Properties

Label 165.6.c.b.34.9
Level $165$
Weight $6$
Character 165.34
Analytic conductor $26.463$
Analytic rank $0$
Dimension $26$
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] = [165,6,Mod(34,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.34");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 165.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: \(26.4633302691\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 34.9
Character \(\chi\) \(=\) 165.34
Dual form 165.6.c.b.34.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.97394i q^{2} +9.00000i q^{3} +7.25990 q^{4} +(47.6857 - 29.1732i) q^{5} +44.7655 q^{6} +155.412i q^{7} -195.276i q^{8} -81.0000 q^{9} +O(q^{10})\) \(q-4.97394i q^{2} +9.00000i q^{3} +7.25990 q^{4} +(47.6857 - 29.1732i) q^{5} +44.7655 q^{6} +155.412i q^{7} -195.276i q^{8} -81.0000 q^{9} +(-145.106 - 237.186i) q^{10} +121.000 q^{11} +65.3391i q^{12} -1173.30i q^{13} +773.008 q^{14} +(262.559 + 429.171i) q^{15} -738.977 q^{16} +898.118i q^{17} +402.889i q^{18} +2407.95 q^{19} +(346.193 - 211.794i) q^{20} -1398.70 q^{21} -601.847i q^{22} +4121.12i q^{23} +1757.49 q^{24} +(1422.85 - 2782.29i) q^{25} -5835.95 q^{26} -729.000i q^{27} +1128.27i q^{28} -75.4479 q^{29} +(2134.67 - 1305.95i) q^{30} +3595.47 q^{31} -2573.22i q^{32} +1089.00i q^{33} +4467.18 q^{34} +(4533.85 + 7410.91i) q^{35} -588.052 q^{36} -16063.1i q^{37} -11977.0i q^{38} +10559.7 q^{39} +(-5696.83 - 9311.90i) q^{40} +15062.8 q^{41} +6957.07i q^{42} +12867.8i q^{43} +878.448 q^{44} +(-3862.54 + 2363.03i) q^{45} +20498.2 q^{46} -6698.84i q^{47} -6650.79i q^{48} -7345.75 q^{49} +(-13838.9 - 7077.18i) q^{50} -8083.06 q^{51} -8518.07i q^{52} -22850.8i q^{53} -3626.00 q^{54} +(5769.97 - 3529.95i) q^{55} +30348.2 q^{56} +21671.6i q^{57} +375.274i q^{58} +13021.3 q^{59} +(1906.15 + 3115.74i) q^{60} +882.310 q^{61} -17883.6i q^{62} -12588.3i q^{63} -36446.3 q^{64} +(-34229.0 - 55949.8i) q^{65} +5416.62 q^{66} -14191.7i q^{67} +6520.24i q^{68} -37090.1 q^{69} +(36861.4 - 22551.1i) q^{70} -78746.0 q^{71} +15817.4i q^{72} -34227.3i q^{73} -79896.8 q^{74} +(25040.6 + 12805.7i) q^{75} +17481.5 q^{76} +18804.8i q^{77} -52523.5i q^{78} +48694.6 q^{79} +(-35238.6 + 21558.3i) q^{80} +6561.00 q^{81} -74921.3i q^{82} +95905.3i q^{83} -10154.5 q^{84} +(26200.9 + 42827.4i) q^{85} +64003.6 q^{86} -679.031i q^{87} -23628.5i q^{88} -1342.55 q^{89} +(11753.6 + 19212.1i) q^{90} +182345. q^{91} +29918.9i q^{92} +32359.2i q^{93} -33319.6 q^{94} +(114825. - 70247.6i) q^{95} +23159.0 q^{96} +80938.9i q^{97} +36537.3i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.97394i 0.879277i −0.898175 0.439639i \(-0.855107\pi\)
0.898175 0.439639i \(-0.144893\pi\)
\(3\) 9.00000i 0.577350i
\(4\) 7.25990 0.226872
\(5\) 47.6857 29.1732i 0.853028 0.521866i
\(6\) 44.7655 0.507651
\(7\) 155.412i 1.19878i 0.800459 + 0.599388i \(0.204589\pi\)
−0.800459 + 0.599388i \(0.795411\pi\)
\(8\) 195.276i 1.07876i
\(9\) −81.0000 −0.333333
\(10\) −145.106 237.186i −0.458864 0.750048i
\(11\) 121.000 0.301511
\(12\) 65.3391i 0.130985i
\(13\) 1173.30i 1.92554i −0.270323 0.962770i \(-0.587131\pi\)
0.270323 0.962770i \(-0.412869\pi\)
\(14\) 773.008 1.05406
\(15\) 262.559 + 429.171i 0.301299 + 0.492496i
\(16\) −738.977 −0.721657
\(17\) 898.118i 0.753721i 0.926270 + 0.376861i \(0.122996\pi\)
−0.926270 + 0.376861i \(0.877004\pi\)
\(18\) 402.889i 0.293092i
\(19\) 2407.95 1.53026 0.765128 0.643879i \(-0.222676\pi\)
0.765128 + 0.643879i \(0.222676\pi\)
\(20\) 346.193 211.794i 0.193528 0.118397i
\(21\) −1398.70 −0.692114
\(22\) 601.847i 0.265112i
\(23\) 4121.12i 1.62441i 0.583372 + 0.812205i \(0.301733\pi\)
−0.583372 + 0.812205i \(0.698267\pi\)
\(24\) 1757.49 0.622823
\(25\) 1422.85 2782.29i 0.455313 0.890332i
\(26\) −5835.95 −1.69308
\(27\) 729.000i 0.192450i
\(28\) 1128.27i 0.271969i
\(29\) −75.4479 −0.0166591 −0.00832957 0.999965i \(-0.502651\pi\)
−0.00832957 + 0.999965i \(0.502651\pi\)
\(30\) 2134.67 1305.95i 0.433040 0.264925i
\(31\) 3595.47 0.671972 0.335986 0.941867i \(-0.390931\pi\)
0.335986 + 0.941867i \(0.390931\pi\)
\(32\) 2573.22i 0.444224i
\(33\) 1089.00i 0.174078i
\(34\) 4467.18 0.662730
\(35\) 4533.85 + 7410.91i 0.625600 + 1.02259i
\(36\) −588.052 −0.0756240
\(37\) 16063.1i 1.92897i −0.264145 0.964483i \(-0.585090\pi\)
0.264145 0.964483i \(-0.414910\pi\)
\(38\) 11977.0i 1.34552i
\(39\) 10559.7 1.11171
\(40\) −5696.83 9311.90i −0.562968 0.920212i
\(41\) 15062.8 1.39941 0.699705 0.714432i \(-0.253315\pi\)
0.699705 + 0.714432i \(0.253315\pi\)
\(42\) 6957.07i 0.608560i
\(43\) 12867.8i 1.06129i 0.847595 + 0.530643i \(0.178050\pi\)
−0.847595 + 0.530643i \(0.821950\pi\)
\(44\) 878.448 0.0684045
\(45\) −3862.54 + 2363.03i −0.284343 + 0.173955i
\(46\) 20498.2 1.42831
\(47\) 6698.84i 0.442339i −0.975235 0.221169i \(-0.929013\pi\)
0.975235 0.221169i \(-0.0709873\pi\)
\(48\) 6650.79i 0.416649i
\(49\) −7345.75 −0.437065
\(50\) −13838.9 7077.18i −0.782848 0.400346i
\(51\) −8083.06 −0.435161
\(52\) 8518.07i 0.436851i
\(53\) 22850.8i 1.11741i −0.829367 0.558705i \(-0.811298\pi\)
0.829367 0.558705i \(-0.188702\pi\)
\(54\) −3626.00 −0.169217
\(55\) 5769.97 3529.95i 0.257198 0.157348i
\(56\) 30348.2 1.29319
\(57\) 21671.6i 0.883493i
\(58\) 375.274i 0.0146480i
\(59\) 13021.3 0.486995 0.243498 0.969901i \(-0.421705\pi\)
0.243498 + 0.969901i \(0.421705\pi\)
\(60\) 1906.15 + 3115.74i 0.0683563 + 0.111733i
\(61\) 882.310 0.0303596 0.0151798 0.999885i \(-0.495168\pi\)
0.0151798 + 0.999885i \(0.495168\pi\)
\(62\) 17883.6i 0.590849i
\(63\) 12588.3i 0.399592i
\(64\) −36446.3 −1.11225
\(65\) −34229.0 55949.8i −1.00487 1.64254i
\(66\) 5416.62 0.153062
\(67\) 14191.7i 0.386231i −0.981176 0.193115i \(-0.938141\pi\)
0.981176 0.193115i \(-0.0618591\pi\)
\(68\) 6520.24i 0.170998i
\(69\) −37090.1 −0.937854
\(70\) 36861.4 22551.1i 0.899139 0.550076i
\(71\) −78746.0 −1.85388 −0.926942 0.375205i \(-0.877572\pi\)
−0.926942 + 0.375205i \(0.877572\pi\)
\(72\) 15817.4i 0.359587i
\(73\) 34227.3i 0.751736i −0.926673 0.375868i \(-0.877345\pi\)
0.926673 0.375868i \(-0.122655\pi\)
\(74\) −79896.8 −1.69610
\(75\) 25040.6 + 12805.7i 0.514033 + 0.262875i
\(76\) 17481.5 0.347172
\(77\) 18804.8i 0.361445i
\(78\) 52523.5i 0.977502i
\(79\) 48694.6 0.877835 0.438917 0.898527i \(-0.355362\pi\)
0.438917 + 0.898527i \(0.355362\pi\)
\(80\) −35238.6 + 21558.3i −0.615594 + 0.376608i
\(81\) 6561.00 0.111111
\(82\) 74921.3i 1.23047i
\(83\) 95905.3i 1.52809i 0.645166 + 0.764043i \(0.276788\pi\)
−0.645166 + 0.764043i \(0.723212\pi\)
\(84\) −10154.5 −0.157021
\(85\) 26200.9 + 42827.4i 0.393341 + 0.642945i
\(86\) 64003.6 0.933165
\(87\) 679.031i 0.00961815i
\(88\) 23628.5i 0.325258i
\(89\) −1342.55 −0.0179662 −0.00898308 0.999960i \(-0.502859\pi\)
−0.00898308 + 0.999960i \(0.502859\pi\)
\(90\) 11753.6 + 19212.1i 0.152955 + 0.250016i
\(91\) 182345. 2.30829
\(92\) 29918.9i 0.368533i
\(93\) 32359.2i 0.387963i
\(94\) −33319.6 −0.388938
\(95\) 114825. 70247.6i 1.30535 0.798587i
\(96\) 23159.0 0.256473
\(97\) 80938.9i 0.873430i 0.899600 + 0.436715i \(0.143858\pi\)
−0.899600 + 0.436715i \(0.856142\pi\)
\(98\) 36537.3i 0.384301i
\(99\) −9801.00 −0.100504
\(100\) 10329.8 20199.1i 0.103298 0.201991i
\(101\) 19225.2 0.187529 0.0937644 0.995594i \(-0.470110\pi\)
0.0937644 + 0.995594i \(0.470110\pi\)
\(102\) 40204.7i 0.382627i
\(103\) 126651.i 1.17630i 0.808753 + 0.588148i \(0.200143\pi\)
−0.808753 + 0.588148i \(0.799857\pi\)
\(104\) −229119. −2.07720
\(105\) −66698.2 + 40804.6i −0.590392 + 0.361190i
\(106\) −113659. −0.982513
\(107\) 77773.3i 0.656706i 0.944555 + 0.328353i \(0.106494\pi\)
−0.944555 + 0.328353i \(0.893506\pi\)
\(108\) 5292.47i 0.0436615i
\(109\) −68872.6 −0.555240 −0.277620 0.960691i \(-0.589546\pi\)
−0.277620 + 0.960691i \(0.589546\pi\)
\(110\) −17557.8 28699.5i −0.138353 0.226148i
\(111\) 144568. 1.11369
\(112\) 114846.i 0.865106i
\(113\) 43794.9i 0.322647i 0.986902 + 0.161323i \(0.0515762\pi\)
−0.986902 + 0.161323i \(0.948424\pi\)
\(114\) 107793. 0.776835
\(115\) 120226. + 196518.i 0.847724 + 1.38567i
\(116\) −547.745 −0.00377949
\(117\) 95037.7i 0.641846i
\(118\) 64767.3i 0.428204i
\(119\) −139578. −0.903543
\(120\) 83807.1 51271.5i 0.531285 0.325030i
\(121\) 14641.0 0.0909091
\(122\) 4388.56i 0.0266945i
\(123\) 135565.i 0.807949i
\(124\) 26102.7 0.152452
\(125\) −13318.4 174184.i −0.0762390 0.997090i
\(126\) −62613.6 −0.351352
\(127\) 209089.i 1.15033i −0.818037 0.575165i \(-0.804938\pi\)
0.818037 0.575165i \(-0.195062\pi\)
\(128\) 98938.8i 0.533755i
\(129\) −115810. −0.612734
\(130\) −278291. + 170253.i −1.44425 + 0.883561i
\(131\) −85677.3 −0.436202 −0.218101 0.975926i \(-0.569986\pi\)
−0.218101 + 0.975926i \(0.569986\pi\)
\(132\) 7906.03i 0.0394933i
\(133\) 374224.i 1.83443i
\(134\) −70588.6 −0.339604
\(135\) −21267.2 34762.9i −0.100433 0.164165i
\(136\) 175381. 0.813085
\(137\) 115510.i 0.525795i 0.964824 + 0.262898i \(0.0846782\pi\)
−0.964824 + 0.262898i \(0.915322\pi\)
\(138\) 184484.i 0.824633i
\(139\) 120621. 0.529523 0.264761 0.964314i \(-0.414707\pi\)
0.264761 + 0.964314i \(0.414707\pi\)
\(140\) 32915.3 + 53802.5i 0.141931 + 0.231997i
\(141\) 60289.5 0.255384
\(142\) 391678.i 1.63008i
\(143\) 141970.i 0.580572i
\(144\) 59857.1 0.240552
\(145\) −3597.79 + 2201.06i −0.0142107 + 0.00869383i
\(146\) −170245. −0.660984
\(147\) 66111.7i 0.252339i
\(148\) 116616.i 0.437628i
\(149\) −49190.8 −0.181517 −0.0907587 0.995873i \(-0.528929\pi\)
−0.0907587 + 0.995873i \(0.528929\pi\)
\(150\) 63694.7 124550.i 0.231140 0.451978i
\(151\) −490808. −1.75174 −0.875870 0.482547i \(-0.839712\pi\)
−0.875870 + 0.482547i \(0.839712\pi\)
\(152\) 470216.i 1.65078i
\(153\) 72747.5i 0.251240i
\(154\) 93534.0 0.317810
\(155\) 171452. 104891.i 0.573211 0.350679i
\(156\) 76662.7 0.252216
\(157\) 273703.i 0.886199i −0.896473 0.443099i \(-0.853879\pi\)
0.896473 0.443099i \(-0.146121\pi\)
\(158\) 242204.i 0.771860i
\(159\) 205657. 0.645137
\(160\) −75068.9 122706.i −0.231825 0.378935i
\(161\) −640470. −1.94730
\(162\) 32634.0i 0.0976974i
\(163\) 64881.0i 0.191271i −0.995416 0.0956354i \(-0.969512\pi\)
0.995416 0.0956354i \(-0.0304883\pi\)
\(164\) 109354. 0.317487
\(165\) 31769.6 + 51929.7i 0.0908451 + 0.148493i
\(166\) 477028. 1.34361
\(167\) 379513.i 1.05302i 0.850170 + 0.526508i \(0.176499\pi\)
−0.850170 + 0.526508i \(0.823501\pi\)
\(168\) 273134.i 0.746625i
\(169\) −1.00535e6 −2.70770
\(170\) 213021. 130322.i 0.565327 0.345856i
\(171\) −195044. −0.510085
\(172\) 93418.8i 0.240776i
\(173\) 509354.i 1.29391i 0.762528 + 0.646955i \(0.223958\pi\)
−0.762528 + 0.646955i \(0.776042\pi\)
\(174\) −3377.46 −0.00845702
\(175\) 432399. + 221128.i 1.06731 + 0.545818i
\(176\) −89416.2 −0.217588
\(177\) 117192.i 0.281167i
\(178\) 6677.76i 0.0157972i
\(179\) −706267. −1.64754 −0.823771 0.566923i \(-0.808134\pi\)
−0.823771 + 0.566923i \(0.808134\pi\)
\(180\) −28041.7 + 17155.3i −0.0645093 + 0.0394655i
\(181\) 250646. 0.568674 0.284337 0.958724i \(-0.408227\pi\)
0.284337 + 0.958724i \(0.408227\pi\)
\(182\) 906974.i 2.02963i
\(183\) 7940.79i 0.0175281i
\(184\) 804758. 1.75235
\(185\) −468611. 765979.i −1.00666 1.64546i
\(186\) 160953. 0.341127
\(187\) 108672.i 0.227256i
\(188\) 48632.9i 0.100354i
\(189\) 113295. 0.230705
\(190\) −349407. 571132.i −0.702180 1.14776i
\(191\) −592850. −1.17588 −0.587938 0.808906i \(-0.700060\pi\)
−0.587938 + 0.808906i \(0.700060\pi\)
\(192\) 328017.i 0.642160i
\(193\) 965415.i 1.86561i 0.360383 + 0.932804i \(0.382646\pi\)
−0.360383 + 0.932804i \(0.617354\pi\)
\(194\) 402585. 0.767986
\(195\) 503549. 308061.i 0.948320 0.580163i
\(196\) −53329.4 −0.0991577
\(197\) 175247.i 0.321725i −0.986977 0.160862i \(-0.948573\pi\)
0.986977 0.160862i \(-0.0514275\pi\)
\(198\) 48749.6i 0.0883707i
\(199\) 48708.5 0.0871911 0.0435955 0.999049i \(-0.486119\pi\)
0.0435955 + 0.999049i \(0.486119\pi\)
\(200\) −543315. 277850.i −0.960454 0.491173i
\(201\) 127725. 0.222990
\(202\) 95625.1i 0.164890i
\(203\) 11725.5i 0.0199706i
\(204\) −58682.2 −0.0987259
\(205\) 718278. 439428.i 1.19373 0.730303i
\(206\) 629956. 1.03429
\(207\) 333811.i 0.541470i
\(208\) 867045.i 1.38958i
\(209\) 291362. 0.461389
\(210\) 202960. + 331753.i 0.317586 + 0.519118i
\(211\) 662206. 1.02397 0.511985 0.858995i \(-0.328910\pi\)
0.511985 + 0.858995i \(0.328910\pi\)
\(212\) 165895.i 0.253509i
\(213\) 708714.i 1.07034i
\(214\) 386840. 0.577427
\(215\) 375394. + 613609.i 0.553849 + 0.905307i
\(216\) −142357. −0.207608
\(217\) 558777.i 0.805544i
\(218\) 342568.i 0.488209i
\(219\) 308046. 0.434015
\(220\) 41889.4 25627.1i 0.0583509 0.0356979i
\(221\) 1.05377e6 1.45132
\(222\) 719071.i 0.979241i
\(223\) 44174.7i 0.0594855i 0.999558 + 0.0297428i \(0.00946881\pi\)
−0.999558 + 0.0297428i \(0.990531\pi\)
\(224\) 399908. 0.532525
\(225\) −115251. + 225365.i −0.151771 + 0.296777i
\(226\) 217833. 0.283696
\(227\) 585184.i 0.753750i 0.926264 + 0.376875i \(0.123001\pi\)
−0.926264 + 0.376875i \(0.876999\pi\)
\(228\) 157333.i 0.200440i
\(229\) −914300. −1.15213 −0.576063 0.817405i \(-0.695412\pi\)
−0.576063 + 0.817405i \(0.695412\pi\)
\(230\) 977472. 597998.i 1.21839 0.745384i
\(231\) −169243. −0.208680
\(232\) 14733.2i 0.0179712i
\(233\) 702641.i 0.847898i −0.905686 0.423949i \(-0.860644\pi\)
0.905686 0.423949i \(-0.139356\pi\)
\(234\) 472712. 0.564361
\(235\) −195426. 319439.i −0.230841 0.377327i
\(236\) 94533.5 0.110486
\(237\) 438251.i 0.506818i
\(238\) 694252.i 0.794465i
\(239\) −572014. −0.647757 −0.323879 0.946099i \(-0.604987\pi\)
−0.323879 + 0.946099i \(0.604987\pi\)
\(240\) −194025. 317148.i −0.217435 0.355413i
\(241\) −485324. −0.538256 −0.269128 0.963104i \(-0.586736\pi\)
−0.269128 + 0.963104i \(0.586736\pi\)
\(242\) 72823.5i 0.0799343i
\(243\) 59049.0i 0.0641500i
\(244\) 6405.48 0.00688775
\(245\) −350287. + 214299.i −0.372828 + 0.228089i
\(246\) 674291. 0.710411
\(247\) 2.82526e6i 2.94657i
\(248\) 702110.i 0.724897i
\(249\) −863148. −0.882240
\(250\) −866383. + 66245.0i −0.876718 + 0.0670352i
\(251\) 25755.4 0.0258039 0.0129019 0.999917i \(-0.495893\pi\)
0.0129019 + 0.999917i \(0.495893\pi\)
\(252\) 91390.1i 0.0906562i
\(253\) 498656.i 0.489778i
\(254\) −1.04000e6 −1.01146
\(255\) −385446. + 235808.i −0.371205 + 0.227096i
\(256\) −674166. −0.642935
\(257\) 243229.i 0.229711i 0.993382 + 0.114856i \(0.0366405\pi\)
−0.993382 + 0.114856i \(0.963359\pi\)
\(258\) 576032.i 0.538763i
\(259\) 2.49639e6 2.31240
\(260\) −248499. 406190.i −0.227977 0.372646i
\(261\) 6111.28 0.00555304
\(262\) 426154.i 0.383542i
\(263\) 46278.0i 0.0412558i −0.999787 0.0206279i \(-0.993433\pi\)
0.999787 0.0206279i \(-0.00656653\pi\)
\(264\) 212656. 0.187788
\(265\) −666631. 1.08966e6i −0.583138 0.953181i
\(266\) 1.86137e6 1.61298
\(267\) 12082.9i 0.0103728i
\(268\) 103030.i 0.0876249i
\(269\) −174634. −0.147146 −0.0735729 0.997290i \(-0.523440\pi\)
−0.0735729 + 0.997290i \(0.523440\pi\)
\(270\) −172909. + 105782.i −0.144347 + 0.0883085i
\(271\) −1.78096e6 −1.47309 −0.736546 0.676387i \(-0.763545\pi\)
−0.736546 + 0.676387i \(0.763545\pi\)
\(272\) 663688.i 0.543929i
\(273\) 1.64111e6i 1.33269i
\(274\) 574538. 0.462320
\(275\) 172165. 336657.i 0.137282 0.268445i
\(276\) −269270. −0.212773
\(277\) 545088.i 0.426842i 0.976960 + 0.213421i \(0.0684607\pi\)
−0.976960 + 0.213421i \(0.931539\pi\)
\(278\) 599960.i 0.465597i
\(279\) −291233. −0.223991
\(280\) 1.44718e6 885354.i 1.10313 0.674873i
\(281\) 85469.5 0.0645722 0.0322861 0.999479i \(-0.489721\pi\)
0.0322861 + 0.999479i \(0.489721\pi\)
\(282\) 299877.i 0.224554i
\(283\) 1.51069e6i 1.12127i 0.828064 + 0.560634i \(0.189442\pi\)
−0.828064 + 0.560634i \(0.810558\pi\)
\(284\) −571688. −0.420594
\(285\) 632228. + 1.03342e6i 0.461065 + 0.753644i
\(286\) −706150. −0.510484
\(287\) 2.34093e6i 1.67758i
\(288\) 208431.i 0.148075i
\(289\) 613242. 0.431904
\(290\) 10947.9 + 17895.2i 0.00764428 + 0.0124951i
\(291\) −728450. −0.504275
\(292\) 248487.i 0.170548i
\(293\) 1.05179e6i 0.715746i 0.933770 + 0.357873i \(0.116498\pi\)
−0.933770 + 0.357873i \(0.883502\pi\)
\(294\) −328836. −0.221876
\(295\) 620931. 379873.i 0.415421 0.254146i
\(296\) −3.13674e6 −2.08089
\(297\) 88209.0i 0.0580259i
\(298\) 244672.i 0.159604i
\(299\) 4.83533e6 3.12787
\(300\) 181792. + 92967.9i 0.116620 + 0.0596389i
\(301\) −1.99980e6 −1.27224
\(302\) 2.44125e6i 1.54026i
\(303\) 173027.i 0.108270i
\(304\) −1.77942e6 −1.10432
\(305\) 42073.6 25739.8i 0.0258976 0.0158436i
\(306\) −361842. −0.220910
\(307\) 1.68373e6i 1.01959i −0.860295 0.509796i \(-0.829721\pi\)
0.860295 0.509796i \(-0.170279\pi\)
\(308\) 136521.i 0.0820016i
\(309\) −1.13986e6 −0.679135
\(310\) −521723. 852794.i −0.308344 0.504011i
\(311\) −2.72412e6 −1.59707 −0.798536 0.601947i \(-0.794392\pi\)
−0.798536 + 0.601947i \(0.794392\pi\)
\(312\) 2.06207e6i 1.19927i
\(313\) 1.69158e6i 0.975959i −0.872855 0.487979i \(-0.837734\pi\)
0.872855 0.487979i \(-0.162266\pi\)
\(314\) −1.36138e6 −0.779214
\(315\) −367242. 600284.i −0.208533 0.340863i
\(316\) 353518. 0.199156
\(317\) 371370.i 0.207567i −0.994600 0.103784i \(-0.966905\pi\)
0.994600 0.103784i \(-0.0330949\pi\)
\(318\) 1.02293e6i 0.567254i
\(319\) −9129.20 −0.00502292
\(320\) −1.73797e6 + 1.06325e6i −0.948783 + 0.580446i
\(321\) −699960. −0.379149
\(322\) 3.18566e6i 1.71222i
\(323\) 2.16262e6i 1.15339i
\(324\) 47632.2 0.0252080
\(325\) −3.26447e6 1.66944e6i −1.71437 0.876722i
\(326\) −322714. −0.168180
\(327\) 619854.i 0.320568i
\(328\) 2.94140e6i 1.50963i
\(329\) 1.04108e6 0.530265
\(330\) 258295. 158020.i 0.130567 0.0798780i
\(331\) 1.54525e6 0.775229 0.387614 0.921822i \(-0.373299\pi\)
0.387614 + 0.921822i \(0.373299\pi\)
\(332\) 696263.i 0.346680i
\(333\) 1.30111e6i 0.642989i
\(334\) 1.88767e6 0.925893
\(335\) −414016. 676740.i −0.201560 0.329465i
\(336\) 1.03361e6 0.499469
\(337\) 1.56563e6i 0.750956i −0.926831 0.375478i \(-0.877479\pi\)
0.926831 0.375478i \(-0.122521\pi\)
\(338\) 5.00055e6i 2.38082i
\(339\) −394154. −0.186280
\(340\) 190216. + 310922.i 0.0892381 + 0.145866i
\(341\) 435052. 0.202607
\(342\) 970138.i 0.448506i
\(343\) 1.47039e6i 0.674833i
\(344\) 2.51277e6 1.14487
\(345\) −1.76867e6 + 1.08204e6i −0.800015 + 0.489433i
\(346\) 2.53350e6 1.13771
\(347\) 2.21769e6i 0.988727i 0.869255 + 0.494364i \(0.164599\pi\)
−0.869255 + 0.494364i \(0.835401\pi\)
\(348\) 4929.70i 0.00218209i
\(349\) 3.10101e6 1.36283 0.681413 0.731899i \(-0.261366\pi\)
0.681413 + 0.731899i \(0.261366\pi\)
\(350\) 1.09988e6 2.15073e6i 0.479925 0.938460i
\(351\) −855339. −0.370570
\(352\) 311359.i 0.133938i
\(353\) 2.34837e6i 1.00307i 0.865138 + 0.501534i \(0.167231\pi\)
−0.865138 + 0.501534i \(0.832769\pi\)
\(354\) 582905. 0.247224
\(355\) −3.75506e6 + 2.29727e6i −1.58141 + 0.967478i
\(356\) −9746.77 −0.00407602
\(357\) 1.25620e6i 0.521661i
\(358\) 3.51293e6i 1.44865i
\(359\) −1.76347e6 −0.722158 −0.361079 0.932535i \(-0.617592\pi\)
−0.361079 + 0.932535i \(0.617592\pi\)
\(360\) 461444. + 754264.i 0.187656 + 0.306737i
\(361\) 3.32213e6 1.34168
\(362\) 1.24670e6i 0.500022i
\(363\) 131769.i 0.0524864i
\(364\) 1.32381e6 0.523686
\(365\) −998519. 1.63215e6i −0.392305 0.641252i
\(366\) 39497.0 0.0154121
\(367\) 2.99827e6i 1.16200i −0.813904 0.580999i \(-0.802662\pi\)
0.813904 0.580999i \(-0.197338\pi\)
\(368\) 3.04541e6i 1.17227i
\(369\) −1.22008e6 −0.466470
\(370\) −3.80994e6 + 2.33084e6i −1.44682 + 0.885134i
\(371\) 3.55128e6 1.33952
\(372\) 234925.i 0.0880179i
\(373\) 2.01705e6i 0.750663i 0.926891 + 0.375331i \(0.122471\pi\)
−0.926891 + 0.375331i \(0.877529\pi\)
\(374\) 540529. 0.199821
\(375\) 1.56766e6 119866.i 0.575670 0.0440166i
\(376\) −1.30813e6 −0.477177
\(377\) 88523.4i 0.0320778i
\(378\) 563523.i 0.202853i
\(379\) −3.78909e6 −1.35499 −0.677497 0.735526i \(-0.736935\pi\)
−0.677497 + 0.735526i \(0.736935\pi\)
\(380\) 833617. 509991.i 0.296147 0.181177i
\(381\) 1.88180e6 0.664144
\(382\) 2.94880e6i 1.03392i
\(383\) 2.72827e6i 0.950366i 0.879887 + 0.475183i \(0.157618\pi\)
−0.879887 + 0.475183i \(0.842382\pi\)
\(384\) −890449. −0.308163
\(385\) 548596. + 896720.i 0.188626 + 0.308322i
\(386\) 4.80192e6 1.64039
\(387\) 1.04229e6i 0.353762i
\(388\) 587608.i 0.198157i
\(389\) −432266. −0.144836 −0.0724181 0.997374i \(-0.523072\pi\)
−0.0724181 + 0.997374i \(0.523072\pi\)
\(390\) −1.53228e6 2.50462e6i −0.510124 0.833836i
\(391\) −3.70125e6 −1.22435
\(392\) 1.43445e6i 0.471488i
\(393\) 771095.i 0.251841i
\(394\) −871667. −0.282885
\(395\) 2.32203e6 1.42057e6i 0.748817 0.458112i
\(396\) −71154.3 −0.0228015
\(397\) 3.90462e6i 1.24338i −0.783265 0.621688i \(-0.786447\pi\)
0.783265 0.621688i \(-0.213553\pi\)
\(398\) 242273.i 0.0766651i
\(399\) −3.36801e6 −1.05911
\(400\) −1.05146e6 + 2.05605e6i −0.328580 + 0.642514i
\(401\) 4.60863e6 1.43124 0.715618 0.698492i \(-0.246145\pi\)
0.715618 + 0.698492i \(0.246145\pi\)
\(402\) 635297.i 0.196070i
\(403\) 4.21858e6i 1.29391i
\(404\) 139573. 0.0425450
\(405\) 312866. 191405.i 0.0947809 0.0579851i
\(406\) −58321.9 −0.0175597
\(407\) 1.94363e6i 0.581605i
\(408\) 1.57843e6i 0.469435i
\(409\) 3.86604e6 1.14277 0.571384 0.820683i \(-0.306407\pi\)
0.571384 + 0.820683i \(0.306407\pi\)
\(410\) −2.18569e6 3.57267e6i −0.642139 1.04962i
\(411\) −1.03959e6 −0.303568
\(412\) 919476.i 0.266868i
\(413\) 2.02366e6i 0.583799i
\(414\) −1.66036e6 −0.476102
\(415\) 2.79786e6 + 4.57331e6i 0.797455 + 1.30350i
\(416\) −3.01917e6 −0.855370
\(417\) 1.08559e6i 0.305720i
\(418\) 1.44922e6i 0.405689i
\(419\) −3.60488e6 −1.00313 −0.501563 0.865121i \(-0.667241\pi\)
−0.501563 + 0.865121i \(0.667241\pi\)
\(420\) −484222. + 296238.i −0.133943 + 0.0819440i
\(421\) 2.69664e6 0.741510 0.370755 0.928731i \(-0.379099\pi\)
0.370755 + 0.928731i \(0.379099\pi\)
\(422\) 3.29377e6i 0.900353i
\(423\) 542606.i 0.147446i
\(424\) −4.46223e6 −1.20542
\(425\) 2.49882e6 + 1.27789e6i 0.671062 + 0.343179i
\(426\) −3.52510e6 −0.941126
\(427\) 137121.i 0.0363944i
\(428\) 564626.i 0.148988i
\(429\) 1.27773e6 0.335193
\(430\) 3.05206e6 1.86719e6i 0.796015 0.486986i
\(431\) −337978. −0.0876385 −0.0438193 0.999039i \(-0.513953\pi\)
−0.0438193 + 0.999039i \(0.513953\pi\)
\(432\) 538714.i 0.138883i
\(433\) 5.43565e6i 1.39326i −0.717431 0.696629i \(-0.754682\pi\)
0.717431 0.696629i \(-0.245318\pi\)
\(434\) 2.77932e6 0.708296
\(435\) −19809.5 32380.1i −0.00501938 0.00820455i
\(436\) −500008. −0.125968
\(437\) 9.92346e6i 2.48576i
\(438\) 1.53220e6i 0.381620i
\(439\) 170878. 0.0423180 0.0211590 0.999776i \(-0.493264\pi\)
0.0211590 + 0.999776i \(0.493264\pi\)
\(440\) −689317. 1.12674e6i −0.169741 0.277454i
\(441\) 595006. 0.145688
\(442\) 5.24137e6i 1.27611i
\(443\) 6.94673e6i 1.68179i −0.541201 0.840893i \(-0.682030\pi\)
0.541201 0.840893i \(-0.317970\pi\)
\(444\) 1.04955e6 0.252665
\(445\) −64020.4 + 39166.4i −0.0153256 + 0.00937592i
\(446\) 219722. 0.0523043
\(447\) 442717.i 0.104799i
\(448\) 5.66418e6i 1.33334i
\(449\) 1.91825e6 0.449045 0.224522 0.974469i \(-0.427918\pi\)
0.224522 + 0.974469i \(0.427918\pi\)
\(450\) 1.12095e6 + 573252.i 0.260949 + 0.133449i
\(451\) 1.82259e6 0.421938
\(452\) 317946.i 0.0731995i
\(453\) 4.41728e6i 1.01137i
\(454\) 2.91067e6 0.662755
\(455\) 8.69525e6 5.31958e6i 1.96904 1.20462i
\(456\) 4.23195e6 0.953077
\(457\) 1.14248e6i 0.255892i −0.991781 0.127946i \(-0.959162\pi\)
0.991781 0.127946i \(-0.0408385\pi\)
\(458\) 4.54768e6i 1.01304i
\(459\) 654728. 0.145054
\(460\) 872830. + 1.42670e6i 0.192325 + 0.314369i
\(461\) 3.63295e6 0.796172 0.398086 0.917348i \(-0.369675\pi\)
0.398086 + 0.917348i \(0.369675\pi\)
\(462\) 841806.i 0.183488i
\(463\) 6.29651e6i 1.36505i 0.730864 + 0.682523i \(0.239117\pi\)
−0.730864 + 0.682523i \(0.760883\pi\)
\(464\) 55754.3 0.0120222
\(465\) 944021. + 1.54307e6i 0.202465 + 0.330943i
\(466\) −3.49490e6 −0.745537
\(467\) 46216.3i 0.00980624i 0.999988 + 0.00490312i \(0.00156072\pi\)
−0.999988 + 0.00490312i \(0.998439\pi\)
\(468\) 689964.i 0.145617i
\(469\) 2.20555e6 0.463004
\(470\) −1.58887e6 + 972039.i −0.331775 + 0.202973i
\(471\) 2.46333e6 0.511647
\(472\) 2.54276e6i 0.525351i
\(473\) 1.55700e6i 0.319990i
\(474\) 2.17983e6 0.445633
\(475\) 3.42616e6 6.69961e6i 0.696745 1.36243i
\(476\) −1.01332e6 −0.204989
\(477\) 1.85092e6i 0.372470i
\(478\) 2.84517e6i 0.569558i
\(479\) −1.87454e6 −0.373299 −0.186649 0.982427i \(-0.559763\pi\)
−0.186649 + 0.982427i \(0.559763\pi\)
\(480\) 1.10435e6 675620.i 0.218778 0.133844i
\(481\) −1.88469e7 −3.71430
\(482\) 2.41397e6i 0.473276i
\(483\) 5.76423e6i 1.12428i
\(484\) 106292. 0.0206247
\(485\) 2.36124e6 + 3.85963e6i 0.455813 + 0.745060i
\(486\) 293706. 0.0564056
\(487\) 2.93849e6i 0.561439i −0.959790 0.280719i \(-0.909427\pi\)
0.959790 0.280719i \(-0.0905730\pi\)
\(488\) 172294.i 0.0327508i
\(489\) 583929. 0.110430
\(490\) 1.06591e6 + 1.74231e6i 0.200553 + 0.327819i
\(491\) 7.56455e6 1.41605 0.708026 0.706186i \(-0.249586\pi\)
0.708026 + 0.706186i \(0.249586\pi\)
\(492\) 984187.i 0.183301i
\(493\) 67761.1i 0.0125563i
\(494\) −1.40527e7 −2.59085
\(495\) −467368. + 285926.i −0.0857325 + 0.0524495i
\(496\) −2.65697e6 −0.484933
\(497\) 1.22380e7i 2.22239i
\(498\) 4.29325e6i 0.775734i
\(499\) 3.96894e6 0.713548 0.356774 0.934191i \(-0.383877\pi\)
0.356774 + 0.934191i \(0.383877\pi\)
\(500\) −96690.3 1.26456e6i −0.0172965 0.226212i
\(501\) −3.41561e6 −0.607959
\(502\) 128106.i 0.0226887i
\(503\) 7.67415e6i 1.35242i −0.736711 0.676208i \(-0.763622\pi\)
0.736711 0.676208i \(-0.236378\pi\)
\(504\) −2.45821e6 −0.431064
\(505\) 916768. 560860.i 0.159967 0.0978648i
\(506\) 2.48028e6 0.430651
\(507\) 9.04815e6i 1.56329i
\(508\) 1.51797e6i 0.260978i
\(509\) 2.34465e6 0.401129 0.200564 0.979681i \(-0.435722\pi\)
0.200564 + 0.979681i \(0.435722\pi\)
\(510\) 1.17290e6 + 1.91719e6i 0.199680 + 0.326392i
\(511\) 5.31932e6 0.901164
\(512\) 6.51930e6i 1.09907i
\(513\) 1.75540e6i 0.294498i
\(514\) 1.20981e6 0.201980
\(515\) 3.69482e6 + 6.03945e6i 0.613868 + 1.00341i
\(516\) −840769. −0.139012
\(517\) 810559.i 0.133370i
\(518\) 1.24169e7i 2.03324i
\(519\) −4.58418e6 −0.747040
\(520\) −1.09257e7 + 6.68412e6i −1.77191 + 1.08402i
\(521\) −4.60694e6 −0.743563 −0.371782 0.928320i \(-0.621253\pi\)
−0.371782 + 0.928320i \(0.621253\pi\)
\(522\) 30397.2i 0.00488266i
\(523\) 3.79276e6i 0.606319i 0.952940 + 0.303159i \(0.0980415\pi\)
−0.952940 + 0.303159i \(0.901959\pi\)
\(524\) −622008. −0.0989619
\(525\) −1.99015e6 + 3.89159e6i −0.315128 + 0.616211i
\(526\) −230184. −0.0362753
\(527\) 3.22915e6i 0.506480i
\(528\) 804746.i 0.125624i
\(529\) −1.05473e7 −1.63871
\(530\) −5.41990e6 + 3.31579e6i −0.838110 + 0.512739i
\(531\) −1.05473e6 −0.162332
\(532\) 2.71683e6i 0.416181i
\(533\) 1.76732e7i 2.69462i
\(534\) −60099.9 −0.00912053
\(535\) 2.26889e6 + 3.70867e6i 0.342712 + 0.560189i
\(536\) −2.77130e6 −0.416650
\(537\) 6.35640e6i 0.951208i
\(538\) 868619.i 0.129382i
\(539\) −888835. −0.131780
\(540\) −154398. 252375.i −0.0227854 0.0372445i
\(541\) −8.95976e6 −1.31614 −0.658072 0.752955i \(-0.728628\pi\)
−0.658072 + 0.752955i \(0.728628\pi\)
\(542\) 8.85837e6i 1.29526i
\(543\) 2.25581e6i 0.328324i
\(544\) 2.31105e6 0.334821
\(545\) −3.28424e6 + 2.00923e6i −0.473635 + 0.289760i
\(546\) 8.16276e6 1.17181
\(547\) 2.79065e6i 0.398783i 0.979920 + 0.199391i \(0.0638965\pi\)
−0.979920 + 0.199391i \(0.936104\pi\)
\(548\) 838588.i 0.119288i
\(549\) −71467.1 −0.0101199
\(550\) −1.67451e6 856339.i −0.236038 0.120709i
\(551\) −181675. −0.0254927
\(552\) 7.24282e6i 1.01172i
\(553\) 7.56770e6i 1.05233i
\(554\) 2.71124e6 0.375313
\(555\) 6.89381e6 4.21750e6i 0.950008 0.581196i
\(556\) 875694. 0.120134
\(557\) 1.22903e7i 1.67851i 0.543736 + 0.839256i \(0.317009\pi\)
−0.543736 + 0.839256i \(0.682991\pi\)
\(558\) 1.44858e6i 0.196950i
\(559\) 1.50978e7 2.04355
\(560\) −3.35041e6 5.47649e6i −0.451469 0.737959i
\(561\) −978050. −0.131206
\(562\) 425120.i 0.0567768i
\(563\) 1.13900e7i 1.51444i −0.653160 0.757220i \(-0.726557\pi\)
0.653160 0.757220i \(-0.273443\pi\)
\(564\) 437696. 0.0579395
\(565\) 1.27764e6 + 2.08839e6i 0.168378 + 0.275227i
\(566\) 7.51408e6 0.985905
\(567\) 1.01966e6i 0.133197i
\(568\) 1.53772e7i 1.99990i
\(569\) −4.71367e6 −0.610350 −0.305175 0.952296i \(-0.598715\pi\)
−0.305175 + 0.952296i \(0.598715\pi\)
\(570\) 5.14019e6 3.14467e6i 0.662662 0.405404i
\(571\) 7.49421e6 0.961913 0.480957 0.876744i \(-0.340289\pi\)
0.480957 + 0.876744i \(0.340289\pi\)
\(572\) 1.03069e6i 0.131715i
\(573\) 5.33565e6i 0.678893i
\(574\) 1.16436e7 1.47506
\(575\) 1.14661e7 + 5.86374e6i 1.44626 + 0.739615i
\(576\) 2.95215e6 0.370751
\(577\) 5.77654e6i 0.722318i −0.932504 0.361159i \(-0.882381\pi\)
0.932504 0.361159i \(-0.117619\pi\)
\(578\) 3.05023e6i 0.379763i
\(579\) −8.68873e6 −1.07711
\(580\) −26119.6 + 15979.4i −0.00322401 + 0.00197239i
\(581\) −1.49048e7 −1.83183
\(582\) 3.62327e6i 0.443397i
\(583\) 2.76495e6i 0.336912i
\(584\) −6.68379e6 −0.810943
\(585\) 2.77255e6 + 4.53194e6i 0.334958 + 0.547513i
\(586\) 5.23153e6 0.629339
\(587\) 1.19273e6i 0.142872i −0.997445 0.0714358i \(-0.977242\pi\)
0.997445 0.0714358i \(-0.0227581\pi\)
\(588\) 479965.i 0.0572487i
\(589\) 8.65771e6 1.02829
\(590\) −1.88947e6 3.08847e6i −0.223465 0.365270i
\(591\) 1.57722e6 0.185748
\(592\) 1.18702e7i 1.39205i
\(593\) 1.14801e7i 1.34064i 0.742074 + 0.670318i \(0.233842\pi\)
−0.742074 + 0.670318i \(0.766158\pi\)
\(594\) −438746. −0.0510208
\(595\) −6.65587e6 + 4.07193e6i −0.770748 + 0.471528i
\(596\) −357120. −0.0411812
\(597\) 438376.i 0.0503398i
\(598\) 2.40506e7i 2.75026i
\(599\) −1.07989e7 −1.22974 −0.614869 0.788630i \(-0.710791\pi\)
−0.614869 + 0.788630i \(0.710791\pi\)
\(600\) 2.50065e6 4.88984e6i 0.283579 0.554519i
\(601\) 6.43742e6 0.726986 0.363493 0.931597i \(-0.381584\pi\)
0.363493 + 0.931597i \(0.381584\pi\)
\(602\) 9.94690e6i 1.11866i
\(603\) 1.14953e6i 0.128744i
\(604\) −3.56322e6 −0.397421
\(605\) 698166. 427124.i 0.0775480 0.0474423i
\(606\) 860626. 0.0951991
\(607\) 2.78009e6i 0.306258i 0.988206 + 0.153129i \(0.0489350\pi\)
−0.988206 + 0.153129i \(0.951065\pi\)
\(608\) 6.19619e6i 0.679776i
\(609\) 105529. 0.0115300
\(610\) −128028. 209271.i −0.0139310 0.0227712i
\(611\) −7.85978e6 −0.851740
\(612\) 528140.i 0.0569994i
\(613\) 1.25907e7i 1.35331i 0.736299 + 0.676657i \(0.236572\pi\)
−0.736299 + 0.676657i \(0.763428\pi\)
\(614\) −8.37477e6 −0.896504
\(615\) 3.95485e6 + 6.46450e6i 0.421641 + 0.689203i
\(616\) 3.67213e6 0.389912
\(617\) 1.20724e6i 0.127668i 0.997961 + 0.0638339i \(0.0203328\pi\)
−0.997961 + 0.0638339i \(0.979667\pi\)
\(618\) 5.66960e6i 0.597147i
\(619\) −1.03935e7 −1.09028 −0.545138 0.838346i \(-0.683523\pi\)
−0.545138 + 0.838346i \(0.683523\pi\)
\(620\) 1.24473e6 761500.i 0.130045 0.0795592i
\(621\) 3.00430e6 0.312618
\(622\) 1.35496e7i 1.40427i
\(623\) 208648.i 0.0215374i
\(624\) −7.80341e6 −0.802274
\(625\) −5.71661e6 7.91756e6i −0.585381 0.810759i
\(626\) −8.41381e6 −0.858138
\(627\) 2.62226e6i 0.266383i
\(628\) 1.98706e6i 0.201054i
\(629\) 1.44265e7 1.45390
\(630\) −2.98578e6 + 1.82664e6i −0.299713 + 0.183359i
\(631\) 389320. 0.0389254 0.0194627 0.999811i \(-0.493804\pi\)
0.0194627 + 0.999811i \(0.493804\pi\)
\(632\) 9.50890e6i 0.946973i
\(633\) 5.95985e6i 0.591189i
\(634\) −1.84717e6 −0.182509
\(635\) −6.09980e6 9.97057e6i −0.600318 0.981264i
\(636\) 1.49305e6 0.146363
\(637\) 8.61880e6i 0.841585i
\(638\) 45408.1i 0.00441654i
\(639\) 6.37843e6 0.617961
\(640\) 2.88636e6 + 4.71797e6i 0.278548 + 0.455308i
\(641\) 9.85176e6 0.947041 0.473520 0.880783i \(-0.342983\pi\)
0.473520 + 0.880783i \(0.342983\pi\)
\(642\) 3.48156e6i 0.333377i
\(643\) 9.41361e6i 0.897901i −0.893557 0.448951i \(-0.851798\pi\)
0.893557 0.448951i \(-0.148202\pi\)
\(644\) −4.64975e6 −0.441789
\(645\) −5.52248e6 + 3.37855e6i −0.522679 + 0.319765i
\(646\) 1.07568e7 1.01415
\(647\) 8.37846e6i 0.786871i −0.919352 0.393435i \(-0.871287\pi\)
0.919352 0.393435i \(-0.128713\pi\)
\(648\) 1.28121e6i 0.119862i
\(649\) 1.57558e6 0.146835
\(650\) −8.30369e6 + 1.62373e7i −0.770882 + 1.50740i
\(651\) −5.02899e6 −0.465081
\(652\) 471030.i 0.0433940i
\(653\) 1.87196e7i 1.71796i 0.512011 + 0.858979i \(0.328901\pi\)
−0.512011 + 0.858979i \(0.671099\pi\)
\(654\) −3.08312e6 −0.281868
\(655\) −4.08558e6 + 2.49948e6i −0.372092 + 0.227639i
\(656\) −1.11310e7 −1.00989
\(657\) 2.77241e6i 0.250579i
\(658\) 5.17826e6i 0.466250i
\(659\) 7.53086e6 0.675509 0.337755 0.941234i \(-0.390333\pi\)
0.337755 + 0.941234i \(0.390333\pi\)
\(660\) 230644. + 377005.i 0.0206102 + 0.0336889i
\(661\) −1.12673e7 −1.00304 −0.501518 0.865147i \(-0.667225\pi\)
−0.501518 + 0.865147i \(0.667225\pi\)
\(662\) 7.68600e6i 0.681641i
\(663\) 9.48389e6i 0.837920i
\(664\) 1.87281e7 1.64844
\(665\) 1.09173e7 + 1.78451e7i 0.957328 + 1.56482i
\(666\) 6.47164e6 0.565365
\(667\) 310930.i 0.0270613i
\(668\) 2.75522e6i 0.238900i
\(669\) −397572. −0.0343440
\(670\) −3.36607e6 + 2.05929e6i −0.289691 + 0.177227i
\(671\) 106759. 0.00915377
\(672\) 3.59917e6i 0.307453i
\(673\) 747965.i 0.0636566i −0.999493 0.0318283i \(-0.989867\pi\)
0.999493 0.0318283i \(-0.0101330\pi\)
\(674\) −7.78735e6 −0.660298
\(675\) −2.02829e6 1.03726e6i −0.171344 0.0876250i
\(676\) −7.29874e6 −0.614301
\(677\) 1.52419e7i 1.27811i −0.769160 0.639056i \(-0.779325\pi\)
0.769160 0.639056i \(-0.220675\pi\)
\(678\) 1.96050e6i 0.163792i
\(679\) −1.25788e7 −1.04705
\(680\) 8.36318e6 5.11643e6i 0.693584 0.424321i
\(681\) −5.26665e6 −0.435178
\(682\) 2.16392e6i 0.178148i
\(683\) 891262.i 0.0731061i −0.999332 0.0365531i \(-0.988362\pi\)
0.999332 0.0365531i \(-0.0116378\pi\)
\(684\) −1.41600e6 −0.115724
\(685\) 3.36978e6 + 5.50816e6i 0.274394 + 0.448518i
\(686\) 7.31362e6 0.593366
\(687\) 8.22870e6i 0.665180i
\(688\) 9.50899e6i 0.765885i
\(689\) −2.68110e7 −2.15162
\(690\) 5.38198e6 + 8.79724e6i 0.430348 + 0.703435i
\(691\) −2.23692e6 −0.178220 −0.0891100 0.996022i \(-0.528402\pi\)
−0.0891100 + 0.996022i \(0.528402\pi\)
\(692\) 3.69786e6i 0.293552i
\(693\) 1.52319e6i 0.120482i
\(694\) 1.10306e7 0.869365
\(695\) 5.75188e6 3.51889e6i 0.451698 0.276340i
\(696\) −132599. −0.0103757
\(697\) 1.35281e7i 1.05476i
\(698\) 1.54243e7i 1.19830i
\(699\) 6.32377e6 0.489534
\(700\) 3.13918e6 + 1.60536e6i 0.242142 + 0.123831i
\(701\) −9.23251e6 −0.709618 −0.354809 0.934939i \(-0.615454\pi\)
−0.354809 + 0.934939i \(0.615454\pi\)
\(702\) 4.25441e6i 0.325834i
\(703\) 3.86791e7i 2.95181i
\(704\) −4.41000e6 −0.335357
\(705\) 2.87495e6 1.75884e6i 0.217850 0.133276i
\(706\) 1.16807e7 0.881975
\(707\) 2.98782e6i 0.224805i
\(708\) 850801.i 0.0637889i
\(709\) 1.91122e7 1.42789 0.713945 0.700201i \(-0.246906\pi\)
0.713945 + 0.700201i \(0.246906\pi\)
\(710\) 1.14265e7 + 1.86774e7i 0.850681 + 1.39050i
\(711\) −3.94426e6 −0.292612
\(712\) 262168.i 0.0193812i
\(713\) 1.48174e7i 1.09156i
\(714\) −6.24827e6 −0.458685
\(715\) −4.14171e6 6.76993e6i −0.302980 0.495244i
\(716\) −5.12743e6 −0.373781
\(717\) 5.14813e6i 0.373983i
\(718\) 8.77140e6i 0.634977i
\(719\) −3.98132e6 −0.287213 −0.143607 0.989635i \(-0.545870\pi\)
−0.143607 + 0.989635i \(0.545870\pi\)
\(720\) 2.85433e6 1.74622e6i 0.205198 0.125536i
\(721\) −1.96831e7 −1.41012
\(722\) 1.65241e7i 1.17971i
\(723\) 4.36792e6i 0.310762i
\(724\) 1.81966e6 0.129016
\(725\) −107351. + 209918.i −0.00758511 + 0.0148322i
\(726\) 655411. 0.0461501
\(727\) 2.31098e6i 0.162166i −0.996707 0.0810832i \(-0.974162\pi\)
0.996707 0.0810832i \(-0.0258380\pi\)
\(728\) 3.56077e7i 2.49009i
\(729\) −531441. −0.0370370
\(730\) −8.11823e6 + 4.96657e6i −0.563838 + 0.344945i
\(731\) −1.15568e7 −0.799914
\(732\) 57649.3i 0.00397664i
\(733\) 1.76034e7i 1.21015i −0.796170 0.605073i \(-0.793144\pi\)
0.796170 0.605073i \(-0.206856\pi\)
\(734\) −1.49132e7 −1.02172
\(735\) −1.92869e6 3.15258e6i −0.131687 0.215253i
\(736\) 1.06045e7 0.721601
\(737\) 1.71719e6i 0.116453i
\(738\) 6.06862e6i 0.410156i
\(739\) 8.91956e6 0.600803 0.300402 0.953813i \(-0.402879\pi\)
0.300402 + 0.953813i \(0.402879\pi\)
\(740\) −3.40207e6 5.56093e6i −0.228383 0.373309i
\(741\) 2.54273e7 1.70120
\(742\) 1.76639e7i 1.17781i
\(743\) 3.22802e6i 0.214519i −0.994231 0.107259i \(-0.965793\pi\)
0.994231 0.107259i \(-0.0342075\pi\)
\(744\) 6.31899e6 0.418519
\(745\) −2.34570e6 + 1.43505e6i −0.154839 + 0.0947277i
\(746\) 1.00327e7 0.660040
\(747\) 7.76833e6i 0.509362i
\(748\) 788950.i 0.0515579i
\(749\) −1.20869e7 −0.787244
\(750\) −596205. 7.79745e6i −0.0387028 0.506173i
\(751\) −2.04930e6 −0.132588 −0.0662942 0.997800i \(-0.521118\pi\)
−0.0662942 + 0.997800i \(0.521118\pi\)
\(752\) 4.95029e6i 0.319217i
\(753\) 231799.i 0.0148979i
\(754\) 440310. 0.0282053
\(755\) −2.34045e7 + 1.43184e7i −1.49428 + 0.914173i
\(756\) 822511. 0.0523404
\(757\) 2.62464e6i 0.166468i 0.996530 + 0.0832340i \(0.0265249\pi\)
−0.996530 + 0.0832340i \(0.973475\pi\)
\(758\) 1.88467e7i 1.19141i
\(759\) −4.48790e6 −0.282773
\(760\) −1.37177e7 2.24226e7i −0.861484 1.40816i
\(761\) 1.90240e7 1.19080 0.595401 0.803428i \(-0.296993\pi\)
0.595401 + 0.803428i \(0.296993\pi\)
\(762\) 9.35999e6i 0.583966i
\(763\) 1.07036e7i 0.665608i
\(764\) −4.30404e6 −0.266773
\(765\) −2.12228e6 3.46902e6i −0.131114 0.214315i
\(766\) 1.35703e7 0.835635
\(767\) 1.52780e7i 0.937729i
\(768\) 6.06749e6i 0.371198i
\(769\) 1.84565e7 1.12547 0.562735 0.826637i \(-0.309749\pi\)
0.562735 + 0.826637i \(0.309749\pi\)
\(770\) 4.46023e6 2.72868e6i 0.271101 0.165854i
\(771\) −2.18906e6 −0.132624
\(772\) 7.00881e6i 0.423254i
\(773\) 6.98835e6i 0.420655i 0.977631 + 0.210327i \(0.0674530\pi\)
−0.977631 + 0.210327i \(0.932547\pi\)
\(774\) −5.18429e6 −0.311055
\(775\) 5.11582e6 1.00036e7i 0.305957 0.598278i
\(776\) 1.58055e7 0.942221
\(777\) 2.24675e7i 1.33506i
\(778\) 2.15007e6i 0.127351i
\(779\) 3.62704e7 2.14145
\(780\) 3.65571e6 2.23649e6i 0.215147 0.131623i
\(781\) −9.52826e6 −0.558967
\(782\) 1.84098e7i 1.07655i
\(783\) 55001.5i 0.00320605i
\(784\) 5.42834e6 0.315411
\(785\) −7.98480e6 1.30517e7i −0.462477 0.755952i
\(786\) −3.83538e6 −0.221438
\(787\) 1.02434e7i 0.589533i −0.955569 0.294766i \(-0.904758\pi\)
0.955569 0.294766i \(-0.0952419\pi\)
\(788\) 1.27227e6i 0.0729903i
\(789\) 416502. 0.0238190
\(790\) −7.06586e6 1.15497e7i −0.402807 0.658418i
\(791\) −6.80623e6 −0.386781
\(792\) 1.91390e6i 0.108419i
\(793\) 1.03522e6i 0.0584587i
\(794\) −1.94213e7 −1.09327
\(795\) 9.80692e6 5.99968e6i 0.550319 0.336675i
\(796\) 353619. 0.0197812
\(797\) 1.36372e7i 0.760466i 0.924891 + 0.380233i \(0.124156\pi\)
−0.924891 + 0.380233i \(0.875844\pi\)
\(798\) 1.67523e7i 0.931252i
\(799\) 6.01634e6 0.333400
\(800\) −7.15943e6 3.66131e6i −0.395506 0.202261i
\(801\) 108746. 0.00598872
\(802\) 2.29231e7i 1.25845i
\(803\) 4.14150e6i 0.226657i
\(804\) 927271. 0.0505902
\(805\) −3.05412e7 + 1.86845e7i −1.66110 + 1.01623i
\(806\) −2.09830e7 −1.13770
\(807\) 1.57171e6i 0.0849547i
\(808\) 3.75423e6i 0.202299i
\(809\) 2.94019e7 1.57944 0.789722 0.613465i \(-0.210225\pi\)
0.789722 + 0.613465i \(0.210225\pi\)
\(810\) −952038. 1.55618e6i −0.0509849 0.0833386i
\(811\) −1.42304e7 −0.759737 −0.379869 0.925040i \(-0.624031\pi\)
−0.379869 + 0.925040i \(0.624031\pi\)
\(812\) 85125.8i 0.00453076i
\(813\) 1.60286e7i 0.850490i
\(814\) −9.66752e6 −0.511392
\(815\) −1.89278e6 3.09390e6i −0.0998176 0.163159i
\(816\) 5.97319e6 0.314037
\(817\) 3.09850e7i 1.62404i
\(818\) 1.92294e7i 1.00481i
\(819\) −1.47699e7 −0.769430
\(820\) 5.21463e6 3.19021e6i 0.270825 0.165685i
\(821\) 2.28257e7 1.18186 0.590931 0.806722i \(-0.298761\pi\)
0.590931 + 0.806722i \(0.298761\pi\)
\(822\) 5.17084e6i 0.266920i
\(823\) 1.12391e6i 0.0578405i 0.999582 + 0.0289202i \(0.00920688\pi\)
−0.999582 + 0.0289202i \(0.990793\pi\)
\(824\) 2.47320e7 1.26894
\(825\) 3.02991e6 + 1.54949e6i 0.154987 + 0.0792598i
\(826\) 1.00656e7 0.513321
\(827\) 2.69107e7i 1.36824i −0.729370 0.684119i \(-0.760187\pi\)
0.729370 0.684119i \(-0.239813\pi\)
\(828\) 2.42343e6i 0.122844i
\(829\) 6.83042e6 0.345192 0.172596 0.984993i \(-0.444784\pi\)
0.172596 + 0.984993i \(0.444784\pi\)
\(830\) 2.27474e7 1.39164e7i 1.14614 0.701184i
\(831\) −4.90580e6 −0.246438
\(832\) 4.27626e7i 2.14169i
\(833\) 6.59734e6i 0.329425i
\(834\) 5.39964e6 0.268813
\(835\) 1.10716e7 + 1.80973e7i 0.549533 + 0.898252i
\(836\) 2.11526e6 0.104676
\(837\) 2.62110e6i 0.129321i
\(838\) 1.79305e7i 0.882026i
\(839\) 1.37641e7 0.675061 0.337531 0.941315i \(-0.390408\pi\)
0.337531 + 0.941315i \(0.390408\pi\)
\(840\) 7.96818e6 + 1.30246e7i 0.389638 + 0.636892i
\(841\) −2.05055e7 −0.999722
\(842\) 1.34129e7i 0.651993i
\(843\) 769225.i 0.0372808i
\(844\) 4.80755e6 0.232310
\(845\) −4.79408e7 + 2.93293e7i −2.30974 + 1.41306i
\(846\) 2.69889e6 0.129646
\(847\) 2.27538e6i 0.108980i
\(848\) 1.68862e7i 0.806387i
\(849\) −1.35962e7 −0.647364
\(850\) 6.35614e6 1.24290e7i 0.301749 0.590049i
\(851\) 6.61979e7 3.13343
\(852\) 5.14519e6i 0.242830i
\(853\) 2.38141e7i 1.12063i 0.828281 + 0.560313i \(0.189319\pi\)
−0.828281 + 0.560313i \(0.810681\pi\)
\(854\) 682032. 0.0320008
\(855\) −9.30082e6 + 5.69006e6i −0.435117 + 0.266196i
\(856\) 1.51873e7 0.708428
\(857\) 1.96463e7i 0.913751i −0.889531 0.456875i \(-0.848969\pi\)
0.889531 0.456875i \(-0.151031\pi\)
\(858\) 6.35535e6i 0.294728i
\(859\) 4.10315e7 1.89729 0.948646 0.316339i \(-0.102454\pi\)
0.948646 + 0.316339i \(0.102454\pi\)
\(860\) 2.72532e6 + 4.45474e6i 0.125653 + 0.205389i
\(861\) −2.10683e7 −0.968550
\(862\) 1.68108e6i 0.0770585i
\(863\) 1.10401e7i 0.504599i 0.967649 + 0.252300i \(0.0811869\pi\)
−0.967649 + 0.252300i \(0.918813\pi\)
\(864\) −1.87588e6 −0.0854909
\(865\) 1.48595e7 + 2.42889e7i 0.675247 + 1.10374i
\(866\) −2.70366e7 −1.22506
\(867\) 5.51918e6i 0.249360i
\(868\) 4.05667e6i 0.182755i
\(869\) 5.89204e6 0.264677
\(870\) −161057. + 98531.3i −0.00721407 + 0.00441343i
\(871\) −1.66512e7 −0.743702
\(872\) 1.34492e7i 0.598970i
\(873\) 6.55605e6i 0.291143i
\(874\) 4.93587e7 2.18567
\(875\) 2.70703e7 2.06983e6i 1.19529 0.0913935i
\(876\) 2.23638e6 0.0984658
\(877\) 2.06101e7i 0.904861i −0.891800 0.452430i \(-0.850557\pi\)
0.891800 0.452430i \(-0.149443\pi\)
\(878\) 849937.i 0.0372092i
\(879\) −9.46608e6 −0.413236
\(880\) −4.26387e6 + 2.60855e6i −0.185608 + 0.113552i
\(881\) −7.17874e6 −0.311608 −0.155804 0.987788i \(-0.549797\pi\)
−0.155804 + 0.987788i \(0.549797\pi\)
\(882\) 2.95952e6i 0.128100i
\(883\) 1.55190e6i 0.0669824i −0.999439 0.0334912i \(-0.989337\pi\)
0.999439 0.0334912i \(-0.0106626\pi\)
\(884\) 7.65023e6 0.329264
\(885\) 3.41886e6 + 5.58837e6i 0.146731 + 0.239843i
\(886\) −3.45526e7 −1.47876
\(887\) 3.39646e7i 1.44950i −0.689014 0.724748i \(-0.741956\pi\)
0.689014 0.724748i \(-0.258044\pi\)
\(888\) 2.82307e7i 1.20140i
\(889\) 3.24949e7 1.37899
\(890\) 194811. + 318434.i 0.00824403 + 0.0134755i
\(891\) 793881. 0.0335013
\(892\) 320704.i 0.0134956i
\(893\) 1.61305e7i 0.676891i
\(894\) −2.20205e6 −0.0921474
\(895\) −3.36788e7 + 2.06040e7i −1.40540 + 0.859795i
\(896\) −1.53762e7 −0.639853
\(897\) 4.35180e7i 1.80587i
\(898\) 9.54127e6i 0.394835i
\(899\) −271271. −0.0111945
\(900\) −836711. + 1.63613e6i −0.0344326 + 0.0673304i
\(901\) 2.05227e7 0.842216
\(902\) 9.06547e6i 0.371000i
\(903\) 1.79982e7i 0.734531i
\(904\) 8.55211e6 0.348058
\(905\) 1.19522e7 7.31212e6i 0.485095 0.296771i
\(906\) −2.19713e7 −0.889272
\(907\) 2.58319e7i 1.04265i −0.853359 0.521324i \(-0.825438\pi\)
0.853359 0.521324i \(-0.174562\pi\)
\(908\) 4.24837e6i 0.171005i
\(909\) −1.55724e6 −0.0625096
\(910\) −2.64593e7 4.32497e7i −1.05919 1.73133i
\(911\) 549431. 0.0219340 0.0109670 0.999940i \(-0.496509\pi\)
0.0109670 + 0.999940i \(0.496509\pi\)
\(912\) 1.60148e7i 0.637579i
\(913\) 1.16045e7i 0.460735i
\(914\) −5.68262e6 −0.225000
\(915\) 231658. + 378662.i 0.00914733 + 0.0149520i
\(916\) −6.63773e6 −0.261385
\(917\) 1.33152e7i 0.522908i
\(918\) 3.25658e6i 0.127542i
\(919\) −3.84177e7 −1.50052 −0.750261 0.661142i \(-0.770072\pi\)
−0.750261 + 0.661142i \(0.770072\pi\)
\(920\) 3.83754e7 2.34773e7i 1.49480 0.914491i
\(921\) 1.51536e7 0.588662
\(922\) 1.80701e7i 0.700055i
\(923\) 9.23930e7i 3.56973i
\(924\) −1.22869e6 −0.0473437
\(925\) −4.46921e7 2.28554e7i −1.71742 0.878283i
\(926\) 3.13185e7 1.20025
\(927\) 1.02588e7i 0.392099i
\(928\) 194144.i 0.00740038i
\(929\) −1.50560e7 −0.572360 −0.286180 0.958176i \(-0.592386\pi\)
−0.286180 + 0.958176i \(0.592386\pi\)
\(930\) 7.67515e6 4.69550e6i 0.290991 0.178022i
\(931\) −1.76882e7 −0.668821
\(932\) 5.10110e6i 0.192364i
\(933\) 2.45170e7i 0.922070i
\(934\) 229877. 0.00862240
\(935\) 3.17031e6 + 5.18211e6i 0.118597 + 0.193855i
\(936\) 1.85586e7 0.692398
\(937\) 1.83320e7i 0.682119i 0.940042 + 0.341059i \(0.110786\pi\)
−0.940042 + 0.341059i \(0.889214\pi\)
\(938\) 1.09703e7i 0.407109i
\(939\) 1.52242e7 0.563470
\(940\) −1.41878e6 2.31909e6i −0.0523714 0.0856049i
\(941\) −3.82211e7 −1.40711 −0.703557 0.710639i \(-0.748406\pi\)
−0.703557 + 0.710639i \(0.748406\pi\)
\(942\) 1.22525e7i 0.449879i
\(943\) 6.20754e7i 2.27321i
\(944\) −9.62245e6 −0.351444
\(945\) 5.40255e6 3.30517e6i 0.196797 0.120397i
\(946\) 7.74444e6 0.281360
\(947\) 3.35057e7i 1.21407i 0.794675 + 0.607035i \(0.207641\pi\)
−0.794675 + 0.607035i \(0.792359\pi\)
\(948\) 3.18166e6i 0.114983i
\(949\) −4.01590e7 −1.44750
\(950\) −3.33235e7 1.70415e7i −1.19796 0.612632i
\(951\) 3.34233e6 0.119839
\(952\) 2.72563e7i 0.974707i
\(953\) 3.29329e7i 1.17462i 0.809362 + 0.587310i \(0.199813\pi\)
−0.809362 + 0.587310i \(0.800187\pi\)
\(954\) 9.20636e6 0.327504
\(955\) −2.82705e7 + 1.72953e7i −1.00306 + 0.613649i
\(956\) −4.15277e6 −0.146958
\(957\) 82162.8i 0.00289998i
\(958\) 9.32386e6i 0.328233i
\(959\) −1.79515e7 −0.630311
\(960\) −9.56929e6 1.56417e7i −0.335121 0.547780i
\(961\) −1.57018e7 −0.548454
\(962\) 9.37433e7i 3.26590i
\(963\) 6.29964e6i 0.218902i
\(964\) −3.52340e6 −0.122115
\(965\) 2.81642e7 + 4.60365e7i 0.973597 + 1.59142i
\(966\) −2.86709e7 −0.988551
\(967\) 2.24586e7i 0.772353i 0.922425 + 0.386177i \(0.126204\pi\)
−0.922425 + 0.386177i \(0.873796\pi\)
\(968\) 2.85904e6i 0.0980691i
\(969\) −1.94636e7 −0.665908
\(970\) 1.91976e7 1.17447e7i 0.655114 0.400786i
\(971\) 3.76102e7 1.28014 0.640069 0.768317i \(-0.278906\pi\)
0.640069 + 0.768317i \(0.278906\pi\)
\(972\) 428690.i 0.0145538i
\(973\) 1.87458e7i 0.634780i
\(974\) −1.46159e7 −0.493660
\(975\) 1.50250e7 2.93802e7i 0.506176 0.989791i
\(976\) −652007. −0.0219092
\(977\) 1.90408e7i 0.638187i −0.947723 0.319094i \(-0.896622\pi\)
0.947723 0.319094i \(-0.103378\pi\)
\(978\) 2.90443e6i 0.0970987i
\(979\) −162448. −0.00541700
\(980\) −2.54305e6 + 1.55579e6i −0.0845843 + 0.0517470i
\(981\) 5.57868e6 0.185080
\(982\) 3.76256e7i 1.24510i
\(983\) 3.59407e7i 1.18632i 0.805083 + 0.593162i \(0.202120\pi\)
−0.805083 + 0.593162i \(0.797880\pi\)
\(984\) 2.64726e7 0.871584
\(985\) −5.11250e6 8.35676e6i −0.167897 0.274440i
\(986\) −337040. −0.0110405
\(987\) 9.36969e6i 0.306149i
\(988\) 2.05111e7i 0.668493i
\(989\) −5.30297e7 −1.72396
\(990\) 1.42218e6 + 2.32466e6i 0.0461176 + 0.0753826i
\(991\) 2.52119e7 0.815495 0.407748 0.913095i \(-0.366314\pi\)
0.407748 + 0.913095i \(0.366314\pi\)
\(992\) 9.25192e6i 0.298506i
\(993\) 1.39073e7i 0.447578i
\(994\) −6.08713e7 −1.95410
\(995\) 2.32270e6 1.42098e6i 0.0743764 0.0455020i
\(996\) −6.26637e6 −0.200156
\(997\) 4.86935e6i 0.155143i 0.996987 + 0.0775716i \(0.0247166\pi\)
−0.996987 + 0.0775716i \(0.975283\pi\)
\(998\) 1.97413e7i 0.627406i
\(999\) −1.17100e7 −0.371230
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 165.6.c.b.34.9 26
5.2 odd 4 825.6.a.y.1.8 13
5.3 odd 4 825.6.a.v.1.6 13
5.4 even 2 inner 165.6.c.b.34.18 yes 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.6.c.b.34.9 26 1.1 even 1 trivial
165.6.c.b.34.18 yes 26 5.4 even 2 inner
825.6.a.v.1.6 13 5.3 odd 4
825.6.a.y.1.8 13 5.2 odd 4