Properties

Label 10.4.b.a.9.1
Level 10
Weight 4
Character 10.9
Analytic conductor 0.590
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 10.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.590019100057\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 9.1
Root \(-1.00000i\)
Character \(\chi\) = 10.9
Dual form 10.4.b.a.9.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.00000i q^{2}\) \(+2.00000i q^{3}\) \(-4.00000 q^{4}\) \(+(-5.00000 + 10.0000i) q^{5}\) \(+4.00000 q^{6}\) \(-26.0000i q^{7}\) \(+8.00000i q^{8}\) \(+23.0000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.00000i q^{2}\) \(+2.00000i q^{3}\) \(-4.00000 q^{4}\) \(+(-5.00000 + 10.0000i) q^{5}\) \(+4.00000 q^{6}\) \(-26.0000i q^{7}\) \(+8.00000i q^{8}\) \(+23.0000 q^{9}\) \(+(20.0000 + 10.0000i) q^{10}\) \(-28.0000 q^{11}\) \(-8.00000i q^{12}\) \(+12.0000i q^{13}\) \(-52.0000 q^{14}\) \(+(-20.0000 - 10.0000i) q^{15}\) \(+16.0000 q^{16}\) \(+64.0000i q^{17}\) \(-46.0000i q^{18}\) \(+60.0000 q^{19}\) \(+(20.0000 - 40.0000i) q^{20}\) \(+52.0000 q^{21}\) \(+56.0000i q^{22}\) \(-58.0000i q^{23}\) \(-16.0000 q^{24}\) \(+(-75.0000 - 100.000i) q^{25}\) \(+24.0000 q^{26}\) \(+100.000i q^{27}\) \(+104.000i q^{28}\) \(-90.0000 q^{29}\) \(+(-20.0000 + 40.0000i) q^{30}\) \(-128.000 q^{31}\) \(-32.0000i q^{32}\) \(-56.0000i q^{33}\) \(+128.000 q^{34}\) \(+(260.000 + 130.000i) q^{35}\) \(-92.0000 q^{36}\) \(-236.000i q^{37}\) \(-120.000i q^{38}\) \(-24.0000 q^{39}\) \(+(-80.0000 - 40.0000i) q^{40}\) \(+242.000 q^{41}\) \(-104.000i q^{42}\) \(+362.000i q^{43}\) \(+112.000 q^{44}\) \(+(-115.000 + 230.000i) q^{45}\) \(-116.000 q^{46}\) \(-226.000i q^{47}\) \(+32.0000i q^{48}\) \(-333.000 q^{49}\) \(+(-200.000 + 150.000i) q^{50}\) \(-128.000 q^{51}\) \(-48.0000i q^{52}\) \(-108.000i q^{53}\) \(+200.000 q^{54}\) \(+(140.000 - 280.000i) q^{55}\) \(+208.000 q^{56}\) \(+120.000i q^{57}\) \(+180.000i q^{58}\) \(+20.0000 q^{59}\) \(+(80.0000 + 40.0000i) q^{60}\) \(+542.000 q^{61}\) \(+256.000i q^{62}\) \(-598.000i q^{63}\) \(-64.0000 q^{64}\) \(+(-120.000 - 60.0000i) q^{65}\) \(-112.000 q^{66}\) \(+434.000i q^{67}\) \(-256.000i q^{68}\) \(+116.000 q^{69}\) \(+(260.000 - 520.000i) q^{70}\) \(-1128.00 q^{71}\) \(+184.000i q^{72}\) \(+632.000i q^{73}\) \(-472.000 q^{74}\) \(+(200.000 - 150.000i) q^{75}\) \(-240.000 q^{76}\) \(+728.000i q^{77}\) \(+48.0000i q^{78}\) \(+720.000 q^{79}\) \(+(-80.0000 + 160.000i) q^{80}\) \(+421.000 q^{81}\) \(-484.000i q^{82}\) \(-478.000i q^{83}\) \(-208.000 q^{84}\) \(+(-640.000 - 320.000i) q^{85}\) \(+724.000 q^{86}\) \(-180.000i q^{87}\) \(-224.000i q^{88}\) \(+490.000 q^{89}\) \(+(460.000 + 230.000i) q^{90}\) \(+312.000 q^{91}\) \(+232.000i q^{92}\) \(-256.000i q^{93}\) \(-452.000 q^{94}\) \(+(-300.000 + 600.000i) q^{95}\) \(+64.0000 q^{96}\) \(-1456.00i q^{97}\) \(+666.000i q^{98}\) \(-644.000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut 40q^{10} \) \(\mathstrut -\mathstrut 56q^{11} \) \(\mathstrut -\mathstrut 104q^{14} \) \(\mathstrut -\mathstrut 40q^{15} \) \(\mathstrut +\mathstrut 32q^{16} \) \(\mathstrut +\mathstrut 120q^{19} \) \(\mathstrut +\mathstrut 40q^{20} \) \(\mathstrut +\mathstrut 104q^{21} \) \(\mathstrut -\mathstrut 32q^{24} \) \(\mathstrut -\mathstrut 150q^{25} \) \(\mathstrut +\mathstrut 48q^{26} \) \(\mathstrut -\mathstrut 180q^{29} \) \(\mathstrut -\mathstrut 40q^{30} \) \(\mathstrut -\mathstrut 256q^{31} \) \(\mathstrut +\mathstrut 256q^{34} \) \(\mathstrut +\mathstrut 520q^{35} \) \(\mathstrut -\mathstrut 184q^{36} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 160q^{40} \) \(\mathstrut +\mathstrut 484q^{41} \) \(\mathstrut +\mathstrut 224q^{44} \) \(\mathstrut -\mathstrut 230q^{45} \) \(\mathstrut -\mathstrut 232q^{46} \) \(\mathstrut -\mathstrut 666q^{49} \) \(\mathstrut -\mathstrut 400q^{50} \) \(\mathstrut -\mathstrut 256q^{51} \) \(\mathstrut +\mathstrut 400q^{54} \) \(\mathstrut +\mathstrut 280q^{55} \) \(\mathstrut +\mathstrut 416q^{56} \) \(\mathstrut +\mathstrut 40q^{59} \) \(\mathstrut +\mathstrut 160q^{60} \) \(\mathstrut +\mathstrut 1084q^{61} \) \(\mathstrut -\mathstrut 128q^{64} \) \(\mathstrut -\mathstrut 240q^{65} \) \(\mathstrut -\mathstrut 224q^{66} \) \(\mathstrut +\mathstrut 232q^{69} \) \(\mathstrut +\mathstrut 520q^{70} \) \(\mathstrut -\mathstrut 2256q^{71} \) \(\mathstrut -\mathstrut 944q^{74} \) \(\mathstrut +\mathstrut 400q^{75} \) \(\mathstrut -\mathstrut 480q^{76} \) \(\mathstrut +\mathstrut 1440q^{79} \) \(\mathstrut -\mathstrut 160q^{80} \) \(\mathstrut +\mathstrut 842q^{81} \) \(\mathstrut -\mathstrut 416q^{84} \) \(\mathstrut -\mathstrut 1280q^{85} \) \(\mathstrut +\mathstrut 1448q^{86} \) \(\mathstrut +\mathstrut 980q^{89} \) \(\mathstrut +\mathstrut 920q^{90} \) \(\mathstrut +\mathstrut 624q^{91} \) \(\mathstrut -\mathstrut 904q^{94} \) \(\mathstrut -\mathstrut 600q^{95} \) \(\mathstrut +\mathstrut 128q^{96} \) \(\mathstrut -\mathstrut 1288q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(-1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 0.707107i
\(3\) 2.00000i 0.384900i 0.981307 + 0.192450i \(0.0616434\pi\)
−0.981307 + 0.192450i \(0.938357\pi\)
\(4\) −4.00000 −0.500000
\(5\) −5.00000 + 10.0000i −0.447214 + 0.894427i
\(6\) 4.00000 0.272166
\(7\) 26.0000i 1.40387i −0.712242 0.701934i \(-0.752320\pi\)
0.712242 0.701934i \(-0.247680\pi\)
\(8\) 8.00000i 0.353553i
\(9\) 23.0000 0.851852
\(10\) 20.0000 + 10.0000i 0.632456 + 0.316228i
\(11\) −28.0000 −0.767483 −0.383742 0.923440i \(-0.625365\pi\)
−0.383742 + 0.923440i \(0.625365\pi\)
\(12\) 8.00000i 0.192450i
\(13\) 12.0000i 0.256015i 0.991773 + 0.128008i \(0.0408582\pi\)
−0.991773 + 0.128008i \(0.959142\pi\)
\(14\) −52.0000 −0.992685
\(15\) −20.0000 10.0000i −0.344265 0.172133i
\(16\) 16.0000 0.250000
\(17\) 64.0000i 0.913075i 0.889704 + 0.456538i \(0.150911\pi\)
−0.889704 + 0.456538i \(0.849089\pi\)
\(18\) 46.0000i 0.602350i
\(19\) 60.0000 0.724471 0.362235 0.932087i \(-0.382014\pi\)
0.362235 + 0.932087i \(0.382014\pi\)
\(20\) 20.0000 40.0000i 0.223607 0.447214i
\(21\) 52.0000 0.540349
\(22\) 56.0000i 0.542693i
\(23\) 58.0000i 0.525819i −0.964821 0.262909i \(-0.915318\pi\)
0.964821 0.262909i \(-0.0846821\pi\)
\(24\) −16.0000 −0.136083
\(25\) −75.0000 100.000i −0.600000 0.800000i
\(26\) 24.0000 0.181030
\(27\) 100.000i 0.712778i
\(28\) 104.000i 0.701934i
\(29\) −90.0000 −0.576296 −0.288148 0.957586i \(-0.593039\pi\)
−0.288148 + 0.957586i \(0.593039\pi\)
\(30\) −20.0000 + 40.0000i −0.121716 + 0.243432i
\(31\) −128.000 −0.741596 −0.370798 0.928714i \(-0.620916\pi\)
−0.370798 + 0.928714i \(0.620916\pi\)
\(32\) 32.0000i 0.176777i
\(33\) 56.0000i 0.295405i
\(34\) 128.000 0.645642
\(35\) 260.000 + 130.000i 1.25566 + 0.627829i
\(36\) −92.0000 −0.425926
\(37\) 236.000i 1.04860i −0.851534 0.524299i \(-0.824327\pi\)
0.851534 0.524299i \(-0.175673\pi\)
\(38\) 120.000i 0.512278i
\(39\) −24.0000 −0.0985404
\(40\) −80.0000 40.0000i −0.316228 0.158114i
\(41\) 242.000 0.921806 0.460903 0.887450i \(-0.347526\pi\)
0.460903 + 0.887450i \(0.347526\pi\)
\(42\) 104.000i 0.382084i
\(43\) 362.000i 1.28383i 0.766778 + 0.641913i \(0.221859\pi\)
−0.766778 + 0.641913i \(0.778141\pi\)
\(44\) 112.000 0.383742
\(45\) −115.000 + 230.000i −0.380960 + 0.761919i
\(46\) −116.000 −0.371810
\(47\) 226.000i 0.701393i −0.936489 0.350697i \(-0.885945\pi\)
0.936489 0.350697i \(-0.114055\pi\)
\(48\) 32.0000i 0.0962250i
\(49\) −333.000 −0.970845
\(50\) −200.000 + 150.000i −0.565685 + 0.424264i
\(51\) −128.000 −0.351443
\(52\) 48.0000i 0.128008i
\(53\) 108.000i 0.279905i −0.990158 0.139952i \(-0.955305\pi\)
0.990158 0.139952i \(-0.0446949\pi\)
\(54\) 200.000 0.504010
\(55\) 140.000 280.000i 0.343229 0.686458i
\(56\) 208.000 0.496342
\(57\) 120.000i 0.278849i
\(58\) 180.000i 0.407503i
\(59\) 20.0000 0.0441318 0.0220659 0.999757i \(-0.492976\pi\)
0.0220659 + 0.999757i \(0.492976\pi\)
\(60\) 80.0000 + 40.0000i 0.172133 + 0.0860663i
\(61\) 542.000 1.13764 0.568820 0.822462i \(-0.307400\pi\)
0.568820 + 0.822462i \(0.307400\pi\)
\(62\) 256.000i 0.524388i
\(63\) 598.000i 1.19589i
\(64\) −64.0000 −0.125000
\(65\) −120.000 60.0000i −0.228987 0.114494i
\(66\) −112.000 −0.208883
\(67\) 434.000i 0.791366i 0.918387 + 0.395683i \(0.129492\pi\)
−0.918387 + 0.395683i \(0.870508\pi\)
\(68\) 256.000i 0.456538i
\(69\) 116.000 0.202388
\(70\) 260.000 520.000i 0.443942 0.887884i
\(71\) −1128.00 −1.88548 −0.942739 0.333531i \(-0.891760\pi\)
−0.942739 + 0.333531i \(0.891760\pi\)
\(72\) 184.000i 0.301175i
\(73\) 632.000i 1.01329i 0.862155 + 0.506644i \(0.169114\pi\)
−0.862155 + 0.506644i \(0.830886\pi\)
\(74\) −472.000 −0.741471
\(75\) 200.000 150.000i 0.307920 0.230940i
\(76\) −240.000 −0.362235
\(77\) 728.000i 1.07745i
\(78\) 48.0000i 0.0696786i
\(79\) 720.000 1.02540 0.512698 0.858569i \(-0.328646\pi\)
0.512698 + 0.858569i \(0.328646\pi\)
\(80\) −80.0000 + 160.000i −0.111803 + 0.223607i
\(81\) 421.000 0.577503
\(82\) 484.000i 0.651815i
\(83\) 478.000i 0.632136i −0.948736 0.316068i \(-0.897637\pi\)
0.948736 0.316068i \(-0.102363\pi\)
\(84\) −208.000 −0.270175
\(85\) −640.000 320.000i −0.816679 0.408340i
\(86\) 724.000 0.907801
\(87\) 180.000i 0.221816i
\(88\) 224.000i 0.271346i
\(89\) 490.000 0.583594 0.291797 0.956480i \(-0.405747\pi\)
0.291797 + 0.956480i \(0.405747\pi\)
\(90\) 460.000 + 230.000i 0.538758 + 0.269379i
\(91\) 312.000 0.359412
\(92\) 232.000i 0.262909i
\(93\) 256.000i 0.285440i
\(94\) −452.000 −0.495960
\(95\) −300.000 + 600.000i −0.323993 + 0.647986i
\(96\) 64.0000 0.0680414
\(97\) 1456.00i 1.52407i −0.647538 0.762033i \(-0.724201\pi\)
0.647538 0.762033i \(-0.275799\pi\)
\(98\) 666.000i 0.686491i
\(99\) −644.000 −0.653782
\(100\) 300.000 + 400.000i 0.300000 + 0.400000i
\(101\) −578.000 −0.569437 −0.284719 0.958611i \(-0.591900\pi\)
−0.284719 + 0.958611i \(0.591900\pi\)
\(102\) 256.000i 0.248508i
\(103\) 1462.00i 1.39859i 0.714831 + 0.699297i \(0.246503\pi\)
−0.714831 + 0.699297i \(0.753497\pi\)
\(104\) −96.0000 −0.0905151
\(105\) −260.000 + 520.000i −0.241651 + 0.483303i
\(106\) −216.000 −0.197922
\(107\) 966.000i 0.872773i −0.899759 0.436387i \(-0.856258\pi\)
0.899759 0.436387i \(-0.143742\pi\)
\(108\) 400.000i 0.356389i
\(109\) −370.000 −0.325134 −0.162567 0.986698i \(-0.551977\pi\)
−0.162567 + 0.986698i \(0.551977\pi\)
\(110\) −560.000 280.000i −0.485399 0.242700i
\(111\) 472.000 0.403606
\(112\) 416.000i 0.350967i
\(113\) 528.000i 0.439558i −0.975550 0.219779i \(-0.929466\pi\)
0.975550 0.219779i \(-0.0705336\pi\)
\(114\) 240.000 0.197176
\(115\) 580.000 + 290.000i 0.470307 + 0.235153i
\(116\) 360.000 0.288148
\(117\) 276.000i 0.218087i
\(118\) 40.0000i 0.0312059i
\(119\) 1664.00 1.28184
\(120\) 80.0000 160.000i 0.0608581 0.121716i
\(121\) −547.000 −0.410969
\(122\) 1084.00i 0.804432i
\(123\) 484.000i 0.354803i
\(124\) 512.000 0.370798
\(125\) 1375.00 250.000i 0.983870 0.178885i
\(126\) −1196.00 −0.845620
\(127\) 1534.00i 1.07181i 0.844277 + 0.535907i \(0.180030\pi\)
−0.844277 + 0.535907i \(0.819970\pi\)
\(128\) 128.000i 0.0883883i
\(129\) −724.000 −0.494145
\(130\) −120.000 + 240.000i −0.0809592 + 0.161918i
\(131\) 12.0000 0.00800340 0.00400170 0.999992i \(-0.498726\pi\)
0.00400170 + 0.999992i \(0.498726\pi\)
\(132\) 224.000i 0.147702i
\(133\) 1560.00i 1.01706i
\(134\) 868.000 0.559580
\(135\) −1000.00 500.000i −0.637528 0.318764i
\(136\) −512.000 −0.322821
\(137\) 1224.00i 0.763309i 0.924305 + 0.381655i \(0.124646\pi\)
−0.924305 + 0.381655i \(0.875354\pi\)
\(138\) 232.000i 0.143110i
\(139\) −3100.00 −1.89164 −0.945822 0.324685i \(-0.894742\pi\)
−0.945822 + 0.324685i \(0.894742\pi\)
\(140\) −1040.00 520.000i −0.627829 0.313914i
\(141\) 452.000 0.269966
\(142\) 2256.00i 1.33323i
\(143\) 336.000i 0.196488i
\(144\) 368.000 0.212963
\(145\) 450.000 900.000i 0.257727 0.515455i
\(146\) 1264.00 0.716503
\(147\) 666.000i 0.373679i
\(148\) 944.000i 0.524299i
\(149\) −250.000 −0.137455 −0.0687275 0.997635i \(-0.521894\pi\)
−0.0687275 + 0.997635i \(0.521894\pi\)
\(150\) −300.000 400.000i −0.163299 0.217732i
\(151\) 2152.00 1.15978 0.579892 0.814694i \(-0.303095\pi\)
0.579892 + 0.814694i \(0.303095\pi\)
\(152\) 480.000i 0.256139i
\(153\) 1472.00i 0.777805i
\(154\) 1456.00 0.761869
\(155\) 640.000 1280.00i 0.331652 0.663304i
\(156\) 96.0000 0.0492702
\(157\) 524.000i 0.266368i 0.991091 + 0.133184i \(0.0425201\pi\)
−0.991091 + 0.133184i \(0.957480\pi\)
\(158\) 1440.00i 0.725065i
\(159\) 216.000 0.107735
\(160\) 320.000 + 160.000i 0.158114 + 0.0790569i
\(161\) −1508.00 −0.738180
\(162\) 842.000i 0.408357i
\(163\) 3518.00i 1.69050i −0.534373 0.845249i \(-0.679452\pi\)
0.534373 0.845249i \(-0.320548\pi\)
\(164\) −968.000 −0.460903
\(165\) 560.000 + 280.000i 0.264218 + 0.132109i
\(166\) −956.000 −0.446988
\(167\) 534.000i 0.247438i 0.992317 + 0.123719i \(0.0394822\pi\)
−0.992317 + 0.123719i \(0.960518\pi\)
\(168\) 416.000i 0.191042i
\(169\) 2053.00 0.934456
\(170\) −640.000 + 1280.00i −0.288740 + 0.577480i
\(171\) 1380.00 0.617142
\(172\) 1448.00i 0.641913i
\(173\) 4252.00i 1.86863i 0.356444 + 0.934317i \(0.383989\pi\)
−0.356444 + 0.934317i \(0.616011\pi\)
\(174\) −360.000 −0.156848
\(175\) −2600.00 + 1950.00i −1.12309 + 0.842321i
\(176\) −448.000 −0.191871
\(177\) 40.0000i 0.0169864i
\(178\) 980.000i 0.412664i
\(179\) −2500.00 −1.04390 −0.521952 0.852975i \(-0.674796\pi\)
−0.521952 + 0.852975i \(0.674796\pi\)
\(180\) 460.000 920.000i 0.190480 0.380960i
\(181\) −2578.00 −1.05868 −0.529340 0.848410i \(-0.677561\pi\)
−0.529340 + 0.848410i \(0.677561\pi\)
\(182\) 624.000i 0.254143i
\(183\) 1084.00i 0.437878i
\(184\) 464.000 0.185905
\(185\) 2360.00 + 1180.00i 0.937895 + 0.468948i
\(186\) −512.000 −0.201837
\(187\) 1792.00i 0.700770i
\(188\) 904.000i 0.350697i
\(189\) 2600.00 1.00065
\(190\) 1200.00 + 600.000i 0.458196 + 0.229098i
\(191\) −768.000 −0.290945 −0.145473 0.989362i \(-0.546470\pi\)
−0.145473 + 0.989362i \(0.546470\pi\)
\(192\) 128.000i 0.0481125i
\(193\) 2608.00i 0.972684i −0.873769 0.486342i \(-0.838331\pi\)
0.873769 0.486342i \(-0.161669\pi\)
\(194\) −2912.00 −1.07768
\(195\) 120.000 240.000i 0.0440686 0.0881372i
\(196\) 1332.00 0.485423
\(197\) 5116.00i 1.85025i −0.379659 0.925127i \(-0.623959\pi\)
0.379659 0.925127i \(-0.376041\pi\)
\(198\) 1288.00i 0.462294i
\(199\) 3480.00 1.23965 0.619826 0.784739i \(-0.287203\pi\)
0.619826 + 0.784739i \(0.287203\pi\)
\(200\) 800.000 600.000i 0.282843 0.212132i
\(201\) −868.000 −0.304597
\(202\) 1156.00i 0.402653i
\(203\) 2340.00i 0.809043i
\(204\) 512.000 0.175721
\(205\) −1210.00 + 2420.00i −0.412244 + 0.824488i
\(206\) 2924.00 0.988955
\(207\) 1334.00i 0.447920i
\(208\) 192.000i 0.0640039i
\(209\) −1680.00 −0.556019
\(210\) 1040.00 + 520.000i 0.341747 + 0.170873i
\(211\) 3132.00 1.02188 0.510938 0.859618i \(-0.329298\pi\)
0.510938 + 0.859618i \(0.329298\pi\)
\(212\) 432.000i 0.139952i
\(213\) 2256.00i 0.725721i
\(214\) −1932.00 −0.617144
\(215\) −3620.00 1810.00i −1.14829 0.574144i
\(216\) −800.000 −0.252005
\(217\) 3328.00i 1.04110i
\(218\) 740.000i 0.229904i
\(219\) −1264.00 −0.390015
\(220\) −560.000 + 1120.00i −0.171615 + 0.343229i
\(221\) −768.000 −0.233761
\(222\) 944.000i 0.285392i
\(223\) 62.0000i 0.0186181i 0.999957 + 0.00930903i \(0.00296320\pi\)
−0.999957 + 0.00930903i \(0.997037\pi\)
\(224\) −832.000 −0.248171
\(225\) −1725.00 2300.00i −0.511111 0.681481i
\(226\) −1056.00 −0.310814
\(227\) 5314.00i 1.55376i 0.629651 + 0.776878i \(0.283198\pi\)
−0.629651 + 0.776878i \(0.716802\pi\)
\(228\) 480.000i 0.139424i
\(229\) 190.000 0.0548277 0.0274139 0.999624i \(-0.491273\pi\)
0.0274139 + 0.999624i \(0.491273\pi\)
\(230\) 580.000 1160.00i 0.166279 0.332557i
\(231\) −1456.00 −0.414709
\(232\) 720.000i 0.203751i
\(233\) 2408.00i 0.677053i −0.940957 0.338526i \(-0.890072\pi\)
0.940957 0.338526i \(-0.109928\pi\)
\(234\) 552.000 0.154211
\(235\) 2260.00 + 1130.00i 0.627345 + 0.313673i
\(236\) −80.0000 −0.0220659
\(237\) 1440.00i 0.394675i
\(238\) 3328.00i 0.906396i
\(239\) 5680.00 1.53727 0.768637 0.639685i \(-0.220935\pi\)
0.768637 + 0.639685i \(0.220935\pi\)
\(240\) −320.000 160.000i −0.0860663 0.0430331i
\(241\) −278.000 −0.0743052 −0.0371526 0.999310i \(-0.511829\pi\)
−0.0371526 + 0.999310i \(0.511829\pi\)
\(242\) 1094.00i 0.290599i
\(243\) 3542.00i 0.935059i
\(244\) −2168.00 −0.568820
\(245\) 1665.00 3330.00i 0.434175 0.868351i
\(246\) 968.000 0.250884
\(247\) 720.000i 0.185476i
\(248\) 1024.00i 0.262194i
\(249\) 956.000 0.243309
\(250\) −500.000 2750.00i −0.126491 0.695701i
\(251\) 3252.00 0.817787 0.408893 0.912582i \(-0.365915\pi\)
0.408893 + 0.912582i \(0.365915\pi\)
\(252\) 2392.00i 0.597944i
\(253\) 1624.00i 0.403557i
\(254\) 3068.00 0.757888
\(255\) 640.000 1280.00i 0.157170 0.314340i
\(256\) 256.000 0.0625000
\(257\) 1536.00i 0.372813i −0.982473 0.186407i \(-0.940316\pi\)
0.982473 0.186407i \(-0.0596842\pi\)
\(258\) 1448.00i 0.349413i
\(259\) −6136.00 −1.47209
\(260\) 480.000 + 240.000i 0.114494 + 0.0572468i
\(261\) −2070.00 −0.490919
\(262\) 24.0000i 0.00565926i
\(263\) 4858.00i 1.13900i −0.821991 0.569500i \(-0.807137\pi\)
0.821991 0.569500i \(-0.192863\pi\)
\(264\) 448.000 0.104441
\(265\) 1080.00 + 540.000i 0.250354 + 0.125177i
\(266\) −3120.00 −0.719171
\(267\) 980.000i 0.224626i
\(268\) 1736.00i 0.395683i
\(269\) −2610.00 −0.591578 −0.295789 0.955253i \(-0.595583\pi\)
−0.295789 + 0.955253i \(0.595583\pi\)
\(270\) −1000.00 + 2000.00i −0.225400 + 0.450800i
\(271\) −5168.00 −1.15843 −0.579213 0.815176i \(-0.696640\pi\)
−0.579213 + 0.815176i \(0.696640\pi\)
\(272\) 1024.00i 0.228269i
\(273\) 624.000i 0.138338i
\(274\) 2448.00 0.539741
\(275\) 2100.00 + 2800.00i 0.460490 + 0.613987i
\(276\) −464.000 −0.101194
\(277\) 1924.00i 0.417336i 0.977987 + 0.208668i \(0.0669127\pi\)
−0.977987 + 0.208668i \(0.933087\pi\)
\(278\) 6200.00i 1.33759i
\(279\) −2944.00 −0.631730
\(280\) −1040.00 + 2080.00i −0.221971 + 0.443942i
\(281\) 3042.00 0.645803 0.322901 0.946433i \(-0.395342\pi\)
0.322901 + 0.946433i \(0.395342\pi\)
\(282\) 904.000i 0.190895i
\(283\) 1718.00i 0.360864i −0.983587 0.180432i \(-0.942250\pi\)
0.983587 0.180432i \(-0.0577496\pi\)
\(284\) 4512.00 0.942739
\(285\) −1200.00 600.000i −0.249410 0.124705i
\(286\) −672.000 −0.138938
\(287\) 6292.00i 1.29409i
\(288\) 736.000i 0.150588i
\(289\) 817.000 0.166294
\(290\) −1800.00 900.000i −0.364482 0.182241i
\(291\) 2912.00 0.586613
\(292\) 2528.00i 0.506644i
\(293\) 2292.00i 0.456997i 0.973544 + 0.228498i \(0.0733816\pi\)
−0.973544 + 0.228498i \(0.926618\pi\)
\(294\) −1332.00 −0.264231
\(295\) −100.000 + 200.000i −0.0197364 + 0.0394727i
\(296\) 1888.00 0.370736
\(297\) 2800.00i 0.547045i
\(298\) 500.000i 0.0971954i
\(299\) 696.000 0.134618
\(300\) −800.000 + 600.000i −0.153960 + 0.115470i
\(301\) 9412.00 1.80232
\(302\) 4304.00i 0.820091i
\(303\) 1156.00i 0.219176i
\(304\) 960.000 0.181118
\(305\) −2710.00 + 5420.00i −0.508768 + 1.01754i
\(306\) 2944.00 0.549991
\(307\) 5406.00i 1.00501i −0.864576 0.502503i \(-0.832413\pi\)
0.864576 0.502503i \(-0.167587\pi\)
\(308\) 2912.00i 0.538723i
\(309\) −2924.00 −0.538319
\(310\) −2560.00 1280.00i −0.469027 0.234513i
\(311\) −5688.00 −1.03710 −0.518548 0.855048i \(-0.673527\pi\)
−0.518548 + 0.855048i \(0.673527\pi\)
\(312\) 192.000i 0.0348393i
\(313\) 7352.00i 1.32767i 0.747881 + 0.663833i \(0.231072\pi\)
−0.747881 + 0.663833i \(0.768928\pi\)
\(314\) 1048.00 0.188351
\(315\) 5980.00 + 2990.00i 1.06963 + 0.534817i
\(316\) −2880.00 −0.512698
\(317\) 3484.00i 0.617290i 0.951177 + 0.308645i \(0.0998755\pi\)
−0.951177 + 0.308645i \(0.900124\pi\)
\(318\) 432.000i 0.0761804i
\(319\) 2520.00 0.442298
\(320\) 320.000 640.000i 0.0559017 0.111803i
\(321\) 1932.00 0.335931
\(322\) 3016.00i 0.521972i
\(323\) 3840.00i 0.661496i
\(324\) −1684.00 −0.288752
\(325\) 1200.00 900.000i 0.204812 0.153609i
\(326\) −7036.00 −1.19536
\(327\) 740.000i 0.125144i
\(328\) 1936.00i 0.325908i
\(329\) −5876.00 −0.984664
\(330\) 560.000 1120.00i 0.0934151 0.186830i
\(331\) −7868.00 −1.30654 −0.653269 0.757125i \(-0.726603\pi\)
−0.653269 + 0.757125i \(0.726603\pi\)
\(332\) 1912.00i 0.316068i
\(333\) 5428.00i 0.893251i
\(334\) 1068.00 0.174965
\(335\) −4340.00 2170.00i −0.707819 0.353910i
\(336\) 832.000 0.135087
\(337\) 656.000i 0.106037i −0.998594 0.0530187i \(-0.983116\pi\)
0.998594 0.0530187i \(-0.0168843\pi\)
\(338\) 4106.00i 0.660760i
\(339\) 1056.00 0.169186
\(340\) 2560.00 + 1280.00i 0.408340 + 0.204170i
\(341\) 3584.00 0.569163
\(342\) 2760.00i 0.436385i
\(343\) 260.000i 0.0409291i
\(344\) −2896.00 −0.453901
\(345\) −580.000 + 1160.00i −0.0905106 + 0.181021i
\(346\) 8504.00 1.32132
\(347\) 5754.00i 0.890176i 0.895487 + 0.445088i \(0.146828\pi\)
−0.895487 + 0.445088i \(0.853172\pi\)
\(348\) 720.000i 0.110908i
\(349\) 3110.00 0.477004 0.238502 0.971142i \(-0.423344\pi\)
0.238502 + 0.971142i \(0.423344\pi\)
\(350\) 3900.00 + 5200.00i 0.595611 + 0.794148i
\(351\) −1200.00 −0.182482
\(352\) 896.000i 0.135673i
\(353\) 7808.00i 1.17727i −0.808397 0.588637i \(-0.799665\pi\)
0.808397 0.588637i \(-0.200335\pi\)
\(354\) 80.0000 0.0120112
\(355\) 5640.00 11280.0i 0.843212 1.68642i
\(356\) −1960.00 −0.291797
\(357\) 3328.00i 0.493379i
\(358\) 5000.00i 0.738151i
\(359\) 9240.00 1.35841 0.679204 0.733949i \(-0.262325\pi\)
0.679204 + 0.733949i \(0.262325\pi\)
\(360\) −1840.00 920.000i −0.269379 0.134690i
\(361\) −3259.00 −0.475142
\(362\) 5156.00i 0.748600i
\(363\) 1094.00i 0.158182i
\(364\) −1248.00 −0.179706
\(365\) −6320.00 3160.00i −0.906312 0.453156i
\(366\) 2168.00 0.309626
\(367\) 3214.00i 0.457137i 0.973528 + 0.228569i \(0.0734046\pi\)
−0.973528 + 0.228569i \(0.926595\pi\)
\(368\) 928.000i 0.131455i
\(369\) 5566.00 0.785242
\(370\) 2360.00 4720.00i 0.331596 0.663192i
\(371\) −2808.00 −0.392949
\(372\) 1024.00i 0.142720i
\(373\) 348.000i 0.0483077i −0.999708 0.0241538i \(-0.992311\pi\)
0.999708 0.0241538i \(-0.00768915\pi\)
\(374\) −3584.00 −0.495519
\(375\) 500.000 + 2750.00i 0.0688530 + 0.378692i
\(376\) 1808.00 0.247980
\(377\) 1080.00i 0.147541i
\(378\) 5200.00i 0.707564i
\(379\) −4940.00 −0.669527 −0.334764 0.942302i \(-0.608656\pi\)
−0.334764 + 0.942302i \(0.608656\pi\)
\(380\) 1200.00 2400.00i 0.161997 0.323993i
\(381\) −3068.00 −0.412542
\(382\) 1536.00i 0.205729i
\(383\) 6142.00i 0.819430i 0.912214 + 0.409715i \(0.134372\pi\)
−0.912214 + 0.409715i \(0.865628\pi\)
\(384\) −256.000 −0.0340207
\(385\) −7280.00 3640.00i −0.963697 0.481848i
\(386\) −5216.00 −0.687791
\(387\) 8326.00i 1.09363i
\(388\) 5824.00i 0.762033i
\(389\) −3050.00 −0.397535 −0.198768 0.980047i \(-0.563694\pi\)
−0.198768 + 0.980047i \(0.563694\pi\)
\(390\) −480.000 240.000i −0.0623224 0.0311612i
\(391\) 3712.00 0.480112
\(392\) 2664.00i 0.343246i
\(393\) 24.0000i 0.00308051i
\(394\) −10232.0 −1.30833
\(395\) −3600.00 + 7200.00i −0.458571 + 0.917143i
\(396\) 2576.00 0.326891
\(397\) 5396.00i 0.682160i −0.940034 0.341080i \(-0.889207\pi\)
0.940034 0.341080i \(-0.110793\pi\)
\(398\) 6960.00i 0.876566i
\(399\) 3120.00 0.391467
\(400\) −1200.00 1600.00i −0.150000 0.200000i
\(401\) 14482.0 1.80348 0.901741 0.432276i \(-0.142289\pi\)
0.901741 + 0.432276i \(0.142289\pi\)
\(402\) 1736.00i 0.215383i
\(403\) 1536.00i 0.189860i
\(404\) 2312.00 0.284719
\(405\) −2105.00 + 4210.00i −0.258267 + 0.516535i
\(406\) 4680.00 0.572080
\(407\) 6608.00i 0.804782i
\(408\) 1024.00i 0.124254i
\(409\) 1090.00 0.131778 0.0658888 0.997827i \(-0.479012\pi\)
0.0658888 + 0.997827i \(0.479012\pi\)
\(410\) 4840.00 + 2420.00i 0.583001 + 0.291501i
\(411\) −2448.00 −0.293798
\(412\) 5848.00i 0.699297i
\(413\) 520.000i 0.0619553i
\(414\) −2668.00 −0.316727
\(415\) 4780.00 + 2390.00i 0.565400 + 0.282700i
\(416\) 384.000 0.0452576
\(417\) 6200.00i 0.728094i
\(418\) 3360.00i 0.393165i
\(419\) 7180.00 0.837150 0.418575 0.908182i \(-0.362530\pi\)
0.418575 + 0.908182i \(0.362530\pi\)
\(420\) 1040.00 2080.00i 0.120826 0.241651i
\(421\) −8138.00 −0.942095 −0.471047 0.882108i \(-0.656124\pi\)
−0.471047 + 0.882108i \(0.656124\pi\)
\(422\) 6264.00i 0.722575i
\(423\) 5198.00i 0.597483i
\(424\) 864.000 0.0989612
\(425\) 6400.00 4800.00i 0.730460 0.547845i
\(426\) −4512.00 −0.513162
\(427\) 14092.0i 1.59710i
\(428\) 3864.00i 0.436387i
\(429\) 672.000 0.0756281
\(430\) −3620.00 + 7240.00i −0.405981 + 0.811962i
\(431\) −208.000 −0.0232460 −0.0116230 0.999932i \(-0.503700\pi\)
−0.0116230 + 0.999932i \(0.503700\pi\)
\(432\) 1600.00i 0.178195i
\(433\) 12992.0i 1.44193i 0.692971 + 0.720965i \(0.256301\pi\)
−0.692971 + 0.720965i \(0.743699\pi\)
\(434\) 6656.00 0.736171
\(435\) 1800.00 + 900.000i 0.198399 + 0.0991993i
\(436\) 1480.00 0.162567
\(437\) 3480.00i 0.380940i
\(438\) 2528.00i 0.275782i
\(439\) −1080.00 −0.117416 −0.0587080 0.998275i \(-0.518698\pi\)
−0.0587080 + 0.998275i \(0.518698\pi\)
\(440\) 2240.00 + 1120.00i 0.242700 + 0.121350i
\(441\) −7659.00 −0.827017
\(442\) 1536.00i 0.165294i
\(443\) 9078.00i 0.973609i −0.873511 0.486805i \(-0.838162\pi\)
0.873511 0.486805i \(-0.161838\pi\)
\(444\) −1888.00 −0.201803
\(445\) −2450.00 + 4900.00i −0.260991 + 0.521983i
\(446\) 124.000 0.0131650
\(447\) 500.000i 0.0529065i
\(448\) 1664.00i 0.175484i
\(449\) −14310.0 −1.50408 −0.752039 0.659119i \(-0.770929\pi\)
−0.752039 + 0.659119i \(0.770929\pi\)
\(450\) −4600.00 + 3450.00i −0.481880 + 0.361410i
\(451\) −6776.00 −0.707471
\(452\) 2112.00i 0.219779i
\(453\) 4304.00i 0.446401i
\(454\) 10628.0 1.09867
\(455\) −1560.00 + 3120.00i −0.160734 + 0.321468i
\(456\) −960.000 −0.0985880
\(457\) 2344.00i 0.239929i 0.992778 + 0.119965i \(0.0382781\pi\)
−0.992778 + 0.119965i \(0.961722\pi\)
\(458\) 380.000i 0.0387691i
\(459\) −6400.00 −0.650820
\(460\) −2320.00 1160.00i −0.235153 0.117577i
\(461\) 11382.0 1.14992 0.574959 0.818182i \(-0.305018\pi\)
0.574959 + 0.818182i \(0.305018\pi\)
\(462\) 2912.00i 0.293244i
\(463\) 16062.0i 1.61223i 0.591756 + 0.806117i \(0.298435\pi\)
−0.591756 + 0.806117i \(0.701565\pi\)
\(464\) −1440.00 −0.144074
\(465\) 2560.00 + 1280.00i 0.255306 + 0.127653i
\(466\) −4816.00 −0.478749
\(467\) 17166.0i 1.70096i −0.526008 0.850479i \(-0.676312\pi\)
0.526008 0.850479i \(-0.323688\pi\)
\(468\) 1104.00i 0.109044i
\(469\) 11284.0 1.11097
\(470\) 2260.00 4520.00i 0.221800 0.443600i
\(471\) −1048.00 −0.102525
\(472\) 160.000i 0.0156030i
\(473\) 10136.0i 0.985315i
\(474\) 2880.00 0.279078
\(475\) −4500.00 6000.00i −0.434682 0.579577i
\(476\) −6656.00 −0.640919
\(477\) 2484.00i 0.238437i
\(478\) 11360.0i 1.08702i
\(479\) −7520.00 −0.717323 −0.358661 0.933468i \(-0.616767\pi\)
−0.358661 + 0.933468i \(0.616767\pi\)
\(480\) −320.000 + 640.000i −0.0304290 + 0.0608581i
\(481\) 2832.00 0.268458
\(482\) 556.000i 0.0525417i
\(483\) 3016.00i 0.284126i
\(484\) 2188.00 0.205485
\(485\) 14560.0 + 7280.00i 1.36317 + 0.681583i
\(486\) 7084.00 0.661187
\(487\) 11814.0i 1.09927i 0.835406 + 0.549634i \(0.185233\pi\)
−0.835406 + 0.549634i \(0.814767\pi\)
\(488\) 4336.00i 0.402216i
\(489\) 7036.00 0.650673
\(490\) −6660.00 3330.00i −0.614017 0.307008i
\(491\) 14052.0 1.29156 0.645782 0.763522i \(-0.276532\pi\)
0.645782 + 0.763522i \(0.276532\pi\)
\(492\) 1936.00i 0.177402i
\(493\) 5760.00i 0.526202i
\(494\) 1440.00 0.131151
\(495\) 3220.00 6440.00i 0.292380 0.584761i
\(496\) −2048.00 −0.185399
\(497\) 29328.0i 2.64696i
\(498\) 1912.00i 0.172046i
\(499\) −7620.00 −0.683603 −0.341802 0.939772i \(-0.611037\pi\)
−0.341802 + 0.939772i \(0.611037\pi\)
\(500\) −5500.00 + 1000.00i −0.491935 + 0.0894427i
\(501\) −1068.00 −0.0952390
\(502\) 6504.00i 0.578262i
\(503\) 1818.00i 0.161154i −0.996748 0.0805772i \(-0.974324\pi\)
0.996748 0.0805772i \(-0.0256763\pi\)
\(504\) 4784.00 0.422810
\(505\) 2890.00 5780.00i 0.254660 0.509320i
\(506\) 3248.00 0.285358
\(507\) 4106.00i 0.359672i
\(508\) 6136.00i 0.535907i
\(509\) −17850.0 −1.55440 −0.777198 0.629256i \(-0.783360\pi\)
−0.777198 + 0.629256i \(0.783360\pi\)
\(510\) −2560.00 1280.00i −0.222272 0.111136i
\(511\) 16432.0 1.42252
\(512\) 512.000i 0.0441942i
\(513\) 6000.00i 0.516387i
\(514\) −3072.00 −0.263619
\(515\) −14620.0 7310.00i −1.25094 0.625470i
\(516\) 2896.00 0.247072
\(517\) 6328.00i 0.538308i
\(518\) 12272.0i 1.04093i
\(519\) −8504.00 −0.719237
\(520\) 480.000 960.000i 0.0404796 0.0809592i
\(521\) −19238.0 −1.61772 −0.808860 0.588001i \(-0.799915\pi\)
−0.808860 + 0.588001i \(0.799915\pi\)
\(522\) 4140.00i 0.347132i
\(523\) 6278.00i 0.524891i −0.964947 0.262445i \(-0.915471\pi\)
0.964947 0.262445i \(-0.0845289\pi\)
\(524\) −48.0000 −0.00400170
\(525\) −3900.00 5200.00i −0.324209 0.432279i
\(526\) −9716.00 −0.805395
\(527\) 8192.00i 0.677133i
\(528\) 896.000i 0.0738511i
\(529\) 8803.00 0.723514
\(530\) 1080.00 2160.00i 0.0885136 0.177027i
\(531\) 460.000 0.0375938
\(532\) 6240.00i 0.508531i
\(533\) 2904.00i 0.235997i
\(534\) 1960.00 0.158834
\(535\) 9660.00 + 4830.00i 0.780632 + 0.390316i
\(536\) −3472.00 −0.279790
\(537\) 5000.00i 0.401799i
\(538\) 5220.00i 0.418309i
\(539\) 9324.00 0.745108
\(540\) 4000.00 + 2000.00i 0.318764 + 0.159382i
\(541\) −9818.00 −0.780238 −0.390119 0.920764i \(-0.627566\pi\)
−0.390119 + 0.920764i \(0.627566\pi\)
\(542\) 10336.0i 0.819131i
\(543\) 5156.00i 0.407486i
\(544\) 2048.00 0.161410
\(545\) 1850.00 3700.00i 0.145404 0.290808i
\(546\) 1248.00 0.0978195
\(547\) 12514.0i 0.978172i 0.872236 + 0.489086i \(0.162670\pi\)
−0.872236 + 0.489086i \(0.837330\pi\)
\(548\) 4896.00i 0.381655i
\(549\) 12466.0 0.969100
\(550\) 5600.00 4200.00i 0.434154 0.325616i
\(551\) −5400.00 −0.417509
\(552\) 928.000i 0.0715549i
\(553\) 18720.0i 1.43952i
\(554\) 3848.00 0.295101
\(555\) −2360.00 + 4720.00i −0.180498 + 0.360996i
\(556\) 12400.0 0.945822
\(557\) 10596.0i 0.806045i −0.915190 0.403022i \(-0.867960\pi\)
0.915190 0.403022i \(-0.132040\pi\)
\(558\) 5888.00i 0.446701i
\(559\) −4344.00 −0.328679
\(560\) 4160.00 + 2080.00i 0.313914 + 0.156957i
\(561\) 3584.00 0.269727
\(562\) 6084.00i 0.456651i
\(563\) 14002.0i 1.04816i 0.851669 + 0.524080i \(0.175591\pi\)
−0.851669 + 0.524080i \(0.824409\pi\)
\(564\) −1808.00 −0.134983
\(565\) 5280.00 + 2640.00i 0.393153 + 0.196576i
\(566\) −3436.00 −0.255169
\(567\) 10946.0i 0.810739i
\(568\) 9024.00i 0.666617i
\(569\) 7330.00 0.540052 0.270026 0.962853i \(-0.412968\pi\)
0.270026 + 0.962853i \(0.412968\pi\)
\(570\) −1200.00 + 2400.00i −0.0881798 + 0.176360i
\(571\) 5812.00 0.425963 0.212981 0.977056i \(-0.431683\pi\)
0.212981 + 0.977056i \(0.431683\pi\)
\(572\) 1344.00i 0.0982438i
\(573\) 1536.00i 0.111985i
\(574\) −12584.0 −0.915063
\(575\) −5800.00 + 4350.00i −0.420655 + 0.315491i
\(576\) −1472.00 −0.106481
\(577\) 16736.0i 1.20750i −0.797173 0.603751i \(-0.793672\pi\)
0.797173 0.603751i \(-0.206328\pi\)
\(578\) 1634.00i 0.117587i
\(579\) 5216.00 0.374386
\(580\) −1800.00 + 3600.00i −0.128864 + 0.257727i
\(581\) −12428.0 −0.887436
\(582\) 5824.00i 0.414798i
\(583\) 3024.00i 0.214822i
\(584\) −5056.00 −0.358251
\(585\) −2760.00 1380.00i −0.195063 0.0975316i
\(586\) 4584.00 0.323146
\(587\) 7434.00i 0.522716i 0.965242 + 0.261358i \(0.0841702\pi\)
−0.965242 + 0.261358i \(0.915830\pi\)
\(588\) 2664.00i 0.186839i
\(589\) −7680.00 −0.537265
\(590\) 400.000 + 200.000i 0.0279114 + 0.0139557i
\(591\) 10232.0 0.712163
\(592\) 3776.00i 0.262150i
\(593\) 25872.0i 1.79163i 0.444429 + 0.895814i \(0.353407\pi\)
−0.444429 + 0.895814i \(0.646593\pi\)
\(594\) −5600.00 −0.386820
\(595\) −8320.00 + 16640.0i −0.573255 + 1.14651i
\(596\) 1000.00 0.0687275
\(597\) 6960.00i 0.477142i
\(598\) 1392.00i 0.0951892i
\(599\) 3720.00 0.253748 0.126874 0.991919i \(-0.459506\pi\)
0.126874 + 0.991919i \(0.459506\pi\)
\(600\) 1200.00 + 1600.00i 0.0816497 + 0.108866i
\(601\) −12958.0 −0.879481 −0.439740 0.898125i \(-0.644930\pi\)
−0.439740 + 0.898125i \(0.644930\pi\)
\(602\) 18824.0i 1.27443i
\(603\) 9982.00i 0.674127i
\(604\) −8608.00 −0.579892
\(605\) 2735.00 5470.00i 0.183791 0.367582i
\(606\) −2312.00 −0.154981
\(607\) 7214.00i 0.482384i 0.970477 + 0.241192i \(0.0775384\pi\)
−0.970477 + 0.241192i \(0.922462\pi\)
\(608\) 1920.00i 0.128070i
\(609\) −4680.00 −0.311401
\(610\) 10840.0 + 5420.00i 0.719506 + 0.359753i
\(611\) 2712.00 0.179568
\(612\) 5888.00i 0.388902i
\(613\) 4828.00i 0.318109i −0.987270 0.159055i \(-0.949155\pi\)
0.987270 0.159055i \(-0.0508446\pi\)
\(614\) −10812.0 −0.710646
\(615\) −4840.00 2420.00i −0.317346 0.158673i
\(616\) −5824.00 −0.380934
\(617\) 27656.0i 1.80452i −0.431193 0.902260i \(-0.641907\pi\)
0.431193 0.902260i \(-0.358093\pi\)
\(618\) 5848.00i 0.380649i
\(619\) 21220.0 1.37787 0.688937 0.724821i \(-0.258078\pi\)
0.688937 + 0.724821i \(0.258078\pi\)
\(620\) −2560.00 + 5120.00i −0.165826 + 0.331652i
\(621\) 5800.00 0.374792
\(622\) 11376.0i 0.733338i
\(623\) 12740.0i 0.819289i
\(624\) −384.000 −0.0246351
\(625\) −4375.00 + 15000.0i −0.280000 + 0.960000i
\(626\) 14704.0 0.938802
\(627\) 3360.00i 0.214012i
\(628\) 2096.00i 0.133184i
\(629\) 15104.0 0.957450
\(630\) 5980.00 11960.0i 0.378173 0.756346i
\(631\) 17672.0 1.11491 0.557457 0.830206i \(-0.311777\pi\)
0.557457 + 0.830206i \(0.311777\pi\)
\(632\) 5760.00i 0.362532i
\(633\) 6264.00i 0.393320i
\(634\) 6968.00 0.436490
\(635\) −15340.0 7670.00i −0.958660 0.479330i
\(636\) −864.000 −0.0538677
\(637\) 3996.00i 0.248551i
\(638\) 5040.00i 0.312752i
\(639\) −25944.0 −1.60615
\(640\) −1280.00 640.000i −0.0790569 0.0395285i
\(641\) 7322.00 0.451173 0.225586 0.974223i \(-0.427570\pi\)
0.225586 + 0.974223i \(0.427570\pi\)
\(642\) 3864.00i 0.237539i
\(643\) 8238.00i 0.505249i −0.967564 0.252624i \(-0.918706\pi\)
0.967564 0.252624i \(-0.0812937\pi\)
\(644\) 6032.00 0.369090
\(645\) 3620.00 7240.00i 0.220988 0.441976i
\(646\) 7680.00 0.467749
\(647\) 6426.00i 0.390467i −0.980757 0.195233i \(-0.937454\pi\)
0.980757 0.195233i \(-0.0625465\pi\)
\(648\) 3368.00i 0.204178i
\(649\) −560.000 −0.0338705
\(650\) −1800.00 2400.00i −0.108618 0.144824i
\(651\) −6656.00 −0.400721
\(652\) 14072.0i 0.845249i
\(653\) 5908.00i 0.354055i −0.984206 0.177027i \(-0.943352\pi\)
0.984206 0.177027i \(-0.0566482\pi\)
\(654\) −1480.00 −0.0884902
\(655\) −60.0000 + 120.000i −0.00357923 + 0.00715845i
\(656\) 3872.00 0.230452
\(657\) 14536.0i 0.863171i
\(658\) 11752.0i 0.696262i
\(659\) 26780.0 1.58301 0.791503 0.611166i \(-0.209299\pi\)
0.791503 + 0.611166i \(0.209299\pi\)
\(660\) −2240.00 1120.00i −0.132109 0.0660545i
\(661\) −24538.0 −1.44390 −0.721950 0.691945i \(-0.756754\pi\)
−0.721950 + 0.691945i \(0.756754\pi\)
\(662\) 15736.0i 0.923863i
\(663\) 1536.00i 0.0899748i
\(664\) 3824.00 0.223494
\(665\) 15600.0 + 7800.00i 0.909687 + 0.454844i
\(666\) −10856.0 −0.631624
\(667\) 5220.00i 0.303027i
\(668\) 2136.00i 0.123719i
\(669\) −124.000 −0.00716609
\(670\) −4340.00 + 8680.00i −0.250252 + 0.500504i
\(671\) −15176.0 −0.873119
\(672\) 1664.00i 0.0955211i
\(673\) 28848.0i 1.65232i −0.563439 0.826158i \(-0.690522\pi\)
0.563439 0.826158i \(-0.309478\pi\)
\(674\) −1312.00 −0.0749798
\(675\) 10000.0 7500.00i 0.570222 0.427667i
\(676\) −8212.00 −0.467228
\(677\) 26884.0i 1.52620i 0.646282 + 0.763099i \(0.276323\pi\)
−0.646282 + 0.763099i \(0.723677\pi\)
\(678\) 2112.00i 0.119633i
\(679\) −37856.0 −2.13959
\(680\) 2560.00 5120.00i 0.144370 0.288740i
\(681\) −10628.0 −0.598041
\(682\) 7168.00i 0.402459i
\(683\) 14282.0i 0.800125i 0.916488 + 0.400063i \(0.131012\pi\)
−0.916488 + 0.400063i \(0.868988\pi\)
\(684\) −5520.00 −0.308571
\(685\) −12240.0 6120.00i −0.682725 0.341362i
\(686\) −520.000 −0.0289412
\(687\) 380.000i 0.0211032i
\(688\) 5792.00i 0.320956i
\(689\) 1296.00 0.0716599
\(690\) 2320.00 + 1160.00i 0.128001 + 0.0640006i
\(691\) −3428.00 −0.188723 −0.0943613 0.995538i \(-0.530081\pi\)
−0.0943613 + 0.995538i \(0.530081\pi\)
\(692\) 17008.0i 0.934317i
\(693\) 16744.0i 0.917824i
\(694\) 11508.0 0.629449
\(695\) 15500.0 31000.0i 0.845969 1.69194i
\(696\) 1440.00 0.0784239
\(697\) 15488.0i 0.841678i
\(698\) 6220.00i 0.337293i
\(699\) 4816.00 0.260598
\(700\) 10400.0 7800.00i 0.561547 0.421160i
\(701\) 26942.0 1.45162 0.725810 0.687895i \(-0.241465\pi\)
0.725810 + 0.687895i \(0.241465\pi\)
\(702\) 2400.00i 0.129034i
\(703\) 14160.0i 0.759679i
\(704\) 1792.00 0.0959354
\(705\) −2260.00 + 4520.00i −0.120733 + 0.241465i
\(706\) −15616.0 −0.832459
\(707\) 15028.0i 0.799415i
\(708\) 160.000i 0.00849318i
\(709\) 1950.00 0.103292 0.0516458 0.998665i \(-0.483553\pi\)
0.0516458 + 0.998665i \(0.483553\pi\)
\(710\) −22560.0 11280.0i −1.19248 0.596241i
\(711\) 16560.0 0.873486
\(712\) 3920.00i 0.206332i
\(713\) 7424.00i 0.389945i
\(714\) 6656.00 0.348872
\(715\) 3360.00 + 1680.00i 0.175744 + 0.0878719i
\(716\) 10000.0 0.521952
\(717\) 11360.0i 0.591697i
\(718\) 18480.0i 0.960540i
\(719\) −12080.0 −0.626576 −0.313288 0.949658i \(-0.601430\pi\)
−0.313288 + 0.949658i \(0.601430\pi\)
\(720\) −1840.00 + 3680.00i −0.0952399 + 0.190480i
\(721\) 38012.0 1.96344
\(722\) 6518.00i 0.335976i
\(723\) 556.000i 0.0286001i
\(724\) 10312.0 0.529340
\(725\) 6750.00 + 9000.00i 0.345778 + 0.461037i
\(726\) −2188.00 −0.111852
\(727\) 17226.0i 0.878785i −0.898295 0.439393i \(-0.855194\pi\)
0.898295 0.439393i \(-0.144806\pi\)
\(728\) 2496.00i 0.127071i
\(729\) 4283.00 0.217599
\(730\) −6320.00 + 12640.0i −0.320430 + 0.640859i
\(731\) −23168.0 −1.17223
\(732\) 4336.00i 0.218939i
\(733\) 788.000i 0.0397073i −0.999803 0.0198536i \(-0.993680\pi\)
0.999803 0.0198536i \(-0.00632003\pi\)
\(734\) 6428.00 0.323245
\(735\) 6660.00 + 3330.00i 0.334228 + 0.167114i
\(736\) −1856.00 −0.0929525
\(737\) 12152.0i 0.607360i
\(738\) 11132.0i 0.555250i
\(739\) 2060.00 0.102542 0.0512709 0.998685i \(-0.483673\pi\)
0.0512709 + 0.998685i \(0.483673\pi\)
\(740\) −9440.00 4720.00i −0.468948 0.234474i
\(741\) −1440.00 −0.0713896
\(742\) 5616.00i 0.277857i
\(743\) 3258.00i 0.160867i −0.996760 0.0804337i \(-0.974369\pi\)
0.996760 0.0804337i \(-0.0256305\pi\)
\(744\) 2048.00 0.100918
\(745\) 1250.00 2500.00i 0.0614718 0.122944i
\(746\) −696.000 −0.0341587
\(747\) 10994.0i 0.538487i
\(748\) 7168.00i 0.350385i
\(749\) −25116.0 −1.22526
\(750\) 5500.00 1000.00i 0.267775 0.0486864i
\(751\) −4528.00 −0.220012 −0.110006 0.993931i \(-0.535087\pi\)
−0.110006 + 0.993931i \(0.535087\pi\)
\(752\) 3616.00i 0.175348i
\(753\) 6504.00i 0.314766i
\(754\) −2160.00 −0.104327
\(755\) −10760.0 + 21520.0i −0.518671 + 1.03734i
\(756\) −10400.0 −0.500323
\(757\) 18236.0i 0.875560i −0.899082 0.437780i \(-0.855765\pi\)
0.899082 0.437780i \(-0.144235\pi\)
\(758\) 9880.00i 0.473427i
\(759\) −3248.00 −0.155329
\(760\) −4800.00 2400.00i −0.229098 0.114549i
\(761\) −18678.0 −0.889720 −0.444860 0.895600i \(-0.646747\pi\)
−0.444860 + 0.895600i \(0.646747\pi\)
\(762\) 6136.00i 0.291711i
\(763\) 9620.00i 0.456445i
\(764\) 3072.00 0.145473
\(765\) −14720.0 7360.00i −0.695690 0.347845i
\(766\) 12284.0 0.579424
\(767\) 240.000i 0.0112984i
\(768\) 512.000i 0.0240563i
\(769\) −27390.0 −1.28441 −0.642203 0.766534i \(-0.721980\pi\)
−0.642203 + 0.766534i \(0.721980\pi\)
\(770\) −7280.00 + 14560.0i −0.340718 + 0.681436i
\(771\) 3072.00 0.143496
\(772\) 10432.0i 0.486342i
\(773\) 9252.00i 0.430493i 0.976560 + 0.215247i \(0.0690555\pi\)
−0.976560 + 0.215247i \(0.930944\pi\)
\(774\) 16652.0 0.773312
\(775\) 9600.00 + 12800.0i 0.444958 + 0.593277i
\(776\) 11648.0 0.538839
\(777\) 12272.0i 0.566609i
\(778\) 6100.00i 0.281100i
\(779\) 14520.0 0.667822
\(780\) −480.000 + 960.000i −0.0220343 + 0.0440686i
\(781\) 31584.0 1.44707
\(782\) 7424.00i 0.339491i
\(783\) 9000.00i 0.410771i
\(784\) −5328.00 −0.242711
\(785\) −5240.00 2620.00i −0.238247 0.119123i
\(786\) 48.0000 0.00217825
\(787\) 5726.00i 0.259352i −0.991556 0.129676i \(-0.958606\pi\)
0.991556 0.129676i \(-0.0413937\pi\)
\(788\) 20464.0i 0.925127i
\(789\) 9716.00 0.438401
\(790\) 14400.0 + 7200.00i 0.648518 + 0.324259i
\(791\) −13728.0 −0.617082
\(792\) 5152.00i 0.231147i
\(793\) 6504.00i 0.291253i
\(794\) −10792.0 −0.482360
\(795\) −1080.00 + 2160.00i −0.0481807 + 0.0963614i
\(796\) −13920.0 −0.619826