Properties

Label 4235.2.a.bb.1.1
Level $4235$
Weight $2$
Character 4235.1
Self dual yes
Analytic conductor $33.817$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4235.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.8166452560\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.580017.1
Defining polynomial: \(x^{5} - 7 x^{3} - 4 x^{2} + 6 x + 3\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.74137\) of defining polynomial
Character \(\chi\) \(=\) 4235.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.74137 q^{2} -3.04102 q^{3} +5.51511 q^{4} -1.00000 q^{5} +8.33658 q^{6} +1.00000 q^{7} -9.63623 q^{8} +6.24783 q^{9} +O(q^{10})\) \(q-2.74137 q^{2} -3.04102 q^{3} +5.51511 q^{4} -1.00000 q^{5} +8.33658 q^{6} +1.00000 q^{7} -9.63623 q^{8} +6.24783 q^{9} +2.74137 q^{10} -16.7716 q^{12} -6.59521 q^{13} -2.74137 q^{14} +3.04102 q^{15} +15.3863 q^{16} +4.86249 q^{17} -17.1276 q^{18} -0.907153 q^{19} -5.51511 q^{20} -3.04102 q^{21} +3.01425 q^{23} +29.3040 q^{24} +1.00000 q^{25} +18.0799 q^{26} -9.87674 q^{27} +5.51511 q^{28} +0.914310 q^{29} -8.33658 q^{30} -5.33352 q^{31} -22.9070 q^{32} -13.3299 q^{34} -1.00000 q^{35} +34.4575 q^{36} -2.76947 q^{37} +2.48684 q^{38} +20.0562 q^{39} +9.63623 q^{40} +5.06780 q^{41} +8.33658 q^{42} -1.67940 q^{43} -6.24783 q^{45} -8.26318 q^{46} +9.45037 q^{47} -46.7900 q^{48} +1.00000 q^{49} -2.74137 q^{50} -14.7869 q^{51} -36.3733 q^{52} -3.38280 q^{53} +27.0758 q^{54} -9.63623 q^{56} +2.75868 q^{57} -2.50646 q^{58} -1.13751 q^{59} +16.7716 q^{60} -10.4208 q^{61} +14.6212 q^{62} +6.24783 q^{63} +32.0240 q^{64} +6.59521 q^{65} +7.50236 q^{67} +26.8172 q^{68} -9.16641 q^{69} +2.74137 q^{70} +3.74697 q^{71} -60.2056 q^{72} -15.8983 q^{73} +7.59215 q^{74} -3.04102 q^{75} -5.00305 q^{76} -54.9814 q^{78} -13.6658 q^{79} -15.3863 q^{80} +11.2919 q^{81} -13.8927 q^{82} -10.1635 q^{83} -16.7716 q^{84} -4.86249 q^{85} +4.60386 q^{86} -2.78044 q^{87} +7.76964 q^{89} +17.1276 q^{90} -6.59521 q^{91} +16.6239 q^{92} +16.2194 q^{93} -25.9070 q^{94} +0.907153 q^{95} +69.6607 q^{96} +11.3919 q^{97} -2.74137 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9} + O(q^{10}) \) \( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9} - 23 q^{12} - 10 q^{13} + 2 q^{15} + 10 q^{16} - 2 q^{17} - 5 q^{18} + 3 q^{19} - 4 q^{20} - 2 q^{21} + 3 q^{23} + 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} + 4 q^{28} - q^{29} - 5 q^{30} - 12 q^{31} - 29 q^{32} - 20 q^{34} - 5 q^{35} + 45 q^{36} + 9 q^{38} + 2 q^{39} + 12 q^{40} + 11 q^{41} + 5 q^{42} - 10 q^{43} - 11 q^{45} - 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} - 6 q^{51} - 30 q^{52} + 4 q^{53} + 34 q^{54} - 12 q^{56} - 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} - 40 q^{61} - q^{62} + 11 q^{63} + 38 q^{64} + 10 q^{65} + 7 q^{67} + 19 q^{68} - 24 q^{69} + 10 q^{71} - 72 q^{72} - 11 q^{73} + 37 q^{74} - 2 q^{75} - 3 q^{76} - 87 q^{78} - 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} - 26 q^{83} - 23 q^{84} + 2 q^{85} - 17 q^{86} - 14 q^{87} + 5 q^{89} + 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} - 44 q^{94} - 3 q^{95} + 84 q^{96} - 5 q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74137 −1.93844 −0.969221 0.246193i \(-0.920820\pi\)
−0.969221 + 0.246193i \(0.920820\pi\)
\(3\) −3.04102 −1.75574 −0.877868 0.478902i \(-0.841035\pi\)
−0.877868 + 0.478902i \(0.841035\pi\)
\(4\) 5.51511 2.75756
\(5\) −1.00000 −0.447214
\(6\) 8.33658 3.40339
\(7\) 1.00000 0.377964
\(8\) −9.63623 −3.40692
\(9\) 6.24783 2.08261
\(10\) 2.74137 0.866898
\(11\) 0 0
\(12\) −16.7716 −4.84154
\(13\) −6.59521 −1.82918 −0.914591 0.404381i \(-0.867487\pi\)
−0.914591 + 0.404381i \(0.867487\pi\)
\(14\) −2.74137 −0.732662
\(15\) 3.04102 0.785189
\(16\) 15.3863 3.84656
\(17\) 4.86249 1.17933 0.589663 0.807649i \(-0.299260\pi\)
0.589663 + 0.807649i \(0.299260\pi\)
\(18\) −17.1276 −4.03702
\(19\) −0.907153 −0.208115 −0.104058 0.994571i \(-0.533183\pi\)
−0.104058 + 0.994571i \(0.533183\pi\)
\(20\) −5.51511 −1.23322
\(21\) −3.04102 −0.663606
\(22\) 0 0
\(23\) 3.01425 0.628515 0.314257 0.949338i \(-0.398245\pi\)
0.314257 + 0.949338i \(0.398245\pi\)
\(24\) 29.3040 5.98166
\(25\) 1.00000 0.200000
\(26\) 18.0799 3.54576
\(27\) −9.87674 −1.90078
\(28\) 5.51511 1.04226
\(29\) 0.914310 0.169783 0.0848915 0.996390i \(-0.472946\pi\)
0.0848915 + 0.996390i \(0.472946\pi\)
\(30\) −8.33658 −1.52204
\(31\) −5.33352 −0.957929 −0.478964 0.877834i \(-0.658988\pi\)
−0.478964 + 0.877834i \(0.658988\pi\)
\(32\) −22.9070 −4.04942
\(33\) 0 0
\(34\) −13.3299 −2.28606
\(35\) −1.00000 −0.169031
\(36\) 34.4575 5.74292
\(37\) −2.76947 −0.455299 −0.227649 0.973743i \(-0.573104\pi\)
−0.227649 + 0.973743i \(0.573104\pi\)
\(38\) 2.48684 0.403419
\(39\) 20.0562 3.21156
\(40\) 9.63623 1.52362
\(41\) 5.06780 0.791457 0.395729 0.918368i \(-0.370492\pi\)
0.395729 + 0.918368i \(0.370492\pi\)
\(42\) 8.33658 1.28636
\(43\) −1.67940 −0.256106 −0.128053 0.991767i \(-0.540873\pi\)
−0.128053 + 0.991767i \(0.540873\pi\)
\(44\) 0 0
\(45\) −6.24783 −0.931372
\(46\) −8.26318 −1.21834
\(47\) 9.45037 1.37848 0.689239 0.724534i \(-0.257945\pi\)
0.689239 + 0.724534i \(0.257945\pi\)
\(48\) −46.7900 −6.75355
\(49\) 1.00000 0.142857
\(50\) −2.74137 −0.387688
\(51\) −14.7869 −2.07059
\(52\) −36.3733 −5.04407
\(53\) −3.38280 −0.464663 −0.232332 0.972637i \(-0.574635\pi\)
−0.232332 + 0.972637i \(0.574635\pi\)
\(54\) 27.0758 3.68455
\(55\) 0 0
\(56\) −9.63623 −1.28770
\(57\) 2.75868 0.365396
\(58\) −2.50646 −0.329115
\(59\) −1.13751 −0.148091 −0.0740457 0.997255i \(-0.523591\pi\)
−0.0740457 + 0.997255i \(0.523591\pi\)
\(60\) 16.7716 2.16520
\(61\) −10.4208 −1.33424 −0.667122 0.744949i \(-0.732474\pi\)
−0.667122 + 0.744949i \(0.732474\pi\)
\(62\) 14.6212 1.85689
\(63\) 6.24783 0.787153
\(64\) 32.0240 4.00300
\(65\) 6.59521 0.818035
\(66\) 0 0
\(67\) 7.50236 0.916559 0.458280 0.888808i \(-0.348466\pi\)
0.458280 + 0.888808i \(0.348466\pi\)
\(68\) 26.8172 3.25206
\(69\) −9.16641 −1.10351
\(70\) 2.74137 0.327656
\(71\) 3.74697 0.444683 0.222342 0.974969i \(-0.428630\pi\)
0.222342 + 0.974969i \(0.428630\pi\)
\(72\) −60.2056 −7.09529
\(73\) −15.8983 −1.86076 −0.930378 0.366600i \(-0.880522\pi\)
−0.930378 + 0.366600i \(0.880522\pi\)
\(74\) 7.59215 0.882570
\(75\) −3.04102 −0.351147
\(76\) −5.00305 −0.573890
\(77\) 0 0
\(78\) −54.9814 −6.22542
\(79\) −13.6658 −1.53753 −0.768763 0.639534i \(-0.779127\pi\)
−0.768763 + 0.639534i \(0.779127\pi\)
\(80\) −15.3863 −1.72024
\(81\) 11.2919 1.25466
\(82\) −13.8927 −1.53419
\(83\) −10.1635 −1.11559 −0.557793 0.829980i \(-0.688352\pi\)
−0.557793 + 0.829980i \(0.688352\pi\)
\(84\) −16.7716 −1.82993
\(85\) −4.86249 −0.527411
\(86\) 4.60386 0.496447
\(87\) −2.78044 −0.298094
\(88\) 0 0
\(89\) 7.76964 0.823580 0.411790 0.911279i \(-0.364904\pi\)
0.411790 + 0.911279i \(0.364904\pi\)
\(90\) 17.1276 1.80541
\(91\) −6.59521 −0.691365
\(92\) 16.6239 1.73317
\(93\) 16.2194 1.68187
\(94\) −25.9070 −2.67210
\(95\) 0.907153 0.0930720
\(96\) 69.6607 7.10971
\(97\) 11.3919 1.15667 0.578334 0.815800i \(-0.303703\pi\)
0.578334 + 0.815800i \(0.303703\pi\)
\(98\) −2.74137 −0.276920
\(99\) 0 0
\(100\) 5.51511 0.551511
\(101\) −1.17248 −0.116666 −0.0583329 0.998297i \(-0.518578\pi\)
−0.0583329 + 0.998297i \(0.518578\pi\)
\(102\) 40.5365 4.01371
\(103\) −8.97905 −0.884732 −0.442366 0.896834i \(-0.645861\pi\)
−0.442366 + 0.896834i \(0.645861\pi\)
\(104\) 63.5529 6.23188
\(105\) 3.04102 0.296774
\(106\) 9.27351 0.900723
\(107\) 6.26036 0.605211 0.302606 0.953116i \(-0.402143\pi\)
0.302606 + 0.953116i \(0.402143\pi\)
\(108\) −54.4713 −5.24151
\(109\) 1.70340 0.163156 0.0815781 0.996667i \(-0.474004\pi\)
0.0815781 + 0.996667i \(0.474004\pi\)
\(110\) 0 0
\(111\) 8.42204 0.799384
\(112\) 15.3863 1.45386
\(113\) −0.107727 −0.0101341 −0.00506706 0.999987i \(-0.501613\pi\)
−0.00506706 + 0.999987i \(0.501613\pi\)
\(114\) −7.56255 −0.708298
\(115\) −3.01425 −0.281080
\(116\) 5.04252 0.468186
\(117\) −41.2057 −3.80947
\(118\) 3.11834 0.287067
\(119\) 4.86249 0.445744
\(120\) −29.3040 −2.67508
\(121\) 0 0
\(122\) 28.5672 2.58635
\(123\) −15.4113 −1.38959
\(124\) −29.4150 −2.64154
\(125\) −1.00000 −0.0894427
\(126\) −17.1276 −1.52585
\(127\) 14.1131 1.25234 0.626170 0.779687i \(-0.284622\pi\)
0.626170 + 0.779687i \(0.284622\pi\)
\(128\) −41.9757 −3.71016
\(129\) 5.10710 0.449655
\(130\) −18.0799 −1.58571
\(131\) 10.3314 0.902662 0.451331 0.892357i \(-0.350949\pi\)
0.451331 + 0.892357i \(0.350949\pi\)
\(132\) 0 0
\(133\) −0.907153 −0.0786602
\(134\) −20.5667 −1.77670
\(135\) 9.87674 0.850054
\(136\) −46.8561 −4.01787
\(137\) 21.6579 1.85036 0.925180 0.379528i \(-0.123913\pi\)
0.925180 + 0.379528i \(0.123913\pi\)
\(138\) 25.1285 2.13908
\(139\) 14.7057 1.24732 0.623660 0.781695i \(-0.285645\pi\)
0.623660 + 0.781695i \(0.285645\pi\)
\(140\) −5.51511 −0.466112
\(141\) −28.7388 −2.42024
\(142\) −10.2718 −0.861993
\(143\) 0 0
\(144\) 96.1307 8.01089
\(145\) −0.914310 −0.0759293
\(146\) 43.5832 3.60697
\(147\) −3.04102 −0.250820
\(148\) −15.2740 −1.25551
\(149\) −4.62867 −0.379196 −0.189598 0.981862i \(-0.560718\pi\)
−0.189598 + 0.981862i \(0.560718\pi\)
\(150\) 8.33658 0.680679
\(151\) −7.04541 −0.573347 −0.286674 0.958028i \(-0.592550\pi\)
−0.286674 + 0.958028i \(0.592550\pi\)
\(152\) 8.74154 0.709032
\(153\) 30.3800 2.45608
\(154\) 0 0
\(155\) 5.33352 0.428399
\(156\) 110.612 8.85606
\(157\) 6.56589 0.524015 0.262007 0.965066i \(-0.415615\pi\)
0.262007 + 0.965066i \(0.415615\pi\)
\(158\) 37.4631 2.98040
\(159\) 10.2872 0.815826
\(160\) 22.9070 1.81095
\(161\) 3.01425 0.237556
\(162\) −30.9553 −2.43208
\(163\) 12.3470 0.967088 0.483544 0.875320i \(-0.339349\pi\)
0.483544 + 0.875320i \(0.339349\pi\)
\(164\) 27.9495 2.18249
\(165\) 0 0
\(166\) 27.8618 2.16250
\(167\) −3.90433 −0.302126 −0.151063 0.988524i \(-0.548270\pi\)
−0.151063 + 0.988524i \(0.548270\pi\)
\(168\) 29.3040 2.26085
\(169\) 30.4967 2.34590
\(170\) 13.3299 1.02236
\(171\) −5.66774 −0.433423
\(172\) −9.26208 −0.706227
\(173\) −5.70167 −0.433490 −0.216745 0.976228i \(-0.569544\pi\)
−0.216745 + 0.976228i \(0.569544\pi\)
\(174\) 7.62221 0.577838
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 3.45920 0.260010
\(178\) −21.2995 −1.59646
\(179\) −19.6283 −1.46708 −0.733542 0.679644i \(-0.762134\pi\)
−0.733542 + 0.679644i \(0.762134\pi\)
\(180\) −34.4575 −2.56831
\(181\) 15.4408 1.14770 0.573852 0.818959i \(-0.305448\pi\)
0.573852 + 0.818959i \(0.305448\pi\)
\(182\) 18.0799 1.34017
\(183\) 31.6898 2.34258
\(184\) −29.0460 −2.14130
\(185\) 2.76947 0.203616
\(186\) −44.4633 −3.26021
\(187\) 0 0
\(188\) 52.1199 3.80123
\(189\) −9.87674 −0.718427
\(190\) −2.48684 −0.180415
\(191\) −6.21529 −0.449723 −0.224861 0.974391i \(-0.572193\pi\)
−0.224861 + 0.974391i \(0.572193\pi\)
\(192\) −97.3857 −7.02821
\(193\) 21.9778 1.58200 0.790999 0.611817i \(-0.209561\pi\)
0.790999 + 0.611817i \(0.209561\pi\)
\(194\) −31.2293 −2.24213
\(195\) −20.0562 −1.43625
\(196\) 5.51511 0.393937
\(197\) 2.95573 0.210587 0.105294 0.994441i \(-0.466422\pi\)
0.105294 + 0.994441i \(0.466422\pi\)
\(198\) 0 0
\(199\) −11.6335 −0.824674 −0.412337 0.911031i \(-0.635287\pi\)
−0.412337 + 0.911031i \(0.635287\pi\)
\(200\) −9.63623 −0.681384
\(201\) −22.8149 −1.60924
\(202\) 3.21420 0.226150
\(203\) 0.914310 0.0641719
\(204\) −81.5517 −5.70976
\(205\) −5.06780 −0.353950
\(206\) 24.6149 1.71500
\(207\) 18.8325 1.30895
\(208\) −101.476 −7.03606
\(209\) 0 0
\(210\) −8.33658 −0.575278
\(211\) 26.2090 1.80430 0.902152 0.431419i \(-0.141987\pi\)
0.902152 + 0.431419i \(0.141987\pi\)
\(212\) −18.6565 −1.28134
\(213\) −11.3946 −0.780747
\(214\) −17.1620 −1.17317
\(215\) 1.67940 0.114534
\(216\) 95.1745 6.47581
\(217\) −5.33352 −0.362063
\(218\) −4.66965 −0.316269
\(219\) 48.3472 3.26700
\(220\) 0 0
\(221\) −32.0691 −2.15720
\(222\) −23.0879 −1.54956
\(223\) 4.57357 0.306269 0.153134 0.988205i \(-0.451063\pi\)
0.153134 + 0.988205i \(0.451063\pi\)
\(224\) −22.9070 −1.53054
\(225\) 6.24783 0.416522
\(226\) 0.295320 0.0196444
\(227\) 8.22365 0.545823 0.272911 0.962039i \(-0.412013\pi\)
0.272911 + 0.962039i \(0.412013\pi\)
\(228\) 15.2144 1.00760
\(229\) −1.84824 −0.122135 −0.0610675 0.998134i \(-0.519450\pi\)
−0.0610675 + 0.998134i \(0.519450\pi\)
\(230\) 8.26318 0.544858
\(231\) 0 0
\(232\) −8.81050 −0.578438
\(233\) −23.2023 −1.52003 −0.760016 0.649904i \(-0.774809\pi\)
−0.760016 + 0.649904i \(0.774809\pi\)
\(234\) 112.960 7.38444
\(235\) −9.45037 −0.616474
\(236\) −6.27351 −0.408371
\(237\) 41.5581 2.69949
\(238\) −13.3299 −0.864048
\(239\) 26.4737 1.71244 0.856222 0.516608i \(-0.172806\pi\)
0.856222 + 0.516608i \(0.172806\pi\)
\(240\) 46.7900 3.02028
\(241\) −10.7031 −0.689449 −0.344724 0.938704i \(-0.612028\pi\)
−0.344724 + 0.938704i \(0.612028\pi\)
\(242\) 0 0
\(243\) −4.70877 −0.302068
\(244\) −57.4717 −3.67925
\(245\) −1.00000 −0.0638877
\(246\) 42.2481 2.69364
\(247\) 5.98286 0.380680
\(248\) 51.3951 3.26359
\(249\) 30.9074 1.95867
\(250\) 2.74137 0.173380
\(251\) −16.9313 −1.06870 −0.534348 0.845265i \(-0.679443\pi\)
−0.534348 + 0.845265i \(0.679443\pi\)
\(252\) 34.4575 2.17062
\(253\) 0 0
\(254\) −38.6894 −2.42759
\(255\) 14.7869 0.925994
\(256\) 51.0229 3.18893
\(257\) −12.5126 −0.780513 −0.390256 0.920706i \(-0.627614\pi\)
−0.390256 + 0.920706i \(0.627614\pi\)
\(258\) −14.0004 −0.871630
\(259\) −2.76947 −0.172087
\(260\) 36.3733 2.25578
\(261\) 5.71245 0.353592
\(262\) −28.3223 −1.74976
\(263\) 22.4525 1.38448 0.692240 0.721667i \(-0.256624\pi\)
0.692240 + 0.721667i \(0.256624\pi\)
\(264\) 0 0
\(265\) 3.38280 0.207804
\(266\) 2.48684 0.152478
\(267\) −23.6277 −1.44599
\(268\) 41.3764 2.52746
\(269\) −13.7295 −0.837101 −0.418551 0.908194i \(-0.637462\pi\)
−0.418551 + 0.908194i \(0.637462\pi\)
\(270\) −27.0758 −1.64778
\(271\) 1.95141 0.118540 0.0592700 0.998242i \(-0.481123\pi\)
0.0592700 + 0.998242i \(0.481123\pi\)
\(272\) 74.8155 4.53635
\(273\) 20.0562 1.21386
\(274\) −59.3724 −3.58682
\(275\) 0 0
\(276\) −50.5538 −3.04298
\(277\) −6.52545 −0.392076 −0.196038 0.980596i \(-0.562808\pi\)
−0.196038 + 0.980596i \(0.562808\pi\)
\(278\) −40.3138 −2.41786
\(279\) −33.3230 −1.99499
\(280\) 9.63623 0.575875
\(281\) 2.41881 0.144294 0.0721472 0.997394i \(-0.477015\pi\)
0.0721472 + 0.997394i \(0.477015\pi\)
\(282\) 78.7837 4.69150
\(283\) 0.799239 0.0475099 0.0237549 0.999718i \(-0.492438\pi\)
0.0237549 + 0.999718i \(0.492438\pi\)
\(284\) 20.6650 1.22624
\(285\) −2.75868 −0.163410
\(286\) 0 0
\(287\) 5.06780 0.299143
\(288\) −143.119 −8.43336
\(289\) 6.64379 0.390811
\(290\) 2.50646 0.147184
\(291\) −34.6429 −2.03080
\(292\) −87.6810 −5.13114
\(293\) −23.9733 −1.40053 −0.700267 0.713881i \(-0.746936\pi\)
−0.700267 + 0.713881i \(0.746936\pi\)
\(294\) 8.33658 0.486199
\(295\) 1.13751 0.0662285
\(296\) 26.6873 1.55117
\(297\) 0 0
\(298\) 12.6889 0.735049
\(299\) −19.8796 −1.14967
\(300\) −16.7716 −0.968309
\(301\) −1.67940 −0.0967990
\(302\) 19.3141 1.11140
\(303\) 3.56553 0.204835
\(304\) −13.9577 −0.800529
\(305\) 10.4208 0.596692
\(306\) −83.2829 −4.76096
\(307\) 19.0748 1.08865 0.544327 0.838873i \(-0.316785\pi\)
0.544327 + 0.838873i \(0.316785\pi\)
\(308\) 0 0
\(309\) 27.3055 1.55336
\(310\) −14.6212 −0.830426
\(311\) 9.18049 0.520578 0.260289 0.965531i \(-0.416182\pi\)
0.260289 + 0.965531i \(0.416182\pi\)
\(312\) −193.266 −10.9415
\(313\) −13.7670 −0.778160 −0.389080 0.921204i \(-0.627207\pi\)
−0.389080 + 0.921204i \(0.627207\pi\)
\(314\) −17.9995 −1.01577
\(315\) −6.24783 −0.352025
\(316\) −75.3686 −4.23982
\(317\) 22.9456 1.28875 0.644376 0.764709i \(-0.277117\pi\)
0.644376 + 0.764709i \(0.277117\pi\)
\(318\) −28.2010 −1.58143
\(319\) 0 0
\(320\) −32.0240 −1.79019
\(321\) −19.0379 −1.06259
\(322\) −8.26318 −0.460489
\(323\) −4.41102 −0.245436
\(324\) 62.2762 3.45979
\(325\) −6.59521 −0.365836
\(326\) −33.8476 −1.87464
\(327\) −5.18008 −0.286459
\(328\) −48.8345 −2.69643
\(329\) 9.45037 0.521016
\(330\) 0 0
\(331\) −3.44016 −0.189088 −0.0945441 0.995521i \(-0.530139\pi\)
−0.0945441 + 0.995521i \(0.530139\pi\)
\(332\) −56.0527 −3.07629
\(333\) −17.3032 −0.948210
\(334\) 10.7032 0.585654
\(335\) −7.50236 −0.409898
\(336\) −46.7900 −2.55260
\(337\) −30.2961 −1.65033 −0.825166 0.564891i \(-0.808918\pi\)
−0.825166 + 0.564891i \(0.808918\pi\)
\(338\) −83.6029 −4.54740
\(339\) 0.327601 0.0177929
\(340\) −26.8172 −1.45437
\(341\) 0 0
\(342\) 15.5374 0.840165
\(343\) 1.00000 0.0539949
\(344\) 16.1831 0.872534
\(345\) 9.16641 0.493503
\(346\) 15.6304 0.840296
\(347\) −3.88350 −0.208477 −0.104239 0.994552i \(-0.533241\pi\)
−0.104239 + 0.994552i \(0.533241\pi\)
\(348\) −15.3344 −0.822012
\(349\) −19.2489 −1.03037 −0.515184 0.857080i \(-0.672276\pi\)
−0.515184 + 0.857080i \(0.672276\pi\)
\(350\) −2.74137 −0.146532
\(351\) 65.1391 3.47687
\(352\) 0 0
\(353\) −26.3031 −1.39997 −0.699986 0.714156i \(-0.746811\pi\)
−0.699986 + 0.714156i \(0.746811\pi\)
\(354\) −9.48296 −0.504014
\(355\) −3.74697 −0.198868
\(356\) 42.8505 2.27107
\(357\) −14.7869 −0.782608
\(358\) 53.8083 2.84386
\(359\) 21.4912 1.13426 0.567131 0.823627i \(-0.308053\pi\)
0.567131 + 0.823627i \(0.308053\pi\)
\(360\) 60.2056 3.17311
\(361\) −18.1771 −0.956688
\(362\) −42.3289 −2.22476
\(363\) 0 0
\(364\) −36.3733 −1.90648
\(365\) 15.8983 0.832156
\(366\) −86.8736 −4.54095
\(367\) −5.20635 −0.271769 −0.135885 0.990725i \(-0.543388\pi\)
−0.135885 + 0.990725i \(0.543388\pi\)
\(368\) 46.3780 2.41762
\(369\) 31.6628 1.64830
\(370\) −7.59215 −0.394697
\(371\) −3.38280 −0.175626
\(372\) 89.4517 4.63785
\(373\) −15.6505 −0.810354 −0.405177 0.914238i \(-0.632790\pi\)
−0.405177 + 0.914238i \(0.632790\pi\)
\(374\) 0 0
\(375\) 3.04102 0.157038
\(376\) −91.0659 −4.69637
\(377\) −6.03006 −0.310564
\(378\) 27.0758 1.39263
\(379\) 19.0890 0.980537 0.490269 0.871571i \(-0.336899\pi\)
0.490269 + 0.871571i \(0.336899\pi\)
\(380\) 5.00305 0.256651
\(381\) −42.9184 −2.19878
\(382\) 17.0384 0.871761
\(383\) 23.3917 1.19526 0.597629 0.801773i \(-0.296110\pi\)
0.597629 + 0.801773i \(0.296110\pi\)
\(384\) 127.649 6.51406
\(385\) 0 0
\(386\) −60.2494 −3.06661
\(387\) −10.4926 −0.533369
\(388\) 62.8274 3.18958
\(389\) 11.3746 0.576715 0.288358 0.957523i \(-0.406891\pi\)
0.288358 + 0.957523i \(0.406891\pi\)
\(390\) 54.9814 2.78409
\(391\) 14.6568 0.741224
\(392\) −9.63623 −0.486703
\(393\) −31.4182 −1.58484
\(394\) −8.10276 −0.408211
\(395\) 13.6658 0.687602
\(396\) 0 0
\(397\) −15.2708 −0.766418 −0.383209 0.923662i \(-0.625181\pi\)
−0.383209 + 0.923662i \(0.625181\pi\)
\(398\) 31.8916 1.59858
\(399\) 2.75868 0.138107
\(400\) 15.3863 0.769313
\(401\) 9.66663 0.482728 0.241364 0.970435i \(-0.422405\pi\)
0.241364 + 0.970435i \(0.422405\pi\)
\(402\) 62.5440 3.11941
\(403\) 35.1757 1.75223
\(404\) −6.46635 −0.321713
\(405\) −11.2919 −0.561100
\(406\) −2.50646 −0.124394
\(407\) 0 0
\(408\) 142.490 7.05433
\(409\) −14.2142 −0.702849 −0.351425 0.936216i \(-0.614303\pi\)
−0.351425 + 0.936216i \(0.614303\pi\)
\(410\) 13.8927 0.686112
\(411\) −65.8623 −3.24875
\(412\) −49.5205 −2.43970
\(413\) −1.13751 −0.0559733
\(414\) −51.6270 −2.53733
\(415\) 10.1635 0.498905
\(416\) 151.076 7.40712
\(417\) −44.7204 −2.18997
\(418\) 0 0
\(419\) 15.2832 0.746633 0.373317 0.927704i \(-0.378221\pi\)
0.373317 + 0.927704i \(0.378221\pi\)
\(420\) 16.7716 0.818370
\(421\) 8.10283 0.394908 0.197454 0.980312i \(-0.436733\pi\)
0.197454 + 0.980312i \(0.436733\pi\)
\(422\) −71.8487 −3.49754
\(423\) 59.0443 2.87083
\(424\) 32.5974 1.58307
\(425\) 4.86249 0.235865
\(426\) 31.2369 1.51343
\(427\) −10.4208 −0.504296
\(428\) 34.5266 1.66890
\(429\) 0 0
\(430\) −4.60386 −0.222018
\(431\) 16.6282 0.800953 0.400476 0.916307i \(-0.368845\pi\)
0.400476 + 0.916307i \(0.368845\pi\)
\(432\) −151.966 −7.31147
\(433\) 35.0842 1.68604 0.843019 0.537884i \(-0.180776\pi\)
0.843019 + 0.537884i \(0.180776\pi\)
\(434\) 14.6212 0.701838
\(435\) 2.78044 0.133312
\(436\) 9.39445 0.449912
\(437\) −2.73439 −0.130804
\(438\) −132.538 −6.33289
\(439\) −24.3254 −1.16099 −0.580493 0.814265i \(-0.697140\pi\)
−0.580493 + 0.814265i \(0.697140\pi\)
\(440\) 0 0
\(441\) 6.24783 0.297516
\(442\) 87.9133 4.18161
\(443\) 5.08137 0.241423 0.120712 0.992688i \(-0.461482\pi\)
0.120712 + 0.992688i \(0.461482\pi\)
\(444\) 46.4485 2.20435
\(445\) −7.76964 −0.368316
\(446\) −12.5378 −0.593684
\(447\) 14.0759 0.665768
\(448\) 32.0240 1.51299
\(449\) −31.8906 −1.50501 −0.752504 0.658588i \(-0.771154\pi\)
−0.752504 + 0.658588i \(0.771154\pi\)
\(450\) −17.1276 −0.807404
\(451\) 0 0
\(452\) −0.594128 −0.0279454
\(453\) 21.4253 1.00665
\(454\) −22.5441 −1.05805
\(455\) 6.59521 0.309188
\(456\) −26.5832 −1.24487
\(457\) 6.92579 0.323975 0.161987 0.986793i \(-0.448210\pi\)
0.161987 + 0.986793i \(0.448210\pi\)
\(458\) 5.06671 0.236752
\(459\) −48.0255 −2.24164
\(460\) −16.6239 −0.775095
\(461\) 26.9670 1.25598 0.627989 0.778222i \(-0.283878\pi\)
0.627989 + 0.778222i \(0.283878\pi\)
\(462\) 0 0
\(463\) −35.4519 −1.64759 −0.823795 0.566888i \(-0.808147\pi\)
−0.823795 + 0.566888i \(0.808147\pi\)
\(464\) 14.0678 0.653081
\(465\) −16.2194 −0.752156
\(466\) 63.6061 2.94649
\(467\) −32.4914 −1.50352 −0.751762 0.659434i \(-0.770796\pi\)
−0.751762 + 0.659434i \(0.770796\pi\)
\(468\) −227.254 −10.5048
\(469\) 7.50236 0.346427
\(470\) 25.9070 1.19500
\(471\) −19.9670 −0.920032
\(472\) 10.9613 0.504536
\(473\) 0 0
\(474\) −113.926 −5.23281
\(475\) −0.907153 −0.0416231
\(476\) 26.8172 1.22916
\(477\) −21.1352 −0.967713
\(478\) −72.5743 −3.31947
\(479\) −20.7343 −0.947375 −0.473687 0.880693i \(-0.657077\pi\)
−0.473687 + 0.880693i \(0.657077\pi\)
\(480\) −69.6607 −3.17956
\(481\) 18.2652 0.832823
\(482\) 29.3412 1.33646
\(483\) −9.16641 −0.417086
\(484\) 0 0
\(485\) −11.3919 −0.517277
\(486\) 12.9085 0.585540
\(487\) 3.50987 0.159047 0.0795236 0.996833i \(-0.474660\pi\)
0.0795236 + 0.996833i \(0.474660\pi\)
\(488\) 100.417 4.54566
\(489\) −37.5474 −1.69795
\(490\) 2.74137 0.123843
\(491\) 0.148819 0.00671611 0.00335805 0.999994i \(-0.498931\pi\)
0.00335805 + 0.999994i \(0.498931\pi\)
\(492\) −84.9951 −3.83187
\(493\) 4.44582 0.200230
\(494\) −16.4012 −0.737927
\(495\) 0 0
\(496\) −82.0629 −3.68473
\(497\) 3.74697 0.168075
\(498\) −84.7285 −3.79678
\(499\) 3.48032 0.155800 0.0779002 0.996961i \(-0.475178\pi\)
0.0779002 + 0.996961i \(0.475178\pi\)
\(500\) −5.51511 −0.246643
\(501\) 11.8732 0.530454
\(502\) 46.4150 2.07160
\(503\) 18.0097 0.803012 0.401506 0.915856i \(-0.368487\pi\)
0.401506 + 0.915856i \(0.368487\pi\)
\(504\) −60.2056 −2.68177
\(505\) 1.17248 0.0521746
\(506\) 0 0
\(507\) −92.7414 −4.11879
\(508\) 77.8356 3.45340
\(509\) −35.1540 −1.55818 −0.779088 0.626915i \(-0.784317\pi\)
−0.779088 + 0.626915i \(0.784317\pi\)
\(510\) −40.5365 −1.79499
\(511\) −15.8983 −0.703300
\(512\) −55.9214 −2.47140
\(513\) 8.95972 0.395581
\(514\) 34.3016 1.51298
\(515\) 8.97905 0.395664
\(516\) 28.1662 1.23995
\(517\) 0 0
\(518\) 7.59215 0.333580
\(519\) 17.3389 0.761095
\(520\) −63.5529 −2.78698
\(521\) −24.5834 −1.07702 −0.538509 0.842620i \(-0.681012\pi\)
−0.538509 + 0.842620i \(0.681012\pi\)
\(522\) −15.6600 −0.685417
\(523\) −16.0636 −0.702411 −0.351205 0.936298i \(-0.614228\pi\)
−0.351205 + 0.936298i \(0.614228\pi\)
\(524\) 56.9791 2.48914
\(525\) −3.04102 −0.132721
\(526\) −61.5506 −2.68373
\(527\) −25.9342 −1.12971
\(528\) 0 0
\(529\) −13.9143 −0.604969
\(530\) −9.27351 −0.402816
\(531\) −7.10699 −0.308417
\(532\) −5.00305 −0.216910
\(533\) −33.4232 −1.44772
\(534\) 64.7722 2.80297
\(535\) −6.26036 −0.270659
\(536\) −72.2945 −3.12265
\(537\) 59.6900 2.57581
\(538\) 37.6376 1.62267
\(539\) 0 0
\(540\) 54.4713 2.34407
\(541\) −24.6520 −1.05987 −0.529937 0.848037i \(-0.677784\pi\)
−0.529937 + 0.848037i \(0.677784\pi\)
\(542\) −5.34955 −0.229783
\(543\) −46.9558 −2.01507
\(544\) −111.385 −4.77559
\(545\) −1.70340 −0.0729656
\(546\) −54.9814 −2.35299
\(547\) 24.6864 1.05552 0.527758 0.849395i \(-0.323033\pi\)
0.527758 + 0.849395i \(0.323033\pi\)
\(548\) 119.446 5.10248
\(549\) −65.1072 −2.77871
\(550\) 0 0
\(551\) −0.829419 −0.0353344
\(552\) 88.3297 3.75956
\(553\) −13.6658 −0.581130
\(554\) 17.8887 0.760017
\(555\) −8.42204 −0.357496
\(556\) 81.1036 3.43956
\(557\) −20.2912 −0.859766 −0.429883 0.902885i \(-0.641445\pi\)
−0.429883 + 0.902885i \(0.641445\pi\)
\(558\) 91.3506 3.86718
\(559\) 11.0760 0.468464
\(560\) −15.3863 −0.650188
\(561\) 0 0
\(562\) −6.63086 −0.279706
\(563\) 11.9397 0.503200 0.251600 0.967831i \(-0.419043\pi\)
0.251600 + 0.967831i \(0.419043\pi\)
\(564\) −158.498 −6.67396
\(565\) 0.107727 0.00453212
\(566\) −2.19101 −0.0920951
\(567\) 11.2919 0.474216
\(568\) −36.1067 −1.51500
\(569\) −18.0100 −0.755017 −0.377509 0.926006i \(-0.623219\pi\)
−0.377509 + 0.926006i \(0.623219\pi\)
\(570\) 7.56255 0.316761
\(571\) −0.0419420 −0.00175522 −0.000877610 1.00000i \(-0.500279\pi\)
−0.000877610 1.00000i \(0.500279\pi\)
\(572\) 0 0
\(573\) 18.9009 0.789595
\(574\) −13.8927 −0.579871
\(575\) 3.01425 0.125703
\(576\) 200.080 8.33669
\(577\) −12.9887 −0.540726 −0.270363 0.962758i \(-0.587144\pi\)
−0.270363 + 0.962758i \(0.587144\pi\)
\(578\) −18.2131 −0.757564
\(579\) −66.8351 −2.77757
\(580\) −5.04252 −0.209379
\(581\) −10.1635 −0.421652
\(582\) 94.9691 3.93659
\(583\) 0 0
\(584\) 153.200 6.33945
\(585\) 41.2057 1.70365
\(586\) 65.7196 2.71485
\(587\) 4.44817 0.183596 0.0917979 0.995778i \(-0.470739\pi\)
0.0917979 + 0.995778i \(0.470739\pi\)
\(588\) −16.7716 −0.691649
\(589\) 4.83832 0.199360
\(590\) −3.11834 −0.128380
\(591\) −8.98846 −0.369736
\(592\) −42.6118 −1.75133
\(593\) 25.1551 1.03300 0.516498 0.856288i \(-0.327235\pi\)
0.516498 + 0.856288i \(0.327235\pi\)
\(594\) 0 0
\(595\) −4.86249 −0.199343
\(596\) −25.5277 −1.04565
\(597\) 35.3776 1.44791
\(598\) 54.4974 2.22856
\(599\) −41.3234 −1.68843 −0.844215 0.536004i \(-0.819933\pi\)
−0.844215 + 0.536004i \(0.819933\pi\)
\(600\) 29.3040 1.19633
\(601\) 36.8476 1.50305 0.751523 0.659707i \(-0.229320\pi\)
0.751523 + 0.659707i \(0.229320\pi\)
\(602\) 4.60386 0.187639
\(603\) 46.8735 1.90884
\(604\) −38.8562 −1.58104
\(605\) 0 0
\(606\) −9.77445 −0.397060
\(607\) −9.84153 −0.399455 −0.199728 0.979851i \(-0.564006\pi\)
−0.199728 + 0.979851i \(0.564006\pi\)
\(608\) 20.7801 0.842746
\(609\) −2.78044 −0.112669
\(610\) −28.5672 −1.15665
\(611\) −62.3271 −2.52149
\(612\) 167.549 6.77278
\(613\) −27.7360 −1.12025 −0.560123 0.828409i \(-0.689246\pi\)
−0.560123 + 0.828409i \(0.689246\pi\)
\(614\) −52.2910 −2.11029
\(615\) 15.4113 0.621444
\(616\) 0 0
\(617\) −6.34939 −0.255617 −0.127808 0.991799i \(-0.540794\pi\)
−0.127808 + 0.991799i \(0.540794\pi\)
\(618\) −74.8546 −3.01109
\(619\) 21.7248 0.873192 0.436596 0.899658i \(-0.356184\pi\)
0.436596 + 0.899658i \(0.356184\pi\)
\(620\) 29.4150 1.18133
\(621\) −29.7710 −1.19467
\(622\) −25.1671 −1.00911
\(623\) 7.76964 0.311284
\(624\) 308.590 12.3535
\(625\) 1.00000 0.0400000
\(626\) 37.7406 1.50842
\(627\) 0 0
\(628\) 36.2116 1.44500
\(629\) −13.4665 −0.536946
\(630\) 17.1276 0.682381
\(631\) −46.9428 −1.86876 −0.934382 0.356272i \(-0.884048\pi\)
−0.934382 + 0.356272i \(0.884048\pi\)
\(632\) 131.687 5.23823
\(633\) −79.7023 −3.16788
\(634\) −62.9023 −2.49817
\(635\) −14.1131 −0.560063
\(636\) 56.7350 2.24969
\(637\) −6.59521 −0.261312
\(638\) 0 0
\(639\) 23.4104 0.926103
\(640\) 41.9757 1.65923
\(641\) −34.5237 −1.36361 −0.681803 0.731536i \(-0.738804\pi\)
−0.681803 + 0.731536i \(0.738804\pi\)
\(642\) 52.1899 2.05977
\(643\) −0.0386672 −0.00152489 −0.000762443 1.00000i \(-0.500243\pi\)
−0.000762443 1.00000i \(0.500243\pi\)
\(644\) 16.6239 0.655075
\(645\) −5.10710 −0.201092
\(646\) 12.0922 0.475763
\(647\) 3.77288 0.148327 0.0741636 0.997246i \(-0.476371\pi\)
0.0741636 + 0.997246i \(0.476371\pi\)
\(648\) −108.811 −4.27452
\(649\) 0 0
\(650\) 18.0799 0.709152
\(651\) 16.2194 0.635687
\(652\) 68.0949 2.66680
\(653\) −47.8327 −1.87184 −0.935918 0.352217i \(-0.885428\pi\)
−0.935918 + 0.352217i \(0.885428\pi\)
\(654\) 14.2005 0.555284
\(655\) −10.3314 −0.403683
\(656\) 77.9744 3.04439
\(657\) −99.3300 −3.87523
\(658\) −25.9070 −1.00996
\(659\) −19.7418 −0.769030 −0.384515 0.923119i \(-0.625631\pi\)
−0.384515 + 0.923119i \(0.625631\pi\)
\(660\) 0 0
\(661\) −15.6196 −0.607530 −0.303765 0.952747i \(-0.598244\pi\)
−0.303765 + 0.952747i \(0.598244\pi\)
\(662\) 9.43075 0.366536
\(663\) 97.5230 3.78748
\(664\) 97.9375 3.80071
\(665\) 0.907153 0.0351779
\(666\) 47.4345 1.83805
\(667\) 2.75596 0.106711
\(668\) −21.5328 −0.833130
\(669\) −13.9083 −0.537727
\(670\) 20.5667 0.794563
\(671\) 0 0
\(672\) 69.6607 2.68722
\(673\) 3.27724 0.126328 0.0631642 0.998003i \(-0.479881\pi\)
0.0631642 + 0.998003i \(0.479881\pi\)
\(674\) 83.0527 3.19907
\(675\) −9.87674 −0.380156
\(676\) 168.193 6.46896
\(677\) −31.4726 −1.20959 −0.604795 0.796381i \(-0.706745\pi\)
−0.604795 + 0.796381i \(0.706745\pi\)
\(678\) −0.898076 −0.0344904
\(679\) 11.3919 0.437179
\(680\) 46.8561 1.79685
\(681\) −25.0083 −0.958321
\(682\) 0 0
\(683\) 35.0569 1.34142 0.670708 0.741721i \(-0.265990\pi\)
0.670708 + 0.741721i \(0.265990\pi\)
\(684\) −31.2582 −1.19519
\(685\) −21.6579 −0.827507
\(686\) −2.74137 −0.104666
\(687\) 5.62054 0.214437
\(688\) −25.8397 −0.985128
\(689\) 22.3103 0.849953
\(690\) −25.1285 −0.956627
\(691\) 36.2261 1.37810 0.689052 0.724712i \(-0.258027\pi\)
0.689052 + 0.724712i \(0.258027\pi\)
\(692\) −31.4454 −1.19537
\(693\) 0 0
\(694\) 10.6461 0.404121
\(695\) −14.7057 −0.557819
\(696\) 26.7929 1.01558
\(697\) 24.6421 0.933386
\(698\) 52.7683 1.99731
\(699\) 70.5587 2.66878
\(700\) 5.51511 0.208452
\(701\) 32.4214 1.22454 0.612269 0.790649i \(-0.290257\pi\)
0.612269 + 0.790649i \(0.290257\pi\)
\(702\) −178.571 −6.73971
\(703\) 2.51234 0.0947546
\(704\) 0 0
\(705\) 28.7388 1.08237
\(706\) 72.1065 2.71377
\(707\) −1.17248 −0.0440955
\(708\) 19.0779 0.716991
\(709\) 38.9574 1.46308 0.731538 0.681801i \(-0.238803\pi\)
0.731538 + 0.681801i \(0.238803\pi\)
\(710\) 10.2718 0.385495
\(711\) −85.3818 −3.20207
\(712\) −74.8701 −2.80587
\(713\) −16.0766 −0.602073
\(714\) 40.5365 1.51704
\(715\) 0 0
\(716\) −108.252 −4.04557
\(717\) −80.5073 −3.00660
\(718\) −58.9154 −2.19870
\(719\) −21.0902 −0.786531 −0.393266 0.919425i \(-0.628655\pi\)
−0.393266 + 0.919425i \(0.628655\pi\)
\(720\) −96.1307 −3.58258
\(721\) −8.97905 −0.334397
\(722\) 49.8301 1.85448
\(723\) 32.5485 1.21049
\(724\) 85.1577 3.16486
\(725\) 0.914310 0.0339566
\(726\) 0 0
\(727\) −48.1383 −1.78535 −0.892675 0.450702i \(-0.851174\pi\)
−0.892675 + 0.450702i \(0.851174\pi\)
\(728\) 63.5529 2.35543
\(729\) −19.5563 −0.724306
\(730\) −43.5832 −1.61309
\(731\) −8.16606 −0.302033
\(732\) 174.773 6.45980
\(733\) 48.4595 1.78989 0.894946 0.446174i \(-0.147214\pi\)
0.894946 + 0.446174i \(0.147214\pi\)
\(734\) 14.2725 0.526809
\(735\) 3.04102 0.112170
\(736\) −69.0473 −2.54512
\(737\) 0 0
\(738\) −86.7994 −3.19513
\(739\) −13.6252 −0.501211 −0.250606 0.968089i \(-0.580630\pi\)
−0.250606 + 0.968089i \(0.580630\pi\)
\(740\) 15.2740 0.561482
\(741\) −18.1940 −0.668375
\(742\) 9.27351 0.340441
\(743\) −15.5807 −0.571602 −0.285801 0.958289i \(-0.592260\pi\)
−0.285801 + 0.958289i \(0.592260\pi\)
\(744\) −156.294 −5.73000
\(745\) 4.62867 0.169582
\(746\) 42.9039 1.57082
\(747\) −63.4997 −2.32333
\(748\) 0 0
\(749\) 6.26036 0.228748
\(750\) −8.33658 −0.304409
\(751\) −30.0749 −1.09745 −0.548725 0.836003i \(-0.684887\pi\)
−0.548725 + 0.836003i \(0.684887\pi\)
\(752\) 145.406 5.30240
\(753\) 51.4886 1.87635
\(754\) 16.5306 0.602010
\(755\) 7.04541 0.256409
\(756\) −54.4713 −1.98110
\(757\) 20.9610 0.761840 0.380920 0.924608i \(-0.375607\pi\)
0.380920 + 0.924608i \(0.375607\pi\)
\(758\) −52.3301 −1.90071
\(759\) 0 0
\(760\) −8.74154 −0.317089
\(761\) 48.0504 1.74182 0.870912 0.491439i \(-0.163529\pi\)
0.870912 + 0.491439i \(0.163529\pi\)
\(762\) 117.655 4.26220
\(763\) 1.70340 0.0616672
\(764\) −34.2780 −1.24014
\(765\) −30.3800 −1.09839
\(766\) −64.1252 −2.31694
\(767\) 7.50213 0.270886
\(768\) −155.162 −5.59893
\(769\) 22.9234 0.826638 0.413319 0.910586i \(-0.364370\pi\)
0.413319 + 0.910586i \(0.364370\pi\)
\(770\) 0 0
\(771\) 38.0510 1.37037
\(772\) 121.210 4.36245
\(773\) −31.4722 −1.13198 −0.565988 0.824413i \(-0.691505\pi\)
−0.565988 + 0.824413i \(0.691505\pi\)
\(774\) 28.7641 1.03391
\(775\) −5.33352 −0.191586
\(776\) −109.775 −3.94068
\(777\) 8.42204 0.302139
\(778\) −31.1820 −1.11793
\(779\) −4.59727 −0.164714
\(780\) −110.612 −3.96055
\(781\) 0 0
\(782\) −40.1796 −1.43682
\(783\) −9.03040 −0.322720
\(784\) 15.3863 0.549509
\(785\) −6.56589 −0.234347
\(786\) 86.1288 3.07211
\(787\) −44.9445 −1.60210 −0.801049 0.598598i \(-0.795725\pi\)
−0.801049 + 0.598598i \(0.795725\pi\)
\(788\) 16.3012 0.580707
\(789\) −68.2786 −2.43078
\(790\) −37.4631 −1.33288
\(791\) −0.107727 −0.00383034
\(792\) 0 0
\(793\) 68.7271 2.44057
\(794\) 41.8629 1.48566
\(795\) −10.2872 −0.364849
\(796\) −64.1598 −2.27409
\(797\) 29.7898 1.05521 0.527605 0.849490i \(-0.323090\pi\)
0.527605 + 0.849490i \(0.323090\pi\)
\(798\) −7.56255 −0.267711
\(799\) 45.9523 1.62568
\(800\) −22.9070 −0.809884
\(801\) 48.5434 1.71520
\(802\) −26.4998 −0.935741
\(803\) 0 0
\(804\) −125.827 −4.43756
\(805\) −3.01425 −0.106238
\(806\) −96.4296 −3.39659
\(807\) 41.7517 1.46973
\(808\) 11.2983 0.397471
\(809\) 28.3849 0.997961 0.498980 0.866613i \(-0.333708\pi\)
0.498980 + 0.866613i \(0.333708\pi\)
\(810\) 30.9553 1.08766
\(811\) 1.22401 0.0429807 0.0214904 0.999769i \(-0.493159\pi\)
0.0214904 + 0.999769i \(0.493159\pi\)
\(812\) 5.04252 0.176958
\(813\) −5.93430 −0.208125
\(814\) 0 0
\(815\) −12.3470 −0.432495
\(816\) −227.516 −7.96464
\(817\) 1.52347 0.0532996
\(818\) 38.9665 1.36243
\(819\) −41.2057 −1.43985
\(820\) −27.9495 −0.976038
\(821\) 9.87864 0.344767 0.172383 0.985030i \(-0.444853\pi\)
0.172383 + 0.985030i \(0.444853\pi\)
\(822\) 180.553 6.29751
\(823\) 13.9342 0.485714 0.242857 0.970062i \(-0.421915\pi\)
0.242857 + 0.970062i \(0.421915\pi\)
\(824\) 86.5242 3.01421
\(825\) 0 0
\(826\) 3.11834 0.108501
\(827\) −30.9317 −1.07560 −0.537801 0.843072i \(-0.680745\pi\)
−0.537801 + 0.843072i \(0.680745\pi\)
\(828\) 103.864 3.60951
\(829\) −39.1431 −1.35950 −0.679749 0.733445i \(-0.737911\pi\)
−0.679749 + 0.733445i \(0.737911\pi\)
\(830\) −27.8618 −0.967099
\(831\) 19.8441 0.688383
\(832\) −211.205 −7.32221
\(833\) 4.86249 0.168475
\(834\) 122.595 4.24512
\(835\) 3.90433 0.135115
\(836\) 0 0
\(837\) 52.6778 1.82081
\(838\) −41.8969 −1.44730
\(839\) 8.38642 0.289531 0.144766 0.989466i \(-0.453757\pi\)
0.144766 + 0.989466i \(0.453757\pi\)
\(840\) −29.3040 −1.01108
\(841\) −28.1640 −0.971174
\(842\) −22.2129 −0.765506
\(843\) −7.35567 −0.253343
\(844\) 144.546 4.97547
\(845\) −30.4967 −1.04912
\(846\) −161.862 −5.56494
\(847\) 0 0
\(848\) −52.0486 −1.78736
\(849\) −2.43051 −0.0834148
\(850\) −13.3299 −0.457211
\(851\) −8.34789 −0.286162
\(852\) −62.8427 −2.15295
\(853\) 6.41870 0.219772 0.109886 0.993944i \(-0.464951\pi\)
0.109886 + 0.993944i \(0.464951\pi\)
\(854\) 28.5672 0.977549
\(855\) 5.66774 0.193833
\(856\) −60.3262 −2.06191
\(857\) −42.0950 −1.43794 −0.718968 0.695043i \(-0.755385\pi\)
−0.718968 + 0.695043i \(0.755385\pi\)
\(858\) 0 0
\(859\) −28.4518 −0.970763 −0.485381 0.874303i \(-0.661319\pi\)
−0.485381 + 0.874303i \(0.661319\pi\)
\(860\) 9.26208 0.315834
\(861\) −15.4113 −0.525216
\(862\) −45.5841 −1.55260
\(863\) 49.5170 1.68558 0.842789 0.538245i \(-0.180912\pi\)
0.842789 + 0.538245i \(0.180912\pi\)
\(864\) 226.246 7.69705
\(865\) 5.70167 0.193863
\(866\) −96.1787 −3.26829
\(867\) −20.2039 −0.686161
\(868\) −29.4150 −0.998410
\(869\) 0 0
\(870\) −7.62221 −0.258417
\(871\) −49.4796 −1.67655
\(872\) −16.4144 −0.555860
\(873\) 71.1744 2.40889
\(874\) 7.49597 0.253555
\(875\) −1.00000 −0.0338062
\(876\) 266.640 9.00894
\(877\) 30.9398 1.04476 0.522381 0.852712i \(-0.325044\pi\)
0.522381 + 0.852712i \(0.325044\pi\)
\(878\) 66.6848 2.25050
\(879\) 72.9033 2.45897
\(880\) 0 0
\(881\) −17.9677 −0.605348 −0.302674 0.953094i \(-0.597879\pi\)
−0.302674 + 0.953094i \(0.597879\pi\)
\(882\) −17.1276 −0.576717
\(883\) 4.90553 0.165084 0.0825421 0.996588i \(-0.473696\pi\)
0.0825421 + 0.996588i \(0.473696\pi\)
\(884\) −176.865 −5.94861
\(885\) −3.45920 −0.116280
\(886\) −13.9299 −0.467985
\(887\) 24.4188 0.819902 0.409951 0.912107i \(-0.365546\pi\)
0.409951 + 0.912107i \(0.365546\pi\)
\(888\) −81.1567 −2.72344
\(889\) 14.1131 0.473340
\(890\) 21.2995 0.713960
\(891\) 0 0
\(892\) 25.2238 0.844554
\(893\) −8.57293 −0.286882
\(894\) −38.5873 −1.29055
\(895\) 19.6283 0.656100
\(896\) −41.9757 −1.40231
\(897\) 60.4544 2.01851
\(898\) 87.4238 2.91737
\(899\) −4.87649 −0.162640
\(900\) 34.4575 1.14858
\(901\) −16.4488 −0.547990
\(902\) 0 0
\(903\) 5.10710 0.169954
\(904\) 1.03808 0.0345262
\(905\) −15.4408 −0.513269
\(906\) −58.7346 −1.95133
\(907\) −33.4445 −1.11051 −0.555253 0.831682i \(-0.687378\pi\)
−0.555253 + 0.831682i \(0.687378\pi\)
\(908\) 45.3544 1.50514
\(909\) −7.32544 −0.242970
\(910\) −18.0799 −0.599343
\(911\) −20.8102 −0.689474 −0.344737 0.938699i \(-0.612032\pi\)
−0.344737 + 0.938699i \(0.612032\pi\)
\(912\) 42.4457 1.40552
\(913\) 0 0
\(914\) −18.9861 −0.628006
\(915\) −31.6898 −1.04763
\(916\) −10.1932 −0.336794
\(917\) 10.3314 0.341174
\(918\) 131.656 4.34529
\(919\) 11.8322 0.390308 0.195154 0.980773i \(-0.437479\pi\)
0.195154 + 0.980773i \(0.437479\pi\)
\(920\) 29.0460 0.957619
\(921\) −58.0068 −1.91139
\(922\) −73.9265 −2.43464
\(923\) −24.7120 −0.813407
\(924\) 0 0
\(925\) −2.76947 −0.0910597
\(926\) 97.1868 3.19376
\(927\) −56.0996 −1.84255
\(928\) −20.9441 −0.687522
\(929\) 57.2642 1.87878 0.939388 0.342855i \(-0.111394\pi\)
0.939388 + 0.342855i \(0.111394\pi\)
\(930\) 44.4633 1.45801
\(931\) −0.907153 −0.0297308
\(932\) −127.963 −4.19158
\(933\) −27.9181 −0.913998
\(934\) 89.0711 2.91449
\(935\) 0 0
\(936\) 397.068 12.9786
\(937\) −49.7345 −1.62476 −0.812378 0.583131i \(-0.801827\pi\)
−0.812378 + 0.583131i \(0.801827\pi\)
\(938\) −20.5667 −0.671528
\(939\) 41.8659 1.36624
\(940\) −52.1199 −1.69996
\(941\) −47.0701 −1.53444 −0.767221 0.641383i \(-0.778361\pi\)
−0.767221 + 0.641383i \(0.778361\pi\)
\(942\) 54.7370 1.78343
\(943\) 15.2756 0.497443
\(944\) −17.5021 −0.569643
\(945\) 9.87674 0.321290
\(946\) 0 0
\(947\) 16.1208 0.523855 0.261927 0.965088i \(-0.415642\pi\)
0.261927 + 0.965088i \(0.415642\pi\)
\(948\) 229.198 7.44400
\(949\) 104.853 3.40366
\(950\) 2.48684 0.0806839
\(951\) −69.7780 −2.26271
\(952\) −46.8561 −1.51861
\(953\) 17.5288 0.567813 0.283907 0.958852i \(-0.408369\pi\)
0.283907 + 0.958852i \(0.408369\pi\)
\(954\) 57.9393 1.87586
\(955\) 6.21529 0.201122
\(956\) 146.006 4.72216
\(957\) 0 0
\(958\) 56.8404 1.83643
\(959\) 21.6579 0.699371
\(960\) 97.3857 3.14311
\(961\) −2.55354 −0.0823721
\(962\) −50.0718 −1.61438
\(963\) 39.1136 1.26042
\(964\) −59.0289 −1.90119
\(965\) −21.9778 −0.707491
\(966\) 25.1285 0.808497
\(967\) −11.5858 −0.372575 −0.186287 0.982495i \(-0.559646\pi\)
−0.186287 + 0.982495i \(0.559646\pi\)
\(968\) 0 0
\(969\) 13.4140 0.430921
\(970\) 31.2293 1.00271
\(971\) 30.6243 0.982782 0.491391 0.870939i \(-0.336489\pi\)
0.491391 + 0.870939i \(0.336489\pi\)
\(972\) −25.9694 −0.832968
\(973\) 14.7057 0.471443
\(974\) −9.62184 −0.308304
\(975\) 20.0562 0.642312
\(976\) −160.337 −5.13225
\(977\) 1.44818 0.0463314 0.0231657 0.999732i \(-0.492625\pi\)
0.0231657 + 0.999732i \(0.492625\pi\)
\(978\) 102.931 3.29138
\(979\) 0 0
\(980\) −5.51511 −0.176174
\(981\) 10.6426 0.339791
\(982\) −0.407968 −0.0130188
\(983\) −60.3589 −1.92515 −0.962574 0.271018i \(-0.912640\pi\)
−0.962574 + 0.271018i \(0.912640\pi\)
\(984\) 148.507 4.73423
\(985\) −2.95573 −0.0941775
\(986\) −12.1876 −0.388133
\(987\) −28.7388 −0.914766
\(988\) 32.9962 1.04975
\(989\) −5.06213 −0.160966
\(990\) 0 0
\(991\) 27.9689 0.888460 0.444230 0.895913i \(-0.353477\pi\)
0.444230 + 0.895913i \(0.353477\pi\)
\(992\) 122.175 3.87905
\(993\) 10.4616 0.331989
\(994\) −10.2718 −0.325803
\(995\) 11.6335 0.368805
\(996\) 170.458 5.40116
\(997\) −4.12371 −0.130599 −0.0652996 0.997866i \(-0.520800\pi\)
−0.0652996 + 0.997866i \(0.520800\pi\)
\(998\) −9.54084 −0.302010
\(999\) 27.3534 0.865422
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 4235.2.a.bb.1.1 yes 5
11.10 odd 2 4235.2.a.ba.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4235.2.a.ba.1.5 5 11.10 odd 2
4235.2.a.bb.1.1 yes 5 1.1 even 1 trivial