Properties

Label 29.6.a.b.1.3
Level $29$
Weight $6$
Character 29.1
Self dual yes
Analytic conductor $4.651$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.65113077458\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \( x^{7} - 3x^{6} - 184x^{5} + 584x^{4} + 10145x^{3} - 34491x^{2} - 149754x + 524902 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(4.90786\) of defining polynomial
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.90786 q^{2} +29.3989 q^{3} -16.7287 q^{4} +64.0801 q^{5} -114.887 q^{6} -138.793 q^{7} +190.425 q^{8} +621.298 q^{9} +O(q^{10})\) \(q-3.90786 q^{2} +29.3989 q^{3} -16.7287 q^{4} +64.0801 q^{5} -114.887 q^{6} -138.793 q^{7} +190.425 q^{8} +621.298 q^{9} -250.416 q^{10} +557.286 q^{11} -491.805 q^{12} -41.1854 q^{13} +542.382 q^{14} +1883.89 q^{15} -208.835 q^{16} -1643.99 q^{17} -2427.94 q^{18} +258.134 q^{19} -1071.97 q^{20} -4080.36 q^{21} -2177.79 q^{22} -2828.17 q^{23} +5598.28 q^{24} +981.257 q^{25} +160.946 q^{26} +11121.6 q^{27} +2321.82 q^{28} +841.000 q^{29} -7361.96 q^{30} -5980.62 q^{31} -5277.49 q^{32} +16383.6 q^{33} +6424.48 q^{34} -8893.86 q^{35} -10393.5 q^{36} -3327.01 q^{37} -1008.75 q^{38} -1210.81 q^{39} +12202.4 q^{40} -3895.80 q^{41} +15945.5 q^{42} -3589.20 q^{43} -9322.64 q^{44} +39812.8 q^{45} +11052.1 q^{46} -7502.91 q^{47} -6139.52 q^{48} +2456.45 q^{49} -3834.61 q^{50} -48331.6 q^{51} +688.976 q^{52} +9015.58 q^{53} -43461.5 q^{54} +35710.9 q^{55} -26429.6 q^{56} +7588.86 q^{57} -3286.51 q^{58} +39101.0 q^{59} -31514.9 q^{60} +3951.11 q^{61} +23371.4 q^{62} -86231.7 q^{63} +27306.4 q^{64} -2639.16 q^{65} -64024.8 q^{66} +62985.3 q^{67} +27501.8 q^{68} -83145.1 q^{69} +34755.9 q^{70} +7121.60 q^{71} +118310. q^{72} -13910.9 q^{73} +13001.5 q^{74} +28847.9 q^{75} -4318.23 q^{76} -77347.2 q^{77} +4731.66 q^{78} -37581.7 q^{79} -13382.1 q^{80} +175987. q^{81} +15224.2 q^{82} -74905.7 q^{83} +68259.0 q^{84} -105347. q^{85} +14026.1 q^{86} +24724.5 q^{87} +106121. q^{88} +102613. q^{89} -155583. q^{90} +5716.23 q^{91} +47311.5 q^{92} -175824. q^{93} +29320.3 q^{94} +16541.2 q^{95} -155153. q^{96} -25501.5 q^{97} -9599.44 q^{98} +346241. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9} + 922 q^{10} + 1106 q^{11} + 214 q^{12} + 408 q^{13} - 2008 q^{14} - 614 q^{15} + 242 q^{16} - 874 q^{17} - 5598 q^{18} + 4288 q^{19} - 6350 q^{20} - 4200 q^{21} - 6114 q^{22} - 4532 q^{23} - 4318 q^{24} + 5527 q^{25} - 19806 q^{26} + 5942 q^{27} - 496 q^{28} + 5887 q^{29} - 16734 q^{30} + 7794 q^{31} + 7898 q^{32} + 34410 q^{33} + 20840 q^{34} + 7088 q^{35} - 572 q^{36} + 5086 q^{37} + 23732 q^{38} + 33394 q^{39} + 22906 q^{40} + 19826 q^{41} - 55440 q^{42} + 19498 q^{43} - 6074 q^{44} + 7854 q^{45} - 12404 q^{46} + 14278 q^{47} - 16406 q^{48} + 38431 q^{49} - 41066 q^{50} + 23892 q^{51} - 34302 q^{52} - 58644 q^{53} - 31194 q^{54} - 25574 q^{55} - 79560 q^{56} - 88540 q^{57} + 3364 q^{58} + 12888 q^{59} - 180822 q^{60} + 102866 q^{61} - 42654 q^{62} - 88632 q^{63} - 10170 q^{64} - 149206 q^{65} + 7710 q^{66} + 102996 q^{67} + 85100 q^{68} - 107244 q^{69} + 349480 q^{70} - 51596 q^{71} + 135568 q^{72} - 17566 q^{73} + 12132 q^{74} + 39356 q^{75} + 360740 q^{76} - 94104 q^{77} + 46386 q^{78} + 212058 q^{79} + 142510 q^{80} - 128285 q^{81} + 201924 q^{82} - 122928 q^{83} - 12328 q^{84} - 109336 q^{85} - 63290 q^{86} + 21866 q^{87} + 136666 q^{88} - 66510 q^{89} + 56084 q^{90} + 194368 q^{91} - 110108 q^{92} - 474274 q^{93} + 438926 q^{94} - 131676 q^{95} - 117018 q^{96} - 118182 q^{97} - 29132 q^{98} + 300668 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.90786 −0.690818 −0.345409 0.938452i \(-0.612260\pi\)
−0.345409 + 0.938452i \(0.612260\pi\)
\(3\) 29.3989 1.88594 0.942972 0.332873i \(-0.108018\pi\)
0.942972 + 0.332873i \(0.108018\pi\)
\(4\) −16.7287 −0.522771
\(5\) 64.0801 1.14630 0.573150 0.819451i \(-0.305721\pi\)
0.573150 + 0.819451i \(0.305721\pi\)
\(6\) −114.887 −1.30284
\(7\) −138.793 −1.07059 −0.535293 0.844666i \(-0.679799\pi\)
−0.535293 + 0.844666i \(0.679799\pi\)
\(8\) 190.425 1.05196
\(9\) 621.298 2.55678
\(10\) −250.416 −0.791884
\(11\) 557.286 1.38866 0.694330 0.719656i \(-0.255701\pi\)
0.694330 + 0.719656i \(0.255701\pi\)
\(12\) −491.805 −0.985916
\(13\) −41.1854 −0.0675903 −0.0337952 0.999429i \(-0.510759\pi\)
−0.0337952 + 0.999429i \(0.510759\pi\)
\(14\) 542.382 0.739580
\(15\) 1883.89 2.16186
\(16\) −208.835 −0.203940
\(17\) −1643.99 −1.37968 −0.689838 0.723964i \(-0.742318\pi\)
−0.689838 + 0.723964i \(0.742318\pi\)
\(18\) −2427.94 −1.76627
\(19\) 258.134 0.164044 0.0820221 0.996631i \(-0.473862\pi\)
0.0820221 + 0.996631i \(0.473862\pi\)
\(20\) −1071.97 −0.599252
\(21\) −4080.36 −2.01907
\(22\) −2177.79 −0.959311
\(23\) −2828.17 −1.11477 −0.557385 0.830254i \(-0.688195\pi\)
−0.557385 + 0.830254i \(0.688195\pi\)
\(24\) 5598.28 1.98393
\(25\) 981.257 0.314002
\(26\) 160.946 0.0466926
\(27\) 11121.6 2.93600
\(28\) 2321.82 0.559671
\(29\) 841.000 0.185695
\(30\) −7361.96 −1.49345
\(31\) −5980.62 −1.11774 −0.558872 0.829254i \(-0.688766\pi\)
−0.558872 + 0.829254i \(0.688766\pi\)
\(32\) −5277.49 −0.911072
\(33\) 16383.6 2.61894
\(34\) 6424.48 0.953105
\(35\) −8893.86 −1.22721
\(36\) −10393.5 −1.33661
\(37\) −3327.01 −0.399531 −0.199765 0.979844i \(-0.564018\pi\)
−0.199765 + 0.979844i \(0.564018\pi\)
\(38\) −1008.75 −0.113325
\(39\) −1210.81 −0.127472
\(40\) 12202.4 1.20586
\(41\) −3895.80 −0.361940 −0.180970 0.983489i \(-0.557924\pi\)
−0.180970 + 0.983489i \(0.557924\pi\)
\(42\) 15945.5 1.39481
\(43\) −3589.20 −0.296023 −0.148012 0.988986i \(-0.547287\pi\)
−0.148012 + 0.988986i \(0.547287\pi\)
\(44\) −9322.64 −0.725951
\(45\) 39812.8 2.93084
\(46\) 11052.1 0.770103
\(47\) −7502.91 −0.495433 −0.247717 0.968833i \(-0.579680\pi\)
−0.247717 + 0.968833i \(0.579680\pi\)
\(48\) −6139.52 −0.384619
\(49\) 2456.45 0.146156
\(50\) −3834.61 −0.216918
\(51\) −48331.6 −2.60199
\(52\) 688.976 0.0353342
\(53\) 9015.58 0.440863 0.220432 0.975402i \(-0.429253\pi\)
0.220432 + 0.975402i \(0.429253\pi\)
\(54\) −43461.5 −2.02824
\(55\) 35710.9 1.59182
\(56\) −26429.6 −1.12621
\(57\) 7588.86 0.309378
\(58\) −3286.51 −0.128282
\(59\) 39101.0 1.46237 0.731187 0.682177i \(-0.238967\pi\)
0.731187 + 0.682177i \(0.238967\pi\)
\(60\) −31514.9 −1.13015
\(61\) 3951.11 0.135955 0.0679773 0.997687i \(-0.478345\pi\)
0.0679773 + 0.997687i \(0.478345\pi\)
\(62\) 23371.4 0.772157
\(63\) −86231.7 −2.73726
\(64\) 27306.4 0.833325
\(65\) −2639.16 −0.0774787
\(66\) −64024.8 −1.80921
\(67\) 62985.3 1.71416 0.857082 0.515180i \(-0.172275\pi\)
0.857082 + 0.515180i \(0.172275\pi\)
\(68\) 27501.8 0.721254
\(69\) −83145.1 −2.10239
\(70\) 34755.9 0.847781
\(71\) 7121.60 0.167661 0.0838304 0.996480i \(-0.473285\pi\)
0.0838304 + 0.996480i \(0.473285\pi\)
\(72\) 118310. 2.68963
\(73\) −13910.9 −0.305525 −0.152763 0.988263i \(-0.548817\pi\)
−0.152763 + 0.988263i \(0.548817\pi\)
\(74\) 13001.5 0.276003
\(75\) 28847.9 0.592190
\(76\) −4318.23 −0.0857575
\(77\) −77347.2 −1.48668
\(78\) 4731.66 0.0880596
\(79\) −37581.7 −0.677499 −0.338749 0.940877i \(-0.610004\pi\)
−0.338749 + 0.940877i \(0.610004\pi\)
\(80\) −13382.1 −0.233776
\(81\) 175987. 2.98035
\(82\) 15224.2 0.250035
\(83\) −74905.7 −1.19349 −0.596746 0.802430i \(-0.703540\pi\)
−0.596746 + 0.802430i \(0.703540\pi\)
\(84\) 68259.0 1.05551
\(85\) −105347. −1.58152
\(86\) 14026.1 0.204498
\(87\) 24724.5 0.350211
\(88\) 106121. 1.46081
\(89\) 102613. 1.37318 0.686590 0.727045i \(-0.259107\pi\)
0.686590 + 0.727045i \(0.259107\pi\)
\(90\) −155583. −2.02468
\(91\) 5716.23 0.0723613
\(92\) 47311.5 0.582769
\(93\) −175824. −2.10800
\(94\) 29320.3 0.342254
\(95\) 16541.2 0.188044
\(96\) −155153. −1.71823
\(97\) −25501.5 −0.275193 −0.137596 0.990488i \(-0.543938\pi\)
−0.137596 + 0.990488i \(0.543938\pi\)
\(98\) −9599.44 −0.100967
\(99\) 346241. 3.55050
\(100\) −16415.1 −0.164151
\(101\) −29590.5 −0.288635 −0.144317 0.989531i \(-0.546099\pi\)
−0.144317 + 0.989531i \(0.546099\pi\)
\(102\) 188873. 1.79750
\(103\) 170152. 1.58032 0.790159 0.612902i \(-0.209998\pi\)
0.790159 + 0.612902i \(0.209998\pi\)
\(104\) −7842.71 −0.0711021
\(105\) −261470. −2.31445
\(106\) −35231.6 −0.304556
\(107\) −200423. −1.69234 −0.846169 0.532915i \(-0.821097\pi\)
−0.846169 + 0.532915i \(0.821097\pi\)
\(108\) −186049. −1.53486
\(109\) −80642.9 −0.650130 −0.325065 0.945692i \(-0.605386\pi\)
−0.325065 + 0.945692i \(0.605386\pi\)
\(110\) −139553. −1.09966
\(111\) −97810.6 −0.753492
\(112\) 28984.7 0.218336
\(113\) 17299.3 0.127448 0.0637240 0.997968i \(-0.479702\pi\)
0.0637240 + 0.997968i \(0.479702\pi\)
\(114\) −29656.2 −0.213724
\(115\) −181229. −1.27786
\(116\) −14068.8 −0.0970761
\(117\) −25588.4 −0.172814
\(118\) −152801. −1.01023
\(119\) 228174. 1.47706
\(120\) 358738. 2.27418
\(121\) 149516. 0.928378
\(122\) −15440.4 −0.0939199
\(123\) −114532. −0.682599
\(124\) 100048. 0.584323
\(125\) −137371. −0.786359
\(126\) 336981. 1.89095
\(127\) 191838. 1.05542 0.527711 0.849424i \(-0.323051\pi\)
0.527711 + 0.849424i \(0.323051\pi\)
\(128\) 62170.3 0.335396
\(129\) −105519. −0.558283
\(130\) 10313.5 0.0535237
\(131\) 112493. 0.572726 0.286363 0.958121i \(-0.407554\pi\)
0.286363 + 0.958121i \(0.407554\pi\)
\(132\) −274076. −1.36910
\(133\) −35827.1 −0.175623
\(134\) −246138. −1.18417
\(135\) 712671. 3.36554
\(136\) −313056. −1.45136
\(137\) −13514.2 −0.0615162 −0.0307581 0.999527i \(-0.509792\pi\)
−0.0307581 + 0.999527i \(0.509792\pi\)
\(138\) 324919. 1.45237
\(139\) 315337. 1.38432 0.692161 0.721743i \(-0.256659\pi\)
0.692161 + 0.721743i \(0.256659\pi\)
\(140\) 148782. 0.641551
\(141\) −220578. −0.934359
\(142\) −27830.2 −0.115823
\(143\) −22952.0 −0.0938600
\(144\) −129749. −0.521430
\(145\) 53891.3 0.212862
\(146\) 54361.7 0.211062
\(147\) 72216.9 0.275642
\(148\) 55656.5 0.208863
\(149\) −1500.22 −0.00553590 −0.00276795 0.999996i \(-0.500881\pi\)
−0.00276795 + 0.999996i \(0.500881\pi\)
\(150\) −112734. −0.409096
\(151\) −141060. −0.503457 −0.251729 0.967798i \(-0.580999\pi\)
−0.251729 + 0.967798i \(0.580999\pi\)
\(152\) 49155.0 0.172567
\(153\) −1.02141e6 −3.52753
\(154\) 302262. 1.02703
\(155\) −383239. −1.28127
\(156\) 20255.2 0.0666384
\(157\) −335858. −1.08744 −0.543721 0.839266i \(-0.682985\pi\)
−0.543721 + 0.839266i \(0.682985\pi\)
\(158\) 146864. 0.468028
\(159\) 265049. 0.831443
\(160\) −338182. −1.04436
\(161\) 392529. 1.19346
\(162\) −687732. −2.05888
\(163\) 208039. 0.613303 0.306651 0.951822i \(-0.400791\pi\)
0.306651 + 0.951822i \(0.400791\pi\)
\(164\) 65171.5 0.189212
\(165\) 1.04986e6 3.00208
\(166\) 292721. 0.824486
\(167\) 235392. 0.653131 0.326565 0.945175i \(-0.394109\pi\)
0.326565 + 0.945175i \(0.394109\pi\)
\(168\) −777001. −2.12397
\(169\) −369597. −0.995432
\(170\) 411681. 1.09254
\(171\) 160378. 0.419425
\(172\) 60042.4 0.154752
\(173\) 126867. 0.322280 0.161140 0.986932i \(-0.448483\pi\)
0.161140 + 0.986932i \(0.448483\pi\)
\(174\) −96619.8 −0.241932
\(175\) −136191. −0.336167
\(176\) −116381. −0.283203
\(177\) 1.14953e6 2.75795
\(178\) −400997. −0.948617
\(179\) −582710. −1.35932 −0.679658 0.733529i \(-0.737872\pi\)
−0.679658 + 0.733529i \(0.737872\pi\)
\(180\) −666016. −1.53216
\(181\) 469745. 1.06578 0.532888 0.846186i \(-0.321107\pi\)
0.532888 + 0.846186i \(0.321107\pi\)
\(182\) −22338.2 −0.0499885
\(183\) 116158. 0.256403
\(184\) −538553. −1.17269
\(185\) −213195. −0.457982
\(186\) 687095. 1.45624
\(187\) −916172. −1.91590
\(188\) 125514. 0.258998
\(189\) −1.54359e6 −3.14325
\(190\) −64640.7 −0.129904
\(191\) 808559. 1.60372 0.801860 0.597512i \(-0.203844\pi\)
0.801860 + 0.597512i \(0.203844\pi\)
\(192\) 802779. 1.57160
\(193\) 397971. 0.769057 0.384528 0.923113i \(-0.374364\pi\)
0.384528 + 0.923113i \(0.374364\pi\)
\(194\) 99656.3 0.190108
\(195\) −77588.6 −0.146121
\(196\) −41093.1 −0.0764062
\(197\) −821639. −1.50840 −0.754198 0.656647i \(-0.771974\pi\)
−0.754198 + 0.656647i \(0.771974\pi\)
\(198\) −1.35306e6 −2.45275
\(199\) 304702. 0.545435 0.272718 0.962094i \(-0.412078\pi\)
0.272718 + 0.962094i \(0.412078\pi\)
\(200\) 186855. 0.330317
\(201\) 1.85170e6 3.23282
\(202\) 115635. 0.199394
\(203\) −116725. −0.198803
\(204\) 808523. 1.36024
\(205\) −249643. −0.414892
\(206\) −664930. −1.09171
\(207\) −1.75714e6 −2.85023
\(208\) 8600.93 0.0137844
\(209\) 143854. 0.227802
\(210\) 1.02179e6 1.59887
\(211\) 657135. 1.01613 0.508064 0.861319i \(-0.330361\pi\)
0.508064 + 0.861319i \(0.330361\pi\)
\(212\) −150819. −0.230470
\(213\) 209367. 0.316199
\(214\) 783222. 1.16910
\(215\) −229996. −0.339331
\(216\) 2.11782e6 3.08855
\(217\) 830067. 1.19664
\(218\) 315141. 0.449121
\(219\) −408965. −0.576204
\(220\) −597396. −0.832157
\(221\) 67708.4 0.0932528
\(222\) 382230. 0.520526
\(223\) −899606. −1.21141 −0.605703 0.795690i \(-0.707108\pi\)
−0.605703 + 0.795690i \(0.707108\pi\)
\(224\) 732478. 0.975381
\(225\) 609653. 0.802835
\(226\) −67603.3 −0.0880434
\(227\) 660017. 0.850139 0.425070 0.905161i \(-0.360250\pi\)
0.425070 + 0.905161i \(0.360250\pi\)
\(228\) −126951. −0.161734
\(229\) −622380. −0.784273 −0.392136 0.919907i \(-0.628264\pi\)
−0.392136 + 0.919907i \(0.628264\pi\)
\(230\) 708218. 0.882769
\(231\) −2.27393e6 −2.80380
\(232\) 160147. 0.195344
\(233\) 24182.1 0.0291813 0.0145906 0.999894i \(-0.495355\pi\)
0.0145906 + 0.999894i \(0.495355\pi\)
\(234\) 99995.7 0.119383
\(235\) −480787. −0.567915
\(236\) −654108. −0.764486
\(237\) −1.10486e6 −1.27772
\(238\) −891672. −1.02038
\(239\) 201571. 0.228262 0.114131 0.993466i \(-0.463592\pi\)
0.114131 + 0.993466i \(0.463592\pi\)
\(240\) −393421. −0.440889
\(241\) −1.01961e6 −1.13081 −0.565407 0.824812i \(-0.691281\pi\)
−0.565407 + 0.824812i \(0.691281\pi\)
\(242\) −584288. −0.641340
\(243\) 2.47129e6 2.68478
\(244\) −66096.7 −0.0710731
\(245\) 157409. 0.167539
\(246\) 447576. 0.471552
\(247\) −10631.3 −0.0110878
\(248\) −1.13886e6 −1.17582
\(249\) −2.20215e6 −2.25086
\(250\) 536827. 0.543231
\(251\) 1.41854e6 1.42121 0.710604 0.703593i \(-0.248422\pi\)
0.710604 + 0.703593i \(0.248422\pi\)
\(252\) 1.44254e6 1.43096
\(253\) −1.57610e6 −1.54804
\(254\) −749676. −0.729104
\(255\) −3.09709e6 −2.98266
\(256\) −1.11676e6 −1.06502
\(257\) −54526.1 −0.0514958 −0.0257479 0.999668i \(-0.508197\pi\)
−0.0257479 + 0.999668i \(0.508197\pi\)
\(258\) 412351. 0.385672
\(259\) 461765. 0.427732
\(260\) 44149.6 0.0405036
\(261\) 522512. 0.474783
\(262\) −439606. −0.395649
\(263\) 2.15754e6 1.92340 0.961702 0.274098i \(-0.0883792\pi\)
0.961702 + 0.274098i \(0.0883792\pi\)
\(264\) 3.11984e6 2.75501
\(265\) 577719. 0.505361
\(266\) 140007. 0.121324
\(267\) 3.01672e6 2.58974
\(268\) −1.05366e6 −0.896115
\(269\) −128043. −0.107888 −0.0539442 0.998544i \(-0.517179\pi\)
−0.0539442 + 0.998544i \(0.517179\pi\)
\(270\) −2.78502e6 −2.32497
\(271\) 691071. 0.571610 0.285805 0.958288i \(-0.407739\pi\)
0.285805 + 0.958288i \(0.407739\pi\)
\(272\) 343322. 0.281371
\(273\) 168051. 0.136469
\(274\) 52811.6 0.0424965
\(275\) 546840. 0.436042
\(276\) 1.39091e6 1.09907
\(277\) 589147. 0.461343 0.230672 0.973032i \(-0.425908\pi\)
0.230672 + 0.973032i \(0.425908\pi\)
\(278\) −1.23229e6 −0.956315
\(279\) −3.71575e6 −2.85783
\(280\) −1.69361e6 −1.29098
\(281\) −1.20853e6 −0.913044 −0.456522 0.889712i \(-0.650905\pi\)
−0.456522 + 0.889712i \(0.650905\pi\)
\(282\) 861985. 0.645472
\(283\) 1.88980e6 1.40265 0.701325 0.712842i \(-0.252592\pi\)
0.701325 + 0.712842i \(0.252592\pi\)
\(284\) −119135. −0.0876481
\(285\) 486295. 0.354640
\(286\) 89693.1 0.0648402
\(287\) 540709. 0.387489
\(288\) −3.27890e6 −2.32941
\(289\) 1.28285e6 0.903506
\(290\) −210600. −0.147049
\(291\) −749718. −0.518998
\(292\) 232710. 0.159720
\(293\) −2.43906e6 −1.65979 −0.829895 0.557920i \(-0.811600\pi\)
−0.829895 + 0.557920i \(0.811600\pi\)
\(294\) −282213. −0.190419
\(295\) 2.50560e6 1.67632
\(296\) −633545. −0.420289
\(297\) 6.19789e6 4.07711
\(298\) 5862.63 0.00382430
\(299\) 116479. 0.0753477
\(300\) −482587. −0.309580
\(301\) 498154. 0.316919
\(302\) 551243. 0.347797
\(303\) −869929. −0.544349
\(304\) −53907.2 −0.0334552
\(305\) 253187. 0.155845
\(306\) 3.99152e6 2.43688
\(307\) −842448. −0.510149 −0.255074 0.966921i \(-0.582100\pi\)
−0.255074 + 0.966921i \(0.582100\pi\)
\(308\) 1.29392e6 0.777194
\(309\) 5.00229e6 2.98039
\(310\) 1.49764e6 0.885123
\(311\) −1.78495e6 −1.04647 −0.523233 0.852190i \(-0.675274\pi\)
−0.523233 + 0.852190i \(0.675274\pi\)
\(312\) −230567. −0.134095
\(313\) 1.79477e6 1.03550 0.517749 0.855533i \(-0.326770\pi\)
0.517749 + 0.855533i \(0.326770\pi\)
\(314\) 1.31248e6 0.751225
\(315\) −5.52574e6 −3.13772
\(316\) 628691. 0.354177
\(317\) −1.00473e6 −0.561564 −0.280782 0.959772i \(-0.590594\pi\)
−0.280782 + 0.959772i \(0.590594\pi\)
\(318\) −1.03577e6 −0.574376
\(319\) 468677. 0.257868
\(320\) 1.74980e6 0.955239
\(321\) −5.89221e6 −3.19165
\(322\) −1.53395e6 −0.824463
\(323\) −424369. −0.226328
\(324\) −2.94403e6 −1.55804
\(325\) −40413.4 −0.0212235
\(326\) −812985. −0.423680
\(327\) −2.37082e6 −1.22611
\(328\) −741856. −0.380746
\(329\) 1.04135e6 0.530404
\(330\) −4.10271e6 −2.07389
\(331\) 3.52272e6 1.76729 0.883646 0.468155i \(-0.155081\pi\)
0.883646 + 0.468155i \(0.155081\pi\)
\(332\) 1.25307e6 0.623923
\(333\) −2.06707e6 −1.02151
\(334\) −919878. −0.451195
\(335\) 4.03610e6 1.96494
\(336\) 852121. 0.411768
\(337\) 2.94676e6 1.41342 0.706708 0.707506i \(-0.250180\pi\)
0.706708 + 0.707506i \(0.250180\pi\)
\(338\) 1.44433e6 0.687662
\(339\) 508582. 0.240360
\(340\) 1.76232e6 0.826773
\(341\) −3.33291e6 −1.55217
\(342\) −626734. −0.289746
\(343\) 1.99175e6 0.914114
\(344\) −683471. −0.311404
\(345\) −5.32795e6 −2.40997
\(346\) −495777. −0.222637
\(347\) −2.31985e6 −1.03428 −0.517138 0.855902i \(-0.673003\pi\)
−0.517138 + 0.855902i \(0.673003\pi\)
\(348\) −413608. −0.183080
\(349\) 1.13664e6 0.499526 0.249763 0.968307i \(-0.419647\pi\)
0.249763 + 0.968307i \(0.419647\pi\)
\(350\) 532216. 0.232230
\(351\) −458046. −0.198445
\(352\) −2.94107e6 −1.26517
\(353\) −942783. −0.402694 −0.201347 0.979520i \(-0.564532\pi\)
−0.201347 + 0.979520i \(0.564532\pi\)
\(354\) −4.49220e6 −1.90524
\(355\) 456352. 0.192189
\(356\) −1.71658e6 −0.717858
\(357\) 6.70808e6 2.78566
\(358\) 2.27715e6 0.939039
\(359\) −2.78926e6 −1.14223 −0.571113 0.820871i \(-0.693488\pi\)
−0.571113 + 0.820871i \(0.693488\pi\)
\(360\) 7.58134e6 3.08312
\(361\) −2.40947e6 −0.973090
\(362\) −1.83570e6 −0.736257
\(363\) 4.39562e6 1.75087
\(364\) −95624.9 −0.0378284
\(365\) −891410. −0.350224
\(366\) −453930. −0.177128
\(367\) −4.20179e6 −1.62843 −0.814215 0.580564i \(-0.802832\pi\)
−0.814215 + 0.580564i \(0.802832\pi\)
\(368\) 590619. 0.227346
\(369\) −2.42045e6 −0.925403
\(370\) 833136. 0.316382
\(371\) −1.25130e6 −0.471982
\(372\) 2.94130e6 1.10200
\(373\) 4.83152e6 1.79809 0.899045 0.437856i \(-0.144262\pi\)
0.899045 + 0.437856i \(0.144262\pi\)
\(374\) 3.58027e6 1.32354
\(375\) −4.03857e6 −1.48303
\(376\) −1.42874e6 −0.521174
\(377\) −34636.9 −0.0125512
\(378\) 6.03214e6 2.17141
\(379\) 2.03959e6 0.729366 0.364683 0.931132i \(-0.381177\pi\)
0.364683 + 0.931132i \(0.381177\pi\)
\(380\) −276713. −0.0983037
\(381\) 5.63984e6 1.99046
\(382\) −3.15973e6 −1.10788
\(383\) 923917. 0.321837 0.160919 0.986968i \(-0.448554\pi\)
0.160919 + 0.986968i \(0.448554\pi\)
\(384\) 1.82774e6 0.632538
\(385\) −4.95642e6 −1.70418
\(386\) −1.55521e6 −0.531278
\(387\) −2.22996e6 −0.756867
\(388\) 426606. 0.143863
\(389\) −3.39429e6 −1.13730 −0.568650 0.822580i \(-0.692534\pi\)
−0.568650 + 0.822580i \(0.692534\pi\)
\(390\) 303205. 0.100943
\(391\) 4.64948e6 1.53802
\(392\) 467768. 0.153750
\(393\) 3.30717e6 1.08013
\(394\) 3.21085e6 1.04203
\(395\) −2.40824e6 −0.776616
\(396\) −5.79214e6 −1.85610
\(397\) −1.00161e6 −0.318949 −0.159475 0.987202i \(-0.550980\pi\)
−0.159475 + 0.987202i \(0.550980\pi\)
\(398\) −1.19073e6 −0.376796
\(399\) −1.05328e6 −0.331216
\(400\) −204920. −0.0640376
\(401\) 5.53448e6 1.71876 0.859381 0.511337i \(-0.170849\pi\)
0.859381 + 0.511337i \(0.170849\pi\)
\(402\) −7.23618e6 −2.23329
\(403\) 246314. 0.0755486
\(404\) 495009. 0.150890
\(405\) 1.12773e7 3.41638
\(406\) 456144. 0.137337
\(407\) −1.85410e6 −0.554812
\(408\) −9.20353e6 −2.73718
\(409\) 1.93289e6 0.571345 0.285672 0.958327i \(-0.407783\pi\)
0.285672 + 0.958327i \(0.407783\pi\)
\(410\) 975569. 0.286615
\(411\) −397304. −0.116016
\(412\) −2.84642e6 −0.826144
\(413\) −5.42694e6 −1.56560
\(414\) 6.86663e6 1.96899
\(415\) −4.79997e6 −1.36810
\(416\) 217355. 0.0615796
\(417\) 9.27057e6 2.61075
\(418\) −562161. −0.157369
\(419\) 1.80082e6 0.501112 0.250556 0.968102i \(-0.419387\pi\)
0.250556 + 0.968102i \(0.419387\pi\)
\(420\) 4.37404e6 1.20993
\(421\) −1.32654e6 −0.364766 −0.182383 0.983228i \(-0.558381\pi\)
−0.182383 + 0.983228i \(0.558381\pi\)
\(422\) −2.56799e6 −0.701959
\(423\) −4.66154e6 −1.26671
\(424\) 1.71679e6 0.463769
\(425\) −1.61318e6 −0.433221
\(426\) −818178. −0.218436
\(427\) −548385. −0.145551
\(428\) 3.35280e6 0.884705
\(429\) −674765. −0.177015
\(430\) 898791. 0.234416
\(431\) 584408. 0.151539 0.0757693 0.997125i \(-0.475859\pi\)
0.0757693 + 0.997125i \(0.475859\pi\)
\(432\) −2.32257e6 −0.598769
\(433\) −707379. −0.181315 −0.0906573 0.995882i \(-0.528897\pi\)
−0.0906573 + 0.995882i \(0.528897\pi\)
\(434\) −3.24378e6 −0.826661
\(435\) 1.58435e6 0.401447
\(436\) 1.34905e6 0.339869
\(437\) −730045. −0.182872
\(438\) 1.59818e6 0.398052
\(439\) 5.06180e6 1.25356 0.626778 0.779198i \(-0.284373\pi\)
0.626778 + 0.779198i \(0.284373\pi\)
\(440\) 6.80023e6 1.67453
\(441\) 1.52619e6 0.373689
\(442\) −264595. −0.0644207
\(443\) −3.33111e6 −0.806453 −0.403227 0.915100i \(-0.632111\pi\)
−0.403227 + 0.915100i \(0.632111\pi\)
\(444\) 1.63624e6 0.393904
\(445\) 6.57545e6 1.57408
\(446\) 3.51553e6 0.836861
\(447\) −44104.8 −0.0104404
\(448\) −3.78993e6 −0.892146
\(449\) 37802.9 0.00884930 0.00442465 0.999990i \(-0.498592\pi\)
0.00442465 + 0.999990i \(0.498592\pi\)
\(450\) −2.38244e6 −0.554613
\(451\) −2.17107e6 −0.502612
\(452\) −289395. −0.0666261
\(453\) −4.14702e6 −0.949491
\(454\) −2.57925e6 −0.587292
\(455\) 366297. 0.0829477
\(456\) 1.44511e6 0.325452
\(457\) −7.55109e6 −1.69129 −0.845647 0.533743i \(-0.820785\pi\)
−0.845647 + 0.533743i \(0.820785\pi\)
\(458\) 2.43217e6 0.541790
\(459\) −1.82838e7 −4.05073
\(460\) 3.03172e6 0.668028
\(461\) 1.97564e6 0.432967 0.216484 0.976286i \(-0.430541\pi\)
0.216484 + 0.976286i \(0.430541\pi\)
\(462\) 8.88618e6 1.93691
\(463\) −8.35199e6 −1.81066 −0.905331 0.424707i \(-0.860377\pi\)
−0.905331 + 0.424707i \(0.860377\pi\)
\(464\) −175630. −0.0378707
\(465\) −1.12668e7 −2.41640
\(466\) −94500.2 −0.0201590
\(467\) −856159. −0.181661 −0.0908306 0.995866i \(-0.528952\pi\)
−0.0908306 + 0.995866i \(0.528952\pi\)
\(468\) 428060. 0.0903420
\(469\) −8.74191e6 −1.83516
\(470\) 1.87885e6 0.392325
\(471\) −9.87387e6 −2.05086
\(472\) 7.44580e6 1.53835
\(473\) −2.00021e6 −0.411076
\(474\) 4.31764e6 0.882675
\(475\) 253296. 0.0515102
\(476\) −3.81705e6 −0.772165
\(477\) 5.60136e6 1.12719
\(478\) −787709. −0.157687
\(479\) 3.97374e6 0.791336 0.395668 0.918394i \(-0.370513\pi\)
0.395668 + 0.918394i \(0.370513\pi\)
\(480\) −9.94220e6 −1.96961
\(481\) 137024. 0.0270044
\(482\) 3.98449e6 0.781186
\(483\) 1.15399e7 2.25080
\(484\) −2.50121e6 −0.485329
\(485\) −1.63414e6 −0.315453
\(486\) −9.65745e6 −1.85469
\(487\) 2.73024e6 0.521649 0.260824 0.965386i \(-0.416006\pi\)
0.260824 + 0.965386i \(0.416006\pi\)
\(488\) 752388. 0.143018
\(489\) 6.11611e6 1.15665
\(490\) −615133. −0.115739
\(491\) 2.52027e6 0.471785 0.235892 0.971779i \(-0.424199\pi\)
0.235892 + 0.971779i \(0.424199\pi\)
\(492\) 1.91597e6 0.356843
\(493\) −1.38260e6 −0.256199
\(494\) 41545.7 0.00765965
\(495\) 2.21871e7 4.06994
\(496\) 1.24896e6 0.227953
\(497\) −988426. −0.179495
\(498\) 8.60568e6 1.55493
\(499\) 8.63079e6 1.55167 0.775834 0.630937i \(-0.217329\pi\)
0.775834 + 0.630937i \(0.217329\pi\)
\(500\) 2.29804e6 0.411085
\(501\) 6.92027e6 1.23177
\(502\) −5.54345e6 −0.981795
\(503\) −8.02315e6 −1.41392 −0.706960 0.707254i \(-0.749934\pi\)
−0.706960 + 0.707254i \(0.749934\pi\)
\(504\) −1.64206e7 −2.87948
\(505\) −1.89616e6 −0.330862
\(506\) 6.15916e6 1.06941
\(507\) −1.08658e7 −1.87733
\(508\) −3.20920e6 −0.551743
\(509\) 5.81312e6 0.994523 0.497261 0.867601i \(-0.334339\pi\)
0.497261 + 0.867601i \(0.334339\pi\)
\(510\) 1.21030e7 2.06048
\(511\) 1.93073e6 0.327092
\(512\) 2.37467e6 0.400340
\(513\) 2.87085e6 0.481634
\(514\) 213080. 0.0355742
\(515\) 1.09034e7 1.81152
\(516\) 1.76518e6 0.291854
\(517\) −4.18126e6 −0.687988
\(518\) −1.80451e6 −0.295485
\(519\) 3.72975e6 0.607801
\(520\) −502561. −0.0815043
\(521\) 381523. 0.0615781 0.0307891 0.999526i \(-0.490198\pi\)
0.0307891 + 0.999526i \(0.490198\pi\)
\(522\) −2.04190e6 −0.327988
\(523\) 1.85496e6 0.296538 0.148269 0.988947i \(-0.452630\pi\)
0.148269 + 0.988947i \(0.452630\pi\)
\(524\) −1.88186e6 −0.299404
\(525\) −4.00388e6 −0.633991
\(526\) −8.43137e6 −1.32872
\(527\) 9.83209e6 1.54212
\(528\) −3.42146e6 −0.534106
\(529\) 1.56219e6 0.242713
\(530\) −2.25764e6 −0.349113
\(531\) 2.42934e7 3.73897
\(532\) 599340. 0.0918108
\(533\) 160450. 0.0244637
\(534\) −1.17889e7 −1.78904
\(535\) −1.28431e7 −1.93993
\(536\) 1.19940e7 1.80323
\(537\) −1.71311e7 −2.56359
\(538\) 500373. 0.0745312
\(539\) 1.36894e6 0.202961
\(540\) −1.19220e7 −1.75941
\(541\) −4.92237e6 −0.723071 −0.361535 0.932358i \(-0.617747\pi\)
−0.361535 + 0.932358i \(0.617747\pi\)
\(542\) −2.70061e6 −0.394878
\(543\) 1.38100e7 2.00999
\(544\) 8.67615e6 1.25698
\(545\) −5.16760e6 −0.745243
\(546\) −656720. −0.0942755
\(547\) −1.35722e6 −0.193947 −0.0969735 0.995287i \(-0.530916\pi\)
−0.0969735 + 0.995287i \(0.530916\pi\)
\(548\) 226075. 0.0321589
\(549\) 2.45481e6 0.347607
\(550\) −2.13697e6 −0.301226
\(551\) 217090. 0.0304622
\(552\) −1.58329e7 −2.21163
\(553\) 5.21607e6 0.725321
\(554\) −2.30230e6 −0.318704
\(555\) −6.26771e6 −0.863727
\(556\) −5.27516e6 −0.723684
\(557\) −629428. −0.0859623 −0.0429811 0.999076i \(-0.513686\pi\)
−0.0429811 + 0.999076i \(0.513686\pi\)
\(558\) 1.45206e7 1.97424
\(559\) 147822. 0.0200083
\(560\) 1.85734e6 0.250278
\(561\) −2.69345e7 −3.61328
\(562\) 4.72276e6 0.630747
\(563\) −706922. −0.0939941 −0.0469971 0.998895i \(-0.514965\pi\)
−0.0469971 + 0.998895i \(0.514965\pi\)
\(564\) 3.68997e6 0.488455
\(565\) 1.10854e6 0.146094
\(566\) −7.38506e6 −0.968975
\(567\) −2.44257e7 −3.19073
\(568\) 1.35613e6 0.176372
\(569\) 1.26921e7 1.64343 0.821716 0.569898i \(-0.193017\pi\)
0.821716 + 0.569898i \(0.193017\pi\)
\(570\) −1.90037e6 −0.244991
\(571\) −8.06713e6 −1.03545 −0.517725 0.855547i \(-0.673221\pi\)
−0.517725 + 0.855547i \(0.673221\pi\)
\(572\) 383956. 0.0490673
\(573\) 2.37708e7 3.02452
\(574\) −2.11301e6 −0.267684
\(575\) −2.77516e6 −0.350040
\(576\) 1.69654e7 2.13063
\(577\) 5.23139e6 0.654150 0.327075 0.944998i \(-0.393937\pi\)
0.327075 + 0.944998i \(0.393937\pi\)
\(578\) −5.01319e6 −0.624158
\(579\) 1.16999e7 1.45040
\(580\) −901530. −0.111278
\(581\) 1.03964e7 1.27774
\(582\) 2.92979e6 0.358533
\(583\) 5.02425e6 0.612209
\(584\) −2.64897e6 −0.321400
\(585\) −1.63971e6 −0.198096
\(586\) 9.53149e6 1.14661
\(587\) −1.22738e7 −1.47022 −0.735111 0.677947i \(-0.762870\pi\)
−0.735111 + 0.677947i \(0.762870\pi\)
\(588\) −1.20809e6 −0.144098
\(589\) −1.54380e6 −0.183359
\(590\) −9.79152e6 −1.15803
\(591\) −2.41553e7 −2.84475
\(592\) 694795. 0.0814803
\(593\) −1.56297e7 −1.82521 −0.912607 0.408838i \(-0.865934\pi\)
−0.912607 + 0.408838i \(0.865934\pi\)
\(594\) −2.42205e7 −2.81654
\(595\) 1.46214e7 1.69316
\(596\) 25096.6 0.00289401
\(597\) 8.95793e6 1.02866
\(598\) −455184. −0.0520515
\(599\) −909739. −0.103598 −0.0517988 0.998658i \(-0.516495\pi\)
−0.0517988 + 0.998658i \(0.516495\pi\)
\(600\) 5.49335e6 0.622959
\(601\) −1.28807e7 −1.45463 −0.727315 0.686303i \(-0.759232\pi\)
−0.727315 + 0.686303i \(0.759232\pi\)
\(602\) −1.94672e6 −0.218933
\(603\) 3.91327e7 4.38274
\(604\) 2.35975e6 0.263193
\(605\) 9.58101e6 1.06420
\(606\) 3.39956e6 0.376046
\(607\) 1.39560e7 1.53741 0.768706 0.639602i \(-0.220901\pi\)
0.768706 + 0.639602i \(0.220901\pi\)
\(608\) −1.36230e6 −0.149456
\(609\) −3.43159e6 −0.374931
\(610\) −989419. −0.107660
\(611\) 309010. 0.0334865
\(612\) 1.70868e7 1.84409
\(613\) −4.77628e6 −0.513380 −0.256690 0.966494i \(-0.582632\pi\)
−0.256690 + 0.966494i \(0.582632\pi\)
\(614\) 3.29216e6 0.352420
\(615\) −7.33925e6 −0.782463
\(616\) −1.47288e7 −1.56393
\(617\) −5.08319e6 −0.537556 −0.268778 0.963202i \(-0.586620\pi\)
−0.268778 + 0.963202i \(0.586620\pi\)
\(618\) −1.95482e7 −2.05891
\(619\) 2.45717e6 0.257755 0.128878 0.991660i \(-0.458863\pi\)
0.128878 + 0.991660i \(0.458863\pi\)
\(620\) 6.41107e6 0.669810
\(621\) −3.14537e7 −3.27297
\(622\) 6.97533e6 0.722917
\(623\) −1.42420e7 −1.47011
\(624\) 252858. 0.0259965
\(625\) −1.18692e7 −1.21540
\(626\) −7.01372e6 −0.715340
\(627\) 4.22916e6 0.429621
\(628\) 5.61845e6 0.568483
\(629\) 5.46958e6 0.551223
\(630\) 2.15938e7 2.16759
\(631\) −1.11683e7 −1.11664 −0.558322 0.829624i \(-0.688555\pi\)
−0.558322 + 0.829624i \(0.688555\pi\)
\(632\) −7.15648e6 −0.712700
\(633\) 1.93191e7 1.91636
\(634\) 3.92632e6 0.387938
\(635\) 1.22930e7 1.20983
\(636\) −4.43391e6 −0.434654
\(637\) −101170. −0.00987874
\(638\) −1.83152e6 −0.178140
\(639\) 4.42463e6 0.428672
\(640\) 3.98388e6 0.384465
\(641\) −9.24222e6 −0.888446 −0.444223 0.895916i \(-0.646520\pi\)
−0.444223 + 0.895916i \(0.646520\pi\)
\(642\) 2.30259e7 2.20485
\(643\) 1.65662e6 0.158014 0.0790069 0.996874i \(-0.474825\pi\)
0.0790069 + 0.996874i \(0.474825\pi\)
\(644\) −6.56649e6 −0.623905
\(645\) −6.76164e6 −0.639960
\(646\) 1.65837e6 0.156351
\(647\) −1.26223e6 −0.118544 −0.0592720 0.998242i \(-0.518878\pi\)
−0.0592720 + 0.998242i \(0.518878\pi\)
\(648\) 3.35122e7 3.13521
\(649\) 2.17904e7 2.03074
\(650\) 157930. 0.0146616
\(651\) 2.44031e7 2.25680
\(652\) −3.48021e6 −0.320617
\(653\) 1.64066e7 1.50569 0.752843 0.658200i \(-0.228682\pi\)
0.752843 + 0.658200i \(0.228682\pi\)
\(654\) 9.26481e6 0.847017
\(655\) 7.20855e6 0.656515
\(656\) 813578. 0.0738141
\(657\) −8.64280e6 −0.781162
\(658\) −4.06944e6 −0.366413
\(659\) −2.46135e6 −0.220780 −0.110390 0.993888i \(-0.535210\pi\)
−0.110390 + 0.993888i \(0.535210\pi\)
\(660\) −1.75628e7 −1.56940
\(661\) −1.29962e7 −1.15694 −0.578471 0.815703i \(-0.696350\pi\)
−0.578471 + 0.815703i \(0.696350\pi\)
\(662\) −1.37663e7 −1.22088
\(663\) 1.99055e6 0.175869
\(664\) −1.42639e7 −1.25550
\(665\) −2.29580e6 −0.201317
\(666\) 8.07780e6 0.705679
\(667\) −2.37849e6 −0.207008
\(668\) −3.93779e6 −0.341438
\(669\) −2.64475e7 −2.28464
\(670\) −1.57725e7 −1.35742
\(671\) 2.20189e6 0.188795
\(672\) 2.15341e7 1.83951
\(673\) −1.00711e7 −0.857119 −0.428559 0.903514i \(-0.640979\pi\)
−0.428559 + 0.903514i \(0.640979\pi\)
\(674\) −1.15155e7 −0.976413
\(675\) 1.09131e7 0.921912
\(676\) 6.18286e6 0.520382
\(677\) 9.82242e6 0.823658 0.411829 0.911261i \(-0.364890\pi\)
0.411829 + 0.911261i \(0.364890\pi\)
\(678\) −1.98747e6 −0.166045
\(679\) 3.53943e6 0.294618
\(680\) −2.00607e7 −1.66369
\(681\) 1.94038e7 1.60331
\(682\) 1.30245e7 1.07226
\(683\) −1.66547e7 −1.36611 −0.683053 0.730369i \(-0.739348\pi\)
−0.683053 + 0.730369i \(0.739348\pi\)
\(684\) −2.68291e6 −0.219263
\(685\) −865992. −0.0705160
\(686\) −7.78349e6 −0.631486
\(687\) −1.82973e7 −1.47909
\(688\) 749548. 0.0603710
\(689\) −371310. −0.0297981
\(690\) 2.08209e7 1.66485
\(691\) 6.35915e6 0.506645 0.253323 0.967382i \(-0.418477\pi\)
0.253323 + 0.967382i \(0.418477\pi\)
\(692\) −2.12231e6 −0.168478
\(693\) −4.80557e7 −3.80112
\(694\) 9.06565e6 0.714497
\(695\) 2.02068e7 1.58685
\(696\) 4.70816e6 0.368407
\(697\) 6.40466e6 0.499360
\(698\) −4.44181e6 −0.345081
\(699\) 710929. 0.0550342
\(700\) 2.27830e6 0.175738
\(701\) −167796. −0.0128969 −0.00644846 0.999979i \(-0.502053\pi\)
−0.00644846 + 0.999979i \(0.502053\pi\)
\(702\) 1.78998e6 0.137090
\(703\) −858814. −0.0655406
\(704\) 1.52175e7 1.15721
\(705\) −1.41346e7 −1.07105
\(706\) 3.68426e6 0.278188
\(707\) 4.10695e6 0.309009
\(708\) −1.92301e7 −1.44178
\(709\) −2.01558e7 −1.50586 −0.752932 0.658099i \(-0.771361\pi\)
−0.752932 + 0.658099i \(0.771361\pi\)
\(710\) −1.78336e6 −0.132768
\(711\) −2.33494e7 −1.73222
\(712\) 1.95400e7 1.44453
\(713\) 1.69142e7 1.24603
\(714\) −2.62142e7 −1.92438
\(715\) −1.47077e6 −0.107592
\(716\) 9.74797e6 0.710610
\(717\) 5.92597e6 0.430488
\(718\) 1.09000e7 0.789071
\(719\) −1.06393e7 −0.767523 −0.383761 0.923432i \(-0.625372\pi\)
−0.383761 + 0.923432i \(0.625372\pi\)
\(720\) −8.31430e6 −0.597715
\(721\) −2.36159e7 −1.69187
\(722\) 9.41585e6 0.672228
\(723\) −2.99754e7 −2.13265
\(724\) −7.85821e6 −0.557157
\(725\) 825237. 0.0583087
\(726\) −1.71774e7 −1.20953
\(727\) 1.07639e7 0.755323 0.377661 0.925944i \(-0.376728\pi\)
0.377661 + 0.925944i \(0.376728\pi\)
\(728\) 1.08851e6 0.0761210
\(729\) 2.98885e7 2.08298
\(730\) 3.48350e6 0.241941
\(731\) 5.90060e6 0.408416
\(732\) −1.94317e6 −0.134040
\(733\) 8.86456e6 0.609393 0.304696 0.952450i \(-0.401445\pi\)
0.304696 + 0.952450i \(0.401445\pi\)
\(734\) 1.64200e7 1.12495
\(735\) 4.62767e6 0.315968
\(736\) 1.49256e7 1.01564
\(737\) 3.51008e7 2.38039
\(738\) 9.45878e6 0.639285
\(739\) 1.34276e7 0.904457 0.452229 0.891902i \(-0.350629\pi\)
0.452229 + 0.891902i \(0.350629\pi\)
\(740\) 3.56647e6 0.239419
\(741\) −312550. −0.0209110
\(742\) 4.88989e6 0.326054
\(743\) −3.76228e6 −0.250023 −0.125011 0.992155i \(-0.539897\pi\)
−0.125011 + 0.992155i \(0.539897\pi\)
\(744\) −3.34812e7 −2.21753
\(745\) −96134.1 −0.00634580
\(746\) −1.88809e7 −1.24215
\(747\) −4.65388e7 −3.05150
\(748\) 1.53263e7 1.00158
\(749\) 2.78172e7 1.81179
\(750\) 1.57821e7 1.02450
\(751\) 1.97179e7 1.27574 0.637870 0.770144i \(-0.279816\pi\)
0.637870 + 0.770144i \(0.279816\pi\)
\(752\) 1.56687e6 0.101039
\(753\) 4.17036e7 2.68032
\(754\) 135356. 0.00867060
\(755\) −9.03915e6 −0.577112
\(756\) 2.58223e7 1.64320
\(757\) −1.91175e7 −1.21253 −0.606264 0.795264i \(-0.707332\pi\)
−0.606264 + 0.795264i \(0.707332\pi\)
\(758\) −7.97043e6 −0.503859
\(759\) −4.63356e7 −2.91951
\(760\) 3.14986e6 0.197814
\(761\) −4.51417e6 −0.282563 −0.141282 0.989969i \(-0.545122\pi\)
−0.141282 + 0.989969i \(0.545122\pi\)
\(762\) −2.20397e7 −1.37505
\(763\) 1.11927e7 0.696020
\(764\) −1.35261e7 −0.838378
\(765\) −6.54519e7 −4.04361
\(766\) −3.61054e6 −0.222331
\(767\) −1.61039e6 −0.0988423
\(768\) −3.28315e7 −2.00857
\(769\) 2.08251e7 1.26990 0.634952 0.772551i \(-0.281020\pi\)
0.634952 + 0.772551i \(0.281020\pi\)
\(770\) 1.93690e7 1.17728
\(771\) −1.60301e6 −0.0971182
\(772\) −6.65753e6 −0.402040
\(773\) −1.68649e7 −1.01516 −0.507581 0.861604i \(-0.669460\pi\)
−0.507581 + 0.861604i \(0.669460\pi\)
\(774\) 8.71436e6 0.522857
\(775\) −5.86853e6 −0.350974
\(776\) −4.85612e6 −0.289491
\(777\) 1.35754e7 0.806679
\(778\) 1.32644e7 0.785667
\(779\) −1.00564e6 −0.0593742
\(780\) 1.29795e6 0.0763875
\(781\) 3.96876e6 0.232824
\(782\) −1.81695e7 −1.06249
\(783\) 9.35324e6 0.545202
\(784\) −512991. −0.0298071
\(785\) −2.15218e7 −1.24654
\(786\) −1.29240e7 −0.746172
\(787\) −532946. −0.0306723 −0.0153361 0.999882i \(-0.504882\pi\)
−0.0153361 + 0.999882i \(0.504882\pi\)
\(788\) 1.37449e7 0.788546
\(789\) 6.34295e7 3.62743
\(790\) 9.41104e6 0.536500
\(791\) −2.40102e6 −0.136444
\(792\) 6.59327e7 3.73498
\(793\) −162728. −0.00918922
\(794\) 3.91414e6 0.220336
\(795\) 1.69843e7 0.953083
\(796\) −5.09726e6 −0.285137
\(797\) 2.74340e6 0.152983 0.0764916 0.997070i \(-0.475628\pi\)
0.0764916 + 0.997070i \(0.475628\pi\)
\(798\) 4.11606e6 0.228810
\(799\) 1.23347e7 0.683537
\(800\) −5.17858e6 −0.286079
\(801\) 6.37533e7 3.51092
\(802\) −2.16279e7 −1.18735
\(803\) −7.75233e6 −0.424271
\(804\) −3.09765e7 −1.69002
\(805\) 2.51533e7 1.36806
\(806\) −962560. −0.0521903
\(807\) −3.76433e6 −0.203471
\(808\) −5.63476e6 −0.303631
\(809\) 3.60884e6 0.193864 0.0969318 0.995291i \(-0.469097\pi\)
0.0969318 + 0.995291i \(0.469097\pi\)
\(810\) −4.40699e7 −2.36010
\(811\) −2.42636e7 −1.29540 −0.647698 0.761897i \(-0.724268\pi\)
−0.647698 + 0.761897i \(0.724268\pi\)
\(812\) 1.95265e6 0.103928
\(813\) 2.03168e7 1.07802
\(814\) 7.24554e6 0.383274
\(815\) 1.33311e7 0.703028
\(816\) 1.00933e7 0.530650
\(817\) −926492. −0.0485609
\(818\) −7.55344e6 −0.394695
\(819\) 3.55149e6 0.185012
\(820\) 4.17620e6 0.216893
\(821\) −2.65430e6 −0.137433 −0.0687167 0.997636i \(-0.521890\pi\)
−0.0687167 + 0.997636i \(0.521890\pi\)
\(822\) 1.55261e6 0.0801460
\(823\) −1.45761e7 −0.750137 −0.375068 0.926997i \(-0.622381\pi\)
−0.375068 + 0.926997i \(0.622381\pi\)
\(824\) 3.24012e7 1.66243
\(825\) 1.60765e7 0.822351
\(826\) 2.12077e7 1.08154
\(827\) −2.56966e7 −1.30651 −0.653254 0.757139i \(-0.726597\pi\)
−0.653254 + 0.757139i \(0.726597\pi\)
\(828\) 2.93945e7 1.49001
\(829\) 5.04257e6 0.254839 0.127419 0.991849i \(-0.459331\pi\)
0.127419 + 0.991849i \(0.459331\pi\)
\(830\) 1.87576e7 0.945108
\(831\) 1.73203e7 0.870067
\(832\) −1.12462e6 −0.0563247
\(833\) −4.03838e6 −0.201648
\(834\) −3.62280e7 −1.80356
\(835\) 1.50839e7 0.748684
\(836\) −2.40649e6 −0.119088
\(837\) −6.65139e7 −3.28170
\(838\) −7.03734e6 −0.346177
\(839\) −6.91282e6 −0.339039 −0.169520 0.985527i \(-0.554222\pi\)
−0.169520 + 0.985527i \(0.554222\pi\)
\(840\) −4.97903e7 −2.43471
\(841\) 707281. 0.0344828
\(842\) 5.18392e6 0.251987
\(843\) −3.55295e7 −1.72195
\(844\) −1.09930e7 −0.531202
\(845\) −2.36838e7 −1.14106
\(846\) 1.82166e7 0.875069
\(847\) −2.07518e7 −0.993909
\(848\) −1.88276e6 −0.0899097
\(849\) 5.55581e7 2.64532
\(850\) 6.30407e6 0.299277
\(851\) 9.40934e6 0.445385
\(852\) −3.50244e6 −0.165299
\(853\) −2.16826e7 −1.02033 −0.510164 0.860077i \(-0.670415\pi\)
−0.510164 + 0.860077i \(0.670415\pi\)
\(854\) 2.14301e6 0.100549
\(855\) 1.02770e7 0.480787
\(856\) −3.81654e7 −1.78027
\(857\) −2.22637e7 −1.03549 −0.517745 0.855535i \(-0.673228\pi\)
−0.517745 + 0.855535i \(0.673228\pi\)
\(858\) 2.63688e6 0.122285
\(859\) −1.56538e7 −0.723828 −0.361914 0.932211i \(-0.617877\pi\)
−0.361914 + 0.932211i \(0.617877\pi\)
\(860\) 3.84752e6 0.177392
\(861\) 1.58963e7 0.730781
\(862\) −2.28378e6 −0.104685
\(863\) 3.14396e7 1.43698 0.718489 0.695538i \(-0.244834\pi\)
0.718489 + 0.695538i \(0.244834\pi\)
\(864\) −5.86940e7 −2.67491
\(865\) 8.12964e6 0.369429
\(866\) 2.76434e6 0.125255
\(867\) 3.77144e7 1.70396
\(868\) −1.38859e7 −0.625569
\(869\) −2.09437e7 −0.940816
\(870\) −6.19141e6 −0.277326
\(871\) −2.59407e6 −0.115861
\(872\) −1.53564e7 −0.683909
\(873\) −1.58440e7 −0.703608
\(874\) 2.85291e6 0.126331
\(875\) 1.90661e7 0.841865
\(876\) 6.84144e6 0.301222
\(877\) 9.99092e6 0.438638 0.219319 0.975653i \(-0.429616\pi\)
0.219319 + 0.975653i \(0.429616\pi\)
\(878\) −1.97808e7 −0.865978
\(879\) −7.17057e7 −3.13027
\(880\) −7.45767e6 −0.324636
\(881\) −2.37367e6 −0.103034 −0.0515169 0.998672i \(-0.516406\pi\)
−0.0515169 + 0.998672i \(0.516406\pi\)
\(882\) −5.96411e6 −0.258151
\(883\) −686405. −0.0296264 −0.0148132 0.999890i \(-0.504715\pi\)
−0.0148132 + 0.999890i \(0.504715\pi\)
\(884\) −1.13267e6 −0.0487498
\(885\) 7.36619e7 3.16144
\(886\) 1.30175e7 0.557112
\(887\) 1.54019e7 0.657302 0.328651 0.944451i \(-0.393406\pi\)
0.328651 + 0.944451i \(0.393406\pi\)
\(888\) −1.86256e7 −0.792641
\(889\) −2.66258e7 −1.12992
\(890\) −2.56959e7 −1.08740
\(891\) 9.80750e7 4.13870
\(892\) 1.50492e7 0.633288
\(893\) −1.93675e6 −0.0812729
\(894\) 172355. 0.00721242
\(895\) −3.73401e7 −1.55818
\(896\) −8.62879e6 −0.359071
\(897\) 3.42436e6 0.142102
\(898\) −147728. −0.00611325
\(899\) −5.02970e6 −0.207560
\(900\) −1.01987e7 −0.419699
\(901\) −1.48215e7 −0.608248
\(902\) 8.48424e6 0.347213
\(903\) 1.46452e7 0.597691
\(904\) 3.29422e6 0.134070
\(905\) 3.01013e7 1.22170
\(906\) 1.62060e7 0.655926
\(907\) −2.67004e7 −1.07770 −0.538852 0.842401i \(-0.681142\pi\)
−0.538852 + 0.842401i \(0.681142\pi\)
\(908\) −1.10412e7 −0.444428
\(909\) −1.83845e7 −0.737976
\(910\) −1.43143e6 −0.0573018
\(911\) 1.90851e7 0.761902 0.380951 0.924595i \(-0.375597\pi\)
0.380951 + 0.924595i \(0.375597\pi\)
\(912\) −1.58482e6 −0.0630946
\(913\) −4.17439e7 −1.65736
\(914\) 2.95086e7 1.16838
\(915\) 7.44344e6 0.293914
\(916\) 1.04116e7 0.409995
\(917\) −1.56132e7 −0.613153
\(918\) 7.14503e7 2.79832
\(919\) 3.04815e7 1.19055 0.595274 0.803523i \(-0.297043\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(920\) −3.45105e7 −1.34425
\(921\) −2.47671e7 −0.962112
\(922\) −7.72051e6 −0.299101
\(923\) −293306. −0.0113322
\(924\) 3.80398e7 1.46574
\(925\) −3.26465e6 −0.125453
\(926\) 3.26384e7 1.25084
\(927\) 1.05715e8 4.04053
\(928\) −4.43837e6 −0.169182
\(929\) −2.44730e7 −0.930352 −0.465176 0.885218i \(-0.654009\pi\)
−0.465176 + 0.885218i \(0.654009\pi\)
\(930\) 4.40291e7 1.66929
\(931\) 634092. 0.0239761
\(932\) −404534. −0.0152551
\(933\) −5.24757e7 −1.97358
\(934\) 3.34575e6 0.125495
\(935\) −5.87084e7 −2.19620
\(936\) −4.87266e6 −0.181793
\(937\) −3.03413e7 −1.12898 −0.564489 0.825441i \(-0.690927\pi\)
−0.564489 + 0.825441i \(0.690927\pi\)
\(938\) 3.41621e7 1.26776
\(939\) 5.27645e7 1.95289
\(940\) 8.04292e6 0.296889
\(941\) 4.32048e7 1.59059 0.795294 0.606224i \(-0.207317\pi\)
0.795294 + 0.606224i \(0.207317\pi\)
\(942\) 3.85857e7 1.41677
\(943\) 1.10180e7 0.403480
\(944\) −8.16565e6 −0.298236
\(945\) −9.89136e7 −3.60310
\(946\) 7.81652e6 0.283979
\(947\) −2.50483e7 −0.907620 −0.453810 0.891099i \(-0.649935\pi\)
−0.453810 + 0.891099i \(0.649935\pi\)
\(948\) 1.84829e7 0.667957
\(949\) 572925. 0.0206506
\(950\) −989842. −0.0355842
\(951\) −2.95379e7 −1.05908
\(952\) 4.34500e7 1.55381
\(953\) 4.30580e7 1.53576 0.767878 0.640596i \(-0.221313\pi\)
0.767878 + 0.640596i \(0.221313\pi\)
\(954\) −2.18893e7 −0.778684
\(955\) 5.18125e7 1.83834
\(956\) −3.37201e6 −0.119328
\(957\) 1.37786e7 0.486324
\(958\) −1.55288e7 −0.546669
\(959\) 1.87568e6 0.0658584
\(960\) 5.14421e7 1.80153
\(961\) 7.13868e6 0.249350
\(962\) −535471. −0.0186551
\(963\) −1.24522e8 −4.32694
\(964\) 1.70567e7 0.591156
\(965\) 2.55020e7 0.881569
\(966\) −4.50965e7 −1.55489
\(967\) −3.26447e7 −1.12266 −0.561328 0.827593i \(-0.689710\pi\)
−0.561328 + 0.827593i \(0.689710\pi\)
\(968\) 2.84716e7 0.976614
\(969\) −1.24760e7 −0.426841
\(970\) 6.38598e6 0.217921
\(971\) −9.02885e6 −0.307315 −0.153658 0.988124i \(-0.549105\pi\)
−0.153658 + 0.988124i \(0.549105\pi\)
\(972\) −4.13414e7 −1.40352
\(973\) −4.37665e7 −1.48204
\(974\) −1.06694e7 −0.360364
\(975\) −1.18811e6 −0.0400263
\(976\) −825128. −0.0277266
\(977\) 8.87743e6 0.297544 0.148772 0.988872i \(-0.452468\pi\)
0.148772 + 0.988872i \(0.452468\pi\)
\(978\) −2.39009e7 −0.799037
\(979\) 5.71848e7 1.90688
\(980\) −2.63325e6 −0.0875843
\(981\) −5.01033e7 −1.66224
\(982\) −9.84886e6 −0.325917
\(983\) −4.56481e7 −1.50674 −0.753371 0.657596i \(-0.771573\pi\)
−0.753371 + 0.657596i \(0.771573\pi\)
\(984\) −2.18098e7 −0.718065
\(985\) −5.26507e7 −1.72907
\(986\) 5.40299e6 0.176987
\(987\) 3.06146e7 1.00031
\(988\) 177848. 0.00579638
\(989\) 1.01508e7 0.329998
\(990\) −8.67041e7 −2.81159
\(991\) −7.74121e6 −0.250395 −0.125197 0.992132i \(-0.539956\pi\)
−0.125197 + 0.992132i \(0.539956\pi\)
\(992\) 3.15627e7 1.01834
\(993\) 1.03564e8 3.33301
\(994\) 3.86263e6 0.123999
\(995\) 1.95253e7 0.625232
\(996\) 3.68390e7 1.17668
\(997\) 5.64996e7 1.80014 0.900072 0.435740i \(-0.143513\pi\)
0.900072 + 0.435740i \(0.143513\pi\)
\(998\) −3.37279e7 −1.07192
\(999\) −3.70016e7 −1.17302
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 29.6.a.b.1.3 7
3.2 odd 2 261.6.a.e.1.5 7
4.3 odd 2 464.6.a.k.1.1 7
5.4 even 2 725.6.a.b.1.5 7
29.28 even 2 841.6.a.b.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.6.a.b.1.3 7 1.1 even 1 trivial
261.6.a.e.1.5 7 3.2 odd 2
464.6.a.k.1.1 7 4.3 odd 2
725.6.a.b.1.5 7 5.4 even 2
841.6.a.b.1.5 7 29.28 even 2