Properties

Label 29.3.c.a.17.2
Level 29
Weight 3
Character 29.17
Analytic conductor 0.790
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 29.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.790192766645\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 18 x^{6} + 91 x^{4} + 126 x^{2} + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 17.2
Root \(3.22189i\) of defining polynomial
Character \(\chi\) \(=\) 29.17
Dual form 29.3.c.a.12.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.07935 + 1.07935i) q^{2} +(-2.14254 + 2.14254i) q^{3} +1.67001i q^{4} +0.488689i q^{5} -4.62511i q^{6} +8.09117 q^{7} +(-6.11992 - 6.11992i) q^{8} -0.180982i q^{9} +O(q^{10})\) \(q+(-1.07935 + 1.07935i) q^{2} +(-2.14254 + 2.14254i) q^{3} +1.67001i q^{4} +0.488689i q^{5} -4.62511i q^{6} +8.09117 q^{7} +(-6.11992 - 6.11992i) q^{8} -0.180982i q^{9} +(-0.527467 - 0.527467i) q^{10} +(11.3195 - 11.3195i) q^{11} +(-3.57807 - 3.57807i) q^{12} +10.0463i q^{13} +(-8.73320 + 8.73320i) q^{14} +(-1.04704 - 1.04704i) q^{15} +6.53103 q^{16} +(-9.69799 + 9.69799i) q^{17} +(0.195342 + 0.195342i) q^{18} +(8.58453 - 8.58453i) q^{19} -0.816116 q^{20} +(-17.3357 + 17.3357i) q^{21} +24.4355i q^{22} -14.4215 q^{23} +26.2244 q^{24} +24.7612 q^{25} +(-10.8434 - 10.8434i) q^{26} +(-18.8951 - 18.8951i) q^{27} +13.5123i q^{28} +(-11.8706 - 26.4592i) q^{29} +2.26024 q^{30} +(31.2221 - 31.2221i) q^{31} +(17.4304 - 17.4304i) q^{32} +48.5052i q^{33} -20.9350i q^{34} +3.95407i q^{35} +0.302241 q^{36} +(-31.2631 - 31.2631i) q^{37} +18.5314i q^{38} +(-21.5246 - 21.5246i) q^{39} +(2.99074 - 2.99074i) q^{40} +(19.6337 + 19.6337i) q^{41} -37.4225i q^{42} +(-50.2394 + 50.2394i) q^{43} +(18.9037 + 18.9037i) q^{44} +0.0884438 q^{45} +(15.5658 - 15.5658i) q^{46} +(42.2268 + 42.2268i) q^{47} +(-13.9930 + 13.9930i) q^{48} +16.4671 q^{49} +(-26.7260 + 26.7260i) q^{50} -41.5567i q^{51} -16.7774 q^{52} +16.5613 q^{53} +40.7889 q^{54} +(5.53173 + 5.53173i) q^{55} +(-49.5173 - 49.5173i) q^{56} +36.7855i q^{57} +(41.3713 + 15.7461i) q^{58} -14.5041 q^{59} +(1.74856 - 1.74856i) q^{60} +(-45.3849 + 45.3849i) q^{61} +67.3992i q^{62} -1.46435i q^{63} +63.7512i q^{64} -4.90950 q^{65} +(-52.3540 - 52.3540i) q^{66} -133.589i q^{67} +(-16.1957 - 16.1957i) q^{68} +(30.8987 - 30.8987i) q^{69} +(-4.26782 - 4.26782i) q^{70} -33.9204i q^{71} +(-1.10759 + 1.10759i) q^{72} +(-22.1752 - 22.1752i) q^{73} +67.4877 q^{74} +(-53.0519 + 53.0519i) q^{75} +(14.3363 + 14.3363i) q^{76} +(91.5883 - 91.5883i) q^{77} +46.4651 q^{78} +(9.72981 - 9.72981i) q^{79} +3.19164i q^{80} +82.5961 q^{81} -42.3833 q^{82} +64.2570 q^{83} +(-28.9508 - 28.9508i) q^{84} +(-4.73930 - 4.73930i) q^{85} -108.452i q^{86} +(82.1233 + 31.2565i) q^{87} -138.549 q^{88} +(-119.740 + 119.740i) q^{89} +(-0.0954618 + 0.0954618i) q^{90} +81.2861i q^{91} -24.0840i q^{92} +133.790i q^{93} -91.1550 q^{94} +(4.19517 + 4.19517i) q^{95} +74.6909i q^{96} +(-33.5755 - 33.5755i) q^{97} +(-17.7737 + 17.7737i) q^{98} +(-2.04863 - 2.04863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 2q^{3} - 4q^{7} - 42q^{8} + O(q^{10}) \) \( 8q + 2q^{2} - 2q^{3} - 4q^{7} - 42q^{8} + 6q^{10} - 6q^{11} + 54q^{12} - 40q^{14} - 10q^{15} - 32q^{16} + 12q^{17} + 20q^{18} - 16q^{19} + 108q^{20} - 36q^{21} + 168q^{24} + 104q^{25} - 54q^{26} - 98q^{27} + 128q^{29} - 220q^{30} - 10q^{31} - 106q^{32} - 252q^{36} - 84q^{37} - 90q^{39} + 226q^{40} + 20q^{41} - 190q^{43} + 42q^{44} + 292q^{45} + 12q^{46} + 58q^{47} + 354q^{48} - 72q^{49} - 60q^{50} - 144q^{52} + 252q^{53} + 400q^{54} - 74q^{55} - 192q^{56} + 326q^{58} - 40q^{59} - 258q^{60} - 208q^{61} + 36q^{65} - 414q^{66} - 296q^{68} + 120q^{69} + 44q^{70} - 636q^{72} - 188q^{73} - 64q^{74} - 12q^{75} + 592q^{76} + 180q^{77} + 600q^{78} - 382q^{79} - 124q^{81} + 228q^{82} + 280q^{83} - 124q^{84} + 32q^{85} + 34q^{87} + 20q^{88} - 64q^{89} + 128q^{90} - 460q^{94} - 380q^{95} - 44q^{97} - 66q^{98} + 552q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07935 + 1.07935i −0.539675 + 0.539675i −0.923433 0.383759i \(-0.874629\pi\)
0.383759 + 0.923433i \(0.374629\pi\)
\(3\) −2.14254 + 2.14254i −0.714181 + 0.714181i −0.967407 0.253226i \(-0.918508\pi\)
0.253226 + 0.967407i \(0.418508\pi\)
\(4\) 1.67001i 0.417502i
\(5\) 0.488689i 0.0977379i 0.998805 + 0.0488689i \(0.0155617\pi\)
−0.998805 + 0.0488689i \(0.984438\pi\)
\(6\) 4.62511i 0.770851i
\(7\) 8.09117 1.15588 0.577941 0.816079i \(-0.303856\pi\)
0.577941 + 0.816079i \(0.303856\pi\)
\(8\) −6.11992 6.11992i −0.764990 0.764990i
\(9\) 0.180982i 0.0201091i
\(10\) −0.527467 0.527467i −0.0527467 0.0527467i
\(11\) 11.3195 11.3195i 1.02905 1.02905i 0.0294830 0.999565i \(-0.490614\pi\)
0.999565 0.0294830i \(-0.00938610\pi\)
\(12\) −3.57807 3.57807i −0.298172 0.298172i
\(13\) 10.0463i 0.772790i 0.922333 + 0.386395i \(0.126280\pi\)
−0.922333 + 0.386395i \(0.873720\pi\)
\(14\) −8.73320 + 8.73320i −0.623800 + 0.623800i
\(15\) −1.04704 1.04704i −0.0698025 0.0698025i
\(16\) 6.53103 0.408189
\(17\) −9.69799 + 9.69799i −0.570470 + 0.570470i −0.932260 0.361790i \(-0.882166\pi\)
0.361790 + 0.932260i \(0.382166\pi\)
\(18\) 0.195342 + 0.195342i 0.0108524 + 0.0108524i
\(19\) 8.58453 8.58453i 0.451818 0.451818i −0.444140 0.895957i \(-0.646491\pi\)
0.895957 + 0.444140i \(0.146491\pi\)
\(20\) −0.816116 −0.0408058
\(21\) −17.3357 + 17.3357i −0.825509 + 0.825509i
\(22\) 24.4355i 1.11070i
\(23\) −14.4215 −0.627022 −0.313511 0.949585i \(-0.601505\pi\)
−0.313511 + 0.949585i \(0.601505\pi\)
\(24\) 26.2244 1.09268
\(25\) 24.7612 0.990447
\(26\) −10.8434 10.8434i −0.417055 0.417055i
\(27\) −18.8951 18.8951i −0.699820 0.699820i
\(28\) 13.5123i 0.482583i
\(29\) −11.8706 26.4592i −0.409333 0.912385i
\(30\) 2.26024 0.0753413
\(31\) 31.2221 31.2221i 1.00717 1.00717i 0.00719198 0.999974i \(-0.497711\pi\)
0.999974 0.00719198i \(-0.00228930\pi\)
\(32\) 17.4304 17.4304i 0.544701 0.544701i
\(33\) 48.5052i 1.46985i
\(34\) 20.9350i 0.615736i
\(35\) 3.95407i 0.112973i
\(36\) 0.302241 0.00839559
\(37\) −31.2631 31.2631i −0.844950 0.844950i 0.144548 0.989498i \(-0.453827\pi\)
−0.989498 + 0.144548i \(0.953827\pi\)
\(38\) 18.5314i 0.487669i
\(39\) −21.5246 21.5246i −0.551912 0.551912i
\(40\) 2.99074 2.99074i 0.0747685 0.0747685i
\(41\) 19.6337 + 19.6337i 0.478871 + 0.478871i 0.904770 0.425900i \(-0.140042\pi\)
−0.425900 + 0.904770i \(0.640042\pi\)
\(42\) 37.4225i 0.891013i
\(43\) −50.2394 + 50.2394i −1.16836 + 1.16836i −0.185764 + 0.982594i \(0.559476\pi\)
−0.982594 + 0.185764i \(0.940524\pi\)
\(44\) 18.9037 + 18.9037i 0.429630 + 0.429630i
\(45\) 0.0884438 0.00196542
\(46\) 15.5658 15.5658i 0.338388 0.338388i
\(47\) 42.2268 + 42.2268i 0.898443 + 0.898443i 0.995298 0.0968555i \(-0.0308785\pi\)
−0.0968555 + 0.995298i \(0.530878\pi\)
\(48\) −13.9930 + 13.9930i −0.291521 + 0.291521i
\(49\) 16.4671 0.336063
\(50\) −26.7260 + 26.7260i −0.534519 + 0.534519i
\(51\) 41.5567i 0.814838i
\(52\) −16.7774 −0.322642
\(53\) 16.5613 0.312477 0.156239 0.987719i \(-0.450063\pi\)
0.156239 + 0.987719i \(0.450063\pi\)
\(54\) 40.7889 0.755350
\(55\) 5.53173 + 5.53173i 0.100577 + 0.100577i
\(56\) −49.5173 49.5173i −0.884238 0.884238i
\(57\) 36.7855i 0.645359i
\(58\) 41.3713 + 15.7461i 0.713298 + 0.271485i
\(59\) −14.5041 −0.245833 −0.122916 0.992417i \(-0.539225\pi\)
−0.122916 + 0.992417i \(0.539225\pi\)
\(60\) 1.74856 1.74856i 0.0291427 0.0291427i
\(61\) −45.3849 + 45.3849i −0.744014 + 0.744014i −0.973348 0.229334i \(-0.926345\pi\)
0.229334 + 0.973348i \(0.426345\pi\)
\(62\) 67.3992i 1.08708i
\(63\) 1.46435i 0.0232437i
\(64\) 63.7512i 0.996112i
\(65\) −4.90950 −0.0755308
\(66\) −52.3540 52.3540i −0.793243 0.793243i
\(67\) 133.589i 1.99386i −0.0782703 0.996932i \(-0.524940\pi\)
0.0782703 0.996932i \(-0.475060\pi\)
\(68\) −16.1957 16.1957i −0.238173 0.238173i
\(69\) 30.8987 30.8987i 0.447807 0.447807i
\(70\) −4.26782 4.26782i −0.0609689 0.0609689i
\(71\) 33.9204i 0.477752i −0.971050 0.238876i \(-0.923221\pi\)
0.971050 0.238876i \(-0.0767790\pi\)
\(72\) −1.10759 + 1.10759i −0.0153832 + 0.0153832i
\(73\) −22.1752 22.1752i −0.303770 0.303770i 0.538717 0.842487i \(-0.318909\pi\)
−0.842487 + 0.538717i \(0.818909\pi\)
\(74\) 67.4877 0.911996
\(75\) −53.0519 + 53.0519i −0.707359 + 0.707359i
\(76\) 14.3363 + 14.3363i 0.188635 + 0.188635i
\(77\) 91.5883 91.5883i 1.18946 1.18946i
\(78\) 46.4651 0.595706
\(79\) 9.72981 9.72981i 0.123162 0.123162i −0.642839 0.766001i \(-0.722244\pi\)
0.766001 + 0.642839i \(0.222244\pi\)
\(80\) 3.19164i 0.0398956i
\(81\) 82.5961 1.01970
\(82\) −42.3833 −0.516869
\(83\) 64.2570 0.774181 0.387091 0.922042i \(-0.373480\pi\)
0.387091 + 0.922042i \(0.373480\pi\)
\(84\) −28.9508 28.9508i −0.344652 0.344652i
\(85\) −4.73930 4.73930i −0.0557565 0.0557565i
\(86\) 108.452i 1.26107i
\(87\) 82.1233 + 31.2565i 0.943946 + 0.359271i
\(88\) −138.549 −1.57442
\(89\) −119.740 + 119.740i −1.34540 + 1.34540i −0.454808 + 0.890590i \(0.650292\pi\)
−0.890590 + 0.454808i \(0.849708\pi\)
\(90\) −0.0954618 + 0.0954618i −0.00106069 + 0.00106069i
\(91\) 81.2861i 0.893254i
\(92\) 24.0840i 0.261783i
\(93\) 133.790i 1.43860i
\(94\) −91.1550 −0.969734
\(95\) 4.19517 + 4.19517i 0.0441597 + 0.0441597i
\(96\) 74.6909i 0.778030i
\(97\) −33.5755 33.5755i −0.346139 0.346139i 0.512530 0.858669i \(-0.328708\pi\)
−0.858669 + 0.512530i \(0.828708\pi\)
\(98\) −17.7737 + 17.7737i −0.181365 + 0.181365i
\(99\) −2.04863 2.04863i −0.0206932 0.0206932i
\(100\) 41.3514i 0.413514i
\(101\) −38.2463 + 38.2463i −0.378676 + 0.378676i −0.870624 0.491948i \(-0.836285\pi\)
0.491948 + 0.870624i \(0.336285\pi\)
\(102\) 44.8542 + 44.8542i 0.439747 + 0.439747i
\(103\) 61.6568 0.598609 0.299305 0.954158i \(-0.403245\pi\)
0.299305 + 0.954158i \(0.403245\pi\)
\(104\) 61.4824 61.4824i 0.591177 0.591177i
\(105\) −8.47176 8.47176i −0.0806835 0.0806835i
\(106\) −17.8754 + 17.8754i −0.168636 + 0.168636i
\(107\) −48.5836 −0.454052 −0.227026 0.973889i \(-0.572900\pi\)
−0.227026 + 0.973889i \(0.572900\pi\)
\(108\) 31.5550 31.5550i 0.292176 0.292176i
\(109\) 82.0131i 0.752414i −0.926536 0.376207i \(-0.877228\pi\)
0.926536 0.376207i \(-0.122772\pi\)
\(110\) −11.9413 −0.108558
\(111\) 133.965 1.20689
\(112\) 52.8437 0.471819
\(113\) 0.444855 + 0.444855i 0.00393677 + 0.00393677i 0.709072 0.705136i \(-0.249114\pi\)
−0.705136 + 0.709072i \(0.749114\pi\)
\(114\) −39.7044 39.7044i −0.348284 0.348284i
\(115\) 7.04763i 0.0612838i
\(116\) 44.1871 19.8241i 0.380923 0.170897i
\(117\) 1.81819 0.0155401
\(118\) 15.6550 15.6550i 0.132670 0.132670i
\(119\) −78.4681 + 78.4681i −0.659396 + 0.659396i
\(120\) 12.8156i 0.106796i
\(121\) 135.264i 1.11788i
\(122\) 97.9722i 0.803051i
\(123\) −84.1321 −0.684001
\(124\) 52.1413 + 52.1413i 0.420494 + 0.420494i
\(125\) 24.3178i 0.194542i
\(126\) 1.58055 + 1.58055i 0.0125440 + 0.0125440i
\(127\) −21.4010 + 21.4010i −0.168512 + 0.168512i −0.786325 0.617813i \(-0.788019\pi\)
0.617813 + 0.786325i \(0.288019\pi\)
\(128\) 0.911922 + 0.911922i 0.00712439 + 0.00712439i
\(129\) 215.280i 1.66884i
\(130\) 5.29907 5.29907i 0.0407621 0.0407621i
\(131\) −46.6907 46.6907i −0.356417 0.356417i 0.506073 0.862491i \(-0.331097\pi\)
−0.862491 + 0.506073i \(0.831097\pi\)
\(132\) −81.0041 −0.613667
\(133\) 69.4589 69.4589i 0.522248 0.522248i
\(134\) 144.189 + 144.189i 1.07604 + 1.07604i
\(135\) 9.23385 9.23385i 0.0683989 0.0683989i
\(136\) 118.702 0.872808
\(137\) 5.76576 5.76576i 0.0420858 0.0420858i −0.685751 0.727837i \(-0.740526\pi\)
0.727837 + 0.685751i \(0.240526\pi\)
\(138\) 66.7010i 0.483340i
\(139\) −223.985 −1.61140 −0.805701 0.592322i \(-0.798211\pi\)
−0.805701 + 0.592322i \(0.798211\pi\)
\(140\) −6.60333 −0.0471667
\(141\) −180.946 −1.28330
\(142\) 36.6120 + 36.6120i 0.257831 + 0.257831i
\(143\) 113.719 + 113.719i 0.795238 + 0.795238i
\(144\) 1.18200i 0.00820831i
\(145\) 12.9303 5.80106i 0.0891746 0.0400073i
\(146\) 47.8696 0.327874
\(147\) −35.2814 + 35.2814i −0.240010 + 0.240010i
\(148\) 52.2097 52.2097i 0.352769 0.352769i
\(149\) 129.230i 0.867316i −0.901078 0.433658i \(-0.857223\pi\)
0.901078 0.433658i \(-0.142777\pi\)
\(150\) 114.523i 0.763487i
\(151\) 59.3971i 0.393359i 0.980468 + 0.196679i \(0.0630158\pi\)
−0.980468 + 0.196679i \(0.936984\pi\)
\(152\) −105.073 −0.691272
\(153\) 1.75516 + 1.75516i 0.0114716 + 0.0114716i
\(154\) 197.712i 1.28384i
\(155\) 15.2579 + 15.2579i 0.0984383 + 0.0984383i
\(156\) 35.9462 35.9462i 0.230425 0.230425i
\(157\) 210.885 + 210.885i 1.34321 + 1.34321i 0.892840 + 0.450374i \(0.148709\pi\)
0.450374 + 0.892840i \(0.351291\pi\)
\(158\) 21.0037i 0.132935i
\(159\) −35.4833 + 35.4833i −0.223165 + 0.223165i
\(160\) 8.51806 + 8.51806i 0.0532379 + 0.0532379i
\(161\) −116.687 −0.724763
\(162\) −89.1500 + 89.1500i −0.550309 + 0.550309i
\(163\) −151.656 151.656i −0.930405 0.930405i 0.0673260 0.997731i \(-0.478553\pi\)
−0.997731 + 0.0673260i \(0.978553\pi\)
\(164\) −32.7885 + 32.7885i −0.199930 + 0.199930i
\(165\) −23.7040 −0.143660
\(166\) −69.3558 + 69.3558i −0.417806 + 0.417806i
\(167\) 117.024i 0.700743i 0.936611 + 0.350371i \(0.113945\pi\)
−0.936611 + 0.350371i \(0.886055\pi\)
\(168\) 212.186 1.26301
\(169\) 68.0725 0.402796
\(170\) 10.2307 0.0601808
\(171\) −1.55364 1.55364i −0.00908563 0.00908563i
\(172\) −83.9003 83.9003i −0.487792 0.487792i
\(173\) 51.3836i 0.297015i −0.988911 0.148508i \(-0.952553\pi\)
0.988911 0.148508i \(-0.0474469\pi\)
\(174\) −122.376 + 54.9030i −0.703313 + 0.315534i
\(175\) 200.347 1.14484
\(176\) 73.9282 73.9282i 0.420047 0.420047i
\(177\) 31.0757 31.0757i 0.175569 0.175569i
\(178\) 258.483i 1.45215i
\(179\) 292.744i 1.63544i 0.575615 + 0.817721i \(0.304763\pi\)
−0.575615 + 0.817721i \(0.695237\pi\)
\(180\) 0.147702i 0.000820567i
\(181\) 175.159 0.967728 0.483864 0.875143i \(-0.339233\pi\)
0.483864 + 0.875143i \(0.339233\pi\)
\(182\) −87.7361 87.7361i −0.482067 0.482067i
\(183\) 194.478i 1.06272i
\(184\) 88.2585 + 88.2585i 0.479666 + 0.479666i
\(185\) 15.2780 15.2780i 0.0825836 0.0825836i
\(186\) −144.406 144.406i −0.776375 0.776375i
\(187\) 219.553i 1.17408i
\(188\) −70.5192 + 70.5192i −0.375102 + 0.375102i
\(189\) −152.884 152.884i −0.808909 0.808909i
\(190\) −9.05611 −0.0476637
\(191\) 46.8745 46.8745i 0.245416 0.245416i −0.573670 0.819086i \(-0.694481\pi\)
0.819086 + 0.573670i \(0.194481\pi\)
\(192\) −136.590 136.590i −0.711404 0.711404i
\(193\) 49.8678 49.8678i 0.258382 0.258382i −0.566014 0.824396i \(-0.691515\pi\)
0.824396 + 0.566014i \(0.191515\pi\)
\(194\) 72.4794 0.373605
\(195\) 10.5188 10.5188i 0.0539427 0.0539427i
\(196\) 27.5002i 0.140307i
\(197\) −59.7514 −0.303307 −0.151653 0.988434i \(-0.548460\pi\)
−0.151653 + 0.988434i \(0.548460\pi\)
\(198\) 4.42237 0.0223352
\(199\) −10.7830 −0.0541859 −0.0270929 0.999633i \(-0.508625\pi\)
−0.0270929 + 0.999633i \(0.508625\pi\)
\(200\) −151.536 151.536i −0.757682 0.757682i
\(201\) 286.220 + 286.220i 1.42398 + 1.42398i
\(202\) 82.5622i 0.408724i
\(203\) −96.0474 214.086i −0.473140 1.05461i
\(204\) 69.4001 0.340197
\(205\) −9.59478 + 9.59478i −0.0468038 + 0.0468038i
\(206\) −66.5492 + 66.5492i −0.323054 + 0.323054i
\(207\) 2.61003i 0.0126088i
\(208\) 65.6125i 0.315445i
\(209\) 194.346i 0.929884i
\(210\) 18.2880 0.0870857
\(211\) 71.2119 + 71.2119i 0.337497 + 0.337497i 0.855424 0.517928i \(-0.173296\pi\)
−0.517928 + 0.855424i \(0.673296\pi\)
\(212\) 27.6575i 0.130460i
\(213\) 72.6759 + 72.6759i 0.341201 + 0.341201i
\(214\) 52.4387 52.4387i 0.245041 0.245041i
\(215\) −24.5515 24.5515i −0.114193 0.114193i
\(216\) 231.273i 1.07071i
\(217\) 252.624 252.624i 1.16417 1.16417i
\(218\) 88.5208 + 88.5208i 0.406059 + 0.406059i
\(219\) 95.0227 0.433894
\(220\) −9.23805 + 9.23805i −0.0419911 + 0.0419911i
\(221\) −97.4286 97.4286i −0.440853 0.440853i
\(222\) −144.595 + 144.595i −0.651330 + 0.651330i
\(223\) −166.943 −0.748625 −0.374312 0.927303i \(-0.622121\pi\)
−0.374312 + 0.927303i \(0.622121\pi\)
\(224\) 141.033 141.033i 0.629610 0.629610i
\(225\) 4.48132i 0.0199170i
\(226\) −0.960307 −0.00424915
\(227\) −120.332 −0.530095 −0.265048 0.964235i \(-0.585388\pi\)
−0.265048 + 0.964235i \(0.585388\pi\)
\(228\) −61.4321 −0.269439
\(229\) 9.30072 + 9.30072i 0.0406145 + 0.0406145i 0.727122 0.686508i \(-0.240857\pi\)
−0.686508 + 0.727122i \(0.740857\pi\)
\(230\) 7.60686 + 7.60686i 0.0330733 + 0.0330733i
\(231\) 392.464i 1.69898i
\(232\) −89.2806 + 234.575i −0.384830 + 1.01110i
\(233\) −235.895 −1.01243 −0.506213 0.862408i \(-0.668955\pi\)
−0.506213 + 0.862408i \(0.668955\pi\)
\(234\) −1.96246 + 1.96246i −0.00838660 + 0.00838660i
\(235\) −20.6358 + 20.6358i −0.0878119 + 0.0878119i
\(236\) 24.2220i 0.102636i
\(237\) 41.6931i 0.175920i
\(238\) 169.389i 0.711719i
\(239\) 389.332 1.62900 0.814501 0.580162i \(-0.197011\pi\)
0.814501 + 0.580162i \(0.197011\pi\)
\(240\) −6.83824 6.83824i −0.0284926 0.0284926i
\(241\) 163.689i 0.679206i 0.940569 + 0.339603i \(0.110293\pi\)
−0.940569 + 0.339603i \(0.889707\pi\)
\(242\) 145.997 + 145.997i 0.603292 + 0.603292i
\(243\) −6.90952 + 6.90952i −0.0284342 + 0.0284342i
\(244\) −75.7931 75.7931i −0.310628 0.310628i
\(245\) 8.04729i 0.0328461i
\(246\) 90.8080 90.8080i 0.369138 0.369138i
\(247\) 86.2425 + 86.2425i 0.349160 + 0.349160i
\(248\) −382.154 −1.54094
\(249\) −137.673 + 137.673i −0.552905 + 0.552905i
\(250\) −26.2474 26.2474i −0.104989 0.104989i
\(251\) −132.018 + 132.018i −0.525968 + 0.525968i −0.919368 0.393399i \(-0.871299\pi\)
0.393399 + 0.919368i \(0.371299\pi\)
\(252\) 2.44549 0.00970431
\(253\) −163.245 + 163.245i −0.645236 + 0.645236i
\(254\) 46.1983i 0.181883i
\(255\) 20.3083 0.0796405
\(256\) −256.973 −1.00380
\(257\) −113.634 −0.442155 −0.221078 0.975256i \(-0.570957\pi\)
−0.221078 + 0.975256i \(0.570957\pi\)
\(258\) 232.363 + 232.363i 0.900630 + 0.900630i
\(259\) −252.955 252.955i −0.976662 0.976662i
\(260\) 8.19892i 0.0315343i
\(261\) −4.78863 + 2.14837i −0.0183472 + 0.00823130i
\(262\) 100.791 0.384699
\(263\) 279.851 279.851i 1.06407 1.06407i 0.0662687 0.997802i \(-0.478891\pi\)
0.997802 0.0662687i \(-0.0211095\pi\)
\(264\) 296.848 296.848i 1.12442 1.12442i
\(265\) 8.09332i 0.0305408i
\(266\) 149.941i 0.563688i
\(267\) 513.098i 1.92171i
\(268\) 223.095 0.832443
\(269\) 302.867 + 302.867i 1.12590 + 1.12590i 0.990837 + 0.135061i \(0.0431231\pi\)
0.135061 + 0.990837i \(0.456877\pi\)
\(270\) 19.9331i 0.0738263i
\(271\) −222.952 222.952i −0.822702 0.822702i 0.163793 0.986495i \(-0.447627\pi\)
−0.986495 + 0.163793i \(0.947627\pi\)
\(272\) −63.3379 + 63.3379i −0.232860 + 0.232860i
\(273\) −174.159 174.159i −0.637945 0.637945i
\(274\) 12.4465i 0.0454253i
\(275\) 280.285 280.285i 1.01922 1.01922i
\(276\) 51.6011 + 51.6011i 0.186961 + 0.186961i
\(277\) 290.196 1.04764 0.523820 0.851829i \(-0.324507\pi\)
0.523820 + 0.851829i \(0.324507\pi\)
\(278\) 241.758 241.758i 0.869633 0.869633i
\(279\) −5.65064 5.65064i −0.0202532 0.0202532i
\(280\) 24.1986 24.1986i 0.0864236 0.0864236i
\(281\) −486.000 −1.72954 −0.864768 0.502171i \(-0.832535\pi\)
−0.864768 + 0.502171i \(0.832535\pi\)
\(282\) 195.303 195.303i 0.692566 0.692566i
\(283\) 95.1009i 0.336046i −0.985783 0.168023i \(-0.946262\pi\)
0.985783 0.168023i \(-0.0537382\pi\)
\(284\) 56.6474 0.199463
\(285\) −17.9767 −0.0630760
\(286\) −245.485 −0.858340
\(287\) 158.860 + 158.860i 0.553518 + 0.553518i
\(288\) −3.15459 3.15459i −0.0109534 0.0109534i
\(289\) 100.898i 0.349128i
\(290\) −7.69496 + 20.2177i −0.0265343 + 0.0697162i
\(291\) 143.874 0.494412
\(292\) 37.0328 37.0328i 0.126825 0.126825i
\(293\) 21.2589 21.2589i 0.0725559 0.0725559i −0.669898 0.742454i \(-0.733662\pi\)
0.742454 + 0.669898i \(0.233662\pi\)
\(294\) 76.1620i 0.259054i
\(295\) 7.08801i 0.0240272i
\(296\) 382.656i 1.29276i
\(297\) −427.768 −1.44030
\(298\) 139.484 + 139.484i 0.468068 + 0.468068i
\(299\) 144.882i 0.484556i
\(300\) −88.5972 88.5972i −0.295324 0.295324i
\(301\) −406.496 + 406.496i −1.35048 + 1.35048i
\(302\) −64.1103 64.1103i −0.212286 0.212286i
\(303\) 163.889i 0.540887i
\(304\) 56.0658 56.0658i 0.184427 0.184427i
\(305\) −22.1791 22.1791i −0.0727183 0.0727183i
\(306\) −3.78886 −0.0123819
\(307\) −193.144 + 193.144i −0.629135 + 0.629135i −0.947850 0.318715i \(-0.896749\pi\)
0.318715 + 0.947850i \(0.396749\pi\)
\(308\) 152.953 + 152.953i 0.496602 + 0.496602i
\(309\) −132.102 + 132.102i −0.427516 + 0.427516i
\(310\) −32.9373 −0.106249
\(311\) 112.842 112.842i 0.362835 0.362835i −0.502021 0.864856i \(-0.667410\pi\)
0.864856 + 0.502021i \(0.167410\pi\)
\(312\) 263.457i 0.844414i
\(313\) 119.788 0.382710 0.191355 0.981521i \(-0.438712\pi\)
0.191355 + 0.981521i \(0.438712\pi\)
\(314\) −455.236 −1.44980
\(315\) 0.715614 0.00227179
\(316\) 16.2489 + 16.2489i 0.0514205 + 0.0514205i
\(317\) 270.382 + 270.382i 0.852942 + 0.852942i 0.990494 0.137553i \(-0.0439237\pi\)
−0.137553 + 0.990494i \(0.543924\pi\)
\(318\) 76.5977i 0.240873i
\(319\) −433.876 165.135i −1.36011 0.517665i
\(320\) −31.1545 −0.0973578
\(321\) 104.092 104.092i 0.324276 0.324276i
\(322\) 125.946 125.946i 0.391136 0.391136i
\(323\) 166.505i 0.515497i
\(324\) 137.936i 0.425729i
\(325\) 248.758i 0.765408i
\(326\) 327.380 1.00423
\(327\) 175.717 + 175.717i 0.537360 + 0.537360i
\(328\) 240.313i 0.732663i
\(329\) 341.665 + 341.665i 1.03849 + 1.03849i
\(330\) 25.5849 25.5849i 0.0775299 0.0775299i
\(331\) −64.5326 64.5326i −0.194962 0.194962i 0.602874 0.797836i \(-0.294022\pi\)
−0.797836 + 0.602874i \(0.794022\pi\)
\(332\) 107.310i 0.323222i
\(333\) −5.65806 + 5.65806i −0.0169912 + 0.0169912i
\(334\) −126.310 126.310i −0.378173 0.378173i
\(335\) 65.2835 0.194876
\(336\) −113.220 + 113.220i −0.336964 + 0.336964i
\(337\) −49.1921 49.1921i −0.145971 0.145971i 0.630345 0.776315i \(-0.282914\pi\)
−0.776315 + 0.630345i \(0.782914\pi\)
\(338\) −73.4740 + 73.4740i −0.217379 + 0.217379i
\(339\) −1.90624 −0.00562313
\(340\) 7.91468 7.91468i 0.0232785 0.0232785i
\(341\) 706.840i 2.07285i
\(342\) 3.35385 0.00980657
\(343\) −263.229 −0.767433
\(344\) 614.923 1.78757
\(345\) 15.0999 + 15.0999i 0.0437677 + 0.0437677i
\(346\) 55.4609 + 55.4609i 0.160292 + 0.160292i
\(347\) 75.0323i 0.216231i 0.994138 + 0.108116i \(0.0344817\pi\)
−0.994138 + 0.108116i \(0.965518\pi\)
\(348\) −52.1987 + 137.147i −0.149996 + 0.394100i
\(349\) 284.109 0.814067 0.407033 0.913413i \(-0.366563\pi\)
0.407033 + 0.913413i \(0.366563\pi\)
\(350\) −216.244 + 216.244i −0.617841 + 0.617841i
\(351\) 189.826 189.826i 0.540813 0.540813i
\(352\) 394.608i 1.12105i
\(353\) 157.587i 0.446422i 0.974770 + 0.223211i \(0.0716538\pi\)
−0.974770 + 0.223211i \(0.928346\pi\)
\(354\) 67.0831i 0.189500i
\(355\) 16.5765 0.0466945
\(356\) −199.968 199.968i −0.561707 0.561707i
\(357\) 336.243i 0.941856i
\(358\) −315.973 315.973i −0.882606 0.882606i
\(359\) −327.012 + 327.012i −0.910896 + 0.910896i −0.996343 0.0854467i \(-0.972768\pi\)
0.0854467 + 0.996343i \(0.472768\pi\)
\(360\) −0.541269 0.541269i −0.00150353 0.00150353i
\(361\) 213.612i 0.591722i
\(362\) −189.058 + 189.058i −0.522259 + 0.522259i
\(363\) 289.808 + 289.808i 0.798369 + 0.798369i
\(364\) −135.749 −0.372936
\(365\) 10.8368 10.8368i 0.0296898 0.0296898i
\(366\) 209.910 + 209.910i 0.573524 + 0.573524i
\(367\) 243.021 243.021i 0.662182 0.662182i −0.293712 0.955894i \(-0.594891\pi\)
0.955894 + 0.293712i \(0.0948906\pi\)
\(368\) −94.1873 −0.255944
\(369\) 3.55334 3.55334i 0.00962965 0.00962965i
\(370\) 32.9805i 0.0891365i
\(371\) 134.000 0.361187
\(372\) −223.430 −0.600618
\(373\) −503.790 −1.35064 −0.675322 0.737523i \(-0.735995\pi\)
−0.675322 + 0.737523i \(0.735995\pi\)
\(374\) −236.975 236.975i −0.633623 0.633623i
\(375\) −52.1018 52.1018i −0.138938 0.138938i
\(376\) 516.850i 1.37460i
\(377\) 265.816 119.256i 0.705082 0.316328i
\(378\) 330.030 0.873095
\(379\) −74.1929 + 74.1929i −0.195760 + 0.195760i −0.798179 0.602420i \(-0.794203\pi\)
0.602420 + 0.798179i \(0.294203\pi\)
\(380\) −7.00597 + 7.00597i −0.0184368 + 0.0184368i
\(381\) 91.7051i 0.240696i
\(382\) 101.188i 0.264890i
\(383\) 561.592i 1.46630i −0.680068 0.733149i \(-0.738050\pi\)
0.680068 0.733149i \(-0.261950\pi\)
\(384\) −3.90766 −0.0101762
\(385\) 44.7582 + 44.7582i 0.116255 + 0.116255i
\(386\) 107.649i 0.278885i
\(387\) 9.09241 + 9.09241i 0.0234946 + 0.0234946i
\(388\) 56.0714 56.0714i 0.144514 0.144514i
\(389\) −111.236 111.236i −0.285953 0.285953i 0.549525 0.835478i \(-0.314809\pi\)
−0.835478 + 0.549525i \(0.814809\pi\)
\(390\) 22.7070i 0.0582230i
\(391\) 139.860 139.860i 0.357697 0.357697i
\(392\) −100.777 100.777i −0.257085 0.257085i
\(393\) 200.074 0.509093
\(394\) 64.4927 64.4927i 0.163687 0.163687i
\(395\) 4.75485 + 4.75485i 0.0120376 + 0.0120376i
\(396\) 3.42123 3.42123i 0.00863947 0.00863947i
\(397\) 695.905 1.75291 0.876455 0.481484i \(-0.159902\pi\)
0.876455 + 0.481484i \(0.159902\pi\)
\(398\) 11.6386 11.6386i 0.0292428 0.0292428i
\(399\) 297.638i 0.745959i
\(400\) 161.716 0.404290
\(401\) 450.193 1.12268 0.561338 0.827587i \(-0.310287\pi\)
0.561338 + 0.827587i \(0.310287\pi\)
\(402\) −617.863 −1.53697
\(403\) 313.666 + 313.666i 0.778328 + 0.778328i
\(404\) −63.8717 63.8717i −0.158098 0.158098i
\(405\) 40.3638i 0.0996638i
\(406\) 334.742 + 127.405i 0.824488 + 0.313804i
\(407\) −707.768 −1.73899
\(408\) −254.324 + 254.324i −0.623343 + 0.623343i
\(409\) −449.447 + 449.447i −1.09889 + 1.09889i −0.104353 + 0.994540i \(0.533277\pi\)
−0.994540 + 0.104353i \(0.966723\pi\)
\(410\) 20.7122i 0.0505177i
\(411\) 24.7068i 0.0601138i
\(412\) 102.967i 0.249921i
\(413\) −117.355 −0.284154
\(414\) −2.81713 2.81713i −0.00680467 0.00680467i
\(415\) 31.4017i 0.0756668i
\(416\) 175.111 + 175.111i 0.420939 + 0.420939i
\(417\) 479.898 479.898i 1.15083 1.15083i
\(418\) 209.767 + 209.767i 0.501835 + 0.501835i
\(419\) 585.961i 1.39848i −0.714889 0.699238i \(-0.753523\pi\)
0.714889 0.699238i \(-0.246477\pi\)
\(420\) 14.1479 14.1479i 0.0336855 0.0336855i
\(421\) −37.5863 37.5863i −0.0892786 0.0892786i 0.661057 0.750336i \(-0.270108\pi\)
−0.750336 + 0.661057i \(0.770108\pi\)
\(422\) −153.725 −0.364277
\(423\) 7.64228 7.64228i 0.0180669 0.0180669i
\(424\) −101.354 101.354i −0.239042 0.239042i
\(425\) −240.134 + 240.134i −0.565020 + 0.565020i
\(426\) −156.885 −0.368276
\(427\) −367.217 + 367.217i −0.859992 + 0.859992i
\(428\) 81.1351i 0.189568i
\(429\) −487.296 −1.13589
\(430\) 52.9992 0.123254
\(431\) 270.174 0.626853 0.313427 0.949612i \(-0.398523\pi\)
0.313427 + 0.949612i \(0.398523\pi\)
\(432\) −123.405 123.405i −0.285659 0.285659i
\(433\) 214.672 + 214.672i 0.495779 + 0.495779i 0.910121 0.414342i \(-0.135988\pi\)
−0.414342 + 0.910121i \(0.635988\pi\)
\(434\) 545.339i 1.25654i
\(435\) −15.2747 + 40.1328i −0.0351143 + 0.0922592i
\(436\) 136.963 0.314135
\(437\) −123.802 + 123.802i −0.283299 + 0.283299i
\(438\) −102.563 + 102.563i −0.234161 + 0.234161i
\(439\) 380.066i 0.865753i 0.901453 + 0.432877i \(0.142501\pi\)
−0.901453 + 0.432877i \(0.857499\pi\)
\(440\) 67.7076i 0.153881i
\(441\) 2.98024i 0.00675792i
\(442\) 210.319 0.475835
\(443\) −248.852 248.852i −0.561743 0.561743i 0.368059 0.929802i \(-0.380022\pi\)
−0.929802 + 0.368059i \(0.880022\pi\)
\(444\) 223.723i 0.503881i
\(445\) −58.5158 58.5158i −0.131496 0.131496i
\(446\) 180.190 180.190i 0.404014 0.404014i
\(447\) 276.881 + 276.881i 0.619420 + 0.619420i
\(448\) 515.822i 1.15139i
\(449\) 133.874 133.874i 0.298159 0.298159i −0.542133 0.840293i \(-0.682383\pi\)
0.840293 + 0.542133i \(0.182383\pi\)
\(450\) 4.83691 + 4.83691i 0.0107487 + 0.0107487i
\(451\) 444.489 0.985562
\(452\) −0.742911 + 0.742911i −0.00164361 + 0.00164361i
\(453\) −127.261 127.261i −0.280929 0.280929i
\(454\) 129.880 129.880i 0.286079 0.286079i
\(455\) −39.7236 −0.0873047
\(456\) 225.124 225.124i 0.493693 0.493693i
\(457\) 476.374i 1.04239i 0.853436 + 0.521197i \(0.174514\pi\)
−0.853436 + 0.521197i \(0.825486\pi\)
\(458\) −20.0775 −0.0438372
\(459\) 366.489 0.798452
\(460\) 11.7696 0.0255861
\(461\) −478.069 478.069i −1.03703 1.03703i −0.999288 0.0377379i \(-0.987985\pi\)
−0.0377379 0.999288i \(-0.512015\pi\)
\(462\) −423.605 423.605i −0.916895 0.916895i
\(463\) 144.158i 0.311357i −0.987808 0.155678i \(-0.950244\pi\)
0.987808 0.155678i \(-0.0497564\pi\)
\(464\) −77.5275 172.806i −0.167085 0.372426i
\(465\) −65.3815 −0.140605
\(466\) 254.613 254.613i 0.546381 0.546381i
\(467\) −63.5129 + 63.5129i −0.136002 + 0.136002i −0.771830 0.635828i \(-0.780659\pi\)
0.635828 + 0.771830i \(0.280659\pi\)
\(468\) 3.03640i 0.00648803i
\(469\) 1080.89i 2.30467i
\(470\) 44.5465i 0.0947797i
\(471\) −903.659 −1.91860
\(472\) 88.7641 + 88.7641i 0.188060 + 0.188060i
\(473\) 1137.37i 2.40459i
\(474\) −45.0014 45.0014i −0.0949396 0.0949396i
\(475\) 212.563 212.563i 0.447501 0.447501i
\(476\) −131.042 131.042i −0.275299 0.275299i
\(477\) 2.99729i 0.00628363i
\(478\) −420.225 + 420.225i −0.879132 + 0.879132i
\(479\) −25.8901 25.8901i −0.0540503 0.0540503i 0.679565 0.733615i \(-0.262169\pi\)
−0.733615 + 0.679565i \(0.762169\pi\)
\(480\) −36.5006 −0.0760430
\(481\) 314.078 314.078i 0.652969 0.652969i
\(482\) −176.677 176.677i −0.366551 0.366551i
\(483\) 250.007 250.007i 0.517612 0.517612i
\(484\) 225.891 0.466718
\(485\) 16.4080 16.4080i 0.0338309 0.0338309i
\(486\) 14.9156i 0.0306905i
\(487\) −383.625 −0.787730 −0.393865 0.919168i \(-0.628862\pi\)
−0.393865 + 0.919168i \(0.628862\pi\)
\(488\) 555.504 1.13833
\(489\) 649.859 1.32896
\(490\) −8.68584 8.68584i −0.0177262 0.0177262i
\(491\) 196.364 + 196.364i 0.399927 + 0.399927i 0.878207 0.478280i \(-0.158740\pi\)
−0.478280 + 0.878207i \(0.658740\pi\)
\(492\) 140.501i 0.285572i
\(493\) 371.722 + 141.479i 0.754000 + 0.286976i
\(494\) −186.172 −0.376866
\(495\) 1.00114 1.00114i 0.00202251 0.00202251i
\(496\) 203.913 203.913i 0.411114 0.411114i
\(497\) 274.456i 0.552225i
\(498\) 297.196i 0.596778i
\(499\) 513.725i 1.02951i 0.857337 + 0.514755i \(0.172117\pi\)
−0.857337 + 0.514755i \(0.827883\pi\)
\(500\) −40.6109 −0.0812218
\(501\) −250.729 250.729i −0.500457 0.500457i
\(502\) 284.987i 0.567703i
\(503\) 195.929 + 195.929i 0.389522 + 0.389522i 0.874517 0.484995i \(-0.161179\pi\)
−0.484995 + 0.874517i \(0.661179\pi\)
\(504\) −8.96173 + 8.96173i −0.0177812 + 0.0177812i
\(505\) −18.6905 18.6905i −0.0370110 0.0370110i
\(506\) 352.396i 0.696435i
\(507\) −145.848 + 145.848i −0.287669 + 0.287669i
\(508\) −35.7399 35.7399i −0.0703541 0.0703541i
\(509\) −802.720 −1.57705 −0.788526 0.615001i \(-0.789155\pi\)
−0.788526 + 0.615001i \(0.789155\pi\)
\(510\) −21.9198 + 21.9198i −0.0429800 + 0.0429800i
\(511\) −179.424 179.424i −0.351122 0.351122i
\(512\) 273.716 273.716i 0.534602 0.534602i
\(513\) −324.412 −0.632381
\(514\) 122.651 122.651i 0.238620 0.238620i
\(515\) 30.1310i 0.0585068i
\(516\) 359.520 0.696744
\(517\) 955.976 1.84908
\(518\) 546.055 1.05416
\(519\) 110.092 + 110.092i 0.212123 + 0.212123i
\(520\) 30.0458 + 30.0458i 0.0577803 + 0.0577803i
\(521\) 913.769i 1.75388i −0.480604 0.876938i \(-0.659583\pi\)
0.480604 0.876938i \(-0.340417\pi\)
\(522\) 2.84976 7.48744i 0.00545931 0.0143438i
\(523\) −280.930 −0.537151 −0.268575 0.963259i \(-0.586553\pi\)
−0.268575 + 0.963259i \(0.586553\pi\)
\(524\) 77.9739 77.9739i 0.148805 0.148805i
\(525\) −429.252 + 429.252i −0.817623 + 0.817623i
\(526\) 604.113i 1.14850i
\(527\) 605.584i 1.14912i
\(528\) 316.789i 0.599979i
\(529\) −321.020 −0.606844
\(530\) −8.73553 8.73553i −0.0164821 0.0164821i
\(531\) 2.62498i 0.00494347i
\(532\) 115.997 + 115.997i 0.218040 + 0.218040i
\(533\) −197.245 + 197.245i −0.370067 + 0.370067i
\(534\) 553.812 + 553.812i 1.03710 + 1.03710i
\(535\) 23.7423i 0.0443781i
\(536\) −817.554 + 817.554i −1.52529 + 1.52529i
\(537\) −627.217 627.217i −1.16800 1.16800i
\(538\) −653.798 −1.21524
\(539\) 186.400 186.400i 0.345825 0.345825i
\(540\) 15.4206 + 15.4206i 0.0285567 + 0.0285567i
\(541\) −17.1635 + 17.1635i −0.0317255 + 0.0317255i −0.722792 0.691066i \(-0.757141\pi\)
0.691066 + 0.722792i \(0.257141\pi\)
\(542\) 481.287 0.887983
\(543\) −375.285 + 375.285i −0.691133 + 0.691133i
\(544\) 338.080i 0.621471i
\(545\) 40.0789 0.0735393
\(546\) 375.957 0.688566
\(547\) 116.845 0.213610 0.106805 0.994280i \(-0.465938\pi\)
0.106805 + 0.994280i \(0.465938\pi\)
\(548\) 9.62887 + 9.62887i 0.0175709 + 0.0175709i
\(549\) 8.21383 + 8.21383i 0.0149614 + 0.0149614i
\(550\) 605.051i 1.10009i
\(551\) −329.044 125.236i −0.597175 0.227288i
\(552\) −378.195 −0.685136
\(553\) 78.7255 78.7255i 0.142361 0.142361i
\(554\) −313.223 + 313.223i −0.565385 + 0.565385i
\(555\) 65.4674i 0.117959i
\(556\) 374.057i 0.672765i
\(557\) 575.508i 1.03323i 0.856218 + 0.516614i \(0.172808\pi\)
−0.856218 + 0.516614i \(0.827192\pi\)
\(558\) 12.1980 0.0218603
\(559\) −504.719 504.719i −0.902896 0.902896i
\(560\) 25.8241i 0.0461145i
\(561\) −470.403 470.403i −0.838507 0.838507i
\(562\) 524.564 524.564i 0.933387 0.933387i
\(563\) 465.411 + 465.411i 0.826662 + 0.826662i 0.987054 0.160391i \(-0.0512756\pi\)
−0.160391 + 0.987054i \(0.551276\pi\)
\(564\) 302.181i 0.535782i
\(565\) −0.217396 + 0.217396i −0.000384771 + 0.000384771i
\(566\) 102.647 + 102.647i 0.181355 + 0.181355i
\(567\) 668.299 1.17866
\(568\) −207.590 + 207.590i −0.365476 + 0.365476i
\(569\) 417.363 + 417.363i 0.733503 + 0.733503i 0.971312 0.237809i \(-0.0764292\pi\)
−0.237809 + 0.971312i \(0.576429\pi\)
\(570\) 19.4031 19.4031i 0.0340405 0.0340405i
\(571\) 24.6693 0.0432037 0.0216019 0.999767i \(-0.493123\pi\)
0.0216019 + 0.999767i \(0.493123\pi\)
\(572\) −189.912 + 189.912i −0.332014 + 0.332014i
\(573\) 200.861i 0.350543i
\(574\) −342.930 −0.597439
\(575\) −357.093 −0.621032
\(576\) 11.5378 0.0200309
\(577\) −152.708 152.708i −0.264659 0.264659i 0.562285 0.826944i \(-0.309922\pi\)
−0.826944 + 0.562285i \(0.809922\pi\)
\(578\) −108.904 108.904i −0.188416 0.188416i
\(579\) 213.688i 0.369063i
\(580\) 9.68782 + 21.5937i 0.0167031 + 0.0372306i
\(581\) 519.915 0.894862
\(582\) −155.290 + 155.290i −0.266822 + 0.266822i
\(583\) 187.466 187.466i 0.321554 0.321554i
\(584\) 271.421i 0.464762i
\(585\) 0.888530i 0.00151886i
\(586\) 45.8915i 0.0783132i
\(587\) 891.866 1.51936 0.759681 0.650295i \(-0.225355\pi\)
0.759681 + 0.650295i \(0.225355\pi\)
\(588\) −58.9203 58.9203i −0.100205 0.100205i
\(589\) 536.055i 0.910111i
\(590\) 7.65044 + 7.65044i 0.0129669 + 0.0129669i
\(591\) 128.020 128.020i 0.216616 0.216616i
\(592\) −204.181 204.181i −0.344900 0.344900i
\(593\) 1124.61i 1.89647i −0.317563 0.948237i \(-0.602864\pi\)
0.317563 0.948237i \(-0.397136\pi\)
\(594\) 461.711 461.711i 0.777291 0.777291i
\(595\) −38.3465 38.3465i −0.0644479 0.0644479i
\(596\) 215.815 0.362106
\(597\) 23.1030 23.1030i 0.0386985 0.0386985i
\(598\) 156.379 + 156.379i 0.261503 + 0.261503i
\(599\) 222.555 222.555i 0.371544 0.371544i −0.496495 0.868040i \(-0.665380\pi\)
0.868040 + 0.496495i \(0.165380\pi\)
\(600\) 649.347 1.08224
\(601\) −196.657 + 196.657i −0.327216 + 0.327216i −0.851527 0.524311i \(-0.824323\pi\)
0.524311 + 0.851527i \(0.324323\pi\)
\(602\) 877.502i 1.45764i
\(603\) −24.1771 −0.0400948
\(604\) −99.1938 −0.164228
\(605\) 66.1019 0.109259
\(606\) 176.893 + 176.893i 0.291903 + 0.291903i
\(607\) −660.823 660.823i −1.08867 1.08867i −0.995666 0.0930047i \(-0.970353\pi\)
−0.0930047 0.995666i \(-0.529647\pi\)
\(608\) 299.264i 0.492211i
\(609\) 664.474 + 252.902i 1.09109 + 0.415274i
\(610\) 47.8780 0.0784885
\(611\) −424.222 + 424.222i −0.694308 + 0.694308i
\(612\) −2.93113 + 2.93113i −0.00478943 + 0.00478943i
\(613\) 299.378i 0.488382i −0.969727 0.244191i \(-0.921478\pi\)
0.969727 0.244191i \(-0.0785224\pi\)
\(614\) 416.941i 0.679057i
\(615\) 41.1145i 0.0668528i
\(616\) −1121.03 −1.81985
\(617\) −419.542 419.542i −0.679972 0.679972i 0.280022 0.959994i \(-0.409658\pi\)
−0.959994 + 0.280022i \(0.909658\pi\)
\(618\) 285.169i 0.461439i
\(619\) 243.311 + 243.311i 0.393072 + 0.393072i 0.875781 0.482709i \(-0.160347\pi\)
−0.482709 + 0.875781i \(0.660347\pi\)
\(620\) −25.4809 + 25.4809i −0.0410982 + 0.0410982i
\(621\) 272.496 + 272.496i 0.438802 + 0.438802i
\(622\) 243.591i 0.391626i
\(623\) −968.840 + 968.840i −1.55512 + 1.55512i
\(624\) −140.578 140.578i −0.225285 0.225285i
\(625\) 607.146 0.971433
\(626\) −129.294 + 129.294i −0.206539 + 0.206539i
\(627\) 416.394 + 416.394i 0.664106 + 0.664106i
\(628\) −352.179 + 352.179i −0.560795 + 0.560795i
\(629\) 606.379 0.964037
\(630\) −0.772398 + 0.772398i −0.00122603 + 0.00122603i
\(631\) 96.3199i 0.152647i −0.997083 0.0763233i \(-0.975682\pi\)
0.997083 0.0763233i \(-0.0243181\pi\)
\(632\) −119.091 −0.188436
\(633\) −305.149 −0.482068
\(634\) −583.674 −0.920622
\(635\) −10.4584 10.4584i −0.0164700 0.0164700i
\(636\) −59.2574 59.2574i −0.0931720 0.0931720i
\(637\) 165.433i 0.259706i
\(638\) 646.542 290.065i 1.01339 0.454647i
\(639\) −6.13897 −0.00960715
\(640\) −0.445646 + 0.445646i −0.000696322 + 0.000696322i
\(641\) −378.246 + 378.246i −0.590088 + 0.590088i −0.937655 0.347567i \(-0.887008\pi\)
0.347567 + 0.937655i \(0.387008\pi\)
\(642\) 224.704i 0.350007i
\(643\) 258.453i 0.401949i −0.979597 0.200974i \(-0.935589\pi\)
0.979597 0.200974i \(-0.0644108\pi\)
\(644\) 194.868i 0.302590i
\(645\) 105.205 0.163109
\(646\) −179.718 179.718i −0.278201 0.278201i
\(647\) 568.930i 0.879336i −0.898160 0.439668i \(-0.855096\pi\)
0.898160 0.439668i \(-0.144904\pi\)
\(648\) −505.482 505.482i −0.780064 0.780064i
\(649\) −164.180 + 164.180i −0.252974 + 0.252974i
\(650\) −268.496 268.496i −0.413071 0.413071i
\(651\) 1082.51i 1.66285i
\(652\) 253.267 253.267i 0.388446 0.388446i
\(653\) 810.018 + 810.018i 1.24046 + 1.24046i 0.959812 + 0.280645i \(0.0905485\pi\)
0.280645 + 0.959812i \(0.409452\pi\)
\(654\) −379.319 −0.579999
\(655\) 22.8172 22.8172i 0.0348355 0.0348355i
\(656\) 128.228 + 128.228i 0.195470 + 0.195470i
\(657\) −4.01331 + 4.01331i −0.00610854 + 0.00610854i
\(658\) −737.551 −1.12090
\(659\) 573.095 573.095i 0.869644 0.869644i −0.122789 0.992433i \(-0.539184\pi\)
0.992433 + 0.122789i \(0.0391839\pi\)
\(660\) 39.5858i 0.0599785i
\(661\) 654.922 0.990804 0.495402 0.868664i \(-0.335021\pi\)
0.495402 + 0.868664i \(0.335021\pi\)
\(662\) 139.306 0.210433
\(663\) 417.490 0.629698
\(664\) −393.248 393.248i −0.592241 0.592241i
\(665\) 33.9438 + 33.9438i 0.0510434 + 0.0510434i
\(666\) 12.2140i 0.0183394i
\(667\) 171.193 + 381.581i 0.256660 + 0.572085i
\(668\) −195.431 −0.292562
\(669\) 357.683 357.683i 0.534653 0.534653i
\(670\) −70.4637 + 70.4637i −0.105170 + 0.105170i
\(671\) 1027.47i 1.53125i
\(672\) 604.337i 0.899311i
\(673\) 395.630i 0.587861i 0.955827 + 0.293930i \(0.0949633\pi\)
−0.955827 + 0.293930i \(0.905037\pi\)
\(674\) 106.191 0.157553
\(675\) −467.866 467.866i −0.693134 0.693134i
\(676\) 113.682i 0.168168i
\(677\) −161.375 161.375i −0.238368 0.238368i 0.577806 0.816174i \(-0.303909\pi\)
−0.816174 + 0.577806i \(0.803909\pi\)
\(678\) 2.05750 2.05750i 0.00303466 0.00303466i
\(679\) −271.665 271.665i −0.400096 0.400096i
\(680\) 58.0083i 0.0853064i
\(681\) 257.816 257.816i 0.378584 0.378584i
\(682\) 762.928 + 762.928i 1.11866 + 1.11866i
\(683\) 635.971 0.931143 0.465572 0.885010i \(-0.345849\pi\)
0.465572 + 0.885010i \(0.345849\pi\)
\(684\) 2.59460 2.59460i 0.00379327 0.00379327i
\(685\) 2.81766 + 2.81766i 0.00411338 + 0.00411338i
\(686\) 284.117 284.117i 0.414164 0.414164i
\(687\) −39.8544 −0.0580122
\(688\) −328.115 + 328.115i −0.476911 + 0.476911i
\(689\) 166.379i 0.241479i
\(690\) −32.5960 −0.0472406
\(691\) −440.160 −0.636990 −0.318495 0.947925i \(-0.603177\pi\)
−0.318495 + 0.947925i \(0.603177\pi\)
\(692\) 85.8112 0.124005
\(693\) −16.5758 16.5758i −0.0239189 0.0239189i
\(694\) −80.9861 80.9861i −0.116695 0.116695i
\(695\) 109.459i 0.157495i
\(696\) −311.300 693.876i −0.447271 0.996948i
\(697\) −380.815 −0.546363
\(698\) −306.653 + 306.653i −0.439331 + 0.439331i
\(699\) 505.416 505.416i 0.723056 0.723056i
\(700\) 334.581i 0.477973i
\(701\) 330.622i 0.471643i 0.971796 + 0.235822i \(0.0757781\pi\)
−0.971796 + 0.235822i \(0.924222\pi\)
\(702\) 409.776i 0.583727i
\(703\) −536.759 −0.763526
\(704\) 721.633 + 721.633i 1.02505 + 1.02505i
\(705\) 88.4262i 0.125427i
\(706\) −170.091 170.091i −0.240922 0.240922i
\(707\) −309.457 + 309.457i −0.437705 + 0.437705i
\(708\) 51.8968 + 51.8968i 0.0733005 + 0.0733005i
\(709\) 740.213i 1.04402i −0.852938 0.522012i \(-0.825182\pi\)
0.852938 0.522012i \(-0.174818\pi\)
\(710\) −17.8919 + 17.8919i −0.0251998 + 0.0251998i
\(711\) −1.76092 1.76092i −0.00247668 0.00247668i
\(712\) 1465.60 2.05843
\(713\) −450.270 + 450.270i −0.631515 + 0.631515i
\(714\) 362.923 + 362.923i 0.508296 + 0.508296i
\(715\) −55.5733 + 55.5733i −0.0777249 + 0.0777249i
\(716\) −488.885 −0.682801
\(717\) −834.160 + 834.160i −1.16340 + 1.16340i
\(718\) 705.920i 0.983175i
\(719\) −177.916 −0.247449 −0.123725 0.992317i \(-0.539484\pi\)
−0.123725 + 0.992317i \(0.539484\pi\)
\(720\) 0.577629 0.000802263
\(721\) 498.876 0.691922
\(722\) −230.562 230.562i −0.319337 0.319337i
\(723\) −350.710 350.710i −0.485076 0.485076i
\(724\) 292.517i 0.404029i
\(725\) −293.931 655.160i −0.405422 0.903670i
\(726\) −625.608 −0.861719
\(727\) −322.555 + 322.555i −0.443680 + 0.443680i −0.893247 0.449567i \(-0.851578\pi\)
0.449567 + 0.893247i \(0.351578\pi\)
\(728\) 497.465 497.465i 0.683330 0.683330i
\(729\) 713.757i 0.979090i
\(730\) 23.3934i 0.0320457i
\(731\) 974.443i 1.33303i
\(732\) 324.780 0.443689
\(733\) 691.012 + 691.012i 0.942718 + 0.942718i 0.998446 0.0557278i \(-0.0177479\pi\)
−0.0557278 + 0.998446i \(0.517748\pi\)
\(734\) 524.609i 0.714726i
\(735\) −17.2417 17.2417i −0.0234580 0.0234580i
\(736\) −251.373 + 251.373i −0.341539 + 0.341539i
\(737\) −1512.16 1512.16i −2.05178 2.05178i
\(738\) 7.67059i 0.0103938i
\(739\) −80.9996 + 80.9996i −0.109607 + 0.109607i −0.759783 0.650176i \(-0.774695\pi\)
0.650176 + 0.759783i \(0.274695\pi\)
\(740\) 25.5143 + 25.5143i 0.0344788 + 0.0344788i
\(741\) −369.557 −0.498727
\(742\) −144.633 + 144.633i −0.194923 + 0.194923i
\(743\) −27.4691 27.4691i −0.0369705 0.0369705i 0.688380 0.725350i \(-0.258322\pi\)
−0.725350 + 0.688380i \(0.758322\pi\)
\(744\) 818.782 818.782i 1.10051 1.10051i
\(745\) 63.1533 0.0847696
\(746\) 543.766 543.766i 0.728909 0.728909i
\(747\) 11.6293i 0.0155681i
\(748\) −366.656 −0.490182
\(749\) −393.098 −0.524831
\(750\) 112.472 0.149963
\(751\) 370.129 + 370.129i 0.492849 + 0.492849i 0.909203 0.416354i \(-0.136692\pi\)
−0.416354 + 0.909203i \(0.636692\pi\)
\(752\) 275.785 + 275.785i 0.366735 + 0.366735i
\(753\) 565.709i 0.751273i
\(754\) −158.190 + 415.627i −0.209801 + 0.551229i
\(755\) −29.0267 −0.0384460
\(756\) 255.317 255.317i 0.337721 0.337721i
\(757\) 361.762 361.762i 0.477889 0.477889i −0.426567 0.904456i \(-0.640277\pi\)
0.904456 + 0.426567i \(0.140277\pi\)
\(758\) 160.160i 0.211293i
\(759\) 699.517i 0.921630i
\(760\) 51.3482i 0.0675634i
\(761\) 955.440 1.25551 0.627753 0.778413i \(-0.283975\pi\)
0.627753 + 0.778413i \(0.283975\pi\)
\(762\) 98.9819 + 98.9819i 0.129897 + 0.129897i
\(763\) 663.582i 0.869702i
\(764\) 78.2809 + 78.2809i 0.102462 + 0.102462i
\(765\) −0.857727 + 0.857727i −0.00112121 + 0.00112121i
\(766\) 606.154 + 606.154i 0.791324 + 0.791324i
\(767\) 145.712i 0.189977i
\(768\) 550.576 550.576i 0.716896 0.716896i
\(769\) −881.047 881.047i −1.14570 1.14570i −0.987388 0.158316i \(-0.949393\pi\)
−0.158316 0.987388i \(-0.550607\pi\)
\(770\) −96.6195 −0.125480
\(771\) 243.466 243.466i 0.315779 0.315779i
\(772\) 83.2796 + 83.2796i 0.107875 + 0.107875i
\(773\) −46.5963 + 46.5963i −0.0602799 + 0.0602799i −0.736604 0.676324i \(-0.763572\pi\)
0.676324 + 0.736604i \(0.263572\pi\)
\(774\) −19.6278 −0.0253589
\(775\) 773.097 773.097i 0.997545 0.997545i
\(776\) 410.959i 0.529586i
\(777\) 1083.94 1.39503
\(778\) 240.124 0.308643
\(779\) 337.092 0.432724
\(780\) 17.5665 + 17.5665i 0.0225212 + 0.0225212i
\(781\) −383.963 383.963i −0.491630 0.491630i
\(782\) 301.915i 0.386080i