Properties

Label 29.3.c.a.12.2
Level $29$
Weight $3$
Character 29.12
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 12.2
Root \(-3.22189i\) of defining polynomial
Character \(\chi\) \(=\) 29.12
Dual form 29.3.c.a.17.2

$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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 0.383759 0.923433i \(-0.374629\pi\)
−0.923433 + 0.383759i \(0.874629\pi\)
\(3\) −2.14254 2.14254i −0.714181 0.714181i 0.253226 0.967407i \(-0.418508\pi\)
−0.967407 + 0.253226i \(0.918508\pi\)
\(4\) 1.67001i 0.417502i
\(5\) 0.488689i 0.0977379i −0.998805 0.0488689i \(-0.984438\pi\)
0.998805 0.0488689i \(-0.0155617\pi\)
\(6\) 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 0.999565 + 0.0294830i \(0.00938610\pi\)
0.0294830 + 0.999565i \(0.490614\pi\)
\(12\) −3.57807 + 3.57807i −0.298172 + 0.298172i
\(13\) 10.0463i 0.772790i −0.922333 0.386395i \(-0.873720\pi\)
0.922333 0.386395i \(-0.126280\pi\)
\(14\) −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 0.361790 0.932260i \(-0.382166\pi\)
−0.932260 + 0.361790i \(0.882166\pi\)
\(18\) 0.195342 0.195342i 0.0108524 0.0108524i
\(19\) 8.58453 + 8.58453i 0.451818 + 0.451818i 0.895957 0.444140i \(-0.146491\pi\)
−0.444140 + 0.895957i \(0.646491\pi\)
\(20\) −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 0.999974 + 0.00719198i \(0.00228930\pi\)
0.00719198 + 0.999974i \(0.497711\pi\)
\(32\) 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 −0.989498 0.144548i \(-0.953827\pi\)
0.144548 + 0.989498i \(0.453827\pi\)
\(38\) 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 −0.425900 0.904770i \(-0.640042\pi\)
0.904770 + 0.425900i \(0.140042\pi\)
\(42\) 37.4225i 0.891013i
\(43\) −50.2394 50.2394i −1.16836 1.16836i −0.982594 0.185764i \(-0.940524\pi\)
−0.185764 0.982594i \(-0.559476\pi\)
\(44\) 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 −0.0968555 0.995298i \(-0.530878\pi\)
0.995298 + 0.0968555i \(0.0308785\pi\)
\(48\) −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 0.229334 0.973348i \(-0.426345\pi\)
−0.973348 + 0.229334i \(0.926345\pi\)
\(62\) 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 \(0.475060\pi\)
−0.0782703 + 0.996932i \(0.524940\pi\)
\(68\) −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 \(0.0767790\pi\)
−0.971050 + 0.238876i \(0.923221\pi\)
\(72\) −1.10759 1.10759i −0.0153832 0.0153832i
\(73\) −22.1752 + 22.1752i −0.303770 + 0.303770i −0.842487 0.538717i \(-0.818909\pi\)
0.538717 + 0.842487i \(0.318909\pi\)
\(74\) 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 0.766001 0.642839i \(-0.222244\pi\)
−0.642839 + 0.766001i \(0.722244\pi\)
\(80\) 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 −0.890590 0.454808i \(-0.849708\pi\)
−0.454808 0.890590i \(-0.650292\pi\)
\(90\) −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 −0.858669 0.512530i \(-0.828708\pi\)
0.512530 + 0.858669i \(0.328708\pi\)
\(98\) −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 0.491948 0.870624i \(-0.336285\pi\)
−0.870624 + 0.491948i \(0.836285\pi\)
\(102\) 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 \(0.122772\pi\)
−0.926536 + 0.376207i \(0.877228\pi\)
\(110\) −11.9413 −0.108558
\(111\) 133.965 1.20689
\(112\) 52.8437 0.471819
\(113\) 0.444855 0.444855i 0.00393677 0.00393677i −0.705136 0.709072i \(-0.749114\pi\)
0.709072 + 0.705136i \(0.249114\pi\)
\(114\) −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 0.617813 0.786325i \(-0.288019\pi\)
−0.786325 + 0.617813i \(0.788019\pi\)
\(128\) 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 −0.862491 0.506073i \(-0.831097\pi\)
0.506073 + 0.862491i \(0.331097\pi\)
\(132\) −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 0.727837 0.685751i \(-0.240526\pi\)
−0.685751 + 0.727837i \(0.740526\pi\)
\(138\) 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 \(0.142777\pi\)
−0.901078 + 0.433658i \(0.857223\pi\)
\(150\) 114.523i 0.763487i
\(151\) 59.3971i 0.393359i −0.980468 0.196679i \(-0.936984\pi\)
0.980468 0.196679i \(-0.0630158\pi\)
\(152\) −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 0.450374 0.892840i \(-0.351291\pi\)
0.892840 0.450374i \(-0.148709\pi\)
\(158\) 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 −0.997731 0.0673260i \(-0.978553\pi\)
0.0673260 + 0.997731i \(0.478553\pi\)
\(164\) −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 \(-0.886055\pi\)
0.936611 0.350371i \(-0.113945\pi\)
\(168\) 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 \(0.0474469\pi\)
−0.988911 + 0.148508i \(0.952553\pi\)
\(174\) −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 \(-0.695237\pi\)
0.575615 0.817721i \(-0.304763\pi\)
\(180\) 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 0.819086 0.573670i \(-0.194481\pi\)
−0.573670 + 0.819086i \(0.694481\pi\)
\(192\) −136.590 + 136.590i −0.711404 + 0.711404i
\(193\) 49.8678 + 49.8678i 0.258382 + 0.258382i 0.824396 0.566014i \(-0.191515\pi\)
−0.566014 + 0.824396i \(0.691515\pi\)
\(194\) 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 −0.517928 0.855424i \(-0.673296\pi\)
0.855424 + 0.517928i \(0.173296\pi\)
\(212\) 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 −0.686508 0.727122i \(-0.740857\pi\)
0.727122 + 0.686508i \(0.240857\pi\)
\(230\) 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 \(-0.889707\pi\)
0.940569 0.339603i \(-0.110293\pi\)
\(242\) 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 0.393399 0.919368i \(-0.371299\pi\)
−0.919368 + 0.393399i \(0.871299\pi\)
\(252\) 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 0.997802 + 0.0662687i \(0.0211095\pi\)
0.0662687 + 0.997802i \(0.478891\pi\)
\(264\) 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 0.135061 0.990837i \(-0.456877\pi\)
0.990837 0.135061i \(-0.0431231\pi\)
\(270\) 19.9331i 0.0738263i
\(271\) −222.952 + 222.952i −0.822702 + 0.822702i −0.986495 0.163793i \(-0.947627\pi\)
0.163793 + 0.986495i \(0.447627\pi\)
\(272\) −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 \(0.0537382\pi\)
−0.985783 + 0.168023i \(0.946262\pi\)
\(284\) 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 0.742454 0.669898i \(-0.233662\pi\)
−0.669898 + 0.742454i \(0.733662\pi\)
\(294\) 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 0.318715 0.947850i \(-0.396749\pi\)
−0.947850 + 0.318715i \(0.896749\pi\)
\(308\) 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 0.864856 0.502021i \(-0.167410\pi\)
−0.502021 + 0.864856i \(0.667410\pi\)
\(312\) 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 −0.137553 0.990494i \(-0.543924\pi\)
0.990494 + 0.137553i \(0.0439237\pi\)
\(318\) 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 −0.797836 0.602874i \(-0.794022\pi\)
0.602874 + 0.797836i \(0.294022\pi\)
\(332\) 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 −0.776315 0.630345i \(-0.782914\pi\)
0.630345 + 0.776315i \(0.282914\pi\)
\(338\) −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 \(-0.965518\pi\)
0.994138 0.108116i \(-0.0344817\pi\)
\(348\) −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 \(-0.928346\pi\)
0.974770 0.223211i \(-0.0716538\pi\)
\(354\) 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 0.0854467 0.996343i \(-0.472768\pi\)
−0.996343 + 0.0854467i \(0.972768\pi\)
\(360\) −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 0.955894 0.293712i \(-0.0948906\pi\)
−0.293712 + 0.955894i \(0.594891\pi\)
\(368\) −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 0.602420 0.798179i \(-0.294203\pi\)
−0.798179 + 0.602420i \(0.794203\pi\)
\(380\) −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 \(0.261950\pi\)
−0.680068 + 0.733149i \(0.738050\pi\)
\(384\) −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 −0.835478 0.549525i \(-0.814809\pi\)
0.549525 + 0.835478i \(0.314809\pi\)
\(390\) 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 −0.994540 0.104353i \(-0.966723\pi\)
−0.104353 0.994540i \(-0.533277\pi\)
\(410\) 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 \(0.246477\pi\)
−0.714889 + 0.699238i \(0.753523\pi\)
\(420\) 14.1479 + 14.1479i 0.0336855 + 0.0336855i
\(421\) −37.5863 + 37.5863i −0.0892786 + 0.0892786i −0.750336 0.661057i \(-0.770108\pi\)
0.661057 + 0.750336i \(0.270108\pi\)
\(422\) −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 −0.414342 0.910121i \(-0.635988\pi\)
0.910121 + 0.414342i \(0.135988\pi\)
\(434\) 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 \(-0.857499\pi\)
0.901453 0.432877i \(-0.142501\pi\)
\(440\) 67.7076i 0.153881i
\(441\) 2.98024i 0.00675792i
\(442\) 210.319 0.475835
\(443\) −248.852 + 248.852i −0.561743 + 0.561743i −0.929802 0.368059i \(-0.880022\pi\)
0.368059 + 0.929802i \(0.380022\pi\)
\(444\) 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 0.840293 0.542133i \(-0.182383\pi\)
−0.542133 + 0.840293i \(0.682383\pi\)
\(450\) 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 \(-0.825486\pi\)
0.853436 0.521197i \(-0.174514\pi\)
\(458\) −20.0775 −0.0438372
\(459\) 366.489 0.798452
\(460\) 11.7696 0.0255861
\(461\) −478.069 + 478.069i −1.03703 + 1.03703i −0.0377379 + 0.999288i \(0.512015\pi\)
−0.999288 + 0.0377379i \(0.987985\pi\)
\(462\) −423.605 + 423.605i −0.916895 + 0.916895i
\(463\) 144.158i 0.311357i 0.987808 + 0.155678i \(0.0497564\pi\)
−0.987808 + 0.155678i \(0.950244\pi\)
\(464\) −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 0.635828 0.771830i \(-0.280659\pi\)
−0.771830 + 0.635828i \(0.780659\pi\)
\(468\) 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 −0.733615 0.679565i \(-0.762169\pi\)
0.679565 + 0.733615i \(0.262169\pi\)
\(480\) −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 −0.478280 0.878207i \(-0.658740\pi\)
0.878207 + 0.478280i \(0.158740\pi\)
\(492\) 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 \(-0.827883\pi\)
0.857337 0.514755i \(-0.172117\pi\)
\(500\) −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 −0.484995 0.874517i \(-0.661179\pi\)
0.874517 + 0.484995i \(0.161179\pi\)
\(504\) −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 \(0.340417\pi\)
−0.480604 + 0.876938i \(0.659583\pi\)
\(522\) 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 0.691066 0.722792i \(-0.257141\pi\)
−0.722792 + 0.691066i \(0.757141\pi\)
\(542\) 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 \(-0.827192\pi\)
0.856218 0.516614i \(-0.172808\pi\)
\(558\) 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 −0.160391 0.987054i \(-0.551276\pi\)
0.987054 + 0.160391i \(0.0512756\pi\)
\(564\) 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 −0.237809 0.971312i \(-0.576429\pi\)
0.971312 + 0.237809i \(0.0764292\pi\)
\(570\) 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 −0.826944 0.562285i \(-0.809922\pi\)
0.562285 + 0.826944i \(0.309922\pi\)
\(578\) −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 \(0.397136\pi\)
−0.317563 + 0.948237i \(0.602864\pi\)
\(594\) 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 0.868040 0.496495i \(-0.165380\pi\)
−0.496495 + 0.868040i \(0.665380\pi\)
\(600\) 649.347 1.08224
\(601\) −196.657 196.657i −0.327216 0.327216i 0.524311 0.851527i \(-0.324323\pi\)
−0.851527 + 0.524311i \(0.824323\pi\)
\(602\) 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 −0.0930047 + 0.995666i \(0.529647\pi\)
−0.995666 + 0.0930047i \(0.970353\pi\)
\(608\) 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 \(0.0785224\pi\)
−0.969727 + 0.244191i \(0.921478\pi\)
\(614\) 416.941i 0.679057i
\(615\) 41.1145i 0.0668528i
\(616\) −1121.03 −1.81985
\(617\) −419.542 + 419.542i −0.679972 + 0.679972i −0.959994 0.280022i \(-0.909658\pi\)
0.280022 + 0.959994i \(0.409658\pi\)
\(618\) 285.169i 0.461439i
\(619\) 243.311 243.311i 0.393072 0.393072i −0.482709 0.875781i \(-0.660347\pi\)
0.875781 + 0.482709i \(0.160347\pi\)
\(620\) −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 \(0.0243181\pi\)
−0.997083 + 0.0763233i \(0.975682\pi\)
\(632\) −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 0.347567 0.937655i \(-0.387008\pi\)
−0.937655 + 0.347567i \(0.887008\pi\)
\(642\) 224.704i 0.350007i
\(643\) 258.453i 0.401949i 0.979597 + 0.200974i \(0.0644108\pi\)
−0.979597 + 0.200974i \(0.935589\pi\)
\(644\) 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 \(0.144904\pi\)
−0.898160 + 0.439668i \(0.855096\pi\)
\(648\) −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 0.280645 0.959812i \(-0.409452\pi\)
0.959812 0.280645i \(-0.0905485\pi\)
\(654\) −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 0.992433 0.122789i \(-0.0391839\pi\)
−0.122789 + 0.992433i \(0.539184\pi\)
\(660\) 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 \(-0.905037\pi\)
0.955827 0.293930i \(-0.0949633\pi\)
\(674\) 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 −0.816174 0.577806i \(-0.803909\pi\)
0.577806 + 0.816174i \(0.303909\pi\)
\(678\) 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 \(-0.924222\pi\)
0.971796 0.235822i \(-0.0757781\pi\)
\(702\) 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 \(0.174818\pi\)
−0.852938 + 0.522012i \(0.825182\pi\)
\(710\) −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 0.449567 0.893247i \(-0.351578\pi\)
−0.893247 + 0.449567i \(0.851578\pi\)
\(728\) 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 −0.0557278 0.998446i \(-0.517748\pi\)
0.998446 + 0.0557278i \(0.0177479\pi\)
\(734\) 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 0.650176 0.759783i \(-0.274695\pi\)
−0.759783 + 0.650176i \(0.774695\pi\)
\(740\) 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 −0.725350 0.688380i \(-0.758322\pi\)
0.688380 + 0.725350i \(0.258322\pi\)
\(744\) 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 −0.416354 0.909203i \(-0.636692\pi\)
0.909203 + 0.416354i \(0.136692\pi\)
\(752\) 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 0.904456 0.426567i \(-0.140277\pi\)
−0.426567 + 0.904456i \(0.640277\pi\)
\(758\) 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 −0.158316 + 0.987388i \(0.550607\pi\)
−0.987388 + 0.158316i \(0.949393\pi\)
\(770\) −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 0.676324 0.736604i \(-0.263572\pi\)
−0.736604 + 0.676324i \(0.763572\pi\)
\(774\) −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