Properties

Label 1075.6.a.a.1.7
Level $1075$
Weight $6$
Character 1075.1
Self dual yes
Analytic conductor $172.413$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(172.412606299\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 4x^{7} - 173x^{6} + 462x^{5} + 9118x^{4} - 14192x^{3} - 167688x^{2} + 106368x + 681984 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-6.09504\) of defining polynomial
Character \(\chi\) \(=\) 1075.1

$q$-expansion

\(f(q)\) \(=\) \(q+8.09504 q^{2} -11.1803 q^{3} +33.5297 q^{4} -90.5052 q^{6} -223.489 q^{7} +12.3830 q^{8} -118.000 q^{9} +O(q^{10})\) \(q+8.09504 q^{2} -11.1803 q^{3} +33.5297 q^{4} -90.5052 q^{6} -223.489 q^{7} +12.3830 q^{8} -118.000 q^{9} -631.897 q^{11} -374.873 q^{12} -28.5724 q^{13} -1809.15 q^{14} -972.709 q^{16} +1743.07 q^{17} -955.217 q^{18} -2027.92 q^{19} +2498.68 q^{21} -5115.23 q^{22} -2980.86 q^{23} -138.447 q^{24} -231.295 q^{26} +4036.10 q^{27} -7493.51 q^{28} +766.139 q^{29} -8355.33 q^{31} -8270.38 q^{32} +7064.81 q^{33} +14110.3 q^{34} -3956.51 q^{36} -14892.6 q^{37} -16416.1 q^{38} +319.449 q^{39} -5342.20 q^{41} +20226.9 q^{42} +1849.00 q^{43} -21187.3 q^{44} -24130.2 q^{46} +6282.09 q^{47} +10875.2 q^{48} +33140.1 q^{49} -19488.1 q^{51} -958.024 q^{52} +915.172 q^{53} +32672.4 q^{54} -2767.47 q^{56} +22672.8 q^{57} +6201.92 q^{58} -14644.5 q^{59} -21324.9 q^{61} -67636.7 q^{62} +26371.7 q^{63} -35822.4 q^{64} +57189.9 q^{66} +12868.9 q^{67} +58444.8 q^{68} +33327.0 q^{69} +56454.6 q^{71} -1461.20 q^{72} +25591.3 q^{73} -120556. q^{74} -67995.4 q^{76} +141222. q^{77} +2585.95 q^{78} +5795.13 q^{79} -16450.9 q^{81} -43245.4 q^{82} +7857.24 q^{83} +83779.9 q^{84} +14967.7 q^{86} -8565.68 q^{87} -7824.80 q^{88} -7560.11 q^{89} +6385.60 q^{91} -99947.5 q^{92} +93415.3 q^{93} +50853.8 q^{94} +92465.6 q^{96} -111712. q^{97} +268271. q^{98} +74563.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 12 q^{2} + 26 q^{3} + 122 q^{4} - 69 q^{6} + 136 q^{7} + 666 q^{8} + 546 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 12 q^{2} + 26 q^{3} + 122 q^{4} - 69 q^{6} + 136 q^{7} + 666 q^{8} + 546 q^{9} - 532 q^{11} + 4195 q^{12} + 2492 q^{13} - 4240 q^{14} + 1882 q^{16} + 2534 q^{17} + 3711 q^{18} - 1678 q^{19} - 2256 q^{21} - 11502 q^{22} + 2488 q^{23} + 19953 q^{24} + 4586 q^{26} + 8960 q^{27} - 18640 q^{28} - 4360 q^{29} + 5704 q^{31} + 18294 q^{32} + 12852 q^{33} + 30007 q^{34} + 67969 q^{36} + 3772 q^{37} + 6559 q^{38} + 11120 q^{39} - 10698 q^{41} - 78698 q^{42} + 14792 q^{43} - 356 q^{44} - 19389 q^{46} + 77864 q^{47} + 118727 q^{48} + 7188 q^{49} - 80246 q^{51} + 60736 q^{52} + 62352 q^{53} + 61026 q^{54} - 144528 q^{56} + 808 q^{57} - 52951 q^{58} - 26224 q^{59} - 82540 q^{61} + 9023 q^{62} + 61768 q^{63} + 153858 q^{64} - 48516 q^{66} - 27784 q^{67} - 40507 q^{68} - 93776 q^{69} - 9504 q^{71} + 186687 q^{72} - 14260 q^{73} - 15239 q^{74} + 1279 q^{76} + 218140 q^{77} - 264170 q^{78} + 160248 q^{79} + 161076 q^{81} + 47781 q^{82} + 77176 q^{83} + 16382 q^{84} + 22188 q^{86} - 268136 q^{87} - 129544 q^{88} - 265692 q^{89} + 401148 q^{91} - 190391 q^{92} + 123860 q^{93} + 248737 q^{94} + 950817 q^{96} - 144742 q^{97} + 292244 q^{98} + 239516 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.09504 1.43101 0.715507 0.698605i \(-0.246196\pi\)
0.715507 + 0.698605i \(0.246196\pi\)
\(3\) −11.1803 −0.717218 −0.358609 0.933488i \(-0.616749\pi\)
−0.358609 + 0.933488i \(0.616749\pi\)
\(4\) 33.5297 1.04780
\(5\) 0 0
\(6\) −90.5052 −1.02635
\(7\) −223.489 −1.72389 −0.861946 0.507000i \(-0.830755\pi\)
−0.861946 + 0.507000i \(0.830755\pi\)
\(8\) 12.3830 0.0684073
\(9\) −118.000 −0.485598
\(10\) 0 0
\(11\) −631.897 −1.57458 −0.787289 0.616584i \(-0.788516\pi\)
−0.787289 + 0.616584i \(0.788516\pi\)
\(12\) −374.873 −0.751504
\(13\) −28.5724 −0.0468909 −0.0234454 0.999725i \(-0.507464\pi\)
−0.0234454 + 0.999725i \(0.507464\pi\)
\(14\) −1809.15 −2.46692
\(15\) 0 0
\(16\) −972.709 −0.949911
\(17\) 1743.07 1.46283 0.731414 0.681933i \(-0.238861\pi\)
0.731414 + 0.681933i \(0.238861\pi\)
\(18\) −955.217 −0.694897
\(19\) −2027.92 −1.28874 −0.644371 0.764713i \(-0.722881\pi\)
−0.644371 + 0.764713i \(0.722881\pi\)
\(20\) 0 0
\(21\) 2498.68 1.23641
\(22\) −5115.23 −2.25324
\(23\) −2980.86 −1.17496 −0.587479 0.809239i \(-0.699880\pi\)
−0.587479 + 0.809239i \(0.699880\pi\)
\(24\) −138.447 −0.0490630
\(25\) 0 0
\(26\) −231.295 −0.0671015
\(27\) 4036.10 1.06550
\(28\) −7493.51 −1.80630
\(29\) 766.139 0.169166 0.0845829 0.996416i \(-0.473044\pi\)
0.0845829 + 0.996416i \(0.473044\pi\)
\(30\) 0 0
\(31\) −8355.33 −1.56156 −0.780781 0.624805i \(-0.785178\pi\)
−0.780781 + 0.624805i \(0.785178\pi\)
\(32\) −8270.38 −1.42774
\(33\) 7064.81 1.12932
\(34\) 14110.3 2.09333
\(35\) 0 0
\(36\) −3956.51 −0.508811
\(37\) −14892.6 −1.78841 −0.894204 0.447661i \(-0.852257\pi\)
−0.894204 + 0.447661i \(0.852257\pi\)
\(38\) −16416.1 −1.84421
\(39\) 319.449 0.0336310
\(40\) 0 0
\(41\) −5342.20 −0.496319 −0.248159 0.968719i \(-0.579826\pi\)
−0.248159 + 0.968719i \(0.579826\pi\)
\(42\) 20226.9 1.76932
\(43\) 1849.00 0.152499
\(44\) −21187.3 −1.64985
\(45\) 0 0
\(46\) −24130.2 −1.68138
\(47\) 6282.09 0.414820 0.207410 0.978254i \(-0.433497\pi\)
0.207410 + 0.978254i \(0.433497\pi\)
\(48\) 10875.2 0.681294
\(49\) 33140.1 1.97181
\(50\) 0 0
\(51\) −19488.1 −1.04917
\(52\) −958.024 −0.0491324
\(53\) 915.172 0.0447521 0.0223760 0.999750i \(-0.492877\pi\)
0.0223760 + 0.999750i \(0.492877\pi\)
\(54\) 32672.4 1.52474
\(55\) 0 0
\(56\) −2767.47 −0.117927
\(57\) 22672.8 0.924310
\(58\) 6201.92 0.242079
\(59\) −14644.5 −0.547704 −0.273852 0.961772i \(-0.588298\pi\)
−0.273852 + 0.961772i \(0.588298\pi\)
\(60\) 0 0
\(61\) −21324.9 −0.733775 −0.366887 0.930265i \(-0.619577\pi\)
−0.366887 + 0.930265i \(0.619577\pi\)
\(62\) −67636.7 −2.23462
\(63\) 26371.7 0.837118
\(64\) −35822.4 −1.09321
\(65\) 0 0
\(66\) 57189.9 1.61607
\(67\) 12868.9 0.350232 0.175116 0.984548i \(-0.443970\pi\)
0.175116 + 0.984548i \(0.443970\pi\)
\(68\) 58444.8 1.53276
\(69\) 33327.0 0.842702
\(70\) 0 0
\(71\) 56454.6 1.32909 0.664544 0.747249i \(-0.268626\pi\)
0.664544 + 0.747249i \(0.268626\pi\)
\(72\) −1461.20 −0.0332184
\(73\) 25591.3 0.562064 0.281032 0.959698i \(-0.409323\pi\)
0.281032 + 0.959698i \(0.409323\pi\)
\(74\) −120556. −2.55924
\(75\) 0 0
\(76\) −67995.4 −1.35035
\(77\) 141222. 2.71440
\(78\) 2585.95 0.0481265
\(79\) 5795.13 0.104471 0.0522355 0.998635i \(-0.483365\pi\)
0.0522355 + 0.998635i \(0.483365\pi\)
\(80\) 0 0
\(81\) −16450.9 −0.278597
\(82\) −43245.4 −0.710240
\(83\) 7857.24 0.125192 0.0625958 0.998039i \(-0.480062\pi\)
0.0625958 + 0.998039i \(0.480062\pi\)
\(84\) 83779.9 1.29551
\(85\) 0 0
\(86\) 14967.7 0.218228
\(87\) −8565.68 −0.121329
\(88\) −7824.80 −0.107713
\(89\) −7560.11 −0.101170 −0.0505852 0.998720i \(-0.516109\pi\)
−0.0505852 + 0.998720i \(0.516109\pi\)
\(90\) 0 0
\(91\) 6385.60 0.0808348
\(92\) −99947.5 −1.23113
\(93\) 93415.3 1.11998
\(94\) 50853.8 0.593613
\(95\) 0 0
\(96\) 92465.6 1.02400
\(97\) −111712. −1.20551 −0.602754 0.797927i \(-0.705930\pi\)
−0.602754 + 0.797927i \(0.705930\pi\)
\(98\) 268271. 2.82168
\(99\) 74563.9 0.764611
\(100\) 0 0
\(101\) 10492.3 0.102345 0.0511724 0.998690i \(-0.483704\pi\)
0.0511724 + 0.998690i \(0.483704\pi\)
\(102\) −157757. −1.50137
\(103\) 11286.6 0.104826 0.0524130 0.998625i \(-0.483309\pi\)
0.0524130 + 0.998625i \(0.483309\pi\)
\(104\) −353.813 −0.00320768
\(105\) 0 0
\(106\) 7408.36 0.0640409
\(107\) −39045.4 −0.329693 −0.164847 0.986319i \(-0.552713\pi\)
−0.164847 + 0.986319i \(0.552713\pi\)
\(108\) 135329. 1.11643
\(109\) −14622.8 −0.117887 −0.0589433 0.998261i \(-0.518773\pi\)
−0.0589433 + 0.998261i \(0.518773\pi\)
\(110\) 0 0
\(111\) 166504. 1.28268
\(112\) 217389. 1.63755
\(113\) 859.121 0.00632934 0.00316467 0.999995i \(-0.498993\pi\)
0.00316467 + 0.999995i \(0.498993\pi\)
\(114\) 183537. 1.32270
\(115\) 0 0
\(116\) 25688.4 0.177252
\(117\) 3371.55 0.0227701
\(118\) −118548. −0.783772
\(119\) −389557. −2.52176
\(120\) 0 0
\(121\) 238242. 1.47930
\(122\) −172626. −1.05004
\(123\) 59727.6 0.355969
\(124\) −280152. −1.63621
\(125\) 0 0
\(126\) 213480. 1.19793
\(127\) −193396. −1.06399 −0.531997 0.846746i \(-0.678558\pi\)
−0.531997 + 0.846746i \(0.678558\pi\)
\(128\) −25331.5 −0.136658
\(129\) −20672.4 −0.109375
\(130\) 0 0
\(131\) −269599. −1.37259 −0.686293 0.727325i \(-0.740763\pi\)
−0.686293 + 0.727325i \(0.740763\pi\)
\(132\) 236881. 1.18330
\(133\) 453216. 2.22165
\(134\) 104175. 0.501187
\(135\) 0 0
\(136\) 21584.6 0.100068
\(137\) −148987. −0.678183 −0.339091 0.940753i \(-0.610120\pi\)
−0.339091 + 0.940753i \(0.610120\pi\)
\(138\) 269784. 1.20592
\(139\) −16355.6 −0.0718008 −0.0359004 0.999355i \(-0.511430\pi\)
−0.0359004 + 0.999355i \(0.511430\pi\)
\(140\) 0 0
\(141\) −70235.8 −0.297516
\(142\) 457003. 1.90194
\(143\) 18054.8 0.0738333
\(144\) 114780. 0.461275
\(145\) 0 0
\(146\) 207163. 0.804322
\(147\) −370518. −1.41422
\(148\) −499345. −1.87390
\(149\) −150536. −0.555489 −0.277744 0.960655i \(-0.589587\pi\)
−0.277744 + 0.960655i \(0.589587\pi\)
\(150\) 0 0
\(151\) 428141. 1.52807 0.764037 0.645172i \(-0.223214\pi\)
0.764037 + 0.645172i \(0.223214\pi\)
\(152\) −25111.8 −0.0881594
\(153\) −205683. −0.710346
\(154\) 1.14320e6 3.88435
\(155\) 0 0
\(156\) 10711.0 0.0352387
\(157\) 434190. 1.40582 0.702912 0.711277i \(-0.251883\pi\)
0.702912 + 0.711277i \(0.251883\pi\)
\(158\) 46911.8 0.149499
\(159\) −10231.9 −0.0320970
\(160\) 0 0
\(161\) 666189. 2.02550
\(162\) −133171. −0.398677
\(163\) 571830. 1.68577 0.842884 0.538095i \(-0.180856\pi\)
0.842884 + 0.538095i \(0.180856\pi\)
\(164\) −179122. −0.520044
\(165\) 0 0
\(166\) 63604.7 0.179151
\(167\) −605744. −1.68073 −0.840365 0.542020i \(-0.817660\pi\)
−0.840365 + 0.542020i \(0.817660\pi\)
\(168\) 30941.2 0.0845793
\(169\) −370477. −0.997801
\(170\) 0 0
\(171\) 239295. 0.625810
\(172\) 61996.4 0.159789
\(173\) 85238.8 0.216532 0.108266 0.994122i \(-0.465470\pi\)
0.108266 + 0.994122i \(0.465470\pi\)
\(174\) −69339.6 −0.173623
\(175\) 0 0
\(176\) 614652. 1.49571
\(177\) 163731. 0.392823
\(178\) −61199.4 −0.144776
\(179\) 77941.8 0.181818 0.0909092 0.995859i \(-0.471023\pi\)
0.0909092 + 0.995859i \(0.471023\pi\)
\(180\) 0 0
\(181\) −347661. −0.788787 −0.394393 0.918942i \(-0.629045\pi\)
−0.394393 + 0.918942i \(0.629045\pi\)
\(182\) 51691.7 0.115676
\(183\) 238420. 0.526277
\(184\) −36912.2 −0.0803757
\(185\) 0 0
\(186\) 756201. 1.60271
\(187\) −1.10144e6 −2.30334
\(188\) 210637. 0.434650
\(189\) −902023. −1.83680
\(190\) 0 0
\(191\) −192163. −0.381142 −0.190571 0.981673i \(-0.561034\pi\)
−0.190571 + 0.981673i \(0.561034\pi\)
\(192\) 400506. 0.784072
\(193\) 271724. 0.525091 0.262546 0.964920i \(-0.415438\pi\)
0.262546 + 0.964920i \(0.415438\pi\)
\(194\) −904313. −1.72510
\(195\) 0 0
\(196\) 1.11118e6 2.06606
\(197\) −76788.1 −0.140971 −0.0704853 0.997513i \(-0.522455\pi\)
−0.0704853 + 0.997513i \(0.522455\pi\)
\(198\) 603598. 1.09417
\(199\) −694776. −1.24369 −0.621845 0.783140i \(-0.713617\pi\)
−0.621845 + 0.783140i \(0.713617\pi\)
\(200\) 0 0
\(201\) −143879. −0.251193
\(202\) 84935.3 0.146457
\(203\) −171223. −0.291624
\(204\) −653432. −1.09932
\(205\) 0 0
\(206\) 91365.3 0.150008
\(207\) 351743. 0.570557
\(208\) 27792.6 0.0445422
\(209\) 1.28143e6 2.02923
\(210\) 0 0
\(211\) −433533. −0.670372 −0.335186 0.942152i \(-0.608799\pi\)
−0.335186 + 0.942152i \(0.608799\pi\)
\(212\) 30685.5 0.0468914
\(213\) −631181. −0.953246
\(214\) −316074. −0.471796
\(215\) 0 0
\(216\) 49979.2 0.0728878
\(217\) 1.86732e6 2.69196
\(218\) −118372. −0.168698
\(219\) −286119. −0.403123
\(220\) 0 0
\(221\) −49803.8 −0.0685933
\(222\) 1.34786e6 1.83553
\(223\) −1.04204e6 −1.40320 −0.701602 0.712569i \(-0.747531\pi\)
−0.701602 + 0.712569i \(0.747531\pi\)
\(224\) 1.84834e6 2.46128
\(225\) 0 0
\(226\) 6954.62 0.00905737
\(227\) −924970. −1.19141 −0.595707 0.803202i \(-0.703128\pi\)
−0.595707 + 0.803202i \(0.703128\pi\)
\(228\) 760211. 0.968495
\(229\) −137140. −0.172812 −0.0864062 0.996260i \(-0.527538\pi\)
−0.0864062 + 0.996260i \(0.527538\pi\)
\(230\) 0 0
\(231\) −1.57890e6 −1.94682
\(232\) 9487.13 0.0115722
\(233\) −428602. −0.517208 −0.258604 0.965983i \(-0.583262\pi\)
−0.258604 + 0.965983i \(0.583262\pi\)
\(234\) 27292.8 0.0325843
\(235\) 0 0
\(236\) −491027. −0.573886
\(237\) −64791.5 −0.0749285
\(238\) −3.15348e6 −3.60868
\(239\) −1.17134e6 −1.32645 −0.663223 0.748422i \(-0.730812\pi\)
−0.663223 + 0.748422i \(0.730812\pi\)
\(240\) 0 0
\(241\) 119252. 0.132258 0.0661291 0.997811i \(-0.478935\pi\)
0.0661291 + 0.997811i \(0.478935\pi\)
\(242\) 1.92858e6 2.11690
\(243\) −796846. −0.865683
\(244\) −715018. −0.768852
\(245\) 0 0
\(246\) 483497. 0.509397
\(247\) 57942.4 0.0604302
\(248\) −103464. −0.106822
\(249\) −87846.6 −0.0897897
\(250\) 0 0
\(251\) −141272. −0.141538 −0.0707690 0.997493i \(-0.522545\pi\)
−0.0707690 + 0.997493i \(0.522545\pi\)
\(252\) 884235. 0.877135
\(253\) 1.88360e6 1.85006
\(254\) −1.56555e6 −1.52259
\(255\) 0 0
\(256\) 941257. 0.897652
\(257\) 196749. 0.185815 0.0929074 0.995675i \(-0.470384\pi\)
0.0929074 + 0.995675i \(0.470384\pi\)
\(258\) −167344. −0.156517
\(259\) 3.32833e6 3.08302
\(260\) 0 0
\(261\) −90404.5 −0.0821465
\(262\) −2.18241e6 −1.96419
\(263\) 1.96879e6 1.75513 0.877565 0.479457i \(-0.159166\pi\)
0.877565 + 0.479457i \(0.159166\pi\)
\(264\) 87483.9 0.0772535
\(265\) 0 0
\(266\) 3.66880e6 3.17922
\(267\) 84524.6 0.0725612
\(268\) 431492. 0.366974
\(269\) −531007. −0.447424 −0.223712 0.974655i \(-0.571818\pi\)
−0.223712 + 0.974655i \(0.571818\pi\)
\(270\) 0 0
\(271\) −1.68769e6 −1.39595 −0.697975 0.716122i \(-0.745916\pi\)
−0.697975 + 0.716122i \(0.745916\pi\)
\(272\) −1.69550e6 −1.38956
\(273\) −71393.2 −0.0579762
\(274\) −1.20606e6 −0.970489
\(275\) 0 0
\(276\) 1.11745e6 0.882986
\(277\) −13630.1 −0.0106733 −0.00533665 0.999986i \(-0.501699\pi\)
−0.00533665 + 0.999986i \(0.501699\pi\)
\(278\) −132399. −0.102748
\(279\) 985930. 0.758291
\(280\) 0 0
\(281\) 1.12070e6 0.846692 0.423346 0.905968i \(-0.360855\pi\)
0.423346 + 0.905968i \(0.360855\pi\)
\(282\) −568562. −0.425750
\(283\) 1.52947e6 1.13521 0.567605 0.823301i \(-0.307870\pi\)
0.567605 + 0.823301i \(0.307870\pi\)
\(284\) 1.89291e6 1.39262
\(285\) 0 0
\(286\) 146154. 0.105657
\(287\) 1.19392e6 0.855600
\(288\) 975907. 0.693309
\(289\) 1.61845e6 1.13987
\(290\) 0 0
\(291\) 1.24898e6 0.864613
\(292\) 858070. 0.588932
\(293\) 1.58484e6 1.07849 0.539246 0.842148i \(-0.318709\pi\)
0.539246 + 0.842148i \(0.318709\pi\)
\(294\) −2.99936e6 −2.02376
\(295\) 0 0
\(296\) −184416. −0.122340
\(297\) −2.55040e6 −1.67771
\(298\) −1.21860e6 −0.794912
\(299\) 85170.4 0.0550948
\(300\) 0 0
\(301\) −413230. −0.262891
\(302\) 3.46582e6 2.18670
\(303\) −117307. −0.0734035
\(304\) 1.97257e6 1.22419
\(305\) 0 0
\(306\) −1.66501e6 −1.01652
\(307\) −695751. −0.421316 −0.210658 0.977560i \(-0.567561\pi\)
−0.210658 + 0.977560i \(0.567561\pi\)
\(308\) 4.73512e6 2.84416
\(309\) −126188. −0.0751831
\(310\) 0 0
\(311\) −988763. −0.579684 −0.289842 0.957075i \(-0.593603\pi\)
−0.289842 + 0.957075i \(0.593603\pi\)
\(312\) 3955.75 0.00230061
\(313\) 3.07551e6 1.77442 0.887208 0.461369i \(-0.152642\pi\)
0.887208 + 0.461369i \(0.152642\pi\)
\(314\) 3.51479e6 2.01176
\(315\) 0 0
\(316\) 194309. 0.109465
\(317\) −904527. −0.505561 −0.252780 0.967524i \(-0.581345\pi\)
−0.252780 + 0.967524i \(0.581345\pi\)
\(318\) −82827.9 −0.0459313
\(319\) −484120. −0.266365
\(320\) 0 0
\(321\) 436540. 0.236462
\(322\) 5.39283e6 2.89852
\(323\) −3.53481e6 −1.88521
\(324\) −551594. −0.291915
\(325\) 0 0
\(326\) 4.62899e6 2.41236
\(327\) 163488. 0.0845505
\(328\) −66152.7 −0.0339518
\(329\) −1.40398e6 −0.715105
\(330\) 0 0
\(331\) −2.09309e6 −1.05007 −0.525034 0.851081i \(-0.675947\pi\)
−0.525034 + 0.851081i \(0.675947\pi\)
\(332\) 263451. 0.131176
\(333\) 1.75733e6 0.868446
\(334\) −4.90353e6 −2.40515
\(335\) 0 0
\(336\) −2.43049e6 −1.17448
\(337\) 647484. 0.310566 0.155283 0.987870i \(-0.450371\pi\)
0.155283 + 0.987870i \(0.450371\pi\)
\(338\) −2.99902e6 −1.42787
\(339\) −9605.25 −0.00453952
\(340\) 0 0
\(341\) 5.27970e6 2.45880
\(342\) 1.93710e6 0.895544
\(343\) −3.65027e6 −1.67529
\(344\) 22896.2 0.0104320
\(345\) 0 0
\(346\) 690012. 0.309860
\(347\) 462018. 0.205985 0.102992 0.994682i \(-0.467158\pi\)
0.102992 + 0.994682i \(0.467158\pi\)
\(348\) −287205. −0.127129
\(349\) 2.85075e6 1.25284 0.626420 0.779486i \(-0.284520\pi\)
0.626420 + 0.779486i \(0.284520\pi\)
\(350\) 0 0
\(351\) −115321. −0.0499621
\(352\) 5.22602e6 2.24810
\(353\) 809444. 0.345740 0.172870 0.984945i \(-0.444696\pi\)
0.172870 + 0.984945i \(0.444696\pi\)
\(354\) 1.32541e6 0.562136
\(355\) 0 0
\(356\) −253488. −0.106007
\(357\) 4.35538e6 1.80865
\(358\) 630942. 0.260185
\(359\) 3.46118e6 1.41739 0.708694 0.705516i \(-0.249285\pi\)
0.708694 + 0.705516i \(0.249285\pi\)
\(360\) 0 0
\(361\) 1.63635e6 0.660856
\(362\) −2.81433e6 −1.12877
\(363\) −2.66363e6 −1.06098
\(364\) 214107. 0.0846990
\(365\) 0 0
\(366\) 1.93002e6 0.753110
\(367\) −2.13602e6 −0.827827 −0.413914 0.910316i \(-0.635838\pi\)
−0.413914 + 0.910316i \(0.635838\pi\)
\(368\) 2.89951e6 1.11611
\(369\) 630381. 0.241011
\(370\) 0 0
\(371\) −204531. −0.0771478
\(372\) 3.13219e6 1.17352
\(373\) −2.37193e6 −0.882734 −0.441367 0.897327i \(-0.645506\pi\)
−0.441367 + 0.897327i \(0.645506\pi\)
\(374\) −8.91622e6 −3.29611
\(375\) 0 0
\(376\) 77791.4 0.0283767
\(377\) −21890.4 −0.00793233
\(378\) −7.30191e6 −2.62849
\(379\) −5.47562e6 −1.95810 −0.979051 0.203616i \(-0.934731\pi\)
−0.979051 + 0.203616i \(0.934731\pi\)
\(380\) 0 0
\(381\) 2.16224e6 0.763116
\(382\) −1.55557e6 −0.545419
\(383\) −3.16966e6 −1.10412 −0.552059 0.833805i \(-0.686158\pi\)
−0.552059 + 0.833805i \(0.686158\pi\)
\(384\) 283214. 0.0980138
\(385\) 0 0
\(386\) 2.19962e6 0.751413
\(387\) −218182. −0.0740529
\(388\) −3.74567e6 −1.26314
\(389\) −311235. −0.104283 −0.0521416 0.998640i \(-0.516605\pi\)
−0.0521416 + 0.998640i \(0.516605\pi\)
\(390\) 0 0
\(391\) −5.19587e6 −1.71876
\(392\) 410376. 0.134886
\(393\) 3.01420e6 0.984444
\(394\) −621603. −0.201731
\(395\) 0 0
\(396\) 2.50011e6 0.801162
\(397\) 496314. 0.158045 0.0790224 0.996873i \(-0.474820\pi\)
0.0790224 + 0.996873i \(0.474820\pi\)
\(398\) −5.62424e6 −1.77974
\(399\) −5.06711e6 −1.59341
\(400\) 0 0
\(401\) −5.63670e6 −1.75051 −0.875253 0.483665i \(-0.839305\pi\)
−0.875253 + 0.483665i \(0.839305\pi\)
\(402\) −1.16471e6 −0.359461
\(403\) 238732. 0.0732230
\(404\) 351802. 0.107237
\(405\) 0 0
\(406\) −1.38606e6 −0.417318
\(407\) 9.41059e6 2.81599
\(408\) −241323. −0.0717707
\(409\) −720515. −0.212978 −0.106489 0.994314i \(-0.533961\pi\)
−0.106489 + 0.994314i \(0.533961\pi\)
\(410\) 0 0
\(411\) 1.66572e6 0.486405
\(412\) 378435. 0.109837
\(413\) 3.27289e6 0.944182
\(414\) 2.84737e6 0.816476
\(415\) 0 0
\(416\) 236305. 0.0669482
\(417\) 182861. 0.0514969
\(418\) 1.03733e7 2.90385
\(419\) −3.94151e6 −1.09680 −0.548400 0.836216i \(-0.684763\pi\)
−0.548400 + 0.836216i \(0.684763\pi\)
\(420\) 0 0
\(421\) 4.39506e6 1.20854 0.604268 0.796781i \(-0.293466\pi\)
0.604268 + 0.796781i \(0.293466\pi\)
\(422\) −3.50947e6 −0.959312
\(423\) −741288. −0.201436
\(424\) 11332.6 0.00306137
\(425\) 0 0
\(426\) −5.10944e6 −1.36411
\(427\) 4.76588e6 1.26495
\(428\) −1.30918e6 −0.345454
\(429\) −201859. −0.0529546
\(430\) 0 0
\(431\) 1.24913e6 0.323903 0.161951 0.986799i \(-0.448221\pi\)
0.161951 + 0.986799i \(0.448221\pi\)
\(432\) −3.92595e6 −1.01213
\(433\) −971902. −0.249117 −0.124558 0.992212i \(-0.539751\pi\)
−0.124558 + 0.992212i \(0.539751\pi\)
\(434\) 1.51160e7 3.85224
\(435\) 0 0
\(436\) −490299. −0.123522
\(437\) 6.04494e6 1.51422
\(438\) −2.31615e6 −0.576874
\(439\) −1.32453e6 −0.328021 −0.164010 0.986459i \(-0.552443\pi\)
−0.164010 + 0.986459i \(0.552443\pi\)
\(440\) 0 0
\(441\) −3.91054e6 −0.957504
\(442\) −403164. −0.0981581
\(443\) −4.76446e6 −1.15346 −0.576732 0.816933i \(-0.695672\pi\)
−0.576732 + 0.816933i \(0.695672\pi\)
\(444\) 5.58284e6 1.34399
\(445\) 0 0
\(446\) −8.43533e6 −2.00801
\(447\) 1.68304e6 0.398407
\(448\) 8.00589e6 1.88458
\(449\) −5.40007e6 −1.26411 −0.632053 0.774926i \(-0.717787\pi\)
−0.632053 + 0.774926i \(0.717787\pi\)
\(450\) 0 0
\(451\) 3.37572e6 0.781493
\(452\) 28806.1 0.00663190
\(453\) −4.78676e6 −1.09596
\(454\) −7.48767e6 −1.70493
\(455\) 0 0
\(456\) 280758. 0.0632295
\(457\) −2.12752e6 −0.476523 −0.238261 0.971201i \(-0.576577\pi\)
−0.238261 + 0.971201i \(0.576577\pi\)
\(458\) −1.11015e6 −0.247297
\(459\) 7.03522e6 1.55864
\(460\) 0 0
\(461\) 2.80905e6 0.615612 0.307806 0.951449i \(-0.400405\pi\)
0.307806 + 0.951449i \(0.400405\pi\)
\(462\) −1.27813e7 −2.78593
\(463\) 2.85342e6 0.618605 0.309302 0.950964i \(-0.399904\pi\)
0.309302 + 0.950964i \(0.399904\pi\)
\(464\) −745230. −0.160692
\(465\) 0 0
\(466\) −3.46955e6 −0.740132
\(467\) 559463. 0.118708 0.0593539 0.998237i \(-0.481096\pi\)
0.0593539 + 0.998237i \(0.481096\pi\)
\(468\) 113047. 0.0238586
\(469\) −2.87606e6 −0.603762
\(470\) 0 0
\(471\) −4.85439e6 −1.00828
\(472\) −181344. −0.0374669
\(473\) −1.16838e6 −0.240121
\(474\) −524490. −0.107224
\(475\) 0 0
\(476\) −1.30617e7 −2.64231
\(477\) −107991. −0.0217315
\(478\) −9.48208e6 −1.89816
\(479\) 5.46747e6 1.08880 0.544399 0.838826i \(-0.316758\pi\)
0.544399 + 0.838826i \(0.316758\pi\)
\(480\) 0 0
\(481\) 425517. 0.0838600
\(482\) 965349. 0.189263
\(483\) −7.44821e6 −1.45273
\(484\) 7.98819e6 1.55001
\(485\) 0 0
\(486\) −6.45050e6 −1.23881
\(487\) −9.34759e6 −1.78598 −0.892991 0.450074i \(-0.851397\pi\)
−0.892991 + 0.450074i \(0.851397\pi\)
\(488\) −264067. −0.0501955
\(489\) −6.39325e6 −1.20906
\(490\) 0 0
\(491\) −1.04964e7 −1.96488 −0.982438 0.186589i \(-0.940257\pi\)
−0.982438 + 0.186589i \(0.940257\pi\)
\(492\) 2.00265e6 0.372986
\(493\) 1.33544e6 0.247460
\(494\) 469046. 0.0864766
\(495\) 0 0
\(496\) 8.12730e6 1.48335
\(497\) −1.26170e7 −2.29120
\(498\) −711122. −0.128490
\(499\) 5.74842e6 1.03347 0.516734 0.856146i \(-0.327148\pi\)
0.516734 + 0.856146i \(0.327148\pi\)
\(500\) 0 0
\(501\) 6.77242e6 1.20545
\(502\) −1.14361e6 −0.202543
\(503\) −3.10341e6 −0.546915 −0.273457 0.961884i \(-0.588167\pi\)
−0.273457 + 0.961884i \(0.588167\pi\)
\(504\) 326562. 0.0572650
\(505\) 0 0
\(506\) 1.52478e7 2.64747
\(507\) 4.14205e6 0.715642
\(508\) −6.48453e6 −1.11486
\(509\) −7.92714e6 −1.35620 −0.678098 0.734972i \(-0.737195\pi\)
−0.678098 + 0.734972i \(0.737195\pi\)
\(510\) 0 0
\(511\) −5.71937e6 −0.968938
\(512\) 8.43012e6 1.42121
\(513\) −8.18488e6 −1.37315
\(514\) 1.59269e6 0.265904
\(515\) 0 0
\(516\) −693141. −0.114603
\(517\) −3.96963e6 −0.653166
\(518\) 2.69429e7 4.41185
\(519\) −952998. −0.155301
\(520\) 0 0
\(521\) −4.37136e6 −0.705541 −0.352771 0.935710i \(-0.614760\pi\)
−0.352771 + 0.935710i \(0.614760\pi\)
\(522\) −731828. −0.117553
\(523\) −1.11680e6 −0.178534 −0.0892671 0.996008i \(-0.528452\pi\)
−0.0892671 + 0.996008i \(0.528452\pi\)
\(524\) −9.03957e6 −1.43820
\(525\) 0 0
\(526\) 1.59374e7 2.51162
\(527\) −1.45640e7 −2.28430
\(528\) −6.87201e6 −1.07275
\(529\) 2.44920e6 0.380527
\(530\) 0 0
\(531\) 1.72806e6 0.265964
\(532\) 1.51962e7 2.32786
\(533\) 152640. 0.0232728
\(534\) 684230. 0.103836
\(535\) 0 0
\(536\) 159357. 0.0239584
\(537\) −871415. −0.130403
\(538\) −4.29852e6 −0.640271
\(539\) −2.09411e7 −3.10476
\(540\) 0 0
\(541\) −6212.12 −0.000912528 0 −0.000456264 1.00000i \(-0.500145\pi\)
−0.000456264 1.00000i \(0.500145\pi\)
\(542\) −1.36619e7 −1.99763
\(543\) 3.88696e6 0.565732
\(544\) −1.44159e7 −2.08855
\(545\) 0 0
\(546\) −577931. −0.0829648
\(547\) 9.82839e6 1.40448 0.702238 0.711942i \(-0.252184\pi\)
0.702238 + 0.711942i \(0.252184\pi\)
\(548\) −4.99549e6 −0.710602
\(549\) 2.51635e6 0.356319
\(550\) 0 0
\(551\) −1.55367e6 −0.218011
\(552\) 412690. 0.0576470
\(553\) −1.29515e6 −0.180097
\(554\) −110336. −0.0152737
\(555\) 0 0
\(556\) −548398. −0.0752332
\(557\) 6.27045e6 0.856369 0.428184 0.903691i \(-0.359153\pi\)
0.428184 + 0.903691i \(0.359153\pi\)
\(558\) 7.98115e6 1.08513
\(559\) −52830.4 −0.00715079
\(560\) 0 0
\(561\) 1.23145e7 1.65200
\(562\) 9.07215e6 1.21163
\(563\) 6.71129e6 0.892350 0.446175 0.894946i \(-0.352786\pi\)
0.446175 + 0.894946i \(0.352786\pi\)
\(564\) −2.35499e6 −0.311739
\(565\) 0 0
\(566\) 1.23812e7 1.62450
\(567\) 3.67659e6 0.480272
\(568\) 699080. 0.0909193
\(569\) −7.01697e6 −0.908592 −0.454296 0.890851i \(-0.650109\pi\)
−0.454296 + 0.890851i \(0.650109\pi\)
\(570\) 0 0
\(571\) 1.61627e6 0.207455 0.103727 0.994606i \(-0.466923\pi\)
0.103727 + 0.994606i \(0.466923\pi\)
\(572\) 605372. 0.0773628
\(573\) 2.14845e6 0.273362
\(574\) 9.66484e6 1.22438
\(575\) 0 0
\(576\) 4.22705e6 0.530861
\(577\) −1.08712e7 −1.35937 −0.679686 0.733503i \(-0.737884\pi\)
−0.679686 + 0.733503i \(0.737884\pi\)
\(578\) 1.31014e7 1.63117
\(579\) −3.03796e6 −0.376605
\(580\) 0 0
\(581\) −1.75600e6 −0.215817
\(582\) 1.01105e7 1.23727
\(583\) −578294. −0.0704656
\(584\) 316898. 0.0384493
\(585\) 0 0
\(586\) 1.28294e7 1.54334
\(587\) −8.65320e6 −1.03653 −0.518264 0.855221i \(-0.673422\pi\)
−0.518264 + 0.855221i \(0.673422\pi\)
\(588\) −1.24233e7 −1.48182
\(589\) 1.69439e7 2.01245
\(590\) 0 0
\(591\) 858517. 0.101107
\(592\) 1.44862e7 1.69883
\(593\) −5.13574e6 −0.599745 −0.299872 0.953979i \(-0.596944\pi\)
−0.299872 + 0.953979i \(0.596944\pi\)
\(594\) −2.06456e7 −2.40083
\(595\) 0 0
\(596\) −5.04743e6 −0.582043
\(597\) 7.76782e6 0.891997
\(598\) 689458. 0.0788415
\(599\) 7.56853e6 0.861875 0.430937 0.902382i \(-0.358183\pi\)
0.430937 + 0.902382i \(0.358183\pi\)
\(600\) 0 0
\(601\) 2.56891e6 0.290110 0.145055 0.989424i \(-0.453664\pi\)
0.145055 + 0.989424i \(0.453664\pi\)
\(602\) −3.34512e6 −0.376201
\(603\) −1.51854e6 −0.170072
\(604\) 1.43554e7 1.60112
\(605\) 0 0
\(606\) −949604. −0.105042
\(607\) −2.62172e6 −0.288812 −0.144406 0.989519i \(-0.546127\pi\)
−0.144406 + 0.989519i \(0.546127\pi\)
\(608\) 1.67716e7 1.83999
\(609\) 1.91433e6 0.209158
\(610\) 0 0
\(611\) −179494. −0.0194513
\(612\) −6.89650e6 −0.744303
\(613\) −537167. −0.0577376 −0.0288688 0.999583i \(-0.509190\pi\)
−0.0288688 + 0.999583i \(0.509190\pi\)
\(614\) −5.63213e6 −0.602909
\(615\) 0 0
\(616\) 1.74875e6 0.185685
\(617\) −1.15522e7 −1.22166 −0.610830 0.791762i \(-0.709164\pi\)
−0.610830 + 0.791762i \(0.709164\pi\)
\(618\) −1.02149e6 −0.107588
\(619\) 2.20752e6 0.231568 0.115784 0.993274i \(-0.463062\pi\)
0.115784 + 0.993274i \(0.463062\pi\)
\(620\) 0 0
\(621\) −1.20311e7 −1.25192
\(622\) −8.00408e6 −0.829536
\(623\) 1.68960e6 0.174407
\(624\) −310731. −0.0319465
\(625\) 0 0
\(626\) 2.48963e7 2.53922
\(627\) −1.43268e7 −1.45540
\(628\) 1.45583e7 1.47303
\(629\) −2.59589e7 −2.61613
\(630\) 0 0
\(631\) −1.43943e7 −1.43919 −0.719594 0.694395i \(-0.755672\pi\)
−0.719594 + 0.694395i \(0.755672\pi\)
\(632\) 71761.3 0.00714657
\(633\) 4.84704e6 0.480803
\(634\) −7.32219e6 −0.723465
\(635\) 0 0
\(636\) −343074. −0.0336314
\(637\) −946893. −0.0924597
\(638\) −3.91897e6 −0.381172
\(639\) −6.66166e6 −0.645402
\(640\) 0 0
\(641\) 4.90224e6 0.471248 0.235624 0.971844i \(-0.424287\pi\)
0.235624 + 0.971844i \(0.424287\pi\)
\(642\) 3.53381e6 0.338381
\(643\) 1.80253e7 1.71931 0.859656 0.510874i \(-0.170678\pi\)
0.859656 + 0.510874i \(0.170678\pi\)
\(644\) 2.23371e7 2.12233
\(645\) 0 0
\(646\) −2.86144e7 −2.69776
\(647\) 1.24242e7 1.16683 0.583415 0.812174i \(-0.301716\pi\)
0.583415 + 0.812174i \(0.301716\pi\)
\(648\) −203712. −0.0190581
\(649\) 9.25383e6 0.862402
\(650\) 0 0
\(651\) −2.08772e7 −1.93073
\(652\) 1.91733e7 1.76635
\(653\) 1.28553e7 1.17977 0.589887 0.807486i \(-0.299172\pi\)
0.589887 + 0.807486i \(0.299172\pi\)
\(654\) 1.32344e6 0.120993
\(655\) 0 0
\(656\) 5.19641e6 0.471459
\(657\) −3.01978e6 −0.272937
\(658\) −1.13652e7 −1.02333
\(659\) −5.18218e6 −0.464835 −0.232417 0.972616i \(-0.574664\pi\)
−0.232417 + 0.972616i \(0.574664\pi\)
\(660\) 0 0
\(661\) 6.47130e6 0.576087 0.288043 0.957617i \(-0.406995\pi\)
0.288043 + 0.957617i \(0.406995\pi\)
\(662\) −1.69436e7 −1.50266
\(663\) 556823. 0.0491964
\(664\) 97296.6 0.00856402
\(665\) 0 0
\(666\) 1.42257e7 1.24276
\(667\) −2.28375e6 −0.198763
\(668\) −2.03104e7 −1.76108
\(669\) 1.16503e7 1.00640
\(670\) 0 0
\(671\) 1.34751e7 1.15539
\(672\) −2.06650e7 −1.76527
\(673\) −6.21171e6 −0.528657 −0.264328 0.964433i \(-0.585150\pi\)
−0.264328 + 0.964433i \(0.585150\pi\)
\(674\) 5.24141e6 0.444425
\(675\) 0 0
\(676\) −1.24220e7 −1.04550
\(677\) −1.85078e7 −1.55197 −0.775984 0.630752i \(-0.782747\pi\)
−0.775984 + 0.630752i \(0.782747\pi\)
\(678\) −77754.9 −0.00649611
\(679\) 2.49663e7 2.07817
\(680\) 0 0
\(681\) 1.03415e7 0.854504
\(682\) 4.27394e7 3.51858
\(683\) 4.91590e6 0.403228 0.201614 0.979465i \(-0.435381\pi\)
0.201614 + 0.979465i \(0.435381\pi\)
\(684\) 8.02348e6 0.655726
\(685\) 0 0
\(686\) −2.95491e7 −2.39736
\(687\) 1.53327e6 0.123944
\(688\) −1.79854e6 −0.144860
\(689\) −26148.7 −0.00209846
\(690\) 0 0
\(691\) −1.07645e7 −0.857630 −0.428815 0.903392i \(-0.641069\pi\)
−0.428815 + 0.903392i \(0.641069\pi\)
\(692\) 2.85803e6 0.226883
\(693\) −1.66642e7 −1.31811
\(694\) 3.74005e6 0.294767
\(695\) 0 0
\(696\) −106069. −0.00829977
\(697\) −9.31185e6 −0.726029
\(698\) 2.30769e7 1.79283
\(699\) 4.79192e6 0.370951
\(700\) 0 0
\(701\) 9.02819e6 0.693914 0.346957 0.937881i \(-0.387215\pi\)
0.346957 + 0.937881i \(0.387215\pi\)
\(702\) −933529. −0.0714966
\(703\) 3.02010e7 2.30480
\(704\) 2.26360e7 1.72135
\(705\) 0 0
\(706\) 6.55248e6 0.494760
\(707\) −2.34490e6 −0.176431
\(708\) 5.48984e6 0.411601
\(709\) 4.91059e6 0.366875 0.183438 0.983031i \(-0.441277\pi\)
0.183438 + 0.983031i \(0.441277\pi\)
\(710\) 0 0
\(711\) −683827. −0.0507308
\(712\) −93617.2 −0.00692079
\(713\) 2.49061e7 1.83477
\(714\) 3.52570e7 2.58821
\(715\) 0 0
\(716\) 2.61336e6 0.190510
\(717\) 1.30960e7 0.951352
\(718\) 2.80184e7 2.02830
\(719\) 1.44751e7 1.04424 0.522119 0.852873i \(-0.325142\pi\)
0.522119 + 0.852873i \(0.325142\pi\)
\(720\) 0 0
\(721\) −2.52242e6 −0.180709
\(722\) 1.32463e7 0.945695
\(723\) −1.33328e6 −0.0948580
\(724\) −1.16570e7 −0.826493
\(725\) 0 0
\(726\) −2.15622e7 −1.51828
\(727\) −1.55189e7 −1.08899 −0.544495 0.838764i \(-0.683279\pi\)
−0.544495 + 0.838764i \(0.683279\pi\)
\(728\) 79073.2 0.00552969
\(729\) 1.29066e7 0.899481
\(730\) 0 0
\(731\) 3.22294e6 0.223079
\(732\) 7.99414e6 0.551435
\(733\) −1.03870e6 −0.0714050 −0.0357025 0.999362i \(-0.511367\pi\)
−0.0357025 + 0.999362i \(0.511367\pi\)
\(734\) −1.72912e7 −1.18463
\(735\) 0 0
\(736\) 2.46529e7 1.67754
\(737\) −8.13184e6 −0.551467
\(738\) 5.10296e6 0.344891
\(739\) 1.33918e6 0.0902046 0.0451023 0.998982i \(-0.485639\pi\)
0.0451023 + 0.998982i \(0.485639\pi\)
\(740\) 0 0
\(741\) −647816. −0.0433417
\(742\) −1.65568e6 −0.110400
\(743\) −1.56518e7 −1.04014 −0.520070 0.854124i \(-0.674094\pi\)
−0.520070 + 0.854124i \(0.674094\pi\)
\(744\) 1.15677e6 0.0766149
\(745\) 0 0
\(746\) −1.92009e7 −1.26321
\(747\) −927157. −0.0607927
\(748\) −3.69310e7 −2.41345
\(749\) 8.72620e6 0.568356
\(750\) 0 0
\(751\) 1.92274e7 1.24400 0.622002 0.783016i \(-0.286320\pi\)
0.622002 + 0.783016i \(0.286320\pi\)
\(752\) −6.11065e6 −0.394042
\(753\) 1.57947e6 0.101514
\(754\) −177204. −0.0113513
\(755\) 0 0
\(756\) −3.02446e7 −1.92461
\(757\) 2.73627e7 1.73548 0.867739 0.497021i \(-0.165573\pi\)
0.867739 + 0.497021i \(0.165573\pi\)
\(758\) −4.43254e7 −2.80207
\(759\) −2.10592e7 −1.32690
\(760\) 0 0
\(761\) 5.86301e6 0.366994 0.183497 0.983020i \(-0.441258\pi\)
0.183497 + 0.983020i \(0.441258\pi\)
\(762\) 1.75034e7 1.09203
\(763\) 3.26803e6 0.203224
\(764\) −6.44317e6 −0.399361
\(765\) 0 0
\(766\) −2.56585e7 −1.58001
\(767\) 418430. 0.0256823
\(768\) −1.05236e7 −0.643813
\(769\) −1.36162e7 −0.830308 −0.415154 0.909751i \(-0.636272\pi\)
−0.415154 + 0.909751i \(0.636272\pi\)
\(770\) 0 0
\(771\) −2.19972e6 −0.133270
\(772\) 9.11083e6 0.550192
\(773\) 9.44787e6 0.568703 0.284351 0.958720i \(-0.408222\pi\)
0.284351 + 0.958720i \(0.408222\pi\)
\(774\) −1.76620e6 −0.105971
\(775\) 0 0
\(776\) −1.38333e6 −0.0824655
\(777\) −3.72118e7 −2.21120
\(778\) −2.51946e6 −0.149231
\(779\) 1.08335e7 0.639627
\(780\) 0 0
\(781\) −3.56735e7 −2.09275
\(782\) −4.20608e7 −2.45958
\(783\) 3.09221e6 0.180246
\(784\) −3.22357e7 −1.87304
\(785\) 0 0
\(786\) 2.44001e7 1.40875
\(787\) −2.97678e7 −1.71320 −0.856602 0.515977i \(-0.827429\pi\)
−0.856602 + 0.515977i \(0.827429\pi\)
\(788\) −2.57468e6 −0.147709
\(789\) −2.20117e7 −1.25881
\(790\) 0 0
\(791\) −192004. −0.0109111
\(792\) 923328. 0.0523050
\(793\) 609304. 0.0344073
\(794\) 4.01768e6 0.226164
\(795\) 0 0
\(796\) −2.32956e7 −1.30314
\(797\) 1.80924e7 1.00891 0.504453 0.863439i \(-0.331694\pi\)
0.504453 + 0.863439i \(0.331694\pi\)
\(798\) −4.10184e7 −2.28019
\(799\) 1.09501e7 0.606810
\(800\) 0 0
\(801\) 892095. 0.0491281
\(802\) −4.56293e7 −2.50500
\(803\) −1.61711e7 −0.885013
\(804\) −4.82422e6 −0.263201
\(805\) 0 0
\(806\) 1.93254e6 0.104783
\(807\) 5.93683e6 0.320901
\(808\) 129926. 0.00700113
\(809\) −1.57182e7 −0.844366 −0.422183 0.906511i \(-0.638736\pi\)
−0.422183 + 0.906511i \(0.638736\pi\)
\(810\) 0 0
\(811\) −1.57562e6 −0.0841202 −0.0420601 0.999115i \(-0.513392\pi\)
−0.0420601 + 0.999115i \(0.513392\pi\)
\(812\) −5.74106e6 −0.305564
\(813\) 1.88690e7 1.00120
\(814\) 7.61791e7 4.02972
\(815\) 0 0
\(816\) 1.89563e7 0.996617
\(817\) −3.74962e6 −0.196531
\(818\) −5.83260e6 −0.304775
\(819\) −753503. −0.0392532
\(820\) 0 0
\(821\) 2.61911e7 1.35611 0.678056 0.735010i \(-0.262823\pi\)
0.678056 + 0.735010i \(0.262823\pi\)
\(822\) 1.34841e7 0.696053
\(823\) 3.66910e7 1.88825 0.944126 0.329585i \(-0.106909\pi\)
0.944126 + 0.329585i \(0.106909\pi\)
\(824\) 139762. 0.00717086
\(825\) 0 0
\(826\) 2.64942e7 1.35114
\(827\) −1.38402e7 −0.703685 −0.351843 0.936059i \(-0.614445\pi\)
−0.351843 + 0.936059i \(0.614445\pi\)
\(828\) 1.17938e7 0.597832
\(829\) −2.83219e7 −1.43132 −0.715660 0.698449i \(-0.753874\pi\)
−0.715660 + 0.698449i \(0.753874\pi\)
\(830\) 0 0
\(831\) 152389. 0.00765509
\(832\) 1.02353e6 0.0512617
\(833\) 5.77657e7 2.88441
\(834\) 1.48027e6 0.0736928
\(835\) 0 0
\(836\) 4.29661e7 2.12623
\(837\) −3.37229e7 −1.66384
\(838\) −3.19067e7 −1.56954
\(839\) 2.80231e7 1.37439 0.687197 0.726471i \(-0.258841\pi\)
0.687197 + 0.726471i \(0.258841\pi\)
\(840\) 0 0
\(841\) −1.99242e7 −0.971383
\(842\) 3.55782e7 1.72943
\(843\) −1.25298e7 −0.607263
\(844\) −1.45362e7 −0.702418
\(845\) 0 0
\(846\) −6.00076e6 −0.288257
\(847\) −5.32444e7 −2.55015
\(848\) −890197. −0.0425105
\(849\) −1.71000e7 −0.814193
\(850\) 0 0
\(851\) 4.43928e7 2.10130
\(852\) −2.11633e7 −0.998815
\(853\) 2.38300e7 1.12138 0.560689 0.828027i \(-0.310537\pi\)
0.560689 + 0.828027i \(0.310537\pi\)
\(854\) 3.85800e7 1.81016
\(855\) 0 0
\(856\) −483501. −0.0225534
\(857\) 3.83129e7 1.78194 0.890971 0.454061i \(-0.150025\pi\)
0.890971 + 0.454061i \(0.150025\pi\)
\(858\) −1.63405e6 −0.0757789
\(859\) 2.68650e7 1.24224 0.621118 0.783717i \(-0.286679\pi\)
0.621118 + 0.783717i \(0.286679\pi\)
\(860\) 0 0
\(861\) −1.33484e7 −0.613652
\(862\) 1.01118e7 0.463510
\(863\) 1.63558e7 0.747558 0.373779 0.927518i \(-0.378062\pi\)
0.373779 + 0.927518i \(0.378062\pi\)
\(864\) −3.33801e7 −1.52126
\(865\) 0 0
\(866\) −7.86758e6 −0.356489
\(867\) −1.80948e7 −0.817535
\(868\) 6.26107e7 2.82065
\(869\) −3.66192e6 −0.164498
\(870\) 0 0
\(871\) −367696. −0.0164227
\(872\) −181075. −0.00806431
\(873\) 1.31820e7 0.585392
\(874\) 4.89341e7 2.16687
\(875\) 0 0
\(876\) −9.59350e6 −0.422393
\(877\) 2.30604e7 1.01243 0.506217 0.862406i \(-0.331043\pi\)
0.506217 + 0.862406i \(0.331043\pi\)
\(878\) −1.07221e7 −0.469402
\(879\) −1.77191e7 −0.773515
\(880\) 0 0
\(881\) −3.15095e7 −1.36774 −0.683868 0.729606i \(-0.739704\pi\)
−0.683868 + 0.729606i \(0.739704\pi\)
\(882\) −3.16560e7 −1.37020
\(883\) −2.86348e7 −1.23593 −0.617963 0.786208i \(-0.712042\pi\)
−0.617963 + 0.786208i \(0.712042\pi\)
\(884\) −1.66991e6 −0.0718723
\(885\) 0 0
\(886\) −3.85685e7 −1.65063
\(887\) 2.45670e7 1.04844 0.524220 0.851583i \(-0.324357\pi\)
0.524220 + 0.851583i \(0.324357\pi\)
\(888\) 2.06183e6 0.0877446
\(889\) 4.32219e7 1.83421
\(890\) 0 0
\(891\) 1.03953e7 0.438673
\(892\) −3.49392e7 −1.47028
\(893\) −1.27396e7 −0.534596
\(894\) 1.36243e7 0.570126
\(895\) 0 0
\(896\) 5.66130e6 0.235584
\(897\) −952233. −0.0395150
\(898\) −4.37138e7 −1.80895
\(899\) −6.40134e6 −0.264163
\(900\) 0 0
\(901\) 1.59521e6 0.0654646
\(902\) 2.73266e7 1.11833
\(903\) 4.62005e6 0.188550
\(904\) 10638.5 0.000432973 0
\(905\) 0 0
\(906\) −3.87490e7 −1.56834
\(907\) −1.90832e7 −0.770254 −0.385127 0.922864i \(-0.625842\pi\)
−0.385127 + 0.922864i \(0.625842\pi\)
\(908\) −3.10140e7 −1.24837
\(909\) −1.23809e6 −0.0496984
\(910\) 0 0
\(911\) −3.04616e7 −1.21606 −0.608032 0.793912i \(-0.708041\pi\)
−0.608032 + 0.793912i \(0.708041\pi\)
\(912\) −2.20540e7 −0.878012
\(913\) −4.96497e6 −0.197124
\(914\) −1.72224e7 −0.681911
\(915\) 0 0
\(916\) −4.59826e6 −0.181073
\(917\) 6.02522e7 2.36619
\(918\) 5.69504e7 2.23044
\(919\) 2.73866e7 1.06967 0.534834 0.844957i \(-0.320374\pi\)
0.534834 + 0.844957i \(0.320374\pi\)
\(920\) 0 0
\(921\) 7.77872e6 0.302175
\(922\) 2.27394e7 0.880950
\(923\) −1.61304e6 −0.0623221
\(924\) −5.29402e7 −2.03989
\(925\) 0 0
\(926\) 2.30986e7 0.885232
\(927\) −1.33182e6 −0.0509033
\(928\) −6.33626e6 −0.241525
\(929\) −2.65451e7 −1.00913 −0.504563 0.863375i \(-0.668346\pi\)
−0.504563 + 0.863375i \(0.668346\pi\)
\(930\) 0 0
\(931\) −6.72054e7 −2.54115
\(932\) −1.43709e7 −0.541932
\(933\) 1.10547e7 0.415760
\(934\) 4.52888e6 0.169873
\(935\) 0 0
\(936\) 41750.0 0.00155764
\(937\) 2.34660e7 0.873151 0.436576 0.899668i \(-0.356191\pi\)
0.436576 + 0.899668i \(0.356191\pi\)
\(938\) −2.32818e7 −0.863993
\(939\) −3.43852e7 −1.27264
\(940\) 0 0
\(941\) −2.18303e7 −0.803686 −0.401843 0.915709i \(-0.631630\pi\)
−0.401843 + 0.915709i \(0.631630\pi\)
\(942\) −3.92965e7 −1.44287
\(943\) 1.59244e7 0.583154
\(944\) 1.42449e7 0.520270
\(945\) 0 0
\(946\) −9.45806e6 −0.343617
\(947\) −1.87197e7 −0.678305 −0.339152 0.940731i \(-0.610140\pi\)
−0.339152 + 0.940731i \(0.610140\pi\)
\(948\) −2.17244e6 −0.0785103
\(949\) −731206. −0.0263557
\(950\) 0 0
\(951\) 1.01129e7 0.362598
\(952\) −4.82390e6 −0.172507
\(953\) −5.37413e7 −1.91680 −0.958399 0.285432i \(-0.907863\pi\)
−0.958399 + 0.285432i \(0.907863\pi\)
\(954\) −874188. −0.0310981
\(955\) 0 0
\(956\) −3.92748e7 −1.38986
\(957\) 5.41262e6 0.191042
\(958\) 4.42594e7 1.55809
\(959\) 3.32969e7 1.16911
\(960\) 0 0
\(961\) 4.11823e7 1.43847
\(962\) 3.44458e6 0.120005
\(963\) 4.60736e6 0.160098
\(964\) 3.99848e6 0.138581
\(965\) 0 0
\(966\) −6.02936e7 −2.07887
\(967\) −1.78136e7 −0.612611 −0.306306 0.951933i \(-0.599093\pi\)
−0.306306 + 0.951933i \(0.599093\pi\)
\(968\) 2.95016e6 0.101195
\(969\) 3.95203e7 1.35211
\(970\) 0 0
\(971\) 3.06231e7 1.04232 0.521160 0.853459i \(-0.325500\pi\)
0.521160 + 0.853459i \(0.325500\pi\)
\(972\) −2.67180e7 −0.907065
\(973\) 3.65529e6 0.123777
\(974\) −7.56691e7 −2.55577
\(975\) 0 0
\(976\) 2.07429e7 0.697021
\(977\) 1.93935e7 0.650011 0.325005 0.945712i \(-0.394634\pi\)
0.325005 + 0.945712i \(0.394634\pi\)
\(978\) −5.17536e7 −1.73019
\(979\) 4.77721e6 0.159301
\(980\) 0 0
\(981\) 1.72550e6 0.0572455
\(982\) −8.49685e7 −2.81177
\(983\) −3.41089e7 −1.12586 −0.562929 0.826505i \(-0.690325\pi\)
−0.562929 + 0.826505i \(0.690325\pi\)
\(984\) 739609. 0.0243509
\(985\) 0 0
\(986\) 1.08104e7 0.354120
\(987\) 1.56969e7 0.512886
\(988\) 1.94279e6 0.0633190
\(989\) −5.51162e6 −0.179179
\(990\) 0 0
\(991\) −1.15321e7 −0.373013 −0.186507 0.982454i \(-0.559717\pi\)
−0.186507 + 0.982454i \(0.559717\pi\)
\(992\) 6.91017e7 2.22951
\(993\) 2.34014e7 0.753128
\(994\) −1.02135e8 −3.27875
\(995\) 0 0
\(996\) −2.94547e6 −0.0940819
\(997\) −3.45745e7 −1.10159 −0.550793 0.834642i \(-0.685675\pi\)
−0.550793 + 0.834642i \(0.685675\pi\)
\(998\) 4.65337e7 1.47891
\(999\) −6.01081e7 −1.90554
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 1075.6.a.a.1.7 8
5.4 even 2 43.6.a.a.1.2 8
15.14 odd 2 387.6.a.c.1.7 8
20.19 odd 2 688.6.a.e.1.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.a.a.1.2 8 5.4 even 2
387.6.a.c.1.7 8 15.14 odd 2
688.6.a.e.1.2 8 20.19 odd 2
1075.6.a.a.1.7 8 1.1 even 1 trivial