Properties

Label 300.3.f.c.199.15
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 199.15
Root \(-1.32811 - 0.485936i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.c.199.16

$q$-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 \(-0.472797\pi\)
0.0853582 + 0.996350i \(0.472797\pi\)
\(8\) 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 \(-0.878100\pi\)
0.927562 0.373669i \(-0.121900\pi\)
\(12\) 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 \(0.263259\pi\)
−0.677048 + 0.735939i \(0.736741\pi\)
\(20\) 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 \(-0.433887\pi\)
0.206209 + 0.978508i \(0.433887\pi\)
\(24\) 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 \(-0.649200\pi\)
0.451748 0.892145i \(-0.350800\pi\)
\(32\) 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 \(-0.428771\pi\)
0.221911 + 0.975067i \(0.428771\pi\)
\(44\) −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 \(-0.438462\pi\)
0.192125 + 0.981370i \(0.438462\pi\)
\(48\) 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 \(-0.828124\pi\)
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 \(0.555997\pi\)
\(62\) −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 \(-0.476969\pi\)
0.0722895 + 0.997384i \(0.476969\pi\)
\(68\) 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 \(0.160730\pi\)
−0.875199 + 0.483763i \(0.839270\pi\)
\(72\) 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 \(0.0470928\pi\)
−0.989076 + 0.147407i \(0.952907\pi\)
\(80\) 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 \(-0.689893\pi\)
−0.561804 + 0.827270i \(0.689893\pi\)
\(84\) 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 \(-0.358225\pi\)
0.430818 + 0.902439i \(0.358225\pi\)
\(104\) −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 \(-0.775447\pi\)
−0.761316 + 0.648381i \(0.775447\pi\)
\(108\) 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 \(-0.251998\pi\)
0.702655 + 0.711531i \(0.251998\pi\)
\(128\) 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 \(0.199615\pi\)
−0.809727 + 0.586806i \(0.800385\pi\)
\(132\) −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 \(-0.974965\pi\)
0.996909 0.0785684i \(-0.0250349\pi\)
\(140\) 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 \(-0.561058\pi\)
0.190646 0.981659i \(-0.438942\pi\)
\(152\) 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 \(-0.282864\pi\)
0.630465 + 0.776218i \(0.282864\pi\)
\(164\) −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 \(-0.488908\pi\)
0.0348381 + 0.999393i \(0.488908\pi\)
\(168\) 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 \(0.0386212\pi\)
−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 \(0.309852\pi\)
\(182\) −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 \(-0.771204\pi\)
0.752606 0.658471i \(-0.228796\pi\)
\(192\) 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 \(0.0991335\pi\)
−0.951894 + 0.306427i \(0.900867\pi\)
\(200\) 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 \(-0.898303\pi\)
0.949395 0.314084i \(-0.101697\pi\)
\(212\) 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 \(-0.331317\pi\)
0.505475 + 0.862841i \(0.331317\pi\)
\(224\) 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 \(-0.423488\pi\)
0.238062 + 0.971250i \(0.423488\pi\)
\(228\) 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 \(-0.948333\pi\)
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 \(0.587310\pi\)
\(242\) 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 \(0.336470\pi\)
−0.491441 + 0.870911i \(0.663530\pi\)
\(252\) 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 \(-0.162676\pi\)
0.872225 + 0.489105i \(0.162676\pi\)
\(264\) −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 \(-0.769508\pi\)
0.749088 0.662470i \(-0.230492\pi\)
\(272\) 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 \(-0.693984\pi\)
−0.572391 + 0.819981i \(0.693984\pi\)
\(284\) 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 \(-0.870541\pi\)
−0.918428 + 0.395587i \(0.870541\pi\)
\(308\) −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 \(0.0204952\pi\)
−0.997928 + 0.0643431i \(0.979505\pi\)
\(312\) −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 \(0.217325\pi\)
−0.775844 + 0.630925i \(0.782675\pi\)
\(332\) −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 \(-0.603925\pi\)
−0.320721 + 0.947174i \(0.603925\pi\)
\(348\) −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 \(0.0471023\pi\)
−0.989071 + 0.147437i \(0.952898\pi\)
\(360\) 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 \(-0.663272\pi\)
−0.490735 + 0.871309i \(0.663272\pi\)
\(368\) 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 \(-0.865572\pi\)
0.912141 0.409876i \(-0.134428\pi\)
\(380\) 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 \(-0.449094\pi\)
0.159244 + 0.987239i \(0.449094\pi\)
\(384\) 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 \(-0.877083\pi\)
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 \(0.640773\pi\)
\(422\) −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 \(-0.792195\pi\)
0.794362 0.607445i \(-0.207805\pi\)
\(432\) 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 \(-0.908934\pi\)
0.959354 0.282206i \(-0.0910662\pi\)
\(440\) 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 \(-0.270549\pi\)
0.660017 + 0.751251i \(0.270549\pi\)
\(444\) 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 \(-0.316575\pi\)
0.544881 + 0.838513i \(0.316575\pi\)
\(464\) −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 \(-0.797575\pi\)
−0.804516 + 0.593931i \(0.797575\pi\)
\(468\) −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 \(0.207583\pi\)
−0.794786 + 0.606890i \(0.792417\pi\)
\(480\) 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 \(-0.306024\pi\)
0.572371 + 0.819995i \(0.306024\pi\)
\(488\) −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 \(0.00849463\pi\)
−0.999644 + 0.0266835i \(0.991505\pi\)
\(492\) −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 \(-0.853024\pi\)
0.895279 0.445506i \(-0.146976\pi\)
\(500\) 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 \(-0.569147\pi\)
−0.215526 + 0.976498i \(0.569147\pi\)
\(504\) 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 \(-0.511868\pi\)
−0.0372751 + 0.999305i \(0.511868\pi\)
\(524\) 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 \(-0.574835\pi\)
−0.232942 + 0.972491i \(0.574835\pi\)
\(548\) −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 \(-0.394305\pi\)
0.325984 + 0.945375i \(0.394305\pi\)
\(564\) 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 \(0.259975\pi\)
−0.684604 + 0.728915i \(0.740025\pi\)
\(572\) −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 \(-0.333564\pi\)
0.499372 + 0.866388i \(0.333564\pi\)
\(588\) −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 \(-0.890093\pi\)
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 \(0.594201\pi\)
\(602\) 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 \(-0.707920\pi\)
−0.607731 + 0.794143i \(0.707920\pi\)
\(608\) 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 \(-0.876223\pi\)
0.925343 0.379130i \(-0.123777\pi\)
\(620\) 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 \(0.0824494\pi\)
−0.966641 + 0.256136i \(0.917551\pi\)
\(632\) 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 \(-0.758827\pi\)
−0.726442 + 0.687228i \(0.758827\pi\)
\(644\) 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 \(-0.621237\pi\)
−0.371734 + 0.928339i \(0.621237\pi\)
\(648\) 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 \(0.0373622\pi\)
−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 \(0.294591\pi\)
\(662\) 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 \(-0.698366\pi\)
−0.583625 + 0.812024i \(0.698366\pi\)
\(684\) 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 \(0.117482\pi\)
−0.932659 + 0.360759i \(0.882518\pi\)
\(692\) 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 \(0.388026\pi\)
−0.344566 + 0.938762i \(0.611974\pi\)
\(720\) 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 \(-0.542039\pi\)
−0.131685 + 0.991292i \(0.542039\pi\)
\(728\) −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 \(0.170989\pi\)
−0.859157 + 0.511712i \(0.829011\pi\)
\(740\) 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 \(-0.218766\pi\)
0.772979 + 0.634432i \(0.218766\pi\)
\(744\) −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 \(0.0926827\pi\)
−0.957908 + 0.287074i \(0.907317\pi\)
\(752\) 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 −0.485172 −0.242586 0.970130i \(-0.577996\pi\)