Properties

Label 4.7.b.a.3.2
Level $4$
Weight $7$
Character 4.3
Analytic conductor $0.920$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 4.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.920216334479\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-15}) \)
Defining polynomial: \(x^{2} - x + 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.2
Root \(0.500000 + 1.93649i\) of defining polynomial
Character \(\chi\) \(=\) 4.3
Dual form 4.7.b.a.3.1

$q$-expansion

\(f(q)\) \(=\) \(q+(2.00000 + 7.74597i) q^{2} -30.9839i q^{3} +(-56.0000 + 30.9839i) q^{4} +10.0000 q^{5} +(240.000 - 61.9677i) q^{6} +309.839i q^{7} +(-352.000 - 371.806i) q^{8} -231.000 q^{9} +O(q^{10})\) \(q+(2.00000 + 7.74597i) q^{2} -30.9839i q^{3} +(-56.0000 + 30.9839i) q^{4} +10.0000 q^{5} +(240.000 - 61.9677i) q^{6} +309.839i q^{7} +(-352.000 - 371.806i) q^{8} -231.000 q^{9} +(20.0000 + 77.4597i) q^{10} -960.500i q^{11} +(960.000 + 1735.10i) q^{12} +1466.00 q^{13} +(-2400.00 + 619.677i) q^{14} -309.839i q^{15} +(2176.00 - 3470.19i) q^{16} -4766.00 q^{17} +(-462.000 - 1789.32i) q^{18} +7529.08i q^{19} +(-560.000 + 309.839i) q^{20} +9600.00 q^{21} +(7440.00 - 1921.00i) q^{22} -10472.5i q^{23} +(-11520.0 + 10906.3i) q^{24} -15525.0 q^{25} +(2932.00 + 11355.6i) q^{26} -15430.0i q^{27} +(-9600.00 - 17351.0i) q^{28} +25498.0 q^{29} +(2400.00 - 619.677i) q^{30} +41890.2i q^{31} +(31232.0 + 9914.84i) q^{32} -29760.0 q^{33} +(-9532.00 - 36917.3i) q^{34} +3098.39i q^{35} +(12936.0 - 7157.27i) q^{36} +1994.00 q^{37} +(-58320.0 + 15058.2i) q^{38} -45422.3i q^{39} +(-3520.00 - 3718.06i) q^{40} +29362.0 q^{41} +(19200.0 + 74361.3i) q^{42} -21533.8i q^{43} +(29760.0 + 53788.0i) q^{44} -2310.00 q^{45} +(81120.0 - 20945.1i) q^{46} -7560.06i q^{47} +(-107520. - 67420.9i) q^{48} +21649.0 q^{49} +(-31050.0 - 120256. i) q^{50} +147669. i q^{51} +(-82096.0 + 45422.3i) q^{52} -192854. q^{53} +(119520. - 30859.9i) q^{54} -9605.00i q^{55} +(115200. - 109063. i) q^{56} +233280. q^{57} +(50996.0 + 197507. i) q^{58} -78420.2i q^{59} +(9600.00 + 17351.0i) q^{60} -10918.0 q^{61} +(-324480. + 83780.4i) q^{62} -71572.7i q^{63} +(-14336.0 + 261752. i) q^{64} +14660.0 q^{65} +(-59520.0 - 230520. i) q^{66} -394146. i q^{67} +(266896. - 147669. i) q^{68} -324480. q^{69} +(-24000.0 + 6196.77i) q^{70} +532241. i q^{71} +(81312.0 + 85887.3i) q^{72} +288626. q^{73} +(3988.00 + 15445.5i) q^{74} +481025. i q^{75} +(-233280. - 421628. i) q^{76} +297600. q^{77} +(351840. - 90844.7i) q^{78} -310706. i q^{79} +(21760.0 - 34701.9i) q^{80} -646479. q^{81} +(58724.0 + 227437. i) q^{82} -204153. i q^{83} +(-537600. + 297445. i) q^{84} -47660.0 q^{85} +(166800. - 43067.6i) q^{86} -790027. i q^{87} +(-357120. + 338096. i) q^{88} +310738. q^{89} +(-4620.00 - 17893.2i) q^{90} +454223. i q^{91} +(324480. + 586463. i) q^{92} +1.29792e6 q^{93} +(58560.0 - 15120.1i) q^{94} +75290.8i q^{95} +(307200. - 967688. i) q^{96} -1.45709e6 q^{97} +(43298.0 + 167692. i) q^{98} +221875. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} - 112 q^{4} + 20 q^{5} + 480 q^{6} - 704 q^{8} - 462 q^{9} + O(q^{10}) \) \( 2 q + 4 q^{2} - 112 q^{4} + 20 q^{5} + 480 q^{6} - 704 q^{8} - 462 q^{9} + 40 q^{10} + 1920 q^{12} + 2932 q^{13} - 4800 q^{14} + 4352 q^{16} - 9532 q^{17} - 924 q^{18} - 1120 q^{20} + 19200 q^{21} + 14880 q^{22} - 23040 q^{24} - 31050 q^{25} + 5864 q^{26} - 19200 q^{28} + 50996 q^{29} + 4800 q^{30} + 62464 q^{32} - 59520 q^{33} - 19064 q^{34} + 25872 q^{36} + 3988 q^{37} - 116640 q^{38} - 7040 q^{40} + 58724 q^{41} + 38400 q^{42} + 59520 q^{44} - 4620 q^{45} + 162240 q^{46} - 215040 q^{48} + 43298 q^{49} - 62100 q^{50} - 164192 q^{52} - 385708 q^{53} + 239040 q^{54} + 230400 q^{56} + 466560 q^{57} + 101992 q^{58} + 19200 q^{60} - 21836 q^{61} - 648960 q^{62} - 28672 q^{64} + 29320 q^{65} - 119040 q^{66} + 533792 q^{68} - 648960 q^{69} - 48000 q^{70} + 162624 q^{72} + 577252 q^{73} + 7976 q^{74} - 466560 q^{76} + 595200 q^{77} + 703680 q^{78} + 43520 q^{80} - 1292958 q^{81} + 117448 q^{82} - 1075200 q^{84} - 95320 q^{85} + 333600 q^{86} - 714240 q^{88} + 621476 q^{89} - 9240 q^{90} + 648960 q^{92} + 2595840 q^{93} + 117120 q^{94} + 614400 q^{96} - 2914172 q^{97} + 86596 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 + 7.74597i 0.250000 + 0.968246i
\(3\) 30.9839i 1.14755i −0.819013 0.573775i \(-0.805478\pi\)
0.819013 0.573775i \(-0.194522\pi\)
\(4\) −56.0000 + 30.9839i −0.875000 + 0.484123i
\(5\) 10.0000 0.0800000 0.0400000 0.999200i \(-0.487264\pi\)
0.0400000 + 0.999200i \(0.487264\pi\)
\(6\) 240.000 61.9677i 1.11111 0.286888i
\(7\) 309.839i 0.903320i 0.892190 + 0.451660i \(0.149168\pi\)
−0.892190 + 0.451660i \(0.850832\pi\)
\(8\) −352.000 371.806i −0.687500 0.726184i
\(9\) −231.000 −0.316872
\(10\) 20.0000 + 77.4597i 0.0200000 + 0.0774597i
\(11\) 960.500i 0.721638i −0.932636 0.360819i \(-0.882497\pi\)
0.932636 0.360819i \(-0.117503\pi\)
\(12\) 960.000 + 1735.10i 0.555556 + 1.00411i
\(13\) 1466.00 0.667274 0.333637 0.942702i \(-0.391724\pi\)
0.333637 + 0.942702i \(0.391724\pi\)
\(14\) −2400.00 + 619.677i −0.874636 + 0.225830i
\(15\) 309.839i 0.0918040i
\(16\) 2176.00 3470.19i 0.531250 0.847215i
\(17\) −4766.00 −0.970079 −0.485040 0.874492i \(-0.661195\pi\)
−0.485040 + 0.874492i \(0.661195\pi\)
\(18\) −462.000 1789.32i −0.0792181 0.306810i
\(19\) 7529.08i 1.09769i 0.835923 + 0.548847i \(0.184933\pi\)
−0.835923 + 0.548847i \(0.815067\pi\)
\(20\) −560.000 + 309.839i −0.0700000 + 0.0387298i
\(21\) 9600.00 1.03661
\(22\) 7440.00 1921.00i 0.698723 0.180409i
\(23\) 10472.5i 0.860734i −0.902654 0.430367i \(-0.858384\pi\)
0.902654 0.430367i \(-0.141616\pi\)
\(24\) −11520.0 + 10906.3i −0.833333 + 0.788941i
\(25\) −15525.0 −0.993600
\(26\) 2932.00 + 11355.6i 0.166818 + 0.646085i
\(27\) 15430.0i 0.783923i
\(28\) −9600.00 17351.0i −0.437318 0.790405i
\(29\) 25498.0 1.04547 0.522736 0.852495i \(-0.324911\pi\)
0.522736 + 0.852495i \(0.324911\pi\)
\(30\) 2400.00 619.677i 0.0888889 0.0229510i
\(31\) 41890.2i 1.40614i 0.711123 + 0.703068i \(0.248187\pi\)
−0.711123 + 0.703068i \(0.751813\pi\)
\(32\) 31232.0 + 9914.84i 0.953125 + 0.302577i
\(33\) −29760.0 −0.828116
\(34\) −9532.00 36917.3i −0.242520 0.939275i
\(35\) 3098.39i 0.0722656i
\(36\) 12936.0 7157.27i 0.277263 0.153405i
\(37\) 1994.00 0.0393659 0.0196829 0.999806i \(-0.493734\pi\)
0.0196829 + 0.999806i \(0.493734\pi\)
\(38\) −58320.0 + 15058.2i −1.06284 + 0.274423i
\(39\) 45422.3i 0.765730i
\(40\) −3520.00 3718.06i −0.0550000 0.0580948i
\(41\) 29362.0 0.426024 0.213012 0.977050i \(-0.431673\pi\)
0.213012 + 0.977050i \(0.431673\pi\)
\(42\) 19200.0 + 74361.3i 0.259151 + 1.00369i
\(43\) 21533.8i 0.270841i −0.990788 0.135421i \(-0.956761\pi\)
0.990788 0.135421i \(-0.0432386\pi\)
\(44\) 29760.0 + 53788.0i 0.349361 + 0.631433i
\(45\) −2310.00 −0.0253498
\(46\) 81120.0 20945.1i 0.833402 0.215183i
\(47\) 7560.06i 0.0728168i −0.999337 0.0364084i \(-0.988408\pi\)
0.999337 0.0364084i \(-0.0115917\pi\)
\(48\) −107520. 67420.9i −0.972222 0.609636i
\(49\) 21649.0 0.184013
\(50\) −31050.0 120256.i −0.248400 0.962049i
\(51\) 147669.i 1.11322i
\(52\) −82096.0 + 45422.3i −0.583864 + 0.323042i
\(53\) −192854. −1.29539 −0.647696 0.761899i \(-0.724267\pi\)
−0.647696 + 0.761899i \(0.724267\pi\)
\(54\) 119520. 30859.9i 0.759031 0.195981i
\(55\) 9605.00i 0.0577310i
\(56\) 115200. 109063.i 0.655977 0.621032i
\(57\) 233280. 1.25966
\(58\) 50996.0 + 197507.i 0.261368 + 1.01227i
\(59\) 78420.2i 0.381831i −0.981606 0.190916i \(-0.938854\pi\)
0.981606 0.190916i \(-0.0611457\pi\)
\(60\) 9600.00 + 17351.0i 0.0444444 + 0.0803285i
\(61\) −10918.0 −0.0481009 −0.0240505 0.999711i \(-0.507656\pi\)
−0.0240505 + 0.999711i \(0.507656\pi\)
\(62\) −324480. + 83780.4i −1.36149 + 0.351534i
\(63\) 71572.7i 0.286237i
\(64\) −14336.0 + 261752.i −0.0546875 + 0.998504i
\(65\) 14660.0 0.0533819
\(66\) −59520.0 230520.i −0.207029 0.801820i
\(67\) 394146.i 1.31049i −0.755418 0.655243i \(-0.772566\pi\)
0.755418 0.655243i \(-0.227434\pi\)
\(68\) 266896. 147669.i 0.848819 0.469638i
\(69\) −324480. −0.987735
\(70\) −24000.0 + 6196.77i −0.0699708 + 0.0180664i
\(71\) 532241.i 1.48708i 0.668694 + 0.743538i \(0.266854\pi\)
−0.668694 + 0.743538i \(0.733146\pi\)
\(72\) 81312.0 + 85887.3i 0.217850 + 0.230108i
\(73\) 288626. 0.741937 0.370968 0.928646i \(-0.379026\pi\)
0.370968 + 0.928646i \(0.379026\pi\)
\(74\) 3988.00 + 15445.5i 0.00984147 + 0.0381159i
\(75\) 481025.i 1.14021i
\(76\) −233280. 421628.i −0.531419 0.960482i
\(77\) 297600. 0.651870
\(78\) 351840. 90844.7i 0.741415 0.191433i
\(79\) 310706.i 0.630186i −0.949061 0.315093i \(-0.897964\pi\)
0.949061 0.315093i \(-0.102036\pi\)
\(80\) 21760.0 34701.9i 0.0425000 0.0677772i
\(81\) −646479. −1.21646
\(82\) 58724.0 + 227437.i 0.106506 + 0.412496i
\(83\) 204153.i 0.357043i −0.983936 0.178522i \(-0.942869\pi\)
0.983936 0.178522i \(-0.0571314\pi\)
\(84\) −537600. + 297445.i −0.907029 + 0.501844i
\(85\) −47660.0 −0.0776064
\(86\) 166800. 43067.6i 0.262241 0.0677104i
\(87\) 790027.i 1.19973i
\(88\) −357120. + 338096.i −0.524042 + 0.496126i
\(89\) 310738. 0.440783 0.220391 0.975412i \(-0.429267\pi\)
0.220391 + 0.975412i \(0.429267\pi\)
\(90\) −4620.00 17893.2i −0.00633745 0.0245448i
\(91\) 454223.i 0.602761i
\(92\) 324480. + 586463.i 0.416701 + 0.753142i
\(93\) 1.29792e6 1.61361
\(94\) 58560.0 15120.1i 0.0705046 0.0182042i
\(95\) 75290.8i 0.0878155i
\(96\) 307200. 967688.i 0.347222 1.09376i
\(97\) −1.45709e6 −1.59650 −0.798252 0.602324i \(-0.794242\pi\)
−0.798252 + 0.602324i \(0.794242\pi\)
\(98\) 43298.0 + 167692.i 0.0460034 + 0.178170i
\(99\) 221875.i 0.228667i
\(100\) 869400. 481025.i 0.869400 0.481025i
\(101\) −639158. −0.620360 −0.310180 0.950678i \(-0.600389\pi\)
−0.310180 + 0.950678i \(0.600389\pi\)
\(102\) −1.14384e6 + 295338.i −1.07787 + 0.278304i
\(103\) 1.38913e6i 1.27125i 0.771997 + 0.635626i \(0.219258\pi\)
−0.771997 + 0.635626i \(0.780742\pi\)
\(104\) −516032. 545068.i −0.458751 0.484564i
\(105\) 96000.0 0.0829284
\(106\) −385708. 1.49384e6i −0.323848 1.25426i
\(107\) 1.14935e6i 0.938209i −0.883143 0.469105i \(-0.844577\pi\)
0.883143 0.469105i \(-0.155423\pi\)
\(108\) 478080. + 864078.i 0.379515 + 0.685933i
\(109\) 1.53574e6 1.18587 0.592936 0.805250i \(-0.297969\pi\)
0.592936 + 0.805250i \(0.297969\pi\)
\(110\) 74400.0 19210.0i 0.0558978 0.0144328i
\(111\) 61781.8i 0.0451743i
\(112\) 1.07520e6 + 674209.i 0.765306 + 0.479889i
\(113\) −601694. −0.417004 −0.208502 0.978022i \(-0.566859\pi\)
−0.208502 + 0.978022i \(0.566859\pi\)
\(114\) 466560. + 1.80698e6i 0.314915 + 1.21966i
\(115\) 104725.i 0.0688587i
\(116\) −1.42789e6 + 790027.i −0.914787 + 0.506137i
\(117\) −338646. −0.211441
\(118\) 607440. 156840.i 0.369707 0.0954579i
\(119\) 1.47669e6i 0.876292i
\(120\) −115200. + 109063.i −0.0666667 + 0.0631153i
\(121\) 849001. 0.479239
\(122\) −21836.0 84570.5i −0.0120252 0.0465735i
\(123\) 909748.i 0.488884i
\(124\) −1.29792e6 2.34585e6i −0.680743 1.23037i
\(125\) −311500. −0.159488
\(126\) 554400. 143145.i 0.277148 0.0715593i
\(127\) 1.67462e6i 0.817531i 0.912640 + 0.408765i \(0.134041\pi\)
−0.912640 + 0.408765i \(0.865959\pi\)
\(128\) −2.05619e6 + 412457.i −0.980469 + 0.196675i
\(129\) −667200. −0.310804
\(130\) 29320.0 + 113556.i 0.0133455 + 0.0516868i
\(131\) 2.84454e6i 1.26531i 0.774433 + 0.632656i \(0.218035\pi\)
−0.774433 + 0.632656i \(0.781965\pi\)
\(132\) 1.66656e6 922080.i 0.724601 0.400910i
\(133\) −2.33280e6 −0.991568
\(134\) 3.05304e6 788292.i 1.26887 0.327622i
\(135\) 154300.i 0.0627139i
\(136\) 1.67763e6 + 1.77203e6i 0.666930 + 0.704456i
\(137\) 3.81003e6 1.48172 0.740862 0.671658i \(-0.234417\pi\)
0.740862 + 0.671658i \(0.234417\pi\)
\(138\) −648960. 2.51341e6i −0.246934 0.956371i
\(139\) 138839.i 0.0516971i 0.999666 + 0.0258485i \(0.00822877\pi\)
−0.999666 + 0.0258485i \(0.991771\pi\)
\(140\) −96000.0 173510.i −0.0349854 0.0632324i
\(141\) −234240. −0.0835610
\(142\) −4.12272e6 + 1.06448e6i −1.43986 + 0.371769i
\(143\) 1.40809e6i 0.481530i
\(144\) −502656. + 801615.i −0.168338 + 0.268459i
\(145\) 254980. 0.0836377
\(146\) 577252. + 2.23569e6i 0.185484 + 0.718377i
\(147\) 670770.i 0.211165i
\(148\) −111664. + 61781.8i −0.0344451 + 0.0190579i
\(149\) −3.27426e6 −0.989816 −0.494908 0.868945i \(-0.664798\pi\)
−0.494908 + 0.868945i \(0.664798\pi\)
\(150\) −3.72600e6 + 962049.i −1.10400 + 0.285052i
\(151\) 5.59352e6i 1.62463i −0.583220 0.812314i \(-0.698207\pi\)
0.583220 0.812314i \(-0.301793\pi\)
\(152\) 2.79936e6 2.65024e6i 0.797128 0.754664i
\(153\) 1.10095e6 0.307391
\(154\) 595200. + 2.30520e6i 0.162967 + 0.631170i
\(155\) 418902.i 0.112491i
\(156\) 1.40736e6 + 2.54365e6i 0.370708 + 0.670014i
\(157\) 816794. 0.211064 0.105532 0.994416i \(-0.466345\pi\)
0.105532 + 0.994416i \(0.466345\pi\)
\(158\) 2.40672e6 621412.i 0.610175 0.157546i
\(159\) 5.97536e6i 1.48653i
\(160\) 312320. + 99148.4i 0.0762500 + 0.0242061i
\(161\) 3.24480e6 0.777518
\(162\) −1.29296e6 5.00760e6i −0.304116 1.17784i
\(163\) 1.84593e6i 0.426237i −0.977026 0.213119i \(-0.931638\pi\)
0.977026 0.213119i \(-0.0683621\pi\)
\(164\) −1.64427e6 + 909748.i −0.372771 + 0.206248i
\(165\) −297600. −0.0662493
\(166\) 1.58136e6 408305.i 0.345706 0.0892608i
\(167\) 7.96515e6i 1.71019i 0.518471 + 0.855095i \(0.326501\pi\)
−0.518471 + 0.855095i \(0.673499\pi\)
\(168\) −3.37920e6 3.56934e6i −0.712666 0.752766i
\(169\) −2.67765e6 −0.554746
\(170\) −95320.0 369173.i −0.0194016 0.0751420i
\(171\) 1.73922e6i 0.347829i
\(172\) 667200. + 1.20589e6i 0.131121 + 0.236986i
\(173\) −5.12653e6 −0.990115 −0.495057 0.868860i \(-0.664853\pi\)
−0.495057 + 0.868860i \(0.664853\pi\)
\(174\) 6.11952e6 1.58005e6i 1.16163 0.299933i
\(175\) 4.81025e6i 0.897538i
\(176\) −3.33312e6 2.09005e6i −0.611382 0.383370i
\(177\) −2.42976e6 −0.438171
\(178\) 621476. + 2.40697e6i 0.110196 + 0.426786i
\(179\) 2.33411e6i 0.406969i −0.979078 0.203485i \(-0.934773\pi\)
0.979078 0.203485i \(-0.0652267\pi\)
\(180\) 129360. 71572.7i 0.0221811 0.0122724i
\(181\) 9.69156e6 1.63440 0.817199 0.576355i \(-0.195525\pi\)
0.817199 + 0.576355i \(0.195525\pi\)
\(182\) −3.51840e6 + 908447.i −0.583621 + 0.150690i
\(183\) 338282.i 0.0551983i
\(184\) −3.89376e6 + 3.68634e6i −0.625051 + 0.591754i
\(185\) 19940.0 0.00314927
\(186\) 2.59584e6 + 1.00536e7i 0.403403 + 1.56237i
\(187\) 4.57774e6i 0.700046i
\(188\) 234240. + 423364.i 0.0352523 + 0.0637147i
\(189\) 4.78080e6 0.708134
\(190\) −583200. + 150582.i −0.0850270 + 0.0219539i
\(191\) 1.14164e7i 1.63844i −0.573479 0.819220i \(-0.694407\pi\)
0.573479 0.819220i \(-0.305593\pi\)
\(192\) 8.11008e6 + 444185.i 1.14583 + 0.0627567i
\(193\) −2.43033e6 −0.338060 −0.169030 0.985611i \(-0.554064\pi\)
−0.169030 + 0.985611i \(0.554064\pi\)
\(194\) −2.91417e6 1.12865e7i −0.399126 1.54581i
\(195\) 454223.i 0.0612584i
\(196\) −1.21234e6 + 670770.i −0.161012 + 0.0890851i
\(197\) −2.23065e6 −0.291764 −0.145882 0.989302i \(-0.546602\pi\)
−0.145882 + 0.989302i \(0.546602\pi\)
\(198\) −1.71864e6 + 443751.i −0.221406 + 0.0571668i
\(199\) 4.89576e6i 0.621242i 0.950534 + 0.310621i \(0.100537\pi\)
−0.950534 + 0.310621i \(0.899463\pi\)
\(200\) 5.46480e6 + 5.77229e6i 0.683100 + 0.721537i
\(201\) −1.22122e7 −1.50385
\(202\) −1.27832e6 4.95090e6i −0.155090 0.600661i
\(203\) 7.90027e6i 0.944395i
\(204\) −4.57536e6 8.26947e6i −0.538933 0.974063i
\(205\) 293620. 0.0340819
\(206\) −1.07602e7 + 2.77826e6i −1.23088 + 0.317813i
\(207\) 2.41916e6i 0.272743i
\(208\) 3.19002e6 5.08730e6i 0.354489 0.565324i
\(209\) 7.23168e6 0.792137
\(210\) 192000. + 743613.i 0.0207321 + 0.0802951i
\(211\) 3.90951e6i 0.416174i 0.978110 + 0.208087i \(0.0667238\pi\)
−0.978110 + 0.208087i \(0.933276\pi\)
\(212\) 1.07998e7 5.97536e6i 1.13347 0.627129i
\(213\) 1.64909e7 1.70650
\(214\) 8.90280e6 2.29869e6i 0.908417 0.234552i
\(215\) 215338.i 0.0216673i
\(216\) −5.73696e6 + 5.43135e6i −0.569273 + 0.538947i
\(217\) −1.29792e7 −1.27019
\(218\) 3.07148e6 + 1.18958e7i 0.296468 + 1.14822i
\(219\) 8.94275e6i 0.851410i
\(220\) 297600. + 537880.i 0.0279489 + 0.0505146i
\(221\) −6.98696e6 −0.647308
\(222\) 478560. 123564.i 0.0437399 0.0112936i
\(223\) 3.33114e6i 0.300385i 0.988657 + 0.150192i \(0.0479893\pi\)
−0.988657 + 0.150192i \(0.952011\pi\)
\(224\) −3.07200e6 + 9.67688e6i −0.273324 + 0.860977i
\(225\) 3.58628e6 0.314844
\(226\) −1.20339e6 4.66070e6i −0.104251 0.403763i
\(227\) 1.35033e7i 1.15442i −0.816597 0.577208i \(-0.804142\pi\)
0.816597 0.577208i \(-0.195858\pi\)
\(228\) −1.30637e7 + 7.22792e6i −1.10220 + 0.609830i
\(229\) 1.59598e6 0.132899 0.0664493 0.997790i \(-0.478833\pi\)
0.0664493 + 0.997790i \(0.478833\pi\)
\(230\) 811200. 209451.i 0.0666721 0.0172147i
\(231\) 9.22080e6i 0.748053i
\(232\) −8.97530e6 9.48032e6i −0.718762 0.759205i
\(233\) 8.04383e6 0.635909 0.317954 0.948106i \(-0.397004\pi\)
0.317954 + 0.948106i \(0.397004\pi\)
\(234\) −677292. 2.62314e6i −0.0528601 0.204726i
\(235\) 75600.6i 0.00582535i
\(236\) 2.42976e6 + 4.39153e6i 0.184853 + 0.334103i
\(237\) −9.62688e6 −0.723170
\(238\) 1.14384e7 2.95338e6i 0.848466 0.219073i
\(239\) 1.12532e7i 0.824296i 0.911117 + 0.412148i \(0.135221\pi\)
−0.911117 + 0.412148i \(0.864779\pi\)
\(240\) −1.07520e6 674209.i −0.0777778 0.0487709i
\(241\) 5.05104e6 0.360853 0.180426 0.983589i \(-0.442252\pi\)
0.180426 + 0.983589i \(0.442252\pi\)
\(242\) 1.69800e6 + 6.57633e6i 0.119810 + 0.464021i
\(243\) 8.78197e6i 0.612031i
\(244\) 611408. 338282.i 0.0420883 0.0232868i
\(245\) 216490. 0.0147211
\(246\) 7.04688e6 1.81950e6i 0.473360 0.122221i
\(247\) 1.10376e7i 0.732462i
\(248\) 1.55750e7 1.47453e7i 1.02111 0.966718i
\(249\) −6.32544e6 −0.409725
\(250\) −623000. 2.41287e6i −0.0398720 0.154424i
\(251\) 4.71590e6i 0.298225i 0.988820 + 0.149112i \(0.0476416\pi\)
−0.988820 + 0.149112i \(0.952358\pi\)
\(252\) 2.21760e6 + 4.00807e6i 0.138574 + 0.250457i
\(253\) −1.00589e7 −0.621138
\(254\) −1.29715e7 + 3.34923e6i −0.791571 + 0.204383i
\(255\) 1.47669e6i 0.0890572i
\(256\) −7.30726e6 1.51023e7i −0.435547 0.900166i
\(257\) 2.34552e7 1.38178 0.690892 0.722958i \(-0.257218\pi\)
0.690892 + 0.722958i \(0.257218\pi\)
\(258\) −1.33440e6 5.16811e6i −0.0777011 0.300935i
\(259\) 617818.i 0.0355600i
\(260\) −820960. + 454223.i −0.0467091 + 0.0258434i
\(261\) −5.89004e6 −0.331281
\(262\) −2.20337e7 + 5.68907e6i −1.22513 + 0.316328i
\(263\) 2.16993e7i 1.19283i −0.802676 0.596415i \(-0.796591\pi\)
0.802676 0.596415i \(-0.203409\pi\)
\(264\) 1.04755e7 + 1.10650e7i 0.569330 + 0.601365i
\(265\) −1.92854e6 −0.103631
\(266\) −4.66560e6 1.80698e7i −0.247892 0.960082i
\(267\) 9.62786e6i 0.505820i
\(268\) 1.22122e7 + 2.20722e7i 0.634436 + 1.14668i
\(269\) −2.94278e7 −1.51182 −0.755911 0.654674i \(-0.772806\pi\)
−0.755911 + 0.654674i \(0.772806\pi\)
\(270\) 1.19520e6 308599.i 0.0607225 0.0156785i
\(271\) 8.51474e6i 0.427822i −0.976853 0.213911i \(-0.931380\pi\)
0.976853 0.213911i \(-0.0686203\pi\)
\(272\) −1.03708e7 + 1.65389e7i −0.515355 + 0.821866i
\(273\) 1.40736e7 0.691699
\(274\) 7.62007e6 + 2.95124e7i 0.370431 + 1.43467i
\(275\) 1.49118e7i 0.717019i
\(276\) 1.81709e7 1.00536e7i 0.864269 0.478185i
\(277\) 2.76226e7 1.29965 0.649824 0.760085i \(-0.274843\pi\)
0.649824 + 0.760085i \(0.274843\pi\)
\(278\) −1.07544e6 + 277677.i −0.0500555 + 0.0129243i
\(279\) 9.67663e6i 0.445566i
\(280\) 1.15200e6 1.09063e6i 0.0524781 0.0496826i
\(281\) 8.64008e6 0.389403 0.194701 0.980863i \(-0.437626\pi\)
0.194701 + 0.980863i \(0.437626\pi\)
\(282\) −468480. 1.81442e6i −0.0208903 0.0809076i
\(283\) 1.27350e7i 0.561873i −0.959726 0.280937i \(-0.909355\pi\)
0.959726 0.280937i \(-0.0906450\pi\)
\(284\) −1.64909e7 2.98055e7i −0.719928 1.30119i
\(285\) 2.33280e6 0.100773
\(286\) 1.09070e7 2.81619e6i 0.466239 0.120382i
\(287\) 9.09748e6i 0.384836i
\(288\) −7.21459e6 2.29033e6i −0.302019 0.0958783i
\(289\) −1.42281e6 −0.0589460
\(290\) 509960. + 1.97507e6i 0.0209094 + 0.0809819i
\(291\) 4.51462e7i 1.83207i
\(292\) −1.61631e7 + 8.94275e6i −0.649195 + 0.359189i
\(293\) −4.45415e7 −1.77077 −0.885385 0.464859i \(-0.846105\pi\)
−0.885385 + 0.464859i \(0.846105\pi\)
\(294\) 5.19576e6 1.34154e6i 0.204459 0.0527912i
\(295\) 784202.i 0.0305465i
\(296\) −701888. 741382.i −0.0270640 0.0285869i
\(297\) −1.48205e7 −0.565709
\(298\) −6.54852e6 2.53623e7i −0.247454 0.958386i
\(299\) 1.53528e7i 0.574345i
\(300\) −1.49040e7 2.69374e7i −0.552000 0.997681i
\(301\) 6.67200e6 0.244656
\(302\) 4.33272e7 1.11870e7i 1.57304 0.406157i
\(303\) 1.98036e7i 0.711895i
\(304\) 2.61274e7 + 1.63833e7i 0.929983 + 0.583150i
\(305\) −109180. −0.00384808
\(306\) 2.20189e6 + 8.52789e6i 0.0768479 + 0.297630i
\(307\) 4.89051e7i 1.69020i −0.534606 0.845102i \(-0.679540\pi\)
0.534606 0.845102i \(-0.320460\pi\)
\(308\) −1.66656e7 + 9.22080e6i −0.570386 + 0.315585i
\(309\) 4.30406e7 1.45883
\(310\) −3.24480e6 + 837804.i −0.108919 + 0.0281227i
\(311\) 5.00220e7i 1.66295i 0.555559 + 0.831477i \(0.312504\pi\)
−0.555559 + 0.831477i \(0.687496\pi\)
\(312\) −1.68883e7 + 1.59887e7i −0.556061 + 0.526440i
\(313\) 1.12719e6 0.0367589 0.0183795 0.999831i \(-0.494149\pi\)
0.0183795 + 0.999831i \(0.494149\pi\)
\(314\) 1.63359e6 + 6.32686e6i 0.0527659 + 0.204362i
\(315\) 715727.i 0.0228990i
\(316\) 9.62688e6 + 1.73995e7i 0.305087 + 0.551413i
\(317\) 3.44882e7 1.08266 0.541330 0.840810i \(-0.317921\pi\)
0.541330 + 0.840810i \(0.317921\pi\)
\(318\) −4.62850e7 + 1.19507e7i −1.43932 + 0.371632i
\(319\) 2.44908e7i 0.754452i
\(320\) −143360. + 2.61752e6i −0.00437500 + 0.0798803i
\(321\) −3.56112e7 −1.07664
\(322\) 6.48960e6 + 2.51341e7i 0.194379 + 0.752828i
\(323\) 3.58836e7i 1.06485i
\(324\) 3.62028e7 2.00304e7i 1.06441 0.588918i
\(325\) −2.27596e7 −0.663003
\(326\) 1.42985e7 3.69185e6i 0.412702 0.106559i
\(327\) 4.75831e7i 1.36085i
\(328\) −1.03354e7 1.09170e7i −0.292891 0.309372i
\(329\) 2.34240e6 0.0657769
\(330\) −595200. 2.30520e6i −0.0165623 0.0641456i
\(331\) 4.02696e7i 1.11044i 0.831705 + 0.555218i \(0.187365\pi\)
−0.831705 + 0.555218i \(0.812635\pi\)
\(332\) 6.32544e6 + 1.14326e7i 0.172853 + 0.312413i
\(333\) −460614. −0.0124740
\(334\) −6.16978e7 + 1.59303e7i −1.65588 + 0.427547i
\(335\) 3.94146e6i 0.104839i
\(336\) 2.08896e7 3.33139e7i 0.550696 0.878228i
\(337\) −3.42531e7 −0.894973 −0.447487 0.894291i \(-0.647681\pi\)
−0.447487 + 0.894291i \(0.647681\pi\)
\(338\) −5.35531e6 2.07410e7i −0.138687 0.537131i
\(339\) 1.86428e7i 0.478533i
\(340\) 2.66896e6 1.47669e6i 0.0679056 0.0375710i
\(341\) 4.02355e7 1.01472
\(342\) 1.34719e7 3.47843e6i 0.336784 0.0869572i
\(343\) 4.31599e7i 1.06954i
\(344\) −8.00640e6 + 7.57989e6i −0.196681 + 0.186203i
\(345\) −3.24480e6 −0.0790188
\(346\) −1.02531e7 3.97100e7i −0.247529 0.958674i
\(347\) 5.45496e7i 1.30558i 0.757539 + 0.652790i \(0.226401\pi\)
−0.757539 + 0.652790i \(0.773599\pi\)
\(348\) 2.44781e7 + 4.42415e7i 0.580817 + 1.04976i
\(349\) 4.70009e7 1.10568 0.552840 0.833287i \(-0.313544\pi\)
0.552840 + 0.833287i \(0.313544\pi\)
\(350\) 3.72600e7 9.62049e6i 0.869038 0.224385i
\(351\) 2.26203e7i 0.523091i
\(352\) 9.52320e6 2.99983e7i 0.218351 0.687811i
\(353\) −1.27231e7 −0.289248 −0.144624 0.989487i \(-0.546197\pi\)
−0.144624 + 0.989487i \(0.546197\pi\)
\(354\) −4.85952e6 1.88208e7i −0.109543 0.424257i
\(355\) 5.32241e6i 0.118966i
\(356\) −1.74013e7 + 9.62786e6i −0.385685 + 0.213393i
\(357\) −4.57536e7 −1.00559
\(358\) 1.80799e7 4.66822e6i 0.394046 0.101742i
\(359\) 2.02153e7i 0.436915i −0.975846 0.218457i \(-0.929898\pi\)
0.975846 0.218457i \(-0.0701025\pi\)
\(360\) 813120. + 858873.i 0.0174280 + 0.0184086i
\(361\) −9.64116e6 −0.204931
\(362\) 1.93831e7 + 7.50705e7i 0.408600 + 1.58250i
\(363\) 2.63053e7i 0.549951i
\(364\) −1.40736e7 2.54365e7i −0.291811 0.527416i
\(365\) 2.88626e6 0.0593549
\(366\) −2.62032e6 + 676564.i −0.0534455 + 0.0137996i
\(367\) 1.11057e7i 0.224672i −0.993670 0.112336i \(-0.964167\pi\)
0.993670 0.112336i \(-0.0358333\pi\)
\(368\) −3.63418e7 2.27883e7i −0.729227 0.457265i
\(369\) −6.78262e6 −0.134995
\(370\) 39880.0 + 154455.i 0.000787318 + 0.00304927i
\(371\) 5.97536e7i 1.17015i
\(372\) −7.26835e7 + 4.02146e7i −1.41191 + 0.781186i
\(373\) 687146. 0.0132411 0.00662053 0.999978i \(-0.497893\pi\)
0.00662053 + 0.999978i \(0.497893\pi\)
\(374\) −3.54590e7 + 9.15548e6i −0.677817 + 0.175011i
\(375\) 9.65147e6i 0.183021i
\(376\) −2.81088e6 + 2.66114e6i −0.0528785 + 0.0500616i
\(377\) 3.73801e7 0.697615
\(378\) 9.56160e6 + 3.70319e7i 0.177033 + 0.685647i
\(379\) 1.48499e7i 0.272775i 0.990656 + 0.136388i \(0.0435492\pi\)
−0.990656 + 0.136388i \(0.956451\pi\)
\(380\) −2.33280e6 4.21628e6i −0.0425135 0.0768385i
\(381\) 5.18861e7 0.938158
\(382\) 8.84314e7 2.28329e7i 1.58641 0.409610i
\(383\) 3.35885e7i 0.597853i −0.954276 0.298926i \(-0.903372\pi\)
0.954276 0.298926i \(-0.0966285\pi\)
\(384\) 1.27795e7 + 6.37088e7i 0.225694 + 1.12514i
\(385\) 2.97600e6 0.0521496
\(386\) −4.86067e6 1.88253e7i −0.0845150 0.327325i
\(387\) 4.97430e6i 0.0858222i
\(388\) 8.15968e7 4.51462e7i 1.39694 0.772904i
\(389\) −1.01122e8 −1.71789 −0.858946 0.512066i \(-0.828880\pi\)
−0.858946 + 0.512066i \(0.828880\pi\)
\(390\) 3.51840e6 908447.i 0.0593132 0.0153146i
\(391\) 4.99122e7i 0.834980i
\(392\) −7.62045e6 8.04924e6i −0.126509 0.133628i
\(393\) 8.81347e7 1.45201
\(394\) −4.46129e6 1.72785e7i −0.0729410 0.282499i
\(395\) 3.10706e6i 0.0504149i
\(396\) −6.87456e6 1.24250e7i −0.110703 0.200084i
\(397\) −3.48266e7 −0.556595 −0.278297 0.960495i \(-0.589770\pi\)
−0.278297 + 0.960495i \(0.589770\pi\)
\(398\) −3.79224e7 + 9.79152e6i −0.601515 + 0.155311i
\(399\) 7.22792e7i 1.13787i
\(400\) −3.37824e7 + 5.38747e7i −0.527850 + 0.841793i
\(401\) −6.88398e7 −1.06760 −0.533798 0.845612i \(-0.679236\pi\)
−0.533798 + 0.845612i \(0.679236\pi\)
\(402\) −2.44243e7 9.45950e7i −0.375962 1.45610i
\(403\) 6.14110e7i 0.938277i
\(404\) 3.57928e7 1.98036e7i 0.542815 0.300331i
\(405\) −6.46479e6 −0.0973171
\(406\) −6.11952e7 + 1.58005e7i −0.914406 + 0.236099i
\(407\) 1.91524e6i 0.0284079i
\(408\) 5.49043e7 5.19795e7i 0.808399 0.765335i
\(409\) 4.59959e7 0.672278 0.336139 0.941812i \(-0.390879\pi\)
0.336139 + 0.941812i \(0.390879\pi\)
\(410\) 587240. + 2.27437e6i 0.00852048 + 0.0329997i
\(411\) 1.18050e8i 1.70035i
\(412\) −4.30406e7 7.77913e7i −0.615442 1.11234i
\(413\) 2.42976e7 0.344916
\(414\) −1.87387e7 + 4.83832e6i −0.264082 + 0.0681857i
\(415\) 2.04153e6i 0.0285635i
\(416\) 4.57861e7 + 1.45352e7i 0.635995 + 0.201902i
\(417\) 4.30176e6 0.0593250
\(418\) 1.44634e7 + 5.60164e7i 0.198034 + 0.766983i
\(419\) 2.71153e7i 0.368615i 0.982869 + 0.184307i \(0.0590042\pi\)
−0.982869 + 0.184307i \(0.940996\pi\)
\(420\) −5.37600e6 + 2.97445e6i −0.0725624 + 0.0401475i
\(421\) −9.42078e7 −1.26253 −0.631263 0.775569i \(-0.717463\pi\)
−0.631263 + 0.775569i \(0.717463\pi\)
\(422\) −3.02830e7 + 7.81903e6i −0.402959 + 0.104044i
\(423\) 1.74637e6i 0.0230737i
\(424\) 6.78846e7 + 7.17044e7i 0.890582 + 0.940693i
\(425\) 7.39922e7 0.963871
\(426\) 3.29818e7 + 1.27738e8i 0.426624 + 1.65231i
\(427\) 3.38282e6i 0.0434505i
\(428\) 3.56112e7 + 6.43634e7i 0.454209 + 0.820933i
\(429\) −4.36282e7 −0.552580
\(430\) 1.66800e6 430676.i 0.0209793 0.00541683i
\(431\) 5.19187e7i 0.648473i −0.945976 0.324236i \(-0.894893\pi\)
0.945976 0.324236i \(-0.105107\pi\)
\(432\) −5.35450e7 3.35756e7i −0.664152 0.416459i
\(433\) 8.40210e7 1.03496 0.517481 0.855695i \(-0.326870\pi\)
0.517481 + 0.855695i \(0.326870\pi\)
\(434\) −2.59584e7 1.00536e8i −0.317548 1.22986i
\(435\) 7.90027e6i 0.0959785i
\(436\) −8.60013e7 + 4.75831e7i −1.03764 + 0.574108i
\(437\) 7.88486e7 0.944822
\(438\) 6.92702e7 1.78855e7i 0.824374 0.212852i
\(439\) 1.48115e8i 1.75068i −0.483512 0.875338i \(-0.660639\pi\)
0.483512 0.875338i \(-0.339361\pi\)
\(440\) −3.57120e6 + 3.38096e6i −0.0419234 + 0.0396901i
\(441\) −5.00092e6 −0.0583088
\(442\) −1.39739e7 5.41207e7i −0.161827 0.626754i
\(443\) 8.03735e7i 0.924489i 0.886752 + 0.462245i \(0.152956\pi\)
−0.886752 + 0.462245i \(0.847044\pi\)
\(444\) 1.91424e6 + 3.45978e6i 0.0218699 + 0.0395275i
\(445\) 3.10738e6 0.0352626
\(446\) −2.58029e7 + 6.66227e6i −0.290846 + 0.0750962i
\(447\) 1.01449e8i 1.13586i
\(448\) −8.11008e7 4.44185e6i −0.901968 0.0494003i
\(449\) −8.80925e7 −0.973196 −0.486598 0.873626i \(-0.661762\pi\)
−0.486598 + 0.873626i \(0.661762\pi\)
\(450\) 7.17255e6 + 2.77792e7i 0.0787111 + 0.304847i
\(451\) 2.82022e7i 0.307435i
\(452\) 3.36949e7 1.86428e7i 0.364879 0.201881i
\(453\) −1.73309e8 −1.86434
\(454\) 1.04596e8 2.70066e7i 1.11776 0.288604i
\(455\) 4.54223e6i 0.0482209i
\(456\) −8.21146e7 8.67350e7i −0.866015 0.914745i
\(457\) −3.75423e7 −0.393344 −0.196672 0.980469i \(-0.563013\pi\)
−0.196672 + 0.980469i \(0.563013\pi\)
\(458\) 3.19196e6 + 1.23624e7i 0.0332247 + 0.128679i
\(459\) 7.35392e7i 0.760468i
\(460\) 3.24480e6 + 5.86463e6i 0.0333361 + 0.0602514i
\(461\) 1.15260e8 1.17646 0.588228 0.808695i \(-0.299826\pi\)
0.588228 + 0.808695i \(0.299826\pi\)
\(462\) 7.14240e7 1.84416e7i 0.724300 0.187013i
\(463\) 1.03415e7i 0.104194i −0.998642 0.0520970i \(-0.983410\pi\)
0.998642 0.0520970i \(-0.0165905\pi\)
\(464\) 5.54836e7 8.84830e7i 0.555407 0.885739i
\(465\) 1.29792e7 0.129089
\(466\) 1.60877e7 + 6.23072e7i 0.158977 + 0.615716i
\(467\) 1.64223e8i 1.61243i 0.591620 + 0.806217i \(0.298489\pi\)
−0.591620 + 0.806217i \(0.701511\pi\)
\(468\) 1.89642e7 1.04926e7i 0.185011 0.102363i
\(469\) 1.22122e8 1.18379
\(470\) 585600. 151201.i 0.00564037 0.00145634i
\(471\) 2.53074e7i 0.242206i
\(472\) −2.91571e7 + 2.76039e7i −0.277280 + 0.262509i
\(473\) −2.06832e7 −0.195449
\(474\) −1.92538e7 7.45695e7i −0.180793 0.700207i
\(475\) 1.16889e8i 1.09067i
\(476\) 4.57536e7 + 8.26947e7i 0.424233 + 0.766755i
\(477\) 4.45493e7 0.410474
\(478\) −8.71670e7 + 2.25064e7i −0.798121 + 0.206074i
\(479\) 7.76230e7i 0.706291i 0.935568 + 0.353146i \(0.114888\pi\)
−0.935568 + 0.353146i \(0.885112\pi\)
\(480\) 3.07200e6 9.67688e6i 0.0277778 0.0875007i
\(481\) 2.92320e6 0.0262678
\(482\) 1.01021e7 + 3.91252e7i 0.0902132 + 0.349394i
\(483\) 1.00536e8i 0.892241i
\(484\) −4.75441e7 + 2.63053e7i −0.419334 + 0.232011i
\(485\) −1.45709e7 −0.127720
\(486\) −6.80249e7 + 1.75639e7i −0.592596 + 0.153008i
\(487\) 1.08071e7i 0.0935670i −0.998905 0.0467835i \(-0.985103\pi\)
0.998905 0.0467835i \(-0.0148971\pi\)
\(488\) 3.84314e6 + 4.05938e6i 0.0330694 + 0.0349302i
\(489\) −5.71939e7 −0.489129
\(490\) 432980. + 1.67692e6i 0.00368027 + 0.0142536i
\(491\) 1.85067e8i 1.56345i −0.623624 0.781724i \(-0.714340\pi\)
0.623624 0.781724i \(-0.285660\pi\)
\(492\) 2.81875e7 + 5.09459e7i 0.236680 + 0.427774i
\(493\) −1.21523e8 −1.01419
\(494\) −8.54971e7 + 2.20753e7i −0.709203 + 0.183115i
\(495\) 2.21875e6i 0.0182934i
\(496\) 1.45367e8 + 9.11530e7i 1.19130 + 0.747010i
\(497\) −1.64909e8 −1.34331
\(498\) −1.26509e7 4.89966e7i −0.102431 0.396715i
\(499\) 6.83704e7i 0.550258i −0.961407 0.275129i \(-0.911279\pi\)
0.961407 0.275129i \(-0.0887206\pi\)
\(500\) 1.74440e7 9.65147e6i 0.139552 0.0772118i
\(501\) 2.46791e8 1.96253
\(502\) −3.65292e7 + 9.43180e6i −0.288755 + 0.0745561i
\(503\) 1.31562e7i 0.103377i 0.998663 + 0.0516887i \(0.0164604\pi\)
−0.998663 + 0.0516887i \(0.983540\pi\)
\(504\) −2.66112e7 + 2.51936e7i −0.207861 + 0.196788i
\(505\) −6.39158e6 −0.0496288
\(506\) −2.01178e7 7.79157e7i −0.155284 0.601414i
\(507\) 8.29640e7i 0.636599i
\(508\) −5.18861e7 9.37785e7i −0.395785 0.715339i
\(509\) 1.34186e8 1.01755 0.508775 0.860900i \(-0.330099\pi\)
0.508775 + 0.860900i \(0.330099\pi\)
\(510\) −1.14384e7 + 2.95338e6i −0.0862293 + 0.0222643i
\(511\) 8.94275e7i 0.670206i
\(512\) 1.02367e8 8.68064e7i 0.762695 0.646758i
\(513\) 1.16173e8 0.860508
\(514\) 4.69105e7 + 1.81683e8i 0.345446 + 1.33791i
\(515\) 1.38913e7i 0.101700i
\(516\) 3.73632e7 2.06724e7i 0.271954 0.150467i
\(517\) −7.26144e6 −0.0525474
\(518\) −4.78560e6 + 1.23564e6i −0.0344308 + 0.00888999i
\(519\) 1.58840e8i 1.13621i
\(520\) −5.16032e6 5.45068e6i −0.0367000 0.0387651i
\(521\) −1.98565e8 −1.40407 −0.702036 0.712142i \(-0.747725\pi\)
−0.702036 + 0.712142i \(0.747725\pi\)
\(522\) −1.17801e7 4.56240e7i −0.0828203 0.320761i
\(523\) 2.15512e8i 1.50649i 0.657740 + 0.753245i \(0.271513\pi\)
−0.657740 + 0.753245i \(0.728487\pi\)
\(524\) −8.81347e7 1.59294e8i −0.612566 1.10715i
\(525\) −1.49040e8 −1.02997
\(526\) 1.68082e8 4.33986e7i 1.15495 0.298207i
\(527\) 1.99649e8i 1.36406i
\(528\) −6.47578e7 + 1.03273e8i −0.439937 + 0.701592i
\(529\) 3.83616e7 0.259137
\(530\) −3.85708e6 1.49384e7i −0.0259078 0.100341i
\(531\) 1.81151e7i 0.120992i
\(532\) 1.30637e8 7.22792e7i 0.867622 0.480041i
\(533\) 4.30447e7 0.284275
\(534\) 7.45771e7 1.92557e7i 0.489758 0.126455i
\(535\) 1.14935e7i 0.0750567i
\(536\) −1.46546e8 + 1.38739e8i −0.951655 + 0.900959i
\(537\) −7.23197e7 −0.467018
\(538\) −5.88556e7 2.27947e8i −0.377956 1.46382i
\(539\) 2.07939e7i 0.132791i
\(540\) 4.78080e6 + 8.64078e6i 0.0303612 + 0.0548746i
\(541\) 1.44188e7 0.0910623 0.0455311 0.998963i \(-0.485502\pi\)
0.0455311 + 0.998963i \(0.485502\pi\)
\(542\) 6.59549e7 1.70295e7i 0.414237 0.106956i
\(543\) 3.00282e8i 1.87556i
\(544\) −1.48852e8 4.72541e7i −0.924607 0.293524i
\(545\) 1.53574e7 0.0948697
\(546\) 2.81472e7 + 1.09014e8i 0.172925 + 0.669735i
\(547\) 4.24129e7i 0.259141i 0.991570 + 0.129571i \(0.0413599\pi\)
−0.991570 + 0.129571i \(0.958640\pi\)
\(548\) −2.13362e8 + 1.18050e8i −1.29651 + 0.717336i
\(549\) 2.52206e6 0.0152419
\(550\) −1.15506e8 + 2.98235e7i −0.694251 + 0.179255i
\(551\) 1.91976e8i 1.14761i
\(552\) 1.14217e8 + 1.20644e8i 0.679068 + 0.717278i
\(553\) 9.62688e7 0.569259
\(554\) 5.52453e7 + 2.13964e8i 0.324912 + 1.25838i
\(555\) 617818.i 0.00361395i
\(556\) −4.30176e6 7.77497e6i −0.0250277 0.0452350i
\(557\) 8.90848e7 0.515511 0.257756 0.966210i \(-0.417017\pi\)
0.257756 + 0.966210i \(0.417017\pi\)
\(558\) 7.49549e7 1.93533e7i 0.431417 0.111391i
\(559\) 3.15685e7i 0.180725i
\(560\) 1.07520e7 + 6.74209e6i 0.0612245 + 0.0383911i
\(561\) 1.41836e8 0.803338
\(562\) 1.72802e7 + 6.69258e7i 0.0973507 + 0.377037i
\(563\) 2.41576e8i 1.35372i −0.736112 0.676860i \(-0.763340\pi\)
0.736112 0.676860i \(-0.236660\pi\)
\(564\) 1.31174e7 7.25766e6i 0.0731159 0.0404538i
\(565\) −6.01694e6 −0.0333603
\(566\) 9.86446e7 2.54699e7i 0.544031 0.140468i
\(567\) 2.00304e8i 1.09886i
\(568\) 1.97891e8 1.87349e8i 1.07989 1.02236i
\(569\) −2.56141e7 −0.139041 −0.0695203 0.997581i \(-0.522147\pi\)
−0.0695203 + 0.997581i \(0.522147\pi\)
\(570\) 4.66560e6 + 1.80698e7i 0.0251932 + 0.0975728i
\(571\) 1.10781e8i 0.595057i 0.954713 + 0.297528i \(0.0961623\pi\)
−0.954713 + 0.297528i \(0.903838\pi\)
\(572\) 4.36282e7 + 7.88532e7i 0.233120 + 0.421339i
\(573\) −3.53725e8 −1.88019
\(574\) −7.04688e7 + 1.81950e7i −0.372616 + 0.0962090i
\(575\) 1.62586e8i 0.855225i
\(576\) 3.31162e6 6.04646e7i 0.0173290 0.316398i
\(577\) 1.07272e8 0.558415 0.279208 0.960231i \(-0.409928\pi\)
0.279208 + 0.960231i \(0.409928\pi\)
\(578\) −2.84563e6 1.10211e7i −0.0147365 0.0570742i
\(579\) 7.53011e7i 0.387941i
\(580\) −1.42789e7 + 7.90027e6i −0.0731830 + 0.0404909i
\(581\) 6.32544e7 0.322524
\(582\) −3.49701e8 + 9.02923e7i −1.77389 + 0.458017i
\(583\) 1.85236e8i 0.934803i
\(584\) −1.01596e8 1.07313e8i −0.510082 0.538783i
\(585\) −3.38646e6 −0.0169152
\(586\) −8.90830e7 3.45017e8i −0.442692 1.71454i
\(587\) 2.16397e7i 0.106988i 0.998568 + 0.0534941i \(0.0170358\pi\)
−0.998568 + 0.0534941i \(0.982964\pi\)
\(588\) 2.07830e7 + 3.75631e7i 0.102230 + 0.184769i
\(589\) −3.15395e8 −1.54351
\(590\) 6.07440e6 1.56840e6i 0.0295765 0.00763663i
\(591\) 6.91140e7i 0.334814i
\(592\) 4.33894e6 6.91956e6i 0.0209131 0.0333514i
\(593\) 2.00341e8 0.960738 0.480369 0.877066i \(-0.340503\pi\)
0.480369 + 0.877066i \(0.340503\pi\)
\(594\) −2.96410e7 1.14799e8i −0.141427 0.547745i
\(595\) 1.47669e7i 0.0701033i
\(596\) 1.83359e8 1.01449e8i 0.866089 0.479193i
\(597\) 1.51690e8 0.712907
\(598\) 1.18922e8 3.07055e7i 0.556107 0.143586i
\(599\) 1.37592e8i 0.640197i −0.947384 0.320098i \(-0.896284\pi\)
0.947384 0.320098i \(-0.103716\pi\)
\(600\) 1.78848e8 1.69321e8i 0.828000 0.783892i
\(601\) −1.90306e8 −0.876655 −0.438327 0.898815i \(-0.644429\pi\)
−0.438327 + 0.898815i \(0.644429\pi\)
\(602\) 1.33440e7 + 5.16811e7i 0.0611641 + 0.236888i
\(603\) 9.10477e7i 0.415257i
\(604\) 1.73309e8 + 3.13237e8i 0.786520 + 1.42155i
\(605\) 8.49001e6 0.0383391
\(606\) −1.53398e8 + 3.96072e7i −0.689289 + 0.177974i
\(607\) 1.25461e8i 0.560974i 0.959858 + 0.280487i \(0.0904960\pi\)
−0.959858 + 0.280487i \(0.909504\pi\)
\(608\) −7.46496e7 + 2.35148e8i −0.332137 + 1.04624i
\(609\) 2.44781e8 1.08374
\(610\) −218360. 845705.i −0.000962019 0.00372588i
\(611\) 1.10831e7i 0.0485888i
\(612\) −6.16530e7 + 3.41116e7i −0.268967 + 0.148815i
\(613\) −9.91111e7 −0.430270 −0.215135 0.976584i \(-0.569019\pi\)
−0.215135 + 0.976584i \(0.569019\pi\)
\(614\) 3.78817e8 9.78102e7i 1.63653 0.422551i
\(615\) 9.09748e6i 0.0391107i
\(616\) −1.04755e8 1.10650e8i −0.448160 0.473378i
\(617\) 3.70827e7 0.157876 0.0789379 0.996880i \(-0.474847\pi\)
0.0789379 + 0.996880i \(0.474847\pi\)
\(618\) 8.60813e7 + 3.33391e8i 0.364706 + 1.41250i
\(619\) 4.05274e8i 1.70874i −0.519662 0.854372i \(-0.673942\pi\)
0.519662 0.854372i \(-0.326058\pi\)
\(620\) −1.29792e7 2.34585e7i −0.0544594 0.0984295i
\(621\) −1.61591e8 −0.674749
\(622\) −3.87469e8 + 1.00044e8i −1.61015 + 0.415738i
\(623\) 9.62786e7i 0.398168i
\(624\) −1.57624e8 9.88390e7i −0.648738 0.406794i
\(625\) 2.39463e8 0.980841
\(626\) 2.25437e6 + 8.73115e6i 0.00918973 + 0.0355917i
\(627\) 2.24065e8i 0.909017i
\(628\) −4.57405e7 + 2.53074e7i −0.184681 + 0.102181i
\(629\) −9.50340e6 −0.0381880
\(630\) 5.54400e6 1.43145e6i 0.0221718 0.00572474i
\(631\) 2.52648e7i 0.100561i −0.998735 0.0502803i \(-0.983989\pi\)
0.998735 0.0502803i \(-0.0160115\pi\)
\(632\) −1.15523e8 + 1.09369e8i −0.457631 + 0.433253i
\(633\) 1.21132e8 0.477581
\(634\) 6.89763e7 + 2.67144e8i 0.270665 + 1.04828i
\(635\) 1.67462e7i 0.0654025i
\(636\) −1.85140e8 3.34620e8i −0.719662 1.30071i
\(637\) 3.17374e7 0.122787
\(638\) 1.89705e8 4.89817e7i 0.730495 0.188613i
\(639\) 1.22948e8i 0.471213i
\(640\) −2.05619e7 + 4.12457e6i −0.0784375 + 0.0157340i
\(641\) −4.21293e8 −1.59959 −0.799797 0.600270i \(-0.795060\pi\)
−0.799797 + 0.600270i \(0.795060\pi\)
\(642\) −7.12224e7 2.75843e8i −0.269161 1.04245i
\(643\) 8.17706e7i 0.307584i 0.988103 + 0.153792i \(0.0491486\pi\)
−0.988103 + 0.153792i \(0.950851\pi\)
\(644\) −1.81709e8 + 1.00536e8i −0.680328 + 0.376414i
\(645\) −6.67200e6 −0.0248643
\(646\) 2.77953e8 7.17672e7i 1.03104 0.266212i
\(647\) 1.84284e8i 0.680416i −0.940350 0.340208i \(-0.889503\pi\)
0.940350 0.340208i \(-0.110497\pi\)
\(648\) 2.27561e8 + 2.40365e8i 0.836319 + 0.883377i
\(649\) −7.53226e7 −0.275544
\(650\) −4.55193e7 1.76295e8i −0.165751 0.641950i
\(651\) 4.02146e8i 1.45761i
\(652\) 5.71939e7 + 1.03372e8i 0.206351 + 0.372958i
\(653\) 6.43842e7 0.231228 0.115614 0.993294i \(-0.463117\pi\)
0.115614 + 0.993294i \(0.463117\pi\)
\(654\) 3.68577e8 9.51662e7i 1.31764 0.340212i
\(655\) 2.84454e7i 0.101225i
\(656\) 6.38917e7 1.01892e8i 0.226325 0.360934i
\(657\) −6.66726e7 −0.235099
\(658\) 4.68480e6 + 1.81442e7i 0.0164442 + 0.0636882i
\(659\) 5.38099e8i 1.88021i 0.340889 + 0.940103i \(0.389272\pi\)
−0.340889 + 0.940103i \(0.610728\pi\)
\(660\) 1.66656e7 9.22080e6i 0.0579681 0.0320728i
\(661\) 2.83897e8 0.983008 0.491504 0.870875i \(-0.336447\pi\)
0.491504 + 0.870875i \(0.336447\pi\)
\(662\) −3.11927e8 + 8.05393e7i −1.07518 + 0.277609i
\(663\) 2.16483e8i 0.742819i
\(664\) −7.59053e7 + 7.18617e7i −0.259279 + 0.245467i
\(665\) −2.33280e7 −0.0793255
\(666\) −921228. 3.56790e6i −0.00311849 0.0120779i
\(667\) 2.67029e8i 0.899872i
\(668\) −2.46791e8 4.46048e8i −0.827942 1.49642i
\(669\) 1.03212e8 0.344707
\(670\) 3.05304e7 7.88292e6i 0.101510 0.0262097i
\(671\) 1.04867e7i 0.0347115i
\(672\) 2.99827e8 + 9.51824e7i 0.988014 + 0.313653i
\(673\) 2.77693e8 0.911002 0.455501 0.890235i \(-0.349460\pi\)
0.455501 + 0.890235i \(0.349460\pi\)
\(674\) −6.85062e7 2.65323e8i −0.223743 0.866554i
\(675\) 2.39550e8i 0.778906i
\(676\) 1.49949e8 8.29640e7i 0.485403 0.268565i
\(677\) −9.23026e7 −0.297473 −0.148737 0.988877i \(-0.547521\pi\)
−0.148737 + 0.988877i \(0.547521\pi\)
\(678\) −1.44407e8 + 3.72856e7i −0.463338 + 0.119633i
\(679\) 4.51462e8i 1.44215i
\(680\) 1.67763e7 + 1.77203e7i 0.0533544 + 0.0563565i
\(681\) −4.18384e8 −1.32475
\(682\) 8.04710e7 + 3.11663e8i 0.253680 + 0.982499i
\(683\) 2.70862e8i 0.850132i −0.905162 0.425066i \(-0.860251\pi\)
0.905162 0.425066i \(-0.139749\pi\)
\(684\) 5.38877e7 + 9.73962e7i 0.168392 + 0.304350i
\(685\) 3.81003e7 0.118538
\(686\) −3.34315e8 + 8.63198e7i −1.03558 + 0.267386i
\(687\) 4.94496e7i 0.152508i
\(688\) −7.47264e7 4.68575e7i −0.229461 0.143884i
\(689\) −2.82724e8 −0.864380
\(690\) −6.48960e6 2.51341e7i −0.0197547 0.0765097i
\(691\) 1.92568e7i 0.0583645i −0.999574 0.0291823i \(-0.990710\pi\)
0.999574 0.0291823i \(-0.00929032\pi\)
\(692\) 2.87086e8 1.58840e8i 0.866350 0.479337i
\(693\) −6.87456e7 −0.206560
\(694\) −4.22539e8 + 1.09099e8i −1.26412 + 0.326395i
\(695\) 1.38839e6i 0.00413577i
\(696\) −2.93737e8 + 2.78089e8i −0.871226 + 0.824815i
\(697\) −1.39939e8 −0.413277
\(698\) 9.40017e7 + 3.64067e8i 0.276420 + 1.07057i
\(699\) 2.49229e8i 0.729738i
\(700\) 1.49040e8 + 2.69374e8i 0.434519 + 0.785346i
\(701\) 3.52234e8 1.02253 0.511266 0.859423i \(-0.329177\pi\)
0.511266 + 0.859423i \(0.329177\pi\)
\(702\) 1.75216e8 4.52407e7i 0.506481 0.130773i
\(703\) 1.50130e7i 0.0432117i
\(704\) 2.51412e8 + 1.37697e7i 0.720558 + 0.0394646i
\(705\) −2.34240e6 −0.00668488
\(706\) −2.54463e7 9.85530e7i −0.0723119 0.280063i
\(707\) 1.98036e8i 0.560384i
\(708\) 1.36067e8 7.52834e7i 0.383400 0.212129i
\(709\) 4.62733e8 1.29835 0.649175 0.760639i \(-0.275114\pi\)
0.649175 + 0.760639i \(0.275114\pi\)
\(710\) −4.12272e7 + 1.06448e7i −0.115188 + 0.0297415i
\(711\) 7.17731e7i 0.199689i
\(712\) −1.09380e8 1.15534e8i −0.303038 0.320089i
\(713\) 4.38697e8 1.21031
\(714\) −9.15072e7 3.54406e8i −0.251397 0.973658i
\(715\) 1.40809e7i 0.0385224i
\(716\) 7.23197e7 + 1.30710e8i 0.197023 + 0.356098i
\(717\) 3.48668e8 0.945921
\(718\) 1.56587e8 4.04306e7i 0.423041 0.109229i
\(719\) 4.60385e8i 1.23861i 0.785150 + 0.619305i \(0.212586\pi\)
−0.785150 + 0.619305i \(0.787414\pi\)
\(720\) −5.02656e6 + 8.01615e6i −0.0134671 + 0.0214767i
\(721\) −4.30406e8 −1.14835
\(722\) −1.92823e7 7.46801e7i −0.0512327 0.198424i
\(723\) 1.56501e8i 0.414097i
\(724\) −5.42727e8 + 3.00282e8i −1.43010 + 0.791250i
\(725\) −3.95856e8 −1.03878
\(726\) 2.03760e8 5.26107e7i 0.532488 0.137488i
\(727\) 4.82173e8i 1.25487i 0.778668 + 0.627437i \(0.215896\pi\)
−0.778668 + 0.627437i \(0.784104\pi\)
\(728\) 1.68883e8 1.59887e8i 0.437716 0.414398i
\(729\) −1.99184e8 −0.514128
\(730\) 5.77252e6 + 2.23569e7i 0.0148387 + 0.0574702i
\(731\) 1.02630e8i 0.262738i
\(732\) −1.04813e7 1.89438e7i −0.0267227 0.0482985i
\(733\) −5.08270e8 −1.29057 −0.645287 0.763941i \(-0.723262\pi\)
−0.645287 + 0.763941i \(0.723262\pi\)
\(734\) 8.60246e7 2.22115e7i 0.217538 0.0561680i
\(735\) 6.70770e6i 0.0168932i
\(736\) 1.03834e8 3.27079e8i 0.260438 0.820387i
\(737\) −3.78577e8 −0.945696
\(738\) −1.35652e7 5.25380e7i −0.0337488 0.130709i
\(739\) 1.27767e8i 0.316582i 0.987392 + 0.158291i \(0.0505984\pi\)
−0.987392 + 0.158291i \(0.949402\pi\)
\(740\) −1.11664e6 + 617818.i −0.00275561 + 0.00152463i
\(741\) 3.41988e8 0.840537
\(742\) 4.62850e8 1.19507e8i 1.13300 0.292538i
\(743\) 2.83312e8i 0.690716i −0.938471 0.345358i \(-0.887758\pi\)
0.938471 0.345358i \(-0.112242\pi\)
\(744\) −4.56868e8 4.82575e8i −1.10936 1.17178i
\(745\) −3.27426e7 −0.0791853
\(746\) 1.37429e6 + 5.32261e6i 0.00331026 + 0.0128206i
\(747\) 4.71593e7i 0.113137i
\(748\) −1.41836e8 2.56354e8i −0.338908 0.612540i
\(749\) 3.56112e8 0.847503
\(750\) −7.47600e7 + 1.93029e7i −0.177209 + 0.0457551i
\(751\) 2.15309e8i 0.508325i −0.967161 0.254163i \(-0.918200\pi\)
0.967161 0.254163i \(-0.0817999\pi\)
\(752\) −2.62349e7 1.64507e7i −0.0616915 0.0386839i
\(753\) 1.46117e8 0.342228
\(754\) 7.47601e7 + 2.89545e8i 0.174404 + 0.675463i
\(755\) 5.59352e7i 0.129970i
\(756\) −2.67725e8 + 1.48128e8i −0.619617 + 0.342824i
\(757\) −3.03985e8 −0.700753 −0.350377 0.936609i \(-0.613946\pi\)
−0.350377 + 0.936609i \(0.613946\pi\)
\(758\) −1.15026e8 + 2.96997e7i −0.264113 + 0.0681938i
\(759\) 3.11663e8i 0.712787i
\(760\) 2.79936e7 2.65024e7i 0.0637702 0.0603731i
\(761\) 8.63611e8 1.95959 0.979793 0.200014i \(-0.0640988\pi\)
0.979793 + 0.200014i \(0.0640988\pi\)
\(762\) 1.03772e8 + 4.01908e8i 0.234539 + 0.908367i
\(763\) 4.75831e8i 1.07122i
\(764\) 3.53725e8 + 6.39321e8i 0.793206 + 1.43364i
\(765\) 1.10095e7 0.0245913
\(766\) 2.60175e8 6.71770e7i 0.578868 0.149463i
\(767\) 1.14964e8i 0.254786i
\(768\) −4.67927e8 + 2.26407e8i −1.03299 + 0.499812i
\(769\) −1.97898e7 −0.0435174 −0.0217587 0.999763i \(-0.506927\pi\)
−0.0217587 + 0.999763i \(0.506927\pi\)