Properties

Label 1575.4.a.p.1.1
Level $1575$
Weight $4$
Character 1575.1
Self dual yes
Analytic conductor $92.928$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(92.9280082590\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{57}) \)
Defining polynomial: \(x^{2} - x - 14\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.27492\) of defining polynomial
Character \(\chi\) \(=\) 1575.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.27492 q^{2} +19.8248 q^{4} -7.00000 q^{7} -62.3746 q^{8} +O(q^{10})\) \(q-5.27492 q^{2} +19.8248 q^{4} -7.00000 q^{7} -62.3746 q^{8} -34.7492 q^{11} +37.2990 q^{13} +36.9244 q^{14} +170.423 q^{16} -10.5498 q^{17} -58.5980 q^{19} +183.299 q^{22} -125.347 q^{23} -196.749 q^{26} -138.773 q^{28} +35.4020 q^{29} +291.794 q^{31} -399.969 q^{32} +55.6495 q^{34} +259.897 q^{37} +309.100 q^{38} +338.248 q^{41} -6.80397 q^{43} -688.894 q^{44} +661.196 q^{46} +250.694 q^{47} +49.0000 q^{49} +739.444 q^{52} -536.900 q^{53} +436.622 q^{56} -186.743 q^{58} +35.8904 q^{59} +57.7940 q^{61} -1539.19 q^{62} +746.423 q^{64} -481.691 q^{67} -209.148 q^{68} -363.752 q^{71} -581.299 q^{73} -1370.94 q^{74} -1161.69 q^{76} +243.244 q^{77} -693.691 q^{79} -1784.23 q^{82} +1334.39 q^{83} +35.8904 q^{86} +2167.47 q^{88} +353.038 q^{89} -261.093 q^{91} -2484.98 q^{92} -1322.39 q^{94} -1445.88 q^{97} -258.471 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} + 17 q^{4} - 14 q^{7} - 87 q^{8} + O(q^{10}) \) \( 2 q - 3 q^{2} + 17 q^{4} - 14 q^{7} - 87 q^{8} + 6 q^{11} - 16 q^{13} + 21 q^{14} + 137 q^{16} - 6 q^{17} + 64 q^{19} + 276 q^{22} + 6 q^{23} - 318 q^{26} - 119 q^{28} + 252 q^{29} + 40 q^{31} - 279 q^{32} + 66 q^{34} + 248 q^{37} + 588 q^{38} + 450 q^{41} - 376 q^{43} - 804 q^{44} + 960 q^{46} - 12 q^{47} + 98 q^{49} + 890 q^{52} - 1104 q^{53} + 609 q^{56} + 306 q^{58} - 804 q^{59} - 428 q^{61} - 2112 q^{62} + 1289 q^{64} - 148 q^{67} - 222 q^{68} - 954 q^{71} - 1072 q^{73} - 1398 q^{74} - 1508 q^{76} - 42 q^{77} - 572 q^{79} - 1530 q^{82} + 1944 q^{83} - 804 q^{86} + 1164 q^{88} - 366 q^{89} + 112 q^{91} - 2856 q^{92} - 1920 q^{94} - 808 q^{97} - 147 q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.27492 −1.86496 −0.932482 0.361215i \(-0.882362\pi\)
−0.932482 + 0.361215i \(0.882362\pi\)
\(3\) 0 0
\(4\) 19.8248 2.47809
\(5\) 0 0
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) −62.3746 −2.75659
\(9\) 0 0
\(10\) 0 0
\(11\) −34.7492 −0.952479 −0.476240 0.879316i \(-0.658000\pi\)
−0.476240 + 0.879316i \(0.658000\pi\)
\(12\) 0 0
\(13\) 37.2990 0.795760 0.397880 0.917437i \(-0.369746\pi\)
0.397880 + 0.917437i \(0.369746\pi\)
\(14\) 36.9244 0.704890
\(15\) 0 0
\(16\) 170.423 2.66286
\(17\) −10.5498 −0.150512 −0.0752562 0.997164i \(-0.523977\pi\)
−0.0752562 + 0.997164i \(0.523977\pi\)
\(18\) 0 0
\(19\) −58.5980 −0.707542 −0.353771 0.935332i \(-0.615101\pi\)
−0.353771 + 0.935332i \(0.615101\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 183.299 1.77634
\(23\) −125.347 −1.13638 −0.568189 0.822898i \(-0.692356\pi\)
−0.568189 + 0.822898i \(0.692356\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −196.749 −1.48406
\(27\) 0 0
\(28\) −138.773 −0.936631
\(29\) 35.4020 0.226689 0.113345 0.993556i \(-0.463844\pi\)
0.113345 + 0.993556i \(0.463844\pi\)
\(30\) 0 0
\(31\) 291.794 1.69057 0.845286 0.534313i \(-0.179430\pi\)
0.845286 + 0.534313i \(0.179430\pi\)
\(32\) −399.969 −2.20954
\(33\) 0 0
\(34\) 55.6495 0.280700
\(35\) 0 0
\(36\) 0 0
\(37\) 259.897 1.15478 0.577389 0.816469i \(-0.304072\pi\)
0.577389 + 0.816469i \(0.304072\pi\)
\(38\) 309.100 1.31954
\(39\) 0 0
\(40\) 0 0
\(41\) 338.248 1.28842 0.644212 0.764847i \(-0.277185\pi\)
0.644212 + 0.764847i \(0.277185\pi\)
\(42\) 0 0
\(43\) −6.80397 −0.0241301 −0.0120651 0.999927i \(-0.503841\pi\)
−0.0120651 + 0.999927i \(0.503841\pi\)
\(44\) −688.894 −2.36033
\(45\) 0 0
\(46\) 661.196 2.11931
\(47\) 250.694 0.778033 0.389016 0.921231i \(-0.372815\pi\)
0.389016 + 0.921231i \(0.372815\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 739.444 1.97197
\(53\) −536.900 −1.39149 −0.695745 0.718289i \(-0.744925\pi\)
−0.695745 + 0.718289i \(0.744925\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 436.622 1.04189
\(57\) 0 0
\(58\) −186.743 −0.422767
\(59\) 35.8904 0.0791955 0.0395977 0.999216i \(-0.487392\pi\)
0.0395977 + 0.999216i \(0.487392\pi\)
\(60\) 0 0
\(61\) 57.7940 0.121308 0.0606538 0.998159i \(-0.480681\pi\)
0.0606538 + 0.998159i \(0.480681\pi\)
\(62\) −1539.19 −3.15286
\(63\) 0 0
\(64\) 746.423 1.45786
\(65\) 0 0
\(66\) 0 0
\(67\) −481.691 −0.878327 −0.439164 0.898407i \(-0.644725\pi\)
−0.439164 + 0.898407i \(0.644725\pi\)
\(68\) −209.148 −0.372984
\(69\) 0 0
\(70\) 0 0
\(71\) −363.752 −0.608021 −0.304010 0.952669i \(-0.598326\pi\)
−0.304010 + 0.952669i \(0.598326\pi\)
\(72\) 0 0
\(73\) −581.299 −0.931999 −0.465999 0.884785i \(-0.654305\pi\)
−0.465999 + 0.884785i \(0.654305\pi\)
\(74\) −1370.94 −2.15362
\(75\) 0 0
\(76\) −1161.69 −1.75336
\(77\) 243.244 0.360003
\(78\) 0 0
\(79\) −693.691 −0.987928 −0.493964 0.869482i \(-0.664453\pi\)
−0.493964 + 0.869482i \(0.664453\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −1784.23 −2.40287
\(83\) 1334.39 1.76468 0.882341 0.470611i \(-0.155967\pi\)
0.882341 + 0.470611i \(0.155967\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 35.8904 0.0450019
\(87\) 0 0
\(88\) 2167.47 2.62560
\(89\) 353.038 0.420472 0.210236 0.977651i \(-0.432577\pi\)
0.210236 + 0.977651i \(0.432577\pi\)
\(90\) 0 0
\(91\) −261.093 −0.300769
\(92\) −2484.98 −2.81605
\(93\) 0 0
\(94\) −1322.39 −1.45100
\(95\) 0 0
\(96\) 0 0
\(97\) −1445.88 −1.51347 −0.756735 0.653722i \(-0.773207\pi\)
−0.756735 + 0.653722i \(0.773207\pi\)
\(98\) −258.471 −0.266424
\(99\) 0 0
\(100\) 0 0
\(101\) −474.852 −0.467817 −0.233909 0.972259i \(-0.575152\pi\)
−0.233909 + 0.972259i \(0.575152\pi\)
\(102\) 0 0
\(103\) 1999.59 1.91287 0.956433 0.291951i \(-0.0943044\pi\)
0.956433 + 0.291951i \(0.0943044\pi\)
\(104\) −2326.51 −2.19359
\(105\) 0 0
\(106\) 2832.10 2.59508
\(107\) 1166.74 1.05414 0.527068 0.849823i \(-0.323291\pi\)
0.527068 + 0.849823i \(0.323291\pi\)
\(108\) 0 0
\(109\) −1337.18 −1.17503 −0.587515 0.809213i \(-0.699894\pi\)
−0.587515 + 0.809213i \(0.699894\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1192.96 −1.00646
\(113\) 906.578 0.754723 0.377361 0.926066i \(-0.376831\pi\)
0.377361 + 0.926066i \(0.376831\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 701.836 0.561757
\(117\) 0 0
\(118\) −189.319 −0.147697
\(119\) 73.8488 0.0568883
\(120\) 0 0
\(121\) −123.495 −0.0927836
\(122\) −304.859 −0.226235
\(123\) 0 0
\(124\) 5784.74 4.18940
\(125\) 0 0
\(126\) 0 0
\(127\) 1714.89 1.19820 0.599101 0.800674i \(-0.295525\pi\)
0.599101 + 0.800674i \(0.295525\pi\)
\(128\) −737.564 −0.509313
\(129\) 0 0
\(130\) 0 0
\(131\) −470.611 −0.313874 −0.156937 0.987609i \(-0.550162\pi\)
−0.156937 + 0.987609i \(0.550162\pi\)
\(132\) 0 0
\(133\) 410.186 0.267426
\(134\) 2540.88 1.63805
\(135\) 0 0
\(136\) 658.042 0.414901
\(137\) −443.910 −0.276831 −0.138415 0.990374i \(-0.544201\pi\)
−0.138415 + 0.990374i \(0.544201\pi\)
\(138\) 0 0
\(139\) 1669.98 1.01904 0.509518 0.860460i \(-0.329824\pi\)
0.509518 + 0.860460i \(0.329824\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1918.76 1.13394
\(143\) −1296.11 −0.757945
\(144\) 0 0
\(145\) 0 0
\(146\) 3066.30 1.73814
\(147\) 0 0
\(148\) 5152.39 2.86165
\(149\) −743.871 −0.408995 −0.204497 0.978867i \(-0.565556\pi\)
−0.204497 + 0.978867i \(0.565556\pi\)
\(150\) 0 0
\(151\) 606.764 0.327005 0.163503 0.986543i \(-0.447721\pi\)
0.163503 + 0.986543i \(0.447721\pi\)
\(152\) 3655.03 1.95041
\(153\) 0 0
\(154\) −1283.09 −0.671393
\(155\) 0 0
\(156\) 0 0
\(157\) −3114.78 −1.58336 −0.791678 0.610939i \(-0.790792\pi\)
−0.791678 + 0.610939i \(0.790792\pi\)
\(158\) 3659.16 1.84245
\(159\) 0 0
\(160\) 0 0
\(161\) 877.430 0.429511
\(162\) 0 0
\(163\) −2413.07 −1.15955 −0.579774 0.814777i \(-0.696859\pi\)
−0.579774 + 0.814777i \(0.696859\pi\)
\(164\) 6705.67 3.19284
\(165\) 0 0
\(166\) −7038.81 −3.29107
\(167\) −610.475 −0.282874 −0.141437 0.989947i \(-0.545172\pi\)
−0.141437 + 0.989947i \(0.545172\pi\)
\(168\) 0 0
\(169\) −805.784 −0.366766
\(170\) 0 0
\(171\) 0 0
\(172\) −134.887 −0.0597968
\(173\) 3793.81 1.66727 0.833636 0.552315i \(-0.186255\pi\)
0.833636 + 0.552315i \(0.186255\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −5922.05 −2.53631
\(177\) 0 0
\(178\) −1862.25 −0.784165
\(179\) 2804.68 1.17112 0.585562 0.810627i \(-0.300874\pi\)
0.585562 + 0.810627i \(0.300874\pi\)
\(180\) 0 0
\(181\) 3106.04 1.27553 0.637763 0.770232i \(-0.279860\pi\)
0.637763 + 0.770232i \(0.279860\pi\)
\(182\) 1377.24 0.560924
\(183\) 0 0
\(184\) 7818.48 3.13253
\(185\) 0 0
\(186\) 0 0
\(187\) 366.598 0.143360
\(188\) 4969.95 1.92804
\(189\) 0 0
\(190\) 0 0
\(191\) −261.952 −0.0992365 −0.0496182 0.998768i \(-0.515800\pi\)
−0.0496182 + 0.998768i \(0.515800\pi\)
\(192\) 0 0
\(193\) −4051.07 −1.51089 −0.755447 0.655210i \(-0.772580\pi\)
−0.755447 + 0.655210i \(0.772580\pi\)
\(194\) 7626.88 2.82257
\(195\) 0 0
\(196\) 971.413 0.354013
\(197\) −2874.83 −1.03971 −0.519855 0.854254i \(-0.674014\pi\)
−0.519855 + 0.854254i \(0.674014\pi\)
\(198\) 0 0
\(199\) −3066.97 −1.09252 −0.546261 0.837615i \(-0.683949\pi\)
−0.546261 + 0.837615i \(0.683949\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 2504.81 0.872463
\(203\) −247.814 −0.0856804
\(204\) 0 0
\(205\) 0 0
\(206\) −10547.7 −3.56743
\(207\) 0 0
\(208\) 6356.60 2.11899
\(209\) 2036.23 0.673919
\(210\) 0 0
\(211\) 595.422 0.194268 0.0971340 0.995271i \(-0.469032\pi\)
0.0971340 + 0.995271i \(0.469032\pi\)
\(212\) −10643.9 −3.44824
\(213\) 0 0
\(214\) −6154.44 −1.96593
\(215\) 0 0
\(216\) 0 0
\(217\) −2042.56 −0.638976
\(218\) 7053.49 2.19139
\(219\) 0 0
\(220\) 0 0
\(221\) −393.498 −0.119772
\(222\) 0 0
\(223\) 3779.79 1.13504 0.567520 0.823360i \(-0.307903\pi\)
0.567520 + 0.823360i \(0.307903\pi\)
\(224\) 2799.79 0.835127
\(225\) 0 0
\(226\) −4782.12 −1.40753
\(227\) 1827.62 0.534376 0.267188 0.963644i \(-0.413906\pi\)
0.267188 + 0.963644i \(0.413906\pi\)
\(228\) 0 0
\(229\) −850.249 −0.245354 −0.122677 0.992447i \(-0.539148\pi\)
−0.122677 + 0.992447i \(0.539148\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −2208.18 −0.624890
\(233\) −6591.10 −1.85321 −0.926604 0.376039i \(-0.877286\pi\)
−0.926604 + 0.376039i \(0.877286\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 711.518 0.196254
\(237\) 0 0
\(238\) −389.547 −0.106095
\(239\) 182.556 0.0494083 0.0247042 0.999695i \(-0.492136\pi\)
0.0247042 + 0.999695i \(0.492136\pi\)
\(240\) 0 0
\(241\) 1523.90 0.407315 0.203657 0.979042i \(-0.434717\pi\)
0.203657 + 0.979042i \(0.434717\pi\)
\(242\) 651.426 0.173038
\(243\) 0 0
\(244\) 1145.75 0.300612
\(245\) 0 0
\(246\) 0 0
\(247\) −2185.65 −0.563034
\(248\) −18200.5 −4.66022
\(249\) 0 0
\(250\) 0 0
\(251\) −2357.73 −0.592903 −0.296451 0.955048i \(-0.595803\pi\)
−0.296451 + 0.955048i \(0.595803\pi\)
\(252\) 0 0
\(253\) 4355.71 1.08238
\(254\) −9045.89 −2.23460
\(255\) 0 0
\(256\) −2080.79 −0.508006
\(257\) 2782.55 0.675372 0.337686 0.941259i \(-0.390356\pi\)
0.337686 + 0.941259i \(0.390356\pi\)
\(258\) 0 0
\(259\) −1819.28 −0.436465
\(260\) 0 0
\(261\) 0 0
\(262\) 2482.44 0.585364
\(263\) 2043.78 0.479183 0.239591 0.970874i \(-0.422987\pi\)
0.239591 + 0.970874i \(0.422987\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2163.70 −0.498740
\(267\) 0 0
\(268\) −9549.41 −2.17658
\(269\) −3452.84 −0.782614 −0.391307 0.920260i \(-0.627977\pi\)
−0.391307 + 0.920260i \(0.627977\pi\)
\(270\) 0 0
\(271\) 2644.29 0.592728 0.296364 0.955075i \(-0.404226\pi\)
0.296364 + 0.955075i \(0.404226\pi\)
\(272\) −1797.93 −0.400793
\(273\) 0 0
\(274\) 2341.59 0.516280
\(275\) 0 0
\(276\) 0 0
\(277\) −2679.49 −0.581208 −0.290604 0.956843i \(-0.593856\pi\)
−0.290604 + 0.956843i \(0.593856\pi\)
\(278\) −8809.01 −1.90046
\(279\) 0 0
\(280\) 0 0
\(281\) 1019.69 0.216476 0.108238 0.994125i \(-0.465479\pi\)
0.108238 + 0.994125i \(0.465479\pi\)
\(282\) 0 0
\(283\) −432.206 −0.0907844 −0.0453922 0.998969i \(-0.514454\pi\)
−0.0453922 + 0.998969i \(0.514454\pi\)
\(284\) −7211.30 −1.50673
\(285\) 0 0
\(286\) 6836.87 1.41354
\(287\) −2367.73 −0.486979
\(288\) 0 0
\(289\) −4801.70 −0.977346
\(290\) 0 0
\(291\) 0 0
\(292\) −11524.1 −2.30958
\(293\) −2245.92 −0.447809 −0.223904 0.974611i \(-0.571880\pi\)
−0.223904 + 0.974611i \(0.571880\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −16211.0 −3.18325
\(297\) 0 0
\(298\) 3923.86 0.762761
\(299\) −4675.33 −0.904284
\(300\) 0 0
\(301\) 47.6278 0.00912034
\(302\) −3200.63 −0.609853
\(303\) 0 0
\(304\) −9986.44 −1.88408
\(305\) 0 0
\(306\) 0 0
\(307\) 3197.08 0.594354 0.297177 0.954822i \(-0.403955\pi\)
0.297177 + 0.954822i \(0.403955\pi\)
\(308\) 4822.26 0.892122
\(309\) 0 0
\(310\) 0 0
\(311\) 3355.60 0.611829 0.305915 0.952059i \(-0.401038\pi\)
0.305915 + 0.952059i \(0.401038\pi\)
\(312\) 0 0
\(313\) 2256.39 0.407472 0.203736 0.979026i \(-0.434692\pi\)
0.203736 + 0.979026i \(0.434692\pi\)
\(314\) 16430.2 2.95290
\(315\) 0 0
\(316\) −13752.3 −2.44818
\(317\) −6139.19 −1.08773 −0.543866 0.839172i \(-0.683040\pi\)
−0.543866 + 0.839172i \(0.683040\pi\)
\(318\) 0 0
\(319\) −1230.19 −0.215917
\(320\) 0 0
\(321\) 0 0
\(322\) −4628.37 −0.801022
\(323\) 618.199 0.106494
\(324\) 0 0
\(325\) 0 0
\(326\) 12728.8 2.16252
\(327\) 0 0
\(328\) −21098.0 −3.55166
\(329\) −1754.86 −0.294069
\(330\) 0 0
\(331\) 7029.81 1.16735 0.583676 0.811987i \(-0.301614\pi\)
0.583676 + 0.811987i \(0.301614\pi\)
\(332\) 26454.0 4.37305
\(333\) 0 0
\(334\) 3220.21 0.527550
\(335\) 0 0
\(336\) 0 0
\(337\) −10328.4 −1.66951 −0.834757 0.550619i \(-0.814392\pi\)
−0.834757 + 0.550619i \(0.814392\pi\)
\(338\) 4250.44 0.684005
\(339\) 0 0
\(340\) 0 0
\(341\) −10139.6 −1.61024
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 424.395 0.0665170
\(345\) 0 0
\(346\) −20012.0 −3.10940
\(347\) 1967.54 0.304389 0.152194 0.988351i \(-0.451366\pi\)
0.152194 + 0.988351i \(0.451366\pi\)
\(348\) 0 0
\(349\) −4365.46 −0.669564 −0.334782 0.942296i \(-0.608663\pi\)
−0.334782 + 0.942296i \(0.608663\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 13898.6 2.10454
\(353\) −6071.59 −0.915462 −0.457731 0.889091i \(-0.651338\pi\)
−0.457731 + 0.889091i \(0.651338\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6998.90 1.04197
\(357\) 0 0
\(358\) −14794.4 −2.18411
\(359\) −9638.04 −1.41693 −0.708463 0.705748i \(-0.750611\pi\)
−0.708463 + 0.705748i \(0.750611\pi\)
\(360\) 0 0
\(361\) −3425.27 −0.499384
\(362\) −16384.1 −2.37881
\(363\) 0 0
\(364\) −5176.10 −0.745334
\(365\) 0 0
\(366\) 0 0
\(367\) −522.725 −0.0743488 −0.0371744 0.999309i \(-0.511836\pi\)
−0.0371744 + 0.999309i \(0.511836\pi\)
\(368\) −21362.0 −3.02601
\(369\) 0 0
\(370\) 0 0
\(371\) 3758.30 0.525934
\(372\) 0 0
\(373\) −3229.84 −0.448351 −0.224175 0.974549i \(-0.571969\pi\)
−0.224175 + 0.974549i \(0.571969\pi\)
\(374\) −1933.77 −0.267361
\(375\) 0 0
\(376\) −15637.0 −2.14472
\(377\) 1320.46 0.180390
\(378\) 0 0
\(379\) 6639.71 0.899892 0.449946 0.893056i \(-0.351443\pi\)
0.449946 + 0.893056i \(0.351443\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1381.77 0.185073
\(383\) −14224.4 −1.89774 −0.948871 0.315664i \(-0.897773\pi\)
−0.948871 + 0.315664i \(0.897773\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 21369.1 2.81777
\(387\) 0 0
\(388\) −28664.2 −3.75052
\(389\) −2921.82 −0.380828 −0.190414 0.981704i \(-0.560983\pi\)
−0.190414 + 0.981704i \(0.560983\pi\)
\(390\) 0 0
\(391\) 1322.39 0.171039
\(392\) −3056.35 −0.393799
\(393\) 0 0
\(394\) 15164.5 1.93902
\(395\) 0 0
\(396\) 0 0
\(397\) −811.940 −0.102645 −0.0513226 0.998682i \(-0.516344\pi\)
−0.0513226 + 0.998682i \(0.516344\pi\)
\(398\) 16178.0 2.03751
\(399\) 0 0
\(400\) 0 0
\(401\) −2338.63 −0.291237 −0.145618 0.989341i \(-0.546517\pi\)
−0.145618 + 0.989341i \(0.546517\pi\)
\(402\) 0 0
\(403\) 10883.6 1.34529
\(404\) −9413.83 −1.15930
\(405\) 0 0
\(406\) 1307.20 0.159791
\(407\) −9031.21 −1.09990
\(408\) 0 0
\(409\) −2727.57 −0.329755 −0.164877 0.986314i \(-0.552723\pi\)
−0.164877 + 0.986314i \(0.552723\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 39641.3 4.74026
\(413\) −251.233 −0.0299331
\(414\) 0 0
\(415\) 0 0
\(416\) −14918.5 −1.75826
\(417\) 0 0
\(418\) −10741.0 −1.25684
\(419\) −13306.3 −1.55144 −0.775721 0.631076i \(-0.782614\pi\)
−0.775721 + 0.631076i \(0.782614\pi\)
\(420\) 0 0
\(421\) −11007.5 −1.27428 −0.637138 0.770750i \(-0.719882\pi\)
−0.637138 + 0.770750i \(0.719882\pi\)
\(422\) −3140.80 −0.362303
\(423\) 0 0
\(424\) 33488.9 3.83577
\(425\) 0 0
\(426\) 0 0
\(427\) −404.558 −0.0458500
\(428\) 23130.2 2.61225
\(429\) 0 0
\(430\) 0 0
\(431\) 6525.62 0.729300 0.364650 0.931145i \(-0.381189\pi\)
0.364650 + 0.931145i \(0.381189\pi\)
\(432\) 0 0
\(433\) 11716.3 1.30034 0.650171 0.759788i \(-0.274697\pi\)
0.650171 + 0.759788i \(0.274697\pi\)
\(434\) 10774.3 1.19167
\(435\) 0 0
\(436\) −26509.2 −2.91183
\(437\) 7345.10 0.804036
\(438\) 0 0
\(439\) −14611.4 −1.58853 −0.794264 0.607573i \(-0.792143\pi\)
−0.794264 + 0.607573i \(0.792143\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 2075.67 0.223370
\(443\) −15239.8 −1.63446 −0.817228 0.576314i \(-0.804490\pi\)
−0.817228 + 0.576314i \(0.804490\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −19938.1 −2.11681
\(447\) 0 0
\(448\) −5224.96 −0.551018
\(449\) −10678.8 −1.12241 −0.561206 0.827676i \(-0.689662\pi\)
−0.561206 + 0.827676i \(0.689662\pi\)
\(450\) 0 0
\(451\) −11753.8 −1.22720
\(452\) 17972.7 1.87027
\(453\) 0 0
\(454\) −9640.53 −0.996592
\(455\) 0 0
\(456\) 0 0
\(457\) −4228.23 −0.432797 −0.216399 0.976305i \(-0.569431\pi\)
−0.216399 + 0.976305i \(0.569431\pi\)
\(458\) 4484.99 0.457577
\(459\) 0 0
\(460\) 0 0
\(461\) −910.121 −0.0919492 −0.0459746 0.998943i \(-0.514639\pi\)
−0.0459746 + 0.998943i \(0.514639\pi\)
\(462\) 0 0
\(463\) −4456.16 −0.447290 −0.223645 0.974671i \(-0.571796\pi\)
−0.223645 + 0.974671i \(0.571796\pi\)
\(464\) 6033.30 0.603640
\(465\) 0 0
\(466\) 34767.5 3.45617
\(467\) −4429.42 −0.438907 −0.219453 0.975623i \(-0.570427\pi\)
−0.219453 + 0.975623i \(0.570427\pi\)
\(468\) 0 0
\(469\) 3371.84 0.331977
\(470\) 0 0
\(471\) 0 0
\(472\) −2238.65 −0.218310
\(473\) 236.432 0.0229835
\(474\) 0 0
\(475\) 0 0
\(476\) 1464.03 0.140975
\(477\) 0 0
\(478\) −962.970 −0.0921448
\(479\) −2752.85 −0.262591 −0.131296 0.991343i \(-0.541914\pi\)
−0.131296 + 0.991343i \(0.541914\pi\)
\(480\) 0 0
\(481\) 9693.90 0.918927
\(482\) −8038.43 −0.759628
\(483\) 0 0
\(484\) −2448.26 −0.229927
\(485\) 0 0
\(486\) 0 0
\(487\) 670.598 0.0623977 0.0311989 0.999513i \(-0.490067\pi\)
0.0311989 + 0.999513i \(0.490067\pi\)
\(488\) −3604.88 −0.334396
\(489\) 0 0
\(490\) 0 0
\(491\) 8244.70 0.757797 0.378898 0.925438i \(-0.376303\pi\)
0.378898 + 0.925438i \(0.376303\pi\)
\(492\) 0 0
\(493\) −373.485 −0.0341195
\(494\) 11529.1 1.05004
\(495\) 0 0
\(496\) 49728.3 4.50175
\(497\) 2546.27 0.229810
\(498\) 0 0
\(499\) 8164.91 0.732488 0.366244 0.930519i \(-0.380644\pi\)
0.366244 + 0.930519i \(0.380644\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 12436.8 1.10574
\(503\) 8175.59 0.724715 0.362357 0.932039i \(-0.381972\pi\)
0.362357 + 0.932039i \(0.381972\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −22976.0 −2.01859
\(507\) 0 0
\(508\) 33997.2 2.96926
\(509\) 878.448 0.0764961 0.0382480 0.999268i \(-0.487822\pi\)
0.0382480 + 0.999268i \(0.487822\pi\)
\(510\) 0 0
\(511\) 4069.09 0.352262
\(512\) 16876.5 1.45673
\(513\) 0 0
\(514\) −14677.7 −1.25955
\(515\) 0 0
\(516\) 0 0
\(517\) −8711.42 −0.741060
\(518\) 9596.55 0.813992
\(519\) 0 0
\(520\) 0 0
\(521\) −11712.6 −0.984910 −0.492455 0.870338i \(-0.663900\pi\)
−0.492455 + 0.870338i \(0.663900\pi\)
\(522\) 0 0
\(523\) 7341.82 0.613834 0.306917 0.951736i \(-0.400703\pi\)
0.306917 + 0.951736i \(0.400703\pi\)
\(524\) −9329.75 −0.777809
\(525\) 0 0
\(526\) −10780.8 −0.893659
\(527\) −3078.38 −0.254452
\(528\) 0 0
\(529\) 3544.92 0.291355
\(530\) 0 0
\(531\) 0 0
\(532\) 8131.84 0.662707
\(533\) 12616.3 1.02528
\(534\) 0 0
\(535\) 0 0
\(536\) 30045.3 2.42119
\(537\) 0 0
\(538\) 18213.4 1.45955
\(539\) −1702.71 −0.136068
\(540\) 0 0
\(541\) −15868.7 −1.26109 −0.630545 0.776153i \(-0.717169\pi\)
−0.630545 + 0.776153i \(0.717169\pi\)
\(542\) −13948.4 −1.10542
\(543\) 0 0
\(544\) 4219.61 0.332563
\(545\) 0 0
\(546\) 0 0
\(547\) −2315.26 −0.180975 −0.0904875 0.995898i \(-0.528843\pi\)
−0.0904875 + 0.995898i \(0.528843\pi\)
\(548\) −8800.41 −0.686013
\(549\) 0 0
\(550\) 0 0
\(551\) −2074.49 −0.160392
\(552\) 0 0
\(553\) 4855.84 0.373402
\(554\) 14134.1 1.08393
\(555\) 0 0
\(556\) 33106.9 2.52526
\(557\) −4819.05 −0.366588 −0.183294 0.983058i \(-0.558676\pi\)
−0.183294 + 0.983058i \(0.558676\pi\)
\(558\) 0 0
\(559\) −253.781 −0.0192018
\(560\) 0 0
\(561\) 0 0
\(562\) −5378.79 −0.403720
\(563\) 2540.86 0.190203 0.0951017 0.995468i \(-0.469682\pi\)
0.0951017 + 0.995468i \(0.469682\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 2279.85 0.169310
\(567\) 0 0
\(568\) 22688.9 1.67607
\(569\) 24220.0 1.78445 0.892227 0.451587i \(-0.149142\pi\)
0.892227 + 0.451587i \(0.149142\pi\)
\(570\) 0 0
\(571\) −11772.1 −0.862778 −0.431389 0.902166i \(-0.641976\pi\)
−0.431389 + 0.902166i \(0.641976\pi\)
\(572\) −25695.1 −1.87826
\(573\) 0 0
\(574\) 12489.6 0.908198
\(575\) 0 0
\(576\) 0 0
\(577\) −10584.3 −0.763655 −0.381827 0.924234i \(-0.624705\pi\)
−0.381827 + 0.924234i \(0.624705\pi\)
\(578\) 25328.6 1.82272
\(579\) 0 0
\(580\) 0 0
\(581\) −9340.74 −0.666987
\(582\) 0 0
\(583\) 18656.8 1.32536
\(584\) 36258.3 2.56914
\(585\) 0 0
\(586\) 11847.0 0.835148
\(587\) −8712.63 −0.612621 −0.306311 0.951932i \(-0.599095\pi\)
−0.306311 + 0.951932i \(0.599095\pi\)
\(588\) 0 0
\(589\) −17098.6 −1.19615
\(590\) 0 0
\(591\) 0 0
\(592\) 44292.4 3.07501
\(593\) −15362.9 −1.06387 −0.531937 0.846784i \(-0.678536\pi\)
−0.531937 + 0.846784i \(0.678536\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −14747.0 −1.01353
\(597\) 0 0
\(598\) 24662.0 1.68646
\(599\) −26003.8 −1.77377 −0.886883 0.461994i \(-0.847134\pi\)
−0.886883 + 0.461994i \(0.847134\pi\)
\(600\) 0 0
\(601\) 20567.7 1.39596 0.697982 0.716115i \(-0.254082\pi\)
0.697982 + 0.716115i \(0.254082\pi\)
\(602\) −251.233 −0.0170091
\(603\) 0 0
\(604\) 12029.0 0.810349
\(605\) 0 0
\(606\) 0 0
\(607\) −19642.1 −1.31342 −0.656711 0.754142i \(-0.728053\pi\)
−0.656711 + 0.754142i \(0.728053\pi\)
\(608\) 23437.4 1.56334
\(609\) 0 0
\(610\) 0 0
\(611\) 9350.65 0.619127
\(612\) 0 0
\(613\) −8454.59 −0.557060 −0.278530 0.960428i \(-0.589847\pi\)
−0.278530 + 0.960428i \(0.589847\pi\)
\(614\) −16864.3 −1.10845
\(615\) 0 0
\(616\) −15172.3 −0.992383
\(617\) −24168.4 −1.57696 −0.788479 0.615061i \(-0.789131\pi\)
−0.788479 + 0.615061i \(0.789131\pi\)
\(618\) 0 0
\(619\) −2037.56 −0.132305 −0.0661523 0.997810i \(-0.521072\pi\)
−0.0661523 + 0.997810i \(0.521072\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −17700.5 −1.14104
\(623\) −2471.27 −0.158923
\(624\) 0 0
\(625\) 0 0
\(626\) −11902.3 −0.759921
\(627\) 0 0
\(628\) −61749.8 −3.92370
\(629\) −2741.87 −0.173808
\(630\) 0 0
\(631\) 12339.5 0.778489 0.389244 0.921135i \(-0.372736\pi\)
0.389244 + 0.921135i \(0.372736\pi\)
\(632\) 43268.7 2.72332
\(633\) 0 0
\(634\) 32383.7 2.02858
\(635\) 0 0
\(636\) 0 0
\(637\) 1827.65 0.113680
\(638\) 6489.15 0.402677
\(639\) 0 0
\(640\) 0 0
\(641\) 10222.6 0.629906 0.314953 0.949107i \(-0.398011\pi\)
0.314953 + 0.949107i \(0.398011\pi\)
\(642\) 0 0
\(643\) 1211.75 0.0743187 0.0371594 0.999309i \(-0.488169\pi\)
0.0371594 + 0.999309i \(0.488169\pi\)
\(644\) 17394.8 1.06437
\(645\) 0 0
\(646\) −3260.95 −0.198607
\(647\) −2817.22 −0.171184 −0.0855922 0.996330i \(-0.527278\pi\)
−0.0855922 + 0.996330i \(0.527278\pi\)
\(648\) 0 0
\(649\) −1247.16 −0.0754320
\(650\) 0 0
\(651\) 0 0
\(652\) −47838.6 −2.87347
\(653\) 20986.2 1.25766 0.628831 0.777542i \(-0.283534\pi\)
0.628831 + 0.777542i \(0.283534\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 57645.1 3.43089
\(657\) 0 0
\(658\) 9256.74 0.548428
\(659\) 2384.09 0.140927 0.0704635 0.997514i \(-0.477552\pi\)
0.0704635 + 0.997514i \(0.477552\pi\)
\(660\) 0 0
\(661\) −7577.10 −0.445862 −0.222931 0.974834i \(-0.571562\pi\)
−0.222931 + 0.974834i \(0.571562\pi\)
\(662\) −37081.7 −2.17707
\(663\) 0 0
\(664\) −83232.2 −4.86451
\(665\) 0 0
\(666\) 0 0
\(667\) −4437.54 −0.257605
\(668\) −12102.5 −0.700989
\(669\) 0 0
\(670\) 0 0
\(671\) −2008.30 −0.115543
\(672\) 0 0
\(673\) −11724.6 −0.671547 −0.335774 0.941943i \(-0.608998\pi\)
−0.335774 + 0.941943i \(0.608998\pi\)
\(674\) 54481.7 3.11358
\(675\) 0 0
\(676\) −15974.5 −0.908880
\(677\) 32304.3 1.83390 0.916952 0.398997i \(-0.130642\pi\)
0.916952 + 0.398997i \(0.130642\pi\)
\(678\) 0 0
\(679\) 10121.1 0.572038
\(680\) 0 0
\(681\) 0 0
\(682\) 53485.6 3.00303
\(683\) 33367.1 1.86934 0.934669 0.355519i \(-0.115696\pi\)
0.934669 + 0.355519i \(0.115696\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1809.30 0.100699
\(687\) 0 0
\(688\) −1159.55 −0.0642551
\(689\) −20025.8 −1.10729
\(690\) 0 0
\(691\) −1043.67 −0.0574577 −0.0287288 0.999587i \(-0.509146\pi\)
−0.0287288 + 0.999587i \(0.509146\pi\)
\(692\) 75211.3 4.13166
\(693\) 0 0
\(694\) −10378.6 −0.567674
\(695\) 0 0
\(696\) 0 0
\(697\) −3568.46 −0.193924
\(698\) 23027.4 1.24871
\(699\) 0 0
\(700\) 0 0
\(701\) 11305.7 0.609143 0.304572 0.952489i \(-0.401487\pi\)
0.304572 + 0.952489i \(0.401487\pi\)
\(702\) 0 0
\(703\) −15229.4 −0.817055
\(704\) −25937.6 −1.38858
\(705\) 0 0
\(706\) 32027.1 1.70730
\(707\) 3323.97 0.176818
\(708\) 0 0
\(709\) −13306.8 −0.704860 −0.352430 0.935838i \(-0.614645\pi\)
−0.352430 + 0.935838i \(0.614645\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −22020.6 −1.15907
\(713\) −36575.6 −1.92113
\(714\) 0 0
\(715\) 0 0
\(716\) 55602.0 2.90216
\(717\) 0 0
\(718\) 50839.9 2.64252
\(719\) −10701.2 −0.555062 −0.277531 0.960717i \(-0.589516\pi\)
−0.277531 + 0.960717i \(0.589516\pi\)
\(720\) 0 0
\(721\) −13997.1 −0.722996
\(722\) 18068.0 0.931333
\(723\) 0 0
\(724\) 61576.5 3.16088
\(725\) 0 0
\(726\) 0 0
\(727\) 2121.14 0.108210 0.0541051 0.998535i \(-0.482769\pi\)
0.0541051 + 0.998535i \(0.482769\pi\)
\(728\) 16285.6 0.829098
\(729\) 0 0
\(730\) 0 0
\(731\) 71.7808 0.00363189
\(732\) 0 0
\(733\) 21584.0 1.08762 0.543809 0.839209i \(-0.316981\pi\)
0.543809 + 0.839209i \(0.316981\pi\)
\(734\) 2757.33 0.138658
\(735\) 0 0
\(736\) 50135.0 2.51087
\(737\) 16738.4 0.836588
\(738\) 0 0
\(739\) −9945.21 −0.495048 −0.247524 0.968882i \(-0.579617\pi\)
−0.247524 + 0.968882i \(0.579617\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −19824.7 −0.980848
\(743\) 2867.01 0.141562 0.0707808 0.997492i \(-0.477451\pi\)
0.0707808 + 0.997492i \(0.477451\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 17037.1 0.836158
\(747\) 0 0
\(748\) 7267.71 0.355259
\(749\) −8167.15 −0.398426
\(750\) 0 0
\(751\) −10824.1 −0.525934 −0.262967 0.964805i \(-0.584701\pi\)
−0.262967 + 0.964805i \(0.584701\pi\)
\(752\) 42724.0 2.07179
\(753\) 0 0
\(754\) −6965.31 −0.336421
\(755\) 0 0
\(756\) 0 0
\(757\) 14512.0 0.696761 0.348381 0.937353i \(-0.386732\pi\)
0.348381 + 0.937353i \(0.386732\pi\)
\(758\) −35023.9 −1.67827
\(759\) 0 0
\(760\) 0 0
\(761\) 33075.8 1.57556 0.787778 0.615959i \(-0.211231\pi\)
0.787778 + 0.615959i \(0.211231\pi\)
\(762\) 0 0
\(763\) 9360.23 0.444120
\(764\) −5193.13 −0.245917
\(765\) 0 0
\(766\) 75032.8 3.53922
\(767\) 1338.68 0.0630206
\(768\) 0 0
\(769\) 6728.44 0.315518 0.157759 0.987478i \(-0.449573\pi\)
0.157759 + 0.987478i \(0.449573\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −80311.5 −3.74414
\(773\) −24233.3 −1.12757 −0.563784 0.825922i \(-0.690655\pi\)
−0.563784 + 0.825922i \(0.690655\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 90186.0 4.17202
\(777\) 0 0
\(778\) 15412.4 0.710231
\(779\) −19820.6 −0.911615
\(780\) 0 0
\(781\) 12640.1 0.579127
\(782\) −6975.51 −0.318982
\(783\) 0 0
\(784\) 8350.72 0.380408
\(785\) 0 0
\(786\) 0 0
\(787\) 17200.4 0.779069 0.389535 0.921012i \(-0.372636\pi\)
0.389535 + 0.921012i \(0.372636\pi\)
\(788\) −56992.7 −2.57650
\(789\) 0 0
\(790\) 0 0
\(791\) −6346.05 −0.285258
\(792\) 0 0
\(793\) 2155.66 0.0965318
\(794\) 4282.92 0.191430
\(795\) 0 0
\(796\) −60801.9 −2.70737
\(797\) −4208.87 −0.187059 −0.0935295 0.995617i \(-0.529815\pi\)
−0.0935295 + 0.995617i \(0.529815\pi\)
\(798\) 0 0
\(799\) −2644.78 −0.117104
\(800\) 0 0
\(801\) 0 0
\(802\) 12336.1 0.543146
\(803\) 20199.7 0.887709
\(804\) 0 0
\(805\) 0 0
\(806\) −57410.2 −2.50892
\(807\) 0 0
\(808\) 29618.7 1.28958
\(809\) 23632.1 1.02702 0.513511 0.858083i \(-0.328344\pi\)
0.513511 + 0.858083i \(0.328344\pi\)
\(810\) 0 0
\(811\) 28425.1 1.23075 0.615377 0.788233i \(-0.289004\pi\)
0.615377 + 0.788233i \(0.289004\pi\)
\(812\) −4912.85 −0.212324
\(813\) 0 0
\(814\) 47638.9 2.05128
\(815\) 0 0
\(816\) 0 0
\(817\) 398.699 0.0170731
\(818\) 14387.7 0.614981
\(819\) 0 0
\(820\) 0 0
\(821\) −39409.6 −1.67528 −0.837640 0.546223i \(-0.816065\pi\)
−0.837640 + 0.546223i \(0.816065\pi\)
\(822\) 0 0
\(823\) −16346.6 −0.692352 −0.346176 0.938170i \(-0.612520\pi\)
−0.346176 + 0.938170i \(0.612520\pi\)
\(824\) −124723. −5.27300
\(825\) 0 0
\(826\) 1325.23 0.0558241
\(827\) −3738.87 −0.157211 −0.0786054 0.996906i \(-0.525047\pi\)
−0.0786054 + 0.996906i \(0.525047\pi\)
\(828\) 0 0
\(829\) −45196.2 −1.89352 −0.946761 0.321937i \(-0.895666\pi\)
−0.946761 + 0.321937i \(0.895666\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 27840.8 1.16010
\(833\) −516.942 −0.0215018
\(834\) 0 0
\(835\) 0 0
\(836\) 40367.8 1.67004
\(837\) 0 0
\(838\) 70189.5 2.89338
\(839\) −15899.7 −0.654254 −0.327127 0.944980i \(-0.606080\pi\)
−0.327127 + 0.944980i \(0.606080\pi\)
\(840\) 0 0
\(841\) −23135.7 −0.948612
\(842\) 58063.4 2.37648
\(843\) 0 0
\(844\) 11804.1 0.481414
\(845\) 0 0
\(846\) 0 0
\(847\) 864.465 0.0350689
\(848\) −91500.0 −3.70534
\(849\) 0 0
\(850\) 0 0
\(851\) −32577.4 −1.31227
\(852\) 0 0
\(853\) −33926.7 −1.36182 −0.680908 0.732369i \(-0.738415\pi\)
−0.680908 + 0.732369i \(0.738415\pi\)
\(854\) 2134.01 0.0855086
\(855\) 0 0
\(856\) −72774.7 −2.90583
\(857\) −35432.4 −1.41231 −0.706154 0.708058i \(-0.749572\pi\)
−0.706154 + 0.708058i \(0.749572\pi\)
\(858\) 0 0
\(859\) −6780.17 −0.269309 −0.134655 0.990893i \(-0.542992\pi\)
−0.134655 + 0.990893i \(0.542992\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −34422.1 −1.36012
\(863\) −30675.1 −1.20995 −0.604977 0.796243i \(-0.706818\pi\)
−0.604977 + 0.796243i \(0.706818\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −61802.4 −2.42509
\(867\) 0 0
\(868\) −40493.2 −1.58344
\(869\) 24105.2 0.940981
\(870\) 0 0
\(871\) −17966.6 −0.698938
\(872\) 83405.8 3.23908
\(873\) 0 0
\(874\) −38744.8 −1.49950
\(875\) 0 0
\(876\) 0 0
\(877\) −40861.3 −1.57330 −0.786652 0.617397i \(-0.788187\pi\)
−0.786652 + 0.617397i \(0.788187\pi\)
\(878\) 77073.9 2.96255
\(879\) 0 0
\(880\) 0 0
\(881\) 43839.0 1.67647 0.838236 0.545308i \(-0.183587\pi\)
0.838236 + 0.545308i \(0.183587\pi\)
\(882\) 0 0
\(883\) −44625.1 −1.70074 −0.850371 0.526183i \(-0.823623\pi\)
−0.850371 + 0.526183i \(0.823623\pi\)
\(884\) −7801.01 −0.296806
\(885\) 0 0
\(886\) 80388.6 3.04820
\(887\) −43967.5 −1.66436 −0.832178 0.554509i \(-0.812906\pi\)
−0.832178 + 0.554509i \(0.812906\pi\)
\(888\) 0 0
\(889\) −12004.2 −0.452878
\(890\) 0 0
\(891\) 0 0
\(892\) 74933.5 2.81273
\(893\) −14690.2 −0.550491
\(894\) 0 0
\(895\) 0 0
\(896\) 5162.95 0.192502
\(897\) 0 0
\(898\) 56329.7 2.09326
\(899\) 10330.1 0.383234
\(900\) 0 0
\(901\) 5664.21 0.209436
\(902\) 62000.4 2.28868
\(903\) 0 0
\(904\) −56547.4 −2.08046
\(905\) 0 0
\(906\) 0 0
\(907\) 13584.3 0.497309 0.248654 0.968592i \(-0.420012\pi\)
0.248654 + 0.968592i \(0.420012\pi\)
\(908\) 36232.1 1.32423
\(909\) 0 0
\(910\) 0 0
\(911\) 16421.6 0.597226 0.298613 0.954374i \(-0.403476\pi\)
0.298613 + 0.954374i \(0.403476\pi\)
\(912\) 0 0
\(913\) −46369.0 −1.68082
\(914\) 22303.6 0.807152
\(915\) 0 0
\(916\) −16856.0 −0.608010
\(917\) 3294.28 0.118633
\(918\) 0 0
\(919\) −29487.3 −1.05843 −0.529214 0.848488i \(-0.677513\pi\)
−0.529214 + 0.848488i \(0.677513\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 4800.81 0.171482
\(923\) −13567.6 −0.483839
\(924\) 0 0
\(925\) 0 0
\(926\) 23505.9 0.834181
\(927\) 0 0
\(928\) −14159.7 −0.500878
\(929\) −3441.85 −0.121554 −0.0607769 0.998151i \(-0.519358\pi\)
−0.0607769 + 0.998151i \(0.519358\pi\)
\(930\) 0 0
\(931\) −2871.30 −0.101077
\(932\) −130667. −4.59242
\(933\) 0 0
\(934\) 23364.8 0.818545
\(935\) 0 0
\(936\) 0 0
\(937\) −5646.60 −0.196869 −0.0984346 0.995144i \(-0.531384\pi\)
−0.0984346 + 0.995144i \(0.531384\pi\)
\(938\) −17786.2 −0.619125
\(939\) 0 0
\(940\) 0 0
\(941\) 44680.1 1.54785 0.773927 0.633275i \(-0.218290\pi\)
0.773927 + 0.633275i \(0.218290\pi\)
\(942\) 0 0
\(943\) −42398.4 −1.46414
\(944\) 6116.54 0.210886
\(945\) 0 0
\(946\) −1247.16 −0.0428633
\(947\) −48924.6 −1.67881 −0.839406 0.543505i \(-0.817097\pi\)
−0.839406 + 0.543505i \(0.817097\pi\)
\(948\) 0 0
\(949\) −21681.9 −0.741647
\(950\) 0 0
\(951\) 0 0
\(952\) −4606.29 −0.156818
\(953\) 52014.3 1.76801 0.884003 0.467482i \(-0.154839\pi\)
0.884003 + 0.467482i \(0.154839\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 3619.14 0.122439
\(957\) 0 0
\(958\) 14521.1 0.489723
\(959\) 3107.37 0.104632
\(960\) 0 0
\(961\) 55352.8 1.85804
\(962\) −51134.5 −1.71377
\(963\) 0 0
\(964\) 30210.9 1.00936
\(965\) 0 0
\(966\) 0 0
\(967\) 47117.7 1.56691 0.783456 0.621448i \(-0.213455\pi\)
0.783456 + 0.621448i \(0.213455\pi\)
\(968\) 7702.95 0.255767
\(969\) 0 0
\(970\) 0 0
\(971\) 8195.04 0.270846 0.135423 0.990788i \(-0.456761\pi\)
0.135423 + 0.990788i \(0.456761\pi\)
\(972\) 0 0
\(973\) −11689.9 −0.385159
\(974\) −3537.35 −0.116370
\(975\) 0 0
\(976\) 9849.42 0.323025
\(977\) 4643.51 0.152056 0.0760282 0.997106i \(-0.475776\pi\)
0.0760282 + 0.997106i \(0.475776\pi\)
\(978\) 0 0
\(979\) −12267.8 −0.400490
\(980\) 0 0
\(981\) 0 0
\(982\) −43490.1 −1.41326
\(983\) 43986.5 1.42721 0.713607 0.700546i \(-0.247060\pi\)
0.713607 + 0.700546i \(0.247060\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 1970.10 0.0636317
\(987\) 0 0
\(988\) −43329.9 −1.39525
\(989\) 852.859 0.0274210
\(990\) 0 0
\(991\) 1595.21 0.0511337 0.0255668 0.999673i \(-0.491861\pi\)
0.0255668 + 0.999673i \(0.491861\pi\)
\(992\) −116709. −3.73539
\(993\) 0 0
\(994\) −13431.3 −0.428588
\(995\) 0 0
\(996\) 0 0
\(997\) −21501.2 −0.682998 −0.341499 0.939882i \(-0.610935\pi\)
−0.341499 + 0.939882i \(0.610935\pi\)
\(998\) −43069.2 −1.36606
\(999\) 0 0
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 1575.4.a.p.1.1 2
3.2 odd 2 525.4.a.n.1.2 2
5.4 even 2 63.4.a.e.1.2 2
15.2 even 4 525.4.d.g.274.4 4
15.8 even 4 525.4.d.g.274.1 4
15.14 odd 2 21.4.a.c.1.1 2
20.19 odd 2 1008.4.a.ba.1.1 2
35.4 even 6 441.4.e.q.226.1 4
35.9 even 6 441.4.e.q.361.1 4
35.19 odd 6 441.4.e.p.361.1 4
35.24 odd 6 441.4.e.p.226.1 4
35.34 odd 2 441.4.a.r.1.2 2
60.59 even 2 336.4.a.m.1.2 2
105.44 odd 6 147.4.e.l.67.2 4
105.59 even 6 147.4.e.m.79.2 4
105.74 odd 6 147.4.e.l.79.2 4
105.89 even 6 147.4.e.m.67.2 4
105.104 even 2 147.4.a.i.1.1 2
120.29 odd 2 1344.4.a.bg.1.1 2
120.59 even 2 1344.4.a.bo.1.1 2
420.419 odd 2 2352.4.a.bz.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.a.c.1.1 2 15.14 odd 2
63.4.a.e.1.2 2 5.4 even 2
147.4.a.i.1.1 2 105.104 even 2
147.4.e.l.67.2 4 105.44 odd 6
147.4.e.l.79.2 4 105.74 odd 6
147.4.e.m.67.2 4 105.89 even 6
147.4.e.m.79.2 4 105.59 even 6
336.4.a.m.1.2 2 60.59 even 2
441.4.a.r.1.2 2 35.34 odd 2
441.4.e.p.226.1 4 35.24 odd 6
441.4.e.p.361.1 4 35.19 odd 6
441.4.e.q.226.1 4 35.4 even 6
441.4.e.q.361.1 4 35.9 even 6
525.4.a.n.1.2 2 3.2 odd 2
525.4.d.g.274.1 4 15.8 even 4
525.4.d.g.274.4 4 15.2 even 4
1008.4.a.ba.1.1 2 20.19 odd 2
1344.4.a.bg.1.1 2 120.29 odd 2
1344.4.a.bo.1.1 2 120.59 even 2
1575.4.a.p.1.1 2 1.1 even 1 trivial
2352.4.a.bz.1.1 2 420.419 odd 2