Properties

Label 162.3.d.c.107.1
Level $162$
Weight $3$
Character 162.107
Analytic conductor $4.414$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.41418028264\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.1
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.3.d.c.53.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.01910 + 2.89778i) q^{5} +(4.19615 - 7.26795i) q^{7} -2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.01910 + 2.89778i) q^{5} +(4.19615 - 7.26795i) q^{7} -2.82843i q^{8} +8.19615 q^{10} +(12.7279 + 7.34847i) q^{11} +(10.5981 + 18.3564i) q^{13} +(-10.2784 + 5.93426i) q^{14} +(-2.00000 + 3.46410i) q^{16} -7.76457i q^{17} +24.3923 q^{19} +(-10.0382 - 5.79555i) q^{20} +(-10.3923 - 18.0000i) q^{22} +(12.7279 - 7.34847i) q^{23} +(4.29423 - 7.43782i) q^{25} -29.9759i q^{26} +16.7846 q^{28} +(30.7387 + 17.7470i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-5.49038 + 9.50962i) q^{34} +48.6381i q^{35} -60.5692 q^{37} +(-29.8744 - 17.2480i) q^{38} +(8.19615 + 14.1962i) q^{40} +(29.1301 - 16.8183i) q^{41} +(-4.58846 + 7.94744i) q^{43} +29.3939i q^{44} -20.7846 q^{46} +(-14.6969 - 8.48528i) q^{47} +(-10.7154 - 18.5596i) q^{49} +(-10.5187 + 6.07296i) q^{50} +(-21.1962 + 36.7128i) q^{52} -25.7605i q^{53} -85.1769 q^{55} +(-20.5569 - 11.8685i) q^{56} +(-25.0981 - 43.4711i) q^{58} +(-53.4083 + 30.8353i) q^{59} +(6.50000 - 11.2583i) q^{61} +11.3137i q^{62} -8.00000 q^{64} +(-106.386 - 61.4217i) q^{65} +(-10.5885 - 18.3397i) q^{67} +(13.4486 - 7.76457i) q^{68} +(34.3923 - 59.5692i) q^{70} +101.214i q^{71} +40.4115 q^{73} +(74.1818 + 42.8289i) q^{74} +(24.3923 + 42.2487i) q^{76} +(106.817 - 61.6706i) q^{77} +(-49.3731 + 85.5167i) q^{79} -23.1822i q^{80} -47.5692 q^{82} +(89.6231 + 51.7439i) q^{83} +(22.5000 + 38.9711i) q^{85} +(11.2394 - 6.48906i) q^{86} +(20.7846 - 36.0000i) q^{88} -134.130i q^{89} +177.885 q^{91} +(25.4558 + 14.6969i) q^{92} +(12.0000 + 20.7846i) q^{94} +(-122.427 + 70.6835i) q^{95} +(37.5692 - 65.0718i) q^{97} +30.3077i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} - 8 q^{7} + 24 q^{10} + 64 q^{13} - 16 q^{16} + 112 q^{19} - 28 q^{25} - 32 q^{28} - 32 q^{31} + 60 q^{34} - 152 q^{37} + 24 q^{40} + 88 q^{43} - 252 q^{49} - 128 q^{52} - 432 q^{55} - 180 q^{58} + 52 q^{61} - 64 q^{64} + 40 q^{67} + 192 q^{70} + 448 q^{73} + 112 q^{76} - 104 q^{79} - 48 q^{82} + 180 q^{85} + 176 q^{91} + 96 q^{94} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.612372 0.353553i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) −5.01910 + 2.89778i −1.00382 + 0.579555i −0.909376 0.415975i \(-0.863440\pi\)
−0.0944434 + 0.995530i \(0.530107\pi\)
\(6\) 0 0
\(7\) 4.19615 7.26795i 0.599450 1.03828i −0.393452 0.919345i \(-0.628719\pi\)
0.992902 0.118933i \(-0.0379475\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) 8.19615 0.819615
\(11\) 12.7279 + 7.34847i 1.15708 + 0.668043i 0.950603 0.310408i \(-0.100466\pi\)
0.206480 + 0.978451i \(0.433799\pi\)
\(12\) 0 0
\(13\) 10.5981 + 18.3564i 0.815237 + 1.41203i 0.909158 + 0.416452i \(0.136726\pi\)
−0.0939212 + 0.995580i \(0.529940\pi\)
\(14\) −10.2784 + 5.93426i −0.734174 + 0.423875i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 7.76457i 0.456739i −0.973574 0.228370i \(-0.926660\pi\)
0.973574 0.228370i \(-0.0733395\pi\)
\(18\) 0 0
\(19\) 24.3923 1.28381 0.641903 0.766786i \(-0.278145\pi\)
0.641903 + 0.766786i \(0.278145\pi\)
\(20\) −10.0382 5.79555i −0.501910 0.289778i
\(21\) 0 0
\(22\) −10.3923 18.0000i −0.472377 0.818182i
\(23\) 12.7279 7.34847i 0.553388 0.319499i −0.197099 0.980384i \(-0.563152\pi\)
0.750487 + 0.660885i \(0.229819\pi\)
\(24\) 0 0
\(25\) 4.29423 7.43782i 0.171769 0.297513i
\(26\) 29.9759i 1.15292i
\(27\) 0 0
\(28\) 16.7846 0.599450
\(29\) 30.7387 + 17.7470i 1.05996 + 0.611966i 0.925420 0.378942i \(-0.123712\pi\)
0.134536 + 0.990909i \(0.457046\pi\)
\(30\) 0 0
\(31\) −4.00000 6.92820i −0.129032 0.223490i 0.794270 0.607565i \(-0.207854\pi\)
−0.923302 + 0.384075i \(0.874520\pi\)
\(32\) 4.89898 2.82843i 0.153093 0.0883883i
\(33\) 0 0
\(34\) −5.49038 + 9.50962i −0.161482 + 0.279695i
\(35\) 48.6381i 1.38966i
\(36\) 0 0
\(37\) −60.5692 −1.63701 −0.818503 0.574502i \(-0.805196\pi\)
−0.818503 + 0.574502i \(0.805196\pi\)
\(38\) −29.8744 17.2480i −0.786167 0.453894i
\(39\) 0 0
\(40\) 8.19615 + 14.1962i 0.204904 + 0.354904i
\(41\) 29.1301 16.8183i 0.710490 0.410201i −0.100753 0.994912i \(-0.532125\pi\)
0.811242 + 0.584710i \(0.198792\pi\)
\(42\) 0 0
\(43\) −4.58846 + 7.94744i −0.106708 + 0.184824i −0.914435 0.404733i \(-0.867364\pi\)
0.807727 + 0.589557i \(0.200698\pi\)
\(44\) 29.3939i 0.668043i
\(45\) 0 0
\(46\) −20.7846 −0.451839
\(47\) −14.6969 8.48528i −0.312701 0.180538i 0.335434 0.942064i \(-0.391117\pi\)
−0.648134 + 0.761526i \(0.724451\pi\)
\(48\) 0 0
\(49\) −10.7154 18.5596i −0.218681 0.378767i
\(50\) −10.5187 + 6.07296i −0.210373 + 0.121459i
\(51\) 0 0
\(52\) −21.1962 + 36.7128i −0.407618 + 0.706016i
\(53\) 25.7605i 0.486046i −0.970020 0.243023i \(-0.921861\pi\)
0.970020 0.243023i \(-0.0781391\pi\)
\(54\) 0 0
\(55\) −85.1769 −1.54867
\(56\) −20.5569 11.8685i −0.367087 0.211938i
\(57\) 0 0
\(58\) −25.0981 43.4711i −0.432725 0.749502i
\(59\) −53.4083 + 30.8353i −0.905225 + 0.522632i −0.878892 0.477021i \(-0.841717\pi\)
−0.0263336 + 0.999653i \(0.508383\pi\)
\(60\) 0 0
\(61\) 6.50000 11.2583i 0.106557 0.184563i −0.807816 0.589435i \(-0.799351\pi\)
0.914373 + 0.404872i \(0.132684\pi\)
\(62\) 11.3137i 0.182479i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) −106.386 61.4217i −1.63670 0.944950i
\(66\) 0 0
\(67\) −10.5885 18.3397i −0.158037 0.273728i 0.776124 0.630580i \(-0.217183\pi\)
−0.934161 + 0.356853i \(0.883850\pi\)
\(68\) 13.4486 7.76457i 0.197774 0.114185i
\(69\) 0 0
\(70\) 34.3923 59.5692i 0.491319 0.850989i
\(71\) 101.214i 1.42555i 0.701392 + 0.712776i \(0.252562\pi\)
−0.701392 + 0.712776i \(0.747438\pi\)
\(72\) 0 0
\(73\) 40.4115 0.553583 0.276791 0.960930i \(-0.410729\pi\)
0.276791 + 0.960930i \(0.410729\pi\)
\(74\) 74.1818 + 42.8289i 1.00246 + 0.578769i
\(75\) 0 0
\(76\) 24.3923 + 42.2487i 0.320951 + 0.555904i
\(77\) 106.817 61.6706i 1.38723 0.800917i
\(78\) 0 0
\(79\) −49.3731 + 85.5167i −0.624976 + 1.08249i 0.363570 + 0.931567i \(0.381558\pi\)
−0.988546 + 0.150923i \(0.951776\pi\)
\(80\) 23.1822i 0.289778i
\(81\) 0 0
\(82\) −47.5692 −0.580112
\(83\) 89.6231 + 51.7439i 1.07980 + 0.623420i 0.930841 0.365424i \(-0.119076\pi\)
0.148954 + 0.988844i \(0.452409\pi\)
\(84\) 0 0
\(85\) 22.5000 + 38.9711i 0.264706 + 0.458484i
\(86\) 11.2394 6.48906i 0.130690 0.0754542i
\(87\) 0 0
\(88\) 20.7846 36.0000i 0.236189 0.409091i
\(89\) 134.130i 1.50708i −0.657403 0.753539i \(-0.728345\pi\)
0.657403 0.753539i \(-0.271655\pi\)
\(90\) 0 0
\(91\) 177.885 1.95478
\(92\) 25.4558 + 14.6969i 0.276694 + 0.159749i
\(93\) 0 0
\(94\) 12.0000 + 20.7846i 0.127660 + 0.221113i
\(95\) −122.427 + 70.6835i −1.28871 + 0.744037i
\(96\) 0 0
\(97\) 37.5692 65.0718i 0.387312 0.670843i −0.604775 0.796396i \(-0.706737\pi\)
0.992087 + 0.125553i \(0.0400705\pi\)
\(98\) 30.3077i 0.309262i
\(99\) 0 0
\(100\) 17.1769 0.171769
\(101\) −25.1920 14.5446i −0.249426 0.144006i 0.370075 0.929002i \(-0.379332\pi\)
−0.619501 + 0.784995i \(0.712665\pi\)
\(102\) 0 0
\(103\) −48.3538 83.7513i −0.469455 0.813119i 0.529936 0.848038i \(-0.322216\pi\)
−0.999390 + 0.0349186i \(0.988883\pi\)
\(104\) 51.9198 29.9759i 0.499228 0.288230i
\(105\) 0 0
\(106\) −18.2154 + 31.5500i −0.171843 + 0.297641i
\(107\) 177.582i 1.65964i −0.558030 0.829821i \(-0.688442\pi\)
0.558030 0.829821i \(-0.311558\pi\)
\(108\) 0 0
\(109\) 61.9423 0.568278 0.284139 0.958783i \(-0.408292\pi\)
0.284139 + 0.958783i \(0.408292\pi\)
\(110\) 104.320 + 60.2292i 0.948364 + 0.547538i
\(111\) 0 0
\(112\) 16.7846 + 29.0718i 0.149863 + 0.259570i
\(113\) −95.0991 + 54.9055i −0.841585 + 0.485889i −0.857803 0.513979i \(-0.828171\pi\)
0.0162179 + 0.999868i \(0.494837\pi\)
\(114\) 0 0
\(115\) −42.5885 + 73.7654i −0.370334 + 0.641438i
\(116\) 70.9881i 0.611966i
\(117\) 0 0
\(118\) 87.2154 0.739113
\(119\) −56.4325 32.5813i −0.474223 0.273793i
\(120\) 0 0
\(121\) 47.5000 + 82.2724i 0.392562 + 0.679937i
\(122\) −15.9217 + 9.19239i −0.130506 + 0.0753474i
\(123\) 0 0
\(124\) 8.00000 13.8564i 0.0645161 0.111745i
\(125\) 95.1140i 0.760912i
\(126\) 0 0
\(127\) 141.177 1.11163 0.555815 0.831306i \(-0.312406\pi\)
0.555815 + 0.831306i \(0.312406\pi\)
\(128\) 9.79796 + 5.65685i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 86.8634 + 150.452i 0.668180 + 1.15732i
\(131\) 46.0598 26.5927i 0.351602 0.202997i −0.313789 0.949493i \(-0.601598\pi\)
0.665391 + 0.746495i \(0.268265\pi\)
\(132\) 0 0
\(133\) 102.354 177.282i 0.769578 1.33295i
\(134\) 29.9487i 0.223498i
\(135\) 0 0
\(136\) −21.9615 −0.161482
\(137\) 1.41555 + 0.817267i 0.0103325 + 0.00596545i 0.505157 0.863027i \(-0.331434\pi\)
−0.494825 + 0.868993i \(0.664768\pi\)
\(138\) 0 0
\(139\) 9.60770 + 16.6410i 0.0691201 + 0.119720i 0.898514 0.438944i \(-0.144647\pi\)
−0.829394 + 0.558664i \(0.811314\pi\)
\(140\) −84.2436 + 48.6381i −0.601740 + 0.347415i
\(141\) 0 0
\(142\) 71.5692 123.962i 0.504009 0.872968i
\(143\) 311.519i 2.17845i
\(144\) 0 0
\(145\) −205.708 −1.41867
\(146\) −49.4938 28.5753i −0.338999 0.195721i
\(147\) 0 0
\(148\) −60.5692 104.909i −0.409251 0.708844i
\(149\) −81.6504 + 47.1409i −0.547989 + 0.316382i −0.748311 0.663348i \(-0.769135\pi\)
0.200321 + 0.979730i \(0.435801\pi\)
\(150\) 0 0
\(151\) −16.0000 + 27.7128i −0.105960 + 0.183529i −0.914130 0.405421i \(-0.867125\pi\)
0.808170 + 0.588949i \(0.200458\pi\)
\(152\) 68.9919i 0.453894i
\(153\) 0 0
\(154\) −174.431 −1.13267
\(155\) 40.1528 + 23.1822i 0.259050 + 0.149563i
\(156\) 0 0
\(157\) −0.146171 0.253175i −0.000931025 0.00161258i 0.865560 0.500806i \(-0.166963\pi\)
−0.866491 + 0.499193i \(0.833630\pi\)
\(158\) 120.939 69.8241i 0.765436 0.441924i
\(159\) 0 0
\(160\) −16.3923 + 28.3923i −0.102452 + 0.177452i
\(161\) 123.341i 0.766094i
\(162\) 0 0
\(163\) 28.7846 0.176593 0.0882963 0.996094i \(-0.471858\pi\)
0.0882963 + 0.996094i \(0.471858\pi\)
\(164\) 58.2602 + 33.6365i 0.355245 + 0.205101i
\(165\) 0 0
\(166\) −73.1769 126.746i −0.440825 0.763531i
\(167\) −48.5564 + 28.0341i −0.290757 + 0.167869i −0.638283 0.769802i \(-0.720355\pi\)
0.347526 + 0.937670i \(0.387022\pi\)
\(168\) 0 0
\(169\) −140.138 + 242.727i −0.829222 + 1.43625i
\(170\) 63.6396i 0.374351i
\(171\) 0 0
\(172\) −18.3538 −0.106708
\(173\) −191.350 110.476i −1.10607 0.638589i −0.168260 0.985743i \(-0.553815\pi\)
−0.937808 + 0.347154i \(0.887148\pi\)
\(174\) 0 0
\(175\) −36.0385 62.4205i −0.205934 0.356688i
\(176\) −50.9117 + 29.3939i −0.289271 + 0.167011i
\(177\) 0 0
\(178\) −94.8442 + 164.275i −0.532833 + 0.922893i
\(179\) 248.347i 1.38741i 0.720258 + 0.693706i \(0.244023\pi\)
−0.720258 + 0.693706i \(0.755977\pi\)
\(180\) 0 0
\(181\) −158.277 −0.874458 −0.437229 0.899350i \(-0.644040\pi\)
−0.437229 + 0.899350i \(0.644040\pi\)
\(182\) −217.863 125.783i −1.19705 0.691118i
\(183\) 0 0
\(184\) −20.7846 36.0000i −0.112960 0.195652i
\(185\) 304.003 175.516i 1.64326 0.948736i
\(186\) 0 0
\(187\) 57.0577 98.8269i 0.305121 0.528486i
\(188\) 33.9411i 0.180538i
\(189\) 0 0
\(190\) 199.923 1.05223
\(191\) 29.9215 + 17.2752i 0.156657 + 0.0904459i 0.576279 0.817253i \(-0.304504\pi\)
−0.419622 + 0.907699i \(0.637837\pi\)
\(192\) 0 0
\(193\) 27.5000 + 47.6314i 0.142487 + 0.246795i 0.928433 0.371501i \(-0.121157\pi\)
−0.785946 + 0.618296i \(0.787823\pi\)
\(194\) −92.0254 + 53.1309i −0.474358 + 0.273871i
\(195\) 0 0
\(196\) 21.4308 37.1192i 0.109341 0.189384i
\(197\) 35.7170i 0.181305i −0.995883 0.0906524i \(-0.971105\pi\)
0.995883 0.0906524i \(-0.0288952\pi\)
\(198\) 0 0
\(199\) −375.138 −1.88512 −0.942559 0.334040i \(-0.891588\pi\)
−0.942559 + 0.334040i \(0.891588\pi\)
\(200\) −21.0373 12.1459i −0.105187 0.0607296i
\(201\) 0 0
\(202\) 20.5692 + 35.6269i 0.101828 + 0.176371i
\(203\) 257.969 148.938i 1.27078 0.733687i
\(204\) 0 0
\(205\) −97.4711 + 168.825i −0.475469 + 0.823536i
\(206\) 136.765i 0.663909i
\(207\) 0 0
\(208\) −84.7846 −0.407618
\(209\) 310.463 + 179.246i 1.48547 + 0.857637i
\(210\) 0 0
\(211\) −153.727 266.263i −0.728563 1.26191i −0.957490 0.288465i \(-0.906855\pi\)
0.228927 0.973444i \(-0.426478\pi\)
\(212\) 44.6184 25.7605i 0.210464 0.121512i
\(213\) 0 0
\(214\) −125.569 + 217.492i −0.586772 + 1.01632i
\(215\) 53.1853i 0.247374i
\(216\) 0 0
\(217\) −67.1384 −0.309394
\(218\) −75.8635 43.7998i −0.347998 0.200917i
\(219\) 0 0
\(220\) −85.1769 147.531i −0.387168 0.670594i
\(221\) 142.530 82.2895i 0.644930 0.372351i
\(222\) 0 0
\(223\) 169.296 293.229i 0.759175 1.31493i −0.184096 0.982908i \(-0.558936\pi\)
0.943272 0.332022i \(-0.107731\pi\)
\(224\) 47.4740i 0.211938i
\(225\) 0 0
\(226\) 155.296 0.687151
\(227\) 107.344 + 61.9752i 0.472882 + 0.273019i 0.717445 0.696615i \(-0.245311\pi\)
−0.244563 + 0.969633i \(0.578645\pi\)
\(228\) 0 0
\(229\) −37.0289 64.1359i −0.161698 0.280069i 0.773780 0.633455i \(-0.218364\pi\)
−0.935478 + 0.353386i \(0.885030\pi\)
\(230\) 104.320 60.2292i 0.453565 0.261866i
\(231\) 0 0
\(232\) 50.1962 86.9423i 0.216363 0.374751i
\(233\) 273.223i 1.17263i 0.810082 + 0.586316i \(0.199422\pi\)
−0.810082 + 0.586316i \(0.800578\pi\)
\(234\) 0 0
\(235\) 98.3538 0.418527
\(236\) −106.817 61.6706i −0.452613 0.261316i
\(237\) 0 0
\(238\) 46.0770 + 79.8076i 0.193601 + 0.335326i
\(239\) −392.210 + 226.443i −1.64105 + 0.947459i −0.660585 + 0.750751i \(0.729692\pi\)
−0.980462 + 0.196708i \(0.936975\pi\)
\(240\) 0 0
\(241\) 191.344 331.418i 0.793959 1.37518i −0.129538 0.991574i \(-0.541350\pi\)
0.923498 0.383604i \(-0.125317\pi\)
\(242\) 134.350i 0.555166i
\(243\) 0 0
\(244\) 26.0000 0.106557
\(245\) 107.563 + 62.1016i 0.439033 + 0.253476i
\(246\) 0 0
\(247\) 258.512 + 447.755i 1.04661 + 1.81277i
\(248\) −19.5959 + 11.3137i −0.0790158 + 0.0456198i
\(249\) 0 0
\(250\) −67.2558 + 116.490i −0.269023 + 0.465962i
\(251\) 73.9307i 0.294544i −0.989096 0.147272i \(-0.952951\pi\)
0.989096 0.147272i \(-0.0470493\pi\)
\(252\) 0 0
\(253\) 216.000 0.853755
\(254\) −172.906 99.8272i −0.680731 0.393020i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −138.398 + 79.9044i −0.538515 + 0.310912i −0.744477 0.667648i \(-0.767301\pi\)
0.205962 + 0.978560i \(0.433968\pi\)
\(258\) 0 0
\(259\) −254.158 + 440.214i −0.981304 + 1.69967i
\(260\) 245.687i 0.944950i
\(261\) 0 0
\(262\) −75.2154 −0.287082
\(263\) −224.392 129.553i −0.853202 0.492596i 0.00852798 0.999964i \(-0.497285\pi\)
−0.861730 + 0.507367i \(0.830619\pi\)
\(264\) 0 0
\(265\) 74.6481 + 129.294i 0.281691 + 0.487903i
\(266\) −250.715 + 144.750i −0.942536 + 0.544174i
\(267\) 0 0
\(268\) 21.1769 36.6795i 0.0790183 0.136864i
\(269\) 24.8168i 0.0922556i 0.998936 + 0.0461278i \(0.0146881\pi\)
−0.998936 + 0.0461278i \(0.985312\pi\)
\(270\) 0 0
\(271\) 98.1154 0.362050 0.181025 0.983479i \(-0.442059\pi\)
0.181025 + 0.983479i \(0.442059\pi\)
\(272\) 26.8973 + 15.5291i 0.0988870 + 0.0570924i
\(273\) 0 0
\(274\) −1.15579 2.00189i −0.00421821 0.00730616i
\(275\) 109.313 63.1120i 0.397503 0.229498i
\(276\) 0 0
\(277\) 0.707658 1.22570i 0.00255472 0.00442491i −0.864745 0.502211i \(-0.832520\pi\)
0.867300 + 0.497786i \(0.165853\pi\)
\(278\) 27.1747i 0.0977506i
\(279\) 0 0
\(280\) 137.569 0.491319
\(281\) 87.2230 + 50.3582i 0.310402 + 0.179211i 0.647106 0.762400i \(-0.275979\pi\)
−0.336704 + 0.941610i \(0.609312\pi\)
\(282\) 0 0
\(283\) 23.6462 + 40.9564i 0.0835554 + 0.144722i 0.904775 0.425890i \(-0.140039\pi\)
−0.821219 + 0.570613i \(0.806706\pi\)
\(284\) −175.308 + 101.214i −0.617282 + 0.356388i
\(285\) 0 0
\(286\) 220.277 381.531i 0.770199 1.33402i
\(287\) 282.288i 0.983582i
\(288\) 0 0
\(289\) 228.711 0.791389
\(290\) 251.939 + 145.457i 0.868757 + 0.501577i
\(291\) 0 0
\(292\) 40.4115 + 69.9948i 0.138396 + 0.239708i
\(293\) −288.920 + 166.808i −0.986074 + 0.569310i −0.904098 0.427324i \(-0.859456\pi\)
−0.0819755 + 0.996634i \(0.526123\pi\)
\(294\) 0 0
\(295\) 178.708 309.531i 0.605789 1.04926i
\(296\) 171.316i 0.578769i
\(297\) 0 0
\(298\) 133.335 0.447432
\(299\) 269.783 + 155.759i 0.902284 + 0.520934i
\(300\) 0 0
\(301\) 38.5077 + 66.6973i 0.127933 + 0.221586i
\(302\) 39.1918 22.6274i 0.129774 0.0749252i
\(303\) 0 0
\(304\) −48.7846 + 84.4974i −0.160476 + 0.277952i
\(305\) 75.3422i 0.247024i
\(306\) 0 0
\(307\) 10.3538 0.0337258 0.0168629 0.999858i \(-0.494632\pi\)
0.0168629 + 0.999858i \(0.494632\pi\)
\(308\) 213.633 + 123.341i 0.693614 + 0.400458i
\(309\) 0 0
\(310\) −32.7846 56.7846i −0.105757 0.183176i
\(311\) −8.26229 + 4.77024i −0.0265669 + 0.0153384i −0.513225 0.858254i \(-0.671549\pi\)
0.486658 + 0.873593i \(0.338216\pi\)
\(312\) 0 0
\(313\) 239.638 415.066i 0.765618 1.32609i −0.174301 0.984692i \(-0.555767\pi\)
0.939919 0.341397i \(-0.110900\pi\)
\(314\) 0.413434i 0.00131667i
\(315\) 0 0
\(316\) −197.492 −0.624976
\(317\) −155.592 89.8311i −0.490827 0.283379i 0.234091 0.972215i \(-0.424789\pi\)
−0.724917 + 0.688836i \(0.758122\pi\)
\(318\) 0 0
\(319\) 260.827 + 451.765i 0.817639 + 1.41619i
\(320\) 40.1528 23.1822i 0.125477 0.0724444i
\(321\) 0 0
\(322\) −87.2154 + 151.061i −0.270855 + 0.469135i
\(323\) 189.396i 0.586365i
\(324\) 0 0
\(325\) 182.042 0.560130
\(326\) −35.2538 20.3538i −0.108141 0.0624349i
\(327\) 0 0
\(328\) −47.5692 82.3923i −0.145028 0.251196i
\(329\) −123.341 + 71.2111i −0.374897 + 0.216447i
\(330\) 0 0
\(331\) −147.727 + 255.870i −0.446305 + 0.773023i −0.998142 0.0609292i \(-0.980594\pi\)
0.551837 + 0.833952i \(0.313927\pi\)
\(332\) 206.976i 0.623420i
\(333\) 0 0
\(334\) 79.2923 0.237402
\(335\) 106.289 + 61.3660i 0.317281 + 0.183182i
\(336\) 0 0
\(337\) −244.631 423.713i −0.725907 1.25731i −0.958600 0.284758i \(-0.908087\pi\)
0.232692 0.972550i \(-0.425246\pi\)
\(338\) 343.268 198.186i 1.01558 0.586348i
\(339\) 0 0
\(340\) −45.0000 + 77.9423i −0.132353 + 0.229242i
\(341\) 117.576i 0.344796i
\(342\) 0 0
\(343\) 231.369 0.674546
\(344\) 22.4788 + 12.9781i 0.0653452 + 0.0377271i
\(345\) 0 0
\(346\) 156.237 + 270.610i 0.451551 + 0.782109i
\(347\) 577.363 333.341i 1.66387 0.960637i 0.693032 0.720907i \(-0.256274\pi\)
0.970840 0.239730i \(-0.0770590\pi\)
\(348\) 0 0
\(349\) −255.985 + 443.378i −0.733480 + 1.27042i 0.221907 + 0.975068i \(0.428772\pi\)
−0.955387 + 0.295357i \(0.904561\pi\)
\(350\) 101.932i 0.291235i
\(351\) 0 0
\(352\) 83.1384 0.236189
\(353\) −508.081 293.340i −1.43932 0.830993i −0.441519 0.897252i \(-0.645560\pi\)
−0.997802 + 0.0662588i \(0.978894\pi\)
\(354\) 0 0
\(355\) −293.296 508.004i −0.826186 1.43100i
\(356\) 232.320 134.130i 0.652584 0.376770i
\(357\) 0 0
\(358\) 175.608 304.161i 0.490524 0.849613i
\(359\) 534.573i 1.48906i −0.667589 0.744530i \(-0.732674\pi\)
0.667589 0.744530i \(-0.267326\pi\)
\(360\) 0 0
\(361\) 233.985 0.648157
\(362\) 193.849 + 111.919i 0.535494 + 0.309168i
\(363\) 0 0
\(364\) 177.885 + 308.105i 0.488694 + 0.846443i
\(365\) −202.829 + 117.104i −0.555697 + 0.320832i
\(366\) 0 0
\(367\) −7.64617 + 13.2436i −0.0208343 + 0.0360860i −0.876255 0.481848i \(-0.839966\pi\)
0.855420 + 0.517934i \(0.173299\pi\)
\(368\) 58.7878i 0.159749i
\(369\) 0 0
\(370\) −496.435 −1.34172
\(371\) −187.226 108.095i −0.504651 0.291361i
\(372\) 0 0
\(373\) −326.492 565.501i −0.875314 1.51609i −0.856427 0.516267i \(-0.827321\pi\)
−0.0188869 0.999822i \(-0.506012\pi\)
\(374\) −139.762 + 80.6918i −0.373696 + 0.215753i
\(375\) 0 0
\(376\) −24.0000 + 41.5692i −0.0638298 + 0.110556i
\(377\) 752.337i 1.99559i
\(378\) 0 0
\(379\) −655.215 −1.72880 −0.864400 0.502804i \(-0.832302\pi\)
−0.864400 + 0.502804i \(0.832302\pi\)
\(380\) −244.855 141.367i −0.644355 0.372018i
\(381\) 0 0
\(382\) −24.4308 42.3154i −0.0639549 0.110773i
\(383\) −259.410 + 149.771i −0.677311 + 0.391046i −0.798841 0.601542i \(-0.794553\pi\)
0.121530 + 0.992588i \(0.461220\pi\)
\(384\) 0 0
\(385\) −357.415 + 619.061i −0.928351 + 1.60795i
\(386\) 77.7817i 0.201507i
\(387\) 0 0
\(388\) 150.277 0.387312
\(389\) 402.319 + 232.279i 1.03424 + 0.597119i 0.918196 0.396126i \(-0.129646\pi\)
0.116043 + 0.993244i \(0.462979\pi\)
\(390\) 0 0
\(391\) −57.0577 98.8269i −0.145928 0.252754i
\(392\) −52.4945 + 30.3077i −0.133914 + 0.0773156i
\(393\) 0 0
\(394\) −25.2558 + 43.7442i −0.0641009 + 0.111026i
\(395\) 572.289i 1.44883i
\(396\) 0 0
\(397\) −185.708 −0.467777 −0.233889 0.972263i \(-0.575145\pi\)
−0.233889 + 0.972263i \(0.575145\pi\)
\(398\) 459.449 + 265.263i 1.15439 + 0.666490i
\(399\) 0 0
\(400\) 17.1769 + 29.7513i 0.0429423 + 0.0743782i
\(401\) −54.4376 + 31.4296i −0.135755 + 0.0783780i −0.566339 0.824172i \(-0.691641\pi\)
0.430585 + 0.902550i \(0.358307\pi\)
\(402\) 0 0
\(403\) 84.7846 146.851i 0.210384 0.364395i
\(404\) 58.1785i 0.144006i
\(405\) 0 0
\(406\) −421.261 −1.03759
\(407\) −770.920 445.091i −1.89415 1.09359i
\(408\) 0 0
\(409\) 163.640 + 283.433i 0.400099 + 0.692991i 0.993737 0.111741i \(-0.0356425\pi\)
−0.593639 + 0.804732i \(0.702309\pi\)
\(410\) 238.755 137.845i 0.582328 0.336207i
\(411\) 0 0
\(412\) 96.7077 167.503i 0.234727 0.406560i
\(413\) 517.558i 1.25317i
\(414\) 0 0
\(415\) −599.769 −1.44523
\(416\) 103.840 + 59.9518i 0.249614 + 0.144115i
\(417\) 0 0
\(418\) −253.492 439.061i −0.606441 1.05039i
\(419\) 562.808 324.937i 1.34322 0.775507i 0.355939 0.934509i \(-0.384161\pi\)
0.987278 + 0.159003i \(0.0508278\pi\)
\(420\) 0 0
\(421\) −1.65956 + 2.87445i −0.00394196 + 0.00682767i −0.867990 0.496582i \(-0.834588\pi\)
0.864048 + 0.503410i \(0.167921\pi\)
\(422\) 434.805i 1.03034i
\(423\) 0 0
\(424\) −72.8616 −0.171843
\(425\) −57.7515 33.3428i −0.135886 0.0784538i
\(426\) 0 0
\(427\) −54.5500 94.4833i −0.127752 0.221272i
\(428\) 307.581 177.582i 0.718646 0.414910i
\(429\) 0 0
\(430\) −37.6077 + 65.1384i −0.0874598 + 0.151485i
\(431\) 803.502i 1.86427i 0.362107 + 0.932136i \(0.382057\pi\)
−0.362107 + 0.932136i \(0.617943\pi\)
\(432\) 0 0
\(433\) −93.1230 −0.215065 −0.107532 0.994202i \(-0.534295\pi\)
−0.107532 + 0.994202i \(0.534295\pi\)
\(434\) 82.2275 + 47.4740i 0.189464 + 0.109387i
\(435\) 0 0
\(436\) 61.9423 + 107.287i 0.142069 + 0.246072i
\(437\) 310.463 179.246i 0.710442 0.410174i
\(438\) 0 0
\(439\) 236.000 408.764i 0.537585 0.931125i −0.461448 0.887167i \(-0.652670\pi\)
0.999033 0.0439580i \(-0.0139968\pi\)
\(440\) 240.917i 0.547538i
\(441\) 0 0
\(442\) −232.750 −0.526584
\(443\) −493.365 284.844i −1.11369 0.642989i −0.173908 0.984762i \(-0.555639\pi\)
−0.939783 + 0.341773i \(0.888973\pi\)
\(444\) 0 0
\(445\) 388.679 + 673.211i 0.873436 + 1.51283i
\(446\) −414.689 + 239.421i −0.929796 + 0.536818i
\(447\) 0 0
\(448\) −33.5692 + 58.1436i −0.0749313 + 0.129785i
\(449\) 559.115i 1.24524i −0.782523 0.622622i \(-0.786067\pi\)
0.782523 0.622622i \(-0.213933\pi\)
\(450\) 0 0
\(451\) 494.354 1.09613
\(452\) −190.198 109.811i −0.420792 0.242945i
\(453\) 0 0
\(454\) −87.6462 151.808i −0.193053 0.334378i
\(455\) −892.820 + 515.470i −1.96224 + 1.13290i
\(456\) 0 0
\(457\) −302.148 + 523.336i −0.661155 + 1.14515i 0.319157 + 0.947702i \(0.396600\pi\)
−0.980312 + 0.197453i \(0.936733\pi\)
\(458\) 104.733i 0.228676i
\(459\) 0 0
\(460\) −170.354 −0.370334
\(461\) 4.44669 + 2.56730i 0.00964575 + 0.00556897i 0.504815 0.863227i \(-0.331561\pi\)
−0.495169 + 0.868796i \(0.664894\pi\)
\(462\) 0 0
\(463\) 80.7461 + 139.856i 0.174398 + 0.302066i 0.939953 0.341305i \(-0.110869\pi\)
−0.765555 + 0.643370i \(0.777536\pi\)
\(464\) −122.955 + 70.9881i −0.264989 + 0.152992i
\(465\) 0 0
\(466\) 193.198 334.629i 0.414588 0.718088i
\(467\) 503.025i 1.07714i −0.842581 0.538570i \(-0.818965\pi\)
0.842581 0.538570i \(-0.181035\pi\)
\(468\) 0 0
\(469\) −177.723 −0.378941
\(470\) −120.458 69.5467i −0.256294 0.147972i
\(471\) 0 0
\(472\) 87.2154 + 151.061i 0.184778 + 0.320046i
\(473\) −116.803 + 67.4363i −0.246941 + 0.142571i
\(474\) 0 0
\(475\) 104.746 181.426i 0.220518 0.381949i
\(476\) 130.325i 0.273793i
\(477\) 0 0
\(478\) 640.477 1.33991
\(479\) −185.153 106.898i −0.386541 0.223170i 0.294119 0.955769i \(-0.404974\pi\)
−0.680660 + 0.732599i \(0.738307\pi\)
\(480\) 0 0
\(481\) −641.917 1111.83i −1.33455 2.31150i
\(482\) −468.696 + 270.602i −0.972398 + 0.561414i
\(483\) 0 0
\(484\) −95.0000 + 164.545i −0.196281 + 0.339969i
\(485\) 435.469i 0.897874i
\(486\) 0 0
\(487\) 8.63071 0.0177222 0.00886110 0.999961i \(-0.497179\pi\)
0.00886110 + 0.999961i \(0.497179\pi\)
\(488\) −31.8434 18.3848i −0.0652528 0.0376737i
\(489\) 0 0
\(490\) −87.8250 152.117i −0.179235 0.310443i
\(491\) 798.873 461.229i 1.62703 0.939367i 0.642060 0.766654i \(-0.278080\pi\)
0.984972 0.172713i \(-0.0552533\pi\)
\(492\) 0 0
\(493\) 137.798 238.673i 0.279509 0.484124i
\(494\) 731.181i 1.48012i
\(495\) 0 0
\(496\) 32.0000 0.0645161
\(497\) 735.619 + 424.710i 1.48012 + 0.854547i
\(498\) 0 0
\(499\) 217.296 + 376.368i 0.435463 + 0.754244i 0.997333 0.0729811i \(-0.0232513\pi\)
−0.561870 + 0.827225i \(0.689918\pi\)
\(500\) 164.742 95.1140i 0.329485 0.190228i
\(501\) 0 0
\(502\) −52.2769 + 90.5462i −0.104137 + 0.180371i
\(503\) 144.087i 0.286454i 0.989690 + 0.143227i \(0.0457480\pi\)
−0.989690 + 0.143227i \(0.954252\pi\)
\(504\) 0 0
\(505\) 168.588 0.333839
\(506\) −264.545 152.735i −0.522816 0.301848i
\(507\) 0 0
\(508\) 141.177 + 244.526i 0.277907 + 0.481350i
\(509\) −603.856 + 348.636i −1.18636 + 0.684943i −0.957477 0.288511i \(-0.906840\pi\)
−0.228880 + 0.973455i \(0.573506\pi\)
\(510\) 0 0
\(511\) 169.573 293.709i 0.331845 0.574773i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 226.004 0.439696
\(515\) 485.385 + 280.237i 0.942496 + 0.544150i
\(516\) 0 0
\(517\) −124.708 216.000i −0.241214 0.417795i
\(518\) 622.557 359.433i 1.20185 0.693887i
\(519\) 0 0
\(520\) −173.727 + 300.904i −0.334090 + 0.578661i
\(521\) 426.962i 0.819504i −0.912197 0.409752i \(-0.865615\pi\)
0.912197 0.409752i \(-0.134385\pi\)
\(522\) 0 0
\(523\) 179.762 0.343712 0.171856 0.985122i \(-0.445024\pi\)
0.171856 + 0.985122i \(0.445024\pi\)
\(524\) 92.1197 + 53.1853i 0.175801 + 0.101499i
\(525\) 0 0
\(526\) 183.215 + 317.338i 0.348318 + 0.603305i
\(527\) −53.7945 + 31.0583i −0.102077 + 0.0589341i
\(528\) 0 0
\(529\) −156.500 + 271.066i −0.295841 + 0.512412i
\(530\) 211.137i 0.398371i
\(531\) 0 0
\(532\) 409.415 0.769578
\(533\) 617.446 + 356.482i 1.15843 + 0.668822i
\(534\) 0 0
\(535\) 514.592 + 891.300i 0.961855 + 1.66598i
\(536\) −51.8726 + 29.9487i −0.0967773 + 0.0558744i
\(537\) 0 0
\(538\) 17.5481 30.3942i 0.0326173 0.0564948i
\(539\) 314.967i 0.584354i
\(540\) 0 0
\(541\) 708.734 1.31005 0.655023 0.755609i \(-0.272659\pi\)
0.655023 + 0.755609i \(0.272659\pi\)
\(542\) −120.166 69.3781i −0.221709 0.128004i
\(543\) 0 0
\(544\) −21.9615 38.0385i −0.0403704 0.0699237i
\(545\) −310.894 + 179.495i −0.570448 + 0.329349i
\(546\) 0 0
\(547\) 98.1154 169.941i 0.179370 0.310678i −0.762295 0.647230i \(-0.775927\pi\)
0.941665 + 0.336552i \(0.109261\pi\)
\(548\) 3.26907i 0.00596545i
\(549\) 0 0
\(550\) −178.508 −0.324560
\(551\) 749.789 + 432.891i 1.36078 + 0.785646i
\(552\) 0 0
\(553\) 414.354 + 717.682i 0.749284 + 1.29780i
\(554\) −1.73340 + 1.00078i −0.00312888 + 0.00180646i
\(555\) 0 0
\(556\) −19.2154 + 33.2820i −0.0345601 + 0.0598598i
\(557\) 353.610i 0.634848i 0.948284 + 0.317424i \(0.102818\pi\)
−0.948284 + 0.317424i \(0.897182\pi\)
\(558\) 0 0
\(559\) −194.515 −0.347970
\(560\) −168.487 97.2761i −0.300870 0.173707i
\(561\) 0 0
\(562\) −71.2173 123.352i −0.126721 0.219487i
\(563\) 323.050 186.513i 0.573801 0.331284i −0.184865 0.982764i \(-0.559185\pi\)
0.758666 + 0.651480i \(0.225851\pi\)
\(564\) 0 0
\(565\) 318.208 551.152i 0.563199 0.975490i
\(566\) 66.8815i 0.118165i
\(567\) 0 0
\(568\) 286.277 0.504009
\(569\) −52.0634 30.0588i −0.0914999 0.0528275i 0.453552 0.891230i \(-0.350157\pi\)
−0.545052 + 0.838402i \(0.683490\pi\)
\(570\) 0 0
\(571\) −43.1000 74.6513i −0.0754815 0.130738i 0.825814 0.563943i \(-0.190716\pi\)
−0.901296 + 0.433205i \(0.857383\pi\)
\(572\) −539.566 + 311.519i −0.943297 + 0.544613i
\(573\) 0 0
\(574\) −199.608 + 345.731i −0.347749 + 0.602318i
\(575\) 126.224i 0.219520i
\(576\) 0 0
\(577\) 709.123 1.22898 0.614491 0.788924i \(-0.289361\pi\)
0.614491 + 0.788924i \(0.289361\pi\)
\(578\) −280.113 161.723i −0.484625 0.279798i
\(579\) 0 0
\(580\) −205.708 356.296i −0.354668 0.614304i
\(581\) 752.144 434.251i 1.29457 0.747419i
\(582\) 0 0
\(583\) 189.300 327.877i 0.324700 0.562396i
\(584\) 114.301i 0.195721i
\(585\) 0 0
\(586\) 471.804 0.805126
\(587\) 833.363 + 481.143i 1.41970 + 0.819664i 0.996272 0.0862666i \(-0.0274937\pi\)
0.423427 + 0.905930i \(0.360827\pi\)
\(588\) 0 0
\(589\) −97.5692 168.995i −0.165652 0.286918i
\(590\) −437.743 + 252.731i −0.741937 + 0.428357i
\(591\) 0 0
\(592\) 121.138 209.818i 0.204626 0.354422i
\(593\) 104.350i 0.175969i −0.996122 0.0879847i \(-0.971957\pi\)
0.996122 0.0879847i \(-0.0280427\pi\)
\(594\) 0 0
\(595\) 377.654 0.634712
\(596\) −163.301 94.2818i −0.273995 0.158191i
\(597\) 0 0
\(598\) −220.277 381.531i −0.368356 0.638011i
\(599\) 247.738 143.031i 0.413585 0.238784i −0.278744 0.960366i \(-0.589918\pi\)
0.692329 + 0.721582i \(0.256585\pi\)
\(600\) 0 0
\(601\) 140.208 242.847i 0.233291 0.404071i −0.725484 0.688239i \(-0.758384\pi\)
0.958775 + 0.284168i \(0.0917173\pi\)
\(602\) 108.916i 0.180924i
\(603\) 0 0
\(604\) −64.0000 −0.105960
\(605\) −476.814 275.289i −0.788123 0.455023i
\(606\) 0 0
\(607\) −368.865 638.894i −0.607686 1.05254i −0.991621 0.129183i \(-0.958765\pi\)
0.383935 0.923360i \(-0.374569\pi\)
\(608\) 119.497 68.9919i 0.196542 0.113473i
\(609\) 0 0
\(610\) 53.2750 92.2750i 0.0873361 0.151270i
\(611\) 359.711i 0.588724i
\(612\) 0 0
\(613\) −679.415 −1.10834 −0.554172 0.832402i \(-0.686965\pi\)
−0.554172 + 0.832402i \(0.686965\pi\)
\(614\) −12.6808 7.32126i −0.0206528 0.0119239i
\(615\) 0 0
\(616\) −174.431 302.123i −0.283167 0.490459i
\(617\) −409.326 + 236.325i −0.663414 + 0.383022i −0.793576 0.608471i \(-0.791783\pi\)
0.130163 + 0.991493i \(0.458450\pi\)
\(618\) 0 0
\(619\) −443.177 + 767.605i −0.715956 + 1.24007i 0.246633 + 0.969109i \(0.420676\pi\)
−0.962590 + 0.270964i \(0.912658\pi\)
\(620\) 92.7289i 0.149563i
\(621\) 0 0
\(622\) 13.4923 0.0216917
\(623\) −974.850 562.830i −1.56477 0.903419i
\(624\) 0 0
\(625\) 382.975 + 663.332i 0.612760 + 1.06133i
\(626\) −586.992 + 338.900i −0.937687 + 0.541374i
\(627\) 0 0
\(628\) 0.292342 0.506351i 0.000465513 0.000806291i
\(629\) 470.294i 0.747685i
\(630\) 0 0
\(631\) −729.108 −1.15548 −0.577740 0.816221i \(-0.696065\pi\)
−0.577740 + 0.816221i \(0.696065\pi\)
\(632\) 241.878 + 139.648i 0.382718 + 0.220962i
\(633\) 0 0
\(634\) 127.040 + 220.040i 0.200379 + 0.347067i
\(635\) −708.581 + 409.099i −1.11588 + 0.644251i
\(636\) 0 0
\(637\) 227.125 393.392i 0.356554 0.617570i
\(638\) 737.730i 1.15632i
\(639\) 0 0
\(640\) −65.5692 −0.102452
\(641\) −753.611 435.098i −1.17568 0.678780i −0.220669 0.975349i \(-0.570824\pi\)
−0.955011 + 0.296569i \(0.904157\pi\)
\(642\) 0 0
\(643\) 309.061 + 535.310i 0.480656 + 0.832520i 0.999754 0.0221949i \(-0.00706543\pi\)
−0.519098 + 0.854715i \(0.673732\pi\)
\(644\) 213.633 123.341i 0.331729 0.191524i
\(645\) 0 0
\(646\) −133.923 + 231.962i −0.207311 + 0.359074i
\(647\) 425.439i 0.657556i 0.944407 + 0.328778i \(0.106637\pi\)
−0.944407 + 0.328778i \(0.893363\pi\)
\(648\) 0 0
\(649\) −906.369 −1.39656
\(650\) −222.955 128.723i −0.343008 0.198036i
\(651\) 0 0
\(652\) 28.7846 + 49.8564i 0.0441482 + 0.0764669i
\(653\) 163.513 94.4042i 0.250403 0.144570i −0.369546 0.929212i \(-0.620487\pi\)
0.619949 + 0.784642i \(0.287153\pi\)
\(654\) 0 0
\(655\) −154.119 + 266.942i −0.235296 + 0.407545i
\(656\) 134.546i 0.205101i
\(657\) 0 0
\(658\) 201.415 0.306102
\(659\) 571.984 + 330.235i 0.867958 + 0.501116i 0.866669 0.498884i \(-0.166256\pi\)
0.00128859 + 0.999999i \(0.499590\pi\)
\(660\) 0 0
\(661\) 294.915 + 510.808i 0.446165 + 0.772781i 0.998133 0.0610847i \(-0.0194560\pi\)
−0.551967 + 0.833866i \(0.686123\pi\)
\(662\) 361.856 208.917i 0.546610 0.315585i
\(663\) 0 0
\(664\) 146.354 253.492i 0.220412 0.381765i
\(665\) 1186.39i 1.78405i
\(666\) 0 0
\(667\) 521.654 0.782090
\(668\) −97.1129 56.0682i −0.145379 0.0839344i
\(669\) 0 0
\(670\) −86.7846 150.315i −0.129529 0.224351i
\(671\) 165.463 95.5301i 0.246592 0.142370i
\(672\) 0 0
\(673\) 195.715 338.989i 0.290810 0.503698i −0.683191 0.730240i \(-0.739408\pi\)
0.974002 + 0.226541i \(0.0727418\pi\)
\(674\) 691.920i 1.02659i
\(675\) 0 0
\(676\) −560.554 −0.829222
\(677\) 600.728 + 346.830i 0.887338 + 0.512305i 0.873071 0.487593i \(-0.162125\pi\)
0.0142672 + 0.999898i \(0.495458\pi\)
\(678\) 0 0
\(679\) −315.292 546.102i −0.464348 0.804274i
\(680\) 110.227 63.6396i 0.162099 0.0935877i
\(681\) 0 0
\(682\) −83.1384 + 144.000i −0.121904 + 0.211144i
\(683\) 678.170i 0.992928i 0.868057 + 0.496464i \(0.165368\pi\)
−0.868057 + 0.496464i \(0.834632\pi\)
\(684\) 0 0
\(685\) −9.47303 −0.0138292
\(686\) −283.368 163.603i −0.413073 0.238488i
\(687\) 0 0
\(688\) −18.3538 31.7898i −0.0266771 0.0462061i
\(689\) 472.869 273.011i 0.686313 0.396243i
\(690\) 0 0
\(691\) −337.888 + 585.240i −0.488985 + 0.846946i −0.999920 0.0126731i \(-0.995966\pi\)
0.510935 + 0.859619i \(0.329299\pi\)
\(692\) 441.904i 0.638589i
\(693\) 0 0
\(694\) −942.831 −1.35855
\(695\) −96.4439 55.6819i −0.138768 0.0801179i
\(696\) 0 0
\(697\) −130.587 226.183i −0.187355 0.324509i
\(698\) 627.031 362.017i 0.898326 0.518649i
\(699\) 0 0
\(700\) 72.0770 124.841i 0.102967 0.178344i
\(701\) 797.260i 1.13732i −0.822573 0.568659i \(-0.807462\pi\)
0.822573 0.568659i \(-0.192538\pi\)
\(702\) 0 0
\(703\) −1477.42 −2.10160
\(704\) −101.823 58.7878i −0.144635 0.0835053i
\(705\) 0 0
\(706\) 414.846 + 718.535i 0.587601 + 1.01775i
\(707\) −211.419 + 122.063i −0.299037 + 0.172649i
\(708\) 0 0
\(709\) −86.7520 + 150.259i −0.122358 + 0.211931i −0.920697 0.390278i \(-0.872379\pi\)
0.798339 + 0.602208i \(0.205712\pi\)
\(710\) 829.567i 1.16840i
\(711\) 0 0
\(712\) −379.377 −0.532833
\(713\) −101.823 58.7878i −0.142810 0.0824513i
\(714\) 0 0
\(715\) −902.711 1563.54i −1.26253 2.18677i
\(716\) −430.149 + 248.347i −0.600767 + 0.346853i
\(717\) 0 0
\(718\) −378.000 + 654.715i −0.526462 + 0.911860i
\(719\) 188.177i 0.261721i −0.991401 0.130860i \(-0.958226\pi\)
0.991401 0.130860i \(-0.0417740\pi\)
\(720\) 0 0
\(721\) −811.600 −1.12566
\(722\) −286.571 165.452i −0.396913 0.229158i
\(723\) 0 0
\(724\) −158.277 274.144i −0.218614 0.378651i
\(725\) 263.998 152.420i 0.364136 0.210234i
\(726\) 0 0
\(727\) −355.888 + 616.417i −0.489530 + 0.847891i −0.999927 0.0120478i \(-0.996165\pi\)
0.510397 + 0.859939i \(0.329498\pi\)
\(728\) 503.134i 0.691118i
\(729\) 0 0
\(730\) 331.219 0.453725
\(731\) 61.7085 + 35.6274i 0.0844165 + 0.0487379i
\(732\) 0 0
\(733\) −613.415 1062.47i −0.836856 1.44948i −0.892510 0.451027i \(-0.851058\pi\)
0.0556546 0.998450i \(-0.482275\pi\)
\(734\) 18.7292 10.8133i 0.0255166 0.0147320i
\(735\) 0 0
\(736\) 41.5692 72.0000i 0.0564799 0.0978261i
\(737\) 311.236i 0.422301i
\(738\) 0 0
\(739\) 741.892 1.00391 0.501957 0.864893i \(-0.332614\pi\)
0.501957 + 0.864893i \(0.332614\pi\)
\(740\) 608.006 + 351.032i 0.821629 + 0.474368i
\(741\) 0 0
\(742\) 152.869 + 264.777i 0.206023 + 0.356842i
\(743\) −677.218 + 390.992i −0.911464 + 0.526234i −0.880902 0.473299i \(-0.843063\pi\)
−0.0305622 + 0.999533i \(0.509730\pi\)
\(744\) 0 0
\(745\) 273.208 473.210i 0.366722 0.635181i
\(746\) 923.460i 1.23788i
\(747\) 0 0
\(748\) 228.231 0.305121
\(749\) −1290.65 745.160i −1.72317 0.994873i
\(750\) 0 0
\(751\) 516.665 + 894.891i 0.687970 + 1.19160i 0.972494 + 0.232930i \(0.0748312\pi\)
−0.284524 + 0.958669i \(0.591835\pi\)
\(752\) 58.7878 33.9411i 0.0781752 0.0451345i
\(753\) 0 0
\(754\) 531.983 921.421i 0.705547 1.22204i
\(755\) 185.458i 0.245639i
\(756\) 0 0
\(757\) 473.877 0.625993 0.312997 0.949754i \(-0.398667\pi\)
0.312997 + 0.949754i \(0.398667\pi\)
\(758\) 802.472 + 463.307i 1.05867 + 0.611223i
\(759\) 0 0
\(760\) 199.923 + 346.277i 0.263057 + 0.455627i
\(761\) 814.458 470.227i 1.07025 0.617907i 0.141998 0.989867i \(-0.454647\pi\)
0.928249 + 0.371960i \(0.121314\pi\)
\(762\) 0 0
\(763\) 259.919 450.193i 0.340654 0.590031i
\(764\) 69.1007i 0.0904459i
\(765\) 0 0
\(766\) 423.615 0.553023
\(767\) −1132.05 653.590i −1.47595 0.852138i
\(768\) 0 0
\(769\) −490.408 849.411i −0.637721 1.10457i −0.985932 0.167149i \(-0.946544\pi\)
0.348210 0.937416i \(-0.386789\pi\)
\(770\) 875.485 505.462i 1.13699 0.656444i
\(771\) 0 0
\(772\) −55.0000 + 95.2628i −0.0712435 + 0.123397i
\(773\) 1042.20i 1.34825i −0.738618 0.674124i \(-0.764521\pi\)
0.738618 0.674124i \(-0.235479\pi\)
\(774\) 0 0
\(775\) −68.7077 −0.0886550
\(776\) −184.051 106.262i −0.237179 0.136935i
\(777\) 0 0
\(778\) −328.492 568.965i −0.422227 0.731318i
\(779\) 710.550 410.236i 0.912131 0.526619i
\(780\) 0 0
\(781\) −743.769 + 1288.25i −0.952329 + 1.64948i
\(782\) 161.384i 0.206373i
\(783\) 0 0
\(784\) 85.7231 0.109341
\(785\) 1.46729 + 0.847142i 0.00186916 + 0.00107916i
\(786\) 0 0
\(787\)