Properties

Label 45.3.g.b.28.2
Level $45$
Weight $3$
Character 45.28
Analytic conductor $1.226$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 45.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.22616118962\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 28.2
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 45.28
Dual form 45.3.g.b.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+(2.22474 - 2.22474i) q^{2} -5.89898i q^{4} +(-2.67423 + 4.22474i) q^{5} +(-1.44949 + 1.44949i) q^{7} +(-4.22474 - 4.22474i) q^{8} +O(q^{10})\) \(q+(2.22474 - 2.22474i) q^{2} -5.89898i q^{4} +(-2.67423 + 4.22474i) q^{5} +(-1.44949 + 1.44949i) q^{7} +(-4.22474 - 4.22474i) q^{8} +(3.44949 + 15.3485i) q^{10} +3.34847 q^{11} +(-10.4495 - 10.4495i) q^{13} +6.44949i q^{14} +4.79796 q^{16} +(2.65153 - 2.65153i) q^{17} +20.6969i q^{19} +(24.9217 + 15.7753i) q^{20} +(7.44949 - 7.44949i) q^{22} +(-16.4495 - 16.4495i) q^{23} +(-10.6969 - 22.5959i) q^{25} -46.4949 q^{26} +(8.55051 + 8.55051i) q^{28} +0.853572i q^{29} -18.6969 q^{31} +(27.5732 - 27.5732i) q^{32} -11.7980i q^{34} +(-2.24745 - 10.0000i) q^{35} +(38.0454 - 38.0454i) q^{37} +(46.0454 + 46.0454i) q^{38} +(29.1464 - 6.55051i) q^{40} +28.6969 q^{41} +(22.4949 + 22.4949i) q^{43} -19.7526i q^{44} -73.1918 q^{46} +(-19.7526 + 19.7526i) q^{47} +44.7980i q^{49} +(-74.0681 - 26.4722i) q^{50} +(-61.6413 + 61.6413i) q^{52} +(-28.6969 - 28.6969i) q^{53} +(-8.95459 + 14.1464i) q^{55} +12.2474 q^{56} +(1.89898 + 1.89898i) q^{58} +111.934i q^{59} +94.0908 q^{61} +(-41.5959 + 41.5959i) q^{62} -103.495i q^{64} +(72.0908 - 16.2020i) q^{65} +(-54.8990 + 54.8990i) q^{67} +(-15.6413 - 15.6413i) q^{68} +(-27.2474 - 17.2474i) q^{70} +68.0000 q^{71} +(-39.7878 - 39.7878i) q^{73} -169.283i q^{74} +122.091 q^{76} +(-4.85357 + 4.85357i) q^{77} -24.4949i q^{79} +(-12.8309 + 20.2702i) q^{80} +(63.8434 - 63.8434i) q^{82} +(21.1464 + 21.1464i) q^{83} +(4.11123 + 18.2929i) q^{85} +100.091 q^{86} +(-14.1464 - 14.1464i) q^{88} -94.1816i q^{89} +30.2929 q^{91} +(-97.0352 + 97.0352i) q^{92} +87.8888i q^{94} +(-87.4393 - 55.3485i) q^{95} +(14.5959 - 14.5959i) q^{97} +(99.6640 + 99.6640i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} + 4q^{5} + 4q^{7} - 12q^{8} + O(q^{10}) \) \( 4q + 4q^{2} + 4q^{5} + 4q^{7} - 12q^{8} + 4q^{10} - 16q^{11} - 32q^{13} - 20q^{16} + 40q^{17} + 36q^{20} + 20q^{22} - 56q^{23} + 16q^{25} - 88q^{26} + 44q^{28} - 16q^{31} + 76q^{32} + 40q^{35} + 64q^{37} + 96q^{38} + 48q^{40} + 56q^{41} - 8q^{43} - 136q^{46} - 128q^{47} - 164q^{50} - 80q^{52} - 56q^{53} - 124q^{55} - 12q^{58} + 200q^{61} - 88q^{62} + 112q^{65} - 200q^{67} + 104q^{68} - 60q^{70} + 272q^{71} + 76q^{73} + 312q^{76} - 88q^{77} - 164q^{80} + 128q^{82} + 16q^{83} + 232q^{85} + 224q^{86} + 12q^{88} - 16q^{91} - 104q^{92} - 144q^{95} - 20q^{97} + 188q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.22474 2.22474i 1.11237 1.11237i 0.119543 0.992829i \(-0.461857\pi\)
0.992829 0.119543i \(-0.0381431\pi\)
\(3\) 0 0
\(4\) 5.89898i 1.47474i
\(5\) −2.67423 + 4.22474i −0.534847 + 0.844949i
\(6\) 0 0
\(7\) −1.44949 + 1.44949i −0.207070 + 0.207070i −0.803021 0.595951i \(-0.796775\pi\)
0.595951 + 0.803021i \(0.296775\pi\)
\(8\) −4.22474 4.22474i −0.528093 0.528093i
\(9\) 0 0
\(10\) 3.44949 + 15.3485i 0.344949 + 1.53485i
\(11\) 3.34847 0.304406 0.152203 0.988349i \(-0.451363\pi\)
0.152203 + 0.988349i \(0.451363\pi\)
\(12\) 0 0
\(13\) −10.4495 10.4495i −0.803807 0.803807i 0.179881 0.983688i \(-0.442429\pi\)
−0.983688 + 0.179881i \(0.942429\pi\)
\(14\) 6.44949i 0.460678i
\(15\) 0 0
\(16\) 4.79796 0.299872
\(17\) 2.65153 2.65153i 0.155972 0.155972i −0.624807 0.780779i \(-0.714822\pi\)
0.780779 + 0.624807i \(0.214822\pi\)
\(18\) 0 0
\(19\) 20.6969i 1.08931i 0.838659 + 0.544656i \(0.183340\pi\)
−0.838659 + 0.544656i \(0.816660\pi\)
\(20\) 24.9217 + 15.7753i 1.24608 + 0.788763i
\(21\) 0 0
\(22\) 7.44949 7.44949i 0.338613 0.338613i
\(23\) −16.4495 16.4495i −0.715195 0.715195i 0.252422 0.967617i \(-0.418773\pi\)
−0.967617 + 0.252422i \(0.918773\pi\)
\(24\) 0 0
\(25\) −10.6969 22.5959i −0.427878 0.903837i
\(26\) −46.4949 −1.78827
\(27\) 0 0
\(28\) 8.55051 + 8.55051i 0.305375 + 0.305375i
\(29\) 0.853572i 0.0294335i 0.999892 + 0.0147168i \(0.00468466\pi\)
−0.999892 + 0.0147168i \(0.995315\pi\)
\(30\) 0 0
\(31\) −18.6969 −0.603127 −0.301564 0.953446i \(-0.597509\pi\)
−0.301564 + 0.953446i \(0.597509\pi\)
\(32\) 27.5732 27.5732i 0.861663 0.861663i
\(33\) 0 0
\(34\) 11.7980i 0.346999i
\(35\) −2.24745 10.0000i −0.0642128 0.285714i
\(36\) 0 0
\(37\) 38.0454 38.0454i 1.02825 1.02825i 0.0286652 0.999589i \(-0.490874\pi\)
0.999589 0.0286652i \(-0.00912566\pi\)
\(38\) 46.0454 + 46.0454i 1.21172 + 1.21172i
\(39\) 0 0
\(40\) 29.1464 6.55051i 0.728661 0.163763i
\(41\) 28.6969 0.699925 0.349963 0.936764i \(-0.386194\pi\)
0.349963 + 0.936764i \(0.386194\pi\)
\(42\) 0 0
\(43\) 22.4949 + 22.4949i 0.523137 + 0.523137i 0.918517 0.395380i \(-0.129387\pi\)
−0.395380 + 0.918517i \(0.629387\pi\)
\(44\) 19.7526i 0.448922i
\(45\) 0 0
\(46\) −73.1918 −1.59113
\(47\) −19.7526 + 19.7526i −0.420267 + 0.420267i −0.885296 0.465029i \(-0.846044\pi\)
0.465029 + 0.885296i \(0.346044\pi\)
\(48\) 0 0
\(49\) 44.7980i 0.914244i
\(50\) −74.0681 26.4722i −1.48136 0.529444i
\(51\) 0 0
\(52\) −61.6413 + 61.6413i −1.18541 + 1.18541i
\(53\) −28.6969 28.6969i −0.541452 0.541452i 0.382503 0.923954i \(-0.375062\pi\)
−0.923954 + 0.382503i \(0.875062\pi\)
\(54\) 0 0
\(55\) −8.95459 + 14.1464i −0.162811 + 0.257208i
\(56\) 12.2474 0.218704
\(57\) 0 0
\(58\) 1.89898 + 1.89898i 0.0327410 + 0.0327410i
\(59\) 111.934i 1.89719i 0.316493 + 0.948595i \(0.397495\pi\)
−0.316493 + 0.948595i \(0.602505\pi\)
\(60\) 0 0
\(61\) 94.0908 1.54247 0.771236 0.636549i \(-0.219639\pi\)
0.771236 + 0.636549i \(0.219639\pi\)
\(62\) −41.5959 + 41.5959i −0.670902 + 0.670902i
\(63\) 0 0
\(64\) 103.495i 1.61711i
\(65\) 72.0908 16.2020i 1.10909 0.249262i
\(66\) 0 0
\(67\) −54.8990 + 54.8990i −0.819388 + 0.819388i −0.986019 0.166631i \(-0.946711\pi\)
0.166631 + 0.986019i \(0.446711\pi\)
\(68\) −15.6413 15.6413i −0.230019 0.230019i
\(69\) 0 0
\(70\) −27.2474 17.2474i −0.389249 0.246392i
\(71\) 68.0000 0.957746 0.478873 0.877884i \(-0.341045\pi\)
0.478873 + 0.877884i \(0.341045\pi\)
\(72\) 0 0
\(73\) −39.7878 39.7878i −0.545038 0.545038i 0.379964 0.925001i \(-0.375936\pi\)
−0.925001 + 0.379964i \(0.875936\pi\)
\(74\) 169.283i 2.28760i
\(75\) 0 0
\(76\) 122.091 1.60646
\(77\) −4.85357 + 4.85357i −0.0630334 + 0.0630334i
\(78\) 0 0
\(79\) 24.4949i 0.310062i −0.987910 0.155031i \(-0.950452\pi\)
0.987910 0.155031i \(-0.0495477\pi\)
\(80\) −12.8309 + 20.2702i −0.160386 + 0.253377i
\(81\) 0 0
\(82\) 63.8434 63.8434i 0.778578 0.778578i
\(83\) 21.1464 + 21.1464i 0.254776 + 0.254776i 0.822926 0.568149i \(-0.192340\pi\)
−0.568149 + 0.822926i \(0.692340\pi\)
\(84\) 0 0
\(85\) 4.11123 + 18.2929i 0.0483674 + 0.215210i
\(86\) 100.091 1.16385
\(87\) 0 0
\(88\) −14.1464 14.1464i −0.160755 0.160755i
\(89\) 94.1816i 1.05822i −0.848553 0.529110i \(-0.822526\pi\)
0.848553 0.529110i \(-0.177474\pi\)
\(90\) 0 0
\(91\) 30.2929 0.332889
\(92\) −97.0352 + 97.0352i −1.05473 + 1.05473i
\(93\) 0 0
\(94\) 87.8888i 0.934987i
\(95\) −87.4393 55.3485i −0.920414 0.582615i
\(96\) 0 0
\(97\) 14.5959 14.5959i 0.150473 0.150473i −0.627856 0.778329i \(-0.716067\pi\)
0.778329 + 0.627856i \(0.216067\pi\)
\(98\) 99.6640 + 99.6640i 1.01698 + 1.01698i
\(99\) 0 0
\(100\) −133.293 + 63.1010i −1.33293 + 0.631010i
\(101\) −173.621 −1.71902 −0.859509 0.511120i \(-0.829231\pi\)
−0.859509 + 0.511120i \(0.829231\pi\)
\(102\) 0 0
\(103\) −64.7526 64.7526i −0.628666 0.628666i 0.319067 0.947732i \(-0.396631\pi\)
−0.947732 + 0.319067i \(0.896631\pi\)
\(104\) 88.2929i 0.848970i
\(105\) 0 0
\(106\) −127.687 −1.20459
\(107\) 4.74235 4.74235i 0.0443210 0.0443210i −0.684599 0.728920i \(-0.740023\pi\)
0.728920 + 0.684599i \(0.240023\pi\)
\(108\) 0 0
\(109\) 39.3031i 0.360579i −0.983614 0.180289i \(-0.942297\pi\)
0.983614 0.180289i \(-0.0577034\pi\)
\(110\) 11.5505 + 51.3939i 0.105005 + 0.467217i
\(111\) 0 0
\(112\) −6.95459 + 6.95459i −0.0620946 + 0.0620946i
\(113\) −14.3587 14.3587i −0.127068 0.127068i 0.640713 0.767781i \(-0.278639\pi\)
−0.767781 + 0.640713i \(0.778639\pi\)
\(114\) 0 0
\(115\) 113.485 25.5051i 0.986823 0.221784i
\(116\) 5.03520 0.0434069
\(117\) 0 0
\(118\) 249.025 + 249.025i 2.11038 + 2.11038i
\(119\) 7.68673i 0.0645944i
\(120\) 0 0
\(121\) −109.788 −0.907337
\(122\) 209.328 209.328i 1.71580 1.71580i
\(123\) 0 0
\(124\) 110.293i 0.889459i
\(125\) 124.068 + 15.2350i 0.992545 + 0.121880i
\(126\) 0 0
\(127\) −114.621 + 114.621i −0.902527 + 0.902527i −0.995654 0.0931273i \(-0.970314\pi\)
0.0931273 + 0.995654i \(0.470314\pi\)
\(128\) −119.957 119.957i −0.937163 0.937163i
\(129\) 0 0
\(130\) 124.338 196.429i 0.956448 1.51099i
\(131\) 26.1362 0.199513 0.0997566 0.995012i \(-0.468194\pi\)
0.0997566 + 0.995012i \(0.468194\pi\)
\(132\) 0 0
\(133\) −30.0000 30.0000i −0.225564 0.225564i
\(134\) 244.272i 1.82293i
\(135\) 0 0
\(136\) −22.4041 −0.164736
\(137\) −14.6311 + 14.6311i −0.106796 + 0.106796i −0.758486 0.651689i \(-0.774061\pi\)
0.651689 + 0.758486i \(0.274061\pi\)
\(138\) 0 0
\(139\) 83.1714i 0.598356i −0.954197 0.299178i \(-0.903288\pi\)
0.954197 0.299178i \(-0.0967124\pi\)
\(140\) −58.9898 + 13.2577i −0.421356 + 0.0946975i
\(141\) 0 0
\(142\) 151.283 151.283i 1.06537 1.06537i
\(143\) −34.9898 34.9898i −0.244684 0.244684i
\(144\) 0 0
\(145\) −3.60612 2.28265i −0.0248698 0.0157424i
\(146\) −177.035 −1.21257
\(147\) 0 0
\(148\) −224.429 224.429i −1.51641 1.51641i
\(149\) 119.146i 0.799640i 0.916594 + 0.399820i \(0.130927\pi\)
−0.916594 + 0.399820i \(0.869073\pi\)
\(150\) 0 0
\(151\) −144.969 −0.960062 −0.480031 0.877251i \(-0.659375\pi\)
−0.480031 + 0.877251i \(0.659375\pi\)
\(152\) 87.4393 87.4393i 0.575258 0.575258i
\(153\) 0 0
\(154\) 21.5959i 0.140233i
\(155\) 50.0000 78.9898i 0.322581 0.509612i
\(156\) 0 0
\(157\) 51.1464 51.1464i 0.325773 0.325773i −0.525203 0.850977i \(-0.676011\pi\)
0.850977 + 0.525203i \(0.176011\pi\)
\(158\) −54.4949 54.4949i −0.344904 0.344904i
\(159\) 0 0
\(160\) 42.7526 + 190.227i 0.267203 + 1.18892i
\(161\) 47.6867 0.296191
\(162\) 0 0
\(163\) 189.394 + 189.394i 1.16193 + 1.16193i 0.984054 + 0.177872i \(0.0569213\pi\)
0.177872 + 0.984054i \(0.443079\pi\)
\(164\) 169.283i 1.03221i
\(165\) 0 0
\(166\) 94.0908 0.566812
\(167\) −97.0352 + 97.0352i −0.581049 + 0.581049i −0.935192 0.354142i \(-0.884773\pi\)
0.354142 + 0.935192i \(0.384773\pi\)
\(168\) 0 0
\(169\) 49.3837i 0.292211i
\(170\) 49.8434 + 31.5505i 0.293196 + 0.185591i
\(171\) 0 0
\(172\) 132.697 132.697i 0.771494 0.771494i
\(173\) 34.6311 + 34.6311i 0.200180 + 0.200180i 0.800077 0.599897i \(-0.204792\pi\)
−0.599897 + 0.800077i \(0.704792\pi\)
\(174\) 0 0
\(175\) 48.2577 + 17.2474i 0.275758 + 0.0985568i
\(176\) 16.0658 0.0912831
\(177\) 0 0
\(178\) −209.530 209.530i −1.17714 1.17714i
\(179\) 183.712i 1.02632i −0.858292 0.513161i \(-0.828474\pi\)
0.858292 0.513161i \(-0.171526\pi\)
\(180\) 0 0
\(181\) −21.7276 −0.120042 −0.0600209 0.998197i \(-0.519117\pi\)
−0.0600209 + 0.998197i \(0.519117\pi\)
\(182\) 67.3939 67.3939i 0.370296 0.370296i
\(183\) 0 0
\(184\) 138.990i 0.755379i
\(185\) 58.9898 + 262.474i 0.318864 + 1.41878i
\(186\) 0 0
\(187\) 8.87857 8.87857i 0.0474790 0.0474790i
\(188\) 116.520 + 116.520i 0.619787 + 0.619787i
\(189\) 0 0
\(190\) −317.666 + 71.3939i −1.67193 + 0.375757i
\(191\) 40.0908 0.209900 0.104950 0.994478i \(-0.466532\pi\)
0.104950 + 0.994478i \(0.466532\pi\)
\(192\) 0 0
\(193\) 77.5653 + 77.5653i 0.401893 + 0.401893i 0.878900 0.477007i \(-0.158278\pi\)
−0.477007 + 0.878900i \(0.658278\pi\)
\(194\) 64.9444i 0.334765i
\(195\) 0 0
\(196\) 264.262 1.34828
\(197\) 67.3031 67.3031i 0.341640 0.341640i −0.515344 0.856984i \(-0.672336\pi\)
0.856984 + 0.515344i \(0.172336\pi\)
\(198\) 0 0
\(199\) 251.394i 1.26329i −0.775259 0.631643i \(-0.782381\pi\)
0.775259 0.631643i \(-0.217619\pi\)
\(200\) −50.2702 + 140.654i −0.251351 + 0.703269i
\(201\) 0 0
\(202\) −386.262 + 386.262i −1.91219 + 1.91219i
\(203\) −1.23724 1.23724i −0.00609480 0.00609480i
\(204\) 0 0
\(205\) −76.7423 + 121.237i −0.374353 + 0.591401i
\(206\) −288.116 −1.39862
\(207\) 0 0
\(208\) −50.1362 50.1362i −0.241040 0.241040i
\(209\) 69.3031i 0.331594i
\(210\) 0 0
\(211\) 264.788 1.25492 0.627459 0.778649i \(-0.284095\pi\)
0.627459 + 0.778649i \(0.284095\pi\)
\(212\) −169.283 + 169.283i −0.798503 + 0.798503i
\(213\) 0 0
\(214\) 21.1010i 0.0986029i
\(215\) −155.192 + 34.8786i −0.721822 + 0.162226i
\(216\) 0 0
\(217\) 27.1010 27.1010i 0.124889 0.124889i
\(218\) −87.4393 87.4393i −0.401098 0.401098i
\(219\) 0 0
\(220\) 83.4495 + 52.8230i 0.379316 + 0.240104i
\(221\) −55.4143 −0.250743
\(222\) 0 0
\(223\) −33.4291 33.4291i −0.149906 0.149906i 0.628170 0.778076i \(-0.283804\pi\)
−0.778076 + 0.628170i \(0.783804\pi\)
\(224\) 79.9342i 0.356849i
\(225\) 0 0
\(226\) −63.8888 −0.282694
\(227\) 21.1714 21.1714i 0.0932662 0.0932662i −0.658934 0.752200i \(-0.728992\pi\)
0.752200 + 0.658934i \(0.228992\pi\)
\(228\) 0 0
\(229\) 243.798i 1.06462i 0.846550 + 0.532310i \(0.178676\pi\)
−0.846550 + 0.532310i \(0.821324\pi\)
\(230\) 195.732 309.217i 0.851009 1.34442i
\(231\) 0 0
\(232\) 3.60612 3.60612i 0.0155436 0.0155436i
\(233\) −161.712 161.712i −0.694042 0.694042i 0.269077 0.963119i \(-0.413281\pi\)
−0.963119 + 0.269077i \(0.913281\pi\)
\(234\) 0 0
\(235\) −30.6265 136.272i −0.130326 0.579883i
\(236\) 660.297 2.79787
\(237\) 0 0
\(238\) 17.1010 + 17.1010i 0.0718530 + 0.0718530i
\(239\) 326.202i 1.36486i −0.730950 0.682431i \(-0.760923\pi\)
0.730950 0.682431i \(-0.239077\pi\)
\(240\) 0 0
\(241\) −133.576 −0.554255 −0.277128 0.960833i \(-0.589382\pi\)
−0.277128 + 0.960833i \(0.589382\pi\)
\(242\) −244.250 + 244.250i −1.00930 + 1.00930i
\(243\) 0 0
\(244\) 555.040i 2.27475i
\(245\) −189.260 119.800i −0.772490 0.488981i
\(246\) 0 0
\(247\) 216.272 216.272i 0.875597 0.875597i
\(248\) 78.9898 + 78.9898i 0.318507 + 0.318507i
\(249\) 0 0
\(250\) 309.914 242.126i 1.23966 0.968504i
\(251\) 404.742 1.61252 0.806260 0.591562i \(-0.201488\pi\)
0.806260 + 0.591562i \(0.201488\pi\)
\(252\) 0 0
\(253\) −55.0806 55.0806i −0.217710 0.217710i
\(254\) 510.005i 2.00789i
\(255\) 0 0
\(256\) −119.767 −0.467841
\(257\) 89.2372 89.2372i 0.347227 0.347227i −0.511849 0.859076i \(-0.671039\pi\)
0.859076 + 0.511849i \(0.171039\pi\)
\(258\) 0 0
\(259\) 110.293i 0.425841i
\(260\) −95.5755 425.262i −0.367598 1.63562i
\(261\) 0 0
\(262\) 58.1464 58.1464i 0.221933 0.221933i
\(263\) 341.843 + 341.843i 1.29978 + 1.29978i 0.928532 + 0.371253i \(0.121072\pi\)
0.371253 + 0.928532i \(0.378928\pi\)
\(264\) 0 0
\(265\) 197.980 44.4949i 0.747093 0.167905i
\(266\) −133.485 −0.501822
\(267\) 0 0
\(268\) 323.848 + 323.848i 1.20839 + 1.20839i
\(269\) 3.50052i 0.0130131i −0.999979 0.00650653i \(-0.997929\pi\)
0.999979 0.00650653i \(-0.00207111\pi\)
\(270\) 0 0
\(271\) −103.576 −0.382197 −0.191099 0.981571i \(-0.561205\pi\)
−0.191099 + 0.981571i \(0.561205\pi\)
\(272\) 12.7219 12.7219i 0.0467718 0.0467718i
\(273\) 0 0
\(274\) 65.1010i 0.237595i
\(275\) −35.8184 75.6617i −0.130249 0.275134i
\(276\) 0 0
\(277\) −285.510 + 285.510i −1.03072 + 1.03072i −0.0312080 + 0.999513i \(0.509935\pi\)
−0.999513 + 0.0312080i \(0.990065\pi\)
\(278\) −185.035 185.035i −0.665594 0.665594i
\(279\) 0 0
\(280\) −32.7526 + 51.7423i −0.116973 + 0.184794i
\(281\) −372.697 −1.32632 −0.663162 0.748476i \(-0.730786\pi\)
−0.663162 + 0.748476i \(0.730786\pi\)
\(282\) 0 0
\(283\) −77.1918 77.1918i −0.272763 0.272763i 0.557449 0.830211i \(-0.311780\pi\)
−0.830211 + 0.557449i \(0.811780\pi\)
\(284\) 401.131i 1.41243i
\(285\) 0 0
\(286\) −155.687 −0.544359
\(287\) −41.5959 + 41.5959i −0.144934 + 0.144934i
\(288\) 0 0
\(289\) 274.939i 0.951345i
\(290\) −13.1010 + 2.94439i −0.0451759 + 0.0101531i
\(291\) 0 0
\(292\) −234.707 + 234.707i −0.803792 + 0.803792i
\(293\) 236.565 + 236.565i 0.807390 + 0.807390i 0.984238 0.176848i \(-0.0565901\pi\)
−0.176848 + 0.984238i \(0.556590\pi\)
\(294\) 0 0
\(295\) −472.893 299.338i −1.60303 1.01471i
\(296\) −321.464 −1.08603
\(297\) 0 0
\(298\) 265.070 + 265.070i 0.889498 + 0.889498i
\(299\) 343.778i 1.14976i
\(300\) 0 0
\(301\) −65.2122 −0.216652
\(302\) −322.520 + 322.520i −1.06795 + 1.06795i
\(303\) 0 0
\(304\) 99.3031i 0.326655i
\(305\) −251.621 + 397.510i −0.824987 + 1.30331i
\(306\) 0 0
\(307\) 168.969 168.969i 0.550389 0.550389i −0.376164 0.926553i \(-0.622757\pi\)
0.926553 + 0.376164i \(0.122757\pi\)
\(308\) 28.6311 + 28.6311i 0.0929582 + 0.0929582i
\(309\) 0 0
\(310\) −64.4949 286.969i −0.208048 0.925708i
\(311\) −354.302 −1.13923 −0.569617 0.821910i \(-0.692909\pi\)
−0.569617 + 0.821910i \(0.692909\pi\)
\(312\) 0 0
\(313\) 152.373 + 152.373i 0.486816 + 0.486816i 0.907300 0.420484i \(-0.138140\pi\)
−0.420484 + 0.907300i \(0.638140\pi\)
\(314\) 227.576i 0.724763i
\(315\) 0 0
\(316\) −144.495 −0.457262
\(317\) 427.217 427.217i 1.34769 1.34769i 0.459519 0.888168i \(-0.348022\pi\)
0.888168 0.459519i \(-0.151978\pi\)
\(318\) 0 0
\(319\) 2.85816i 0.00895975i
\(320\) 437.240 + 276.770i 1.36637 + 0.864905i
\(321\) 0 0
\(322\) 106.091 106.091i 0.329475 0.329475i
\(323\) 54.8786 + 54.8786i 0.169903 + 0.169903i
\(324\) 0 0
\(325\) −124.338 + 347.893i −0.382579 + 1.07044i
\(326\) 842.706 2.58499
\(327\) 0 0
\(328\) −121.237 121.237i −0.369626 0.369626i
\(329\) 57.2622i 0.174049i
\(330\) 0 0
\(331\) 489.423 1.47862 0.739310 0.673365i \(-0.235152\pi\)
0.739310 + 0.673365i \(0.235152\pi\)
\(332\) 124.742 124.742i 0.375730 0.375730i
\(333\) 0 0
\(334\) 431.757i 1.29269i
\(335\) −85.1214 378.747i −0.254094 1.13059i
\(336\) 0 0
\(337\) 292.192 292.192i 0.867038 0.867038i −0.125105 0.992143i \(-0.539927\pi\)
0.992143 + 0.125105i \(0.0399269\pi\)
\(338\) 109.866 + 109.866i 0.325048 + 0.325048i
\(339\) 0 0
\(340\) 107.909 24.2520i 0.317380 0.0713295i
\(341\) −62.6061 −0.183596
\(342\) 0 0
\(343\) −135.959 135.959i −0.396382 0.396382i
\(344\) 190.070i 0.552530i
\(345\) 0 0
\(346\) 154.091 0.445349
\(347\) −320.050 + 320.050i −0.922334 + 0.922334i −0.997194 0.0748598i \(-0.976149\pi\)
0.0748598 + 0.997194i \(0.476149\pi\)
\(348\) 0 0
\(349\) 574.009i 1.64473i −0.568964 0.822363i \(-0.692655\pi\)
0.568964 0.822363i \(-0.307345\pi\)
\(350\) 145.732 68.9898i 0.416378 0.197114i
\(351\) 0 0
\(352\) 92.3281 92.3281i 0.262296 0.262296i
\(353\) −266.520 266.520i −0.755014 0.755014i 0.220396 0.975410i \(-0.429265\pi\)
−0.975410 + 0.220396i \(0.929265\pi\)
\(354\) 0 0
\(355\) −181.848 + 287.283i −0.512248 + 0.809247i
\(356\) −555.576 −1.56061
\(357\) 0 0
\(358\) −408.712 408.712i −1.14165 1.14165i
\(359\) 216.272i 0.602430i −0.953556 0.301215i \(-0.902608\pi\)
0.953556 0.301215i \(-0.0973922\pi\)
\(360\) 0 0
\(361\) −67.3633 −0.186602
\(362\) −48.3383 + 48.3383i −0.133531 + 0.133531i
\(363\) 0 0
\(364\) 178.697i 0.490926i
\(365\) 274.495 61.6913i 0.752041 0.169017i
\(366\) 0 0
\(367\) −240.510 + 240.510i −0.655340 + 0.655340i −0.954274 0.298934i \(-0.903369\pi\)
0.298934 + 0.954274i \(0.403369\pi\)
\(368\) −78.9240 78.9240i −0.214467 0.214467i
\(369\) 0 0
\(370\) 715.176 + 452.702i 1.93291 + 1.22352i
\(371\) 83.1918 0.224237
\(372\) 0 0
\(373\) −330.207 330.207i −0.885272 0.885272i 0.108792 0.994065i \(-0.465302\pi\)
−0.994065 + 0.108792i \(0.965302\pi\)
\(374\) 39.5051i 0.105629i
\(375\) 0 0
\(376\) 166.899 0.443880
\(377\) 8.91939 8.91939i 0.0236589 0.0236589i
\(378\) 0 0
\(379\) 210.000i 0.554090i 0.960857 + 0.277045i \(0.0893551\pi\)
−0.960857 + 0.277045i \(0.910645\pi\)
\(380\) −326.499 + 515.803i −0.859209 + 1.35738i
\(381\) 0 0
\(382\) 89.1918 89.1918i 0.233486 0.233486i
\(383\) −170.631 170.631i −0.445512 0.445512i 0.448347 0.893859i \(-0.352013\pi\)
−0.893859 + 0.448347i \(0.852013\pi\)
\(384\) 0 0
\(385\) −7.52551 33.4847i −0.0195468 0.0869732i
\(386\) 345.126 0.894109
\(387\) 0 0
\(388\) −86.1010 86.1010i −0.221910 0.221910i
\(389\) 547.337i 1.40704i 0.710677 + 0.703518i \(0.248389\pi\)
−0.710677 + 0.703518i \(0.751611\pi\)
\(390\) 0 0
\(391\) −87.2327 −0.223101
\(392\) 189.260 189.260i 0.482806 0.482806i
\(393\) 0 0
\(394\) 299.464i 0.760062i
\(395\) 103.485 + 65.5051i 0.261987 + 0.165836i
\(396\) 0 0
\(397\) 45.2577 45.2577i 0.113999 0.113999i −0.647806 0.761805i \(-0.724313\pi\)
0.761805 + 0.647806i \(0.224313\pi\)
\(398\) −559.287 559.287i −1.40524 1.40524i
\(399\) 0 0
\(400\) −51.3235 108.414i −0.128309 0.271036i
\(401\) 520.302 1.29751 0.648756 0.760997i \(-0.275290\pi\)
0.648756 + 0.760997i \(0.275290\pi\)
\(402\) 0 0
\(403\) 195.373 + 195.373i 0.484798 + 0.484798i
\(404\) 1024.19i 2.53511i
\(405\) 0 0
\(406\) −5.50510 −0.0135594
\(407\) 127.394 127.394i 0.313007 0.313007i
\(408\) 0 0
\(409\) 347.110i 0.848680i −0.905503 0.424340i \(-0.860506\pi\)
0.905503 0.424340i \(-0.139494\pi\)
\(410\) 98.9898 + 440.454i 0.241439 + 1.07428i
\(411\) 0 0
\(412\) −381.974 + 381.974i −0.927121 + 0.927121i
\(413\) −162.247 162.247i −0.392851 0.392851i
\(414\) 0 0
\(415\) −145.889 + 32.7878i −0.351539 + 0.0790066i
\(416\) −576.252 −1.38522
\(417\) 0 0
\(418\) 154.182 + 154.182i 0.368856 + 0.368856i
\(419\) 583.398i 1.39236i −0.717868 0.696180i \(-0.754882\pi\)
0.717868 0.696180i \(-0.245118\pi\)
\(420\) 0 0
\(421\) 213.151 0.506297 0.253148 0.967427i \(-0.418534\pi\)
0.253148 + 0.967427i \(0.418534\pi\)
\(422\) 589.085 589.085i 1.39594 1.39594i
\(423\) 0 0
\(424\) 242.474i 0.571874i
\(425\) −88.2770 31.5505i −0.207711 0.0742365i
\(426\) 0 0
\(427\) −136.384 + 136.384i −0.319400 + 0.319400i
\(428\) −27.9750 27.9750i −0.0653622 0.0653622i
\(429\) 0 0
\(430\) −267.666 + 422.858i −0.622480 + 0.983391i
\(431\) −187.364 −0.434720 −0.217360 0.976092i \(-0.569745\pi\)
−0.217360 + 0.976092i \(0.569745\pi\)
\(432\) 0 0
\(433\) 154.848 + 154.848i 0.357617 + 0.357617i 0.862934 0.505317i \(-0.168624\pi\)
−0.505317 + 0.862934i \(0.668624\pi\)
\(434\) 120.586i 0.277847i
\(435\) 0 0
\(436\) −231.848 −0.531761
\(437\) 340.454 340.454i 0.779071 0.779071i
\(438\) 0 0
\(439\) 252.929i 0.576147i 0.957608 + 0.288074i \(0.0930148\pi\)
−0.957608 + 0.288074i \(0.906985\pi\)
\(440\) 97.5959 21.9342i 0.221809 0.0498504i
\(441\) 0 0
\(442\) −123.283 + 123.283i −0.278920 + 0.278920i
\(443\) 421.131 + 421.131i 0.950633 + 0.950633i 0.998838 0.0482041i \(-0.0153498\pi\)
−0.0482041 + 0.998838i \(0.515350\pi\)
\(444\) 0 0
\(445\) 397.893 + 251.864i 0.894142 + 0.565986i
\(446\) −148.742 −0.333503
\(447\) 0 0
\(448\) 150.015 + 150.015i 0.334854 + 0.334854i
\(449\) 297.909i 0.663495i 0.943368 + 0.331747i \(0.107638\pi\)
−0.943368 + 0.331747i \(0.892362\pi\)
\(450\) 0 0
\(451\) 96.0908 0.213062
\(452\) −84.7015 + 84.7015i −0.187393 + 0.187393i
\(453\) 0 0
\(454\) 94.2020i 0.207493i
\(455\) −81.0102 + 127.980i −0.178044 + 0.281274i
\(456\) 0 0
\(457\) 285.747 285.747i 0.625267 0.625267i −0.321607 0.946873i \(-0.604223\pi\)
0.946873 + 0.321607i \(0.104223\pi\)
\(458\) 542.388 + 542.388i 1.18425 + 1.18425i
\(459\) 0 0
\(460\) −150.454 669.444i −0.327074 1.45531i
\(461\) −526.620 −1.14234 −0.571171 0.820831i \(-0.693511\pi\)
−0.571171 + 0.820831i \(0.693511\pi\)
\(462\) 0 0
\(463\) 335.702 + 335.702i 0.725057 + 0.725057i 0.969631 0.244573i \(-0.0786479\pi\)
−0.244573 + 0.969631i \(0.578648\pi\)
\(464\) 4.09540i 0.00882630i
\(465\) 0 0
\(466\) −719.535 −1.54407
\(467\) −488.742 + 488.742i −1.04656 + 1.04656i −0.0476956 + 0.998862i \(0.515188\pi\)
−0.998862 + 0.0476956i \(0.984812\pi\)
\(468\) 0 0
\(469\) 159.151i 0.339341i
\(470\) −371.308 235.035i −0.790016 0.500075i
\(471\) 0 0
\(472\) 472.893 472.893i 1.00189 1.00189i
\(473\) 75.3235 + 75.3235i 0.159246 + 0.159246i
\(474\) 0 0
\(475\) 467.666 221.394i 0.984561 0.466092i
\(476\) 45.3439 0.0952603
\(477\) 0 0
\(478\) −725.716 725.716i −1.51823 1.51823i
\(479\) 184.949i 0.386115i −0.981187 0.193057i \(-0.938160\pi\)
0.981187 0.193057i \(-0.0618404\pi\)
\(480\) 0 0
\(481\) −795.110 −1.65304
\(482\) −297.171 + 297.171i −0.616538 + 0.616538i
\(483\) 0 0
\(484\) 647.636i 1.33809i
\(485\) 22.6311 + 100.697i 0.0466621 + 0.207623i
\(486\) 0 0
\(487\) −120.682 + 120.682i −0.247807 + 0.247807i −0.820070 0.572263i \(-0.806066\pi\)
0.572263 + 0.820070i \(0.306066\pi\)
\(488\) −397.510 397.510i −0.814569 0.814569i
\(489\) 0 0
\(490\) −687.580 + 154.530i −1.40322 + 0.315368i
\(491\) 105.682 0.215239 0.107619 0.994192i \(-0.465677\pi\)
0.107619 + 0.994192i \(0.465677\pi\)
\(492\) 0 0
\(493\) 2.26327 + 2.26327i 0.00459082 + 0.00459082i
\(494\) 962.302i 1.94798i
\(495\) 0 0
\(496\) −89.7071 −0.180861
\(497\) −98.5653 + 98.5653i −0.198321 + 0.198321i
\(498\) 0 0
\(499\) 739.585i 1.48213i 0.671431 + 0.741067i \(0.265680\pi\)
−0.671431 + 0.741067i \(0.734320\pi\)
\(500\) 89.8707 731.875i 0.179741 1.46375i
\(501\) 0 0
\(502\) 900.448 900.448i 1.79372 1.79372i
\(503\) 406.409 + 406.409i 0.807970 + 0.807970i 0.984326 0.176357i \(-0.0564312\pi\)
−0.176357 + 0.984326i \(0.556431\pi\)
\(504\) 0 0
\(505\) 464.303 733.504i 0.919412 1.45248i
\(506\) −245.081 −0.484349
\(507\) 0 0
\(508\) 676.146 + 676.146i 1.33100 + 1.33100i
\(509\) 194.511i 0.382143i 0.981576 + 0.191071i \(0.0611962\pi\)
−0.981576 + 0.191071i \(0.938804\pi\)
\(510\) 0 0
\(511\) 115.344 0.225722
\(512\) 213.376 213.376i 0.416750 0.416750i
\(513\) 0 0
\(514\) 397.060i 0.772491i
\(515\) 446.727 100.399i 0.867430 0.194950i
\(516\) 0 0
\(517\) −66.1408 + 66.1408i −0.127932 + 0.127932i
\(518\) 245.373 + 245.373i 0.473694 + 0.473694i
\(519\) 0 0
\(520\) −373.015 236.116i −0.717336 0.454069i
\(521\) 589.605 1.13168 0.565840 0.824515i \(-0.308552\pi\)
0.565840 + 0.824515i \(0.308552\pi\)
\(522\) 0 0
\(523\) −141.546 141.546i −0.270642 0.270642i 0.558716 0.829359i \(-0.311294\pi\)
−0.829359 + 0.558716i \(0.811294\pi\)
\(524\) 154.177i 0.294231i
\(525\) 0 0
\(526\) 1521.03 2.89169
\(527\) −49.5755 + 49.5755i −0.0940712 + 0.0940712i
\(528\) 0 0
\(529\) 12.1714i 0.0230084i
\(530\) 341.464 539.444i 0.644272 1.01782i
\(531\) 0 0
\(532\) −176.969 + 176.969i −0.332649 + 0.332649i
\(533\) −299.868 299.868i −0.562605 0.562605i
\(534\) 0 0
\(535\) 7.35306 + 32.7173i 0.0137440 + 0.0611539i
\(536\) 463.868 0.865426
\(537\) 0 0
\(538\) −7.78775 7.78775i −0.0144754 0.0144754i
\(539\) 150.005i 0.278302i
\(540\) 0 0
\(541\) 431.303 0.797233 0.398617 0.917118i \(-0.369490\pi\)
0.398617 + 0.917118i \(0.369490\pi\)
\(542\) −230.429 + 230.429i −0.425146 + 0.425146i
\(543\) 0 0
\(544\) 146.222i 0.268791i
\(545\) 166.045 + 105.106i 0.304670 + 0.192854i
\(546\) 0 0
\(547\) −446.222 + 446.222i −0.815763 + 0.815763i −0.985491 0.169728i \(-0.945711\pi\)
0.169728 + 0.985491i \(0.445711\pi\)
\(548\) 86.3087 + 86.3087i 0.157498 + 0.157498i
\(549\) 0 0
\(550\) −248.015 88.6413i −0.450936 0.161166i
\(551\) −17.6663 −0.0320623
\(552\) 0 0
\(553\) 35.5051 + 35.5051i 0.0642045 + 0.0642045i
\(554\) 1270.37i 2.29309i
\(555\) 0 0
\(556\) −490.627 −0.882422
\(557\) −214.091 + 214.091i −0.384364 + 0.384364i −0.872672 0.488308i \(-0.837614\pi\)
0.488308 + 0.872672i \(0.337614\pi\)
\(558\) 0 0
\(559\) 470.120i 0.841003i
\(560\) −10.7832 47.9796i −0.0192557 0.0856778i
\(561\) 0 0
\(562\) −829.156 + 829.156i −1.47537 + 1.47537i
\(563\) −672.009 672.009i −1.19362 1.19362i −0.976043 0.217579i \(-0.930184\pi\)
−0.217579 0.976043i \(-0.569816\pi\)
\(564\) 0 0
\(565\) 99.0602 22.2633i 0.175328 0.0394040i
\(566\) −343.464 −0.606827
\(567\) 0 0
\(568\) −287.283 287.283i −0.505779 0.505779i
\(569\) 972.161i 1.70854i −0.519827 0.854272i \(-0.674003\pi\)
0.519827 0.854272i \(-0.325997\pi\)
\(570\) 0 0
\(571\) −924.030 −1.61827 −0.809133 0.587626i \(-0.800063\pi\)
−0.809133 + 0.587626i \(0.800063\pi\)
\(572\) −206.404 + 206.404i −0.360846 + 0.360846i
\(573\) 0 0
\(574\) 185.081i 0.322440i
\(575\) −195.732 + 547.650i −0.340404 + 0.952436i
\(576\) 0 0
\(577\) −497.879 + 497.879i −0.862874 + 0.862874i −0.991671 0.128797i \(-0.958889\pi\)
0.128797 + 0.991671i \(0.458889\pi\)
\(578\) 611.669 + 611.669i 1.05825 + 1.05825i
\(579\) 0 0
\(580\) −13.4653 + 21.2724i −0.0232161 + 0.0366766i
\(581\) −61.3031 −0.105513
\(582\) 0 0
\(583\) −96.0908 96.0908i −0.164821 0.164821i
\(584\) 336.186i 0.575661i
\(585\) 0 0
\(586\) 1052.59 1.79624
\(587\) −292.783 + 292.783i −0.498779 + 0.498779i −0.911058 0.412279i \(-0.864733\pi\)
0.412279 + 0.911058i \(0.364733\pi\)
\(588\) 0 0
\(589\) 386.969i 0.656994i
\(590\) −1718.02 + 386.116i −2.91190 + 0.654434i
\(591\) 0 0
\(592\) 182.540 182.540i 0.308345 0.308345i
\(593\) −451.258 451.258i −0.760974 0.760974i 0.215524 0.976498i \(-0.430854\pi\)
−0.976498 + 0.215524i \(0.930854\pi\)
\(594\) 0 0
\(595\) −32.4745 20.5561i −0.0545790 0.0345481i
\(596\) 702.842 1.17927
\(597\) 0 0
\(598\) 764.817 + 764.817i 1.27896 + 1.27896i
\(599\) 32.8582i 0.0548550i 0.999624 + 0.0274275i \(0.00873154\pi\)
−0.999624 + 0.0274275i \(0.991268\pi\)
\(600\) 0 0
\(601\) −184.484 −0.306961 −0.153481 0.988152i \(-0.549048\pi\)
−0.153481 + 0.988152i \(0.549048\pi\)
\(602\) −145.081 + 145.081i −0.240998 + 0.240998i
\(603\) 0 0
\(604\) 855.171i 1.41585i
\(605\) 293.598 463.825i 0.485286 0.766653i
\(606\) 0 0
\(607\) 136.389 136.389i 0.224694 0.224694i −0.585778 0.810472i \(-0.699211\pi\)
0.810472 + 0.585778i \(0.199211\pi\)
\(608\) 570.681 + 570.681i 0.938620 + 0.938620i
\(609\) 0 0
\(610\) 324.565 + 1444.15i 0.532074 + 2.36746i
\(611\) 412.808 0.675627
\(612\) 0 0
\(613\) −12.7128 12.7128i −0.0207386 0.0207386i 0.696661 0.717400i \(-0.254668\pi\)
−0.717400 + 0.696661i \(0.754668\pi\)
\(614\) 751.828i 1.22447i
\(615\) 0 0
\(616\) 41.0102 0.0665750
\(617\) 398.752 398.752i 0.646275 0.646275i −0.305816 0.952091i \(-0.598929\pi\)
0.952091 + 0.305816i \(0.0989292\pi\)
\(618\) 0 0
\(619\) 819.131i 1.32331i −0.749807 0.661656i \(-0.769854\pi\)
0.749807 0.661656i \(-0.230146\pi\)
\(620\) −465.959 294.949i −0.751547 0.475724i
\(621\) 0 0
\(622\) −788.232 + 788.232i −1.26725 + 1.26725i
\(623\) 136.515 + 136.515i 0.219126 + 0.219126i
\(624\) 0 0
\(625\) −396.151 + 483.414i −0.633842 + 0.773463i
\(626\) 677.984 1.08304
\(627\) 0 0
\(628\) −301.712 301.712i −0.480433 0.480433i
\(629\) 201.757i 0.320759i
\(630\) 0 0
\(631\) 105.485 0.167171 0.0835853 0.996501i \(-0.473363\pi\)
0.0835853 + 0.996501i \(0.473363\pi\)
\(632\) −103.485 + 103.485i −0.163742 + 0.163742i
\(633\) 0 0
\(634\) 1900.90i 2.99826i
\(635\) −177.721 790.767i −0.279875 1.24530i
\(636\) 0 0
\(637\) 468.116 468.116i 0.734876 0.734876i
\(638\) 6.35867 + 6.35867i 0.00996657 + 0.00996657i
\(639\) 0 0
\(640\) 827.580 185.994i 1.29309 0.290616i
\(641\) −164.788 −0.257079 −0.128540 0.991704i \(-0.541029\pi\)
−0.128540 + 0.991704i \(0.541029\pi\)
\(642\) 0 0
\(643\) −764.372 764.372i −1.18876 1.18876i −0.977411 0.211349i \(-0.932214\pi\)
−0.211349 0.977411i \(-0.567786\pi\)
\(644\) 281.303i 0.436806i
\(645\) 0 0
\(646\) 244.182 0.377990
\(647\) −321.287 + 321.287i −0.496580 + 0.496580i −0.910372 0.413792i \(-0.864204\pi\)
0.413792 + 0.910372i \(0.364204\pi\)
\(648\) 0 0
\(649\) 374.808i 0.577516i
\(650\) 497.353 + 1050.59i 0.765159 + 1.61630i
\(651\) 0 0
\(652\) 1117.23 1117.23i 1.71354 1.71354i
\(653\) 169.823 + 169.823i 0.260066 + 0.260066i 0.825081 0.565015i \(-0.191130\pi\)
−0.565015 + 0.825081i \(0.691130\pi\)
\(654\) 0 0
\(655\) −69.8944 + 110.419i −0.106709 + 0.168578i
\(656\) 137.687 0.209888
\(657\) 0 0
\(658\) −127.394 127.394i −0.193608 0.193608i
\(659\) 958.763i 1.45488i 0.686174 + 0.727438i \(0.259289\pi\)
−0.686174 + 0.727438i \(0.740711\pi\)
\(660\) 0 0
\(661\) 396.393 0.599687 0.299843 0.953988i \(-0.403066\pi\)
0.299843 + 0.953988i \(0.403066\pi\)
\(662\) 1088.84 1088.84i 1.64478 1.64478i
\(663\) 0 0
\(664\) 178.677i 0.269091i
\(665\) 206.969 46.5153i 0.311232 0.0699478i
\(666\) 0 0
\(667\) 14.0408 14.0408i 0.0210507 0.0210507i
\(668\) 572.409 + 572.409i 0.856899 + 0.856899i
\(669\) 0 0
\(670\) −1031.99 653.242i −1.54028 0.974988i
\(671\) 315.060 0.469538
\(672\) 0 0
\(673\) 164.707 + 164.707i 0.244736 + 0.244736i 0.818806 0.574070i \(-0.194636\pi\)
−0.574070 + 0.818806i \(0.694636\pi\)
\(674\) 1300.10i 1.92894i
\(675\) 0 0
\(676\) 291.313 0.430937
\(677\) −544.388 + 544.388i −0.804119 + 0.804119i −0.983736 0.179618i \(-0.942514\pi\)
0.179618 + 0.983736i \(0.442514\pi\)
\(678\) 0 0
\(679\) 42.3133i 0.0623170i
\(680\) 59.9138 94.6515i 0.0881085 0.139193i
\(681\) 0 0
\(682\) −139.283 + 139.283i −0.204227 + 0.204227i
\(683\) −786.590 786.590i −1.15167 1.15167i −0.986218 0.165452i \(-0.947092\pi\)
−0.165452 0.986218i \(-0.552908\pi\)
\(684\) 0 0
\(685\) −22.6857 100.940i −0.0331178 0.147357i
\(686\) −604.949 −0.881850
\(687\) 0 0
\(688\) 107.930 + 107.930i 0.156874 + 0.156874i
\(689\) 599.737i 0.870445i
\(690\) 0 0
\(691\) 356.879 0.516467 0.258233 0.966083i \(-0.416860\pi\)
0.258233 + 0.966083i \(0.416860\pi\)
\(692\) 204.288 204.288i 0.295214 0.295214i
\(693\) 0 0
\(694\) 1424.06i 2.05196i
\(695\) 351.378 + 222.420i 0.505580 + 0.320029i
\(696\) 0 0
\(697\) 76.0908 76.0908i 0.109169 0.109169i
\(698\) −1277.02 1277.02i −1.82955 1.82955i
\(699\) 0 0
\(700\) 101.742 284.671i 0.145346 0.406673i
\(701\) −885.680 −1.26345 −0.631726 0.775192i \(-0.717653\pi\)
−0.631726 + 0.775192i \(0.717653\pi\)
\(702\) 0 0
\(703\) 787.423 + 787.423i 1.12009 + 1.12009i
\(704\) 346.549i 0.492258i
\(705\) 0 0
\(706\) −1185.88 −1.67971
\(707\) 251.662 251.662i 0.355957 0.355957i
\(708\) 0 0
\(709\) 731.049i 1.03110i 0.856860 + 0.515549i \(0.172412\pi\)
−0.856860 + 0.515549i \(0.827588\pi\)
\(710\) 234.565 + 1043.70i 0.330374 + 1.46999i
\(711\) 0 0
\(712\) −397.893 + 397.893i −0.558839 + 0.558839i
\(713\) 307.555 + 307.555i 0.431354 + 0.431354i
\(714\) 0 0
\(715\) 241.394 54.2520i 0.337614 0.0758770i
\(716\) −1083.71 −1.51356
\(717\) 0 0
\(718\) −481.151 481.151i −0.670127 0.670127i
\(719\) 629.271i 0.875204i 0.899169 + 0.437602i \(0.144172\pi\)
−0.899169 + 0.437602i \(0.855828\pi\)
\(720\) 0 0
\(721\) 187.716 0.260356
\(722\) −149.866 + 149.866i −0.207571 + 0.207571i
\(723\) 0 0
\(724\) 128.170i 0.177031i
\(725\) 19.2872 9.13061i 0.0266031 0.0125939i
\(726\) 0 0
\(727\) −15.8740 + 15.8740i −0.0218349 + 0.0218349i −0.717940 0.696105i \(-0.754915\pi\)
0.696105 + 0.717940i \(0.254915\pi\)
\(728\) −127.980 127.980i −0.175796 0.175796i
\(729\) 0 0
\(730\) 473.434 747.929i 0.648539 1.02456i
\(731\) 119.292 0.163190
\(732\) 0 0
\(733\) −393.237 393.237i −0.536476 0.536476i 0.386016 0.922492i \(-0.373851\pi\)
−0.922492 + 0.386016i \(0.873851\pi\)
\(734\) 1070.15i 1.45796i
\(735\) 0 0
\(736\) −907.131 −1.23251
\(737\) −183.828 + 183.828i −0.249427 + 0.249427i
\(738\) 0 0
\(739\) 192.334i 0.260262i 0.991497 + 0.130131i \(0.0415398\pi\)
−0.991497 + 0.130131i \(0.958460\pi\)
\(740\) 1548.33 347.980i 2.09234 0.470243i
\(741\) 0 0
\(742\) 185.081 185.081i 0.249435 0.249435i
\(743\) 44.7015 + 44.7015i 0.0601636 + 0.0601636i 0.736548 0.676385i \(-0.236454\pi\)
−0.676385 + 0.736548i \(0.736454\pi\)
\(744\) 0 0
\(745\) −503.363 318.626i −0.675655 0.427685i
\(746\) −1469.25 −1.96951
\(747\) 0 0
\(748\) −52.3745 52.3745i −0.0700194 0.0700194i
\(749\) 13.7480i 0.0183551i
\(750\) 0 0
\(751\) 227.787 0.303311 0.151656 0.988433i \(-0.451540\pi\)
0.151656 + 0.988433i \(0.451540\pi\)
\(752\) −94.7719 + 94.7719i −0.126027 + 0.126027i
\(753\) 0 0
\(754\) 39.6867i 0.0526349i
\(755\) 387.682 612.459i 0.513486 0.811204i
\(756\) 0 0
\(757\) −235.925 + 235.925i −0.311658 + 0.311658i −0.845552 0.533894i \(-0.820728\pi\)
0.533894 + 0.845552i \(0.320728\pi\)
\(758\) 467.196 + 467.196i 0.616354 + 0.616354i
\(759\) 0 0
\(760\) 135.576 + 603.242i 0.178389 + 0.793739i
\(761\) 881.242 1.15801 0.579003 0.815326i \(-0.303442\pi\)
0.579003 + 0.815326i \(0.303442\pi\)
\(762\) 0 0
\(763\) 56.9694 + 56.9694i 0.0746650 + 0.0746650i
\(764\) 236.495i 0.309548i
\(765\) 0 0
\(766\) −759.221 −0.991151
\(767\) 1169.66 1169.66i 1.52497 1.52497i
\(768\) 0 0
\(769\) 1208.40i 1.57139i 0.618612 + 0.785697i \(0.287696\pi\)
−0.618612 + 0.785697i \(0.712304\pi\)
\(770\) −91.2372 57.7526i −0.118490 0.0750033i
\(771\) 0 0
\(772\) 457.556 457.556i 0.592689 0.592689i
\(773\) 815.226 + 815.226i 1.05463 + 1.05463i 0.998419 + 0.0562070i \(0.0179007\pi\)
0.0562070 + 0.998419i \(0.482099\pi\)
\(774\) 0 0
\(775\) 200.000 + 422.474i 0.258065 + 0.545128i
\(776\) −123.328 −0.158928
\(777\) 0 0
\(778\) 1217.69 + 1217.69i 1.56515 + 1.56515i
\(779\) 593.939i 0.762437i
\(780\) 0 0
\(781\) 227.696 0.291544
\(782\) −194.070 + 194.070i −0.248172 + 0.248172i
\(783\) 0 0
\(784\) 214.939i 0.274157i
\(785\) 79.3031 + 352.858i 0.101023 + 0.449501i
\(786\) 0 0
\(787\) 813.010 813.010i 1.03305 1.03305i 0.0336150 0.999435i \(-0.489298\pi\)
0.999435 0.0336150i \(-0.0107020\pi\)
\(788\) −397.019 397.019i −0.503832 0.503832i
\(789\) 0