Properties

Label 144.3.m.c.91.4
Level $144$
Weight $3$
Character 144.91
Analytic conductor $3.924$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 91.4
Root \(-0.455024 - 1.94755i\) of defining polynomial
Character \(\chi\) \(=\) 144.91
Dual form 144.3.m.c.19.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.455024 + 1.94755i) q^{2} +(-3.58591 - 1.77236i) q^{4} +(3.40572 + 3.40572i) q^{5} +12.1303 q^{7} +(5.08344 - 6.17727i) q^{8} +O(q^{10})\) \(q+(-0.455024 + 1.94755i) q^{2} +(-3.58591 - 1.77236i) q^{4} +(3.40572 + 3.40572i) q^{5} +12.1303 q^{7} +(5.08344 - 6.17727i) q^{8} +(-8.18251 + 5.08314i) q^{10} +(-9.81086 + 9.81086i) q^{11} +(-7.76859 + 7.76859i) q^{13} +(-5.51959 + 23.6244i) q^{14} +(9.71745 + 12.7111i) q^{16} -9.73087 q^{17} +(11.2823 + 11.2823i) q^{19} +(-6.17643 - 18.2488i) q^{20} +(-14.6430 - 23.5713i) q^{22} +20.2635 q^{23} -1.80207i q^{25} +(-11.5948 - 18.6646i) q^{26} +(-43.4982 - 21.4994i) q^{28} +(16.4069 - 16.4069i) q^{29} +26.3542i q^{31} +(-29.1771 + 13.1414i) q^{32} +(4.42778 - 18.9514i) q^{34} +(41.3125 + 41.3125i) q^{35} +(-23.7263 - 23.7263i) q^{37} +(-27.1066 + 16.8392i) q^{38} +(38.3509 - 3.72526i) q^{40} -24.7452i q^{41} +(29.8844 - 29.8844i) q^{43} +(52.5692 - 17.7924i) q^{44} +(-9.22036 + 39.4641i) q^{46} -31.3325i q^{47} +98.1448 q^{49} +(3.50963 + 0.819987i) q^{50} +(41.6262 - 14.0887i) q^{52} +(-36.8742 - 36.8742i) q^{53} -66.8262 q^{55} +(61.6638 - 74.9322i) q^{56} +(24.4877 + 39.4188i) q^{58} +(14.1325 - 14.1325i) q^{59} +(-42.5199 + 42.5199i) q^{61} +(-51.3260 - 11.9918i) q^{62} +(-12.3172 - 62.8036i) q^{64} -52.9153 q^{65} +(48.7789 + 48.7789i) q^{67} +(34.8940 + 17.2467i) q^{68} +(-99.2565 + 61.6601i) q^{70} -7.73935 q^{71} -85.4163i q^{73} +(57.0041 - 35.4121i) q^{74} +(-20.4610 - 60.4537i) q^{76} +(-119.009 + 119.009i) q^{77} -105.294i q^{79} +(-10.1954 + 76.3854i) q^{80} +(48.1926 + 11.2597i) q^{82} +(62.1229 + 62.1229i) q^{83} +(-33.1407 - 33.1407i) q^{85} +(44.6033 + 71.7996i) q^{86} +(10.7313 + 110.477i) q^{88} -127.172i q^{89} +(-94.2355 + 94.2355i) q^{91} +(-72.6629 - 35.9142i) q^{92} +(61.0215 + 14.2570i) q^{94} +76.8489i q^{95} -147.348 q^{97} +(-44.6582 + 191.142i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} + 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} + 12q^{8} - 56q^{10} - 32q^{11} + 44q^{14} + 32q^{16} - 32q^{19} - 80q^{20} + 32q^{22} + 128q^{23} + 100q^{26} - 120q^{28} - 32q^{29} - 160q^{32} + 96q^{34} - 96q^{35} - 96q^{37} - 168q^{38} + 48q^{40} + 160q^{43} - 88q^{44} + 136q^{46} + 112q^{49} + 236q^{50} - 48q^{52} + 160q^{53} - 256q^{55} + 224q^{56} + 144q^{58} + 128q^{59} - 32q^{61} + 276q^{62} - 408q^{64} + 32q^{65} + 320q^{67} + 448q^{68} - 384q^{70} - 512q^{71} - 348q^{74} + 72q^{76} - 224q^{77} - 552q^{80} - 40q^{82} + 160q^{83} + 160q^{85} - 528q^{86} + 480q^{88} - 480q^{91} - 496q^{92} + 312q^{94} + 440q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.455024 + 1.94755i −0.227512 + 0.973775i
\(3\) 0 0
\(4\) −3.58591 1.77236i −0.896477 0.443091i
\(5\) 3.40572 + 3.40572i 0.681145 + 0.681145i 0.960258 0.279113i \(-0.0900405\pi\)
−0.279113 + 0.960258i \(0.590040\pi\)
\(6\) 0 0
\(7\) 12.1303 1.73290 0.866452 0.499261i \(-0.166395\pi\)
0.866452 + 0.499261i \(0.166395\pi\)
\(8\) 5.08344 6.17727i 0.635430 0.772158i
\(9\) 0 0
\(10\) −8.18251 + 5.08314i −0.818251 + 0.508314i
\(11\) −9.81086 + 9.81086i −0.891896 + 0.891896i −0.994702 0.102805i \(-0.967218\pi\)
0.102805 + 0.994702i \(0.467218\pi\)
\(12\) 0 0
\(13\) −7.76859 + 7.76859i −0.597584 + 0.597584i −0.939669 0.342085i \(-0.888867\pi\)
0.342085 + 0.939669i \(0.388867\pi\)
\(14\) −5.51959 + 23.6244i −0.394256 + 1.68746i
\(15\) 0 0
\(16\) 9.71745 + 12.7111i 0.607341 + 0.794442i
\(17\) −9.73087 −0.572404 −0.286202 0.958169i \(-0.592393\pi\)
−0.286202 + 0.958169i \(0.592393\pi\)
\(18\) 0 0
\(19\) 11.2823 + 11.2823i 0.593806 + 0.593806i 0.938657 0.344851i \(-0.112071\pi\)
−0.344851 + 0.938657i \(0.612071\pi\)
\(20\) −6.17643 18.2488i −0.308821 0.912440i
\(21\) 0 0
\(22\) −14.6430 23.5713i −0.665589 1.07142i
\(23\) 20.2635 0.881020 0.440510 0.897748i \(-0.354798\pi\)
0.440510 + 0.897748i \(0.354798\pi\)
\(24\) 0 0
\(25\) 1.80207i 0.0720830i
\(26\) −11.5948 18.6646i −0.445955 0.717870i
\(27\) 0 0
\(28\) −43.4982 21.4994i −1.55351 0.767834i
\(29\) 16.4069 16.4069i 0.565754 0.565754i −0.365182 0.930936i \(-0.618993\pi\)
0.930936 + 0.365182i \(0.118993\pi\)
\(30\) 0 0
\(31\) 26.3542i 0.850134i 0.905162 + 0.425067i \(0.139749\pi\)
−0.905162 + 0.425067i \(0.860251\pi\)
\(32\) −29.1771 + 13.1414i −0.911785 + 0.410668i
\(33\) 0 0
\(34\) 4.42778 18.9514i 0.130229 0.557393i
\(35\) 41.3125 + 41.3125i 1.18036 + 1.18036i
\(36\) 0 0
\(37\) −23.7263 23.7263i −0.641250 0.641250i 0.309613 0.950863i \(-0.399801\pi\)
−0.950863 + 0.309613i \(0.899801\pi\)
\(38\) −27.1066 + 16.8392i −0.713332 + 0.443136i
\(39\) 0 0
\(40\) 38.3509 3.72526i 0.958772 0.0931315i
\(41\) 24.7452i 0.603542i −0.953380 0.301771i \(-0.902422\pi\)
0.953380 0.301771i \(-0.0975779\pi\)
\(42\) 0 0
\(43\) 29.8844 29.8844i 0.694987 0.694987i −0.268338 0.963325i \(-0.586474\pi\)
0.963325 + 0.268338i \(0.0864744\pi\)
\(44\) 52.5692 17.7924i 1.19476 0.404373i
\(45\) 0 0
\(46\) −9.22036 + 39.4641i −0.200443 + 0.857915i
\(47\) 31.3325i 0.666648i −0.942812 0.333324i \(-0.891830\pi\)
0.942812 0.333324i \(-0.108170\pi\)
\(48\) 0 0
\(49\) 98.1448 2.00295
\(50\) 3.50963 + 0.819987i 0.0701926 + 0.0163997i
\(51\) 0 0
\(52\) 41.6262 14.0887i 0.800504 0.270936i
\(53\) −36.8742 36.8742i −0.695739 0.695739i 0.267750 0.963489i \(-0.413720\pi\)
−0.963489 + 0.267750i \(0.913720\pi\)
\(54\) 0 0
\(55\) −66.8262 −1.21502
\(56\) 61.6638 74.9322i 1.10114 1.33808i
\(57\) 0 0
\(58\) 24.4877 + 39.4188i 0.422202 + 0.679634i
\(59\) 14.1325 14.1325i 0.239534 0.239534i −0.577123 0.816657i \(-0.695825\pi\)
0.816657 + 0.577123i \(0.195825\pi\)
\(60\) 0 0
\(61\) −42.5199 + 42.5199i −0.697048 + 0.697048i −0.963773 0.266725i \(-0.914059\pi\)
0.266725 + 0.963773i \(0.414059\pi\)
\(62\) −51.3260 11.9918i −0.827839 0.193416i
\(63\) 0 0
\(64\) −12.3172 62.8036i −0.192457 0.981305i
\(65\) −52.9153 −0.814082
\(66\) 0 0
\(67\) 48.7789 + 48.7789i 0.728044 + 0.728044i 0.970230 0.242186i \(-0.0778644\pi\)
−0.242186 + 0.970230i \(0.577864\pi\)
\(68\) 34.8940 + 17.2467i 0.513147 + 0.253627i
\(69\) 0 0
\(70\) −99.2565 + 61.6601i −1.41795 + 0.880858i
\(71\) −7.73935 −0.109005 −0.0545025 0.998514i \(-0.517357\pi\)
−0.0545025 + 0.998514i \(0.517357\pi\)
\(72\) 0 0
\(73\) 85.4163i 1.17009i −0.811002 0.585043i \(-0.801077\pi\)
0.811002 0.585043i \(-0.198923\pi\)
\(74\) 57.0041 35.4121i 0.770326 0.478541i
\(75\) 0 0
\(76\) −20.4610 60.4537i −0.269223 0.795443i
\(77\) −119.009 + 119.009i −1.54557 + 1.54557i
\(78\) 0 0
\(79\) 105.294i 1.33283i −0.745581 0.666416i \(-0.767828\pi\)
0.745581 0.666416i \(-0.232172\pi\)
\(80\) −10.1954 + 76.3854i −0.127443 + 0.954817i
\(81\) 0 0
\(82\) 48.1926 + 11.2597i 0.587715 + 0.137313i
\(83\) 62.1229 + 62.1229i 0.748469 + 0.748469i 0.974192 0.225723i \(-0.0724743\pi\)
−0.225723 + 0.974192i \(0.572474\pi\)
\(84\) 0 0
\(85\) −33.1407 33.1407i −0.389890 0.389890i
\(86\) 44.6033 + 71.7996i 0.518643 + 0.834879i
\(87\) 0 0
\(88\) 10.7313 + 110.477i 0.121947 + 1.25542i
\(89\) 127.172i 1.42890i −0.699685 0.714451i \(-0.746676\pi\)
0.699685 0.714451i \(-0.253324\pi\)
\(90\) 0 0
\(91\) −94.2355 + 94.2355i −1.03555 + 1.03555i
\(92\) −72.6629 35.9142i −0.789814 0.390372i
\(93\) 0 0
\(94\) 61.0215 + 14.2570i 0.649165 + 0.151670i
\(95\) 76.8489i 0.808936i
\(96\) 0 0
\(97\) −147.348 −1.51905 −0.759525 0.650478i \(-0.774569\pi\)
−0.759525 + 0.650478i \(0.774569\pi\)
\(98\) −44.6582 + 191.142i −0.455696 + 1.95043i
\(99\) 0 0
\(100\) −3.19393 + 6.46207i −0.0319393 + 0.0646207i
\(101\) −12.7690 12.7690i −0.126426 0.126426i 0.641063 0.767489i \(-0.278494\pi\)
−0.767489 + 0.641063i \(0.778494\pi\)
\(102\) 0 0
\(103\) −17.7621 −0.172448 −0.0862240 0.996276i \(-0.527480\pi\)
−0.0862240 + 0.996276i \(0.527480\pi\)
\(104\) 8.49746 + 87.4798i 0.0817063 + 0.841152i
\(105\) 0 0
\(106\) 88.5929 55.0357i 0.835782 0.519204i
\(107\) 15.8889 15.8889i 0.148494 0.148494i −0.628951 0.777445i \(-0.716515\pi\)
0.777445 + 0.628951i \(0.216515\pi\)
\(108\) 0 0
\(109\) −79.3257 + 79.3257i −0.727758 + 0.727758i −0.970173 0.242414i \(-0.922061\pi\)
0.242414 + 0.970173i \(0.422061\pi\)
\(110\) 30.4075 130.147i 0.276432 1.18316i
\(111\) 0 0
\(112\) 117.876 + 154.189i 1.05246 + 1.37669i
\(113\) 167.538 1.48263 0.741317 0.671155i \(-0.234201\pi\)
0.741317 + 0.671155i \(0.234201\pi\)
\(114\) 0 0
\(115\) 69.0118 + 69.0118i 0.600102 + 0.600102i
\(116\) −87.9125 + 29.7546i −0.757866 + 0.256505i
\(117\) 0 0
\(118\) 21.0932 + 33.9545i 0.178756 + 0.287750i
\(119\) −118.039 −0.991921
\(120\) 0 0
\(121\) 71.5059i 0.590958i
\(122\) −63.4621 102.157i −0.520181 0.837355i
\(123\) 0 0
\(124\) 46.7092 94.5035i 0.376687 0.762125i
\(125\) 91.2805 91.2805i 0.730244 0.730244i
\(126\) 0 0
\(127\) 198.247i 1.56100i −0.625156 0.780500i \(-0.714965\pi\)
0.625156 0.780500i \(-0.285035\pi\)
\(128\) 127.918 + 4.58871i 0.999357 + 0.0358493i
\(129\) 0 0
\(130\) 24.0778 103.055i 0.185213 0.792733i
\(131\) −134.339 134.339i −1.02549 1.02549i −0.999667 0.0258197i \(-0.991780\pi\)
−0.0258197 0.999667i \(-0.508220\pi\)
\(132\) 0 0
\(133\) 136.858 + 136.858i 1.02901 + 1.02901i
\(134\) −117.195 + 72.8039i −0.874590 + 0.543313i
\(135\) 0 0
\(136\) −49.4663 + 60.1102i −0.363723 + 0.441987i
\(137\) 255.937i 1.86816i 0.357069 + 0.934078i \(0.383776\pi\)
−0.357069 + 0.934078i \(0.616224\pi\)
\(138\) 0 0
\(139\) −21.7231 + 21.7231i −0.156281 + 0.156281i −0.780917 0.624635i \(-0.785248\pi\)
0.624635 + 0.780917i \(0.285248\pi\)
\(140\) −74.9220 221.364i −0.535157 1.58117i
\(141\) 0 0
\(142\) 3.52159 15.0728i 0.0247999 0.106146i
\(143\) 152.433i 1.06597i
\(144\) 0 0
\(145\) 111.755 0.770722
\(146\) 166.353 + 38.8665i 1.13940 + 0.266209i
\(147\) 0 0
\(148\) 43.0286 + 127.132i 0.290734 + 0.858998i
\(149\) 34.2444 + 34.2444i 0.229828 + 0.229828i 0.812621 0.582793i \(-0.198040\pi\)
−0.582793 + 0.812621i \(0.698040\pi\)
\(150\) 0 0
\(151\) −14.4645 −0.0957913 −0.0478956 0.998852i \(-0.515251\pi\)
−0.0478956 + 0.998852i \(0.515251\pi\)
\(152\) 127.047 12.3409i 0.835835 0.0811898i
\(153\) 0 0
\(154\) −177.624 285.928i −1.15340 1.85667i
\(155\) −89.7550 + 89.7550i −0.579064 + 0.579064i
\(156\) 0 0
\(157\) 31.4652 31.4652i 0.200415 0.200415i −0.599763 0.800178i \(-0.704738\pi\)
0.800178 + 0.599763i \(0.204738\pi\)
\(158\) 205.065 + 47.9111i 1.29788 + 0.303235i
\(159\) 0 0
\(160\) −144.125 54.6133i −0.900782 0.341333i
\(161\) 245.802 1.52672
\(162\) 0 0
\(163\) 31.4002 + 31.4002i 0.192640 + 0.192640i 0.796836 0.604196i \(-0.206506\pi\)
−0.604196 + 0.796836i \(0.706506\pi\)
\(164\) −43.8576 + 88.7341i −0.267424 + 0.541062i
\(165\) 0 0
\(166\) −149.255 + 92.7201i −0.899126 + 0.558555i
\(167\) −36.4796 −0.218441 −0.109220 0.994018i \(-0.534835\pi\)
−0.109220 + 0.994018i \(0.534835\pi\)
\(168\) 0 0
\(169\) 48.2981i 0.285788i
\(170\) 79.6229 49.4633i 0.468370 0.290961i
\(171\) 0 0
\(172\) −160.129 + 54.1967i −0.930982 + 0.315097i
\(173\) −97.6419 + 97.6419i −0.564404 + 0.564404i −0.930555 0.366151i \(-0.880675\pi\)
0.366151 + 0.930555i \(0.380675\pi\)
\(174\) 0 0
\(175\) 21.8598i 0.124913i
\(176\) −220.043 29.3700i −1.25024 0.166875i
\(177\) 0 0
\(178\) 247.674 + 57.8664i 1.39143 + 0.325092i
\(179\) −89.7427 89.7427i −0.501356 0.501356i 0.410503 0.911859i \(-0.365353\pi\)
−0.911859 + 0.410503i \(0.865353\pi\)
\(180\) 0 0
\(181\) −115.497 115.497i −0.638108 0.638108i 0.311981 0.950088i \(-0.399008\pi\)
−0.950088 + 0.311981i \(0.899008\pi\)
\(182\) −140.649 226.408i −0.772796 1.24400i
\(183\) 0 0
\(184\) 103.008 125.173i 0.559827 0.680287i
\(185\) 161.610i 0.873569i
\(186\) 0 0
\(187\) 95.4682 95.4682i 0.510525 0.510525i
\(188\) −55.5325 + 112.355i −0.295386 + 0.597634i
\(189\) 0 0
\(190\) −149.667 34.9681i −0.787722 0.184043i
\(191\) 62.6278i 0.327894i 0.986469 + 0.163947i \(0.0524227\pi\)
−0.986469 + 0.163947i \(0.947577\pi\)
\(192\) 0 0
\(193\) 223.342 1.15721 0.578607 0.815607i \(-0.303597\pi\)
0.578607 + 0.815607i \(0.303597\pi\)
\(194\) 67.0468 286.967i 0.345602 1.47921i
\(195\) 0 0
\(196\) −351.938 173.948i −1.79560 0.887491i
\(197\) −29.0959 29.0959i −0.147695 0.147695i 0.629393 0.777087i \(-0.283304\pi\)
−0.777087 + 0.629393i \(0.783304\pi\)
\(198\) 0 0
\(199\) 11.6967 0.0587776 0.0293888 0.999568i \(-0.490644\pi\)
0.0293888 + 0.999568i \(0.490644\pi\)
\(200\) −11.1319 9.16074i −0.0556595 0.0458037i
\(201\) 0 0
\(202\) 30.6786 19.0581i 0.151874 0.0943472i
\(203\) 199.021 199.021i 0.980398 0.980398i
\(204\) 0 0
\(205\) 84.2755 84.2755i 0.411100 0.411100i
\(206\) 8.08220 34.5927i 0.0392340 0.167926i
\(207\) 0 0
\(208\) −174.238 23.2562i −0.837682 0.111809i
\(209\) −221.378 −1.05923
\(210\) 0 0
\(211\) −0.215765 0.215765i −0.00102258 0.00102258i 0.706595 0.707618i \(-0.250230\pi\)
−0.707618 + 0.706595i \(0.750230\pi\)
\(212\) 66.8728 + 197.582i 0.315438 + 0.931989i
\(213\) 0 0
\(214\) 23.7146 + 38.1742i 0.110816 + 0.178384i
\(215\) 203.556 0.946773
\(216\) 0 0
\(217\) 319.684i 1.47320i
\(218\) −118.396 190.586i −0.543099 0.874247i
\(219\) 0 0
\(220\) 239.632 + 118.440i 1.08924 + 0.538365i
\(221\) 75.5951 75.5951i 0.342059 0.342059i
\(222\) 0 0
\(223\) 371.347i 1.66523i 0.553850 + 0.832617i \(0.313158\pi\)
−0.553850 + 0.832617i \(0.686842\pi\)
\(224\) −353.928 + 159.409i −1.58004 + 0.711648i
\(225\) 0 0
\(226\) −76.2337 + 326.288i −0.337317 + 1.44375i
\(227\) 209.823 + 209.823i 0.924330 + 0.924330i 0.997332 0.0730018i \(-0.0232579\pi\)
−0.0730018 + 0.997332i \(0.523258\pi\)
\(228\) 0 0
\(229\) 152.751 + 152.751i 0.667037 + 0.667037i 0.957029 0.289992i \(-0.0936527\pi\)
−0.289992 + 0.957029i \(0.593653\pi\)
\(230\) −165.806 + 103.002i −0.720895 + 0.447834i
\(231\) 0 0
\(232\) −17.9462 184.753i −0.0773544 0.796350i
\(233\) 272.899i 1.17124i 0.810586 + 0.585619i \(0.199149\pi\)
−0.810586 + 0.585619i \(0.800851\pi\)
\(234\) 0 0
\(235\) 106.710 106.710i 0.454084 0.454084i
\(236\) −75.7259 + 25.6299i −0.320873 + 0.108601i
\(237\) 0 0
\(238\) 53.7104 229.886i 0.225674 0.965908i
\(239\) 104.650i 0.437866i −0.975740 0.218933i \(-0.929742\pi\)
0.975740 0.218933i \(-0.0702576\pi\)
\(240\) 0 0
\(241\) 148.875 0.617737 0.308869 0.951105i \(-0.400050\pi\)
0.308869 + 0.951105i \(0.400050\pi\)
\(242\) 139.261 + 32.5369i 0.575460 + 0.134450i
\(243\) 0 0
\(244\) 227.833 77.1117i 0.933743 0.316031i
\(245\) 334.254 + 334.254i 1.36430 + 1.36430i
\(246\) 0 0
\(247\) −175.295 −0.709698
\(248\) 162.797 + 133.970i 0.656438 + 0.540201i
\(249\) 0 0
\(250\) 136.239 + 219.308i 0.544954 + 0.877233i
\(251\) −143.712 + 143.712i −0.572558 + 0.572558i −0.932843 0.360284i \(-0.882680\pi\)
0.360284 + 0.932843i \(0.382680\pi\)
\(252\) 0 0
\(253\) −198.802 + 198.802i −0.785778 + 0.785778i
\(254\) 386.096 + 90.2071i 1.52006 + 0.355146i
\(255\) 0 0
\(256\) −67.1424 + 247.038i −0.262275 + 0.964993i
\(257\) −134.023 −0.521489 −0.260745 0.965408i \(-0.583968\pi\)
−0.260745 + 0.965408i \(0.583968\pi\)
\(258\) 0 0
\(259\) −287.807 287.807i −1.11122 1.11122i
\(260\) 189.749 + 93.7853i 0.729806 + 0.360713i
\(261\) 0 0
\(262\) 322.759 200.504i 1.23190 0.765283i
\(263\) −290.386 −1.10413 −0.552066 0.833801i \(-0.686160\pi\)
−0.552066 + 0.833801i \(0.686160\pi\)
\(264\) 0 0
\(265\) 251.166i 0.947798i
\(266\) −328.812 + 204.264i −1.23613 + 0.767911i
\(267\) 0 0
\(268\) −88.4627 261.371i −0.330085 0.975264i
\(269\) 74.2628 74.2628i 0.276070 0.276070i −0.555468 0.831538i \(-0.687461\pi\)
0.831538 + 0.555468i \(0.187461\pi\)
\(270\) 0 0
\(271\) 70.8329i 0.261376i −0.991424 0.130688i \(-0.958281\pi\)
0.991424 0.130688i \(-0.0417186\pi\)
\(272\) −94.5593 123.690i −0.347644 0.454742i
\(273\) 0 0
\(274\) −498.451 116.458i −1.81916 0.425028i
\(275\) 17.6799 + 17.6799i 0.0642906 + 0.0642906i
\(276\) 0 0
\(277\) −96.6953 96.6953i −0.349081 0.349081i 0.510686 0.859767i \(-0.329391\pi\)
−0.859767 + 0.510686i \(0.829391\pi\)
\(278\) −32.4223 52.1914i −0.116627 0.187739i
\(279\) 0 0
\(280\) 465.209 45.1886i 1.66146 0.161388i
\(281\) 138.151i 0.491640i −0.969316 0.245820i \(-0.920943\pi\)
0.969316 0.245820i \(-0.0790572\pi\)
\(282\) 0 0
\(283\) −295.011 + 295.011i −1.04244 + 1.04244i −0.0433821 + 0.999059i \(0.513813\pi\)
−0.999059 + 0.0433821i \(0.986187\pi\)
\(284\) 27.7526 + 13.7170i 0.0977204 + 0.0482991i
\(285\) 0 0
\(286\) 296.871 + 69.3607i 1.03801 + 0.242520i
\(287\) 300.168i 1.04588i
\(288\) 0 0
\(289\) −194.310 −0.672353
\(290\) −50.8510 + 217.648i −0.175348 + 0.750510i
\(291\) 0 0
\(292\) −151.389 + 306.295i −0.518455 + 1.04896i
\(293\) 33.4759 + 33.4759i 0.114252 + 0.114252i 0.761922 0.647669i \(-0.224256\pi\)
−0.647669 + 0.761922i \(0.724256\pi\)
\(294\) 0 0
\(295\) 96.2630 0.326315
\(296\) −267.174 + 25.9523i −0.902616 + 0.0876768i
\(297\) 0 0
\(298\) −82.2748 + 51.1107i −0.276090 + 0.171513i
\(299\) −157.418 + 157.418i −0.526483 + 0.526483i
\(300\) 0 0
\(301\) 362.508 362.508i 1.20434 1.20434i
\(302\) 6.58169 28.1703i 0.0217937 0.0932792i
\(303\) 0 0
\(304\) −33.7749 + 253.046i −0.111102 + 0.832387i
\(305\) −289.622 −0.949582
\(306\) 0 0
\(307\) −92.6638 92.6638i −0.301836 0.301836i 0.539896 0.841732i \(-0.318464\pi\)
−0.841732 + 0.539896i \(0.818464\pi\)
\(308\) 637.682 215.828i 2.07040 0.700739i
\(309\) 0 0
\(310\) −133.962 215.643i −0.432135 0.695623i
\(311\) 18.5610 0.0596817 0.0298408 0.999555i \(-0.490500\pi\)
0.0298408 + 0.999555i \(0.490500\pi\)
\(312\) 0 0
\(313\) 55.1534i 0.176209i 0.996111 + 0.0881045i \(0.0280809\pi\)
−0.996111 + 0.0881045i \(0.971919\pi\)
\(314\) 46.9626 + 75.5975i 0.149563 + 0.240756i
\(315\) 0 0
\(316\) −186.619 + 377.573i −0.590566 + 1.19485i
\(317\) −62.2977 + 62.2977i −0.196523 + 0.196523i −0.798507 0.601985i \(-0.794377\pi\)
0.601985 + 0.798507i \(0.294377\pi\)
\(318\) 0 0
\(319\) 321.931i 1.00919i
\(320\) 171.943 255.841i 0.537320 0.799502i
\(321\) 0 0
\(322\) −111.846 + 478.712i −0.347348 + 1.48668i
\(323\) −109.787 109.787i −0.339897 0.339897i
\(324\) 0 0
\(325\) 13.9996 + 13.9996i 0.0430756 + 0.0430756i
\(326\) −75.4414 + 46.8657i −0.231415 + 0.143760i
\(327\) 0 0
\(328\) −152.858 125.791i −0.466030 0.383509i
\(329\) 380.073i 1.15524i
\(330\) 0 0
\(331\) 373.767 373.767i 1.12921 1.12921i 0.138899 0.990307i \(-0.455644\pi\)
0.990307 0.138899i \(-0.0443564\pi\)
\(332\) −112.663 332.871i −0.339345 1.00262i
\(333\) 0 0
\(334\) 16.5991 71.0459i 0.0496979 0.212712i
\(335\) 332.255i 0.991807i
\(336\) 0 0
\(337\) −519.936 −1.54284 −0.771419 0.636328i \(-0.780453\pi\)
−0.771419 + 0.636328i \(0.780453\pi\)
\(338\) −94.0630 21.9768i −0.278293 0.0650201i
\(339\) 0 0
\(340\) 60.1020 + 177.577i 0.176771 + 0.522284i
\(341\) −258.557 258.557i −0.758231 0.758231i
\(342\) 0 0
\(343\) 596.142 1.73802
\(344\) −32.6883 336.520i −0.0950240 0.978255i
\(345\) 0 0
\(346\) −145.733 234.592i −0.421194 0.678011i
\(347\) −122.160 + 122.160i −0.352045 + 0.352045i −0.860870 0.508825i \(-0.830080\pi\)
0.508825 + 0.860870i \(0.330080\pi\)
\(348\) 0 0
\(349\) −279.483 + 279.483i −0.800810 + 0.800810i −0.983222 0.182412i \(-0.941609\pi\)
0.182412 + 0.983222i \(0.441609\pi\)
\(350\) 42.5730 + 9.94671i 0.121637 + 0.0284192i
\(351\) 0 0
\(352\) 157.324 415.181i 0.446944 1.17949i
\(353\) 212.266 0.601320 0.300660 0.953731i \(-0.402793\pi\)
0.300660 + 0.953731i \(0.402793\pi\)
\(354\) 0 0
\(355\) −26.3581 26.3581i −0.0742482 0.0742482i
\(356\) −225.396 + 456.028i −0.633134 + 1.28098i
\(357\) 0 0
\(358\) 215.614 133.943i 0.602272 0.374144i
\(359\) 435.033 1.21179 0.605895 0.795545i \(-0.292815\pi\)
0.605895 + 0.795545i \(0.292815\pi\)
\(360\) 0 0
\(361\) 106.419i 0.294789i
\(362\) 277.491 172.383i 0.766551 0.476196i
\(363\) 0 0
\(364\) 504.939 170.900i 1.38720 0.469505i
\(365\) 290.905 290.905i 0.796999 0.796999i
\(366\) 0 0
\(367\) 125.535i 0.342058i −0.985266 0.171029i \(-0.945291\pi\)
0.985266 0.171029i \(-0.0547091\pi\)
\(368\) 196.909 + 257.570i 0.535079 + 0.699919i
\(369\) 0 0
\(370\) 314.744 + 73.5365i 0.850660 + 0.198747i
\(371\) −447.295 447.295i −1.20565 1.20565i
\(372\) 0 0
\(373\) −302.389 302.389i −0.810694 0.810694i 0.174044 0.984738i \(-0.444317\pi\)
−0.984738 + 0.174044i \(0.944317\pi\)
\(374\) 142.489 + 229.370i 0.380986 + 0.613287i
\(375\) 0 0
\(376\) −193.549 159.277i −0.514758 0.423608i
\(377\) 254.917i 0.676171i
\(378\) 0 0
\(379\) 189.784 189.784i 0.500751 0.500751i −0.410921 0.911671i \(-0.634793\pi\)
0.911671 + 0.410921i \(0.134793\pi\)
\(380\) 136.204 275.573i 0.358432 0.725192i
\(381\) 0 0
\(382\) −121.971 28.4972i −0.319296 0.0745999i
\(383\) 639.916i 1.67080i 0.549644 + 0.835399i \(0.314763\pi\)
−0.549644 + 0.835399i \(0.685237\pi\)
\(384\) 0 0
\(385\) −810.623 −2.10551
\(386\) −101.626 + 434.970i −0.263280 + 1.12687i
\(387\) 0 0
\(388\) 528.376 + 261.154i 1.36179 + 0.673078i
\(389\) −499.333 499.333i −1.28363 1.28363i −0.938586 0.345046i \(-0.887863\pi\)
−0.345046 0.938586i \(-0.612137\pi\)
\(390\) 0 0
\(391\) −197.181 −0.504300
\(392\) 498.913 606.266i 1.27274 1.54660i
\(393\) 0 0
\(394\) 69.9050 43.4264i 0.177424 0.110219i
\(395\) 358.601 358.601i 0.907851 0.907851i
\(396\) 0 0
\(397\) 492.518 492.518i 1.24060 1.24060i 0.280846 0.959753i \(-0.409385\pi\)
0.959753 0.280846i \(-0.0906151\pi\)
\(398\) −5.32230 + 22.7800i −0.0133726 + 0.0572361i
\(399\) 0 0
\(400\) 22.9063 17.5116i 0.0572657 0.0437789i
\(401\) −705.045 −1.75822 −0.879109 0.476621i \(-0.841862\pi\)
−0.879109 + 0.476621i \(0.841862\pi\)
\(402\) 0 0
\(403\) −204.735 204.735i −0.508026 0.508026i
\(404\) 23.1572 + 68.4200i 0.0573198 + 0.169356i
\(405\) 0 0
\(406\) 297.044 + 478.162i 0.731635 + 1.17774i
\(407\) 465.550 1.14386
\(408\) 0 0
\(409\) 279.815i 0.684144i 0.939674 + 0.342072i \(0.111129\pi\)
−0.939674 + 0.342072i \(0.888871\pi\)
\(410\) 125.783 + 202.478i 0.306789 + 0.493849i
\(411\) 0 0
\(412\) 63.6934 + 31.4810i 0.154596 + 0.0764102i
\(413\) 171.432 171.432i 0.415090 0.415090i
\(414\) 0 0
\(415\) 423.147i 1.01963i
\(416\) 124.575 328.755i 0.299459 0.790276i
\(417\) 0 0
\(418\) 100.732 431.146i 0.240987 1.03145i
\(419\) 573.583 + 573.583i 1.36893 + 1.36893i 0.861965 + 0.506968i \(0.169234\pi\)
0.506968 + 0.861965i \(0.330766\pi\)
\(420\) 0 0
\(421\) −213.341 213.341i −0.506749 0.506749i 0.406778 0.913527i \(-0.366652\pi\)
−0.913527 + 0.406778i \(0.866652\pi\)
\(422\) 0.518392 0.322035i 0.00122842 0.000763117i
\(423\) 0 0
\(424\) −415.229 + 40.3338i −0.979314 + 0.0951269i
\(425\) 17.5358i 0.0412606i
\(426\) 0 0
\(427\) −515.781 + 515.781i −1.20792 + 1.20792i
\(428\) −85.1369 + 28.8152i −0.198918 + 0.0673251i
\(429\) 0 0
\(430\) −92.6230 + 396.436i −0.215402 + 0.921944i
\(431\) 166.900i 0.387239i −0.981077 0.193619i \(-0.937977\pi\)
0.981077 0.193619i \(-0.0620227\pi\)
\(432\) 0 0
\(433\) 233.153 0.538459 0.269230 0.963076i \(-0.413231\pi\)
0.269230 + 0.963076i \(0.413231\pi\)
\(434\) −622.602 145.464i −1.43457 0.335171i
\(435\) 0 0
\(436\) 425.048 143.860i 0.974882 0.329955i
\(437\) 228.619 + 228.619i 0.523155 + 0.523155i
\(438\) 0 0
\(439\) 440.480 1.00337 0.501686 0.865050i \(-0.332713\pi\)
0.501686 + 0.865050i \(0.332713\pi\)
\(440\) −339.707 + 412.803i −0.772061 + 0.938189i
\(441\) 0 0
\(442\) 112.828 + 181.623i 0.255266 + 0.410912i
\(443\) 312.524 312.524i 0.705473 0.705473i −0.260107 0.965580i \(-0.583758\pi\)
0.965580 + 0.260107i \(0.0837579\pi\)
\(444\) 0 0
\(445\) 433.114 433.114i 0.973290 0.973290i
\(446\) −723.217 168.972i −1.62156 0.378861i
\(447\) 0 0
\(448\) −149.412 761.827i −0.333509 1.70051i
\(449\) 734.338 1.63550 0.817748 0.575576i \(-0.195222\pi\)
0.817748 + 0.575576i \(0.195222\pi\)
\(450\) 0 0
\(451\) 242.772 + 242.772i 0.538297 + 0.538297i
\(452\) −600.774 296.938i −1.32915 0.656942i
\(453\) 0 0
\(454\) −504.115 + 313.166i −1.11039 + 0.689794i
\(455\) −641.880 −1.41073
\(456\) 0 0
\(457\) 692.749i 1.51586i 0.652335 + 0.757931i \(0.273789\pi\)
−0.652335 + 0.757931i \(0.726211\pi\)
\(458\) −366.997 + 227.986i −0.801303 + 0.497785i
\(459\) 0 0
\(460\) −125.156 369.784i −0.272078 0.803878i
\(461\) −298.447 + 298.447i −0.647391 + 0.647391i −0.952362 0.304971i \(-0.901353\pi\)
0.304971 + 0.952362i \(0.401353\pi\)
\(462\) 0 0
\(463\) 281.830i 0.608705i 0.952560 + 0.304352i \(0.0984400\pi\)
−0.952560 + 0.304352i \(0.901560\pi\)
\(464\) 367.982 + 49.1159i 0.793065 + 0.105853i
\(465\) 0 0
\(466\) −531.484 124.175i −1.14052 0.266471i
\(467\) −198.116 198.116i −0.424232 0.424232i 0.462426 0.886658i \(-0.346979\pi\)
−0.886658 + 0.462426i \(0.846979\pi\)
\(468\) 0 0
\(469\) 591.704 + 591.704i 1.26163 + 1.26163i
\(470\) 159.267 + 256.378i 0.338866 + 0.545485i
\(471\) 0 0
\(472\) −15.4585 159.142i −0.0327510 0.337166i
\(473\) 586.384i 1.23971i
\(474\) 0 0
\(475\) 20.3316 20.3316i 0.0428033 0.0428033i
\(476\) 423.276 + 209.207i 0.889234 + 0.439512i
\(477\) 0 0
\(478\) 203.811 + 47.6182i 0.426383 + 0.0996197i
\(479\) 917.713i 1.91589i 0.286945 + 0.957947i \(0.407360\pi\)
−0.286945 + 0.957947i \(0.592640\pi\)
\(480\) 0 0
\(481\) 368.639 0.766401
\(482\) −67.7416 + 289.941i −0.140543 + 0.601537i
\(483\) 0 0
\(484\) −126.735 + 256.413i −0.261848 + 0.529780i
\(485\) −501.826 501.826i −1.03469 1.03469i
\(486\) 0 0
\(487\) −426.183 −0.875119 −0.437559 0.899190i \(-0.644157\pi\)
−0.437559 + 0.899190i \(0.644157\pi\)
\(488\) 46.5093 + 478.805i 0.0953059 + 0.981157i
\(489\) 0 0
\(490\) −803.070 + 498.883i −1.63892 + 1.01813i
\(491\) 266.299 266.299i 0.542361 0.542361i −0.381859 0.924220i \(-0.624716\pi\)
0.924220 + 0.381859i \(0.124716\pi\)
\(492\) 0 0
\(493\) −159.653 + 159.653i −0.323840 + 0.323840i
\(494\) 79.7636 341.396i 0.161465 0.691086i
\(495\) 0 0
\(496\) −334.989 + 256.095i −0.675382 + 0.516321i
\(497\) −93.8809 −0.188895
\(498\) 0 0
\(499\) −264.104 264.104i −0.529266 0.529266i 0.391088 0.920353i \(-0.372099\pi\)
−0.920353 + 0.391088i \(0.872099\pi\)
\(500\) −489.106 + 165.541i −0.978211 + 0.331082i
\(501\) 0 0
\(502\) −214.494 345.279i −0.427279 0.687807i
\(503\) 574.766 1.14268 0.571338 0.820715i \(-0.306425\pi\)
0.571338 + 0.820715i \(0.306425\pi\)
\(504\) 0 0
\(505\) 86.9756i 0.172229i
\(506\) −296.717 477.636i −0.586398 0.943946i
\(507\) 0 0
\(508\) −351.366 + 710.895i −0.691665 + 1.39940i
\(509\) −170.592 + 170.592i −0.335152 + 0.335152i −0.854539 0.519387i \(-0.826160\pi\)
0.519387 + 0.854539i \(0.326160\pi\)
\(510\) 0 0
\(511\) 1036.13i 2.02765i
\(512\) −450.568 243.172i −0.880016 0.474944i
\(513\) 0 0
\(514\) 60.9835 261.016i 0.118645 0.507813i
\(515\) −60.4930 60.4930i −0.117462 0.117462i
\(516\) 0 0
\(517\) 307.398 + 307.398i 0.594581 + 0.594581i
\(518\) 691.478 429.560i 1.33490 0.829266i
\(519\) 0 0
\(520\) −268.992 + 326.872i −0.517293 + 0.628600i
\(521\) 37.1210i 0.0712496i −0.999365 0.0356248i \(-0.988658\pi\)
0.999365 0.0356248i \(-0.0113421\pi\)
\(522\) 0 0
\(523\) −199.555 + 199.555i −0.381558 + 0.381558i −0.871663 0.490105i \(-0.836958\pi\)
0.490105 + 0.871663i \(0.336958\pi\)
\(524\) 243.629 + 719.823i 0.464941 + 1.37371i
\(525\) 0 0
\(526\) 132.133 565.542i 0.251203 1.07518i
\(527\) 256.449i 0.486620i
\(528\) 0 0
\(529\) −118.392 −0.223804
\(530\) 489.159 + 114.287i 0.922942 + 0.215635i
\(531\) 0 0
\(532\) −248.198 733.323i −0.466538 1.37843i
\(533\) 192.236 + 192.236i 0.360667 + 0.360667i
\(534\) 0 0
\(535\) 108.226 0.202292
\(536\) 549.286 53.3555i 1.02479 0.0995439i
\(537\) 0 0
\(538\) 110.839 + 178.422i 0.206021 + 0.331639i
\(539\) −962.884 + 962.884i −1.78643 + 1.78643i
\(540\) 0 0
\(541\) 278.121 278.121i 0.514086 0.514086i −0.401690 0.915776i \(-0.631577\pi\)
0.915776 + 0.401690i \(0.131577\pi\)
\(542\) 137.951 + 32.2307i 0.254521 + 0.0594661i
\(543\) 0 0
\(544\) 283.919 127.877i 0.521910 0.235068i
\(545\) −540.323 −0.991418
\(546\) 0 0
\(547\) 724.938 + 724.938i 1.32530 + 1.32530i 0.909421 + 0.415876i \(0.136525\pi\)
0.415876 + 0.909421i \(0.363475\pi\)
\(548\) 453.614 917.767i 0.827763 1.67476i
\(549\) 0 0
\(550\) −42.4773 + 26.3877i −0.0772314 + 0.0479777i
\(551\) 370.215 0.671897
\(552\) 0 0
\(553\) 1277.25i 2.30967i
\(554\) 232.318 144.320i 0.419346 0.260506i
\(555\) 0 0
\(556\) 116.398 39.3958i 0.209350 0.0708558i
\(557\) −268.298 + 268.298i −0.481685 + 0.481685i −0.905669 0.423985i \(-0.860631\pi\)
0.423985 + 0.905669i \(0.360631\pi\)
\(558\) 0 0
\(559\) 464.320i 0.830625i
\(560\) −123.674 + 926.579i −0.220846 + 1.65461i
\(561\) 0 0
\(562\) 269.056 + 62.8619i 0.478747 + 0.111854i
\(563\) 78.4662 + 78.4662i 0.139372 + 0.139372i 0.773350 0.633979i \(-0.218579\pi\)
−0.633979 + 0.773350i \(0.718579\pi\)
\(564\) 0 0
\(565\) 570.587 + 570.587i 1.00989 + 1.00989i
\(566\) −440.311 708.785i −0.777935 1.25227i
\(567\) 0 0
\(568\) −39.3426 + 47.8080i −0.0692651 + 0.0841691i
\(569\) 801.999i 1.40949i −0.709461 0.704744i \(-0.751062\pi\)
0.709461 0.704744i \(-0.248938\pi\)
\(570\) 0 0
\(571\) 79.9964 79.9964i 0.140099 0.140099i −0.633579 0.773678i \(-0.718415\pi\)
0.773678 + 0.633579i \(0.218415\pi\)
\(572\) −270.167 + 546.611i −0.472320 + 0.955613i
\(573\) 0 0
\(574\) 584.592 + 136.583i 1.01845 + 0.237950i
\(575\) 36.5163i 0.0635066i
\(576\) 0 0
\(577\) −237.186 −0.411068 −0.205534 0.978650i \(-0.565893\pi\)
−0.205534 + 0.978650i \(0.565893\pi\)
\(578\) 88.4158 378.429i 0.152968 0.654721i
\(579\) 0 0
\(580\) −400.742 198.070i −0.690934 0.341500i
\(581\) 753.571 + 753.571i 1.29702 + 1.29702i
\(582\) 0 0
\(583\) 723.534 1.24105
\(584\) −527.639 434.209i −0.903492 0.743509i
\(585\) 0 0
\(586\) −80.4283 + 49.9637i −0.137250 + 0.0852622i
\(587\) 267.958 267.958i 0.456487 0.456487i −0.441014 0.897500i \(-0.645381\pi\)
0.897500 + 0.441014i \(0.145381\pi\)
\(588\) 0 0
\(589\) −297.336 + 297.336i −0.504815 + 0.504815i
\(590\) −43.8020 + 187.477i −0.0742407 + 0.317758i
\(591\) 0 0
\(592\) 71.0273 532.145i 0.119979 0.898893i
\(593\) 607.086 1.02375 0.511877 0.859059i \(-0.328950\pi\)
0.511877 + 0.859059i \(0.328950\pi\)
\(594\) 0 0
\(595\) −402.007 402.007i −0.675642 0.675642i
\(596\) −62.1037 183.491i −0.104201 0.307871i
\(597\) 0 0
\(598\) −234.951 378.210i −0.392895 0.632457i
\(599\) −575.392 −0.960587 −0.480294 0.877108i \(-0.659470\pi\)
−0.480294 + 0.877108i \(0.659470\pi\)
\(600\) 0 0
\(601\) 310.094i 0.515963i 0.966150 + 0.257981i \(0.0830573\pi\)
−0.966150 + 0.257981i \(0.916943\pi\)
\(602\) 541.052 + 870.952i 0.898758 + 1.44676i
\(603\) 0 0
\(604\) 51.8683 + 25.6363i 0.0858746 + 0.0424443i
\(605\) 243.529 243.529i 0.402528 0.402528i
\(606\) 0 0
\(607\) 556.510i 0.916820i 0.888741 + 0.458410i \(0.151581\pi\)
−0.888741 + 0.458410i \(0.848419\pi\)
\(608\) −477.451 180.920i −0.785281 0.297566i
\(609\) 0 0
\(610\) 131.785 564.054i 0.216041 0.924679i
\(611\) 243.409 + 243.409i 0.398378 + 0.398378i
\(612\) 0 0
\(613\) −326.241 326.241i −0.532204 0.532204i 0.389024 0.921228i \(-0.372812\pi\)
−0.921228 + 0.389024i \(0.872812\pi\)
\(614\) 222.632 138.303i 0.362592 0.225249i
\(615\) 0 0
\(616\) 130.175 + 1340.12i 0.211323 + 2.17553i
\(617\) 502.068i 0.813725i −0.913490 0.406862i \(-0.866623\pi\)
0.913490 0.406862i \(-0.133377\pi\)
\(618\) 0 0
\(619\) 304.429 304.429i 0.491808 0.491808i −0.417067 0.908876i \(-0.636942\pi\)
0.908876 + 0.417067i \(0.136942\pi\)
\(620\) 480.932 162.774i 0.775696 0.262539i
\(621\) 0 0
\(622\) −8.44570 + 36.1485i −0.0135783 + 0.0581166i
\(623\) 1542.64i 2.47615i
\(624\) 0 0
\(625\) 576.701 0.922721
\(626\) −107.414 25.0961i −0.171588 0.0400896i
\(627\) 0 0
\(628\) −168.599 + 57.0635i −0.268470 + 0.0908654i
\(629\) 230.877 + 230.877i 0.367054 + 0.367054i
\(630\) 0 0
\(631\) 8.60592 0.0136385 0.00681927 0.999977i \(-0.497829\pi\)
0.00681927 + 0.999977i \(0.497829\pi\)
\(632\) −650.427 535.254i −1.02916 0.846921i
\(633\) 0 0
\(634\) −92.9809 149.675i −0.146658 0.236080i
\(635\) 675.174 675.174i 1.06327 1.06327i
\(636\) 0 0
\(637\) −762.446 + 762.446i −1.19693 + 1.19693i
\(638\) −626.977 146.486i −0.982723 0.229603i
\(639\) 0 0
\(640\) 420.025 + 451.280i 0.656289 + 0.705126i
\(641\) 445.780 0.695445 0.347722 0.937598i \(-0.386955\pi\)
0.347722 + 0.937598i \(0.386955\pi\)
\(642\) 0 0
\(643\) −118.001 118.001i −0.183517 0.183517i 0.609369 0.792886i \(-0.291423\pi\)
−0.792886 + 0.609369i \(0.791423\pi\)
\(644\) −881.424 435.651i −1.36867 0.676477i
\(645\) 0 0
\(646\) 263.771 163.860i 0.408314 0.253653i
\(647\) −1081.35 −1.67132 −0.835662 0.549243i \(-0.814916\pi\)
−0.835662 + 0.549243i \(0.814916\pi\)
\(648\) 0 0
\(649\) 277.305i 0.427280i
\(650\) −33.6350 + 20.8947i −0.0517462 + 0.0321458i
\(651\) 0 0
\(652\) −56.9457 168.251i −0.0873400 0.258054i
\(653\) 586.227 586.227i 0.897744 0.897744i −0.0974927 0.995236i \(-0.531082\pi\)
0.995236 + 0.0974927i \(0.0310823\pi\)
\(654\) 0 0
\(655\) 915.041i 1.39701i
\(656\) 314.538 240.461i 0.479479 0.366556i
\(657\) 0 0
\(658\) 740.211 + 172.942i 1.12494 + 0.262830i
\(659\) −469.999 469.999i −0.713201 0.713201i 0.254003 0.967204i \(-0.418253\pi\)
−0.967204 + 0.254003i \(0.918253\pi\)
\(660\) 0 0
\(661\) −884.745 884.745i −1.33849 1.33849i −0.897519 0.440976i \(-0.854632\pi\)
−0.440976 0.897519i \(-0.645368\pi\)
\(662\) 557.857 + 898.003i 0.842685 + 1.35650i
\(663\) 0 0
\(664\) 699.548 67.9515i 1.05354 0.102337i
\(665\) 932.202i 1.40181i
\(666\) 0 0
\(667\) 332.460 332.460i 0.498441 0.498441i
\(668\) 130.813 + 64.6552i 0.195827 + 0.0967892i
\(669\) 0 0
\(670\) −647.084 151.184i −0.965797 0.225648i
\(671\) 834.314i 1.24339i
\(672\) 0 0
\(673\) 684.329 1.01683 0.508417 0.861111i \(-0.330231\pi\)
0.508417 + 0.861111i \(0.330231\pi\)
\(674\) 236.584 1012.60i 0.351014 1.50238i
\(675\) 0 0
\(676\) 85.6018 173.192i 0.126630 0.256202i
\(677\) 383.762 + 383.762i 0.566857 + 0.566857i 0.931246 0.364390i \(-0.118722\pi\)
−0.364390 + 0.931246i \(0.618722\pi\)
\(678\) 0 0
\(679\) −1787.38 −2.63237
\(680\) −373.188 + 36.2500i −0.548805 + 0.0533089i
\(681\) 0 0
\(682\) 621.202 385.903i 0.910854 0.565840i
\(683\) −903.626 + 903.626i −1.32302 + 1.32302i −0.411709 + 0.911315i \(0.635068\pi\)
−0.911315 + 0.411709i \(0.864932\pi\)
\(684\) 0 0
\(685\) −871.652 + 871.652i −1.27248 + 1.27248i
\(686\) −271.259 + 1161.02i −0.395421 + 1.69244i
\(687\) 0 0
\(688\) 670.263 + 89.4625i 0.974220 + 0.130033i
\(689\) 572.920 0.831524
\(690\) 0 0
\(691\) −63.6870 63.6870i −0.0921665 0.0921665i 0.659520 0.751687i \(-0.270759\pi\)
−0.751687 + 0.659520i \(0.770759\pi\)
\(692\) 523.192 177.078i 0.756057 0.255893i
\(693\) 0 0
\(694\) −182.326 293.497i −0.262718 0.422907i
\(695\) −147.966 −0.212901
\(696\) 0 0
\(697\) 240.793i 0.345470i
\(698\) −417.135 671.478i −0.597615 0.962003i
\(699\) 0 0
\(700\) −38.7434 + 78.3870i −0.0553478 + 0.111981i
\(701\) −218.312 + 218.312i −0.311430 + 0.311430i −0.845463 0.534033i \(-0.820676\pi\)
0.534033 + 0.845463i \(0.320676\pi\)
\(702\) 0 0
\(703\) 535.374i 0.761557i
\(704\) 736.999 + 495.314i 1.04687 + 0.703571i
\(705\) 0 0
\(706\) −96.5861 + 413.399i −0.136808 + 0.585551i
\(707\) −154.893 154.893i −0.219084 0.219084i
\(708\) 0 0
\(709\) −822.199 822.199i −1.15966 1.15966i −0.984548 0.175112i \(-0.943971\pi\)
−0.175112 0.984548i \(-0.556029\pi\)
\(710\) 63.3273 39.3402i 0.0891934 0.0554087i
\(711\) 0 0
\(712\) −785.577 646.473i −1.10334 0.907968i
\(713\) 534.026i 0.748985i
\(714\) 0 0
\(715\) 519.145 519.145i 0.726077 0.726077i
\(716\) 162.752 + 480.866i 0.227307 + 0.671600i
\(717\) 0 0
\(718\) −197.950 + 847.248i −0.275697 + 1.18001i
\(719\) 340.913i 0.474149i 0.971491 + 0.237074i \(0.0761885\pi\)
−0.971491 + 0.237074i \(0.923811\pi\)
\(720\) 0 0
\(721\) −215.461 −0.298836
\(722\) 207.256 + 48.4231i 0.287058 + 0.0670680i
\(723\) 0 0
\(724\) 209.460 + 618.867i 0.289309 + 0.854788i
\(725\) −29.5664 29.5664i −0.0407813 0.0407813i
\(726\) 0 0
\(727\) −803.090 −1.10466 −0.552331 0.833625i \(-0.686262\pi\)
−0.552331 + 0.833625i \(0.686262\pi\)
\(728\) 103.077 + 1061.16i 0.141589 + 1.45763i
\(729\) 0 0
\(730\) 434.183 + 698.920i 0.594771 + 0.957424i
\(731\) −290.802 + 290.802i −0.397813 + 0.397813i
\(732\) 0 0
\(733\) 481.592 481.592i 0.657015 0.657015i −0.297658 0.954673i \(-0.596205\pi\)
0.954673 + 0.297658i \(0.0962054\pi\)
\(734\) 244.486 + 57.1215i 0.333087 + 0.0778222i
\(735\) 0 0
\(736\) −591.229 + 266.290i −0.803301 + 0.361807i
\(737\) −957.127 −1.29868
\(738\) 0 0
\(739\) 173.622 + 173.622i 0.234941 + 0.234941i 0.814752 0.579810i \(-0.196873\pi\)
−0.579810 + 0.814752i \(0.696873\pi\)
\(740\) −286.432 + 579.519i −0.387071 + 0.783134i
\(741\) 0 0
\(742\) 1074.66 667.600i 1.44833 0.899731i
\(743\) −1316.22 −1.77149 −0.885744 0.464173i \(-0.846351\pi\)
−0.885744 + 0.464173i \(0.846351\pi\)
\(744\) 0 0
\(745\) 233.254i 0.313093i
\(746\) 726.512 451.323i 0.973876 0.604991i
\(747\) 0 0
\(748\) −511.545 + 173.136i −0.683883 + 0.231465i
\(749\) 192.737 192.737i 0.257326 0.257326i
\(750\) 0 0
\(751\) 322.977i 0.430062i 0.976607 + 0.215031i \(0.0689853\pi\)
−0.976607 + 0.215031i \(0.931015\pi\)
\(752\) 398.269 304.472i 0.529613 0.404882i
\(753\) 0 0
\(754\) −496.463 115.993i −0.658439 0.153837i
\(755\) −49.2621 49.2621i −0.0652478 0.0652478i
\(756\) 0 0
\(757\) −80.2744 80.2744i −0.106043 0.106043i 0.652095 0.758138i \(-0.273890\pi\)
−0.758138 + 0.652095i \(0.773890\pi\)
\(758\) 283.258 + 455.971i 0.373692 + 0.601545i
\(759\) 0 0
\(760\) 474.716 + 390.657i 0.624627 + 0.514023i
\(761\) 596.664i 0.784053i −0.919954 0.392027i \(-0.871774\pi\)
0.919954 0.392027i \(-0.128226\pi\)
\(762\) 0 0
\(763\) −962.246 + 962.246i −1.26113 + 1.26113i
\(764\) 110.999 224.578i 0.145287 0.293950i
\(765\) 0 0
\(766\) −1246.27 291.177i −1.62698 0.380127i
\(767\) 219.580i 0.286284i
\(768\) 0 0
\(769\) 1515.31 1.97050 0.985249 0.171129i \(-0.0547416\pi\)
0.985249 + 0.171129i \(0.0547416\pi\)
\(770\) 368.853 1578.73i 0.479030 2.05030i
\(771\) 0 0
\(772\) −800.884 395.844i −1.03741 0.512751i
\(773\) −607.901 607.901i −0.786418 0.786418i 0.194487 0.980905i \(-0.437696\pi\)
−0.980905 + 0.194487i \(0.937696\pi\)
\(774\) 0 0
\(775\) 47.4922 0.0612802
\(776\) −749.034 + 910.207i −0.965250 + 1.17295i
\(777\) 0 0
\(778\) 1199.68 745.267i 1.54201 0.957927i
\(779\) 279.184 279.184i 0.358387 0.358387i
\(780\) 0 0
\(781\) 75.9297 75.9297i 0.0972211 0.0972211i
\(782\) 89.7221 384.020i 0.114734 0.491074i
\(783\) 0 0
\(784\) 953.717 + 1247.52i 1.21648 + 1.59123i
\(785\)