Properties

Label 45.3.g.b.37.2
Level $45$
Weight $3$
Character 45.37
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 37.2
Root \(1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 45.37
Dual form 45.3.g.b.28.2

$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

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

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 0.992829 + 0.119543i \(0.0381431\pi\)
0.119543 + 0.992829i \(0.461857\pi\)
\(3\) 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 0.595951 0.803021i \(-0.296775\pi\)
−0.803021 + 0.595951i \(0.796775\pi\)
\(8\) −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 −0.983688 0.179881i \(-0.942429\pi\)
0.179881 + 0.983688i \(0.442429\pi\)
\(14\) 6.44949i 0.460678i
\(15\) 0 0
\(16\) 4.79796 0.299872
\(17\) 2.65153 + 2.65153i 0.155972 + 0.155972i 0.780779 0.624807i \(-0.214822\pi\)
−0.624807 + 0.780779i \(0.714822\pi\)
\(18\) 0 0
\(19\) 20.6969i 1.08931i −0.838659 0.544656i \(-0.816660\pi\)
0.838659 0.544656i \(-0.183340\pi\)
\(20\) 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 −0.967617 0.252422i \(-0.918773\pi\)
0.252422 + 0.967617i \(0.418773\pi\)
\(24\) 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 \(-0.995315\pi\)
0.999892 0.0147168i \(-0.00468466\pi\)
\(30\) 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 0.999589 + 0.0286652i \(0.00912566\pi\)
0.0286652 + 0.999589i \(0.490874\pi\)
\(38\) 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 −0.395380 0.918517i \(-0.629387\pi\)
0.918517 + 0.395380i \(0.129387\pi\)
\(44\) 19.7526i 0.448922i
\(45\) 0 0
\(46\) −73.1918 −1.59113
\(47\) −19.7526 19.7526i −0.420267 0.420267i 0.465029 0.885296i \(-0.346044\pi\)
−0.885296 + 0.465029i \(0.846044\pi\)
\(48\) 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 −0.923954 0.382503i \(-0.875062\pi\)
0.382503 + 0.923954i \(0.375062\pi\)
\(54\) 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 \(-0.602505\pi\)
0.316493 0.948595i \(-0.397495\pi\)
\(60\) 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 0.166631 0.986019i \(-0.446711\pi\)
−0.986019 + 0.166631i \(0.946711\pi\)
\(68\) −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 −0.925001 0.379964i \(-0.875936\pi\)
0.379964 + 0.925001i \(0.375936\pi\)
\(74\) 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 \(0.0495477\pi\)
−0.987910 + 0.155031i \(0.950452\pi\)
\(80\) −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 −0.568149 0.822926i \(-0.692340\pi\)
0.822926 + 0.568149i \(0.192340\pi\)
\(84\) 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 \(0.177474\pi\)
−0.848553 + 0.529110i \(0.822526\pi\)
\(90\) 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 0.778329 0.627856i \(-0.216067\pi\)
−0.627856 + 0.778329i \(0.716067\pi\)
\(98\) 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 −0.947732 0.319067i \(-0.896631\pi\)
0.319067 + 0.947732i \(0.396631\pi\)
\(104\) 88.2929i 0.848970i
\(105\) 0 0
\(106\) −127.687 −1.20459
\(107\) 4.74235 + 4.74235i 0.0443210 + 0.0443210i 0.728920 0.684599i \(-0.240023\pi\)
−0.684599 + 0.728920i \(0.740023\pi\)
\(108\) 0 0
\(109\) 39.3031i 0.360579i 0.983614 + 0.180289i \(0.0577034\pi\)
−0.983614 + 0.180289i \(0.942297\pi\)
\(110\) 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 −0.767781 0.640713i \(-0.778639\pi\)
0.640713 + 0.767781i \(0.278639\pi\)
\(114\) 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 0.0931273 0.995654i \(-0.470314\pi\)
−0.995654 + 0.0931273i \(0.970314\pi\)
\(128\) −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 0.651689 0.758486i \(-0.274061\pi\)
−0.758486 + 0.651689i \(0.774061\pi\)
\(138\) 0 0
\(139\) 83.1714i 0.598356i 0.954197 + 0.299178i \(0.0967124\pi\)
−0.954197 + 0.299178i \(0.903288\pi\)
\(140\) −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 \(-0.869073\pi\)
0.916594 0.399820i \(-0.130927\pi\)
\(150\) 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 0.850977 0.525203i \(-0.176011\pi\)
−0.525203 + 0.850977i \(0.676011\pi\)
\(158\) −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 0.177872 0.984054i \(-0.443079\pi\)
0.984054 0.177872i \(-0.0569213\pi\)
\(164\) 169.283i 1.03221i
\(165\) 0 0
\(166\) 94.0908 0.566812
\(167\) −97.0352 97.0352i −0.581049 0.581049i 0.354142 0.935192i \(-0.384773\pi\)
−0.935192 + 0.354142i \(0.884773\pi\)
\(168\) 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 −0.599897 0.800077i \(-0.704792\pi\)
0.800077 + 0.599897i \(0.204792\pi\)
\(174\) 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 \(0.171526\pi\)
−0.858292 + 0.513161i \(0.828474\pi\)
\(180\) 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 −0.477007 0.878900i \(-0.658278\pi\)
0.878900 + 0.477007i \(0.158278\pi\)
\(194\) 64.9444i 0.334765i
\(195\) 0 0
\(196\) 264.262 1.34828
\(197\) 67.3031 + 67.3031i 0.341640 + 0.341640i 0.856984 0.515344i \(-0.172336\pi\)
−0.515344 + 0.856984i \(0.672336\pi\)
\(198\) 0 0
\(199\) 251.394i 1.26329i 0.775259 + 0.631643i \(0.217619\pi\)
−0.775259 + 0.631643i \(0.782381\pi\)
\(200\) −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 −0.778076 0.628170i \(-0.783804\pi\)
0.628170 + 0.778076i \(0.283804\pi\)
\(224\) 79.9342i 0.356849i
\(225\) 0 0
\(226\) −63.8888 −0.282694
\(227\) 21.1714 + 21.1714i 0.0932662 + 0.0932662i 0.752200 0.658934i \(-0.228992\pi\)
−0.658934 + 0.752200i \(0.728992\pi\)
\(228\) 0 0
\(229\) 243.798i 1.06462i −0.846550 0.532310i \(-0.821324\pi\)
0.846550 0.532310i \(-0.178676\pi\)
\(230\) 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 −0.963119 0.269077i \(-0.913281\pi\)
0.269077 + 0.963119i \(0.413281\pi\)
\(234\) 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 \(0.239077\pi\)
−0.730950 + 0.682431i \(0.760923\pi\)
\(240\) 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 0.859076 0.511849i \(-0.171039\pi\)
−0.511849 + 0.859076i \(0.671039\pi\)
\(258\) 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 0.371253 0.928532i \(-0.378928\pi\)
0.928532 0.371253i \(-0.121072\pi\)
\(264\) 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 \(0.00207111\pi\)
−0.999979 + 0.00650653i \(0.997929\pi\)
\(270\) 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 −0.999513 0.0312080i \(-0.990065\pi\)
−0.0312080 0.999513i \(-0.509935\pi\)
\(278\) −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 −0.830211 0.557449i \(-0.811780\pi\)
0.557449 + 0.830211i \(0.311780\pi\)
\(284\) 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 −0.176848 0.984238i \(-0.556590\pi\)
0.984238 + 0.176848i \(0.0565901\pi\)
\(294\) 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 0.926553 0.376164i \(-0.122757\pi\)
−0.376164 + 0.926553i \(0.622757\pi\)
\(308\) 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 −0.420484 0.907300i \(-0.638140\pi\)
0.907300 + 0.420484i \(0.138140\pi\)
\(314\) 227.576i 0.724763i
\(315\) 0 0
\(316\) −144.495 −0.457262
\(317\) 427.217 + 427.217i 1.34769 + 1.34769i 0.888168 + 0.459519i \(0.151978\pi\)
0.459519 + 0.888168i \(0.348022\pi\)
\(318\) 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 0.992143 0.125105i \(-0.0399269\pi\)
−0.125105 + 0.992143i \(0.539927\pi\)
\(338\) 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 0.0748598 0.997194i \(-0.476149\pi\)
−0.997194 + 0.0748598i \(0.976149\pi\)
\(348\) 0 0
\(349\) 574.009i 1.64473i 0.568964 + 0.822363i \(0.307345\pi\)
−0.568964 + 0.822363i \(0.692655\pi\)
\(350\) 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 −0.975410 0.220396i \(-0.929265\pi\)
0.220396 + 0.975410i \(0.429265\pi\)
\(354\) 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 \(0.0973922\pi\)
−0.953556 + 0.301215i \(0.902608\pi\)
\(360\) 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 0.298934 0.954274i \(-0.403369\pi\)
−0.954274 + 0.298934i \(0.903369\pi\)
\(368\) −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 −0.994065 0.108792i \(-0.965302\pi\)
0.108792 + 0.994065i \(0.465302\pi\)
\(374\) 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 \(-0.910645\pi\)
0.960857 0.277045i \(-0.0893551\pi\)
\(380\) −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 −0.893859 0.448347i \(-0.852013\pi\)
0.448347 + 0.893859i \(0.352013\pi\)
\(384\) 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 \(-0.751611\pi\)
0.710677 0.703518i \(-0.248389\pi\)
\(390\) 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 0.761805 0.647806i \(-0.224313\pi\)
−0.647806 + 0.761805i \(0.724313\pi\)
\(398\) −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 \(0.139494\pi\)
−0.905503 + 0.424340i \(0.860506\pi\)
\(410\) 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 \(0.245118\pi\)
−0.717868 + 0.696180i \(0.754882\pi\)
\(420\) 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 −0.505317 0.862934i \(-0.668624\pi\)
0.862934 + 0.505317i \(0.168624\pi\)
\(434\) 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 \(-0.906985\pi\)
0.957608 0.288074i \(-0.0930148\pi\)
\(440\) 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 −0.0482041 0.998838i \(-0.515350\pi\)
0.998838 + 0.0482041i \(0.0153498\pi\)
\(444\) 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 \(-0.892362\pi\)
0.943368 0.331747i \(-0.107638\pi\)
\(450\) 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 0.946873 0.321607i \(-0.104223\pi\)
−0.321607 + 0.946873i \(0.604223\pi\)
\(458\) 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 −0.244573 0.969631i \(-0.578648\pi\)
0.969631 + 0.244573i \(0.0786479\pi\)
\(464\) 4.09540i 0.00882630i
\(465\) 0 0
\(466\) −719.535 −1.54407
\(467\) −488.742 488.742i −1.04656 1.04656i −0.998862 0.0476956i \(-0.984812\pi\)
−0.0476956 0.998862i \(-0.515188\pi\)
\(468\) 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 \(0.0618404\pi\)
−0.981187 + 0.193057i \(0.938160\pi\)
\(480\) 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 0.572263 0.820070i \(-0.306066\pi\)
−0.820070 + 0.572263i \(0.806066\pi\)
\(488\) −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 \(-0.734320\pi\)
0.671431 0.741067i \(-0.265680\pi\)
\(500\) 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 −0.176357 0.984326i \(-0.556431\pi\)
0.984326 + 0.176357i \(0.0564312\pi\)
\(504\) 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 \(-0.938804\pi\)
0.981576 0.191071i \(-0.0611962\pi\)
\(510\) 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 −0.829359 0.558716i \(-0.811294\pi\)
0.558716 + 0.829359i \(0.311294\pi\)
\(524\) 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 0.169728 0.985491i \(-0.445711\pi\)
−0.985491 + 0.169728i \(0.945711\pi\)
\(548\) 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 0.488308 0.872672i \(-0.337614\pi\)
−0.872672 + 0.488308i \(0.837614\pi\)
\(558\) 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 −0.217579 + 0.976043i \(0.569816\pi\)
−0.976043 + 0.217579i \(0.930184\pi\)
\(564\) 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 \(0.325997\pi\)
−0.519827 + 0.854272i \(0.674003\pi\)
\(570\) 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 0.128797 0.991671i \(-0.458889\pi\)
−0.991671 + 0.128797i \(0.958889\pi\)
\(578\) 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 0.412279 0.911058i \(-0.364733\pi\)
−0.911058 + 0.412279i \(0.864733\pi\)
\(588\) 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 −0.976498 0.215524i \(-0.930854\pi\)
0.215524 + 0.976498i \(0.430854\pi\)
\(594\) 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 \(-0.991268\pi\)
0.999624 0.0274275i \(-0.00873154\pi\)
\(600\) 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 0.810472 0.585778i \(-0.199211\pi\)
−0.585778 + 0.810472i \(0.699211\pi\)
\(608\) 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 −0.717400 0.696661i \(-0.754668\pi\)
0.696661 + 0.717400i \(0.254668\pi\)
\(614\) 751.828i 1.22447i
\(615\) 0 0
\(616\) 41.0102 0.0665750
\(617\) 398.752 + 398.752i 0.646275 + 0.646275i 0.952091 0.305816i \(-0.0989292\pi\)
−0.305816 + 0.952091i \(0.598929\pi\)
\(618\) 0 0
\(619\) 819.131i 1.32331i 0.749807 + 0.661656i \(0.230146\pi\)
−0.749807 + 0.661656i \(0.769854\pi\)
\(620\) −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 −0.211349 + 0.977411i \(0.567786\pi\)
−0.977411 + 0.211349i \(0.932214\pi\)
\(644\) 281.303i 0.436806i
\(645\) 0 0
\(646\) 244.182 0.377990
\(647\) −321.287 321.287i −0.496580 0.496580i 0.413792 0.910372i \(-0.364204\pi\)
−0.910372 + 0.413792i \(0.864204\pi\)
\(648\) 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 −0.565015 0.825081i \(-0.691130\pi\)
0.825081 + 0.565015i \(0.191130\pi\)
\(654\) 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 \(-0.740711\pi\)
0.686174 0.727438i \(-0.259289\pi\)
\(660\) 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 −0.574070 0.818806i \(-0.694636\pi\)
0.818806 + 0.574070i \(0.194636\pi\)
\(674\) 1300.10i 1.92894i
\(675\) 0 0
\(676\) 291.313 0.430937
\(677\) −544.388 544.388i −0.804119 0.804119i 0.179618 0.983736i \(-0.442514\pi\)
−0.983736 + 0.179618i \(0.942514\pi\)
\(678\) 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 −0.165452 + 0.986218i \(0.552908\pi\)
−0.986218 + 0.165452i \(0.947092\pi\)
\(684\) 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 \(-0.827588\pi\)
0.856860 0.515549i \(-0.172412\pi\)
\(710\) 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 \(-0.855828\pi\)
0.899169 0.437602i \(-0.144172\pi\)
\(720\) 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 0.696105 0.717940i \(-0.254915\pi\)
−0.717940 + 0.696105i \(0.754915\pi\)
\(728\) −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 −0.922492 0.386016i \(-0.873851\pi\)
0.386016 + 0.922492i \(0.373851\pi\)
\(734\) 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 \(-0.958460\pi\)
0.991497 0.130131i \(-0.0415398\pi\)
\(740\) 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 −0.676385 0.736548i \(-0.736454\pi\)
0.736548 + 0.676385i \(0.236454\pi\)
\(744\) 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 0.533894 0.845552i \(-0.320728\pi\)
−0.845552 + 0.533894i \(0.820728\pi\)
\(758\) 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 \(-0.712304\pi\)
0.618612 0.785697i \(-0.287696\pi\)
\(770\) −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 0.0562070 0.998419i \(-0.482099\pi\)
0.998419 0.0562070i \(-0.0179007\pi\)
\(774\) 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 0.999435 + 0.0336150i \(0.0107020\pi\)
0.0336150 + 0.999435i \(0.489298\pi\)
\(788\) −397.019 + 397.019i −0.503832 + 0.503832i
\(789\) 0