Properties

Label 429.2.b.b.298.2
Level $429$
Weight $2$
Character 429.298
Analytic conductor $3.426$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
Defining polynomial: \(x^{14} + 23 x^{12} + 201 x^{10} + 835 x^{8} + 1695 x^{6} + 1565 x^{4} + 511 x^{2} + 49\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 298.2
Root \(-2.53441i\) of defining polynomial
Character \(\chi\) \(=\) 429.298
Dual form 429.2.b.b.298.13

$q$-expansion

\(f(q)\) \(=\) \(q-2.53441i q^{2} +1.00000 q^{3} -4.42325 q^{4} -3.70100i q^{5} -2.53441i q^{6} -0.957295i q^{7} +6.14151i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.53441i q^{2} +1.00000 q^{3} -4.42325 q^{4} -3.70100i q^{5} -2.53441i q^{6} -0.957295i q^{7} +6.14151i q^{8} +1.00000 q^{9} -9.37985 q^{10} +1.00000i q^{11} -4.42325 q^{12} +(-2.10857 + 2.92471i) q^{13} -2.42618 q^{14} -3.70100i q^{15} +6.71863 q^{16} +2.05542 q^{17} -2.53441i q^{18} -7.67886i q^{19} +16.3704i q^{20} -0.957295i q^{21} +2.53441 q^{22} +4.20997 q^{23} +6.14151i q^{24} -8.69737 q^{25} +(7.41243 + 5.34397i) q^{26} +1.00000 q^{27} +4.23435i q^{28} +1.97786 q^{29} -9.37985 q^{30} +10.5475i q^{31} -4.74476i q^{32} +1.00000i q^{33} -5.20928i q^{34} -3.54294 q^{35} -4.42325 q^{36} -8.30741i q^{37} -19.4614 q^{38} +(-2.10857 + 2.92471i) q^{39} +22.7297 q^{40} +5.23142i q^{41} -2.42618 q^{42} -5.26116 q^{43} -4.42325i q^{44} -3.70100i q^{45} -10.6698i q^{46} -1.24656i q^{47} +6.71863 q^{48} +6.08359 q^{49} +22.0427i q^{50} +2.05542 q^{51} +(9.32671 - 12.9367i) q^{52} +2.98297 q^{53} -2.53441i q^{54} +3.70100 q^{55} +5.87924 q^{56} -7.67886i q^{57} -5.01271i q^{58} -12.3548i q^{59} +16.3704i q^{60} -0.183851 q^{61} +26.7317 q^{62} -0.957295i q^{63} +1.41208 q^{64} +(10.8244 + 7.80379i) q^{65} +2.53441 q^{66} -1.40691i q^{67} -9.09163 q^{68} +4.20997 q^{69} +8.97928i q^{70} -12.1582i q^{71} +6.14151i q^{72} -3.32573i q^{73} -21.0544 q^{74} -8.69737 q^{75} +33.9655i q^{76} +0.957295 q^{77} +(7.41243 + 5.34397i) q^{78} -3.64911 q^{79} -24.8656i q^{80} +1.00000 q^{81} +13.2586 q^{82} -3.31957i q^{83} +4.23435i q^{84} -7.60710i q^{85} +13.3340i q^{86} +1.97786 q^{87} -6.14151 q^{88} +5.24302i q^{89} -9.37985 q^{90} +(2.79981 + 2.01852i) q^{91} -18.6217 q^{92} +10.5475i q^{93} -3.15929 q^{94} -28.4194 q^{95} -4.74476i q^{96} -9.82293i q^{97} -15.4183i q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} + O(q^{10}) \) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} - 18q^{12} + 16q^{14} + 34q^{16} + 4q^{17} + 6q^{22} - 8q^{23} - 26q^{25} - 6q^{26} + 14q^{27} - 24q^{29} - 8q^{35} - 18q^{36} - 32q^{38} - 20q^{40} + 16q^{42} + 32q^{43} + 34q^{48} - 46q^{49} + 4q^{51} + 4q^{52} + 20q^{53} + 12q^{55} - 32q^{56} - 20q^{61} + 72q^{62} - 58q^{64} + 12q^{65} + 6q^{66} - 20q^{68} - 8q^{69} - 26q^{75} - 12q^{77} - 6q^{78} + 12q^{79} + 14q^{81} + 20q^{82} - 24q^{87} - 30q^{88} + 16q^{91} - 24q^{92} + 64q^{94} - 36q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.53441i 1.79210i −0.443953 0.896050i \(-0.646424\pi\)
0.443953 0.896050i \(-0.353576\pi\)
\(3\) 1.00000 0.577350
\(4\) −4.42325 −2.21162
\(5\) 3.70100i 1.65514i −0.561366 0.827568i \(-0.689724\pi\)
0.561366 0.827568i \(-0.310276\pi\)
\(6\) 2.53441i 1.03467i
\(7\) 0.957295i 0.361823i −0.983499 0.180912i \(-0.942095\pi\)
0.983499 0.180912i \(-0.0579048\pi\)
\(8\) 6.14151i 2.17135i
\(9\) 1.00000 0.333333
\(10\) −9.37985 −2.96617
\(11\) 1.00000i 0.301511i
\(12\) −4.42325 −1.27688
\(13\) −2.10857 + 2.92471i −0.584811 + 0.811170i
\(14\) −2.42618 −0.648424
\(15\) 3.70100i 0.955593i
\(16\) 6.71863 1.67966
\(17\) 2.05542 0.498512 0.249256 0.968438i \(-0.419814\pi\)
0.249256 + 0.968438i \(0.419814\pi\)
\(18\) 2.53441i 0.597367i
\(19\) 7.67886i 1.76165i −0.473442 0.880825i \(-0.656988\pi\)
0.473442 0.880825i \(-0.343012\pi\)
\(20\) 16.3704i 3.66054i
\(21\) 0.957295i 0.208899i
\(22\) 2.53441 0.540339
\(23\) 4.20997 0.877840 0.438920 0.898526i \(-0.355361\pi\)
0.438920 + 0.898526i \(0.355361\pi\)
\(24\) 6.14151i 1.25363i
\(25\) −8.69737 −1.73947
\(26\) 7.41243 + 5.34397i 1.45370 + 1.04804i
\(27\) 1.00000 0.192450
\(28\) 4.23435i 0.800217i
\(29\) 1.97786 0.367279 0.183640 0.982994i \(-0.441212\pi\)
0.183640 + 0.982994i \(0.441212\pi\)
\(30\) −9.37985 −1.71252
\(31\) 10.5475i 1.89439i 0.320664 + 0.947193i \(0.396094\pi\)
−0.320664 + 0.947193i \(0.603906\pi\)
\(32\) 4.74476i 0.838763i
\(33\) 1.00000i 0.174078i
\(34\) 5.20928i 0.893384i
\(35\) −3.54294 −0.598867
\(36\) −4.42325 −0.737208
\(37\) 8.30741i 1.36573i −0.730545 0.682865i \(-0.760734\pi\)
0.730545 0.682865i \(-0.239266\pi\)
\(38\) −19.4614 −3.15705
\(39\) −2.10857 + 2.92471i −0.337641 + 0.468329i
\(40\) 22.7297 3.59388
\(41\) 5.23142i 0.817011i 0.912756 + 0.408505i \(0.133950\pi\)
−0.912756 + 0.408505i \(0.866050\pi\)
\(42\) −2.42618 −0.374368
\(43\) −5.26116 −0.802320 −0.401160 0.916008i \(-0.631393\pi\)
−0.401160 + 0.916008i \(0.631393\pi\)
\(44\) 4.42325i 0.666830i
\(45\) 3.70100i 0.551712i
\(46\) 10.6698i 1.57318i
\(47\) 1.24656i 0.181829i −0.995859 0.0909145i \(-0.971021\pi\)
0.995859 0.0909145i \(-0.0289790\pi\)
\(48\) 6.71863 0.969751
\(49\) 6.08359 0.869084
\(50\) 22.0427i 3.11731i
\(51\) 2.05542 0.287816
\(52\) 9.32671 12.9367i 1.29338 1.79400i
\(53\) 2.98297 0.409743 0.204871 0.978789i \(-0.434322\pi\)
0.204871 + 0.978789i \(0.434322\pi\)
\(54\) 2.53441i 0.344890i
\(55\) 3.70100 0.499042
\(56\) 5.87924 0.785646
\(57\) 7.67886i 1.01709i
\(58\) 5.01271i 0.658202i
\(59\) 12.3548i 1.60846i −0.594321 0.804228i \(-0.702579\pi\)
0.594321 0.804228i \(-0.297421\pi\)
\(60\) 16.3704i 2.11341i
\(61\) −0.183851 −0.0235397 −0.0117698 0.999931i \(-0.503747\pi\)
−0.0117698 + 0.999931i \(0.503747\pi\)
\(62\) 26.7317 3.39493
\(63\) 0.957295i 0.120608i
\(64\) 1.41208 0.176510
\(65\) 10.8244 + 7.80379i 1.34260 + 0.967941i
\(66\) 2.53441 0.311965
\(67\) 1.40691i 0.171881i −0.996300 0.0859407i \(-0.972610\pi\)
0.996300 0.0859407i \(-0.0273896\pi\)
\(68\) −9.09163 −1.10252
\(69\) 4.20997 0.506821
\(70\) 8.97928i 1.07323i
\(71\) 12.1582i 1.44291i −0.692459 0.721457i \(-0.743473\pi\)
0.692459 0.721457i \(-0.256527\pi\)
\(72\) 6.14151i 0.723784i
\(73\) 3.32573i 0.389247i −0.980878 0.194624i \(-0.937651\pi\)
0.980878 0.194624i \(-0.0623485\pi\)
\(74\) −21.0544 −2.44752
\(75\) −8.69737 −1.00429
\(76\) 33.9655i 3.89611i
\(77\) 0.957295 0.109094
\(78\) 7.41243 + 5.34397i 0.839293 + 0.605086i
\(79\) −3.64911 −0.410557 −0.205279 0.978704i \(-0.565810\pi\)
−0.205279 + 0.978704i \(0.565810\pi\)
\(80\) 24.8656i 2.78006i
\(81\) 1.00000 0.111111
\(82\) 13.2586 1.46417
\(83\) 3.31957i 0.364370i −0.983264 0.182185i \(-0.941683\pi\)
0.983264 0.182185i \(-0.0583170\pi\)
\(84\) 4.23435i 0.462006i
\(85\) 7.60710i 0.825106i
\(86\) 13.3340i 1.43784i
\(87\) 1.97786 0.212049
\(88\) −6.14151 −0.654687
\(89\) 5.24302i 0.555759i 0.960616 + 0.277879i \(0.0896316\pi\)
−0.960616 + 0.277879i \(0.910368\pi\)
\(90\) −9.37985 −0.988723
\(91\) 2.79981 + 2.01852i 0.293500 + 0.211598i
\(92\) −18.6217 −1.94145
\(93\) 10.5475i 1.09372i
\(94\) −3.15929 −0.325856
\(95\) −28.4194 −2.91577
\(96\) 4.74476i 0.484260i
\(97\) 9.82293i 0.997368i −0.866784 0.498684i \(-0.833817\pi\)
0.866784 0.498684i \(-0.166183\pi\)
\(98\) 15.4183i 1.55749i
\(99\) 1.00000i 0.100504i
\(100\) 38.4706 3.84706
\(101\) 8.42338 0.838157 0.419079 0.907950i \(-0.362353\pi\)
0.419079 + 0.907950i \(0.362353\pi\)
\(102\) 5.20928i 0.515796i
\(103\) 13.4029 1.32063 0.660314 0.750989i \(-0.270423\pi\)
0.660314 + 0.750989i \(0.270423\pi\)
\(104\) −17.9622 12.9498i −1.76134 1.26983i
\(105\) −3.54294 −0.345756
\(106\) 7.56008i 0.734300i
\(107\) −8.05792 −0.778988 −0.389494 0.921029i \(-0.627350\pi\)
−0.389494 + 0.921029i \(0.627350\pi\)
\(108\) −4.42325 −0.425627
\(109\) 14.3600i 1.37544i 0.725976 + 0.687720i \(0.241388\pi\)
−0.725976 + 0.687720i \(0.758612\pi\)
\(110\) 9.37985i 0.894334i
\(111\) 8.30741i 0.788504i
\(112\) 6.43171i 0.607739i
\(113\) 18.6675 1.75609 0.878046 0.478577i \(-0.158847\pi\)
0.878046 + 0.478577i \(0.158847\pi\)
\(114\) −19.4614 −1.82273
\(115\) 15.5811i 1.45294i
\(116\) −8.74857 −0.812284
\(117\) −2.10857 + 2.92471i −0.194937 + 0.270390i
\(118\) −31.3121 −2.88251
\(119\) 1.96764i 0.180373i
\(120\) 22.7297 2.07493
\(121\) −1.00000 −0.0909091
\(122\) 0.465954i 0.0421855i
\(123\) 5.23142i 0.471701i
\(124\) 46.6542i 4.18967i
\(125\) 13.6840i 1.22393i
\(126\) −2.42618 −0.216141
\(127\) −6.60130 −0.585770 −0.292885 0.956148i \(-0.594615\pi\)
−0.292885 + 0.956148i \(0.594615\pi\)
\(128\) 13.0683i 1.15509i
\(129\) −5.26116 −0.463220
\(130\) 19.7780 27.4334i 1.73465 2.40607i
\(131\) 5.81083 0.507694 0.253847 0.967244i \(-0.418304\pi\)
0.253847 + 0.967244i \(0.418304\pi\)
\(132\) 4.42325i 0.384994i
\(133\) −7.35093 −0.637406
\(134\) −3.56569 −0.308029
\(135\) 3.70100i 0.318531i
\(136\) 12.6234i 1.08245i
\(137\) 5.64208i 0.482035i 0.970521 + 0.241018i \(0.0774812\pi\)
−0.970521 + 0.241018i \(0.922519\pi\)
\(138\) 10.6698i 0.908274i
\(139\) −4.46820 −0.378987 −0.189494 0.981882i \(-0.560685\pi\)
−0.189494 + 0.981882i \(0.560685\pi\)
\(140\) 15.6713 1.32447
\(141\) 1.24656i 0.104979i
\(142\) −30.8139 −2.58585
\(143\) −2.92471 2.10857i −0.244577 0.176327i
\(144\) 6.71863 0.559886
\(145\) 7.32005i 0.607897i
\(146\) −8.42877 −0.697570
\(147\) 6.08359 0.501766
\(148\) 36.7457i 3.02048i
\(149\) 7.39749i 0.606026i 0.952986 + 0.303013i \(0.0979925\pi\)
−0.952986 + 0.303013i \(0.902007\pi\)
\(150\) 22.0427i 1.79978i
\(151\) 23.7454i 1.93237i 0.257841 + 0.966187i \(0.416989\pi\)
−0.257841 + 0.966187i \(0.583011\pi\)
\(152\) 47.1598 3.82516
\(153\) 2.05542 0.166171
\(154\) 2.42618i 0.195507i
\(155\) 39.0362 3.13547
\(156\) 9.32671 12.9367i 0.746734 1.03577i
\(157\) 12.9704 1.03515 0.517576 0.855637i \(-0.326834\pi\)
0.517576 + 0.855637i \(0.326834\pi\)
\(158\) 9.24836i 0.735760i
\(159\) 2.98297 0.236565
\(160\) −17.5603 −1.38827
\(161\) 4.03018i 0.317623i
\(162\) 2.53441i 0.199122i
\(163\) 18.6880i 1.46376i 0.681436 + 0.731878i \(0.261356\pi\)
−0.681436 + 0.731878i \(0.738644\pi\)
\(164\) 23.1399i 1.80692i
\(165\) 3.70100 0.288122
\(166\) −8.41316 −0.652988
\(167\) 25.0420i 1.93781i 0.247437 + 0.968904i \(0.420412\pi\)
−0.247437 + 0.968904i \(0.579588\pi\)
\(168\) 5.87924 0.453593
\(169\) −4.10791 12.3339i −0.315993 0.948762i
\(170\) −19.2795 −1.47867
\(171\) 7.67886i 0.587217i
\(172\) 23.2714 1.77443
\(173\) 3.16333 0.240503 0.120252 0.992743i \(-0.461630\pi\)
0.120252 + 0.992743i \(0.461630\pi\)
\(174\) 5.01271i 0.380013i
\(175\) 8.32595i 0.629383i
\(176\) 6.71863i 0.506436i
\(177\) 12.3548i 0.928642i
\(178\) 13.2880 0.995976
\(179\) −1.24977 −0.0934123 −0.0467062 0.998909i \(-0.514872\pi\)
−0.0467062 + 0.998909i \(0.514872\pi\)
\(180\) 16.3704i 1.22018i
\(181\) −16.0712 −1.19456 −0.597281 0.802032i \(-0.703752\pi\)
−0.597281 + 0.802032i \(0.703752\pi\)
\(182\) 5.11576 7.09588i 0.379205 0.525982i
\(183\) −0.183851 −0.0135906
\(184\) 25.8556i 1.90610i
\(185\) −30.7457 −2.26047
\(186\) 26.7317 1.96006
\(187\) 2.05542i 0.150307i
\(188\) 5.51383i 0.402137i
\(189\) 0.957295i 0.0696329i
\(190\) 72.0265i 5.22535i
\(191\) 15.2909 1.10641 0.553207 0.833044i \(-0.313404\pi\)
0.553207 + 0.833044i \(0.313404\pi\)
\(192\) 1.41208 0.101908
\(193\) 6.76152i 0.486705i 0.969938 + 0.243353i \(0.0782472\pi\)
−0.969938 + 0.243353i \(0.921753\pi\)
\(194\) −24.8954 −1.78738
\(195\) 10.8244 + 7.80379i 0.775148 + 0.558841i
\(196\) −26.9092 −1.92209
\(197\) 11.3320i 0.807374i 0.914897 + 0.403687i \(0.132272\pi\)
−0.914897 + 0.403687i \(0.867728\pi\)
\(198\) 2.53441 0.180113
\(199\) −21.5642 −1.52864 −0.764321 0.644836i \(-0.776926\pi\)
−0.764321 + 0.644836i \(0.776926\pi\)
\(200\) 53.4150i 3.77701i
\(201\) 1.40691i 0.0992358i
\(202\) 21.3483i 1.50206i
\(203\) 1.89339i 0.132890i
\(204\) −9.09163 −0.636541
\(205\) 19.3615 1.35226
\(206\) 33.9685i 2.36670i
\(207\) 4.20997 0.292613
\(208\) −14.1667 + 19.6501i −0.982282 + 1.36249i
\(209\) 7.67886 0.531158
\(210\) 8.97928i 0.619629i
\(211\) −23.5992 −1.62463 −0.812317 0.583217i \(-0.801794\pi\)
−0.812317 + 0.583217i \(0.801794\pi\)
\(212\) −13.1944 −0.906197
\(213\) 12.1582i 0.833067i
\(214\) 20.4221i 1.39603i
\(215\) 19.4715i 1.32795i
\(216\) 6.14151i 0.417877i
\(217\) 10.0971 0.685433
\(218\) 36.3942 2.46493
\(219\) 3.32573i 0.224732i
\(220\) −16.3704 −1.10369
\(221\) −4.33399 + 6.01151i −0.291535 + 0.404378i
\(222\) −21.0544 −1.41308
\(223\) 14.7201i 0.985730i 0.870106 + 0.492865i \(0.164050\pi\)
−0.870106 + 0.492865i \(0.835950\pi\)
\(224\) −4.54213 −0.303484
\(225\) −8.69737 −0.579825
\(226\) 47.3112i 3.14709i
\(227\) 0.0358913i 0.00238219i −0.999999 0.00119109i \(-0.999621\pi\)
0.999999 0.00119109i \(-0.000379137\pi\)
\(228\) 33.9655i 2.24942i
\(229\) 8.37257i 0.553275i 0.960974 + 0.276637i \(0.0892201\pi\)
−0.960974 + 0.276637i \(0.910780\pi\)
\(230\) −39.4889 −2.60382
\(231\) 0.957295 0.0629854
\(232\) 12.1471i 0.797493i
\(233\) 18.0020 1.17935 0.589674 0.807641i \(-0.299256\pi\)
0.589674 + 0.807641i \(0.299256\pi\)
\(234\) 7.41243 + 5.34397i 0.484566 + 0.349347i
\(235\) −4.61350 −0.300952
\(236\) 54.6483i 3.55730i
\(237\) −3.64911 −0.237035
\(238\) −4.98682 −0.323247
\(239\) 5.74497i 0.371611i 0.982587 + 0.185806i \(0.0594895\pi\)
−0.982587 + 0.185806i \(0.940511\pi\)
\(240\) 24.8656i 1.60507i
\(241\) 16.1458i 1.04004i −0.854153 0.520022i \(-0.825924\pi\)
0.854153 0.520022i \(-0.174076\pi\)
\(242\) 2.53441i 0.162918i
\(243\) 1.00000 0.0641500
\(244\) 0.813218 0.0520609
\(245\) 22.5153i 1.43845i
\(246\) 13.2586 0.845336
\(247\) 22.4585 + 16.1914i 1.42900 + 1.03023i
\(248\) −64.7776 −4.11338
\(249\) 3.31957i 0.210369i
\(250\) 34.6808 2.19341
\(251\) 6.83631 0.431504 0.215752 0.976448i \(-0.430780\pi\)
0.215752 + 0.976448i \(0.430780\pi\)
\(252\) 4.23435i 0.266739i
\(253\) 4.20997i 0.264679i
\(254\) 16.7304i 1.04976i
\(255\) 7.60710i 0.476375i
\(256\) −30.2963 −1.89352
\(257\) 26.8038 1.67197 0.835987 0.548749i \(-0.184896\pi\)
0.835987 + 0.548749i \(0.184896\pi\)
\(258\) 13.3340i 0.830136i
\(259\) −7.95264 −0.494153
\(260\) −47.8788 34.5181i −2.96932 2.14072i
\(261\) 1.97786 0.122426
\(262\) 14.7270i 0.909839i
\(263\) −11.9518 −0.736980 −0.368490 0.929632i \(-0.620125\pi\)
−0.368490 + 0.929632i \(0.620125\pi\)
\(264\) −6.14151 −0.377984
\(265\) 11.0400i 0.678180i
\(266\) 18.6303i 1.14230i
\(267\) 5.24302i 0.320868i
\(268\) 6.22311i 0.380137i
\(269\) 4.59663 0.280261 0.140131 0.990133i \(-0.455248\pi\)
0.140131 + 0.990133i \(0.455248\pi\)
\(270\) −9.37985 −0.570840
\(271\) 19.8969i 1.20865i 0.796738 + 0.604326i \(0.206557\pi\)
−0.796738 + 0.604326i \(0.793443\pi\)
\(272\) 13.8096 0.837330
\(273\) 2.79981 + 2.01852i 0.169452 + 0.122166i
\(274\) 14.2994 0.863856
\(275\) 8.69737i 0.524471i
\(276\) −18.6217 −1.12090
\(277\) 11.2319 0.674857 0.337428 0.941351i \(-0.390443\pi\)
0.337428 + 0.941351i \(0.390443\pi\)
\(278\) 11.3243i 0.679183i
\(279\) 10.5475i 0.631462i
\(280\) 21.7590i 1.30035i
\(281\) 30.2946i 1.80722i −0.428352 0.903612i \(-0.640906\pi\)
0.428352 0.903612i \(-0.359094\pi\)
\(282\) −3.15929 −0.188133
\(283\) 15.3889 0.914777 0.457389 0.889267i \(-0.348785\pi\)
0.457389 + 0.889267i \(0.348785\pi\)
\(284\) 53.7788i 3.19118i
\(285\) −28.4194 −1.68342
\(286\) −5.34397 + 7.41243i −0.315996 + 0.438306i
\(287\) 5.00801 0.295614
\(288\) 4.74476i 0.279588i
\(289\) −12.7753 −0.751485
\(290\) −18.5520 −1.08941
\(291\) 9.82293i 0.575831i
\(292\) 14.7105i 0.860869i
\(293\) 6.95822i 0.406503i 0.979127 + 0.203252i \(0.0651510\pi\)
−0.979127 + 0.203252i \(0.934849\pi\)
\(294\) 15.4183i 0.899215i
\(295\) −45.7250 −2.66221
\(296\) 51.0200 2.96548
\(297\) 1.00000i 0.0580259i
\(298\) 18.7483 1.08606
\(299\) −8.87700 + 12.3130i −0.513370 + 0.712077i
\(300\) 38.4706 2.22110
\(301\) 5.03648i 0.290298i
\(302\) 60.1807 3.46301
\(303\) 8.42338 0.483910
\(304\) 51.5914i 2.95897i
\(305\) 0.680431i 0.0389614i
\(306\) 5.20928i 0.297795i
\(307\) 12.6233i 0.720447i −0.932866 0.360224i \(-0.882700\pi\)
0.932866 0.360224i \(-0.117300\pi\)
\(308\) −4.23435 −0.241275
\(309\) 13.4029 0.762465
\(310\) 98.9339i 5.61907i
\(311\) −2.12116 −0.120280 −0.0601399 0.998190i \(-0.519155\pi\)
−0.0601399 + 0.998190i \(0.519155\pi\)
\(312\) −17.9622 12.9498i −1.01691 0.733137i
\(313\) 21.5919 1.22045 0.610224 0.792229i \(-0.291079\pi\)
0.610224 + 0.792229i \(0.291079\pi\)
\(314\) 32.8724i 1.85510i
\(315\) −3.54294 −0.199622
\(316\) 16.1409 0.907999
\(317\) 15.7684i 0.885640i −0.896611 0.442820i \(-0.853978\pi\)
0.896611 0.442820i \(-0.146022\pi\)
\(318\) 7.56008i 0.423948i
\(319\) 1.97786i 0.110739i
\(320\) 5.22612i 0.292149i
\(321\) −8.05792 −0.449749
\(322\) −10.2141 −0.569212
\(323\) 15.7833i 0.878205i
\(324\) −4.42325 −0.245736
\(325\) 18.3390 25.4373i 1.01726 1.41101i
\(326\) 47.3631 2.62320
\(327\) 14.3600i 0.794111i
\(328\) −32.1288 −1.77402
\(329\) −1.19332 −0.0657900
\(330\) 9.37985i 0.516344i
\(331\) 11.6602i 0.640902i −0.947265 0.320451i \(-0.896166\pi\)
0.947265 0.320451i \(-0.103834\pi\)
\(332\) 14.6833i 0.805850i
\(333\) 8.30741i 0.455243i
\(334\) 63.4668 3.47275
\(335\) −5.20697 −0.284487
\(336\) 6.43171i 0.350879i
\(337\) 7.63508 0.415909 0.207955 0.978138i \(-0.433319\pi\)
0.207955 + 0.978138i \(0.433319\pi\)
\(338\) −31.2592 + 10.4111i −1.70028 + 0.566291i
\(339\) 18.6675 1.01388
\(340\) 33.6481i 1.82482i
\(341\) −10.5475 −0.571179
\(342\) −19.4614 −1.05235
\(343\) 12.5248i 0.676278i
\(344\) 32.3115i 1.74212i
\(345\) 15.5811i 0.838858i
\(346\) 8.01717i 0.431006i
\(347\) −17.7823 −0.954606 −0.477303 0.878739i \(-0.658386\pi\)
−0.477303 + 0.878739i \(0.658386\pi\)
\(348\) −8.74857 −0.468972
\(349\) 12.1663i 0.651245i 0.945500 + 0.325622i \(0.105574\pi\)
−0.945500 + 0.325622i \(0.894426\pi\)
\(350\) 21.1014 1.12792
\(351\) −2.10857 + 2.92471i −0.112547 + 0.156110i
\(352\) 4.74476 0.252896
\(353\) 32.9025i 1.75122i 0.483014 + 0.875612i \(0.339542\pi\)
−0.483014 + 0.875612i \(0.660458\pi\)
\(354\) −31.3121 −1.66422
\(355\) −44.9975 −2.38822
\(356\) 23.1912i 1.22913i
\(357\) 1.96764i 0.104139i
\(358\) 3.16744i 0.167404i
\(359\) 7.29760i 0.385153i 0.981282 + 0.192576i \(0.0616843\pi\)
−0.981282 + 0.192576i \(0.938316\pi\)
\(360\) 22.7297 1.19796
\(361\) −39.9648 −2.10341
\(362\) 40.7310i 2.14078i
\(363\) −1.00000 −0.0524864
\(364\) −12.3843 8.92841i −0.649112 0.467976i
\(365\) −12.3085 −0.644257
\(366\) 0.465954i 0.0243558i
\(367\) −8.94917 −0.467143 −0.233571 0.972340i \(-0.575041\pi\)
−0.233571 + 0.972340i \(0.575041\pi\)
\(368\) 28.2852 1.47447
\(369\) 5.23142i 0.272337i
\(370\) 77.9222i 4.05098i
\(371\) 2.85558i 0.148254i
\(372\) 46.6542i 2.41891i
\(373\) −18.1913 −0.941908 −0.470954 0.882158i \(-0.656090\pi\)
−0.470954 + 0.882158i \(0.656090\pi\)
\(374\) 5.20928 0.269366
\(375\) 13.6840i 0.706637i
\(376\) 7.65574 0.394815
\(377\) −4.17045 + 5.78468i −0.214789 + 0.297926i
\(378\) −2.42618 −0.124789
\(379\) 20.1063i 1.03279i −0.856350 0.516396i \(-0.827273\pi\)
0.856350 0.516396i \(-0.172727\pi\)
\(380\) 125.706 6.44859
\(381\) −6.60130 −0.338195
\(382\) 38.7536i 1.98281i
\(383\) 7.99092i 0.408317i 0.978938 + 0.204158i \(0.0654458\pi\)
−0.978938 + 0.204158i \(0.934554\pi\)
\(384\) 13.0683i 0.666890i
\(385\) 3.54294i 0.180565i
\(386\) 17.1365 0.872224
\(387\) −5.26116 −0.267440
\(388\) 43.4493i 2.20580i
\(389\) −4.31617 −0.218839 −0.109419 0.993996i \(-0.534899\pi\)
−0.109419 + 0.993996i \(0.534899\pi\)
\(390\) 19.7780 27.4334i 1.00150 1.38914i
\(391\) 8.65326 0.437614
\(392\) 37.3624i 1.88709i
\(393\) 5.81083 0.293117
\(394\) 28.7201 1.44690
\(395\) 13.5054i 0.679528i
\(396\) 4.42325i 0.222277i
\(397\) 23.4560i 1.17722i 0.808416 + 0.588612i \(0.200325\pi\)
−0.808416 + 0.588612i \(0.799675\pi\)
\(398\) 54.6525i 2.73948i
\(399\) −7.35093 −0.368007
\(400\) −58.4344 −2.92172
\(401\) 2.38235i 0.118969i −0.998229 0.0594844i \(-0.981054\pi\)
0.998229 0.0594844i \(-0.0189457\pi\)
\(402\) −3.56569 −0.177841
\(403\) −30.8484 22.2401i −1.53667 1.10786i
\(404\) −37.2587 −1.85369
\(405\) 3.70100i 0.183904i
\(406\) −4.79864 −0.238153
\(407\) 8.30741 0.411783
\(408\) 12.6234i 0.624951i
\(409\) 10.3945i 0.513973i 0.966415 + 0.256987i \(0.0827296\pi\)
−0.966415 + 0.256987i \(0.917270\pi\)
\(410\) 49.0700i 2.42339i
\(411\) 5.64208i 0.278303i
\(412\) −59.2844 −2.92073
\(413\) −11.8272 −0.581977
\(414\) 10.6698i 0.524392i
\(415\) −12.2857 −0.603082
\(416\) 13.8771 + 10.0046i 0.680379 + 0.490517i
\(417\) −4.46820 −0.218808
\(418\) 19.4614i 0.951888i
\(419\) 13.6447 0.666586 0.333293 0.942823i \(-0.391840\pi\)
0.333293 + 0.942823i \(0.391840\pi\)
\(420\) 15.6713 0.764682
\(421\) 6.41040i 0.312424i −0.987724 0.156212i \(-0.950072\pi\)
0.987724 0.156212i \(-0.0499283\pi\)
\(422\) 59.8100i 2.91151i
\(423\) 1.24656i 0.0606097i
\(424\) 18.3200i 0.889696i
\(425\) −17.8768 −0.867150
\(426\) −30.8139 −1.49294
\(427\) 0.175999i 0.00851721i
\(428\) 35.6422 1.72283
\(429\) −2.92471 2.10857i −0.141207 0.101802i
\(430\) 49.3489 2.37982
\(431\) 15.8350i 0.762747i −0.924421 0.381374i \(-0.875451\pi\)
0.924421 0.381374i \(-0.124549\pi\)
\(432\) 6.71863 0.323250
\(433\) 10.6273 0.510716 0.255358 0.966847i \(-0.417807\pi\)
0.255358 + 0.966847i \(0.417807\pi\)
\(434\) 25.5901i 1.22836i
\(435\) 7.32005i 0.350970i
\(436\) 63.5179i 3.04196i
\(437\) 32.3278i 1.54645i
\(438\) −8.42877 −0.402742
\(439\) 17.2195 0.821841 0.410920 0.911671i \(-0.365207\pi\)
0.410920 + 0.911671i \(0.365207\pi\)
\(440\) 22.7297i 1.08360i
\(441\) 6.08359 0.289695
\(442\) 15.2357 + 10.9841i 0.724686 + 0.522461i
\(443\) −25.1359 −1.19424 −0.597120 0.802152i \(-0.703689\pi\)
−0.597120 + 0.802152i \(0.703689\pi\)
\(444\) 36.7457i 1.74387i
\(445\) 19.4044 0.919857
\(446\) 37.3068 1.76653
\(447\) 7.39749i 0.349889i
\(448\) 1.35178i 0.0638656i
\(449\) 2.01596i 0.0951392i −0.998868 0.0475696i \(-0.984852\pi\)
0.998868 0.0475696i \(-0.0151476\pi\)
\(450\) 22.0427i 1.03910i
\(451\) −5.23142 −0.246338
\(452\) −82.5710 −3.88382
\(453\) 23.7454i 1.11566i
\(454\) −0.0909634 −0.00426912
\(455\) 7.47053 10.3621i 0.350224 0.485783i
\(456\) 47.1598 2.20846
\(457\) 33.7659i 1.57950i −0.613426 0.789752i \(-0.710209\pi\)
0.613426 0.789752i \(-0.289791\pi\)
\(458\) 21.2195 0.991524
\(459\) 2.05542 0.0959388
\(460\) 68.9190i 3.21337i
\(461\) 16.7600i 0.780589i −0.920690 0.390294i \(-0.872373\pi\)
0.920690 0.390294i \(-0.127627\pi\)
\(462\) 2.42618i 0.112876i
\(463\) 27.5446i 1.28011i 0.768330 + 0.640054i \(0.221088\pi\)
−0.768330 + 0.640054i \(0.778912\pi\)
\(464\) 13.2885 0.616904
\(465\) 39.0362 1.81026
\(466\) 45.6244i 2.11351i
\(467\) −22.9318 −1.06116 −0.530578 0.847636i \(-0.678025\pi\)
−0.530578 + 0.847636i \(0.678025\pi\)
\(468\) 9.32671 12.9367i 0.431127 0.598001i
\(469\) −1.34683 −0.0621907
\(470\) 11.6925i 0.539336i
\(471\) 12.9704 0.597646
\(472\) 75.8770 3.49252
\(473\) 5.26116i 0.241909i
\(474\) 9.24836i 0.424791i
\(475\) 66.7859i 3.06435i
\(476\) 8.70337i 0.398918i
\(477\) 2.98297 0.136581
\(478\) 14.5601 0.665965
\(479\) 5.71495i 0.261123i −0.991440 0.130561i \(-0.958322\pi\)
0.991440 0.130561i \(-0.0416780\pi\)
\(480\) −17.5603 −0.801516
\(481\) 24.2968 + 17.5167i 1.10784 + 0.798693i
\(482\) −40.9202 −1.86386
\(483\) 4.03018i 0.183380i
\(484\) 4.42325 0.201057
\(485\) −36.3546 −1.65078
\(486\) 2.53441i 0.114963i
\(487\) 10.4987i 0.475742i −0.971297 0.237871i \(-0.923550\pi\)
0.971297 0.237871i \(-0.0764496\pi\)
\(488\) 1.12912i 0.0511129i
\(489\) 18.6880i 0.845100i
\(490\) −57.0631 −2.57785
\(491\) −13.0458 −0.588747 −0.294373 0.955691i \(-0.595111\pi\)
−0.294373 + 0.955691i \(0.595111\pi\)
\(492\) 23.1399i 1.04323i
\(493\) 4.06533 0.183093
\(494\) 41.0356 56.9190i 1.84628 2.56091i
\(495\) 3.70100 0.166347
\(496\) 70.8647i 3.18192i
\(497\) −11.6390 −0.522080
\(498\) −8.41316 −0.377003
\(499\) 38.6395i 1.72974i 0.501995 + 0.864870i \(0.332600\pi\)
−0.501995 + 0.864870i \(0.667400\pi\)
\(500\) 60.5276i 2.70688i
\(501\) 25.0420i 1.11879i
\(502\) 17.3260i 0.773298i
\(503\) 0.330867 0.0147526 0.00737631 0.999973i \(-0.497652\pi\)
0.00737631 + 0.999973i \(0.497652\pi\)
\(504\) 5.87924 0.261882
\(505\) 31.1749i 1.38726i
\(506\) 10.6698 0.474331
\(507\) −4.10791 12.3339i −0.182439 0.547768i
\(508\) 29.1992 1.29550
\(509\) 44.2090i 1.95953i −0.200157 0.979764i \(-0.564145\pi\)
0.200157 0.979764i \(-0.435855\pi\)
\(510\) −19.2795 −0.853712
\(511\) −3.18370 −0.140839
\(512\) 50.6468i 2.23829i
\(513\) 7.67886i 0.339030i
\(514\) 67.9318i 2.99635i
\(515\) 49.6041i 2.18582i
\(516\) 23.2714 1.02447
\(517\) 1.24656 0.0548235
\(518\) 20.1553i 0.885571i
\(519\) 3.16333 0.138855
\(520\) −47.9271 + 66.4779i −2.10174 + 2.91525i
\(521\) 9.66049 0.423234 0.211617 0.977353i \(-0.432127\pi\)
0.211617 + 0.977353i \(0.432127\pi\)
\(522\) 5.01271i 0.219401i
\(523\) 21.7358 0.950440 0.475220 0.879867i \(-0.342368\pi\)
0.475220 + 0.879867i \(0.342368\pi\)
\(524\) −25.7027 −1.12283
\(525\) 8.32595i 0.363374i
\(526\) 30.2908i 1.32074i
\(527\) 21.6795i 0.944375i
\(528\) 6.71863i 0.292391i
\(529\) −5.27614 −0.229398
\(530\) −27.9798 −1.21537
\(531\) 12.3548i 0.536152i
\(532\) 32.5150 1.40970
\(533\) −15.3004 11.0308i −0.662734 0.477797i
\(534\) 13.2880 0.575027
\(535\) 29.8223i 1.28933i
\(536\) 8.64056 0.373215
\(537\) −1.24977 −0.0539316
\(538\) 11.6497i 0.502256i
\(539\) 6.08359i 0.262039i
\(540\) 16.3704i 0.704471i
\(541\) 18.0139i 0.774478i 0.921979 + 0.387239i \(0.126571\pi\)
−0.921979 + 0.387239i \(0.873429\pi\)
\(542\) 50.4270 2.16602
\(543\) −16.0712 −0.689681
\(544\) 9.75247i 0.418134i
\(545\) 53.1464 2.27654
\(546\) 5.11576 7.09588i 0.218934 0.303676i
\(547\) 23.2740 0.995125 0.497563 0.867428i \(-0.334228\pi\)
0.497563 + 0.867428i \(0.334228\pi\)
\(548\) 24.9563i 1.06608i
\(549\) −0.183851 −0.00784656
\(550\) −22.0427 −0.939906
\(551\) 15.1877i 0.647018i
\(552\) 25.8556i 1.10049i
\(553\) 3.49328i 0.148549i
\(554\) 28.4662i 1.20941i
\(555\) −30.7457 −1.30508
\(556\) 19.7639 0.838178
\(557\) 11.5996i 0.491491i 0.969334 + 0.245745i \(0.0790327\pi\)
−0.969334 + 0.245745i \(0.920967\pi\)
\(558\) 26.7317 1.13164
\(559\) 11.0935 15.3874i 0.469205 0.650818i
\(560\) −23.8037 −1.00589
\(561\) 2.05542i 0.0867799i
\(562\) −76.7790 −3.23873
\(563\) −26.5695 −1.11977 −0.559885 0.828570i \(-0.689155\pi\)
−0.559885 + 0.828570i \(0.689155\pi\)
\(564\) 5.51383i 0.232174i
\(565\) 69.0884i 2.90657i
\(566\) 39.0019i 1.63937i
\(567\) 0.957295i 0.0402026i
\(568\) 74.6698 3.13308
\(569\) 22.7470 0.953603 0.476802 0.879011i \(-0.341796\pi\)
0.476802 + 0.879011i \(0.341796\pi\)
\(570\) 72.0265i 3.01686i
\(571\) 29.4622 1.23296 0.616478 0.787372i \(-0.288559\pi\)
0.616478 + 0.787372i \(0.288559\pi\)
\(572\) 12.9367 + 9.32671i 0.540912 + 0.389969i
\(573\) 15.2909 0.638788
\(574\) 12.6924i 0.529769i
\(575\) −36.6157 −1.52698
\(576\) 1.41208 0.0588368
\(577\) 26.6537i 1.10961i 0.831981 + 0.554803i \(0.187207\pi\)
−0.831981 + 0.554803i \(0.812793\pi\)
\(578\) 32.3778i 1.34674i
\(579\) 6.76152i 0.280999i
\(580\) 32.3784i 1.34444i
\(581\) −3.17781 −0.131838
\(582\) −24.8954 −1.03195
\(583\) 2.98297i 0.123542i
\(584\) 20.4250 0.845193
\(585\) 10.8244 + 7.80379i 0.447532 + 0.322647i
\(586\) 17.6350 0.728495
\(587\) 10.9203i 0.450729i −0.974275 0.225364i \(-0.927643\pi\)
0.974275 0.225364i \(-0.0723573\pi\)
\(588\) −26.9092 −1.10972
\(589\) 80.9927 3.33725
\(590\) 115.886i 4.77095i
\(591\) 11.3320i 0.466138i
\(592\) 55.8144i 2.29396i
\(593\) 19.3064i 0.792820i 0.918074 + 0.396410i \(0.129744\pi\)
−0.918074 + 0.396410i \(0.870256\pi\)
\(594\) 2.53441 0.103988
\(595\) −7.28224 −0.298543
\(596\) 32.7209i 1.34030i
\(597\) −21.5642 −0.882562
\(598\) 31.2061 + 22.4980i 1.27611 + 0.920011i
\(599\) 2.01132 0.0821802 0.0410901 0.999155i \(-0.486917\pi\)
0.0410901 + 0.999155i \(0.486917\pi\)
\(600\) 53.4150i 2.18066i
\(601\) −40.1233 −1.63667 −0.818333 0.574745i \(-0.805101\pi\)
−0.818333 + 0.574745i \(0.805101\pi\)
\(602\) 12.7645 0.520243
\(603\) 1.40691i 0.0572938i
\(604\) 105.032i 4.27369i
\(605\) 3.70100i 0.150467i
\(606\) 21.3483i 0.867216i
\(607\) −35.4310 −1.43810 −0.719049 0.694959i \(-0.755422\pi\)
−0.719049 + 0.694959i \(0.755422\pi\)
\(608\) −36.4343 −1.47761
\(609\) 1.89339i 0.0767242i
\(610\) 1.72449 0.0698227
\(611\) 3.64582 + 2.62845i 0.147494 + 0.106336i
\(612\) −9.09163 −0.367507
\(613\) 0.644081i 0.0260142i −0.999915 0.0130071i \(-0.995860\pi\)
0.999915 0.0130071i \(-0.00414040\pi\)
\(614\) −31.9925 −1.29111
\(615\) 19.3615 0.780730
\(616\) 5.87924i 0.236881i
\(617\) 23.5775i 0.949194i −0.880203 0.474597i \(-0.842594\pi\)
0.880203 0.474597i \(-0.157406\pi\)
\(618\) 33.9685i 1.36641i
\(619\) 5.86810i 0.235859i −0.993022 0.117929i \(-0.962374\pi\)
0.993022 0.117929i \(-0.0376256\pi\)
\(620\) −172.667 −6.93447
\(621\) 4.20997 0.168940
\(622\) 5.37589i 0.215553i
\(623\) 5.01911 0.201087
\(624\) −14.1667 + 19.6501i −0.567121 + 0.786633i
\(625\) 7.15745 0.286298
\(626\) 54.7229i 2.18717i
\(627\) 7.67886 0.306664
\(628\) −57.3714 −2.28937
\(629\) 17.0752i 0.680833i
\(630\) 8.97928i 0.357743i
\(631\) 11.0386i 0.439441i 0.975563 + 0.219721i \(0.0705146\pi\)
−0.975563 + 0.219721i \(0.929485\pi\)
\(632\) 22.4111i 0.891465i
\(633\) −23.5992 −0.937982
\(634\) −39.9636 −1.58716
\(635\) 24.4314i 0.969529i
\(636\) −13.1944 −0.523193
\(637\) −12.8276 + 17.7928i −0.508250 + 0.704975i
\(638\) 5.01271 0.198455
\(639\) 12.1582i 0.480972i
\(640\) −48.3658 −1.91183
\(641\) −11.2924 −0.446022 −0.223011 0.974816i \(-0.571589\pi\)
−0.223011 + 0.974816i \(0.571589\pi\)
\(642\) 20.4221i 0.805996i
\(643\) 2.73168i 0.107727i −0.998548 0.0538634i \(-0.982846\pi\)
0.998548 0.0538634i \(-0.0171536\pi\)
\(644\) 17.8265i 0.702463i
\(645\) 19.4715i 0.766691i
\(646\) −40.0013 −1.57383
\(647\) 10.3135 0.405465 0.202733 0.979234i \(-0.435018\pi\)
0.202733 + 0.979234i \(0.435018\pi\)
\(648\) 6.14151i 0.241261i
\(649\) 12.3548 0.484968
\(650\) −64.4687 46.4785i −2.52867 1.82304i
\(651\) 10.0971 0.395735
\(652\) 82.6616i 3.23728i
\(653\) −1.95601 −0.0765446 −0.0382723 0.999267i \(-0.512185\pi\)
−0.0382723 + 0.999267i \(0.512185\pi\)
\(654\) 36.3942 1.42313
\(655\) 21.5058i 0.840303i
\(656\) 35.1480i 1.37230i
\(657\) 3.32573i 0.129749i
\(658\) 3.02437i 0.117902i
\(659\) −21.0277 −0.819121 −0.409561 0.912283i \(-0.634318\pi\)
−0.409561 + 0.912283i \(0.634318\pi\)
\(660\) −16.3704 −0.637218
\(661\) 25.7516i 1.00162i 0.865557 + 0.500810i \(0.166964\pi\)
−0.865557 + 0.500810i \(0.833036\pi\)
\(662\) −29.5517 −1.14856
\(663\) −4.33399 + 6.01151i −0.168318 + 0.233468i
\(664\) 20.3872 0.791176
\(665\) 27.2058i 1.05499i
\(666\) −21.0544 −0.815841
\(667\) 8.32673 0.322412
\(668\) 110.767i 4.28570i
\(669\) 14.7201i 0.569111i
\(670\) 13.1966i 0.509830i
\(671\) 0.183851i 0.00709748i
\(672\) −4.54213 −0.175217
\(673\) 18.2077 0.701856 0.350928 0.936403i \(-0.385866\pi\)
0.350928 + 0.936403i \(0.385866\pi\)
\(674\) 19.3504i 0.745351i
\(675\) −8.69737 −0.334762
\(676\) 18.1703 + 54.5559i 0.698857 + 2.09830i
\(677\) −10.3281 −0.396941 −0.198470 0.980107i \(-0.563597\pi\)
−0.198470 + 0.980107i \(0.563597\pi\)
\(678\) 47.3112i 1.81697i
\(679\) −9.40344 −0.360871
\(680\) 46.7191 1.79160
\(681\) 0.0358913i 0.00137536i
\(682\) 26.7317i 1.02361i
\(683\) 33.4285i 1.27911i −0.768747 0.639553i \(-0.779119\pi\)
0.768747 0.639553i \(-0.220881\pi\)
\(684\) 33.9655i 1.29870i
\(685\) 20.8813 0.797834
\(686\) −31.7431 −1.21196
\(687\) 8.37257i 0.319433i
\(688\) −35.3478 −1.34762
\(689\) −6.28979 + 8.72434i −0.239622 + 0.332371i
\(690\) −39.4889 −1.50332
\(691\) 38.8290i 1.47712i 0.674186 + 0.738562i \(0.264495\pi\)
−0.674186 + 0.738562i \(0.735505\pi\)
\(692\) −13.9922 −0.531903
\(693\) 0.957295 0.0363646
\(694\) 45.0678i 1.71075i
\(695\) 16.5368i 0.627276i
\(696\) 12.1471i 0.460433i
\(697\) 10.7528i 0.407290i
\(698\) 30.8343 1.16710
\(699\) 18.0020 0.680897
\(700\) 36.8277i 1.39196i
\(701\) −47.5275 −1.79509 −0.897544 0.440925i \(-0.854650\pi\)
−0.897544 + 0.440925i \(0.854650\pi\)
\(702\) 7.41243 + 5.34397i 0.279764 + 0.201695i
\(703\) −63.7914 −2.40594
\(704\) 1.41208i 0.0532199i
\(705\) −4.61350 −0.173755
\(706\) 83.3886 3.13837
\(707\) 8.06365i 0.303265i
\(708\) 54.6483i 2.05381i
\(709\) 28.9052i 1.08556i −0.839875 0.542780i \(-0.817372\pi\)
0.839875 0.542780i \(-0.182628\pi\)
\(710\) 114.042i 4.27993i
\(711\) −3.64911 −0.136852
\(712\) −32.2001 −1.20675
\(713\) 44.4046i 1.66297i
\(714\) −4.98682 −0.186627
\(715\) −7.80379 + 10.8244i −0.291845 + 0.404808i
\(716\) 5.52805 0.206593
\(717\) 5.74497i 0.214550i
\(718\) 18.4951 0.690233
\(719\) −47.9212 −1.78716 −0.893579 0.448906i \(-0.851814\pi\)
−0.893579 + 0.448906i \(0.851814\pi\)
\(720\) 24.8656i 0.926687i
\(721\) 12.8305i 0.477834i
\(722\) 101.287i 3.76953i
\(723\) 16.1458i 0.600469i
\(724\) 71.0869 2.64192
\(725\) −17.2022 −0.638873
\(726\) 2.53441i 0.0940609i
\(727\) −23.4347 −0.869146 −0.434573 0.900636i \(-0.643101\pi\)
−0.434573 + 0.900636i \(0.643101\pi\)
\(728\) −12.3968 + 17.1951i −0.459454 + 0.637292i
\(729\) 1.00000 0.0370370
\(730\) 31.1949i 1.15457i
\(731\) −10.8139 −0.399966
\(732\) 0.813218 0.0300574
\(733\) 38.8733i 1.43582i −0.696136 0.717910i \(-0.745099\pi\)
0.696136 0.717910i \(-0.254901\pi\)
\(734\) 22.6809i 0.837167i
\(735\) 22.5153i 0.830491i
\(736\) 19.9753i 0.736299i
\(737\) 1.40691 0.0518242
\(738\) 13.2586 0.488055
\(739\) 29.3240i 1.07870i 0.842082 + 0.539350i \(0.181330\pi\)
−0.842082 + 0.539350i \(0.818670\pi\)
\(740\) 135.996 4.99930
\(741\) 22.4585 + 16.1914i 0.825032 + 0.594805i
\(742\) −7.23723 −0.265687
\(743\) 40.8183i 1.49748i −0.662864 0.748740i \(-0.730659\pi\)
0.662864 0.748740i \(-0.269341\pi\)
\(744\) −64.7776 −2.37486
\(745\) 27.3781 1.00305
\(746\) 46.1042i 1.68799i
\(747\) 3.31957i 0.121457i
\(748\) 9.09163i 0.332423i
\(749\) 7.71380i 0.281856i
\(750\) 34.6808 1.26636
\(751\) −4.36042 −0.159114 −0.0795570 0.996830i \(-0.525351\pi\)
−0.0795570 + 0.996830i \(0.525351\pi\)
\(752\) 8.37515i 0.305410i
\(753\) 6.83631 0.249129
\(754\) 14.6608 + 10.5696i 0.533913 + 0.384923i
\(755\) 87.8817 3.19834
\(756\) 4.23435i 0.154002i
\(757\) 40.1387 1.45887 0.729433 0.684052i \(-0.239784\pi\)
0.729433 + 0.684052i \(0.239784\pi\)
\(758\) −50.9577 −1.85087
\(759\) 4.20997i 0.152812i
\(760\) 174.538i 6.33117i
\(761\) 38.2425i 1.38629i −0.720799 0.693144i \(-0.756225\pi\)
0.720799 0.693144i \(-0.243775\pi\)
\(762\) 16.7304i 0.606079i
\(763\) 13.7468 0.497667
\(764\) −67.6357 −2.44697
\(765\) 7.60710i 0.275035i
\(766\) 20.2523 0.731745
\(767\) 36.1342 + 26.0509i 1.30473 + 0.940642i
\(768\) −30.2963 −1.09323
\(769\) 35.0140i 1.26264i 0.775523 + 0.631319i \(0.217486\pi\)
−0.775523 + 0.631319i \(0.782514\pi\)
\(770\) −8.97928 −0.323591
\(771\) 26.8038 0.965315
\(772\) 29.9079i 1.07641i
\(773\) 5.69564i 0.204858i 0.994740 + 0.102429i \(0.0326614\pi\)
−0.994740 + 0.102429i \(0.967339\pi\)
\(774\) 13.3340i 0.479279i
\(775\) 91.7355i 3.29524i
\(776\) 60.3277 2.16564
\(777\) −7.95264 −0.285299
\(778\) 10.9390i 0.392181i
\(779\) 40.1713 1.43929
\(780\) −47.8788 34.5181i −1.71434 1.23595i
\(781\) 12.1582 0.435055
\(782\) 21.9309i 0.784248i
\(783\) 1.97786 0.0706830
\(784\) 40.8734 1.45976
\(785\) 48.0035i 1.71332i
\(786\) 14.7270i 0.525296i
\(787\) 31.2092i 1.11249i 0.831019 + 0.556244i \(0.187758\pi\)
−0.831019 + 0.556244i \(0.812242\pi\)
\(788\) 50.1244i 1.78561i
\(789\) −11.9518 −0.425496
\(790\) 34.2282 1.21778
\(791\) 17.8703i 0.635395i