Properties

Label 4730.2.a.w.1.2
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 1
Dimension 8
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: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.86277\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.86277 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.86277 q^{6} -1.78911 q^{7} -1.00000 q^{8} +5.19548 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.86277 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.86277 q^{6} -1.78911 q^{7} -1.00000 q^{8} +5.19548 q^{9} -1.00000 q^{10} +1.00000 q^{11} -2.86277 q^{12} -5.69835 q^{13} +1.78911 q^{14} -2.86277 q^{15} +1.00000 q^{16} +0.963912 q^{17} -5.19548 q^{18} +4.63919 q^{19} +1.00000 q^{20} +5.12181 q^{21} -1.00000 q^{22} -7.69835 q^{23} +2.86277 q^{24} +1.00000 q^{25} +5.69835 q^{26} -6.28516 q^{27} -1.78911 q^{28} +10.1449 q^{29} +2.86277 q^{30} -2.96582 q^{31} -1.00000 q^{32} -2.86277 q^{33} -0.963912 q^{34} -1.78911 q^{35} +5.19548 q^{36} +4.30018 q^{37} -4.63919 q^{38} +16.3131 q^{39} -1.00000 q^{40} -4.75298 q^{41} -5.12181 q^{42} -1.00000 q^{43} +1.00000 q^{44} +5.19548 q^{45} +7.69835 q^{46} +7.87220 q^{47} -2.86277 q^{48} -3.79910 q^{49} -1.00000 q^{50} -2.75946 q^{51} -5.69835 q^{52} -3.39384 q^{53} +6.28516 q^{54} +1.00000 q^{55} +1.78911 q^{56} -13.2810 q^{57} -10.1449 q^{58} -6.29216 q^{59} -2.86277 q^{60} +3.05059 q^{61} +2.96582 q^{62} -9.29527 q^{63} +1.00000 q^{64} -5.69835 q^{65} +2.86277 q^{66} +13.2850 q^{67} +0.963912 q^{68} +22.0386 q^{69} +1.78911 q^{70} -13.7617 q^{71} -5.19548 q^{72} -6.67878 q^{73} -4.30018 q^{74} -2.86277 q^{75} +4.63919 q^{76} -1.78911 q^{77} -16.3131 q^{78} -6.14424 q^{79} +1.00000 q^{80} +2.40656 q^{81} +4.75298 q^{82} +2.53212 q^{83} +5.12181 q^{84} +0.963912 q^{85} +1.00000 q^{86} -29.0426 q^{87} -1.00000 q^{88} -3.42413 q^{89} -5.19548 q^{90} +10.1950 q^{91} -7.69835 q^{92} +8.49049 q^{93} -7.87220 q^{94} +4.63919 q^{95} +2.86277 q^{96} +17.9695 q^{97} +3.79910 q^{98} +5.19548 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{2} - 7q^{3} + 8q^{4} + 8q^{5} + 7q^{6} - 6q^{7} - 8q^{8} + 7q^{9} + O(q^{10}) \) \( 8q - 8q^{2} - 7q^{3} + 8q^{4} + 8q^{5} + 7q^{6} - 6q^{7} - 8q^{8} + 7q^{9} - 8q^{10} + 8q^{11} - 7q^{12} - 2q^{13} + 6q^{14} - 7q^{15} + 8q^{16} - 8q^{17} - 7q^{18} + 8q^{20} + 14q^{21} - 8q^{22} - 18q^{23} + 7q^{24} + 8q^{25} + 2q^{26} - 22q^{27} - 6q^{28} + 8q^{29} + 7q^{30} - 11q^{31} - 8q^{32} - 7q^{33} + 8q^{34} - 6q^{35} + 7q^{36} - 17q^{37} - 6q^{39} - 8q^{40} + 12q^{41} - 14q^{42} - 8q^{43} + 8q^{44} + 7q^{45} + 18q^{46} - 19q^{47} - 7q^{48} - 2q^{49} - 8q^{50} - q^{51} - 2q^{52} - 7q^{53} + 22q^{54} + 8q^{55} + 6q^{56} - 3q^{57} - 8q^{58} + q^{59} - 7q^{60} + 6q^{61} + 11q^{62} - 15q^{63} + 8q^{64} - 2q^{65} + 7q^{66} - 22q^{67} - 8q^{68} + 8q^{69} + 6q^{70} - 14q^{71} - 7q^{72} - 13q^{73} + 17q^{74} - 7q^{75} - 6q^{77} + 6q^{78} - 8q^{79} + 8q^{80} + 28q^{81} - 12q^{82} - 4q^{83} + 14q^{84} - 8q^{85} + 8q^{86} - 30q^{87} - 8q^{88} + 5q^{89} - 7q^{90} - 8q^{91} - 18q^{92} + q^{93} + 19q^{94} + 7q^{96} - 23q^{97} + 2q^{98} + 7q^{99} + O(q^{100}) \)

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
\(3\) −2.86277 −1.65282 −0.826412 0.563066i \(-0.809622\pi\)
−0.826412 + 0.563066i \(0.809622\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 2.86277 1.16872
\(7\) −1.78911 −0.676219 −0.338109 0.941107i \(-0.609787\pi\)
−0.338109 + 0.941107i \(0.609787\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.19548 1.73183
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) −2.86277 −0.826412
\(13\) −5.69835 −1.58044 −0.790219 0.612824i \(-0.790033\pi\)
−0.790219 + 0.612824i \(0.790033\pi\)
\(14\) 1.78911 0.478159
\(15\) −2.86277 −0.739165
\(16\) 1.00000 0.250000
\(17\) 0.963912 0.233783 0.116892 0.993145i \(-0.462707\pi\)
0.116892 + 0.993145i \(0.462707\pi\)
\(18\) −5.19548 −1.22459
\(19\) 4.63919 1.06430 0.532152 0.846649i \(-0.321383\pi\)
0.532152 + 0.846649i \(0.321383\pi\)
\(20\) 1.00000 0.223607
\(21\) 5.12181 1.11767
\(22\) −1.00000 −0.213201
\(23\) −7.69835 −1.60522 −0.802609 0.596506i \(-0.796555\pi\)
−0.802609 + 0.596506i \(0.796555\pi\)
\(24\) 2.86277 0.584361
\(25\) 1.00000 0.200000
\(26\) 5.69835 1.11754
\(27\) −6.28516 −1.20958
\(28\) −1.78911 −0.338109
\(29\) 10.1449 1.88386 0.941931 0.335807i \(-0.109009\pi\)
0.941931 + 0.335807i \(0.109009\pi\)
\(30\) 2.86277 0.522669
\(31\) −2.96582 −0.532678 −0.266339 0.963879i \(-0.585814\pi\)
−0.266339 + 0.963879i \(0.585814\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.86277 −0.498345
\(34\) −0.963912 −0.165310
\(35\) −1.78911 −0.302414
\(36\) 5.19548 0.865913
\(37\) 4.30018 0.706945 0.353472 0.935445i \(-0.385001\pi\)
0.353472 + 0.935445i \(0.385001\pi\)
\(38\) −4.63919 −0.752577
\(39\) 16.3131 2.61219
\(40\) −1.00000 −0.158114
\(41\) −4.75298 −0.742291 −0.371145 0.928575i \(-0.621035\pi\)
−0.371145 + 0.928575i \(0.621035\pi\)
\(42\) −5.12181 −0.790313
\(43\) −1.00000 −0.152499
\(44\) 1.00000 0.150756
\(45\) 5.19548 0.774496
\(46\) 7.69835 1.13506
\(47\) 7.87220 1.14828 0.574139 0.818758i \(-0.305337\pi\)
0.574139 + 0.818758i \(0.305337\pi\)
\(48\) −2.86277 −0.413206
\(49\) −3.79910 −0.542728
\(50\) −1.00000 −0.141421
\(51\) −2.75946 −0.386402
\(52\) −5.69835 −0.790219
\(53\) −3.39384 −0.466180 −0.233090 0.972455i \(-0.574884\pi\)
−0.233090 + 0.972455i \(0.574884\pi\)
\(54\) 6.28516 0.855302
\(55\) 1.00000 0.134840
\(56\) 1.78911 0.239080
\(57\) −13.2810 −1.75911
\(58\) −10.1449 −1.33209
\(59\) −6.29216 −0.819170 −0.409585 0.912272i \(-0.634326\pi\)
−0.409585 + 0.912272i \(0.634326\pi\)
\(60\) −2.86277 −0.369583
\(61\) 3.05059 0.390588 0.195294 0.980745i \(-0.437434\pi\)
0.195294 + 0.980745i \(0.437434\pi\)
\(62\) 2.96582 0.376660
\(63\) −9.29527 −1.17109
\(64\) 1.00000 0.125000
\(65\) −5.69835 −0.706794
\(66\) 2.86277 0.352383
\(67\) 13.2850 1.62303 0.811513 0.584334i \(-0.198644\pi\)
0.811513 + 0.584334i \(0.198644\pi\)
\(68\) 0.963912 0.116892
\(69\) 22.0386 2.65314
\(70\) 1.78911 0.213839
\(71\) −13.7617 −1.63321 −0.816605 0.577197i \(-0.804146\pi\)
−0.816605 + 0.577197i \(0.804146\pi\)
\(72\) −5.19548 −0.612293
\(73\) −6.67878 −0.781692 −0.390846 0.920456i \(-0.627817\pi\)
−0.390846 + 0.920456i \(0.627817\pi\)
\(74\) −4.30018 −0.499886
\(75\) −2.86277 −0.330565
\(76\) 4.63919 0.532152
\(77\) −1.78911 −0.203888
\(78\) −16.3131 −1.84709
\(79\) −6.14424 −0.691281 −0.345641 0.938367i \(-0.612338\pi\)
−0.345641 + 0.938367i \(0.612338\pi\)
\(80\) 1.00000 0.111803
\(81\) 2.40656 0.267395
\(82\) 4.75298 0.524879
\(83\) 2.53212 0.277936 0.138968 0.990297i \(-0.455622\pi\)
0.138968 + 0.990297i \(0.455622\pi\)
\(84\) 5.12181 0.558835
\(85\) 0.963912 0.104551
\(86\) 1.00000 0.107833
\(87\) −29.0426 −3.11369
\(88\) −1.00000 −0.106600
\(89\) −3.42413 −0.362957 −0.181479 0.983395i \(-0.558088\pi\)
−0.181479 + 0.983395i \(0.558088\pi\)
\(90\) −5.19548 −0.547651
\(91\) 10.1950 1.06872
\(92\) −7.69835 −0.802609
\(93\) 8.49049 0.880423
\(94\) −7.87220 −0.811955
\(95\) 4.63919 0.475971
\(96\) 2.86277 0.292181
\(97\) 17.9695 1.82453 0.912263 0.409606i \(-0.134334\pi\)
0.912263 + 0.409606i \(0.134334\pi\)
\(98\) 3.79910 0.383767
\(99\) 5.19548 0.522165
\(100\) 1.00000 0.100000
\(101\) 17.6924 1.76046 0.880228 0.474551i \(-0.157389\pi\)
0.880228 + 0.474551i \(0.157389\pi\)
\(102\) 2.75946 0.273228
\(103\) 18.9702 1.86918 0.934592 0.355721i \(-0.115764\pi\)
0.934592 + 0.355721i \(0.115764\pi\)
\(104\) 5.69835 0.558769
\(105\) 5.12181 0.499838
\(106\) 3.39384 0.329639
\(107\) −9.14536 −0.884115 −0.442058 0.896987i \(-0.645751\pi\)
−0.442058 + 0.896987i \(0.645751\pi\)
\(108\) −6.28516 −0.604790
\(109\) 17.3644 1.66321 0.831605 0.555368i \(-0.187422\pi\)
0.831605 + 0.555368i \(0.187422\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −12.3104 −1.16846
\(112\) −1.78911 −0.169055
\(113\) 8.57368 0.806544 0.403272 0.915080i \(-0.367873\pi\)
0.403272 + 0.915080i \(0.367873\pi\)
\(114\) 13.2810 1.24388
\(115\) −7.69835 −0.717875
\(116\) 10.1449 0.941931
\(117\) −29.6057 −2.73704
\(118\) 6.29216 0.579240
\(119\) −1.72454 −0.158089
\(120\) 2.86277 0.261334
\(121\) 1.00000 0.0909091
\(122\) −3.05059 −0.276187
\(123\) 13.6067 1.22688
\(124\) −2.96582 −0.266339
\(125\) 1.00000 0.0894427
\(126\) 9.29527 0.828088
\(127\) −4.68579 −0.415797 −0.207898 0.978150i \(-0.566662\pi\)
−0.207898 + 0.978150i \(0.566662\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.86277 0.252053
\(130\) 5.69835 0.499779
\(131\) 1.13992 0.0995956 0.0497978 0.998759i \(-0.484142\pi\)
0.0497978 + 0.998759i \(0.484142\pi\)
\(132\) −2.86277 −0.249173
\(133\) −8.30002 −0.719703
\(134\) −13.2850 −1.14765
\(135\) −6.28516 −0.540940
\(136\) −0.963912 −0.0826548
\(137\) 7.41533 0.633534 0.316767 0.948503i \(-0.397403\pi\)
0.316767 + 0.948503i \(0.397403\pi\)
\(138\) −22.0386 −1.87605
\(139\) −8.58170 −0.727890 −0.363945 0.931420i \(-0.618570\pi\)
−0.363945 + 0.931420i \(0.618570\pi\)
\(140\) −1.78911 −0.151207
\(141\) −22.5363 −1.89790
\(142\) 13.7617 1.15485
\(143\) −5.69835 −0.476520
\(144\) 5.19548 0.432956
\(145\) 10.1449 0.842489
\(146\) 6.67878 0.552740
\(147\) 10.8760 0.897034
\(148\) 4.30018 0.353472
\(149\) −6.05872 −0.496350 −0.248175 0.968715i \(-0.579831\pi\)
−0.248175 + 0.968715i \(0.579831\pi\)
\(150\) 2.86277 0.233745
\(151\) −17.4306 −1.41848 −0.709239 0.704968i \(-0.750961\pi\)
−0.709239 + 0.704968i \(0.750961\pi\)
\(152\) −4.63919 −0.376288
\(153\) 5.00798 0.404872
\(154\) 1.78911 0.144170
\(155\) −2.96582 −0.238221
\(156\) 16.3131 1.30609
\(157\) −11.1720 −0.891623 −0.445811 0.895127i \(-0.647085\pi\)
−0.445811 + 0.895127i \(0.647085\pi\)
\(158\) 6.14424 0.488810
\(159\) 9.71580 0.770513
\(160\) −1.00000 −0.0790569
\(161\) 13.7732 1.08548
\(162\) −2.40656 −0.189077
\(163\) −10.9817 −0.860151 −0.430075 0.902793i \(-0.641513\pi\)
−0.430075 + 0.902793i \(0.641513\pi\)
\(164\) −4.75298 −0.371145
\(165\) −2.86277 −0.222867
\(166\) −2.53212 −0.196530
\(167\) 17.3594 1.34331 0.671656 0.740864i \(-0.265583\pi\)
0.671656 + 0.740864i \(0.265583\pi\)
\(168\) −5.12181 −0.395156
\(169\) 19.4712 1.49779
\(170\) −0.963912 −0.0739287
\(171\) 24.1028 1.84319
\(172\) −1.00000 −0.0762493
\(173\) −5.17703 −0.393602 −0.196801 0.980443i \(-0.563055\pi\)
−0.196801 + 0.980443i \(0.563055\pi\)
\(174\) 29.0426 2.20171
\(175\) −1.78911 −0.135244
\(176\) 1.00000 0.0753778
\(177\) 18.0130 1.35394
\(178\) 3.42413 0.256650
\(179\) −18.7696 −1.40291 −0.701453 0.712716i \(-0.747465\pi\)
−0.701453 + 0.712716i \(0.747465\pi\)
\(180\) 5.19548 0.387248
\(181\) 9.94319 0.739071 0.369536 0.929217i \(-0.379517\pi\)
0.369536 + 0.929217i \(0.379517\pi\)
\(182\) −10.1950 −0.755701
\(183\) −8.73315 −0.645573
\(184\) 7.69835 0.567530
\(185\) 4.30018 0.316155
\(186\) −8.49049 −0.622553
\(187\) 0.963912 0.0704882
\(188\) 7.87220 0.574139
\(189\) 11.2448 0.817940
\(190\) −4.63919 −0.336562
\(191\) 21.4314 1.55072 0.775360 0.631519i \(-0.217568\pi\)
0.775360 + 0.631519i \(0.217568\pi\)
\(192\) −2.86277 −0.206603
\(193\) 19.5355 1.40620 0.703098 0.711093i \(-0.251799\pi\)
0.703098 + 0.711093i \(0.251799\pi\)
\(194\) −17.9695 −1.29013
\(195\) 16.3131 1.16821
\(196\) −3.79910 −0.271364
\(197\) −2.65052 −0.188842 −0.0944210 0.995532i \(-0.530100\pi\)
−0.0944210 + 0.995532i \(0.530100\pi\)
\(198\) −5.19548 −0.369227
\(199\) −17.8560 −1.26578 −0.632889 0.774243i \(-0.718131\pi\)
−0.632889 + 0.774243i \(0.718131\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −38.0321 −2.68258
\(202\) −17.6924 −1.24483
\(203\) −18.1503 −1.27390
\(204\) −2.75946 −0.193201
\(205\) −4.75298 −0.331962
\(206\) −18.9702 −1.32171
\(207\) −39.9966 −2.77996
\(208\) −5.69835 −0.395110
\(209\) 4.63919 0.320900
\(210\) −5.12181 −0.353438
\(211\) −25.8794 −1.78161 −0.890805 0.454385i \(-0.849859\pi\)
−0.890805 + 0.454385i \(0.849859\pi\)
\(212\) −3.39384 −0.233090
\(213\) 39.3966 2.69941
\(214\) 9.14536 0.625164
\(215\) −1.00000 −0.0681994
\(216\) 6.28516 0.427651
\(217\) 5.30618 0.360207
\(218\) −17.3644 −1.17607
\(219\) 19.1198 1.29200
\(220\) 1.00000 0.0674200
\(221\) −5.49271 −0.369480
\(222\) 12.3104 0.826223
\(223\) −19.7769 −1.32436 −0.662178 0.749346i \(-0.730368\pi\)
−0.662178 + 0.749346i \(0.730368\pi\)
\(224\) 1.78911 0.119540
\(225\) 5.19548 0.346365
\(226\) −8.57368 −0.570313
\(227\) 22.0963 1.46658 0.733291 0.679915i \(-0.237983\pi\)
0.733291 + 0.679915i \(0.237983\pi\)
\(228\) −13.2810 −0.879553
\(229\) 8.96277 0.592276 0.296138 0.955145i \(-0.404301\pi\)
0.296138 + 0.955145i \(0.404301\pi\)
\(230\) 7.69835 0.507614
\(231\) 5.12181 0.336990
\(232\) −10.1449 −0.666046
\(233\) 0.510127 0.0334195 0.0167098 0.999860i \(-0.494681\pi\)
0.0167098 + 0.999860i \(0.494681\pi\)
\(234\) 29.6057 1.93538
\(235\) 7.87220 0.513526
\(236\) −6.29216 −0.409585
\(237\) 17.5896 1.14257
\(238\) 1.72454 0.111785
\(239\) −15.8249 −1.02363 −0.511815 0.859096i \(-0.671027\pi\)
−0.511815 + 0.859096i \(0.671027\pi\)
\(240\) −2.86277 −0.184791
\(241\) 13.1540 0.847323 0.423662 0.905821i \(-0.360745\pi\)
0.423662 + 0.905821i \(0.360745\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 11.9660 0.767622
\(244\) 3.05059 0.195294
\(245\) −3.79910 −0.242715
\(246\) −13.6067 −0.867532
\(247\) −26.4358 −1.68207
\(248\) 2.96582 0.188330
\(249\) −7.24887 −0.459379
\(250\) −1.00000 −0.0632456
\(251\) −23.9069 −1.50899 −0.754496 0.656304i \(-0.772119\pi\)
−0.754496 + 0.656304i \(0.772119\pi\)
\(252\) −9.29527 −0.585547
\(253\) −7.69835 −0.483991
\(254\) 4.68579 0.294013
\(255\) −2.75946 −0.172804
\(256\) 1.00000 0.0625000
\(257\) 0.683199 0.0426168 0.0213084 0.999773i \(-0.493217\pi\)
0.0213084 + 0.999773i \(0.493217\pi\)
\(258\) −2.86277 −0.178229
\(259\) −7.69348 −0.478050
\(260\) −5.69835 −0.353397
\(261\) 52.7076 3.26252
\(262\) −1.13992 −0.0704248
\(263\) 11.8338 0.729704 0.364852 0.931066i \(-0.381120\pi\)
0.364852 + 0.931066i \(0.381120\pi\)
\(264\) 2.86277 0.176192
\(265\) −3.39384 −0.208482
\(266\) 8.30002 0.508907
\(267\) 9.80252 0.599905
\(268\) 13.2850 0.811513
\(269\) −6.01316 −0.366629 −0.183314 0.983054i \(-0.558683\pi\)
−0.183314 + 0.983054i \(0.558683\pi\)
\(270\) 6.28516 0.382503
\(271\) −7.55873 −0.459160 −0.229580 0.973290i \(-0.573735\pi\)
−0.229580 + 0.973290i \(0.573735\pi\)
\(272\) 0.963912 0.0584458
\(273\) −29.1859 −1.76641
\(274\) −7.41533 −0.447976
\(275\) 1.00000 0.0603023
\(276\) 22.0386 1.32657
\(277\) −20.5243 −1.23318 −0.616592 0.787283i \(-0.711487\pi\)
−0.616592 + 0.787283i \(0.711487\pi\)
\(278\) 8.58170 0.514696
\(279\) −15.4089 −0.922505
\(280\) 1.78911 0.106920
\(281\) −5.72185 −0.341337 −0.170669 0.985328i \(-0.554593\pi\)
−0.170669 + 0.985328i \(0.554593\pi\)
\(282\) 22.5363 1.34202
\(283\) 6.15248 0.365727 0.182864 0.983138i \(-0.441463\pi\)
0.182864 + 0.983138i \(0.441463\pi\)
\(284\) −13.7617 −0.816605
\(285\) −13.2810 −0.786697
\(286\) 5.69835 0.336951
\(287\) 8.50359 0.501951
\(288\) −5.19548 −0.306146
\(289\) −16.0709 −0.945345
\(290\) −10.1449 −0.595729
\(291\) −51.4426 −3.01562
\(292\) −6.67878 −0.390846
\(293\) 8.37551 0.489303 0.244651 0.969611i \(-0.421326\pi\)
0.244651 + 0.969611i \(0.421326\pi\)
\(294\) −10.8760 −0.634298
\(295\) −6.29216 −0.366344
\(296\) −4.30018 −0.249943
\(297\) −6.28516 −0.364702
\(298\) 6.05872 0.350972
\(299\) 43.8679 2.53695
\(300\) −2.86277 −0.165282
\(301\) 1.78911 0.103122
\(302\) 17.4306 1.00302
\(303\) −50.6493 −2.90972
\(304\) 4.63919 0.266076
\(305\) 3.05059 0.174676
\(306\) −5.00798 −0.286287
\(307\) 4.00958 0.228839 0.114419 0.993433i \(-0.463499\pi\)
0.114419 + 0.993433i \(0.463499\pi\)
\(308\) −1.78911 −0.101944
\(309\) −54.3073 −3.08943
\(310\) 2.96582 0.168448
\(311\) 1.53007 0.0867620 0.0433810 0.999059i \(-0.486187\pi\)
0.0433810 + 0.999059i \(0.486187\pi\)
\(312\) −16.3131 −0.923547
\(313\) 7.69308 0.434839 0.217419 0.976078i \(-0.430236\pi\)
0.217419 + 0.976078i \(0.430236\pi\)
\(314\) 11.1720 0.630473
\(315\) −9.29527 −0.523729
\(316\) −6.14424 −0.345641
\(317\) −8.45749 −0.475020 −0.237510 0.971385i \(-0.576331\pi\)
−0.237510 + 0.971385i \(0.576331\pi\)
\(318\) −9.71580 −0.544835
\(319\) 10.1449 0.568006
\(320\) 1.00000 0.0559017
\(321\) 26.1811 1.46129
\(322\) −13.7732 −0.767549
\(323\) 4.47178 0.248816
\(324\) 2.40656 0.133698
\(325\) −5.69835 −0.316088
\(326\) 10.9817 0.608219
\(327\) −49.7104 −2.74899
\(328\) 4.75298 0.262439
\(329\) −14.0842 −0.776487
\(330\) 2.86277 0.157591
\(331\) −23.3024 −1.28082 −0.640409 0.768034i \(-0.721235\pi\)
−0.640409 + 0.768034i \(0.721235\pi\)
\(332\) 2.53212 0.138968
\(333\) 22.3415 1.22431
\(334\) −17.3594 −0.949864
\(335\) 13.2850 0.725839
\(336\) 5.12181 0.279418
\(337\) −27.5049 −1.49829 −0.749143 0.662408i \(-0.769535\pi\)
−0.749143 + 0.662408i \(0.769535\pi\)
\(338\) −19.4712 −1.05909
\(339\) −24.5445 −1.33308
\(340\) 0.963912 0.0522755
\(341\) −2.96582 −0.160608
\(342\) −24.1028 −1.30333
\(343\) 19.3207 1.04322
\(344\) 1.00000 0.0539164
\(345\) 22.0386 1.18652
\(346\) 5.17703 0.278319
\(347\) −0.00414127 −0.000222315 0 −0.000111158 1.00000i \(-0.500035\pi\)
−0.000111158 1.00000i \(0.500035\pi\)
\(348\) −29.0426 −1.55685
\(349\) −33.8734 −1.81320 −0.906601 0.421989i \(-0.861332\pi\)
−0.906601 + 0.421989i \(0.861332\pi\)
\(350\) 1.78911 0.0956318
\(351\) 35.8150 1.91167
\(352\) −1.00000 −0.0533002
\(353\) −25.3439 −1.34892 −0.674460 0.738311i \(-0.735624\pi\)
−0.674460 + 0.738311i \(0.735624\pi\)
\(354\) −18.0130 −0.957382
\(355\) −13.7617 −0.730394
\(356\) −3.42413 −0.181479
\(357\) 4.93698 0.261292
\(358\) 18.7696 0.992004
\(359\) 19.5704 1.03289 0.516443 0.856322i \(-0.327256\pi\)
0.516443 + 0.856322i \(0.327256\pi\)
\(360\) −5.19548 −0.273826
\(361\) 2.52212 0.132743
\(362\) −9.94319 −0.522602
\(363\) −2.86277 −0.150257
\(364\) 10.1950 0.534361
\(365\) −6.67878 −0.349583
\(366\) 8.73315 0.456489
\(367\) −21.1977 −1.10651 −0.553255 0.833012i \(-0.686614\pi\)
−0.553255 + 0.833012i \(0.686614\pi\)
\(368\) −7.69835 −0.401304
\(369\) −24.6940 −1.28552
\(370\) −4.30018 −0.223556
\(371\) 6.07194 0.315240
\(372\) 8.49049 0.440211
\(373\) −29.9681 −1.55169 −0.775845 0.630924i \(-0.782676\pi\)
−0.775845 + 0.630924i \(0.782676\pi\)
\(374\) −0.963912 −0.0498427
\(375\) −2.86277 −0.147833
\(376\) −7.87220 −0.405978
\(377\) −57.8092 −2.97733
\(378\) −11.2448 −0.578371
\(379\) −27.3318 −1.40394 −0.701969 0.712207i \(-0.747696\pi\)
−0.701969 + 0.712207i \(0.747696\pi\)
\(380\) 4.63919 0.237986
\(381\) 13.4144 0.687239
\(382\) −21.4314 −1.09653
\(383\) −3.43388 −0.175463 −0.0877316 0.996144i \(-0.527962\pi\)
−0.0877316 + 0.996144i \(0.527962\pi\)
\(384\) 2.86277 0.146090
\(385\) −1.78911 −0.0911813
\(386\) −19.5355 −0.994331
\(387\) −5.19548 −0.264101
\(388\) 17.9695 0.912263
\(389\) 7.61138 0.385912 0.192956 0.981207i \(-0.438192\pi\)
0.192956 + 0.981207i \(0.438192\pi\)
\(390\) −16.3131 −0.826046
\(391\) −7.42054 −0.375273
\(392\) 3.79910 0.191883
\(393\) −3.26335 −0.164614
\(394\) 2.65052 0.133531
\(395\) −6.14424 −0.309150
\(396\) 5.19548 0.261083
\(397\) 5.57754 0.279929 0.139964 0.990157i \(-0.455301\pi\)
0.139964 + 0.990157i \(0.455301\pi\)
\(398\) 17.8560 0.895040
\(399\) 23.7611 1.18954
\(400\) 1.00000 0.0500000
\(401\) −31.5987 −1.57796 −0.788982 0.614416i \(-0.789392\pi\)
−0.788982 + 0.614416i \(0.789392\pi\)
\(402\) 38.0321 1.89687
\(403\) 16.9003 0.841865
\(404\) 17.6924 0.880228
\(405\) 2.40656 0.119583
\(406\) 18.1503 0.900786
\(407\) 4.30018 0.213152
\(408\) 2.75946 0.136614
\(409\) 32.6528 1.61458 0.807289 0.590157i \(-0.200934\pi\)
0.807289 + 0.590157i \(0.200934\pi\)
\(410\) 4.75298 0.234733
\(411\) −21.2284 −1.04712
\(412\) 18.9702 0.934592
\(413\) 11.2574 0.553938
\(414\) 39.9966 1.96573
\(415\) 2.53212 0.124297
\(416\) 5.69835 0.279385
\(417\) 24.5675 1.20307
\(418\) −4.63919 −0.226910
\(419\) −14.9133 −0.728562 −0.364281 0.931289i \(-0.618685\pi\)
−0.364281 + 0.931289i \(0.618685\pi\)
\(420\) 5.12181 0.249919
\(421\) −7.00096 −0.341206 −0.170603 0.985340i \(-0.554572\pi\)
−0.170603 + 0.985340i \(0.554572\pi\)
\(422\) 25.8794 1.25979
\(423\) 40.8998 1.98862
\(424\) 3.39384 0.164819
\(425\) 0.963912 0.0467566
\(426\) −39.3966 −1.90877
\(427\) −5.45783 −0.264123
\(428\) −9.14536 −0.442058
\(429\) 16.3131 0.787604
\(430\) 1.00000 0.0482243
\(431\) 1.71755 0.0827313 0.0413656 0.999144i \(-0.486829\pi\)
0.0413656 + 0.999144i \(0.486829\pi\)
\(432\) −6.28516 −0.302395
\(433\) −3.58605 −0.172334 −0.0861672 0.996281i \(-0.527462\pi\)
−0.0861672 + 0.996281i \(0.527462\pi\)
\(434\) −5.30618 −0.254705
\(435\) −29.0426 −1.39249
\(436\) 17.3644 0.831605
\(437\) −35.7141 −1.70844
\(438\) −19.1198 −0.913581
\(439\) 37.3617 1.78318 0.891589 0.452846i \(-0.149591\pi\)
0.891589 + 0.452846i \(0.149591\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −19.7381 −0.939910
\(442\) 5.49271 0.261262
\(443\) −27.7099 −1.31654 −0.658269 0.752783i \(-0.728711\pi\)
−0.658269 + 0.752783i \(0.728711\pi\)
\(444\) −12.3104 −0.584228
\(445\) −3.42413 −0.162320
\(446\) 19.7769 0.936461
\(447\) 17.3448 0.820379
\(448\) −1.78911 −0.0845274
\(449\) 30.4230 1.43575 0.717875 0.696172i \(-0.245115\pi\)
0.717875 + 0.696172i \(0.245115\pi\)
\(450\) −5.19548 −0.244917
\(451\) −4.75298 −0.223809
\(452\) 8.57368 0.403272
\(453\) 49.8998 2.34449
\(454\) −22.0963 −1.03703
\(455\) 10.1950 0.477947
\(456\) 13.2810 0.621938
\(457\) −32.9666 −1.54211 −0.771057 0.636766i \(-0.780272\pi\)
−0.771057 + 0.636766i \(0.780272\pi\)
\(458\) −8.96277 −0.418803
\(459\) −6.05834 −0.282779
\(460\) −7.69835 −0.358938
\(461\) −34.8994 −1.62543 −0.812713 0.582664i \(-0.802010\pi\)
−0.812713 + 0.582664i \(0.802010\pi\)
\(462\) −5.12181 −0.238288
\(463\) −25.0883 −1.16595 −0.582975 0.812490i \(-0.698112\pi\)
−0.582975 + 0.812490i \(0.698112\pi\)
\(464\) 10.1449 0.470965
\(465\) 8.49049 0.393737
\(466\) −0.510127 −0.0236312
\(467\) −31.7044 −1.46711 −0.733553 0.679632i \(-0.762139\pi\)
−0.733553 + 0.679632i \(0.762139\pi\)
\(468\) −29.6057 −1.36852
\(469\) −23.7684 −1.09752
\(470\) −7.87220 −0.363117
\(471\) 31.9829 1.47370
\(472\) 6.29216 0.289620
\(473\) −1.00000 −0.0459800
\(474\) −17.5896 −0.807916
\(475\) 4.63919 0.212861
\(476\) −1.72454 −0.0790443
\(477\) −17.6326 −0.807342
\(478\) 15.8249 0.723815
\(479\) 19.7689 0.903263 0.451631 0.892205i \(-0.350842\pi\)
0.451631 + 0.892205i \(0.350842\pi\)
\(480\) 2.86277 0.130667
\(481\) −24.5039 −1.11728
\(482\) −13.1540 −0.599148
\(483\) −39.4295 −1.79410
\(484\) 1.00000 0.0454545
\(485\) 17.9695 0.815953
\(486\) −11.9660 −0.542791
\(487\) −13.6035 −0.616432 −0.308216 0.951316i \(-0.599732\pi\)
−0.308216 + 0.951316i \(0.599732\pi\)
\(488\) −3.05059 −0.138094
\(489\) 31.4381 1.42168
\(490\) 3.79910 0.171626
\(491\) 14.9396 0.674214 0.337107 0.941466i \(-0.390552\pi\)
0.337107 + 0.941466i \(0.390552\pi\)
\(492\) 13.6067 0.613438
\(493\) 9.77880 0.440415
\(494\) 26.4358 1.18940
\(495\) 5.19548 0.233519
\(496\) −2.96582 −0.133169
\(497\) 24.6211 1.10441
\(498\) 7.24887 0.324830
\(499\) −25.6559 −1.14852 −0.574259 0.818674i \(-0.694710\pi\)
−0.574259 + 0.818674i \(0.694710\pi\)
\(500\) 1.00000 0.0447214
\(501\) −49.6961 −2.22026
\(502\) 23.9069 1.06702
\(503\) −8.99905 −0.401248 −0.200624 0.979668i \(-0.564297\pi\)
−0.200624 + 0.979668i \(0.564297\pi\)
\(504\) 9.29527 0.414044
\(505\) 17.6924 0.787300
\(506\) 7.69835 0.342233
\(507\) −55.7417 −2.47558
\(508\) −4.68579 −0.207898
\(509\) −23.2606 −1.03101 −0.515504 0.856887i \(-0.672395\pi\)
−0.515504 + 0.856887i \(0.672395\pi\)
\(510\) 2.75946 0.122191
\(511\) 11.9490 0.528595
\(512\) −1.00000 −0.0441942
\(513\) −29.1581 −1.28736
\(514\) −0.683199 −0.0301346
\(515\) 18.9702 0.835925
\(516\) 2.86277 0.126027
\(517\) 7.87220 0.346219
\(518\) 7.69348 0.338032
\(519\) 14.8207 0.650555
\(520\) 5.69835 0.249889
\(521\) −4.44877 −0.194904 −0.0974521 0.995240i \(-0.531069\pi\)
−0.0974521 + 0.995240i \(0.531069\pi\)
\(522\) −52.7076 −2.30695
\(523\) −23.7929 −1.04039 −0.520196 0.854047i \(-0.674141\pi\)
−0.520196 + 0.854047i \(0.674141\pi\)
\(524\) 1.13992 0.0497978
\(525\) 5.12181 0.223534
\(526\) −11.8338 −0.515978
\(527\) −2.85879 −0.124531
\(528\) −2.86277 −0.124586
\(529\) 36.2646 1.57672
\(530\) 3.39384 0.147419
\(531\) −32.6908 −1.41866
\(532\) −8.30002 −0.359851
\(533\) 27.0841 1.17314
\(534\) −9.80252 −0.424197
\(535\) −9.14536 −0.395388
\(536\) −13.2850 −0.573827
\(537\) 53.7331 2.31876
\(538\) 6.01316 0.259246
\(539\) −3.79910 −0.163639
\(540\) −6.28516 −0.270470
\(541\) 5.52084 0.237359 0.118680 0.992933i \(-0.462134\pi\)
0.118680 + 0.992933i \(0.462134\pi\)
\(542\) 7.55873 0.324675
\(543\) −28.4651 −1.22155
\(544\) −0.963912 −0.0413274
\(545\) 17.3644 0.743810
\(546\) 29.1859 1.24904
\(547\) −6.94755 −0.297056 −0.148528 0.988908i \(-0.547453\pi\)
−0.148528 + 0.988908i \(0.547453\pi\)
\(548\) 7.41533 0.316767
\(549\) 15.8493 0.676430
\(550\) −1.00000 −0.0426401
\(551\) 47.0642 2.00500
\(552\) −22.0386 −0.938027
\(553\) 10.9927 0.467457
\(554\) 20.5243 0.871992
\(555\) −12.3104 −0.522549
\(556\) −8.58170 −0.363945
\(557\) 20.6608 0.875427 0.437714 0.899114i \(-0.355788\pi\)
0.437714 + 0.899114i \(0.355788\pi\)
\(558\) 15.4089 0.652310
\(559\) 5.69835 0.241015
\(560\) −1.78911 −0.0756036
\(561\) −2.75946 −0.116505
\(562\) 5.72185 0.241362
\(563\) 26.3414 1.11016 0.555080 0.831797i \(-0.312688\pi\)
0.555080 + 0.831797i \(0.312688\pi\)
\(564\) −22.5363 −0.948950
\(565\) 8.57368 0.360698
\(566\) −6.15248 −0.258608
\(567\) −4.30559 −0.180818
\(568\) 13.7617 0.577427
\(569\) 23.6886 0.993079 0.496540 0.868014i \(-0.334604\pi\)
0.496540 + 0.868014i \(0.334604\pi\)
\(570\) 13.2810 0.556278
\(571\) −30.6960 −1.28459 −0.642293 0.766459i \(-0.722017\pi\)
−0.642293 + 0.766459i \(0.722017\pi\)
\(572\) −5.69835 −0.238260
\(573\) −61.3532 −2.56307
\(574\) −8.50359 −0.354933
\(575\) −7.69835 −0.321043
\(576\) 5.19548 0.216478
\(577\) 6.09731 0.253835 0.126917 0.991913i \(-0.459492\pi\)
0.126917 + 0.991913i \(0.459492\pi\)
\(578\) 16.0709 0.668460
\(579\) −55.9257 −2.32419
\(580\) 10.1449 0.421244
\(581\) −4.53023 −0.187945
\(582\) 51.4426 2.13236
\(583\) −3.39384 −0.140559
\(584\) 6.67878 0.276370
\(585\) −29.6057 −1.22404
\(586\) −8.37551 −0.345989
\(587\) −41.7141 −1.72172 −0.860862 0.508838i \(-0.830075\pi\)
−0.860862 + 0.508838i \(0.830075\pi\)
\(588\) 10.8760 0.448517
\(589\) −13.7590 −0.566931
\(590\) 6.29216 0.259044
\(591\) 7.58785 0.312123
\(592\) 4.30018 0.176736
\(593\) −32.1860 −1.32172 −0.660860 0.750509i \(-0.729808\pi\)
−0.660860 + 0.750509i \(0.729808\pi\)
\(594\) 6.28516 0.257883
\(595\) −1.72454 −0.0706993
\(596\) −6.05872 −0.248175
\(597\) 51.1177 2.09211
\(598\) −43.8679 −1.79389
\(599\) −3.79741 −0.155158 −0.0775790 0.996986i \(-0.524719\pi\)
−0.0775790 + 0.996986i \(0.524719\pi\)
\(600\) 2.86277 0.116872
\(601\) 12.5830 0.513270 0.256635 0.966508i \(-0.417386\pi\)
0.256635 + 0.966508i \(0.417386\pi\)
\(602\) −1.78911 −0.0729186
\(603\) 69.0221 2.81080
\(604\) −17.4306 −0.709239
\(605\) 1.00000 0.0406558
\(606\) 50.6493 2.05749
\(607\) 26.3562 1.06976 0.534882 0.844927i \(-0.320356\pi\)
0.534882 + 0.844927i \(0.320356\pi\)
\(608\) −4.63919 −0.188144
\(609\) 51.9603 2.10554
\(610\) −3.05059 −0.123515
\(611\) −44.8586 −1.81478
\(612\) 5.00798 0.202436
\(613\) −15.0486 −0.607807 −0.303904 0.952703i \(-0.598290\pi\)
−0.303904 + 0.952703i \(0.598290\pi\)
\(614\) −4.00958 −0.161814
\(615\) 13.6067 0.548675
\(616\) 1.78911 0.0720852
\(617\) −25.6626 −1.03314 −0.516569 0.856246i \(-0.672791\pi\)
−0.516569 + 0.856246i \(0.672791\pi\)
\(618\) 54.3073 2.18456
\(619\) 27.2160 1.09390 0.546951 0.837165i \(-0.315788\pi\)
0.546951 + 0.837165i \(0.315788\pi\)
\(620\) −2.96582 −0.119110
\(621\) 48.3854 1.94164
\(622\) −1.53007 −0.0613500
\(623\) 6.12614 0.245439
\(624\) 16.3131 0.653046
\(625\) 1.00000 0.0400000
\(626\) −7.69308 −0.307477
\(627\) −13.2810 −0.530391
\(628\) −11.1720 −0.445811
\(629\) 4.14499 0.165272
\(630\) 9.29527 0.370332
\(631\) 47.1711 1.87785 0.938926 0.344120i \(-0.111823\pi\)
0.938926 + 0.344120i \(0.111823\pi\)
\(632\) 6.14424 0.244405
\(633\) 74.0868 2.94469
\(634\) 8.45749 0.335890
\(635\) −4.68579 −0.185950
\(636\) 9.71580 0.385257
\(637\) 21.6486 0.857748
\(638\) −10.1449 −0.401641
\(639\) −71.4984 −2.82843
\(640\) −1.00000 −0.0395285
\(641\) 13.7227 0.542013 0.271007 0.962577i \(-0.412643\pi\)
0.271007 + 0.962577i \(0.412643\pi\)
\(642\) −26.1811 −1.03329
\(643\) −29.5431 −1.16507 −0.582533 0.812807i \(-0.697938\pi\)
−0.582533 + 0.812807i \(0.697938\pi\)
\(644\) 13.7732 0.542739
\(645\) 2.86277 0.112722
\(646\) −4.47178 −0.175940
\(647\) −14.5082 −0.570377 −0.285189 0.958471i \(-0.592056\pi\)
−0.285189 + 0.958471i \(0.592056\pi\)
\(648\) −2.40656 −0.0945384
\(649\) −6.29216 −0.246989
\(650\) 5.69835 0.223508
\(651\) −15.1904 −0.595358
\(652\) −10.9817 −0.430075
\(653\) 29.9274 1.17115 0.585575 0.810618i \(-0.300869\pi\)
0.585575 + 0.810618i \(0.300869\pi\)
\(654\) 49.7104 1.94383
\(655\) 1.13992 0.0445405
\(656\) −4.75298 −0.185573
\(657\) −34.6994 −1.35375
\(658\) 14.0842 0.549059
\(659\) 13.1076 0.510600 0.255300 0.966862i \(-0.417826\pi\)
0.255300 + 0.966862i \(0.417826\pi\)
\(660\) −2.86277 −0.111433
\(661\) −7.21039 −0.280452 −0.140226 0.990120i \(-0.544783\pi\)
−0.140226 + 0.990120i \(0.544783\pi\)
\(662\) 23.3024 0.905675
\(663\) 15.7244 0.610685
\(664\) −2.53212 −0.0982651
\(665\) −8.30002 −0.321861
\(666\) −22.3415 −0.865715
\(667\) −78.0991 −3.02401
\(668\) 17.3594 0.671656
\(669\) 56.6167 2.18893
\(670\) −13.2850 −0.513246
\(671\) 3.05059 0.117767
\(672\) −5.12181 −0.197578
\(673\) −49.8510 −1.92161 −0.960807 0.277218i \(-0.910588\pi\)
−0.960807 + 0.277218i \(0.910588\pi\)
\(674\) 27.5049 1.05945
\(675\) −6.28516 −0.241916
\(676\) 19.4712 0.748893
\(677\) −39.0926 −1.50245 −0.751225 0.660046i \(-0.770537\pi\)
−0.751225 + 0.660046i \(0.770537\pi\)
\(678\) 24.5445 0.942627
\(679\) −32.1493 −1.23378
\(680\) −0.963912 −0.0369643
\(681\) −63.2567 −2.42400
\(682\) 2.96582 0.113567
\(683\) −45.4437 −1.73885 −0.869427 0.494061i \(-0.835512\pi\)
−0.869427 + 0.494061i \(0.835512\pi\)
\(684\) 24.1028 0.921595
\(685\) 7.41533 0.283325
\(686\) −19.3207 −0.737669
\(687\) −25.6584 −0.978928
\(688\) −1.00000 −0.0381246
\(689\) 19.3393 0.736769
\(690\) −22.0386 −0.838997
\(691\) 18.7419 0.712974 0.356487 0.934300i \(-0.383974\pi\)
0.356487 + 0.934300i \(0.383974\pi\)
\(692\) −5.17703 −0.196801
\(693\) −9.29527 −0.353098
\(694\) 0.00414127 0.000157200 0
\(695\) −8.58170 −0.325522
\(696\) 29.0426 1.10086
\(697\) −4.58145 −0.173535
\(698\) 33.8734 1.28213
\(699\) −1.46038 −0.0552366
\(700\) −1.78911 −0.0676219
\(701\) 8.03137 0.303341 0.151670 0.988431i \(-0.451535\pi\)
0.151670 + 0.988431i \(0.451535\pi\)
\(702\) −35.8150 −1.35175
\(703\) 19.9494 0.752404
\(704\) 1.00000 0.0376889
\(705\) −22.5363 −0.848767
\(706\) 25.3439 0.953831
\(707\) −31.6535 −1.19045
\(708\) 18.0130 0.676971
\(709\) −34.3852 −1.29136 −0.645682 0.763607i \(-0.723427\pi\)
−0.645682 + 0.763607i \(0.723427\pi\)
\(710\) 13.7617 0.516466
\(711\) −31.9223 −1.19718
\(712\) 3.42413 0.128325
\(713\) 22.8320 0.855064
\(714\) −4.93698 −0.184762
\(715\) −5.69835 −0.213106
\(716\) −18.7696 −0.701453
\(717\) 45.3032 1.69188
\(718\) −19.5704 −0.730360
\(719\) 3.32459 0.123986 0.0619932 0.998077i \(-0.480254\pi\)
0.0619932 + 0.998077i \(0.480254\pi\)
\(720\) 5.19548 0.193624
\(721\) −33.9396 −1.26398
\(722\) −2.52212 −0.0938636
\(723\) −37.6569 −1.40048
\(724\) 9.94319 0.369536
\(725\) 10.1449 0.376772
\(726\) 2.86277 0.106248
\(727\) 22.5702 0.837083 0.418541 0.908198i \(-0.362542\pi\)
0.418541 + 0.908198i \(0.362542\pi\)
\(728\) −10.1950 −0.377850
\(729\) −41.4758 −1.53614
\(730\) 6.67878 0.247193
\(731\) −0.963912 −0.0356516
\(732\) −8.73315 −0.322787
\(733\) −0.126810 −0.00468382 −0.00234191 0.999997i \(-0.500745\pi\)
−0.00234191 + 0.999997i \(0.500745\pi\)
\(734\) 21.1977 0.782421
\(735\) 10.8760 0.401166
\(736\) 7.69835 0.283765
\(737\) 13.2850 0.489361
\(738\) 24.6940 0.908998
\(739\) −15.7206 −0.578291 −0.289146 0.957285i \(-0.593371\pi\)
−0.289146 + 0.957285i \(0.593371\pi\)
\(740\) 4.30018 0.158078
\(741\) 75.6796 2.78016
\(742\) −6.07194 −0.222908
\(743\) 52.0569 1.90978 0.954891 0.296955i \(-0.0959712\pi\)
0.954891 + 0.296955i \(0.0959712\pi\)
\(744\) −8.49049 −0.311276
\(745\) −6.05872 −0.221974
\(746\) 29.9681 1.09721
\(747\) 13.1555 0.481336
\(748\) 0.963912 0.0352441
\(749\) 16.3620 0.597855
\(750\) 2.86277 0.104534
\(751\) −46.3717 −1.69213 −0.846064 0.533081i \(-0.821034\pi\)
−0.846064 + 0.533081i \(0.821034\pi\)
\(752\) 7.87220 0.287070
\(753\) 68.4402 2.49410
\(754\) 57.8092 2.10529
\(755\) −17.4306 −0.634363
\(756\) 11.2448 0.408970
\(757\) −18.9255 −0.687860 −0.343930 0.938995i \(-0.611758\pi\)
−0.343930 + 0.938995i \(0.611758\pi\)
\(758\) 27.3318 0.992735
\(759\) 22.0386 0.799952
\(760\) −4.63919 −0.168281
\(761\) −17.4661 −0.633146 −0.316573 0.948568i \(-0.602532\pi\)
−0.316573 + 0.948568i \(0.602532\pi\)
\(762\) −13.4144 −0.485951
\(763\) −31.0668 −1.12469
\(764\) 21.4314 0.775360
\(765\) 5.00798 0.181064
\(766\) 3.43388 0.124071
\(767\) 35.8550 1.29465
\(768\) −2.86277 −0.103301
\(769\) 20.4588 0.737762 0.368881 0.929477i \(-0.379741\pi\)
0.368881 + 0.929477i \(0.379741\pi\)
\(770\) 1.78911 0.0644749
\(771\) −1.95585 −0.0704381
\(772\) 19.5355 0.703098
\(773\) 33.4427 1.20285 0.601425 0.798930i \(-0.294600\pi\)
0.601425 + 0.798930i \(0.294600\pi\)
\(774\) 5.19548 0.186748
\(775\) −2.96582 −0.106536
\(776\) −17.9695 −0.645067
\(777\) 22.0247 0.790132
\(778\) −7.61138 −0.272881
\(779\) −22.0500 −0.790023
\(780\) 16.3131 0.584103
\(781\) −13.7617 −0.492431
\(782\) 7.42054 0.265358
\(783\) −63.7623 −2.27868
\(784\) −3.79910 −0.135682
\(785\) −11.1720 −0.398746
\(786\) 3.26335 0.116400
\(787\) −16.4745 −0.587253 −0.293626 0.955920i \(-0.594862\pi\)
−0.293626 + 0.955920i \(0.594862\pi\)
\(788\) −2.65052 −0.0944210
\(789\) −33.8775 −1.20607
\(790\) 6.14424 0.218602
\(791\) −15.3392 −0.545400
\(792\) −5.19548 −0.184613
\(793\) −17.3833 −0.617300
\(794\) −5.57754 −0.197939
\(795\) 9.71580 0.344584
\(796\) −17.8560 −0.632889
\(797\) 16.2469 0.575493 0.287747 0.957707i \(-0.407094\pi\)
0.287747 + 0.957707i \(0.407094\pi\)
\(798\) −23.7611 −0.841133
\(799\) 7.58811 0.268448
\(800\) −1.00000 −0.0353553
\(801\) −17.7900 −0.628579
\(802\) 31.5987 1.11579
\(803\) −6.67878 −0.235689
\(804\) −38.0321 −1.34129
\(805\) 13.7732 0.485441
\(806\) −16.9003 −0.595288
\(807\) 17.2143 0.605973
\(808\) −17.6924 −0.622415
\(809\) 5.85235 0.205758 0.102879 0.994694i \(-0.467195\pi\)
0.102879 + 0.994694i \(0.467195\pi\)
\(810\) −2.40656 −0.0845577
\(811\) −27.1463 −0.953235 −0.476617 0.879111i \(-0.658137\pi\)
−0.476617 + 0.879111i \(0.658137\pi\)
\(812\) −18.1503 −0.636952
\(813\) 21.6389 0.758911
\(814\) −4.30018 −0.150721
\(815\) −10.9817 −0.384671
\(816\) −2.75946 −0.0966005
\(817\) −4.63919 −0.162305
\(818\) −32.6528 −1.14168
\(819\) 52.9677 1.85084
\(820\) −4.75298 −0.165981
\(821\) 17.2934 0.603542 0.301771 0.953380i \(-0.402422\pi\)
0.301771 + 0.953380i \(0.402422\pi\)
\(822\) 21.2284 0.740426
\(823\) −16.7932 −0.585374 −0.292687 0.956208i \(-0.594549\pi\)
−0.292687 + 0.956208i \(0.594549\pi\)
\(824\) −18.9702 −0.660857
\(825\) −2.86277 −0.0996690
\(826\) −11.2574 −0.391693
\(827\) 48.8017 1.69700 0.848501 0.529193i \(-0.177505\pi\)
0.848501 + 0.529193i \(0.177505\pi\)
\(828\) −39.9966 −1.38998
\(829\) 2.98161 0.103556 0.0517778 0.998659i \(-0.483511\pi\)
0.0517778 + 0.998659i \(0.483511\pi\)
\(830\) −2.53212 −0.0878910
\(831\) 58.7563 2.03823
\(832\) −5.69835 −0.197555
\(833\) −3.66199 −0.126881
\(834\) −24.5675 −0.850702
\(835\) 17.3594 0.600747
\(836\) 4.63919 0.160450
\(837\) 18.6407 0.644316
\(838\) 14.9133 0.515171
\(839\) 21.1431 0.729939 0.364970 0.931019i \(-0.381079\pi\)
0.364970 + 0.931019i \(0.381079\pi\)
\(840\) −5.12181 −0.176719
\(841\) 73.9191 2.54894
\(842\) 7.00096 0.241269
\(843\) 16.3804 0.564170
\(844\) −25.8794 −0.890805
\(845\) 19.4712 0.669830
\(846\) −40.8998 −1.40616
\(847\) −1.78911 −0.0614745
\(848\) −3.39384 −0.116545
\(849\) −17.6132 −0.604482
\(850\) −0.963912 −0.0330619
\(851\) −33.1043 −1.13480
\(852\) 39.3966 1.34970
\(853\) 39.7047 1.35946 0.679732 0.733460i \(-0.262096\pi\)
0.679732 + 0.733460i \(0.262096\pi\)
\(854\) 5.45783 0.186763
\(855\) 24.1028 0.824299
\(856\) 9.14536 0.312582
\(857\) −11.9015 −0.406546 −0.203273 0.979122i \(-0.565158\pi\)
−0.203273 + 0.979122i \(0.565158\pi\)
\(858\) −16.3131 −0.556920
\(859\) −11.7263 −0.400098 −0.200049 0.979786i \(-0.564110\pi\)
−0.200049 + 0.979786i \(0.564110\pi\)
\(860\) −1.00000 −0.0340997
\(861\) −24.3439 −0.829636
\(862\) −1.71755 −0.0584999
\(863\) 56.9557 1.93879 0.969396 0.245500i \(-0.0789523\pi\)
0.969396 + 0.245500i \(0.0789523\pi\)
\(864\) 6.28516 0.213825
\(865\) −5.17703 −0.176024
\(866\) 3.58605 0.121859
\(867\) 46.0073 1.56249
\(868\) 5.30618 0.180103
\(869\) −6.14424 −0.208429
\(870\) 29.0426 0.984636
\(871\) −75.7029 −2.56509
\(872\) −17.3644 −0.588033
\(873\) 93.3601 3.15976
\(874\) 35.7141 1.20805
\(875\) −1.78911 −0.0604829
\(876\) 19.1198 0.645999
\(877\) 26.9437 0.909823 0.454912 0.890537i \(-0.349671\pi\)
0.454912 + 0.890537i \(0.349671\pi\)
\(878\) −37.3617 −1.26090
\(879\) −23.9772 −0.808731
\(880\) 1.00000 0.0337100
\(881\) 45.3039 1.52633 0.763163 0.646206i \(-0.223645\pi\)
0.763163 + 0.646206i \(0.223645\pi\)
\(882\) 19.7381 0.664617
\(883\) 15.5465 0.523181 0.261591 0.965179i \(-0.415753\pi\)
0.261591 + 0.965179i \(0.415753\pi\)
\(884\) −5.49271 −0.184740
\(885\) 18.0130 0.605502
\(886\) 27.7099 0.930933
\(887\) −0.617981 −0.0207498 −0.0103749 0.999946i \(-0.503302\pi\)
−0.0103749 + 0.999946i \(0.503302\pi\)
\(888\) 12.3104 0.413111
\(889\) 8.38339 0.281170
\(890\) 3.42413 0.114777
\(891\) 2.40656 0.0806226
\(892\) −19.7769 −0.662178
\(893\) 36.5206 1.22212
\(894\) −17.3448 −0.580096
\(895\) −18.7696 −0.627399
\(896\) 1.78911 0.0597699
\(897\) −125.584 −4.19313
\(898\) −30.4230 −1.01523
\(899\) −30.0880 −1.00349
\(900\) 5.19548 0.173183
\(901\) −3.27136 −0.108985
\(902\) 4.75298 0.158257
\(903\) −5.12181 −0.170443
\(904\) −8.57368 −0.285156
\(905\) 9.94319 0.330523
\(906\) −49.8998 −1.65781
\(907\) −23.0711 −0.766063 −0.383031 0.923735i \(-0.625120\pi\)
−0.383031 + 0.923735i \(0.625120\pi\)
\(908\) 22.0963 0.733291
\(909\) 91.9203 3.04880
\(910\) −10.1950 −0.337960
\(911\) 8.30052 0.275009 0.137504 0.990501i \(-0.456092\pi\)
0.137504 + 0.990501i \(0.456092\pi\)
\(912\) −13.2810 −0.439777
\(913\) 2.53212 0.0838008
\(914\) 32.9666 1.09044
\(915\) −8.73315 −0.288709
\(916\) 8.96277 0.296138
\(917\) −2.03945 −0.0673485
\(918\) 6.05834 0.199955
\(919\) 13.4450 0.443510 0.221755 0.975102i \(-0.428821\pi\)
0.221755 + 0.975102i \(0.428821\pi\)
\(920\) 7.69835 0.253807
\(921\) −11.4785 −0.378230
\(922\) 34.8994 1.14935
\(923\) 78.4188 2.58119
\(924\) 5.12181 0.168495
\(925\) 4.30018 0.141389
\(926\) 25.0883 0.824451
\(927\) 98.5590 3.23710
\(928\) −10.1449 −0.333023
\(929\) 29.2727 0.960408 0.480204 0.877157i \(-0.340563\pi\)
0.480204 + 0.877157i \(0.340563\pi\)
\(930\) −8.49049 −0.278414
\(931\) −17.6247 −0.577628
\(932\) 0.510127 0.0167098
\(933\) −4.38023 −0.143402
\(934\) 31.7044 1.03740
\(935\) 0.963912 0.0315233
\(936\) 29.6057 0.967691
\(937\) −6.94493 −0.226881 −0.113440 0.993545i \(-0.536187\pi\)
−0.113440 + 0.993545i \(0.536187\pi\)
\(938\) 23.7684 0.776065
\(939\) −22.0236 −0.718712
\(940\) 7.87220 0.256763
\(941\) 14.7555 0.481015 0.240507 0.970647i \(-0.422686\pi\)
0.240507 + 0.970647i \(0.422686\pi\)
\(942\) −31.9829 −1.04206
\(943\) 36.5901 1.19154
\(944\) −6.29216 −0.204792
\(945\) 11.2448 0.365794
\(946\) 1.00000 0.0325128
\(947\) 10.4291 0.338899 0.169450 0.985539i \(-0.445801\pi\)
0.169450 + 0.985539i \(0.445801\pi\)
\(948\) 17.5896 0.571283
\(949\) 38.0580 1.23542
\(950\) −4.63919 −0.150515
\(951\) 24.2119 0.785124
\(952\) 1.72454 0.0558927
\(953\) −48.9621 −1.58604 −0.793019 0.609197i \(-0.791492\pi\)
−0.793019 + 0.609197i \(0.791492\pi\)
\(954\) 17.6326 0.570877
\(955\) 21.4314 0.693503
\(956\) −15.8249 −0.511815
\(957\) −29.0426 −0.938813
\(958\) −19.7689 −0.638703
\(959\) −13.2668 −0.428408
\(960\) −2.86277 −0.0923956
\(961\) −22.2039 −0.716254
\(962\) 24.5039 0.790038
\(963\) −47.5145 −1.53113
\(964\) 13.1540 0.423662
\(965\) 19.5355 0.628870
\(966\) 39.4295 1.26862
\(967\) −33.0672 −1.06337 −0.531684 0.846943i \(-0.678441\pi\)
−0.531684 + 0.846943i \(0.678441\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −12.8017 −0.411249
\(970\) −17.9695 −0.576966
\(971\) 52.0985 1.67192 0.835960 0.548790i \(-0.184911\pi\)
0.835960 + 0.548790i \(0.184911\pi\)
\(972\) 11.9660 0.383811
\(973\) 15.3536 0.492213
\(974\) 13.6035 0.435883
\(975\) 16.3131 0.522437
\(976\) 3.05059 0.0976470
\(977\) −2.81985 −0.0902149 −0.0451074 0.998982i \(-0.514363\pi\)
−0.0451074 + 0.998982i \(0.514363\pi\)
\(978\) −31.4381 −1.00528
\(979\) −3.42413 −0.109436
\(980\) −3.79910 −0.121358
\(981\) 90.2165 2.88039
\(982\) −14.9396 −0.476741
\(983\) −49.2812 −1.57183 −0.785914 0.618336i \(-0.787807\pi\)
−0.785914 + 0.618336i \(0.787807\pi\)
\(984\) −13.6067 −0.433766
\(985\) −2.65052 −0.0844527
\(986\) −9.77880 −0.311420
\(987\) 40.3199 1.28340
\(988\) −26.4358 −0.841034
\(989\) 7.69835 0.244793
\(990\) −5.19548 −0.165123
\(991\) −8.33102 −0.264644 −0.132322 0.991207i \(-0.542243\pi\)
−0.132322 + 0.991207i \(0.542243\pi\)
\(992\) 2.96582 0.0941650
\(993\) 66.7097 2.11697
\(994\) −24.6211 −0.780934
\(995\) −17.8560 −0.566073
\(996\) −7.24887 −0.229689
\(997\) −38.6185 −1.22306 −0.611530 0.791221i \(-0.709446\pi\)
−0.611530 + 0.791221i \(0.709446\pi\)
\(998\) 25.6559 0.812124
\(999\) −27.0273 −0.855106
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.w.1.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.w.1.2 8 1.1 even 1 trivial