Properties

Label 300.3.f.c.199.4
Level $300$
Weight $3$
Character 300.199
Analytic conductor $8.174$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 8 x^{14} - 14 x^{13} + 23 x^{12} - 26 x^{11} + 18 x^{10} - 10 x^{9} + 9 x^{8} - 20 x^{7} + 72 x^{6} - 208 x^{5} + 368 x^{4} - 448 x^{3} + 512 x^{2} - 512 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{20}\cdot 5^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 199.4
Root \(1.21868 + 0.717516i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.c.199.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.92737 + 0.534079i) q^{2} +1.73205 q^{3} +(3.42952 - 2.05874i) q^{4} +(-3.33830 + 0.925051i) q^{6} +11.9716 q^{7} +(-5.51043 + 5.79958i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-1.92737 + 0.534079i) q^{2} +1.73205 q^{3} +(3.42952 - 2.05874i) q^{4} +(-3.33830 + 0.925051i) q^{6} +11.9716 q^{7} +(-5.51043 + 5.79958i) q^{8} +3.00000 q^{9} -14.5382i q^{11} +(5.94010 - 3.56583i) q^{12} +22.4802i q^{13} +(-23.0738 + 6.39379i) q^{14} +(7.52322 - 14.1209i) q^{16} -12.6890i q^{17} +(-5.78211 + 1.60224i) q^{18} -8.76336i q^{19} +20.7355 q^{21} +(7.76455 + 28.0205i) q^{22} +4.99653 q^{23} +(-9.54435 + 10.0452i) q^{24} +(-12.0062 - 43.3278i) q^{26} +5.19615 q^{27} +(41.0570 - 24.6464i) q^{28} -2.74712 q^{29} +16.3466i q^{31} +(-6.95833 + 31.2343i) q^{32} -25.1809i q^{33} +(6.77695 + 24.4565i) q^{34} +(10.2886 - 6.17621i) q^{36} -32.4872i q^{37} +(4.68032 + 16.8902i) q^{38} +38.9369i q^{39} +42.7586 q^{41} +(-39.9650 + 11.0744i) q^{42} +16.5435 q^{43} +(-29.9303 - 49.8591i) q^{44} +(-9.63018 + 2.66854i) q^{46} +48.5912 q^{47} +(13.0306 - 24.4582i) q^{48} +94.3200 q^{49} -21.9781i q^{51} +(46.2809 + 77.0964i) q^{52} +94.1066i q^{53} +(-10.0149 + 2.77515i) q^{54} +(-65.9689 + 69.4305i) q^{56} -15.1786i q^{57} +(5.29471 - 1.46718i) q^{58} +43.2650i q^{59} +56.7678 q^{61} +(-8.73038 - 31.5060i) q^{62} +35.9149 q^{63} +(-3.27028 - 63.9164i) q^{64} +(13.4486 + 48.5330i) q^{66} -61.1106 q^{67} +(-26.1234 - 43.5173i) q^{68} +8.65425 q^{69} -39.6643i q^{71} +(-16.5313 + 17.3987i) q^{72} -99.5452i q^{73} +(17.3507 + 62.6149i) q^{74} +(-18.0414 - 30.0541i) q^{76} -174.046i q^{77} +(-20.7954 - 75.0459i) q^{78} -10.7780i q^{79} +9.00000 q^{81} +(-82.4118 + 22.8365i) q^{82} -140.263 q^{83} +(71.1127 - 42.6889i) q^{84} +(-31.8855 + 8.83554i) q^{86} -4.75815 q^{87} +(84.3156 + 80.1118i) q^{88} -54.8723 q^{89} +269.125i q^{91} +(17.1357 - 10.2865i) q^{92} +28.3132i q^{93} +(-93.6533 + 25.9515i) q^{94} +(-12.0522 + 54.0994i) q^{96} -14.1601i q^{97} +(-181.790 + 50.3743i) q^{98} -43.6146i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{4} - 12q^{6} + 48q^{9} + O(q^{10}) \) \( 16q + 16q^{4} - 12q^{6} + 48q^{9} - 44q^{14} + 80q^{16} + 48q^{21} + 72q^{24} - 132q^{26} + 64q^{29} - 248q^{34} + 48q^{36} - 32q^{41} - 80q^{44} - 152q^{46} - 32q^{49} - 36q^{54} - 344q^{56} + 272q^{61} - 32q^{64} - 216q^{66} + 192q^{69} + 216q^{74} + 240q^{76} + 144q^{81} + 288q^{84} + 428q^{86} - 256q^{89} - 24q^{94} + 192q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.92737 + 0.534079i −0.963686 + 0.267039i
\(3\) 1.73205 0.577350
\(4\) 3.42952 2.05874i 0.857380 0.514684i
\(5\) 0 0
\(6\) −3.33830 + 0.925051i −0.556384 + 0.154175i
\(7\) 11.9716 1.71023 0.855117 0.518436i \(-0.173485\pi\)
0.855117 + 0.518436i \(0.173485\pi\)
\(8\) −5.51043 + 5.79958i −0.688804 + 0.724948i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 14.5382i 1.32166i −0.750537 0.660828i \(-0.770205\pi\)
0.750537 0.660828i \(-0.229795\pi\)
\(12\) 5.94010 3.56583i 0.495009 0.297153i
\(13\) 22.4802i 1.72925i 0.502418 + 0.864625i \(0.332444\pi\)
−0.502418 + 0.864625i \(0.667556\pi\)
\(14\) −23.0738 + 6.39379i −1.64813 + 0.456699i
\(15\) 0 0
\(16\) 7.52322 14.1209i 0.470201 0.882559i
\(17\) 12.6890i 0.746414i −0.927748 0.373207i \(-0.878258\pi\)
0.927748 0.373207i \(-0.121742\pi\)
\(18\) −5.78211 + 1.60224i −0.321229 + 0.0890131i
\(19\) 8.76336i 0.461229i −0.973045 0.230615i \(-0.925926\pi\)
0.973045 0.230615i \(-0.0740737\pi\)
\(20\) 0 0
\(21\) 20.7355 0.987404
\(22\) 7.76455 + 28.0205i 0.352934 + 1.27366i
\(23\) 4.99653 0.217241 0.108620 0.994083i \(-0.465357\pi\)
0.108620 + 0.994083i \(0.465357\pi\)
\(24\) −9.54435 + 10.0452i −0.397681 + 0.418549i
\(25\) 0 0
\(26\) −12.0062 43.3278i −0.461778 1.66645i
\(27\) 5.19615 0.192450
\(28\) 41.0570 24.6464i 1.46632 0.880229i
\(29\) −2.74712 −0.0947282 −0.0473641 0.998878i \(-0.515082\pi\)
−0.0473641 + 0.998878i \(0.515082\pi\)
\(30\) 0 0
\(31\) 16.3466i 0.527310i 0.964617 + 0.263655i \(0.0849281\pi\)
−0.964617 + 0.263655i \(0.915072\pi\)
\(32\) −6.95833 + 31.2343i −0.217448 + 0.976072i
\(33\) 25.1809i 0.763058i
\(34\) 6.77695 + 24.4565i 0.199322 + 0.719309i
\(35\) 0 0
\(36\) 10.2886 6.17621i 0.285793 0.171561i
\(37\) 32.4872i 0.878032i −0.898479 0.439016i \(-0.855327\pi\)
0.898479 0.439016i \(-0.144673\pi\)
\(38\) 4.68032 + 16.8902i 0.123166 + 0.444480i
\(39\) 38.9369i 0.998383i
\(40\) 0 0
\(41\) 42.7586 1.04289 0.521447 0.853284i \(-0.325393\pi\)
0.521447 + 0.853284i \(0.325393\pi\)
\(42\) −39.9650 + 11.0744i −0.951547 + 0.263676i
\(43\) 16.5435 0.384733 0.192367 0.981323i \(-0.438384\pi\)
0.192367 + 0.981323i \(0.438384\pi\)
\(44\) −29.9303 49.8591i −0.680235 1.13316i
\(45\) 0 0
\(46\) −9.63018 + 2.66854i −0.209352 + 0.0580118i
\(47\) 48.5912 1.03386 0.516928 0.856029i \(-0.327076\pi\)
0.516928 + 0.856029i \(0.327076\pi\)
\(48\) 13.0306 24.4582i 0.271471 0.509546i
\(49\) 94.3200 1.92490
\(50\) 0 0
\(51\) 21.9781i 0.430943i
\(52\) 46.2809 + 77.0964i 0.890017 + 1.48262i
\(53\) 94.1066i 1.77560i 0.460233 + 0.887798i \(0.347766\pi\)
−0.460233 + 0.887798i \(0.652234\pi\)
\(54\) −10.0149 + 2.77515i −0.185461 + 0.0513917i
\(55\) 0 0
\(56\) −65.9689 + 69.4305i −1.17802 + 1.23983i
\(57\) 15.1786i 0.266291i
\(58\) 5.29471 1.46718i 0.0912882 0.0252961i
\(59\) 43.2650i 0.733305i 0.930358 + 0.366653i \(0.119496\pi\)
−0.930358 + 0.366653i \(0.880504\pi\)
\(60\) 0 0
\(61\) 56.7678 0.930620 0.465310 0.885148i \(-0.345943\pi\)
0.465310 + 0.885148i \(0.345943\pi\)
\(62\) −8.73038 31.5060i −0.140813 0.508161i
\(63\) 35.9149 0.570078
\(64\) −3.27028 63.9164i −0.0510981 0.998694i
\(65\) 0 0
\(66\) 13.4486 + 48.5330i 0.203767 + 0.735348i
\(67\) −61.1106 −0.912098 −0.456049 0.889955i \(-0.650736\pi\)
−0.456049 + 0.889955i \(0.650736\pi\)
\(68\) −26.1234 43.5173i −0.384167 0.639961i
\(69\) 8.65425 0.125424
\(70\) 0 0
\(71\) 39.6643i 0.558652i −0.960196 0.279326i \(-0.909889\pi\)
0.960196 0.279326i \(-0.0901110\pi\)
\(72\) −16.5313 + 17.3987i −0.229601 + 0.241649i
\(73\) 99.5452i 1.36363i −0.731523 0.681817i \(-0.761190\pi\)
0.731523 0.681817i \(-0.238810\pi\)
\(74\) 17.3507 + 62.6149i 0.234469 + 0.846147i
\(75\) 0 0
\(76\) −18.0414 30.0541i −0.237387 0.395449i
\(77\) 174.046i 2.26034i
\(78\) −20.7954 75.0459i −0.266607 0.962127i
\(79\) 10.7780i 0.136430i −0.997671 0.0682151i \(-0.978270\pi\)
0.997671 0.0682151i \(-0.0217304\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −82.4118 + 22.8365i −1.00502 + 0.278494i
\(83\) −140.263 −1.68991 −0.844955 0.534837i \(-0.820373\pi\)
−0.844955 + 0.534837i \(0.820373\pi\)
\(84\) 71.1127 42.6889i 0.846580 0.508201i
\(85\) 0 0
\(86\) −31.8855 + 8.83554i −0.370762 + 0.102739i
\(87\) −4.75815 −0.0546913
\(88\) 84.3156 + 80.1118i 0.958131 + 0.910362i
\(89\) −54.8723 −0.616543 −0.308271 0.951298i \(-0.599751\pi\)
−0.308271 + 0.951298i \(0.599751\pi\)
\(90\) 0 0
\(91\) 269.125i 2.95742i
\(92\) 17.1357 10.2865i 0.186258 0.111810i
\(93\) 28.3132i 0.304443i
\(94\) −93.6533 + 25.9515i −0.996312 + 0.276080i
\(95\) 0 0
\(96\) −12.0522 + 54.0994i −0.125544 + 0.563535i
\(97\) 14.1601i 0.145980i −0.997333 0.0729902i \(-0.976746\pi\)
0.997333 0.0729902i \(-0.0232542\pi\)
\(98\) −181.790 + 50.3743i −1.85500 + 0.514023i
\(99\) 43.6146i 0.440552i
\(100\) 0 0
\(101\) −163.410 −1.61792 −0.808962 0.587861i \(-0.799970\pi\)
−0.808962 + 0.587861i \(0.799970\pi\)
\(102\) 11.7380 + 42.3599i 0.115079 + 0.415293i
\(103\) −169.591 −1.64651 −0.823255 0.567672i \(-0.807844\pi\)
−0.823255 + 0.567672i \(0.807844\pi\)
\(104\) −130.376 123.876i −1.25362 1.19111i
\(105\) 0 0
\(106\) −50.2603 181.378i −0.474154 1.71112i
\(107\) 8.14840 0.0761532 0.0380766 0.999275i \(-0.487877\pi\)
0.0380766 + 0.999275i \(0.487877\pi\)
\(108\) 17.8203 10.6975i 0.165003 0.0990510i
\(109\) 25.2322 0.231488 0.115744 0.993279i \(-0.463075\pi\)
0.115744 + 0.993279i \(0.463075\pi\)
\(110\) 0 0
\(111\) 56.2695i 0.506932i
\(112\) 90.0652 169.051i 0.804153 1.50938i
\(113\) 97.8142i 0.865613i 0.901487 + 0.432806i \(0.142477\pi\)
−0.901487 + 0.432806i \(0.857523\pi\)
\(114\) 8.10655 + 29.2548i 0.0711101 + 0.256621i
\(115\) 0 0
\(116\) −9.42129 + 5.65559i −0.0812180 + 0.0487551i
\(117\) 67.4407i 0.576417i
\(118\) −23.1069 83.3877i −0.195821 0.706676i
\(119\) 151.909i 1.27654i
\(120\) 0 0
\(121\) −90.3597 −0.746774
\(122\) −109.413 + 30.3185i −0.896825 + 0.248512i
\(123\) 74.0601 0.602115
\(124\) 33.6534 + 56.0611i 0.271398 + 0.452105i
\(125\) 0 0
\(126\) −69.2213 + 19.1814i −0.549376 + 0.152233i
\(127\) −167.563 −1.31939 −0.659695 0.751533i \(-0.729315\pi\)
−0.659695 + 0.751533i \(0.729315\pi\)
\(128\) 40.4394 + 121.444i 0.315933 + 0.948782i
\(129\) 28.6542 0.222126
\(130\) 0 0
\(131\) 82.0465i 0.626309i −0.949702 0.313155i \(-0.898614\pi\)
0.949702 0.313155i \(-0.101386\pi\)
\(132\) −51.8409 86.3585i −0.392734 0.654231i
\(133\) 104.912i 0.788810i
\(134\) 117.783 32.6378i 0.878976 0.243566i
\(135\) 0 0
\(136\) 73.5911 + 69.9221i 0.541111 + 0.514133i
\(137\) 254.459i 1.85737i 0.370874 + 0.928683i \(0.379058\pi\)
−0.370874 + 0.928683i \(0.620942\pi\)
\(138\) −16.6800 + 4.62205i −0.120869 + 0.0334931i
\(139\) 78.9483i 0.567974i −0.958828 0.283987i \(-0.908343\pi\)
0.958828 0.283987i \(-0.0916572\pi\)
\(140\) 0 0
\(141\) 84.1624 0.596897
\(142\) 21.1838 + 76.4478i 0.149182 + 0.538365i
\(143\) 326.823 2.28547
\(144\) 22.5696 42.3628i 0.156734 0.294186i
\(145\) 0 0
\(146\) 53.1650 + 191.861i 0.364144 + 1.31411i
\(147\) 163.367 1.11134
\(148\) −66.8825 111.415i −0.451909 0.752807i
\(149\) 32.3433 0.217069 0.108534 0.994093i \(-0.465384\pi\)
0.108534 + 0.994093i \(0.465384\pi\)
\(150\) 0 0
\(151\) 38.7953i 0.256922i −0.991715 0.128461i \(-0.958996\pi\)
0.991715 0.128461i \(-0.0410038\pi\)
\(152\) 50.8238 + 48.2899i 0.334367 + 0.317697i
\(153\) 38.0671i 0.248805i
\(154\) 92.9543 + 335.452i 0.603600 + 2.17826i
\(155\) 0 0
\(156\) 80.1608 + 133.535i 0.513851 + 0.855993i
\(157\) 44.2021i 0.281542i −0.990042 0.140771i \(-0.955042\pi\)
0.990042 0.140771i \(-0.0449581\pi\)
\(158\) 5.75629 + 20.7732i 0.0364322 + 0.131476i
\(159\) 162.997i 1.02514i
\(160\) 0 0
\(161\) 59.8167 0.371532
\(162\) −17.3463 + 4.80671i −0.107076 + 0.0296710i
\(163\) −52.9366 −0.324764 −0.162382 0.986728i \(-0.551918\pi\)
−0.162382 + 0.986728i \(0.551918\pi\)
\(164\) 146.642 88.0287i 0.894156 0.536760i
\(165\) 0 0
\(166\) 270.338 74.9112i 1.62854 0.451272i
\(167\) 179.273 1.07349 0.536745 0.843744i \(-0.319654\pi\)
0.536745 + 0.843744i \(0.319654\pi\)
\(168\) −114.261 + 120.257i −0.680128 + 0.715816i
\(169\) −336.361 −1.99030
\(170\) 0 0
\(171\) 26.2901i 0.153743i
\(172\) 56.7364 34.0587i 0.329863 0.198016i
\(173\) 177.276i 1.02471i −0.858772 0.512357i \(-0.828772\pi\)
0.858772 0.512357i \(-0.171228\pi\)
\(174\) 9.17071 2.54122i 0.0527053 0.0146047i
\(175\) 0 0
\(176\) −205.293 109.374i −1.16644 0.621444i
\(177\) 74.9372i 0.423374i
\(178\) 105.759 29.3061i 0.594154 0.164641i
\(179\) 102.849i 0.574573i 0.957845 + 0.287286i \(0.0927532\pi\)
−0.957845 + 0.287286i \(0.907247\pi\)
\(180\) 0 0
\(181\) −115.413 −0.637640 −0.318820 0.947815i \(-0.603286\pi\)
−0.318820 + 0.947815i \(0.603286\pi\)
\(182\) −143.734 518.704i −0.789747 2.85002i
\(183\) 98.3247 0.537294
\(184\) −27.5331 + 28.9778i −0.149636 + 0.157488i
\(185\) 0 0
\(186\) −15.1215 54.5700i −0.0812982 0.293387i
\(187\) −184.476 −0.986503
\(188\) 166.645 100.036i 0.886407 0.532109i
\(189\) 62.2064 0.329135
\(190\) 0 0
\(191\) 191.305i 1.00160i −0.865563 0.500799i \(-0.833040\pi\)
0.865563 0.500799i \(-0.166960\pi\)
\(192\) −5.66429 110.706i −0.0295015 0.576596i
\(193\) 160.332i 0.830734i 0.909654 + 0.415367i \(0.136347\pi\)
−0.909654 + 0.415367i \(0.863653\pi\)
\(194\) 7.56261 + 27.2918i 0.0389825 + 0.140679i
\(195\) 0 0
\(196\) 323.472 194.180i 1.65037 0.990714i
\(197\) 355.081i 1.80244i 0.433362 + 0.901220i \(0.357327\pi\)
−0.433362 + 0.901220i \(0.642673\pi\)
\(198\) 23.2936 + 84.0616i 0.117645 + 0.424554i
\(199\) 88.2032i 0.443232i 0.975134 + 0.221616i \(0.0711332\pi\)
−0.975134 + 0.221616i \(0.928867\pi\)
\(200\) 0 0
\(201\) −105.847 −0.526600
\(202\) 314.952 87.2740i 1.55917 0.432049i
\(203\) −32.8875 −0.162007
\(204\) −45.2470 75.3742i −0.221799 0.369482i
\(205\) 0 0
\(206\) 326.864 90.5747i 1.58672 0.439683i
\(207\) 14.9896 0.0724135
\(208\) 317.442 + 169.124i 1.52617 + 0.813095i
\(209\) −127.404 −0.609586
\(210\) 0 0
\(211\) 190.584i 0.903243i 0.892210 + 0.451622i \(0.149154\pi\)
−0.892210 + 0.451622i \(0.850846\pi\)
\(212\) 193.741 + 322.741i 0.913871 + 1.52236i
\(213\) 68.7006i 0.322538i
\(214\) −15.7050 + 4.35188i −0.0733878 + 0.0203359i
\(215\) 0 0
\(216\) −28.6330 + 30.1355i −0.132560 + 0.139516i
\(217\) 195.696i 0.901824i
\(218\) −48.6318 + 13.4760i −0.223082 + 0.0618164i
\(219\) 172.417i 0.787294i
\(220\) 0 0
\(221\) 285.253 1.29074
\(222\) 30.0523 + 108.452i 0.135371 + 0.488523i
\(223\) −79.2869 −0.355547 −0.177773 0.984071i \(-0.556889\pi\)
−0.177773 + 0.984071i \(0.556889\pi\)
\(224\) −83.3026 + 373.926i −0.371887 + 1.66931i
\(225\) 0 0
\(226\) −52.2405 188.524i −0.231153 0.834178i
\(227\) −353.645 −1.55791 −0.778953 0.627082i \(-0.784249\pi\)
−0.778953 + 0.627082i \(0.784249\pi\)
\(228\) −31.2487 52.0552i −0.137056 0.228312i
\(229\) 22.7911 0.0995244 0.0497622 0.998761i \(-0.484154\pi\)
0.0497622 + 0.998761i \(0.484154\pi\)
\(230\) 0 0
\(231\) 301.457i 1.30501i
\(232\) 15.1378 15.9321i 0.0652491 0.0686730i
\(233\) 189.710i 0.814205i −0.913382 0.407103i \(-0.866539\pi\)
0.913382 0.407103i \(-0.133461\pi\)
\(234\) −36.0187 129.983i −0.153926 0.555484i
\(235\) 0 0
\(236\) 89.0712 + 148.378i 0.377420 + 0.628721i
\(237\) 18.6680i 0.0787680i
\(238\) 81.1311 + 292.784i 0.340887 + 1.23019i
\(239\) 267.778i 1.12041i 0.828355 + 0.560204i \(0.189277\pi\)
−0.828355 + 0.560204i \(0.810723\pi\)
\(240\) 0 0
\(241\) −301.663 −1.25171 −0.625857 0.779938i \(-0.715251\pi\)
−0.625857 + 0.779938i \(0.715251\pi\)
\(242\) 174.157 48.2592i 0.719656 0.199418i
\(243\) 15.5885 0.0641500
\(244\) 194.686 116.870i 0.797895 0.478975i
\(245\) 0 0
\(246\) −142.741 + 39.5539i −0.580249 + 0.160788i
\(247\) 197.002 0.797580
\(248\) −94.8035 90.0769i −0.382272 0.363213i
\(249\) −242.942 −0.975670
\(250\) 0 0
\(251\) 63.1891i 0.251749i −0.992046 0.125875i \(-0.959826\pi\)
0.992046 0.125875i \(-0.0401737\pi\)
\(252\) 123.171 73.9393i 0.488773 0.293410i
\(253\) 72.6407i 0.287117i
\(254\) 322.955 89.4916i 1.27148 0.352329i
\(255\) 0 0
\(256\) −142.802 212.470i −0.557822 0.829961i
\(257\) 150.719i 0.586456i −0.956043 0.293228i \(-0.905271\pi\)
0.956043 0.293228i \(-0.0947295\pi\)
\(258\) −55.2273 + 15.3036i −0.214059 + 0.0593163i
\(259\) 388.925i 1.50164i
\(260\) 0 0
\(261\) −8.24135 −0.0315761
\(262\) 43.8193 + 158.134i 0.167249 + 0.603565i
\(263\) 203.755 0.774735 0.387368 0.921925i \(-0.373384\pi\)
0.387368 + 0.921925i \(0.373384\pi\)
\(264\) 146.039 + 138.758i 0.553177 + 0.525598i
\(265\) 0 0
\(266\) 56.0311 + 202.204i 0.210643 + 0.760165i
\(267\) −95.0416 −0.355961
\(268\) −209.580 + 125.810i −0.782014 + 0.469442i
\(269\) −76.3986 −0.284010 −0.142005 0.989866i \(-0.545355\pi\)
−0.142005 + 0.989866i \(0.545355\pi\)
\(270\) 0 0
\(271\) 169.216i 0.624414i −0.950014 0.312207i \(-0.898932\pi\)
0.950014 0.312207i \(-0.101068\pi\)
\(272\) −179.181 95.4624i −0.658755 0.350965i
\(273\) 466.139i 1.70747i
\(274\) −135.901 490.437i −0.495990 1.78992i
\(275\) 0 0
\(276\) 29.6799 17.8168i 0.107536 0.0645537i
\(277\) 273.891i 0.988774i 0.869242 + 0.494387i \(0.164607\pi\)
−0.869242 + 0.494387i \(0.835393\pi\)
\(278\) 42.1646 + 152.163i 0.151671 + 0.547348i
\(279\) 49.0399i 0.175770i
\(280\) 0 0
\(281\) −311.672 −1.10915 −0.554577 0.832133i \(-0.687120\pi\)
−0.554577 + 0.832133i \(0.687120\pi\)
\(282\) −162.212 + 44.9494i −0.575221 + 0.159395i
\(283\) −264.566 −0.934861 −0.467431 0.884030i \(-0.654820\pi\)
−0.467431 + 0.884030i \(0.654820\pi\)
\(284\) −81.6583 136.029i −0.287529 0.478977i
\(285\) 0 0
\(286\) −629.909 + 174.549i −2.20248 + 0.610311i
\(287\) 511.891 1.78359
\(288\) −20.8750 + 93.7029i −0.0724826 + 0.325357i
\(289\) 127.988 0.442866
\(290\) 0 0
\(291\) 24.5260i 0.0842818i
\(292\) −204.937 341.392i −0.701840 1.16915i
\(293\) 121.281i 0.413927i 0.978349 + 0.206964i \(0.0663582\pi\)
−0.978349 + 0.206964i \(0.933642\pi\)
\(294\) −314.869 + 87.2508i −1.07098 + 0.296772i
\(295\) 0 0
\(296\) 188.412 + 179.018i 0.636527 + 0.604792i
\(297\) 75.5428i 0.254353i
\(298\) −62.3375 + 17.2739i −0.209186 + 0.0579659i
\(299\) 112.323i 0.375663i
\(300\) 0 0
\(301\) 198.053 0.657984
\(302\) 20.7197 + 74.7729i 0.0686083 + 0.247592i
\(303\) −283.035 −0.934109
\(304\) −123.747 65.9286i −0.407062 0.216870i
\(305\) 0 0
\(306\) 20.3308 + 73.3695i 0.0664407 + 0.239770i
\(307\) −161.768 −0.526932 −0.263466 0.964669i \(-0.584866\pi\)
−0.263466 + 0.964669i \(0.584866\pi\)
\(308\) −358.315 596.895i −1.16336 1.93797i
\(309\) −293.739 −0.950613
\(310\) 0 0
\(311\) 26.3813i 0.0848273i 0.999100 + 0.0424137i \(0.0135047\pi\)
−0.999100 + 0.0424137i \(0.986495\pi\)
\(312\) −225.818 214.559i −0.723775 0.687690i
\(313\) 5.39902i 0.0172493i 0.999963 + 0.00862463i \(0.00274534\pi\)
−0.999963 + 0.00862463i \(0.997255\pi\)
\(314\) 23.6074 + 85.1938i 0.0751827 + 0.271318i
\(315\) 0 0
\(316\) −22.1890 36.9633i −0.0702184 0.116972i
\(317\) 270.157i 0.852231i −0.904669 0.426116i \(-0.859882\pi\)
0.904669 0.426116i \(-0.140118\pi\)
\(318\) −87.0535 314.157i −0.273753 0.987914i
\(319\) 39.9382i 0.125198i
\(320\) 0 0
\(321\) 14.1134 0.0439671
\(322\) −115.289 + 31.9468i −0.358040 + 0.0992137i
\(323\) −111.199 −0.344268
\(324\) 30.8657 18.5286i 0.0952644 0.0571871i
\(325\) 0 0
\(326\) 102.028 28.2723i 0.312971 0.0867248i
\(327\) 43.7034 0.133650
\(328\) −235.619 + 247.982i −0.718349 + 0.756043i
\(329\) 581.716 1.76813
\(330\) 0 0
\(331\) 480.728i 1.45235i 0.687510 + 0.726174i \(0.258704\pi\)
−0.687510 + 0.726174i \(0.741296\pi\)
\(332\) −481.033 + 288.763i −1.44890 + 0.869770i
\(333\) 97.4616i 0.292677i
\(334\) −345.526 + 95.7459i −1.03451 + 0.286664i
\(335\) 0 0
\(336\) 155.997 292.805i 0.464278 0.871442i
\(337\) 568.382i 1.68659i −0.537448 0.843297i \(-0.680612\pi\)
0.537448 0.843297i \(-0.319388\pi\)
\(338\) 648.293 179.643i 1.91803 0.531489i
\(339\) 169.419i 0.499762i
\(340\) 0 0
\(341\) 237.651 0.696923
\(342\) 14.0410 + 50.6707i 0.0410554 + 0.148160i
\(343\) 542.554 1.58179
\(344\) −91.1620 + 95.9455i −0.265006 + 0.278911i
\(345\) 0 0
\(346\) 94.6791 + 341.676i 0.273639 + 0.987503i
\(347\) −370.184 −1.06681 −0.533406 0.845859i \(-0.679088\pi\)
−0.533406 + 0.845859i \(0.679088\pi\)
\(348\) −16.3182 + 9.79576i −0.0468913 + 0.0281487i
\(349\) 488.570 1.39991 0.699957 0.714185i \(-0.253203\pi\)
0.699957 + 0.714185i \(0.253203\pi\)
\(350\) 0 0
\(351\) 116.811i 0.332794i
\(352\) 454.091 + 101.162i 1.29003 + 0.287391i
\(353\) 649.728i 1.84059i −0.391226 0.920295i \(-0.627949\pi\)
0.391226 0.920295i \(-0.372051\pi\)
\(354\) −40.0224 144.432i −0.113058 0.407999i
\(355\) 0 0
\(356\) −188.186 + 112.968i −0.528612 + 0.317325i
\(357\) 263.113i 0.737012i
\(358\) −54.9292 198.227i −0.153434 0.553708i
\(359\) 405.910i 1.13067i −0.824862 0.565334i \(-0.808747\pi\)
0.824862 0.565334i \(-0.191253\pi\)
\(360\) 0 0
\(361\) 284.204 0.787268
\(362\) 222.443 61.6395i 0.614484 0.170275i
\(363\) −156.508 −0.431150
\(364\) 554.058 + 922.970i 1.52214 + 2.53563i
\(365\) 0 0
\(366\) −189.508 + 52.5131i −0.517782 + 0.143479i
\(367\) −46.2347 −0.125980 −0.0629900 0.998014i \(-0.520064\pi\)
−0.0629900 + 0.998014i \(0.520064\pi\)
\(368\) 37.5900 70.5558i 0.102147 0.191728i
\(369\) 128.276 0.347631
\(370\) 0 0
\(371\) 1126.61i 3.03668i
\(372\) 58.2893 + 97.1006i 0.156692 + 0.261023i
\(373\) 138.262i 0.370676i 0.982675 + 0.185338i \(0.0593380\pi\)
−0.982675 + 0.185338i \(0.940662\pi\)
\(374\) 355.554 98.5247i 0.950679 0.263435i
\(375\) 0 0
\(376\) −267.759 + 281.809i −0.712124 + 0.749491i
\(377\) 61.7559i 0.163809i
\(378\) −119.895 + 33.2231i −0.317182 + 0.0878919i
\(379\) 254.516i 0.671546i −0.941943 0.335773i \(-0.891002\pi\)
0.941943 0.335773i \(-0.108998\pi\)
\(380\) 0 0
\(381\) −290.227 −0.761750
\(382\) 102.172 + 368.716i 0.267466 + 0.965226i
\(383\) −62.7205 −0.163761 −0.0818805 0.996642i \(-0.526093\pi\)
−0.0818805 + 0.996642i \(0.526093\pi\)
\(384\) 70.0431 + 210.347i 0.182404 + 0.547779i
\(385\) 0 0
\(386\) −85.6298 309.019i −0.221839 0.800567i
\(387\) 49.6306 0.128244
\(388\) −29.1519 48.5623i −0.0751338 0.125161i
\(389\) −110.130 −0.283112 −0.141556 0.989930i \(-0.545210\pi\)
−0.141556 + 0.989930i \(0.545210\pi\)
\(390\) 0 0
\(391\) 63.4012i 0.162152i
\(392\) −519.744 + 547.016i −1.32588 + 1.39545i
\(393\) 142.109i 0.361600i
\(394\) −189.641 684.372i −0.481322 1.73698i
\(395\) 0 0
\(396\) −89.7910 149.577i −0.226745 0.377720i
\(397\) 292.953i 0.737916i −0.929446 0.368958i \(-0.879715\pi\)
0.929446 0.368958i \(-0.120285\pi\)
\(398\) −47.1074 170.000i −0.118360 0.427136i
\(399\) 181.712i 0.455419i
\(400\) 0 0
\(401\) 518.103 1.29203 0.646014 0.763325i \(-0.276435\pi\)
0.646014 + 0.763325i \(0.276435\pi\)
\(402\) 204.006 56.5304i 0.507477 0.140623i
\(403\) −367.476 −0.911851
\(404\) −560.419 + 336.419i −1.38718 + 0.832720i
\(405\) 0 0
\(406\) 63.3864 17.5645i 0.156124 0.0432623i
\(407\) −472.306 −1.16046
\(408\) 127.464 + 121.109i 0.312411 + 0.296835i
\(409\) 181.984 0.444948 0.222474 0.974939i \(-0.428587\pi\)
0.222474 + 0.974939i \(0.428587\pi\)
\(410\) 0 0
\(411\) 440.736i 1.07235i
\(412\) −581.614 + 349.142i −1.41168 + 0.847432i
\(413\) 517.953i 1.25412i
\(414\) −28.8905 + 8.00563i −0.0697839 + 0.0193373i
\(415\) 0 0
\(416\) −702.155 156.425i −1.68787 0.376022i
\(417\) 136.743i 0.327920i
\(418\) 245.554 68.0435i 0.587450 0.162784i
\(419\) 163.347i 0.389849i 0.980818 + 0.194925i \(0.0624462\pi\)
−0.980818 + 0.194925i \(0.937554\pi\)
\(420\) 0 0
\(421\) −467.206 −1.10975 −0.554876 0.831933i \(-0.687234\pi\)
−0.554876 + 0.831933i \(0.687234\pi\)
\(422\) −101.787 367.327i −0.241201 0.870442i
\(423\) 145.774 0.344619
\(424\) −545.779 518.568i −1.28721 1.22304i
\(425\) 0 0
\(426\) 36.6915 + 132.411i 0.0861303 + 0.310825i
\(427\) 679.603 1.59158
\(428\) 27.9451 16.7754i 0.0652923 0.0391948i
\(429\) 566.073 1.31952
\(430\) 0 0
\(431\) 685.527i 1.59055i −0.606248 0.795275i \(-0.707326\pi\)
0.606248 0.795275i \(-0.292674\pi\)
\(432\) 39.0918 73.3746i 0.0904902 0.169849i
\(433\) 592.777i 1.36900i 0.729013 + 0.684500i \(0.239979\pi\)
−0.729013 + 0.684500i \(0.760021\pi\)
\(434\) −104.517 377.178i −0.240822 0.869074i
\(435\) 0 0
\(436\) 86.5343 51.9464i 0.198473 0.119143i
\(437\) 43.7864i 0.100198i
\(438\) 92.0844 + 332.312i 0.210238 + 0.758704i
\(439\) 464.439i 1.05795i 0.848638 + 0.528974i \(0.177423\pi\)
−0.848638 + 0.528974i \(0.822577\pi\)
\(440\) 0 0
\(441\) 282.960 0.641633
\(442\) −549.788 + 152.347i −1.24386 + 0.344677i
\(443\) −54.2868 −0.122544 −0.0612718 0.998121i \(-0.519516\pi\)
−0.0612718 + 0.998121i \(0.519516\pi\)
\(444\) −115.844 192.977i −0.260910 0.434633i
\(445\) 0 0
\(446\) 152.815 42.3454i 0.342635 0.0949449i
\(447\) 56.0202 0.125325
\(448\) −39.1506 765.184i −0.0873897 1.70800i
\(449\) 428.051 0.953343 0.476671 0.879082i \(-0.341843\pi\)
0.476671 + 0.879082i \(0.341843\pi\)
\(450\) 0 0
\(451\) 621.634i 1.37835i
\(452\) 201.374 + 335.456i 0.445517 + 0.742159i
\(453\) 67.1954i 0.148334i
\(454\) 681.605 188.874i 1.50133 0.416022i
\(455\) 0 0
\(456\) 88.0294 + 83.6405i 0.193047 + 0.183422i
\(457\) 66.5848i 0.145700i 0.997343 + 0.0728498i \(0.0232094\pi\)
−0.997343 + 0.0728498i \(0.976791\pi\)
\(458\) −43.9269 + 12.1722i −0.0959103 + 0.0265769i
\(459\) 65.9342i 0.143648i
\(460\) 0 0
\(461\) −238.626 −0.517627 −0.258814 0.965927i \(-0.583332\pi\)
−0.258814 + 0.965927i \(0.583332\pi\)
\(462\) 161.002 + 581.019i 0.348488 + 1.25762i
\(463\) 386.958 0.835762 0.417881 0.908502i \(-0.362773\pi\)
0.417881 + 0.908502i \(0.362773\pi\)
\(464\) −20.6672 + 38.7919i −0.0445413 + 0.0836032i
\(465\) 0 0
\(466\) 101.320 + 365.641i 0.217425 + 0.784638i
\(467\) 235.964 0.505276 0.252638 0.967561i \(-0.418702\pi\)
0.252638 + 0.967561i \(0.418702\pi\)
\(468\) 138.843 + 231.289i 0.296672 + 0.494208i
\(469\) −731.593 −1.55990
\(470\) 0 0
\(471\) 76.5602i 0.162548i
\(472\) −250.919 238.409i −0.531608 0.505104i
\(473\) 240.513i 0.508485i
\(474\) 9.97018 + 35.9802i 0.0210341 + 0.0759076i
\(475\) 0 0
\(476\) −312.740 520.974i −0.657016 1.09448i
\(477\) 282.320i 0.591866i
\(478\) −143.014 516.107i −0.299193 1.07972i
\(479\) 529.496i 1.10542i 0.833374 + 0.552710i \(0.186406\pi\)
−0.833374 + 0.552710i \(0.813594\pi\)
\(480\) 0 0
\(481\) 730.320 1.51834
\(482\) 581.417 161.112i 1.20626 0.334257i
\(483\) 103.606 0.214504
\(484\) −309.890 + 186.027i −0.640270 + 0.384353i
\(485\) 0 0
\(486\) −30.0447 + 8.32546i −0.0618205 + 0.0171306i
\(487\) 880.801 1.80863 0.904314 0.426869i \(-0.140383\pi\)
0.904314 + 0.426869i \(0.140383\pi\)
\(488\) −312.815 + 329.230i −0.641015 + 0.674651i
\(489\) −91.6888 −0.187503
\(490\) 0 0
\(491\) 86.4466i 0.176062i −0.996118 0.0880312i \(-0.971942\pi\)
0.996118 0.0880312i \(-0.0280575\pi\)
\(492\) 253.991 152.470i 0.516241 0.309899i
\(493\) 34.8583i 0.0707065i
\(494\) −379.697 + 105.215i −0.768617 + 0.212985i
\(495\) 0 0
\(496\) 230.830 + 122.979i 0.465383 + 0.247942i
\(497\) 474.846i 0.955425i
\(498\) 468.239 129.750i 0.940239 0.260542i
\(499\) 874.536i 1.75258i 0.481786 + 0.876289i \(0.339988\pi\)
−0.481786 + 0.876289i \(0.660012\pi\)
\(500\) 0 0
\(501\) 310.510 0.619780
\(502\) 33.7479 + 121.789i 0.0672269 + 0.242607i
\(503\) 17.5479 0.0348865 0.0174433 0.999848i \(-0.494447\pi\)
0.0174433 + 0.999848i \(0.494447\pi\)
\(504\) −197.907 + 208.291i −0.392672 + 0.413277i
\(505\) 0 0
\(506\) 38.7958 + 140.006i 0.0766716 + 0.276691i
\(507\) −582.595 −1.14910
\(508\) −574.659 + 344.967i −1.13122 + 0.679069i
\(509\) −609.132 −1.19672 −0.598362 0.801226i \(-0.704181\pi\)
−0.598362 + 0.801226i \(0.704181\pi\)
\(510\) 0 0
\(511\) 1191.72i 2.33213i
\(512\) 388.709 + 333.241i 0.759197 + 0.650861i
\(513\) 45.5357i 0.0887636i
\(514\) 80.4959 + 290.492i 0.156607 + 0.565159i
\(515\) 0 0
\(516\) 98.2703 58.9915i 0.190446 0.114325i
\(517\) 706.430i 1.36640i
\(518\) 207.716 + 749.602i 0.400997 + 1.44711i
\(519\) 307.050i 0.591619i
\(520\) 0 0
\(521\) 433.724 0.832484 0.416242 0.909254i \(-0.363347\pi\)
0.416242 + 0.909254i \(0.363347\pi\)
\(522\) 15.8841 4.40153i 0.0304294 0.00843205i
\(523\) −473.223 −0.904823 −0.452412 0.891809i \(-0.649436\pi\)
−0.452412 + 0.891809i \(0.649436\pi\)
\(524\) −168.912 281.380i −0.322351 0.536985i
\(525\) 0 0
\(526\) −392.712 + 108.821i −0.746601 + 0.206885i
\(527\) 207.423 0.393592
\(528\) −355.579 189.442i −0.673444 0.358791i
\(529\) −504.035 −0.952807
\(530\) 0 0
\(531\) 129.795i 0.244435i
\(532\) −215.985 359.797i −0.405988 0.676310i
\(533\) 961.224i 1.80342i
\(534\) 183.181 50.7597i 0.343035 0.0950556i
\(535\) 0 0
\(536\) 336.746 354.416i 0.628257 0.661223i
\(537\) 178.139i 0.331730i
\(538\) 147.249 40.8029i 0.273696 0.0758418i
\(539\) 1371.24i 2.54405i
\(540\) 0 0
\(541\) 294.889 0.545081 0.272540 0.962144i \(-0.412136\pi\)
0.272540 + 0.962144i \(0.412136\pi\)
\(542\) 90.3747 + 326.142i 0.166743 + 0.601739i
\(543\) −199.901 −0.368141
\(544\) 396.333 + 88.2946i 0.728554 + 0.162306i
\(545\) 0 0
\(546\) −248.955 898.422i −0.455961 1.64546i
\(547\) −966.695 −1.76727 −0.883634 0.468179i \(-0.844910\pi\)
−0.883634 + 0.468179i \(0.844910\pi\)
\(548\) 523.864 + 872.673i 0.955956 + 1.59247i
\(549\) 170.303 0.310207
\(550\) 0 0
\(551\) 24.0740i 0.0436914i
\(552\) −47.6887 + 50.1910i −0.0863925 + 0.0909258i
\(553\) 129.030i 0.233327i
\(554\) −146.279 527.889i −0.264042 0.952868i
\(555\) 0 0
\(556\) −162.534 270.755i −0.292327 0.486969i
\(557\) 74.2603i 0.133322i −0.997776 0.0666609i \(-0.978765\pi\)
0.997776 0.0666609i \(-0.0212346\pi\)
\(558\) −26.1911 94.5180i −0.0469375 0.169387i
\(559\) 371.903i 0.665300i
\(560\) 0 0
\(561\) −319.522 −0.569558
\(562\) 600.708 166.457i 1.06887 0.296187i
\(563\) −663.688 −1.17884 −0.589421 0.807826i \(-0.700644\pi\)
−0.589421 + 0.807826i \(0.700644\pi\)
\(564\) 288.637 173.268i 0.511767 0.307213i
\(565\) 0 0
\(566\) 509.916 141.299i 0.900912 0.249645i
\(567\) 107.745 0.190026
\(568\) 230.036 + 218.567i 0.404993 + 0.384802i
\(569\) 667.450 1.17302 0.586511 0.809941i \(-0.300501\pi\)
0.586511 + 0.809941i \(0.300501\pi\)
\(570\) 0 0
\(571\) 185.898i 0.325565i −0.986662 0.162782i \(-0.947953\pi\)
0.986662 0.162782i \(-0.0520469\pi\)
\(572\) 1120.84 672.841i 1.95952 1.17630i
\(573\) 331.350i 0.578273i
\(574\) −986.603 + 273.390i −1.71882 + 0.476289i
\(575\) 0 0
\(576\) −9.81084 191.749i −0.0170327 0.332898i
\(577\) 664.331i 1.15135i 0.817678 + 0.575676i \(0.195261\pi\)
−0.817678 + 0.575676i \(0.804739\pi\)
\(578\) −246.681 + 68.3557i −0.426783 + 0.118263i
\(579\) 277.703i 0.479625i
\(580\) 0 0
\(581\) −1679.17 −2.89014
\(582\) 13.0988 + 47.2707i 0.0225066 + 0.0812212i
\(583\) 1368.14 2.34673
\(584\) 577.321 + 548.537i 0.988563 + 0.939276i
\(585\) 0 0
\(586\) −64.7734 233.753i −0.110535 0.398896i
\(587\) 763.083 1.29997 0.649986 0.759946i \(-0.274775\pi\)
0.649986 + 0.759946i \(0.274775\pi\)
\(588\) 560.270 336.329i 0.952841 0.571989i
\(589\) 143.251 0.243211
\(590\) 0 0
\(591\) 615.018i 1.04064i
\(592\) −458.750 244.408i −0.774915 0.412852i
\(593\) 286.193i 0.482618i 0.970448 + 0.241309i \(0.0775768\pi\)
−0.970448 + 0.241309i \(0.922423\pi\)
\(594\) 40.3458 + 145.599i 0.0679222 + 0.245116i
\(595\) 0 0
\(596\) 110.922 66.5862i 0.186111 0.111722i
\(597\) 152.772i 0.255900i
\(598\) −59.9895 216.489i −0.100317 0.362021i
\(599\) 604.151i 1.00860i 0.863529 + 0.504300i \(0.168249\pi\)
−0.863529 + 0.504300i \(0.831751\pi\)
\(600\) 0 0
\(601\) 275.562 0.458505 0.229253 0.973367i \(-0.426372\pi\)
0.229253 + 0.973367i \(0.426372\pi\)
\(602\) −381.722 + 105.776i −0.634089 + 0.175707i
\(603\) −183.332 −0.304033
\(604\) −79.8692 133.049i −0.132234 0.220280i
\(605\) 0 0
\(606\) 545.514 151.163i 0.900188 0.249444i
\(607\) 52.1487 0.0859121 0.0429561 0.999077i \(-0.486322\pi\)
0.0429561 + 0.999077i \(0.486322\pi\)
\(608\) 273.717 + 60.9784i 0.450193 + 0.100293i
\(609\) −56.9628 −0.0935349
\(610\) 0 0
\(611\) 1092.34i 1.78779i
\(612\) −78.3702 130.552i −0.128056 0.213320i
\(613\) 898.128i 1.46513i −0.680695 0.732567i \(-0.738322\pi\)
0.680695 0.732567i \(-0.261678\pi\)
\(614\) 311.787 86.3968i 0.507796 0.140711i
\(615\) 0 0
\(616\) 1009.39 + 959.070i 1.63863 + 1.55693i
\(617\) 636.868i 1.03220i 0.856528 + 0.516101i \(0.172617\pi\)
−0.856528 + 0.516101i \(0.827383\pi\)
\(618\) 566.145 156.880i 0.916092 0.253851i
\(619\) 190.559i 0.307849i −0.988083 0.153925i \(-0.950809\pi\)
0.988083 0.153925i \(-0.0491913\pi\)
\(620\) 0 0
\(621\) 25.9628 0.0418080
\(622\) −14.0897 50.8466i −0.0226522 0.0817469i
\(623\) −656.911 −1.05443
\(624\) 549.826 + 292.931i 0.881132 + 0.469441i
\(625\) 0 0
\(626\) −2.88350 10.4059i −0.00460623 0.0166229i
\(627\) −220.669 −0.351945
\(628\) −91.0004 151.592i −0.144905 0.241388i
\(629\) −412.231 −0.655376
\(630\) 0 0
\(631\) 578.160i 0.916261i −0.888885 0.458130i \(-0.848519\pi\)
0.888885 0.458130i \(-0.151481\pi\)
\(632\) 62.5078 + 59.3913i 0.0989047 + 0.0939736i
\(633\) 330.102i 0.521488i
\(634\) 144.285 + 520.693i 0.227579 + 0.821283i
\(635\) 0 0
\(636\) 335.569 + 559.003i 0.527624 + 0.878936i
\(637\) 2120.34i 3.32863i
\(638\) −21.3301 76.9757i −0.0334328 0.120652i
\(639\) 118.993i 0.186217i
\(640\) 0 0
\(641\) −35.3085 −0.0550834 −0.0275417 0.999621i \(-0.508768\pi\)
−0.0275417 + 0.999621i \(0.508768\pi\)
\(642\) −27.2018 + 7.53768i −0.0423704 + 0.0117409i
\(643\) 1045.67 1.62623 0.813117 0.582100i \(-0.197769\pi\)
0.813117 + 0.582100i \(0.197769\pi\)
\(644\) 205.143 123.147i 0.318544 0.191222i
\(645\) 0 0
\(646\) 214.321 59.3888i 0.331766 0.0919331i
\(647\) −2.71164 −0.00419110 −0.00209555 0.999998i \(-0.500667\pi\)
−0.00209555 + 0.999998i \(0.500667\pi\)
\(648\) −49.5939 + 52.1962i −0.0765338 + 0.0805497i
\(649\) 628.996 0.969177
\(650\) 0 0
\(651\) 338.955i 0.520668i
\(652\) −181.547 + 108.982i −0.278446 + 0.167151i
\(653\) 206.765i 0.316639i −0.987388 0.158319i \(-0.949392\pi\)
0.987388 0.158319i \(-0.0506076\pi\)
\(654\) −84.2327 + 23.3411i −0.128796 + 0.0356897i
\(655\) 0 0
\(656\) 321.682 603.792i 0.490370 0.920415i
\(657\) 298.636i 0.454544i
\(658\) −1121.18 + 310.682i −1.70393 + 0.472161i
\(659\) 708.330i 1.07486i −0.843309 0.537428i \(-0.819396\pi\)
0.843309 0.537428i \(-0.180604\pi\)
\(660\) 0 0
\(661\) 1229.66 1.86031 0.930155 0.367167i \(-0.119672\pi\)
0.930155 + 0.367167i \(0.119672\pi\)
\(662\) −256.746 926.540i −0.387834 1.39961i
\(663\) 494.072 0.745207
\(664\) 772.907 813.464i 1.16402 1.22510i
\(665\) 0 0
\(666\) 52.0521 + 187.845i 0.0781564 + 0.282049i
\(667\) −13.7261 −0.0205788
\(668\) 614.820 369.076i 0.920390 0.552508i
\(669\) −137.329 −0.205275
\(670\) 0 0
\(671\) 825.303i 1.22996i
\(672\) −144.284 + 647.658i −0.214709 + 0.963777i
\(673\) 753.492i 1.11960i −0.828627 0.559801i \(-0.810878\pi\)
0.828627 0.559801i \(-0.189122\pi\)
\(674\) 303.561 + 1095.48i 0.450387 + 1.62535i
\(675\) 0 0
\(676\) −1153.56 + 692.479i −1.70645 + 1.02438i
\(677\) 332.246i 0.490762i −0.969427 0.245381i \(-0.921087\pi\)
0.969427 0.245381i \(-0.0789131\pi\)
\(678\) −90.4832 326.534i −0.133456 0.481613i
\(679\) 169.520i 0.249661i
\(680\) 0 0
\(681\) −612.531 −0.899458
\(682\) −458.041 + 126.924i −0.671615 + 0.186106i
\(683\) 1120.62 1.64074 0.820368 0.571835i \(-0.193768\pi\)
0.820368 + 0.571835i \(0.193768\pi\)
\(684\) −54.1243 90.1623i −0.0791291 0.131816i
\(685\) 0 0
\(686\) −1045.70 + 289.767i −1.52435 + 0.422400i
\(687\) 39.4753 0.0574605
\(688\) 124.461 233.610i 0.180902 0.339550i
\(689\) −2115.54 −3.07045
\(690\) 0 0
\(691\) 331.115i 0.479182i −0.970874 0.239591i \(-0.922987\pi\)
0.970874 0.239591i \(-0.0770134\pi\)
\(692\) −364.964 607.970i −0.527404 0.878570i
\(693\) 522.139i 0.753447i
\(694\) 713.482 197.707i 1.02807 0.284881i
\(695\) 0 0
\(696\) 26.2194 27.5953i 0.0376716 0.0396484i
\(697\) 542.566i 0.778431i
\(698\) −941.655 + 260.935i −1.34908 + 0.373832i
\(699\) 328.587i 0.470081i
\(700\) 0 0
\(701\) −564.971 −0.805949 −0.402975 0.915211i \(-0.632024\pi\)
−0.402975 + 0.915211i \(0.632024\pi\)
\(702\) −62.3861 225.138i −0.0888691 0.320709i
\(703\) −284.697 −0.404974
\(704\) −929.230 + 47.5440i −1.31993 + 0.0675341i
\(705\) 0 0
\(706\) 347.006 + 1252.27i 0.491510 + 1.77375i
\(707\) −1956.29 −2.76703
\(708\) 154.276 + 256.999i 0.217904 + 0.362992i
\(709\) −1.56083 −0.00220146 −0.00110073 0.999999i \(-0.500350\pi\)
−0.00110073 + 0.999999i \(0.500350\pi\)
\(710\) 0 0
\(711\) 32.3339i 0.0454767i
\(712\) 302.370 318.236i 0.424677 0.446961i
\(713\) 81.6765i 0.114553i
\(714\) 140.523 + 507.117i 0.196811 + 0.710248i
\(715\) 0 0
\(716\) 211.738 + 352.721i 0.295723 + 0.492627i
\(717\) 463.804i 0.646868i
\(718\) 216.788 + 782.339i 0.301933 + 1.08961i
\(719\) 75.0325i 0.104357i 0.998638 + 0.0521784i \(0.0166164\pi\)
−0.998638 + 0.0521784i \(0.983384\pi\)
\(720\) 0 0
\(721\) −2030.28 −2.81592
\(722\) −547.766 + 151.787i −0.758678 + 0.210231i
\(723\) −522.496 −0.722678
\(724\) −395.810 + 237.604i −0.546699 + 0.328183i
\(725\) 0 0
\(726\) 301.648 83.5874i 0.415493 0.115134i
\(727\) 1229.26 1.69087 0.845433 0.534082i \(-0.179343\pi\)
0.845433 + 0.534082i \(0.179343\pi\)
\(728\) −1560.81 1483.00i −2.14397 2.03708i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 209.922i 0.287170i
\(732\) 337.207 202.425i 0.460665 0.276536i
\(733\) 691.736i 0.943705i −0.881678 0.471852i \(-0.843586\pi\)
0.881678 0.471852i \(-0.156414\pi\)
\(734\) 89.1114 24.6930i 0.121405 0.0336416i
\(735\) 0 0
\(736\) −34.7676 + 156.063i −0.0472385 + 0.212042i
\(737\) 888.438i 1.20548i
\(738\) −247.235 + 68.5094i −0.335007 + 0.0928312i
\(739\) 71.4311i 0.0966591i 0.998831 + 0.0483296i \(0.0153898\pi\)
−0.998831 + 0.0483296i \(0.984610\pi\)
\(740\) 0 0
\(741\) 341.218 0.460483
\(742\) −601.698 2171.40i −0.810914 2.92641i
\(743\) −1006.92 −1.35521 −0.677605 0.735426i \(-0.736982\pi\)
−0.677605 + 0.735426i \(0.736982\pi\)
\(744\) −164.205 156.018i −0.220705 0.209701i
\(745\) 0 0
\(746\) −73.8428 266.482i −0.0989850 0.357215i
\(747\) −420.788 −0.563303
\(748\) −632.664 + 379.787i −0.845808 + 0.507737i
\(749\) 97.5496 0.130240
\(750\) 0 0
\(751\) 1110.14i 1.47822i 0.673587 + 0.739108i \(0.264753\pi\)
−0.673587 + 0.739108i \(0.735247\pi\)
\(752\) 365.562 686.154i 0.486120 0.912439i
\(753\) 109.447i 0.145347i
\(754\) 32.9825 + 119.026i 0.0437433 + 0.157860i
\(755\) 0 0
\(756\) 213.338 128.067i 0.282193 0.169400i
\(757\) 326.752i 0.431641i 0.976433 + 0.215821i \(0.0692426\pi\)
−0.976433 + 0.215821i \(0.930757\pi\)
\(758\) 135.932 + 490.547i 0.179329 + 0.647160i
\(759\) 125.817i 0.165767i
\(760\) 0 0
\(761\) 162.162 0.213091 0.106546 0.994308i \(-0.466021\pi\)
0.106546 + 0.994308i \(0.466021\pi\)
\(762\) 559.375 155.004i 0.734088 0.203417i
\(763\) 302.070 0.395898
\(764\) −393.847 656.085i −0.515507 0.858750i
\(765\) 0 0
\(766\) 120.886 33.4977i 0.157814 0.0437306i
\(767\) −972.608 −1.26807
\(768\) −247.341 368.009i −0.322059 0.479178i
\(769\) 154.694 0.201162 0.100581 0.994929i \(-0.467930\pi\)
0.100581 + 0.994929i \(0.467930\pi\)
\(770\) 0 0
\(771\) 261.053i 0.338590i
\(772\) 330.081 + 549.861i 0.427566 + 0.712255i
\(773\) 208.302i 0.269472i 0.990882 + 0.134736i \(0.0430187\pi\)
−0.990882 + 0.134736i \(0.956981\pi\)
\(774\) −95.6566 + 26.5066i −0.123587 + 0.0342463i
\(775\) 0 0
\(776\) 82.1226 + 78.0283i 0.105828 + 0.100552i
\(777\) 673.637i 0.866972i
\(778\) 212.262 58.8183i 0.272831 0.0756019i
\(779\) 374.709i 0.481013i
\(780\) 0 0
\(781\) −576.648 −0.738346
\(782\) 33.8612 + 122.198i 0.0433008 + 0.156263i
\(783\) −14.2744 −0.0182304
\(784\) 709.590 1331.89i 0.905089 1.69884i
\(785\) 0 0
\(786\) 75.8972 + 273.896i 0.0965613 + 0.348468i
\(787\) 377.158 0.479235