Properties

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

$q$-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 \(0.229795\pi\)
−0.750537 + 0.660828i \(0.770205\pi\)
\(12\) 5.94010 + 3.56583i 0.495009 + 0.297153i
\(13\) 22.4802i 1.72925i −0.502418 0.864625i \(-0.667556\pi\)
0.502418 0.864625i \(-0.332444\pi\)
\(14\) −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 \(0.121742\pi\)
−0.927748 + 0.373207i \(0.878258\pi\)
\(18\) −5.78211 1.60224i −0.321229 0.0890131i
\(19\) 8.76336i 0.461229i 0.973045 + 0.230615i \(0.0740737\pi\)
−0.973045 + 0.230615i \(0.925926\pi\)
\(20\) 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 \(-0.915072\pi\)
0.964617 0.263655i \(-0.0849281\pi\)
\(32\) −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 \(0.144673\pi\)
−0.898479 + 0.439016i \(0.855327\pi\)
\(38\) 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 \(-0.652234\pi\)
0.460233 0.887798i \(-0.347766\pi\)
\(54\) −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 \(-0.880504\pi\)
0.930358 0.366653i \(-0.119496\pi\)
\(60\) 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 \(0.0901110\pi\)
−0.960196 + 0.279326i \(0.909889\pi\)
\(72\) −16.5313 17.3987i −0.229601 0.241649i
\(73\) 99.5452i 1.36363i 0.731523 + 0.681817i \(0.238810\pi\)
−0.731523 + 0.681817i \(0.761190\pi\)
\(74\) 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 \(0.0217304\pi\)
−0.997671 + 0.0682151i \(0.978270\pi\)
\(80\) 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 \(0.0232542\pi\)
−0.997333 + 0.0729902i \(0.976746\pi\)
\(98\) −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 \(-0.857523\pi\)
0.901487 0.432806i \(-0.142477\pi\)
\(114\) 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 \(0.101386\pi\)
−0.949702 + 0.313155i \(0.898614\pi\)
\(132\) −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 \(-0.620942\pi\)
0.370874 0.928683i \(-0.379058\pi\)
\(138\) −16.6800 4.62205i −0.120869 0.0334931i
\(139\) 78.9483i 0.567974i 0.958828 + 0.283987i \(0.0916572\pi\)
−0.958828 + 0.283987i \(0.908343\pi\)
\(140\) 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 \(0.0410038\pi\)
−0.991715 + 0.128461i \(0.958996\pi\)
\(152\) 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 \(0.0449581\pi\)
−0.990042 + 0.140771i \(0.955042\pi\)
\(158\) 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 \(0.171228\pi\)
−0.858772 + 0.512357i \(0.828772\pi\)
\(174\) 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 \(-0.907247\pi\)
0.957845 0.287286i \(-0.0927532\pi\)
\(180\) 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 \(0.166960\pi\)
−0.865563 + 0.500799i \(0.833040\pi\)
\(192\) −5.66429 + 110.706i −0.0295015 + 0.576596i
\(193\) 160.332i 0.830734i −0.909654 0.415367i \(-0.863653\pi\)
0.909654 0.415367i \(-0.136347\pi\)
\(194\) 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 \(-0.642673\pi\)
0.433362 0.901220i \(-0.357327\pi\)
\(198\) 23.2936 84.0616i 0.117645 0.424554i
\(199\) 88.2032i 0.443232i −0.975134 0.221616i \(-0.928867\pi\)
0.975134 0.221616i \(-0.0711332\pi\)
\(200\) 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 \(-0.850846\pi\)
0.892210 0.451622i \(-0.149154\pi\)
\(212\) 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 \(0.133461\pi\)
−0.913382 + 0.407103i \(0.866539\pi\)
\(234\) −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 \(-0.810723\pi\)
0.828355 0.560204i \(-0.189277\pi\)
\(240\) 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 \(0.0401737\pi\)
−0.992046 + 0.125875i \(0.959826\pi\)
\(252\) 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 \(0.0947295\pi\)
−0.956043 + 0.293228i \(0.905271\pi\)
\(258\) −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 \(0.101068\pi\)
−0.950014 + 0.312207i \(0.898932\pi\)
\(272\) −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 \(-0.835393\pi\)
0.869242 0.494387i \(-0.164607\pi\)
\(278\) 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 \(-0.933642\pi\)
0.978349 0.206964i \(-0.0663582\pi\)
\(294\) −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 \(-0.986495\pi\)
0.999100 0.0424137i \(-0.0135047\pi\)
\(312\) −225.818 + 214.559i −0.723775 + 0.687690i
\(313\) 5.39902i 0.0172493i −0.999963 0.00862463i \(-0.997255\pi\)
0.999963 0.00862463i \(-0.00274534\pi\)
\(314\) 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 \(0.140118\pi\)
−0.904669 + 0.426116i \(0.859882\pi\)
\(318\) −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 \(-0.741296\pi\)
0.687510 0.726174i \(-0.258704\pi\)
\(332\) −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 \(0.319388\pi\)
−0.537448 + 0.843297i \(0.680612\pi\)
\(338\) 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 \(0.372051\pi\)
−0.391226 + 0.920295i \(0.627949\pi\)
\(354\) −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 \(0.191253\pi\)
−0.824862 + 0.565334i \(0.808747\pi\)
\(360\) 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 \(-0.940662\pi\)
0.982675 0.185338i \(-0.0593380\pi\)
\(374\) 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 \(0.108998\pi\)
−0.941943 + 0.335773i \(0.891002\pi\)
\(380\) 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 \(0.120285\pi\)
−0.929446 + 0.368958i \(0.879715\pi\)
\(398\) −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 \(-0.937554\pi\)
0.980818 0.194925i \(-0.0624462\pi\)
\(420\) 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 \(0.292674\pi\)
−0.606248 + 0.795275i \(0.707326\pi\)
\(432\) 39.0918 + 73.3746i 0.0904902 + 0.169849i
\(433\) 592.777i 1.36900i −0.729013 0.684500i \(-0.760021\pi\)
0.729013 0.684500i \(-0.239979\pi\)
\(434\) −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 \(-0.822577\pi\)
0.848638 0.528974i \(-0.177423\pi\)
\(440\) 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 \(-0.976791\pi\)
0.997343 0.0728498i \(-0.0232094\pi\)
\(458\) −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 \(-0.813594\pi\)
0.833374 0.552710i \(-0.186406\pi\)
\(480\) 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 \(0.0280575\pi\)
−0.996118 + 0.0880312i \(0.971942\pi\)
\(492\) 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 \(-0.660012\pi\)
0.481786 0.876289i \(-0.339988\pi\)
\(500\) 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 \(0.0212346\pi\)
−0.997776 + 0.0666609i \(0.978765\pi\)
\(558\) −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 \(0.0520469\pi\)
−0.986662 + 0.162782i \(0.947953\pi\)
\(572\) 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 \(-0.804739\pi\)
0.817678 0.575676i \(-0.195261\pi\)
\(578\) −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 \(-0.922423\pi\)
0.970448 0.241309i \(-0.0775768\pi\)
\(594\) 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 \(-0.831751\pi\)
0.863529 0.504300i \(-0.168249\pi\)
\(600\) 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 \(0.261678\pi\)
−0.680695 + 0.732567i \(0.738322\pi\)
\(614\) 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 \(-0.827383\pi\)
0.856528 0.516101i \(-0.172617\pi\)
\(618\) 566.145 + 156.880i 0.916092 + 0.253851i
\(619\) 190.559i 0.307849i 0.988083 + 0.153925i \(0.0491913\pi\)
−0.988083 + 0.153925i \(0.950809\pi\)
\(620\) 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 \(0.151481\pi\)
−0.888885 + 0.458130i \(0.848519\pi\)
\(632\) 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 \(0.0506076\pi\)
−0.987388 + 0.158319i \(0.949392\pi\)
\(654\) −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 \(0.180604\pi\)
−0.843309 + 0.537428i \(0.819396\pi\)
\(660\) 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 \(0.189122\pi\)
−0.828627 + 0.559801i \(0.810878\pi\)
\(674\) 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 \(0.0789131\pi\)
−0.969427 + 0.245381i \(0.921087\pi\)
\(678\) −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 \(0.0770134\pi\)
−0.970874 + 0.239591i \(0.922987\pi\)
\(692\) −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 \(-0.983384\pi\)
0.998638 0.0521784i \(-0.0166164\pi\)
\(720\) 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 \(0.156414\pi\)
−0.881678 + 0.471852i \(0.843586\pi\)
\(734\) 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 \(-0.984610\pi\)
0.998831 0.0483296i \(-0.0153898\pi\)
\(740\) 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 \(-0.735247\pi\)
0.673587 0.739108i \(-0.264753\pi\)
\(752\) 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 \(-0.930757\pi\)
0.976433 0.215821i \(-0.0692426\pi\)
\(758\) 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 \(-0.956981\pi\)
0.990882 0.134736i \(-0.0430187\pi\)
\(774\) −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 0.239617