Properties

Label 165.6.c.b.34.15
Level $165$
Weight $6$
Character 165.34
Analytic conductor $26.463$
Analytic rank $0$
Dimension $26$
Inner twists $2$

Related objects

Downloads

Learn more

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 34.15
Character \(\chi\) \(=\) 165.34
Dual form 165.6.c.b.34.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.31741i q^{2} -9.00000i q^{3} +30.2644 q^{4} +(-35.6376 + 43.0693i) q^{5} +11.8567 q^{6} -87.4786i q^{7} +82.0279i q^{8} -81.0000 q^{9} +O(q^{10})\) \(q+1.31741i q^{2} -9.00000i q^{3} +30.2644 q^{4} +(-35.6376 + 43.0693i) q^{5} +11.8567 q^{6} -87.4786i q^{7} +82.0279i q^{8} -81.0000 q^{9} +(-56.7399 - 46.9494i) q^{10} +121.000 q^{11} -272.380i q^{12} -521.292i q^{13} +115.245 q^{14} +(387.623 + 320.739i) q^{15} +860.397 q^{16} -68.1523i q^{17} -106.710i q^{18} +1588.76 q^{19} +(-1078.55 + 1303.47i) q^{20} -787.308 q^{21} +159.407i q^{22} -191.904i q^{23} +738.251 q^{24} +(-584.921 - 3069.77i) q^{25} +686.756 q^{26} +729.000i q^{27} -2647.49i q^{28} +4252.98 q^{29} +(-422.545 + 510.659i) q^{30} -83.6771 q^{31} +3758.39i q^{32} -1089.00i q^{33} +89.7846 q^{34} +(3767.64 + 3117.53i) q^{35} -2451.42 q^{36} -14445.4i q^{37} +2093.06i q^{38} -4691.63 q^{39} +(-3532.88 - 2923.28i) q^{40} +6151.94 q^{41} -1037.21i q^{42} -1408.62i q^{43} +3662.00 q^{44} +(2886.65 - 3488.61i) q^{45} +252.816 q^{46} -14797.5i q^{47} -7743.57i q^{48} +9154.49 q^{49} +(4044.15 - 770.582i) q^{50} -613.371 q^{51} -15776.6i q^{52} -10938.4i q^{53} -960.393 q^{54} +(-4312.15 + 5211.38i) q^{55} +7175.69 q^{56} -14298.9i q^{57} +5602.92i q^{58} +16099.1 q^{59} +(11731.2 + 9706.97i) q^{60} +41095.0 q^{61} -110.237i q^{62} +7085.77i q^{63} +22581.4 q^{64} +(22451.7 + 18577.6i) q^{65} +1434.66 q^{66} -1254.02i q^{67} -2062.59i q^{68} -1727.14 q^{69} +(-4107.07 + 4963.53i) q^{70} +47638.4 q^{71} -6644.26i q^{72} +7358.01i q^{73} +19030.5 q^{74} +(-27627.9 + 5264.29i) q^{75} +48083.1 q^{76} -10584.9i q^{77} -6180.81i q^{78} -90184.5 q^{79} +(-30662.5 + 37056.7i) q^{80} +6561.00 q^{81} +8104.64i q^{82} -10857.0i q^{83} -23827.4 q^{84} +(2935.27 + 2428.79i) q^{85} +1855.73 q^{86} -38276.8i q^{87} +9925.37i q^{88} -112869. q^{89} +(4595.93 + 3802.90i) q^{90} -45601.9 q^{91} -5807.86i q^{92} +753.094i q^{93} +19494.4 q^{94} +(-56619.8 + 68426.9i) q^{95} +33825.5 q^{96} +96993.9i q^{97} +12060.2i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.31741i 0.232888i 0.993197 + 0.116444i \(0.0371495\pi\)
−0.993197 + 0.116444i \(0.962851\pi\)
\(3\) 9.00000i 0.577350i
\(4\) 30.2644 0.945763
\(5\) −35.6376 + 43.0693i −0.637505 + 0.770446i
\(6\) 11.8567 0.134458
\(7\) 87.4786i 0.674772i −0.941366 0.337386i \(-0.890457\pi\)
0.941366 0.337386i \(-0.109543\pi\)
\(8\) 82.0279i 0.453144i
\(9\) −81.0000 −0.333333
\(10\) −56.7399 46.9494i −0.179427 0.148467i
\(11\) 121.000 0.301511
\(12\) 272.380i 0.546037i
\(13\) 521.292i 0.855506i −0.903896 0.427753i \(-0.859305\pi\)
0.903896 0.427753i \(-0.140695\pi\)
\(14\) 115.245 0.157146
\(15\) 387.623 + 320.739i 0.444817 + 0.368064i
\(16\) 860.397 0.840232
\(17\) 68.1523i 0.0571950i −0.999591 0.0285975i \(-0.990896\pi\)
0.999591 0.0285975i \(-0.00910411\pi\)
\(18\) 106.710i 0.0776292i
\(19\) 1588.76 1.00966 0.504830 0.863219i \(-0.331555\pi\)
0.504830 + 0.863219i \(0.331555\pi\)
\(20\) −1078.55 + 1303.47i −0.602929 + 0.728660i
\(21\) −787.308 −0.389580
\(22\) 159.407i 0.0702183i
\(23\) 191.904i 0.0756422i −0.999285 0.0378211i \(-0.987958\pi\)
0.999285 0.0378211i \(-0.0120417\pi\)
\(24\) 738.251 0.261623
\(25\) −584.921 3069.77i −0.187175 0.982327i
\(26\) 686.756 0.199237
\(27\) 729.000i 0.192450i
\(28\) 2647.49i 0.638174i
\(29\) 4252.98 0.939071 0.469535 0.882914i \(-0.344421\pi\)
0.469535 + 0.882914i \(0.344421\pi\)
\(30\) −422.545 + 510.659i −0.0857175 + 0.103592i
\(31\) −83.6771 −0.0156388 −0.00781938 0.999969i \(-0.502489\pi\)
−0.00781938 + 0.999969i \(0.502489\pi\)
\(32\) 3758.39i 0.648824i
\(33\) 1089.00i 0.174078i
\(34\) 89.7846 0.0133200
\(35\) 3767.64 + 3117.53i 0.519875 + 0.430170i
\(36\) −2451.42 −0.315254
\(37\) 14445.4i 1.73470i −0.497695 0.867352i \(-0.665820\pi\)
0.497695 0.867352i \(-0.334180\pi\)
\(38\) 2093.06i 0.235138i
\(39\) −4691.63 −0.493926
\(40\) −3532.88 2923.28i −0.349123 0.288882i
\(41\) 6151.94 0.571548 0.285774 0.958297i \(-0.407749\pi\)
0.285774 + 0.958297i \(0.407749\pi\)
\(42\) 1037.21i 0.0907283i
\(43\) 1408.62i 0.116177i −0.998311 0.0580886i \(-0.981499\pi\)
0.998311 0.0580886i \(-0.0185006\pi\)
\(44\) 3662.00 0.285158
\(45\) 2886.65 3488.61i 0.212502 0.256815i
\(46\) 252.816 0.0176161
\(47\) 14797.5i 0.977110i −0.872533 0.488555i \(-0.837524\pi\)
0.872533 0.488555i \(-0.162476\pi\)
\(48\) 7743.57i 0.485108i
\(49\) 9154.49 0.544683
\(50\) 4044.15 770.582i 0.228772 0.0435907i
\(51\) −613.371 −0.0330216
\(52\) 15776.6i 0.809106i
\(53\) 10938.4i 0.534891i −0.963573 0.267445i \(-0.913820\pi\)
0.963573 0.267445i \(-0.0861795\pi\)
\(54\) −960.393 −0.0448192
\(55\) −4312.15 + 5211.38i −0.192215 + 0.232298i
\(56\) 7175.69 0.305769
\(57\) 14298.9i 0.582928i
\(58\) 5602.92i 0.218698i
\(59\) 16099.1 0.602103 0.301052 0.953608i \(-0.402662\pi\)
0.301052 + 0.953608i \(0.402662\pi\)
\(60\) 11731.2 + 9706.97i 0.420692 + 0.348101i
\(61\) 41095.0 1.41405 0.707025 0.707189i \(-0.250037\pi\)
0.707025 + 0.707189i \(0.250037\pi\)
\(62\) 110.237i 0.00364208i
\(63\) 7085.77i 0.224924i
\(64\) 22581.4 0.689129
\(65\) 22451.7 + 18577.6i 0.659121 + 0.545389i
\(66\) 1434.66 0.0405405
\(67\) 1254.02i 0.0341286i −0.999854 0.0170643i \(-0.994568\pi\)
0.999854 0.0170643i \(-0.00543199\pi\)
\(68\) 2062.59i 0.0540930i
\(69\) −1727.14 −0.0436721
\(70\) −4107.07 + 4963.53i −0.100181 + 0.121073i
\(71\) 47638.4 1.12153 0.560765 0.827975i \(-0.310507\pi\)
0.560765 + 0.827975i \(0.310507\pi\)
\(72\) 6644.26i 0.151048i
\(73\) 7358.01i 0.161604i 0.996730 + 0.0808022i \(0.0257482\pi\)
−0.996730 + 0.0808022i \(0.974252\pi\)
\(74\) 19030.5 0.403991
\(75\) −27627.9 + 5264.29i −0.567147 + 0.108065i
\(76\) 48083.1 0.954900
\(77\) 10584.9i 0.203451i
\(78\) 6180.81i 0.115029i
\(79\) −90184.5 −1.62579 −0.812895 0.582411i \(-0.802110\pi\)
−0.812895 + 0.582411i \(0.802110\pi\)
\(80\) −30662.5 + 37056.7i −0.535652 + 0.647353i
\(81\) 6561.00 0.111111
\(82\) 8104.64i 0.133106i
\(83\) 10857.0i 0.172987i −0.996252 0.0864935i \(-0.972434\pi\)
0.996252 0.0864935i \(-0.0275662\pi\)
\(84\) −23827.4 −0.368450
\(85\) 2935.27 + 2428.79i 0.0440657 + 0.0364621i
\(86\) 1855.73 0.0270563
\(87\) 38276.8i 0.542173i
\(88\) 9925.37i 0.136628i
\(89\) −112869. −1.51043 −0.755216 0.655476i \(-0.772468\pi\)
−0.755216 + 0.655476i \(0.772468\pi\)
\(90\) 4595.93 + 3802.90i 0.0598091 + 0.0494890i
\(91\) −45601.9 −0.577271
\(92\) 5807.86i 0.0715396i
\(93\) 753.094i 0.00902905i
\(94\) 19494.4 0.227557
\(95\) −56619.8 + 68426.9i −0.643664 + 0.777889i
\(96\) 33825.5 0.374599
\(97\) 96993.9i 1.04668i 0.852123 + 0.523341i \(0.175315\pi\)
−0.852123 + 0.523341i \(0.824685\pi\)
\(98\) 12060.2i 0.126850i
\(99\) −9801.00 −0.100504
\(100\) −17702.3 92904.9i −0.177023 0.929049i
\(101\) −55750.8 −0.543810 −0.271905 0.962324i \(-0.587654\pi\)
−0.271905 + 0.962324i \(0.587654\pi\)
\(102\) 808.062i 0.00769031i
\(103\) 107469.i 0.998139i −0.866562 0.499069i \(-0.833675\pi\)
0.866562 0.499069i \(-0.166325\pi\)
\(104\) 42760.5 0.387667
\(105\) 28057.8 33908.8i 0.248359 0.300150i
\(106\) 14410.4 0.124569
\(107\) 25673.1i 0.216780i 0.994108 + 0.108390i \(0.0345696\pi\)
−0.994108 + 0.108390i \(0.965430\pi\)
\(108\) 22062.8i 0.182012i
\(109\) −98829.6 −0.796748 −0.398374 0.917223i \(-0.630425\pi\)
−0.398374 + 0.917223i \(0.630425\pi\)
\(110\) −6865.53 5680.88i −0.0540994 0.0447645i
\(111\) −130009. −1.00153
\(112\) 75266.4i 0.566965i
\(113\) 12055.0i 0.0888120i 0.999014 + 0.0444060i \(0.0141395\pi\)
−0.999014 + 0.0444060i \(0.985860\pi\)
\(114\) 18837.5 0.135757
\(115\) 8265.16 + 6839.00i 0.0582783 + 0.0482223i
\(116\) 128714. 0.888139
\(117\) 42224.7i 0.285169i
\(118\) 21209.1i 0.140222i
\(119\) −5961.87 −0.0385936
\(120\) −26309.5 + 31795.9i −0.166786 + 0.201566i
\(121\) 14641.0 0.0909091
\(122\) 54139.1i 0.329315i
\(123\) 55367.5i 0.329983i
\(124\) −2532.44 −0.0147906
\(125\) 153058. + 84207.2i 0.876155 + 0.482030i
\(126\) −9334.87 −0.0523820
\(127\) 57953.4i 0.318838i 0.987211 + 0.159419i \(0.0509620\pi\)
−0.987211 + 0.159419i \(0.949038\pi\)
\(128\) 150017.i 0.809313i
\(129\) −12677.5 −0.0670750
\(130\) −24474.4 + 29578.1i −0.127014 + 0.153501i
\(131\) −124350. −0.633095 −0.316548 0.948577i \(-0.602524\pi\)
−0.316548 + 0.948577i \(0.602524\pi\)
\(132\) 32958.0i 0.164636i
\(133\) 138983.i 0.681291i
\(134\) 1652.06 0.00794812
\(135\) −31397.5 25979.8i −0.148272 0.122688i
\(136\) 5590.39 0.0259176
\(137\) 408683.i 1.86031i 0.367170 + 0.930154i \(0.380327\pi\)
−0.367170 + 0.930154i \(0.619673\pi\)
\(138\) 2275.35i 0.0101707i
\(139\) −378463. −1.66145 −0.830723 0.556686i \(-0.812073\pi\)
−0.830723 + 0.556686i \(0.812073\pi\)
\(140\) 114025. + 94350.2i 0.491679 + 0.406839i
\(141\) −133177. −0.564135
\(142\) 62759.4i 0.261191i
\(143\) 63076.4i 0.257945i
\(144\) −69692.2 −0.280077
\(145\) −151566. + 183173.i −0.598662 + 0.723503i
\(146\) −9693.52 −0.0376357
\(147\) 82390.4i 0.314473i
\(148\) 437182.i 1.64062i
\(149\) 271317. 1.00118 0.500588 0.865686i \(-0.333117\pi\)
0.500588 + 0.865686i \(0.333117\pi\)
\(150\) −6935.24 36397.4i −0.0251671 0.132081i
\(151\) −146748. −0.523758 −0.261879 0.965101i \(-0.584342\pi\)
−0.261879 + 0.965101i \(0.584342\pi\)
\(152\) 130323.i 0.457522i
\(153\) 5520.34i 0.0190650i
\(154\) 13944.7 0.0473813
\(155\) 2982.05 3603.91i 0.00996979 0.0120488i
\(156\) −141990. −0.467138
\(157\) 365562.i 1.18362i 0.806077 + 0.591810i \(0.201586\pi\)
−0.806077 + 0.591810i \(0.798414\pi\)
\(158\) 118810.i 0.378626i
\(159\) −98445.8 −0.308819
\(160\) −161871. 133940.i −0.499884 0.413628i
\(161\) −16787.5 −0.0510412
\(162\) 8643.54i 0.0258764i
\(163\) 16695.2i 0.0492180i 0.999697 + 0.0246090i \(0.00783408\pi\)
−0.999697 + 0.0246090i \(0.992166\pi\)
\(164\) 186185. 0.540549
\(165\) 46902.4 + 38809.4i 0.134117 + 0.110975i
\(166\) 14303.1 0.0402865
\(167\) 568590.i 1.57764i 0.614623 + 0.788821i \(0.289308\pi\)
−0.614623 + 0.788821i \(0.710692\pi\)
\(168\) 64581.2i 0.176536i
\(169\) 99547.4 0.268110
\(170\) −3199.71 + 3866.96i −0.00849157 + 0.0102624i
\(171\) −128690. −0.336554
\(172\) 42630.9i 0.109876i
\(173\) 552203.i 1.40276i 0.712788 + 0.701380i \(0.247432\pi\)
−0.712788 + 0.701380i \(0.752568\pi\)
\(174\) 50426.3 0.126265
\(175\) −268539. + 51168.1i −0.662846 + 0.126300i
\(176\) 104108. 0.253339
\(177\) 144892.i 0.347624i
\(178\) 148695.i 0.351761i
\(179\) 179962. 0.419807 0.209903 0.977722i \(-0.432685\pi\)
0.209903 + 0.977722i \(0.432685\pi\)
\(180\) 87362.7 105581.i 0.200976 0.242887i
\(181\) 612439. 1.38953 0.694763 0.719239i \(-0.255509\pi\)
0.694763 + 0.719239i \(0.255509\pi\)
\(182\) 60076.5i 0.134439i
\(183\) 369855.i 0.816402i
\(184\) 15741.5 0.0342768
\(185\) 622153. + 514800.i 1.33650 + 1.10588i
\(186\) −992.135 −0.00210275
\(187\) 8246.43i 0.0172449i
\(188\) 447838.i 0.924115i
\(189\) 63771.9 0.129860
\(190\) −90146.4 74591.5i −0.181161 0.149901i
\(191\) 65407.8 0.129732 0.0648659 0.997894i \(-0.479338\pi\)
0.0648659 + 0.997894i \(0.479338\pi\)
\(192\) 203232.i 0.397869i
\(193\) 661050.i 1.27744i −0.769439 0.638721i \(-0.779464\pi\)
0.769439 0.638721i \(-0.220536\pi\)
\(194\) −127781. −0.243759
\(195\) 167199. 202065.i 0.314881 0.380544i
\(196\) 277055. 0.515141
\(197\) 590186.i 1.08349i −0.840544 0.541743i \(-0.817765\pi\)
0.840544 0.541743i \(-0.182235\pi\)
\(198\) 12911.9i 0.0234061i
\(199\) 342750. 0.613543 0.306771 0.951783i \(-0.400751\pi\)
0.306771 + 0.951783i \(0.400751\pi\)
\(200\) 251807. 47979.8i 0.445136 0.0848172i
\(201\) −11286.2 −0.0197041
\(202\) 73446.7i 0.126647i
\(203\) 372045.i 0.633658i
\(204\) −18563.3 −0.0312306
\(205\) −219240. + 264959.i −0.364364 + 0.440347i
\(206\) 141581. 0.232454
\(207\) 15544.2i 0.0252141i
\(208\) 448518.i 0.718823i
\(209\) 192241. 0.304424
\(210\) 44671.8 + 36963.6i 0.0699013 + 0.0578397i
\(211\) −214655. −0.331921 −0.165960 0.986132i \(-0.553072\pi\)
−0.165960 + 0.986132i \(0.553072\pi\)
\(212\) 331045.i 0.505880i
\(213\) 428746.i 0.647516i
\(214\) −33822.1 −0.0504854
\(215\) 60668.0 + 50199.7i 0.0895083 + 0.0740636i
\(216\) −59798.3 −0.0872076
\(217\) 7319.96i 0.0105526i
\(218\) 130199.i 0.185553i
\(219\) 66222.1 0.0933023
\(220\) −130505. + 157719.i −0.181790 + 0.219699i
\(221\) −35527.3 −0.0489307
\(222\) 171275.i 0.233244i
\(223\) 118747.i 0.159904i 0.996799 + 0.0799521i \(0.0254767\pi\)
−0.996799 + 0.0799521i \(0.974523\pi\)
\(224\) 328779. 0.437808
\(225\) 47378.6 + 248651.i 0.0623916 + 0.327442i
\(226\) −15881.4 −0.0206832
\(227\) 2183.16i 0.00281204i 0.999999 + 0.00140602i \(0.000447550\pi\)
−0.999999 + 0.00140602i \(0.999552\pi\)
\(228\) 432747.i 0.551312i
\(229\) −123704. −0.155881 −0.0779407 0.996958i \(-0.524834\pi\)
−0.0779407 + 0.996958i \(0.524834\pi\)
\(230\) −9009.77 + 10888.6i −0.0112304 + 0.0135723i
\(231\) −95264.2 −0.117463
\(232\) 348863.i 0.425534i
\(233\) 1.16587e6i 1.40689i −0.710748 0.703446i \(-0.751644\pi\)
0.710748 0.703446i \(-0.248356\pi\)
\(234\) −55627.3 −0.0664122
\(235\) 637317. + 527347.i 0.752811 + 0.622912i
\(236\) 487229. 0.569447
\(237\) 811661.i 0.938650i
\(238\) 7854.24i 0.00898797i
\(239\) −770619. −0.872659 −0.436330 0.899787i \(-0.643722\pi\)
−0.436330 + 0.899787i \(0.643722\pi\)
\(240\) 333510. + 275963.i 0.373750 + 0.309259i
\(241\) −1.42541e6 −1.58087 −0.790434 0.612547i \(-0.790145\pi\)
−0.790434 + 0.612547i \(0.790145\pi\)
\(242\) 19288.2i 0.0211716i
\(243\) 59049.0i 0.0641500i
\(244\) 1.24372e6 1.33736
\(245\) −326244. + 394277.i −0.347238 + 0.419649i
\(246\) 72941.7 0.0768490
\(247\) 828211.i 0.863771i
\(248\) 6863.86i 0.00708662i
\(249\) −97712.7 −0.0998741
\(250\) −110935. + 201640.i −0.112259 + 0.204046i
\(251\) −668745. −0.670002 −0.335001 0.942218i \(-0.608737\pi\)
−0.335001 + 0.942218i \(0.608737\pi\)
\(252\) 214447.i 0.212725i
\(253\) 23220.4i 0.0228070i
\(254\) −76348.5 −0.0742534
\(255\) 21859.1 26417.4i 0.0210514 0.0254413i
\(256\) 524969. 0.500650
\(257\) 1.08696e6i 1.02655i 0.858223 + 0.513276i \(0.171568\pi\)
−0.858223 + 0.513276i \(0.828432\pi\)
\(258\) 16701.5i 0.0156209i
\(259\) −1.26366e6 −1.17053
\(260\) 679487. + 562241.i 0.623373 + 0.515809i
\(261\) −344491. −0.313024
\(262\) 163821.i 0.147440i
\(263\) 865881.i 0.771914i −0.922517 0.385957i \(-0.873871\pi\)
0.922517 0.385957i \(-0.126129\pi\)
\(264\) 89328.3 0.0788823
\(265\) 471110. + 389819.i 0.412105 + 0.340996i
\(266\) 183098. 0.158664
\(267\) 1.01582e6i 0.872049i
\(268\) 37952.2i 0.0322775i
\(269\) −455847. −0.384094 −0.192047 0.981386i \(-0.561513\pi\)
−0.192047 + 0.981386i \(0.561513\pi\)
\(270\) 34226.1 41363.4i 0.0285725 0.0345308i
\(271\) 1.93670e6 1.60191 0.800955 0.598725i \(-0.204326\pi\)
0.800955 + 0.598725i \(0.204326\pi\)
\(272\) 58638.1i 0.0480571i
\(273\) 410417.i 0.333288i
\(274\) −538403. −0.433243
\(275\) −70775.5 371442.i −0.0564353 0.296183i
\(276\) −52270.8 −0.0413034
\(277\) 1.67891e6i 1.31470i −0.753584 0.657352i \(-0.771677\pi\)
0.753584 0.657352i \(-0.228323\pi\)
\(278\) 498591.i 0.386930i
\(279\) 6777.85 0.00521292
\(280\) −255724. + 309051.i −0.194929 + 0.235578i
\(281\) −1.66433e6 −1.25740 −0.628700 0.777648i \(-0.716413\pi\)
−0.628700 + 0.777648i \(0.716413\pi\)
\(282\) 175449.i 0.131380i
\(283\) 529051.i 0.392673i −0.980537 0.196337i \(-0.937095\pi\)
0.980537 0.196337i \(-0.0629045\pi\)
\(284\) 1.44175e6 1.06070
\(285\) 615842. + 509578.i 0.449115 + 0.371620i
\(286\) 83097.5 0.0600721
\(287\) 538163.i 0.385664i
\(288\) 304430.i 0.216275i
\(289\) 1.41521e6 0.996729
\(290\) −241314. 199675.i −0.168495 0.139421i
\(291\) 872945. 0.604302
\(292\) 222686.i 0.152839i
\(293\) 1.17586e6i 0.800178i 0.916476 + 0.400089i \(0.131021\pi\)
−0.916476 + 0.400089i \(0.868979\pi\)
\(294\) 108542. 0.0732369
\(295\) −573733. + 693375.i −0.383844 + 0.463888i
\(296\) 1.18493e6 0.786071
\(297\) 88209.0i 0.0580259i
\(298\) 357436.i 0.233162i
\(299\) −100038. −0.0647123
\(300\) −836144. + 159321.i −0.536386 + 0.102204i
\(301\) −123224. −0.0783931
\(302\) 193328.i 0.121977i
\(303\) 501757.i 0.313969i
\(304\) 1.36697e6 0.848349
\(305\) −1.46453e6 + 1.76993e6i −0.901464 + 1.08945i
\(306\) −7272.55 −0.00444000
\(307\) 1.53089e6i 0.927037i 0.886087 + 0.463518i \(0.153413\pi\)
−0.886087 + 0.463518i \(0.846587\pi\)
\(308\) 320346.i 0.192417i
\(309\) −967223. −0.576276
\(310\) 4747.83 + 3928.59i 0.00280602 + 0.00232184i
\(311\) −1.11621e6 −0.654400 −0.327200 0.944955i \(-0.606105\pi\)
−0.327200 + 0.944955i \(0.606105\pi\)
\(312\) 384844.i 0.223820i
\(313\) 864587.i 0.498824i −0.968397 0.249412i \(-0.919763\pi\)
0.968397 0.249412i \(-0.0802374\pi\)
\(314\) −481596. −0.275651
\(315\) −305179. 252520.i −0.173292 0.143390i
\(316\) −2.72938e6 −1.53761
\(317\) 1.80604e6i 1.00943i −0.863285 0.504717i \(-0.831597\pi\)
0.863285 0.504717i \(-0.168403\pi\)
\(318\) 129694.i 0.0719202i
\(319\) 514611. 0.283140
\(320\) −804746. + 972563.i −0.439323 + 0.530937i
\(321\) 231058. 0.125158
\(322\) 22116.0i 0.0118869i
\(323\) 108278.i 0.0577476i
\(324\) 198565. 0.105085
\(325\) −1.60025e6 + 304915.i −0.840386 + 0.160129i
\(326\) −21994.5 −0.0114623
\(327\) 889466.i 0.460003i
\(328\) 504630.i 0.258994i
\(329\) −1.29446e6 −0.659326
\(330\) −51127.9 + 61789.8i −0.0258448 + 0.0312343i
\(331\) 1.85701e6 0.931634 0.465817 0.884881i \(-0.345761\pi\)
0.465817 + 0.884881i \(0.345761\pi\)
\(332\) 328580.i 0.163605i
\(333\) 1.17008e6i 0.578235i
\(334\) −749068. −0.367413
\(335\) 54009.8 + 44690.3i 0.0262942 + 0.0217571i
\(336\) −677397. −0.327337
\(337\) 2.18068e6i 1.04597i 0.852343 + 0.522983i \(0.175181\pi\)
−0.852343 + 0.522983i \(0.824819\pi\)
\(338\) 131145.i 0.0624395i
\(339\) 108495. 0.0512757
\(340\) 88834.2 + 73505.8i 0.0416757 + 0.0344845i
\(341\) −10124.9 −0.00471527
\(342\) 169538.i 0.0783792i
\(343\) 2.27108e6i 1.04231i
\(344\) 115546. 0.0526451
\(345\) 61551.0 74386.4i 0.0278411 0.0336470i
\(346\) −727478. −0.326685
\(347\) 2.59930e6i 1.15886i 0.815021 + 0.579432i \(0.196726\pi\)
−0.815021 + 0.579432i \(0.803274\pi\)
\(348\) 1.15843e6i 0.512767i
\(349\) −1.17216e6 −0.515138 −0.257569 0.966260i \(-0.582921\pi\)
−0.257569 + 0.966260i \(0.582921\pi\)
\(350\) −67409.5 353777.i −0.0294138 0.154369i
\(351\) 380022. 0.164642
\(352\) 454765.i 0.195628i
\(353\) 1.57881e6i 0.674364i −0.941440 0.337182i \(-0.890526\pi\)
0.941440 0.337182i \(-0.109474\pi\)
\(354\) 190882. 0.0809574
\(355\) −1.69772e6 + 2.05175e6i −0.714982 + 0.864079i
\(356\) −3.41593e6 −1.42851
\(357\) 53656.8i 0.0222820i
\(358\) 237085.i 0.0977678i
\(359\) −3.19520e6 −1.30847 −0.654233 0.756293i \(-0.727008\pi\)
−0.654233 + 0.756293i \(0.727008\pi\)
\(360\) 286163. + 236785.i 0.116374 + 0.0962939i
\(361\) 48073.9 0.0194152
\(362\) 806834.i 0.323603i
\(363\) 131769.i 0.0524864i
\(364\) −1.38012e6 −0.545962
\(365\) −316904. 262222.i −0.124507 0.103024i
\(366\) 487252. 0.190130
\(367\) 2.52046e6i 0.976819i 0.872615 + 0.488409i \(0.162423\pi\)
−0.872615 + 0.488409i \(0.837577\pi\)
\(368\) 165114.i 0.0635570i
\(369\) −498307. −0.190516
\(370\) −678203. + 819631.i −0.257546 + 0.311253i
\(371\) −956879. −0.360929
\(372\) 22792.0i 0.00853934i
\(373\) 1.66879e6i 0.621053i −0.950565 0.310527i \(-0.899495\pi\)
0.950565 0.310527i \(-0.100505\pi\)
\(374\) 10863.9 0.00401614
\(375\) 757865. 1.37752e6i 0.278300 0.505848i
\(376\) 1.21381e6 0.442772
\(377\) 2.21705e6i 0.803380i
\(378\) 84013.9i 0.0302428i
\(379\) 3.13030e6 1.11941 0.559704 0.828692i \(-0.310915\pi\)
0.559704 + 0.828692i \(0.310915\pi\)
\(380\) −1.71357e6 + 2.07090e6i −0.608754 + 0.735699i
\(381\) 521581. 0.184081
\(382\) 86169.0i 0.0302129i
\(383\) 4.30969e6i 1.50124i −0.660737 0.750618i \(-0.729756\pi\)
0.660737 0.750618i \(-0.270244\pi\)
\(384\) 1.35016e6 0.467257
\(385\) 455884. + 377221.i 0.156748 + 0.129701i
\(386\) 870875. 0.297500
\(387\) 114098.i 0.0387258i
\(388\) 2.93546e6i 0.989914i
\(389\) 2.45755e6 0.823432 0.411716 0.911312i \(-0.364929\pi\)
0.411716 + 0.911312i \(0.364929\pi\)
\(390\) 266203. + 220269.i 0.0886239 + 0.0733318i
\(391\) −13078.7 −0.00432636
\(392\) 750923.i 0.246820i
\(393\) 1.11915e6i 0.365518i
\(394\) 777518. 0.252330
\(395\) 3.21396e6 3.88418e6i 1.03645 1.25258i
\(396\) −296622. −0.0950528
\(397\) 5.93203e6i 1.88898i 0.328544 + 0.944489i \(0.393442\pi\)
−0.328544 + 0.944489i \(0.606558\pi\)
\(398\) 451543.i 0.142887i
\(399\) −1.25085e6 −0.393343
\(400\) −503265. 2.64122e6i −0.157270 0.825382i
\(401\) 4.56758e6 1.41849 0.709243 0.704964i \(-0.249037\pi\)
0.709243 + 0.704964i \(0.249037\pi\)
\(402\) 14868.6i 0.00458885i
\(403\) 43620.2i 0.0133791i
\(404\) −1.68727e6 −0.514316
\(405\) −233818. + 282577.i −0.0708339 + 0.0856051i
\(406\) 490136. 0.147571
\(407\) 1.74789e6i 0.523033i
\(408\) 50313.5i 0.0149635i
\(409\) 5.87934e6 1.73788 0.868941 0.494915i \(-0.164801\pi\)
0.868941 + 0.494915i \(0.164801\pi\)
\(410\) −349061. 288830.i −0.102551 0.0848560i
\(411\) 3.67814e6 1.07405
\(412\) 3.25249e6i 0.944003i
\(413\) 1.40833e6i 0.406282i
\(414\) −20478.1 −0.00587205
\(415\) 467601. + 386916.i 0.133277 + 0.110280i
\(416\) 1.95922e6 0.555072
\(417\) 3.40616e6i 0.959236i
\(418\) 253260.i 0.0708966i
\(419\) −6.12464e6 −1.70430 −0.852149 0.523299i \(-0.824701\pi\)
−0.852149 + 0.523299i \(0.824701\pi\)
\(420\) 849152. 1.02623e6i 0.234889 0.283871i
\(421\) −2.83114e6 −0.778495 −0.389248 0.921133i \(-0.627265\pi\)
−0.389248 + 0.921133i \(0.627265\pi\)
\(422\) 282789.i 0.0773003i
\(423\) 1.19860e6i 0.325703i
\(424\) 897256. 0.242383
\(425\) −209212. + 39863.7i −0.0561842 + 0.0107055i
\(426\) 564834. 0.150799
\(427\) 3.59494e6i 0.954161i
\(428\) 776983.i 0.205023i
\(429\) −567687. −0.148924
\(430\) −66133.6 + 79924.7i −0.0172485 + 0.0208454i
\(431\) 6.20538e6 1.60907 0.804536 0.593904i \(-0.202414\pi\)
0.804536 + 0.593904i \(0.202414\pi\)
\(432\) 627230.i 0.161703i
\(433\) 422736.i 0.108355i −0.998531 0.0541775i \(-0.982746\pi\)
0.998531 0.0541775i \(-0.0172537\pi\)
\(434\) −9643.40 −0.00245757
\(435\) 1.64855e6 + 1.36409e6i 0.417715 + 0.345638i
\(436\) −2.99102e6 −0.753535
\(437\) 304890.i 0.0763730i
\(438\) 87241.7i 0.0217290i
\(439\) 4.07012e6 1.00797 0.503983 0.863713i \(-0.331867\pi\)
0.503983 + 0.863713i \(0.331867\pi\)
\(440\) −427478. 353717.i −0.105265 0.0871011i
\(441\) −741514. −0.181561
\(442\) 46804.0i 0.0113953i
\(443\) 4.95245e6i 1.19898i −0.800384 0.599488i \(-0.795371\pi\)
0.800384 0.599488i \(-0.204629\pi\)
\(444\) −3.93464e6 −0.947212
\(445\) 4.02240e6 4.86120e6i 0.962908 1.16371i
\(446\) −156438. −0.0372397
\(447\) 2.44185e6i 0.578029i
\(448\) 1.97539e6i 0.465004i
\(449\) −7.34037e6 −1.71831 −0.859157 0.511713i \(-0.829011\pi\)
−0.859157 + 0.511713i \(0.829011\pi\)
\(450\) −327576. + 62417.1i −0.0762572 + 0.0145302i
\(451\) 744385. 0.172328
\(452\) 364838.i 0.0839952i
\(453\) 1.32073e6i 0.302392i
\(454\) −2876.12 −0.000654888
\(455\) 1.62514e6 1.96404e6i 0.368013 0.444756i
\(456\) 1.17291e6 0.264150
\(457\) 2.07655e6i 0.465106i 0.972584 + 0.232553i \(0.0747080\pi\)
−0.972584 + 0.232553i \(0.925292\pi\)
\(458\) 162969.i 0.0363029i
\(459\) 49683.0 0.0110072
\(460\) 250140. + 206978.i 0.0551174 + 0.0456069i
\(461\) −1.68917e6 −0.370186 −0.185093 0.982721i \(-0.559259\pi\)
−0.185093 + 0.982721i \(0.559259\pi\)
\(462\) 125502.i 0.0273556i
\(463\) 1.35953e6i 0.294739i 0.989082 + 0.147369i \(0.0470806\pi\)
−0.989082 + 0.147369i \(0.952919\pi\)
\(464\) 3.65925e6 0.789037
\(465\) −32435.2 26838.5i −0.00695639 0.00575606i
\(466\) 1.53593e6 0.327648
\(467\) 8.47580e6i 1.79841i −0.437528 0.899205i \(-0.644146\pi\)
0.437528 0.899205i \(-0.355854\pi\)
\(468\) 1.27791e6i 0.269702i
\(469\) −109700. −0.0230290
\(470\) −694733. + 839608.i −0.145069 + 0.175320i
\(471\) 3.29006e6 0.683363
\(472\) 1.32057e6i 0.272840i
\(473\) 170442.i 0.0350288i
\(474\) −1.06929e6 −0.218600
\(475\) −929302. 4.87714e6i −0.188983 0.991817i
\(476\) −180433. −0.0365004
\(477\) 886013.i 0.178297i
\(478\) 1.01522e6i 0.203232i
\(479\) 3.52896e6 0.702762 0.351381 0.936233i \(-0.385712\pi\)
0.351381 + 0.936233i \(0.385712\pi\)
\(480\) −1.20546e6 + 1.45684e6i −0.238808 + 0.288608i
\(481\) −7.53028e6 −1.48405
\(482\) 1.87784e6i 0.368165i
\(483\) 151087.i 0.0294687i
\(484\) 443101. 0.0859785
\(485\) −4.17745e6 3.45663e6i −0.806413 0.667265i
\(486\) 77791.8 0.0149397
\(487\) 4.66713e6i 0.891719i 0.895103 + 0.445859i \(0.147102\pi\)
−0.895103 + 0.445859i \(0.852898\pi\)
\(488\) 3.37094e6i 0.640768i
\(489\) 150257. 0.0284160
\(490\) −519425. 429798.i −0.0977311 0.0808675i
\(491\) −7.22516e6 −1.35252 −0.676260 0.736663i \(-0.736400\pi\)
−0.676260 + 0.736663i \(0.736400\pi\)
\(492\) 1.67566e6i 0.312086i
\(493\) 289850.i 0.0537102i
\(494\) 1.09109e6 0.201162
\(495\) 349284. 422122.i 0.0640717 0.0774328i
\(496\) −71995.6 −0.0131402
\(497\) 4.16734e6i 0.756777i
\(498\) 128728.i 0.0232594i
\(499\) 1.04815e7 1.88440 0.942202 0.335046i \(-0.108752\pi\)
0.942202 + 0.335046i \(0.108752\pi\)
\(500\) 4.63221e6 + 2.54848e6i 0.828635 + 0.455886i
\(501\) 5.11731e6 0.910852
\(502\) 881012.i 0.156035i
\(503\) 8.37701e6i 1.47628i 0.674647 + 0.738140i \(0.264296\pi\)
−0.674647 + 0.738140i \(0.735704\pi\)
\(504\) −581230. −0.101923
\(505\) 1.98682e6 2.40114e6i 0.346682 0.418977i
\(506\) 30590.8 0.00531146
\(507\) 895926.i 0.154793i
\(508\) 1.75393e6i 0.301545i
\(509\) −3.17550e6 −0.543272 −0.271636 0.962400i \(-0.587565\pi\)
−0.271636 + 0.962400i \(0.587565\pi\)
\(510\) 34802.6 + 28797.4i 0.00592497 + 0.00490261i
\(511\) 643668. 0.109046
\(512\) 5.49216e6i 0.925908i
\(513\) 1.15821e6i 0.194309i
\(514\) −1.43198e6 −0.239071
\(515\) 4.62862e6 + 3.82995e6i 0.769012 + 0.636318i
\(516\) −383678. −0.0634371
\(517\) 1.79050e6i 0.294610i
\(518\) 1.66477e6i 0.272602i
\(519\) 4.96982e6 0.809884
\(520\) −1.52388e6 + 1.84166e6i −0.247140 + 0.298677i
\(521\) 3.72507e6 0.601230 0.300615 0.953746i \(-0.402808\pi\)
0.300615 + 0.953746i \(0.402808\pi\)
\(522\) 453837.i 0.0728993i
\(523\) 3.77963e6i 0.604219i 0.953273 + 0.302110i \(0.0976909\pi\)
−0.953273 + 0.302110i \(0.902309\pi\)
\(524\) −3.76339e6 −0.598758
\(525\) 460513. + 2.41685e6i 0.0729195 + 0.382694i
\(526\) 1.14072e6 0.179769
\(527\) 5702.79i 0.000894460i
\(528\) 936973.i 0.146266i
\(529\) 6.39952e6 0.994278
\(530\) −513553. + 620646.i −0.0794137 + 0.0959741i
\(531\) −1.30403e6 −0.200701
\(532\) 4.20624e6i 0.644340i
\(533\) 3.20696e6i 0.488962i
\(534\) −1.33826e6 −0.203089
\(535\) −1.10572e6 914929.i −0.167017 0.138198i
\(536\) 102865. 0.0154652
\(537\) 1.61966e6i 0.242375i
\(538\) 600538.i 0.0894509i
\(539\) 1.10769e6 0.164228
\(540\) −950227. 786264.i −0.140231 0.116034i
\(541\) −6.08511e6 −0.893871 −0.446936 0.894566i \(-0.647485\pi\)
−0.446936 + 0.894566i \(0.647485\pi\)
\(542\) 2.55142e6i 0.373065i
\(543\) 5.51195e6i 0.802243i
\(544\) 256143. 0.0371095
\(545\) 3.52205e6 4.25652e6i 0.507931 0.613851i
\(546\) −540689. −0.0776186
\(547\) 2.49034e6i 0.355870i −0.984042 0.177935i \(-0.943058\pi\)
0.984042 0.177935i \(-0.0569416\pi\)
\(548\) 1.23685e7i 1.75941i
\(549\) −3.32870e6 −0.471350
\(550\) 489342. 93240.4i 0.0689773 0.0131431i
\(551\) 6.75698e6 0.948143
\(552\) 141673.i 0.0197897i
\(553\) 7.88922e6i 1.09704i
\(554\) 2.21181e6 0.306178
\(555\) 4.63320e6 5.59937e6i 0.638481 0.771626i
\(556\) −1.14540e7 −1.57133
\(557\) 5.36235e6i 0.732347i 0.930547 + 0.366173i \(0.119332\pi\)
−0.930547 + 0.366173i \(0.880668\pi\)
\(558\) 8929.21i 0.00121403i
\(559\) −734300. −0.0993903
\(560\) 3.24167e6 + 2.68231e6i 0.436816 + 0.361443i
\(561\) −74217.9 −0.00995638
\(562\) 2.19261e6i 0.292833i
\(563\) 479316.i 0.0637310i 0.999492 + 0.0318655i \(0.0101448\pi\)
−0.999492 + 0.0318655i \(0.989855\pi\)
\(564\) −4.03054e6 −0.533538
\(565\) −519201. 429612.i −0.0684249 0.0566181i
\(566\) 696978. 0.0914488
\(567\) 573947.i 0.0749746i
\(568\) 3.90768e6i 0.508215i
\(569\) −3.08333e6 −0.399245 −0.199623 0.979873i \(-0.563972\pi\)
−0.199623 + 0.979873i \(0.563972\pi\)
\(570\) −671324. + 811317.i −0.0865456 + 0.104593i
\(571\) −5.85646e6 −0.751701 −0.375850 0.926680i \(-0.622649\pi\)
−0.375850 + 0.926680i \(0.622649\pi\)
\(572\) 1.90897e6i 0.243955i
\(573\) 588670.i 0.0749007i
\(574\) 708982. 0.0898164
\(575\) −589101. + 112249.i −0.0743054 + 0.0141583i
\(576\) −1.82909e6 −0.229710
\(577\) 5.66144e6i 0.707925i −0.935260 0.353963i \(-0.884834\pi\)
0.935260 0.353963i \(-0.115166\pi\)
\(578\) 1.86442e6i 0.232126i
\(579\) −5.94945e6 −0.737531
\(580\) −4.58706e6 + 5.54362e6i −0.566193 + 0.684263i
\(581\) −949753. −0.116727
\(582\) 1.15003e6i 0.140735i
\(583\) 1.32355e6i 0.161276i
\(584\) −603562. −0.0732301
\(585\) −1.81859e6 1.50479e6i −0.219707 0.181796i
\(586\) −1.54909e6 −0.186352
\(587\) 1.39978e7i 1.67674i −0.545104 0.838368i \(-0.683510\pi\)
0.545104 0.838368i \(-0.316490\pi\)
\(588\) 2.49350e6i 0.297417i
\(589\) −132943. −0.0157899
\(590\) −913460. 755842.i −0.108034 0.0893925i
\(591\) −5.31167e6 −0.625551
\(592\) 1.24288e7i 1.45755i
\(593\) 1.27936e7i 1.49402i 0.664810 + 0.747012i \(0.268512\pi\)
−0.664810 + 0.747012i \(0.731488\pi\)
\(594\) −116208. −0.0135135
\(595\) 212467. 256773.i 0.0246036 0.0297343i
\(596\) 8.21124e6 0.946876
\(597\) 3.08475e6i 0.354229i
\(598\) 131791.i 0.0150707i
\(599\) 1.21733e7 1.38625 0.693125 0.720818i \(-0.256234\pi\)
0.693125 + 0.720818i \(0.256234\pi\)
\(600\) −431819. 2.26626e6i −0.0489692 0.256999i
\(601\) −6.74801e6 −0.762060 −0.381030 0.924563i \(-0.624431\pi\)
−0.381030 + 0.924563i \(0.624431\pi\)
\(602\) 162336.i 0.0182568i
\(603\) 101576.i 0.0113762i
\(604\) −4.44125e6 −0.495351
\(605\) −521770. + 630577.i −0.0579550 + 0.0700406i
\(606\) −661020. −0.0731195
\(607\) 1.16658e7i 1.28512i 0.766234 + 0.642561i \(0.222128\pi\)
−0.766234 + 0.642561i \(0.777872\pi\)
\(608\) 5.97120e6i 0.655092i
\(609\) −3.34840e6 −0.365843
\(610\) −2.33173e6 1.92939e6i −0.253719 0.209940i
\(611\) −7.71382e6 −0.835923
\(612\) 167070.i 0.0180310i
\(613\) 1.36615e7i 1.46841i 0.678928 + 0.734204i \(0.262445\pi\)
−0.678928 + 0.734204i \(0.737555\pi\)
\(614\) −2.01681e6 −0.215895
\(615\) 2.38464e6 + 1.97316e6i 0.254234 + 0.210366i
\(616\) 868258. 0.0921928
\(617\) 1.15742e7i 1.22399i 0.790862 + 0.611995i \(0.209633\pi\)
−0.790862 + 0.611995i \(0.790367\pi\)
\(618\) 1.27423e6i 0.134207i
\(619\) −9.22658e6 −0.967863 −0.483932 0.875106i \(-0.660792\pi\)
−0.483932 + 0.875106i \(0.660792\pi\)
\(620\) 90250.1 109070.i 0.00942906 0.0113953i
\(621\) 139898. 0.0145574
\(622\) 1.47050e6i 0.152402i
\(623\) 9.87366e6i 1.01920i
\(624\) −4.03667e6 −0.415013
\(625\) −9.08136e6 + 3.59115e6i −0.929931 + 0.367734i
\(626\) 1.13902e6 0.116170
\(627\) 1.73016e6i 0.175759i
\(628\) 1.10635e7i 1.11942i
\(629\) −984487. −0.0992164
\(630\) 332673. 402046.i 0.0333938 0.0403575i
\(631\) 1.03002e7 1.02985 0.514923 0.857237i \(-0.327821\pi\)
0.514923 + 0.857237i \(0.327821\pi\)
\(632\) 7.39764e6i 0.736717i
\(633\) 1.93189e6i 0.191635i
\(634\) 2.37929e6 0.235085
\(635\) −2.49601e6 2.06532e6i −0.245647 0.203261i
\(636\) −2.97941e6 −0.292070
\(637\) 4.77217e6i 0.465980i
\(638\) 677954.i 0.0659399i
\(639\) −3.85871e6 −0.373844
\(640\) −6.46114e6 5.34626e6i −0.623532 0.515941i
\(641\) −3.06165e6 −0.294313 −0.147157 0.989113i \(-0.547012\pi\)
−0.147157 + 0.989113i \(0.547012\pi\)
\(642\) 304399.i 0.0291478i
\(643\) 1.62044e6i 0.154563i 0.997009 + 0.0772813i \(0.0246240\pi\)
−0.997009 + 0.0772813i \(0.975376\pi\)
\(644\) −508064. −0.0482729
\(645\) 451797. 546012.i 0.0427606 0.0516777i
\(646\) 142647. 0.0134487
\(647\) 1.57992e6i 0.148380i 0.997244 + 0.0741900i \(0.0236371\pi\)
−0.997244 + 0.0741900i \(0.976363\pi\)
\(648\) 538185.i 0.0503494i
\(649\) 1.94799e6 0.181541
\(650\) −401698. 2.10818e6i −0.0372921 0.195716i
\(651\) 65879.6 0.00609254
\(652\) 505272.i 0.0465486i
\(653\) 1.29080e6i 0.118462i −0.998244 0.0592308i \(-0.981135\pi\)
0.998244 0.0592308i \(-0.0188648\pi\)
\(654\) −1.17179e6 −0.107129
\(655\) 4.43155e6 5.35568e6i 0.403601 0.487766i
\(656\) 5.29311e6 0.480232
\(657\) 595999.i 0.0538681i
\(658\) 1.70534e6i 0.153549i
\(659\) −1.44401e7 −1.29525 −0.647627 0.761957i \(-0.724239\pi\)
−0.647627 + 0.761957i \(0.724239\pi\)
\(660\) 1.41947e6 + 1.17454e6i 0.126843 + 0.104956i
\(661\) 8.80403e6 0.783751 0.391875 0.920018i \(-0.371826\pi\)
0.391875 + 0.920018i \(0.371826\pi\)
\(662\) 2.44645e6i 0.216966i
\(663\) 319745.i 0.0282501i
\(664\) 890574. 0.0783880
\(665\) 5.98589e6 + 4.95302e6i 0.524898 + 0.434326i
\(666\) −1.54147e6 −0.134664
\(667\) 816163.i 0.0710334i
\(668\) 1.72081e7i 1.49208i
\(669\) 1.06872e6 0.0923207
\(670\) −58875.5 + 71153.1i −0.00506697 + 0.00612360i
\(671\) 4.97250e6 0.426352
\(672\) 2.95901e6i 0.252769i
\(673\) 1.43891e7i 1.22461i −0.790623 0.612303i \(-0.790243\pi\)
0.790623 0.612303i \(-0.209757\pi\)
\(674\) −2.87286e6 −0.243593
\(675\) 2.23786e6 426408.i 0.189049 0.0360218i
\(676\) 3.01274e6 0.253569
\(677\) 1.21710e7i 1.02060i 0.859997 + 0.510299i \(0.170465\pi\)
−0.859997 + 0.510299i \(0.829535\pi\)
\(678\) 142933.i 0.0119415i
\(679\) 8.48489e6 0.706272
\(680\) −199228. + 240774.i −0.0165226 + 0.0199681i
\(681\) 19648.4 0.00162353
\(682\) 13338.7i 0.00109813i
\(683\) 5.96383e6i 0.489186i 0.969626 + 0.244593i \(0.0786543\pi\)
−0.969626 + 0.244593i \(0.921346\pi\)
\(684\) −3.89473e6 −0.318300
\(685\) −1.76017e7 1.45645e7i −1.43327 1.18596i
\(686\) 2.99194e6 0.242741
\(687\) 1.11333e6i 0.0899982i
\(688\) 1.21197e6i 0.0976158i
\(689\) −5.70212e6 −0.457602
\(690\) 97997.5 + 81088.0i 0.00783596 + 0.00648386i
\(691\) −1.10524e7 −0.880565 −0.440283 0.897859i \(-0.645122\pi\)
−0.440283 + 0.897859i \(0.645122\pi\)
\(692\) 1.67121e7i 1.32668i
\(693\) 857378.i 0.0678171i
\(694\) −3.42434e6 −0.269885
\(695\) 1.34875e7 1.63001e7i 1.05918 1.28005i
\(696\) 3.13977e6 0.245682
\(697\) 419269.i 0.0326897i
\(698\) 1.54422e6i 0.119969i
\(699\) −1.04928e7 −0.812270
\(700\) −8.12719e6 + 1.54857e6i −0.626896 + 0.119450i
\(701\) −9.86637e6 −0.758337 −0.379168 0.925328i \(-0.623790\pi\)
−0.379168 + 0.925328i \(0.623790\pi\)
\(702\) 500645.i 0.0383431i
\(703\) 2.29503e7i 1.75146i
\(704\) 2.73235e6 0.207780
\(705\) 4.74612e6 5.73585e6i 0.359639 0.434635i
\(706\) 2.07995e6 0.157051
\(707\) 4.87700e6i 0.366948i
\(708\) 4.38506e6i 0.328770i
\(709\) 1.65852e7 1.23910 0.619550 0.784957i \(-0.287315\pi\)
0.619550 + 0.784957i \(0.287315\pi\)
\(710\) −2.70300e6 2.23659e6i −0.201233 0.166510i
\(711\) 7.30495e6 0.541930
\(712\) 9.25844e6i 0.684444i
\(713\) 16058.0i 0.00118295i
\(714\) −70688.1 −0.00518921
\(715\) 2.71665e6 + 2.24789e6i 0.198733 + 0.164441i
\(716\) 5.44646e6 0.397038
\(717\) 6.93557e6i 0.503830i
\(718\) 4.20940e6i 0.304725i
\(719\) 1.70621e6 0.123086 0.0615430 0.998104i \(-0.480398\pi\)
0.0615430 + 0.998104i \(0.480398\pi\)
\(720\) 2.48366e6 3.00159e6i 0.178551 0.215784i
\(721\) −9.40126e6 −0.673516
\(722\) 63333.1i 0.00452156i
\(723\) 1.28286e7i 0.912715i
\(724\) 1.85351e7 1.31416
\(725\) −2.48766e6 1.30557e7i −0.175770 0.922474i
\(726\) 173594. 0.0122234
\(727\) 4.79877e6i 0.336739i 0.985724 + 0.168370i \(0.0538502\pi\)
−0.985724 + 0.168370i \(0.946150\pi\)
\(728\) 3.74063e6i 0.261587i
\(729\) −531441. −0.0370370
\(730\) 345454. 417493.i 0.0239929 0.0289962i
\(731\) −96000.4 −0.00664476
\(732\) 1.11935e7i 0.772123i
\(733\) 2.10050e7i 1.44398i 0.691902 + 0.721991i \(0.256773\pi\)
−0.691902 + 0.721991i \(0.743227\pi\)
\(734\) −3.32048e6 −0.227489
\(735\) 3.54849e6 + 2.93620e6i 0.242285 + 0.200478i
\(736\) 721250. 0.0490785
\(737\) 151737.i 0.0102901i
\(738\) 656475.i 0.0443688i
\(739\) 1.45144e7 0.977660 0.488830 0.872379i \(-0.337424\pi\)
0.488830 + 0.872379i \(0.337424\pi\)
\(740\) 1.88291e7 + 1.55801e7i 1.26401 + 1.04590i
\(741\) −7.45390e6 −0.498698
\(742\) 1.26060e6i 0.0840560i
\(743\) 1.33510e7i 0.887245i −0.896214 0.443622i \(-0.853693\pi\)
0.896214 0.443622i \(-0.146307\pi\)
\(744\) −61774.7 −0.00409146
\(745\) −9.66907e6 + 1.16854e7i −0.638255 + 0.771353i
\(746\) 2.19848e6 0.144636
\(747\) 879414.i 0.0576623i
\(748\) 249573.i 0.0163096i
\(749\) 2.24585e6 0.146277
\(750\) 1.81476e6 + 998419.i 0.117806 + 0.0648127i
\(751\) 1.03902e7 0.672242 0.336121 0.941819i \(-0.390885\pi\)
0.336121 + 0.941819i \(0.390885\pi\)
\(752\) 1.27317e7i 0.820999i
\(753\) 6.01870e6i 0.386826i
\(754\) 2.92076e6 0.187097
\(755\) 5.22976e6 6.32034e6i 0.333898 0.403527i
\(756\) 1.93002e6 0.122817
\(757\) 1.09141e7i 0.692227i −0.938193 0.346113i \(-0.887501\pi\)
0.938193 0.346113i \(-0.112499\pi\)
\(758\) 4.12390e6i 0.260696i
\(759\) −208983. −0.0131676
\(760\) −5.61291e6 4.64440e6i −0.352496 0.291673i
\(761\) 1.04145e7 0.651894 0.325947 0.945388i \(-0.394317\pi\)
0.325947 + 0.945388i \(0.394317\pi\)
\(762\) 687136.i 0.0428702i
\(763\) 8.64548e6i 0.537623i
\(764\) 1.97953e6 0.122696
\(765\) −237757. 196732.i −0.0146886 0.0121540i
\(766\) 5.67763e6 0.349619
\(767\) 8.39232e6i 0.515103i
\(768\) 4.72472e6i 0.289050i
\(769\) 9.42825e6 0.574930 0.287465 0.957791i \(-0.407187\pi\)
0.287465 + 0.957791i \(0.407187\pi\)
\(770\) −496955. + 600587.i −0.0302058 + 0.0365047i
\(771\) 9.78265e6 0.592681
\(772\) 2.00063e7i 1.20816i
\(773\) 1.18529e7i 0.713469i 0.934206 + 0.356734i \(0.116110\pi\)
−0.934206 + 0.356734i \(0.883890\pi\)
\(774\) −150314. −0.00901875
\(775\) 48944.5 +