Properties

Label 300.3.c.b.151.1
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 12)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +1.73205i q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 + 1.73205i) q^{6} -6.92820i q^{7} -8.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +1.73205i q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 + 1.73205i) q^{6} -6.92820i q^{7} -8.00000 q^{8} -3.00000 q^{9} -6.92820i q^{11} +(6.00000 - 3.46410i) q^{12} -2.00000 q^{13} +(-12.0000 - 6.92820i) q^{14} +(-8.00000 + 13.8564i) q^{16} -10.0000 q^{17} +(-3.00000 + 5.19615i) q^{18} -20.7846i q^{19} +12.0000 q^{21} +(-12.0000 - 6.92820i) q^{22} -27.7128i q^{23} -13.8564i q^{24} +(-2.00000 + 3.46410i) q^{26} -5.19615i q^{27} +(-24.0000 + 13.8564i) q^{28} -26.0000 q^{29} -6.92820i q^{31} +(16.0000 + 27.7128i) q^{32} +12.0000 q^{33} +(-10.0000 + 17.3205i) q^{34} +(6.00000 + 10.3923i) q^{36} -26.0000 q^{37} +(-36.0000 - 20.7846i) q^{38} -3.46410i q^{39} +58.0000 q^{41} +(12.0000 - 20.7846i) q^{42} -48.4974i q^{43} +(-24.0000 + 13.8564i) q^{44} +(-48.0000 - 27.7128i) q^{46} +69.2820i q^{47} +(-24.0000 - 13.8564i) q^{48} +1.00000 q^{49} -17.3205i q^{51} +(4.00000 + 6.92820i) q^{52} +74.0000 q^{53} +(-9.00000 - 5.19615i) q^{54} +55.4256i q^{56} +36.0000 q^{57} +(-26.0000 + 45.0333i) q^{58} +90.0666i q^{59} +26.0000 q^{61} +(-12.0000 - 6.92820i) q^{62} +20.7846i q^{63} +64.0000 q^{64} +(12.0000 - 20.7846i) q^{66} +6.92820i q^{67} +(20.0000 + 34.6410i) q^{68} +48.0000 q^{69} +24.0000 q^{72} +46.0000 q^{73} +(-26.0000 + 45.0333i) q^{74} +(-72.0000 + 41.5692i) q^{76} -48.0000 q^{77} +(-6.00000 - 3.46410i) q^{78} -117.779i q^{79} +9.00000 q^{81} +(58.0000 - 100.459i) q^{82} +48.4974i q^{83} +(-24.0000 - 41.5692i) q^{84} +(-84.0000 - 48.4974i) q^{86} -45.0333i q^{87} +55.4256i q^{88} +82.0000 q^{89} +13.8564i q^{91} +(-96.0000 + 55.4256i) q^{92} +12.0000 q^{93} +(120.000 + 69.2820i) q^{94} +(-48.0000 + 27.7128i) q^{96} -2.00000 q^{97} +(1.00000 - 1.73205i) q^{98} +20.7846i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 4q^{4} + 6q^{6} - 16q^{8} - 6q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 4q^{4} + 6q^{6} - 16q^{8} - 6q^{9} + 12q^{12} - 4q^{13} - 24q^{14} - 16q^{16} - 20q^{17} - 6q^{18} + 24q^{21} - 24q^{22} - 4q^{26} - 48q^{28} - 52q^{29} + 32q^{32} + 24q^{33} - 20q^{34} + 12q^{36} - 52q^{37} - 72q^{38} + 116q^{41} + 24q^{42} - 48q^{44} - 96q^{46} - 48q^{48} + 2q^{49} + 8q^{52} + 148q^{53} - 18q^{54} + 72q^{57} - 52q^{58} + 52q^{61} - 24q^{62} + 128q^{64} + 24q^{66} + 40q^{68} + 96q^{69} + 48q^{72} + 92q^{73} - 52q^{74} - 144q^{76} - 96q^{77} - 12q^{78} + 18q^{81} + 116q^{82} - 48q^{84} - 168q^{86} + 164q^{89} - 192q^{92} + 24q^{93} + 240q^{94} - 96q^{96} - 4q^{97} + 2q^{98} + O(q^{100}) \)

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
\(7\) 6.92820i 0.989743i −0.868966 0.494872i \(-0.835215\pi\)
0.868966 0.494872i \(-0.164785\pi\)
\(8\) −8.00000 −1.00000
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 6.92820i 0.629837i −0.949119 0.314918i \(-0.898023\pi\)
0.949119 0.314918i \(-0.101977\pi\)
\(12\) 6.00000 3.46410i 0.500000 0.288675i
\(13\) −2.00000 −0.153846 −0.0769231 0.997037i \(-0.524510\pi\)
−0.0769231 + 0.997037i \(0.524510\pi\)
\(14\) −12.0000 6.92820i −0.857143 0.494872i
\(15\) 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
\(19\) 20.7846i 1.09393i −0.837157 0.546963i \(-0.815784\pi\)
0.837157 0.546963i \(-0.184216\pi\)
\(20\) 0 0
\(21\) 12.0000 0.571429
\(22\) −12.0000 6.92820i −0.545455 0.314918i
\(23\) 27.7128i 1.20490i −0.798155 0.602452i \(-0.794190\pi\)
0.798155 0.602452i \(-0.205810\pi\)
\(24\) 13.8564i 0.577350i
\(25\) 0 0
\(26\) −2.00000 + 3.46410i −0.0769231 + 0.133235i
\(27\) 5.19615i 0.192450i
\(28\) −24.0000 + 13.8564i −0.857143 + 0.494872i
\(29\) −26.0000 −0.896552 −0.448276 0.893895i \(-0.647962\pi\)
−0.448276 + 0.893895i \(0.647962\pi\)
\(30\) 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
\(33\) 12.0000 0.363636
\(34\) −10.0000 + 17.3205i −0.294118 + 0.509427i
\(35\) 0 0
\(36\) 6.00000 + 10.3923i 0.166667 + 0.288675i
\(37\) −26.0000 −0.702703 −0.351351 0.936244i \(-0.614278\pi\)
−0.351351 + 0.936244i \(0.614278\pi\)
\(38\) −36.0000 20.7846i −0.947368 0.546963i
\(39\) 3.46410i 0.0888231i
\(40\) 0 0
\(41\) 58.0000 1.41463 0.707317 0.706896i \(-0.249905\pi\)
0.707317 + 0.706896i \(0.249905\pi\)
\(42\) 12.0000 20.7846i 0.285714 0.494872i
\(43\) 48.4974i 1.12785i −0.825827 0.563924i \(-0.809291\pi\)
0.825827 0.563924i \(-0.190709\pi\)
\(44\) −24.0000 + 13.8564i −0.545455 + 0.314918i
\(45\) 0 0
\(46\) −48.0000 27.7128i −1.04348 0.602452i
\(47\) 69.2820i 1.47409i 0.675846 + 0.737043i \(0.263778\pi\)
−0.675846 + 0.737043i \(0.736222\pi\)
\(48\) −24.0000 13.8564i −0.500000 0.288675i
\(49\) 1.00000 0.0204082
\(50\) 0 0
\(51\) 17.3205i 0.339618i
\(52\) 4.00000 + 6.92820i 0.0769231 + 0.133235i
\(53\) 74.0000 1.39623 0.698113 0.715987i \(-0.254023\pi\)
0.698113 + 0.715987i \(0.254023\pi\)
\(54\) −9.00000 5.19615i −0.166667 0.0962250i
\(55\) 0 0
\(56\) 55.4256i 0.989743i
\(57\) 36.0000 0.631579
\(58\) −26.0000 + 45.0333i −0.448276 + 0.776437i
\(59\) 90.0666i 1.52655i 0.646072 + 0.763277i \(0.276411\pi\)
−0.646072 + 0.763277i \(0.723589\pi\)
\(60\) 0 0
\(61\) 26.0000 0.426230 0.213115 0.977027i \(-0.431639\pi\)
0.213115 + 0.977027i \(0.431639\pi\)
\(62\) −12.0000 6.92820i −0.193548 0.111745i
\(63\) 20.7846i 0.329914i
\(64\) 64.0000 1.00000
\(65\) 0 0
\(66\) 12.0000 20.7846i 0.181818 0.314918i
\(67\) 6.92820i 0.103406i 0.998663 + 0.0517030i \(0.0164649\pi\)
−0.998663 + 0.0517030i \(0.983535\pi\)
\(68\) 20.0000 + 34.6410i 0.294118 + 0.509427i
\(69\) 48.0000 0.695652
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 24.0000 0.333333
\(73\) 46.0000 0.630137 0.315068 0.949069i \(-0.397973\pi\)
0.315068 + 0.949069i \(0.397973\pi\)
\(74\) −26.0000 + 45.0333i −0.351351 + 0.608558i
\(75\) 0 0
\(76\) −72.0000 + 41.5692i −0.947368 + 0.546963i
\(77\) −48.0000 −0.623377
\(78\) −6.00000 3.46410i −0.0769231 0.0444116i
\(79\) 117.779i 1.49088i −0.666573 0.745440i \(-0.732240\pi\)
0.666573 0.745440i \(-0.267760\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 58.0000 100.459i 0.707317 1.22511i
\(83\) 48.4974i 0.584306i 0.956372 + 0.292153i \(0.0943717\pi\)
−0.956372 + 0.292153i \(0.905628\pi\)
\(84\) −24.0000 41.5692i −0.285714 0.494872i
\(85\) 0 0
\(86\) −84.0000 48.4974i −0.976744 0.563924i
\(87\) 45.0333i 0.517624i
\(88\) 55.4256i 0.629837i
\(89\) 82.0000 0.921348 0.460674 0.887569i \(-0.347608\pi\)
0.460674 + 0.887569i \(0.347608\pi\)
\(90\) 0 0
\(91\) 13.8564i 0.152268i
\(92\) −96.0000 + 55.4256i −1.04348 + 0.602452i
\(93\) 12.0000 0.129032
\(94\) 120.000 + 69.2820i 1.27660 + 0.737043i
\(95\) 0 0
\(96\) −48.0000 + 27.7128i −0.500000 + 0.288675i
\(97\) −2.00000 −0.0206186 −0.0103093 0.999947i \(-0.503282\pi\)
−0.0103093 + 0.999947i \(0.503282\pi\)
\(98\) 1.00000 1.73205i 0.0102041 0.0176740i
\(99\) 20.7846i 0.209946i
\(100\) 0 0
\(101\) −74.0000 −0.732673 −0.366337 0.930482i \(-0.619388\pi\)
−0.366337 + 0.930482i \(0.619388\pi\)
\(102\) −30.0000 17.3205i −0.294118 0.169809i
\(103\) 76.2102i 0.739905i −0.929051 0.369953i \(-0.879374\pi\)
0.929051 0.369953i \(-0.120626\pi\)
\(104\) 16.0000 0.153846
\(105\) 0 0
\(106\) 74.0000 128.172i 0.698113 1.20917i
\(107\) 20.7846i 0.194249i 0.995272 + 0.0971243i \(0.0309645\pi\)
−0.995272 + 0.0971243i \(0.969036\pi\)
\(108\) −18.0000 + 10.3923i −0.166667 + 0.0962250i
\(109\) −46.0000 −0.422018 −0.211009 0.977484i \(-0.567675\pi\)
−0.211009 + 0.977484i \(0.567675\pi\)
\(110\) 0 0
\(111\) 45.0333i 0.405706i
\(112\) 96.0000 + 55.4256i 0.857143 + 0.494872i
\(113\) 110.000 0.973451 0.486726 0.873555i \(-0.338191\pi\)
0.486726 + 0.873555i \(0.338191\pi\)
\(114\) 36.0000 62.3538i 0.315789 0.546963i
\(115\) 0 0
\(116\) 52.0000 + 90.0666i 0.448276 + 0.776437i
\(117\) 6.00000 0.0512821
\(118\) 156.000 + 90.0666i 1.32203 + 0.763277i
\(119\) 69.2820i 0.582202i
\(120\) 0 0
\(121\) 73.0000 0.603306
\(122\) 26.0000 45.0333i 0.213115 0.369126i
\(123\) 100.459i 0.816739i
\(124\) −24.0000 + 13.8564i −0.193548 + 0.111745i
\(125\) 0 0
\(126\) 36.0000 + 20.7846i 0.285714 + 0.164957i
\(127\) 145.492i 1.14561i −0.819692 0.572804i \(-0.805856\pi\)
0.819692 0.572804i \(-0.194144\pi\)
\(128\) 64.0000 110.851i 0.500000 0.866025i
\(129\) 84.0000 0.651163
\(130\) 0 0
\(131\) 117.779i 0.899080i −0.893260 0.449540i \(-0.851588\pi\)
0.893260 0.449540i \(-0.148412\pi\)
\(132\) −24.0000 41.5692i −0.181818 0.314918i
\(133\) −144.000 −1.08271
\(134\) 12.0000 + 6.92820i 0.0895522 + 0.0517030i
\(135\) 0 0
\(136\) 80.0000 0.588235
\(137\) −10.0000 −0.0729927 −0.0364964 0.999334i \(-0.511620\pi\)
−0.0364964 + 0.999334i \(0.511620\pi\)
\(138\) 48.0000 83.1384i 0.347826 0.602452i
\(139\) 48.4974i 0.348902i −0.984666 0.174451i \(-0.944185\pi\)
0.984666 0.174451i \(-0.0558151\pi\)
\(140\) 0 0
\(141\) −120.000 −0.851064
\(142\) 0 0
\(143\) 13.8564i 0.0968979i
\(144\) 24.0000 41.5692i 0.166667 0.288675i
\(145\) 0 0
\(146\) 46.0000 79.6743i 0.315068 0.545715i
\(147\) 1.73205i 0.0117827i
\(148\) 52.0000 + 90.0666i 0.351351 + 0.608558i
\(149\) −2.00000 −0.0134228 −0.00671141 0.999977i \(-0.502136\pi\)
−0.00671141 + 0.999977i \(0.502136\pi\)
\(150\) 0 0
\(151\) 90.0666i 0.596468i 0.954493 + 0.298234i \(0.0963975\pi\)
−0.954493 + 0.298234i \(0.903602\pi\)
\(152\) 166.277i 1.09393i
\(153\) 30.0000 0.196078
\(154\) −48.0000 + 83.1384i −0.311688 + 0.539860i
\(155\) 0 0
\(156\) −12.0000 + 6.92820i −0.0769231 + 0.0444116i
\(157\) 214.000 1.36306 0.681529 0.731791i \(-0.261315\pi\)
0.681529 + 0.731791i \(0.261315\pi\)
\(158\) −204.000 117.779i −1.29114 0.745440i
\(159\) 128.172i 0.806112i
\(160\) 0 0
\(161\) −192.000 −1.19255
\(162\) 9.00000 15.5885i 0.0555556 0.0962250i
\(163\) 20.7846i 0.127513i 0.997965 + 0.0637565i \(0.0203081\pi\)
−0.997965 + 0.0637565i \(0.979692\pi\)
\(164\) −116.000 200.918i −0.707317 1.22511i
\(165\) 0 0
\(166\) 84.0000 + 48.4974i 0.506024 + 0.292153i
\(167\) 96.9948i 0.580807i 0.956904 + 0.290404i \(0.0937896\pi\)
−0.956904 + 0.290404i \(0.906210\pi\)
\(168\) −96.0000 −0.571429
\(169\) −165.000 −0.976331
\(170\) 0 0
\(171\) 62.3538i 0.364642i
\(172\) −168.000 + 96.9948i −0.976744 + 0.563924i
\(173\) −334.000 −1.93064 −0.965318 0.261077i \(-0.915922\pi\)
−0.965318 + 0.261077i \(0.915922\pi\)
\(174\) −78.0000 45.0333i −0.448276 0.258812i
\(175\) 0 0
\(176\) 96.0000 + 55.4256i 0.545455 + 0.314918i
\(177\) −156.000 −0.881356
\(178\) 82.0000 142.028i 0.460674 0.797911i
\(179\) 187.061i 1.04504i 0.852628 + 0.522518i \(0.175007\pi\)
−0.852628 + 0.522518i \(0.824993\pi\)
\(180\) 0 0
\(181\) 2.00000 0.0110497 0.00552486 0.999985i \(-0.498241\pi\)
0.00552486 + 0.999985i \(0.498241\pi\)
\(182\) 24.0000 + 13.8564i 0.131868 + 0.0761341i
\(183\) 45.0333i 0.246084i
\(184\) 221.703i 1.20490i
\(185\) 0 0
\(186\) 12.0000 20.7846i 0.0645161 0.111745i
\(187\) 69.2820i 0.370492i
\(188\) 240.000 138.564i 1.27660 0.737043i
\(189\) −36.0000 −0.190476
\(190\) 0 0
\(191\) 221.703i 1.16075i 0.814351 + 0.580373i \(0.197093\pi\)
−0.814351 + 0.580373i \(0.802907\pi\)
\(192\) 110.851i 0.577350i
\(193\) −290.000 −1.50259 −0.751295 0.659966i \(-0.770571\pi\)
−0.751295 + 0.659966i \(0.770571\pi\)
\(194\) −2.00000 + 3.46410i −0.0103093 + 0.0178562i
\(195\) 0 0
\(196\) −2.00000 3.46410i −0.0102041 0.0176740i
\(197\) 26.0000 0.131980 0.0659898 0.997820i \(-0.478980\pi\)
0.0659898 + 0.997820i \(0.478980\pi\)
\(198\) 36.0000 + 20.7846i 0.181818 + 0.104973i
\(199\) 394.908i 1.98446i −0.124416 0.992230i \(-0.539706\pi\)
0.124416 0.992230i \(-0.460294\pi\)
\(200\) 0 0
\(201\) −12.0000 −0.0597015
\(202\) −74.0000 + 128.172i −0.366337 + 0.634514i
\(203\) 180.133i 0.887356i
\(204\) −60.0000 + 34.6410i −0.294118 + 0.169809i
\(205\) 0 0
\(206\) −132.000 76.2102i −0.640777 0.369953i
\(207\) 83.1384i 0.401635i
\(208\) 16.0000 27.7128i 0.0769231 0.133235i
\(209\) −144.000 −0.688995
\(210\) 0 0
\(211\) 242.487i 1.14923i 0.818425 + 0.574614i \(0.194848\pi\)
−0.818425 + 0.574614i \(0.805152\pi\)
\(212\) −148.000 256.344i −0.698113 1.20917i
\(213\) 0 0
\(214\) 36.0000 + 20.7846i 0.168224 + 0.0971243i
\(215\) 0 0
\(216\) 41.5692i 0.192450i
\(217\) −48.0000 −0.221198
\(218\) −46.0000 + 79.6743i −0.211009 + 0.365479i
\(219\) 79.6743i 0.363810i
\(220\) 0 0
\(221\) 20.0000 0.0904977
\(222\) −78.0000 45.0333i −0.351351 0.202853i
\(223\) 339.482i 1.52234i −0.648552 0.761170i \(-0.724625\pi\)
0.648552 0.761170i \(-0.275375\pi\)
\(224\) 192.000 110.851i 0.857143 0.494872i
\(225\) 0 0
\(226\) 110.000 190.526i 0.486726 0.843034i
\(227\) 284.056i 1.25135i −0.780084 0.625675i \(-0.784824\pi\)
0.780084 0.625675i \(-0.215176\pi\)
\(228\) −72.0000 124.708i −0.315789 0.546963i
\(229\) −142.000 −0.620087 −0.310044 0.950722i \(-0.600344\pi\)
−0.310044 + 0.950722i \(0.600344\pi\)
\(230\) 0 0
\(231\) 83.1384i 0.359907i
\(232\) 208.000 0.896552
\(233\) −82.0000 −0.351931 −0.175966 0.984396i \(-0.556305\pi\)
−0.175966 + 0.984396i \(0.556305\pi\)
\(234\) 6.00000 10.3923i 0.0256410 0.0444116i
\(235\) 0 0
\(236\) 312.000 180.133i 1.32203 0.763277i
\(237\) 204.000 0.860759
\(238\) 120.000 + 69.2820i 0.504202 + 0.291101i
\(239\) 387.979i 1.62334i −0.584113 0.811672i \(-0.698558\pi\)
0.584113 0.811672i \(-0.301442\pi\)
\(240\) 0 0
\(241\) −46.0000 −0.190871 −0.0954357 0.995436i \(-0.530424\pi\)
−0.0954357 + 0.995436i \(0.530424\pi\)
\(242\) 73.0000 126.440i 0.301653 0.522478i
\(243\) 15.5885i 0.0641500i
\(244\) −52.0000 90.0666i −0.213115 0.369126i
\(245\) 0 0
\(246\) 174.000 + 100.459i 0.707317 + 0.408370i
\(247\) 41.5692i 0.168296i
\(248\) 55.4256i 0.223490i
\(249\) −84.0000 −0.337349
\(250\) 0 0
\(251\) 145.492i 0.579650i −0.957080 0.289825i \(-0.906403\pi\)
0.957080 0.289825i \(-0.0935972\pi\)
\(252\) 72.0000 41.5692i 0.285714 0.164957i
\(253\) −192.000 −0.758893
\(254\) −252.000 145.492i −0.992126 0.572804i
\(255\) 0 0
\(256\) −128.000 221.703i −0.500000 0.866025i
\(257\) 254.000 0.988327 0.494163 0.869369i \(-0.335474\pi\)
0.494163 + 0.869369i \(0.335474\pi\)
\(258\) 84.0000 145.492i 0.325581 0.563924i
\(259\) 180.133i 0.695495i
\(260\) 0 0
\(261\) 78.0000 0.298851
\(262\) −204.000 117.779i −0.778626 0.449540i
\(263\) 152.420i 0.579546i 0.957095 + 0.289773i \(0.0935797\pi\)
−0.957095 + 0.289773i \(0.906420\pi\)
\(264\) −96.0000 −0.363636
\(265\) 0 0
\(266\) −144.000 + 249.415i −0.541353 + 0.937652i
\(267\) 142.028i 0.531941i
\(268\) 24.0000 13.8564i 0.0895522 0.0517030i
\(269\) 262.000 0.973978 0.486989 0.873408i \(-0.338095\pi\)
0.486989 + 0.873408i \(0.338095\pi\)
\(270\) 0 0
\(271\) 20.7846i 0.0766960i −0.999264 0.0383480i \(-0.987790\pi\)
0.999264 0.0383480i \(-0.0122095\pi\)
\(272\) 80.0000 138.564i 0.294118 0.509427i
\(273\) −24.0000 −0.0879121
\(274\) −10.0000 + 17.3205i −0.0364964 + 0.0632135i
\(275\) 0 0
\(276\) −96.0000 166.277i −0.347826 0.602452i
\(277\) −290.000 −1.04693 −0.523466 0.852047i \(-0.675361\pi\)
−0.523466 + 0.852047i \(0.675361\pi\)
\(278\) −84.0000 48.4974i −0.302158 0.174451i
\(279\) 20.7846i 0.0744968i
\(280\) 0 0
\(281\) 226.000 0.804270 0.402135 0.915580i \(-0.368268\pi\)
0.402135 + 0.915580i \(0.368268\pi\)
\(282\) −120.000 + 207.846i −0.425532 + 0.737043i
\(283\) 297.913i 1.05270i 0.850269 + 0.526348i \(0.176439\pi\)
−0.850269 + 0.526348i \(0.823561\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 24.0000 + 13.8564i 0.0839161 + 0.0484490i
\(287\) 401.836i 1.40012i
\(288\) −48.0000 83.1384i −0.166667 0.288675i
\(289\) −189.000 −0.653979
\(290\) 0 0
\(291\) 3.46410i 0.0119041i
\(292\) −92.0000 159.349i −0.315068 0.545715i
\(293\) 362.000 1.23549 0.617747 0.786377i \(-0.288045\pi\)
0.617747 + 0.786377i \(0.288045\pi\)
\(294\) 3.00000 + 1.73205i 0.0102041 + 0.00589133i
\(295\) 0 0
\(296\) 208.000 0.702703
\(297\) −36.0000 −0.121212
\(298\) −2.00000 + 3.46410i −0.00671141 + 0.0116245i
\(299\) 55.4256i 0.185370i
\(300\) 0 0
\(301\) −336.000 −1.11628
\(302\) 156.000 + 90.0666i 0.516556 + 0.298234i
\(303\) 128.172i 0.423009i
\(304\) 288.000 + 166.277i 0.947368 + 0.546963i
\(305\) 0 0
\(306\) 30.0000 51.9615i 0.0980392 0.169809i
\(307\) 145.492i 0.473916i 0.971520 + 0.236958i \(0.0761504\pi\)
−0.971520 + 0.236958i \(0.923850\pi\)
\(308\) 96.0000 + 166.277i 0.311688 + 0.539860i
\(309\) 132.000 0.427184
\(310\) 0 0
\(311\) 235.559i 0.757424i 0.925515 + 0.378712i \(0.123633\pi\)
−0.925515 + 0.378712i \(0.876367\pi\)
\(312\) 27.7128i 0.0888231i
\(313\) 478.000 1.52716 0.763578 0.645715i \(-0.223441\pi\)
0.763578 + 0.645715i \(0.223441\pi\)
\(314\) 214.000 370.659i 0.681529 1.18044i
\(315\) 0 0
\(316\) −408.000 + 235.559i −1.29114 + 0.745440i
\(317\) 170.000 0.536278 0.268139 0.963380i \(-0.413591\pi\)
0.268139 + 0.963380i \(0.413591\pi\)
\(318\) 222.000 + 128.172i 0.698113 + 0.403056i
\(319\) 180.133i 0.564681i
\(320\) 0 0
\(321\) −36.0000 −0.112150
\(322\) −192.000 + 332.554i −0.596273 + 1.03278i
\(323\) 207.846i 0.643486i
\(324\) −18.0000 31.1769i −0.0555556 0.0962250i
\(325\) 0 0
\(326\) 36.0000 + 20.7846i 0.110429 + 0.0637565i
\(327\) 79.6743i 0.243652i
\(328\) −464.000 −1.41463
\(329\) 480.000 1.45897
\(330\) 0 0
\(331\) 408.764i 1.23494i −0.786596 0.617468i \(-0.788158\pi\)
0.786596 0.617468i \(-0.211842\pi\)
\(332\) 168.000 96.9948i 0.506024 0.292153i
\(333\) 78.0000 0.234234
\(334\) 168.000 + 96.9948i 0.502994 + 0.290404i
\(335\) 0 0
\(336\) −96.0000 + 166.277i −0.285714 + 0.494872i
\(337\) −338.000 −1.00297 −0.501484 0.865167i \(-0.667212\pi\)
−0.501484 + 0.865167i \(0.667212\pi\)
\(338\) −165.000 + 285.788i −0.488166 + 0.845528i
\(339\) 190.526i 0.562022i
\(340\) 0 0
\(341\) −48.0000 −0.140762
\(342\) 108.000 + 62.3538i 0.315789 + 0.182321i
\(343\) 346.410i 1.00994i
\(344\) 387.979i 1.12785i
\(345\) 0 0
\(346\) −334.000 + 578.505i −0.965318 + 1.67198i
\(347\) 200.918i 0.579014i 0.957176 + 0.289507i \(0.0934914\pi\)
−0.957176 + 0.289507i \(0.906509\pi\)
\(348\) −156.000 + 90.0666i −0.448276 + 0.258812i
\(349\) 506.000 1.44986 0.724928 0.688824i \(-0.241873\pi\)
0.724928 + 0.688824i \(0.241873\pi\)
\(350\) 0 0
\(351\) 10.3923i 0.0296077i
\(352\) 192.000 110.851i 0.545455 0.314918i
\(353\) −178.000 −0.504249 −0.252125 0.967695i \(-0.581129\pi\)
−0.252125 + 0.967695i \(0.581129\pi\)
\(354\) −156.000 + 270.200i −0.440678 + 0.763277i
\(355\) 0 0
\(356\) −164.000 284.056i −0.460674 0.797911i
\(357\) −120.000 −0.336134
\(358\) 324.000 + 187.061i 0.905028 + 0.522518i
\(359\) 166.277i 0.463167i −0.972815 0.231583i \(-0.925609\pi\)
0.972815 0.231583i \(-0.0743906\pi\)
\(360\) 0 0
\(361\) −71.0000 −0.196676
\(362\) 2.00000 3.46410i 0.00552486 0.00956934i
\(363\) 126.440i 0.348319i
\(364\) 48.0000 27.7128i 0.131868 0.0761341i
\(365\) 0 0
\(366\) 78.0000 + 45.0333i 0.213115 + 0.123042i
\(367\) 200.918i 0.547460i 0.961807 + 0.273730i \(0.0882575\pi\)
−0.961807 + 0.273730i \(0.911742\pi\)
\(368\) 384.000 + 221.703i 1.04348 + 0.602452i
\(369\) −174.000 −0.471545
\(370\) 0 0
\(371\) 512.687i 1.38191i
\(372\) −24.0000 41.5692i −0.0645161 0.111745i
\(373\) 310.000 0.831099 0.415550 0.909571i \(-0.363589\pi\)
0.415550 + 0.909571i \(0.363589\pi\)
\(374\) 120.000 + 69.2820i 0.320856 + 0.185246i
\(375\) 0 0
\(376\) 554.256i 1.47409i
\(377\) 52.0000 0.137931
\(378\) −36.0000 + 62.3538i −0.0952381 + 0.164957i
\(379\) 436.477i 1.15165i 0.817572 + 0.575827i \(0.195320\pi\)
−0.817572 + 0.575827i \(0.804680\pi\)
\(380\) 0 0
\(381\) 252.000 0.661417
\(382\) 384.000 + 221.703i 1.00524 + 0.580373i
\(383\) 609.682i 1.59186i −0.605390 0.795929i \(-0.706983\pi\)
0.605390 0.795929i \(-0.293017\pi\)
\(384\) 192.000 + 110.851i 0.500000 + 0.288675i
\(385\) 0 0
\(386\) −290.000 + 502.295i −0.751295 + 1.30128i
\(387\) 145.492i 0.375949i
\(388\) 4.00000 + 6.92820i 0.0103093 + 0.0178562i
\(389\) −578.000 −1.48586 −0.742931 0.669368i \(-0.766565\pi\)
−0.742931 + 0.669368i \(0.766565\pi\)
\(390\) 0 0
\(391\) 277.128i 0.708768i
\(392\) −8.00000 −0.0204082
\(393\) 204.000 0.519084
\(394\) 26.0000 45.0333i 0.0659898 0.114298i
\(395\) 0 0
\(396\) 72.0000 41.5692i 0.181818 0.104973i
\(397\) −26.0000 −0.0654912 −0.0327456 0.999464i \(-0.510425\pi\)
−0.0327456 + 0.999464i \(0.510425\pi\)
\(398\) −684.000 394.908i −1.71859 0.992230i
\(399\) 249.415i 0.625101i
\(400\) 0 0
\(401\) 250.000 0.623441 0.311721 0.950174i \(-0.399095\pi\)
0.311721 + 0.950174i \(0.399095\pi\)
\(402\) −12.0000 + 20.7846i −0.0298507 + 0.0517030i
\(403\) 13.8564i 0.0343831i
\(404\) 148.000 + 256.344i 0.366337 + 0.634514i
\(405\) 0 0
\(406\) 312.000 + 180.133i 0.768473 + 0.443678i
\(407\) 180.133i 0.442588i
\(408\) 138.564i 0.339618i
\(409\) 290.000 0.709046 0.354523 0.935047i \(-0.384643\pi\)
0.354523 + 0.935047i \(0.384643\pi\)
\(410\) 0 0
\(411\) 17.3205i 0.0421424i
\(412\) −264.000 + 152.420i −0.640777 + 0.369953i
\(413\) 624.000 1.51090
\(414\) 144.000 + 83.1384i 0.347826 + 0.200817i
\(415\) 0 0
\(416\) −32.0000 55.4256i −0.0769231 0.133235i
\(417\) 84.0000 0.201439
\(418\) −144.000 + 249.415i −0.344498 + 0.596687i
\(419\) 339.482i 0.810219i 0.914268 + 0.405110i \(0.132767\pi\)
−0.914268 + 0.405110i \(0.867233\pi\)
\(420\) 0 0
\(421\) 674.000 1.60095 0.800475 0.599366i \(-0.204581\pi\)
0.800475 + 0.599366i \(0.204581\pi\)
\(422\) 420.000 + 242.487i 0.995261 + 0.574614i
\(423\) 207.846i 0.491362i
\(424\) −592.000 −1.39623
\(425\) 0 0
\(426\) 0 0
\(427\) 180.133i 0.421858i
\(428\) 72.0000 41.5692i 0.168224 0.0971243i
\(429\) −24.0000 −0.0559441
\(430\) 0 0
\(431\) 540.400i 1.25383i −0.779088 0.626914i \(-0.784318\pi\)
0.779088 0.626914i \(-0.215682\pi\)
\(432\) 72.0000 + 41.5692i 0.166667 + 0.0962250i
\(433\) 334.000 0.771363 0.385681 0.922632i \(-0.373966\pi\)
0.385681 + 0.922632i \(0.373966\pi\)
\(434\) −48.0000 + 83.1384i −0.110599 + 0.191563i
\(435\) 0 0
\(436\) 92.0000 + 159.349i 0.211009 + 0.365479i
\(437\) −576.000 −1.31808
\(438\) 138.000 + 79.6743i 0.315068 + 0.181905i
\(439\) 117.779i 0.268290i −0.990962 0.134145i \(-0.957171\pi\)
0.990962 0.134145i \(-0.0428288\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.00680272
\(442\) 20.0000 34.6410i 0.0452489 0.0783733i
\(443\) 76.2102i 0.172032i −0.996294 0.0860161i \(-0.972586\pi\)
0.996294 0.0860161i \(-0.0274136\pi\)
\(444\) −156.000 + 90.0666i −0.351351 + 0.202853i
\(445\) 0 0
\(446\) −588.000 339.482i −1.31839 0.761170i
\(447\) 3.46410i 0.00774967i
\(448\) 443.405i 0.989743i
\(449\) 394.000 0.877506 0.438753 0.898608i \(-0.355420\pi\)
0.438753 + 0.898608i \(0.355420\pi\)
\(450\) 0 0
\(451\) 401.836i 0.890988i
\(452\) −220.000 381.051i −0.486726 0.843034i
\(453\) −156.000 −0.344371
\(454\) −492.000 284.056i −1.08370 0.625675i
\(455\) 0 0
\(456\) −288.000 −0.631579
\(457\) 478.000 1.04595 0.522976 0.852347i \(-0.324822\pi\)
0.522976 + 0.852347i \(0.324822\pi\)
\(458\) −142.000 + 245.951i −0.310044 + 0.537011i
\(459\) 51.9615i 0.113206i
\(460\) 0 0
\(461\) 142.000 0.308026 0.154013 0.988069i \(-0.450780\pi\)
0.154013 + 0.988069i \(0.450780\pi\)
\(462\) −144.000 83.1384i −0.311688 0.179953i
\(463\) 630.466i 1.36170i 0.732423 + 0.680849i \(0.238389\pi\)
−0.732423 + 0.680849i \(0.761611\pi\)
\(464\) 208.000 360.267i 0.448276 0.776437i
\(465\) 0 0
\(466\) −82.0000 + 142.028i −0.175966 + 0.304781i
\(467\) 20.7846i 0.0445067i 0.999752 + 0.0222533i \(0.00708404\pi\)
−0.999752 + 0.0222533i \(0.992916\pi\)
\(468\) −12.0000 20.7846i −0.0256410 0.0444116i
\(469\) 48.0000 0.102345
\(470\) 0 0
\(471\) 370.659i 0.786962i
\(472\) 720.533i 1.52655i
\(473\) −336.000 −0.710359
\(474\) 204.000 353.338i 0.430380 0.745440i
\(475\) 0 0
\(476\) 240.000 138.564i 0.504202 0.291101i
\(477\) −222.000 −0.465409
\(478\) −672.000 387.979i −1.40586 0.811672i
\(479\) 734.390i 1.53317i −0.642141 0.766586i \(-0.721954\pi\)
0.642141 0.766586i \(-0.278046\pi\)
\(480\) 0 0
\(481\) 52.0000 0.108108
\(482\) −46.0000 + 79.6743i −0.0954357 + 0.165299i
\(483\) 332.554i 0.688517i
\(484\) −146.000 252.879i −0.301653 0.522478i
\(485\) 0 0
\(486\) 27.0000 + 15.5885i 0.0555556 + 0.0320750i
\(487\) 103.923i 0.213394i 0.994292 + 0.106697i \(0.0340275\pi\)
−0.994292 + 0.106697i \(0.965972\pi\)
\(488\) −208.000 −0.426230
\(489\) −36.0000 −0.0736196
\(490\) 0 0
\(491\) 921.451i 1.87668i 0.345711 + 0.938341i \(0.387638\pi\)
−0.345711 + 0.938341i \(0.612362\pi\)
\(492\) 348.000 200.918i 0.707317 0.408370i
\(493\) 260.000 0.527383
\(494\) 72.0000 + 41.5692i 0.145749 + 0.0841482i
\(495\) 0 0
\(496\) 96.0000 + 55.4256i 0.193548 + 0.111745i
\(497\) 0 0
\(498\) −84.0000 + 145.492i −0.168675 + 0.292153i
\(499\) 76.2102i 0.152726i 0.997080 + 0.0763630i \(0.0243308\pi\)
−0.997080 + 0.0763630i \(0.975669\pi\)
\(500\) 0 0
\(501\) −168.000 −0.335329
\(502\) −252.000 145.492i −0.501992 0.289825i
\(503\) 581.969i 1.15700i −0.815684 0.578498i \(-0.803639\pi\)
0.815684 0.578498i \(-0.196361\pi\)
\(504\) 166.277i 0.329914i
\(505\) 0 0
\(506\) −192.000 + 332.554i −0.379447 + 0.657221i
\(507\) 285.788i 0.563685i
\(508\) −504.000 + 290.985i −0.992126 + 0.572804i
\(509\) −842.000 −1.65422 −0.827112 0.562037i \(-0.810018\pi\)
−0.827112 + 0.562037i \(0.810018\pi\)
\(510\) 0 0
\(511\) 318.697i 0.623674i
\(512\) −512.000 −1.00000
\(513\) −108.000 −0.210526
\(514\) 254.000 439.941i 0.494163 0.855916i
\(515\) 0 0
\(516\) −168.000 290.985i −0.325581 0.563924i
\(517\) 480.000 0.928433
\(518\) 312.000 + 180.133i 0.602317 + 0.347748i
\(519\) 578.505i 1.11465i
\(520\) 0 0
\(521\) −326.000 −0.625720 −0.312860 0.949799i \(-0.601287\pi\)
−0.312860 + 0.949799i \(0.601287\pi\)
\(522\) 78.0000 135.100i 0.149425 0.258812i
\(523\) 311.769i 0.596117i 0.954548 + 0.298058i \(0.0963390\pi\)
−0.954548 + 0.298058i \(0.903661\pi\)
\(524\) −408.000 + 235.559i −0.778626 + 0.449540i
\(525\) 0 0
\(526\) 264.000 + 152.420i 0.501901 + 0.289773i
\(527\) 69.2820i 0.131465i
\(528\) −96.0000 + 166.277i −0.181818 + 0.314918i
\(529\) −239.000 −0.451796
\(530\) 0 0
\(531\) 270.200i 0.508851i
\(532\) 288.000 + 498.831i 0.541353 + 0.937652i
\(533\) −116.000 −0.217636
\(534\) 246.000 + 142.028i 0.460674 + 0.265970i
\(535\) 0 0
\(536\) 55.4256i 0.103406i
\(537\) −324.000 −0.603352
\(538\) 262.000 453.797i 0.486989 0.843489i
\(539\) 6.92820i 0.0128538i
\(540\) 0 0
\(541\) 530.000 0.979667 0.489834 0.871816i \(-0.337058\pi\)
0.489834 + 0.871816i \(0.337058\pi\)
\(542\) −36.0000 20.7846i −0.0664207 0.0383480i
\(543\) 3.46410i 0.00637956i
\(544\) −160.000 277.128i −0.294118 0.509427i
\(545\) 0 0
\(546\) −24.0000 + 41.5692i −0.0439560 + 0.0761341i
\(547\) 339.482i 0.620625i −0.950635 0.310313i \(-0.899566\pi\)
0.950635 0.310313i \(-0.100434\pi\)
\(548\) 20.0000 + 34.6410i 0.0364964 + 0.0632135i
\(549\) −78.0000 −0.142077
\(550\) 0 0
\(551\) 540.400i 0.980762i
\(552\) −384.000 −0.695652
\(553\) −816.000 −1.47559
\(554\) −290.000 + 502.295i −0.523466 + 0.906669i
\(555\) 0 0
\(556\) −168.000 + 96.9948i −0.302158 + 0.174451i
\(557\) −766.000 −1.37522 −0.687612 0.726078i \(-0.741341\pi\)
−0.687612 + 0.726078i \(0.741341\pi\)
\(558\) 36.0000 + 20.7846i 0.0645161 + 0.0372484i
\(559\) 96.9948i 0.173515i
\(560\) 0 0
\(561\) −120.000 −0.213904
\(562\) 226.000 391.443i 0.402135 0.696519i
\(563\) 491.902i 0.873717i 0.899530 + 0.436858i \(0.143909\pi\)
−0.899530 + 0.436858i \(0.856091\pi\)
\(564\) 240.000 + 415.692i 0.425532 + 0.737043i
\(565\) 0 0
\(566\) 516.000 + 297.913i 0.911661 + 0.526348i
\(567\) 62.3538i 0.109971i
\(568\) 0 0
\(569\) −422.000 −0.741652 −0.370826 0.928702i \(-0.620925\pi\)
−0.370826 + 0.928702i \(0.620925\pi\)
\(570\) 0 0
\(571\) 284.056i 0.497472i 0.968571 + 0.248736i \(0.0800151\pi\)
−0.968571 + 0.248736i \(0.919985\pi\)
\(572\) 48.0000 27.7128i 0.0839161 0.0484490i
\(573\) −384.000 −0.670157
\(574\) −696.000 401.836i −1.21254 0.700062i
\(575\) 0 0
\(576\) −192.000 −0.333333
\(577\) 46.0000 0.0797227 0.0398614 0.999205i \(-0.487308\pi\)
0.0398614 + 0.999205i \(0.487308\pi\)
\(578\) −189.000 + 327.358i −0.326990 + 0.566363i
\(579\) 502.295i 0.867521i
\(580\) 0 0
\(581\) 336.000 0.578313
\(582\) −6.00000 3.46410i −0.0103093 0.00595206i
\(583\) 512.687i 0.879395i
\(584\) −368.000 −0.630137
\(585\) 0 0
\(586\) 362.000 627.002i 0.617747 1.06997i
\(587\) 630.466i 1.07405i 0.843567 + 0.537024i \(0.180452\pi\)
−0.843567 + 0.537024i \(0.819548\pi\)
\(588\) 6.00000 3.46410i 0.0102041 0.00589133i
\(589\) −144.000 −0.244482
\(590\) 0 0
\(591\) 45.0333i 0.0761985i
\(592\) 208.000 360.267i 0.351351 0.608558i
\(593\) −82.0000 −0.138280 −0.0691400 0.997607i \(-0.522026\pi\)
−0.0691400 + 0.997607i \(0.522026\pi\)
\(594\) −36.0000 + 62.3538i −0.0606061 + 0.104973i
\(595\) 0 0
\(596\) 4.00000 + 6.92820i 0.00671141 + 0.0116245i
\(597\) 684.000 1.14573
\(598\) 96.0000 + 55.4256i 0.160535 + 0.0926850i
\(599\) 55.4256i 0.0925303i −0.998929 0.0462651i \(-0.985268\pi\)
0.998929 0.0462651i \(-0.0147319\pi\)
\(600\) 0 0
\(601\) −334.000 −0.555740 −0.277870 0.960619i \(-0.589629\pi\)
−0.277870 + 0.960619i \(0.589629\pi\)
\(602\) −336.000 + 581.969i −0.558140 + 0.966726i
\(603\) 20.7846i 0.0344687i
\(604\) 312.000 180.133i 0.516556 0.298234i
\(605\) 0 0
\(606\) −222.000 128.172i −0.366337 0.211505i
\(607\) 367.195i 0.604934i −0.953160 0.302467i \(-0.902190\pi\)
0.953160 0.302467i \(-0.0978102\pi\)
\(608\) 576.000 332.554i 0.947368 0.546963i
\(609\) −312.000 −0.512315
\(610\) 0 0
\(611\) 138.564i 0.226782i
\(612\) −60.0000 103.923i −0.0980392 0.169809i
\(613\) 214.000 0.349103 0.174551 0.984648i \(-0.444152\pi\)
0.174551 + 0.984648i \(0.444152\pi\)
\(614\) 252.000 + 145.492i 0.410423 + 0.236958i
\(615\) 0 0
\(616\) 384.000 0.623377
\(617\) 1118.00 1.81199 0.905997 0.423285i \(-0.139123\pi\)
0.905997 + 0.423285i \(0.139123\pi\)
\(618\) 132.000 228.631i 0.213592 0.369953i
\(619\) 672.036i 1.08568i 0.839836 + 0.542840i \(0.182651\pi\)
−0.839836 + 0.542840i \(0.817349\pi\)
\(620\) 0 0
\(621\) −144.000 −0.231884
\(622\) 408.000 + 235.559i 0.655949 + 0.378712i
\(623\) 568.113i 0.911898i
\(624\) 48.0000 + 27.7128i 0.0769231 + 0.0444116i
\(625\) 0 0
\(626\) 478.000 827.920i 0.763578 1.32256i
\(627\) 249.415i 0.397792i
\(628\) −428.000 741.318i −0.681529 1.18044i
\(629\) 260.000 0.413355
\(630\) 0 0
\(631\) 145.492i 0.230574i 0.993332 + 0.115287i \(0.0367788\pi\)
−0.993332 + 0.115287i \(0.963221\pi\)
\(632\) 942.236i 1.49088i
\(633\) −420.000 −0.663507
\(634\) 170.000 294.449i 0.268139 0.464430i
\(635\) 0 0
\(636\) 444.000 256.344i 0.698113 0.403056i
\(637\) −2.00000 −0.00313972
\(638\) 312.000 + 180.133i 0.489028 + 0.282341i
\(639\) 0 0
\(640\) 0 0
\(641\) 10.0000 0.0156006 0.00780031 0.999970i \(-0.497517\pi\)
0.00780031 + 0.999970i \(0.497517\pi\)
\(642\) −36.0000 + 62.3538i −0.0560748 + 0.0971243i
\(643\) 1212.44i 1.88559i 0.333370 + 0.942796i \(0.391814\pi\)
−0.333370 + 0.942796i \(0.608186\pi\)
\(644\) 384.000 + 665.108i 0.596273 + 1.03278i
\(645\) 0 0
\(646\) 360.000 + 207.846i 0.557276 + 0.321743i
\(647\) 332.554i 0.513993i −0.966412 0.256997i \(-0.917267\pi\)
0.966412 0.256997i \(-0.0827330\pi\)
\(648\) −72.0000 −0.111111
\(649\) 624.000 0.961479
\(650\) 0 0
\(651\) 83.1384i 0.127709i
\(652\) 72.0000 41.5692i 0.110429 0.0637565i
\(653\) −670.000 −1.02603 −0.513017 0.858379i \(-0.671472\pi\)
−0.513017 + 0.858379i \(0.671472\pi\)
\(654\) −138.000 79.6743i −0.211009 0.121826i
\(655\) 0 0
\(656\) −464.000 + 803.672i −0.707317 + 1.22511i
\(657\) −138.000 −0.210046
\(658\) 480.000 831.384i 0.729483 1.26350i
\(659\) 824.456i 1.25107i 0.780195 + 0.625536i \(0.215120\pi\)
−0.780195 + 0.625536i \(0.784880\pi\)
\(660\) 0 0
\(661\) −1222.00 −1.84871 −0.924357 0.381529i \(-0.875398\pi\)
−0.924357 + 0.381529i \(0.875398\pi\)
\(662\) −708.000 408.764i −1.06949 0.617468i
\(663\) 34.6410i 0.0522489i
\(664\) 387.979i 0.584306i
\(665\) 0 0
\(666\) 78.0000 135.100i 0.117117 0.202853i
\(667\) 720.533i 1.08026i
\(668\) 336.000 193.990i 0.502994 0.290404i
\(669\) 588.000 0.878924
\(670\) 0 0
\(671\) 180.133i 0.268455i
\(672\) 192.000 + 332.554i 0.285714 + 0.494872i
\(673\) 334.000 0.496285 0.248143 0.968724i \(-0.420180\pi\)
0.248143 + 0.968724i \(0.420180\pi\)
\(674\) −338.000 + 585.433i −0.501484 + 0.868595i
\(675\) 0 0
\(676\) 330.000 + 571.577i 0.488166 + 0.845528i
\(677\) −1006.00 −1.48597 −0.742984 0.669309i \(-0.766590\pi\)
−0.742984 + 0.669309i \(0.766590\pi\)
\(678\) 330.000 + 190.526i 0.486726 + 0.281011i
\(679\) 13.8564i 0.0204071i
\(680\) 0 0
\(681\) 492.000 0.722467
\(682\) −48.0000 + 83.1384i −0.0703812 + 0.121904i
\(683\) 187.061i 0.273882i −0.990579 0.136941i \(-0.956273\pi\)
0.990579 0.136941i \(-0.0437271\pi\)
\(684\) 216.000 124.708i 0.315789 0.182321i
\(685\) 0 0
\(686\) −600.000 346.410i −0.874636 0.504971i
\(687\) 245.951i 0.358008i
\(688\) 672.000 + 387.979i 0.976744 + 0.563924i
\(689\) −148.000 −0.214804
\(690\) 0 0
\(691\) 990.733i 1.43377i −0.697193 0.716884i \(-0.745568\pi\)
0.697193 0.716884i \(-0.254432\pi\)
\(692\) 668.000 + 1157.01i 0.965318 + 1.67198i
\(693\) 144.000 0.207792
\(694\) 348.000 + 200.918i 0.501441 + 0.289507i
\(695\) 0 0
\(696\) 360.267i 0.517624i
\(697\) −580.000 −0.832138
\(698\) 506.000 876.418i 0.724928 1.25561i
\(699\) 142.028i 0.203188i
\(700\) 0 0
\(701\) −1034.00 −1.47504 −0.737518 0.675328i \(-0.764002\pi\)
−0.737518 + 0.675328i \(0.764002\pi\)
\(702\) 18.0000 + 10.3923i 0.0256410 + 0.0148039i
\(703\) 540.400i 0.768705i
\(704\) 443.405i 0.629837i
\(705\) 0 0
\(706\) −178.000 + 308.305i −0.252125 + 0.436693i
\(707\) 512.687i 0.725158i
\(708\) 312.000 + 540.400i 0.440678 + 0.763277i
\(709\) 530.000 0.747532 0.373766 0.927523i \(-0.378066\pi\)
0.373766 + 0.927523i \(0.378066\pi\)
\(710\) 0 0
\(711\) 353.338i 0.496960i
\(712\) −656.000 −0.921348
\(713\) −192.000 −0.269285
\(714\) −120.000 + 207.846i −0.168067 + 0.291101i
\(715\) 0 0
\(716\) 648.000 374.123i 0.905028 0.522518i
\(717\) 672.000 0.937238
\(718\) −288.000 166.277i −0.401114 0.231583i
\(719\) 706.677i 0.982861i 0.870917 + 0.491430i \(0.163526\pi\)
−0.870917 + 0.491430i \(0.836474\pi\)
\(720\) 0 0
\(721\) −528.000 −0.732316
\(722\) −71.0000 + 122.976i −0.0983380 + 0.170326i
\(723\) 79.6743i 0.110200i
\(724\) −4.00000 6.92820i −0.00552486 0.00956934i
\(725\) 0 0
\(726\) 219.000 + 126.440i 0.301653 + 0.174159i
\(727\) 242.487i 0.333545i 0.985995 + 0.166772i \(0.0533345\pi\)
−0.985995 + 0.166772i \(0.946665\pi\)
\(728\) 110.851i 0.152268i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 484.974i 0.663439i
\(732\) 156.000 90.0666i 0.213115 0.123042i
\(733\) −194.000 −0.264666 −0.132333 0.991205i \(-0.542247\pi\)
−0.132333 + 0.991205i \(0.542247\pi\)
\(734\) 348.000 + 200.918i 0.474114 + 0.273730i
\(735\) 0 0
\(736\) 768.000 443.405i 1.04348 0.602452i
\(737\) 48.0000 0.0651289
\(738\) −174.000 + 301.377i −0.235772 + 0.408370i
\(739\) 1351.00i 1.82815i 0.405550 + 0.914073i \(0.367080\pi\)
−0.405550 + 0.914073i \(0.632920\pi\)
\(740\) 0 0
\(741\) −72.0000 −0.0971660
\(742\) −888.000 512.687i −1.19677 0.690953i
\(743\) 678.964i 0.913814i 0.889514 + 0.456907i \(0.151043\pi\)
−0.889514 + 0.456907i \(0.848957\pi\)
\(744\) −96.0000 −0.129032
\(745\) 0 0
\(746\) 310.000 536.936i 0.415550 0.719753i
\(747\) 145.492i 0.194769i
\(748\) 240.000 138.564i 0.320856 0.185246i
\(749\) 144.000 0.192256
\(750\) 0 0
\(751\) 658.179i 0.876404i 0.898877 + 0.438202i \(0.144385\pi\)
−0.898877 + 0.438202i \(0.855615\pi\)
\(752\) −960.000 554.256i −1.27660 0.737043i
\(753\) 252.000 0.334661
\(754\) 52.0000 90.0666i 0.0689655 0.119452i
\(755\) 0 0
\(756\) 72.0000 + 124.708i 0.0952381 + 0.164957i
\(757\) 1006.00 1.32893 0.664465 0.747319i \(-0.268659\pi\)
0.664465 + 0.747319i \(0.268659\pi\)
\(758\) 756.000 + 436.477i 0.997361 + 0.575827i
\(759\) 332.554i 0.438147i
\(760\) 0 0
\(761\) −758.000 −0.996058 −0.498029 0.867160i \(-0.665943\pi\)
−0.498029 + 0.867160i \(0.665943\pi\)
\(762\) 252.000 436.477i 0.330709 0.572804i
\(763\) 318.697i 0.417690i
\(764\) 768.000 443.405i 1.00524 0.580373i
\(765\) 0 0
\(766\) −1056.00 609.682i −1.37859 0.795929i
\(767\) 180.133i 0.234854i
\(768\) 384.000 221.703i 0.500000 0.288675i
\(769\) 2.00000 0.00260078 0.00130039 0.999999i \(-0.499586\pi\)
0.00130039 + 0.999999i \(0.499586\pi\)
\(770\) 0 0
\(771\) 439.941i 0.570611i
\(772\) 580.000 + 1004.59i 0.751295 + 1.30128i
\(773\) −262.000 −0.338939 −0.169470 0.985535i \(-0.554205\pi\)
−0.169470 + 0.985535i \(0.554205\pi\)
\(774\) 252.000 + 145.492i 0.325581 + 0.187975i
\(775\) 0 0
\(776\) 16.0000 0.0206186
\(777\) −312.000 −0.401544
\(778\) −578.000 + 1001.13i −0.742931 + 1.28679i
\(779\) 1205.51i 1.54751i
\(780\) 0 0
\(781\) 0 0
\(782\) 480.000 + 277.128i 0.613811 + 0.354384i
\(783\) 135.100i 0.172541i
\(784\) −8.00000 + 13.8564i −0.0102041 + 0.0176740i
\(785\) 0 0
\(786\) 204.000 353.338i 0.259542 0.449540i
\(787\) 1447.99i 1.83989i −0.392046 0.919946i \(-0.628233\pi\)
0.392046 0.919946i \(-0.371767\pi\)