Properties

Label 403.2.c.b.311.1
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 311.1
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.32

$q$-expansion

\(f(q)\) \(=\) \(q-2.71381i q^{2} +0.265781 q^{3} -5.36475 q^{4} +0.954130i q^{5} -0.721280i q^{6} +4.28452i q^{7} +9.13130i q^{8} -2.92936 q^{9} +O(q^{10})\) \(q-2.71381i q^{2} +0.265781 q^{3} -5.36475 q^{4} +0.954130i q^{5} -0.721280i q^{6} +4.28452i q^{7} +9.13130i q^{8} -2.92936 q^{9} +2.58933 q^{10} +0.0225126i q^{11} -1.42585 q^{12} +(0.755896 + 3.52543i) q^{13} +11.6274 q^{14} +0.253590i q^{15} +14.0511 q^{16} -4.73883 q^{17} +7.94972i q^{18} -1.51732i q^{19} -5.11868i q^{20} +1.13875i q^{21} +0.0610950 q^{22} -7.63808 q^{23} +2.42693i q^{24} +4.08964 q^{25} +(9.56733 - 2.05136i) q^{26} -1.57591 q^{27} -22.9854i q^{28} -2.41622 q^{29} +0.688195 q^{30} +1.00000i q^{31} -19.8694i q^{32} +0.00598344i q^{33} +12.8603i q^{34} -4.08799 q^{35} +15.7153 q^{36} -2.46547i q^{37} -4.11771 q^{38} +(0.200903 + 0.936992i) q^{39} -8.71245 q^{40} +6.00514i q^{41} +3.09034 q^{42} +9.18930 q^{43} -0.120775i q^{44} -2.79499i q^{45} +20.7283i q^{46} -6.05875i q^{47} +3.73452 q^{48} -11.3571 q^{49} -11.0985i q^{50} -1.25949 q^{51} +(-4.05519 - 18.9130i) q^{52} -5.67923 q^{53} +4.27673i q^{54} -0.0214800 q^{55} -39.1232 q^{56} -0.403275i q^{57} +6.55717i q^{58} +8.26538i q^{59} -1.36045i q^{60} +9.28373 q^{61} +2.71381 q^{62} -12.5509i q^{63} -25.8194 q^{64} +(-3.36371 + 0.721223i) q^{65} +0.0162379 q^{66} +7.52898i q^{67} +25.4227 q^{68} -2.03006 q^{69} +11.0940i q^{70} -13.2469i q^{71} -26.7489i q^{72} +1.76582i q^{73} -6.69081 q^{74} +1.08695 q^{75} +8.14005i q^{76} -0.0964559 q^{77} +(2.54282 - 0.545212i) q^{78} +10.0714 q^{79} +13.4066i q^{80} +8.36923 q^{81} +16.2968 q^{82} +13.3518i q^{83} -6.10909i q^{84} -4.52146i q^{85} -24.9380i q^{86} -0.642187 q^{87} -0.205570 q^{88} +6.66565i q^{89} -7.58507 q^{90} +(-15.1048 + 3.23865i) q^{91} +40.9764 q^{92} +0.265781i q^{93} -16.4423 q^{94} +1.44772 q^{95} -5.28090i q^{96} +10.9110i q^{97} +30.8210i q^{98} -0.0659476i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.71381i 1.91895i −0.281790 0.959476i \(-0.590928\pi\)
0.281790 0.959476i \(-0.409072\pi\)
\(3\) 0.265781 0.153449 0.0767245 0.997052i \(-0.475554\pi\)
0.0767245 + 0.997052i \(0.475554\pi\)
\(4\) −5.36475 −2.68238
\(5\) 0.954130i 0.426700i 0.976976 + 0.213350i \(0.0684375\pi\)
−0.976976 + 0.213350i \(0.931563\pi\)
\(6\) 0.721280i 0.294461i
\(7\) 4.28452i 1.61940i 0.586847 + 0.809698i \(0.300369\pi\)
−0.586847 + 0.809698i \(0.699631\pi\)
\(8\) 9.13130i 3.22840i
\(9\) −2.92936 −0.976453
\(10\) 2.58933 0.818817
\(11\) 0.0225126i 0.00678782i 0.999994 + 0.00339391i \(0.00108032\pi\)
−0.999994 + 0.00339391i \(0.998920\pi\)
\(12\) −1.42585 −0.411608
\(13\) 0.755896 + 3.52543i 0.209648 + 0.977777i
\(14\) 11.6274 3.10754
\(15\) 0.253590i 0.0654767i
\(16\) 14.0511 3.51277
\(17\) −4.73883 −1.14933 −0.574667 0.818387i \(-0.694869\pi\)
−0.574667 + 0.818387i \(0.694869\pi\)
\(18\) 7.94972i 1.87377i
\(19\) 1.51732i 0.348097i −0.984737 0.174048i \(-0.944315\pi\)
0.984737 0.174048i \(-0.0556849\pi\)
\(20\) 5.11868i 1.14457i
\(21\) 1.13875i 0.248495i
\(22\) 0.0610950 0.0130255
\(23\) −7.63808 −1.59265 −0.796325 0.604869i \(-0.793226\pi\)
−0.796325 + 0.604869i \(0.793226\pi\)
\(24\) 2.42693i 0.495395i
\(25\) 4.08964 0.817927
\(26\) 9.56733 2.05136i 1.87631 0.402304i
\(27\) −1.57591 −0.303285
\(28\) 22.9854i 4.34383i
\(29\) −2.41622 −0.448681 −0.224341 0.974511i \(-0.572023\pi\)
−0.224341 + 0.974511i \(0.572023\pi\)
\(30\) 0.688195 0.125647
\(31\) 1.00000i 0.179605i
\(32\) 19.8694i 3.51244i
\(33\) 0.00598344i 0.00104158i
\(34\) 12.8603i 2.20552i
\(35\) −4.08799 −0.690996
\(36\) 15.7153 2.61922
\(37\) 2.46547i 0.405321i −0.979249 0.202660i \(-0.935041\pi\)
0.979249 0.202660i \(-0.0649587\pi\)
\(38\) −4.11771 −0.667981
\(39\) 0.200903 + 0.936992i 0.0321702 + 0.150039i
\(40\) −8.71245 −1.37756
\(41\) 6.00514i 0.937845i 0.883239 + 0.468922i \(0.155358\pi\)
−0.883239 + 0.468922i \(0.844642\pi\)
\(42\) 3.09034 0.476849
\(43\) 9.18930 1.40136 0.700678 0.713478i \(-0.252881\pi\)
0.700678 + 0.713478i \(0.252881\pi\)
\(44\) 0.120775i 0.0182075i
\(45\) 2.79499i 0.416653i
\(46\) 20.7283i 3.05622i
\(47\) 6.05875i 0.883759i −0.897074 0.441880i \(-0.854312\pi\)
0.897074 0.441880i \(-0.145688\pi\)
\(48\) 3.73452 0.539031
\(49\) −11.3571 −1.62244
\(50\) 11.0985i 1.56956i
\(51\) −1.25949 −0.176364
\(52\) −4.05519 18.9130i −0.562354 2.62277i
\(53\) −5.67923 −0.780103 −0.390051 0.920793i \(-0.627543\pi\)
−0.390051 + 0.920793i \(0.627543\pi\)
\(54\) 4.27673i 0.581989i
\(55\) −0.0214800 −0.00289636
\(56\) −39.1232 −5.22806
\(57\) 0.403275i 0.0534151i
\(58\) 6.55717i 0.860998i
\(59\) 8.26538i 1.07606i 0.842926 + 0.538030i \(0.180831\pi\)
−0.842926 + 0.538030i \(0.819169\pi\)
\(60\) 1.36045i 0.175633i
\(61\) 9.28373 1.18866 0.594330 0.804221i \(-0.297417\pi\)
0.594330 + 0.804221i \(0.297417\pi\)
\(62\) 2.71381 0.344654
\(63\) 12.5509i 1.58126i
\(64\) −25.8194 −3.22743
\(65\) −3.36371 + 0.721223i −0.417217 + 0.0894567i
\(66\) 0.0162379 0.00199875
\(67\) 7.52898i 0.919812i 0.887968 + 0.459906i \(0.152117\pi\)
−0.887968 + 0.459906i \(0.847883\pi\)
\(68\) 25.4227 3.08295
\(69\) −2.03006 −0.244391
\(70\) 11.0940i 1.32599i
\(71\) 13.2469i 1.57212i −0.618151 0.786060i \(-0.712118\pi\)
0.618151 0.786060i \(-0.287882\pi\)
\(72\) 26.7489i 3.15238i
\(73\) 1.76582i 0.206673i 0.994646 + 0.103337i \(0.0329519\pi\)
−0.994646 + 0.103337i \(0.967048\pi\)
\(74\) −6.69081 −0.777791
\(75\) 1.08695 0.125510
\(76\) 8.14005i 0.933727i
\(77\) −0.0964559 −0.0109922
\(78\) 2.54282 0.545212i 0.287917 0.0617331i
\(79\) 10.0714 1.13312 0.566559 0.824021i \(-0.308274\pi\)
0.566559 + 0.824021i \(0.308274\pi\)
\(80\) 13.4066i 1.49890i
\(81\) 8.36923 0.929915
\(82\) 16.2968 1.79968
\(83\) 13.3518i 1.46555i 0.680469 + 0.732777i \(0.261776\pi\)
−0.680469 + 0.732777i \(0.738224\pi\)
\(84\) 6.10909i 0.666556i
\(85\) 4.52146i 0.490421i
\(86\) 24.9380i 2.68913i
\(87\) −0.642187 −0.0688497
\(88\) −0.205570 −0.0219138
\(89\) 6.66565i 0.706558i 0.935518 + 0.353279i \(0.114933\pi\)
−0.935518 + 0.353279i \(0.885067\pi\)
\(90\) −7.58507 −0.799537
\(91\) −15.1048 + 3.23865i −1.58341 + 0.339503i
\(92\) 40.9764 4.27209
\(93\) 0.265781i 0.0275602i
\(94\) −16.4423 −1.69589
\(95\) 1.44772 0.148533
\(96\) 5.28090i 0.538980i
\(97\) 10.9110i 1.10784i 0.832568 + 0.553922i \(0.186870\pi\)
−0.832568 + 0.553922i \(0.813130\pi\)
\(98\) 30.8210i 3.11339i
\(99\) 0.0659476i 0.00662799i
\(100\) −21.9399 −2.19399
\(101\) 14.9766 1.49022 0.745111 0.666940i \(-0.232396\pi\)
0.745111 + 0.666940i \(0.232396\pi\)
\(102\) 3.41802i 0.338435i
\(103\) −15.9516 −1.57176 −0.785880 0.618379i \(-0.787790\pi\)
−0.785880 + 0.618379i \(0.787790\pi\)
\(104\) −32.1917 + 6.90231i −3.15666 + 0.676827i
\(105\) −1.08651 −0.106033
\(106\) 15.4124i 1.49698i
\(107\) 0.382486 0.0369763 0.0184882 0.999829i \(-0.494115\pi\)
0.0184882 + 0.999829i \(0.494115\pi\)
\(108\) 8.45439 0.813524
\(109\) 1.44742i 0.138638i 0.997595 + 0.0693188i \(0.0220826\pi\)
−0.997595 + 0.0693188i \(0.977917\pi\)
\(110\) 0.0582926i 0.00555798i
\(111\) 0.655276i 0.0621960i
\(112\) 60.2021i 5.68857i
\(113\) −3.43980 −0.323589 −0.161795 0.986824i \(-0.551728\pi\)
−0.161795 + 0.986824i \(0.551728\pi\)
\(114\) −1.09441 −0.102501
\(115\) 7.28773i 0.679584i
\(116\) 12.9624 1.20353
\(117\) −2.21429 10.3272i −0.204711 0.954754i
\(118\) 22.4306 2.06491
\(119\) 20.3036i 1.86123i
\(120\) −2.31561 −0.211385
\(121\) 10.9995 0.999954
\(122\) 25.1943i 2.28098i
\(123\) 1.59605i 0.143911i
\(124\) 5.36475i 0.481769i
\(125\) 8.67270i 0.775710i
\(126\) −34.0607 −3.03437
\(127\) −16.2398 −1.44105 −0.720525 0.693429i \(-0.756099\pi\)
−0.720525 + 0.693429i \(0.756099\pi\)
\(128\) 30.3303i 2.68085i
\(129\) 2.44235 0.215036
\(130\) 1.95726 + 9.12848i 0.171663 + 0.800620i
\(131\) −4.33413 −0.378675 −0.189338 0.981912i \(-0.560634\pi\)
−0.189338 + 0.981912i \(0.560634\pi\)
\(132\) 0.0320997i 0.00279392i
\(133\) 6.50098 0.563707
\(134\) 20.4322 1.76507
\(135\) 1.50363i 0.129412i
\(136\) 43.2717i 3.71051i
\(137\) 5.03448i 0.430124i 0.976600 + 0.215062i \(0.0689954\pi\)
−0.976600 + 0.215062i \(0.931005\pi\)
\(138\) 5.50919i 0.468974i
\(139\) −6.21851 −0.527447 −0.263724 0.964598i \(-0.584951\pi\)
−0.263724 + 0.964598i \(0.584951\pi\)
\(140\) 21.9311 1.85351
\(141\) 1.61030i 0.135612i
\(142\) −35.9496 −3.01682
\(143\) −0.0793666 + 0.0170172i −0.00663697 + 0.00142305i
\(144\) −41.1607 −3.43006
\(145\) 2.30539i 0.191452i
\(146\) 4.79209 0.396596
\(147\) −3.01851 −0.248962
\(148\) 13.2266i 1.08722i
\(149\) 16.2180i 1.32863i −0.747451 0.664317i \(-0.768722\pi\)
0.747451 0.664317i \(-0.231278\pi\)
\(150\) 2.94977i 0.240848i
\(151\) 12.8028i 1.04187i 0.853595 + 0.520937i \(0.174417\pi\)
−0.853595 + 0.520937i \(0.825583\pi\)
\(152\) 13.8551 1.12380
\(153\) 13.8817 1.12227
\(154\) 0.261763i 0.0210934i
\(155\) −0.954130 −0.0766376
\(156\) −1.07780 5.02673i −0.0862927 0.402461i
\(157\) −6.29883 −0.502701 −0.251351 0.967896i \(-0.580875\pi\)
−0.251351 + 0.967896i \(0.580875\pi\)
\(158\) 27.3318i 2.17440i
\(159\) −1.50943 −0.119706
\(160\) 18.9580 1.49876
\(161\) 32.7255i 2.57913i
\(162\) 22.7125i 1.78446i
\(163\) 17.1448i 1.34288i −0.741058 0.671441i \(-0.765675\pi\)
0.741058 0.671441i \(-0.234325\pi\)
\(164\) 32.2161i 2.51565i
\(165\) −0.00570898 −0.000444444
\(166\) 36.2343 2.81233
\(167\) 1.18249i 0.0915038i 0.998953 + 0.0457519i \(0.0145684\pi\)
−0.998953 + 0.0457519i \(0.985432\pi\)
\(168\) −10.3982 −0.802241
\(169\) −11.8572 + 5.32971i −0.912096 + 0.409977i
\(170\) −12.2704 −0.941095
\(171\) 4.44478i 0.339900i
\(172\) −49.2983 −3.75896
\(173\) 24.0917 1.83166 0.915828 0.401571i \(-0.131536\pi\)
0.915828 + 0.401571i \(0.131536\pi\)
\(174\) 1.74277i 0.132119i
\(175\) 17.5221i 1.32455i
\(176\) 0.316327i 0.0238441i
\(177\) 2.19678i 0.165120i
\(178\) 18.0893 1.35585
\(179\) −15.1454 −1.13202 −0.566009 0.824399i \(-0.691513\pi\)
−0.566009 + 0.824399i \(0.691513\pi\)
\(180\) 14.9944i 1.11762i
\(181\) 6.94767 0.516416 0.258208 0.966089i \(-0.416868\pi\)
0.258208 + 0.966089i \(0.416868\pi\)
\(182\) 8.78907 + 40.9914i 0.651489 + 3.03848i
\(183\) 2.46744 0.182399
\(184\) 69.7456i 5.14172i
\(185\) 2.35238 0.172950
\(186\) 0.721280 0.0528868
\(187\) 0.106684i 0.00780148i
\(188\) 32.5037i 2.37058i
\(189\) 6.75203i 0.491138i
\(190\) 3.92884i 0.285028i
\(191\) 0.202104 0.0146237 0.00731187 0.999973i \(-0.497673\pi\)
0.00731187 + 0.999973i \(0.497673\pi\)
\(192\) −6.86233 −0.495246
\(193\) 2.83360i 0.203967i 0.994786 + 0.101983i \(0.0325189\pi\)
−0.994786 + 0.101983i \(0.967481\pi\)
\(194\) 29.6104 2.12590
\(195\) −0.894013 + 0.191688i −0.0640216 + 0.0137270i
\(196\) 60.9281 4.35201
\(197\) 17.4170i 1.24091i 0.784241 + 0.620456i \(0.213053\pi\)
−0.784241 + 0.620456i \(0.786947\pi\)
\(198\) −0.178969 −0.0127188
\(199\) 0.880069 0.0623865 0.0311932 0.999513i \(-0.490069\pi\)
0.0311932 + 0.999513i \(0.490069\pi\)
\(200\) 37.3437i 2.64060i
\(201\) 2.00106i 0.141144i
\(202\) 40.6435i 2.85967i
\(203\) 10.3524i 0.726593i
\(204\) 6.75687 0.473075
\(205\) −5.72968 −0.400178
\(206\) 43.2897i 3.01613i
\(207\) 22.3747 1.55515
\(208\) 10.6212 + 49.5360i 0.736444 + 3.43471i
\(209\) 0.0341589 0.00236282
\(210\) 2.94858i 0.203472i
\(211\) −5.82491 −0.401003 −0.200502 0.979693i \(-0.564257\pi\)
−0.200502 + 0.979693i \(0.564257\pi\)
\(212\) 30.4677 2.09253
\(213\) 3.52078i 0.241240i
\(214\) 1.03799i 0.0709558i
\(215\) 8.76779i 0.597958i
\(216\) 14.3901i 0.979125i
\(217\) −4.28452 −0.290852
\(218\) 3.92802 0.266039
\(219\) 0.469321i 0.0317138i
\(220\) 0.115235 0.00776914
\(221\) −3.58206 16.7064i −0.240955 1.12379i
\(222\) −1.77829 −0.119351
\(223\) 13.5018i 0.904151i −0.891980 0.452075i \(-0.850684\pi\)
0.891980 0.452075i \(-0.149316\pi\)
\(224\) 85.1306 5.68803
\(225\) −11.9800 −0.798668
\(226\) 9.33496i 0.620952i
\(227\) 12.9771i 0.861322i 0.902514 + 0.430661i \(0.141720\pi\)
−0.902514 + 0.430661i \(0.858280\pi\)
\(228\) 2.16347i 0.143280i
\(229\) 20.8066i 1.37494i −0.726212 0.687470i \(-0.758721\pi\)
0.726212 0.687470i \(-0.241279\pi\)
\(230\) −19.7775 −1.30409
\(231\) −0.0256362 −0.00168674
\(232\) 22.0633i 1.44852i
\(233\) 14.1051 0.924057 0.462028 0.886865i \(-0.347122\pi\)
0.462028 + 0.886865i \(0.347122\pi\)
\(234\) −28.0261 + 6.00916i −1.83213 + 0.392831i
\(235\) 5.78083 0.377100
\(236\) 44.3417i 2.88640i
\(237\) 2.67678 0.173876
\(238\) −55.1001 −3.57161
\(239\) 23.8483i 1.54262i −0.636459 0.771310i \(-0.719602\pi\)
0.636459 0.771310i \(-0.280398\pi\)
\(240\) 3.56322i 0.230005i
\(241\) 16.4903i 1.06224i −0.847298 0.531118i \(-0.821772\pi\)
0.847298 0.531118i \(-0.178228\pi\)
\(242\) 29.8505i 1.91886i
\(243\) 6.95213 0.445979
\(244\) −49.8049 −3.18843
\(245\) 10.8362i 0.692297i
\(246\) 4.33138 0.276159
\(247\) 5.34920 1.14694i 0.340361 0.0729777i
\(248\) −9.13130 −0.579838
\(249\) 3.54867i 0.224888i
\(250\) 23.5360 1.48855
\(251\) −9.32651 −0.588684 −0.294342 0.955700i \(-0.595100\pi\)
−0.294342 + 0.955700i \(0.595100\pi\)
\(252\) 67.3325i 4.24155i
\(253\) 0.171953i 0.0108106i
\(254\) 44.0717i 2.76531i
\(255\) 1.20172i 0.0752546i
\(256\) 30.6717 1.91698
\(257\) 21.1698 1.32054 0.660269 0.751029i \(-0.270442\pi\)
0.660269 + 0.751029i \(0.270442\pi\)
\(258\) 6.62806i 0.412645i
\(259\) 10.5633 0.656375
\(260\) 18.0455 3.86918i 1.11913 0.239957i
\(261\) 7.07799 0.438116
\(262\) 11.7620i 0.726659i
\(263\) −15.0683 −0.929150 −0.464575 0.885534i \(-0.653793\pi\)
−0.464575 + 0.885534i \(0.653793\pi\)
\(264\) −0.0546366 −0.00336265
\(265\) 5.41873i 0.332870i
\(266\) 17.6424i 1.08173i
\(267\) 1.77161i 0.108421i
\(268\) 40.3912i 2.46728i
\(269\) −3.39090 −0.206747 −0.103373 0.994643i \(-0.532964\pi\)
−0.103373 + 0.994643i \(0.532964\pi\)
\(270\) −4.08056 −0.248335
\(271\) 21.0667i 1.27971i 0.768494 + 0.639857i \(0.221006\pi\)
−0.768494 + 0.639857i \(0.778994\pi\)
\(272\) −66.5857 −4.03735
\(273\) −4.01456 + 0.860773i −0.242972 + 0.0520963i
\(274\) 13.6626 0.825388
\(275\) 0.0920685i 0.00555194i
\(276\) 10.8908 0.655548
\(277\) −2.38224 −0.143135 −0.0715675 0.997436i \(-0.522800\pi\)
−0.0715675 + 0.997436i \(0.522800\pi\)
\(278\) 16.8758i 1.01215i
\(279\) 2.92936i 0.175376i
\(280\) 37.3287i 2.23081i
\(281\) 6.89508i 0.411326i 0.978623 + 0.205663i \(0.0659350\pi\)
−0.978623 + 0.205663i \(0.934065\pi\)
\(282\) −4.37005 −0.260233
\(283\) 8.31358 0.494191 0.247095 0.968991i \(-0.420524\pi\)
0.247095 + 0.968991i \(0.420524\pi\)
\(284\) 71.0664i 4.21702i
\(285\) 0.384777 0.0227922
\(286\) 0.0461814 + 0.215386i 0.00273077 + 0.0127360i
\(287\) −25.7291 −1.51874
\(288\) 58.2045i 3.42973i
\(289\) 5.45650 0.320971
\(290\) −6.25639 −0.367388
\(291\) 2.89994i 0.169998i
\(292\) 9.47317i 0.554375i
\(293\) 8.52889i 0.498263i −0.968470 0.249132i \(-0.919855\pi\)
0.968470 0.249132i \(-0.0801451\pi\)
\(294\) 8.19165i 0.477747i
\(295\) −7.88625 −0.459155
\(296\) 22.5129 1.30854
\(297\) 0.0354780i 0.00205864i
\(298\) −44.0127 −2.54959
\(299\) −5.77359 26.9275i −0.333895 1.55726i
\(300\) −5.83122 −0.336665
\(301\) 39.3717i 2.26935i
\(302\) 34.7442 1.99931
\(303\) 3.98049 0.228673
\(304\) 21.3200i 1.22279i
\(305\) 8.85789i 0.507201i
\(306\) 37.6724i 2.15359i
\(307\) 27.0437i 1.54346i 0.635949 + 0.771731i \(0.280609\pi\)
−0.635949 + 0.771731i \(0.719391\pi\)
\(308\) 0.517462 0.0294851
\(309\) −4.23965 −0.241185
\(310\) 2.58933i 0.147064i
\(311\) 13.0421 0.739547 0.369773 0.929122i \(-0.379435\pi\)
0.369773 + 0.929122i \(0.379435\pi\)
\(312\) −8.55596 + 1.83451i −0.484386 + 0.103858i
\(313\) 8.35791 0.472417 0.236208 0.971702i \(-0.424095\pi\)
0.236208 + 0.971702i \(0.424095\pi\)
\(314\) 17.0938i 0.964660i
\(315\) 11.9752 0.674726
\(316\) −54.0304 −3.03945
\(317\) 17.9533i 1.00836i 0.863599 + 0.504180i \(0.168205\pi\)
−0.863599 + 0.504180i \(0.831795\pi\)
\(318\) 4.09632i 0.229710i
\(319\) 0.0543956i 0.00304557i
\(320\) 24.6351i 1.37714i
\(321\) 0.101658 0.00567398
\(322\) −88.8108 −4.94923
\(323\) 7.19032i 0.400080i
\(324\) −44.8989 −2.49438
\(325\) 3.09134 + 14.4177i 0.171477 + 0.799750i
\(326\) −46.5277 −2.57693
\(327\) 0.384697i 0.0212738i
\(328\) −54.8347 −3.02774
\(329\) 25.9588 1.43116
\(330\) 0.0154931i 0.000852866i
\(331\) 21.7321i 1.19450i 0.802054 + 0.597252i \(0.203741\pi\)
−0.802054 + 0.597252i \(0.796259\pi\)
\(332\) 71.6293i 3.93117i
\(333\) 7.22225i 0.395777i
\(334\) 3.20905 0.175591
\(335\) −7.18363 −0.392484
\(336\) 16.0006i 0.872905i
\(337\) 35.0375 1.90862 0.954308 0.298824i \(-0.0965945\pi\)
0.954308 + 0.298824i \(0.0965945\pi\)
\(338\) 14.4638 + 32.1783i 0.786727 + 1.75027i
\(339\) −0.914235 −0.0496544
\(340\) 24.2565i 1.31549i
\(341\) −0.0225126 −0.00121913
\(342\) 12.0623 0.652253
\(343\) 18.6681i 1.00798i
\(344\) 83.9102i 4.52414i
\(345\) 1.93694i 0.104281i
\(346\) 65.3802i 3.51486i
\(347\) −25.4611 −1.36682 −0.683412 0.730033i \(-0.739504\pi\)
−0.683412 + 0.730033i \(0.739504\pi\)
\(348\) 3.44518 0.184681
\(349\) 17.4958i 0.936531i 0.883588 + 0.468265i \(0.155121\pi\)
−0.883588 + 0.468265i \(0.844879\pi\)
\(350\) 47.5517 2.54174
\(351\) −1.19123 5.55577i −0.0635829 0.296545i
\(352\) 0.447312 0.0238418
\(353\) 32.1393i 1.71060i 0.518132 + 0.855301i \(0.326628\pi\)
−0.518132 + 0.855301i \(0.673372\pi\)
\(354\) 5.96165 0.316858
\(355\) 12.6393 0.670823
\(356\) 35.7596i 1.89525i
\(357\) 5.39632i 0.285604i
\(358\) 41.1016i 2.17229i
\(359\) 11.0850i 0.585042i 0.956259 + 0.292521i \(0.0944941\pi\)
−0.956259 + 0.292521i \(0.905506\pi\)
\(360\) 25.5219 1.34512
\(361\) 16.6977 0.878829
\(362\) 18.8546i 0.990978i
\(363\) 2.92346 0.153442
\(364\) 81.0333 17.3746i 4.24730 0.910674i
\(365\) −1.68482 −0.0881874
\(366\) 6.69617i 0.350014i
\(367\) −9.66148 −0.504325 −0.252163 0.967685i \(-0.581142\pi\)
−0.252163 + 0.967685i \(0.581142\pi\)
\(368\) −107.323 −5.59462
\(369\) 17.5912i 0.915762i
\(370\) 6.38390i 0.331883i
\(371\) 24.3328i 1.26330i
\(372\) 1.42585i 0.0739270i
\(373\) −21.0438 −1.08961 −0.544804 0.838564i \(-0.683396\pi\)
−0.544804 + 0.838564i \(0.683396\pi\)
\(374\) −0.289519 −0.0149707
\(375\) 2.30504i 0.119032i
\(376\) 55.3242 2.85313
\(377\) −1.82641 8.51821i −0.0940650 0.438710i
\(378\) −18.3237 −0.942471
\(379\) 4.22803i 0.217179i −0.994087 0.108590i \(-0.965367\pi\)
0.994087 0.108590i \(-0.0346334\pi\)
\(380\) −7.76667 −0.398422
\(381\) −4.31624 −0.221128
\(382\) 0.548472i 0.0280623i
\(383\) 2.50461i 0.127979i −0.997951 0.0639897i \(-0.979618\pi\)
0.997951 0.0639897i \(-0.0203825\pi\)
\(384\) 8.06123i 0.411373i
\(385\) 0.0920315i 0.00469036i
\(386\) 7.68984 0.391403
\(387\) −26.9188 −1.36836
\(388\) 58.5349i 2.97166i
\(389\) 11.6085 0.588575 0.294288 0.955717i \(-0.404918\pi\)
0.294288 + 0.955717i \(0.404918\pi\)
\(390\) 0.520203 + 2.42618i 0.0263415 + 0.122854i
\(391\) 36.1956 1.83049
\(392\) 103.705i 5.23790i
\(393\) −1.15193 −0.0581073
\(394\) 47.2665 2.38125
\(395\) 9.60940i 0.483501i
\(396\) 0.353793i 0.0177788i
\(397\) 9.50682i 0.477134i 0.971126 + 0.238567i \(0.0766776\pi\)
−0.971126 + 0.238567i \(0.923322\pi\)
\(398\) 2.38834i 0.119717i
\(399\) 1.72784 0.0865002
\(400\) 57.4638 2.87319
\(401\) 30.7755i 1.53685i 0.639937 + 0.768427i \(0.278960\pi\)
−0.639937 + 0.768427i \(0.721040\pi\)
\(402\) 5.43050 0.270849
\(403\) −3.52543 + 0.755896i −0.175614 + 0.0376538i
\(404\) −80.3456 −3.99734
\(405\) 7.98534i 0.396795i
\(406\) −28.0943 −1.39430
\(407\) 0.0555042 0.00275124
\(408\) 11.5008i 0.569375i
\(409\) 13.7197i 0.678395i 0.940715 + 0.339197i \(0.110155\pi\)
−0.940715 + 0.339197i \(0.889845\pi\)
\(410\) 15.5493i 0.767923i
\(411\) 1.33807i 0.0660021i
\(412\) 85.5766 4.21606
\(413\) −35.4132 −1.74257
\(414\) 60.7206i 2.98426i
\(415\) −12.7394 −0.625352
\(416\) 70.0479 15.0192i 3.43438 0.736375i
\(417\) −1.65276 −0.0809362
\(418\) 0.0927006i 0.00453414i
\(419\) 8.82161 0.430964 0.215482 0.976508i \(-0.430868\pi\)
0.215482 + 0.976508i \(0.430868\pi\)
\(420\) 5.82887 0.284420
\(421\) 9.49222i 0.462623i 0.972880 + 0.231311i \(0.0743016\pi\)
−0.972880 + 0.231311i \(0.925698\pi\)
\(422\) 15.8077i 0.769506i
\(423\) 17.7483i 0.862949i
\(424\) 51.8588i 2.51849i
\(425\) −19.3801 −0.940072
\(426\) −9.55473 −0.462928
\(427\) 39.7763i 1.92491i
\(428\) −2.05194 −0.0991845
\(429\) −0.0210942 + 0.00452286i −0.00101844 + 0.000218366i
\(430\) 23.7941 1.14745
\(431\) 24.5182i 1.18100i −0.807038 0.590499i \(-0.798931\pi\)
0.807038 0.590499i \(-0.201069\pi\)
\(432\) −22.1433 −1.06537
\(433\) 24.3795 1.17160 0.585801 0.810455i \(-0.300780\pi\)
0.585801 + 0.810455i \(0.300780\pi\)
\(434\) 11.6274i 0.558131i
\(435\) 0.612730i 0.0293782i
\(436\) 7.76505i 0.371878i
\(437\) 11.5894i 0.554397i
\(438\) 1.27365 0.0608572
\(439\) 6.37491 0.304258 0.152129 0.988361i \(-0.451387\pi\)
0.152129 + 0.988361i \(0.451387\pi\)
\(440\) 0.196140i 0.00935062i
\(441\) 33.2691 1.58424
\(442\) −45.3379 + 9.72102i −2.15651 + 0.462382i
\(443\) 20.4425 0.971252 0.485626 0.874167i \(-0.338592\pi\)
0.485626 + 0.874167i \(0.338592\pi\)
\(444\) 3.51539i 0.166833i
\(445\) −6.35990 −0.301488
\(446\) −36.6414 −1.73502
\(447\) 4.31045i 0.203878i
\(448\) 110.624i 5.22649i
\(449\) 0.809817i 0.0382176i −0.999817 0.0191088i \(-0.993917\pi\)
0.999817 0.0191088i \(-0.00608289\pi\)
\(450\) 32.5115i 1.53261i
\(451\) −0.135192 −0.00636592
\(452\) 18.4537 0.867988
\(453\) 3.40273i 0.159874i
\(454\) 35.2174 1.65284
\(455\) −3.09009 14.4119i −0.144866 0.675640i
\(456\) 3.68243 0.172445
\(457\) 3.62678i 0.169654i −0.996396 0.0848269i \(-0.972966\pi\)
0.996396 0.0848269i \(-0.0270337\pi\)
\(458\) −56.4652 −2.63845
\(459\) 7.46799 0.348576
\(460\) 39.0969i 1.82290i
\(461\) 31.7766i 1.47998i −0.672615 0.739992i \(-0.734829\pi\)
0.672615 0.739992i \(-0.265171\pi\)
\(462\) 0.0695717i 0.00323677i
\(463\) 7.74173i 0.359788i 0.983686 + 0.179894i \(0.0575756\pi\)
−0.983686 + 0.179894i \(0.942424\pi\)
\(464\) −33.9506 −1.57612
\(465\) −0.253590 −0.0117600
\(466\) 38.2786i 1.77322i
\(467\) −12.1610 −0.562746 −0.281373 0.959598i \(-0.590790\pi\)
−0.281373 + 0.959598i \(0.590790\pi\)
\(468\) 11.8791 + 55.4031i 0.549113 + 2.56101i
\(469\) −32.2581 −1.48954
\(470\) 15.6881i 0.723637i
\(471\) −1.67411 −0.0771390
\(472\) −75.4736 −3.47396
\(473\) 0.206875i 0.00951214i
\(474\) 7.26427i 0.333659i
\(475\) 6.20528i 0.284718i
\(476\) 108.924i 4.99252i
\(477\) 16.6365 0.761734
\(478\) −64.7198 −2.96022
\(479\) 15.1807i 0.693624i −0.937935 0.346812i \(-0.887264\pi\)
0.937935 0.346812i \(-0.112736\pi\)
\(480\) 5.03867 0.229983
\(481\) 8.69183 1.86364i 0.396313 0.0849745i
\(482\) −44.7516 −2.03838
\(483\) 8.69783i 0.395765i
\(484\) −59.0096 −2.68225
\(485\) −10.4105 −0.472717
\(486\) 18.8667i 0.855813i
\(487\) 12.5401i 0.568246i 0.958788 + 0.284123i \(0.0917024\pi\)
−0.958788 + 0.284123i \(0.908298\pi\)
\(488\) 84.7725i 3.83747i
\(489\) 4.55676i 0.206064i
\(490\) −29.4073 −1.32848
\(491\) −34.6948 −1.56576 −0.782878 0.622175i \(-0.786249\pi\)
−0.782878 + 0.622175i \(0.786249\pi\)
\(492\) 8.56244i 0.386024i
\(493\) 11.4501 0.515685
\(494\) −3.11256 14.5167i −0.140041 0.653137i
\(495\) 0.0629226 0.00282816
\(496\) 14.0511i 0.630912i
\(497\) 56.7567 2.54588
\(498\) 9.63041 0.431549
\(499\) 26.7370i 1.19691i −0.801156 0.598456i \(-0.795781\pi\)
0.801156 0.598456i \(-0.204219\pi\)
\(500\) 46.5269i 2.08075i
\(501\) 0.314284i 0.0140412i
\(502\) 25.3104i 1.12966i
\(503\) −4.00119 −0.178404 −0.0892021 0.996014i \(-0.528432\pi\)
−0.0892021 + 0.996014i \(0.528432\pi\)
\(504\) 114.606 5.10496
\(505\) 14.2896i 0.635878i
\(506\) −0.466649 −0.0207451
\(507\) −3.15143 + 1.41654i −0.139960 + 0.0629106i
\(508\) 87.1226 3.86544
\(509\) 20.2683i 0.898379i −0.893437 0.449189i \(-0.851713\pi\)
0.893437 0.449189i \(-0.148287\pi\)
\(510\) −3.26124 −0.144410
\(511\) −7.56567 −0.334686
\(512\) 22.5766i 0.997755i
\(513\) 2.39116i 0.105572i
\(514\) 57.4509i 2.53405i
\(515\) 15.2199i 0.670670i
\(516\) −13.1026 −0.576809
\(517\) 0.136398 0.00599880
\(518\) 28.6669i 1.25955i
\(519\) 6.40312 0.281066
\(520\) −6.58570 30.7151i −0.288802 1.34695i
\(521\) −14.2096 −0.622532 −0.311266 0.950323i \(-0.600753\pi\)
−0.311266 + 0.950323i \(0.600753\pi\)
\(522\) 19.2083i 0.840725i
\(523\) −4.58600 −0.200532 −0.100266 0.994961i \(-0.531969\pi\)
−0.100266 + 0.994961i \(0.531969\pi\)
\(524\) 23.2516 1.01575
\(525\) 4.65705i 0.203251i
\(526\) 40.8924i 1.78299i
\(527\) 4.73883i 0.206427i
\(528\) 0.0840739i 0.00365885i
\(529\) 35.3403 1.53654
\(530\) −14.7054 −0.638761
\(531\) 24.2123i 1.05072i
\(532\) −34.8762 −1.51207
\(533\) −21.1707 + 4.53926i −0.917003 + 0.196617i
\(534\) 4.80780 0.208054
\(535\) 0.364942i 0.0157778i
\(536\) −68.7494 −2.96952
\(537\) −4.02536 −0.173707
\(538\) 9.20225i 0.396737i
\(539\) 0.255678i 0.0110129i
\(540\) 8.06659i 0.347131i
\(541\) 9.43063i 0.405454i 0.979235 + 0.202727i \(0.0649805\pi\)
−0.979235 + 0.202727i \(0.935020\pi\)
\(542\) 57.1711 2.45571
\(543\) 1.84656 0.0792435
\(544\) 94.1575i 4.03697i
\(545\) −1.38103 −0.0591567
\(546\) 2.33597 + 10.8948i 0.0999704 + 0.466252i
\(547\) 33.3713 1.42686 0.713428 0.700729i \(-0.247142\pi\)
0.713428 + 0.700729i \(0.247142\pi\)
\(548\) 27.0087i 1.15376i
\(549\) −27.1954 −1.16067
\(550\) 0.249856 0.0106539
\(551\) 3.66618i 0.156185i
\(552\) 18.5371i 0.788991i
\(553\) 43.1510i 1.83497i
\(554\) 6.46494i 0.274669i
\(555\) 0.625218 0.0265390
\(556\) 33.3608 1.41481
\(557\) 27.1006i 1.14829i 0.818754 + 0.574144i \(0.194665\pi\)
−0.818754 + 0.574144i \(0.805335\pi\)
\(558\) −7.94972 −0.336539
\(559\) 6.94615 + 32.3962i 0.293791 + 1.37021i
\(560\) −57.4407 −2.42731
\(561\) 0.0283545i 0.00119713i
\(562\) 18.7119 0.789315
\(563\) 40.6775 1.71435 0.857176 0.515023i \(-0.172217\pi\)
0.857176 + 0.515023i \(0.172217\pi\)
\(564\) 8.63888i 0.363762i
\(565\) 3.28202i 0.138076i
\(566\) 22.5615i 0.948329i
\(567\) 35.8581i 1.50590i
\(568\) 120.962 5.07543
\(569\) 29.6678 1.24374 0.621870 0.783120i \(-0.286373\pi\)
0.621870 + 0.783120i \(0.286373\pi\)
\(570\) 1.04421i 0.0437372i
\(571\) −31.9473 −1.33695 −0.668476 0.743733i \(-0.733053\pi\)
−0.668476 + 0.743733i \(0.733053\pi\)
\(572\) 0.425783 0.0912932i 0.0178029 0.00381716i
\(573\) 0.0537155 0.00224400
\(574\) 69.8239i 2.91439i
\(575\) −31.2370 −1.30267
\(576\) 75.6344 3.15143
\(577\) 3.17220i 0.132061i 0.997818 + 0.0660303i \(0.0210334\pi\)
−0.997818 + 0.0660303i \(0.978967\pi\)
\(578\) 14.8079i 0.615927i
\(579\) 0.753118i 0.0312985i
\(580\) 12.3679i 0.513547i
\(581\) −57.2062 −2.37331
\(582\) 7.86988 0.326217
\(583\) 0.127855i 0.00529520i
\(584\) −16.1242 −0.667224
\(585\) 9.85353 2.11272i 0.407393 0.0873503i
\(586\) −23.1458 −0.956143
\(587\) 18.0414i 0.744650i −0.928102 0.372325i \(-0.878561\pi\)
0.928102 0.372325i \(-0.121439\pi\)
\(588\) 16.1936 0.667811
\(589\) 1.51732 0.0625201
\(590\) 21.4018i 0.881097i
\(591\) 4.62912i 0.190417i
\(592\) 34.6425i 1.42380i
\(593\) 4.22088i 0.173331i −0.996237 0.0866653i \(-0.972379\pi\)
0.996237 0.0866653i \(-0.0276211\pi\)
\(594\) −0.0962805 −0.00395043
\(595\) 19.3723 0.794186
\(596\) 87.0058i 3.56390i
\(597\) 0.233906 0.00957314
\(598\) −73.0760 + 15.6684i −2.98830 + 0.640729i
\(599\) 46.9779 1.91947 0.959733 0.280915i \(-0.0906380\pi\)
0.959733 + 0.280915i \(0.0906380\pi\)
\(600\) 9.92526i 0.405197i
\(601\) −32.9398 −1.34364 −0.671821 0.740713i \(-0.734488\pi\)
−0.671821 + 0.740713i \(0.734488\pi\)
\(602\) 106.847 4.35477
\(603\) 22.0551i 0.898153i
\(604\) 68.6837i 2.79470i
\(605\) 10.4949i 0.426680i
\(606\) 10.8023i 0.438813i
\(607\) −27.8658 −1.13104 −0.565518 0.824736i \(-0.691324\pi\)
−0.565518 + 0.824736i \(0.691324\pi\)
\(608\) −30.1482 −1.22267
\(609\) 2.75146i 0.111495i
\(610\) 24.0386 0.973295
\(611\) 21.3597 4.57978i 0.864119 0.185278i
\(612\) −74.4721 −3.01036
\(613\) 40.6326i 1.64114i −0.571548 0.820568i \(-0.693657\pi\)
0.571548 0.820568i \(-0.306343\pi\)
\(614\) 73.3913 2.96183
\(615\) −1.52284 −0.0614070
\(616\) 0.880767i 0.0354871i
\(617\) 14.7457i 0.593641i 0.954933 + 0.296820i \(0.0959263\pi\)
−0.954933 + 0.296820i \(0.904074\pi\)
\(618\) 11.5056i 0.462823i
\(619\) 0.164280i 0.00660296i −0.999995 0.00330148i \(-0.998949\pi\)
0.999995 0.00330148i \(-0.00105090\pi\)
\(620\) 5.11868 0.205571
\(621\) 12.0370 0.483027
\(622\) 35.3936i 1.41916i
\(623\) −28.5591 −1.14420
\(624\) 2.82290 + 13.1658i 0.113007 + 0.527052i
\(625\) 12.1733 0.486932
\(626\) 22.6818i 0.906545i
\(627\) 0.00907879 0.000362572
\(628\) 33.7917 1.34843
\(629\) 11.6834i 0.465849i
\(630\) 32.4984i 1.29477i
\(631\) 13.1950i 0.525284i −0.964893 0.262642i \(-0.915406\pi\)
0.964893 0.262642i \(-0.0845938\pi\)
\(632\) 91.9647i 3.65816i
\(633\) −1.54815 −0.0615336
\(634\) 48.7219 1.93499
\(635\) 15.4949i 0.614896i
\(636\) 8.09775 0.321097
\(637\) −8.58478 40.0386i −0.340142 1.58639i
\(638\) −0.147619 −0.00584430
\(639\) 38.8050i 1.53510i
\(640\) −28.9391 −1.14392
\(641\) −18.4650 −0.729324 −0.364662 0.931140i \(-0.618816\pi\)
−0.364662 + 0.931140i \(0.618816\pi\)
\(642\) 0.275880i 0.0108881i
\(643\) 26.0213i 1.02618i −0.858335 0.513090i \(-0.828501\pi\)
0.858335 0.513090i \(-0.171499\pi\)
\(644\) 175.564i 6.91820i
\(645\) 2.33032i 0.0917561i
\(646\) 19.5131 0.767734
\(647\) 2.83219 0.111345 0.0556724 0.998449i \(-0.482270\pi\)
0.0556724 + 0.998449i \(0.482270\pi\)
\(648\) 76.4220i 3.00214i
\(649\) −0.186076 −0.00730410
\(650\) 39.1269 8.38930i 1.53468 0.329055i
\(651\) −1.13875 −0.0446310
\(652\) 91.9776i 3.60212i
\(653\) −9.50505 −0.371961 −0.185981 0.982553i \(-0.559546\pi\)
−0.185981 + 0.982553i \(0.559546\pi\)
\(654\) 1.04399 0.0408234
\(655\) 4.13533i 0.161581i
\(656\) 84.3787i 3.29443i
\(657\) 5.17271i 0.201807i
\(658\) 70.4472i 2.74632i
\(659\) −5.62723 −0.219206 −0.109603 0.993975i \(-0.534958\pi\)
−0.109603 + 0.993975i \(0.534958\pi\)
\(660\) 0.0306273 0.00119217
\(661\) 39.1535i 1.52289i −0.648228 0.761447i \(-0.724489\pi\)
0.648228 0.761447i \(-0.275511\pi\)
\(662\) 58.9767 2.29219
\(663\) −0.952045 4.44025i −0.0369744 0.172445i
\(664\) −121.920 −4.73140
\(665\) 6.20279i 0.240534i
\(666\) 19.5998 0.759476
\(667\) 18.4553 0.714593
\(668\) 6.34376i 0.245448i
\(669\) 3.58854i 0.138741i
\(670\) 19.4950i 0.753158i
\(671\) 0.209001i 0.00806841i
\(672\) 22.6261 0.872822
\(673\) −28.2120 −1.08749 −0.543747 0.839249i \(-0.682995\pi\)
−0.543747 + 0.839249i \(0.682995\pi\)
\(674\) 95.0852i 3.66254i
\(675\) −6.44491 −0.248065
\(676\) 63.6112 28.5926i 2.44658 1.09971i
\(677\) 26.9041 1.03401 0.517004 0.855983i \(-0.327047\pi\)
0.517004 + 0.855983i \(0.327047\pi\)
\(678\) 2.48106i 0.0952845i
\(679\) −46.7484 −1.79404
\(680\) 41.2868 1.58328
\(681\) 3.44908i 0.132169i
\(682\) 0.0610950i 0.00233945i
\(683\) 0.580132i 0.0221981i −0.999938 0.0110991i \(-0.996467\pi\)
0.999938 0.0110991i \(-0.00353301\pi\)
\(684\) 23.8451i 0.911741i
\(685\) −4.80355 −0.183534
\(686\) −50.6616 −1.93427
\(687\) 5.53002i 0.210983i
\(688\) 129.120 4.92264
\(689\) −4.29291 20.0217i −0.163547 0.762767i
\(690\) −5.25649 −0.200111
\(691\) 25.1489i 0.956708i 0.878167 + 0.478354i \(0.158766\pi\)
−0.878167 + 0.478354i \(0.841234\pi\)
\(692\) −129.246 −4.91319
\(693\) 0.282554 0.0107333
\(694\) 69.0965i 2.62287i
\(695\) 5.93327i 0.225062i
\(696\) 5.86400i 0.222274i
\(697\) 28.4573i 1.07790i
\(698\) 47.4804 1.79716
\(699\) 3.74888 0.141796
\(700\) 94.0019i 3.55294i
\(701\) 14.5697 0.550289 0.275144 0.961403i \(-0.411274\pi\)
0.275144 + 0.961403i \(0.411274\pi\)
\(702\) −15.0773 + 3.23276i −0.569055 + 0.122013i
\(703\) −3.74090 −0.141091
\(704\) 0.581264i 0.0219072i
\(705\) 1.53644 0.0578656
\(706\) 87.2198 3.28256
\(707\) 64.1673i 2.41326i
\(708\) 11.7852i 0.442915i
\(709\) 16.7626i 0.629531i −0.949169 0.314766i \(-0.898074\pi\)
0.949169 0.314766i \(-0.101926\pi\)
\(710\) 34.3006i 1.28728i
\(711\) −29.5027 −1.10644
\(712\) −60.8661 −2.28105
\(713\) 7.63808i 0.286048i
\(714\) −14.6446 −0.548060
\(715\) −0.0162366 0.0757261i −0.000607216 0.00283200i
\(716\) 81.2512 3.03650
\(717\) 6.33845i 0.236714i
\(718\) 30.0825 1.12267
\(719\) −17.1883 −0.641016 −0.320508 0.947246i \(-0.603854\pi\)
−0.320508 + 0.947246i \(0.603854\pi\)
\(720\) 39.2727i 1.46361i
\(721\) 68.3451i 2.54530i
\(722\) 45.3145i 1.68643i
\(723\) 4.38282i 0.162999i
\(724\) −37.2726 −1.38522
\(725\) −9.88147 −0.366989
\(726\) 7.93371i 0.294448i
\(727\) 37.3532 1.38535 0.692676 0.721249i \(-0.256431\pi\)
0.692676 + 0.721249i \(0.256431\pi\)
\(728\) −29.5731 137.926i −1.09605 5.11188i
\(729\) −23.2600 −0.861480
\(730\) 4.57227i 0.169227i
\(731\) −43.5465 −1.61063
\(732\) −13.2372 −0.489262
\(733\) 2.21871i 0.0819498i −0.999160 0.0409749i \(-0.986954\pi\)
0.999160 0.0409749i \(-0.0130464\pi\)
\(734\) 26.2194i 0.967776i
\(735\) 2.88005i 0.106232i
\(736\) 151.764i 5.59409i
\(737\) −0.169497 −0.00624352
\(738\) −47.7392 −1.75730
\(739\) 34.3388i 1.26317i 0.775306 + 0.631586i \(0.217596\pi\)
−0.775306 + 0.631586i \(0.782404\pi\)
\(740\) −12.6199 −0.463918
\(741\) 1.42172 0.304834i 0.0522281 0.0111984i
\(742\) −66.0345 −2.42420
\(743\) 25.2755i 0.927268i −0.886027 0.463634i \(-0.846545\pi\)
0.886027 0.463634i \(-0.153455\pi\)
\(744\) −2.42693 −0.0889756
\(745\) 15.4741 0.566928
\(746\) 57.1089i 2.09090i
\(747\) 39.1123i 1.43105i
\(748\) 0.572331i 0.0209265i
\(749\) 1.63877i 0.0598793i
\(750\) 6.25544 0.228416
\(751\) −24.0110 −0.876172 −0.438086 0.898933i \(-0.644343\pi\)
−0.438086 + 0.898933i \(0.644343\pi\)
\(752\) 85.1320i 3.10444i
\(753\) −2.47881 −0.0903330
\(754\) −23.1168 + 4.95653i −0.841864 + 0.180506i
\(755\) −12.2155 −0.444567
\(756\) 36.2230i 1.31742i
\(757\) 25.2359 0.917214 0.458607 0.888639i \(-0.348349\pi\)
0.458607 + 0.888639i \(0.348349\pi\)
\(758\) −11.4741 −0.416756
\(759\) 0.0457020i 0.00165888i
\(760\) 13.2196i 0.479524i
\(761\) 38.2689i 1.38725i 0.720338 + 0.693623i \(0.243987\pi\)
−0.720338 + 0.693623i \(0.756013\pi\)
\(762\) 11.7134i 0.424333i
\(763\) −6.20149 −0.224509
\(764\) −1.08424 −0.0392264
\(765\) 13.2450i 0.478873i
\(766\) −6.79702 −0.245586
\(767\) −29.1390 + 6.24776i −1.05215 + 0.225594i
\(768\) 8.15198 0.294159
\(769\) 2.61840i 0.0944220i −0.998885 0.0472110i \(-0.984967\pi\)
0.998885 0.0472110i \(-0.0150333\pi\)
\(770\) −0.249756 −0.00900057
\(771\) 5.62655 0.202635
\(772\) 15.2016i 0.547116i
\(773\) 6.45442i 0.232149i −0.993240 0.116075i \(-0.962969\pi\)
0.993240 0.116075i \(-0.0370312\pi\)
\(774\) 73.0524i 2.62581i
\(775\) 4.08964i 0.146904i
\(776\) −99.6316 −3.57657
\(777\) 2.80754 0.100720
\(778\) 31.5033i 1.12945i
\(779\) 9.11171 0.326461
\(780\) 4.79616 1.02836i 0.171730 0.0368211i
\(781\) 0.298223 0.0106713
\(782\) 98.2278i 3.51262i