Properties

Label 6025.2.a.p.1.13
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $46$
CM no
Inner twists $2$

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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 1.13
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.45267 q^{2} +2.41257 q^{3} +0.110263 q^{4} -3.50468 q^{6} -1.25057 q^{7} +2.74517 q^{8} +2.82049 q^{9} +O(q^{10})\) \(q-1.45267 q^{2} +2.41257 q^{3} +0.110263 q^{4} -3.50468 q^{6} -1.25057 q^{7} +2.74517 q^{8} +2.82049 q^{9} +2.46616 q^{11} +0.266016 q^{12} +2.06969 q^{13} +1.81667 q^{14} -4.20837 q^{16} -1.42467 q^{17} -4.09725 q^{18} -0.479813 q^{19} -3.01709 q^{21} -3.58253 q^{22} -2.87475 q^{23} +6.62292 q^{24} -3.00659 q^{26} -0.433079 q^{27} -0.137891 q^{28} -9.26441 q^{29} +0.180654 q^{31} +0.623041 q^{32} +5.94979 q^{33} +2.06958 q^{34} +0.310994 q^{36} +0.824807 q^{37} +0.697012 q^{38} +4.99327 q^{39} +1.12498 q^{41} +4.38285 q^{42} -3.43795 q^{43} +0.271925 q^{44} +4.17607 q^{46} -3.00871 q^{47} -10.1530 q^{48} -5.43607 q^{49} -3.43711 q^{51} +0.228209 q^{52} -12.3733 q^{53} +0.629123 q^{54} -3.43303 q^{56} -1.15758 q^{57} +13.4582 q^{58} +0.433111 q^{59} -3.88745 q^{61} -0.262432 q^{62} -3.52722 q^{63} +7.51166 q^{64} -8.64311 q^{66} +5.24447 q^{67} -0.157087 q^{68} -6.93552 q^{69} +14.3247 q^{71} +7.74273 q^{72} -4.35588 q^{73} -1.19818 q^{74} -0.0529054 q^{76} -3.08411 q^{77} -7.25360 q^{78} -7.28837 q^{79} -9.50630 q^{81} -1.63423 q^{82} -1.09208 q^{83} -0.332672 q^{84} +4.99422 q^{86} -22.3510 q^{87} +6.77004 q^{88} -12.2161 q^{89} -2.58830 q^{91} -0.316977 q^{92} +0.435841 q^{93} +4.37068 q^{94} +1.50313 q^{96} -9.80240 q^{97} +7.89684 q^{98} +6.95579 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45267 −1.02720 −0.513598 0.858031i \(-0.671688\pi\)
−0.513598 + 0.858031i \(0.671688\pi\)
\(3\) 2.41257 1.39290 0.696449 0.717607i \(-0.254762\pi\)
0.696449 + 0.717607i \(0.254762\pi\)
\(4\) 0.110263 0.0551313
\(5\) 0 0
\(6\) −3.50468 −1.43078
\(7\) −1.25057 −0.472671 −0.236336 0.971671i \(-0.575946\pi\)
−0.236336 + 0.971671i \(0.575946\pi\)
\(8\) 2.74517 0.970565
\(9\) 2.82049 0.940164
\(10\) 0 0
\(11\) 2.46616 0.743576 0.371788 0.928318i \(-0.378745\pi\)
0.371788 + 0.928318i \(0.378745\pi\)
\(12\) 0.266016 0.0767922
\(13\) 2.06969 0.574029 0.287015 0.957926i \(-0.407337\pi\)
0.287015 + 0.957926i \(0.407337\pi\)
\(14\) 1.81667 0.485526
\(15\) 0 0
\(16\) −4.20837 −1.05209
\(17\) −1.42467 −0.345532 −0.172766 0.984963i \(-0.555271\pi\)
−0.172766 + 0.984963i \(0.555271\pi\)
\(18\) −4.09725 −0.965732
\(19\) −0.479813 −0.110077 −0.0550384 0.998484i \(-0.517528\pi\)
−0.0550384 + 0.998484i \(0.517528\pi\)
\(20\) 0 0
\(21\) −3.01709 −0.658383
\(22\) −3.58253 −0.763798
\(23\) −2.87475 −0.599426 −0.299713 0.954029i \(-0.596891\pi\)
−0.299713 + 0.954029i \(0.596891\pi\)
\(24\) 6.62292 1.35190
\(25\) 0 0
\(26\) −3.00659 −0.589640
\(27\) −0.433079 −0.0833461
\(28\) −0.137891 −0.0260590
\(29\) −9.26441 −1.72036 −0.860179 0.509992i \(-0.829648\pi\)
−0.860179 + 0.509992i \(0.829648\pi\)
\(30\) 0 0
\(31\) 0.180654 0.0324465 0.0162232 0.999868i \(-0.494836\pi\)
0.0162232 + 0.999868i \(0.494836\pi\)
\(32\) 0.623041 0.110139
\(33\) 5.94979 1.03573
\(34\) 2.06958 0.354929
\(35\) 0 0
\(36\) 0.310994 0.0518324
\(37\) 0.824807 0.135597 0.0677987 0.997699i \(-0.478402\pi\)
0.0677987 + 0.997699i \(0.478402\pi\)
\(38\) 0.697012 0.113070
\(39\) 4.99327 0.799564
\(40\) 0 0
\(41\) 1.12498 0.175693 0.0878464 0.996134i \(-0.472002\pi\)
0.0878464 + 0.996134i \(0.472002\pi\)
\(42\) 4.38285 0.676288
\(43\) −3.43795 −0.524282 −0.262141 0.965030i \(-0.584429\pi\)
−0.262141 + 0.965030i \(0.584429\pi\)
\(44\) 0.271925 0.0409943
\(45\) 0 0
\(46\) 4.17607 0.615728
\(47\) −3.00871 −0.438866 −0.219433 0.975628i \(-0.570421\pi\)
−0.219433 + 0.975628i \(0.570421\pi\)
\(48\) −10.1530 −1.46546
\(49\) −5.43607 −0.776582
\(50\) 0 0
\(51\) −3.43711 −0.481291
\(52\) 0.228209 0.0316470
\(53\) −12.3733 −1.69961 −0.849804 0.527099i \(-0.823280\pi\)
−0.849804 + 0.527099i \(0.823280\pi\)
\(54\) 0.629123 0.0856128
\(55\) 0 0
\(56\) −3.43303 −0.458758
\(57\) −1.15758 −0.153326
\(58\) 13.4582 1.76714
\(59\) 0.433111 0.0563863 0.0281931 0.999602i \(-0.491025\pi\)
0.0281931 + 0.999602i \(0.491025\pi\)
\(60\) 0 0
\(61\) −3.88745 −0.497737 −0.248868 0.968537i \(-0.580059\pi\)
−0.248868 + 0.968537i \(0.580059\pi\)
\(62\) −0.262432 −0.0333289
\(63\) −3.52722 −0.444388
\(64\) 7.51166 0.938957
\(65\) 0 0
\(66\) −8.64311 −1.06389
\(67\) 5.24447 0.640714 0.320357 0.947297i \(-0.396197\pi\)
0.320357 + 0.947297i \(0.396197\pi\)
\(68\) −0.157087 −0.0190496
\(69\) −6.93552 −0.834939
\(70\) 0 0
\(71\) 14.3247 1.70003 0.850013 0.526762i \(-0.176594\pi\)
0.850013 + 0.526762i \(0.176594\pi\)
\(72\) 7.74273 0.912490
\(73\) −4.35588 −0.509818 −0.254909 0.966965i \(-0.582045\pi\)
−0.254909 + 0.966965i \(0.582045\pi\)
\(74\) −1.19818 −0.139285
\(75\) 0 0
\(76\) −0.0529054 −0.00606867
\(77\) −3.08411 −0.351467
\(78\) −7.25360 −0.821309
\(79\) −7.28837 −0.820005 −0.410003 0.912084i \(-0.634472\pi\)
−0.410003 + 0.912084i \(0.634472\pi\)
\(80\) 0 0
\(81\) −9.50630 −1.05626
\(82\) −1.63423 −0.180471
\(83\) −1.09208 −0.119871 −0.0599357 0.998202i \(-0.519090\pi\)
−0.0599357 + 0.998202i \(0.519090\pi\)
\(84\) −0.332672 −0.0362975
\(85\) 0 0
\(86\) 4.99422 0.538541
\(87\) −22.3510 −2.39628
\(88\) 6.77004 0.721689
\(89\) −12.2161 −1.29490 −0.647452 0.762106i \(-0.724166\pi\)
−0.647452 + 0.762106i \(0.724166\pi\)
\(90\) 0 0
\(91\) −2.58830 −0.271327
\(92\) −0.316977 −0.0330471
\(93\) 0.435841 0.0451946
\(94\) 4.37068 0.450801
\(95\) 0 0
\(96\) 1.50313 0.153412
\(97\) −9.80240 −0.995283 −0.497642 0.867383i \(-0.665801\pi\)
−0.497642 + 0.867383i \(0.665801\pi\)
\(98\) 7.89684 0.797702
\(99\) 6.95579 0.699083
\(100\) 0 0
\(101\) −10.5462 −1.04939 −0.524695 0.851291i \(-0.675820\pi\)
−0.524695 + 0.851291i \(0.675820\pi\)
\(102\) 4.99300 0.494380
\(103\) 7.56058 0.744966 0.372483 0.928039i \(-0.378506\pi\)
0.372483 + 0.928039i \(0.378506\pi\)
\(104\) 5.68166 0.557133
\(105\) 0 0
\(106\) 17.9744 1.74583
\(107\) 4.30799 0.416469 0.208234 0.978079i \(-0.433228\pi\)
0.208234 + 0.978079i \(0.433228\pi\)
\(108\) −0.0477524 −0.00459498
\(109\) −3.03421 −0.290625 −0.145313 0.989386i \(-0.546419\pi\)
−0.145313 + 0.989386i \(0.546419\pi\)
\(110\) 0 0
\(111\) 1.98990 0.188873
\(112\) 5.26286 0.497294
\(113\) 5.48438 0.515927 0.257964 0.966155i \(-0.416949\pi\)
0.257964 + 0.966155i \(0.416949\pi\)
\(114\) 1.68159 0.157495
\(115\) 0 0
\(116\) −1.02152 −0.0948455
\(117\) 5.83755 0.539681
\(118\) −0.629169 −0.0579197
\(119\) 1.78165 0.163323
\(120\) 0 0
\(121\) −4.91804 −0.447095
\(122\) 5.64720 0.511273
\(123\) 2.71410 0.244722
\(124\) 0.0199194 0.00178882
\(125\) 0 0
\(126\) 5.12390 0.456474
\(127\) 1.82445 0.161894 0.0809471 0.996718i \(-0.474206\pi\)
0.0809471 + 0.996718i \(0.474206\pi\)
\(128\) −12.1581 −1.07463
\(129\) −8.29429 −0.730271
\(130\) 0 0
\(131\) 10.7564 0.939789 0.469895 0.882722i \(-0.344292\pi\)
0.469895 + 0.882722i \(0.344292\pi\)
\(132\) 0.656039 0.0571009
\(133\) 0.600040 0.0520301
\(134\) −7.61851 −0.658139
\(135\) 0 0
\(136\) −3.91096 −0.335362
\(137\) 18.0907 1.54560 0.772798 0.634653i \(-0.218857\pi\)
0.772798 + 0.634653i \(0.218857\pi\)
\(138\) 10.0751 0.857646
\(139\) 9.24847 0.784445 0.392222 0.919870i \(-0.371706\pi\)
0.392222 + 0.919870i \(0.371706\pi\)
\(140\) 0 0
\(141\) −7.25873 −0.611296
\(142\) −20.8091 −1.74626
\(143\) 5.10420 0.426834
\(144\) −11.8697 −0.989138
\(145\) 0 0
\(146\) 6.32768 0.523683
\(147\) −13.1149 −1.08170
\(148\) 0.0909453 0.00747566
\(149\) 17.0170 1.39408 0.697042 0.717030i \(-0.254499\pi\)
0.697042 + 0.717030i \(0.254499\pi\)
\(150\) 0 0
\(151\) −9.18436 −0.747413 −0.373706 0.927547i \(-0.621913\pi\)
−0.373706 + 0.927547i \(0.621913\pi\)
\(152\) −1.31717 −0.106837
\(153\) −4.01826 −0.324857
\(154\) 4.48021 0.361025
\(155\) 0 0
\(156\) 0.550571 0.0440810
\(157\) 0.176439 0.0140814 0.00704069 0.999975i \(-0.497759\pi\)
0.00704069 + 0.999975i \(0.497759\pi\)
\(158\) 10.5876 0.842306
\(159\) −29.8515 −2.36738
\(160\) 0 0
\(161\) 3.59507 0.283331
\(162\) 13.8096 1.08498
\(163\) 9.16744 0.718050 0.359025 0.933328i \(-0.383109\pi\)
0.359025 + 0.933328i \(0.383109\pi\)
\(164\) 0.124043 0.00968616
\(165\) 0 0
\(166\) 1.58644 0.123131
\(167\) 22.5003 1.74112 0.870562 0.492058i \(-0.163755\pi\)
0.870562 + 0.492058i \(0.163755\pi\)
\(168\) −8.28243 −0.639003
\(169\) −8.71638 −0.670491
\(170\) 0 0
\(171\) −1.35331 −0.103490
\(172\) −0.379077 −0.0289043
\(173\) −5.08571 −0.386659 −0.193330 0.981134i \(-0.561929\pi\)
−0.193330 + 0.981134i \(0.561929\pi\)
\(174\) 32.4688 2.46145
\(175\) 0 0
\(176\) −10.3785 −0.782310
\(177\) 1.04491 0.0785403
\(178\) 17.7460 1.33012
\(179\) −15.3122 −1.14449 −0.572244 0.820084i \(-0.693927\pi\)
−0.572244 + 0.820084i \(0.693927\pi\)
\(180\) 0 0
\(181\) −18.4259 −1.36958 −0.684792 0.728738i \(-0.740107\pi\)
−0.684792 + 0.728738i \(0.740107\pi\)
\(182\) 3.75995 0.278706
\(183\) −9.37874 −0.693297
\(184\) −7.89167 −0.581782
\(185\) 0 0
\(186\) −0.633135 −0.0464237
\(187\) −3.51346 −0.256930
\(188\) −0.331749 −0.0241952
\(189\) 0.541596 0.0393953
\(190\) 0 0
\(191\) −13.7148 −0.992368 −0.496184 0.868217i \(-0.665266\pi\)
−0.496184 + 0.868217i \(0.665266\pi\)
\(192\) 18.1224 1.30787
\(193\) 12.4066 0.893047 0.446524 0.894772i \(-0.352662\pi\)
0.446524 + 0.894772i \(0.352662\pi\)
\(194\) 14.2397 1.02235
\(195\) 0 0
\(196\) −0.599395 −0.0428139
\(197\) −7.72970 −0.550718 −0.275359 0.961341i \(-0.588797\pi\)
−0.275359 + 0.961341i \(0.588797\pi\)
\(198\) −10.1045 −0.718095
\(199\) −5.15173 −0.365196 −0.182598 0.983188i \(-0.558451\pi\)
−0.182598 + 0.983188i \(0.558451\pi\)
\(200\) 0 0
\(201\) 12.6526 0.892449
\(202\) 15.3202 1.07793
\(203\) 11.5858 0.813164
\(204\) −0.378984 −0.0265342
\(205\) 0 0
\(206\) −10.9831 −0.765226
\(207\) −8.10819 −0.563558
\(208\) −8.71002 −0.603931
\(209\) −1.18330 −0.0818504
\(210\) 0 0
\(211\) −20.6216 −1.41965 −0.709823 0.704380i \(-0.751225\pi\)
−0.709823 + 0.704380i \(0.751225\pi\)
\(212\) −1.36431 −0.0937015
\(213\) 34.5593 2.36796
\(214\) −6.25810 −0.427795
\(215\) 0 0
\(216\) −1.18888 −0.0808928
\(217\) −0.225921 −0.0153365
\(218\) 4.40772 0.298529
\(219\) −10.5089 −0.710124
\(220\) 0 0
\(221\) −2.94862 −0.198346
\(222\) −2.89068 −0.194010
\(223\) 0.789803 0.0528891 0.0264446 0.999650i \(-0.491581\pi\)
0.0264446 + 0.999650i \(0.491581\pi\)
\(224\) −0.779156 −0.0520596
\(225\) 0 0
\(226\) −7.96702 −0.529958
\(227\) 1.06248 0.0705190 0.0352595 0.999378i \(-0.488774\pi\)
0.0352595 + 0.999378i \(0.488774\pi\)
\(228\) −0.127638 −0.00845303
\(229\) 18.7377 1.23822 0.619110 0.785304i \(-0.287493\pi\)
0.619110 + 0.785304i \(0.287493\pi\)
\(230\) 0 0
\(231\) −7.44063 −0.489558
\(232\) −25.4324 −1.66972
\(233\) 20.6141 1.35047 0.675237 0.737601i \(-0.264041\pi\)
0.675237 + 0.737601i \(0.264041\pi\)
\(234\) −8.48005 −0.554358
\(235\) 0 0
\(236\) 0.0477559 0.00310865
\(237\) −17.5837 −1.14218
\(238\) −2.58815 −0.167765
\(239\) −17.2630 −1.11665 −0.558324 0.829623i \(-0.688555\pi\)
−0.558324 + 0.829623i \(0.688555\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 7.14431 0.459254
\(243\) −21.6354 −1.38791
\(244\) −0.428640 −0.0274409
\(245\) 0 0
\(246\) −3.94270 −0.251377
\(247\) −0.993065 −0.0631872
\(248\) 0.495927 0.0314914
\(249\) −2.63472 −0.166969
\(250\) 0 0
\(251\) −21.5943 −1.36302 −0.681510 0.731809i \(-0.738677\pi\)
−0.681510 + 0.731809i \(0.738677\pi\)
\(252\) −0.388920 −0.0244997
\(253\) −7.08959 −0.445719
\(254\) −2.65034 −0.166297
\(255\) 0 0
\(256\) 2.63841 0.164900
\(257\) −22.2276 −1.38652 −0.693261 0.720687i \(-0.743827\pi\)
−0.693261 + 0.720687i \(0.743827\pi\)
\(258\) 12.0489 0.750132
\(259\) −1.03148 −0.0640930
\(260\) 0 0
\(261\) −26.1302 −1.61742
\(262\) −15.6255 −0.965348
\(263\) −3.89765 −0.240339 −0.120170 0.992753i \(-0.538344\pi\)
−0.120170 + 0.992753i \(0.538344\pi\)
\(264\) 16.3332 1.00524
\(265\) 0 0
\(266\) −0.871663 −0.0534451
\(267\) −29.4722 −1.80367
\(268\) 0.578268 0.0353234
\(269\) 6.60591 0.402769 0.201385 0.979512i \(-0.435456\pi\)
0.201385 + 0.979512i \(0.435456\pi\)
\(270\) 0 0
\(271\) −16.8832 −1.02558 −0.512791 0.858513i \(-0.671388\pi\)
−0.512791 + 0.858513i \(0.671388\pi\)
\(272\) 5.99552 0.363532
\(273\) −6.24444 −0.377931
\(274\) −26.2799 −1.58763
\(275\) 0 0
\(276\) −0.764728 −0.0460312
\(277\) −27.0001 −1.62228 −0.811140 0.584852i \(-0.801153\pi\)
−0.811140 + 0.584852i \(0.801153\pi\)
\(278\) −13.4350 −0.805778
\(279\) 0.509534 0.0305050
\(280\) 0 0
\(281\) −9.48720 −0.565959 −0.282979 0.959126i \(-0.591323\pi\)
−0.282979 + 0.959126i \(0.591323\pi\)
\(282\) 10.5446 0.627920
\(283\) 13.7557 0.817690 0.408845 0.912604i \(-0.365932\pi\)
0.408845 + 0.912604i \(0.365932\pi\)
\(284\) 1.57947 0.0937246
\(285\) 0 0
\(286\) −7.41474 −0.438442
\(287\) −1.40687 −0.0830449
\(288\) 1.75728 0.103549
\(289\) −14.9703 −0.880607
\(290\) 0 0
\(291\) −23.6490 −1.38633
\(292\) −0.480291 −0.0281069
\(293\) −11.4782 −0.670561 −0.335280 0.942118i \(-0.608831\pi\)
−0.335280 + 0.942118i \(0.608831\pi\)
\(294\) 19.0517 1.11112
\(295\) 0 0
\(296\) 2.26424 0.131606
\(297\) −1.06804 −0.0619742
\(298\) −24.7201 −1.43200
\(299\) −5.94984 −0.344088
\(300\) 0 0
\(301\) 4.29940 0.247813
\(302\) 13.3419 0.767739
\(303\) −25.4435 −1.46169
\(304\) 2.01923 0.115811
\(305\) 0 0
\(306\) 5.83722 0.333692
\(307\) 11.8355 0.675485 0.337743 0.941238i \(-0.390337\pi\)
0.337743 + 0.941238i \(0.390337\pi\)
\(308\) −0.340062 −0.0193768
\(309\) 18.2404 1.03766
\(310\) 0 0
\(311\) −5.53844 −0.314056 −0.157028 0.987594i \(-0.550191\pi\)
−0.157028 + 0.987594i \(0.550191\pi\)
\(312\) 13.7074 0.776029
\(313\) 24.8522 1.40473 0.702365 0.711817i \(-0.252127\pi\)
0.702365 + 0.711817i \(0.252127\pi\)
\(314\) −0.256309 −0.0144643
\(315\) 0 0
\(316\) −0.803634 −0.0452079
\(317\) −15.8127 −0.888130 −0.444065 0.895994i \(-0.646464\pi\)
−0.444065 + 0.895994i \(0.646464\pi\)
\(318\) 43.3645 2.43176
\(319\) −22.8475 −1.27922
\(320\) 0 0
\(321\) 10.3933 0.580098
\(322\) −5.22247 −0.291037
\(323\) 0.683574 0.0380351
\(324\) −1.04819 −0.0582327
\(325\) 0 0
\(326\) −13.3173 −0.737578
\(327\) −7.32025 −0.404811
\(328\) 3.08827 0.170521
\(329\) 3.76261 0.207439
\(330\) 0 0
\(331\) 23.4865 1.29093 0.645467 0.763789i \(-0.276663\pi\)
0.645467 + 0.763789i \(0.276663\pi\)
\(332\) −0.120416 −0.00660866
\(333\) 2.32636 0.127484
\(334\) −32.6856 −1.78848
\(335\) 0 0
\(336\) 12.6970 0.692679
\(337\) 11.1318 0.606385 0.303193 0.952929i \(-0.401947\pi\)
0.303193 + 0.952929i \(0.401947\pi\)
\(338\) 12.6621 0.688725
\(339\) 13.2315 0.718634
\(340\) 0 0
\(341\) 0.445523 0.0241264
\(342\) 1.96592 0.106305
\(343\) 15.5522 0.839739
\(344\) −9.43776 −0.508850
\(345\) 0 0
\(346\) 7.38788 0.397175
\(347\) 4.44891 0.238830 0.119415 0.992844i \(-0.461898\pi\)
0.119415 + 0.992844i \(0.461898\pi\)
\(348\) −2.46448 −0.132110
\(349\) 0.902138 0.0482903 0.0241452 0.999708i \(-0.492314\pi\)
0.0241452 + 0.999708i \(0.492314\pi\)
\(350\) 0 0
\(351\) −0.896340 −0.0478431
\(352\) 1.53652 0.0818968
\(353\) −0.455388 −0.0242379 −0.0121189 0.999927i \(-0.503858\pi\)
−0.0121189 + 0.999927i \(0.503858\pi\)
\(354\) −1.51791 −0.0806763
\(355\) 0 0
\(356\) −1.34698 −0.0713897
\(357\) 4.29834 0.227493
\(358\) 22.2436 1.17561
\(359\) −8.65154 −0.456611 −0.228305 0.973590i \(-0.573318\pi\)
−0.228305 + 0.973590i \(0.573318\pi\)
\(360\) 0 0
\(361\) −18.7698 −0.987883
\(362\) 26.7668 1.40683
\(363\) −11.8651 −0.622757
\(364\) −0.285392 −0.0149586
\(365\) 0 0
\(366\) 13.6243 0.712151
\(367\) 23.7645 1.24050 0.620249 0.784405i \(-0.287031\pi\)
0.620249 + 0.784405i \(0.287031\pi\)
\(368\) 12.0980 0.630651
\(369\) 3.17300 0.165180
\(370\) 0 0
\(371\) 15.4737 0.803355
\(372\) 0.0480570 0.00249164
\(373\) −7.72073 −0.399764 −0.199882 0.979820i \(-0.564056\pi\)
−0.199882 + 0.979820i \(0.564056\pi\)
\(374\) 5.10391 0.263917
\(375\) 0 0
\(376\) −8.25944 −0.425948
\(377\) −19.1745 −0.987536
\(378\) −0.786762 −0.0404667
\(379\) 27.7660 1.42624 0.713122 0.701040i \(-0.247281\pi\)
0.713122 + 0.701040i \(0.247281\pi\)
\(380\) 0 0
\(381\) 4.40162 0.225502
\(382\) 19.9231 1.01936
\(383\) −2.17131 −0.110949 −0.0554744 0.998460i \(-0.517667\pi\)
−0.0554744 + 0.998460i \(0.517667\pi\)
\(384\) −29.3322 −1.49685
\(385\) 0 0
\(386\) −18.0228 −0.917334
\(387\) −9.69670 −0.492911
\(388\) −1.08084 −0.0548712
\(389\) −16.3022 −0.826556 −0.413278 0.910605i \(-0.635616\pi\)
−0.413278 + 0.910605i \(0.635616\pi\)
\(390\) 0 0
\(391\) 4.09555 0.207121
\(392\) −14.9230 −0.753723
\(393\) 25.9505 1.30903
\(394\) 11.2287 0.565696
\(395\) 0 0
\(396\) 0.766963 0.0385413
\(397\) 4.91814 0.246835 0.123417 0.992355i \(-0.460615\pi\)
0.123417 + 0.992355i \(0.460615\pi\)
\(398\) 7.48378 0.375128
\(399\) 1.44764 0.0724726
\(400\) 0 0
\(401\) 2.97380 0.148504 0.0742522 0.997239i \(-0.476343\pi\)
0.0742522 + 0.997239i \(0.476343\pi\)
\(402\) −18.3802 −0.916720
\(403\) 0.373899 0.0186252
\(404\) −1.16285 −0.0578542
\(405\) 0 0
\(406\) −16.8304 −0.835278
\(407\) 2.03411 0.100827
\(408\) −9.43545 −0.467125
\(409\) −24.3914 −1.20608 −0.603039 0.797712i \(-0.706044\pi\)
−0.603039 + 0.797712i \(0.706044\pi\)
\(410\) 0 0
\(411\) 43.6451 2.15286
\(412\) 0.833649 0.0410709
\(413\) −0.541636 −0.0266522
\(414\) 11.7786 0.578885
\(415\) 0 0
\(416\) 1.28950 0.0632231
\(417\) 22.3126 1.09265
\(418\) 1.71895 0.0840764
\(419\) −29.8864 −1.46005 −0.730023 0.683422i \(-0.760491\pi\)
−0.730023 + 0.683422i \(0.760491\pi\)
\(420\) 0 0
\(421\) −5.05042 −0.246142 −0.123071 0.992398i \(-0.539274\pi\)
−0.123071 + 0.992398i \(0.539274\pi\)
\(422\) 29.9564 1.45825
\(423\) −8.48605 −0.412606
\(424\) −33.9669 −1.64958
\(425\) 0 0
\(426\) −50.2034 −2.43236
\(427\) 4.86153 0.235266
\(428\) 0.475010 0.0229605
\(429\) 12.3142 0.594537
\(430\) 0 0
\(431\) 10.0234 0.482808 0.241404 0.970425i \(-0.422392\pi\)
0.241404 + 0.970425i \(0.422392\pi\)
\(432\) 1.82256 0.0876878
\(433\) −26.9755 −1.29636 −0.648179 0.761488i \(-0.724469\pi\)
−0.648179 + 0.761488i \(0.724469\pi\)
\(434\) 0.328190 0.0157536
\(435\) 0 0
\(436\) −0.334560 −0.0160225
\(437\) 1.37934 0.0659828
\(438\) 15.2660 0.729436
\(439\) 24.6330 1.17567 0.587835 0.808981i \(-0.299980\pi\)
0.587835 + 0.808981i \(0.299980\pi\)
\(440\) 0 0
\(441\) −15.3324 −0.730114
\(442\) 4.28339 0.203740
\(443\) −10.5621 −0.501819 −0.250910 0.968010i \(-0.580730\pi\)
−0.250910 + 0.968010i \(0.580730\pi\)
\(444\) 0.219412 0.0104128
\(445\) 0 0
\(446\) −1.14733 −0.0543275
\(447\) 41.0546 1.94182
\(448\) −9.39386 −0.443818
\(449\) −5.95137 −0.280863 −0.140431 0.990090i \(-0.544849\pi\)
−0.140431 + 0.990090i \(0.544849\pi\)
\(450\) 0 0
\(451\) 2.77439 0.130641
\(452\) 0.604722 0.0284437
\(453\) −22.1579 −1.04107
\(454\) −1.54343 −0.0724369
\(455\) 0 0
\(456\) −3.17776 −0.148812
\(457\) 8.98781 0.420432 0.210216 0.977655i \(-0.432583\pi\)
0.210216 + 0.977655i \(0.432583\pi\)
\(458\) −27.2197 −1.27190
\(459\) 0.616993 0.0287988
\(460\) 0 0
\(461\) 17.2131 0.801693 0.400846 0.916145i \(-0.368716\pi\)
0.400846 + 0.916145i \(0.368716\pi\)
\(462\) 10.8088 0.502871
\(463\) −17.5090 −0.813711 −0.406856 0.913492i \(-0.633375\pi\)
−0.406856 + 0.913492i \(0.633375\pi\)
\(464\) 38.9880 1.80997
\(465\) 0 0
\(466\) −29.9456 −1.38720
\(467\) −4.34976 −0.201283 −0.100641 0.994923i \(-0.532089\pi\)
−0.100641 + 0.994923i \(0.532089\pi\)
\(468\) 0.643663 0.0297533
\(469\) −6.55858 −0.302847
\(470\) 0 0
\(471\) 0.425672 0.0196139
\(472\) 1.18897 0.0547266
\(473\) −8.47854 −0.389844
\(474\) 25.5434 1.17325
\(475\) 0 0
\(476\) 0.196449 0.00900422
\(477\) −34.8989 −1.59791
\(478\) 25.0775 1.14702
\(479\) −28.5754 −1.30565 −0.652823 0.757511i \(-0.726415\pi\)
−0.652823 + 0.757511i \(0.726415\pi\)
\(480\) 0 0
\(481\) 1.70710 0.0778369
\(482\) −1.45267 −0.0661675
\(483\) 8.67336 0.394652
\(484\) −0.542276 −0.0246489
\(485\) 0 0
\(486\) 31.4292 1.42566
\(487\) 15.6356 0.708516 0.354258 0.935148i \(-0.384734\pi\)
0.354258 + 0.935148i \(0.384734\pi\)
\(488\) −10.6717 −0.483086
\(489\) 22.1171 1.00017
\(490\) 0 0
\(491\) −15.4298 −0.696338 −0.348169 0.937432i \(-0.613196\pi\)
−0.348169 + 0.937432i \(0.613196\pi\)
\(492\) 0.299263 0.0134918
\(493\) 13.1987 0.594439
\(494\) 1.44260 0.0649057
\(495\) 0 0
\(496\) −0.760260 −0.0341367
\(497\) −17.9140 −0.803553
\(498\) 3.82739 0.171509
\(499\) 1.64702 0.0737308 0.0368654 0.999320i \(-0.488263\pi\)
0.0368654 + 0.999320i \(0.488263\pi\)
\(500\) 0 0
\(501\) 54.2835 2.42521
\(502\) 31.3695 1.40009
\(503\) −39.2147 −1.74850 −0.874249 0.485477i \(-0.838646\pi\)
−0.874249 + 0.485477i \(0.838646\pi\)
\(504\) −9.68283 −0.431308
\(505\) 0 0
\(506\) 10.2989 0.457840
\(507\) −21.0289 −0.933925
\(508\) 0.201169 0.00892543
\(509\) −1.68682 −0.0747669 −0.0373835 0.999301i \(-0.511902\pi\)
−0.0373835 + 0.999301i \(0.511902\pi\)
\(510\) 0 0
\(511\) 5.44734 0.240976
\(512\) 20.4834 0.905247
\(513\) 0.207797 0.00917447
\(514\) 32.2895 1.42423
\(515\) 0 0
\(516\) −0.914549 −0.0402608
\(517\) −7.41998 −0.326330
\(518\) 1.49840 0.0658360
\(519\) −12.2696 −0.538577
\(520\) 0 0
\(521\) 16.3399 0.715862 0.357931 0.933748i \(-0.383482\pi\)
0.357931 + 0.933748i \(0.383482\pi\)
\(522\) 37.9586 1.66140
\(523\) 15.6795 0.685617 0.342808 0.939405i \(-0.388622\pi\)
0.342808 + 0.939405i \(0.388622\pi\)
\(524\) 1.18603 0.0518118
\(525\) 0 0
\(526\) 5.66201 0.246875
\(527\) −0.257372 −0.0112113
\(528\) −25.0389 −1.08968
\(529\) −14.7358 −0.640689
\(530\) 0 0
\(531\) 1.22159 0.0530123
\(532\) 0.0661620 0.00286848
\(533\) 2.32837 0.100853
\(534\) 42.8135 1.85272
\(535\) 0 0
\(536\) 14.3970 0.621855
\(537\) −36.9417 −1.59415
\(538\) −9.59623 −0.413723
\(539\) −13.4062 −0.577448
\(540\) 0 0
\(541\) −3.92084 −0.168570 −0.0842851 0.996442i \(-0.526861\pi\)
−0.0842851 + 0.996442i \(0.526861\pi\)
\(542\) 24.5258 1.05347
\(543\) −44.4537 −1.90769
\(544\) −0.887626 −0.0380566
\(545\) 0 0
\(546\) 9.07114 0.388209
\(547\) 36.8903 1.57732 0.788658 0.614832i \(-0.210776\pi\)
0.788658 + 0.614832i \(0.210776\pi\)
\(548\) 1.99473 0.0852106
\(549\) −10.9645 −0.467954
\(550\) 0 0
\(551\) 4.44519 0.189371
\(552\) −19.0392 −0.810363
\(553\) 9.11462 0.387593
\(554\) 39.2224 1.66640
\(555\) 0 0
\(556\) 1.01976 0.0432474
\(557\) 0.602249 0.0255181 0.0127591 0.999919i \(-0.495939\pi\)
0.0127591 + 0.999919i \(0.495939\pi\)
\(558\) −0.740187 −0.0313346
\(559\) −7.11549 −0.300953
\(560\) 0 0
\(561\) −8.47647 −0.357877
\(562\) 13.7818 0.581350
\(563\) −7.05189 −0.297202 −0.148601 0.988897i \(-0.547477\pi\)
−0.148601 + 0.988897i \(0.547477\pi\)
\(564\) −0.800366 −0.0337015
\(565\) 0 0
\(566\) −19.9825 −0.839928
\(567\) 11.8883 0.499262
\(568\) 39.3237 1.64999
\(569\) 32.0383 1.34311 0.671557 0.740953i \(-0.265626\pi\)
0.671557 + 0.740953i \(0.265626\pi\)
\(570\) 0 0
\(571\) 27.2459 1.14020 0.570102 0.821574i \(-0.306904\pi\)
0.570102 + 0.821574i \(0.306904\pi\)
\(572\) 0.562802 0.0235319
\(573\) −33.0879 −1.38227
\(574\) 2.04372 0.0853034
\(575\) 0 0
\(576\) 21.1866 0.882773
\(577\) 2.31753 0.0964802 0.0482401 0.998836i \(-0.484639\pi\)
0.0482401 + 0.998836i \(0.484639\pi\)
\(578\) 21.7470 0.904556
\(579\) 29.9318 1.24392
\(580\) 0 0
\(581\) 1.36572 0.0566598
\(582\) 34.3543 1.42403
\(583\) −30.5146 −1.26379
\(584\) −11.9577 −0.494811
\(585\) 0 0
\(586\) 16.6740 0.688797
\(587\) 3.75229 0.154874 0.0774369 0.996997i \(-0.475326\pi\)
0.0774369 + 0.996997i \(0.475326\pi\)
\(588\) −1.44608 −0.0596354
\(589\) −0.0866804 −0.00357160
\(590\) 0 0
\(591\) −18.6484 −0.767094
\(592\) −3.47109 −0.142661
\(593\) 34.1569 1.40266 0.701328 0.712839i \(-0.252591\pi\)
0.701328 + 0.712839i \(0.252591\pi\)
\(594\) 1.55152 0.0636596
\(595\) 0 0
\(596\) 1.87633 0.0768577
\(597\) −12.4289 −0.508681
\(598\) 8.64317 0.353446
\(599\) −19.0779 −0.779503 −0.389752 0.920920i \(-0.627439\pi\)
−0.389752 + 0.920920i \(0.627439\pi\)
\(600\) 0 0
\(601\) 22.3859 0.913140 0.456570 0.889687i \(-0.349078\pi\)
0.456570 + 0.889687i \(0.349078\pi\)
\(602\) −6.24562 −0.254553
\(603\) 14.7920 0.602376
\(604\) −1.01269 −0.0412058
\(605\) 0 0
\(606\) 36.9611 1.50144
\(607\) −39.6985 −1.61131 −0.805656 0.592384i \(-0.798187\pi\)
−0.805656 + 0.592384i \(0.798187\pi\)
\(608\) −0.298943 −0.0121237
\(609\) 27.9515 1.13265
\(610\) 0 0
\(611\) −6.22711 −0.251922
\(612\) −0.443063 −0.0179098
\(613\) −22.1222 −0.893505 −0.446753 0.894658i \(-0.647420\pi\)
−0.446753 + 0.894658i \(0.647420\pi\)
\(614\) −17.1931 −0.693856
\(615\) 0 0
\(616\) −8.46642 −0.341122
\(617\) 4.59367 0.184934 0.0924670 0.995716i \(-0.470525\pi\)
0.0924670 + 0.995716i \(0.470525\pi\)
\(618\) −26.4974 −1.06588
\(619\) −11.6527 −0.468364 −0.234182 0.972193i \(-0.575241\pi\)
−0.234182 + 0.972193i \(0.575241\pi\)
\(620\) 0 0
\(621\) 1.24499 0.0499598
\(622\) 8.04555 0.322597
\(623\) 15.2771 0.612064
\(624\) −21.0135 −0.841215
\(625\) 0 0
\(626\) −36.1022 −1.44293
\(627\) −2.85479 −0.114009
\(628\) 0.0194546 0.000776324 0
\(629\) −1.17507 −0.0468533
\(630\) 0 0
\(631\) −3.75293 −0.149402 −0.0747010 0.997206i \(-0.523800\pi\)
−0.0747010 + 0.997206i \(0.523800\pi\)
\(632\) −20.0078 −0.795869
\(633\) −49.7509 −1.97742
\(634\) 22.9707 0.912284
\(635\) 0 0
\(636\) −3.29150 −0.130517
\(637\) −11.2510 −0.445781
\(638\) 33.1900 1.31401
\(639\) 40.4026 1.59830
\(640\) 0 0
\(641\) 30.9147 1.22106 0.610529 0.791994i \(-0.290957\pi\)
0.610529 + 0.791994i \(0.290957\pi\)
\(642\) −15.0981 −0.595875
\(643\) −22.1044 −0.871712 −0.435856 0.900017i \(-0.643554\pi\)
−0.435856 + 0.900017i \(0.643554\pi\)
\(644\) 0.396402 0.0156204
\(645\) 0 0
\(646\) −0.993010 −0.0390695
\(647\) 32.9443 1.29517 0.647586 0.761992i \(-0.275778\pi\)
0.647586 + 0.761992i \(0.275778\pi\)
\(648\) −26.0965 −1.02517
\(649\) 1.06812 0.0419275
\(650\) 0 0
\(651\) −0.545050 −0.0213622
\(652\) 1.01083 0.0395870
\(653\) 40.1758 1.57220 0.786100 0.618100i \(-0.212097\pi\)
0.786100 + 0.618100i \(0.212097\pi\)
\(654\) 10.6339 0.415820
\(655\) 0 0
\(656\) −4.73434 −0.184845
\(657\) −12.2857 −0.479312
\(658\) −5.46585 −0.213081
\(659\) −24.7128 −0.962672 −0.481336 0.876536i \(-0.659848\pi\)
−0.481336 + 0.876536i \(0.659848\pi\)
\(660\) 0 0
\(661\) 12.9928 0.505361 0.252681 0.967550i \(-0.418688\pi\)
0.252681 + 0.967550i \(0.418688\pi\)
\(662\) −34.1182 −1.32604
\(663\) −7.11375 −0.276275
\(664\) −2.99795 −0.116343
\(665\) 0 0
\(666\) −3.37944 −0.130951
\(667\) 26.6328 1.03123
\(668\) 2.48094 0.0959904
\(669\) 1.90545 0.0736691
\(670\) 0 0
\(671\) −9.58708 −0.370105
\(672\) −1.87977 −0.0725137
\(673\) −6.53422 −0.251876 −0.125938 0.992038i \(-0.540194\pi\)
−0.125938 + 0.992038i \(0.540194\pi\)
\(674\) −16.1708 −0.622876
\(675\) 0 0
\(676\) −0.961090 −0.0369650
\(677\) −3.97121 −0.152626 −0.0763130 0.997084i \(-0.524315\pi\)
−0.0763130 + 0.997084i \(0.524315\pi\)
\(678\) −19.2210 −0.738178
\(679\) 12.2586 0.470442
\(680\) 0 0
\(681\) 2.56330 0.0982258
\(682\) −0.647200 −0.0247826
\(683\) −28.9357 −1.10719 −0.553596 0.832785i \(-0.686745\pi\)
−0.553596 + 0.832785i \(0.686745\pi\)
\(684\) −0.149219 −0.00570554
\(685\) 0 0
\(686\) −22.5923 −0.862577
\(687\) 45.2060 1.72471
\(688\) 14.4682 0.551593
\(689\) −25.6090 −0.975624
\(690\) 0 0
\(691\) 43.7038 1.66257 0.831285 0.555847i \(-0.187606\pi\)
0.831285 + 0.555847i \(0.187606\pi\)
\(692\) −0.560763 −0.0213170
\(693\) −8.69870 −0.330436
\(694\) −6.46282 −0.245325
\(695\) 0 0
\(696\) −61.3574 −2.32575
\(697\) −1.60272 −0.0607075
\(698\) −1.31051 −0.0496036
\(699\) 49.7329 1.88107
\(700\) 0 0
\(701\) −25.3881 −0.958894 −0.479447 0.877571i \(-0.659163\pi\)
−0.479447 + 0.877571i \(0.659163\pi\)
\(702\) 1.30209 0.0491442
\(703\) −0.395753 −0.0149261
\(704\) 18.5250 0.698186
\(705\) 0 0
\(706\) 0.661531 0.0248970
\(707\) 13.1888 0.496016
\(708\) 0.115215 0.00433003
\(709\) 47.6484 1.78947 0.894737 0.446594i \(-0.147363\pi\)
0.894737 + 0.446594i \(0.147363\pi\)
\(710\) 0 0
\(711\) −20.5568 −0.770939
\(712\) −33.5353 −1.25679
\(713\) −0.519335 −0.0194493
\(714\) −6.24409 −0.233679
\(715\) 0 0
\(716\) −1.68836 −0.0630970
\(717\) −41.6481 −1.55538
\(718\) 12.5679 0.469028
\(719\) −22.1579 −0.826351 −0.413175 0.910651i \(-0.635580\pi\)
−0.413175 + 0.910651i \(0.635580\pi\)
\(720\) 0 0
\(721\) −9.45504 −0.352124
\(722\) 27.2664 1.01475
\(723\) 2.41257 0.0897244
\(724\) −2.03168 −0.0755069
\(725\) 0 0
\(726\) 17.2361 0.639693
\(727\) −11.4060 −0.423026 −0.211513 0.977375i \(-0.567839\pi\)
−0.211513 + 0.977375i \(0.567839\pi\)
\(728\) −7.10532 −0.263341
\(729\) −23.6779 −0.876961
\(730\) 0 0
\(731\) 4.89793 0.181157
\(732\) −1.03412 −0.0382223
\(733\) 32.1861 1.18882 0.594411 0.804162i \(-0.297385\pi\)
0.594411 + 0.804162i \(0.297385\pi\)
\(734\) −34.5221 −1.27423
\(735\) 0 0
\(736\) −1.79108 −0.0660202
\(737\) 12.9337 0.476420
\(738\) −4.60934 −0.169672
\(739\) 6.90721 0.254086 0.127043 0.991897i \(-0.459451\pi\)
0.127043 + 0.991897i \(0.459451\pi\)
\(740\) 0 0
\(741\) −2.39584 −0.0880133
\(742\) −22.4783 −0.825203
\(743\) −31.6170 −1.15991 −0.579957 0.814647i \(-0.696931\pi\)
−0.579957 + 0.814647i \(0.696931\pi\)
\(744\) 1.19646 0.0438643
\(745\) 0 0
\(746\) 11.2157 0.410636
\(747\) −3.08020 −0.112699
\(748\) −0.387403 −0.0141649
\(749\) −5.38744 −0.196853
\(750\) 0 0
\(751\) −14.3963 −0.525327 −0.262664 0.964887i \(-0.584601\pi\)
−0.262664 + 0.964887i \(0.584601\pi\)
\(752\) 12.6618 0.461727
\(753\) −52.0978 −1.89855
\(754\) 27.8543 1.01439
\(755\) 0 0
\(756\) 0.0597177 0.00217191
\(757\) 31.1923 1.13370 0.566852 0.823820i \(-0.308161\pi\)
0.566852 + 0.823820i \(0.308161\pi\)
\(758\) −40.3350 −1.46503
\(759\) −17.1041 −0.620841
\(760\) 0 0
\(761\) 4.10282 0.148727 0.0743636 0.997231i \(-0.476307\pi\)
0.0743636 + 0.997231i \(0.476307\pi\)
\(762\) −6.39412 −0.231635
\(763\) 3.79450 0.137370
\(764\) −1.51223 −0.0547105
\(765\) 0 0
\(766\) 3.15421 0.113966
\(767\) 0.896407 0.0323674
\(768\) 6.36534 0.229689
\(769\) −13.7105 −0.494413 −0.247206 0.968963i \(-0.579513\pi\)
−0.247206 + 0.968963i \(0.579513\pi\)
\(770\) 0 0
\(771\) −53.6257 −1.93128
\(772\) 1.36798 0.0492348
\(773\) −34.2990 −1.23365 −0.616825 0.787100i \(-0.711582\pi\)
−0.616825 + 0.787100i \(0.711582\pi\)
\(774\) 14.0861 0.506316
\(775\) 0 0
\(776\) −26.9093 −0.965987
\(777\) −2.48851 −0.0892750
\(778\) 23.6818 0.849035
\(779\) −0.539781 −0.0193397
\(780\) 0 0
\(781\) 35.3270 1.26410
\(782\) −5.94951 −0.212754
\(783\) 4.01222 0.143385
\(784\) 22.8770 0.817035
\(785\) 0 0
\(786\) −37.6976 −1.34463
\(787\) 1.05124 0.0374728 0.0187364 0.999824i \(-0.494036\pi\)
0.0187364 + 0.999824i \(0.494036\pi\)
\(788\) −0.852296 −0.0303618
\(789\) −9.40335 −0.334768
\(790\) 0 0
\(791\) −6.85861 −0.243864
\(792\) 19.0948 0.678506
\(793\) −8.04582 −0.285716
\(794\) −7.14446 −0.253547
\(795\) 0 0
\(796\) −0.568042 −0.0201337
\(797\) −46.9746 −1.66393 −0.831963 0.554832i \(-0.812783\pi\)
−0.831963 + 0.554832i \(0.812783\pi\)
\(798\) −2.10295 −0.0744435
\(799\) 4.28642 0.151642
\(800\) 0 0
\(801\) −34.4554 −1.21742
\(802\) −4.31996 −0.152543
\(803\) −10.7423 −0.379088
\(804\) 1.39511 0.0492018
\(805\) 0 0
\(806\) −0.543153 −0.0191318
\(807\) 15.9372 0.561016
\(808\) −28.9512 −1.01850
\(809\) −40.7051 −1.43111 −0.715557 0.698554i \(-0.753827\pi\)
−0.715557 + 0.698554i \(0.753827\pi\)
\(810\) 0 0
\(811\) −9.80946 −0.344457 −0.172228 0.985057i \(-0.555097\pi\)
−0.172228 + 0.985057i \(0.555097\pi\)
\(812\) 1.27748 0.0448307
\(813\) −40.7319 −1.42853
\(814\) −2.95490 −0.103569
\(815\) 0 0
\(816\) 14.4646 0.506363
\(817\) 1.64957 0.0577113
\(818\) 35.4328 1.23888
\(819\) −7.30026 −0.255092
\(820\) 0 0
\(821\) −7.27965 −0.254061 −0.127031 0.991899i \(-0.540545\pi\)
−0.127031 + 0.991899i \(0.540545\pi\)
\(822\) −63.4022 −2.21140
\(823\) −10.9222 −0.380725 −0.190362 0.981714i \(-0.560966\pi\)
−0.190362 + 0.981714i \(0.560966\pi\)
\(824\) 20.7551 0.723039
\(825\) 0 0
\(826\) 0.786821 0.0273770
\(827\) −19.4083 −0.674894 −0.337447 0.941344i \(-0.609563\pi\)
−0.337447 + 0.941344i \(0.609563\pi\)
\(828\) −0.894030 −0.0310697
\(829\) 28.4668 0.988692 0.494346 0.869265i \(-0.335408\pi\)
0.494346 + 0.869265i \(0.335408\pi\)
\(830\) 0 0
\(831\) −65.1397 −2.25967
\(832\) 15.5468 0.538989
\(833\) 7.74459 0.268334
\(834\) −32.4129 −1.12237
\(835\) 0 0
\(836\) −0.130473 −0.00451252
\(837\) −0.0782376 −0.00270429
\(838\) 43.4152 1.49975
\(839\) −19.8074 −0.683826 −0.341913 0.939732i \(-0.611075\pi\)
−0.341913 + 0.939732i \(0.611075\pi\)
\(840\) 0 0
\(841\) 56.8293 1.95963
\(842\) 7.33662 0.252836
\(843\) −22.8885 −0.788322
\(844\) −2.27378 −0.0782669
\(845\) 0 0
\(846\) 12.3275 0.423827
\(847\) 6.15036 0.211329
\(848\) 52.0715 1.78814
\(849\) 33.1865 1.13896
\(850\) 0 0
\(851\) −2.37111 −0.0812806
\(852\) 3.81059 0.130549
\(853\) −8.54067 −0.292427 −0.146214 0.989253i \(-0.546709\pi\)
−0.146214 + 0.989253i \(0.546709\pi\)
\(854\) −7.06222 −0.241664
\(855\) 0 0
\(856\) 11.8262 0.404210
\(857\) −9.52177 −0.325257 −0.162629 0.986687i \(-0.551997\pi\)
−0.162629 + 0.986687i \(0.551997\pi\)
\(858\) −17.8886 −0.610705
\(859\) −32.9092 −1.12285 −0.561423 0.827529i \(-0.689746\pi\)
−0.561423 + 0.827529i \(0.689746\pi\)
\(860\) 0 0
\(861\) −3.39417 −0.115673
\(862\) −14.5607 −0.495939
\(863\) 2.93045 0.0997538 0.0498769 0.998755i \(-0.484117\pi\)
0.0498769 + 0.998755i \(0.484117\pi\)
\(864\) −0.269826 −0.00917967
\(865\) 0 0
\(866\) 39.1866 1.33161
\(867\) −36.1169 −1.22660
\(868\) −0.0249106 −0.000845522 0
\(869\) −17.9743 −0.609736
\(870\) 0 0
\(871\) 10.8544 0.367788
\(872\) −8.32944 −0.282071
\(873\) −27.6476 −0.935729
\(874\) −2.00373 −0.0677773
\(875\) 0 0
\(876\) −1.15873 −0.0391500
\(877\) 47.5268 1.60487 0.802434 0.596741i \(-0.203538\pi\)
0.802434 + 0.596741i \(0.203538\pi\)
\(878\) −35.7838 −1.20764
\(879\) −27.6918 −0.934022
\(880\) 0 0
\(881\) −14.8772 −0.501227 −0.250614 0.968087i \(-0.580632\pi\)
−0.250614 + 0.968087i \(0.580632\pi\)
\(882\) 22.2730 0.749970
\(883\) −18.1229 −0.609884 −0.304942 0.952371i \(-0.598637\pi\)
−0.304942 + 0.952371i \(0.598637\pi\)
\(884\) −0.325122 −0.0109351
\(885\) 0 0
\(886\) 15.3433 0.515467
\(887\) 29.7170 0.997799 0.498899 0.866660i \(-0.333738\pi\)
0.498899 + 0.866660i \(0.333738\pi\)
\(888\) 5.46263 0.183314
\(889\) −2.28161 −0.0765227
\(890\) 0 0
\(891\) −23.4441 −0.785407
\(892\) 0.0870857 0.00291584
\(893\) 1.44362 0.0483089
\(894\) −59.6390 −1.99463
\(895\) 0 0
\(896\) 15.2045 0.507948
\(897\) −14.3544 −0.479279
\(898\) 8.64540 0.288501
\(899\) −1.67366 −0.0558196
\(900\) 0 0
\(901\) 17.6279 0.587269
\(902\) −4.03028 −0.134194
\(903\) 10.3726 0.345178
\(904\) 15.0556 0.500741
\(905\) 0 0
\(906\) 32.1882 1.06938
\(907\) 42.0265 1.39547 0.697733 0.716358i \(-0.254192\pi\)
0.697733 + 0.716358i \(0.254192\pi\)
\(908\) 0.117151 0.00388780
\(909\) −29.7455 −0.986597
\(910\) 0 0
\(911\) −48.7145 −1.61398 −0.806992 0.590562i \(-0.798906\pi\)
−0.806992 + 0.590562i \(0.798906\pi\)
\(912\) 4.87153 0.161313
\(913\) −2.69325 −0.0891335
\(914\) −13.0564 −0.431866
\(915\) 0 0
\(916\) 2.06606 0.0682647
\(917\) −13.4516 −0.444211
\(918\) −0.896290 −0.0295820
\(919\) 14.6475 0.483177 0.241589 0.970379i \(-0.422332\pi\)
0.241589 + 0.970379i \(0.422332\pi\)
\(920\) 0 0
\(921\) 28.5539 0.940882
\(922\) −25.0050 −0.823495
\(923\) 29.6477 0.975865
\(924\) −0.820423 −0.0269899
\(925\) 0 0
\(926\) 25.4349 0.835841
\(927\) 21.3246 0.700390
\(928\) −5.77211 −0.189479
\(929\) 45.7110 1.49973 0.749864 0.661592i \(-0.230119\pi\)
0.749864 + 0.661592i \(0.230119\pi\)
\(930\) 0 0
\(931\) 2.60830 0.0854836
\(932\) 2.27296 0.0744533
\(933\) −13.3619 −0.437448
\(934\) 6.31878 0.206757
\(935\) 0 0
\(936\) 16.0251 0.523796
\(937\) −39.7753 −1.29940 −0.649701 0.760190i \(-0.725106\pi\)
−0.649701 + 0.760190i \(0.725106\pi\)
\(938\) 9.52748 0.311083
\(939\) 59.9577 1.95665
\(940\) 0 0
\(941\) 18.0359 0.587953 0.293977 0.955813i \(-0.405021\pi\)
0.293977 + 0.955813i \(0.405021\pi\)
\(942\) −0.618362 −0.0201473
\(943\) −3.23404 −0.105315
\(944\) −1.82269 −0.0593235
\(945\) 0 0
\(946\) 12.3166 0.400446
\(947\) 34.4377 1.11908 0.559538 0.828805i \(-0.310979\pi\)
0.559538 + 0.828805i \(0.310979\pi\)
\(948\) −1.93882 −0.0629700
\(949\) −9.01534 −0.292650
\(950\) 0 0
\(951\) −38.1493 −1.23707
\(952\) 4.89093 0.158516
\(953\) 30.0386 0.973045 0.486522 0.873668i \(-0.338265\pi\)
0.486522 + 0.873668i \(0.338265\pi\)
\(954\) 50.6967 1.64137
\(955\) 0 0
\(956\) −1.90346 −0.0615622
\(957\) −55.1213 −1.78182
\(958\) 41.5108 1.34115
\(959\) −22.6237 −0.730558
\(960\) 0 0
\(961\) −30.9674 −0.998947
\(962\) −2.47985 −0.0799537
\(963\) 12.1506 0.391549
\(964\) 0.110263 0.00355132
\(965\) 0 0
\(966\) −12.5996 −0.405384
\(967\) −47.3839 −1.52376 −0.761882 0.647716i \(-0.775724\pi\)
−0.761882 + 0.647716i \(0.775724\pi\)
\(968\) −13.5009 −0.433934
\(969\) 1.64917 0.0529790
\(970\) 0 0
\(971\) 6.81587 0.218732 0.109366 0.994002i \(-0.465118\pi\)
0.109366 + 0.994002i \(0.465118\pi\)
\(972\) −2.38557 −0.0765173
\(973\) −11.5659 −0.370784
\(974\) −22.7134 −0.727784
\(975\) 0 0
\(976\) 16.3598 0.523665
\(977\) −51.4729 −1.64676 −0.823382 0.567488i \(-0.807915\pi\)
−0.823382 + 0.567488i \(0.807915\pi\)
\(978\) −32.1289 −1.02737
\(979\) −30.1269 −0.962860
\(980\) 0 0
\(981\) −8.55797 −0.273235
\(982\) 22.4145 0.715275
\(983\) −17.8746 −0.570112 −0.285056 0.958511i \(-0.592012\pi\)
−0.285056 + 0.958511i \(0.592012\pi\)
\(984\) 7.45067 0.237519
\(985\) 0 0
\(986\) −19.1734 −0.610606
\(987\) 9.07756 0.288942
\(988\) −0.109498 −0.00348359
\(989\) 9.88323 0.314268
\(990\) 0 0
\(991\) 28.7353 0.912805 0.456403 0.889773i \(-0.349138\pi\)
0.456403 + 0.889773i \(0.349138\pi\)
\(992\) 0.112555 0.00357363
\(993\) 56.6627 1.79814
\(994\) 26.0232 0.825407
\(995\) 0 0
\(996\) −0.290511 −0.00920519
\(997\) −44.7201 −1.41630 −0.708150 0.706062i \(-0.750470\pi\)
−0.708150 + 0.706062i \(0.750470\pi\)
\(998\) −2.39258 −0.0757359
\(999\) −0.357207 −0.0113015
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.1.13 46
5.2 odd 4 1205.2.b.c.724.13 46
5.3 odd 4 1205.2.b.c.724.34 yes 46
5.4 even 2 inner 6025.2.a.p.1.34 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.13 46 5.2 odd 4
1205.2.b.c.724.34 yes 46 5.3 odd 4
6025.2.a.p.1.13 46 1.1 even 1 trivial
6025.2.a.p.1.34 46 5.4 even 2 inner