Properties

Label 690.3.k.a.277.19
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 277.19
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.19

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.45244 + 2.27502i) q^{5} +2.44949 q^{6} +(-3.57605 - 3.57605i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.45244 + 2.27502i) q^{5} +2.44949 q^{6} +(-3.57605 - 3.57605i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-6.72747 - 2.17742i) q^{10} +15.2817 q^{11} +(2.44949 + 2.44949i) q^{12} +(9.30559 - 9.30559i) q^{13} -7.15211i q^{14} +(-2.66678 + 8.23943i) q^{15} -4.00000 q^{16} +(7.64975 + 7.64975i) q^{17} +(3.00000 - 3.00000i) q^{18} -16.6289i q^{19} +(-4.55005 - 8.90489i) q^{20} -8.75951 q^{21} +(15.2817 + 15.2817i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(14.6485 - 20.2588i) q^{25} +18.6112 q^{26} +(-3.67423 - 3.67423i) q^{27} +(7.15211 - 7.15211i) q^{28} +28.4867i q^{29} +(-10.9062 + 5.57265i) q^{30} +46.8375 q^{31} +(-4.00000 - 4.00000i) q^{32} +(18.7162 - 18.7162i) q^{33} +15.2995i q^{34} +(24.0578 + 7.78657i) q^{35} +6.00000 q^{36} +(38.8008 + 38.8008i) q^{37} +(16.6289 - 16.6289i) q^{38} -22.7940i q^{39} +(4.35484 - 13.4549i) q^{40} +49.1688 q^{41} +(-8.75951 - 8.75951i) q^{42} +(-39.9675 + 39.9675i) q^{43} +30.5635i q^{44} +(6.82507 + 13.3573i) q^{45} -6.78233 q^{46} +(42.2681 + 42.2681i) q^{47} +(-4.89898 + 4.89898i) q^{48} -23.4237i q^{49} +(34.9074 - 5.61032i) q^{50} +18.7380 q^{51} +(18.6112 + 18.6112i) q^{52} +(40.9030 - 40.9030i) q^{53} -7.34847i q^{54} +(-68.0411 + 34.7664i) q^{55} +14.3042 q^{56} +(-20.3661 - 20.3661i) q^{57} +(-28.4867 + 28.4867i) q^{58} -115.558i q^{59} +(-16.4789 - 5.33357i) q^{60} -39.5522 q^{61} +(46.8375 + 46.8375i) q^{62} +(-10.7282 + 10.7282i) q^{63} -8.00000i q^{64} +(-20.2622 + 62.6031i) q^{65} +37.4325 q^{66} +(30.0611 + 30.0611i) q^{67} +(-15.2995 + 15.2995i) q^{68} +8.30662i q^{69} +(16.2712 + 31.8444i) q^{70} -109.516 q^{71} +(6.00000 + 6.00000i) q^{72} +(37.5852 - 37.5852i) q^{73} +77.6015i q^{74} +(-6.87121 - 42.7526i) q^{75} +33.2577 q^{76} +(-54.6484 - 54.6484i) q^{77} +(22.7940 - 22.7940i) q^{78} -116.711i q^{79} +(17.8098 - 9.10010i) q^{80} -9.00000 q^{81} +(49.1688 + 49.1688i) q^{82} +(97.5863 - 97.5863i) q^{83} -17.5190i q^{84} +(-51.4635 - 16.6567i) q^{85} -79.9350 q^{86} +(34.8890 + 34.8890i) q^{87} +(-30.5635 + 30.5635i) q^{88} +26.3345i q^{89} +(-6.53226 + 20.1824i) q^{90} -66.5546 q^{91} +(-6.78233 - 6.78233i) q^{92} +(57.3640 - 57.3640i) q^{93} +84.5362i q^{94} +(37.8311 + 74.0391i) q^{95} -9.79796 q^{96} +(-70.0462 - 70.0462i) q^{97} +(23.4237 - 23.4237i) q^{98} -45.8452i 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
\(5\) −4.45244 + 2.27502i −0.890489 + 0.455005i
\(6\) 2.44949 0.408248
\(7\) −3.57605 3.57605i −0.510865 0.510865i 0.403927 0.914791i \(-0.367645\pi\)
−0.914791 + 0.403927i \(0.867645\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −6.72747 2.17742i −0.672747 0.217742i
\(11\) 15.2817 1.38925 0.694625 0.719372i \(-0.255570\pi\)
0.694625 + 0.719372i \(0.255570\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) 9.30559 9.30559i 0.715815 0.715815i −0.251931 0.967745i \(-0.581065\pi\)
0.967745 + 0.251931i \(0.0810654\pi\)
\(14\) 7.15211i 0.510865i
\(15\) −2.66678 + 8.23943i −0.177786 + 0.549296i
\(16\) −4.00000 −0.250000
\(17\) 7.64975 + 7.64975i 0.449986 + 0.449986i 0.895350 0.445364i \(-0.146926\pi\)
−0.445364 + 0.895350i \(0.646926\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 16.6289i 0.875203i −0.899169 0.437602i \(-0.855828\pi\)
0.899169 0.437602i \(-0.144172\pi\)
\(20\) −4.55005 8.90489i −0.227502 0.445244i
\(21\) −8.75951 −0.417119
\(22\) 15.2817 + 15.2817i 0.694625 + 0.694625i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 14.6485 20.2588i 0.585941 0.810354i
\(26\) 18.6112 0.715815
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 7.15211 7.15211i 0.255432 0.255432i
\(29\) 28.4867i 0.982301i 0.871075 + 0.491150i \(0.163423\pi\)
−0.871075 + 0.491150i \(0.836577\pi\)
\(30\) −10.9062 + 5.57265i −0.363541 + 0.185755i
\(31\) 46.8375 1.51089 0.755443 0.655214i \(-0.227422\pi\)
0.755443 + 0.655214i \(0.227422\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 18.7162 18.7162i 0.567159 0.567159i
\(34\) 15.2995i 0.449986i
\(35\) 24.0578 + 7.78657i 0.687366 + 0.222473i
\(36\) 6.00000 0.166667
\(37\) 38.8008 + 38.8008i 1.04867 + 1.04867i 0.998753 + 0.0499156i \(0.0158952\pi\)
0.0499156 + 0.998753i \(0.484105\pi\)
\(38\) 16.6289 16.6289i 0.437602 0.437602i
\(39\) 22.7940i 0.584460i
\(40\) 4.35484 13.4549i 0.108871 0.336373i
\(41\) 49.1688 1.19924 0.599620 0.800285i \(-0.295319\pi\)
0.599620 + 0.800285i \(0.295319\pi\)
\(42\) −8.75951 8.75951i −0.208560 0.208560i
\(43\) −39.9675 + 39.9675i −0.929477 + 0.929477i −0.997672 0.0681954i \(-0.978276\pi\)
0.0681954 + 0.997672i \(0.478276\pi\)
\(44\) 30.5635i 0.694625i
\(45\) 6.82507 + 13.3573i 0.151668 + 0.296830i
\(46\) −6.78233 −0.147442
\(47\) 42.2681 + 42.2681i 0.899322 + 0.899322i 0.995376 0.0960544i \(-0.0306223\pi\)
−0.0960544 + 0.995376i \(0.530622\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 23.4237i 0.478034i
\(50\) 34.9074 5.61032i 0.698147 0.112206i
\(51\) 18.7380 0.367412
\(52\) 18.6112 + 18.6112i 0.357907 + 0.357907i
\(53\) 40.9030 40.9030i 0.771756 0.771756i −0.206658 0.978413i \(-0.566259\pi\)
0.978413 + 0.206658i \(0.0662587\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −68.0411 + 34.7664i −1.23711 + 0.632115i
\(56\) 14.3042 0.255432
\(57\) −20.3661 20.3661i −0.357300 0.357300i
\(58\) −28.4867 + 28.4867i −0.491150 + 0.491150i
\(59\) 115.558i 1.95860i −0.202409 0.979301i \(-0.564877\pi\)
0.202409 0.979301i \(-0.435123\pi\)
\(60\) −16.4789 5.33357i −0.274648 0.0888928i
\(61\) −39.5522 −0.648397 −0.324199 0.945989i \(-0.605095\pi\)
−0.324199 + 0.945989i \(0.605095\pi\)
\(62\) 46.8375 + 46.8375i 0.755443 + 0.755443i
\(63\) −10.7282 + 10.7282i −0.170288 + 0.170288i
\(64\) 8.00000i 0.125000i
\(65\) −20.2622 + 62.6031i −0.311726 + 0.963124i
\(66\) 37.4325 0.567159
\(67\) 30.0611 + 30.0611i 0.448673 + 0.448673i 0.894913 0.446240i \(-0.147237\pi\)
−0.446240 + 0.894913i \(0.647237\pi\)
\(68\) −15.2995 + 15.2995i −0.224993 + 0.224993i
\(69\) 8.30662i 0.120386i
\(70\) 16.2712 + 31.8444i 0.232446 + 0.454920i
\(71\) −109.516 −1.54247 −0.771237 0.636548i \(-0.780362\pi\)
−0.771237 + 0.636548i \(0.780362\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 37.5852 37.5852i 0.514865 0.514865i −0.401148 0.916013i \(-0.631389\pi\)
0.916013 + 0.401148i \(0.131389\pi\)
\(74\) 77.6015i 1.04867i
\(75\) −6.87121 42.7526i −0.0916162 0.570035i
\(76\) 33.2577 0.437602
\(77\) −54.6484 54.6484i −0.709719 0.709719i
\(78\) 22.7940 22.7940i 0.292230 0.292230i
\(79\) 116.711i 1.47736i −0.674057 0.738679i \(-0.735450\pi\)
0.674057 0.738679i \(-0.264550\pi\)
\(80\) 17.8098 9.10010i 0.222622 0.113751i
\(81\) −9.00000 −0.111111
\(82\) 49.1688 + 49.1688i 0.599620 + 0.599620i
\(83\) 97.5863 97.5863i 1.17574 1.17574i 0.194920 0.980819i \(-0.437555\pi\)
0.980819 0.194920i \(-0.0624447\pi\)
\(84\) 17.5190i 0.208560i
\(85\) −51.4635 16.6567i −0.605453 0.195961i
\(86\) −79.9350 −0.929477
\(87\) 34.8890 + 34.8890i 0.401023 + 0.401023i
\(88\) −30.5635 + 30.5635i −0.347312 + 0.347312i
\(89\) 26.3345i 0.295893i 0.988995 + 0.147946i \(0.0472663\pi\)
−0.988995 + 0.147946i \(0.952734\pi\)
\(90\) −6.53226 + 20.1824i −0.0725807 + 0.224249i
\(91\) −66.5546 −0.731369
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 57.3640 57.3640i 0.616817 0.616817i
\(94\) 84.5362i 0.899322i
\(95\) 37.8311 + 74.0391i 0.398222 + 0.779359i
\(96\) −9.79796 −0.102062
\(97\) −70.0462 70.0462i −0.722126 0.722126i 0.246912 0.969038i \(-0.420584\pi\)
−0.969038 + 0.246912i \(0.920584\pi\)
\(98\) 23.4237 23.4237i 0.239017 0.239017i
\(99\) 45.8452i 0.463083i
\(100\) 40.5177 + 29.2970i 0.405177 + 0.292970i
\(101\) 157.618 1.56057 0.780285 0.625424i \(-0.215074\pi\)
0.780285 + 0.625424i \(0.215074\pi\)
\(102\) 18.7380 + 18.7380i 0.183706 + 0.183706i
\(103\) −133.113 + 133.113i −1.29236 + 1.29236i −0.359032 + 0.933325i \(0.616893\pi\)
−0.933325 + 0.359032i \(0.883107\pi\)
\(104\) 37.2224i 0.357907i
\(105\) 39.0012 19.9281i 0.371440 0.189791i
\(106\) 81.8061 0.771756
\(107\) −14.8025 14.8025i −0.138341 0.138341i 0.634545 0.772886i \(-0.281188\pi\)
−0.772886 + 0.634545i \(0.781188\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 0.102683i 0.000942049i −1.00000 0.000471024i \(-0.999850\pi\)
1.00000 0.000471024i \(-0.000149932\pi\)
\(110\) −102.807 33.2748i −0.934613 0.302498i
\(111\) 95.0421 0.856235
\(112\) 14.3042 + 14.3042i 0.127716 + 0.127716i
\(113\) −54.9742 + 54.9742i −0.486497 + 0.486497i −0.907199 0.420702i \(-0.861784\pi\)
0.420702 + 0.907199i \(0.361784\pi\)
\(114\) 40.7322i 0.357300i
\(115\) 7.38399 22.8140i 0.0642086 0.198382i
\(116\) −56.9734 −0.491150
\(117\) −27.9168 27.9168i −0.238605 0.238605i
\(118\) 115.558 115.558i 0.979301 0.979301i
\(119\) 54.7119i 0.459764i
\(120\) −11.1453 21.8124i −0.0928775 0.181770i
\(121\) 112.532 0.930014
\(122\) −39.5522 39.5522i −0.324199 0.324199i
\(123\) 60.2193 60.2193i 0.489587 0.489587i
\(124\) 93.6750i 0.755443i
\(125\) −19.1324 + 123.527i −0.153059 + 0.988217i
\(126\) −21.4563 −0.170288
\(127\) −159.860 159.860i −1.25874 1.25874i −0.951696 0.307042i \(-0.900661\pi\)
−0.307042 0.951696i \(-0.599339\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 97.9000i 0.758914i
\(130\) −82.8653 + 42.3409i −0.637425 + 0.325699i
\(131\) −249.753 −1.90651 −0.953257 0.302161i \(-0.902292\pi\)
−0.953257 + 0.302161i \(0.902292\pi\)
\(132\) 37.4325 + 37.4325i 0.283579 + 0.283579i
\(133\) −59.4657 + 59.4657i −0.447111 + 0.447111i
\(134\) 60.1222i 0.448673i
\(135\) 24.7183 + 8.00035i 0.183099 + 0.0592619i
\(136\) −30.5990 −0.224993
\(137\) 24.1535 + 24.1535i 0.176303 + 0.176303i 0.789742 0.613439i \(-0.210214\pi\)
−0.613439 + 0.789742i \(0.710214\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 107.895i 0.776221i 0.921613 + 0.388111i \(0.126872\pi\)
−0.921613 + 0.388111i \(0.873128\pi\)
\(140\) −15.5731 + 48.1156i −0.111237 + 0.343683i
\(141\) 103.535 0.734293
\(142\) −109.516 109.516i −0.771237 0.771237i
\(143\) 142.206 142.206i 0.994445 0.994445i
\(144\) 12.0000i 0.0833333i
\(145\) −64.8080 126.836i −0.446952 0.874728i
\(146\) 75.1703 0.514865
\(147\) −28.6880 28.6880i −0.195157 0.195157i
\(148\) −77.6015 + 77.6015i −0.524335 + 0.524335i
\(149\) 149.146i 1.00098i 0.865741 + 0.500492i \(0.166847\pi\)
−0.865741 + 0.500492i \(0.833153\pi\)
\(150\) 35.8814 49.6238i 0.239209 0.330826i
\(151\) −87.3637 −0.578568 −0.289284 0.957243i \(-0.593417\pi\)
−0.289284 + 0.957243i \(0.593417\pi\)
\(152\) 33.2577 + 33.2577i 0.218801 + 0.218801i
\(153\) 22.9493 22.9493i 0.149995 0.149995i
\(154\) 109.297i 0.709719i
\(155\) −208.541 + 106.556i −1.34543 + 0.687461i
\(156\) 45.5879 0.292230
\(157\) 81.1651 + 81.1651i 0.516975 + 0.516975i 0.916655 0.399680i \(-0.130879\pi\)
−0.399680 + 0.916655i \(0.630879\pi\)
\(158\) 116.711 116.711i 0.738679 0.738679i
\(159\) 100.192i 0.630136i
\(160\) 26.9099 + 8.70968i 0.168187 + 0.0544355i
\(161\) 24.2540 0.150646
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −56.4577 + 56.4577i −0.346366 + 0.346366i −0.858754 0.512388i \(-0.828761\pi\)
0.512388 + 0.858754i \(0.328761\pi\)
\(164\) 98.3376i 0.599620i
\(165\) −40.7531 + 125.913i −0.246989 + 0.763109i
\(166\) 195.173 1.17574
\(167\) 161.337 + 161.337i 0.966088 + 0.966088i 0.999444 0.0333553i \(-0.0106193\pi\)
−0.0333553 + 0.999444i \(0.510619\pi\)
\(168\) 17.5190 17.5190i 0.104280 0.104280i
\(169\) 4.18809i 0.0247816i
\(170\) −34.8068 68.1202i −0.204746 0.400707i
\(171\) −49.8866 −0.291734
\(172\) −79.9350 79.9350i −0.464738 0.464738i
\(173\) −113.686 + 113.686i −0.657146 + 0.657146i −0.954704 0.297558i \(-0.903828\pi\)
0.297558 + 0.954704i \(0.403828\pi\)
\(174\) 69.7779i 0.401023i
\(175\) −124.831 + 20.0628i −0.713318 + 0.114645i
\(176\) −61.1270 −0.347312
\(177\) −141.528 141.528i −0.799596 0.799596i
\(178\) −26.3345 + 26.3345i −0.147946 + 0.147946i
\(179\) 202.276i 1.13003i −0.825080 0.565016i \(-0.808870\pi\)
0.825080 0.565016i \(-0.191130\pi\)
\(180\) −26.7147 + 13.6501i −0.148415 + 0.0758342i
\(181\) −119.692 −0.661281 −0.330640 0.943757i \(-0.607265\pi\)
−0.330640 + 0.943757i \(0.607265\pi\)
\(182\) −66.5546 66.5546i −0.365685 0.365685i
\(183\) −48.4414 + 48.4414i −0.264707 + 0.264707i
\(184\) 13.5647i 0.0737210i
\(185\) −261.031 84.4855i −1.41098 0.456679i
\(186\) 114.728 0.616817
\(187\) 116.902 + 116.902i 0.625142 + 0.625142i
\(188\) −84.5362 + 84.5362i −0.449661 + 0.449661i
\(189\) 26.2785i 0.139040i
\(190\) −36.2080 + 111.870i −0.190568 + 0.588790i
\(191\) 354.419 1.85560 0.927798 0.373084i \(-0.121700\pi\)
0.927798 + 0.373084i \(0.121700\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) 89.8493 89.8493i 0.465541 0.465541i −0.434926 0.900466i \(-0.643225\pi\)
0.900466 + 0.434926i \(0.143225\pi\)
\(194\) 140.092i 0.722126i
\(195\) 51.8568 + 101.489i 0.265932 + 0.520455i
\(196\) 46.8473 0.239017
\(197\) 244.917 + 244.917i 1.24323 + 1.24323i 0.958652 + 0.284582i \(0.0918548\pi\)
0.284582 + 0.958652i \(0.408145\pi\)
\(198\) 45.8452 45.8452i 0.231542 0.231542i
\(199\) 201.091i 1.01051i 0.862971 + 0.505253i \(0.168601\pi\)
−0.862971 + 0.505253i \(0.831399\pi\)
\(200\) 11.2206 + 69.8147i 0.0561032 + 0.349074i
\(201\) 73.6343 0.366340
\(202\) 157.618 + 157.618i 0.780285 + 0.780285i
\(203\) 101.870 101.870i 0.501823 0.501823i
\(204\) 37.4760i 0.183706i
\(205\) −218.921 + 111.860i −1.06791 + 0.545660i
\(206\) −266.226 −1.29236
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) −37.2224 + 37.2224i −0.178954 + 0.178954i
\(209\) 254.118i 1.21588i
\(210\) 58.9293 + 19.0731i 0.280616 + 0.0908244i
\(211\) −56.8261 −0.269318 −0.134659 0.990892i \(-0.542994\pi\)
−0.134659 + 0.990892i \(0.542994\pi\)
\(212\) 81.8061 + 81.8061i 0.385878 + 0.385878i
\(213\) −134.129 + 134.129i −0.629712 + 0.629712i
\(214\) 29.6049i 0.138341i
\(215\) 87.0260 268.880i 0.404772 1.25061i
\(216\) 14.6969 0.0680414
\(217\) −167.493 167.493i −0.771859 0.771859i
\(218\) 0.102683 0.102683i 0.000471024 0.000471024i
\(219\) 92.0645i 0.420386i
\(220\) −69.5327 136.082i −0.316058 0.618556i
\(221\) 142.371 0.644213
\(222\) 95.0421 + 95.0421i 0.428117 + 0.428117i
\(223\) 50.8364 50.8364i 0.227966 0.227966i −0.583876 0.811843i \(-0.698465\pi\)
0.811843 + 0.583876i \(0.198465\pi\)
\(224\) 28.6084i 0.127716i
\(225\) −60.7765 43.9456i −0.270118 0.195314i
\(226\) −109.948 −0.486497
\(227\) −75.8315 75.8315i −0.334060 0.334060i 0.520066 0.854126i \(-0.325907\pi\)
−0.854126 + 0.520066i \(0.825907\pi\)
\(228\) 40.7322 40.7322i 0.178650 0.178650i
\(229\) 70.0263i 0.305792i −0.988242 0.152896i \(-0.951140\pi\)
0.988242 0.152896i \(-0.0488599\pi\)
\(230\) 30.1979 15.4300i 0.131295 0.0670868i
\(231\) −133.861 −0.579483
\(232\) −56.9734 56.9734i −0.245575 0.245575i
\(233\) 4.02362 4.02362i 0.0172687 0.0172687i −0.698420 0.715688i \(-0.746113\pi\)
0.715688 + 0.698420i \(0.246113\pi\)
\(234\) 55.8336i 0.238605i
\(235\) −284.357 92.0354i −1.21003 0.391640i
\(236\) 231.115 0.979301
\(237\) −142.942 142.942i −0.603129 0.603129i
\(238\) 54.7119 54.7119i 0.229882 0.229882i
\(239\) 268.560i 1.12368i −0.827245 0.561842i \(-0.810093\pi\)
0.827245 0.561842i \(-0.189907\pi\)
\(240\) 10.6671 32.9577i 0.0444464 0.137324i
\(241\) −265.941 −1.10349 −0.551745 0.834013i \(-0.686038\pi\)
−0.551745 + 0.834013i \(0.686038\pi\)
\(242\) 112.532 + 112.532i 0.465007 + 0.465007i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 79.1045i 0.324199i
\(245\) 53.2894 + 104.293i 0.217508 + 0.425684i
\(246\) 120.439 0.489587
\(247\) −154.741 154.741i −0.626483 0.626483i
\(248\) −93.6750 + 93.6750i −0.377722 + 0.377722i
\(249\) 239.037i 0.959987i
\(250\) −142.659 + 104.395i −0.570638 + 0.417579i
\(251\) 167.641 0.667893 0.333947 0.942592i \(-0.391619\pi\)
0.333947 + 0.942592i \(0.391619\pi\)
\(252\) −21.4563 21.4563i −0.0851442 0.0851442i
\(253\) −51.8229 + 51.8229i −0.204834 + 0.204834i
\(254\) 319.719i 1.25874i
\(255\) −83.4299 + 42.6294i −0.327176 + 0.167174i
\(256\) 16.0000 0.0625000
\(257\) 64.2388 + 64.2388i 0.249956 + 0.249956i 0.820953 0.570996i \(-0.193443\pi\)
−0.570996 + 0.820953i \(0.693443\pi\)
\(258\) −97.9000 + 97.9000i −0.379457 + 0.379457i
\(259\) 277.507i 1.07146i
\(260\) −125.206 40.5244i −0.481562 0.155863i
\(261\) 85.4602 0.327434
\(262\) −249.753 249.753i −0.953257 0.953257i
\(263\) −26.1375 + 26.1375i −0.0993820 + 0.0993820i −0.755050 0.655668i \(-0.772387\pi\)
0.655668 + 0.755050i \(0.272387\pi\)
\(264\) 74.8650i 0.283579i
\(265\) −89.0631 + 275.174i −0.336087 + 1.03839i
\(266\) −118.931 −0.447111
\(267\) 32.2530 + 32.2530i 0.120798 + 0.120798i
\(268\) −60.1222 + 60.1222i −0.224336 + 0.224336i
\(269\) 114.873i 0.427036i −0.976939 0.213518i \(-0.931508\pi\)
0.976939 0.213518i \(-0.0684922\pi\)
\(270\) 16.7180 + 32.7187i 0.0619183 + 0.121180i
\(271\) 263.414 0.972007 0.486004 0.873957i \(-0.338454\pi\)
0.486004 + 0.873957i \(0.338454\pi\)
\(272\) −30.5990 30.5990i −0.112496 0.112496i
\(273\) −81.5124 + 81.5124i −0.298580 + 0.298580i
\(274\) 48.3070i 0.176303i
\(275\) 223.855 309.590i 0.814018 1.12578i
\(276\) −16.6132 −0.0601929
\(277\) −247.635 247.635i −0.893990 0.893990i 0.100906 0.994896i \(-0.467826\pi\)
−0.994896 + 0.100906i \(0.967826\pi\)
\(278\) −107.895 + 107.895i −0.388111 + 0.388111i
\(279\) 140.512i 0.503629i
\(280\) −63.6887 + 32.5425i −0.227460 + 0.116223i
\(281\) −503.134 −1.79051 −0.895257 0.445550i \(-0.853008\pi\)
−0.895257 + 0.445550i \(0.853008\pi\)
\(282\) 103.535 + 103.535i 0.367147 + 0.367147i
\(283\) −334.802 + 334.802i −1.18304 + 1.18304i −0.204093 + 0.978951i \(0.565425\pi\)
−0.978951 + 0.204093i \(0.934575\pi\)
\(284\) 219.031i 0.771237i
\(285\) 137.012 + 44.3456i 0.480745 + 0.155598i
\(286\) 284.411 0.994445
\(287\) −175.830 175.830i −0.612649 0.612649i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 171.963i 0.595026i
\(290\) 62.0275 191.644i 0.213888 0.660840i
\(291\) −171.578 −0.589614
\(292\) 75.1703 + 75.1703i 0.257433 + 0.257433i
\(293\) −103.910 + 103.910i −0.354642 + 0.354642i −0.861833 0.507192i \(-0.830684\pi\)
0.507192 + 0.861833i \(0.330684\pi\)
\(294\) 57.3760i 0.195157i
\(295\) 262.896 + 514.513i 0.891174 + 1.74411i
\(296\) −155.203 −0.524335
\(297\) −56.1487 56.1487i −0.189053 0.189053i
\(298\) −149.146 + 149.146i −0.500492 + 0.500492i
\(299\) 63.1136i 0.211082i
\(300\) 85.5052 13.7424i 0.285017 0.0458081i
\(301\) 285.852 0.949674
\(302\) −87.3637 87.3637i −0.289284 0.289284i
\(303\) 193.041 193.041i 0.637100 0.637100i
\(304\) 66.5154i 0.218801i
\(305\) 176.104 89.9823i 0.577391 0.295024i
\(306\) 45.8985 0.149995
\(307\) 15.9914 + 15.9914i 0.0520893 + 0.0520893i 0.732672 0.680582i \(-0.238273\pi\)
−0.680582 + 0.732672i \(0.738273\pi\)
\(308\) 109.297 109.297i 0.354859 0.354859i
\(309\) 326.058i 1.05521i
\(310\) −315.098 101.985i −1.01644 0.328983i
\(311\) 430.485 1.38420 0.692098 0.721804i \(-0.256687\pi\)
0.692098 + 0.721804i \(0.256687\pi\)
\(312\) 45.5879 + 45.5879i 0.146115 + 0.146115i
\(313\) −215.563 + 215.563i −0.688699 + 0.688699i −0.961944 0.273246i \(-0.911903\pi\)
0.273246 + 0.961944i \(0.411903\pi\)
\(314\) 162.330i 0.516975i
\(315\) 23.3597 72.1734i 0.0741578 0.229122i
\(316\) 233.423 0.738679
\(317\) −74.4937 74.4937i −0.234996 0.234996i 0.579778 0.814774i \(-0.303139\pi\)
−0.814774 + 0.579778i \(0.803139\pi\)
\(318\) 100.192 100.192i 0.315068 0.315068i
\(319\) 435.327i 1.36466i
\(320\) 18.2002 + 35.6196i 0.0568756 + 0.111311i
\(321\) −36.2585 −0.112955
\(322\) 24.2540 + 24.2540i 0.0753229 + 0.0753229i
\(323\) 127.207 127.207i 0.393829 0.393829i
\(324\) 18.0000i 0.0555556i
\(325\) −52.2074 324.834i −0.160638 0.999488i
\(326\) −112.915 −0.346366
\(327\) −0.125761 0.125761i −0.000384590 0.000384590i
\(328\) −98.3376 + 98.3376i −0.299810 + 0.299810i
\(329\) 302.306i 0.918864i
\(330\) −166.666 + 85.1598i −0.505049 + 0.258060i
\(331\) 316.884 0.957354 0.478677 0.877991i \(-0.341116\pi\)
0.478677 + 0.877991i \(0.341116\pi\)
\(332\) 195.173 + 195.173i 0.587870 + 0.587870i
\(333\) 116.402 116.402i 0.349556 0.349556i
\(334\) 322.673i 0.966088i
\(335\) −202.235 65.4556i −0.603687 0.195390i
\(336\) 35.0380 0.104280
\(337\) 81.9442 + 81.9442i 0.243158 + 0.243158i 0.818155 0.574997i \(-0.194997\pi\)
−0.574997 + 0.818155i \(0.694997\pi\)
\(338\) 4.18809 4.18809i 0.0123908 0.0123908i
\(339\) 134.659i 0.397223i
\(340\) 33.3134 102.927i 0.0979807 0.302726i
\(341\) 715.758 2.09900
\(342\) −49.8866 49.8866i −0.145867 0.145867i
\(343\) −258.991 + 258.991i −0.755076 + 0.755076i
\(344\) 159.870i 0.464738i
\(345\) −18.8978 36.9848i −0.0547762 0.107202i
\(346\) −227.372 −0.657146
\(347\) 253.677 + 253.677i 0.731058 + 0.731058i 0.970829 0.239771i \(-0.0770724\pi\)
−0.239771 + 0.970829i \(0.577072\pi\)
\(348\) −69.7779 + 69.7779i −0.200511 + 0.200511i
\(349\) 162.699i 0.466186i −0.972454 0.233093i \(-0.925115\pi\)
0.972454 0.233093i \(-0.0748847\pi\)
\(350\) −144.893 104.768i −0.413981 0.299337i
\(351\) −68.3819 −0.194820
\(352\) −61.1270 61.1270i −0.173656 0.173656i
\(353\) 19.9049 19.9049i 0.0563877 0.0563877i −0.678351 0.734738i \(-0.737305\pi\)
0.734738 + 0.678351i \(0.237305\pi\)
\(354\) 283.057i 0.799596i
\(355\) 487.612 249.151i 1.37356 0.701833i
\(356\) −52.6689 −0.147946
\(357\) −67.0081 67.0081i −0.187698 0.187698i
\(358\) 202.276 202.276i 0.565016 0.565016i
\(359\) 414.391i 1.15429i −0.816641 0.577146i \(-0.804166\pi\)
0.816641 0.577146i \(-0.195834\pi\)
\(360\) −40.3648 13.0645i −0.112124 0.0362903i
\(361\) 84.4810 0.234019
\(362\) −119.692 119.692i −0.330640 0.330640i
\(363\) 137.823 137.823i 0.379677 0.379677i
\(364\) 133.109i 0.365685i
\(365\) −81.8387 + 252.853i −0.224215 + 0.692748i
\(366\) −96.8828 −0.264707
\(367\) 105.693 + 105.693i 0.287991 + 0.287991i 0.836286 0.548294i \(-0.184723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 147.506i 0.399746i
\(370\) −176.545 345.516i −0.477150 0.933828i
\(371\) −292.543 −0.788526
\(372\) 114.728 + 114.728i 0.308408 + 0.308408i
\(373\) −322.018 + 322.018i −0.863319 + 0.863319i −0.991722 0.128403i \(-0.959015\pi\)
0.128403 + 0.991722i \(0.459015\pi\)
\(374\) 233.803i 0.625142i
\(375\) 127.857 + 174.721i 0.340952 + 0.465924i
\(376\) −169.072 −0.449661
\(377\) 265.086 + 265.086i 0.703145 + 0.703145i
\(378\) −26.2785 + 26.2785i −0.0695199 + 0.0695199i
\(379\) 46.2839i 0.122121i 0.998134 + 0.0610605i \(0.0194483\pi\)
−0.998134 + 0.0610605i \(0.980552\pi\)
\(380\) −148.078 + 75.6621i −0.389679 + 0.199111i
\(381\) −391.575 −1.02776
\(382\) 354.419 + 354.419i 0.927798 + 0.927798i
\(383\) −456.507 + 456.507i −1.19192 + 1.19192i −0.215397 + 0.976527i \(0.569105\pi\)
−0.976527 + 0.215397i \(0.930895\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 367.645 + 118.992i 0.954922 + 0.309071i
\(386\) 179.699 0.465541
\(387\) 119.902 + 119.902i 0.309826 + 0.309826i
\(388\) 140.092 140.092i 0.361063 0.361063i
\(389\) 423.277i 1.08812i −0.839048 0.544058i \(-0.816887\pi\)
0.839048 0.544058i \(-0.183113\pi\)
\(390\) −49.6320 + 153.346i −0.127262 + 0.393194i
\(391\) −51.8832 −0.132693
\(392\) 46.8473 + 46.8473i 0.119509 + 0.119509i
\(393\) −305.884 + 305.884i −0.778331 + 0.778331i
\(394\) 489.834i 1.24323i
\(395\) 265.521 + 519.651i 0.672206 + 1.31557i
\(396\) 91.6905 0.231542
\(397\) 114.959 + 114.959i 0.289569 + 0.289569i 0.836910 0.547341i \(-0.184360\pi\)
−0.547341 + 0.836910i \(0.684360\pi\)
\(398\) −201.091 + 201.091i −0.505253 + 0.505253i
\(399\) 145.661i 0.365064i
\(400\) −58.5941 + 81.0354i −0.146485 + 0.202588i
\(401\) −545.562 −1.36050 −0.680252 0.732978i \(-0.738130\pi\)
−0.680252 + 0.732978i \(0.738130\pi\)
\(402\) 73.6343 + 73.6343i 0.183170 + 0.183170i
\(403\) 435.850 435.850i 1.08151 1.08151i
\(404\) 315.235i 0.780285i
\(405\) 40.0720 20.4752i 0.0989432 0.0505561i
\(406\) 203.740 0.501823
\(407\) 592.943 + 592.943i 1.45686 + 1.45686i
\(408\) −37.4760 + 37.4760i −0.0918529 + 0.0918529i
\(409\) 400.154i 0.978371i 0.872180 + 0.489185i \(0.162706\pi\)
−0.872180 + 0.489185i \(0.837294\pi\)
\(410\) −330.782 107.061i −0.806785 0.261125i
\(411\) 59.1637 0.143951
\(412\) −266.226 266.226i −0.646179 0.646179i
\(413\) −413.240 + 413.240i −1.00058 + 1.00058i
\(414\) 20.3470i 0.0491473i
\(415\) −212.486 + 656.509i −0.512015 + 1.58195i
\(416\) −74.4447 −0.178954
\(417\) 132.144 + 132.144i 0.316891 + 0.316891i
\(418\) 254.118 254.118i 0.607938 0.607938i
\(419\) 100.320i 0.239428i −0.992808 0.119714i \(-0.961802\pi\)
0.992808 0.119714i \(-0.0381978\pi\)
\(420\) 39.8562 + 78.0025i 0.0948957 + 0.185720i
\(421\) 115.474 0.274286 0.137143 0.990551i \(-0.456208\pi\)
0.137143 + 0.990551i \(0.456208\pi\)
\(422\) −56.8261 56.8261i −0.134659 0.134659i
\(423\) 126.804 126.804i 0.299774 0.299774i
\(424\) 163.612i 0.385878i
\(425\) 267.033 42.9176i 0.628312 0.100983i
\(426\) −268.257 −0.629712
\(427\) 141.441 + 141.441i 0.331243 + 0.331243i
\(428\) 29.6049 29.6049i 0.0691704 0.0691704i
\(429\) 348.331i 0.811961i
\(430\) 355.906 181.854i 0.827689 0.422916i
\(431\) 341.266 0.791801 0.395901 0.918293i \(-0.370432\pi\)
0.395901 + 0.918293i \(0.370432\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) −364.495 + 364.495i −0.841791 + 0.841791i −0.989092 0.147301i \(-0.952941\pi\)
0.147301 + 0.989092i \(0.452941\pi\)
\(434\) 334.987i 0.771859i
\(435\) −234.714 75.9679i −0.539573 0.174639i
\(436\) 0.205367 0.000471024
\(437\) 56.3912 + 56.3912i 0.129042 + 0.129042i
\(438\) 92.0645 92.0645i 0.210193 0.210193i
\(439\) 745.512i 1.69821i −0.528228 0.849103i \(-0.677143\pi\)
0.528228 0.849103i \(-0.322857\pi\)
\(440\) 66.5495 205.615i 0.151249 0.467307i
\(441\) −70.2710 −0.159345
\(442\) 142.371 + 142.371i 0.322106 + 0.322106i
\(443\) 426.726 426.726i 0.963264 0.963264i −0.0360845 0.999349i \(-0.511489\pi\)
0.999349 + 0.0360845i \(0.0114886\pi\)
\(444\) 190.084i 0.428117i
\(445\) −59.9116 117.253i −0.134633 0.263489i
\(446\) 101.673 0.227966
\(447\) 182.666 + 182.666i 0.408650 + 0.408650i
\(448\) −28.6084 + 28.6084i −0.0638581 + 0.0638581i
\(449\) 183.403i 0.408470i −0.978922 0.204235i \(-0.934529\pi\)
0.978922 0.204235i \(-0.0654707\pi\)
\(450\) −16.8310 104.722i −0.0374021 0.232716i
\(451\) 751.385 1.66604
\(452\) −109.948 109.948i −0.243248 0.243248i
\(453\) −106.998 + 106.998i −0.236199 + 0.236199i
\(454\) 151.663i 0.334060i
\(455\) 296.331 151.413i 0.651276 0.332777i
\(456\) 81.4644 0.178650
\(457\) −68.1150 68.1150i −0.149048 0.149048i 0.628645 0.777693i \(-0.283610\pi\)
−0.777693 + 0.628645i \(0.783610\pi\)
\(458\) 70.0263 70.0263i 0.152896 0.152896i
\(459\) 56.2140i 0.122471i
\(460\) 45.6279 + 14.7680i 0.0991911 + 0.0321043i
\(461\) −386.997 −0.839472 −0.419736 0.907646i \(-0.637877\pi\)
−0.419736 + 0.907646i \(0.637877\pi\)
\(462\) −133.861 133.861i −0.289742 0.289742i
\(463\) −111.577 + 111.577i −0.240986 + 0.240986i −0.817258 0.576272i \(-0.804507\pi\)
0.576272 + 0.817258i \(0.304507\pi\)
\(464\) 113.947i 0.245575i
\(465\) −124.905 + 385.914i −0.268614 + 0.829923i
\(466\) 8.04723 0.0172687
\(467\) −8.27939 8.27939i −0.0177289 0.0177289i 0.698187 0.715916i \(-0.253991\pi\)
−0.715916 + 0.698187i \(0.753991\pi\)
\(468\) 55.8336 55.8336i 0.119302 0.119302i
\(469\) 215.000i 0.458422i
\(470\) −192.322 376.393i −0.409196 0.800836i
\(471\) 198.813 0.422108
\(472\) 231.115 + 231.115i 0.489651 + 0.489651i
\(473\) −610.773 + 610.773i −1.29128 + 1.29128i
\(474\) 285.883i 0.603129i
\(475\) −336.881 243.588i −0.709224 0.512817i
\(476\) 109.424 0.229882
\(477\) −122.709 122.709i −0.257252 0.257252i
\(478\) 268.560 268.560i 0.561842 0.561842i
\(479\) 391.487i 0.817301i 0.912691 + 0.408651i \(0.134001\pi\)
−0.912691 + 0.408651i \(0.865999\pi\)
\(480\) 43.6249 22.2906i 0.0908851 0.0464388i
\(481\) 722.128 1.50131
\(482\) −265.941 265.941i −0.551745 0.551745i
\(483\) 29.7049 29.7049i 0.0615009 0.0615009i
\(484\) 225.063i 0.465007i
\(485\) 471.234 + 152.520i 0.971616 + 0.314474i
\(486\) −22.0454 −0.0453609
\(487\) −282.428 282.428i −0.579933 0.579933i 0.354951 0.934885i \(-0.384497\pi\)
−0.934885 + 0.354951i \(0.884497\pi\)
\(488\) 79.1045 79.1045i 0.162099 0.162099i
\(489\) 138.292i 0.282807i
\(490\) −51.0032 + 157.582i −0.104088 + 0.321596i
\(491\) 15.3095 0.0311802 0.0155901 0.999878i \(-0.495037\pi\)
0.0155901 + 0.999878i \(0.495037\pi\)
\(492\) 120.439 + 120.439i 0.244794 + 0.244794i
\(493\) −217.916 + 217.916i −0.442021 + 0.442021i
\(494\) 309.483i 0.626483i
\(495\) 104.299 + 204.123i 0.210705 + 0.412370i
\(496\) −187.350 −0.377722
\(497\) 391.634 + 391.634i 0.787996 + 0.787996i
\(498\) 239.037 239.037i 0.479993 0.479993i
\(499\) 823.731i 1.65076i −0.564575 0.825382i \(-0.690960\pi\)
0.564575 0.825382i \(-0.309040\pi\)
\(500\) −247.054 38.2647i −0.494109 0.0765294i
\(501\) 395.193 0.788808
\(502\) 167.641 + 167.641i 0.333947 + 0.333947i
\(503\) −230.664 + 230.664i −0.458577 + 0.458577i −0.898188 0.439611i \(-0.855116\pi\)
0.439611 + 0.898188i \(0.355116\pi\)
\(504\) 42.9127i 0.0851442i
\(505\) −701.784 + 358.584i −1.38967 + 0.710067i
\(506\) −103.646 −0.204834
\(507\) −5.12934 5.12934i −0.0101170 0.0101170i
\(508\) 319.719 319.719i 0.629369 0.629369i
\(509\) 879.412i 1.72772i 0.503728 + 0.863862i \(0.331961\pi\)
−0.503728 + 0.863862i \(0.668039\pi\)
\(510\) −126.059 40.8005i −0.247175 0.0800009i
\(511\) −268.813 −0.526053
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −61.0983 + 61.0983i −0.119100 + 0.119100i
\(514\) 128.478i 0.249956i
\(515\) 289.842 895.512i 0.562801 1.73886i
\(516\) −195.800 −0.379457
\(517\) 645.931 + 645.931i 1.24938 + 1.24938i
\(518\) 277.507 277.507i 0.535728 0.535728i
\(519\) 278.473i 0.536557i
\(520\) −84.6818 165.731i −0.162850 0.318713i
\(521\) −207.118 −0.397540 −0.198770 0.980046i \(-0.563695\pi\)
−0.198770 + 0.980046i \(0.563695\pi\)
\(522\) 85.4602 + 85.4602i 0.163717 + 0.163717i
\(523\) 222.354 222.354i 0.425151 0.425151i −0.461822 0.886973i \(-0.652804\pi\)
0.886973 + 0.461822i \(0.152804\pi\)
\(524\) 499.507i 0.953257i
\(525\) −128.314 + 177.458i −0.244407 + 0.338014i
\(526\) −52.2749 −0.0993820
\(527\) 358.295 + 358.295i 0.679877 + 0.679877i
\(528\) −74.8650 + 74.8650i −0.141790 + 0.141790i
\(529\) 23.0000i 0.0434783i
\(530\) −364.237 + 186.111i −0.687240 + 0.351153i
\(531\) −346.673 −0.652867
\(532\) −118.931 118.931i −0.223555 0.223555i
\(533\) 457.545 457.545i 0.858433 0.858433i
\(534\) 64.5060i 0.120798i
\(535\) 99.5832 + 32.2312i 0.186137 + 0.0602452i
\(536\) −120.244 −0.224336
\(537\) −247.736 247.736i −0.461333 0.461333i
\(538\) 114.873 114.873i 0.213518 0.213518i
\(539\) 357.955i 0.664109i
\(540\) −16.0007 + 49.4366i −0.0296309 + 0.0915493i
\(541\) 209.995 0.388160 0.194080 0.980986i \(-0.437828\pi\)
0.194080 + 0.980986i \(0.437828\pi\)
\(542\) 263.414 + 263.414i 0.486004 + 0.486004i
\(543\) −146.592 + 146.592i −0.269967 + 0.269967i
\(544\) 61.1980i 0.112496i
\(545\) 0.233607 + 0.457192i 0.000428637 + 0.000838884i
\(546\) −163.025 −0.298580
\(547\) −56.6666 56.6666i −0.103595 0.103595i 0.653409 0.757005i \(-0.273338\pi\)
−0.757005 + 0.653409i \(0.773338\pi\)
\(548\) −48.3070 + 48.3070i −0.0881514 + 0.0881514i
\(549\) 118.657i 0.216132i
\(550\) 533.446 85.7355i 0.969901 0.155883i
\(551\) 473.702 0.859713
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) −417.366 + 417.366i −0.754731 + 0.754731i
\(554\) 495.271i 0.893990i
\(555\) −423.169 + 216.223i −0.762468 + 0.389591i
\(556\) −215.789 −0.388111
\(557\) −51.0912 51.0912i −0.0917256 0.0917256i 0.659755 0.751481i \(-0.270660\pi\)
−0.751481 + 0.659755i \(0.770660\pi\)
\(558\) 140.512 140.512i 0.251814 0.251814i
\(559\) 743.842i 1.33067i
\(560\) −96.2312 31.1463i −0.171841 0.0556184i
\(561\) 286.349 0.510426
\(562\) −503.134 503.134i −0.895257 0.895257i
\(563\) −189.263 + 189.263i −0.336169 + 0.336169i −0.854923 0.518755i \(-0.826396\pi\)
0.518755 + 0.854923i \(0.326396\pi\)
\(564\) 207.071i 0.367147i
\(565\) 119.702 369.837i 0.211862 0.654579i
\(566\) −669.603 −1.18304
\(567\) 32.1845 + 32.1845i 0.0567628 + 0.0567628i
\(568\) 219.031 219.031i 0.385618 0.385618i
\(569\) 743.025i 1.30584i 0.757426 + 0.652921i \(0.226457\pi\)
−0.757426 + 0.652921i \(0.773543\pi\)
\(570\) 92.6668 + 181.358i 0.162573 + 0.318172i
\(571\) 630.678 1.10452 0.552258 0.833673i \(-0.313766\pi\)
0.552258 + 0.833673i \(0.313766\pi\)
\(572\) 284.411 + 284.411i 0.497223 + 0.497223i
\(573\) 434.072 434.072i 0.757544 0.757544i
\(574\) 351.661i 0.612649i
\(575\) 19.0255 + 118.377i 0.0330879 + 0.205872i
\(576\) −24.0000 −0.0416667
\(577\) 87.5513 + 87.5513i 0.151735 + 0.151735i 0.778893 0.627157i \(-0.215782\pi\)
−0.627157 + 0.778893i \(0.715782\pi\)
\(578\) 171.963 171.963i 0.297513 0.297513i
\(579\) 220.085i 0.380112i
\(580\) 253.671 129.616i 0.437364 0.223476i
\(581\) −697.948 −1.20129
\(582\) −171.578 171.578i −0.294807 0.294807i
\(583\) 625.070 625.070i 1.07216 1.07216i
\(584\) 150.341i 0.257433i
\(585\) 187.809 + 60.7865i 0.321041 + 0.103909i
\(586\) −207.820 −0.354642
\(587\) −358.680 358.680i −0.611039 0.611039i 0.332178 0.943217i \(-0.392217\pi\)
−0.943217 + 0.332178i \(0.892217\pi\)
\(588\) 57.3760 57.3760i 0.0975783 0.0975783i
\(589\) 778.854i 1.32233i
\(590\) −251.617 + 777.410i −0.426470 + 1.31764i
\(591\) 599.922 1.01510
\(592\) −155.203 155.203i −0.262167 0.262167i
\(593\) 388.968 388.968i 0.655933 0.655933i −0.298482 0.954415i \(-0.596480\pi\)
0.954415 + 0.298482i \(0.0964804\pi\)
\(594\) 112.297i 0.189053i
\(595\) 124.471 + 243.602i 0.209195 + 0.409414i
\(596\) −298.293 −0.500492
\(597\) 246.285 + 246.285i 0.412538 + 0.412538i
\(598\) −63.1136 + 63.1136i −0.105541 + 0.105541i
\(599\) 430.104i 0.718036i 0.933331 + 0.359018i \(0.116888\pi\)
−0.933331 + 0.359018i \(0.883112\pi\)
\(600\) 99.2477 + 71.7628i 0.165413 + 0.119605i
\(601\) 613.240 1.02037 0.510183 0.860066i \(-0.329578\pi\)
0.510183 + 0.860066i \(0.329578\pi\)
\(602\) 285.852 + 285.852i 0.474837 + 0.474837i
\(603\) 90.1833 90.1833i 0.149558 0.149558i
\(604\) 174.727i 0.289284i
\(605\) −501.041 + 256.013i −0.828168 + 0.423161i
\(606\) 386.083 0.637100
\(607\) −332.149 332.149i −0.547198 0.547198i 0.378432 0.925629i \(-0.376464\pi\)
−0.925629 + 0.378432i \(0.876464\pi\)
\(608\) −66.5154 + 66.5154i −0.109400 + 0.109400i
\(609\) 249.530i 0.409737i
\(610\) 266.086 + 86.1218i 0.436207 + 0.141183i
\(611\) 786.660 1.28750
\(612\) 45.8985 + 45.8985i 0.0749976 + 0.0749976i
\(613\) −766.001 + 766.001i −1.24959 + 1.24959i −0.293693 + 0.955900i \(0.594884\pi\)
−0.955900 + 0.293693i \(0.905116\pi\)
\(614\) 31.9828i 0.0520893i
\(615\) −131.123 + 405.123i −0.213207 + 0.658737i
\(616\) 218.593 0.354859
\(617\) 255.443 + 255.443i 0.414008 + 0.414008i 0.883132 0.469124i \(-0.155430\pi\)
−0.469124 + 0.883132i \(0.655430\pi\)
\(618\) −326.058 + 326.058i −0.527603 + 0.527603i
\(619\) 750.831i 1.21297i −0.795093 0.606487i \(-0.792578\pi\)
0.795093 0.606487i \(-0.207422\pi\)
\(620\) −213.113 417.083i −0.343730 0.672714i
\(621\) 24.9199 0.0401286
\(622\) 430.485 + 430.485i 0.692098 + 0.692098i
\(623\) 94.1735 94.1735i 0.151161 0.151161i
\(624\) 91.1758i 0.146115i
\(625\) −195.842 593.524i −0.313346 0.949639i
\(626\) −431.125 −0.688699
\(627\) −311.230 311.230i −0.496379 0.496379i
\(628\) −162.330 + 162.330i −0.258488 + 0.258488i
\(629\) 593.632i 0.943772i
\(630\) 95.5331 48.8137i 0.151640 0.0774820i
\(631\) 695.761 1.10263 0.551316 0.834297i \(-0.314126\pi\)
0.551316 + 0.834297i \(0.314126\pi\)
\(632\) 233.423 + 233.423i 0.369340 + 0.369340i
\(633\) −69.5975 + 69.5975i −0.109949 + 0.109949i
\(634\) 148.987i 0.234996i
\(635\) 1075.45 + 348.082i 1.69362 + 0.548160i
\(636\) 200.383 0.315068
\(637\) −217.971 217.971i −0.342184 0.342184i
\(638\) −435.327 + 435.327i −0.682330 + 0.682330i
\(639\) 328.547i 0.514158i
\(640\) −17.4194 + 53.8198i −0.0272177 + 0.0840934i
\(641\) −108.436 −0.169168 −0.0845838 0.996416i \(-0.526956\pi\)
−0.0845838 + 0.996416i \(0.526956\pi\)
\(642\) −36.2585 36.2585i −0.0564774 0.0564774i
\(643\) 748.186 748.186i 1.16359 1.16359i 0.179901 0.983685i \(-0.442422\pi\)
0.983685 0.179901i \(-0.0575778\pi\)
\(644\) 48.5080i 0.0753229i
\(645\) −222.725 435.894i −0.345310 0.675805i
\(646\) 254.413 0.393829
\(647\) 175.618 + 175.618i 0.271435 + 0.271435i 0.829678 0.558243i \(-0.188524\pi\)
−0.558243 + 0.829678i \(0.688524\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 1765.92i 2.72099i
\(650\) 272.626 377.041i 0.419425 0.580063i
\(651\) −410.273 −0.630220
\(652\) −112.915 112.915i −0.173183 0.173183i
\(653\) −752.118 + 752.118i −1.15179 + 1.15179i −0.165595 + 0.986194i \(0.552954\pi\)
−0.986194 + 0.165595i \(0.947046\pi\)
\(654\) 0.251522i 0.000384590i
\(655\) 1112.01 568.195i 1.69773 0.867473i
\(656\) −196.675 −0.299810
\(657\) −112.755 112.755i −0.171622 0.171622i
\(658\) 302.306 302.306i 0.459432 0.459432i
\(659\) 651.736i 0.988977i −0.869184 0.494488i \(-0.835355\pi\)
0.869184 0.494488i \(-0.164645\pi\)
\(660\) −251.826 81.5062i −0.381554 0.123494i
\(661\) −104.721 −0.158428 −0.0792141 0.996858i \(-0.525241\pi\)
−0.0792141 + 0.996858i \(0.525241\pi\)
\(662\) 316.884 + 316.884i 0.478677 + 0.478677i
\(663\) 174.368 174.368i 0.262999 0.262999i
\(664\) 390.345i 0.587870i
\(665\) 129.482 400.054i 0.194709 0.601585i
\(666\) 232.805 0.349556
\(667\) −96.6032 96.6032i −0.144832 0.144832i
\(668\) −322.673 + 322.673i −0.483044 + 0.483044i
\(669\) 124.523i 0.186134i
\(670\) −136.779 267.691i −0.204148 0.399538i
\(671\) −604.427 −0.900786
\(672\) 35.0380 + 35.0380i 0.0521399 + 0.0521399i
\(673\) 175.443 175.443i 0.260688 0.260688i −0.564646 0.825333i \(-0.690987\pi\)
0.825333 + 0.564646i \(0.190987\pi\)
\(674\) 163.888i 0.243158i
\(675\) −128.258 + 20.6136i −0.190012 + 0.0305387i
\(676\) 8.37618 0.0123908
\(677\) 366.104 + 366.104i 0.540775 + 0.540775i 0.923756 0.382981i \(-0.125103\pi\)
−0.382981 + 0.923756i \(0.625103\pi\)
\(678\) −134.659 + 134.659i −0.198612 + 0.198612i
\(679\) 500.978i 0.737818i
\(680\) 136.240 69.6135i 0.200354 0.102373i
\(681\) −185.749 −0.272758
\(682\) 715.758 + 715.758i 1.04950 + 1.04950i
\(683\) −397.528 + 397.528i −0.582032 + 0.582032i −0.935461 0.353429i \(-0.885016\pi\)
0.353429 + 0.935461i \(0.385016\pi\)
\(684\) 99.7732i 0.145867i
\(685\) −162.492 52.5923i −0.237214 0.0767770i
\(686\) −517.982 −0.755076
\(687\) −85.7644 85.7644i −0.124839 0.124839i
\(688\) 159.870 159.870i 0.232369 0.232369i
\(689\) 761.254i 1.10487i
\(690\) 18.0870 55.8826i 0.0262131 0.0809892i
\(691\) −827.604 −1.19769 −0.598846 0.800865i \(-0.704374\pi\)
−0.598846 + 0.800865i \(0.704374\pi\)
\(692\) −227.372 227.372i −0.328573 0.328573i
\(693\) −163.945 + 163.945i −0.236573 + 0.236573i
\(694\) 507.354i 0.731058i
\(695\) −245.463 480.395i −0.353184 0.691216i
\(696\) −139.556 −0.200511
\(697\) 376.129 + 376.129i 0.539640 + 0.539640i
\(698\) 162.699 162.699i 0.233093 0.233093i
\(699\) 9.85581i 0.0140999i
\(700\) −40.1256 249.661i −0.0573223 0.356659i
\(701\) −1107.02 −1.57920 −0.789600 0.613621i \(-0.789712\pi\)
−0.789600 + 0.613621i \(0.789712\pi\)
\(702\) −68.3819 68.3819i −0.0974101 0.0974101i
\(703\) 645.212 645.212i 0.917798 0.917798i
\(704\) 122.254i 0.173656i
\(705\) −460.985 + 235.545i −0.653880 + 0.334107i
\(706\) 39.8097 0.0563877
\(707\) −563.649 563.649i −0.797241 0.797241i
\(708\) 283.057 283.057i 0.399798 0.399798i
\(709\) 369.641i 0.521356i 0.965426 + 0.260678i \(0.0839460\pi\)
−0.965426 + 0.260678i \(0.916054\pi\)
\(710\) 736.763 + 238.461i 1.03769 + 0.335861i
\(711\) −350.134 −0.492453
\(712\) −52.6689 52.6689i −0.0739732 0.0739732i
\(713\) −158.834 + 158.834i −0.222768 + 0.222768i
\(714\) 134.016i 0.187698i
\(715\) −309.641 + 956.684i −0.433065 + 1.33802i
\(716\) 404.551 0.565016
\(717\) −328.918 328.918i −0.458742 0.458742i
\(718\) 414.391 414.391i 0.577146 0.577146i
\(719\) 700.854i 0.974762i 0.873189 + 0.487381i \(0.162048\pi\)
−0.873189 + 0.487381i \(0.837952\pi\)
\(720\) −27.3003 53.4293i −0.0379171 0.0742074i
\(721\) 952.037 1.32044
\(722\) 84.4810 + 84.4810i 0.117010 + 0.117010i
\(723\) −325.710 + 325.710i −0.450498 + 0.450498i
\(724\) 239.384i 0.330640i
\(725\) 577.108 + 417.288i 0.796011 + 0.575570i
\(726\) 275.645 0.379677
\(727\) −160.008 160.008i −0.220093 0.220093i 0.588445 0.808538i \(-0.299740\pi\)
−0.808538 + 0.588445i \(0.799740\pi\)
\(728\) 133.109 133.109i 0.182842 0.182842i
\(729\) 27.0000i 0.0370370i
\(730\) −334.692 + 171.014i −0.458482 + 0.234266i
\(731\) −611.483 −0.836502
\(732\) −96.8828 96.8828i −0.132354 0.132354i
\(733\) −104.240 + 104.240i −0.142210 + 0.142210i −0.774628 0.632417i \(-0.782063\pi\)
0.632417 + 0.774628i \(0.282063\pi\)
\(734\) 211.386i 0.287991i
\(735\) 192.998 + 62.4659i 0.262582 + 0.0849876i
\(736\) 27.1293 0.0368605
\(737\) 459.386 + 459.386i 0.623319 + 0.623319i
\(738\) 147.506 147.506i 0.199873 0.199873i
\(739\) 761.948i 1.03105i 0.856874 + 0.515526i \(0.172403\pi\)
−0.856874 + 0.515526i \(0.827597\pi\)
\(740\) 168.971 522.062i 0.228339 0.705489i
\(741\) −379.037 −0.511521
\(742\) −292.543 292.543i −0.394263 0.394263i
\(743\) −222.730 + 222.730i −0.299772 + 0.299772i −0.840924 0.541153i \(-0.817988\pi\)
0.541153 + 0.840924i \(0.317988\pi\)
\(744\) 229.456i 0.308408i
\(745\) −339.312 664.066i −0.455452 0.891364i
\(746\) −644.036 −0.863319
\(747\) −292.759 292.759i −0.391913 0.391913i
\(748\) −233.803 + 233.803i −0.312571 + 0.312571i
\(749\) 105.869i 0.141347i
\(750\) −46.8645 + 302.578i −0.0624860 + 0.403438i
\(751\) −276.810 −0.368589 −0.184294 0.982871i \(-0.559000\pi\)
−0.184294 + 0.982871i \(0.559000\pi\)
\(752\) −169.072 169.072i −0.224830 0.224830i
\(753\) 205.318 205.318i 0.272666 0.272666i
\(754\) 530.172i 0.703145i
\(755\) 388.982 198.755i 0.515208 0.263251i
\(756\) −52.5571 −0.0695199
\(757\) −762.159 762.159i −1.00681 1.00681i −0.999977 0.00683824i \(-0.997823\pi\)
−0.00683824 0.999977i \(-0.502177\pi\)
\(758\) −46.2839 + 46.2839i −0.0610605 + 0.0610605i
\(759\) 126.940i 0.167246i
\(760\) −223.740 72.4160i −0.294395 0.0952842i
\(761\) 458.239 0.602153 0.301077 0.953600i \(-0.402654\pi\)
0.301077 + 0.953600i \(0.402654\pi\)
\(762\) −391.575 391.575i −0.513878 0.513878i
\(763\) −0.367201 + 0.367201i −0.000481260 + 0.000481260i
\(764\) 708.837i 0.927798i
\(765\) −49.9702 + 154.390i −0.0653205 + 0.201818i
\(766\) −913.014 −1.19192
\(767\) −1075.33 1075.33i −1.40200 1.40200i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 493.914i 0.642281i 0.947032 + 0.321141i \(0.104066\pi\)
−0.947032 + 0.321141i \(0.895934\pi\)
\(770\) 248.653 + 486.638i 0.322926 + 0.631997i
\(771\) 157.352 0.204088
\(772\) 179.699 + 179.699i 0.232770 + 0.232770i
\(773\) −429.285 + 429.285i −0.555349 + 0.555349i −0.927980 0.372631i \(-0.878456\pi\)
0.372631 + 0.927980i \(0.378456\pi\)
\(774\) 239.805i 0.309826i
\(775\) 686.100 948.873i 0.885290 1.22435i
\(776\) 280.185 0.361063
\(777\) −339.876 339.876i −0.437420 0.437420i
\(778\) 423.277 423.277i 0.544058 0.544058i
\(779\) 817.621i