Properties

Label 1148.2.k.b.337.6
Level $1148$
Weight $2$
Character 1148.337
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 337.6
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.898855 - 0.898855i) q^{3} +3.17533i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.38412i q^{9} +O(q^{10})\) \(q+(-0.898855 - 0.898855i) q^{3} +3.17533i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.38412i q^{9} +(-3.23064 - 3.23064i) q^{11} +(3.60315 + 3.60315i) q^{13} +(2.85416 - 2.85416i) q^{15} +(-4.90397 + 4.90397i) q^{17} +(1.76734 - 1.76734i) q^{19} +1.27117i q^{21} +7.82290 q^{23} -5.08271 q^{25} +(-3.94069 + 3.94069i) q^{27} +(-1.94379 - 1.94379i) q^{29} -10.1342 q^{31} +5.80775i q^{33} +(2.24530 - 2.24530i) q^{35} -10.4792 q^{37} -6.47742i q^{39} +(-6.28688 + 1.21455i) q^{41} -2.44432i q^{43} +4.39504 q^{45} +(-3.19148 + 3.19148i) q^{47} +1.00000i q^{49} +8.81592 q^{51} +(-0.796549 - 0.796549i) q^{53} +(10.2583 - 10.2583i) q^{55} -3.17716 q^{57} -11.7853 q^{59} -14.3630i q^{61} +(-0.978721 + 0.978721i) q^{63} +(-11.4412 + 11.4412i) q^{65} +(-4.45771 + 4.45771i) q^{67} +(-7.03165 - 7.03165i) q^{69} +(0.431860 + 0.431860i) q^{71} +6.43168i q^{73} +(4.56862 + 4.56862i) q^{75} +4.56881i q^{77} +(0.490820 + 0.490820i) q^{79} +2.93185 q^{81} -2.68754 q^{83} +(-15.5717 - 15.5717i) q^{85} +3.49437i q^{87} +(9.23786 + 9.23786i) q^{89} -5.09563i q^{91} +(9.10915 + 9.10915i) q^{93} +(5.61187 + 5.61187i) q^{95} +(5.19074 - 5.19074i) q^{97} +(-4.47159 + 4.47159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.898855 0.898855i −0.518954 0.518954i 0.398301 0.917255i \(-0.369600\pi\)
−0.917255 + 0.398301i \(0.869600\pi\)
\(4\) 0 0
\(5\) 3.17533i 1.42005i 0.704177 + 0.710025i \(0.251316\pi\)
−0.704177 + 0.710025i \(0.748684\pi\)
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 0 0
\(9\) 1.38412i 0.461373i
\(10\) 0 0
\(11\) −3.23064 3.23064i −0.974074 0.974074i 0.0255985 0.999672i \(-0.491851\pi\)
−0.999672 + 0.0255985i \(0.991851\pi\)
\(12\) 0 0
\(13\) 3.60315 + 3.60315i 0.999335 + 0.999335i 1.00000 0.000664865i \(-0.000211633\pi\)
−0.000664865 1.00000i \(0.500212\pi\)
\(14\) 0 0
\(15\) 2.85416 2.85416i 0.736941 0.736941i
\(16\) 0 0
\(17\) −4.90397 + 4.90397i −1.18939 + 1.18939i −0.212151 + 0.977237i \(0.568047\pi\)
−0.977237 + 0.212151i \(0.931953\pi\)
\(18\) 0 0
\(19\) 1.76734 1.76734i 0.405455 0.405455i −0.474695 0.880150i \(-0.657442\pi\)
0.880150 + 0.474695i \(0.157442\pi\)
\(20\) 0 0
\(21\) 1.27117i 0.277393i
\(22\) 0 0
\(23\) 7.82290 1.63119 0.815593 0.578625i \(-0.196411\pi\)
0.815593 + 0.578625i \(0.196411\pi\)
\(24\) 0 0
\(25\) −5.08271 −1.01654
\(26\) 0 0
\(27\) −3.94069 + 3.94069i −0.758386 + 0.758386i
\(28\) 0 0
\(29\) −1.94379 1.94379i −0.360953 0.360953i 0.503211 0.864164i \(-0.332152\pi\)
−0.864164 + 0.503211i \(0.832152\pi\)
\(30\) 0 0
\(31\) −10.1342 −1.82015 −0.910075 0.414443i \(-0.863977\pi\)
−0.910075 + 0.414443i \(0.863977\pi\)
\(32\) 0 0
\(33\) 5.80775i 1.01100i
\(34\) 0 0
\(35\) 2.24530 2.24530i 0.379524 0.379524i
\(36\) 0 0
\(37\) −10.4792 −1.72277 −0.861387 0.507949i \(-0.830404\pi\)
−0.861387 + 0.507949i \(0.830404\pi\)
\(38\) 0 0
\(39\) 6.47742i 1.03722i
\(40\) 0 0
\(41\) −6.28688 + 1.21455i −0.981846 + 0.189680i
\(42\) 0 0
\(43\) 2.44432i 0.372755i −0.982478 0.186378i \(-0.940325\pi\)
0.982478 0.186378i \(-0.0596748\pi\)
\(44\) 0 0
\(45\) 4.39504 0.655173
\(46\) 0 0
\(47\) −3.19148 + 3.19148i −0.465525 + 0.465525i −0.900461 0.434936i \(-0.856771\pi\)
0.434936 + 0.900461i \(0.356771\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 8.81592 1.23448
\(52\) 0 0
\(53\) −0.796549 0.796549i −0.109414 0.109414i 0.650280 0.759695i \(-0.274652\pi\)
−0.759695 + 0.650280i \(0.774652\pi\)
\(54\) 0 0
\(55\) 10.2583 10.2583i 1.38323 1.38323i
\(56\) 0 0
\(57\) −3.17716 −0.420825
\(58\) 0 0
\(59\) −11.7853 −1.53431 −0.767156 0.641461i \(-0.778329\pi\)
−0.767156 + 0.641461i \(0.778329\pi\)
\(60\) 0 0
\(61\) 14.3630i 1.83899i −0.393101 0.919495i \(-0.628598\pi\)
0.393101 0.919495i \(-0.371402\pi\)
\(62\) 0 0
\(63\) −0.978721 + 0.978721i −0.123307 + 0.123307i
\(64\) 0 0
\(65\) −11.4412 + 11.4412i −1.41911 + 1.41911i
\(66\) 0 0
\(67\) −4.45771 + 4.45771i −0.544596 + 0.544596i −0.924873 0.380276i \(-0.875829\pi\)
0.380276 + 0.924873i \(0.375829\pi\)
\(68\) 0 0
\(69\) −7.03165 7.03165i −0.846511 0.846511i
\(70\) 0 0
\(71\) 0.431860 + 0.431860i 0.0512524 + 0.0512524i 0.732268 0.681016i \(-0.238462\pi\)
−0.681016 + 0.732268i \(0.738462\pi\)
\(72\) 0 0
\(73\) 6.43168i 0.752772i 0.926463 + 0.376386i \(0.122833\pi\)
−0.926463 + 0.376386i \(0.877167\pi\)
\(74\) 0 0
\(75\) 4.56862 + 4.56862i 0.527538 + 0.527538i
\(76\) 0 0
\(77\) 4.56881i 0.520664i
\(78\) 0 0
\(79\) 0.490820 + 0.490820i 0.0552215 + 0.0552215i 0.734178 0.678957i \(-0.237568\pi\)
−0.678957 + 0.734178i \(0.737568\pi\)
\(80\) 0 0
\(81\) 2.93185 0.325761
\(82\) 0 0
\(83\) −2.68754 −0.294996 −0.147498 0.989062i \(-0.547122\pi\)
−0.147498 + 0.989062i \(0.547122\pi\)
\(84\) 0 0
\(85\) −15.5717 15.5717i −1.68899 1.68899i
\(86\) 0 0
\(87\) 3.49437i 0.374636i
\(88\) 0 0
\(89\) 9.23786 + 9.23786i 0.979211 + 0.979211i 0.999788 0.0205770i \(-0.00655032\pi\)
−0.0205770 + 0.999788i \(0.506550\pi\)
\(90\) 0 0
\(91\) 5.09563i 0.534167i
\(92\) 0 0
\(93\) 9.10915 + 9.10915i 0.944575 + 0.944575i
\(94\) 0 0
\(95\) 5.61187 + 5.61187i 0.575766 + 0.575766i
\(96\) 0 0
\(97\) 5.19074 5.19074i 0.527040 0.527040i −0.392649 0.919689i \(-0.628441\pi\)
0.919689 + 0.392649i \(0.128441\pi\)
\(98\) 0 0
\(99\) −4.47159 + 4.47159i −0.449412 + 0.449412i
\(100\) 0 0
\(101\) −9.45064 + 9.45064i −0.940374 + 0.940374i −0.998320 0.0579460i \(-0.981545\pi\)
0.0579460 + 0.998320i \(0.481545\pi\)
\(102\) 0 0
\(103\) 4.04846i 0.398906i −0.979907 0.199453i \(-0.936083\pi\)
0.979907 0.199453i \(-0.0639165\pi\)
\(104\) 0 0
\(105\) −4.03639 −0.393911
\(106\) 0 0
\(107\) −17.4119 −1.68327 −0.841634 0.540048i \(-0.818406\pi\)
−0.841634 + 0.540048i \(0.818406\pi\)
\(108\) 0 0
\(109\) 0.978729 0.978729i 0.0937452 0.0937452i −0.658679 0.752424i \(-0.728884\pi\)
0.752424 + 0.658679i \(0.228884\pi\)
\(110\) 0 0
\(111\) 9.41930 + 9.41930i 0.894041 + 0.894041i
\(112\) 0 0
\(113\) 5.12924 0.482518 0.241259 0.970461i \(-0.422440\pi\)
0.241259 + 0.970461i \(0.422440\pi\)
\(114\) 0 0
\(115\) 24.8403i 2.31637i
\(116\) 0 0
\(117\) 4.98720 4.98720i 0.461066 0.461066i
\(118\) 0 0
\(119\) 6.93527 0.635755
\(120\) 0 0
\(121\) 9.87403i 0.897639i
\(122\) 0 0
\(123\) 6.74270 + 4.55929i 0.607968 + 0.411098i
\(124\) 0 0
\(125\) 0.262626i 0.0234900i
\(126\) 0 0
\(127\) −0.889564 −0.0789360 −0.0394680 0.999221i \(-0.512566\pi\)
−0.0394680 + 0.999221i \(0.512566\pi\)
\(128\) 0 0
\(129\) −2.19709 + 2.19709i −0.193443 + 0.193443i
\(130\) 0 0
\(131\) 10.6279i 0.928565i 0.885687 + 0.464283i \(0.153688\pi\)
−0.885687 + 0.464283i \(0.846312\pi\)
\(132\) 0 0
\(133\) −2.49939 −0.216725
\(134\) 0 0
\(135\) −12.5130 12.5130i −1.07695 1.07695i
\(136\) 0 0
\(137\) 0.0781818 0.0781818i 0.00667952 0.00667952i −0.703759 0.710439i \(-0.748497\pi\)
0.710439 + 0.703759i \(0.248497\pi\)
\(138\) 0 0
\(139\) 9.09143 0.771125 0.385563 0.922682i \(-0.374007\pi\)
0.385563 + 0.922682i \(0.374007\pi\)
\(140\) 0 0
\(141\) 5.73735 0.483172
\(142\) 0 0
\(143\) 23.2810i 1.94685i
\(144\) 0 0
\(145\) 6.17217 6.17217i 0.512571 0.512571i
\(146\) 0 0
\(147\) 0.898855 0.898855i 0.0741363 0.0741363i
\(148\) 0 0
\(149\) −11.3092 + 11.3092i −0.926484 + 0.926484i −0.997477 0.0709928i \(-0.977383\pi\)
0.0709928 + 0.997477i \(0.477383\pi\)
\(150\) 0 0
\(151\) −1.64619 1.64619i −0.133965 0.133965i 0.636945 0.770910i \(-0.280198\pi\)
−0.770910 + 0.636945i \(0.780198\pi\)
\(152\) 0 0
\(153\) 6.78769 + 6.78769i 0.548752 + 0.548752i
\(154\) 0 0
\(155\) 32.1793i 2.58471i
\(156\) 0 0
\(157\) 7.30693 + 7.30693i 0.583157 + 0.583157i 0.935769 0.352613i \(-0.114707\pi\)
−0.352613 + 0.935769i \(0.614707\pi\)
\(158\) 0 0
\(159\) 1.43196i 0.113562i
\(160\) 0 0
\(161\) −5.53162 5.53162i −0.435953 0.435953i
\(162\) 0 0
\(163\) −3.53525 −0.276902 −0.138451 0.990369i \(-0.544212\pi\)
−0.138451 + 0.990369i \(0.544212\pi\)
\(164\) 0 0
\(165\) −18.4415 −1.43567
\(166\) 0 0
\(167\) 10.1679 + 10.1679i 0.786816 + 0.786816i 0.980971 0.194155i \(-0.0621964\pi\)
−0.194155 + 0.980971i \(0.562196\pi\)
\(168\) 0 0
\(169\) 12.9654i 0.997341i
\(170\) 0 0
\(171\) −2.44621 2.44621i −0.187066 0.187066i
\(172\) 0 0
\(173\) 11.5873i 0.880964i −0.897761 0.440482i \(-0.854807\pi\)
0.897761 0.440482i \(-0.145193\pi\)
\(174\) 0 0
\(175\) 3.59402 + 3.59402i 0.271682 + 0.271682i
\(176\) 0 0
\(177\) 10.5932 + 10.5932i 0.796237 + 0.796237i
\(178\) 0 0
\(179\) 11.3428 11.3428i 0.847797 0.847797i −0.142061 0.989858i \(-0.545373\pi\)
0.989858 + 0.142061i \(0.0453728\pi\)
\(180\) 0 0
\(181\) 11.4097 11.4097i 0.848076 0.848076i −0.141817 0.989893i \(-0.545294\pi\)
0.989893 + 0.141817i \(0.0452944\pi\)
\(182\) 0 0
\(183\) −12.9102 + 12.9102i −0.954351 + 0.954351i
\(184\) 0 0
\(185\) 33.2750i 2.44643i
\(186\) 0 0
\(187\) 31.6859 2.31710
\(188\) 0 0
\(189\) 5.57297 0.405374
\(190\) 0 0
\(191\) 10.7086 10.7086i 0.774846 0.774846i −0.204103 0.978949i \(-0.565428\pi\)
0.978949 + 0.204103i \(0.0654279\pi\)
\(192\) 0 0
\(193\) −1.24930 1.24930i −0.0899268 0.0899268i 0.660712 0.750639i \(-0.270254\pi\)
−0.750639 + 0.660712i \(0.770254\pi\)
\(194\) 0 0
\(195\) 20.5679 1.47290
\(196\) 0 0
\(197\) 8.32237i 0.592945i −0.955041 0.296472i \(-0.904190\pi\)
0.955041 0.296472i \(-0.0958103\pi\)
\(198\) 0 0
\(199\) 16.7332 16.7332i 1.18619 1.18619i 0.208073 0.978113i \(-0.433281\pi\)
0.978113 0.208073i \(-0.0667190\pi\)
\(200\) 0 0
\(201\) 8.01368 0.565241
\(202\) 0 0
\(203\) 2.74893i 0.192937i
\(204\) 0 0
\(205\) −3.85659 19.9629i −0.269356 1.39427i
\(206\) 0 0
\(207\) 10.8278i 0.752586i
\(208\) 0 0
\(209\) −11.4192 −0.789886
\(210\) 0 0
\(211\) −8.31690 + 8.31690i −0.572559 + 0.572559i −0.932843 0.360284i \(-0.882680\pi\)
0.360284 + 0.932843i \(0.382680\pi\)
\(212\) 0 0
\(213\) 0.776360i 0.0531953i
\(214\) 0 0
\(215\) 7.76151 0.529331
\(216\) 0 0
\(217\) 7.16594 + 7.16594i 0.486456 + 0.486456i
\(218\) 0 0
\(219\) 5.78115 5.78115i 0.390654 0.390654i
\(220\) 0 0
\(221\) −35.3395 −2.37719
\(222\) 0 0
\(223\) −7.07610 −0.473851 −0.236925 0.971528i \(-0.576140\pi\)
−0.236925 + 0.971528i \(0.576140\pi\)
\(224\) 0 0
\(225\) 7.03508i 0.469005i
\(226\) 0 0
\(227\) 15.8504 15.8504i 1.05203 1.05203i 0.0534569 0.998570i \(-0.482976\pi\)
0.998570 0.0534569i \(-0.0170240\pi\)
\(228\) 0 0
\(229\) −10.9365 + 10.9365i −0.722704 + 0.722704i −0.969155 0.246452i \(-0.920735\pi\)
0.246452 + 0.969155i \(0.420735\pi\)
\(230\) 0 0
\(231\) 4.10670 4.10670i 0.270201 0.270201i
\(232\) 0 0
\(233\) 7.18801 + 7.18801i 0.470902 + 0.470902i 0.902207 0.431304i \(-0.141946\pi\)
−0.431304 + 0.902207i \(0.641946\pi\)
\(234\) 0 0
\(235\) −10.1340 10.1340i −0.661068 0.661068i
\(236\) 0 0
\(237\) 0.882351i 0.0573149i
\(238\) 0 0
\(239\) 12.0190 + 12.0190i 0.777445 + 0.777445i 0.979396 0.201950i \(-0.0647279\pi\)
−0.201950 + 0.979396i \(0.564728\pi\)
\(240\) 0 0
\(241\) 29.2447i 1.88382i −0.335870 0.941908i \(-0.609030\pi\)
0.335870 0.941908i \(-0.390970\pi\)
\(242\) 0 0
\(243\) 9.18675 + 9.18675i 0.589330 + 0.589330i
\(244\) 0 0
\(245\) −3.17533 −0.202864
\(246\) 0 0
\(247\) 12.7360 0.810370
\(248\) 0 0
\(249\) 2.41571 + 2.41571i 0.153089 + 0.153089i
\(250\) 0 0
\(251\) 12.0031i 0.757632i 0.925472 + 0.378816i \(0.123669\pi\)
−0.925472 + 0.378816i \(0.876331\pi\)
\(252\) 0 0
\(253\) −25.2729 25.2729i −1.58890 1.58890i
\(254\) 0 0
\(255\) 27.9934i 1.75302i
\(256\) 0 0
\(257\) 1.48650 + 1.48650i 0.0927255 + 0.0927255i 0.751948 0.659222i \(-0.229114\pi\)
−0.659222 + 0.751948i \(0.729114\pi\)
\(258\) 0 0
\(259\) 7.40993 + 7.40993i 0.460431 + 0.460431i
\(260\) 0 0
\(261\) −2.69044 + 2.69044i −0.166534 + 0.166534i
\(262\) 0 0
\(263\) −9.58843 + 9.58843i −0.591248 + 0.591248i −0.937968 0.346721i \(-0.887295\pi\)
0.346721 + 0.937968i \(0.387295\pi\)
\(264\) 0 0
\(265\) 2.52930 2.52930i 0.155374 0.155374i
\(266\) 0 0
\(267\) 16.6070i 1.01633i
\(268\) 0 0
\(269\) −22.9772 −1.40095 −0.700474 0.713678i \(-0.747028\pi\)
−0.700474 + 0.713678i \(0.747028\pi\)
\(270\) 0 0
\(271\) −13.5441 −0.822743 −0.411371 0.911468i \(-0.634950\pi\)
−0.411371 + 0.911468i \(0.634950\pi\)
\(272\) 0 0
\(273\) −4.58023 + 4.58023i −0.277208 + 0.277208i
\(274\) 0 0
\(275\) 16.4204 + 16.4204i 0.990187 + 0.990187i
\(276\) 0 0
\(277\) 32.8570 1.97419 0.987094 0.160145i \(-0.0511961\pi\)
0.987094 + 0.160145i \(0.0511961\pi\)
\(278\) 0 0
\(279\) 14.0269i 0.839769i
\(280\) 0 0
\(281\) −4.67777 + 4.67777i −0.279053 + 0.279053i −0.832731 0.553678i \(-0.813224\pi\)
0.553678 + 0.832731i \(0.313224\pi\)
\(282\) 0 0
\(283\) −3.80539 −0.226207 −0.113103 0.993583i \(-0.536079\pi\)
−0.113103 + 0.993583i \(0.536079\pi\)
\(284\) 0 0
\(285\) 10.0885i 0.597592i
\(286\) 0 0
\(287\) 5.30431 + 3.58668i 0.313104 + 0.211715i
\(288\) 0 0
\(289\) 31.0979i 1.82929i
\(290\) 0 0
\(291\) −9.33145 −0.547019
\(292\) 0 0
\(293\) −5.65650 + 5.65650i −0.330456 + 0.330456i −0.852760 0.522303i \(-0.825073\pi\)
0.522303 + 0.852760i \(0.325073\pi\)
\(294\) 0 0
\(295\) 37.4221i 2.17880i
\(296\) 0 0
\(297\) 25.4619 1.47745
\(298\) 0 0
\(299\) 28.1871 + 28.1871i 1.63010 + 1.63010i
\(300\) 0 0
\(301\) −1.72839 + 1.72839i −0.0996230 + 0.0996230i
\(302\) 0 0
\(303\) 16.9895 0.976022
\(304\) 0 0
\(305\) 45.6072 2.61146
\(306\) 0 0
\(307\) 8.30419i 0.473945i −0.971516 0.236973i \(-0.923845\pi\)
0.971516 0.236973i \(-0.0761552\pi\)
\(308\) 0 0
\(309\) −3.63897 + 3.63897i −0.207014 + 0.207014i
\(310\) 0 0
\(311\) −6.99226 + 6.99226i −0.396495 + 0.396495i −0.876995 0.480500i \(-0.840455\pi\)
0.480500 + 0.876995i \(0.340455\pi\)
\(312\) 0 0
\(313\) 5.57929 5.57929i 0.315360 0.315360i −0.531622 0.846982i \(-0.678417\pi\)
0.846982 + 0.531622i \(0.178417\pi\)
\(314\) 0 0
\(315\) −3.10776 3.10776i −0.175102 0.175102i
\(316\) 0 0
\(317\) −2.94928 2.94928i −0.165648 0.165648i 0.619415 0.785064i \(-0.287370\pi\)
−0.785064 + 0.619415i \(0.787370\pi\)
\(318\) 0 0
\(319\) 12.5594i 0.703189i
\(320\) 0 0
\(321\) 15.6507 + 15.6507i 0.873539 + 0.873539i
\(322\) 0 0
\(323\) 17.3339i 0.964486i
\(324\) 0 0
\(325\) −18.3138 18.3138i −1.01587 1.01587i
\(326\) 0 0
\(327\) −1.75947 −0.0972990
\(328\) 0 0
\(329\) 4.51343 0.248833
\(330\) 0 0
\(331\) 18.1383 + 18.1383i 0.996970 + 0.996970i 0.999995 0.00302502i \(-0.000962895\pi\)
−0.00302502 + 0.999995i \(0.500963\pi\)
\(332\) 0 0
\(333\) 14.5045i 0.794842i
\(334\) 0 0
\(335\) −14.1547 14.1547i −0.773354 0.773354i
\(336\) 0 0
\(337\) 0.453144i 0.0246843i −0.999924 0.0123422i \(-0.996071\pi\)
0.999924 0.0123422i \(-0.00392873\pi\)
\(338\) 0 0
\(339\) −4.61044 4.61044i −0.250405 0.250405i
\(340\) 0 0
\(341\) 32.7398 + 32.7398i 1.77296 + 1.77296i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 0 0
\(345\) 22.3278 22.3278i 1.20209 1.20209i
\(346\) 0 0
\(347\) −17.0961 + 17.0961i −0.917767 + 0.917767i −0.996867 0.0790998i \(-0.974795\pi\)
0.0790998 + 0.996867i \(0.474795\pi\)
\(348\) 0 0
\(349\) 27.1989i 1.45592i 0.685618 + 0.727962i \(0.259532\pi\)
−0.685618 + 0.727962i \(0.740468\pi\)
\(350\) 0 0
\(351\) −28.3978 −1.51576
\(352\) 0 0
\(353\) −18.1032 −0.963536 −0.481768 0.876299i \(-0.660005\pi\)
−0.481768 + 0.876299i \(0.660005\pi\)
\(354\) 0 0
\(355\) −1.37130 + 1.37130i −0.0727810 + 0.0727810i
\(356\) 0 0
\(357\) −6.23380 6.23380i −0.329927 0.329927i
\(358\) 0 0
\(359\) 16.1281 0.851209 0.425605 0.904909i \(-0.360061\pi\)
0.425605 + 0.904909i \(0.360061\pi\)
\(360\) 0 0
\(361\) 12.7530i 0.671213i
\(362\) 0 0
\(363\) 8.87532 8.87532i 0.465834 0.465834i
\(364\) 0 0
\(365\) −20.4227 −1.06897
\(366\) 0 0
\(367\) 30.5280i 1.59355i −0.604278 0.796774i \(-0.706538\pi\)
0.604278 0.796774i \(-0.293462\pi\)
\(368\) 0 0
\(369\) 1.68108 + 8.70180i 0.0875135 + 0.452998i
\(370\) 0 0
\(371\) 1.12649i 0.0584844i
\(372\) 0 0
\(373\) 17.4217 0.902060 0.451030 0.892509i \(-0.351057\pi\)
0.451030 + 0.892509i \(0.351057\pi\)
\(374\) 0 0
\(375\) −0.236063 + 0.236063i −0.0121902 + 0.0121902i
\(376\) 0 0
\(377\) 14.0075i 0.721425i
\(378\) 0 0
\(379\) −31.9163 −1.63943 −0.819715 0.572772i \(-0.805868\pi\)
−0.819715 + 0.572772i \(0.805868\pi\)
\(380\) 0 0
\(381\) 0.799589 + 0.799589i 0.0409642 + 0.0409642i
\(382\) 0 0
\(383\) −3.59095 + 3.59095i −0.183489 + 0.183489i −0.792874 0.609385i \(-0.791416\pi\)
0.609385 + 0.792874i \(0.291416\pi\)
\(384\) 0 0
\(385\) −14.5075 −0.739369
\(386\) 0 0
\(387\) −3.38323 −0.171979
\(388\) 0 0
\(389\) 25.4500i 1.29037i 0.764028 + 0.645183i \(0.223219\pi\)
−0.764028 + 0.645183i \(0.776781\pi\)
\(390\) 0 0
\(391\) −38.3633 + 38.3633i −1.94011 + 1.94011i
\(392\) 0 0
\(393\) 9.55295 9.55295i 0.481883 0.481883i
\(394\) 0 0
\(395\) −1.55851 + 1.55851i −0.0784173 + 0.0784173i
\(396\) 0 0
\(397\) −4.45110 4.45110i −0.223394 0.223394i 0.586532 0.809926i \(-0.300493\pi\)
−0.809926 + 0.586532i \(0.800493\pi\)
\(398\) 0 0
\(399\) 2.24659 + 2.24659i 0.112470 + 0.112470i
\(400\) 0 0
\(401\) 25.9816i 1.29746i 0.761019 + 0.648730i \(0.224700\pi\)
−0.761019 + 0.648730i \(0.775300\pi\)
\(402\) 0 0
\(403\) −36.5150 36.5150i −1.81894 1.81894i
\(404\) 0 0
\(405\) 9.30959i 0.462597i
\(406\) 0 0
\(407\) 33.8546 + 33.8546i 1.67811 + 1.67811i
\(408\) 0 0
\(409\) −29.9120 −1.47905 −0.739527 0.673127i \(-0.764951\pi\)
−0.739527 + 0.673127i \(0.764951\pi\)
\(410\) 0 0
\(411\) −0.140548 −0.00693273
\(412\) 0 0
\(413\) 8.33344 + 8.33344i 0.410062 + 0.410062i
\(414\) 0 0
\(415\) 8.53382i 0.418909i
\(416\) 0 0
\(417\) −8.17188 8.17188i −0.400179 0.400179i
\(418\) 0 0
\(419\) 27.6599i 1.35127i −0.737235 0.675637i \(-0.763869\pi\)
0.737235 0.675637i \(-0.236131\pi\)
\(420\) 0 0
\(421\) −1.33229 1.33229i −0.0649320 0.0649320i 0.673895 0.738827i \(-0.264620\pi\)
−0.738827 + 0.673895i \(0.764620\pi\)
\(422\) 0 0
\(423\) 4.41739 + 4.41739i 0.214781 + 0.214781i
\(424\) 0 0
\(425\) 24.9255 24.9255i 1.20906 1.20906i
\(426\) 0 0
\(427\) −10.1562 + 10.1562i −0.491491 + 0.491491i
\(428\) 0 0
\(429\) −20.9262 + 20.9262i −1.01033 + 1.01033i
\(430\) 0 0
\(431\) 3.34284i 0.161019i −0.996754 0.0805095i \(-0.974345\pi\)
0.996754 0.0805095i \(-0.0256547\pi\)
\(432\) 0 0
\(433\) 5.36464 0.257808 0.128904 0.991657i \(-0.458854\pi\)
0.128904 + 0.991657i \(0.458854\pi\)
\(434\) 0 0
\(435\) −11.0958 −0.532002
\(436\) 0 0
\(437\) 13.8257 13.8257i 0.661373 0.661373i
\(438\) 0 0
\(439\) −20.1275 20.1275i −0.960635 0.960635i 0.0386189 0.999254i \(-0.487704\pi\)
−0.999254 + 0.0386189i \(0.987704\pi\)
\(440\) 0 0
\(441\) 1.38412 0.0659105
\(442\) 0 0
\(443\) 17.5644i 0.834511i −0.908789 0.417256i \(-0.862992\pi\)
0.908789 0.417256i \(-0.137008\pi\)
\(444\) 0 0
\(445\) −29.3332 + 29.3332i −1.39053 + 1.39053i
\(446\) 0 0
\(447\) 20.3306 0.961605
\(448\) 0 0
\(449\) 6.11739i 0.288698i −0.989527 0.144349i \(-0.953891\pi\)
0.989527 0.144349i \(-0.0461087\pi\)
\(450\) 0 0
\(451\) 24.2344 + 16.3869i 1.14115 + 0.771628i
\(452\) 0 0
\(453\) 2.95937i 0.139043i
\(454\) 0 0
\(455\) 16.1803 0.758544
\(456\) 0 0
\(457\) −4.69840 + 4.69840i −0.219782 + 0.219782i −0.808406 0.588625i \(-0.799670\pi\)
0.588625 + 0.808406i \(0.299670\pi\)
\(458\) 0 0
\(459\) 38.6500i 1.80403i
\(460\) 0 0
\(461\) 22.9832 1.07044 0.535218 0.844714i \(-0.320229\pi\)
0.535218 + 0.844714i \(0.320229\pi\)
\(462\) 0 0
\(463\) 13.7403 + 13.7403i 0.638568 + 0.638568i 0.950202 0.311634i \(-0.100876\pi\)
−0.311634 + 0.950202i \(0.600876\pi\)
\(464\) 0 0
\(465\) −28.9245 + 28.9245i −1.34134 + 1.34134i
\(466\) 0 0
\(467\) −31.9109 −1.47666 −0.738329 0.674440i \(-0.764385\pi\)
−0.738329 + 0.674440i \(0.764385\pi\)
\(468\) 0 0
\(469\) 6.30416 0.291099
\(470\) 0 0
\(471\) 13.1357i 0.605263i
\(472\) 0 0
\(473\) −7.89671 + 7.89671i −0.363091 + 0.363091i
\(474\) 0 0
\(475\) −8.98286 + 8.98286i −0.412162 + 0.412162i
\(476\) 0 0
\(477\) −1.10252 + 1.10252i −0.0504809 + 0.0504809i
\(478\) 0 0
\(479\) 20.0784 + 20.0784i 0.917405 + 0.917405i 0.996840 0.0794347i \(-0.0253115\pi\)
−0.0794347 + 0.996840i \(0.525312\pi\)
\(480\) 0 0
\(481\) −37.7583 37.7583i −1.72163 1.72163i
\(482\) 0 0
\(483\) 9.94425i 0.452479i
\(484\) 0 0
\(485\) 16.4823 + 16.4823i 0.748423 + 0.748423i
\(486\) 0 0
\(487\) 30.1236i 1.36503i −0.730872 0.682515i \(-0.760886\pi\)
0.730872 0.682515i \(-0.239114\pi\)
\(488\) 0 0
\(489\) 3.17767 + 3.17767i 0.143699 + 0.143699i
\(490\) 0 0
\(491\) −5.91261 −0.266832 −0.133416 0.991060i \(-0.542595\pi\)
−0.133416 + 0.991060i \(0.542595\pi\)
\(492\) 0 0
\(493\) 19.0646 0.858626
\(494\) 0 0
\(495\) −14.1988 14.1988i −0.638187 0.638187i
\(496\) 0 0
\(497\) 0.610743i 0.0273956i
\(498\) 0 0
\(499\) 0.844691 + 0.844691i 0.0378136 + 0.0378136i 0.725761 0.687947i \(-0.241488\pi\)
−0.687947 + 0.725761i \(0.741488\pi\)
\(500\) 0 0
\(501\) 18.2789i 0.816643i
\(502\) 0 0
\(503\) 10.5141 + 10.5141i 0.468800 + 0.468800i 0.901526 0.432725i \(-0.142448\pi\)
−0.432725 + 0.901526i \(0.642448\pi\)
\(504\) 0 0
\(505\) −30.0089 30.0089i −1.33538 1.33538i
\(506\) 0 0
\(507\) 11.6540 11.6540i 0.517574 0.517574i
\(508\) 0 0
\(509\) −0.254782 + 0.254782i −0.0112930 + 0.0112930i −0.712731 0.701438i \(-0.752542\pi\)
0.701438 + 0.712731i \(0.252542\pi\)
\(510\) 0 0
\(511\) 4.54789 4.54789i 0.201187 0.201187i
\(512\) 0 0
\(513\) 13.9290i 0.614982i
\(514\) 0 0
\(515\) 12.8552 0.566467
\(516\) 0 0
\(517\) 20.6210 0.906911
\(518\) 0 0
\(519\) −10.4153 + 10.4153i −0.457180 + 0.457180i
\(520\) 0 0
\(521\) 11.0165 + 11.0165i 0.482644 + 0.482644i 0.905975 0.423331i \(-0.139139\pi\)
−0.423331 + 0.905975i \(0.639139\pi\)
\(522\) 0 0
\(523\) −24.4937 −1.07104 −0.535518 0.844524i \(-0.679884\pi\)
−0.535518 + 0.844524i \(0.679884\pi\)
\(524\) 0 0
\(525\) 6.46100i 0.281981i
\(526\) 0 0
\(527\) 49.6977 49.6977i 2.16487 2.16487i
\(528\) 0 0
\(529\) 38.1977 1.66077
\(530\) 0 0
\(531\) 16.3122i 0.707890i
\(532\) 0 0
\(533\) −27.0288 18.2764i −1.17075 0.791639i
\(534\) 0 0
\(535\) 55.2884i 2.39032i
\(536\) 0 0
\(537\) −20.3910 −0.879936
\(538\) 0 0
\(539\) 3.23064 3.23064i 0.139153 0.139153i
\(540\) 0 0
\(541\) 40.7307i 1.75115i −0.483084 0.875574i \(-0.660484\pi\)
0.483084 0.875574i \(-0.339516\pi\)
\(542\) 0 0
\(543\) −20.5113 −0.880225
\(544\) 0 0
\(545\) 3.10779 + 3.10779i 0.133123 + 0.133123i
\(546\) 0 0
\(547\) 1.83965 1.83965i 0.0786578 0.0786578i −0.666683 0.745341i \(-0.732287\pi\)
0.745341 + 0.666683i \(0.232287\pi\)
\(548\) 0 0
\(549\) −19.8801 −0.848461
\(550\) 0 0
\(551\) −6.87066 −0.292700
\(552\) 0 0
\(553\) 0.694124i 0.0295171i
\(554\) 0 0
\(555\) −29.9094 + 29.9094i −1.26958 + 1.26958i
\(556\) 0 0
\(557\) 8.99669 8.99669i 0.381202 0.381202i −0.490333 0.871535i \(-0.663125\pi\)
0.871535 + 0.490333i \(0.163125\pi\)
\(558\) 0 0
\(559\) 8.80725 8.80725i 0.372507 0.372507i
\(560\) 0 0
\(561\) −28.4810 28.4810i −1.20247 1.20247i
\(562\) 0 0
\(563\) −9.11108 9.11108i −0.383986 0.383986i 0.488550 0.872536i \(-0.337526\pi\)
−0.872536 + 0.488550i \(0.837526\pi\)
\(564\) 0 0
\(565\) 16.2870i 0.685199i
\(566\) 0 0
\(567\) −2.07313 2.07313i −0.0870634 0.0870634i
\(568\) 0 0
\(569\) 23.8699i 1.00068i 0.865830 + 0.500339i \(0.166791\pi\)
−0.865830 + 0.500339i \(0.833209\pi\)
\(570\) 0 0
\(571\) 18.4625 + 18.4625i 0.772632 + 0.772632i 0.978566 0.205934i \(-0.0660232\pi\)
−0.205934 + 0.978566i \(0.566023\pi\)
\(572\) 0 0
\(573\) −19.2509 −0.804219
\(574\) 0 0
\(575\) −39.7615 −1.65817
\(576\) 0 0
\(577\) 16.2481 + 16.2481i 0.676416 + 0.676416i 0.959187 0.282772i \(-0.0912538\pi\)
−0.282772 + 0.959187i \(0.591254\pi\)
\(578\) 0 0
\(579\) 2.24588i 0.0933357i
\(580\) 0 0
\(581\) 1.90038 + 1.90038i 0.0788410 + 0.0788410i
\(582\) 0 0
\(583\) 5.14672i 0.213155i
\(584\) 0 0
\(585\) 15.8360 + 15.8360i 0.654737 + 0.654737i
\(586\) 0 0
\(587\) −25.6552 25.6552i −1.05890 1.05890i −0.998153 0.0607512i \(-0.980650\pi\)
−0.0607512 0.998153i \(-0.519350\pi\)
\(588\) 0 0
\(589\) −17.9105 + 17.9105i −0.737989 + 0.737989i
\(590\) 0 0
\(591\) −7.48061 + 7.48061i −0.307711 + 0.307711i
\(592\) 0 0
\(593\) 32.9511 32.9511i 1.35314 1.35314i 0.471013 0.882126i \(-0.343888\pi\)
0.882126 0.471013i \(-0.156112\pi\)
\(594\) 0 0
\(595\) 22.0217i 0.902803i
\(596\) 0 0
\(597\) −30.0815 −1.23115
\(598\) 0 0
\(599\) 1.28943 0.0526846 0.0263423 0.999653i \(-0.491614\pi\)
0.0263423 + 0.999653i \(0.491614\pi\)
\(600\) 0 0
\(601\) 12.2813 12.2813i 0.500966 0.500966i −0.410772 0.911738i \(-0.634741\pi\)
0.911738 + 0.410772i \(0.134741\pi\)
\(602\) 0 0
\(603\) 6.17001 + 6.17001i 0.251262 + 0.251262i
\(604\) 0 0
\(605\) −31.3533 −1.27469
\(606\) 0 0
\(607\) 7.06614i 0.286806i −0.989664 0.143403i \(-0.954196\pi\)
0.989664 0.143403i \(-0.0458045\pi\)
\(608\) 0 0
\(609\) 2.47089 2.47089i 0.100126 0.100126i
\(610\) 0 0
\(611\) −22.9988 −0.930430
\(612\) 0 0
\(613\) 19.8614i 0.802194i 0.916036 + 0.401097i \(0.131371\pi\)
−0.916036 + 0.401097i \(0.868629\pi\)
\(614\) 0 0
\(615\) −14.4772 + 21.4103i −0.583779 + 0.863345i
\(616\) 0 0
\(617\) 33.9650i 1.36738i 0.729773 + 0.683690i \(0.239626\pi\)
−0.729773 + 0.683690i \(0.760374\pi\)
\(618\) 0 0
\(619\) −18.9560 −0.761905 −0.380953 0.924595i \(-0.624404\pi\)
−0.380953 + 0.924595i \(0.624404\pi\)
\(620\) 0 0
\(621\) −30.8276 + 30.8276i −1.23707 + 1.23707i
\(622\) 0 0
\(623\) 13.0643i 0.523410i
\(624\) 0 0
\(625\) −24.5796 −0.983185
\(626\) 0 0
\(627\) 10.2642 + 10.2642i 0.409914 + 0.409914i
\(628\) 0 0
\(629\) 51.3898 51.3898i 2.04905 2.04905i
\(630\) 0 0
\(631\) −24.9884 −0.994772 −0.497386 0.867529i \(-0.665707\pi\)
−0.497386 + 0.867529i \(0.665707\pi\)
\(632\) 0 0
\(633\) 14.9514 0.594264
\(634\) 0 0
\(635\) 2.82466i 0.112093i
\(636\) 0 0
\(637\) −3.60315 + 3.60315i −0.142762 + 0.142762i
\(638\) 0 0
\(639\) 0.597747 0.597747i 0.0236465 0.0236465i
\(640\) 0 0
\(641\) 2.92515 2.92515i 0.115536 0.115536i −0.646975 0.762511i \(-0.723966\pi\)
0.762511 + 0.646975i \(0.223966\pi\)
\(642\) 0 0
\(643\) 8.25587 + 8.25587i 0.325580 + 0.325580i 0.850903 0.525323i \(-0.176056\pi\)
−0.525323 + 0.850903i \(0.676056\pi\)
\(644\) 0 0
\(645\) −6.97647 6.97647i −0.274698 0.274698i
\(646\) 0 0
\(647\) 24.7889i 0.974553i −0.873248 0.487276i \(-0.837990\pi\)
0.873248 0.487276i \(-0.162010\pi\)
\(648\) 0 0
\(649\) 38.0739 + 38.0739i 1.49453 + 1.49453i
\(650\) 0 0
\(651\) 12.8823i 0.504896i
\(652\) 0 0
\(653\) 29.9864 + 29.9864i 1.17346 + 1.17346i 0.981380 + 0.192077i \(0.0615223\pi\)
0.192077 + 0.981380i \(0.438478\pi\)
\(654\) 0 0
\(655\) −33.7471 −1.31861
\(656\) 0 0
\(657\) 8.90222 0.347309
\(658\) 0 0
\(659\) 13.6460 + 13.6460i 0.531574 + 0.531574i 0.921041 0.389467i \(-0.127341\pi\)
−0.389467 + 0.921041i \(0.627341\pi\)
\(660\) 0 0
\(661\) 37.0565i 1.44133i 0.693284 + 0.720665i \(0.256163\pi\)
−0.693284 + 0.720665i \(0.743837\pi\)
\(662\) 0 0
\(663\) 31.7651 + 31.7651i 1.23365 + 1.23365i
\(664\) 0 0
\(665\) 7.93639i 0.307760i
\(666\) 0 0
\(667\) −15.2061 15.2061i −0.588781 0.588781i
\(668\) 0 0
\(669\) 6.36038 + 6.36038i 0.245907 + 0.245907i
\(670\) 0 0
\(671\) −46.4016 + 46.4016i −1.79131 + 1.79131i
\(672\) 0 0
\(673\) −17.9693 + 17.9693i −0.692665 + 0.692665i −0.962817 0.270153i \(-0.912926\pi\)
0.270153 + 0.962817i \(0.412926\pi\)
\(674\) 0 0
\(675\) 20.0294 20.0294i 0.770931 0.770931i
\(676\) 0 0
\(677\) 48.3118i 1.85678i 0.371613 + 0.928388i \(0.378805\pi\)
−0.371613 + 0.928388i \(0.621195\pi\)
\(678\) 0 0
\(679\) −7.34082 −0.281715
\(680\) 0 0
\(681\) −28.4944 −1.09191
\(682\) 0 0
\(683\) 19.6184 19.6184i 0.750677 0.750677i −0.223928 0.974606i \(-0.571888\pi\)
0.974606 + 0.223928i \(0.0718882\pi\)
\(684\) 0 0
\(685\) 0.248253 + 0.248253i 0.00948525 + 0.00948525i
\(686\) 0 0
\(687\) 19.6606 0.750100
\(688\) 0 0
\(689\) 5.74017i 0.218683i
\(690\) 0 0
\(691\) −20.2232 + 20.2232i −0.769328 + 0.769328i −0.977988 0.208660i \(-0.933090\pi\)
0.208660 + 0.977988i \(0.433090\pi\)
\(692\) 0 0
\(693\) 6.32378 0.240221
\(694\) 0 0
\(695\) 28.8683i 1.09504i
\(696\) 0 0
\(697\) 24.8746 36.7868i 0.942192 1.39340i
\(698\) 0 0
\(699\) 12.9220i 0.488754i
\(700\) 0 0
\(701\) −17.0207 −0.642862 −0.321431 0.946933i \(-0.604164\pi\)
−0.321431 + 0.946933i \(0.604164\pi\)
\(702\) 0 0
\(703\) −18.5203 + 18.5203i −0.698507 + 0.698507i
\(704\) 0 0
\(705\) 18.2180i 0.686128i
\(706\) 0 0
\(707\) 13.3652 0.502651
\(708\) 0 0
\(709\) −30.7522 30.7522i −1.15492 1.15492i −0.985552 0.169370i \(-0.945827\pi\)
−0.169370 0.985552i \(-0.554173\pi\)
\(710\) 0 0
\(711\) 0.679353 0.679353i 0.0254777 0.0254777i
\(712\) 0 0
\(713\) −79.2786 −2.96901
\(714\) 0 0
\(715\) 73.9247 2.76463
\(716\) 0 0
\(717\) 21.6067i 0.806917i
\(718\) 0 0
\(719\) −14.5626 + 14.5626i −0.543093 + 0.543093i −0.924434 0.381341i \(-0.875462\pi\)
0.381341 + 0.924434i \(0.375462\pi\)
\(720\) 0 0
\(721\) −2.86269 + 2.86269i −0.106612 + 0.106612i
\(722\) 0 0
\(723\) −26.2867 + 26.2867i −0.977614 + 0.977614i
\(724\) 0 0
\(725\) 9.87972 + 9.87972i 0.366924 + 0.366924i
\(726\) 0 0
\(727\) 13.3854 + 13.3854i 0.496437 + 0.496437i 0.910327 0.413890i \(-0.135830\pi\)
−0.413890 + 0.910327i \(0.635830\pi\)
\(728\) 0 0
\(729\) 25.3107i 0.937432i
\(730\) 0 0
\(731\) 11.9869 + 11.9869i 0.443350 + 0.443350i
\(732\) 0 0
\(733\) 18.6444i 0.688647i 0.938851 + 0.344323i \(0.111892\pi\)
−0.938851 + 0.344323i \(0.888108\pi\)
\(734\) 0 0
\(735\) 2.85416 + 2.85416i 0.105277 + 0.105277i
\(736\) 0 0
\(737\) 28.8025 1.06095
\(738\) 0 0
\(739\) 12.9718 0.477176 0.238588 0.971121i \(-0.423315\pi\)
0.238588 + 0.971121i \(0.423315\pi\)
\(740\) 0 0
\(741\) −11.4478 11.4478i −0.420545 0.420545i
\(742\) 0 0
\(743\) 19.7381i 0.724119i −0.932155 0.362060i \(-0.882074\pi\)
0.932155 0.362060i \(-0.117926\pi\)
\(744\) 0 0
\(745\) −35.9104 35.9104i −1.31565 1.31565i
\(746\) 0 0
\(747\) 3.71988i 0.136103i
\(748\) 0 0
\(749\) 12.3120 + 12.3120i 0.449872 + 0.449872i
\(750\) 0 0
\(751\) 0.359210 + 0.359210i 0.0131077 + 0.0131077i 0.713630 0.700523i \(-0.247050\pi\)
−0.700523 + 0.713630i \(0.747050\pi\)
\(752\) 0 0
\(753\) 10.7891 10.7891i 0.393176 0.393176i
\(754\) 0 0
\(755\) 5.22719 5.22719i 0.190237 0.190237i
\(756\) 0 0
\(757\) 16.3008 16.3008i 0.592463 0.592463i −0.345833 0.938296i \(-0.612404\pi\)
0.938296 + 0.345833i \(0.112404\pi\)
\(758\) 0 0
\(759\) 45.4334i 1.64913i
\(760\) 0 0
\(761\) 23.1815 0.840328 0.420164 0.907448i \(-0.361972\pi\)
0.420164 + 0.907448i \(0.361972\pi\)
\(762\) 0 0
\(763\) −1.38413 −0.0501089
\(764\) 0 0
\(765\) −21.5531 + 21.5531i −0.779255 + 0.779255i
\(766\) 0 0
\(767\) −42.4641 42.4641i −1.53329 1.53329i
\(768\) 0 0
\(769\) 27.0527 0.975546 0.487773 0.872971i \(-0.337809\pi\)
0.487773 + 0.872971i \(0.337809\pi\)
\(770\) 0 0
\(771\) 2.67230i 0.0962405i
\(772\) 0 0
\(773\) −33.0614 + 33.0614i −1.18913 + 1.18913i −0.211827 + 0.977307i \(0.567941\pi\)
−0.977307 + 0.211827i \(0.932059\pi\)
\(774\) 0 0
\(775\) 51.5090 1.85026
\(776\) 0 0
\(777\) 13.3209i 0.477885i
\(778\) 0 0
\(779\) −8.96452 + 13.2575i −0.321187 + 0.475001i
\(780\) 0 0
\(781\) 2.79037i 0.0998472i
\(782\) 0 0
\(783\) 15.3197 0.547483
\(784\) 0 0
\(785\) −23.2019 + 23.2019i −0.828112 + 0.828112i
\(786\) 0 0
\(787\) 26.7178i 0.952385i 0.879341 + 0.476193i \(0.157983\pi\)
−0.879341 + 0.476193i \(0.842017\pi\)
\(788\) 0 0
\(789\) 17.2372 0.613661
\(790\) 0 0
\(791\) −3.62692 3.62692i −0.128958 0.128958i
\(792\) 0 0
\(793\) 51.7520 51.7520i 1.83777 1.83777i
\(794\) 0 0
\(795\) −4.54695 −0.161264
\(796\) 0 0
\(797\) −10.7130 −0.379475 −0.189738 0.981835i \(-0.560764\pi\)
−0.189738 + 0.981835i \(0.560764\pi\)
\(798\) 0 0
\(799\) 31.3018i 1.10738i
\(800\) 0 0
\(801\) 12.7863