Properties

Label 690.3.k.a.277.17
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.17
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.17

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.38409 + 3.68075i) q^{5} +2.44949 q^{6} +(-0.957772 - 0.957772i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.38409 + 3.68075i) q^{5} +2.44949 q^{6} +(-0.957772 - 0.957772i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-0.296667 + 7.06484i) q^{10} -8.07242 q^{11} +(2.44949 + 2.44949i) q^{12} +(-16.4529 + 16.4529i) q^{13} -1.91554i q^{14} +(8.65263 + 0.363341i) q^{15} -4.00000 q^{16} +(10.2171 + 10.2171i) q^{17} +(3.00000 - 3.00000i) q^{18} +22.2917i q^{19} +(-7.36151 + 6.76817i) q^{20} -2.34605 q^{21} +(-8.07242 - 8.07242i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(-2.09590 + 24.9120i) q^{25} -32.9058 q^{26} +(-3.67423 - 3.67423i) q^{27} +(1.91554 - 1.91554i) q^{28} +9.67981i q^{29} +(8.28929 + 9.01597i) q^{30} +56.2127 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-9.88665 + 9.88665i) q^{33} +20.4342i q^{34} +(0.284139 - 6.76651i) q^{35} +6.00000 q^{36} +(-21.1313 - 21.1313i) q^{37} +(-22.2917 + 22.2917i) q^{38} +40.3012i q^{39} +(-14.1297 - 0.593334i) q^{40} +0.341891 q^{41} +(-2.34605 - 2.34605i) q^{42} +(10.7117 - 10.7117i) q^{43} -16.1448i q^{44} +(11.0423 - 10.1523i) q^{45} -6.78233 q^{46} +(11.4105 + 11.4105i) q^{47} +(-4.89898 + 4.89898i) q^{48} -47.1653i q^{49} +(-27.0079 + 22.8161i) q^{50} +25.0267 q^{51} +(-32.9058 - 32.9058i) q^{52} +(1.59872 - 1.59872i) q^{53} -7.34847i q^{54} +(-27.3178 - 29.7126i) q^{55} +3.83109 q^{56} +(27.3017 + 27.3017i) q^{57} +(-9.67981 + 9.67981i) q^{58} -10.4110i q^{59} +(-0.726682 + 17.3053i) q^{60} +11.0126 q^{61} +(56.2127 + 56.2127i) q^{62} +(-2.87332 + 2.87332i) q^{63} -8.00000i q^{64} +(-116.237 - 4.88103i) q^{65} -19.7733 q^{66} +(86.5905 + 86.5905i) q^{67} +(-20.4342 + 20.4342i) q^{68} +8.30662i q^{69} +(7.05065 - 6.48237i) q^{70} -127.113 q^{71} +(6.00000 + 6.00000i) q^{72} +(-28.1347 + 28.1347i) q^{73} -42.2626i q^{74} +(27.9439 + 33.0778i) q^{75} -44.5834 q^{76} +(7.73154 + 7.73154i) q^{77} +(-40.3012 + 40.3012i) q^{78} +72.7818i q^{79} +(-13.5363 - 14.7230i) q^{80} -9.00000 q^{81} +(0.341891 + 0.341891i) q^{82} +(61.3355 - 61.3355i) q^{83} -4.69211i q^{84} +(-3.03107 + 72.1822i) q^{85} +21.4234 q^{86} +(11.8553 + 11.8553i) q^{87} +(16.1448 - 16.1448i) q^{88} +58.5171i q^{89} +(21.1945 + 0.890001i) q^{90} +31.5163 q^{91} +(-6.78233 - 6.78233i) q^{92} +(68.8462 - 68.8462i) q^{93} +22.8211i q^{94} +(-82.0504 + 75.4371i) q^{95} -9.79796 q^{96} +(-101.479 - 101.479i) q^{97} +(47.1653 - 47.1653i) q^{98} +24.2172i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 3.38409 + 3.68075i 0.676817 + 0.736151i
\(6\) 2.44949 0.408248
\(7\) −0.957772 0.957772i −0.136825 0.136825i 0.635377 0.772202i \(-0.280845\pi\)
−0.772202 + 0.635377i \(0.780845\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −0.296667 + 7.06484i −0.0296667 + 0.706484i
\(11\) −8.07242 −0.733856 −0.366928 0.930249i \(-0.619590\pi\)
−0.366928 + 0.930249i \(0.619590\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) −16.4529 + 16.4529i −1.26561 + 1.26561i −0.317274 + 0.948334i \(0.602767\pi\)
−0.948334 + 0.317274i \(0.897233\pi\)
\(14\) 1.91554i 0.136825i
\(15\) 8.65263 + 0.363341i 0.576842 + 0.0242227i
\(16\) −4.00000 −0.250000
\(17\) 10.2171 + 10.2171i 0.601006 + 0.601006i 0.940579 0.339574i \(-0.110283\pi\)
−0.339574 + 0.940579i \(0.610283\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 22.2917i 1.17325i 0.809859 + 0.586624i \(0.199543\pi\)
−0.809859 + 0.586624i \(0.800457\pi\)
\(20\) −7.36151 + 6.76817i −0.368075 + 0.338409i
\(21\) −2.34605 −0.111717
\(22\) −8.07242 8.07242i −0.366928 0.366928i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −2.09590 + 24.9120i −0.0838362 + 0.996480i
\(26\) −32.9058 −1.26561
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 1.91554 1.91554i 0.0684123 0.0684123i
\(29\) 9.67981i 0.333787i 0.985975 + 0.166893i \(0.0533736\pi\)
−0.985975 + 0.166893i \(0.946626\pi\)
\(30\) 8.28929 + 9.01597i 0.276310 + 0.300532i
\(31\) 56.2127 1.81331 0.906656 0.421871i \(-0.138627\pi\)
0.906656 + 0.421871i \(0.138627\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −9.88665 + 9.88665i −0.299595 + 0.299595i
\(34\) 20.4342i 0.601006i
\(35\) 0.284139 6.76651i 0.00811826 0.193329i
\(36\) 6.00000 0.166667
\(37\) −21.1313 21.1313i −0.571116 0.571116i 0.361325 0.932440i \(-0.382325\pi\)
−0.932440 + 0.361325i \(0.882325\pi\)
\(38\) −22.2917 + 22.2917i −0.586624 + 0.586624i
\(39\) 40.3012i 1.03336i
\(40\) −14.1297 0.593334i −0.353242 0.0148333i
\(41\) 0.341891 0.00833881 0.00416941 0.999991i \(-0.498673\pi\)
0.00416941 + 0.999991i \(0.498673\pi\)
\(42\) −2.34605 2.34605i −0.0558584 0.0558584i
\(43\) 10.7117 10.7117i 0.249109 0.249109i −0.571496 0.820605i \(-0.693637\pi\)
0.820605 + 0.571496i \(0.193637\pi\)
\(44\) 16.1448i 0.366928i
\(45\) 11.0423 10.1523i 0.245384 0.225606i
\(46\) −6.78233 −0.147442
\(47\) 11.4105 + 11.4105i 0.242777 + 0.242777i 0.817998 0.575221i \(-0.195084\pi\)
−0.575221 + 0.817998i \(0.695084\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 47.1653i 0.962558i
\(50\) −27.0079 + 22.8161i −0.540158 + 0.456322i
\(51\) 25.0267 0.490719
\(52\) −32.9058 32.9058i −0.632804 0.632804i
\(53\) 1.59872 1.59872i 0.0301645 0.0301645i −0.691864 0.722028i \(-0.743210\pi\)
0.722028 + 0.691864i \(0.243210\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −27.3178 29.7126i −0.496687 0.540229i
\(56\) 3.83109 0.0684123
\(57\) 27.3017 + 27.3017i 0.478977 + 0.478977i
\(58\) −9.67981 + 9.67981i −0.166893 + 0.166893i
\(59\) 10.4110i 0.176458i −0.996100 0.0882289i \(-0.971879\pi\)
0.996100 0.0882289i \(-0.0281207\pi\)
\(60\) −0.726682 + 17.3053i −0.0121114 + 0.288421i
\(61\) 11.0126 0.180534 0.0902671 0.995918i \(-0.471228\pi\)
0.0902671 + 0.995918i \(0.471228\pi\)
\(62\) 56.2127 + 56.2127i 0.906656 + 0.906656i
\(63\) −2.87332 + 2.87332i −0.0456082 + 0.0456082i
\(64\) 8.00000i 0.125000i
\(65\) −116.237 4.88103i −1.78826 0.0750928i
\(66\) −19.7733 −0.299595
\(67\) 86.5905 + 86.5905i 1.29240 + 1.29240i 0.933301 + 0.359094i \(0.116914\pi\)
0.359094 + 0.933301i \(0.383086\pi\)
\(68\) −20.4342 + 20.4342i −0.300503 + 0.300503i
\(69\) 8.30662i 0.120386i
\(70\) 7.05065 6.48237i 0.100724 0.0926053i
\(71\) −127.113 −1.79032 −0.895162 0.445741i \(-0.852940\pi\)
−0.895162 + 0.445741i \(0.852940\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) −28.1347 + 28.1347i −0.385407 + 0.385407i −0.873046 0.487638i \(-0.837858\pi\)
0.487638 + 0.873046i \(0.337858\pi\)
\(74\) 42.2626i 0.571116i
\(75\) 27.9439 + 33.0778i 0.372585 + 0.441037i
\(76\) −44.5834 −0.586624
\(77\) 7.73154 + 7.73154i 0.100410 + 0.100410i
\(78\) −40.3012 + 40.3012i −0.516682 + 0.516682i
\(79\) 72.7818i 0.921289i 0.887585 + 0.460645i \(0.152382\pi\)
−0.887585 + 0.460645i \(0.847618\pi\)
\(80\) −13.5363 14.7230i −0.169204 0.184038i
\(81\) −9.00000 −0.111111
\(82\) 0.341891 + 0.341891i 0.00416941 + 0.00416941i
\(83\) 61.3355 61.3355i 0.738982 0.738982i −0.233399 0.972381i \(-0.574985\pi\)
0.972381 + 0.233399i \(0.0749849\pi\)
\(84\) 4.69211i 0.0558584i
\(85\) −3.03107 + 72.1822i −0.0356597 + 0.849202i
\(86\) 21.4234 0.249109
\(87\) 11.8553 + 11.8553i 0.136268 + 0.136268i
\(88\) 16.1448 16.1448i 0.183464 0.183464i
\(89\) 58.5171i 0.657495i 0.944418 + 0.328748i \(0.106627\pi\)
−0.944418 + 0.328748i \(0.893373\pi\)
\(90\) 21.1945 + 0.890001i 0.235495 + 0.00988890i
\(91\) 31.5163 0.346333
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 68.8462 68.8462i 0.740281 0.740281i
\(94\) 22.8211i 0.242777i
\(95\) −82.0504 + 75.4371i −0.863688 + 0.794075i
\(96\) −9.79796 −0.102062
\(97\) −101.479 101.479i −1.04618 1.04618i −0.998881 0.0472966i \(-0.984939\pi\)
−0.0472966 0.998881i \(-0.515061\pi\)
\(98\) 47.1653 47.1653i 0.481279 0.481279i
\(99\) 24.2172i 0.244619i
\(100\) −49.8240 4.19181i −0.498240 0.0419181i
\(101\) 197.512 1.95557 0.977783 0.209620i \(-0.0672227\pi\)
0.977783 + 0.209620i \(0.0672227\pi\)
\(102\) 25.0267 + 25.0267i 0.245360 + 0.245360i
\(103\) 80.9301 80.9301i 0.785729 0.785729i −0.195062 0.980791i \(-0.562491\pi\)
0.980791 + 0.195062i \(0.0624908\pi\)
\(104\) 65.8116i 0.632804i
\(105\) −7.93925 8.63524i −0.0756119 0.0822404i
\(106\) 3.19744 0.0301645
\(107\) 70.4148 + 70.4148i 0.658082 + 0.658082i 0.954926 0.296844i \(-0.0959340\pi\)
−0.296844 + 0.954926i \(0.595934\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 92.6182i 0.849708i −0.905262 0.424854i \(-0.860325\pi\)
0.905262 0.424854i \(-0.139675\pi\)
\(110\) 2.39482 57.0303i 0.0217711 0.518458i
\(111\) −51.7608 −0.466314
\(112\) 3.83109 + 3.83109i 0.0342061 + 0.0342061i
\(113\) −61.6480 + 61.6480i −0.545557 + 0.545557i −0.925153 0.379595i \(-0.876063\pi\)
0.379595 + 0.925153i \(0.376063\pi\)
\(114\) 54.6033i 0.478977i
\(115\) −23.9580 1.00605i −0.208331 0.00874823i
\(116\) −19.3596 −0.166893
\(117\) 49.3587 + 49.3587i 0.421869 + 0.421869i
\(118\) 10.4110 10.4110i 0.0882289 0.0882289i
\(119\) 19.5713i 0.164465i
\(120\) −18.0319 + 16.5786i −0.150266 + 0.138155i
\(121\) −55.8361 −0.461455
\(122\) 11.0126 + 11.0126i 0.0902671 + 0.0902671i
\(123\) 0.418730 0.418730i 0.00340431 0.00340431i
\(124\) 112.425i 0.906656i
\(125\) −98.7876 + 76.5898i −0.790301 + 0.612719i
\(126\) −5.74663 −0.0456082
\(127\) 78.6155 + 78.6155i 0.619020 + 0.619020i 0.945280 0.326260i \(-0.105789\pi\)
−0.326260 + 0.945280i \(0.605789\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 26.2381i 0.203396i
\(130\) −111.356 121.118i −0.856586 0.931678i
\(131\) 12.2443 0.0934677 0.0467338 0.998907i \(-0.485119\pi\)
0.0467338 + 0.998907i \(0.485119\pi\)
\(132\) −19.7733 19.7733i −0.149798 0.149798i
\(133\) 21.3504 21.3504i 0.160529 0.160529i
\(134\) 173.181i 1.29240i
\(135\) 1.09002 25.9579i 0.00807425 0.192281i
\(136\) −40.8684 −0.300503
\(137\) 57.0677 + 57.0677i 0.416552 + 0.416552i 0.884014 0.467461i \(-0.154831\pi\)
−0.467461 + 0.884014i \(0.654831\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 258.802i 1.86189i −0.365164 0.930943i \(-0.618987\pi\)
0.365164 0.930943i \(-0.381013\pi\)
\(140\) 13.5330 + 0.568278i 0.0966644 + 0.00405913i
\(141\) 27.9500 0.198227
\(142\) −127.113 127.113i −0.895162 0.895162i
\(143\) 132.815 132.815i 0.928774 0.928774i
\(144\) 12.0000i 0.0833333i
\(145\) −35.6290 + 32.7573i −0.245717 + 0.225913i
\(146\) −56.2695 −0.385407
\(147\) −57.7655 57.7655i −0.392963 0.392963i
\(148\) 42.2626 42.2626i 0.285558 0.285558i
\(149\) 189.848i 1.27415i −0.770803 0.637074i \(-0.780145\pi\)
0.770803 0.637074i \(-0.219855\pi\)
\(150\) −5.13390 + 61.0217i −0.0342260 + 0.406811i
\(151\) 87.3704 0.578612 0.289306 0.957237i \(-0.406576\pi\)
0.289306 + 0.957237i \(0.406576\pi\)
\(152\) −44.5834 44.5834i −0.293312 0.293312i
\(153\) 30.6513 30.6513i 0.200335 0.200335i
\(154\) 15.4631i 0.100410i
\(155\) 190.229 + 206.905i 1.22728 + 1.33487i
\(156\) −80.6024 −0.516682
\(157\) −141.182 141.182i −0.899247 0.899247i 0.0961225 0.995370i \(-0.469356\pi\)
−0.995370 + 0.0961225i \(0.969356\pi\)
\(158\) −72.7818 + 72.7818i −0.460645 + 0.460645i
\(159\) 3.91605i 0.0246292i
\(160\) 1.18667 28.2594i 0.00741667 0.176621i
\(161\) 6.49593 0.0403474
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −4.11911 + 4.11911i −0.0252706 + 0.0252706i −0.719629 0.694359i \(-0.755688\pi\)
0.694359 + 0.719629i \(0.255688\pi\)
\(164\) 0.683783i 0.00416941i
\(165\) −69.8476 2.93304i −0.423319 0.0177760i
\(166\) 122.671 0.738982
\(167\) −189.466 189.466i −1.13453 1.13453i −0.989415 0.145113i \(-0.953646\pi\)
−0.145113 0.989415i \(-0.546354\pi\)
\(168\) 4.69211 4.69211i 0.0279292 0.0279292i
\(169\) 372.396i 2.20353i
\(170\) −75.2132 + 69.1511i −0.442431 + 0.406771i
\(171\) 66.8752 0.391083
\(172\) 21.4234 + 21.4234i 0.124554 + 0.124554i
\(173\) −36.0695 + 36.0695i −0.208494 + 0.208494i −0.803627 0.595133i \(-0.797099\pi\)
0.595133 + 0.803627i \(0.297099\pi\)
\(174\) 23.7106i 0.136268i
\(175\) 25.8674 21.8526i 0.147814 0.124872i
\(176\) 32.2897 0.183464
\(177\) −12.7508 12.7508i −0.0720386 0.0720386i
\(178\) −58.5171 + 58.5171i −0.328748 + 0.328748i
\(179\) 253.350i 1.41536i 0.706531 + 0.707682i \(0.250259\pi\)
−0.706531 + 0.707682i \(0.749741\pi\)
\(180\) 20.3045 + 22.0845i 0.112803 + 0.122692i
\(181\) 67.8558 0.374894 0.187447 0.982275i \(-0.439979\pi\)
0.187447 + 0.982275i \(0.439979\pi\)
\(182\) 31.5163 + 31.5163i 0.173166 + 0.173166i
\(183\) 13.4876 13.4876i 0.0737028 0.0737028i
\(184\) 13.5647i 0.0737210i
\(185\) 6.26895 149.289i 0.0338862 0.806968i
\(186\) 137.692 0.740281
\(187\) −82.4767 82.4767i −0.441052 0.441052i
\(188\) −22.8211 + 22.8211i −0.121389 + 0.121389i
\(189\) 7.03816i 0.0372389i
\(190\) −157.487 6.61322i −0.828882 0.0348064i
\(191\) −29.7286 −0.155647 −0.0778235 0.996967i \(-0.524797\pi\)
−0.0778235 + 0.996967i \(0.524797\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) 99.2409 99.2409i 0.514202 0.514202i −0.401610 0.915811i \(-0.631549\pi\)
0.915811 + 0.401610i \(0.131549\pi\)
\(194\) 202.958i 1.04618i
\(195\) −148.339 + 136.383i −0.760712 + 0.699399i
\(196\) 94.3307 0.481279
\(197\) 80.0266 + 80.0266i 0.406227 + 0.406227i 0.880420 0.474194i \(-0.157260\pi\)
−0.474194 + 0.880420i \(0.657260\pi\)
\(198\) −24.2172 + 24.2172i −0.122309 + 0.122309i
\(199\) 262.310i 1.31814i −0.752082 0.659070i \(-0.770950\pi\)
0.752082 0.659070i \(-0.229050\pi\)
\(200\) −45.6322 54.0158i −0.228161 0.270079i
\(201\) 212.103 1.05524
\(202\) 197.512 + 197.512i 0.977783 + 0.977783i
\(203\) 9.27105 9.27105i 0.0456702 0.0456702i
\(204\) 50.0533i 0.245360i
\(205\) 1.15699 + 1.25842i 0.00564385 + 0.00613862i
\(206\) 161.860 0.785729
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) 65.8116 65.8116i 0.316402 0.316402i
\(209\) 179.948i 0.860996i
\(210\) 0.695996 16.5745i 0.00331427 0.0789262i
\(211\) 269.701 1.27820 0.639102 0.769122i \(-0.279306\pi\)
0.639102 + 0.769122i \(0.279306\pi\)
\(212\) 3.19744 + 3.19744i 0.0150823 + 0.0150823i
\(213\) −155.681 + 155.681i −0.730897 + 0.730897i
\(214\) 140.830i 0.658082i
\(215\) 75.6763 + 3.17780i 0.351983 + 0.0147805i
\(216\) 14.6969 0.0680414
\(217\) −53.8389 53.8389i −0.248106 0.248106i
\(218\) 92.6182 92.6182i 0.424854 0.424854i
\(219\) 68.9157i 0.314684i
\(220\) 59.4252 54.6355i 0.270114 0.248343i
\(221\) −336.202 −1.52128
\(222\) −51.7608 51.7608i −0.233157 0.233157i
\(223\) 2.67761 2.67761i 0.0120072 0.0120072i −0.701078 0.713085i \(-0.747297\pi\)
0.713085 + 0.701078i \(0.247297\pi\)
\(224\) 7.66218i 0.0342061i
\(225\) 74.7360 + 6.28771i 0.332160 + 0.0279454i
\(226\) −123.296 −0.545557
\(227\) 145.152 + 145.152i 0.639437 + 0.639437i 0.950417 0.310979i \(-0.100657\pi\)
−0.310979 + 0.950417i \(0.600657\pi\)
\(228\) −54.6033 + 54.6033i −0.239488 + 0.239488i
\(229\) 59.4180i 0.259467i −0.991549 0.129734i \(-0.958588\pi\)
0.991549 0.129734i \(-0.0414123\pi\)
\(230\) −22.9520 24.9641i −0.0997913 0.108540i
\(231\) 18.9383 0.0819841
\(232\) −19.3596 19.3596i −0.0834467 0.0834467i
\(233\) −236.967 + 236.967i −1.01702 + 1.01702i −0.0171724 + 0.999853i \(0.505466\pi\)
−0.999853 + 0.0171724i \(0.994534\pi\)
\(234\) 98.7174i 0.421869i
\(235\) −3.38513 + 80.6137i −0.0144048 + 0.343037i
\(236\) 20.8220 0.0882289
\(237\) 89.1392 + 89.1392i 0.376115 + 0.376115i
\(238\) 19.5713 19.5713i 0.0822324 0.0822324i
\(239\) 258.221i 1.08042i 0.841530 + 0.540210i \(0.181655\pi\)
−0.841530 + 0.540210i \(0.818345\pi\)
\(240\) −34.6105 1.45336i −0.144210 0.00605569i
\(241\) 380.361 1.57826 0.789130 0.614226i \(-0.210532\pi\)
0.789130 + 0.614226i \(0.210532\pi\)
\(242\) −55.8361 55.8361i −0.230728 0.230728i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 22.0252i 0.0902671i
\(245\) 173.604 159.612i 0.708588 0.651476i
\(246\) 0.837459 0.00340431
\(247\) −366.764 366.764i −1.48487 1.48487i
\(248\) −112.425 + 112.425i −0.453328 + 0.453328i
\(249\) 150.241i 0.603376i
\(250\) −175.377 22.1978i −0.701510 0.0887912i
\(251\) 115.175 0.458864 0.229432 0.973325i \(-0.426313\pi\)
0.229432 + 0.973325i \(0.426313\pi\)
\(252\) −5.74663 5.74663i −0.0228041 0.0228041i
\(253\) 27.3749 27.3749i 0.108201 0.108201i
\(254\) 157.231i 0.619020i
\(255\) 84.6925 + 92.1170i 0.332127 + 0.361243i
\(256\) 16.0000 0.0625000
\(257\) 265.052 + 265.052i 1.03133 + 1.03133i 0.999493 + 0.0318362i \(0.0101355\pi\)
0.0318362 + 0.999493i \(0.489865\pi\)
\(258\) 26.2381 26.2381i 0.101698 0.101698i
\(259\) 40.4779i 0.156285i
\(260\) 9.76206 232.474i 0.0375464 0.894132i
\(261\) 29.0394 0.111262
\(262\) 12.2443 + 12.2443i 0.0467338 + 0.0467338i
\(263\) 11.8740 11.8740i 0.0451481 0.0451481i −0.684172 0.729320i \(-0.739836\pi\)
0.729320 + 0.684172i \(0.239836\pi\)
\(264\) 39.5466i 0.149798i
\(265\) 11.2947 + 0.474287i 0.0426215 + 0.00178976i
\(266\) 42.7008 0.160529
\(267\) 71.6685 + 71.6685i 0.268421 + 0.268421i
\(268\) −173.181 + 173.181i −0.646198 + 0.646198i
\(269\) 170.641i 0.634353i 0.948367 + 0.317177i \(0.102735\pi\)
−0.948367 + 0.317177i \(0.897265\pi\)
\(270\) 27.0479 24.8679i 0.100177 0.0921032i
\(271\) 95.8232 0.353591 0.176796 0.984248i \(-0.443427\pi\)
0.176796 + 0.984248i \(0.443427\pi\)
\(272\) −40.8684 40.8684i −0.150251 0.150251i
\(273\) 38.5994 38.5994i 0.141390 0.141390i
\(274\) 114.135i 0.416552i
\(275\) 16.9190 201.100i 0.0615237 0.731273i
\(276\) −16.6132 −0.0601929
\(277\) 98.3010 + 98.3010i 0.354877 + 0.354877i 0.861921 0.507043i \(-0.169262\pi\)
−0.507043 + 0.861921i \(0.669262\pi\)
\(278\) 258.802 258.802i 0.930943 0.930943i
\(279\) 168.638i 0.604437i
\(280\) 12.9647 + 14.1013i 0.0463026 + 0.0503618i
\(281\) 155.796 0.554433 0.277216 0.960808i \(-0.410588\pi\)
0.277216 + 0.960808i \(0.410588\pi\)
\(282\) 27.9500 + 27.9500i 0.0991135 + 0.0991135i
\(283\) 141.426 141.426i 0.499737 0.499737i −0.411619 0.911356i \(-0.635036\pi\)
0.911356 + 0.411619i \(0.135036\pi\)
\(284\) 254.226i 0.895162i
\(285\) −8.09950 + 192.882i −0.0284193 + 0.676779i
\(286\) 265.629 0.928774
\(287\) −0.327454 0.327454i −0.00114095 0.00114095i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 80.2219i 0.277584i
\(290\) −68.3863 2.87168i −0.235815 0.00990234i
\(291\) −248.572 −0.854200
\(292\) −56.2695 56.2695i −0.192704 0.192704i
\(293\) 182.330 182.330i 0.622287 0.622287i −0.323829 0.946116i \(-0.604970\pi\)
0.946116 + 0.323829i \(0.104970\pi\)
\(294\) 115.531i 0.392963i
\(295\) 38.3204 35.2318i 0.129900 0.119430i
\(296\) 84.5251 0.285558
\(297\) 29.6600 + 29.6600i 0.0998652 + 0.0998652i
\(298\) 189.848 189.848i 0.637074 0.637074i
\(299\) 111.589i 0.373207i
\(300\) −66.1556 + 55.8878i −0.220519 + 0.186293i
\(301\) −20.5187 −0.0681684
\(302\) 87.3704 + 87.3704i 0.289306 + 0.289306i
\(303\) 241.902 241.902i 0.798356 0.798356i
\(304\) 89.1669i 0.293312i
\(305\) 37.2675 + 40.5346i 0.122189 + 0.132900i
\(306\) 61.3026 0.200335
\(307\) 360.897 + 360.897i 1.17556 + 1.17556i 0.980864 + 0.194696i \(0.0623719\pi\)
0.194696 + 0.980864i \(0.437628\pi\)
\(308\) −15.4631 + 15.4631i −0.0502048 + 0.0502048i
\(309\) 198.237i 0.641545i
\(310\) −16.6764 + 397.134i −0.0537949 + 1.28108i
\(311\) 171.586 0.551723 0.275862 0.961197i \(-0.411037\pi\)
0.275862 + 0.961197i \(0.411037\pi\)
\(312\) −80.6024 80.6024i −0.258341 0.258341i
\(313\) −416.142 + 416.142i −1.32953 + 1.32953i −0.423746 + 0.905781i \(0.639285\pi\)
−0.905781 + 0.423746i \(0.860715\pi\)
\(314\) 282.364i 0.899247i
\(315\) −20.2995 0.852418i −0.0644429 0.00270609i
\(316\) −145.564 −0.460645
\(317\) 224.319 + 224.319i 0.707630 + 0.707630i 0.966036 0.258407i \(-0.0831975\pi\)
−0.258407 + 0.966036i \(0.583197\pi\)
\(318\) 3.91605 3.91605i 0.0123146 0.0123146i
\(319\) 78.1395i 0.244951i
\(320\) 29.4460 27.0727i 0.0920189 0.0846022i
\(321\) 172.480 0.537322
\(322\) 6.49593 + 6.49593i 0.0201737 + 0.0201737i
\(323\) −227.757 + 227.757i −0.705129 + 0.705129i
\(324\) 18.0000i 0.0555556i
\(325\) −375.391 444.358i −1.15505 1.36726i
\(326\) −8.23822 −0.0252706
\(327\) −113.434 113.434i −0.346892 0.346892i
\(328\) −0.683783 + 0.683783i −0.00208470 + 0.00208470i
\(329\) 21.8574i 0.0664358i
\(330\) −66.9146 72.7807i −0.202771 0.220547i
\(331\) 269.054 0.812853 0.406426 0.913684i \(-0.366775\pi\)
0.406426 + 0.913684i \(0.366775\pi\)
\(332\) 122.671 + 122.671i 0.369491 + 0.369491i
\(333\) −63.3938 + 63.3938i −0.190372 + 0.190372i
\(334\) 378.932i 1.13453i
\(335\) −25.6885 + 611.748i −0.0766822 + 1.82611i
\(336\) 9.38421 0.0279292
\(337\) −94.3863 94.3863i −0.280078 0.280078i 0.553062 0.833140i \(-0.313459\pi\)
−0.833140 + 0.553062i \(0.813459\pi\)
\(338\) 372.396 372.396i 1.10176 1.10176i
\(339\) 151.006i 0.445445i
\(340\) −144.364 6.06215i −0.424601 0.0178298i
\(341\) −453.772 −1.33071
\(342\) 66.8752 + 66.8752i 0.195541 + 0.195541i
\(343\) −92.1045 + 92.1045i −0.268526 + 0.268526i
\(344\) 42.8467i 0.124554i
\(345\) −30.5746 + 28.1103i −0.0886221 + 0.0814793i
\(346\) −72.1389 −0.208494
\(347\) 150.970 + 150.970i 0.435072 + 0.435072i 0.890349 0.455278i \(-0.150460\pi\)
−0.455278 + 0.890349i \(0.650460\pi\)
\(348\) −23.7106 + 23.7106i −0.0681339 + 0.0681339i
\(349\) 417.741i 1.19697i −0.801135 0.598483i \(-0.795770\pi\)
0.801135 0.598483i \(-0.204230\pi\)
\(350\) 47.7200 + 4.01480i 0.136343 + 0.0114709i
\(351\) 120.904 0.344455
\(352\) 32.2897 + 32.2897i 0.0917320 + 0.0917320i
\(353\) −367.544 + 367.544i −1.04120 + 1.04120i −0.0420875 + 0.999114i \(0.513401\pi\)
−0.999114 + 0.0420875i \(0.986599\pi\)
\(354\) 25.5017i 0.0720386i
\(355\) −430.162 467.872i −1.21172 1.31795i
\(356\) −117.034 −0.328748
\(357\) −23.9698 23.9698i −0.0671424 0.0671424i
\(358\) −253.350 + 253.350i −0.707682 + 0.707682i
\(359\) 392.377i 1.09297i −0.837468 0.546486i \(-0.815965\pi\)
0.837468 0.546486i \(-0.184035\pi\)
\(360\) −1.78000 + 42.3891i −0.00494445 + 0.117747i
\(361\) −135.921 −0.376512
\(362\) 67.8558 + 67.8558i 0.187447 + 0.187447i
\(363\) −68.3850 + 68.3850i −0.188388 + 0.188388i
\(364\) 63.0325i 0.173166i
\(365\) −198.767 8.34664i −0.544568 0.0228675i
\(366\) 26.9752 0.0737028
\(367\) −400.857 400.857i −1.09225 1.09225i −0.995288 0.0969643i \(-0.969087\pi\)
−0.0969643 0.995288i \(-0.530913\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 1.02567i 0.00277960i
\(370\) 155.558 143.020i 0.420427 0.386541i
\(371\) −3.06242 −0.00825450
\(372\) 137.692 + 137.692i 0.370141 + 0.370141i
\(373\) −239.306 + 239.306i −0.641572 + 0.641572i −0.950942 0.309370i \(-0.899882\pi\)
0.309370 + 0.950942i \(0.399882\pi\)
\(374\) 164.953i 0.441052i
\(375\) −27.1866 + 214.793i −0.0724977 + 0.572780i
\(376\) −45.6422 −0.121389
\(377\) −159.261 159.261i −0.422443 0.422443i
\(378\) −7.03816 + 7.03816i −0.0186195 + 0.0186195i
\(379\) 164.467i 0.433951i −0.976177 0.216975i \(-0.930381\pi\)
0.976177 0.216975i \(-0.0696191\pi\)
\(380\) −150.874 164.101i −0.397038 0.431844i
\(381\) 192.568 0.505428
\(382\) −29.7286 29.7286i −0.0778235 0.0778235i
\(383\) −97.6018 + 97.6018i −0.254835 + 0.254835i −0.822949 0.568115i \(-0.807673\pi\)
0.568115 + 0.822949i \(0.307673\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −2.29369 + 54.6221i −0.00595764 + 0.141876i
\(386\) 198.482 0.514202
\(387\) −32.1350 32.1350i −0.0830362 0.0830362i
\(388\) 202.958 202.958i 0.523089 0.523089i
\(389\) 591.161i 1.51969i −0.650102 0.759847i \(-0.725274\pi\)
0.650102 0.759847i \(-0.274726\pi\)
\(390\) −284.722 11.9560i −0.730056 0.0306565i
\(391\) −69.2957 −0.177227
\(392\) 94.3307 + 94.3307i 0.240640 + 0.240640i
\(393\) 14.9961 14.9961i 0.0381580 0.0381580i
\(394\) 160.053i 0.406227i
\(395\) −267.892 + 246.300i −0.678208 + 0.623545i
\(396\) −48.4345 −0.122309
\(397\) −2.74699 2.74699i −0.00691938 0.00691938i 0.703639 0.710558i \(-0.251557\pi\)
−0.710558 + 0.703639i \(0.751557\pi\)
\(398\) 262.310 262.310i 0.659070 0.659070i
\(399\) 52.2976i 0.131072i
\(400\) 8.38362 99.6480i 0.0209590 0.249120i
\(401\) 259.213 0.646416 0.323208 0.946328i \(-0.395239\pi\)
0.323208 + 0.946328i \(0.395239\pi\)
\(402\) 212.103 + 212.103i 0.527618 + 0.527618i
\(403\) −924.861 + 924.861i −2.29494 + 2.29494i
\(404\) 395.024i 0.977783i
\(405\) −30.4568 33.1268i −0.0752019 0.0817945i
\(406\) 18.5421 0.0456702
\(407\) 170.580 + 170.580i 0.419117 + 0.419117i
\(408\) −50.0533 + 50.0533i −0.122680 + 0.122680i
\(409\) 67.6142i 0.165316i 0.996578 + 0.0826579i \(0.0263409\pi\)
−0.996578 + 0.0826579i \(0.973659\pi\)
\(410\) −0.101428 + 2.41541i −0.000247385 + 0.00589124i
\(411\) 139.787 0.340114
\(412\) 161.860 + 161.860i 0.392864 + 0.392864i
\(413\) −9.97137 + 9.97137i −0.0241438 + 0.0241438i
\(414\) 20.3470i 0.0491473i
\(415\) 433.326 + 18.1962i 1.04416 + 0.0438463i
\(416\) 131.623 0.316402
\(417\) −316.967 316.967i −0.760112 0.760112i
\(418\) 179.948 179.948i 0.430498 0.430498i
\(419\) 659.542i 1.57408i 0.616899 + 0.787042i \(0.288389\pi\)
−0.616899 + 0.787042i \(0.711611\pi\)
\(420\) 17.2705 15.8785i 0.0411202 0.0378059i
\(421\) 162.043 0.384900 0.192450 0.981307i \(-0.438357\pi\)
0.192450 + 0.981307i \(0.438357\pi\)
\(422\) 269.701 + 269.701i 0.639102 + 0.639102i
\(423\) 34.2316 34.2316i 0.0809258 0.0809258i
\(424\) 6.39488i 0.0150823i
\(425\) −275.942 + 233.114i −0.649276 + 0.548504i
\(426\) −311.362 −0.730897
\(427\) −10.5475 10.5475i −0.0247015 0.0247015i
\(428\) −140.830 + 140.830i −0.329041 + 0.329041i
\(429\) 325.328i 0.758341i
\(430\) 72.4985 + 78.8541i 0.168601 + 0.183382i
\(431\) −536.271 −1.24425 −0.622124 0.782918i \(-0.713730\pi\)
−0.622124 + 0.782918i \(0.713730\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) 185.531 185.531i 0.428479 0.428479i −0.459631 0.888110i \(-0.652018\pi\)
0.888110 + 0.459631i \(0.152018\pi\)
\(434\) 107.678i 0.248106i
\(435\) −3.51708 + 83.7558i −0.00808523 + 0.192542i
\(436\) 185.236 0.424854
\(437\) −75.5949 75.5949i −0.172986 0.172986i
\(438\) −68.9157 + 68.9157i −0.157342 + 0.157342i
\(439\) 568.595i 1.29521i 0.761978 + 0.647603i \(0.224228\pi\)
−0.761978 + 0.647603i \(0.775772\pi\)
\(440\) 114.061 + 4.78964i 0.259229 + 0.0108855i
\(441\) −141.496 −0.320853
\(442\) −336.202 336.202i −0.760638 0.760638i
\(443\) −543.783 + 543.783i −1.22750 + 1.22750i −0.262594 + 0.964907i \(0.584578\pi\)
−0.964907 + 0.262594i \(0.915422\pi\)
\(444\) 103.522i 0.233157i
\(445\) −215.387 + 198.027i −0.484016 + 0.445004i
\(446\) 5.35522 0.0120072
\(447\) −232.515 232.515i −0.520168 0.520168i
\(448\) −7.66218 + 7.66218i −0.0171031 + 0.0171031i
\(449\) 357.234i 0.795622i −0.917467 0.397811i \(-0.869770\pi\)
0.917467 0.397811i \(-0.130230\pi\)
\(450\) 68.4483 + 81.0237i 0.152107 + 0.180053i
\(451\) −2.75989 −0.00611949
\(452\) −123.296 123.296i −0.272779 0.272779i
\(453\) 107.006 107.006i 0.236217 0.236217i
\(454\) 290.304i 0.639437i
\(455\) 106.654 + 116.004i 0.234404 + 0.254953i
\(456\) −109.207 −0.239488
\(457\) −10.4610 10.4610i −0.0228906 0.0228906i 0.695569 0.718459i \(-0.255152\pi\)
−0.718459 + 0.695569i \(0.755152\pi\)
\(458\) 59.4180 59.4180i 0.129734 0.129734i
\(459\) 75.0800i 0.163573i
\(460\) 2.01209 47.9161i 0.00437411 0.104165i
\(461\) 12.5540 0.0272321 0.0136160 0.999907i \(-0.495666\pi\)
0.0136160 + 0.999907i \(0.495666\pi\)
\(462\) 18.9383 + 18.9383i 0.0409920 + 0.0409920i
\(463\) −245.657 + 245.657i −0.530577 + 0.530577i −0.920744 0.390167i \(-0.872417\pi\)
0.390167 + 0.920744i \(0.372417\pi\)
\(464\) 38.7193i 0.0834467i
\(465\) 486.387 + 20.4244i 1.04599 + 0.0439234i
\(466\) −473.934 −1.01702
\(467\) −125.860 125.860i −0.269507 0.269507i 0.559395 0.828901i \(-0.311034\pi\)
−0.828901 + 0.559395i \(0.811034\pi\)
\(468\) −98.7174 + 98.7174i −0.210935 + 0.210935i
\(469\) 165.868i 0.353663i
\(470\) −83.9988 + 77.2285i −0.178721 + 0.164316i
\(471\) −345.823 −0.734232
\(472\) 20.8220 + 20.8220i 0.0441144 + 0.0441144i
\(473\) −86.4691 + 86.4691i −0.182810 + 0.182810i
\(474\) 178.278i 0.376115i
\(475\) −555.331 46.7213i −1.16912 0.0983607i
\(476\) 39.1426 0.0822324
\(477\) −4.79616 4.79616i −0.0100548 0.0100548i
\(478\) −258.221 + 258.221i −0.540210 + 0.540210i
\(479\) 268.187i 0.559890i 0.960016 + 0.279945i \(0.0903162\pi\)
−0.960016 + 0.279945i \(0.909684\pi\)
\(480\) −33.1571 36.0639i −0.0690774 0.0751331i
\(481\) 695.342 1.44562
\(482\) 380.361 + 380.361i 0.789130 + 0.789130i
\(483\) 7.95585 7.95585i 0.0164717 0.0164717i
\(484\) 111.672i 0.230728i
\(485\) 30.1055 716.935i 0.0620732 1.47822i
\(486\) −22.0454 −0.0453609
\(487\) 489.385 + 489.385i 1.00490 + 1.00490i 0.999988 + 0.00490986i \(0.00156286\pi\)
0.00490986 + 0.999988i \(0.498437\pi\)
\(488\) −22.0252 + 22.0252i −0.0451335 + 0.0451335i
\(489\) 10.0897i 0.0206334i
\(490\) 333.216 + 13.9924i 0.680032 + 0.0285559i
\(491\) 467.500 0.952138 0.476069 0.879408i \(-0.342061\pi\)
0.476069 + 0.879408i \(0.342061\pi\)
\(492\) 0.837459 + 0.837459i 0.00170215 + 0.00170215i
\(493\) −98.8996 + 98.8996i −0.200608 + 0.200608i
\(494\) 733.527i 1.48487i
\(495\) −89.1377 + 81.9533i −0.180076 + 0.165562i
\(496\) −224.851 −0.453328
\(497\) 121.745 + 121.745i 0.244960 + 0.244960i
\(498\) 150.241 150.241i 0.301688 0.301688i
\(499\) 344.871i 0.691124i −0.938396 0.345562i \(-0.887688\pi\)
0.938396 0.345562i \(-0.112312\pi\)
\(500\) −153.180 197.575i −0.306359 0.395151i
\(501\) −464.095 −0.926338
\(502\) 115.175 + 115.175i 0.229432 + 0.229432i
\(503\) −334.082 + 334.082i −0.664178 + 0.664178i −0.956362 0.292184i \(-0.905618\pi\)
0.292184 + 0.956362i \(0.405618\pi\)
\(504\) 11.4933i 0.0228041i
\(505\) 668.398 + 726.994i 1.32356 + 1.43959i
\(506\) 54.7498 0.108201
\(507\) −456.090 456.090i −0.899586 0.899586i
\(508\) −157.231 + 157.231i −0.309510 + 0.309510i
\(509\) 526.240i 1.03387i −0.856025 0.516935i \(-0.827073\pi\)
0.856025 0.516935i \(-0.172927\pi\)
\(510\) −7.42459 + 176.809i −0.0145580 + 0.346685i
\(511\) 53.8933 0.105466
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 81.9050 81.9050i 0.159659 0.159659i
\(514\) 530.103i 1.03133i
\(515\) 571.758 + 24.0093i 1.11021 + 0.0466200i
\(516\) 52.4763 0.101698
\(517\) −92.1106 92.1106i −0.178164 0.178164i
\(518\) −40.4779 + 40.4779i −0.0781426 + 0.0781426i
\(519\) 88.3518i 0.170235i
\(520\) 242.236 222.712i 0.465839 0.428293i
\(521\) −924.134 −1.77377 −0.886885 0.461991i \(-0.847135\pi\)
−0.886885 + 0.461991i \(0.847135\pi\)
\(522\) 29.0394 + 29.0394i 0.0556311 + 0.0556311i
\(523\) −234.911 + 234.911i −0.449161 + 0.449161i −0.895076 0.445914i \(-0.852879\pi\)
0.445914 + 0.895076i \(0.352879\pi\)
\(524\) 24.4885i 0.0467338i
\(525\) 4.91710 58.4448i 0.00936591 0.111324i
\(526\) 23.7479 0.0451481
\(527\) 574.330 + 574.330i 1.08981 + 1.08981i
\(528\) 39.5466 39.5466i 0.0748989 0.0748989i
\(529\) 23.0000i 0.0434783i
\(530\) 10.8204 + 11.7690i 0.0204159 + 0.0222057i
\(531\) −31.2330 −0.0588193
\(532\) 42.7008 + 42.7008i 0.0802646 + 0.0802646i
\(533\) −5.62511 + 5.62511i −0.0105537 + 0.0105537i
\(534\) 143.337i 0.268421i
\(535\) −20.8897 + 497.470i −0.0390463 + 0.929850i
\(536\) −346.362 −0.646198
\(537\) 310.289 + 310.289i 0.577820 + 0.577820i
\(538\) −170.641 + 170.641i −0.317177 + 0.317177i
\(539\) 380.738i 0.706379i
\(540\) 51.9158 + 2.18005i 0.0961403 + 0.00403712i
\(541\) −264.669 −0.489222 −0.244611 0.969621i \(-0.578660\pi\)
−0.244611 + 0.969621i \(0.578660\pi\)
\(542\) 95.8232 + 95.8232i 0.176796 + 0.176796i
\(543\) 83.1061 83.1061i 0.153050 0.153050i
\(544\) 81.7368i 0.150251i
\(545\) 340.905 313.428i 0.625513 0.575097i
\(546\) 77.1988 0.141390
\(547\) 200.828 + 200.828i 0.367145 + 0.367145i 0.866435 0.499290i \(-0.166406\pi\)
−0.499290 + 0.866435i \(0.666406\pi\)
\(548\) −114.135 + 114.135i −0.208276 + 0.208276i
\(549\) 33.0377i 0.0601780i
\(550\) 218.019 184.181i 0.396398 0.334874i
\(551\) −215.780 −0.391615
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) 69.7084 69.7084i 0.126055 0.126055i
\(554\) 196.602i 0.354877i
\(555\) −175.163 190.519i −0.315609 0.343277i
\(556\) 517.604 0.930943
\(557\) 361.253 + 361.253i 0.648570 + 0.648570i 0.952647 0.304077i \(-0.0983481\pi\)
−0.304077 + 0.952647i \(0.598348\pi\)
\(558\) 168.638 168.638i 0.302219 0.302219i
\(559\) 352.476i 0.630548i
\(560\) −1.13656 + 27.0660i −0.00202957 + 0.0483322i
\(561\) −202.026 −0.360117
\(562\) 155.796 + 155.796i 0.277216 + 0.277216i
\(563\) −210.985 + 210.985i −0.374752 + 0.374752i −0.869205 0.494453i \(-0.835369\pi\)
0.494453 + 0.869205i \(0.335369\pi\)
\(564\) 55.9000i 0.0991135i
\(565\) −435.533 18.2889i −0.770855 0.0323697i
\(566\) 282.851 0.499737
\(567\) 8.61995 + 8.61995i 0.0152027 + 0.0152027i
\(568\) 254.226 254.226i 0.447581 0.447581i
\(569\) 1065.34i 1.87230i −0.351600 0.936150i \(-0.614362\pi\)
0.351600 0.936150i \(-0.385638\pi\)
\(570\) −200.981 + 184.782i −0.352599 + 0.324180i
\(571\) −192.279 −0.336740 −0.168370 0.985724i \(-0.553850\pi\)
−0.168370 + 0.985724i \(0.553850\pi\)
\(572\) 265.629 + 265.629i 0.464387 + 0.464387i
\(573\) −36.4099 + 36.4099i −0.0635427 + 0.0635427i
\(574\) 0.654908i 0.00114095i
\(575\) −77.3731 91.5882i −0.134562 0.159284i
\(576\) −24.0000 −0.0416667
\(577\) −474.911 474.911i −0.823069 0.823069i 0.163478 0.986547i \(-0.447729\pi\)
−0.986547 + 0.163478i \(0.947729\pi\)
\(578\) 80.2219 80.2219i 0.138792 0.138792i
\(579\) 243.090i 0.419844i
\(580\) −65.5147 71.2580i −0.112956 0.122859i
\(581\) −117.491 −0.202222
\(582\) −248.572 248.572i −0.427100 0.427100i
\(583\) −12.9055 + 12.9055i −0.0221364 + 0.0221364i
\(584\) 112.539i 0.192704i
\(585\) −14.6431 + 348.711i −0.0250309 + 0.596088i
\(586\) 364.660 0.622287
\(587\) 344.230 + 344.230i 0.586423 + 0.586423i 0.936661 0.350238i \(-0.113899\pi\)
−0.350238 + 0.936661i \(0.613899\pi\)
\(588\) 115.531 115.531i 0.196481 0.196481i
\(589\) 1253.08i 2.12746i
\(590\) 73.5521 + 3.08860i 0.124665 + 0.00523492i
\(591\) 196.024 0.331683
\(592\) 84.5251 + 84.5251i 0.142779 + 0.142779i
\(593\) −430.072 + 430.072i −0.725248 + 0.725248i −0.969669 0.244421i \(-0.921402\pi\)
0.244421 + 0.969669i \(0.421402\pi\)
\(594\) 59.3199i 0.0998652i
\(595\) 72.0371 66.2310i 0.121071 0.111313i
\(596\) 379.696 0.637074
\(597\) −321.262 321.262i −0.538128 0.538128i
\(598\) 111.589 111.589i 0.186604 0.186604i
\(599\) 1172.10i 1.95677i −0.206803 0.978383i \(-0.566306\pi\)
0.206803 0.978383i \(-0.433694\pi\)
\(600\) −122.043 10.2678i −0.203406 0.0171130i
\(601\) 812.766 1.35236 0.676178 0.736738i \(-0.263635\pi\)
0.676178 + 0.736738i \(0.263635\pi\)
\(602\) −20.5187 20.5187i −0.0340842 0.0340842i
\(603\) 259.772 259.772i 0.430799 0.430799i
\(604\) 174.741i 0.289306i
\(605\) −188.954 205.519i −0.312321 0.339701i
\(606\) 483.804 0.798356
\(607\) 194.117 + 194.117i 0.319798 + 0.319798i 0.848689 0.528892i \(-0.177392\pi\)
−0.528892 + 0.848689i \(0.677392\pi\)
\(608\) 89.1669 89.1669i 0.146656 0.146656i
\(609\) 22.7094i 0.0372896i
\(610\) −3.26707 + 77.8022i −0.00535585 + 0.127545i
\(611\) −375.473 −0.614522
\(612\) 61.3026 + 61.3026i 0.100168 + 0.100168i
\(613\) 750.016 750.016i 1.22352 1.22352i 0.257143 0.966373i \(-0.417219\pi\)
0.966373 0.257143i \(-0.0827812\pi\)
\(614\) 721.793i 1.17556i
\(615\) 2.95826 + 0.124223i 0.00481018 + 0.000201989i
\(616\) −30.9261 −0.0502048
\(617\) −399.144 399.144i −0.646911 0.646911i 0.305334 0.952245i \(-0.401232\pi\)
−0.952245 + 0.305334i \(0.901232\pi\)
\(618\) 198.237 198.237i 0.320773 0.320773i
\(619\) 611.969i 0.988642i 0.869280 + 0.494321i \(0.164583\pi\)
−0.869280 + 0.494321i \(0.835417\pi\)
\(620\) −413.810 + 380.457i −0.667435 + 0.613640i
\(621\) 24.9199 0.0401286
\(622\) 171.586 + 171.586i 0.275862 + 0.275862i
\(623\) 56.0460 56.0460i 0.0899615 0.0899615i
\(624\) 161.205i 0.258341i
\(625\) −616.214 104.426i −0.985943 0.167082i
\(626\) −832.284 −1.32953
\(627\) −220.390 220.390i −0.351500 0.351500i
\(628\) 282.364 282.364i 0.449624 0.449624i
\(629\) 431.801i 0.686487i
\(630\) −19.4471 21.1519i −0.0308684 0.0335745i
\(631\) −163.115 −0.258503 −0.129251 0.991612i \(-0.541257\pi\)
−0.129251 + 0.991612i \(0.541257\pi\)
\(632\) −145.564 145.564i −0.230322 0.230322i
\(633\) 330.315 330.315i 0.521824 0.521824i
\(634\) 448.637i 0.707630i
\(635\) −23.3226 + 555.406i −0.0367285 + 0.874655i
\(636\) 7.83210 0.0123146
\(637\) 776.007 + 776.007i 1.21822 + 1.21822i
\(638\) 78.1395 78.1395i 0.122476 0.122476i
\(639\) 381.339i 0.596775i
\(640\) 56.5187 + 2.37333i 0.0883105 + 0.00370834i
\(641\) −292.715 −0.456653 −0.228327 0.973585i \(-0.573325\pi\)
−0.228327 + 0.973585i \(0.573325\pi\)
\(642\) 172.480 + 172.480i 0.268661 + 0.268661i
\(643\) 177.031 177.031i 0.275320 0.275320i −0.555917 0.831238i \(-0.687633\pi\)
0.831238 + 0.555917i \(0.187633\pi\)
\(644\) 12.9919i 0.0201737i
\(645\) 96.5761 88.7922i 0.149730 0.137662i
\(646\) −455.513 −0.705129
\(647\) 514.177 + 514.177i 0.794710 + 0.794710i 0.982256 0.187546i \(-0.0600533\pi\)
−0.187546 + 0.982256i \(0.560053\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 84.0420i 0.129495i
\(650\) 68.9674 819.749i 0.106104 1.26115i
\(651\) −131.878 −0.202577
\(652\) −8.23822 8.23822i −0.0126353 0.0126353i
\(653\) −490.962 + 490.962i −0.751855 + 0.751855i −0.974825 0.222970i \(-0.928425\pi\)
0.222970 + 0.974825i \(0.428425\pi\)
\(654\) 226.867i 0.346892i
\(655\) 41.4357 + 45.0681i 0.0632605 + 0.0688063i
\(656\) −1.36757 −0.00208470
\(657\) 84.4042 + 84.4042i 0.128469 + 0.128469i
\(658\) 21.8574 21.8574i 0.0332179 0.0332179i
\(659\) 629.616i 0.955411i −0.878520 0.477705i \(-0.841469\pi\)
0.878520 0.477705i \(-0.158531\pi\)
\(660\) 5.86608 139.695i 0.00888801 0.211659i
\(661\) −1084.09 −1.64008 −0.820041 0.572304i \(-0.806050\pi\)
−0.820041 + 0.572304i \(0.806050\pi\)
\(662\) 269.054 + 269.054i 0.406426 + 0.406426i
\(663\) −411.761 + 411.761i −0.621058 + 0.621058i
\(664\) 245.342i 0.369491i
\(665\) 150.837 + 6.33395i 0.226823 + 0.00952474i
\(666\) −126.788 −0.190372
\(667\) −32.8258 32.8258i −0.0492142 0.0492142i
\(668\) 378.932 378.932i 0.567264 0.567264i
\(669\) 6.55878i 0.00980386i
\(670\) −637.437 + 586.060i −0.951398 + 0.874716i
\(671\) −88.8982 −0.132486
\(672\) 9.38421 + 9.38421i 0.0139646 + 0.0139646i
\(673\) 646.098 646.098i 0.960026 0.960026i −0.0392051 0.999231i \(-0.512483\pi\)
0.999231 + 0.0392051i \(0.0124826\pi\)
\(674\) 188.773i 0.280078i
\(675\) 99.2333 83.8316i 0.147012 0.124195i
\(676\) 744.792 1.10176
\(677\) −77.7169 77.7169i −0.114796 0.114796i 0.647375 0.762171i \(-0.275867\pi\)
−0.762171 + 0.647375i \(0.775867\pi\)
\(678\) −151.006 + 151.006i −0.222723 + 0.222723i
\(679\) 194.388i 0.286286i
\(680\) −138.302 150.426i −0.203386 0.221215i
\(681\) 355.549 0.522098
\(682\) −453.772 453.772i −0.665355 0.665355i
\(683\) −458.185 + 458.185i −0.670841 + 0.670841i −0.957910 0.287069i \(-0.907319\pi\)
0.287069 + 0.957910i \(0.407319\pi\)
\(684\) 133.750i 0.195541i
\(685\) −16.9301 + 403.174i −0.0247155 + 0.588575i
\(686\) −184.209 −0.268526
\(687\) −72.7719 72.7719i −0.105927 0.105927i
\(688\) −42.8467 + 42.8467i −0.0622772 + 0.0622772i
\(689\) 52.6072i 0.0763530i
\(690\) −58.6850 2.46430i −0.0850507 0.00357145i
\(691\) 564.193 0.816487 0.408244 0.912873i \(-0.366141\pi\)
0.408244 + 0.912873i \(0.366141\pi\)
\(692\) −72.1389 72.1389i −0.104247 0.104247i
\(693\) 23.1946 23.1946i 0.0334698 0.0334698i
\(694\) 301.940i 0.435072i
\(695\) 952.587 875.809i 1.37063 1.26016i
\(696\) −47.4212 −0.0681339
\(697\) 3.49314 + 3.49314i 0.00501167 + 0.00501167i
\(698\) 417.741 417.741i 0.598483 0.598483i
\(699\) 580.448i 0.830397i
\(700\) 43.7052 + 51.7348i 0.0624360 + 0.0739069i
\(701\) −607.326 −0.866371 −0.433185 0.901305i \(-0.642610\pi\)
−0.433185 + 0.901305i \(0.642610\pi\)
\(702\) 120.904 + 120.904i 0.172227 + 0.172227i
\(703\) 471.053 471.053i 0.670061 0.670061i
\(704\) 64.5793i 0.0917320i
\(705\) 94.5852 + 102.877i 0.134163 + 0.145925i
\(706\) −735.088 −1.04120
\(707\) −189.172 189.172i −0.267569 0.267569i
\(708\) 25.5017 25.5017i 0.0360193 0.0360193i
\(709\) 1335.32i 1.88338i 0.336482 + 0.941690i \(0.390763\pi\)
−0.336482 + 0.941690i \(0.609237\pi\)
\(710\) 37.7102 898.033i 0.0531130 1.26484i
\(711\) 218.346 0.307096
\(712\) −117.034 117.034i −0.164374 0.164374i
\(713\) −190.626 + 190.626i −0.267358 + 0.267358i
\(714\) 47.9397i 0.0671424i
\(715\) 938.315 + 39.4017i 1.31233 + 0.0551073i
\(716\) −506.701 −0.707682
\(717\) 316.254 + 316.254i 0.441080 + 0.441080i
\(718\) 392.377 392.377i 0.546486 0.546486i
\(719\) 669.180i 0.930709i 0.885124 + 0.465354i \(0.154073\pi\)
−0.885124 + 0.465354i \(0.845927\pi\)
\(720\) −44.1691 + 40.6090i −0.0613459 + 0.0564015i
\(721\) −155.025 −0.215014
\(722\) −135.921 135.921i −0.188256 0.188256i
\(723\) 465.845 465.845i 0.644322 0.644322i
\(724\) 135.712i 0.187447i
\(725\) −241.143 20.2880i −0.332612 0.0279834i
\(726\) −136.770 −0.188388
\(727\) −129.796 129.796i −0.178536 0.178536i 0.612181 0.790717i \(-0.290292\pi\)
−0.790717 + 0.612181i \(0.790292\pi\)
\(728\) −63.0325 + 63.0325i −0.0865831 + 0.0865831i
\(729\) 27.0000i 0.0370370i
\(730\) −190.421 207.114i −0.260850 0.283718i
\(731\) 218.884 0.299432
\(732\) 26.9752 + 26.9752i 0.0368514 + 0.0368514i
\(733\) −381.755 + 381.755i −0.520811 + 0.520811i −0.917816 0.397005i \(-0.870050\pi\)
0.397005 + 0.917816i \(0.370050\pi\)
\(734\) 801.713i 1.09225i
\(735\) 17.1371 408.104i 0.0233158 0.555244i
\(736\) 27.1293 0.0368605
\(737\) −698.995 698.995i −0.948432 0.948432i
\(738\) 1.02567 1.02567i 0.00138980 0.00138980i
\(739\) 1025.05i 1.38707i −0.720422 0.693536i \(-0.756052\pi\)
0.720422 0.693536i \(-0.243948\pi\)
\(740\) 298.578 + 12.5379i 0.403484 + 0.0169431i
\(741\) −898.384 −1.21239
\(742\) −3.06242 3.06242i −0.00412725 0.00412725i
\(743\) −260.972 + 260.972i −0.351241 + 0.351241i −0.860571 0.509330i \(-0.829893\pi\)
0.509330 + 0.860571i \(0.329893\pi\)
\(744\) 275.385i 0.370141i
\(745\) 698.784 642.462i 0.937965 0.862365i
\(746\) −478.612 −0.641572
\(747\) −184.006 184.006i −0.246327 0.246327i
\(748\) 164.953 164.953i 0.220526 0.220526i
\(749\) 134.883i 0.180084i
\(750\) −241.979 + 187.606i −0.322639 + 0.250141i
\(751\) 972.680 1.29518 0.647590 0.761989i \(-0.275777\pi\)
0.647590 + 0.761989i \(0.275777\pi\)
\(752\) −45.6422 45.6422i −0.0606944 0.0606944i
\(753\) 141.060 141.060i 0.187331 0.187331i
\(754\) 318.522i 0.422443i
\(755\) 295.669 + 321.589i 0.391615 + 0.425946i
\(756\) −14.0763 −0.0186195
\(757\) −697.433 697.433i −0.921312 0.921312i 0.0758101 0.997122i \(-0.475846\pi\)
−0.997122 + 0.0758101i \(0.975846\pi\)
\(758\) 164.467 164.467i 0.216975 0.216975i
\(759\) 67.0545i 0.0883459i
\(760\) 13.2264 314.975i 0.0174032 0.414441i
\(761\) −545.853 −0.717284 −0.358642 0.933475i \(-0.616760\pi\)
−0.358642 + 0.933475i \(0.616760\pi\)
\(762\) 192.568 + 192.568i 0.252714 + 0.252714i
\(763\) −88.7071 + 88.7071i −0.116261 + 0.116261i
\(764\) 59.4572i 0.0778235i
\(765\) 216.547 + 9.09322i 0.283067 + 0.0118866i
\(766\) −195.204 −0.254835
\(767\) 171.291 + 171.291i 0.223326 + 0.223326i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 113.856i 0.148057i −0.997256 0.0740286i \(-0.976414\pi\)
0.997256 0.0740286i \(-0.0235856\pi\)
\(770\) −56.9158 + 52.3284i −0.0739166 + 0.0679589i
\(771\) 649.241 0.842077
\(772\) 198.482 + 198.482i 0.257101 + 0.257101i
\(773\) 155.336 155.336i 0.200952 0.200952i −0.599456 0.800408i \(-0.704616\pi\)
0.800408 + 0.599456i \(0.204616\pi\)
\(774\) 64.2701i 0.0830362i
\(775\) −117.816 + 1400.37i −0.152021 + 1.80693i
\(776\) 405.917 0.523089
\(777\) 49.5751 + 49.5751i 0.0638032 + 0.0638032i
\(778\) 591.161 591.161i 0.759847 0.759847i
\(779\) 7.62135i