Properties

Label 354.6.c.a.353.16
Level $354$
Weight $6$
Character 354.353
Analytic conductor $56.776$
Analytic rank $0$
Dimension $50$
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] = [354,6,Mod(353,354)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(354, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("354.353");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 354.c (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: \(56.7758722138\)
Analytic rank: \(0\)
Dimension: \(50\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 353.16
Character \(\chi\) \(=\) 354.353
Dual form 354.6.c.a.353.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000 q^{2} +(-9.75722 + 12.1572i) q^{3} +16.0000 q^{4} -43.2791i q^{5} +(39.0289 - 48.6287i) q^{6} -5.13563 q^{7} -64.0000 q^{8} +(-52.5934 - 237.240i) q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +(-9.75722 + 12.1572i) q^{3} +16.0000 q^{4} -43.2791i q^{5} +(39.0289 - 48.6287i) q^{6} -5.13563 q^{7} -64.0000 q^{8} +(-52.5934 - 237.240i) q^{9} +173.116i q^{10} +262.706 q^{11} +(-156.115 + 194.515i) q^{12} +296.127i q^{13} +20.5425 q^{14} +(526.151 + 422.283i) q^{15} +256.000 q^{16} +1334.77i q^{17} +(210.374 + 948.961i) q^{18} -1340.55 q^{19} -692.465i q^{20} +(50.1095 - 62.4347i) q^{21} -1050.82 q^{22} -1858.55 q^{23} +(624.462 - 778.059i) q^{24} +1251.92 q^{25} -1184.51i q^{26} +(3397.33 + 1675.42i) q^{27} -82.1701 q^{28} +1127.52i q^{29} +(-2104.60 - 1689.13i) q^{30} -6100.77i q^{31} -1024.00 q^{32} +(-2563.28 + 3193.76i) q^{33} -5339.10i q^{34} +222.265i q^{35} +(-841.494 - 3795.84i) q^{36} -6962.90i q^{37} +5362.21 q^{38} +(-3600.06 - 2889.37i) q^{39} +2769.86i q^{40} -1648.54i q^{41} +(-200.438 + 249.739i) q^{42} +1565.02i q^{43} +4203.29 q^{44} +(-10267.5 + 2276.19i) q^{45} +7434.22 q^{46} -13521.2 q^{47} +(-2497.85 + 3112.23i) q^{48} -16780.6 q^{49} -5007.69 q^{50} +(-16227.1 - 13023.7i) q^{51} +4738.02i q^{52} +12816.2i q^{53} +(-13589.3 - 6701.67i) q^{54} -11369.7i q^{55} +328.680 q^{56} +(13080.1 - 16297.3i) q^{57} -4510.09i q^{58} +(14183.6 + 22666.1i) q^{59} +(8418.41 + 6756.53i) q^{60} -50754.6i q^{61} +24403.1i q^{62} +(270.100 + 1218.38i) q^{63} +4096.00 q^{64} +12816.1 q^{65} +(10253.1 - 12775.0i) q^{66} +1305.77i q^{67} +21356.4i q^{68} +(18134.3 - 22594.8i) q^{69} -889.061i q^{70} +17624.9i q^{71} +(3365.98 + 15183.4i) q^{72} +16392.2i q^{73} +27851.6i q^{74} +(-12215.3 + 15219.8i) q^{75} -21448.8 q^{76} -1349.16 q^{77} +(14400.2 + 11557.5i) q^{78} +66615.5 q^{79} -11079.4i q^{80} +(-53516.9 + 24954.5i) q^{81} +6594.17i q^{82} +52720.6 q^{83} +(801.751 - 998.955i) q^{84} +57767.8 q^{85} -6260.06i q^{86} +(-13707.5 - 11001.5i) q^{87} -16813.2 q^{88} +89751.0 q^{89} +(41070.1 - 9104.77i) q^{90} -1520.80i q^{91} -29736.9 q^{92} +(74168.1 + 59526.5i) q^{93} +54085.0 q^{94} +58017.8i q^{95} +(9991.39 - 12448.9i) q^{96} -24987.9i q^{97} +67122.5 q^{98} +(-13816.6 - 62324.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9} - 652 q^{11} - 208 q^{12} - 152 q^{14} - 2107 q^{15} + 12800 q^{16} - 204 q^{18} - 894 q^{19} - 3801 q^{21} + 2608 q^{22} + 2456 q^{23} + 832 q^{24} - 23956 q^{25} + 9890 q^{27} + 608 q^{28} + 8428 q^{30} - 51200 q^{32} - 9744 q^{33} + 816 q^{36} + 3576 q^{38} + 1388 q^{39} + 15204 q^{42} - 10432 q^{44} + 33067 q^{45} - 9824 q^{46} - 27144 q^{47} - 3328 q^{48} + 85768 q^{49} + 95824 q^{50} + 3338 q^{51} - 39560 q^{54} - 2432 q^{56} - 63969 q^{57} - 23840 q^{59} - 33712 q^{60} + 94781 q^{63} + 204800 q^{64} - 9400 q^{65} + 38976 q^{66} - 115930 q^{69} - 3264 q^{72} + 24248 q^{75} - 14304 q^{76} - 150240 q^{77} - 5552 q^{78} - 68658 q^{79} + 47095 q^{81} - 175140 q^{83} - 60816 q^{84} - 138524 q^{85} + 138261 q^{87} + 41728 q^{88} + 104908 q^{89} - 132268 q^{90} + 39296 q^{92} - 91204 q^{93} + 108576 q^{94} + 13312 q^{96} - 343072 q^{98} - 111406 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.00000 −0.707107
\(3\) −9.75722 + 12.1572i −0.625926 + 0.779883i
\(4\) 16.0000 0.500000
\(5\) 43.2791i 0.774200i −0.922038 0.387100i \(-0.873477\pi\)
0.922038 0.387100i \(-0.126523\pi\)
\(6\) 39.0289 48.6287i 0.442596 0.551460i
\(7\) −5.13563 −0.0396140 −0.0198070 0.999804i \(-0.506305\pi\)
−0.0198070 + 0.999804i \(0.506305\pi\)
\(8\) −64.0000 −0.353553
\(9\) −52.5934 237.240i −0.216434 0.976297i
\(10\) 173.116i 0.547442i
\(11\) 262.706 0.654618 0.327309 0.944917i \(-0.393858\pi\)
0.327309 + 0.944917i \(0.393858\pi\)
\(12\) −156.115 + 194.515i −0.312963 + 0.389941i
\(13\) 296.127i 0.485981i 0.970029 + 0.242990i \(0.0781283\pi\)
−0.970029 + 0.242990i \(0.921872\pi\)
\(14\) 20.5425 0.0280113
\(15\) 526.151 + 422.283i 0.603785 + 0.484591i
\(16\) 256.000 0.250000
\(17\) 1334.77i 1.12017i 0.828434 + 0.560087i \(0.189232\pi\)
−0.828434 + 0.560087i \(0.810768\pi\)
\(18\) 210.374 + 948.961i 0.153042 + 0.690346i
\(19\) −1340.55 −0.851922 −0.425961 0.904742i \(-0.640064\pi\)
−0.425961 + 0.904742i \(0.640064\pi\)
\(20\) 692.465i 0.387100i
\(21\) 50.1095 62.4347i 0.0247954 0.0308943i
\(22\) −1050.82 −0.462885
\(23\) −1858.55 −0.732581 −0.366290 0.930501i \(-0.619372\pi\)
−0.366290 + 0.930501i \(0.619372\pi\)
\(24\) 624.462 778.059i 0.221298 0.275730i
\(25\) 1251.92 0.400615
\(26\) 1184.51i 0.343640i
\(27\) 3397.33 + 1675.42i 0.896869 + 0.442297i
\(28\) −82.1701 −0.0198070
\(29\) 1127.52i 0.248960i 0.992222 + 0.124480i \(0.0397263\pi\)
−0.992222 + 0.124480i \(0.960274\pi\)
\(30\) −2104.60 1689.13i −0.426940 0.342658i
\(31\) 6100.77i 1.14020i −0.821576 0.570099i \(-0.806905\pi\)
0.821576 0.570099i \(-0.193095\pi\)
\(32\) −1024.00 −0.176777
\(33\) −2563.28 + 3193.76i −0.409742 + 0.510525i
\(34\) 5339.10i 0.792083i
\(35\) 222.265i 0.0306691i
\(36\) −841.494 3795.84i −0.108217 0.488149i
\(37\) 6962.90i 0.836153i −0.908412 0.418077i \(-0.862704\pi\)
0.908412 0.418077i \(-0.137296\pi\)
\(38\) 5362.21 0.602399
\(39\) −3600.06 2889.37i −0.379008 0.304188i
\(40\) 2769.86i 0.273721i
\(41\) 1648.54i 0.153158i −0.997064 0.0765791i \(-0.975600\pi\)
0.997064 0.0765791i \(-0.0243998\pi\)
\(42\) −200.438 + 249.739i −0.0175330 + 0.0218455i
\(43\) 1565.02i 0.129077i 0.997915 + 0.0645383i \(0.0205575\pi\)
−0.997915 + 0.0645383i \(0.979443\pi\)
\(44\) 4203.29 0.327309
\(45\) −10267.5 + 2276.19i −0.755849 + 0.167563i
\(46\) 7434.22 0.518013
\(47\) −13521.2 −0.892837 −0.446418 0.894824i \(-0.647301\pi\)
−0.446418 + 0.894824i \(0.647301\pi\)
\(48\) −2497.85 + 3112.23i −0.156481 + 0.194971i
\(49\) −16780.6 −0.998431
\(50\) −5007.69 −0.283278
\(51\) −16227.1 13023.7i −0.873605 0.701146i
\(52\) 4738.02i 0.242990i
\(53\) 12816.2i 0.626714i 0.949635 + 0.313357i \(0.101454\pi\)
−0.949635 + 0.313357i \(0.898546\pi\)
\(54\) −13589.3 6701.67i −0.634182 0.312751i
\(55\) 11369.7i 0.506805i
\(56\) 328.680 0.0140057
\(57\) 13080.1 16297.3i 0.533240 0.664399i
\(58\) 4510.09i 0.176042i
\(59\) 14183.6 + 22666.1i 0.530464 + 0.847707i
\(60\) 8418.41 + 6756.53i 0.301892 + 0.242296i
\(61\) 50754.6i 1.74643i −0.487336 0.873215i \(-0.662031\pi\)
0.487336 0.873215i \(-0.337969\pi\)
\(62\) 24403.1i 0.806242i
\(63\) 270.100 + 1218.38i 0.00857381 + 0.0386750i
\(64\) 4096.00 0.125000
\(65\) 12816.1 0.376246
\(66\) 10253.1 12775.0i 0.289732 0.360996i
\(67\) 1305.77i 0.0355368i 0.999842 + 0.0177684i \(0.00565615\pi\)
−0.999842 + 0.0177684i \(0.994344\pi\)
\(68\) 21356.4i 0.560087i
\(69\) 18134.3 22594.8i 0.458541 0.571327i
\(70\) 889.061i 0.0216864i
\(71\) 17624.9i 0.414936i 0.978242 + 0.207468i \(0.0665222\pi\)
−0.978242 + 0.207468i \(0.933478\pi\)
\(72\) 3365.98 + 15183.4i 0.0765209 + 0.345173i
\(73\) 16392.2i 0.360023i 0.983664 + 0.180012i \(0.0576135\pi\)
−0.983664 + 0.180012i \(0.942386\pi\)
\(74\) 27851.6i 0.591250i
\(75\) −12215.3 + 15219.8i −0.250755 + 0.312433i
\(76\) −21448.8 −0.425961
\(77\) −1349.16 −0.0259320
\(78\) 14400.2 + 11557.5i 0.267999 + 0.215093i
\(79\) 66615.5 1.20090 0.600451 0.799662i \(-0.294988\pi\)
0.600451 + 0.799662i \(0.294988\pi\)
\(80\) 11079.4i 0.193550i
\(81\) −53516.9 + 24954.5i −0.906313 + 0.422607i
\(82\) 6594.17i 0.108299i
\(83\) 52720.6 0.840011 0.420005 0.907522i \(-0.362028\pi\)
0.420005 + 0.907522i \(0.362028\pi\)
\(84\) 801.751 998.955i 0.0123977 0.0154471i
\(85\) 57767.8 0.867239
\(86\) 6260.06i 0.0912709i
\(87\) −13707.5 11001.5i −0.194160 0.155831i
\(88\) −16813.2 −0.231442
\(89\) 89751.0 1.20106 0.600529 0.799603i \(-0.294957\pi\)
0.600529 + 0.799603i \(0.294957\pi\)
\(90\) 41070.1 9104.77i 0.534466 0.118485i
\(91\) 1520.80i 0.0192516i
\(92\) −29736.9 −0.366290
\(93\) 74168.1 + 59526.5i 0.889221 + 0.713680i
\(94\) 54085.0 0.631331
\(95\) 58017.8i 0.659557i
\(96\) 9991.39 12448.9i 0.110649 0.137865i
\(97\) 24987.9i 0.269650i −0.990869 0.134825i \(-0.956953\pi\)
0.990869 0.134825i \(-0.0430473\pi\)
\(98\) 67122.5 0.705997
\(99\) −13816.6 62324.4i −0.141681 0.639102i
\(100\) 20030.8 0.200308
\(101\) 118534. 1.15622 0.578110 0.815959i \(-0.303790\pi\)
0.578110 + 0.815959i \(0.303790\pi\)
\(102\) 64908.3 + 52094.8i 0.617732 + 0.495785i
\(103\) 21499.7i 0.199682i −0.995003 0.0998409i \(-0.968167\pi\)
0.995003 0.0998409i \(-0.0318334\pi\)
\(104\) 18952.1i 0.171820i
\(105\) −2702.12 2168.69i −0.0239183 0.0191966i
\(106\) 51264.8i 0.443154i
\(107\) 172067.i 1.45291i 0.687216 + 0.726453i \(0.258833\pi\)
−0.687216 + 0.726453i \(0.741167\pi\)
\(108\) 54357.4 + 26806.7i 0.448434 + 0.221148i
\(109\) 220183.i 1.77508i −0.460733 0.887539i \(-0.652413\pi\)
0.460733 0.887539i \(-0.347587\pi\)
\(110\) 45478.7i 0.358365i
\(111\) 84649.2 + 67938.6i 0.652102 + 0.523370i
\(112\) −1314.72 −0.00990350
\(113\) 171524. 1.26366 0.631829 0.775108i \(-0.282305\pi\)
0.631829 + 0.775108i \(0.282305\pi\)
\(114\) −52320.2 + 65189.2i −0.377057 + 0.469801i
\(115\) 80436.5i 0.567164i
\(116\) 18040.4i 0.124480i
\(117\) 70253.1 15574.3i 0.474462 0.105183i
\(118\) −56734.4 90664.2i −0.375095 0.599420i
\(119\) 6854.91i 0.0443746i
\(120\) −33673.7 27026.1i −0.213470 0.171329i
\(121\) −92036.7 −0.571475
\(122\) 203018.i 1.23491i
\(123\) 20041.6 + 16085.2i 0.119445 + 0.0958657i
\(124\) 97612.3i 0.570099i
\(125\) 189429.i 1.08436i
\(126\) −1080.40 4873.51i −0.00606260 0.0273474i
\(127\) 265527. 1.46083 0.730416 0.683003i \(-0.239326\pi\)
0.730416 + 0.683003i \(0.239326\pi\)
\(128\) −16384.0 −0.0883883
\(129\) −19026.2 15270.2i −0.100665 0.0807924i
\(130\) −51264.3 −0.266046
\(131\) 23529.0 0.119791 0.0598956 0.998205i \(-0.480923\pi\)
0.0598956 + 0.998205i \(0.480923\pi\)
\(132\) −41012.4 + 51100.1i −0.204871 + 0.255263i
\(133\) 6884.58 0.0337480
\(134\) 5223.06i 0.0251283i
\(135\) 72510.5 147033.i 0.342426 0.694355i
\(136\) 85425.6i 0.396042i
\(137\) 232717.i 1.05932i −0.848210 0.529660i \(-0.822319\pi\)
0.848210 0.529660i \(-0.177681\pi\)
\(138\) −72537.3 + 90379.0i −0.324238 + 0.403989i
\(139\) 315311. 1.38421 0.692105 0.721797i \(-0.256683\pi\)
0.692105 + 0.721797i \(0.256683\pi\)
\(140\) 3556.25i 0.0153346i
\(141\) 131930. 164380.i 0.558850 0.696308i
\(142\) 70499.6i 0.293404i
\(143\) 77794.2i 0.318132i
\(144\) −13463.9 60733.5i −0.0541084 0.244074i
\(145\) 48798.1 0.192745
\(146\) 65568.9i 0.254575i
\(147\) 163732. 204005.i 0.624944 0.778659i
\(148\) 111406.i 0.418077i
\(149\) −388721. −1.43441 −0.717204 0.696863i \(-0.754579\pi\)
−0.717204 + 0.696863i \(0.754579\pi\)
\(150\) 48861.1 60879.3i 0.177311 0.220923i
\(151\) 1572.47i 0.00561230i 0.999996 + 0.00280615i \(0.000893227\pi\)
−0.999996 + 0.00280615i \(0.999107\pi\)
\(152\) 85795.3 0.301200
\(153\) 316662. 70200.3i 1.09362 0.242444i
\(154\) 5396.64 0.0183367
\(155\) −264036. −0.882741
\(156\) −57601.0 46229.9i −0.189504 0.152094i
\(157\) 99590.7i 0.322455i 0.986917 + 0.161228i \(0.0515454\pi\)
−0.986917 + 0.161228i \(0.948455\pi\)
\(158\) −266462. −0.849166
\(159\) −155809. 125050.i −0.488764 0.392277i
\(160\) 44317.8i 0.136860i
\(161\) 9544.85 0.0290205
\(162\) 214067. 99818.2i 0.640860 0.298829i
\(163\) 580713. 1.71196 0.855978 0.517012i \(-0.172956\pi\)
0.855978 + 0.517012i \(0.172956\pi\)
\(164\) 26376.7i 0.0765791i
\(165\) 138223. + 110936.i 0.395248 + 0.317222i
\(166\) −210882. −0.593977
\(167\) 101767.i 0.282367i 0.989983 + 0.141184i \(0.0450908\pi\)
−0.989983 + 0.141184i \(0.954909\pi\)
\(168\) −3207.01 + 3995.82i −0.00876651 + 0.0109228i
\(169\) 283602. 0.763823
\(170\) −231071. −0.613230
\(171\) 70504.2 + 318033.i 0.184385 + 0.831729i
\(172\) 25040.2i 0.0645383i
\(173\) 64078.2 0.162778 0.0813888 0.996682i \(-0.474064\pi\)
0.0813888 + 0.996682i \(0.474064\pi\)
\(174\) 54829.9 + 44005.9i 0.137292 + 0.110189i
\(175\) −6429.41 −0.0158700
\(176\) 67252.7 0.163655
\(177\) −413947. 48725.3i −0.993143 0.116902i
\(178\) −359004. −0.849276
\(179\) 412538. 0.962347 0.481173 0.876625i \(-0.340211\pi\)
0.481173 + 0.876625i \(0.340211\pi\)
\(180\) −164281. + 36419.1i −0.377924 + 0.0837815i
\(181\) 37016.7 0.0839850 0.0419925 0.999118i \(-0.486629\pi\)
0.0419925 + 0.999118i \(0.486629\pi\)
\(182\) 6083.19i 0.0136130i
\(183\) 617032. + 495224.i 1.36201 + 1.09314i
\(184\) 118947. 0.259006
\(185\) −301348. −0.647350
\(186\) −296672. 238106.i −0.628774 0.504648i
\(187\) 350653.i 0.733286i
\(188\) −216340. −0.446418
\(189\) −17447.5 8604.33i −0.0355286 0.0175211i
\(190\) 232071.i 0.466377i
\(191\) −155943. −0.309301 −0.154651 0.987969i \(-0.549425\pi\)
−0.154651 + 0.987969i \(0.549425\pi\)
\(192\) −39965.6 + 49795.8i −0.0782407 + 0.0974853i
\(193\) −520302. −1.00545 −0.502727 0.864445i \(-0.667670\pi\)
−0.502727 + 0.864445i \(0.667670\pi\)
\(194\) 99951.7i 0.190671i
\(195\) −125049. + 155807.i −0.235502 + 0.293428i
\(196\) −268490. −0.499215
\(197\) 264785.i 0.486103i 0.970013 + 0.243052i \(0.0781484\pi\)
−0.970013 + 0.243052i \(0.921852\pi\)
\(198\) 55266.4 + 249298.i 0.100184 + 0.451913i
\(199\) 79805.9 0.142857 0.0714286 0.997446i \(-0.477244\pi\)
0.0714286 + 0.997446i \(0.477244\pi\)
\(200\) −80123.0 −0.141639
\(201\) −15874.4 12740.6i −0.0277145 0.0222434i
\(202\) −474137. −0.817571
\(203\) 5790.54i 0.00986231i
\(204\) −259633. 208379.i −0.436802 0.350573i
\(205\) −71347.4 −0.118575
\(206\) 85998.6i 0.141196i
\(207\) 97747.7 + 440924.i 0.158555 + 0.715217i
\(208\) 75808.4i 0.121495i
\(209\) −352171. −0.557683
\(210\) 10808.5 + 8674.76i 0.0169128 + 0.0135741i
\(211\) 115465.i 0.178543i 0.996007 + 0.0892717i \(0.0284540\pi\)
−0.996007 + 0.0892717i \(0.971546\pi\)
\(212\) 205059.i 0.313357i
\(213\) −214269. 171970.i −0.323601 0.259719i
\(214\) 688267.i 1.02736i
\(215\) 67732.4 0.0999310
\(216\) −217429. 107227.i −0.317091 0.156376i
\(217\) 31331.3i 0.0451678i
\(218\) 880732.i 1.25517i
\(219\) −199283. 159942.i −0.280776 0.225348i
\(220\) 181915.i 0.253402i
\(221\) −395262. −0.544383
\(222\) −338597. 271754.i −0.461105 0.370078i
\(223\) 949938. 1.27918 0.639592 0.768715i \(-0.279103\pi\)
0.639592 + 0.768715i \(0.279103\pi\)
\(224\) 5258.89 0.00700283
\(225\) −65842.8 297006.i −0.0867066 0.391119i
\(226\) −686097. −0.893541
\(227\) −372043. −0.479213 −0.239607 0.970870i \(-0.577018\pi\)
−0.239607 + 0.970870i \(0.577018\pi\)
\(228\) 209281. 260757.i 0.266620 0.332199i
\(229\) 354826.i 0.447122i −0.974690 0.223561i \(-0.928232\pi\)
0.974690 0.223561i \(-0.0717683\pi\)
\(230\) 321746.i 0.401045i
\(231\) 13164.0 16402.0i 0.0162315 0.0202239i
\(232\) 72161.4i 0.0880208i
\(233\) 1.25262e6 1.51158 0.755790 0.654814i \(-0.227253\pi\)
0.755790 + 0.654814i \(0.227253\pi\)
\(234\) −281013. + 62297.2i −0.335495 + 0.0743753i
\(235\) 585187.i 0.691234i
\(236\) 226937. + 362657.i 0.265232 + 0.423854i
\(237\) −649982. + 809855.i −0.751675 + 0.936562i
\(238\) 27419.6i 0.0313776i
\(239\) 168819.i 0.191174i −0.995421 0.0955868i \(-0.969527\pi\)
0.995421 0.0955868i \(-0.0304727\pi\)
\(240\) 134695. + 108105.i 0.150946 + 0.121148i
\(241\) 340564. 0.377708 0.188854 0.982005i \(-0.439523\pi\)
0.188854 + 0.982005i \(0.439523\pi\)
\(242\) 368147. 0.404094
\(243\) 218799. 894100.i 0.237700 0.971338i
\(244\) 812074.i 0.873215i
\(245\) 726250.i 0.772985i
\(246\) −80166.4 64340.7i −0.0844607 0.0677873i
\(247\) 396973.i 0.414017i
\(248\) 390449.i 0.403121i
\(249\) −514406. + 640933.i −0.525785 + 0.655110i
\(250\) 757716.i 0.766755i
\(251\) 44476.4i 0.0445600i −0.999752 0.0222800i \(-0.992907\pi\)
0.999752 0.0222800i \(-0.00709253\pi\)
\(252\) 4321.60 + 19494.1i 0.00428690 + 0.0193375i
\(253\) −488253. −0.479561
\(254\) −1.06211e6 −1.03296
\(255\) −563653. + 702293.i −0.542827 + 0.676344i
\(256\) 65536.0 0.0625000
\(257\) 485768.i 0.458771i −0.973336 0.229386i \(-0.926328\pi\)
0.973336 0.229386i \(-0.0736717\pi\)
\(258\) 76104.6 + 61080.8i 0.0711806 + 0.0571288i
\(259\) 35758.9i 0.0331234i
\(260\) 205057. 0.188123
\(261\) 267494. 59300.2i 0.243059 0.0538834i
\(262\) −94115.9 −0.0847051
\(263\) 1.65840e6i 1.47843i −0.673471 0.739214i \(-0.735197\pi\)
0.673471 0.739214i \(-0.264803\pi\)
\(264\) 164050. 204401.i 0.144866 0.180498i
\(265\) 554673. 0.485202
\(266\) −27538.3 −0.0238635
\(267\) −875720. + 1.09112e6i −0.751773 + 0.936684i
\(268\) 20892.3i 0.0177684i
\(269\) 548436. 0.462110 0.231055 0.972941i \(-0.425782\pi\)
0.231055 + 0.972941i \(0.425782\pi\)
\(270\) −290042. + 588134.i −0.242132 + 0.490983i
\(271\) −653560. −0.540583 −0.270292 0.962779i \(-0.587120\pi\)
−0.270292 + 0.962779i \(0.587120\pi\)
\(272\) 341702.i 0.280044i
\(273\) 18488.6 + 14838.7i 0.0150140 + 0.0120501i
\(274\) 930869.i 0.749053i
\(275\) 328887. 0.262250
\(276\) 290149. 361516.i 0.229271 0.285664i
\(277\) −1.01496e6 −0.794784 −0.397392 0.917649i \(-0.630085\pi\)
−0.397392 + 0.917649i \(0.630085\pi\)
\(278\) −1.26124e6 −0.978785
\(279\) −1.44735e6 + 320860.i −1.11317 + 0.246777i
\(280\) 14225.0i 0.0108432i
\(281\) 1.98324e6i 1.49834i −0.662378 0.749170i \(-0.730453\pi\)
0.662378 0.749170i \(-0.269547\pi\)
\(282\) −527719. + 657520.i −0.395166 + 0.492364i
\(283\) 2.06818e6i 1.53505i −0.641021 0.767523i \(-0.721489\pi\)
0.641021 0.767523i \(-0.278511\pi\)
\(284\) 281998.i 0.207468i
\(285\) −705332. 566093.i −0.514377 0.412834i
\(286\) 311177.i 0.224953i
\(287\) 8466.30i 0.00606721i
\(288\) 53855.6 + 242934.i 0.0382604 + 0.172587i
\(289\) −361767. −0.254791
\(290\) −195192. −0.136291
\(291\) 303782. + 243813.i 0.210295 + 0.168781i
\(292\) 262275.i 0.180012i
\(293\) 438652.i 0.298505i −0.988799 0.149252i \(-0.952313\pi\)
0.988799 0.149252i \(-0.0476866\pi\)
\(294\) −654929. + 816019.i −0.441902 + 0.550595i
\(295\) 980966. 613853.i 0.656295 0.410685i
\(296\) 445626.i 0.295625i
\(297\) 892499. + 440142.i 0.587106 + 0.289535i
\(298\) 1.55489e6 1.01428
\(299\) 550367.i 0.356020i
\(300\) −195444. + 243517.i −0.125378 + 0.156216i
\(301\) 8037.34i 0.00511324i
\(302\) 6289.90i 0.00396850i
\(303\) −1.15657e6 + 1.44104e6i −0.723708 + 0.901716i
\(304\) −343181. −0.212980
\(305\) −2.19661e6 −1.35208
\(306\) −1.26665e6 + 280801.i −0.773309 + 0.171434i
\(307\) 815525. 0.493846 0.246923 0.969035i \(-0.420581\pi\)
0.246923 + 0.969035i \(0.420581\pi\)
\(308\) −21586.6 −0.0129660
\(309\) 261375. + 209777.i 0.155728 + 0.124986i
\(310\) 1.05614e6 0.624192
\(311\) 1.29979e6i 0.762028i 0.924569 + 0.381014i \(0.124425\pi\)
−0.924569 + 0.381014i \(0.875575\pi\)
\(312\) 230404. + 184920.i 0.134000 + 0.107547i
\(313\) 1.44214e6i 0.832045i 0.909354 + 0.416023i \(0.136576\pi\)
−0.909354 + 0.416023i \(0.863424\pi\)
\(314\) 398363.i 0.228010i
\(315\) 52730.3 11689.7i 0.0299422 0.00663784i
\(316\) 1.06585e6 0.600451
\(317\) 167603.i 0.0936769i −0.998902 0.0468384i \(-0.985085\pi\)
0.998902 0.0468384i \(-0.0149146\pi\)
\(318\) 623235. + 500202.i 0.345608 + 0.277381i
\(319\) 296207.i 0.162974i
\(320\) 177271.i 0.0967749i
\(321\) −2.09184e6 1.67889e6i −1.13310 0.909412i
\(322\) −38179.4 −0.0205206
\(323\) 1.78933e6i 0.954301i
\(324\) −856270. + 399273.i −0.453156 + 0.211304i
\(325\) 370727.i 0.194691i
\(326\) −2.32285e6 −1.21054
\(327\) 2.67680e6 + 2.14837e6i 1.38435 + 1.11107i
\(328\) 105507.i 0.0541496i
\(329\) 69440.1 0.0353688
\(330\) −552892. 443745.i −0.279483 0.224310i
\(331\) 73742.6 0.0369955 0.0184977 0.999829i \(-0.494112\pi\)
0.0184977 + 0.999829i \(0.494112\pi\)
\(332\) 843529. 0.420005
\(333\) −1.65188e6 + 366203.i −0.816334 + 0.180972i
\(334\) 407067.i 0.199664i
\(335\) 56512.3 0.0275126
\(336\) 12828.0 15983.3i 0.00619886 0.00772357i
\(337\) 3.49548e6i 1.67661i −0.545202 0.838305i \(-0.683547\pi\)
0.545202 0.838305i \(-0.316453\pi\)
\(338\) −1.13441e6 −0.540104
\(339\) −1.67360e6 + 2.08525e6i −0.790956 + 0.985504i
\(340\) 924285. 0.433619
\(341\) 1.60271e6i 0.746394i
\(342\) −282017. 1.27213e6i −0.130380 0.588121i
\(343\) 172494. 0.0791658
\(344\) 100161.i 0.0456355i
\(345\) −977880. 784836.i −0.442321 0.355002i
\(346\) −256313. −0.115101
\(347\) 81574.5 0.0363689 0.0181845 0.999835i \(-0.494211\pi\)
0.0181845 + 0.999835i \(0.494211\pi\)
\(348\) −219320. 176024.i −0.0970799 0.0779153i
\(349\) 3.25809e6i 1.43186i −0.698173 0.715929i \(-0.746003\pi\)
0.698173 0.715929i \(-0.253997\pi\)
\(350\) 25717.6 0.0112218
\(351\) −496136. + 1.00604e6i −0.214948 + 0.435861i
\(352\) −269011. −0.115721
\(353\) 1.76544e6 0.754077 0.377039 0.926198i \(-0.376942\pi\)
0.377039 + 0.926198i \(0.376942\pi\)
\(354\) 1.65579e6 + 194901.i 0.702258 + 0.0826621i
\(355\) 762789. 0.321243
\(356\) 1.43602e6 0.600529
\(357\) 83336.3 + 66884.9i 0.0346070 + 0.0277752i
\(358\) −1.65015e6 −0.680482
\(359\) 2.73460e6i 1.11985i −0.828545 0.559923i \(-0.810831\pi\)
0.828545 0.559923i \(-0.189169\pi\)
\(360\) 657122. 145676.i 0.267233 0.0592424i
\(361\) −679020. −0.274230
\(362\) −148067. −0.0593864
\(363\) 898022. 1.11891e6i 0.357701 0.445684i
\(364\) 24332.7i 0.00962582i
\(365\) 709440. 0.278730
\(366\) −2.46813e6 1.98090e6i −0.963086 0.772963i
\(367\) 1.54107e6i 0.597252i 0.954370 + 0.298626i \(0.0965284\pi\)
−0.954370 + 0.298626i \(0.903472\pi\)
\(368\) −475790. −0.183145
\(369\) −391100. + 86702.4i −0.149528 + 0.0331486i
\(370\) 1.20539e6 0.457745
\(371\) 65819.3i 0.0248267i
\(372\) 1.18669e6 + 952425.i 0.444610 + 0.356840i
\(373\) 1.35221e6 0.503236 0.251618 0.967827i \(-0.419037\pi\)
0.251618 + 0.967827i \(0.419037\pi\)
\(374\) 1.40261e6i 0.518512i
\(375\) 2.30292e6 + 1.84830e6i 0.845670 + 0.678726i
\(376\) 865360. 0.315665
\(377\) −333889. −0.120990
\(378\) 69789.8 + 34417.3i 0.0251225 + 0.0123893i
\(379\) 856323. 0.306224 0.153112 0.988209i \(-0.451070\pi\)
0.153112 + 0.988209i \(0.451070\pi\)
\(380\) 928285.i 0.329779i
\(381\) −2.59081e6 + 3.22806e6i −0.914372 + 1.13928i
\(382\) 623771. 0.218709
\(383\) 3.33532e6i 1.16183i 0.813966 + 0.580913i \(0.197304\pi\)
−0.813966 + 0.580913i \(0.802696\pi\)
\(384\) 159862. 199183.i 0.0553245 0.0689325i
\(385\) 58390.4i 0.0200766i
\(386\) 2.08121e6 0.710963
\(387\) 371285. 82309.5i 0.126017 0.0279365i
\(388\) 399807.i 0.134825i
\(389\) 2.94144e6i 0.985565i 0.870152 + 0.492783i \(0.164020\pi\)
−0.870152 + 0.492783i \(0.835980\pi\)
\(390\) 500197. 623229.i 0.166525 0.207485i
\(391\) 2.48075e6i 0.820619i
\(392\) 1.07396e6 0.352999
\(393\) −229577. + 286046.i −0.0749804 + 0.0934230i
\(394\) 1.05914e6i 0.343727i
\(395\) 2.88306e6i 0.929737i
\(396\) −221065. 997190.i −0.0708407 0.319551i
\(397\) 1.44954e6i 0.461589i 0.973003 + 0.230794i \(0.0741324\pi\)
−0.973003 + 0.230794i \(0.925868\pi\)
\(398\) −319224. −0.101015
\(399\) −67174.3 + 83697.0i −0.0211238 + 0.0263195i
\(400\) 320492. 0.100154
\(401\) −9021.61 −0.00280171 −0.00140085 0.999999i \(-0.500446\pi\)
−0.00140085 + 0.999999i \(0.500446\pi\)
\(402\) 63497.6 + 50962.6i 0.0195971 + 0.0157285i
\(403\) 1.80660e6 0.554114
\(404\) 1.89655e6 0.578110
\(405\) 1.08001e6 + 2.31616e6i 0.327182 + 0.701667i
\(406\) 23162.2i 0.00697371i
\(407\) 1.82919e6i 0.547361i
\(408\) 1.03853e6 + 833516.i 0.308866 + 0.247893i
\(409\) 1.87499e6i 0.554232i 0.960836 + 0.277116i \(0.0893786\pi\)
−0.960836 + 0.277116i \(0.910621\pi\)
\(410\) 285389. 0.0838452
\(411\) 2.82918e6 + 2.27067e6i 0.826146 + 0.663056i
\(412\) 343994.i 0.0998409i
\(413\) −72841.7 116404.i −0.0210138 0.0335811i
\(414\) −390991. 1.76370e6i −0.112115 0.505735i
\(415\) 2.28170e6i 0.650336i
\(416\) 303234.i 0.0859100i
\(417\) −3.07656e6 + 3.83329e6i −0.866413 + 1.07952i
\(418\) 1.40868e6 0.394342
\(419\) 6.23979e6 1.73634 0.868171 0.496265i \(-0.165296\pi\)
0.868171 + 0.496265i \(0.165296\pi\)
\(420\) −43233.9 34699.1i −0.0119592 0.00959830i
\(421\) 3.47111e6i 0.954472i −0.878775 0.477236i \(-0.841639\pi\)
0.878775 0.477236i \(-0.158361\pi\)
\(422\) 461860.i 0.126249i
\(423\) 711128. + 3.20778e6i 0.193240 + 0.871674i
\(424\) 820237.i 0.221577i
\(425\) 1.67103e6i 0.448759i
\(426\) 857075. + 687880.i 0.228821 + 0.183649i
\(427\) 260657.i 0.0691830i
\(428\) 2.75307e6i 0.726453i
\(429\) −945757. 759055.i −0.248105 0.199127i
\(430\) −270930. −0.0706619
\(431\) −1.55792e6 −0.403973 −0.201986 0.979388i \(-0.564740\pi\)
−0.201986 + 0.979388i \(0.564740\pi\)
\(432\) 869718. + 428907.i 0.224217 + 0.110574i
\(433\) 4.97595e6 1.27543 0.637714 0.770273i \(-0.279880\pi\)
0.637714 + 0.770273i \(0.279880\pi\)
\(434\) 125325.i 0.0319385i
\(435\) −476134. + 593247.i −0.120644 + 0.150318i
\(436\) 3.52293e6i 0.887539i
\(437\) 2.49149e6 0.624102
\(438\) 797132. + 639770.i 0.198539 + 0.159345i
\(439\) 2.37372e6 0.587852 0.293926 0.955828i \(-0.405038\pi\)
0.293926 + 0.955828i \(0.405038\pi\)
\(440\) 727658.i 0.179183i
\(441\) 882550. + 3.98104e6i 0.216094 + 0.974765i
\(442\) 1.58105e6 0.384937
\(443\) −512210. −0.124005 −0.0620024 0.998076i \(-0.519749\pi\)
−0.0620024 + 0.998076i \(0.519749\pi\)
\(444\) 1.35439e6 + 1.08702e6i 0.326051 + 0.261685i
\(445\) 3.88434e6i 0.929859i
\(446\) −3.79975e6 −0.904520
\(447\) 3.79284e6 4.72575e6i 0.897833 1.11867i
\(448\) −21035.5 −0.00495175
\(449\) 2.22031e6i 0.519753i 0.965642 + 0.259876i \(0.0836819\pi\)
−0.965642 + 0.259876i \(0.916318\pi\)
\(450\) 263371. + 1.18803e6i 0.0613108 + 0.276563i
\(451\) 433082.i 0.100260i
\(452\) 2.74439e6 0.631829
\(453\) −19116.8 15343.0i −0.00437694 0.00351289i
\(454\) 1.48817e6 0.338855
\(455\) −65818.7 −0.0149046
\(456\) −837124. + 1.04303e6i −0.188529 + 0.234900i
\(457\) 784209.i 0.175647i −0.996136 0.0878237i \(-0.972009\pi\)
0.996136 0.0878237i \(-0.0279912\pi\)
\(458\) 1.41930e6i 0.316163i
\(459\) −2.23631e6 + 4.53468e6i −0.495450 + 1.00465i
\(460\) 1.28698e6i 0.283582i
\(461\) 4.67620e6i 1.02480i −0.858746 0.512402i \(-0.828756\pi\)
0.858746 0.512402i \(-0.171244\pi\)
\(462\) −52656.2 + 65607.8i −0.0114774 + 0.0143005i
\(463\) 2.00844e6i 0.435417i −0.976014 0.217709i \(-0.930142\pi\)
0.976014 0.217709i \(-0.0698583\pi\)
\(464\) 288646.i 0.0622401i
\(465\) 2.57625e6 3.20993e6i 0.552530 0.688434i
\(466\) −5.01050e6 −1.06885
\(467\) 8.02525e6 1.70281 0.851406 0.524508i \(-0.175751\pi\)
0.851406 + 0.524508i \(0.175751\pi\)
\(468\) 1.12405e6 249189.i 0.237231 0.0525913i
\(469\) 6705.93i 0.00140775i
\(470\) 2.34075e6i 0.488776i
\(471\) −1.21074e6 971728.i −0.251477 0.201833i
\(472\) −907750. 1.45063e6i −0.187547 0.299710i
\(473\) 411139.i 0.0844959i
\(474\) 2.59993e6 3.23942e6i 0.531515 0.662250i
\(475\) −1.67827e6 −0.341293
\(476\) 109679.i 0.0221873i
\(477\) 3.04052e6 674048.i 0.611859 0.135642i
\(478\) 675278.i 0.135180i
\(479\) 2.59531e6i 0.516834i 0.966033 + 0.258417i \(0.0832008\pi\)
−0.966033 + 0.258417i \(0.916799\pi\)
\(480\) −538778. 432418.i −0.106735 0.0856645i
\(481\) 2.06190e6 0.406354
\(482\) −1.36226e6 −0.267080
\(483\) −93131.2 + 116038.i −0.0181647 + 0.0226326i
\(484\) −1.47259e6 −0.285738
\(485\) −1.08145e6 −0.208763
\(486\) −875197. + 3.57640e6i −0.168080 + 0.686840i
\(487\) 751189. 0.143525 0.0717624 0.997422i \(-0.477138\pi\)
0.0717624 + 0.997422i \(0.477138\pi\)
\(488\) 3.24830e6i 0.617456i
\(489\) −5.66615e6 + 7.05983e6i −1.07156 + 1.33512i
\(490\) 2.90500e6i 0.546583i
\(491\) 1.04218e6i 0.195093i −0.995231 0.0975463i \(-0.968901\pi\)
0.995231 0.0975463i \(-0.0310994\pi\)
\(492\) 320666. + 257363.i 0.0597227 + 0.0479328i
\(493\) −1.50499e6 −0.278879
\(494\) 1.58789e6i 0.292754i
\(495\) −2.69734e6 + 597969.i −0.494792 + 0.109690i
\(496\) 1.56180e6i 0.285050i
\(497\) 90515.0i 0.0164373i
\(498\) 2.05762e6 2.56373e6i 0.371786 0.463233i
\(499\) −4.89287e6 −0.879655 −0.439827 0.898082i \(-0.644960\pi\)
−0.439827 + 0.898082i \(0.644960\pi\)
\(500\) 3.03087e6i 0.542178i
\(501\) −1.23719e6 992959.i −0.220213 0.176741i
\(502\) 177905.i 0.0315087i
\(503\) −4.85721e6 −0.855987 −0.427994 0.903782i \(-0.640779\pi\)
−0.427994 + 0.903782i \(0.640779\pi\)
\(504\) −17286.4 77976.2i −0.00303130 0.0136737i
\(505\) 5.13005e6i 0.895145i
\(506\) 1.95301e6 0.339101
\(507\) −2.76717e6 + 3.44780e6i −0.478096 + 0.595692i
\(508\) 4.24844e6 0.730416
\(509\) 6.13492e6 1.04958 0.524788 0.851233i \(-0.324144\pi\)
0.524788 + 0.851233i \(0.324144\pi\)
\(510\) 2.25461e6 2.80917e6i 0.383837 0.478248i
\(511\) 84184.4i 0.0142620i
\(512\) −262144. −0.0441942
\(513\) −4.55430e6 2.24598e6i −0.764062 0.376802i
\(514\) 1.94307e6i 0.324400i
\(515\) −930485. −0.154594
\(516\) −304418. 244323.i −0.0503323 0.0403962i
\(517\) −3.55211e6 −0.584467
\(518\) 143036.i 0.0234218i
\(519\) −625225. + 779009.i −0.101887 + 0.126947i
\(520\) −820229. −0.133023
\(521\) 8.88459e6i 1.43398i 0.697083 + 0.716990i \(0.254481\pi\)
−0.697083 + 0.716990i \(0.745519\pi\)
\(522\) −1.06997e6 + 237201.i −0.171869 + 0.0381013i
\(523\) −9.38714e6 −1.50065 −0.750325 0.661069i \(-0.770103\pi\)
−0.750325 + 0.661069i \(0.770103\pi\)
\(524\) 376463. 0.0598956
\(525\) 62733.1 78163.4i 0.00993342 0.0123767i
\(526\) 6.63360e6i 1.04541i
\(527\) 8.14315e6 1.27722
\(528\) −656199. + 817602.i −0.102436 + 0.127631i
\(529\) −2.98212e6 −0.463325
\(530\) −2.21869e6 −0.343090
\(531\) 4.63134e6 4.55700e6i 0.712804 0.701363i
\(532\) 110153. 0.0168740
\(533\) 488177. 0.0744319
\(534\) 3.50288e6 4.36447e6i 0.531584 0.662336i
\(535\) 7.44689e6 1.12484
\(536\) 83569.0i 0.0125642i
\(537\) −4.02523e6 + 5.01530e6i −0.602358 + 0.750517i
\(538\) −2.19374e6 −0.326761
\(539\) −4.40837e6 −0.653591
\(540\) 1.16017e6 2.35254e6i 0.171213 0.347178i
\(541\) 3.12504e6i 0.459052i 0.973303 + 0.229526i \(0.0737176\pi\)
−0.973303 + 0.229526i \(0.926282\pi\)
\(542\) 2.61424e6 0.382250
\(543\) −361180. + 450019.i −0.0525684 + 0.0654984i
\(544\) 1.36681e6i 0.198021i
\(545\) −9.52931e6 −1.37426
\(546\) −73954.3 59355.0i −0.0106165 0.00852070i
\(547\) −1.07410e6 −0.153489 −0.0767444 0.997051i \(-0.524453\pi\)
−0.0767444 + 0.997051i \(0.524453\pi\)
\(548\) 3.72348e6i 0.529660i
\(549\) −1.20410e7 + 2.66936e6i −1.70503 + 0.377986i
\(550\) −1.31555e6 −0.185439
\(551\) 1.51150e6i 0.212095i
\(552\) −1.16060e6 + 1.44606e6i −0.162119 + 0.201995i
\(553\) −342112. −0.0475725
\(554\) 4.05983e6 0.561997
\(555\) 2.94032e6 3.66354e6i 0.405193 0.504857i
\(556\) 5.04498e6 0.692105
\(557\) 5.89668e6i 0.805321i −0.915349 0.402661i \(-0.868085\pi\)
0.915349 0.402661i \(-0.131915\pi\)
\(558\) 5.78939e6 1.28344e6i 0.787132 0.174498i
\(559\) −463443. −0.0627287
\(560\) 56899.9i 0.00766728i
\(561\) −4.26295e6 3.42140e6i −0.571877 0.458983i
\(562\) 7.93298e6i 1.05949i
\(563\) 8.58589e6 1.14160 0.570800 0.821089i \(-0.306633\pi\)
0.570800 + 0.821089i \(0.306633\pi\)
\(564\) 2.11088e6 2.63008e6i 0.279425 0.348154i
\(565\) 7.42341e6i 0.978323i
\(566\) 8.27271e6i 1.08544i
\(567\) 274843. 128157.i 0.0359027 0.0167412i
\(568\) 1.12799e6i 0.146702i
\(569\) −1.86963e6 −0.242089 −0.121045 0.992647i \(-0.538624\pi\)
−0.121045 + 0.992647i \(0.538624\pi\)
\(570\) 2.82133e6 + 2.26437e6i 0.363720 + 0.291918i
\(571\) 1.46089e6i 0.187511i −0.995595 0.0937555i \(-0.970113\pi\)
0.995595 0.0937555i \(-0.0298872\pi\)
\(572\) 1.24471e6i 0.159066i
\(573\) 1.52157e6 1.89582e6i 0.193600 0.241219i
\(574\) 33865.2i 0.00429017i
\(575\) −2.32677e6 −0.293483
\(576\) −215423. 971736.i −0.0270542 0.122037i
\(577\) 4.34585e6 0.543419 0.271709 0.962379i \(-0.412411\pi\)
0.271709 + 0.962379i \(0.412411\pi\)
\(578\) 1.44707e6 0.180165
\(579\) 5.07670e6 6.32539e6i 0.629339 0.784135i
\(580\) 780770. 0.0963725
\(581\) −270753. −0.0332762
\(582\) −1.21513e6 975250.i −0.148701 0.119346i
\(583\) 3.36689e6i 0.410258i
\(584\) 1.04910e6i 0.127287i
\(585\) −674041. 3.04049e6i −0.0814323 0.367328i
\(586\) 1.75461e6i 0.211075i
\(587\) −1.24558e7 −1.49203 −0.746013 0.665931i \(-0.768034\pi\)
−0.746013 + 0.665931i \(0.768034\pi\)
\(588\) 2.61972e6 3.26408e6i 0.312472 0.389329i
\(589\) 8.17840e6i 0.971359i
\(590\) −3.92386e6 + 2.45541e6i −0.464070 + 0.290398i
\(591\) −3.21904e6 2.58357e6i −0.379103 0.304264i
\(592\) 1.78250e6i 0.209038i
\(593\) 5.16014e6i 0.602594i 0.953530 + 0.301297i \(0.0974196\pi\)
−0.953530 + 0.301297i \(0.902580\pi\)
\(594\) −3.57000e6 1.76057e6i −0.415147 0.204732i
\(595\) −296674. −0.0343548
\(596\) −6.21954e6 −0.717204
\(597\) −778684. + 970214.i −0.0894181 + 0.111412i
\(598\) 2.20147e6i 0.251744i
\(599\) 1.08002e6i 0.122989i −0.998107 0.0614943i \(-0.980413\pi\)
0.998107 0.0614943i \(-0.0195866\pi\)
\(600\) 781778. 974069.i 0.0886554 0.110462i
\(601\) 5.28734e6i 0.597105i 0.954393 + 0.298553i \(0.0965039\pi\)
−0.954393 + 0.298553i \(0.903496\pi\)
\(602\) 32149.4i 0.00361561i
\(603\) 309780. 68674.7i 0.0346945 0.00769136i
\(604\) 25159.6i 0.00280615i
\(605\) 3.98326e6i 0.442436i
\(606\) 4.62626e6 5.76417e6i 0.511739 0.637610i
\(607\) −5.30029e6 −0.583886 −0.291943 0.956436i \(-0.594302\pi\)
−0.291943 + 0.956436i \(0.594302\pi\)
\(608\) 1.37273e6 0.150600
\(609\) 70396.5 + 56499.5i 0.00769145 + 0.00617308i
\(610\) 8.78645e6 0.956068
\(611\) 4.00400e6i 0.433901i
\(612\) 5.06660e6 1.12321e6i 0.546812 0.121222i
\(613\) 5.94190e6i 0.638667i −0.947642 0.319333i \(-0.896541\pi\)
0.947642 0.319333i \(-0.103459\pi\)
\(614\) −3.26210e6 −0.349202
\(615\) 696152. 867382.i 0.0742192 0.0924746i
\(616\) 86346.2 0.00916836
\(617\) 3.58168e6i 0.378768i 0.981903 + 0.189384i \(0.0606491\pi\)
−0.981903 + 0.189384i \(0.939351\pi\)
\(618\) −1.04550e6 839107.i −0.110117 0.0883784i
\(619\) 3.86115e6 0.405032 0.202516 0.979279i \(-0.435088\pi\)
0.202516 + 0.979279i \(0.435088\pi\)
\(620\) −4.22457e6 −0.441371
\(621\) −6.31413e6 3.11386e6i −0.657029 0.324018i
\(622\) 5.19914e6i 0.538835i
\(623\) −460928. −0.0475787
\(624\) −921615. 739679.i −0.0947520 0.0760470i
\(625\) −4.28606e6 −0.438892
\(626\) 5.76856e6i 0.588345i
\(627\) 3.43621e6 4.28140e6i 0.349068 0.434927i
\(628\) 1.59345e6i 0.161228i
\(629\) 9.29391e6 0.936638
\(630\) −210921. + 46758.8i −0.0211723 + 0.00469366i
\(631\) −9.39799e6 −0.939640 −0.469820 0.882762i \(-0.655681\pi\)
−0.469820 + 0.882762i \(0.655681\pi\)
\(632\) −4.26339e6 −0.424583
\(633\) −1.40373e6 1.12662e6i −0.139243 0.111755i
\(634\) 670410.i 0.0662396i
\(635\) 1.14918e7i 1.13098i
\(636\) −2.49294e6 2.00081e6i −0.244382 0.196138i
\(637\) 4.96919e6i 0.485218i
\(638\) 1.18483e6i 0.115240i
\(639\) 4.18134e6 926953.i 0.405101 0.0898061i
\(640\) 709084.i 0.0684302i
\(641\) 1.45277e7i 1.39653i −0.715837 0.698267i \(-0.753955\pi\)
0.715837 0.698267i \(-0.246045\pi\)
\(642\) 8.36738e6 + 6.71557e6i 0.801220 + 0.643051i
\(643\) 8.06246e6 0.769024 0.384512 0.923120i \(-0.374370\pi\)
0.384512 + 0.923120i \(0.374370\pi\)
\(644\) 152718. 0.0145102
\(645\) −660880. + 823434.i −0.0625494 + 0.0779345i
\(646\) 7.15734e6i 0.674793i
\(647\) 1.30624e7i 1.22677i 0.789784 + 0.613385i \(0.210192\pi\)
−0.789784 + 0.613385i \(0.789808\pi\)
\(648\) 3.42508e6 1.59709e6i 0.320430 0.149414i
\(649\) 3.72611e6 + 5.95450e6i 0.347252 + 0.554924i
\(650\) 1.48291e6i 0.137667i
\(651\) −380900. 305706.i −0.0352256 0.0282717i
\(652\) 9.29141e6 0.855978
\(653\) 8.12008e6i 0.745208i 0.927990 + 0.372604i \(0.121535\pi\)
−0.927990 + 0.372604i \(0.878465\pi\)
\(654\) −1.07072e7 8.59349e6i −0.978885 0.785643i
\(655\) 1.01831e6i 0.0927422i
\(656\) 422027.i 0.0382896i
\(657\) 3.88889e6 862122.i 0.351490 0.0779212i
\(658\) −277761. −0.0250095
\(659\) −1.16495e7 −1.04495 −0.522475 0.852655i \(-0.674991\pi\)
−0.522475 + 0.852655i \(0.674991\pi\)
\(660\) 2.21157e6 + 1.77498e6i 0.197624 + 0.158611i
\(661\) −4.25595e6 −0.378873 −0.189436 0.981893i \(-0.560666\pi\)
−0.189436 + 0.981893i \(0.560666\pi\)
\(662\) −294971. −0.0261598
\(663\) 3.85666e6 4.80527e6i 0.340743 0.424555i
\(664\) −3.37412e6 −0.296989
\(665\) 297958.i 0.0261277i
\(666\) 6.60752e6 1.46481e6i 0.577236 0.127966i
\(667\) 2.09556e6i 0.182384i
\(668\) 1.62827e6i 0.141184i
\(669\) −9.26875e6 + 1.15485e7i −0.800674 + 0.997613i
\(670\) −226049. −0.0194543
\(671\) 1.33335e7i 1.14324i
\(672\) −51312.1 + 63933.1i −0.00438325 + 0.00546139i
\(673\) 1.68599e7i 1.43488i 0.696619 + 0.717441i \(0.254687\pi\)
−0.696619 + 0.717441i \(0.745313\pi\)
\(674\) 1.39819e7i 1.18554i
\(675\) 4.25320e6 + 2.09749e6i 0.359299 + 0.177191i
\(676\) 4.53763e6 0.381911
\(677\) 18963.6i 0.00159019i −1.00000 0.000795094i \(-0.999747\pi\)
1.00000 0.000795094i \(-0.000253086\pi\)
\(678\) 6.69440e6 8.34099e6i 0.559290 0.696857i
\(679\) 128329.i 0.0106819i
\(680\) −3.69714e6 −0.306615
\(681\) 3.63011e6 4.52299e6i 0.299952 0.373730i
\(682\) 6.41083e6i 0.527781i
\(683\) 7.53196e6 0.617812 0.308906 0.951093i \(-0.400037\pi\)
0.308906 + 0.951093i \(0.400037\pi\)
\(684\) 1.12807e6 + 5.08853e6i 0.0921923 + 0.415864i
\(685\) −1.00718e7 −0.820125
\(686\) −689975. −0.0559787
\(687\) 4.31368e6 + 3.46211e6i 0.348703 + 0.279865i
\(688\) 400644.i 0.0322692i
\(689\) −3.79522e6 −0.304571
\(690\) 3.91152e6 + 3.13935e6i 0.312768 + 0.251025i
\(691\) 2.00757e7i 1.59947i 0.600353 + 0.799735i \(0.295027\pi\)
−0.600353 + 0.799735i \(0.704973\pi\)
\(692\) 1.02525e6 0.0813888
\(693\) 70956.9 + 320075.i 0.00561257 + 0.0253174i
\(694\) −326298. −0.0257167
\(695\) 1.36464e7i 1.07166i
\(696\) 877278. + 704095.i 0.0686459 + 0.0550945i
\(697\) 2.20043e6 0.171564
\(698\) 1.30324e7i 1.01248i
\(699\) −1.22221e7 + 1.52284e7i −0.946137 + 1.17885i
\(700\) −102871. −0.00793498
\(701\) 2.02660e6 0.155766 0.0778832 0.996962i \(-0.475184\pi\)
0.0778832 + 0.996962i \(0.475184\pi\)
\(702\) 1.98454e6 4.02416e6i 0.151991 0.308200i
\(703\) 9.33413e6i 0.712337i
\(704\) 1.07604e6 0.0818273
\(705\) −7.11422e6 5.70980e6i −0.539081 0.432661i
\(706\) −7.06175e6 −0.533213
\(707\) −608748. −0.0458025
\(708\) −6.62316e6 779605.i −0.496572 0.0584510i
\(709\) −1.86937e7 −1.39662 −0.698311 0.715794i \(-0.746065\pi\)
−0.698311 + 0.715794i \(0.746065\pi\)
\(710\) −3.05116e6 −0.227153
\(711\) −3.50353e6 1.58039e7i −0.259916 1.17244i
\(712\) −5.74406e6 −0.424638
\(713\) 1.13386e7i 0.835288i
\(714\) −333345. 267539.i −0.0244708 0.0196400i
\(715\) 3.36686e6 0.246297
\(716\) 6.60061e6 0.481173
\(717\) 2.05237e6 + 1.64721e6i 0.149093 + 0.119660i
\(718\) 1.09384e7i 0.791850i
\(719\) 2.52490e7 1.82147 0.910736 0.412990i \(-0.135516\pi\)
0.910736 + 0.412990i \(0.135516\pi\)
\(720\) −2.62849e6 + 582706.i −0.188962 + 0.0418907i
\(721\) 110414.i 0.00791019i
\(722\) 2.71608e6 0.193910
\(723\) −3.32296e6 + 4.14029e6i −0.236417 + 0.294568i
\(724\) 592268. 0.0419925
\(725\) 1.41157e6i 0.0997373i
\(726\) −3.59209e6 + 4.47562e6i −0.252933 + 0.315146i
\(727\) −3.88302e6 −0.272479 −0.136240 0.990676i \(-0.543502\pi\)
−0.136240 + 0.990676i \(0.543502\pi\)
\(728\) 97331.0i 0.00680648i
\(729\) 8.73486e6 + 1.13839e7i 0.608747 + 0.793364i
\(730\) −2.83776e6 −0.197092
\(731\) −2.08894e6 −0.144588
\(732\) 9.87252e6 + 7.92358e6i 0.681005 + 0.546568i
\(733\) −1.94836e7 −1.33939 −0.669697 0.742635i \(-0.733576\pi\)
−0.669697 + 0.742635i \(0.733576\pi\)
\(734\) 6.16429e6i 0.422321i
\(735\) −8.82914e6 7.08618e6i −0.602837 0.483831i
\(736\) 1.90316e6 0.129503
\(737\) 343032.i 0.0232630i
\(738\) 1.56440e6 346810.i 0.105732 0.0234396i
\(739\) 1.83794e7i 1.23800i 0.785392 + 0.618998i \(0.212461\pi\)
−0.785392 + 0.618998i \(0.787539\pi\)
\(740\) −4.82157e6 −0.323675
\(741\) 4.82607e6 + 3.87335e6i 0.322885 + 0.259144i
\(742\) 263277.i 0.0175551i
\(743\) 1.41912e7i 0.943077i −0.881845 0.471539i \(-0.843699\pi\)
0.881845 0.471539i \(-0.156301\pi\)
\(744\) −4.74676e6 3.80970e6i −0.314387 0.252324i
\(745\) 1.68235e7i 1.11052i
\(746\) −5.40884e6 −0.355842
\(747\) −2.77275e6 1.25074e7i −0.181807 0.820100i
\(748\) 5.61045e6i 0.366643i
\(749\) 883672.i 0.0575554i
\(750\) −9.21169e6 7.39320e6i −0.597979 0.479932i
\(751\) 3.45413e6i 0.223480i 0.993737 + 0.111740i \(0.0356424\pi\)
−0.993737 + 0.111740i \(0.964358\pi\)
\(752\) −3.46144e6 −0.223209
\(753\) 540707. + 433966.i 0.0347516 + 0.0278912i
\(754\) 1.33556e6 0.0855528
\(755\) 68055.2 0.00434504
\(756\) −279159. 137669.i −0.0177643 0.00876057i
\(757\) 1.30006e7 0.824564 0.412282 0.911056i \(-0.364732\pi\)
0.412282 + 0.911056i \(0.364732\pi\)
\(758\) −3.42529e6 −0.216533
\(759\) 4.76399e6 5.93577e6i 0.300169 0.374001i
\(760\) 3.71314e6i 0.233189i
\(761\) 7.83517e6i 0.490441i −0.969467 0.245221i \(-0.921140\pi\)
0.969467 0.245221i \(-0.0788604\pi\)
\(762\) 1.03632e7 1.29122e7i 0.646559 0.805591i
\(763\) 1.13078e6i 0.0703179i
\(764\) −2.49508e6 −0.154651
\(765\) −3.03821e6 1.37049e7i −0.187700 0.846683i
\(766\) 1.33413e7i 0.821535i
\(767\) −6.71202e6 + 4.20014e6i −0.411969 + 0.257795i
\(768\) −639449. + 796732.i −0.0391204 + 0.0487427i
\(769\) 1.56964e7i 0.957161i −0.878044 0.478581i \(-0.841151\pi\)
0.878044 0.478581i \(-0.158849\pi\)
\(770\) 233562.i 0.0141963i
\(771\) 5.90556e6 + 4.73975e6i 0.357788 + 0.287157i
\(772\) −8.32483e6 −0.502727
\(773\) −2.41197e7 −1.45186 −0.725929 0.687770i \(-0.758590\pi\)
−0.725929 + 0.687770i \(0.758590\pi\)
\(774\) −1.48514e6 + 329238.i −0.0891076 + 0.0197541i
\(775\) 7.63769e6i 0.456781i
\(776\) 1.59923e6i 0.0953357i
\(777\) −434727. 348907.i −0.0258323 0.0207328i
\(778\) 1.17657e7i 0.696900i
\(779\) 2.20996e6i 0.130479i
\(780\) −2.00079e6 + 2.49292e6i −0.117751 + 0.146714i
\(781\) 4.63016e6i 0.271624i
\(782\) 9.92301e6i 0.580265i
\(783\) −1.88907e6 + 3.83057e6i −0.110114 + 0.223285i
\(784\) −4.29584e6 −0.249608
\(785\) 4.31019e6 0.249645
\(786\) 918309. 1.14418e6i 0.0530191 0.0660600i
\(787\) −1.37090e7 −0.788985 −0.394492 0.918899i \(-0.629080\pi\)
−0.394492 + 0.918899i \(0.629080\pi\)
\(788\) 4.23657e6i 0.243052i
\(789\) 2.01615e7 + 1.61814e7i 1.15300 + 0.925386i
\(790\) 1.15322e7i 0.657424i
\(791\) −880885. −0.0500585
\(792\) 884262. + 3.98876e6i 0.0500920 + 0.225957i
\(793\) 1.50298e7 0.848731
\(794\) 5.79817e6i 0.326392i
\(795\) −5.41207e6 + 6.74325e6i −0.303700 + 0.378401i
\(796\) 1.27689e6 0.0714286
\(797\) −1.32372e7 −0.738157 −0.369079 0.929398i \(-0.620327\pi\)
−0.369079 + 0.929398i \(0.620327\pi\)
\(798\) 268697. 334788.i 0.0149368 0.0186107i
\(799\) 1.80478e7i 1.00013i
\(800\) −1.28197e6 −0.0708194
\(801\) −4.72031e6 2.12925e7i −0.259950 1.17259i
\(802\) 36086.4 0.00198111
\(803\) 4.30633e6i 0.235678i
\(804\) −253991. 203850.i −0.0138573 0.0111217i
\(805\) 413092.i 0.0224676i
\(806\) −7.22640e6 −0.391818
\(807\) −5.35121e6 + 6.66743e6i −0.289247 + 0.360392i
\(808\) −7.58620e6 −0.408786
\(809\) −2.44918e7 −1.31568 −0.657840 0.753158i \(-0.728530\pi\)
−0.657840 + 0.753158i \(0.728530\pi\)
\(810\) −4.32004e6 9.26464e6i −0.231353 0.496153i
\(811\) 1.54861e7i 0.826779i 0.910554 + 0.413389i \(0.135655\pi\)
−0.910554 + 0.413389i \(0.864345\pi\)
\(812\) 92648.6i 0.00493116i
\(813\) 6.37693e6 7.94544e6i 0.338365 0.421591i
\(814\) 7.31678e6i 0.387043i
\(815\) 2.51327e7i 1.32540i
\(816\) −4.15413e6 3.33406e6i −0.218401 0.175287i
\(817\) 2.09798e6i 0.109963i
\(818\) 7.49998e6i 0.391901i
\(819\) −360794. + 79983.9i −0.0187953 + 0.00416670i
\(820\) −1.14156e6 −0.0592875
\(821\) −2.89142e7 −1.49711 −0.748554 0.663073i \(-0.769252\pi\)
−0.748554 + 0.663073i \(0.769252\pi\)
\(822\) −1.13167e7 9.08269e6i −0.584173 0.468851i
\(823\) 1.88475e7i 0.969961i 0.874525 + 0.484980i \(0.161173\pi\)
−0.874525 + 0.484980i \(0.838827\pi\)
\(824\) 1.37598e6i 0.0705982i
\(825\) −3.20902e6 + 3.99834e6i −0.164149 + 0.204524i
\(826\) 291367. + 465618.i 0.0148590 + 0.0237454i
\(827\) 1.33149e7i 0.676979i 0.940970 + 0.338490i \(0.109916\pi\)
−0.940970 + 0.338490i \(0.890084\pi\)
\(828\) 1.56396e6 + 7.05478e6i 0.0792776 + 0.357608i
\(829\) −3.82902e7 −1.93509 −0.967545 0.252700i \(-0.918681\pi\)
−0.967545 + 0.252700i \(0.918681\pi\)
\(830\) 9.12679e6i 0.459857i
\(831\) 9.90317e6 1.23390e7i 0.497476 0.619838i
\(832\) 1.21293e6i 0.0607476i
\(833\) 2.23984e7i 1.11842i
\(834\) 1.23062e7 1.53332e7i 0.612647 0.763337i
\(835\) 4.40437e6 0.218609
\(836\) −5.63473e6 −0.278842
\(837\) 1.02213e7 2.07264e7i 0.504306 1.02261i
\(838\) −2.49592e7 −1.22778
\(839\) −3.15083e7 −1.54532 −0.772662 0.634818i \(-0.781075\pi\)
−0.772662 + 0.634818i \(0.781075\pi\)
\(840\) 172935. + 138796.i 0.00845641 + 0.00678703i
\(841\) 1.92398e7 0.938019
\(842\) 1.38844e7i 0.674914i
\(843\) 2.41106e7 + 1.93509e7i 1.16853 + 0.937850i
\(844\) 1.84744e6i 0.0892717i
\(845\) 1.22740e7i 0.591351i
\(846\) −2.84451e6 1.28311e7i −0.136641 0.616367i
\(847\) 472666. 0.0226384
\(848\) 3.28095e6i 0.156679i
\(849\) 2.51432e7 + 2.01797e7i 1.19716 + 0.960825i
\(850\) 6.68414e6i 0.317320i
\(851\) 1.29409e7i 0.612550i
\(852\) −3.42830e6 2.75152e6i −0.161801 0.129859i
\(853\) −4.06416e6 −0.191248 −0.0956242 0.995418i \(-0.530485\pi\)
−0.0956242 + 0.995418i \(0.530485\pi\)
\(854\) 1.04263e6i 0.0489198i
\(855\) 1.37642e7 3.05136e6i 0.643924 0.142750i
\(856\) 1.10123e7i 0.513680i
\(857\) 8.69830e6 0.404559 0.202280 0.979328i \(-0.435165\pi\)
0.202280 + 0.979328i \(0.435165\pi\)
\(858\) 3.78303e6 + 3.03622e6i 0.175437 + 0.140804i
\(859\) 1.70914e7i 0.790303i 0.918616 + 0.395151i \(0.129308\pi\)
−0.918616 + 0.395151i \(0.870692\pi\)
\(860\) 1.08372e6 0.0499655
\(861\) −102926. 82607.6i −0.00473171 0.00379762i
\(862\) 6.23168e6 0.285652
\(863\) 1.68836e7 0.771682 0.385841 0.922565i \(-0.373911\pi\)
0.385841 + 0.922565i \(0.373911\pi\)
\(864\) −3.47887e6 1.71563e6i −0.158545 0.0781878i
\(865\) 2.77324e6i 0.126022i
\(866\) −1.99038e7 −0.901864
\(867\) 3.52984e6 4.39806e6i 0.159480 0.198707i
\(868\) 501301.i 0.0225839i
\(869\) 1.75003e7 0.786132
\(870\) 1.90454e6 2.37299e6i 0.0853082 0.106291i
\(871\) −386672. −0.0172702
\(872\) 1.40917e7i 0.627585i
\(873\) −5.92814e6 + 1.31420e6i −0.263259 + 0.0583614i
\(874\) −9.96595e6 −0.441306
\(875\) 972838.i 0.0429557i
\(876\) −3.18853e6 2.55908e6i −0.140388 0.112674i
\(877\) 920002. 0.0403915 0.0201957 0.999796i \(-0.493571\pi\)
0.0201957 + 0.999796i \(0.493571\pi\)
\(878\) −9.49487e6 −0.415674
\(879\) 5.33276e6 + 4.28002e6i 0.232798 + 0.186842i
\(880\) 2.91063e6i 0.126701i
\(881\) 6.50122e6 0.282199 0.141099 0.989995i \(-0.454936\pi\)
0.141099 + 0.989995i \(0.454936\pi\)
\(882\) −3.53020e6 1.59242e7i −0.152802 0.689263i
\(883\) 3.31385e7 1.43031 0.715156 0.698965i \(-0.246356\pi\)
0.715156 + 0.698965i \(0.246356\pi\)
\(884\) −6.32420e6 −0.272192
\(885\) −2.10879e6 + 1.79153e7i −0.0905054 + 0.768891i
\(886\) 2.04884e6 0.0876846
\(887\) 4.39283e7 1.87472 0.937358 0.348369i \(-0.113264\pi\)
0.937358 + 0.348369i \(0.113264\pi\)
\(888\) −5.41755e6 4.34807e6i −0.230553 0.185039i
\(889\) −1.36365e6 −0.0578694
\(890\) 1.55374e7i 0.657509i
\(891\) −1.40592e7 + 6.55570e6i −0.593289 + 0.276646i
\(892\) 1.51990e7 0.639592
\(893\) 1.81259e7 0.760627
\(894\) −1.51714e7 + 1.89030e7i −0.634864 + 0.791019i
\(895\) 1.78543e7i 0.745048i
\(896\) 84142.2 0.00350142
\(897\) 6.69091e6 + 5.37005e6i 0.277654 + 0.222842i
\(898\) 8.88122e6i 0.367521i
\(899\) 6.87875e6 0.283864
\(900\) −1.05349e6 4.75210e6i −0.0433533 0.195560i
\(901\) −1.71067e7 −0.702029
\(902\) 1.73233e6i 0.0708946i
\(903\) 97711.3 + 78422.1i 0.00398773 + 0.00320051i
\(904\) −1.09775e7 −0.446770
\(905\) 1.60205e6i 0.0650211i
\(906\) 76467.3 + 61371.9i 0.00309496 + 0.00248399i
\(907\) −1.96151e6 −0.0791723 −0.0395862 0.999216i \(-0.512604\pi\)
−0.0395862 + 0.999216i \(0.512604\pi\)
\(908\) −5.95269e6 −0.239607
\(909\) −6.23412e6 2.81211e7i −0.250245 1.12881i
\(910\) 263275. 0.0105391
\(911\) 3.45674e7i 1.37997i −0.723821 0.689987i \(-0.757616\pi\)
0.723821 0.689987i \(-0.242384\pi\)
\(912\) 3.34849e6 4.17211e6i 0.133310 0.166100i
\(913\) 1.38500e7 0.549886
\(914\) 3.13684e6i 0.124201i
\(915\) 2.14328e7 2.67046e7i 0.846305 1.05447i
\(916\) 5.67721e6i 0.223561i
\(917\) −120836. −0.00474540
\(918\) 8.94522e6 1.81387e7i 0.350336 0.710395i
\(919\) 2.45944e7i 0.960612i −0.877101 0.480306i \(-0.840526\pi\)
0.877101 0.480306i \(-0.159474\pi\)
\(920\) 5.14794e6i 0.200523i
\(921\) −7.95725e6 + 9.91447e6i −0.309111 + 0.385142i
\(922\) 1.87048e7i 0.724646i
\(923\) −5.21920e6 −0.201651
\(924\) 210625. 262431.i 0.00811577 0.0101120i
\(925\) 8.71701e6i 0.334976i
\(926\) 8.03375e6i 0.307887i
\(927\) −5.10058e6 + 1.13074e6i −0.194949 + 0.0432179i
\(928\) 1.15458e6i 0.0440104i
\(929\) 2.25317e7 0.856552 0.428276 0.903648i \(-0.359121\pi\)
0.428276 + 0.903648i \(0.359121\pi\)
\(930\) −1.03050e7 + 1.28397e7i −0.390698 + 0.486797i
\(931\) 2.24953e7 0.850585
\(932\) 2.00420e7 0.755790
\(933\) −1.58017e7 1.26823e7i −0.594292 0.476973i
\(934\) −3.21010e7 −1.20407
\(935\) 1.51759e7 0.567710
\(936\) −4.49620e6 + 996755.i −0.167747 + 0.0371877i
\(937\) 1.16192e7i 0.432344i 0.976355 + 0.216172i \(0.0693571\pi\)
−0.976355 + 0.216172i \(0.930643\pi\)
\(938\) 26823.7i 0.000995433i
\(939\) −1.75323e7 1.40713e7i −0.648897 0.520798i
\(940\) 9.36299e6i 0.345617i
\(941\) −2.31486e6 −0.0852218 −0.0426109 0.999092i \(-0.513568\pi\)
−0.0426109 + 0.999092i \(0.513568\pi\)
\(942\) 4.84296e6 + 3.88691e6i 0.177821 + 0.142718i
\(943\) 3.06390e6i 0.112201i
\(944\) 3.63100e6 + 5.80251e6i 0.132616 + 0.211927i
\(945\) −372387. + 755110.i −0.0135649 + 0.0275062i
\(946\) 1.64455e6i 0.0597476i
\(947\) 5.80247e6i 0.210251i 0.994459 + 0.105125i \(0.0335244\pi\)
−0.994459 + 0.105125i \(0.966476\pi\)
\(948\) −1.03997e7 + 1.29577e7i −0.375838 + 0.468281i
\(949\) −4.85417e6 −0.174964
\(950\) 6.71307e6 0.241330
\(951\) 2.03757e6 + 1.63533e6i 0.0730570 + 0.0586348i
\(952\) 438714.i 0.0156888i
\(953\) 8.74975e6i 0.312078i 0.987751 + 0.156039i \(0.0498726\pi\)
−0.987751 + 0.156039i \(0.950127\pi\)
\(954\) −1.21621e7 + 2.69619e6i −0.432650 + 0.0959135i
\(955\) 6.74906e6i 0.239461i
\(956\) 2.70111e6i 0.0955868i
\(957\) −3.60103e6 2.89015e6i −0.127101 0.102010i
\(958\) 1.03813e7i 0.365457i
\(959\) 1.19515e6i 0.0419639i
\(960\) 2.15511e6 + 1.72967e6i 0.0754731 + 0.0605739i
\(961\) −8.59024e6 −0.300052
\(962\) −8.24760e6 −0.287336
\(963\) 4.08212e7 9.04958e6i 1.41847 0.314458i
\(964\) 5.44903e6 0.188854
\(965\) 2.25182e7i 0.778421i
\(966\) 372525. 464153.i 0.0128444 0.0160036i
\(967\) 94538.9i 0.00325121i 0.999999 + 0.00162560i \(0.000517446\pi\)
−0.999999 + 0.00162560i \(0.999483\pi\)
\(968\) 5.89035e6 0.202047
\(969\) 2.17532e7 + 1.74589e7i 0.744243 + 0.597322i
\(970\) 4.32582e6 0.147618
\(971\) 6.08747e6i 0.207200i 0.994619 + 0.103600i \(0.0330361\pi\)
−0.994619 + 0.103600i \(0.966964\pi\)
\(972\) 3.50079e6 1.43056e7i 0.118850 0.485669i
\(973\) −1.61932e6 −0.0548341
\(974\) −3.00476e6 −0.101487
\(975\) −4.50699e6 3.61727e6i −0.151836 0.121862i
\(976\) 1.29932e7i 0.436607i
\(977\) 5.01560e7 1.68107 0.840537 0.541754i \(-0.182240\pi\)
0.840537 + 0.541754i \(0.182240\pi\)
\(978\) 2.26646e7 2.82393e7i 0.757706 0.944076i
\(979\) 2.35781e7 0.786234
\(980\) 1.16200e7i 0.386492i
\(981\) −5.22363e7 + 1.15802e7i −1.73300 + 0.384187i
\(982\) 4.16874e6i 0.137951i
\(983\) 4.76773e7 1.57372 0.786861 0.617131i \(-0.211705\pi\)
0.786861 + 0.617131i \(0.211705\pi\)
\(984\) −1.28266e6 1.02945e6i −0.0422303 0.0338936i
\(985\) 1.14597e7 0.376341
\(986\) 6.01995e6 0.197197
\(987\) −677542. + 844195.i −0.0221383 + 0.0275835i
\(988\) 6.35157e6i 0.207009i
\(989\) 2.90867e6i 0.0945591i
\(990\) 1.07894e7 2.39188e6i 0.349871 0.0775623i
\(991\) 2.87525e7i 0.930019i 0.885306 + 0.465010i \(0.153949\pi\)
−0.885306 + 0.465010i \(0.846051\pi\)
\(992\) 6.24719e6i 0.201560i
\(993\) −719523. + 896501.i −0.0231564 + 0.0288521i
\(994\) 362060.i 0.0116229i
\(995\) 3.45393e6i 0.110600i
\(996\) −8.23050e6 + 1.02549e7i −0.262892 + 0.327555i
\(997\) 171824. 0.00547452 0.00273726 0.999996i \(-0.499129\pi\)
0.00273726 + 0.999996i \(0.499129\pi\)
\(998\) 1.95715e7 0.622010
\(999\) 1.16658e7 2.36553e7i 0.369828 0.749920i
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 354.6.c.a.353.16 yes 50
3.2 odd 2 354.6.c.b.353.15 yes 50
59.58 odd 2 354.6.c.b.353.16 yes 50
177.176 even 2 inner 354.6.c.a.353.15 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
354.6.c.a.353.15 50 177.176 even 2 inner
354.6.c.a.353.16 yes 50 1.1 even 1 trivial
354.6.c.b.353.15 yes 50 3.2 odd 2
354.6.c.b.353.16 yes 50 59.58 odd 2