) −2.66175 −0.206592
\(167\) 1.88127i 0.145577i −0.997347 0.0727885i \(-0.976810\pi\)
0.997347 0.0727885i \(-0.0231898\pi\)
\(168\) 0 0
\(169\) −2.16695 + 12.8181i −0.166688 + 0.986010i
\(170\) −24.1004 −1.84841
\(171\) 31.9690i 2.44473i
\(172\) 3.37638 0.257447
\(173\) 5.57113 0.423565 0.211783 0.977317i \(-0.432073\pi\)
0.211783 + 0.977317i \(0.432073\pi\)
\(174\) 2.67292i 0.202634i
\(175\) 0 0
\(176\) 10.7614i 0.811170i
\(177\) 18.4080i 1.38363i
\(178\) −15.5909 −1.16858
\(179\) 4.66142 0.348411 0.174205 0.984709i \(-0.444264\pi\)
0.174205 + 0.984709i \(0.444264\pi\)
\(180\) 5.64164i 0.420503i
\(181\) −12.5360 −0.931794 −0.465897 0.884839i \(-0.654268\pi\)
−0.465897 + 0.884839i \(0.654268\pi\)
\(182\) 0 0
\(183\) −8.34701 −0.617029
\(184\) 7.13879i 0.526278i
\(185\) 1.99068 0.146358
\(186\) −38.0248 −2.78811
\(187\) 12.7326i 0.931098i
\(188\) 0.172472i 0.0125788i
\(189\) 0 0
\(190\) 24.0305i 1.74336i
\(191\) −1.31764 −0.0953408 −0.0476704 0.998863i \(-0.515180\pi\)
−0.0476704 + 0.998863i \(0.515180\pi\)
\(192\) 18.9847 1.37010
\(193\) 15.1445i 1.09012i −0.838396 0.545061i \(-0.816506\pi\)
0.838396 0.545061i \(-0.183494\pi\)
\(194\) −15.0914 −1.08350
\(195\) 24.2989 20.5359i 1.74008 1.47061i
\(196\) 0 0
\(197\) 9.90571i 0.705753i −0.935670 0.352876i \(-0.885204\pi\)
0.935670 0.352876i \(-0.114796\pi\)
\(198\) −21.5665 −1.53266
\(199\) 8.57326 0.607742 0.303871 0.952713i \(-0.401721\pi\)
0.303871 + 0.952713i \(0.401721\pi\)
\(200\) 9.41225i 0.665547i
\(201\) 12.6199i 0.890142i
\(202\) 3.12413i 0.219813i
\(203\) 0 0
\(204\) 5.15852 0.361169
\(205\) 33.2311 2.32096
\(206\) 4.61530i 0.321564i
\(207\) −16.6614 −1.15805
\(208\) 10.5629 + 12.4984i 0.732403 + 0.866611i
\(209\) −12.6957 −0.878177
\(210\) 0 0
\(211\) −1.44515 −0.0994881 −0.0497440 0.998762i \(-0.515841\pi\)
−0.0497440 + 0.998762i \(0.515841\pi\)
\(212\) −2.53490 −0.174098
\(213\) 3.74841i 0.256837i
\(214\) 18.9366i 1.29448i
\(215\) 31.0134i 2.11510i
\(216\) 22.7610i 1.54869i
\(217\) 0 0
\(218\) 5.38950 0.365023
\(219\) 32.5328i 2.19836i
\(220\) 2.24043 0.151050
\(221\) −12.4977 14.7878i −0.840686 0.994735i
\(222\) −3.08307 −0.206922
\(223\) 14.9949i 1.00413i −0.864829 0.502067i \(-0.832573\pi\)
0.864829 0.502067i \(-0.167427\pi\)
\(224\) 0 0
\(225\) −21.9675 −1.46450
\(226\) 15.8202i 1.05234i
\(227\) 1.14220i 0.0758105i −0.999281 0.0379052i \(-0.987932\pi\)
0.999281 0.0379052i \(-0.0120685\pi\)
\(228\) 5.14356i 0.340641i
\(229\) 6.26935i 0.414290i 0.978310 + 0.207145i \(0.0664172\pi\)
−0.978310 + 0.207145i \(0.933583\pi\)
\(230\) 12.5241 0.825814
\(231\) 0 0
\(232\) 1.49863i 0.0983900i
\(233\) 6.16695 0.404010 0.202005 0.979384i \(-0.435254\pi\)
0.202005 + 0.979384i \(0.435254\pi\)
\(234\) −25.0476 + 21.1686i −1.63741 + 1.38384i
\(235\) −1.58423 −0.103343
\(236\) 1.97124i 0.128317i
\(237\) −18.8433 −1.22400
\(238\) 0 0
\(239\) 27.4589i 1.77617i −0.459684 0.888083i \(-0.652037\pi\)
0.459684 0.888083i \(-0.347963\pi\)
\(240\) 40.0474i 2.58505i
\(241\) 9.79378i 0.630873i −0.948947 0.315436i \(-0.897849\pi\)
0.948947 0.315436i \(-0.102151\pi\)
\(242\) 8.19278i 0.526652i
\(243\) 0.525262 0.0336956
\(244\) −0.893848 −0.0572227
\(245\) 0 0
\(246\) −51.4668 −3.28140
\(247\) −14.7449 + 12.4615i −0.938198 + 0.792904i
\(248\) 21.3194 1.35378
\(249\) 5.23319i 0.331640i
\(250\) −5.92747 −0.374886
\(251\) −12.4945 −0.788644 −0.394322 0.918972i \(-0.629021\pi\)
−0.394322 + 0.918972i \(0.629021\pi\)
\(252\) 0 0
\(253\) 6.61665i 0.415985i
\(254\) 7.76176i 0.487016i
\(255\) 47.3830i 2.96724i
\(256\) 7.51022 0.469389
\(257\) −19.1929 −1.19722 −0.598610 0.801040i \(-0.704280\pi\)
−0.598610 + 0.801040i \(0.704280\pi\)
\(258\) 48.0321i 2.99035i
\(259\) 0 0
\(260\) 2.60207 2.19910i 0.161374 0.136383i
\(261\) 3.49770 0.216502
\(262\) 34.3439i 2.12178i
\(263\) 28.8153 1.77683 0.888415 0.459041i \(-0.151807\pi\)
0.888415 + 0.459041i \(0.151807\pi\)
\(264\) 18.1673 1.11812
\(265\) 23.2840i 1.43033i
\(266\) 0 0
\(267\) 30.6527i 1.87592i
\(268\) 1.35142i 0.0825511i
\(269\) 8.15419 0.497170 0.248585 0.968610i \(-0.420035\pi\)
0.248585 + 0.968610i \(0.420035\pi\)
\(270\) 39.9313 2.43014
\(271\) 18.5788i 1.12858i −0.825577 0.564290i \(-0.809150\pi\)
0.825577 0.564290i \(-0.190850\pi\)
\(272\) −24.3720 −1.47777
\(273\) 0 0
\(274\) 1.57640 0.0952336
\(275\) 8.72384i 0.526067i
\(276\) −2.68069 −0.161359
\(277\) 17.2342 1.03550 0.517752 0.855531i \(-0.326769\pi\)
0.517752 + 0.855531i \(0.326769\pi\)
\(278\) 12.9406i 0.776124i
\(279\) 49.7580i 2.97893i
\(280\) 0 0
\(281\) 11.4691i 0.684191i 0.939665 + 0.342096i \(0.111137\pi\)
−0.939665 + 0.342096i \(0.888863\pi\)
\(282\) 2.45358 0.146108
\(283\) −1.45575 −0.0865355 −0.0432678 0.999064i \(-0.513777\pi\)
−0.0432678 + 0.999064i \(0.513777\pi\)
\(284\) 0.401402i 0.0238188i
\(285\) 47.2456 2.79859
\(286\) 8.40658 + 9.94702i 0.497092 + 0.588180i
\(287\) 0 0
\(288\) 10.7334i 0.632472i
\(289\) 11.8363 0.696252
\(290\) −2.62916 −0.154389
\(291\) 29.6707i 1.73932i
\(292\) 3.48380i 0.203874i
\(293\) 30.6962i 1.79329i 0.442750 + 0.896645i \(0.354003\pi\)
−0.442750 + 0.896645i \(0.645997\pi\)
\(294\) 0 0
\(295\) 18.1066 1.05421
\(296\) 1.72859 0.100472
\(297\) 21.0963i 1.22413i
\(298\) −6.57107 −0.380652
\(299\) 6.49460 + 7.68469i 0.375592 + 0.444417i
\(300\) −3.53441 −0.204059
\(301\) 0 0
\(302\) 18.6536 1.07339
\(303\) 6.14226 0.352864
\(304\) 24.3013i 1.39378i
\(305\) 8.21034i 0.470123i
\(306\) 48.8430i 2.79217i
\(307\) 21.2602i 1.21339i 0.794936 + 0.606693i \(0.207504\pi\)
−0.794936 + 0.606693i \(0.792496\pi\)
\(308\) 0 0
\(309\) 9.07401 0.516202
\(310\) 37.4022i 2.12430i
\(311\) −4.44647 −0.252136 −0.126068 0.992022i \(-0.540236\pi\)
−0.126068 + 0.992022i \(0.540236\pi\)
\(312\) 21.0998 17.8322i 1.19454 1.00955i
\(313\) −2.28687 −0.129261 −0.0646307 0.997909i \(-0.520587\pi\)
−0.0646307 + 0.997909i \(0.520587\pi\)
\(314\) 33.8254i 1.90888i
\(315\) 0 0
\(316\) −2.01785 −0.113513
\(317\) 8.10086i 0.454990i −0.973779 0.227495i \(-0.926947\pi\)
0.973779 0.227495i \(-0.0730535\pi\)
\(318\) 36.0613i 2.02222i
\(319\) 1.38902i 0.0777703i
\(320\) 18.6738i 1.04390i
\(321\) 37.2307 2.07801
\(322\) 0 0
\(323\) 28.7527i 1.59984i
\(324\) −2.80209 −0.155672
\(325\) 8.56292 + 10.1320i 0.474985 + 0.562022i
\(326\) 17.3124 0.958847
\(327\) 10.5961i 0.585967i
\(328\) 28.8560 1.59330
\(329\) 0 0
\(330\) 31.8722i 1.75451i
\(331\) 11.7858i 0.647804i −0.946091 0.323902i \(-0.895005\pi\)
0.946091 0.323902i \(-0.104995\pi\)
\(332\) 0.560401i 0.0307560i
\(333\) 4.03441i 0.221084i
\(334\) −2.86592 −0.156816
\(335\) −12.4133 −0.678212
\(336\) 0 0
\(337\) −2.63045 −0.143290 −0.0716450 0.997430i \(-0.522825\pi\)
−0.0716450 + 0.997430i \(0.522825\pi\)
\(338\) 19.5271 + 3.30112i 1.06213 + 0.179557i
\(339\) −31.1035 −1.68931
\(340\) 5.07405i 0.275179i
\(341\) 19.7601 1.07007
\(342\) −48.7014 −2.63347
\(343\) 0 0
\(344\) 26.9302i 1.45198i
\(345\) 24.6232i 1.32567i
\(346\) 8.48704i 0.456266i
\(347\) 4.82463 0.259000 0.129500 0.991579i \(-0.458663\pi\)
0.129500 + 0.991579i \(0.458663\pi\)
\(348\) 0.562753 0.0301667
\(349\) 17.5231i 0.937991i 0.883201 + 0.468995i \(0.155384\pi\)
−0.883201 + 0.468995i \(0.844616\pi\)
\(350\) 0 0
\(351\) 20.7071 + 24.5016i 1.10527 + 1.30780i
\(352\) 4.26250 0.227192
\(353\) 6.59724i 0.351136i −0.984467 0.175568i \(-0.943824\pi\)
0.984467 0.175568i \(-0.0561761\pi\)
\(354\) −28.0426 −1.49045
\(355\) −3.68704 −0.195688
\(356\) 3.28248i 0.173971i
\(357\) 0 0
\(358\) 7.10118i 0.375309i
\(359\) 23.0484i 1.21645i −0.793764 0.608225i \(-0.791882\pi\)
0.793764 0.608225i \(-0.208118\pi\)
\(360\) −44.9981 −2.37161
\(361\) −9.66934 −0.508912
\(362\) 19.0973i 1.00373i
\(363\) −16.1076 −0.845428
\(364\) 0 0
\(365\) −32.0001 −1.67496
\(366\) 12.7158i 0.664665i
\(367\) −15.9318 −0.831631 −0.415815 0.909449i \(-0.636504\pi\)
−0.415815 + 0.909449i \(0.636504\pi\)
\(368\) 12.6652 0.660222
\(369\) 67.3478i 3.50599i
\(370\) 3.03259i 0.157657i
\(371\) 0 0
\(372\) 8.00568i 0.415075i
\(373\) 23.4289 1.21310 0.606552 0.795044i \(-0.292552\pi\)
0.606552 + 0.795044i \(0.292552\pi\)
\(374\) −19.3967 −1.00298
\(375\) 11.6538i 0.601800i
\(376\) −1.37565 −0.0709437
\(377\) −1.36340 1.61323i −0.0702186 0.0830856i
\(378\) 0 0
\(379\) 30.1041i 1.54634i −0.634196 0.773172i \(-0.718669\pi\)
0.634196 0.773172i \(-0.281331\pi\)
\(380\) 5.05934 0.259539
\(381\) 15.2602 0.781802
\(382\) 2.00728i 0.102701i
\(383\) 12.8597i 0.657101i 0.944486 + 0.328551i \(0.106560\pi\)
−0.944486 + 0.328551i \(0.893440\pi\)
\(384\) 39.6898i 2.02541i
\(385\) 0 0
\(386\) −23.0710 −1.17428
\(387\) −62.8532 −3.19501
\(388\) 3.17731i 0.161304i
\(389\) −36.8531 −1.86853 −0.934264 0.356582i \(-0.883942\pi\)
−0.934264 + 0.356582i \(0.883942\pi\)
\(390\) −31.2843 37.0169i −1.58414 1.87442i
\(391\) −14.9852 −0.757833
\(392\) 0 0
\(393\) −67.5226 −3.40606
\(394\) −15.0903 −0.760239
\(395\) 18.5347i 0.932583i
\(396\) 4.54057i 0.228172i
\(397\) 20.3087i 1.01926i −0.860393 0.509631i \(-0.829782\pi\)
0.860393 0.509631i \(-0.170218\pi\)
\(398\) 13.0605i 0.654662i
\(399\) 0 0
\(400\) 16.6987 0.834935
\(401\) 19.6699i 0.982268i 0.871084 + 0.491134i \(0.163417\pi\)
−0.871084 + 0.491134i \(0.836583\pi\)
\(402\) 19.2252 0.958864
\(403\) 22.9497 19.3956i 1.14321 0.966163i
\(404\) 0.657750 0.0327243
\(405\) 25.7383i 1.27895i
\(406\) 0 0
\(407\) 1.60216 0.0794162
\(408\) 41.1446i 2.03696i
\(409\) 23.1755i 1.14595i −0.819572 0.572976i \(-0.805789\pi\)
0.819572 0.572976i \(-0.194211\pi\)
\(410\) 50.6241i 2.50015i
\(411\) 3.09931i 0.152877i
\(412\) 0.971699 0.0478722
\(413\) 0 0
\(414\) 25.3819i 1.24745i
\(415\) −5.14750 −0.252681
\(416\) 4.95053 4.18387i 0.242720 0.205131i
\(417\) −25.4421 −1.24590
\(418\) 19.3405i 0.945975i
\(419\) 28.6478 1.39953 0.699767 0.714371i \(-0.253287\pi\)
0.699767 + 0.714371i \(0.253287\pi\)
\(420\) 0 0
\(421\) 36.3249i 1.77037i 0.465241 + 0.885184i \(0.345968\pi\)
−0.465241 + 0.885184i \(0.654032\pi\)
\(422\) 2.20153i 0.107169i
\(423\) 3.21067i 0.156108i
\(424\) 20.2185i 0.981898i
\(425\) −19.7575 −0.958377
\(426\) 5.71031 0.276666
\(427\) 0 0
\(428\) 3.98688 0.192713
\(429\) 19.5565 16.5279i 0.944198 0.797976i
\(430\) 47.2456 2.27839
\(431\) 7.93131i 0.382038i −0.981586 0.191019i \(-0.938821\pi\)
0.981586 0.191019i \(-0.0611792\pi\)
\(432\) 40.3814 1.94285
\(433\) −9.60994 −0.461824 −0.230912 0.972975i \(-0.574171\pi\)
−0.230912 + 0.972975i \(0.574171\pi\)
\(434\) 0 0
\(435\) 5.16911i 0.247840i
\(436\) 1.13470i 0.0543421i
\(437\) 14.9417i 0.714760i
\(438\) 49.5603 2.36808
\(439\) −3.46690 −0.165466 −0.0827332 0.996572i \(-0.526365\pi\)
−0.0827332 + 0.996572i \(0.526365\pi\)
\(440\) 17.8698i 0.851910i
\(441\) 0 0
\(442\) −22.5277 + 19.0389i −1.07153 + 0.905590i
\(443\) 2.45667 0.116720 0.0583600 0.998296i \(-0.481413\pi\)
0.0583600 + 0.998296i \(0.481413\pi\)
\(444\) 0.649106i 0.0308052i
\(445\) −30.1508 −1.42929
\(446\) −22.8432 −1.08166
\(447\) 12.9192i 0.611056i
\(448\) 0 0
\(449\) 22.7487i 1.07358i −0.843716 0.536790i \(-0.819637\pi\)
0.843716 0.536790i \(-0.180363\pi\)
\(450\) 33.4652i 1.57757i
\(451\) 26.7454 1.25939
\(452\) −3.33075 −0.156665
\(453\) 36.6742i 1.72311i
\(454\) −1.74002 −0.0816633
\(455\) 0 0
\(456\) 41.0254 1.92119
\(457\) 12.2568i 0.573349i −0.958028 0.286675i \(-0.907450\pi\)
0.958028 0.286675i \(-0.0925499\pi\)
\(458\) 9.55070 0.446275
\(459\) −47.7781 −2.23009
\(460\) 2.63680i 0.122942i
\(461\) 24.0650i 1.12082i −0.828216 0.560409i \(-0.810644\pi\)
0.828216 0.560409i \(-0.189356\pi\)
\(462\) 0 0
\(463\) 19.3956i 0.901390i 0.892678 + 0.450695i \(0.148824\pi\)
−0.892678 + 0.450695i \(0.851176\pi\)
\(464\) −2.65879 −0.123431
\(465\) −73.5352 −3.41012
\(466\) 9.39470i 0.435201i
\(467\) −17.8782 −0.827307 −0.413653 0.910434i \(-0.635747\pi\)
−0.413653 + 0.910434i \(0.635747\pi\)
\(468\) 4.45681 + 5.27349i 0.206016 + 0.243767i
\(469\) 0 0
\(470\) 2.41340i 0.111322i
\(471\) 66.5031 3.06430
\(472\) 15.7227 0.723696
\(473\) 24.9605i 1.14769i
\(474\) 28.7057i 1.31850i
\(475\) 19.7002i 0.903906i
\(476\) 0 0
\(477\) 47.1886 2.16062
\(478\) −41.8307 −1.91329
\(479\) 20.7671i 0.948875i −0.880289 0.474437i \(-0.842652\pi\)
0.880289 0.474437i \(-0.157348\pi\)
\(480\) −15.8625 −0.724019
\(481\) 1.86078 1.57261i 0.0848441 0.0717048i
\(482\) −14.9198 −0.679578
\(483\) 0 0
\(484\) −1.72490 −0.0784043
\(485\) −29.1848 −1.32522
\(486\) 0.800181i 0.0362970i
\(487\) 19.1987i 0.869977i 0.900436 + 0.434988i \(0.143248\pi\)
−0.900436 + 0.434988i \(0.856752\pi\)
\(488\) 7.12938i 0.322732i
\(489\) 34.0374i 1.53923i
\(490\) 0 0
\(491\) −7.91648 −0.357266 −0.178633 0.983916i \(-0.557167\pi\)
−0.178633 + 0.983916i \(0.557167\pi\)
\(492\) 10.8357i 0.488513i
\(493\) 3.14581 0.141680
\(494\) 18.9837 + 22.4624i 0.854119 + 1.01063i
\(495\) −41.7069 −1.87459
\(496\) 37.8237i 1.69833i
\(497\) 0 0
\(498\) 7.97222 0.357244
\(499\) 39.1750i 1.75371i −0.480753 0.876856i \(-0.659637\pi\)
0.480753 0.876856i \(-0.340363\pi\)
\(500\) 1.24796i 0.0558105i
\(501\) 5.63459i 0.251735i
\(502\) 19.0340i 0.849530i
\(503\) −16.1533 −0.720239 −0.360120 0.932906i \(-0.617264\pi\)
−0.360120 + 0.932906i \(0.617264\pi\)
\(504\) 0 0
\(505\) 6.04169i 0.268852i
\(506\) 10.0798 0.448101
\(507\) 6.49022 38.3916i 0.288241 1.70503i
\(508\) 1.63415 0.0725036
\(509\) 24.3177i 1.07786i −0.842350 0.538930i \(-0.818829\pi\)
0.842350 0.538930i \(-0.181171\pi\)
\(510\) 72.1830 3.19632
\(511\) 0 0
\(512\) 15.0621i 0.665658i
\(513\) 47.6396i 2.10334i
\(514\) 29.2384i 1.28965i
\(515\) 8.92543i 0.393302i
\(516\) −10.1126 −0.445183
\(517\) −1.27503 −0.0560759
\(518\) 0 0
\(519\) −16.6861 −0.732439
\(520\) 17.5402 + 20.7543i 0.769188 + 0.910136i
\(521\) 34.4550 1.50950 0.754750 0.656012i \(-0.227758\pi\)
0.754750 + 0.656012i \(0.227758\pi\)
\(522\) 5.32838i 0.233217i
\(523\) −34.6865 −1.51674 −0.758368 0.651827i \(-0.774003\pi\)
−0.758368 + 0.651827i \(0.774003\pi\)
\(524\) −7.23072 −0.315875
\(525\) 0 0
\(526\) 43.8971i 1.91401i
\(527\) 44.7520i 1.94943i
\(528\) 32.2314i 1.40269i
\(529\) −15.2128 −0.661424
\(530\) −35.4708 −1.54075
\(531\) 36.6956i 1.59246i
\(532\) 0 0
\(533\) 31.0626 26.2521i 1.34547 1.13710i
\(534\) 46.6962 2.02074
\(535\) 36.6211i 1.58327i
\(536\) −10.7790 −0.465582
\(537\) −13.9614 −0.602480
\(538\) 12.4221i 0.535553i
\(539\) 0 0
\(540\) 8.40708i 0.361783i
\(541\) 12.2568i 0.526961i −0.964665 0.263481i \(-0.915129\pi\)
0.964665 0.263481i \(-0.0848705\pi\)
\(542\) −28.3028 −1.21571
\(543\) 37.5466 1.61128
\(544\) 9.65356i 0.413893i
\(545\) 10.4226 0.446456
\(546\) 0 0
\(547\) −16.4110 −0.701686 −0.350843 0.936434i \(-0.614105\pi\)
−0.350843 + 0.936434i \(0.614105\pi\)
\(548\) 0.331892i 0.0141777i
\(549\) 16.6395 0.710155
\(550\) 13.2899 0.566681
\(551\) 3.13669i 0.133627i
\(552\) 21.3814i 0.910052i
\(553\) 0 0
\(554\) 26.2545i 1.11545i
\(555\) −5.96229 −0.253085
\(556\) −2.72449 −0.115544
\(557\) 35.6541i 1.51071i 0.655315 + 0.755356i \(0.272536\pi\)
−0.655315 + 0.755356i \(0.727464\pi\)
\(558\) 75.8010 3.20891
\(559\) 24.5001 + 28.9896i 1.03624 + 1.22613i
\(560\) 0 0
\(561\) 38.1353i 1.61007i
\(562\) 17.4720 0.737013
\(563\) 10.7748 0.454103 0.227052 0.973883i \(-0.427091\pi\)
0.227052 + 0.973883i \(0.427091\pi\)
\(564\) 0.516572i 0.0217516i
\(565\) 30.5943i 1.28711i
\(566\) 2.21769i 0.0932163i
\(567\) 0 0
\(568\) −3.20161 −0.134336
\(569\) −20.9328 −0.877550 −0.438775 0.898597i \(-0.644587\pi\)
−0.438775 + 0.898597i \(0.644587\pi\)
\(570\) 71.9738i 3.01465i
\(571\) −32.2668 −1.35032 −0.675161 0.737670i \(-0.735926\pi\)
−0.675161 + 0.737670i \(0.735926\pi\)
\(572\) 2.09423 1.76991i 0.0875642 0.0740036i
\(573\) 3.94645 0.164865
\(574\) 0 0
\(575\) 10.2672 0.428173
\(576\) −37.8453 −1.57689
\(577\) 0.197896i 0.00823851i 0.999992 + 0.00411925i \(0.00131120\pi\)
−0.999992 + 0.00411925i \(0.998689\pi\)
\(578\) 18.0313i 0.750005i
\(579\) 45.3592i 1.88506i
\(580\) 0.553539i 0.0229844i
\(581\) 0 0
\(582\) 45.2001 1.87361
\(583\) 18.7397i 0.776120i
\(584\) −27.7870 −1.14984
\(585\) −48.4390 + 40.9376i −2.00271 + 1.69256i
\(586\) 46.7624 1.93174
\(587\) 10.1251i 0.417907i 0.977926 + 0.208954i \(0.0670058\pi\)
−0.977926 + 0.208954i \(0.932994\pi\)
\(588\) 0 0
\(589\) 44.6222 1.83863
\(590\) 27.5835i 1.13559i
\(591\) 29.6686i 1.22040i
\(592\) 3.06677i 0.126044i
\(593\) 29.9345i 1.22926i −0.788815 0.614631i \(-0.789305\pi\)
0.788815 0.614631i \(-0.210695\pi\)
\(594\) 32.1380 1.31864
\(595\) 0 0
\(596\) 1.38346i 0.0566688i
\(597\) −25.6778 −1.05092
\(598\) 11.7068 9.89384i 0.478727 0.404589i
\(599\) 26.8872 1.09858 0.549291 0.835631i \(-0.314898\pi\)
0.549291 + 0.835631i \(0.314898\pi\)
\(600\) 28.1906i 1.15088i
\(601\) −24.7432 −1.00930 −0.504649 0.863325i \(-0.668378\pi\)
−0.504649 + 0.863325i \(0.668378\pi\)
\(602\) 0 0
\(603\) 25.1574i 1.02449i
\(604\) 3.92730i 0.159799i
\(605\) 15.8438i 0.644143i
\(606\) 9.35709i 0.380106i
\(607\) 3.09235 0.125515 0.0627573 0.998029i \(-0.480011\pi\)
0.0627573 + 0.998029i \(0.480011\pi\)
\(608\) 9.62557 0.390369
\(609\) 0 0
\(610\) −12.5076 −0.506417
\(611\) −1.48084 + 1.25151i −0.0599086 + 0.0506308i
\(612\) −10.2833 −0.415679
\(613\) 31.3605i 1.26664i −0.773891 0.633319i \(-0.781692\pi\)
0.773891 0.633319i \(-0.218308\pi\)
\(614\) 32.3877 1.30706
\(615\) −99.5305 −4.01346
\(616\) 0 0
\(617\) 12.5311i 0.504484i −0.967664 0.252242i \(-0.918832\pi\)
0.967664 0.252242i \(-0.0811678\pi\)
\(618\) 13.8233i 0.556055i
\(619\) 11.6112i 0.466692i −0.972394 0.233346i \(-0.925032\pi\)
0.972394 0.233346i \(-0.0749675\pi\)
\(620\) −7.87459 −0.316251
\(621\) 24.8286 0.996336
\(622\) 6.77374i 0.271602i
\(623\) 0 0
\(624\) −31.6369 37.4341i −1.26649 1.49856i
\(625\) −29.8593 −1.19437
\(626\) 3.48380i 0.139241i
\(627\) 38.0248 1.51856
\(628\) 7.12155 0.284181
\(629\) 3.62852i 0.144679i
\(630\) 0 0
\(631\) 12.7037i 0.505728i −0.967502 0.252864i \(-0.918628\pi\)
0.967502 0.252864i \(-0.0813725\pi\)
\(632\) 16.0945i 0.640204i
\(633\) 4.32836 0.172037
\(634\) −12.3408 −0.490116
\(635\) 15.0103i 0.595665i
\(636\) 7.59228 0.301054
\(637\) 0 0
\(638\) −2.11603 −0.0837744
\(639\) 7.47233i 0.295601i
\(640\) 39.0399 1.54319
\(641\) 40.3015 1.59181 0.795906 0.605420i \(-0.206995\pi\)
0.795906 + 0.605420i \(0.206995\pi\)
\(642\) 56.7170i 2.23844i
\(643\) 11.6643i 0.459997i −0.973191 0.229998i \(-0.926128\pi\)
0.973191 0.229998i \(-0.0738721\pi\)
\(644\) 0 0
\(645\) 92.8882i 3.65747i
\(646\) −43.8017 −1.72336
\(647\) 11.0387 0.433977 0.216988 0.976174i \(-0.430377\pi\)
0.216988 + 0.976174i \(0.430377\pi\)
\(648\) 22.3496i 0.877976i
\(649\) 14.5727 0.572030
\(650\) 15.4350 13.0447i 0.605412 0.511656i
\(651\) 0 0
\(652\) 3.64493i 0.142747i
\(653\) 19.1260 0.748458 0.374229 0.927336i \(-0.377907\pi\)
0.374229 + 0.927336i \(0.377907\pi\)
\(654\) −16.1421 −0.631206
\(655\) 66.4170i 2.59513i
\(656\) 51.1947i 1.99882i
\(657\) 64.8529i 2.53015i
\(658\) 0 0
\(659\) 28.8233 1.12279 0.561397 0.827546i \(-0.310264\pi\)
0.561397 + 0.827546i \(0.310264\pi\)
\(660\) −6.71032 −0.261199
\(661\) 48.2385i 1.87626i 0.346281 + 0.938131i \(0.387444\pi\)
−0.346281 + 0.938131i \(0.612556\pi\)
\(662\) −17.9544 −0.697816
\(663\) 37.4319 + 44.2910i 1.45373 + 1.72012i
\(664\) −4.46979 −0.173462
\(665\) 0 0
\(666\) 6.14600 0.238153
\(667\) −1.63476 −0.0632982
\(668\) 0.603386i 0.0233457i
\(669\) 44.9112i 1.73637i
\(670\) 18.9104i 0.730572i
\(671\) 6.60794i 0.255097i
\(672\) 0 0
\(673\) 33.0426 1.27370 0.636849 0.770989i \(-0.280238\pi\)
0.636849 + 0.770989i \(0.280238\pi\)
\(674\) 4.00722i 0.154352i
\(675\) 32.7356 1.26000
\(676\) 0.695012 4.11120i 0.0267312 0.158123i
\(677\) 15.7186 0.604117 0.302058 0.953289i \(-0.402326\pi\)
0.302058 + 0.953289i \(0.402326\pi\)
\(678\) 47.3830i 1.81973i
\(679\) 0 0
\(680\) −40.4710 −1.55199
\(681\) 3.42100i 0.131093i
\(682\) 30.1024i 1.15268i
\(683\) 33.3629i 1.27660i 0.769789 + 0.638298i \(0.220361\pi\)
−0.769789 + 0.638298i \(0.779639\pi\)
\(684\) 10.2535i 0.392053i
\(685\) 3.04856 0.116479
\(686\) 0 0
\(687\) 18.7773i 0.716400i
\(688\) 47.7781 1.82152
\(689\) −18.3941 21.7646i −0.700758 0.829166i
\(690\) −37.5109 −1.42802
\(691\) 45.3507i 1.72522i 0.505869 + 0.862610i \(0.331172\pi\)
−0.505869 + 0.862610i \(0.668828\pi\)
\(692\) −1.78685 −0.0679257
\(693\) 0 0
\(694\) 7.34981i 0.278995i
\(695\) 25.0255i 0.949270i
\(696\) 4.48855i 0.170138i
\(697\) 60.5721i 2.29433i
\(698\) 26.6946 1.01041
\(699\) −18.4706 −0.698623
\(700\) 0 0
\(701\) −23.5681 −0.890155 −0.445077 0.895492i \(-0.646824\pi\)
−0.445077 + 0.895492i \(0.646824\pi\)
\(702\) 37.3256 31.5452i 1.40876 1.19060i
\(703\) 3.61800 0.136456
\(704\) 15.0293i 0.566438i
\(705\) 4.74491 0.178704
\(706\) −10.0502 −0.378244
\(707\) 0 0
\(708\) 5.90405i 0.221888i
\(709\) 8.66932i 0.325583i 0.986660 + 0.162792i \(0.0520498\pi\)
−0.986660 + 0.162792i \(0.947950\pi\)
\(710\) 5.61681i 0.210795i
\(711\) 37.5634 1.40874
\(712\) −26.1812 −0.981183
\(713\) 23.2560i 0.870943i
\(714\) 0 0
\(715\) 16.2573 + 19.2363i 0.607988 + 0.719398i
\(716\) −1.49507 −0.0558735
\(717\) 82.2420i 3.07138i
\(718\) −35.1119 −1.31036
\(719\) −11.0038 −0.410373 −0.205186 0.978723i \(-0.565780\pi\)
−0.205186 + 0.978723i \(0.565780\pi\)
\(720\) 79.8331i 2.97520i
\(721\) 0 0
\(722\) 14.7302i 0.548202i
\(723\) 29.3333i 1.09092i
\(724\) 4.02071 0.149429
\(725\) −2.15538 −0.0800488
\(726\) 24.5382i 0.910698i
\(727\) 40.7049 1.50966 0.754831 0.655919i \(-0.227719\pi\)
0.754831 + 0.655919i \(0.227719\pi\)
\(728\) 0 0
\(729\) −27.7827 −1.02899
\(730\) 48.7488i 1.80427i
\(731\) −56.5298 −2.09083
\(732\) 2.67716 0.0989508
\(733\) 10.3536i 0.382418i 0.981549 + 0.191209i \(0.0612409\pi\)
−0.981549 + 0.191209i \(0.938759\pi\)
\(734\) 24.2704i 0.895835i
\(735\) 0 0
\(736\) 5.01660i 0.184914i
\(737\) −9.99062 −0.368009
\(738\) 102.597 3.77666
\(739\) 48.5321i 1.78528i −0.450770 0.892640i \(-0.648850\pi\)
0.450770 0.892640i \(-0.351150\pi\)
\(740\) −0.638477 −0.0234709
\(741\) 44.1626 37.3234i 1.62235 1.37111i
\(742\) 0 0
\(743\) 24.5215i 0.899608i 0.893127 + 0.449804i \(0.148506\pi\)
−0.893127 + 0.449804i \(0.851494\pi\)
\(744\) −63.8537 −2.34099
\(745\) −12.7076 −0.465572
\(746\) 35.6915i 1.30676i
\(747\) 10.4322i 0.381694i
\(748\) 4.08376i 0.149317i
\(749\) 0 0
\(750\) 17.7534 0.648261
\(751\) 28.0663 1.02415 0.512077 0.858939i \(-0.328876\pi\)
0.512077 + 0.858939i \(0.328876\pi\)
\(752\) 2.44060i 0.0889996i
\(753\) 37.4222 1.36374
\(754\) −2.45759 + 2.07700i −0.0895001 + 0.0756397i
\(755\) 36.0738 1.31286
\(756\) 0 0
\(757\) 5.70864 0.207484 0.103742 0.994604i \(-0.466918\pi\)
0.103742 + 0.994604i \(0.466918\pi\)
\(758\) −45.8605 −1.66573
\(759\) 19.8175i 0.719331i
\(760\) 40.3536i 1.46378i
\(761\) 7.69598i 0.278979i 0.990224 + 0.139490i \(0.0445462\pi\)
−0.990224 + 0.139490i \(0.955454\pi\)
\(762\) 23.2473i 0.842159i
\(763\) 0 0
\(764\) 0.422610 0.0152895
\(765\) 94.4563i 3.41508i
\(766\) 19.5904 0.707832
\(767\) 16.9250 14.3039i 0.611126 0.516485i
\(768\) −22.4939 −0.811677
\(769\) 15.0754i 0.543634i 0.962349 + 0.271817i \(0.0876245\pi\)
−0.962349 + 0.271817i \(0.912375\pi\)
\(770\) 0 0
\(771\) 57.4847 2.07026
\(772\) 4.85733i 0.174819i
\(773\) 21.2624i 0.764755i 0.924006 + 0.382378i \(0.124895\pi\)
−0.924006 + 0.382378i \(0.875105\pi\)
\(774\) 95.7503i 3.44167i
\(775\) 30.6622i 1.10142i
\(776\) −25.3424 −0.909740
\(777\) 0 0
\(778\) 56.1419i 2.01278i
\(779\) 60.3966 2.16393
\(780\) −7.79347 + 6.58654i −0.279051 + 0.235836i
\(781\) −2.96744 −0.106183
\(782\) 22.8283i 0.816340i
\(783\) −5.21221 −0.186269
\(784\) 0 0
\(785\) 65.4142i 2.33473i
\(786\) 102.864i 3.66902i
\(787\) 9.28939i 0.331131i −0.986199 0.165565i \(-0.947055\pi\)
0.986199 0.165565i \(-0.0529449\pi\)
\(788\) 3.17709i 0.113179i
\(789\) −86.3048 −3.07253
\(790\) −28.2357 −1.00458
\(791\) 0 0
\(792\) −36.2158 −1.28687
\(793\) −6.48604 7.67456i −0.230326 0.272532i
\(794\) −30.9381 −1.09795
\(795\) 69.7381i 2.47335i