Properties

Label 5610.2.a.i.1.1
Level $5610$
Weight $2$
Character 5610.1
Self dual yes
Analytic conductor $44.796$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5610.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.7960755339\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 5610.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} -2.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -6.00000 q^{19} +1.00000 q^{20} -2.00000 q^{21} +1.00000 q^{22} -6.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} +2.00000 q^{28} +2.00000 q^{29} +1.00000 q^{30} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +2.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} +6.00000 q^{38} +4.00000 q^{39} -1.00000 q^{40} -2.00000 q^{41} +2.00000 q^{42} -2.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} +6.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} -4.00000 q^{52} -4.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -2.00000 q^{56} +6.00000 q^{57} -2.00000 q^{58} +14.0000 q^{59} -1.00000 q^{60} +10.0000 q^{61} +2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} -1.00000 q^{66} +8.00000 q^{67} -1.00000 q^{68} +6.00000 q^{69} -2.00000 q^{70} -6.00000 q^{71} -1.00000 q^{72} +4.00000 q^{73} +6.00000 q^{74} -1.00000 q^{75} -6.00000 q^{76} -2.00000 q^{77} -4.00000 q^{78} +14.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +12.0000 q^{83} -2.00000 q^{84} -1.00000 q^{85} +2.00000 q^{86} -2.00000 q^{87} +1.00000 q^{88} +6.00000 q^{89} -1.00000 q^{90} -8.00000 q^{91} -6.00000 q^{92} -8.00000 q^{94} -6.00000 q^{95} +1.00000 q^{96} +14.0000 q^{97} +3.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.00000 0.408248
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) −1.00000 −0.301511
\(12\) −1.00000 −0.288675
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −2.00000 −0.534522
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.00000 −0.436436
\(22\) 1.00000 0.213201
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 4.00000 0.784465
\(27\) −1.00000 −0.192450
\(28\) 2.00000 0.377964
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 1.00000 0.182574
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) 1.00000 0.171499
\(35\) 2.00000 0.338062
\(36\) 1.00000 0.166667
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 6.00000 0.973329
\(39\) 4.00000 0.640513
\(40\) −1.00000 −0.158114
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 2.00000 0.308607
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) −1.00000 −0.150756
\(45\) 1.00000 0.149071
\(46\) 6.00000 0.884652
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.00000 −0.428571
\(50\) −1.00000 −0.141421
\(51\) 1.00000 0.140028
\(52\) −4.00000 −0.554700
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 1.00000 0.136083
\(55\) −1.00000 −0.134840
\(56\) −2.00000 −0.267261
\(57\) 6.00000 0.794719
\(58\) −2.00000 −0.262613
\(59\) 14.0000 1.82264 0.911322 0.411693i \(-0.135063\pi\)
0.911322 + 0.411693i \(0.135063\pi\)
\(60\) −1.00000 −0.129099
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 0 0
\(63\) 2.00000 0.251976
\(64\) 1.00000 0.125000
\(65\) −4.00000 −0.496139
\(66\) −1.00000 −0.123091
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) −1.00000 −0.121268
\(69\) 6.00000 0.722315
\(70\) −2.00000 −0.239046
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) −1.00000 −0.117851
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 6.00000 0.697486
\(75\) −1.00000 −0.115470
\(76\) −6.00000 −0.688247
\(77\) −2.00000 −0.227921
\(78\) −4.00000 −0.452911
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 2.00000 0.220863
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) −2.00000 −0.218218
\(85\) −1.00000 −0.108465
\(86\) 2.00000 0.215666
\(87\) −2.00000 −0.214423
\(88\) 1.00000 0.106600
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −1.00000 −0.105409
\(91\) −8.00000 −0.838628
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) −6.00000 −0.615587
\(96\) 1.00000 0.102062
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 3.00000 0.303046
\(99\) −1.00000 −0.100504
\(100\) 1.00000 0.100000
\(101\) 18.0000 1.79107 0.895533 0.444994i \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) −1.00000 −0.0990148
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 4.00000 0.392232
\(105\) −2.00000 −0.195180
\(106\) 4.00000 0.388514
\(107\) 20.0000 1.93347 0.966736 0.255774i \(-0.0823304\pi\)
0.966736 + 0.255774i \(0.0823304\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 1.00000 0.0953463
\(111\) 6.00000 0.569495
\(112\) 2.00000 0.188982
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) −6.00000 −0.561951
\(115\) −6.00000 −0.559503
\(116\) 2.00000 0.185695
\(117\) −4.00000 −0.369800
\(118\) −14.0000 −1.28880
\(119\) −2.00000 −0.183340
\(120\) 1.00000 0.0912871
\(121\) 1.00000 0.0909091
\(122\) −10.0000 −0.905357
\(123\) 2.00000 0.180334
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) −2.00000 −0.178174
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.00000 0.176090
\(130\) 4.00000 0.350823
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 1.00000 0.0870388
\(133\) −12.0000 −1.04053
\(134\) −8.00000 −0.691095
\(135\) −1.00000 −0.0860663
\(136\) 1.00000 0.0857493
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) −6.00000 −0.510754
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 2.00000 0.169031
\(141\) −8.00000 −0.673722
\(142\) 6.00000 0.503509
\(143\) 4.00000 0.334497
\(144\) 1.00000 0.0833333
\(145\) 2.00000 0.166091
\(146\) −4.00000 −0.331042
\(147\) 3.00000 0.247436
\(148\) −6.00000 −0.493197
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 1.00000 0.0816497
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 6.00000 0.486664
\(153\) −1.00000 −0.0808452
\(154\) 2.00000 0.161165
\(155\) 0 0
\(156\) 4.00000 0.320256
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) −14.0000 −1.11378
\(159\) 4.00000 0.317221
\(160\) −1.00000 −0.0790569
\(161\) −12.0000 −0.945732
\(162\) −1.00000 −0.0785674
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −2.00000 −0.156174
\(165\) 1.00000 0.0778499
\(166\) −12.0000 −0.931381
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 2.00000 0.154303
\(169\) 3.00000 0.230769
\(170\) 1.00000 0.0766965
\(171\) −6.00000 −0.458831
\(172\) −2.00000 −0.152499
\(173\) 14.0000 1.06440 0.532200 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) 2.00000 0.151620
\(175\) 2.00000 0.151186
\(176\) −1.00000 −0.0753778
\(177\) −14.0000 −1.05230
\(178\) −6.00000 −0.449719
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 1.00000 0.0745356
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 8.00000 0.592999
\(183\) −10.0000 −0.739221
\(184\) 6.00000 0.442326
\(185\) −6.00000 −0.441129
\(186\) 0 0
\(187\) 1.00000 0.0731272
\(188\) 8.00000 0.583460
\(189\) −2.00000 −0.145479
\(190\) 6.00000 0.435286
\(191\) −4.00000 −0.289430 −0.144715 0.989473i \(-0.546227\pi\)
−0.144715 + 0.989473i \(0.546227\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −16.0000 −1.15171 −0.575853 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) −14.0000 −1.00514
\(195\) 4.00000 0.286446
\(196\) −3.00000 −0.214286
\(197\) −22.0000 −1.56744 −0.783718 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) 1.00000 0.0710669
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −8.00000 −0.564276
\(202\) −18.0000 −1.26648
\(203\) 4.00000 0.280745
\(204\) 1.00000 0.0700140
\(205\) −2.00000 −0.139686
\(206\) 16.0000 1.11477
\(207\) −6.00000 −0.417029
\(208\) −4.00000 −0.277350
\(209\) 6.00000 0.415029
\(210\) 2.00000 0.138013
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −4.00000 −0.274721
\(213\) 6.00000 0.411113
\(214\) −20.0000 −1.36717
\(215\) −2.00000 −0.136399
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) −4.00000 −0.270295
\(220\) −1.00000 −0.0674200
\(221\) 4.00000 0.269069
\(222\) −6.00000 −0.402694
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) −2.00000 −0.133631
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 6.00000 0.397360
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 6.00000 0.395628
\(231\) 2.00000 0.131590
\(232\) −2.00000 −0.131306
\(233\) −22.0000 −1.44127 −0.720634 0.693316i \(-0.756149\pi\)
−0.720634 + 0.693316i \(0.756149\pi\)
\(234\) 4.00000 0.261488
\(235\) 8.00000 0.521862
\(236\) 14.0000 0.911322
\(237\) −14.0000 −0.909398
\(238\) 2.00000 0.129641
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −4.00000 −0.257663 −0.128831 0.991667i \(-0.541123\pi\)
−0.128831 + 0.991667i \(0.541123\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) 10.0000 0.640184
\(245\) −3.00000 −0.191663
\(246\) −2.00000 −0.127515
\(247\) 24.0000 1.52708
\(248\) 0 0
\(249\) −12.0000 −0.760469
\(250\) −1.00000 −0.0632456
\(251\) 10.0000 0.631194 0.315597 0.948893i \(-0.397795\pi\)
0.315597 + 0.948893i \(0.397795\pi\)
\(252\) 2.00000 0.125988
\(253\) 6.00000 0.377217
\(254\) −4.00000 −0.250982
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) −2.00000 −0.124515
\(259\) −12.0000 −0.745644
\(260\) −4.00000 −0.248069
\(261\) 2.00000 0.123797
\(262\) −12.0000 −0.741362
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) −1.00000 −0.0615457
\(265\) −4.00000 −0.245718
\(266\) 12.0000 0.735767
\(267\) −6.00000 −0.367194
\(268\) 8.00000 0.488678
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 1.00000 0.0608581
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 8.00000 0.484182
\(274\) −2.00000 −0.120824
\(275\) −1.00000 −0.0603023
\(276\) 6.00000 0.361158
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 4.00000 0.239904
\(279\) 0 0
\(280\) −2.00000 −0.119523
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 8.00000 0.476393
\(283\) 28.0000 1.66443 0.832214 0.554455i \(-0.187073\pi\)
0.832214 + 0.554455i \(0.187073\pi\)
\(284\) −6.00000 −0.356034
\(285\) 6.00000 0.355409
\(286\) −4.00000 −0.236525
\(287\) −4.00000 −0.236113
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −2.00000 −0.117444
\(291\) −14.0000 −0.820695
\(292\) 4.00000 0.234082
\(293\) 2.00000 0.116841 0.0584206 0.998292i \(-0.481394\pi\)
0.0584206 + 0.998292i \(0.481394\pi\)
\(294\) −3.00000 −0.174964
\(295\) 14.0000 0.815112
\(296\) 6.00000 0.348743
\(297\) 1.00000 0.0580259
\(298\) −6.00000 −0.347571
\(299\) 24.0000 1.38796
\(300\) −1.00000 −0.0577350
\(301\) −4.00000 −0.230556
\(302\) 8.00000 0.460348
\(303\) −18.0000 −1.03407
\(304\) −6.00000 −0.344124
\(305\) 10.0000 0.572598
\(306\) 1.00000 0.0571662
\(307\) −30.0000 −1.71219 −0.856095 0.516818i \(-0.827116\pi\)
−0.856095 + 0.516818i \(0.827116\pi\)
\(308\) −2.00000 −0.113961
\(309\) 16.0000 0.910208
\(310\) 0 0
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) −4.00000 −0.226455
\(313\) −18.0000 −1.01742 −0.508710 0.860938i \(-0.669877\pi\)
−0.508710 + 0.860938i \(0.669877\pi\)
\(314\) 18.0000 1.01580
\(315\) 2.00000 0.112687
\(316\) 14.0000 0.787562
\(317\) 34.0000 1.90963 0.954815 0.297200i \(-0.0960529\pi\)
0.954815 + 0.297200i \(0.0960529\pi\)
\(318\) −4.00000 −0.224309
\(319\) −2.00000 −0.111979
\(320\) 1.00000 0.0559017
\(321\) −20.0000 −1.11629
\(322\) 12.0000 0.668734
\(323\) 6.00000 0.333849
\(324\) 1.00000 0.0555556
\(325\) −4.00000 −0.221880
\(326\) 4.00000 0.221540
\(327\) 2.00000 0.110600
\(328\) 2.00000 0.110432
\(329\) 16.0000 0.882109
\(330\) −1.00000 −0.0550482
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 12.0000 0.658586
\(333\) −6.00000 −0.328798
\(334\) −8.00000 −0.437741
\(335\) 8.00000 0.437087
\(336\) −2.00000 −0.109109
\(337\) −12.0000 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) −3.00000 −0.163178
\(339\) 0 0
\(340\) −1.00000 −0.0542326
\(341\) 0 0
\(342\) 6.00000 0.324443
\(343\) −20.0000 −1.07990
\(344\) 2.00000 0.107833
\(345\) 6.00000 0.323029
\(346\) −14.0000 −0.752645
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) −2.00000 −0.107211
\(349\) 16.0000 0.856460 0.428230 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) −2.00000 −0.106904
\(351\) 4.00000 0.213504
\(352\) 1.00000 0.0533002
\(353\) 10.0000 0.532246 0.266123 0.963939i \(-0.414257\pi\)
0.266123 + 0.963939i \(0.414257\pi\)
\(354\) 14.0000 0.744092
\(355\) −6.00000 −0.318447
\(356\) 6.00000 0.317999
\(357\) 2.00000 0.105851
\(358\) 6.00000 0.317110
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 17.0000 0.894737
\(362\) −10.0000 −0.525588
\(363\) −1.00000 −0.0524864
\(364\) −8.00000 −0.419314
\(365\) 4.00000 0.209370
\(366\) 10.0000 0.522708
\(367\) −28.0000 −1.46159 −0.730794 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) −6.00000 −0.312772
\(369\) −2.00000 −0.104116
\(370\) 6.00000 0.311925
\(371\) −8.00000 −0.415339
\(372\) 0 0
\(373\) 12.0000 0.621336 0.310668 0.950518i \(-0.399447\pi\)
0.310668 + 0.950518i \(0.399447\pi\)
\(374\) −1.00000 −0.0517088
\(375\) −1.00000 −0.0516398
\(376\) −8.00000 −0.412568
\(377\) −8.00000 −0.412021
\(378\) 2.00000 0.102869
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) −6.00000 −0.307794
\(381\) −4.00000 −0.204926
\(382\) 4.00000 0.204658
\(383\) −12.0000 −0.613171 −0.306586 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) 1.00000 0.0510310
\(385\) −2.00000 −0.101929
\(386\) 16.0000 0.814379
\(387\) −2.00000 −0.101666
\(388\) 14.0000 0.710742
\(389\) 12.0000 0.608424 0.304212 0.952604i \(-0.401607\pi\)
0.304212 + 0.952604i \(0.401607\pi\)
\(390\) −4.00000 −0.202548
\(391\) 6.00000 0.303433
\(392\) 3.00000 0.151523
\(393\) −12.0000 −0.605320
\(394\) 22.0000 1.10834
\(395\) 14.0000 0.704416
\(396\) −1.00000 −0.0502519
\(397\) −18.0000 −0.903394 −0.451697 0.892171i \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) −8.00000 −0.401004
\(399\) 12.0000 0.600751
\(400\) 1.00000 0.0500000
\(401\) −12.0000 −0.599251 −0.299626 0.954057i \(-0.596862\pi\)
−0.299626 + 0.954057i \(0.596862\pi\)
\(402\) 8.00000 0.399004
\(403\) 0 0
\(404\) 18.0000 0.895533
\(405\) 1.00000 0.0496904
\(406\) −4.00000 −0.198517
\(407\) 6.00000 0.297409
\(408\) −1.00000 −0.0495074
\(409\) −2.00000 −0.0988936 −0.0494468 0.998777i \(-0.515746\pi\)
−0.0494468 + 0.998777i \(0.515746\pi\)
\(410\) 2.00000 0.0987730
\(411\) −2.00000 −0.0986527
\(412\) −16.0000 −0.788263
\(413\) 28.0000 1.37779
\(414\) 6.00000 0.294884
\(415\) 12.0000 0.589057
\(416\) 4.00000 0.196116
\(417\) 4.00000 0.195881
\(418\) −6.00000 −0.293470
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) −2.00000 −0.0975900
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) −20.0000 −0.973585
\(423\) 8.00000 0.388973
\(424\) 4.00000 0.194257
\(425\) −1.00000 −0.0485071
\(426\) −6.00000 −0.290701
\(427\) 20.0000 0.967868
\(428\) 20.0000 0.966736
\(429\) −4.00000 −0.193122
\(430\) 2.00000 0.0964486
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −18.0000 −0.865025 −0.432512 0.901628i \(-0.642373\pi\)
−0.432512 + 0.901628i \(0.642373\pi\)
\(434\) 0 0
\(435\) −2.00000 −0.0958927
\(436\) −2.00000 −0.0957826
\(437\) 36.0000 1.72211
\(438\) 4.00000 0.191127
\(439\) 6.00000 0.286364 0.143182 0.989696i \(-0.454267\pi\)
0.143182 + 0.989696i \(0.454267\pi\)
\(440\) 1.00000 0.0476731
\(441\) −3.00000 −0.142857
\(442\) −4.00000 −0.190261
\(443\) 18.0000 0.855206 0.427603 0.903967i \(-0.359358\pi\)
0.427603 + 0.903967i \(0.359358\pi\)
\(444\) 6.00000 0.284747
\(445\) 6.00000 0.284427
\(446\) −16.0000 −0.757622
\(447\) −6.00000 −0.283790
\(448\) 2.00000 0.0944911
\(449\) −24.0000 −1.13263 −0.566315 0.824189i \(-0.691631\pi\)
−0.566315 + 0.824189i \(0.691631\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 2.00000 0.0941763
\(452\) 0 0
\(453\) 8.00000 0.375873
\(454\) 4.00000 0.187729
\(455\) −8.00000 −0.375046
\(456\) −6.00000 −0.280976
\(457\) −2.00000 −0.0935561 −0.0467780 0.998905i \(-0.514895\pi\)
−0.0467780 + 0.998905i \(0.514895\pi\)
\(458\) 14.0000 0.654177
\(459\) 1.00000 0.0466760
\(460\) −6.00000 −0.279751
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) −2.00000 −0.0930484
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 2.00000 0.0928477
\(465\) 0 0
\(466\) 22.0000 1.01913
\(467\) 2.00000 0.0925490 0.0462745 0.998929i \(-0.485265\pi\)
0.0462745 + 0.998929i \(0.485265\pi\)
\(468\) −4.00000 −0.184900
\(469\) 16.0000 0.738811
\(470\) −8.00000 −0.369012
\(471\) 18.0000 0.829396
\(472\) −14.0000 −0.644402
\(473\) 2.00000 0.0919601
\(474\) 14.0000 0.643041
\(475\) −6.00000 −0.275299
\(476\) −2.00000 −0.0916698
\(477\) −4.00000 −0.183147
\(478\) −16.0000 −0.731823
\(479\) 4.00000 0.182765 0.0913823 0.995816i \(-0.470871\pi\)
0.0913823 + 0.995816i \(0.470871\pi\)
\(480\) 1.00000 0.0456435
\(481\) 24.0000 1.09431
\(482\) 4.00000 0.182195
\(483\) 12.0000 0.546019
\(484\) 1.00000 0.0454545
\(485\) 14.0000 0.635707
\(486\) 1.00000 0.0453609
\(487\) −28.0000 −1.26880 −0.634401 0.773004i \(-0.718753\pi\)
−0.634401 + 0.773004i \(0.718753\pi\)
\(488\) −10.0000 −0.452679
\(489\) 4.00000 0.180886
\(490\) 3.00000 0.135526
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 2.00000 0.0901670
\(493\) −2.00000 −0.0900755
\(494\) −24.0000 −1.07981
\(495\) −1.00000 −0.0449467
\(496\) 0 0
\(497\) −12.0000 −0.538274
\(498\) 12.0000 0.537733
\(499\) −36.0000 −1.61158 −0.805791 0.592200i \(-0.798259\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) 1.00000 0.0447214
\(501\) −8.00000 −0.357414
\(502\) −10.0000 −0.446322
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 18.0000 0.800989
\(506\) −6.00000 −0.266733
\(507\) −3.00000 −0.133235
\(508\) 4.00000 0.177471
\(509\) 20.0000 0.886484 0.443242 0.896402i \(-0.353828\pi\)
0.443242 + 0.896402i \(0.353828\pi\)
\(510\) −1.00000 −0.0442807
\(511\) 8.00000 0.353899
\(512\) −1.00000 −0.0441942
\(513\) 6.00000 0.264906
\(514\) −18.0000 −0.793946
\(515\) −16.0000 −0.705044
\(516\) 2.00000 0.0880451
\(517\) −8.00000 −0.351840
\(518\) 12.0000 0.527250
\(519\) −14.0000 −0.614532
\(520\) 4.00000 0.175412
\(521\) 12.0000 0.525730 0.262865 0.964833i \(-0.415333\pi\)
0.262865 + 0.964833i \(0.415333\pi\)
\(522\) −2.00000 −0.0875376
\(523\) 34.0000 1.48672 0.743358 0.668894i \(-0.233232\pi\)
0.743358 + 0.668894i \(0.233232\pi\)
\(524\) 12.0000 0.524222
\(525\) −2.00000 −0.0872872
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 1.00000 0.0435194
\(529\) 13.0000 0.565217
\(530\) 4.00000 0.173749
\(531\) 14.0000 0.607548
\(532\) −12.0000 −0.520266
\(533\) 8.00000 0.346518
\(534\) 6.00000 0.259645
\(535\) 20.0000 0.864675
\(536\) −8.00000 −0.345547
\(537\) 6.00000 0.258919
\(538\) −6.00000 −0.258678
\(539\) 3.00000 0.129219
\(540\) −1.00000 −0.0430331
\(541\) 42.0000 1.80572 0.902861 0.429934i \(-0.141463\pi\)
0.902861 + 0.429934i \(0.141463\pi\)
\(542\) −20.0000 −0.859074
\(543\) −10.0000 −0.429141
\(544\) 1.00000 0.0428746
\(545\) −2.00000 −0.0856706
\(546\) −8.00000 −0.342368
\(547\) 32.0000 1.36822 0.684111 0.729378i \(-0.260191\pi\)
0.684111 + 0.729378i \(0.260191\pi\)
\(548\) 2.00000 0.0854358
\(549\) 10.0000 0.426790
\(550\) 1.00000 0.0426401
\(551\) −12.0000 −0.511217
\(552\) −6.00000 −0.255377
\(553\) 28.0000 1.19068
\(554\) 2.00000 0.0849719
\(555\) 6.00000 0.254686
\(556\) −4.00000 −0.169638
\(557\) 10.0000 0.423714 0.211857 0.977301i \(-0.432049\pi\)
0.211857 + 0.977301i \(0.432049\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 2.00000 0.0845154
\(561\) −1.00000 −0.0422200
\(562\) −18.0000 −0.759284
\(563\) 28.0000 1.18006 0.590030 0.807382i \(-0.299116\pi\)
0.590030 + 0.807382i \(0.299116\pi\)
\(564\) −8.00000 −0.336861
\(565\) 0 0
\(566\) −28.0000 −1.17693
\(567\) 2.00000 0.0839921
\(568\) 6.00000 0.251754
\(569\) 14.0000 0.586911 0.293455 0.955973i \(-0.405195\pi\)
0.293455 + 0.955973i \(0.405195\pi\)
\(570\) −6.00000 −0.251312
\(571\) −36.0000 −1.50655 −0.753277 0.657704i \(-0.771528\pi\)
−0.753277 + 0.657704i \(0.771528\pi\)
\(572\) 4.00000 0.167248
\(573\) 4.00000 0.167102
\(574\) 4.00000 0.166957
\(575\) −6.00000 −0.250217
\(576\) 1.00000 0.0416667
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 16.0000 0.664937
\(580\) 2.00000 0.0830455
\(581\) 24.0000 0.995688
\(582\) 14.0000 0.580319
\(583\) 4.00000 0.165663
\(584\) −4.00000 −0.165521
\(585\) −4.00000 −0.165380
\(586\) −2.00000 −0.0826192
\(587\) 2.00000 0.0825488 0.0412744 0.999148i \(-0.486858\pi\)
0.0412744 + 0.999148i \(0.486858\pi\)
\(588\) 3.00000 0.123718
\(589\) 0 0
\(590\) −14.0000 −0.576371
\(591\) 22.0000 0.904959
\(592\) −6.00000 −0.246598
\(593\) −46.0000 −1.88899 −0.944497 0.328521i \(-0.893450\pi\)
−0.944497 + 0.328521i \(0.893450\pi\)
\(594\) −1.00000 −0.0410305
\(595\) −2.00000 −0.0819920
\(596\) 6.00000 0.245770
\(597\) −8.00000 −0.327418
\(598\) −24.0000 −0.981433
\(599\) 36.0000 1.47092 0.735460 0.677568i \(-0.236966\pi\)
0.735460 + 0.677568i \(0.236966\pi\)
\(600\) 1.00000 0.0408248
\(601\) −16.0000 −0.652654 −0.326327 0.945257i \(-0.605811\pi\)
−0.326327 + 0.945257i \(0.605811\pi\)
\(602\) 4.00000 0.163028
\(603\) 8.00000 0.325785
\(604\) −8.00000 −0.325515
\(605\) 1.00000 0.0406558
\(606\) 18.0000 0.731200
\(607\) −30.0000 −1.21766 −0.608831 0.793300i \(-0.708361\pi\)
−0.608831 + 0.793300i \(0.708361\pi\)
\(608\) 6.00000 0.243332
\(609\) −4.00000 −0.162088
\(610\) −10.0000 −0.404888
\(611\) −32.0000 −1.29458
\(612\) −1.00000 −0.0404226
\(613\) −20.0000 −0.807792 −0.403896 0.914805i \(-0.632344\pi\)
−0.403896 + 0.914805i \(0.632344\pi\)
\(614\) 30.0000 1.21070
\(615\) 2.00000 0.0806478
\(616\) 2.00000 0.0805823
\(617\) 4.00000 0.161034 0.0805170 0.996753i \(-0.474343\pi\)
0.0805170 + 0.996753i \(0.474343\pi\)
\(618\) −16.0000 −0.643614
\(619\) 44.0000 1.76851 0.884255 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(620\) 0 0
\(621\) 6.00000 0.240772
\(622\) 30.0000 1.20289
\(623\) 12.0000 0.480770
\(624\) 4.00000 0.160128
\(625\) 1.00000 0.0400000
\(626\) 18.0000 0.719425
\(627\) −6.00000 −0.239617
\(628\) −18.0000 −0.718278
\(629\) 6.00000 0.239236
\(630\) −2.00000 −0.0796819
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) −14.0000 −0.556890
\(633\) −20.0000 −0.794929
\(634\) −34.0000 −1.35031
\(635\) 4.00000 0.158735
\(636\) 4.00000 0.158610
\(637\) 12.0000 0.475457
\(638\) 2.00000 0.0791808
\(639\) −6.00000 −0.237356
\(640\) −1.00000 −0.0395285
\(641\) 28.0000 1.10593 0.552967 0.833203i \(-0.313496\pi\)
0.552967 + 0.833203i \(0.313496\pi\)
\(642\) 20.0000 0.789337
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) −12.0000 −0.472866
\(645\) 2.00000 0.0787499
\(646\) −6.00000 −0.236067
\(647\) −8.00000 −0.314512 −0.157256 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −14.0000 −0.549548
\(650\) 4.00000 0.156893
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) −34.0000 −1.33052 −0.665261 0.746611i \(-0.731680\pi\)
−0.665261 + 0.746611i \(0.731680\pi\)
\(654\) −2.00000 −0.0782062
\(655\) 12.0000 0.468879
\(656\) −2.00000 −0.0780869
\(657\) 4.00000 0.156055
\(658\) −16.0000 −0.623745
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 1.00000 0.0389249
\(661\) −6.00000 −0.233373 −0.116686 0.993169i \(-0.537227\pi\)
−0.116686 + 0.993169i \(0.537227\pi\)
\(662\) −4.00000 −0.155464
\(663\) −4.00000 −0.155347
\(664\) −12.0000 −0.465690
\(665\) −12.0000 −0.465340
\(666\) 6.00000 0.232495
\(667\) −12.0000 −0.464642
\(668\) 8.00000 0.309529
\(669\) −16.0000 −0.618596
\(670\) −8.00000 −0.309067
\(671\) −10.0000 −0.386046
\(672\) 2.00000 0.0771517
\(673\) 32.0000 1.23351 0.616755 0.787155i \(-0.288447\pi\)
0.616755 + 0.787155i \(0.288447\pi\)
\(674\) 12.0000 0.462223
\(675\) −1.00000 −0.0384900
\(676\) 3.00000 0.115385
\(677\) −22.0000 −0.845529 −0.422764 0.906240i \(-0.638940\pi\)
−0.422764 + 0.906240i \(0.638940\pi\)
\(678\) 0 0
\(679\) 28.0000 1.07454
\(680\) 1.00000 0.0383482
\(681\) 4.00000 0.153280
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −6.00000 −0.229416
\(685\) 2.00000 0.0764161
\(686\) 20.0000 0.763604
\(687\) 14.0000 0.534133
\(688\) −2.00000 −0.0762493
\(689\) 16.0000 0.609551
\(690\) −6.00000 −0.228416
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 14.0000 0.532200
\(693\) −2.00000 −0.0759737
\(694\) −12.0000 −0.455514
\(695\) −4.00000 −0.151729
\(696\) 2.00000 0.0758098
\(697\) 2.00000 0.0757554
\(698\) −16.0000 −0.605609
\(699\) 22.0000 0.832116
\(700\) 2.00000 0.0755929
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) −4.00000 −0.150970
\(703\) 36.0000 1.35777
\(704\) −1.00000 −0.0376889
\(705\) −8.00000 −0.301297
\(706\) −10.0000 −0.376355
\(707\) 36.0000 1.35392
\(708\) −14.0000 −0.526152
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 6.00000 0.225176
\(711\) 14.0000 0.525041
\(712\) −6.00000 −0.224860
\(713\) 0 0
\(714\) −2.00000 −0.0748481
\(715\) 4.00000 0.149592
\(716\) −6.00000 −0.224231
\(717\) −16.0000 −0.597531
\(718\) −24.0000 −0.895672
\(719\) 14.0000 0.522112 0.261056 0.965324i \(-0.415929\pi\)
0.261056 + 0.965324i \(0.415929\pi\)
\(720\) 1.00000 0.0372678
\(721\) −32.0000 −1.19174
\(722\) −17.0000 −0.632674
\(723\) 4.00000 0.148762
\(724\) 10.0000 0.371647
\(725\) 2.00000 0.0742781
\(726\) 1.00000 0.0371135
\(727\) 40.0000 1.48352 0.741759 0.670667i \(-0.233992\pi\)
0.741759 + 0.670667i \(0.233992\pi\)
\(728\) 8.00000 0.296500
\(729\) 1.00000 0.0370370
\(730\) −4.00000 −0.148047
\(731\) 2.00000 0.0739727
\(732\) −10.0000 −0.369611
\(733\) −36.0000 −1.32969 −0.664845 0.746981i \(-0.731502\pi\)
−0.664845 + 0.746981i \(0.731502\pi\)
\(734\) 28.0000 1.03350
\(735\) 3.00000 0.110657
\(736\) 6.00000 0.221163
\(737\) −8.00000 −0.294684
\(738\) 2.00000 0.0736210
\(739\) 50.0000 1.83928 0.919640 0.392763i \(-0.128481\pi\)
0.919640 + 0.392763i \(0.128481\pi\)
\(740\) −6.00000 −0.220564
\(741\) −24.0000 −0.881662
\(742\) 8.00000 0.293689
\(743\) −12.0000 −0.440237 −0.220119 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 0 0
\(745\) 6.00000 0.219823
\(746\) −12.0000 −0.439351
\(747\) 12.0000 0.439057
\(748\) 1.00000 0.0365636
\(749\) 40.0000 1.46157
\(750\) 1.00000 0.0365148
\(751\) −20.0000 −0.729810 −0.364905 0.931045i \(-0.618899\pi\)
−0.364905 + 0.931045i \(0.618899\pi\)
\(752\) 8.00000 0.291730
\(753\) −10.0000 −0.364420
\(754\) 8.00000 0.291343
\(755\) −8.00000 −0.291150
\(756\) −2.00000 −0.0727393
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −12.0000 −0.435860
\(759\) −6.00000 −0.217786
\(760\) 6.00000 0.217643
\(761\) −38.0000 −1.37750 −0.688749 0.724999i \(-0.741840\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 4.00000 0.144905
\(763\) −4.00000 −0.144810
\(764\) −4.00000 −0.144715
\(765\) −1.00000 −0.0361551
\(766\) 12.0000 0.433578
\(767\) −56.0000 −2.02204
\(768\) −1.00000 −0.0360844
\(769\) −38.0000 −1.37032 −0.685158 0.728395i \(-0.740267\pi\)
−0.685158 + 0.728395i \(0.740267\pi\)
\(770\) 2.00000 0.0720750
\(771\) −18.0000 −0.648254
\(772\) −16.0000 −0.575853
\(773\) −32.0000 −1.15096 −0.575480 0.817816i \(-0.695185\pi\)
−0.575480 + 0.817816i \(0.695185\pi\)
\(774\) 2.00000 0.0718885
\(775\) 0 0
\(776\) −14.0000 −0.502571
\(777\) 12.0000 0.430498
\(778\) −12.0000 −0.430221
\(779\) 12.0000 0.429945
\(780\) 4.00000 0.143223
\(781\) 6.00000 0.214697
\(782\) −6.00000 −0.214560
\(783\) −2.00000 −0.0714742
\(784\) −3.00000 −0.107143
\(785\) −18.0000 −0.642448
\(786\) 12.0000 0.428026
\(787\) 48.0000 1.71102 0.855508 0.517790i \(-0.173245\pi\)
0.855508 + 0.517790i \(0.173245\pi\)
\(788\) −22.0000 −0.783718
\(789\) 24.0000 0.854423
\(790\) −14.0000 −0.498098
\(791\) 0 0
\(792\) 1.00000 0.0355335
\(793\) −40.0000 −1.42044
\(794\) 18.0000 0.638796
\(795\) 4.00000 0.141865
\(796\) 8.00000 0.283552
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) −12.0000 −0.424795
\(799\) −8.00000 −0.283020
\(800\) −1.00000 −0.0353553
\(801\) 6.00000 0.212000
\(802\) 12.0000 0.423735
\(803\) −4.00000 −0.141157
\(804\) −8.00000 −0.282138
\(805\) −12.0000 −0.422944
\(806\) 0 0
\(807\) −6.00000 −0.211210
\(808\) −18.0000 −0.633238
\(809\) 26.0000 0.914111 0.457056 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −32.0000 −1.12367 −0.561836 0.827249i \(-0.689905\pi\)
−0.561836 + 0.827249i \(0.689905\pi\)
\(812\) 4.00000 0.140372
\(813\) −20.0000 −0.701431
\(814\) −6.00000 −0.210300
\(815\) −4.00000 −0.140114
\(816\) 1.00000 0.0350070
\(817\) 12.0000 0.419827
\(818\) 2.00000 0.0699284
\(819\) −8.00000 −0.279543
\(820\) −2.00000 −0.0698430
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 2.00000 0.0697580
\(823\) −40.0000 −1.39431 −0.697156 0.716919i \(-0.745552\pi\)
−0.697156 + 0.716919i \(0.745552\pi\)
\(824\) 16.0000 0.557386
\(825\) 1.00000 0.0348155
\(826\) −28.0000 −0.974245
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) −6.00000 −0.208514
\(829\) −26.0000 −0.903017 −0.451509 0.892267i \(-0.649114\pi\)
−0.451509 + 0.892267i \(0.649114\pi\)
\(830\) −12.0000 −0.416526
\(831\) 2.00000 0.0693792
\(832\) −4.00000 −0.138675
\(833\) 3.00000 0.103944
\(834\) −4.00000 −0.138509
\(835\) 8.00000 0.276851
\(836\) 6.00000 0.207514
\(837\) 0 0
\(838\) −20.0000 −0.690889
\(839\) −22.0000 −0.759524 −0.379762 0.925084i \(-0.623994\pi\)
−0.379762 + 0.925084i \(0.623994\pi\)
\(840\) 2.00000 0.0690066
\(841\) −25.0000 −0.862069
\(842\) 2.00000 0.0689246
\(843\) −18.0000 −0.619953
\(844\) 20.0000 0.688428
\(845\) 3.00000 0.103203
\(846\) −8.00000 −0.275046
\(847\) 2.00000 0.0687208
\(848\) −4.00000 −0.137361
\(849\) −28.0000 −0.960958
\(850\) 1.00000 0.0342997
\(851\) 36.0000 1.23406
\(852\) 6.00000 0.205557
\(853\) 14.0000 0.479351 0.239675 0.970853i \(-0.422959\pi\)
0.239675 + 0.970853i \(0.422959\pi\)
\(854\) −20.0000 −0.684386
\(855\) −6.00000 −0.205196
\(856\) −20.0000 −0.683586
\(857\) −42.0000 −1.43469 −0.717346 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) 4.00000 0.136558
\(859\) −20.0000 −0.682391 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) −2.00000 −0.0681994
\(861\) 4.00000 0.136320
\(862\) 0 0
\(863\) 52.0000 1.77010 0.885050 0.465495i \(-0.154124\pi\)
0.885050 + 0.465495i \(0.154124\pi\)
\(864\) 1.00000 0.0340207
\(865\) 14.0000 0.476014
\(866\) 18.0000 0.611665
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) −14.0000 −0.474917
\(870\) 2.00000 0.0678064
\(871\) −32.0000 −1.08428
\(872\) 2.00000 0.0677285
\(873\) 14.0000 0.473828
\(874\) −36.0000 −1.21772
\(875\) 2.00000 0.0676123
\(876\) −4.00000 −0.135147
\(877\) 38.0000 1.28317 0.641584 0.767052i \(-0.278277\pi\)
0.641584 + 0.767052i \(0.278277\pi\)
\(878\) −6.00000 −0.202490
\(879\) −2.00000 −0.0674583
\(880\) −1.00000 −0.0337100
\(881\) 24.0000 0.808581 0.404290 0.914631i \(-0.367519\pi\)
0.404290 + 0.914631i \(0.367519\pi\)
\(882\) 3.00000 0.101015
\(883\) 36.0000 1.21150 0.605748 0.795656i \(-0.292874\pi\)
0.605748 + 0.795656i \(0.292874\pi\)
\(884\) 4.00000 0.134535
\(885\) −14.0000 −0.470605
\(886\) −18.0000 −0.604722
\(887\) 24.0000 0.805841 0.402921 0.915235i \(-0.367995\pi\)
0.402921 + 0.915235i \(0.367995\pi\)
\(888\) −6.00000 −0.201347
\(889\) 8.00000 0.268311
\(890\) −6.00000 −0.201120
\(891\) −1.00000 −0.0335013
\(892\) 16.0000 0.535720
\(893\) −48.0000 −1.60626
\(894\) 6.00000 0.200670
\(895\) −6.00000 −0.200558
\(896\) −2.00000 −0.0668153
\(897\) −24.0000 −0.801337
\(898\) 24.0000 0.800890
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 4.00000 0.133259
\(902\) −2.00000 −0.0665927
\(903\) 4.00000 0.133112
\(904\) 0 0
\(905\) 10.0000 0.332411
\(906\) −8.00000 −0.265782
\(907\) 28.0000 0.929725 0.464862 0.885383i \(-0.346104\pi\)
0.464862 + 0.885383i \(0.346104\pi\)
\(908\) −4.00000 −0.132745
\(909\) 18.0000 0.597022
\(910\) 8.00000 0.265197
\(911\) −22.0000 −0.728893 −0.364446 0.931224i \(-0.618742\pi\)
−0.364446 + 0.931224i \(0.618742\pi\)
\(912\) 6.00000 0.198680
\(913\) −12.0000 −0.397142
\(914\) 2.00000 0.0661541
\(915\) −10.0000 −0.330590
\(916\) −14.0000 −0.462573
\(917\) 24.0000 0.792550
\(918\) −1.00000 −0.0330049
\(919\) 56.0000 1.84727 0.923635 0.383274i \(-0.125203\pi\)
0.923635 + 0.383274i \(0.125203\pi\)
\(920\) 6.00000 0.197814
\(921\) 30.0000 0.988534
\(922\) −14.0000 −0.461065
\(923\) 24.0000 0.789970
\(924\) 2.00000 0.0657952
\(925\) −6.00000 −0.197279
\(926\) −16.0000 −0.525793
\(927\) −16.0000 −0.525509
\(928\) −2.00000 −0.0656532
\(929\) −32.0000 −1.04989 −0.524943 0.851137i \(-0.675913\pi\)
−0.524943 + 0.851137i \(0.675913\pi\)
\(930\) 0 0
\(931\) 18.0000 0.589926
\(932\) −22.0000 −0.720634
\(933\) 30.0000 0.982156
\(934\) −2.00000 −0.0654420
\(935\) 1.00000 0.0327035
\(936\) 4.00000 0.130744
\(937\) −18.0000 −0.588034 −0.294017 0.955800i \(-0.594992\pi\)
−0.294017 + 0.955800i \(0.594992\pi\)
\(938\) −16.0000 −0.522419
\(939\) 18.0000 0.587408
\(940\) 8.00000 0.260931
\(941\) 6.00000 0.195594 0.0977972 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) −18.0000 −0.586472
\(943\) 12.0000 0.390774
\(944\) 14.0000 0.455661
\(945\) −2.00000 −0.0650600
\(946\) −2.00000 −0.0650256
\(947\) 48.0000 1.55979 0.779895 0.625910i \(-0.215272\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(948\) −14.0000 −0.454699
\(949\) −16.0000 −0.519382
\(950\) 6.00000 0.194666
\(951\) −34.0000 −1.10253
\(952\) 2.00000 0.0648204
\(953\) 42.0000 1.36051 0.680257 0.732974i \(-0.261868\pi\)
0.680257 + 0.732974i \(0.261868\pi\)
\(954\) 4.00000 0.129505
\(955\) −4.00000 −0.129437
\(956\) 16.0000 0.517477
\(957\) 2.00000 0.0646508
\(958\) −4.00000 −0.129234
\(959\) 4.00000 0.129167
\(960\) −1.00000 −0.0322749
\(961\) −31.0000 −1.00000
\(962\) −24.0000 −0.773791
\(963\) 20.0000 0.644491
\(964\) −4.00000 −0.128831
\(965\) −16.0000 −0.515058
\(966\) −12.0000 −0.386094
\(967\) −52.0000 −1.67221 −0.836104 0.548572i \(-0.815172\pi\)
−0.836104 + 0.548572i \(0.815172\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −6.00000 −0.192748
\(970\) −14.0000 −0.449513
\(971\) −2.00000 −0.0641831 −0.0320915 0.999485i \(-0.510217\pi\)
−0.0320915 + 0.999485i \(0.510217\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −8.00000 −0.256468
\(974\) 28.0000 0.897178
\(975\) 4.00000 0.128103
\(976\) 10.0000 0.320092
\(977\) 42.0000 1.34370 0.671850 0.740688i \(-0.265500\pi\)
0.671850 + 0.740688i \(0.265500\pi\)
\(978\) −4.00000 −0.127906
\(979\) −6.00000 −0.191761
\(980\) −3.00000 −0.0958315
\(981\) −2.00000 −0.0638551
\(982\) 12.0000 0.382935
\(983\) −6.00000 −0.191370 −0.0956851 0.995412i \(-0.530504\pi\)
−0.0956851 + 0.995412i \(0.530504\pi\)
\(984\) −2.00000 −0.0637577
\(985\) −22.0000 −0.700978
\(986\) 2.00000 0.0636930
\(987\) −16.0000 −0.509286
\(988\) 24.0000 0.763542
\(989\) 12.0000 0.381578
\(990\) 1.00000 0.0317821
\(991\) 28.0000 0.889449 0.444725 0.895667i \(-0.353302\pi\)
0.444725 + 0.895667i \(0.353302\pi\)
\(992\) 0 0
\(993\) −4.00000 −0.126936
\(994\) 12.0000 0.380617
\(995\) 8.00000 0.253617
\(996\) −12.0000 −0.380235
\(997\) −38.0000 −1.20347 −0.601736 0.798695i \(-0.705524\pi\)
−0.601736 + 0.798695i \(0.705524\pi\)
\(998\) 36.0000 1.13956
\(999\) 6.00000 0.189832
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 5610.2.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.i.1.1 1 1.1 even 1 trivial