Properties

Label 6025.2.a.p.1.6
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 1.6
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.95888 q^{2} +0.350465 q^{3} +1.83721 q^{4} -0.686519 q^{6} +1.14869 q^{7} +0.318879 q^{8} -2.87717 q^{9} +O(q^{10})\) \(q-1.95888 q^{2} +0.350465 q^{3} +1.83721 q^{4} -0.686519 q^{6} +1.14869 q^{7} +0.318879 q^{8} -2.87717 q^{9} +0.395421 q^{11} +0.643879 q^{12} -0.595326 q^{13} -2.25014 q^{14} -4.29907 q^{16} -7.79008 q^{17} +5.63604 q^{18} +3.25574 q^{19} +0.402575 q^{21} -0.774582 q^{22} +3.49975 q^{23} +0.111756 q^{24} +1.16617 q^{26} -2.05974 q^{27} +2.11038 q^{28} +6.23795 q^{29} -9.01707 q^{31} +7.78361 q^{32} +0.138581 q^{33} +15.2598 q^{34} -5.28598 q^{36} +0.667693 q^{37} -6.37760 q^{38} -0.208641 q^{39} +6.05766 q^{41} -0.788596 q^{42} +9.26190 q^{43} +0.726472 q^{44} -6.85559 q^{46} +13.6965 q^{47} -1.50667 q^{48} -5.68052 q^{49} -2.73015 q^{51} -1.09374 q^{52} +0.719285 q^{53} +4.03479 q^{54} +0.366293 q^{56} +1.14102 q^{57} -12.2194 q^{58} -10.8402 q^{59} +2.84725 q^{61} +17.6634 q^{62} -3.30498 q^{63} -6.64902 q^{64} -0.271464 q^{66} +1.17890 q^{67} -14.3120 q^{68} +1.22654 q^{69} -14.0182 q^{71} -0.917471 q^{72} -4.89629 q^{73} -1.30793 q^{74} +5.98148 q^{76} +0.454215 q^{77} +0.408703 q^{78} +13.1124 q^{79} +7.90966 q^{81} -11.8662 q^{82} +5.86352 q^{83} +0.739616 q^{84} -18.1429 q^{86} +2.18618 q^{87} +0.126092 q^{88} -11.3538 q^{89} -0.683844 q^{91} +6.42979 q^{92} -3.16017 q^{93} -26.8298 q^{94} +2.72788 q^{96} +0.175389 q^{97} +11.1275 q^{98} -1.13769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.95888 −1.38514 −0.692569 0.721352i \(-0.743521\pi\)
−0.692569 + 0.721352i \(0.743521\pi\)
\(3\) 0.350465 0.202341 0.101171 0.994869i \(-0.467741\pi\)
0.101171 + 0.994869i \(0.467741\pi\)
\(4\) 1.83721 0.918607
\(5\) 0 0
\(6\) −0.686519 −0.280270
\(7\) 1.14869 0.434163 0.217082 0.976153i \(-0.430346\pi\)
0.217082 + 0.976153i \(0.430346\pi\)
\(8\) 0.318879 0.112741
\(9\) −2.87717 −0.959058
\(10\) 0 0
\(11\) 0.395421 0.119224 0.0596119 0.998222i \(-0.481014\pi\)
0.0596119 + 0.998222i \(0.481014\pi\)
\(12\) 0.643879 0.185872
\(13\) −0.595326 −0.165114 −0.0825569 0.996586i \(-0.526309\pi\)
−0.0825569 + 0.996586i \(0.526309\pi\)
\(14\) −2.25014 −0.601376
\(15\) 0 0
\(16\) −4.29907 −1.07477
\(17\) −7.79008 −1.88937 −0.944686 0.327977i \(-0.893633\pi\)
−0.944686 + 0.327977i \(0.893633\pi\)
\(18\) 5.63604 1.32843
\(19\) 3.25574 0.746917 0.373459 0.927647i \(-0.378172\pi\)
0.373459 + 0.927647i \(0.378172\pi\)
\(20\) 0 0
\(21\) 0.402575 0.0878490
\(22\) −0.774582 −0.165141
\(23\) 3.49975 0.729748 0.364874 0.931057i \(-0.381112\pi\)
0.364874 + 0.931057i \(0.381112\pi\)
\(24\) 0.111756 0.0228121
\(25\) 0 0
\(26\) 1.16617 0.228705
\(27\) −2.05974 −0.396398
\(28\) 2.11038 0.398825
\(29\) 6.23795 1.15836 0.579179 0.815200i \(-0.303373\pi\)
0.579179 + 0.815200i \(0.303373\pi\)
\(30\) 0 0
\(31\) −9.01707 −1.61951 −0.809757 0.586766i \(-0.800401\pi\)
−0.809757 + 0.586766i \(0.800401\pi\)
\(32\) 7.78361 1.37596
\(33\) 0.138581 0.0241239
\(34\) 15.2598 2.61704
\(35\) 0 0
\(36\) −5.28598 −0.880997
\(37\) 0.667693 0.109768 0.0548840 0.998493i \(-0.482521\pi\)
0.0548840 + 0.998493i \(0.482521\pi\)
\(38\) −6.37760 −1.03458
\(39\) −0.208641 −0.0334093
\(40\) 0 0
\(41\) 6.05766 0.946048 0.473024 0.881050i \(-0.343162\pi\)
0.473024 + 0.881050i \(0.343162\pi\)
\(42\) −0.788596 −0.121683
\(43\) 9.26190 1.41243 0.706213 0.707999i \(-0.250402\pi\)
0.706213 + 0.707999i \(0.250402\pi\)
\(44\) 0.726472 0.109520
\(45\) 0 0
\(46\) −6.85559 −1.01080
\(47\) 13.6965 1.99784 0.998921 0.0464433i \(-0.0147887\pi\)
0.998921 + 0.0464433i \(0.0147887\pi\)
\(48\) −1.50667 −0.217470
\(49\) −5.68052 −0.811502
\(50\) 0 0
\(51\) −2.73015 −0.382297
\(52\) −1.09374 −0.151675
\(53\) 0.719285 0.0988013 0.0494007 0.998779i \(-0.484269\pi\)
0.0494007 + 0.998779i \(0.484269\pi\)
\(54\) 4.03479 0.549066
\(55\) 0 0
\(56\) 0.366293 0.0489479
\(57\) 1.14102 0.151132
\(58\) −12.2194 −1.60449
\(59\) −10.8402 −1.41127 −0.705635 0.708576i \(-0.749338\pi\)
−0.705635 + 0.708576i \(0.749338\pi\)
\(60\) 0 0
\(61\) 2.84725 0.364553 0.182276 0.983247i \(-0.441653\pi\)
0.182276 + 0.983247i \(0.441653\pi\)
\(62\) 17.6634 2.24325
\(63\) −3.30498 −0.416388
\(64\) −6.64902 −0.831128
\(65\) 0 0
\(66\) −0.271464 −0.0334149
\(67\) 1.17890 0.144026 0.0720129 0.997404i \(-0.477058\pi\)
0.0720129 + 0.997404i \(0.477058\pi\)
\(68\) −14.3120 −1.73559
\(69\) 1.22654 0.147658
\(70\) 0 0
\(71\) −14.0182 −1.66366 −0.831828 0.555033i \(-0.812706\pi\)
−0.831828 + 0.555033i \(0.812706\pi\)
\(72\) −0.917471 −0.108125
\(73\) −4.89629 −0.573067 −0.286534 0.958070i \(-0.592503\pi\)
−0.286534 + 0.958070i \(0.592503\pi\)
\(74\) −1.30793 −0.152044
\(75\) 0 0
\(76\) 5.98148 0.686123
\(77\) 0.454215 0.0517626
\(78\) 0.408703 0.0462765
\(79\) 13.1124 1.47526 0.737632 0.675203i \(-0.235944\pi\)
0.737632 + 0.675203i \(0.235944\pi\)
\(80\) 0 0
\(81\) 7.90966 0.878851
\(82\) −11.8662 −1.31041
\(83\) 5.86352 0.643604 0.321802 0.946807i \(-0.395711\pi\)
0.321802 + 0.946807i \(0.395711\pi\)
\(84\) 0.739616 0.0806987
\(85\) 0 0
\(86\) −18.1429 −1.95640
\(87\) 2.18618 0.234383
\(88\) 0.126092 0.0134414
\(89\) −11.3538 −1.20350 −0.601751 0.798683i \(-0.705530\pi\)
−0.601751 + 0.798683i \(0.705530\pi\)
\(90\) 0 0
\(91\) −0.683844 −0.0716863
\(92\) 6.42979 0.670352
\(93\) −3.16017 −0.327694
\(94\) −26.8298 −2.76729
\(95\) 0 0
\(96\) 2.72788 0.278413
\(97\) 0.175389 0.0178081 0.00890404 0.999960i \(-0.497166\pi\)
0.00890404 + 0.999960i \(0.497166\pi\)
\(98\) 11.1275 1.12404
\(99\) −1.13769 −0.114343
\(100\) 0 0
\(101\) −11.2535 −1.11976 −0.559882 0.828572i \(-0.689154\pi\)
−0.559882 + 0.828572i \(0.689154\pi\)
\(102\) 5.34804 0.529534
\(103\) 9.35760 0.922032 0.461016 0.887392i \(-0.347485\pi\)
0.461016 + 0.887392i \(0.347485\pi\)
\(104\) −0.189837 −0.0186151
\(105\) 0 0
\(106\) −1.40899 −0.136853
\(107\) −11.7603 −1.13691 −0.568456 0.822714i \(-0.692459\pi\)
−0.568456 + 0.822714i \(0.692459\pi\)
\(108\) −3.78419 −0.364134
\(109\) −4.89496 −0.468852 −0.234426 0.972134i \(-0.575321\pi\)
−0.234426 + 0.972134i \(0.575321\pi\)
\(110\) 0 0
\(111\) 0.234003 0.0222106
\(112\) −4.93829 −0.466625
\(113\) 7.26082 0.683041 0.341520 0.939874i \(-0.389058\pi\)
0.341520 + 0.939874i \(0.389058\pi\)
\(114\) −2.23512 −0.209339
\(115\) 0 0
\(116\) 11.4604 1.06408
\(117\) 1.71286 0.158354
\(118\) 21.2346 1.95480
\(119\) −8.94837 −0.820296
\(120\) 0 0
\(121\) −10.8436 −0.985786
\(122\) −5.57742 −0.504956
\(123\) 2.12300 0.191424
\(124\) −16.5663 −1.48770
\(125\) 0 0
\(126\) 6.47405 0.576754
\(127\) 12.5876 1.11697 0.558483 0.829516i \(-0.311384\pi\)
0.558483 + 0.829516i \(0.311384\pi\)
\(128\) −2.54258 −0.224735
\(129\) 3.24597 0.285792
\(130\) 0 0
\(131\) −14.3195 −1.25110 −0.625552 0.780182i \(-0.715126\pi\)
−0.625552 + 0.780182i \(0.715126\pi\)
\(132\) 0.254603 0.0221604
\(133\) 3.73982 0.324284
\(134\) −2.30933 −0.199495
\(135\) 0 0
\(136\) −2.48409 −0.213009
\(137\) −5.34099 −0.456312 −0.228156 0.973625i \(-0.573270\pi\)
−0.228156 + 0.973625i \(0.573270\pi\)
\(138\) −2.40264 −0.204527
\(139\) −13.1396 −1.11448 −0.557241 0.830351i \(-0.688140\pi\)
−0.557241 + 0.830351i \(0.688140\pi\)
\(140\) 0 0
\(141\) 4.80015 0.404245
\(142\) 27.4600 2.30439
\(143\) −0.235404 −0.0196855
\(144\) 12.3692 1.03077
\(145\) 0 0
\(146\) 9.59125 0.793777
\(147\) −1.99082 −0.164200
\(148\) 1.22669 0.100834
\(149\) −6.09589 −0.499395 −0.249697 0.968324i \(-0.580331\pi\)
−0.249697 + 0.968324i \(0.580331\pi\)
\(150\) 0 0
\(151\) −2.45933 −0.200137 −0.100069 0.994981i \(-0.531906\pi\)
−0.100069 + 0.994981i \(0.531906\pi\)
\(152\) 1.03819 0.0842081
\(153\) 22.4134 1.81202
\(154\) −0.889753 −0.0716983
\(155\) 0 0
\(156\) −0.383318 −0.0306900
\(157\) −2.93713 −0.234409 −0.117204 0.993108i \(-0.537393\pi\)
−0.117204 + 0.993108i \(0.537393\pi\)
\(158\) −25.6857 −2.04344
\(159\) 0.252084 0.0199916
\(160\) 0 0
\(161\) 4.02012 0.316830
\(162\) −15.4941 −1.21733
\(163\) 23.5480 1.84443 0.922213 0.386683i \(-0.126379\pi\)
0.922213 + 0.386683i \(0.126379\pi\)
\(164\) 11.1292 0.869046
\(165\) 0 0
\(166\) −11.4859 −0.891481
\(167\) −15.3378 −1.18688 −0.593439 0.804879i \(-0.702230\pi\)
−0.593439 + 0.804879i \(0.702230\pi\)
\(168\) 0.128373 0.00990418
\(169\) −12.6456 −0.972737
\(170\) 0 0
\(171\) −9.36732 −0.716337
\(172\) 17.0161 1.29746
\(173\) −7.62958 −0.580066 −0.290033 0.957017i \(-0.593666\pi\)
−0.290033 + 0.957017i \(0.593666\pi\)
\(174\) −4.28247 −0.324653
\(175\) 0 0
\(176\) −1.69994 −0.128138
\(177\) −3.79910 −0.285558
\(178\) 22.2408 1.66702
\(179\) 13.4465 1.00504 0.502520 0.864566i \(-0.332406\pi\)
0.502520 + 0.864566i \(0.332406\pi\)
\(180\) 0 0
\(181\) 24.3051 1.80658 0.903292 0.429027i \(-0.141144\pi\)
0.903292 + 0.429027i \(0.141144\pi\)
\(182\) 1.33957 0.0992954
\(183\) 0.997861 0.0737640
\(184\) 1.11600 0.0822725
\(185\) 0 0
\(186\) 6.19039 0.453901
\(187\) −3.08036 −0.225258
\(188\) 25.1634 1.83523
\(189\) −2.36600 −0.172101
\(190\) 0 0
\(191\) 16.5298 1.19605 0.598026 0.801476i \(-0.295952\pi\)
0.598026 + 0.801476i \(0.295952\pi\)
\(192\) −2.33025 −0.168171
\(193\) −14.0074 −1.00828 −0.504138 0.863623i \(-0.668190\pi\)
−0.504138 + 0.863623i \(0.668190\pi\)
\(194\) −0.343566 −0.0246666
\(195\) 0 0
\(196\) −10.4363 −0.745451
\(197\) −25.8379 −1.84087 −0.920437 0.390892i \(-0.872167\pi\)
−0.920437 + 0.390892i \(0.872167\pi\)
\(198\) 2.22861 0.158380
\(199\) −5.06385 −0.358967 −0.179483 0.983761i \(-0.557443\pi\)
−0.179483 + 0.983761i \(0.557443\pi\)
\(200\) 0 0
\(201\) 0.413164 0.0291423
\(202\) 22.0443 1.55103
\(203\) 7.16546 0.502916
\(204\) −5.01587 −0.351181
\(205\) 0 0
\(206\) −18.3304 −1.27714
\(207\) −10.0694 −0.699871
\(208\) 2.55935 0.177459
\(209\) 1.28739 0.0890503
\(210\) 0 0
\(211\) −12.2747 −0.845026 −0.422513 0.906357i \(-0.638852\pi\)
−0.422513 + 0.906357i \(0.638852\pi\)
\(212\) 1.32148 0.0907596
\(213\) −4.91289 −0.336626
\(214\) 23.0370 1.57478
\(215\) 0 0
\(216\) −0.656810 −0.0446902
\(217\) −10.3578 −0.703133
\(218\) 9.58864 0.649425
\(219\) −1.71598 −0.115955
\(220\) 0 0
\(221\) 4.63764 0.311961
\(222\) −0.458384 −0.0307647
\(223\) 20.5388 1.37538 0.687689 0.726005i \(-0.258625\pi\)
0.687689 + 0.726005i \(0.258625\pi\)
\(224\) 8.94094 0.597392
\(225\) 0 0
\(226\) −14.2231 −0.946106
\(227\) 15.6294 1.03736 0.518679 0.854969i \(-0.326424\pi\)
0.518679 + 0.854969i \(0.326424\pi\)
\(228\) 2.09630 0.138831
\(229\) −7.68533 −0.507861 −0.253930 0.967222i \(-0.581723\pi\)
−0.253930 + 0.967222i \(0.581723\pi\)
\(230\) 0 0
\(231\) 0.159186 0.0104737
\(232\) 1.98915 0.130594
\(233\) −28.4122 −1.86135 −0.930673 0.365851i \(-0.880778\pi\)
−0.930673 + 0.365851i \(0.880778\pi\)
\(234\) −3.35528 −0.219342
\(235\) 0 0
\(236\) −19.9157 −1.29640
\(237\) 4.59545 0.298507
\(238\) 17.5288 1.13622
\(239\) −2.95254 −0.190984 −0.0954918 0.995430i \(-0.530442\pi\)
−0.0954918 + 0.995430i \(0.530442\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 21.2414 1.36545
\(243\) 8.95129 0.574225
\(244\) 5.23100 0.334881
\(245\) 0 0
\(246\) −4.15870 −0.265149
\(247\) −1.93822 −0.123326
\(248\) −2.87536 −0.182585
\(249\) 2.05496 0.130228
\(250\) 0 0
\(251\) 12.1180 0.764879 0.382439 0.923981i \(-0.375084\pi\)
0.382439 + 0.923981i \(0.375084\pi\)
\(252\) −6.07195 −0.382497
\(253\) 1.38387 0.0870034
\(254\) −24.6575 −1.54715
\(255\) 0 0
\(256\) 18.2787 1.14242
\(257\) −28.0054 −1.74693 −0.873464 0.486888i \(-0.838132\pi\)
−0.873464 + 0.486888i \(0.838132\pi\)
\(258\) −6.35847 −0.395861
\(259\) 0.766971 0.0476572
\(260\) 0 0
\(261\) −17.9477 −1.11093
\(262\) 28.0503 1.73295
\(263\) −9.93706 −0.612746 −0.306373 0.951912i \(-0.599115\pi\)
−0.306373 + 0.951912i \(0.599115\pi\)
\(264\) 0.0441907 0.00271975
\(265\) 0 0
\(266\) −7.32587 −0.449178
\(267\) −3.97912 −0.243518
\(268\) 2.16589 0.132303
\(269\) −19.8870 −1.21253 −0.606266 0.795262i \(-0.707333\pi\)
−0.606266 + 0.795262i \(0.707333\pi\)
\(270\) 0 0
\(271\) 7.60072 0.461711 0.230855 0.972988i \(-0.425848\pi\)
0.230855 + 0.972988i \(0.425848\pi\)
\(272\) 33.4901 2.03064
\(273\) −0.239663 −0.0145051
\(274\) 10.4624 0.632055
\(275\) 0 0
\(276\) 2.25342 0.135640
\(277\) −2.57322 −0.154610 −0.0773048 0.997008i \(-0.524631\pi\)
−0.0773048 + 0.997008i \(0.524631\pi\)
\(278\) 25.7388 1.54371
\(279\) 25.9437 1.55321
\(280\) 0 0
\(281\) −4.36381 −0.260323 −0.130161 0.991493i \(-0.541550\pi\)
−0.130161 + 0.991493i \(0.541550\pi\)
\(282\) −9.40292 −0.559936
\(283\) −9.97677 −0.593058 −0.296529 0.955024i \(-0.595829\pi\)
−0.296529 + 0.955024i \(0.595829\pi\)
\(284\) −25.7545 −1.52825
\(285\) 0 0
\(286\) 0.461129 0.0272671
\(287\) 6.95836 0.410739
\(288\) −22.3948 −1.31963
\(289\) 43.6853 2.56972
\(290\) 0 0
\(291\) 0.0614678 0.00360330
\(292\) −8.99553 −0.526424
\(293\) 8.13620 0.475322 0.237661 0.971348i \(-0.423619\pi\)
0.237661 + 0.971348i \(0.423619\pi\)
\(294\) 3.89978 0.227440
\(295\) 0 0
\(296\) 0.212913 0.0123753
\(297\) −0.814465 −0.0472601
\(298\) 11.9411 0.691731
\(299\) −2.08349 −0.120491
\(300\) 0 0
\(301\) 10.6390 0.613223
\(302\) 4.81753 0.277217
\(303\) −3.94396 −0.226574
\(304\) −13.9967 −0.802763
\(305\) 0 0
\(306\) −43.9052 −2.50989
\(307\) −16.9541 −0.967624 −0.483812 0.875172i \(-0.660748\pi\)
−0.483812 + 0.875172i \(0.660748\pi\)
\(308\) 0.834490 0.0475495
\(309\) 3.27951 0.186565
\(310\) 0 0
\(311\) 17.6072 0.998412 0.499206 0.866483i \(-0.333625\pi\)
0.499206 + 0.866483i \(0.333625\pi\)
\(312\) −0.0665313 −0.00376659
\(313\) 0.775970 0.0438604 0.0219302 0.999760i \(-0.493019\pi\)
0.0219302 + 0.999760i \(0.493019\pi\)
\(314\) 5.75349 0.324688
\(315\) 0 0
\(316\) 24.0903 1.35519
\(317\) −20.2080 −1.13499 −0.567496 0.823376i \(-0.692088\pi\)
−0.567496 + 0.823376i \(0.692088\pi\)
\(318\) −0.493803 −0.0276911
\(319\) 2.46661 0.138104
\(320\) 0 0
\(321\) −4.12157 −0.230044
\(322\) −7.87494 −0.438853
\(323\) −25.3624 −1.41120
\(324\) 14.5317 0.807318
\(325\) 0 0
\(326\) −46.1278 −2.55478
\(327\) −1.71551 −0.0948680
\(328\) 1.93166 0.106658
\(329\) 15.7330 0.867389
\(330\) 0 0
\(331\) 3.47783 0.191159 0.0955794 0.995422i \(-0.469530\pi\)
0.0955794 + 0.995422i \(0.469530\pi\)
\(332\) 10.7725 0.591219
\(333\) −1.92107 −0.105274
\(334\) 30.0450 1.64399
\(335\) 0 0
\(336\) −1.73070 −0.0944174
\(337\) −28.8161 −1.56971 −0.784857 0.619677i \(-0.787263\pi\)
−0.784857 + 0.619677i \(0.787263\pi\)
\(338\) 24.7712 1.34738
\(339\) 2.54466 0.138207
\(340\) 0 0
\(341\) −3.56554 −0.193085
\(342\) 18.3495 0.992225
\(343\) −14.5660 −0.786488
\(344\) 2.95343 0.159238
\(345\) 0 0
\(346\) 14.9454 0.803472
\(347\) −2.81946 −0.151356 −0.0756782 0.997132i \(-0.524112\pi\)
−0.0756782 + 0.997132i \(0.524112\pi\)
\(348\) 4.01648 0.215306
\(349\) −2.99211 −0.160164 −0.0800820 0.996788i \(-0.525518\pi\)
−0.0800820 + 0.996788i \(0.525518\pi\)
\(350\) 0 0
\(351\) 1.22622 0.0654507
\(352\) 3.07780 0.164047
\(353\) 21.1653 1.12652 0.563259 0.826281i \(-0.309547\pi\)
0.563259 + 0.826281i \(0.309547\pi\)
\(354\) 7.44198 0.395537
\(355\) 0 0
\(356\) −20.8594 −1.10555
\(357\) −3.13609 −0.165979
\(358\) −26.3401 −1.39212
\(359\) −21.1263 −1.11500 −0.557501 0.830176i \(-0.688240\pi\)
−0.557501 + 0.830176i \(0.688240\pi\)
\(360\) 0 0
\(361\) −8.40018 −0.442115
\(362\) −47.6108 −2.50237
\(363\) −3.80032 −0.199465
\(364\) −1.25637 −0.0658515
\(365\) 0 0
\(366\) −1.95469 −0.102173
\(367\) −7.88596 −0.411644 −0.205822 0.978589i \(-0.565987\pi\)
−0.205822 + 0.978589i \(0.565987\pi\)
\(368\) −15.0457 −0.784310
\(369\) −17.4290 −0.907315
\(370\) 0 0
\(371\) 0.826233 0.0428959
\(372\) −5.80590 −0.301022
\(373\) 37.2140 1.92687 0.963434 0.267944i \(-0.0863443\pi\)
0.963434 + 0.267944i \(0.0863443\pi\)
\(374\) 6.03405 0.312014
\(375\) 0 0
\(376\) 4.36754 0.225238
\(377\) −3.71361 −0.191261
\(378\) 4.63472 0.238384
\(379\) −2.84659 −0.146219 −0.0731097 0.997324i \(-0.523292\pi\)
−0.0731097 + 0.997324i \(0.523292\pi\)
\(380\) 0 0
\(381\) 4.41150 0.226008
\(382\) −32.3799 −1.65670
\(383\) 25.2530 1.29037 0.645183 0.764028i \(-0.276781\pi\)
0.645183 + 0.764028i \(0.276781\pi\)
\(384\) −0.891087 −0.0454731
\(385\) 0 0
\(386\) 27.4388 1.39660
\(387\) −26.6481 −1.35460
\(388\) 0.322227 0.0163586
\(389\) −24.4296 −1.23863 −0.619315 0.785143i \(-0.712589\pi\)
−0.619315 + 0.785143i \(0.712589\pi\)
\(390\) 0 0
\(391\) −27.2633 −1.37877
\(392\) −1.81140 −0.0914895
\(393\) −5.01850 −0.253150
\(394\) 50.6133 2.54986
\(395\) 0 0
\(396\) −2.09019 −0.105036
\(397\) 38.2694 1.92069 0.960343 0.278822i \(-0.0899439\pi\)
0.960343 + 0.278822i \(0.0899439\pi\)
\(398\) 9.91947 0.497218
\(399\) 1.31068 0.0656159
\(400\) 0 0
\(401\) −16.9783 −0.847856 −0.423928 0.905696i \(-0.639349\pi\)
−0.423928 + 0.905696i \(0.639349\pi\)
\(402\) −0.809338 −0.0403661
\(403\) 5.36809 0.267404
\(404\) −20.6751 −1.02862
\(405\) 0 0
\(406\) −14.0363 −0.696609
\(407\) 0.264020 0.0130870
\(408\) −0.870588 −0.0431005
\(409\) −22.7177 −1.12332 −0.561659 0.827369i \(-0.689837\pi\)
−0.561659 + 0.827369i \(0.689837\pi\)
\(410\) 0 0
\(411\) −1.87183 −0.0923306
\(412\) 17.1919 0.846985
\(413\) −12.4520 −0.612721
\(414\) 19.7247 0.969418
\(415\) 0 0
\(416\) −4.63379 −0.227190
\(417\) −4.60495 −0.225505
\(418\) −2.52183 −0.123347
\(419\) −16.7307 −0.817346 −0.408673 0.912681i \(-0.634008\pi\)
−0.408673 + 0.912681i \(0.634008\pi\)
\(420\) 0 0
\(421\) −24.0746 −1.17333 −0.586663 0.809831i \(-0.699559\pi\)
−0.586663 + 0.809831i \(0.699559\pi\)
\(422\) 24.0447 1.17048
\(423\) −39.4073 −1.91605
\(424\) 0.229365 0.0111389
\(425\) 0 0
\(426\) 9.62377 0.466273
\(427\) 3.27060 0.158275
\(428\) −21.6062 −1.04437
\(429\) −0.0825009 −0.00398318
\(430\) 0 0
\(431\) 22.8880 1.10248 0.551239 0.834348i \(-0.314155\pi\)
0.551239 + 0.834348i \(0.314155\pi\)
\(432\) 8.85499 0.426036
\(433\) −27.4679 −1.32002 −0.660011 0.751256i \(-0.729448\pi\)
−0.660011 + 0.751256i \(0.729448\pi\)
\(434\) 20.2897 0.973936
\(435\) 0 0
\(436\) −8.99309 −0.430691
\(437\) 11.3943 0.545062
\(438\) 3.36140 0.160614
\(439\) −0.960670 −0.0458503 −0.0229251 0.999737i \(-0.507298\pi\)
−0.0229251 + 0.999737i \(0.507298\pi\)
\(440\) 0 0
\(441\) 16.3438 0.778278
\(442\) −9.08457 −0.432109
\(443\) −22.0797 −1.04904 −0.524519 0.851399i \(-0.675755\pi\)
−0.524519 + 0.851399i \(0.675755\pi\)
\(444\) 0.429913 0.0204028
\(445\) 0 0
\(446\) −40.2330 −1.90509
\(447\) −2.13640 −0.101048
\(448\) −7.63765 −0.360845
\(449\) 20.6202 0.973128 0.486564 0.873645i \(-0.338250\pi\)
0.486564 + 0.873645i \(0.338250\pi\)
\(450\) 0 0
\(451\) 2.39533 0.112791
\(452\) 13.3397 0.627446
\(453\) −0.861907 −0.0404959
\(454\) −30.6161 −1.43689
\(455\) 0 0
\(456\) 0.363848 0.0170388
\(457\) 17.3096 0.809711 0.404855 0.914381i \(-0.367322\pi\)
0.404855 + 0.914381i \(0.367322\pi\)
\(458\) 15.0546 0.703457
\(459\) 16.0456 0.748943
\(460\) 0 0
\(461\) 9.15093 0.426201 0.213101 0.977030i \(-0.431644\pi\)
0.213101 + 0.977030i \(0.431644\pi\)
\(462\) −0.311827 −0.0145075
\(463\) −14.2244 −0.661063 −0.330532 0.943795i \(-0.607228\pi\)
−0.330532 + 0.943795i \(0.607228\pi\)
\(464\) −26.8174 −1.24497
\(465\) 0 0
\(466\) 55.6562 2.57822
\(467\) −16.2381 −0.751411 −0.375705 0.926739i \(-0.622600\pi\)
−0.375705 + 0.926739i \(0.622600\pi\)
\(468\) 3.14688 0.145465
\(469\) 1.35419 0.0625307
\(470\) 0 0
\(471\) −1.02936 −0.0474305
\(472\) −3.45670 −0.159108
\(473\) 3.66235 0.168395
\(474\) −9.00194 −0.413473
\(475\) 0 0
\(476\) −16.4401 −0.753529
\(477\) −2.06951 −0.0947562
\(478\) 5.78367 0.264539
\(479\) 32.4129 1.48098 0.740492 0.672066i \(-0.234593\pi\)
0.740492 + 0.672066i \(0.234593\pi\)
\(480\) 0 0
\(481\) −0.397495 −0.0181242
\(482\) −1.95888 −0.0892246
\(483\) 1.40891 0.0641077
\(484\) −19.9221 −0.905549
\(485\) 0 0
\(486\) −17.5345 −0.795381
\(487\) 20.8714 0.945772 0.472886 0.881123i \(-0.343212\pi\)
0.472886 + 0.881123i \(0.343212\pi\)
\(488\) 0.907929 0.0411000
\(489\) 8.25276 0.373203
\(490\) 0 0
\(491\) −1.44239 −0.0650941 −0.0325471 0.999470i \(-0.510362\pi\)
−0.0325471 + 0.999470i \(0.510362\pi\)
\(492\) 3.90040 0.175844
\(493\) −48.5941 −2.18857
\(494\) 3.79675 0.170824
\(495\) 0 0
\(496\) 38.7650 1.74060
\(497\) −16.1026 −0.722299
\(498\) −4.02541 −0.180383
\(499\) 12.2754 0.549524 0.274762 0.961512i \(-0.411401\pi\)
0.274762 + 0.961512i \(0.411401\pi\)
\(500\) 0 0
\(501\) −5.37537 −0.240154
\(502\) −23.7376 −1.05946
\(503\) −22.8011 −1.01665 −0.508325 0.861165i \(-0.669735\pi\)
−0.508325 + 0.861165i \(0.669735\pi\)
\(504\) −1.05389 −0.0469439
\(505\) 0 0
\(506\) −2.71084 −0.120512
\(507\) −4.43183 −0.196825
\(508\) 23.1260 1.02605
\(509\) −34.5559 −1.53166 −0.765831 0.643041i \(-0.777672\pi\)
−0.765831 + 0.643041i \(0.777672\pi\)
\(510\) 0 0
\(511\) −5.62431 −0.248805
\(512\) −30.7206 −1.35767
\(513\) −6.70598 −0.296076
\(514\) 54.8592 2.41974
\(515\) 0 0
\(516\) 5.96354 0.262530
\(517\) 5.41589 0.238190
\(518\) −1.50240 −0.0660118
\(519\) −2.67390 −0.117371
\(520\) 0 0
\(521\) −16.4128 −0.719056 −0.359528 0.933134i \(-0.617062\pi\)
−0.359528 + 0.933134i \(0.617062\pi\)
\(522\) 35.1573 1.53879
\(523\) 22.5542 0.986228 0.493114 0.869965i \(-0.335859\pi\)
0.493114 + 0.869965i \(0.335859\pi\)
\(524\) −26.3081 −1.14927
\(525\) 0 0
\(526\) 19.4655 0.848737
\(527\) 70.2437 3.05986
\(528\) −0.595770 −0.0259276
\(529\) −10.7517 −0.467467
\(530\) 0 0
\(531\) 31.1890 1.35349
\(532\) 6.87086 0.297889
\(533\) −3.60628 −0.156205
\(534\) 7.79462 0.337306
\(535\) 0 0
\(536\) 0.375927 0.0162376
\(537\) 4.71253 0.203361
\(538\) 38.9562 1.67952
\(539\) −2.24619 −0.0967504
\(540\) 0 0
\(541\) −23.0909 −0.992757 −0.496379 0.868106i \(-0.665337\pi\)
−0.496379 + 0.868106i \(0.665337\pi\)
\(542\) −14.8889 −0.639533
\(543\) 8.51808 0.365546
\(544\) −60.6350 −2.59970
\(545\) 0 0
\(546\) 0.469472 0.0200915
\(547\) −14.5566 −0.622395 −0.311198 0.950345i \(-0.600730\pi\)
−0.311198 + 0.950345i \(0.600730\pi\)
\(548\) −9.81254 −0.419171
\(549\) −8.19203 −0.349627
\(550\) 0 0
\(551\) 20.3091 0.865197
\(552\) 0.391118 0.0166471
\(553\) 15.0621 0.640506
\(554\) 5.04063 0.214156
\(555\) 0 0
\(556\) −24.1402 −1.02377
\(557\) 8.58684 0.363836 0.181918 0.983314i \(-0.441769\pi\)
0.181918 + 0.983314i \(0.441769\pi\)
\(558\) −50.8206 −2.15141
\(559\) −5.51385 −0.233211
\(560\) 0 0
\(561\) −1.07956 −0.0455790
\(562\) 8.54818 0.360583
\(563\) −6.54355 −0.275778 −0.137889 0.990448i \(-0.544032\pi\)
−0.137889 + 0.990448i \(0.544032\pi\)
\(564\) 8.81890 0.371343
\(565\) 0 0
\(566\) 19.5433 0.821466
\(567\) 9.08573 0.381565
\(568\) −4.47012 −0.187562
\(569\) −45.8495 −1.92211 −0.961056 0.276355i \(-0.910874\pi\)
−0.961056 + 0.276355i \(0.910874\pi\)
\(570\) 0 0
\(571\) −8.61219 −0.360409 −0.180205 0.983629i \(-0.557676\pi\)
−0.180205 + 0.983629i \(0.557676\pi\)
\(572\) −0.432488 −0.0180832
\(573\) 5.79311 0.242011
\(574\) −13.6306 −0.568930
\(575\) 0 0
\(576\) 19.1304 0.797100
\(577\) −8.25954 −0.343849 −0.171925 0.985110i \(-0.554999\pi\)
−0.171925 + 0.985110i \(0.554999\pi\)
\(578\) −85.5743 −3.55942
\(579\) −4.90911 −0.204015
\(580\) 0 0
\(581\) 6.73535 0.279429
\(582\) −0.120408 −0.00499107
\(583\) 0.284420 0.0117795
\(584\) −1.56133 −0.0646081
\(585\) 0 0
\(586\) −15.9378 −0.658386
\(587\) −9.63478 −0.397670 −0.198835 0.980033i \(-0.563716\pi\)
−0.198835 + 0.980033i \(0.563716\pi\)
\(588\) −3.65756 −0.150835
\(589\) −29.3572 −1.20964
\(590\) 0 0
\(591\) −9.05527 −0.372484
\(592\) −2.87046 −0.117975
\(593\) −22.0788 −0.906668 −0.453334 0.891341i \(-0.649766\pi\)
−0.453334 + 0.891341i \(0.649766\pi\)
\(594\) 1.59544 0.0654617
\(595\) 0 0
\(596\) −11.1995 −0.458747
\(597\) −1.77470 −0.0726337
\(598\) 4.08131 0.166897
\(599\) −26.5132 −1.08330 −0.541650 0.840604i \(-0.682200\pi\)
−0.541650 + 0.840604i \(0.682200\pi\)
\(600\) 0 0
\(601\) 31.0912 1.26823 0.634117 0.773237i \(-0.281364\pi\)
0.634117 + 0.773237i \(0.281364\pi\)
\(602\) −20.8406 −0.849399
\(603\) −3.39190 −0.138129
\(604\) −4.51831 −0.183847
\(605\) 0 0
\(606\) 7.72574 0.313837
\(607\) −5.83591 −0.236872 −0.118436 0.992962i \(-0.537788\pi\)
−0.118436 + 0.992962i \(0.537788\pi\)
\(608\) 25.3414 1.02773
\(609\) 2.51124 0.101761
\(610\) 0 0
\(611\) −8.15389 −0.329871
\(612\) 41.1782 1.66453
\(613\) 7.15782 0.289101 0.144551 0.989497i \(-0.453826\pi\)
0.144551 + 0.989497i \(0.453826\pi\)
\(614\) 33.2111 1.34029
\(615\) 0 0
\(616\) 0.144840 0.00583576
\(617\) 7.92936 0.319224 0.159612 0.987180i \(-0.448976\pi\)
0.159612 + 0.987180i \(0.448976\pi\)
\(618\) −6.42417 −0.258418
\(619\) −27.1369 −1.09072 −0.545362 0.838200i \(-0.683608\pi\)
−0.545362 + 0.838200i \(0.683608\pi\)
\(620\) 0 0
\(621\) −7.20859 −0.289271
\(622\) −34.4904 −1.38294
\(623\) −13.0420 −0.522517
\(624\) 0.896962 0.0359072
\(625\) 0 0
\(626\) −1.52003 −0.0607527
\(627\) 0.451184 0.0180185
\(628\) −5.39614 −0.215329
\(629\) −5.20138 −0.207393
\(630\) 0 0
\(631\) 21.9630 0.874333 0.437167 0.899380i \(-0.355982\pi\)
0.437167 + 0.899380i \(0.355982\pi\)
\(632\) 4.18129 0.166323
\(633\) −4.30185 −0.170983
\(634\) 39.5850 1.57212
\(635\) 0 0
\(636\) 0.463132 0.0183644
\(637\) 3.38176 0.133990
\(638\) −4.83180 −0.191293
\(639\) 40.3329 1.59554
\(640\) 0 0
\(641\) 8.90572 0.351755 0.175877 0.984412i \(-0.443724\pi\)
0.175877 + 0.984412i \(0.443724\pi\)
\(642\) 8.07367 0.318642
\(643\) −33.1787 −1.30844 −0.654221 0.756303i \(-0.727003\pi\)
−0.654221 + 0.756303i \(0.727003\pi\)
\(644\) 7.38582 0.291042
\(645\) 0 0
\(646\) 49.6820 1.95471
\(647\) 45.8517 1.80262 0.901309 0.433176i \(-0.142607\pi\)
0.901309 + 0.433176i \(0.142607\pi\)
\(648\) 2.52223 0.0990824
\(649\) −4.28643 −0.168257
\(650\) 0 0
\(651\) −3.63004 −0.142273
\(652\) 43.2628 1.69430
\(653\) −12.5825 −0.492390 −0.246195 0.969220i \(-0.579180\pi\)
−0.246195 + 0.969220i \(0.579180\pi\)
\(654\) 3.36048 0.131405
\(655\) 0 0
\(656\) −26.0423 −1.01678
\(657\) 14.0875 0.549605
\(658\) −30.8191 −1.20145
\(659\) 47.3761 1.84551 0.922756 0.385385i \(-0.125931\pi\)
0.922756 + 0.385385i \(0.125931\pi\)
\(660\) 0 0
\(661\) 14.2092 0.552675 0.276338 0.961061i \(-0.410879\pi\)
0.276338 + 0.961061i \(0.410879\pi\)
\(662\) −6.81266 −0.264781
\(663\) 1.62533 0.0631225
\(664\) 1.86975 0.0725605
\(665\) 0 0
\(666\) 3.76314 0.145819
\(667\) 21.8313 0.845310
\(668\) −28.1789 −1.09027
\(669\) 7.19812 0.278295
\(670\) 0 0
\(671\) 1.12586 0.0434634
\(672\) 3.13349 0.120877
\(673\) −4.54188 −0.175077 −0.0875384 0.996161i \(-0.527900\pi\)
−0.0875384 + 0.996161i \(0.527900\pi\)
\(674\) 56.4473 2.17427
\(675\) 0 0
\(676\) −23.2326 −0.893563
\(677\) −33.7570 −1.29739 −0.648694 0.761050i \(-0.724684\pi\)
−0.648694 + 0.761050i \(0.724684\pi\)
\(678\) −4.98469 −0.191436
\(679\) 0.201467 0.00773161
\(680\) 0 0
\(681\) 5.47755 0.209900
\(682\) 6.98446 0.267449
\(683\) −17.9641 −0.687376 −0.343688 0.939084i \(-0.611676\pi\)
−0.343688 + 0.939084i \(0.611676\pi\)
\(684\) −17.2098 −0.658032
\(685\) 0 0
\(686\) 28.5330 1.08939
\(687\) −2.69344 −0.102761
\(688\) −39.8176 −1.51803
\(689\) −0.428209 −0.0163135
\(690\) 0 0
\(691\) −23.3108 −0.886785 −0.443392 0.896328i \(-0.646225\pi\)
−0.443392 + 0.896328i \(0.646225\pi\)
\(692\) −14.0172 −0.532853
\(693\) −1.30686 −0.0496433
\(694\) 5.52298 0.209650
\(695\) 0 0
\(696\) 0.697128 0.0264246
\(697\) −47.1897 −1.78744
\(698\) 5.86119 0.221849
\(699\) −9.95749 −0.376627
\(700\) 0 0
\(701\) −31.4253 −1.18692 −0.593458 0.804865i \(-0.702238\pi\)
−0.593458 + 0.804865i \(0.702238\pi\)
\(702\) −2.40202 −0.0906583
\(703\) 2.17383 0.0819876
\(704\) −2.62916 −0.0990902
\(705\) 0 0
\(706\) −41.4604 −1.56038
\(707\) −12.9268 −0.486161
\(708\) −6.97975 −0.262315
\(709\) −33.0144 −1.23988 −0.619941 0.784648i \(-0.712844\pi\)
−0.619941 + 0.784648i \(0.712844\pi\)
\(710\) 0 0
\(711\) −37.7268 −1.41486
\(712\) −3.62050 −0.135684
\(713\) −31.5575 −1.18184
\(714\) 6.14322 0.229904
\(715\) 0 0
\(716\) 24.7041 0.923236
\(717\) −1.03476 −0.0386438
\(718\) 41.3839 1.54443
\(719\) 29.1086 1.08557 0.542785 0.839872i \(-0.317370\pi\)
0.542785 + 0.839872i \(0.317370\pi\)
\(720\) 0 0
\(721\) 10.7490 0.400312
\(722\) 16.4550 0.612390
\(723\) 0.350465 0.0130339
\(724\) 44.6536 1.65954
\(725\) 0 0
\(726\) 7.44437 0.276286
\(727\) 38.7905 1.43866 0.719330 0.694668i \(-0.244449\pi\)
0.719330 + 0.694668i \(0.244449\pi\)
\(728\) −0.218064 −0.00808198
\(729\) −20.5919 −0.762661
\(730\) 0 0
\(731\) −72.1509 −2.66860
\(732\) 1.83328 0.0677601
\(733\) 41.6461 1.53823 0.769117 0.639108i \(-0.220696\pi\)
0.769117 + 0.639108i \(0.220696\pi\)
\(734\) 15.4477 0.570183
\(735\) 0 0
\(736\) 27.2407 1.00411
\(737\) 0.466162 0.0171713
\(738\) 34.1412 1.25676
\(739\) −27.7225 −1.01979 −0.509894 0.860237i \(-0.670315\pi\)
−0.509894 + 0.860237i \(0.670315\pi\)
\(740\) 0 0
\(741\) −0.679280 −0.0249540
\(742\) −1.61849 −0.0594167
\(743\) 0.633484 0.0232403 0.0116201 0.999932i \(-0.496301\pi\)
0.0116201 + 0.999932i \(0.496301\pi\)
\(744\) −1.00771 −0.0369445
\(745\) 0 0
\(746\) −72.8978 −2.66898
\(747\) −16.8704 −0.617254
\(748\) −5.65928 −0.206924
\(749\) −13.5089 −0.493605
\(750\) 0 0
\(751\) −42.8427 −1.56335 −0.781677 0.623684i \(-0.785635\pi\)
−0.781677 + 0.623684i \(0.785635\pi\)
\(752\) −58.8823 −2.14722
\(753\) 4.24692 0.154766
\(754\) 7.27452 0.264923
\(755\) 0 0
\(756\) −4.34685 −0.158093
\(757\) −52.4715 −1.90711 −0.953554 0.301221i \(-0.902606\pi\)
−0.953554 + 0.301221i \(0.902606\pi\)
\(758\) 5.57612 0.202534
\(759\) 0.484999 0.0176044
\(760\) 0 0
\(761\) 18.1523 0.658022 0.329011 0.944326i \(-0.393285\pi\)
0.329011 + 0.944326i \(0.393285\pi\)
\(762\) −8.64160 −0.313052
\(763\) −5.62278 −0.203558
\(764\) 30.3687 1.09870
\(765\) 0 0
\(766\) −49.4676 −1.78734
\(767\) 6.45343 0.233020
\(768\) 6.40603 0.231158
\(769\) −1.59167 −0.0573971 −0.0286986 0.999588i \(-0.509136\pi\)
−0.0286986 + 0.999588i \(0.509136\pi\)
\(770\) 0 0
\(771\) −9.81491 −0.353475
\(772\) −25.7346 −0.926209
\(773\) −8.08891 −0.290938 −0.145469 0.989363i \(-0.546469\pi\)
−0.145469 + 0.989363i \(0.546469\pi\)
\(774\) 52.2004 1.87631
\(775\) 0 0
\(776\) 0.0559280 0.00200770
\(777\) 0.268796 0.00964302
\(778\) 47.8547 1.71567
\(779\) 19.7222 0.706619
\(780\) 0 0
\(781\) −5.54310 −0.198348
\(782\) 53.4056 1.90978
\(783\) −12.8486 −0.459171
\(784\) 24.4210 0.872177
\(785\) 0 0
\(786\) 9.83064 0.350647
\(787\) 13.2956 0.473936 0.236968 0.971518i \(-0.423846\pi\)
0.236968 + 0.971518i \(0.423846\pi\)
\(788\) −47.4697 −1.69104
\(789\) −3.48259 −0.123984
\(790\) 0 0
\(791\) 8.34042 0.296551
\(792\) −0.362787 −0.0128911
\(793\) −1.69504 −0.0601927
\(794\) −74.9652 −2.66041
\(795\) 0 0
\(796\) −9.30337 −0.329749
\(797\) 15.6546 0.554515 0.277258 0.960796i \(-0.410574\pi\)
0.277258 + 0.960796i \(0.410574\pi\)
\(798\) −2.56746 −0.0908871
\(799\) −106.697 −3.77467
\(800\) 0 0
\(801\) 32.6669 1.15423
\(802\) 33.2585 1.17440
\(803\) −1.93609 −0.0683233
\(804\) 0.759070 0.0267703
\(805\) 0 0
\(806\) −10.5155 −0.370391
\(807\) −6.96969 −0.245345
\(808\) −3.58851 −0.126243
\(809\) −52.3375 −1.84009 −0.920045 0.391813i \(-0.871848\pi\)
−0.920045 + 0.391813i \(0.871848\pi\)
\(810\) 0 0
\(811\) 32.0875 1.12675 0.563373 0.826203i \(-0.309504\pi\)
0.563373 + 0.826203i \(0.309504\pi\)
\(812\) 13.1645 0.461982
\(813\) 2.66378 0.0934230
\(814\) −0.517183 −0.0181273
\(815\) 0 0
\(816\) 11.7371 0.410881
\(817\) 30.1543 1.05497
\(818\) 44.5013 1.55595
\(819\) 1.96754 0.0687513
\(820\) 0 0
\(821\) −37.5310 −1.30984 −0.654920 0.755698i \(-0.727298\pi\)
−0.654920 + 0.755698i \(0.727298\pi\)
\(822\) 3.66669 0.127891
\(823\) −36.0696 −1.25731 −0.628654 0.777685i \(-0.716394\pi\)
−0.628654 + 0.777685i \(0.716394\pi\)
\(824\) 2.98395 0.103951
\(825\) 0 0
\(826\) 24.3919 0.848703
\(827\) −40.8256 −1.41964 −0.709822 0.704381i \(-0.751225\pi\)
−0.709822 + 0.704381i \(0.751225\pi\)
\(828\) −18.4996 −0.642906
\(829\) 9.33570 0.324242 0.162121 0.986771i \(-0.448166\pi\)
0.162121 + 0.986771i \(0.448166\pi\)
\(830\) 0 0
\(831\) −0.901823 −0.0312839
\(832\) 3.95834 0.137231
\(833\) 44.2517 1.53323
\(834\) 9.02055 0.312356
\(835\) 0 0
\(836\) 2.36520 0.0818022
\(837\) 18.5728 0.641971
\(838\) 32.7733 1.13214
\(839\) −38.9297 −1.34400 −0.672002 0.740549i \(-0.734565\pi\)
−0.672002 + 0.740549i \(0.734565\pi\)
\(840\) 0 0
\(841\) 9.91200 0.341793
\(842\) 47.1593 1.62522
\(843\) −1.52936 −0.0526740
\(844\) −22.5513 −0.776246
\(845\) 0 0
\(846\) 77.1941 2.65399
\(847\) −12.4560 −0.427992
\(848\) −3.09226 −0.106189
\(849\) −3.49651 −0.120000
\(850\) 0 0
\(851\) 2.33676 0.0801030
\(852\) −9.02604 −0.309227
\(853\) −18.9683 −0.649462 −0.324731 0.945806i \(-0.605274\pi\)
−0.324731 + 0.945806i \(0.605274\pi\)
\(854\) −6.40671 −0.219233
\(855\) 0 0
\(856\) −3.75012 −0.128176
\(857\) −9.99880 −0.341552 −0.170776 0.985310i \(-0.554628\pi\)
−0.170776 + 0.985310i \(0.554628\pi\)
\(858\) 0.161609 0.00551726
\(859\) 38.2098 1.30370 0.651852 0.758347i \(-0.273993\pi\)
0.651852 + 0.758347i \(0.273993\pi\)
\(860\) 0 0
\(861\) 2.43866 0.0831094
\(862\) −44.8349 −1.52708
\(863\) −30.2182 −1.02864 −0.514320 0.857598i \(-0.671956\pi\)
−0.514320 + 0.857598i \(0.671956\pi\)
\(864\) −16.0322 −0.545428
\(865\) 0 0
\(866\) 53.8063 1.82841
\(867\) 15.3102 0.519961
\(868\) −19.0295 −0.645903
\(869\) 5.18493 0.175887
\(870\) 0 0
\(871\) −0.701831 −0.0237806
\(872\) −1.56090 −0.0528588
\(873\) −0.504625 −0.0170790
\(874\) −22.3200 −0.754985
\(875\) 0 0
\(876\) −3.15262 −0.106517
\(877\) −51.3849 −1.73515 −0.867573 0.497310i \(-0.834321\pi\)
−0.867573 + 0.497310i \(0.834321\pi\)
\(878\) 1.88184 0.0635090
\(879\) 2.85145 0.0961771
\(880\) 0 0
\(881\) −37.5670 −1.26566 −0.632832 0.774289i \(-0.718107\pi\)
−0.632832 + 0.774289i \(0.718107\pi\)
\(882\) −32.0156 −1.07802
\(883\) −33.6934 −1.13387 −0.566937 0.823761i \(-0.691872\pi\)
−0.566937 + 0.823761i \(0.691872\pi\)
\(884\) 8.52033 0.286570
\(885\) 0 0
\(886\) 43.2515 1.45306
\(887\) 3.08274 0.103508 0.0517541 0.998660i \(-0.483519\pi\)
0.0517541 + 0.998660i \(0.483519\pi\)
\(888\) 0.0746187 0.00250404
\(889\) 14.4592 0.484945
\(890\) 0 0
\(891\) 3.12764 0.104780
\(892\) 37.7341 1.26343
\(893\) 44.5922 1.49222
\(894\) 4.18494 0.139965
\(895\) 0 0
\(896\) −2.92064 −0.0975716
\(897\) −0.730191 −0.0243804
\(898\) −40.3926 −1.34792
\(899\) −56.2480 −1.87598
\(900\) 0 0
\(901\) −5.60328 −0.186672
\(902\) −4.69216 −0.156232
\(903\) 3.72861 0.124080
\(904\) 2.31533 0.0770066
\(905\) 0 0
\(906\) 1.68837 0.0560925
\(907\) −15.3474 −0.509603 −0.254801 0.966993i \(-0.582010\pi\)
−0.254801 + 0.966993i \(0.582010\pi\)
\(908\) 28.7145 0.952925
\(909\) 32.3783 1.07392
\(910\) 0 0
\(911\) 1.34862 0.0446818 0.0223409 0.999750i \(-0.492888\pi\)
0.0223409 + 0.999750i \(0.492888\pi\)
\(912\) −4.90534 −0.162432
\(913\) 2.31856 0.0767330
\(914\) −33.9075 −1.12156
\(915\) 0 0
\(916\) −14.1196 −0.466525
\(917\) −16.4487 −0.543184
\(918\) −31.4313 −1.03739
\(919\) 34.5210 1.13874 0.569371 0.822081i \(-0.307187\pi\)
0.569371 + 0.822081i \(0.307187\pi\)
\(920\) 0 0
\(921\) −5.94183 −0.195790
\(922\) −17.9256 −0.590348
\(923\) 8.34541 0.274693
\(924\) 0.292459 0.00962121
\(925\) 0 0
\(926\) 27.8639 0.915663
\(927\) −26.9234 −0.884282
\(928\) 48.5538 1.59386
\(929\) 25.8554 0.848287 0.424144 0.905595i \(-0.360575\pi\)
0.424144 + 0.905595i \(0.360575\pi\)
\(930\) 0 0
\(931\) −18.4943 −0.606125
\(932\) −52.1993 −1.70985
\(933\) 6.17070 0.202020
\(934\) 31.8086 1.04081
\(935\) 0 0
\(936\) 0.546195 0.0178529
\(937\) 7.11017 0.232279 0.116140 0.993233i \(-0.462948\pi\)
0.116140 + 0.993233i \(0.462948\pi\)
\(938\) −2.65270 −0.0866136
\(939\) 0.271950 0.00887476
\(940\) 0 0
\(941\) −16.9120 −0.551317 −0.275658 0.961256i \(-0.588896\pi\)
−0.275658 + 0.961256i \(0.588896\pi\)
\(942\) 2.01640 0.0656978
\(943\) 21.2003 0.690377
\(944\) 46.6027 1.51679
\(945\) 0 0
\(946\) −7.17410 −0.233250
\(947\) −44.2056 −1.43649 −0.718244 0.695791i \(-0.755054\pi\)
−0.718244 + 0.695791i \(0.755054\pi\)
\(948\) 8.44282 0.274210
\(949\) 2.91489 0.0946213
\(950\) 0 0
\(951\) −7.08218 −0.229655
\(952\) −2.85345 −0.0924808
\(953\) −39.1355 −1.26772 −0.633862 0.773446i \(-0.718531\pi\)
−0.633862 + 0.773446i \(0.718531\pi\)
\(954\) 4.05392 0.131250
\(955\) 0 0
\(956\) −5.42444 −0.175439
\(957\) 0.864462 0.0279441
\(958\) −63.4930 −2.05137
\(959\) −6.13513 −0.198114
\(960\) 0 0
\(961\) 50.3075 1.62282
\(962\) 0.778645 0.0251045
\(963\) 33.8364 1.09036
\(964\) 1.83721 0.0591727
\(965\) 0 0
\(966\) −2.75989 −0.0887980
\(967\) 38.7564 1.24632 0.623161 0.782094i \(-0.285848\pi\)
0.623161 + 0.782094i \(0.285848\pi\)
\(968\) −3.45781 −0.111138
\(969\) −8.88865 −0.285544
\(970\) 0 0
\(971\) −35.9268 −1.15295 −0.576473 0.817116i \(-0.695572\pi\)
−0.576473 + 0.817116i \(0.695572\pi\)
\(972\) 16.4454 0.527487
\(973\) −15.0932 −0.483867
\(974\) −40.8845 −1.31003
\(975\) 0 0
\(976\) −12.2405 −0.391810
\(977\) 1.39554 0.0446474 0.0223237 0.999751i \(-0.492894\pi\)
0.0223237 + 0.999751i \(0.492894\pi\)
\(978\) −16.1662 −0.516937
\(979\) −4.48954 −0.143486
\(980\) 0 0
\(981\) 14.0837 0.449656
\(982\) 2.82547 0.0901643
\(983\) 3.40982 0.108756 0.0543782 0.998520i \(-0.482682\pi\)
0.0543782 + 0.998520i \(0.482682\pi\)
\(984\) 0.676980 0.0215813
\(985\) 0 0
\(986\) 95.1900 3.03147
\(987\) 5.51387 0.175508
\(988\) −3.56093 −0.113288
\(989\) 32.4143 1.03072
\(990\) 0 0
\(991\) −21.1169 −0.670799 −0.335400 0.942076i \(-0.608871\pi\)
−0.335400 + 0.942076i \(0.608871\pi\)
\(992\) −70.1854 −2.22839
\(993\) 1.21886 0.0386793
\(994\) 31.5430 1.00048
\(995\) 0 0
\(996\) 3.77539 0.119628
\(997\) 12.2441 0.387775 0.193888 0.981024i \(-0.437890\pi\)
0.193888 + 0.981024i \(0.437890\pi\)
\(998\) −24.0461 −0.761166
\(999\) −1.37528 −0.0435118
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.1.6 46
5.2 odd 4 1205.2.b.c.724.6 46
5.3 odd 4 1205.2.b.c.724.41 yes 46
5.4 even 2 inner 6025.2.a.p.1.41 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.6 46 5.2 odd 4
1205.2.b.c.724.41 yes 46 5.3 odd 4
6025.2.a.p.1.6 46 1.1 even 1 trivial
6025.2.a.p.1.41 46 5.4 even 2 inner