Properties

Label 403.2.c.b.311.7
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.7
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.26

$q$-expansion

\(f(q)\) \(=\) \(q-1.88981i q^{2} -0.327950 q^{3} -1.57140 q^{4} +1.75790i q^{5} +0.619765i q^{6} -0.652358i q^{7} -0.809976i q^{8} -2.89245 q^{9} +O(q^{10})\) \(q-1.88981i q^{2} -0.327950 q^{3} -1.57140 q^{4} +1.75790i q^{5} +0.619765i q^{6} -0.652358i q^{7} -0.809976i q^{8} -2.89245 q^{9} +3.32211 q^{10} -4.04168i q^{11} +0.515341 q^{12} +(-0.515318 - 3.56854i) q^{13} -1.23284 q^{14} -0.576505i q^{15} -4.67350 q^{16} -2.05056 q^{17} +5.46619i q^{18} -7.52193i q^{19} -2.76237i q^{20} +0.213941i q^{21} -7.63802 q^{22} -1.17786 q^{23} +0.265632i q^{24} +1.90978 q^{25} +(-6.74387 + 0.973855i) q^{26} +1.93243 q^{27} +1.02511i q^{28} +6.42057 q^{29} -1.08949 q^{30} +1.00000i q^{31} +7.21210i q^{32} +1.32547i q^{33} +3.87518i q^{34} +1.14678 q^{35} +4.54519 q^{36} +4.69077i q^{37} -14.2150 q^{38} +(0.168999 + 1.17030i) q^{39} +1.42386 q^{40} +5.09819i q^{41} +0.404309 q^{42} +2.44144 q^{43} +6.35109i q^{44} -5.08465i q^{45} +2.22594i q^{46} +1.20893i q^{47} +1.53268 q^{48} +6.57443 q^{49} -3.60912i q^{50} +0.672482 q^{51} +(0.809770 + 5.60759i) q^{52} +0.419540 q^{53} -3.65193i q^{54} +7.10488 q^{55} -0.528394 q^{56} +2.46682i q^{57} -12.1337i q^{58} +10.2580i q^{59} +0.905919i q^{60} -12.7823 q^{61} +1.88981 q^{62} +1.88691i q^{63} +4.28253 q^{64} +(6.27314 - 0.905879i) q^{65} +2.50489 q^{66} -11.5333i q^{67} +3.22225 q^{68} +0.386280 q^{69} -2.16721i q^{70} +6.53421i q^{71} +2.34282i q^{72} -0.170013i q^{73} +8.86469 q^{74} -0.626311 q^{75} +11.8200i q^{76} -2.63662 q^{77} +(2.21165 - 0.319376i) q^{78} +8.39155 q^{79} -8.21557i q^{80} +8.04360 q^{81} +9.63464 q^{82} -13.1610i q^{83} -0.336186i q^{84} -3.60469i q^{85} -4.61387i q^{86} -2.10563 q^{87} -3.27366 q^{88} +7.61808i q^{89} -9.60904 q^{90} +(-2.32796 + 0.336172i) q^{91} +1.85089 q^{92} -0.327950i q^{93} +2.28465 q^{94} +13.2228 q^{95} -2.36521i q^{96} -18.9945i q^{97} -12.4245i q^{98} +11.6903i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.88981i 1.33630i −0.744026 0.668150i \(-0.767086\pi\)
0.744026 0.668150i \(-0.232914\pi\)
\(3\) −0.327950 −0.189342 −0.0946711 0.995509i \(-0.530180\pi\)
−0.0946711 + 0.995509i \(0.530180\pi\)
\(4\) −1.57140 −0.785699
\(5\) 1.75790i 0.786158i 0.919505 + 0.393079i \(0.128590\pi\)
−0.919505 + 0.393079i \(0.871410\pi\)
\(6\) 0.619765i 0.253018i
\(7\) 0.652358i 0.246568i −0.992371 0.123284i \(-0.960657\pi\)
0.992371 0.123284i \(-0.0393426\pi\)
\(8\) 0.809976i 0.286370i
\(9\) −2.89245 −0.964150
\(10\) 3.32211 1.05054
\(11\) 4.04168i 1.21861i −0.792935 0.609306i \(-0.791448\pi\)
0.792935 0.609306i \(-0.208552\pi\)
\(12\) 0.515341 0.148766
\(13\) −0.515318 3.56854i −0.142923 0.989734i
\(14\) −1.23284 −0.329489
\(15\) 0.576505i 0.148853i
\(16\) −4.67350 −1.16838
\(17\) −2.05056 −0.497334 −0.248667 0.968589i \(-0.579992\pi\)
−0.248667 + 0.968589i \(0.579992\pi\)
\(18\) 5.46619i 1.28839i
\(19\) 7.52193i 1.72565i −0.505504 0.862824i \(-0.668693\pi\)
0.505504 0.862824i \(-0.331307\pi\)
\(20\) 2.76237i 0.617684i
\(21\) 0.213941i 0.0466857i
\(22\) −7.63802 −1.62843
\(23\) −1.17786 −0.245601 −0.122801 0.992431i \(-0.539188\pi\)
−0.122801 + 0.992431i \(0.539188\pi\)
\(24\) 0.265632i 0.0542219i
\(25\) 1.90978 0.381955
\(26\) −6.74387 + 0.973855i −1.32258 + 0.190989i
\(27\) 1.93243 0.371896
\(28\) 1.02511i 0.193728i
\(29\) 6.42057 1.19227 0.596135 0.802884i \(-0.296702\pi\)
0.596135 + 0.802884i \(0.296702\pi\)
\(30\) −1.08949 −0.198912
\(31\) 1.00000i 0.179605i
\(32\) 7.21210i 1.27493i
\(33\) 1.32547i 0.230735i
\(34\) 3.87518i 0.664588i
\(35\) 1.14678 0.193842
\(36\) 4.54519 0.757532
\(37\) 4.69077i 0.771158i 0.922675 + 0.385579i \(0.125998\pi\)
−0.922675 + 0.385579i \(0.874002\pi\)
\(38\) −14.2150 −2.30599
\(39\) 0.168999 + 1.17030i 0.0270614 + 0.187398i
\(40\) 1.42386 0.225132
\(41\) 5.09819i 0.796204i 0.917341 + 0.398102i \(0.130331\pi\)
−0.917341 + 0.398102i \(0.869669\pi\)
\(42\) 0.404309 0.0623862
\(43\) 2.44144 0.372317 0.186158 0.982520i \(-0.440396\pi\)
0.186158 + 0.982520i \(0.440396\pi\)
\(44\) 6.35109i 0.957463i
\(45\) 5.08465i 0.757974i
\(46\) 2.22594i 0.328197i
\(47\) 1.20893i 0.176341i 0.996105 + 0.0881703i \(0.0281020\pi\)
−0.996105 + 0.0881703i \(0.971898\pi\)
\(48\) 1.53268 0.221223
\(49\) 6.57443 0.939204
\(50\) 3.60912i 0.510407i
\(51\) 0.672482 0.0941663
\(52\) 0.809770 + 5.60759i 0.112295 + 0.777633i
\(53\) 0.419540 0.0576282 0.0288141 0.999585i \(-0.490827\pi\)
0.0288141 + 0.999585i \(0.490827\pi\)
\(54\) 3.65193i 0.496965i
\(55\) 7.10488 0.958022
\(56\) −0.528394 −0.0706097
\(57\) 2.46682i 0.326738i
\(58\) 12.1337i 1.59323i
\(59\) 10.2580i 1.33548i 0.744397 + 0.667738i \(0.232737\pi\)
−0.744397 + 0.667738i \(0.767263\pi\)
\(60\) 0.905919i 0.116954i
\(61\) −12.7823 −1.63661 −0.818303 0.574788i \(-0.805085\pi\)
−0.818303 + 0.574788i \(0.805085\pi\)
\(62\) 1.88981 0.240007
\(63\) 1.88691i 0.237728i
\(64\) 4.28253 0.535316
\(65\) 6.27314 0.905879i 0.778087 0.112360i
\(66\) 2.50489 0.308331
\(67\) 11.5333i 1.40902i −0.709693 0.704511i \(-0.751166\pi\)
0.709693 0.704511i \(-0.248834\pi\)
\(68\) 3.22225 0.390755
\(69\) 0.386280 0.0465027
\(70\) 2.16721i 0.259031i
\(71\) 6.53421i 0.775468i 0.921771 + 0.387734i \(0.126742\pi\)
−0.921771 + 0.387734i \(0.873258\pi\)
\(72\) 2.34282i 0.276103i
\(73\) 0.170013i 0.0198985i −0.999951 0.00994926i \(-0.996833\pi\)
0.999951 0.00994926i \(-0.00316700\pi\)
\(74\) 8.86469 1.03050
\(75\) −0.626311 −0.0723202
\(76\) 11.8200i 1.35584i
\(77\) −2.63662 −0.300471
\(78\) 2.21165 0.319376i 0.250421 0.0361622i
\(79\) 8.39155 0.944124 0.472062 0.881565i \(-0.343510\pi\)
0.472062 + 0.881565i \(0.343510\pi\)
\(80\) 8.21557i 0.918528i
\(81\) 8.04360 0.893734
\(82\) 9.63464 1.06397
\(83\) 13.1610i 1.44461i −0.691576 0.722304i \(-0.743083\pi\)
0.691576 0.722304i \(-0.256917\pi\)
\(84\) 0.336186i 0.0366810i
\(85\) 3.60469i 0.390983i
\(86\) 4.61387i 0.497527i
\(87\) −2.10563 −0.225747
\(88\) −3.27366 −0.348974
\(89\) 7.61808i 0.807515i 0.914866 + 0.403758i \(0.132296\pi\)
−0.914866 + 0.403758i \(0.867704\pi\)
\(90\) −9.60904 −1.01288
\(91\) −2.32796 + 0.336172i −0.244037 + 0.0352404i
\(92\) 1.85089 0.192969
\(93\) 0.327950i 0.0340069i
\(94\) 2.28465 0.235644
\(95\) 13.2228 1.35663
\(96\) 2.36521i 0.241398i
\(97\) 18.9945i 1.92860i −0.264812 0.964300i \(-0.585310\pi\)
0.264812 0.964300i \(-0.414690\pi\)
\(98\) 12.4245i 1.25506i
\(99\) 11.6903i 1.17492i
\(100\) −3.00102 −0.300102
\(101\) −12.9992 −1.29347 −0.646733 0.762717i \(-0.723865\pi\)
−0.646733 + 0.762717i \(0.723865\pi\)
\(102\) 1.27087i 0.125834i
\(103\) −7.58987 −0.747852 −0.373926 0.927458i \(-0.621989\pi\)
−0.373926 + 0.927458i \(0.621989\pi\)
\(104\) −2.89043 + 0.417395i −0.283430 + 0.0409290i
\(105\) −0.376087 −0.0367024
\(106\) 0.792853i 0.0770087i
\(107\) 14.5830 1.40979 0.704895 0.709312i \(-0.250994\pi\)
0.704895 + 0.709312i \(0.250994\pi\)
\(108\) −3.03662 −0.292199
\(109\) 4.51756i 0.432703i −0.976315 0.216352i \(-0.930584\pi\)
0.976315 0.216352i \(-0.0694158\pi\)
\(110\) 13.4269i 1.28021i
\(111\) 1.53834i 0.146013i
\(112\) 3.04880i 0.288084i
\(113\) −12.3097 −1.15800 −0.578998 0.815329i \(-0.696556\pi\)
−0.578998 + 0.815329i \(0.696556\pi\)
\(114\) 4.66183 0.436620
\(115\) 2.07057i 0.193082i
\(116\) −10.0893 −0.936766
\(117\) 1.49053 + 10.3218i 0.137800 + 0.954251i
\(118\) 19.3857 1.78460
\(119\) 1.33770i 0.122627i
\(120\) −0.466955 −0.0426270
\(121\) −5.33516 −0.485015
\(122\) 24.1562i 2.18700i
\(123\) 1.67195i 0.150755i
\(124\) 1.57140i 0.141116i
\(125\) 12.1467i 1.08644i
\(126\) 3.56591 0.317677
\(127\) 20.8813 1.85292 0.926459 0.376396i \(-0.122837\pi\)
0.926459 + 0.376396i \(0.122837\pi\)
\(128\) 6.33102i 0.559588i
\(129\) −0.800672 −0.0704952
\(130\) −1.71194 11.8551i −0.150147 1.03976i
\(131\) 8.64964 0.755723 0.377861 0.925862i \(-0.376660\pi\)
0.377861 + 0.925862i \(0.376660\pi\)
\(132\) 2.08284i 0.181288i
\(133\) −4.90699 −0.425490
\(134\) −21.7959 −1.88288
\(135\) 3.39703i 0.292369i
\(136\) 1.66091i 0.142421i
\(137\) 14.7125i 1.25697i −0.777821 0.628486i \(-0.783675\pi\)
0.777821 0.628486i \(-0.216325\pi\)
\(138\) 0.729998i 0.0621416i
\(139\) 15.5107 1.31560 0.657801 0.753192i \(-0.271487\pi\)
0.657801 + 0.753192i \(0.271487\pi\)
\(140\) −1.80205 −0.152301
\(141\) 0.396469i 0.0333887i
\(142\) 12.3484 1.03626
\(143\) −14.4229 + 2.08275i −1.20610 + 0.174168i
\(144\) 13.5179 1.12649
\(145\) 11.2867i 0.937313i
\(146\) −0.321293 −0.0265904
\(147\) −2.15609 −0.177831
\(148\) 7.37108i 0.605899i
\(149\) 1.96195i 0.160729i 0.996766 + 0.0803645i \(0.0256084\pi\)
−0.996766 + 0.0803645i \(0.974392\pi\)
\(150\) 1.18361i 0.0966415i
\(151\) 3.06613i 0.249518i −0.992187 0.124759i \(-0.960184\pi\)
0.992187 0.124759i \(-0.0398158\pi\)
\(152\) −6.09258 −0.494174
\(153\) 5.93114 0.479504
\(154\) 4.98272i 0.401519i
\(155\) −1.75790 −0.141198
\(156\) −0.265564 1.83901i −0.0212622 0.147239i
\(157\) 9.92590 0.792173 0.396086 0.918213i \(-0.370368\pi\)
0.396086 + 0.918213i \(0.370368\pi\)
\(158\) 15.8585i 1.26163i
\(159\) −0.137588 −0.0109115
\(160\) −12.6782 −1.00230
\(161\) 0.768388i 0.0605575i
\(162\) 15.2009i 1.19430i
\(163\) 9.23484i 0.723328i −0.932308 0.361664i \(-0.882209\pi\)
0.932308 0.361664i \(-0.117791\pi\)
\(164\) 8.01129i 0.625577i
\(165\) −2.33005 −0.181394
\(166\) −24.8718 −1.93043
\(167\) 18.2427i 1.41166i 0.708379 + 0.705832i \(0.249427\pi\)
−0.708379 + 0.705832i \(0.750573\pi\)
\(168\) 0.173287 0.0133694
\(169\) −12.4689 + 3.67786i −0.959146 + 0.282912i
\(170\) −6.81219 −0.522471
\(171\) 21.7568i 1.66378i
\(172\) −3.83648 −0.292529
\(173\) −0.0577833 −0.00439318 −0.00219659 0.999998i \(-0.500699\pi\)
−0.00219659 + 0.999998i \(0.500699\pi\)
\(174\) 3.97925i 0.301666i
\(175\) 1.24586i 0.0941779i
\(176\) 18.8888i 1.42380i
\(177\) 3.36411i 0.252862i
\(178\) 14.3968 1.07908
\(179\) 12.4809 0.932867 0.466433 0.884556i \(-0.345539\pi\)
0.466433 + 0.884556i \(0.345539\pi\)
\(180\) 7.99001i 0.595540i
\(181\) 9.94653 0.739319 0.369660 0.929167i \(-0.379474\pi\)
0.369660 + 0.929167i \(0.379474\pi\)
\(182\) 0.635302 + 4.39942i 0.0470917 + 0.326106i
\(183\) 4.19196 0.309878
\(184\) 0.954041i 0.0703329i
\(185\) −8.24593 −0.606253
\(186\) −0.619765 −0.0454434
\(187\) 8.28771i 0.606057i
\(188\) 1.89971i 0.138551i
\(189\) 1.26064i 0.0916978i
\(190\) 24.9887i 1.81287i
\(191\) −26.3529 −1.90683 −0.953413 0.301669i \(-0.902456\pi\)
−0.953413 + 0.301669i \(0.902456\pi\)
\(192\) −1.40446 −0.101358
\(193\) 0.942300i 0.0678282i 0.999425 + 0.0339141i \(0.0107973\pi\)
−0.999425 + 0.0339141i \(0.989203\pi\)
\(194\) −35.8961 −2.57719
\(195\) −2.05728 + 0.297083i −0.147325 + 0.0212746i
\(196\) −10.3311 −0.737932
\(197\) 10.5101i 0.748812i −0.927265 0.374406i \(-0.877847\pi\)
0.927265 0.374406i \(-0.122153\pi\)
\(198\) 22.0926 1.57005
\(199\) 10.5659 0.748994 0.374497 0.927228i \(-0.377815\pi\)
0.374497 + 0.927228i \(0.377815\pi\)
\(200\) 1.54687i 0.109380i
\(201\) 3.78236i 0.266787i
\(202\) 24.5660i 1.72846i
\(203\) 4.18851i 0.293976i
\(204\) −1.05674 −0.0739864
\(205\) −8.96213 −0.625942
\(206\) 14.3435i 0.999356i
\(207\) 3.40691 0.236796
\(208\) 2.40834 + 16.6776i 0.166988 + 1.15638i
\(209\) −30.4012 −2.10290
\(210\) 0.710736i 0.0490454i
\(211\) −0.214908 −0.0147949 −0.00739745 0.999973i \(-0.502355\pi\)
−0.00739745 + 0.999973i \(0.502355\pi\)
\(212\) −0.659265 −0.0452785
\(213\) 2.14290i 0.146829i
\(214\) 27.5591i 1.88390i
\(215\) 4.29182i 0.292700i
\(216\) 1.56522i 0.106500i
\(217\) 0.652358 0.0442849
\(218\) −8.53734 −0.578222
\(219\) 0.0557558i 0.00376763i
\(220\) −11.1646 −0.752717
\(221\) 1.05669 + 7.31750i 0.0710807 + 0.492228i
\(222\) −2.90718 −0.195117
\(223\) 7.54869i 0.505497i −0.967532 0.252749i \(-0.918665\pi\)
0.967532 0.252749i \(-0.0813346\pi\)
\(224\) 4.70487 0.314357
\(225\) −5.52393 −0.368262
\(226\) 23.2630i 1.54743i
\(227\) 17.5811i 1.16690i 0.812149 + 0.583450i \(0.198298\pi\)
−0.812149 + 0.583450i \(0.801702\pi\)
\(228\) 3.87636i 0.256718i
\(229\) 2.48342i 0.164109i 0.996628 + 0.0820544i \(0.0261481\pi\)
−0.996628 + 0.0820544i \(0.973852\pi\)
\(230\) −3.91299 −0.258015
\(231\) 0.864680 0.0568918
\(232\) 5.20051i 0.341430i
\(233\) −1.73165 −0.113444 −0.0567220 0.998390i \(-0.518065\pi\)
−0.0567220 + 0.998390i \(0.518065\pi\)
\(234\) 19.5063 2.81683i 1.27517 0.184142i
\(235\) −2.12518 −0.138632
\(236\) 16.1194i 1.04928i
\(237\) −2.75201 −0.178762
\(238\) 2.52800 0.163866
\(239\) 1.40954i 0.0911755i −0.998960 0.0455878i \(-0.985484\pi\)
0.998960 0.0455878i \(-0.0145161\pi\)
\(240\) 2.69430i 0.173916i
\(241\) 0.348571i 0.0224534i −0.999937 0.0112267i \(-0.996426\pi\)
0.999937 0.0112267i \(-0.00357365\pi\)
\(242\) 10.0825i 0.648125i
\(243\) −8.43519 −0.541118
\(244\) 20.0861 1.28588
\(245\) 11.5572i 0.738363i
\(246\) −3.15968 −0.201454
\(247\) −26.8423 + 3.87618i −1.70793 + 0.246636i
\(248\) 0.809976 0.0514336
\(249\) 4.31615i 0.273525i
\(250\) 22.9550 1.45180
\(251\) −7.54455 −0.476208 −0.238104 0.971240i \(-0.576526\pi\)
−0.238104 + 0.971240i \(0.576526\pi\)
\(252\) 2.96509i 0.186783i
\(253\) 4.76054i 0.299293i
\(254\) 39.4618i 2.47606i
\(255\) 1.18216i 0.0740296i
\(256\) 20.5295 1.28309
\(257\) −22.3905 −1.39668 −0.698341 0.715765i \(-0.746078\pi\)
−0.698341 + 0.715765i \(0.746078\pi\)
\(258\) 1.51312i 0.0942028i
\(259\) 3.06006 0.190143
\(260\) −9.85761 + 1.42350i −0.611343 + 0.0882816i
\(261\) −18.5712 −1.14953
\(262\) 16.3462i 1.00987i
\(263\) 19.5006 1.20246 0.601230 0.799076i \(-0.294678\pi\)
0.601230 + 0.799076i \(0.294678\pi\)
\(264\) 1.07360 0.0660755
\(265\) 0.737511i 0.0453049i
\(266\) 9.27330i 0.568582i
\(267\) 2.49835i 0.152897i
\(268\) 18.1235i 1.10707i
\(269\) 22.4446 1.36847 0.684236 0.729261i \(-0.260136\pi\)
0.684236 + 0.729261i \(0.260136\pi\)
\(270\) 6.41975 0.390693
\(271\) 19.0371i 1.15642i −0.815887 0.578211i \(-0.803751\pi\)
0.815887 0.578211i \(-0.196249\pi\)
\(272\) 9.58330 0.581073
\(273\) 0.763456 0.110248i 0.0462064 0.00667249i
\(274\) −27.8039 −1.67969
\(275\) 7.71870i 0.465455i
\(276\) −0.607001 −0.0365372
\(277\) 3.01871 0.181377 0.0906883 0.995879i \(-0.471093\pi\)
0.0906883 + 0.995879i \(0.471093\pi\)
\(278\) 29.3124i 1.75804i
\(279\) 2.89245i 0.173166i
\(280\) 0.928866i 0.0555104i
\(281\) 28.7820i 1.71699i −0.512820 0.858496i \(-0.671399\pi\)
0.512820 0.858496i \(-0.328601\pi\)
\(282\) −0.749253 −0.0446174
\(283\) −1.28804 −0.0765662 −0.0382831 0.999267i \(-0.512189\pi\)
−0.0382831 + 0.999267i \(0.512189\pi\)
\(284\) 10.2678i 0.609285i
\(285\) −4.33643 −0.256868
\(286\) 3.93601 + 27.2566i 0.232741 + 1.61171i
\(287\) 3.32584 0.196318
\(288\) 20.8606i 1.22922i
\(289\) −12.7952 −0.752659
\(290\) 21.3298 1.25253
\(291\) 6.22925i 0.365165i
\(292\) 0.267158i 0.0156343i
\(293\) 21.1020i 1.23279i −0.787436 0.616397i \(-0.788592\pi\)
0.787436 0.616397i \(-0.211408\pi\)
\(294\) 4.07460i 0.237636i
\(295\) −18.0325 −1.04990
\(296\) 3.79942 0.220837
\(297\) 7.81026i 0.453197i
\(298\) 3.70772 0.214782
\(299\) 0.606974 + 4.20325i 0.0351022 + 0.243080i
\(300\) 0.984185 0.0568219
\(301\) 1.59269i 0.0918014i
\(302\) −5.79442 −0.333431
\(303\) 4.26308 0.244908
\(304\) 35.1538i 2.01621i
\(305\) 22.4700i 1.28663i
\(306\) 11.2088i 0.640762i
\(307\) 2.44457i 0.139519i 0.997564 + 0.0697595i \(0.0222232\pi\)
−0.997564 + 0.0697595i \(0.977777\pi\)
\(308\) 4.14318 0.236080
\(309\) 2.48910 0.141600
\(310\) 3.32211i 0.188683i
\(311\) 19.4882 1.10508 0.552538 0.833487i \(-0.313659\pi\)
0.552538 + 0.833487i \(0.313659\pi\)
\(312\) 0.947917 0.136885i 0.0536652 0.00774958i
\(313\) 17.7760 1.00476 0.502380 0.864647i \(-0.332458\pi\)
0.502380 + 0.864647i \(0.332458\pi\)
\(314\) 18.7581i 1.05858i
\(315\) −3.31701 −0.186892
\(316\) −13.1865 −0.741797
\(317\) 2.03343i 0.114209i 0.998368 + 0.0571044i \(0.0181868\pi\)
−0.998368 + 0.0571044i \(0.981813\pi\)
\(318\) 0.260016i 0.0145810i
\(319\) 25.9499i 1.45291i
\(320\) 7.52827i 0.420843i
\(321\) −4.78249 −0.266933
\(322\) 1.45211 0.0809230
\(323\) 15.4242i 0.858224i
\(324\) −12.6397 −0.702206
\(325\) −0.984141 6.81510i −0.0545903 0.378034i
\(326\) −17.4521 −0.966584
\(327\) 1.48153i 0.0819290i
\(328\) 4.12941 0.228009
\(329\) 0.788655 0.0434799
\(330\) 4.40336i 0.242397i
\(331\) 18.5709i 1.02075i 0.859952 + 0.510376i \(0.170494\pi\)
−0.859952 + 0.510376i \(0.829506\pi\)
\(332\) 20.6812i 1.13503i
\(333\) 13.5678i 0.743512i
\(334\) 34.4754 1.88641
\(335\) 20.2745 1.10771
\(336\) 0.999853i 0.0545465i
\(337\) 33.2525 1.81138 0.905689 0.423942i \(-0.139354\pi\)
0.905689 + 0.423942i \(0.139354\pi\)
\(338\) 6.95047 + 23.5639i 0.378056 + 1.28171i
\(339\) 4.03696 0.219258
\(340\) 5.66440i 0.307195i
\(341\) 4.04168 0.218869
\(342\) 41.1163 2.22331
\(343\) 8.85538i 0.478146i
\(344\) 1.97751i 0.106620i
\(345\) 0.679044i 0.0365585i
\(346\) 0.109200i 0.00587061i
\(347\) 20.9692 1.12569 0.562843 0.826564i \(-0.309708\pi\)
0.562843 + 0.826564i \(0.309708\pi\)
\(348\) 3.30878 0.177369
\(349\) 30.4835i 1.63175i 0.578231 + 0.815873i \(0.303743\pi\)
−0.578231 + 0.815873i \(0.696257\pi\)
\(350\) −2.35444 −0.125850
\(351\) −0.995816 6.89595i −0.0531527 0.368078i
\(352\) 29.1490 1.55365
\(353\) 10.5824i 0.563243i −0.959526 0.281621i \(-0.909128\pi\)
0.959526 0.281621i \(-0.0908722\pi\)
\(354\) −6.35754 −0.337899
\(355\) −11.4865 −0.609640
\(356\) 11.9710i 0.634464i
\(357\) 0.438699i 0.0232184i
\(358\) 23.5866i 1.24659i
\(359\) 21.8192i 1.15157i 0.817600 + 0.575786i \(0.195304\pi\)
−0.817600 + 0.575786i \(0.804696\pi\)
\(360\) −4.11844 −0.217061
\(361\) −37.5794 −1.97786
\(362\) 18.7971i 0.987953i
\(363\) 1.74967 0.0918337
\(364\) 3.65816 0.528260i 0.191740 0.0276883i
\(365\) 0.298866 0.0156434
\(366\) 7.92202i 0.414091i
\(367\) −20.1551 −1.05209 −0.526044 0.850457i \(-0.676325\pi\)
−0.526044 + 0.850457i \(0.676325\pi\)
\(368\) 5.50475 0.286955
\(369\) 14.7463i 0.767659i
\(370\) 15.5833i 0.810136i
\(371\) 0.273690i 0.0142093i
\(372\) 0.515341i 0.0267192i
\(373\) −29.0660 −1.50498 −0.752491 0.658602i \(-0.771148\pi\)
−0.752491 + 0.658602i \(0.771148\pi\)
\(374\) 15.6622 0.809874
\(375\) 3.98352i 0.205708i
\(376\) 0.979205 0.0504986
\(377\) −3.30863 22.9120i −0.170403 1.18003i
\(378\) −2.38237 −0.122536
\(379\) 12.4985i 0.642003i −0.947079 0.321002i \(-0.895981\pi\)
0.947079 0.321002i \(-0.104019\pi\)
\(380\) −20.7783 −1.06591
\(381\) −6.84804 −0.350835
\(382\) 49.8020i 2.54809i
\(383\) 5.69126i 0.290810i −0.989372 0.145405i \(-0.953551\pi\)
0.989372 0.145405i \(-0.0464485\pi\)
\(384\) 2.07626i 0.105954i
\(385\) 4.63492i 0.236218i
\(386\) 1.78077 0.0906389
\(387\) −7.06175 −0.358969
\(388\) 29.8479i 1.51530i
\(389\) 23.5136 1.19219 0.596093 0.802915i \(-0.296719\pi\)
0.596093 + 0.802915i \(0.296719\pi\)
\(390\) 0.561432 + 3.88787i 0.0284292 + 0.196870i
\(391\) 2.41528 0.122146
\(392\) 5.32513i 0.268960i
\(393\) −2.83665 −0.143090
\(394\) −19.8621 −1.00064
\(395\) 14.7515i 0.742231i
\(396\) 18.3702i 0.923137i
\(397\) 8.32867i 0.418004i 0.977915 + 0.209002i \(0.0670215\pi\)
−0.977915 + 0.209002i \(0.932979\pi\)
\(398\) 19.9675i 1.00088i
\(399\) 1.60925 0.0805632
\(400\) −8.92534 −0.446267
\(401\) 32.6105i 1.62849i 0.580520 + 0.814246i \(0.302849\pi\)
−0.580520 + 0.814246i \(0.697151\pi\)
\(402\) 7.14797 0.356508
\(403\) 3.56854 0.515318i 0.177761 0.0256698i
\(404\) 20.4269 1.01628
\(405\) 14.1399i 0.702616i
\(406\) −7.91550 −0.392840
\(407\) 18.9586 0.939743
\(408\) 0.544694i 0.0269664i
\(409\) 22.2951i 1.10242i 0.834366 + 0.551211i \(0.185834\pi\)
−0.834366 + 0.551211i \(0.814166\pi\)
\(410\) 16.9368i 0.836447i
\(411\) 4.82496i 0.237998i
\(412\) 11.9267 0.587587
\(413\) 6.69187 0.329286
\(414\) 6.43842i 0.316431i
\(415\) 23.1358 1.13569
\(416\) 25.7366 3.71652i 1.26184 0.182218i
\(417\) −5.08674 −0.249099
\(418\) 57.4527i 2.81010i
\(419\) −30.9395 −1.51149 −0.755747 0.654864i \(-0.772726\pi\)
−0.755747 + 0.654864i \(0.772726\pi\)
\(420\) 0.590983 0.0288370
\(421\) 5.10402i 0.248754i −0.992235 0.124377i \(-0.960307\pi\)
0.992235 0.124377i \(-0.0396933\pi\)
\(422\) 0.406137i 0.0197704i
\(423\) 3.49677i 0.170019i
\(424\) 0.339817i 0.0165030i
\(425\) −3.91611 −0.189959
\(426\) −4.04967 −0.196207
\(427\) 8.33863i 0.403534i
\(428\) −22.9157 −1.10767
\(429\) 4.72999 0.683038i 0.228366 0.0329774i
\(430\) 8.11075 0.391135
\(431\) 24.6933i 1.18944i −0.803935 0.594718i \(-0.797264\pi\)
0.803935 0.594718i \(-0.202736\pi\)
\(432\) −9.03122 −0.434515
\(433\) −4.59601 −0.220870 −0.110435 0.993883i \(-0.535224\pi\)
−0.110435 + 0.993883i \(0.535224\pi\)
\(434\) 1.23284i 0.0591780i
\(435\) 3.70149i 0.177473i
\(436\) 7.09888i 0.339975i
\(437\) 8.85980i 0.423822i
\(438\) 0.105368 0.00503468
\(439\) −22.3774 −1.06801 −0.534007 0.845480i \(-0.679314\pi\)
−0.534007 + 0.845480i \(0.679314\pi\)
\(440\) 5.75479i 0.274349i
\(441\) −19.0162 −0.905533
\(442\) 13.8287 1.99695i 0.657765 0.0949852i
\(443\) 27.0807 1.28664 0.643322 0.765596i \(-0.277556\pi\)
0.643322 + 0.765596i \(0.277556\pi\)
\(444\) 2.41735i 0.114722i
\(445\) −13.3919 −0.634835
\(446\) −14.2656 −0.675497
\(447\) 0.643422i 0.0304328i
\(448\) 2.79374i 0.131992i
\(449\) 33.4114i 1.57678i 0.615175 + 0.788391i \(0.289085\pi\)
−0.615175 + 0.788391i \(0.710915\pi\)
\(450\) 10.4392i 0.492108i
\(451\) 20.6052 0.970263
\(452\) 19.3434 0.909837
\(453\) 1.00554i 0.0472443i
\(454\) 33.2251 1.55933
\(455\) −0.590957 4.09233i −0.0277045 0.191851i
\(456\) 1.99806 0.0935680
\(457\) 25.7519i 1.20462i −0.798262 0.602311i \(-0.794247\pi\)
0.798262 0.602311i \(-0.205753\pi\)
\(458\) 4.69320 0.219299
\(459\) −3.96256 −0.184957
\(460\) 3.25369i 0.151704i
\(461\) 7.17831i 0.334327i −0.985929 0.167164i \(-0.946539\pi\)
0.985929 0.167164i \(-0.0534608\pi\)
\(462\) 1.63409i 0.0760245i
\(463\) 2.14846i 0.0998475i 0.998753 + 0.0499238i \(0.0158978\pi\)
−0.998753 + 0.0499238i \(0.984102\pi\)
\(464\) −30.0065 −1.39302
\(465\) 0.576505 0.0267348
\(466\) 3.27249i 0.151595i
\(467\) −7.19142 −0.332779 −0.166390 0.986060i \(-0.553211\pi\)
−0.166390 + 0.986060i \(0.553211\pi\)
\(468\) −2.34222 16.2197i −0.108269 0.749755i
\(469\) −7.52387 −0.347420
\(470\) 4.01620i 0.185254i
\(471\) −3.25520 −0.149992
\(472\) 8.30872 0.382440
\(473\) 9.86753i 0.453709i
\(474\) 5.20079i 0.238880i
\(475\) 14.3652i 0.659120i
\(476\) 2.10206i 0.0963477i
\(477\) −1.21350 −0.0555622
\(478\) −2.66377 −0.121838
\(479\) 25.8734i 1.18219i 0.806603 + 0.591094i \(0.201304\pi\)
−0.806603 + 0.591094i \(0.798696\pi\)
\(480\) 4.15781 0.189777
\(481\) 16.7392 2.41724i 0.763242 0.110217i
\(482\) −0.658734 −0.0300045
\(483\) 0.251993i 0.0114661i
\(484\) 8.38367 0.381076
\(485\) 33.3905 1.51618
\(486\) 15.9410i 0.723096i
\(487\) 1.91760i 0.0868946i −0.999056 0.0434473i \(-0.986166\pi\)
0.999056 0.0434473i \(-0.0138341\pi\)
\(488\) 10.3534i 0.468674i
\(489\) 3.02857i 0.136957i
\(490\) 21.8410 0.986675
\(491\) 5.36083 0.241931 0.120965 0.992657i \(-0.461401\pi\)
0.120965 + 0.992657i \(0.461401\pi\)
\(492\) 2.62731i 0.118448i
\(493\) −13.1658 −0.592956
\(494\) 7.32527 + 50.7269i 0.329579 + 2.28231i
\(495\) −20.5505 −0.923676
\(496\) 4.67350i 0.209846i
\(497\) 4.26264 0.191206
\(498\) 8.15673 0.365512
\(499\) 22.3837i 1.00203i −0.865438 0.501016i \(-0.832960\pi\)
0.865438 0.501016i \(-0.167040\pi\)
\(500\) 19.0873i 0.853612i
\(501\) 5.98271i 0.267288i
\(502\) 14.2578i 0.636357i
\(503\) 1.51578 0.0675852 0.0337926 0.999429i \(-0.489241\pi\)
0.0337926 + 0.999429i \(0.489241\pi\)
\(504\) 1.52835 0.0680783
\(505\) 22.8513i 1.01687i
\(506\) 8.99654 0.399945
\(507\) 4.08918 1.20616i 0.181607 0.0535672i
\(508\) −32.8129 −1.45584
\(509\) 15.8794i 0.703842i 0.936030 + 0.351921i \(0.114471\pi\)
−0.936030 + 0.351921i \(0.885529\pi\)
\(510\) 2.23406 0.0989258
\(511\) −0.110909 −0.00490634
\(512\) 26.1349i 1.15501i
\(513\) 14.5356i 0.641762i
\(514\) 42.3139i 1.86639i
\(515\) 13.3423i 0.587930i
\(516\) 1.25817 0.0553881
\(517\) 4.88611 0.214891
\(518\) 5.78295i 0.254088i
\(519\) 0.0189500 0.000831815
\(520\) −0.733741 5.08110i −0.0321767 0.222821i
\(521\) −15.5542 −0.681440 −0.340720 0.940165i \(-0.610671\pi\)
−0.340720 + 0.940165i \(0.610671\pi\)
\(522\) 35.0961i 1.53611i
\(523\) −33.1558 −1.44980 −0.724901 0.688853i \(-0.758115\pi\)
−0.724901 + 0.688853i \(0.758115\pi\)
\(524\) −13.5920 −0.593771
\(525\) 0.408579i 0.0178319i
\(526\) 36.8525i 1.60685i
\(527\) 2.05056i 0.0893238i
\(528\) 6.19459i 0.269585i
\(529\) −21.6126 −0.939680
\(530\) 1.39376 0.0605410
\(531\) 29.6707i 1.28760i
\(532\) 7.71084 0.334307
\(533\) 18.1931 2.62719i 0.788030 0.113796i
\(534\) −4.72142 −0.204316
\(535\) 25.6355i 1.10832i
\(536\) −9.34174 −0.403502
\(537\) −4.09312 −0.176631
\(538\) 42.4161i 1.82869i
\(539\) 26.5717i 1.14453i
\(540\) 5.33808i 0.229715i
\(541\) 38.6097i 1.65996i 0.557792 + 0.829981i \(0.311649\pi\)
−0.557792 + 0.829981i \(0.688351\pi\)
\(542\) −35.9766 −1.54533
\(543\) −3.26197 −0.139984
\(544\) 14.7889i 0.634067i
\(545\) 7.94143 0.340173
\(546\) −0.208347 1.44279i −0.00891645 0.0617457i
\(547\) −9.56630 −0.409026 −0.204513 0.978864i \(-0.565561\pi\)
−0.204513 + 0.978864i \(0.565561\pi\)
\(548\) 23.1192i 0.987602i
\(549\) 36.9721 1.57793
\(550\) −14.5869 −0.621988
\(551\) 48.2951i 2.05744i
\(552\) 0.312878i 0.0133170i
\(553\) 5.47430i 0.232791i
\(554\) 5.70480i 0.242374i
\(555\) 2.70425 0.114789
\(556\) −24.3735 −1.03367
\(557\) 6.45936i 0.273692i 0.990592 + 0.136846i \(0.0436965\pi\)
−0.990592 + 0.136846i \(0.956303\pi\)
\(558\) −5.46619 −0.231402
\(559\) −1.25812 8.71238i −0.0532128 0.368494i
\(560\) −5.35949 −0.226480
\(561\) 2.71796i 0.114752i
\(562\) −54.3927 −2.29442
\(563\) 3.68120 0.155144 0.0775721 0.996987i \(-0.475283\pi\)
0.0775721 + 0.996987i \(0.475283\pi\)
\(564\) 0.623011i 0.0262335i
\(565\) 21.6392i 0.910368i
\(566\) 2.43416i 0.102315i
\(567\) 5.24731i 0.220366i
\(568\) 5.29255 0.222071
\(569\) −27.0122 −1.13241 −0.566205 0.824265i \(-0.691589\pi\)
−0.566205 + 0.824265i \(0.691589\pi\)
\(570\) 8.19505i 0.343253i
\(571\) 26.6613 1.11574 0.557870 0.829928i \(-0.311619\pi\)
0.557870 + 0.829928i \(0.311619\pi\)
\(572\) 22.6641 3.27283i 0.947633 0.136844i
\(573\) 8.64242 0.361042
\(574\) 6.28523i 0.262340i
\(575\) −2.24945 −0.0938087
\(576\) −12.3870 −0.516125
\(577\) 6.72496i 0.279964i −0.990154 0.139982i \(-0.955296\pi\)
0.990154 0.139982i \(-0.0447044\pi\)
\(578\) 24.1806i 1.00578i
\(579\) 0.309027i 0.0128427i
\(580\) 17.7360i 0.736446i
\(581\) −8.58568 −0.356194
\(582\) 11.7721 0.487971
\(583\) 1.69565i 0.0702265i
\(584\) −0.137707 −0.00569834
\(585\) −18.1447 + 2.62021i −0.750193 + 0.108332i
\(586\) −39.8789 −1.64738
\(587\) 28.7519i 1.18672i −0.804938 0.593359i \(-0.797801\pi\)
0.804938 0.593359i \(-0.202199\pi\)
\(588\) 3.38807 0.139722
\(589\) 7.52193 0.309936
\(590\) 34.0782i 1.40298i
\(591\) 3.44678i 0.141782i
\(592\) 21.9223i 0.901003i
\(593\) 1.97573i 0.0811335i 0.999177 + 0.0405668i \(0.0129163\pi\)
−0.999177 + 0.0405668i \(0.987084\pi\)
\(594\) −14.7599 −0.605608
\(595\) −2.35155 −0.0964040
\(596\) 3.08300i 0.126285i
\(597\) −3.46508 −0.141816
\(598\) 7.94336 1.14707i 0.324828 0.0469071i
\(599\) 7.67011 0.313392 0.156696 0.987647i \(-0.449916\pi\)
0.156696 + 0.987647i \(0.449916\pi\)
\(600\) 0.507297i 0.0207103i
\(601\) −34.0529 −1.38905 −0.694523 0.719470i \(-0.744385\pi\)
−0.694523 + 0.719470i \(0.744385\pi\)
\(602\) −3.00990 −0.122674
\(603\) 33.3596i 1.35851i
\(604\) 4.81811i 0.196046i
\(605\) 9.37870i 0.381298i
\(606\) 8.05643i 0.327270i
\(607\) 32.5479 1.32108 0.660540 0.750791i \(-0.270328\pi\)
0.660540 + 0.750791i \(0.270328\pi\)
\(608\) 54.2489 2.20008
\(609\) 1.37362i 0.0556620i
\(610\) −42.4642 −1.71933
\(611\) 4.31411 0.622983i 0.174530 0.0252032i
\(612\) −9.32019 −0.376746
\(613\) 17.8597i 0.721348i 0.932692 + 0.360674i \(0.117453\pi\)
−0.932692 + 0.360674i \(0.882547\pi\)
\(614\) 4.61978 0.186439
\(615\) 2.93913 0.118517
\(616\) 2.13560i 0.0860458i
\(617\) 14.9164i 0.600511i 0.953859 + 0.300255i \(0.0970719\pi\)
−0.953859 + 0.300255i \(0.902928\pi\)
\(618\) 4.70394i 0.189220i
\(619\) 12.1473i 0.488242i 0.969745 + 0.244121i \(0.0784994\pi\)
−0.969745 + 0.244121i \(0.921501\pi\)
\(620\) 2.76237 0.110939
\(621\) −2.27614 −0.0913383
\(622\) 36.8292i 1.47671i
\(623\) 4.96971 0.199107
\(624\) −0.789816 5.46941i −0.0316179 0.218952i
\(625\) −11.8039 −0.472155
\(626\) 33.5934i 1.34266i
\(627\) 9.97009 0.398167
\(628\) −15.5975 −0.622410
\(629\) 9.61872i 0.383523i
\(630\) 6.26853i 0.249744i
\(631\) 18.8097i 0.748800i 0.927267 + 0.374400i \(0.122151\pi\)
−0.927267 + 0.374400i \(0.877849\pi\)
\(632\) 6.79696i 0.270369i
\(633\) 0.0704793 0.00280130
\(634\) 3.84281 0.152617
\(635\) 36.7073i 1.45669i
\(636\) 0.216206 0.00857313
\(637\) −3.38792 23.4611i −0.134234 0.929562i
\(638\) −49.0404 −1.94153
\(639\) 18.8999i 0.747667i
\(640\) −11.1293 −0.439925
\(641\) −2.35909 −0.0931783 −0.0465892 0.998914i \(-0.514835\pi\)
−0.0465892 + 0.998914i \(0.514835\pi\)
\(642\) 9.03802i 0.356702i
\(643\) 17.9916i 0.709518i 0.934958 + 0.354759i \(0.115437\pi\)
−0.934958 + 0.354759i \(0.884563\pi\)
\(644\) 1.20744i 0.0475800i
\(645\) 1.40750i 0.0554204i
\(646\) 29.1488 1.14684
\(647\) −43.8760 −1.72494 −0.862472 0.506105i \(-0.831085\pi\)
−0.862472 + 0.506105i \(0.831085\pi\)
\(648\) 6.51513i 0.255938i
\(649\) 41.4595 1.62743
\(650\) −12.8793 + 1.85984i −0.505167 + 0.0729491i
\(651\) −0.213941 −0.00838500
\(652\) 14.5116i 0.568319i
\(653\) −0.256698 −0.0100454 −0.00502269 0.999987i \(-0.501599\pi\)
−0.00502269 + 0.999987i \(0.501599\pi\)
\(654\) 2.79982 0.109482
\(655\) 15.2052i 0.594118i
\(656\) 23.8264i 0.930265i
\(657\) 0.491754i 0.0191851i
\(658\) 1.49041i 0.0581023i
\(659\) 8.42299 0.328113 0.164056 0.986451i \(-0.447542\pi\)
0.164056 + 0.986451i \(0.447542\pi\)
\(660\) 3.66143 0.142521
\(661\) 11.7394i 0.456609i 0.973590 + 0.228304i \(0.0733181\pi\)
−0.973590 + 0.228304i \(0.926682\pi\)
\(662\) 35.0956 1.36403
\(663\) −0.346542 2.39978i −0.0134586 0.0931996i
\(664\) −10.6601 −0.413692
\(665\) 8.62601i 0.334502i
\(666\) −25.6407 −0.993556
\(667\) −7.56255 −0.292823
\(668\) 28.6666i 1.10914i
\(669\) 2.47559i 0.0957120i
\(670\) 38.3151i 1.48024i
\(671\) 51.6619i 1.99439i
\(672\) −1.54296 −0.0595211
\(673\) −17.2708 −0.665742 −0.332871 0.942972i \(-0.608017\pi\)
−0.332871 + 0.942972i \(0.608017\pi\)
\(674\) 62.8410i 2.42055i
\(675\) 3.69051 0.142048
\(676\) 19.5936 5.77939i 0.753600 0.222284i
\(677\) 14.1990 0.545713 0.272857 0.962055i \(-0.412032\pi\)
0.272857 + 0.962055i \(0.412032\pi\)
\(678\) 7.62910i 0.292994i
\(679\) −12.3912 −0.475531
\(680\) −2.91971 −0.111966
\(681\) 5.76574i 0.220943i
\(682\) 7.63802i 0.292475i
\(683\) 10.1038i 0.386611i 0.981139 + 0.193305i \(0.0619208\pi\)
−0.981139 + 0.193305i \(0.938079\pi\)
\(684\) 34.1886i 1.30723i
\(685\) 25.8631 0.988179
\(686\) −16.7350 −0.638947
\(687\) 0.814437i 0.0310727i
\(688\) −11.4101 −0.435006
\(689\) −0.216196 1.49714i −0.00823643 0.0570366i
\(690\) 1.28327 0.0488531
\(691\) 9.41120i 0.358019i 0.983847 + 0.179009i \(0.0572893\pi\)
−0.983847 + 0.179009i \(0.942711\pi\)
\(692\) 0.0908006 0.00345172
\(693\) 7.62629 0.289699
\(694\) 39.6279i 1.50426i
\(695\) 27.2663i 1.03427i
\(696\) 1.70551i 0.0646471i
\(697\) 10.4542i 0.395979i
\(698\) 57.6082 2.18050
\(699\) 0.567894 0.0214797
\(700\) 1.95774i 0.0739955i
\(701\) −22.3912 −0.845703 −0.422852 0.906199i \(-0.638971\pi\)
−0.422852 + 0.906199i \(0.638971\pi\)
\(702\) −13.0321 + 1.88191i −0.491863 + 0.0710280i
\(703\) 35.2837 1.33075
\(704\) 17.3086i 0.652342i
\(705\) 0.696954 0.0262488
\(706\) −19.9987 −0.752662
\(707\) 8.48011i 0.318927i
\(708\) 5.28636i 0.198673i
\(709\) 20.3716i 0.765072i 0.923941 + 0.382536i \(0.124949\pi\)
−0.923941 + 0.382536i \(0.875051\pi\)
\(710\) 21.7074i 0.814663i
\(711\) −24.2721 −0.910276
\(712\) 6.17047 0.231248
\(713\) 1.17786i 0.0441113i
\(714\) −0.829059 −0.0310268
\(715\) −3.66127 25.3540i −0.136924 0.948187i
\(716\) −19.6125 −0.732953
\(717\) 0.462259i 0.0172634i
\(718\) 41.2342 1.53885
\(719\) 14.9478 0.557459 0.278730 0.960370i \(-0.410087\pi\)
0.278730 + 0.960370i \(0.410087\pi\)
\(720\) 23.7631i 0.885599i
\(721\) 4.95131i 0.184396i
\(722\) 71.0181i 2.64302i
\(723\) 0.114314i 0.00425138i
\(724\) −15.6300 −0.580883
\(725\) 12.2618 0.455393
\(726\) 3.30655i 0.122717i
\(727\) 27.0908 1.00474 0.502372 0.864652i \(-0.332461\pi\)
0.502372 + 0.864652i \(0.332461\pi\)
\(728\) 0.272291 + 1.88559i 0.0100918 + 0.0698848i
\(729\) −21.3645 −0.791277
\(730\) 0.564802i 0.0209043i
\(731\) −5.00633 −0.185166
\(732\) −6.58724 −0.243471
\(733\) 16.9857i 0.627382i 0.949525 + 0.313691i \(0.101566\pi\)
−0.949525 + 0.313691i \(0.898434\pi\)
\(734\) 38.0894i 1.40591i
\(735\) 3.79019i 0.139803i
\(736\) 8.49487i 0.313125i
\(737\) −46.6141 −1.71705
\(738\) −27.8677 −1.02582
\(739\) 4.03178i 0.148311i 0.997247 + 0.0741557i \(0.0236262\pi\)
−0.997247 + 0.0741557i \(0.976374\pi\)
\(740\) 12.9576 0.476332
\(741\) 8.80293 1.27120i 0.323384 0.0466985i
\(742\) −0.517224 −0.0189879
\(743\) 5.56680i 0.204226i −0.994773 0.102113i \(-0.967440\pi\)
0.994773 0.102113i \(-0.0325603\pi\)
\(744\) −0.265632 −0.00973854
\(745\) −3.44892 −0.126359
\(746\) 54.9294i 2.01111i
\(747\) 38.0675i 1.39282i
\(748\) 13.0233i 0.476179i
\(749\) 9.51332i 0.347609i
\(750\) −7.52811 −0.274888
\(751\) −2.33856 −0.0853354 −0.0426677 0.999089i \(-0.513586\pi\)
−0.0426677 + 0.999089i \(0.513586\pi\)
\(752\) 5.64994i 0.206032i
\(753\) 2.47424 0.0901662
\(754\) −43.2995 + 6.25270i −1.57687 + 0.227710i
\(755\) 5.38996 0.196161
\(756\) 1.98096i 0.0720469i
\(757\) 8.27850 0.300887 0.150444 0.988619i \(-0.451930\pi\)
0.150444 + 0.988619i \(0.451930\pi\)
\(758\) −23.6198 −0.857909
\(759\) 1.56122i 0.0566687i
\(760\) 10.7102i 0.388499i
\(761\) 26.7917i 0.971199i 0.874181 + 0.485600i \(0.161399\pi\)
−0.874181 + 0.485600i \(0.838601\pi\)
\(762\) 12.9415i 0.468822i
\(763\) −2.94706 −0.106691
\(764\) 41.4108 1.49819
\(765\) 10.4264i 0.376966i
\(766\) −10.7554 −0.388610
\(767\) 36.6060 5.28612i 1.32177 0.190871i
\(768\) −6.73266 −0.242944
\(769\) 43.5055i 1.56885i 0.620224 + 0.784425i \(0.287042\pi\)
−0.620224 + 0.784425i \(0.712958\pi\)
\(770\) −8.75915 −0.315658
\(771\) 7.34298 0.264451
\(772\) 1.48073i 0.0532926i
\(773\) 34.3969i 1.23717i −0.785718 0.618585i \(-0.787706\pi\)
0.785718 0.618585i \(-0.212294\pi\)
\(774\) 13.3454i 0.479690i
\(775\) 1.90978i 0.0686012i
\(776\) −15.3851 −0.552293
\(777\) −1.00355 −0.0360021
\(778\) 44.4363i 1.59312i
\(779\) 38.3482 1.37397
\(780\) 3.23281 0.466836i 0.115753 0.0167154i
\(781\) 26.4092 0.944994
\(782\) 4.56443i