Properties

Label 690.3.k.b.277.14
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.14
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.14

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-1.86672 + 4.63846i) q^{5} -2.44949 q^{6} +(2.71586 + 2.71586i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-1.86672 + 4.63846i) q^{5} -2.44949 q^{6} +(2.71586 + 2.71586i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.50519 - 2.77174i) q^{10} -20.1942 q^{11} +(2.44949 + 2.44949i) q^{12} +(0.746801 - 0.746801i) q^{13} -5.43173i q^{14} +(3.39468 + 7.96719i) q^{15} -4.00000 q^{16} +(0.556028 + 0.556028i) q^{17} +(-3.00000 + 3.00000i) q^{18} -19.9846i q^{19} +(-9.27693 - 3.73345i) q^{20} +6.65248 q^{21} +(20.1942 + 20.1942i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-18.0307 - 17.3175i) q^{25} -1.49360 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-5.43173 + 5.43173i) q^{28} -48.8362i q^{29} +(4.57252 - 11.3619i) q^{30} +50.2284 q^{31} +(4.00000 + 4.00000i) q^{32} +(-24.7327 + 24.7327i) q^{33} -1.11206i q^{34} +(-17.6672 + 7.52767i) q^{35} +6.00000 q^{36} +(-16.5528 - 16.5528i) q^{37} +(-19.9846 + 19.9846i) q^{38} -1.82928i q^{39} +(5.54348 + 13.0104i) q^{40} +57.2091 q^{41} +(-6.65248 - 6.65248i) q^{42} +(58.6184 - 58.6184i) q^{43} -40.3884i q^{44} +(13.9154 + 5.60017i) q^{45} +6.78233 q^{46} +(-41.3244 - 41.3244i) q^{47} +(-4.89898 + 4.89898i) q^{48} -34.2482i q^{49} +(0.713239 + 35.3481i) q^{50} +1.36199 q^{51} +(1.49360 + 1.49360i) q^{52} +(28.0837 - 28.0837i) q^{53} +7.34847i q^{54} +(37.6970 - 93.6701i) q^{55} +10.8635 q^{56} +(-24.4761 - 24.4761i) q^{57} +(-48.8362 + 48.8362i) q^{58} +46.2872i q^{59} +(-15.9344 + 6.78935i) q^{60} -80.6788 q^{61} +(-50.2284 - 50.2284i) q^{62} +(8.14759 - 8.14759i) q^{63} -8.00000i q^{64} +(2.06994 + 4.85808i) q^{65} +49.4655 q^{66} +(3.70461 + 3.70461i) q^{67} +(-1.11206 + 1.11206i) q^{68} +8.30662i q^{69} +(25.1949 + 10.1395i) q^{70} -45.0042 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-19.9215 + 19.9215i) q^{73} +33.1057i q^{74} +(-43.2925 + 0.873535i) q^{75} +39.9693 q^{76} +(-54.8447 - 54.8447i) q^{77} +(-1.82928 + 1.82928i) q^{78} -11.9143i q^{79} +(7.46689 - 18.5539i) q^{80} -9.00000 q^{81} +(-57.2091 - 57.2091i) q^{82} +(51.9727 - 51.9727i) q^{83} +13.3050i q^{84} +(-3.61707 + 1.54117i) q^{85} -117.237 q^{86} +(-59.8118 - 59.8118i) q^{87} +(-40.3884 + 40.3884i) q^{88} +153.052i q^{89} +(-8.31522 - 19.5156i) q^{90} +4.05642 q^{91} +(-6.78233 - 6.78233i) q^{92} +(61.5170 - 61.5170i) q^{93} +82.6487i q^{94} +(92.6980 + 37.3058i) q^{95} +9.79796 q^{96} +(109.557 + 109.557i) q^{97} +(-34.2482 + 34.2482i) q^{98} +60.5826i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

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
\(5\) −1.86672 + 4.63846i −0.373345 + 0.927693i
\(6\) −2.44949 −0.408248
\(7\) 2.71586 + 2.71586i 0.387980 + 0.387980i 0.873967 0.485986i \(-0.161539\pi\)
−0.485986 + 0.873967i \(0.661539\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 6.50519 2.77174i 0.650519 0.277174i
\(11\) −20.1942 −1.83584 −0.917918 0.396770i \(-0.870131\pi\)
−0.917918 + 0.396770i \(0.870131\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) 0.746801 0.746801i 0.0574462 0.0574462i −0.677800 0.735246i \(-0.737066\pi\)
0.735246 + 0.677800i \(0.237066\pi\)
\(14\) 5.43173i 0.387980i
\(15\) 3.39468 + 7.96719i 0.226312 + 0.531146i
\(16\) −4.00000 −0.250000
\(17\) 0.556028 + 0.556028i 0.0327075 + 0.0327075i 0.723271 0.690564i \(-0.242638\pi\)
−0.690564 + 0.723271i \(0.742638\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 19.9846i 1.05182i −0.850539 0.525911i \(-0.823724\pi\)
0.850539 0.525911i \(-0.176276\pi\)
\(20\) −9.27693 3.73345i −0.463846 0.186672i
\(21\) 6.65248 0.316785
\(22\) 20.1942 + 20.1942i 0.917918 + 0.917918i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −18.0307 17.3175i −0.721228 0.692698i
\(26\) −1.49360 −0.0574462
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) −5.43173 + 5.43173i −0.193990 + 0.193990i
\(29\) 48.8362i 1.68401i −0.539473 0.842003i \(-0.681377\pi\)
0.539473 0.842003i \(-0.318623\pi\)
\(30\) 4.57252 11.3619i 0.152417 0.378729i
\(31\) 50.2284 1.62027 0.810136 0.586242i \(-0.199393\pi\)
0.810136 + 0.586242i \(0.199393\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −24.7327 + 24.7327i −0.749477 + 0.749477i
\(34\) 1.11206i 0.0327075i
\(35\) −17.6672 + 7.52767i −0.504777 + 0.215076i
\(36\) 6.00000 0.166667
\(37\) −16.5528 16.5528i −0.447374 0.447374i 0.447106 0.894481i \(-0.352455\pi\)
−0.894481 + 0.447106i \(0.852455\pi\)
\(38\) −19.9846 + 19.9846i −0.525911 + 0.525911i
\(39\) 1.82928i 0.0469047i
\(40\) 5.54348 + 13.0104i 0.138587 + 0.325259i
\(41\) 57.2091 1.39534 0.697672 0.716418i \(-0.254219\pi\)
0.697672 + 0.716418i \(0.254219\pi\)
\(42\) −6.65248 6.65248i −0.158392 0.158392i
\(43\) 58.6184 58.6184i 1.36322 1.36322i 0.493437 0.869781i \(-0.335740\pi\)
0.869781 0.493437i \(-0.164260\pi\)
\(44\) 40.3884i 0.917918i
\(45\) 13.9154 + 5.60017i 0.309231 + 0.124448i
\(46\) 6.78233 0.147442
\(47\) −41.3244 41.3244i −0.879242 0.879242i 0.114214 0.993456i \(-0.463565\pi\)
−0.993456 + 0.114214i \(0.963565\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 34.2482i 0.698942i
\(50\) 0.713239 + 35.3481i 0.0142648 + 0.706963i
\(51\) 1.36199 0.0267056
\(52\) 1.49360 + 1.49360i 0.0287231 + 0.0287231i
\(53\) 28.0837 28.0837i 0.529882 0.529882i −0.390655 0.920537i \(-0.627752\pi\)
0.920537 + 0.390655i \(0.127752\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 37.6970 93.6701i 0.685400 1.70309i
\(56\) 10.8635 0.193990
\(57\) −24.4761 24.4761i −0.429405 0.429405i
\(58\) −48.8362 + 48.8362i −0.842003 + 0.842003i
\(59\) 46.2872i 0.784529i 0.919852 + 0.392265i \(0.128308\pi\)
−0.919852 + 0.392265i \(0.871692\pi\)
\(60\) −15.9344 + 6.78935i −0.265573 + 0.113156i
\(61\) −80.6788 −1.32260 −0.661302 0.750120i \(-0.729996\pi\)
−0.661302 + 0.750120i \(0.729996\pi\)
\(62\) −50.2284 50.2284i −0.810136 0.810136i
\(63\) 8.14759 8.14759i 0.129327 0.129327i
\(64\) 8.00000i 0.125000i
\(65\) 2.06994 + 4.85808i 0.0318452 + 0.0747397i
\(66\) 49.4655 0.749477
\(67\) 3.70461 + 3.70461i 0.0552926 + 0.0552926i 0.734212 0.678920i \(-0.237552\pi\)
−0.678920 + 0.734212i \(0.737552\pi\)
\(68\) −1.11206 + 1.11206i −0.0163538 + 0.0163538i
\(69\) 8.30662i 0.120386i
\(70\) 25.1949 + 10.1395i 0.359927 + 0.144850i
\(71\) −45.0042 −0.633862 −0.316931 0.948449i \(-0.602652\pi\)
−0.316931 + 0.948449i \(0.602652\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −19.9215 + 19.9215i −0.272897 + 0.272897i −0.830265 0.557369i \(-0.811811\pi\)
0.557369 + 0.830265i \(0.311811\pi\)
\(74\) 33.1057i 0.447374i
\(75\) −43.2925 + 0.873535i −0.577233 + 0.0116471i
\(76\) 39.9693 0.525911
\(77\) −54.8447 54.8447i −0.712269 0.712269i
\(78\) −1.82928 + 1.82928i −0.0234523 + 0.0234523i
\(79\) 11.9143i 0.150814i −0.997153 0.0754069i \(-0.975974\pi\)
0.997153 0.0754069i \(-0.0240256\pi\)
\(80\) 7.46689 18.5539i 0.0933361 0.231923i
\(81\) −9.00000 −0.111111
\(82\) −57.2091 57.2091i −0.697672 0.697672i
\(83\) 51.9727 51.9727i 0.626177 0.626177i −0.320927 0.947104i \(-0.603994\pi\)
0.947104 + 0.320927i \(0.103994\pi\)
\(84\) 13.3050i 0.158392i
\(85\) −3.61707 + 1.54117i −0.0425537 + 0.0181314i
\(86\) −117.237 −1.36322
\(87\) −59.8118 59.8118i −0.687492 0.687492i
\(88\) −40.3884 + 40.3884i −0.458959 + 0.458959i
\(89\) 153.052i 1.71968i 0.510562 + 0.859841i \(0.329437\pi\)
−0.510562 + 0.859841i \(0.670563\pi\)
\(90\) −8.31522 19.5156i −0.0923914 0.216840i
\(91\) 4.05642 0.0445760
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 61.5170 61.5170i 0.661473 0.661473i
\(94\) 82.6487i 0.879242i
\(95\) 92.6980 + 37.3058i 0.975768 + 0.392692i
\(96\) 9.79796 0.102062
\(97\) 109.557 + 109.557i 1.12946 + 1.12946i 0.990265 + 0.139192i \(0.0444504\pi\)
0.139192 + 0.990265i \(0.455550\pi\)
\(98\) −34.2482 + 34.2482i −0.349471 + 0.349471i
\(99\) 60.5826i 0.611945i
\(100\) 34.6349 36.0614i 0.346349 0.360614i
\(101\) −186.217 −1.84373 −0.921866 0.387508i \(-0.873336\pi\)
−0.921866 + 0.387508i \(0.873336\pi\)
\(102\) −1.36199 1.36199i −0.0133528 0.0133528i
\(103\) −69.1652 + 69.1652i −0.671507 + 0.671507i −0.958063 0.286556i \(-0.907489\pi\)
0.286556 + 0.958063i \(0.407489\pi\)
\(104\) 2.98720i 0.0287231i
\(105\) −12.4183 + 30.8573i −0.118270 + 0.293879i
\(106\) −56.1675 −0.529882
\(107\) −95.3930 95.3930i −0.891524 0.891524i 0.103143 0.994667i \(-0.467110\pi\)
−0.994667 + 0.103143i \(0.967110\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 86.6994i 0.795407i −0.917514 0.397704i \(-0.869807\pi\)
0.917514 0.397704i \(-0.130193\pi\)
\(110\) −131.367 + 55.9731i −1.19425 + 0.508846i
\(111\) −40.5460 −0.365280
\(112\) −10.8635 10.8635i −0.0969951 0.0969951i
\(113\) −106.499 + 106.499i −0.942470 + 0.942470i −0.998433 0.0559628i \(-0.982177\pi\)
0.0559628 + 0.998433i \(0.482177\pi\)
\(114\) 48.9522i 0.429405i
\(115\) −9.39943 22.0602i −0.0817342 0.191827i
\(116\) 97.6723 0.842003
\(117\) −2.24040 2.24040i −0.0191487 0.0191487i
\(118\) 46.2872 46.2872i 0.392265 0.392265i
\(119\) 3.02019i 0.0253798i
\(120\) 22.7237 + 9.14504i 0.189364 + 0.0762086i
\(121\) 286.806 2.37030
\(122\) 80.6788 + 80.6788i 0.661302 + 0.661302i
\(123\) 70.0665 70.0665i 0.569647 0.569647i
\(124\) 100.457i 0.810136i
\(125\) 113.985 51.3078i 0.911877 0.410463i
\(126\) −16.2952 −0.129327
\(127\) −165.125 165.125i −1.30020 1.30020i −0.928254 0.371947i \(-0.878690\pi\)
−0.371947 0.928254i \(-0.621310\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 143.585i 1.11306i
\(130\) 2.78814 6.92802i 0.0214472 0.0532925i
\(131\) −98.3677 −0.750898 −0.375449 0.926843i \(-0.622512\pi\)
−0.375449 + 0.926843i \(0.622512\pi\)
\(132\) −49.4655 49.4655i −0.374739 0.374739i
\(133\) 54.2755 54.2755i 0.408087 0.408087i
\(134\) 7.40921i 0.0552926i
\(135\) 23.9016 10.1840i 0.177049 0.0754372i
\(136\) 2.22411 0.0163538
\(137\) −151.564 151.564i −1.10631 1.10631i −0.993632 0.112676i \(-0.964058\pi\)
−0.112676 0.993632i \(-0.535942\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 24.6988i 0.177689i −0.996045 0.0888446i \(-0.971683\pi\)
0.996045 0.0888446i \(-0.0283175\pi\)
\(140\) −15.0553 35.3344i −0.107538 0.252389i
\(141\) −101.224 −0.717898
\(142\) 45.0042 + 45.0042i 0.316931 + 0.316931i
\(143\) −15.0811 + 15.0811i −0.105462 + 0.105462i
\(144\) 12.0000i 0.0833333i
\(145\) 226.525 + 91.1636i 1.56224 + 0.628714i
\(146\) 39.8429 0.272897
\(147\) −41.9453 41.9453i −0.285342 0.285342i
\(148\) 33.1057 33.1057i 0.223687 0.223687i
\(149\) 26.1452i 0.175471i 0.996144 + 0.0877355i \(0.0279630\pi\)
−0.996144 + 0.0877355i \(0.972037\pi\)
\(150\) 44.1660 + 42.4189i 0.294440 + 0.282793i
\(151\) 149.368 0.989191 0.494596 0.869123i \(-0.335316\pi\)
0.494596 + 0.869123i \(0.335316\pi\)
\(152\) −39.9693 39.9693i −0.262956 0.262956i
\(153\) 1.66808 1.66808i 0.0109025 0.0109025i
\(154\) 109.689i 0.712269i
\(155\) −93.7626 + 232.983i −0.604920 + 1.50312i
\(156\) 3.65856 0.0234523
\(157\) −93.1332 93.1332i −0.593205 0.593205i 0.345291 0.938496i \(-0.387780\pi\)
−0.938496 + 0.345291i \(0.887780\pi\)
\(158\) −11.9143 + 11.9143i −0.0754069 + 0.0754069i
\(159\) 68.7908i 0.432647i
\(160\) −26.0207 + 11.0870i −0.162630 + 0.0692935i
\(161\) −18.4199 −0.114409
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 160.565 160.565i 0.985062 0.985062i −0.0148284 0.999890i \(-0.504720\pi\)
0.999890 + 0.0148284i \(0.00472019\pi\)
\(164\) 114.418i 0.697672i
\(165\) −68.5528 160.891i −0.415471 0.975098i
\(166\) −103.945 −0.626177
\(167\) −197.089 197.089i −1.18017 1.18017i −0.979699 0.200473i \(-0.935752\pi\)
−0.200473 0.979699i \(-0.564248\pi\)
\(168\) 13.3050 13.3050i 0.0791962 0.0791962i
\(169\) 167.885i 0.993400i
\(170\) 5.15823 + 2.07590i 0.0303425 + 0.0122112i
\(171\) −59.9539 −0.350608
\(172\) 117.237 + 117.237i 0.681609 + 0.681609i
\(173\) 17.1387 17.1387i 0.0990678 0.0990678i −0.655836 0.754904i \(-0.727684\pi\)
0.754904 + 0.655836i \(0.227684\pi\)
\(174\) 119.624i 0.687492i
\(175\) −1.93706 96.0007i −0.0110689 0.548576i
\(176\) 80.7768 0.458959
\(177\) 56.6900 + 56.6900i 0.320283 + 0.320283i
\(178\) 153.052 153.052i 0.859841 0.859841i
\(179\) 118.734i 0.663318i −0.943399 0.331659i \(-0.892392\pi\)
0.943399 0.331659i \(-0.107608\pi\)
\(180\) −11.2003 + 27.8308i −0.0622241 + 0.154615i
\(181\) −20.8622 −0.115261 −0.0576303 0.998338i \(-0.518354\pi\)
−0.0576303 + 0.998338i \(0.518354\pi\)
\(182\) −4.05642 4.05642i −0.0222880 0.0222880i
\(183\) −98.8109 + 98.8109i −0.539951 + 0.539951i
\(184\) 13.5647i 0.0737210i
\(185\) 107.679 45.8802i 0.582051 0.248001i
\(186\) −123.034 −0.661473
\(187\) −11.2285 11.2285i −0.0600457 0.0600457i
\(188\) 82.6487 82.6487i 0.439621 0.439621i
\(189\) 19.9574i 0.105595i
\(190\) −55.3922 130.004i −0.291538 0.684230i
\(191\) 252.640 1.32272 0.661361 0.750068i \(-0.269979\pi\)
0.661361 + 0.750068i \(0.269979\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) −31.5274 + 31.5274i −0.163354 + 0.163354i −0.784051 0.620697i \(-0.786850\pi\)
0.620697 + 0.784051i \(0.286850\pi\)
\(194\) 219.115i 1.12946i
\(195\) 8.48506 + 3.41476i 0.0435131 + 0.0175116i
\(196\) 68.4963 0.349471
\(197\) 125.808 + 125.808i 0.638618 + 0.638618i 0.950214 0.311597i \(-0.100864\pi\)
−0.311597 + 0.950214i \(0.600864\pi\)
\(198\) 60.5826 60.5826i 0.305973 0.305973i
\(199\) 213.068i 1.07069i 0.844633 + 0.535346i \(0.179819\pi\)
−0.844633 + 0.535346i \(0.820181\pi\)
\(200\) −70.6963 + 1.42648i −0.353481 + 0.00713239i
\(201\) 9.07439 0.0451462
\(202\) 186.217 + 186.217i 0.921866 + 0.921866i
\(203\) 132.632 132.632i 0.653361 0.653361i
\(204\) 2.72397i 0.0133528i
\(205\) −106.793 + 265.362i −0.520944 + 1.29445i
\(206\) 138.330 0.671507
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) −2.98720 + 2.98720i −0.0143616 + 0.0143616i
\(209\) 403.574i 1.93097i
\(210\) 43.2756 18.4389i 0.206074 0.0878045i
\(211\) 381.486 1.80799 0.903996 0.427540i \(-0.140620\pi\)
0.903996 + 0.427540i \(0.140620\pi\)
\(212\) 56.1675 + 56.1675i 0.264941 + 0.264941i
\(213\) −55.1186 + 55.1186i −0.258773 + 0.258773i
\(214\) 190.786i 0.891524i
\(215\) 162.475 + 381.324i 0.755698 + 1.77360i
\(216\) −14.6969 −0.0680414
\(217\) 136.414 + 136.414i 0.628634 + 0.628634i
\(218\) −86.6994 + 86.6994i −0.397704 + 0.397704i
\(219\) 48.7974i 0.222819i
\(220\) 187.340 + 75.3940i 0.851546 + 0.342700i
\(221\) 0.830485 0.00375785
\(222\) 40.5460 + 40.5460i 0.182640 + 0.182640i
\(223\) −43.6482 + 43.6482i −0.195732 + 0.195732i −0.798167 0.602436i \(-0.794197\pi\)
0.602436 + 0.798167i \(0.294197\pi\)
\(224\) 21.7269i 0.0969951i
\(225\) −51.9524 + 54.0921i −0.230899 + 0.240409i
\(226\) 212.998 0.942470
\(227\) 148.529 + 148.529i 0.654314 + 0.654314i 0.954029 0.299714i \(-0.0968914\pi\)
−0.299714 + 0.954029i \(0.596891\pi\)
\(228\) 48.9522 48.9522i 0.214702 0.214702i
\(229\) 176.625i 0.771289i 0.922647 + 0.385645i \(0.126021\pi\)
−0.922647 + 0.385645i \(0.873979\pi\)
\(230\) −12.6607 + 31.4596i −0.0550467 + 0.136781i
\(231\) −134.341 −0.581565
\(232\) −97.6723 97.6723i −0.421001 0.421001i
\(233\) −86.0763 + 86.0763i −0.369426 + 0.369426i −0.867268 0.497842i \(-0.834126\pi\)
0.497842 + 0.867268i \(0.334126\pi\)
\(234\) 4.48081i 0.0191487i
\(235\) 268.823 114.540i 1.14393 0.487406i
\(236\) −92.5745 −0.392265
\(237\) −14.5920 14.5920i −0.0615694 0.0615694i
\(238\) 3.02019 3.02019i 0.0126899 0.0126899i
\(239\) 83.0954i 0.347680i −0.984774 0.173840i \(-0.944383\pi\)
0.984774 0.173840i \(-0.0556175\pi\)
\(240\) −13.5787 31.8688i −0.0565779 0.132787i
\(241\) −458.620 −1.90299 −0.951494 0.307667i \(-0.900452\pi\)
−0.951494 + 0.307667i \(0.900452\pi\)
\(242\) −286.806 286.806i −1.18515 1.18515i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 161.358i 0.661302i
\(245\) 158.859 + 63.9318i 0.648404 + 0.260946i
\(246\) −140.133 −0.569647
\(247\) −14.9245 14.9245i −0.0604233 0.0604233i
\(248\) 100.457 100.457i 0.405068 0.405068i
\(249\) 127.307i 0.511271i
\(250\) −165.293 62.6769i −0.661170 0.250707i
\(251\) 297.824 1.18655 0.593275 0.805000i \(-0.297835\pi\)
0.593275 + 0.805000i \(0.297835\pi\)
\(252\) 16.2952 + 16.2952i 0.0646634 + 0.0646634i
\(253\) 68.4819 68.4819i 0.270679 0.270679i
\(254\) 330.251i 1.30020i
\(255\) −2.54245 + 6.31752i −0.00997039 + 0.0247746i
\(256\) 16.0000 0.0625000
\(257\) −133.100 133.100i −0.517899 0.517899i 0.399036 0.916935i \(-0.369345\pi\)
−0.916935 + 0.399036i \(0.869345\pi\)
\(258\) −143.585 + 143.585i −0.556532 + 0.556532i
\(259\) 89.9105i 0.347145i
\(260\) −9.71616 + 4.13988i −0.0373699 + 0.0159226i
\(261\) −146.508 −0.561335
\(262\) 98.3677 + 98.3677i 0.375449 + 0.375449i
\(263\) 107.267 107.267i 0.407860 0.407860i −0.473132 0.880992i \(-0.656877\pi\)
0.880992 + 0.473132i \(0.156877\pi\)
\(264\) 98.9310i 0.374739i
\(265\) 77.8408 + 182.690i 0.293739 + 0.689396i
\(266\) −108.551 −0.408087
\(267\) 187.449 + 187.449i 0.702057 + 0.702057i
\(268\) −7.40921 + 7.40921i −0.0276463 + 0.0276463i
\(269\) 68.2440i 0.253695i −0.991922 0.126848i \(-0.959514\pi\)
0.991922 0.126848i \(-0.0404859\pi\)
\(270\) −34.0856 13.7176i −0.126243 0.0508058i
\(271\) −166.004 −0.612560 −0.306280 0.951941i \(-0.599084\pi\)
−0.306280 + 0.951941i \(0.599084\pi\)
\(272\) −2.22411 2.22411i −0.00817688 0.00817688i
\(273\) 4.96808 4.96808i 0.0181981 0.0181981i
\(274\) 303.128i 1.10631i
\(275\) 364.115 + 349.712i 1.32406 + 1.27168i
\(276\) −16.6132 −0.0601929
\(277\) 166.997 + 166.997i 0.602878 + 0.602878i 0.941075 0.338197i \(-0.109817\pi\)
−0.338197 + 0.941075i \(0.609817\pi\)
\(278\) −24.6988 + 24.6988i −0.0888446 + 0.0888446i
\(279\) 150.685i 0.540091i
\(280\) −20.2791 + 50.3897i −0.0724252 + 0.179963i
\(281\) −138.196 −0.491802 −0.245901 0.969295i \(-0.579084\pi\)
−0.245901 + 0.969295i \(0.579084\pi\)
\(282\) 101.224 + 101.224i 0.358949 + 0.358949i
\(283\) −55.6688 + 55.6688i −0.196710 + 0.196710i −0.798588 0.601878i \(-0.794419\pi\)
0.601878 + 0.798588i \(0.294419\pi\)
\(284\) 90.0083i 0.316931i
\(285\) 159.221 67.8413i 0.558672 0.238040i
\(286\) 30.1621 0.105462
\(287\) 155.372 + 155.372i 0.541366 + 0.541366i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 288.382i 0.997860i
\(290\) −135.361 317.688i −0.466763 1.09548i
\(291\) 268.360 0.922198
\(292\) −39.8429 39.8429i −0.136448 0.136448i
\(293\) 147.374 147.374i 0.502984 0.502984i −0.409380 0.912364i \(-0.634255\pi\)
0.912364 + 0.409380i \(0.134255\pi\)
\(294\) 83.8905i 0.285342i
\(295\) −214.702 86.4054i −0.727802 0.292900i
\(296\) −66.2114 −0.223687
\(297\) 74.1982 + 74.1982i 0.249826 + 0.249826i
\(298\) 26.1452 26.1452i 0.0877355 0.0877355i
\(299\) 5.06505i 0.0169400i
\(300\) −1.74707 86.5849i −0.00582357 0.288616i
\(301\) 318.399 1.05780
\(302\) −149.368 149.368i −0.494596 0.494596i
\(303\) −228.068 + 228.068i −0.752701 + 0.752701i
\(304\) 79.9385i 0.262956i
\(305\) 150.605 374.226i 0.493787 1.22697i
\(306\) −3.33617 −0.0109025
\(307\) −299.704 299.704i −0.976234 0.976234i 0.0234903 0.999724i \(-0.492522\pi\)
−0.999724 + 0.0234903i \(0.992522\pi\)
\(308\) 109.689 109.689i 0.356134 0.356134i
\(309\) 169.419i 0.548283i
\(310\) 326.745 139.220i 1.05402 0.449098i
\(311\) −259.066 −0.833009 −0.416504 0.909134i \(-0.636745\pi\)
−0.416504 + 0.909134i \(0.636745\pi\)
\(312\) −3.65856 3.65856i −0.0117262 0.0117262i
\(313\) −163.064 + 163.064i −0.520972 + 0.520972i −0.917865 0.396893i \(-0.870088\pi\)
0.396893 + 0.917865i \(0.370088\pi\)
\(314\) 186.266i 0.593205i
\(315\) 22.5830 + 53.0016i 0.0716921 + 0.168259i
\(316\) 23.8286 0.0754069
\(317\) −147.096 147.096i −0.464025 0.464025i 0.435947 0.899972i \(-0.356413\pi\)
−0.899972 + 0.435947i \(0.856413\pi\)
\(318\) −68.7908 + 68.7908i −0.216323 + 0.216323i
\(319\) 986.207i 3.09156i
\(320\) 37.1077 + 14.9338i 0.115962 + 0.0466681i
\(321\) −233.664 −0.727926
\(322\) 18.4199 + 18.4199i 0.0572046 + 0.0572046i
\(323\) 11.1120 11.1120i 0.0344025 0.0344025i
\(324\) 18.0000i 0.0555556i
\(325\) −26.3980 + 0.532647i −0.0812247 + 0.00163892i
\(326\) −321.130 −0.985062
\(327\) −106.185 106.185i −0.324724 0.324724i
\(328\) 114.418 114.418i 0.348836 0.348836i
\(329\) 224.463i 0.682257i
\(330\) −92.3384 + 229.444i −0.279813 + 0.695284i
\(331\) 354.624 1.07137 0.535686 0.844417i \(-0.320053\pi\)
0.535686 + 0.844417i \(0.320053\pi\)
\(332\) 103.945 + 103.945i 0.313088 + 0.313088i
\(333\) −49.6585 + 49.6585i −0.149125 + 0.149125i
\(334\) 394.177i 1.18017i
\(335\) −24.0991 + 10.2682i −0.0719378 + 0.0306514i
\(336\) −26.6099 −0.0791962
\(337\) −70.1245 70.1245i −0.208084 0.208084i 0.595368 0.803453i \(-0.297006\pi\)
−0.803453 + 0.595368i \(0.797006\pi\)
\(338\) 167.885 167.885i 0.496700 0.496700i
\(339\) 260.868i 0.769524i
\(340\) −3.08233 7.23413i −0.00906568 0.0212769i
\(341\) −1014.32 −2.97456
\(342\) 59.9539 + 59.9539i 0.175304 + 0.175304i
\(343\) 226.091 226.091i 0.659156 0.659156i
\(344\) 234.474i 0.681609i
\(345\) −38.5300 15.5062i −0.111681 0.0449454i
\(346\) −34.2775 −0.0990678
\(347\) −70.2036 70.2036i −0.202316 0.202316i 0.598676 0.800992i \(-0.295694\pi\)
−0.800992 + 0.598676i \(0.795694\pi\)
\(348\) 119.624 119.624i 0.343746 0.343746i
\(349\) 361.402i 1.03554i −0.855521 0.517769i \(-0.826763\pi\)
0.855521 0.517769i \(-0.173237\pi\)
\(350\) −94.0637 + 97.9378i −0.268753 + 0.279822i
\(351\) −5.48785 −0.0156349
\(352\) −80.7768 80.7768i −0.229480 0.229480i
\(353\) 176.815 176.815i 0.500892 0.500892i −0.410823 0.911715i \(-0.634759\pi\)
0.911715 + 0.410823i \(0.134759\pi\)
\(354\) 113.380i 0.320283i
\(355\) 84.0103 208.750i 0.236649 0.588029i
\(356\) −306.103 −0.859841
\(357\) 3.69897 + 3.69897i 0.0103612 + 0.0103612i
\(358\) −118.734 + 118.734i −0.331659 + 0.331659i
\(359\) 247.653i 0.689841i 0.938632 + 0.344921i \(0.112094\pi\)
−0.938632 + 0.344921i \(0.887906\pi\)
\(360\) 39.0311 16.6304i 0.108420 0.0461957i
\(361\) −38.3856 −0.106331
\(362\) 20.8622 + 20.8622i 0.0576303 + 0.0576303i
\(363\) 351.264 351.264i 0.967669 0.967669i
\(364\) 8.11284i 0.0222880i
\(365\) −55.2171 129.593i −0.151280 0.355049i
\(366\) 197.622 0.539951
\(367\) 227.941 + 227.941i 0.621094 + 0.621094i 0.945811 0.324717i \(-0.105269\pi\)
−0.324717 + 0.945811i \(0.605269\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 171.627i 0.465114i
\(370\) −153.560 61.7992i −0.415026 0.167025i
\(371\) 152.543 0.411168
\(372\) 123.034 + 123.034i 0.330737 + 0.330737i
\(373\) 96.9161 96.9161i 0.259829 0.259829i −0.565156 0.824984i \(-0.691184\pi\)
0.824984 + 0.565156i \(0.191184\pi\)
\(374\) 22.4571i 0.0600457i
\(375\) 76.7632 202.441i 0.204702 0.539843i
\(376\) −165.297 −0.439621
\(377\) −36.4709 36.4709i −0.0967398 0.0967398i
\(378\) −19.9574 + 19.9574i −0.0527975 + 0.0527975i
\(379\) 233.612i 0.616390i 0.951323 + 0.308195i \(0.0997249\pi\)
−0.951323 + 0.308195i \(0.900275\pi\)
\(380\) −74.6115 + 185.396i −0.196346 + 0.487884i
\(381\) −404.473 −1.06161
\(382\) −252.640 252.640i −0.661361 0.661361i
\(383\) 159.974 159.974i 0.417687 0.417687i −0.466719 0.884406i \(-0.654564\pi\)
0.884406 + 0.466719i \(0.154564\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 356.775 152.015i 0.926688 0.394845i
\(386\) 63.0548 0.163354
\(387\) −175.855 175.855i −0.454406 0.454406i
\(388\) −219.115 + 219.115i −0.564729 + 0.564729i
\(389\) 218.431i 0.561520i 0.959778 + 0.280760i \(0.0905865\pi\)
−0.959778 + 0.280760i \(0.909413\pi\)
\(390\) −5.07030 11.8998i −0.0130008 0.0305124i
\(391\) −3.77117 −0.00964493
\(392\) −68.4963 68.4963i −0.174736 0.174736i
\(393\) −120.475 + 120.475i −0.306553 + 0.306553i
\(394\) 251.615i 0.638618i
\(395\) 55.2640 + 22.2407i 0.139909 + 0.0563055i
\(396\) −121.165 −0.305973
\(397\) −349.255 349.255i −0.879735 0.879735i 0.113772 0.993507i \(-0.463707\pi\)
−0.993507 + 0.113772i \(0.963707\pi\)
\(398\) 213.068 213.068i 0.535346 0.535346i
\(399\) 132.947i 0.333201i
\(400\) 72.1228 + 69.2698i 0.180307 + 0.173175i
\(401\) 18.8951 0.0471199 0.0235599 0.999722i \(-0.492500\pi\)
0.0235599 + 0.999722i \(0.492500\pi\)
\(402\) −9.07439 9.07439i −0.0225731 0.0225731i
\(403\) 37.5107 37.5107i 0.0930786 0.0930786i
\(404\) 372.434i 0.921866i
\(405\) 16.8005 41.7462i 0.0414827 0.103077i
\(406\) −265.265 −0.653361
\(407\) 334.272 + 334.272i 0.821306 + 0.821306i
\(408\) 2.72397 2.72397i 0.00667640 0.00667640i
\(409\) 455.514i 1.11373i −0.830605 0.556863i \(-0.812005\pi\)
0.830605 0.556863i \(-0.187995\pi\)
\(410\) 372.156 158.569i 0.907697 0.386753i
\(411\) −371.255 −0.903296
\(412\) −138.330 138.330i −0.335753 0.335753i
\(413\) −125.710 + 125.710i −0.304382 + 0.304382i
\(414\) 20.3470i 0.0491473i
\(415\) 144.055 + 338.092i 0.347120 + 0.814679i
\(416\) 5.97441 0.0143616
\(417\) −30.2497 30.2497i −0.0725413 0.0725413i
\(418\) 403.574 403.574i 0.965487 0.965487i
\(419\) 348.362i 0.831414i 0.909499 + 0.415707i \(0.136466\pi\)
−0.909499 + 0.415707i \(0.863534\pi\)
\(420\) −61.7146 24.8367i −0.146939 0.0591349i
\(421\) −394.574 −0.937231 −0.468615 0.883402i \(-0.655247\pi\)
−0.468615 + 0.883402i \(0.655247\pi\)
\(422\) −381.486 381.486i −0.903996 0.903996i
\(423\) −123.973 + 123.973i −0.293081 + 0.293081i
\(424\) 112.335i 0.264941i
\(425\) −0.396581 19.6546i −0.000933131 0.0462460i
\(426\) 110.237 0.258773
\(427\) −219.113 219.113i −0.513144 0.513144i
\(428\) 190.786 190.786i 0.445762 0.445762i
\(429\) 36.9409i 0.0861093i
\(430\) 218.849 543.799i 0.508950 1.26465i
\(431\) 719.875 1.67024 0.835122 0.550065i \(-0.185397\pi\)
0.835122 + 0.550065i \(0.185397\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) −543.789 + 543.789i −1.25586 + 1.25586i −0.302815 + 0.953049i \(0.597926\pi\)
−0.953049 + 0.302815i \(0.902074\pi\)
\(434\) 272.827i 0.628634i
\(435\) 389.087 165.783i 0.894453 0.381110i
\(436\) 173.399 0.397704
\(437\) 67.7712 + 67.7712i 0.155083 + 0.155083i
\(438\) 48.7974 48.7974i 0.111410 0.111410i
\(439\) 478.471i 1.08991i 0.838465 + 0.544956i \(0.183453\pi\)
−0.838465 + 0.544956i \(0.816547\pi\)
\(440\) −111.946 262.734i −0.254423 0.597123i
\(441\) −102.745 −0.232981
\(442\) −0.830485 0.830485i −0.00187893 0.00187893i
\(443\) 324.161 324.161i 0.731741 0.731741i −0.239223 0.970965i \(-0.576893\pi\)
0.970965 + 0.239223i \(0.0768928\pi\)
\(444\) 81.0921i 0.182640i
\(445\) −709.924 285.705i −1.59534 0.642034i
\(446\) 87.2963 0.195732
\(447\) 32.0212 + 32.0212i 0.0716357 + 0.0716357i
\(448\) 21.7269 21.7269i 0.0484976 0.0484976i
\(449\) 316.099i 0.704007i −0.935999 0.352003i \(-0.885501\pi\)
0.935999 0.352003i \(-0.114499\pi\)
\(450\) 106.044 2.13972i 0.235654 0.00475492i
\(451\) −1155.29 −2.56162
\(452\) −212.998 212.998i −0.471235 0.471235i
\(453\) 182.938 182.938i 0.403836 0.403836i
\(454\) 297.059i 0.654314i
\(455\) −7.57221 + 18.8156i −0.0166422 + 0.0413529i
\(456\) −97.9043 −0.214702
\(457\) −572.671 572.671i −1.25311 1.25311i −0.954318 0.298791i \(-0.903417\pi\)
−0.298791 0.954318i \(-0.596583\pi\)
\(458\) 176.625 176.625i 0.385645 0.385645i
\(459\) 4.08596i 0.00890186i
\(460\) 44.1203 18.7989i 0.0959137 0.0408671i
\(461\) 664.538 1.44151 0.720757 0.693187i \(-0.243794\pi\)
0.720757 + 0.693187i \(0.243794\pi\)
\(462\) 134.341 + 134.341i 0.290782 + 0.290782i
\(463\) −32.2968 + 32.2968i −0.0697555 + 0.0697555i −0.741124 0.671368i \(-0.765707\pi\)
0.671368 + 0.741124i \(0.265707\pi\)
\(464\) 195.345i 0.421001i
\(465\) 170.509 + 400.180i 0.366687 + 0.860602i
\(466\) 172.153 0.369426
\(467\) 107.272 + 107.272i 0.229705 + 0.229705i 0.812569 0.582864i \(-0.198068\pi\)
−0.582864 + 0.812569i \(0.698068\pi\)
\(468\) 4.48081 4.48081i 0.00957437 0.00957437i
\(469\) 20.1224i 0.0429049i
\(470\) −383.363 154.282i −0.815666 0.328260i
\(471\) −228.129 −0.484350
\(472\) 92.5745 + 92.5745i 0.196132 + 0.196132i
\(473\) −1183.75 + 1183.75i −2.50265 + 2.50265i
\(474\) 29.1839i 0.0615694i
\(475\) −346.083 + 360.337i −0.728596 + 0.758604i
\(476\) −6.04039 −0.0126899
\(477\) −84.2512 84.2512i −0.176627 0.176627i
\(478\) −83.0954 + 83.0954i −0.173840 + 0.173840i
\(479\) 199.437i 0.416360i 0.978091 + 0.208180i \(0.0667540\pi\)
−0.978091 + 0.208180i \(0.933246\pi\)
\(480\) −18.2901 + 45.4475i −0.0381043 + 0.0946822i
\(481\) −24.7234 −0.0513999
\(482\) 458.620 + 458.620i 0.951494 + 0.951494i
\(483\) −22.5597 + 22.5597i −0.0467074 + 0.0467074i
\(484\) 573.611i 1.18515i
\(485\) −712.691 + 303.665i −1.46947 + 0.626113i
\(486\) 22.0454 0.0453609
\(487\) −202.028 202.028i −0.414842 0.414842i 0.468580 0.883421i \(-0.344766\pi\)
−0.883421 + 0.468580i \(0.844766\pi\)
\(488\) −161.358 + 161.358i −0.330651 + 0.330651i
\(489\) 393.302i 0.804299i
\(490\) −94.9271 222.791i −0.193729 0.454675i
\(491\) 642.465 1.30848 0.654241 0.756286i \(-0.272988\pi\)
0.654241 + 0.756286i \(0.272988\pi\)
\(492\) 140.133 + 140.133i 0.284823 + 0.284823i
\(493\) 27.1543 27.1543i 0.0550797 0.0550797i
\(494\) 29.8491i 0.0604233i
\(495\) −281.010 113.091i −0.567697 0.228467i
\(496\) −200.914 −0.405068
\(497\) −122.225 122.225i −0.245926 0.245926i
\(498\) −127.307 + 127.307i −0.255636 + 0.255636i
\(499\) 745.571i 1.49413i −0.664751 0.747065i \(-0.731462\pi\)
0.664751 0.747065i \(-0.268538\pi\)
\(500\) 102.616 + 227.969i 0.205231 + 0.455939i
\(501\) −482.767 −0.963606
\(502\) −297.824 297.824i −0.593275 0.593275i
\(503\) 133.917 133.917i 0.266237 0.266237i −0.561345 0.827582i \(-0.689716\pi\)
0.827582 + 0.561345i \(0.189716\pi\)
\(504\) 32.5904i 0.0646634i
\(505\) 347.615 863.761i 0.688347 1.71042i
\(506\) −136.964 −0.270679
\(507\) 205.616 + 205.616i 0.405554 + 0.405554i
\(508\) 330.251 330.251i 0.650100 0.650100i
\(509\) 553.510i 1.08745i 0.839265 + 0.543723i \(0.182986\pi\)
−0.839265 + 0.543723i \(0.817014\pi\)
\(510\) 8.85997 3.77507i 0.0173725 0.00740210i
\(511\) −108.208 −0.211757
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −73.4282 + 73.4282i −0.143135 + 0.143135i
\(514\) 266.200i 0.517899i
\(515\) −191.708 449.933i −0.372249 0.873656i
\(516\) 287.170 0.556532
\(517\) 834.512 + 834.512i 1.61414 + 1.61414i
\(518\) −89.9105 + 89.9105i −0.173572 + 0.173572i
\(519\) 41.9812i 0.0808885i
\(520\) 13.8560 + 5.57628i 0.0266462 + 0.0107236i
\(521\) 516.860 0.992053 0.496027 0.868307i \(-0.334792\pi\)
0.496027 + 0.868307i \(0.334792\pi\)
\(522\) 146.508 + 146.508i 0.280668 + 0.280668i
\(523\) −346.867 + 346.867i −0.663225 + 0.663225i −0.956139 0.292914i \(-0.905375\pi\)
0.292914 + 0.956139i \(0.405375\pi\)
\(524\) 196.735i 0.375449i
\(525\) −119.949 115.204i −0.228474 0.219436i
\(526\) −214.534 −0.407860
\(527\) 27.9284 + 27.9284i 0.0529951 + 0.0529951i
\(528\) 98.9310 98.9310i 0.187369 0.187369i
\(529\) 23.0000i 0.0434783i
\(530\) 104.849 260.531i 0.197828 0.491568i
\(531\) 138.862 0.261510
\(532\) 108.551 + 108.551i 0.204043 + 0.204043i
\(533\) 42.7238 42.7238i 0.0801572 0.0801572i
\(534\) 374.898i 0.702057i
\(535\) 620.549 264.405i 1.15991 0.494215i
\(536\) 14.8184 0.0276463
\(537\) −145.419 145.419i −0.270798 0.270798i
\(538\) −68.2440 + 68.2440i −0.126848 + 0.126848i
\(539\) 691.614i 1.28314i
\(540\) 20.3681 + 47.8032i 0.0377186 + 0.0885244i
\(541\) −99.7425 −0.184367 −0.0921835 0.995742i \(-0.529385\pi\)
−0.0921835 + 0.995742i \(0.529385\pi\)
\(542\) 166.004 + 166.004i 0.306280 + 0.306280i
\(543\) −25.5508 + 25.5508i −0.0470550 + 0.0470550i
\(544\) 4.44823i 0.00817688i
\(545\) 402.152 + 161.844i 0.737893 + 0.296961i
\(546\) −9.93616 −0.0181981
\(547\) −187.087 187.087i −0.342023 0.342023i 0.515104 0.857127i \(-0.327753\pi\)
−0.857127 + 0.515104i \(0.827753\pi\)
\(548\) 303.128 303.128i 0.553154 0.553154i
\(549\) 242.036i 0.440868i
\(550\) −14.4033 713.827i −0.0261878 1.29787i
\(551\) −975.973 −1.77128
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 32.3576 32.3576i 0.0585128 0.0585128i
\(554\) 333.995i 0.602878i
\(555\) 75.6882 188.071i 0.136375 0.338867i
\(556\) 49.3976 0.0888446
\(557\) −471.806 471.806i −0.847049 0.847049i 0.142715 0.989764i \(-0.454417\pi\)
−0.989764 + 0.142715i \(0.954417\pi\)
\(558\) −150.685 + 150.685i −0.270045 + 0.270045i
\(559\) 87.5526i 0.156624i
\(560\) 70.6688 30.1107i 0.126194 0.0537691i
\(561\) −27.5042 −0.0490271
\(562\) 138.196 + 138.196i 0.245901 + 0.245901i
\(563\) −49.5630 + 49.5630i −0.0880338 + 0.0880338i −0.749752 0.661719i \(-0.769827\pi\)
0.661719 + 0.749752i \(0.269827\pi\)
\(564\) 202.447i 0.358949i
\(565\) −295.188 692.797i −0.522457 1.22619i
\(566\) 111.338 0.196710
\(567\) −24.4428 24.4428i −0.0431089 0.0431089i
\(568\) −90.0083 + 90.0083i −0.158465 + 0.158465i
\(569\) 485.455i 0.853172i 0.904447 + 0.426586i \(0.140284\pi\)
−0.904447 + 0.426586i \(0.859716\pi\)
\(570\) −227.063 91.3801i −0.398356 0.160316i
\(571\) 159.599 0.279508 0.139754 0.990186i \(-0.455369\pi\)
0.139754 + 0.990186i \(0.455369\pi\)
\(572\) −30.1621 30.1621i −0.0527310 0.0527310i
\(573\) 309.419 309.419i 0.539999 0.539999i
\(574\) 310.744i 0.541366i
\(575\) 119.871 2.41871i 0.208472 0.00420645i
\(576\) −24.0000 −0.0416667
\(577\) 676.144 + 676.144i 1.17183 + 1.17183i 0.981774 + 0.190052i \(0.0608658\pi\)
0.190052 + 0.981774i \(0.439134\pi\)
\(578\) −288.382 + 288.382i −0.498930 + 0.498930i
\(579\) 77.2260i 0.133378i
\(580\) −182.327 + 453.050i −0.314357 + 0.781120i
\(581\) 282.301 0.485889
\(582\) −268.360 268.360i −0.461099 0.461099i
\(583\) −567.129 + 567.129i −0.972776 + 0.972776i
\(584\) 79.6858i 0.136448i
\(585\) 14.5742 6.20982i 0.0249132 0.0106151i
\(586\) −294.748 −0.502984
\(587\) −9.46267 9.46267i −0.0161204 0.0161204i 0.699001 0.715121i \(-0.253628\pi\)
−0.715121 + 0.699001i \(0.753628\pi\)
\(588\) 83.8905 83.8905i 0.142671 0.142671i
\(589\) 1003.80i 1.70424i
\(590\) 128.296 + 301.107i 0.217451 + 0.510351i
\(591\) 308.165 0.521429
\(592\) 66.2114 + 66.2114i 0.111844 + 0.111844i
\(593\) 464.745 464.745i 0.783719 0.783719i −0.196738 0.980456i \(-0.563035\pi\)
0.980456 + 0.196738i \(0.0630347\pi\)
\(594\) 148.396i 0.249826i
\(595\) −14.0091 5.63786i −0.0235446 0.00947540i
\(596\) −52.2903 −0.0877355
\(597\) 260.953 + 260.953i 0.437108 + 0.437108i
\(598\) 5.06505 5.06505i 0.00846999 0.00846999i
\(599\) 711.019i 1.18701i −0.804830 0.593505i \(-0.797744\pi\)
0.804830 0.593505i \(-0.202256\pi\)
\(600\) −84.8378 + 88.3320i −0.141396 + 0.147220i
\(601\) −103.335 −0.171938 −0.0859689 0.996298i \(-0.527399\pi\)
−0.0859689 + 0.996298i \(0.527399\pi\)
\(602\) −318.399 318.399i −0.528902 0.528902i
\(603\) 11.1138 11.1138i 0.0184309 0.0184309i
\(604\) 298.736i 0.494596i
\(605\) −535.387 + 1330.34i −0.884937 + 2.19891i
\(606\) 456.137 0.752701
\(607\) −12.5607 12.5607i −0.0206931 0.0206931i 0.696685 0.717378i \(-0.254658\pi\)
−0.717378 + 0.696685i \(0.754658\pi\)
\(608\) 79.9385 79.9385i 0.131478 0.131478i
\(609\) 324.882i 0.533467i
\(610\) −524.831 + 223.621i −0.860378 + 0.366591i
\(611\) −61.7222 −0.101018
\(612\) 3.33617 + 3.33617i 0.00545126 + 0.00545126i
\(613\) −227.704 + 227.704i −0.371459 + 0.371459i −0.868008 0.496550i \(-0.834600\pi\)
0.496550 + 0.868008i \(0.334600\pi\)
\(614\) 599.408i 0.976234i
\(615\) 194.206 + 455.796i 0.315783 + 0.741131i
\(616\) −219.379 −0.356134
\(617\) −735.380 735.380i −1.19186 1.19186i −0.976543 0.215320i \(-0.930920\pi\)
−0.215320 0.976543i \(-0.569080\pi\)
\(618\) 169.419 169.419i 0.274142 0.274142i
\(619\) 216.723i 0.350118i 0.984558 + 0.175059i \(0.0560116\pi\)
−0.984558 + 0.175059i \(0.943988\pi\)
\(620\) −465.966 187.525i −0.751558 0.302460i
\(621\) 24.9199 0.0401286
\(622\) 259.066 + 259.066i 0.416504 + 0.416504i
\(623\) −415.667 + 415.667i −0.667203 + 0.667203i
\(624\) 7.31713i 0.0117262i
\(625\) 25.2117 + 624.491i 0.0403387 + 0.999186i
\(626\) 326.128 0.520972
\(627\) 494.275 + 494.275i 0.788317 + 0.788317i
\(628\) 186.266 186.266i 0.296603 0.296603i
\(629\) 18.4077i 0.0292650i
\(630\) 30.4186 75.5846i 0.0482835 0.119976i
\(631\) −702.127 −1.11272 −0.556361 0.830941i \(-0.687803\pi\)
−0.556361 + 0.830941i \(0.687803\pi\)
\(632\) −23.8286 23.8286i −0.0377034 0.0377034i
\(633\) 467.224 467.224i 0.738110 0.738110i
\(634\) 294.192i 0.464025i
\(635\) 1074.17 457.685i 1.69161 0.720764i
\(636\) 137.582 0.216323
\(637\) −25.5766 25.5766i −0.0401516 0.0401516i
\(638\) 986.207 986.207i 1.54578 1.54578i
\(639\) 135.013i 0.211287i
\(640\) −22.1739 52.0415i −0.0346468 0.0813148i
\(641\) −121.421 −0.189424 −0.0947122 0.995505i \(-0.530193\pi\)
−0.0947122 + 0.995505i \(0.530193\pi\)
\(642\) 233.664 + 233.664i 0.363963 + 0.363963i
\(643\) −219.567 + 219.567i −0.341473 + 0.341473i −0.856921 0.515448i \(-0.827626\pi\)
0.515448 + 0.856921i \(0.327626\pi\)
\(644\) 36.8398i 0.0572046i
\(645\) 666.015 + 268.034i 1.03258 + 0.415556i
\(646\) −22.2240 −0.0344025
\(647\) −460.289 460.289i −0.711420 0.711420i 0.255412 0.966832i \(-0.417789\pi\)
−0.966832 + 0.255412i \(0.917789\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 934.734i 1.44027i
\(650\) 26.9307 + 25.8654i 0.0414318 + 0.0397929i
\(651\) 334.144 0.513278
\(652\) 321.130 + 321.130i 0.492531 + 0.492531i
\(653\) −444.922 + 444.922i −0.681351 + 0.681351i −0.960304 0.278954i \(-0.910012\pi\)
0.278954 + 0.960304i \(0.410012\pi\)
\(654\) 212.369i 0.324724i
\(655\) 183.625 456.275i 0.280344 0.696603i
\(656\) −228.836 −0.348836
\(657\) 59.7644 + 59.7644i 0.0909655 + 0.0909655i
\(658\) −224.463 + 224.463i −0.341129 + 0.341129i
\(659\) 215.293i 0.326697i 0.986568 + 0.163348i \(0.0522295\pi\)
−0.986568 + 0.163348i \(0.947771\pi\)
\(660\) 321.782 137.106i 0.487549 0.207736i
\(661\) 460.077 0.696032 0.348016 0.937489i \(-0.386855\pi\)
0.348016 + 0.937489i \(0.386855\pi\)
\(662\) −354.624 354.624i −0.535686 0.535686i
\(663\) 1.01713 1.01713i 0.00153414 0.00153414i
\(664\) 207.891i 0.313088i
\(665\) 150.438 + 353.072i 0.226222 + 0.530936i
\(666\) 99.3171 0.149125
\(667\) 165.611 + 165.611i 0.248293 + 0.248293i
\(668\) 394.177 394.177i 0.590086 0.590086i
\(669\) 106.916i 0.159814i
\(670\) 34.3674 + 13.8309i 0.0512946 + 0.0206432i
\(671\) 1629.24 2.42808
\(672\) 26.6099 + 26.6099i 0.0395981 + 0.0395981i
\(673\) −380.727 + 380.727i −0.565716 + 0.565716i −0.930925 0.365210i \(-0.880997\pi\)
0.365210 + 0.930925i \(0.380997\pi\)
\(674\) 140.249i 0.208084i
\(675\) 2.62061 + 129.877i 0.00388238 + 0.192411i
\(676\) −335.769 −0.496700
\(677\) 88.2870 + 88.2870i 0.130409 + 0.130409i 0.769299 0.638889i \(-0.220606\pi\)
−0.638889 + 0.769299i \(0.720606\pi\)
\(678\) 260.868 260.868i 0.384762 0.384762i
\(679\) 595.086i 0.876415i
\(680\) −4.15180 + 10.3165i −0.00610559 + 0.0151713i
\(681\) 363.821 0.534246
\(682\) 1014.32 + 1014.32i 1.48728 + 1.48728i
\(683\) 367.133 367.133i 0.537530 0.537530i −0.385273 0.922803i \(-0.625893\pi\)
0.922803 + 0.385273i \(0.125893\pi\)
\(684\) 119.908i 0.175304i
\(685\) 985.953 420.097i 1.43935 0.613280i
\(686\) −452.181 −0.659156
\(687\) 216.321 + 216.321i 0.314877 + 0.314877i
\(688\) −234.474 + 234.474i −0.340805 + 0.340805i
\(689\) 41.9459i 0.0608794i
\(690\) 23.0238 + 54.0361i 0.0333678 + 0.0783132i
\(691\) 557.637 0.807001 0.403500 0.914979i \(-0.367793\pi\)
0.403500 + 0.914979i \(0.367793\pi\)
\(692\) 34.2775 + 34.2775i 0.0495339 + 0.0495339i
\(693\) −164.534 + 164.534i −0.237423 + 0.237423i
\(694\) 140.407i 0.202316i
\(695\) 114.565 + 46.1058i 0.164841 + 0.0663393i
\(696\) −239.247 −0.343746
\(697\) 31.8099 + 31.8099i 0.0456382 + 0.0456382i
\(698\) −361.402 + 361.402i −0.517769 + 0.517769i
\(699\) 210.843i 0.301635i
\(700\) 192.001 3.87412i 0.274288 0.00553445i
\(701\) 780.433 1.11331 0.556657 0.830742i \(-0.312084\pi\)
0.556657 + 0.830742i \(0.312084\pi\)
\(702\) 5.48785 + 5.48785i 0.00781744 + 0.00781744i
\(703\) −330.803 + 330.803i −0.470558 + 0.470558i
\(704\) 161.554i 0.229480i
\(705\) 188.956 469.522i 0.268023 0.665989i
\(706\) −353.630 −0.500892
\(707\) −505.740 505.740i −0.715332 0.715332i
\(708\) −113.380 + 113.380i −0.160141 + 0.160141i
\(709\) 954.304i 1.34599i 0.739649 + 0.672993i \(0.234992\pi\)
−0.739649 + 0.672993i \(0.765008\pi\)
\(710\) −292.761 + 124.740i −0.412339 + 0.175690i
\(711\) −35.7429 −0.0502712
\(712\) 306.103 + 306.103i 0.429920 + 0.429920i
\(713\) −170.333 + 170.333i −0.238896 + 0.238896i
\(714\) 7.39793i 0.0103612i
\(715\) −41.8008 98.1051i −0.0584626 0.137210i
\(716\) 237.468 0.331659
\(717\) −101.771 101.771i −0.141940 0.141940i
\(718\) 247.653 247.653i 0.344921 0.344921i
\(719\) 898.190i 1.24922i 0.780937 + 0.624610i \(0.214742\pi\)
−0.780937 + 0.624610i \(0.785258\pi\)
\(720\) −55.6616 22.4007i −0.0773077 0.0311120i
\(721\) −375.687 −0.521063
\(722\) 38.3856 + 38.3856i 0.0531656 + 0.0531656i
\(723\) −561.693 + 561.693i −0.776892 + 0.776892i
\(724\) 41.7244i 0.0576303i
\(725\) −845.718 + 880.550i −1.16651 + 1.21455i
\(726\) −702.528 −0.967669
\(727\) 112.049 + 112.049i 0.154125 + 0.154125i 0.779958 0.625832i \(-0.215241\pi\)
−0.625832 + 0.779958i \(0.715241\pi\)
\(728\) 8.11284 8.11284i 0.0111440 0.0111440i
\(729\) 27.0000i 0.0370370i
\(730\) −74.3757 + 184.810i −0.101884 + 0.253164i
\(731\) 65.1870 0.0891750
\(732\) −197.622 197.622i −0.269975 0.269975i
\(733\) −717.264 + 717.264i −0.978532 + 0.978532i −0.999774 0.0212427i \(-0.993238\pi\)
0.0212427 + 0.999774i \(0.493238\pi\)
\(734\) 455.883i 0.621094i
\(735\) 272.862 116.261i 0.371241 0.158179i
\(736\) −27.1293 −0.0368605
\(737\) −74.8115 74.8115i −0.101508 0.101508i
\(738\) −171.627 + 171.627i −0.232557 + 0.232557i
\(739\) 756.398i 1.02354i −0.859122 0.511772i \(-0.828989\pi\)
0.859122 0.511772i \(-0.171011\pi\)
\(740\) 91.7604 + 215.359i 0.124001 + 0.291025i
\(741\) −36.5575 −0.0493354
\(742\) −152.543 152.543i −0.205584 0.205584i
\(743\) 611.505 611.505i 0.823022 0.823022i −0.163518 0.986540i \(-0.552284\pi\)
0.986540 + 0.163518i \(0.0522843\pi\)
\(744\) 246.068i 0.330737i
\(745\) −121.273 48.8058i −0.162783 0.0655111i
\(746\) −193.832 −0.259829
\(747\) −155.918 155.918i −0.208726 0.208726i
\(748\) 22.4571 22.4571i 0.0300228 0.0300228i
\(749\) 518.149i 0.691788i
\(750\) −279.204 + 125.678i −0.372272 + 0.167571i
\(751\) 720.817 0.959809 0.479905 0.877321i \(-0.340671\pi\)
0.479905 + 0.877321i \(0.340671\pi\)
\(752\) 165.297 + 165.297i 0.219810 + 0.219810i
\(753\) 364.758 364.758i 0.484407 0.484407i
\(754\) 72.9418i 0.0967398i
\(755\) −278.828 + 692.838i −0.369309 + 0.917666i
\(756\) 39.9149 0.0527975
\(757\) −704.669 704.669i −0.930870 0.930870i 0.0668903 0.997760i \(-0.478692\pi\)
−0.997760 + 0.0668903i \(0.978692\pi\)
\(758\) 233.612 233.612i 0.308195 0.308195i
\(759\) 167.746i 0.221009i
\(760\) 260.008 110.784i 0.342115 0.145769i
\(761\) 522.214 0.686221 0.343111 0.939295i \(-0.388519\pi\)
0.343111 + 0.939295i \(0.388519\pi\)
\(762\) 404.473 + 404.473i 0.530805 + 0.530805i
\(763\) 235.464 235.464i 0.308602 0.308602i
\(764\) 505.280i 0.661361i
\(765\) 4.62350 + 10.8512i 0.00604379 + 0.0141846i
\(766\) −319.948 −0.417687
\(767\) 34.5674 + 34.5674i 0.0450683 + 0.0450683i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 478.937i 0.622805i −0.950278 0.311403i \(-0.899201\pi\)
0.950278 0.311403i \(-0.100799\pi\)
\(770\) −508.790 204.760i −0.660766 0.265922i
\(771\) −326.027 −0.422862
\(772\) −63.0548 63.0548i −0.0816772 0.0816772i
\(773\) −149.986 + 149.986i −0.194031 + 0.194031i −0.797435 0.603405i \(-0.793810\pi\)
0.603405 + 0.797435i \(0.293810\pi\)
\(774\) 351.710i 0.454406i
\(775\) −905.654 869.829i −1.16859 1.12236i
\(776\) 438.229 0.564729
\(777\) −110.117 110.117i −0.141721 0.141721i
\(778\) 218.431 218.431i 0.280760 0.280760i