Properties

Label 162.3.d.c.53.4
Level $162$
Weight $3$
Character 162.53
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 53.4
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 162.53
Dual form 162.3.d.c.107.4

$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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 \(-0.136560\pi\)
0.0944434 + 0.995530i \(0.469893\pi\)
\(6\) 0 0
\(7\) 4.19615 + 7.26795i 0.599450 + 1.03828i 0.992902 + 0.118933i \(0.0379475\pi\)
−0.393452 + 0.919345i \(0.628719\pi\)
\(8\) 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 \(-0.899534\pi\)
−0.206480 + 0.978451i \(0.566201\pi\)
\(12\) 0 0
\(13\) 10.5981 18.3564i 0.815237 1.41203i −0.0939212 0.995580i \(-0.529940\pi\)
0.909158 0.416452i \(-0.136726\pi\)
\(14\) 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 \(-0.436848\pi\)
−0.750487 + 0.660885i \(0.770181\pi\)
\(24\) 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 \(-0.876288\pi\)
−0.134536 + 0.990909i \(0.542954\pi\)
\(30\) 0 0
\(31\) −4.00000 + 6.92820i −0.129032 + 0.223490i −0.923302 0.384075i \(-0.874520\pi\)
0.794270 + 0.607565i \(0.207854\pi\)
\(32\) −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 \(-0.467875\pi\)
−0.811242 + 0.584710i \(0.801208\pi\)
\(42\) 0 0
\(43\) −4.58846 7.94744i −0.106708 0.184824i 0.807727 0.589557i \(-0.200698\pi\)
−0.914435 + 0.404733i \(0.867364\pi\)
\(44\) 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 \(-0.608883\pi\)
0.648134 + 0.761526i \(0.275549\pi\)
\(48\) 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 \(-0.158283\pi\)
0.0263336 + 0.999653i \(0.491617\pi\)
\(60\) 0 0
\(61\) 6.50000 + 11.2583i 0.106557 + 0.184563i 0.914373 0.404872i \(-0.132684\pi\)
−0.807816 + 0.589435i \(0.799351\pi\)
\(62\) 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 −0.934161 0.356853i \(-0.883850\pi\)
0.776124 + 0.630580i \(0.217183\pi\)
\(68\) −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 −0.988546 0.150923i \(-0.951776\pi\)
0.363570 0.931567i \(-0.381558\pi\)
\(80\) 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 \(-0.880924\pi\)
−0.148954 + 0.988844i \(0.547591\pi\)
\(84\) 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 0.992087 0.125553i \(-0.0400705\pi\)
−0.604775 + 0.796396i \(0.706737\pi\)
\(98\) 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 \(-0.620668\pi\)
0.619501 + 0.784995i \(0.287335\pi\)
\(102\) 0 0
\(103\) −48.3538 + 83.7513i −0.469455 + 0.813119i −0.999390 0.0349186i \(-0.988883\pi\)
0.529936 + 0.848038i \(0.322216\pi\)
\(104\) −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 \(-0.171829\pi\)
−0.0162179 + 0.999868i \(0.505163\pi\)
\(114\) 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 \(-0.398402\pi\)
−0.665391 + 0.746495i \(0.731735\pi\)
\(132\) 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 \(-0.668566\pi\)
0.494825 + 0.868993i \(0.335232\pi\)
\(138\) 0 0
\(139\) 9.60770 16.6410i 0.0691201 0.119720i −0.829394 0.558664i \(-0.811314\pi\)
0.898514 + 0.438944i \(0.144647\pi\)
\(140\) 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 \(-0.230865\pi\)
−0.200321 + 0.979730i \(0.564199\pi\)
\(150\) 0 0
\(151\) −16.0000 27.7128i −0.105960 0.183529i 0.808170 0.588949i \(-0.200458\pi\)
−0.914130 + 0.405421i \(0.867125\pi\)
\(152\) 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 −0.866491 0.499193i \(-0.833630\pi\)
0.865560 + 0.500806i \(0.166963\pi\)
\(158\) −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 \(-0.279645\pi\)
−0.347526 + 0.937670i \(0.612978\pi\)
\(168\) 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 \(-0.446185\pi\)
0.937808 + 0.347154i \(0.112852\pi\)
\(174\) 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 \(-0.695496\pi\)
0.419622 + 0.907699i \(0.362163\pi\)
\(192\) 0 0
\(193\) 27.5000 47.6314i 0.142487 0.246795i −0.785946 0.618296i \(-0.787823\pi\)
0.928433 + 0.371501i \(0.121157\pi\)
\(194\) 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 0.228927 + 0.973444i \(0.426478\pi\)
−0.957490 + 0.288465i \(0.906855\pi\)
\(212\) −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 0.943272 + 0.332022i \(0.107731\pi\)
−0.184096 + 0.982908i \(0.558936\pi\)
\(224\) 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 \(-0.754689\pi\)
0.244563 + 0.969633i \(0.421355\pi\)
\(228\) 0 0
\(229\) −37.0289 + 64.1359i −0.161698 + 0.280069i −0.935478 0.353386i \(-0.885030\pi\)
0.773780 + 0.633455i \(0.218364\pi\)
\(230\) −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 0.980462 + 0.196708i \(0.0630252\pi\)
0.660585 + 0.750751i \(0.270308\pi\)
\(240\) 0 0
\(241\) 191.344 + 331.418i 0.793959 + 1.37518i 0.923498 + 0.383604i \(0.125317\pi\)
−0.129538 + 0.991574i \(0.541350\pi\)
\(242\) 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 \(-0.232699\pi\)
−0.205962 + 0.978560i \(0.566032\pi\)
\(258\) 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 \(-0.502715\pi\)
0.861730 + 0.507367i \(0.169381\pi\)
\(264\) 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 0.867300 0.497786i \(-0.165853\pi\)
−0.864745 + 0.502211i \(0.832520\pi\)
\(278\) 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 \(-0.724021\pi\)
0.336704 + 0.941610i \(0.390688\pi\)
\(282\) 0 0
\(283\) 23.6462 40.9564i 0.0835554 0.144722i −0.821219 0.570613i \(-0.806706\pi\)
0.904775 + 0.425890i \(0.140039\pi\)
\(284\) 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 \(-0.140544\pi\)
0.0819755 + 0.996634i \(0.473877\pi\)
\(294\) 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 \(-0.328451\pi\)
−0.486658 + 0.873593i \(0.661784\pi\)
\(312\) 0 0
\(313\) 239.638 + 415.066i 0.765618 + 1.32609i 0.939919 + 0.341397i \(0.110900\pi\)
−0.174301 + 0.984692i \(0.555767\pi\)
\(314\) 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 \(-0.575211\pi\)
0.724917 + 0.688836i \(0.241878\pi\)
\(318\) 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 0.551837 0.833952i \(-0.313927\pi\)
−0.998142 + 0.0609292i \(0.980594\pi\)
\(332\) 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 0.232692 + 0.972550i \(0.425246\pi\)
−0.958600 + 0.284758i \(0.908087\pi\)
\(338\) −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 −0.970840 0.239730i \(-0.922941\pi\)
−0.693032 0.720907i \(-0.743726\pi\)
\(348\) 0 0
\(349\) −255.985 443.378i −0.733480 1.27042i −0.955387 0.295357i \(-0.904561\pi\)
0.221907 0.975068i \(-0.428772\pi\)
\(350\) 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 \(-0.354440\pi\)
0.997802 + 0.0662588i \(0.0211063\pi\)
\(354\) 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 0.855420 0.517934i \(-0.173299\pi\)
−0.876255 + 0.481848i \(0.839966\pi\)
\(368\) 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 −0.0188869 + 0.999822i \(0.506012\pi\)
−0.856427 + 0.516267i \(0.827321\pi\)
\(374\) 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 \(-0.205447\pi\)
−0.121530 + 0.992588i \(0.538780\pi\)
\(384\) 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 \(-0.870354\pi\)
−0.116043 + 0.993244i \(0.537021\pi\)
\(390\) 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 \(-0.308359\pi\)
−0.430585 + 0.902550i \(0.641693\pi\)
\(402\) 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 −0.593639 0.804732i \(-0.702309\pi\)
0.993737 + 0.111741i \(0.0356425\pi\)
\(410\) −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 \(-0.615839\pi\)
−0.987278 + 0.159003i \(0.949172\pi\)
\(420\) 0 0
\(421\) −1.65956 2.87445i −0.00394196 0.00682767i 0.864048 0.503410i \(-0.167921\pi\)
−0.867990 + 0.496582i \(0.834588\pi\)
\(422\) 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 0.999033 + 0.0439580i \(0.0139968\pi\)
−0.461448 + 0.887167i \(0.652670\pi\)
\(440\) 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 \(-0.444361\pi\)
0.939783 + 0.341773i \(0.111027\pi\)
\(444\) 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 −0.980312 0.197453i \(-0.936733\pi\)
0.319157 0.947702i \(-0.396600\pi\)
\(458\) 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 \(-0.668439\pi\)
0.495169 + 0.868796i \(0.335106\pi\)
\(462\) 0 0
\(463\) 80.7461 139.856i 0.174398 0.302066i −0.765555 0.643370i \(-0.777536\pi\)
0.939953 + 0.341305i \(0.110869\pi\)
\(464\) 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 \(-0.595026\pi\)
0.680660 + 0.732599i \(0.261693\pi\)
\(480\) 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 −0.984972 0.172713i \(-0.944747\pi\)
−0.642060 0.766654i \(-0.721920\pi\)
\(492\) 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 −0.561870 0.827225i \(-0.689918\pi\)
0.997333 + 0.0729811i \(0.0232513\pi\)
\(500\) −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 \(-0.0931602\pi\)
0.228880 + 0.973455i \(0.426494\pi\)
\(510\) 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 0.941665 0.336552i \(-0.109261\pi\)
−0.762295 + 0.647230i \(0.775927\pi\)
\(548\) 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 \(-0.440815\pi\)
−0.758666 + 0.651480i \(0.774149\pi\)
\(564\) 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 \(-0.649843\pi\)
0.545052 + 0.838402i \(0.316510\pi\)
\(570\) 0 0
\(571\) −43.1000 + 74.6513i −0.0754815 + 0.130738i −0.901296 0.433205i \(-0.857383\pi\)
0.825814 + 0.563943i \(0.190716\pi\)
\(572\) 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 \(-0.972506\pi\)
−0.423427 + 0.905930i \(0.639173\pi\)
\(588\) 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 \(-0.410082\pi\)
−0.692329 + 0.721582i \(0.743415\pi\)
\(600\) 0 0
\(601\) 140.208 + 242.847i 0.233291 + 0.404071i 0.958775 0.284168i \(-0.0917173\pi\)
−0.725484 + 0.688239i \(0.758384\pi\)
\(602\) 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 0.383935 + 0.923360i \(0.374569\pi\)
−0.991621 + 0.129183i \(0.958765\pi\)
\(608\) −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 \(-0.208217\pi\)
−0.130163 + 0.991493i \(0.541550\pi\)
\(618\) 0 0
\(619\) −443.177 767.605i −0.715956 1.24007i −0.962590 0.270964i \(-0.912658\pi\)
0.246633 0.969109i \(-0.420676\pi\)
\(620\) 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 \(-0.429176\pi\)
0.955011 + 0.296569i \(0.0958425\pi\)
\(642\) 0 0
\(643\) 309.061 535.310i 0.480656 0.832520i −0.519098 0.854715i \(-0.673732\pi\)
0.999754 + 0.0221949i \(0.00706543\pi\)
\(644\) −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 \(-0.379513\pi\)
−0.619949 + 0.784642i \(0.712847\pi\)
\(654\) 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 \(-0.833744\pi\)
−0.00128859 + 0.999999i \(0.500410\pi\)
\(660\) 0 0
\(661\) 294.915 510.808i 0.446165 0.772781i −0.551967 0.833866i \(-0.686123\pi\)
0.998133 + 0.0610847i \(0.0194560\pi\)
\(662\) −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 0.974002 0.226541i \(-0.0727418\pi\)
−0.683191 + 0.730240i \(0.739408\pi\)
\(674\) 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 \(-0.837875\pi\)
−0.0142672 + 0.999898i \(0.504542\pi\)
\(678\) 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 0.510935 0.859619i \(-0.329299\pi\)
−0.999920 + 0.0126731i \(0.995966\pi\)
\(692\) 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 0.798339 0.602208i \(-0.205712\pi\)
−0.920697 + 0.390278i \(0.872379\pi\)
\(710\) 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 0.510397 0.859939i \(-0.329498\pi\)
−0.999927 + 0.0120478i \(0.996165\pi\)
\(728\) 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 0.0556546 + 0.998450i \(0.482275\pi\)
−0.892510 + 0.451027i \(0.851058\pi\)
\(734\) −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 \(-0.156937\pi\)
0.0305622 + 0.999533i \(0.490270\pi\)
\(744\) 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 −0.284524 0.958669i \(-0.591835\pi\)
0.972494 0.232930i \(-0.0748312\pi\)
\(752\) −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 \(-0.545353\pi\)
−0.928249 + 0.371960i \(0.878686\pi\)
\(762\) 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 0.348210 + 0.937416i \(0.386789\pi\)
−0.985932 + 0.167149i \(0.946544\pi\)
\(770\) −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
\(787\) 72.3501