Properties

Label 147.6.c.c.146.5
Level $147$
Weight $6$
Character 147.146
Analytic conductor $23.576$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.5764215125\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + 7244325760 x^{4} - 29387167488 x^{2} + 90230547456 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{8}\cdot 7^{4} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.5
Root \(3.16536 + 1.82752i\) of defining polynomial
Character \(\chi\) \(=\) 147.146
Dual form 147.6.c.c.146.11

$q$-expansion

\(f(q)\) \(=\) \(q-3.65505i q^{2} +(-15.5635 + 0.882561i) q^{3} +18.6406 q^{4} +74.3244 q^{5} +(3.22580 + 56.8851i) q^{6} -185.094i q^{8} +(241.442 - 27.4714i) q^{9} +O(q^{10})\) \(q-3.65505i q^{2} +(-15.5635 + 0.882561i) q^{3} +18.6406 q^{4} +74.3244 q^{5} +(3.22580 + 56.8851i) q^{6} -185.094i q^{8} +(241.442 - 27.4714i) q^{9} -271.659i q^{10} +39.3914i q^{11} +(-290.113 + 16.4515i) q^{12} +589.288i q^{13} +(-1156.74 + 65.5958i) q^{15} -80.0263 q^{16} +1237.51 q^{17} +(-100.409 - 882.482i) q^{18} +2767.79i q^{19} +1385.45 q^{20} +143.977 q^{22} +463.253i q^{23} +(163.357 + 2880.70i) q^{24} +2399.11 q^{25} +2153.88 q^{26} +(-3733.43 + 640.637i) q^{27} -5294.57i q^{29} +(239.756 + 4227.95i) q^{30} -2846.74i q^{31} -5630.50i q^{32} +(-34.7653 - 613.066i) q^{33} -4523.16i q^{34} +(4500.64 - 512.084i) q^{36} +7847.11 q^{37} +10116.4 q^{38} +(-520.083 - 9171.36i) q^{39} -13757.0i q^{40} +12162.5 q^{41} +5350.18 q^{43} +734.281i q^{44} +(17945.0 - 2041.79i) q^{45} +1693.21 q^{46} +6755.99 q^{47} +(1245.49 - 70.6281i) q^{48} -8768.86i q^{50} +(-19259.9 + 1092.18i) q^{51} +10984.7i q^{52} -16011.8i q^{53} +(2341.56 + 13645.9i) q^{54} +2927.74i q^{55} +(-2442.74 - 43076.3i) q^{57} -19351.9 q^{58} +7746.64 q^{59} +(-21562.4 + 1222.75i) q^{60} +5617.58i q^{61} -10405.0 q^{62} -23140.6 q^{64} +43798.5i q^{65} +(-2240.79 + 127.069i) q^{66} -12887.4 q^{67} +23068.0 q^{68} +(-408.849 - 7209.82i) q^{69} +60637.7i q^{71} +(-5084.79 - 44689.5i) q^{72} -51641.4i q^{73} -28681.6i q^{74} +(-37338.5 + 2117.36i) q^{75} +51593.3i q^{76} +(-33521.7 + 1900.93i) q^{78} +67372.2 q^{79} -5947.90 q^{80} +(57539.6 - 13265.5i) q^{81} -44454.5i q^{82} -8712.06 q^{83} +91977.1 q^{85} -19555.1i q^{86} +(4672.78 + 82401.9i) q^{87} +7291.11 q^{88} -18112.0 q^{89} +(-7462.85 - 65589.9i) q^{90} +8635.34i q^{92} +(2512.42 + 44305.1i) q^{93} -24693.4i q^{94} +205714. i q^{95} +(4969.26 + 87630.1i) q^{96} -18641.1i q^{97} +(1082.14 + 9510.75i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 172 q^{4} + 1212 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 172 q^{4} + 1212 q^{9} + 1188 q^{15} + 5716 q^{16} + 876 q^{18} - 21900 q^{22} + 13156 q^{25} - 900 q^{30} - 15132 q^{36} + 20932 q^{37} + 34836 q^{39} + 111052 q^{43} - 163392 q^{46} - 63192 q^{51} - 31368 q^{57} + 83412 q^{58} - 120132 q^{60} - 158884 q^{64} + 204404 q^{67} - 661728 q^{72} - 277512 q^{78} + 502616 q^{79} - 358524 q^{81} + 205152 q^{85} + 719028 q^{88} - 35352 q^{93} + 215472 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.65505i 0.646127i −0.946377 0.323064i \(-0.895287\pi\)
0.946377 0.323064i \(-0.104713\pi\)
\(3\) −15.5635 + 0.882561i −0.998396 + 0.0566163i
\(4\) 18.6406 0.582520
\(5\) 74.3244 1.32955 0.664777 0.747042i \(-0.268526\pi\)
0.664777 + 0.747042i \(0.268526\pi\)
\(6\) 3.22580 + 56.8851i 0.0365813 + 0.645091i
\(7\) 0 0
\(8\) 185.094i 1.02251i
\(9\) 241.442 27.4714i 0.993589 0.113051i
\(10\) 271.659i 0.859061i
\(11\) 39.3914i 0.0981567i 0.998795 + 0.0490783i \(0.0156284\pi\)
−0.998795 + 0.0490783i \(0.984372\pi\)
\(12\) −290.113 + 16.4515i −0.581586 + 0.0329801i
\(13\) 589.288i 0.967096i 0.875318 + 0.483548i \(0.160652\pi\)
−0.875318 + 0.483548i \(0.839348\pi\)
\(14\) 0 0
\(15\) −1156.74 + 65.5958i −1.32742 + 0.0752745i
\(16\) −80.0263 −0.0781507
\(17\) 1237.51 1.03855 0.519274 0.854608i \(-0.326203\pi\)
0.519274 + 0.854608i \(0.326203\pi\)
\(18\) −100.409 882.482i −0.0730453 0.641985i
\(19\) 2767.79i 1.75893i 0.475964 + 0.879465i \(0.342099\pi\)
−0.475964 + 0.879465i \(0.657901\pi\)
\(20\) 1385.45 0.774492
\(21\) 0 0
\(22\) 143.977 0.0634217
\(23\) 463.253i 0.182599i 0.995823 + 0.0912997i \(0.0291021\pi\)
−0.995823 + 0.0912997i \(0.970898\pi\)
\(24\) 163.357 + 2880.70i 0.0578907 + 1.02087i
\(25\) 2399.11 0.767716
\(26\) 2153.88 0.624867
\(27\) −3733.43 + 640.637i −0.985595 + 0.169123i
\(28\) 0 0
\(29\) 5294.57i 1.16906i −0.811373 0.584529i \(-0.801279\pi\)
0.811373 0.584529i \(-0.198721\pi\)
\(30\) 239.756 + 4227.95i 0.0486369 + 0.857683i
\(31\) 2846.74i 0.532039i −0.963968 0.266019i \(-0.914291\pi\)
0.963968 0.266019i \(-0.0857085\pi\)
\(32\) 5630.50i 0.972014i
\(33\) −34.7653 613.066i −0.00555727 0.0979992i
\(34\) 4523.16i 0.671034i
\(35\) 0 0
\(36\) 4500.64 512.084i 0.578785 0.0658545i
\(37\) 7847.11 0.942336 0.471168 0.882044i \(-0.343833\pi\)
0.471168 + 0.882044i \(0.343833\pi\)
\(38\) 10116.4 1.13649
\(39\) −520.083 9171.36i −0.0547534 0.965544i
\(40\) 13757.0i 1.35948i
\(41\) 12162.5 1.12996 0.564980 0.825105i \(-0.308884\pi\)
0.564980 + 0.825105i \(0.308884\pi\)
\(42\) 0 0
\(43\) 5350.18 0.441262 0.220631 0.975357i \(-0.429188\pi\)
0.220631 + 0.975357i \(0.429188\pi\)
\(44\) 734.281i 0.0571782i
\(45\) 17945.0 2041.79i 1.32103 0.150307i
\(46\) 1693.21 0.117982
\(47\) 6755.99 0.446112 0.223056 0.974806i \(-0.428397\pi\)
0.223056 + 0.974806i \(0.428397\pi\)
\(48\) 1245.49 70.6281i 0.0780253 0.00442460i
\(49\) 0 0
\(50\) 8768.86i 0.496042i
\(51\) −19259.9 + 1092.18i −1.03688 + 0.0587987i
\(52\) 10984.7i 0.563352i
\(53\) 16011.8i 0.782977i −0.920183 0.391489i \(-0.871960\pi\)
0.920183 0.391489i \(-0.128040\pi\)
\(54\) 2341.56 + 13645.9i 0.109275 + 0.636820i
\(55\) 2927.74i 0.130505i
\(56\) 0 0
\(57\) −2442.74 43076.3i −0.0995841 1.75611i
\(58\) −19351.9 −0.755360
\(59\) 7746.64 0.289723 0.144862 0.989452i \(-0.453726\pi\)
0.144862 + 0.989452i \(0.453726\pi\)
\(60\) −21562.4 + 1222.75i −0.773250 + 0.0438489i
\(61\) 5617.58i 0.193297i 0.995319 + 0.0966484i \(0.0308122\pi\)
−0.995319 + 0.0966484i \(0.969188\pi\)
\(62\) −10405.0 −0.343765
\(63\) 0 0
\(64\) −23140.6 −0.706195
\(65\) 43798.5i 1.28581i
\(66\) −2240.79 + 127.069i −0.0633199 + 0.00359070i
\(67\) −12887.4 −0.350734 −0.175367 0.984503i \(-0.556111\pi\)
−0.175367 + 0.984503i \(0.556111\pi\)
\(68\) 23068.0 0.604975
\(69\) −408.849 7209.82i −0.0103381 0.182306i
\(70\) 0 0
\(71\) 60637.7i 1.42757i 0.700366 + 0.713784i \(0.253020\pi\)
−0.700366 + 0.713784i \(0.746980\pi\)
\(72\) −5084.79 44689.5i −0.115596 1.01595i
\(73\) 51641.4i 1.13420i −0.823648 0.567101i \(-0.808065\pi\)
0.823648 0.567101i \(-0.191935\pi\)
\(74\) 28681.6i 0.608869i
\(75\) −37338.5 + 2117.36i −0.766484 + 0.0434652i
\(76\) 51593.3i 1.02461i
\(77\) 0 0
\(78\) −33521.7 + 1900.93i −0.623864 + 0.0353776i
\(79\) 67372.2 1.21454 0.607272 0.794494i \(-0.292264\pi\)
0.607272 + 0.794494i \(0.292264\pi\)
\(80\) −5947.90 −0.103906
\(81\) 57539.6 13265.5i 0.974439 0.224652i
\(82\) 44454.5i 0.730097i
\(83\) −8712.06 −0.138812 −0.0694058 0.997589i \(-0.522110\pi\)
−0.0694058 + 0.997589i \(0.522110\pi\)
\(84\) 0 0
\(85\) 91977.1 1.38081
\(86\) 19555.1i 0.285112i
\(87\) 4672.78 + 82401.9i 0.0661877 + 1.16718i
\(88\) 7291.11 0.100366
\(89\) −18112.0 −0.242378 −0.121189 0.992629i \(-0.538671\pi\)
−0.121189 + 0.992629i \(0.538671\pi\)
\(90\) −7462.85 65589.9i −0.0971177 0.853554i
\(91\) 0 0
\(92\) 8635.34i 0.106368i
\(93\) 2512.42 + 44305.1i 0.0301221 + 0.531185i
\(94\) 24693.4i 0.288245i
\(95\) 205714.i 2.33859i
\(96\) 4969.26 + 87630.1i 0.0550318 + 0.970454i
\(97\) 18641.1i 0.201160i −0.994929 0.100580i \(-0.967930\pi\)
0.994929 0.100580i \(-0.0320698\pi\)
\(98\) 0 0
\(99\) 1082.14 + 9510.75i 0.0110967 + 0.0975274i
\(100\) 44721.0 0.447210
\(101\) −170598. −1.66407 −0.832034 0.554725i \(-0.812824\pi\)
−0.832034 + 0.554725i \(0.812824\pi\)
\(102\) 3991.96 + 70395.9i 0.0379914 + 0.669957i
\(103\) 58887.8i 0.546931i −0.961882 0.273465i \(-0.911830\pi\)
0.961882 0.273465i \(-0.0881699\pi\)
\(104\) 109074. 0.988864
\(105\) 0 0
\(106\) −58523.7 −0.505903
\(107\) 147582.i 1.24616i −0.782157 0.623082i \(-0.785880\pi\)
0.782157 0.623082i \(-0.214120\pi\)
\(108\) −69593.5 + 11941.9i −0.574129 + 0.0985175i
\(109\) 26156.0 0.210865 0.105433 0.994426i \(-0.466377\pi\)
0.105433 + 0.994426i \(0.466377\pi\)
\(110\) 10701.0 0.0843226
\(111\) −122128. + 6925.56i −0.940824 + 0.0533516i
\(112\) 0 0
\(113\) 19094.4i 0.140672i 0.997523 + 0.0703362i \(0.0224072\pi\)
−0.997523 + 0.0703362i \(0.977593\pi\)
\(114\) −157446. + 8928.33i −1.13467 + 0.0643440i
\(115\) 34431.0i 0.242776i
\(116\) 98694.2i 0.681000i
\(117\) 16188.6 + 142279.i 0.109331 + 0.960896i
\(118\) 28314.3i 0.187198i
\(119\) 0 0
\(120\) 12141.4 + 214106.i 0.0769688 + 1.35730i
\(121\) 159499. 0.990365
\(122\) 20532.5 0.124894
\(123\) −189290. + 10734.1i −1.12815 + 0.0639741i
\(124\) 53065.0i 0.309923i
\(125\) −53951.2 −0.308835
\(126\) 0 0
\(127\) −42178.1 −0.232048 −0.116024 0.993246i \(-0.537015\pi\)
−0.116024 + 0.993246i \(0.537015\pi\)
\(128\) 95596.2i 0.515722i
\(129\) −83267.2 + 4721.86i −0.440555 + 0.0249827i
\(130\) 160085. 0.830794
\(131\) −283072. −1.44118 −0.720590 0.693361i \(-0.756129\pi\)
−0.720590 + 0.693361i \(0.756129\pi\)
\(132\) −648.048 11427.9i −0.00323722 0.0570865i
\(133\) 0 0
\(134\) 47104.0i 0.226619i
\(135\) −277485. + 47615.0i −1.31040 + 0.224858i
\(136\) 229055.i 1.06192i
\(137\) 263686.i 1.20029i 0.799891 + 0.600145i \(0.204890\pi\)
−0.799891 + 0.600145i \(0.795110\pi\)
\(138\) −26352.2 + 1494.36i −0.117793 + 0.00667972i
\(139\) 363744.i 1.59683i 0.602108 + 0.798415i \(0.294328\pi\)
−0.602108 + 0.798415i \(0.705672\pi\)
\(140\) 0 0
\(141\) −105147. + 5962.57i −0.445397 + 0.0252572i
\(142\) 221634. 0.922390
\(143\) −23212.9 −0.0949269
\(144\) −19321.7 + 2198.43i −0.0776497 + 0.00883501i
\(145\) 393516.i 1.55433i
\(146\) −188752. −0.732839
\(147\) 0 0
\(148\) 146275. 0.548929
\(149\) 385877.i 1.42391i 0.702224 + 0.711957i \(0.252191\pi\)
−0.702224 + 0.711957i \(0.747809\pi\)
\(150\) 7739.06 + 136474.i 0.0280841 + 0.495246i
\(151\) −276533. −0.986970 −0.493485 0.869754i \(-0.664277\pi\)
−0.493485 + 0.869754i \(0.664277\pi\)
\(152\) 512300. 1.79852
\(153\) 298787. 33996.1i 1.03189 0.117409i
\(154\) 0 0
\(155\) 211582.i 0.707375i
\(156\) −9694.67 170960.i −0.0318949 0.562449i
\(157\) 378991.i 1.22710i −0.789656 0.613550i \(-0.789741\pi\)
0.789656 0.613550i \(-0.210259\pi\)
\(158\) 246248.i 0.784749i
\(159\) 14131.3 + 249198.i 0.0443293 + 0.781722i
\(160\) 418484.i 1.29235i
\(161\) 0 0
\(162\) −48486.0 210310.i −0.145154 0.629611i
\(163\) −231513. −0.682505 −0.341252 0.939972i \(-0.610851\pi\)
−0.341252 + 0.939972i \(0.610851\pi\)
\(164\) 226717. 0.658224
\(165\) −2583.91 45565.8i −0.00738869 0.130295i
\(166\) 31843.0i 0.0896899i
\(167\) −173708. −0.481981 −0.240990 0.970527i \(-0.577472\pi\)
−0.240990 + 0.970527i \(0.577472\pi\)
\(168\) 0 0
\(169\) 24032.3 0.0647260
\(170\) 336181.i 0.892176i
\(171\) 76034.9 + 668260.i 0.198849 + 1.74765i
\(172\) 99730.7 0.257044
\(173\) −490510. −1.24604 −0.623021 0.782205i \(-0.714095\pi\)
−0.623021 + 0.782205i \(0.714095\pi\)
\(174\) 301183. 17079.2i 0.754148 0.0427657i
\(175\) 0 0
\(176\) 3152.35i 0.00767101i
\(177\) −120564. + 6836.88i −0.289259 + 0.0164031i
\(178\) 66200.4i 0.156607i
\(179\) 641321.i 1.49604i −0.663677 0.748019i \(-0.731005\pi\)
0.663677 0.748019i \(-0.268995\pi\)
\(180\) 334507. 38060.3i 0.769527 0.0875571i
\(181\) 46939.3i 0.106498i 0.998581 + 0.0532489i \(0.0169577\pi\)
−0.998581 + 0.0532489i \(0.983042\pi\)
\(182\) 0 0
\(183\) −4957.85 87428.9i −0.0109437 0.192987i
\(184\) 85745.4 0.186709
\(185\) 583232. 1.25289
\(186\) 161937. 9183.01i 0.343213 0.0194627i
\(187\) 48747.3i 0.101940i
\(188\) 125936. 0.259869
\(189\) 0 0
\(190\) 751894. 1.51103
\(191\) 761400.i 1.51018i 0.655620 + 0.755091i \(0.272407\pi\)
−0.655620 + 0.755091i \(0.727593\pi\)
\(192\) 360148. 20423.0i 0.705062 0.0399821i
\(193\) 556313. 1.07504 0.537522 0.843250i \(-0.319361\pi\)
0.537522 + 0.843250i \(0.319361\pi\)
\(194\) −68133.9 −0.129975
\(195\) −38654.8 681656.i −0.0727976 1.28374i
\(196\) 0 0
\(197\) 545896.i 1.00218i −0.865396 0.501088i \(-0.832933\pi\)
0.865396 0.501088i \(-0.167067\pi\)
\(198\) 34762.2 3955.26i 0.0630151 0.00716988i
\(199\) 211201.i 0.378062i 0.981971 + 0.189031i \(0.0605346\pi\)
−0.981971 + 0.189031i \(0.939465\pi\)
\(200\) 444061.i 0.784996i
\(201\) 200572. 11373.9i 0.350171 0.0198573i
\(202\) 623544.i 1.07520i
\(203\) 0 0
\(204\) −359017. + 20358.9i −0.604004 + 0.0342514i
\(205\) 903969. 1.50234
\(206\) −215238. −0.353387
\(207\) 12726.2 + 111849.i 0.0206430 + 0.181429i
\(208\) 47158.6i 0.0755792i
\(209\) −109027. −0.172651
\(210\) 0 0
\(211\) −670640. −1.03701 −0.518506 0.855074i \(-0.673512\pi\)
−0.518506 + 0.855074i \(0.673512\pi\)
\(212\) 298469.i 0.456100i
\(213\) −53516.5 943732.i −0.0808236 1.42528i
\(214\) −539420. −0.805180
\(215\) 397649. 0.586683
\(216\) 118578. + 691035.i 0.172930 + 1.00778i
\(217\) 0 0
\(218\) 95601.5i 0.136246i
\(219\) 45576.7 + 803718.i 0.0642144 + 1.13238i
\(220\) 54575.0i 0.0760216i
\(221\) 729250.i 1.00437i
\(222\) 25313.2 + 446384.i 0.0344719 + 0.607892i
\(223\) 18729.0i 0.0252204i −0.999920 0.0126102i \(-0.995986\pi\)
0.999920 0.0126102i \(-0.00401406\pi\)
\(224\) 0 0
\(225\) 579247. 65906.9i 0.762794 0.0867910i
\(226\) 69790.8 0.0908923
\(227\) 447047. 0.575822 0.287911 0.957657i \(-0.407039\pi\)
0.287911 + 0.957657i \(0.407039\pi\)
\(228\) −45534.2 802970.i −0.0580097 1.02297i
\(229\) 22000.4i 0.0277231i −0.999904 0.0138616i \(-0.995588\pi\)
0.999904 0.0138616i \(-0.00441241\pi\)
\(230\) 125847. 0.156864
\(231\) 0 0
\(232\) −979993. −1.19537
\(233\) 533090.i 0.643296i −0.946859 0.321648i \(-0.895763\pi\)
0.946859 0.321648i \(-0.104237\pi\)
\(234\) 520036. 59170.0i 0.620861 0.0706418i
\(235\) 502135. 0.593131
\(236\) 144402. 0.168770
\(237\) −1.04854e6 + 59460.1i −1.21259 + 0.0687629i
\(238\) 0 0
\(239\) 269068.i 0.304697i −0.988327 0.152348i \(-0.951316\pi\)
0.988327 0.152348i \(-0.0486836\pi\)
\(240\) 92569.9 5249.39i 0.103739 0.00588275i
\(241\) 266824.i 0.295926i 0.988993 + 0.147963i \(0.0472716\pi\)
−0.988993 + 0.147963i \(0.952728\pi\)
\(242\) 582977.i 0.639902i
\(243\) −883808. + 257239.i −0.960157 + 0.279461i
\(244\) 104715.i 0.112599i
\(245\) 0 0
\(246\) 39233.8 + 691865.i 0.0413354 + 0.728926i
\(247\) −1.63102e6 −1.70105
\(248\) −526914. −0.544014
\(249\) 135590. 7688.92i 0.138589 0.00785899i
\(250\) 197194.i 0.199546i
\(251\) 947580. 0.949361 0.474681 0.880158i \(-0.342564\pi\)
0.474681 + 0.880158i \(0.342564\pi\)
\(252\) 0 0
\(253\) −18248.2 −0.0179233
\(254\) 154163.i 0.149932i
\(255\) −1.43148e6 + 81175.4i −1.37859 + 0.0781761i
\(256\) −1.08991e6 −1.03942
\(257\) −526317. −0.497066 −0.248533 0.968623i \(-0.579948\pi\)
−0.248533 + 0.968623i \(0.579948\pi\)
\(258\) 17258.6 + 304346.i 0.0161420 + 0.284654i
\(259\) 0 0
\(260\) 816432.i 0.749008i
\(261\) −145449. 1.27833e6i −0.132163 1.16156i
\(262\) 1.03464e6i 0.931186i
\(263\) 1.36537e6i 1.21720i 0.793477 + 0.608601i \(0.208269\pi\)
−0.793477 + 0.608601i \(0.791731\pi\)
\(264\) −113475. + 6434.85i −0.100205 + 0.00568236i
\(265\) 1.19006e6i 1.04101i
\(266\) 0 0
\(267\) 281886. 15985.0i 0.241989 0.0137225i
\(268\) −240229. −0.204310
\(269\) −29229.0 −0.0246283 −0.0123141 0.999924i \(-0.503920\pi\)
−0.0123141 + 0.999924i \(0.503920\pi\)
\(270\) 174035. + 1.01422e6i 0.145287 + 0.846686i
\(271\) 423724.i 0.350477i 0.984526 + 0.175239i \(0.0560697\pi\)
−0.984526 + 0.175239i \(0.943930\pi\)
\(272\) −99033.3 −0.0811632
\(273\) 0 0
\(274\) 963785. 0.775540
\(275\) 94504.4i 0.0753564i
\(276\) −7621.21 134396.i −0.00602215 0.106197i
\(277\) −746981. −0.584938 −0.292469 0.956275i \(-0.594477\pi\)
−0.292469 + 0.956275i \(0.594477\pi\)
\(278\) 1.32950e6 1.03175
\(279\) −78203.9 687323.i −0.0601475 0.528628i
\(280\) 0 0
\(281\) 841921.i 0.636071i 0.948079 + 0.318035i \(0.103023\pi\)
−0.948079 + 0.318035i \(0.896977\pi\)
\(282\) 21793.5 + 384315.i 0.0163194 + 0.287783i
\(283\) 1.39274e6i 1.03373i −0.856068 0.516863i \(-0.827100\pi\)
0.856068 0.516863i \(-0.172900\pi\)
\(284\) 1.13033e6i 0.831587i
\(285\) −181555. 3.20162e6i −0.132403 2.33484i
\(286\) 84844.2i 0.0613348i
\(287\) 0 0
\(288\) −154678. 1.35944e6i −0.109887 0.965782i
\(289\) 111574. 0.0785809
\(290\) −1.43832e6 −1.00429
\(291\) 16451.9 + 290119.i 0.0113889 + 0.200837i
\(292\) 962628.i 0.660696i
\(293\) 537097. 0.365497 0.182748 0.983160i \(-0.441501\pi\)
0.182748 + 0.983160i \(0.441501\pi\)
\(294\) 0 0
\(295\) 575764. 0.385203
\(296\) 1.45245e6i 0.963547i
\(297\) −25235.6 147065.i −0.0166006 0.0967427i
\(298\) 1.41040e6 0.920029
\(299\) −272990. −0.176591
\(300\) −696013. + 39469.0i −0.446492 + 0.0253194i
\(301\) 0 0
\(302\) 1.01074e6i 0.637708i
\(303\) 2.65510e6 150563.i 1.66140 0.0942134i
\(304\) 221496.i 0.137462i
\(305\) 417523.i 0.256999i
\(306\) −124257. 1.09208e6i −0.0758610 0.666732i
\(307\) 511397.i 0.309679i −0.987940 0.154840i \(-0.950514\pi\)
0.987940 0.154840i \(-0.0494861\pi\)
\(308\) 0 0
\(309\) 51972.1 + 916497.i 0.0309652 + 0.546053i
\(310\) −773342. −0.457054
\(311\) −2.41299e6 −1.41467 −0.707335 0.706878i \(-0.750103\pi\)
−0.707335 + 0.706878i \(0.750103\pi\)
\(312\) −1.69756e6 + 96264.1i −0.987278 + 0.0559858i
\(313\) 2.72163e6i 1.57025i 0.619339 + 0.785124i \(0.287401\pi\)
−0.619339 + 0.785124i \(0.712599\pi\)
\(314\) −1.38523e6 −0.792862
\(315\) 0 0
\(316\) 1.25586e6 0.707495
\(317\) 1.65080e6i 0.922672i 0.887226 + 0.461336i \(0.152630\pi\)
−0.887226 + 0.461336i \(0.847370\pi\)
\(318\) 910831. 51650.7i 0.505091 0.0286424i
\(319\) 208561. 0.114751
\(320\) −1.71991e6 −0.938925
\(321\) 130250. + 2.29689e6i 0.0705532 + 1.24416i
\(322\) 0 0
\(323\) 3.42516e6i 1.82673i
\(324\) 1.07258e6 247277.i 0.567630 0.130865i
\(325\) 1.41377e6i 0.742455i
\(326\) 846190.i 0.440985i
\(327\) −407078. + 23084.3i −0.210527 + 0.0119384i
\(328\) 2.25120e6i 1.15539i
\(329\) 0 0
\(330\) −166545. + 9444.31i −0.0841873 + 0.00477403i
\(331\) −2.62569e6 −1.31727 −0.658633 0.752464i \(-0.728865\pi\)
−0.658633 + 0.752464i \(0.728865\pi\)
\(332\) −162398. −0.0808605
\(333\) 1.89462e6 215571.i 0.936295 0.106532i
\(334\) 634912.i 0.311421i
\(335\) −957847. −0.466320
\(336\) 0 0
\(337\) −3.01254e6 −1.44497 −0.722483 0.691388i \(-0.756999\pi\)
−0.722483 + 0.691388i \(0.756999\pi\)
\(338\) 87839.2i 0.0418212i
\(339\) −16851.9 297174.i −0.00796436 0.140447i
\(340\) 1.71451e6 0.804347
\(341\) 112137. 0.0522232
\(342\) 2.44252e6 277911.i 1.12921 0.128482i
\(343\) 0 0
\(344\) 990285.i 0.451195i
\(345\) −30387.5 535866.i −0.0137451 0.242386i
\(346\) 1.79284e6i 0.805101i
\(347\) 2.90956e6i 1.29719i −0.761134 0.648595i \(-0.775357\pi\)
0.761134 0.648595i \(-0.224643\pi\)
\(348\) 87103.7 + 1.53602e6i 0.0385557 + 0.679907i
\(349\) 3.93286e6i 1.72840i 0.503147 + 0.864201i \(0.332176\pi\)
−0.503147 + 0.864201i \(0.667824\pi\)
\(350\) 0 0
\(351\) −377520. 2.20007e6i −0.163558 0.953165i
\(352\) 221793. 0.0954096
\(353\) 1.93598e6 0.826922 0.413461 0.910522i \(-0.364320\pi\)
0.413461 + 0.910522i \(0.364320\pi\)
\(354\) 24989.1 + 440669.i 0.0105985 + 0.186898i
\(355\) 4.50686e6i 1.89803i
\(356\) −337620. −0.141190
\(357\) 0 0
\(358\) −2.34406e6 −0.966631
\(359\) 1.39251e6i 0.570247i −0.958491 0.285123i \(-0.907965\pi\)
0.958491 0.285123i \(-0.0920346\pi\)
\(360\) −377924. 3.32152e6i −0.153691 1.35077i
\(361\) −5.18454e6 −2.09383
\(362\) 171565. 0.0688111
\(363\) −2.48236e6 + 140768.i −0.988777 + 0.0560708i
\(364\) 0 0
\(365\) 3.83821e6i 1.50798i
\(366\) −319557. + 18121.2i −0.124694 + 0.00707105i
\(367\) 985240.i 0.381836i 0.981606 + 0.190918i \(0.0611465\pi\)
−0.981606 + 0.190918i \(0.938854\pi\)
\(368\) 37072.5i 0.0142703i
\(369\) 2.93654e6 334120.i 1.12272 0.127743i
\(370\) 2.13174e6i 0.809524i
\(371\) 0 0
\(372\) 46833.1 + 825875.i 0.0175467 + 0.309426i
\(373\) 2.51585e6 0.936296 0.468148 0.883650i \(-0.344921\pi\)
0.468148 + 0.883650i \(0.344921\pi\)
\(374\) 178173. 0.0658664
\(375\) 839667. 47615.2i 0.308339 0.0174851i
\(376\) 1.25049e6i 0.456154i
\(377\) 3.12003e6 1.13059
\(378\) 0 0
\(379\) −627888. −0.224535 −0.112268 0.993678i \(-0.535811\pi\)
−0.112268 + 0.993678i \(0.535811\pi\)
\(380\) 3.83464e6i 1.36228i
\(381\) 656437. 37224.8i 0.231676 0.0131377i
\(382\) 2.78295e6 0.975770
\(383\) 3.10523e6 1.08167 0.540837 0.841127i \(-0.318107\pi\)
0.540837 + 0.841127i \(0.318107\pi\)
\(384\) 84369.5 + 1.48781e6i 0.0291983 + 0.514895i
\(385\) 0 0
\(386\) 2.03335e6i 0.694615i
\(387\) 1.29176e6 146977.i 0.438434 0.0498852i
\(388\) 347481.i 0.117180i
\(389\) 669791.i 0.224422i 0.993684 + 0.112211i \(0.0357932\pi\)
−0.993684 + 0.112211i \(0.964207\pi\)
\(390\) −2.49148e6 + 141285.i −0.829462 + 0.0470365i
\(391\) 573281.i 0.189638i
\(392\) 0 0
\(393\) 4.40558e6 249828.i 1.43887 0.0815943i
\(394\) −1.99527e6 −0.647533
\(395\) 5.00740e6 1.61480
\(396\) 20171.7 + 177286.i 0.00646405 + 0.0568117i
\(397\) 3.49472e6i 1.11285i −0.830898 0.556425i \(-0.812173\pi\)
0.830898 0.556425i \(-0.187827\pi\)
\(398\) 771949. 0.244276
\(399\) 0 0
\(400\) −191992. −0.0599975
\(401\) 2.81146e6i 0.873115i −0.899676 0.436558i \(-0.856198\pi\)
0.899676 0.436558i \(-0.143802\pi\)
\(402\) −41572.1 733101.i −0.0128303 0.226255i
\(403\) 1.67755e6 0.514532
\(404\) −3.18006e6 −0.969353
\(405\) 4.27660e6 985950.i 1.29557 0.298688i
\(406\) 0 0
\(407\) 309109.i 0.0924965i
\(408\) 202155. + 3.56489e6i 0.0601222 + 1.06022i
\(409\) 2.79035e6i 0.824803i 0.911002 + 0.412402i \(0.135310\pi\)
−0.911002 + 0.412402i \(0.864690\pi\)
\(410\) 3.30405e6i 0.970704i
\(411\) −232719. 4.10387e6i −0.0679560 1.19836i
\(412\) 1.09771e6i 0.318598i
\(413\) 0 0
\(414\) 408813. 46514.9i 0.117226 0.0133380i
\(415\) −647518. −0.184557
\(416\) 3.31799e6 0.940030
\(417\) −321026. 5.66111e6i −0.0904066 1.59427i
\(418\) 398499.i 0.111554i
\(419\) −3.40729e6 −0.948144 −0.474072 0.880486i \(-0.657216\pi\)
−0.474072 + 0.880486i \(0.657216\pi\)
\(420\) 0 0
\(421\) 3.77099e6 1.03693 0.518465 0.855099i \(-0.326504\pi\)
0.518465 + 0.855099i \(0.326504\pi\)
\(422\) 2.45122e6i 0.670041i
\(423\) 1.63118e6 185596.i 0.443252 0.0504334i
\(424\) −2.96368e6 −0.800601
\(425\) 2.96892e6 0.797309
\(426\) −3.44938e6 + 195605.i −0.920911 + 0.0522223i
\(427\) 0 0
\(428\) 2.75103e6i 0.725915i
\(429\) 361273. 20486.8i 0.0947746 0.00537441i
\(430\) 1.45342e6i 0.379071i
\(431\) 3.00701e6i 0.779726i −0.920873 0.389863i \(-0.872522\pi\)
0.920873 0.389863i \(-0.127478\pi\)
\(432\) 298773. 51267.8i 0.0770249 0.0132171i
\(433\) 1.50880e6i 0.386734i −0.981126 0.193367i \(-0.938059\pi\)
0.981126 0.193367i \(-0.0619408\pi\)
\(434\) 0 0
\(435\) 347302. + 6.12447e6i 0.0880002 + 1.55183i
\(436\) 487565. 0.122833
\(437\) −1.28219e6 −0.321179
\(438\) 2.93763e6 166585.i 0.731664 0.0414906i
\(439\) 1.97163e6i 0.488275i −0.969741 0.244138i \(-0.921495\pi\)
0.969741 0.244138i \(-0.0785049\pi\)
\(440\) 541907. 0.133442
\(441\) 0 0
\(442\) 2.66544e6 0.648954
\(443\) 2.13681e6i 0.517316i −0.965969 0.258658i \(-0.916720\pi\)
0.965969 0.258658i \(-0.0832803\pi\)
\(444\) −2.27655e6 + 129097.i −0.548049 + 0.0310784i
\(445\) −1.34617e6 −0.322254
\(446\) −68455.3 −0.0162956
\(447\) −340560. 6.00558e6i −0.0806167 1.42163i
\(448\) 0 0
\(449\) 5.91347e6i 1.38429i −0.721759 0.692144i \(-0.756666\pi\)
0.721759 0.692144i \(-0.243334\pi\)
\(450\) −240893. 2.11717e6i −0.0560780 0.492862i
\(451\) 479098.i 0.110913i
\(452\) 355931.i 0.0819445i
\(453\) 4.30380e6 244057.i 0.985387 0.0558786i
\(454\) 1.63398e6i 0.372054i
\(455\) 0 0
\(456\) −7.97316e6 + 452136.i −1.79564 + 0.101826i
\(457\) −7.51891e6 −1.68409 −0.842044 0.539410i \(-0.818647\pi\)
−0.842044 + 0.539410i \(0.818647\pi\)
\(458\) −80412.5 −0.0179126
\(459\) −4.62016e6 + 792795.i −1.02359 + 0.175642i
\(460\) 641816.i 0.141422i
\(461\) 929187. 0.203634 0.101817 0.994803i \(-0.467534\pi\)
0.101817 + 0.994803i \(0.467534\pi\)
\(462\) 0 0
\(463\) 1.21496e6 0.263396 0.131698 0.991290i \(-0.457957\pi\)
0.131698 + 0.991290i \(0.457957\pi\)
\(464\) 423705.i 0.0913627i
\(465\) 186734. + 3.29295e6i 0.0400489 + 0.706240i
\(466\) −1.94847e6 −0.415651
\(467\) −3.03117e6 −0.643159 −0.321580 0.946883i \(-0.604214\pi\)
−0.321580 + 0.946883i \(0.604214\pi\)
\(468\) 301765. + 2.65217e6i 0.0636876 + 0.559741i
\(469\) 0 0
\(470\) 1.83532e6i 0.383238i
\(471\) 334483. + 5.89841e6i 0.0694739 + 1.22513i
\(472\) 1.43386e6i 0.296245i
\(473\) 210751.i 0.0433129i
\(474\) 217329. + 3.83248e6i 0.0444296 + 0.783490i
\(475\) 6.64023e6i 1.35036i
\(476\) 0 0
\(477\) −439865. 3.86591e6i −0.0885164 0.777958i
\(478\) −983457. −0.196873
\(479\) −81905.2 −0.0163107 −0.00815535 0.999967i \(-0.502596\pi\)
−0.00815535 + 0.999967i \(0.502596\pi\)
\(480\) 369337. + 6.51305e6i 0.0731678 + 1.29027i
\(481\) 4.62421e6i 0.911329i
\(482\) 975255. 0.191206
\(483\) 0 0
\(484\) 2.97317e6 0.576907
\(485\) 1.38549e6i 0.267453i
\(486\) 940222. + 3.23036e6i 0.180567 + 0.620383i
\(487\) 4.41516e6 0.843575 0.421787 0.906695i \(-0.361403\pi\)
0.421787 + 0.906695i \(0.361403\pi\)
\(488\) 1.03978e6 0.197648
\(489\) 3.60314e6 204324.i 0.681410 0.0386409i
\(490\) 0 0
\(491\) 9.60786e6i 1.79855i 0.437381 + 0.899276i \(0.355906\pi\)
−0.437381 + 0.899276i \(0.644094\pi\)
\(492\) −3.52849e6 + 200091.i −0.657168 + 0.0372662i
\(493\) 6.55209e6i 1.21412i
\(494\) 5.96147e6i 1.09910i
\(495\) 80429.1 + 706880.i 0.0147537 + 0.129668i
\(496\) 227814.i 0.0415792i
\(497\) 0 0
\(498\) −28103.4 495587.i −0.00507791 0.0895460i
\(499\) 1.00695e7 1.81032 0.905160 0.425071i \(-0.139751\pi\)
0.905160 + 0.425071i \(0.139751\pi\)
\(500\) −1.00568e6 −0.179902
\(501\) 2.70350e6 153308.i 0.481208 0.0272880i
\(502\) 3.46345e6i 0.613408i
\(503\) −2.68345e6 −0.472904 −0.236452 0.971643i \(-0.575985\pi\)
−0.236452 + 0.971643i \(0.575985\pi\)
\(504\) 0 0
\(505\) −1.26796e7 −2.21247
\(506\) 66698.0i 0.0115808i
\(507\) −374026. + 21210.0i −0.0646222 + 0.00366455i
\(508\) −786227. −0.135173
\(509\) −7.51287e6 −1.28532 −0.642661 0.766151i \(-0.722169\pi\)
−0.642661 + 0.766151i \(0.722169\pi\)
\(510\) 296700. + 5.23213e6i 0.0505117 + 0.890745i
\(511\) 0 0
\(512\) 924585.i 0.155873i
\(513\) −1.77315e6 1.03333e7i −0.297475 1.73359i
\(514\) 1.92371e6i 0.321168i
\(515\) 4.37680e6i 0.727174i
\(516\) −1.55215e6 + 88018.4i −0.256632 + 0.0145529i
\(517\) 266128.i 0.0437889i
\(518\) 0 0
\(519\) 7.63403e6 432905.i 1.24404 0.0705463i
\(520\) 8.10683e6 1.31475
\(521\) −9.46018e6 −1.52688 −0.763440 0.645878i \(-0.776491\pi\)
−0.763440 + 0.645878i \(0.776491\pi\)
\(522\) −4.67237e6 + 531624.i −0.750517 + 0.0853942i
\(523\) 1.32587e6i 0.211957i −0.994368 0.105979i \(-0.966202\pi\)
0.994368 0.105979i \(-0.0337975\pi\)
\(524\) −5.27664e6 −0.839517
\(525\) 0 0
\(526\) 4.99051e6 0.786466
\(527\) 3.52287e6i 0.552548i
\(528\) 2782.14 + 49061.4i 0.000434304 + 0.00765871i
\(529\) 6.22174e6 0.966657
\(530\) −4.34974e6 −0.672626
\(531\) 1.87037e6 212811.i 0.287866 0.0327535i
\(532\) 0 0
\(533\) 7.16721e6i 1.09278i
\(534\) −58425.9 1.03031e6i −0.00886650 0.156356i
\(535\) 1.09690e7i 1.65684i
\(536\) 2.38538e6i 0.358629i
\(537\) 566005. + 9.98116e6i 0.0847002 + 1.49364i
\(538\) 106833.i 0.0159130i
\(539\) 0 0
\(540\) −5.17249e6 + 887573.i −0.763335 + 0.130984i
\(541\) 6.92295e6 1.01695 0.508473 0.861078i \(-0.330210\pi\)
0.508473 + 0.861078i \(0.330210\pi\)
\(542\) 1.54873e6 0.226453
\(543\) −41426.8 730538.i −0.00602951 0.106327i
\(544\) 6.96780e6i 1.00948i
\(545\) 1.94403e6 0.280357
\(546\) 0 0
\(547\) −9.97756e6 −1.42579 −0.712896 0.701270i \(-0.752617\pi\)
−0.712896 + 0.701270i \(0.752617\pi\)
\(548\) 4.91528e6i 0.699193i
\(549\) 154323. + 1.35632e6i 0.0218524 + 0.192058i
\(550\) 345418. 0.0486898
\(551\) 1.46542e7 2.05629
\(552\) −1.33449e6 + 75675.5i −0.186410 + 0.0105708i
\(553\) 0 0
\(554\) 2.73025e6i 0.377944i
\(555\) −9.07710e6 + 514738.i −1.25088 + 0.0709338i
\(556\) 6.78041e6i 0.930185i
\(557\) 1.25386e7i 1.71242i 0.516628 + 0.856210i \(0.327187\pi\)
−0.516628 + 0.856210i \(0.672813\pi\)
\(558\) −2.51220e6 + 285839.i −0.341561 + 0.0388629i
\(559\) 3.15280e6i 0.426743i
\(560\) 0 0
\(561\) −43022.4 758676.i −0.00577149 0.101777i
\(562\) 3.07726e6 0.410982
\(563\) −6.87659e6 −0.914329 −0.457164 0.889382i \(-0.651135\pi\)
−0.457164 + 0.889382i \(0.651135\pi\)
\(564\) −1.96000e6 + 111146.i −0.259452 + 0.0147128i
\(565\) 1.41918e6i 0.187032i
\(566\) −5.09055e6 −0.667918
\(567\) 0 0
\(568\) 1.12237e7 1.45970
\(569\) 2.64936e6i 0.343053i 0.985180 + 0.171526i \(0.0548699\pi\)
−0.985180 + 0.171526i \(0.945130\pi\)
\(570\) −1.17021e7 + 663592.i −1.50860 + 0.0855488i
\(571\) 1.09557e6 0.140621 0.0703105 0.997525i \(-0.477601\pi\)
0.0703105 + 0.997525i \(0.477601\pi\)
\(572\) −432703. −0.0552968
\(573\) −671982. 1.18500e7i −0.0855009 1.50776i
\(574\) 0 0
\(575\) 1.11140e6i 0.140184i
\(576\) −5.58712e6 + 635704.i −0.701668 + 0.0798360i
\(577\) 2.90428e6i 0.363161i 0.983376 + 0.181581i \(0.0581214\pi\)
−0.983376 + 0.181581i \(0.941879\pi\)
\(578\) 407807.i 0.0507733i
\(579\) −8.65816e6 + 490980.i −1.07332 + 0.0608650i
\(580\) 7.33539e6i 0.905426i
\(581\) 0 0
\(582\) 1.06040e6 60132.3i 0.129766 0.00735869i
\(583\) 630726. 0.0768545
\(584\) −9.55850e6 −1.15973
\(585\) 1.20321e6 + 1.05748e7i 0.145362 + 1.27756i
\(586\) 1.96311e6i 0.236157i
\(587\) −2.80932e6 −0.336516 −0.168258 0.985743i \(-0.553814\pi\)
−0.168258 + 0.985743i \(0.553814\pi\)
\(588\) 0 0
\(589\) 7.87916e6 0.935819
\(590\) 2.10444e6i 0.248890i
\(591\) 481786. + 8.49602e6i 0.0567395 + 1.00057i
\(592\) −627976. −0.0736442
\(593\) −471223. −0.0550288 −0.0275144 0.999621i \(-0.508759\pi\)
−0.0275144 + 0.999621i \(0.508759\pi\)
\(594\) −537529. + 92237.3i −0.0625081 + 0.0107261i
\(595\) 0 0
\(596\) 7.19300e6i 0.829458i
\(597\) −186398. 3.28701e6i −0.0214045 0.377455i
\(598\) 997791.i 0.114100i
\(599\) 1.73472e6i 0.197544i 0.995110 + 0.0987719i \(0.0314914\pi\)
−0.995110 + 0.0987719i \(0.968509\pi\)
\(600\) 391911. + 6.91112e6i 0.0444436 + 0.783737i
\(601\) 3.42903e6i 0.387244i −0.981076 0.193622i \(-0.937976\pi\)
0.981076 0.193622i \(-0.0620235\pi\)
\(602\) 0 0
\(603\) −3.11156e6 + 354034.i −0.348486 + 0.0396508i
\(604\) −5.15475e6 −0.574930
\(605\) 1.18547e7 1.31674
\(606\) −550316. 9.70451e6i −0.0608738 1.07347i
\(607\) 9.81466e6i 1.08119i −0.841282 0.540597i \(-0.818198\pi\)
0.841282 0.540597i \(-0.181802\pi\)
\(608\) 1.55840e7 1.70970
\(609\) 0 0
\(610\) 1.52607e6 0.166054
\(611\) 3.98122e6i 0.431433i
\(612\) 5.56958e6 633709.i 0.601096 0.0683930i
\(613\) −2.75780e6 −0.296422 −0.148211 0.988956i \(-0.547352\pi\)
−0.148211 + 0.988956i \(0.547352\pi\)
\(614\) −1.86918e6 −0.200092
\(615\) −1.40689e7 + 797808.i −1.49993 + 0.0850571i
\(616\) 0 0
\(617\) 5.46419e6i 0.577847i −0.957352 0.288923i \(-0.906703\pi\)
0.957352 0.288923i \(-0.0932973\pi\)
\(618\) 3.34984e6 189960.i 0.352820 0.0200074i
\(619\) 4.24390e6i 0.445183i −0.974912 0.222591i \(-0.928548\pi\)
0.974912 0.222591i \(-0.0714516\pi\)
\(620\) 3.94402e6i 0.412060i
\(621\) −296777. 1.72952e6i −0.0308817 0.179969i
\(622\) 8.81960e6i 0.914057i
\(623\) 0 0
\(624\) 41620.3 + 733950.i 0.00427901 + 0.0754580i
\(625\) −1.15071e7 −1.17833
\(626\) 9.94768e6 1.01458
\(627\) 1.69684e6 96222.9i 0.172374 0.00977484i
\(628\) 7.06464e6i 0.714810i
\(629\) 9.71088e6 0.978660
\(630\) 0 0
\(631\) 1.97794e6 0.197761 0.0988804 0.995099i \(-0.468474\pi\)
0.0988804 + 0.995099i \(0.468474\pi\)
\(632\) 1.24702e7i 1.24188i
\(633\) 1.04375e7 591881.i 1.03535 0.0587118i
\(634\) 6.03376e6 0.596163
\(635\) −3.13486e6 −0.308521
\(636\) 263417. + 4.64521e6i 0.0258227 + 0.455368i
\(637\) 0 0
\(638\) 762299.i 0.0741436i
\(639\) 1.66580e6 + 1.46405e7i 0.161388 + 1.41842i
\(640\) 7.10513e6i 0.685681i
\(641\) 6.87312e6i 0.660707i −0.943857 0.330353i \(-0.892832\pi\)
0.943857 0.330353i \(-0.107168\pi\)
\(642\) 8.39524e6 476071.i 0.803888 0.0455863i
\(643\) 4.81869e6i 0.459623i 0.973235 + 0.229811i \(0.0738109\pi\)
−0.973235 + 0.229811i \(0.926189\pi\)
\(644\) 0 0
\(645\) −6.18878e6 + 350949.i −0.585742 + 0.0332158i
\(646\) 1.25191e7 1.18030
\(647\) −7.50407e6 −0.704752 −0.352376 0.935859i \(-0.614626\pi\)
−0.352376 + 0.935859i \(0.614626\pi\)
\(648\) −2.45536e6 1.06502e7i −0.229709 0.996372i
\(649\) 305151.i 0.0284383i
\(650\) 5.16739e6 0.479720
\(651\) 0 0
\(652\) −4.31554e6 −0.397573
\(653\) 1.40288e7i 1.28747i −0.765248 0.643735i \(-0.777384\pi\)
0.765248 0.643735i \(-0.222616\pi\)
\(654\) 84374.1 + 1.48789e6i 0.00771374 + 0.136027i
\(655\) −2.10391e7 −1.91613
\(656\) −973319. −0.0883071
\(657\) −1.41866e6 1.24684e7i −0.128223 1.12693i
\(658\) 0 0
\(659\) 4.93455e6i 0.442623i −0.975203 0.221311i \(-0.928966\pi\)
0.975203 0.221311i \(-0.0710337\pi\)
\(660\) −48165.7 849375.i −0.00430406 0.0758996i
\(661\) 1.83713e7i 1.63544i −0.575615 0.817721i \(-0.695237\pi\)
0.575615 0.817721i \(-0.304763\pi\)
\(662\) 9.59702e6i 0.851121i
\(663\) −643608. 1.13496e7i −0.0568640 1.00276i
\(664\) 1.61255e6i 0.141936i
\(665\) 0 0
\(666\) −787923. 6.92494e6i −0.0688332 0.604965i
\(667\) 2.45273e6 0.213469
\(668\) −3.23804e6 −0.280763
\(669\) 16529.5 + 291488.i 0.00142789 + 0.0251800i
\(670\) 3.50097e6i 0.301302i
\(671\) −221284. −0.0189734
\(672\) 0 0
\(673\) 5.27763e6 0.449160 0.224580 0.974456i \(-0.427899\pi\)
0.224580 + 0.974456i \(0.427899\pi\)
\(674\) 1.10110e7i 0.933632i
\(675\) −8.95691e6 + 1.53696e6i −0.756657 + 0.129838i
\(676\) 447978. 0.0377042
\(677\) 1.37062e7 1.14933 0.574666 0.818388i \(-0.305132\pi\)
0.574666 + 0.818388i \(0.305132\pi\)
\(678\) −1.08619e6 + 61594.6i −0.0907465 + 0.00514599i
\(679\) 0 0
\(680\) 1.70244e7i 1.41189i
\(681\) −6.95759e6 + 394546.i −0.574899 + 0.0326009i
\(682\) 409866.i 0.0337428i
\(683\) 1.56582e7i 1.28437i −0.766549 0.642186i \(-0.778028\pi\)
0.766549 0.642186i \(-0.221972\pi\)
\(684\) 1.41734e6 + 1.24568e7i 0.115833 + 1.01804i
\(685\) 1.95983e7i 1.59585i
\(686\) 0 0
\(687\) 19416.7 + 342402.i 0.00156958 + 0.0276786i
\(688\) −428155. −0.0344850
\(689\) 9.43554e6 0.757214
\(690\) −1.95861e6 + 111068.i −0.156612 + 0.00888106i
\(691\) 4.22151e6i 0.336336i 0.985758 + 0.168168i \(0.0537850\pi\)
−0.985758 + 0.168168i \(0.946215\pi\)
\(692\) −9.14342e6 −0.725844
\(693\) 0 0
\(694\) −1.06346e7 −0.838150
\(695\) 2.70350e7i 2.12307i
\(696\) 1.52521e7 864904.i 1.19345 0.0676776i
\(697\) 1.50512e7 1.17352
\(698\) 1.43748e7 1.11677
\(699\) 470485. + 8.29673e6i 0.0364211 + 0.642264i
\(700\) 0 0
\(701\) 2.08992e7i 1.60633i −0.595758 0.803164i \(-0.703148\pi\)
0.595758 0.803164i \(-0.296852\pi\)
\(702\) −8.04134e6 + 1.37985e6i −0.615865 + 0.105679i
\(703\) 2.17191e7i 1.65750i
\(704\) 911541.i 0.0693177i
\(705\) −7.81495e6 + 443164.i −0.592179 + 0.0335809i
\(706\) 7.07610e6i 0.534297i
\(707\) 0 0
\(708\) −2.24740e6 + 127444.i −0.168499 + 0.00955511i
\(709\) 2.06100e6 0.153979 0.0769895 0.997032i \(-0.475469\pi\)
0.0769895 + 0.997032i \(0.475469\pi\)
\(710\) 1.64728e7 1.22637
\(711\) 1.62665e7 1.85081e6i 1.20676 0.137305i
\(712\) 3.35243e6i 0.247833i
\(713\) 1.31876e6 0.0971499
\(714\) 0 0
\(715\) −1.72528e6 −0.126210
\(716\) 1.19546e7i 0.871472i
\(717\) 237469. + 4.18763e6i 0.0172508 + 0.304208i
\(718\) −5.08970e6 −0.368452
\(719\) −2.24934e7 −1.62268 −0.811339 0.584575i \(-0.801261\pi\)
−0.811339 + 0.584575i \(0.801261\pi\)
\(720\) −1.43607e6 + 163397.i −0.103239 + 0.0117466i
\(721\) 0 0
\(722\) 1.89497e7i 1.35288i
\(723\) −235489. 4.15271e6i −0.0167542 0.295451i
\(724\) 874979.i 0.0620370i
\(725\) 1.27023e7i 0.897504i
\(726\) 514513. + 9.07314e6i 0.0362289 + 0.638875i
\(727\) 2.23831e7i 1.57067i −0.619073 0.785334i \(-0.712491\pi\)
0.619073 0.785334i \(-0.287509\pi\)
\(728\) 0 0
\(729\) 1.35281e7 4.78355e6i 0.942795 0.333374i
\(730\) −1.40288e7 −0.974350
\(731\) 6.62090e6 0.458272
\(732\) −92417.6 1.62973e6i −0.00637495 0.112419i
\(733\) 1.24379e7i 0.855040i 0.904006 + 0.427520i \(0.140613\pi\)
−0.904006 + 0.427520i \(0.859387\pi\)
\(734\) 3.60110e6 0.246715
\(735\) 0 0
\(736\) 2.60835e6 0.177489
\(737\) 507652.i 0.0344269i
\(738\) −1.22123e6 1.07332e7i −0.0825382 0.725417i
\(739\) −1.34548e7 −0.906291 −0.453145 0.891437i \(-0.649698\pi\)
−0.453145 + 0.891437i \(0.649698\pi\)
\(740\) 1.08718e7 0.729832
\(741\) 2.53844e7 1.43948e6i 1.69832 0.0963073i
\(742\) 0 0
\(743\) 1.80287e7i 1.19810i 0.800713 + 0.599049i \(0.204454\pi\)
−0.800713 + 0.599049i \(0.795546\pi\)
\(744\) 8.20060e6 465034.i 0.543142 0.0308001i
\(745\) 2.86801e7i 1.89317i
\(746\) 9.19556e6i 0.604966i
\(747\) −2.10346e6 + 239332.i −0.137922 + 0.0156928i
\(748\) 908680.i 0.0593823i
\(749\) 0 0
\(750\) −174036. 3.06902e6i −0.0112976 0.199226i
\(751\) 8.24075e6 0.533171 0.266586 0.963811i \(-0.414105\pi\)
0.266586 + 0.963811i \(0.414105\pi\)
\(752\) −540657. −0.0348640
\(753\) −1.47476e7 + 836297.i −0.947838 + 0.0537493i
\(754\) 1.14039e7i 0.730505i
\(755\) −2.05531e7 −1.31223
\(756\) 0 0
\(757\) −1.17983e7 −0.748308 −0.374154 0.927367i \(-0.622067\pi\)
−0.374154 + 0.927367i \(0.622067\pi\)
\(758\) 2.29496e6i 0.145078i
\(759\) 284005. 16105.2i 0.0178946 0.00101475i
\(760\) 3.80764e7 2.39123
\(761\) −1.22420e7 −0.766286 −0.383143 0.923689i \(-0.625158\pi\)
−0.383143 + 0.923689i \(0.625158\pi\)
\(762\) −136058. 2.39931e6i −0.00848862 0.149692i
\(763\) 0 0
\(764\) 1.41930e7i 0.879711i
\(765\) 2.22072e7 2.52674e6i 1.37195 0.156101i
\(766\) 1.13498e7i 0.698899i
\(767\) 4.56500e6i 0.280190i
\(768\) 1.69627e7 961910.i 1.03775 0.0588479i
\(769\) 2.89879e6i 0.176767i −0.996087 0.0883834i \(-0.971830\pi\)
0.996087 0.0883834i \(-0.0281701\pi\)
\(770\) 0 0
\(771\) 8.19131e6 464507.i 0.496269 0.0281421i
\(772\) 1.03700e7 0.626234
\(773\) 3.49988e6 0.210671 0.105336 0.994437i \(-0.466408\pi\)
0.105336 + 0.994437i \(0.466408\pi\)
\(774\) −537207. 4.72144e6i −0.0322322 0.283284i
\(775\) 6.82964e6i 0.408455i
\(776\) −3.45035e6 −0.205688
\(777\) 0 0
\(778\) 2.44812e6 0.145005
\(779\) 3.36632e7i 1.98752i
\(780\)