Properties

Label 8034.2.a.z.1.13
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + 6361 x^{6} - 14618 x^{5} - 7015 x^{4} + 15763 x^{3} + 1118 x^{2} - 6316 x + 1552\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(-2.41893\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.41893 q^{5} +1.00000 q^{6} -0.257176 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.41893 q^{5} +1.00000 q^{6} -0.257176 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.41893 q^{10} +1.56925 q^{11} -1.00000 q^{12} +1.00000 q^{13} +0.257176 q^{14} -2.41893 q^{15} +1.00000 q^{16} +4.26992 q^{17} -1.00000 q^{18} +1.38482 q^{19} +2.41893 q^{20} +0.257176 q^{21} -1.56925 q^{22} +8.56848 q^{23} +1.00000 q^{24} +0.851240 q^{25} -1.00000 q^{26} -1.00000 q^{27} -0.257176 q^{28} +10.3349 q^{29} +2.41893 q^{30} +7.55065 q^{31} -1.00000 q^{32} -1.56925 q^{33} -4.26992 q^{34} -0.622092 q^{35} +1.00000 q^{36} -2.82902 q^{37} -1.38482 q^{38} -1.00000 q^{39} -2.41893 q^{40} +10.3277 q^{41} -0.257176 q^{42} -6.51464 q^{43} +1.56925 q^{44} +2.41893 q^{45} -8.56848 q^{46} +9.53966 q^{47} -1.00000 q^{48} -6.93386 q^{49} -0.851240 q^{50} -4.26992 q^{51} +1.00000 q^{52} -12.5020 q^{53} +1.00000 q^{54} +3.79591 q^{55} +0.257176 q^{56} -1.38482 q^{57} -10.3349 q^{58} -4.00889 q^{59} -2.41893 q^{60} +12.4048 q^{61} -7.55065 q^{62} -0.257176 q^{63} +1.00000 q^{64} +2.41893 q^{65} +1.56925 q^{66} +9.28134 q^{67} +4.26992 q^{68} -8.56848 q^{69} +0.622092 q^{70} -0.286350 q^{71} -1.00000 q^{72} -15.7947 q^{73} +2.82902 q^{74} -0.851240 q^{75} +1.38482 q^{76} -0.403573 q^{77} +1.00000 q^{78} +9.06214 q^{79} +2.41893 q^{80} +1.00000 q^{81} -10.3277 q^{82} -6.84929 q^{83} +0.257176 q^{84} +10.3286 q^{85} +6.51464 q^{86} -10.3349 q^{87} -1.56925 q^{88} -14.0981 q^{89} -2.41893 q^{90} -0.257176 q^{91} +8.56848 q^{92} -7.55065 q^{93} -9.53966 q^{94} +3.34978 q^{95} +1.00000 q^{96} +13.3988 q^{97} +6.93386 q^{98} +1.56925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + 3q^{10} + 5q^{11} - 14q^{12} + 14q^{13} - 4q^{14} + 3q^{15} + 14q^{16} - 7q^{17} - 14q^{18} + 31q^{19} - 3q^{20} - 4q^{21} - 5q^{22} + 14q^{23} + 14q^{24} + 11q^{25} - 14q^{26} - 14q^{27} + 4q^{28} + 9q^{29} - 3q^{30} + 23q^{31} - 14q^{32} - 5q^{33} + 7q^{34} - 2q^{35} + 14q^{36} + 12q^{37} - 31q^{38} - 14q^{39} + 3q^{40} - 5q^{41} + 4q^{42} - 2q^{43} + 5q^{44} - 3q^{45} - 14q^{46} - 11q^{47} - 14q^{48} + 52q^{49} - 11q^{50} + 7q^{51} + 14q^{52} + 6q^{53} + 14q^{54} + 30q^{55} - 4q^{56} - 31q^{57} - 9q^{58} - 4q^{59} + 3q^{60} + 12q^{61} - 23q^{62} + 4q^{63} + 14q^{64} - 3q^{65} + 5q^{66} + 24q^{67} - 7q^{68} - 14q^{69} + 2q^{70} + 20q^{71} - 14q^{72} + 2q^{73} - 12q^{74} - 11q^{75} + 31q^{76} - 28q^{77} + 14q^{78} + 59q^{79} - 3q^{80} + 14q^{81} + 5q^{82} + q^{83} - 4q^{84} - 29q^{85} + 2q^{86} - 9q^{87} - 5q^{88} + 6q^{89} + 3q^{90} + 4q^{91} + 14q^{92} - 23q^{93} + 11q^{94} - 58q^{95} + 14q^{96} - 6q^{97} - 52q^{98} + 5q^{99} + O(q^{100}) \)

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
\(5\) 2.41893 1.08178 0.540890 0.841093i \(-0.318088\pi\)
0.540890 + 0.841093i \(0.318088\pi\)
\(6\) 1.00000 0.408248
\(7\) −0.257176 −0.0972034 −0.0486017 0.998818i \(-0.515476\pi\)
−0.0486017 + 0.998818i \(0.515476\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −2.41893 −0.764934
\(11\) 1.56925 0.473146 0.236573 0.971614i \(-0.423976\pi\)
0.236573 + 0.971614i \(0.423976\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) 0.257176 0.0687332
\(15\) −2.41893 −0.624566
\(16\) 1.00000 0.250000
\(17\) 4.26992 1.03561 0.517804 0.855500i \(-0.326750\pi\)
0.517804 + 0.855500i \(0.326750\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.38482 0.317699 0.158849 0.987303i \(-0.449222\pi\)
0.158849 + 0.987303i \(0.449222\pi\)
\(20\) 2.41893 0.540890
\(21\) 0.257176 0.0561204
\(22\) −1.56925 −0.334565
\(23\) 8.56848 1.78665 0.893326 0.449409i \(-0.148365\pi\)
0.893326 + 0.449409i \(0.148365\pi\)
\(24\) 1.00000 0.204124
\(25\) 0.851240 0.170248
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −0.257176 −0.0486017
\(29\) 10.3349 1.91915 0.959573 0.281459i \(-0.0908182\pi\)
0.959573 + 0.281459i \(0.0908182\pi\)
\(30\) 2.41893 0.441635
\(31\) 7.55065 1.35614 0.678069 0.734998i \(-0.262817\pi\)
0.678069 + 0.734998i \(0.262817\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.56925 −0.273171
\(34\) −4.26992 −0.732285
\(35\) −0.622092 −0.105153
\(36\) 1.00000 0.166667
\(37\) −2.82902 −0.465088 −0.232544 0.972586i \(-0.574705\pi\)
−0.232544 + 0.972586i \(0.574705\pi\)
\(38\) −1.38482 −0.224647
\(39\) −1.00000 −0.160128
\(40\) −2.41893 −0.382467
\(41\) 10.3277 1.61291 0.806455 0.591296i \(-0.201384\pi\)
0.806455 + 0.591296i \(0.201384\pi\)
\(42\) −0.257176 −0.0396831
\(43\) −6.51464 −0.993474 −0.496737 0.867901i \(-0.665469\pi\)
−0.496737 + 0.867901i \(0.665469\pi\)
\(44\) 1.56925 0.236573
\(45\) 2.41893 0.360593
\(46\) −8.56848 −1.26335
\(47\) 9.53966 1.39150 0.695751 0.718283i \(-0.255072\pi\)
0.695751 + 0.718283i \(0.255072\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.93386 −0.990552
\(50\) −0.851240 −0.120384
\(51\) −4.26992 −0.597908
\(52\) 1.00000 0.138675
\(53\) −12.5020 −1.71728 −0.858640 0.512580i \(-0.828690\pi\)
−0.858640 + 0.512580i \(0.828690\pi\)
\(54\) 1.00000 0.136083
\(55\) 3.79591 0.511840
\(56\) 0.257176 0.0343666
\(57\) −1.38482 −0.183423
\(58\) −10.3349 −1.35704
\(59\) −4.00889 −0.521913 −0.260957 0.965351i \(-0.584038\pi\)
−0.260957 + 0.965351i \(0.584038\pi\)
\(60\) −2.41893 −0.312283
\(61\) 12.4048 1.58827 0.794134 0.607743i \(-0.207925\pi\)
0.794134 + 0.607743i \(0.207925\pi\)
\(62\) −7.55065 −0.958934
\(63\) −0.257176 −0.0324011
\(64\) 1.00000 0.125000
\(65\) 2.41893 0.300032
\(66\) 1.56925 0.193161
\(67\) 9.28134 1.13390 0.566948 0.823753i \(-0.308124\pi\)
0.566948 + 0.823753i \(0.308124\pi\)
\(68\) 4.26992 0.517804
\(69\) −8.56848 −1.03152
\(70\) 0.622092 0.0743542
\(71\) −0.286350 −0.0339834 −0.0169917 0.999856i \(-0.505409\pi\)
−0.0169917 + 0.999856i \(0.505409\pi\)
\(72\) −1.00000 −0.117851
\(73\) −15.7947 −1.84863 −0.924313 0.381635i \(-0.875361\pi\)
−0.924313 + 0.381635i \(0.875361\pi\)
\(74\) 2.82902 0.328867
\(75\) −0.851240 −0.0982928
\(76\) 1.38482 0.158849
\(77\) −0.403573 −0.0459914
\(78\) 1.00000 0.113228
\(79\) 9.06214 1.01957 0.509785 0.860302i \(-0.329725\pi\)
0.509785 + 0.860302i \(0.329725\pi\)
\(80\) 2.41893 0.270445
\(81\) 1.00000 0.111111
\(82\) −10.3277 −1.14050
\(83\) −6.84929 −0.751808 −0.375904 0.926659i \(-0.622668\pi\)
−0.375904 + 0.926659i \(0.622668\pi\)
\(84\) 0.257176 0.0280602
\(85\) 10.3286 1.12030
\(86\) 6.51464 0.702492
\(87\) −10.3349 −1.10802
\(88\) −1.56925 −0.167282
\(89\) −14.0981 −1.49440 −0.747199 0.664600i \(-0.768602\pi\)
−0.747199 + 0.664600i \(0.768602\pi\)
\(90\) −2.41893 −0.254978
\(91\) −0.257176 −0.0269594
\(92\) 8.56848 0.893326
\(93\) −7.55065 −0.782966
\(94\) −9.53966 −0.983940
\(95\) 3.34978 0.343680
\(96\) 1.00000 0.102062
\(97\) 13.3988 1.36044 0.680220 0.733008i \(-0.261884\pi\)
0.680220 + 0.733008i \(0.261884\pi\)
\(98\) 6.93386 0.700426
\(99\) 1.56925 0.157715
\(100\) 0.851240 0.0851240
\(101\) −3.46177 −0.344459 −0.172229 0.985057i \(-0.555097\pi\)
−0.172229 + 0.985057i \(0.555097\pi\)
\(102\) 4.26992 0.422785
\(103\) −1.00000 −0.0985329
\(104\) −1.00000 −0.0980581
\(105\) 0.622092 0.0607099
\(106\) 12.5020 1.21430
\(107\) −14.7757 −1.42842 −0.714209 0.699932i \(-0.753213\pi\)
−0.714209 + 0.699932i \(0.753213\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −7.20934 −0.690530 −0.345265 0.938505i \(-0.612211\pi\)
−0.345265 + 0.938505i \(0.612211\pi\)
\(110\) −3.79591 −0.361926
\(111\) 2.82902 0.268519
\(112\) −0.257176 −0.0243008
\(113\) 9.35198 0.879760 0.439880 0.898057i \(-0.355021\pi\)
0.439880 + 0.898057i \(0.355021\pi\)
\(114\) 1.38482 0.129700
\(115\) 20.7266 1.93276
\(116\) 10.3349 0.959573
\(117\) 1.00000 0.0924500
\(118\) 4.00889 0.369048
\(119\) −1.09812 −0.100664
\(120\) 2.41893 0.220817
\(121\) −8.53746 −0.776133
\(122\) −12.4048 −1.12307
\(123\) −10.3277 −0.931214
\(124\) 7.55065 0.678069
\(125\) −10.0356 −0.897609
\(126\) 0.257176 0.0229111
\(127\) −10.9282 −0.969723 −0.484862 0.874591i \(-0.661130\pi\)
−0.484862 + 0.874591i \(0.661130\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 6.51464 0.573582
\(130\) −2.41893 −0.212155
\(131\) 19.8225 1.73190 0.865949 0.500132i \(-0.166715\pi\)
0.865949 + 0.500132i \(0.166715\pi\)
\(132\) −1.56925 −0.136586
\(133\) −0.356141 −0.0308814
\(134\) −9.28134 −0.801786
\(135\) −2.41893 −0.208189
\(136\) −4.26992 −0.366142
\(137\) −7.15001 −0.610867 −0.305433 0.952213i \(-0.598801\pi\)
−0.305433 + 0.952213i \(0.598801\pi\)
\(138\) 8.56848 0.729398
\(139\) 3.85007 0.326559 0.163279 0.986580i \(-0.447793\pi\)
0.163279 + 0.986580i \(0.447793\pi\)
\(140\) −0.622092 −0.0525763
\(141\) −9.53966 −0.803384
\(142\) 0.286350 0.0240299
\(143\) 1.56925 0.131227
\(144\) 1.00000 0.0833333
\(145\) 24.9995 2.07609
\(146\) 15.7947 1.30718
\(147\) 6.93386 0.571895
\(148\) −2.82902 −0.232544
\(149\) −10.1252 −0.829490 −0.414745 0.909938i \(-0.636129\pi\)
−0.414745 + 0.909938i \(0.636129\pi\)
\(150\) 0.851240 0.0695035
\(151\) 15.0201 1.22232 0.611159 0.791508i \(-0.290704\pi\)
0.611159 + 0.791508i \(0.290704\pi\)
\(152\) −1.38482 −0.112323
\(153\) 4.26992 0.345202
\(154\) 0.403573 0.0325208
\(155\) 18.2645 1.46704
\(156\) −1.00000 −0.0800641
\(157\) 22.4063 1.78822 0.894109 0.447849i \(-0.147810\pi\)
0.894109 + 0.447849i \(0.147810\pi\)
\(158\) −9.06214 −0.720946
\(159\) 12.5020 0.991472
\(160\) −2.41893 −0.191234
\(161\) −2.20361 −0.173669
\(162\) −1.00000 −0.0785674
\(163\) 3.77020 0.295305 0.147652 0.989039i \(-0.452828\pi\)
0.147652 + 0.989039i \(0.452828\pi\)
\(164\) 10.3277 0.806455
\(165\) −3.79591 −0.295511
\(166\) 6.84929 0.531608
\(167\) 11.1628 0.863801 0.431900 0.901921i \(-0.357843\pi\)
0.431900 + 0.901921i \(0.357843\pi\)
\(168\) −0.257176 −0.0198416
\(169\) 1.00000 0.0769231
\(170\) −10.3286 −0.792171
\(171\) 1.38482 0.105900
\(172\) −6.51464 −0.496737
\(173\) −13.9420 −1.05999 −0.529994 0.848001i \(-0.677806\pi\)
−0.529994 + 0.848001i \(0.677806\pi\)
\(174\) 10.3349 0.783488
\(175\) −0.218919 −0.0165487
\(176\) 1.56925 0.118287
\(177\) 4.00889 0.301327
\(178\) 14.0981 1.05670
\(179\) −1.46855 −0.109765 −0.0548824 0.998493i \(-0.517478\pi\)
−0.0548824 + 0.998493i \(0.517478\pi\)
\(180\) 2.41893 0.180297
\(181\) −16.8574 −1.25300 −0.626499 0.779422i \(-0.715513\pi\)
−0.626499 + 0.779422i \(0.715513\pi\)
\(182\) 0.257176 0.0190631
\(183\) −12.4048 −0.916987
\(184\) −8.56848 −0.631677
\(185\) −6.84321 −0.503123
\(186\) 7.55065 0.553641
\(187\) 6.70056 0.489993
\(188\) 9.53966 0.695751
\(189\) 0.257176 0.0187068
\(190\) −3.34978 −0.243018
\(191\) 10.5816 0.765660 0.382830 0.923819i \(-0.374949\pi\)
0.382830 + 0.923819i \(0.374949\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 6.61573 0.476210 0.238105 0.971239i \(-0.423474\pi\)
0.238105 + 0.971239i \(0.423474\pi\)
\(194\) −13.3988 −0.961976
\(195\) −2.41893 −0.173223
\(196\) −6.93386 −0.495276
\(197\) −18.2594 −1.30093 −0.650463 0.759538i \(-0.725425\pi\)
−0.650463 + 0.759538i \(0.725425\pi\)
\(198\) −1.56925 −0.111522
\(199\) −5.58471 −0.395890 −0.197945 0.980213i \(-0.563427\pi\)
−0.197945 + 0.980213i \(0.563427\pi\)
\(200\) −0.851240 −0.0601918
\(201\) −9.28134 −0.654655
\(202\) 3.46177 0.243569
\(203\) −2.65789 −0.186548
\(204\) −4.26992 −0.298954
\(205\) 24.9819 1.74481
\(206\) 1.00000 0.0696733
\(207\) 8.56848 0.595551
\(208\) 1.00000 0.0693375
\(209\) 2.17312 0.150318
\(210\) −0.622092 −0.0429284
\(211\) −15.0750 −1.03780 −0.518902 0.854834i \(-0.673659\pi\)
−0.518902 + 0.854834i \(0.673659\pi\)
\(212\) −12.5020 −0.858640
\(213\) 0.286350 0.0196204
\(214\) 14.7757 1.01004
\(215\) −15.7585 −1.07472
\(216\) 1.00000 0.0680414
\(217\) −1.94185 −0.131821
\(218\) 7.20934 0.488278
\(219\) 15.7947 1.06730
\(220\) 3.79591 0.255920
\(221\) 4.26992 0.287226
\(222\) −2.82902 −0.189871
\(223\) −22.1745 −1.48492 −0.742458 0.669892i \(-0.766340\pi\)
−0.742458 + 0.669892i \(0.766340\pi\)
\(224\) 0.257176 0.0171833
\(225\) 0.851240 0.0567493
\(226\) −9.35198 −0.622084
\(227\) 15.2505 1.01221 0.506107 0.862471i \(-0.331084\pi\)
0.506107 + 0.862471i \(0.331084\pi\)
\(228\) −1.38482 −0.0917117
\(229\) −2.61103 −0.172542 −0.0862708 0.996272i \(-0.527495\pi\)
−0.0862708 + 0.996272i \(0.527495\pi\)
\(230\) −20.7266 −1.36667
\(231\) 0.403573 0.0265531
\(232\) −10.3349 −0.678521
\(233\) 12.0453 0.789112 0.394556 0.918872i \(-0.370898\pi\)
0.394556 + 0.918872i \(0.370898\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 23.0758 1.50530
\(236\) −4.00889 −0.260957
\(237\) −9.06214 −0.588650
\(238\) 1.09812 0.0711805
\(239\) −16.0683 −1.03937 −0.519685 0.854358i \(-0.673951\pi\)
−0.519685 + 0.854358i \(0.673951\pi\)
\(240\) −2.41893 −0.156141
\(241\) 3.41064 0.219699 0.109849 0.993948i \(-0.464963\pi\)
0.109849 + 0.993948i \(0.464963\pi\)
\(242\) 8.53746 0.548809
\(243\) −1.00000 −0.0641500
\(244\) 12.4048 0.794134
\(245\) −16.7725 −1.07156
\(246\) 10.3277 0.658467
\(247\) 1.38482 0.0881137
\(248\) −7.55065 −0.479467
\(249\) 6.84929 0.434056
\(250\) 10.0356 0.634705
\(251\) 18.3812 1.16021 0.580106 0.814541i \(-0.303011\pi\)
0.580106 + 0.814541i \(0.303011\pi\)
\(252\) −0.257176 −0.0162006
\(253\) 13.4461 0.845348
\(254\) 10.9282 0.685698
\(255\) −10.3286 −0.646805
\(256\) 1.00000 0.0625000
\(257\) 27.4438 1.71190 0.855950 0.517059i \(-0.172973\pi\)
0.855950 + 0.517059i \(0.172973\pi\)
\(258\) −6.51464 −0.405584
\(259\) 0.727555 0.0452081
\(260\) 2.41893 0.150016
\(261\) 10.3349 0.639716
\(262\) −19.8225 −1.22464
\(263\) −24.1083 −1.48658 −0.743290 0.668969i \(-0.766736\pi\)
−0.743290 + 0.668969i \(0.766736\pi\)
\(264\) 1.56925 0.0965805
\(265\) −30.2415 −1.85772
\(266\) 0.356141 0.0218364
\(267\) 14.0981 0.862791
\(268\) 9.28134 0.566948
\(269\) −11.7471 −0.716233 −0.358117 0.933677i \(-0.616581\pi\)
−0.358117 + 0.933677i \(0.616581\pi\)
\(270\) 2.41893 0.147212
\(271\) 20.2824 1.23207 0.616035 0.787719i \(-0.288738\pi\)
0.616035 + 0.787719i \(0.288738\pi\)
\(272\) 4.26992 0.258902
\(273\) 0.257176 0.0155650
\(274\) 7.15001 0.431948
\(275\) 1.33581 0.0805522
\(276\) −8.56848 −0.515762
\(277\) −26.9165 −1.61725 −0.808627 0.588322i \(-0.799789\pi\)
−0.808627 + 0.588322i \(0.799789\pi\)
\(278\) −3.85007 −0.230912
\(279\) 7.55065 0.452046
\(280\) 0.622092 0.0371771
\(281\) −18.6951 −1.11526 −0.557628 0.830091i \(-0.688289\pi\)
−0.557628 + 0.830091i \(0.688289\pi\)
\(282\) 9.53966 0.568078
\(283\) −23.9981 −1.42654 −0.713270 0.700889i \(-0.752787\pi\)
−0.713270 + 0.700889i \(0.752787\pi\)
\(284\) −0.286350 −0.0169917
\(285\) −3.34978 −0.198424
\(286\) −1.56925 −0.0927916
\(287\) −2.65603 −0.156780
\(288\) −1.00000 −0.0589256
\(289\) 1.23219 0.0724819
\(290\) −24.9995 −1.46802
\(291\) −13.3988 −0.785450
\(292\) −15.7947 −0.924313
\(293\) −16.2925 −0.951815 −0.475908 0.879495i \(-0.657880\pi\)
−0.475908 + 0.879495i \(0.657880\pi\)
\(294\) −6.93386 −0.404391
\(295\) −9.69724 −0.564595
\(296\) 2.82902 0.164433
\(297\) −1.56925 −0.0910570
\(298\) 10.1252 0.586538
\(299\) 8.56848 0.495528
\(300\) −0.851240 −0.0491464
\(301\) 1.67541 0.0965690
\(302\) −15.0201 −0.864309
\(303\) 3.46177 0.198873
\(304\) 1.38482 0.0794247
\(305\) 30.0063 1.71816
\(306\) −4.26992 −0.244095
\(307\) −9.48598 −0.541393 −0.270697 0.962665i \(-0.587254\pi\)
−0.270697 + 0.962665i \(0.587254\pi\)
\(308\) −0.403573 −0.0229957
\(309\) 1.00000 0.0568880
\(310\) −18.2645 −1.03736
\(311\) 5.00459 0.283784 0.141892 0.989882i \(-0.454681\pi\)
0.141892 + 0.989882i \(0.454681\pi\)
\(312\) 1.00000 0.0566139
\(313\) 17.0166 0.961835 0.480917 0.876766i \(-0.340304\pi\)
0.480917 + 0.876766i \(0.340304\pi\)
\(314\) −22.4063 −1.26446
\(315\) −0.622092 −0.0350509
\(316\) 9.06214 0.509785
\(317\) −23.2420 −1.30540 −0.652701 0.757615i \(-0.726364\pi\)
−0.652701 + 0.757615i \(0.726364\pi\)
\(318\) −12.5020 −0.701076
\(319\) 16.2181 0.908037
\(320\) 2.41893 0.135223
\(321\) 14.7757 0.824698
\(322\) 2.20361 0.122802
\(323\) 5.91305 0.329011
\(324\) 1.00000 0.0555556
\(325\) 0.851240 0.0472183
\(326\) −3.77020 −0.208812
\(327\) 7.20934 0.398678
\(328\) −10.3277 −0.570250
\(329\) −2.45337 −0.135259
\(330\) 3.79591 0.208958
\(331\) −0.342089 −0.0188029 −0.00940146 0.999956i \(-0.502993\pi\)
−0.00940146 + 0.999956i \(0.502993\pi\)
\(332\) −6.84929 −0.375904
\(333\) −2.82902 −0.155029
\(334\) −11.1628 −0.610799
\(335\) 22.4509 1.22663
\(336\) 0.257176 0.0140301
\(337\) 25.7894 1.40484 0.702418 0.711764i \(-0.252104\pi\)
0.702418 + 0.711764i \(0.252104\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −9.35198 −0.507930
\(340\) 10.3286 0.560150
\(341\) 11.8488 0.641651
\(342\) −1.38482 −0.0748823
\(343\) 3.58345 0.193488
\(344\) 6.51464 0.351246
\(345\) −20.7266 −1.11588
\(346\) 13.9420 0.749525
\(347\) 18.4618 0.991079 0.495540 0.868585i \(-0.334970\pi\)
0.495540 + 0.868585i \(0.334970\pi\)
\(348\) −10.3349 −0.554010
\(349\) −20.4645 −1.09544 −0.547719 0.836662i \(-0.684504\pi\)
−0.547719 + 0.836662i \(0.684504\pi\)
\(350\) 0.218919 0.0117017
\(351\) −1.00000 −0.0533761
\(352\) −1.56925 −0.0836412
\(353\) 10.0583 0.535351 0.267676 0.963509i \(-0.413744\pi\)
0.267676 + 0.963509i \(0.413744\pi\)
\(354\) −4.00889 −0.213070
\(355\) −0.692661 −0.0367626
\(356\) −14.0981 −0.747199
\(357\) 1.09812 0.0581187
\(358\) 1.46855 0.0776155
\(359\) 14.8765 0.785149 0.392575 0.919720i \(-0.371584\pi\)
0.392575 + 0.919720i \(0.371584\pi\)
\(360\) −2.41893 −0.127489
\(361\) −17.0823 −0.899068
\(362\) 16.8574 0.886004
\(363\) 8.53746 0.448100
\(364\) −0.257176 −0.0134797
\(365\) −38.2063 −1.99981
\(366\) 12.4048 0.648407
\(367\) −10.7987 −0.563688 −0.281844 0.959460i \(-0.590946\pi\)
−0.281844 + 0.959460i \(0.590946\pi\)
\(368\) 8.56848 0.446663
\(369\) 10.3277 0.537636
\(370\) 6.84321 0.355761
\(371\) 3.21521 0.166925
\(372\) −7.55065 −0.391483
\(373\) 27.3303 1.41511 0.707554 0.706659i \(-0.249799\pi\)
0.707554 + 0.706659i \(0.249799\pi\)
\(374\) −6.70056 −0.346478
\(375\) 10.0356 0.518235
\(376\) −9.53966 −0.491970
\(377\) 10.3349 0.532276
\(378\) −0.257176 −0.0132277
\(379\) 8.62300 0.442934 0.221467 0.975168i \(-0.428916\pi\)
0.221467 + 0.975168i \(0.428916\pi\)
\(380\) 3.34978 0.171840
\(381\) 10.9282 0.559870
\(382\) −10.5816 −0.541403
\(383\) 5.34302 0.273015 0.136508 0.990639i \(-0.456412\pi\)
0.136508 + 0.990639i \(0.456412\pi\)
\(384\) 1.00000 0.0510310
\(385\) −0.976216 −0.0497526
\(386\) −6.61573 −0.336732
\(387\) −6.51464 −0.331158
\(388\) 13.3988 0.680220
\(389\) −30.3993 −1.54131 −0.770654 0.637254i \(-0.780070\pi\)
−0.770654 + 0.637254i \(0.780070\pi\)
\(390\) 2.41893 0.122487
\(391\) 36.5867 1.85027
\(392\) 6.93386 0.350213
\(393\) −19.8225 −0.999912
\(394\) 18.2594 0.919893
\(395\) 21.9207 1.10295
\(396\) 1.56925 0.0788577
\(397\) −35.9897 −1.80627 −0.903136 0.429354i \(-0.858741\pi\)
−0.903136 + 0.429354i \(0.858741\pi\)
\(398\) 5.58471 0.279936
\(399\) 0.356141 0.0178294
\(400\) 0.851240 0.0425620
\(401\) −15.2475 −0.761423 −0.380712 0.924694i \(-0.624321\pi\)
−0.380712 + 0.924694i \(0.624321\pi\)
\(402\) 9.28134 0.462911
\(403\) 7.55065 0.376125
\(404\) −3.46177 −0.172229
\(405\) 2.41893 0.120198
\(406\) 2.65789 0.131909
\(407\) −4.43943 −0.220054
\(408\) 4.26992 0.211392
\(409\) 18.7585 0.927550 0.463775 0.885953i \(-0.346495\pi\)
0.463775 + 0.885953i \(0.346495\pi\)
\(410\) −24.9819 −1.23377
\(411\) 7.15001 0.352684
\(412\) −1.00000 −0.0492665
\(413\) 1.03099 0.0507317
\(414\) −8.56848 −0.421118
\(415\) −16.5680 −0.813291
\(416\) −1.00000 −0.0490290
\(417\) −3.85007 −0.188539
\(418\) −2.17312 −0.106291
\(419\) 12.8880 0.629621 0.314811 0.949154i \(-0.398059\pi\)
0.314811 + 0.949154i \(0.398059\pi\)
\(420\) 0.622092 0.0303550
\(421\) −13.2438 −0.645462 −0.322731 0.946491i \(-0.604601\pi\)
−0.322731 + 0.946491i \(0.604601\pi\)
\(422\) 15.0750 0.733839
\(423\) 9.53966 0.463834
\(424\) 12.5020 0.607150
\(425\) 3.63473 0.176310
\(426\) −0.286350 −0.0138737
\(427\) −3.19021 −0.154385
\(428\) −14.7757 −0.714209
\(429\) −1.56925 −0.0757640
\(430\) 15.7585 0.759942
\(431\) −13.7422 −0.661937 −0.330969 0.943642i \(-0.607375\pi\)
−0.330969 + 0.943642i \(0.607375\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 21.5048 1.03346 0.516729 0.856149i \(-0.327150\pi\)
0.516729 + 0.856149i \(0.327150\pi\)
\(434\) 1.94185 0.0932116
\(435\) −24.9995 −1.19863
\(436\) −7.20934 −0.345265
\(437\) 11.8658 0.567617
\(438\) −15.7947 −0.754699
\(439\) 2.91356 0.139057 0.0695283 0.997580i \(-0.477851\pi\)
0.0695283 + 0.997580i \(0.477851\pi\)
\(440\) −3.79591 −0.180963
\(441\) −6.93386 −0.330184
\(442\) −4.26992 −0.203099
\(443\) −29.2420 −1.38933 −0.694664 0.719335i \(-0.744447\pi\)
−0.694664 + 0.719335i \(0.744447\pi\)
\(444\) 2.82902 0.134259
\(445\) −34.1024 −1.61661
\(446\) 22.1745 1.04999
\(447\) 10.1252 0.478906
\(448\) −0.257176 −0.0121504
\(449\) 34.2300 1.61541 0.807706 0.589585i \(-0.200709\pi\)
0.807706 + 0.589585i \(0.200709\pi\)
\(450\) −0.851240 −0.0401279
\(451\) 16.2067 0.763142
\(452\) 9.35198 0.439880
\(453\) −15.0201 −0.705706
\(454\) −15.2505 −0.715743
\(455\) −0.622092 −0.0291641
\(456\) 1.38482 0.0648500
\(457\) −4.90047 −0.229234 −0.114617 0.993410i \(-0.536564\pi\)
−0.114617 + 0.993410i \(0.536564\pi\)
\(458\) 2.61103 0.122005
\(459\) −4.26992 −0.199303
\(460\) 20.7266 0.966382
\(461\) 12.2479 0.570443 0.285221 0.958462i \(-0.407933\pi\)
0.285221 + 0.958462i \(0.407933\pi\)
\(462\) −0.403573 −0.0187759
\(463\) 33.1408 1.54018 0.770091 0.637934i \(-0.220211\pi\)
0.770091 + 0.637934i \(0.220211\pi\)
\(464\) 10.3349 0.479787
\(465\) −18.2645 −0.846997
\(466\) −12.0453 −0.557987
\(467\) −23.1797 −1.07263 −0.536314 0.844019i \(-0.680184\pi\)
−0.536314 + 0.844019i \(0.680184\pi\)
\(468\) 1.00000 0.0462250
\(469\) −2.38694 −0.110219
\(470\) −23.0758 −1.06441
\(471\) −22.4063 −1.03243
\(472\) 4.00889 0.184524
\(473\) −10.2231 −0.470058
\(474\) 9.06214 0.416238
\(475\) 1.17881 0.0540876
\(476\) −1.09812 −0.0503322
\(477\) −12.5020 −0.572427
\(478\) 16.0683 0.734946
\(479\) −7.47120 −0.341368 −0.170684 0.985326i \(-0.554598\pi\)
−0.170684 + 0.985326i \(0.554598\pi\)
\(480\) 2.41893 0.110409
\(481\) −2.82902 −0.128992
\(482\) −3.41064 −0.155351
\(483\) 2.20361 0.100268
\(484\) −8.53746 −0.388066
\(485\) 32.4107 1.47170
\(486\) 1.00000 0.0453609
\(487\) −13.0822 −0.592813 −0.296406 0.955062i \(-0.595788\pi\)
−0.296406 + 0.955062i \(0.595788\pi\)
\(488\) −12.4048 −0.561537
\(489\) −3.77020 −0.170494
\(490\) 16.7725 0.757707
\(491\) −29.2439 −1.31976 −0.659879 0.751372i \(-0.729392\pi\)
−0.659879 + 0.751372i \(0.729392\pi\)
\(492\) −10.3277 −0.465607
\(493\) 44.1293 1.98748
\(494\) −1.38482 −0.0623058
\(495\) 3.79591 0.170613
\(496\) 7.55065 0.339034
\(497\) 0.0736422 0.00330331
\(498\) −6.84929 −0.306924
\(499\) 20.8225 0.932142 0.466071 0.884747i \(-0.345669\pi\)
0.466071 + 0.884747i \(0.345669\pi\)
\(500\) −10.0356 −0.448805
\(501\) −11.1628 −0.498715
\(502\) −18.3812 −0.820393
\(503\) 12.1548 0.541957 0.270978 0.962585i \(-0.412653\pi\)
0.270978 + 0.962585i \(0.412653\pi\)
\(504\) 0.257176 0.0114555
\(505\) −8.37379 −0.372629
\(506\) −13.4461 −0.597751
\(507\) −1.00000 −0.0444116
\(508\) −10.9282 −0.484862
\(509\) 5.21062 0.230957 0.115478 0.993310i \(-0.463160\pi\)
0.115478 + 0.993310i \(0.463160\pi\)
\(510\) 10.3286 0.457360
\(511\) 4.06201 0.179693
\(512\) −1.00000 −0.0441942
\(513\) −1.38482 −0.0611411
\(514\) −27.4438 −1.21050
\(515\) −2.41893 −0.106591
\(516\) 6.51464 0.286791
\(517\) 14.9701 0.658384
\(518\) −0.727555 −0.0319670
\(519\) 13.9420 0.611984
\(520\) −2.41893 −0.106077
\(521\) −33.9850 −1.48891 −0.744456 0.667672i \(-0.767291\pi\)
−0.744456 + 0.667672i \(0.767291\pi\)
\(522\) −10.3349 −0.452347
\(523\) 37.6173 1.64489 0.822444 0.568846i \(-0.192610\pi\)
0.822444 + 0.568846i \(0.192610\pi\)
\(524\) 19.8225 0.865949
\(525\) 0.218919 0.00955439
\(526\) 24.1083 1.05117
\(527\) 32.2407 1.40443
\(528\) −1.56925 −0.0682928
\(529\) 50.4189 2.19213
\(530\) 30.2415 1.31361
\(531\) −4.00889 −0.173971
\(532\) −0.356141 −0.0154407
\(533\) 10.3277 0.447341
\(534\) −14.0981 −0.610085
\(535\) −35.7414 −1.54523
\(536\) −9.28134 −0.400893
\(537\) 1.46855 0.0633728
\(538\) 11.7471 0.506453
\(539\) −10.8809 −0.468676
\(540\) −2.41893 −0.104094
\(541\) 29.9167 1.28622 0.643110 0.765774i \(-0.277644\pi\)
0.643110 + 0.765774i \(0.277644\pi\)
\(542\) −20.2824 −0.871205
\(543\) 16.8574 0.723419
\(544\) −4.26992 −0.183071
\(545\) −17.4389 −0.747001
\(546\) −0.257176 −0.0110061
\(547\) 31.6336 1.35255 0.676276 0.736648i \(-0.263592\pi\)
0.676276 + 0.736648i \(0.263592\pi\)
\(548\) −7.15001 −0.305433
\(549\) 12.4048 0.529422
\(550\) −1.33581 −0.0569590
\(551\) 14.3120 0.609710
\(552\) 8.56848 0.364699
\(553\) −2.33057 −0.0991057
\(554\) 26.9165 1.14357
\(555\) 6.84321 0.290478
\(556\) 3.85007 0.163279
\(557\) 13.8220 0.585659 0.292829 0.956165i \(-0.405403\pi\)
0.292829 + 0.956165i \(0.405403\pi\)
\(558\) −7.55065 −0.319645
\(559\) −6.51464 −0.275540
\(560\) −0.622092 −0.0262882
\(561\) −6.70056 −0.282898
\(562\) 18.6951 0.788606
\(563\) 0.435298 0.0183456 0.00917281 0.999958i \(-0.497080\pi\)
0.00917281 + 0.999958i \(0.497080\pi\)
\(564\) −9.53966 −0.401692
\(565\) 22.6218 0.951707
\(566\) 23.9981 1.00872
\(567\) −0.257176 −0.0108004
\(568\) 0.286350 0.0120150
\(569\) 10.2054 0.427831 0.213916 0.976852i \(-0.431378\pi\)
0.213916 + 0.976852i \(0.431378\pi\)
\(570\) 3.34978 0.140307
\(571\) 22.7820 0.953396 0.476698 0.879067i \(-0.341834\pi\)
0.476698 + 0.879067i \(0.341834\pi\)
\(572\) 1.56925 0.0656136
\(573\) −10.5816 −0.442054
\(574\) 2.65603 0.110860
\(575\) 7.29384 0.304174
\(576\) 1.00000 0.0416667
\(577\) 16.3459 0.680490 0.340245 0.940337i \(-0.389490\pi\)
0.340245 + 0.940337i \(0.389490\pi\)
\(578\) −1.23219 −0.0512525
\(579\) −6.61573 −0.274940
\(580\) 24.9995 1.03805
\(581\) 1.76147 0.0730782
\(582\) 13.3988 0.555397
\(583\) −19.6187 −0.812524
\(584\) 15.7947 0.653588
\(585\) 2.41893 0.100011
\(586\) 16.2925 0.673035
\(587\) −45.6887 −1.88577 −0.942887 0.333112i \(-0.891901\pi\)
−0.942887 + 0.333112i \(0.891901\pi\)
\(588\) 6.93386 0.285948
\(589\) 10.4563 0.430843
\(590\) 9.69724 0.399229
\(591\) 18.2594 0.751089
\(592\) −2.82902 −0.116272
\(593\) −5.09918 −0.209398 −0.104699 0.994504i \(-0.533388\pi\)
−0.104699 + 0.994504i \(0.533388\pi\)
\(594\) 1.56925 0.0643870
\(595\) −2.65628 −0.108897
\(596\) −10.1252 −0.414745
\(597\) 5.58471 0.228567
\(598\) −8.56848 −0.350391
\(599\) −2.52897 −0.103331 −0.0516654 0.998664i \(-0.516453\pi\)
−0.0516654 + 0.998664i \(0.516453\pi\)
\(600\) 0.851240 0.0347517
\(601\) −13.9478 −0.568943 −0.284471 0.958685i \(-0.591818\pi\)
−0.284471 + 0.958685i \(0.591818\pi\)
\(602\) −1.67541 −0.0682846
\(603\) 9.28134 0.377965
\(604\) 15.0201 0.611159
\(605\) −20.6516 −0.839605
\(606\) −3.46177 −0.140625
\(607\) −26.2324 −1.06474 −0.532371 0.846511i \(-0.678699\pi\)
−0.532371 + 0.846511i \(0.678699\pi\)
\(608\) −1.38482 −0.0561617
\(609\) 2.65789 0.107703
\(610\) −30.0063 −1.21492
\(611\) 9.53966 0.385933
\(612\) 4.26992 0.172601
\(613\) −18.5862 −0.750688 −0.375344 0.926886i \(-0.622475\pi\)
−0.375344 + 0.926886i \(0.622475\pi\)
\(614\) 9.48598 0.382823
\(615\) −24.9819 −1.00737
\(616\) 0.403573 0.0162604
\(617\) 8.44285 0.339896 0.169948 0.985453i \(-0.445640\pi\)
0.169948 + 0.985453i \(0.445640\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 33.6205 1.35132 0.675662 0.737212i \(-0.263858\pi\)
0.675662 + 0.737212i \(0.263858\pi\)
\(620\) 18.2645 0.733521
\(621\) −8.56848 −0.343841
\(622\) −5.00459 −0.200666
\(623\) 3.62570 0.145261
\(624\) −1.00000 −0.0400320
\(625\) −28.5316 −1.14126
\(626\) −17.0166 −0.680120
\(627\) −2.17312 −0.0867861
\(628\) 22.4063 0.894109
\(629\) −12.0797 −0.481648
\(630\) 0.622092 0.0247847
\(631\) −27.1072 −1.07912 −0.539560 0.841947i \(-0.681409\pi\)
−0.539560 + 0.841947i \(0.681409\pi\)
\(632\) −9.06214 −0.360473
\(633\) 15.0750 0.599177
\(634\) 23.2420 0.923059
\(635\) −26.4347 −1.04903
\(636\) 12.5020 0.495736
\(637\) −6.93386 −0.274730
\(638\) −16.2181 −0.642079
\(639\) −0.286350 −0.0113278
\(640\) −2.41893 −0.0956168
\(641\) −7.16304 −0.282923 −0.141462 0.989944i \(-0.545180\pi\)
−0.141462 + 0.989944i \(0.545180\pi\)
\(642\) −14.7757 −0.583149
\(643\) 43.7819 1.72659 0.863294 0.504701i \(-0.168397\pi\)
0.863294 + 0.504701i \(0.168397\pi\)
\(644\) −2.20361 −0.0868343
\(645\) 15.7585 0.620490
\(646\) −5.91305 −0.232646
\(647\) −40.6556 −1.59834 −0.799169 0.601107i \(-0.794727\pi\)
−0.799169 + 0.601107i \(0.794727\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −6.29095 −0.246941
\(650\) −0.851240 −0.0333884
\(651\) 1.94185 0.0761070
\(652\) 3.77020 0.147652
\(653\) −42.1850 −1.65083 −0.825413 0.564530i \(-0.809058\pi\)
−0.825413 + 0.564530i \(0.809058\pi\)
\(654\) −7.20934 −0.281908
\(655\) 47.9493 1.87353
\(656\) 10.3277 0.403227
\(657\) −15.7947 −0.616209
\(658\) 2.45337 0.0956423
\(659\) 32.0508 1.24852 0.624261 0.781216i \(-0.285400\pi\)
0.624261 + 0.781216i \(0.285400\pi\)
\(660\) −3.79591 −0.147755
\(661\) 26.4456 1.02861 0.514307 0.857606i \(-0.328049\pi\)
0.514307 + 0.857606i \(0.328049\pi\)
\(662\) 0.342089 0.0132957
\(663\) −4.26992 −0.165830
\(664\) 6.84929 0.265804
\(665\) −0.861482 −0.0334069
\(666\) 2.82902 0.109622
\(667\) 88.5546 3.42885
\(668\) 11.1628 0.431900
\(669\) 22.1745 0.857317
\(670\) −22.4509 −0.867356
\(671\) 19.4662 0.751483
\(672\) −0.257176 −0.00992078
\(673\) −29.5184 −1.13785 −0.568925 0.822390i \(-0.692640\pi\)
−0.568925 + 0.822390i \(0.692640\pi\)
\(674\) −25.7894 −0.993370
\(675\) −0.851240 −0.0327643
\(676\) 1.00000 0.0384615
\(677\) 22.0651 0.848030 0.424015 0.905655i \(-0.360620\pi\)
0.424015 + 0.905655i \(0.360620\pi\)
\(678\) 9.35198 0.359161
\(679\) −3.44584 −0.132239
\(680\) −10.3286 −0.396086
\(681\) −15.2505 −0.584402
\(682\) −11.8488 −0.453716
\(683\) −1.67975 −0.0642737 −0.0321369 0.999483i \(-0.510231\pi\)
−0.0321369 + 0.999483i \(0.510231\pi\)
\(684\) 1.38482 0.0529498
\(685\) −17.2954 −0.660823
\(686\) −3.58345 −0.136817
\(687\) 2.61103 0.0996169
\(688\) −6.51464 −0.248368
\(689\) −12.5020 −0.476288
\(690\) 20.7266 0.789048
\(691\) −34.2647 −1.30349 −0.651745 0.758438i \(-0.725963\pi\)
−0.651745 + 0.758438i \(0.725963\pi\)
\(692\) −13.9420 −0.529994
\(693\) −0.403573 −0.0153305
\(694\) −18.4618 −0.700799
\(695\) 9.31306 0.353265
\(696\) 10.3349 0.391744
\(697\) 44.0982 1.67034
\(698\) 20.4645 0.774592
\(699\) −12.0453 −0.455594
\(700\) −0.218919 −0.00827434
\(701\) −9.73279 −0.367602 −0.183801 0.982963i \(-0.558840\pi\)
−0.183801 + 0.982963i \(0.558840\pi\)
\(702\) 1.00000 0.0377426
\(703\) −3.91767 −0.147758
\(704\) 1.56925 0.0591433
\(705\) −23.0758 −0.869085
\(706\) −10.0583 −0.378550
\(707\) 0.890284 0.0334826
\(708\) 4.00889 0.150663
\(709\) 43.2474 1.62419 0.812096 0.583524i \(-0.198327\pi\)
0.812096 + 0.583524i \(0.198327\pi\)
\(710\) 0.692661 0.0259951
\(711\) 9.06214 0.339857
\(712\) 14.0981 0.528350
\(713\) 64.6977 2.42295
\(714\) −1.09812 −0.0410961
\(715\) 3.79591 0.141959
\(716\) −1.46855 −0.0548824
\(717\) 16.0683 0.600081
\(718\) −14.8765 −0.555184
\(719\) 36.1888 1.34961 0.674807 0.737995i \(-0.264227\pi\)
0.674807 + 0.737995i \(0.264227\pi\)
\(720\) 2.41893 0.0901483
\(721\) 0.257176 0.00957773
\(722\) 17.0823 0.635737
\(723\) −3.41064 −0.126843
\(724\) −16.8574 −0.626499
\(725\) 8.79750 0.326731
\(726\) −8.53746 −0.316855
\(727\) 39.2177 1.45450 0.727252 0.686370i \(-0.240797\pi\)
0.727252 + 0.686370i \(0.240797\pi\)
\(728\) 0.257176 0.00953157
\(729\) 1.00000 0.0370370
\(730\) 38.2063 1.41408
\(731\) −27.8170 −1.02885
\(732\) −12.4048 −0.458493
\(733\) −14.5729 −0.538261 −0.269131 0.963104i \(-0.586736\pi\)
−0.269131 + 0.963104i \(0.586736\pi\)
\(734\) 10.7987 0.398588
\(735\) 16.7725 0.618665
\(736\) −8.56848 −0.315839
\(737\) 14.5647 0.536499
\(738\) −10.3277 −0.380166
\(739\) −13.0285 −0.479261 −0.239631 0.970864i \(-0.577026\pi\)
−0.239631 + 0.970864i \(0.577026\pi\)
\(740\) −6.84321 −0.251561
\(741\) −1.38482 −0.0508725
\(742\) −3.21521 −0.118034
\(743\) 13.9766 0.512751 0.256376 0.966577i \(-0.417472\pi\)
0.256376 + 0.966577i \(0.417472\pi\)
\(744\) 7.55065 0.276820
\(745\) −24.4922 −0.897326
\(746\) −27.3303 −1.00063
\(747\) −6.84929 −0.250603
\(748\) 6.70056 0.244997
\(749\) 3.79995 0.138847
\(750\) −10.0356 −0.366447
\(751\) −6.09636 −0.222459 −0.111230 0.993795i \(-0.535479\pi\)
−0.111230 + 0.993795i \(0.535479\pi\)
\(752\) 9.53966 0.347875
\(753\) −18.3812 −0.669848
\(754\) −10.3349 −0.376376
\(755\) 36.3326 1.32228
\(756\) 0.257176 0.00935340
\(757\) 35.0595 1.27426 0.637130 0.770756i \(-0.280121\pi\)
0.637130 + 0.770756i \(0.280121\pi\)
\(758\) −8.62300 −0.313202
\(759\) −13.4461 −0.488062
\(760\) −3.34978 −0.121509
\(761\) −18.3039 −0.663515 −0.331758 0.943365i \(-0.607642\pi\)
−0.331758 + 0.943365i \(0.607642\pi\)
\(762\) −10.9282 −0.395888
\(763\) 1.85407 0.0671218
\(764\) 10.5816 0.382830
\(765\) 10.3286 0.373433
\(766\) −5.34302 −0.193051
\(767\) −4.00889 −0.144753
\(768\) −1.00000 −0.0360844
\(769\) −28.0075 −1.00998 −0.504989 0.863126i \(-0.668503\pi\)
−0.504989 + 0.863126i \(0.668503\pi\)
\(770\) 0.976216 0.0351804
\(771\) −27.4438 −0.988365
\(772\) 6.61573 0.238105
\(773\) 16.9295 0.608910 0.304455 0.952527i \(-0.401526\pi\)
0.304455 + 0.952527i \(0.401526\pi\)
\(774\) 6.51464 0.234164
\(775\) 6.42742 0.230880
\(776\) −13.3988 −0.480988
\(777\) −0.727555 −0.0261009
\(778\) 30.3993 1.08987
\(779\) 14.3019 0.512419
\(780\) −2.41893 −0.0866117
\(781\) −0.449354 −0.0160791
\(782\) −36.5867 −1.30834
\(783\) −10.3349 −0.369340
\(784\) −6.93386 −0.247638
\(785\) 54.1994 1.93446
\(786\) 19.8225 0.707044
\(787\) 4.30348 0.153402 0.0767012 0.997054i \(-0.475561\pi\)
0.0767012 + 0.997054i \(0.475561\pi\)
\(788\) −18.2594 −0.650463
\(789\) 24.1083 0.858278
\(790\) −21.9207 −0.779904
\(791\) −2.40510 −0.0855156
\(792\) −1.56925 −0.0557608
\(793\) 12.4048 0.440506
\(794\) 35.9897 1.27723
\(795\) 30.2415 1.07255
\(796\) −5.58471 −0.197945
\(797\) 9.26665 0.328242 0.164121 0.986440i \(-0.447521\pi\)
0.164121 + 0.986440i \(0.447521\pi\)
\(798\) −0.356141 −0.0126073
\(799\) 40.7335 1.44105
\(800\) −0.851240 −0.0300959
\(801\) −14.0981 −0.498133
\(802\) 15.2475 0.538408
\(803\) −24.7858 −0.874670
\(804\) −9.28134 −0.327328
\(805\) −5.33038 −0.187871
\(806\) −7.55065 −0.265960
\(807\) 11.7471 0.413517
\(808\) 3.46177 0.121785
\(809\) −25.8177 −0.907701 −0.453850 0.891078i \(-0.649950\pi\)
−0.453850 + 0.891078i \(0.649950\pi\)
\(810\) −2.41893 −0.0849927
\(811\) 27.7188 0.973339 0.486669 0.873586i \(-0.338212\pi\)
0.486669 + 0.873586i \(0.338212\pi\)
\(812\) −2.65789 −0.0932738
\(813\) −20.2824 −0.711336
\(814\) 4.43943 0.155602
\(815\) 9.11986 0.319455
\(816\) −4.26992 −0.149477
\(817\) −9.02158 −0.315625
\(818\) −18.7585 −0.655877
\(819\) −0.257176 −0.00898645
\(820\) 24.9819 0.872406
\(821\) 8.58538 0.299632 0.149816 0.988714i \(-0.452132\pi\)
0.149816 + 0.988714i \(0.452132\pi\)
\(822\) −7.15001 −0.249385
\(823\) −25.0310 −0.872527 −0.436263 0.899819i \(-0.643698\pi\)
−0.436263 + 0.899819i \(0.643698\pi\)
\(824\) 1.00000 0.0348367
\(825\) −1.33581 −0.0465068
\(826\) −1.03099 −0.0358727
\(827\) 3.21644 0.111847 0.0559233 0.998435i \(-0.482190\pi\)
0.0559233 + 0.998435i \(0.482190\pi\)
\(828\) 8.56848 0.297775
\(829\) −27.9871 −0.972034 −0.486017 0.873949i \(-0.661551\pi\)
−0.486017 + 0.873949i \(0.661551\pi\)
\(830\) 16.5680 0.575083
\(831\) 26.9165 0.933721
\(832\) 1.00000 0.0346688
\(833\) −29.6070 −1.02582
\(834\) 3.85007 0.133317
\(835\) 27.0020 0.934442
\(836\) 2.17312 0.0751589
\(837\) −7.55065 −0.260989
\(838\) −12.8880 −0.445209
\(839\) 28.7827 0.993688 0.496844 0.867840i \(-0.334492\pi\)
0.496844 + 0.867840i \(0.334492\pi\)
\(840\) −0.622092 −0.0214642
\(841\) 77.8106 2.68312
\(842\) 13.2438 0.456411
\(843\) 18.6951 0.643894
\(844\) −15.0750 −0.518902
\(845\) 2.41893 0.0832138
\(846\) −9.53966 −0.327980
\(847\) 2.19563 0.0754427
\(848\) −12.5020 −0.429320
\(849\) 23.9981 0.823614
\(850\) −3.63473 −0.124670
\(851\) −24.2404 −0.830950
\(852\) 0.286350 0.00981018
\(853\) 6.26327 0.214450 0.107225 0.994235i \(-0.465803\pi\)
0.107225 + 0.994235i \(0.465803\pi\)
\(854\) 3.19021 0.109167
\(855\) 3.34978 0.114560
\(856\) 14.7757 0.505022
\(857\) −38.6866 −1.32151 −0.660755 0.750601i \(-0.729764\pi\)
−0.660755 + 0.750601i \(0.729764\pi\)
\(858\) 1.56925 0.0535732
\(859\) 3.86346 0.131820 0.0659098 0.997826i \(-0.479005\pi\)
0.0659098 + 0.997826i \(0.479005\pi\)
\(860\) −15.7585 −0.537360
\(861\) 2.65603 0.0905171
\(862\) 13.7422 0.468060
\(863\) 1.04093 0.0354336 0.0177168 0.999843i \(-0.494360\pi\)
0.0177168 + 0.999843i \(0.494360\pi\)
\(864\) 1.00000 0.0340207
\(865\) −33.7247 −1.14667
\(866\) −21.5048 −0.730764
\(867\) −1.23219 −0.0418475
\(868\) −1.94185 −0.0659106
\(869\) 14.2208 0.482406
\(870\) 24.9995 0.847562
\(871\) 9.28134 0.314486
\(872\) 7.20934 0.244139
\(873\) 13.3988 0.453480
\(874\) −11.8658 −0.401366
\(875\) 2.58091 0.0872506
\(876\) 15.7947 0.533652
\(877\) −22.7979 −0.769831 −0.384915 0.922952i \(-0.625769\pi\)
−0.384915 + 0.922952i \(0.625769\pi\)
\(878\) −2.91356 −0.0983279
\(879\) 16.2925 0.549531
\(880\) 3.79591 0.127960
\(881\) 26.3482 0.887694 0.443847 0.896103i \(-0.353613\pi\)
0.443847 + 0.896103i \(0.353613\pi\)
\(882\) 6.93386 0.233475
\(883\) 22.9812 0.773379 0.386690 0.922210i \(-0.373618\pi\)
0.386690 + 0.922210i \(0.373618\pi\)
\(884\) 4.26992 0.143613
\(885\) 9.69724 0.325969
\(886\) 29.2420 0.982403
\(887\) 27.5466 0.924924 0.462462 0.886639i \(-0.346966\pi\)
0.462462 + 0.886639i \(0.346966\pi\)
\(888\) −2.82902 −0.0949356
\(889\) 2.81048 0.0942604
\(890\) 34.1024 1.14312
\(891\) 1.56925 0.0525718
\(892\) −22.1745 −0.742458
\(893\) 13.2107 0.442078
\(894\) −10.1252 −0.338638
\(895\) −3.55233 −0.118741
\(896\) 0.257176 0.00859165
\(897\) −8.56848 −0.286093
\(898\) −34.2300 −1.14227
\(899\) 78.0354 2.60263
\(900\) 0.851240 0.0283747
\(901\) −53.3824 −1.77843
\(902\) −16.2067 −0.539623
\(903\) −1.67541 −0.0557541
\(904\) −9.35198 −0.311042
\(905\) −40.7769 −1.35547
\(906\) 15.0201 0.499009
\(907\) −26.5420 −0.881312 −0.440656 0.897676i \(-0.645254\pi\)
−0.440656 + 0.897676i \(0.645254\pi\)
\(908\) 15.2505 0.506107
\(909\) −3.46177 −0.114820
\(910\) 0.622092 0.0206221
\(911\) 32.1818 1.06623 0.533115 0.846043i \(-0.321021\pi\)
0.533115 + 0.846043i \(0.321021\pi\)
\(912\) −1.38482 −0.0458558
\(913\) −10.7482 −0.355715
\(914\) 4.90047 0.162093
\(915\) −30.0063 −0.991978
\(916\) −2.61103 −0.0862708
\(917\) −5.09787 −0.168346
\(918\) 4.26992 0.140928
\(919\) −37.8115 −1.24729 −0.623643 0.781709i \(-0.714348\pi\)
−0.623643 + 0.781709i \(0.714348\pi\)
\(920\) −20.7266 −0.683336
\(921\) 9.48598 0.312574
\(922\) −12.2479 −0.403364
\(923\) −0.286350 −0.00942531
\(924\) 0.403573 0.0132766
\(925\) −2.40817 −0.0791803
\(926\) −33.1408 −1.08907
\(927\) −1.00000 −0.0328443
\(928\) −10.3349 −0.339260
\(929\) −3.13069 −0.102715 −0.0513573 0.998680i \(-0.516355\pi\)
−0.0513573 + 0.998680i \(0.516355\pi\)
\(930\) 18.2645 0.598918
\(931\) −9.60212 −0.314697
\(932\) 12.0453 0.394556
\(933\) −5.00459 −0.163843
\(934\) 23.1797 0.758462
\(935\) 16.2082 0.530065
\(936\) −1.00000 −0.0326860
\(937\) 32.1463 1.05017 0.525087 0.851049i \(-0.324033\pi\)
0.525087 + 0.851049i \(0.324033\pi\)
\(938\) 2.38694 0.0779363
\(939\) −17.0166 −0.555316
\(940\) 23.0758 0.752649
\(941\) 46.2552 1.50788 0.753938 0.656946i \(-0.228152\pi\)
0.753938 + 0.656946i \(0.228152\pi\)
\(942\) 22.4063 0.730037
\(943\) 88.4924 2.88171
\(944\) −4.00889 −0.130478
\(945\) 0.622092 0.0202366
\(946\) 10.2231 0.332381
\(947\) 15.2368 0.495129 0.247564 0.968871i \(-0.420370\pi\)
0.247564 + 0.968871i \(0.420370\pi\)
\(948\) −9.06214 −0.294325
\(949\) −15.7947 −0.512717
\(950\) −1.17881 −0.0382457
\(951\) 23.2420 0.753674
\(952\) 1.09812 0.0355903
\(953\) −7.86823 −0.254877 −0.127438 0.991846i \(-0.540676\pi\)
−0.127438 + 0.991846i \(0.540676\pi\)
\(954\) 12.5020 0.404767
\(955\) 25.5963 0.828276
\(956\) −16.0683 −0.519685
\(957\) −16.2181 −0.524255
\(958\) 7.47120 0.241384
\(959\) 1.83881 0.0593783
\(960\) −2.41893 −0.0780707
\(961\) 26.0124 0.839109
\(962\) 2.82902 0.0912112
\(963\) −14.7757 −0.476139
\(964\) 3.41064 0.109849
\(965\) 16.0030 0.515155
\(966\) −2.20361 −0.0708999
\(967\) −4.92886 −0.158501 −0.0792507 0.996855i \(-0.525253\pi\)
−0.0792507 + 0.996855i \(0.525253\pi\)
\(968\) 8.53746 0.274404
\(969\) −5.91305 −0.189955
\(970\) −32.4107 −1.04065
\(971\) 12.0048 0.385252 0.192626 0.981272i \(-0.438300\pi\)
0.192626 + 0.981272i \(0.438300\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −0.990145 −0.0317426
\(974\) 13.0822 0.419182
\(975\) −0.851240 −0.0272615
\(976\) 12.4048 0.397067
\(977\) 0.539082 0.0172468 0.00862339 0.999963i \(-0.497255\pi\)
0.00862339 + 0.999963i \(0.497255\pi\)
\(978\) 3.77020 0.120558
\(979\) −22.1235 −0.707069
\(980\) −16.7725 −0.535779
\(981\) −7.20934 −0.230177
\(982\) 29.2439 0.933210
\(983\) −42.9713 −1.37057 −0.685286 0.728274i \(-0.740323\pi\)
−0.685286 + 0.728274i \(0.740323\pi\)
\(984\) 10.3277 0.329234
\(985\) −44.1682 −1.40731
\(986\) −44.1293 −1.40536
\(987\) 2.45337 0.0780916
\(988\) 1.38482 0.0440569
\(989\) −55.8206 −1.77499
\(990\) −3.79591 −0.120642
\(991\) 49.6660 1.57769 0.788846 0.614592i \(-0.210679\pi\)
0.788846 + 0.614592i \(0.210679\pi\)
\(992\) −7.55065 −0.239734
\(993\) 0.342089 0.0108559
\(994\) −0.0736422 −0.00233579
\(995\) −13.5090 −0.428265
\(996\) 6.84929 0.217028
\(997\) 46.7267 1.47985 0.739924 0.672690i \(-0.234861\pi\)
0.739924 + 0.672690i \(0.234861\pi\)
\(998\) −20.8225 −0.659124
\(999\) 2.82902 0.0895062
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 8034.2.a.z.1.13 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.z.1.13 14 1.1 even 1 trivial