Properties

Label 4020.2.q.k.841.1
Level 4020
Weight 2
Character 4020.841
Analytic conductor 32.100
Analytic rank 0
Dimension 14
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.q (of order \(3\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 841.1
Root \(0.295122 - 0.511167i\)
Character \(\chi\) = 4020.841
Dual form 4020.2.q.k.3781.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{5} +(-1.59463 + 2.76199i) q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{5} +(-1.59463 + 2.76199i) q^{7} +1.00000 q^{9} +(2.11819 - 3.66882i) q^{11} +(1.09024 + 1.88836i) q^{13} -1.00000 q^{15} +(-2.56215 - 4.43778i) q^{17} +(-0.325805 - 0.564312i) q^{19} +(1.59463 - 2.76199i) q^{21} +(4.02246 + 6.96710i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-3.94885 + 6.83962i) q^{29} +(4.23779 - 7.34007i) q^{31} +(-2.11819 + 3.66882i) q^{33} +(-1.59463 + 2.76199i) q^{35} +(-1.75252 - 3.03546i) q^{37} +(-1.09024 - 1.88836i) q^{39} +(0.135436 - 0.234583i) q^{41} +8.32328 q^{43} +1.00000 q^{45} +(-0.171569 + 0.297167i) q^{47} +(-1.58571 - 2.74654i) q^{49} +(2.56215 + 4.43778i) q^{51} +7.89678 q^{53} +(2.11819 - 3.66882i) q^{55} +(0.325805 + 0.564312i) q^{57} -4.39987 q^{59} +(-7.05670 - 12.2226i) q^{61} +(-1.59463 + 2.76199i) q^{63} +(1.09024 + 1.88836i) q^{65} +(5.59464 - 5.97495i) q^{67} +(-4.02246 - 6.96710i) q^{69} +(1.45116 - 2.51348i) q^{71} +(3.18520 + 5.51693i) q^{73} -1.00000 q^{75} +(6.75549 + 11.7008i) q^{77} +(0.598566 - 1.03675i) q^{79} +1.00000 q^{81} +(0.963958 + 1.66962i) q^{83} +(-2.56215 - 4.43778i) q^{85} +(3.94885 - 6.83962i) q^{87} -3.23796 q^{89} -6.95417 q^{91} +(-4.23779 + 7.34007i) q^{93} +(-0.325805 - 0.564312i) q^{95} +(5.58794 + 9.67860i) q^{97} +(2.11819 - 3.66882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{3} + 14q^{5} + 3q^{7} + 14q^{9} + 6q^{11} + 9q^{13} - 14q^{15} - 12q^{17} + 14q^{19} - 3q^{21} + 6q^{23} + 14q^{25} - 14q^{27} - q^{29} + 7q^{31} - 6q^{33} + 3q^{35} - 2q^{37} - 9q^{39} - 18q^{41} - 6q^{43} + 14q^{45} + 7q^{47} + 12q^{51} - 12q^{53} + 6q^{55} - 14q^{57} - 2q^{59} + 3q^{63} + 9q^{65} + 25q^{67} - 6q^{69} + 22q^{71} - 15q^{73} - 14q^{75} + q^{77} + 9q^{79} + 14q^{81} - q^{83} - 12q^{85} + q^{87} - 12q^{89} - 38q^{91} - 7q^{93} + 14q^{95} + 16q^{97} + 6q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.59463 + 2.76199i −0.602715 + 1.04393i 0.389693 + 0.920945i \(0.372581\pi\)
−0.992408 + 0.122988i \(0.960752\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.11819 3.66882i 0.638660 1.10619i −0.347068 0.937840i \(-0.612823\pi\)
0.985727 0.168351i \(-0.0538441\pi\)
\(12\) 0 0
\(13\) 1.09024 + 1.88836i 0.302380 + 0.523737i 0.976674 0.214725i \(-0.0688857\pi\)
−0.674295 + 0.738462i \(0.735552\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −2.56215 4.43778i −0.621413 1.07632i −0.989223 0.146418i \(-0.953225\pi\)
0.367810 0.929901i \(-0.380108\pi\)
\(18\) 0 0
\(19\) −0.325805 0.564312i −0.0747449 0.129462i 0.826230 0.563332i \(-0.190481\pi\)
−0.900975 + 0.433870i \(0.857148\pi\)
\(20\) 0 0
\(21\) 1.59463 2.76199i 0.347978 0.602715i
\(22\) 0 0
\(23\) 4.02246 + 6.96710i 0.838741 + 1.45274i 0.890948 + 0.454105i \(0.150041\pi\)
−0.0522075 + 0.998636i \(0.516626\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −3.94885 + 6.83962i −0.733284 + 1.27008i 0.222188 + 0.975004i \(0.428680\pi\)
−0.955472 + 0.295081i \(0.904653\pi\)
\(30\) 0 0
\(31\) 4.23779 7.34007i 0.761129 1.31831i −0.181139 0.983457i \(-0.557979\pi\)
0.942269 0.334857i \(-0.108688\pi\)
\(32\) 0 0
\(33\) −2.11819 + 3.66882i −0.368730 + 0.638660i
\(34\) 0 0
\(35\) −1.59463 + 2.76199i −0.269542 + 0.466861i
\(36\) 0 0
\(37\) −1.75252 3.03546i −0.288113 0.499026i 0.685246 0.728311i \(-0.259694\pi\)
−0.973359 + 0.229285i \(0.926361\pi\)
\(38\) 0 0
\(39\) −1.09024 1.88836i −0.174579 0.302380i
\(40\) 0 0
\(41\) 0.135436 0.234583i 0.0211516 0.0366356i −0.855256 0.518206i \(-0.826600\pi\)
0.876407 + 0.481570i \(0.159933\pi\)
\(42\) 0 0
\(43\) 8.32328 1.26929 0.634644 0.772804i \(-0.281147\pi\)
0.634644 + 0.772804i \(0.281147\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −0.171569 + 0.297167i −0.0250260 + 0.0433462i −0.878267 0.478170i \(-0.841300\pi\)
0.853241 + 0.521517i \(0.174634\pi\)
\(48\) 0 0
\(49\) −1.58571 2.74654i −0.226530 0.392362i
\(50\) 0 0
\(51\) 2.56215 + 4.43778i 0.358773 + 0.621413i
\(52\) 0 0
\(53\) 7.89678 1.08471 0.542353 0.840151i \(-0.317534\pi\)
0.542353 + 0.840151i \(0.317534\pi\)
\(54\) 0 0
\(55\) 2.11819 3.66882i 0.285617 0.494704i
\(56\) 0 0
\(57\) 0.325805 + 0.564312i 0.0431540 + 0.0747449i
\(58\) 0 0
\(59\) −4.39987 −0.572814 −0.286407 0.958108i \(-0.592461\pi\)
−0.286407 + 0.958108i \(0.592461\pi\)
\(60\) 0 0
\(61\) −7.05670 12.2226i −0.903518 1.56494i −0.822894 0.568195i \(-0.807642\pi\)
−0.0806243 0.996745i \(-0.525691\pi\)
\(62\) 0 0
\(63\) −1.59463 + 2.76199i −0.200905 + 0.347978i
\(64\) 0 0
\(65\) 1.09024 + 1.88836i 0.135228 + 0.234222i
\(66\) 0 0
\(67\) 5.59464 5.97495i 0.683493 0.729957i
\(68\) 0 0
\(69\) −4.02246 6.96710i −0.484247 0.838741i
\(70\) 0 0
\(71\) 1.45116 2.51348i 0.172221 0.298295i −0.766975 0.641677i \(-0.778239\pi\)
0.939196 + 0.343382i \(0.111572\pi\)
\(72\) 0 0
\(73\) 3.18520 + 5.51693i 0.372800 + 0.645708i 0.989995 0.141102i \(-0.0450646\pi\)
−0.617195 + 0.786810i \(0.711731\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 6.75549 + 11.7008i 0.769859 + 1.33344i
\(78\) 0 0
\(79\) 0.598566 1.03675i 0.0673440 0.116643i −0.830387 0.557187i \(-0.811881\pi\)
0.897731 + 0.440543i \(0.145214\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0.963958 + 1.66962i 0.105808 + 0.183265i 0.914068 0.405561i \(-0.132924\pi\)
−0.808260 + 0.588826i \(0.799590\pi\)
\(84\) 0 0
\(85\) −2.56215 4.43778i −0.277904 0.481345i
\(86\) 0 0
\(87\) 3.94885 6.83962i 0.423362 0.733284i
\(88\) 0 0
\(89\) −3.23796 −0.343223 −0.171612 0.985165i \(-0.554897\pi\)
−0.171612 + 0.985165i \(0.554897\pi\)
\(90\) 0 0
\(91\) −6.95417 −0.728995
\(92\) 0 0
\(93\) −4.23779 + 7.34007i −0.439438 + 0.761129i
\(94\) 0 0
\(95\) −0.325805 0.564312i −0.0334269 0.0578971i
\(96\) 0 0
\(97\) 5.58794 + 9.67860i 0.567370 + 0.982713i 0.996825 + 0.0796248i \(0.0253722\pi\)
−0.429455 + 0.903088i \(0.641294\pi\)
\(98\) 0 0
\(99\) 2.11819 3.66882i 0.212887 0.368730i
\(100\) 0 0
\(101\) −7.11803 + 12.3288i −0.708270 + 1.22676i 0.257228 + 0.966351i \(0.417191\pi\)
−0.965498 + 0.260409i \(0.916142\pi\)
\(102\) 0 0
\(103\) 5.69947 9.87177i 0.561585 0.972694i −0.435773 0.900057i \(-0.643525\pi\)
0.997358 0.0726378i \(-0.0231417\pi\)
\(104\) 0 0
\(105\) 1.59463 2.76199i 0.155620 0.269542i
\(106\) 0 0
\(107\) 8.78848 0.849615 0.424807 0.905284i \(-0.360342\pi\)
0.424807 + 0.905284i \(0.360342\pi\)
\(108\) 0 0
\(109\) 2.52859 0.242195 0.121098 0.992641i \(-0.461359\pi\)
0.121098 + 0.992641i \(0.461359\pi\)
\(110\) 0 0
\(111\) 1.75252 + 3.03546i 0.166342 + 0.288113i
\(112\) 0 0
\(113\) −8.82932 + 15.2928i −0.830593 + 1.43863i 0.0669763 + 0.997755i \(0.478665\pi\)
−0.897569 + 0.440874i \(0.854669\pi\)
\(114\) 0 0
\(115\) 4.02246 + 6.96710i 0.375096 + 0.649686i
\(116\) 0 0
\(117\) 1.09024 + 1.88836i 0.100793 + 0.174579i
\(118\) 0 0
\(119\) 16.3428 1.49814
\(120\) 0 0
\(121\) −3.47349 6.01627i −0.315772 0.546933i
\(122\) 0 0
\(123\) −0.135436 + 0.234583i −0.0122119 + 0.0211516i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −5.93915 + 10.2869i −0.527015 + 0.912816i 0.472490 + 0.881336i \(0.343355\pi\)
−0.999504 + 0.0314799i \(0.989978\pi\)
\(128\) 0 0
\(129\) −8.32328 −0.732824
\(130\) 0 0
\(131\) 1.93949 0.169454 0.0847271 0.996404i \(-0.472998\pi\)
0.0847271 + 0.996404i \(0.472998\pi\)
\(132\) 0 0
\(133\) 2.07816 0.180199
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) −15.7104 −1.34223 −0.671115 0.741353i \(-0.734184\pi\)
−0.671115 + 0.741353i \(0.734184\pi\)
\(138\) 0 0
\(139\) 15.1789 1.28746 0.643730 0.765253i \(-0.277386\pi\)
0.643730 + 0.765253i \(0.277386\pi\)
\(140\) 0 0
\(141\) 0.171569 0.297167i 0.0144487 0.0250260i
\(142\) 0 0
\(143\) 9.23740 0.772470
\(144\) 0 0
\(145\) −3.94885 + 6.83962i −0.327934 + 0.567999i
\(146\) 0 0
\(147\) 1.58571 + 2.74654i 0.130787 + 0.226530i
\(148\) 0 0
\(149\) 10.2647 0.840916 0.420458 0.907312i \(-0.361869\pi\)
0.420458 + 0.907312i \(0.361869\pi\)
\(150\) 0 0
\(151\) 8.87873 + 15.3784i 0.722541 + 1.25148i 0.959978 + 0.280075i \(0.0903594\pi\)
−0.237437 + 0.971403i \(0.576307\pi\)
\(152\) 0 0
\(153\) −2.56215 4.43778i −0.207138 0.358773i
\(154\) 0 0
\(155\) 4.23779 7.34007i 0.340387 0.589568i
\(156\) 0 0
\(157\) 11.3542 + 19.6661i 0.906167 + 1.56953i 0.819343 + 0.573303i \(0.194338\pi\)
0.0868237 + 0.996224i \(0.472328\pi\)
\(158\) 0 0
\(159\) −7.89678 −0.626255
\(160\) 0 0
\(161\) −25.6574 −2.02209
\(162\) 0 0
\(163\) −3.63817 + 6.30150i −0.284964 + 0.493571i −0.972600 0.232484i \(-0.925315\pi\)
0.687637 + 0.726055i \(0.258648\pi\)
\(164\) 0 0
\(165\) −2.11819 + 3.66882i −0.164901 + 0.285617i
\(166\) 0 0
\(167\) 8.49804 14.7190i 0.657598 1.13899i −0.323638 0.946181i \(-0.604906\pi\)
0.981236 0.192812i \(-0.0617607\pi\)
\(168\) 0 0
\(169\) 4.12273 7.14078i 0.317133 0.549291i
\(170\) 0 0
\(171\) −0.325805 0.564312i −0.0249150 0.0431540i
\(172\) 0 0
\(173\) 4.74878 + 8.22513i 0.361043 + 0.625345i 0.988133 0.153602i \(-0.0490873\pi\)
−0.627090 + 0.778947i \(0.715754\pi\)
\(174\) 0 0
\(175\) −1.59463 + 2.76199i −0.120543 + 0.208787i
\(176\) 0 0
\(177\) 4.39987 0.330714
\(178\) 0 0
\(179\) 2.79245 0.208717 0.104359 0.994540i \(-0.466721\pi\)
0.104359 + 0.994540i \(0.466721\pi\)
\(180\) 0 0
\(181\) 0.424877 0.735909i 0.0315809 0.0546997i −0.849803 0.527100i \(-0.823279\pi\)
0.881384 + 0.472401i \(0.156612\pi\)
\(182\) 0 0
\(183\) 7.05670 + 12.2226i 0.521647 + 0.903518i
\(184\) 0 0
\(185\) −1.75252 3.03546i −0.128848 0.223171i
\(186\) 0 0
\(187\) −21.7085 −1.58749
\(188\) 0 0
\(189\) 1.59463 2.76199i 0.115993 0.200905i
\(190\) 0 0
\(191\) 7.32457 + 12.6865i 0.529987 + 0.917965i 0.999388 + 0.0349798i \(0.0111367\pi\)
−0.469401 + 0.882985i \(0.655530\pi\)
\(192\) 0 0
\(193\) 17.5891 1.26609 0.633047 0.774113i \(-0.281804\pi\)
0.633047 + 0.774113i \(0.281804\pi\)
\(194\) 0 0
\(195\) −1.09024 1.88836i −0.0780741 0.135228i
\(196\) 0 0
\(197\) 11.2607 19.5041i 0.802293 1.38961i −0.115811 0.993271i \(-0.536947\pi\)
0.918103 0.396341i \(-0.129720\pi\)
\(198\) 0 0
\(199\) −0.782789 1.35583i −0.0554904 0.0961123i 0.836946 0.547286i \(-0.184339\pi\)
−0.892436 + 0.451173i \(0.851006\pi\)
\(200\) 0 0
\(201\) −5.59464 + 5.97495i −0.394615 + 0.421441i
\(202\) 0 0
\(203\) −12.5940 21.8134i −0.883922 1.53100i
\(204\) 0 0
\(205\) 0.135436 0.234583i 0.00945928 0.0163840i
\(206\) 0 0
\(207\) 4.02246 + 6.96710i 0.279580 + 0.484247i
\(208\) 0 0
\(209\) −2.76048 −0.190946
\(210\) 0 0
\(211\) 10.6933 + 18.5213i 0.736156 + 1.27506i 0.954214 + 0.299124i \(0.0966946\pi\)
−0.218058 + 0.975936i \(0.569972\pi\)
\(212\) 0 0
\(213\) −1.45116 + 2.51348i −0.0994316 + 0.172221i
\(214\) 0 0
\(215\) 8.32328 0.567643
\(216\) 0 0
\(217\) 13.5154 + 23.4094i 0.917488 + 1.58914i
\(218\) 0 0
\(219\) −3.18520 5.51693i −0.215236 0.372800i
\(220\) 0 0
\(221\) 5.58675 9.67653i 0.375805 0.650914i
\(222\) 0 0
\(223\) 14.6790 0.982979 0.491490 0.870883i \(-0.336453\pi\)
0.491490 + 0.870883i \(0.336453\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 11.3434 19.6473i 0.752888 1.30404i −0.193529 0.981094i \(-0.561994\pi\)
0.946417 0.322946i \(-0.104673\pi\)
\(228\) 0 0
\(229\) −0.410433 0.710890i −0.0271221 0.0469769i 0.852146 0.523305i \(-0.175301\pi\)
−0.879268 + 0.476328i \(0.841968\pi\)
\(230\) 0 0
\(231\) −6.75549 11.7008i −0.444478 0.769859i
\(232\) 0 0
\(233\) −10.2133 + 17.6899i −0.669093 + 1.15890i 0.309065 + 0.951041i \(0.399984\pi\)
−0.978158 + 0.207862i \(0.933349\pi\)
\(234\) 0 0
\(235\) −0.171569 + 0.297167i −0.0111919 + 0.0193850i
\(236\) 0 0
\(237\) −0.598566 + 1.03675i −0.0388811 + 0.0673440i
\(238\) 0 0
\(239\) 13.4875 23.3611i 0.872436 1.51110i 0.0129662 0.999916i \(-0.495873\pi\)
0.859470 0.511187i \(-0.170794\pi\)
\(240\) 0 0
\(241\) −4.12596 −0.265776 −0.132888 0.991131i \(-0.542425\pi\)
−0.132888 + 0.991131i \(0.542425\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −1.58571 2.74654i −0.101307 0.175470i
\(246\) 0 0
\(247\) 0.710415 1.23048i 0.0452027 0.0782933i
\(248\) 0 0
\(249\) −0.963958 1.66962i −0.0610884 0.105808i
\(250\) 0 0
\(251\) 2.26482 + 3.92278i 0.142954 + 0.247604i 0.928608 0.371063i \(-0.121007\pi\)
−0.785654 + 0.618666i \(0.787673\pi\)
\(252\) 0 0
\(253\) 34.0814 2.14268
\(254\) 0 0
\(255\) 2.56215 + 4.43778i 0.160448 + 0.277904i
\(256\) 0 0
\(257\) −1.27099 + 2.20142i −0.0792821 + 0.137321i −0.902940 0.429766i \(-0.858596\pi\)
0.823658 + 0.567086i \(0.191929\pi\)
\(258\) 0 0
\(259\) 11.1785 0.694599
\(260\) 0 0
\(261\) −3.94885 + 6.83962i −0.244428 + 0.423362i
\(262\) 0 0
\(263\) 22.9781 1.41689 0.708446 0.705765i \(-0.249397\pi\)
0.708446 + 0.705765i \(0.249397\pi\)
\(264\) 0 0
\(265\) 7.89678 0.485095
\(266\) 0 0
\(267\) 3.23796 0.198160
\(268\) 0 0
\(269\) 12.7893 0.779777 0.389889 0.920862i \(-0.372513\pi\)
0.389889 + 0.920862i \(0.372513\pi\)
\(270\) 0 0
\(271\) −3.91554 −0.237852 −0.118926 0.992903i \(-0.537945\pi\)
−0.118926 + 0.992903i \(0.537945\pi\)
\(272\) 0 0
\(273\) 6.95417 0.420885
\(274\) 0 0
\(275\) 2.11819 3.66882i 0.127732 0.221238i
\(276\) 0 0
\(277\) 21.4499 1.28880 0.644401 0.764688i \(-0.277107\pi\)
0.644401 + 0.764688i \(0.277107\pi\)
\(278\) 0 0
\(279\) 4.23779 7.34007i 0.253710 0.439438i
\(280\) 0 0
\(281\) −3.76695 6.52455i −0.224717 0.389222i 0.731517 0.681823i \(-0.238813\pi\)
−0.956235 + 0.292601i \(0.905479\pi\)
\(282\) 0 0
\(283\) 2.37594 0.141235 0.0706175 0.997503i \(-0.477503\pi\)
0.0706175 + 0.997503i \(0.477503\pi\)
\(284\) 0 0
\(285\) 0.325805 + 0.564312i 0.0192990 + 0.0334269i
\(286\) 0 0
\(287\) 0.431943 + 0.748146i 0.0254968 + 0.0441617i
\(288\) 0 0
\(289\) −4.62925 + 8.01810i −0.272309 + 0.471653i
\(290\) 0 0
\(291\) −5.58794 9.67860i −0.327571 0.567370i
\(292\) 0 0
\(293\) −0.957295 −0.0559258 −0.0279629 0.999609i \(-0.508902\pi\)
−0.0279629 + 0.999609i \(0.508902\pi\)
\(294\) 0 0
\(295\) −4.39987 −0.256170
\(296\) 0 0
\(297\) −2.11819 + 3.66882i −0.122910 + 0.212887i
\(298\) 0 0
\(299\) −8.77093 + 15.1917i −0.507236 + 0.878559i
\(300\) 0 0
\(301\) −13.2726 + 22.9888i −0.765019 + 1.32505i
\(302\) 0 0
\(303\) 7.11803 12.3288i 0.408920 0.708270i
\(304\) 0 0
\(305\) −7.05670 12.2226i −0.404066 0.699862i
\(306\) 0 0
\(307\) −13.7000 23.7291i −0.781900 1.35429i −0.930834 0.365443i \(-0.880917\pi\)
0.148934 0.988847i \(-0.452416\pi\)
\(308\) 0 0
\(309\) −5.69947 + 9.87177i −0.324231 + 0.561585i
\(310\) 0 0
\(311\) −7.11121 −0.403240 −0.201620 0.979464i \(-0.564621\pi\)
−0.201620 + 0.979464i \(0.564621\pi\)
\(312\) 0 0
\(313\) −23.4103 −1.32323 −0.661616 0.749843i \(-0.730129\pi\)
−0.661616 + 0.749843i \(0.730129\pi\)
\(314\) 0 0
\(315\) −1.59463 + 2.76199i −0.0898474 + 0.155620i
\(316\) 0 0
\(317\) 0.400887 + 0.694356i 0.0225160 + 0.0389989i 0.877064 0.480374i \(-0.159499\pi\)
−0.854548 + 0.519373i \(0.826166\pi\)
\(318\) 0 0
\(319\) 16.7289 + 28.9753i 0.936637 + 1.62230i
\(320\) 0 0
\(321\) −8.78848 −0.490525
\(322\) 0 0
\(323\) −1.66953 + 2.89170i −0.0928949 + 0.160899i
\(324\) 0 0
\(325\) 1.09024 + 1.88836i 0.0604759 + 0.104747i
\(326\) 0 0
\(327\) −2.52859 −0.139831
\(328\) 0 0
\(329\) −0.547180 0.947744i −0.0301670 0.0522508i
\(330\) 0 0
\(331\) −6.38166 + 11.0534i −0.350768 + 0.607547i −0.986384 0.164458i \(-0.947413\pi\)
0.635617 + 0.772005i \(0.280746\pi\)
\(332\) 0 0
\(333\) −1.75252 3.03546i −0.0960376 0.166342i
\(334\) 0 0
\(335\) 5.59464 5.97495i 0.305668 0.326447i
\(336\) 0 0
\(337\) 8.07382 + 13.9843i 0.439809 + 0.761772i 0.997674 0.0681599i \(-0.0217128\pi\)
−0.557865 + 0.829931i \(0.688379\pi\)
\(338\) 0 0
\(339\) 8.82932 15.2928i 0.479543 0.830593i
\(340\) 0 0
\(341\) −17.9529 31.0954i −0.972205 1.68391i
\(342\) 0 0
\(343\) −12.2103 −0.659297
\(344\) 0 0
\(345\) −4.02246 6.96710i −0.216562 0.375096i
\(346\) 0 0
\(347\) −2.53654 + 4.39341i −0.136169 + 0.235851i −0.926043 0.377417i \(-0.876812\pi\)
0.789875 + 0.613268i \(0.210146\pi\)
\(348\) 0 0
\(349\) 4.95651 0.265316 0.132658 0.991162i \(-0.457649\pi\)
0.132658 + 0.991162i \(0.457649\pi\)
\(350\) 0 0
\(351\) −1.09024 1.88836i −0.0581930 0.100793i
\(352\) 0 0
\(353\) −0.676718 1.17211i −0.0360181 0.0623851i 0.847454 0.530868i \(-0.178134\pi\)
−0.883473 + 0.468483i \(0.844801\pi\)
\(354\) 0 0
\(355\) 1.45116 2.51348i 0.0770194 0.133402i
\(356\) 0 0
\(357\) −16.3428 −0.864952
\(358\) 0 0
\(359\) −21.5436 −1.13703 −0.568514 0.822674i \(-0.692481\pi\)
−0.568514 + 0.822674i \(0.692481\pi\)
\(360\) 0 0
\(361\) 9.28770 16.0868i 0.488826 0.846672i
\(362\) 0 0
\(363\) 3.47349 + 6.01627i 0.182311 + 0.315772i
\(364\) 0 0
\(365\) 3.18520 + 5.51693i 0.166721 + 0.288769i
\(366\) 0 0
\(367\) 8.20139 14.2052i 0.428109 0.741507i −0.568596 0.822617i \(-0.692513\pi\)
0.996705 + 0.0811103i \(0.0258466\pi\)
\(368\) 0 0
\(369\) 0.135436 0.234583i 0.00705053 0.0122119i
\(370\) 0 0
\(371\) −12.5925 + 21.8108i −0.653768 + 1.13236i
\(372\) 0 0
\(373\) 12.8529 22.2619i 0.665498 1.15268i −0.313652 0.949538i \(-0.601552\pi\)
0.979150 0.203139i \(-0.0651142\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −17.2209 −0.886920
\(378\) 0 0
\(379\) 11.7431 + 20.3397i 0.603204 + 1.04478i 0.992333 + 0.123597i \(0.0394428\pi\)
−0.389129 + 0.921183i \(0.627224\pi\)
\(380\) 0 0
\(381\) 5.93915 10.2869i 0.304272 0.527015i
\(382\) 0 0
\(383\) 15.5127 + 26.8688i 0.792663 + 1.37293i 0.924313 + 0.381636i \(0.124639\pi\)
−0.131650 + 0.991296i \(0.542027\pi\)
\(384\) 0 0
\(385\) 6.75549 + 11.7008i 0.344292 + 0.596330i
\(386\) 0 0
\(387\) 8.32328 0.423096
\(388\) 0 0
\(389\) 5.23358 + 9.06483i 0.265353 + 0.459605i 0.967656 0.252273i \(-0.0811782\pi\)
−0.702303 + 0.711878i \(0.747845\pi\)
\(390\) 0 0
\(391\) 20.6123 35.7016i 1.04241 1.80551i
\(392\) 0 0
\(393\) −1.93949 −0.0978345
\(394\) 0 0
\(395\) 0.598566 1.03675i 0.0301171 0.0521644i
\(396\) 0 0
\(397\) −5.59361 −0.280735 −0.140368 0.990099i \(-0.544828\pi\)
−0.140368 + 0.990099i \(0.544828\pi\)
\(398\) 0 0
\(399\) −2.07816 −0.104038
\(400\) 0 0
\(401\) −21.0340 −1.05039 −0.525193 0.850983i \(-0.676007\pi\)
−0.525193 + 0.850983i \(0.676007\pi\)
\(402\) 0 0
\(403\) 18.4809 0.920600
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −14.8487 −0.736024
\(408\) 0 0
\(409\) 13.6119 23.5765i 0.673066 1.16579i −0.303964 0.952684i \(-0.598310\pi\)
0.977030 0.213102i \(-0.0683566\pi\)
\(410\) 0 0
\(411\) 15.7104 0.774937
\(412\) 0 0
\(413\) 7.01617 12.1524i 0.345243 0.597979i
\(414\) 0 0
\(415\) 0.963958 + 1.66962i 0.0473188 + 0.0819586i
\(416\) 0 0
\(417\) −15.1789 −0.743315
\(418\) 0 0
\(419\) 3.91227 + 6.77625i 0.191127 + 0.331042i 0.945624 0.325262i \(-0.105452\pi\)
−0.754497 + 0.656303i \(0.772119\pi\)
\(420\) 0 0
\(421\) −2.08243 3.60688i −0.101492 0.175789i 0.810808 0.585313i \(-0.199028\pi\)
−0.912299 + 0.409524i \(0.865695\pi\)
\(422\) 0 0
\(423\) −0.171569 + 0.297167i −0.00834199 + 0.0144487i
\(424\) 0 0
\(425\) −2.56215 4.43778i −0.124283 0.215264i
\(426\) 0 0
\(427\) 45.0114 2.17826
\(428\) 0 0
\(429\) −9.23740 −0.445986
\(430\) 0 0
\(431\) 3.27726 5.67638i 0.157860 0.273422i −0.776237 0.630442i \(-0.782874\pi\)
0.934097 + 0.357020i \(0.116207\pi\)
\(432\) 0 0
\(433\) −18.2476 + 31.6057i −0.876922 + 1.51887i −0.0222211 + 0.999753i \(0.507074\pi\)
−0.854701 + 0.519121i \(0.826260\pi\)
\(434\) 0 0
\(435\) 3.94885 6.83962i 0.189333 0.327934i
\(436\) 0 0
\(437\) 2.62108 4.53984i 0.125383 0.217170i
\(438\) 0 0
\(439\) −13.4752 23.3397i −0.643136 1.11394i −0.984729 0.174096i \(-0.944300\pi\)
0.341593 0.939848i \(-0.389034\pi\)
\(440\) 0 0
\(441\) −1.58571 2.74654i −0.0755101 0.130787i
\(442\) 0 0
\(443\) −15.6017 + 27.0229i −0.741257 + 1.28390i 0.210666 + 0.977558i \(0.432437\pi\)
−0.951923 + 0.306337i \(0.900896\pi\)
\(444\) 0 0
\(445\) −3.23796 −0.153494
\(446\) 0 0
\(447\) −10.2647 −0.485503
\(448\) 0 0
\(449\) −8.51529 + 14.7489i −0.401861 + 0.696044i −0.993951 0.109828i \(-0.964970\pi\)
0.592089 + 0.805872i \(0.298303\pi\)
\(450\) 0 0
\(451\) −0.573761 0.993783i −0.0270173 0.0467954i
\(452\) 0 0
\(453\) −8.87873 15.3784i −0.417159 0.722541i
\(454\) 0 0
\(455\) −6.95417 −0.326016
\(456\) 0 0
\(457\) −0.837395 + 1.45041i −0.0391717 + 0.0678474i −0.884947 0.465693i \(-0.845805\pi\)
0.845775 + 0.533540i \(0.179139\pi\)
\(458\) 0 0
\(459\) 2.56215 + 4.43778i 0.119591 + 0.207138i
\(460\) 0 0
\(461\) −35.3135 −1.64471 −0.822357 0.568972i \(-0.807341\pi\)
−0.822357 + 0.568972i \(0.807341\pi\)
\(462\) 0 0
\(463\) 8.00755 + 13.8695i 0.372143 + 0.644570i 0.989895 0.141803i \(-0.0452899\pi\)
−0.617752 + 0.786373i \(0.711957\pi\)
\(464\) 0 0
\(465\) −4.23779 + 7.34007i −0.196523 + 0.340387i
\(466\) 0 0
\(467\) −3.66214 6.34301i −0.169464 0.293519i 0.768768 0.639528i \(-0.220870\pi\)
−0.938231 + 0.346008i \(0.887537\pi\)
\(468\) 0 0
\(469\) 7.58135 + 24.9802i 0.350074 + 1.15348i
\(470\) 0 0
\(471\) −11.3542 19.6661i −0.523176 0.906167i
\(472\) 0 0
\(473\) 17.6303 30.5366i 0.810643 1.40408i
\(474\) 0 0
\(475\) −0.325805 0.564312i −0.0149490 0.0258924i
\(476\) 0 0
\(477\) 7.89678 0.361569
\(478\) 0 0
\(479\) 15.2111 + 26.3464i 0.695012 + 1.20380i 0.970177 + 0.242399i \(0.0779344\pi\)
−0.275164 + 0.961397i \(0.588732\pi\)
\(480\) 0 0
\(481\) 3.82136 6.61878i 0.174239 0.301790i
\(482\) 0 0
\(483\) 25.6574 1.16745
\(484\) 0 0
\(485\) 5.58794 + 9.67860i 0.253735 + 0.439483i
\(486\) 0 0
\(487\) 1.39290 + 2.41258i 0.0631185 + 0.109324i 0.895858 0.444341i \(-0.146562\pi\)
−0.832739 + 0.553665i \(0.813229\pi\)
\(488\) 0 0
\(489\) 3.63817 6.30150i 0.164524 0.284964i
\(490\) 0 0
\(491\) 8.67676 0.391577 0.195788 0.980646i \(-0.437273\pi\)
0.195788 + 0.980646i \(0.437273\pi\)
\(492\) 0 0
\(493\) 40.4703 1.82269
\(494\) 0 0
\(495\) 2.11819 3.66882i 0.0952057 0.164901i
\(496\) 0 0
\(497\) 4.62813 + 8.01615i 0.207600 + 0.359574i
\(498\) 0 0
\(499\) 2.35666 + 4.08185i 0.105499 + 0.182729i 0.913942 0.405845i \(-0.133023\pi\)
−0.808443 + 0.588574i \(0.799690\pi\)
\(500\) 0 0
\(501\) −8.49804 + 14.7190i −0.379664 + 0.657598i
\(502\) 0 0
\(503\) 7.84252 13.5836i 0.349681 0.605665i −0.636512 0.771267i \(-0.719623\pi\)
0.986193 + 0.165602i \(0.0529568\pi\)
\(504\) 0 0
\(505\) −7.11803 + 12.3288i −0.316748 + 0.548624i
\(506\) 0 0
\(507\) −4.12273 + 7.14078i −0.183097 + 0.317133i
\(508\) 0 0
\(509\) −1.49842 −0.0664163 −0.0332082 0.999448i \(-0.510572\pi\)
−0.0332082 + 0.999448i \(0.510572\pi\)
\(510\) 0 0
\(511\) −20.3169 −0.898767
\(512\) 0 0
\(513\) 0.325805 + 0.564312i 0.0143847 + 0.0249150i
\(514\) 0 0
\(515\) 5.69947 9.87177i 0.251149 0.435002i
\(516\) 0 0
\(517\) 0.726834 + 1.25891i 0.0319661 + 0.0553670i
\(518\) 0 0
\(519\) −4.74878 8.22513i −0.208448 0.361043i
\(520\) 0 0
\(521\) 17.8113 0.780328 0.390164 0.920745i \(-0.372418\pi\)
0.390164 + 0.920745i \(0.372418\pi\)
\(522\) 0 0
\(523\) 0.689611 + 1.19444i 0.0301546 + 0.0522293i 0.880709 0.473658i \(-0.157067\pi\)
−0.850554 + 0.525887i \(0.823733\pi\)
\(524\) 0 0
\(525\) 1.59463 2.76199i 0.0695955 0.120543i
\(526\) 0 0
\(527\) −43.4315 −1.89190
\(528\) 0 0
\(529\) −20.8603 + 36.1312i −0.906972 + 1.57092i
\(530\) 0 0
\(531\) −4.39987 −0.190938
\(532\) 0 0
\(533\) 0.590635 0.0255832
\(534\) 0 0
\(535\) 8.78848 0.379959
\(536\) 0 0
\(537\) −2.79245 −0.120503
\(538\) 0 0
\(539\) −13.4354 −0.578703
\(540\) 0 0
\(541\) 34.7368 1.49345 0.746726 0.665132i \(-0.231625\pi\)
0.746726 + 0.665132i \(0.231625\pi\)
\(542\) 0 0
\(543\) −0.424877 + 0.735909i −0.0182332 + 0.0315809i
\(544\) 0 0
\(545\) 2.52859 0.108313
\(546\) 0 0
\(547\) 12.7913 22.1552i 0.546917 0.947289i −0.451566 0.892238i \(-0.649134\pi\)
0.998484 0.0550511i \(-0.0175322\pi\)
\(548\) 0 0
\(549\) −7.05670 12.2226i −0.301173 0.521647i
\(550\) 0 0
\(551\) 5.14623 0.219237
\(552\) 0 0
\(553\) 1.90899 + 3.30646i 0.0811784 + 0.140605i
\(554\) 0 0
\(555\) 1.75252 + 3.03546i 0.0743904 + 0.128848i
\(556\) 0 0
\(557\) −5.78484 + 10.0196i −0.245112 + 0.424546i −0.962163 0.272474i \(-0.912158\pi\)
0.717051 + 0.697020i \(0.245491\pi\)
\(558\) 0 0
\(559\) 9.07442 + 15.7173i 0.383807 + 0.664773i
\(560\) 0 0
\(561\) 21.7085 0.916536
\(562\) 0 0
\(563\) −22.9163 −0.965809 −0.482904 0.875673i \(-0.660418\pi\)
−0.482904 + 0.875673i \(0.660418\pi\)
\(564\) 0 0
\(565\) −8.82932 + 15.2928i −0.371452 + 0.643374i
\(566\) 0 0
\(567\) −1.59463 + 2.76199i −0.0669683 + 0.115993i
\(568\) 0 0
\(569\) −6.47148 + 11.2089i −0.271299 + 0.469903i −0.969195 0.246296i \(-0.920786\pi\)
0.697896 + 0.716199i \(0.254120\pi\)
\(570\) 0 0
\(571\) −6.16229 + 10.6734i −0.257884 + 0.446668i −0.965675 0.259754i \(-0.916359\pi\)
0.707791 + 0.706422i \(0.249692\pi\)
\(572\) 0 0
\(573\) −7.32457 12.6865i −0.305988 0.529987i
\(574\) 0 0
\(575\) 4.02246 + 6.96710i 0.167748 + 0.290548i
\(576\) 0 0
\(577\) −2.13548 + 3.69876i −0.0889012 + 0.153981i −0.907047 0.421030i \(-0.861669\pi\)
0.818146 + 0.575011i \(0.195002\pi\)
\(578\) 0 0
\(579\) −17.5891 −0.730980
\(580\) 0 0
\(581\) −6.14864 −0.255089
\(582\) 0 0
\(583\) 16.7269 28.9719i 0.692758 1.19989i
\(584\) 0 0
\(585\) 1.09024 + 1.88836i 0.0450761 + 0.0780741i
\(586\) 0 0
\(587\) 7.02283 + 12.1639i 0.289863 + 0.502058i 0.973777 0.227505i \(-0.0730568\pi\)
−0.683914 + 0.729563i \(0.739723\pi\)
\(588\) 0 0
\(589\) −5.52278 −0.227562
\(590\) 0 0
\(591\) −11.2607 + 19.5041i −0.463204 + 0.802293i
\(592\) 0 0
\(593\) −19.6100 33.9655i −0.805286 1.39480i −0.916098 0.400954i \(-0.868679\pi\)
0.110813 0.993841i \(-0.464655\pi\)
\(594\) 0 0
\(595\) 16.3428 0.669989
\(596\) 0 0
\(597\) 0.782789 + 1.35583i 0.0320374 + 0.0554904i
\(598\) 0 0
\(599\) 22.7801 39.4562i 0.930768 1.61214i 0.148756 0.988874i \(-0.452473\pi\)
0.782012 0.623263i \(-0.214193\pi\)
\(600\) 0 0
\(601\) 0.697116 + 1.20744i 0.0284360 + 0.0492525i 0.879893 0.475172i \(-0.157614\pi\)
−0.851457 + 0.524424i \(0.824281\pi\)
\(602\) 0 0
\(603\) 5.59464 5.97495i 0.227831 0.243319i
\(604\) 0 0
\(605\) −3.47349 6.01627i −0.141218 0.244596i
\(606\) 0 0
\(607\) −15.9376 + 27.6047i −0.646886 + 1.12044i 0.336977 + 0.941513i \(0.390596\pi\)
−0.983862 + 0.178926i \(0.942738\pi\)
\(608\) 0 0
\(609\) 12.5940 + 21.8134i 0.510333 + 0.883922i
\(610\) 0 0
\(611\) −0.748210 −0.0302693
\(612\) 0 0
\(613\) 16.1889 + 28.0400i 0.653863 + 1.13252i 0.982178 + 0.187955i \(0.0601861\pi\)
−0.328315 + 0.944568i \(0.606481\pi\)
\(614\) 0 0
\(615\) −0.135436 + 0.234583i −0.00546132 + 0.00945928i
\(616\) 0 0
\(617\) −46.7023 −1.88016 −0.940081 0.340951i \(-0.889251\pi\)
−0.940081 + 0.340951i \(0.889251\pi\)
\(618\) 0 0
\(619\) −2.04658 3.54477i −0.0822588 0.142476i 0.821961 0.569544i \(-0.192880\pi\)
−0.904220 + 0.427067i \(0.859547\pi\)
\(620\) 0 0
\(621\) −4.02246 6.96710i −0.161416 0.279580i
\(622\) 0 0
\(623\) 5.16336 8.94321i 0.206866 0.358302i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 2.76048 0.110243
\(628\) 0 0
\(629\) −8.98045 + 15.5546i −0.358074 + 0.620203i
\(630\) 0 0
\(631\) −8.16830 14.1479i −0.325175 0.563219i 0.656373 0.754437i \(-0.272090\pi\)
−0.981548 + 0.191217i \(0.938756\pi\)
\(632\) 0 0
\(633\) −10.6933 18.5213i −0.425020 0.736156i
\(634\) 0 0
\(635\) −5.93915 + 10.2869i −0.235688 + 0.408224i
\(636\) 0 0
\(637\) 3.45763 5.98879i 0.136996 0.237285i
\(638\) 0 0
\(639\) 1.45116 2.51348i 0.0574069 0.0994316i
\(640\) 0 0
\(641\) −19.3268 + 33.4750i −0.763363 + 1.32218i 0.177745 + 0.984077i \(0.443120\pi\)
−0.941108 + 0.338106i \(0.890214\pi\)
\(642\) 0 0
\(643\) −4.00953 −0.158120 −0.0790602 0.996870i \(-0.525192\pi\)
−0.0790602 + 0.996870i \(0.525192\pi\)
\(644\) 0 0
\(645\) −8.32328 −0.327729
\(646\) 0 0
\(647\) 19.7253 + 34.1652i 0.775482 + 1.34317i 0.934523 + 0.355902i \(0.115826\pi\)
−0.159041 + 0.987272i \(0.550840\pi\)
\(648\) 0 0
\(649\) −9.31977 + 16.1423i −0.365833 + 0.633641i
\(650\) 0 0
\(651\) −13.5154 23.4094i −0.529712 0.917488i
\(652\) 0 0
\(653\) −0.542419 0.939496i −0.0212265 0.0367653i 0.855217 0.518270i \(-0.173424\pi\)
−0.876444 + 0.481505i \(0.840090\pi\)
\(654\) 0 0
\(655\) 1.93949 0.0757823
\(656\) 0 0
\(657\) 3.18520 + 5.51693i 0.124267 + 0.215236i
\(658\) 0 0
\(659\) −8.14677 + 14.1106i −0.317353 + 0.549672i −0.979935 0.199318i \(-0.936127\pi\)
0.662582 + 0.748990i \(0.269461\pi\)
\(660\) 0 0
\(661\) −24.1025 −0.937479 −0.468740 0.883336i \(-0.655292\pi\)
−0.468740 + 0.883336i \(0.655292\pi\)
\(662\) 0 0
\(663\) −5.58675 + 9.67653i −0.216971 + 0.375805i
\(664\) 0 0
\(665\) 2.07816 0.0805876
\(666\) 0 0
\(667\) −63.5364 −2.46014
\(668\) 0 0
\(669\) −14.6790 −0.567523
\(670\) 0 0
\(671\) −59.7899 −2.30816
\(672\) 0 0
\(673\) −14.9779 −0.577356 −0.288678 0.957426i \(-0.593216\pi\)
−0.288678 + 0.957426i \(0.593216\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) 16.9425 29.3452i 0.651152 1.12783i −0.331691 0.943388i \(-0.607619\pi\)
0.982844 0.184441i \(-0.0590475\pi\)
\(678\) 0 0
\(679\) −35.6429 −1.36785
\(680\) 0 0
\(681\) −11.3434 + 19.6473i −0.434680 + 0.752888i
\(682\) 0 0
\(683\) −14.5645 25.2264i −0.557294 0.965262i −0.997721 0.0674735i \(-0.978506\pi\)
0.440427 0.897789i \(-0.354827\pi\)
\(684\) 0 0
\(685\) −15.7104 −0.600264
\(686\) 0 0
\(687\) 0.410433 + 0.710890i 0.0156590 + 0.0271221i
\(688\) 0 0
\(689\) 8.60942 + 14.9120i 0.327993 + 0.568100i
\(690\) 0 0
\(691\) −4.89874 + 8.48487i −0.186357 + 0.322780i −0.944033 0.329851i \(-0.893001\pi\)
0.757676 + 0.652631i \(0.226335\pi\)
\(692\) 0 0
\(693\) 6.75549 + 11.7008i 0.256620 + 0.444478i
\(694\) 0 0
\(695\) 15.1789 0.575770
\(696\) 0 0
\(697\) −1.38803 −0.0525755
\(698\) 0 0
\(699\) 10.2133 17.6899i 0.386301 0.669093i
\(700\) 0 0
\(701\) 9.65402 16.7213i 0.364627 0.631553i −0.624089 0.781353i \(-0.714530\pi\)
0.988716 + 0.149800i \(0.0478630\pi\)
\(702\) 0 0
\(703\) −1.14196 + 1.97794i −0.0430699 + 0.0745993i
\(704\) 0 0
\(705\) 0.171569 0.297167i 0.00646167 0.0111919i
\(706\) 0 0
\(707\) −22.7013 39.3198i −0.853770 1.47877i
\(708\) 0 0
\(709\) −13.2319 22.9182i −0.496933 0.860712i 0.503061 0.864251i \(-0.332207\pi\)
−0.999994 + 0.00353836i \(0.998874\pi\)
\(710\) 0 0
\(711\) 0.598566 1.03675i 0.0224480 0.0388811i
\(712\) 0 0
\(713\) 68.1853 2.55356
\(714\) 0 0
\(715\) 9.23740 0.345459
\(716\) 0 0
\(717\) −13.4875 + 23.3611i −0.503701 + 0.872436i
\(718\) 0 0
\(719\) −6.78309 11.7487i −0.252967 0.438151i 0.711375 0.702813i \(-0.248073\pi\)
−0.964341 + 0.264662i \(0.914740\pi\)
\(720\) 0 0
\(721\) 18.1771 + 31.4837i 0.676952 + 1.17251i
\(722\) 0 0
\(723\) 4.12596 0.153446
\(724\) 0 0
\(725\) −3.94885 + 6.83962i −0.146657 + 0.254017i
\(726\) 0 0
\(727\) −16.1213 27.9229i −0.597906 1.03560i −0.993130 0.117018i \(-0.962666\pi\)
0.395224 0.918585i \(-0.370667\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −21.3255 36.9369i −0.788753 1.36616i
\(732\) 0 0
\(733\) 12.6254 21.8679i 0.466330 0.807708i −0.532930 0.846159i \(-0.678909\pi\)
0.999260 + 0.0384513i \(0.0122424\pi\)
\(734\) 0 0
\(735\) 1.58571 + 2.74654i 0.0584899 + 0.101307i
\(736\) 0 0
\(737\) −10.0705 33.1818i −0.370952 1.22227i
\(738\) 0 0
\(739\) −26.7641 46.3568i −0.984534 1.70526i −0.643990 0.765034i \(-0.722722\pi\)
−0.340544 0.940229i \(-0.610611\pi\)
\(740\) 0 0
\(741\) −0.710415 + 1.23048i −0.0260978 + 0.0452027i
\(742\) 0 0
\(743\) −7.08937 12.2792i −0.260084 0.450478i 0.706180 0.708032i \(-0.250417\pi\)
−0.966264 + 0.257554i \(0.917084\pi\)
\(744\) 0 0
\(745\) 10.2647 0.376069
\(746\) 0 0
\(747\) 0.963958 + 1.66962i 0.0352694 + 0.0610884i
\(748\) 0 0
\(749\) −14.0144 + 24.2737i −0.512075 + 0.886941i
\(750\) 0 0
\(751\) −28.8789 −1.05381 −0.526904 0.849925i \(-0.676647\pi\)
−0.526904 + 0.849925i \(0.676647\pi\)
\(752\) 0 0
\(753\) −2.26482 3.92278i −0.0825345 0.142954i
\(754\) 0 0
\(755\) 8.87873 + 15.3784i 0.323130 + 0.559678i
\(756\) 0 0
\(757\) 20.5487 35.5915i 0.746857 1.29359i −0.202466 0.979289i \(-0.564895\pi\)
0.949322 0.314304i \(-0.101771\pi\)
\(758\) 0 0
\(759\) −34.0814 −1.23708
\(760\) 0 0
\(761\) 19.8369 0.719087 0.359544 0.933128i \(-0.382932\pi\)
0.359544 + 0.933128i \(0.382932\pi\)
\(762\) 0 0
\(763\) −4.03218 + 6.98394i −0.145975 + 0.252836i
\(764\) 0 0
\(765\) −2.56215 4.43778i −0.0926348 0.160448i
\(766\) 0 0
\(767\) −4.79693 8.30853i −0.173207 0.300004i
\(768\) 0 0
\(769\) 10.9558 18.9760i 0.395077 0.684293i −0.598034 0.801470i \(-0.704051\pi\)
0.993111 + 0.117178i \(0.0373847\pi\)
\(770\) 0 0
\(771\) 1.27099 2.20142i 0.0457736 0.0792821i
\(772\) 0 0
\(773\) −23.4893 + 40.6847i −0.844852 + 1.46333i 0.0408971 + 0.999163i \(0.486978\pi\)
−0.885749 + 0.464164i \(0.846355\pi\)
\(774\) 0 0
\(775\) 4.23779 7.34007i 0.152226 0.263663i
\(776\) 0 0
\(777\) −11.1785 −0.401027
\(778\) 0 0
\(779\) −0.176504 −0.00632389
\(780\) 0 0
\(781\) −6.14766 10.6481i −0.219981 0.381018i
\(782\) 0 0
\(783\) 3.94885 6.83962i 0.141121 0.244428i
\(784\) 0 0
\(785\) 11.3542 + 19.6661i 0.405250 + 0.701914i
\(786\) 0 0
\(787\) 6.55363 + 11.3512i 0.233612 + 0.404627i 0.958868 0.283851i \(-0.0916123\pi\)
−0.725257 + 0.688479i \(0.758279\pi\)
\(788\) 0 0
\(789\) −22.9781 −0.818043
\(790\) 0 0
\(791\) −28.1591 48.7729i −1.00122 1.73417i
\(792\) 0 0
\(793\) 15.3871 26.6512i 0.546411 0.946411i