Properties

Label 300.3.c.f.151.8
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
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.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.6080256576.2
Defining polynomial: \(x^{8} - 3 x^{7} + 7 x^{6} - 12 x^{5} + 12 x^{4} - 48 x^{3} + 112 x^{2} - 192 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.8
Root \(0.375825 - 1.96437i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.f.151.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.88911 + 0.656712i) q^{2} -1.73205i q^{3} +(3.13746 + 2.48120i) q^{4} +(1.13746 - 3.27203i) q^{6} +9.55505i q^{7} +(4.29756 + 6.74766i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(1.88911 + 0.656712i) q^{2} -1.73205i q^{3} +(3.13746 + 2.48120i) q^{4} +(1.13746 - 3.27203i) q^{6} +9.55505i q^{7} +(4.29756 + 6.74766i) q^{8} -3.00000 q^{9} +9.92480i q^{11} +(4.29756 - 5.43424i) q^{12} +7.55643 q^{13} +(-6.27492 + 18.0505i) q^{14} +(3.68729 + 15.5693i) q^{16} +17.1903 q^{17} +(-5.66732 - 1.97014i) q^{18} -26.1762i q^{19} +16.5498 q^{21} +(-6.51774 + 18.7490i) q^{22} +1.67451i q^{23} +(11.6873 - 7.44360i) q^{24} +(14.2749 + 4.96240i) q^{26} +5.19615i q^{27} +(-23.7080 + 29.9786i) q^{28} +0.350497 q^{29} -46.0258i q^{31} +(-3.25887 + 31.8336i) q^{32} +17.1903 q^{33} +(32.4743 + 11.2890i) q^{34} +(-9.41238 - 7.44360i) q^{36} +22.6693 q^{37} +(17.1903 - 49.4498i) q^{38} -13.0881i q^{39} -77.2990 q^{41} +(31.2644 + 10.8685i) q^{42} +41.7994i q^{43} +(-24.6254 + 31.1386i) q^{44} +(-1.09967 + 3.16332i) q^{46} +14.0866i q^{47} +(26.9669 - 6.38658i) q^{48} -42.2990 q^{49} -29.7744i q^{51} +(23.7080 + 18.7490i) q^{52} -22.6693 q^{53} +(-3.41238 + 9.81609i) q^{54} +(-64.4743 + 41.0634i) q^{56} -45.3386 q^{57} +(0.662126 + 0.230175i) q^{58} -94.7802i q^{59} +38.0000 q^{61} +(30.2257 - 86.9478i) q^{62} -28.6652i q^{63} +(-27.0619 + 57.9970i) q^{64} +(32.4743 + 11.2890i) q^{66} -29.8477i q^{67} +(53.9337 + 42.6525i) q^{68} +2.90033 q^{69} +7.19630i q^{71} +(-12.8927 - 20.2430i) q^{72} -34.3805 q^{73} +(42.8248 + 14.8872i) q^{74} +(64.9485 - 82.1269i) q^{76} -94.8320 q^{77} +(8.59513 - 24.7249i) q^{78} -46.0258i q^{79} +9.00000 q^{81} +(-146.026 - 50.7632i) q^{82} -24.1336i q^{83} +(51.9244 + 41.0634i) q^{84} +(-27.4502 + 78.9636i) q^{86} -0.607078i q^{87} +(-66.9692 + 42.6525i) q^{88} -100.199 q^{89} +72.2021i q^{91} +(-4.15479 + 5.25370i) q^{92} -79.7191 q^{93} +(-9.25083 + 26.6111i) q^{94} +(55.1375 + 5.64452i) q^{96} +131.861 q^{97} +(-79.9074 - 27.7783i) q^{98} -29.7744i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 10q^{4} - 6q^{6} - 24q^{9} + O(q^{10}) \) \( 8q + 10q^{4} - 6q^{6} - 24q^{9} - 20q^{14} - 46q^{16} + 72q^{21} + 18q^{24} + 84q^{26} + 184q^{29} - 12q^{34} - 30q^{36} - 256q^{41} - 348q^{44} + 112q^{46} + 24q^{49} + 18q^{54} - 244q^{56} + 304q^{61} + 10q^{64} - 12q^{66} + 144q^{69} + 252q^{74} - 24q^{76} + 72q^{81} + 204q^{84} - 280q^{86} - 560q^{89} - 376q^{94} + 426q^{96} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.88911 + 0.656712i 0.944554 + 0.328356i
\(3\) 1.73205i 0.577350i
\(4\) 3.13746 + 2.48120i 0.784365 + 0.620300i
\(5\) 0 0
\(6\) 1.13746 3.27203i 0.189576 0.545339i
\(7\) 9.55505i 1.36501i 0.730882 + 0.682504i \(0.239109\pi\)
−0.730882 + 0.682504i \(0.760891\pi\)
\(8\) 4.29756 + 6.74766i 0.537196 + 0.843458i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 9.92480i 0.902255i 0.892460 + 0.451127i \(0.148978\pi\)
−0.892460 + 0.451127i \(0.851022\pi\)
\(12\) 4.29756 5.43424i 0.358130 0.452853i
\(13\) 7.55643 0.581264 0.290632 0.956835i \(-0.406134\pi\)
0.290632 + 0.956835i \(0.406134\pi\)
\(14\) −6.27492 + 18.0505i −0.448208 + 1.28932i
\(15\) 0 0
\(16\) 3.68729 + 15.5693i 0.230456 + 0.973083i
\(17\) 17.1903 1.01119 0.505596 0.862770i \(-0.331273\pi\)
0.505596 + 0.862770i \(0.331273\pi\)
\(18\) −5.66732 1.97014i −0.314851 0.109452i
\(19\) 26.1762i 1.37770i −0.724905 0.688849i \(-0.758116\pi\)
0.724905 0.688849i \(-0.241884\pi\)
\(20\) 0 0
\(21\) 16.5498 0.788087
\(22\) −6.51774 + 18.7490i −0.296261 + 0.852228i
\(23\) 1.67451i 0.0728047i 0.999337 + 0.0364023i \(0.0115898\pi\)
−0.999337 + 0.0364023i \(0.988410\pi\)
\(24\) 11.6873 7.44360i 0.486971 0.310150i
\(25\) 0 0
\(26\) 14.2749 + 4.96240i 0.549035 + 0.190862i
\(27\) 5.19615i 0.192450i
\(28\) −23.7080 + 29.9786i −0.846714 + 1.07066i
\(29\) 0.350497 0.0120861 0.00604305 0.999982i \(-0.498076\pi\)
0.00604305 + 0.999982i \(0.498076\pi\)
\(30\) 0 0
\(31\) 46.0258i 1.48470i −0.670010 0.742352i \(-0.733710\pi\)
0.670010 0.742352i \(-0.266290\pi\)
\(32\) −3.25887 + 31.8336i −0.101840 + 0.994801i
\(33\) 17.1903 0.520917
\(34\) 32.4743 + 11.2890i 0.955125 + 0.332031i
\(35\) 0 0
\(36\) −9.41238 7.44360i −0.261455 0.206767i
\(37\) 22.6693 0.612684 0.306342 0.951922i \(-0.400895\pi\)
0.306342 + 0.951922i \(0.400895\pi\)
\(38\) 17.1903 49.4498i 0.452375 1.30131i
\(39\) 13.0881i 0.335593i
\(40\) 0 0
\(41\) −77.2990 −1.88534 −0.942671 0.333724i \(-0.891695\pi\)
−0.942671 + 0.333724i \(0.891695\pi\)
\(42\) 31.2644 + 10.8685i 0.744391 + 0.258773i
\(43\) 41.7994i 0.972079i 0.873937 + 0.486039i \(0.161559\pi\)
−0.873937 + 0.486039i \(0.838441\pi\)
\(44\) −24.6254 + 31.1386i −0.559668 + 0.707697i
\(45\) 0 0
\(46\) −1.09967 + 3.16332i −0.0239058 + 0.0687679i
\(47\) 14.0866i 0.299715i 0.988708 + 0.149857i \(0.0478814\pi\)
−0.988708 + 0.149857i \(0.952119\pi\)
\(48\) 26.9669 6.38658i 0.561810 0.133054i
\(49\) −42.2990 −0.863245
\(50\) 0 0
\(51\) 29.7744i 0.583812i
\(52\) 23.7080 + 18.7490i 0.455923 + 0.360558i
\(53\) −22.6693 −0.427723 −0.213861 0.976864i \(-0.568604\pi\)
−0.213861 + 0.976864i \(0.568604\pi\)
\(54\) −3.41238 + 9.81609i −0.0631921 + 0.181780i
\(55\) 0 0
\(56\) −64.4743 + 41.0634i −1.15133 + 0.733276i
\(57\) −45.3386 −0.795414
\(58\) 0.662126 + 0.230175i 0.0114160 + 0.00396854i
\(59\) 94.7802i 1.60644i −0.595680 0.803222i \(-0.703117\pi\)
0.595680 0.803222i \(-0.296883\pi\)
\(60\) 0 0
\(61\) 38.0000 0.622951 0.311475 0.950254i \(-0.399177\pi\)
0.311475 + 0.950254i \(0.399177\pi\)
\(62\) 30.2257 86.9478i 0.487512 1.40238i
\(63\) 28.6652i 0.455002i
\(64\) −27.0619 + 57.9970i −0.422842 + 0.906203i
\(65\) 0 0
\(66\) 32.4743 + 11.2890i 0.492034 + 0.171046i
\(67\) 29.8477i 0.445488i −0.974877 0.222744i \(-0.928499\pi\)
0.974877 0.222744i \(-0.0715013\pi\)
\(68\) 53.9337 + 42.6525i 0.793143 + 0.627242i
\(69\) 2.90033 0.0420338
\(70\) 0 0
\(71\) 7.19630i 0.101356i 0.998715 + 0.0506782i \(0.0161383\pi\)
−0.998715 + 0.0506782i \(0.983862\pi\)
\(72\) −12.8927 20.2430i −0.179065 0.281153i
\(73\) −34.3805 −0.470966 −0.235483 0.971878i \(-0.575667\pi\)
−0.235483 + 0.971878i \(0.575667\pi\)
\(74\) 42.8248 + 14.8872i 0.578713 + 0.201178i
\(75\) 0 0
\(76\) 64.9485 82.1269i 0.854586 1.08062i
\(77\) −94.8320 −1.23158
\(78\) 8.59513 24.7249i 0.110194 0.316986i
\(79\) 46.0258i 0.582606i −0.956631 0.291303i \(-0.905911\pi\)
0.956631 0.291303i \(-0.0940887\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −146.026 50.7632i −1.78081 0.619063i
\(83\) 24.1336i 0.290767i −0.989375 0.145383i \(-0.953558\pi\)
0.989375 0.145383i \(-0.0464415\pi\)
\(84\) 51.9244 + 41.0634i 0.618148 + 0.488851i
\(85\) 0 0
\(86\) −27.4502 + 78.9636i −0.319188 + 0.918181i
\(87\) 0.607078i 0.00697791i
\(88\) −66.9692 + 42.6525i −0.761014 + 0.484687i
\(89\) −100.199 −1.12584 −0.562918 0.826513i \(-0.690321\pi\)
−0.562918 + 0.826513i \(0.690321\pi\)
\(90\) 0 0
\(91\) 72.2021i 0.793430i
\(92\) −4.15479 + 5.25370i −0.0451607 + 0.0571054i
\(93\) −79.7191 −0.857195
\(94\) −9.25083 + 26.6111i −0.0984131 + 0.283097i
\(95\) 0 0
\(96\) 55.1375 + 5.64452i 0.574349 + 0.0587971i
\(97\) 131.861 1.35939 0.679696 0.733494i \(-0.262112\pi\)
0.679696 + 0.733494i \(0.262112\pi\)
\(98\) −79.9074 27.7783i −0.815382 0.283452i
\(99\) 29.7744i 0.300752i
\(100\) 0 0
\(101\) 29.4502 0.291586 0.145793 0.989315i \(-0.453427\pi\)
0.145793 + 0.989315i \(0.453427\pi\)
\(102\) 19.5532 56.2471i 0.191698 0.551442i
\(103\) 143.786i 1.39598i −0.716107 0.697991i \(-0.754078\pi\)
0.716107 0.697991i \(-0.245922\pi\)
\(104\) 32.4743 + 50.9882i 0.312252 + 0.490272i
\(105\) 0 0
\(106\) −42.8248 14.8872i −0.404007 0.140445i
\(107\) 35.1014i 0.328050i −0.986456 0.164025i \(-0.947552\pi\)
0.986456 0.164025i \(-0.0524478\pi\)
\(108\) −12.8927 + 16.3027i −0.119377 + 0.150951i
\(109\) 151.498 1.38989 0.694947 0.719061i \(-0.255428\pi\)
0.694947 + 0.719061i \(0.255428\pi\)
\(110\) 0 0
\(111\) 39.2644i 0.353733i
\(112\) −148.766 + 35.2323i −1.32827 + 0.314574i
\(113\) 32.3031 0.285868 0.142934 0.989732i \(-0.454346\pi\)
0.142934 + 0.989732i \(0.454346\pi\)
\(114\) −85.6495 29.7744i −0.751311 0.261179i
\(115\) 0 0
\(116\) 1.09967 + 0.869652i 0.00947990 + 0.00749700i
\(117\) −22.6693 −0.193755
\(118\) 62.2433 179.050i 0.527486 1.51737i
\(119\) 164.254i 1.38028i
\(120\) 0 0
\(121\) 22.4983 0.185937
\(122\) 71.7861 + 24.9551i 0.588411 + 0.204550i
\(123\) 133.886i 1.08850i
\(124\) 114.199 144.404i 0.920962 1.16455i
\(125\) 0 0
\(126\) 18.8248 54.1516i 0.149403 0.429774i
\(127\) 192.053i 1.51223i −0.654438 0.756116i \(-0.727095\pi\)
0.654438 0.756116i \(-0.272905\pi\)
\(128\) −89.2102 + 91.7908i −0.696954 + 0.717115i
\(129\) 72.3987 0.561230
\(130\) 0 0
\(131\) 42.4277i 0.323876i 0.986801 + 0.161938i \(0.0517744\pi\)
−0.986801 + 0.161938i \(0.948226\pi\)
\(132\) 53.9337 + 42.6525i 0.408589 + 0.323125i
\(133\) 250.115 1.88057
\(134\) 19.6013 56.3855i 0.146279 0.420787i
\(135\) 0 0
\(136\) 73.8762 + 115.994i 0.543208 + 0.852897i
\(137\) −206.854 −1.50988 −0.754942 0.655791i \(-0.772335\pi\)
−0.754942 + 0.655791i \(0.772335\pi\)
\(138\) 5.47904 + 1.90468i 0.0397032 + 0.0138020i
\(139\) 46.0258i 0.331121i 0.986200 + 0.165561i \(0.0529433\pi\)
−0.986200 + 0.165561i \(0.947057\pi\)
\(140\) 0 0
\(141\) 24.3987 0.173040
\(142\) −4.72590 + 13.5946i −0.0332810 + 0.0957366i
\(143\) 74.9961i 0.524448i
\(144\) −11.0619 46.7080i −0.0768186 0.324361i
\(145\) 0 0
\(146\) −64.9485 22.5781i −0.444853 0.154645i
\(147\) 73.2640i 0.498395i
\(148\) 71.1240 + 56.2471i 0.480567 + 0.380048i
\(149\) −11.6495 −0.0781846 −0.0390923 0.999236i \(-0.512447\pi\)
−0.0390923 + 0.999236i \(0.512447\pi\)
\(150\) 0 0
\(151\) 125.424i 0.830624i −0.909679 0.415312i \(-0.863672\pi\)
0.909679 0.415312i \(-0.136328\pi\)
\(152\) 176.628 112.494i 1.16203 0.740093i
\(153\) −51.5708 −0.337064
\(154\) −179.148 62.2773i −1.16330 0.404398i
\(155\) 0 0
\(156\) 32.4743 41.0634i 0.208168 0.263227i
\(157\) 197.220 1.25618 0.628090 0.778140i \(-0.283837\pi\)
0.628090 + 0.778140i \(0.283837\pi\)
\(158\) 30.2257 86.9478i 0.191302 0.550303i
\(159\) 39.2644i 0.246946i
\(160\) 0 0
\(161\) −16.0000 −0.0993789
\(162\) 17.0020 + 5.91041i 0.104950 + 0.0364840i
\(163\) 18.4196i 0.113004i 0.998402 + 0.0565018i \(0.0179947\pi\)
−0.998402 + 0.0565018i \(0.982005\pi\)
\(164\) −242.522 191.794i −1.47880 1.16948i
\(165\) 0 0
\(166\) 15.8488 45.5910i 0.0954749 0.274645i
\(167\) 92.8920i 0.556240i 0.960546 + 0.278120i \(0.0897112\pi\)
−0.960546 + 0.278120i \(0.910289\pi\)
\(168\) 71.1240 + 111.673i 0.423357 + 0.664718i
\(169\) −111.900 −0.662132
\(170\) 0 0
\(171\) 78.5287i 0.459232i
\(172\) −103.713 + 131.144i −0.602981 + 0.762464i
\(173\) −117.501 −0.679198 −0.339599 0.940570i \(-0.610291\pi\)
−0.339599 + 0.940570i \(0.610291\pi\)
\(174\) 0.398675 1.14684i 0.00229124 0.00659101i
\(175\) 0 0
\(176\) −154.522 + 36.5956i −0.877968 + 0.207930i
\(177\) −164.164 −0.927481
\(178\) −189.287 65.8021i −1.06341 0.369675i
\(179\) 231.988i 1.29602i 0.761631 + 0.648011i \(0.224399\pi\)
−0.761631 + 0.648011i \(0.775601\pi\)
\(180\) 0 0
\(181\) −218.096 −1.20495 −0.602476 0.798137i \(-0.705819\pi\)
−0.602476 + 0.798137i \(0.705819\pi\)
\(182\) −47.4160 + 136.398i −0.260527 + 0.749437i
\(183\) 65.8179i 0.359661i
\(184\) −11.2990 + 7.19630i −0.0614076 + 0.0391103i
\(185\) 0 0
\(186\) −150.598 52.3525i −0.809667 0.281465i
\(187\) 170.610i 0.912352i
\(188\) −34.9516 + 44.1961i −0.185913 + 0.235085i
\(189\) −49.6495 −0.262696
\(190\) 0 0
\(191\) 137.208i 0.718366i 0.933267 + 0.359183i \(0.116945\pi\)
−0.933267 + 0.359183i \(0.883055\pi\)
\(192\) 100.454 + 46.8725i 0.523197 + 0.244128i
\(193\) −37.0290 −0.191860 −0.0959301 0.995388i \(-0.530583\pi\)
−0.0959301 + 0.995388i \(0.530583\pi\)
\(194\) 249.100 + 86.5947i 1.28402 + 0.446364i
\(195\) 0 0
\(196\) −132.711 104.952i −0.677099 0.535471i
\(197\) 194.572 0.987674 0.493837 0.869554i \(-0.335594\pi\)
0.493837 + 0.869554i \(0.335594\pi\)
\(198\) 19.5532 56.2471i 0.0987536 0.284076i
\(199\) 176.037i 0.884610i 0.896865 + 0.442305i \(0.145839\pi\)
−0.896865 + 0.442305i \(0.854161\pi\)
\(200\) 0 0
\(201\) −51.6977 −0.257202
\(202\) 55.6345 + 19.3403i 0.275419 + 0.0957440i
\(203\) 3.34901i 0.0164976i
\(204\) 73.8762 93.4159i 0.362138 0.457921i
\(205\) 0 0
\(206\) 94.4261 271.628i 0.458379 1.31858i
\(207\) 5.02352i 0.0242682i
\(208\) 27.8628 + 117.649i 0.133956 + 0.565618i
\(209\) 259.794 1.24303
\(210\) 0 0
\(211\) 20.7193i 0.0981955i 0.998794 + 0.0490978i \(0.0156346\pi\)
−0.998794 + 0.0490978i \(0.984365\pi\)
\(212\) −71.1240 56.2471i −0.335490 0.265316i
\(213\) 12.4644 0.0585181
\(214\) 23.0515 66.3103i 0.107717 0.309861i
\(215\) 0 0
\(216\) −35.0619 + 22.3308i −0.162324 + 0.103383i
\(217\) 439.779 2.02663
\(218\) 286.197 + 99.4908i 1.31283 + 0.456380i
\(219\) 59.5488i 0.271912i
\(220\) 0 0
\(221\) 129.897 0.587769
\(222\) 25.7854 74.1746i 0.116150 0.334120i
\(223\) 97.0265i 0.435096i −0.976050 0.217548i \(-0.930194\pi\)
0.976050 0.217548i \(-0.0698059\pi\)
\(224\) −304.172 31.1386i −1.35791 0.139012i
\(225\) 0 0
\(226\) 61.0241 + 21.2138i 0.270018 + 0.0938666i
\(227\) 407.256i 1.79408i 0.441948 + 0.897040i \(0.354287\pi\)
−0.441948 + 0.897040i \(0.645713\pi\)
\(228\) −142.248 112.494i −0.623895 0.493395i
\(229\) 7.89702 0.0344848 0.0172424 0.999851i \(-0.494511\pi\)
0.0172424 + 0.999851i \(0.494511\pi\)
\(230\) 0 0
\(231\) 164.254i 0.711055i
\(232\) 1.50628 + 2.36503i 0.00649260 + 0.0101941i
\(233\) 28.1483 0.120808 0.0604042 0.998174i \(-0.480761\pi\)
0.0604042 + 0.998174i \(0.480761\pi\)
\(234\) −42.8248 14.8872i −0.183012 0.0636205i
\(235\) 0 0
\(236\) 235.169 297.369i 0.996477 1.26004i
\(237\) −79.7191 −0.336368
\(238\) −107.867 + 310.293i −0.453225 + 1.30375i
\(239\) 296.005i 1.23851i −0.785189 0.619257i \(-0.787434\pi\)
0.785189 0.619257i \(-0.212566\pi\)
\(240\) 0 0
\(241\) 465.794 1.93276 0.966378 0.257127i \(-0.0827758\pi\)
0.966378 + 0.257127i \(0.0827758\pi\)
\(242\) 42.5018 + 14.7749i 0.175627 + 0.0610534i
\(243\) 15.5885i 0.0641500i
\(244\) 119.223 + 94.2856i 0.488621 + 0.386416i
\(245\) 0 0
\(246\) −87.9244 + 252.925i −0.357416 + 1.02815i
\(247\) 197.799i 0.800806i
\(248\) 310.567 197.799i 1.25229 0.797577i
\(249\) −41.8007 −0.167874
\(250\) 0 0
\(251\) 141.676i 0.564445i −0.959349 0.282223i \(-0.908928\pi\)
0.959349 0.282223i \(-0.0910716\pi\)
\(252\) 71.1240 89.9357i 0.282238 0.356888i
\(253\) −16.6191 −0.0656883
\(254\) 126.124 362.810i 0.496550 1.42838i
\(255\) 0 0
\(256\) −228.808 + 114.817i −0.893780 + 0.448505i
\(257\) −41.7549 −0.162470 −0.0812352 0.996695i \(-0.525887\pi\)
−0.0812352 + 0.996695i \(0.525887\pi\)
\(258\) 136.769 + 47.5451i 0.530112 + 0.184283i
\(259\) 216.606i 0.836318i
\(260\) 0 0
\(261\) −1.05149 −0.00402870
\(262\) −27.8628 + 80.1505i −0.106346 + 0.305918i
\(263\) 203.283i 0.772939i 0.922302 + 0.386469i \(0.126306\pi\)
−0.922302 + 0.386469i \(0.873694\pi\)
\(264\) 73.8762 + 115.994i 0.279834 + 0.439371i
\(265\) 0 0
\(266\) 472.495 + 164.254i 1.77630 + 0.617495i
\(267\) 173.550i 0.650001i
\(268\) 74.0580 93.6458i 0.276336 0.349425i
\(269\) 244.048 0.907242 0.453621 0.891195i \(-0.350132\pi\)
0.453621 + 0.891195i \(0.350132\pi\)
\(270\) 0 0
\(271\) 466.585i 1.72172i 0.508845 + 0.860858i \(0.330073\pi\)
−0.508845 + 0.860858i \(0.669927\pi\)
\(272\) 63.3855 + 267.641i 0.233035 + 0.983973i
\(273\) 125.058 0.458087
\(274\) −390.770 135.844i −1.42617 0.495780i
\(275\) 0 0
\(276\) 9.09967 + 7.19630i 0.0329698 + 0.0260736i
\(277\) −494.181 −1.78405 −0.892023 0.451990i \(-0.850714\pi\)
−0.892023 + 0.451990i \(0.850714\pi\)
\(278\) −30.2257 + 86.9478i −0.108726 + 0.312762i
\(279\) 138.078i 0.494902i
\(280\) 0 0
\(281\) −43.4020 −0.154455 −0.0772277 0.997013i \(-0.524607\pi\)
−0.0772277 + 0.997013i \(0.524607\pi\)
\(282\) 46.0917 + 16.0229i 0.163446 + 0.0568188i
\(283\) 310.785i 1.09818i 0.835763 + 0.549090i \(0.185026\pi\)
−0.835763 + 0.549090i \(0.814974\pi\)
\(284\) −17.8555 + 22.5781i −0.0628714 + 0.0795003i
\(285\) 0 0
\(286\) −49.2508 + 141.676i −0.172206 + 0.495370i
\(287\) 738.596i 2.57351i
\(288\) 9.77660 95.5009i 0.0339465 0.331600i
\(289\) 6.50497 0.0225085
\(290\) 0 0
\(291\) 228.390i 0.784845i
\(292\) −107.867 85.3049i −0.369409 0.292140i
\(293\) −245.207 −0.836886 −0.418443 0.908243i \(-0.637424\pi\)
−0.418443 + 0.908243i \(0.637424\pi\)
\(294\) −48.1134 + 138.404i −0.163651 + 0.470761i
\(295\) 0 0
\(296\) 97.4228 + 152.965i 0.329131 + 0.516773i
\(297\) −51.5708 −0.173639
\(298\) −22.0072 7.65037i −0.0738496 0.0256724i
\(299\) 12.6533i 0.0423187i
\(300\) 0 0
\(301\) −399.395 −1.32689
\(302\) 82.3676 236.940i 0.272740 0.784569i
\(303\) 51.0092i 0.168347i
\(304\) 407.547 96.5195i 1.34061 0.317498i
\(305\) 0 0
\(306\) −97.4228 33.8671i −0.318375 0.110677i
\(307\) 337.514i 1.09939i 0.835364 + 0.549697i \(0.185257\pi\)
−0.835364 + 0.549697i \(0.814743\pi\)
\(308\) −297.531 235.297i −0.966011 0.763952i
\(309\) −249.045 −0.805970
\(310\) 0 0
\(311\) 427.756i 1.37542i −0.725986 0.687710i \(-0.758616\pi\)
0.725986 0.687710i \(-0.241384\pi\)
\(312\) 88.3142 56.2471i 0.283058 0.180279i
\(313\) 83.8739 0.267968 0.133984 0.990984i \(-0.457223\pi\)
0.133984 + 0.990984i \(0.457223\pi\)
\(314\) 372.571 + 129.517i 1.18653 + 0.412475i
\(315\) 0 0
\(316\) 114.199 144.404i 0.361390 0.456975i
\(317\) −112.204 −0.353957 −0.176978 0.984215i \(-0.556632\pi\)
−0.176978 + 0.984215i \(0.556632\pi\)
\(318\) −25.7854 + 74.1746i −0.0810861 + 0.233254i
\(319\) 3.47861i 0.0109047i
\(320\) 0 0
\(321\) −60.7974 −0.189400
\(322\) −30.2257 10.5074i −0.0938687 0.0326317i
\(323\) 449.976i 1.39312i
\(324\) 28.2371 + 22.3308i 0.0871516 + 0.0689222i
\(325\) 0 0
\(326\) −12.0964 + 34.7966i −0.0371054 + 0.106738i
\(327\) 262.403i 0.802455i
\(328\) −332.197 521.588i −1.01280 1.59021i
\(329\) −134.598 −0.409113
\(330\) 0 0
\(331\) 132.621i 0.400666i −0.979728 0.200333i \(-0.935798\pi\)
0.979728 0.200333i \(-0.0642025\pi\)
\(332\) 59.8803 75.7182i 0.180362 0.228067i
\(333\) −68.0079 −0.204228
\(334\) −61.0033 + 175.483i −0.182645 + 0.525398i
\(335\) 0 0
\(336\) 61.0241 + 257.670i 0.181619 + 0.766874i
\(337\) −20.7739 −0.0616437 −0.0308219 0.999525i \(-0.509812\pi\)
−0.0308219 + 0.999525i \(0.509812\pi\)
\(338\) −211.392 73.4863i −0.625420 0.217415i
\(339\) 55.9506i 0.165046i
\(340\) 0 0
\(341\) 456.797 1.33958
\(342\) −51.5708 + 148.349i −0.150792 + 0.433770i
\(343\) 64.0283i 0.186672i
\(344\) −282.048 + 179.636i −0.819907 + 0.522196i
\(345\) 0 0
\(346\) −221.973 77.1645i −0.641539 0.223019i
\(347\) 8.89616i 0.0256374i 0.999918 + 0.0128187i \(0.00408042\pi\)
−0.999918 + 0.0128187i \(0.995920\pi\)
\(348\) 1.50628 1.90468i 0.00432840 0.00547323i
\(349\) −19.4020 −0.0555931 −0.0277965 0.999614i \(-0.508849\pi\)
−0.0277965 + 0.999614i \(0.508849\pi\)
\(350\) 0 0
\(351\) 39.2644i 0.111864i
\(352\) −315.942 32.3436i −0.897564 0.0918853i
\(353\) 80.2902 0.227451 0.113726 0.993512i \(-0.463722\pi\)
0.113726 + 0.993512i \(0.463722\pi\)
\(354\) −310.124 107.809i −0.876056 0.304544i
\(355\) 0 0
\(356\) −314.371 248.615i −0.883065 0.698356i
\(357\) 284.496 0.796907
\(358\) −152.349 + 438.251i −0.425557 + 1.22416i
\(359\) 314.115i 0.874972i −0.899225 0.437486i \(-0.855869\pi\)
0.899225 0.437486i \(-0.144131\pi\)
\(360\) 0 0
\(361\) −324.196 −0.898050
\(362\) −412.008 143.227i −1.13814 0.395653i
\(363\) 38.9683i 0.107351i
\(364\) −179.148 + 226.531i −0.492164 + 0.622338i
\(365\) 0 0
\(366\) 43.2234 124.337i 0.118097 0.339719i
\(367\) 476.800i 1.29918i −0.760283 0.649592i \(-0.774940\pi\)
0.760283 0.649592i \(-0.225060\pi\)
\(368\) −26.0709 + 6.17440i −0.0708450 + 0.0167783i
\(369\) 231.897 0.628447
\(370\) 0 0
\(371\) 216.606i 0.583844i
\(372\) −250.115 197.799i −0.672353 0.531718i
\(373\) −86.1333 −0.230920 −0.115460 0.993312i \(-0.536834\pi\)
−0.115460 + 0.993312i \(0.536834\pi\)
\(374\) −112.042 + 322.300i −0.299576 + 0.861766i
\(375\) 0 0
\(376\) −95.0515 + 60.5380i −0.252797 + 0.161005i
\(377\) 2.64850 0.00702521
\(378\) −93.7933 32.6054i −0.248130 0.0862577i
\(379\) 638.035i 1.68347i −0.539891 0.841735i \(-0.681534\pi\)
0.539891 0.841735i \(-0.318466\pi\)
\(380\) 0 0
\(381\) −332.646 −0.873087
\(382\) −90.1061 + 259.201i −0.235880 + 0.678535i
\(383\) 216.742i 0.565907i −0.959134 0.282953i \(-0.908686\pi\)
0.959134 0.282953i \(-0.0913142\pi\)
\(384\) 158.986 + 154.517i 0.414027 + 0.402387i
\(385\) 0 0
\(386\) −69.9518 24.3174i −0.181222 0.0629985i
\(387\) 125.398i 0.324026i
\(388\) 413.708 + 327.174i 1.06626 + 0.843231i
\(389\) −476.640 −1.22529 −0.612647 0.790356i \(-0.709895\pi\)
−0.612647 + 0.790356i \(0.709895\pi\)
\(390\) 0 0
\(391\) 28.7852i 0.0736195i
\(392\) −181.783 285.419i −0.463731 0.728111i
\(393\) 73.4869 0.186990
\(394\) 367.567 + 127.778i 0.932912 + 0.324309i
\(395\) 0 0
\(396\) 73.8762 93.4159i 0.186556 0.235899i
\(397\) −43.0792 −0.108512 −0.0542559 0.998527i \(-0.517279\pi\)
−0.0542559 + 0.998527i \(0.517279\pi\)
\(398\) −115.606 + 332.554i −0.290467 + 0.835562i
\(399\) 433.213i 1.08575i
\(400\) 0 0
\(401\) −168.694 −0.420684 −0.210342 0.977628i \(-0.567458\pi\)
−0.210342 + 0.977628i \(0.567458\pi\)
\(402\) −97.6625 33.9505i −0.242942 0.0844540i
\(403\) 347.791i 0.863005i
\(404\) 92.3987 + 73.0718i 0.228710 + 0.180871i
\(405\) 0 0
\(406\) −2.19934 + 6.32665i −0.00541709 + 0.0155829i
\(407\) 224.988i 0.552797i
\(408\) 200.908 127.957i 0.492421 0.313621i
\(409\) −373.890 −0.914157 −0.457079 0.889426i \(-0.651104\pi\)
−0.457079 + 0.889426i \(0.651104\pi\)
\(410\) 0 0
\(411\) 358.282i 0.871732i
\(412\) 356.762 451.123i 0.865927 1.09496i
\(413\) 905.630 2.19281
\(414\) 3.29901 9.48997i 0.00796862 0.0229226i
\(415\) 0 0
\(416\) −24.6254 + 240.549i −0.0591957 + 0.578242i
\(417\) 79.7191 0.191173
\(418\) 490.779 + 170.610i 1.17411 + 0.408158i
\(419\) 87.5839i 0.209031i −0.994523 0.104515i \(-0.966671\pi\)
0.994523 0.104515i \(-0.0333291\pi\)
\(420\) 0 0
\(421\) 70.3023 0.166989 0.0834944 0.996508i \(-0.473392\pi\)
0.0834944 + 0.996508i \(0.473392\pi\)
\(422\) −13.6066 + 39.1409i −0.0322431 + 0.0927510i
\(423\) 42.2597i 0.0999048i
\(424\) −97.4228 152.965i −0.229771 0.360766i
\(425\) 0 0
\(426\) 23.5465 + 8.18550i 0.0552735 + 0.0192148i
\(427\) 363.092i 0.850332i
\(428\) 87.0935 110.129i 0.203490 0.257311i
\(429\) 129.897 0.302790
\(430\) 0 0
\(431\) 247.370i 0.573944i 0.957939 + 0.286972i \(0.0926487\pi\)
−0.957939 + 0.286972i \(0.907351\pi\)
\(432\) −80.9006 + 19.1597i −0.187270 + 0.0443512i
\(433\) −636.247 −1.46939 −0.734696 0.678397i \(-0.762675\pi\)
−0.734696 + 0.678397i \(0.762675\pi\)
\(434\) 830.791 + 288.808i 1.91426 + 0.665457i
\(435\) 0 0
\(436\) 475.320 + 375.898i 1.09018 + 0.862151i
\(437\) 43.8323 0.100303
\(438\) −39.1064 + 112.494i −0.0892840 + 0.256836i
\(439\) 769.786i 1.75350i −0.480947 0.876750i \(-0.659707\pi\)
0.480947 0.876750i \(-0.340293\pi\)
\(440\) 0 0
\(441\) 126.897 0.287748
\(442\) 245.390 + 85.3049i 0.555180 + 0.192998i
\(443\) 612.214i 1.38197i 0.722868 + 0.690986i \(0.242823\pi\)
−0.722868 + 0.690986i \(0.757177\pi\)
\(444\) 97.4228 123.190i 0.219421 0.277456i
\(445\) 0 0
\(446\) 63.7185 183.294i 0.142867 0.410972i
\(447\) 20.1775i 0.0451399i
\(448\) −554.165 258.578i −1.23697 0.577182i
\(449\) −175.897 −0.391753 −0.195876 0.980629i \(-0.562755\pi\)
−0.195876 + 0.980629i \(0.562755\pi\)
\(450\) 0 0
\(451\) 767.177i 1.70106i
\(452\) 101.350 + 80.1505i 0.224225 + 0.177324i
\(453\) −217.241 −0.479561
\(454\) −267.450 + 769.351i −0.589097 + 1.69461i
\(455\) 0 0
\(456\) −194.846 305.929i −0.427293 0.670898i
\(457\) −365.357 −0.799469 −0.399734 0.916631i \(-0.630898\pi\)
−0.399734 + 0.916631i \(0.630898\pi\)
\(458\) 14.9183 + 5.18607i 0.0325728 + 0.0113233i
\(459\) 89.3232i 0.194604i
\(460\) 0 0
\(461\) 308.350 0.668873 0.334437 0.942418i \(-0.391454\pi\)
0.334437 + 0.942418i \(0.391454\pi\)
\(462\) −107.867 + 310.293i −0.233479 + 0.671630i
\(463\) 92.6302i 0.200065i 0.994984 + 0.100033i \(0.0318947\pi\)
−0.994984 + 0.100033i \(0.968105\pi\)
\(464\) 1.29238 + 5.45700i 0.00278531 + 0.0117608i
\(465\) 0 0
\(466\) 53.1752 + 18.4854i 0.114110 + 0.0396681i
\(467\) 606.103i 1.29786i 0.760846 + 0.648932i \(0.224784\pi\)
−0.760846 + 0.648932i \(0.775216\pi\)
\(468\) −71.1240 56.2471i −0.151974 0.120186i
\(469\) 285.196 0.608094
\(470\) 0 0
\(471\) 341.596i 0.725256i
\(472\) 639.545 407.324i 1.35497 0.862975i
\(473\) −414.851 −0.877063
\(474\) −150.598 52.3525i −0.317717 0.110448i
\(475\) 0 0
\(476\) −407.547 + 515.339i −0.856190 + 1.08265i
\(477\) 68.0079 0.142574
\(478\) 194.390 559.185i 0.406673 1.16984i
\(479\) 138.947i 0.290078i 0.989426 + 0.145039i \(0.0463307\pi\)
−0.989426 + 0.145039i \(0.953669\pi\)
\(480\) 0 0
\(481\) 171.299 0.356131
\(482\) 879.935 + 305.893i 1.82559 + 0.634632i
\(483\) 27.7128i 0.0573764i
\(484\) 70.5876 + 55.8229i 0.145842 + 0.115337i
\(485\) 0 0
\(486\) 10.2371 29.4483i 0.0210640 0.0605932i
\(487\) 201.243i 0.413230i −0.978422 0.206615i \(-0.933755\pi\)
0.978422 0.206615i \(-0.0662447\pi\)
\(488\) 163.307 + 256.411i 0.334646 + 0.525433i
\(489\) 31.9036 0.0652426
\(490\) 0 0
\(491\) 347.368i 0.707470i 0.935346 + 0.353735i \(0.115089\pi\)
−0.935346 + 0.353735i \(0.884911\pi\)
\(492\) −332.197 + 420.061i −0.675198 + 0.853783i
\(493\) 6.02513 0.0122214
\(494\) 129.897 373.664i 0.262949 0.756404i
\(495\) 0 0
\(496\) 716.591 169.711i 1.44474 0.342159i
\(497\) −68.7610 −0.138352
\(498\) −78.9660 27.4510i −0.158566 0.0551225i
\(499\) 672.277i 1.34725i 0.739074 + 0.673625i \(0.235264\pi\)
−0.739074 + 0.673625i \(0.764736\pi\)
\(500\) 0 0
\(501\) 160.894 0.321145
\(502\) 93.0401 267.641i 0.185339 0.533149i
\(503\) 436.350i 0.867496i −0.901034 0.433748i \(-0.857191\pi\)
0.901034 0.433748i \(-0.142809\pi\)
\(504\) 193.423 123.190i 0.383775 0.244425i
\(505\) 0 0
\(506\) −31.3954 10.9140i −0.0620462 0.0215692i
\(507\) 193.817i 0.382282i
\(508\) 476.523 602.559i 0.938037 1.18614i
\(509\) 109.547 0.215219 0.107610 0.994193i \(-0.465680\pi\)
0.107610 + 0.994193i \(0.465680\pi\)
\(510\) 0 0
\(511\) 328.508i 0.642872i
\(512\) −507.644 + 66.6415i −0.991493 + 0.130159i
\(513\) 136.016 0.265138
\(514\) −78.8796 27.4210i −0.153462 0.0533482i
\(515\) 0 0
\(516\) 227.148 + 179.636i 0.440209 + 0.348131i
\(517\) −139.807 −0.270419
\(518\) −142.248 + 409.193i −0.274610 + 0.789947i
\(519\) 203.518i 0.392135i
\(520\) 0 0
\(521\) −743.100 −1.42629 −0.713147 0.701014i \(-0.752731\pi\)
−0.713147 + 0.701014i \(0.752731\pi\)
\(522\) −1.98638 0.690526i −0.00380532 0.00132285i
\(523\) 366.211i 0.700212i 0.936710 + 0.350106i \(0.113854\pi\)
−0.936710 + 0.350106i \(0.886146\pi\)
\(524\) −105.272 + 133.115i −0.200900 + 0.254037i
\(525\) 0 0
\(526\) −133.498 + 384.023i −0.253799 + 0.730083i
\(527\) 791.196i 1.50132i
\(528\) 63.3855 + 267.641i 0.120048 + 0.506895i
\(529\) 526.196 0.994699
\(530\) 0 0
\(531\) 284.341i 0.535481i
\(532\) 784.727 + 620.586i 1.47505 + 1.16652i
\(533\) −584.105 −1.09588
\(534\) −113.973 + 327.855i −0.213432 + 0.613961i
\(535\) 0 0
\(536\) 201.402 128.272i 0.375750 0.239314i
\(537\) 401.815 0.748259
\(538\) 461.033 + 160.269i 0.856939 + 0.297898i
\(539\) 419.809i 0.778867i
\(540\) 0 0
\(541\) 170.688 0.315504 0.157752 0.987479i \(-0.449575\pi\)
0.157752 + 0.987479i \(0.449575\pi\)
\(542\) −306.412 + 881.430i −0.565336 + 1.62625i
\(543\) 377.754i 0.695680i
\(544\) −56.0208 + 547.228i −0.102979 + 1.00593i
\(545\) 0 0
\(546\) 236.248 + 82.1269i 0.432688 + 0.150416i
\(547\) 507.600i 0.927971i 0.885843 + 0.463986i \(0.153581\pi\)
−0.885843 + 0.463986i \(0.846419\pi\)
\(548\) −648.997 513.247i −1.18430 0.936581i
\(549\) −114.000 −0.207650
\(550\) 0 0
\(551\) 9.17469i 0.0166510i
\(552\) 12.4644 + 19.5705i 0.0225804 + 0.0354537i
\(553\) 439.779 0.795261
\(554\) −933.561 324.534i −1.68513 0.585802i
\(555\) 0 0
\(556\) −114.199 + 144.404i −0.205394 + 0.259720i
\(557\) 788.492 1.41561 0.707803 0.706410i \(-0.249686\pi\)
0.707803 + 0.706410i \(0.249686\pi\)
\(558\) −90.6772 + 260.843i −0.162504 + 0.467461i
\(559\) 315.854i 0.565035i
\(560\) 0 0
\(561\) 295.505 0.526747
\(562\) −81.9910 28.5026i −0.145892 0.0507164i
\(563\) 936.102i 1.66270i 0.555747 + 0.831351i \(0.312432\pi\)
−0.555747 + 0.831351i \(0.687568\pi\)
\(564\) 76.5498 + 60.5380i 0.135727 + 0.107337i
\(565\) 0 0
\(566\) −204.096 + 587.107i −0.360594 + 1.03729i
\(567\) 85.9955i 0.151667i
\(568\) −48.5582 + 30.9266i −0.0854898 + 0.0544482i
\(569\) 95.4983 0.167835 0.0839177 0.996473i \(-0.473257\pi\)
0.0839177 + 0.996473i \(0.473257\pi\)
\(570\) 0 0
\(571\) 889.123i 1.55713i 0.627562 + 0.778566i \(0.284053\pi\)
−0.627562 + 0.778566i \(0.715947\pi\)
\(572\) −186.080 + 235.297i −0.325315 + 0.411359i
\(573\) 237.651 0.414749
\(574\) 485.045 1395.29i 0.845026 2.43081i
\(575\) 0 0
\(576\) 81.1856 173.991i 0.140947 0.302068i
\(577\) −522.147 −0.904934 −0.452467 0.891781i \(-0.649456\pi\)
−0.452467 + 0.891781i \(0.649456\pi\)
\(578\) 12.2886 + 4.27189i 0.0212605 + 0.00739081i
\(579\) 64.1361i 0.110771i
\(580\) 0 0
\(581\) 230.598 0.396898
\(582\) 149.986 431.453i 0.257709 0.741329i
\(583\) 224.988i 0.385915i
\(584\) −147.752 231.988i −0.253001 0.397240i
\(585\) 0 0
\(586\) −463.223 161.031i −0.790484 0.274796i
\(587\) 95.8440i 0.163278i 0.996662 + 0.0816388i \(0.0260154\pi\)
−0.996662 + 0.0816388i \(0.973985\pi\)
\(588\) −181.783 + 229.863i −0.309154 + 0.390923i
\(589\) −1204.78 −2.04547
\(590\) 0 0
\(591\) 337.008i 0.570234i
\(592\) 83.5883 + 352.946i 0.141197 + 0.596192i
\(593\) 878.624 1.48166 0.740829 0.671693i \(-0.234433\pi\)
0.740829 + 0.671693i \(0.234433\pi\)
\(594\) −97.4228 33.8671i −0.164011 0.0570154i
\(595\) 0 0
\(596\) −36.5498 28.9047i −0.0613252 0.0484979i
\(597\) 304.906 0.510730
\(598\) −8.30957 + 23.9034i −0.0138956 + 0.0399723i
\(599\) 967.652i 1.61545i 0.589563 + 0.807723i \(0.299300\pi\)
−0.589563 + 0.807723i \(0.700700\pi\)
\(600\) 0 0
\(601\) 279.704 0.465398 0.232699 0.972549i \(-0.425244\pi\)
0.232699 + 0.972549i \(0.425244\pi\)
\(602\) −754.501 262.288i −1.25332 0.435694i
\(603\) 89.5430i 0.148496i
\(604\) 311.203 393.513i 0.515236 0.651512i
\(605\) 0 0
\(606\) 33.4983 96.3619i 0.0552778 0.159013i
\(607\) 747.564i 1.23157i 0.787914 + 0.615786i \(0.211161\pi\)
−0.787914 + 0.615786i \(0.788839\pi\)
\(608\) 833.285 + 85.3049i 1.37053 + 0.140304i
\(609\) 5.80066 0.00952490
\(610\) 0 0
\(611\) 106.444i 0.174213i
\(612\) −161.801 127.957i −0.264381 0.209081i
\(613\) 457.152 0.745761 0.372881 0.927879i \(-0.378370\pi\)
0.372881 + 0.927879i \(0.378370\pi\)
\(614\) −221.650 + 637.600i −0.360993 + 1.03844i
\(615\) 0 0
\(616\) −407.547 639.894i −0.661601 1.03879i
\(617\) 764.888 1.23969 0.619844 0.784725i \(-0.287196\pi\)
0.619844 + 0.784725i \(0.287196\pi\)
\(618\) −470.473 163.551i −0.761283 0.264645i
\(619\) 365.359i 0.590240i −0.955460 0.295120i \(-0.904640\pi\)
0.955460 0.295120i \(-0.0953597\pi\)
\(620\) 0 0
\(621\) −8.70099 −0.0140113
\(622\) 280.912 808.077i 0.451627 1.29916i
\(623\) 957.410i 1.53677i
\(624\) 203.773 48.2598i 0.326560 0.0773393i
\(625\) 0 0
\(626\) 158.447 + 55.0810i 0.253110 + 0.0879888i
\(627\) 449.976i 0.717666i
\(628\) 618.771 + 489.343i 0.985304 + 0.779209i
\(629\) 389.691 0.619541
\(630\) 0 0
\(631\) 62.1578i 0.0985067i −0.998786 0.0492534i \(-0.984316\pi\)
0.998786 0.0492534i \(-0.0156842\pi\)
\(632\) 310.567 197.799i 0.491403 0.312973i
\(633\) 35.8868 0.0566932
\(634\) −211.966 73.6859i −0.334331 0.116224i
\(635\) 0 0
\(636\) −97.4228 + 123.190i −0.153180 + 0.193696i
\(637\) −319.630 −0.501773
\(638\) −2.28444 + 6.57147i −0.00358063 + 0.0103001i
\(639\) 21.5889i 0.0337855i
\(640\) 0 0
\(641\) −1111.69 −1.73431 −0.867154 0.498041i \(-0.834053\pi\)
−0.867154 + 0.498041i \(0.834053\pi\)
\(642\) −114.853 39.9264i −0.178898 0.0621906i
\(643\) 468.983i 0.729367i −0.931132 0.364683i \(-0.881177\pi\)
0.931132 0.364683i \(-0.118823\pi\)
\(644\) −50.1993 39.6992i −0.0779493 0.0616447i
\(645\) 0 0
\(646\) 295.505 850.054i 0.457438 1.31587i
\(647\) 96.7647i 0.149559i −0.997200 0.0747795i \(-0.976175\pi\)
0.997200 0.0747795i \(-0.0238253\pi\)
\(648\) 38.6781 + 60.7290i 0.0596884 + 0.0937175i
\(649\) 940.675 1.44942
\(650\) 0 0
\(651\) 761.720i 1.17008i
\(652\) −45.7027 + 57.7907i −0.0700961 + 0.0886360i
\(653\) −920.353 −1.40942 −0.704712 0.709494i \(-0.748924\pi\)
−0.704712 + 0.709494i \(0.748924\pi\)
\(654\) 172.323 495.707i 0.263491 0.757962i
\(655\) 0 0
\(656\) −285.024 1203.49i −0.434488 1.83459i
\(657\) 103.142 0.156989
\(658\) −254.270 88.3921i −0.386429 0.134335i
\(659\) 591.020i 0.896844i −0.893822 0.448422i \(-0.851986\pi\)
0.893822 0.448422i \(-0.148014\pi\)
\(660\) 0 0
\(661\) −306.193 −0.463226 −0.231613 0.972808i \(-0.574400\pi\)
−0.231613 + 0.972808i \(0.574400\pi\)
\(662\) 87.0935 250.535i 0.131561 0.378451i
\(663\) 224.988i 0.339349i
\(664\) 162.846 103.716i 0.245249 0.156198i
\(665\) 0 0
\(666\) −128.474 44.6616i −0.192904 0.0670595i
\(667\) 0.586909i 0.000879924i
\(668\) −230.484 + 291.445i −0.345035 + 0.436295i
\(669\) −168.055 −0.251203
\(670\) 0 0
\(671\) 377.142i 0.562060i
\(672\) −53.9337 + 526.841i −0.0802585 + 0.783990i
\(673\) −556.892 −0.827476 −0.413738 0.910396i \(-0.635777\pi\)
−0.413738 + 0.910396i \(0.635777\pi\)
\(674\) −39.2442 13.6425i −0.0582258 0.0202411i
\(675\) 0 0
\(676\) −351.083 277.647i −0.519353 0.410721i
\(677\) 58.1920 0.0859557 0.0429779 0.999076i \(-0.486316\pi\)
0.0429779 + 0.999076i \(0.486316\pi\)
\(678\) 36.7435 105.697i 0.0541939 0.155895i
\(679\) 1259.94i 1.85558i
\(680\) 0 0
\(681\) 705.389 1.03581
\(682\) 862.940 + 299.984i 1.26531 + 0.439860i
\(683\) 357.274i 0.523096i 0.965191 + 0.261548i \(0.0842329\pi\)
−0.965191 + 0.261548i \(0.915767\pi\)
\(684\) −194.846 + 246.381i −0.284862 + 0.360206i
\(685\) 0 0
\(686\) −42.0482 + 120.956i −0.0612947 + 0.176321i
\(687\) 13.6780i 0.0199098i
\(688\) −650.788 + 154.127i −0.945913 + 0.224021i
\(689\) −171.299 −0.248620
\(690\) 0 0
\(691\) 614.707i 0.889590i 0.895632 + 0.444795i \(0.146724\pi\)
−0.895632 + 0.444795i \(0.853276\pi\)
\(692\) −368.655 291.544i −0.532739 0.421307i
\(693\) 284.496 0.410528
\(694\) −5.84222 + 16.8058i −0.00841818 + 0.0242159i
\(695\) 0 0
\(696\) 4.09636 2.60896i 0.00588557 0.00374850i
\(697\) −1328.79 −1.90644
\(698\) −36.6524 12.7415i −0.0525107 0.0182543i
\(699\) 48.7543i 0.0697487i
\(700\) 0 0
\(701\) −886.028 −1.26395 −0.631975 0.774989i \(-0.717755\pi\)
−0.631975 + 0.774989i \(0.717755\pi\)
\(702\) −25.7854 + 74.1746i −0.0367313 + 0.105662i
\(703\) 593.397i 0.844093i
\(704\) −575.609 268.584i −0.817626 0.381511i
\(705\) 0 0
\(706\) 151.677 + 52.7276i 0.214840 + 0.0746849i
\(707\) 281.398i 0.398017i
\(708\) −515.058 407.324i −0.727483 0.575316i
\(709\) 760.887 1.07318 0.536592 0.843842i \(-0.319712\pi\)
0.536592 + 0.843842i \(0.319712\pi\)
\(710\) 0 0
\(711\) 138.078i 0.194202i
\(712\) −430.613 676.111i −0.604794 0.949594i
\(713\) 77.0706 0.108093
\(714\) 537.444 + 186.832i 0.752722 + 0.261669i
\(715\) 0 0
\(716\) −575.609 + 727.853i −0.803923 + 1.01655i
\(717\) −512.695 −0.715056
\(718\) 206.283 593.397i 0.287302 0.826458i
\(719\) 575.877i 0.800942i 0.916309 + 0.400471i \(0.131154\pi\)
−0.916309 + 0.400471i \(0.868846\pi\)
\(720\) 0 0
\(721\) 1373.88 1.90553
\(722\) −612.441 212.903i −0.848257 0.294880i
\(723\) 806.779i 1.11588i
\(724\) −684.268 541.141i −0.945122 0.747432i
\(725\) 0 0
\(726\) 25.5909 73.6153i 0.0352492 0.101398i
\(727\) 327.332i 0.450250i −0.974330 0.225125i \(-0.927721\pi\)
0.974330 0.225125i \(-0.0722790\pi\)
\(728\) −487.195 + 310.293i −0.669224 + 0.426227i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 718.542i 0.982958i
\(732\) 163.307 206.501i 0.223098 0.282105i
\(733\) −947.567 −1.29272 −0.646362 0.763031i \(-0.723710\pi\)
−0.646362 + 0.763031i \(0.723710\pi\)
\(734\) 313.120 900.727i 0.426595 1.22715i
\(735\) 0 0
\(736\) −53.3056 5.45700i −0.0724261 0.00741440i
\(737\) 296.232 0.401943
\(738\) 438.079 + 152.290i 0.593602 + 0.206354i
\(739\) 183.234i 0.247948i −0.992285 0.123974i \(-0.960436\pi\)
0.992285 0.123974i \(-0.0395640\pi\)
\(740\) 0 0
\(741\) −342.598 −0.462345
\(742\) 142.248 409.193i 0.191709 0.551473i
\(743\) 183.712i 0.247258i 0.992329 + 0.123629i \(0.0394532\pi\)
−0.992329 + 0.123629i \(0.960547\pi\)
\(744\) −342.598 537.918i −0.460481 0.723008i
\(745\) 0 0
\(746\) −162.715 56.5648i −0.218117 0.0758241i
\(747\) 72.4009i 0.0969222i
\(748\) −423.317 + 535.281i −0.565932 + 0.715617i
\(749\) 335.395 0.447791
\(750\) 0 0
\(751\) 345.748i 0.460384i −0.973145 0.230192i \(-0.926065\pi\)
0.973145 0.230192i \(-0.0739354\pi\)
\(752\) −219.319 + 51.9414i −0.291647 + 0.0690710i
\(753\) −245.390 −0.325882
\(754\) 5.00331 + 1.73930i 0.00663569 + 0.00230677i
\(755\) 0 0
\(756\) −155.773 123.190i −0.206049 0.162950i
\(757\) −549.335 −0.725674 −0.362837 0.931853i \(-0.618192\pi\)
−0.362837 + 0.931853i \(0.618192\pi\)
\(758\) 419.005 1205.32i 0.552778 1.59013i
\(759\) 28.7852i 0.0379252i
\(760\) 0 0
\(761\) 251.485 0.330467 0.165233 0.986255i \(-0.447162\pi\)
0.165233 + 0.986255i \(0.447162\pi\)
\(762\) −628.405 218.453i −0.824678 0.286683i
\(763\) 1447.57i 1.89721i
\(764\) −340.440 + 430.484i −0.445602 + 0.563461i
\(765\) 0 0
\(766\) 142.337 409.450i 0.185819 0.534529i
\(767\) 716.200i 0.933768i
\(768\) 198.869 + 396.307i 0.258945 + 0.516024i
\(769\) −583.691 −0.759026 −0.379513 0.925186i \(-0.623908\pi\)
−0.379513 + 0.925186i \(0.623908\pi\)
\(770\) 0 0
\(771\) 72.3216i 0.0938024i
\(772\) −116.177 91.8764i −0.150488 0.119011i
\(773\) 1328.04 1.71803 0.859015 0.511951i \(-0.171077\pi\)
0.859015 + 0.511951i \(0.171077\pi\)
\(774\) 82.3505 236.891i 0.106396 0.306060i
\(775\) 0 0
\(776\) 566.681 + 889.753i 0.730259 + 1.14659i
\(777\) 375.173 0.482848
\(778\) −900.424 313.015i −1.15736 0.402333i
\(779\) 2023.40i 2.59743i
\(780\) 0 0
\(781\) −71.4219 −0.0914492
\(782\) −18.9036 + 54.3784i −0.0241734 + 0.0695376i
\(783\) 1.82123i 0.00232597i
\(784\) −155.969 658.567i −0.198940 0.840009i
\(785\) 0 0
\(786\) 138.825 + 48.2598i 0.176622 + 0.0613992i
\(787\) 1318.83i 1.67577i −0.545850 0.837883i \(-0.683793\pi\)