Properties

Label 29.6.a.b.1.1
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 1.1
Root \(9.56883\) of defining polynomial
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q-8.56883 q^{2} +18.3274 q^{3} +41.4249 q^{4} -84.3249 q^{5} -157.045 q^{6} +216.816 q^{7} -80.7606 q^{8} +92.8952 q^{9} +O(q^{10})\) \(q-8.56883 q^{2} +18.3274 q^{3} +41.4249 q^{4} -84.3249 q^{5} -157.045 q^{6} +216.816 q^{7} -80.7606 q^{8} +92.8952 q^{9} +722.566 q^{10} +380.662 q^{11} +759.213 q^{12} +1058.05 q^{13} -1857.86 q^{14} -1545.46 q^{15} -633.574 q^{16} +801.385 q^{17} -796.004 q^{18} -288.487 q^{19} -3493.15 q^{20} +3973.69 q^{21} -3261.83 q^{22} +334.571 q^{23} -1480.13 q^{24} +3985.69 q^{25} -9066.22 q^{26} -2751.04 q^{27} +8981.59 q^{28} +841.000 q^{29} +13242.8 q^{30} -3280.54 q^{31} +8013.32 q^{32} +6976.57 q^{33} -6866.93 q^{34} -18283.0 q^{35} +3848.18 q^{36} -11158.5 q^{37} +2472.00 q^{38} +19391.3 q^{39} +6810.13 q^{40} -887.943 q^{41} -34049.9 q^{42} +13247.9 q^{43} +15768.9 q^{44} -7833.38 q^{45} -2866.89 q^{46} -2338.13 q^{47} -11611.8 q^{48} +30202.3 q^{49} -34152.7 q^{50} +14687.3 q^{51} +43829.4 q^{52} +1850.38 q^{53} +23573.2 q^{54} -32099.3 q^{55} -17510.2 q^{56} -5287.23 q^{57} -7206.39 q^{58} +7102.05 q^{59} -64020.6 q^{60} +9622.02 q^{61} +28110.4 q^{62} +20141.2 q^{63} -48390.5 q^{64} -89219.6 q^{65} -59781.1 q^{66} +11714.6 q^{67} +33197.3 q^{68} +6131.84 q^{69} +156664. q^{70} -67084.1 q^{71} -7502.27 q^{72} -2340.00 q^{73} +95615.2 q^{74} +73047.5 q^{75} -11950.6 q^{76} +82533.8 q^{77} -166161. q^{78} +33928.9 q^{79} +53426.0 q^{80} -72993.0 q^{81} +7608.63 q^{82} -97350.5 q^{83} +164610. q^{84} -67576.7 q^{85} -113519. q^{86} +15413.4 q^{87} -30742.5 q^{88} +101586. q^{89} +67122.9 q^{90} +229401. q^{91} +13859.6 q^{92} -60124.0 q^{93} +20035.1 q^{94} +24326.7 q^{95} +146864. q^{96} -84674.6 q^{97} -258798. q^{98} +35361.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.56883 −1.51477 −0.757385 0.652968i \(-0.773523\pi\)
−0.757385 + 0.652968i \(0.773523\pi\)
\(3\) 18.3274 1.17571 0.587853 0.808968i \(-0.299973\pi\)
0.587853 + 0.808968i \(0.299973\pi\)
\(4\) 41.4249 1.29453
\(5\) −84.3249 −1.50845 −0.754225 0.656616i \(-0.771987\pi\)
−0.754225 + 0.656616i \(0.771987\pi\)
\(6\) −157.045 −1.78092
\(7\) 216.816 1.67242 0.836212 0.548406i \(-0.184765\pi\)
0.836212 + 0.548406i \(0.184765\pi\)
\(8\) −80.7606 −0.446143
\(9\) 92.8952 0.382285
\(10\) 722.566 2.28496
\(11\) 380.662 0.948546 0.474273 0.880378i \(-0.342711\pi\)
0.474273 + 0.880378i \(0.342711\pi\)
\(12\) 759.213 1.52199
\(13\) 1058.05 1.73638 0.868192 0.496228i \(-0.165282\pi\)
0.868192 + 0.496228i \(0.165282\pi\)
\(14\) −1857.86 −2.53334
\(15\) −1545.46 −1.77349
\(16\) −633.574 −0.618724
\(17\) 801.385 0.672541 0.336271 0.941765i \(-0.390834\pi\)
0.336271 + 0.941765i \(0.390834\pi\)
\(18\) −796.004 −0.579074
\(19\) −288.487 −0.183334 −0.0916669 0.995790i \(-0.529219\pi\)
−0.0916669 + 0.995790i \(0.529219\pi\)
\(20\) −3493.15 −1.95273
\(21\) 3973.69 1.96628
\(22\) −3261.83 −1.43683
\(23\) 334.571 0.131877 0.0659385 0.997824i \(-0.478996\pi\)
0.0659385 + 0.997824i \(0.478996\pi\)
\(24\) −1480.13 −0.524533
\(25\) 3985.69 1.27542
\(26\) −9066.22 −2.63022
\(27\) −2751.04 −0.726252
\(28\) 8981.59 2.16500
\(29\) 841.000 0.185695
\(30\) 13242.8 2.68644
\(31\) −3280.54 −0.613115 −0.306557 0.951852i \(-0.599177\pi\)
−0.306557 + 0.951852i \(0.599177\pi\)
\(32\) 8013.32 1.38337
\(33\) 6976.57 1.11521
\(34\) −6866.93 −1.01875
\(35\) −18283.0 −2.52277
\(36\) 3848.18 0.494879
\(37\) −11158.5 −1.33999 −0.669994 0.742366i \(-0.733703\pi\)
−0.669994 + 0.742366i \(0.733703\pi\)
\(38\) 2472.00 0.277709
\(39\) 19391.3 2.04148
\(40\) 6810.13 0.672985
\(41\) −887.943 −0.0824946 −0.0412473 0.999149i \(-0.513133\pi\)
−0.0412473 + 0.999149i \(0.513133\pi\)
\(42\) −34049.9 −2.97846
\(43\) 13247.9 1.09264 0.546318 0.837578i \(-0.316029\pi\)
0.546318 + 0.837578i \(0.316029\pi\)
\(44\) 15768.9 1.22792
\(45\) −7833.38 −0.576657
\(46\) −2866.89 −0.199763
\(47\) −2338.13 −0.154392 −0.0771959 0.997016i \(-0.524597\pi\)
−0.0771959 + 0.997016i \(0.524597\pi\)
\(48\) −11611.8 −0.727438
\(49\) 30202.3 1.79700
\(50\) −34152.7 −1.93197
\(51\) 14687.3 0.790711
\(52\) 43829.4 2.24780
\(53\) 1850.38 0.0904840 0.0452420 0.998976i \(-0.485594\pi\)
0.0452420 + 0.998976i \(0.485594\pi\)
\(54\) 23573.2 1.10010
\(55\) −32099.3 −1.43083
\(56\) −17510.2 −0.746141
\(57\) −5287.23 −0.215547
\(58\) −7206.39 −0.281286
\(59\) 7102.05 0.265616 0.132808 0.991142i \(-0.457601\pi\)
0.132808 + 0.991142i \(0.457601\pi\)
\(60\) −64020.6 −2.29584
\(61\) 9622.02 0.331087 0.165543 0.986203i \(-0.447062\pi\)
0.165543 + 0.986203i \(0.447062\pi\)
\(62\) 28110.4 0.928728
\(63\) 20141.2 0.639343
\(64\) −48390.5 −1.47676
\(65\) −89219.6 −2.61925
\(66\) −59781.1 −1.68929
\(67\) 11714.6 0.318816 0.159408 0.987213i \(-0.449042\pi\)
0.159408 + 0.987213i \(0.449042\pi\)
\(68\) 33197.3 0.870624
\(69\) 6131.84 0.155049
\(70\) 156664. 3.82142
\(71\) −67084.1 −1.57933 −0.789667 0.613536i \(-0.789747\pi\)
−0.789667 + 0.613536i \(0.789747\pi\)
\(72\) −7502.27 −0.170554
\(73\) −2340.00 −0.0513935 −0.0256967 0.999670i \(-0.508180\pi\)
−0.0256967 + 0.999670i \(0.508180\pi\)
\(74\) 95615.2 2.02977
\(75\) 73047.5 1.49952
\(76\) −11950.6 −0.237331
\(77\) 82533.8 1.58637
\(78\) −166161. −3.09237
\(79\) 33928.9 0.611649 0.305825 0.952088i \(-0.401068\pi\)
0.305825 + 0.952088i \(0.401068\pi\)
\(80\) 53426.0 0.933314
\(81\) −72993.0 −1.23614
\(82\) 7608.63 0.124960
\(83\) −97350.5 −1.55111 −0.775555 0.631279i \(-0.782530\pi\)
−0.775555 + 0.631279i \(0.782530\pi\)
\(84\) 164610. 2.54541
\(85\) −67576.7 −1.01449
\(86\) −113519. −1.65509
\(87\) 15413.4 0.218323
\(88\) −30742.5 −0.423187
\(89\) 101586. 1.35943 0.679716 0.733475i \(-0.262103\pi\)
0.679716 + 0.733475i \(0.262103\pi\)
\(90\) 67122.9 0.873504
\(91\) 229401. 2.90397
\(92\) 13859.6 0.170719
\(93\) −60124.0 −0.720843
\(94\) 20035.1 0.233868
\(95\) 24326.7 0.276550
\(96\) 146864. 1.62643
\(97\) −84674.6 −0.913743 −0.456871 0.889533i \(-0.651030\pi\)
−0.456871 + 0.889533i \(0.651030\pi\)
\(98\) −258798. −2.72205
\(99\) 35361.7 0.362615
\(100\) 165107. 1.65107
\(101\) 59936.3 0.584637 0.292318 0.956321i \(-0.405573\pi\)
0.292318 + 0.956321i \(0.405573\pi\)
\(102\) −125853. −1.19774
\(103\) −196075. −1.82108 −0.910542 0.413417i \(-0.864335\pi\)
−0.910542 + 0.413417i \(0.864335\pi\)
\(104\) −85448.3 −0.774676
\(105\) −335081. −2.96604
\(106\) −15855.6 −0.137063
\(107\) 82447.0 0.696170 0.348085 0.937463i \(-0.386832\pi\)
0.348085 + 0.937463i \(0.386832\pi\)
\(108\) −113961. −0.940153
\(109\) −152195. −1.22697 −0.613484 0.789707i \(-0.710233\pi\)
−0.613484 + 0.789707i \(0.710233\pi\)
\(110\) 275054. 2.16738
\(111\) −204507. −1.57543
\(112\) −137369. −1.03477
\(113\) 168561. 1.24182 0.620912 0.783880i \(-0.286762\pi\)
0.620912 + 0.783880i \(0.286762\pi\)
\(114\) 45305.4 0.326504
\(115\) −28212.7 −0.198930
\(116\) 34838.4 0.240388
\(117\) 98287.3 0.663793
\(118\) −60856.3 −0.402347
\(119\) 173753. 1.12477
\(120\) 124812. 0.791232
\(121\) −16147.1 −0.100261
\(122\) −82449.5 −0.501520
\(123\) −16273.7 −0.0969893
\(124\) −135896. −0.793695
\(125\) −72577.8 −0.415460
\(126\) −172586. −0.968457
\(127\) −21587.4 −0.118766 −0.0593829 0.998235i \(-0.518913\pi\)
−0.0593829 + 0.998235i \(0.518913\pi\)
\(128\) 158224. 0.853585
\(129\) 242800. 1.28462
\(130\) 764508. 3.96756
\(131\) 137802. 0.701581 0.350790 0.936454i \(-0.385913\pi\)
0.350790 + 0.936454i \(0.385913\pi\)
\(132\) 289004. 1.44367
\(133\) −62548.7 −0.306612
\(134\) −100380. −0.482933
\(135\) 231981. 1.09551
\(136\) −64720.3 −0.300050
\(137\) −422084. −1.92131 −0.960654 0.277747i \(-0.910412\pi\)
−0.960654 + 0.277747i \(0.910412\pi\)
\(138\) −52542.7 −0.234863
\(139\) 79419.8 0.348652 0.174326 0.984688i \(-0.444225\pi\)
0.174326 + 0.984688i \(0.444225\pi\)
\(140\) −757372. −3.26580
\(141\) −42852.0 −0.181519
\(142\) 574833. 2.39233
\(143\) 402758. 1.64704
\(144\) −58855.9 −0.236529
\(145\) −70917.3 −0.280112
\(146\) 20051.0 0.0778493
\(147\) 553530. 2.11275
\(148\) −462239. −1.73465
\(149\) −144641. −0.533736 −0.266868 0.963733i \(-0.585989\pi\)
−0.266868 + 0.963733i \(0.585989\pi\)
\(150\) −625932. −2.27143
\(151\) −446697. −1.59430 −0.797152 0.603779i \(-0.793661\pi\)
−0.797152 + 0.603779i \(0.793661\pi\)
\(152\) 23298.4 0.0817931
\(153\) 74444.8 0.257102
\(154\) −707218. −2.40299
\(155\) 276632. 0.924853
\(156\) 803282. 2.64275
\(157\) −136908. −0.443282 −0.221641 0.975128i \(-0.571141\pi\)
−0.221641 + 0.975128i \(0.571141\pi\)
\(158\) −290731. −0.926508
\(159\) 33912.8 0.106383
\(160\) −675723. −2.08674
\(161\) 72540.5 0.220554
\(162\) 625465. 1.87247
\(163\) 5407.16 0.0159404 0.00797022 0.999968i \(-0.497463\pi\)
0.00797022 + 0.999968i \(0.497463\pi\)
\(164\) −36783.0 −0.106792
\(165\) −588299. −1.68224
\(166\) 834180. 2.34958
\(167\) −303826. −0.843013 −0.421506 0.906825i \(-0.638498\pi\)
−0.421506 + 0.906825i \(0.638498\pi\)
\(168\) −320917. −0.877243
\(169\) 748167. 2.01503
\(170\) 579054. 1.53673
\(171\) −26799.1 −0.0700857
\(172\) 548792. 1.41445
\(173\) −45069.8 −0.114491 −0.0572454 0.998360i \(-0.518232\pi\)
−0.0572454 + 0.998360i \(0.518232\pi\)
\(174\) −132075. −0.330709
\(175\) 864163. 2.13305
\(176\) −241178. −0.586888
\(177\) 130162. 0.312286
\(178\) −870471. −2.05923
\(179\) 348392. 0.812710 0.406355 0.913715i \(-0.366800\pi\)
0.406355 + 0.913715i \(0.366800\pi\)
\(180\) −324497. −0.746500
\(181\) −754876. −1.71269 −0.856346 0.516403i \(-0.827271\pi\)
−0.856346 + 0.516403i \(0.827271\pi\)
\(182\) −1.96570e6 −4.39885
\(183\) 176347. 0.389261
\(184\) −27020.2 −0.0588361
\(185\) 940939. 2.02131
\(186\) 515193. 1.09191
\(187\) 305057. 0.637936
\(188\) −96856.9 −0.199865
\(189\) −596469. −1.21460
\(190\) −208451. −0.418909
\(191\) −559504. −1.10974 −0.554868 0.831938i \(-0.687231\pi\)
−0.554868 + 0.831938i \(0.687231\pi\)
\(192\) −886874. −1.73624
\(193\) 915469. 1.76909 0.884546 0.466453i \(-0.154468\pi\)
0.884546 + 0.466453i \(0.154468\pi\)
\(194\) 725563. 1.38411
\(195\) −1.63517e6 −3.07947
\(196\) 1.25113e6 2.32627
\(197\) 149660. 0.274751 0.137375 0.990519i \(-0.456133\pi\)
0.137375 + 0.990519i \(0.456133\pi\)
\(198\) −303009. −0.549278
\(199\) 2043.12 0.00365731 0.00182865 0.999998i \(-0.499418\pi\)
0.00182865 + 0.999998i \(0.499418\pi\)
\(200\) −321887. −0.569021
\(201\) 214698. 0.374834
\(202\) −513584. −0.885591
\(203\) 182342. 0.310562
\(204\) 608422. 1.02360
\(205\) 74875.7 0.124439
\(206\) 1.68014e6 2.75852
\(207\) 31080.1 0.0504146
\(208\) −670350. −1.07434
\(209\) −109816. −0.173900
\(210\) 2.87125e6 4.49286
\(211\) −94629.7 −0.146326 −0.0731630 0.997320i \(-0.523309\pi\)
−0.0731630 + 0.997320i \(0.523309\pi\)
\(212\) 76652.0 0.117134
\(213\) −1.22948e6 −1.85683
\(214\) −706474. −1.05454
\(215\) −1.11713e6 −1.64819
\(216\) 222175. 0.324012
\(217\) −711275. −1.02539
\(218\) 1.30413e6 1.85857
\(219\) −42886.1 −0.0604236
\(220\) −1.32971e6 −1.85226
\(221\) 847902. 1.16779
\(222\) 1.75238e6 2.38642
\(223\) 33151.7 0.0446420 0.0223210 0.999751i \(-0.492894\pi\)
0.0223210 + 0.999751i \(0.492894\pi\)
\(224\) 1.73742e6 2.31358
\(225\) 370252. 0.487574
\(226\) −1.44437e6 −1.88108
\(227\) −886146. −1.14141 −0.570704 0.821156i \(-0.693329\pi\)
−0.570704 + 0.821156i \(0.693329\pi\)
\(228\) −219023. −0.279031
\(229\) −51324.5 −0.0646749 −0.0323375 0.999477i \(-0.510295\pi\)
−0.0323375 + 0.999477i \(0.510295\pi\)
\(230\) 241750. 0.301333
\(231\) 1.51263e6 1.86511
\(232\) −67919.6 −0.0828467
\(233\) −854399. −1.03103 −0.515515 0.856881i \(-0.672399\pi\)
−0.515515 + 0.856881i \(0.672399\pi\)
\(234\) −842208. −1.00549
\(235\) 197163. 0.232892
\(236\) 294202. 0.343847
\(237\) 621831. 0.719120
\(238\) −1.48886e6 −1.70377
\(239\) 750885. 0.850313 0.425156 0.905120i \(-0.360219\pi\)
0.425156 + 0.905120i \(0.360219\pi\)
\(240\) 979163. 1.09730
\(241\) −71808.1 −0.0796400 −0.0398200 0.999207i \(-0.512678\pi\)
−0.0398200 + 0.999207i \(0.512678\pi\)
\(242\) 138362. 0.151872
\(243\) −669273. −0.727089
\(244\) 398591. 0.428601
\(245\) −2.54680e6 −2.71069
\(246\) 139447. 0.146917
\(247\) −305233. −0.318338
\(248\) 264939. 0.273537
\(249\) −1.78419e6 −1.82365
\(250\) 621907. 0.629326
\(251\) 897843. 0.899531 0.449765 0.893147i \(-0.351508\pi\)
0.449765 + 0.893147i \(0.351508\pi\)
\(252\) 834347. 0.827647
\(253\) 127359. 0.125091
\(254\) 184979. 0.179903
\(255\) −1.23851e6 −1.19275
\(256\) 192703. 0.183776
\(257\) 848562. 0.801402 0.400701 0.916209i \(-0.368767\pi\)
0.400701 + 0.916209i \(0.368767\pi\)
\(258\) −2.08051e6 −1.94590
\(259\) −2.41934e6 −2.24103
\(260\) −3.69591e6 −3.39069
\(261\) 78124.9 0.0709885
\(262\) −1.18080e6 −1.06273
\(263\) −592909. −0.528565 −0.264283 0.964445i \(-0.585135\pi\)
−0.264283 + 0.964445i \(0.585135\pi\)
\(264\) −563432. −0.497544
\(265\) −156033. −0.136491
\(266\) 535969. 0.464447
\(267\) 1.86181e6 1.59829
\(268\) 485276. 0.412716
\(269\) 833107. 0.701973 0.350986 0.936381i \(-0.385846\pi\)
0.350986 + 0.936381i \(0.385846\pi\)
\(270\) −1.98781e6 −1.65945
\(271\) 728989. 0.602973 0.301487 0.953470i \(-0.402517\pi\)
0.301487 + 0.953470i \(0.402517\pi\)
\(272\) −507736. −0.416117
\(273\) 4.20434e6 3.41422
\(274\) 3.61676e6 2.91034
\(275\) 1.51720e6 1.20980
\(276\) 254011. 0.200715
\(277\) 1.44549e6 1.13192 0.565961 0.824432i \(-0.308505\pi\)
0.565961 + 0.824432i \(0.308505\pi\)
\(278\) −680535. −0.528127
\(279\) −304747. −0.234384
\(280\) 1.47655e6 1.12552
\(281\) 1.71312e6 1.29426 0.647131 0.762379i \(-0.275969\pi\)
0.647131 + 0.762379i \(0.275969\pi\)
\(282\) 367191. 0.274960
\(283\) 2.14168e6 1.58960 0.794799 0.606872i \(-0.207576\pi\)
0.794799 + 0.606872i \(0.207576\pi\)
\(284\) −2.77896e6 −2.04449
\(285\) 445845. 0.325141
\(286\) −3.45117e6 −2.49489
\(287\) −192520. −0.137966
\(288\) 744399. 0.528841
\(289\) −777639. −0.547688
\(290\) 607678. 0.424306
\(291\) −1.55187e6 −1.07429
\(292\) −96934.1 −0.0665303
\(293\) 663344. 0.451408 0.225704 0.974196i \(-0.427532\pi\)
0.225704 + 0.974196i \(0.427532\pi\)
\(294\) −4.74311e6 −3.20033
\(295\) −598880. −0.400668
\(296\) 901166. 0.597827
\(297\) −1.04722e6 −0.688883
\(298\) 1.23941e6 0.808488
\(299\) 353992. 0.228989
\(300\) 3.02599e6 1.94117
\(301\) 2.87236e6 1.82735
\(302\) 3.82768e6 2.41500
\(303\) 1.09848e6 0.687361
\(304\) 182778. 0.113433
\(305\) −811376. −0.499428
\(306\) −637905. −0.389451
\(307\) 615215. 0.372547 0.186274 0.982498i \(-0.440359\pi\)
0.186274 + 0.982498i \(0.440359\pi\)
\(308\) 3.41896e6 2.05360
\(309\) −3.59356e6 −2.14106
\(310\) −2.37041e6 −1.40094
\(311\) −1.17303e6 −0.687712 −0.343856 0.939022i \(-0.611733\pi\)
−0.343856 + 0.939022i \(0.611733\pi\)
\(312\) −1.56605e6 −0.910792
\(313\) −2.58664e6 −1.49237 −0.746184 0.665740i \(-0.768116\pi\)
−0.746184 + 0.665740i \(0.768116\pi\)
\(314\) 1.17314e6 0.671470
\(315\) −1.69840e6 −0.964416
\(316\) 1.40550e6 0.791798
\(317\) −934239. −0.522167 −0.261084 0.965316i \(-0.584080\pi\)
−0.261084 + 0.965316i \(0.584080\pi\)
\(318\) −290593. −0.161145
\(319\) 320137. 0.176141
\(320\) 4.08052e6 2.22762
\(321\) 1.51104e6 0.818491
\(322\) −621587. −0.334089
\(323\) −231189. −0.123299
\(324\) −3.02373e6 −1.60022
\(325\) 4.21704e6 2.21462
\(326\) −46333.1 −0.0241461
\(327\) −2.78934e6 −1.44255
\(328\) 71710.7 0.0368044
\(329\) −506945. −0.258209
\(330\) 5.04103e6 2.54821
\(331\) −3.77955e6 −1.89614 −0.948070 0.318061i \(-0.896968\pi\)
−0.948070 + 0.318061i \(0.896968\pi\)
\(332\) −4.03274e6 −2.00796
\(333\) −1.03657e6 −0.512257
\(334\) 2.60344e6 1.27697
\(335\) −987831. −0.480918
\(336\) −2.51762e6 −1.21658
\(337\) 2.10980e6 1.01197 0.505983 0.862544i \(-0.331130\pi\)
0.505983 + 0.862544i \(0.331130\pi\)
\(338\) −6.41092e6 −3.05231
\(339\) 3.08929e6 1.46002
\(340\) −2.79936e6 −1.31329
\(341\) −1.24878e6 −0.581567
\(342\) 229637. 0.106164
\(343\) 2.90431e6 1.33293
\(344\) −1.06991e6 −0.487472
\(345\) −517067. −0.233883
\(346\) 386196. 0.173427
\(347\) 37808.7 0.0168565 0.00842827 0.999964i \(-0.497317\pi\)
0.00842827 + 0.999964i \(0.497317\pi\)
\(348\) 638498. 0.282626
\(349\) 632608. 0.278017 0.139008 0.990291i \(-0.455608\pi\)
0.139008 + 0.990291i \(0.455608\pi\)
\(350\) −7.40487e6 −3.23108
\(351\) −2.91072e6 −1.26105
\(352\) 3.05037e6 1.31219
\(353\) −2.76871e6 −1.18261 −0.591304 0.806449i \(-0.701387\pi\)
−0.591304 + 0.806449i \(0.701387\pi\)
\(354\) −1.11534e6 −0.473041
\(355\) 5.65687e6 2.38235
\(356\) 4.20818e6 1.75982
\(357\) 3.18445e6 1.32240
\(358\) −2.98531e6 −1.23107
\(359\) −2.50490e6 −1.02578 −0.512889 0.858455i \(-0.671425\pi\)
−0.512889 + 0.858455i \(0.671425\pi\)
\(360\) 632628. 0.257272
\(361\) −2.39287e6 −0.966389
\(362\) 6.46841e6 2.59433
\(363\) −295935. −0.117877
\(364\) 9.50293e6 3.75928
\(365\) 197320. 0.0775245
\(366\) −1.51109e6 −0.589640
\(367\) 3.09219e6 1.19840 0.599199 0.800600i \(-0.295486\pi\)
0.599199 + 0.800600i \(0.295486\pi\)
\(368\) −211976. −0.0815955
\(369\) −82485.6 −0.0315364
\(370\) −8.06275e6 −3.06181
\(371\) 401193. 0.151328
\(372\) −2.49063e6 −0.933151
\(373\) 2.44054e6 0.908266 0.454133 0.890934i \(-0.349949\pi\)
0.454133 + 0.890934i \(0.349949\pi\)
\(374\) −2.61398e6 −0.966327
\(375\) −1.33017e6 −0.488458
\(376\) 188829. 0.0688809
\(377\) 889816. 0.322439
\(378\) 5.11105e6 1.83984
\(379\) 2.64306e6 0.945168 0.472584 0.881286i \(-0.343321\pi\)
0.472584 + 0.881286i \(0.343321\pi\)
\(380\) 1.00773e6 0.358002
\(381\) −395642. −0.139634
\(382\) 4.79430e6 1.68099
\(383\) −460287. −0.160336 −0.0801682 0.996781i \(-0.525546\pi\)
−0.0801682 + 0.996781i \(0.525546\pi\)
\(384\) 2.89984e6 1.00356
\(385\) −6.95965e6 −2.39296
\(386\) −7.84450e6 −2.67977
\(387\) 1.23066e6 0.417698
\(388\) −3.50764e6 −1.18287
\(389\) −2.72948e6 −0.914547 −0.457273 0.889326i \(-0.651174\pi\)
−0.457273 + 0.889326i \(0.651174\pi\)
\(390\) 1.40115e7 4.66469
\(391\) 268120. 0.0886927
\(392\) −2.43915e6 −0.801722
\(393\) 2.52556e6 0.824853
\(394\) −1.28241e6 −0.416184
\(395\) −2.86106e6 −0.922643
\(396\) 1.46486e6 0.469415
\(397\) 530743. 0.169008 0.0845041 0.996423i \(-0.473069\pi\)
0.0845041 + 0.996423i \(0.473069\pi\)
\(398\) −17507.2 −0.00553998
\(399\) −1.14636e6 −0.360486
\(400\) −2.52523e6 −0.789134
\(401\) 1.65453e6 0.513822 0.256911 0.966435i \(-0.417295\pi\)
0.256911 + 0.966435i \(0.417295\pi\)
\(402\) −1.83971e6 −0.567787
\(403\) −3.47097e6 −1.06460
\(404\) 2.48286e6 0.756829
\(405\) 6.15513e6 1.86466
\(406\) −1.56246e6 −0.470429
\(407\) −4.24762e6 −1.27104
\(408\) −1.18616e6 −0.352770
\(409\) −5.20484e6 −1.53851 −0.769253 0.638944i \(-0.779372\pi\)
−0.769253 + 0.638944i \(0.779372\pi\)
\(410\) −641597. −0.188496
\(411\) −7.73571e6 −2.25889
\(412\) −8.12240e6 −2.35744
\(413\) 1.53984e6 0.444222
\(414\) −266320. −0.0763665
\(415\) 8.20907e6 2.33977
\(416\) 8.47846e6 2.40206
\(417\) 1.45556e6 0.409912
\(418\) 940997. 0.263419
\(419\) 191911. 0.0534030 0.0267015 0.999643i \(-0.491500\pi\)
0.0267015 + 0.999643i \(0.491500\pi\)
\(420\) −1.38807e7 −3.83962
\(421\) 5.00002e6 1.37488 0.687442 0.726239i \(-0.258734\pi\)
0.687442 + 0.726239i \(0.258734\pi\)
\(422\) 810866. 0.221650
\(423\) −217201. −0.0590216
\(424\) −149438. −0.0403688
\(425\) 3.19407e6 0.857773
\(426\) 1.05352e7 2.81267
\(427\) 2.08621e6 0.553718
\(428\) 3.41536e6 0.901212
\(429\) 7.38153e6 1.93644
\(430\) 9.57247e6 2.49662
\(431\) −3.04923e6 −0.790672 −0.395336 0.918537i \(-0.629372\pi\)
−0.395336 + 0.918537i \(0.629372\pi\)
\(432\) 1.74298e6 0.449349
\(433\) 3.79886e6 0.973719 0.486860 0.873480i \(-0.338142\pi\)
0.486860 + 0.873480i \(0.338142\pi\)
\(434\) 6.09480e6 1.55323
\(435\) −1.29973e6 −0.329330
\(436\) −6.30465e6 −1.58835
\(437\) −96519.5 −0.0241775
\(438\) 367484. 0.0915279
\(439\) 3.28829e6 0.814345 0.407173 0.913351i \(-0.366515\pi\)
0.407173 + 0.913351i \(0.366515\pi\)
\(440\) 2.59236e6 0.638357
\(441\) 2.80565e6 0.686968
\(442\) −7.26553e6 −1.76893
\(443\) 97599.9 0.0236287 0.0118144 0.999930i \(-0.496239\pi\)
0.0118144 + 0.999930i \(0.496239\pi\)
\(444\) −8.47167e6 −2.03944
\(445\) −8.56621e6 −2.05064
\(446\) −284072. −0.0676224
\(447\) −2.65091e6 −0.627517
\(448\) −1.04918e7 −2.46977
\(449\) 4.55742e6 1.06685 0.533424 0.845848i \(-0.320905\pi\)
0.533424 + 0.845848i \(0.320905\pi\)
\(450\) −3.17263e6 −0.738563
\(451\) −338006. −0.0782499
\(452\) 6.98261e6 1.60758
\(453\) −8.18682e6 −1.87443
\(454\) 7.59324e6 1.72897
\(455\) −1.93443e7 −4.38050
\(456\) 427000. 0.0961647
\(457\) 491699. 0.110131 0.0550654 0.998483i \(-0.482463\pi\)
0.0550654 + 0.998483i \(0.482463\pi\)
\(458\) 439791. 0.0979677
\(459\) −2.20464e6 −0.488434
\(460\) −1.16871e6 −0.257520
\(461\) 2.55180e6 0.559234 0.279617 0.960112i \(-0.409792\pi\)
0.279617 + 0.960112i \(0.409792\pi\)
\(462\) −1.29615e7 −2.82521
\(463\) −6.25797e6 −1.35669 −0.678345 0.734743i \(-0.737303\pi\)
−0.678345 + 0.734743i \(0.737303\pi\)
\(464\) −532835. −0.114894
\(465\) 5.06995e6 1.08736
\(466\) 7.32120e6 1.56177
\(467\) 2.34350e6 0.497247 0.248624 0.968600i \(-0.420022\pi\)
0.248624 + 0.968600i \(0.420022\pi\)
\(468\) 4.07155e6 0.859300
\(469\) 2.53991e6 0.533195
\(470\) −1.68945e6 −0.352778
\(471\) −2.50918e6 −0.521169
\(472\) −573565. −0.118503
\(473\) 5.04297e6 1.03641
\(474\) −5.32837e6 −1.08930
\(475\) −1.14982e6 −0.233828
\(476\) 7.19771e6 1.45605
\(477\) 171892. 0.0345907
\(478\) −6.43421e6 −1.28803
\(479\) 4.98927e6 0.993570 0.496785 0.867874i \(-0.334514\pi\)
0.496785 + 0.867874i \(0.334514\pi\)
\(480\) −1.23843e7 −2.45339
\(481\) −1.18062e7 −2.32674
\(482\) 615312. 0.120636
\(483\) 1.32948e6 0.259307
\(484\) −668892. −0.129790
\(485\) 7.14018e6 1.37834
\(486\) 5.73489e6 1.10137
\(487\) −1.75440e6 −0.335202 −0.167601 0.985855i \(-0.553602\pi\)
−0.167601 + 0.985855i \(0.553602\pi\)
\(488\) −777080. −0.147712
\(489\) 99099.5 0.0187413
\(490\) 2.18231e7 4.10608
\(491\) 2.28688e6 0.428094 0.214047 0.976823i \(-0.431335\pi\)
0.214047 + 0.976823i \(0.431335\pi\)
\(492\) −674137. −0.125555
\(493\) 673965. 0.124888
\(494\) 2.61549e6 0.482209
\(495\) −2.98187e6 −0.546986
\(496\) 2.07847e6 0.379349
\(497\) −1.45449e7 −2.64132
\(498\) 1.52884e7 2.76241
\(499\) 6.03762e6 1.08546 0.542730 0.839907i \(-0.317391\pi\)
0.542730 + 0.839907i \(0.317391\pi\)
\(500\) −3.00653e6 −0.537824
\(501\) −5.56836e6 −0.991135
\(502\) −7.69347e6 −1.36258
\(503\) −1.11239e6 −0.196036 −0.0980182 0.995185i \(-0.531250\pi\)
−0.0980182 + 0.995185i \(0.531250\pi\)
\(504\) −1.62661e6 −0.285238
\(505\) −5.05412e6 −0.881896
\(506\) −1.09132e6 −0.189485
\(507\) 1.37120e7 2.36909
\(508\) −894257. −0.153746
\(509\) −3.45813e6 −0.591625 −0.295813 0.955246i \(-0.595590\pi\)
−0.295813 + 0.955246i \(0.595590\pi\)
\(510\) 1.06126e7 1.80674
\(511\) −507349. −0.0859517
\(512\) −6.71440e6 −1.13196
\(513\) 793639. 0.133146
\(514\) −7.27118e6 −1.21394
\(515\) 1.65340e7 2.74701
\(516\) 1.00580e7 1.66298
\(517\) −890039. −0.146448
\(518\) 2.07309e7 3.39465
\(519\) −826015. −0.134608
\(520\) 7.20542e6 1.16856
\(521\) −9.29125e6 −1.49961 −0.749807 0.661656i \(-0.769854\pi\)
−0.749807 + 0.661656i \(0.769854\pi\)
\(522\) −669439. −0.107531
\(523\) 1.62992e6 0.260563 0.130282 0.991477i \(-0.458412\pi\)
0.130282 + 0.991477i \(0.458412\pi\)
\(524\) 5.70844e6 0.908216
\(525\) 1.58379e7 2.50784
\(526\) 5.08054e6 0.800655
\(527\) −2.62898e6 −0.412345
\(528\) −4.42017e6 −0.690008
\(529\) −6.32441e6 −0.982608
\(530\) 1.33702e6 0.206752
\(531\) 659746. 0.101541
\(532\) −2.59107e6 −0.396918
\(533\) −939484. −0.143242
\(534\) −1.59535e7 −2.42105
\(535\) −6.95233e6 −1.05014
\(536\) −946076. −0.142238
\(537\) 6.38514e6 0.955509
\(538\) −7.13876e6 −1.06333
\(539\) 1.14969e7 1.70454
\(540\) 9.60979e6 1.41817
\(541\) −1.04884e7 −1.54070 −0.770348 0.637624i \(-0.779917\pi\)
−0.770348 + 0.637624i \(0.779917\pi\)
\(542\) −6.24659e6 −0.913366
\(543\) −1.38349e7 −2.01362
\(544\) 6.42176e6 0.930372
\(545\) 1.28338e7 1.85082
\(546\) −3.60263e7 −5.17176
\(547\) 4.48107e6 0.640345 0.320172 0.947359i \(-0.396259\pi\)
0.320172 + 0.947359i \(0.396259\pi\)
\(548\) −1.74848e7 −2.48719
\(549\) 893839. 0.126569
\(550\) −1.30007e7 −1.83256
\(551\) −242618. −0.0340442
\(552\) −495211. −0.0691739
\(553\) 7.35634e6 1.02294
\(554\) −1.23862e7 −1.71460
\(555\) 1.72450e7 2.37646
\(556\) 3.28996e6 0.451339
\(557\) −720322. −0.0983759 −0.0491879 0.998790i \(-0.515663\pi\)
−0.0491879 + 0.998790i \(0.515663\pi\)
\(558\) 2.61132e6 0.355038
\(559\) 1.40169e7 1.89724
\(560\) 1.15836e7 1.56090
\(561\) 5.59092e6 0.750025
\(562\) −1.46795e7 −1.96051
\(563\) 1.26872e7 1.68692 0.843458 0.537196i \(-0.180516\pi\)
0.843458 + 0.537196i \(0.180516\pi\)
\(564\) −1.77514e6 −0.234982
\(565\) −1.42139e7 −1.87323
\(566\) −1.83517e7 −2.40788
\(567\) −1.58261e7 −2.06736
\(568\) 5.41775e6 0.704609
\(569\) −7.93605e6 −1.02760 −0.513799 0.857910i \(-0.671762\pi\)
−0.513799 + 0.857910i \(0.671762\pi\)
\(570\) −3.82038e6 −0.492514
\(571\) 9.14124e6 1.17332 0.586658 0.809835i \(-0.300443\pi\)
0.586658 + 0.809835i \(0.300443\pi\)
\(572\) 1.66842e7 2.13214
\(573\) −1.02543e7 −1.30472
\(574\) 1.64967e6 0.208987
\(575\) 1.33350e6 0.168199
\(576\) −4.49524e6 −0.564543
\(577\) 2.52312e6 0.315499 0.157750 0.987479i \(-0.449576\pi\)
0.157750 + 0.987479i \(0.449576\pi\)
\(578\) 6.66346e6 0.829622
\(579\) 1.67782e7 2.07993
\(580\) −2.93774e6 −0.362613
\(581\) −2.11072e7 −2.59412
\(582\) 1.32977e7 1.62731
\(583\) 704371. 0.0858283
\(584\) 188979. 0.0229288
\(585\) −8.28807e6 −1.00130
\(586\) −5.68408e6 −0.683780
\(587\) −1.02895e7 −1.23254 −0.616268 0.787536i \(-0.711356\pi\)
−0.616268 + 0.787536i \(0.711356\pi\)
\(588\) 2.29299e7 2.73502
\(589\) 946395. 0.112405
\(590\) 5.13170e6 0.606920
\(591\) 2.74288e6 0.323026
\(592\) 7.06972e6 0.829083
\(593\) −573757. −0.0670025 −0.0335013 0.999439i \(-0.510666\pi\)
−0.0335013 + 0.999439i \(0.510666\pi\)
\(594\) 8.97343e6 1.04350
\(595\) −1.46517e7 −1.69667
\(596\) −5.99176e6 −0.690937
\(597\) 37445.2 0.00429992
\(598\) −3.03330e6 −0.346866
\(599\) 1.61434e7 1.83835 0.919173 0.393853i \(-0.128858\pi\)
0.919173 + 0.393853i \(0.128858\pi\)
\(600\) −5.89936e6 −0.669001
\(601\) 3.97295e6 0.448670 0.224335 0.974512i \(-0.427979\pi\)
0.224335 + 0.974512i \(0.427979\pi\)
\(602\) −2.46127e7 −2.76802
\(603\) 1.08823e6 0.121878
\(604\) −1.85044e7 −2.06387
\(605\) 1.36160e6 0.151238
\(606\) −9.41268e6 −1.04119
\(607\) 5.65644e6 0.623119 0.311560 0.950227i \(-0.399149\pi\)
0.311560 + 0.950227i \(0.399149\pi\)
\(608\) −2.31174e6 −0.253618
\(609\) 3.34187e6 0.365129
\(610\) 6.95255e6 0.756518
\(611\) −2.47385e6 −0.268084
\(612\) 3.08387e6 0.332826
\(613\) 7.65406e6 0.822699 0.411349 0.911478i \(-0.365058\pi\)
0.411349 + 0.911478i \(0.365058\pi\)
\(614\) −5.27168e6 −0.564323
\(615\) 1.37228e6 0.146304
\(616\) −6.66548e6 −0.707749
\(617\) −1.06193e7 −1.12301 −0.561505 0.827473i \(-0.689778\pi\)
−0.561505 + 0.827473i \(0.689778\pi\)
\(618\) 3.07926e7 3.24321
\(619\) −4.45953e6 −0.467802 −0.233901 0.972260i \(-0.575149\pi\)
−0.233901 + 0.972260i \(0.575149\pi\)
\(620\) 1.14594e7 1.19725
\(621\) −920418. −0.0957759
\(622\) 1.00515e7 1.04173
\(623\) 2.20254e7 2.27355
\(624\) −1.22858e7 −1.26311
\(625\) −6.33517e6 −0.648722
\(626\) 2.21645e7 2.26059
\(627\) −2.01265e6 −0.204456
\(628\) −5.67141e6 −0.573841
\(629\) −8.94224e6 −0.901197
\(630\) 1.45533e7 1.46087
\(631\) 1.51771e7 1.51745 0.758725 0.651411i \(-0.225823\pi\)
0.758725 + 0.651411i \(0.225823\pi\)
\(632\) −2.74012e6 −0.272883
\(633\) −1.73432e6 −0.172036
\(634\) 8.00534e6 0.790964
\(635\) 1.82036e6 0.179152
\(636\) 1.40483e6 0.137715
\(637\) 3.19554e7 3.12029
\(638\) −2.74320e6 −0.266812
\(639\) −6.23180e6 −0.603755
\(640\) −1.33422e7 −1.28759
\(641\) 1.33769e7 1.28591 0.642957 0.765903i \(-0.277708\pi\)
0.642957 + 0.765903i \(0.277708\pi\)
\(642\) −1.29479e7 −1.23983
\(643\) −5.68424e6 −0.542182 −0.271091 0.962554i \(-0.587384\pi\)
−0.271091 + 0.962554i \(0.587384\pi\)
\(644\) 3.00498e6 0.285514
\(645\) −2.04741e7 −1.93778
\(646\) 1.98102e6 0.186770
\(647\) −1.93095e7 −1.81347 −0.906735 0.421702i \(-0.861433\pi\)
−0.906735 + 0.421702i \(0.861433\pi\)
\(648\) 5.89496e6 0.551497
\(649\) 2.70348e6 0.251949
\(650\) −3.61351e7 −3.35464
\(651\) −1.30359e7 −1.20556
\(652\) 223991. 0.0206354
\(653\) 151435. 0.0138977 0.00694884 0.999976i \(-0.497788\pi\)
0.00694884 + 0.999976i \(0.497788\pi\)
\(654\) 2.39014e7 2.18514
\(655\) −1.16201e7 −1.05830
\(656\) 562577. 0.0510414
\(657\) −217374. −0.0196469
\(658\) 4.34392e6 0.391127
\(659\) −9.74503e6 −0.874117 −0.437058 0.899433i \(-0.643980\pi\)
−0.437058 + 0.899433i \(0.643980\pi\)
\(660\) −2.43702e7 −2.17771
\(661\) −8.52857e6 −0.759229 −0.379614 0.925145i \(-0.623943\pi\)
−0.379614 + 0.925145i \(0.623943\pi\)
\(662\) 3.23864e7 2.87222
\(663\) 1.55399e7 1.37298
\(664\) 7.86208e6 0.692018
\(665\) 5.27441e6 0.462509
\(666\) 8.88220e6 0.775952
\(667\) 281374. 0.0244889
\(668\) −1.25860e7 −1.09130
\(669\) 607586. 0.0524859
\(670\) 8.46456e6 0.728480
\(671\) 3.66274e6 0.314051
\(672\) 3.18424e7 2.72009
\(673\) −1.53606e7 −1.30729 −0.653643 0.756803i \(-0.726760\pi\)
−0.653643 + 0.756803i \(0.726760\pi\)
\(674\) −1.80785e7 −1.53290
\(675\) −1.09648e7 −0.926277
\(676\) 3.09928e7 2.60852
\(677\) −2.37603e6 −0.199241 −0.0996207 0.995025i \(-0.531763\pi\)
−0.0996207 + 0.995025i \(0.531763\pi\)
\(678\) −2.64716e7 −2.21159
\(679\) −1.83588e7 −1.52817
\(680\) 5.45753e6 0.452610
\(681\) −1.62408e7 −1.34196
\(682\) 1.07006e7 0.880941
\(683\) −6.86181e6 −0.562842 −0.281421 0.959584i \(-0.590806\pi\)
−0.281421 + 0.959584i \(0.590806\pi\)
\(684\) −1.11015e6 −0.0907280
\(685\) 3.55922e7 2.89820
\(686\) −2.48865e7 −2.01908
\(687\) −940647. −0.0760387
\(688\) −8.39351e6 −0.676040
\(689\) 1.95779e6 0.157115
\(690\) 4.43066e6 0.354279
\(691\) 1.86887e7 1.48896 0.744480 0.667645i \(-0.232698\pi\)
0.744480 + 0.667645i \(0.232698\pi\)
\(692\) −1.86701e6 −0.148212
\(693\) 7.66699e6 0.606446
\(694\) −323977. −0.0255338
\(695\) −6.69706e6 −0.525923
\(696\) −1.24479e6 −0.0974034
\(697\) −711584. −0.0554810
\(698\) −5.42071e6 −0.421132
\(699\) −1.56589e7 −1.21219
\(700\) 3.57979e7 2.76129
\(701\) −5.85780e6 −0.450235 −0.225118 0.974332i \(-0.572277\pi\)
−0.225118 + 0.974332i \(0.572277\pi\)
\(702\) 2.49415e7 1.91020
\(703\) 3.21908e6 0.245665
\(704\) −1.84204e7 −1.40078
\(705\) 3.61349e6 0.273813
\(706\) 2.37246e7 1.79138
\(707\) 1.29952e7 0.977761
\(708\) 5.39197e6 0.404263
\(709\) −3.17834e6 −0.237457 −0.118728 0.992927i \(-0.537882\pi\)
−0.118728 + 0.992927i \(0.537882\pi\)
\(710\) −4.84727e7 −3.60871
\(711\) 3.15184e6 0.233824
\(712\) −8.20412e6 −0.606502
\(713\) −1.09758e6 −0.0808557
\(714\) −2.72870e7 −2.00314
\(715\) −3.39626e7 −2.48448
\(716\) 1.44321e7 1.05208
\(717\) 1.37618e7 0.999718
\(718\) 2.14640e7 1.55382
\(719\) 2.62515e7 1.89379 0.946894 0.321546i \(-0.104202\pi\)
0.946894 + 0.321546i \(0.104202\pi\)
\(720\) 4.96302e6 0.356792
\(721\) −4.25123e7 −3.04563
\(722\) 2.05041e7 1.46386
\(723\) −1.31606e6 −0.0936332
\(724\) −3.12707e7 −2.21713
\(725\) 3.35197e6 0.236840
\(726\) 2.53582e6 0.178557
\(727\) −1.53808e7 −1.07930 −0.539651 0.841889i \(-0.681444\pi\)
−0.539651 + 0.841889i \(0.681444\pi\)
\(728\) −1.85266e7 −1.29559
\(729\) 5.47123e6 0.381300
\(730\) −1.69080e6 −0.117432
\(731\) 1.06167e7 0.734842
\(732\) 7.30516e6 0.503909
\(733\) 1.07403e7 0.738338 0.369169 0.929362i \(-0.379642\pi\)
0.369169 + 0.929362i \(0.379642\pi\)
\(734\) −2.64965e7 −1.81530
\(735\) −4.66764e7 −3.18698
\(736\) 2.68103e6 0.182434
\(737\) 4.45930e6 0.302411
\(738\) 706805. 0.0477704
\(739\) 1.50225e7 1.01189 0.505943 0.862567i \(-0.331145\pi\)
0.505943 + 0.862567i \(0.331145\pi\)
\(740\) 3.89783e7 2.61664
\(741\) −5.59413e6 −0.374272
\(742\) −3.43776e6 −0.229227
\(743\) −1.20298e7 −0.799440 −0.399720 0.916637i \(-0.630893\pi\)
−0.399720 + 0.916637i \(0.630893\pi\)
\(744\) 4.85565e6 0.321599
\(745\) 1.21969e7 0.805115
\(746\) −2.09126e7 −1.37581
\(747\) −9.04339e6 −0.592966
\(748\) 1.26370e7 0.825827
\(749\) 1.78758e7 1.16429
\(750\) 1.13980e7 0.739902
\(751\) 1.27308e7 0.823674 0.411837 0.911258i \(-0.364887\pi\)
0.411837 + 0.911258i \(0.364887\pi\)
\(752\) 1.48138e6 0.0955259
\(753\) 1.64552e7 1.05758
\(754\) −7.62469e6 −0.488420
\(755\) 3.76677e7 2.40493
\(756\) −2.47087e7 −1.57234
\(757\) −2.61540e7 −1.65882 −0.829408 0.558643i \(-0.811322\pi\)
−0.829408 + 0.558643i \(0.811322\pi\)
\(758\) −2.26479e7 −1.43171
\(759\) 2.33416e6 0.147071
\(760\) −1.96463e6 −0.123381
\(761\) 1.26786e7 0.793612 0.396806 0.917903i \(-0.370119\pi\)
0.396806 + 0.917903i \(0.370119\pi\)
\(762\) 3.39019e6 0.211513
\(763\) −3.29983e7 −2.05201
\(764\) −2.31774e7 −1.43658
\(765\) −6.27755e6 −0.387826
\(766\) 3.94412e6 0.242873
\(767\) 7.51429e6 0.461211
\(768\) 3.53175e6 0.216066
\(769\) 2.28743e7 1.39486 0.697431 0.716652i \(-0.254326\pi\)
0.697431 + 0.716652i \(0.254326\pi\)
\(770\) 5.96361e7 3.62479
\(771\) 1.55520e7 0.942213
\(772\) 3.79232e7 2.29014
\(773\) 2.65876e7 1.60041 0.800204 0.599728i \(-0.204725\pi\)
0.800204 + 0.599728i \(0.204725\pi\)
\(774\) −1.05454e7 −0.632716
\(775\) −1.30752e7 −0.781980
\(776\) 6.83837e6 0.407660
\(777\) −4.43403e7 −2.63479
\(778\) 2.33885e7 1.38533
\(779\) 256160. 0.0151240
\(780\) −6.77367e7 −3.98646
\(781\) −2.55364e7 −1.49807
\(782\) −2.29748e6 −0.134349
\(783\) −2.31362e6 −0.134862
\(784\) −1.91354e7 −1.11185
\(785\) 1.15448e7 0.668669
\(786\) −2.16411e7 −1.24946
\(787\) −9.06273e6 −0.521582 −0.260791 0.965395i \(-0.583983\pi\)
−0.260791 + 0.965395i \(0.583983\pi\)
\(788\) 6.19963e6 0.355673
\(789\) −1.08665e7 −0.621437
\(790\) 2.45159e7 1.39759
\(791\) 3.65467e7 2.07686
\(792\) −2.85583e6 −0.161778
\(793\) 1.01805e7 0.574894
\(794\) −4.54785e6 −0.256009
\(795\) −2.85969e6 −0.160473
\(796\) 84636.1 0.00473449
\(797\) −2.52271e7 −1.40676 −0.703382 0.710812i \(-0.748328\pi\)
−0.703382 + 0.710812i \(0.748328\pi\)
\(798\) 9.82295e6 0.546053
\(799\) −1.87374e6 −0.103835
\(800\) 3.19386e7 1.76438
\(801\) 9.43683e6 0.519690
\(802\) −1.41774e7 −0.778322
\(803\) −890748. −0.0487491
\(804\) 8.89386e6 0.485233
\(805\) −6.11697e6 −0.332695
\(806\) 2.97421e7 1.61263
\(807\) 1.52687e7 0.825314
\(808\) −4.84049e6 −0.260832
\(809\) −8.69627e6 −0.467156 −0.233578 0.972338i \(-0.575043\pi\)
−0.233578 + 0.972338i \(0.575043\pi\)
\(810\) −5.27423e7 −2.82453
\(811\) 1.94112e7 1.03633 0.518166 0.855280i \(-0.326615\pi\)
0.518166 + 0.855280i \(0.326615\pi\)
\(812\) 7.55352e6 0.402031
\(813\) 1.33605e7 0.708919
\(814\) 3.63971e7 1.92533
\(815\) −455959. −0.0240454
\(816\) −9.30551e6 −0.489232
\(817\) −3.82184e6 −0.200317
\(818\) 4.45994e7 2.33048
\(819\) 2.13103e7 1.11014
\(820\) 3.10172e6 0.161090
\(821\) 1.78189e7 0.922620 0.461310 0.887239i \(-0.347380\pi\)
0.461310 + 0.887239i \(0.347380\pi\)
\(822\) 6.62861e7 3.42171
\(823\) −1.73515e7 −0.892969 −0.446485 0.894791i \(-0.647324\pi\)
−0.446485 + 0.894791i \(0.647324\pi\)
\(824\) 1.58352e7 0.812464
\(825\) 2.78065e7 1.42236
\(826\) −1.31946e7 −0.672894
\(827\) 8.83226e6 0.449064 0.224532 0.974467i \(-0.427915\pi\)
0.224532 + 0.974467i \(0.427915\pi\)
\(828\) 1.28749e6 0.0652631
\(829\) −1.69640e7 −0.857316 −0.428658 0.903467i \(-0.641014\pi\)
−0.428658 + 0.903467i \(0.641014\pi\)
\(830\) −7.03422e7 −3.54422
\(831\) 2.64922e7 1.33081
\(832\) −5.11993e7 −2.56422
\(833\) 2.42036e7 1.20856
\(834\) −1.24725e7 −0.620922
\(835\) 2.56201e7 1.27164
\(836\) −4.54913e6 −0.225119
\(837\) 9.02490e6 0.445275
\(838\) −1.64446e6 −0.0808933
\(839\) −2.68046e7 −1.31463 −0.657316 0.753615i \(-0.728308\pi\)
−0.657316 + 0.753615i \(0.728308\pi\)
\(840\) 2.70613e7 1.32328
\(841\) 707281. 0.0344828
\(842\) −4.28443e7 −2.08263
\(843\) 3.13971e7 1.52167
\(844\) −3.92003e6 −0.189423
\(845\) −6.30891e7 −3.03957
\(846\) 1.86116e6 0.0894042
\(847\) −3.50095e6 −0.167678
\(848\) −1.17235e6 −0.0559847
\(849\) 3.92514e7 1.86890
\(850\) −2.73695e7 −1.29933
\(851\) −3.73331e6 −0.176714
\(852\) −5.09311e7 −2.40372
\(853\) 2.65626e7 1.24997 0.624983 0.780638i \(-0.285106\pi\)
0.624983 + 0.780638i \(0.285106\pi\)
\(854\) −1.78764e7 −0.838755
\(855\) 2.25983e6 0.105721
\(856\) −6.65846e6 −0.310591
\(857\) −1.81681e7 −0.845003 −0.422501 0.906362i \(-0.638848\pi\)
−0.422501 + 0.906362i \(0.638848\pi\)
\(858\) −6.32511e7 −2.93325
\(859\) 2.68029e7 1.23936 0.619681 0.784854i \(-0.287262\pi\)
0.619681 + 0.784854i \(0.287262\pi\)
\(860\) −4.62769e7 −2.13362
\(861\) −3.52841e6 −0.162207
\(862\) 2.61283e7 1.19769
\(863\) −2.87179e7 −1.31258 −0.656291 0.754508i \(-0.727876\pi\)
−0.656291 + 0.754508i \(0.727876\pi\)
\(864\) −2.20450e7 −1.00467
\(865\) 3.80051e6 0.172704
\(866\) −3.25518e7 −1.47496
\(867\) −1.42521e7 −0.643921
\(868\) −2.94645e7 −1.32739
\(869\) 1.29155e7 0.580178
\(870\) 1.11372e7 0.498859
\(871\) 1.23946e7 0.553587
\(872\) 1.22913e7 0.547404
\(873\) −7.86586e6 −0.349310
\(874\) 827060. 0.0366234
\(875\) −1.57360e7 −0.694825
\(876\) −1.77655e6 −0.0782201
\(877\) 139217. 0.00611213 0.00305606 0.999995i \(-0.499027\pi\)
0.00305606 + 0.999995i \(0.499027\pi\)
\(878\) −2.81768e7 −1.23355
\(879\) 1.21574e7 0.530723
\(880\) 2.03373e7 0.885292
\(881\) −8.68118e6 −0.376824 −0.188412 0.982090i \(-0.560334\pi\)
−0.188412 + 0.982090i \(0.560334\pi\)
\(882\) −2.40411e7 −1.04060
\(883\) −2.65874e7 −1.14756 −0.573778 0.819011i \(-0.694523\pi\)
−0.573778 + 0.819011i \(0.694523\pi\)
\(884\) 3.51243e7 1.51174
\(885\) −1.09759e7 −0.471068
\(886\) −836317. −0.0357921
\(887\) −4.43687e7 −1.89351 −0.946754 0.321956i \(-0.895660\pi\)
−0.946754 + 0.321956i \(0.895660\pi\)
\(888\) 1.65161e7 0.702869
\(889\) −4.68050e6 −0.198627
\(890\) 7.34024e7 3.10624
\(891\) −2.77857e7 −1.17254
\(892\) 1.37331e6 0.0577904
\(893\) 674521. 0.0283052
\(894\) 2.27152e7 0.950544
\(895\) −2.93781e7 −1.22593
\(896\) 3.43055e7 1.42756
\(897\) 6.48776e6 0.269224
\(898\) −3.90517e7 −1.61603
\(899\) −2.75894e6 −0.113853
\(900\) 1.53376e7 0.631179
\(901\) 1.48287e6 0.0608542
\(902\) 2.89632e6 0.118531
\(903\) 5.26429e7 2.14843
\(904\) −1.36131e7 −0.554031
\(905\) 6.36548e7 2.58351
\(906\) 7.01515e7 2.83934
\(907\) −1.96923e7 −0.794839 −0.397420 0.917637i \(-0.630094\pi\)
−0.397420 + 0.917637i \(0.630094\pi\)
\(908\) −3.67085e7 −1.47758
\(909\) 5.56779e6 0.223498
\(910\) 1.65758e8 6.63545
\(911\) 4.33698e6 0.173138 0.0865688 0.996246i \(-0.472410\pi\)
0.0865688 + 0.996246i \(0.472410\pi\)
\(912\) 3.34985e6 0.133364
\(913\) −3.70577e7 −1.47130
\(914\) −4.21329e6 −0.166823
\(915\) −1.48704e7 −0.587180
\(916\) −2.12611e6 −0.0837236
\(917\) 2.98777e7 1.17334
\(918\) 1.88912e7 0.739865
\(919\) 2.13300e7 0.833110 0.416555 0.909110i \(-0.363237\pi\)
0.416555 + 0.909110i \(0.363237\pi\)
\(920\) 2.27847e6 0.0887512
\(921\) 1.12753e7 0.438006
\(922\) −2.18659e7 −0.847112
\(923\) −7.09781e7 −2.74233
\(924\) 6.26607e7 2.41443
\(925\) −4.44743e7 −1.70905
\(926\) 5.36235e7 2.05507
\(927\) −1.82145e7 −0.696172
\(928\) 6.73921e6 0.256885
\(929\) 4.41448e7 1.67819 0.839093 0.543988i \(-0.183086\pi\)
0.839093 + 0.543988i \(0.183086\pi\)
\(930\) −4.34436e7 −1.64709
\(931\) −8.71296e6 −0.329452
\(932\) −3.53934e7 −1.33470
\(933\) −2.14986e7 −0.808547
\(934\) −2.00810e7 −0.753215
\(935\) −2.57239e7 −0.962295
\(936\) −7.93774e6 −0.296147
\(937\) 5.10338e7 1.89893 0.949466 0.313871i \(-0.101626\pi\)
0.949466 + 0.313871i \(0.101626\pi\)
\(938\) −2.17641e7 −0.807669
\(939\) −4.74066e7 −1.75459
\(940\) 8.16745e6 0.301486
\(941\) 4.69231e7 1.72748 0.863739 0.503939i \(-0.168116\pi\)
0.863739 + 0.503939i \(0.168116\pi\)
\(942\) 2.15007e7 0.789452
\(943\) −297080. −0.0108791
\(944\) −4.49967e6 −0.164343
\(945\) 5.02972e7 1.83217
\(946\) −4.32124e7 −1.56993
\(947\) 1.22405e7 0.443533 0.221766 0.975100i \(-0.428818\pi\)
0.221766 + 0.975100i \(0.428818\pi\)
\(948\) 2.57593e7 0.930922
\(949\) −2.47582e6 −0.0892388
\(950\) 9.85263e6 0.354195
\(951\) −1.71222e7 −0.613915
\(952\) −1.40324e7 −0.501811
\(953\) −4.02315e7 −1.43494 −0.717470 0.696590i \(-0.754700\pi\)
−0.717470 + 0.696590i \(0.754700\pi\)
\(954\) −1.47291e6 −0.0523969
\(955\) 4.71801e7 1.67398
\(956\) 3.11053e7 1.10075
\(957\) 5.86730e6 0.207090
\(958\) −4.27523e7 −1.50503
\(959\) −9.15146e7 −3.21324
\(960\) 7.47856e7 2.61903
\(961\) −1.78672e7 −0.624090
\(962\) 1.01165e8 3.52447
\(963\) 7.65893e6 0.266135
\(964\) −2.97465e6 −0.103096
\(965\) −7.71969e7 −2.66859
\(966\) −1.13921e7 −0.392791
\(967\) 1.72628e7 0.593668 0.296834 0.954929i \(-0.404069\pi\)
0.296834 + 0.954929i \(0.404069\pi\)
\(968\) 1.30405e6 0.0447306
\(969\) −4.23711e6 −0.144964
\(970\) −6.11830e7 −2.08786
\(971\) 1.32907e7 0.452378 0.226189 0.974083i \(-0.427373\pi\)
0.226189 + 0.974083i \(0.427373\pi\)
\(972\) −2.77246e7 −0.941238
\(973\) 1.72195e7 0.583093
\(974\) 1.50332e7 0.507754
\(975\) 7.72876e7 2.60374
\(976\) −6.09626e6 −0.204851
\(977\) −4.16592e7 −1.39629 −0.698144 0.715957i \(-0.745990\pi\)
−0.698144 + 0.715957i \(0.745990\pi\)
\(978\) −849167. −0.0283887
\(979\) 3.86699e7 1.28948
\(980\) −1.05501e8 −3.50907
\(981\) −1.41382e7 −0.469051
\(982\) −1.95959e7 −0.648464
\(983\) 2.91834e6 0.0963278 0.0481639 0.998839i \(-0.484663\pi\)
0.0481639 + 0.998839i \(0.484663\pi\)
\(984\) 1.31427e6 0.0432711
\(985\) −1.26200e7 −0.414448
\(986\) −5.77509e6 −0.189176
\(987\) −9.29100e6 −0.303577
\(988\) −1.26442e7 −0.412098
\(989\) 4.43236e6 0.144094
\(990\) 2.55512e7 0.828558
\(991\) −5.12994e7 −1.65931 −0.829657 0.558274i \(-0.811464\pi\)
−0.829657 + 0.558274i \(0.811464\pi\)
\(992\) −2.62881e7 −0.848163
\(993\) −6.92696e7 −2.22930
\(994\) 1.24633e8 4.00099
\(995\) −172286. −0.00551686
\(996\) −7.39097e7 −2.36077
\(997\) 3.15013e7 1.00367 0.501834 0.864964i \(-0.332659\pi\)
0.501834 + 0.864964i \(0.332659\pi\)
\(998\) −5.17353e7 −1.64422
\(999\) 3.06974e7 0.973169
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.1.1 7
3.2 odd 2 261.6.a.e.1.7 7
4.3 odd 2 464.6.a.k.1.2 7
5.4 even 2 725.6.a.b.1.7 7
29.28 even 2 841.6.a.b.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.6.a.b.1.1 7 1.1 even 1 trivial
261.6.a.e.1.7 7 3.2 odd 2
464.6.a.k.1.2 7 4.3 odd 2
725.6.a.b.1.7 7 5.4 even 2
841.6.a.b.1.7 7 29.28 even 2