Properties

Label 4598.2.a.cc.1.8
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $10$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \( x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 418)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(2.10092\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.10092 q^{3} +1.00000 q^{4} +2.46005 q^{5} -2.10092 q^{6} -3.09995 q^{7} -1.00000 q^{8} +1.41386 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.10092 q^{3} +1.00000 q^{4} +2.46005 q^{5} -2.10092 q^{6} -3.09995 q^{7} -1.00000 q^{8} +1.41386 q^{9} -2.46005 q^{10} +2.10092 q^{12} -3.97832 q^{13} +3.09995 q^{14} +5.16836 q^{15} +1.00000 q^{16} -2.14576 q^{17} -1.41386 q^{18} -1.00000 q^{19} +2.46005 q^{20} -6.51275 q^{21} -2.55940 q^{23} -2.10092 q^{24} +1.05183 q^{25} +3.97832 q^{26} -3.33234 q^{27} -3.09995 q^{28} +6.50365 q^{29} -5.16836 q^{30} +1.48635 q^{31} -1.00000 q^{32} +2.14576 q^{34} -7.62603 q^{35} +1.41386 q^{36} -1.74921 q^{37} +1.00000 q^{38} -8.35814 q^{39} -2.46005 q^{40} +5.48529 q^{41} +6.51275 q^{42} +4.59472 q^{43} +3.47817 q^{45} +2.55940 q^{46} -3.40634 q^{47} +2.10092 q^{48} +2.60971 q^{49} -1.05183 q^{50} -4.50808 q^{51} -3.97832 q^{52} -11.7609 q^{53} +3.33234 q^{54} +3.09995 q^{56} -2.10092 q^{57} -6.50365 q^{58} -6.65028 q^{59} +5.16836 q^{60} -6.34059 q^{61} -1.48635 q^{62} -4.38291 q^{63} +1.00000 q^{64} -9.78686 q^{65} +14.1154 q^{67} -2.14576 q^{68} -5.37710 q^{69} +7.62603 q^{70} -15.9696 q^{71} -1.41386 q^{72} -3.17623 q^{73} +1.74921 q^{74} +2.20981 q^{75} -1.00000 q^{76} +8.35814 q^{78} +7.25669 q^{79} +2.46005 q^{80} -11.2426 q^{81} -5.48529 q^{82} +11.2166 q^{83} -6.51275 q^{84} -5.27868 q^{85} -4.59472 q^{86} +13.6636 q^{87} -4.63686 q^{89} -3.47817 q^{90} +12.3326 q^{91} -2.55940 q^{92} +3.12270 q^{93} +3.40634 q^{94} -2.46005 q^{95} -2.10092 q^{96} -5.47081 q^{97} -2.60971 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} - 2 q^{6} - 11 q^{7} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} - 2 q^{6} - 11 q^{7} - 10 q^{8} + 12 q^{9} + 3 q^{10} + 2 q^{12} - 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 10 q^{19} - 3 q^{20} + q^{21} + 14 q^{23} - 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} - 11 q^{28} - 16 q^{29} - q^{30} + 12 q^{31} - 10 q^{32} + 12 q^{34} + 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} - 11 q^{39} + 3 q^{40} + 5 q^{41} - q^{42} - 22 q^{43} - 2 q^{45} - 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} - 5 q^{50} - 8 q^{51} - 11 q^{52} + 2 q^{53} - 2 q^{54} + 11 q^{56} - 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} - 35 q^{61} - 12 q^{62} - 38 q^{63} + 10 q^{64} - 4 q^{65} + 9 q^{67} - 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} - 12 q^{72} - 5 q^{73} + q^{74} - 15 q^{75} - 10 q^{76} + 11 q^{78} - 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} - 7 q^{83} + q^{84} - 35 q^{85} + 22 q^{86} - 8 q^{87} + 22 q^{89} + 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} - 8 q^{94} + 3 q^{95} - 2 q^{96} + 32 q^{97} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 2.10092 1.21297 0.606483 0.795096i \(-0.292580\pi\)
0.606483 + 0.795096i \(0.292580\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.46005 1.10017 0.550083 0.835110i \(-0.314596\pi\)
0.550083 + 0.835110i \(0.314596\pi\)
\(6\) −2.10092 −0.857697
\(7\) −3.09995 −1.17167 −0.585836 0.810430i \(-0.699234\pi\)
−0.585836 + 0.810430i \(0.699234\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.41386 0.471288
\(10\) −2.46005 −0.777935
\(11\) 0 0
\(12\) 2.10092 0.606483
\(13\) −3.97832 −1.10339 −0.551694 0.834047i \(-0.686018\pi\)
−0.551694 + 0.834047i \(0.686018\pi\)
\(14\) 3.09995 0.828497
\(15\) 5.16836 1.33447
\(16\) 1.00000 0.250000
\(17\) −2.14576 −0.520424 −0.260212 0.965551i \(-0.583792\pi\)
−0.260212 + 0.965551i \(0.583792\pi\)
\(18\) −1.41386 −0.333251
\(19\) −1.00000 −0.229416
\(20\) 2.46005 0.550083
\(21\) −6.51275 −1.42120
\(22\) 0 0
\(23\) −2.55940 −0.533672 −0.266836 0.963742i \(-0.585978\pi\)
−0.266836 + 0.963742i \(0.585978\pi\)
\(24\) −2.10092 −0.428848
\(25\) 1.05183 0.210366
\(26\) 3.97832 0.780213
\(27\) −3.33234 −0.641310
\(28\) −3.09995 −0.585836
\(29\) 6.50365 1.20770 0.603849 0.797099i \(-0.293633\pi\)
0.603849 + 0.797099i \(0.293633\pi\)
\(30\) −5.16836 −0.943609
\(31\) 1.48635 0.266956 0.133478 0.991052i \(-0.457385\pi\)
0.133478 + 0.991052i \(0.457385\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 2.14576 0.367995
\(35\) −7.62603 −1.28903
\(36\) 1.41386 0.235644
\(37\) −1.74921 −0.287569 −0.143784 0.989609i \(-0.545927\pi\)
−0.143784 + 0.989609i \(0.545927\pi\)
\(38\) 1.00000 0.162221
\(39\) −8.35814 −1.33837
\(40\) −2.46005 −0.388968
\(41\) 5.48529 0.856659 0.428329 0.903623i \(-0.359102\pi\)
0.428329 + 0.903623i \(0.359102\pi\)
\(42\) 6.51275 1.00494
\(43\) 4.59472 0.700689 0.350344 0.936621i \(-0.386065\pi\)
0.350344 + 0.936621i \(0.386065\pi\)
\(44\) 0 0
\(45\) 3.47817 0.518495
\(46\) 2.55940 0.377363
\(47\) −3.40634 −0.496866 −0.248433 0.968649i \(-0.579916\pi\)
−0.248433 + 0.968649i \(0.579916\pi\)
\(48\) 2.10092 0.303242
\(49\) 2.60971 0.372815
\(50\) −1.05183 −0.148751
\(51\) −4.50808 −0.631257
\(52\) −3.97832 −0.551694
\(53\) −11.7609 −1.61548 −0.807742 0.589536i \(-0.799311\pi\)
−0.807742 + 0.589536i \(0.799311\pi\)
\(54\) 3.33234 0.453475
\(55\) 0 0
\(56\) 3.09995 0.414249
\(57\) −2.10092 −0.278274
\(58\) −6.50365 −0.853971
\(59\) −6.65028 −0.865793 −0.432896 0.901444i \(-0.642508\pi\)
−0.432896 + 0.901444i \(0.642508\pi\)
\(60\) 5.16836 0.667233
\(61\) −6.34059 −0.811829 −0.405915 0.913911i \(-0.633047\pi\)
−0.405915 + 0.913911i \(0.633047\pi\)
\(62\) −1.48635 −0.188766
\(63\) −4.38291 −0.552195
\(64\) 1.00000 0.125000
\(65\) −9.78686 −1.21391
\(66\) 0 0
\(67\) 14.1154 1.72447 0.862236 0.506506i \(-0.169063\pi\)
0.862236 + 0.506506i \(0.169063\pi\)
\(68\) −2.14576 −0.260212
\(69\) −5.37710 −0.647326
\(70\) 7.62603 0.911485
\(71\) −15.9696 −1.89524 −0.947619 0.319404i \(-0.896517\pi\)
−0.947619 + 0.319404i \(0.896517\pi\)
\(72\) −1.41386 −0.166626
\(73\) −3.17623 −0.371749 −0.185875 0.982573i \(-0.559512\pi\)
−0.185875 + 0.982573i \(0.559512\pi\)
\(74\) 1.74921 0.203342
\(75\) 2.20981 0.255167
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 8.35814 0.946373
\(79\) 7.25669 0.816442 0.408221 0.912883i \(-0.366149\pi\)
0.408221 + 0.912883i \(0.366149\pi\)
\(80\) 2.46005 0.275042
\(81\) −11.2426 −1.24918
\(82\) −5.48529 −0.605749
\(83\) 11.2166 1.23118 0.615588 0.788068i \(-0.288918\pi\)
0.615588 + 0.788068i \(0.288918\pi\)
\(84\) −6.51275 −0.710600
\(85\) −5.27868 −0.572553
\(86\) −4.59472 −0.495462
\(87\) 13.6636 1.46490
\(88\) 0 0
\(89\) −4.63686 −0.491506 −0.245753 0.969332i \(-0.579035\pi\)
−0.245753 + 0.969332i \(0.579035\pi\)
\(90\) −3.47817 −0.366632
\(91\) 12.3326 1.29281
\(92\) −2.55940 −0.266836
\(93\) 3.12270 0.323809
\(94\) 3.40634 0.351338
\(95\) −2.46005 −0.252395
\(96\) −2.10092 −0.214424
\(97\) −5.47081 −0.555477 −0.277738 0.960657i \(-0.589585\pi\)
−0.277738 + 0.960657i \(0.589585\pi\)
\(98\) −2.60971 −0.263620
\(99\) 0 0
\(100\) 1.05183 0.105183
\(101\) −5.80492 −0.577611 −0.288806 0.957388i \(-0.593258\pi\)
−0.288806 + 0.957388i \(0.593258\pi\)
\(102\) 4.50808 0.446366
\(103\) −9.56301 −0.942271 −0.471136 0.882061i \(-0.656156\pi\)
−0.471136 + 0.882061i \(0.656156\pi\)
\(104\) 3.97832 0.390107
\(105\) −16.0217 −1.56356
\(106\) 11.7609 1.14232
\(107\) −14.5663 −1.40818 −0.704090 0.710111i \(-0.748645\pi\)
−0.704090 + 0.710111i \(0.748645\pi\)
\(108\) −3.33234 −0.320655
\(109\) −3.38080 −0.323822 −0.161911 0.986805i \(-0.551766\pi\)
−0.161911 + 0.986805i \(0.551766\pi\)
\(110\) 0 0
\(111\) −3.67496 −0.348811
\(112\) −3.09995 −0.292918
\(113\) 11.3668 1.06930 0.534650 0.845074i \(-0.320444\pi\)
0.534650 + 0.845074i \(0.320444\pi\)
\(114\) 2.10092 0.196769
\(115\) −6.29625 −0.587128
\(116\) 6.50365 0.603849
\(117\) −5.62481 −0.520014
\(118\) 6.65028 0.612208
\(119\) 6.65177 0.609766
\(120\) −5.16836 −0.471805
\(121\) 0 0
\(122\) 6.34059 0.574050
\(123\) 11.5242 1.03910
\(124\) 1.48635 0.133478
\(125\) −9.71268 −0.868729
\(126\) 4.38291 0.390461
\(127\) −13.3466 −1.18432 −0.592160 0.805820i \(-0.701725\pi\)
−0.592160 + 0.805820i \(0.701725\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 9.65314 0.849912
\(130\) 9.78686 0.858364
\(131\) −4.58757 −0.400818 −0.200409 0.979712i \(-0.564227\pi\)
−0.200409 + 0.979712i \(0.564227\pi\)
\(132\) 0 0
\(133\) 3.09995 0.268800
\(134\) −14.1154 −1.21939
\(135\) −8.19772 −0.705548
\(136\) 2.14576 0.183998
\(137\) −13.6371 −1.16509 −0.582546 0.812798i \(-0.697943\pi\)
−0.582546 + 0.812798i \(0.697943\pi\)
\(138\) 5.37710 0.457729
\(139\) −5.78982 −0.491086 −0.245543 0.969386i \(-0.578966\pi\)
−0.245543 + 0.969386i \(0.578966\pi\)
\(140\) −7.62603 −0.644517
\(141\) −7.15646 −0.602682
\(142\) 15.9696 1.34014
\(143\) 0 0
\(144\) 1.41386 0.117822
\(145\) 15.9993 1.32867
\(146\) 3.17623 0.262866
\(147\) 5.48278 0.452212
\(148\) −1.74921 −0.143784
\(149\) −10.3503 −0.847926 −0.423963 0.905679i \(-0.639361\pi\)
−0.423963 + 0.905679i \(0.639361\pi\)
\(150\) −2.20981 −0.180430
\(151\) −12.1731 −0.990632 −0.495316 0.868713i \(-0.664948\pi\)
−0.495316 + 0.868713i \(0.664948\pi\)
\(152\) 1.00000 0.0811107
\(153\) −3.03382 −0.245270
\(154\) 0 0
\(155\) 3.65649 0.293696
\(156\) −8.35814 −0.669186
\(157\) 3.72389 0.297199 0.148599 0.988897i \(-0.452524\pi\)
0.148599 + 0.988897i \(0.452524\pi\)
\(158\) −7.25669 −0.577312
\(159\) −24.7087 −1.95953
\(160\) −2.46005 −0.194484
\(161\) 7.93402 0.625289
\(162\) 11.2426 0.883301
\(163\) −19.8920 −1.55806 −0.779032 0.626984i \(-0.784289\pi\)
−0.779032 + 0.626984i \(0.784289\pi\)
\(164\) 5.48529 0.428329
\(165\) 0 0
\(166\) −11.2166 −0.870573
\(167\) −21.9867 −1.70138 −0.850690 0.525667i \(-0.823816\pi\)
−0.850690 + 0.525667i \(0.823816\pi\)
\(168\) 6.51275 0.502470
\(169\) 2.82705 0.217465
\(170\) 5.27868 0.404856
\(171\) −1.41386 −0.108121
\(172\) 4.59472 0.350344
\(173\) −25.4819 −1.93735 −0.968675 0.248333i \(-0.920117\pi\)
−0.968675 + 0.248333i \(0.920117\pi\)
\(174\) −13.6636 −1.03584
\(175\) −3.26062 −0.246480
\(176\) 0 0
\(177\) −13.9717 −1.05018
\(178\) 4.63686 0.347547
\(179\) 22.7884 1.70329 0.851643 0.524122i \(-0.175607\pi\)
0.851643 + 0.524122i \(0.175607\pi\)
\(180\) 3.47817 0.259248
\(181\) −1.54547 −0.114874 −0.0574368 0.998349i \(-0.518293\pi\)
−0.0574368 + 0.998349i \(0.518293\pi\)
\(182\) −12.3326 −0.914154
\(183\) −13.3211 −0.984722
\(184\) 2.55940 0.188682
\(185\) −4.30315 −0.316374
\(186\) −3.12270 −0.228967
\(187\) 0 0
\(188\) −3.40634 −0.248433
\(189\) 10.3301 0.751405
\(190\) 2.46005 0.178471
\(191\) 7.14404 0.516925 0.258462 0.966021i \(-0.416784\pi\)
0.258462 + 0.966021i \(0.416784\pi\)
\(192\) 2.10092 0.151621
\(193\) −12.0980 −0.870833 −0.435417 0.900229i \(-0.643399\pi\)
−0.435417 + 0.900229i \(0.643399\pi\)
\(194\) 5.47081 0.392781
\(195\) −20.5614 −1.47243
\(196\) 2.60971 0.186408
\(197\) 18.2516 1.30037 0.650186 0.759775i \(-0.274691\pi\)
0.650186 + 0.759775i \(0.274691\pi\)
\(198\) 0 0
\(199\) 23.9705 1.69923 0.849613 0.527406i \(-0.176835\pi\)
0.849613 + 0.527406i \(0.176835\pi\)
\(200\) −1.05183 −0.0743756
\(201\) 29.6554 2.09173
\(202\) 5.80492 0.408433
\(203\) −20.1610 −1.41503
\(204\) −4.50808 −0.315629
\(205\) 13.4941 0.942467
\(206\) 9.56301 0.666286
\(207\) −3.61865 −0.251513
\(208\) −3.97832 −0.275847
\(209\) 0 0
\(210\) 16.0217 1.10560
\(211\) 20.7466 1.42826 0.714129 0.700015i \(-0.246823\pi\)
0.714129 + 0.700015i \(0.246823\pi\)
\(212\) −11.7609 −0.807742
\(213\) −33.5508 −2.29886
\(214\) 14.5663 0.995734
\(215\) 11.3032 0.770874
\(216\) 3.33234 0.226737
\(217\) −4.60761 −0.312785
\(218\) 3.38080 0.228977
\(219\) −6.67300 −0.450920
\(220\) 0 0
\(221\) 8.53654 0.574230
\(222\) 3.67496 0.246647
\(223\) 28.3845 1.90077 0.950384 0.311080i \(-0.100691\pi\)
0.950384 + 0.311080i \(0.100691\pi\)
\(224\) 3.09995 0.207124
\(225\) 1.48715 0.0991430
\(226\) −11.3668 −0.756109
\(227\) −8.50634 −0.564585 −0.282293 0.959328i \(-0.591095\pi\)
−0.282293 + 0.959328i \(0.591095\pi\)
\(228\) −2.10092 −0.139137
\(229\) −1.70730 −0.112822 −0.0564109 0.998408i \(-0.517966\pi\)
−0.0564109 + 0.998408i \(0.517966\pi\)
\(230\) 6.29625 0.415162
\(231\) 0 0
\(232\) −6.50365 −0.426986
\(233\) 9.95632 0.652260 0.326130 0.945325i \(-0.394255\pi\)
0.326130 + 0.945325i \(0.394255\pi\)
\(234\) 5.62481 0.367705
\(235\) −8.37977 −0.546636
\(236\) −6.65028 −0.432896
\(237\) 15.2457 0.990317
\(238\) −6.65177 −0.431170
\(239\) 16.2786 1.05297 0.526487 0.850183i \(-0.323509\pi\)
0.526487 + 0.850183i \(0.323509\pi\)
\(240\) 5.16836 0.333616
\(241\) −5.95144 −0.383366 −0.191683 0.981457i \(-0.561395\pi\)
−0.191683 + 0.981457i \(0.561395\pi\)
\(242\) 0 0
\(243\) −13.6227 −0.873899
\(244\) −6.34059 −0.405915
\(245\) 6.42000 0.410159
\(246\) −11.5242 −0.734753
\(247\) 3.97832 0.253135
\(248\) −1.48635 −0.0943832
\(249\) 23.5651 1.49338
\(250\) 9.71268 0.614284
\(251\) −21.0594 −1.32926 −0.664630 0.747173i \(-0.731411\pi\)
−0.664630 + 0.747173i \(0.731411\pi\)
\(252\) −4.38291 −0.276098
\(253\) 0 0
\(254\) 13.3466 0.837441
\(255\) −11.0901 −0.694488
\(256\) 1.00000 0.0625000
\(257\) 1.27738 0.0796811 0.0398405 0.999206i \(-0.487315\pi\)
0.0398405 + 0.999206i \(0.487315\pi\)
\(258\) −9.65314 −0.600978
\(259\) 5.42248 0.336936
\(260\) −9.78686 −0.606955
\(261\) 9.19528 0.569174
\(262\) 4.58757 0.283421
\(263\) 8.85896 0.546267 0.273134 0.961976i \(-0.411940\pi\)
0.273134 + 0.961976i \(0.411940\pi\)
\(264\) 0 0
\(265\) −28.9324 −1.77730
\(266\) −3.09995 −0.190070
\(267\) −9.74167 −0.596181
\(268\) 14.1154 0.862236
\(269\) 26.0234 1.58667 0.793337 0.608783i \(-0.208342\pi\)
0.793337 + 0.608783i \(0.208342\pi\)
\(270\) 8.19772 0.498897
\(271\) 17.0826 1.03770 0.518848 0.854867i \(-0.326361\pi\)
0.518848 + 0.854867i \(0.326361\pi\)
\(272\) −2.14576 −0.130106
\(273\) 25.9098 1.56813
\(274\) 13.6371 0.823845
\(275\) 0 0
\(276\) −5.37710 −0.323663
\(277\) 8.49406 0.510359 0.255179 0.966894i \(-0.417865\pi\)
0.255179 + 0.966894i \(0.417865\pi\)
\(278\) 5.78982 0.347251
\(279\) 2.10150 0.125813
\(280\) 7.62603 0.455742
\(281\) 29.4238 1.75527 0.877637 0.479325i \(-0.159119\pi\)
0.877637 + 0.479325i \(0.159119\pi\)
\(282\) 7.15646 0.426161
\(283\) −17.0589 −1.01405 −0.507024 0.861932i \(-0.669255\pi\)
−0.507024 + 0.861932i \(0.669255\pi\)
\(284\) −15.9696 −0.947619
\(285\) −5.16836 −0.306147
\(286\) 0 0
\(287\) −17.0041 −1.00372
\(288\) −1.41386 −0.0833128
\(289\) −12.3957 −0.729159
\(290\) −15.9993 −0.939510
\(291\) −11.4937 −0.673775
\(292\) −3.17623 −0.185875
\(293\) 20.5142 1.19845 0.599227 0.800579i \(-0.295475\pi\)
0.599227 + 0.800579i \(0.295475\pi\)
\(294\) −5.48278 −0.319762
\(295\) −16.3600 −0.952516
\(296\) 1.74921 0.101671
\(297\) 0 0
\(298\) 10.3503 0.599575
\(299\) 10.1821 0.588847
\(300\) 2.20981 0.127584
\(301\) −14.2434 −0.820977
\(302\) 12.1731 0.700483
\(303\) −12.1957 −0.700623
\(304\) −1.00000 −0.0573539
\(305\) −15.5982 −0.893147
\(306\) 3.03382 0.173432
\(307\) 5.64603 0.322236 0.161118 0.986935i \(-0.448490\pi\)
0.161118 + 0.986935i \(0.448490\pi\)
\(308\) 0 0
\(309\) −20.0911 −1.14294
\(310\) −3.65649 −0.207674
\(311\) 8.41613 0.477235 0.238617 0.971114i \(-0.423306\pi\)
0.238617 + 0.971114i \(0.423306\pi\)
\(312\) 8.35814 0.473186
\(313\) 31.3766 1.77351 0.886756 0.462239i \(-0.152954\pi\)
0.886756 + 0.462239i \(0.152954\pi\)
\(314\) −3.72389 −0.210151
\(315\) −10.7822 −0.607507
\(316\) 7.25669 0.408221
\(317\) 7.20289 0.404555 0.202277 0.979328i \(-0.435166\pi\)
0.202277 + 0.979328i \(0.435166\pi\)
\(318\) 24.7087 1.38560
\(319\) 0 0
\(320\) 2.46005 0.137521
\(321\) −30.6027 −1.70808
\(322\) −7.93402 −0.442146
\(323\) 2.14576 0.119393
\(324\) −11.2426 −0.624588
\(325\) −4.18452 −0.232115
\(326\) 19.8920 1.10172
\(327\) −7.10279 −0.392785
\(328\) −5.48529 −0.302875
\(329\) 10.5595 0.582164
\(330\) 0 0
\(331\) 20.4083 1.12174 0.560870 0.827904i \(-0.310467\pi\)
0.560870 + 0.827904i \(0.310467\pi\)
\(332\) 11.2166 0.615588
\(333\) −2.47315 −0.135528
\(334\) 21.9867 1.20306
\(335\) 34.7246 1.89721
\(336\) −6.51275 −0.355300
\(337\) −32.1119 −1.74925 −0.874623 0.484803i \(-0.838891\pi\)
−0.874623 + 0.484803i \(0.838891\pi\)
\(338\) −2.82705 −0.153771
\(339\) 23.8807 1.29702
\(340\) −5.27868 −0.286277
\(341\) 0 0
\(342\) 1.41386 0.0764530
\(343\) 13.6097 0.734855
\(344\) −4.59472 −0.247731
\(345\) −13.2279 −0.712167
\(346\) 25.4819 1.36991
\(347\) 1.12968 0.0606444 0.0303222 0.999540i \(-0.490347\pi\)
0.0303222 + 0.999540i \(0.490347\pi\)
\(348\) 13.6636 0.732448
\(349\) −21.1559 −1.13245 −0.566225 0.824251i \(-0.691597\pi\)
−0.566225 + 0.824251i \(0.691597\pi\)
\(350\) 3.26062 0.174288
\(351\) 13.2571 0.707614
\(352\) 0 0
\(353\) −0.0272714 −0.00145151 −0.000725755 1.00000i \(-0.500231\pi\)
−0.000725755 1.00000i \(0.500231\pi\)
\(354\) 13.9717 0.742588
\(355\) −39.2858 −2.08508
\(356\) −4.63686 −0.245753
\(357\) 13.9748 0.739626
\(358\) −22.7884 −1.20441
\(359\) 15.1154 0.797758 0.398879 0.917004i \(-0.369399\pi\)
0.398879 + 0.917004i \(0.369399\pi\)
\(360\) −3.47817 −0.183316
\(361\) 1.00000 0.0526316
\(362\) 1.54547 0.0812279
\(363\) 0 0
\(364\) 12.3326 0.646404
\(365\) −7.81367 −0.408986
\(366\) 13.3211 0.696304
\(367\) 21.4714 1.12080 0.560399 0.828223i \(-0.310648\pi\)
0.560399 + 0.828223i \(0.310648\pi\)
\(368\) −2.55940 −0.133418
\(369\) 7.75546 0.403733
\(370\) 4.30315 0.223710
\(371\) 36.4582 1.89282
\(372\) 3.12270 0.161904
\(373\) −18.3417 −0.949697 −0.474848 0.880068i \(-0.657497\pi\)
−0.474848 + 0.880068i \(0.657497\pi\)
\(374\) 0 0
\(375\) −20.4056 −1.05374
\(376\) 3.40634 0.175669
\(377\) −25.8736 −1.33256
\(378\) −10.3301 −0.531323
\(379\) 12.3232 0.633003 0.316501 0.948592i \(-0.397492\pi\)
0.316501 + 0.948592i \(0.397492\pi\)
\(380\) −2.46005 −0.126198
\(381\) −28.0402 −1.43654
\(382\) −7.14404 −0.365521
\(383\) 28.7507 1.46909 0.734546 0.678558i \(-0.237395\pi\)
0.734546 + 0.678558i \(0.237395\pi\)
\(384\) −2.10092 −0.107212
\(385\) 0 0
\(386\) 12.0980 0.615772
\(387\) 6.49631 0.330226
\(388\) −5.47081 −0.277738
\(389\) 2.72988 0.138410 0.0692052 0.997602i \(-0.477954\pi\)
0.0692052 + 0.997602i \(0.477954\pi\)
\(390\) 20.5614 1.04117
\(391\) 5.49187 0.277736
\(392\) −2.60971 −0.131810
\(393\) −9.63812 −0.486179
\(394\) −18.2516 −0.919502
\(395\) 17.8518 0.898222
\(396\) 0 0
\(397\) 7.21330 0.362025 0.181013 0.983481i \(-0.442062\pi\)
0.181013 + 0.983481i \(0.442062\pi\)
\(398\) −23.9705 −1.20153
\(399\) 6.51275 0.326045
\(400\) 1.05183 0.0525915
\(401\) −1.18981 −0.0594164 −0.0297082 0.999559i \(-0.509458\pi\)
−0.0297082 + 0.999559i \(0.509458\pi\)
\(402\) −29.6554 −1.47908
\(403\) −5.91317 −0.294556
\(404\) −5.80492 −0.288806
\(405\) −27.6573 −1.37430
\(406\) 20.1610 1.00057
\(407\) 0 0
\(408\) 4.50808 0.223183
\(409\) 11.7792 0.582442 0.291221 0.956656i \(-0.405939\pi\)
0.291221 + 0.956656i \(0.405939\pi\)
\(410\) −13.4941 −0.666425
\(411\) −28.6504 −1.41322
\(412\) −9.56301 −0.471136
\(413\) 20.6156 1.01443
\(414\) 3.61865 0.177847
\(415\) 27.5932 1.35450
\(416\) 3.97832 0.195053
\(417\) −12.1640 −0.595672
\(418\) 0 0
\(419\) 20.0798 0.980963 0.490482 0.871452i \(-0.336821\pi\)
0.490482 + 0.871452i \(0.336821\pi\)
\(420\) −16.0217 −0.781778
\(421\) 0.885182 0.0431412 0.0215706 0.999767i \(-0.493133\pi\)
0.0215706 + 0.999767i \(0.493133\pi\)
\(422\) −20.7466 −1.00993
\(423\) −4.81611 −0.234167
\(424\) 11.7609 0.571160
\(425\) −2.25698 −0.109480
\(426\) 33.5508 1.62554
\(427\) 19.6555 0.951198
\(428\) −14.5663 −0.704090
\(429\) 0 0
\(430\) −11.3032 −0.545090
\(431\) −20.3046 −0.978038 −0.489019 0.872273i \(-0.662645\pi\)
−0.489019 + 0.872273i \(0.662645\pi\)
\(432\) −3.33234 −0.160327
\(433\) −36.1713 −1.73828 −0.869140 0.494566i \(-0.835327\pi\)
−0.869140 + 0.494566i \(0.835327\pi\)
\(434\) 4.60761 0.221172
\(435\) 33.6132 1.61163
\(436\) −3.38080 −0.161911
\(437\) 2.55940 0.122433
\(438\) 6.67300 0.318848
\(439\) 21.4914 1.02573 0.512864 0.858470i \(-0.328584\pi\)
0.512864 + 0.858470i \(0.328584\pi\)
\(440\) 0 0
\(441\) 3.68977 0.175703
\(442\) −8.53654 −0.406042
\(443\) −24.5995 −1.16876 −0.584379 0.811481i \(-0.698662\pi\)
−0.584379 + 0.811481i \(0.698662\pi\)
\(444\) −3.67496 −0.174406
\(445\) −11.4069 −0.540739
\(446\) −28.3845 −1.34405
\(447\) −21.7451 −1.02851
\(448\) −3.09995 −0.146459
\(449\) 35.2701 1.66450 0.832251 0.554400i \(-0.187052\pi\)
0.832251 + 0.554400i \(0.187052\pi\)
\(450\) −1.48715 −0.0701047
\(451\) 0 0
\(452\) 11.3668 0.534650
\(453\) −25.5747 −1.20160
\(454\) 8.50634 0.399222
\(455\) 30.3388 1.42230
\(456\) 2.10092 0.0983846
\(457\) −7.37055 −0.344780 −0.172390 0.985029i \(-0.555149\pi\)
−0.172390 + 0.985029i \(0.555149\pi\)
\(458\) 1.70730 0.0797770
\(459\) 7.15042 0.333753
\(460\) −6.29625 −0.293564
\(461\) −36.4875 −1.69939 −0.849696 0.527272i \(-0.823215\pi\)
−0.849696 + 0.527272i \(0.823215\pi\)
\(462\) 0 0
\(463\) −16.2208 −0.753844 −0.376922 0.926245i \(-0.623018\pi\)
−0.376922 + 0.926245i \(0.623018\pi\)
\(464\) 6.50365 0.301924
\(465\) 7.68199 0.356244
\(466\) −9.95632 −0.461217
\(467\) 4.27354 0.197756 0.0988779 0.995100i \(-0.468475\pi\)
0.0988779 + 0.995100i \(0.468475\pi\)
\(468\) −5.62481 −0.260007
\(469\) −43.7571 −2.02052
\(470\) 8.37977 0.386530
\(471\) 7.82359 0.360492
\(472\) 6.65028 0.306104
\(473\) 0 0
\(474\) −15.2457 −0.700260
\(475\) −1.05183 −0.0482613
\(476\) 6.65177 0.304883
\(477\) −16.6283 −0.761359
\(478\) −16.2786 −0.744564
\(479\) −39.1936 −1.79080 −0.895402 0.445260i \(-0.853111\pi\)
−0.895402 + 0.445260i \(0.853111\pi\)
\(480\) −5.16836 −0.235902
\(481\) 6.95893 0.317300
\(482\) 5.95144 0.271081
\(483\) 16.6687 0.758454
\(484\) 0 0
\(485\) −13.4585 −0.611117
\(486\) 13.6227 0.617940
\(487\) 3.27438 0.148376 0.0741882 0.997244i \(-0.476363\pi\)
0.0741882 + 0.997244i \(0.476363\pi\)
\(488\) 6.34059 0.287025
\(489\) −41.7916 −1.88988
\(490\) −6.42000 −0.290026
\(491\) 40.6503 1.83452 0.917260 0.398288i \(-0.130396\pi\)
0.917260 + 0.398288i \(0.130396\pi\)
\(492\) 11.5242 0.519549
\(493\) −13.9553 −0.628515
\(494\) −3.97832 −0.178993
\(495\) 0 0
\(496\) 1.48635 0.0667390
\(497\) 49.5049 2.22060
\(498\) −23.5651 −1.05598
\(499\) −14.1445 −0.633195 −0.316598 0.948560i \(-0.602540\pi\)
−0.316598 + 0.948560i \(0.602540\pi\)
\(500\) −9.71268 −0.434364
\(501\) −46.1923 −2.06372
\(502\) 21.0594 0.939928
\(503\) −27.7402 −1.23688 −0.618438 0.785834i \(-0.712234\pi\)
−0.618438 + 0.785834i \(0.712234\pi\)
\(504\) 4.38291 0.195230
\(505\) −14.2804 −0.635468
\(506\) 0 0
\(507\) 5.93940 0.263778
\(508\) −13.3466 −0.592160
\(509\) 4.86817 0.215778 0.107889 0.994163i \(-0.465591\pi\)
0.107889 + 0.994163i \(0.465591\pi\)
\(510\) 11.0901 0.491077
\(511\) 9.84616 0.435568
\(512\) −1.00000 −0.0441942
\(513\) 3.33234 0.147127
\(514\) −1.27738 −0.0563430
\(515\) −23.5254 −1.03666
\(516\) 9.65314 0.424956
\(517\) 0 0
\(518\) −5.42248 −0.238250
\(519\) −53.5353 −2.34994
\(520\) 9.78686 0.429182
\(521\) 18.6548 0.817281 0.408641 0.912695i \(-0.366003\pi\)
0.408641 + 0.912695i \(0.366003\pi\)
\(522\) −9.19528 −0.402466
\(523\) −8.39239 −0.366974 −0.183487 0.983022i \(-0.558738\pi\)
−0.183487 + 0.983022i \(0.558738\pi\)
\(524\) −4.58757 −0.200409
\(525\) −6.85031 −0.298972
\(526\) −8.85896 −0.386269
\(527\) −3.18935 −0.138930
\(528\) 0 0
\(529\) −16.4495 −0.715194
\(530\) 28.9324 1.25674
\(531\) −9.40259 −0.408038
\(532\) 3.09995 0.134400
\(533\) −21.8223 −0.945227
\(534\) 9.74167 0.421563
\(535\) −35.8338 −1.54923
\(536\) −14.1154 −0.609693
\(537\) 47.8766 2.06603
\(538\) −26.0234 −1.12195
\(539\) 0 0
\(540\) −8.19772 −0.352774
\(541\) −32.0199 −1.37664 −0.688322 0.725405i \(-0.741653\pi\)
−0.688322 + 0.725405i \(0.741653\pi\)
\(542\) −17.0826 −0.733762
\(543\) −3.24690 −0.139338
\(544\) 2.14576 0.0919989
\(545\) −8.31693 −0.356258
\(546\) −25.9098 −1.10884
\(547\) 25.7176 1.09961 0.549803 0.835295i \(-0.314703\pi\)
0.549803 + 0.835295i \(0.314703\pi\)
\(548\) −13.6371 −0.582546
\(549\) −8.96474 −0.382606
\(550\) 0 0
\(551\) −6.50365 −0.277065
\(552\) 5.37710 0.228864
\(553\) −22.4954 −0.956602
\(554\) −8.49406 −0.360878
\(555\) −9.04057 −0.383751
\(556\) −5.78982 −0.245543
\(557\) 37.3111 1.58092 0.790461 0.612512i \(-0.209841\pi\)
0.790461 + 0.612512i \(0.209841\pi\)
\(558\) −2.10150 −0.0889634
\(559\) −18.2793 −0.773131
\(560\) −7.62603 −0.322259
\(561\) 0 0
\(562\) −29.4238 −1.24117
\(563\) 0.758990 0.0319876 0.0159938 0.999872i \(-0.494909\pi\)
0.0159938 + 0.999872i \(0.494909\pi\)
\(564\) −7.15646 −0.301341
\(565\) 27.9629 1.17641
\(566\) 17.0589 0.717041
\(567\) 34.8515 1.46362
\(568\) 15.9696 0.670068
\(569\) −31.2487 −1.31001 −0.655007 0.755623i \(-0.727334\pi\)
−0.655007 + 0.755623i \(0.727334\pi\)
\(570\) 5.16836 0.216479
\(571\) −20.5848 −0.861445 −0.430723 0.902484i \(-0.641741\pi\)
−0.430723 + 0.902484i \(0.641741\pi\)
\(572\) 0 0
\(573\) 15.0091 0.627012
\(574\) 17.0041 0.709739
\(575\) −2.69206 −0.112267
\(576\) 1.41386 0.0589110
\(577\) 12.5133 0.520934 0.260467 0.965483i \(-0.416124\pi\)
0.260467 + 0.965483i \(0.416124\pi\)
\(578\) 12.3957 0.515593
\(579\) −25.4169 −1.05629
\(580\) 15.9993 0.664334
\(581\) −34.7708 −1.44254
\(582\) 11.4937 0.476431
\(583\) 0 0
\(584\) 3.17623 0.131433
\(585\) −13.8373 −0.572102
\(586\) −20.5142 −0.847435
\(587\) 12.0214 0.496178 0.248089 0.968737i \(-0.420197\pi\)
0.248089 + 0.968737i \(0.420197\pi\)
\(588\) 5.48278 0.226106
\(589\) −1.48635 −0.0612439
\(590\) 16.3600 0.673531
\(591\) 38.3451 1.57731
\(592\) −1.74921 −0.0718922
\(593\) −33.2839 −1.36680 −0.683402 0.730042i \(-0.739500\pi\)
−0.683402 + 0.730042i \(0.739500\pi\)
\(594\) 0 0
\(595\) 16.3637 0.670844
\(596\) −10.3503 −0.423963
\(597\) 50.3602 2.06110
\(598\) −10.1821 −0.416378
\(599\) −14.8580 −0.607081 −0.303541 0.952819i \(-0.598169\pi\)
−0.303541 + 0.952819i \(0.598169\pi\)
\(600\) −2.20981 −0.0902152
\(601\) 30.9531 1.26260 0.631301 0.775538i \(-0.282521\pi\)
0.631301 + 0.775538i \(0.282521\pi\)
\(602\) 14.2434 0.580518
\(603\) 19.9573 0.812724
\(604\) −12.1731 −0.495316
\(605\) 0 0
\(606\) 12.1957 0.495415
\(607\) 29.4283 1.19446 0.597229 0.802071i \(-0.296268\pi\)
0.597229 + 0.802071i \(0.296268\pi\)
\(608\) 1.00000 0.0405554
\(609\) −42.3567 −1.71638
\(610\) 15.5982 0.631551
\(611\) 13.5515 0.548236
\(612\) −3.03382 −0.122635
\(613\) 21.5787 0.871554 0.435777 0.900055i \(-0.356474\pi\)
0.435777 + 0.900055i \(0.356474\pi\)
\(614\) −5.64603 −0.227855
\(615\) 28.3500 1.14318
\(616\) 0 0
\(617\) −21.8270 −0.878721 −0.439360 0.898311i \(-0.644795\pi\)
−0.439360 + 0.898311i \(0.644795\pi\)
\(618\) 20.0911 0.808183
\(619\) 41.5379 1.66955 0.834775 0.550592i \(-0.185598\pi\)
0.834775 + 0.550592i \(0.185598\pi\)
\(620\) 3.65649 0.146848
\(621\) 8.52881 0.342249
\(622\) −8.41613 −0.337456
\(623\) 14.3740 0.575884
\(624\) −8.35814 −0.334593
\(625\) −29.1528 −1.16611
\(626\) −31.3766 −1.25406
\(627\) 0 0
\(628\) 3.72389 0.148599
\(629\) 3.75340 0.149658
\(630\) 10.7822 0.429572
\(631\) 1.40462 0.0559171 0.0279585 0.999609i \(-0.491099\pi\)
0.0279585 + 0.999609i \(0.491099\pi\)
\(632\) −7.25669 −0.288656
\(633\) 43.5870 1.73243
\(634\) −7.20289 −0.286063
\(635\) −32.8333 −1.30295
\(636\) −24.7087 −0.979765
\(637\) −10.3822 −0.411360
\(638\) 0 0
\(639\) −22.5788 −0.893203
\(640\) −2.46005 −0.0972419
\(641\) −12.6801 −0.500832 −0.250416 0.968138i \(-0.580567\pi\)
−0.250416 + 0.968138i \(0.580567\pi\)
\(642\) 30.6027 1.20779
\(643\) 4.42309 0.174429 0.0872147 0.996190i \(-0.472203\pi\)
0.0872147 + 0.996190i \(0.472203\pi\)
\(644\) 7.93402 0.312644
\(645\) 23.7472 0.935044
\(646\) −2.14576 −0.0844239
\(647\) −24.5901 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(648\) 11.2426 0.441650
\(649\) 0 0
\(650\) 4.18452 0.164130
\(651\) −9.68022 −0.379398
\(652\) −19.8920 −0.779032
\(653\) 19.5368 0.764533 0.382267 0.924052i \(-0.375144\pi\)
0.382267 + 0.924052i \(0.375144\pi\)
\(654\) 7.10279 0.277741
\(655\) −11.2856 −0.440967
\(656\) 5.48529 0.214165
\(657\) −4.49076 −0.175201
\(658\) −10.5595 −0.411652
\(659\) 35.3980 1.37891 0.689456 0.724328i \(-0.257850\pi\)
0.689456 + 0.724328i \(0.257850\pi\)
\(660\) 0 0
\(661\) −26.3898 −1.02644 −0.513222 0.858256i \(-0.671548\pi\)
−0.513222 + 0.858256i \(0.671548\pi\)
\(662\) −20.4083 −0.793190
\(663\) 17.9346 0.696522
\(664\) −11.2166 −0.435287
\(665\) 7.62603 0.295725
\(666\) 2.47315 0.0958326
\(667\) −16.6455 −0.644514
\(668\) −21.9867 −0.850690
\(669\) 59.6336 2.30557
\(670\) −34.7246 −1.34153
\(671\) 0 0
\(672\) 6.51275 0.251235
\(673\) −4.02795 −0.155266 −0.0776331 0.996982i \(-0.524736\pi\)
−0.0776331 + 0.996982i \(0.524736\pi\)
\(674\) 32.1119 1.23690
\(675\) −3.50506 −0.134910
\(676\) 2.82705 0.108733
\(677\) 21.6069 0.830419 0.415210 0.909726i \(-0.363708\pi\)
0.415210 + 0.909726i \(0.363708\pi\)
\(678\) −23.8807 −0.917135
\(679\) 16.9593 0.650837
\(680\) 5.27868 0.202428
\(681\) −17.8711 −0.684823
\(682\) 0 0
\(683\) 3.73163 0.142787 0.0713935 0.997448i \(-0.477255\pi\)
0.0713935 + 0.997448i \(0.477255\pi\)
\(684\) −1.41386 −0.0540605
\(685\) −33.5478 −1.28180
\(686\) −13.6097 −0.519621
\(687\) −3.58691 −0.136849
\(688\) 4.59472 0.175172
\(689\) 46.7887 1.78251
\(690\) 13.2279 0.503578
\(691\) 42.4147 1.61353 0.806765 0.590872i \(-0.201216\pi\)
0.806765 + 0.590872i \(0.201216\pi\)
\(692\) −25.4819 −0.968675
\(693\) 0 0
\(694\) −1.12968 −0.0428820
\(695\) −14.2432 −0.540277
\(696\) −13.6636 −0.517919
\(697\) −11.7701 −0.445826
\(698\) 21.1559 0.800763
\(699\) 20.9174 0.791170
\(700\) −3.26062 −0.123240
\(701\) −51.9082 −1.96054 −0.980272 0.197654i \(-0.936668\pi\)
−0.980272 + 0.197654i \(0.936668\pi\)
\(702\) −13.2571 −0.500358
\(703\) 1.74921 0.0659728
\(704\) 0 0
\(705\) −17.6052 −0.663051
\(706\) 0.0272714 0.00102637
\(707\) 17.9950 0.676771
\(708\) −13.9717 −0.525089
\(709\) −42.1161 −1.58170 −0.790852 0.612008i \(-0.790362\pi\)
−0.790852 + 0.612008i \(0.790362\pi\)
\(710\) 39.2858 1.47437
\(711\) 10.2600 0.384779
\(712\) 4.63686 0.173774
\(713\) −3.80416 −0.142467
\(714\) −13.9748 −0.522995
\(715\) 0 0
\(716\) 22.7884 0.851643
\(717\) 34.2000 1.27722
\(718\) −15.1154 −0.564100
\(719\) −6.37162 −0.237621 −0.118811 0.992917i \(-0.537908\pi\)
−0.118811 + 0.992917i \(0.537908\pi\)
\(720\) 3.47817 0.129624
\(721\) 29.6449 1.10403
\(722\) −1.00000 −0.0372161
\(723\) −12.5035 −0.465010
\(724\) −1.54547 −0.0574368
\(725\) 6.84074 0.254059
\(726\) 0 0
\(727\) −36.8358 −1.36616 −0.683082 0.730342i \(-0.739361\pi\)
−0.683082 + 0.730342i \(0.739361\pi\)
\(728\) −12.3326 −0.457077
\(729\) 5.10748 0.189166
\(730\) 7.81367 0.289197
\(731\) −9.85919 −0.364655
\(732\) −13.3211 −0.492361
\(733\) −7.23710 −0.267308 −0.133654 0.991028i \(-0.542671\pi\)
−0.133654 + 0.991028i \(0.542671\pi\)
\(734\) −21.4714 −0.792524
\(735\) 13.4879 0.497509
\(736\) 2.55940 0.0943408
\(737\) 0 0
\(738\) −7.75546 −0.285482
\(739\) 19.6497 0.722825 0.361413 0.932406i \(-0.382295\pi\)
0.361413 + 0.932406i \(0.382295\pi\)
\(740\) −4.30315 −0.158187
\(741\) 8.35814 0.307044
\(742\) −36.4582 −1.33842
\(743\) 7.72331 0.283341 0.141670 0.989914i \(-0.454753\pi\)
0.141670 + 0.989914i \(0.454753\pi\)
\(744\) −3.12270 −0.114484
\(745\) −25.4621 −0.932860
\(746\) 18.3417 0.671537
\(747\) 15.8587 0.580239
\(748\) 0 0
\(749\) 45.1549 1.64992
\(750\) 20.4056 0.745106
\(751\) −45.4390 −1.65809 −0.829046 0.559181i \(-0.811116\pi\)
−0.829046 + 0.559181i \(0.811116\pi\)
\(752\) −3.40634 −0.124217
\(753\) −44.2442 −1.61235
\(754\) 25.8736 0.942261
\(755\) −29.9464 −1.08986
\(756\) 10.3301 0.375702
\(757\) −0.394649 −0.0143438 −0.00717189 0.999974i \(-0.502283\pi\)
−0.00717189 + 0.999974i \(0.502283\pi\)
\(758\) −12.3232 −0.447601
\(759\) 0 0
\(760\) 2.46005 0.0892353
\(761\) 37.5003 1.35938 0.679692 0.733498i \(-0.262114\pi\)
0.679692 + 0.733498i \(0.262114\pi\)
\(762\) 28.0402 1.01579
\(763\) 10.4803 0.379413
\(764\) 7.14404 0.258462
\(765\) −7.46334 −0.269838
\(766\) −28.7507 −1.03881
\(767\) 26.4570 0.955305
\(768\) 2.10092 0.0758104
\(769\) 0.388213 0.0139993 0.00699965 0.999976i \(-0.497772\pi\)
0.00699965 + 0.999976i \(0.497772\pi\)
\(770\) 0 0
\(771\) 2.68368 0.0966505
\(772\) −12.0980 −0.435417
\(773\) −32.5057 −1.16915 −0.584574 0.811341i \(-0.698738\pi\)
−0.584574 + 0.811341i \(0.698738\pi\)
\(774\) −6.49631 −0.233505
\(775\) 1.56339 0.0561585
\(776\) 5.47081 0.196391
\(777\) 11.3922 0.408693
\(778\) −2.72988 −0.0978709
\(779\) −5.48529 −0.196531
\(780\) −20.5614 −0.736216
\(781\) 0 0
\(782\) −5.49187 −0.196389
\(783\) −21.6724 −0.774508
\(784\) 2.60971 0.0932038
\(785\) 9.16094 0.326968
\(786\) 9.63812 0.343781
\(787\) −11.8225 −0.421425 −0.210713 0.977548i \(-0.567578\pi\)
−0.210713 + 0.977548i \(0.567578\pi\)
\(788\) 18.2516 0.650186
\(789\) 18.6120 0.662604
\(790\) −17.8518 −0.635139
\(791\) −35.2366 −1.25287
\(792\) 0 0
\(793\) 25.2249 0.895763
\(794\) −7.21330 −0.255991
\(795\) −60.7846 −2.15581
\(796\) 23.9705 0.849613
\(797\) 27.4045 0.970719 0.485359 0.874315i \(-0.338689\pi\)
0.485359 + 0.874315i \(0.338689\pi\)
\(798\) −6.51275 −0.230549
\(799\) 7.30921 0.258581
\(800\) −1.05183 −0.0371878
\(801\) −6.55589 −0.231641
\(802\) 1.18981 0.0420137
\(803\) 0 0
\(804\) 29.6554 1.04586
\(805\) 19.5181 0.687922
\(806\) 5.91317 0.208283
\(807\) 54.6731 1.92458
\(808\) 5.80492 0.204216
\(809\) 9.23218 0.324586 0.162293 0.986743i \(-0.448111\pi\)
0.162293 + 0.986743i \(0.448111\pi\)
\(810\) 27.6573 0.971778
\(811\) −28.3825 −0.996646 −0.498323 0.866992i \(-0.666051\pi\)
−0.498323 + 0.866992i \(0.666051\pi\)
\(812\) −20.1610 −0.707513
\(813\) 35.8892 1.25869
\(814\) 0 0
\(815\) −48.9353 −1.71413
\(816\) −4.50808 −0.157814
\(817\) −4.59472 −0.160749
\(818\) −11.7792 −0.411849
\(819\) 17.4366 0.609285
\(820\) 13.4941 0.471233
\(821\) 29.3170 1.02317 0.511584 0.859233i \(-0.329059\pi\)
0.511584 + 0.859233i \(0.329059\pi\)
\(822\) 28.6504 0.999296
\(823\) −19.1547 −0.667692 −0.333846 0.942628i \(-0.608347\pi\)
−0.333846 + 0.942628i \(0.608347\pi\)
\(824\) 9.56301 0.333143
\(825\) 0 0
\(826\) −20.6156 −0.717307
\(827\) −19.0633 −0.662896 −0.331448 0.943473i \(-0.607537\pi\)
−0.331448 + 0.943473i \(0.607537\pi\)
\(828\) −3.61865 −0.125757
\(829\) −3.45420 −0.119969 −0.0599847 0.998199i \(-0.519105\pi\)
−0.0599847 + 0.998199i \(0.519105\pi\)
\(830\) −27.5932 −0.957775
\(831\) 17.8453 0.619048
\(832\) −3.97832 −0.137923
\(833\) −5.59981 −0.194022
\(834\) 12.1640 0.421203
\(835\) −54.0883 −1.87180
\(836\) 0 0
\(837\) −4.95302 −0.171202
\(838\) −20.0798 −0.693646
\(839\) 16.7961 0.579865 0.289932 0.957047i \(-0.406367\pi\)
0.289932 + 0.957047i \(0.406367\pi\)
\(840\) 16.0217 0.552800
\(841\) 13.2975 0.458533
\(842\) −0.885182 −0.0305054
\(843\) 61.8170 2.12909
\(844\) 20.7466 0.714129
\(845\) 6.95466 0.239248
\(846\) 4.81611 0.165581
\(847\) 0 0
\(848\) −11.7609 −0.403871
\(849\) −35.8395 −1.23001
\(850\) 2.25698 0.0774138
\(851\) 4.47694 0.153467
\(852\) −33.5508 −1.14943
\(853\) −5.53724 −0.189592 −0.0947958 0.995497i \(-0.530220\pi\)
−0.0947958 + 0.995497i \(0.530220\pi\)
\(854\) −19.6555 −0.672598
\(855\) −3.47817 −0.118951
\(856\) 14.5663 0.497867
\(857\) 26.5793 0.907932 0.453966 0.891019i \(-0.350009\pi\)
0.453966 + 0.891019i \(0.350009\pi\)
\(858\) 0 0
\(859\) 19.7426 0.673610 0.336805 0.941574i \(-0.390654\pi\)
0.336805 + 0.941574i \(0.390654\pi\)
\(860\) 11.3032 0.385437
\(861\) −35.7243 −1.21748
\(862\) 20.3046 0.691577
\(863\) −22.8417 −0.777539 −0.388770 0.921335i \(-0.627100\pi\)
−0.388770 + 0.921335i \(0.627100\pi\)
\(864\) 3.33234 0.113369
\(865\) −62.6866 −2.13141
\(866\) 36.1713 1.22915
\(867\) −26.0424 −0.884445
\(868\) −4.60761 −0.156392
\(869\) 0 0
\(870\) −33.6132 −1.13959
\(871\) −56.1557 −1.90276
\(872\) 3.38080 0.114488
\(873\) −7.73499 −0.261790
\(874\) −2.55940 −0.0865730
\(875\) 30.1089 1.01787
\(876\) −6.67300 −0.225460
\(877\) 39.1209 1.32102 0.660510 0.750817i \(-0.270340\pi\)
0.660510 + 0.750817i \(0.270340\pi\)
\(878\) −21.4914 −0.725300
\(879\) 43.0987 1.45368
\(880\) 0 0
\(881\) 39.7517 1.33927 0.669635 0.742691i \(-0.266451\pi\)
0.669635 + 0.742691i \(0.266451\pi\)
\(882\) −3.68977 −0.124241
\(883\) −24.1017 −0.811088 −0.405544 0.914075i \(-0.632918\pi\)
−0.405544 + 0.914075i \(0.632918\pi\)
\(884\) 8.53654 0.287115
\(885\) −34.3710 −1.15537
\(886\) 24.5995 0.826437
\(887\) −40.9484 −1.37491 −0.687457 0.726225i \(-0.741273\pi\)
−0.687457 + 0.726225i \(0.741273\pi\)
\(888\) 3.67496 0.123323
\(889\) 41.3739 1.38764
\(890\) 11.4069 0.382360
\(891\) 0 0
\(892\) 28.3845 0.950384
\(893\) 3.40634 0.113989
\(894\) 21.7451 0.727264
\(895\) 56.0606 1.87390
\(896\) 3.09995 0.103562
\(897\) 21.3918 0.714252
\(898\) −35.2701 −1.17698
\(899\) 9.66669 0.322402
\(900\) 1.48715 0.0495715
\(901\) 25.2361 0.840737
\(902\) 0 0
\(903\) −29.9243 −0.995818
\(904\) −11.3668 −0.378054
\(905\) −3.80192 −0.126380
\(906\) 25.5747 0.849662
\(907\) −54.8992 −1.82290 −0.911449 0.411413i \(-0.865035\pi\)
−0.911449 + 0.411413i \(0.865035\pi\)
\(908\) −8.50634 −0.282293
\(909\) −8.20737 −0.272221
\(910\) −30.3388 −1.00572
\(911\) 46.8459 1.55207 0.776037 0.630687i \(-0.217227\pi\)
0.776037 + 0.630687i \(0.217227\pi\)
\(912\) −2.10092 −0.0695684
\(913\) 0 0
\(914\) 7.37055 0.243796
\(915\) −32.7705 −1.08336
\(916\) −1.70730 −0.0564109
\(917\) 14.2213 0.469627
\(918\) −7.15042 −0.235999
\(919\) −1.76516 −0.0582272 −0.0291136 0.999576i \(-0.509268\pi\)
−0.0291136 + 0.999576i \(0.509268\pi\)
\(920\) 6.29625 0.207581
\(921\) 11.8619 0.390861
\(922\) 36.4875 1.20165
\(923\) 63.5320 2.09118
\(924\) 0 0
\(925\) −1.83988 −0.0604947
\(926\) 16.2208 0.533048
\(927\) −13.5208 −0.444081
\(928\) −6.50365 −0.213493
\(929\) −28.8886 −0.947805 −0.473902 0.880577i \(-0.657155\pi\)
−0.473902 + 0.880577i \(0.657155\pi\)
\(930\) −7.68199 −0.251902
\(931\) −2.60971 −0.0855297
\(932\) 9.95632 0.326130
\(933\) 17.6816 0.578870
\(934\) −4.27354 −0.139835
\(935\) 0 0
\(936\) 5.62481 0.183853
\(937\) 25.1445 0.821436 0.410718 0.911762i \(-0.365278\pi\)
0.410718 + 0.911762i \(0.365278\pi\)
\(938\) 43.7571 1.42872
\(939\) 65.9198 2.15121
\(940\) −8.37977 −0.273318
\(941\) −0.744662 −0.0242753 −0.0121376 0.999926i \(-0.503864\pi\)
−0.0121376 + 0.999926i \(0.503864\pi\)
\(942\) −7.82359 −0.254906
\(943\) −14.0391 −0.457175
\(944\) −6.65028 −0.216448
\(945\) 25.4125 0.826670
\(946\) 0 0
\(947\) 54.6088 1.77455 0.887273 0.461244i \(-0.152597\pi\)
0.887273 + 0.461244i \(0.152597\pi\)
\(948\) 15.2457 0.495158
\(949\) 12.6361 0.410184
\(950\) 1.05183 0.0341259
\(951\) 15.1327 0.490712
\(952\) −6.65177 −0.215585
\(953\) 29.4684 0.954574 0.477287 0.878747i \(-0.341620\pi\)
0.477287 + 0.878747i \(0.341620\pi\)
\(954\) 16.6283 0.538362
\(955\) 17.5747 0.568703
\(956\) 16.2786 0.526487
\(957\) 0 0
\(958\) 39.1936 1.26629
\(959\) 42.2742 1.36511
\(960\) 5.16836 0.166808
\(961\) −28.7908 −0.928734
\(962\) −6.95893 −0.224365
\(963\) −20.5948 −0.663659
\(964\) −5.95144 −0.191683
\(965\) −29.7616 −0.958061
\(966\) −16.6687 −0.536308
\(967\) −30.8647 −0.992541 −0.496271 0.868168i \(-0.665298\pi\)
−0.496271 + 0.868168i \(0.665298\pi\)
\(968\) 0 0
\(969\) 4.50808 0.144820
\(970\) 13.4585 0.432125
\(971\) −10.8297 −0.347541 −0.173771 0.984786i \(-0.555595\pi\)
−0.173771 + 0.984786i \(0.555595\pi\)
\(972\) −13.6227 −0.436949
\(973\) 17.9482 0.575392
\(974\) −3.27438 −0.104918
\(975\) −8.79134 −0.281548
\(976\) −6.34059 −0.202957
\(977\) 5.53214 0.176989 0.0884945 0.996077i \(-0.471794\pi\)
0.0884945 + 0.996077i \(0.471794\pi\)
\(978\) 41.7916 1.33635
\(979\) 0 0
\(980\) 6.42000 0.205079
\(981\) −4.77999 −0.152613
\(982\) −40.6503 −1.29720
\(983\) 22.2474 0.709583 0.354791 0.934945i \(-0.384552\pi\)
0.354791 + 0.934945i \(0.384552\pi\)
\(984\) −11.5242 −0.367377
\(985\) 44.8998 1.43063
\(986\) 13.9553 0.444427
\(987\) 22.1847 0.706146
\(988\) 3.97832 0.126567
\(989\) −11.7597 −0.373938
\(990\) 0 0
\(991\) −8.28887 −0.263305 −0.131652 0.991296i \(-0.542028\pi\)
−0.131652 + 0.991296i \(0.542028\pi\)
\(992\) −1.48635 −0.0471916
\(993\) 42.8761 1.36063
\(994\) −49.5049 −1.57020
\(995\) 58.9686 1.86943
\(996\) 23.5651 0.746688
\(997\) −27.5534 −0.872624 −0.436312 0.899795i \(-0.643716\pi\)
−0.436312 + 0.899795i \(0.643716\pi\)
\(998\) 14.1445 0.447736
\(999\) 5.82898 0.184421
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 4598.2.a.cc.1.8 10
11.3 even 5 418.2.f.h.229.2 yes 20
11.4 even 5 418.2.f.h.115.2 20
11.10 odd 2 4598.2.a.cd.1.8 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.h.115.2 20 11.4 even 5
418.2.f.h.229.2 yes 20 11.3 even 5
4598.2.a.cc.1.8 10 1.1 even 1 trivial
4598.2.a.cd.1.8 10 11.10 odd 2