Properties

Label 6037.2.a.b.1.20
Level $6037$
Weight $2$
Character 6037.1
Self dual yes
Analytic conductor $48.206$
Analytic rank $0$
Dimension $259$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.38263 q^{2} -0.344809 q^{3} +3.67692 q^{4} +0.273793 q^{5} +0.821552 q^{6} +0.727572 q^{7} -3.99549 q^{8} -2.88111 q^{9} +O(q^{10})\) \(q-2.38263 q^{2} -0.344809 q^{3} +3.67692 q^{4} +0.273793 q^{5} +0.821552 q^{6} +0.727572 q^{7} -3.99549 q^{8} -2.88111 q^{9} -0.652346 q^{10} +3.88366 q^{11} -1.26784 q^{12} -3.75219 q^{13} -1.73354 q^{14} -0.0944060 q^{15} +2.16593 q^{16} -5.98659 q^{17} +6.86461 q^{18} +5.86992 q^{19} +1.00671 q^{20} -0.250873 q^{21} -9.25334 q^{22} -2.71732 q^{23} +1.37768 q^{24} -4.92504 q^{25} +8.94009 q^{26} +2.02786 q^{27} +2.67523 q^{28} -1.73212 q^{29} +0.224935 q^{30} -10.6688 q^{31} +2.83038 q^{32} -1.33912 q^{33} +14.2638 q^{34} +0.199204 q^{35} -10.5936 q^{36} -0.0898831 q^{37} -13.9858 q^{38} +1.29379 q^{39} -1.09394 q^{40} -0.491956 q^{41} +0.597738 q^{42} +7.22234 q^{43} +14.2799 q^{44} -0.788825 q^{45} +6.47437 q^{46} -5.73624 q^{47} -0.746830 q^{48} -6.47064 q^{49} +11.7345 q^{50} +2.06423 q^{51} -13.7965 q^{52} +11.0244 q^{53} -4.83163 q^{54} +1.06332 q^{55} -2.90701 q^{56} -2.02400 q^{57} +4.12699 q^{58} -5.61526 q^{59} -0.347124 q^{60} -7.48540 q^{61} +25.4197 q^{62} -2.09621 q^{63} -11.0756 q^{64} -1.02732 q^{65} +3.19063 q^{66} +5.34242 q^{67} -22.0122 q^{68} +0.936956 q^{69} -0.474629 q^{70} -1.48365 q^{71} +11.5114 q^{72} +9.78980 q^{73} +0.214158 q^{74} +1.69820 q^{75} +21.5832 q^{76} +2.82565 q^{77} -3.08262 q^{78} -1.65606 q^{79} +0.593014 q^{80} +7.94410 q^{81} +1.17215 q^{82} -12.9137 q^{83} -0.922442 q^{84} -1.63908 q^{85} -17.2082 q^{86} +0.597249 q^{87} -15.5171 q^{88} +16.6571 q^{89} +1.87948 q^{90} -2.72999 q^{91} -9.99138 q^{92} +3.67868 q^{93} +13.6673 q^{94} +1.60714 q^{95} -0.975941 q^{96} +5.76518 q^{97} +15.4171 q^{98} -11.1893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38263 −1.68477 −0.842387 0.538873i \(-0.818850\pi\)
−0.842387 + 0.538873i \(0.818850\pi\)
\(3\) −0.344809 −0.199075 −0.0995377 0.995034i \(-0.531736\pi\)
−0.0995377 + 0.995034i \(0.531736\pi\)
\(4\) 3.67692 1.83846
\(5\) 0.273793 0.122444 0.0612219 0.998124i \(-0.480500\pi\)
0.0612219 + 0.998124i \(0.480500\pi\)
\(6\) 0.821552 0.335397
\(7\) 0.727572 0.274996 0.137498 0.990502i \(-0.456094\pi\)
0.137498 + 0.990502i \(0.456094\pi\)
\(8\) −3.99549 −1.41262
\(9\) −2.88111 −0.960369
\(10\) −0.652346 −0.206290
\(11\) 3.88366 1.17097 0.585484 0.810684i \(-0.300904\pi\)
0.585484 + 0.810684i \(0.300904\pi\)
\(12\) −1.26784 −0.365993
\(13\) −3.75219 −1.04067 −0.520336 0.853962i \(-0.674193\pi\)
−0.520336 + 0.853962i \(0.674193\pi\)
\(14\) −1.73354 −0.463307
\(15\) −0.0944060 −0.0243755
\(16\) 2.16593 0.541481
\(17\) −5.98659 −1.45196 −0.725980 0.687716i \(-0.758614\pi\)
−0.725980 + 0.687716i \(0.758614\pi\)
\(18\) 6.86461 1.61800
\(19\) 5.86992 1.34665 0.673326 0.739346i \(-0.264865\pi\)
0.673326 + 0.739346i \(0.264865\pi\)
\(20\) 1.00671 0.225108
\(21\) −0.250873 −0.0547450
\(22\) −9.25334 −1.97282
\(23\) −2.71732 −0.566600 −0.283300 0.959031i \(-0.591429\pi\)
−0.283300 + 0.959031i \(0.591429\pi\)
\(24\) 1.37768 0.281218
\(25\) −4.92504 −0.985008
\(26\) 8.94009 1.75330
\(27\) 2.02786 0.390261
\(28\) 2.67523 0.505571
\(29\) −1.73212 −0.321646 −0.160823 0.986983i \(-0.551415\pi\)
−0.160823 + 0.986983i \(0.551415\pi\)
\(30\) 0.224935 0.0410673
\(31\) −10.6688 −1.91616 −0.958082 0.286494i \(-0.907510\pi\)
−0.958082 + 0.286494i \(0.907510\pi\)
\(32\) 2.83038 0.500346
\(33\) −1.33912 −0.233111
\(34\) 14.2638 2.44622
\(35\) 0.199204 0.0336716
\(36\) −10.5936 −1.76560
\(37\) −0.0898831 −0.0147767 −0.00738835 0.999973i \(-0.502352\pi\)
−0.00738835 + 0.999973i \(0.502352\pi\)
\(38\) −13.9858 −2.26880
\(39\) 1.29379 0.207172
\(40\) −1.09394 −0.172966
\(41\) −0.491956 −0.0768306 −0.0384153 0.999262i \(-0.512231\pi\)
−0.0384153 + 0.999262i \(0.512231\pi\)
\(42\) 0.597738 0.0922330
\(43\) 7.22234 1.10140 0.550698 0.834704i \(-0.314361\pi\)
0.550698 + 0.834704i \(0.314361\pi\)
\(44\) 14.2799 2.15278
\(45\) −0.788825 −0.117591
\(46\) 6.47437 0.954593
\(47\) −5.73624 −0.836717 −0.418358 0.908282i \(-0.637394\pi\)
−0.418358 + 0.908282i \(0.637394\pi\)
\(48\) −0.746830 −0.107796
\(49\) −6.47064 −0.924377
\(50\) 11.7345 1.65951
\(51\) 2.06423 0.289050
\(52\) −13.7965 −1.91323
\(53\) 11.0244 1.51431 0.757156 0.653235i \(-0.226588\pi\)
0.757156 + 0.653235i \(0.226588\pi\)
\(54\) −4.83163 −0.657502
\(55\) 1.06332 0.143378
\(56\) −2.90701 −0.388465
\(57\) −2.02400 −0.268085
\(58\) 4.12699 0.541901
\(59\) −5.61526 −0.731045 −0.365522 0.930803i \(-0.619110\pi\)
−0.365522 + 0.930803i \(0.619110\pi\)
\(60\) −0.347124 −0.0448135
\(61\) −7.48540 −0.958407 −0.479203 0.877704i \(-0.659074\pi\)
−0.479203 + 0.877704i \(0.659074\pi\)
\(62\) 25.4197 3.22830
\(63\) −2.09621 −0.264098
\(64\) −11.0756 −1.38445
\(65\) −1.02732 −0.127424
\(66\) 3.19063 0.392739
\(67\) 5.34242 0.652680 0.326340 0.945252i \(-0.394185\pi\)
0.326340 + 0.945252i \(0.394185\pi\)
\(68\) −22.0122 −2.66937
\(69\) 0.936956 0.112796
\(70\) −0.474629 −0.0567290
\(71\) −1.48365 −0.176077 −0.0880387 0.996117i \(-0.528060\pi\)
−0.0880387 + 0.996117i \(0.528060\pi\)
\(72\) 11.5114 1.35664
\(73\) 9.78980 1.14581 0.572905 0.819622i \(-0.305816\pi\)
0.572905 + 0.819622i \(0.305816\pi\)
\(74\) 0.214158 0.0248954
\(75\) 1.69820 0.196091
\(76\) 21.5832 2.47577
\(77\) 2.82565 0.322012
\(78\) −3.08262 −0.349038
\(79\) −1.65606 −0.186321 −0.0931606 0.995651i \(-0.529697\pi\)
−0.0931606 + 0.995651i \(0.529697\pi\)
\(80\) 0.593014 0.0663010
\(81\) 7.94410 0.882678
\(82\) 1.17215 0.129442
\(83\) −12.9137 −1.41746 −0.708732 0.705478i \(-0.750733\pi\)
−0.708732 + 0.705478i \(0.750733\pi\)
\(84\) −0.922442 −0.100647
\(85\) −1.63908 −0.177783
\(86\) −17.2082 −1.85560
\(87\) 0.597249 0.0640318
\(88\) −15.5171 −1.65413
\(89\) 16.6571 1.76565 0.882823 0.469706i \(-0.155640\pi\)
0.882823 + 0.469706i \(0.155640\pi\)
\(90\) 1.87948 0.198114
\(91\) −2.72999 −0.286181
\(92\) −9.99138 −1.04167
\(93\) 3.67868 0.381461
\(94\) 13.6673 1.40968
\(95\) 1.60714 0.164889
\(96\) −0.975941 −0.0996065
\(97\) 5.76518 0.585365 0.292682 0.956210i \(-0.405452\pi\)
0.292682 + 0.956210i \(0.405452\pi\)
\(98\) 15.4171 1.55737
\(99\) −11.1893 −1.12456
\(100\) −18.1090 −1.81090
\(101\) −9.67986 −0.963182 −0.481591 0.876396i \(-0.659941\pi\)
−0.481591 + 0.876396i \(0.659941\pi\)
\(102\) −4.91829 −0.486983
\(103\) 7.41314 0.730438 0.365219 0.930922i \(-0.380994\pi\)
0.365219 + 0.930922i \(0.380994\pi\)
\(104\) 14.9919 1.47007
\(105\) −0.0686872 −0.00670319
\(106\) −26.2669 −2.55127
\(107\) 1.92792 0.186380 0.0931898 0.995648i \(-0.470294\pi\)
0.0931898 + 0.995648i \(0.470294\pi\)
\(108\) 7.45628 0.717481
\(109\) −0.673701 −0.0645288 −0.0322644 0.999479i \(-0.510272\pi\)
−0.0322644 + 0.999479i \(0.510272\pi\)
\(110\) −2.53349 −0.241559
\(111\) 0.0309925 0.00294168
\(112\) 1.57587 0.148905
\(113\) 17.4808 1.64445 0.822227 0.569160i \(-0.192732\pi\)
0.822227 + 0.569160i \(0.192732\pi\)
\(114\) 4.82244 0.451663
\(115\) −0.743982 −0.0693767
\(116\) −6.36886 −0.591334
\(117\) 10.8105 0.999428
\(118\) 13.3791 1.23165
\(119\) −4.35567 −0.399284
\(120\) 0.377198 0.0344334
\(121\) 4.08285 0.371168
\(122\) 17.8349 1.61470
\(123\) 0.169631 0.0152951
\(124\) −39.2282 −3.52280
\(125\) −2.71740 −0.243052
\(126\) 4.99450 0.444945
\(127\) −11.6371 −1.03262 −0.516312 0.856400i \(-0.672696\pi\)
−0.516312 + 0.856400i \(0.672696\pi\)
\(128\) 20.7283 1.83214
\(129\) −2.49033 −0.219261
\(130\) 2.44773 0.214680
\(131\) 12.6074 1.10151 0.550756 0.834666i \(-0.314339\pi\)
0.550756 + 0.834666i \(0.314339\pi\)
\(132\) −4.92385 −0.428566
\(133\) 4.27079 0.370324
\(134\) −12.7290 −1.09962
\(135\) 0.555212 0.0477850
\(136\) 23.9194 2.05107
\(137\) 17.4647 1.49211 0.746055 0.665884i \(-0.231945\pi\)
0.746055 + 0.665884i \(0.231945\pi\)
\(138\) −2.23242 −0.190036
\(139\) −2.93875 −0.249261 −0.124631 0.992203i \(-0.539775\pi\)
−0.124631 + 0.992203i \(0.539775\pi\)
\(140\) 0.732457 0.0619039
\(141\) 1.97791 0.166570
\(142\) 3.53500 0.296651
\(143\) −14.5723 −1.21859
\(144\) −6.24026 −0.520022
\(145\) −0.474241 −0.0393835
\(146\) −23.3255 −1.93043
\(147\) 2.23113 0.184021
\(148\) −0.330493 −0.0271664
\(149\) 1.01379 0.0830527 0.0415264 0.999137i \(-0.486778\pi\)
0.0415264 + 0.999137i \(0.486778\pi\)
\(150\) −4.04617 −0.330369
\(151\) 9.77957 0.795850 0.397925 0.917418i \(-0.369730\pi\)
0.397925 + 0.917418i \(0.369730\pi\)
\(152\) −23.4532 −1.90231
\(153\) 17.2480 1.39442
\(154\) −6.73247 −0.542518
\(155\) −2.92102 −0.234622
\(156\) 4.75716 0.380878
\(157\) 16.0977 1.28474 0.642368 0.766396i \(-0.277952\pi\)
0.642368 + 0.766396i \(0.277952\pi\)
\(158\) 3.94578 0.313909
\(159\) −3.80129 −0.301462
\(160\) 0.774938 0.0612642
\(161\) −1.97705 −0.155813
\(162\) −18.9278 −1.48711
\(163\) 19.8423 1.55417 0.777083 0.629399i \(-0.216699\pi\)
0.777083 + 0.629399i \(0.216699\pi\)
\(164\) −1.80888 −0.141250
\(165\) −0.366641 −0.0285430
\(166\) 30.7686 2.38811
\(167\) 18.4378 1.42676 0.713378 0.700779i \(-0.247164\pi\)
0.713378 + 0.700779i \(0.247164\pi\)
\(168\) 1.00236 0.0773339
\(169\) 1.07895 0.0829964
\(170\) 3.90533 0.299525
\(171\) −16.9119 −1.29328
\(172\) 26.5560 2.02488
\(173\) −6.79800 −0.516843 −0.258421 0.966032i \(-0.583202\pi\)
−0.258421 + 0.966032i \(0.583202\pi\)
\(174\) −1.42302 −0.107879
\(175\) −3.58332 −0.270874
\(176\) 8.41173 0.634058
\(177\) 1.93619 0.145533
\(178\) −39.6876 −2.97471
\(179\) −2.04452 −0.152815 −0.0764074 0.997077i \(-0.524345\pi\)
−0.0764074 + 0.997077i \(0.524345\pi\)
\(180\) −2.90045 −0.216187
\(181\) −6.07758 −0.451743 −0.225872 0.974157i \(-0.572523\pi\)
−0.225872 + 0.974157i \(0.572523\pi\)
\(182\) 6.50456 0.482150
\(183\) 2.58103 0.190795
\(184\) 10.8570 0.800391
\(185\) −0.0246093 −0.00180931
\(186\) −8.76493 −0.642676
\(187\) −23.2499 −1.70020
\(188\) −21.0917 −1.53827
\(189\) 1.47541 0.107320
\(190\) −3.82922 −0.277801
\(191\) −15.4641 −1.11895 −0.559473 0.828849i \(-0.688996\pi\)
−0.559473 + 0.828849i \(0.688996\pi\)
\(192\) 3.81897 0.275610
\(193\) 1.30655 0.0940479 0.0470239 0.998894i \(-0.485026\pi\)
0.0470239 + 0.998894i \(0.485026\pi\)
\(194\) −13.7363 −0.986207
\(195\) 0.354230 0.0253669
\(196\) −23.7921 −1.69943
\(197\) 9.53093 0.679051 0.339525 0.940597i \(-0.389734\pi\)
0.339525 + 0.940597i \(0.389734\pi\)
\(198\) 26.6598 1.89463
\(199\) −19.5842 −1.38828 −0.694142 0.719838i \(-0.744216\pi\)
−0.694142 + 0.719838i \(0.744216\pi\)
\(200\) 19.6779 1.39144
\(201\) −1.84211 −0.129933
\(202\) 23.0635 1.62274
\(203\) −1.26024 −0.0884515
\(204\) 7.59001 0.531407
\(205\) −0.134694 −0.00940742
\(206\) −17.6628 −1.23062
\(207\) 7.82889 0.544145
\(208\) −8.12697 −0.563504
\(209\) 22.7968 1.57689
\(210\) 0.163656 0.0112934
\(211\) −3.19828 −0.220179 −0.110089 0.993922i \(-0.535114\pi\)
−0.110089 + 0.993922i \(0.535114\pi\)
\(212\) 40.5357 2.78400
\(213\) 0.511577 0.0350527
\(214\) −4.59353 −0.314007
\(215\) 1.97742 0.134859
\(216\) −8.10228 −0.551291
\(217\) −7.76229 −0.526938
\(218\) 1.60518 0.108716
\(219\) −3.37561 −0.228103
\(220\) 3.90974 0.263595
\(221\) 22.4628 1.51101
\(222\) −0.0738436 −0.00495606
\(223\) −11.6024 −0.776956 −0.388478 0.921458i \(-0.626999\pi\)
−0.388478 + 0.921458i \(0.626999\pi\)
\(224\) 2.05931 0.137593
\(225\) 14.1896 0.945971
\(226\) −41.6502 −2.77053
\(227\) 23.5533 1.56329 0.781644 0.623725i \(-0.214382\pi\)
0.781644 + 0.623725i \(0.214382\pi\)
\(228\) −7.44209 −0.492865
\(229\) −13.1287 −0.867569 −0.433784 0.901017i \(-0.642822\pi\)
−0.433784 + 0.901017i \(0.642822\pi\)
\(230\) 1.77263 0.116884
\(231\) −0.974308 −0.0641047
\(232\) 6.92066 0.454363
\(233\) 17.5241 1.14804 0.574022 0.818840i \(-0.305382\pi\)
0.574022 + 0.818840i \(0.305382\pi\)
\(234\) −25.7573 −1.68381
\(235\) −1.57054 −0.102451
\(236\) −20.6469 −1.34400
\(237\) 0.571024 0.0370920
\(238\) 10.3780 0.672703
\(239\) 14.5925 0.943908 0.471954 0.881623i \(-0.343549\pi\)
0.471954 + 0.881623i \(0.343549\pi\)
\(240\) −0.204476 −0.0131989
\(241\) −26.4569 −1.70424 −0.852121 0.523345i \(-0.824684\pi\)
−0.852121 + 0.523345i \(0.824684\pi\)
\(242\) −9.72793 −0.625335
\(243\) −8.82277 −0.565981
\(244\) −27.5232 −1.76199
\(245\) −1.77161 −0.113184
\(246\) −0.404167 −0.0257687
\(247\) −22.0251 −1.40142
\(248\) 42.6269 2.70681
\(249\) 4.45276 0.282182
\(250\) 6.47456 0.409487
\(251\) 7.47031 0.471522 0.235761 0.971811i \(-0.424242\pi\)
0.235761 + 0.971811i \(0.424242\pi\)
\(252\) −7.70762 −0.485534
\(253\) −10.5532 −0.663471
\(254\) 27.7269 1.73974
\(255\) 0.565170 0.0353923
\(256\) −27.2367 −1.70229
\(257\) 29.8196 1.86010 0.930048 0.367437i \(-0.119765\pi\)
0.930048 + 0.367437i \(0.119765\pi\)
\(258\) 5.93353 0.369405
\(259\) −0.0653965 −0.00406354
\(260\) −3.77739 −0.234264
\(261\) 4.99041 0.308899
\(262\) −30.0387 −1.85580
\(263\) −11.5992 −0.715237 −0.357618 0.933868i \(-0.616411\pi\)
−0.357618 + 0.933868i \(0.616411\pi\)
\(264\) 5.35045 0.329297
\(265\) 3.01838 0.185418
\(266\) −10.1757 −0.623913
\(267\) −5.74350 −0.351497
\(268\) 19.6437 1.19993
\(269\) −4.85687 −0.296128 −0.148064 0.988978i \(-0.547304\pi\)
−0.148064 + 0.988978i \(0.547304\pi\)
\(270\) −1.32286 −0.0805070
\(271\) 1.68960 0.102636 0.0513180 0.998682i \(-0.483658\pi\)
0.0513180 + 0.998682i \(0.483658\pi\)
\(272\) −12.9665 −0.786210
\(273\) 0.941325 0.0569716
\(274\) −41.6119 −2.51387
\(275\) −19.1272 −1.15341
\(276\) 3.44511 0.207372
\(277\) 11.0402 0.663341 0.331671 0.943395i \(-0.392388\pi\)
0.331671 + 0.943395i \(0.392388\pi\)
\(278\) 7.00194 0.419949
\(279\) 30.7378 1.84022
\(280\) −0.795917 −0.0475651
\(281\) −26.7476 −1.59563 −0.797813 0.602905i \(-0.794010\pi\)
−0.797813 + 0.602905i \(0.794010\pi\)
\(282\) −4.71262 −0.280632
\(283\) −25.8292 −1.53539 −0.767694 0.640817i \(-0.778596\pi\)
−0.767694 + 0.640817i \(0.778596\pi\)
\(284\) −5.45528 −0.323712
\(285\) −0.554156 −0.0328254
\(286\) 34.7203 2.05305
\(287\) −0.357933 −0.0211281
\(288\) −8.15463 −0.480516
\(289\) 18.8392 1.10819
\(290\) 1.12994 0.0663523
\(291\) −1.98788 −0.116532
\(292\) 35.9964 2.10653
\(293\) 0.702917 0.0410648 0.0205324 0.999789i \(-0.493464\pi\)
0.0205324 + 0.999789i \(0.493464\pi\)
\(294\) −5.31596 −0.310033
\(295\) −1.53742 −0.0895119
\(296\) 0.359127 0.0208738
\(297\) 7.87552 0.456984
\(298\) −2.41548 −0.139925
\(299\) 10.1959 0.589645
\(300\) 6.24414 0.360506
\(301\) 5.25477 0.302880
\(302\) −23.3011 −1.34083
\(303\) 3.33770 0.191746
\(304\) 12.7138 0.729187
\(305\) −2.04945 −0.117351
\(306\) −41.0956 −2.34928
\(307\) −24.5056 −1.39861 −0.699303 0.714825i \(-0.746506\pi\)
−0.699303 + 0.714825i \(0.746506\pi\)
\(308\) 10.3897 0.592007
\(309\) −2.55612 −0.145412
\(310\) 6.95972 0.395285
\(311\) 29.4419 1.66950 0.834750 0.550629i \(-0.185612\pi\)
0.834750 + 0.550629i \(0.185612\pi\)
\(312\) −5.16932 −0.292655
\(313\) −13.0304 −0.736524 −0.368262 0.929722i \(-0.620047\pi\)
−0.368262 + 0.929722i \(0.620047\pi\)
\(314\) −38.3549 −2.16449
\(315\) −0.573927 −0.0323372
\(316\) −6.08921 −0.342545
\(317\) −4.15175 −0.233186 −0.116593 0.993180i \(-0.537197\pi\)
−0.116593 + 0.993180i \(0.537197\pi\)
\(318\) 9.05707 0.507895
\(319\) −6.72696 −0.376637
\(320\) −3.03242 −0.169517
\(321\) −0.664765 −0.0371036
\(322\) 4.71057 0.262510
\(323\) −35.1408 −1.95528
\(324\) 29.2098 1.62277
\(325\) 18.4797 1.02507
\(326\) −47.2767 −2.61842
\(327\) 0.232298 0.0128461
\(328\) 1.96560 0.108532
\(329\) −4.17353 −0.230094
\(330\) 0.873571 0.0480885
\(331\) −8.52272 −0.468451 −0.234225 0.972182i \(-0.575255\pi\)
−0.234225 + 0.972182i \(0.575255\pi\)
\(332\) −47.4828 −2.60596
\(333\) 0.258963 0.0141911
\(334\) −43.9304 −2.40376
\(335\) 1.46271 0.0799166
\(336\) −0.543373 −0.0296434
\(337\) 34.3300 1.87007 0.935037 0.354551i \(-0.115366\pi\)
0.935037 + 0.354551i \(0.115366\pi\)
\(338\) −2.57075 −0.139830
\(339\) −6.02752 −0.327370
\(340\) −6.02678 −0.326848
\(341\) −41.4338 −2.24377
\(342\) 40.2947 2.17889
\(343\) −9.80086 −0.529197
\(344\) −28.8568 −1.55585
\(345\) 0.256531 0.0138112
\(346\) 16.1971 0.870763
\(347\) 2.95835 0.158812 0.0794062 0.996842i \(-0.474698\pi\)
0.0794062 + 0.996842i \(0.474698\pi\)
\(348\) 2.19604 0.117720
\(349\) −15.4111 −0.824937 −0.412469 0.910972i \(-0.635333\pi\)
−0.412469 + 0.910972i \(0.635333\pi\)
\(350\) 8.53773 0.456361
\(351\) −7.60891 −0.406134
\(352\) 10.9923 0.585889
\(353\) 20.6918 1.10131 0.550657 0.834732i \(-0.314377\pi\)
0.550657 + 0.834732i \(0.314377\pi\)
\(354\) −4.61323 −0.245190
\(355\) −0.406213 −0.0215596
\(356\) 61.2468 3.24607
\(357\) 1.50187 0.0794876
\(358\) 4.87134 0.257458
\(359\) −3.92504 −0.207156 −0.103578 0.994621i \(-0.533029\pi\)
−0.103578 + 0.994621i \(0.533029\pi\)
\(360\) 3.15174 0.166112
\(361\) 15.4559 0.813470
\(362\) 14.4806 0.761085
\(363\) −1.40780 −0.0738905
\(364\) −10.0380 −0.526133
\(365\) 2.68037 0.140297
\(366\) −6.14964 −0.321447
\(367\) 4.98451 0.260189 0.130095 0.991502i \(-0.458472\pi\)
0.130095 + 0.991502i \(0.458472\pi\)
\(368\) −5.88551 −0.306804
\(369\) 1.41738 0.0737857
\(370\) 0.0586349 0.00304828
\(371\) 8.02101 0.416430
\(372\) 13.5262 0.701302
\(373\) −31.0404 −1.60721 −0.803607 0.595161i \(-0.797088\pi\)
−0.803607 + 0.595161i \(0.797088\pi\)
\(374\) 55.3959 2.86445
\(375\) 0.936984 0.0483856
\(376\) 22.9191 1.18196
\(377\) 6.49924 0.334728
\(378\) −3.51536 −0.180811
\(379\) 27.1565 1.39494 0.697469 0.716615i \(-0.254310\pi\)
0.697469 + 0.716615i \(0.254310\pi\)
\(380\) 5.90933 0.303142
\(381\) 4.01257 0.205570
\(382\) 36.8453 1.88517
\(383\) −22.8145 −1.16577 −0.582883 0.812556i \(-0.698075\pi\)
−0.582883 + 0.812556i \(0.698075\pi\)
\(384\) −7.14730 −0.364734
\(385\) 0.773641 0.0394284
\(386\) −3.11304 −0.158449
\(387\) −20.8083 −1.05775
\(388\) 21.1981 1.07617
\(389\) 16.3515 0.829056 0.414528 0.910037i \(-0.363947\pi\)
0.414528 + 0.910037i \(0.363947\pi\)
\(390\) −0.843998 −0.0427375
\(391\) 16.2675 0.822681
\(392\) 25.8534 1.30579
\(393\) −4.34714 −0.219284
\(394\) −22.7087 −1.14405
\(395\) −0.453417 −0.0228139
\(396\) −41.1420 −2.06747
\(397\) −9.75609 −0.489644 −0.244822 0.969568i \(-0.578730\pi\)
−0.244822 + 0.969568i \(0.578730\pi\)
\(398\) 46.6618 2.33895
\(399\) −1.47261 −0.0737225
\(400\) −10.6673 −0.533363
\(401\) −4.79423 −0.239412 −0.119706 0.992809i \(-0.538195\pi\)
−0.119706 + 0.992809i \(0.538195\pi\)
\(402\) 4.38907 0.218907
\(403\) 40.0312 1.99410
\(404\) −35.5921 −1.77077
\(405\) 2.17503 0.108078
\(406\) 3.00269 0.149021
\(407\) −0.349076 −0.0173031
\(408\) −8.24760 −0.408317
\(409\) 1.51745 0.0750329 0.0375164 0.999296i \(-0.488055\pi\)
0.0375164 + 0.999296i \(0.488055\pi\)
\(410\) 0.320925 0.0158494
\(411\) −6.02198 −0.297043
\(412\) 27.2576 1.34288
\(413\) −4.08551 −0.201035
\(414\) −18.6533 −0.916762
\(415\) −3.53568 −0.173560
\(416\) −10.6201 −0.520695
\(417\) 1.01331 0.0496218
\(418\) −54.3163 −2.65670
\(419\) 24.8570 1.21434 0.607172 0.794570i \(-0.292304\pi\)
0.607172 + 0.794570i \(0.292304\pi\)
\(420\) −0.252558 −0.0123236
\(421\) 16.3819 0.798406 0.399203 0.916863i \(-0.369287\pi\)
0.399203 + 0.916863i \(0.369287\pi\)
\(422\) 7.62031 0.370951
\(423\) 16.5267 0.803557
\(424\) −44.0477 −2.13915
\(425\) 29.4842 1.43019
\(426\) −1.21890 −0.0590558
\(427\) −5.44617 −0.263558
\(428\) 7.08883 0.342652
\(429\) 5.02464 0.242592
\(430\) −4.71147 −0.227207
\(431\) −10.4937 −0.505465 −0.252733 0.967536i \(-0.581329\pi\)
−0.252733 + 0.967536i \(0.581329\pi\)
\(432\) 4.39219 0.211319
\(433\) 31.5907 1.51815 0.759077 0.651001i \(-0.225651\pi\)
0.759077 + 0.651001i \(0.225651\pi\)
\(434\) 18.4947 0.887772
\(435\) 0.163522 0.00784029
\(436\) −2.47715 −0.118634
\(437\) −15.9504 −0.763013
\(438\) 8.04283 0.384301
\(439\) 19.7169 0.941037 0.470518 0.882390i \(-0.344067\pi\)
0.470518 + 0.882390i \(0.344067\pi\)
\(440\) −4.24848 −0.202538
\(441\) 18.6426 0.887743
\(442\) −53.5206 −2.54572
\(443\) 23.6026 1.12139 0.560696 0.828022i \(-0.310534\pi\)
0.560696 + 0.828022i \(0.310534\pi\)
\(444\) 0.113957 0.00540816
\(445\) 4.56058 0.216192
\(446\) 27.6443 1.30900
\(447\) −0.349563 −0.0165338
\(448\) −8.05830 −0.380719
\(449\) −17.6689 −0.833845 −0.416923 0.908942i \(-0.636891\pi\)
−0.416923 + 0.908942i \(0.636891\pi\)
\(450\) −33.8085 −1.59375
\(451\) −1.91059 −0.0899662
\(452\) 64.2755 3.02327
\(453\) −3.37208 −0.158434
\(454\) −56.1188 −2.63379
\(455\) −0.747451 −0.0350411
\(456\) 8.08687 0.378702
\(457\) −30.1256 −1.40922 −0.704609 0.709596i \(-0.748878\pi\)
−0.704609 + 0.709596i \(0.748878\pi\)
\(458\) 31.2808 1.46166
\(459\) −12.1399 −0.566644
\(460\) −2.73556 −0.127546
\(461\) 2.65047 0.123445 0.0617223 0.998093i \(-0.480341\pi\)
0.0617223 + 0.998093i \(0.480341\pi\)
\(462\) 2.32141 0.108002
\(463\) −18.2005 −0.845851 −0.422925 0.906165i \(-0.638997\pi\)
−0.422925 + 0.906165i \(0.638997\pi\)
\(464\) −3.75164 −0.174165
\(465\) 1.00719 0.0467075
\(466\) −41.7535 −1.93419
\(467\) −17.4549 −0.807718 −0.403859 0.914821i \(-0.632331\pi\)
−0.403859 + 0.914821i \(0.632331\pi\)
\(468\) 39.7493 1.83741
\(469\) 3.88700 0.179485
\(470\) 3.74202 0.172606
\(471\) −5.55063 −0.255760
\(472\) 22.4357 1.03269
\(473\) 28.0492 1.28970
\(474\) −1.36054 −0.0624916
\(475\) −28.9096 −1.32646
\(476\) −16.0155 −0.734069
\(477\) −31.7623 −1.45430
\(478\) −34.7684 −1.59027
\(479\) −16.5224 −0.754927 −0.377464 0.926024i \(-0.623204\pi\)
−0.377464 + 0.926024i \(0.623204\pi\)
\(480\) −0.267205 −0.0121962
\(481\) 0.337259 0.0153777
\(482\) 63.0371 2.87126
\(483\) 0.681703 0.0310186
\(484\) 15.0123 0.682379
\(485\) 1.57846 0.0716743
\(486\) 21.0214 0.953549
\(487\) 13.0562 0.591632 0.295816 0.955245i \(-0.404408\pi\)
0.295816 + 0.955245i \(0.404408\pi\)
\(488\) 29.9078 1.35386
\(489\) −6.84178 −0.309396
\(490\) 4.22110 0.190690
\(491\) 4.15659 0.187584 0.0937922 0.995592i \(-0.470101\pi\)
0.0937922 + 0.995592i \(0.470101\pi\)
\(492\) 0.623719 0.0281194
\(493\) 10.3695 0.467017
\(494\) 52.4776 2.36108
\(495\) −3.06353 −0.137696
\(496\) −23.1077 −1.03757
\(497\) −1.07947 −0.0484206
\(498\) −10.6093 −0.475413
\(499\) 23.2813 1.04221 0.521107 0.853491i \(-0.325519\pi\)
0.521107 + 0.853491i \(0.325519\pi\)
\(500\) −9.99168 −0.446841
\(501\) −6.35750 −0.284032
\(502\) −17.7990 −0.794407
\(503\) −7.95766 −0.354815 −0.177407 0.984138i \(-0.556771\pi\)
−0.177407 + 0.984138i \(0.556771\pi\)
\(504\) 8.37540 0.373070
\(505\) −2.65027 −0.117936
\(506\) 25.1443 1.11780
\(507\) −0.372033 −0.0165225
\(508\) −42.7887 −1.89844
\(509\) 22.3243 0.989507 0.494754 0.869033i \(-0.335258\pi\)
0.494754 + 0.869033i \(0.335258\pi\)
\(510\) −1.34659 −0.0596280
\(511\) 7.12279 0.315094
\(512\) 23.4383 1.03583
\(513\) 11.9034 0.525546
\(514\) −71.0491 −3.13384
\(515\) 2.02966 0.0894376
\(516\) −9.15674 −0.403103
\(517\) −22.2776 −0.979770
\(518\) 0.155816 0.00684614
\(519\) 2.34401 0.102891
\(520\) 4.10466 0.180001
\(521\) 5.20158 0.227885 0.113943 0.993487i \(-0.463652\pi\)
0.113943 + 0.993487i \(0.463652\pi\)
\(522\) −11.8903 −0.520425
\(523\) 7.32280 0.320204 0.160102 0.987100i \(-0.448818\pi\)
0.160102 + 0.987100i \(0.448818\pi\)
\(524\) 46.3564 2.02509
\(525\) 1.23556 0.0539243
\(526\) 27.6366 1.20501
\(527\) 63.8694 2.78219
\(528\) −2.90044 −0.126225
\(529\) −15.6162 −0.678964
\(530\) −7.19169 −0.312387
\(531\) 16.1782 0.702073
\(532\) 15.7034 0.680827
\(533\) 1.84591 0.0799554
\(534\) 13.6846 0.592192
\(535\) 0.527851 0.0228210
\(536\) −21.3456 −0.921989
\(537\) 0.704969 0.0304217
\(538\) 11.5721 0.498909
\(539\) −25.1298 −1.08242
\(540\) 2.04147 0.0878510
\(541\) 28.7856 1.23759 0.618794 0.785553i \(-0.287621\pi\)
0.618794 + 0.785553i \(0.287621\pi\)
\(542\) −4.02569 −0.172918
\(543\) 2.09560 0.0899310
\(544\) −16.9443 −0.726482
\(545\) −0.184454 −0.00790115
\(546\) −2.24283 −0.0959842
\(547\) −1.52056 −0.0650146 −0.0325073 0.999471i \(-0.510349\pi\)
−0.0325073 + 0.999471i \(0.510349\pi\)
\(548\) 64.2164 2.74319
\(549\) 21.5662 0.920424
\(550\) 45.5730 1.94324
\(551\) −10.1674 −0.433145
\(552\) −3.74360 −0.159338
\(553\) −1.20490 −0.0512377
\(554\) −26.3047 −1.11758
\(555\) 0.00848551 0.000360190 0
\(556\) −10.8055 −0.458257
\(557\) −10.6899 −0.452947 −0.226474 0.974017i \(-0.572720\pi\)
−0.226474 + 0.974017i \(0.572720\pi\)
\(558\) −73.2368 −3.10036
\(559\) −27.0996 −1.14619
\(560\) 0.431461 0.0182325
\(561\) 8.01677 0.338468
\(562\) 63.7295 2.68827
\(563\) −5.98815 −0.252371 −0.126185 0.992007i \(-0.540273\pi\)
−0.126185 + 0.992007i \(0.540273\pi\)
\(564\) 7.27261 0.306232
\(565\) 4.78611 0.201353
\(566\) 61.5415 2.58678
\(567\) 5.77990 0.242733
\(568\) 5.92793 0.248730
\(569\) 28.1697 1.18094 0.590468 0.807061i \(-0.298943\pi\)
0.590468 + 0.807061i \(0.298943\pi\)
\(570\) 1.32035 0.0553033
\(571\) 34.0126 1.42338 0.711692 0.702491i \(-0.247929\pi\)
0.711692 + 0.702491i \(0.247929\pi\)
\(572\) −53.5811 −2.24034
\(573\) 5.33217 0.222754
\(574\) 0.852823 0.0355961
\(575\) 13.3829 0.558106
\(576\) 31.9100 1.32958
\(577\) −5.05806 −0.210570 −0.105285 0.994442i \(-0.533575\pi\)
−0.105285 + 0.994442i \(0.533575\pi\)
\(578\) −44.8869 −1.86705
\(579\) −0.450512 −0.0187226
\(580\) −1.74375 −0.0724051
\(581\) −9.39566 −0.389798
\(582\) 4.73639 0.196330
\(583\) 42.8149 1.77321
\(584\) −39.1151 −1.61859
\(585\) 2.95983 0.122374
\(586\) −1.67479 −0.0691850
\(587\) −40.5291 −1.67282 −0.836408 0.548107i \(-0.815349\pi\)
−0.836408 + 0.548107i \(0.815349\pi\)
\(588\) 8.20371 0.338315
\(589\) −62.6247 −2.58041
\(590\) 3.66309 0.150807
\(591\) −3.28635 −0.135182
\(592\) −0.194680 −0.00800131
\(593\) 21.8112 0.895678 0.447839 0.894114i \(-0.352194\pi\)
0.447839 + 0.894114i \(0.352194\pi\)
\(594\) −18.7644 −0.769914
\(595\) −1.19255 −0.0488898
\(596\) 3.72762 0.152689
\(597\) 6.75279 0.276373
\(598\) −24.2931 −0.993418
\(599\) 8.96796 0.366421 0.183210 0.983074i \(-0.441351\pi\)
0.183210 + 0.983074i \(0.441351\pi\)
\(600\) −6.78513 −0.277002
\(601\) 1.89642 0.0773567 0.0386784 0.999252i \(-0.487685\pi\)
0.0386784 + 0.999252i \(0.487685\pi\)
\(602\) −12.5202 −0.510285
\(603\) −15.3921 −0.626814
\(604\) 35.9587 1.46314
\(605\) 1.11785 0.0454472
\(606\) −7.95250 −0.323048
\(607\) 28.4699 1.15556 0.577779 0.816193i \(-0.303919\pi\)
0.577779 + 0.816193i \(0.303919\pi\)
\(608\) 16.6141 0.673791
\(609\) 0.434542 0.0176085
\(610\) 4.88307 0.197710
\(611\) 21.5235 0.870747
\(612\) 63.4196 2.56358
\(613\) −41.3037 −1.66824 −0.834120 0.551583i \(-0.814024\pi\)
−0.834120 + 0.551583i \(0.814024\pi\)
\(614\) 58.3877 2.35634
\(615\) 0.0464436 0.00187279
\(616\) −11.2898 −0.454881
\(617\) 20.4279 0.822396 0.411198 0.911546i \(-0.365111\pi\)
0.411198 + 0.911546i \(0.365111\pi\)
\(618\) 6.09028 0.244987
\(619\) 44.7266 1.79771 0.898857 0.438241i \(-0.144398\pi\)
0.898857 + 0.438241i \(0.144398\pi\)
\(620\) −10.7404 −0.431344
\(621\) −5.51034 −0.221122
\(622\) −70.1493 −2.81273
\(623\) 12.1192 0.485546
\(624\) 2.80225 0.112180
\(625\) 23.8812 0.955247
\(626\) 31.0467 1.24088
\(627\) −7.86053 −0.313919
\(628\) 59.1901 2.36194
\(629\) 0.538093 0.0214552
\(630\) 1.36746 0.0544808
\(631\) 38.3115 1.52516 0.762578 0.646897i \(-0.223933\pi\)
0.762578 + 0.646897i \(0.223933\pi\)
\(632\) 6.61677 0.263201
\(633\) 1.10279 0.0438321
\(634\) 9.89208 0.392865
\(635\) −3.18615 −0.126438
\(636\) −13.9771 −0.554227
\(637\) 24.2791 0.961972
\(638\) 16.0279 0.634549
\(639\) 4.27457 0.169099
\(640\) 5.67525 0.224334
\(641\) 32.1230 1.26878 0.634391 0.773013i \(-0.281251\pi\)
0.634391 + 0.773013i \(0.281251\pi\)
\(642\) 1.58389 0.0625111
\(643\) 18.2031 0.717859 0.358930 0.933365i \(-0.383142\pi\)
0.358930 + 0.933365i \(0.383142\pi\)
\(644\) −7.26945 −0.286456
\(645\) −0.681833 −0.0268471
\(646\) 83.7274 3.29421
\(647\) 19.2504 0.756809 0.378405 0.925640i \(-0.376473\pi\)
0.378405 + 0.925640i \(0.376473\pi\)
\(648\) −31.7406 −1.24689
\(649\) −21.8078 −0.856031
\(650\) −44.0303 −1.72701
\(651\) 2.67650 0.104900
\(652\) 72.9585 2.85727
\(653\) 40.7440 1.59444 0.797218 0.603691i \(-0.206304\pi\)
0.797218 + 0.603691i \(0.206304\pi\)
\(654\) −0.553480 −0.0216428
\(655\) 3.45181 0.134873
\(656\) −1.06554 −0.0416023
\(657\) −28.2055 −1.10040
\(658\) 9.94398 0.387657
\(659\) 15.6498 0.609632 0.304816 0.952411i \(-0.401405\pi\)
0.304816 + 0.952411i \(0.401405\pi\)
\(660\) −1.34811 −0.0524752
\(661\) −26.2188 −1.01979 −0.509897 0.860235i \(-0.670316\pi\)
−0.509897 + 0.860235i \(0.670316\pi\)
\(662\) 20.3065 0.789234
\(663\) −7.74538 −0.300806
\(664\) 51.5966 2.00234
\(665\) 1.16931 0.0453439
\(666\) −0.617013 −0.0239088
\(667\) 4.70671 0.182245
\(668\) 67.7943 2.62304
\(669\) 4.00062 0.154673
\(670\) −3.48511 −0.134641
\(671\) −29.0708 −1.12226
\(672\) −0.710067 −0.0273914
\(673\) 37.6070 1.44964 0.724821 0.688937i \(-0.241922\pi\)
0.724821 + 0.688937i \(0.241922\pi\)
\(674\) −81.7956 −3.15065
\(675\) −9.98727 −0.384410
\(676\) 3.96723 0.152586
\(677\) −0.525690 −0.0202039 −0.0101020 0.999949i \(-0.503216\pi\)
−0.0101020 + 0.999949i \(0.503216\pi\)
\(678\) 14.3614 0.551545
\(679\) 4.19458 0.160973
\(680\) 6.54894 0.251140
\(681\) −8.12138 −0.311212
\(682\) 98.7215 3.78024
\(683\) −43.0885 −1.64874 −0.824368 0.566054i \(-0.808469\pi\)
−0.824368 + 0.566054i \(0.808469\pi\)
\(684\) −62.1836 −2.37765
\(685\) 4.78171 0.182700
\(686\) 23.3518 0.891577
\(687\) 4.52689 0.172712
\(688\) 15.6431 0.596386
\(689\) −41.3655 −1.57590
\(690\) −0.611219 −0.0232687
\(691\) −39.1263 −1.48843 −0.744217 0.667938i \(-0.767177\pi\)
−0.744217 + 0.667938i \(0.767177\pi\)
\(692\) −24.9957 −0.950196
\(693\) −8.14099 −0.309251
\(694\) −7.04865 −0.267563
\(695\) −0.804606 −0.0305205
\(696\) −2.38630 −0.0904526
\(697\) 2.94514 0.111555
\(698\) 36.7189 1.38983
\(699\) −6.04247 −0.228547
\(700\) −13.1756 −0.497991
\(701\) 40.7626 1.53958 0.769791 0.638296i \(-0.220360\pi\)
0.769791 + 0.638296i \(0.220360\pi\)
\(702\) 18.1292 0.684243
\(703\) −0.527607 −0.0198991
\(704\) −43.0139 −1.62115
\(705\) 0.541536 0.0203954
\(706\) −49.3009 −1.85546
\(707\) −7.04280 −0.264872
\(708\) 7.11923 0.267557
\(709\) −27.1855 −1.02097 −0.510487 0.859886i \(-0.670535\pi\)
−0.510487 + 0.859886i \(0.670535\pi\)
\(710\) 0.967856 0.0363230
\(711\) 4.77128 0.178937
\(712\) −66.5532 −2.49419
\(713\) 28.9904 1.08570
\(714\) −3.57841 −0.133919
\(715\) −3.98978 −0.149209
\(716\) −7.51756 −0.280944
\(717\) −5.03161 −0.187909
\(718\) 9.35192 0.349011
\(719\) 26.6368 0.993384 0.496692 0.867927i \(-0.334548\pi\)
0.496692 + 0.867927i \(0.334548\pi\)
\(720\) −1.70854 −0.0636734
\(721\) 5.39359 0.200868
\(722\) −36.8258 −1.37051
\(723\) 9.12258 0.339273
\(724\) −22.3468 −0.830513
\(725\) 8.53074 0.316824
\(726\) 3.35427 0.124489
\(727\) −21.0462 −0.780560 −0.390280 0.920696i \(-0.627622\pi\)
−0.390280 + 0.920696i \(0.627622\pi\)
\(728\) 10.9077 0.404265
\(729\) −20.7901 −0.770005
\(730\) −6.38634 −0.236369
\(731\) −43.2372 −1.59918
\(732\) 9.49025 0.350770
\(733\) −3.09646 −0.114370 −0.0571852 0.998364i \(-0.518213\pi\)
−0.0571852 + 0.998364i \(0.518213\pi\)
\(734\) −11.8762 −0.438360
\(735\) 0.610867 0.0225322
\(736\) −7.69105 −0.283496
\(737\) 20.7482 0.764268
\(738\) −3.37709 −0.124312
\(739\) 51.3521 1.88902 0.944508 0.328488i \(-0.106539\pi\)
0.944508 + 0.328488i \(0.106539\pi\)
\(740\) −0.0904866 −0.00332635
\(741\) 7.59443 0.278989
\(742\) −19.1111 −0.701591
\(743\) 10.2072 0.374468 0.187234 0.982315i \(-0.440048\pi\)
0.187234 + 0.982315i \(0.440048\pi\)
\(744\) −14.6981 −0.538859
\(745\) 0.277567 0.0101693
\(746\) 73.9579 2.70779
\(747\) 37.2058 1.36129
\(748\) −85.4881 −3.12576
\(749\) 1.40270 0.0512537
\(750\) −2.23248 −0.0815188
\(751\) 46.0065 1.67880 0.839401 0.543513i \(-0.182906\pi\)
0.839401 + 0.543513i \(0.182906\pi\)
\(752\) −12.4243 −0.453067
\(753\) −2.57583 −0.0938684
\(754\) −15.4853 −0.563940
\(755\) 2.67757 0.0974468
\(756\) 5.42498 0.197305
\(757\) 33.6523 1.22311 0.611557 0.791201i \(-0.290544\pi\)
0.611557 + 0.791201i \(0.290544\pi\)
\(758\) −64.7040 −2.35015
\(759\) 3.63882 0.132081
\(760\) −6.42131 −0.232925
\(761\) 38.4039 1.39214 0.696071 0.717973i \(-0.254930\pi\)
0.696071 + 0.717973i \(0.254930\pi\)
\(762\) −9.56046 −0.346339
\(763\) −0.490166 −0.0177452
\(764\) −56.8604 −2.05714
\(765\) 4.72237 0.170738
\(766\) 54.3585 1.96405
\(767\) 21.0695 0.760777
\(768\) 9.39144 0.338884
\(769\) −25.8361 −0.931675 −0.465838 0.884870i \(-0.654247\pi\)
−0.465838 + 0.884870i \(0.654247\pi\)
\(770\) −1.84330 −0.0664279
\(771\) −10.2821 −0.370300
\(772\) 4.80410 0.172903
\(773\) −15.2744 −0.549381 −0.274691 0.961533i \(-0.588575\pi\)
−0.274691 + 0.961533i \(0.588575\pi\)
\(774\) 49.5786 1.78206
\(775\) 52.5440 1.88744
\(776\) −23.0347 −0.826898
\(777\) 0.0225493 0.000808951 0
\(778\) −38.9597 −1.39677
\(779\) −2.88774 −0.103464
\(780\) 1.30248 0.0466361
\(781\) −5.76202 −0.206181
\(782\) −38.7594 −1.38603
\(783\) −3.51248 −0.125526
\(784\) −14.0149 −0.500533
\(785\) 4.40743 0.157308
\(786\) 10.3576 0.369444
\(787\) 14.0074 0.499311 0.249656 0.968335i \(-0.419683\pi\)
0.249656 + 0.968335i \(0.419683\pi\)
\(788\) 35.0445 1.24841
\(789\) 3.99950 0.142386
\(790\) 1.08032 0.0384362
\(791\) 12.7185 0.452219
\(792\) 44.7066 1.58858
\(793\) 28.0866 0.997386
\(794\) 23.2451 0.824939
\(795\) −1.04077 −0.0369121
\(796\) −72.0095 −2.55231
\(797\) 3.84541 0.136212 0.0681058 0.997678i \(-0.478304\pi\)
0.0681058 + 0.997678i \(0.478304\pi\)
\(798\) 3.50867 0.124206
\(799\) 34.3405 1.21488
\(800\) −13.9397 −0.492844
\(801\) −47.9908 −1.69567
\(802\) 11.4229 0.403356
\(803\) 38.0203 1.34171
\(804\) −6.77331 −0.238876
\(805\) −0.541300 −0.0190783
\(806\) −95.3796 −3.35960
\(807\) 1.67469 0.0589519
\(808\) 38.6758 1.36061
\(809\) 29.7136 1.04467 0.522337 0.852739i \(-0.325060\pi\)
0.522337 + 0.852739i \(0.325060\pi\)
\(810\) −5.18230 −0.182088
\(811\) −9.95679 −0.349630 −0.174815 0.984601i \(-0.555933\pi\)
−0.174815 + 0.984601i \(0.555933\pi\)
\(812\) −4.63381 −0.162615
\(813\) −0.582589 −0.0204323
\(814\) 0.831719 0.0291517
\(815\) 5.43266 0.190298
\(816\) 4.47096 0.156515
\(817\) 42.3945 1.48320
\(818\) −3.61551 −0.126413
\(819\) 7.86540 0.274839
\(820\) −0.495259 −0.0172952
\(821\) 32.6096 1.13808 0.569041 0.822309i \(-0.307314\pi\)
0.569041 + 0.822309i \(0.307314\pi\)
\(822\) 14.3482 0.500449
\(823\) −2.71197 −0.0945335 −0.0472667 0.998882i \(-0.515051\pi\)
−0.0472667 + 0.998882i \(0.515051\pi\)
\(824\) −29.6191 −1.03183
\(825\) 6.59522 0.229616
\(826\) 9.73425 0.338698
\(827\) −5.62022 −0.195434 −0.0977170 0.995214i \(-0.531154\pi\)
−0.0977170 + 0.995214i \(0.531154\pi\)
\(828\) 28.7862 1.00039
\(829\) −19.6826 −0.683603 −0.341802 0.939772i \(-0.611037\pi\)
−0.341802 + 0.939772i \(0.611037\pi\)
\(830\) 8.42421 0.292409
\(831\) −3.80676 −0.132055
\(832\) 41.5578 1.44076
\(833\) 38.7370 1.34216
\(834\) −2.41433 −0.0836014
\(835\) 5.04812 0.174697
\(836\) 83.8221 2.89905
\(837\) −21.6347 −0.747805
\(838\) −59.2251 −2.04590
\(839\) −10.6069 −0.366189 −0.183095 0.983095i \(-0.558611\pi\)
−0.183095 + 0.983095i \(0.558611\pi\)
\(840\) 0.274439 0.00946905
\(841\) −25.9998 −0.896544
\(842\) −39.0321 −1.34513
\(843\) 9.22279 0.317650
\(844\) −11.7598 −0.404790
\(845\) 0.295409 0.0101624
\(846\) −39.3771 −1.35381
\(847\) 2.97057 0.102070
\(848\) 23.8779 0.819971
\(849\) 8.90614 0.305658
\(850\) −70.2498 −2.40955
\(851\) 0.244241 0.00837248
\(852\) 1.88103 0.0644430
\(853\) 44.6221 1.52783 0.763915 0.645317i \(-0.223275\pi\)
0.763915 + 0.645317i \(0.223275\pi\)
\(854\) 12.9762 0.444036
\(855\) −4.63034 −0.158354
\(856\) −7.70300 −0.263283
\(857\) 16.6250 0.567898 0.283949 0.958839i \(-0.408355\pi\)
0.283949 + 0.958839i \(0.408355\pi\)
\(858\) −11.9719 −0.408713
\(859\) −15.0058 −0.511991 −0.255996 0.966678i \(-0.582403\pi\)
−0.255996 + 0.966678i \(0.582403\pi\)
\(860\) 7.27083 0.247933
\(861\) 0.123419 0.00420609
\(862\) 25.0027 0.851595
\(863\) −16.6937 −0.568259 −0.284130 0.958786i \(-0.591705\pi\)
−0.284130 + 0.958786i \(0.591705\pi\)
\(864\) 5.73961 0.195266
\(865\) −1.86124 −0.0632841
\(866\) −75.2690 −2.55775
\(867\) −6.49593 −0.220613
\(868\) −28.5413 −0.968756
\(869\) −6.43158 −0.218176
\(870\) −0.389613 −0.0132091
\(871\) −20.0458 −0.679226
\(872\) 2.69176 0.0911547
\(873\) −16.6101 −0.562166
\(874\) 38.0040 1.28550
\(875\) −1.97711 −0.0668384
\(876\) −12.4119 −0.419358
\(877\) 18.3947 0.621146 0.310573 0.950550i \(-0.399479\pi\)
0.310573 + 0.950550i \(0.399479\pi\)
\(878\) −46.9781 −1.58543
\(879\) −0.242372 −0.00817500
\(880\) 2.30307 0.0776364
\(881\) −4.10415 −0.138272 −0.0691362 0.997607i \(-0.522024\pi\)
−0.0691362 + 0.997607i \(0.522024\pi\)
\(882\) −44.4184 −1.49565
\(883\) −17.4459 −0.587102 −0.293551 0.955943i \(-0.594837\pi\)
−0.293551 + 0.955943i \(0.594837\pi\)
\(884\) 82.5941 2.77794
\(885\) 0.530115 0.0178196
\(886\) −56.2362 −1.88929
\(887\) 39.2535 1.31800 0.659002 0.752141i \(-0.270979\pi\)
0.659002 + 0.752141i \(0.270979\pi\)
\(888\) −0.123830 −0.00415547
\(889\) −8.46682 −0.283968
\(890\) −10.8662 −0.364235
\(891\) 30.8522 1.03359
\(892\) −42.6613 −1.42840
\(893\) −33.6713 −1.12677
\(894\) 0.832879 0.0278556
\(895\) −0.559775 −0.0187112
\(896\) 15.0813 0.503832
\(897\) −3.51564 −0.117384
\(898\) 42.0984 1.40484
\(899\) 18.4795 0.616326
\(900\) 52.1739 1.73913
\(901\) −65.9982 −2.19872
\(902\) 4.55223 0.151573
\(903\) −1.81189 −0.0602960
\(904\) −69.8443 −2.32299
\(905\) −1.66400 −0.0553131
\(906\) 8.03442 0.266926
\(907\) −51.1491 −1.69838 −0.849188 0.528090i \(-0.822908\pi\)
−0.849188 + 0.528090i \(0.822908\pi\)
\(908\) 86.6037 2.87404
\(909\) 27.8887 0.925010
\(910\) 1.78090 0.0590362
\(911\) 39.4156 1.30590 0.652948 0.757403i \(-0.273532\pi\)
0.652948 + 0.757403i \(0.273532\pi\)
\(912\) −4.38383 −0.145163
\(913\) −50.1525 −1.65981
\(914\) 71.7782 2.37421
\(915\) 0.706667 0.0233617
\(916\) −48.2732 −1.59499
\(917\) 9.17278 0.302912
\(918\) 28.9250 0.954667
\(919\) −18.1319 −0.598116 −0.299058 0.954235i \(-0.596672\pi\)
−0.299058 + 0.954235i \(0.596672\pi\)
\(920\) 2.97257 0.0980028
\(921\) 8.44974 0.278428
\(922\) −6.31508 −0.207976
\(923\) 5.56696 0.183239
\(924\) −3.58246 −0.117854
\(925\) 0.442678 0.0145552
\(926\) 43.3651 1.42507
\(927\) −21.3580 −0.701490
\(928\) −4.90255 −0.160934
\(929\) 3.60431 0.118254 0.0591268 0.998250i \(-0.481168\pi\)
0.0591268 + 0.998250i \(0.481168\pi\)
\(930\) −2.39977 −0.0786916
\(931\) −37.9821 −1.24481
\(932\) 64.4349 2.11064
\(933\) −10.1518 −0.332356
\(934\) 41.5886 1.36082
\(935\) −6.36565 −0.208179
\(936\) −43.1931 −1.41181
\(937\) −23.6915 −0.773969 −0.386984 0.922086i \(-0.626483\pi\)
−0.386984 + 0.922086i \(0.626483\pi\)
\(938\) −9.26127 −0.302391
\(939\) 4.49301 0.146624
\(940\) −5.77476 −0.188352
\(941\) 30.5075 0.994516 0.497258 0.867603i \(-0.334340\pi\)
0.497258 + 0.867603i \(0.334340\pi\)
\(942\) 13.2251 0.430897
\(943\) 1.33680 0.0435322
\(944\) −12.1622 −0.395847
\(945\) 0.403957 0.0131407
\(946\) −66.8307 −2.17285
\(947\) 21.3639 0.694235 0.347118 0.937822i \(-0.387160\pi\)
0.347118 + 0.937822i \(0.387160\pi\)
\(948\) 2.09961 0.0681922
\(949\) −36.7332 −1.19241
\(950\) 68.8808 2.23479
\(951\) 1.43156 0.0464215
\(952\) 17.4031 0.564036
\(953\) 21.1411 0.684829 0.342414 0.939549i \(-0.388755\pi\)
0.342414 + 0.939549i \(0.388755\pi\)
\(954\) 75.6779 2.45016
\(955\) −4.23396 −0.137008
\(956\) 53.6554 1.73534
\(957\) 2.31951 0.0749793
\(958\) 39.3667 1.27188
\(959\) 12.7068 0.410325
\(960\) 1.04560 0.0337467
\(961\) 82.8222 2.67168
\(962\) −0.803563 −0.0259079
\(963\) −5.55456 −0.178993
\(964\) −97.2802 −3.13318
\(965\) 0.357725 0.0115156
\(966\) −1.62425 −0.0522592
\(967\) 14.9665 0.481291 0.240646 0.970613i \(-0.422641\pi\)
0.240646 + 0.970613i \(0.422641\pi\)
\(968\) −16.3130 −0.524320
\(969\) 12.1168 0.389249
\(970\) −3.76089 −0.120755
\(971\) 5.33394 0.171174 0.0855871 0.996331i \(-0.472723\pi\)
0.0855871 + 0.996331i \(0.472723\pi\)
\(972\) −32.4406 −1.04053
\(973\) −2.13815 −0.0685459
\(974\) −31.1080 −0.996766
\(975\) −6.37196 −0.204066
\(976\) −16.2128 −0.518959
\(977\) −12.3985 −0.396663 −0.198331 0.980135i \(-0.563552\pi\)
−0.198331 + 0.980135i \(0.563552\pi\)
\(978\) 16.3014 0.521262
\(979\) 64.6905 2.06752
\(980\) −6.51409 −0.208085
\(981\) 1.94100 0.0619715
\(982\) −9.90362 −0.316037
\(983\) −53.8935 −1.71894 −0.859468 0.511190i \(-0.829205\pi\)
−0.859468 + 0.511190i \(0.829205\pi\)
\(984\) −0.677758 −0.0216061
\(985\) 2.60950 0.0831455
\(986\) −24.7066 −0.786818
\(987\) 1.43907 0.0458061
\(988\) −80.9845 −2.57646
\(989\) −19.6254 −0.624052
\(990\) 7.29927 0.231986
\(991\) 37.9367 1.20510 0.602549 0.798082i \(-0.294152\pi\)
0.602549 + 0.798082i \(0.294152\pi\)
\(992\) −30.1966 −0.958744
\(993\) 2.93871 0.0932571
\(994\) 2.57197 0.0815778
\(995\) −5.36200 −0.169987
\(996\) 16.3725 0.518782
\(997\) −38.2290 −1.21072 −0.605362 0.795951i \(-0.706971\pi\)
−0.605362 + 0.795951i \(0.706971\pi\)
\(998\) −55.4707 −1.75589
\(999\) −0.182270 −0.00576677
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 6037.2.a.b.1.20 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.20 259 1.1 even 1 trivial