Properties

Label 690.3.k.a.277.11
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 277.11
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-0.335340 + 4.98874i) q^{5} +2.44949 q^{6} +(-8.75117 - 8.75117i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-0.335340 + 4.98874i) q^{5} +2.44949 q^{6} +(-8.75117 - 8.75117i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-5.32408 + 4.65340i) q^{10} -1.73874 q^{11} +(2.44949 + 2.44949i) q^{12} +(2.77410 - 2.77410i) q^{13} -17.5023i q^{14} +(5.69923 + 6.52064i) q^{15} -4.00000 q^{16} +(-13.9720 - 13.9720i) q^{17} +(3.00000 - 3.00000i) q^{18} +3.58863i q^{19} +(-9.97748 - 0.670679i) q^{20} -21.4359 q^{21} +(-1.73874 - 1.73874i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(-24.7751 - 3.34584i) q^{25} +5.54821 q^{26} +(-3.67423 - 3.67423i) q^{27} +(17.5023 - 17.5023i) q^{28} -39.9985i q^{29} +(-0.821411 + 12.2199i) q^{30} -29.7104 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-2.12951 + 2.12951i) q^{33} -27.9439i q^{34} +(46.5919 - 40.7227i) q^{35} +6.00000 q^{36} +(-36.2049 - 36.2049i) q^{37} +(-3.58863 + 3.58863i) q^{38} -6.79514i q^{39} +(-9.30681 - 10.6482i) q^{40} +53.7996 q^{41} +(-21.4359 - 21.4359i) q^{42} +(-17.3527 + 17.3527i) q^{43} -3.47748i q^{44} +(14.9662 + 1.00602i) q^{45} +6.78233 q^{46} +(-41.7185 - 41.7185i) q^{47} +(-4.89898 + 4.89898i) q^{48} +104.166i q^{49} +(-21.4292 - 28.1209i) q^{50} -34.2242 q^{51} +(5.54821 + 5.54821i) q^{52} +(40.3864 - 40.3864i) q^{53} -7.34847i q^{54} +(0.583069 - 8.67413i) q^{55} +35.0047 q^{56} +(4.39515 + 4.39515i) q^{57} +(39.9985 - 39.9985i) q^{58} +88.9048i q^{59} +(-13.0413 + 11.3985i) q^{60} +5.38439 q^{61} +(-29.7104 - 29.7104i) q^{62} +(-26.2535 + 26.2535i) q^{63} -8.00000i q^{64} +(12.9090 + 14.7696i) q^{65} -4.25903 q^{66} +(11.2357 + 11.2357i) q^{67} +(27.9439 - 27.9439i) q^{68} -8.30662i q^{69} +(87.3146 + 5.86922i) q^{70} -47.6451 q^{71} +(6.00000 + 6.00000i) q^{72} +(65.5909 - 65.5909i) q^{73} -72.4098i q^{74} +(-34.4410 + 26.2454i) q^{75} -7.17725 q^{76} +(15.2160 + 15.2160i) q^{77} +(6.79514 - 6.79514i) q^{78} +13.2923i q^{79} +(1.34136 - 19.9550i) q^{80} -9.00000 q^{81} +(53.7996 + 53.7996i) q^{82} +(-102.840 + 102.840i) q^{83} -42.8718i q^{84} +(74.3879 - 65.0172i) q^{85} -34.7055 q^{86} +(-48.9880 - 48.9880i) q^{87} +(3.47748 - 3.47748i) q^{88} -77.1039i q^{89} +(13.9602 + 15.9722i) q^{90} -48.5533 q^{91} +(6.78233 + 6.78233i) q^{92} +(-36.3877 + 36.3877i) q^{93} -83.4371i q^{94} +(-17.9027 - 1.20341i) q^{95} -9.79796 q^{96} +(-21.6454 - 21.6454i) q^{97} +(-104.166 + 104.166i) q^{98} +5.21622i 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
\(5\) −0.335340 + 4.98874i −0.0670679 + 0.997748i
\(6\) 2.44949 0.408248
\(7\) −8.75117 8.75117i −1.25017 1.25017i −0.955645 0.294522i \(-0.904840\pi\)
−0.294522 0.955645i \(-0.595160\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −5.32408 + 4.65340i −0.532408 + 0.465340i
\(11\) −1.73874 −0.158067 −0.0790337 0.996872i \(-0.525183\pi\)
−0.0790337 + 0.996872i \(0.525183\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) 2.77410 2.77410i 0.213393 0.213393i −0.592314 0.805707i \(-0.701786\pi\)
0.805707 + 0.592314i \(0.201786\pi\)
\(14\) 17.5023i 1.25017i
\(15\) 5.69923 + 6.52064i 0.379949 + 0.434709i
\(16\) −4.00000 −0.250000
\(17\) −13.9720 13.9720i −0.821881 0.821881i 0.164497 0.986378i \(-0.447400\pi\)
−0.986378 + 0.164497i \(0.947400\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 3.58863i 0.188875i 0.995531 + 0.0944375i \(0.0301053\pi\)
−0.995531 + 0.0944375i \(0.969895\pi\)
\(20\) −9.97748 0.670679i −0.498874 0.0335340i
\(21\) −21.4359 −1.02076
\(22\) −1.73874 1.73874i −0.0790337 0.0790337i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −24.7751 3.34584i −0.991004 0.133834i
\(26\) 5.54821 0.213393
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 17.5023 17.5023i 0.625083 0.625083i
\(29\) 39.9985i 1.37926i −0.724162 0.689630i \(-0.757773\pi\)
0.724162 0.689630i \(-0.242227\pi\)
\(30\) −0.821411 + 12.2199i −0.0273804 + 0.407329i
\(31\) −29.7104 −0.958401 −0.479201 0.877705i \(-0.659073\pi\)
−0.479201 + 0.877705i \(0.659073\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −2.12951 + 2.12951i −0.0645307 + 0.0645307i
\(34\) 27.9439i 0.821881i
\(35\) 46.5919 40.7227i 1.33120 1.16351i
\(36\) 6.00000 0.166667
\(37\) −36.2049 36.2049i −0.978511 0.978511i 0.0212627 0.999774i \(-0.493231\pi\)
−0.999774 + 0.0212627i \(0.993231\pi\)
\(38\) −3.58863 + 3.58863i −0.0944375 + 0.0944375i
\(39\) 6.79514i 0.174234i
\(40\) −9.30681 10.6482i −0.232670 0.266204i
\(41\) 53.7996 1.31218 0.656092 0.754681i \(-0.272208\pi\)
0.656092 + 0.754681i \(0.272208\pi\)
\(42\) −21.4359 21.4359i −0.510378 0.510378i
\(43\) −17.3527 + 17.3527i −0.403552 + 0.403552i −0.879483 0.475931i \(-0.842111\pi\)
0.475931 + 0.879483i \(0.342111\pi\)
\(44\) 3.47748i 0.0790337i
\(45\) 14.9662 + 1.00602i 0.332583 + 0.0223560i
\(46\) 6.78233 0.147442
\(47\) −41.7185 41.7185i −0.887629 0.887629i 0.106666 0.994295i \(-0.465982\pi\)
−0.994295 + 0.106666i \(0.965982\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 104.166i 2.12583i
\(50\) −21.4292 28.1209i −0.428585 0.562419i
\(51\) −34.2242 −0.671063
\(52\) 5.54821 + 5.54821i 0.106696 + 0.106696i
\(53\) 40.3864 40.3864i 0.762008 0.762008i −0.214677 0.976685i \(-0.568870\pi\)
0.976685 + 0.214677i \(0.0688700\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 0.583069 8.67413i 0.0106012 0.157711i
\(56\) 35.0047 0.625083
\(57\) 4.39515 + 4.39515i 0.0771079 + 0.0771079i
\(58\) 39.9985 39.9985i 0.689630 0.689630i
\(59\) 88.9048i 1.50686i 0.657528 + 0.753430i \(0.271602\pi\)
−0.657528 + 0.753430i \(0.728398\pi\)
\(60\) −13.0413 + 11.3985i −0.217355 + 0.189974i
\(61\) 5.38439 0.0882686 0.0441343 0.999026i \(-0.485947\pi\)
0.0441343 + 0.999026i \(0.485947\pi\)
\(62\) −29.7104 29.7104i −0.479201 0.479201i
\(63\) −26.2535 + 26.2535i −0.416722 + 0.416722i
\(64\) 8.00000i 0.125000i
\(65\) 12.9090 + 14.7696i 0.198600 + 0.227224i
\(66\) −4.25903 −0.0645307
\(67\) 11.2357 + 11.2357i 0.167697 + 0.167697i 0.785967 0.618269i \(-0.212166\pi\)
−0.618269 + 0.785967i \(0.712166\pi\)
\(68\) 27.9439 27.9439i 0.410940 0.410940i
\(69\) 8.30662i 0.120386i
\(70\) 87.3146 + 5.86922i 1.24735 + 0.0838461i
\(71\) −47.6451 −0.671057 −0.335529 0.942030i \(-0.608915\pi\)
−0.335529 + 0.942030i \(0.608915\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 65.5909 65.5909i 0.898505 0.898505i −0.0967990 0.995304i \(-0.530860\pi\)
0.995304 + 0.0967990i \(0.0308604\pi\)
\(74\) 72.4098i 0.978511i
\(75\) −34.4410 + 26.2454i −0.459213 + 0.349938i
\(76\) −7.17725 −0.0944375
\(77\) 15.2160 + 15.2160i 0.197611 + 0.197611i
\(78\) 6.79514 6.79514i 0.0871172 0.0871172i
\(79\) 13.2923i 0.168257i 0.996455 + 0.0841284i \(0.0268106\pi\)
−0.996455 + 0.0841284i \(0.973189\pi\)
\(80\) 1.34136 19.9550i 0.0167670 0.249437i
\(81\) −9.00000 −0.111111
\(82\) 53.7996 + 53.7996i 0.656092 + 0.656092i
\(83\) −102.840 + 102.840i −1.23904 + 1.23904i −0.278648 + 0.960393i \(0.589886\pi\)
−0.960393 + 0.278648i \(0.910114\pi\)
\(84\) 42.8718i 0.510378i
\(85\) 74.3879 65.0172i 0.875152 0.764908i
\(86\) −34.7055 −0.403552
\(87\) −48.9880 48.9880i −0.563080 0.563080i
\(88\) 3.47748 3.47748i 0.0395168 0.0395168i
\(89\) 77.1039i 0.866336i −0.901313 0.433168i \(-0.857396\pi\)
0.901313 0.433168i \(-0.142604\pi\)
\(90\) 13.9602 + 15.9722i 0.155113 + 0.177469i
\(91\) −48.5533 −0.533553
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) −36.3877 + 36.3877i −0.391266 + 0.391266i
\(94\) 83.4371i 0.887629i
\(95\) −17.9027 1.20341i −0.188450 0.0126675i
\(96\) −9.79796 −0.102062
\(97\) −21.6454 21.6454i −0.223148 0.223148i 0.586674 0.809823i \(-0.300437\pi\)
−0.809823 + 0.586674i \(0.800437\pi\)
\(98\) −104.166 + 104.166i −1.06292 + 1.06292i
\(99\) 5.21622i 0.0526891i
\(100\) 6.69169 49.5502i 0.0669169 0.495502i
\(101\) 144.025 1.42599 0.712994 0.701170i \(-0.247339\pi\)
0.712994 + 0.701170i \(0.247339\pi\)
\(102\) −34.2242 34.2242i −0.335531 0.335531i
\(103\) −56.4397 + 56.4397i −0.547958 + 0.547958i −0.925850 0.377891i \(-0.876649\pi\)
0.377891 + 0.925850i \(0.376649\pi\)
\(104\) 11.0964i 0.106696i
\(105\) 7.18830 106.938i 0.0684600 1.01846i
\(106\) 80.7728 0.762008
\(107\) −140.286 140.286i −1.31108 1.31108i −0.920620 0.390461i \(-0.872316\pi\)
−0.390461 0.920620i \(-0.627684\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 95.5699i 0.876788i 0.898783 + 0.438394i \(0.144453\pi\)
−0.898783 + 0.438394i \(0.855547\pi\)
\(110\) 9.25720 8.09106i 0.0841563 0.0735551i
\(111\) −88.6836 −0.798951
\(112\) 35.0047 + 35.0047i 0.312542 + 0.312542i
\(113\) −77.4278 + 77.4278i −0.685202 + 0.685202i −0.961168 0.275966i \(-0.911002\pi\)
0.275966 + 0.961168i \(0.411002\pi\)
\(114\) 8.79030i 0.0771079i
\(115\) 15.7805 + 18.0548i 0.137221 + 0.156999i
\(116\) 79.9971 0.689630
\(117\) −8.32231 8.32231i −0.0711309 0.0711309i
\(118\) −88.9048 + 88.9048i −0.753430 + 0.753430i
\(119\) 244.542i 2.05498i
\(120\) −24.4397 1.64282i −0.203665 0.0136902i
\(121\) −117.977 −0.975015
\(122\) 5.38439 + 5.38439i 0.0441343 + 0.0441343i
\(123\) 65.8907 65.8907i 0.535697 0.535697i
\(124\) 59.4209i 0.479201i
\(125\) 24.9996 122.475i 0.199997 0.979797i
\(126\) −52.5070 −0.416722
\(127\) 134.001 + 134.001i 1.05513 + 1.05513i 0.998389 + 0.0567374i \(0.0180698\pi\)
0.0567374 + 0.998389i \(0.481930\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 42.5054i 0.329499i
\(130\) −1.86053 + 27.6786i −0.0143118 + 0.212912i
\(131\) −110.981 −0.847181 −0.423590 0.905854i \(-0.639230\pi\)
−0.423590 + 0.905854i \(0.639230\pi\)
\(132\) −4.25903 4.25903i −0.0322654 0.0322654i
\(133\) 31.4047 31.4047i 0.236125 0.236125i
\(134\) 22.4715i 0.167697i
\(135\) 19.5619 17.0977i 0.144903 0.126650i
\(136\) 55.8879 0.410940
\(137\) −29.9855 29.9855i −0.218872 0.218872i 0.589151 0.808023i \(-0.299462\pi\)
−0.808023 + 0.589151i \(0.799462\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 153.082i 1.10131i −0.834734 0.550653i \(-0.814379\pi\)
0.834734 0.550653i \(-0.185621\pi\)
\(140\) 81.4454 + 93.1838i 0.581753 + 0.665599i
\(141\) −102.189 −0.724746
\(142\) −47.6451 47.6451i −0.335529 0.335529i
\(143\) −4.82345 + 4.82345i −0.0337304 + 0.0337304i
\(144\) 12.0000i 0.0833333i
\(145\) 199.542 + 13.4131i 1.37615 + 0.0925041i
\(146\) 131.182 0.898505
\(147\) 127.577 + 127.577i 0.867868 + 0.867868i
\(148\) 72.4098 72.4098i 0.489256 0.489256i
\(149\) 42.7618i 0.286992i −0.989651 0.143496i \(-0.954166\pi\)
0.989651 0.143496i \(-0.0458344\pi\)
\(150\) −60.6863 8.19561i −0.404576 0.0546374i
\(151\) 237.809 1.57490 0.787448 0.616382i \(-0.211402\pi\)
0.787448 + 0.616382i \(0.211402\pi\)
\(152\) −7.17725 7.17725i −0.0472188 0.0472188i
\(153\) −41.9159 + 41.9159i −0.273960 + 0.273960i
\(154\) 30.4320i 0.197611i
\(155\) 9.96308 148.218i 0.0642780 0.956243i
\(156\) 13.5903 0.0871172
\(157\) 124.621 + 124.621i 0.793766 + 0.793766i 0.982104 0.188338i \(-0.0603102\pi\)
−0.188338 + 0.982104i \(0.560310\pi\)
\(158\) −13.2923 + 13.2923i −0.0841284 + 0.0841284i
\(159\) 98.9261i 0.622177i
\(160\) 21.2963 18.6136i 0.133102 0.116335i
\(161\) −59.3533 −0.368654
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −102.091 + 102.091i −0.626322 + 0.626322i −0.947141 0.320818i \(-0.896042\pi\)
0.320818 + 0.947141i \(0.396042\pi\)
\(164\) 107.599i 0.656092i
\(165\) −9.90949 11.3377i −0.0600575 0.0687134i
\(166\) −205.681 −1.23904
\(167\) 135.570 + 135.570i 0.811797 + 0.811797i 0.984903 0.173106i \(-0.0553804\pi\)
−0.173106 + 0.984903i \(0.555380\pi\)
\(168\) 42.8718 42.8718i 0.255189 0.255189i
\(169\) 153.609i 0.908927i
\(170\) 139.405 + 9.37071i 0.820030 + 0.0551218i
\(171\) 10.7659 0.0629584
\(172\) −34.7055 34.7055i −0.201776 0.201776i
\(173\) 161.164 161.164i 0.931582 0.931582i −0.0662225 0.997805i \(-0.521095\pi\)
0.997805 + 0.0662225i \(0.0210947\pi\)
\(174\) 97.9760i 0.563080i
\(175\) 187.531 + 246.091i 1.07161 + 1.40623i
\(176\) 6.95496 0.0395168
\(177\) 108.886 + 108.886i 0.615173 + 0.615173i
\(178\) 77.1039 77.1039i 0.433168 0.433168i
\(179\) 138.437i 0.773393i −0.922207 0.386697i \(-0.873616\pi\)
0.922207 0.386697i \(-0.126384\pi\)
\(180\) −2.01204 + 29.9325i −0.0111780 + 0.166291i
\(181\) −235.431 −1.30072 −0.650362 0.759624i \(-0.725383\pi\)
−0.650362 + 0.759624i \(0.725383\pi\)
\(182\) −48.5533 48.5533i −0.266776 0.266776i
\(183\) 6.59450 6.59450i 0.0360355 0.0360355i
\(184\) 13.5647i 0.0737210i
\(185\) 192.758 168.476i 1.04193 0.910681i
\(186\) −72.7754 −0.391266
\(187\) 24.2936 + 24.2936i 0.129913 + 0.129913i
\(188\) 83.4371 83.4371i 0.443814 0.443814i
\(189\) 64.3077i 0.340252i
\(190\) −16.6993 19.1061i −0.0878912 0.100559i
\(191\) 179.526 0.939927 0.469964 0.882686i \(-0.344267\pi\)
0.469964 + 0.882686i \(0.344267\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) 121.477 121.477i 0.629413 0.629413i −0.318508 0.947920i \(-0.603182\pi\)
0.947920 + 0.318508i \(0.103182\pi\)
\(194\) 43.2908i 0.223148i
\(195\) 33.8992 + 2.27868i 0.173842 + 0.0116855i
\(196\) −208.332 −1.06292
\(197\) −59.5411 59.5411i −0.302239 0.302239i 0.539650 0.841889i \(-0.318556\pi\)
−0.841889 + 0.539650i \(0.818556\pi\)
\(198\) −5.21622 + 5.21622i −0.0263446 + 0.0263446i
\(199\) 276.890i 1.39141i 0.718328 + 0.695705i \(0.244908\pi\)
−0.718328 + 0.695705i \(0.755092\pi\)
\(200\) 56.2419 42.8585i 0.281209 0.214292i
\(201\) 27.5218 0.136924
\(202\) 144.025 + 144.025i 0.712994 + 0.712994i
\(203\) −350.034 + 350.034i −1.72430 + 1.72430i
\(204\) 68.4484i 0.335531i
\(205\) −18.0411 + 268.392i −0.0880055 + 1.30923i
\(206\) −112.879 −0.547958
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) −11.0964 + 11.0964i −0.0533482 + 0.0533482i
\(209\) 6.23969i 0.0298550i
\(210\) 114.126 99.7498i 0.543459 0.474999i
\(211\) −144.999 −0.687197 −0.343598 0.939117i \(-0.611646\pi\)
−0.343598 + 0.939117i \(0.611646\pi\)
\(212\) 80.7728 + 80.7728i 0.381004 + 0.381004i
\(213\) −58.3531 + 58.3531i −0.273958 + 0.273958i
\(214\) 280.571i 1.31108i
\(215\) −80.7493 92.3874i −0.375578 0.429709i
\(216\) 14.6969 0.0680414
\(217\) 260.001 + 260.001i 1.19816 + 1.19816i
\(218\) −95.5699 + 95.5699i −0.438394 + 0.438394i
\(219\) 160.664i 0.733626i
\(220\) 17.3483 + 1.16614i 0.0788557 + 0.00530062i
\(221\) −77.5194 −0.350767
\(222\) −88.6836 88.6836i −0.399476 0.399476i
\(223\) 84.8740 84.8740i 0.380601 0.380601i −0.490718 0.871319i \(-0.663265\pi\)
0.871319 + 0.490718i \(0.163265\pi\)
\(224\) 70.0093i 0.312542i
\(225\) −10.0375 + 74.3253i −0.0446113 + 0.330335i
\(226\) −154.856 −0.685202
\(227\) −111.797 111.797i −0.492500 0.492500i 0.416593 0.909093i \(-0.363224\pi\)
−0.909093 + 0.416593i \(0.863224\pi\)
\(228\) −8.79030 + 8.79030i −0.0385540 + 0.0385540i
\(229\) 86.7814i 0.378958i −0.981885 0.189479i \(-0.939320\pi\)
0.981885 0.189479i \(-0.0606799\pi\)
\(230\) −2.27438 + 33.8353i −0.00988862 + 0.147110i
\(231\) 37.2715 0.161348
\(232\) 79.9971 + 79.9971i 0.344815 + 0.344815i
\(233\) −186.872 + 186.872i −0.802027 + 0.802027i −0.983412 0.181385i \(-0.941942\pi\)
0.181385 + 0.983412i \(0.441942\pi\)
\(234\) 16.6446i 0.0711309i
\(235\) 222.113 194.133i 0.945162 0.826099i
\(236\) −177.810 −0.753430
\(237\) 16.2797 + 16.2797i 0.0686906 + 0.0686906i
\(238\) −244.542 + 244.542i −1.02749 + 1.02749i
\(239\) 240.834i 1.00767i 0.863798 + 0.503837i \(0.168079\pi\)
−0.863798 + 0.503837i \(0.831921\pi\)
\(240\) −22.7969 26.0826i −0.0949872 0.108677i
\(241\) −293.854 −1.21931 −0.609655 0.792667i \(-0.708692\pi\)
−0.609655 + 0.792667i \(0.708692\pi\)
\(242\) −117.977 117.977i −0.487507 0.487507i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 10.7688i 0.0441343i
\(245\) −519.656 34.9309i −2.12105 0.142575i
\(246\) 131.781 0.535697
\(247\) 9.95522 + 9.95522i 0.0403045 + 0.0403045i
\(248\) 59.4209 59.4209i 0.239600 0.239600i
\(249\) 251.907i 1.01167i
\(250\) 147.474 97.4749i 0.589897 0.389900i
\(251\) −123.272 −0.491125 −0.245563 0.969381i \(-0.578973\pi\)
−0.245563 + 0.969381i \(0.578973\pi\)
\(252\) −52.5070 52.5070i −0.208361 0.208361i
\(253\) −5.89636 + 5.89636i −0.0233058 + 0.0233058i
\(254\) 268.002i 1.05513i
\(255\) 11.4767 170.736i 0.0450068 0.669552i
\(256\) 16.0000 0.0625000
\(257\) 53.3120 + 53.3120i 0.207440 + 0.207440i 0.803178 0.595739i \(-0.203141\pi\)
−0.595739 + 0.803178i \(0.703141\pi\)
\(258\) −42.5054 + 42.5054i −0.164749 + 0.164749i
\(259\) 633.670i 2.44660i
\(260\) −29.5391 + 25.8180i −0.113612 + 0.0993002i
\(261\) −119.996 −0.459753
\(262\) −110.981 110.981i −0.423590 0.423590i
\(263\) 143.800 143.800i 0.546769 0.546769i −0.378736 0.925505i \(-0.623641\pi\)
0.925505 + 0.378736i \(0.123641\pi\)
\(264\) 8.51806i 0.0322654i
\(265\) 187.934 + 215.020i 0.709186 + 0.811398i
\(266\) 62.8093 0.236125
\(267\) −94.4326 94.4326i −0.353680 0.353680i
\(268\) −22.4715 + 22.4715i −0.0838487 + 0.0838487i
\(269\) 46.8246i 0.174069i 0.996205 + 0.0870345i \(0.0277390\pi\)
−0.996205 + 0.0870345i \(0.972261\pi\)
\(270\) 36.6596 + 2.46423i 0.135776 + 0.00912679i
\(271\) −47.0979 −0.173793 −0.0868965 0.996217i \(-0.527695\pi\)
−0.0868965 + 0.996217i \(0.527695\pi\)
\(272\) 55.8879 + 55.8879i 0.205470 + 0.205470i
\(273\) −59.4654 + 59.4654i −0.217822 + 0.217822i
\(274\) 59.9710i 0.218872i
\(275\) 43.0775 + 5.81756i 0.156645 + 0.0211548i
\(276\) 16.6132 0.0601929
\(277\) −153.177 153.177i −0.552987 0.552987i 0.374315 0.927302i \(-0.377878\pi\)
−0.927302 + 0.374315i \(0.877878\pi\)
\(278\) 153.082 153.082i 0.550653 0.550653i
\(279\) 89.1313i 0.319467i
\(280\) −11.7384 + 174.629i −0.0419230 + 0.623676i
\(281\) −155.385 −0.552973 −0.276486 0.961018i \(-0.589170\pi\)
−0.276486 + 0.961018i \(0.589170\pi\)
\(282\) −102.189 102.189i −0.362373 0.362373i
\(283\) 226.643 226.643i 0.800858 0.800858i −0.182372 0.983230i \(-0.558377\pi\)
0.983230 + 0.182372i \(0.0583775\pi\)
\(284\) 95.2902i 0.335529i
\(285\) −23.4001 + 20.4524i −0.0821058 + 0.0717628i
\(286\) −9.64690 −0.0337304
\(287\) −470.809 470.809i −1.64045 1.64045i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 101.432i 0.350976i
\(290\) 186.129 + 212.955i 0.641825 + 0.734329i
\(291\) −53.0202 −0.182200
\(292\) 131.182 + 131.182i 0.449252 + 0.449252i
\(293\) 199.400 199.400i 0.680545 0.680545i −0.279578 0.960123i \(-0.590194\pi\)
0.960123 + 0.279578i \(0.0901945\pi\)
\(294\) 255.153i 0.867868i
\(295\) −443.523 29.8133i −1.50347 0.101062i
\(296\) 144.820 0.489256
\(297\) 6.38854 + 6.38854i 0.0215102 + 0.0215102i
\(298\) 42.7618 42.7618i 0.143496 0.143496i
\(299\) 18.8149i 0.0629260i
\(300\) −52.4907 68.8820i −0.174969 0.229607i
\(301\) 303.713 1.00901
\(302\) 237.809 + 237.809i 0.787448 + 0.787448i
\(303\) 176.394 176.394i 0.582157 0.582157i
\(304\) 14.3545i 0.0472188i
\(305\) −1.80560 + 26.8613i −0.00591999 + 0.0880699i
\(306\) −83.8318 −0.273960
\(307\) 134.159 + 134.159i 0.437001 + 0.437001i 0.891001 0.454000i \(-0.150004\pi\)
−0.454000 + 0.891001i \(0.650004\pi\)
\(308\) −30.4320 + 30.4320i −0.0988053 + 0.0988053i
\(309\) 138.249i 0.447406i
\(310\) 158.181 138.255i 0.510261 0.445983i
\(311\) 84.5518 0.271871 0.135935 0.990718i \(-0.456596\pi\)
0.135935 + 0.990718i \(0.456596\pi\)
\(312\) 13.5903 + 13.5903i 0.0435586 + 0.0435586i
\(313\) −40.9857 + 40.9857i −0.130945 + 0.130945i −0.769541 0.638597i \(-0.779515\pi\)
0.638597 + 0.769541i \(0.279515\pi\)
\(314\) 249.242i 0.793766i
\(315\) −122.168 139.776i −0.387835 0.443733i
\(316\) −26.5846 −0.0841284
\(317\) 87.6597 + 87.6597i 0.276529 + 0.276529i 0.831722 0.555193i \(-0.187356\pi\)
−0.555193 + 0.831722i \(0.687356\pi\)
\(318\) 98.9261 98.9261i 0.311088 0.311088i
\(319\) 69.5471i 0.218016i
\(320\) 39.9099 + 2.68272i 0.124719 + 0.00838349i
\(321\) −343.628 −1.07049
\(322\) −59.3533 59.3533i −0.184327 0.184327i
\(323\) 50.1402 50.1402i 0.155233 0.155233i
\(324\) 18.0000i 0.0555556i
\(325\) −78.0104 + 59.4470i −0.240032 + 0.182914i
\(326\) −204.181 −0.626322
\(327\) 117.049 + 117.049i 0.357947 + 0.357947i
\(328\) −107.599 + 107.599i −0.328046 + 0.328046i
\(329\) 730.172i 2.21937i
\(330\) 1.42822 21.2472i 0.00432794 0.0643854i
\(331\) 531.734 1.60645 0.803224 0.595677i \(-0.203116\pi\)
0.803224 + 0.595677i \(0.203116\pi\)
\(332\) −205.681 205.681i −0.619521 0.619521i
\(333\) −108.615 + 108.615i −0.326170 + 0.326170i
\(334\) 271.140i 0.811797i
\(335\) −59.8199 + 52.2844i −0.178567 + 0.156073i
\(336\) 85.7436 0.255189
\(337\) −80.0946 80.0946i −0.237670 0.237670i 0.578215 0.815884i \(-0.303750\pi\)
−0.815884 + 0.578215i \(0.803750\pi\)
\(338\) −153.609 + 153.609i −0.454464 + 0.454464i
\(339\) 189.659i 0.559465i
\(340\) 130.034 + 148.776i 0.382454 + 0.437576i
\(341\) 51.6587 0.151492
\(342\) 10.7659 + 10.7659i 0.0314792 + 0.0314792i
\(343\) 482.765 482.765i 1.40748 1.40748i
\(344\) 69.4110i 0.201776i
\(345\) 41.4396 + 2.78554i 0.120115 + 0.00807403i
\(346\) 322.327 0.931582
\(347\) −434.081 434.081i −1.25095 1.25095i −0.955293 0.295662i \(-0.904460\pi\)
−0.295662 0.955293i \(-0.595540\pi\)
\(348\) 97.9760 97.9760i 0.281540 0.281540i
\(349\) 302.420i 0.866534i −0.901266 0.433267i \(-0.857361\pi\)
0.901266 0.433267i \(-0.142639\pi\)
\(350\) −58.5601 + 433.622i −0.167315 + 1.23892i
\(351\) −20.3854 −0.0580781
\(352\) 6.95496 + 6.95496i 0.0197584 + 0.0197584i
\(353\) 361.731 361.731i 1.02473 1.02473i 0.0250482 0.999686i \(-0.492026\pi\)
0.999686 0.0250482i \(-0.00797392\pi\)
\(354\) 217.771i 0.615173i
\(355\) 15.9773 237.689i 0.0450064 0.669547i
\(356\) 154.208 0.433168
\(357\) 299.502 + 299.502i 0.838940 + 0.838940i
\(358\) 138.437 138.437i 0.386697 0.386697i
\(359\) 234.342i 0.652763i −0.945238 0.326382i \(-0.894171\pi\)
0.945238 0.326382i \(-0.105829\pi\)
\(360\) −31.9445 + 27.9204i −0.0887347 + 0.0775567i
\(361\) 348.122 0.964326
\(362\) −235.431 235.431i −0.650362 0.650362i
\(363\) −144.491 + 144.491i −0.398048 + 0.398048i
\(364\) 97.1066i 0.266776i
\(365\) 305.221 + 349.211i 0.836221 + 0.956743i
\(366\) 13.1890 0.0360355
\(367\) −38.3418 38.3418i −0.104473 0.104473i 0.652938 0.757411i \(-0.273536\pi\)
−0.757411 + 0.652938i \(0.773536\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 161.399i 0.437395i
\(370\) 361.234 + 24.2819i 0.976308 + 0.0656267i
\(371\) −706.856 −1.90527
\(372\) −72.7754 72.7754i −0.195633 0.195633i
\(373\) 437.210 437.210i 1.17215 1.17215i 0.190449 0.981697i \(-0.439006\pi\)
0.981697 0.190449i \(-0.0609944\pi\)
\(374\) 48.5873i 0.129913i
\(375\) −119.382 180.618i −0.318352 0.481649i
\(376\) 166.874 0.443814
\(377\) −110.960 110.960i −0.294324 0.294324i
\(378\) −64.3077 + 64.3077i −0.170126 + 0.170126i
\(379\) 208.519i 0.550183i −0.961418 0.275091i \(-0.911292\pi\)
0.961418 0.275091i \(-0.0887081\pi\)
\(380\) 2.40682 35.8055i 0.00633373 0.0942249i
\(381\) 328.234 0.861507
\(382\) 179.526 + 179.526i 0.469964 + 0.469964i
\(383\) 197.844 197.844i 0.516563 0.516563i −0.399967 0.916530i \(-0.630978\pi\)
0.916530 + 0.399967i \(0.130978\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −81.0113 + 70.8062i −0.210419 + 0.183912i
\(386\) 242.953 0.629413
\(387\) 52.0582 + 52.0582i 0.134517 + 0.134517i
\(388\) 43.2908 43.2908i 0.111574 0.111574i
\(389\) 334.345i 0.859498i −0.902948 0.429749i \(-0.858602\pi\)
0.902948 0.429749i \(-0.141398\pi\)
\(390\) 31.6205 + 36.1779i 0.0810783 + 0.0927638i
\(391\) −94.7625 −0.242359
\(392\) −208.332 208.332i −0.531458 0.531458i
\(393\) −135.923 + 135.923i −0.345860 + 0.345860i
\(394\) 119.082i 0.302239i
\(395\) −66.3118 4.45743i −0.167878 0.0112846i
\(396\) −10.4324 −0.0263446
\(397\) −314.687 314.687i −0.792662 0.792662i 0.189264 0.981926i \(-0.439390\pi\)
−0.981926 + 0.189264i \(0.939390\pi\)
\(398\) −276.890 + 276.890i −0.695705 + 0.695705i
\(399\) 76.9254i 0.192796i
\(400\) 99.1004 + 13.3834i 0.247751 + 0.0334584i
\(401\) 57.4442 0.143252 0.0716262 0.997432i \(-0.477181\pi\)
0.0716262 + 0.997432i \(0.477181\pi\)
\(402\) 27.5218 + 27.5218i 0.0684622 + 0.0684622i
\(403\) −82.4198 + 82.4198i −0.204516 + 0.204516i
\(404\) 288.050i 0.712994i
\(405\) 3.01806 44.8987i 0.00745199 0.110861i
\(406\) −700.068 −1.72430
\(407\) 62.9510 + 62.9510i 0.154671 + 0.154671i
\(408\) 68.4484 68.4484i 0.167766 0.167766i
\(409\) 576.404i 1.40930i 0.709554 + 0.704651i \(0.248896\pi\)
−0.709554 + 0.704651i \(0.751104\pi\)
\(410\) −286.433 + 250.351i −0.698618 + 0.610612i
\(411\) −73.4492 −0.178709
\(412\) −112.879 112.879i −0.273979 0.273979i
\(413\) 778.020 778.020i 1.88383 1.88383i
\(414\) 20.3470i 0.0491473i
\(415\) −478.558 547.531i −1.15315 1.31935i
\(416\) −22.1928 −0.0533482
\(417\) −187.486 187.486i −0.449606 0.449606i
\(418\) 6.23969 6.23969i 0.0149275 0.0149275i
\(419\) 647.383i 1.54507i −0.634974 0.772533i \(-0.718989\pi\)
0.634974 0.772533i \(-0.281011\pi\)
\(420\) 213.876 + 14.3766i 0.509229 + 0.0342300i
\(421\) 13.3066 0.0316071 0.0158035 0.999875i \(-0.494969\pi\)
0.0158035 + 0.999875i \(0.494969\pi\)
\(422\) −144.999 144.999i −0.343598 0.343598i
\(423\) −125.156 + 125.156i −0.295876 + 0.295876i
\(424\) 161.546i 0.381004i
\(425\) 299.409 + 392.905i 0.704492 + 0.924482i
\(426\) −116.706 −0.273958
\(427\) −47.1197 47.1197i −0.110350 0.110350i
\(428\) 280.571 280.571i 0.655540 0.655540i
\(429\) 11.8150i 0.0275408i
\(430\) 11.6381 173.137i 0.0270654 0.402643i
\(431\) 21.3553 0.0495483 0.0247741 0.999693i \(-0.492113\pi\)
0.0247741 + 0.999693i \(0.492113\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) 503.307 503.307i 1.16237 1.16237i 0.178416 0.983955i \(-0.442903\pi\)
0.983955 0.178416i \(-0.0570973\pi\)
\(434\) 520.002i 1.19816i
\(435\) 260.816 227.961i 0.599577 0.524048i
\(436\) −191.140 −0.438394
\(437\) 12.1696 + 12.1696i 0.0278481 + 0.0278481i
\(438\) 160.664 160.664i 0.366813 0.366813i
\(439\) 260.712i 0.593878i −0.954896 0.296939i \(-0.904034\pi\)
0.954896 0.296939i \(-0.0959658\pi\)
\(440\) 16.1821 + 18.5144i 0.0367776 + 0.0420782i
\(441\) 312.497 0.708611
\(442\) −77.5194 77.5194i −0.175383 0.175383i
\(443\) −554.518 + 554.518i −1.25173 + 1.25173i −0.296790 + 0.954943i \(0.595916\pi\)
−0.954943 + 0.296790i \(0.904084\pi\)
\(444\) 177.367i 0.399476i
\(445\) 384.651 + 25.8560i 0.864385 + 0.0581033i
\(446\) 169.748 0.380601
\(447\) −52.3723 52.3723i −0.117164 0.117164i
\(448\) −70.0093 + 70.0093i −0.156271 + 0.156271i
\(449\) 23.2629i 0.0518105i 0.999664 + 0.0259053i \(0.00824682\pi\)
−0.999664 + 0.0259053i \(0.991753\pi\)
\(450\) −84.3628 + 64.2877i −0.187473 + 0.142862i
\(451\) −93.5435 −0.207414
\(452\) −154.856 154.856i −0.342601 0.342601i
\(453\) 291.256 291.256i 0.642948 0.642948i
\(454\) 223.595i 0.492500i
\(455\) 16.2818 242.220i 0.0357843 0.532351i
\(456\) −17.5806 −0.0385540
\(457\) −164.757 164.757i −0.360519 0.360519i 0.503485 0.864004i \(-0.332051\pi\)
−0.864004 + 0.503485i \(0.832051\pi\)
\(458\) 86.7814 86.7814i 0.189479 0.189479i
\(459\) 102.673i 0.223688i
\(460\) −36.1097 + 31.5609i −0.0784993 + 0.0686107i
\(461\) −751.058 −1.62919 −0.814596 0.580028i \(-0.803042\pi\)
−0.814596 + 0.580028i \(0.803042\pi\)
\(462\) 37.2715 + 37.2715i 0.0806742 + 0.0806742i
\(463\) 412.426 412.426i 0.890770 0.890770i −0.103826 0.994595i \(-0.533108\pi\)
0.994595 + 0.103826i \(0.0331085\pi\)
\(464\) 159.994i 0.344815i
\(465\) −169.327 193.731i −0.364143 0.416626i
\(466\) −373.745 −0.802027
\(467\) −281.477 281.477i −0.602734 0.602734i 0.338303 0.941037i \(-0.390147\pi\)
−0.941037 + 0.338303i \(0.890147\pi\)
\(468\) 16.6446 16.6446i 0.0355654 0.0355654i
\(469\) 196.651i 0.419300i
\(470\) 416.246 + 27.9798i 0.885630 + 0.0595314i
\(471\) 305.258 0.648107
\(472\) −177.810 177.810i −0.376715 0.376715i
\(473\) 30.1719 30.1719i 0.0637884 0.0637884i
\(474\) 32.5593i 0.0686906i
\(475\) 12.0070 88.9086i 0.0252779 0.187176i
\(476\) −489.084 −1.02749
\(477\) −121.159 121.159i −0.254003 0.254003i
\(478\) −240.834 + 240.834i −0.503837 + 0.503837i
\(479\) 779.801i 1.62798i 0.580882 + 0.813988i \(0.302708\pi\)
−0.580882 + 0.813988i \(0.697292\pi\)
\(480\) 3.28564 48.8795i 0.00684509 0.101832i
\(481\) −200.872 −0.417614
\(482\) −293.854 293.854i −0.609655 0.609655i
\(483\) −72.6926 + 72.6926i −0.150502 + 0.150502i
\(484\) 235.954i 0.487507i
\(485\) 115.242 100.725i 0.237612 0.207680i
\(486\) −22.0454 −0.0453609
\(487\) −74.5332 74.5332i −0.153046 0.153046i 0.626431 0.779477i \(-0.284515\pi\)
−0.779477 + 0.626431i \(0.784515\pi\)
\(488\) −10.7688 + 10.7688i −0.0220672 + 0.0220672i
\(489\) 250.070i 0.511390i
\(490\) −484.726 554.587i −0.989236 1.13181i
\(491\) 542.009 1.10389 0.551944 0.833881i \(-0.313886\pi\)
0.551944 + 0.833881i \(0.313886\pi\)
\(492\) 131.781 + 131.781i 0.267849 + 0.267849i
\(493\) −558.858 + 558.858i −1.13359 + 1.13359i
\(494\) 19.9104i 0.0403045i
\(495\) −26.0224 1.74921i −0.0525705 0.00353375i
\(496\) 118.842 0.239600
\(497\) 416.950 + 416.950i 0.838934 + 0.838934i
\(498\) −251.907 + 251.907i −0.505837 + 0.505837i
\(499\) 418.049i 0.837773i 0.908039 + 0.418887i \(0.137580\pi\)
−0.908039 + 0.418887i \(0.862420\pi\)
\(500\) 244.949 + 49.9993i 0.489898 + 0.0999985i
\(501\) 332.078 0.662829
\(502\) −123.272 123.272i −0.245563 0.245563i
\(503\) 664.763 664.763i 1.32160 1.32160i 0.409114 0.912483i \(-0.365838\pi\)
0.912483 0.409114i \(-0.134162\pi\)
\(504\) 105.014i 0.208361i
\(505\) −48.2972 + 718.503i −0.0956380 + 1.42278i
\(506\) −11.7927 −0.0233058
\(507\) 188.131 + 188.131i 0.371068 + 0.371068i
\(508\) −268.002 + 268.002i −0.527563 + 0.527563i
\(509\) 157.871i 0.310160i 0.987902 + 0.155080i \(0.0495635\pi\)
−0.987902 + 0.155080i \(0.950436\pi\)
\(510\) 182.212 159.259i 0.357279 0.312273i
\(511\) −1147.99 −2.24656
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 13.1855 13.1855i 0.0257026 0.0257026i
\(514\) 106.624i 0.207440i
\(515\) −262.637 300.490i −0.509974 0.583475i
\(516\) −85.0107 −0.164749
\(517\) 72.5377 + 72.5377i 0.140305 + 0.140305i
\(518\) −633.670 + 633.670i −1.22330 + 1.22330i
\(519\) 394.769i 0.760634i
\(520\) −55.3572 3.72107i −0.106456 0.00715590i
\(521\) 27.4189 0.0526275 0.0263137 0.999654i \(-0.491623\pi\)
0.0263137 + 0.999654i \(0.491623\pi\)
\(522\) −119.996 119.996i −0.229877 0.229877i
\(523\) −698.589 + 698.589i −1.33573 + 1.33573i −0.435587 + 0.900147i \(0.643459\pi\)
−0.900147 + 0.435587i \(0.856541\pi\)
\(524\) 221.961i 0.423590i
\(525\) 531.076 + 71.7212i 1.01157 + 0.136612i
\(526\) 287.600 0.546769
\(527\) 415.113 + 415.113i 0.787691 + 0.787691i
\(528\) 8.51806 8.51806i 0.0161327 0.0161327i
\(529\) 23.0000i 0.0434783i
\(530\) −27.0863 + 402.955i −0.0511062 + 0.760292i
\(531\) 266.714 0.502287
\(532\) 62.8093 + 62.8093i 0.118063 + 0.118063i
\(533\) 149.246 149.246i 0.280010 0.280010i
\(534\) 188.865i 0.353680i
\(535\) 746.892 652.805i 1.39606 1.22020i
\(536\) −44.9429 −0.0838487
\(537\) −169.551 169.551i −0.315737 0.315737i
\(538\) −46.8246 + 46.8246i −0.0870345 + 0.0870345i
\(539\) 181.117i 0.336025i
\(540\) 34.1954 + 39.1238i 0.0633248 + 0.0724516i
\(541\) −120.670 −0.223050 −0.111525 0.993762i \(-0.535573\pi\)
−0.111525 + 0.993762i \(0.535573\pi\)
\(542\) −47.0979 47.0979i −0.0868965 0.0868965i
\(543\) −288.343 + 288.343i −0.531018 + 0.531018i
\(544\) 111.776i 0.205470i
\(545\) −476.774 32.0484i −0.874814 0.0588043i
\(546\) −118.931 −0.217822
\(547\) 196.495 + 196.495i 0.359224 + 0.359224i 0.863527 0.504303i \(-0.168251\pi\)
−0.504303 + 0.863527i \(0.668251\pi\)
\(548\) 59.9710 59.9710i 0.109436 0.109436i
\(549\) 16.1532i 0.0294229i
\(550\) 37.2599 + 48.8950i 0.0677453 + 0.0889000i
\(551\) 143.540 0.260508
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 116.323 116.323i 0.210349 0.210349i
\(554\) 306.355i 0.552987i
\(555\) 29.7391 442.419i 0.0535840 0.797152i
\(556\) 306.163 0.550653
\(557\) 52.0135 + 52.0135i 0.0933815 + 0.0933815i 0.752254 0.658873i \(-0.228966\pi\)
−0.658873 + 0.752254i \(0.728966\pi\)
\(558\) −89.1313 + 89.1313i −0.159734 + 0.159734i
\(559\) 96.2766i 0.172230i
\(560\) −186.368 + 162.891i −0.332799 + 0.290876i
\(561\) 59.5070 0.106073
\(562\) −155.385 155.385i −0.276486 0.276486i
\(563\) 89.0061 89.0061i 0.158093 0.158093i −0.623628 0.781721i \(-0.714342\pi\)
0.781721 + 0.623628i \(0.214342\pi\)
\(564\) 204.378i 0.362373i
\(565\) −360.303 412.232i −0.637704 0.729614i
\(566\) 453.285 0.800858
\(567\) 78.7605 + 78.7605i 0.138907 + 0.138907i
\(568\) 95.2902 95.2902i 0.167764 0.167764i
\(569\) 443.631i 0.779667i −0.920885 0.389834i \(-0.872533\pi\)
0.920885 0.389834i \(-0.127467\pi\)
\(570\) −43.8526 2.94774i −0.0769343 0.00517147i
\(571\) −586.293 −1.02678 −0.513391 0.858155i \(-0.671611\pi\)
−0.513391 + 0.858155i \(0.671611\pi\)
\(572\) −9.64690 9.64690i −0.0168652 0.0168652i
\(573\) 219.874 219.874i 0.383724 0.383724i
\(574\) 941.618i 1.64045i
\(575\) −95.3627 + 72.6701i −0.165848 + 0.126383i
\(576\) −24.0000 −0.0416667
\(577\) 214.728 + 214.728i 0.372146 + 0.372146i 0.868258 0.496112i \(-0.165240\pi\)
−0.496112 + 0.868258i \(0.665240\pi\)
\(578\) −101.432 + 101.432i −0.175488 + 0.175488i
\(579\) 297.556i 0.513913i
\(580\) −26.8262 + 399.085i −0.0462520 + 0.688077i
\(581\) 1799.95 3.09802
\(582\) −53.0202 53.0202i −0.0911000 0.0911000i
\(583\) −70.2215 + 70.2215i −0.120449 + 0.120449i
\(584\) 262.363i 0.449252i
\(585\) 44.3087 38.7271i 0.0757413 0.0662001i
\(586\) 398.800 0.680545
\(587\) −24.5722 24.5722i −0.0418606 0.0418606i 0.685867 0.727727i \(-0.259423\pi\)
−0.727727 + 0.685867i \(0.759423\pi\)
\(588\) −255.153 + 255.153i −0.433934 + 0.433934i
\(589\) 106.620i 0.181018i
\(590\) −413.710 473.336i −0.701203 0.802265i
\(591\) −145.845 −0.246777
\(592\) 144.820 + 144.820i 0.244628 + 0.244628i
\(593\) 741.247 741.247i 1.25000 1.25000i 0.294274 0.955721i \(-0.404922\pi\)
0.955721 0.294274i \(-0.0950779\pi\)
\(594\) 12.7771i 0.0215102i
\(595\) −1219.96 82.0047i −2.05035 0.137823i
\(596\) 85.5237 0.143496
\(597\) 339.120 + 339.120i 0.568041 + 0.568041i
\(598\) 18.8149 18.8149i 0.0314630 0.0314630i
\(599\) 611.907i 1.02155i −0.859715 0.510774i \(-0.829359\pi\)
0.859715 0.510774i \(-0.170641\pi\)
\(600\) 16.3912 121.373i 0.0273187 0.202288i
\(601\) −586.294 −0.975530 −0.487765 0.872975i \(-0.662188\pi\)
−0.487765 + 0.872975i \(0.662188\pi\)
\(602\) 303.713 + 303.713i 0.504507 + 0.504507i
\(603\) 33.7072 33.7072i 0.0558992 0.0558992i
\(604\) 475.618i 0.787448i
\(605\) 39.5623 588.556i 0.0653922 0.972819i
\(606\) 352.787 0.582157
\(607\) −709.112 709.112i −1.16822 1.16822i −0.982626 0.185599i \(-0.940577\pi\)
−0.185599 0.982626i \(-0.559423\pi\)
\(608\) 14.3545 14.3545i 0.0236094 0.0236094i
\(609\) 857.404i 1.40789i
\(610\) −28.6669 + 25.0557i −0.0469949 + 0.0410749i
\(611\) −231.463 −0.378827
\(612\) −83.8318 83.8318i −0.136980 0.136980i
\(613\) 43.1064 43.1064i 0.0703205 0.0703205i −0.671072 0.741392i \(-0.734166\pi\)
0.741392 + 0.671072i \(0.234166\pi\)
\(614\) 268.319i 0.437001i
\(615\) 306.616 + 350.808i 0.498563 + 0.570419i
\(616\) −60.8640 −0.0988053
\(617\) −15.4469 15.4469i −0.0250354 0.0250354i 0.694478 0.719514i \(-0.255635\pi\)
−0.719514 + 0.694478i \(0.755635\pi\)
\(618\) −138.249 + 138.249i −0.223703 + 0.223703i
\(619\) 174.136i 0.281319i −0.990058 0.140659i \(-0.955078\pi\)
0.990058 0.140659i \(-0.0449222\pi\)
\(620\) 296.435 + 19.9262i 0.478122 + 0.0321390i
\(621\) −24.9199 −0.0401286
\(622\) 84.5518 + 84.5518i 0.135935 + 0.135935i
\(623\) −674.749 + 674.749i −1.08306 + 1.08306i
\(624\) 27.1806i 0.0435586i
\(625\) 602.611 + 165.787i 0.964177 + 0.265260i
\(626\) −81.9714 −0.130945
\(627\) −7.64203 7.64203i −0.0121882 0.0121882i
\(628\) −249.242 + 249.242i −0.396883 + 0.396883i
\(629\) 1011.71i 1.60844i
\(630\) 17.6077 261.944i 0.0279487 0.415784i
\(631\) −444.988 −0.705210 −0.352605 0.935772i \(-0.614704\pi\)
−0.352605 + 0.935772i \(0.614704\pi\)
\(632\) −26.5846 26.5846i −0.0420642 0.0420642i
\(633\) −177.586 + 177.586i −0.280547 + 0.280547i
\(634\) 175.319i 0.276529i
\(635\) −713.433 + 623.561i −1.12352 + 0.981986i
\(636\) 197.852 0.311088
\(637\) 288.967 + 288.967i 0.453637 + 0.453637i
\(638\) −69.5471 + 69.5471i −0.109008 + 0.109008i
\(639\) 142.935i 0.223686i
\(640\) 37.2272 + 42.5927i 0.0581675 + 0.0665510i
\(641\) −711.126 −1.10940 −0.554701 0.832050i \(-0.687167\pi\)
−0.554701 + 0.832050i \(0.687167\pi\)
\(642\) −343.628 343.628i −0.535246 0.535246i
\(643\) −2.97562 + 2.97562i −0.00462772 + 0.00462772i −0.709417 0.704789i \(-0.751042\pi\)
0.704789 + 0.709417i \(0.251042\pi\)
\(644\) 118.707i 0.184327i
\(645\) −212.048 14.2537i −0.328757 0.0220988i
\(646\) 100.280 0.155233
\(647\) −667.250 667.250i −1.03130 1.03130i −0.999494 0.0318041i \(-0.989875\pi\)
−0.0318041 0.999494i \(-0.510125\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 154.582i 0.238185i
\(650\) −137.457 18.5634i −0.211473 0.0285591i
\(651\) 636.870 0.978294
\(652\) −204.181 204.181i −0.313161 0.313161i
\(653\) 551.195 551.195i 0.844097 0.844097i −0.145292 0.989389i \(-0.546412\pi\)
0.989389 + 0.145292i \(0.0464121\pi\)
\(654\) 234.097i 0.357947i
\(655\) 37.2162 553.654i 0.0568186 0.845273i
\(656\) −215.198 −0.328046
\(657\) −196.773 196.773i −0.299502 0.299502i
\(658\) −730.172 + 730.172i −1.10968 + 1.10968i
\(659\) 728.798i 1.10591i −0.833209 0.552957i \(-0.813499\pi\)
0.833209 0.552957i \(-0.186501\pi\)
\(660\) 22.6754 19.8190i 0.0343567 0.0300287i
\(661\) −1033.34 −1.56330 −0.781652 0.623715i \(-0.785623\pi\)
−0.781652 + 0.623715i \(0.785623\pi\)
\(662\) 531.734 + 531.734i 0.803224 + 0.803224i
\(663\) −94.9415 + 94.9415i −0.143200 + 0.143200i
\(664\) 411.362i 0.619521i
\(665\) 146.139 + 167.201i 0.219757 + 0.251430i
\(666\) −217.229 −0.326170
\(667\) −135.642 135.642i −0.203361 0.203361i
\(668\) −271.140 + 271.140i −0.405898 + 0.405898i
\(669\) 207.898i 0.310759i
\(670\) −112.104 7.53557i −0.167320 0.0112471i
\(671\) −9.36205 −0.0139524
\(672\) 85.7436 + 85.7436i 0.127595 + 0.127595i
\(673\) 249.793 249.793i 0.371164 0.371164i −0.496737 0.867901i \(-0.665469\pi\)
0.867901 + 0.496737i \(0.165469\pi\)
\(674\) 160.189i 0.237670i
\(675\) 78.7361 + 103.323i 0.116646 + 0.153071i
\(676\) −307.217 −0.454464
\(677\) −395.782 395.782i −0.584611 0.584611i 0.351556 0.936167i \(-0.385653\pi\)
−0.936167 + 0.351556i \(0.885653\pi\)
\(678\) −189.659 + 189.659i −0.279732 + 0.279732i
\(679\) 378.845i 0.557946i
\(680\) −18.7414 + 278.810i −0.0275609 + 0.410015i
\(681\) −273.847 −0.402124
\(682\) 51.6587 + 51.6587i 0.0757460 + 0.0757460i
\(683\) 623.632 623.632i 0.913078 0.913078i −0.0834349 0.996513i \(-0.526589\pi\)
0.996513 + 0.0834349i \(0.0265891\pi\)
\(684\) 21.5318i 0.0314792i
\(685\) 159.645 139.535i 0.233059 0.203700i
\(686\) 965.531 1.40748
\(687\) −106.285 106.285i −0.154709 0.154709i
\(688\) 69.4110 69.4110i 0.100888 0.100888i
\(689\) 224.072i 0.325214i
\(690\) 38.6541 + 44.2251i 0.0560204 + 0.0640944i
\(691\) −1294.08 −1.87276 −0.936382 0.350982i \(-0.885848\pi\)
−0.936382 + 0.350982i \(0.885848\pi\)
\(692\) 322.327 + 322.327i 0.465791 + 0.465791i
\(693\) 45.6480 45.6480i 0.0658702 0.0658702i
\(694\) 868.163i 1.25095i
\(695\) 763.685 + 51.3343i 1.09883 + 0.0738623i
\(696\) 195.952 0.281540
\(697\) −751.686 751.686i −1.07846 1.07846i
\(698\) 302.420 302.420i 0.433267 0.433267i
\(699\) 457.742i 0.654853i
\(700\) −492.182 + 375.062i −0.703117 + 0.535803i
\(701\) 389.671 0.555879 0.277940 0.960599i \(-0.410348\pi\)
0.277940 + 0.960599i \(0.410348\pi\)
\(702\) −20.3854 20.3854i −0.0290391 0.0290391i
\(703\) 129.926 129.926i 0.184816 0.184816i
\(704\) 13.9099i 0.0197584i
\(705\) 34.2681 509.795i 0.0486072 0.723114i
\(706\) 723.463 1.02473
\(707\) −1260.39 1260.39i −1.78272 1.78272i
\(708\) −217.771 + 217.771i −0.307587 + 0.307587i
\(709\) 89.4778i 0.126203i −0.998007 0.0631014i \(-0.979901\pi\)
0.998007 0.0631014i \(-0.0200992\pi\)
\(710\) 253.666 221.712i 0.357276 0.312270i
\(711\) 39.8769 0.0560856
\(712\) 154.208 + 154.208i 0.216584 + 0.216584i
\(713\) −100.753 + 100.753i −0.141309 + 0.141309i
\(714\) 599.003i 0.838940i
\(715\) −22.4454 25.6804i −0.0313922 0.0359167i
\(716\) 276.875 0.386697
\(717\) 294.961 + 294.961i 0.411382 + 0.411382i
\(718\) 234.342 234.342i 0.326382 0.326382i
\(719\) 1170.94i 1.62857i −0.580463 0.814287i \(-0.697128\pi\)
0.580463 0.814287i \(-0.302872\pi\)
\(720\) −59.8649 4.02407i −0.0831457 0.00558899i
\(721\) 987.827 1.37008
\(722\) 348.122 + 348.122i 0.482163 + 0.482163i
\(723\) −359.896 + 359.896i −0.497781 + 0.497781i
\(724\) 470.862i 0.650362i
\(725\) −133.829 + 990.967i −0.184592 + 1.36685i
\(726\) −288.983 −0.398048
\(727\) 629.817 + 629.817i 0.866323 + 0.866323i 0.992063 0.125740i \(-0.0401306\pi\)
−0.125740 + 0.992063i \(0.540131\pi\)
\(728\) 97.1066 97.1066i 0.133388 0.133388i
\(729\) 27.0000i 0.0370370i
\(730\) −43.9904 + 654.432i −0.0602608 + 0.896482i
\(731\) 484.904 0.663343
\(732\) 13.1890 + 13.1890i 0.0180178 + 0.0180178i
\(733\) −689.739 + 689.739i −0.940980 + 0.940980i −0.998353 0.0573724i \(-0.981728\pi\)
0.0573724 + 0.998353i \(0.481728\pi\)
\(734\) 76.6835i 0.104473i
\(735\) −679.228 + 593.665i −0.924120 + 0.807708i
\(736\) −27.1293 −0.0368605
\(737\) −19.5360 19.5360i −0.0265075 0.0265075i
\(738\) 161.399 161.399i 0.218697 0.218697i
\(739\) 474.009i 0.641420i 0.947177 + 0.320710i \(0.103922\pi\)
−0.947177 + 0.320710i \(0.896078\pi\)
\(740\) 336.952 + 385.516i 0.455341 + 0.520967i
\(741\) 24.3852 0.0329085
\(742\) −706.856 706.856i −0.952636 0.952636i
\(743\) −932.902 + 932.902i −1.25559 + 1.25559i −0.302410 + 0.953178i \(0.597791\pi\)
−0.953178 + 0.302410i \(0.902209\pi\)
\(744\) 145.551i 0.195633i
\(745\) 213.328 + 14.3397i 0.286346 + 0.0192480i
\(746\) 874.421 1.17215
\(747\) 308.521 + 308.521i 0.413014 + 0.413014i
\(748\) −48.5873 + 48.5873i −0.0649563 + 0.0649563i
\(749\) 2455.33i 3.27814i
\(750\) 61.2363 300.000i 0.0816484 0.400000i
\(751\) −847.215 −1.12812 −0.564058 0.825735i \(-0.690761\pi\)
−0.564058 + 0.825735i \(0.690761\pi\)
\(752\) 166.874 + 166.874i 0.221907 + 0.221907i
\(753\) −150.977 + 150.977i −0.200501 + 0.200501i
\(754\) 221.920i 0.294324i
\(755\) −79.7468 + 1186.37i −0.105625 + 1.57135i
\(756\) −128.615 −0.170126
\(757\) 440.710 + 440.710i 0.582180 + 0.582180i 0.935502 0.353322i \(-0.114948\pi\)
−0.353322 + 0.935502i \(0.614948\pi\)
\(758\) 208.519 208.519i 0.275091 0.275091i
\(759\) 14.4431i 0.0190291i
\(760\) 38.2123 33.3986i 0.0502793 0.0439456i
\(761\) 822.127 1.08032 0.540162 0.841561i \(-0.318363\pi\)
0.540162 + 0.841561i \(0.318363\pi\)
\(762\) 328.234 + 328.234i 0.430754 + 0.430754i
\(763\) 836.348 836.348i 1.09613 1.09613i
\(764\) 359.052i 0.469964i
\(765\) −195.052 223.164i −0.254969 0.291717i
\(766\) 395.687 0.516563
\(767\) 246.631 + 246.631i 0.321553 + 0.321553i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 432.890i 0.562925i 0.959572 + 0.281463i \(0.0908196\pi\)
−0.959572 + 0.281463i \(0.909180\pi\)
\(770\) −151.818 10.2051i −0.197166 0.0132533i
\(771\) 130.587 0.169374
\(772\) 242.953 + 242.953i 0.314706 + 0.314706i
\(773\) 497.327 497.327i 0.643372 0.643372i −0.308011 0.951383i \(-0.599663\pi\)
0.951383 + 0.308011i \(0.0996633\pi\)
\(774\) 104.116i 0.134517i
\(775\) 736.079 + 99.4065i 0.949779 + 0.128266i
\(776\) 86.5816 0.111574
\(777\) 776.085 + 776.085i 0.998822 + 0.998822i
\(778\) 334.345 334.345i 0.429749 0.429749i
\(779\)