Properties

Label 8033.2.a.c.1.7
Level $8033$
Weight $2$
Character 8033.1
Self dual yes
Analytic conductor $64.144$
Analytic rank $1$
Dimension $154$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8033,2,Mod(1,8033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8033, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8033 = 29 \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8033.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(64.1438279437\)
Analytic rank: \(1\)
Dimension: \(154\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 8033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.66581 q^{2} -3.36665 q^{3} +5.10653 q^{4} -1.10799 q^{5} +8.97484 q^{6} -4.45627 q^{7} -8.28140 q^{8} +8.33433 q^{9} +O(q^{10})\) \(q-2.66581 q^{2} -3.36665 q^{3} +5.10653 q^{4} -1.10799 q^{5} +8.97484 q^{6} -4.45627 q^{7} -8.28140 q^{8} +8.33433 q^{9} +2.95369 q^{10} -4.32851 q^{11} -17.1919 q^{12} -5.75777 q^{13} +11.8796 q^{14} +3.73022 q^{15} +11.8636 q^{16} -6.70001 q^{17} -22.2177 q^{18} -7.99128 q^{19} -5.65799 q^{20} +15.0027 q^{21} +11.5390 q^{22} -2.90229 q^{23} +27.8806 q^{24} -3.77236 q^{25} +15.3491 q^{26} -17.9588 q^{27} -22.7561 q^{28} +1.00000 q^{29} -9.94404 q^{30} -7.11406 q^{31} -15.0632 q^{32} +14.5726 q^{33} +17.8609 q^{34} +4.93751 q^{35} +42.5595 q^{36} +5.50479 q^{37} +21.3032 q^{38} +19.3844 q^{39} +9.17572 q^{40} -2.93502 q^{41} -39.9943 q^{42} -1.55429 q^{43} -22.1036 q^{44} -9.23437 q^{45} +7.73696 q^{46} -5.22730 q^{47} -39.9404 q^{48} +12.8584 q^{49} +10.0564 q^{50} +22.5566 q^{51} -29.4022 q^{52} -2.60392 q^{53} +47.8748 q^{54} +4.79595 q^{55} +36.9042 q^{56} +26.9039 q^{57} -2.66581 q^{58} +6.36172 q^{59} +19.0485 q^{60} -13.9229 q^{61} +18.9647 q^{62} -37.1400 q^{63} +16.4284 q^{64} +6.37956 q^{65} -38.8477 q^{66} -0.349472 q^{67} -34.2138 q^{68} +9.77101 q^{69} -13.1624 q^{70} -6.97042 q^{71} -69.0199 q^{72} +11.1466 q^{73} -14.6747 q^{74} +12.7002 q^{75} -40.8077 q^{76} +19.2890 q^{77} -51.6751 q^{78} +0.734753 q^{79} -13.1447 q^{80} +35.4581 q^{81} +7.82421 q^{82} +4.15474 q^{83} +76.6117 q^{84} +7.42355 q^{85} +4.14343 q^{86} -3.36665 q^{87} +35.8461 q^{88} +2.52229 q^{89} +24.6170 q^{90} +25.6582 q^{91} -14.8206 q^{92} +23.9506 q^{93} +13.9350 q^{94} +8.85427 q^{95} +50.7124 q^{96} +5.34178 q^{97} -34.2779 q^{98} -36.0752 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66581 −1.88501 −0.942505 0.334192i \(-0.891537\pi\)
−0.942505 + 0.334192i \(0.891537\pi\)
\(3\) −3.36665 −1.94374 −0.971868 0.235526i \(-0.924319\pi\)
−0.971868 + 0.235526i \(0.924319\pi\)
\(4\) 5.10653 2.55326
\(5\) −1.10799 −0.495509 −0.247754 0.968823i \(-0.579693\pi\)
−0.247754 + 0.968823i \(0.579693\pi\)
\(6\) 8.97484 3.66396
\(7\) −4.45627 −1.68431 −0.842156 0.539234i \(-0.818714\pi\)
−0.842156 + 0.539234i \(0.818714\pi\)
\(8\) −8.28140 −2.92792
\(9\) 8.33433 2.77811
\(10\) 2.95369 0.934039
\(11\) −4.32851 −1.30509 −0.652547 0.757748i \(-0.726300\pi\)
−0.652547 + 0.757748i \(0.726300\pi\)
\(12\) −17.1919 −4.96287
\(13\) −5.75777 −1.59692 −0.798459 0.602049i \(-0.794351\pi\)
−0.798459 + 0.602049i \(0.794351\pi\)
\(14\) 11.8796 3.17495
\(15\) 3.73022 0.963138
\(16\) 11.8636 2.96589
\(17\) −6.70001 −1.62499 −0.812495 0.582968i \(-0.801891\pi\)
−0.812495 + 0.582968i \(0.801891\pi\)
\(18\) −22.2177 −5.23677
\(19\) −7.99128 −1.83333 −0.916663 0.399661i \(-0.869128\pi\)
−0.916663 + 0.399661i \(0.869128\pi\)
\(20\) −5.65799 −1.26516
\(21\) 15.0027 3.27386
\(22\) 11.5390 2.46012
\(23\) −2.90229 −0.605170 −0.302585 0.953122i \(-0.597850\pi\)
−0.302585 + 0.953122i \(0.597850\pi\)
\(24\) 27.8806 5.69110
\(25\) −3.77236 −0.754471
\(26\) 15.3491 3.01021
\(27\) −17.9588 −3.45618
\(28\) −22.7561 −4.30049
\(29\) 1.00000 0.185695
\(30\) −9.94404 −1.81553
\(31\) −7.11406 −1.27772 −0.638862 0.769322i \(-0.720594\pi\)
−0.638862 + 0.769322i \(0.720594\pi\)
\(32\) −15.0632 −2.66282
\(33\) 14.5726 2.53676
\(34\) 17.8609 3.06312
\(35\) 4.93751 0.834591
\(36\) 42.5595 7.09325
\(37\) 5.50479 0.904983 0.452491 0.891769i \(-0.350535\pi\)
0.452491 + 0.891769i \(0.350535\pi\)
\(38\) 21.3032 3.45584
\(39\) 19.3844 3.10399
\(40\) 9.17572 1.45081
\(41\) −2.93502 −0.458374 −0.229187 0.973382i \(-0.573607\pi\)
−0.229187 + 0.973382i \(0.573607\pi\)
\(42\) −39.9943 −6.17126
\(43\) −1.55429 −0.237027 −0.118513 0.992952i \(-0.537813\pi\)
−0.118513 + 0.992952i \(0.537813\pi\)
\(44\) −22.1036 −3.33225
\(45\) −9.23437 −1.37658
\(46\) 7.73696 1.14075
\(47\) −5.22730 −0.762480 −0.381240 0.924476i \(-0.624503\pi\)
−0.381240 + 0.924476i \(0.624503\pi\)
\(48\) −39.9404 −5.76491
\(49\) 12.8584 1.83691
\(50\) 10.0564 1.42219
\(51\) 22.5566 3.15855
\(52\) −29.4022 −4.07735
\(53\) −2.60392 −0.357676 −0.178838 0.983879i \(-0.557234\pi\)
−0.178838 + 0.983879i \(0.557234\pi\)
\(54\) 47.8748 6.51493
\(55\) 4.79595 0.646686
\(56\) 36.9042 4.93153
\(57\) 26.9039 3.56350
\(58\) −2.66581 −0.350038
\(59\) 6.36172 0.828226 0.414113 0.910226i \(-0.364092\pi\)
0.414113 + 0.910226i \(0.364092\pi\)
\(60\) 19.0485 2.45915
\(61\) −13.9229 −1.78265 −0.891324 0.453367i \(-0.850223\pi\)
−0.891324 + 0.453367i \(0.850223\pi\)
\(62\) 18.9647 2.40852
\(63\) −37.1400 −4.67921
\(64\) 16.4284 2.05354
\(65\) 6.37956 0.791287
\(66\) −38.8477 −4.78182
\(67\) −0.349472 −0.0426948 −0.0213474 0.999772i \(-0.506796\pi\)
−0.0213474 + 0.999772i \(0.506796\pi\)
\(68\) −34.2138 −4.14903
\(69\) 9.77101 1.17629
\(70\) −13.1624 −1.57321
\(71\) −6.97042 −0.827237 −0.413618 0.910450i \(-0.635735\pi\)
−0.413618 + 0.910450i \(0.635735\pi\)
\(72\) −69.0199 −8.13408
\(73\) 11.1466 1.30461 0.652307 0.757955i \(-0.273801\pi\)
0.652307 + 0.757955i \(0.273801\pi\)
\(74\) −14.6747 −1.70590
\(75\) 12.7002 1.46649
\(76\) −40.8077 −4.68096
\(77\) 19.2890 2.19819
\(78\) −51.6751 −5.85105
\(79\) 0.734753 0.0826661 0.0413331 0.999145i \(-0.486840\pi\)
0.0413331 + 0.999145i \(0.486840\pi\)
\(80\) −13.1447 −1.46962
\(81\) 35.4581 3.93979
\(82\) 7.82421 0.864039
\(83\) 4.15474 0.456042 0.228021 0.973656i \(-0.426775\pi\)
0.228021 + 0.973656i \(0.426775\pi\)
\(84\) 76.6117 8.35902
\(85\) 7.42355 0.805197
\(86\) 4.14343 0.446798
\(87\) −3.36665 −0.360943
\(88\) 35.8461 3.82121
\(89\) 2.52229 0.267362 0.133681 0.991024i \(-0.457320\pi\)
0.133681 + 0.991024i \(0.457320\pi\)
\(90\) 24.6170 2.59486
\(91\) 25.6582 2.68971
\(92\) −14.8206 −1.54516
\(93\) 23.9506 2.48356
\(94\) 13.9350 1.43728
\(95\) 8.85427 0.908429
\(96\) 50.7124 5.17581
\(97\) 5.34178 0.542376 0.271188 0.962526i \(-0.412584\pi\)
0.271188 + 0.962526i \(0.412584\pi\)
\(98\) −34.2779 −3.46259
\(99\) −36.0752 −3.62570
\(100\) −19.2636 −1.92636
\(101\) −5.05772 −0.503262 −0.251631 0.967823i \(-0.580967\pi\)
−0.251631 + 0.967823i \(0.580967\pi\)
\(102\) −60.1315 −5.95391
\(103\) −12.9852 −1.27947 −0.639733 0.768598i \(-0.720955\pi\)
−0.639733 + 0.768598i \(0.720955\pi\)
\(104\) 47.6824 4.67564
\(105\) −16.6229 −1.62223
\(106\) 6.94156 0.674223
\(107\) 1.43422 0.138651 0.0693257 0.997594i \(-0.477915\pi\)
0.0693257 + 0.997594i \(0.477915\pi\)
\(108\) −91.7072 −8.82453
\(109\) −5.33818 −0.511304 −0.255652 0.966769i \(-0.582290\pi\)
−0.255652 + 0.966769i \(0.582290\pi\)
\(110\) −12.7851 −1.21901
\(111\) −18.5327 −1.75905
\(112\) −52.8672 −4.99548
\(113\) −9.94896 −0.935920 −0.467960 0.883750i \(-0.655011\pi\)
−0.467960 + 0.883750i \(0.655011\pi\)
\(114\) −71.7205 −6.71724
\(115\) 3.21572 0.299867
\(116\) 5.10653 0.474129
\(117\) −47.9872 −4.43642
\(118\) −16.9591 −1.56121
\(119\) 29.8571 2.73699
\(120\) −30.8914 −2.81999
\(121\) 7.73598 0.703271
\(122\) 37.1158 3.36031
\(123\) 9.88120 0.890958
\(124\) −36.3281 −3.26236
\(125\) 9.71969 0.869356
\(126\) 99.0082 8.82035
\(127\) −18.7585 −1.66455 −0.832273 0.554367i \(-0.812961\pi\)
−0.832273 + 0.554367i \(0.812961\pi\)
\(128\) −13.6685 −1.20814
\(129\) 5.23274 0.460717
\(130\) −17.0067 −1.49158
\(131\) 5.88061 0.513791 0.256896 0.966439i \(-0.417300\pi\)
0.256896 + 0.966439i \(0.417300\pi\)
\(132\) 74.4152 6.47701
\(133\) 35.6113 3.08789
\(134\) 0.931624 0.0804801
\(135\) 19.8982 1.71257
\(136\) 55.4854 4.75784
\(137\) −13.0288 −1.11312 −0.556561 0.830807i \(-0.687880\pi\)
−0.556561 + 0.830807i \(0.687880\pi\)
\(138\) −26.0476 −2.21732
\(139\) −14.9439 −1.26752 −0.633762 0.773528i \(-0.718490\pi\)
−0.633762 + 0.773528i \(0.718490\pi\)
\(140\) 25.2135 2.13093
\(141\) 17.5985 1.48206
\(142\) 18.5818 1.55935
\(143\) 24.9226 2.08413
\(144\) 98.8748 8.23957
\(145\) −1.10799 −0.0920137
\(146\) −29.7147 −2.45921
\(147\) −43.2896 −3.57046
\(148\) 28.1104 2.31066
\(149\) 5.10797 0.418461 0.209231 0.977866i \(-0.432904\pi\)
0.209231 + 0.977866i \(0.432904\pi\)
\(150\) −33.8563 −2.76435
\(151\) −16.1551 −1.31469 −0.657343 0.753592i \(-0.728320\pi\)
−0.657343 + 0.753592i \(0.728320\pi\)
\(152\) 66.1790 5.36783
\(153\) −55.8401 −4.51440
\(154\) −51.4208 −4.14360
\(155\) 7.88232 0.633123
\(156\) 98.9869 7.92530
\(157\) −3.26552 −0.260617 −0.130308 0.991474i \(-0.541597\pi\)
−0.130308 + 0.991474i \(0.541597\pi\)
\(158\) −1.95871 −0.155826
\(159\) 8.76650 0.695228
\(160\) 16.6898 1.31945
\(161\) 12.9334 1.01930
\(162\) −94.5244 −7.42654
\(163\) 24.4925 1.91840 0.959199 0.282730i \(-0.0912402\pi\)
0.959199 + 0.282730i \(0.0912402\pi\)
\(164\) −14.9878 −1.17035
\(165\) −16.1463 −1.25699
\(166\) −11.0757 −0.859644
\(167\) 9.92242 0.767820 0.383910 0.923371i \(-0.374577\pi\)
0.383910 + 0.923371i \(0.374577\pi\)
\(168\) −124.243 −9.58559
\(169\) 20.1519 1.55015
\(170\) −19.7898 −1.51780
\(171\) −66.6020 −5.09318
\(172\) −7.93701 −0.605191
\(173\) 5.40800 0.411163 0.205581 0.978640i \(-0.434091\pi\)
0.205581 + 0.978640i \(0.434091\pi\)
\(174\) 8.97484 0.680381
\(175\) 16.8106 1.27076
\(176\) −51.3515 −3.87077
\(177\) −21.4177 −1.60985
\(178\) −6.72394 −0.503980
\(179\) −0.384232 −0.0287188 −0.0143594 0.999897i \(-0.504571\pi\)
−0.0143594 + 0.999897i \(0.504571\pi\)
\(180\) −47.1555 −3.51477
\(181\) −14.1508 −1.05182 −0.525909 0.850541i \(-0.676275\pi\)
−0.525909 + 0.850541i \(0.676275\pi\)
\(182\) −68.3998 −5.07013
\(183\) 46.8736 3.46500
\(184\) 24.0351 1.77189
\(185\) −6.09926 −0.448427
\(186\) −63.8476 −4.68153
\(187\) 29.0010 2.12077
\(188\) −26.6933 −1.94681
\(189\) 80.0294 5.82128
\(190\) −23.6038 −1.71240
\(191\) −9.88678 −0.715382 −0.357691 0.933840i \(-0.616436\pi\)
−0.357691 + 0.933840i \(0.616436\pi\)
\(192\) −55.3085 −3.99155
\(193\) −14.0061 −1.00818 −0.504091 0.863651i \(-0.668172\pi\)
−0.504091 + 0.863651i \(0.668172\pi\)
\(194\) −14.2402 −1.02238
\(195\) −21.4777 −1.53805
\(196\) 65.6615 4.69011
\(197\) −5.76858 −0.410994 −0.205497 0.978658i \(-0.565881\pi\)
−0.205497 + 0.978658i \(0.565881\pi\)
\(198\) 96.1696 6.83447
\(199\) −11.8468 −0.839800 −0.419900 0.907570i \(-0.637935\pi\)
−0.419900 + 0.907570i \(0.637935\pi\)
\(200\) 31.2404 2.20903
\(201\) 1.17655 0.0829874
\(202\) 13.4829 0.948653
\(203\) −4.45627 −0.312769
\(204\) 115.186 8.06462
\(205\) 3.25198 0.227128
\(206\) 34.6159 2.41181
\(207\) −24.1887 −1.68123
\(208\) −68.3077 −4.73628
\(209\) 34.5903 2.39266
\(210\) 44.3133 3.05791
\(211\) −4.38911 −0.302159 −0.151079 0.988522i \(-0.548275\pi\)
−0.151079 + 0.988522i \(0.548275\pi\)
\(212\) −13.2970 −0.913242
\(213\) 23.4670 1.60793
\(214\) −3.82336 −0.261359
\(215\) 1.72214 0.117449
\(216\) 148.724 10.1194
\(217\) 31.7022 2.15209
\(218\) 14.2305 0.963814
\(219\) −37.5268 −2.53583
\(220\) 24.4906 1.65116
\(221\) 38.5771 2.59498
\(222\) 49.4046 3.31582
\(223\) 8.11508 0.543426 0.271713 0.962378i \(-0.412410\pi\)
0.271713 + 0.962378i \(0.412410\pi\)
\(224\) 67.1255 4.48501
\(225\) −31.4401 −2.09600
\(226\) 26.5220 1.76422
\(227\) 1.17650 0.0780868 0.0390434 0.999238i \(-0.487569\pi\)
0.0390434 + 0.999238i \(0.487569\pi\)
\(228\) 137.385 9.09856
\(229\) −0.0269009 −0.00177766 −0.000888832 1.00000i \(-0.500283\pi\)
−0.000888832 1.00000i \(0.500283\pi\)
\(230\) −8.57248 −0.565252
\(231\) −64.9393 −4.27269
\(232\) −8.28140 −0.543700
\(233\) 19.7364 1.29298 0.646488 0.762924i \(-0.276237\pi\)
0.646488 + 0.762924i \(0.276237\pi\)
\(234\) 127.925 8.36269
\(235\) 5.79180 0.377815
\(236\) 32.4863 2.11468
\(237\) −2.47365 −0.160681
\(238\) −79.5931 −5.15926
\(239\) 12.5020 0.808687 0.404344 0.914607i \(-0.367500\pi\)
0.404344 + 0.914607i \(0.367500\pi\)
\(240\) 44.2537 2.85656
\(241\) −8.73806 −0.562868 −0.281434 0.959581i \(-0.590810\pi\)
−0.281434 + 0.959581i \(0.590810\pi\)
\(242\) −20.6226 −1.32567
\(243\) −65.4985 −4.20173
\(244\) −71.0978 −4.55157
\(245\) −14.2469 −0.910204
\(246\) −26.3414 −1.67946
\(247\) 46.0120 2.92767
\(248\) 58.9144 3.74107
\(249\) −13.9876 −0.886425
\(250\) −25.9108 −1.63874
\(251\) 24.2161 1.52851 0.764254 0.644916i \(-0.223108\pi\)
0.764254 + 0.644916i \(0.223108\pi\)
\(252\) −189.657 −11.9472
\(253\) 12.5626 0.789804
\(254\) 50.0065 3.13768
\(255\) −24.9925 −1.56509
\(256\) 3.58087 0.223805
\(257\) −3.54015 −0.220828 −0.110414 0.993886i \(-0.535218\pi\)
−0.110414 + 0.993886i \(0.535218\pi\)
\(258\) −13.9495 −0.868457
\(259\) −24.5309 −1.52427
\(260\) 32.5774 2.02036
\(261\) 8.33433 0.515882
\(262\) −15.6766 −0.968502
\(263\) −26.2570 −1.61907 −0.809537 0.587068i \(-0.800282\pi\)
−0.809537 + 0.587068i \(0.800282\pi\)
\(264\) −120.681 −7.42742
\(265\) 2.88512 0.177232
\(266\) −94.9329 −5.82071
\(267\) −8.49167 −0.519682
\(268\) −1.78459 −0.109011
\(269\) 24.5324 1.49577 0.747884 0.663830i \(-0.231070\pi\)
0.747884 + 0.663830i \(0.231070\pi\)
\(270\) −53.0448 −3.22821
\(271\) −24.8018 −1.50660 −0.753301 0.657676i \(-0.771540\pi\)
−0.753301 + 0.657676i \(0.771540\pi\)
\(272\) −79.4859 −4.81954
\(273\) −86.3821 −5.22809
\(274\) 34.7322 2.09825
\(275\) 16.3287 0.984656
\(276\) 49.8959 3.00338
\(277\) 1.00000 0.0600842
\(278\) 39.8375 2.38930
\(279\) −59.2910 −3.54966
\(280\) −40.8895 −2.44361
\(281\) −1.75991 −0.104987 −0.0524936 0.998621i \(-0.516717\pi\)
−0.0524936 + 0.998621i \(0.516717\pi\)
\(282\) −46.9141 −2.79370
\(283\) 4.98113 0.296097 0.148049 0.988980i \(-0.452701\pi\)
0.148049 + 0.988980i \(0.452701\pi\)
\(284\) −35.5946 −2.11215
\(285\) −29.8092 −1.76575
\(286\) −66.4387 −3.92860
\(287\) 13.0793 0.772045
\(288\) −125.541 −7.39760
\(289\) 27.8901 1.64060
\(290\) 2.95369 0.173447
\(291\) −17.9839 −1.05423
\(292\) 56.9205 3.33102
\(293\) 0.564979 0.0330064 0.0165032 0.999864i \(-0.494747\pi\)
0.0165032 + 0.999864i \(0.494747\pi\)
\(294\) 115.402 6.73036
\(295\) −7.04873 −0.410393
\(296\) −45.5874 −2.64971
\(297\) 77.7349 4.51064
\(298\) −13.6169 −0.788804
\(299\) 16.7107 0.966407
\(300\) 64.8539 3.74434
\(301\) 6.92633 0.399227
\(302\) 43.0665 2.47820
\(303\) 17.0276 0.978208
\(304\) −94.8051 −5.43744
\(305\) 15.4265 0.883318
\(306\) 148.859 8.50970
\(307\) −26.1812 −1.49424 −0.747119 0.664690i \(-0.768563\pi\)
−0.747119 + 0.664690i \(0.768563\pi\)
\(308\) 98.4998 5.61255
\(309\) 43.7165 2.48694
\(310\) −21.0127 −1.19344
\(311\) −5.93303 −0.336431 −0.168216 0.985750i \(-0.553800\pi\)
−0.168216 + 0.985750i \(0.553800\pi\)
\(312\) −160.530 −9.08822
\(313\) −18.0557 −1.02057 −0.510286 0.860005i \(-0.670460\pi\)
−0.510286 + 0.860005i \(0.670460\pi\)
\(314\) 8.70524 0.491265
\(315\) 41.1508 2.31859
\(316\) 3.75203 0.211068
\(317\) 22.5229 1.26501 0.632507 0.774555i \(-0.282026\pi\)
0.632507 + 0.774555i \(0.282026\pi\)
\(318\) −23.3698 −1.31051
\(319\) −4.32851 −0.242350
\(320\) −18.2025 −1.01755
\(321\) −4.82852 −0.269502
\(322\) −34.4780 −1.92138
\(323\) 53.5417 2.97914
\(324\) 181.068 10.0593
\(325\) 21.7204 1.20483
\(326\) −65.2922 −3.61620
\(327\) 17.9718 0.993841
\(328\) 24.3061 1.34208
\(329\) 23.2943 1.28425
\(330\) 43.0429 2.36943
\(331\) 13.9915 0.769042 0.384521 0.923116i \(-0.374367\pi\)
0.384521 + 0.923116i \(0.374367\pi\)
\(332\) 21.2163 1.16440
\(333\) 45.8788 2.51414
\(334\) −26.4512 −1.44735
\(335\) 0.387212 0.0211556
\(336\) 177.985 9.70990
\(337\) −6.15743 −0.335417 −0.167708 0.985837i \(-0.553637\pi\)
−0.167708 + 0.985837i \(0.553637\pi\)
\(338\) −53.7211 −2.92205
\(339\) 33.4947 1.81918
\(340\) 37.9086 2.05588
\(341\) 30.7933 1.66755
\(342\) 177.548 9.60070
\(343\) −26.1064 −1.40961
\(344\) 12.8717 0.693994
\(345\) −10.8262 −0.582863
\(346\) −14.4167 −0.775046
\(347\) −18.8041 −1.00946 −0.504728 0.863278i \(-0.668407\pi\)
−0.504728 + 0.863278i \(0.668407\pi\)
\(348\) −17.1919 −0.921582
\(349\) −14.9830 −0.802021 −0.401010 0.916074i \(-0.631341\pi\)
−0.401010 + 0.916074i \(0.631341\pi\)
\(350\) −44.8139 −2.39540
\(351\) 103.403 5.51923
\(352\) 65.2010 3.47522
\(353\) 12.3216 0.655811 0.327905 0.944711i \(-0.393657\pi\)
0.327905 + 0.944711i \(0.393657\pi\)
\(354\) 57.0954 3.03459
\(355\) 7.72316 0.409903
\(356\) 12.8801 0.682646
\(357\) −100.518 −5.31999
\(358\) 1.02429 0.0541353
\(359\) 8.37134 0.441823 0.220911 0.975294i \(-0.429097\pi\)
0.220911 + 0.975294i \(0.429097\pi\)
\(360\) 76.4735 4.03051
\(361\) 44.8606 2.36108
\(362\) 37.7232 1.98269
\(363\) −26.0443 −1.36697
\(364\) 131.024 6.86754
\(365\) −12.3504 −0.646447
\(366\) −124.956 −6.53156
\(367\) −17.3782 −0.907137 −0.453569 0.891221i \(-0.649849\pi\)
−0.453569 + 0.891221i \(0.649849\pi\)
\(368\) −34.4315 −1.79487
\(369\) −24.4615 −1.27341
\(370\) 16.2595 0.845289
\(371\) 11.6038 0.602439
\(372\) 122.304 6.34118
\(373\) −21.0646 −1.09068 −0.545342 0.838213i \(-0.683600\pi\)
−0.545342 + 0.838213i \(0.683600\pi\)
\(374\) −77.3112 −3.99767
\(375\) −32.7228 −1.68980
\(376\) 43.2893 2.23248
\(377\) −5.75777 −0.296540
\(378\) −213.343 −10.9732
\(379\) 24.6186 1.26457 0.632286 0.774735i \(-0.282117\pi\)
0.632286 + 0.774735i \(0.282117\pi\)
\(380\) 45.2146 2.31946
\(381\) 63.1532 3.23544
\(382\) 26.3562 1.34850
\(383\) −14.6477 −0.748462 −0.374231 0.927336i \(-0.622093\pi\)
−0.374231 + 0.927336i \(0.622093\pi\)
\(384\) 46.0170 2.34830
\(385\) −21.3720 −1.08922
\(386\) 37.3376 1.90043
\(387\) −12.9539 −0.658486
\(388\) 27.2779 1.38483
\(389\) 0.770700 0.0390760 0.0195380 0.999809i \(-0.493780\pi\)
0.0195380 + 0.999809i \(0.493780\pi\)
\(390\) 57.2555 2.89925
\(391\) 19.4454 0.983396
\(392\) −106.485 −5.37831
\(393\) −19.7980 −0.998675
\(394\) 15.3779 0.774728
\(395\) −0.814099 −0.0409618
\(396\) −184.219 −9.25736
\(397\) 29.1697 1.46398 0.731992 0.681313i \(-0.238591\pi\)
0.731992 + 0.681313i \(0.238591\pi\)
\(398\) 31.5814 1.58303
\(399\) −119.891 −6.00205
\(400\) −44.7536 −2.23768
\(401\) 14.7192 0.735043 0.367522 0.930015i \(-0.380206\pi\)
0.367522 + 0.930015i \(0.380206\pi\)
\(402\) −3.13645 −0.156432
\(403\) 40.9611 2.04042
\(404\) −25.8274 −1.28496
\(405\) −39.2873 −1.95220
\(406\) 11.8796 0.589573
\(407\) −23.8275 −1.18109
\(408\) −186.800 −9.24798
\(409\) 17.4378 0.862244 0.431122 0.902294i \(-0.358118\pi\)
0.431122 + 0.902294i \(0.358118\pi\)
\(410\) −8.66915 −0.428139
\(411\) 43.8633 2.16362
\(412\) −66.3090 −3.26681
\(413\) −28.3496 −1.39499
\(414\) 64.4824 3.16914
\(415\) −4.60342 −0.225973
\(416\) 86.7302 4.25230
\(417\) 50.3108 2.46373
\(418\) −92.2111 −4.51019
\(419\) 3.17712 0.155213 0.0776063 0.996984i \(-0.475272\pi\)
0.0776063 + 0.996984i \(0.475272\pi\)
\(420\) −84.8851 −4.14197
\(421\) 0.705545 0.0343862 0.0171931 0.999852i \(-0.494527\pi\)
0.0171931 + 0.999852i \(0.494527\pi\)
\(422\) 11.7005 0.569572
\(423\) −43.5660 −2.11825
\(424\) 21.5641 1.04725
\(425\) 25.2748 1.22601
\(426\) −62.5584 −3.03096
\(427\) 62.0443 3.00254
\(428\) 7.32389 0.354013
\(429\) −83.9055 −4.05100
\(430\) −4.59088 −0.221392
\(431\) 26.2543 1.26463 0.632313 0.774713i \(-0.282106\pi\)
0.632313 + 0.774713i \(0.282106\pi\)
\(432\) −213.056 −10.2506
\(433\) 3.45592 0.166081 0.0830405 0.996546i \(-0.473537\pi\)
0.0830405 + 0.996546i \(0.473537\pi\)
\(434\) −84.5119 −4.05670
\(435\) 3.73022 0.178850
\(436\) −27.2595 −1.30549
\(437\) 23.1931 1.10947
\(438\) 100.039 4.78006
\(439\) 13.2029 0.630141 0.315071 0.949068i \(-0.397972\pi\)
0.315071 + 0.949068i \(0.397972\pi\)
\(440\) −39.7172 −1.89344
\(441\) 107.166 5.10313
\(442\) −102.839 −4.89156
\(443\) 21.8804 1.03957 0.519784 0.854298i \(-0.326012\pi\)
0.519784 + 0.854298i \(0.326012\pi\)
\(444\) −94.6378 −4.49131
\(445\) −2.79468 −0.132480
\(446\) −21.6332 −1.02436
\(447\) −17.1968 −0.813379
\(448\) −73.2092 −3.45881
\(449\) 2.53849 0.119799 0.0598993 0.998204i \(-0.480922\pi\)
0.0598993 + 0.998204i \(0.480922\pi\)
\(450\) 83.8131 3.95099
\(451\) 12.7043 0.598221
\(452\) −50.8046 −2.38965
\(453\) 54.3887 2.55540
\(454\) −3.13631 −0.147194
\(455\) −28.4290 −1.33277
\(456\) −222.802 −10.4336
\(457\) 7.27784 0.340443 0.170222 0.985406i \(-0.445552\pi\)
0.170222 + 0.985406i \(0.445552\pi\)
\(458\) 0.0717127 0.00335091
\(459\) 120.324 5.61626
\(460\) 16.4211 0.765640
\(461\) 10.1036 0.470573 0.235287 0.971926i \(-0.424397\pi\)
0.235287 + 0.971926i \(0.424397\pi\)
\(462\) 173.116 8.05407
\(463\) −3.87135 −0.179917 −0.0899585 0.995946i \(-0.528673\pi\)
−0.0899585 + 0.995946i \(0.528673\pi\)
\(464\) 11.8636 0.550752
\(465\) −26.5370 −1.23062
\(466\) −52.6135 −2.43727
\(467\) 23.2730 1.07694 0.538472 0.842643i \(-0.319002\pi\)
0.538472 + 0.842643i \(0.319002\pi\)
\(468\) −245.048 −11.3273
\(469\) 1.55734 0.0719113
\(470\) −15.4398 −0.712186
\(471\) 10.9939 0.506570
\(472\) −52.6840 −2.42498
\(473\) 6.72775 0.309342
\(474\) 6.59429 0.302886
\(475\) 30.1460 1.38319
\(476\) 152.466 6.98826
\(477\) −21.7020 −0.993664
\(478\) −33.3279 −1.52438
\(479\) 18.3285 0.837450 0.418725 0.908113i \(-0.362477\pi\)
0.418725 + 0.908113i \(0.362477\pi\)
\(480\) −56.1889 −2.56466
\(481\) −31.6953 −1.44518
\(482\) 23.2940 1.06101
\(483\) −43.5423 −1.98124
\(484\) 39.5040 1.79564
\(485\) −5.91864 −0.268752
\(486\) 174.606 7.92031
\(487\) −24.6474 −1.11688 −0.558441 0.829544i \(-0.688600\pi\)
−0.558441 + 0.829544i \(0.688600\pi\)
\(488\) 115.301 5.21945
\(489\) −82.4576 −3.72886
\(490\) 37.9796 1.71574
\(491\) −23.1001 −1.04249 −0.521245 0.853407i \(-0.674532\pi\)
−0.521245 + 0.853407i \(0.674532\pi\)
\(492\) 50.4586 2.27485
\(493\) −6.70001 −0.301753
\(494\) −122.659 −5.51869
\(495\) 39.9710 1.79656
\(496\) −84.3981 −3.78959
\(497\) 31.0621 1.39332
\(498\) 37.2881 1.67092
\(499\) −1.66936 −0.0747307 −0.0373654 0.999302i \(-0.511897\pi\)
−0.0373654 + 0.999302i \(0.511897\pi\)
\(500\) 49.6339 2.21969
\(501\) −33.4053 −1.49244
\(502\) −64.5555 −2.88125
\(503\) −30.7057 −1.36910 −0.684549 0.728966i \(-0.740001\pi\)
−0.684549 + 0.728966i \(0.740001\pi\)
\(504\) 307.572 13.7003
\(505\) 5.60390 0.249370
\(506\) −33.4895 −1.48879
\(507\) −67.8445 −3.01308
\(508\) −95.7906 −4.25002
\(509\) −43.5643 −1.93095 −0.965477 0.260487i \(-0.916117\pi\)
−0.965477 + 0.260487i \(0.916117\pi\)
\(510\) 66.6252 2.95021
\(511\) −49.6724 −2.19738
\(512\) 17.7911 0.786262
\(513\) 143.514 6.33630
\(514\) 9.43735 0.416264
\(515\) 14.3874 0.633986
\(516\) 26.7211 1.17633
\(517\) 22.6264 0.995108
\(518\) 65.3945 2.87327
\(519\) −18.2069 −0.799192
\(520\) −52.8317 −2.31682
\(521\) −35.8719 −1.57157 −0.785787 0.618497i \(-0.787742\pi\)
−0.785787 + 0.618497i \(0.787742\pi\)
\(522\) −22.2177 −0.972443
\(523\) −9.26124 −0.404966 −0.202483 0.979286i \(-0.564901\pi\)
−0.202483 + 0.979286i \(0.564901\pi\)
\(524\) 30.0295 1.31184
\(525\) −56.5955 −2.47003
\(526\) 69.9960 3.05197
\(527\) 47.6643 2.07629
\(528\) 172.883 7.52375
\(529\) −14.5767 −0.633769
\(530\) −7.69118 −0.334084
\(531\) 53.0207 2.30090
\(532\) 181.850 7.88420
\(533\) 16.8992 0.731986
\(534\) 22.6371 0.979605
\(535\) −1.58910 −0.0687030
\(536\) 2.89411 0.125007
\(537\) 1.29357 0.0558218
\(538\) −65.3987 −2.81954
\(539\) −55.6575 −2.39734
\(540\) 101.611 4.37263
\(541\) −31.4531 −1.35227 −0.676137 0.736776i \(-0.736347\pi\)
−0.676137 + 0.736776i \(0.736347\pi\)
\(542\) 66.1168 2.83996
\(543\) 47.6407 2.04446
\(544\) 100.923 4.32705
\(545\) 5.91465 0.253356
\(546\) 230.278 9.85499
\(547\) 40.2618 1.72147 0.860736 0.509052i \(-0.170004\pi\)
0.860736 + 0.509052i \(0.170004\pi\)
\(548\) −66.5317 −2.84209
\(549\) −116.038 −4.95239
\(550\) −43.5291 −1.85609
\(551\) −7.99128 −0.340440
\(552\) −80.9176 −3.44408
\(553\) −3.27426 −0.139236
\(554\) −2.66581 −0.113259
\(555\) 20.5341 0.871623
\(556\) −76.3113 −3.23632
\(557\) 18.4929 0.783568 0.391784 0.920057i \(-0.371858\pi\)
0.391784 + 0.920057i \(0.371858\pi\)
\(558\) 158.058 6.69114
\(559\) 8.94923 0.378512
\(560\) 58.5764 2.47531
\(561\) −97.6364 −4.12221
\(562\) 4.69157 0.197902
\(563\) −5.12018 −0.215790 −0.107895 0.994162i \(-0.534411\pi\)
−0.107895 + 0.994162i \(0.534411\pi\)
\(564\) 89.8671 3.78409
\(565\) 11.0234 0.463756
\(566\) −13.2787 −0.558146
\(567\) −158.011 −6.63583
\(568\) 57.7248 2.42208
\(569\) −17.3938 −0.729188 −0.364594 0.931167i \(-0.618792\pi\)
−0.364594 + 0.931167i \(0.618792\pi\)
\(570\) 79.4657 3.32845
\(571\) −36.0678 −1.50939 −0.754696 0.656075i \(-0.772216\pi\)
−0.754696 + 0.656075i \(0.772216\pi\)
\(572\) 127.268 5.32133
\(573\) 33.2853 1.39051
\(574\) −34.8668 −1.45531
\(575\) 10.9485 0.456583
\(576\) 136.919 5.70497
\(577\) −24.0492 −1.00118 −0.500590 0.865684i \(-0.666884\pi\)
−0.500590 + 0.865684i \(0.666884\pi\)
\(578\) −74.3497 −3.09254
\(579\) 47.1537 1.95964
\(580\) −5.65799 −0.234935
\(581\) −18.5146 −0.768117
\(582\) 47.9416 1.98724
\(583\) 11.2711 0.466801
\(584\) −92.3097 −3.81980
\(585\) 53.1694 2.19828
\(586\) −1.50613 −0.0622175
\(587\) 5.47614 0.226024 0.113012 0.993594i \(-0.463950\pi\)
0.113012 + 0.993594i \(0.463950\pi\)
\(588\) −221.059 −9.11633
\(589\) 56.8505 2.34248
\(590\) 18.7906 0.773595
\(591\) 19.4208 0.798864
\(592\) 65.3064 2.68408
\(593\) 29.5768 1.21457 0.607286 0.794483i \(-0.292258\pi\)
0.607286 + 0.794483i \(0.292258\pi\)
\(594\) −207.226 −8.50260
\(595\) −33.0814 −1.35620
\(596\) 26.0840 1.06844
\(597\) 39.8841 1.63235
\(598\) −44.5476 −1.82169
\(599\) −1.71453 −0.0700540 −0.0350270 0.999386i \(-0.511152\pi\)
−0.0350270 + 0.999386i \(0.511152\pi\)
\(600\) −105.175 −4.29377
\(601\) −9.09289 −0.370907 −0.185453 0.982653i \(-0.559375\pi\)
−0.185453 + 0.982653i \(0.559375\pi\)
\(602\) −18.4642 −0.752547
\(603\) −2.91261 −0.118611
\(604\) −82.4966 −3.35674
\(605\) −8.57140 −0.348477
\(606\) −45.3922 −1.84393
\(607\) 17.6703 0.717214 0.358607 0.933489i \(-0.383252\pi\)
0.358607 + 0.933489i \(0.383252\pi\)
\(608\) 120.374 4.88181
\(609\) 15.0027 0.607940
\(610\) −41.1240 −1.66506
\(611\) 30.0976 1.21762
\(612\) −285.149 −11.5265
\(613\) −5.00671 −0.202219 −0.101110 0.994875i \(-0.532239\pi\)
−0.101110 + 0.994875i \(0.532239\pi\)
\(614\) 69.7939 2.81665
\(615\) −10.9483 −0.441477
\(616\) −159.740 −6.43611
\(617\) −38.6754 −1.55701 −0.778506 0.627637i \(-0.784022\pi\)
−0.778506 + 0.627637i \(0.784022\pi\)
\(618\) −116.540 −4.68791
\(619\) −22.4207 −0.901164 −0.450582 0.892735i \(-0.648783\pi\)
−0.450582 + 0.892735i \(0.648783\pi\)
\(620\) 40.2513 1.61653
\(621\) 52.1218 2.09158
\(622\) 15.8163 0.634176
\(623\) −11.2400 −0.450321
\(624\) 229.968 9.20609
\(625\) 8.09245 0.323698
\(626\) 48.1331 1.92379
\(627\) −116.454 −4.65071
\(628\) −16.6755 −0.665423
\(629\) −36.8822 −1.47059
\(630\) −109.700 −4.37056
\(631\) −28.2285 −1.12376 −0.561880 0.827219i \(-0.689922\pi\)
−0.561880 + 0.827219i \(0.689922\pi\)
\(632\) −6.08478 −0.242040
\(633\) 14.7766 0.587317
\(634\) −60.0417 −2.38456
\(635\) 20.7842 0.824797
\(636\) 44.7663 1.77510
\(637\) −74.0355 −2.93339
\(638\) 11.5390 0.456832
\(639\) −58.0938 −2.29815
\(640\) 15.1446 0.598642
\(641\) −34.9886 −1.38197 −0.690984 0.722870i \(-0.742822\pi\)
−0.690984 + 0.722870i \(0.742822\pi\)
\(642\) 12.8719 0.508014
\(643\) 4.53293 0.178761 0.0893807 0.995998i \(-0.471511\pi\)
0.0893807 + 0.995998i \(0.471511\pi\)
\(644\) 66.0448 2.60253
\(645\) −5.79783 −0.228289
\(646\) −142.732 −5.61571
\(647\) 1.60769 0.0632046 0.0316023 0.999501i \(-0.489939\pi\)
0.0316023 + 0.999501i \(0.489939\pi\)
\(648\) −293.643 −11.5354
\(649\) −27.5368 −1.08091
\(650\) −57.9023 −2.27111
\(651\) −106.730 −4.18309
\(652\) 125.071 4.89818
\(653\) −22.2198 −0.869527 −0.434763 0.900545i \(-0.643168\pi\)
−0.434763 + 0.900545i \(0.643168\pi\)
\(654\) −47.9093 −1.87340
\(655\) −6.51566 −0.254588
\(656\) −34.8198 −1.35949
\(657\) 92.8997 3.62436
\(658\) −62.0980 −2.42083
\(659\) 17.4171 0.678476 0.339238 0.940701i \(-0.389831\pi\)
0.339238 + 0.940701i \(0.389831\pi\)
\(660\) −82.4514 −3.20942
\(661\) 12.2302 0.475699 0.237849 0.971302i \(-0.423558\pi\)
0.237849 + 0.971302i \(0.423558\pi\)
\(662\) −37.2986 −1.44965
\(663\) −129.876 −5.04395
\(664\) −34.4071 −1.33525
\(665\) −39.4570 −1.53008
\(666\) −122.304 −4.73918
\(667\) −2.90229 −0.112377
\(668\) 50.6691 1.96045
\(669\) −27.3206 −1.05628
\(670\) −1.03223 −0.0398786
\(671\) 60.2655 2.32652
\(672\) −225.988 −8.71768
\(673\) 3.63996 0.140310 0.0701552 0.997536i \(-0.477651\pi\)
0.0701552 + 0.997536i \(0.477651\pi\)
\(674\) 16.4145 0.632264
\(675\) 67.7471 2.60759
\(676\) 102.906 3.95794
\(677\) 28.9773 1.11369 0.556844 0.830617i \(-0.312012\pi\)
0.556844 + 0.830617i \(0.312012\pi\)
\(678\) −89.2903 −3.42917
\(679\) −23.8044 −0.913530
\(680\) −61.4774 −2.35755
\(681\) −3.96085 −0.151780
\(682\) −82.0889 −3.14335
\(683\) 43.9545 1.68187 0.840937 0.541134i \(-0.182005\pi\)
0.840937 + 0.541134i \(0.182005\pi\)
\(684\) −340.105 −13.0042
\(685\) 14.4358 0.551562
\(686\) 69.5946 2.65714
\(687\) 0.0905660 0.00345531
\(688\) −18.4394 −0.702995
\(689\) 14.9928 0.571180
\(690\) 28.8605 1.09870
\(691\) −32.4109 −1.23297 −0.616485 0.787366i \(-0.711444\pi\)
−0.616485 + 0.787366i \(0.711444\pi\)
\(692\) 27.6161 1.04981
\(693\) 160.761 6.10680
\(694\) 50.1280 1.90283
\(695\) 16.5577 0.628069
\(696\) 27.8806 1.05681
\(697\) 19.6647 0.744853
\(698\) 39.9417 1.51182
\(699\) −66.4456 −2.51320
\(700\) 85.8440 3.24460
\(701\) −34.7606 −1.31289 −0.656444 0.754375i \(-0.727940\pi\)
−0.656444 + 0.754375i \(0.727940\pi\)
\(702\) −275.652 −10.4038
\(703\) −43.9904 −1.65913
\(704\) −71.1103 −2.68007
\(705\) −19.4990 −0.734373
\(706\) −32.8469 −1.23621
\(707\) 22.5386 0.847650
\(708\) −109.370 −4.11038
\(709\) −10.7733 −0.404601 −0.202300 0.979324i \(-0.564842\pi\)
−0.202300 + 0.979324i \(0.564842\pi\)
\(710\) −20.5885 −0.772671
\(711\) 6.12367 0.229656
\(712\) −20.8881 −0.782814
\(713\) 20.6471 0.773240
\(714\) 267.962 10.0282
\(715\) −27.6140 −1.03270
\(716\) −1.96209 −0.0733267
\(717\) −42.0899 −1.57187
\(718\) −22.3164 −0.832840
\(719\) 26.7574 0.997882 0.498941 0.866636i \(-0.333722\pi\)
0.498941 + 0.866636i \(0.333722\pi\)
\(720\) −109.552 −4.08278
\(721\) 57.8654 2.15502
\(722\) −119.590 −4.45067
\(723\) 29.4180 1.09407
\(724\) −72.2612 −2.68557
\(725\) −3.77236 −0.140102
\(726\) 69.4292 2.57676
\(727\) −39.9725 −1.48250 −0.741248 0.671231i \(-0.765766\pi\)
−0.741248 + 0.671231i \(0.765766\pi\)
\(728\) −212.486 −7.87524
\(729\) 114.136 4.22727
\(730\) 32.9237 1.21856
\(731\) 10.4137 0.385166
\(732\) 239.361 8.84705
\(733\) 18.2900 0.675557 0.337778 0.941226i \(-0.390325\pi\)
0.337778 + 0.941226i \(0.390325\pi\)
\(734\) 46.3271 1.70996
\(735\) 47.9645 1.76920
\(736\) 43.7177 1.61146
\(737\) 1.51269 0.0557207
\(738\) 65.2096 2.40040
\(739\) −8.35613 −0.307385 −0.153693 0.988119i \(-0.549117\pi\)
−0.153693 + 0.988119i \(0.549117\pi\)
\(740\) −31.1460 −1.14495
\(741\) −154.906 −5.69062
\(742\) −30.9335 −1.13560
\(743\) 0.443321 0.0162639 0.00813193 0.999967i \(-0.497411\pi\)
0.00813193 + 0.999967i \(0.497411\pi\)
\(744\) −198.344 −7.27165
\(745\) −5.65959 −0.207351
\(746\) 56.1542 2.05595
\(747\) 34.6270 1.26694
\(748\) 148.095 5.41487
\(749\) −6.39128 −0.233532
\(750\) 87.2327 3.18529
\(751\) −49.0327 −1.78923 −0.894614 0.446840i \(-0.852549\pi\)
−0.894614 + 0.446840i \(0.852549\pi\)
\(752\) −62.0143 −2.26143
\(753\) −81.5272 −2.97101
\(754\) 15.3491 0.558981
\(755\) 17.8997 0.651438
\(756\) 408.672 14.8633
\(757\) −19.0583 −0.692687 −0.346343 0.938108i \(-0.612577\pi\)
−0.346343 + 0.938108i \(0.612577\pi\)
\(758\) −65.6284 −2.38373
\(759\) −42.2939 −1.53517
\(760\) −73.3258 −2.65980
\(761\) −39.9263 −1.44733 −0.723664 0.690153i \(-0.757543\pi\)
−0.723664 + 0.690153i \(0.757543\pi\)
\(762\) −168.354 −6.09883
\(763\) 23.7884 0.861196
\(764\) −50.4871 −1.82656
\(765\) 61.8703 2.23693
\(766\) 39.0479 1.41086
\(767\) −36.6293 −1.32261
\(768\) −12.0555 −0.435017
\(769\) −1.91460 −0.0690422 −0.0345211 0.999404i \(-0.510991\pi\)
−0.0345211 + 0.999404i \(0.510991\pi\)
\(770\) 56.9738 2.05319
\(771\) 11.9184 0.429232
\(772\) −71.5226 −2.57415
\(773\) −15.7324 −0.565854 −0.282927 0.959141i \(-0.591305\pi\)
−0.282927 + 0.959141i \(0.591305\pi\)
\(774\) 34.5327 1.24125
\(775\) 26.8368 0.964005
\(776\) −44.2374 −1.58803
\(777\) 82.5868 2.96279
\(778\) −2.05454 −0.0736587
\(779\) 23.4546 0.840349
\(780\) −109.677 −3.92705
\(781\) 30.1715 1.07962
\(782\) −51.8377 −1.85371
\(783\) −17.9588 −0.641796
\(784\) 152.546 5.44807
\(785\) 3.61817 0.129138
\(786\) 52.7775 1.88251
\(787\) −17.4189 −0.620917 −0.310459 0.950587i \(-0.600483\pi\)
−0.310459 + 0.950587i \(0.600483\pi\)
\(788\) −29.4574 −1.04938
\(789\) 88.3981 3.14705
\(790\) 2.17023 0.0772134
\(791\) 44.3353 1.57638
\(792\) 298.753 10.6157
\(793\) 80.1650 2.84674
\(794\) −77.7607 −2.75962
\(795\) −9.71320 −0.344492
\(796\) −60.4962 −2.14423
\(797\) −48.8965 −1.73200 −0.866001 0.500043i \(-0.833318\pi\)
−0.866001 + 0.500043i \(0.833318\pi\)
\(798\) 319.606 11.3139
\(799\) 35.0229 1.23902
\(800\) 56.8236 2.00902
\(801\) 21.0216 0.742762
\(802\) −39.2386 −1.38556
\(803\) −48.2483 −1.70264
\(804\) 6.00808 0.211889
\(805\) −14.3301 −0.505070
\(806\) −109.195 −3.84621
\(807\) −82.5920 −2.90738
\(808\) 41.8850 1.47351
\(809\) 51.7985 1.82114 0.910570 0.413355i \(-0.135643\pi\)
0.910570 + 0.413355i \(0.135643\pi\)
\(810\) 104.732 3.67992
\(811\) −14.4334 −0.506826 −0.253413 0.967358i \(-0.581553\pi\)
−0.253413 + 0.967358i \(0.581553\pi\)
\(812\) −22.7561 −0.798581
\(813\) 83.4990 2.92844
\(814\) 63.5196 2.22636
\(815\) −27.1374 −0.950583
\(816\) 267.601 9.36792
\(817\) 12.4208 0.434547
\(818\) −46.4858 −1.62534
\(819\) 213.844 7.47231
\(820\) 16.6063 0.579918
\(821\) 4.70525 0.164214 0.0821071 0.996624i \(-0.473835\pi\)
0.0821071 + 0.996624i \(0.473835\pi\)
\(822\) −116.931 −4.07844
\(823\) 54.5921 1.90296 0.951480 0.307711i \(-0.0995629\pi\)
0.951480 + 0.307711i \(0.0995629\pi\)
\(824\) 107.535 3.74617
\(825\) −54.9729 −1.91391
\(826\) 75.5745 2.62957
\(827\) 8.81000 0.306354 0.153177 0.988199i \(-0.451050\pi\)
0.153177 + 0.988199i \(0.451050\pi\)
\(828\) −123.520 −4.29262
\(829\) 2.67669 0.0929654 0.0464827 0.998919i \(-0.485199\pi\)
0.0464827 + 0.998919i \(0.485199\pi\)
\(830\) 12.2718 0.425961
\(831\) −3.36665 −0.116788
\(832\) −94.5907 −3.27934
\(833\) −86.1511 −2.98496
\(834\) −134.119 −4.64416
\(835\) −10.9940 −0.380461
\(836\) 176.636 6.10910
\(837\) 127.760 4.41604
\(838\) −8.46960 −0.292577
\(839\) −40.3416 −1.39275 −0.696373 0.717680i \(-0.745204\pi\)
−0.696373 + 0.717680i \(0.745204\pi\)
\(840\) 137.661 4.74974
\(841\) 1.00000 0.0344828
\(842\) −1.88085 −0.0648183
\(843\) 5.92499 0.204068
\(844\) −22.4131 −0.771491
\(845\) −22.3282 −0.768112
\(846\) 116.139 3.99293
\(847\) −34.4736 −1.18453
\(848\) −30.8918 −1.06083
\(849\) −16.7697 −0.575535
\(850\) −67.3778 −2.31104
\(851\) −15.9765 −0.547668
\(852\) 119.835 4.10547
\(853\) 8.28156 0.283555 0.141778 0.989899i \(-0.454718\pi\)
0.141778 + 0.989899i \(0.454718\pi\)
\(854\) −165.398 −5.65981
\(855\) 73.7944 2.52372
\(856\) −11.8774 −0.405960
\(857\) −45.7888 −1.56412 −0.782058 0.623206i \(-0.785830\pi\)
−0.782058 + 0.623206i \(0.785830\pi\)
\(858\) 223.676 7.63617
\(859\) −50.9471 −1.73829 −0.869146 0.494556i \(-0.835331\pi\)
−0.869146 + 0.494556i \(0.835331\pi\)
\(860\) 8.79414 0.299878
\(861\) −44.0333 −1.50065
\(862\) −69.9889 −2.38383
\(863\) 0.804565 0.0273877 0.0136939 0.999906i \(-0.495641\pi\)
0.0136939 + 0.999906i \(0.495641\pi\)
\(864\) 270.517 9.20316
\(865\) −5.99202 −0.203735
\(866\) −9.21282 −0.313064
\(867\) −93.8963 −3.18888
\(868\) 161.888 5.49484
\(869\) −3.18038 −0.107887
\(870\) −9.94404 −0.337135
\(871\) 2.01218 0.0681801
\(872\) 44.2076 1.49706
\(873\) 44.5202 1.50678
\(874\) −61.8282 −2.09137
\(875\) −43.3136 −1.46427
\(876\) −191.632 −6.47463
\(877\) 26.8808 0.907699 0.453850 0.891078i \(-0.350050\pi\)
0.453850 + 0.891078i \(0.350050\pi\)
\(878\) −35.1965 −1.18782
\(879\) −1.90209 −0.0641558
\(880\) 56.8970 1.91800
\(881\) 13.8169 0.465505 0.232752 0.972536i \(-0.425227\pi\)
0.232752 + 0.972536i \(0.425227\pi\)
\(882\) −285.683 −9.61946
\(883\) 43.6135 1.46771 0.733856 0.679306i \(-0.237719\pi\)
0.733856 + 0.679306i \(0.237719\pi\)
\(884\) 196.995 6.62566
\(885\) 23.7306 0.797696
\(886\) −58.3288 −1.95960
\(887\) −18.8824 −0.634008 −0.317004 0.948424i \(-0.602677\pi\)
−0.317004 + 0.948424i \(0.602677\pi\)
\(888\) 153.477 5.15034
\(889\) 83.5928 2.80361
\(890\) 7.45006 0.249727
\(891\) −153.481 −5.14180
\(892\) 41.4399 1.38751
\(893\) 41.7728 1.39787
\(894\) 45.8432 1.53323
\(895\) 0.425725 0.0142304
\(896\) 60.9105 2.03488
\(897\) −56.2592 −1.87844
\(898\) −6.76711 −0.225821
\(899\) −7.11406 −0.237267
\(900\) −160.550 −5.35165
\(901\) 17.4463 0.581221
\(902\) −33.8672 −1.12765
\(903\) −23.3185 −0.775992
\(904\) 82.3913 2.74030
\(905\) 15.6789 0.521185
\(906\) −144.990 −4.81696
\(907\) −8.07972 −0.268283 −0.134141 0.990962i \(-0.542828\pi\)
−0.134141 + 0.990962i \(0.542828\pi\)
\(908\) 6.00781 0.199376
\(909\) −42.1527 −1.39812
\(910\) 75.7863 2.51229
\(911\) −25.6534 −0.849935 −0.424967 0.905209i \(-0.639714\pi\)
−0.424967 + 0.905209i \(0.639714\pi\)
\(912\) 319.175 10.5690
\(913\) −17.9838 −0.595178
\(914\) −19.4013 −0.641739
\(915\) −51.9356 −1.71694
\(916\) −0.137370 −0.00453884
\(917\) −26.2056 −0.865385
\(918\) −320.761 −10.5867
\(919\) −0.259809 −0.00857031 −0.00428516 0.999991i \(-0.501364\pi\)
−0.00428516 + 0.999991i \(0.501364\pi\)
\(920\) −26.6306 −0.877986
\(921\) 88.1428 2.90440
\(922\) −26.9343 −0.887035
\(923\) 40.1341 1.32103
\(924\) −331.614 −10.9093
\(925\) −20.7660 −0.682783
\(926\) 10.3203 0.339145
\(927\) −108.223 −3.55450
\(928\) −15.0632 −0.494472
\(929\) 38.1853 1.25282 0.626409 0.779495i \(-0.284524\pi\)
0.626409 + 0.779495i \(0.284524\pi\)
\(930\) 70.7425 2.31974
\(931\) −102.755 −3.36765
\(932\) 100.785 3.30131
\(933\) 19.9744 0.653933
\(934\) −62.0413 −2.03005
\(935\) −32.1329 −1.05086
\(936\) 397.401 12.9895
\(937\) −11.2206 −0.366562 −0.183281 0.983061i \(-0.558672\pi\)
−0.183281 + 0.983061i \(0.558672\pi\)
\(938\) −4.15157 −0.135554
\(939\) 60.7874 1.98372
\(940\) 29.5760 0.964662
\(941\) −5.85844 −0.190980 −0.0954898 0.995430i \(-0.530442\pi\)
−0.0954898 + 0.995430i \(0.530442\pi\)
\(942\) −29.3075 −0.954890
\(943\) 8.51831 0.277394
\(944\) 75.4727 2.45643
\(945\) −88.6719 −2.88450
\(946\) −17.9349 −0.583113
\(947\) 8.63521 0.280607 0.140303 0.990109i \(-0.455192\pi\)
0.140303 + 0.990109i \(0.455192\pi\)
\(948\) −12.6318 −0.410261
\(949\) −64.1797 −2.08336
\(950\) −80.3633 −2.60733
\(951\) −75.8268 −2.45885
\(952\) −247.258 −8.01368
\(953\) 23.4163 0.758528 0.379264 0.925288i \(-0.376177\pi\)
0.379264 + 0.925288i \(0.376177\pi\)
\(954\) 57.8532 1.87307
\(955\) 10.9545 0.354478
\(956\) 63.8418 2.06479
\(957\) 14.5726 0.471064
\(958\) −48.8602 −1.57860
\(959\) 58.0597 1.87485
\(960\) 61.2813 1.97785
\(961\) 19.6099 0.632577
\(962\) 84.4937 2.72419
\(963\) 11.9533 0.385189
\(964\) −44.6211 −1.43715
\(965\) 15.5186 0.499563
\(966\) 116.075 3.73466
\(967\) −15.3480 −0.493560 −0.246780 0.969072i \(-0.579372\pi\)
−0.246780 + 0.969072i \(0.579372\pi\)
\(968\) −64.0648 −2.05912
\(969\) −180.256 −5.79066
\(970\) 15.7780 0.506600
\(971\) −41.9796 −1.34719 −0.673594 0.739101i \(-0.735250\pi\)
−0.673594 + 0.739101i \(0.735250\pi\)
\(972\) −334.470 −10.7281
\(973\) 66.5940 2.13491
\(974\) 65.7053 2.10533
\(975\) −73.1248 −2.34187
\(976\) −165.175 −5.28714
\(977\) −4.93207 −0.157791 −0.0788955 0.996883i \(-0.525139\pi\)
−0.0788955 + 0.996883i \(0.525139\pi\)
\(978\) 219.816 7.02894
\(979\) −10.9178 −0.348933
\(980\) −72.7524 −2.32399
\(981\) −44.4901 −1.42046
\(982\) 61.5803 1.96511
\(983\) −35.9897 −1.14789 −0.573947 0.818893i \(-0.694588\pi\)
−0.573947 + 0.818893i \(0.694588\pi\)
\(984\) −81.8302 −2.60865
\(985\) 6.39153 0.203651
\(986\) 17.8609 0.568808
\(987\) −78.4236 −2.49625
\(988\) 234.961 7.47512
\(989\) 4.51100 0.143441
\(990\) −106.555 −3.38654
\(991\) 13.1905 0.419010 0.209505 0.977808i \(-0.432815\pi\)
0.209505 + 0.977808i \(0.432815\pi\)
\(992\) 107.160 3.40234
\(993\) −47.1044 −1.49481
\(994\) −82.8055 −2.62643
\(995\) 13.1262 0.416128
\(996\) −71.4278 −2.26328
\(997\) 5.61341 0.177778 0.0888892 0.996042i \(-0.471668\pi\)
0.0888892 + 0.996042i \(0.471668\pi\)
\(998\) 4.45019 0.140868
\(999\) −98.8597 −3.12778
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 8033.2.a.c.1.7 154
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8033.2.a.c.1.7 154 1.1 even 1 trivial