Properties

Label 6025.2.a.p.1.10
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $46$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(46\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.83307 q^{2} -2.40621 q^{3} +1.36013 q^{4} +4.41073 q^{6} -0.302396 q^{7} +1.17293 q^{8} +2.78983 q^{9} +O(q^{10})\) \(q-1.83307 q^{2} -2.40621 q^{3} +1.36013 q^{4} +4.41073 q^{6} -0.302396 q^{7} +1.17293 q^{8} +2.78983 q^{9} -5.09885 q^{11} -3.27275 q^{12} +4.63318 q^{13} +0.554311 q^{14} -4.87031 q^{16} -1.03451 q^{17} -5.11394 q^{18} -8.55559 q^{19} +0.727627 q^{21} +9.34653 q^{22} +1.34508 q^{23} -2.82231 q^{24} -8.49293 q^{26} +0.505718 q^{27} -0.411297 q^{28} +10.3038 q^{29} +0.459299 q^{31} +6.58174 q^{32} +12.2689 q^{33} +1.89632 q^{34} +3.79452 q^{36} -1.55014 q^{37} +15.6830 q^{38} -11.1484 q^{39} +5.44165 q^{41} -1.33379 q^{42} +5.45885 q^{43} -6.93509 q^{44} -2.46562 q^{46} -10.3833 q^{47} +11.7190 q^{48} -6.90856 q^{49} +2.48924 q^{51} +6.30172 q^{52} +4.20240 q^{53} -0.927014 q^{54} -0.354689 q^{56} +20.5865 q^{57} -18.8875 q^{58} -5.01849 q^{59} -6.46168 q^{61} -0.841924 q^{62} -0.843632 q^{63} -2.32413 q^{64} -22.4897 q^{66} -14.8239 q^{67} -1.40707 q^{68} -3.23654 q^{69} -6.08615 q^{71} +3.27227 q^{72} +13.8254 q^{73} +2.84152 q^{74} -11.6367 q^{76} +1.54187 q^{77} +20.4357 q^{78} +2.63720 q^{79} -9.58634 q^{81} -9.97491 q^{82} -2.13404 q^{83} +0.989665 q^{84} -10.0064 q^{86} -24.7930 q^{87} -5.98059 q^{88} -2.74947 q^{89} -1.40106 q^{91} +1.82948 q^{92} -1.10517 q^{93} +19.0333 q^{94} -15.8370 q^{96} +10.5373 q^{97} +12.6638 q^{98} -14.2249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.83307 −1.29617 −0.648086 0.761567i \(-0.724430\pi\)
−0.648086 + 0.761567i \(0.724430\pi\)
\(3\) −2.40621 −1.38922 −0.694612 0.719385i \(-0.744424\pi\)
−0.694612 + 0.719385i \(0.744424\pi\)
\(4\) 1.36013 0.680064
\(5\) 0 0
\(6\) 4.41073 1.80067
\(7\) −0.302396 −0.114295 −0.0571474 0.998366i \(-0.518201\pi\)
−0.0571474 + 0.998366i \(0.518201\pi\)
\(8\) 1.17293 0.414693
\(9\) 2.78983 0.929943
\(10\) 0 0
\(11\) −5.09885 −1.53736 −0.768681 0.639633i \(-0.779086\pi\)
−0.768681 + 0.639633i \(0.779086\pi\)
\(12\) −3.27275 −0.944761
\(13\) 4.63318 1.28501 0.642507 0.766280i \(-0.277894\pi\)
0.642507 + 0.766280i \(0.277894\pi\)
\(14\) 0.554311 0.148146
\(15\) 0 0
\(16\) −4.87031 −1.21758
\(17\) −1.03451 −0.250906 −0.125453 0.992100i \(-0.540038\pi\)
−0.125453 + 0.992100i \(0.540038\pi\)
\(18\) −5.11394 −1.20537
\(19\) −8.55559 −1.96279 −0.981394 0.192006i \(-0.938501\pi\)
−0.981394 + 0.192006i \(0.938501\pi\)
\(20\) 0 0
\(21\) 0.727627 0.158781
\(22\) 9.34653 1.99269
\(23\) 1.34508 0.280469 0.140234 0.990118i \(-0.455214\pi\)
0.140234 + 0.990118i \(0.455214\pi\)
\(24\) −2.82231 −0.576101
\(25\) 0 0
\(26\) −8.49293 −1.66560
\(27\) 0.505718 0.0973255
\(28\) −0.411297 −0.0777278
\(29\) 10.3038 1.91336 0.956681 0.291138i \(-0.0940340\pi\)
0.956681 + 0.291138i \(0.0940340\pi\)
\(30\) 0 0
\(31\) 0.459299 0.0824925 0.0412462 0.999149i \(-0.486867\pi\)
0.0412462 + 0.999149i \(0.486867\pi\)
\(32\) 6.58174 1.16350
\(33\) 12.2689 2.13574
\(34\) 1.89632 0.325217
\(35\) 0 0
\(36\) 3.79452 0.632420
\(37\) −1.55014 −0.254842 −0.127421 0.991849i \(-0.540670\pi\)
−0.127421 + 0.991849i \(0.540670\pi\)
\(38\) 15.6830 2.54411
\(39\) −11.1484 −1.78517
\(40\) 0 0
\(41\) 5.44165 0.849844 0.424922 0.905230i \(-0.360302\pi\)
0.424922 + 0.905230i \(0.360302\pi\)
\(42\) −1.33379 −0.205808
\(43\) 5.45885 0.832467 0.416234 0.909258i \(-0.363350\pi\)
0.416234 + 0.909258i \(0.363350\pi\)
\(44\) −6.93509 −1.04550
\(45\) 0 0
\(46\) −2.46562 −0.363536
\(47\) −10.3833 −1.51456 −0.757280 0.653090i \(-0.773472\pi\)
−0.757280 + 0.653090i \(0.773472\pi\)
\(48\) 11.7190 1.69149
\(49\) −6.90856 −0.986937
\(50\) 0 0
\(51\) 2.48924 0.348564
\(52\) 6.30172 0.873891
\(53\) 4.20240 0.577244 0.288622 0.957443i \(-0.406803\pi\)
0.288622 + 0.957443i \(0.406803\pi\)
\(54\) −0.927014 −0.126151
\(55\) 0 0
\(56\) −0.354689 −0.0473973
\(57\) 20.5865 2.72675
\(58\) −18.8875 −2.48005
\(59\) −5.01849 −0.653352 −0.326676 0.945136i \(-0.605929\pi\)
−0.326676 + 0.945136i \(0.605929\pi\)
\(60\) 0 0
\(61\) −6.46168 −0.827333 −0.413667 0.910428i \(-0.635752\pi\)
−0.413667 + 0.910428i \(0.635752\pi\)
\(62\) −0.841924 −0.106924
\(63\) −0.843632 −0.106288
\(64\) −2.32413 −0.290516
\(65\) 0 0
\(66\) −22.4897 −2.76829
\(67\) −14.8239 −1.81103 −0.905516 0.424311i \(-0.860516\pi\)
−0.905516 + 0.424311i \(0.860516\pi\)
\(68\) −1.40707 −0.170632
\(69\) −3.23654 −0.389634
\(70\) 0 0
\(71\) −6.08615 −0.722293 −0.361147 0.932509i \(-0.617615\pi\)
−0.361147 + 0.932509i \(0.617615\pi\)
\(72\) 3.27227 0.385640
\(73\) 13.8254 1.61814 0.809070 0.587712i \(-0.199971\pi\)
0.809070 + 0.587712i \(0.199971\pi\)
\(74\) 2.84152 0.330320
\(75\) 0 0
\(76\) −11.6367 −1.33482
\(77\) 1.54187 0.175713
\(78\) 20.4357 2.31389
\(79\) 2.63720 0.296708 0.148354 0.988934i \(-0.452602\pi\)
0.148354 + 0.988934i \(0.452602\pi\)
\(80\) 0 0
\(81\) −9.58634 −1.06515
\(82\) −9.97491 −1.10154
\(83\) −2.13404 −0.234242 −0.117121 0.993118i \(-0.537367\pi\)
−0.117121 + 0.993118i \(0.537367\pi\)
\(84\) 0.989665 0.107981
\(85\) 0 0
\(86\) −10.0064 −1.07902
\(87\) −24.7930 −2.65809
\(88\) −5.98059 −0.637533
\(89\) −2.74947 −0.291443 −0.145722 0.989326i \(-0.546550\pi\)
−0.145722 + 0.989326i \(0.546550\pi\)
\(90\) 0 0
\(91\) −1.40106 −0.146871
\(92\) 1.82948 0.190737
\(93\) −1.10517 −0.114600
\(94\) 19.0333 1.96313
\(95\) 0 0
\(96\) −15.8370 −1.61636
\(97\) 10.5373 1.06990 0.534950 0.844884i \(-0.320331\pi\)
0.534950 + 0.844884i \(0.320331\pi\)
\(98\) 12.6638 1.27924
\(99\) −14.2249 −1.42966
\(100\) 0 0
\(101\) −6.99997 −0.696523 −0.348262 0.937397i \(-0.613228\pi\)
−0.348262 + 0.937397i \(0.613228\pi\)
\(102\) −4.56295 −0.451799
\(103\) 0.931512 0.0917846 0.0458923 0.998946i \(-0.485387\pi\)
0.0458923 + 0.998946i \(0.485387\pi\)
\(104\) 5.43439 0.532886
\(105\) 0 0
\(106\) −7.70327 −0.748208
\(107\) 9.32032 0.901029 0.450515 0.892769i \(-0.351241\pi\)
0.450515 + 0.892769i \(0.351241\pi\)
\(108\) 0.687841 0.0661875
\(109\) 6.86942 0.657971 0.328986 0.944335i \(-0.393293\pi\)
0.328986 + 0.944335i \(0.393293\pi\)
\(110\) 0 0
\(111\) 3.72997 0.354033
\(112\) 1.47276 0.139163
\(113\) 3.92833 0.369546 0.184773 0.982781i \(-0.440845\pi\)
0.184773 + 0.982781i \(0.440845\pi\)
\(114\) −37.7364 −3.53434
\(115\) 0 0
\(116\) 14.0144 1.30121
\(117\) 12.9258 1.19499
\(118\) 9.19922 0.846857
\(119\) 0.312832 0.0286772
\(120\) 0 0
\(121\) 14.9983 1.36348
\(122\) 11.8447 1.07237
\(123\) −13.0937 −1.18062
\(124\) 0.624705 0.0561001
\(125\) 0 0
\(126\) 1.54643 0.137767
\(127\) 19.0590 1.69121 0.845604 0.533810i \(-0.179240\pi\)
0.845604 + 0.533810i \(0.179240\pi\)
\(128\) −8.90319 −0.786938
\(129\) −13.1351 −1.15648
\(130\) 0 0
\(131\) 11.9830 1.04696 0.523481 0.852038i \(-0.324633\pi\)
0.523481 + 0.852038i \(0.324633\pi\)
\(132\) 16.6872 1.45244
\(133\) 2.58717 0.224337
\(134\) 27.1733 2.34741
\(135\) 0 0
\(136\) −1.21341 −0.104049
\(137\) −11.4620 −0.979266 −0.489633 0.871929i \(-0.662869\pi\)
−0.489633 + 0.871929i \(0.662869\pi\)
\(138\) 5.93279 0.505033
\(139\) 16.6366 1.41110 0.705551 0.708660i \(-0.250700\pi\)
0.705551 + 0.708660i \(0.250700\pi\)
\(140\) 0 0
\(141\) 24.9844 2.10406
\(142\) 11.1563 0.936217
\(143\) −23.6239 −1.97553
\(144\) −13.5873 −1.13228
\(145\) 0 0
\(146\) −25.3429 −2.09739
\(147\) 16.6234 1.37108
\(148\) −2.10839 −0.173309
\(149\) 16.2343 1.32997 0.664983 0.746858i \(-0.268439\pi\)
0.664983 + 0.746858i \(0.268439\pi\)
\(150\) 0 0
\(151\) −7.40916 −0.602949 −0.301474 0.953474i \(-0.597479\pi\)
−0.301474 + 0.953474i \(0.597479\pi\)
\(152\) −10.0351 −0.813954
\(153\) −2.88611 −0.233328
\(154\) −2.82635 −0.227754
\(155\) 0 0
\(156\) −15.1632 −1.21403
\(157\) 16.4755 1.31489 0.657444 0.753503i \(-0.271638\pi\)
0.657444 + 0.753503i \(0.271638\pi\)
\(158\) −4.83416 −0.384585
\(159\) −10.1118 −0.801921
\(160\) 0 0
\(161\) −0.406747 −0.0320561
\(162\) 17.5724 1.38062
\(163\) 21.5566 1.68845 0.844224 0.535991i \(-0.180062\pi\)
0.844224 + 0.535991i \(0.180062\pi\)
\(164\) 7.40134 0.577948
\(165\) 0 0
\(166\) 3.91184 0.303618
\(167\) −2.83253 −0.219188 −0.109594 0.993976i \(-0.534955\pi\)
−0.109594 + 0.993976i \(0.534955\pi\)
\(168\) 0.853454 0.0658454
\(169\) 8.46640 0.651261
\(170\) 0 0
\(171\) −23.8686 −1.82528
\(172\) 7.42473 0.566131
\(173\) −22.2673 −1.69296 −0.846478 0.532424i \(-0.821281\pi\)
−0.846478 + 0.532424i \(0.821281\pi\)
\(174\) 45.4472 3.44534
\(175\) 0 0
\(176\) 24.8330 1.87186
\(177\) 12.0755 0.907652
\(178\) 5.03996 0.377761
\(179\) 1.82748 0.136592 0.0682962 0.997665i \(-0.478244\pi\)
0.0682962 + 0.997665i \(0.478244\pi\)
\(180\) 0 0
\(181\) 12.5134 0.930114 0.465057 0.885281i \(-0.346034\pi\)
0.465057 + 0.885281i \(0.346034\pi\)
\(182\) 2.56823 0.190370
\(183\) 15.5481 1.14935
\(184\) 1.57768 0.116308
\(185\) 0 0
\(186\) 2.02584 0.148542
\(187\) 5.27481 0.385733
\(188\) −14.1226 −1.03000
\(189\) −0.152927 −0.0111238
\(190\) 0 0
\(191\) 3.47735 0.251612 0.125806 0.992055i \(-0.459848\pi\)
0.125806 + 0.992055i \(0.459848\pi\)
\(192\) 5.59234 0.403592
\(193\) −4.00614 −0.288368 −0.144184 0.989551i \(-0.546056\pi\)
−0.144184 + 0.989551i \(0.546056\pi\)
\(194\) −19.3155 −1.38677
\(195\) 0 0
\(196\) −9.39652 −0.671180
\(197\) −5.14600 −0.366638 −0.183319 0.983054i \(-0.558684\pi\)
−0.183319 + 0.983054i \(0.558684\pi\)
\(198\) 26.0752 1.85308
\(199\) 10.3802 0.735835 0.367917 0.929858i \(-0.380071\pi\)
0.367917 + 0.929858i \(0.380071\pi\)
\(200\) 0 0
\(201\) 35.6695 2.51593
\(202\) 12.8314 0.902815
\(203\) −3.11582 −0.218687
\(204\) 3.38569 0.237046
\(205\) 0 0
\(206\) −1.70752 −0.118969
\(207\) 3.75254 0.260820
\(208\) −22.5650 −1.56460
\(209\) 43.6237 3.01751
\(210\) 0 0
\(211\) −12.4398 −0.856394 −0.428197 0.903685i \(-0.640851\pi\)
−0.428197 + 0.903685i \(0.640851\pi\)
\(212\) 5.71580 0.392563
\(213\) 14.6445 1.00343
\(214\) −17.0847 −1.16789
\(215\) 0 0
\(216\) 0.593171 0.0403602
\(217\) −0.138890 −0.00942846
\(218\) −12.5921 −0.852844
\(219\) −33.2668 −2.24796
\(220\) 0 0
\(221\) −4.79308 −0.322417
\(222\) −6.83727 −0.458888
\(223\) −2.52846 −0.169318 −0.0846591 0.996410i \(-0.526980\pi\)
−0.0846591 + 0.996410i \(0.526980\pi\)
\(224\) −1.99029 −0.132982
\(225\) 0 0
\(226\) −7.20088 −0.478996
\(227\) −11.2535 −0.746922 −0.373461 0.927646i \(-0.621829\pi\)
−0.373461 + 0.927646i \(0.621829\pi\)
\(228\) 28.0003 1.85436
\(229\) 21.9401 1.44985 0.724923 0.688830i \(-0.241875\pi\)
0.724923 + 0.688830i \(0.241875\pi\)
\(230\) 0 0
\(231\) −3.71006 −0.244104
\(232\) 12.0856 0.793457
\(233\) −1.43595 −0.0940720 −0.0470360 0.998893i \(-0.514978\pi\)
−0.0470360 + 0.998893i \(0.514978\pi\)
\(234\) −23.6938 −1.54891
\(235\) 0 0
\(236\) −6.82579 −0.444321
\(237\) −6.34564 −0.412194
\(238\) −0.573441 −0.0371706
\(239\) −27.7962 −1.79799 −0.898994 0.437961i \(-0.855701\pi\)
−0.898994 + 0.437961i \(0.855701\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −27.4928 −1.76731
\(243\) 21.5496 1.38241
\(244\) −8.78870 −0.562639
\(245\) 0 0
\(246\) 24.0017 1.53029
\(247\) −39.6396 −2.52221
\(248\) 0.538724 0.0342090
\(249\) 5.13495 0.325414
\(250\) 0 0
\(251\) −8.17551 −0.516034 −0.258017 0.966140i \(-0.583069\pi\)
−0.258017 + 0.966140i \(0.583069\pi\)
\(252\) −1.14745 −0.0722824
\(253\) −6.85837 −0.431182
\(254\) −34.9363 −2.19210
\(255\) 0 0
\(256\) 20.9684 1.31052
\(257\) 2.28257 0.142383 0.0711913 0.997463i \(-0.477320\pi\)
0.0711913 + 0.997463i \(0.477320\pi\)
\(258\) 24.0775 1.49900
\(259\) 0.468757 0.0291272
\(260\) 0 0
\(261\) 28.7457 1.77932
\(262\) −21.9657 −1.35704
\(263\) 6.59117 0.406429 0.203214 0.979134i \(-0.434861\pi\)
0.203214 + 0.979134i \(0.434861\pi\)
\(264\) 14.3905 0.885676
\(265\) 0 0
\(266\) −4.74246 −0.290779
\(267\) 6.61580 0.404880
\(268\) −20.1625 −1.23162
\(269\) 17.1330 1.04462 0.522310 0.852756i \(-0.325071\pi\)
0.522310 + 0.852756i \(0.325071\pi\)
\(270\) 0 0
\(271\) 9.21261 0.559626 0.279813 0.960055i \(-0.409728\pi\)
0.279813 + 0.960055i \(0.409728\pi\)
\(272\) 5.03838 0.305497
\(273\) 3.37123 0.204036
\(274\) 21.0106 1.26930
\(275\) 0 0
\(276\) −4.40211 −0.264976
\(277\) −21.1695 −1.27195 −0.635977 0.771708i \(-0.719403\pi\)
−0.635977 + 0.771708i \(0.719403\pi\)
\(278\) −30.4960 −1.82903
\(279\) 1.28136 0.0767132
\(280\) 0 0
\(281\) −28.2982 −1.68813 −0.844066 0.536240i \(-0.819844\pi\)
−0.844066 + 0.536240i \(0.819844\pi\)
\(282\) −45.7980 −2.72723
\(283\) 26.7052 1.58746 0.793730 0.608270i \(-0.208136\pi\)
0.793730 + 0.608270i \(0.208136\pi\)
\(284\) −8.27794 −0.491206
\(285\) 0 0
\(286\) 43.3042 2.56063
\(287\) −1.64553 −0.0971328
\(288\) 18.3619 1.08199
\(289\) −15.9298 −0.937046
\(290\) 0 0
\(291\) −25.3549 −1.48633
\(292\) 18.8043 1.10044
\(293\) −20.6913 −1.20880 −0.604399 0.796682i \(-0.706587\pi\)
−0.604399 + 0.796682i \(0.706587\pi\)
\(294\) −30.4718 −1.77715
\(295\) 0 0
\(296\) −1.81821 −0.105681
\(297\) −2.57858 −0.149624
\(298\) −29.7585 −1.72387
\(299\) 6.23201 0.360406
\(300\) 0 0
\(301\) −1.65073 −0.0951467
\(302\) 13.5815 0.781526
\(303\) 16.8434 0.967627
\(304\) 41.6684 2.38984
\(305\) 0 0
\(306\) 5.29042 0.302433
\(307\) 20.2769 1.15727 0.578633 0.815588i \(-0.303586\pi\)
0.578633 + 0.815588i \(0.303586\pi\)
\(308\) 2.09714 0.119496
\(309\) −2.24141 −0.127509
\(310\) 0 0
\(311\) 12.3238 0.698820 0.349410 0.936970i \(-0.386382\pi\)
0.349410 + 0.936970i \(0.386382\pi\)
\(312\) −13.0763 −0.740298
\(313\) 10.5428 0.595912 0.297956 0.954580i \(-0.403695\pi\)
0.297956 + 0.954580i \(0.403695\pi\)
\(314\) −30.2007 −1.70432
\(315\) 0 0
\(316\) 3.58693 0.201780
\(317\) 20.9718 1.17790 0.588948 0.808171i \(-0.299542\pi\)
0.588948 + 0.808171i \(0.299542\pi\)
\(318\) 18.5357 1.03943
\(319\) −52.5374 −2.94153
\(320\) 0 0
\(321\) −22.4266 −1.25173
\(322\) 0.745593 0.0415503
\(323\) 8.85085 0.492474
\(324\) −13.0386 −0.724369
\(325\) 0 0
\(326\) −39.5147 −2.18852
\(327\) −16.5292 −0.914069
\(328\) 6.38267 0.352424
\(329\) 3.13987 0.173107
\(330\) 0 0
\(331\) −19.2909 −1.06033 −0.530163 0.847896i \(-0.677869\pi\)
−0.530163 + 0.847896i \(0.677869\pi\)
\(332\) −2.90257 −0.159299
\(333\) −4.32464 −0.236989
\(334\) 5.19221 0.284105
\(335\) 0 0
\(336\) −3.54377 −0.193328
\(337\) −27.5023 −1.49815 −0.749074 0.662487i \(-0.769501\pi\)
−0.749074 + 0.662487i \(0.769501\pi\)
\(338\) −15.5195 −0.844147
\(339\) −9.45237 −0.513382
\(340\) 0 0
\(341\) −2.34190 −0.126821
\(342\) 43.7527 2.36588
\(343\) 4.20589 0.227097
\(344\) 6.40284 0.345218
\(345\) 0 0
\(346\) 40.8175 2.19436
\(347\) −23.2293 −1.24701 −0.623506 0.781819i \(-0.714292\pi\)
−0.623506 + 0.781819i \(0.714292\pi\)
\(348\) −33.7216 −1.80767
\(349\) −31.5500 −1.68883 −0.844416 0.535688i \(-0.820052\pi\)
−0.844416 + 0.535688i \(0.820052\pi\)
\(350\) 0 0
\(351\) 2.34309 0.125065
\(352\) −33.5593 −1.78872
\(353\) −5.60734 −0.298449 −0.149224 0.988803i \(-0.547678\pi\)
−0.149224 + 0.988803i \(0.547678\pi\)
\(354\) −22.1352 −1.17647
\(355\) 0 0
\(356\) −3.73963 −0.198200
\(357\) −0.752737 −0.0398391
\(358\) −3.34989 −0.177047
\(359\) 23.8284 1.25761 0.628806 0.777562i \(-0.283544\pi\)
0.628806 + 0.777562i \(0.283544\pi\)
\(360\) 0 0
\(361\) 54.1981 2.85253
\(362\) −22.9379 −1.20559
\(363\) −36.0890 −1.89418
\(364\) −1.90561 −0.0998813
\(365\) 0 0
\(366\) −28.5007 −1.48976
\(367\) 10.7773 0.562568 0.281284 0.959625i \(-0.409240\pi\)
0.281284 + 0.959625i \(0.409240\pi\)
\(368\) −6.55096 −0.341492
\(369\) 15.1813 0.790306
\(370\) 0 0
\(371\) −1.27079 −0.0659760
\(372\) −1.50317 −0.0779356
\(373\) −6.83088 −0.353689 −0.176845 0.984239i \(-0.556589\pi\)
−0.176845 + 0.984239i \(0.556589\pi\)
\(374\) −9.66908 −0.499976
\(375\) 0 0
\(376\) −12.1789 −0.628077
\(377\) 47.7393 2.45870
\(378\) 0.280325 0.0144184
\(379\) −11.4240 −0.586813 −0.293406 0.955988i \(-0.594789\pi\)
−0.293406 + 0.955988i \(0.594789\pi\)
\(380\) 0 0
\(381\) −45.8598 −2.34947
\(382\) −6.37421 −0.326133
\(383\) 38.2543 1.95470 0.977352 0.211618i \(-0.0678733\pi\)
0.977352 + 0.211618i \(0.0678733\pi\)
\(384\) 21.4229 1.09323
\(385\) 0 0
\(386\) 7.34351 0.373775
\(387\) 15.2293 0.774147
\(388\) 14.3321 0.727600
\(389\) −0.100947 −0.00511820 −0.00255910 0.999997i \(-0.500815\pi\)
−0.00255910 + 0.999997i \(0.500815\pi\)
\(390\) 0 0
\(391\) −1.39150 −0.0703712
\(392\) −8.10324 −0.409276
\(393\) −28.8336 −1.45446
\(394\) 9.43296 0.475226
\(395\) 0 0
\(396\) −19.3477 −0.972258
\(397\) 18.7984 0.943466 0.471733 0.881741i \(-0.343629\pi\)
0.471733 + 0.881741i \(0.343629\pi\)
\(398\) −19.0276 −0.953769
\(399\) −6.22528 −0.311654
\(400\) 0 0
\(401\) 16.1807 0.808026 0.404013 0.914753i \(-0.367615\pi\)
0.404013 + 0.914753i \(0.367615\pi\)
\(402\) −65.3844 −3.26108
\(403\) 2.12801 0.106004
\(404\) −9.52086 −0.473680
\(405\) 0 0
\(406\) 5.71149 0.283457
\(407\) 7.90396 0.391785
\(408\) 2.91971 0.144547
\(409\) 3.76534 0.186184 0.0930919 0.995658i \(-0.470325\pi\)
0.0930919 + 0.995658i \(0.470325\pi\)
\(410\) 0 0
\(411\) 27.5800 1.36042
\(412\) 1.26698 0.0624194
\(413\) 1.51757 0.0746748
\(414\) −6.87866 −0.338068
\(415\) 0 0
\(416\) 30.4944 1.49511
\(417\) −40.0312 −1.96034
\(418\) −79.9651 −3.91122
\(419\) 13.7453 0.671500 0.335750 0.941951i \(-0.391010\pi\)
0.335750 + 0.941951i \(0.391010\pi\)
\(420\) 0 0
\(421\) 16.6746 0.812669 0.406335 0.913724i \(-0.366807\pi\)
0.406335 + 0.913724i \(0.366807\pi\)
\(422\) 22.8030 1.11003
\(423\) −28.9676 −1.40845
\(424\) 4.92911 0.239379
\(425\) 0 0
\(426\) −26.8444 −1.30061
\(427\) 1.95398 0.0945599
\(428\) 12.6768 0.612757
\(429\) 56.8440 2.74445
\(430\) 0 0
\(431\) 5.57968 0.268764 0.134382 0.990930i \(-0.457095\pi\)
0.134382 + 0.990930i \(0.457095\pi\)
\(432\) −2.46300 −0.118501
\(433\) −10.9860 −0.527953 −0.263977 0.964529i \(-0.585034\pi\)
−0.263977 + 0.964529i \(0.585034\pi\)
\(434\) 0.254594 0.0122209
\(435\) 0 0
\(436\) 9.34329 0.447462
\(437\) −11.5080 −0.550501
\(438\) 60.9801 2.91374
\(439\) −17.3442 −0.827795 −0.413897 0.910324i \(-0.635833\pi\)
−0.413897 + 0.910324i \(0.635833\pi\)
\(440\) 0 0
\(441\) −19.2737 −0.917794
\(442\) 8.78602 0.417908
\(443\) 23.6992 1.12598 0.562991 0.826463i \(-0.309651\pi\)
0.562991 + 0.826463i \(0.309651\pi\)
\(444\) 5.07323 0.240765
\(445\) 0 0
\(446\) 4.63483 0.219466
\(447\) −39.0631 −1.84762
\(448\) 0.702808 0.0332045
\(449\) −27.2306 −1.28509 −0.642546 0.766247i \(-0.722122\pi\)
−0.642546 + 0.766247i \(0.722122\pi\)
\(450\) 0 0
\(451\) −27.7462 −1.30652
\(452\) 5.34303 0.251315
\(453\) 17.8280 0.837631
\(454\) 20.6284 0.968140
\(455\) 0 0
\(456\) 24.1465 1.13076
\(457\) 23.5359 1.10096 0.550481 0.834848i \(-0.314444\pi\)
0.550481 + 0.834848i \(0.314444\pi\)
\(458\) −40.2177 −1.87925
\(459\) −0.523171 −0.0244195
\(460\) 0 0
\(461\) −37.9663 −1.76827 −0.884133 0.467236i \(-0.845250\pi\)
−0.884133 + 0.467236i \(0.845250\pi\)
\(462\) 6.80078 0.316401
\(463\) −6.08858 −0.282960 −0.141480 0.989941i \(-0.545186\pi\)
−0.141480 + 0.989941i \(0.545186\pi\)
\(464\) −50.1825 −2.32967
\(465\) 0 0
\(466\) 2.63218 0.121934
\(467\) −29.4171 −1.36126 −0.680630 0.732628i \(-0.738294\pi\)
−0.680630 + 0.732628i \(0.738294\pi\)
\(468\) 17.5807 0.812669
\(469\) 4.48270 0.206992
\(470\) 0 0
\(471\) −39.6434 −1.82667
\(472\) −5.88633 −0.270940
\(473\) −27.8339 −1.27980
\(474\) 11.6320 0.534274
\(475\) 0 0
\(476\) 0.425491 0.0195023
\(477\) 11.7240 0.536804
\(478\) 50.9523 2.33050
\(479\) −17.9285 −0.819173 −0.409587 0.912271i \(-0.634327\pi\)
−0.409587 + 0.912271i \(0.634327\pi\)
\(480\) 0 0
\(481\) −7.18211 −0.327476
\(482\) −1.83307 −0.0834938
\(483\) 0.978717 0.0445331
\(484\) 20.3996 0.927253
\(485\) 0 0
\(486\) −39.5018 −1.79184
\(487\) 22.6663 1.02711 0.513554 0.858057i \(-0.328329\pi\)
0.513554 + 0.858057i \(0.328329\pi\)
\(488\) −7.57908 −0.343089
\(489\) −51.8697 −2.34563
\(490\) 0 0
\(491\) 14.3512 0.647661 0.323831 0.946115i \(-0.395029\pi\)
0.323831 + 0.946115i \(0.395029\pi\)
\(492\) −17.8092 −0.802899
\(493\) −10.6594 −0.480073
\(494\) 72.6620 3.26922
\(495\) 0 0
\(496\) −2.23693 −0.100441
\(497\) 1.84043 0.0825544
\(498\) −9.41270 −0.421793
\(499\) −16.1552 −0.723206 −0.361603 0.932332i \(-0.617770\pi\)
−0.361603 + 0.932332i \(0.617770\pi\)
\(500\) 0 0
\(501\) 6.81565 0.304501
\(502\) 14.9862 0.668869
\(503\) −17.0723 −0.761215 −0.380607 0.924737i \(-0.624285\pi\)
−0.380607 + 0.924737i \(0.624285\pi\)
\(504\) −0.989520 −0.0440767
\(505\) 0 0
\(506\) 12.5718 0.558886
\(507\) −20.3719 −0.904748
\(508\) 25.9226 1.15013
\(509\) −24.9620 −1.10642 −0.553211 0.833041i \(-0.686598\pi\)
−0.553211 + 0.833041i \(0.686598\pi\)
\(510\) 0 0
\(511\) −4.18074 −0.184945
\(512\) −20.6300 −0.911727
\(513\) −4.32672 −0.191029
\(514\) −4.18409 −0.184552
\(515\) 0 0
\(516\) −17.8654 −0.786482
\(517\) 52.9429 2.32843
\(518\) −0.859263 −0.0377538
\(519\) 53.5798 2.35189
\(520\) 0 0
\(521\) −31.2003 −1.36691 −0.683456 0.729992i \(-0.739524\pi\)
−0.683456 + 0.729992i \(0.739524\pi\)
\(522\) −52.6928 −2.30630
\(523\) −21.0227 −0.919257 −0.459628 0.888111i \(-0.652017\pi\)
−0.459628 + 0.888111i \(0.652017\pi\)
\(524\) 16.2984 0.712000
\(525\) 0 0
\(526\) −12.0820 −0.526802
\(527\) −0.475149 −0.0206978
\(528\) −59.7533 −2.60043
\(529\) −21.1908 −0.921337
\(530\) 0 0
\(531\) −14.0007 −0.607580
\(532\) 3.51889 0.152563
\(533\) 25.2122 1.09206
\(534\) −12.1272 −0.524795
\(535\) 0 0
\(536\) −17.3874 −0.751022
\(537\) −4.39730 −0.189757
\(538\) −31.4060 −1.35401
\(539\) 35.2257 1.51728
\(540\) 0 0
\(541\) −19.9902 −0.859445 −0.429722 0.902961i \(-0.641389\pi\)
−0.429722 + 0.902961i \(0.641389\pi\)
\(542\) −16.8873 −0.725372
\(543\) −30.1098 −1.29214
\(544\) −6.80887 −0.291928
\(545\) 0 0
\(546\) −6.17968 −0.264466
\(547\) 1.94389 0.0831148 0.0415574 0.999136i \(-0.486768\pi\)
0.0415574 + 0.999136i \(0.486768\pi\)
\(548\) −15.5898 −0.665963
\(549\) −18.0270 −0.769372
\(550\) 0 0
\(551\) −88.1548 −3.75552
\(552\) −3.79623 −0.161578
\(553\) −0.797478 −0.0339122
\(554\) 38.8051 1.64867
\(555\) 0 0
\(556\) 22.6279 0.959639
\(557\) −5.46031 −0.231361 −0.115680 0.993286i \(-0.536905\pi\)
−0.115680 + 0.993286i \(0.536905\pi\)
\(558\) −2.34882 −0.0994336
\(559\) 25.2919 1.06973
\(560\) 0 0
\(561\) −12.6923 −0.535869
\(562\) 51.8725 2.18811
\(563\) 31.3778 1.32242 0.661208 0.750202i \(-0.270044\pi\)
0.661208 + 0.750202i \(0.270044\pi\)
\(564\) 33.9819 1.43090
\(565\) 0 0
\(566\) −48.9524 −2.05762
\(567\) 2.89887 0.121741
\(568\) −7.13862 −0.299530
\(569\) −35.0427 −1.46907 −0.734533 0.678573i \(-0.762599\pi\)
−0.734533 + 0.678573i \(0.762599\pi\)
\(570\) 0 0
\(571\) −1.82647 −0.0764356 −0.0382178 0.999269i \(-0.512168\pi\)
−0.0382178 + 0.999269i \(0.512168\pi\)
\(572\) −32.1315 −1.34349
\(573\) −8.36722 −0.349546
\(574\) 3.01637 0.125901
\(575\) 0 0
\(576\) −6.48393 −0.270164
\(577\) −13.8070 −0.574792 −0.287396 0.957812i \(-0.592790\pi\)
−0.287396 + 0.957812i \(0.592790\pi\)
\(578\) 29.2003 1.21457
\(579\) 9.63959 0.400608
\(580\) 0 0
\(581\) 0.645326 0.0267726
\(582\) 46.4772 1.92654
\(583\) −21.4274 −0.887433
\(584\) 16.2162 0.671031
\(585\) 0 0
\(586\) 37.9285 1.56681
\(587\) 11.7903 0.486637 0.243319 0.969946i \(-0.421764\pi\)
0.243319 + 0.969946i \(0.421764\pi\)
\(588\) 22.6100 0.932419
\(589\) −3.92957 −0.161915
\(590\) 0 0
\(591\) 12.3823 0.509342
\(592\) 7.54968 0.310290
\(593\) 1.87116 0.0768392 0.0384196 0.999262i \(-0.487768\pi\)
0.0384196 + 0.999262i \(0.487768\pi\)
\(594\) 4.72671 0.193939
\(595\) 0 0
\(596\) 22.0807 0.904462
\(597\) −24.9770 −1.02224
\(598\) −11.4237 −0.467149
\(599\) −25.0996 −1.02554 −0.512772 0.858525i \(-0.671381\pi\)
−0.512772 + 0.858525i \(0.671381\pi\)
\(600\) 0 0
\(601\) 17.2895 0.705254 0.352627 0.935764i \(-0.385288\pi\)
0.352627 + 0.935764i \(0.385288\pi\)
\(602\) 3.02590 0.123327
\(603\) −41.3562 −1.68416
\(604\) −10.0774 −0.410044
\(605\) 0 0
\(606\) −30.8750 −1.25421
\(607\) −24.4282 −0.991510 −0.495755 0.868462i \(-0.665109\pi\)
−0.495755 + 0.868462i \(0.665109\pi\)
\(608\) −56.3106 −2.28370
\(609\) 7.49730 0.303806
\(610\) 0 0
\(611\) −48.1078 −1.94623
\(612\) −3.92547 −0.158678
\(613\) 0.229288 0.00926086 0.00463043 0.999989i \(-0.498526\pi\)
0.00463043 + 0.999989i \(0.498526\pi\)
\(614\) −37.1690 −1.50002
\(615\) 0 0
\(616\) 1.80850 0.0728667
\(617\) −30.1386 −1.21333 −0.606667 0.794956i \(-0.707494\pi\)
−0.606667 + 0.794956i \(0.707494\pi\)
\(618\) 4.10865 0.165274
\(619\) −24.6422 −0.990455 −0.495227 0.868763i \(-0.664915\pi\)
−0.495227 + 0.868763i \(0.664915\pi\)
\(620\) 0 0
\(621\) 0.680232 0.0272968
\(622\) −22.5904 −0.905791
\(623\) 0.831429 0.0333105
\(624\) 54.2961 2.17358
\(625\) 0 0
\(626\) −19.3256 −0.772405
\(627\) −104.968 −4.19200
\(628\) 22.4088 0.894207
\(629\) 1.60364 0.0639413
\(630\) 0 0
\(631\) −12.0079 −0.478027 −0.239014 0.971016i \(-0.576824\pi\)
−0.239014 + 0.971016i \(0.576824\pi\)
\(632\) 3.09325 0.123043
\(633\) 29.9328 1.18972
\(634\) −38.4427 −1.52676
\(635\) 0 0
\(636\) −13.7534 −0.545357
\(637\) −32.0086 −1.26823
\(638\) 96.3044 3.81273
\(639\) −16.9793 −0.671691
\(640\) 0 0
\(641\) −21.7431 −0.858799 −0.429400 0.903115i \(-0.641275\pi\)
−0.429400 + 0.903115i \(0.641275\pi\)
\(642\) 41.1094 1.62246
\(643\) −28.4439 −1.12172 −0.560860 0.827911i \(-0.689529\pi\)
−0.560860 + 0.827911i \(0.689529\pi\)
\(644\) −0.553227 −0.0218002
\(645\) 0 0
\(646\) −16.2242 −0.638332
\(647\) −10.8334 −0.425903 −0.212952 0.977063i \(-0.568308\pi\)
−0.212952 + 0.977063i \(0.568308\pi\)
\(648\) −11.2441 −0.441710
\(649\) 25.5885 1.00444
\(650\) 0 0
\(651\) 0.334198 0.0130982
\(652\) 29.3198 1.14825
\(653\) −29.1679 −1.14143 −0.570714 0.821149i \(-0.693333\pi\)
−0.570714 + 0.821149i \(0.693333\pi\)
\(654\) 30.2992 1.18479
\(655\) 0 0
\(656\) −26.5025 −1.03475
\(657\) 38.5705 1.50478
\(658\) −5.75558 −0.224376
\(659\) 3.98489 0.155229 0.0776147 0.996983i \(-0.475270\pi\)
0.0776147 + 0.996983i \(0.475270\pi\)
\(660\) 0 0
\(661\) 10.7056 0.416399 0.208200 0.978086i \(-0.433240\pi\)
0.208200 + 0.978086i \(0.433240\pi\)
\(662\) 35.3615 1.37437
\(663\) 11.5331 0.447910
\(664\) −2.50308 −0.0971384
\(665\) 0 0
\(666\) 7.92734 0.307178
\(667\) 13.8594 0.536638
\(668\) −3.85260 −0.149062
\(669\) 6.08400 0.235221
\(670\) 0 0
\(671\) 32.9471 1.27191
\(672\) 4.78905 0.184741
\(673\) 9.82304 0.378650 0.189325 0.981914i \(-0.439370\pi\)
0.189325 + 0.981914i \(0.439370\pi\)
\(674\) 50.4136 1.94186
\(675\) 0 0
\(676\) 11.5154 0.442899
\(677\) 26.9422 1.03547 0.517737 0.855540i \(-0.326775\pi\)
0.517737 + 0.855540i \(0.326775\pi\)
\(678\) 17.3268 0.665432
\(679\) −3.18643 −0.122284
\(680\) 0 0
\(681\) 27.0783 1.03764
\(682\) 4.29285 0.164382
\(683\) 44.7069 1.71066 0.855331 0.518082i \(-0.173354\pi\)
0.855331 + 0.518082i \(0.173354\pi\)
\(684\) −32.4644 −1.24131
\(685\) 0 0
\(686\) −7.70967 −0.294356
\(687\) −52.7925 −2.01416
\(688\) −26.5863 −1.01359
\(689\) 19.4705 0.741767
\(690\) 0 0
\(691\) 38.1949 1.45300 0.726502 0.687164i \(-0.241145\pi\)
0.726502 + 0.687164i \(0.241145\pi\)
\(692\) −30.2864 −1.15132
\(693\) 4.30155 0.163403
\(694\) 42.5807 1.61634
\(695\) 0 0
\(696\) −29.0804 −1.10229
\(697\) −5.62945 −0.213231
\(698\) 57.8332 2.18902
\(699\) 3.45519 0.130687
\(700\) 0 0
\(701\) 20.1487 0.761008 0.380504 0.924779i \(-0.375751\pi\)
0.380504 + 0.924779i \(0.375751\pi\)
\(702\) −4.29503 −0.162105
\(703\) 13.2624 0.500201
\(704\) 11.8504 0.446629
\(705\) 0 0
\(706\) 10.2786 0.386841
\(707\) 2.11676 0.0796091
\(708\) 16.4242 0.617261
\(709\) 29.3168 1.10102 0.550508 0.834830i \(-0.314434\pi\)
0.550508 + 0.834830i \(0.314434\pi\)
\(710\) 0 0
\(711\) 7.35733 0.275921
\(712\) −3.22493 −0.120859
\(713\) 0.617794 0.0231366
\(714\) 1.37982 0.0516383
\(715\) 0 0
\(716\) 2.48561 0.0928916
\(717\) 66.8834 2.49781
\(718\) −43.6789 −1.63008
\(719\) 3.26007 0.121580 0.0607900 0.998151i \(-0.480638\pi\)
0.0607900 + 0.998151i \(0.480638\pi\)
\(720\) 0 0
\(721\) −0.281685 −0.0104905
\(722\) −99.3487 −3.69738
\(723\) −2.40621 −0.0894878
\(724\) 17.0198 0.632536
\(725\) 0 0
\(726\) 66.1534 2.45518
\(727\) −20.1773 −0.748336 −0.374168 0.927361i \(-0.622072\pi\)
−0.374168 + 0.927361i \(0.622072\pi\)
\(728\) −1.64334 −0.0609061
\(729\) −23.0937 −0.855321
\(730\) 0 0
\(731\) −5.64724 −0.208871
\(732\) 21.1474 0.781632
\(733\) −13.8239 −0.510599 −0.255299 0.966862i \(-0.582174\pi\)
−0.255299 + 0.966862i \(0.582174\pi\)
\(734\) −19.7554 −0.729185
\(735\) 0 0
\(736\) 8.85297 0.326325
\(737\) 75.5851 2.78421
\(738\) −27.8283 −1.02437
\(739\) 7.81411 0.287447 0.143723 0.989618i \(-0.454092\pi\)
0.143723 + 0.989618i \(0.454092\pi\)
\(740\) 0 0
\(741\) 95.3811 3.50391
\(742\) 2.32944 0.0855163
\(743\) −34.4155 −1.26258 −0.631291 0.775546i \(-0.717475\pi\)
−0.631291 + 0.775546i \(0.717475\pi\)
\(744\) −1.29628 −0.0475240
\(745\) 0 0
\(746\) 12.5214 0.458442
\(747\) −5.95362 −0.217831
\(748\) 7.17442 0.262323
\(749\) −2.81842 −0.102983
\(750\) 0 0
\(751\) −32.6623 −1.19187 −0.595933 0.803034i \(-0.703218\pi\)
−0.595933 + 0.803034i \(0.703218\pi\)
\(752\) 50.5699 1.84409
\(753\) 19.6720 0.716886
\(754\) −87.5092 −3.18690
\(755\) 0 0
\(756\) −0.208000 −0.00756489
\(757\) 17.6525 0.641590 0.320795 0.947149i \(-0.396050\pi\)
0.320795 + 0.947149i \(0.396050\pi\)
\(758\) 20.9410 0.760611
\(759\) 16.5026 0.599008
\(760\) 0 0
\(761\) −40.8281 −1.48002 −0.740008 0.672598i \(-0.765178\pi\)
−0.740008 + 0.672598i \(0.765178\pi\)
\(762\) 84.0639 3.04532
\(763\) −2.07728 −0.0752027
\(764\) 4.72964 0.171112
\(765\) 0 0
\(766\) −70.1227 −2.53363
\(767\) −23.2516 −0.839566
\(768\) −50.4542 −1.82061
\(769\) −12.1935 −0.439709 −0.219854 0.975533i \(-0.570558\pi\)
−0.219854 + 0.975533i \(0.570558\pi\)
\(770\) 0 0
\(771\) −5.49232 −0.197801
\(772\) −5.44886 −0.196109
\(773\) −37.8215 −1.36035 −0.680173 0.733052i \(-0.738095\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(774\) −27.9162 −1.00343
\(775\) 0 0
\(776\) 12.3595 0.443680
\(777\) −1.12793 −0.0404641
\(778\) 0.185042 0.00663407
\(779\) −46.5566 −1.66806
\(780\) 0 0
\(781\) 31.0324 1.11043
\(782\) 2.55071 0.0912132
\(783\) 5.21080 0.186219
\(784\) 33.6468 1.20167
\(785\) 0 0
\(786\) 52.8539 1.88524
\(787\) 13.9696 0.497964 0.248982 0.968508i \(-0.419904\pi\)
0.248982 + 0.968508i \(0.419904\pi\)
\(788\) −6.99922 −0.249337
\(789\) −15.8597 −0.564620
\(790\) 0 0
\(791\) −1.18791 −0.0422372
\(792\) −16.6848 −0.592869
\(793\) −29.9381 −1.06313
\(794\) −34.4587 −1.22289
\(795\) 0 0
\(796\) 14.1184 0.500415
\(797\) −12.1732 −0.431198 −0.215599 0.976482i \(-0.569170\pi\)
−0.215599 + 0.976482i \(0.569170\pi\)
\(798\) 11.4113 0.403957
\(799\) 10.7416 0.380012
\(800\) 0 0
\(801\) −7.67055 −0.271026
\(802\) −29.6603 −1.04734
\(803\) −70.4937 −2.48767
\(804\) 48.5150 1.71099
\(805\) 0 0
\(806\) −3.90079 −0.137399
\(807\) −41.2256 −1.45121
\(808\) −8.21047 −0.288843
\(809\) −25.0091 −0.879271 −0.439636 0.898176i \(-0.644892\pi\)
−0.439636 + 0.898176i \(0.644892\pi\)
\(810\) 0 0
\(811\) 39.0119 1.36989 0.684947 0.728593i \(-0.259826\pi\)
0.684947 + 0.728593i \(0.259826\pi\)
\(812\) −4.23791 −0.148721
\(813\) −22.1674 −0.777446
\(814\) −14.4885 −0.507821
\(815\) 0 0
\(816\) −12.1234 −0.424404
\(817\) −46.7037 −1.63396
\(818\) −6.90210 −0.241326
\(819\) −3.90870 −0.136581
\(820\) 0 0
\(821\) −18.5556 −0.647595 −0.323797 0.946126i \(-0.604960\pi\)
−0.323797 + 0.946126i \(0.604960\pi\)
\(822\) −50.5559 −1.76334
\(823\) 50.5534 1.76218 0.881090 0.472949i \(-0.156810\pi\)
0.881090 + 0.472949i \(0.156810\pi\)
\(824\) 1.09260 0.0380624
\(825\) 0 0
\(826\) −2.78180 −0.0967914
\(827\) −14.1845 −0.493242 −0.246621 0.969112i \(-0.579320\pi\)
−0.246621 + 0.969112i \(0.579320\pi\)
\(828\) 5.10394 0.177374
\(829\) −56.2077 −1.95217 −0.976087 0.217381i \(-0.930249\pi\)
−0.976087 + 0.217381i \(0.930249\pi\)
\(830\) 0 0
\(831\) 50.9382 1.76703
\(832\) −10.7681 −0.373318
\(833\) 7.14697 0.247628
\(834\) 73.3798 2.54093
\(835\) 0 0
\(836\) 59.3338 2.05210
\(837\) 0.232276 0.00802862
\(838\) −25.1960 −0.870380
\(839\) −9.83492 −0.339539 −0.169770 0.985484i \(-0.554302\pi\)
−0.169770 + 0.985484i \(0.554302\pi\)
\(840\) 0 0
\(841\) 77.1677 2.66095
\(842\) −30.5656 −1.05336
\(843\) 68.0914 2.34519
\(844\) −16.9198 −0.582402
\(845\) 0 0
\(846\) 53.0996 1.82560
\(847\) −4.53542 −0.155839
\(848\) −20.4670 −0.702839
\(849\) −64.2583 −2.20534
\(850\) 0 0
\(851\) −2.08507 −0.0714753
\(852\) 19.9184 0.682394
\(853\) −34.2541 −1.17284 −0.586419 0.810008i \(-0.699463\pi\)
−0.586419 + 0.810008i \(0.699463\pi\)
\(854\) −3.58178 −0.122566
\(855\) 0 0
\(856\) 10.9321 0.373650
\(857\) −45.4343 −1.55201 −0.776004 0.630729i \(-0.782756\pi\)
−0.776004 + 0.630729i \(0.782756\pi\)
\(858\) −104.199 −3.55729
\(859\) 8.81001 0.300594 0.150297 0.988641i \(-0.451977\pi\)
0.150297 + 0.988641i \(0.451977\pi\)
\(860\) 0 0
\(861\) 3.95949 0.134939
\(862\) −10.2279 −0.348364
\(863\) −26.7733 −0.911374 −0.455687 0.890140i \(-0.650606\pi\)
−0.455687 + 0.890140i \(0.650606\pi\)
\(864\) 3.32850 0.113238
\(865\) 0 0
\(866\) 20.1380 0.684319
\(867\) 38.3304 1.30177
\(868\) −0.188908 −0.00641196
\(869\) −13.4467 −0.456148
\(870\) 0 0
\(871\) −68.6821 −2.32720
\(872\) 8.05734 0.272856
\(873\) 29.3972 0.994945
\(874\) 21.0948 0.713544
\(875\) 0 0
\(876\) −45.2470 −1.52876
\(877\) −28.5732 −0.964850 −0.482425 0.875937i \(-0.660244\pi\)
−0.482425 + 0.875937i \(0.660244\pi\)
\(878\) 31.7931 1.07296
\(879\) 49.7875 1.67929
\(880\) 0 0
\(881\) 13.4524 0.453224 0.226612 0.973985i \(-0.427235\pi\)
0.226612 + 0.973985i \(0.427235\pi\)
\(882\) 35.3299 1.18962
\(883\) −2.30504 −0.0775706 −0.0387853 0.999248i \(-0.512349\pi\)
−0.0387853 + 0.999248i \(0.512349\pi\)
\(884\) −6.51919 −0.219264
\(885\) 0 0
\(886\) −43.4421 −1.45947
\(887\) −7.50871 −0.252118 −0.126059 0.992023i \(-0.540233\pi\)
−0.126059 + 0.992023i \(0.540233\pi\)
\(888\) 4.37498 0.146815
\(889\) −5.76335 −0.193296
\(890\) 0 0
\(891\) 48.8793 1.63752
\(892\) −3.43903 −0.115147
\(893\) 88.8353 2.97276
\(894\) 71.6052 2.39484
\(895\) 0 0
\(896\) 2.69229 0.0899430
\(897\) −14.9955 −0.500685
\(898\) 49.9155 1.66570
\(899\) 4.73251 0.157838
\(900\) 0 0
\(901\) −4.34743 −0.144834
\(902\) 50.8606 1.69347
\(903\) 3.97201 0.132180
\(904\) 4.60765 0.153248
\(905\) 0 0
\(906\) −32.6798 −1.08571
\(907\) −27.9423 −0.927810 −0.463905 0.885885i \(-0.653552\pi\)
−0.463905 + 0.885885i \(0.653552\pi\)
\(908\) −15.3062 −0.507954
\(909\) −19.5287 −0.647727
\(910\) 0 0
\(911\) 21.0515 0.697468 0.348734 0.937222i \(-0.386612\pi\)
0.348734 + 0.937222i \(0.386612\pi\)
\(912\) −100.263 −3.32003
\(913\) 10.8812 0.360114
\(914\) −43.1428 −1.42704
\(915\) 0 0
\(916\) 29.8414 0.985987
\(917\) −3.62361 −0.119662
\(918\) 0.959006 0.0316519
\(919\) 5.21572 0.172051 0.0860253 0.996293i \(-0.472583\pi\)
0.0860253 + 0.996293i \(0.472583\pi\)
\(920\) 0 0
\(921\) −48.7905 −1.60770
\(922\) 69.5946 2.29198
\(923\) −28.1983 −0.928157
\(924\) −5.04615 −0.166006
\(925\) 0 0
\(926\) 11.1608 0.366765
\(927\) 2.59876 0.0853544
\(928\) 67.8167 2.22619
\(929\) −51.1232 −1.67730 −0.838649 0.544672i \(-0.816654\pi\)
−0.838649 + 0.544672i \(0.816654\pi\)
\(930\) 0 0
\(931\) 59.1068 1.93715
\(932\) −1.95307 −0.0639750
\(933\) −29.6536 −0.970817
\(934\) 53.9234 1.76443
\(935\) 0 0
\(936\) 15.1610 0.495553
\(937\) 23.5517 0.769400 0.384700 0.923042i \(-0.374305\pi\)
0.384700 + 0.923042i \(0.374305\pi\)
\(938\) −8.21708 −0.268297
\(939\) −25.3680 −0.827855
\(940\) 0 0
\(941\) 45.4674 1.48219 0.741097 0.671398i \(-0.234306\pi\)
0.741097 + 0.671398i \(0.234306\pi\)
\(942\) 72.6690 2.36768
\(943\) 7.31947 0.238355
\(944\) 24.4416 0.795506
\(945\) 0 0
\(946\) 51.0213 1.65885
\(947\) 22.5514 0.732821 0.366411 0.930453i \(-0.380587\pi\)
0.366411 + 0.930453i \(0.380587\pi\)
\(948\) −8.63088 −0.280318
\(949\) 64.0556 2.07933
\(950\) 0 0
\(951\) −50.4626 −1.63636
\(952\) 0.366929 0.0118922
\(953\) 0.231111 0.00748642 0.00374321 0.999993i \(-0.498808\pi\)
0.00374321 + 0.999993i \(0.498808\pi\)
\(954\) −21.4908 −0.695790
\(955\) 0 0
\(956\) −37.8064 −1.22275
\(957\) 126.416 4.08644
\(958\) 32.8641 1.06179
\(959\) 3.46606 0.111925
\(960\) 0 0
\(961\) −30.7890 −0.993195
\(962\) 13.1653 0.424465
\(963\) 26.0021 0.837905
\(964\) 1.36013 0.0438068
\(965\) 0 0
\(966\) −1.79405 −0.0577227
\(967\) −3.83002 −0.123165 −0.0615825 0.998102i \(-0.519615\pi\)
−0.0615825 + 0.998102i \(0.519615\pi\)
\(968\) 17.5919 0.565425
\(969\) −21.2970 −0.684157
\(970\) 0 0
\(971\) −37.2292 −1.19474 −0.597371 0.801965i \(-0.703788\pi\)
−0.597371 + 0.801965i \(0.703788\pi\)
\(972\) 29.3102 0.940124
\(973\) −5.03085 −0.161282
\(974\) −41.5488 −1.33131
\(975\) 0 0
\(976\) 31.4704 1.00734
\(977\) −3.50188 −0.112035 −0.0560175 0.998430i \(-0.517840\pi\)
−0.0560175 + 0.998430i \(0.517840\pi\)
\(978\) 95.0806 3.04034
\(979\) 14.0191 0.448054
\(980\) 0 0
\(981\) 19.1645 0.611875
\(982\) −26.3067 −0.839481
\(983\) 52.1048 1.66188 0.830942 0.556358i \(-0.187802\pi\)
0.830942 + 0.556358i \(0.187802\pi\)
\(984\) −15.3580 −0.489596
\(985\) 0 0
\(986\) 19.5393 0.622258
\(987\) −7.55517 −0.240484
\(988\) −53.9149 −1.71526
\(989\) 7.34260 0.233481
\(990\) 0 0
\(991\) 55.2696 1.75570 0.877848 0.478939i \(-0.158978\pi\)
0.877848 + 0.478939i \(0.158978\pi\)
\(992\) 3.02298 0.0959798
\(993\) 46.4180 1.47303
\(994\) −3.37362 −0.107005
\(995\) 0 0
\(996\) 6.98419 0.221302
\(997\) 4.93251 0.156214 0.0781071 0.996945i \(-0.475112\pi\)
0.0781071 + 0.996945i \(0.475112\pi\)
\(998\) 29.6135 0.937399
\(999\) −0.783936 −0.0248026
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 6025.2.a.p.1.10 46
5.2 odd 4 1205.2.b.c.724.10 46
5.3 odd 4 1205.2.b.c.724.37 yes 46
5.4 even 2 inner 6025.2.a.p.1.37 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.10 46 5.2 odd 4
1205.2.b.c.724.37 yes 46 5.3 odd 4
6025.2.a.p.1.10 46 1.1 even 1 trivial
6025.2.a.p.1.37 46 5.4 even 2 inner