Properties

Label 128.5.f.b.31.7
Level $128$
Weight $5$
Character 128.31
Analytic conductor $13.231$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 128.f (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2313552747\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} - 1048576 x + 2097152\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{42} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.7
Root \(0.153862 + 2.82424i\) of defining polynomial
Character \(\chi\) \(=\) 128.31
Dual form 128.5.f.b.95.7

$q$-expansion

\(f(q)\) \(=\) \(q+(9.42589 + 9.42589i) q^{3} +(2.84710 + 2.84710i) q^{5} -76.7794 q^{7} +96.6949i q^{9} +O(q^{10})\) \(q+(9.42589 + 9.42589i) q^{3} +(2.84710 + 2.84710i) q^{5} -76.7794 q^{7} +96.6949i q^{9} +(-121.488 + 121.488i) q^{11} +(-27.1604 + 27.1604i) q^{13} +53.6729i q^{15} -88.0613 q^{17} +(261.112 + 261.112i) q^{19} +(-723.714 - 723.714i) q^{21} +93.4210 q^{23} -608.788i q^{25} +(-147.938 + 147.938i) q^{27} +(-272.522 + 272.522i) q^{29} +1232.20i q^{31} -2290.26 q^{33} +(-218.599 - 218.599i) q^{35} +(1046.16 + 1046.16i) q^{37} -512.021 q^{39} -915.267i q^{41} +(-1116.82 + 1116.82i) q^{43} +(-275.300 + 275.300i) q^{45} +1720.70i q^{47} +3494.07 q^{49} +(-830.056 - 830.056i) q^{51} +(-734.019 - 734.019i) q^{53} -691.775 q^{55} +4922.43i q^{57} +(1202.73 - 1202.73i) q^{59} +(-580.221 + 580.221i) q^{61} -7424.17i q^{63} -154.657 q^{65} +(1483.97 + 1483.97i) q^{67} +(880.576 + 880.576i) q^{69} +5571.73 q^{71} -6615.21i q^{73} +(5738.37 - 5738.37i) q^{75} +(9327.75 - 9327.75i) q^{77} -5391.66i q^{79} +5043.39 q^{81} +(2554.07 + 2554.07i) q^{83} +(-250.719 - 250.719i) q^{85} -5137.52 q^{87} +10962.7i q^{89} +(2085.35 - 2085.35i) q^{91} +(-11614.6 + 11614.6i) q^{93} +1486.83i q^{95} +4713.20 q^{97} +(-11747.2 - 11747.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{3} + 2q^{5} - 4q^{7} + O(q^{10}) \) \( 14q + 2q^{3} + 2q^{5} - 4q^{7} - 94q^{11} + 2q^{13} - 4q^{17} + 706q^{19} + 164q^{21} + 1148q^{23} + 1664q^{27} - 862q^{29} - 4q^{33} - 1340q^{35} + 1826q^{37} + 2684q^{39} - 1694q^{43} - 1410q^{45} + 682q^{49} + 3012q^{51} + 482q^{53} - 11780q^{55} + 2786q^{59} + 3778q^{61} - 2020q^{65} - 7998q^{67} - 9628q^{69} + 19964q^{71} - 17570q^{75} + 9508q^{77} + 1454q^{81} + 17282q^{83} - 9948q^{85} - 49284q^{87} + 28036q^{91} - 8896q^{93} - 4q^{97} - 49214q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 9.42589 + 9.42589i 1.04732 + 1.04732i 0.998823 + 0.0484980i \(0.0154435\pi\)
0.0484980 + 0.998823i \(0.484557\pi\)
\(4\) 0 0
\(5\) 2.84710 + 2.84710i 0.113884 + 0.113884i 0.761752 0.647868i \(-0.224339\pi\)
−0.647868 + 0.761752i \(0.724339\pi\)
\(6\) 0 0
\(7\) −76.7794 −1.56693 −0.783463 0.621439i \(-0.786549\pi\)
−0.783463 + 0.621439i \(0.786549\pi\)
\(8\) 0 0
\(9\) 96.6949i 1.19376i
\(10\) 0 0
\(11\) −121.488 + 121.488i −1.00403 + 1.00403i −0.00403849 + 0.999992i \(0.501285\pi\)
−0.999992 + 0.00403849i \(0.998715\pi\)
\(12\) 0 0
\(13\) −27.1604 + 27.1604i −0.160712 + 0.160712i −0.782882 0.622170i \(-0.786251\pi\)
0.622170 + 0.782882i \(0.286251\pi\)
\(14\) 0 0
\(15\) 53.6729i 0.238546i
\(16\) 0 0
\(17\) −88.0613 −0.304710 −0.152355 0.988326i \(-0.548686\pi\)
−0.152355 + 0.988326i \(0.548686\pi\)
\(18\) 0 0
\(19\) 261.112 + 261.112i 0.723302 + 0.723302i 0.969276 0.245974i \(-0.0791078\pi\)
−0.245974 + 0.969276i \(0.579108\pi\)
\(20\) 0 0
\(21\) −723.714 723.714i −1.64107 1.64107i
\(22\) 0 0
\(23\) 93.4210 0.176599 0.0882996 0.996094i \(-0.471857\pi\)
0.0882996 + 0.996094i \(0.471857\pi\)
\(24\) 0 0
\(25\) 608.788i 0.974061i
\(26\) 0 0
\(27\) −147.938 + 147.938i −0.202933 + 0.202933i
\(28\) 0 0
\(29\) −272.522 + 272.522i −0.324045 + 0.324045i −0.850316 0.526272i \(-0.823590\pi\)
0.526272 + 0.850316i \(0.323590\pi\)
\(30\) 0 0
\(31\) 1232.20i 1.28220i 0.767455 + 0.641102i \(0.221523\pi\)
−0.767455 + 0.641102i \(0.778477\pi\)
\(32\) 0 0
\(33\) −2290.26 −2.10308
\(34\) 0 0
\(35\) −218.599 218.599i −0.178448 0.178448i
\(36\) 0 0
\(37\) 1046.16 + 1046.16i 0.764177 + 0.764177i 0.977075 0.212898i \(-0.0682901\pi\)
−0.212898 + 0.977075i \(0.568290\pi\)
\(38\) 0 0
\(39\) −512.021 −0.336635
\(40\) 0 0
\(41\) 915.267i 0.544478i −0.962230 0.272239i \(-0.912236\pi\)
0.962230 0.272239i \(-0.0877641\pi\)
\(42\) 0 0
\(43\) −1116.82 + 1116.82i −0.604013 + 0.604013i −0.941375 0.337362i \(-0.890465\pi\)
0.337362 + 0.941375i \(0.390465\pi\)
\(44\) 0 0
\(45\) −275.300 + 275.300i −0.135951 + 0.135951i
\(46\) 0 0
\(47\) 1720.70i 0.778949i 0.921037 + 0.389475i \(0.127343\pi\)
−0.921037 + 0.389475i \(0.872657\pi\)
\(48\) 0 0
\(49\) 3494.07 1.45526
\(50\) 0 0
\(51\) −830.056 830.056i −0.319130 0.319130i
\(52\) 0 0
\(53\) −734.019 734.019i −0.261310 0.261310i 0.564276 0.825586i \(-0.309155\pi\)
−0.825586 + 0.564276i \(0.809155\pi\)
\(54\) 0 0
\(55\) −691.775 −0.228686
\(56\) 0 0
\(57\) 4922.43i 1.51506i
\(58\) 0 0
\(59\) 1202.73 1202.73i 0.345512 0.345512i −0.512923 0.858435i \(-0.671437\pi\)
0.858435 + 0.512923i \(0.171437\pi\)
\(60\) 0 0
\(61\) −580.221 + 580.221i −0.155932 + 0.155932i −0.780761 0.624830i \(-0.785168\pi\)
0.624830 + 0.780761i \(0.285168\pi\)
\(62\) 0 0
\(63\) 7424.17i 1.87054i
\(64\) 0 0
\(65\) −154.657 −0.0366051
\(66\) 0 0
\(67\) 1483.97 + 1483.97i 0.330580 + 0.330580i 0.852807 0.522227i \(-0.174899\pi\)
−0.522227 + 0.852807i \(0.674899\pi\)
\(68\) 0 0
\(69\) 880.576 + 880.576i 0.184956 + 0.184956i
\(70\) 0 0
\(71\) 5571.73 1.10528 0.552641 0.833419i \(-0.313620\pi\)
0.552641 + 0.833419i \(0.313620\pi\)
\(72\) 0 0
\(73\) 6615.21i 1.24136i −0.784064 0.620681i \(-0.786856\pi\)
0.784064 0.620681i \(-0.213144\pi\)
\(74\) 0 0
\(75\) 5738.37 5738.37i 1.02015 1.02015i
\(76\) 0 0
\(77\) 9327.75 9327.75i 1.57324 1.57324i
\(78\) 0 0
\(79\) 5391.66i 0.863910i −0.901895 0.431955i \(-0.857824\pi\)
0.901895 0.431955i \(-0.142176\pi\)
\(80\) 0 0
\(81\) 5043.39 0.768692
\(82\) 0 0
\(83\) 2554.07 + 2554.07i 0.370747 + 0.370747i 0.867749 0.497002i \(-0.165566\pi\)
−0.497002 + 0.867749i \(0.665566\pi\)
\(84\) 0 0
\(85\) −250.719 250.719i −0.0347017 0.0347017i
\(86\) 0 0
\(87\) −5137.52 −0.678758
\(88\) 0 0
\(89\) 10962.7i 1.38400i 0.721898 + 0.691999i \(0.243270\pi\)
−0.721898 + 0.691999i \(0.756730\pi\)
\(90\) 0 0
\(91\) 2085.35 2085.35i 0.251824 0.251824i
\(92\) 0 0
\(93\) −11614.6 + 11614.6i −1.34288 + 1.34288i
\(94\) 0 0
\(95\) 1486.83i 0.164745i
\(96\) 0 0
\(97\) 4713.20 0.500925 0.250462 0.968126i \(-0.419417\pi\)
0.250462 + 0.968126i \(0.419417\pi\)
\(98\) 0 0
\(99\) −11747.2 11747.2i −1.19858 1.19858i
\(100\) 0 0
\(101\) 11381.0 + 11381.0i 1.11568 + 1.11568i 0.992369 + 0.123307i \(0.0393499\pi\)
0.123307 + 0.992369i \(0.460650\pi\)
\(102\) 0 0
\(103\) 175.758 0.0165668 0.00828342 0.999966i \(-0.497363\pi\)
0.00828342 + 0.999966i \(0.497363\pi\)
\(104\) 0 0
\(105\) 4120.97i 0.373784i
\(106\) 0 0
\(107\) −15151.8 + 15151.8i −1.32342 + 1.32342i −0.412432 + 0.910988i \(0.635321\pi\)
−0.910988 + 0.412432i \(0.864679\pi\)
\(108\) 0 0
\(109\) 2349.51 2349.51i 0.197754 0.197754i −0.601283 0.799036i \(-0.705343\pi\)
0.799036 + 0.601283i \(0.205343\pi\)
\(110\) 0 0
\(111\) 19721.9i 1.60068i
\(112\) 0 0
\(113\) −8526.30 −0.667734 −0.333867 0.942620i \(-0.608354\pi\)
−0.333867 + 0.942620i \(0.608354\pi\)
\(114\) 0 0
\(115\) 265.979 + 265.979i 0.0201118 + 0.0201118i
\(116\) 0 0
\(117\) −2626.27 2626.27i −0.191852 0.191852i
\(118\) 0 0
\(119\) 6761.29 0.477459
\(120\) 0 0
\(121\) 14877.5i 1.01615i
\(122\) 0 0
\(123\) 8627.21 8627.21i 0.570243 0.570243i
\(124\) 0 0
\(125\) 3512.72 3512.72i 0.224814 0.224814i
\(126\) 0 0
\(127\) 2844.31i 0.176347i 0.996105 + 0.0881737i \(0.0281031\pi\)
−0.996105 + 0.0881737i \(0.971897\pi\)
\(128\) 0 0
\(129\) −21054.1 −1.26519
\(130\) 0 0
\(131\) 6989.87 + 6989.87i 0.407311 + 0.407311i 0.880800 0.473489i \(-0.157006\pi\)
−0.473489 + 0.880800i \(0.657006\pi\)
\(132\) 0 0
\(133\) −20048.0 20048.0i −1.13336 1.13336i
\(134\) 0 0
\(135\) −842.390 −0.0462217
\(136\) 0 0
\(137\) 3669.69i 0.195519i 0.995210 + 0.0977594i \(0.0311676\pi\)
−0.995210 + 0.0977594i \(0.968832\pi\)
\(138\) 0 0
\(139\) −4401.33 + 4401.33i −0.227800 + 0.227800i −0.811773 0.583973i \(-0.801497\pi\)
0.583973 + 0.811773i \(0.301497\pi\)
\(140\) 0 0
\(141\) −16219.1 + 16219.1i −0.815810 + 0.815810i
\(142\) 0 0
\(143\) 6599.30i 0.322720i
\(144\) 0 0
\(145\) −1551.79 −0.0738071
\(146\) 0 0
\(147\) 32934.7 + 32934.7i 1.52412 + 1.52412i
\(148\) 0 0
\(149\) −15737.5 15737.5i −0.708863 0.708863i 0.257433 0.966296i \(-0.417123\pi\)
−0.966296 + 0.257433i \(0.917123\pi\)
\(150\) 0 0
\(151\) −41972.2 −1.84080 −0.920402 0.390974i \(-0.872138\pi\)
−0.920402 + 0.390974i \(0.872138\pi\)
\(152\) 0 0
\(153\) 8515.08i 0.363752i
\(154\) 0 0
\(155\) −3508.19 + 3508.19i −0.146023 + 0.146023i
\(156\) 0 0
\(157\) 24735.4 24735.4i 1.00351 1.00351i 0.00351271 0.999994i \(-0.498882\pi\)
0.999994 0.00351271i \(-0.00111813\pi\)
\(158\) 0 0
\(159\) 13837.6i 0.547350i
\(160\) 0 0
\(161\) −7172.80 −0.276718
\(162\) 0 0
\(163\) −24429.8 24429.8i −0.919483 0.919483i 0.0775084 0.996992i \(-0.475304\pi\)
−0.996992 + 0.0775084i \(0.975304\pi\)
\(164\) 0 0
\(165\) −6520.60 6520.60i −0.239508 0.239508i
\(166\) 0 0
\(167\) 52178.2 1.87093 0.935463 0.353425i \(-0.114983\pi\)
0.935463 + 0.353425i \(0.114983\pi\)
\(168\) 0 0
\(169\) 27085.6i 0.948343i
\(170\) 0 0
\(171\) −25248.2 + 25248.2i −0.863452 + 0.863452i
\(172\) 0 0
\(173\) −26316.2 + 26316.2i −0.879289 + 0.879289i −0.993461 0.114172i \(-0.963578\pi\)
0.114172 + 0.993461i \(0.463578\pi\)
\(174\) 0 0
\(175\) 46742.4i 1.52628i
\(176\) 0 0
\(177\) 22673.5 0.723723
\(178\) 0 0
\(179\) −4815.78 4815.78i −0.150301 0.150301i 0.627952 0.778252i \(-0.283894\pi\)
−0.778252 + 0.627952i \(0.783894\pi\)
\(180\) 0 0
\(181\) 23924.9 + 23924.9i 0.730286 + 0.730286i 0.970676 0.240391i \(-0.0772755\pi\)
−0.240391 + 0.970676i \(0.577276\pi\)
\(182\) 0 0
\(183\) −10938.2 −0.326621
\(184\) 0 0
\(185\) 5957.04i 0.174055i
\(186\) 0 0
\(187\) 10698.4 10698.4i 0.305939 0.305939i
\(188\) 0 0
\(189\) 11358.6 11358.6i 0.317981 0.317981i
\(190\) 0 0
\(191\) 45079.4i 1.23569i −0.786298 0.617847i \(-0.788005\pi\)
0.786298 0.617847i \(-0.211995\pi\)
\(192\) 0 0
\(193\) 50286.0 1.34999 0.674997 0.737820i \(-0.264145\pi\)
0.674997 + 0.737820i \(0.264145\pi\)
\(194\) 0 0
\(195\) −1457.78 1457.78i −0.0383373 0.0383373i
\(196\) 0 0
\(197\) 25662.2 + 25662.2i 0.661243 + 0.661243i 0.955673 0.294430i \(-0.0951297\pi\)
−0.294430 + 0.955673i \(0.595130\pi\)
\(198\) 0 0
\(199\) −44599.1 −1.12621 −0.563106 0.826385i \(-0.690394\pi\)
−0.563106 + 0.826385i \(0.690394\pi\)
\(200\) 0 0
\(201\) 27975.5i 0.692447i
\(202\) 0 0
\(203\) 20924.0 20924.0i 0.507754 0.507754i
\(204\) 0 0
\(205\) 2605.86 2605.86i 0.0620073 0.0620073i
\(206\) 0 0
\(207\) 9033.33i 0.210818i
\(208\) 0 0
\(209\) −63443.8 −1.45244
\(210\) 0 0
\(211\) −25828.5 25828.5i −0.580143 0.580143i 0.354800 0.934942i \(-0.384549\pi\)
−0.934942 + 0.354800i \(0.884549\pi\)
\(212\) 0 0
\(213\) 52518.5 + 52518.5i 1.15759 + 1.15759i
\(214\) 0 0
\(215\) −6359.40 −0.137575
\(216\) 0 0
\(217\) 94607.4i 2.00912i
\(218\) 0 0
\(219\) 62354.3 62354.3i 1.30010 1.30010i
\(220\) 0 0
\(221\) 2391.78 2391.78i 0.0489707 0.0489707i
\(222\) 0 0
\(223\) 72650.0i 1.46092i −0.682957 0.730459i \(-0.739306\pi\)
0.682957 0.730459i \(-0.260694\pi\)
\(224\) 0 0
\(225\) 58866.7 1.16280
\(226\) 0 0
\(227\) −18858.2 18858.2i −0.365972 0.365972i 0.500034 0.866006i \(-0.333321\pi\)
−0.866006 + 0.500034i \(0.833321\pi\)
\(228\) 0 0
\(229\) −41675.9 41675.9i −0.794721 0.794721i 0.187537 0.982258i \(-0.439950\pi\)
−0.982258 + 0.187537i \(0.939950\pi\)
\(230\) 0 0
\(231\) 175845. 3.29538
\(232\) 0 0
\(233\) 2767.61i 0.0509792i 0.999675 + 0.0254896i \(0.00811447\pi\)
−0.999675 + 0.0254896i \(0.991886\pi\)
\(234\) 0 0
\(235\) −4899.00 + 4899.00i −0.0887099 + 0.0887099i
\(236\) 0 0
\(237\) 50821.2 50821.2i 0.904791 0.904791i
\(238\) 0 0
\(239\) 49981.8i 0.875016i 0.899215 + 0.437508i \(0.144139\pi\)
−0.899215 + 0.437508i \(0.855861\pi\)
\(240\) 0 0
\(241\) −44076.0 −0.758872 −0.379436 0.925218i \(-0.623882\pi\)
−0.379436 + 0.925218i \(0.623882\pi\)
\(242\) 0 0
\(243\) 59521.4 + 59521.4i 1.00800 + 1.00800i
\(244\) 0 0
\(245\) 9947.97 + 9947.97i 0.165730 + 0.165730i
\(246\) 0 0
\(247\) −14183.8 −0.232487
\(248\) 0 0
\(249\) 48148.8i 0.776582i
\(250\) 0 0
\(251\) 31786.2 31786.2i 0.504534 0.504534i −0.408309 0.912844i \(-0.633881\pi\)
0.912844 + 0.408309i \(0.133881\pi\)
\(252\) 0 0
\(253\) −11349.5 + 11349.5i −0.177311 + 0.177311i
\(254\) 0 0
\(255\) 4726.51i 0.0726876i
\(256\) 0 0
\(257\) 70865.6 1.07292 0.536462 0.843924i \(-0.319760\pi\)
0.536462 + 0.843924i \(0.319760\pi\)
\(258\) 0 0
\(259\) −80323.4 80323.4i −1.19741 1.19741i
\(260\) 0 0
\(261\) −26351.5 26351.5i −0.386833 0.386833i
\(262\) 0 0
\(263\) −113289. −1.63786 −0.818929 0.573894i \(-0.805432\pi\)
−0.818929 + 0.573894i \(0.805432\pi\)
\(264\) 0 0
\(265\) 4179.65i 0.0595180i
\(266\) 0 0
\(267\) −103333. + 103333.i −1.44949 + 1.44949i
\(268\) 0 0
\(269\) −70652.7 + 70652.7i −0.976393 + 0.976393i −0.999728 0.0233352i \(-0.992572\pi\)
0.0233352 + 0.999728i \(0.492572\pi\)
\(270\) 0 0
\(271\) 110180.i 1.50025i −0.661294 0.750126i \(-0.729993\pi\)
0.661294 0.750126i \(-0.270007\pi\)
\(272\) 0 0
\(273\) 39312.7 0.527481
\(274\) 0 0
\(275\) 73960.2 + 73960.2i 0.977987 + 0.977987i
\(276\) 0 0
\(277\) −34611.0 34611.0i −0.451081 0.451081i 0.444632 0.895713i \(-0.353334\pi\)
−0.895713 + 0.444632i \(0.853334\pi\)
\(278\) 0 0
\(279\) −119147. −1.53065
\(280\) 0 0
\(281\) 147980.i 1.87408i 0.349216 + 0.937042i \(0.386448\pi\)
−0.349216 + 0.937042i \(0.613552\pi\)
\(282\) 0 0
\(283\) −39761.2 + 39761.2i −0.496463 + 0.496463i −0.910335 0.413872i \(-0.864176\pi\)
0.413872 + 0.910335i \(0.364176\pi\)
\(284\) 0 0
\(285\) −14014.7 + 14014.7i −0.172541 + 0.172541i
\(286\) 0 0
\(287\) 70273.6i 0.853156i
\(288\) 0 0
\(289\) −75766.2 −0.907152
\(290\) 0 0
\(291\) 44426.1 + 44426.1i 0.524629 + 0.524629i
\(292\) 0 0
\(293\) 708.909 + 708.909i 0.00825763 + 0.00825763i 0.711224 0.702966i \(-0.248141\pi\)
−0.702966 + 0.711224i \(0.748141\pi\)
\(294\) 0 0
\(295\) 6848.56 0.0786965
\(296\) 0 0
\(297\) 35945.3i 0.407502i
\(298\) 0 0
\(299\) −2537.35 + 2537.35i −0.0283816 + 0.0283816i
\(300\) 0 0
\(301\) 85748.8 85748.8i 0.946444 0.946444i
\(302\) 0 0
\(303\) 214552.i 2.33694i
\(304\) 0 0
\(305\) −3303.90 −0.0355162
\(306\) 0 0
\(307\) 20597.1 + 20597.1i 0.218539 + 0.218539i 0.807883 0.589344i \(-0.200614\pi\)
−0.589344 + 0.807883i \(0.700614\pi\)
\(308\) 0 0
\(309\) 1656.67 + 1656.67i 0.0173508 + 0.0173508i
\(310\) 0 0
\(311\) 82310.6 0.851011 0.425505 0.904956i \(-0.360096\pi\)
0.425505 + 0.904956i \(0.360096\pi\)
\(312\) 0 0
\(313\) 120415.i 1.22911i −0.788872 0.614557i \(-0.789335\pi\)
0.788872 0.614557i \(-0.210665\pi\)
\(314\) 0 0
\(315\) 21137.4 21137.4i 0.213025 0.213025i
\(316\) 0 0
\(317\) −14795.3 + 14795.3i −0.147233 + 0.147233i −0.776881 0.629648i \(-0.783199\pi\)
0.629648 + 0.776881i \(0.283199\pi\)
\(318\) 0 0
\(319\) 66216.1i 0.650702i
\(320\) 0 0
\(321\) −285639. −2.77209
\(322\) 0 0
\(323\) −22993.9 22993.9i −0.220398 0.220398i
\(324\) 0 0
\(325\) 16534.9 + 16534.9i 0.156543 + 0.156543i
\(326\) 0 0
\(327\) 44292.5 0.414224
\(328\) 0 0
\(329\) 132114.i 1.22056i
\(330\) 0 0
\(331\) −82868.2 + 82868.2i −0.756366 + 0.756366i −0.975659 0.219293i \(-0.929625\pi\)
0.219293 + 0.975659i \(0.429625\pi\)
\(332\) 0 0
\(333\) −101158. + 101158.i −0.912247 + 0.912247i
\(334\) 0 0
\(335\) 8450.04i 0.0752955i
\(336\) 0 0
\(337\) 78854.4 0.694331 0.347165 0.937804i \(-0.387144\pi\)
0.347165 + 0.937804i \(0.387144\pi\)
\(338\) 0 0
\(339\) −80368.0 80368.0i −0.699332 0.699332i
\(340\) 0 0
\(341\) −149697. 149697.i −1.28737 1.28737i
\(342\) 0 0
\(343\) −83925.2 −0.713352
\(344\) 0 0
\(345\) 5014.18i 0.0421271i
\(346\) 0 0
\(347\) 59543.0 59543.0i 0.494506 0.494506i −0.415216 0.909723i \(-0.636294\pi\)
0.909723 + 0.415216i \(0.136294\pi\)
\(348\) 0 0
\(349\) 756.172 756.172i 0.00620826 0.00620826i −0.703996 0.710204i \(-0.748603\pi\)
0.710204 + 0.703996i \(0.248603\pi\)
\(350\) 0 0
\(351\) 8036.11i 0.0652276i
\(352\) 0 0
\(353\) 23723.5 0.190384 0.0951918 0.995459i \(-0.469654\pi\)
0.0951918 + 0.995459i \(0.469654\pi\)
\(354\) 0 0
\(355\) 15863.3 + 15863.3i 0.125874 + 0.125874i
\(356\) 0 0
\(357\) 63731.2 + 63731.2i 0.500053 + 0.500053i
\(358\) 0 0
\(359\) 146064. 1.13333 0.566663 0.823950i \(-0.308234\pi\)
0.566663 + 0.823950i \(0.308234\pi\)
\(360\) 0 0
\(361\) 6038.12i 0.0463327i
\(362\) 0 0
\(363\) 140234. 140234.i 1.06424 1.06424i
\(364\) 0 0
\(365\) 18834.2 18834.2i 0.141371 0.141371i
\(366\) 0 0
\(367\) 151129.i 1.12206i 0.827797 + 0.561028i \(0.189594\pi\)
−0.827797 + 0.561028i \(0.810406\pi\)
\(368\) 0 0
\(369\) 88501.7 0.649978
\(370\) 0 0
\(371\) 56357.5 + 56357.5i 0.409453 + 0.409453i
\(372\) 0 0
\(373\) −26207.7 26207.7i −0.188370 0.188370i 0.606621 0.794991i \(-0.292524\pi\)
−0.794991 + 0.606621i \(0.792524\pi\)
\(374\) 0 0
\(375\) 66221.0 0.470905
\(376\) 0 0
\(377\) 14803.6i 0.104156i
\(378\) 0 0
\(379\) −110424. + 110424.i −0.768752 + 0.768752i −0.977887 0.209135i \(-0.932935\pi\)
0.209135 + 0.977887i \(0.432935\pi\)
\(380\) 0 0
\(381\) −26810.1 + 26810.1i −0.184692 + 0.184692i
\(382\) 0 0
\(383\) 10514.9i 0.0716819i −0.999358 0.0358409i \(-0.988589\pi\)
0.999358 0.0358409i \(-0.0114110\pi\)
\(384\) 0 0
\(385\) 53114.1 0.358334
\(386\) 0 0
\(387\) −107991. 107991.i −0.721049 0.721049i
\(388\) 0 0
\(389\) 166762. + 166762.i 1.10204 + 1.10204i 0.994164 + 0.107877i \(0.0344054\pi\)
0.107877 + 0.994164i \(0.465595\pi\)
\(390\) 0 0
\(391\) −8226.78 −0.0538116
\(392\) 0 0
\(393\) 131772.i 0.853172i
\(394\) 0 0
\(395\) 15350.6 15350.6i 0.0983855 0.0983855i
\(396\) 0 0
\(397\) 192542. 192542.i 1.22164 1.22164i 0.254594 0.967048i \(-0.418058\pi\)
0.967048 0.254594i \(-0.0819419\pi\)
\(398\) 0 0
\(399\) 377941.i 2.37399i
\(400\) 0 0
\(401\) 91157.6 0.566897 0.283448 0.958987i \(-0.408522\pi\)
0.283448 + 0.958987i \(0.408522\pi\)
\(402\) 0 0
\(403\) −33467.0 33467.0i −0.206066 0.206066i
\(404\) 0 0
\(405\) 14359.0 + 14359.0i 0.0875417 + 0.0875417i
\(406\) 0 0
\(407\) −254191. −1.53451
\(408\) 0 0
\(409\) 107774.i 0.644272i 0.946693 + 0.322136i \(0.104401\pi\)
−0.946693 + 0.322136i \(0.895599\pi\)
\(410\) 0 0
\(411\) −34590.1 + 34590.1i −0.204771 + 0.204771i
\(412\) 0 0
\(413\) −92344.5 + 92344.5i −0.541391 + 0.541391i
\(414\) 0 0
\(415\) 14543.4i 0.0844442i
\(416\) 0 0
\(417\) −82972.9 −0.477160
\(418\) 0 0
\(419\) 118524. + 118524.i 0.675115 + 0.675115i 0.958891 0.283776i \(-0.0915871\pi\)
−0.283776 + 0.958891i \(0.591587\pi\)
\(420\) 0 0
\(421\) 226616. + 226616.i 1.27858 + 1.27858i 0.941464 + 0.337113i \(0.109451\pi\)
0.337113 + 0.941464i \(0.390549\pi\)
\(422\) 0 0
\(423\) −166383. −0.929882
\(424\) 0 0
\(425\) 53610.7i 0.296807i
\(426\) 0 0
\(427\) 44549.0 44549.0i 0.244333 0.244333i
\(428\) 0 0
\(429\) 62204.3 62204.3i 0.337991 0.337991i
\(430\) 0 0
\(431\) 5397.51i 0.0290562i 0.999894 + 0.0145281i \(0.00462460\pi\)
−0.999894 + 0.0145281i \(0.995375\pi\)
\(432\) 0 0
\(433\) 163835. 0.873840 0.436920 0.899500i \(-0.356069\pi\)
0.436920 + 0.899500i \(0.356069\pi\)
\(434\) 0 0
\(435\) −14627.0 14627.0i −0.0772997 0.0772997i
\(436\) 0 0
\(437\) 24393.4 + 24393.4i 0.127735 + 0.127735i
\(438\) 0 0
\(439\) 158472. 0.822289 0.411144 0.911570i \(-0.365129\pi\)
0.411144 + 0.911570i \(0.365129\pi\)
\(440\) 0 0
\(441\) 337859.i 1.73723i
\(442\) 0 0
\(443\) 137929. 137929.i 0.702826 0.702826i −0.262190 0.965016i \(-0.584445\pi\)
0.965016 + 0.262190i \(0.0844448\pi\)
\(444\) 0 0
\(445\) −31211.8 + 31211.8i −0.157615 + 0.157615i
\(446\) 0 0
\(447\) 296680.i 1.48482i
\(448\) 0 0
\(449\) 327336. 1.62368 0.811841 0.583879i \(-0.198466\pi\)
0.811841 + 0.583879i \(0.198466\pi\)
\(450\) 0 0
\(451\) 111194. + 111194.i 0.546672 + 0.546672i
\(452\) 0 0
\(453\) −395625. 395625.i −1.92791 1.92791i
\(454\) 0 0
\(455\) 11874.4 0.0573575
\(456\) 0 0
\(457\) 154510.i 0.739817i −0.929068 0.369909i \(-0.879389\pi\)
0.929068 0.369909i \(-0.120611\pi\)
\(458\) 0 0
\(459\) 13027.6 13027.6i 0.0618358 0.0618358i
\(460\) 0 0
\(461\) −19296.3 + 19296.3i −0.0907971 + 0.0907971i −0.751046 0.660249i \(-0.770451\pi\)
0.660249 + 0.751046i \(0.270451\pi\)
\(462\) 0 0
\(463\) 26503.6i 0.123635i −0.998087 0.0618176i \(-0.980310\pi\)
0.998087 0.0618176i \(-0.0196897\pi\)
\(464\) 0 0
\(465\) −66135.7 −0.305865
\(466\) 0 0
\(467\) −111797. 111797.i −0.512622 0.512622i 0.402707 0.915329i \(-0.368069\pi\)
−0.915329 + 0.402707i \(0.868069\pi\)
\(468\) 0 0
\(469\) −113939. 113939.i −0.517994 0.517994i
\(470\) 0 0
\(471\) 466307. 2.10199
\(472\) 0 0
\(473\) 271360.i 1.21290i
\(474\) 0 0
\(475\) 158962. 158962.i 0.704541 0.704541i
\(476\) 0 0
\(477\) 70975.8 70975.8i 0.311942 0.311942i
\(478\) 0 0
\(479\) 225380.i 0.982301i 0.871075 + 0.491150i \(0.163423\pi\)
−0.871075 + 0.491150i \(0.836577\pi\)
\(480\) 0 0
\(481\) −56828.1 −0.245625
\(482\) 0 0
\(483\) −67610.1 67610.1i −0.289813 0.289813i
\(484\) 0 0
\(485\) 13419.0 + 13419.0i 0.0570473 + 0.0570473i
\(486\) 0 0
\(487\) 8483.58 0.0357702 0.0178851 0.999840i \(-0.494307\pi\)
0.0178851 + 0.999840i \(0.494307\pi\)
\(488\) 0 0
\(489\) 460544.i 1.92599i
\(490\) 0 0
\(491\) −69265.0 + 69265.0i −0.287310 + 0.287310i −0.836016 0.548706i \(-0.815121\pi\)
0.548706 + 0.836016i \(0.315121\pi\)
\(492\) 0 0
\(493\) 23998.6 23998.6i 0.0987399 0.0987399i
\(494\) 0 0
\(495\) 66891.1i 0.272997i
\(496\) 0 0
\(497\) −427794. −1.73190
\(498\) 0 0
\(499\) −86869.4 86869.4i −0.348872 0.348872i 0.510817 0.859689i \(-0.329343\pi\)
−0.859689 + 0.510817i \(0.829343\pi\)
\(500\) 0 0
\(501\) 491827. + 491827.i 1.95946 + 1.95946i
\(502\) 0 0
\(503\) 112271. 0.443745 0.221872 0.975076i \(-0.428783\pi\)
0.221872 + 0.975076i \(0.428783\pi\)
\(504\) 0 0
\(505\) 64805.7i 0.254115i
\(506\) 0 0
\(507\) −255306. + 255306.i −0.993220 + 0.993220i
\(508\) 0 0
\(509\) 167589. 167589.i 0.646861 0.646861i −0.305372 0.952233i \(-0.598781\pi\)
0.952233 + 0.305372i \(0.0987808\pi\)
\(510\) 0 0
\(511\) 507912.i 1.94512i
\(512\) 0 0
\(513\) −77256.9 −0.293564
\(514\) 0 0
\(515\) 500.399 + 500.399i 0.00188670 + 0.00188670i
\(516\) 0 0
\(517\) −209044. 209044.i −0.782089 0.782089i
\(518\) 0 0
\(519\) −496108. −1.84180
\(520\) 0 0
\(521\) 287463.i 1.05903i 0.848302 + 0.529513i \(0.177625\pi\)
−0.848302 + 0.529513i \(0.822375\pi\)
\(522\) 0 0
\(523\) 203069. 203069.i 0.742404 0.742404i −0.230636 0.973040i \(-0.574081\pi\)
0.973040 + 0.230636i \(0.0740807\pi\)
\(524\) 0 0
\(525\) −440588. + 440588.i −1.59851 + 1.59851i
\(526\) 0 0
\(527\) 108509.i 0.390701i
\(528\) 0 0
\(529\) −271114. −0.968813
\(530\) 0 0
\(531\) 116297. + 116297.i 0.412459 + 0.412459i
\(532\) 0 0
\(533\) 24859.0 + 24859.0i 0.0875042 + 0.0875042i
\(534\) 0 0
\(535\) −86277.6 −0.301433
\(536\) 0 0
\(537\) 90786.1i 0.314826i
\(538\) 0 0
\(539\) −424486. + 424486.i −1.46112 + 1.46112i
\(540\) 0 0
\(541\) −308972. + 308972.i −1.05566 + 1.05566i −0.0573036 + 0.998357i \(0.518250\pi\)
−0.998357 + 0.0573036i \(0.981750\pi\)
\(542\) 0 0
\(543\) 451027.i 1.52969i
\(544\) 0 0
\(545\) 13378.6 0.0450420
\(546\) 0 0
\(547\) 8623.13 + 8623.13i 0.0288198 + 0.0288198i 0.721370 0.692550i \(-0.243513\pi\)
−0.692550 + 0.721370i \(0.743513\pi\)
\(548\) 0 0
\(549\) −56104.4 56104.4i −0.186145 0.186145i
\(550\) 0 0
\(551\) −142317. −0.468765
\(552\) 0 0
\(553\) 413968.i 1.35368i
\(554\) 0 0
\(555\) −56150.4 + 56150.4i −0.182292 + 0.182292i
\(556\) 0 0
\(557\) 208785. 208785.i 0.672961 0.672961i −0.285437 0.958398i \(-0.592139\pi\)
0.958398 + 0.285437i \(0.0921387\pi\)
\(558\) 0 0
\(559\) 60666.5i 0.194145i
\(560\) 0 0
\(561\) 201683. 0.640832
\(562\) 0 0
\(563\) −127891. 127891.i −0.403480 0.403480i 0.475977 0.879458i \(-0.342094\pi\)
−0.879458 + 0.475977i \(0.842094\pi\)
\(564\) 0 0
\(565\) −24275.2 24275.2i −0.0760443 0.0760443i
\(566\) 0 0
\(567\) −387228. −1.20448
\(568\) 0 0
\(569\) 488561.i 1.50902i −0.656290 0.754509i \(-0.727875\pi\)
0.656290 0.754509i \(-0.272125\pi\)
\(570\) 0 0
\(571\) 17324.2 17324.2i 0.0531352 0.0531352i −0.680040 0.733175i \(-0.738038\pi\)
0.733175 + 0.680040i \(0.238038\pi\)
\(572\) 0 0
\(573\) 424913. 424913.i 1.29417 1.29417i
\(574\) 0 0
\(575\) 56873.6i 0.172018i
\(576\) 0 0
\(577\) −9362.93 −0.0281229 −0.0140615 0.999901i \(-0.504476\pi\)
−0.0140615 + 0.999901i \(0.504476\pi\)
\(578\) 0 0
\(579\) 473990. + 473990.i 1.41388 + 1.41388i
\(580\) 0 0
\(581\) −196100. 196100.i −0.580932 0.580932i
\(582\) 0 0
\(583\) 178348. 0.524725
\(584\) 0 0
\(585\) 14954.5i 0.0436978i
\(586\) 0 0
\(587\) −46301.5 + 46301.5i −0.134375 + 0.134375i −0.771095 0.636720i \(-0.780291\pi\)
0.636720 + 0.771095i \(0.280291\pi\)
\(588\) 0 0
\(589\) −321742. + 321742.i −0.927422 + 0.927422i
\(590\) 0 0
\(591\) 483778.i 1.38507i
\(592\) 0 0
\(593\) −194145. −0.552099 −0.276049 0.961143i \(-0.589025\pi\)
−0.276049 + 0.961143i \(0.589025\pi\)
\(594\) 0 0
\(595\) 19250.1 + 19250.1i 0.0543749 + 0.0543749i
\(596\) 0 0
\(597\) −420387. 420387.i −1.17951 1.17951i
\(598\) 0 0
\(599\) 474516. 1.32250 0.661252 0.750164i \(-0.270025\pi\)
0.661252 + 0.750164i \(0.270025\pi\)
\(600\) 0 0
\(601\) 87515.3i 0.242290i 0.992635 + 0.121145i \(0.0386566\pi\)
−0.992635 + 0.121145i \(0.961343\pi\)
\(602\) 0 0
\(603\) −143493. + 143493.i −0.394634 + 0.394634i
\(604\) 0 0
\(605\) 42357.8 42357.8i 0.115724 0.115724i
\(606\) 0 0
\(607\) 687260.i 1.86528i −0.360808 0.932640i \(-0.617499\pi\)
0.360808 0.932640i \(-0.382501\pi\)
\(608\) 0 0
\(609\) 394456. 1.06356
\(610\) 0 0
\(611\) −46734.8 46734.8i −0.125187 0.125187i
\(612\) 0 0
\(613\) 220862. + 220862.i 0.587761 + 0.587761i 0.937025 0.349263i \(-0.113568\pi\)
−0.349263 + 0.937025i \(0.613568\pi\)
\(614\) 0 0
\(615\) 49125.1 0.129883
\(616\) 0 0
\(617\) 518967.i 1.36323i 0.731711 + 0.681615i \(0.238722\pi\)
−0.731711 + 0.681615i \(0.761278\pi\)
\(618\) 0 0
\(619\) 77555.3 77555.3i 0.202409 0.202409i −0.598622 0.801031i \(-0.704285\pi\)
0.801031 + 0.598622i \(0.204285\pi\)
\(620\) 0 0
\(621\) −13820.5 + 13820.5i −0.0358378 + 0.0358378i
\(622\) 0 0
\(623\) 841705.i 2.16862i
\(624\) 0 0
\(625\) −360490. −0.922855
\(626\) 0 0
\(627\) −598015. 598015.i −1.52117 1.52117i
\(628\) 0 0
\(629\) −92126.1 92126.1i −0.232853 0.232853i
\(630\) 0 0
\(631\) 344653. 0.865612 0.432806 0.901487i \(-0.357523\pi\)
0.432806 + 0.901487i \(0.357523\pi\)
\(632\) 0 0
\(633\) 486914.i 1.21519i
\(634\) 0 0
\(635\) −8098.03 + 8098.03i −0.0200832 + 0.0200832i
\(636\) 0 0
\(637\) −94900.2 + 94900.2i −0.233877 + 0.233877i
\(638\) 0 0
\(639\) 538758.i 1.31945i
\(640\) 0 0
\(641\) −183353. −0.446243 −0.223122 0.974791i \(-0.571625\pi\)
−0.223122 + 0.974791i \(0.571625\pi\)
\(642\) 0 0
\(643\) 541900. + 541900.i 1.31068 + 1.31068i 0.920913 + 0.389768i \(0.127445\pi\)
0.389768 + 0.920913i \(0.372555\pi\)
\(644\) 0 0
\(645\) −59943.0 59943.0i −0.144085 0.144085i
\(646\) 0 0
\(647\) −358562. −0.856555 −0.428278 0.903647i \(-0.640879\pi\)
−0.428278 + 0.903647i \(0.640879\pi\)
\(648\) 0 0
\(649\) 292233.i 0.693808i
\(650\) 0 0
\(651\) 891760. 891760.i 2.10419 2.10419i
\(652\) 0 0
\(653\) 73642.4 73642.4i 0.172704 0.172704i −0.615463 0.788166i \(-0.711031\pi\)
0.788166 + 0.615463i \(0.211031\pi\)
\(654\) 0 0
\(655\) 39801.7i 0.0927725i
\(656\) 0 0
\(657\) 639657. 1.48189
\(658\) 0 0
\(659\) −22081.7 22081.7i −0.0508467 0.0508467i 0.681226 0.732073i \(-0.261447\pi\)
−0.732073 + 0.681226i \(0.761447\pi\)
\(660\) 0 0
\(661\) −20869.3 20869.3i −0.0477644 0.0477644i 0.682821 0.730586i \(-0.260753\pi\)
−0.730586 + 0.682821i \(0.760753\pi\)
\(662\) 0 0
\(663\) 45089.3 0.102576
\(664\) 0 0
\(665\) 114157.i 0.258143i
\(666\) 0 0
\(667\) −25459.3 + 25459.3i −0.0572261 + 0.0572261i
\(668\) 0 0
\(669\) 684791. 684791.i 1.53005 1.53005i
\(670\) 0 0
\(671\) 140979.i 0.313120i
\(672\) 0 0
\(673\) 379771. 0.838479 0.419239 0.907876i \(-0.362297\pi\)
0.419239 + 0.907876i \(0.362297\pi\)
\(674\) 0 0
\(675\) 90063.0 + 90063.0i 0.197669 + 0.197669i
\(676\) 0 0
\(677\) 156167. + 156167.i 0.340731 + 0.340731i 0.856642 0.515911i \(-0.172546\pi\)
−0.515911 + 0.856642i \(0.672546\pi\)
\(678\) 0 0
\(679\) −361877. −0.784912
\(680\) 0 0
\(681\) 355511.i 0.766581i
\(682\) 0 0
\(683\) −164044. + 164044.i −0.351656 + 0.351656i −0.860725 0.509070i \(-0.829990\pi\)
0.509070 + 0.860725i \(0.329990\pi\)
\(684\) 0 0
\(685\) −10448.0 + 10448.0i −0.0222665 + 0.0222665i
\(686\) 0 0
\(687\) 785666.i 1.66466i
\(688\) 0 0
\(689\) 39872.4 0.0839912
\(690\) 0 0
\(691\) 288207. + 288207.i 0.603599 + 0.603599i 0.941266 0.337667i \(-0.109638\pi\)
−0.337667 + 0.941266i \(0.609638\pi\)
\(692\) 0 0
\(693\) 901945. + 901945.i 1.87808 + 1.87808i
\(694\) 0 0
\(695\) −25062.1 −0.0518856
\(696\) 0 0
\(697\) 80599.7i 0.165908i
\(698\) 0 0
\(699\) −26087.2 + 26087.2i −0.0533916 + 0.0533916i
\(700\) 0 0
\(701\) −323248. + 323248.i −0.657808 + 0.657808i −0.954861 0.297053i \(-0.903996\pi\)
0.297053 + 0.954861i \(0.403996\pi\)
\(702\) 0 0
\(703\) 546329.i 1.10546i
\(704\) 0 0
\(705\) −92355.0 −0.185816
\(706\) 0 0
\(707\) −873826. 873826.i −1.74818 1.74818i
\(708\) 0 0
\(709\) 580085. + 580085.i 1.15398 + 1.15398i 0.985747 + 0.168235i \(0.0538067\pi\)
0.168235 + 0.985747i \(0.446193\pi\)
\(710\) 0 0
\(711\) 521346. 1.03130
\(712\) 0 0
\(713\) 115113.i 0.226436i
\(714\) 0 0
\(715\) 18788.9 18788.9i 0.0367526 0.0367526i
\(716\) 0 0
\(717\) −471123. + 471123.i −0.916423 + 0.916423i
\(718\) 0 0
\(719\) 332243.i 0.642684i 0.946963 + 0.321342i \(0.104134\pi\)
−0.946963 + 0.321342i \(0.895866\pi\)
\(720\) 0 0
\(721\) −13494.5 −0.0259590
\(722\) 0 0
\(723\) −415456. 415456.i −0.794783 0.794783i
\(724\) 0 0
\(725\) 165908. + 165908.i 0.315639 + 0.315639i
\(726\) 0 0
\(727\) 362311. 0.685508 0.342754 0.939425i \(-0.388640\pi\)
0.342754 + 0.939425i \(0.388640\pi\)
\(728\) 0 0
\(729\) 713570.i 1.34271i
\(730\) 0 0
\(731\) 98348.7 98348.7i 0.184049 0.184049i
\(732\) 0 0
\(733\) −377844. + 377844.i −0.703242 + 0.703242i −0.965105 0.261863i \(-0.915663\pi\)
0.261863 + 0.965105i \(0.415663\pi\)
\(734\) 0 0
\(735\) 187537.i 0.347146i
\(736\) 0 0
\(737\) −360569. −0.663825
\(738\) 0 0
\(739\) −467502. 467502.i −0.856042 0.856042i 0.134828 0.990869i \(-0.456952\pi\)
−0.990869 + 0.134828i \(0.956952\pi\)
\(740\) 0 0
\(741\) −133695. 133695.i −0.243489 0.243489i
\(742\) 0 0
\(743\) −555820. −1.00683 −0.503415 0.864045i \(-0.667923\pi\)
−0.503415 + 0.864045i \(0.667923\pi\)
\(744\) 0 0
\(745\) 89612.4i 0.161456i
\(746\) 0 0
\(747\) −246966. + 246966.i −0.442584 + 0.442584i
\(748\) 0 0
\(749\) 1.16335e6 1.16335e6i 2.07370 2.07370i
\(750\) 0 0
\(751\) 308308.i 0.546644i −0.961923 0.273322i \(-0.911878\pi\)
0.961923 0.273322i \(-0.0881224\pi\)
\(752\) 0 0
\(753\) 599226. 1.05682
\(754\) 0 0
\(755\) −119499. 119499.i −0.209638 0.209638i
\(756\) 0 0
\(757\) −34980.2 34980.2i −0.0610423 0.0610423i 0.675927 0.736969i \(-0.263744\pi\)
−0.736969 + 0.675927i \(0.763744\pi\)
\(758\) 0 0
\(759\) −213958. −0.371403
\(760\) 0 0
\(761\) 545745.i 0.942368i 0.882035 + 0.471184i \(0.156173\pi\)
−0.882035 + 0.471184i \(0.843827\pi\)
\(762\) 0 0
\(763\) −180394. + 180394.i −0.309866 + 0.309866i
\(764\) 0 0
\(765\) 24243.3 24243.3i 0.0414256 0.0414256i
\(766\) 0 0
\(767\) 65332.9i 0.111056i
\(768\) 0 0
\(769\) 510362. 0.863030 0.431515 0.902106i \(-0.357979\pi\)
0.431515 + 0.902106i \(0.357979\pi\)
\(770\) 0 0
\(771\) 667972. + 667972.i 1.12370 + 1.12370i
\(772\) 0 0
\(773\) −596763. 596763.i −0.998718 0.998718i 0.00128103 0.999999i \(-0.499592\pi\)
−0.999999 + 0.00128103i \(0.999592\pi\)
\(774\) 0 0
\(775\) 750148. 1.24895
\(776\) 0 0
\(777\) 1.51424e6i 2.50814i
\(778\) 0 0
\(779\) 238987. 238987.i 0.393822 0.393822i
\(780\) 0 0
\(781\) −676897. + 676897.i −1.10974 + 1.10974i
\(782\) 0 0
\(783\) 80632.7i 0.131519i
\(784\) 0 0
\(785\) 140849. 0.228567
\(786\) 0 0
\(787\) 463254. + 463254.i 0.747945 + 0.747945i 0.974093 0.226148i \(-0.0726132\pi\)
−0.226148 + 0.974093i \(0.572613\pi\)
\(788\) 0 0
\(789\) −1.06785e6 1.06785e6i −1.71536 1.71536i
\(790\) 0 0
\(791\) 654644. 1.04629
\(792\) 0 0
\(793\) 31518.0i 0.0501202i
\(794\) 0 0
\(795\) 39396.9 39396.9i 0.0623344 0.0623344i
\(796\) 0 0