Properties

Label 300.3.f.c.199.1
Level $300$
Weight $3$
Character 300.199
Analytic conductor $8.174$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 199.1
Root \(-0.485936 - 1.32811i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.c.199.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.99209 - 0.177680i) q^{2} -1.73205 q^{3} +(3.93686 + 0.707911i) q^{4} +(3.45040 + 0.307751i) q^{6} -1.19501 q^{7} +(-7.71680 - 2.10973i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-1.99209 - 0.177680i) q^{2} -1.73205 q^{3} +(3.93686 + 0.707911i) q^{4} +(3.45040 + 0.307751i) q^{6} -1.19501 q^{7} +(-7.71680 - 2.10973i) q^{8} +3.00000 q^{9} +8.22072i q^{11} +(-6.81884 - 1.22614i) q^{12} -11.1863i q^{13} +(2.38058 + 0.212331i) q^{14} +(14.9977 + 5.57389i) q^{16} +20.9256i q^{17} +(-5.97628 - 0.533041i) q^{18} -27.9657i q^{19} +2.06983 q^{21} +(1.46066 - 16.3764i) q^{22} -9.48564 q^{23} +(13.3659 + 3.65415i) q^{24} +(-1.98759 + 22.2842i) q^{26} -5.19615 q^{27} +(-4.70460 - 0.845964i) q^{28} -40.4205 q^{29} +55.3130i q^{31} +(-28.8865 - 13.7685i) q^{32} -14.2387i q^{33} +(3.71807 - 41.6858i) q^{34} +(11.8106 + 2.12373i) q^{36} +50.1890i q^{37} +(-4.96895 + 55.7102i) q^{38} +19.3753i q^{39} -73.6361 q^{41} +(-4.12328 - 0.367767i) q^{42} -19.0843 q^{43} +(-5.81954 + 32.3638i) q^{44} +(18.8963 + 1.68541i) q^{46} -18.0598 q^{47} +(-25.9768 - 9.65427i) q^{48} -47.5719 q^{49} -36.2442i q^{51} +(7.91894 - 44.0391i) q^{52} +57.2212i q^{53} +(10.3512 + 0.923254i) q^{54} +(9.22169 + 2.52115i) q^{56} +48.4380i q^{57} +(80.5213 + 7.18193i) q^{58} +60.6645i q^{59} -21.3518 q^{61} +(9.82804 - 110.189i) q^{62} -3.58504 q^{63} +(55.0981 + 32.5607i) q^{64} +(-2.52994 + 28.3648i) q^{66} -9.68679 q^{67} +(-14.8135 + 82.3812i) q^{68} +16.4296 q^{69} -68.6944i q^{71} +(-23.1504 - 6.32918i) q^{72} -84.7825i q^{73} +(8.91760 - 99.9811i) q^{74} +(19.7972 - 110.097i) q^{76} -9.82388i q^{77} +(3.44261 - 38.5974i) q^{78} -23.2903i q^{79} +9.00000 q^{81} +(146.690 + 13.0837i) q^{82} +93.2595 q^{83} +(8.14861 + 1.46525i) q^{84} +(38.0177 + 3.39091i) q^{86} +70.0104 q^{87} +(17.3435 - 63.4377i) q^{88} -62.9898 q^{89} +13.3678i q^{91} +(-37.3436 - 6.71499i) q^{92} -95.8049i q^{93} +(35.9767 + 3.20887i) q^{94} +(50.0328 + 23.8478i) q^{96} +91.3962i q^{97} +(94.7677 + 8.45260i) q^{98} +24.6622i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{4} - 12q^{6} + 48q^{9} + O(q^{10}) \) \( 16q + 16q^{4} - 12q^{6} + 48q^{9} - 44q^{14} + 80q^{16} + 48q^{21} + 72q^{24} - 132q^{26} + 64q^{29} - 248q^{34} + 48q^{36} - 32q^{41} - 80q^{44} - 152q^{46} - 32q^{49} - 36q^{54} - 344q^{56} + 272q^{61} - 32q^{64} - 216q^{66} + 192q^{69} + 216q^{74} + 240q^{76} + 144q^{81} + 288q^{84} + 428q^{86} - 256q^{89} - 24q^{94} + 192q^{96} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99209 0.177680i −0.996046 0.0888402i
\(3\) −1.73205 −0.577350
\(4\) 3.93686 + 0.707911i 0.984215 + 0.176978i
\(5\) 0 0
\(6\) 3.45040 + 0.307751i 0.575067 + 0.0512919i
\(7\) −1.19501 −0.170716 −0.0853582 0.996350i \(-0.527203\pi\)
−0.0853582 + 0.996350i \(0.527203\pi\)
\(8\) −7.71680 2.10973i −0.964600 0.263716i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 8.22072i 0.747338i 0.927562 + 0.373669i \(0.121900\pi\)
−0.927562 + 0.373669i \(0.878100\pi\)
\(12\) −6.81884 1.22614i −0.568237 0.102178i
\(13\) 11.1863i 0.860488i −0.902713 0.430244i \(-0.858428\pi\)
0.902713 0.430244i \(-0.141572\pi\)
\(14\) 2.38058 + 0.212331i 0.170041 + 0.0151665i
\(15\) 0 0
\(16\) 14.9977 + 5.57389i 0.937358 + 0.348368i
\(17\) 20.9256i 1.23092i 0.788169 + 0.615459i \(0.211030\pi\)
−0.788169 + 0.615459i \(0.788970\pi\)
\(18\) −5.97628 0.533041i −0.332015 0.0296134i
\(19\) 27.9657i 1.47188i −0.677048 0.735939i \(-0.736741\pi\)
0.677048 0.735939i \(-0.263259\pi\)
\(20\) 0 0
\(21\) 2.06983 0.0985631
\(22\) 1.46066 16.3764i 0.0663937 0.744383i
\(23\) −9.48564 −0.412419 −0.206209 0.978508i \(-0.566113\pi\)
−0.206209 + 0.978508i \(0.566113\pi\)
\(24\) 13.3659 + 3.65415i 0.556912 + 0.152256i
\(25\) 0 0
\(26\) −1.98759 + 22.2842i −0.0764459 + 0.857085i
\(27\) −5.19615 −0.192450
\(28\) −4.70460 0.845964i −0.168022 0.0302130i
\(29\) −40.4205 −1.39381 −0.696905 0.717163i \(-0.745440\pi\)
−0.696905 + 0.717163i \(0.745440\pi\)
\(30\) 0 0
\(31\) 55.3130i 1.78429i 0.451748 + 0.892145i \(0.350800\pi\)
−0.451748 + 0.892145i \(0.649200\pi\)
\(32\) −28.8865 13.7685i −0.902702 0.430266i
\(33\) 14.2387i 0.431476i
\(34\) 3.71807 41.6858i 0.109355 1.22605i
\(35\) 0 0
\(36\) 11.8106 + 2.12373i 0.328072 + 0.0589926i
\(37\) 50.1890i 1.35646i 0.734850 + 0.678230i \(0.237253\pi\)
−0.734850 + 0.678230i \(0.762747\pi\)
\(38\) −4.96895 + 55.7102i −0.130762 + 1.46606i
\(39\) 19.3753i 0.496803i
\(40\) 0 0
\(41\) −73.6361 −1.79600 −0.898001 0.439994i \(-0.854981\pi\)
−0.898001 + 0.439994i \(0.854981\pi\)
\(42\) −4.12328 0.367767i −0.0981734 0.00875637i
\(43\) −19.0843 −0.443822 −0.221911 0.975067i \(-0.571229\pi\)
−0.221911 + 0.975067i \(0.571229\pi\)
\(44\) −5.81954 + 32.3638i −0.132262 + 0.735541i
\(45\) 0 0
\(46\) 18.8963 + 1.68541i 0.410788 + 0.0366394i
\(47\) −18.0598 −0.384251 −0.192125 0.981370i \(-0.561538\pi\)
−0.192125 + 0.981370i \(0.561538\pi\)
\(48\) −25.9768 9.65427i −0.541184 0.201131i
\(49\) −47.5719 −0.970856
\(50\) 0 0
\(51\) 36.2442i 0.710671i
\(52\) 7.91894 44.0391i 0.152287 0.846905i
\(53\) 57.2212i 1.07965i 0.841779 + 0.539823i \(0.181509\pi\)
−0.841779 + 0.539823i \(0.818491\pi\)
\(54\) 10.3512 + 0.923254i 0.191689 + 0.0170973i
\(55\) 0 0
\(56\) 9.22169 + 2.52115i 0.164673 + 0.0450206i
\(57\) 48.4380i 0.849789i
\(58\) 80.5213 + 7.18193i 1.38830 + 0.123826i
\(59\) 60.6645i 1.02821i 0.857727 + 0.514106i \(0.171876\pi\)
−0.857727 + 0.514106i \(0.828124\pi\)
\(60\) 0 0
\(61\) −21.3518 −0.350030 −0.175015 0.984566i \(-0.555997\pi\)
−0.175015 + 0.984566i \(0.555997\pi\)
\(62\) 9.82804 110.189i 0.158517 1.77724i
\(63\) −3.58504 −0.0569054
\(64\) 55.0981 + 32.5607i 0.860908 + 0.508761i
\(65\) 0 0
\(66\) −2.52994 + 28.3648i −0.0383324 + 0.429770i
\(67\) −9.68679 −0.144579 −0.0722895 0.997384i \(-0.523031\pi\)
−0.0722895 + 0.997384i \(0.523031\pi\)
\(68\) −14.8135 + 82.3812i −0.217845 + 1.21149i
\(69\) 16.4296 0.238110
\(70\) 0 0
\(71\) 68.6944i 0.967527i −0.875199 0.483763i \(-0.839270\pi\)
0.875199 0.483763i \(-0.160730\pi\)
\(72\) −23.1504 6.32918i −0.321533 0.0879053i
\(73\) 84.7825i 1.16140i −0.814116 0.580702i \(-0.802778\pi\)
0.814116 0.580702i \(-0.197222\pi\)
\(74\) 8.91760 99.9811i 0.120508 1.35110i
\(75\) 0 0
\(76\) 19.7972 110.097i 0.260490 1.44864i
\(77\) 9.82388i 0.127583i
\(78\) 3.44261 38.5974i 0.0441361 0.494839i
\(79\) 23.2903i 0.294814i −0.989076 0.147407i \(-0.952907\pi\)
0.989076 0.147407i \(-0.0470928\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 146.690 + 13.0837i 1.78890 + 0.159557i
\(83\) 93.2595 1.12361 0.561804 0.827270i \(-0.310107\pi\)
0.561804 + 0.827270i \(0.310107\pi\)
\(84\) 8.14861 + 1.46525i 0.0970073 + 0.0174435i
\(85\) 0 0
\(86\) 38.0177 + 3.39091i 0.442067 + 0.0394292i
\(87\) 70.0104 0.804717
\(88\) 17.3435 63.4377i 0.197085 0.720883i
\(89\) −62.9898 −0.707750 −0.353875 0.935293i \(-0.615136\pi\)
−0.353875 + 0.935293i \(0.615136\pi\)
\(90\) 0 0
\(91\) 13.3678i 0.146899i
\(92\) −37.3436 6.71499i −0.405909 0.0729890i
\(93\) 95.8049i 1.03016i
\(94\) 35.9767 + 3.20887i 0.382731 + 0.0341369i
\(95\) 0 0
\(96\) 50.0328 + 23.8478i 0.521175 + 0.248414i
\(97\) 91.3962i 0.942229i 0.882072 + 0.471115i \(0.156148\pi\)
−0.882072 + 0.471115i \(0.843852\pi\)
\(98\) 94.7677 + 8.45260i 0.967017 + 0.0862510i
\(99\) 24.6622i 0.249113i
\(100\) 0 0
\(101\) −29.9780 −0.296811 −0.148406 0.988927i \(-0.547414\pi\)
−0.148406 + 0.988927i \(0.547414\pi\)
\(102\) −6.43989 + 72.2019i −0.0631362 + 0.707861i
\(103\) −88.7485 −0.861636 −0.430818 0.902439i \(-0.641775\pi\)
−0.430818 + 0.902439i \(0.641775\pi\)
\(104\) −23.6001 + 86.3228i −0.226924 + 0.830027i
\(105\) 0 0
\(106\) 10.1671 113.990i 0.0959159 1.07538i
\(107\) 162.922 1.52263 0.761316 0.648381i \(-0.224553\pi\)
0.761316 + 0.648381i \(0.224553\pi\)
\(108\) −20.4565 3.67841i −0.189412 0.0340594i
\(109\) 103.352 0.948182 0.474091 0.880476i \(-0.342777\pi\)
0.474091 + 0.880476i \(0.342777\pi\)
\(110\) 0 0
\(111\) 86.9299i 0.783152i
\(112\) −17.9225 6.66088i −0.160022 0.0594722i
\(113\) 31.2691i 0.276717i 0.990382 + 0.138359i \(0.0441827\pi\)
−0.990382 + 0.138359i \(0.955817\pi\)
\(114\) 8.60647 96.4929i 0.0754954 0.846429i
\(115\) 0 0
\(116\) −159.130 28.6141i −1.37181 0.246673i
\(117\) 33.5590i 0.286829i
\(118\) 10.7789 120.849i 0.0913465 1.02415i
\(119\) 25.0064i 0.210138i
\(120\) 0 0
\(121\) 53.4198 0.441486
\(122\) 42.5348 + 3.79380i 0.348646 + 0.0310967i
\(123\) 127.541 1.03692
\(124\) −39.1567 + 217.760i −0.315780 + 1.75613i
\(125\) 0 0
\(126\) 7.14174 + 0.636992i 0.0566804 + 0.00505549i
\(127\) −178.474 −1.40531 −0.702655 0.711531i \(-0.748002\pi\)
−0.702655 + 0.711531i \(0.748002\pi\)
\(128\) −103.975 74.6537i −0.812305 0.583232i
\(129\) 33.0550 0.256240
\(130\) 0 0
\(131\) 153.743i 1.17361i −0.809727 0.586806i \(-0.800385\pi\)
0.809727 0.586806i \(-0.199615\pi\)
\(132\) 10.0797 56.0558i 0.0763617 0.424665i
\(133\) 33.4194i 0.251274i
\(134\) 19.2970 + 1.72115i 0.144007 + 0.0128444i
\(135\) 0 0
\(136\) 44.1473 161.479i 0.324613 1.18734i
\(137\) 52.9928i 0.386809i −0.981119 0.193405i \(-0.938047\pi\)
0.981119 0.193405i \(-0.0619530\pi\)
\(138\) −32.7293 2.91922i −0.237169 0.0211537i
\(139\) 21.8420i 0.157137i 0.996909 + 0.0785684i \(0.0250349\pi\)
−0.996909 + 0.0785684i \(0.974965\pi\)
\(140\) 0 0
\(141\) 31.2804 0.221847
\(142\) −12.2056 + 136.846i −0.0859552 + 0.963701i
\(143\) 91.9598 0.643076
\(144\) 44.9932 + 16.7217i 0.312453 + 0.116123i
\(145\) 0 0
\(146\) −15.0642 + 168.895i −0.103179 + 1.15681i
\(147\) 82.3970 0.560524
\(148\) −35.5294 + 197.587i −0.240063 + 1.33505i
\(149\) 3.12940 0.0210027 0.0105013 0.999945i \(-0.496657\pi\)
0.0105013 + 0.999945i \(0.496657\pi\)
\(150\) 0 0
\(151\) 296.461i 1.96332i 0.190646 + 0.981659i \(0.438942\pi\)
−0.190646 + 0.981659i \(0.561058\pi\)
\(152\) −58.9999 + 215.806i −0.388157 + 1.41977i
\(153\) 62.7769i 0.410306i
\(154\) −1.74551 + 19.5701i −0.0113345 + 0.127078i
\(155\) 0 0
\(156\) −13.7160 + 76.2779i −0.0879231 + 0.488961i
\(157\) 265.686i 1.69227i −0.532972 0.846133i \(-0.678925\pi\)
0.532972 0.846133i \(-0.321075\pi\)
\(158\) −4.13824 + 46.3965i −0.0261914 + 0.293649i
\(159\) 99.1101i 0.623334i
\(160\) 0 0
\(161\) 11.3355 0.0704067
\(162\) −17.9288 1.59912i −0.110672 0.00987113i
\(163\) −205.531 −1.26093 −0.630465 0.776218i \(-0.717136\pi\)
−0.630465 + 0.776218i \(0.717136\pi\)
\(164\) −289.895 52.1278i −1.76765 0.317852i
\(165\) 0 0
\(166\) −185.781 16.5704i −1.11917 0.0998215i
\(167\) −11.6359 −0.0696763 −0.0348381 0.999393i \(-0.511092\pi\)
−0.0348381 + 0.999393i \(0.511092\pi\)
\(168\) −15.9724 4.36677i −0.0950740 0.0259927i
\(169\) 43.8657 0.259560
\(170\) 0 0
\(171\) 83.8970i 0.490626i
\(172\) −75.1323 13.5100i −0.436816 0.0785466i
\(173\) 106.062i 0.613077i 0.951858 + 0.306538i \(0.0991708\pi\)
−0.951858 + 0.306538i \(0.900829\pi\)
\(174\) −139.467 12.4395i −0.801535 0.0714912i
\(175\) 0 0
\(176\) −45.8214 + 123.292i −0.260349 + 0.700523i
\(177\) 105.074i 0.593639i
\(178\) 125.481 + 11.1920i 0.704951 + 0.0628766i
\(179\) 43.3304i 0.242069i −0.992648 0.121035i \(-0.961379\pi\)
0.992648 0.121035i \(-0.0386212\pi\)
\(180\) 0 0
\(181\) 203.614 1.12494 0.562469 0.826819i \(-0.309852\pi\)
0.562469 + 0.826819i \(0.309852\pi\)
\(182\) 2.37520 26.6300i 0.0130506 0.146319i
\(183\) 36.9824 0.202090
\(184\) 73.1988 + 20.0121i 0.397819 + 0.108761i
\(185\) 0 0
\(186\) −17.0227 + 190.852i −0.0915197 + 1.02609i
\(187\) −172.024 −0.919913
\(188\) −71.0988 12.7847i −0.378185 0.0680038i
\(189\) 6.20948 0.0328544
\(190\) 0 0
\(191\) 251.536i 1.31694i 0.752606 + 0.658471i \(0.228796\pi\)
−0.752606 + 0.658471i \(0.771204\pi\)
\(192\) −95.4327 56.3968i −0.497045 0.293733i
\(193\) 281.811i 1.46016i 0.683360 + 0.730081i \(0.260518\pi\)
−0.683360 + 0.730081i \(0.739482\pi\)
\(194\) 16.2393 182.070i 0.0837078 0.938503i
\(195\) 0 0
\(196\) −187.284 33.6767i −0.955531 0.171820i
\(197\) 243.485i 1.23596i −0.786193 0.617982i \(-0.787951\pi\)
0.786193 0.617982i \(-0.212049\pi\)
\(198\) 4.38198 49.1293i 0.0221312 0.248128i
\(199\) 121.958i 0.612853i −0.951894 0.306427i \(-0.900867\pi\)
0.951894 0.306427i \(-0.0991335\pi\)
\(200\) 0 0
\(201\) 16.7780 0.0834727
\(202\) 59.7188 + 5.32649i 0.295638 + 0.0263688i
\(203\) 48.3031 0.237946
\(204\) 25.6577 142.688i 0.125773 0.699453i
\(205\) 0 0
\(206\) 176.795 + 15.7689i 0.858229 + 0.0765479i
\(207\) −28.4569 −0.137473
\(208\) 62.3515 167.770i 0.299767 0.806585i
\(209\) 229.898 1.09999
\(210\) 0 0
\(211\) 132.543i 0.628168i 0.949395 + 0.314084i \(0.101697\pi\)
−0.949395 + 0.314084i \(0.898303\pi\)
\(212\) −40.5076 + 225.272i −0.191073 + 1.06260i
\(213\) 118.982i 0.558602i
\(214\) −324.555 28.9480i −1.51661 0.135271i
\(215\) 0 0
\(216\) 40.0977 + 10.9625i 0.185637 + 0.0507521i
\(217\) 66.0998i 0.304608i
\(218\) −205.886 18.3636i −0.944433 0.0842366i
\(219\) 146.848i 0.670537i
\(220\) 0 0
\(221\) 234.081 1.05919
\(222\) −15.4457 + 173.172i −0.0695754 + 0.780056i
\(223\) −225.442 −1.01095 −0.505475 0.862841i \(-0.668683\pi\)
−0.505475 + 0.862841i \(0.668683\pi\)
\(224\) 34.5198 + 16.4536i 0.154106 + 0.0734534i
\(225\) 0 0
\(226\) 5.55590 62.2908i 0.0245836 0.275623i
\(227\) −108.080 −0.476124 −0.238062 0.971250i \(-0.576512\pi\)
−0.238062 + 0.971250i \(0.576512\pi\)
\(228\) −34.2898 + 190.693i −0.150394 + 0.836375i
\(229\) 57.3495 0.250435 0.125217 0.992129i \(-0.460037\pi\)
0.125217 + 0.992129i \(0.460037\pi\)
\(230\) 0 0
\(231\) 17.0155i 0.0736600i
\(232\) 311.917 + 85.2762i 1.34447 + 0.367570i
\(233\) 285.320i 1.22455i −0.790646 0.612274i \(-0.790255\pi\)
0.790646 0.612274i \(-0.209745\pi\)
\(234\) −5.96278 + 66.8527i −0.0254820 + 0.285695i
\(235\) 0 0
\(236\) −42.9451 + 238.828i −0.181971 + 1.01198i
\(237\) 40.3400i 0.170211i
\(238\) −4.44315 + 49.8151i −0.0186687 + 0.209307i
\(239\) 77.2471i 0.323210i 0.986856 + 0.161605i \(0.0516670\pi\)
−0.986856 + 0.161605i \(0.948333\pi\)
\(240\) 0 0
\(241\) −130.557 −0.541732 −0.270866 0.962617i \(-0.587310\pi\)
−0.270866 + 0.962617i \(0.587310\pi\)
\(242\) −106.417 9.49164i −0.439740 0.0392217i
\(243\) −15.5885 −0.0641500
\(244\) −84.0591 15.1152i −0.344504 0.0619475i
\(245\) 0 0
\(246\) −254.074 22.6616i −1.03282 0.0921203i
\(247\) −312.834 −1.26653
\(248\) 116.695 426.840i 0.470546 1.72113i
\(249\) −161.530 −0.648715
\(250\) 0 0
\(251\) 437.197i 1.74182i −0.491441 0.870911i \(-0.663530\pi\)
0.491441 0.870911i \(-0.336470\pi\)
\(252\) −14.1138 2.53789i −0.0560072 0.0100710i
\(253\) 77.9788i 0.308216i
\(254\) 355.537 + 31.7114i 1.39975 + 0.124848i
\(255\) 0 0
\(256\) 193.863 + 167.191i 0.757279 + 0.653091i
\(257\) 74.3682i 0.289370i 0.989478 + 0.144685i \(0.0462169\pi\)
−0.989478 + 0.144685i \(0.953783\pi\)
\(258\) −65.8486 5.87323i −0.255227 0.0227644i
\(259\) 59.9766i 0.231570i
\(260\) 0 0
\(261\) −121.261 −0.464603
\(262\) −27.3172 + 306.271i −0.104264 + 1.16897i
\(263\) −458.790 −1.74445 −0.872225 0.489105i \(-0.837324\pi\)
−0.872225 + 0.489105i \(0.837324\pi\)
\(264\) −30.0398 + 109.877i −0.113787 + 0.416202i
\(265\) 0 0
\(266\) 5.93797 66.5745i 0.0223232 0.250280i
\(267\) 109.101 0.408620
\(268\) −38.1355 6.85739i −0.142297 0.0255873i
\(269\) 320.405 1.19110 0.595549 0.803319i \(-0.296935\pi\)
0.595549 + 0.803319i \(0.296935\pi\)
\(270\) 0 0
\(271\) 359.059i 1.32494i 0.749088 + 0.662470i \(0.230492\pi\)
−0.749088 + 0.662470i \(0.769508\pi\)
\(272\) −116.637 + 313.837i −0.428813 + 1.15381i
\(273\) 23.1538i 0.0848124i
\(274\) −9.41579 + 105.567i −0.0343642 + 0.385280i
\(275\) 0 0
\(276\) 64.6810 + 11.6307i 0.234352 + 0.0421402i
\(277\) 138.027i 0.498293i 0.968466 + 0.249147i \(0.0801501\pi\)
−0.968466 + 0.249147i \(0.919850\pi\)
\(278\) 3.88090 43.5113i 0.0139601 0.156516i
\(279\) 165.939i 0.594764i
\(280\) 0 0
\(281\) 462.504 1.64592 0.822960 0.568099i \(-0.192321\pi\)
0.822960 + 0.568099i \(0.192321\pi\)
\(282\) −62.3135 5.55792i −0.220970 0.0197089i
\(283\) 323.973 1.14478 0.572391 0.819981i \(-0.306016\pi\)
0.572391 + 0.819981i \(0.306016\pi\)
\(284\) 48.6295 270.440i 0.171231 0.952254i
\(285\) 0 0
\(286\) −183.192 16.3394i −0.640533 0.0571309i
\(287\) 87.9962 0.306607
\(288\) −86.6594 41.3055i −0.300901 0.143422i
\(289\) −148.882 −0.515161
\(290\) 0 0
\(291\) 158.303i 0.543996i
\(292\) 60.0185 333.777i 0.205543 1.14307i
\(293\) 150.416i 0.513365i −0.966496 0.256683i \(-0.917371\pi\)
0.966496 0.256683i \(-0.0826295\pi\)
\(294\) −164.142 14.6403i −0.558308 0.0497970i
\(295\) 0 0
\(296\) 105.885 387.299i 0.357720 1.30844i
\(297\) 42.7161i 0.143825i
\(298\) −6.23406 0.556033i −0.0209196 0.00186588i
\(299\) 106.110i 0.354882i
\(300\) 0 0
\(301\) 22.8060 0.0757676
\(302\) 52.6753 590.577i 0.174421 1.95555i
\(303\) 51.9233 0.171364
\(304\) 155.878 419.421i 0.512755 1.37968i
\(305\) 0 0
\(306\) 11.1542 125.057i 0.0364517 0.408684i
\(307\) 563.915 1.83686 0.918428 0.395587i \(-0.129459\pi\)
0.918428 + 0.395587i \(0.129459\pi\)
\(308\) 6.95443 38.6752i 0.0225793 0.125569i
\(309\) 153.717 0.497466
\(310\) 0 0
\(311\) 40.0214i 0.128686i −0.997928 0.0643431i \(-0.979505\pi\)
0.997928 0.0643431i \(-0.0204952\pi\)
\(312\) 40.8766 149.515i 0.131015 0.479216i
\(313\) 1.82657i 0.00583568i −0.999996 0.00291784i \(-0.999071\pi\)
0.999996 0.00291784i \(-0.000928778\pi\)
\(314\) −47.2071 + 529.270i −0.150341 + 1.68557i
\(315\) 0 0
\(316\) 16.4875 91.6908i 0.0521756 0.290161i
\(317\) 246.416i 0.777338i 0.921378 + 0.388669i \(0.127065\pi\)
−0.921378 + 0.388669i \(0.872935\pi\)
\(318\) −17.6099 + 197.436i −0.0553771 + 0.620869i
\(319\) 332.286i 1.04165i
\(320\) 0 0
\(321\) −282.189 −0.879092
\(322\) −22.5813 2.01409i −0.0701283 0.00625494i
\(323\) 585.199 1.81176
\(324\) 35.4317 + 6.37120i 0.109357 + 0.0196642i
\(325\) 0 0
\(326\) 409.438 + 36.5189i 1.25594 + 0.112021i
\(327\) −179.011 −0.547433
\(328\) 568.235 + 155.352i 1.73242 + 0.473634i
\(329\) 21.5817 0.0655978
\(330\) 0 0
\(331\) 417.672i 1.26185i −0.775844 0.630925i \(-0.782675\pi\)
0.775844 0.630925i \(-0.217325\pi\)
\(332\) 367.149 + 66.0194i 1.10587 + 0.198854i
\(333\) 150.567i 0.452153i
\(334\) 23.1798 + 2.06748i 0.0694007 + 0.00619005i
\(335\) 0 0
\(336\) 31.0427 + 11.5370i 0.0923889 + 0.0343363i
\(337\) 317.379i 0.941779i −0.882192 0.470889i \(-0.843933\pi\)
0.882192 0.470889i \(-0.156067\pi\)
\(338\) −87.3845 7.79408i −0.258534 0.0230594i
\(339\) 54.1596i 0.159763i
\(340\) 0 0
\(341\) −454.713 −1.33347
\(342\) −14.9068 + 167.131i −0.0435873 + 0.488686i
\(343\) 115.405 0.336457
\(344\) 147.270 + 40.2627i 0.428110 + 0.117043i
\(345\) 0 0
\(346\) 18.8452 211.286i 0.0544659 0.610653i
\(347\) 222.581 0.641443 0.320721 0.947174i \(-0.396075\pi\)
0.320721 + 0.947174i \(0.396075\pi\)
\(348\) 275.621 + 49.5611i 0.792014 + 0.142417i
\(349\) −560.812 −1.60691 −0.803455 0.595366i \(-0.797007\pi\)
−0.803455 + 0.595366i \(0.797007\pi\)
\(350\) 0 0
\(351\) 58.1259i 0.165601i
\(352\) 113.187 237.468i 0.321554 0.674624i
\(353\) 304.856i 0.863616i −0.901966 0.431808i \(-0.857876\pi\)
0.901966 0.431808i \(-0.142124\pi\)
\(354\) −18.6696 + 209.317i −0.0527390 + 0.591291i
\(355\) 0 0
\(356\) −247.982 44.5911i −0.696578 0.125256i
\(357\) 43.3124i 0.121323i
\(358\) −7.69896 + 86.3181i −0.0215055 + 0.241112i
\(359\) 105.860i 0.294874i −0.989071 0.147437i \(-0.952898\pi\)
0.989071 0.147437i \(-0.0471023\pi\)
\(360\) 0 0
\(361\) −421.079 −1.16642
\(362\) −405.617 36.1782i −1.12049 0.0999396i
\(363\) −92.5257 −0.254892
\(364\) −9.46324 + 52.6273i −0.0259979 + 0.144581i
\(365\) 0 0
\(366\) −73.6724 6.57105i −0.201291 0.0179537i
\(367\) 360.200 0.981470 0.490735 0.871309i \(-0.336728\pi\)
0.490735 + 0.871309i \(0.336728\pi\)
\(368\) −142.263 52.8719i −0.386584 0.143674i
\(369\) −220.908 −0.598667
\(370\) 0 0
\(371\) 68.3802i 0.184313i
\(372\) 67.8214 377.171i 0.182316 1.01390i
\(373\) 135.489i 0.363242i 0.983369 + 0.181621i \(0.0581344\pi\)
−0.983369 + 0.181621i \(0.941866\pi\)
\(374\) 342.687 + 30.5652i 0.916275 + 0.0817252i
\(375\) 0 0
\(376\) 139.364 + 38.1012i 0.370648 + 0.101333i
\(377\) 452.158i 1.19936i
\(378\) −12.3698 1.10330i −0.0327245 0.00291879i
\(379\) 310.686i 0.819753i 0.912141 + 0.409876i \(0.134428\pi\)
−0.912141 + 0.409876i \(0.865572\pi\)
\(380\) 0 0
\(381\) 309.126 0.811356
\(382\) 44.6930 501.083i 0.116997 1.31173i
\(383\) −121.981 −0.318487 −0.159244 0.987239i \(-0.550906\pi\)
−0.159244 + 0.987239i \(0.550906\pi\)
\(384\) 180.090 + 129.304i 0.468985 + 0.336729i
\(385\) 0 0
\(386\) 50.0723 561.394i 0.129721 1.45439i
\(387\) −57.2530 −0.147941
\(388\) −64.7004 + 359.814i −0.166754 + 0.927356i
\(389\) −544.266 −1.39914 −0.699570 0.714564i \(-0.746625\pi\)
−0.699570 + 0.714564i \(0.746625\pi\)
\(390\) 0 0
\(391\) 198.493i 0.507654i
\(392\) 367.103 + 100.364i 0.936488 + 0.256030i
\(393\) 266.291i 0.677586i
\(394\) −43.2625 + 485.044i −0.109803 + 1.23108i
\(395\) 0 0
\(396\) −17.4586 + 97.0915i −0.0440874 + 0.245180i
\(397\) 504.528i 1.27085i 0.772162 + 0.635425i \(0.219175\pi\)
−0.772162 + 0.635425i \(0.780825\pi\)
\(398\) −21.6695 + 242.951i −0.0544460 + 0.610430i
\(399\) 57.8841i 0.145073i
\(400\) 0 0
\(401\) −278.018 −0.693312 −0.346656 0.937992i \(-0.612683\pi\)
−0.346656 + 0.937992i \(0.612683\pi\)
\(402\) −33.4233 2.98112i −0.0831426 0.00741573i
\(403\) 618.750 1.53536
\(404\) −118.019 21.2217i −0.292126 0.0525290i
\(405\) 0 0
\(406\) −96.2242 8.58251i −0.237005 0.0211392i
\(407\) −412.590 −1.01373
\(408\) −76.4654 + 279.690i −0.187415 + 0.685514i
\(409\) 296.549 0.725059 0.362530 0.931972i \(-0.381913\pi\)
0.362530 + 0.931972i \(0.381913\pi\)
\(410\) 0 0
\(411\) 91.7863i 0.223324i
\(412\) −349.390 62.8261i −0.848035 0.152490i
\(413\) 72.4950i 0.175533i
\(414\) 56.6888 + 5.05623i 0.136929 + 0.0122131i
\(415\) 0 0
\(416\) −154.019 + 323.134i −0.370239 + 0.776764i
\(417\) 37.8315i 0.0907230i
\(418\) −457.978 40.8483i −1.09564 0.0977233i
\(419\) 315.615i 0.753258i 0.926364 + 0.376629i \(0.122917\pi\)
−0.926364 + 0.376629i \(0.877083\pi\)
\(420\) 0 0
\(421\) −360.355 −0.855951 −0.427975 0.903790i \(-0.640773\pi\)
−0.427975 + 0.903790i \(0.640773\pi\)
\(422\) 23.5504 264.039i 0.0558066 0.625684i
\(423\) −54.1793 −0.128084
\(424\) 120.721 441.565i 0.284720 1.04143i
\(425\) 0 0
\(426\) 21.1408 237.023i 0.0496263 0.556393i
\(427\) 25.5157 0.0597558
\(428\) 641.400 + 115.334i 1.49860 + 0.269472i
\(429\) −159.279 −0.371280
\(430\) 0 0
\(431\) 523.617i 1.21489i 0.794362 + 0.607445i \(0.207805\pi\)
−0.794362 + 0.607445i \(0.792195\pi\)
\(432\) −77.9305 28.9628i −0.180395 0.0670435i
\(433\) 21.5381i 0.0497415i 0.999691 + 0.0248707i \(0.00791742\pi\)
−0.999691 + 0.0248707i \(0.992083\pi\)
\(434\) −11.7446 + 131.677i −0.0270614 + 0.303403i
\(435\) 0 0
\(436\) 406.882 + 73.1639i 0.933215 + 0.167807i
\(437\) 265.272i 0.607030i
\(438\) 26.0919 292.534i 0.0595706 0.667886i
\(439\) 247.777i 0.564412i 0.959354 + 0.282206i \(0.0910662\pi\)
−0.959354 + 0.282206i \(0.908934\pi\)
\(440\) 0 0
\(441\) −142.716 −0.323619
\(442\) −466.311 41.5916i −1.05500 0.0940987i
\(443\) −584.775 −1.32003 −0.660017 0.751251i \(-0.729451\pi\)
−0.660017 + 0.751251i \(0.729451\pi\)
\(444\) 61.5386 342.231i 0.138601 0.770790i
\(445\) 0 0
\(446\) 449.101 + 40.0566i 1.00695 + 0.0898130i
\(447\) −5.42028 −0.0121259
\(448\) −65.8430 38.9105i −0.146971 0.0868538i
\(449\) −152.093 −0.338738 −0.169369 0.985553i \(-0.554173\pi\)
−0.169369 + 0.985553i \(0.554173\pi\)
\(450\) 0 0
\(451\) 605.342i 1.34222i
\(452\) −22.1357 + 123.102i −0.0489728 + 0.272349i
\(453\) 513.485i 1.13352i
\(454\) 215.306 + 19.2037i 0.474242 + 0.0422990i
\(455\) 0 0
\(456\) 102.191 373.786i 0.224103 0.819707i
\(457\) 602.441i 1.31825i 0.752033 + 0.659126i \(0.229074\pi\)
−0.752033 + 0.659126i \(0.770926\pi\)
\(458\) −114.246 10.1899i −0.249444 0.0222487i
\(459\) 108.733i 0.236890i
\(460\) 0 0
\(461\) −504.912 −1.09525 −0.547626 0.836723i \(-0.684468\pi\)
−0.547626 + 0.836723i \(0.684468\pi\)
\(462\) 3.02331 33.8964i 0.00654397 0.0733687i
\(463\) −504.560 −1.08976 −0.544881 0.838513i \(-0.683425\pi\)
−0.544881 + 0.838513i \(0.683425\pi\)
\(464\) −606.215 225.300i −1.30650 0.485559i
\(465\) 0 0
\(466\) −50.6957 + 568.383i −0.108789 + 1.21971i
\(467\) 751.418 1.60903 0.804516 0.593931i \(-0.202425\pi\)
0.804516 + 0.593931i \(0.202425\pi\)
\(468\) 23.7568 132.117i 0.0507624 0.282302i
\(469\) 11.5759 0.0246820
\(470\) 0 0
\(471\) 460.181i 0.977030i
\(472\) 127.986 468.136i 0.271156 0.991814i
\(473\) 156.887i 0.331685i
\(474\) 7.16763 80.3611i 0.0151216 0.169538i
\(475\) 0 0
\(476\) 17.7023 98.4468i 0.0371898 0.206821i
\(477\) 171.664i 0.359882i
\(478\) 13.7253 153.883i 0.0287140 0.321932i
\(479\) 581.401i 1.21378i −0.794786 0.606890i \(-0.792417\pi\)
0.794786 0.606890i \(-0.207583\pi\)
\(480\) 0 0
\(481\) 561.431 1.16722
\(482\) 260.082 + 23.1975i 0.539590 + 0.0481276i
\(483\) −19.6336 −0.0406493
\(484\) 210.306 + 37.8164i 0.434517 + 0.0781331i
\(485\) 0 0
\(486\) 31.0536 + 2.76976i 0.0638964 + 0.00569910i
\(487\) −557.489 −1.14474 −0.572371 0.819995i \(-0.693976\pi\)
−0.572371 + 0.819995i \(0.693976\pi\)
\(488\) 164.768 + 45.0465i 0.337639 + 0.0923084i
\(489\) 355.991 0.727998
\(490\) 0 0
\(491\) 26.2032i 0.0533670i −0.999644 0.0266835i \(-0.991505\pi\)
0.999644 0.0266835i \(-0.00849463\pi\)
\(492\) 502.113 + 90.2880i 1.02055 + 0.183512i
\(493\) 845.824i 1.71567i
\(494\) 623.193 + 55.5844i 1.26152 + 0.112519i
\(495\) 0 0
\(496\) −308.309 + 829.569i −0.621590 + 1.67252i
\(497\) 82.0908i 0.165173i
\(498\) 321.783 + 28.7007i 0.646150 + 0.0576320i
\(499\) 444.615i 0.891011i 0.895279 + 0.445506i \(0.146976\pi\)
−0.895279 + 0.445506i \(0.853024\pi\)
\(500\) 0 0
\(501\) 20.1540 0.0402276
\(502\) −77.6814 + 870.937i −0.154744 + 1.73493i
\(503\) 216.819 0.431052 0.215526 0.976498i \(-0.430853\pi\)
0.215526 + 0.976498i \(0.430853\pi\)
\(504\) 27.6651 + 7.56346i 0.0548910 + 0.0150069i
\(505\) 0 0
\(506\) −13.8553 + 155.341i −0.0273820 + 0.306998i
\(507\) −75.9777 −0.149857
\(508\) −702.628 126.344i −1.38313 0.248708i
\(509\) −202.830 −0.398488 −0.199244 0.979950i \(-0.563849\pi\)
−0.199244 + 0.979950i \(0.563849\pi\)
\(510\) 0 0
\(511\) 101.316i 0.198271i
\(512\) −356.487 367.506i −0.696264 0.717786i
\(513\) 145.314i 0.283263i
\(514\) 13.2138 148.148i 0.0257077 0.288226i
\(515\) 0 0
\(516\) 130.133 + 23.4000i 0.252196 + 0.0453489i
\(517\) 148.464i 0.287165i
\(518\) −10.6567 + 119.479i −0.0205727 + 0.230654i
\(519\) 183.705i 0.353960i
\(520\) 0 0
\(521\) 769.410 1.47679 0.738397 0.674366i \(-0.235583\pi\)
0.738397 + 0.674366i \(0.235583\pi\)
\(522\) 241.564 + 21.5458i 0.462766 + 0.0412754i
\(523\) 38.9898 0.0745502 0.0372751 0.999305i \(-0.488132\pi\)
0.0372751 + 0.999305i \(0.488132\pi\)
\(524\) 108.837 605.266i 0.207703 1.15509i
\(525\) 0 0
\(526\) 913.953 + 81.5180i 1.73755 + 0.154977i
\(527\) −1157.46 −2.19632
\(528\) 79.3650 213.548i 0.150313 0.404447i
\(529\) −439.023 −0.829911
\(530\) 0 0
\(531\) 181.994i 0.342737i
\(532\) −23.6579 + 131.567i −0.0444698 + 0.247307i
\(533\) 823.718i 1.54544i
\(534\) −217.340 19.3852i −0.407004 0.0363018i
\(535\) 0 0
\(536\) 74.7510 + 20.4365i 0.139461 + 0.0381277i
\(537\) 75.0504i 0.139759i
\(538\) −638.277 56.9297i −1.18639 0.105817i
\(539\) 391.076i 0.725558i
\(540\) 0 0
\(541\) −32.0904 −0.0593168 −0.0296584 0.999560i \(-0.509442\pi\)
−0.0296584 + 0.999560i \(0.509442\pi\)
\(542\) 63.7977 715.278i 0.117708 1.31970i
\(543\) −352.669 −0.649483
\(544\) 288.115 604.467i 0.529622 1.11115i
\(545\) 0 0
\(546\) −4.11397 + 46.1245i −0.00753475 + 0.0844770i
\(547\) 254.839 0.465885 0.232942 0.972491i \(-0.425165\pi\)
0.232942 + 0.972491i \(0.425165\pi\)
\(548\) 37.5142 208.625i 0.0684566 0.380703i
\(549\) −64.0554 −0.116677
\(550\) 0 0
\(551\) 1130.39i 2.05152i
\(552\) −126.784 34.6620i −0.229681 0.0627934i
\(553\) 27.8323i 0.0503296i
\(554\) 24.5247 274.963i 0.0442685 0.496323i
\(555\) 0 0
\(556\) −15.4622 + 85.9890i −0.0278097 + 0.154656i
\(557\) 577.439i 1.03670i −0.855170 0.518348i \(-0.826547\pi\)
0.855170 0.518348i \(-0.173453\pi\)
\(558\) 29.4841 330.566i 0.0528389 0.592412i
\(559\) 213.484i 0.381903i
\(560\) 0 0
\(561\) 297.954 0.531112
\(562\) −921.350 82.1778i −1.63941 0.146224i
\(563\) −367.058 −0.651967 −0.325984 0.945375i \(-0.605695\pi\)
−0.325984 + 0.945375i \(0.605695\pi\)
\(564\) 123.147 + 22.1438i 0.218345 + 0.0392620i
\(565\) 0 0
\(566\) −645.384 57.5636i −1.14025 0.101703i
\(567\) −10.7551 −0.0189685
\(568\) −144.926 + 530.101i −0.255152 + 0.933277i
\(569\) 522.006 0.917410 0.458705 0.888589i \(-0.348313\pi\)
0.458705 + 0.888589i \(0.348313\pi\)
\(570\) 0 0
\(571\) 832.421i 1.45783i −0.684604 0.728915i \(-0.740025\pi\)
0.684604 0.728915i \(-0.259975\pi\)
\(572\) 362.033 + 65.0994i 0.632925 + 0.113810i
\(573\) 435.673i 0.760337i
\(574\) −175.296 15.6352i −0.305394 0.0272390i
\(575\) 0 0
\(576\) 165.294 + 97.6821i 0.286969 + 0.169587i
\(577\) 427.659i 0.741177i −0.928797 0.370588i \(-0.879156\pi\)
0.928797 0.370588i \(-0.120844\pi\)
\(578\) 296.586 + 26.4533i 0.513124 + 0.0457670i
\(579\) 488.112i 0.843025i
\(580\) 0 0
\(581\) −111.446 −0.191818
\(582\) −28.1273 + 315.354i −0.0483287 + 0.541845i
\(583\) −470.400 −0.806861
\(584\) −178.868 + 654.250i −0.306281 + 1.12029i
\(585\) 0 0
\(586\) −26.7260 + 299.642i −0.0456074 + 0.511335i
\(587\) −586.262 −0.998743 −0.499372 0.866388i \(-0.666436\pi\)
−0.499372 + 0.866388i \(0.666436\pi\)
\(588\) 324.385 + 58.3298i 0.551676 + 0.0992003i
\(589\) 1546.87 2.62626
\(590\) 0 0
\(591\) 421.728i 0.713584i
\(592\) −279.748 + 752.721i −0.472548 + 1.27149i
\(593\) 518.375i 0.874156i 0.899424 + 0.437078i \(0.143987\pi\)
−0.899424 + 0.437078i \(0.856013\pi\)
\(594\) −7.58981 + 85.0944i −0.0127775 + 0.143257i
\(595\) 0 0
\(596\) 12.3200 + 2.21534i 0.0206712 + 0.00371701i
\(597\) 211.237i 0.353831i
\(598\) 18.8536 211.380i 0.0315277 0.353478i
\(599\) 405.480i 0.676928i 0.940979 + 0.338464i \(0.109907\pi\)
−0.940979 + 0.338464i \(0.890093\pi\)
\(600\) 0 0
\(601\) −350.551 −0.583279 −0.291640 0.956528i \(-0.594201\pi\)
−0.291640 + 0.956528i \(0.594201\pi\)
\(602\) −45.4317 4.05219i −0.0754680 0.00673121i
\(603\) −29.0604 −0.0481930
\(604\) −209.868 + 1167.13i −0.347464 + 1.93233i
\(605\) 0 0
\(606\) −103.436 9.22576i −0.170687 0.0152240i
\(607\) 737.786 1.21546 0.607731 0.794143i \(-0.292080\pi\)
0.607731 + 0.794143i \(0.292080\pi\)
\(608\) −385.046 + 807.829i −0.633299 + 1.32867i
\(609\) −83.6634 −0.137378
\(610\) 0 0
\(611\) 202.023i 0.330643i
\(612\) −44.4404 + 247.144i −0.0726151 + 0.403830i
\(613\) 345.495i 0.563614i 0.959471 + 0.281807i \(0.0909338\pi\)
−0.959471 + 0.281807i \(0.909066\pi\)
\(614\) −1123.37 100.197i −1.82959 0.163187i
\(615\) 0 0
\(616\) −20.7257 + 75.8090i −0.0336456 + 0.123066i
\(617\) 862.171i 1.39736i −0.715434 0.698680i \(-0.753771\pi\)
0.715434 0.698680i \(-0.246229\pi\)
\(618\) −306.218 27.3125i −0.495499 0.0441950i
\(619\) 469.363i 0.758260i 0.925343 + 0.379130i \(0.123777\pi\)
−0.925343 + 0.379130i \(0.876223\pi\)
\(620\) 0 0
\(621\) 49.2888 0.0793701
\(622\) −7.11102 + 79.7264i −0.0114325 + 0.128177i
\(623\) 75.2737 0.120824
\(624\) −107.996 + 290.586i −0.173070 + 0.465682i
\(625\) 0 0
\(626\) −0.324545 + 3.63869i −0.000518443 + 0.00581260i
\(627\) −398.195 −0.635080
\(628\) 188.082 1045.97i 0.299494 1.66555i
\(629\) −1050.24 −1.66969
\(630\) 0 0
\(631\) 323.243i 0.512271i −0.966641 0.256136i \(-0.917551\pi\)
0.966641 0.256136i \(-0.0824494\pi\)
\(632\) −49.1362 + 179.727i −0.0777472 + 0.284378i
\(633\) 229.572i 0.362673i
\(634\) 43.7833 490.883i 0.0690588 0.774264i
\(635\) 0 0
\(636\) 70.1611 390.183i 0.110316 0.613495i
\(637\) 532.156i 0.835410i
\(638\) −59.0406 + 661.943i −0.0925402 + 1.03753i
\(639\) 206.083i 0.322509i
\(640\) 0 0
\(641\) −44.1100 −0.0688144 −0.0344072 0.999408i \(-0.510954\pi\)
−0.0344072 + 0.999408i \(0.510954\pi\)
\(642\) 562.146 + 50.1394i 0.875616 + 0.0780987i
\(643\) 934.204 1.45288 0.726442 0.687228i \(-0.241173\pi\)
0.726442 + 0.687228i \(0.241173\pi\)
\(644\) 44.6262 + 8.02451i 0.0692953 + 0.0124604i
\(645\) 0 0
\(646\) −1165.77 103.978i −1.80460 0.160957i
\(647\) 481.023 0.743467 0.371734 0.928339i \(-0.378763\pi\)
0.371734 + 0.928339i \(0.378763\pi\)
\(648\) −69.4512 18.9875i −0.107178 0.0293018i
\(649\) −498.706 −0.768422
\(650\) 0 0
\(651\) 114.488i 0.175865i
\(652\) −809.148 145.498i −1.24103 0.223156i
\(653\) 1131.38i 1.73259i 0.499536 + 0.866293i \(0.333504\pi\)
−0.499536 + 0.866293i \(0.666496\pi\)
\(654\) 356.606 + 31.8067i 0.545268 + 0.0486340i
\(655\) 0 0
\(656\) −1104.37 410.440i −1.68350 0.625670i
\(657\) 254.348i 0.387135i
\(658\) −42.9927 3.83464i −0.0653385 0.00582772i
\(659\) 154.348i 0.234215i −0.993119 0.117107i \(-0.962638\pi\)
0.993119 0.117107i \(-0.0373622\pi\)
\(660\) 0 0
\(661\) 795.115 1.20290 0.601448 0.798912i \(-0.294591\pi\)
0.601448 + 0.798912i \(0.294591\pi\)
\(662\) −74.2122 + 832.042i −0.112103 + 1.25686i
\(663\) −405.441 −0.611524
\(664\) −719.665 196.752i −1.08383 0.296313i
\(665\) 0 0
\(666\) 26.7528 299.943i 0.0401694 0.450365i
\(667\) 383.414 0.574834
\(668\) −45.8090 8.23721i −0.0685764 0.0123311i
\(669\) 390.477 0.583672
\(670\) 0 0
\(671\) 175.527i 0.261591i
\(672\) −59.7900 28.4984i −0.0889732 0.0424083i
\(673\) 197.215i 0.293039i 0.989208 + 0.146520i \(0.0468071\pi\)
−0.989208 + 0.146520i \(0.953193\pi\)
\(674\) −56.3921 + 632.249i −0.0836678 + 0.938055i
\(675\) 0 0
\(676\) 172.693 + 31.0530i 0.255463 + 0.0459364i
\(677\) 530.367i 0.783408i −0.920091 0.391704i \(-0.871886\pi\)
0.920091 0.391704i \(-0.128114\pi\)
\(678\) −9.62309 + 107.891i −0.0141934 + 0.159131i
\(679\) 109.220i 0.160854i
\(680\) 0 0
\(681\) 187.200 0.274891
\(682\) 905.830 + 80.7935i 1.32820 + 0.118466i
\(683\) 797.231 1.16725 0.583625 0.812024i \(-0.301634\pi\)
0.583625 + 0.812024i \(0.301634\pi\)
\(684\) 59.3916 330.291i 0.0868299 0.482881i
\(685\) 0 0
\(686\) −229.897 20.5052i −0.335127 0.0298909i
\(687\) −99.3323 −0.144588
\(688\) −286.221 106.374i −0.416020 0.154613i
\(689\) 640.096 0.929022
\(690\) 0 0
\(691\) 498.569i 0.721518i −0.932659 0.360759i \(-0.882518\pi\)
0.932659 0.360759i \(-0.117482\pi\)
\(692\) −75.0827 + 417.552i −0.108501 + 0.603399i
\(693\) 29.4716i 0.0425276i
\(694\) −443.401 39.5482i −0.638906 0.0569859i
\(695\) 0 0
\(696\) −540.256 147.703i −0.776230 0.212217i
\(697\) 1540.88i 2.21073i
\(698\) 1117.19 + 99.6452i 1.60056 + 0.142758i
\(699\) 494.188i 0.706993i
\(700\) 0 0
\(701\) −455.939 −0.650412 −0.325206 0.945643i \(-0.605434\pi\)
−0.325206 + 0.945643i \(0.605434\pi\)
\(702\) 10.3278 115.792i 0.0147120 0.164946i
\(703\) 1403.57 1.99654
\(704\) −267.672 + 452.946i −0.380216 + 0.643389i
\(705\) 0 0
\(706\) −54.1670 + 607.302i −0.0767238 + 0.860201i
\(707\) 35.8241 0.0506706
\(708\) 74.3831 413.662i 0.105061 0.584268i
\(709\) 44.4190 0.0626502 0.0313251 0.999509i \(-0.490027\pi\)
0.0313251 + 0.999509i \(0.490027\pi\)
\(710\) 0 0
\(711\) 69.8710i 0.0982715i
\(712\) 486.080 + 132.891i 0.682696 + 0.186645i
\(713\) 524.679i 0.735875i
\(714\) 7.69576 86.2823i 0.0107784 0.120843i
\(715\) 0 0
\(716\) 30.6741 170.586i 0.0428409 0.238248i
\(717\) 133.796i 0.186605i
\(718\) −18.8092 + 210.882i −0.0261966 + 0.293708i
\(719\) 1349.94i 1.87752i −0.344566 0.938762i \(-0.611974\pi\)
0.344566 0.938762i \(-0.388026\pi\)
\(720\) 0 0
\(721\) 106.056 0.147095
\(722\) 838.827 + 74.8174i 1.16181 + 0.103625i
\(723\) 226.132 0.312769
\(724\) 801.599 + 144.140i 1.10718 + 0.199089i
\(725\) 0 0
\(726\) 184.320 + 16.4400i 0.253884 + 0.0226446i
\(727\) 191.470 0.263370 0.131685 0.991292i \(-0.457961\pi\)
0.131685 + 0.991292i \(0.457961\pi\)
\(728\) 28.2025 103.157i 0.0387397 0.141699i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 399.351i 0.546308i
\(732\) 145.595 + 26.1803i 0.198900 + 0.0357654i
\(733\) 358.832i 0.489539i −0.969581 0.244769i \(-0.921288\pi\)
0.969581 0.244769i \(-0.0787122\pi\)
\(734\) −717.551 64.0004i −0.977589 0.0871940i
\(735\) 0 0
\(736\) 274.007 + 130.603i 0.372291 + 0.177450i
\(737\) 79.6324i 0.108049i
\(738\) 440.069 + 39.2510i 0.596300 + 0.0531857i
\(739\) 756.311i 1.02342i −0.859157 0.511712i \(-0.829011\pi\)
0.859157 0.511712i \(-0.170989\pi\)
\(740\) 0 0
\(741\) 541.844 0.731233
\(742\) −12.1498 + 136.220i −0.0163744 + 0.183584i
\(743\) −1148.65 −1.54596 −0.772979 0.634432i \(-0.781234\pi\)
−0.772979 + 0.634432i \(0.781234\pi\)
\(744\) −202.122 + 739.308i −0.271670 + 0.993693i
\(745\) 0 0
\(746\) 24.0738 269.907i 0.0322705 0.361805i
\(747\) 279.778 0.374536
\(748\) −677.233 121.777i −0.905392 0.162804i
\(749\) −194.694 −0.259938
\(750\) 0 0
\(751\) 431.186i 0.574149i −0.957908 0.287074i \(-0.907317\pi\)
0.957908 0.287074i \(-0.0926827\pi\)
\(752\) −270.856 100.663i −0.360180 0.133861i
\(753\) 757.248i 1.00564i
\(754\) 80.3395 900.739i 0.106551 1.19461i
\(755\) 0 0
\(756\) 24.4458 + 4.39576i 0.0323358 + 0.00581449i
\(757\) 645.657i 0.852916i −0.904507 0.426458i \(-0.859761\pi\)
0.904507 0.426458i \(-0.140239\pi\)
\(758\) 55.2029 618.916i 0.0728270 0.816511i
\(759\) 135.063i 0.177949i
\(760\) 0 0
\(761\) −291.287 −0.382768 −0.191384 0.981515i \(-0.561298\pi\)
−0.191384 + 0.981515i \(0.561298\pi\)
\(762\) −615.808 54.9257i −0.808147 0.0720810i
\(763\) −123.507 −0.161870
\(764\) −178.065 + 990.261i −0.233069 + 1.29615i
\(765\) 0 0
\(766\) 242.997 + 21.6736i 0.317228 + 0.0282945i
\(767\) 678.614 0.884764
\(768\) −335.781 289.584i −0.437215 0.377063i
\(769\) 724.076 0.941582 0.470791 0.882245i \(-0.343969\pi\)
0.470791 + 0.882245i \(0.343969\pi\)
\(770\) 0 0
\(771\) 128.809i 0.167068i
\(772\) −199.497 + 1109.45i −0.258416 + 1.43711i
\(773\) 399.686i 0.517058i 0.966003 + 0.258529i \(0.0832378\pi\)
−0.966003 + 0.258529i \(0.916762\pi\)
\(774\) 114.053 + 10.1727i 0.147356 + 0.0131431i
\(775\) 0 0
\(776\) 192.821 705.287i 0.248481 0.908875i
\(777\) 103.882i 0.133697i
\(778\) 1084.23 + 96.7053i 1.39361 + 0.124300i
\(779\) 2059.28i 2.64349i
\(780\) 0 0
\(781\) 564.717 0.723070
\(782\) −35.2683 + 395.416i −0.0451001 + 0.505647i
\(783\) 210.031 0.268239
\(784\) −713.471 265.161i −0.910039 0.338215i
\(785\) 0 0
\(786\) 47.3147 530.476i 0.0601968 0.674906i
\(787\) 381.830