Properties

Label 300.3.c.g.151.4
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 151.4
Root \(0.845613 + 0.488215i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.g.151.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.177680 + 1.99209i) q^{2} -1.73205i q^{3} +(-3.93686 - 0.707911i) q^{4} +(3.45040 + 0.307751i) q^{6} +1.19501i q^{7} +(2.10973 - 7.71680i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-0.177680 + 1.99209i) q^{2} -1.73205i q^{3} +(-3.93686 - 0.707911i) q^{4} +(3.45040 + 0.307751i) q^{6} +1.19501i q^{7} +(2.10973 - 7.71680i) q^{8} -3.00000 q^{9} +8.22072i q^{11} +(-1.22614 + 6.81884i) q^{12} +11.1863 q^{13} +(-2.38058 - 0.212331i) q^{14} +(14.9977 + 5.57389i) q^{16} +20.9256 q^{17} +(0.533041 - 5.97628i) q^{18} +27.9657i q^{19} +2.06983 q^{21} +(-16.3764 - 1.46066i) q^{22} -9.48564i q^{23} +(-13.3659 - 3.65415i) q^{24} +(-1.98759 + 22.2842i) q^{26} +5.19615i q^{27} +(0.845964 - 4.70460i) q^{28} +40.4205 q^{29} +55.3130i q^{31} +(-13.7685 + 28.8865i) q^{32} +14.2387 q^{33} +(-3.71807 + 41.6858i) q^{34} +(11.8106 + 2.12373i) q^{36} +50.1890 q^{37} +(-55.7102 - 4.96895i) q^{38} -19.3753i q^{39} -73.6361 q^{41} +(-0.367767 + 4.12328i) q^{42} -19.0843i q^{43} +(5.81954 - 32.3638i) q^{44} +(18.8963 + 1.68541i) q^{46} +18.0598i q^{47} +(9.65427 - 25.9768i) q^{48} +47.5719 q^{49} -36.2442i q^{51} +(-44.0391 - 7.91894i) q^{52} -57.2212 q^{53} +(-10.3512 - 0.923254i) q^{54} +(9.22169 + 2.52115i) q^{56} +48.4380 q^{57} +(-7.18193 + 80.5213i) q^{58} -60.6645i q^{59} -21.3518 q^{61} +(-110.189 - 9.82804i) q^{62} -3.58504i q^{63} +(-55.0981 - 32.5607i) q^{64} +(-2.52994 + 28.3648i) q^{66} +9.68679i q^{67} +(-82.3812 - 14.8135i) q^{68} -16.4296 q^{69} -68.6944i q^{71} +(-6.32918 + 23.1504i) q^{72} +84.7825 q^{73} +(-8.91760 + 99.9811i) q^{74} +(19.7972 - 110.097i) q^{76} -9.82388 q^{77} +(38.5974 + 3.44261i) q^{78} +23.2903i q^{79} +9.00000 q^{81} +(13.0837 - 146.690i) q^{82} +93.2595i q^{83} +(-8.14861 - 1.46525i) q^{84} +(38.0177 + 3.39091i) q^{86} -70.0104i q^{87} +(63.4377 + 17.3435i) q^{88} +62.9898 q^{89} +13.3678i q^{91} +(-6.71499 + 37.3436i) q^{92} +95.8049 q^{93} +(-35.9767 - 3.20887i) q^{94} +(50.0328 + 23.8478i) q^{96} +91.3962 q^{97} +(-8.45260 + 94.7677i) q^{98} -24.6622i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 8q^{4} - 6q^{6} + 20q^{8} - 24q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 8q^{4} - 6q^{6} + 20q^{8} - 24q^{9} + 8q^{13} + 22q^{14} + 40q^{16} - 6q^{18} + 24q^{21} + 4q^{22} - 36q^{24} - 66q^{26} + 104q^{28} - 32q^{29} + 112q^{32} + 124q^{34} + 24q^{36} - 176q^{37} - 170q^{38} - 16q^{41} + 54q^{42} + 40q^{44} - 76q^{46} + 24q^{48} + 16q^{49} + 56q^{52} - 304q^{53} + 18q^{54} - 172q^{56} + 72q^{57} - 12q^{58} + 136q^{61} - 238q^{62} + 16q^{64} - 108q^{66} + 88q^{68} - 96q^{69} - 60q^{72} + 240q^{73} - 108q^{74} + 120q^{76} - 384q^{77} + 150q^{78} + 72q^{81} + 320q^{82} - 144q^{84} + 214q^{86} - 200q^{88} + 128q^{89} + 312q^{92} + 72q^{93} + 12q^{94} + 96q^{96} + 216q^{97} + 60q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.177680 + 1.99209i −0.0888402 + 0.996046i
\(3\) 1.73205i 0.577350i
\(4\) −3.93686 0.707911i −0.984215 0.176978i
\(5\) 0 0
\(6\) 3.45040 + 0.307751i 0.575067 + 0.0512919i
\(7\) 1.19501i 0.170716i 0.996350 + 0.0853582i \(0.0272035\pi\)
−0.996350 + 0.0853582i \(0.972797\pi\)
\(8\) 2.10973 7.71680i 0.263716 0.964600i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 8.22072i 0.747338i 0.927562 + 0.373669i \(0.121900\pi\)
−0.927562 + 0.373669i \(0.878100\pi\)
\(12\) −1.22614 + 6.81884i −0.102178 + 0.568237i
\(13\) 11.1863 0.860488 0.430244 0.902713i \(-0.358428\pi\)
0.430244 + 0.902713i \(0.358428\pi\)
\(14\) −2.38058 0.212331i −0.170041 0.0151665i
\(15\) 0 0
\(16\) 14.9977 + 5.57389i 0.937358 + 0.348368i
\(17\) 20.9256 1.23092 0.615459 0.788169i \(-0.288970\pi\)
0.615459 + 0.788169i \(0.288970\pi\)
\(18\) 0.533041 5.97628i 0.0296134 0.332015i
\(19\) 27.9657i 1.47188i 0.677048 + 0.735939i \(0.263259\pi\)
−0.677048 + 0.735939i \(0.736741\pi\)
\(20\) 0 0
\(21\) 2.06983 0.0985631
\(22\) −16.3764 1.46066i −0.744383 0.0663937i
\(23\) 9.48564i 0.412419i −0.978508 0.206209i \(-0.933887\pi\)
0.978508 0.206209i \(-0.0661128\pi\)
\(24\) −13.3659 3.65415i −0.556912 0.152256i
\(25\) 0 0
\(26\) −1.98759 + 22.2842i −0.0764459 + 0.857085i
\(27\) 5.19615i 0.192450i
\(28\) 0.845964 4.70460i 0.0302130 0.168022i
\(29\) 40.4205 1.39381 0.696905 0.717163i \(-0.254560\pi\)
0.696905 + 0.717163i \(0.254560\pi\)
\(30\) 0 0
\(31\) 55.3130i 1.78429i 0.451748 + 0.892145i \(0.350800\pi\)
−0.451748 + 0.892145i \(0.649200\pi\)
\(32\) −13.7685 + 28.8865i −0.430266 + 0.902702i
\(33\) 14.2387 0.431476
\(34\) −3.71807 + 41.6858i −0.109355 + 1.22605i
\(35\) 0 0
\(36\) 11.8106 + 2.12373i 0.328072 + 0.0589926i
\(37\) 50.1890 1.35646 0.678230 0.734850i \(-0.262747\pi\)
0.678230 + 0.734850i \(0.262747\pi\)
\(38\) −55.7102 4.96895i −1.46606 0.130762i
\(39\) 19.3753i 0.496803i
\(40\) 0 0
\(41\) −73.6361 −1.79600 −0.898001 0.439994i \(-0.854981\pi\)
−0.898001 + 0.439994i \(0.854981\pi\)
\(42\) −0.367767 + 4.12328i −0.00875637 + 0.0981734i
\(43\) 19.0843i 0.443822i −0.975067 0.221911i \(-0.928771\pi\)
0.975067 0.221911i \(-0.0712294\pi\)
\(44\) 5.81954 32.3638i 0.132262 0.735541i
\(45\) 0 0
\(46\) 18.8963 + 1.68541i 0.410788 + 0.0366394i
\(47\) 18.0598i 0.384251i 0.981370 + 0.192125i \(0.0615380\pi\)
−0.981370 + 0.192125i \(0.938462\pi\)
\(48\) 9.65427 25.9768i 0.201131 0.541184i
\(49\) 47.5719 0.970856
\(50\) 0 0
\(51\) 36.2442i 0.710671i
\(52\) −44.0391 7.91894i −0.846905 0.152287i
\(53\) −57.2212 −1.07965 −0.539823 0.841779i \(-0.681509\pi\)
−0.539823 + 0.841779i \(0.681509\pi\)
\(54\) −10.3512 0.923254i −0.191689 0.0170973i
\(55\) 0 0
\(56\) 9.22169 + 2.52115i 0.164673 + 0.0450206i
\(57\) 48.4380 0.849789
\(58\) −7.18193 + 80.5213i −0.123826 + 1.38830i
\(59\) 60.6645i 1.02821i −0.857727 0.514106i \(-0.828124\pi\)
0.857727 0.514106i \(-0.171876\pi\)
\(60\) 0 0
\(61\) −21.3518 −0.350030 −0.175015 0.984566i \(-0.555997\pi\)
−0.175015 + 0.984566i \(0.555997\pi\)
\(62\) −110.189 9.82804i −1.77724 0.158517i
\(63\) 3.58504i 0.0569054i
\(64\) −55.0981 32.5607i −0.860908 0.508761i
\(65\) 0 0
\(66\) −2.52994 + 28.3648i −0.0383324 + 0.429770i
\(67\) 9.68679i 0.144579i 0.997384 + 0.0722895i \(0.0230305\pi\)
−0.997384 + 0.0722895i \(0.976969\pi\)
\(68\) −82.3812 14.8135i −1.21149 0.217845i
\(69\) −16.4296 −0.238110
\(70\) 0 0
\(71\) 68.6944i 0.967527i −0.875199 0.483763i \(-0.839270\pi\)
0.875199 0.483763i \(-0.160730\pi\)
\(72\) −6.32918 + 23.1504i −0.0879053 + 0.321533i
\(73\) 84.7825 1.16140 0.580702 0.814116i \(-0.302778\pi\)
0.580702 + 0.814116i \(0.302778\pi\)
\(74\) −8.91760 + 99.9811i −0.120508 + 1.35110i
\(75\) 0 0
\(76\) 19.7972 110.097i 0.260490 1.44864i
\(77\) −9.82388 −0.127583
\(78\) 38.5974 + 3.44261i 0.494839 + 0.0441361i
\(79\) 23.2903i 0.294814i 0.989076 + 0.147407i \(0.0470928\pi\)
−0.989076 + 0.147407i \(0.952907\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 13.0837 146.690i 0.159557 1.78890i
\(83\) 93.2595i 1.12361i 0.827270 + 0.561804i \(0.189893\pi\)
−0.827270 + 0.561804i \(0.810107\pi\)
\(84\) −8.14861 1.46525i −0.0970073 0.0174435i
\(85\) 0 0
\(86\) 38.0177 + 3.39091i 0.442067 + 0.0394292i
\(87\) 70.0104i 0.804717i
\(88\) 63.4377 + 17.3435i 0.720883 + 0.197085i
\(89\) 62.9898 0.707750 0.353875 0.935293i \(-0.384864\pi\)
0.353875 + 0.935293i \(0.384864\pi\)
\(90\) 0 0
\(91\) 13.3678i 0.146899i
\(92\) −6.71499 + 37.3436i −0.0729890 + 0.405909i
\(93\) 95.8049 1.03016
\(94\) −35.9767 3.20887i −0.382731 0.0341369i
\(95\) 0 0
\(96\) 50.0328 + 23.8478i 0.521175 + 0.248414i
\(97\) 91.3962 0.942229 0.471115 0.882072i \(-0.343852\pi\)
0.471115 + 0.882072i \(0.343852\pi\)
\(98\) −8.45260 + 94.7677i −0.0862510 + 0.967017i
\(99\) 24.6622i 0.249113i
\(100\) 0 0
\(101\) −29.9780 −0.296811 −0.148406 0.988927i \(-0.547414\pi\)
−0.148406 + 0.988927i \(0.547414\pi\)
\(102\) 72.2019 + 6.43989i 0.707861 + 0.0631362i
\(103\) 88.7485i 0.861636i −0.902439 0.430818i \(-0.858225\pi\)
0.902439 0.430818i \(-0.141775\pi\)
\(104\) 23.6001 86.3228i 0.226924 0.830027i
\(105\) 0 0
\(106\) 10.1671 113.990i 0.0959159 1.07538i
\(107\) 162.922i 1.52263i −0.648381 0.761316i \(-0.724553\pi\)
0.648381 0.761316i \(-0.275447\pi\)
\(108\) 3.67841 20.4565i 0.0340594 0.189412i
\(109\) −103.352 −0.948182 −0.474091 0.880476i \(-0.657223\pi\)
−0.474091 + 0.880476i \(0.657223\pi\)
\(110\) 0 0
\(111\) 86.9299i 0.783152i
\(112\) −6.66088 + 17.9225i −0.0594722 + 0.160022i
\(113\) −31.2691 −0.276717 −0.138359 0.990382i \(-0.544183\pi\)
−0.138359 + 0.990382i \(0.544183\pi\)
\(114\) −8.60647 + 96.4929i −0.0754954 + 0.846429i
\(115\) 0 0
\(116\) −159.130 28.6141i −1.37181 0.246673i
\(117\) −33.5590 −0.286829
\(118\) 120.849 + 10.7789i 1.02415 + 0.0913465i
\(119\) 25.0064i 0.210138i
\(120\) 0 0
\(121\) 53.4198 0.441486
\(122\) 3.79380 42.5348i 0.0310967 0.348646i
\(123\) 127.541i 1.03692i
\(124\) 39.1567 217.760i 0.315780 1.75613i
\(125\) 0 0
\(126\) 7.14174 + 0.636992i 0.0566804 + 0.00505549i
\(127\) 178.474i 1.40531i 0.711531 + 0.702655i \(0.248002\pi\)
−0.711531 + 0.702655i \(0.751998\pi\)
\(128\) 74.6537 103.975i 0.583232 0.812305i
\(129\) −33.0550 −0.256240
\(130\) 0 0
\(131\) 153.743i 1.17361i −0.809727 0.586806i \(-0.800385\pi\)
0.809727 0.586806i \(-0.199615\pi\)
\(132\) −56.0558 10.0797i −0.424665 0.0763617i
\(133\) −33.4194 −0.251274
\(134\) −19.2970 1.72115i −0.144007 0.0128444i
\(135\) 0 0
\(136\) 44.1473 161.479i 0.324613 1.18734i
\(137\) −52.9928 −0.386809 −0.193405 0.981119i \(-0.561953\pi\)
−0.193405 + 0.981119i \(0.561953\pi\)
\(138\) 2.91922 32.7293i 0.0211537 0.237169i
\(139\) 21.8420i 0.157137i −0.996909 0.0785684i \(-0.974965\pi\)
0.996909 0.0785684i \(-0.0250349\pi\)
\(140\) 0 0
\(141\) 31.2804 0.221847
\(142\) 136.846 + 12.2056i 0.963701 + 0.0859552i
\(143\) 91.9598i 0.643076i
\(144\) −44.9932 16.7217i −0.312453 0.116123i
\(145\) 0 0
\(146\) −15.0642 + 168.895i −0.103179 + 1.15681i
\(147\) 82.3970i 0.560524i
\(148\) −197.587 35.5294i −1.33505 0.240063i
\(149\) −3.12940 −0.0210027 −0.0105013 0.999945i \(-0.503343\pi\)
−0.0105013 + 0.999945i \(0.503343\pi\)
\(150\) 0 0
\(151\) 296.461i 1.96332i 0.190646 + 0.981659i \(0.438942\pi\)
−0.190646 + 0.981659i \(0.561058\pi\)
\(152\) 215.806 + 58.9999i 1.41977 + 0.388157i
\(153\) −62.7769 −0.410306
\(154\) 1.74551 19.5701i 0.0113345 0.127078i
\(155\) 0 0
\(156\) −13.7160 + 76.2779i −0.0879231 + 0.488961i
\(157\) −265.686 −1.69227 −0.846133 0.532972i \(-0.821075\pi\)
−0.846133 + 0.532972i \(0.821075\pi\)
\(158\) −46.3965 4.13824i −0.293649 0.0261914i
\(159\) 99.1101i 0.623334i
\(160\) 0 0
\(161\) 11.3355 0.0704067
\(162\) −1.59912 + 17.9288i −0.00987113 + 0.110672i
\(163\) 205.531i 1.26093i −0.776218 0.630465i \(-0.782864\pi\)
0.776218 0.630465i \(-0.217136\pi\)
\(164\) 289.895 + 52.1278i 1.76765 + 0.317852i
\(165\) 0 0
\(166\) −185.781 16.5704i −1.11917 0.0998215i
\(167\) 11.6359i 0.0696763i 0.999393 + 0.0348381i \(0.0110916\pi\)
−0.999393 + 0.0348381i \(0.988908\pi\)
\(168\) 4.36677 15.9724i 0.0259927 0.0950740i
\(169\) −43.8657 −0.259560
\(170\) 0 0
\(171\) 83.8970i 0.490626i
\(172\) −13.5100 + 75.1323i −0.0785466 + 0.436816i
\(173\) −106.062 −0.613077 −0.306538 0.951858i \(-0.599171\pi\)
−0.306538 + 0.951858i \(0.599171\pi\)
\(174\) 139.467 + 12.4395i 0.801535 + 0.0714912i
\(175\) 0 0
\(176\) −45.8214 + 123.292i −0.260349 + 0.700523i
\(177\) −105.074 −0.593639
\(178\) −11.1920 + 125.481i −0.0628766 + 0.704951i
\(179\) 43.3304i 0.242069i 0.992648 + 0.121035i \(0.0386212\pi\)
−0.992648 + 0.121035i \(0.961379\pi\)
\(180\) 0 0
\(181\) 203.614 1.12494 0.562469 0.826819i \(-0.309852\pi\)
0.562469 + 0.826819i \(0.309852\pi\)
\(182\) −26.6300 2.37520i −0.146319 0.0130506i
\(183\) 36.9824i 0.202090i
\(184\) −73.1988 20.0121i −0.397819 0.108761i
\(185\) 0 0
\(186\) −17.0227 + 190.852i −0.0915197 + 1.02609i
\(187\) 172.024i 0.919913i
\(188\) 12.7847 71.0988i 0.0680038 0.378185i
\(189\) −6.20948 −0.0328544
\(190\) 0 0
\(191\) 251.536i 1.31694i 0.752606 + 0.658471i \(0.228796\pi\)
−0.752606 + 0.658471i \(0.771204\pi\)
\(192\) −56.3968 + 95.4327i −0.293733 + 0.497045i
\(193\) −281.811 −1.46016 −0.730081 0.683360i \(-0.760518\pi\)
−0.730081 + 0.683360i \(0.760518\pi\)
\(194\) −16.2393 + 182.070i −0.0837078 + 0.938503i
\(195\) 0 0
\(196\) −187.284 33.6767i −0.955531 0.171820i
\(197\) −243.485 −1.23596 −0.617982 0.786193i \(-0.712049\pi\)
−0.617982 + 0.786193i \(0.712049\pi\)
\(198\) 49.1293 + 4.38198i 0.248128 + 0.0221312i
\(199\) 121.958i 0.612853i 0.951894 + 0.306427i \(0.0991335\pi\)
−0.951894 + 0.306427i \(0.900867\pi\)
\(200\) 0 0
\(201\) 16.7780 0.0834727
\(202\) 5.32649 59.7188i 0.0263688 0.295638i
\(203\) 48.3031i 0.237946i
\(204\) −25.6577 + 142.688i −0.125773 + 0.699453i
\(205\) 0 0
\(206\) 176.795 + 15.7689i 0.858229 + 0.0765479i
\(207\) 28.4569i 0.137473i
\(208\) 167.770 + 62.3515i 0.806585 + 0.299767i
\(209\) −229.898 −1.09999
\(210\) 0 0
\(211\) 132.543i 0.628168i 0.949395 + 0.314084i \(0.101697\pi\)
−0.949395 + 0.314084i \(0.898303\pi\)
\(212\) 225.272 + 40.5076i 1.06260 + 0.191073i
\(213\) −118.982 −0.558602
\(214\) 324.555 + 28.9480i 1.51661 + 0.135271i
\(215\) 0 0
\(216\) 40.0977 + 10.9625i 0.185637 + 0.0507521i
\(217\) −66.0998 −0.304608
\(218\) 18.3636 205.886i 0.0842366 0.944433i
\(219\) 146.848i 0.670537i
\(220\) 0 0
\(221\) 234.081 1.05919
\(222\) 173.172 + 15.4457i 0.780056 + 0.0695754i
\(223\) 225.442i 1.01095i −0.862841 0.505475i \(-0.831317\pi\)
0.862841 0.505475i \(-0.168683\pi\)
\(224\) −34.5198 16.4536i −0.154106 0.0734534i
\(225\) 0 0
\(226\) 5.55590 62.2908i 0.0245836 0.275623i
\(227\) 108.080i 0.476124i 0.971250 + 0.238062i \(0.0765122\pi\)
−0.971250 + 0.238062i \(0.923488\pi\)
\(228\) −190.693 34.2898i −0.836375 0.150394i
\(229\) −57.3495 −0.250435 −0.125217 0.992129i \(-0.539963\pi\)
−0.125217 + 0.992129i \(0.539963\pi\)
\(230\) 0 0
\(231\) 17.0155i 0.0736600i
\(232\) 85.2762 311.917i 0.367570 1.34447i
\(233\) 285.320 1.22455 0.612274 0.790646i \(-0.290255\pi\)
0.612274 + 0.790646i \(0.290255\pi\)
\(234\) 5.96278 66.8527i 0.0254820 0.285695i
\(235\) 0 0
\(236\) −42.9451 + 238.828i −0.181971 + 1.01198i
\(237\) 40.3400 0.170211
\(238\) −49.8151 4.44315i −0.209307 0.0186687i
\(239\) 77.2471i 0.323210i −0.986856 0.161605i \(-0.948333\pi\)
0.986856 0.161605i \(-0.0516670\pi\)
\(240\) 0 0
\(241\) −130.557 −0.541732 −0.270866 0.962617i \(-0.587310\pi\)
−0.270866 + 0.962617i \(0.587310\pi\)
\(242\) −9.49164 + 106.417i −0.0392217 + 0.439740i
\(243\) 15.5885i 0.0641500i
\(244\) 84.0591 + 15.1152i 0.344504 + 0.0619475i
\(245\) 0 0
\(246\) −254.074 22.6616i −1.03282 0.0921203i
\(247\) 312.834i 1.26653i
\(248\) 426.840 + 116.695i 1.72113 + 0.470546i
\(249\) 161.530 0.648715
\(250\) 0 0
\(251\) 437.197i 1.74182i −0.491441 0.870911i \(-0.663530\pi\)
0.491441 0.870911i \(-0.336470\pi\)
\(252\) −2.53789 + 14.1138i −0.0100710 + 0.0560072i
\(253\) 77.9788 0.308216
\(254\) −355.537 31.7114i −1.39975 0.124848i
\(255\) 0 0
\(256\) 193.863 + 167.191i 0.757279 + 0.653091i
\(257\) 74.3682 0.289370 0.144685 0.989478i \(-0.453783\pi\)
0.144685 + 0.989478i \(0.453783\pi\)
\(258\) 5.87323 65.8486i 0.0227644 0.255227i
\(259\) 59.9766i 0.231570i
\(260\) 0 0
\(261\) −121.261 −0.464603
\(262\) 306.271 + 27.3172i 1.16897 + 0.104264i
\(263\) 458.790i 1.74445i −0.489105 0.872225i \(-0.662676\pi\)
0.489105 0.872225i \(-0.337324\pi\)
\(264\) 30.0398 109.877i 0.113787 0.416202i
\(265\) 0 0
\(266\) 5.93797 66.5745i 0.0223232 0.250280i
\(267\) 109.101i 0.408620i
\(268\) 6.85739 38.1355i 0.0255873 0.142297i
\(269\) −320.405 −1.19110 −0.595549 0.803319i \(-0.703065\pi\)
−0.595549 + 0.803319i \(0.703065\pi\)
\(270\) 0 0
\(271\) 359.059i 1.32494i 0.749088 + 0.662470i \(0.230492\pi\)
−0.749088 + 0.662470i \(0.769508\pi\)
\(272\) 313.837 + 116.637i 1.15381 + 0.428813i
\(273\) 23.1538 0.0848124
\(274\) 9.41579 105.567i 0.0343642 0.385280i
\(275\) 0 0
\(276\) 64.6810 + 11.6307i 0.234352 + 0.0421402i
\(277\) 138.027 0.498293 0.249147 0.968466i \(-0.419850\pi\)
0.249147 + 0.968466i \(0.419850\pi\)
\(278\) 43.5113 + 3.88090i 0.156516 + 0.0139601i
\(279\) 165.939i 0.594764i
\(280\) 0 0
\(281\) 462.504 1.64592 0.822960 0.568099i \(-0.192321\pi\)
0.822960 + 0.568099i \(0.192321\pi\)
\(282\) −5.55792 + 62.3135i −0.0197089 + 0.220970i
\(283\) 323.973i 1.14478i 0.819981 + 0.572391i \(0.193984\pi\)
−0.819981 + 0.572391i \(0.806016\pi\)
\(284\) −48.6295 + 270.440i −0.171231 + 0.952254i
\(285\) 0 0
\(286\) −183.192 16.3394i −0.640533 0.0571309i
\(287\) 87.9962i 0.306607i
\(288\) 41.3055 86.6594i 0.143422 0.300901i
\(289\) 148.882 0.515161
\(290\) 0 0
\(291\) 158.303i 0.543996i
\(292\) −333.777 60.0185i −1.14307 0.205543i
\(293\) 150.416 0.513365 0.256683 0.966496i \(-0.417371\pi\)
0.256683 + 0.966496i \(0.417371\pi\)
\(294\) 164.142 + 14.6403i 0.558308 + 0.0497970i
\(295\) 0 0
\(296\) 105.885 387.299i 0.357720 1.30844i
\(297\) −42.7161 −0.143825
\(298\) 0.556033 6.23406i 0.00186588 0.0209196i
\(299\) 106.110i 0.354882i
\(300\) 0 0
\(301\) 22.8060 0.0757676
\(302\) −590.577 52.6753i −1.95555 0.174421i
\(303\) 51.9233i 0.171364i
\(304\) −155.878 + 419.421i −0.512755 + 1.37968i
\(305\) 0 0
\(306\) 11.1542 125.057i 0.0364517 0.408684i
\(307\) 563.915i 1.83686i −0.395587 0.918428i \(-0.629459\pi\)
0.395587 0.918428i \(-0.370541\pi\)
\(308\) 38.6752 + 6.95443i 0.125569 + 0.0225793i
\(309\) −153.717 −0.497466
\(310\) 0 0
\(311\) 40.0214i 0.128686i −0.997928 0.0643431i \(-0.979505\pi\)
0.997928 0.0643431i \(-0.0204952\pi\)
\(312\) −149.515 40.8766i −0.479216 0.131015i
\(313\) 1.82657 0.00583568 0.00291784 0.999996i \(-0.499071\pi\)
0.00291784 + 0.999996i \(0.499071\pi\)
\(314\) 47.2071 529.270i 0.150341 1.68557i
\(315\) 0 0
\(316\) 16.4875 91.6908i 0.0521756 0.290161i
\(317\) 246.416 0.777338 0.388669 0.921378i \(-0.372935\pi\)
0.388669 + 0.921378i \(0.372935\pi\)
\(318\) −197.436 17.6099i −0.620869 0.0553771i
\(319\) 332.286i 1.04165i
\(320\) 0 0
\(321\) −282.189 −0.879092
\(322\) −2.01409 + 22.5813i −0.00625494 + 0.0701283i
\(323\) 585.199i 1.81176i
\(324\) −35.4317 6.37120i −0.109357 0.0196642i
\(325\) 0 0
\(326\) 409.438 + 36.5189i 1.25594 + 0.112021i
\(327\) 179.011i 0.547433i
\(328\) −155.352 + 568.235i −0.473634 + 1.73242i
\(329\) −21.5817 −0.0655978
\(330\) 0 0
\(331\) 417.672i 1.26185i −0.775844 0.630925i \(-0.782675\pi\)
0.775844 0.630925i \(-0.217325\pi\)
\(332\) 66.0194 367.149i 0.198854 1.10587i
\(333\) −150.567 −0.452153
\(334\) −23.1798 2.06748i −0.0694007 0.00619005i
\(335\) 0 0
\(336\) 31.0427 + 11.5370i 0.0923889 + 0.0343363i
\(337\) −317.379 −0.941779 −0.470889 0.882192i \(-0.656067\pi\)
−0.470889 + 0.882192i \(0.656067\pi\)
\(338\) 7.79408 87.3845i 0.0230594 0.258534i
\(339\) 54.1596i 0.159763i
\(340\) 0 0
\(341\) −454.713 −1.33347
\(342\) 167.131 + 14.9068i 0.488686 + 0.0435873i
\(343\) 115.405i 0.336457i
\(344\) −147.270 40.2627i −0.428110 0.117043i
\(345\) 0 0
\(346\) 18.8452 211.286i 0.0544659 0.610653i
\(347\) 222.581i 0.641443i −0.947174 0.320721i \(-0.896075\pi\)
0.947174 0.320721i \(-0.103925\pi\)
\(348\) −49.5611 + 275.621i −0.142417 + 0.792014i
\(349\) 560.812 1.60691 0.803455 0.595366i \(-0.202993\pi\)
0.803455 + 0.595366i \(0.202993\pi\)
\(350\) 0 0
\(351\) 58.1259i 0.165601i
\(352\) −237.468 113.187i −0.674624 0.321554i
\(353\) 304.856 0.863616 0.431808 0.901966i \(-0.357876\pi\)
0.431808 + 0.901966i \(0.357876\pi\)
\(354\) 18.6696 209.317i 0.0527390 0.591291i
\(355\) 0 0
\(356\) −247.982 44.5911i −0.696578 0.125256i
\(357\) 43.3124 0.121323
\(358\) −86.3181 7.69896i −0.241112 0.0215055i
\(359\) 105.860i 0.294874i 0.989071 + 0.147437i \(0.0471023\pi\)
−0.989071 + 0.147437i \(0.952898\pi\)
\(360\) 0 0
\(361\) −421.079 −1.16642
\(362\) −36.1782 + 405.617i −0.0999396 + 1.12049i
\(363\) 92.5257i 0.254892i
\(364\) 9.46324 52.6273i 0.0259979 0.144581i
\(365\) 0 0
\(366\) −73.6724 6.57105i −0.201291 0.0179537i
\(367\) 360.200i 0.981470i −0.871309 0.490735i \(-0.836728\pi\)
0.871309 0.490735i \(-0.163272\pi\)
\(368\) 52.8719 142.263i 0.143674 0.386584i
\(369\) 220.908 0.598667
\(370\) 0 0
\(371\) 68.3802i 0.184313i
\(372\) −377.171 67.8214i −1.01390 0.182316i
\(373\) −135.489 −0.363242 −0.181621 0.983369i \(-0.558134\pi\)
−0.181621 + 0.983369i \(0.558134\pi\)
\(374\) −342.687 30.5652i −0.916275 0.0817252i
\(375\) 0 0
\(376\) 139.364 + 38.1012i 0.370648 + 0.101333i
\(377\) 452.158 1.19936
\(378\) 1.10330 12.3698i 0.00291879 0.0327245i
\(379\) 310.686i 0.819753i −0.912141 0.409876i \(-0.865572\pi\)
0.912141 0.409876i \(-0.134428\pi\)
\(380\) 0 0
\(381\) 309.126 0.811356
\(382\) −501.083 44.6930i −1.31173 0.116997i
\(383\) 121.981i 0.318487i −0.987239 0.159244i \(-0.949094\pi\)
0.987239 0.159244i \(-0.0509056\pi\)
\(384\) −180.090 129.304i −0.468985 0.336729i
\(385\) 0 0
\(386\) 50.0723 561.394i 0.129721 1.45439i
\(387\) 57.2530i 0.147941i
\(388\) −359.814 64.7004i −0.927356 0.166754i
\(389\) 544.266 1.39914 0.699570 0.714564i \(-0.253375\pi\)
0.699570 + 0.714564i \(0.253375\pi\)
\(390\) 0 0
\(391\) 198.493i 0.507654i
\(392\) 100.364 367.103i 0.256030 0.936488i
\(393\) −266.291 −0.677586
\(394\) 43.2625 485.044i 0.109803 1.23108i
\(395\) 0 0
\(396\) −17.4586 + 97.0915i −0.0440874 + 0.245180i
\(397\) 504.528 1.27085 0.635425 0.772162i \(-0.280825\pi\)
0.635425 + 0.772162i \(0.280825\pi\)
\(398\) −242.951 21.6695i −0.610430 0.0544460i
\(399\) 57.8841i 0.145073i
\(400\) 0 0
\(401\) −278.018 −0.693312 −0.346656 0.937992i \(-0.612683\pi\)
−0.346656 + 0.937992i \(0.612683\pi\)
\(402\) −2.98112 + 33.4233i −0.00741573 + 0.0831426i
\(403\) 618.750i 1.53536i
\(404\) 118.019 + 21.2217i 0.292126 + 0.0525290i
\(405\) 0 0
\(406\) −96.2242 8.58251i −0.237005 0.0211392i
\(407\) 412.590i 1.01373i
\(408\) −279.690 76.4654i −0.685514 0.187415i
\(409\) −296.549 −0.725059 −0.362530 0.931972i \(-0.618087\pi\)
−0.362530 + 0.931972i \(0.618087\pi\)
\(410\) 0 0
\(411\) 91.7863i 0.223324i
\(412\) −62.8261 + 349.390i −0.152490 + 0.848035i
\(413\) 72.4950 0.175533
\(414\) −56.6888 5.05623i −0.136929 0.0122131i
\(415\) 0 0
\(416\) −154.019 + 323.134i −0.370239 + 0.776764i
\(417\) −37.8315 −0.0907230
\(418\) 40.8483 457.978i 0.0977233 1.09564i
\(419\) 315.615i 0.753258i −0.926364 0.376629i \(-0.877083\pi\)
0.926364 0.376629i \(-0.122917\pi\)
\(420\) 0 0
\(421\) −360.355 −0.855951 −0.427975 0.903790i \(-0.640773\pi\)
−0.427975 + 0.903790i \(0.640773\pi\)
\(422\) −264.039 23.5504i −0.625684 0.0558066i
\(423\) 54.1793i 0.128084i
\(424\) −120.721 + 441.565i −0.284720 + 1.04143i
\(425\) 0 0
\(426\) 21.1408 237.023i 0.0496263 0.556393i
\(427\) 25.5157i 0.0597558i
\(428\) −115.334 + 641.400i −0.269472 + 1.49860i
\(429\) 159.279 0.371280
\(430\) 0 0
\(431\) 523.617i 1.21489i 0.794362 + 0.607445i \(0.207805\pi\)
−0.794362 + 0.607445i \(0.792195\pi\)
\(432\) −28.9628 + 77.9305i −0.0670435 + 0.180395i
\(433\) −21.5381 −0.0497415 −0.0248707 0.999691i \(-0.507917\pi\)
−0.0248707 + 0.999691i \(0.507917\pi\)
\(434\) 11.7446 131.677i 0.0270614 0.303403i
\(435\) 0 0
\(436\) 406.882 + 73.1639i 0.933215 + 0.167807i
\(437\) 265.272 0.607030
\(438\) 292.534 + 26.0919i 0.667886 + 0.0595706i
\(439\) 247.777i 0.564412i −0.959354 0.282206i \(-0.908934\pi\)
0.959354 0.282206i \(-0.0910662\pi\)
\(440\) 0 0
\(441\) −142.716 −0.323619
\(442\) −41.5916 + 466.311i −0.0940987 + 1.05500i
\(443\) 584.775i 1.32003i −0.751251 0.660017i \(-0.770549\pi\)
0.751251 0.660017i \(-0.229451\pi\)
\(444\) −61.5386 + 342.231i −0.138601 + 0.770790i
\(445\) 0 0
\(446\) 449.101 + 40.0566i 1.00695 + 0.0898130i
\(447\) 5.42028i 0.0121259i
\(448\) 38.9105 65.8430i 0.0868538 0.146971i
\(449\) 152.093 0.338738 0.169369 0.985553i \(-0.445827\pi\)
0.169369 + 0.985553i \(0.445827\pi\)
\(450\) 0 0
\(451\) 605.342i 1.34222i
\(452\) 123.102 + 22.1357i 0.272349 + 0.0489728i
\(453\) 513.485 1.13352
\(454\) −215.306 19.2037i −0.474242 0.0422990i
\(455\) 0 0
\(456\) 102.191 373.786i 0.224103 0.819707i
\(457\) 602.441 1.31825 0.659126 0.752033i \(-0.270926\pi\)
0.659126 + 0.752033i \(0.270926\pi\)
\(458\) 10.1899 114.246i 0.0222487 0.249444i
\(459\) 108.733i 0.236890i
\(460\) 0 0
\(461\) −504.912 −1.09525 −0.547626 0.836723i \(-0.684468\pi\)
−0.547626 + 0.836723i \(0.684468\pi\)
\(462\) −33.8964 3.02331i −0.0733687 0.00654397i
\(463\) 504.560i 1.08976i −0.838513 0.544881i \(-0.816575\pi\)
0.838513 0.544881i \(-0.183425\pi\)
\(464\) 606.215 + 225.300i 1.30650 + 0.485559i
\(465\) 0 0
\(466\) −50.6957 + 568.383i −0.108789 + 1.21971i
\(467\) 751.418i 1.60903i −0.593931 0.804516i \(-0.702425\pi\)
0.593931 0.804516i \(-0.297575\pi\)
\(468\) 132.117 + 23.7568i 0.282302 + 0.0507624i
\(469\) −11.5759 −0.0246820
\(470\) 0 0
\(471\) 460.181i 0.977030i
\(472\) −468.136 127.986i −0.991814 0.271156i
\(473\) 156.887 0.331685
\(474\) −7.16763 + 80.3611i −0.0151216 + 0.169538i
\(475\) 0 0
\(476\) 17.7023 98.4468i 0.0371898 0.206821i
\(477\) 171.664 0.359882
\(478\) 153.883 + 13.7253i 0.321932 + 0.0287140i
\(479\) 581.401i 1.21378i 0.794786 + 0.606890i \(0.207583\pi\)
−0.794786 + 0.606890i \(0.792417\pi\)
\(480\) 0 0
\(481\) 561.431 1.16722
\(482\) 23.1975 260.082i 0.0481276 0.539590i
\(483\) 19.6336i 0.0406493i
\(484\) −210.306 37.8164i −0.434517 0.0781331i
\(485\) 0 0
\(486\) 31.0536 + 2.76976i 0.0638964 + 0.00569910i
\(487\) 557.489i 1.14474i 0.819995 + 0.572371i \(0.193976\pi\)
−0.819995 + 0.572371i \(0.806024\pi\)
\(488\) −45.0465 + 164.768i −0.0923084 + 0.337639i
\(489\) −355.991 −0.727998
\(490\) 0 0
\(491\) 26.2032i 0.0533670i −0.999644 0.0266835i \(-0.991505\pi\)
0.999644 0.0266835i \(-0.00849463\pi\)
\(492\) 90.2880 502.113i 0.183512 1.02055i
\(493\) 845.824 1.71567
\(494\) −623.193 55.5844i −1.26152 0.112519i
\(495\) 0 0
\(496\) −308.309 + 829.569i −0.621590 + 1.67252i
\(497\) 82.0908 0.165173
\(498\) −28.7007 + 321.783i −0.0576320 + 0.646150i
\(499\) 444.615i 0.891011i −0.895279 0.445506i \(-0.853024\pi\)
0.895279 0.445506i \(-0.146976\pi\)
\(500\) 0 0
\(501\) 20.1540 0.0402276
\(502\) 870.937 + 77.6814i 1.73493 + 0.154744i
\(503\) 216.819i 0.431052i 0.976498 + 0.215526i \(0.0691466\pi\)
−0.976498 + 0.215526i \(0.930853\pi\)
\(504\) −27.6651 7.56346i −0.0548910 0.0150069i
\(505\) 0 0
\(506\) −13.8553 + 155.341i −0.0273820 + 0.306998i
\(507\) 75.9777i 0.149857i
\(508\) 126.344 702.628i 0.248708 1.38313i
\(509\) 202.830 0.398488 0.199244 0.979950i \(-0.436151\pi\)
0.199244 + 0.979950i \(0.436151\pi\)
\(510\) 0 0
\(511\) 101.316i 0.198271i
\(512\) −367.506 + 356.487i −0.717786 + 0.696264i
\(513\) −145.314 −0.283263
\(514\) −13.2138 + 148.148i −0.0257077 + 0.288226i
\(515\) 0 0
\(516\) 130.133 + 23.4000i 0.252196 + 0.0453489i
\(517\) −148.464 −0.287165
\(518\) −119.479 10.6567i −0.230654 0.0205727i
\(519\) 183.705i 0.353960i
\(520\) 0 0
\(521\) 769.410 1.47679 0.738397 0.674366i \(-0.235583\pi\)
0.738397 + 0.674366i \(0.235583\pi\)
\(522\) 21.5458 241.564i 0.0412754 0.462766i
\(523\) 38.9898i 0.0745502i 0.999305 + 0.0372751i \(0.0118678\pi\)
−0.999305 + 0.0372751i \(0.988132\pi\)
\(524\) −108.837 + 605.266i −0.207703 + 1.15509i
\(525\) 0 0
\(526\) 913.953 + 81.5180i 1.73755 + 0.154977i
\(527\) 1157.46i 2.19632i
\(528\) 213.548 + 79.3650i 0.404447 + 0.150313i
\(529\) 439.023 0.829911
\(530\) 0 0
\(531\) 181.994i 0.342737i
\(532\) 131.567 + 23.6579i 0.247307 + 0.0444698i
\(533\) −823.718 −1.54544
\(534\) 217.340 + 19.3852i 0.407004 + 0.0363018i
\(535\) 0 0
\(536\) 74.7510 + 20.4365i 0.139461 + 0.0381277i
\(537\) 75.0504 0.139759
\(538\) 56.9297 638.277i 0.105817 1.18639i
\(539\) 391.076i 0.725558i
\(540\) 0 0
\(541\) −32.0904 −0.0593168 −0.0296584 0.999560i \(-0.509442\pi\)
−0.0296584 + 0.999560i \(0.509442\pi\)
\(542\) −715.278 63.7977i −1.31970 0.117708i
\(543\) 352.669i 0.649483i
\(544\) −288.115 + 604.467i −0.529622 + 1.11115i
\(545\) 0 0
\(546\) −4.11397 + 46.1245i −0.00753475 + 0.0844770i
\(547\) 254.839i 0.465885i −0.972491 0.232942i \(-0.925165\pi\)
0.972491 0.232942i \(-0.0748354\pi\)
\(548\) 208.625 + 37.5142i 0.380703 + 0.0684566i
\(549\) 64.0554 0.116677
\(550\) 0 0
\(551\) 1130.39i 2.05152i
\(552\) −34.6620 + 126.784i −0.0627934 + 0.229681i
\(553\) −27.8323 −0.0503296
\(554\) −24.5247 + 274.963i −0.0442685 + 0.496323i
\(555\) 0 0
\(556\) −15.4622 + 85.9890i −0.0278097 + 0.154656i
\(557\) −577.439 −1.03670 −0.518348 0.855170i \(-0.673453\pi\)
−0.518348 + 0.855170i \(0.673453\pi\)
\(558\) 330.566 + 29.4841i 0.592412 + 0.0528389i
\(559\) 213.484i 0.381903i
\(560\) 0 0
\(561\) 297.954 0.531112
\(562\) −82.1778 + 921.350i −0.146224 + 1.63941i
\(563\) 367.058i 0.651967i −0.945375 0.325984i \(-0.894305\pi\)
0.945375 0.325984i \(-0.105695\pi\)
\(564\) −123.147 22.1438i −0.218345 0.0392620i
\(565\) 0 0
\(566\) −645.384 57.5636i −1.14025 0.101703i
\(567\) 10.7551i 0.0189685i
\(568\) −530.101 144.926i −0.933277 0.255152i
\(569\) −522.006 −0.917410 −0.458705 0.888589i \(-0.651687\pi\)
−0.458705 + 0.888589i \(0.651687\pi\)
\(570\) 0 0
\(571\) 832.421i 1.45783i −0.684604 0.728915i \(-0.740025\pi\)
0.684604 0.728915i \(-0.259975\pi\)
\(572\) 65.0994 362.033i 0.113810 0.632925i
\(573\) 435.673 0.760337
\(574\) 175.296 + 15.6352i 0.305394 + 0.0272390i
\(575\) 0 0
\(576\) 165.294 + 97.6821i 0.286969 + 0.169587i
\(577\) −427.659 −0.741177 −0.370588 0.928797i \(-0.620844\pi\)
−0.370588 + 0.928797i \(0.620844\pi\)
\(578\) −26.4533 + 296.586i −0.0457670 + 0.513124i
\(579\) 488.112i 0.843025i
\(580\) 0 0
\(581\) −111.446 −0.191818
\(582\) 315.354 + 28.1273i 0.541845 + 0.0483287i
\(583\) 470.400i 0.806861i
\(584\) 178.868 654.250i 0.306281 1.12029i
\(585\) 0 0
\(586\) −26.7260 + 299.642i −0.0456074 + 0.511335i
\(587\) 586.262i 0.998743i 0.866388 + 0.499372i \(0.166436\pi\)
−0.866388 + 0.499372i \(0.833564\pi\)
\(588\) −58.3298 + 324.385i −0.0992003 + 0.551676i
\(589\) −1546.87 −2.62626
\(590\) 0 0
\(591\) 421.728i 0.713584i
\(592\) 752.721 + 279.748i 1.27149 + 0.472548i
\(593\) −518.375 −0.874156 −0.437078 0.899424i \(-0.643987\pi\)
−0.437078 + 0.899424i \(0.643987\pi\)
\(594\) 7.58981 85.0944i 0.0127775 0.143257i
\(595\) 0 0
\(596\) 12.3200 + 2.21534i 0.0206712 + 0.00371701i
\(597\) 211.237 0.353831
\(598\) 211.380 + 18.8536i 0.353478 + 0.0315277i
\(599\) 405.480i 0.676928i −0.940979 0.338464i \(-0.890093\pi\)
0.940979 0.338464i \(-0.109907\pi\)
\(600\) 0 0
\(601\) −350.551 −0.583279 −0.291640 0.956528i \(-0.594201\pi\)
−0.291640 + 0.956528i \(0.594201\pi\)
\(602\) −4.05219 + 45.4317i −0.00673121 + 0.0754680i
\(603\) 29.0604i 0.0481930i
\(604\) 209.868 1167.13i 0.347464 1.93233i
\(605\) 0 0
\(606\) −103.436 9.22576i −0.170687 0.0152240i
\(607\) 737.786i 1.21546i −0.794143 0.607731i \(-0.792080\pi\)
0.794143 0.607731i \(-0.207920\pi\)
\(608\) −807.829 385.046i −1.32867 0.633299i
\(609\) 83.6634 0.137378
\(610\) 0 0
\(611\) 202.023i 0.330643i
\(612\) 247.144 + 44.4404i 0.403830 + 0.0726151i
\(613\) −345.495 −0.563614 −0.281807 0.959471i \(-0.590934\pi\)
−0.281807 + 0.959471i \(0.590934\pi\)
\(614\) 1123.37 + 100.197i 1.82959 + 0.163187i
\(615\) 0 0
\(616\) −20.7257 + 75.8090i −0.0336456 + 0.123066i
\(617\) −862.171 −1.39736 −0.698680 0.715434i \(-0.746229\pi\)
−0.698680 + 0.715434i \(0.746229\pi\)
\(618\) 27.3125 306.218i 0.0441950 0.495499i
\(619\) 469.363i 0.758260i −0.925343 0.379130i \(-0.876223\pi\)
0.925343 0.379130i \(-0.123777\pi\)
\(620\) 0 0
\(621\) 49.2888 0.0793701
\(622\) 79.7264 + 7.11102i 0.128177 + 0.0114325i
\(623\) 75.2737i 0.120824i
\(624\) 107.996 290.586i 0.173070 0.465682i
\(625\) 0 0
\(626\) −0.324545 + 3.63869i −0.000518443 + 0.00581260i
\(627\) 398.195i 0.635080i
\(628\) 1045.97 + 188.082i 1.66555 + 0.299494i
\(629\) 1050.24 1.66969
\(630\) 0 0
\(631\) 323.243i 0.512271i −0.966641 0.256136i \(-0.917551\pi\)
0.966641 0.256136i \(-0.0824494\pi\)
\(632\) 179.727 + 49.1362i 0.284378 + 0.0777472i
\(633\) 229.572 0.362673
\(634\) −43.7833 + 490.883i −0.0690588 + 0.774264i
\(635\) 0 0
\(636\) 70.1611 390.183i 0.110316 0.613495i
\(637\) 532.156 0.835410
\(638\) −661.943 59.0406i −1.03753 0.0925402i
\(639\) 206.083i 0.322509i
\(640\) 0 0
\(641\) −44.1100 −0.0688144 −0.0344072 0.999408i \(-0.510954\pi\)
−0.0344072 + 0.999408i \(0.510954\pi\)
\(642\) 50.1394 562.146i 0.0780987 0.875616i
\(643\) 934.204i 1.45288i 0.687228 + 0.726442i \(0.258827\pi\)
−0.687228 + 0.726442i \(0.741173\pi\)
\(644\) −44.6262 8.02451i −0.0692953 0.0124604i
\(645\) 0 0
\(646\) −1165.77 103.978i −1.80460 0.160957i
\(647\) 481.023i 0.743467i −0.928339 0.371734i \(-0.878763\pi\)
0.928339 0.371734i \(-0.121237\pi\)
\(648\) 18.9875 69.4512i 0.0293018 0.107178i
\(649\) 498.706 0.768422
\(650\) 0 0
\(651\) 114.488i 0.175865i
\(652\) −145.498 + 809.148i −0.223156 + 1.24103i
\(653\) −1131.38 −1.73259 −0.866293 0.499536i \(-0.833504\pi\)
−0.866293 + 0.499536i \(0.833504\pi\)
\(654\) −356.606 31.8067i −0.545268 0.0486340i
\(655\) 0 0
\(656\) −1104.37 410.440i −1.68350 0.625670i
\(657\) −254.348 −0.387135
\(658\) 3.83464 42.9927i 0.00582772 0.0653385i
\(659\) 154.348i 0.234215i 0.993119 + 0.117107i \(0.0373622\pi\)
−0.993119 + 0.117107i \(0.962638\pi\)
\(660\) 0 0
\(661\) 795.115 1.20290 0.601448 0.798912i \(-0.294591\pi\)
0.601448 + 0.798912i \(0.294591\pi\)
\(662\) 832.042 + 74.2122i 1.25686 + 0.112103i
\(663\) 405.441i 0.611524i
\(664\) 719.665 + 196.752i 1.08383 + 0.296313i
\(665\) 0 0
\(666\) 26.7528 299.943i 0.0401694 0.450365i
\(667\) 383.414i 0.574834i
\(668\) 8.23721 45.8090i 0.0123311 0.0685764i
\(669\) −390.477 −0.583672
\(670\) 0 0
\(671\) 175.527i 0.261591i
\(672\) −28.4984 + 59.7900i −0.0424083 + 0.0889732i
\(673\) −197.215 −0.293039 −0.146520 0.989208i \(-0.546807\pi\)
−0.146520 + 0.989208i \(0.546807\pi\)
\(674\) 56.3921 632.249i 0.0836678 0.938055i
\(675\) 0 0
\(676\) 172.693 + 31.0530i 0.255463 + 0.0459364i
\(677\) −530.367 −0.783408 −0.391704 0.920091i \(-0.628114\pi\)
−0.391704 + 0.920091i \(0.628114\pi\)
\(678\) −107.891 9.62309i −0.159131 0.0141934i
\(679\) 109.220i 0.160854i
\(680\) 0 0
\(681\) 187.200 0.274891
\(682\) 80.7935 905.830i 0.118466 1.32820i
\(683\) 797.231i 1.16725i 0.812024 + 0.583625i \(0.198366\pi\)
−0.812024 + 0.583625i \(0.801634\pi\)
\(684\) −59.3916 + 330.291i −0.0868299 + 0.482881i
\(685\) 0 0
\(686\) −229.897 20.5052i −0.335127 0.0298909i
\(687\) 99.3323i 0.144588i
\(688\) 106.374 286.221i 0.154613 0.416020i
\(689\) −640.096 −0.929022
\(690\) 0 0
\(691\) 498.569i 0.721518i −0.932659 0.360759i \(-0.882518\pi\)
0.932659 0.360759i \(-0.117482\pi\)
\(692\) 417.552 + 75.0827i 0.603399 + 0.108501i
\(693\) 29.4716 0.0425276
\(694\) 443.401 + 39.5482i 0.638906 + 0.0569859i
\(695\) 0 0
\(696\) −540.256 147.703i −0.776230 0.212217i
\(697\) −1540.88 −2.21073
\(698\) −99.6452 + 1117.19i −0.142758 + 1.60056i
\(699\) 494.188i 0.706993i
\(700\) 0 0
\(701\) −455.939 −0.650412 −0.325206 0.945643i \(-0.605434\pi\)
−0.325206 + 0.945643i \(0.605434\pi\)
\(702\) −115.792 10.3278i −0.164946 0.0147120i
\(703\) 1403.57i 1.99654i
\(704\) 267.672 452.946i 0.380216 0.643389i
\(705\) 0 0
\(706\) −54.1670 + 607.302i −0.0767238 + 0.860201i
\(707\) 35.8241i 0.0506706i
\(708\) 413.662 + 74.3831i 0.584268 + 0.105061i
\(709\) −44.4190 −0.0626502 −0.0313251 0.999509i \(-0.509973\pi\)
−0.0313251 + 0.999509i \(0.509973\pi\)
\(710\) 0 0
\(711\) 69.8710i 0.0982715i
\(712\) 132.891 486.080i 0.186645 0.682696i
\(713\) 524.679 0.735875
\(714\) −7.69576 + 86.2823i −0.0107784 + 0.120843i
\(715\) 0 0
\(716\) 30.6741 170.586i 0.0428409 0.238248i
\(717\) −133.796 −0.186605
\(718\) −210.882 18.8092i −0.293708 0.0261966i
\(719\) 1349.94i 1.87752i 0.344566 + 0.938762i \(0.388026\pi\)
−0.344566 + 0.938762i \(0.611974\pi\)
\(720\) 0 0
\(721\) 106.056 0.147095
\(722\) 74.8174 838.827i 0.103625 1.16181i
\(723\) 226.132i 0.312769i
\(724\) −801.599 144.140i −1.10718 0.199089i
\(725\) 0 0
\(726\) 184.320 + 16.4400i 0.253884 + 0.0226446i
\(727\) 191.470i 0.263370i −0.991292 0.131685i \(-0.957961\pi\)
0.991292 0.131685i \(-0.0420387\pi\)
\(728\) 103.157 + 28.2025i 0.141699 + 0.0387397i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 399.351i 0.546308i
\(732\) 26.1803 145.595i 0.0357654 0.198900i
\(733\) 358.832 0.489539 0.244769 0.969581i \(-0.421288\pi\)
0.244769 + 0.969581i \(0.421288\pi\)
\(734\) 717.551 + 64.0004i 0.977589 + 0.0871940i
\(735\) 0 0
\(736\) 274.007 + 130.603i 0.372291 + 0.177450i
\(737\) −79.6324 −0.108049
\(738\) −39.2510 + 440.069i −0.0531857 + 0.596300i
\(739\) 756.311i 1.02342i 0.859157 + 0.511712i \(0.170989\pi\)
−0.859157 + 0.511712i \(0.829011\pi\)
\(740\) 0 0
\(741\) 541.844 0.731233
\(742\) 136.220 + 12.1498i 0.183584 + 0.0163744i
\(743\) 1148.65i 1.54596i −0.634432 0.772979i \(-0.718766\pi\)
0.634432 0.772979i \(-0.281234\pi\)
\(744\) 202.122 739.308i 0.271670 0.993693i
\(745\) 0 0
\(746\) 24.0738 269.907i 0.0322705 0.361805i
\(747\) 279.778i 0.374536i
\(748\) 121.777 677.233i 0.162804 0.905392i
\(749\) 194.694 0.259938
\(750\) 0 0
\(751\) 431.186i 0.574149i −0.957908 0.287074i \(-0.907317\pi\)
0.957908 0.287074i \(-0.0926827\pi\)
\(752\) −100.663 + 270.856i −0.133861 + 0.360180i
\(753\) −757.248 −1.00564
\(754\) −80.3395 + 900.739i −0.106551 + 1.19461i
\(755\) 0 0
\(756\) 24.4458 + 4.39576i 0.0323358 + 0.00581449i
\(757\) −645.657 −0.852916 −0.426458 0.904507i \(-0.640239\pi\)
−0.426458 + 0.904507i \(0.640239\pi\)
\(758\) 618.916 + 55.2029i 0.816511 + 0.0728270i
\(759\) 135.063i 0.177949i
\(760\) 0 0
\(761\) −291.287 −0.382768 −0.191384 0.981515i \(-0.561298\pi\)
−0.191384 + 0.981515i \(0.561298\pi\)
\(762\) −54.9257 + 615.808i −0.0720810 + 0.808147i
\(763\) 123.507i 0.161870i
\(764\) 178.065 990.261i 0.233069 1.29615i
\(765\) 0 0
\(766\) 242.997 + 21.6736i 0.317228 + 0.0282945i
\(767\) 678.614i 0.884764i
\(768\) 289.584 335.781i 0.377063 0.437215i
\(769\) −724.076 −0.941582 −0.470791 0.882245i \(-0.656031\pi\)
−0.470791 + 0.882245i \(0.656031\pi\)
\(770\) 0 0
\(771\) 128.809i 0.167068i
\(772\) 1109.45 + 199.497i 1.43711 + 0.258416i
\(773\) −399.686 −0.517058 −0.258529 0.966003i \(-0.583238\pi\)
−0.258529 + 0.966003i \(0.583238\pi\)
\(774\) −114.053 10.1727i −0.147356 0.0131431i
\(775\) 0 0
\(776\) 192.821 705.287i 0.248481 0.908875i
\(777\) 103.882 0.133697
\(778\) −96.7053 + 1084.23i −0.124300 + 1.39361i
\(779\) 2059.28i 2.64349i
\(780\) 0 0
\(781\) 564.717 0.723070
\(782\) 395.416 + 35.2683i 0.505647 + 0.0451001i
\(783\) 210.031i 0.268239i
\(784\) 713.471 + 265.161i 0.910039 + 0.338215i
\(785\) 0 0
\(786\) 47.3147 530.476i 0.0601968 0.674906i
\(787\) 381.830i