Properties

Label 12.5.d.a.7.3
Level $12$
Weight $5$
Character 12.7
Analytic conductor $1.240$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [12,5,Mod(7,12)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(12, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("12.7");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 12.d (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(1.24043955701\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{13})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 4x^{2} + 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 7.3
Root \(-0.651388 + 1.12824i\) of defining polynomial
Character \(\chi\) \(=\) 12.7
Dual form 12.5.d.a.7.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.30278 - 2.25647i) q^{2} +5.19615i q^{3} +(5.81665 - 14.9053i) q^{4} -22.8444 q^{5} +(11.7250 + 17.1617i) q^{6} +56.8882i q^{7} +(-14.4222 - 62.3538i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(3.30278 - 2.25647i) q^{2} +5.19615i q^{3} +(5.81665 - 14.9053i) q^{4} -22.8444 q^{5} +(11.7250 + 17.1617i) q^{6} +56.8882i q^{7} +(-14.4222 - 62.3538i) q^{8} -27.0000 q^{9} +(-75.4500 + 51.5478i) q^{10} -134.561i q^{11} +(77.4500 + 30.2242i) q^{12} +247.066 q^{13} +(128.367 + 187.889i) q^{14} -118.703i q^{15} +(-188.333 - 173.397i) q^{16} -92.3112 q^{17} +(-89.1749 + 60.9248i) q^{18} +29.5600i q^{19} +(-132.878 + 340.502i) q^{20} -295.600 q^{21} +(-303.633 - 444.425i) q^{22} +571.038i q^{23} +(324.000 - 74.9400i) q^{24} -103.133 q^{25} +(816.005 - 557.499i) q^{26} -140.296i q^{27} +(847.933 + 330.899i) q^{28} +20.0891 q^{29} +(-267.850 - 392.050i) q^{30} +474.736i q^{31} +(-1013.29 - 147.724i) q^{32} +699.199 q^{33} +(-304.883 + 208.298i) q^{34} -1299.58i q^{35} +(-157.050 + 402.442i) q^{36} -755.867 q^{37} +(66.7013 + 97.6300i) q^{38} +1283.79i q^{39} +(329.467 + 1424.44i) q^{40} +541.822 q^{41} +(-976.299 + 667.013i) q^{42} -3097.06i q^{43} +(-2005.67 - 782.695i) q^{44} +616.799 q^{45} +(1288.53 + 1886.01i) q^{46} +1050.16i q^{47} +(900.999 - 978.607i) q^{48} -835.266 q^{49} +(-340.625 + 232.717i) q^{50} -479.663i q^{51} +(1437.10 - 3682.59i) q^{52} +1768.35 q^{53} +(-316.574 - 463.367i) q^{54} +3073.97i q^{55} +(3547.20 - 820.453i) q^{56} -153.598 q^{57} +(66.3499 - 45.3306i) q^{58} +2582.98i q^{59} +(-1769.30 - 690.454i) q^{60} -2403.33 q^{61} +(1071.23 + 1567.95i) q^{62} -1535.98i q^{63} +(-3680.00 + 1798.56i) q^{64} -5644.09 q^{65} +(2309.30 - 1577.72i) q^{66} +379.816i q^{67} +(-536.942 + 1375.92i) q^{68} -2967.20 q^{69} +(-2932.46 - 4292.21i) q^{70} -702.517i q^{71} +(389.400 + 1683.55i) q^{72} +9824.92 q^{73} +(-2496.46 + 1705.59i) q^{74} -535.894i q^{75} +(440.599 + 171.940i) q^{76} +7654.93 q^{77} +(2896.85 + 4240.09i) q^{78} -3756.40i q^{79} +(4302.36 + 3961.16i) q^{80} +729.000 q^{81} +(1789.52 - 1222.61i) q^{82} -10433.6i q^{83} +(-1719.40 + 4405.99i) q^{84} +2108.79 q^{85} +(-6988.43 - 10228.9i) q^{86} +104.386i q^{87} +(-8390.39 + 1940.67i) q^{88} -11923.5 q^{89} +(2037.15 - 1391.79i) q^{90} +14055.2i q^{91} +(8511.46 + 3321.53i) q^{92} -2466.80 q^{93} +(2369.66 + 3468.45i) q^{94} -675.280i q^{95} +(767.597 - 5265.20i) q^{96} -2199.06 q^{97} +(-2758.70 + 1884.76i) q^{98} +3633.15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{2} - 20 q^{4} + 24 q^{5} - 18 q^{6} - 108 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{2} - 20 q^{4} + 24 q^{5} - 18 q^{6} - 108 q^{9} - 172 q^{10} + 180 q^{12} + 296 q^{13} + 600 q^{14} + 112 q^{16} - 600 q^{17} - 162 q^{18} - 1368 q^{20} - 144 q^{21} - 1128 q^{22} + 1296 q^{24} + 972 q^{25} + 1692 q^{26} + 1488 q^{28} + 888 q^{29} - 1980 q^{30} - 2784 q^{32} + 720 q^{33} - 484 q^{34} + 540 q^{36} - 4408 q^{37} + 4680 q^{38} + 1664 q^{40} + 552 q^{41} - 2088 q^{42} - 3696 q^{44} - 648 q^{45} - 384 q^{46} + 1008 q^{48} - 572 q^{49} - 1038 q^{50} + 6008 q^{52} + 5112 q^{53} + 486 q^{54} + 1728 q^{56} + 5616 q^{57} - 124 q^{58} - 2664 q^{60} + 4232 q^{61} - 7224 q^{62} - 14720 q^{64} - 18192 q^{65} + 4824 q^{66} + 5496 q^{68} - 9792 q^{69} + 6096 q^{70} + 8840 q^{73} - 4116 q^{74} - 1872 q^{76} + 20928 q^{77} + 9900 q^{78} + 25632 q^{80} + 2916 q^{81} + 3740 q^{82} - 10512 q^{84} - 10256 q^{85} - 19560 q^{86} - 8640 q^{88} - 25080 q^{89} + 4644 q^{90} + 18816 q^{92} - 17136 q^{93} - 5232 q^{94} - 8352 q^{96} + 23048 q^{97} - 5850 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.30278 2.25647i 0.825694 0.564118i
\(3\) 5.19615i 0.577350i
\(4\) 5.81665 14.9053i 0.363541 0.931578i
\(5\) −22.8444 −0.913776 −0.456888 0.889524i \(-0.651036\pi\)
−0.456888 + 0.889524i \(0.651036\pi\)
\(6\) 11.7250 + 17.1617i 0.325694 + 0.476715i
\(7\) 56.8882i 1.16098i 0.814266 + 0.580492i \(0.197140\pi\)
−0.814266 + 0.580492i \(0.802860\pi\)
\(8\) −14.4222 62.3538i −0.225347 0.974279i
\(9\) −27.0000 −0.333333
\(10\) −75.4500 + 51.5478i −0.754500 + 0.515478i
\(11\) 134.561i 1.11207i −0.831157 0.556037i \(-0.812321\pi\)
0.831157 0.556037i \(-0.187679\pi\)
\(12\) 77.4500 + 30.2242i 0.537847 + 0.209890i
\(13\) 247.066 1.46193 0.730966 0.682414i \(-0.239070\pi\)
0.730966 + 0.682414i \(0.239070\pi\)
\(14\) 128.367 + 187.889i 0.654932 + 0.958617i
\(15\) 118.703i 0.527569i
\(16\) −188.333 173.397i −0.735676 0.677334i
\(17\) −92.3112 −0.319416 −0.159708 0.987164i \(-0.551055\pi\)
−0.159708 + 0.987164i \(0.551055\pi\)
\(18\) −89.1749 + 60.9248i −0.275231 + 0.188039i
\(19\) 29.5600i 0.0818836i 0.999162 + 0.0409418i \(0.0130358\pi\)
−0.999162 + 0.0409418i \(0.986964\pi\)
\(20\) −132.878 + 340.502i −0.332195 + 0.851254i
\(21\) −295.600 −0.670294
\(22\) −303.633 444.425i −0.627342 0.918233i
\(23\) 571.038i 1.07947i 0.841836 + 0.539733i \(0.181475\pi\)
−0.841836 + 0.539733i \(0.818525\pi\)
\(24\) 324.000 74.9400i 0.562500 0.130104i
\(25\) −103.133 −0.165013
\(26\) 816.005 557.499i 1.20711 0.824703i
\(27\) 140.296i 0.192450i
\(28\) 847.933 + 330.899i 1.08155 + 0.422065i
\(29\) 20.0891 0.0238872 0.0119436 0.999929i \(-0.496198\pi\)
0.0119436 + 0.999929i \(0.496198\pi\)
\(30\) −267.850 392.050i −0.297611 0.435611i
\(31\) 474.736i 0.494002i 0.969015 + 0.247001i \(0.0794452\pi\)
−0.969015 + 0.247001i \(0.920555\pi\)
\(32\) −1013.29 147.724i −0.989540 0.144262i
\(33\) 699.199 0.642056
\(34\) −304.883 + 208.298i −0.263740 + 0.180188i
\(35\) 1299.58i 1.06088i
\(36\) −157.050 + 402.442i −0.121180 + 0.310526i
\(37\) −755.867 −0.552131 −0.276065 0.961139i \(-0.589031\pi\)
−0.276065 + 0.961139i \(0.589031\pi\)
\(38\) 66.7013 + 97.6300i 0.0461920 + 0.0676108i
\(39\) 1283.79i 0.844047i
\(40\) 329.467 + 1424.44i 0.205917 + 0.890273i
\(41\) 541.822 0.322321 0.161161 0.986928i \(-0.448476\pi\)
0.161161 + 0.986928i \(0.448476\pi\)
\(42\) −976.299 + 667.013i −0.553458 + 0.378125i
\(43\) 3097.06i 1.67499i −0.546444 0.837496i \(-0.684019\pi\)
0.546444 0.837496i \(-0.315981\pi\)
\(44\) −2005.67 782.695i −1.03598 0.404284i
\(45\) 616.799 0.304592
\(46\) 1288.53 + 1886.01i 0.608947 + 0.891309i
\(47\) 1050.16i 0.475401i 0.971338 + 0.237701i \(0.0763937\pi\)
−0.971338 + 0.237701i \(0.923606\pi\)
\(48\) 900.999 978.607i 0.391059 0.424743i
\(49\) −835.266 −0.347882
\(50\) −340.625 + 232.717i −0.136250 + 0.0930867i
\(51\) 479.663i 0.184415i
\(52\) 1437.10 3682.59i 0.531472 1.36190i
\(53\) 1768.35 0.629532 0.314766 0.949169i \(-0.398074\pi\)
0.314766 + 0.949169i \(0.398074\pi\)
\(54\) −316.574 463.367i −0.108565 0.158905i
\(55\) 3073.97i 1.01619i
\(56\) 3547.20 820.453i 1.13112 0.261624i
\(57\) −153.598 −0.0472755
\(58\) 66.3499 45.3306i 0.0197235 0.0134752i
\(59\) 2582.98i 0.742024i 0.928628 + 0.371012i \(0.120989\pi\)
−0.928628 + 0.371012i \(0.879011\pi\)
\(60\) −1769.30 690.454i −0.491472 0.191793i
\(61\) −2403.33 −0.645883 −0.322941 0.946419i \(-0.604672\pi\)
−0.322941 + 0.946419i \(0.604672\pi\)
\(62\) 1071.23 + 1567.95i 0.278676 + 0.407895i
\(63\) 1535.98i 0.386994i
\(64\) −3680.00 + 1798.56i −0.898438 + 0.439101i
\(65\) −5644.09 −1.33588
\(66\) 2309.30 1577.72i 0.530142 0.362196i
\(67\) 379.816i 0.0846104i 0.999105 + 0.0423052i \(0.0134702\pi\)
−0.999105 + 0.0423052i \(0.986530\pi\)
\(68\) −536.942 + 1375.92i −0.116121 + 0.297561i
\(69\) −2967.20 −0.623230
\(70\) −2932.46 4292.21i −0.598462 0.875962i
\(71\) 702.517i 0.139361i −0.997569 0.0696803i \(-0.977802\pi\)
0.997569 0.0696803i \(-0.0221979\pi\)
\(72\) 389.400 + 1683.55i 0.0751157 + 0.324760i
\(73\) 9824.92 1.84367 0.921836 0.387581i \(-0.126689\pi\)
0.921836 + 0.387581i \(0.126689\pi\)
\(74\) −2496.46 + 1705.59i −0.455891 + 0.311467i
\(75\) 535.894i 0.0952701i
\(76\) 440.599 + 171.940i 0.0762810 + 0.0297680i
\(77\) 7654.93 1.29110
\(78\) 2896.85 + 4240.09i 0.476142 + 0.696924i
\(79\) 3756.40i 0.601890i −0.953641 0.300945i \(-0.902698\pi\)
0.953641 0.300945i \(-0.0973021\pi\)
\(80\) 4302.36 + 3961.16i 0.672243 + 0.618931i
\(81\) 729.000 0.111111
\(82\) 1789.52 1222.61i 0.266139 0.181827i
\(83\) 10433.6i 1.51452i −0.653111 0.757262i \(-0.726537\pi\)
0.653111 0.757262i \(-0.273463\pi\)
\(84\) −1719.40 + 4405.99i −0.243679 + 0.624431i
\(85\) 2108.79 0.291875
\(86\) −6988.43 10228.9i −0.944893 1.38303i
\(87\) 104.386i 0.0137913i
\(88\) −8390.39 + 1940.67i −1.08347 + 0.250603i
\(89\) −11923.5 −1.50530 −0.752651 0.658419i \(-0.771225\pi\)
−0.752651 + 0.658419i \(0.771225\pi\)
\(90\) 2037.15 1391.79i 0.251500 0.171826i
\(91\) 14055.2i 1.69728i
\(92\) 8511.46 + 3321.53i 1.00561 + 0.392430i
\(93\) −2466.80 −0.285212
\(94\) 2369.66 + 3468.45i 0.268183 + 0.392536i
\(95\) 675.280i 0.0748233i
\(96\) 767.597 5265.20i 0.0832896 0.571311i
\(97\) −2199.06 −0.233718 −0.116859 0.993148i \(-0.537283\pi\)
−0.116859 + 0.993148i \(0.537283\pi\)
\(98\) −2758.70 + 1884.76i −0.287244 + 0.196247i
\(99\) 3633.15i 0.370691i
\(100\) −599.889 + 1537.22i −0.0599889 + 0.153722i
\(101\) −874.835 −0.0857597 −0.0428799 0.999080i \(-0.513653\pi\)
−0.0428799 + 0.999080i \(0.513653\pi\)
\(102\) −1082.35 1584.22i −0.104032 0.152270i
\(103\) 3036.94i 0.286260i −0.989704 0.143130i \(-0.954283\pi\)
0.989704 0.143130i \(-0.0457168\pi\)
\(104\) −3563.24 15405.5i −0.329442 1.42433i
\(105\) 6752.80 0.612499
\(106\) 5840.48 3990.25i 0.519801 0.355131i
\(107\) 19057.6i 1.66457i 0.554350 + 0.832284i \(0.312967\pi\)
−0.554350 + 0.832284i \(0.687033\pi\)
\(108\) −2091.15 816.054i −0.179282 0.0699635i
\(109\) −13132.7 −1.10535 −0.552675 0.833397i \(-0.686393\pi\)
−0.552675 + 0.833397i \(0.686393\pi\)
\(110\) 6936.32 + 10152.6i 0.573250 + 0.839060i
\(111\) 3927.60i 0.318773i
\(112\) 9864.26 10713.9i 0.786373 0.854108i
\(113\) 14541.5 1.13882 0.569408 0.822055i \(-0.307173\pi\)
0.569408 + 0.822055i \(0.307173\pi\)
\(114\) −507.300 + 346.590i −0.0390351 + 0.0266690i
\(115\) 13045.0i 0.986391i
\(116\) 116.852 299.434i 0.00868397 0.0222528i
\(117\) −6670.79 −0.487311
\(118\) 5828.44 + 8531.02i 0.418589 + 0.612685i
\(119\) 5251.42i 0.370836i
\(120\) −7401.59 + 1711.96i −0.513999 + 0.118886i
\(121\) −3465.66 −0.236709
\(122\) −7937.66 + 5423.05i −0.533301 + 0.364354i
\(123\) 2815.39i 0.186092i
\(124\) 7076.06 + 2761.38i 0.460202 + 0.179590i
\(125\) 16633.8 1.06456
\(126\) −3465.90 5073.00i −0.218311 0.319539i
\(127\) 25959.7i 1.60951i −0.593609 0.804753i \(-0.702298\pi\)
0.593609 0.804753i \(-0.297702\pi\)
\(128\) −8095.81 + 14244.1i −0.494129 + 0.869388i
\(129\) 16092.8 0.967057
\(130\) −18641.2 + 12735.7i −1.10303 + 0.753594i
\(131\) 16440.3i 0.958003i 0.877814 + 0.479002i \(0.159001\pi\)
−0.877814 + 0.479002i \(0.840999\pi\)
\(132\) 4067.00 10421.7i 0.233414 0.598126i
\(133\) −1681.61 −0.0950655
\(134\) 857.045 + 1254.45i 0.0477303 + 0.0698623i
\(135\) 3204.98i 0.175856i
\(136\) 1331.33 + 5755.96i 0.0719794 + 0.311200i
\(137\) −31618.7 −1.68462 −0.842312 0.538990i \(-0.818806\pi\)
−0.842312 + 0.538990i \(0.818806\pi\)
\(138\) −9799.99 + 6695.41i −0.514597 + 0.351576i
\(139\) 12895.9i 0.667453i 0.942670 + 0.333726i \(0.108306\pi\)
−0.942670 + 0.333726i \(0.891694\pi\)
\(140\) −19370.5 7559.19i −0.988292 0.385673i
\(141\) −5456.80 −0.274473
\(142\) −1585.21 2320.25i −0.0786159 0.115069i
\(143\) 33245.5i 1.62578i
\(144\) 5084.99 + 4681.73i 0.245225 + 0.225778i
\(145\) −458.924 −0.0218276
\(146\) 32449.5 22169.7i 1.52231 1.04005i
\(147\) 4340.17i 0.200850i
\(148\) −4396.62 + 11266.4i −0.200722 + 0.514353i
\(149\) 31474.8 1.41772 0.708859 0.705350i \(-0.249210\pi\)
0.708859 + 0.705350i \(0.249210\pi\)
\(150\) −1209.23 1769.94i −0.0537436 0.0786640i
\(151\) 39479.3i 1.73147i 0.500502 + 0.865735i \(0.333149\pi\)
−0.500502 + 0.865735i \(0.666851\pi\)
\(152\) 1843.18 426.320i 0.0797774 0.0184522i
\(153\) 2492.40 0.106472
\(154\) 25282.5 17273.1i 1.06605 0.728333i
\(155\) 10845.1i 0.451408i
\(156\) 19135.3 + 7467.39i 0.786296 + 0.306845i
\(157\) 2619.07 0.106255 0.0531273 0.998588i \(-0.483081\pi\)
0.0531273 + 0.998588i \(0.483081\pi\)
\(158\) −8476.21 12406.5i −0.339537 0.496977i
\(159\) 9188.64i 0.363460i
\(160\) 23148.0 + 3374.67i 0.904218 + 0.131823i
\(161\) −32485.3 −1.25324
\(162\) 2407.72 1644.97i 0.0917438 0.0626798i
\(163\) 7123.14i 0.268100i −0.990975 0.134050i \(-0.957202\pi\)
0.990975 0.134050i \(-0.0427982\pi\)
\(164\) 3151.59 8075.99i 0.117177 0.300267i
\(165\) −15972.8 −0.586696
\(166\) −23543.0 34459.7i −0.854371 1.25053i
\(167\) 48670.8i 1.74516i 0.488472 + 0.872580i \(0.337555\pi\)
−0.488472 + 0.872580i \(0.662445\pi\)
\(168\) 4263.20 + 18431.8i 0.151049 + 0.653053i
\(169\) 32480.8 1.13724
\(170\) 6964.87 4758.44i 0.240999 0.164652i
\(171\) 798.119i 0.0272945i
\(172\) −46162.4 18014.5i −1.56039 0.608928i
\(173\) −27575.9 −0.921377 −0.460689 0.887562i \(-0.652397\pi\)
−0.460689 + 0.887562i \(0.652397\pi\)
\(174\) 235.545 + 344.764i 0.00777991 + 0.0113874i
\(175\) 5867.05i 0.191577i
\(176\) −23332.5 + 25342.3i −0.753245 + 0.818126i
\(177\) −13421.6 −0.428408
\(178\) −39380.7 + 26905.1i −1.24292 + 0.849169i
\(179\) 42280.0i 1.31956i −0.751459 0.659780i \(-0.770649\pi\)
0.751459 0.659780i \(-0.229351\pi\)
\(180\) 3587.71 9193.55i 0.110732 0.283751i
\(181\) −1006.79 −0.0307313 −0.0153657 0.999882i \(-0.504891\pi\)
−0.0153657 + 0.999882i \(0.504891\pi\)
\(182\) 31715.1 + 46421.1i 0.957466 + 1.40143i
\(183\) 12488.1i 0.372901i
\(184\) 35606.4 8235.62i 1.05170 0.243254i
\(185\) 17267.3 0.504524
\(186\) −8147.29 + 5566.27i −0.235498 + 0.160894i
\(187\) 12421.5i 0.355214i
\(188\) 15652.9 + 6108.43i 0.442874 + 0.172828i
\(189\) 7981.19 0.223431
\(190\) −1523.75 2230.30i −0.0422092 0.0617811i
\(191\) 6906.62i 0.189321i −0.995510 0.0946605i \(-0.969823\pi\)
0.995510 0.0946605i \(-0.0301766\pi\)
\(192\) −9345.59 19121.8i −0.253515 0.518713i
\(193\) 28207.8 0.757278 0.378639 0.925545i \(-0.376392\pi\)
0.378639 + 0.925545i \(0.376392\pi\)
\(194\) −7262.99 + 4962.11i −0.192980 + 0.131845i
\(195\) 29327.5i 0.771270i
\(196\) −4858.45 + 12449.8i −0.126469 + 0.324080i
\(197\) 38453.6 0.990843 0.495422 0.868653i \(-0.335014\pi\)
0.495422 + 0.868653i \(0.335014\pi\)
\(198\) 8198.10 + 11999.5i 0.209114 + 0.306078i
\(199\) 5490.10i 0.138635i −0.997595 0.0693176i \(-0.977918\pi\)
0.997595 0.0693176i \(-0.0220822\pi\)
\(200\) 1487.40 + 6430.73i 0.0371851 + 0.160768i
\(201\) −1973.58 −0.0488498
\(202\) −2889.38 + 1974.04i −0.0708113 + 0.0483787i
\(203\) 1142.83i 0.0277326i
\(204\) −7149.50 2790.03i −0.171797 0.0670423i
\(205\) −12377.6 −0.294529
\(206\) −6852.77 10030.3i −0.161485 0.236363i
\(207\) 15418.0i 0.359822i
\(208\) −46530.8 42840.7i −1.07551 0.990215i
\(209\) 3977.62 0.0910606
\(210\) 22303.0 15237.5i 0.505737 0.345522i
\(211\) 46471.5i 1.04381i −0.853004 0.521905i \(-0.825222\pi\)
0.853004 0.521905i \(-0.174778\pi\)
\(212\) 10285.9 26357.8i 0.228861 0.586458i
\(213\) 3650.38 0.0804599
\(214\) 43003.0 + 62943.1i 0.939013 + 1.37442i
\(215\) 70750.5i 1.53057i
\(216\) −8748.00 + 2023.38i −0.187500 + 0.0433680i
\(217\) −27006.9 −0.573529
\(218\) −43374.2 + 29633.5i −0.912681 + 0.623548i
\(219\) 51051.8i 1.06444i
\(220\) 45818.2 + 17880.2i 0.946658 + 0.369426i
\(221\) −22807.0 −0.466964
\(222\) −8862.53 12972.0i −0.179826 0.263209i
\(223\) 48307.2i 0.971409i 0.874123 + 0.485704i \(0.161437\pi\)
−0.874123 + 0.485704i \(0.838563\pi\)
\(224\) 8403.75 57644.1i 0.167486 1.14884i
\(225\) 2784.59 0.0550042
\(226\) 48027.4 32812.6i 0.940313 0.642427i
\(227\) 19108.6i 0.370832i −0.982660 0.185416i \(-0.940637\pi\)
0.982660 0.185416i \(-0.0593633\pi\)
\(228\) −893.427 + 2289.42i −0.0171866 + 0.0440408i
\(229\) −73378.5 −1.39926 −0.699629 0.714506i \(-0.746651\pi\)
−0.699629 + 0.714506i \(0.746651\pi\)
\(230\) −29435.7 43084.8i −0.556441 0.814457i
\(231\) 39776.2i 0.745417i
\(232\) −289.730 1252.63i −0.00538291 0.0232728i
\(233\) −34041.9 −0.627049 −0.313524 0.949580i \(-0.601510\pi\)
−0.313524 + 0.949580i \(0.601510\pi\)
\(234\) −22032.1 + 15052.5i −0.402369 + 0.274901i
\(235\) 23990.3i 0.434411i
\(236\) 38500.0 + 15024.3i 0.691253 + 0.269756i
\(237\) 19518.8 0.347501
\(238\) −11849.7 17344.2i −0.209196 0.306197i
\(239\) 35114.3i 0.614735i −0.951591 0.307368i \(-0.900552\pi\)
0.951591 0.307368i \(-0.0994482\pi\)
\(240\) −20582.8 + 22355.7i −0.357340 + 0.388120i
\(241\) −19621.0 −0.337821 −0.168910 0.985631i \(-0.554025\pi\)
−0.168910 + 0.985631i \(0.554025\pi\)
\(242\) −11446.3 + 7820.17i −0.195449 + 0.133532i
\(243\) 3788.00i 0.0641500i
\(244\) −13979.3 + 35822.2i −0.234805 + 0.601690i
\(245\) 19081.2 0.317887
\(246\) 6352.85 + 9298.60i 0.104978 + 0.153655i
\(247\) 7303.28i 0.119708i
\(248\) 29601.6 6846.74i 0.481296 0.111322i
\(249\) 54214.3 0.874411
\(250\) 54937.6 37533.7i 0.879002 0.600539i
\(251\) 560.729i 0.00890032i 0.999990 + 0.00445016i \(0.00141654\pi\)
−0.999990 + 0.00445016i \(0.998583\pi\)
\(252\) −22894.2 8934.27i −0.360516 0.140688i
\(253\) 76839.4 1.20045
\(254\) −58577.5 85739.2i −0.907952 1.32896i
\(255\) 10957.6i 0.168514i
\(256\) 5402.70 + 65312.9i 0.0824386 + 0.996596i
\(257\) 80511.1 1.21896 0.609480 0.792801i \(-0.291378\pi\)
0.609480 + 0.792801i \(0.291378\pi\)
\(258\) 53150.9 36313.0i 0.798493 0.545534i
\(259\) 42999.9i 0.641015i
\(260\) −32829.7 + 84126.5i −0.485647 + 1.24448i
\(261\) −542.406 −0.00796240
\(262\) 37097.1 + 54298.6i 0.540427 + 0.791017i
\(263\) 34821.7i 0.503430i −0.967801 0.251715i \(-0.919005\pi\)
0.967801 0.251715i \(-0.0809945\pi\)
\(264\) −10084.0 43597.8i −0.144685 0.625542i
\(265\) −40397.0 −0.575251
\(266\) −5553.99 + 3794.52i −0.0784950 + 0.0536282i
\(267\) 61956.3i 0.869087i
\(268\) 5661.26 + 2209.26i 0.0788212 + 0.0307593i
\(269\) −28469.5 −0.393438 −0.196719 0.980460i \(-0.563029\pi\)
−0.196719 + 0.980460i \(0.563029\pi\)
\(270\) 7231.96 + 10585.3i 0.0992038 + 0.145204i
\(271\) 37653.7i 0.512706i −0.966583 0.256353i \(-0.917479\pi\)
0.966583 0.256353i \(-0.0825210\pi\)
\(272\) 17385.2 + 16006.5i 0.234987 + 0.216351i
\(273\) −73032.8 −0.979924
\(274\) −104429. + 71346.8i −1.39098 + 0.950327i
\(275\) 13877.7i 0.183506i
\(276\) −17259.2 + 44226.9i −0.226570 + 0.580588i
\(277\) 25920.1 0.337814 0.168907 0.985632i \(-0.445976\pi\)
0.168907 + 0.985632i \(0.445976\pi\)
\(278\) 29099.2 + 42592.1i 0.376522 + 0.551112i
\(279\) 12817.9i 0.164667i
\(280\) −81033.6 + 18742.8i −1.03359 + 0.239066i
\(281\) 49815.6 0.630889 0.315444 0.948944i \(-0.397846\pi\)
0.315444 + 0.948944i \(0.397846\pi\)
\(282\) −18022.6 + 12313.1i −0.226631 + 0.154835i
\(283\) 73403.9i 0.916530i 0.888816 + 0.458265i \(0.151529\pi\)
−0.888816 + 0.458265i \(0.848471\pi\)
\(284\) −10471.2 4086.30i −0.129825 0.0506633i
\(285\) 3508.86 0.0431993
\(286\) −75017.6 109802.i −0.917131 1.34239i
\(287\) 30823.3i 0.374209i
\(288\) 27358.8 + 3988.55i 0.329847 + 0.0480873i
\(289\) −74999.6 −0.897974
\(290\) −1515.72 + 1035.55i −0.0180229 + 0.0123133i
\(291\) 11426.6i 0.134937i
\(292\) 57148.2 146443.i 0.670250 1.71752i
\(293\) −130683. −1.52224 −0.761120 0.648611i \(-0.775350\pi\)
−0.761120 + 0.648611i \(0.775350\pi\)
\(294\) −9793.48 14334.6i −0.113303 0.165841i
\(295\) 59006.8i 0.678044i
\(296\) 10901.3 + 47131.2i 0.124421 + 0.537929i
\(297\) −18878.4 −0.214019
\(298\) 103954. 71022.0i 1.17060 0.799761i
\(299\) 141084.i 1.57811i
\(300\) −7987.64 3117.11i −0.0887516 0.0346346i
\(301\) 176186. 1.94464
\(302\) 89083.9 + 130391.i 0.976754 + 1.42966i
\(303\) 4545.78i 0.0495134i
\(304\) 5125.62 5567.12i 0.0554625 0.0602398i
\(305\) 54902.6 0.590192
\(306\) 8231.84 5624.04i 0.0879132 0.0600628i
\(307\) 139512.i 1.48025i 0.672469 + 0.740126i \(0.265234\pi\)
−0.672469 + 0.740126i \(0.734766\pi\)
\(308\) 44526.1 114099.i 0.469368 1.20276i
\(309\) 15780.4 0.165273
\(310\) −24471.6 35818.8i −0.254647 0.372725i
\(311\) 132034.i 1.36510i −0.730837 0.682552i \(-0.760870\pi\)
0.730837 0.682552i \(-0.239130\pi\)
\(312\) 80049.5 18515.2i 0.822337 0.190203i
\(313\) 39526.3 0.403458 0.201729 0.979441i \(-0.435344\pi\)
0.201729 + 0.979441i \(0.435344\pi\)
\(314\) 8650.20 5909.86i 0.0877338 0.0599402i
\(315\) 35088.6i 0.353626i
\(316\) −55990.0 21849.7i −0.560708 0.218812i
\(317\) −91959.1 −0.915116 −0.457558 0.889180i \(-0.651276\pi\)
−0.457558 + 0.889180i \(0.651276\pi\)
\(318\) 20733.9 + 30348.0i 0.205035 + 0.300107i
\(319\) 2703.21i 0.0265643i
\(320\) 84067.4 41087.0i 0.820971 0.401241i
\(321\) −99026.4 −0.961039
\(322\) −107292. + 73302.2i −1.03479 + 0.706977i
\(323\) 2728.72i 0.0261549i
\(324\) 4240.34 10865.9i 0.0403934 0.103509i
\(325\) −25480.7 −0.241237
\(326\) −16073.2 23526.1i −0.151240 0.221368i
\(327\) 68239.3i 0.638174i
\(328\) −7814.26 33784.7i −0.0726341 0.314031i
\(329\) −59741.8 −0.551933
\(330\) −52754.6 + 36042.2i −0.484431 + 0.330966i
\(331\) 3244.08i 0.0296098i 0.999890 + 0.0148049i \(0.00471272\pi\)
−0.999890 + 0.0148049i \(0.995287\pi\)
\(332\) −155515. 60688.4i −1.41090 0.550591i
\(333\) 20408.4 0.184044
\(334\) 109824. + 160749.i 0.984477 + 1.44097i
\(335\) 8676.68i 0.0773150i
\(336\) 55671.2 + 51256.2i 0.493119 + 0.454013i
\(337\) 5591.21 0.0492318 0.0246159 0.999697i \(-0.492164\pi\)
0.0246159 + 0.999697i \(0.492164\pi\)
\(338\) 107277. 73292.1i 0.939016 0.641540i
\(339\) 75560.0i 0.657495i
\(340\) 12266.1 31432.1i 0.106108 0.271904i
\(341\) 63881.0 0.549367
\(342\) −1800.94 2636.01i −0.0153973 0.0225369i
\(343\) 89071.8i 0.757098i
\(344\) −193113. + 44666.4i −1.63191 + 0.377454i
\(345\) 67783.9 0.569493
\(346\) −91077.0 + 62224.3i −0.760775 + 0.519766i
\(347\) 170630.i 1.41708i −0.705668 0.708542i \(-0.749353\pi\)
0.705668 0.708542i \(-0.250647\pi\)
\(348\) 1555.90 + 607.178i 0.0128477 + 0.00501369i
\(349\) −96101.4 −0.789003 −0.394502 0.918895i \(-0.629083\pi\)
−0.394502 + 0.918895i \(0.629083\pi\)
\(350\) −13238.8 19377.5i −0.108072 0.158184i
\(351\) 34662.5i 0.281349i
\(352\) −19877.9 + 136349.i −0.160430 + 1.10044i
\(353\) 205914. 1.65248 0.826242 0.563316i \(-0.190474\pi\)
0.826242 + 0.563316i \(0.190474\pi\)
\(354\) −44328.5 + 30285.4i −0.353734 + 0.241673i
\(355\) 16048.6i 0.127344i
\(356\) −69354.9 + 177723.i −0.547239 + 1.40231i
\(357\) 27287.2 0.214103
\(358\) −95403.8 139641.i −0.744388 1.08955i
\(359\) 78435.2i 0.608586i −0.952578 0.304293i \(-0.901580\pi\)
0.952578 0.304293i \(-0.0984202\pi\)
\(360\) −8895.60 38459.8i −0.0686389 0.296758i
\(361\) 129447. 0.993295
\(362\) −3325.20 + 2271.79i −0.0253747 + 0.0173361i
\(363\) 18008.1i 0.136664i
\(364\) 209496. + 81754.0i 1.58115 + 0.617030i
\(365\) −224445. −1.68470
\(366\) −28179.0 41245.3i −0.210360 0.307902i
\(367\) 221785.i 1.64664i −0.567574 0.823322i \(-0.692118\pi\)
0.567574 0.823322i \(-0.307882\pi\)
\(368\) 99016.5 107545.i 0.731159 0.794138i
\(369\) −14629.2 −0.107440
\(370\) 57030.1 38963.3i 0.416582 0.284611i
\(371\) 100599.i 0.730876i
\(372\) −14348.5 + 36768.3i −0.103686 + 0.265698i
\(373\) −25883.8 −0.186042 −0.0930208 0.995664i \(-0.529652\pi\)
−0.0930208 + 0.995664i \(0.529652\pi\)
\(374\) 28028.7 + 41025.4i 0.200383 + 0.293298i
\(375\) 86431.6i 0.614625i
\(376\) 65481.6 15145.6i 0.463173 0.107130i
\(377\) 4963.35 0.0349214
\(378\) 26360.1 18009.3i 0.184486 0.126042i
\(379\) 147801.i 1.02896i −0.857503 0.514479i \(-0.827985\pi\)
0.857503 0.514479i \(-0.172015\pi\)
\(380\) −10065.2 3927.87i −0.0697038 0.0272013i
\(381\) 134891. 0.929249
\(382\) −15584.6 22811.0i −0.106800 0.156321i
\(383\) 226231.i 1.54225i 0.636683 + 0.771126i \(0.280306\pi\)
−0.636683 + 0.771126i \(0.719694\pi\)
\(384\) −74014.3 42067.1i −0.501942 0.285286i
\(385\) −174872. −1.17978
\(386\) 93164.2 63650.2i 0.625280 0.427194i
\(387\) 83620.6i 0.558330i
\(388\) −12791.2 + 32777.5i −0.0849662 + 0.217727i
\(389\) 256419. 1.69453 0.847267 0.531167i \(-0.178246\pi\)
0.847267 + 0.531167i \(0.178246\pi\)
\(390\) −66176.8 96862.3i −0.435088 0.636833i
\(391\) 52713.2i 0.344799i
\(392\) 12046.4 + 52082.0i 0.0783943 + 0.338934i
\(393\) −85426.3 −0.553103
\(394\) 127004. 86769.6i 0.818133 0.558953i
\(395\) 85812.7i 0.549993i
\(396\) 54153.0 + 21132.8i 0.345328 + 0.134761i
\(397\) −56667.7 −0.359546 −0.179773 0.983708i \(-0.557536\pi\)
−0.179773 + 0.983708i \(0.557536\pi\)
\(398\) −12388.3 18132.6i −0.0782067 0.114470i
\(399\) 8737.92i 0.0548861i
\(400\) 19423.3 + 17883.0i 0.121396 + 0.111769i
\(401\) 10912.0 0.0678605 0.0339302 0.999424i \(-0.489198\pi\)
0.0339302 + 0.999424i \(0.489198\pi\)
\(402\) −6518.30 + 4453.34i −0.0403350 + 0.0275571i
\(403\) 117291.i 0.722198i
\(404\) −5088.61 + 13039.6i −0.0311772 + 0.0798919i
\(405\) −16653.6 −0.101531
\(406\) 2578.77 + 3774.52i 0.0156445 + 0.0228987i
\(407\) 101710.i 0.614010i
\(408\) −29908.8 + 6917.80i −0.179671 + 0.0415573i
\(409\) −289576. −1.73108 −0.865538 0.500844i \(-0.833023\pi\)
−0.865538 + 0.500844i \(0.833023\pi\)
\(410\) −40880.4 + 27929.7i −0.243191 + 0.166149i
\(411\) 164296.i 0.972618i
\(412\) −45266.3 17664.8i −0.266674 0.104067i
\(413\) −146941. −0.861477
\(414\) −34790.4 50922.3i −0.202982 0.297103i
\(415\) 238348.i 1.38394i
\(416\) −250350. 36497.7i −1.44664 0.210901i
\(417\) −67008.8 −0.385354
\(418\) 13137.2 8975.39i 0.0751882 0.0513690i
\(419\) 69837.9i 0.397798i 0.980020 + 0.198899i \(0.0637366\pi\)
−0.980020 + 0.198899i \(0.936263\pi\)
\(420\) 39278.7 100652.i 0.222668 0.570591i
\(421\) 16207.0 0.0914405 0.0457203 0.998954i \(-0.485442\pi\)
0.0457203 + 0.998954i \(0.485442\pi\)
\(422\) −104862. 153485.i −0.588832 0.861867i
\(423\) 28354.4i 0.158467i
\(424\) −25503.6 110264.i −0.141863 0.613339i
\(425\) 9520.32 0.0527077
\(426\) 12056.4 8236.99i 0.0664352 0.0453889i
\(427\) 136721.i 0.749859i
\(428\) 284059. + 110852.i 1.55067 + 0.605138i
\(429\) 172749. 0.938643
\(430\) 159647. + 233673.i 0.863421 + 1.26378i
\(431\) 105264.i 0.566662i −0.959022 0.283331i \(-0.908560\pi\)
0.959022 0.283331i \(-0.0914395\pi\)
\(432\) −24327.0 + 26422.4i −0.130353 + 0.141581i
\(433\) 131799. 0.702970 0.351485 0.936193i \(-0.385677\pi\)
0.351485 + 0.936193i \(0.385677\pi\)
\(434\) −89197.7 + 60940.3i −0.473559 + 0.323538i
\(435\) 2384.64i 0.0126021i
\(436\) −76388.1 + 195746.i −0.401840 + 1.02972i
\(437\) −16879.9 −0.0883906
\(438\) 115197. + 168613.i 0.600473 + 0.878905i
\(439\) 149053.i 0.773414i −0.922203 0.386707i \(-0.873612\pi\)
0.922203 0.386707i \(-0.126388\pi\)
\(440\) 191674. 44333.4i 0.990049 0.228995i
\(441\) 22552.2 0.115961
\(442\) −75326.4 + 51463.4i −0.385569 + 0.263423i
\(443\) 248933.i 1.26845i −0.773147 0.634227i \(-0.781318\pi\)
0.773147 0.634227i \(-0.218682\pi\)
\(444\) −58541.9 22845.5i −0.296962 0.115887i
\(445\) 272385. 1.37551
\(446\) 109004. + 159548.i 0.547990 + 0.802086i
\(447\) 163548.i 0.818520i
\(448\) −102317. 209349.i −0.509789 1.04307i
\(449\) 243749. 1.20906 0.604532 0.796581i \(-0.293360\pi\)
0.604532 + 0.796581i \(0.293360\pi\)
\(450\) 9196.87 6283.35i 0.0454167 0.0310289i
\(451\) 72908.1i 0.358445i
\(452\) 84583.1 216745.i 0.414006 1.06090i
\(453\) −205140. −0.999665
\(454\) −43118.1 63111.5i −0.209193 0.306194i
\(455\) 321082.i 1.55093i
\(456\) 2215.22 + 9577.43i 0.0106534 + 0.0460595i
\(457\) 343278. 1.64367 0.821833 0.569729i \(-0.192952\pi\)
0.821833 + 0.569729i \(0.192952\pi\)
\(458\) −242353. + 165577.i −1.15536 + 0.789347i
\(459\) 12950.9i 0.0614716i
\(460\) −194439. 75878.4i −0.918900 0.358593i
\(461\) −155524. −0.731804 −0.365902 0.930653i \(-0.619239\pi\)
−0.365902 + 0.930653i \(0.619239\pi\)
\(462\) 89753.9 + 131372.i 0.420503 + 0.615486i
\(463\) 321457.i 1.49955i 0.661694 + 0.749774i \(0.269838\pi\)
−0.661694 + 0.749774i \(0.730162\pi\)
\(464\) −3783.45 3483.40i −0.0175732 0.0161796i
\(465\) 56352.6 0.260620
\(466\) −112433. + 76814.6i −0.517750 + 0.353730i
\(467\) 81219.7i 0.372415i −0.982510 0.186208i \(-0.940380\pi\)
0.982510 0.186208i \(-0.0596197\pi\)
\(468\) −38801.7 + 99429.9i −0.177157 + 0.453968i
\(469\) −21607.1 −0.0982313
\(470\) −54133.5 79234.7i −0.245059 0.358690i
\(471\) 13609.1i 0.0613461i
\(472\) 161059. 37252.3i 0.722938 0.167213i
\(473\) −416743. −1.86271
\(474\) 64466.3 44043.7i 0.286930 0.196032i
\(475\) 3048.61i 0.0135118i
\(476\) −78273.7 30545.7i −0.345463 0.134814i
\(477\) −47745.6 −0.209844
\(478\) −79234.5 115975.i −0.346784 0.507583i
\(479\) 346051.i 1.50824i 0.656738 + 0.754119i \(0.271936\pi\)
−0.656738 + 0.754119i \(0.728064\pi\)
\(480\) −17535.3 + 120280.i −0.0761080 + 0.522050i
\(481\) −186749. −0.807178
\(482\) −64803.6 + 44274.2i −0.278936 + 0.190571i
\(483\) 168799.i 0.723560i
\(484\) −20158.5 + 51656.5i −0.0860534 + 0.220513i
\(485\) 50236.2 0.213566
\(486\) 8547.51 + 12510.9i 0.0361882 + 0.0529683i
\(487\) 94439.7i 0.398196i 0.979980 + 0.199098i \(0.0638012\pi\)
−0.979980 + 0.199098i \(0.936199\pi\)
\(488\) 34661.3 + 149857.i 0.145548 + 0.629270i
\(489\) 37012.9 0.154787
\(490\) 63020.8 43056.1i 0.262477 0.179326i
\(491\) 175728.i 0.728915i −0.931220 0.364458i \(-0.881254\pi\)
0.931220 0.364458i \(-0.118746\pi\)
\(492\) 41964.1 + 16376.1i 0.173359 + 0.0676521i
\(493\) −1854.45 −0.00762995
\(494\) 16479.7 + 24121.1i 0.0675296 + 0.0988424i
\(495\) 82997.1i 0.338729i
\(496\) 82318.0 89408.5i 0.334604 0.363426i
\(497\) 39964.9 0.161795
\(498\) 179058. 122333.i 0.721996 0.493271i
\(499\) 37294.6i 0.149777i −0.997192 0.0748885i \(-0.976140\pi\)
0.997192 0.0748885i \(-0.0238601\pi\)
\(500\) 96752.9 247930.i 0.387011 0.991722i
\(501\) −252901. −1.00757
\(502\) 1265.27 + 1851.96i 0.00502084 + 0.00734894i
\(503\) 250727.i 0.990979i 0.868614 + 0.495489i \(0.165011\pi\)
−0.868614 + 0.495489i \(0.834989\pi\)
\(504\) −95774.3 + 22152.2i −0.377040 + 0.0872080i
\(505\) 19985.1 0.0783652
\(506\) 253783. 173386.i 0.991202 0.677194i
\(507\) 168775.i 0.656588i
\(508\) −386936. 150999.i −1.49938 0.585121i
\(509\) 151144. 0.583383 0.291692 0.956512i \(-0.405782\pi\)
0.291692 + 0.956512i \(0.405782\pi\)
\(510\) 24725.6 + 36190.6i 0.0950618 + 0.139141i
\(511\) 558922.i 2.14047i
\(512\) 165221. + 203523.i 0.630267 + 0.776378i
\(513\) 4147.15 0.0157585
\(514\) 265910. 181671.i 1.00649 0.687638i
\(515\) 69377.0i 0.261578i
\(516\) 93606.2 239867.i 0.351565 0.900889i
\(517\) 141311. 0.528682
\(518\) −97028.2 142019.i −0.361608 0.529282i
\(519\) 143289.i 0.531957i
\(520\) 81400.2 + 351930.i 0.301036 + 1.30152i
\(521\) −179715. −0.662079 −0.331039 0.943617i \(-0.607399\pi\)
−0.331039 + 0.943617i \(0.607399\pi\)
\(522\) −1791.45 + 1223.93i −0.00657450 + 0.00449173i
\(523\) 305226.i 1.11588i −0.829881 0.557941i \(-0.811592\pi\)
0.829881 0.557941i \(-0.188408\pi\)
\(524\) 245047. + 95627.5i 0.892455 + 0.348273i
\(525\) 30486.1 0.110607
\(526\) −78574.3 115008.i −0.283994 0.415679i
\(527\) 43823.5i 0.157792i
\(528\) −131682. 121239.i −0.472346 0.434886i
\(529\) −46243.2 −0.165248
\(530\) −133422. + 91154.8i −0.474982 + 0.324510i
\(531\) 69740.6i 0.247341i
\(532\) −9781.36 + 25064.9i −0.0345602 + 0.0885609i
\(533\) 133866. 0.471211
\(534\) −139803. 204628.i −0.490268 0.717600i
\(535\) 435360.i 1.52104i
\(536\) 23683.0 5477.79i 0.0824341 0.0190667i
\(537\) 219694. 0.761849
\(538\) −94028.5 + 64240.8i −0.324859 + 0.221945i
\(539\) 112394.i 0.386871i
\(540\) 47771.1 + 18642.3i 0.163824 + 0.0639310i
\(541\) −282083. −0.963789 −0.481895 0.876229i \(-0.660051\pi\)
−0.481895 + 0.876229i \(0.660051\pi\)
\(542\) −84964.5 124362.i −0.289227 0.423338i
\(543\) 5231.43i 0.0177427i
\(544\) 93537.9 + 13636.6i 0.316075 + 0.0460795i
\(545\) 300008. 1.01004
\(546\) −241211. + 164797.i −0.809117 + 0.552793i
\(547\) 296270.i 0.990176i 0.868843 + 0.495088i \(0.164864\pi\)
−0.868843 + 0.495088i \(0.835136\pi\)
\(548\) −183915. + 471285.i −0.612430 + 1.56936i
\(549\) 64889.9 0.215294
\(550\) 31314.6 + 45834.8i 0.103519 + 0.151520i
\(551\) 593.834i 0.00195597i
\(552\) 42793.6 + 185016.i 0.140443 + 0.607200i
\(553\) 213695. 0.698785
\(554\) 85608.4 58488.1i 0.278931 0.190567i
\(555\) 89723.7i 0.291287i
\(556\) 192216. + 75010.7i 0.621785 + 0.242646i
\(557\) −116573. −0.375739 −0.187869 0.982194i \(-0.560158\pi\)
−0.187869 + 0.982194i \(0.560158\pi\)
\(558\) −28923.2 42334.6i −0.0928919 0.135965i
\(559\) 765179.i 2.44872i
\(560\) −225343. + 244753.i −0.718569 + 0.780463i
\(561\) −64543.9 −0.205083
\(562\) 164530. 112408.i 0.520921 0.355896i
\(563\) 117383.i 0.370329i 0.982708 + 0.185164i \(0.0592817\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(564\) −31740.3 + 81335.0i −0.0997822 + 0.255693i
\(565\) −332193. −1.04062
\(566\) 165634. + 242437.i 0.517031 + 0.756773i
\(567\) 41471.5i 0.128998i
\(568\) −43804.6 + 10131.8i −0.135776 + 0.0314045i
\(569\) −222193. −0.686288 −0.343144 0.939283i \(-0.611492\pi\)
−0.343144 + 0.939283i \(0.611492\pi\)
\(570\) 11589.0 7917.65i 0.0356694 0.0243695i
\(571\) 117091.i 0.359131i 0.983746 + 0.179565i \(0.0574691\pi\)
−0.983746 + 0.179565i \(0.942531\pi\)
\(572\) −495533. 193378.i −1.51454 0.591036i
\(573\) 35887.9 0.109305
\(574\) 69551.9 + 101802.i 0.211098 + 0.308982i
\(575\) 58892.8i 0.178126i
\(576\) 99360.0 48561.1i 0.299479 0.146367i
\(577\) −335932. −1.00902 −0.504510 0.863406i \(-0.668327\pi\)
−0.504510 + 0.863406i \(0.668327\pi\)
\(578\) −247707. + 169235.i −0.741451 + 0.506563i
\(579\) 146572.i 0.437214i
\(580\) −2669.40 + 6840.38i −0.00793521 + 0.0203341i
\(581\) 593546. 1.75834
\(582\) −25783.9 37739.6i −0.0761207 0.111417i
\(583\) 237952.i 0.700086i
\(584\) −141697. 612622.i −0.415466 1.79625i
\(585\) 152390. 0.445293
\(586\) −431616. + 294882.i −1.25690 + 0.858723i
\(587\) 396842.i 1.15170i −0.817554 0.575852i \(-0.804670\pi\)
0.817554 0.575852i \(-0.195330\pi\)
\(588\) −64691.3 25245.3i −0.187108 0.0730172i
\(589\) −14033.2 −0.0404507
\(590\) −133147. 194886.i −0.382497 0.559857i
\(591\) 199811.i 0.572064i
\(592\) 142355. + 131065.i 0.406189 + 0.373977i
\(593\) 13679.6 0.0389012 0.0194506 0.999811i \(-0.493808\pi\)
0.0194506 + 0.999811i \(0.493808\pi\)
\(594\) −62351.1 + 42598.6i −0.176714 + 0.120732i
\(595\) 119965.i 0.338862i
\(596\) 183078. 469139.i 0.515399 1.32072i
\(597\) 28527.4 0.0800411
\(598\) 318353. + 465970.i 0.890239 + 1.30303i
\(599\) 124021.i 0.345654i 0.984952 + 0.172827i \(0.0552902\pi\)
−0.984952 + 0.172827i \(0.944710\pi\)
\(600\) −33415.1 + 7728.78i −0.0928196 + 0.0214688i
\(601\) 484678. 1.34185 0.670926 0.741525i \(-0.265897\pi\)
0.670926 + 0.741525i \(0.265897\pi\)
\(602\) 581903. 397559.i 1.60567 1.09701i
\(603\) 10255.0i 0.0282035i
\(604\) 588448. + 229637.i 1.61300 + 0.629460i
\(605\) 79170.9 0.216299
\(606\) −10257.4 15013.7i −0.0279314 0.0408829i
\(607\) 298924.i 0.811303i 0.914028 + 0.405651i \(0.132955\pi\)
−0.914028 + 0.405651i \(0.867045\pi\)
\(608\) 4366.72 29952.8i 0.0118127 0.0810271i
\(609\) −5938.34 −0.0160114
\(610\) 181331. 123886.i 0.487318 0.332938i
\(611\) 259460.i 0.695004i
\(612\) 14497.4 37149.9i 0.0387069 0.0991870i
\(613\) −155694. −0.414334 −0.207167 0.978306i \(-0.566424\pi\)
−0.207167 + 0.978306i \(0.566424\pi\)
\(614\) 314806. + 460777.i 0.835037 + 1.22223i
\(615\) 64315.9i 0.170047i
\(616\) −110401. 477314.i −0.290945 1.25789i
\(617\) −625050. −1.64189 −0.820946 0.571007i \(-0.806553\pi\)
−0.820946 + 0.571007i \(0.806553\pi\)
\(618\) 52119.1 35608.0i 0.136465 0.0932333i
\(619\) 368822.i 0.962576i 0.876563 + 0.481288i \(0.159831\pi\)
−0.876563 + 0.481288i \(0.840169\pi\)
\(620\) −161649. 63082.0i −0.420522 0.164105i
\(621\) 80114.4 0.207743
\(622\) −297932. 436079.i −0.770080 1.12716i
\(623\) 678307.i 1.74763i
\(624\) 222607. 241781.i 0.571701 0.620945i
\(625\) −315531. −0.807758
\(626\) 130547. 89190.1i 0.333133 0.227598i
\(627\) 20668.3i 0.0525739i
\(628\) 15234.2 39037.9i 0.0386279 0.0989845i
\(629\) 69775.0 0.176359
\(630\) 79176.5 + 115890.i 0.199487 + 0.291987i
\(631\) 457172.i 1.14821i 0.818782 + 0.574105i \(0.194650\pi\)
−0.818782 + 0.574105i \(0.805350\pi\)
\(632\) −234226. + 54175.5i −0.586409 + 0.135634i
\(633\) 241473. 0.602644
\(634\) −303720. + 207503.i −0.755606 + 0.516234i
\(635\) 593035.i 1.47073i
\(636\) 136959. + 53447.1i 0.338592 + 0.132133i
\(637\) −206366. −0.508580
\(638\) −6099.73 8928.11i −0.0149854 0.0219340i
\(639\) 18967.9i 0.0464535i
\(640\) 184944. 325397.i 0.451524 0.794427i
\(641\) −728866. −1.77391 −0.886955 0.461855i \(-0.847184\pi\)
−0.886955 + 0.461855i \(0.847184\pi\)
\(642\) −327062. + 223450.i −0.793524 + 0.542140i
\(643\) 201261.i 0.486786i −0.969928 0.243393i \(-0.921740\pi\)
0.969928 0.243393i \(-0.0782604\pi\)
\(644\) −188956. + 484202.i −0.455605 + 1.16749i
\(645\) −367630. −0.883673
\(646\) −6157.28 9012.34i −0.0147545 0.0215960i
\(647\) 284857.i 0.680484i −0.940338 0.340242i \(-0.889491\pi\)
0.940338 0.340242i \(-0.110509\pi\)
\(648\) −10513.8 45455.9i −0.0250386 0.108253i
\(649\) 347569. 0.825186
\(650\) −84157.0 + 57496.5i −0.199188 + 0.136086i
\(651\) 140332.i 0.331127i
\(652\) −106172. 41432.8i −0.249756 0.0974652i
\(653\) 639617. 1.50001 0.750005 0.661433i \(-0.230051\pi\)
0.750005 + 0.661433i \(0.230051\pi\)
\(654\) −153980. 225379.i −0.360006 0.526936i
\(655\) 375569.i 0.875401i
\(656\) −102043. 93950.5i −0.237124 0.218319i
\(657\) −265273. −0.614557
\(658\) −197314. + 134806.i −0.455728 + 0.311356i
\(659\) 372398.i 0.857505i 0.903422 + 0.428753i \(0.141047\pi\)
−0.903422 + 0.428753i \(0.858953\pi\)
\(660\) −92908.2 + 238079.i −0.213288 + 0.546553i
\(661\) −137125. −0.313843 −0.156922 0.987611i \(-0.550157\pi\)
−0.156922 + 0.987611i \(0.550157\pi\)
\(662\) 7320.19 + 10714.5i 0.0167035 + 0.0244487i
\(663\) 118509.i 0.269602i
\(664\) −650572. + 150475.i −1.47557 + 0.341293i
\(665\) 38415.5 0.0868686
\(666\) 67404.4 46051.0i 0.151964 0.103822i
\(667\) 11471.7i 0.0257854i
\(668\) 725450. + 283101.i 1.62575 + 0.634437i
\(669\) −251011. −0.560843
\(670\) −19578.7 28657.1i −0.0436148 0.0638385i
\(671\) 323394.i 0.718269i
\(672\) 299528. + 43667.2i 0.663283 + 0.0966978i
\(673\) 840931. 1.85665 0.928325 0.371770i \(-0.121249\pi\)
0.928325 + 0.371770i \(0.121249\pi\)
\(674\) 18466.5 12616.4i 0.0406504 0.0277726i
\(675\) 14469.1i 0.0317567i
\(676\) 188930. 484135.i 0.413435 1.05943i
\(677\) 207006. 0.451653 0.225827 0.974168i \(-0.427492\pi\)
0.225827 + 0.974168i \(0.427492\pi\)
\(678\) 170499. + 249558.i 0.370905 + 0.542890i
\(679\) 125100.i 0.271343i
\(680\) −30413.5 131491.i −0.0657731 0.284367i
\(681\) 99291.3 0.214100
\(682\) 210985. 144146.i 0.453609 0.309908i
\(683\) 241334.i 0.517341i −0.965966 0.258670i \(-0.916716\pi\)
0.965966 0.258670i \(-0.0832844\pi\)
\(684\) −11896.2 4642.38i −0.0254270 0.00992268i
\(685\) 722311. 1.53937
\(686\) 200988. + 294184.i 0.427093 + 0.625131i
\(687\) 381286.i 0.807862i
\(688\) −537022. + 583279.i −1.13453 + 1.23225i
\(689\) 436901. 0.920333
\(690\) 223875. 152953.i 0.470227 0.321262i
\(691\) 628208.i 1.31567i −0.753161 0.657836i \(-0.771472\pi\)
0.753161 0.657836i \(-0.228528\pi\)
\(692\) −160399. + 411026.i −0.334958 + 0.858335i
\(693\) −206683. −0.430367
\(694\) −385022. 563552.i −0.799404 1.17008i
\(695\) 294598.i 0.609903i
\(696\) 6508.88 1505.48i 0.0134365 0.00310782i
\(697\) −50016.2 −0.102954
\(698\) −317401. + 216850.i −0.651475 + 0.445091i
\(699\) 176887.i 0.362027i
\(700\) −87449.8 34126.6i −0.178469 0.0696461i
\(701\) −470333. −0.957127 −0.478563 0.878053i \(-0.658842\pi\)
−0.478563 + 0.878053i \(0.658842\pi\)
\(702\) −78214.9 114482.i −0.158714 0.232308i
\(703\) 22343.4i 0.0452105i
\(704\) 242016. + 495184.i 0.488313 + 0.999129i
\(705\) 124657. 0.250807
\(706\) 680089. 464640.i 1.36445 0.932196i
\(707\) 49767.8i 0.0995656i
\(708\) −78068.7 + 200052.i −0.155744 + 0.399095i
\(709\) −666498. −1.32589 −0.662944 0.748669i \(-0.730693\pi\)
−0.662944 + 0.748669i \(0.730693\pi\)
\(710\) 36213.2 + 53004.9i 0.0718373 + 0.105147i
\(711\) 101423.i 0.200630i
\(712\) 171963. + 743476.i 0.339215 + 1.46658i
\(713\) −271092. −0.533259
\(714\) 90123.4 61572.7i 0.176783 0.120779i
\(715\) 759474.i 1.48560i
\(716\) −630195. 245928.i −1.22927 0.479714i
\(717\) 182459. 0.354918
\(718\) −176987. 259054.i −0.343315 0.502506i
\(719\) 551482.i 1.06678i −0.845870 0.533388i \(-0.820918\pi\)
0.845870 0.533388i \(-0.179082\pi\)
\(720\) −116164. 106951.i −0.224081 0.206310i
\(721\) 172766. 0.332344
\(722\) 427535. 292094.i 0.820158 0.560336i
\(723\) 101953.i 0.195041i
\(724\) −5856.14 + 15006.4i −0.0111721 + 0.0286286i
\(725\) −2071.85 −0.00394169
\(726\) −40634.8 59476.7i −0.0770947 0.112843i
\(727\) 735388.i 1.39139i 0.718339 + 0.695694i \(0.244903\pi\)
−0.718339 + 0.695694i \(0.755097\pi\)
\(728\) 876393. 202706.i 1.65362 0.382477i
\(729\) −19683.0 −0.0370370
\(730\) −741290. + 506453.i −1.39105 + 0.950372i
\(731\) 285893.i 0.535019i
\(732\) −186138. 72638.8i −0.347386 0.135565i
\(733\) 372734. 0.693731 0.346866 0.937915i \(-0.387246\pi\)
0.346866 + 0.937915i \(0.387246\pi\)
\(734\) −500452. 732506.i −0.928902 1.35962i
\(735\) 99148.6i 0.183532i
\(736\) 84356.0 578626.i 0.155726 1.06817i
\(737\) 51108.4 0.0940931
\(738\) −48316.9 + 33010.4i −0.0887129 + 0.0606091i
\(739\) 962125.i 1.76174i 0.473356 + 0.880871i \(0.343043\pi\)
−0.473356 + 0.880871i \(0.656957\pi\)
\(740\) 100438. 257374.i 0.183415 0.470004i
\(741\) −37949.0 −0.0691136
\(742\) 226998. + 332254.i 0.412301 + 0.603480i
\(743\) 557423.i 1.00973i 0.863197 + 0.504867i \(0.168459\pi\)
−0.863197 + 0.504867i \(0.831541\pi\)
\(744\) 35576.7 + 153815.i 0.0642717 + 0.277876i
\(745\) −719022. −1.29548
\(746\) −85488.3 + 58406.1i −0.153613 + 0.104949i
\(747\) 281706.i 0.504841i
\(748\) 185145. + 72251.5i 0.330910 + 0.129135i
\(749\) −1.08415e6 −1.93254
\(750\) 195031. + 285464.i 0.346721 + 0.507492i
\(751\) 619927.i 1.09916i −0.835441 0.549580i \(-0.814788\pi\)
0.835441 0.549580i \(-0.185212\pi\)
\(752\) 182095. 197780.i 0.322005 0.349741i
\(753\) −2913.64 −0.00513860
\(754\) 16392.8 11199.7i 0.0288344 0.0196998i
\(755\) 901881.i 1.58218i
\(756\) 46423.8 118962.i 0.0812264 0.208144i
\(757\) −66502.8 −0.116051 −0.0580254 0.998315i \(-0.518480\pi\)
−0.0580254 + 0.998315i \(0.518480\pi\)
\(758\) −333508. 488152.i −0.580454 0.849604i
\(759\) 399269.i 0.693078i
\(760\) −42106.3 + 9739.03i −0.0728987 + 0.0168612i
\(761\) 417057. 0.720156 0.360078 0.932922i \(-0.382750\pi\)
0.360078 + 0.932922i \(0.382750\pi\)
\(762\) 445514. 304377.i 0.767275 0.524207i
\(763\) 747093.i 1.28329i
\(764\) −102945. 40173.4i −0.176367 0.0688260i
\(765\) −56937.5 −0.0972916
\(766\) 510485. + 747192.i 0.870013 + 1.27343i
\(767\) 638169.i 1.08479i
\(768\) −339376. + 28073.2i −0.575385 + 0.0475959i
\(769\) −284602. −0.481266 −0.240633 0.970616i \(-0.577355\pi\)
−0.240633 + 0.970616i \(0.577355\pi\)
\(770\) −577564. + 394595.i −0.974134 + 0.665534i
\(771\) 418348.i 0.703767i
\(772\) 164075. 420445.i 0.275301 0.705463i
\(773\) 690220. 1.15512 0.577562 0.816347i \(-0.304004\pi\)
0.577562 + 0.816347i \(0.304004\pi\)
\(774\) 188688. + 276180.i 0.314964 + 0.461010i
\(775\) 48960.9i 0.0815167i
\(776\) 31715.3 + 137120.i 0.0526677 + 0.227707i
\(777\) 223434. 0.370090
\(778\) 846893. 578602.i 1.39917 0.955918i
\(779\) 16016.2i 0.0263928i
\(780\) −437134. 170588.i −0.718498 0.280388i
\(781\) −94531.3 −0.154979
\(782\) −118946. 174100.i −0.194507 0.284698i
\(783\) 2818.43i 0.00459709i
\(784\) 157308. + 144833.i 0.255929 + 0.235632i
\(785\) −59831.1 −0.0970929
\(786\) −282144. + 192762.i −0.456694 + 0.312016i
\(787\) 855688.i 1.38155i −0.723071 0.690774i \(-0.757270\pi\)
0.723071 0.690774i \(-0.242730\pi\)
\(788\) 223672. 573161.i 0.360212 0.923048i
\(789\) 180939. 0.290655
\(790\) 193634. + 283420.i 0.310261 + 0.454126i
\(791\) 827242.i 1.32215i
\(792\) 226541. 52398.0i 0.361157 0.0835342i
\(793\) −593782. −0.944236
\(794\) −187161. + 127869.i −0.296875 + 0.202827i
\(795\) 209909.i 0.332122i
\(796\) −81831.3 31934.0i −0.129150 0.0503996i
\(797\) 579975. 0.913046 0.456523 0.889712i \(-0.349095\pi\)
0.456523 + 0.889712i \(0.349095\pi\)
\(798\) −19716.9 28859.4i −0.0309623 0.0453191i
\(799\) 96941.7i 0.151851i
\(800\) 104503. + 15235.2i 0.163287 + 0.0238050i
\(801\) 321935. 0.501768
\(802\) 36040.0 24622.7i 0.0560320 0.0382814i
\(803\) 1.32205e6i 2.05030i
\(804\) −11479.6 + 29416.7i −0.0177589 + 0.0455075i
\(805\) 742108. 1.14518
\(806\) 264665. + 387387.i 0.407405 + 0.596314i
\(807\) 147932.i 0.227151i
\(808\) 12617.1 + 54549.3i 0.0193257 + 0.0835539i
\(809\) −60860.6 −0.0929907 −0.0464953 0.998919i \(-0.514805\pi\)
−0.0464953 + 0.998919i \(0.514805\pi\)
\(810\) −55003.0 + 37578.4i −0.0838333 + 0.0572753i
\(811\) 103330.i 0.157103i −0.996910 0.0785515i \(-0.974970\pi\)
0.996910 0.0785515i \(-0.0250295\pi\)
\(812\) 17034.2 + 6647.47i 0.0258351 + 0.0100819i
\(813\) 195654. 0.296011
\(814\) 229506. + 335926.i 0.346375 + 0.506985i
\(815\) 162724.i 0.244983i
\(816\) −83172.3 + 90336.4i −0.124910 + 0.135670i
\(817\) 91549.0 0.137154
\(818\) −956404. + 653421.i −1.42934 + 0.976531i
\(819\) 379489.i 0.565759i
\(820\) −71996.2 + 184491.i −0.107073 + 0.274377i
\(821\) 533333. 0.791247 0.395623 0.918413i \(-0.370529\pi\)
0.395623 + 0.918413i \(0.370529\pi\)
\(822\) −370729. 542632.i −0.548672 0.803085i
\(823\) 728807.i 1.07600i 0.842945 + 0.538000i \(0.180820\pi\)
−0.842945 + 0.538000i \(0.819180\pi\)
\(824\) −189365. + 43799.3i −0.278897 + 0.0645079i
\(825\) −72110.5 −0.105947
\(826\) −485314. + 331569.i −0.711317 + 0.485975i
\(827\) 768434.i 1.12356i 0.827287 + 0.561779i \(0.189883\pi\)
−0.827287 + 0.561779i \(0.810117\pi\)
\(828\) −229809. 89681.3i −0.335203 0.130810i
\(829\) −401672. −0.584471 −0.292235 0.956346i \(-0.594399\pi\)
−0.292235 + 0.956346i \(0.594399\pi\)
\(830\) 537827. + 787211.i 0.780704 + 1.14271i
\(831\) 134685.i 0.195037i
\(832\) −909205. + 444364.i −1.31345 + 0.641936i
\(833\) 77104.4 0.111119
\(834\) −221315. + 151204.i −0.318185 + 0.217385i
\(835\) 1.11185e6i 1.59469i
\(836\) 23136.4 59287.4i 0.0331043 0.0848301i
\(837\) 66603.7 0.0950708
\(838\) 157587. + 230659.i 0.224405 + 0.328460i
\(839\) 429703.i 0.610443i −0.952281 0.305221i \(-0.901270\pi\)
0.952281 0.305221i \(-0.0987305\pi\)
\(840\) −97390.3 421063.i −0.138025 0.596745i
\(841\) −706877. −0.999429
\(842\) 53528.1 36570.7i 0.0755019 0.0515833i
\(843\) 258849.i 0.364244i
\(844\) −692669. 270308.i −0.972391 0.379468i
\(845\) −742006. −1.03919
\(846\) −63980.9 93648.1i −0.0893942 0.130845i
\(847\) 197155.i 0.274815i
\(848\) −333040. 306628.i −0.463132 0.426403i
\(849\) −381418. −0.529159
\(850\) 31443.5 21482.4i 0.0435204 0.0297334i
\(851\) 431629.i 0.596007i
\(852\) 21233.0 54409.9i 0.0292504 0.0749547i
\(853\) −732176. −1.00628 −0.503138 0.864206i \(-0.667821\pi\)
−0.503138 + 0.864206i \(0.667821\pi\)
\(854\) −308507. 451559.i −0.423009 0.619154i
\(855\) 18232.6i 0.0249411i
\(856\) 1.18832e6 274853.i 1.62175 0.375105i
\(857\) 430159. 0.585689 0.292844 0.956160i \(-0.405398\pi\)
0.292844 + 0.956160i \(0.405398\pi\)
\(858\) 570550. 389803.i 0.775031 0.529506i
\(859\) 489975.i 0.664030i 0.943274 + 0.332015i \(0.107728\pi\)
−0.943274 + 0.332015i \(0.892272\pi\)
\(860\) 1.05455e6 + 411531.i 1.42584 + 0.556424i
\(861\) −160162. −0.216050
\(862\) −237525. 347662.i −0.319665 0.467890i
\(863\) 999093.i 1.34148i 0.741692 + 0.670740i \(0.234023\pi\)
−0.741692 + 0.670740i \(0.765977\pi\)
\(864\) −20725.1 + 142160.i −0.0277632 + 0.190437i
\(865\) 629955. 0.841933
\(866\) 435303. 297401.i 0.580438 0.396559i
\(867\) 389710.i 0.518445i
\(868\) −157090. + 402544.i −0.208501 + 0.534287i
\(869\) −505464. −0.669347
\(870\) −5380.88 7875.93i −0.00710910 0.0104055i
\(871\) 93839.8i 0.123695i
\(872\) 189402. + 818872.i 0.249087 + 1.07692i
\(873\) 59374.5 0.0779062
\(874\) −55750.4 + 38089.0i −0.0729836 + 0.0498628i
\(875\) 946265.i 1.23594i
\(876\) 760940. + 296951.i 0.991613 + 0.386969i
\(877\) 634599. 0.825087 0.412544 0.910938i \(-0.364640\pi\)
0.412544 + 0.910938i \(0.364640\pi\)
\(878\) −336334. 492289.i −0.436297 0.638603i
\(879\) 679047.i 0.878865i
\(880\) 533018. 578930.i 0.688298 0.747585i
\(881\) 312649. 0.402815 0.201407 0.979508i \(-0.435448\pi\)
0.201407 + 0.979508i \(0.435448\pi\)
\(882\) 74484.8 50888.4i 0.0957481 0.0654156i
\(883\) 209047.i 0.268116i 0.990973 + 0.134058i \(0.0428008\pi\)
−0.990973 + 0.134058i \(0.957199\pi\)
\(884\) −132660. + 339944.i −0.169761 + 0.435014i
\(885\) 306608. 0.391469
\(886\) −561710. 822169.i −0.715558 1.04735i
\(887\) 178008.i 0.226252i −0.993581 0.113126i \(-0.963914\pi\)
0.993581 0.113126i \(-0.0360864\pi\)
\(888\) −244901. + 56644.7i −0.310574 + 0.0718345i
\(889\) 1.47680e6 1.86861
\(890\) 899628. 614631.i 1.13575 0.775951i
\(891\) 98095.0i 0.123564i
\(892\) 720031. + 280986.i 0.904943 + 0.353147i
\(893\) −31042.8 −0.0389276
\(894\) 369041. + 540161.i 0.461742 + 0.675847i
\(895\) 965863.i 1.20578i
\(896\) −810319. 460556.i −1.00935 0.573676i
\(897\) −733095. −0.911120
\(898\) 805047. 550012.i 0.998317 0.682055i
\(899\) 9537.04i 0.0118003i
\(900\) 16197.0 41505.0i 0.0199963 0.0512407i
\(901\) −163239. −0.201082
\(902\) −164515. 240799.i −0.202205 0.295966i
\(903\) 915490.i 1.12274i
\(904\) −209721. 906720.i −0.256629 1.10952i
\(905\) 22999.5 0.0280815
\(906\) −677532. + 462894.i −0.825417 + 0.563929i
\(907\) 62871.2i 0.0764253i 0.999270 + 0.0382126i \(0.0121664\pi\)
−0.999270 + 0.0382126i \(0.987834\pi\)
\(908\) −284819. 111148.i −0.345459 0.134813i
\(909\) 23620.5 0.0285866
\(910\) −724513. 1.06046e6i −0.874910 1.28060i
\(911\) 1.45791e6i 1.75669i −0.478027 0.878345i \(-0.658648\pi\)
0.478027 0.878345i \(-0.341352\pi\)
\(912\) 28927.6 + 26633.5i 0.0347795 + 0.0320213i
\(913\) −1.40395e6 −1.68426
\(914\) 1.13377e6 774598.i 1.35716 0.927222i
\(915\) 285282.i 0.340748i
\(916\) −426817. + 1.09372e6i −0.508687 + 1.30352i
\(917\) −935258. −1.11223
\(918\) 29223.4 + 42773.9i 0.0346773 + 0.0507567i
\(919\) 315989.i 0.374146i 0.982346 + 0.187073i \(0.0599001\pi\)
−0.982346 + 0.187073i \(0.940100\pi\)
\(920\) −813407. + 188138.i −0.961020 + 0.222280i
\(921\) −724927. −0.854623
\(922\) −513660. + 350935.i −0.604246 + 0.412824i
\(923\) 173568.i 0.203736i
\(924\) 592874. + 231364.i 0.694414 + 0.270989i
\(925\) 77954.8 0.0911086
\(926\) 725358. + 1.06170e6i 0.845923 + 1.23817i
\(927\) 81997.3i 0.0954201i
\(928\) −20356.1 2967.65i −0.0236373 0.00344601i
\(929\) 122547. 0.141994 0.0709971 0.997477i \(-0.477382\pi\)
0.0709971 + 0.997477i \(0.477382\pi\)
\(930\) 186120. 127158.i 0.215193 0.147021i
\(931\) 24690.4i 0.0284859i
\(932\) −198010. + 507403.i −0.227958 + 0.584145i
\(933\) 686070. 0.788143
\(934\) −183270. 268250.i −0.210086 0.307501i
\(935\) 283761.i 0.324586i
\(936\) 96207.6 + 415950.i 0.109814 + 0.474776i
\(937\) 495399. 0.564256 0.282128 0.959377i \(-0.408960\pi\)
0.282128 + 0.959377i \(0.408960\pi\)
\(938\) −71363.3 + 48755.7i −0.0811090 + 0.0554141i
\(939\) 205385.i 0.232936i
\(940\) −357582. 139543.i −0.404687 0.157926i
\(941\) −1.14226e6 −1.28999 −0.644994 0.764188i \(-0.723140\pi\)
−0.644994 + 0.764188i \(0.723140\pi\)
\(942\) 30708.5 + 44947.8i 0.0346065 + 0.0506531i
\(943\) 309401.i 0.347935i
\(944\) 447883. 486461.i 0.502598 0.545889i
\(945\) −182326. −0.204166
\(946\) −1.37641e6 + 940370.i −1.53803 + 1.05079i
\(947\) 527337.i 0.588015i 0.955803 + 0.294007i \(0.0949890\pi\)
−0.955803 + 0.294007i \(0.905011\pi\)
\(948\) 113534. 290933.i 0.126331 0.323725i
\(949\) 2.42741e6 2.69532
\(950\) −6879.10 10068.9i −0.00762227 0.0111566i
\(951\) 477833.i 0.528342i
\(952\) −327446. + 75737.0i −0.361298 + 0.0835669i
\(953\) −259379. −0.285594 −0.142797 0.989752i \(-0.545610\pi\)
−0.142797 + 0.989752i \(0.545610\pi\)
\(954\) −157693. + 107737.i −0.173267 + 0.118377i
\(955\) 157778.i 0.172997i
\(956\) −523387. 204248.i −0.572674 0.223481i
\(957\) 14046.3 0.0153369
\(958\) 780856. + 1.14293e6i 0.850824 + 1.24534i
\(959\) 1.79873e6i 1.95582i
\(960\) 213494. + 436827.i 0.231656 + 0.473988i
\(961\) 698146. 0.755962
\(962\) −616791. + 421395.i −0.666482 + 0.455344i
\(963\) 514556.i 0.554856i
\(964\) −114128. + 292455.i −0.122812 + 0.314706i
\(965\) −644391. −0.691982
\(966\) −380890. 557504.i −0.408174 0.597439i
\(967\) 1.03870e6i 1.11081i −0.831581 0.555403i \(-0.812564\pi\)
0.831581 0.555403i \(-0.187436\pi\)
\(968\) 49982.4 + 216097.i 0.0533417 + 0.230621i
\(969\) 14178.8 0.0151005
\(970\) 165919. 113357.i 0.176341 0.120477i
\(971\) 1.15698e6i 1.22713i −0.789646 0.613563i \(-0.789736\pi\)
0.789646 0.613563i \(-0.210264\pi\)
\(972\) 56461.0 + 22033.5i 0.0597608 + 0.0233212i
\(973\) −733622. −0.774902
\(974\) 213101. + 311913.i 0.224630 + 0.328788i
\(975\) 132402.i 0.139278i
\(976\) 452626. + 416731.i 0.475160 + 0.437478i
\(977\) 1.09732e6 1.14960 0.574799 0.818295i \(-0.305080\pi\)
0.574799 + 0.818295i \(0.305080\pi\)
\(978\) 122245. 83518.7i 0.127807 0.0873184i
\(979\) 1.60444e6i 1.67401i
\(980\) 110988. 284409.i 0.115565 0.296136i
\(981\) 354582. 0.368450
\(982\) −396525. 580389.i −0.411195 0.601861i
\(983\) 1.71299e6i 1.77276i 0.462963 + 0.886378i \(0.346786\pi\)
−0.462963 + 0.886378i \(0.653214\pi\)
\(984\) 175550. 40604.1i 0.181306 0.0419353i
\(985\) −878451. −0.905409
\(986\) −6124.84 + 4184.52i −0.00630000 + 0.00430419i
\(987\) 310427.i 0.318659i
\(988\) 108857. + 42480.6i 0.111518 + 0.0435188i
\(989\) 1.76854e6 1.80810
\(990\) −187281. 274121.i −0.191083 0.279687i
\(991\) 1.03974e6i 1.05872i −0.848399 0.529358i \(-0.822433\pi\)
0.848399 0.529358i \(-0.177567\pi\)
\(992\) 70130.0 481045.i 0.0712657 0.488835i
\(993\) −16856.8 −0.0170953
\(994\) 131995. 90179.7i 0.133593 0.0912717i
\(995\) 125418.i 0.126682i
\(996\) 315346. 808078.i 0.317884 0.814582i
\(997\) −1.11868e6 −1.12542 −0.562709 0.826655i \(-0.690241\pi\)
−0.562709 + 0.826655i \(0.690241\pi\)
\(998\) −84154.4 123176.i −0.0844920 0.123670i
\(999\) 106045.i 0.106258i
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 12.5.d.a.7.3 4
3.2 odd 2 36.5.d.b.19.2 4
4.3 odd 2 inner 12.5.d.a.7.4 yes 4
5.2 odd 4 300.5.f.a.199.6 8
5.3 odd 4 300.5.f.a.199.3 8
5.4 even 2 300.5.c.a.151.2 4
8.3 odd 2 192.5.g.d.127.4 4
8.5 even 2 192.5.g.d.127.2 4
12.11 even 2 36.5.d.b.19.1 4
16.3 odd 4 768.5.b.g.127.7 8
16.5 even 4 768.5.b.g.127.6 8
16.11 odd 4 768.5.b.g.127.2 8
16.13 even 4 768.5.b.g.127.3 8
20.3 even 4 300.5.f.a.199.5 8
20.7 even 4 300.5.f.a.199.4 8
20.19 odd 2 300.5.c.a.151.1 4
24.5 odd 2 576.5.g.m.127.2 4
24.11 even 2 576.5.g.m.127.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.5.d.a.7.3 4 1.1 even 1 trivial
12.5.d.a.7.4 yes 4 4.3 odd 2 inner
36.5.d.b.19.1 4 12.11 even 2
36.5.d.b.19.2 4 3.2 odd 2
192.5.g.d.127.2 4 8.5 even 2
192.5.g.d.127.4 4 8.3 odd 2
300.5.c.a.151.1 4 20.19 odd 2
300.5.c.a.151.2 4 5.4 even 2
300.5.f.a.199.3 8 5.3 odd 4
300.5.f.a.199.4 8 20.7 even 4
300.5.f.a.199.5 8 20.3 even 4
300.5.f.a.199.6 8 5.2 odd 4
576.5.g.m.127.1 4 24.11 even 2
576.5.g.m.127.2 4 24.5 odd 2
768.5.b.g.127.2 8 16.11 odd 4
768.5.b.g.127.3 8 16.13 even 4
768.5.b.g.127.6 8 16.5 even 4
768.5.b.g.127.7 8 16.3 odd 4