Properties

Label 300.3.c.a.151.2
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.2
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.a.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} -1.73205i q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 + 1.73205i) q^{6} -10.3923i q^{7} +8.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} -1.73205i q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 + 1.73205i) q^{6} -10.3923i q^{7} +8.00000 q^{8} -3.00000 q^{9} +10.3923i q^{11} +(-6.00000 + 3.46410i) q^{12} -18.0000 q^{13} +(18.0000 + 10.3923i) q^{14} +(-8.00000 + 13.8564i) q^{16} -10.0000 q^{17} +(3.00000 - 5.19615i) q^{18} +13.8564i q^{19} -18.0000 q^{21} +(-18.0000 - 10.3923i) q^{22} -6.92820i q^{23} -13.8564i q^{24} +(18.0000 - 31.1769i) q^{26} +5.19615i q^{27} +(-36.0000 + 20.7846i) q^{28} -36.0000 q^{29} -6.92820i q^{31} +(-16.0000 - 27.7128i) q^{32} +18.0000 q^{33} +(10.0000 - 17.3205i) q^{34} +(6.00000 + 10.3923i) q^{36} -54.0000 q^{37} +(-24.0000 - 13.8564i) q^{38} +31.1769i q^{39} +18.0000 q^{41} +(18.0000 - 31.1769i) q^{42} -20.7846i q^{43} +(36.0000 - 20.7846i) q^{44} +(12.0000 + 6.92820i) q^{46} +(24.0000 + 13.8564i) q^{48} -59.0000 q^{49} +17.3205i q^{51} +(36.0000 + 62.3538i) q^{52} +26.0000 q^{53} +(-9.00000 - 5.19615i) q^{54} -83.1384i q^{56} +24.0000 q^{57} +(36.0000 - 62.3538i) q^{58} -31.1769i q^{59} -74.0000 q^{61} +(12.0000 + 6.92820i) q^{62} +31.1769i q^{63} +64.0000 q^{64} +(-18.0000 + 31.1769i) q^{66} -41.5692i q^{67} +(20.0000 + 34.6410i) q^{68} -12.0000 q^{69} -103.923i q^{71} -24.0000 q^{72} -36.0000 q^{73} +(54.0000 - 93.5307i) q^{74} +(48.0000 - 27.7128i) q^{76} +108.000 q^{77} +(-54.0000 - 31.1769i) q^{78} +90.0666i q^{79} +9.00000 q^{81} +(-18.0000 + 31.1769i) q^{82} +90.0666i q^{83} +(36.0000 + 62.3538i) q^{84} +(36.0000 + 20.7846i) q^{86} +62.3538i q^{87} +83.1384i q^{88} -18.0000 q^{89} +187.061i q^{91} +(-24.0000 + 13.8564i) q^{92} -12.0000 q^{93} +(-48.0000 + 27.7128i) q^{96} +72.0000 q^{97} +(59.0000 - 102.191i) q^{98} -31.1769i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{4} + 6q^{6} + 16q^{8} - 6q^{9} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{4} + 6q^{6} + 16q^{8} - 6q^{9} - 12q^{12} - 36q^{13} + 36q^{14} - 16q^{16} - 20q^{17} + 6q^{18} - 36q^{21} - 36q^{22} + 36q^{26} - 72q^{28} - 72q^{29} - 32q^{32} + 36q^{33} + 20q^{34} + 12q^{36} - 108q^{37} - 48q^{38} + 36q^{41} + 36q^{42} + 72q^{44} + 24q^{46} + 48q^{48} - 118q^{49} + 72q^{52} + 52q^{53} - 18q^{54} + 48q^{57} + 72q^{58} - 148q^{61} + 24q^{62} + 128q^{64} - 36q^{66} + 40q^{68} - 24q^{69} - 48q^{72} - 72q^{73} + 108q^{74} + 96q^{76} + 216q^{77} - 108q^{78} + 18q^{81} - 36q^{82} + 72q^{84} + 72q^{86} - 36q^{89} - 48q^{92} - 24q^{93} - 96q^{96} + 144q^{97} + 118q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.500000 + 0.866025i
\(3\) 1.73205i 0.577350i
\(4\) −2.00000 3.46410i −0.500000 0.866025i
\(5\) 0 0
\(6\) 3.00000 + 1.73205i 0.500000 + 0.288675i
\(7\) 10.3923i 1.48461i −0.670059 0.742307i \(-0.733731\pi\)
0.670059 0.742307i \(-0.266269\pi\)
\(8\) 8.00000 1.00000
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 10.3923i 0.944755i 0.881396 + 0.472377i \(0.156604\pi\)
−0.881396 + 0.472377i \(0.843396\pi\)
\(12\) −6.00000 + 3.46410i −0.500000 + 0.288675i
\(13\) −18.0000 −1.38462 −0.692308 0.721602i \(-0.743406\pi\)
−0.692308 + 0.721602i \(0.743406\pi\)
\(14\) 18.0000 + 10.3923i 1.28571 + 0.742307i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(17\) −10.0000 −0.588235 −0.294118 0.955769i \(-0.595026\pi\)
−0.294118 + 0.955769i \(0.595026\pi\)
\(18\) 3.00000 5.19615i 0.166667 0.288675i
\(19\) 13.8564i 0.729285i 0.931148 + 0.364642i \(0.118809\pi\)
−0.931148 + 0.364642i \(0.881191\pi\)
\(20\) 0 0
\(21\) −18.0000 −0.857143
\(22\) −18.0000 10.3923i −0.818182 0.472377i
\(23\) 6.92820i 0.301226i −0.988593 0.150613i \(-0.951875\pi\)
0.988593 0.150613i \(-0.0481248\pi\)
\(24\) 13.8564i 0.577350i
\(25\) 0 0
\(26\) 18.0000 31.1769i 0.692308 1.19911i
\(27\) 5.19615i 0.192450i
\(28\) −36.0000 + 20.7846i −1.28571 + 0.742307i
\(29\) −36.0000 −1.24138 −0.620690 0.784056i \(-0.713147\pi\)
−0.620690 + 0.784056i \(0.713147\pi\)
\(30\) 0 0
\(31\) 6.92820i 0.223490i −0.993737 0.111745i \(-0.964356\pi\)
0.993737 0.111745i \(-0.0356441\pi\)
\(32\) −16.0000 27.7128i −0.500000 0.866025i
\(33\) 18.0000 0.545455
\(34\) 10.0000 17.3205i 0.294118 0.509427i
\(35\) 0 0
\(36\) 6.00000 + 10.3923i 0.166667 + 0.288675i
\(37\) −54.0000 −1.45946 −0.729730 0.683736i \(-0.760354\pi\)
−0.729730 + 0.683736i \(0.760354\pi\)
\(38\) −24.0000 13.8564i −0.631579 0.364642i
\(39\) 31.1769i 0.799408i
\(40\) 0 0
\(41\) 18.0000 0.439024 0.219512 0.975610i \(-0.429553\pi\)
0.219512 + 0.975610i \(0.429553\pi\)
\(42\) 18.0000 31.1769i 0.428571 0.742307i
\(43\) 20.7846i 0.483363i −0.970356 0.241682i \(-0.922301\pi\)
0.970356 0.241682i \(-0.0776989\pi\)
\(44\) 36.0000 20.7846i 0.818182 0.472377i
\(45\) 0 0
\(46\) 12.0000 + 6.92820i 0.260870 + 0.150613i
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 24.0000 + 13.8564i 0.500000 + 0.288675i
\(49\) −59.0000 −1.20408
\(50\) 0 0
\(51\) 17.3205i 0.339618i
\(52\) 36.0000 + 62.3538i 0.692308 + 1.19911i
\(53\) 26.0000 0.490566 0.245283 0.969452i \(-0.421119\pi\)
0.245283 + 0.969452i \(0.421119\pi\)
\(54\) −9.00000 5.19615i −0.166667 0.0962250i
\(55\) 0 0
\(56\) 83.1384i 1.48461i
\(57\) 24.0000 0.421053
\(58\) 36.0000 62.3538i 0.620690 1.07507i
\(59\) 31.1769i 0.528422i −0.964465 0.264211i \(-0.914888\pi\)
0.964465 0.264211i \(-0.0851116\pi\)
\(60\) 0 0
\(61\) −74.0000 −1.21311 −0.606557 0.795040i \(-0.707450\pi\)
−0.606557 + 0.795040i \(0.707450\pi\)
\(62\) 12.0000 + 6.92820i 0.193548 + 0.111745i
\(63\) 31.1769i 0.494872i
\(64\) 64.0000 1.00000
\(65\) 0 0
\(66\) −18.0000 + 31.1769i −0.272727 + 0.472377i
\(67\) 41.5692i 0.620436i −0.950665 0.310218i \(-0.899598\pi\)
0.950665 0.310218i \(-0.100402\pi\)
\(68\) 20.0000 + 34.6410i 0.294118 + 0.509427i
\(69\) −12.0000 −0.173913
\(70\) 0 0
\(71\) 103.923i 1.46370i −0.681463 0.731852i \(-0.738656\pi\)
0.681463 0.731852i \(-0.261344\pi\)
\(72\) −24.0000 −0.333333
\(73\) −36.0000 −0.493151 −0.246575 0.969124i \(-0.579305\pi\)
−0.246575 + 0.969124i \(0.579305\pi\)
\(74\) 54.0000 93.5307i 0.729730 1.26393i
\(75\) 0 0
\(76\) 48.0000 27.7128i 0.631579 0.364642i
\(77\) 108.000 1.40260
\(78\) −54.0000 31.1769i −0.692308 0.399704i
\(79\) 90.0666i 1.14008i 0.821616 + 0.570042i \(0.193073\pi\)
−0.821616 + 0.570042i \(0.806927\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −18.0000 + 31.1769i −0.219512 + 0.380206i
\(83\) 90.0666i 1.08514i 0.840011 + 0.542570i \(0.182549\pi\)
−0.840011 + 0.542570i \(0.817451\pi\)
\(84\) 36.0000 + 62.3538i 0.428571 + 0.742307i
\(85\) 0 0
\(86\) 36.0000 + 20.7846i 0.418605 + 0.241682i
\(87\) 62.3538i 0.716711i
\(88\) 83.1384i 0.944755i
\(89\) −18.0000 −0.202247 −0.101124 0.994874i \(-0.532244\pi\)
−0.101124 + 0.994874i \(0.532244\pi\)
\(90\) 0 0
\(91\) 187.061i 2.05562i
\(92\) −24.0000 + 13.8564i −0.260870 + 0.150613i
\(93\) −12.0000 −0.129032
\(94\) 0 0
\(95\) 0 0
\(96\) −48.0000 + 27.7128i −0.500000 + 0.288675i
\(97\) 72.0000 0.742268 0.371134 0.928579i \(-0.378969\pi\)
0.371134 + 0.928579i \(0.378969\pi\)
\(98\) 59.0000 102.191i 0.602041 1.04277i
\(99\) 31.1769i 0.314918i
\(100\) 0 0
\(101\) 36.0000 0.356436 0.178218 0.983991i \(-0.442967\pi\)
0.178218 + 0.983991i \(0.442967\pi\)
\(102\) −30.0000 17.3205i −0.294118 0.169809i
\(103\) 10.3923i 0.100896i −0.998727 0.0504481i \(-0.983935\pi\)
0.998727 0.0504481i \(-0.0160649\pi\)
\(104\) −144.000 −1.38462
\(105\) 0 0
\(106\) −26.0000 + 45.0333i −0.245283 + 0.424843i
\(107\) 187.061i 1.74824i 0.485712 + 0.874119i \(0.338561\pi\)
−0.485712 + 0.874119i \(0.661439\pi\)
\(108\) 18.0000 10.3923i 0.166667 0.0962250i
\(109\) −26.0000 −0.238532 −0.119266 0.992862i \(-0.538054\pi\)
−0.119266 + 0.992862i \(0.538054\pi\)
\(110\) 0 0
\(111\) 93.5307i 0.842619i
\(112\) 144.000 + 83.1384i 1.28571 + 0.742307i
\(113\) 10.0000 0.0884956 0.0442478 0.999021i \(-0.485911\pi\)
0.0442478 + 0.999021i \(0.485911\pi\)
\(114\) −24.0000 + 41.5692i −0.210526 + 0.364642i
\(115\) 0 0
\(116\) 72.0000 + 124.708i 0.620690 + 1.07507i
\(117\) 54.0000 0.461538
\(118\) 54.0000 + 31.1769i 0.457627 + 0.264211i
\(119\) 103.923i 0.873303i
\(120\) 0 0
\(121\) 13.0000 0.107438
\(122\) 74.0000 128.172i 0.606557 1.05059i
\(123\) 31.1769i 0.253471i
\(124\) −24.0000 + 13.8564i −0.193548 + 0.111745i
\(125\) 0 0
\(126\) −54.0000 31.1769i −0.428571 0.247436i
\(127\) 218.238i 1.71841i −0.511629 0.859206i \(-0.670958\pi\)
0.511629 0.859206i \(-0.329042\pi\)
\(128\) −64.0000 + 110.851i −0.500000 + 0.866025i
\(129\) −36.0000 −0.279070
\(130\) 0 0
\(131\) 135.100i 1.03130i −0.856800 0.515649i \(-0.827551\pi\)
0.856800 0.515649i \(-0.172449\pi\)
\(132\) −36.0000 62.3538i −0.272727 0.472377i
\(133\) 144.000 1.08271
\(134\) 72.0000 + 41.5692i 0.537313 + 0.310218i
\(135\) 0 0
\(136\) −80.0000 −0.588235
\(137\) −110.000 −0.802920 −0.401460 0.915877i \(-0.631497\pi\)
−0.401460 + 0.915877i \(0.631497\pi\)
\(138\) 12.0000 20.7846i 0.0869565 0.150613i
\(139\) 187.061i 1.34577i −0.739749 0.672883i \(-0.765056\pi\)
0.739749 0.672883i \(-0.234944\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 180.000 + 103.923i 1.26761 + 0.731852i
\(143\) 187.061i 1.30812i
\(144\) 24.0000 41.5692i 0.166667 0.288675i
\(145\) 0 0
\(146\) 36.0000 62.3538i 0.246575 0.427081i
\(147\) 102.191i 0.695177i
\(148\) 108.000 + 187.061i 0.729730 + 1.26393i
\(149\) 288.000 1.93289 0.966443 0.256881i \(-0.0826950\pi\)
0.966443 + 0.256881i \(0.0826950\pi\)
\(150\) 0 0
\(151\) 187.061i 1.23882i −0.785069 0.619409i \(-0.787372\pi\)
0.785069 0.619409i \(-0.212628\pi\)
\(152\) 110.851i 0.729285i
\(153\) 30.0000 0.196078
\(154\) −108.000 + 187.061i −0.701299 + 1.21468i
\(155\) 0 0
\(156\) 108.000 62.3538i 0.692308 0.399704i
\(157\) −234.000 −1.49045 −0.745223 0.666815i \(-0.767657\pi\)
−0.745223 + 0.666815i \(0.767657\pi\)
\(158\) −156.000 90.0666i −0.987342 0.570042i
\(159\) 45.0333i 0.283228i
\(160\) 0 0
\(161\) −72.0000 −0.447205
\(162\) −9.00000 + 15.5885i −0.0555556 + 0.0962250i
\(163\) 124.708i 0.765078i −0.923939 0.382539i \(-0.875050\pi\)
0.923939 0.382539i \(-0.124950\pi\)
\(164\) −36.0000 62.3538i −0.219512 0.380206i
\(165\) 0 0
\(166\) −156.000 90.0666i −0.939759 0.542570i
\(167\) 131.636i 0.788239i −0.919059 0.394119i \(-0.871050\pi\)
0.919059 0.394119i \(-0.128950\pi\)
\(168\) −144.000 −0.857143
\(169\) 155.000 0.917160
\(170\) 0 0
\(171\) 41.5692i 0.243095i
\(172\) −72.0000 + 41.5692i −0.418605 + 0.241682i
\(173\) −146.000 −0.843931 −0.421965 0.906612i \(-0.638660\pi\)
−0.421965 + 0.906612i \(0.638660\pi\)
\(174\) −108.000 62.3538i −0.620690 0.358355i
\(175\) 0 0
\(176\) −144.000 83.1384i −0.818182 0.472377i
\(177\) −54.0000 −0.305085
\(178\) 18.0000 31.1769i 0.101124 0.175151i
\(179\) 72.7461i 0.406403i −0.979137 0.203201i \(-0.934865\pi\)
0.979137 0.203201i \(-0.0651346\pi\)
\(180\) 0 0
\(181\) 262.000 1.44751 0.723757 0.690055i \(-0.242414\pi\)
0.723757 + 0.690055i \(0.242414\pi\)
\(182\) −324.000 187.061i −1.78022 1.02781i
\(183\) 128.172i 0.700392i
\(184\) 55.4256i 0.301226i
\(185\) 0 0
\(186\) 12.0000 20.7846i 0.0645161 0.111745i
\(187\) 103.923i 0.555738i
\(188\) 0 0
\(189\) 54.0000 0.285714
\(190\) 0 0
\(191\) 187.061i 0.979380i 0.871897 + 0.489690i \(0.162890\pi\)
−0.871897 + 0.489690i \(0.837110\pi\)
\(192\) 110.851i 0.577350i
\(193\) −180.000 −0.932642 −0.466321 0.884615i \(-0.654421\pi\)
−0.466321 + 0.884615i \(0.654421\pi\)
\(194\) −72.0000 + 124.708i −0.371134 + 0.642823i
\(195\) 0 0
\(196\) 118.000 + 204.382i 0.602041 + 1.04277i
\(197\) 154.000 0.781726 0.390863 0.920449i \(-0.372177\pi\)
0.390863 + 0.920449i \(0.372177\pi\)
\(198\) 54.0000 + 31.1769i 0.272727 + 0.157459i
\(199\) 187.061i 0.940007i −0.882664 0.470004i \(-0.844253\pi\)
0.882664 0.470004i \(-0.155747\pi\)
\(200\) 0 0
\(201\) −72.0000 −0.358209
\(202\) −36.0000 + 62.3538i −0.178218 + 0.308682i
\(203\) 374.123i 1.84297i
\(204\) 60.0000 34.6410i 0.294118 0.169809i
\(205\) 0 0
\(206\) 18.0000 + 10.3923i 0.0873786 + 0.0504481i
\(207\) 20.7846i 0.100409i
\(208\) 144.000 249.415i 0.692308 1.19911i
\(209\) −144.000 −0.688995
\(210\) 0 0
\(211\) 242.487i 1.14923i −0.818425 0.574614i \(-0.805152\pi\)
0.818425 0.574614i \(-0.194848\pi\)
\(212\) −52.0000 90.0666i −0.245283 0.424843i
\(213\) −180.000 −0.845070
\(214\) −324.000 187.061i −1.51402 0.874119i
\(215\) 0 0
\(216\) 41.5692i 0.192450i
\(217\) −72.0000 −0.331797
\(218\) 26.0000 45.0333i 0.119266 0.206575i
\(219\) 62.3538i 0.284721i
\(220\) 0 0
\(221\) 180.000 0.814480
\(222\) −162.000 93.5307i −0.729730 0.421310i
\(223\) 93.5307i 0.419420i −0.977764 0.209710i \(-0.932748\pi\)
0.977764 0.209710i \(-0.0672521\pi\)
\(224\) −288.000 + 166.277i −1.28571 + 0.742307i
\(225\) 0 0
\(226\) −10.0000 + 17.3205i −0.0442478 + 0.0766394i
\(227\) 214.774i 0.946142i 0.881024 + 0.473071i \(0.156855\pi\)
−0.881024 + 0.473071i \(0.843145\pi\)
\(228\) −48.0000 83.1384i −0.210526 0.364642i
\(229\) 338.000 1.47598 0.737991 0.674810i \(-0.235775\pi\)
0.737991 + 0.674810i \(0.235775\pi\)
\(230\) 0 0
\(231\) 187.061i 0.809790i
\(232\) −288.000 −1.24138
\(233\) 182.000 0.781116 0.390558 0.920578i \(-0.372282\pi\)
0.390558 + 0.920578i \(0.372282\pi\)
\(234\) −54.0000 + 93.5307i −0.230769 + 0.399704i
\(235\) 0 0
\(236\) −108.000 + 62.3538i −0.457627 + 0.264211i
\(237\) 156.000 0.658228
\(238\) −180.000 103.923i −0.756303 0.436651i
\(239\) 353.338i 1.47840i −0.673484 0.739202i \(-0.735203\pi\)
0.673484 0.739202i \(-0.264797\pi\)
\(240\) 0 0
\(241\) −106.000 −0.439834 −0.219917 0.975519i \(-0.570579\pi\)
−0.219917 + 0.975519i \(0.570579\pi\)
\(242\) −13.0000 + 22.5167i −0.0537190 + 0.0930441i
\(243\) 15.5885i 0.0641500i
\(244\) 148.000 + 256.344i 0.606557 + 1.05059i
\(245\) 0 0
\(246\) 54.0000 + 31.1769i 0.219512 + 0.126735i
\(247\) 249.415i 1.00978i
\(248\) 55.4256i 0.223490i
\(249\) 156.000 0.626506
\(250\) 0 0
\(251\) 322.161i 1.28351i 0.766909 + 0.641756i \(0.221794\pi\)
−0.766909 + 0.641756i \(0.778206\pi\)
\(252\) 108.000 62.3538i 0.428571 0.247436i
\(253\) 72.0000 0.284585
\(254\) 378.000 + 218.238i 1.48819 + 0.859206i
\(255\) 0 0
\(256\) −128.000 221.703i −0.500000 0.866025i
\(257\) −14.0000 −0.0544747 −0.0272374 0.999629i \(-0.508671\pi\)
−0.0272374 + 0.999629i \(0.508671\pi\)
\(258\) 36.0000 62.3538i 0.139535 0.241682i
\(259\) 561.184i 2.16674i
\(260\) 0 0
\(261\) 108.000 0.413793
\(262\) 234.000 + 135.100i 0.893130 + 0.515649i
\(263\) 187.061i 0.711260i −0.934627 0.355630i \(-0.884266\pi\)
0.934627 0.355630i \(-0.115734\pi\)
\(264\) 144.000 0.545455
\(265\) 0 0
\(266\) −144.000 + 249.415i −0.541353 + 0.937652i
\(267\) 31.1769i 0.116767i
\(268\) −144.000 + 83.1384i −0.537313 + 0.310218i
\(269\) −108.000 −0.401487 −0.200743 0.979644i \(-0.564336\pi\)
−0.200743 + 0.979644i \(0.564336\pi\)
\(270\) 0 0
\(271\) 325.626i 1.20157i 0.799411 + 0.600785i \(0.205145\pi\)
−0.799411 + 0.600785i \(0.794855\pi\)
\(272\) 80.0000 138.564i 0.294118 0.509427i
\(273\) 324.000 1.18681
\(274\) 110.000 190.526i 0.401460 0.695349i
\(275\) 0 0
\(276\) 24.0000 + 41.5692i 0.0869565 + 0.150613i
\(277\) −270.000 −0.974729 −0.487365 0.873199i \(-0.662042\pi\)
−0.487365 + 0.873199i \(0.662042\pi\)
\(278\) 324.000 + 187.061i 1.16547 + 0.672883i
\(279\) 20.7846i 0.0744968i
\(280\) 0 0
\(281\) −234.000 −0.832740 −0.416370 0.909195i \(-0.636698\pi\)
−0.416370 + 0.909195i \(0.636698\pi\)
\(282\) 0 0
\(283\) 83.1384i 0.293775i 0.989153 + 0.146888i \(0.0469256\pi\)
−0.989153 + 0.146888i \(0.953074\pi\)
\(284\) −360.000 + 207.846i −1.26761 + 0.731852i
\(285\) 0 0
\(286\) 324.000 + 187.061i 1.13287 + 0.654061i
\(287\) 187.061i 0.651782i
\(288\) 48.0000 + 83.1384i 0.166667 + 0.288675i
\(289\) −189.000 −0.653979
\(290\) 0 0
\(291\) 124.708i 0.428549i
\(292\) 72.0000 + 124.708i 0.246575 + 0.427081i
\(293\) 58.0000 0.197952 0.0989761 0.995090i \(-0.468443\pi\)
0.0989761 + 0.995090i \(0.468443\pi\)
\(294\) −177.000 102.191i −0.602041 0.347588i
\(295\) 0 0
\(296\) −432.000 −1.45946
\(297\) −54.0000 −0.181818
\(298\) −288.000 + 498.831i −0.966443 + 1.67393i
\(299\) 124.708i 0.417082i
\(300\) 0 0
\(301\) −216.000 −0.717608
\(302\) 324.000 + 187.061i 1.07285 + 0.619409i
\(303\) 62.3538i 0.205788i
\(304\) −192.000 110.851i −0.631579 0.364642i
\(305\) 0 0
\(306\) −30.0000 + 51.9615i −0.0980392 + 0.169809i
\(307\) 270.200i 0.880130i 0.897966 + 0.440065i \(0.145045\pi\)
−0.897966 + 0.440065i \(0.854955\pi\)
\(308\) −216.000 374.123i −0.701299 1.21468i
\(309\) −18.0000 −0.0582524
\(310\) 0 0
\(311\) 270.200i 0.868810i 0.900718 + 0.434405i \(0.143041\pi\)
−0.900718 + 0.434405i \(0.856959\pi\)
\(312\) 249.415i 0.799408i
\(313\) −468.000 −1.49521 −0.747604 0.664145i \(-0.768796\pi\)
−0.747604 + 0.664145i \(0.768796\pi\)
\(314\) 234.000 405.300i 0.745223 1.29076i
\(315\) 0 0
\(316\) 312.000 180.133i 0.987342 0.570042i
\(317\) −250.000 −0.788644 −0.394322 0.918972i \(-0.629020\pi\)
−0.394322 + 0.918972i \(0.629020\pi\)
\(318\) 78.0000 + 45.0333i 0.245283 + 0.141614i
\(319\) 374.123i 1.17280i
\(320\) 0 0
\(321\) 324.000 1.00935
\(322\) 72.0000 124.708i 0.223602 0.387291i
\(323\) 138.564i 0.428991i
\(324\) −18.0000 31.1769i −0.0555556 0.0962250i
\(325\) 0 0
\(326\) 216.000 + 124.708i 0.662577 + 0.382539i
\(327\) 45.0333i 0.137717i
\(328\) 144.000 0.439024
\(329\) 0 0
\(330\) 0 0
\(331\) 374.123i 1.13028i −0.824995 0.565140i \(-0.808822\pi\)
0.824995 0.565140i \(-0.191178\pi\)
\(332\) 312.000 180.133i 0.939759 0.542570i
\(333\) 162.000 0.486486
\(334\) 228.000 + 131.636i 0.682635 + 0.394119i
\(335\) 0 0
\(336\) 144.000 249.415i 0.428571 0.742307i
\(337\) 468.000 1.38872 0.694362 0.719626i \(-0.255687\pi\)
0.694362 + 0.719626i \(0.255687\pi\)
\(338\) −155.000 + 268.468i −0.458580 + 0.794284i
\(339\) 17.3205i 0.0510929i
\(340\) 0 0
\(341\) 72.0000 0.211144
\(342\) 72.0000 + 41.5692i 0.210526 + 0.121547i
\(343\) 103.923i 0.302983i
\(344\) 166.277i 0.483363i
\(345\) 0 0
\(346\) 146.000 252.879i 0.421965 0.730865i
\(347\) 561.184i 1.61725i 0.588327 + 0.808623i \(0.299787\pi\)
−0.588327 + 0.808623i \(0.700213\pi\)
\(348\) 216.000 124.708i 0.620690 0.358355i
\(349\) −434.000 −1.24355 −0.621777 0.783195i \(-0.713589\pi\)
−0.621777 + 0.783195i \(0.713589\pi\)
\(350\) 0 0
\(351\) 93.5307i 0.266469i
\(352\) 288.000 166.277i 0.818182 0.472377i
\(353\) 158.000 0.447592 0.223796 0.974636i \(-0.428155\pi\)
0.223796 + 0.974636i \(0.428155\pi\)
\(354\) 54.0000 93.5307i 0.152542 0.264211i
\(355\) 0 0
\(356\) 36.0000 + 62.3538i 0.101124 + 0.175151i
\(357\) 180.000 0.504202
\(358\) 126.000 + 72.7461i 0.351955 + 0.203201i
\(359\) 457.261i 1.27371i 0.770984 + 0.636854i \(0.219765\pi\)
−0.770984 + 0.636854i \(0.780235\pi\)
\(360\) 0 0
\(361\) 169.000 0.468144
\(362\) −262.000 + 453.797i −0.723757 + 1.25358i
\(363\) 22.5167i 0.0620294i
\(364\) 648.000 374.123i 1.78022 1.02781i
\(365\) 0 0
\(366\) −222.000 128.172i −0.606557 0.350196i
\(367\) 218.238i 0.594655i −0.954776 0.297328i \(-0.903905\pi\)
0.954776 0.297328i \(-0.0960953\pi\)
\(368\) 96.0000 + 55.4256i 0.260870 + 0.150613i
\(369\) −54.0000 −0.146341
\(370\) 0 0
\(371\) 270.200i 0.728302i
\(372\) 24.0000 + 41.5692i 0.0645161 + 0.111745i
\(373\) 270.000 0.723861 0.361930 0.932205i \(-0.382118\pi\)
0.361930 + 0.932205i \(0.382118\pi\)
\(374\) 180.000 + 103.923i 0.481283 + 0.277869i
\(375\) 0 0
\(376\) 0 0
\(377\) 648.000 1.71883
\(378\) −54.0000 + 93.5307i −0.142857 + 0.247436i
\(379\) 325.626i 0.859170i −0.903026 0.429585i \(-0.858660\pi\)
0.903026 0.429585i \(-0.141340\pi\)
\(380\) 0 0
\(381\) −378.000 −0.992126
\(382\) −324.000 187.061i −0.848168 0.489690i
\(383\) 55.4256i 0.144714i 0.997379 + 0.0723572i \(0.0230522\pi\)
−0.997379 + 0.0723572i \(0.976948\pi\)
\(384\) 192.000 + 110.851i 0.500000 + 0.288675i
\(385\) 0 0
\(386\) 180.000 311.769i 0.466321 0.807692i
\(387\) 62.3538i 0.161121i
\(388\) −144.000 249.415i −0.371134 0.642823i
\(389\) −288.000 −0.740360 −0.370180 0.928960i \(-0.620704\pi\)
−0.370180 + 0.928960i \(0.620704\pi\)
\(390\) 0 0
\(391\) 69.2820i 0.177192i
\(392\) −472.000 −1.20408
\(393\) −234.000 −0.595420
\(394\) −154.000 + 266.736i −0.390863 + 0.676994i
\(395\) 0 0
\(396\) −108.000 + 62.3538i −0.272727 + 0.157459i
\(397\) 306.000 0.770781 0.385390 0.922754i \(-0.374067\pi\)
0.385390 + 0.922754i \(0.374067\pi\)
\(398\) 324.000 + 187.061i 0.814070 + 0.470004i
\(399\) 249.415i 0.625101i
\(400\) 0 0
\(401\) −450.000 −1.12219 −0.561097 0.827750i \(-0.689621\pi\)
−0.561097 + 0.827750i \(0.689621\pi\)
\(402\) 72.0000 124.708i 0.179104 0.310218i
\(403\) 124.708i 0.309448i
\(404\) −72.0000 124.708i −0.178218 0.308682i
\(405\) 0 0
\(406\) −648.000 374.123i −1.59606 0.921485i
\(407\) 561.184i 1.37883i
\(408\) 138.564i 0.339618i
\(409\) −50.0000 −0.122249 −0.0611247 0.998130i \(-0.519469\pi\)
−0.0611247 + 0.998130i \(0.519469\pi\)
\(410\) 0 0
\(411\) 190.526i 0.463566i
\(412\) −36.0000 + 20.7846i −0.0873786 + 0.0504481i
\(413\) −324.000 −0.784504
\(414\) −36.0000 20.7846i −0.0869565 0.0502044i
\(415\) 0 0
\(416\) 288.000 + 498.831i 0.692308 + 1.19911i
\(417\) −324.000 −0.776978
\(418\) 144.000 249.415i 0.344498 0.596687i
\(419\) 737.854i 1.76099i 0.474058 + 0.880494i \(0.342789\pi\)
−0.474058 + 0.880494i \(0.657211\pi\)
\(420\) 0 0
\(421\) −286.000 −0.679335 −0.339667 0.940546i \(-0.610315\pi\)
−0.339667 + 0.940546i \(0.610315\pi\)
\(422\) 420.000 + 242.487i 0.995261 + 0.574614i
\(423\) 0 0
\(424\) 208.000 0.490566
\(425\) 0 0
\(426\) 180.000 311.769i 0.422535 0.731852i
\(427\) 769.031i 1.80101i
\(428\) 648.000 374.123i 1.51402 0.874119i
\(429\) −324.000 −0.755245
\(430\) 0 0
\(431\) 124.708i 0.289345i −0.989480 0.144672i \(-0.953787\pi\)
0.989480 0.144672i \(-0.0462128\pi\)
\(432\) −72.0000 41.5692i −0.166667 0.0962250i
\(433\) 36.0000 0.0831409 0.0415704 0.999136i \(-0.486764\pi\)
0.0415704 + 0.999136i \(0.486764\pi\)
\(434\) 72.0000 124.708i 0.165899 0.287345i
\(435\) 0 0
\(436\) 52.0000 + 90.0666i 0.119266 + 0.206575i
\(437\) 96.0000 0.219680
\(438\) −108.000 62.3538i −0.246575 0.142360i
\(439\) 782.887i 1.78334i 0.452684 + 0.891671i \(0.350466\pi\)
−0.452684 + 0.891671i \(0.649534\pi\)
\(440\) 0 0
\(441\) 177.000 0.401361
\(442\) −180.000 + 311.769i −0.407240 + 0.705360i
\(443\) 214.774i 0.484818i 0.970174 + 0.242409i \(0.0779376\pi\)
−0.970174 + 0.242409i \(0.922062\pi\)
\(444\) 324.000 187.061i 0.729730 0.421310i
\(445\) 0 0
\(446\) 162.000 + 93.5307i 0.363229 + 0.209710i
\(447\) 498.831i 1.11595i
\(448\) 665.108i 1.48461i
\(449\) 54.0000 0.120267 0.0601336 0.998190i \(-0.480847\pi\)
0.0601336 + 0.998190i \(0.480847\pi\)
\(450\) 0 0
\(451\) 187.061i 0.414770i
\(452\) −20.0000 34.6410i −0.0442478 0.0766394i
\(453\) −324.000 −0.715232
\(454\) −372.000 214.774i −0.819383 0.473071i
\(455\) 0 0
\(456\) 192.000 0.421053
\(457\) −288.000 −0.630197 −0.315098 0.949059i \(-0.602038\pi\)
−0.315098 + 0.949059i \(0.602038\pi\)
\(458\) −338.000 + 585.433i −0.737991 + 1.27824i
\(459\) 51.9615i 0.113206i
\(460\) 0 0
\(461\) −288.000 −0.624729 −0.312364 0.949962i \(-0.601121\pi\)
−0.312364 + 0.949962i \(0.601121\pi\)
\(462\) 324.000 + 187.061i 0.701299 + 0.404895i
\(463\) 405.300i 0.875378i −0.899126 0.437689i \(-0.855797\pi\)
0.899126 0.437689i \(-0.144203\pi\)
\(464\) 288.000 498.831i 0.620690 1.07507i
\(465\) 0 0
\(466\) −182.000 + 315.233i −0.390558 + 0.676466i
\(467\) 575.041i 1.23135i −0.788000 0.615675i \(-0.788883\pi\)
0.788000 0.615675i \(-0.211117\pi\)
\(468\) −108.000 187.061i −0.230769 0.399704i
\(469\) −432.000 −0.921109
\(470\) 0 0
\(471\) 405.300i 0.860509i
\(472\) 249.415i 0.528422i
\(473\) 216.000 0.456660
\(474\) −156.000 + 270.200i −0.329114 + 0.570042i
\(475\) 0 0
\(476\) 360.000 207.846i 0.756303 0.436651i
\(477\) −78.0000 −0.163522
\(478\) 612.000 + 353.338i 1.28033 + 0.739202i
\(479\) 145.492i 0.303742i −0.988400 0.151871i \(-0.951470\pi\)
0.988400 0.151871i \(-0.0485298\pi\)
\(480\) 0 0
\(481\) 972.000 2.02079
\(482\) 106.000 183.597i 0.219917 0.380907i
\(483\) 124.708i 0.258194i
\(484\) −26.0000 45.0333i −0.0537190 0.0930441i
\(485\) 0 0
\(486\) 27.0000 + 15.5885i 0.0555556 + 0.0320750i
\(487\) 259.808i 0.533486i 0.963768 + 0.266743i \(0.0859475\pi\)
−0.963768 + 0.266743i \(0.914053\pi\)
\(488\) −592.000 −1.21311
\(489\) −216.000 −0.441718
\(490\) 0 0
\(491\) 72.7461i 0.148159i 0.997252 + 0.0740796i \(0.0236019\pi\)
−0.997252 + 0.0740796i \(0.976398\pi\)
\(492\) −108.000 + 62.3538i −0.219512 + 0.126735i
\(493\) 360.000 0.730223
\(494\) 432.000 + 249.415i 0.874494 + 0.504889i
\(495\) 0 0
\(496\) 96.0000 + 55.4256i 0.193548 + 0.111745i
\(497\) −1080.00 −2.17304
\(498\) −156.000 + 270.200i −0.313253 + 0.542570i
\(499\) 443.405i 0.888587i −0.895881 0.444294i \(-0.853455\pi\)
0.895881 0.444294i \(-0.146545\pi\)
\(500\) 0 0
\(501\) −228.000 −0.455090
\(502\) −558.000 322.161i −1.11155 0.641756i
\(503\) 110.851i 0.220380i −0.993911 0.110190i \(-0.964854\pi\)
0.993911 0.110190i \(-0.0351460\pi\)
\(504\) 249.415i 0.494872i
\(505\) 0 0
\(506\) −72.0000 + 124.708i −0.142292 + 0.246458i
\(507\) 268.468i 0.529522i
\(508\) −756.000 + 436.477i −1.48819 + 0.859206i
\(509\) −252.000 −0.495088 −0.247544 0.968877i \(-0.579624\pi\)
−0.247544 + 0.968877i \(0.579624\pi\)
\(510\) 0 0
\(511\) 374.123i 0.732139i
\(512\) 512.000 1.00000
\(513\) −72.0000 −0.140351
\(514\) 14.0000 24.2487i 0.0272374 0.0471765i
\(515\) 0 0
\(516\) 72.0000 + 124.708i 0.139535 + 0.241682i
\(517\) 0 0
\(518\) −972.000 561.184i −1.87645 1.08337i
\(519\) 252.879i 0.487244i
\(520\) 0 0
\(521\) 54.0000 0.103647 0.0518234 0.998656i \(-0.483497\pi\)
0.0518234 + 0.998656i \(0.483497\pi\)
\(522\) −108.000 + 187.061i −0.206897 + 0.358355i
\(523\) 623.538i 1.19223i 0.802898 + 0.596117i \(0.203291\pi\)
−0.802898 + 0.596117i \(0.796709\pi\)
\(524\) −468.000 + 270.200i −0.893130 + 0.515649i
\(525\) 0 0
\(526\) 324.000 + 187.061i 0.615970 + 0.355630i
\(527\) 69.2820i 0.131465i
\(528\) −144.000 + 249.415i −0.272727 + 0.472377i
\(529\) 481.000 0.909263
\(530\) 0 0
\(531\) 93.5307i 0.176141i
\(532\) −288.000 498.831i −0.541353 0.937652i
\(533\) −324.000 −0.607880
\(534\) −54.0000 31.1769i −0.101124 0.0583837i
\(535\) 0 0
\(536\) 332.554i 0.620436i
\(537\) −126.000 −0.234637
\(538\) 108.000 187.061i 0.200743 0.347698i
\(539\) 613.146i 1.13756i
\(540\) 0 0
\(541\) −650.000 −1.20148 −0.600739 0.799445i \(-0.705127\pi\)
−0.600739 + 0.799445i \(0.705127\pi\)
\(542\) −564.000 325.626i −1.04059 0.600785i
\(543\) 453.797i 0.835722i
\(544\) 160.000 + 277.128i 0.294118 + 0.509427i
\(545\) 0 0
\(546\) −324.000 + 561.184i −0.593407 + 1.02781i
\(547\) 685.892i 1.25392i 0.779053 + 0.626958i \(0.215700\pi\)
−0.779053 + 0.626958i \(0.784300\pi\)
\(548\) 220.000 + 381.051i 0.401460 + 0.695349i
\(549\) 222.000 0.404372
\(550\) 0 0
\(551\) 498.831i 0.905319i
\(552\) −96.0000 −0.173913
\(553\) 936.000 1.69259
\(554\) 270.000 467.654i 0.487365 0.844140i
\(555\) 0 0
\(556\) −648.000 + 374.123i −1.16547 + 0.672883i
\(557\) −574.000 −1.03052 −0.515260 0.857034i \(-0.672305\pi\)
−0.515260 + 0.857034i \(0.672305\pi\)
\(558\) −36.0000 20.7846i −0.0645161 0.0372484i
\(559\) 374.123i 0.669272i
\(560\) 0 0
\(561\) −180.000 −0.320856
\(562\) 234.000 405.300i 0.416370 0.721174i
\(563\) 561.184i 0.996775i −0.866954 0.498388i \(-0.833926\pi\)
0.866954 0.498388i \(-0.166074\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −144.000 83.1384i −0.254417 0.146888i
\(567\) 93.5307i 0.164957i
\(568\) 831.384i 1.46370i
\(569\) 198.000 0.347979 0.173989 0.984748i \(-0.444334\pi\)
0.173989 + 0.984748i \(0.444334\pi\)
\(570\) 0 0
\(571\) 180.133i 0.315470i 0.987481 + 0.157735i \(0.0504192\pi\)
−0.987481 + 0.157735i \(0.949581\pi\)
\(572\) −648.000 + 374.123i −1.13287 + 0.654061i
\(573\) 324.000 0.565445
\(574\) 324.000 + 187.061i 0.564460 + 0.325891i
\(575\) 0 0
\(576\) −192.000 −0.333333
\(577\) 504.000 0.873484 0.436742 0.899587i \(-0.356132\pi\)
0.436742 + 0.899587i \(0.356132\pi\)
\(578\) 189.000 327.358i 0.326990 0.566363i
\(579\) 311.769i 0.538461i
\(580\) 0 0
\(581\) 936.000 1.61102
\(582\) 216.000 + 124.708i 0.371134 + 0.214274i
\(583\) 270.200i 0.463465i
\(584\) −288.000 −0.493151
\(585\) 0 0
\(586\) −58.0000 + 100.459i −0.0989761 + 0.171432i
\(587\) 408.764i 0.696361i 0.937427 + 0.348181i \(0.113200\pi\)
−0.937427 + 0.348181i \(0.886800\pi\)
\(588\) 354.000 204.382i 0.602041 0.347588i
\(589\) 96.0000 0.162988
\(590\) 0 0
\(591\) 266.736i 0.451330i
\(592\) 432.000 748.246i 0.729730 1.26393i
\(593\) −998.000 −1.68297 −0.841484 0.540282i \(-0.818318\pi\)
−0.841484 + 0.540282i \(0.818318\pi\)
\(594\) 54.0000 93.5307i 0.0909091 0.157459i
\(595\) 0 0
\(596\) −576.000 997.661i −0.966443 1.67393i
\(597\) −324.000 −0.542714
\(598\) −216.000 124.708i −0.361204 0.208541i
\(599\) 540.400i 0.902170i −0.892481 0.451085i \(-0.851037\pi\)
0.892481 0.451085i \(-0.148963\pi\)
\(600\) 0 0
\(601\) −614.000 −1.02163 −0.510815 0.859690i \(-0.670656\pi\)
−0.510815 + 0.859690i \(0.670656\pi\)
\(602\) 216.000 374.123i 0.358804 0.621467i
\(603\) 124.708i 0.206812i
\(604\) −648.000 + 374.123i −1.07285 + 0.619409i
\(605\) 0 0
\(606\) 108.000 + 62.3538i 0.178218 + 0.102894i
\(607\) 654.715i 1.07861i −0.842111 0.539304i \(-0.818687\pi\)
0.842111 0.539304i \(-0.181313\pi\)
\(608\) 384.000 221.703i 0.631579 0.364642i
\(609\) 648.000 1.06404
\(610\) 0 0
\(611\) 0 0
\(612\) −60.0000 103.923i −0.0980392 0.169809i
\(613\) −414.000 −0.675367 −0.337684 0.941260i \(-0.609643\pi\)
−0.337684 + 0.941260i \(0.609643\pi\)
\(614\) −468.000 270.200i −0.762215 0.440065i
\(615\) 0 0
\(616\) 864.000 1.40260
\(617\) −58.0000 −0.0940032 −0.0470016 0.998895i \(-0.514967\pi\)
−0.0470016 + 0.998895i \(0.514967\pi\)
\(618\) 18.0000 31.1769i 0.0291262 0.0504481i
\(619\) 187.061i 0.302199i 0.988519 + 0.151100i \(0.0482815\pi\)
−0.988519 + 0.151100i \(0.951719\pi\)
\(620\) 0 0
\(621\) 36.0000 0.0579710
\(622\) −468.000 270.200i −0.752412 0.434405i
\(623\) 187.061i 0.300259i
\(624\) −432.000 249.415i −0.692308 0.399704i
\(625\) 0 0
\(626\) 468.000 810.600i 0.747604 1.29489i
\(627\) 249.415i 0.397792i
\(628\) 468.000 + 810.600i 0.745223 + 1.29076i
\(629\) 540.000 0.858506
\(630\) 0 0
\(631\) 824.456i 1.30659i −0.757105 0.653293i \(-0.773387\pi\)
0.757105 0.653293i \(-0.226613\pi\)
\(632\) 720.533i 1.14008i
\(633\) −420.000 −0.663507
\(634\) 250.000 433.013i 0.394322 0.682985i
\(635\) 0 0
\(636\) −156.000 + 90.0666i −0.245283 + 0.141614i
\(637\) 1062.00 1.66719
\(638\) 648.000 + 374.123i 1.01567 + 0.586400i
\(639\) 311.769i 0.487902i
\(640\) 0 0
\(641\) 810.000 1.26365 0.631825 0.775111i \(-0.282306\pi\)
0.631825 + 0.775111i \(0.282306\pi\)
\(642\) −324.000 + 561.184i −0.504673 + 0.874119i
\(643\) 415.692i 0.646489i 0.946316 + 0.323244i \(0.104774\pi\)
−0.946316 + 0.323244i \(0.895226\pi\)
\(644\) 144.000 + 249.415i 0.223602 + 0.387291i
\(645\) 0 0
\(646\) 240.000 + 138.564i 0.371517 + 0.214495i
\(647\) 983.805i 1.52056i −0.649593 0.760282i \(-0.725061\pi\)
0.649593 0.760282i \(-0.274939\pi\)
\(648\) 72.0000 0.111111
\(649\) 324.000 0.499230
\(650\) 0 0
\(651\) 124.708i 0.191563i
\(652\) −432.000 + 249.415i −0.662577 + 0.382539i
\(653\) 950.000 1.45482 0.727412 0.686201i \(-0.240723\pi\)
0.727412 + 0.686201i \(0.240723\pi\)
\(654\) −78.0000 45.0333i −0.119266 0.0688583i
\(655\) 0 0
\(656\) −144.000 + 249.415i −0.219512 + 0.380206i
\(657\) 108.000 0.164384
\(658\) 0 0
\(659\) 1132.76i 1.71891i −0.511212 0.859455i \(-0.670803\pi\)
0.511212 0.859455i \(-0.329197\pi\)
\(660\) 0 0
\(661\) −242.000 −0.366112 −0.183056 0.983102i \(-0.558599\pi\)
−0.183056 + 0.983102i \(0.558599\pi\)
\(662\) 648.000 + 374.123i 0.978852 + 0.565140i
\(663\) 311.769i 0.470240i
\(664\) 720.533i 1.08514i
\(665\) 0 0
\(666\) −162.000 + 280.592i −0.243243 + 0.421310i
\(667\) 249.415i 0.373936i
\(668\) −456.000 + 263.272i −0.682635 + 0.394119i
\(669\) −162.000 −0.242152
\(670\) 0 0
\(671\) 769.031i 1.14610i
\(672\) 288.000 + 498.831i 0.428571 + 0.742307i
\(673\) −324.000 −0.481426 −0.240713 0.970596i \(-0.577381\pi\)
−0.240713 + 0.970596i \(0.577381\pi\)
\(674\) −468.000 + 810.600i −0.694362 + 1.20267i
\(675\) 0 0
\(676\) −310.000 536.936i −0.458580 0.794284i
\(677\) 806.000 1.19055 0.595273 0.803523i \(-0.297044\pi\)
0.595273 + 0.803523i \(0.297044\pi\)
\(678\) 30.0000 + 17.3205i 0.0442478 + 0.0255465i
\(679\) 748.246i 1.10198i
\(680\) 0 0
\(681\) 372.000 0.546256
\(682\) −72.0000 + 124.708i −0.105572 + 0.182856i
\(683\) 575.041i 0.841934i −0.907076 0.420967i \(-0.861691\pi\)
0.907076 0.420967i \(-0.138309\pi\)
\(684\) −144.000 + 83.1384i −0.210526 + 0.121547i
\(685\) 0 0
\(686\) −180.000 103.923i −0.262391 0.151491i
\(687\) 585.433i 0.852159i
\(688\) 288.000 + 166.277i 0.418605 + 0.241682i
\(689\) −468.000 −0.679245
\(690\) 0 0
\(691\) 775.959i 1.12295i 0.827494 + 0.561475i \(0.189766\pi\)
−0.827494 + 0.561475i \(0.810234\pi\)
\(692\) 292.000 + 505.759i 0.421965 + 0.730865i
\(693\) −324.000 −0.467532
\(694\) −972.000 561.184i −1.40058 0.808623i
\(695\) 0 0
\(696\) 498.831i 0.716711i
\(697\) −180.000 −0.258250
\(698\) 434.000 751.710i 0.621777 1.07695i
\(699\) 315.233i 0.450977i
\(700\) 0 0
\(701\) 756.000 1.07846 0.539230 0.842159i \(-0.318715\pi\)
0.539230 + 0.842159i \(0.318715\pi\)
\(702\) 162.000 + 93.5307i 0.230769 + 0.133235i
\(703\) 748.246i 1.06436i
\(704\) 665.108i 0.944755i
\(705\) 0 0
\(706\) −158.000 + 273.664i −0.223796 + 0.387626i
\(707\) 374.123i 0.529170i
\(708\) 108.000 + 187.061i 0.152542 + 0.264211i
\(709\) −310.000 −0.437236 −0.218618 0.975811i \(-0.570155\pi\)
−0.218618 + 0.975811i \(0.570155\pi\)
\(710\) 0 0
\(711\) 270.200i 0.380028i
\(712\) −144.000 −0.202247
\(713\) −48.0000 −0.0673212
\(714\) −180.000 + 311.769i −0.252101 + 0.436651i
\(715\) 0 0
\(716\) −252.000 + 145.492i −0.351955 + 0.203201i
\(717\) −612.000 −0.853556
\(718\) −792.000 457.261i −1.10306 0.636854i
\(719\) 83.1384i 0.115631i 0.998327 + 0.0578153i \(0.0184135\pi\)
−0.998327 + 0.0578153i \(0.981587\pi\)
\(720\) 0 0
\(721\) −108.000 −0.149792
\(722\) −169.000 + 292.717i −0.234072 + 0.405425i
\(723\) 183.597i 0.253938i
\(724\) −524.000 907.595i −0.723757 1.25358i
\(725\) 0 0
\(726\) 39.0000 + 22.5167i 0.0537190 + 0.0310147i
\(727\) 1091.19i 1.50095i 0.660898 + 0.750476i \(0.270176\pi\)
−0.660898 + 0.750476i \(0.729824\pi\)
\(728\) 1496.49i 2.05562i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 207.846i 0.284331i
\(732\) 444.000 256.344i 0.606557 0.350196i
\(733\) −1206.00 −1.64529 −0.822647 0.568553i \(-0.807503\pi\)
−0.822647 + 0.568553i \(0.807503\pi\)
\(734\) 378.000 + 218.238i 0.514986 + 0.297328i
\(735\) 0 0
\(736\) −192.000 + 110.851i −0.260870 + 0.150613i
\(737\) 432.000 0.586160
\(738\) 54.0000 93.5307i 0.0731707 0.126735i
\(739\) 484.974i 0.656257i 0.944633 + 0.328129i \(0.106418\pi\)
−0.944633 + 0.328129i \(0.893582\pi\)
\(740\) 0 0
\(741\) −432.000 −0.582996
\(742\) 468.000 + 270.200i 0.630728 + 0.364151i
\(743\) 1122.37i 1.51059i 0.655385 + 0.755295i \(0.272507\pi\)
−0.655385 + 0.755295i \(0.727493\pi\)
\(744\) −96.0000 −0.129032
\(745\) 0 0
\(746\) −270.000 + 467.654i −0.361930 + 0.626882i
\(747\) 270.200i 0.361713i
\(748\) −360.000 + 207.846i −0.481283 + 0.277869i
\(749\) 1944.00 2.59546
\(750\) 0 0
\(751\) 242.487i 0.322886i −0.986882 0.161443i \(-0.948385\pi\)
0.986882 0.161443i \(-0.0516147\pi\)
\(752\) 0 0
\(753\) 558.000 0.741036
\(754\) −648.000 + 1122.37i −0.859416 + 1.48855i
\(755\) 0 0
\(756\) −108.000 187.061i −0.142857 0.247436i
\(757\) −846.000 −1.11757 −0.558785 0.829313i \(-0.688732\pi\)
−0.558785 + 0.829313i \(0.688732\pi\)
\(758\) 564.000 + 325.626i 0.744063 + 0.429585i
\(759\) 124.708i 0.164305i
\(760\) 0 0
\(761\) −1458.00 −1.91590 −0.957950 0.286935i \(-0.907364\pi\)
−0.957950 + 0.286935i \(0.907364\pi\)
\(762\) 378.000 654.715i 0.496063 0.859206i
\(763\) 270.200i 0.354128i
\(764\) 648.000 374.123i 0.848168 0.489690i
\(765\) 0 0
\(766\) −96.0000 55.4256i −0.125326 0.0723572i
\(767\) 561.184i 0.731662i
\(768\) −384.000 + 221.703i −0.500000 + 0.288675i
\(769\) 1282.00 1.66710 0.833550 0.552444i \(-0.186305\pi\)
0.833550 + 0.552444i \(0.186305\pi\)
\(770\) 0 0
\(771\) 24.2487i 0.0314510i
\(772\) 360.000 + 623.538i 0.466321 + 0.807692i
\(773\) 422.000 0.545925 0.272962 0.962025i \(-0.411997\pi\)
0.272962 + 0.962025i \(0.411997\pi\)
\(774\) −108.000 62.3538i −0.139535 0.0805605i
\(775\) 0 0
\(776\) 576.000 0.742268
\(777\) 972.000 1.25097
\(778\) 288.000 498.831i 0.370180 0.641170i
\(779\) 249.415i 0.320174i
\(780\) 0 0
\(781\) 1080.00 1.38284
\(782\) −120.000 69.2820i −0.153453 0.0885959i
\(783\) 187.061i 0.238904i
\(784\) 472.000 817.528i 0.602041 1.04277i
\(785\) 0 0
\(786\) 234.000 405.300i 0.297710 0.515649i
\(787\) 1205.51i 1.53178i