Properties

Label 162.3.d.c.107.4
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 107.4
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.3.d.c.53.4

$q$-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 0.0944434 0.995530i \(-0.469893\pi\)
0.909376 + 0.415975i \(0.136560\pi\)
\(6\) 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 −0.206480 0.978451i \(-0.566201\pi\)
−0.950603 + 0.310408i \(0.899534\pi\)
\(12\) 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 \(0.0733395\pi\)
−0.973574 + 0.228370i \(0.926660\pi\)
\(18\) 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 −0.750487 0.660885i \(-0.770181\pi\)
0.197099 + 0.980384i \(0.436848\pi\)
\(24\) 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 −0.134536 0.990909i \(-0.542954\pi\)
−0.925420 + 0.378942i \(0.876288\pi\)
\(30\) 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 −0.811242 0.584710i \(-0.801208\pi\)
0.100753 + 0.994912i \(0.467875\pi\)
\(42\) 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 0.648134 0.761526i \(-0.275549\pi\)
−0.335434 + 0.942064i \(0.608883\pi\)
\(48\) 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 \(0.0781391\pi\)
−0.970020 + 0.243023i \(0.921861\pi\)
\(54\) 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 0.0263336 0.999653i \(-0.491617\pi\)
0.878892 + 0.477021i \(0.158283\pi\)
\(60\) 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 \(-0.747438\pi\)
0.701392 0.712776i \(-0.252562\pi\)
\(72\) 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 −0.148954 0.988844i \(-0.547591\pi\)
−0.930841 + 0.365424i \(0.880924\pi\)
\(84\) 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 \(0.271655\pi\)
−0.657403 + 0.753539i \(0.728345\pi\)
\(90\) 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 0.619501 0.784995i \(-0.287335\pi\)
−0.370075 + 0.929002i \(0.620668\pi\)
\(102\) 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 \(0.311558\pi\)
−0.558030 + 0.829821i \(0.688442\pi\)
\(108\) 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 −0.0162179 0.999868i \(-0.505163\pi\)
0.857803 + 0.513979i \(0.171829\pi\)
\(114\) 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 −0.665391 0.746495i \(-0.731735\pi\)
0.313789 + 0.949493i \(0.398402\pi\)
\(132\) 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 0.494825 0.868993i \(-0.335232\pi\)
−0.505157 + 0.863027i \(0.668566\pi\)
\(138\) 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 −0.200321 0.979730i \(-0.564199\pi\)
0.748311 + 0.663348i \(0.230865\pi\)
\(150\) 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 −0.347526 0.937670i \(-0.612978\pi\)
0.638283 + 0.769802i \(0.279645\pi\)
\(168\) 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 0.937808 0.347154i \(-0.112852\pi\)
0.168260 + 0.985743i \(0.446185\pi\)
\(174\) 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 \(-0.755977\pi\)
0.720258 0.693706i \(-0.244023\pi\)
\(180\) 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 0.419622 0.907699i \(-0.362163\pi\)
−0.576279 + 0.817253i \(0.695496\pi\)
\(192\) 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 \(0.0288952\pi\)
−0.995883 + 0.0906524i \(0.971105\pi\)
\(198\) 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 0.244563 0.969633i \(-0.421355\pi\)
−0.717445 + 0.696615i \(0.754689\pi\)
\(228\) 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 \(-0.800578\pi\)
0.810082 0.586316i \(-0.199422\pi\)
\(234\) 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 \(-0.270308\pi\)
0.980462 0.196708i \(-0.0630252\pi\)
\(240\) 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 \(0.0470493\pi\)
−0.989096 + 0.147272i \(0.952951\pi\)
\(252\) 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 −0.205962 0.978560i \(-0.566032\pi\)
0.744477 + 0.667648i \(0.232699\pi\)
\(258\) 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 0.861730 0.507367i \(-0.169381\pi\)
−0.00852798 + 0.999964i \(0.502715\pi\)
\(264\) 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 \(-0.985312\pi\)
0.998936 0.0461278i \(-0.0146881\pi\)
\(270\) 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 0.336704 0.941610i \(-0.390688\pi\)
−0.647106 + 0.762400i \(0.724021\pi\)
\(282\) 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 0.0819755 0.996634i \(-0.473877\pi\)
0.904098 + 0.427324i \(0.140544\pi\)
\(294\) 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 −0.486658 0.873593i \(-0.661784\pi\)
0.513225 + 0.858254i \(0.328451\pi\)
\(312\) 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 0.724917 0.688836i \(-0.241878\pi\)
−0.234091 + 0.972215i \(0.575211\pi\)
\(318\) 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 \(0.743726\pi\)
−0.970840 + 0.239730i \(0.922941\pi\)
\(348\) 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 0.997802 0.0662588i \(-0.0211063\pi\)
0.441519 + 0.897252i \(0.354440\pi\)
\(354\) 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 \(0.267326\pi\)
−0.667589 + 0.744530i \(0.732674\pi\)
\(360\) 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 −0.121530 0.992588i \(-0.538780\pi\)
0.798841 + 0.601542i \(0.205447\pi\)
\(384\) 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 −0.116043 0.993244i \(-0.537021\pi\)
−0.918196 + 0.396126i \(0.870354\pi\)
\(390\) 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 −0.430585 0.902550i \(-0.641693\pi\)
0.566339 + 0.824172i \(0.308359\pi\)
\(402\) 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 −0.987278 0.159003i \(-0.949172\pi\)
−0.355939 + 0.934509i \(0.615839\pi\)
\(420\) 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 \(-0.617943\pi\)
0.362107 0.932136i \(-0.382057\pi\)
\(432\) 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 0.939783 0.341773i \(-0.111027\pi\)
0.173908 + 0.984762i \(0.444361\pi\)
\(444\) 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 \(0.213933\pi\)
−0.782523 + 0.622622i \(0.786067\pi\)
\(450\) 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 0.495169 0.868796i \(-0.335106\pi\)
−0.504815 + 0.863227i \(0.668439\pi\)
\(462\) 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 \(0.181035\pi\)
−0.842581 + 0.538570i \(0.818965\pi\)
\(468\) 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 0.680660 0.732599i \(-0.261693\pi\)
−0.294119 + 0.955769i \(0.595026\pi\)
\(480\) 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 \(0.721920\pi\)
−0.984972 + 0.172713i \(0.944747\pi\)
\(492\) 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 \(-0.954252\pi\)
0.989690 0.143227i \(-0.0457480\pi\)
\(504\) 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 0.228880 0.973455i \(-0.426494\pi\)
0.957477 + 0.288511i \(0.0931602\pi\)
\(510\) 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 \(0.134385\pi\)
−0.912197 + 0.409752i \(0.865615\pi\)
\(522\) 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 \(-0.897182\pi\)
0.948284 0.317424i \(-0.102818\pi\)
\(558\) 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 −0.758666 0.651480i \(-0.774149\pi\)
0.184865 + 0.982764i \(0.440815\pi\)
\(564\) 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 0.545052 0.838402i \(-0.316510\pi\)
−0.453552 + 0.891230i \(0.649843\pi\)
\(570\) 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 −0.423427 0.905930i \(-0.639173\pi\)
−0.996272 + 0.0862666i \(0.972506\pi\)
\(588\) 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 \(0.0280427\pi\)
−0.996122 + 0.0879847i \(0.971957\pi\)
\(594\) 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 −0.692329 0.721582i \(-0.743415\pi\)
0.278744 + 0.960366i \(0.410082\pi\)
\(600\) 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 −0.130163 0.991493i \(-0.541550\pi\)
0.793576 + 0.608471i \(0.208217\pi\)
\(618\) 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 0.955011 0.296569i \(-0.0958425\pi\)
0.220669 + 0.975349i \(0.429176\pi\)
\(642\) 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 \(-0.893363\pi\)
0.944407 0.328778i \(-0.106637\pi\)
\(648\) 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 −0.619949 0.784642i \(-0.712847\pi\)
0.369546 + 0.929212i \(0.379513\pi\)
\(654\) 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 −0.00128859 0.999999i \(-0.500410\pi\)
−0.866669 + 0.498884i \(0.833744\pi\)
\(660\) 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 −0.0142672 0.999898i \(-0.504542\pi\)
−0.873071 + 0.487593i \(0.837875\pi\)
\(678\) 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 \(-0.834632\pi\)
0.868057 0.496464i \(-0.165368\pi\)
\(684\) 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 \(0.192538\pi\)
−0.822573 + 0.568659i \(0.807462\pi\)
\(702\) 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 \(0.0417740\pi\)
−0.991401 + 0.130860i \(0.958226\pi\)
\(720\) 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 0.0305622 0.999533i \(-0.490270\pi\)
0.880902 + 0.473299i \(0.156937\pi\)
\(744\) 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 −0.928249 0.371960i \(-0.878686\pi\)
−0.141998 + 0.989867i \(0.545353\pi\)
\(762\) 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 \(0.235479\pi\)
−0.738618 + 0.674124i \(0.764521\pi\)
\(774\) 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
\(787\) 72.3501 + 125.314i