Properties

Label 900.3.f.e.199.2
Level $900$
Weight $3$
Character 900.199
Analytic conductor $24.523$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.5232237924\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{20})\)
Defining polynomial: \(x^{8} - x^{6} + x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 199.2
Root \(0.951057 - 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 900.199
Dual form 900.3.f.e.199.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.90211 + 0.618034i) q^{2} +(3.23607 - 2.35114i) q^{4} -5.25731 q^{7} +(-4.70228 + 6.47214i) q^{8} +O(q^{10})\) \(q+(-1.90211 + 0.618034i) q^{2} +(3.23607 - 2.35114i) q^{4} -5.25731 q^{7} +(-4.70228 + 6.47214i) q^{8} -19.9192i q^{11} -8.47214i q^{13} +(10.0000 - 3.24920i) q^{14} +(4.94427 - 15.2169i) q^{16} +11.8885i q^{17} +15.2169i q^{19} +(12.3107 + 37.8885i) q^{22} -0.555029 q^{23} +(5.23607 + 16.1150i) q^{26} +(-17.0130 + 12.3607i) q^{28} -10.9443 q^{29} -8.29451i q^{31} +32.0000i q^{32} +(-7.34752 - 22.6134i) q^{34} +18.3607i q^{37} +(-9.40456 - 28.9443i) q^{38} +14.5836 q^{41} -22.2703 q^{43} +(-46.8328 - 64.4598i) q^{44} +(1.05573 - 0.343027i) q^{46} -53.3902 q^{47} -21.3607 q^{49} +(-19.9192 - 27.4164i) q^{52} +66.3607i q^{53} +(24.7214 - 34.0260i) q^{56} +(20.8172 - 6.76393i) q^{58} +17.4370i q^{59} +90.1378 q^{61} +(5.12629 + 15.7771i) q^{62} +(-19.7771 - 60.8676i) q^{64} +50.2220 q^{67} +(27.9516 + 38.4721i) q^{68} +80.7868i q^{71} -5.55418i q^{73} +(-11.3475 - 34.9241i) q^{74} +(35.7771 + 49.2429i) q^{76} +104.721i q^{77} +13.8448i q^{79} +(-27.7396 + 9.01316i) q^{82} -76.2155 q^{83} +(42.3607 - 13.7638i) q^{86} +(128.920 + 93.6656i) q^{88} -111.443 q^{89} +44.5407i q^{91} +(-1.79611 + 1.30495i) q^{92} +(101.554 - 32.9970i) q^{94} +92.8328i q^{97} +(40.6304 - 13.2016i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{4} + O(q^{10}) \) \( 8q + 8q^{4} + 80q^{14} - 32q^{16} + 24q^{26} - 16q^{29} - 184q^{34} + 224q^{41} - 160q^{44} + 80q^{46} + 8q^{49} - 160q^{56} + 256q^{61} + 128q^{64} - 216q^{74} + 160q^{86} - 176q^{89} + 240q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(451\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.90211 + 0.618034i −0.951057 + 0.309017i
\(3\) 0 0
\(4\) 3.23607 2.35114i 0.809017 0.587785i
\(5\) 0 0
\(6\) 0 0
\(7\) −5.25731 −0.751044 −0.375522 0.926813i \(-0.622537\pi\)
−0.375522 + 0.926813i \(0.622537\pi\)
\(8\) −4.70228 + 6.47214i −0.587785 + 0.809017i
\(9\) 0 0
\(10\) 0 0
\(11\) 19.9192i 1.81084i −0.424522 0.905418i \(-0.639558\pi\)
0.424522 0.905418i \(-0.360442\pi\)
\(12\) 0 0
\(13\) 8.47214i 0.651703i −0.945421 0.325851i \(-0.894349\pi\)
0.945421 0.325851i \(-0.105651\pi\)
\(14\) 10.0000 3.24920i 0.714286 0.232085i
\(15\) 0 0
\(16\) 4.94427 15.2169i 0.309017 0.951057i
\(17\) 11.8885i 0.699326i 0.936876 + 0.349663i \(0.113704\pi\)
−0.936876 + 0.349663i \(0.886296\pi\)
\(18\) 0 0
\(19\) 15.2169i 0.800890i 0.916321 + 0.400445i \(0.131144\pi\)
−0.916321 + 0.400445i \(0.868856\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 12.3107 + 37.8885i 0.559579 + 1.72221i
\(23\) −0.555029 −0.0241317 −0.0120659 0.999927i \(-0.503841\pi\)
−0.0120659 + 0.999927i \(0.503841\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 5.23607 + 16.1150i 0.201387 + 0.619806i
\(27\) 0 0
\(28\) −17.0130 + 12.3607i −0.607608 + 0.441453i
\(29\) −10.9443 −0.377389 −0.188694 0.982036i \(-0.560426\pi\)
−0.188694 + 0.982036i \(0.560426\pi\)
\(30\) 0 0
\(31\) 8.29451i 0.267565i −0.991011 0.133782i \(-0.957288\pi\)
0.991011 0.133782i \(-0.0427123\pi\)
\(32\) 32.0000i 1.00000i
\(33\) 0 0
\(34\) −7.34752 22.6134i −0.216104 0.665099i
\(35\) 0 0
\(36\) 0 0
\(37\) 18.3607i 0.496235i 0.968730 + 0.248117i \(0.0798118\pi\)
−0.968730 + 0.248117i \(0.920188\pi\)
\(38\) −9.40456 28.9443i −0.247489 0.761691i
\(39\) 0 0
\(40\) 0 0
\(41\) 14.5836 0.355697 0.177849 0.984058i \(-0.443086\pi\)
0.177849 + 0.984058i \(0.443086\pi\)
\(42\) 0 0
\(43\) −22.2703 −0.517915 −0.258957 0.965889i \(-0.583379\pi\)
−0.258957 + 0.965889i \(0.583379\pi\)
\(44\) −46.8328 64.4598i −1.06438 1.46500i
\(45\) 0 0
\(46\) 1.05573 0.343027i 0.0229506 0.00745711i
\(47\) −53.3902 −1.13596 −0.567981 0.823042i \(-0.692275\pi\)
−0.567981 + 0.823042i \(0.692275\pi\)
\(48\) 0 0
\(49\) −21.3607 −0.435932
\(50\) 0 0
\(51\) 0 0
\(52\) −19.9192 27.4164i −0.383061 0.527239i
\(53\) 66.3607i 1.25209i 0.779788 + 0.626044i \(0.215327\pi\)
−0.779788 + 0.626044i \(0.784673\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 24.7214 34.0260i 0.441453 0.607608i
\(57\) 0 0
\(58\) 20.8172 6.76393i 0.358918 0.116620i
\(59\) 17.4370i 0.295543i 0.989022 + 0.147771i \(0.0472100\pi\)
−0.989022 + 0.147771i \(0.952790\pi\)
\(60\) 0 0
\(61\) 90.1378 1.47767 0.738834 0.673887i \(-0.235377\pi\)
0.738834 + 0.673887i \(0.235377\pi\)
\(62\) 5.12629 + 15.7771i 0.0826820 + 0.254469i
\(63\) 0 0
\(64\) −19.7771 60.8676i −0.309017 0.951057i
\(65\) 0 0
\(66\) 0 0
\(67\) 50.2220 0.749582 0.374791 0.927109i \(-0.377715\pi\)
0.374791 + 0.927109i \(0.377715\pi\)
\(68\) 27.9516 + 38.4721i 0.411054 + 0.565767i
\(69\) 0 0
\(70\) 0 0
\(71\) 80.7868i 1.13784i 0.822392 + 0.568921i \(0.192639\pi\)
−0.822392 + 0.568921i \(0.807361\pi\)
\(72\) 0 0
\(73\) 5.55418i 0.0760846i −0.999276 0.0380423i \(-0.987888\pi\)
0.999276 0.0380423i \(-0.0121122\pi\)
\(74\) −11.3475 34.9241i −0.153345 0.471947i
\(75\) 0 0
\(76\) 35.7771 + 49.2429i 0.470751 + 0.647933i
\(77\) 104.721i 1.36002i
\(78\) 0 0
\(79\) 13.8448i 0.175251i 0.996154 + 0.0876253i \(0.0279278\pi\)
−0.996154 + 0.0876253i \(0.972072\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −27.7396 + 9.01316i −0.338288 + 0.109917i
\(83\) −76.2155 −0.918260 −0.459130 0.888369i \(-0.651839\pi\)
−0.459130 + 0.888369i \(0.651839\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 42.3607 13.7638i 0.492566 0.160044i
\(87\) 0 0
\(88\) 128.920 + 93.6656i 1.46500 + 1.06438i
\(89\) −111.443 −1.25217 −0.626083 0.779757i \(-0.715343\pi\)
−0.626083 + 0.779757i \(0.715343\pi\)
\(90\) 0 0
\(91\) 44.5407i 0.489458i
\(92\) −1.79611 + 1.30495i −0.0195230 + 0.0141843i
\(93\) 0 0
\(94\) 101.554 32.9970i 1.08036 0.351031i
\(95\) 0 0
\(96\) 0 0
\(97\) 92.8328i 0.957039i 0.878077 + 0.478520i \(0.158826\pi\)
−0.878077 + 0.478520i \(0.841174\pi\)
\(98\) 40.6304 13.2016i 0.414596 0.134710i
\(99\) 0 0
\(100\) 0 0
\(101\) −64.1115 −0.634767 −0.317383 0.948297i \(-0.602804\pi\)
−0.317383 + 0.948297i \(0.602804\pi\)
\(102\) 0 0
\(103\) −137.769 −1.33757 −0.668783 0.743458i \(-0.733184\pi\)
−0.668783 + 0.743458i \(0.733184\pi\)
\(104\) 54.8328 + 39.8384i 0.527239 + 0.383061i
\(105\) 0 0
\(106\) −41.0132 126.226i −0.386917 1.19081i
\(107\) 51.3320 0.479739 0.239869 0.970805i \(-0.422895\pi\)
0.239869 + 0.970805i \(0.422895\pi\)
\(108\) 0 0
\(109\) −133.469 −1.22449 −0.612243 0.790669i \(-0.709733\pi\)
−0.612243 + 0.790669i \(0.709733\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −25.9936 + 80.0000i −0.232085 + 0.714286i
\(113\) 170.721i 1.51081i −0.655259 0.755404i \(-0.727441\pi\)
0.655259 0.755404i \(-0.272559\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −35.4164 + 25.7315i −0.305314 + 0.221824i
\(117\) 0 0
\(118\) −10.7767 33.1672i −0.0913277 0.281078i
\(119\) 62.5018i 0.525225i
\(120\) 0 0
\(121\) −275.774 −2.27912
\(122\) −171.452 + 55.7082i −1.40535 + 0.456625i
\(123\) 0 0
\(124\) −19.5016 26.8416i −0.157271 0.216464i
\(125\) 0 0
\(126\) 0 0
\(127\) −198.637 −1.56407 −0.782035 0.623235i \(-0.785818\pi\)
−0.782035 + 0.623235i \(0.785818\pi\)
\(128\) 75.2365 + 103.554i 0.587785 + 0.809017i
\(129\) 0 0
\(130\) 0 0
\(131\) 7.77041i 0.0593161i −0.999560 0.0296580i \(-0.990558\pi\)
0.999560 0.0296580i \(-0.00944183\pi\)
\(132\) 0 0
\(133\) 80.0000i 0.601504i
\(134\) −95.5279 + 31.0389i −0.712895 + 0.231633i
\(135\) 0 0
\(136\) −76.9443 55.9033i −0.565767 0.411054i
\(137\) 0.832816i 0.00607895i 0.999995 + 0.00303947i \(0.000967496\pi\)
−0.999995 + 0.00303947i \(0.999033\pi\)
\(138\) 0 0
\(139\) 237.658i 1.70977i 0.518817 + 0.854885i \(0.326373\pi\)
−0.518817 + 0.854885i \(0.673627\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −49.9290 153.666i −0.351613 1.08215i
\(143\) −168.758 −1.18013
\(144\) 0 0
\(145\) 0 0
\(146\) 3.43267 + 10.5647i 0.0235114 + 0.0723607i
\(147\) 0 0
\(148\) 43.1685 + 59.4164i 0.291679 + 0.401462i
\(149\) −36.9706 −0.248125 −0.124062 0.992274i \(-0.539592\pi\)
−0.124062 + 0.992274i \(0.539592\pi\)
\(150\) 0 0
\(151\) 282.723i 1.87234i 0.351552 + 0.936168i \(0.385654\pi\)
−0.351552 + 0.936168i \(0.614346\pi\)
\(152\) −98.4859 71.5542i −0.647933 0.470751i
\(153\) 0 0
\(154\) −64.7214 199.192i −0.420269 1.29345i
\(155\) 0 0
\(156\) 0 0
\(157\) 204.748i 1.30413i −0.758165 0.652063i \(-0.773904\pi\)
0.758165 0.652063i \(-0.226096\pi\)
\(158\) −8.55656 26.3344i −0.0541554 0.166673i
\(159\) 0 0
\(160\) 0 0
\(161\) 2.91796 0.0181240
\(162\) 0 0
\(163\) −107.235 −0.657885 −0.328943 0.944350i \(-0.606692\pi\)
−0.328943 + 0.944350i \(0.606692\pi\)
\(164\) 47.1935 34.2881i 0.287765 0.209074i
\(165\) 0 0
\(166\) 144.971 47.1038i 0.873317 0.283758i
\(167\) −33.2090 −0.198856 −0.0994280 0.995045i \(-0.531701\pi\)
−0.0994280 + 0.995045i \(0.531701\pi\)
\(168\) 0 0
\(169\) 97.2229 0.575284
\(170\) 0 0
\(171\) 0 0
\(172\) −72.0683 + 52.3607i −0.419002 + 0.304423i
\(173\) 226.361i 1.30844i 0.756303 + 0.654222i \(0.227004\pi\)
−0.756303 + 0.654222i \(0.772996\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −303.108 98.4859i −1.72221 0.559579i
\(177\) 0 0
\(178\) 211.977 68.8754i 1.19088 0.386940i
\(179\) 224.337i 1.25328i 0.779308 + 0.626641i \(0.215571\pi\)
−0.779308 + 0.626641i \(0.784429\pi\)
\(180\) 0 0
\(181\) 86.2229 0.476370 0.238185 0.971220i \(-0.423448\pi\)
0.238185 + 0.971220i \(0.423448\pi\)
\(182\) −27.5276 84.7214i −0.151251 0.465502i
\(183\) 0 0
\(184\) 2.60990 3.59222i 0.0141843 0.0195230i
\(185\) 0 0
\(186\) 0 0
\(187\) 236.810 1.26636
\(188\) −172.774 + 125.528i −0.919012 + 0.667701i
\(189\) 0 0
\(190\) 0 0
\(191\) 31.0198i 0.162407i 0.996698 + 0.0812036i \(0.0258764\pi\)
−0.996698 + 0.0812036i \(0.974124\pi\)
\(192\) 0 0
\(193\) 110.223i 0.571103i 0.958363 + 0.285552i \(0.0921768\pi\)
−0.958363 + 0.285552i \(0.907823\pi\)
\(194\) −57.3738 176.579i −0.295741 0.910198i
\(195\) 0 0
\(196\) −69.1246 + 50.2220i −0.352677 + 0.256235i
\(197\) 172.525i 0.875760i −0.899033 0.437880i \(-0.855729\pi\)
0.899033 0.437880i \(-0.144271\pi\)
\(198\) 0 0
\(199\) 272.208i 1.36788i 0.729538 + 0.683940i \(0.239735\pi\)
−0.729538 + 0.683940i \(0.760265\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 121.947 39.6231i 0.603699 0.196154i
\(203\) 57.5374 0.283436
\(204\) 0 0
\(205\) 0 0
\(206\) 262.053 85.1461i 1.27210 0.413330i
\(207\) 0 0
\(208\) −128.920 41.8885i −0.619806 0.201387i
\(209\) 303.108 1.45028
\(210\) 0 0
\(211\) 205.266i 0.972826i −0.873729 0.486413i \(-0.838305\pi\)
0.873729 0.486413i \(-0.161695\pi\)
\(212\) 156.023 + 214.748i 0.735959 + 1.01296i
\(213\) 0 0
\(214\) −97.6393 + 31.7249i −0.456259 + 0.148247i
\(215\) 0 0
\(216\) 0 0
\(217\) 43.6068i 0.200953i
\(218\) 253.873 82.4884i 1.16456 0.378387i
\(219\) 0 0
\(220\) 0 0
\(221\) 100.721 0.455753
\(222\) 0 0
\(223\) −235.731 −1.05709 −0.528545 0.848905i \(-0.677262\pi\)
−0.528545 + 0.848905i \(0.677262\pi\)
\(224\) 168.234i 0.751044i
\(225\) 0 0
\(226\) 105.512 + 324.731i 0.466865 + 1.43686i
\(227\) 58.5165 0.257782 0.128891 0.991659i \(-0.458858\pi\)
0.128891 + 0.991659i \(0.458858\pi\)
\(228\) 0 0
\(229\) −162.721 −0.710574 −0.355287 0.934757i \(-0.615617\pi\)
−0.355287 + 0.934757i \(0.615617\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 51.4631 70.8328i 0.221824 0.305314i
\(233\) 319.050i 1.36931i −0.728867 0.684656i \(-0.759953\pi\)
0.728867 0.684656i \(-0.240047\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 40.9969 + 56.4274i 0.173716 + 0.239099i
\(237\) 0 0
\(238\) 38.6282 + 118.885i 0.162303 + 0.499519i
\(239\) 236.810i 0.990837i 0.868654 + 0.495419i \(0.164985\pi\)
−0.868654 + 0.495419i \(0.835015\pi\)
\(240\) 0 0
\(241\) −0.917961 −0.00380897 −0.00190448 0.999998i \(-0.500606\pi\)
−0.00190448 + 0.999998i \(0.500606\pi\)
\(242\) 524.553 170.438i 2.16758 0.704288i
\(243\) 0 0
\(244\) 291.692 211.927i 1.19546 0.868552i
\(245\) 0 0
\(246\) 0 0
\(247\) 128.920 0.521942
\(248\) 53.6832 + 39.0031i 0.216464 + 0.157271i
\(249\) 0 0
\(250\) 0 0
\(251\) 136.690i 0.544582i 0.962215 + 0.272291i \(0.0877813\pi\)
−0.962215 + 0.272291i \(0.912219\pi\)
\(252\) 0 0
\(253\) 11.0557i 0.0436985i
\(254\) 377.830 122.764i 1.48752 0.483324i
\(255\) 0 0
\(256\) −207.108 150.473i −0.809017 0.587785i
\(257\) 274.944i 1.06982i −0.844908 0.534911i \(-0.820345\pi\)
0.844908 0.534911i \(-0.179655\pi\)
\(258\) 0 0
\(259\) 96.5278i 0.372694i
\(260\) 0 0
\(261\) 0 0
\(262\) 4.80238 + 14.7802i 0.0183297 + 0.0564130i
\(263\) 406.385 1.54519 0.772596 0.634899i \(-0.218958\pi\)
0.772596 + 0.634899i \(0.218958\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 49.4427 + 152.169i 0.185875 + 0.572064i
\(267\) 0 0
\(268\) 162.522 118.079i 0.606424 0.440593i
\(269\) −348.525 −1.29563 −0.647816 0.761797i \(-0.724317\pi\)
−0.647816 + 0.761797i \(0.724317\pi\)
\(270\) 0 0
\(271\) 247.849i 0.914571i −0.889320 0.457286i \(-0.848822\pi\)
0.889320 0.457286i \(-0.151178\pi\)
\(272\) 180.907 + 58.7802i 0.665099 + 0.216104i
\(273\) 0 0
\(274\) −0.514708 1.58411i −0.00187850 0.00578142i
\(275\) 0 0
\(276\) 0 0
\(277\) 54.7539i 0.197667i 0.995104 + 0.0988337i \(0.0315112\pi\)
−0.995104 + 0.0988337i \(0.968489\pi\)
\(278\) −146.881 452.053i −0.528348 1.62609i
\(279\) 0 0
\(280\) 0 0
\(281\) 50.3607 0.179220 0.0896098 0.995977i \(-0.471438\pi\)
0.0896098 + 0.995977i \(0.471438\pi\)
\(282\) 0 0
\(283\) 147.336 0.520621 0.260310 0.965525i \(-0.416175\pi\)
0.260310 + 0.965525i \(0.416175\pi\)
\(284\) 189.941 + 261.432i 0.668807 + 0.920534i
\(285\) 0 0
\(286\) 320.997 104.298i 1.12237 0.364679i
\(287\) −76.6705 −0.267145
\(288\) 0 0
\(289\) 147.663 0.510943
\(290\) 0 0
\(291\) 0 0
\(292\) −13.0586 17.9737i −0.0447214 0.0615537i
\(293\) 178.859i 0.610441i −0.952282 0.305220i \(-0.901270\pi\)
0.952282 0.305220i \(-0.0987301\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −118.833 86.3371i −0.401462 0.291679i
\(297\) 0 0
\(298\) 70.3222 22.8491i 0.235981 0.0766748i
\(299\) 4.70228i 0.0157267i
\(300\) 0 0
\(301\) 117.082 0.388977
\(302\) −174.732 537.771i −0.578584 1.78070i
\(303\) 0 0
\(304\) 231.554 + 75.2365i 0.761691 + 0.247489i
\(305\) 0 0
\(306\) 0 0
\(307\) −284.550 −0.926873 −0.463436 0.886130i \(-0.653384\pi\)
−0.463436 + 0.886130i \(0.653384\pi\)
\(308\) 246.215 + 338.885i 0.799398 + 1.10028i
\(309\) 0 0
\(310\) 0 0
\(311\) 282.199i 0.907392i −0.891157 0.453696i \(-0.850105\pi\)
0.891157 0.453696i \(-0.149895\pi\)
\(312\) 0 0
\(313\) 567.548i 1.81325i −0.421935 0.906626i \(-0.638649\pi\)
0.421935 0.906626i \(-0.361351\pi\)
\(314\) 126.541 + 389.453i 0.402997 + 1.24030i
\(315\) 0 0
\(316\) 32.5511 + 44.8027i 0.103010 + 0.141781i
\(317\) 161.141i 0.508331i 0.967161 + 0.254165i \(0.0818008\pi\)
−0.967161 + 0.254165i \(0.918199\pi\)
\(318\) 0 0
\(319\) 218.001i 0.683389i
\(320\) 0 0
\(321\) 0 0
\(322\) −5.55029 + 1.80340i −0.0172369 + 0.00560062i
\(323\) −180.907 −0.560083
\(324\) 0 0
\(325\) 0 0
\(326\) 203.974 66.2751i 0.625686 0.203298i
\(327\) 0 0
\(328\) −68.5762 + 94.3870i −0.209074 + 0.287765i
\(329\) 280.689 0.853158
\(330\) 0 0
\(331\) 331.966i 1.00292i 0.865181 + 0.501459i \(0.167203\pi\)
−0.865181 + 0.501459i \(0.832797\pi\)
\(332\) −246.639 + 179.193i −0.742888 + 0.539739i
\(333\) 0 0
\(334\) 63.1672 20.5243i 0.189123 0.0614499i
\(335\) 0 0
\(336\) 0 0
\(337\) 269.108i 0.798541i 0.916833 + 0.399271i \(0.130737\pi\)
−0.916833 + 0.399271i \(0.869263\pi\)
\(338\) −184.929 + 60.0871i −0.547127 + 0.177772i
\(339\) 0 0
\(340\) 0 0
\(341\) −165.220 −0.484516
\(342\) 0 0
\(343\) 369.908 1.07845
\(344\) 104.721 144.137i 0.304423 0.419002i
\(345\) 0 0
\(346\) −139.899 430.564i −0.404331 1.24440i
\(347\) 503.075 1.44978 0.724892 0.688863i \(-0.241890\pi\)
0.724892 + 0.688863i \(0.241890\pi\)
\(348\) 0 0
\(349\) 0.504658 0.00144601 0.000723006 1.00000i \(-0.499770\pi\)
0.000723006 1.00000i \(0.499770\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 637.414 1.81084
\(353\) 335.994i 0.951824i 0.879493 + 0.475912i \(0.157882\pi\)
−0.879493 + 0.475912i \(0.842118\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −360.636 + 262.018i −1.01302 + 0.736004i
\(357\) 0 0
\(358\) −138.648 426.715i −0.387285 1.19194i
\(359\) 98.4859i 0.274334i 0.990548 + 0.137167i \(0.0437997\pi\)
−0.990548 + 0.137167i \(0.956200\pi\)
\(360\) 0 0
\(361\) 129.446 0.358576
\(362\) −164.006 + 53.2887i −0.453054 + 0.147206i
\(363\) 0 0
\(364\) 104.721 + 144.137i 0.287696 + 0.395980i
\(365\) 0 0
\(366\) 0 0
\(367\) 498.473 1.35824 0.679118 0.734029i \(-0.262362\pi\)
0.679118 + 0.734029i \(0.262362\pi\)
\(368\) −2.74421 + 8.44582i −0.00745711 + 0.0229506i
\(369\) 0 0
\(370\) 0 0
\(371\) 348.879i 0.940374i
\(372\) 0 0
\(373\) 600.354i 1.60953i 0.593594 + 0.804765i \(0.297709\pi\)
−0.593594 + 0.804765i \(0.702291\pi\)
\(374\) −450.440 + 146.357i −1.20438 + 0.391328i
\(375\) 0 0
\(376\) 251.056 345.549i 0.667701 0.919012i
\(377\) 92.7214i 0.245945i
\(378\) 0 0
\(379\) 303.490i 0.800765i −0.916348 0.400383i \(-0.868877\pi\)
0.916348 0.400383i \(-0.131123\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −19.1713 59.0031i −0.0501866 0.154458i
\(383\) −332.583 −0.868362 −0.434181 0.900826i \(-0.642962\pi\)
−0.434181 + 0.900826i \(0.642962\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −68.1215 209.656i −0.176481 0.543151i
\(387\) 0 0
\(388\) 218.263 + 300.413i 0.562534 + 0.774261i
\(389\) 392.354 1.00862 0.504312 0.863522i \(-0.331746\pi\)
0.504312 + 0.863522i \(0.331746\pi\)
\(390\) 0 0
\(391\) 6.59849i 0.0168759i
\(392\) 100.444 138.249i 0.256235 0.352677i
\(393\) 0 0
\(394\) 106.626 + 328.162i 0.270625 + 0.832897i
\(395\) 0 0
\(396\) 0 0
\(397\) 334.190i 0.841789i −0.907110 0.420895i \(-0.861716\pi\)
0.907110 0.420895i \(-0.138284\pi\)
\(398\) −168.234 517.771i −0.422698 1.30093i
\(399\) 0 0
\(400\) 0 0
\(401\) −121.003 −0.301753 −0.150877 0.988553i \(-0.548210\pi\)
−0.150877 + 0.988553i \(0.548210\pi\)
\(402\) 0 0
\(403\) −70.2722 −0.174373
\(404\) −207.469 + 150.735i −0.513537 + 0.373107i
\(405\) 0 0
\(406\) −109.443 + 35.5601i −0.269563 + 0.0875864i
\(407\) 365.730 0.898599
\(408\) 0 0
\(409\) 607.410 1.48511 0.742555 0.669785i \(-0.233614\pi\)
0.742555 + 0.669785i \(0.233614\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −445.831 + 323.915i −1.08211 + 0.786201i
\(413\) 91.6718i 0.221966i
\(414\) 0 0
\(415\) 0 0
\(416\) 271.108 0.651703
\(417\) 0 0
\(418\) −576.546 + 187.331i −1.37930 + 0.448161i
\(419\) 466.760i 1.11398i −0.830518 0.556992i \(-0.811955\pi\)
0.830518 0.556992i \(-0.188045\pi\)
\(420\) 0 0
\(421\) −73.0883 −0.173606 −0.0868031 0.996225i \(-0.527665\pi\)
−0.0868031 + 0.996225i \(0.527665\pi\)
\(422\) 126.862 + 390.440i 0.300620 + 0.925212i
\(423\) 0 0
\(424\) −429.495 312.047i −1.01296 0.735959i
\(425\) 0 0
\(426\) 0 0
\(427\) −473.882 −1.10979
\(428\) 166.114 120.689i 0.388117 0.281983i
\(429\) 0 0
\(430\) 0 0
\(431\) 463.630i 1.07571i 0.843038 + 0.537853i \(0.180765\pi\)
−0.843038 + 0.537853i \(0.819235\pi\)
\(432\) 0 0
\(433\) 99.8359i 0.230568i −0.993333 0.115284i \(-0.963222\pi\)
0.993333 0.115284i \(-0.0367778\pi\)
\(434\) −26.9505 82.9451i −0.0620979 0.191118i
\(435\) 0 0
\(436\) −431.915 + 313.805i −0.990630 + 0.719735i
\(437\) 8.44582i 0.0193268i
\(438\) 0 0
\(439\) 374.086i 0.852133i −0.904692 0.426066i \(-0.859899\pi\)
0.904692 0.426066i \(-0.140101\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −191.583 + 62.2492i −0.433447 + 0.140835i
\(443\) −290.100 −0.654854 −0.327427 0.944877i \(-0.606182\pi\)
−0.327427 + 0.944877i \(0.606182\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 448.387 145.690i 1.00535 0.326659i
\(447\) 0 0
\(448\) 103.974 + 320.000i 0.232085 + 0.714286i
\(449\) 299.921 0.667976 0.333988 0.942577i \(-0.391606\pi\)
0.333988 + 0.942577i \(0.391606\pi\)
\(450\) 0 0
\(451\) 290.493i 0.644109i
\(452\) −401.390 552.466i −0.888031 1.22227i
\(453\) 0 0
\(454\) −111.305 + 36.1652i −0.245165 + 0.0796590i
\(455\) 0 0
\(456\) 0 0
\(457\) 822.328i 1.79941i −0.436503 0.899703i \(-0.643783\pi\)
0.436503 0.899703i \(-0.356217\pi\)
\(458\) 309.514 100.567i 0.675796 0.219579i
\(459\) 0 0
\(460\) 0 0
\(461\) 456.885 0.991075 0.495537 0.868587i \(-0.334971\pi\)
0.495537 + 0.868587i \(0.334971\pi\)
\(462\) 0 0
\(463\) −400.249 −0.864469 −0.432234 0.901761i \(-0.642275\pi\)
−0.432234 + 0.901761i \(0.642275\pi\)
\(464\) −54.1115 + 166.538i −0.116620 + 0.358918i
\(465\) 0 0
\(466\) 197.183 + 606.868i 0.423140 + 1.30229i
\(467\) −913.145 −1.95534 −0.977672 0.210139i \(-0.932608\pi\)
−0.977672 + 0.210139i \(0.932608\pi\)
\(468\) 0 0
\(469\) −264.033 −0.562969
\(470\) 0 0
\(471\) 0 0
\(472\) −112.855 81.9938i −0.239099 0.173716i
\(473\) 443.607i 0.937858i
\(474\) 0 0
\(475\) 0 0
\(476\) −146.950 202.260i −0.308720 0.424916i
\(477\) 0 0
\(478\) −146.357 450.440i −0.306186 0.942342i
\(479\) 526.131i 1.09840i −0.835692 0.549198i \(-0.814933\pi\)
0.835692 0.549198i \(-0.185067\pi\)
\(480\) 0 0
\(481\) 155.554 0.323397
\(482\) 1.74606 0.567331i 0.00362254 0.00117704i
\(483\) 0 0
\(484\) −892.423 + 648.384i −1.84385 + 1.33964i
\(485\) 0 0
\(486\) 0 0
\(487\) 443.541 0.910762 0.455381 0.890297i \(-0.349503\pi\)
0.455381 + 0.890297i \(0.349503\pi\)
\(488\) −423.853 + 583.384i −0.868552 + 1.19546i
\(489\) 0 0
\(490\) 0 0
\(491\) 287.163i 0.584854i 0.956288 + 0.292427i \(0.0944628\pi\)
−0.956288 + 0.292427i \(0.905537\pi\)
\(492\) 0 0
\(493\) 130.111i 0.263918i
\(494\) −245.220 + 79.6767i −0.496396 + 0.161289i
\(495\) 0 0
\(496\) −126.217 41.0103i −0.254469 0.0826820i
\(497\) 424.721i 0.854570i
\(498\) 0 0
\(499\) 810.936i 1.62512i −0.582876 0.812561i \(-0.698073\pi\)
0.582876 0.812561i \(-0.301927\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −84.4791 260.000i −0.168285 0.517928i
\(503\) 642.471 1.27728 0.638639 0.769506i \(-0.279498\pi\)
0.638639 + 0.769506i \(0.279498\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −6.83282 21.0292i −0.0135036 0.0415598i
\(507\) 0 0
\(508\) −642.802 + 467.023i −1.26536 + 0.919337i
\(509\) −915.050 −1.79774 −0.898870 0.438216i \(-0.855611\pi\)
−0.898870 + 0.438216i \(0.855611\pi\)
\(510\) 0 0
\(511\) 29.2000i 0.0571429i
\(512\) 486.941 + 158.217i 0.951057 + 0.309017i
\(513\) 0 0
\(514\) 169.925 + 522.975i 0.330593 + 1.01746i
\(515\) 0 0
\(516\) 0 0
\(517\) 1063.49i 2.05704i
\(518\) 59.6575 + 183.607i 0.115169 + 0.354453i
\(519\) 0 0
\(520\) 0 0
\(521\) −1006.98 −1.93279 −0.966396 0.257058i \(-0.917247\pi\)
−0.966396 + 0.257058i \(0.917247\pi\)
\(522\) 0 0
\(523\) 774.173 1.48025 0.740127 0.672467i \(-0.234765\pi\)
0.740127 + 0.672467i \(0.234765\pi\)
\(524\) −18.2693 25.1456i −0.0348651 0.0479877i
\(525\) 0 0
\(526\) −772.991 + 251.160i −1.46956 + 0.477490i
\(527\) 98.6096 0.187115
\(528\) 0 0
\(529\) −528.692 −0.999418
\(530\) 0 0
\(531\) 0 0
\(532\) −188.091 258.885i −0.353555 0.486627i
\(533\) 123.554i 0.231809i
\(534\) 0 0
\(535\) 0 0
\(536\) −236.158 + 325.043i −0.440593 + 0.606424i
\(537\) 0 0
\(538\) 662.933 215.400i 1.23222 0.400372i
\(539\) 425.487i 0.789401i
\(540\) 0 0
\(541\) −259.115 −0.478955 −0.239477 0.970902i \(-0.576976\pi\)
−0.239477 + 0.970902i \(0.576976\pi\)
\(542\) 153.179 + 471.437i 0.282618 + 0.869809i
\(543\) 0 0
\(544\) −380.433 −0.699326
\(545\) 0 0
\(546\) 0 0
\(547\) −149.818 −0.273890 −0.136945 0.990579i \(-0.543728\pi\)
−0.136945 + 0.990579i \(0.543728\pi\)
\(548\) 1.95807 + 2.69505i 0.00357312 + 0.00491797i
\(549\) 0 0
\(550\) 0 0
\(551\) 166.538i 0.302247i
\(552\) 0 0
\(553\) 72.7864i 0.131621i
\(554\) −33.8398 104.148i −0.0610826 0.187993i
\(555\) 0 0
\(556\) 558.768 + 769.078i 1.00498 + 1.38323i
\(557\) 511.698i 0.918668i 0.888264 + 0.459334i \(0.151912\pi\)
−0.888264 + 0.459334i \(0.848088\pi\)
\(558\) 0 0
\(559\) 188.677i 0.337526i
\(560\) 0 0
\(561\) 0 0
\(562\) −95.7917 + 31.1246i −0.170448 + 0.0553819i
\(563\) 490.726 0.871627 0.435814 0.900037i \(-0.356461\pi\)
0.435814 + 0.900037i \(0.356461\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −280.249 + 91.0585i −0.495140 + 0.160881i
\(567\) 0 0
\(568\) −522.863 379.882i −0.920534 0.668807i
\(569\) −232.748 −0.409047 −0.204523 0.978862i \(-0.565564\pi\)
−0.204523 + 0.978862i \(0.565564\pi\)
\(570\) 0 0
\(571\) 210.755i 0.369098i −0.982823 0.184549i \(-0.940918\pi\)
0.982823 0.184549i \(-0.0590824\pi\)
\(572\) −546.113 + 396.774i −0.954742 + 0.693661i
\(573\) 0 0
\(574\) 145.836 47.3850i 0.254070 0.0825522i
\(575\) 0 0
\(576\) 0 0
\(577\) 341.712i 0.592222i −0.955154 0.296111i \(-0.904310\pi\)
0.955154 0.296111i \(-0.0956898\pi\)
\(578\) −280.871 + 91.2605i −0.485936 + 0.157890i
\(579\) 0 0
\(580\) 0 0
\(581\) 400.689 0.689654
\(582\) 0 0
\(583\) 1321.85 2.26733
\(584\) 35.9474 + 26.1173i 0.0615537 + 0.0447214i
\(585\) 0 0
\(586\) 110.541 + 340.210i 0.188637 + 0.580564i
\(587\) −618.412 −1.05351 −0.526756 0.850016i \(-0.676592\pi\)
−0.526756 + 0.850016i \(0.676592\pi\)
\(588\) 0 0
\(589\) 126.217 0.214290
\(590\) 0 0
\(591\) 0 0
\(592\) 279.393 + 90.7802i 0.471947 + 0.153345i
\(593\) 120.663i 0.203478i −0.994811 0.101739i \(-0.967559\pi\)
0.994811 0.101739i \(-0.0324407\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −119.639 + 86.9231i −0.200737 + 0.145844i
\(597\) 0 0
\(598\) −2.90617 8.94427i −0.00485982 0.0149570i
\(599\) 849.927i 1.41891i −0.704751 0.709455i \(-0.748941\pi\)
0.704751 0.709455i \(-0.251059\pi\)
\(600\) 0 0
\(601\) −11.3576 −0.0188978 −0.00944890 0.999955i \(-0.503008\pi\)
−0.00944890 + 0.999955i \(0.503008\pi\)
\(602\) −222.703 + 72.3607i −0.369939 + 0.120200i
\(603\) 0 0
\(604\) 664.721 + 914.910i 1.10053 + 1.51475i
\(605\) 0 0
\(606\) 0 0
\(607\) −1115.12 −1.83710 −0.918550 0.395305i \(-0.870639\pi\)
−0.918550 + 0.395305i \(0.870639\pi\)
\(608\) −486.941 −0.800890
\(609\) 0 0
\(610\) 0 0
\(611\) 452.329i 0.740309i
\(612\) 0 0
\(613\) 499.475i 0.814805i 0.913249 + 0.407402i \(0.133565\pi\)
−0.913249 + 0.407402i \(0.866435\pi\)
\(614\) 541.246 175.862i 0.881508 0.286419i
\(615\) 0 0
\(616\) −677.771 492.429i −1.10028 0.799398i
\(617\) 545.935i 0.884822i 0.896813 + 0.442411i \(0.145877\pi\)
−0.896813 + 0.442411i \(0.854123\pi\)
\(618\) 0 0
\(619\) 455.011i 0.735075i −0.930009 0.367537i \(-0.880201\pi\)
0.930009 0.367537i \(-0.119799\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 174.408 + 536.774i 0.280399 + 0.862981i
\(623\) 585.889 0.940432
\(624\) 0 0
\(625\) 0 0
\(626\) 350.764 + 1079.54i 0.560326 + 1.72451i
\(627\) 0 0
\(628\) −481.391 662.577i −0.766546 1.05506i
\(629\) −218.282 −0.347030
\(630\) 0 0
\(631\) 267.706i 0.424257i 0.977242 + 0.212128i \(0.0680395\pi\)
−0.977242 + 0.212128i \(0.931960\pi\)
\(632\) −89.6054 65.1021i −0.141781 0.103010i
\(633\) 0 0
\(634\) −99.5905 306.508i −0.157083 0.483451i
\(635\) 0 0
\(636\) 0 0
\(637\) 180.971i 0.284098i
\(638\) −134.732 414.663i −0.211179 0.649941i
\(639\) 0 0
\(640\) 0 0
\(641\) 418.571 0.652997 0.326499 0.945198i \(-0.394131\pi\)
0.326499 + 0.945198i \(0.394131\pi\)
\(642\) 0 0
\(643\) −439.339 −0.683265 −0.341633 0.939834i \(-0.610980\pi\)
−0.341633 + 0.939834i \(0.610980\pi\)
\(644\) 9.44272 6.86054i 0.0146626 0.0106530i
\(645\) 0 0
\(646\) 344.105 111.807i 0.532671 0.173075i
\(647\) −419.644 −0.648600 −0.324300 0.945954i \(-0.605129\pi\)
−0.324300 + 0.945954i \(0.605129\pi\)
\(648\) 0 0
\(649\) 347.331 0.535179
\(650\) 0 0
\(651\) 0 0
\(652\) −347.021 + 252.125i −0.532240 + 0.386695i
\(653\) 370.085i 0.566746i 0.959010 + 0.283373i \(0.0914534\pi\)
−0.959010 + 0.283373i \(0.908547\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 72.1052 221.917i 0.109917 0.338288i
\(657\) 0 0
\(658\) −533.902 + 173.475i −0.811401 + 0.263640i
\(659\) 322.823i 0.489868i −0.969540 0.244934i \(-0.921234\pi\)
0.969540 0.244934i \(-0.0787664\pi\)
\(660\) 0 0
\(661\) −812.735 −1.22955 −0.614777 0.788701i \(-0.710754\pi\)
−0.614777 + 0.788701i \(0.710754\pi\)
\(662\) −205.166 631.437i −0.309919 0.953832i
\(663\) 0 0
\(664\) 358.387 493.277i 0.539739 0.742888i
\(665\) 0 0
\(666\) 0 0
\(667\) 6.07439 0.00910703
\(668\) −107.466 + 78.0789i −0.160878 + 0.116885i
\(669\) 0 0
\(670\) 0 0
\(671\) 1795.47i 2.67581i
\(672\) 0 0
\(673\) 467.378i 0.694469i 0.937778 + 0.347235i \(0.112879\pi\)
−0.937778 + 0.347235i \(0.887121\pi\)
\(674\) −166.318 511.875i −0.246763 0.759458i
\(675\) 0 0
\(676\) 314.620 228.585i 0.465414 0.338143i
\(677\) 548.237i 0.809803i 0.914360 + 0.404902i \(0.132694\pi\)
−0.914360 + 0.404902i \(0.867306\pi\)
\(678\) 0 0
\(679\) 488.051i 0.718779i
\(680\) 0 0
\(681\) 0 0
\(682\) 314.267 102.111i 0.460802 0.149724i
\(683\) 23.9663 0.0350898 0.0175449 0.999846i \(-0.494415\pi\)
0.0175449 + 0.999846i \(0.494415\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −703.607 + 228.616i −1.02567 + 0.333259i
\(687\) 0 0
\(688\) −110.111 + 338.885i −0.160044 + 0.492566i
\(689\) 562.217 0.815989
\(690\) 0 0
\(691\) 186.981i 0.270595i −0.990805 0.135298i \(-0.956801\pi\)
0.990805 0.135298i \(-0.0431990\pi\)
\(692\) 532.206 + 732.519i 0.769084 + 1.05855i
\(693\) 0 0
\(694\) −956.906 + 310.917i −1.37883 + 0.448008i
\(695\) 0 0
\(696\) 0 0
\(697\) 173.378i 0.248748i
\(698\) −0.959917 + 0.311896i −0.00137524 + 0.000446842i
\(699\) 0 0
\(700\) 0 0
\(701\) 706.636 1.00804 0.504020 0.863692i \(-0.331854\pi\)
0.504020 + 0.863692i \(0.331854\pi\)
\(702\) 0 0
\(703\) −279.393 −0.397429
\(704\) −1212.43 + 393.943i −1.72221 + 0.559579i
\(705\) 0 0
\(706\) −207.656 639.098i −0.294130 0.905238i
\(707\) 337.054 0.476738
\(708\) 0 0
\(709\) 188.597 0.266005 0.133002 0.991116i \(-0.457538\pi\)
0.133002 + 0.991116i \(0.457538\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 524.035 721.272i 0.736004 1.01302i
\(713\) 4.60369i 0.00645679i
\(714\) 0 0
\(715\) 0 0
\(716\) 527.449 + 725.971i 0.736661 + 1.01393i
\(717\) 0 0
\(718\) −60.8676 187.331i −0.0847738 0.260907i
\(719\) 156.085i 0.217086i 0.994092 + 0.108543i \(0.0346186\pi\)
−0.994092 + 0.108543i \(0.965381\pi\)
\(720\) 0 0
\(721\) 724.296 1.00457
\(722\) −246.221 + 80.0019i −0.341026 + 0.110806i
\(723\) 0 0
\(724\) 279.023 202.722i 0.385391 0.280003i
\(725\) 0 0
\(726\) 0 0
\(727\) −715.164 −0.983719 −0.491859 0.870675i \(-0.663683\pi\)
−0.491859 + 0.870675i \(0.663683\pi\)
\(728\) −288.273 209.443i −0.395980 0.287696i
\(729\) 0 0
\(730\) 0 0
\(731\) 264.762i 0.362191i
\(732\) 0 0
\(733\) 1233.29i 1.68252i 0.540632 + 0.841259i \(0.318185\pi\)
−0.540632 + 0.841259i \(0.681815\pi\)
\(734\) −948.152 + 308.073i −1.29176 + 0.419718i
\(735\) 0 0
\(736\) 17.7609i 0.0241317i
\(737\) 1000.38i 1.35737i
\(738\) 0 0
\(739\) 8.55656i 0.0115786i −0.999983 0.00578928i \(-0.998157\pi\)
0.999983 0.00578928i \(-0.00184280\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 215.619 + 663.607i 0.290592 + 0.894349i
\(743\) −1010.56 −1.36011 −0.680053 0.733163i \(-0.738043\pi\)
−0.680053 + 0.733163i \(0.738043\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −371.039 1141.94i −0.497372 1.53075i
\(747\) 0 0
\(748\) 766.334 556.774i 1.02451 0.744350i
\(749\) −269.868 −0.360305
\(750\) 0 0
\(751\) 1104.31i 1.47046i −0.677820 0.735228i \(-0.737075\pi\)
0.677820 0.735228i \(-0.262925\pi\)
\(752\) −263.976 + 812.433i −0.351031 + 1.08036i
\(753\) 0 0
\(754\) −57.3050 176.367i −0.0760013 0.233908i
\(755\) 0 0
\(756\) 0 0
\(757\) 875.633i 1.15671i 0.815783 + 0.578357i \(0.196306\pi\)
−0.815783 + 0.578357i \(0.803694\pi\)
\(758\) 187.567 + 577.272i 0.247450 + 0.761573i
\(759\) 0 0
\(760\) 0 0
\(761\) 647.207 0.850470 0.425235 0.905083i \(-0.360192\pi\)
0.425235 + 0.905083i \(0.360192\pi\)
\(762\) 0 0
\(763\) 701.688 0.919644
\(764\) 72.9318 + 100.382i 0.0954605 + 0.131390i
\(765\) 0 0
\(766\) 632.610 205.547i 0.825861 0.268339i
\(767\) 147.729 0.192606
\(768\) 0 0
\(769\) −631.430 −0.821106 −0.410553 0.911837i \(-0.634664\pi\)
−0.410553 + 0.911837i \(0.634664\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 259.150 + 356.689i 0.335686 + 0.462032i
\(773\) 421.522i 0.545306i 0.962112 + 0.272653i \(0.0879011\pi\)
−0.962112 + 0.272653i \(0.912099\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −600.827 436.526i −0.774261 0.562534i
\(777\) 0 0
\(778\) −746.303 + 242.488i −0.959258 + 0.311682i
\(779\) 221.917i 0.284874i
\(780\) 0 0
\(781\) 1609.21 2.06044
\(782\) 4.07809 + 12.5511i 0.00521495 + 0.0160500i
\(783\) 0 0
\(784\) −105.613 + 325.043i −0.134710 + 0.414596i
\(785\) 0 0
\(786\) 0 0
\(787\) 838.633 1.06561 0.532804 0.846239i \(-0.321138\pi\)
0.532804 + 0.846239i \(0.321138\pi\)
\(788\) −405.630 558.302i −0.514759 0.708505i
\(789\) 0 0
\(790\) 0 0
\(791\) 897.535i 1.13468i
\(792\) 0 0
\(793\) 763.659i 0.963001i
\(794\) 206.541 + 635.668i 0.260127 + 0.800589i
\(795\) 0 0
\(796\) 640.000 + 880.884i 0.804020 + 1.10664i