Properties

Label 8035.2.a.e.1.7
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.59466 q^{2}\) \(-3.04599 q^{3}\) \(+4.73224 q^{4}\) \(+1.00000 q^{5}\) \(+7.90331 q^{6}\) \(-0.447166 q^{7}\) \(-7.08923 q^{8}\) \(+6.27808 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.59466 q^{2}\) \(-3.04599 q^{3}\) \(+4.73224 q^{4}\) \(+1.00000 q^{5}\) \(+7.90331 q^{6}\) \(-0.447166 q^{7}\) \(-7.08923 q^{8}\) \(+6.27808 q^{9}\) \(-2.59466 q^{10}\) \(-0.526592 q^{11}\) \(-14.4144 q^{12}\) \(-3.03214 q^{13}\) \(+1.16024 q^{14}\) \(-3.04599 q^{15}\) \(+8.92964 q^{16}\) \(+2.90689 q^{17}\) \(-16.2895 q^{18}\) \(-1.44327 q^{19}\) \(+4.73224 q^{20}\) \(+1.36206 q^{21}\) \(+1.36633 q^{22}\) \(-5.83121 q^{23}\) \(+21.5938 q^{24}\) \(+1.00000 q^{25}\) \(+7.86736 q^{26}\) \(-9.98501 q^{27}\) \(-2.11610 q^{28}\) \(+4.16733 q^{29}\) \(+7.90331 q^{30}\) \(-6.11330 q^{31}\) \(-8.99088 q^{32}\) \(+1.60400 q^{33}\) \(-7.54238 q^{34}\) \(-0.447166 q^{35}\) \(+29.7094 q^{36}\) \(+5.15081 q^{37}\) \(+3.74480 q^{38}\) \(+9.23587 q^{39}\) \(-7.08923 q^{40}\) \(-2.69925 q^{41}\) \(-3.53409 q^{42}\) \(-8.24891 q^{43}\) \(-2.49196 q^{44}\) \(+6.27808 q^{45}\) \(+15.1300 q^{46}\) \(-10.4887 q^{47}\) \(-27.1996 q^{48}\) \(-6.80004 q^{49}\) \(-2.59466 q^{50}\) \(-8.85436 q^{51}\) \(-14.3488 q^{52}\) \(-10.6720 q^{53}\) \(+25.9077 q^{54}\) \(-0.526592 q^{55}\) \(+3.17006 q^{56}\) \(+4.39620 q^{57}\) \(-10.8128 q^{58}\) \(+0.466252 q^{59}\) \(-14.4144 q^{60}\) \(+1.09388 q^{61}\) \(+15.8619 q^{62}\) \(-2.80734 q^{63}\) \(+5.46896 q^{64}\) \(-3.03214 q^{65}\) \(-4.16182 q^{66}\) \(+6.42470 q^{67}\) \(+13.7561 q^{68}\) \(+17.7618 q^{69}\) \(+1.16024 q^{70}\) \(+3.65939 q^{71}\) \(-44.5068 q^{72}\) \(-0.671565 q^{73}\) \(-13.3646 q^{74}\) \(-3.04599 q^{75}\) \(-6.82992 q^{76}\) \(+0.235474 q^{77}\) \(-23.9639 q^{78}\) \(-6.67379 q^{79}\) \(+8.92964 q^{80}\) \(+11.5800 q^{81}\) \(+7.00363 q^{82}\) \(-12.3639 q^{83}\) \(+6.44562 q^{84}\) \(+2.90689 q^{85}\) \(+21.4031 q^{86}\) \(-12.6937 q^{87}\) \(+3.73313 q^{88}\) \(+3.93445 q^{89}\) \(-16.2895 q^{90}\) \(+1.35587 q^{91}\) \(-27.5947 q^{92}\) \(+18.6211 q^{93}\) \(+27.2147 q^{94}\) \(-1.44327 q^{95}\) \(+27.3862 q^{96}\) \(+9.02693 q^{97}\) \(+17.6438 q^{98}\) \(-3.30599 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59466 −1.83470 −0.917350 0.398082i \(-0.869676\pi\)
−0.917350 + 0.398082i \(0.869676\pi\)
\(3\) −3.04599 −1.75861 −0.879303 0.476263i \(-0.841991\pi\)
−0.879303 + 0.476263i \(0.841991\pi\)
\(4\) 4.73224 2.36612
\(5\) 1.00000 0.447214
\(6\) 7.90331 3.22651
\(7\) −0.447166 −0.169013 −0.0845064 0.996423i \(-0.526931\pi\)
−0.0845064 + 0.996423i \(0.526931\pi\)
\(8\) −7.08923 −2.50642
\(9\) 6.27808 2.09269
\(10\) −2.59466 −0.820502
\(11\) −0.526592 −0.158773 −0.0793867 0.996844i \(-0.525296\pi\)
−0.0793867 + 0.996844i \(0.525296\pi\)
\(12\) −14.4144 −4.16107
\(13\) −3.03214 −0.840964 −0.420482 0.907301i \(-0.638139\pi\)
−0.420482 + 0.907301i \(0.638139\pi\)
\(14\) 1.16024 0.310088
\(15\) −3.04599 −0.786472
\(16\) 8.92964 2.23241
\(17\) 2.90689 0.705024 0.352512 0.935807i \(-0.385328\pi\)
0.352512 + 0.935807i \(0.385328\pi\)
\(18\) −16.2895 −3.83946
\(19\) −1.44327 −0.331110 −0.165555 0.986201i \(-0.552941\pi\)
−0.165555 + 0.986201i \(0.552941\pi\)
\(20\) 4.73224 1.05816
\(21\) 1.36206 0.297227
\(22\) 1.36633 0.291302
\(23\) −5.83121 −1.21589 −0.607945 0.793979i \(-0.708006\pi\)
−0.607945 + 0.793979i \(0.708006\pi\)
\(24\) 21.5938 4.40781
\(25\) 1.00000 0.200000
\(26\) 7.86736 1.54292
\(27\) −9.98501 −1.92162
\(28\) −2.11610 −0.399905
\(29\) 4.16733 0.773854 0.386927 0.922110i \(-0.373537\pi\)
0.386927 + 0.922110i \(0.373537\pi\)
\(30\) 7.90331 1.44294
\(31\) −6.11330 −1.09798 −0.548991 0.835828i \(-0.684988\pi\)
−0.548991 + 0.835828i \(0.684988\pi\)
\(32\) −8.99088 −1.58938
\(33\) 1.60400 0.279220
\(34\) −7.54238 −1.29351
\(35\) −0.447166 −0.0755848
\(36\) 29.7094 4.95157
\(37\) 5.15081 0.846788 0.423394 0.905946i \(-0.360839\pi\)
0.423394 + 0.905946i \(0.360839\pi\)
\(38\) 3.74480 0.607487
\(39\) 9.23587 1.47892
\(40\) −7.08923 −1.12091
\(41\) −2.69925 −0.421552 −0.210776 0.977534i \(-0.567599\pi\)
−0.210776 + 0.977534i \(0.567599\pi\)
\(42\) −3.53409 −0.545322
\(43\) −8.24891 −1.25795 −0.628973 0.777427i \(-0.716524\pi\)
−0.628973 + 0.777427i \(0.716524\pi\)
\(44\) −2.49196 −0.375677
\(45\) 6.27808 0.935881
\(46\) 15.1300 2.23079
\(47\) −10.4887 −1.52994 −0.764970 0.644066i \(-0.777246\pi\)
−0.764970 + 0.644066i \(0.777246\pi\)
\(48\) −27.1996 −3.92593
\(49\) −6.80004 −0.971435
\(50\) −2.59466 −0.366940
\(51\) −8.85436 −1.23986
\(52\) −14.3488 −1.98982
\(53\) −10.6720 −1.46591 −0.732954 0.680279i \(-0.761859\pi\)
−0.732954 + 0.680279i \(0.761859\pi\)
\(54\) 25.9077 3.52559
\(55\) −0.526592 −0.0710057
\(56\) 3.17006 0.423617
\(57\) 4.39620 0.582291
\(58\) −10.8128 −1.41979
\(59\) 0.466252 0.0607008 0.0303504 0.999539i \(-0.490338\pi\)
0.0303504 + 0.999539i \(0.490338\pi\)
\(60\) −14.4144 −1.86089
\(61\) 1.09388 0.140057 0.0700285 0.997545i \(-0.477691\pi\)
0.0700285 + 0.997545i \(0.477691\pi\)
\(62\) 15.8619 2.01447
\(63\) −2.80734 −0.353692
\(64\) 5.46896 0.683620
\(65\) −3.03214 −0.376090
\(66\) −4.16182 −0.512285
\(67\) 6.42470 0.784902 0.392451 0.919773i \(-0.371627\pi\)
0.392451 + 0.919773i \(0.371627\pi\)
\(68\) 13.7561 1.66817
\(69\) 17.7618 2.13827
\(70\) 1.16024 0.138675
\(71\) 3.65939 0.434290 0.217145 0.976139i \(-0.430326\pi\)
0.217145 + 0.976139i \(0.430326\pi\)
\(72\) −44.5068 −5.24517
\(73\) −0.671565 −0.0786007 −0.0393004 0.999227i \(-0.512513\pi\)
−0.0393004 + 0.999227i \(0.512513\pi\)
\(74\) −13.3646 −1.55360
\(75\) −3.04599 −0.351721
\(76\) −6.82992 −0.783446
\(77\) 0.235474 0.0268347
\(78\) −23.9639 −2.71338
\(79\) −6.67379 −0.750860 −0.375430 0.926851i \(-0.622505\pi\)
−0.375430 + 0.926851i \(0.622505\pi\)
\(80\) 8.92964 0.998364
\(81\) 11.5800 1.28667
\(82\) 7.00363 0.773422
\(83\) −12.3639 −1.35711 −0.678555 0.734550i \(-0.737393\pi\)
−0.678555 + 0.734550i \(0.737393\pi\)
\(84\) 6.44562 0.703274
\(85\) 2.90689 0.315296
\(86\) 21.4031 2.30795
\(87\) −12.6937 −1.36090
\(88\) 3.73313 0.397953
\(89\) 3.93445 0.417050 0.208525 0.978017i \(-0.433134\pi\)
0.208525 + 0.978017i \(0.433134\pi\)
\(90\) −16.2895 −1.71706
\(91\) 1.35587 0.142134
\(92\) −27.5947 −2.87695
\(93\) 18.6211 1.93092
\(94\) 27.2147 2.80698
\(95\) −1.44327 −0.148077
\(96\) 27.3862 2.79509
\(97\) 9.02693 0.916546 0.458273 0.888811i \(-0.348468\pi\)
0.458273 + 0.888811i \(0.348468\pi\)
\(98\) 17.6438 1.78229
\(99\) −3.30599 −0.332264
\(100\) 4.73224 0.473224
\(101\) 0.363640 0.0361835 0.0180918 0.999836i \(-0.494241\pi\)
0.0180918 + 0.999836i \(0.494241\pi\)
\(102\) 22.9740 2.27477
\(103\) 2.85316 0.281130 0.140565 0.990071i \(-0.455108\pi\)
0.140565 + 0.990071i \(0.455108\pi\)
\(104\) 21.4955 2.10781
\(105\) 1.36206 0.132924
\(106\) 27.6901 2.68950
\(107\) 6.89874 0.666926 0.333463 0.942763i \(-0.391783\pi\)
0.333463 + 0.942763i \(0.391783\pi\)
\(108\) −47.2515 −4.54678
\(109\) 7.92796 0.759361 0.379681 0.925118i \(-0.376034\pi\)
0.379681 + 0.925118i \(0.376034\pi\)
\(110\) 1.36633 0.130274
\(111\) −15.6893 −1.48917
\(112\) −3.99303 −0.377306
\(113\) −5.47524 −0.515067 −0.257533 0.966269i \(-0.582910\pi\)
−0.257533 + 0.966269i \(0.582910\pi\)
\(114\) −11.4066 −1.06833
\(115\) −5.83121 −0.543763
\(116\) 19.7208 1.83103
\(117\) −19.0360 −1.75988
\(118\) −1.20976 −0.111368
\(119\) −1.29986 −0.119158
\(120\) 21.5938 1.97123
\(121\) −10.7227 −0.974791
\(122\) −2.83824 −0.256963
\(123\) 8.22191 0.741344
\(124\) −28.9296 −2.59796
\(125\) 1.00000 0.0894427
\(126\) 7.28409 0.648918
\(127\) 3.12251 0.277078 0.138539 0.990357i \(-0.455759\pi\)
0.138539 + 0.990357i \(0.455759\pi\)
\(128\) 3.79167 0.335140
\(129\) 25.1261 2.21223
\(130\) 7.86736 0.690013
\(131\) 8.06592 0.704723 0.352361 0.935864i \(-0.385379\pi\)
0.352361 + 0.935864i \(0.385379\pi\)
\(132\) 7.59050 0.660668
\(133\) 0.645382 0.0559618
\(134\) −16.6699 −1.44006
\(135\) −9.98501 −0.859373
\(136\) −20.6076 −1.76709
\(137\) 17.4076 1.48723 0.743617 0.668605i \(-0.233108\pi\)
0.743617 + 0.668605i \(0.233108\pi\)
\(138\) −46.0858 −3.92309
\(139\) −1.12101 −0.0950827 −0.0475414 0.998869i \(-0.515139\pi\)
−0.0475414 + 0.998869i \(0.515139\pi\)
\(140\) −2.11610 −0.178843
\(141\) 31.9486 2.69056
\(142\) −9.49487 −0.796792
\(143\) 1.59670 0.133523
\(144\) 56.0610 4.67175
\(145\) 4.16733 0.346078
\(146\) 1.74248 0.144209
\(147\) 20.7129 1.70837
\(148\) 24.3749 2.00360
\(149\) −3.03657 −0.248765 −0.124383 0.992234i \(-0.539695\pi\)
−0.124383 + 0.992234i \(0.539695\pi\)
\(150\) 7.90331 0.645302
\(151\) −0.427998 −0.0348299 −0.0174150 0.999848i \(-0.505544\pi\)
−0.0174150 + 0.999848i \(0.505544\pi\)
\(152\) 10.2317 0.829901
\(153\) 18.2497 1.47540
\(154\) −0.610974 −0.0492337
\(155\) −6.11330 −0.491032
\(156\) 43.7064 3.49931
\(157\) 12.5778 1.00382 0.501909 0.864920i \(-0.332631\pi\)
0.501909 + 0.864920i \(0.332631\pi\)
\(158\) 17.3162 1.37760
\(159\) 32.5067 2.57795
\(160\) −8.99088 −0.710791
\(161\) 2.60752 0.205501
\(162\) −30.0462 −2.36065
\(163\) −19.2512 −1.50787 −0.753934 0.656950i \(-0.771846\pi\)
−0.753934 + 0.656950i \(0.771846\pi\)
\(164\) −12.7735 −0.997444
\(165\) 1.60400 0.124871
\(166\) 32.0800 2.48989
\(167\) 1.35606 0.104935 0.0524675 0.998623i \(-0.483291\pi\)
0.0524675 + 0.998623i \(0.483291\pi\)
\(168\) −9.65599 −0.744976
\(169\) −3.80614 −0.292780
\(170\) −7.54238 −0.578474
\(171\) −9.06099 −0.692911
\(172\) −39.0358 −2.97645
\(173\) −14.4768 −1.10065 −0.550327 0.834949i \(-0.685497\pi\)
−0.550327 + 0.834949i \(0.685497\pi\)
\(174\) 32.9357 2.49685
\(175\) −0.447166 −0.0338025
\(176\) −4.70228 −0.354447
\(177\) −1.42020 −0.106749
\(178\) −10.2085 −0.765162
\(179\) 8.11108 0.606250 0.303125 0.952951i \(-0.401970\pi\)
0.303125 + 0.952951i \(0.401970\pi\)
\(180\) 29.7094 2.21441
\(181\) 10.4243 0.774832 0.387416 0.921905i \(-0.373368\pi\)
0.387416 + 0.921905i \(0.373368\pi\)
\(182\) −3.51801 −0.260772
\(183\) −3.33195 −0.246305
\(184\) 41.3388 3.04754
\(185\) 5.15081 0.378695
\(186\) −48.3153 −3.54265
\(187\) −1.53074 −0.111939
\(188\) −49.6352 −3.62002
\(189\) 4.46495 0.324778
\(190\) 3.74480 0.271676
\(191\) 22.6517 1.63902 0.819510 0.573065i \(-0.194246\pi\)
0.819510 + 0.573065i \(0.194246\pi\)
\(192\) −16.6584 −1.20222
\(193\) −4.16273 −0.299640 −0.149820 0.988713i \(-0.547869\pi\)
−0.149820 + 0.988713i \(0.547869\pi\)
\(194\) −23.4218 −1.68159
\(195\) 9.23587 0.661395
\(196\) −32.1795 −2.29853
\(197\) −1.36985 −0.0975978 −0.0487989 0.998809i \(-0.515539\pi\)
−0.0487989 + 0.998809i \(0.515539\pi\)
\(198\) 8.57790 0.609605
\(199\) −13.3176 −0.944057 −0.472028 0.881583i \(-0.656478\pi\)
−0.472028 + 0.881583i \(0.656478\pi\)
\(200\) −7.08923 −0.501284
\(201\) −19.5696 −1.38033
\(202\) −0.943521 −0.0663859
\(203\) −1.86349 −0.130791
\(204\) −41.9010 −2.93366
\(205\) −2.69925 −0.188524
\(206\) −7.40296 −0.515789
\(207\) −36.6088 −2.54449
\(208\) −27.0759 −1.87737
\(209\) 0.760016 0.0525714
\(210\) −3.53409 −0.243875
\(211\) −21.6939 −1.49347 −0.746734 0.665123i \(-0.768379\pi\)
−0.746734 + 0.665123i \(0.768379\pi\)
\(212\) −50.5023 −3.46851
\(213\) −11.1465 −0.763745
\(214\) −17.8999 −1.22361
\(215\) −8.24891 −0.562571
\(216\) 70.7860 4.81638
\(217\) 2.73366 0.185573
\(218\) −20.5703 −1.39320
\(219\) 2.04558 0.138228
\(220\) −2.49196 −0.168008
\(221\) −8.81409 −0.592900
\(222\) 40.7084 2.73217
\(223\) 4.79401 0.321031 0.160515 0.987033i \(-0.448684\pi\)
0.160515 + 0.987033i \(0.448684\pi\)
\(224\) 4.02041 0.268625
\(225\) 6.27808 0.418539
\(226\) 14.2064 0.944993
\(227\) 10.5678 0.701410 0.350705 0.936486i \(-0.385942\pi\)
0.350705 + 0.936486i \(0.385942\pi\)
\(228\) 20.8039 1.37777
\(229\) −11.7036 −0.773398 −0.386699 0.922206i \(-0.626385\pi\)
−0.386699 + 0.922206i \(0.626385\pi\)
\(230\) 15.1300 0.997641
\(231\) −0.717252 −0.0471917
\(232\) −29.5432 −1.93960
\(233\) 23.5118 1.54031 0.770154 0.637858i \(-0.220179\pi\)
0.770154 + 0.637858i \(0.220179\pi\)
\(234\) 49.3919 3.22885
\(235\) −10.4887 −0.684210
\(236\) 2.20642 0.143626
\(237\) 20.3283 1.32047
\(238\) 3.37269 0.218619
\(239\) 4.52136 0.292462 0.146231 0.989250i \(-0.453286\pi\)
0.146231 + 0.989250i \(0.453286\pi\)
\(240\) −27.1996 −1.75573
\(241\) −27.8144 −1.79168 −0.895842 0.444373i \(-0.853426\pi\)
−0.895842 + 0.444373i \(0.853426\pi\)
\(242\) 27.8217 1.78845
\(243\) −5.31769 −0.341130
\(244\) 5.17651 0.331392
\(245\) −6.80004 −0.434439
\(246\) −21.3330 −1.36014
\(247\) 4.37620 0.278451
\(248\) 43.3386 2.75201
\(249\) 37.6602 2.38662
\(250\) −2.59466 −0.164100
\(251\) −14.5703 −0.919667 −0.459833 0.888005i \(-0.652091\pi\)
−0.459833 + 0.888005i \(0.652091\pi\)
\(252\) −13.2850 −0.836878
\(253\) 3.07067 0.193051
\(254\) −8.10184 −0.508355
\(255\) −8.85436 −0.554482
\(256\) −20.7760 −1.29850
\(257\) 26.0470 1.62477 0.812383 0.583125i \(-0.198170\pi\)
0.812383 + 0.583125i \(0.198170\pi\)
\(258\) −65.1936 −4.05878
\(259\) −2.30326 −0.143118
\(260\) −14.3488 −0.889875
\(261\) 26.1628 1.61944
\(262\) −20.9283 −1.29295
\(263\) −3.38709 −0.208857 −0.104428 0.994532i \(-0.533301\pi\)
−0.104428 + 0.994532i \(0.533301\pi\)
\(264\) −11.3711 −0.699843
\(265\) −10.6720 −0.655574
\(266\) −1.67455 −0.102673
\(267\) −11.9843 −0.733427
\(268\) 30.4032 1.85717
\(269\) 7.22310 0.440400 0.220200 0.975455i \(-0.429329\pi\)
0.220200 + 0.975455i \(0.429329\pi\)
\(270\) 25.9077 1.57669
\(271\) 13.2490 0.804819 0.402409 0.915460i \(-0.368173\pi\)
0.402409 + 0.915460i \(0.368173\pi\)
\(272\) 25.9575 1.57390
\(273\) −4.12996 −0.249957
\(274\) −45.1668 −2.72863
\(275\) −0.526592 −0.0317547
\(276\) 84.0533 5.05941
\(277\) −28.2945 −1.70005 −0.850027 0.526740i \(-0.823414\pi\)
−0.850027 + 0.526740i \(0.823414\pi\)
\(278\) 2.90863 0.174448
\(279\) −38.3798 −2.29774
\(280\) 3.17006 0.189447
\(281\) 13.9299 0.830986 0.415493 0.909596i \(-0.363609\pi\)
0.415493 + 0.909596i \(0.363609\pi\)
\(282\) −82.8957 −4.93637
\(283\) −2.39974 −0.142650 −0.0713249 0.997453i \(-0.522723\pi\)
−0.0713249 + 0.997453i \(0.522723\pi\)
\(284\) 17.3171 1.02758
\(285\) 4.39620 0.260409
\(286\) −4.14289 −0.244974
\(287\) 1.20701 0.0712477
\(288\) −56.4454 −3.32608
\(289\) −8.55000 −0.502941
\(290\) −10.8128 −0.634949
\(291\) −27.4960 −1.61184
\(292\) −3.17801 −0.185979
\(293\) 1.23713 0.0722742 0.0361371 0.999347i \(-0.488495\pi\)
0.0361371 + 0.999347i \(0.488495\pi\)
\(294\) −53.7428 −3.13435
\(295\) 0.466252 0.0271462
\(296\) −36.5153 −2.12241
\(297\) 5.25803 0.305102
\(298\) 7.87885 0.456409
\(299\) 17.6810 1.02252
\(300\) −14.4144 −0.832215
\(301\) 3.68863 0.212609
\(302\) 1.11051 0.0639025
\(303\) −1.10764 −0.0636325
\(304\) −12.8879 −0.739172
\(305\) 1.09388 0.0626354
\(306\) −47.3516 −2.70691
\(307\) −5.35381 −0.305558 −0.152779 0.988260i \(-0.548822\pi\)
−0.152779 + 0.988260i \(0.548822\pi\)
\(308\) 1.11432 0.0634943
\(309\) −8.69070 −0.494396
\(310\) 15.8619 0.900897
\(311\) 12.1029 0.686293 0.343147 0.939282i \(-0.388507\pi\)
0.343147 + 0.939282i \(0.388507\pi\)
\(312\) −65.4752 −3.70681
\(313\) −30.0426 −1.69811 −0.849053 0.528307i \(-0.822827\pi\)
−0.849053 + 0.528307i \(0.822827\pi\)
\(314\) −32.6351 −1.84171
\(315\) −2.80734 −0.158176
\(316\) −31.5820 −1.77663
\(317\) −0.169978 −0.00954689 −0.00477344 0.999989i \(-0.501519\pi\)
−0.00477344 + 0.999989i \(0.501519\pi\)
\(318\) −84.3438 −4.72977
\(319\) −2.19448 −0.122867
\(320\) 5.46896 0.305724
\(321\) −21.0135 −1.17286
\(322\) −6.76561 −0.377033
\(323\) −4.19544 −0.233440
\(324\) 54.7995 3.04442
\(325\) −3.03214 −0.168193
\(326\) 49.9502 2.76649
\(327\) −24.1485 −1.33542
\(328\) 19.1356 1.05659
\(329\) 4.69020 0.258579
\(330\) −4.16182 −0.229101
\(331\) −8.61589 −0.473572 −0.236786 0.971562i \(-0.576094\pi\)
−0.236786 + 0.971562i \(0.576094\pi\)
\(332\) −58.5088 −3.21109
\(333\) 32.3372 1.77207
\(334\) −3.51850 −0.192524
\(335\) 6.42470 0.351019
\(336\) 12.1627 0.663532
\(337\) −13.2080 −0.719485 −0.359743 0.933052i \(-0.617135\pi\)
−0.359743 + 0.933052i \(0.617135\pi\)
\(338\) 9.87563 0.537164
\(339\) 16.6775 0.905799
\(340\) 13.7561 0.746029
\(341\) 3.21922 0.174330
\(342\) 23.5101 1.27128
\(343\) 6.17091 0.333198
\(344\) 58.4784 3.15294
\(345\) 17.7618 0.956264
\(346\) 37.5624 2.01937
\(347\) 14.4897 0.777848 0.388924 0.921270i \(-0.372847\pi\)
0.388924 + 0.921270i \(0.372847\pi\)
\(348\) −60.0695 −3.22006
\(349\) −3.03684 −0.162558 −0.0812790 0.996691i \(-0.525900\pi\)
−0.0812790 + 0.996691i \(0.525900\pi\)
\(350\) 1.16024 0.0620175
\(351\) 30.2759 1.61601
\(352\) 4.73452 0.252351
\(353\) −0.797555 −0.0424496 −0.0212248 0.999775i \(-0.506757\pi\)
−0.0212248 + 0.999775i \(0.506757\pi\)
\(354\) 3.68493 0.195852
\(355\) 3.65939 0.194220
\(356\) 18.6188 0.986792
\(357\) 3.95937 0.209552
\(358\) −21.0455 −1.11229
\(359\) −1.14239 −0.0602931 −0.0301465 0.999545i \(-0.509597\pi\)
−0.0301465 + 0.999545i \(0.509597\pi\)
\(360\) −44.5068 −2.34571
\(361\) −16.9170 −0.890366
\(362\) −27.0475 −1.42158
\(363\) 32.6613 1.71427
\(364\) 6.41630 0.336305
\(365\) −0.671565 −0.0351513
\(366\) 8.64527 0.451896
\(367\) 0.209999 0.0109619 0.00548093 0.999985i \(-0.498255\pi\)
0.00548093 + 0.999985i \(0.498255\pi\)
\(368\) −52.0706 −2.71437
\(369\) −16.9461 −0.882180
\(370\) −13.3646 −0.694791
\(371\) 4.77214 0.247757
\(372\) 88.1195 4.56878
\(373\) 13.9461 0.722102 0.361051 0.932546i \(-0.382418\pi\)
0.361051 + 0.932546i \(0.382418\pi\)
\(374\) 3.97176 0.205375
\(375\) −3.04599 −0.157294
\(376\) 74.3571 3.83467
\(377\) −12.6359 −0.650783
\(378\) −11.5850 −0.595869
\(379\) −9.30438 −0.477934 −0.238967 0.971028i \(-0.576809\pi\)
−0.238967 + 0.971028i \(0.576809\pi\)
\(380\) −6.82992 −0.350368
\(381\) −9.51114 −0.487271
\(382\) −58.7734 −3.00711
\(383\) −31.6519 −1.61734 −0.808668 0.588266i \(-0.799811\pi\)
−0.808668 + 0.588266i \(0.799811\pi\)
\(384\) −11.5494 −0.589378
\(385\) 0.235474 0.0120009
\(386\) 10.8008 0.549749
\(387\) −51.7873 −2.63250
\(388\) 42.7176 2.16866
\(389\) −35.8514 −1.81774 −0.908869 0.417082i \(-0.863053\pi\)
−0.908869 + 0.417082i \(0.863053\pi\)
\(390\) −23.9639 −1.21346
\(391\) −16.9507 −0.857232
\(392\) 48.2071 2.43483
\(393\) −24.5687 −1.23933
\(394\) 3.55429 0.179063
\(395\) −6.67379 −0.335795
\(396\) −15.6447 −0.786177
\(397\) −13.5293 −0.679018 −0.339509 0.940603i \(-0.610261\pi\)
−0.339509 + 0.940603i \(0.610261\pi\)
\(398\) 34.5545 1.73206
\(399\) −1.96583 −0.0984146
\(400\) 8.92964 0.446482
\(401\) 7.39160 0.369119 0.184559 0.982821i \(-0.440914\pi\)
0.184559 + 0.982821i \(0.440914\pi\)
\(402\) 50.7764 2.53249
\(403\) 18.5364 0.923363
\(404\) 1.72083 0.0856146
\(405\) 11.5800 0.575417
\(406\) 4.83511 0.239962
\(407\) −2.71237 −0.134447
\(408\) 62.7706 3.10761
\(409\) 6.28057 0.310554 0.155277 0.987871i \(-0.450373\pi\)
0.155277 + 0.987871i \(0.450373\pi\)
\(410\) 7.00363 0.345885
\(411\) −53.0236 −2.61546
\(412\) 13.5018 0.665187
\(413\) −0.208492 −0.0102592
\(414\) 94.9872 4.66837
\(415\) −12.3639 −0.606918
\(416\) 27.2616 1.33661
\(417\) 3.41459 0.167213
\(418\) −1.97198 −0.0964528
\(419\) 2.73127 0.133431 0.0667156 0.997772i \(-0.478748\pi\)
0.0667156 + 0.997772i \(0.478748\pi\)
\(420\) 6.44562 0.314514
\(421\) −1.48262 −0.0722583 −0.0361291 0.999347i \(-0.511503\pi\)
−0.0361291 + 0.999347i \(0.511503\pi\)
\(422\) 56.2882 2.74006
\(423\) −65.8491 −3.20169
\(424\) 75.6560 3.67418
\(425\) 2.90689 0.141005
\(426\) 28.9213 1.40124
\(427\) −0.489146 −0.0236714
\(428\) 32.6465 1.57803
\(429\) −4.86354 −0.234814
\(430\) 21.4031 1.03215
\(431\) −7.93114 −0.382030 −0.191015 0.981587i \(-0.561178\pi\)
−0.191015 + 0.981587i \(0.561178\pi\)
\(432\) −89.1625 −4.28983
\(433\) −17.5130 −0.841622 −0.420811 0.907148i \(-0.638254\pi\)
−0.420811 + 0.907148i \(0.638254\pi\)
\(434\) −7.09291 −0.340470
\(435\) −12.6937 −0.608614
\(436\) 37.5170 1.79674
\(437\) 8.41603 0.402593
\(438\) −5.30759 −0.253606
\(439\) −12.9932 −0.620131 −0.310066 0.950715i \(-0.600351\pi\)
−0.310066 + 0.950715i \(0.600351\pi\)
\(440\) 3.73313 0.177970
\(441\) −42.6912 −2.03291
\(442\) 22.8695 1.08779
\(443\) 0.223033 0.0105966 0.00529832 0.999986i \(-0.498313\pi\)
0.00529832 + 0.999986i \(0.498313\pi\)
\(444\) −74.2457 −3.52355
\(445\) 3.93445 0.186511
\(446\) −12.4388 −0.588995
\(447\) 9.24936 0.437480
\(448\) −2.44553 −0.115541
\(449\) 37.3943 1.76474 0.882372 0.470552i \(-0.155945\pi\)
0.882372 + 0.470552i \(0.155945\pi\)
\(450\) −16.2895 −0.767892
\(451\) 1.42140 0.0669313
\(452\) −25.9101 −1.21871
\(453\) 1.30368 0.0612521
\(454\) −27.4198 −1.28688
\(455\) 1.35587 0.0635641
\(456\) −31.1657 −1.45947
\(457\) 22.7286 1.06320 0.531600 0.846996i \(-0.321591\pi\)
0.531600 + 0.846996i \(0.321591\pi\)
\(458\) 30.3669 1.41895
\(459\) −29.0253 −1.35479
\(460\) −27.5947 −1.28661
\(461\) 22.1669 1.03241 0.516207 0.856464i \(-0.327344\pi\)
0.516207 + 0.856464i \(0.327344\pi\)
\(462\) 1.86102 0.0865826
\(463\) 27.8894 1.29613 0.648065 0.761585i \(-0.275579\pi\)
0.648065 + 0.761585i \(0.275579\pi\)
\(464\) 37.2127 1.72756
\(465\) 18.6211 0.863532
\(466\) −61.0050 −2.82600
\(467\) −3.89609 −0.180289 −0.0901447 0.995929i \(-0.528733\pi\)
−0.0901447 + 0.995929i \(0.528733\pi\)
\(468\) −90.0830 −4.16409
\(469\) −2.87290 −0.132658
\(470\) 27.2147 1.25532
\(471\) −38.3119 −1.76532
\(472\) −3.30537 −0.152142
\(473\) 4.34381 0.199729
\(474\) −52.7450 −2.42266
\(475\) −1.44327 −0.0662219
\(476\) −6.15126 −0.281942
\(477\) −66.9994 −3.06769
\(478\) −11.7314 −0.536580
\(479\) −31.2021 −1.42566 −0.712830 0.701337i \(-0.752587\pi\)
−0.712830 + 0.701337i \(0.752587\pi\)
\(480\) 27.3862 1.25000
\(481\) −15.6180 −0.712118
\(482\) 72.1688 3.28720
\(483\) −7.94248 −0.361395
\(484\) −50.7424 −2.30647
\(485\) 9.02693 0.409892
\(486\) 13.7976 0.625871
\(487\) 13.7078 0.621161 0.310581 0.950547i \(-0.399477\pi\)
0.310581 + 0.950547i \(0.399477\pi\)
\(488\) −7.75477 −0.351042
\(489\) 58.6390 2.65175
\(490\) 17.6438 0.797065
\(491\) 18.7542 0.846367 0.423184 0.906044i \(-0.360913\pi\)
0.423184 + 0.906044i \(0.360913\pi\)
\(492\) 38.9081 1.75411
\(493\) 12.1140 0.545585
\(494\) −11.3547 −0.510874
\(495\) −3.30599 −0.148593
\(496\) −54.5896 −2.45114
\(497\) −1.63635 −0.0734005
\(498\) −97.7154 −4.37873
\(499\) −13.9627 −0.625058 −0.312529 0.949908i \(-0.601176\pi\)
−0.312529 + 0.949908i \(0.601176\pi\)
\(500\) 4.73224 0.211632
\(501\) −4.13054 −0.184539
\(502\) 37.8048 1.68731
\(503\) −25.5731 −1.14025 −0.570124 0.821559i \(-0.693105\pi\)
−0.570124 + 0.821559i \(0.693105\pi\)
\(504\) 19.9019 0.886501
\(505\) 0.363640 0.0161818
\(506\) −7.96733 −0.354191
\(507\) 11.5935 0.514885
\(508\) 14.7765 0.655600
\(509\) −20.1717 −0.894095 −0.447048 0.894510i \(-0.647525\pi\)
−0.447048 + 0.894510i \(0.647525\pi\)
\(510\) 22.9740 1.01731
\(511\) 0.300301 0.0132845
\(512\) 46.3233 2.04722
\(513\) 14.4111 0.636266
\(514\) −67.5829 −2.98096
\(515\) 2.85316 0.125725
\(516\) 118.903 5.23441
\(517\) 5.52328 0.242914
\(518\) 5.97618 0.262578
\(519\) 44.0963 1.93561
\(520\) 21.4955 0.942641
\(521\) −1.34970 −0.0591316 −0.0295658 0.999563i \(-0.509412\pi\)
−0.0295658 + 0.999563i \(0.509412\pi\)
\(522\) −67.8835 −2.97118
\(523\) −8.42608 −0.368447 −0.184223 0.982884i \(-0.558977\pi\)
−0.184223 + 0.982884i \(0.558977\pi\)
\(524\) 38.1699 1.66746
\(525\) 1.36206 0.0594453
\(526\) 8.78833 0.383189
\(527\) −17.7707 −0.774103
\(528\) 14.3231 0.623333
\(529\) 11.0030 0.478390
\(530\) 27.6901 1.20278
\(531\) 2.92717 0.127028
\(532\) 3.05411 0.132412
\(533\) 8.18450 0.354510
\(534\) 31.0951 1.34562
\(535\) 6.89874 0.298258
\(536\) −45.5462 −1.96729
\(537\) −24.7063 −1.06616
\(538\) −18.7415 −0.808002
\(539\) 3.58085 0.154238
\(540\) −47.2515 −2.03338
\(541\) −7.56298 −0.325158 −0.162579 0.986696i \(-0.551981\pi\)
−0.162579 + 0.986696i \(0.551981\pi\)
\(542\) −34.3766 −1.47660
\(543\) −31.7523 −1.36262
\(544\) −26.1355 −1.12055
\(545\) 7.92796 0.339597
\(546\) 10.7158 0.458596
\(547\) 24.0653 1.02896 0.514479 0.857503i \(-0.327985\pi\)
0.514479 + 0.857503i \(0.327985\pi\)
\(548\) 82.3772 3.51898
\(549\) 6.86747 0.293096
\(550\) 1.36633 0.0582603
\(551\) −6.01460 −0.256230
\(552\) −125.918 −5.35941
\(553\) 2.98429 0.126905
\(554\) 73.4146 3.11909
\(555\) −15.6893 −0.665975
\(556\) −5.30489 −0.224977
\(557\) 18.9519 0.803017 0.401509 0.915855i \(-0.368486\pi\)
0.401509 + 0.915855i \(0.368486\pi\)
\(558\) 99.5824 4.21566
\(559\) 25.0118 1.05789
\(560\) −3.99303 −0.168736
\(561\) 4.66264 0.196857
\(562\) −36.1432 −1.52461
\(563\) 43.4991 1.83327 0.916635 0.399726i \(-0.130895\pi\)
0.916635 + 0.399726i \(0.130895\pi\)
\(564\) 151.189 6.36619
\(565\) −5.47524 −0.230345
\(566\) 6.22650 0.261719
\(567\) −5.17819 −0.217464
\(568\) −25.9423 −1.08851
\(569\) −26.3909 −1.10636 −0.553182 0.833060i \(-0.686587\pi\)
−0.553182 + 0.833060i \(0.686587\pi\)
\(570\) −11.4066 −0.477771
\(571\) −34.2432 −1.43303 −0.716517 0.697570i \(-0.754265\pi\)
−0.716517 + 0.697570i \(0.754265\pi\)
\(572\) 7.55597 0.315931
\(573\) −68.9969 −2.88239
\(574\) −3.13178 −0.130718
\(575\) −5.83121 −0.243178
\(576\) 34.3346 1.43061
\(577\) 16.2091 0.674795 0.337397 0.941362i \(-0.390453\pi\)
0.337397 + 0.941362i \(0.390453\pi\)
\(578\) 22.1843 0.922746
\(579\) 12.6796 0.526948
\(580\) 19.7208 0.818862
\(581\) 5.52869 0.229369
\(582\) 71.3426 2.95725
\(583\) 5.61977 0.232747
\(584\) 4.76088 0.197007
\(585\) −19.0360 −0.787042
\(586\) −3.20994 −0.132601
\(587\) −21.7083 −0.895997 −0.447998 0.894034i \(-0.647863\pi\)
−0.447998 + 0.894034i \(0.647863\pi\)
\(588\) 98.0184 4.04221
\(589\) 8.82317 0.363552
\(590\) −1.20976 −0.0498052
\(591\) 4.17256 0.171636
\(592\) 45.9948 1.89038
\(593\) −28.3799 −1.16542 −0.582711 0.812680i \(-0.698008\pi\)
−0.582711 + 0.812680i \(0.698008\pi\)
\(594\) −13.6428 −0.559770
\(595\) −1.29986 −0.0532891
\(596\) −14.3698 −0.588609
\(597\) 40.5652 1.66022
\(598\) −45.8762 −1.87602
\(599\) 14.0896 0.575687 0.287844 0.957677i \(-0.407062\pi\)
0.287844 + 0.957677i \(0.407062\pi\)
\(600\) 21.5938 0.881561
\(601\) −5.65538 −0.230688 −0.115344 0.993326i \(-0.536797\pi\)
−0.115344 + 0.993326i \(0.536797\pi\)
\(602\) −9.57072 −0.390073
\(603\) 40.3348 1.64256
\(604\) −2.02539 −0.0824119
\(605\) −10.7227 −0.435940
\(606\) 2.87396 0.116747
\(607\) −1.22678 −0.0497934 −0.0248967 0.999690i \(-0.507926\pi\)
−0.0248967 + 0.999690i \(0.507926\pi\)
\(608\) 12.9763 0.526258
\(609\) 5.67617 0.230010
\(610\) −2.83824 −0.114917
\(611\) 31.8033 1.28662
\(612\) 86.3619 3.49097
\(613\) −27.3025 −1.10274 −0.551368 0.834262i \(-0.685894\pi\)
−0.551368 + 0.834262i \(0.685894\pi\)
\(614\) 13.8913 0.560607
\(615\) 8.22191 0.331539
\(616\) −1.66933 −0.0672592
\(617\) 38.1583 1.53620 0.768098 0.640332i \(-0.221203\pi\)
0.768098 + 0.640332i \(0.221203\pi\)
\(618\) 22.5494 0.907069
\(619\) −2.56929 −0.103268 −0.0516341 0.998666i \(-0.516443\pi\)
−0.0516341 + 0.998666i \(0.516443\pi\)
\(620\) −28.9296 −1.16184
\(621\) 58.2247 2.33647
\(622\) −31.4029 −1.25914
\(623\) −1.75935 −0.0704868
\(624\) 82.4730 3.30156
\(625\) 1.00000 0.0400000
\(626\) 77.9501 3.11551
\(627\) −2.31501 −0.0924524
\(628\) 59.5213 2.37516
\(629\) 14.9728 0.597006
\(630\) 7.28409 0.290205
\(631\) 12.0819 0.480972 0.240486 0.970653i \(-0.422693\pi\)
0.240486 + 0.970653i \(0.422693\pi\)
\(632\) 47.3120 1.88197
\(633\) 66.0794 2.62642
\(634\) 0.441033 0.0175157
\(635\) 3.12251 0.123913
\(636\) 153.830 6.09975
\(637\) 20.6187 0.816941
\(638\) 5.69393 0.225425
\(639\) 22.9740 0.908836
\(640\) 3.79167 0.149879
\(641\) −8.41522 −0.332381 −0.166191 0.986094i \(-0.553147\pi\)
−0.166191 + 0.986094i \(0.553147\pi\)
\(642\) 54.5228 2.15184
\(643\) 6.45576 0.254590 0.127295 0.991865i \(-0.459370\pi\)
0.127295 + 0.991865i \(0.459370\pi\)
\(644\) 12.3394 0.486240
\(645\) 25.1261 0.989340
\(646\) 10.8857 0.428293
\(647\) 4.47445 0.175909 0.0879544 0.996125i \(-0.471967\pi\)
0.0879544 + 0.996125i \(0.471967\pi\)
\(648\) −82.0936 −3.22494
\(649\) −0.245525 −0.00963768
\(650\) 7.86736 0.308583
\(651\) −8.32671 −0.326349
\(652\) −91.1013 −3.56780
\(653\) 16.4975 0.645598 0.322799 0.946468i \(-0.395376\pi\)
0.322799 + 0.946468i \(0.395376\pi\)
\(654\) 62.6571 2.45009
\(655\) 8.06592 0.315162
\(656\) −24.1033 −0.941077
\(657\) −4.21614 −0.164487
\(658\) −12.1695 −0.474415
\(659\) 44.7558 1.74344 0.871720 0.490004i \(-0.163005\pi\)
0.871720 + 0.490004i \(0.163005\pi\)
\(660\) 7.59050 0.295460
\(661\) 38.6038 1.50151 0.750756 0.660579i \(-0.229689\pi\)
0.750756 + 0.660579i \(0.229689\pi\)
\(662\) 22.3553 0.868863
\(663\) 26.8476 1.04268
\(664\) 87.6503 3.40149
\(665\) 0.645382 0.0250269
\(666\) −83.9039 −3.25121
\(667\) −24.3006 −0.940922
\(668\) 6.41720 0.248289
\(669\) −14.6025 −0.564567
\(670\) −16.6699 −0.644014
\(671\) −0.576029 −0.0222373
\(672\) −12.2461 −0.472405
\(673\) 26.6709 1.02809 0.514045 0.857763i \(-0.328147\pi\)
0.514045 + 0.857763i \(0.328147\pi\)
\(674\) 34.2702 1.32004
\(675\) −9.98501 −0.384323
\(676\) −18.0116 −0.692754
\(677\) 37.5231 1.44213 0.721065 0.692867i \(-0.243653\pi\)
0.721065 + 0.692867i \(0.243653\pi\)
\(678\) −43.2725 −1.66187
\(679\) −4.03653 −0.154908
\(680\) −20.6076 −0.790266
\(681\) −32.1895 −1.23350
\(682\) −8.35276 −0.319844
\(683\) 6.46157 0.247245 0.123623 0.992329i \(-0.460549\pi\)
0.123623 + 0.992329i \(0.460549\pi\)
\(684\) −42.8788 −1.63951
\(685\) 17.4076 0.665112
\(686\) −16.0114 −0.611317
\(687\) 35.6492 1.36010
\(688\) −73.6597 −2.80825
\(689\) 32.3589 1.23277
\(690\) −46.0858 −1.75446
\(691\) 9.59956 0.365184 0.182592 0.983189i \(-0.441551\pi\)
0.182592 + 0.983189i \(0.441551\pi\)
\(692\) −68.5079 −2.60428
\(693\) 1.47832 0.0561569
\(694\) −37.5958 −1.42712
\(695\) −1.12101 −0.0425223
\(696\) 89.9883 3.41100
\(697\) −7.84642 −0.297205
\(698\) 7.87954 0.298245
\(699\) −71.6168 −2.70880
\(700\) −2.11610 −0.0799809
\(701\) −30.7087 −1.15985 −0.579926 0.814669i \(-0.696919\pi\)
−0.579926 + 0.814669i \(0.696919\pi\)
\(702\) −78.5556 −2.96489
\(703\) −7.43403 −0.280380
\(704\) −2.87991 −0.108541
\(705\) 31.9486 1.20325
\(706\) 2.06938 0.0778822
\(707\) −0.162607 −0.00611548
\(708\) −6.72073 −0.252581
\(709\) 16.5207 0.620449 0.310224 0.950663i \(-0.399596\pi\)
0.310224 + 0.950663i \(0.399596\pi\)
\(710\) −9.49487 −0.356336
\(711\) −41.8986 −1.57132
\(712\) −27.8922 −1.04530
\(713\) 35.6479 1.33503
\(714\) −10.2732 −0.384465
\(715\) 1.59670 0.0597132
\(716\) 38.3836 1.43446
\(717\) −13.7720 −0.514326
\(718\) 2.96411 0.110620
\(719\) 31.9748 1.19246 0.596230 0.802814i \(-0.296665\pi\)
0.596230 + 0.802814i \(0.296665\pi\)
\(720\) 56.0610 2.08927
\(721\) −1.27583 −0.0475145
\(722\) 43.8937 1.63355
\(723\) 84.7225 3.15086
\(724\) 49.3303 1.83335
\(725\) 4.16733 0.154771
\(726\) −84.7448 −3.14517
\(727\) 0.587554 0.0217912 0.0108956 0.999941i \(-0.496532\pi\)
0.0108956 + 0.999941i \(0.496532\pi\)
\(728\) −9.61206 −0.356247
\(729\) −18.5424 −0.686757
\(730\) 1.74248 0.0644921
\(731\) −23.9786 −0.886882
\(732\) −15.7676 −0.582788
\(733\) 45.0404 1.66361 0.831803 0.555071i \(-0.187309\pi\)
0.831803 + 0.555071i \(0.187309\pi\)
\(734\) −0.544875 −0.0201117
\(735\) 20.7129 0.764006
\(736\) 52.4277 1.93251
\(737\) −3.38319 −0.124622
\(738\) 43.9694 1.61853
\(739\) 0.119486 0.00439536 0.00219768 0.999998i \(-0.499300\pi\)
0.00219768 + 0.999998i \(0.499300\pi\)
\(740\) 24.3749 0.896038
\(741\) −13.3299 −0.489686
\(742\) −12.3821 −0.454560
\(743\) −24.1611 −0.886385 −0.443193 0.896426i \(-0.646154\pi\)
−0.443193 + 0.896426i \(0.646154\pi\)
\(744\) −132.009 −4.83969
\(745\) −3.03657 −0.111251
\(746\) −36.1854 −1.32484
\(747\) −77.6213 −2.84001
\(748\) −7.24385 −0.264862
\(749\) −3.08488 −0.112719
\(750\) 7.90331 0.288588
\(751\) 17.5941 0.642017 0.321008 0.947076i \(-0.395978\pi\)
0.321008 + 0.947076i \(0.395978\pi\)
\(752\) −93.6606 −3.41545
\(753\) 44.3809 1.61733
\(754\) 32.7859 1.19399
\(755\) −0.427998 −0.0155764
\(756\) 21.1292 0.768463
\(757\) 25.7937 0.937490 0.468745 0.883334i \(-0.344706\pi\)
0.468745 + 0.883334i \(0.344706\pi\)
\(758\) 24.1417 0.876865
\(759\) −9.35323 −0.339501
\(760\) 10.2317 0.371143
\(761\) −11.3894 −0.412864 −0.206432 0.978461i \(-0.566185\pi\)
−0.206432 + 0.978461i \(0.566185\pi\)
\(762\) 24.6782 0.893995
\(763\) −3.54511 −0.128342
\(764\) 107.193 3.87812
\(765\) 18.2497 0.659818
\(766\) 82.1258 2.96732
\(767\) −1.41374 −0.0510472
\(768\) 63.2836 2.28355
\(769\) −43.2041 −1.55798 −0.778991 0.627036i \(-0.784268\pi\)
−0.778991 + 0.627036i \(0.784268\pi\)
\(770\) −0.610974 −0.0220180
\(771\) −79.3389 −2.85732
\(772\) −19.6990 −0.708984
\(773\) −8.10310 −0.291448 −0.145724 0.989325i \(-0.546551\pi\)
−0.145724 + 0.989325i \(0.546551\pi\)
\(774\) 134.370 4.82984
\(775\) −6.11330 −0.219596
\(776\) −63.9940 −2.29725
\(777\) 7.01573 0.251688
\(778\) 93.0221 3.33500
\(779\) 3.89576 0.139580
\(780\) 43.7064 1.56494
\(781\) −1.92701 −0.0689537
\(782\) 43.9812 1.57276
\(783\) −41.6108 −1.48705
\(784\) −60.7219 −2.16864
\(785\) 12.5778 0.448921
\(786\) 63.7475 2.27380
\(787\) 14.7698 0.526486 0.263243 0.964730i \(-0.415208\pi\)
0.263243 + 0.964730i \(0.415208\pi\)
\(788\) −6.48246 −0.230928
\(789\) 10.3170 0.367297
\(790\) 17.3162 0.616082
\(791\) 2.44834 0.0870529
\(792\) 23.4369 0.832794
\(793\) −3.31680 −0.117783
\(794\) 35.1040 1.24579
\(795\) 32.5067 1.15290
\(796\) −63.0219 −2.23375
\(797\) −36.2454 −1.28388 −0.641939 0.766755i \(-0.721870\pi\)
−0.641939 + 0.766755i \(0.721870\pi\)
\(798\) 5.10066 0.180561
\(799\) −30.4896 −1.07864
\(800\) −8.99088 −0.317875
\(801\) 24.7008 0.872759
\(802\) −19.1787 −0.677222
\(803\) 0.353641 0.0124797
\(804\) −92.6080 −3.26603
\(805\) 2.60752 0.0919029
\(806\) −48.0955 −1.69409
\(807\) −22.0015 −0.774490
\(808\) −2.57793 −0.0906912
\(809\) −3.82482 −0.134473 −0.0672367 0.997737i \(-0.521418\pi\)
−0.0672367 + 0.997737i \(0.521418\pi\)
\(810\) −30.0462 −1.05572
\(811\) 16.9602 0.595554 0.297777 0.954636i \(-0.403755\pi\)
0.297777 + 0.954636i \(0.403755\pi\)
\(812\) −8.81847 −0.309468
\(813\) −40.3563 −1.41536
\(814\) 7.03768 0.246671
\(815\) −19.2512 −0.674339
\(816\) −79.0662 −2.76787
\(817\) 11.9054 0.416518
\(818\) −16.2959 −0.569774
\(819\) 8.51224 0.297442
\(820\) −12.7735 −0.446071
\(821\) 45.0003 1.57052 0.785261 0.619165i \(-0.212529\pi\)
0.785261 + 0.619165i \(0.212529\pi\)
\(822\) 137.578 4.79858
\(823\) 24.9823 0.870830 0.435415 0.900230i \(-0.356602\pi\)
0.435415 + 0.900230i \(0.356602\pi\)
\(824\) −20.2267 −0.704630
\(825\) 1.60400 0.0558440
\(826\) 0.540965 0.0188226
\(827\) −26.9876 −0.938452 −0.469226 0.883078i \(-0.655467\pi\)
−0.469226 + 0.883078i \(0.655467\pi\)
\(828\) −173.242 −6.02056
\(829\) 32.4619 1.12745 0.563723 0.825964i \(-0.309368\pi\)
0.563723 + 0.825964i \(0.309368\pi\)
\(830\) 32.0800 1.11351
\(831\) 86.1849 2.98972
\(832\) −16.5826 −0.574900
\(833\) −19.7670 −0.684885
\(834\) −8.85968 −0.306786
\(835\) 1.35606 0.0469283
\(836\) 3.59658 0.124390
\(837\) 61.0414 2.10990
\(838\) −7.08670 −0.244806
\(839\) −43.1730 −1.49050 −0.745249 0.666786i \(-0.767670\pi\)
−0.745249 + 0.666786i \(0.767670\pi\)
\(840\) −9.65599 −0.333163
\(841\) −11.6334 −0.401151
\(842\) 3.84688 0.132572
\(843\) −42.4303 −1.46138
\(844\) −102.661 −3.53373
\(845\) −3.80614 −0.130935
\(846\) 170.856 5.87414
\(847\) 4.79482 0.164752
\(848\) −95.2968 −3.27250
\(849\) 7.30959 0.250865
\(850\) −7.54238 −0.258701
\(851\) −30.0354 −1.02960
\(852\) −52.7479 −1.80711
\(853\) 22.1495 0.758385 0.379193 0.925318i \(-0.376202\pi\)
0.379193 + 0.925318i \(0.376202\pi\)
\(854\) 1.26917 0.0434299
\(855\) −9.06099 −0.309879
\(856\) −48.9067 −1.67160
\(857\) −17.0655 −0.582947 −0.291474 0.956579i \(-0.594146\pi\)
−0.291474 + 0.956579i \(0.594146\pi\)
\(858\) 12.6192 0.430813
\(859\) 12.8417 0.438152 0.219076 0.975708i \(-0.429696\pi\)
0.219076 + 0.975708i \(0.429696\pi\)
\(860\) −39.0358 −1.33111
\(861\) −3.67655 −0.125297
\(862\) 20.5786 0.700910
\(863\) 37.3315 1.27078 0.635389 0.772192i \(-0.280840\pi\)
0.635389 + 0.772192i \(0.280840\pi\)
\(864\) 89.7740 3.05417
\(865\) −14.4768 −0.492227
\(866\) 45.4403 1.54412
\(867\) 26.0432 0.884475
\(868\) 12.9363 0.439088
\(869\) 3.51436 0.119217
\(870\) 32.9357 1.11662
\(871\) −19.4806 −0.660074
\(872\) −56.2032 −1.90328
\(873\) 56.6718 1.91805
\(874\) −21.8367 −0.738637
\(875\) −0.447166 −0.0151170
\(876\) 9.68019 0.327063
\(877\) −20.9514 −0.707477 −0.353738 0.935344i \(-0.615090\pi\)
−0.353738 + 0.935344i \(0.615090\pi\)
\(878\) 33.7129 1.13775
\(879\) −3.76830 −0.127102
\(880\) −4.70228 −0.158514
\(881\) 31.8826 1.07415 0.537076 0.843534i \(-0.319529\pi\)
0.537076 + 0.843534i \(0.319529\pi\)
\(882\) 110.769 3.72979
\(883\) −34.9160 −1.17502 −0.587508 0.809218i \(-0.699891\pi\)
−0.587508 + 0.809218i \(0.699891\pi\)
\(884\) −41.7104 −1.40287
\(885\) −1.42020 −0.0477395
\(886\) −0.578695 −0.0194416
\(887\) −17.6502 −0.592636 −0.296318 0.955089i \(-0.595759\pi\)
−0.296318 + 0.955089i \(0.595759\pi\)
\(888\) 111.225 3.73248
\(889\) −1.39628 −0.0468297
\(890\) −10.2085 −0.342191
\(891\) −6.09795 −0.204289
\(892\) 22.6864 0.759598
\(893\) 15.1381 0.506578
\(894\) −23.9989 −0.802644
\(895\) 8.11108 0.271123
\(896\) −1.69551 −0.0566429
\(897\) −53.8563 −1.79821
\(898\) −97.0253 −3.23777
\(899\) −25.4761 −0.849677
\(900\) 29.7094 0.990313
\(901\) −31.0222 −1.03350
\(902\) −3.68806 −0.122799
\(903\) −11.2355 −0.373895
\(904\) 38.8152 1.29098
\(905\) 10.4243 0.346515
\(906\) −3.38260 −0.112379
\(907\) 50.3820 1.67291 0.836454 0.548037i \(-0.184625\pi\)
0.836454 + 0.548037i \(0.184625\pi\)
\(908\) 50.0094 1.65962
\(909\) 2.28296 0.0757210
\(910\) −3.51801 −0.116621
\(911\) −5.46932 −0.181207 −0.0906034 0.995887i \(-0.528880\pi\)
−0.0906034 + 0.995887i \(0.528880\pi\)
\(912\) 39.2565 1.29991
\(913\) 6.51071 0.215473
\(914\) −58.9729 −1.95065
\(915\) −3.33195 −0.110151
\(916\) −55.3845 −1.82995
\(917\) −3.60680 −0.119107
\(918\) 75.3107 2.48562
\(919\) −21.1968 −0.699216 −0.349608 0.936896i \(-0.613685\pi\)
−0.349608 + 0.936896i \(0.613685\pi\)
\(920\) 41.3388 1.36290
\(921\) 16.3077 0.537356
\(922\) −57.5154 −1.89417
\(923\) −11.0958 −0.365222
\(924\) −3.39421 −0.111661
\(925\) 5.15081 0.169358
\(926\) −72.3634 −2.37801
\(927\) 17.9123 0.588318
\(928\) −37.4679 −1.22995
\(929\) −14.8202 −0.486236 −0.243118 0.969997i \(-0.578170\pi\)
−0.243118 + 0.969997i \(0.578170\pi\)
\(930\) −48.3153 −1.58432
\(931\) 9.81432 0.321651
\(932\) 111.264 3.64456
\(933\) −36.8654 −1.20692
\(934\) 10.1090 0.330777
\(935\) −1.53074 −0.0500607
\(936\) 134.951 4.41100
\(937\) 43.9141 1.43461 0.717305 0.696759i \(-0.245375\pi\)
0.717305 + 0.696759i \(0.245375\pi\)
\(938\) 7.45420 0.243388
\(939\) 91.5095 2.98630
\(940\) −49.6352 −1.61892
\(941\) 2.93756 0.0957616 0.0478808 0.998853i \(-0.484753\pi\)
0.0478808 + 0.998853i \(0.484753\pi\)
\(942\) 99.4063 3.23883
\(943\) 15.7399 0.512562
\(944\) 4.16346 0.135509
\(945\) 4.46495 0.145245
\(946\) −11.2707 −0.366442
\(947\) 9.95436 0.323473 0.161737 0.986834i \(-0.448291\pi\)
0.161737 + 0.986834i \(0.448291\pi\)
\(948\) 96.1985 3.12438
\(949\) 2.03628 0.0661004
\(950\) 3.74480 0.121497
\(951\) 0.517750 0.0167892
\(952\) 9.21501 0.298660
\(953\) 51.4352 1.66615 0.833074 0.553161i \(-0.186579\pi\)
0.833074 + 0.553161i \(0.186579\pi\)
\(954\) 173.841 5.62830
\(955\) 22.6517 0.732992
\(956\) 21.3962 0.692001
\(957\) 6.68438 0.216075
\(958\) 80.9587 2.61566
\(959\) −7.78410 −0.251362
\(960\) −16.6584 −0.537648
\(961\) 6.37247 0.205564
\(962\) 40.5232 1.30652
\(963\) 43.3108 1.39567
\(964\) −131.625 −4.23934
\(965\) −4.16273 −0.134003
\(966\) 20.6080 0.663052
\(967\) −55.9389 −1.79887 −0.899437 0.437050i \(-0.856023\pi\)
−0.899437 + 0.437050i \(0.856023\pi\)
\(968\) 76.0157 2.44324
\(969\) 12.7793 0.410529
\(970\) −23.4218 −0.752028
\(971\) 39.8119 1.27763 0.638813 0.769362i \(-0.279426\pi\)
0.638813 + 0.769362i \(0.279426\pi\)
\(972\) −25.1646 −0.807156
\(973\) 0.501277 0.0160702
\(974\) −35.5671 −1.13964
\(975\) 9.23587 0.295785
\(976\) 9.76795 0.312665
\(977\) 20.3296 0.650402 0.325201 0.945645i \(-0.394568\pi\)
0.325201 + 0.945645i \(0.394568\pi\)
\(978\) −152.148 −4.86516
\(979\) −2.07185 −0.0662166
\(980\) −32.1795 −1.02793
\(981\) 49.7724 1.58911
\(982\) −48.6608 −1.55283
\(983\) −23.6556 −0.754496 −0.377248 0.926112i \(-0.623130\pi\)
−0.377248 + 0.926112i \(0.623130\pi\)
\(984\) −58.2870 −1.85812
\(985\) −1.36985 −0.0436471
\(986\) −31.4316 −1.00099
\(987\) −14.2863 −0.454739
\(988\) 20.7093 0.658849
\(989\) 48.1011 1.52953
\(990\) 8.57790 0.272624
\(991\) −46.1214 −1.46509 −0.732547 0.680716i \(-0.761669\pi\)
−0.732547 + 0.680716i \(0.761669\pi\)
\(992\) 54.9639 1.74511
\(993\) 26.2440 0.832827
\(994\) 4.24578 0.134668
\(995\) −13.3176 −0.422195
\(996\) 178.217 5.64703
\(997\) 16.9418 0.536551 0.268275 0.963342i \(-0.413546\pi\)
0.268275 + 0.963342i \(0.413546\pi\)
\(998\) 36.2285 1.14679
\(999\) −51.4309 −1.62720
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 \(a_p\))