Properties

Label 1.34.a.a.1.2
Level 1
Weight 34
Character 1.1
Self dual yes
Analytic conductor 6.898
Analytic rank 1
Dimension 2
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 34 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.89828288810\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\mathbb{Q}[x]/(x^{2} - \cdots)\)
Defining polynomial: \(x^{2} - x - 589050\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-766.996\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+49679.4 q^{2} -1.55221e7 q^{3} -6.12189e9 q^{4} +2.04307e10 q^{5} -7.71130e11 q^{6} -1.22168e14 q^{7} -7.30875e14 q^{8} -5.31812e15 q^{9} +O(q^{10})\) \(q+49679.4 q^{2} -1.55221e7 q^{3} -6.12189e9 q^{4} +2.04307e10 q^{5} -7.71130e11 q^{6} -1.22168e14 q^{7} -7.30875e14 q^{8} -5.31812e15 q^{9} +1.01499e15 q^{10} +2.15763e17 q^{11} +9.50247e16 q^{12} -1.07762e18 q^{13} -6.06926e18 q^{14} -3.17129e17 q^{15} +1.62772e19 q^{16} +2.54532e20 q^{17} -2.64201e20 q^{18} -1.22020e21 q^{19} -1.25075e20 q^{20} +1.89631e21 q^{21} +1.07190e22 q^{22} -5.11280e21 q^{23} +1.13447e22 q^{24} -1.15998e23 q^{25} -5.35354e22 q^{26} +1.68837e23 q^{27} +7.47901e23 q^{28} -1.64733e23 q^{29} -1.57548e22 q^{30} -6.75706e24 q^{31} +7.08681e24 q^{32} -3.34910e24 q^{33} +1.26450e25 q^{34} -2.49599e24 q^{35} +3.25570e25 q^{36} -7.46520e25 q^{37} -6.06190e25 q^{38} +1.67269e25 q^{39} -1.49323e25 q^{40} +4.96453e26 q^{41} +9.42077e25 q^{42} -1.99347e26 q^{43} -1.32088e27 q^{44} -1.08653e26 q^{45} -2.54001e26 q^{46} +2.16452e27 q^{47} -2.52656e26 q^{48} +7.19411e27 q^{49} -5.76271e27 q^{50} -3.95088e27 q^{51} +6.59706e27 q^{52} -3.60439e28 q^{53} +8.38773e27 q^{54} +4.40819e27 q^{55} +8.92898e28 q^{56} +1.89401e28 q^{57} -8.18385e27 q^{58} -1.87520e29 q^{59} +1.94143e27 q^{60} +4.18340e27 q^{61} -3.35687e29 q^{62} +6.49706e29 q^{63} +2.12249e29 q^{64} -2.20165e28 q^{65} -1.66381e29 q^{66} +4.85975e29 q^{67} -1.55822e30 q^{68} +7.93615e28 q^{69} -1.23999e29 q^{70} -3.42819e30 q^{71} +3.88688e30 q^{72} +7.01467e30 q^{73} -3.70867e30 q^{74} +1.80053e30 q^{75} +7.46995e30 q^{76} -2.63594e31 q^{77} +8.30984e29 q^{78} -2.95630e30 q^{79} +3.32554e29 q^{80} +2.69431e31 q^{81} +2.46635e31 q^{82} -1.23020e31 q^{83} -1.16090e31 q^{84} +5.20028e30 q^{85} -9.90343e30 q^{86} +2.55701e30 q^{87} -1.57696e32 q^{88} +7.05623e31 q^{89} -5.39783e30 q^{90} +1.31651e32 q^{91} +3.13000e31 q^{92} +1.04884e32 q^{93} +1.07532e32 q^{94} -2.49297e31 q^{95} -1.10002e32 q^{96} -7.71791e32 q^{97} +3.57399e32 q^{98} -1.14745e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 121680q^{2} + 37919880q^{3} + 14652233984q^{4} - 181061536500q^{5} - 9928922193216q^{6} - 67153080066800q^{7} - 2818750585098240q^{8} - 8021136954970854q^{9} + O(q^{10}) \) \( 2q - 121680q^{2} + 37919880q^{3} + 14652233984q^{4} - 181061536500q^{5} - 9928922193216q^{6} - 67153080066800q^{7} - 2818750585098240q^{8} - 8021136954970854q^{9} + 35542592216532000q^{10} + 133871815441914264q^{11} + 1205235433330467840q^{12} - 2981610478259443940q^{13} - 15496641262468340352q^{14} - 11085280069139874000q^{15} + \)\(19\!\cdots\!72\)\(q^{16} - 79361149261175525340q^{17} + \)\(19\!\cdots\!80\)\(q^{18} - \)\(13\!\cdots\!00\)\(q^{19} - \)\(43\!\cdots\!00\)\(q^{20} + \)\(48\!\cdots\!24\)\(q^{21} + \)\(24\!\cdots\!40\)\(q^{22} + \)\(26\!\cdots\!40\)\(q^{23} - \)\(10\!\cdots\!00\)\(q^{24} - \)\(19\!\cdots\!50\)\(q^{25} + \)\(27\!\cdots\!04\)\(q^{26} - \)\(27\!\cdots\!40\)\(q^{27} + \)\(18\!\cdots\!60\)\(q^{28} - \)\(16\!\cdots\!00\)\(q^{29} + \)\(18\!\cdots\!00\)\(q^{30} - \)\(62\!\cdots\!16\)\(q^{31} - \)\(57\!\cdots\!80\)\(q^{32} - \)\(77\!\cdots\!40\)\(q^{33} + \)\(69\!\cdots\!08\)\(q^{34} - \)\(13\!\cdots\!00\)\(q^{35} - \)\(23\!\cdots\!68\)\(q^{36} - \)\(10\!\cdots\!20\)\(q^{37} - \)\(36\!\cdots\!60\)\(q^{38} - \)\(85\!\cdots\!48\)\(q^{39} + \)\(40\!\cdots\!00\)\(q^{40} + \)\(27\!\cdots\!44\)\(q^{41} - \)\(40\!\cdots\!40\)\(q^{42} + \)\(15\!\cdots\!00\)\(q^{43} - \)\(30\!\cdots\!12\)\(q^{44} + \)\(43\!\cdots\!00\)\(q^{45} - \)\(56\!\cdots\!76\)\(q^{46} + \)\(54\!\cdots\!40\)\(q^{47} + \)\(93\!\cdots\!40\)\(q^{48} + \)\(24\!\cdots\!14\)\(q^{49} + \)\(72\!\cdots\!00\)\(q^{50} - \)\(21\!\cdots\!96\)\(q^{51} - \)\(32\!\cdots\!00\)\(q^{52} - \)\(26\!\cdots\!20\)\(q^{53} + \)\(84\!\cdots\!00\)\(q^{54} + \)\(20\!\cdots\!00\)\(q^{55} - \)\(25\!\cdots\!00\)\(q^{56} + \)\(11\!\cdots\!20\)\(q^{57} + \)\(25\!\cdots\!60\)\(q^{58} - \)\(30\!\cdots\!00\)\(q^{59} - \)\(22\!\cdots\!00\)\(q^{60} - \)\(57\!\cdots\!36\)\(q^{61} - \)\(42\!\cdots\!60\)\(q^{62} + \)\(50\!\cdots\!20\)\(q^{63} + \)\(86\!\cdots\!24\)\(q^{64} + \)\(36\!\cdots\!00\)\(q^{65} + \)\(58\!\cdots\!88\)\(q^{66} + \)\(15\!\cdots\!60\)\(q^{67} - \)\(84\!\cdots\!20\)\(q^{68} + \)\(17\!\cdots\!12\)\(q^{69} + \)\(17\!\cdots\!00\)\(q^{70} - \)\(26\!\cdots\!76\)\(q^{71} + \)\(95\!\cdots\!80\)\(q^{72} + \)\(94\!\cdots\!40\)\(q^{73} + \)\(14\!\cdots\!28\)\(q^{74} - \)\(22\!\cdots\!00\)\(q^{75} + \)\(45\!\cdots\!00\)\(q^{76} - \)\(30\!\cdots\!00\)\(q^{77} + \)\(18\!\cdots\!00\)\(q^{78} - \)\(85\!\cdots\!00\)\(q^{79} - \)\(35\!\cdots\!00\)\(q^{80} + \)\(18\!\cdots\!42\)\(q^{81} + \)\(62\!\cdots\!40\)\(q^{82} + \)\(29\!\cdots\!20\)\(q^{83} + \)\(49\!\cdots\!08\)\(q^{84} + \)\(72\!\cdots\!00\)\(q^{85} - \)\(31\!\cdots\!36\)\(q^{86} - \)\(78\!\cdots\!20\)\(q^{87} + \)\(13\!\cdots\!20\)\(q^{88} + \)\(13\!\cdots\!00\)\(q^{89} - \)\(98\!\cdots\!00\)\(q^{90} + \)\(26\!\cdots\!44\)\(q^{91} + \)\(68\!\cdots\!60\)\(q^{92} + \)\(13\!\cdots\!60\)\(q^{93} - \)\(45\!\cdots\!12\)\(q^{94} + \)\(33\!\cdots\!00\)\(q^{95} - \)\(79\!\cdots\!76\)\(q^{96} - \)\(36\!\cdots\!60\)\(q^{97} + \)\(11\!\cdots\!40\)\(q^{98} - \)\(92\!\cdots\!28\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 49679.4 0.536021 0.268010 0.963416i \(-0.413634\pi\)
0.268010 + 0.963416i \(0.413634\pi\)
\(3\) −1.55221e7 −0.208185 −0.104093 0.994568i \(-0.533194\pi\)
−0.104093 + 0.994568i \(0.533194\pi\)
\(4\) −6.12189e9 −0.712682
\(5\) 2.04307e10 0.0598796 0.0299398 0.999552i \(-0.490468\pi\)
0.0299398 + 0.999552i \(0.490468\pi\)
\(6\) −7.71130e11 −0.111592
\(7\) −1.22168e14 −1.38944 −0.694722 0.719278i \(-0.744473\pi\)
−0.694722 + 0.719278i \(0.744473\pi\)
\(8\) −7.30875e14 −0.918033
\(9\) −5.31812e15 −0.956659
\(10\) 1.01499e15 0.0320967
\(11\) 2.15763e17 1.41578 0.707892 0.706321i \(-0.249646\pi\)
0.707892 + 0.706321i \(0.249646\pi\)
\(12\) 9.50247e16 0.148370
\(13\) −1.07762e18 −0.449158 −0.224579 0.974456i \(-0.572101\pi\)
−0.224579 + 0.974456i \(0.572101\pi\)
\(14\) −6.06926e18 −0.744771
\(15\) −3.17129e17 −0.0124661
\(16\) 1.62772e19 0.220597
\(17\) 2.54532e20 1.26863 0.634316 0.773074i \(-0.281282\pi\)
0.634316 + 0.773074i \(0.281282\pi\)
\(18\) −2.64201e20 −0.512789
\(19\) −1.22020e21 −0.970505 −0.485252 0.874374i \(-0.661272\pi\)
−0.485252 + 0.874374i \(0.661272\pi\)
\(20\) −1.25075e20 −0.0426751
\(21\) 1.89631e21 0.289262
\(22\) 1.07190e22 0.758890
\(23\) −5.11280e21 −0.173840 −0.0869199 0.996215i \(-0.527702\pi\)
−0.0869199 + 0.996215i \(0.527702\pi\)
\(24\) 1.13447e22 0.191121
\(25\) −1.15998e23 −0.996414
\(26\) −5.35354e22 −0.240758
\(27\) 1.68837e23 0.407348
\(28\) 7.47901e23 0.990231
\(29\) −1.64733e23 −0.122240 −0.0611201 0.998130i \(-0.519467\pi\)
−0.0611201 + 0.998130i \(0.519467\pi\)
\(30\) −1.57548e22 −0.00668208
\(31\) −6.75706e24 −1.66836 −0.834181 0.551491i \(-0.814059\pi\)
−0.834181 + 0.551491i \(0.814059\pi\)
\(32\) 7.08681e24 1.03628
\(33\) −3.34910e24 −0.294746
\(34\) 1.26450e25 0.680013
\(35\) −2.49599e24 −0.0831994
\(36\) 3.25570e25 0.681793
\(37\) −7.46520e25 −0.994748 −0.497374 0.867536i \(-0.665702\pi\)
−0.497374 + 0.867536i \(0.665702\pi\)
\(38\) −6.06190e25 −0.520211
\(39\) 1.67269e25 0.0935082
\(40\) −1.49323e25 −0.0549715
\(41\) 4.96453e26 1.21603 0.608016 0.793925i \(-0.291966\pi\)
0.608016 + 0.793925i \(0.291966\pi\)
\(42\) 9.42077e25 0.155051
\(43\) −1.99347e26 −0.222525 −0.111263 0.993791i \(-0.535489\pi\)
−0.111263 + 0.993791i \(0.535489\pi\)
\(44\) −1.32088e27 −1.00900
\(45\) −1.08653e26 −0.0572844
\(46\) −2.54001e26 −0.0931818
\(47\) 2.16452e27 0.556862 0.278431 0.960456i \(-0.410186\pi\)
0.278431 + 0.960456i \(0.410186\pi\)
\(48\) −2.52656e26 −0.0459250
\(49\) 7.19411e27 0.930555
\(50\) −5.76271e27 −0.534099
\(51\) −3.95088e27 −0.264111
\(52\) 6.59706e27 0.320107
\(53\) −3.60439e28 −1.27726 −0.638631 0.769513i \(-0.720499\pi\)
−0.638631 + 0.769513i \(0.720499\pi\)
\(54\) 8.38773e27 0.218347
\(55\) 4.40819e27 0.0847766
\(56\) 8.92898e28 1.27556
\(57\) 1.89401e28 0.202045
\(58\) −8.18385e27 −0.0655233
\(59\) −1.87520e29 −1.13237 −0.566186 0.824278i \(-0.691582\pi\)
−0.566186 + 0.824278i \(0.691582\pi\)
\(60\) 1.94143e27 0.00888434
\(61\) 4.18340e27 0.0145743 0.00728715 0.999973i \(-0.497680\pi\)
0.00728715 + 0.999973i \(0.497680\pi\)
\(62\) −3.35687e29 −0.894276
\(63\) 6.49706e29 1.32922
\(64\) 2.12249e29 0.334870
\(65\) −2.20165e28 −0.0268954
\(66\) −1.66381e29 −0.157990
\(67\) 4.85975e29 0.360064 0.180032 0.983661i \(-0.442380\pi\)
0.180032 + 0.983661i \(0.442380\pi\)
\(68\) −1.55822e30 −0.904130
\(69\) 7.93615e28 0.0361909
\(70\) −1.23999e29 −0.0445966
\(71\) −3.42819e30 −0.975667 −0.487834 0.872937i \(-0.662213\pi\)
−0.487834 + 0.872937i \(0.662213\pi\)
\(72\) 3.88688e30 0.878244
\(73\) 7.01467e30 1.26235 0.631175 0.775640i \(-0.282573\pi\)
0.631175 + 0.775640i \(0.282573\pi\)
\(74\) −3.70867e30 −0.533206
\(75\) 1.80053e30 0.207439
\(76\) 7.46995e30 0.691661
\(77\) −2.63594e31 −1.96715
\(78\) 8.30984e29 0.0501224
\(79\) −2.95630e30 −0.144511 −0.0722555 0.997386i \(-0.523020\pi\)
−0.0722555 + 0.997386i \(0.523020\pi\)
\(80\) 3.32554e29 0.0132092
\(81\) 2.69431e31 0.871855
\(82\) 2.46635e31 0.651818
\(83\) −1.23020e31 −0.266187 −0.133094 0.991103i \(-0.542491\pi\)
−0.133094 + 0.991103i \(0.542491\pi\)
\(84\) −1.16090e31 −0.206152
\(85\) 5.20028e30 0.0759652
\(86\) −9.90343e30 −0.119278
\(87\) 2.55701e30 0.0254486
\(88\) −1.57696e32 −1.29974
\(89\) 7.05623e31 0.482656 0.241328 0.970444i \(-0.422417\pi\)
0.241328 + 0.970444i \(0.422417\pi\)
\(90\) −5.39783e30 −0.0307056
\(91\) 1.31651e32 0.624080
\(92\) 3.13000e31 0.123892
\(93\) 1.04884e32 0.347329
\(94\) 1.07532e32 0.298490
\(95\) −2.49297e31 −0.0581135
\(96\) −1.10002e32 −0.215738
\(97\) −7.71791e32 −1.27575 −0.637875 0.770140i \(-0.720187\pi\)
−0.637875 + 0.770140i \(0.720187\pi\)
\(98\) 3.57399e32 0.498797
\(99\) −1.14745e33 −1.35442
\(100\) 7.10126e32 0.710126
\(101\) 1.88601e33 1.60045 0.800224 0.599701i \(-0.204714\pi\)
0.800224 + 0.599701i \(0.204714\pi\)
\(102\) −1.96278e32 −0.141569
\(103\) −4.05317e32 −0.248874 −0.124437 0.992227i \(-0.539713\pi\)
−0.124437 + 0.992227i \(0.539713\pi\)
\(104\) 7.87604e32 0.412342
\(105\) 3.87431e31 0.0173209
\(106\) −1.79064e33 −0.684640
\(107\) −1.13905e33 −0.373003 −0.186501 0.982455i \(-0.559715\pi\)
−0.186501 + 0.982455i \(0.559715\pi\)
\(108\) −1.03360e33 −0.290309
\(109\) 5.47789e32 0.132153 0.0660764 0.997815i \(-0.478952\pi\)
0.0660764 + 0.997815i \(0.478952\pi\)
\(110\) 2.18997e32 0.0454421
\(111\) 1.15876e33 0.207092
\(112\) −1.98855e33 −0.306507
\(113\) 7.05689e33 0.939332 0.469666 0.882844i \(-0.344374\pi\)
0.469666 + 0.882844i \(0.344374\pi\)
\(114\) 9.40936e32 0.108300
\(115\) −1.04458e32 −0.0104095
\(116\) 1.00848e33 0.0871183
\(117\) 5.73090e33 0.429691
\(118\) −9.31588e33 −0.606975
\(119\) −3.10958e34 −1.76269
\(120\) 2.31781e32 0.0114443
\(121\) 2.33284e34 1.00444
\(122\) 2.07829e32 0.00781213
\(123\) −7.70601e33 −0.253160
\(124\) 4.13660e34 1.18901
\(125\) −4.74838e33 −0.119545
\(126\) 3.22771e34 0.712492
\(127\) −1.88228e34 −0.364689 −0.182344 0.983235i \(-0.558369\pi\)
−0.182344 + 0.983235i \(0.558369\pi\)
\(128\) −5.03308e34 −0.856780
\(129\) 3.09428e33 0.0463265
\(130\) −1.09377e33 −0.0144165
\(131\) −1.26378e35 −1.46790 −0.733949 0.679204i \(-0.762325\pi\)
−0.733949 + 0.679204i \(0.762325\pi\)
\(132\) 2.05028e34 0.210060
\(133\) 1.49070e35 1.34846
\(134\) 2.41430e34 0.193002
\(135\) 3.44947e33 0.0243918
\(136\) −1.86031e35 −1.16465
\(137\) 2.95759e35 1.64077 0.820387 0.571809i \(-0.193758\pi\)
0.820387 + 0.571809i \(0.193758\pi\)
\(138\) 3.94263e33 0.0193991
\(139\) −8.22498e34 −0.359245 −0.179622 0.983736i \(-0.557488\pi\)
−0.179622 + 0.983736i \(0.557488\pi\)
\(140\) 1.52802e34 0.0592947
\(141\) −3.35980e34 −0.115931
\(142\) −1.70310e35 −0.522978
\(143\) −2.32510e35 −0.635911
\(144\) −8.65639e34 −0.211036
\(145\) −3.36562e33 −0.00731970
\(146\) 3.48485e35 0.676646
\(147\) −1.11668e35 −0.193728
\(148\) 4.57011e35 0.708939
\(149\) 5.29045e35 0.734378 0.367189 0.930146i \(-0.380320\pi\)
0.367189 + 0.930146i \(0.380320\pi\)
\(150\) 8.94495e34 0.111192
\(151\) −5.18728e35 −0.577856 −0.288928 0.957351i \(-0.593299\pi\)
−0.288928 + 0.957351i \(0.593299\pi\)
\(152\) 8.91816e35 0.890955
\(153\) −1.35363e36 −1.21365
\(154\) −1.30952e36 −1.05444
\(155\) −1.38052e35 −0.0999009
\(156\) −1.02400e35 −0.0666416
\(157\) 1.31075e36 0.767669 0.383835 0.923402i \(-0.374603\pi\)
0.383835 + 0.923402i \(0.374603\pi\)
\(158\) −1.46867e35 −0.0774609
\(159\) 5.59478e35 0.265908
\(160\) 1.44789e35 0.0620519
\(161\) 6.24622e35 0.241541
\(162\) 1.33852e36 0.467332
\(163\) 1.61518e36 0.509478 0.254739 0.967010i \(-0.418010\pi\)
0.254739 + 0.967010i \(0.418010\pi\)
\(164\) −3.03923e36 −0.866643
\(165\) −6.84245e34 −0.0176493
\(166\) −6.11157e35 −0.142682
\(167\) −6.45682e35 −0.136520 −0.0682601 0.997668i \(-0.521745\pi\)
−0.0682601 + 0.997668i \(0.521745\pi\)
\(168\) −1.38597e36 −0.265552
\(169\) −4.59487e36 −0.798257
\(170\) 2.58347e35 0.0407189
\(171\) 6.48919e36 0.928442
\(172\) 1.22038e36 0.158590
\(173\) −6.58049e36 −0.777137 −0.388569 0.921420i \(-0.627030\pi\)
−0.388569 + 0.921420i \(0.627030\pi\)
\(174\) 1.27031e35 0.0136410
\(175\) 1.41713e37 1.38446
\(176\) 3.51200e36 0.312317
\(177\) 2.91071e36 0.235743
\(178\) 3.50549e36 0.258714
\(179\) −2.08823e37 −1.40508 −0.702542 0.711642i \(-0.747952\pi\)
−0.702542 + 0.711642i \(0.747952\pi\)
\(180\) 6.65163e35 0.0408255
\(181\) −2.42658e37 −1.35925 −0.679624 0.733561i \(-0.737857\pi\)
−0.679624 + 0.733561i \(0.737857\pi\)
\(182\) 6.54034e36 0.334520
\(183\) −6.49353e34 −0.00303416
\(184\) 3.73682e36 0.159591
\(185\) −1.52520e36 −0.0595652
\(186\) 5.21058e36 0.186175
\(187\) 5.49185e37 1.79611
\(188\) −1.32510e37 −0.396865
\(189\) −2.06265e37 −0.565987
\(190\) −1.23849e36 −0.0311500
\(191\) 4.06968e37 0.938664 0.469332 0.883022i \(-0.344495\pi\)
0.469332 + 0.883022i \(0.344495\pi\)
\(192\) −3.29455e36 −0.0697150
\(193\) −5.23242e37 −1.01627 −0.508133 0.861279i \(-0.669664\pi\)
−0.508133 + 0.861279i \(0.669664\pi\)
\(194\) −3.83421e37 −0.683829
\(195\) 3.41743e35 0.00559924
\(196\) −4.40416e37 −0.663189
\(197\) 1.35006e38 1.86922 0.934611 0.355672i \(-0.115748\pi\)
0.934611 + 0.355672i \(0.115748\pi\)
\(198\) −5.70048e37 −0.725999
\(199\) −9.91562e37 −1.16210 −0.581051 0.813867i \(-0.697358\pi\)
−0.581051 + 0.813867i \(0.697358\pi\)
\(200\) 8.47800e37 0.914741
\(201\) −7.54336e36 −0.0749601
\(202\) 9.36960e37 0.857874
\(203\) 2.01252e37 0.169846
\(204\) 2.41868e37 0.188227
\(205\) 1.01429e37 0.0728155
\(206\) −2.01359e37 −0.133402
\(207\) 2.71905e37 0.166305
\(208\) −1.75406e37 −0.0990828
\(209\) −2.63274e38 −1.37403
\(210\) 1.92473e36 0.00928437
\(211\) −2.07128e38 −0.923802 −0.461901 0.886931i \(-0.652832\pi\)
−0.461901 + 0.886931i \(0.652832\pi\)
\(212\) 2.20657e38 0.910282
\(213\) 5.32127e37 0.203120
\(214\) −5.65876e37 −0.199937
\(215\) −4.07280e36 −0.0133247
\(216\) −1.23399e38 −0.373959
\(217\) 8.25499e38 2.31809
\(218\) 2.72139e37 0.0708367
\(219\) −1.08883e38 −0.262803
\(220\) −2.69865e37 −0.0604187
\(221\) −2.74288e38 −0.569816
\(222\) 5.75665e37 0.111006
\(223\) −4.51334e38 −0.808106 −0.404053 0.914736i \(-0.632399\pi\)
−0.404053 + 0.914736i \(0.632399\pi\)
\(224\) −8.65784e38 −1.43985
\(225\) 6.16891e38 0.953229
\(226\) 3.50582e38 0.503501
\(227\) −2.43217e38 −0.324764 −0.162382 0.986728i \(-0.551918\pi\)
−0.162382 + 0.986728i \(0.551918\pi\)
\(228\) −1.15949e38 −0.143994
\(229\) 3.41418e38 0.394458 0.197229 0.980357i \(-0.436806\pi\)
0.197229 + 0.980357i \(0.436806\pi\)
\(230\) −5.18943e36 −0.00557969
\(231\) 4.09153e38 0.409533
\(232\) 1.20399e38 0.112221
\(233\) −6.99608e37 −0.0607410 −0.0303705 0.999539i \(-0.509669\pi\)
−0.0303705 + 0.999539i \(0.509669\pi\)
\(234\) 2.84708e38 0.230323
\(235\) 4.42228e37 0.0333447
\(236\) 1.14798e39 0.807020
\(237\) 4.58880e37 0.0300851
\(238\) −1.54482e39 −0.944840
\(239\) −1.63523e39 −0.933282 −0.466641 0.884447i \(-0.654536\pi\)
−0.466641 + 0.884447i \(0.654536\pi\)
\(240\) −5.16195e36 −0.00274997
\(241\) −3.64560e38 −0.181338 −0.0906689 0.995881i \(-0.528900\pi\)
−0.0906689 + 0.995881i \(0.528900\pi\)
\(242\) 1.15894e39 0.538403
\(243\) −1.35679e39 −0.588856
\(244\) −2.56103e37 −0.0103868
\(245\) 1.46981e38 0.0557213
\(246\) −3.82830e38 −0.135699
\(247\) 1.31491e39 0.435910
\(248\) 4.93857e39 1.53161
\(249\) 1.90953e38 0.0554164
\(250\) −2.35897e38 −0.0640784
\(251\) 1.94693e39 0.495147 0.247573 0.968869i \(-0.420367\pi\)
0.247573 + 0.968869i \(0.420367\pi\)
\(252\) −3.97743e39 −0.947313
\(253\) −1.10315e39 −0.246120
\(254\) −9.35105e38 −0.195481
\(255\) −8.07194e37 −0.0158149
\(256\) −4.32361e39 −0.794122
\(257\) −5.64464e39 −0.972164 −0.486082 0.873913i \(-0.661574\pi\)
−0.486082 + 0.873913i \(0.661574\pi\)
\(258\) 1.53722e38 0.0248320
\(259\) 9.12012e39 1.38215
\(260\) 1.34783e38 0.0191679
\(261\) 8.76071e38 0.116942
\(262\) −6.27840e39 −0.786824
\(263\) 9.75930e39 1.14855 0.574274 0.818663i \(-0.305285\pi\)
0.574274 + 0.818663i \(0.305285\pi\)
\(264\) 2.44777e39 0.270586
\(265\) −7.36404e38 −0.0764820
\(266\) 7.40572e39 0.722804
\(267\) −1.09528e39 −0.100482
\(268\) −2.97508e39 −0.256611
\(269\) −1.08142e40 −0.877168 −0.438584 0.898690i \(-0.644520\pi\)
−0.438584 + 0.898690i \(0.644520\pi\)
\(270\) 1.71368e38 0.0130745
\(271\) −6.19121e39 −0.444408 −0.222204 0.975000i \(-0.571325\pi\)
−0.222204 + 0.975000i \(0.571325\pi\)
\(272\) 4.14306e39 0.279856
\(273\) −2.04350e39 −0.129924
\(274\) 1.46931e40 0.879489
\(275\) −2.50280e40 −1.41071
\(276\) −4.85842e38 −0.0257926
\(277\) −5.15662e39 −0.257898 −0.128949 0.991651i \(-0.541160\pi\)
−0.128949 + 0.991651i \(0.541160\pi\)
\(278\) −4.08612e39 −0.192563
\(279\) 3.59349e40 1.59605
\(280\) 1.82426e39 0.0763798
\(281\) −1.28386e40 −0.506832 −0.253416 0.967357i \(-0.581554\pi\)
−0.253416 + 0.967357i \(0.581554\pi\)
\(282\) −1.66913e39 −0.0621412
\(283\) 3.83806e40 1.34783 0.673915 0.738809i \(-0.264611\pi\)
0.673915 + 0.738809i \(0.264611\pi\)
\(284\) 2.09870e40 0.695340
\(285\) 3.86961e38 0.0120984
\(286\) −1.15510e40 −0.340862
\(287\) −6.06509e40 −1.68961
\(288\) −3.76885e40 −0.991364
\(289\) 2.45321e40 0.609426
\(290\) −1.67202e38 −0.00392351
\(291\) 1.19798e40 0.265593
\(292\) −4.29430e40 −0.899654
\(293\) 1.90344e40 0.376897 0.188449 0.982083i \(-0.439654\pi\)
0.188449 + 0.982083i \(0.439654\pi\)
\(294\) −5.54760e39 −0.103842
\(295\) −3.83117e39 −0.0678060
\(296\) 5.45613e40 0.913212
\(297\) 3.64287e40 0.576717
\(298\) 2.62827e40 0.393642
\(299\) 5.50964e39 0.0780816
\(300\) −1.10227e40 −0.147838
\(301\) 2.43538e40 0.309186
\(302\) −2.57701e40 −0.309743
\(303\) −2.92749e40 −0.333190
\(304\) −1.98614e40 −0.214090
\(305\) 8.54701e37 0.000872703 0
\(306\) −6.72478e40 −0.650540
\(307\) −1.48955e41 −1.36544 −0.682718 0.730682i \(-0.739202\pi\)
−0.682718 + 0.730682i \(0.739202\pi\)
\(308\) 1.61369e41 1.40195
\(309\) 6.29138e39 0.0518121
\(310\) −6.85834e39 −0.0535489
\(311\) −7.37928e39 −0.0546345 −0.0273173 0.999627i \(-0.508696\pi\)
−0.0273173 + 0.999627i \(0.508696\pi\)
\(312\) −1.22253e40 −0.0858437
\(313\) −2.63324e40 −0.175391 −0.0876957 0.996147i \(-0.527950\pi\)
−0.0876957 + 0.996147i \(0.527950\pi\)
\(314\) 6.51171e40 0.411487
\(315\) 1.32740e40 0.0795934
\(316\) 1.80981e40 0.102990
\(317\) 1.79226e41 0.968109 0.484054 0.875038i \(-0.339164\pi\)
0.484054 + 0.875038i \(0.339164\pi\)
\(318\) 2.77946e40 0.142532
\(319\) −3.55433e40 −0.173066
\(320\) 4.33641e39 0.0200519
\(321\) 1.76805e40 0.0776538
\(322\) 3.10309e40 0.129471
\(323\) −3.10581e41 −1.23121
\(324\) −1.64942e41 −0.621355
\(325\) 1.25001e41 0.447548
\(326\) 8.02413e40 0.273091
\(327\) −8.50285e39 −0.0275123
\(328\) −3.62845e41 −1.11636
\(329\) −2.64436e41 −0.773728
\(330\) −3.39929e39 −0.00946038
\(331\) 6.16181e41 1.63135 0.815674 0.578512i \(-0.196366\pi\)
0.815674 + 0.578512i \(0.196366\pi\)
\(332\) 7.53115e40 0.189707
\(333\) 3.97009e41 0.951635
\(334\) −3.20771e40 −0.0731777
\(335\) 9.92883e39 0.0215605
\(336\) 3.08666e40 0.0638102
\(337\) 4.51357e41 0.888437 0.444218 0.895919i \(-0.353481\pi\)
0.444218 + 0.895919i \(0.353481\pi\)
\(338\) −2.28271e41 −0.427882
\(339\) −1.09538e41 −0.195555
\(340\) −3.18355e40 −0.0541390
\(341\) −1.45792e42 −2.36204
\(342\) 3.22379e41 0.497664
\(343\) 6.55899e40 0.0964903
\(344\) 1.45697e41 0.204286
\(345\) 1.62141e39 0.00216710
\(346\) −3.26915e41 −0.416562
\(347\) 8.17900e41 0.993720 0.496860 0.867831i \(-0.334486\pi\)
0.496860 + 0.867831i \(0.334486\pi\)
\(348\) −1.56537e40 −0.0181368
\(349\) −1.22969e42 −1.35886 −0.679432 0.733739i \(-0.737774\pi\)
−0.679432 + 0.733739i \(0.737774\pi\)
\(350\) 7.04021e41 0.742101
\(351\) −1.81942e41 −0.182964
\(352\) 1.52907e42 1.46715
\(353\) 1.62570e41 0.148853 0.0744266 0.997226i \(-0.476287\pi\)
0.0744266 + 0.997226i \(0.476287\pi\)
\(354\) 1.44602e41 0.126363
\(355\) −7.00404e40 −0.0584226
\(356\) −4.31974e41 −0.343980
\(357\) 4.82673e41 0.366967
\(358\) −1.03742e42 −0.753155
\(359\) 3.64036e41 0.252398 0.126199 0.992005i \(-0.459722\pi\)
0.126199 + 0.992005i \(0.459722\pi\)
\(360\) 7.94120e40 0.0525890
\(361\) −9.18755e40 −0.0581207
\(362\) −1.20551e42 −0.728585
\(363\) −3.62106e41 −0.209111
\(364\) −8.05951e41 −0.444771
\(365\) 1.43315e41 0.0755891
\(366\) −3.22595e39 −0.00162637
\(367\) 1.35581e42 0.653442 0.326721 0.945121i \(-0.394056\pi\)
0.326721 + 0.945121i \(0.394056\pi\)
\(368\) −8.32218e40 −0.0383485
\(369\) −2.64020e42 −1.16333
\(370\) −7.57709e40 −0.0319282
\(371\) 4.40343e42 1.77469
\(372\) −6.42088e41 −0.247535
\(373\) 1.93457e42 0.713493 0.356746 0.934201i \(-0.383886\pi\)
0.356746 + 0.934201i \(0.383886\pi\)
\(374\) 2.72832e42 0.962752
\(375\) 7.37049e40 0.0248874
\(376\) −1.58200e42 −0.511218
\(377\) 1.77519e41 0.0549052
\(378\) −1.02471e42 −0.303381
\(379\) −5.45789e42 −1.54696 −0.773478 0.633823i \(-0.781485\pi\)
−0.773478 + 0.633823i \(0.781485\pi\)
\(380\) 1.52617e41 0.0414164
\(381\) 2.92169e41 0.0759229
\(382\) 2.02180e42 0.503143
\(383\) −5.06942e42 −1.20831 −0.604155 0.796867i \(-0.706489\pi\)
−0.604155 + 0.796867i \(0.706489\pi\)
\(384\) 7.81241e41 0.178369
\(385\) −5.38542e41 −0.117792
\(386\) −2.59944e42 −0.544740
\(387\) 1.06015e42 0.212881
\(388\) 4.72482e42 0.909204
\(389\) 7.51028e42 1.38512 0.692560 0.721360i \(-0.256483\pi\)
0.692560 + 0.721360i \(0.256483\pi\)
\(390\) 1.69776e40 0.00300131
\(391\) −1.30137e42 −0.220539
\(392\) −5.25800e42 −0.854280
\(393\) 1.96166e42 0.305595
\(394\) 6.70703e42 1.00194
\(395\) −6.03993e40 −0.00865327
\(396\) 7.02458e42 0.965272
\(397\) −1.26926e43 −1.67304 −0.836519 0.547938i \(-0.815413\pi\)
−0.836519 + 0.547938i \(0.815413\pi\)
\(398\) −4.92603e42 −0.622911
\(399\) −2.31389e42 −0.280730
\(400\) −1.88812e42 −0.219806
\(401\) 5.29553e42 0.591598 0.295799 0.955250i \(-0.404414\pi\)
0.295799 + 0.955250i \(0.404414\pi\)
\(402\) −3.74750e41 −0.0401802
\(403\) 7.28153e42 0.749358
\(404\) −1.15459e43 −1.14061
\(405\) 5.50467e41 0.0522064
\(406\) 9.99807e41 0.0910410
\(407\) −1.61071e43 −1.40835
\(408\) 2.88760e42 0.242462
\(409\) 1.80907e43 1.45888 0.729442 0.684042i \(-0.239780\pi\)
0.729442 + 0.684042i \(0.239780\pi\)
\(410\) 5.03894e41 0.0390306
\(411\) −4.59081e42 −0.341585
\(412\) 2.48130e42 0.177368
\(413\) 2.29090e43 1.57337
\(414\) 1.35081e42 0.0891432
\(415\) −2.51339e41 −0.0159392
\(416\) −7.63687e42 −0.465453
\(417\) 1.27669e42 0.0747896
\(418\) −1.30793e43 −0.736506
\(419\) 9.59306e42 0.519309 0.259654 0.965702i \(-0.416391\pi\)
0.259654 + 0.965702i \(0.416391\pi\)
\(420\) −2.37181e41 −0.0123443
\(421\) −1.95406e43 −0.977875 −0.488938 0.872319i \(-0.662615\pi\)
−0.488938 + 0.872319i \(0.662615\pi\)
\(422\) −1.02900e43 −0.495177
\(423\) −1.15112e43 −0.532727
\(424\) 2.63436e43 1.17257
\(425\) −2.95252e43 −1.26408
\(426\) 2.64358e42 0.108876
\(427\) −5.11080e41 −0.0202502
\(428\) 6.97316e42 0.265832
\(429\) 3.60904e42 0.132387
\(430\) −2.02334e41 −0.00714233
\(431\) 4.01382e43 1.36359 0.681794 0.731544i \(-0.261200\pi\)
0.681794 + 0.731544i \(0.261200\pi\)
\(432\) 2.74819e42 0.0898596
\(433\) −1.24146e43 −0.390735 −0.195367 0.980730i \(-0.562590\pi\)
−0.195367 + 0.980730i \(0.562590\pi\)
\(434\) 4.10103e43 1.24255
\(435\) 5.22416e40 0.00152386
\(436\) −3.35350e42 −0.0941829
\(437\) 6.23865e42 0.168712
\(438\) −5.40922e42 −0.140868
\(439\) −6.07044e43 −1.52249 −0.761247 0.648462i \(-0.775413\pi\)
−0.761247 + 0.648462i \(0.775413\pi\)
\(440\) −3.22184e42 −0.0778278
\(441\) −3.82592e43 −0.890223
\(442\) −1.36265e43 −0.305433
\(443\) 6.61294e43 1.42802 0.714009 0.700137i \(-0.246878\pi\)
0.714009 + 0.700137i \(0.246878\pi\)
\(444\) −7.09379e42 −0.147591
\(445\) 1.44164e42 0.0289013
\(446\) −2.24220e43 −0.433162
\(447\) −8.21191e42 −0.152887
\(448\) −2.59301e43 −0.465283
\(449\) −1.54504e43 −0.267225 −0.133612 0.991034i \(-0.542658\pi\)
−0.133612 + 0.991034i \(0.542658\pi\)
\(450\) 3.06468e43 0.510950
\(451\) 1.07116e44 1.72164
\(452\) −4.32015e43 −0.669444
\(453\) 8.05175e42 0.120301
\(454\) −1.20829e43 −0.174080
\(455\) 2.68972e42 0.0373697
\(456\) −1.38429e43 −0.185484
\(457\) 7.12331e43 0.920586 0.460293 0.887767i \(-0.347744\pi\)
0.460293 + 0.887767i \(0.347744\pi\)
\(458\) 1.69615e43 0.211438
\(459\) 4.29745e43 0.516774
\(460\) 6.39482e41 0.00741864
\(461\) −1.34004e44 −1.49986 −0.749932 0.661515i \(-0.769914\pi\)
−0.749932 + 0.661515i \(0.769914\pi\)
\(462\) 2.03265e43 0.219518
\(463\) −5.53073e43 −0.576363 −0.288182 0.957576i \(-0.593051\pi\)
−0.288182 + 0.957576i \(0.593051\pi\)
\(464\) −2.68139e42 −0.0269658
\(465\) 2.14286e42 0.0207979
\(466\) −3.47561e42 −0.0325584
\(467\) −3.51798e43 −0.318101 −0.159050 0.987270i \(-0.550843\pi\)
−0.159050 + 0.987270i \(0.550843\pi\)
\(468\) −3.50840e43 −0.306233
\(469\) −5.93707e43 −0.500288
\(470\) 2.19696e42 0.0178734
\(471\) −2.03456e43 −0.159818
\(472\) 1.37054e44 1.03955
\(473\) −4.30116e43 −0.315048
\(474\) 2.27969e42 0.0161262
\(475\) 1.41541e44 0.967025
\(476\) 1.90365e44 1.25624
\(477\) 1.91686e44 1.22190
\(478\) −8.12372e43 −0.500258
\(479\) −2.90520e44 −1.72838 −0.864192 0.503162i \(-0.832170\pi\)
−0.864192 + 0.503162i \(0.832170\pi\)
\(480\) −2.24743e42 −0.0129183
\(481\) 8.04464e43 0.446799
\(482\) −1.81112e43 −0.0972008
\(483\) −9.69546e42 −0.0502853
\(484\) −1.42814e44 −0.715849
\(485\) −1.57683e43 −0.0763915
\(486\) −6.74045e43 −0.315639
\(487\) −1.45706e44 −0.659551 −0.329776 0.944059i \(-0.606973\pi\)
−0.329776 + 0.944059i \(0.606973\pi\)
\(488\) −3.05755e42 −0.0133797
\(489\) −2.50710e43 −0.106066
\(490\) 7.30194e42 0.0298678
\(491\) 1.43984e44 0.569469 0.284735 0.958606i \(-0.408095\pi\)
0.284735 + 0.958606i \(0.408095\pi\)
\(492\) 4.71753e43 0.180423
\(493\) −4.19299e43 −0.155078
\(494\) 6.53241e43 0.233657
\(495\) −2.34433e43 −0.0811023
\(496\) −1.09986e44 −0.368035
\(497\) 4.18816e44 1.35564
\(498\) 9.48646e42 0.0297043
\(499\) 1.76176e44 0.533687 0.266843 0.963740i \(-0.414019\pi\)
0.266843 + 0.963740i \(0.414019\pi\)
\(500\) 2.90690e43 0.0851972
\(501\) 1.00224e43 0.0284215
\(502\) 9.67224e43 0.265409
\(503\) −2.43829e44 −0.647460 −0.323730 0.946149i \(-0.604937\pi\)
−0.323730 + 0.946149i \(0.604937\pi\)
\(504\) −4.74854e44 −1.22027
\(505\) 3.85326e43 0.0958343
\(506\) −5.48039e43 −0.131925
\(507\) 7.13222e43 0.166185
\(508\) 1.15231e44 0.259907
\(509\) 3.49786e44 0.763763 0.381882 0.924211i \(-0.375276\pi\)
0.381882 + 0.924211i \(0.375276\pi\)
\(510\) −4.01010e42 −0.00847709
\(511\) −8.56970e44 −1.75396
\(512\) 2.17544e44 0.431114
\(513\) −2.06015e44 −0.395333
\(514\) −2.80422e44 −0.521100
\(515\) −8.28092e42 −0.0149025
\(516\) −1.89429e43 −0.0330161
\(517\) 4.67023e44 0.788396
\(518\) 4.53082e44 0.740860
\(519\) 1.02143e44 0.161789
\(520\) 1.60913e43 0.0246909
\(521\) −3.31981e44 −0.493505 −0.246752 0.969079i \(-0.579363\pi\)
−0.246752 + 0.969079i \(0.579363\pi\)
\(522\) 4.35227e43 0.0626834
\(523\) 1.02645e45 1.43238 0.716190 0.697905i \(-0.245884\pi\)
0.716190 + 0.697905i \(0.245884\pi\)
\(524\) 7.73674e44 1.04614
\(525\) −2.19968e44 −0.288225
\(526\) 4.84837e44 0.615645
\(527\) −1.71989e45 −2.11654
\(528\) −5.45137e43 −0.0650199
\(529\) −8.38864e44 −0.969780
\(530\) −3.65842e43 −0.0409960
\(531\) 9.97254e44 1.08329
\(532\) −9.12591e44 −0.961024
\(533\) −5.34987e44 −0.546191
\(534\) −5.44127e43 −0.0538604
\(535\) −2.32717e43 −0.0223353
\(536\) −3.55187e44 −0.330550
\(537\) 3.24137e44 0.292518
\(538\) −5.37245e44 −0.470180
\(539\) 1.55222e45 1.31746
\(540\) −2.11172e43 −0.0173836
\(541\) 4.08746e44 0.326361 0.163180 0.986596i \(-0.447825\pi\)
0.163180 + 0.986596i \(0.447825\pi\)
\(542\) −3.07576e44 −0.238212
\(543\) 3.76657e44 0.282976
\(544\) 1.80382e45 1.31465
\(545\) 1.11917e43 0.00791326
\(546\) −1.01520e44 −0.0696422
\(547\) 7.54748e44 0.502355 0.251178 0.967941i \(-0.419182\pi\)
0.251178 + 0.967941i \(0.419182\pi\)
\(548\) −1.81060e45 −1.16935
\(549\) −2.22479e43 −0.0139426
\(550\) −1.24338e45 −0.756169
\(551\) 2.01008e44 0.118635
\(552\) −5.80033e43 −0.0332245
\(553\) 3.61166e44 0.200790
\(554\) −2.56178e44 −0.138239
\(555\) 2.36743e43 0.0124006
\(556\) 5.03524e44 0.256027
\(557\) −3.77046e45 −1.86116 −0.930581 0.366087i \(-0.880697\pi\)
−0.930581 + 0.366087i \(0.880697\pi\)
\(558\) 1.78523e45 0.855517
\(559\) 2.14819e44 0.0999491
\(560\) −4.06276e43 −0.0183535
\(561\) −8.52453e44 −0.373924
\(562\) −6.37816e44 −0.271673
\(563\) 1.99523e45 0.825284 0.412642 0.910893i \(-0.364606\pi\)
0.412642 + 0.910893i \(0.364606\pi\)
\(564\) 2.05683e44 0.0826216
\(565\) 1.44177e44 0.0562468
\(566\) 1.90672e45 0.722465
\(567\) −3.29159e45 −1.21139
\(568\) 2.50558e45 0.895695
\(569\) 2.38895e45 0.829574 0.414787 0.909919i \(-0.363856\pi\)
0.414787 + 0.909919i \(0.363856\pi\)
\(570\) 1.92240e43 0.00648499
\(571\) 9.25875e44 0.303429 0.151714 0.988424i \(-0.451521\pi\)
0.151714 + 0.988424i \(0.451521\pi\)
\(572\) 1.42340e45 0.453202
\(573\) −6.31701e44 −0.195416
\(574\) −3.01310e45 −0.905665
\(575\) 5.93074e44 0.173217
\(576\) −1.12877e45 −0.320356
\(577\) −3.73598e45 −1.03040 −0.515198 0.857071i \(-0.672281\pi\)
−0.515198 + 0.857071i \(0.672281\pi\)
\(578\) 1.21874e45 0.326665
\(579\) 8.12183e44 0.211572
\(580\) 2.06040e43 0.00521661
\(581\) 1.50292e45 0.369853
\(582\) 5.95151e44 0.142363
\(583\) −7.77694e45 −1.80833
\(584\) −5.12684e45 −1.15888
\(585\) 1.17087e44 0.0257298
\(586\) 9.45617e44 0.202025
\(587\) 6.35230e45 1.31948 0.659739 0.751495i \(-0.270667\pi\)
0.659739 + 0.751495i \(0.270667\pi\)
\(588\) 6.83618e44 0.138066
\(589\) 8.24499e45 1.61915
\(590\) −1.90330e44 −0.0363454
\(591\) −2.09558e45 −0.389145
\(592\) −1.21512e45 −0.219438
\(593\) 7.20521e45 1.26545 0.632724 0.774378i \(-0.281937\pi\)
0.632724 + 0.774378i \(0.281937\pi\)
\(594\) 1.80976e45 0.309132
\(595\) −6.35310e44 −0.105549
\(596\) −3.23876e45 −0.523377
\(597\) 1.53912e45 0.241933
\(598\) 2.73716e44 0.0418534
\(599\) −6.37291e45 −0.947971 −0.473985 0.880533i \(-0.657185\pi\)
−0.473985 + 0.880533i \(0.657185\pi\)
\(600\) −1.31597e45 −0.190436
\(601\) −8.13523e45 −1.14536 −0.572679 0.819780i \(-0.694096\pi\)
−0.572679 + 0.819780i \(0.694096\pi\)
\(602\) 1.20989e45 0.165730
\(603\) −2.58447e45 −0.344458
\(604\) 3.17559e45 0.411827
\(605\) 4.76616e44 0.0601458
\(606\) −1.45436e45 −0.178597
\(607\) 8.31211e45 0.993339 0.496670 0.867940i \(-0.334556\pi\)
0.496670 + 0.867940i \(0.334556\pi\)
\(608\) −8.64734e45 −1.00571
\(609\) −3.12386e44 −0.0353595
\(610\) 4.24610e42 0.000467787 0
\(611\) −2.33253e45 −0.250119
\(612\) 8.28679e45 0.864944
\(613\) −2.99559e44 −0.0304358 −0.0152179 0.999884i \(-0.504844\pi\)
−0.0152179 + 0.999884i \(0.504844\pi\)
\(614\) −7.40000e45 −0.731903
\(615\) −1.57440e44 −0.0151591
\(616\) 1.92654e46 1.80591
\(617\) 9.03503e45 0.824564 0.412282 0.911056i \(-0.364732\pi\)
0.412282 + 0.911056i \(0.364732\pi\)
\(618\) 3.12552e44 0.0277723
\(619\) −1.15706e46 −1.00106 −0.500528 0.865720i \(-0.666861\pi\)
−0.500528 + 0.865720i \(0.666861\pi\)
\(620\) 8.45138e44 0.0711975
\(621\) −8.63230e44 −0.0708133
\(622\) −3.66598e44 −0.0292853
\(623\) −8.62048e45 −0.670623
\(624\) 2.72267e44 0.0206276
\(625\) 1.34069e46 0.989256
\(626\) −1.30818e45 −0.0940135
\(627\) 4.08658e45 0.286052
\(628\) −8.02424e45 −0.547104
\(629\) −1.90013e46 −1.26197
\(630\) 6.59444e44 0.0426638
\(631\) −1.43742e46 −0.905939 −0.452970 0.891526i \(-0.649635\pi\)
−0.452970 + 0.891526i \(0.649635\pi\)
\(632\) 2.16068e45 0.132666
\(633\) 3.21507e45 0.192322
\(634\) 8.90387e45 0.518927
\(635\) −3.84563e44 −0.0218374
\(636\) −3.42506e45 −0.189507
\(637\) −7.75250e45 −0.417966
\(638\) −1.76577e45 −0.0927668
\(639\) 1.82315e46 0.933381
\(640\) −1.02830e45 −0.0513037
\(641\) 1.34213e46 0.652586 0.326293 0.945269i \(-0.394200\pi\)
0.326293 + 0.945269i \(0.394200\pi\)
\(642\) 8.78360e44 0.0416241
\(643\) 3.48572e46 1.60995 0.804973 0.593312i \(-0.202180\pi\)
0.804973 + 0.593312i \(0.202180\pi\)
\(644\) −3.82387e45 −0.172142
\(645\) 6.32185e43 0.00277402
\(646\) −1.54295e46 −0.659956
\(647\) 3.47978e46 1.45088 0.725440 0.688285i \(-0.241636\pi\)
0.725440 + 0.688285i \(0.241636\pi\)
\(648\) −1.96920e46 −0.800392
\(649\) −4.04598e46 −1.60319
\(650\) 6.21000e45 0.239895
\(651\) −1.28135e46 −0.482594
\(652\) −9.88796e45 −0.363096
\(653\) 1.19815e46 0.428986 0.214493 0.976726i \(-0.431190\pi\)
0.214493 + 0.976726i \(0.431190\pi\)
\(654\) −4.22417e44 −0.0147472
\(655\) −2.58200e45 −0.0878972
\(656\) 8.08085e45 0.268252
\(657\) −3.73049e46 −1.20764
\(658\) −1.31370e46 −0.414735
\(659\) −2.00047e46 −0.615918 −0.307959 0.951400i \(-0.599646\pi\)
−0.307959 + 0.951400i \(0.599646\pi\)
\(660\) 4.18887e44 0.0125783
\(661\) 3.80588e46 1.11463 0.557316 0.830301i \(-0.311831\pi\)
0.557316 + 0.830301i \(0.311831\pi\)
\(662\) 3.06115e46 0.874437
\(663\) 4.25754e45 0.118628
\(664\) 8.99123e45 0.244369
\(665\) 3.04561e45 0.0807454
\(666\) 1.97232e46 0.510096
\(667\) 8.42247e44 0.0212502
\(668\) 3.95279e45 0.0972954
\(669\) 7.00567e45 0.168236
\(670\) 4.93259e44 0.0115569
\(671\) 9.02622e44 0.0206341
\(672\) 1.34388e46 0.299756
\(673\) −5.38328e46 −1.17165 −0.585825 0.810437i \(-0.699230\pi\)
−0.585825 + 0.810437i \(0.699230\pi\)
\(674\) 2.24231e46 0.476221
\(675\) −1.95847e46 −0.405887
\(676\) 2.81293e46 0.568903
\(677\) −9.38585e46 −1.85251 −0.926255 0.376898i \(-0.876991\pi\)
−0.926255 + 0.376898i \(0.876991\pi\)
\(678\) −5.44178e45 −0.104822
\(679\) 9.42884e46 1.77258
\(680\) −3.80076e45 −0.0697386
\(681\) 3.77525e45 0.0676111
\(682\) −7.24288e46 −1.26610
\(683\) 1.22152e46 0.208430 0.104215 0.994555i \(-0.466767\pi\)
0.104215 + 0.994555i \(0.466767\pi\)
\(684\) −3.97261e46 −0.661683
\(685\) 6.04258e45 0.0982489
\(686\) 3.25847e45 0.0517208
\(687\) −5.29953e45 −0.0821205
\(688\) −3.24480e45 −0.0490883
\(689\) 3.88416e46 0.573693
\(690\) 8.05510e43 0.00116161
\(691\) −1.01396e47 −1.42768 −0.713841 0.700308i \(-0.753046\pi\)
−0.713841 + 0.700308i \(0.753046\pi\)
\(692\) 4.02850e46 0.553851
\(693\) 1.40182e47 1.88189
\(694\) 4.06328e46 0.532655
\(695\) −1.68042e45 −0.0215115
\(696\) −1.86885e45 −0.0233627
\(697\) 1.26363e47 1.54270
\(698\) −6.10903e46 −0.728379
\(699\) 1.08594e45 0.0126454
\(700\) −8.67549e46 −0.986681
\(701\) −1.07227e47 −1.19112 −0.595560 0.803311i \(-0.703070\pi\)
−0.595560 + 0.803311i \(0.703070\pi\)
\(702\) −9.03876e45 −0.0980724
\(703\) 9.10906e46 0.965408
\(704\) 4.57954e46 0.474103
\(705\) −6.86432e44 −0.00694188
\(706\) 8.07639e45 0.0797884
\(707\) −2.30411e47 −2.22373
\(708\) −1.78190e46 −0.168010
\(709\) −3.54939e45 −0.0326957 −0.0163478 0.999866i \(-0.505204\pi\)
−0.0163478 + 0.999866i \(0.505204\pi\)
\(710\) −3.47957e45 −0.0313157
\(711\) 1.57219e46 0.138248
\(712\) −5.15722e46 −0.443094
\(713\) 3.45475e46 0.290028
\(714\) 2.39789e46 0.196702
\(715\) −4.75035e45 −0.0380781
\(716\) 1.27839e47 1.00138
\(717\) 2.53822e46 0.194296
\(718\) 1.80851e46 0.135290
\(719\) 6.94896e46 0.508035 0.254017 0.967200i \(-0.418248\pi\)
0.254017 + 0.967200i \(0.418248\pi\)
\(720\) −1.76857e45 −0.0126367
\(721\) 4.95169e46 0.345797
\(722\) −4.56432e45 −0.0311539
\(723\) 5.65875e45 0.0377519
\(724\) 1.48553e47 0.968711
\(725\) 1.91087e46 0.121802
\(726\) −1.79892e46 −0.112088
\(727\) −1.73359e47 −1.05592 −0.527958 0.849270i \(-0.677042\pi\)
−0.527958 + 0.849270i \(0.677042\pi\)
\(728\) −9.62203e46 −0.572926
\(729\) −1.28718e47 −0.749264
\(730\) 7.11980e45 0.0405173
\(731\) −5.07401e46 −0.282303
\(732\) 3.97527e44 0.00216239
\(733\) 4.59301e46 0.244277 0.122138 0.992513i \(-0.461025\pi\)
0.122138 + 0.992513i \(0.461025\pi\)
\(734\) 6.73556e46 0.350259
\(735\) −2.28146e45 −0.0116004
\(736\) −3.62334e46 −0.180146
\(737\) 1.04855e47 0.509773
\(738\) −1.31164e47 −0.623568
\(739\) −3.24514e47 −1.50869 −0.754346 0.656477i \(-0.772046\pi\)
−0.754346 + 0.656477i \(0.772046\pi\)
\(740\) 9.33708e45 0.0424510
\(741\) −2.04102e46 −0.0907502
\(742\) 2.18760e47 0.951268
\(743\) 3.63726e47 1.54689 0.773443 0.633866i \(-0.218533\pi\)
0.773443 + 0.633866i \(0.218533\pi\)
\(744\) −7.66571e46 −0.318859
\(745\) 1.08088e46 0.0439743
\(746\) 9.61085e46 0.382447
\(747\) 6.54236e46 0.254651
\(748\) −3.36205e47 −1.28005
\(749\) 1.39156e47 0.518267
\(750\) 3.66162e45 0.0133402
\(751\) 2.28361e47 0.813885 0.406943 0.913454i \(-0.366595\pi\)
0.406943 + 0.913454i \(0.366595\pi\)
\(752\) 3.52323e46 0.122842
\(753\) −3.02205e46 −0.103082
\(754\) 8.81906e45 0.0294303
\(755\) −1.05980e46 −0.0346018
\(756\) 1.26273e47 0.403369
\(757\) −1.23646e47 −0.386453 −0.193226 0.981154i \(-0.561895\pi\)
−0.193226 + 0.981154i \(0.561895\pi\)
\(758\) −2.71145e47 −0.829201
\(759\) 1.71233e46 0.0512386
\(760\) 1.82205e46 0.0533501
\(761\) −1.65073e47 −0.472966 −0.236483 0.971636i \(-0.575995\pi\)
−0.236483 + 0.971636i \(0.575995\pi\)
\(762\) 1.45148e46 0.0406962
\(763\) −6.69225e46 −0.183619
\(764\) −2.49141e47 −0.668968
\(765\) −2.76557e46 −0.0726728
\(766\) −2.51846e47 −0.647679
\(767\) 2.02075e47 0.508614
\(768\) 6.71116e46 0.165325
\(769\) −2.15810e47 −0.520339 −0.260170 0.965563i \(-0.583778\pi\)
−0.260170 + 0.965563i \(0.583778\pi\)
\(770\) −2.67544e46 −0.0631392
\(771\) 8.76167e46 0.202390
\(772\) 3.20323e47 0.724274
\(773\) 5.97126e46 0.132161 0.0660806 0.997814i \(-0.478951\pi\)
0.0660806 + 0.997814i \(0.478951\pi\)
\(774\) 5.26677e46 0.114109
\(775\) 7.83805e47 1.66238
\(776\) 5.64083e47 1.17118
\(777\) −1.41564e47 −0.287743
\(778\) 3.73106e47 0.742453
\(779\) −6.05774e47 −1.18016
\(780\) −2.09211e45 −0.00399047
\(781\) −7.39675e47 −1.38133
\(782\) −6.46514e46 −0.118213
\(783\) −2.78131e46 −0.0497943
\(784\) 1.17100e47 0.205277
\(785\) 2.67795e46 0.0459677
\(786\) 9.74541e46 0.163805
\(787\) 2.40999e47 0.396673 0.198336 0.980134i \(-0.436446\pi\)
0.198336 + 0.980134i \(0.436446\pi\)
\(788\) −8.26493e47 −1.33216
\(789\) −1.51485e47 −0.239111
\(790\) −3.00060e45 −0.00463833
\(791\) −8.62128e47 −1.30515
\(792\) 8.38645e47 1.24340
\(793\) −4.50811e45 −0.00654616
\(794\) −6.30559e47 −0.896783
\(795\) 1.14306e46 0.0159225
\(796\) 6.07023e47 0.828209
\(797\) 5.30320e47 0.708722 0.354361 0.935109i \(-0.384698\pi\)
0.354361 + 0.935109i \(0.384698\pi\)
\(798\) −1.14953e47 −0.150477
\(799\) 5.50941e47 0.706452
\(800\) −8.22055e47 −1.03256
\(801\) −3.75259e47 −0.461737
\(802\) 2.63079e47 0.317109
\(803\) 1.51350e48 1.78722
\(804\) 4.61796e46 0.0534226
\(805\) 1.27615e46 0.0144634
\(806\) 3.61742e47 0.401672
\(807\) 1.67860e47 0.182614
\(808\) −1.37844e48 −1.46926
\(809\) 6.52623e47 0.681572 0.340786 0.940141i \(-0.389307\pi\)
0.340786 + 0.940141i \(0.389307\pi\)
\(810\) 2.73469e46 0.0279837
\(811\) −4.54256e47 −0.455466 −0.227733 0.973724i \(-0.573131\pi\)
−0.227733 + 0.973724i \(0.573131\pi\)
\(812\) −1.23204e47 −0.121046
\(813\) 9.61007e46 0.0925194
\(814\) −8.00193e47 −0.754904
\(815\) 3.29994e46 0.0305074
\(816\) −6.43091e46 −0.0582619
\(817\) 2.43243e47 0.215962
\(818\) 8.98736e47 0.781993
\(819\) −7.00135e47 −0.597032
\(820\) −6.20938e46 −0.0518943
\(821\) −3.88660e47 −0.318352 −0.159176 0.987250i \(-0.550884\pi\)
−0.159176 + 0.987250i \(0.550884\pi\)
\(822\) −2.28069e47 −0.183097
\(823\) −2.16262e48 −1.70170 −0.850849 0.525410i \(-0.823912\pi\)
−0.850849 + 0.525410i \(0.823912\pi\)
\(824\) 2.96236e47 0.228475
\(825\) 3.88488e47 0.293689
\(826\) 1.13811e48 0.843358
\(827\) −5.70292e47 −0.414244 −0.207122 0.978315i \(-0.566410\pi\)
−0.207122 + 0.978315i \(0.566410\pi\)
\(828\) −1.66457e47 −0.118523
\(829\) 1.81254e48 1.26514 0.632569 0.774504i \(-0.282001\pi\)
0.632569 + 0.774504i \(0.282001\pi\)
\(830\) −1.24864e46 −0.00854375
\(831\) 8.00417e46 0.0536907
\(832\) −2.28723e47 −0.150410
\(833\) 1.83113e48 1.18053
\(834\) 6.34253e46 0.0400888
\(835\) −1.31918e46 −0.00817478
\(836\) 1.61174e48 0.979242
\(837\) −1.14084e48 −0.679603
\(838\) 4.76578e47 0.278360
\(839\) −1.88483e47 −0.107945 −0.0539723 0.998542i \(-0.517188\pi\)
−0.0539723 + 0.998542i \(0.517188\pi\)
\(840\) −2.83163e46 −0.0159012
\(841\) −1.78894e48 −0.985057
\(842\) −9.70766e47 −0.524162
\(843\) 1.99283e47 0.105515
\(844\) 1.26802e48 0.658377
\(845\) −9.38766e46 −0.0477993
\(846\) −5.71870e47 −0.285553
\(847\) −2.84999e48 −1.39562
\(848\) −5.86693e47 −0.281760
\(849\) −5.95748e47 −0.280599
\(850\) −1.46680e48 −0.677575
\(851\) 3.81681e47 0.172927
\(852\) −3.25762e47 −0.144760
\(853\) 3.65000e48 1.59087 0.795434 0.606040i \(-0.207243\pi\)
0.795434 + 0.606040i \(0.207243\pi\)
\(854\) −2.53901e46 −0.0108545
\(855\) 1.32579e47 0.0555948
\(856\) 8.32507e47 0.342429
\(857\) −1.58574e48 −0.639807 −0.319903 0.947450i \(-0.603650\pi\)
−0.319903 + 0.947450i \(0.603650\pi\)
\(858\) 1.79295e47 0.0709625
\(859\) 2.88906e48 1.12168 0.560840 0.827924i \(-0.310478\pi\)
0.560840 + 0.827924i \(0.310478\pi\)
\(860\) 2.49332e46 0.00949629
\(861\) 9.41431e47 0.351752
\(862\) 1.99404e48 0.730912
\(863\) 3.38580e46 0.0121754 0.00608770 0.999981i \(-0.498062\pi\)
0.00608770 + 0.999981i \(0.498062\pi\)
\(864\) 1.19652e48 0.422126
\(865\) −1.34444e47 −0.0465347
\(866\) −6.16750e47 −0.209442
\(867\) −3.80791e47 −0.126874
\(868\) −5.05361e48 −1.65206
\(869\) −6.37858e47 −0.204596
\(870\) 2.59533e45 0.000816818 0
\(871\) −5.23695e47 −0.161726
\(872\) −4.00366e47 −0.121321
\(873\) 4.10448e48 1.22046
\(874\) 3.09933e47 0.0904334
\(875\) 5.80101e47 0.166100
\(876\) 6.66567e47 0.187295
\(877\) −4.24252e48 −1.16985 −0.584925 0.811087i \(-0.698876\pi\)
−0.584925 + 0.811087i \(0.698876\pi\)
\(878\) −3.01576e48 −0.816089
\(879\) −2.95454e47 −0.0784646
\(880\) 7.17528e46 0.0187014
\(881\) −2.17405e48 −0.556119 −0.278059 0.960564i \(-0.589691\pi\)
−0.278059 + 0.960564i \(0.589691\pi\)
\(882\) −1.90069e48 −0.477178
\(883\) 4.77705e48 1.17708 0.588542 0.808466i \(-0.299702\pi\)
0.588542 + 0.808466i \(0.299702\pi\)
\(884\) 1.67916e48 0.406098
\(885\) 5.94679e46 0.0141162
\(886\) 3.28527e48 0.765447
\(887\) −5.12275e48 −1.17156 −0.585779 0.810471i \(-0.699211\pi\)
−0.585779 + 0.810471i \(0.699211\pi\)
\(888\) −8.46907e47 −0.190117
\(889\) 2.29955e48 0.506714
\(890\) 7.16199e46 0.0154917
\(891\) 5.81331e48 1.23436
\(892\) 2.76302e48 0.575922
\(893\) −2.64116e48 −0.540437
\(894\) −4.07963e47 −0.0819505
\(895\) −4.26640e47 −0.0841359
\(896\) 6.14883e48 1.19045
\(897\) −8.55214e46 −0.0162555
\(898\) −7.67570e47 −0.143238
\(899\) 1.11311e48 0.203941
\(900\) −3.77654e48 −0.679348
\(901\) −9.17434e48 −1.62038
\(902\) 5.32147e48 0.922834
\(903\) −3.78023e47 −0.0643681
\(904\) −5.15770e48 −0.862338
\(905\) −4.95769e47 −0.0813912
\(906\) 4.00007e47 0.0644840
\(907\) 7.71888e48 1.22190 0.610948 0.791671i \(-0.290789\pi\)
0.610948 + 0.791671i \(0.290789\pi\)
\(908\) 1.48895e48 0.231453
\(909\) −1.00300e49 −1.53108
\(910\) 1.33624e47 0.0200309
\(911\) −1.06274e49 −1.56450 −0.782250 0.622964i \(-0.785928\pi\)
−0.782250 + 0.622964i \(0.785928\pi\)
\(912\) 3.08292e47 0.0445704
\(913\) −2.65432e48 −0.376864
\(914\) 3.53882e48 0.493454
\(915\) −1.32668e45 −0.000181684 0
\(916\) −2.09012e48 −0.281123
\(917\) 1.54394e49 2.03956
\(918\) 2.13495e48 0.277002
\(919\) 8.89051e48 1.13298 0.566488 0.824070i \(-0.308302\pi\)
0.566488 + 0.824070i \(0.308302\pi\)
\(920\) 7.63460e46 0.00955624
\(921\) 2.31210e48 0.284264
\(922\) −6.65723e48 −0.803959
\(923\) 3.69428e48 0.438229
\(924\) −2.50479e48 −0.291866
\(925\) 8.65948e48 0.991182
\(926\) −2.74764e48 −0.308943
\(927\) 2.15552e48 0.238088
\(928\) −1.16743e48 −0.126675
\(929\) −7.35883e48 −0.784422 −0.392211 0.919875i \(-0.628290\pi\)
−0.392211 + 0.919875i \(0.628290\pi\)
\(930\) 1.06456e47 0.0111481
\(931\) −8.77828e48 −0.903108
\(932\) 4.28292e47 0.0432890
\(933\) 1.14542e47 0.0113741
\(934\) −1.74771e48 −0.170509
\(935\) 1.12203e48 0.107550
\(936\) −4.18858e48 −0.394471
\(937\) −7.92924e48 −0.733717 −0.366858 0.930277i \(-0.619567\pi\)
−0.366858 + 0.930277i \(0.619567\pi\)
\(938\) −2.94950e48 −0.268165
\(939\) 4.08734e47 0.0365140
\(940\) −2.70727e47 −0.0237641
\(941\) 1.44230e49 1.24402 0.622008 0.783011i \(-0.286317\pi\)
0.622008 + 0.783011i \(0.286317\pi\)
\(942\) −1.01076e48 −0.0856656
\(943\) −2.53827e48 −0.211395
\(944\) −3.05229e48 −0.249797
\(945\) −4.21416e47 −0.0338911
\(946\) −2.13679e48 −0.168872
\(947\) 9.83625e48 0.763932 0.381966 0.924176i \(-0.375247\pi\)
0.381966 + 0.924176i \(0.375247\pi\)
\(948\) −2.80921e47 −0.0214411
\(949\) −7.55913e48 −0.566995
\(950\) 7.03168e48 0.518346
\(951\) −2.78198e48 −0.201546
\(952\) 2.27271e49 1.61821
\(953\) −8.19274e48 −0.573319 −0.286660 0.958033i \(-0.592545\pi\)
−0.286660 + 0.958033i \(0.592545\pi\)
\(954\) 9.52286e48 0.654967
\(955\) 8.31467e47 0.0562068
\(956\) 1.00107e49 0.665133
\(957\) 5.51707e47 0.0360298
\(958\) −1.44329e49 −0.926450
\(959\) −3.61324e49 −2.27976
\(960\) −6.73102e46 −0.00417451
\(961\) 2.92544e49 1.78343
\(962\) 3.99653e48 0.239494
\(963\) 6.05763e48 0.356837
\(964\) 2.23180e48 0.129236
\(965\) −1.06902e48 −0.0608536
\(966\) −4.81665e47 −0.0269540
\(967\) −1.65015e49 −0.907791 −0.453895 0.891055i \(-0.649966\pi\)
−0.453895 + 0.891055i \(0.649966\pi\)
\(968\) −1.70501e49 −0.922113
\(969\) 4.82088e48 0.256321
\(970\) −7.83358e47 −0.0409474
\(971\) −3.28602e49 −1.68870 −0.844352 0.535789i \(-0.820014\pi\)
−0.844352 + 0.535789i \(0.820014\pi\)
\(972\) 8.30611e48 0.419666
\(973\) 1.00483e49 0.499151
\(974\) −7.23857e48 −0.353533
\(975\) −1.94029e48 −0.0931730
\(976\) 6.80939e46 0.00321504
\(977\) 1.17177e49 0.543977 0.271989 0.962300i \(-0.412319\pi\)
0.271989 + 0.962300i \(0.412319\pi\)
\(978\) −1.24552e48 −0.0568536
\(979\) 1.52247e49 0.683336
\(980\) −8.99802e47 −0.0397115
\(981\) −2.91321e48 −0.126425
\(982\) 7.15306e48 0.305247
\(983\) 3.61572e49 1.51726 0.758632 0.651519i \(-0.225868\pi\)
0.758632 + 0.651519i \(0.225868\pi\)
\(984\) 5.63213e48 0.232409
\(985\) 2.75828e48 0.111928
\(986\) −2.08305e48 −0.0831249
\(987\) 4.10461e48 0.161079
\(988\) −8.04975e48 −0.310665
\(989\) 1.01922e48 0.0386838
\(990\) −1.16465e48 −0.0434725
\(991\) 2.27623e49 0.835603 0.417802 0.908538i \(-0.362801\pi\)
0.417802 + 0.908538i \(0.362801\pi\)
\(992\) −4.78860e49 −1.72889
\(993\) −9.56445e48 −0.339623
\(994\) 2.08065e49 0.726649
\(995\) −2.02584e48 −0.0695863
\(996\) −1.16900e48 −0.0394942
\(997\) −5.01160e49 −1.66535 −0.832676 0.553761i \(-0.813192\pi\)
−0.832676 + 0.553761i \(0.813192\pi\)
\(998\) 8.75230e48 0.286067
\(999\) −1.26040e49 −0.405209
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 1.34.a.a.1.2 2
3.2 odd 2 9.34.a.b.1.1 2
4.3 odd 2 16.34.a.b.1.2 2
5.2 odd 4 25.34.b.a.24.3 4
5.3 odd 4 25.34.b.a.24.2 4
5.4 even 2 25.34.a.a.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.34.a.a.1.2 2 1.1 even 1 trivial
9.34.a.b.1.1 2 3.2 odd 2
16.34.a.b.1.2 2 4.3 odd 2
25.34.a.a.1.1 2 5.4 even 2
25.34.b.a.24.2 4 5.3 odd 4
25.34.b.a.24.3 4 5.2 odd 4