Properties

Label 4730.2.a.z.1.2
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.88983\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.88983 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.88983 q^{6} -3.45622 q^{7} -1.00000 q^{8} +0.571445 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.88983 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.88983 q^{6} -3.45622 q^{7} -1.00000 q^{8} +0.571445 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.88983 q^{12} -1.07751 q^{13} +3.45622 q^{14} -1.88983 q^{15} +1.00000 q^{16} +4.59357 q^{17} -0.571445 q^{18} -6.77604 q^{19} +1.00000 q^{20} +6.53165 q^{21} -1.00000 q^{22} +8.70472 q^{23} +1.88983 q^{24} +1.00000 q^{25} +1.07751 q^{26} +4.58955 q^{27} -3.45622 q^{28} -5.36254 q^{29} +1.88983 q^{30} -4.60842 q^{31} -1.00000 q^{32} -1.88983 q^{33} -4.59357 q^{34} -3.45622 q^{35} +0.571445 q^{36} -7.21267 q^{37} +6.77604 q^{38} +2.03630 q^{39} -1.00000 q^{40} -7.42557 q^{41} -6.53165 q^{42} +1.00000 q^{43} +1.00000 q^{44} +0.571445 q^{45} -8.70472 q^{46} +11.0724 q^{47} -1.88983 q^{48} +4.94542 q^{49} -1.00000 q^{50} -8.68106 q^{51} -1.07751 q^{52} -11.2984 q^{53} -4.58955 q^{54} +1.00000 q^{55} +3.45622 q^{56} +12.8055 q^{57} +5.36254 q^{58} +12.0322 q^{59} -1.88983 q^{60} -7.57534 q^{61} +4.60842 q^{62} -1.97504 q^{63} +1.00000 q^{64} -1.07751 q^{65} +1.88983 q^{66} +6.54539 q^{67} +4.59357 q^{68} -16.4504 q^{69} +3.45622 q^{70} -9.42496 q^{71} -0.571445 q^{72} -15.2890 q^{73} +7.21267 q^{74} -1.88983 q^{75} -6.77604 q^{76} -3.45622 q^{77} -2.03630 q^{78} -17.5153 q^{79} +1.00000 q^{80} -10.3878 q^{81} +7.42557 q^{82} +11.9844 q^{83} +6.53165 q^{84} +4.59357 q^{85} -1.00000 q^{86} +10.1343 q^{87} -1.00000 q^{88} +2.04961 q^{89} -0.571445 q^{90} +3.72409 q^{91} +8.70472 q^{92} +8.70912 q^{93} -11.0724 q^{94} -6.77604 q^{95} +1.88983 q^{96} +17.4928 q^{97} -4.94542 q^{98} +0.571445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} - 10q^{10} + 10q^{11} + 8q^{12} + 7q^{13} - 3q^{14} + 8q^{15} + 10q^{16} + 2q^{17} - 14q^{18} - 7q^{19} + 10q^{20} - 2q^{21} - 10q^{22} + 12q^{23} - 8q^{24} + 10q^{25} - 7q^{26} + 23q^{27} + 3q^{28} - 12q^{29} - 8q^{30} + 16q^{31} - 10q^{32} + 8q^{33} - 2q^{34} + 3q^{35} + 14q^{36} + 19q^{37} + 7q^{38} + 6q^{39} - 10q^{40} + 9q^{41} + 2q^{42} + 10q^{43} + 10q^{44} + 14q^{45} - 12q^{46} + 29q^{47} + 8q^{48} + 23q^{49} - 10q^{50} - 7q^{51} + 7q^{52} + 6q^{53} - 23q^{54} + 10q^{55} - 3q^{56} + 23q^{57} + 12q^{58} + 29q^{59} + 8q^{60} - 4q^{61} - 16q^{62} + 10q^{64} + 7q^{65} - 8q^{66} + 45q^{67} + 2q^{68} + 24q^{69} - 3q^{70} - 18q^{71} - 14q^{72} + 3q^{73} - 19q^{74} + 8q^{75} - 7q^{76} + 3q^{77} - 6q^{78} - 14q^{79} + 10q^{80} + 6q^{81} - 9q^{82} + 23q^{83} - 2q^{84} + 2q^{85} - 10q^{86} + 25q^{87} - 10q^{88} + q^{89} - 14q^{90} + q^{91} + 12q^{92} + 35q^{93} - 29q^{94} - 7q^{95} - 8q^{96} + 30q^{97} - 23q^{98} + 14q^{99} + O(q^{100}) \)

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 −0.707107
\(3\) −1.88983 −1.09109 −0.545546 0.838081i \(-0.683678\pi\)
−0.545546 + 0.838081i \(0.683678\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.88983 0.771518
\(7\) −3.45622 −1.30633 −0.653163 0.757217i \(-0.726558\pi\)
−0.653163 + 0.757217i \(0.726558\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.571445 0.190482
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) −1.88983 −0.545546
\(13\) −1.07751 −0.298846 −0.149423 0.988773i \(-0.547742\pi\)
−0.149423 + 0.988773i \(0.547742\pi\)
\(14\) 3.45622 0.923712
\(15\) −1.88983 −0.487951
\(16\) 1.00000 0.250000
\(17\) 4.59357 1.11410 0.557052 0.830477i \(-0.311932\pi\)
0.557052 + 0.830477i \(0.311932\pi\)
\(18\) −0.571445 −0.134691
\(19\) −6.77604 −1.55453 −0.777265 0.629174i \(-0.783393\pi\)
−0.777265 + 0.629174i \(0.783393\pi\)
\(20\) 1.00000 0.223607
\(21\) 6.53165 1.42532
\(22\) −1.00000 −0.213201
\(23\) 8.70472 1.81506 0.907529 0.419989i \(-0.137966\pi\)
0.907529 + 0.419989i \(0.137966\pi\)
\(24\) 1.88983 0.385759
\(25\) 1.00000 0.200000
\(26\) 1.07751 0.211316
\(27\) 4.58955 0.883259
\(28\) −3.45622 −0.653163
\(29\) −5.36254 −0.995798 −0.497899 0.867235i \(-0.665895\pi\)
−0.497899 + 0.867235i \(0.665895\pi\)
\(30\) 1.88983 0.345034
\(31\) −4.60842 −0.827698 −0.413849 0.910346i \(-0.635816\pi\)
−0.413849 + 0.910346i \(0.635816\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.88983 −0.328977
\(34\) −4.59357 −0.787791
\(35\) −3.45622 −0.584207
\(36\) 0.571445 0.0952408
\(37\) −7.21267 −1.18576 −0.592878 0.805293i \(-0.702008\pi\)
−0.592878 + 0.805293i \(0.702008\pi\)
\(38\) 6.77604 1.09922
\(39\) 2.03630 0.326069
\(40\) −1.00000 −0.158114
\(41\) −7.42557 −1.15968 −0.579839 0.814731i \(-0.696885\pi\)
−0.579839 + 0.814731i \(0.696885\pi\)
\(42\) −6.53165 −1.00786
\(43\) 1.00000 0.152499
\(44\) 1.00000 0.150756
\(45\) 0.571445 0.0851859
\(46\) −8.70472 −1.28344
\(47\) 11.0724 1.61507 0.807534 0.589820i \(-0.200801\pi\)
0.807534 + 0.589820i \(0.200801\pi\)
\(48\) −1.88983 −0.272773
\(49\) 4.94542 0.706489
\(50\) −1.00000 −0.141421
\(51\) −8.68106 −1.21559
\(52\) −1.07751 −0.149423
\(53\) −11.2984 −1.55196 −0.775980 0.630757i \(-0.782744\pi\)
−0.775980 + 0.630757i \(0.782744\pi\)
\(54\) −4.58955 −0.624558
\(55\) 1.00000 0.134840
\(56\) 3.45622 0.461856
\(57\) 12.8055 1.69613
\(58\) 5.36254 0.704135
\(59\) 12.0322 1.56646 0.783231 0.621731i \(-0.213570\pi\)
0.783231 + 0.621731i \(0.213570\pi\)
\(60\) −1.88983 −0.243976
\(61\) −7.57534 −0.969923 −0.484962 0.874535i \(-0.661166\pi\)
−0.484962 + 0.874535i \(0.661166\pi\)
\(62\) 4.60842 0.585271
\(63\) −1.97504 −0.248831
\(64\) 1.00000 0.125000
\(65\) −1.07751 −0.133648
\(66\) 1.88983 0.232622
\(67\) 6.54539 0.799647 0.399824 0.916592i \(-0.369071\pi\)
0.399824 + 0.916592i \(0.369071\pi\)
\(68\) 4.59357 0.557052
\(69\) −16.4504 −1.98040
\(70\) 3.45622 0.413097
\(71\) −9.42496 −1.11854 −0.559268 0.828987i \(-0.688918\pi\)
−0.559268 + 0.828987i \(0.688918\pi\)
\(72\) −0.571445 −0.0673454
\(73\) −15.2890 −1.78944 −0.894720 0.446628i \(-0.852625\pi\)
−0.894720 + 0.446628i \(0.852625\pi\)
\(74\) 7.21267 0.838455
\(75\) −1.88983 −0.218218
\(76\) −6.77604 −0.777265
\(77\) −3.45622 −0.393872
\(78\) −2.03630 −0.230565
\(79\) −17.5153 −1.97063 −0.985313 0.170759i \(-0.945378\pi\)
−0.985313 + 0.170759i \(0.945378\pi\)
\(80\) 1.00000 0.111803
\(81\) −10.3878 −1.15420
\(82\) 7.42557 0.820017
\(83\) 11.9844 1.31546 0.657731 0.753253i \(-0.271516\pi\)
0.657731 + 0.753253i \(0.271516\pi\)
\(84\) 6.53165 0.712661
\(85\) 4.59357 0.498243
\(86\) −1.00000 −0.107833
\(87\) 10.1343 1.08651
\(88\) −1.00000 −0.106600
\(89\) 2.04961 0.217258 0.108629 0.994082i \(-0.465354\pi\)
0.108629 + 0.994082i \(0.465354\pi\)
\(90\) −0.571445 −0.0602356
\(91\) 3.72409 0.390391
\(92\) 8.70472 0.907529
\(93\) 8.70912 0.903094
\(94\) −11.0724 −1.14203
\(95\) −6.77604 −0.695207
\(96\) 1.88983 0.192880
\(97\) 17.4928 1.77612 0.888062 0.459725i \(-0.152052\pi\)
0.888062 + 0.459725i \(0.152052\pi\)
\(98\) −4.94542 −0.499563
\(99\) 0.571445 0.0574323
\(100\) 1.00000 0.100000
\(101\) 6.35009 0.631857 0.315929 0.948783i \(-0.397684\pi\)
0.315929 + 0.948783i \(0.397684\pi\)
\(102\) 8.68106 0.859553
\(103\) −16.4883 −1.62464 −0.812321 0.583211i \(-0.801796\pi\)
−0.812321 + 0.583211i \(0.801796\pi\)
\(104\) 1.07751 0.105658
\(105\) 6.53165 0.637423
\(106\) 11.2984 1.09740
\(107\) 8.99548 0.869626 0.434813 0.900521i \(-0.356814\pi\)
0.434813 + 0.900521i \(0.356814\pi\)
\(108\) 4.58955 0.441630
\(109\) −3.22082 −0.308499 −0.154249 0.988032i \(-0.549296\pi\)
−0.154249 + 0.988032i \(0.549296\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 13.6307 1.29377
\(112\) −3.45622 −0.326582
\(113\) 1.08010 0.101607 0.0508036 0.998709i \(-0.483822\pi\)
0.0508036 + 0.998709i \(0.483822\pi\)
\(114\) −12.8055 −1.19935
\(115\) 8.70472 0.811719
\(116\) −5.36254 −0.497899
\(117\) −0.615734 −0.0569247
\(118\) −12.0322 −1.10766
\(119\) −15.8764 −1.45538
\(120\) 1.88983 0.172517
\(121\) 1.00000 0.0909091
\(122\) 7.57534 0.685839
\(123\) 14.0330 1.26532
\(124\) −4.60842 −0.413849
\(125\) 1.00000 0.0894427
\(126\) 1.97504 0.175950
\(127\) −9.67459 −0.858481 −0.429240 0.903190i \(-0.641219\pi\)
−0.429240 + 0.903190i \(0.641219\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.88983 −0.166390
\(130\) 1.07751 0.0945034
\(131\) 16.5621 1.44704 0.723518 0.690305i \(-0.242524\pi\)
0.723518 + 0.690305i \(0.242524\pi\)
\(132\) −1.88983 −0.164488
\(133\) 23.4194 2.03072
\(134\) −6.54539 −0.565436
\(135\) 4.58955 0.395005
\(136\) −4.59357 −0.393896
\(137\) 10.1048 0.863310 0.431655 0.902039i \(-0.357930\pi\)
0.431655 + 0.902039i \(0.357930\pi\)
\(138\) 16.4504 1.40035
\(139\) 16.7883 1.42396 0.711980 0.702199i \(-0.247798\pi\)
0.711980 + 0.702199i \(0.247798\pi\)
\(140\) −3.45622 −0.292103
\(141\) −20.9248 −1.76219
\(142\) 9.42496 0.790925
\(143\) −1.07751 −0.0901055
\(144\) 0.571445 0.0476204
\(145\) −5.36254 −0.445334
\(146\) 15.2890 1.26533
\(147\) −9.34599 −0.770844
\(148\) −7.21267 −0.592878
\(149\) −8.89973 −0.729094 −0.364547 0.931185i \(-0.618776\pi\)
−0.364547 + 0.931185i \(0.618776\pi\)
\(150\) 1.88983 0.154304
\(151\) 12.7841 1.04036 0.520178 0.854058i \(-0.325866\pi\)
0.520178 + 0.854058i \(0.325866\pi\)
\(152\) 6.77604 0.549609
\(153\) 2.62497 0.212216
\(154\) 3.45622 0.278510
\(155\) −4.60842 −0.370158
\(156\) 2.03630 0.163034
\(157\) 1.70031 0.135699 0.0678496 0.997696i \(-0.478386\pi\)
0.0678496 + 0.997696i \(0.478386\pi\)
\(158\) 17.5153 1.39344
\(159\) 21.3521 1.69333
\(160\) −1.00000 −0.0790569
\(161\) −30.0854 −2.37106
\(162\) 10.3878 0.816141
\(163\) 10.3010 0.806835 0.403418 0.915016i \(-0.367822\pi\)
0.403418 + 0.915016i \(0.367822\pi\)
\(164\) −7.42557 −0.579839
\(165\) −1.88983 −0.147123
\(166\) −11.9844 −0.930172
\(167\) 9.69317 0.750080 0.375040 0.927009i \(-0.377629\pi\)
0.375040 + 0.927009i \(0.377629\pi\)
\(168\) −6.53165 −0.503928
\(169\) −11.8390 −0.910691
\(170\) −4.59357 −0.352311
\(171\) −3.87213 −0.296109
\(172\) 1.00000 0.0762493
\(173\) −15.4912 −1.17778 −0.588889 0.808214i \(-0.700434\pi\)
−0.588889 + 0.808214i \(0.700434\pi\)
\(174\) −10.1343 −0.768277
\(175\) −3.45622 −0.261265
\(176\) 1.00000 0.0753778
\(177\) −22.7388 −1.70915
\(178\) −2.04961 −0.153625
\(179\) 19.4443 1.45333 0.726667 0.686989i \(-0.241068\pi\)
0.726667 + 0.686989i \(0.241068\pi\)
\(180\) 0.571445 0.0425930
\(181\) −6.81662 −0.506675 −0.253338 0.967378i \(-0.581528\pi\)
−0.253338 + 0.967378i \(0.581528\pi\)
\(182\) −3.72409 −0.276048
\(183\) 14.3161 1.05828
\(184\) −8.70472 −0.641720
\(185\) −7.21267 −0.530286
\(186\) −8.70912 −0.638584
\(187\) 4.59357 0.335915
\(188\) 11.0724 0.807534
\(189\) −15.8625 −1.15382
\(190\) 6.77604 0.491585
\(191\) −8.02035 −0.580332 −0.290166 0.956976i \(-0.593711\pi\)
−0.290166 + 0.956976i \(0.593711\pi\)
\(192\) −1.88983 −0.136386
\(193\) −9.01693 −0.649053 −0.324526 0.945877i \(-0.605205\pi\)
−0.324526 + 0.945877i \(0.605205\pi\)
\(194\) −17.4928 −1.25591
\(195\) 2.03630 0.145822
\(196\) 4.94542 0.353244
\(197\) −25.1470 −1.79165 −0.895825 0.444408i \(-0.853414\pi\)
−0.895825 + 0.444408i \(0.853414\pi\)
\(198\) −0.571445 −0.0406108
\(199\) −5.50392 −0.390163 −0.195081 0.980787i \(-0.562497\pi\)
−0.195081 + 0.980787i \(0.562497\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −12.3697 −0.872489
\(202\) −6.35009 −0.446791
\(203\) 18.5341 1.30084
\(204\) −8.68106 −0.607795
\(205\) −7.42557 −0.518624
\(206\) 16.4883 1.14880
\(207\) 4.97426 0.345735
\(208\) −1.07751 −0.0747115
\(209\) −6.77604 −0.468708
\(210\) −6.53165 −0.450726
\(211\) −10.3421 −0.711982 −0.355991 0.934489i \(-0.615857\pi\)
−0.355991 + 0.934489i \(0.615857\pi\)
\(212\) −11.2984 −0.775980
\(213\) 17.8115 1.22043
\(214\) −8.99548 −0.614919
\(215\) 1.00000 0.0681994
\(216\) −4.58955 −0.312279
\(217\) 15.9277 1.08124
\(218\) 3.22082 0.218142
\(219\) 28.8935 1.95244
\(220\) 1.00000 0.0674200
\(221\) −4.94960 −0.332946
\(222\) −13.6307 −0.914832
\(223\) −14.5630 −0.975209 −0.487605 0.873065i \(-0.662129\pi\)
−0.487605 + 0.873065i \(0.662129\pi\)
\(224\) 3.45622 0.230928
\(225\) 0.571445 0.0380963
\(226\) −1.08010 −0.0718471
\(227\) −17.2021 −1.14174 −0.570872 0.821039i \(-0.693395\pi\)
−0.570872 + 0.821039i \(0.693395\pi\)
\(228\) 12.8055 0.848067
\(229\) 13.8155 0.912954 0.456477 0.889735i \(-0.349111\pi\)
0.456477 + 0.889735i \(0.349111\pi\)
\(230\) −8.70472 −0.573972
\(231\) 6.53165 0.429751
\(232\) 5.36254 0.352068
\(233\) 9.04894 0.592816 0.296408 0.955061i \(-0.404211\pi\)
0.296408 + 0.955061i \(0.404211\pi\)
\(234\) 0.615734 0.0402518
\(235\) 11.0724 0.722281
\(236\) 12.0322 0.783231
\(237\) 33.1009 2.15013
\(238\) 15.8764 1.02911
\(239\) 22.8641 1.47896 0.739479 0.673180i \(-0.235072\pi\)
0.739479 + 0.673180i \(0.235072\pi\)
\(240\) −1.88983 −0.121988
\(241\) −4.14263 −0.266850 −0.133425 0.991059i \(-0.542598\pi\)
−0.133425 + 0.991059i \(0.542598\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 5.86247 0.376077
\(244\) −7.57534 −0.484962
\(245\) 4.94542 0.315951
\(246\) −14.0330 −0.894714
\(247\) 7.30121 0.464565
\(248\) 4.60842 0.292635
\(249\) −22.6485 −1.43529
\(250\) −1.00000 −0.0632456
\(251\) −2.52626 −0.159456 −0.0797281 0.996817i \(-0.525405\pi\)
−0.0797281 + 0.996817i \(0.525405\pi\)
\(252\) −1.97504 −0.124416
\(253\) 8.70472 0.547261
\(254\) 9.67459 0.607038
\(255\) −8.68106 −0.543629
\(256\) 1.00000 0.0625000
\(257\) 10.6223 0.662599 0.331300 0.943526i \(-0.392513\pi\)
0.331300 + 0.943526i \(0.392513\pi\)
\(258\) 1.88983 0.117655
\(259\) 24.9285 1.54898
\(260\) −1.07751 −0.0668240
\(261\) −3.06439 −0.189681
\(262\) −16.5621 −1.02321
\(263\) 21.1937 1.30686 0.653431 0.756986i \(-0.273329\pi\)
0.653431 + 0.756986i \(0.273329\pi\)
\(264\) 1.88983 0.116311
\(265\) −11.2984 −0.694058
\(266\) −23.4194 −1.43594
\(267\) −3.87341 −0.237049
\(268\) 6.54539 0.399824
\(269\) −4.15461 −0.253311 −0.126655 0.991947i \(-0.540424\pi\)
−0.126655 + 0.991947i \(0.540424\pi\)
\(270\) −4.58955 −0.279311
\(271\) 18.9427 1.15069 0.575343 0.817912i \(-0.304868\pi\)
0.575343 + 0.817912i \(0.304868\pi\)
\(272\) 4.59357 0.278526
\(273\) −7.03788 −0.425952
\(274\) −10.1048 −0.610452
\(275\) 1.00000 0.0603023
\(276\) −16.4504 −0.990198
\(277\) 17.5473 1.05432 0.527158 0.849767i \(-0.323258\pi\)
0.527158 + 0.849767i \(0.323258\pi\)
\(278\) −16.7883 −1.00689
\(279\) −2.63346 −0.157661
\(280\) 3.45622 0.206548
\(281\) 13.4738 0.803780 0.401890 0.915688i \(-0.368353\pi\)
0.401890 + 0.915688i \(0.368353\pi\)
\(282\) 20.9248 1.24606
\(283\) 12.9479 0.769670 0.384835 0.922985i \(-0.374258\pi\)
0.384835 + 0.922985i \(0.374258\pi\)
\(284\) −9.42496 −0.559268
\(285\) 12.8055 0.758534
\(286\) 1.07751 0.0637142
\(287\) 25.6644 1.51492
\(288\) −0.571445 −0.0336727
\(289\) 4.10091 0.241230
\(290\) 5.36254 0.314899
\(291\) −33.0583 −1.93791
\(292\) −15.2890 −0.894720
\(293\) 24.7492 1.44586 0.722932 0.690919i \(-0.242794\pi\)
0.722932 + 0.690919i \(0.242794\pi\)
\(294\) 9.34599 0.545069
\(295\) 12.0322 0.700543
\(296\) 7.21267 0.419228
\(297\) 4.58955 0.266313
\(298\) 8.89973 0.515548
\(299\) −9.37938 −0.542423
\(300\) −1.88983 −0.109109
\(301\) −3.45622 −0.199213
\(302\) −12.7841 −0.735643
\(303\) −12.0006 −0.689415
\(304\) −6.77604 −0.388632
\(305\) −7.57534 −0.433763
\(306\) −2.62497 −0.150060
\(307\) −19.0895 −1.08949 −0.544747 0.838601i \(-0.683374\pi\)
−0.544747 + 0.838601i \(0.683374\pi\)
\(308\) −3.45622 −0.196936
\(309\) 31.1601 1.77263
\(310\) 4.60842 0.261741
\(311\) 12.7689 0.724057 0.362029 0.932167i \(-0.382084\pi\)
0.362029 + 0.932167i \(0.382084\pi\)
\(312\) −2.03630 −0.115283
\(313\) −14.5767 −0.823926 −0.411963 0.911201i \(-0.635157\pi\)
−0.411963 + 0.911201i \(0.635157\pi\)
\(314\) −1.70031 −0.0959539
\(315\) −1.97504 −0.111281
\(316\) −17.5153 −0.985313
\(317\) 26.4861 1.48761 0.743805 0.668397i \(-0.233019\pi\)
0.743805 + 0.668397i \(0.233019\pi\)
\(318\) −21.3521 −1.19737
\(319\) −5.36254 −0.300244
\(320\) 1.00000 0.0559017
\(321\) −16.9999 −0.948842
\(322\) 30.0854 1.67659
\(323\) −31.1262 −1.73191
\(324\) −10.3878 −0.577099
\(325\) −1.07751 −0.0597692
\(326\) −10.3010 −0.570519
\(327\) 6.08680 0.336601
\(328\) 7.42557 0.410008
\(329\) −38.2684 −2.10981
\(330\) 1.88983 0.104032
\(331\) 25.6588 1.41033 0.705166 0.709042i \(-0.250872\pi\)
0.705166 + 0.709042i \(0.250872\pi\)
\(332\) 11.9844 0.657731
\(333\) −4.12164 −0.225864
\(334\) −9.69317 −0.530387
\(335\) 6.54539 0.357613
\(336\) 6.53165 0.356331
\(337\) 26.1800 1.42612 0.713059 0.701104i \(-0.247309\pi\)
0.713059 + 0.701104i \(0.247309\pi\)
\(338\) 11.8390 0.643956
\(339\) −2.04120 −0.110863
\(340\) 4.59357 0.249121
\(341\) −4.60842 −0.249560
\(342\) 3.87213 0.209381
\(343\) 7.10106 0.383421
\(344\) −1.00000 −0.0539164
\(345\) −16.4504 −0.885660
\(346\) 15.4912 0.832814
\(347\) 0.381914 0.0205022 0.0102511 0.999947i \(-0.496737\pi\)
0.0102511 + 0.999947i \(0.496737\pi\)
\(348\) 10.1343 0.543254
\(349\) 36.1193 1.93342 0.966710 0.255875i \(-0.0823636\pi\)
0.966710 + 0.255875i \(0.0823636\pi\)
\(350\) 3.45622 0.184742
\(351\) −4.94526 −0.263959
\(352\) −1.00000 −0.0533002
\(353\) 13.8626 0.737833 0.368917 0.929463i \(-0.379729\pi\)
0.368917 + 0.929463i \(0.379729\pi\)
\(354\) 22.7388 1.20855
\(355\) −9.42496 −0.500225
\(356\) 2.04961 0.108629
\(357\) 30.0036 1.58796
\(358\) −19.4443 −1.02766
\(359\) −6.72567 −0.354967 −0.177484 0.984124i \(-0.556796\pi\)
−0.177484 + 0.984124i \(0.556796\pi\)
\(360\) −0.571445 −0.0301178
\(361\) 26.9147 1.41656
\(362\) 6.81662 0.358273
\(363\) −1.88983 −0.0991902
\(364\) 3.72409 0.195195
\(365\) −15.2890 −0.800262
\(366\) −14.3161 −0.748314
\(367\) −18.1752 −0.948737 −0.474368 0.880326i \(-0.657323\pi\)
−0.474368 + 0.880326i \(0.657323\pi\)
\(368\) 8.70472 0.453765
\(369\) −4.24330 −0.220897
\(370\) 7.21267 0.374969
\(371\) 39.0498 2.02737
\(372\) 8.70912 0.451547
\(373\) 10.2057 0.528429 0.264214 0.964464i \(-0.414887\pi\)
0.264214 + 0.964464i \(0.414887\pi\)
\(374\) −4.59357 −0.237528
\(375\) −1.88983 −0.0975902
\(376\) −11.0724 −0.571013
\(377\) 5.77816 0.297590
\(378\) 15.8625 0.815877
\(379\) −15.2049 −0.781023 −0.390512 0.920598i \(-0.627702\pi\)
−0.390512 + 0.920598i \(0.627702\pi\)
\(380\) −6.77604 −0.347603
\(381\) 18.2833 0.936681
\(382\) 8.02035 0.410357
\(383\) 3.18647 0.162821 0.0814106 0.996681i \(-0.474058\pi\)
0.0814106 + 0.996681i \(0.474058\pi\)
\(384\) 1.88983 0.0964398
\(385\) −3.45622 −0.176145
\(386\) 9.01693 0.458950
\(387\) 0.571445 0.0290482
\(388\) 17.4928 0.888062
\(389\) 6.25531 0.317157 0.158578 0.987346i \(-0.449309\pi\)
0.158578 + 0.987346i \(0.449309\pi\)
\(390\) −2.03630 −0.103112
\(391\) 39.9857 2.02217
\(392\) −4.94542 −0.249782
\(393\) −31.2995 −1.57885
\(394\) 25.1470 1.26689
\(395\) −17.5153 −0.881291
\(396\) 0.571445 0.0287162
\(397\) 16.0927 0.807668 0.403834 0.914832i \(-0.367677\pi\)
0.403834 + 0.914832i \(0.367677\pi\)
\(398\) 5.50392 0.275887
\(399\) −44.2587 −2.21571
\(400\) 1.00000 0.0500000
\(401\) −22.0145 −1.09935 −0.549675 0.835379i \(-0.685248\pi\)
−0.549675 + 0.835379i \(0.685248\pi\)
\(402\) 12.3697 0.616943
\(403\) 4.96560 0.247354
\(404\) 6.35009 0.315929
\(405\) −10.3878 −0.516173
\(406\) −18.5341 −0.919831
\(407\) −7.21267 −0.357519
\(408\) 8.68106 0.429776
\(409\) 16.4582 0.813806 0.406903 0.913471i \(-0.366609\pi\)
0.406903 + 0.913471i \(0.366609\pi\)
\(410\) 7.42557 0.366723
\(411\) −19.0963 −0.941950
\(412\) −16.4883 −0.812321
\(413\) −41.5860 −2.04631
\(414\) −4.97426 −0.244472
\(415\) 11.9844 0.588293
\(416\) 1.07751 0.0528290
\(417\) −31.7269 −1.55367
\(418\) 6.77604 0.331427
\(419\) 19.9866 0.976409 0.488204 0.872729i \(-0.337652\pi\)
0.488204 + 0.872729i \(0.337652\pi\)
\(420\) 6.53165 0.318712
\(421\) 28.4459 1.38637 0.693185 0.720760i \(-0.256207\pi\)
0.693185 + 0.720760i \(0.256207\pi\)
\(422\) 10.3421 0.503447
\(423\) 6.32724 0.307641
\(424\) 11.2984 0.548701
\(425\) 4.59357 0.222821
\(426\) −17.8115 −0.862972
\(427\) 26.1820 1.26704
\(428\) 8.99548 0.434813
\(429\) 2.03630 0.0983134
\(430\) −1.00000 −0.0482243
\(431\) −4.26692 −0.205530 −0.102765 0.994706i \(-0.532769\pi\)
−0.102765 + 0.994706i \(0.532769\pi\)
\(432\) 4.58955 0.220815
\(433\) 2.49978 0.120132 0.0600659 0.998194i \(-0.480869\pi\)
0.0600659 + 0.998194i \(0.480869\pi\)
\(434\) −15.9277 −0.764554
\(435\) 10.1343 0.485901
\(436\) −3.22082 −0.154249
\(437\) −58.9835 −2.82156
\(438\) −28.8935 −1.38059
\(439\) −20.6046 −0.983403 −0.491702 0.870764i \(-0.663625\pi\)
−0.491702 + 0.870764i \(0.663625\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 2.82604 0.134573
\(442\) 4.94960 0.235428
\(443\) 21.0118 0.998302 0.499151 0.866515i \(-0.333645\pi\)
0.499151 + 0.866515i \(0.333645\pi\)
\(444\) 13.6307 0.646884
\(445\) 2.04961 0.0971608
\(446\) 14.5630 0.689577
\(447\) 16.8189 0.795509
\(448\) −3.45622 −0.163291
\(449\) 37.0426 1.74815 0.874075 0.485792i \(-0.161469\pi\)
0.874075 + 0.485792i \(0.161469\pi\)
\(450\) −0.571445 −0.0269382
\(451\) −7.42557 −0.349656
\(452\) 1.08010 0.0508036
\(453\) −24.1598 −1.13512
\(454\) 17.2021 0.807336
\(455\) 3.72409 0.174588
\(456\) −12.8055 −0.599674
\(457\) 23.7135 1.10927 0.554636 0.832093i \(-0.312858\pi\)
0.554636 + 0.832093i \(0.312858\pi\)
\(458\) −13.8155 −0.645556
\(459\) 21.0824 0.984043
\(460\) 8.70472 0.405859
\(461\) 18.1272 0.844269 0.422135 0.906533i \(-0.361281\pi\)
0.422135 + 0.906533i \(0.361281\pi\)
\(462\) −6.53165 −0.303880
\(463\) −1.95012 −0.0906296 −0.0453148 0.998973i \(-0.514429\pi\)
−0.0453148 + 0.998973i \(0.514429\pi\)
\(464\) −5.36254 −0.248949
\(465\) 8.70912 0.403876
\(466\) −9.04894 −0.419184
\(467\) −10.8915 −0.503999 −0.252000 0.967727i \(-0.581088\pi\)
−0.252000 + 0.967727i \(0.581088\pi\)
\(468\) −0.615734 −0.0284623
\(469\) −22.6223 −1.04460
\(470\) −11.0724 −0.510730
\(471\) −3.21329 −0.148060
\(472\) −12.0322 −0.553828
\(473\) 1.00000 0.0459800
\(474\) −33.1009 −1.52037
\(475\) −6.77604 −0.310906
\(476\) −15.8764 −0.727692
\(477\) −6.45643 −0.295620
\(478\) −22.8641 −1.04578
\(479\) −20.1081 −0.918763 −0.459381 0.888239i \(-0.651929\pi\)
−0.459381 + 0.888239i \(0.651929\pi\)
\(480\) 1.88983 0.0862584
\(481\) 7.77168 0.354358
\(482\) 4.14263 0.188692
\(483\) 56.8561 2.58704
\(484\) 1.00000 0.0454545
\(485\) 17.4928 0.794306
\(486\) −5.86247 −0.265927
\(487\) 0.0886944 0.00401913 0.00200956 0.999998i \(-0.499360\pi\)
0.00200956 + 0.999998i \(0.499360\pi\)
\(488\) 7.57534 0.342920
\(489\) −19.4671 −0.880331
\(490\) −4.94542 −0.223411
\(491\) 17.0693 0.770328 0.385164 0.922848i \(-0.374145\pi\)
0.385164 + 0.922848i \(0.374145\pi\)
\(492\) 14.0330 0.632658
\(493\) −24.6332 −1.10942
\(494\) −7.30121 −0.328497
\(495\) 0.571445 0.0256845
\(496\) −4.60842 −0.206924
\(497\) 32.5747 1.46117
\(498\) 22.6485 1.01490
\(499\) 19.6472 0.879530 0.439765 0.898113i \(-0.355062\pi\)
0.439765 + 0.898113i \(0.355062\pi\)
\(500\) 1.00000 0.0447214
\(501\) −18.3184 −0.818406
\(502\) 2.52626 0.112753
\(503\) −30.5714 −1.36311 −0.681555 0.731767i \(-0.738696\pi\)
−0.681555 + 0.731767i \(0.738696\pi\)
\(504\) 1.97504 0.0879751
\(505\) 6.35009 0.282575
\(506\) −8.70472 −0.386972
\(507\) 22.3736 0.993648
\(508\) −9.67459 −0.429240
\(509\) −41.9122 −1.85773 −0.928863 0.370424i \(-0.879212\pi\)
−0.928863 + 0.370424i \(0.879212\pi\)
\(510\) 8.68106 0.384404
\(511\) 52.8420 2.33759
\(512\) −1.00000 −0.0441942
\(513\) −31.0989 −1.37305
\(514\) −10.6223 −0.468528
\(515\) −16.4883 −0.726562
\(516\) −1.88983 −0.0831950
\(517\) 11.0724 0.486962
\(518\) −24.9285 −1.09530
\(519\) 29.2758 1.28506
\(520\) 1.07751 0.0472517
\(521\) 24.5762 1.07670 0.538351 0.842721i \(-0.319047\pi\)
0.538351 + 0.842721i \(0.319047\pi\)
\(522\) 3.06439 0.134125
\(523\) −8.55331 −0.374010 −0.187005 0.982359i \(-0.559878\pi\)
−0.187005 + 0.982359i \(0.559878\pi\)
\(524\) 16.5621 0.723518
\(525\) 6.53165 0.285064
\(526\) −21.1937 −0.924091
\(527\) −21.1691 −0.922142
\(528\) −1.88983 −0.0822441
\(529\) 52.7721 2.29444
\(530\) 11.2984 0.490773
\(531\) 6.87575 0.298382
\(532\) 23.4194 1.01536
\(533\) 8.00109 0.346565
\(534\) 3.87341 0.167619
\(535\) 8.99548 0.388909
\(536\) −6.54539 −0.282718
\(537\) −36.7463 −1.58572
\(538\) 4.15461 0.179118
\(539\) 4.94542 0.213014
\(540\) 4.58955 0.197503
\(541\) 43.8421 1.88492 0.942459 0.334321i \(-0.108507\pi\)
0.942459 + 0.334321i \(0.108507\pi\)
\(542\) −18.9427 −0.813658
\(543\) 12.8822 0.552829
\(544\) −4.59357 −0.196948
\(545\) −3.22082 −0.137965
\(546\) 7.03788 0.301194
\(547\) 30.2464 1.29324 0.646620 0.762812i \(-0.276182\pi\)
0.646620 + 0.762812i \(0.276182\pi\)
\(548\) 10.1048 0.431655
\(549\) −4.32889 −0.184752
\(550\) −1.00000 −0.0426401
\(551\) 36.3367 1.54800
\(552\) 16.4504 0.700176
\(553\) 60.5367 2.57428
\(554\) −17.5473 −0.745514
\(555\) 13.6307 0.578591
\(556\) 16.7883 0.711980
\(557\) 26.2412 1.11188 0.555938 0.831224i \(-0.312359\pi\)
0.555938 + 0.831224i \(0.312359\pi\)
\(558\) 2.63346 0.111483
\(559\) −1.07751 −0.0455736
\(560\) −3.45622 −0.146052
\(561\) −8.68106 −0.366514
\(562\) −13.4738 −0.568358
\(563\) −22.3309 −0.941135 −0.470567 0.882364i \(-0.655951\pi\)
−0.470567 + 0.882364i \(0.655951\pi\)
\(564\) −20.9248 −0.881094
\(565\) 1.08010 0.0454401
\(566\) −12.9479 −0.544239
\(567\) 35.9024 1.50776
\(568\) 9.42496 0.395462
\(569\) −19.1033 −0.800853 −0.400427 0.916329i \(-0.631138\pi\)
−0.400427 + 0.916329i \(0.631138\pi\)
\(570\) −12.8055 −0.536365
\(571\) 16.3831 0.685612 0.342806 0.939406i \(-0.388623\pi\)
0.342806 + 0.939406i \(0.388623\pi\)
\(572\) −1.07751 −0.0450527
\(573\) 15.1571 0.633196
\(574\) −25.6644 −1.07121
\(575\) 8.70472 0.363012
\(576\) 0.571445 0.0238102
\(577\) −7.26312 −0.302368 −0.151184 0.988506i \(-0.548309\pi\)
−0.151184 + 0.988506i \(0.548309\pi\)
\(578\) −4.10091 −0.170575
\(579\) 17.0404 0.708176
\(580\) −5.36254 −0.222667
\(581\) −41.4208 −1.71842
\(582\) 33.0583 1.37031
\(583\) −11.2984 −0.467934
\(584\) 15.2890 0.632663
\(585\) −0.615734 −0.0254575
\(586\) −24.7492 −1.02238
\(587\) 14.7950 0.610657 0.305328 0.952247i \(-0.401234\pi\)
0.305328 + 0.952247i \(0.401234\pi\)
\(588\) −9.34599 −0.385422
\(589\) 31.2269 1.28668
\(590\) −12.0322 −0.495359
\(591\) 47.5235 1.95485
\(592\) −7.21267 −0.296439
\(593\) 14.6562 0.601859 0.300929 0.953646i \(-0.402703\pi\)
0.300929 + 0.953646i \(0.402703\pi\)
\(594\) −4.58955 −0.188311
\(595\) −15.8764 −0.650868
\(596\) −8.89973 −0.364547
\(597\) 10.4015 0.425703
\(598\) 9.37938 0.383551
\(599\) 2.16647 0.0885196 0.0442598 0.999020i \(-0.485907\pi\)
0.0442598 + 0.999020i \(0.485907\pi\)
\(600\) 1.88983 0.0771518
\(601\) 0.578261 0.0235878 0.0117939 0.999930i \(-0.496246\pi\)
0.0117939 + 0.999930i \(0.496246\pi\)
\(602\) 3.45622 0.140865
\(603\) 3.74033 0.152318
\(604\) 12.7841 0.520178
\(605\) 1.00000 0.0406558
\(606\) 12.0006 0.487490
\(607\) 10.8521 0.440472 0.220236 0.975447i \(-0.429317\pi\)
0.220236 + 0.975447i \(0.429317\pi\)
\(608\) 6.77604 0.274805
\(609\) −35.0262 −1.41933
\(610\) 7.57534 0.306717
\(611\) −11.9305 −0.482657
\(612\) 2.62497 0.106108
\(613\) −46.8590 −1.89262 −0.946309 0.323262i \(-0.895220\pi\)
−0.946309 + 0.323262i \(0.895220\pi\)
\(614\) 19.0895 0.770388
\(615\) 14.0330 0.565867
\(616\) 3.45622 0.139255
\(617\) 21.8229 0.878556 0.439278 0.898351i \(-0.355234\pi\)
0.439278 + 0.898351i \(0.355234\pi\)
\(618\) −31.1601 −1.25344
\(619\) 9.61180 0.386331 0.193165 0.981166i \(-0.438125\pi\)
0.193165 + 0.981166i \(0.438125\pi\)
\(620\) −4.60842 −0.185079
\(621\) 39.9507 1.60317
\(622\) −12.7689 −0.511986
\(623\) −7.08389 −0.283810
\(624\) 2.03630 0.0815171
\(625\) 1.00000 0.0400000
\(626\) 14.5767 0.582603
\(627\) 12.8055 0.511404
\(628\) 1.70031 0.0678496
\(629\) −33.1319 −1.32106
\(630\) 1.97504 0.0786873
\(631\) −5.74932 −0.228877 −0.114438 0.993430i \(-0.536507\pi\)
−0.114438 + 0.993430i \(0.536507\pi\)
\(632\) 17.5153 0.696721
\(633\) 19.5448 0.776838
\(634\) −26.4861 −1.05190
\(635\) −9.67459 −0.383924
\(636\) 21.3521 0.846666
\(637\) −5.32872 −0.211131
\(638\) 5.36254 0.212305
\(639\) −5.38584 −0.213061
\(640\) −1.00000 −0.0395285
\(641\) −5.71092 −0.225568 −0.112784 0.993620i \(-0.535977\pi\)
−0.112784 + 0.993620i \(0.535977\pi\)
\(642\) 16.9999 0.670933
\(643\) −39.1330 −1.54325 −0.771627 0.636075i \(-0.780557\pi\)
−0.771627 + 0.636075i \(0.780557\pi\)
\(644\) −30.0854 −1.18553
\(645\) −1.88983 −0.0744119
\(646\) 31.1262 1.22464
\(647\) −1.14254 −0.0449179 −0.0224589 0.999748i \(-0.507149\pi\)
−0.0224589 + 0.999748i \(0.507149\pi\)
\(648\) 10.3878 0.408071
\(649\) 12.0322 0.472306
\(650\) 1.07751 0.0422632
\(651\) −30.1006 −1.17974
\(652\) 10.3010 0.403418
\(653\) −12.3063 −0.481582 −0.240791 0.970577i \(-0.577407\pi\)
−0.240791 + 0.970577i \(0.577407\pi\)
\(654\) −6.08680 −0.238013
\(655\) 16.5621 0.647134
\(656\) −7.42557 −0.289920
\(657\) −8.73681 −0.340855
\(658\) 38.2684 1.49186
\(659\) −34.7802 −1.35484 −0.677422 0.735595i \(-0.736903\pi\)
−0.677422 + 0.735595i \(0.736903\pi\)
\(660\) −1.88983 −0.0735614
\(661\) 29.2294 1.13689 0.568446 0.822720i \(-0.307545\pi\)
0.568446 + 0.822720i \(0.307545\pi\)
\(662\) −25.6588 −0.997256
\(663\) 9.35388 0.363275
\(664\) −11.9844 −0.465086
\(665\) 23.4194 0.908167
\(666\) 4.12164 0.159710
\(667\) −46.6794 −1.80743
\(668\) 9.69317 0.375040
\(669\) 27.5215 1.06404
\(670\) −6.54539 −0.252871
\(671\) −7.57534 −0.292443
\(672\) −6.53165 −0.251964
\(673\) −24.2715 −0.935597 −0.467799 0.883835i \(-0.654953\pi\)
−0.467799 + 0.883835i \(0.654953\pi\)
\(674\) −26.1800 −1.00842
\(675\) 4.58955 0.176652
\(676\) −11.8390 −0.455345
\(677\) 3.54176 0.136121 0.0680605 0.997681i \(-0.478319\pi\)
0.0680605 + 0.997681i \(0.478319\pi\)
\(678\) 2.04120 0.0783918
\(679\) −60.4588 −2.32020
\(680\) −4.59357 −0.176155
\(681\) 32.5090 1.24575
\(682\) 4.60842 0.176466
\(683\) −25.3591 −0.970338 −0.485169 0.874420i \(-0.661242\pi\)
−0.485169 + 0.874420i \(0.661242\pi\)
\(684\) −3.87213 −0.148055
\(685\) 10.1048 0.386084
\(686\) −7.10106 −0.271120
\(687\) −26.1089 −0.996117
\(688\) 1.00000 0.0381246
\(689\) 12.1741 0.463797
\(690\) 16.4504 0.626256
\(691\) −46.6313 −1.77394 −0.886968 0.461830i \(-0.847193\pi\)
−0.886968 + 0.461830i \(0.847193\pi\)
\(692\) −15.4912 −0.588889
\(693\) −1.97504 −0.0750254
\(694\) −0.381914 −0.0144973
\(695\) 16.7883 0.636815
\(696\) −10.1343 −0.384138
\(697\) −34.1099 −1.29200
\(698\) −36.1193 −1.36713
\(699\) −17.1009 −0.646817
\(700\) −3.45622 −0.130633
\(701\) −4.84094 −0.182840 −0.0914198 0.995812i \(-0.529141\pi\)
−0.0914198 + 0.995812i \(0.529141\pi\)
\(702\) 4.94526 0.186647
\(703\) 48.8733 1.84329
\(704\) 1.00000 0.0376889
\(705\) −20.9248 −0.788075
\(706\) −13.8626 −0.521727
\(707\) −21.9473 −0.825412
\(708\) −22.7388 −0.854577
\(709\) −31.1161 −1.16859 −0.584295 0.811541i \(-0.698629\pi\)
−0.584295 + 0.811541i \(0.698629\pi\)
\(710\) 9.42496 0.353712
\(711\) −10.0090 −0.375368
\(712\) −2.04961 −0.0768124
\(713\) −40.1150 −1.50232
\(714\) −30.0036 −1.12286
\(715\) −1.07751 −0.0402964
\(716\) 19.4443 0.726667
\(717\) −43.2092 −1.61368
\(718\) 6.72567 0.251000
\(719\) 4.25998 0.158870 0.0794352 0.996840i \(-0.474688\pi\)
0.0794352 + 0.996840i \(0.474688\pi\)
\(720\) 0.571445 0.0212965
\(721\) 56.9872 2.12231
\(722\) −26.9147 −1.00166
\(723\) 7.82886 0.291158
\(724\) −6.81662 −0.253338
\(725\) −5.36254 −0.199160
\(726\) 1.88983 0.0701380
\(727\) 11.4378 0.424203 0.212101 0.977248i \(-0.431969\pi\)
0.212101 + 0.977248i \(0.431969\pi\)
\(728\) −3.72409 −0.138024
\(729\) 20.0843 0.743863
\(730\) 15.2890 0.565871
\(731\) 4.59357 0.169899
\(732\) 14.3161 0.529138
\(733\) −2.21227 −0.0817121 −0.0408560 0.999165i \(-0.513009\pi\)
−0.0408560 + 0.999165i \(0.513009\pi\)
\(734\) 18.1752 0.670858
\(735\) −9.34599 −0.344732
\(736\) −8.70472 −0.320860
\(737\) 6.54539 0.241103
\(738\) 4.24330 0.156198
\(739\) 33.0428 1.21550 0.607749 0.794129i \(-0.292073\pi\)
0.607749 + 0.794129i \(0.292073\pi\)
\(740\) −7.21267 −0.265143
\(741\) −13.7980 −0.506883
\(742\) −39.0498 −1.43356
\(743\) 32.8702 1.20589 0.602945 0.797783i \(-0.293994\pi\)
0.602945 + 0.797783i \(0.293994\pi\)
\(744\) −8.70912 −0.319292
\(745\) −8.89973 −0.326061
\(746\) −10.2057 −0.373656
\(747\) 6.84844 0.250571
\(748\) 4.59357 0.167958
\(749\) −31.0903 −1.13602
\(750\) 1.88983 0.0690067
\(751\) −31.8864 −1.16355 −0.581777 0.813349i \(-0.697642\pi\)
−0.581777 + 0.813349i \(0.697642\pi\)
\(752\) 11.0724 0.403767
\(753\) 4.77420 0.173981
\(754\) −5.77816 −0.210428
\(755\) 12.7841 0.465261
\(756\) −15.8625 −0.576912
\(757\) 41.6726 1.51462 0.757308 0.653058i \(-0.226514\pi\)
0.757308 + 0.653058i \(0.226514\pi\)
\(758\) 15.2049 0.552267
\(759\) −16.4504 −0.597112
\(760\) 6.77604 0.245793
\(761\) −22.7206 −0.823620 −0.411810 0.911270i \(-0.635103\pi\)
−0.411810 + 0.911270i \(0.635103\pi\)
\(762\) −18.2833 −0.662334
\(763\) 11.1319 0.403000
\(764\) −8.02035 −0.290166
\(765\) 2.62497 0.0949061
\(766\) −3.18647 −0.115132
\(767\) −12.9648 −0.468131
\(768\) −1.88983 −0.0681932
\(769\) −49.3991 −1.78138 −0.890689 0.454613i \(-0.849778\pi\)
−0.890689 + 0.454613i \(0.849778\pi\)
\(770\) 3.45622 0.124553
\(771\) −20.0743 −0.722957
\(772\) −9.01693 −0.324526
\(773\) 52.5239 1.88916 0.944578 0.328288i \(-0.106472\pi\)
0.944578 + 0.328288i \(0.106472\pi\)
\(774\) −0.571445 −0.0205402
\(775\) −4.60842 −0.165540
\(776\) −17.4928 −0.627954
\(777\) −47.1106 −1.69008
\(778\) −6.25531 −0.224264
\(779\) 50.3159 1.80275
\(780\) 2.03630 0.0729112
\(781\) −9.42496 −0.337251
\(782\) −39.9857 −1.42989
\(783\) −24.6116 −0.879548
\(784\) 4.94542 0.176622
\(785\) 1.70031 0.0606866
\(786\) 31.2995 1.11642
\(787\) −6.04865 −0.215611 −0.107806 0.994172i \(-0.534382\pi\)
−0.107806 + 0.994172i \(0.534382\pi\)
\(788\) −25.1470 −0.895825
\(789\) −40.0525 −1.42591
\(790\) 17.5153 0.623167
\(791\) −3.73305 −0.132732
\(792\) −0.571445 −0.0203054
\(793\) 8.16247 0.289858
\(794\) −16.0927 −0.571108
\(795\) 21.3521 0.757281
\(796\) −5.50392 −0.195081
\(797\) 15.7906 0.559333 0.279666 0.960097i \(-0.409776\pi\)
0.279666 + 0.960097i \(0.409776\pi\)
\(798\) 44.2587 1.56674
\(799\) 50.8617 1.79936
\(800\) −1.00000 −0.0353553
\(801\) 1.17124 0.0413837
\(802\) 22.0145 0.777358
\(803\) −15.2890 −0.539536
\(804\) −12.3697 −0.436244
\(805\) −30.0854 −1.06037
\(806\) −4.96560 −0.174906
\(807\) 7.85149 0.276385
\(808\) −6.35009 −0.223395
\(809\) −7.73591 −0.271980 −0.135990 0.990710i \(-0.543422\pi\)
−0.135990 + 0.990710i \(0.543422\pi\)
\(810\) 10.3878 0.364990
\(811\) −1.69537 −0.0595327 −0.0297663 0.999557i \(-0.509476\pi\)
−0.0297663 + 0.999557i \(0.509476\pi\)
\(812\) 18.5341 0.650419
\(813\) −35.7984 −1.25550
\(814\) 7.21267 0.252804
\(815\) 10.3010 0.360828
\(816\) −8.68106 −0.303898
\(817\) −6.77604 −0.237063
\(818\) −16.4582 −0.575448
\(819\) 2.12811 0.0743622
\(820\) −7.42557 −0.259312
\(821\) 14.2645 0.497836 0.248918 0.968525i \(-0.419925\pi\)
0.248918 + 0.968525i \(0.419925\pi\)
\(822\) 19.0963 0.666059
\(823\) 11.4395 0.398757 0.199379 0.979923i \(-0.436108\pi\)
0.199379 + 0.979923i \(0.436108\pi\)
\(824\) 16.4883 0.574398
\(825\) −1.88983 −0.0657953
\(826\) 41.5860 1.44696
\(827\) 6.31733 0.219675 0.109837 0.993950i \(-0.464967\pi\)
0.109837 + 0.993950i \(0.464967\pi\)
\(828\) 4.97426 0.172868
\(829\) 41.6164 1.44540 0.722699 0.691163i \(-0.242901\pi\)
0.722699 + 0.691163i \(0.242901\pi\)
\(830\) −11.9844 −0.415986
\(831\) −33.1614 −1.15036
\(832\) −1.07751 −0.0373558
\(833\) 22.7172 0.787103
\(834\) 31.7269 1.09861
\(835\) 9.69317 0.335446
\(836\) −6.77604 −0.234354
\(837\) −21.1506 −0.731071
\(838\) −19.9866 −0.690425
\(839\) −12.8606 −0.443999 −0.221999 0.975047i \(-0.571258\pi\)
−0.221999 + 0.975047i \(0.571258\pi\)
\(840\) −6.53165 −0.225363
\(841\) −0.243206 −0.00838642
\(842\) −28.4459 −0.980311
\(843\) −25.4632 −0.876998
\(844\) −10.3421 −0.355991
\(845\) −11.8390 −0.407273
\(846\) −6.32724 −0.217535
\(847\) −3.45622 −0.118757
\(848\) −11.2984 −0.387990
\(849\) −24.4692 −0.839781
\(850\) −4.59357 −0.157558
\(851\) −62.7842 −2.15222
\(852\) 17.8115 0.610213
\(853\) −41.6895 −1.42742 −0.713710 0.700441i \(-0.752986\pi\)
−0.713710 + 0.700441i \(0.752986\pi\)
\(854\) −26.1820 −0.895930
\(855\) −3.87213 −0.132424
\(856\) −8.99548 −0.307459
\(857\) −14.9183 −0.509599 −0.254800 0.966994i \(-0.582009\pi\)
−0.254800 + 0.966994i \(0.582009\pi\)
\(858\) −2.03630 −0.0695181
\(859\) 16.9198 0.577296 0.288648 0.957435i \(-0.406794\pi\)
0.288648 + 0.957435i \(0.406794\pi\)
\(860\) 1.00000 0.0340997
\(861\) −48.5012 −1.65292
\(862\) 4.26692 0.145332
\(863\) 7.18409 0.244549 0.122275 0.992496i \(-0.460981\pi\)
0.122275 + 0.992496i \(0.460981\pi\)
\(864\) −4.58955 −0.156140
\(865\) −15.4912 −0.526718
\(866\) −2.49978 −0.0849461
\(867\) −7.75001 −0.263204
\(868\) 15.9277 0.540622
\(869\) −17.5153 −0.594166
\(870\) −10.1343 −0.343584
\(871\) −7.05269 −0.238971
\(872\) 3.22082 0.109071
\(873\) 9.99616 0.338319
\(874\) 58.9835 1.99515
\(875\) −3.45622 −0.116841
\(876\) 28.8935 0.976222
\(877\) 20.6988 0.698947 0.349474 0.936946i \(-0.386360\pi\)
0.349474 + 0.936946i \(0.386360\pi\)
\(878\) 20.6046 0.695371
\(879\) −46.7717 −1.57757
\(880\) 1.00000 0.0337100
\(881\) −16.8633 −0.568140 −0.284070 0.958804i \(-0.591685\pi\)
−0.284070 + 0.958804i \(0.591685\pi\)
\(882\) −2.82604 −0.0951576
\(883\) −50.7983 −1.70950 −0.854749 0.519042i \(-0.826289\pi\)
−0.854749 + 0.519042i \(0.826289\pi\)
\(884\) −4.94960 −0.166473
\(885\) −22.7388 −0.764357
\(886\) −21.0118 −0.705906
\(887\) 38.9950 1.30932 0.654662 0.755921i \(-0.272811\pi\)
0.654662 + 0.755921i \(0.272811\pi\)
\(888\) −13.6307 −0.457416
\(889\) 33.4375 1.12146
\(890\) −2.04961 −0.0687031
\(891\) −10.3878 −0.348004
\(892\) −14.5630 −0.487605
\(893\) −75.0267 −2.51067
\(894\) −16.8189 −0.562510
\(895\) 19.4443 0.649951
\(896\) 3.45622 0.115464
\(897\) 17.7254 0.591834
\(898\) −37.0426 −1.23613
\(899\) 24.7128 0.824220
\(900\) 0.571445 0.0190482
\(901\) −51.9002 −1.72905
\(902\) 7.42557 0.247244
\(903\) 6.53165 0.217360
\(904\) −1.08010 −0.0359236
\(905\) −6.81662 −0.226592
\(906\) 24.1598 0.802654
\(907\) −26.9022 −0.893271 −0.446636 0.894716i \(-0.647378\pi\)
−0.446636 + 0.894716i \(0.647378\pi\)
\(908\) −17.2021 −0.570872
\(909\) 3.62872 0.120357
\(910\) −3.72409 −0.123452
\(911\) −35.0920 −1.16265 −0.581325 0.813671i \(-0.697466\pi\)
−0.581325 + 0.813671i \(0.697466\pi\)
\(912\) 12.8055 0.424034
\(913\) 11.9844 0.396627
\(914\) −23.7135 −0.784374
\(915\) 14.3161 0.473275
\(916\) 13.8155 0.456477
\(917\) −57.2421 −1.89030
\(918\) −21.0824 −0.695824
\(919\) 9.80966 0.323591 0.161795 0.986824i \(-0.448272\pi\)
0.161795 + 0.986824i \(0.448272\pi\)
\(920\) −8.70472 −0.286986
\(921\) 36.0758 1.18874
\(922\) −18.1272 −0.596988
\(923\) 10.1554 0.334270
\(924\) 6.53165 0.214875
\(925\) −7.21267 −0.237151
\(926\) 1.95012 0.0640848
\(927\) −9.42216 −0.309464
\(928\) 5.36254 0.176034
\(929\) −5.90224 −0.193646 −0.0968230 0.995302i \(-0.530868\pi\)
−0.0968230 + 0.995302i \(0.530868\pi\)
\(930\) −8.70912 −0.285583
\(931\) −33.5104 −1.09826
\(932\) 9.04894 0.296408
\(933\) −24.1310 −0.790013
\(934\) 10.8915 0.356381
\(935\) 4.59357 0.150226
\(936\) 0.615734 0.0201259
\(937\) −11.8302 −0.386477 −0.193238 0.981152i \(-0.561899\pi\)
−0.193238 + 0.981152i \(0.561899\pi\)
\(938\) 22.6223 0.738644
\(939\) 27.5475 0.898979
\(940\) 11.0724 0.361140
\(941\) 22.5149 0.733966 0.366983 0.930228i \(-0.380391\pi\)
0.366983 + 0.930228i \(0.380391\pi\)
\(942\) 3.21329 0.104694
\(943\) −64.6375 −2.10489
\(944\) 12.0322 0.391616
\(945\) −15.8625 −0.516006
\(946\) −1.00000 −0.0325128
\(947\) 7.12502 0.231532 0.115766 0.993277i \(-0.463068\pi\)
0.115766 + 0.993277i \(0.463068\pi\)
\(948\) 33.1009 1.07507
\(949\) 16.4740 0.534767
\(950\) 6.77604 0.219844
\(951\) −50.0542 −1.62312
\(952\) 15.8764 0.514556
\(953\) 41.5431 1.34571 0.672857 0.739773i \(-0.265067\pi\)
0.672857 + 0.739773i \(0.265067\pi\)
\(954\) 6.45643 0.209035
\(955\) −8.02035 −0.259533
\(956\) 22.8641 0.739479
\(957\) 10.1343 0.327594
\(958\) 20.1081 0.649663
\(959\) −34.9243 −1.12776
\(960\) −1.88983 −0.0609939
\(961\) −9.76242 −0.314917
\(962\) −7.77168 −0.250569
\(963\) 5.14042 0.165648
\(964\) −4.14263 −0.133425
\(965\) −9.01693 −0.290265
\(966\) −56.8561 −1.82932
\(967\) 54.8016 1.76230 0.881150 0.472837i \(-0.156770\pi\)
0.881150 + 0.472837i \(0.156770\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 58.8231 1.88967
\(970\) −17.4928 −0.561659
\(971\) 38.1471 1.22420 0.612100 0.790781i \(-0.290325\pi\)
0.612100 + 0.790781i \(0.290325\pi\)
\(972\) 5.86247 0.188039
\(973\) −58.0238 −1.86016
\(974\) −0.0886944 −0.00284195
\(975\) 2.03630 0.0652137
\(976\) −7.57534 −0.242481
\(977\) −37.0437 −1.18513 −0.592567 0.805521i \(-0.701885\pi\)
−0.592567 + 0.805521i \(0.701885\pi\)
\(978\) 19.4671 0.622488
\(979\) 2.04961 0.0655058
\(980\) 4.94542 0.157976
\(981\) −1.84052 −0.0587634
\(982\) −17.0693 −0.544704
\(983\) 2.73678 0.0872899 0.0436449 0.999047i \(-0.486103\pi\)
0.0436449 + 0.999047i \(0.486103\pi\)
\(984\) −14.0330 −0.447357
\(985\) −25.1470 −0.801250
\(986\) 24.6332 0.784481
\(987\) 72.3207 2.30199
\(988\) 7.30121 0.232283
\(989\) 8.70472 0.276794
\(990\) −0.571445 −0.0181617
\(991\) 29.5784 0.939589 0.469794 0.882776i \(-0.344328\pi\)
0.469794 + 0.882776i \(0.344328\pi\)
\(992\) 4.60842 0.146318
\(993\) −48.4906 −1.53880
\(994\) −32.5747 −1.03321
\(995\) −5.50392 −0.174486
\(996\) −22.6485 −0.717645
\(997\) 44.8319 1.41984 0.709920 0.704283i \(-0.248731\pi\)
0.709920 + 0.704283i \(0.248731\pi\)
\(998\) −19.6472 −0.621921
\(999\) −33.1029 −1.04733
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4730.2.a.z.1.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.z.1.2 10 1.1 even 1 trivial