Properties

Label 300.3.c.g.151.6
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.4069419264.1
Defining polynomial: \(x^{8} - 7 x^{6} + 50 x^{4} - 84 x^{3} + 55 x^{2} - 12 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.6
Root \(-2.65095 + 1.53053i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.g.151.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.534079 + 1.92737i) q^{2} +1.73205i q^{3} +(-3.42952 + 2.05874i) q^{4} +(-3.33830 + 0.925051i) q^{6} -11.9716i q^{7} +(-5.79958 - 5.51043i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(0.534079 + 1.92737i) q^{2} +1.73205i q^{3} +(-3.42952 + 2.05874i) q^{4} +(-3.33830 + 0.925051i) q^{6} -11.9716i q^{7} +(-5.79958 - 5.51043i) q^{8} -3.00000 q^{9} -14.5382i q^{11} +(-3.56583 - 5.94010i) q^{12} -22.4802 q^{13} +(23.0738 - 6.39379i) q^{14} +(7.52322 - 14.1209i) q^{16} -12.6890 q^{17} +(-1.60224 - 5.78211i) q^{18} +8.76336i q^{19} +20.7355 q^{21} +(28.0205 - 7.76455i) q^{22} +4.99653i q^{23} +(9.54435 - 10.0452i) q^{24} +(-12.0062 - 43.3278i) q^{26} -5.19615i q^{27} +(24.6464 + 41.0570i) q^{28} +2.74712 q^{29} +16.3466i q^{31} +(31.2343 + 6.95833i) q^{32} +25.1809 q^{33} +(-6.77695 - 24.4565i) q^{34} +(10.2886 - 6.17621i) q^{36} -32.4872 q^{37} +(-16.8902 + 4.68032i) q^{38} -38.9369i q^{39} +42.7586 q^{41} +(11.0744 + 39.9650i) q^{42} +16.5435i q^{43} +(29.9303 + 49.8591i) q^{44} +(-9.63018 + 2.66854i) q^{46} -48.5912i q^{47} +(24.4582 + 13.0306i) q^{48} -94.3200 q^{49} -21.9781i q^{51} +(77.0964 - 46.2809i) q^{52} -94.1066 q^{53} +(10.0149 - 2.77515i) q^{54} +(-65.9689 + 69.4305i) q^{56} -15.1786 q^{57} +(1.46718 + 5.29471i) q^{58} -43.2650i q^{59} +56.7678 q^{61} +(-31.5060 + 8.73038i) q^{62} +35.9149i q^{63} +(3.27028 + 63.9164i) q^{64} +(13.4486 + 48.5330i) q^{66} +61.1106i q^{67} +(43.5173 - 26.1234i) q^{68} -8.65425 q^{69} -39.6643i q^{71} +(17.3987 + 16.5313i) q^{72} +99.5452 q^{73} +(-17.3507 - 62.6149i) q^{74} +(-18.0414 - 30.0541i) q^{76} -174.046 q^{77} +(75.0459 - 20.7954i) q^{78} +10.7780i q^{79} +9.00000 q^{81} +(22.8365 + 82.4118i) q^{82} -140.263i q^{83} +(-71.1127 + 42.6889i) q^{84} +(-31.8855 + 8.83554i) q^{86} +4.75815i q^{87} +(-80.1118 + 84.3156i) q^{88} +54.8723 q^{89} +269.125i q^{91} +(-10.2865 - 17.1357i) q^{92} -28.3132 q^{93} +(93.6533 - 25.9515i) q^{94} +(-12.0522 + 54.0994i) q^{96} -14.1601 q^{97} +(-50.3743 - 181.790i) q^{98} +43.6146i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 8q^{4} - 6q^{6} + 20q^{8} - 24q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 8q^{4} - 6q^{6} + 20q^{8} - 24q^{9} + 8q^{13} + 22q^{14} + 40q^{16} - 6q^{18} + 24q^{21} + 4q^{22} - 36q^{24} - 66q^{26} + 104q^{28} - 32q^{29} + 112q^{32} + 124q^{34} + 24q^{36} - 176q^{37} - 170q^{38} - 16q^{41} + 54q^{42} + 40q^{44} - 76q^{46} + 24q^{48} + 16q^{49} + 56q^{52} - 304q^{53} + 18q^{54} - 172q^{56} + 72q^{57} - 12q^{58} + 136q^{61} - 238q^{62} + 16q^{64} - 108q^{66} + 88q^{68} - 96q^{69} - 60q^{72} + 240q^{73} - 108q^{74} + 120q^{76} - 384q^{77} + 150q^{78} + 72q^{81} + 320q^{82} - 144q^{84} + 214q^{86} - 200q^{88} + 128q^{89} + 312q^{92} + 72q^{93} + 12q^{94} + 96q^{96} + 216q^{97} + 60q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.534079 + 1.92737i 0.267039 + 0.963686i
\(3\) 1.73205i 0.577350i
\(4\) −3.42952 + 2.05874i −0.857380 + 0.514684i
\(5\) 0 0
\(6\) −3.33830 + 0.925051i −0.556384 + 0.154175i
\(7\) 11.9716i 1.71023i −0.518436 0.855117i \(-0.673485\pi\)
0.518436 0.855117i \(-0.326515\pi\)
\(8\) −5.79958 5.51043i −0.724948 0.688804i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 14.5382i 1.32166i −0.750537 0.660828i \(-0.770205\pi\)
0.750537 0.660828i \(-0.229795\pi\)
\(12\) −3.56583 5.94010i −0.297153 0.495009i
\(13\) −22.4802 −1.72925 −0.864625 0.502418i \(-0.832444\pi\)
−0.864625 + 0.502418i \(0.832444\pi\)
\(14\) 23.0738 6.39379i 1.64813 0.456699i
\(15\) 0 0
\(16\) 7.52322 14.1209i 0.470201 0.882559i
\(17\) −12.6890 −0.746414 −0.373207 0.927748i \(-0.621742\pi\)
−0.373207 + 0.927748i \(0.621742\pi\)
\(18\) −1.60224 5.78211i −0.0890131 0.321229i
\(19\) 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
\(22\) 28.0205 7.76455i 1.27366 0.352934i
\(23\) 4.99653i 0.217241i 0.994083 + 0.108620i \(0.0346433\pi\)
−0.994083 + 0.108620i \(0.965357\pi\)
\(24\) 9.54435 10.0452i 0.397681 0.418549i
\(25\) 0 0
\(26\) −12.0062 43.3278i −0.461778 1.66645i
\(27\) 5.19615i 0.192450i
\(28\) 24.6464 + 41.0570i 0.880229 + 1.46632i
\(29\) 2.74712 0.0947282 0.0473641 0.998878i \(-0.484918\pi\)
0.0473641 + 0.998878i \(0.484918\pi\)
\(30\) 0 0
\(31\) 16.3466i 0.527310i 0.964617 + 0.263655i \(0.0849281\pi\)
−0.964617 + 0.263655i \(0.915072\pi\)
\(32\) 31.2343 + 6.95833i 0.976072 + 0.217448i
\(33\) 25.1809 0.763058
\(34\) −6.77695 24.4565i −0.199322 0.719309i
\(35\) 0 0
\(36\) 10.2886 6.17621i 0.285793 0.171561i
\(37\) −32.4872 −0.878032 −0.439016 0.898479i \(-0.644673\pi\)
−0.439016 + 0.898479i \(0.644673\pi\)
\(38\) −16.8902 + 4.68032i −0.444480 + 0.123166i
\(39\) 38.9369i 0.998383i
\(40\) 0 0
\(41\) 42.7586 1.04289 0.521447 0.853284i \(-0.325393\pi\)
0.521447 + 0.853284i \(0.325393\pi\)
\(42\) 11.0744 + 39.9650i 0.263676 + 0.951547i
\(43\) 16.5435i 0.384733i 0.981323 + 0.192367i \(0.0616163\pi\)
−0.981323 + 0.192367i \(0.938384\pi\)
\(44\) 29.9303 + 49.8591i 0.680235 + 1.13316i
\(45\) 0 0
\(46\) −9.63018 + 2.66854i −0.209352 + 0.0580118i
\(47\) 48.5912i 1.03386i −0.856029 0.516928i \(-0.827076\pi\)
0.856029 0.516928i \(-0.172924\pi\)
\(48\) 24.4582 + 13.0306i 0.509546 + 0.271471i
\(49\) −94.3200 −1.92490
\(50\) 0 0
\(51\) 21.9781i 0.430943i
\(52\) 77.0964 46.2809i 1.48262 0.890017i
\(53\) −94.1066 −1.77560 −0.887798 0.460233i \(-0.847766\pi\)
−0.887798 + 0.460233i \(0.847766\pi\)
\(54\) 10.0149 2.77515i 0.185461 0.0513917i
\(55\) 0 0
\(56\) −65.9689 + 69.4305i −1.17802 + 1.23983i
\(57\) −15.1786 −0.266291
\(58\) 1.46718 + 5.29471i 0.0252961 + 0.0912882i
\(59\) 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 \(0.345943\pi\)
\(62\) −31.5060 + 8.73038i −0.508161 + 0.140813i
\(63\) 35.9149i 0.570078i
\(64\) 3.27028 + 63.9164i 0.0510981 + 0.998694i
\(65\) 0 0
\(66\) 13.4486 + 48.5330i 0.203767 + 0.735348i
\(67\) 61.1106i 0.912098i 0.889955 + 0.456049i \(0.150736\pi\)
−0.889955 + 0.456049i \(0.849264\pi\)
\(68\) 43.5173 26.1234i 0.639961 0.384167i
\(69\) −8.65425 −0.125424
\(70\) 0 0
\(71\) 39.6643i 0.558652i −0.960196 0.279326i \(-0.909889\pi\)
0.960196 0.279326i \(-0.0901110\pi\)
\(72\) 17.3987 + 16.5313i 0.241649 + 0.229601i
\(73\) 99.5452 1.36363 0.681817 0.731523i \(-0.261190\pi\)
0.681817 + 0.731523i \(0.261190\pi\)
\(74\) −17.3507 62.6149i −0.234469 0.846147i
\(75\) 0 0
\(76\) −18.0414 30.0541i −0.237387 0.395449i
\(77\) −174.046 −2.26034
\(78\) 75.0459 20.7954i 0.962127 0.266607i
\(79\) 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
\(82\) 22.8365 + 82.4118i 0.278494 + 1.00502i
\(83\) 140.263i 1.68991i −0.534837 0.844955i \(-0.679627\pi\)
0.534837 0.844955i \(-0.320373\pi\)
\(84\) −71.1127 + 42.6889i −0.846580 + 0.508201i
\(85\) 0 0
\(86\) −31.8855 + 8.83554i −0.370762 + 0.102739i
\(87\) 4.75815i 0.0546913i
\(88\) −80.1118 + 84.3156i −0.910362 + 0.958131i
\(89\) 54.8723 0.616543 0.308271 0.951298i \(-0.400249\pi\)
0.308271 + 0.951298i \(0.400249\pi\)
\(90\) 0 0
\(91\) 269.125i 2.95742i
\(92\) −10.2865 17.1357i −0.111810 0.186258i
\(93\) −28.3132 −0.304443
\(94\) 93.6533 25.9515i 0.996312 0.276080i
\(95\) 0 0
\(96\) −12.0522 + 54.0994i −0.125544 + 0.563535i
\(97\) −14.1601 −0.145980 −0.0729902 0.997333i \(-0.523254\pi\)
−0.0729902 + 0.997333i \(0.523254\pi\)
\(98\) −50.3743 181.790i −0.514023 1.85500i
\(99\) 43.6146i 0.440552i
\(100\) 0 0
\(101\) −163.410 −1.61792 −0.808962 0.587861i \(-0.799970\pi\)
−0.808962 + 0.587861i \(0.799970\pi\)
\(102\) 42.3599 11.7380i 0.415293 0.115079i
\(103\) 169.591i 1.64651i −0.567672 0.823255i \(-0.692156\pi\)
0.567672 0.823255i \(-0.307844\pi\)
\(104\) 130.376 + 123.876i 1.25362 + 1.19111i
\(105\) 0 0
\(106\) −50.2603 181.378i −0.474154 1.71112i
\(107\) 8.14840i 0.0761532i −0.999275 0.0380766i \(-0.987877\pi\)
0.999275 0.0380766i \(-0.0121231\pi\)
\(108\) 10.6975 + 17.8203i 0.0990510 + 0.165003i
\(109\) −25.2322 −0.231488 −0.115744 0.993279i \(-0.536925\pi\)
−0.115744 + 0.993279i \(0.536925\pi\)
\(110\) 0 0
\(111\) 56.2695i 0.506932i
\(112\) −169.051 90.0652i −1.50938 0.804153i
\(113\) −97.8142 −0.865613 −0.432806 0.901487i \(-0.642477\pi\)
−0.432806 + 0.901487i \(0.642477\pi\)
\(114\) −8.10655 29.2548i −0.0711101 0.256621i
\(115\) 0 0
\(116\) −9.42129 + 5.65559i −0.0812180 + 0.0487551i
\(117\) 67.4407 0.576417
\(118\) 83.3877 23.1069i 0.706676 0.195821i
\(119\) 151.909i 1.27654i
\(120\) 0 0
\(121\) −90.3597 −0.746774
\(122\) 30.3185 + 109.413i 0.248512 + 0.896825i
\(123\) 74.0601i 0.602115i
\(124\) −33.6534 56.0611i −0.271398 0.452105i
\(125\) 0 0
\(126\) −69.2213 + 19.1814i −0.549376 + 0.152233i
\(127\) 167.563i 1.31939i 0.751533 + 0.659695i \(0.229315\pi\)
−0.751533 + 0.659695i \(0.770685\pi\)
\(128\) −121.444 + 40.4394i −0.948782 + 0.315933i
\(129\) −28.6542 −0.222126
\(130\) 0 0
\(131\) 82.0465i 0.626309i −0.949702 0.313155i \(-0.898614\pi\)
0.949702 0.313155i \(-0.101386\pi\)
\(132\) −86.3585 + 51.8409i −0.654231 + 0.392734i
\(133\) 104.912 0.788810
\(134\) −117.783 + 32.6378i −0.878976 + 0.243566i
\(135\) 0 0
\(136\) 73.5911 + 69.9221i 0.541111 + 0.514133i
\(137\) 254.459 1.85737 0.928683 0.370874i \(-0.120942\pi\)
0.928683 + 0.370874i \(0.120942\pi\)
\(138\) −4.62205 16.6800i −0.0334931 0.120869i
\(139\) 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
\(142\) 76.4478 21.1838i 0.538365 0.149182i
\(143\) 326.823i 2.28547i
\(144\) −22.5696 + 42.3628i −0.156734 + 0.294186i
\(145\) 0 0
\(146\) 53.1650 + 191.861i 0.364144 + 1.31411i
\(147\) 163.367i 1.11134i
\(148\) 111.415 66.8825i 0.752807 0.451909i
\(149\) −32.3433 −0.217069 −0.108534 0.994093i \(-0.534616\pi\)
−0.108534 + 0.994093i \(0.534616\pi\)
\(150\) 0 0
\(151\) 38.7953i 0.256922i −0.991715 0.128461i \(-0.958996\pi\)
0.991715 0.128461i \(-0.0410038\pi\)
\(152\) 48.2899 50.8238i 0.317697 0.334367i
\(153\) 38.0671 0.248805
\(154\) −92.9543 335.452i −0.603600 2.17826i
\(155\) 0 0
\(156\) 80.1608 + 133.535i 0.513851 + 0.855993i
\(157\) −44.2021 −0.281542 −0.140771 0.990042i \(-0.544958\pi\)
−0.140771 + 0.990042i \(0.544958\pi\)
\(158\) −20.7732 + 5.75629i −0.131476 + 0.0364322i
\(159\) 162.997i 1.02514i
\(160\) 0 0
\(161\) 59.8167 0.371532
\(162\) 4.80671 + 17.3463i 0.0296710 + 0.107076i
\(163\) 52.9366i 0.324764i −0.986728 0.162382i \(-0.948082\pi\)
0.986728 0.162382i \(-0.0519177\pi\)
\(164\) −146.642 + 88.0287i −0.894156 + 0.536760i
\(165\) 0 0
\(166\) 270.338 74.9112i 1.62854 0.451272i
\(167\) 179.273i 1.07349i −0.843744 0.536745i \(-0.819654\pi\)
0.843744 0.536745i \(-0.180346\pi\)
\(168\) −120.257 114.261i −0.715816 0.680128i
\(169\) 336.361 1.99030
\(170\) 0 0
\(171\) 26.2901i 0.153743i
\(172\) −34.0587 56.7364i −0.198016 0.329863i
\(173\) 177.276 1.02471 0.512357 0.858772i \(-0.328772\pi\)
0.512357 + 0.858772i \(0.328772\pi\)
\(174\) −9.17071 + 2.54122i −0.0527053 + 0.0146047i
\(175\) 0 0
\(176\) −205.293 109.374i −1.16644 0.621444i
\(177\) 74.9372 0.423374
\(178\) 29.3061 + 105.759i 0.164641 + 0.594154i
\(179\) 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 \(0.603286\pi\)
\(182\) −518.704 + 143.734i −2.85002 + 0.789747i
\(183\) 98.3247i 0.537294i
\(184\) 27.5331 28.9778i 0.149636 0.157488i
\(185\) 0 0
\(186\) −15.1215 54.5700i −0.0812982 0.293387i
\(187\) 184.476i 0.986503i
\(188\) 100.036 + 166.645i 0.532109 + 0.886407i
\(189\) −62.2064 −0.329135
\(190\) 0 0
\(191\) 191.305i 1.00160i −0.865563 0.500799i \(-0.833040\pi\)
0.865563 0.500799i \(-0.166960\pi\)
\(192\) −110.706 + 5.66429i −0.576596 + 0.0295015i
\(193\) −160.332 −0.830734 −0.415367 0.909654i \(-0.636347\pi\)
−0.415367 + 0.909654i \(0.636347\pi\)
\(194\) −7.56261 27.2918i −0.0389825 0.140679i
\(195\) 0 0
\(196\) 323.472 194.180i 1.65037 0.990714i
\(197\) 355.081 1.80244 0.901220 0.433362i \(-0.142673\pi\)
0.901220 + 0.433362i \(0.142673\pi\)
\(198\) −84.0616 + 23.2936i −0.424554 + 0.117645i
\(199\) 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
\(202\) −87.2740 314.952i −0.432049 1.55917i
\(203\) 32.8875i 0.162007i
\(204\) 45.2470 + 75.3742i 0.221799 + 0.369482i
\(205\) 0 0
\(206\) 326.864 90.5747i 1.58672 0.439683i
\(207\) 14.9896i 0.0724135i
\(208\) −169.124 + 317.442i −0.813095 + 1.52617i
\(209\) 127.404 0.609586
\(210\) 0 0
\(211\) 190.584i 0.903243i 0.892210 + 0.451622i \(0.149154\pi\)
−0.892210 + 0.451622i \(0.850846\pi\)
\(212\) 322.741 193.741i 1.52236 0.913871i
\(213\) 68.7006 0.322538
\(214\) 15.7050 4.35188i 0.0733878 0.0203359i
\(215\) 0 0
\(216\) −28.6330 + 30.1355i −0.132560 + 0.139516i
\(217\) 195.696 0.901824
\(218\) −13.4760 48.6318i −0.0618164 0.223082i
\(219\) 172.417i 0.787294i
\(220\) 0 0
\(221\) 285.253 1.29074
\(222\) 108.452 30.0523i 0.488523 0.135371i
\(223\) 79.2869i 0.355547i −0.984071 0.177773i \(-0.943111\pi\)
0.984071 0.177773i \(-0.0568894\pi\)
\(224\) 83.3026 373.926i 0.371887 1.66931i
\(225\) 0 0
\(226\) −52.2405 188.524i −0.231153 0.834178i
\(227\) 353.645i 1.55791i 0.627082 + 0.778953i \(0.284249\pi\)
−0.627082 + 0.778953i \(0.715751\pi\)
\(228\) 52.0552 31.2487i 0.228312 0.137056i
\(229\) −22.7911 −0.0995244 −0.0497622 0.998761i \(-0.515846\pi\)
−0.0497622 + 0.998761i \(0.515846\pi\)
\(230\) 0 0
\(231\) 301.457i 1.30501i
\(232\) −15.9321 15.1378i −0.0686730 0.0652491i
\(233\) 189.710 0.814205 0.407103 0.913382i \(-0.366539\pi\)
0.407103 + 0.913382i \(0.366539\pi\)
\(234\) 36.0187 + 129.983i 0.153926 + 0.555484i
\(235\) 0 0
\(236\) 89.0712 + 148.378i 0.377420 + 0.628721i
\(237\) −18.6680 −0.0787680
\(238\) −292.784 + 81.1311i −1.23019 + 0.340887i
\(239\) 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 \(0.715251\pi\)
\(242\) −48.2592 174.157i −0.199418 0.719656i
\(243\) 15.5885i 0.0641500i
\(244\) −194.686 + 116.870i −0.797895 + 0.478975i
\(245\) 0 0
\(246\) −142.741 + 39.5539i −0.580249 + 0.160788i
\(247\) 197.002i 0.797580i
\(248\) 90.0769 94.8035i 0.363213 0.382272i
\(249\) 242.942 0.975670
\(250\) 0 0
\(251\) 63.1891i 0.251749i −0.992046 0.125875i \(-0.959826\pi\)
0.992046 0.125875i \(-0.0401737\pi\)
\(252\) −73.9393 123.171i −0.293410 0.488773i
\(253\) 72.6407 0.287117
\(254\) −322.955 + 89.4916i −1.27148 + 0.352329i
\(255\) 0 0
\(256\) −142.802 212.470i −0.557822 0.829961i
\(257\) −150.719 −0.586456 −0.293228 0.956043i \(-0.594729\pi\)
−0.293228 + 0.956043i \(0.594729\pi\)
\(258\) −15.3036 55.2273i −0.0593163 0.214059i
\(259\) 388.925i 1.50164i
\(260\) 0 0
\(261\) −8.24135 −0.0315761
\(262\) 158.134 43.8193i 0.603565 0.167249i
\(263\) 203.755i 0.774735i 0.921925 + 0.387368i \(0.126616\pi\)
−0.921925 + 0.387368i \(0.873384\pi\)
\(264\) −146.039 138.758i −0.553177 0.525598i
\(265\) 0 0
\(266\) 56.0311 + 202.204i 0.210643 + 0.760165i
\(267\) 95.0416i 0.355961i
\(268\) −125.810 209.580i −0.469442 0.782014i
\(269\) 76.3986 0.284010 0.142005 0.989866i \(-0.454645\pi\)
0.142005 + 0.989866i \(0.454645\pi\)
\(270\) 0 0
\(271\) 169.216i 0.624414i −0.950014 0.312207i \(-0.898932\pi\)
0.950014 0.312207i \(-0.101068\pi\)
\(272\) −95.4624 + 179.181i −0.350965 + 0.658755i
\(273\) −466.139 −1.70747
\(274\) 135.901 + 490.437i 0.495990 + 1.78992i
\(275\) 0 0
\(276\) 29.6799 17.8168i 0.107536 0.0645537i
\(277\) 273.891 0.988774 0.494387 0.869242i \(-0.335393\pi\)
0.494387 + 0.869242i \(0.335393\pi\)
\(278\) −152.163 + 42.1646i −0.547348 + 0.151671i
\(279\) 49.0399i 0.175770i
\(280\) 0 0
\(281\) −311.672 −1.10915 −0.554577 0.832133i \(-0.687120\pi\)
−0.554577 + 0.832133i \(0.687120\pi\)
\(282\) 44.9494 + 162.212i 0.159395 + 0.575221i
\(283\) 264.566i 0.934861i −0.884030 0.467431i \(-0.845180\pi\)
0.884030 0.467431i \(-0.154820\pi\)
\(284\) 81.6583 + 136.029i 0.287529 + 0.478977i
\(285\) 0 0
\(286\) −629.909 + 174.549i −2.20248 + 0.610311i
\(287\) 511.891i 1.78359i
\(288\) −93.7029 20.8750i −0.325357 0.0724826i
\(289\) −127.988 −0.442866
\(290\) 0 0
\(291\) 24.5260i 0.0842818i
\(292\) −341.392 + 204.937i −1.16915 + 0.701840i
\(293\) −121.281 −0.413927 −0.206964 0.978349i \(-0.566358\pi\)
−0.206964 + 0.978349i \(0.566358\pi\)
\(294\) 314.869 87.2508i 1.07098 0.296772i
\(295\) 0 0
\(296\) 188.412 + 179.018i 0.636527 + 0.604792i
\(297\) −75.5428 −0.254353
\(298\) −17.2739 62.3375i −0.0579659 0.209186i
\(299\) 112.323i 0.375663i
\(300\) 0 0
\(301\) 198.053 0.657984
\(302\) 74.7729 20.7197i 0.247592 0.0686083i
\(303\) 283.035i 0.934109i
\(304\) 123.747 + 65.9286i 0.407062 + 0.216870i
\(305\) 0 0
\(306\) 20.3308 + 73.3695i 0.0664407 + 0.239770i
\(307\) 161.768i 0.526932i 0.964669 + 0.263466i \(0.0848656\pi\)
−0.964669 + 0.263466i \(0.915134\pi\)
\(308\) 596.895 358.315i 1.93797 1.16336i
\(309\) 293.739 0.950613
\(310\) 0 0
\(311\) 26.3813i 0.0848273i 0.999100 + 0.0424137i \(0.0135047\pi\)
−0.999100 + 0.0424137i \(0.986495\pi\)
\(312\) −214.559 + 225.818i −0.687690 + 0.723775i
\(313\) −5.39902 −0.0172493 −0.00862463 0.999963i \(-0.502745\pi\)
−0.00862463 + 0.999963i \(0.502745\pi\)
\(314\) −23.6074 85.1938i −0.0751827 0.271318i
\(315\) 0 0
\(316\) −22.1890 36.9633i −0.0702184 0.116972i
\(317\) −270.157 −0.852231 −0.426116 0.904669i \(-0.640118\pi\)
−0.426116 + 0.904669i \(0.640118\pi\)
\(318\) 314.157 87.0535i 0.987914 0.273753i
\(319\) 39.9382i 0.125198i
\(320\) 0 0
\(321\) 14.1134 0.0439671
\(322\) 31.9468 + 115.289i 0.0992137 + 0.358040i
\(323\) 111.199i 0.344268i
\(324\) −30.8657 + 18.5286i −0.0952644 + 0.0571871i
\(325\) 0 0
\(326\) 102.028 28.2723i 0.312971 0.0867248i
\(327\) 43.7034i 0.133650i
\(328\) −247.982 235.619i −0.756043 0.718349i
\(329\) −581.716 −1.76813
\(330\) 0 0
\(331\) 480.728i 1.45235i 0.687510 + 0.726174i \(0.258704\pi\)
−0.687510 + 0.726174i \(0.741296\pi\)
\(332\) 288.763 + 481.033i 0.869770 + 1.44890i
\(333\) 97.4616 0.292677
\(334\) 345.526 95.7459i 1.03451 0.286664i
\(335\) 0 0
\(336\) 155.997 292.805i 0.464278 0.871442i
\(337\) −568.382 −1.68659 −0.843297 0.537448i \(-0.819388\pi\)
−0.843297 + 0.537448i \(0.819388\pi\)
\(338\) 179.643 + 648.293i 0.531489 + 1.91803i
\(339\) 169.419i 0.499762i
\(340\) 0 0
\(341\) 237.651 0.696923
\(342\) 50.6707 14.0410i 0.148160 0.0410554i
\(343\) 542.554i 1.58179i
\(344\) 91.1620 95.9455i 0.265006 0.278911i
\(345\) 0 0
\(346\) 94.6791 + 341.676i 0.273639 + 0.987503i
\(347\) 370.184i 1.06681i 0.845859 + 0.533406i \(0.179088\pi\)
−0.845859 + 0.533406i \(0.820912\pi\)
\(348\) −9.79576 16.3182i −0.0281487 0.0468913i
\(349\) −488.570 −1.39991 −0.699957 0.714185i \(-0.746797\pi\)
−0.699957 + 0.714185i \(0.746797\pi\)
\(350\) 0 0
\(351\) 116.811i 0.332794i
\(352\) 101.162 454.091i 0.287391 1.29003i
\(353\) 649.728 1.84059 0.920295 0.391226i \(-0.127949\pi\)
0.920295 + 0.391226i \(0.127949\pi\)
\(354\) 40.0224 + 144.432i 0.113058 + 0.407999i
\(355\) 0 0
\(356\) −188.186 + 112.968i −0.528612 + 0.317325i
\(357\) −263.113 −0.737012
\(358\) 198.227 54.9292i 0.553708 0.153434i
\(359\) 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
\(362\) −61.6395 222.443i −0.170275 0.614484i
\(363\) 156.508i 0.431150i
\(364\) −554.058 922.970i −1.52214 2.53563i
\(365\) 0 0
\(366\) −189.508 + 52.5131i −0.517782 + 0.143479i
\(367\) 46.2347i 0.125980i 0.998014 + 0.0629900i \(0.0200636\pi\)
−0.998014 + 0.0629900i \(0.979936\pi\)
\(368\) 70.5558 + 37.5900i 0.191728 + 0.102147i
\(369\) −128.276 −0.347631
\(370\) 0 0
\(371\) 1126.61i 3.03668i
\(372\) 97.1006 58.2893i 0.261023 0.156692i
\(373\) −138.262 −0.370676 −0.185338 0.982675i \(-0.559338\pi\)
−0.185338 + 0.982675i \(0.559338\pi\)
\(374\) −355.554 + 98.5247i −0.950679 + 0.263435i
\(375\) 0 0
\(376\) −267.759 + 281.809i −0.712124 + 0.749491i
\(377\) −61.7559 −0.163809
\(378\) −33.2231 119.895i −0.0878919 0.317182i
\(379\) 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
\(382\) 368.716 102.172i 0.965226 0.267466i
\(383\) 62.7205i 0.163761i −0.996642 0.0818805i \(-0.973907\pi\)
0.996642 0.0818805i \(-0.0260926\pi\)
\(384\) −70.0431 210.347i −0.182404 0.547779i
\(385\) 0 0
\(386\) −85.6298 309.019i −0.221839 0.800567i
\(387\) 49.6306i 0.128244i
\(388\) 48.5623 29.1519i 0.125161 0.0751338i
\(389\) 110.130 0.283112 0.141556 0.989930i \(-0.454790\pi\)
0.141556 + 0.989930i \(0.454790\pi\)
\(390\) 0 0
\(391\) 63.4012i 0.162152i
\(392\) 547.016 + 519.744i 1.39545 + 1.32588i
\(393\) 142.109 0.361600
\(394\) 189.641 + 684.372i 0.481322 + 1.73698i
\(395\) 0 0
\(396\) −89.7910 149.577i −0.226745 0.377720i
\(397\) −292.953 −0.737916 −0.368958 0.929446i \(-0.620285\pi\)
−0.368958 + 0.929446i \(0.620285\pi\)
\(398\) 170.000 47.1074i 0.427136 0.118360i
\(399\) 181.712i 0.455419i
\(400\) 0 0
\(401\) 518.103 1.29203 0.646014 0.763325i \(-0.276435\pi\)
0.646014 + 0.763325i \(0.276435\pi\)
\(402\) −56.5304 204.006i −0.140623 0.507477i
\(403\) 367.476i 0.911851i
\(404\) 560.419 336.419i 1.38718 0.832720i
\(405\) 0 0
\(406\) 63.3864 17.5645i 0.156124 0.0432623i
\(407\) 472.306i 1.16046i
\(408\) −121.109 + 127.464i −0.296835 + 0.312411i
\(409\) −181.984 −0.444948 −0.222474 0.974939i \(-0.571413\pi\)
−0.222474 + 0.974939i \(0.571413\pi\)
\(410\) 0 0
\(411\) 440.736i 1.07235i
\(412\) 349.142 + 581.614i 0.847432 + 1.41168i
\(413\) −517.953 −1.25412
\(414\) 28.8905 8.00563i 0.0697839 0.0193373i
\(415\) 0 0
\(416\) −702.155 156.425i −1.68787 0.376022i
\(417\) −136.743 −0.327920
\(418\) 68.0435 + 245.554i 0.162784 + 0.587450i
\(419\) 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 \(0.687234\pi\)
\(422\) −367.327 + 101.787i −0.870442 + 0.241201i
\(423\) 145.774i 0.344619i
\(424\) 545.779 + 518.568i 1.28721 + 1.22304i
\(425\) 0 0
\(426\) 36.6915 + 132.411i 0.0861303 + 0.310825i
\(427\) 679.603i 1.59158i
\(428\) 16.7754 + 27.9451i 0.0391948 + 0.0652923i
\(429\) −566.073 −1.31952
\(430\) 0 0
\(431\) 685.527i 1.59055i −0.606248 0.795275i \(-0.707326\pi\)
0.606248 0.795275i \(-0.292674\pi\)
\(432\) −73.3746 39.0918i −0.169849 0.0904902i
\(433\) −592.777 −1.36900 −0.684500 0.729013i \(-0.739979\pi\)
−0.684500 + 0.729013i \(0.739979\pi\)
\(434\) 104.517 + 377.178i 0.240822 + 0.869074i
\(435\) 0 0
\(436\) 86.5343 51.9464i 0.198473 0.119143i
\(437\) −43.7864 −0.100198
\(438\) −332.312 + 92.0844i −0.758704 + 0.210238i
\(439\) 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
\(442\) 152.347 + 549.788i 0.344677 + 1.24386i
\(443\) 54.2868i 0.122544i −0.998121 0.0612718i \(-0.980484\pi\)
0.998121 0.0612718i \(-0.0195156\pi\)
\(444\) 115.844 + 192.977i 0.260910 + 0.434633i
\(445\) 0 0
\(446\) 152.815 42.3454i 0.342635 0.0949449i
\(447\) 56.0202i 0.125325i
\(448\) 765.184 39.1506i 1.70800 0.0873897i
\(449\) −428.051 −0.953343 −0.476671 0.879082i \(-0.658157\pi\)
−0.476671 + 0.879082i \(0.658157\pi\)
\(450\) 0 0
\(451\) 621.634i 1.37835i
\(452\) 335.456 201.374i 0.742159 0.445517i
\(453\) 67.1954 0.148334
\(454\) −681.605 + 188.874i −1.50133 + 0.416022i
\(455\) 0 0
\(456\) 88.0294 + 83.6405i 0.193047 + 0.183422i
\(457\) 66.5848 0.145700 0.0728498 0.997343i \(-0.476791\pi\)
0.0728498 + 0.997343i \(0.476791\pi\)
\(458\) −12.1722 43.9269i −0.0265769 0.0959103i
\(459\) 65.9342i 0.143648i
\(460\) 0 0
\(461\) −238.626 −0.517627 −0.258814 0.965927i \(-0.583332\pi\)
−0.258814 + 0.965927i \(0.583332\pi\)
\(462\) 581.019 161.002i 1.25762 0.348488i
\(463\) 386.958i 0.835762i 0.908502 + 0.417881i \(0.137227\pi\)
−0.908502 + 0.417881i \(0.862773\pi\)
\(464\) 20.6672 38.7919i 0.0445413 0.0836032i
\(465\) 0 0
\(466\) 101.320 + 365.641i 0.217425 + 0.784638i
\(467\) 235.964i 0.505276i −0.967561 0.252638i \(-0.918702\pi\)
0.967561 0.252638i \(-0.0812981\pi\)
\(468\) −231.289 + 138.843i −0.494208 + 0.296672i
\(469\) 731.593 1.55990
\(470\) 0 0
\(471\) 76.5602i 0.162548i
\(472\) −238.409 + 250.919i −0.505104 + 0.531608i
\(473\) 240.513 0.508485
\(474\) −9.97018 35.9802i −0.0210341 0.0759076i
\(475\) 0 0
\(476\) −312.740 520.974i −0.657016 1.09448i
\(477\) 282.320 0.591866
\(478\) 516.107 143.014i 1.07972 0.299193i
\(479\) 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
\(482\) −161.112 581.417i −0.334257 1.20626i
\(483\) 103.606i 0.214504i
\(484\) 309.890 186.027i 0.640270 0.384353i
\(485\) 0 0
\(486\) −30.0447 + 8.32546i −0.0618205 + 0.0171306i
\(487\) 880.801i 1.80863i −0.426869 0.904314i \(-0.640383\pi\)
0.426869 0.904314i \(-0.359617\pi\)
\(488\) −329.230 312.815i −0.674651 0.641015i
\(489\) 91.6888 0.187503
\(490\) 0 0
\(491\) 86.4466i 0.176062i −0.996118 0.0880312i \(-0.971942\pi\)
0.996118 0.0880312i \(-0.0280575\pi\)
\(492\) −152.470 253.991i −0.309899 0.516241i
\(493\) −34.8583 −0.0707065
\(494\) 379.697 105.215i 0.768617 0.212985i
\(495\) 0 0
\(496\) 230.830 + 122.979i 0.465383 + 0.247942i
\(497\) −474.846 −0.955425
\(498\) 129.750 + 468.239i 0.260542 + 0.940239i
\(499\) 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
\(502\) 121.789 33.7479i 0.242607 0.0672269i
\(503\) 17.5479i 0.0348865i 0.999848 + 0.0174433i \(0.00555265\pi\)
−0.999848 + 0.0174433i \(0.994447\pi\)
\(504\) 197.907 208.291i 0.392672 0.413277i
\(505\) 0 0
\(506\) 38.7958 + 140.006i 0.0766716 + 0.276691i
\(507\) 582.595i 1.14910i
\(508\) −344.967 574.659i −0.679069 1.13122i
\(509\) 609.132 1.19672 0.598362 0.801226i \(-0.295819\pi\)
0.598362 + 0.801226i \(0.295819\pi\)
\(510\) 0 0
\(511\) 1191.72i 2.33213i
\(512\) 333.241 388.709i 0.650861 0.759197i
\(513\) 45.5357 0.0887636
\(514\) −80.4959 290.492i −0.156607 0.565159i
\(515\) 0 0
\(516\) 98.2703 58.9915i 0.190446 0.114325i
\(517\) −706.430 −1.36640
\(518\) −749.602 + 207.716i −1.44711 + 0.400997i
\(519\) 307.050i 0.591619i
\(520\) 0 0
\(521\) 433.724 0.832484 0.416242 0.909254i \(-0.363347\pi\)
0.416242 + 0.909254i \(0.363347\pi\)
\(522\) −4.40153 15.8841i −0.00843205 0.0304294i
\(523\) 473.223i 0.904823i −0.891809 0.452412i \(-0.850564\pi\)
0.891809 0.452412i \(-0.149436\pi\)
\(524\) 168.912 + 281.380i 0.322351 + 0.536985i
\(525\) 0 0
\(526\) −392.712 + 108.821i −0.746601 + 0.206885i
\(527\) 207.423i 0.393592i
\(528\) 189.442 355.579i 0.358791 0.673444i
\(529\) 504.035 0.952807
\(530\) 0 0
\(531\) 129.795i 0.244435i
\(532\) −359.797 + 215.985i −0.676310 + 0.405988i
\(533\) −961.224 −1.80342
\(534\) −183.181 + 50.7597i −0.343035 + 0.0950556i
\(535\) 0 0
\(536\) 336.746 354.416i 0.628257 0.661223i
\(537\) 178.139 0.331730
\(538\) 40.8029 + 147.249i 0.0758418 + 0.273696i
\(539\) 1371.24i 2.54405i
\(540\) 0 0
\(541\) 294.889 0.545081 0.272540 0.962144i \(-0.412136\pi\)
0.272540 + 0.962144i \(0.412136\pi\)
\(542\) 326.142 90.3747i 0.601739 0.166743i
\(543\) 199.901i 0.368141i
\(544\) −396.333 88.2946i −0.728554 0.162306i
\(545\) 0 0
\(546\) −248.955 898.422i −0.455961 1.64546i
\(547\) 966.695i 1.76727i 0.468179 + 0.883634i \(0.344910\pi\)
−0.468179 + 0.883634i \(0.655090\pi\)
\(548\) −872.673 + 523.864i −1.59247 + 0.955956i
\(549\) −170.303 −0.310207
\(550\) 0 0
\(551\) 24.0740i 0.0436914i
\(552\) 50.1910 + 47.6887i 0.0909258 + 0.0863925i
\(553\) 129.030 0.233327
\(554\) 146.279 + 527.889i 0.264042 + 0.952868i
\(555\) 0 0
\(556\) −162.534 270.755i −0.292327 0.486969i
\(557\) −74.2603 −0.133322 −0.0666609 0.997776i \(-0.521235\pi\)
−0.0666609 + 0.997776i \(0.521235\pi\)
\(558\) 94.5180 26.1911i 0.169387 0.0469375i
\(559\) 371.903i 0.665300i
\(560\) 0 0
\(561\) −319.522 −0.569558
\(562\) −166.457 600.708i −0.296187 1.06887i
\(563\) 663.688i 1.17884i −0.807826 0.589421i \(-0.799356\pi\)
0.807826 0.589421i \(-0.200644\pi\)
\(564\) −288.637 + 173.268i −0.511767 + 0.307213i
\(565\) 0 0
\(566\) 509.916 141.299i 0.900912 0.249645i
\(567\) 107.745i 0.190026i
\(568\) −218.567 + 230.036i −0.384802 + 0.404993i
\(569\) −667.450 −1.17302 −0.586511 0.809941i \(-0.699499\pi\)
−0.586511 + 0.809941i \(0.699499\pi\)
\(570\) 0 0
\(571\) 185.898i 0.325565i −0.986662 0.162782i \(-0.947953\pi\)
0.986662 0.162782i \(-0.0520469\pi\)
\(572\) −672.841 1120.84i −1.17630 1.95952i
\(573\) 331.350 0.578273
\(574\) 986.603 273.390i 1.71882 0.476289i
\(575\) 0 0
\(576\) −9.81084 191.749i −0.0170327 0.332898i
\(577\) 664.331 1.15135 0.575676 0.817678i \(-0.304739\pi\)
0.575676 + 0.817678i \(0.304739\pi\)
\(578\) −68.3557 246.681i −0.118263 0.426783i
\(579\) 277.703i 0.479625i
\(580\) 0 0
\(581\) −1679.17 −2.89014
\(582\) 47.2707 13.0988i 0.0812212 0.0225066i
\(583\) 1368.14i 2.34673i
\(584\) −577.321 548.537i −0.988563 0.939276i
\(585\) 0 0
\(586\) −64.7734 233.753i −0.110535 0.398896i
\(587\) 763.083i 1.29997i −0.759946 0.649986i \(-0.774775\pi\)
0.759946 0.649986i \(-0.225225\pi\)
\(588\) 336.329 + 560.270i 0.571989 + 0.952841i
\(589\) −143.251 −0.243211
\(590\) 0 0
\(591\) 615.018i 1.04064i
\(592\) −244.408 + 458.750i −0.412852 + 0.774915i
\(593\) −286.193 −0.482618 −0.241309 0.970448i \(-0.577577\pi\)
−0.241309 + 0.970448i \(0.577577\pi\)
\(594\) −40.3458 145.599i −0.0679222 0.245116i
\(595\) 0 0
\(596\) 110.922 66.5862i 0.186111 0.111722i
\(597\) 152.772 0.255900
\(598\) 216.489 59.9895i 0.362021 0.100317i
\(599\) 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 \(0.426372\pi\)
\(602\) 105.776 + 381.722i 0.175707 + 0.634089i
\(603\) 183.332i 0.304033i
\(604\) 79.8692 + 133.049i 0.132234 + 0.220280i
\(605\) 0 0
\(606\) 545.514 151.163i 0.900188 0.249444i
\(607\) 52.1487i 0.0859121i −0.999077 0.0429561i \(-0.986322\pi\)
0.999077 0.0429561i \(-0.0136775\pi\)
\(608\) −60.9784 + 273.717i −0.100293 + 0.450193i
\(609\) 56.9628 0.0935349
\(610\) 0 0
\(611\) 1092.34i 1.78779i
\(612\) −130.552 + 78.3702i −0.213320 + 0.128056i
\(613\) 898.128 1.46513 0.732567 0.680695i \(-0.238322\pi\)
0.732567 + 0.680695i \(0.238322\pi\)
\(614\) −311.787 + 86.3968i −0.507796 + 0.140711i
\(615\) 0 0
\(616\) 1009.39 + 959.070i 1.63863 + 1.55693i
\(617\) 636.868 1.03220 0.516101 0.856528i \(-0.327383\pi\)
0.516101 + 0.856528i \(0.327383\pi\)
\(618\) 156.880 + 566.145i 0.253851 + 0.916092i
\(619\) 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
\(622\) −50.8466 + 14.0897i −0.0817469 + 0.0226522i
\(623\) 656.911i 1.05443i
\(624\) −549.826 292.931i −0.881132 0.469441i
\(625\) 0 0
\(626\) −2.88350 10.4059i −0.00460623 0.0166229i
\(627\) 220.669i 0.351945i
\(628\) 151.592 91.0004i 0.241388 0.144905i
\(629\) 412.231 0.655376
\(630\) 0 0
\(631\) 578.160i 0.916261i −0.888885 0.458130i \(-0.848519\pi\)
0.888885 0.458130i \(-0.151481\pi\)
\(632\) 59.3913 62.5078i 0.0939736 0.0989047i
\(633\) −330.102 −0.521488
\(634\) −144.285 520.693i −0.227579 0.821283i
\(635\) 0 0
\(636\) 335.569 + 559.003i 0.527624 + 0.878936i
\(637\) 2120.34 3.32863
\(638\) 76.9757 21.3301i 0.120652 0.0334328i
\(639\) 118.993i 0.186217i
\(640\) 0 0
\(641\) −35.3085 −0.0550834 −0.0275417 0.999621i \(-0.508768\pi\)
−0.0275417 + 0.999621i \(0.508768\pi\)
\(642\) 7.53768 + 27.2018i 0.0117409 + 0.0423704i
\(643\) 1045.67i 1.62623i 0.582100 + 0.813117i \(0.302231\pi\)
−0.582100 + 0.813117i \(0.697769\pi\)
\(644\) −205.143 + 123.147i −0.318544 + 0.191222i
\(645\) 0 0
\(646\) 214.321 59.3888i 0.331766 0.0919331i
\(647\) 2.71164i 0.00419110i 0.999998 + 0.00209555i \(0.000667035\pi\)
−0.999998 + 0.00209555i \(0.999333\pi\)
\(648\) −52.1962 49.5939i −0.0805497 0.0765338i
\(649\) −628.996 −0.969177
\(650\) 0 0
\(651\) 338.955i 0.520668i
\(652\) 108.982 + 181.547i 0.167151 + 0.278446i
\(653\) 206.765 0.316639 0.158319 0.987388i \(-0.449392\pi\)
0.158319 + 0.987388i \(0.449392\pi\)
\(654\) 84.2327 23.3411i 0.128796 0.0356897i
\(655\) 0 0
\(656\) 321.682 603.792i 0.490370 0.920415i
\(657\) −298.636 −0.454544
\(658\) −310.682 1121.18i −0.472161 1.70393i
\(659\) 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 \(0.119672\pi\)
\(662\) −926.540 + 256.746i −1.39961 + 0.387834i
\(663\) 494.072i 0.745207i
\(664\) −772.907 + 813.464i −1.16402 + 1.22510i
\(665\) 0 0
\(666\) 52.0521 + 187.845i 0.0781564 + 0.282049i
\(667\) 13.7261i 0.0205788i
\(668\) 369.076 + 614.820i 0.552508 + 0.920390i
\(669\) 137.329 0.205275
\(670\) 0 0
\(671\) 825.303i 1.22996i
\(672\) 647.658 + 144.284i 0.963777 + 0.214709i
\(673\) 753.492 1.11960 0.559801 0.828627i \(-0.310878\pi\)
0.559801 + 0.828627i \(0.310878\pi\)
\(674\) −303.561 1095.48i −0.450387 1.62535i
\(675\) 0 0
\(676\) −1153.56 + 692.479i −1.70645 + 1.02438i
\(677\) −332.246 −0.490762 −0.245381 0.969427i \(-0.578913\pi\)
−0.245381 + 0.969427i \(0.578913\pi\)
\(678\) 326.534 90.4832i 0.481613 0.133456i
\(679\) 169.520i 0.249661i
\(680\) 0 0
\(681\) −612.531 −0.899458
\(682\) 126.924 + 458.041i 0.186106 + 0.671615i
\(683\) 1120.62i 1.64074i 0.571835 + 0.820368i \(0.306232\pi\)
−0.571835 + 0.820368i \(0.693768\pi\)
\(684\) 54.1243 + 90.1623i 0.0791291 + 0.131816i
\(685\) 0 0
\(686\) −1045.70 + 289.767i −1.52435 + 0.422400i
\(687\) 39.4753i 0.0574605i
\(688\) 233.610 + 124.461i 0.339550 + 0.180902i
\(689\) 2115.54 3.07045
\(690\) 0 0
\(691\) 331.115i 0.479182i −0.970874 0.239591i \(-0.922987\pi\)
0.970874 0.239591i \(-0.0770134\pi\)
\(692\) −607.970 + 364.964i −0.878570 + 0.527404i
\(693\) 522.139 0.753447
\(694\) −713.482 + 197.707i −1.02807 + 0.284881i
\(695\) 0 0
\(696\) 26.2194 27.5953i 0.0376716 0.0396484i
\(697\) −542.566 −0.778431
\(698\) −260.935 941.655i −0.373832 1.34908i
\(699\) 328.587i 0.470081i
\(700\) 0 0
\(701\) −564.971 −0.805949 −0.402975 0.915211i \(-0.632024\pi\)
−0.402975 + 0.915211i \(0.632024\pi\)
\(702\) −225.138 + 62.3861i −0.320709 + 0.0888691i
\(703\) 284.697i 0.404974i
\(704\) 929.230 47.5440i 1.31993 0.0675341i
\(705\) 0 0
\(706\) 347.006 + 1252.27i 0.491510 + 1.77375i
\(707\) 1956.29i 2.76703i
\(708\) −256.999 + 154.276i −0.362992 + 0.217904i
\(709\) 1.56083 0.00220146 0.00110073 0.999999i \(-0.499650\pi\)
0.00110073 + 0.999999i \(0.499650\pi\)
\(710\) 0 0
\(711\) 32.3339i 0.0454767i
\(712\) −318.236 302.370i −0.446961 0.424677i
\(713\) −81.6765 −0.114553
\(714\) −140.523 507.117i −0.196811 0.710248i
\(715\) 0 0
\(716\) 211.738 + 352.721i 0.295723 + 0.492627i
\(717\) 463.804 0.646868
\(718\) −782.339 + 216.788i −1.08961 + 0.301933i
\(719\) 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
\(722\) 151.787 + 547.766i 0.210231 + 0.758678i
\(723\) 522.496i 0.722678i
\(724\) 395.810 237.604i 0.546699 0.328183i
\(725\) 0 0
\(726\) 301.648 83.5874i 0.415493 0.115134i
\(727\) 1229.26i 1.69087i −0.534082 0.845433i \(-0.679343\pi\)
0.534082 0.845433i \(-0.320657\pi\)
\(728\) 1483.00 1560.81i 2.03708 2.14397i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 209.922i 0.287170i
\(732\) −202.425 337.207i −0.276536 0.460665i
\(733\) 691.736 0.943705 0.471852 0.881678i \(-0.343586\pi\)
0.471852 + 0.881678i \(0.343586\pi\)
\(734\) −89.1114 + 24.6930i −0.121405 + 0.0336416i
\(735\) 0 0
\(736\) −34.7676 + 156.063i −0.0472385 + 0.212042i
\(737\) 888.438 1.20548
\(738\) −68.5094 247.235i −0.0928312 0.335007i
\(739\) 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
\(742\) −2171.40 + 601.698i −2.92641 + 0.810914i
\(743\) 1006.92i 1.35521i −0.735426 0.677605i \(-0.763018\pi\)
0.735426 0.677605i \(-0.236982\pi\)
\(744\) 164.205 + 156.018i 0.220705 + 0.209701i
\(745\) 0 0
\(746\) −73.8428 266.482i −0.0989850 0.357215i
\(747\) 420.788i 0.563303i
\(748\) −379.787 632.664i −0.507737 0.845808i
\(749\) −97.5496 −0.130240
\(750\) 0 0
\(751\) 1110.14i 1.47822i 0.673587 + 0.739108i \(0.264753\pi\)
−0.673587 + 0.739108i \(0.735247\pi\)
\(752\) −686.154 365.562i −0.912439 0.486120i
\(753\) 109.447 0.145347
\(754\) −32.9825 119.026i −0.0437433 0.157860i
\(755\) 0 0
\(756\) 213.338 128.067i 0.282193 0.169400i
\(757\) 326.752 0.431641 0.215821 0.976433i \(-0.430757\pi\)
0.215821 + 0.976433i \(0.430757\pi\)
\(758\) −490.547 + 135.932i −0.647160 + 0.179329i
\(759\) 125.817i 0.165767i
\(760\) 0 0
\(761\) 162.162 0.213091 0.106546 0.994308i \(-0.466021\pi\)
0.106546 + 0.994308i \(0.466021\pi\)
\(762\) −155.004 559.375i −0.203417 0.734088i
\(763\) 302.070i 0.395898i
\(764\) 393.847 + 656.085i 0.515507 + 0.858750i
\(765\) 0 0
\(766\) 120.886 33.4977i 0.157814 0.0437306i
\(767\) 972.608i 1.26807i
\(768\) 368.009 247.341i 0.479178 0.322059i
\(769\) −154.694 −0.201162 −0.100581 0.994929i \(-0.532070\pi\)
−0.100581 + 0.994929i \(0.532070\pi\)
\(770\) 0 0
\(771\) 261.053i 0.338590i
\(772\) 549.861 330.081i 0.712255 0.427566i
\(773\) −208.302 −0.269472 −0.134736 0.990882i \(-0.543019\pi\)
−0.134736 + 0.990882i \(0.543019\pi\)
\(774\) 95.6566 26.5066i 0.123587 0.0342463i
\(775\) 0 0
\(776\) 82.1226 + 78.0283i 0.105828 + 0.100552i
\(777\) −673.637 −0.866972
\(778\) 58.8183 + 212.262i 0.0756019 + 0.272831i
\(779\) 374.709i 0.481013i
\(780\) 0 0
\(781\) −576.648 −0.738346
\(782\) 122.198 33.8612i 0.156263 0.0433008i
\(783\) 14.2744i 0.0182304i
\(784\) −709.590 + 1331.89i −0.905089 + 1.69884i
\(785\) 0 0
\(786\) 75.8972 + 273.896i 0.0965613 + 0.348468i
\(787\)