Properties

Label 48.7.l.a.19.5
Level $48$
Weight $7$
Character 48.19
Analytic conductor $11.043$
Analytic rank $0$
Dimension $48$
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] = [48,7,Mod(19,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.19");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 48.l (of order \(4\), degree \(2\), 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: \(11.0425960138\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.5
Character \(\chi\) \(=\) 48.19
Dual form 48.7.l.a.43.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.21738 - 3.45101i) q^{2} +(11.0227 - 11.0227i) q^{3} +(40.1811 + 49.8145i) q^{4} +(-26.8357 + 26.8357i) q^{5} +(-117.594 + 41.5155i) q^{6} -81.4485 q^{7} +(-118.092 - 498.195i) q^{8} -243.000i q^{9} +O(q^{10})\) \(q+(-7.21738 - 3.45101i) q^{2} +(11.0227 - 11.0227i) q^{3} +(40.1811 + 49.8145i) q^{4} +(-26.8357 + 26.8357i) q^{5} +(-117.594 + 41.5155i) q^{6} -81.4485 q^{7} +(-118.092 - 498.195i) q^{8} -243.000i q^{9} +(286.294 - 101.073i) q^{10} +(-775.312 - 775.312i) q^{11} +(991.994 + 106.186i) q^{12} +(-35.8378 - 35.8378i) q^{13} +(587.845 + 281.080i) q^{14} +591.604i q^{15} +(-866.966 + 4003.20i) q^{16} -3927.21 q^{17} +(-838.596 + 1753.82i) q^{18} +(-8023.59 + 8023.59i) q^{19} +(-2415.09 - 258.520i) q^{20} +(-897.783 + 897.783i) q^{21} +(2920.11 + 8271.32i) q^{22} -12220.5 q^{23} +(-6793.15 - 4189.77i) q^{24} +14184.7i q^{25} +(134.978 + 382.332i) q^{26} +(-2678.52 - 2678.52i) q^{27} +(-3272.69 - 4057.32i) q^{28} +(-4983.96 - 4983.96i) q^{29} +(2041.63 - 4269.83i) q^{30} -1910.12i q^{31} +(20072.3 - 25900.7i) q^{32} -17092.1 q^{33} +(28344.1 + 13552.8i) q^{34} +(2185.73 - 2185.73i) q^{35} +(12104.9 - 9764.00i) q^{36} +(-2913.71 + 2913.71i) q^{37} +(85598.7 - 30219.8i) q^{38} -790.059 q^{39} +(16538.5 + 10200.3i) q^{40} +4731.95i q^{41} +(9577.89 - 3381.38i) q^{42} +(-9752.98 - 9752.98i) q^{43} +(7468.91 - 69774.6i) q^{44} +(6521.08 + 6521.08i) q^{45} +(88200.2 + 42173.2i) q^{46} -190994. i q^{47} +(34569.7 + 53682.4i) q^{48} -111015. q^{49} +(48951.5 - 102376. i) q^{50} +(-43288.4 + 43288.4i) q^{51} +(345.241 - 3225.24i) q^{52} +(-89261.5 + 89261.5i) q^{53} +(10088.3 + 28575.5i) q^{54} +41612.1 q^{55} +(9618.38 + 40577.2i) q^{56} +176883. i q^{57} +(18771.4 + 53170.9i) q^{58} +(-65576.0 - 65576.0i) q^{59} +(-29470.5 + 23771.3i) q^{60} +(46807.2 + 46807.2i) q^{61} +(-6591.83 + 13786.0i) q^{62} +19792.0i q^{63} +(-234253. + 117665. i) q^{64} +1923.47 q^{65} +(123360. + 58984.9i) q^{66} +(156153. - 156153. i) q^{67} +(-157799. - 195632. i) q^{68} +(-134703. + 134703. i) q^{69} +(-23318.2 + 8232.25i) q^{70} +260179. q^{71} +(-121061. + 28696.2i) q^{72} +239064. i q^{73} +(31084.5 - 10974.1i) q^{74} +(156354. + 156354. i) q^{75} +(-722087. - 77294.7i) q^{76} +(63148.0 + 63148.0i) q^{77} +(5702.15 + 2726.50i) q^{78} -845707. i q^{79} +(-84163.0 - 130694. i) q^{80} -59049.0 q^{81} +(16330.0 - 34152.3i) q^{82} +(124933. - 124933. i) q^{83} +(-80796.4 - 8648.73i) q^{84} +(105389. - 105389. i) q^{85} +(36733.3 + 104049. i) q^{86} -109874. q^{87} +(-294699. + 477814. i) q^{88} +921193. i q^{89} +(-24560.8 - 69569.4i) q^{90} +(2918.94 + 2918.94i) q^{91} +(-491034. - 608760. i) q^{92} +(-21054.6 - 21054.6i) q^{93} +(-659123. + 1.37848e6i) q^{94} -430637. i q^{95} +(-64244.5 - 506746. i) q^{96} +1.39151e6 q^{97} +(801238. + 383114. i) q^{98} +(-188401. + 188401. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.21738 3.45101i −0.902172 0.431376i
\(3\) 11.0227 11.0227i 0.408248 0.408248i
\(4\) 40.1811 + 49.8145i 0.627829 + 0.778351i
\(5\) −26.8357 + 26.8357i −0.214686 + 0.214686i −0.806254 0.591569i \(-0.798509\pi\)
0.591569 + 0.806254i \(0.298509\pi\)
\(6\) −117.594 + 41.5155i −0.544419 + 0.192202i
\(7\) −81.4485 −0.237459 −0.118730 0.992927i \(-0.537882\pi\)
−0.118730 + 0.992927i \(0.537882\pi\)
\(8\) −118.092 498.195i −0.230647 0.973037i
\(9\) 243.000i 0.333333i
\(10\) 286.294 101.073i 0.286294 0.101073i
\(11\) −775.312 775.312i −0.582503 0.582503i 0.353087 0.935590i \(-0.385132\pi\)
−0.935590 + 0.353087i \(0.885132\pi\)
\(12\) 991.994 + 106.186i 0.574071 + 0.0614505i
\(13\) −35.8378 35.8378i −0.0163122 0.0163122i 0.698904 0.715216i \(-0.253672\pi\)
−0.715216 + 0.698904i \(0.753672\pi\)
\(14\) 587.845 + 281.080i 0.214229 + 0.102434i
\(15\) 591.604i 0.175290i
\(16\) −866.966 + 4003.20i −0.211662 + 0.977343i
\(17\) −3927.21 −0.799350 −0.399675 0.916657i \(-0.630877\pi\)
−0.399675 + 0.916657i \(0.630877\pi\)
\(18\) −838.596 + 1753.82i −0.143792 + 0.300724i
\(19\) −8023.59 + 8023.59i −1.16979 + 1.16979i −0.187531 + 0.982259i \(0.560048\pi\)
−0.982259 + 0.187531i \(0.939952\pi\)
\(20\) −2415.09 258.520i −0.301887 0.0323150i
\(21\) −897.783 + 897.783i −0.0969423 + 0.0969423i
\(22\) 2920.11 + 8271.32i 0.274240 + 0.776796i
\(23\) −12220.5 −1.00440 −0.502200 0.864751i \(-0.667476\pi\)
−0.502200 + 0.864751i \(0.667476\pi\)
\(24\) −6793.15 4189.77i −0.491402 0.303079i
\(25\) 14184.7i 0.907820i
\(26\) 134.978 + 382.332i 0.00767969 + 0.0217530i
\(27\) −2678.52 2678.52i −0.136083 0.136083i
\(28\) −3272.69 4057.32i −0.149084 0.184827i
\(29\) −4983.96 4983.96i −0.204353 0.204353i 0.597509 0.801862i \(-0.296157\pi\)
−0.801862 + 0.597509i \(0.796157\pi\)
\(30\) 2041.63 4269.83i 0.0756160 0.158142i
\(31\) 1910.12i 0.0641172i −0.999486 0.0320586i \(-0.989794\pi\)
0.999486 0.0320586i \(-0.0102063\pi\)
\(32\) 20072.3 25900.7i 0.612558 0.790426i
\(33\) −17092.1 −0.475612
\(34\) 28344.1 + 13552.8i 0.721152 + 0.344821i
\(35\) 2185.73 2185.73i 0.0509791 0.0509791i
\(36\) 12104.9 9764.00i 0.259450 0.209276i
\(37\) −2913.71 + 2913.71i −0.0575229 + 0.0575229i −0.735283 0.677760i \(-0.762951\pi\)
0.677760 + 0.735283i \(0.262951\pi\)
\(38\) 85598.7 30219.8i 1.55997 0.550732i
\(39\) −790.059 −0.0133188
\(40\) 16538.5 + 10200.3i 0.258414 + 0.159380i
\(41\) 4731.95i 0.0686576i 0.999411 + 0.0343288i \(0.0109294\pi\)
−0.999411 + 0.0343288i \(0.989071\pi\)
\(42\) 9577.89 3381.38i 0.129277 0.0456400i
\(43\) −9752.98 9752.98i −0.122668 0.122668i 0.643108 0.765776i \(-0.277645\pi\)
−0.765776 + 0.643108i \(0.777645\pi\)
\(44\) 7468.91 69774.6i 0.0876797 0.819104i
\(45\) 6521.08 + 6521.08i 0.0715619 + 0.0715619i
\(46\) 88200.2 + 42173.2i 0.906142 + 0.433275i
\(47\) 190994.i 1.83961i −0.392373 0.919806i \(-0.628346\pi\)
0.392373 0.919806i \(-0.371654\pi\)
\(48\) 34569.7 + 53682.4i 0.312588 + 0.485409i
\(49\) −111015. −0.943613
\(50\) 48951.5 102376.i 0.391612 0.819010i
\(51\) −43288.4 + 43288.4i −0.326333 + 0.326333i
\(52\) 345.241 3225.24i 0.00245534 0.0229378i
\(53\) −89261.5 + 89261.5i −0.599566 + 0.599566i −0.940197 0.340631i \(-0.889359\pi\)
0.340631 + 0.940197i \(0.389359\pi\)
\(54\) 10088.3 + 28575.5i 0.0640672 + 0.181473i
\(55\) 41612.1 0.250110
\(56\) 9618.38 + 40577.2i 0.0547694 + 0.231057i
\(57\) 176883.i 0.955129i
\(58\) 18771.4 + 53170.9i 0.0962085 + 0.272515i
\(59\) −65576.0 65576.0i −0.319293 0.319293i 0.529203 0.848495i \(-0.322491\pi\)
−0.848495 + 0.529203i \(0.822491\pi\)
\(60\) −29470.5 + 23771.3i −0.136437 + 0.110052i
\(61\) 46807.2 + 46807.2i 0.206216 + 0.206216i 0.802657 0.596441i \(-0.203419\pi\)
−0.596441 + 0.802657i \(0.703419\pi\)
\(62\) −6591.83 + 13786.0i −0.0276586 + 0.0578448i
\(63\) 19792.0i 0.0791531i
\(64\) −234253. + 117665.i −0.893603 + 0.448857i
\(65\) 1923.47 0.00700397
\(66\) 123360. + 58984.9i 0.429084 + 0.205168i
\(67\) 156153. 156153.i 0.519190 0.519190i −0.398136 0.917326i \(-0.630343\pi\)
0.917326 + 0.398136i \(0.130343\pi\)
\(68\) −157799. 195632.i −0.501855 0.622175i
\(69\) −134703. + 134703.i −0.410045 + 0.410045i
\(70\) −23318.2 + 8232.25i −0.0679831 + 0.0240007i
\(71\) 260179. 0.726938 0.363469 0.931606i \(-0.381592\pi\)
0.363469 + 0.931606i \(0.381592\pi\)
\(72\) −121061. + 28696.2i −0.324346 + 0.0768825i
\(73\) 239064.i 0.614535i 0.951623 + 0.307267i \(0.0994146\pi\)
−0.951623 + 0.307267i \(0.900585\pi\)
\(74\) 31084.5 10974.1i 0.0767095 0.0270815i
\(75\) 156354. + 156354.i 0.370616 + 0.370616i
\(76\) −722087. 77294.7i −1.64494 0.176079i
\(77\) 63148.0 + 63148.0i 0.138321 + 0.138321i
\(78\) 5702.15 + 2726.50i 0.0120159 + 0.00574542i
\(79\) 845707.i 1.71529i −0.514239 0.857647i \(-0.671926\pi\)
0.514239 0.857647i \(-0.328074\pi\)
\(80\) −84163.0 130694.i −0.164381 0.255262i
\(81\) −59049.0 −0.111111
\(82\) 16330.0 34152.3i 0.0296173 0.0619410i
\(83\) 124933. 124933.i 0.218496 0.218496i −0.589368 0.807864i \(-0.700623\pi\)
0.807864 + 0.589368i \(0.200623\pi\)
\(84\) −80796.4 8648.73i −0.136318 0.0145920i
\(85\) 105389. 105389.i 0.171609 0.171609i
\(86\) 36733.3 + 104049.i 0.0577517 + 0.163584i
\(87\) −109874. −0.166853
\(88\) −294699. + 477814.i −0.432444 + 0.701150i
\(89\) 921193.i 1.30671i 0.757050 + 0.653357i \(0.226640\pi\)
−0.757050 + 0.653357i \(0.773360\pi\)
\(90\) −24560.8 69569.4i −0.0336910 0.0954312i
\(91\) 2918.94 + 2918.94i 0.00387347 + 0.00387347i
\(92\) −491034. 608760.i −0.630592 0.781776i
\(93\) −21054.6 21054.6i −0.0261757 0.0261757i
\(94\) −659123. + 1.37848e6i −0.793565 + 1.65965i
\(95\) 430637.i 0.502274i
\(96\) −64244.5 506746.i −0.0726143 0.572766i
\(97\) 1.39151e6 1.52465 0.762326 0.647193i \(-0.224057\pi\)
0.762326 + 0.647193i \(0.224057\pi\)
\(98\) 801238. + 383114.i 0.851301 + 0.407052i
\(99\) −188401. + 188401.i −0.194168 + 0.194168i
\(100\) −706603. + 569956.i −0.706603 + 0.569956i
\(101\) −373244. + 373244.i −0.362267 + 0.362267i −0.864647 0.502380i \(-0.832458\pi\)
0.502380 + 0.864647i \(0.332458\pi\)
\(102\) 461818. 163040.i 0.435181 0.153636i
\(103\) 1.80911e6 1.65559 0.827795 0.561030i \(-0.189595\pi\)
0.827795 + 0.561030i \(0.189595\pi\)
\(104\) −13622.1 + 22086.4i −0.0121100 + 0.0196347i
\(105\) 48185.3i 0.0416242i
\(106\) 952277. 336192.i 0.799550 0.282273i
\(107\) −691978. 691978.i −0.564860 0.564860i 0.365824 0.930684i \(-0.380787\pi\)
−0.930684 + 0.365824i \(0.880787\pi\)
\(108\) 25803.3 241055.i 0.0204835 0.191357i
\(109\) −822525. 822525.i −0.635140 0.635140i 0.314213 0.949353i \(-0.398260\pi\)
−0.949353 + 0.314213i \(0.898260\pi\)
\(110\) −300330. 143604.i −0.225642 0.107892i
\(111\) 64233.8i 0.0469672i
\(112\) 70613.1 326054.i 0.0502610 0.232079i
\(113\) 1.51173e6 1.04770 0.523852 0.851809i \(-0.324495\pi\)
0.523852 + 0.851809i \(0.324495\pi\)
\(114\) 610426. 1.27663e6i 0.412020 0.861691i
\(115\) 327947. 327947.i 0.215630 0.215630i
\(116\) 48012.7 448534.i 0.0307597 0.287357i
\(117\) −8708.59 + 8708.59i −0.00543739 + 0.00543739i
\(118\) 246983. + 699590.i 0.150322 + 0.425792i
\(119\) 319865. 0.189813
\(120\) 294734. 69863.4i 0.170564 0.0404302i
\(121\) 569345.i 0.321380i
\(122\) −176293. 499357.i −0.0970858 0.275000i
\(123\) 52158.9 + 52158.9i 0.0280294 + 0.0280294i
\(124\) 95151.4 76750.5i 0.0499057 0.0402546i
\(125\) −799964. 799964.i −0.409582 0.409582i
\(126\) 68302.4 142846.i 0.0341448 0.0714097i
\(127\) 1.28506e6i 0.627352i −0.949530 0.313676i \(-0.898439\pi\)
0.949530 0.313676i \(-0.101561\pi\)
\(128\) 2.09675e6 40825.5i 0.999810 0.0194671i
\(129\) −215008. −0.100158
\(130\) −13882.4 6637.90i −0.00631879 0.00302135i
\(131\) −2.67757e6 + 2.67757e6i −1.19104 + 1.19104i −0.214268 + 0.976775i \(0.568737\pi\)
−0.976775 + 0.214268i \(0.931263\pi\)
\(132\) −686777. 851432.i −0.298603 0.370193i
\(133\) 653509. 653509.i 0.277777 0.277777i
\(134\) −1.66590e6 + 588130.i −0.692365 + 0.244432i
\(135\) 143760. 0.0584300
\(136\) 463770. + 1.95652e6i 0.184368 + 0.777798i
\(137\) 4.39546e6i 1.70940i 0.519125 + 0.854698i \(0.326258\pi\)
−0.519125 + 0.854698i \(0.673742\pi\)
\(138\) 1.43707e6 507342.i 0.546815 0.193047i
\(139\) −297733. 297733.i −0.110862 0.110862i 0.649500 0.760362i \(-0.274978\pi\)
−0.760362 + 0.649500i \(0.774978\pi\)
\(140\) 196706. + 21056.1i 0.0716858 + 0.00767349i
\(141\) −2.10527e6 2.10527e6i −0.751019 0.751019i
\(142\) −1.87781e6 897881.i −0.655823 0.313584i
\(143\) 55570.9i 0.0190038i
\(144\) 972777. + 210673.i 0.325781 + 0.0705538i
\(145\) 267496. 0.0877433
\(146\) 825014. 1.72542e6i 0.265096 0.554416i
\(147\) −1.22369e6 + 1.22369e6i −0.385228 + 0.385228i
\(148\) −262221. 28069.0i −0.0808875 0.00865848i
\(149\) −3.12091e6 + 3.12091e6i −0.943457 + 0.943457i −0.998485 0.0550275i \(-0.982475\pi\)
0.0550275 + 0.998485i \(0.482475\pi\)
\(150\) −588885. 1.66804e6i −0.174484 0.494234i
\(151\) 802843. 0.233185 0.116592 0.993180i \(-0.462803\pi\)
0.116592 + 0.993180i \(0.462803\pi\)
\(152\) 4.94483e6 + 3.04979e6i 1.40806 + 0.868440i
\(153\) 954312.i 0.266450i
\(154\) −237838. 673687.i −0.0651208 0.184457i
\(155\) 51259.3 + 51259.3i 0.0137650 + 0.0137650i
\(156\) −31745.4 39356.4i −0.00836194 0.0103667i
\(157\) −5.01290e6 5.01290e6i −1.29536 1.29536i −0.931425 0.363932i \(-0.881434\pi\)
−0.363932 0.931425i \(-0.618566\pi\)
\(158\) −2.91854e6 + 6.10378e6i −0.739937 + 1.54749i
\(159\) 1.96781e6i 0.489543i
\(160\) 156409. + 1.23372e6i 0.0381857 + 0.301200i
\(161\) 995345. 0.238504
\(162\) 426179. + 203779.i 0.100241 + 0.0479307i
\(163\) −5.05411e6 + 5.05411e6i −1.16703 + 1.16703i −0.184127 + 0.982903i \(0.558946\pi\)
−0.982903 + 0.184127i \(0.941054\pi\)
\(164\) −235720. + 190135.i −0.0534398 + 0.0431053i
\(165\) 458677. 458677.i 0.102107 0.102107i
\(166\) −1.33284e6 + 470544.i −0.291375 + 0.102867i
\(167\) −3.16978e6 −0.680581 −0.340291 0.940320i \(-0.610525\pi\)
−0.340291 + 0.940320i \(0.610525\pi\)
\(168\) 553292. + 341250.i 0.116688 + 0.0719690i
\(169\) 4.82424e6i 0.999468i
\(170\) −1.12433e6 + 396935.i −0.228849 + 0.0807928i
\(171\) 1.94973e6 + 1.94973e6i 0.389930 + 0.389930i
\(172\) 93954.7 877725.i 0.0184643 0.172494i
\(173\) −131325. 131325.i −0.0253635 0.0253635i 0.694311 0.719675i \(-0.255709\pi\)
−0.719675 + 0.694311i \(0.755709\pi\)
\(174\) 792998. + 379175.i 0.150531 + 0.0719766i
\(175\) 1.15532e6i 0.215570i
\(176\) 3.77589e6 2.43156e6i 0.692599 0.446012i
\(177\) −1.44565e6 −0.260701
\(178\) 3.17905e6 6.64859e6i 0.563685 1.17888i
\(179\) −3.48505e6 + 3.48505e6i −0.607646 + 0.607646i −0.942330 0.334685i \(-0.891370\pi\)
0.334685 + 0.942330i \(0.391370\pi\)
\(180\) −62820.3 + 586868.i −0.0107717 + 0.100629i
\(181\) 3.29758e6 3.29758e6i 0.556108 0.556108i −0.372089 0.928197i \(-0.621358\pi\)
0.928197 + 0.372089i \(0.121358\pi\)
\(182\) −10993.8 31140.3i −0.00182361 0.00516546i
\(183\) 1.03188e6 0.168375
\(184\) 1.44314e6 + 6.08821e6i 0.231662 + 0.977319i
\(185\) 156383.i 0.0246987i
\(186\) 79299.5 + 224619.i 0.0123234 + 0.0349066i
\(187\) 3.04481e6 + 3.04481e6i 0.465624 + 0.465624i
\(188\) 9.51427e6 7.67435e6i 1.43187 1.15496i
\(189\) 218161. + 218161.i 0.0323141 + 0.0323141i
\(190\) −1.48613e6 + 3.10807e6i −0.216669 + 0.453138i
\(191\) 1.00627e7i 1.44415i −0.691815 0.722075i \(-0.743188\pi\)
0.691815 0.722075i \(-0.256812\pi\)
\(192\) −1.28511e6 + 3.87909e6i −0.181567 + 0.548057i
\(193\) 7.50788e6 1.04435 0.522174 0.852839i \(-0.325121\pi\)
0.522174 + 0.852839i \(0.325121\pi\)
\(194\) −1.00430e7 4.80211e6i −1.37550 0.657699i
\(195\) 21201.8 21201.8i 0.00285936 0.00285936i
\(196\) −4.46071e6 5.53016e6i −0.592428 0.734463i
\(197\) 9.83000e6 9.83000e6i 1.28574 1.28574i 0.348398 0.937347i \(-0.386726\pi\)
0.937347 0.348398i \(-0.113274\pi\)
\(198\) 2.00993e6 709586.i 0.258932 0.0914133i
\(199\) 1.08179e7 1.37272 0.686362 0.727260i \(-0.259207\pi\)
0.686362 + 0.727260i \(0.259207\pi\)
\(200\) 7.06674e6 1.67509e6i 0.883343 0.209386i
\(201\) 3.44246e6i 0.423917i
\(202\) 3.98191e6 1.40577e6i 0.483100 0.170554i
\(203\) 405936. + 405936.i 0.0485255 + 0.0485255i
\(204\) −3.89577e6 417016.i −0.458884 0.0491205i
\(205\) −126985. 126985.i −0.0147398 0.0147398i
\(206\) −1.30570e7 6.24325e6i −1.49363 0.714183i
\(207\) 2.96959e6i 0.334800i
\(208\) 174536. 112396.i 0.0193952 0.0124899i
\(209\) 1.24416e7 1.36281
\(210\) −166288. + 347771.i −0.0179557 + 0.0375522i
\(211\) −9.63203e6 + 9.63203e6i −1.02535 + 1.02535i −0.0256759 + 0.999670i \(0.508174\pi\)
−0.999670 + 0.0256759i \(0.991826\pi\)
\(212\) −8.03314e6 859895.i −0.843097 0.0902480i
\(213\) 2.86788e6 2.86788e6i 0.296771 0.296771i
\(214\) 2.60624e6 + 7.38229e6i 0.265934 + 0.753269i
\(215\) 523456. 0.0526702
\(216\) −1.01811e6 + 1.65073e6i −0.101026 + 0.163801i
\(217\) 155576.i 0.0152252i
\(218\) 3.09793e6 + 8.77501e6i 0.299021 + 0.846990i
\(219\) 2.63514e6 + 2.63514e6i 0.250883 + 0.250883i
\(220\) 1.67202e6 + 2.07288e6i 0.157026 + 0.194674i
\(221\) 140743. + 140743.i 0.0130391 + 0.0130391i
\(222\) 221672. 463600.i 0.0202605 0.0423725i
\(223\) 1.26994e7i 1.14517i 0.819847 + 0.572583i \(0.194058\pi\)
−0.819847 + 0.572583i \(0.805942\pi\)
\(224\) −1.63486e6 + 2.10957e6i −0.145457 + 0.187694i
\(225\) 3.44688e6 0.302607
\(226\) −1.09107e7 5.21699e6i −0.945209 0.451954i
\(227\) 9.66433e6 9.66433e6i 0.826217 0.826217i −0.160774 0.986991i \(-0.551399\pi\)
0.986991 + 0.160774i \(0.0513990\pi\)
\(228\) −8.81135e6 + 7.10736e6i −0.743426 + 0.599658i
\(229\) −7.46532e6 + 7.46532e6i −0.621644 + 0.621644i −0.945952 0.324308i \(-0.894869\pi\)
0.324308 + 0.945952i \(0.394869\pi\)
\(230\) −3.49866e6 + 1.23517e6i −0.287554 + 0.101518i
\(231\) 1.39212e6 0.112938
\(232\) −1.89442e6 + 3.07155e6i −0.151710 + 0.245977i
\(233\) 1.57383e7i 1.24420i 0.782938 + 0.622100i \(0.213720\pi\)
−0.782938 + 0.622100i \(0.786280\pi\)
\(234\) 92906.6 32799.7i 0.00725102 0.00255990i
\(235\) 5.12546e6 + 5.12546e6i 0.394938 + 0.394938i
\(236\) 631722. 5.90155e6i 0.0480607 0.448983i
\(237\) −9.32198e6 9.32198e6i −0.700266 0.700266i
\(238\) −2.30859e6 1.10386e6i −0.171244 0.0818809i
\(239\) 1.79587e7i 1.31547i −0.753249 0.657736i \(-0.771514\pi\)
0.753249 0.657736i \(-0.228486\pi\)
\(240\) −2.36831e6 512900.i −0.171319 0.0371022i
\(241\) −1.76960e7 −1.26423 −0.632113 0.774876i \(-0.717812\pi\)
−0.632113 + 0.774876i \(0.717812\pi\)
\(242\) −1.96482e6 + 4.10918e6i −0.138636 + 0.289940i
\(243\) −650880. + 650880.i −0.0453609 + 0.0453609i
\(244\) −450914. + 4.21244e6i −0.0310402 + 0.289977i
\(245\) 2.97917e6 2.97917e6i 0.202580 0.202580i
\(246\) −196450. 556452.i −0.0131961 0.0373785i
\(247\) 575096. 0.0381636
\(248\) −951610. + 225568.i −0.0623884 + 0.0147885i
\(249\) 2.75420e6i 0.178401i
\(250\) 3.01296e6 + 8.53433e6i 0.192829 + 0.546197i
\(251\) −1.70291e7 1.70291e7i −1.07689 1.07689i −0.996786 0.0801047i \(-0.974475\pi\)
−0.0801047 0.996786i \(-0.525525\pi\)
\(252\) −985928. + 795263.i −0.0616089 + 0.0496946i
\(253\) 9.47473e6 + 9.47473e6i 0.585066 + 0.585066i
\(254\) −4.43475e6 + 9.27475e6i −0.270625 + 0.565980i
\(255\) 2.32335e6i 0.140118i
\(256\) −1.52740e7 6.94127e6i −0.910399 0.413732i
\(257\) −3.32789e6 −0.196051 −0.0980256 0.995184i \(-0.531253\pi\)
−0.0980256 + 0.995184i \(0.531253\pi\)
\(258\) 1.55180e6 + 741996.i 0.0903599 + 0.0432059i
\(259\) 237317. 237317.i 0.0136593 0.0136593i
\(260\) 77286.9 + 95816.5i 0.00439730 + 0.00545155i
\(261\) −1.21110e6 + 1.21110e6i −0.0681176 + 0.0681176i
\(262\) 2.85654e7 1.00847e7i 1.58831 0.560738i
\(263\) −528417. −0.0290476 −0.0145238 0.999895i \(-0.504623\pi\)
−0.0145238 + 0.999895i \(0.504623\pi\)
\(264\) 2.01843e6 + 8.51518e6i 0.109699 + 0.462788i
\(265\) 4.79079e6i 0.257436i
\(266\) −6.97189e6 + 2.46136e6i −0.370429 + 0.130776i
\(267\) 1.01540e7 + 1.01540e7i 0.533464 + 0.533464i
\(268\) 1.40531e7 + 1.50429e6i 0.730074 + 0.0781496i
\(269\) 7.17633e6 + 7.17633e6i 0.368677 + 0.368677i 0.866994 0.498318i \(-0.166049\pi\)
−0.498318 + 0.866994i \(0.666049\pi\)
\(270\) −1.03757e6 496117.i −0.0527139 0.0252053i
\(271\) 4.41346e6i 0.221754i 0.993834 + 0.110877i \(0.0353660\pi\)
−0.993834 + 0.110877i \(0.964634\pi\)
\(272\) 3.40475e6 1.57214e7i 0.169192 0.781239i
\(273\) 64349.1 0.00316268
\(274\) 1.51688e7 3.17237e7i 0.737393 1.54217i
\(275\) 1.09976e7 1.09976e7i 0.528808 0.528808i
\(276\) −1.21227e7 1.29766e6i −0.576597 0.0617209i
\(277\) −2.55357e7 + 2.55357e7i −1.20146 + 1.20146i −0.227732 + 0.973724i \(0.573131\pi\)
−0.973724 + 0.227732i \(0.926869\pi\)
\(278\) 1.12137e6 + 3.17633e6i 0.0521933 + 0.147840i
\(279\) −464158. −0.0213724
\(280\) −1.34704e6 830803.i −0.0613628 0.0378464i
\(281\) 1.23501e7i 0.556610i 0.960493 + 0.278305i \(0.0897725\pi\)
−0.960493 + 0.278305i \(0.910227\pi\)
\(282\) 7.92922e6 + 2.24599e7i 0.353576 + 1.00152i
\(283\) −1.87645e7 1.87645e7i −0.827901 0.827901i 0.159325 0.987226i \(-0.449068\pi\)
−0.987226 + 0.159325i \(0.949068\pi\)
\(284\) 1.04543e7 + 1.29607e7i 0.456393 + 0.565813i
\(285\) −4.74679e6 4.74679e6i −0.205053 0.205053i
\(286\) 191776. 401076.i 0.00819777 0.0171447i
\(287\) 385411.i 0.0163034i
\(288\) −6.29386e6 4.87757e6i −0.263475 0.204186i
\(289\) −8.71461e6 −0.361039
\(290\) −1.93062e6 923133.i −0.0791595 0.0378504i
\(291\) 1.53382e7 1.53382e7i 0.622437 0.622437i
\(292\) −1.19089e7 + 9.60586e6i −0.478324 + 0.385823i
\(293\) −2.33597e7 + 2.33597e7i −0.928675 + 0.928675i −0.997620 0.0689457i \(-0.978036\pi\)
0.0689457 + 0.997620i \(0.478036\pi\)
\(294\) 1.30548e7 4.60885e6i 0.513721 0.181364i
\(295\) 3.51956e6 0.137095
\(296\) 1.79568e6 + 1.10751e6i 0.0692394 + 0.0427044i
\(297\) 4.15337e6i 0.158537i
\(298\) 3.32951e7 1.17545e7i 1.25815 0.444176i
\(299\) 437957. + 437957.i 0.0163839 + 0.0163839i
\(300\) −1.50622e6 + 1.40711e7i −0.0557860 + 0.521153i
\(301\) 794366. + 794366.i 0.0291287 + 0.0291287i
\(302\) −5.79442e6 2.77062e6i −0.210373 0.100590i
\(303\) 8.22831e6i 0.295790i
\(304\) −2.51638e7 3.90762e7i −0.895686 1.39089i
\(305\) −2.51221e6 −0.0885434
\(306\) 3.29334e6 6.88763e6i 0.114940 0.240384i
\(307\) 4.10516e6 4.10516e6i 0.141878 0.141878i −0.632600 0.774478i \(-0.718012\pi\)
0.774478 + 0.632600i \(0.218012\pi\)
\(308\) −608331. + 5.68304e6i −0.0208204 + 0.194504i
\(309\) 1.99413e7 1.99413e7i 0.675892 0.675892i
\(310\) −193061. 546854.i −0.00648053 0.0183564i
\(311\) −4.81011e7 −1.59909 −0.799547 0.600604i \(-0.794927\pi\)
−0.799547 + 0.600604i \(0.794927\pi\)
\(312\) 93299.3 + 393604.i 0.00307195 + 0.0129597i
\(313\) 1.59905e7i 0.521469i −0.965411 0.260734i \(-0.916035\pi\)
0.965411 0.260734i \(-0.0839647\pi\)
\(314\) 1.88804e7 + 5.34795e7i 0.609849 + 1.72742i
\(315\) −531132. 531132.i −0.0169930 0.0169930i
\(316\) 4.21284e7 3.39814e7i 1.33510 1.07691i
\(317\) 2.98537e7 + 2.98537e7i 0.937173 + 0.937173i 0.998140 0.0609665i \(-0.0194183\pi\)
−0.0609665 + 0.998140i \(0.519418\pi\)
\(318\) 6.79092e6 1.42024e7i 0.211177 0.441652i
\(319\) 7.72825e6i 0.238072i
\(320\) 3.12871e6 9.44397e6i 0.0954806 0.288207i
\(321\) −1.52549e7 −0.461207
\(322\) −7.18378e6 3.43495e6i −0.215172 0.102885i
\(323\) 3.15103e7 3.15103e7i 0.935072 0.935072i
\(324\) −2.37265e6 2.94150e6i −0.0697588 0.0864835i
\(325\) 508348. 508348.i 0.0148085 0.0148085i
\(326\) 5.39192e7 1.90356e7i 1.55629 0.549432i
\(327\) −1.81329e7 −0.518590
\(328\) 2.35744e6 558804.i 0.0668065 0.0158357i
\(329\) 1.55562e7i 0.436833i
\(330\) −4.89335e6 + 1.72755e6i −0.136165 + 0.0480716i
\(331\) −1.52731e7 1.52731e7i −0.421156 0.421156i 0.464446 0.885602i \(-0.346254\pi\)
−0.885602 + 0.464446i \(0.846254\pi\)
\(332\) 1.12434e7 + 1.20354e6i 0.307245 + 0.0328885i
\(333\) 708031. + 708031.i 0.0191743 + 0.0191743i
\(334\) 2.28775e7 + 1.09390e7i 0.614001 + 0.293587i
\(335\) 8.38096e6i 0.222925i
\(336\) −2.81565e6 4.37235e6i −0.0742269 0.115265i
\(337\) −3.20323e7 −0.836948 −0.418474 0.908229i \(-0.637435\pi\)
−0.418474 + 0.908229i \(0.637435\pi\)
\(338\) −1.66485e7 + 3.48184e7i −0.431147 + 0.901692i
\(339\) 1.66633e7 1.66633e7i 0.427723 0.427723i
\(340\) 9.48458e6 + 1.01526e6i 0.241313 + 0.0258310i
\(341\) −1.48093e6 + 1.48093e6i −0.0373485 + 0.0373485i
\(342\) −7.34340e6 2.08005e7i −0.183577 0.519990i
\(343\) 1.86244e7 0.461529
\(344\) −3.70714e6 + 6.01063e6i −0.0910676 + 0.147654i
\(345\) 7.22972e6i 0.176061i
\(346\) 494619. + 1.40103e6i 0.0119410 + 0.0338235i
\(347\) 4.52698e6 + 4.52698e6i 0.108348 + 0.108348i 0.759202 0.650855i \(-0.225589\pi\)
−0.650855 + 0.759202i \(0.725589\pi\)
\(348\) −4.41483e6 5.47329e6i −0.104755 0.129871i
\(349\) 3.42959e7 + 3.42959e7i 0.806801 + 0.806801i 0.984148 0.177348i \(-0.0567517\pi\)
−0.177348 + 0.984148i \(0.556752\pi\)
\(350\) −3.98703e6 + 8.33839e6i −0.0929919 + 0.194481i
\(351\) 191984.i 0.00443961i
\(352\) −3.56434e7 + 4.51881e6i −0.817242 + 0.103609i
\(353\) −1.61140e6 −0.0366335 −0.0183168 0.999832i \(-0.505831\pi\)
−0.0183168 + 0.999832i \(0.505831\pi\)
\(354\) 1.04338e7 + 4.98895e6i 0.235198 + 0.112460i
\(355\) −6.98209e6 + 6.98209e6i −0.156063 + 0.156063i
\(356\) −4.58887e7 + 3.70145e7i −1.01708 + 0.820393i
\(357\) 3.52578e6 3.52578e6i 0.0774909 0.0774909i
\(358\) 3.71799e7 1.31260e7i 0.810325 0.286077i
\(359\) −2.80317e7 −0.605850 −0.302925 0.953014i \(-0.597963\pi\)
−0.302925 + 0.953014i \(0.597963\pi\)
\(360\) 2.47868e6 4.01885e6i 0.0531268 0.0861380i
\(361\) 8.17100e7i 1.73682i
\(362\) −3.51798e7 + 1.24199e7i −0.741597 + 0.261814i
\(363\) −6.27572e6 6.27572e6i −0.131203 0.131203i
\(364\) −28119.4 + 262691.i −0.000583044 + 0.00544680i
\(365\) −6.41546e6 6.41546e6i −0.131932 0.131932i
\(366\) −7.44750e6 3.56104e6i −0.151903 0.0726330i
\(367\) 1.29660e7i 0.262305i 0.991362 + 0.131153i \(0.0418678\pi\)
−0.991362 + 0.131153i \(0.958132\pi\)
\(368\) 1.05948e7 4.89212e7i 0.212593 0.981644i
\(369\) 1.14986e6 0.0228859
\(370\) −539678. + 1.12867e6i −0.0106544 + 0.0222825i
\(371\) 7.27022e6 7.27022e6i 0.142372 0.142372i
\(372\) 202828. 1.89482e6i 0.00394003 0.0368078i
\(373\) −1.21108e7 + 1.21108e7i −0.233370 + 0.233370i −0.814098 0.580728i \(-0.802768\pi\)
0.580728 + 0.814098i \(0.302768\pi\)
\(374\) −1.14679e7 3.24832e7i −0.219214 0.620932i
\(375\) −1.76355e7 −0.334422
\(376\) −9.51523e7 + 2.25548e7i −1.79001 + 0.424302i
\(377\) 357229.i 0.00666687i
\(378\) −821675. 2.32743e6i −0.0152133 0.0430924i
\(379\) 7.52090e6 + 7.52090e6i 0.138150 + 0.138150i 0.772800 0.634650i \(-0.218856\pi\)
−0.634650 + 0.772800i \(0.718856\pi\)
\(380\) 2.14520e7 1.73035e7i 0.390946 0.315342i
\(381\) −1.41648e7 1.41648e7i −0.256116 0.256116i
\(382\) −3.47263e7 + 7.26260e7i −0.622972 + 1.30287i
\(383\) 6.40799e7i 1.14058i 0.821444 + 0.570290i \(0.193169\pi\)
−0.821444 + 0.570290i \(0.806831\pi\)
\(384\) 2.26619e7 2.35619e7i 0.400224 0.416118i
\(385\) −3.38924e6 −0.0593909
\(386\) −5.41872e7 2.59098e7i −0.942182 0.450507i
\(387\) −2.36997e6 + 2.36997e6i −0.0408894 + 0.0408894i
\(388\) 5.59123e7 + 6.93173e7i 0.957221 + 1.18672i
\(389\) 2.83762e7 2.83762e7i 0.482065 0.482065i −0.423725 0.905791i \(-0.639278\pi\)
0.905791 + 0.423725i \(0.139278\pi\)
\(390\) −226189. + 79853.7i −0.00381309 + 0.00134617i
\(391\) 4.79926e7 0.802868
\(392\) 1.31099e7 + 5.53072e7i 0.217642 + 0.918171i
\(393\) 5.90282e7i 0.972483i
\(394\) −1.04870e8 + 3.70234e7i −1.71460 + 0.605323i
\(395\) 2.26951e7 + 2.26951e7i 0.368249 + 0.368249i
\(396\) −1.69552e7 1.81494e6i −0.273035 0.0292266i
\(397\) 8.65284e7 + 8.65284e7i 1.38289 + 1.38289i 0.839446 + 0.543443i \(0.182880\pi\)
0.543443 + 0.839446i \(0.317120\pi\)
\(398\) −7.80768e7 3.73326e7i −1.23843 0.592160i
\(399\) 1.44069e7i 0.226804i
\(400\) −5.67841e7 1.22976e7i −0.887252 0.192151i
\(401\) −5.90588e7 −0.915907 −0.457954 0.888976i \(-0.651417\pi\)
−0.457954 + 0.888976i \(0.651417\pi\)
\(402\) −1.18800e7 + 2.48455e7i −0.182868 + 0.382446i
\(403\) −68454.4 + 68454.4i −0.00104589 + 0.00104589i
\(404\) −3.35903e7 3.59562e6i −0.509412 0.0545292i
\(405\) 1.58462e6 1.58462e6i 0.0238540 0.0238540i
\(406\) −1.52891e6 4.33069e6i −0.0228456 0.0647111i
\(407\) 4.51806e6 0.0670145
\(408\) 2.66781e7 + 1.64541e7i 0.392803 + 0.242267i
\(409\) 7.26547e7i 1.06192i −0.847395 0.530962i \(-0.821831\pi\)
0.847395 0.530962i \(-0.178169\pi\)
\(410\) 478273. + 1.35473e6i 0.00693944 + 0.0196563i
\(411\) 4.84499e7 + 4.84499e7i 0.697858 + 0.697858i
\(412\) 7.26919e7 + 9.01198e7i 1.03943 + 1.28863i
\(413\) 5.34107e6 + 5.34107e6i 0.0758190 + 0.0758190i
\(414\) 1.02481e7 2.14327e7i 0.144425 0.302047i
\(415\) 6.70534e6i 0.0938160i
\(416\) −1.64757e6 + 208876.i −0.0228857 + 0.00290141i
\(417\) −6.56364e6 −0.0905183
\(418\) −8.97954e7 4.29360e7i −1.22949 0.587885i
\(419\) 1.95758e7 1.95758e7i 0.266120 0.266120i −0.561415 0.827535i \(-0.689743\pi\)
0.827535 + 0.561415i \(0.189743\pi\)
\(420\) 2.40032e6 1.93613e6i 0.0323983 0.0261329i
\(421\) 3.85272e7 3.85272e7i 0.516323 0.516323i −0.400134 0.916457i \(-0.631036\pi\)
0.916457 + 0.400134i \(0.131036\pi\)
\(422\) 1.02758e8 3.62778e7i 1.36735 0.482729i
\(423\) −4.64116e7 −0.613204
\(424\) 5.50107e7 + 3.39286e7i 0.721688 + 0.445111i
\(425\) 5.57062e7i 0.725666i
\(426\) −3.05956e7 + 1.08015e7i −0.395759 + 0.139719i
\(427\) −3.81238e6 3.81238e6i −0.0489680 0.0489680i
\(428\) 6.66612e6 6.22750e7i 0.0850241 0.794296i
\(429\) 612542. + 612542.i 0.00775825 + 0.00775825i
\(430\) −3.77798e6 1.80645e6i −0.0475176 0.0227207i
\(431\) 7.68903e6i 0.0960373i −0.998846 0.0480186i \(-0.984709\pi\)
0.998846 0.0480186i \(-0.0152907\pi\)
\(432\) 1.30448e7 8.40045e6i 0.161803 0.104196i
\(433\) 6.11798e7 0.753607 0.376803 0.926293i \(-0.377023\pi\)
0.376803 + 0.926293i \(0.377023\pi\)
\(434\) 536895. 1.12285e6i 0.00656780 0.0137358i
\(435\) 2.94853e6 2.94853e6i 0.0358210 0.0358210i
\(436\) 7.92373e6 7.40235e7i 0.0956027 0.893121i
\(437\) 9.80526e7 9.80526e7i 1.17494 1.17494i
\(438\) −9.92489e6 2.81126e7i −0.118115 0.334564i
\(439\) 2.46496e7 0.291351 0.145676 0.989332i \(-0.453464\pi\)
0.145676 + 0.989332i \(0.453464\pi\)
\(440\) −4.91403e6 2.07309e7i −0.0576873 0.243366i
\(441\) 2.69767e7i 0.314538i
\(442\) −530088. 1.50150e6i −0.00613877 0.0173883i
\(443\) 4.36137e7 + 4.36137e7i 0.501662 + 0.501662i 0.911954 0.410292i \(-0.134573\pi\)
−0.410292 + 0.911954i \(0.634573\pi\)
\(444\) −3.19978e6 + 2.58098e6i −0.0365570 + 0.0294874i
\(445\) −2.47209e7 2.47209e7i −0.280533 0.280533i
\(446\) 4.38257e7 9.16563e7i 0.493997 1.03314i
\(447\) 6.88017e7i 0.770330i
\(448\) 1.90795e7 9.58366e6i 0.212194 0.106585i
\(449\) 1.69871e6 0.0187664 0.00938320 0.999956i \(-0.497013\pi\)
0.00938320 + 0.999956i \(0.497013\pi\)
\(450\) −2.48774e7 1.18952e7i −0.273003 0.130537i
\(451\) 3.66874e6 3.66874e6i 0.0399933 0.0399933i
\(452\) 6.07428e7 + 7.53060e7i 0.657779 + 0.815481i
\(453\) 8.84950e6 8.84950e6i 0.0951972 0.0951972i
\(454\) −1.03103e8 + 3.63994e7i −1.10180 + 0.388980i
\(455\) −156663. −0.00166316
\(456\) 8.81224e7 2.08884e7i 0.929376 0.220298i
\(457\) 1.26874e8i 1.32931i −0.747151 0.664654i \(-0.768579\pi\)
0.747151 0.664654i \(-0.231421\pi\)
\(458\) 7.96429e7 2.81171e7i 0.828992 0.292667i
\(459\) 1.05191e7 + 1.05191e7i 0.108778 + 0.108778i
\(460\) 2.95138e7 + 3.15925e6i 0.303215 + 0.0324572i
\(461\) −9.90837e7 9.90837e7i −1.01135 1.01135i −0.999935 0.0114105i \(-0.996368\pi\)
−0.0114105 0.999935i \(-0.503632\pi\)
\(462\) −1.00475e7 4.80423e6i −0.101890 0.0487189i
\(463\) 7.82203e7i 0.788091i −0.919091 0.394045i \(-0.871075\pi\)
0.919091 0.394045i \(-0.128925\pi\)
\(464\) 2.42727e7 1.56309e7i 0.242977 0.156469i
\(465\) 1.13003e6 0.0112391
\(466\) 5.43130e7 1.13589e8i 0.536718 1.12248i
\(467\) −4.15449e7 + 4.15449e7i −0.407913 + 0.407913i −0.881010 0.473097i \(-0.843136\pi\)
0.473097 + 0.881010i \(0.343136\pi\)
\(468\) −783734. 83893.6i −0.00764594 0.000818448i
\(469\) −1.27184e7 + 1.27184e7i −0.123286 + 0.123286i
\(470\) −1.93044e7 5.46804e7i −0.185935 0.526670i
\(471\) −1.10511e8 −1.05766
\(472\) −2.49257e7 + 4.04136e7i −0.237040 + 0.384328i
\(473\) 1.51232e7i 0.142909i
\(474\) 3.51100e7 + 9.94504e7i 0.329682 + 0.933838i
\(475\) −1.13812e8 1.13812e8i −1.06196 1.06196i
\(476\) 1.28525e7 + 1.59339e7i 0.119170 + 0.147741i
\(477\) 2.16906e7 + 2.16906e7i 0.199855 + 0.199855i
\(478\) −6.19757e7 + 1.29615e8i −0.567463 + 1.18678i
\(479\) 1.47963e8i 1.34631i 0.739499 + 0.673157i \(0.235062\pi\)
−0.739499 + 0.673157i \(0.764938\pi\)
\(480\) 1.53229e7 + 1.18749e7i 0.138554 + 0.107375i
\(481\) 208842. 0.00187664
\(482\) 1.27719e8 + 6.10692e7i 1.14055 + 0.545357i
\(483\) 1.09714e7 1.09714e7i 0.0973689 0.0973689i
\(484\) 2.83616e7 2.28769e7i 0.250147 0.201772i
\(485\) −3.73421e7 + 3.73421e7i −0.327321 + 0.327321i
\(486\) 6.94384e6 2.45145e6i 0.0604910 0.0213557i
\(487\) 1.46672e8 1.26988 0.634938 0.772563i \(-0.281026\pi\)
0.634938 + 0.772563i \(0.281026\pi\)
\(488\) 1.77916e7 2.88467e7i 0.153093 0.248220i
\(489\) 1.11420e8i 0.952875i
\(490\) −3.17829e7 + 1.12206e7i −0.270150 + 0.0953739i
\(491\) 5.09913e7 + 5.09913e7i 0.430776 + 0.430776i 0.888892 0.458116i \(-0.151476\pi\)
−0.458116 + 0.888892i \(0.651476\pi\)
\(492\) −502469. + 4.69407e6i −0.00421905 + 0.0394143i
\(493\) 1.95731e7 + 1.95731e7i 0.163350 + 0.163350i
\(494\) −4.15068e6 1.98466e6i −0.0344301 0.0164629i
\(495\) 1.01117e7i 0.0833700i
\(496\) 7.64657e6 + 1.65600e6i 0.0626645 + 0.0135711i
\(497\) −2.11912e7 −0.172618
\(498\) −9.50479e6 + 1.98781e7i −0.0769581 + 0.160949i
\(499\) −1.49891e8 + 1.49891e8i −1.20635 + 1.20635i −0.234152 + 0.972200i \(0.575231\pi\)
−0.972200 + 0.234152i \(0.924769\pi\)
\(500\) 7.70640e6 7.19932e7i 0.0616512 0.575946i
\(501\) −3.49396e7 + 3.49396e7i −0.277846 + 0.277846i
\(502\) 6.41380e7 + 1.81674e8i 0.506996 + 1.43609i
\(503\) −1.74504e8 −1.37120 −0.685600 0.727979i \(-0.740460\pi\)
−0.685600 + 0.727979i \(0.740460\pi\)
\(504\) 9.86027e6 2.33727e6i 0.0770189 0.0182565i
\(505\) 2.00325e7i 0.155547i
\(506\) −3.56853e7 1.01080e8i −0.275447 0.780214i
\(507\) −5.31762e7 5.31762e7i −0.408031 0.408031i
\(508\) 6.40145e7 5.16350e7i 0.488301 0.393870i
\(509\) −9.29471e7 9.29471e7i −0.704827 0.704827i 0.260616 0.965443i \(-0.416074\pi\)
−0.965443 + 0.260616i \(0.916074\pi\)
\(510\) −8.01791e6 + 1.67685e7i −0.0604437 + 0.126411i
\(511\) 1.94714e7i 0.145927i
\(512\) 8.62835e7 + 1.02808e8i 0.642862 + 0.765982i
\(513\) 4.29826e7 0.318376
\(514\) 2.40186e7 + 1.14846e7i 0.176872 + 0.0845719i
\(515\) −4.85487e7 + 4.85487e7i −0.355432 + 0.355432i
\(516\) −8.63927e6 1.07105e7i −0.0628822 0.0779583i
\(517\) −1.48080e8 + 1.48080e8i −1.07158 + 1.07158i
\(518\) −2.53179e6 + 893823.i −0.0182154 + 0.00643076i
\(519\) −2.89512e6 −0.0207092
\(520\) −227145. 958261.i −0.00161545 0.00681513i
\(521\) 7.09637e7i 0.501791i −0.968014 0.250895i \(-0.919275\pi\)
0.968014 0.250895i \(-0.0807251\pi\)
\(522\) 1.29205e7 4.56146e6i 0.0908382 0.0320695i
\(523\) −5.50191e7 5.50191e7i −0.384599 0.384599i 0.488157 0.872756i \(-0.337669\pi\)
−0.872756 + 0.488157i \(0.837669\pi\)
\(524\) −2.40970e8 2.57942e7i −1.67482 0.179279i
\(525\) −1.27348e7 1.27348e7i −0.0880062 0.0880062i
\(526\) 3.81379e6 + 1.82357e6i 0.0262059 + 0.0125304i
\(527\) 7.50142e6i 0.0512521i
\(528\) 1.48182e7 6.84229e7i 0.100669 0.464836i
\(529\) 1.30573e6 0.00882036
\(530\) −1.65331e7 + 3.45770e7i −0.111052 + 0.232252i
\(531\) −1.59350e7 + 1.59350e7i −0.106431 + 0.106431i
\(532\) 5.88129e7 + 6.29553e6i 0.390605 + 0.0418117i
\(533\) 169583. 169583.i 0.00111995 0.00111995i
\(534\) −3.82438e7 1.08327e8i −0.251152 0.711400i
\(535\) 3.71395e7 0.242535
\(536\) −9.62350e7 5.93543e7i −0.624941 0.385441i
\(537\) 7.68294e7i 0.496141i
\(538\) −2.70287e7 7.65598e7i −0.173571 0.491648i
\(539\) 8.60713e7 + 8.60713e7i 0.549658 + 0.549658i
\(540\) 5.77642e6 + 7.16132e6i 0.0366841 + 0.0454791i
\(541\) 9.74560e7 + 9.74560e7i 0.615484 + 0.615484i 0.944370 0.328886i \(-0.106673\pi\)
−0.328886 + 0.944370i \(0.606673\pi\)
\(542\) 1.52309e7 3.18536e7i 0.0956595 0.200060i
\(543\) 7.26965e7i 0.454061i
\(544\) −7.88281e7 + 1.01717e8i −0.489648 + 0.631827i
\(545\) 4.41461e7 0.272711
\(546\) −464432. 222070.i −0.00285328 0.00136430i
\(547\) −6.39041e6 + 6.39041e6i −0.0390451 + 0.0390451i −0.726360 0.687315i \(-0.758789\pi\)
0.687315 + 0.726360i \(0.258789\pi\)
\(548\) −2.18958e8 + 1.76614e8i −1.33051 + 1.07321i
\(549\) 1.13742e7 1.13742e7i 0.0687388 0.0687388i
\(550\) −1.17326e8 + 4.14208e7i −0.705191 + 0.248961i
\(551\) 7.99785e7 0.478100
\(552\) 8.30159e7 + 5.12013e7i 0.493565 + 0.304413i
\(553\) 6.88816e7i 0.407312i
\(554\) 2.72424e8 9.61766e7i 1.60220 0.565640i
\(555\) −1.72376e6 1.72376e6i −0.0100832 0.0100832i
\(556\) 2.86819e6 2.67946e7i 0.0166872 0.155892i
\(557\) −2.14251e8 2.14251e8i −1.23982 1.23982i −0.960075 0.279741i \(-0.909751\pi\)
−0.279741 0.960075i \(-0.590249\pi\)
\(558\) 3.35000e6 + 1.60181e6i 0.0192816 + 0.00921955i
\(559\) 699051.i 0.00400197i
\(560\) 6.85495e6 + 1.06449e7i 0.0390337 + 0.0606144i
\(561\) 6.71241e7 0.380180
\(562\) 4.26202e7 8.91352e7i 0.240108 0.502158i
\(563\) 3.29830e7 3.29830e7i 0.184827 0.184827i −0.608628 0.793455i \(-0.708280\pi\)
0.793455 + 0.608628i \(0.208280\pi\)
\(564\) 2.02810e7 1.89465e8i 0.113045 1.05607i
\(565\) −4.05683e7 + 4.05683e7i −0.224927 + 0.224927i
\(566\) 7.06741e7 + 2.00187e8i 0.389772 + 1.10405i
\(567\) 4.80945e6 0.0263844
\(568\) −3.07249e7 1.29620e8i −0.167666 0.707338i
\(569\) 3.50326e8i 1.90167i 0.309694 + 0.950836i \(0.399773\pi\)
−0.309694 + 0.950836i \(0.600227\pi\)
\(570\) 1.78781e7 + 5.06406e7i 0.0965379 + 0.273447i
\(571\) −1.89558e8 1.89558e8i −1.01820 1.01820i −0.999831 0.0183727i \(-0.994151\pi\)
−0.0183727 0.999831i \(-0.505849\pi\)
\(572\) −2.76824e6 + 2.23290e6i −0.0147916 + 0.0119311i
\(573\) −1.10918e8 1.10918e8i −0.589572 0.589572i
\(574\) −1.33006e6 + 2.78165e6i −0.00703290 + 0.0147085i
\(575\) 1.73345e8i 0.911815i
\(576\) 2.85927e7 + 5.69234e7i 0.149619 + 0.297868i
\(577\) 2.39174e8 1.24505 0.622525 0.782600i \(-0.286107\pi\)
0.622525 + 0.782600i \(0.286107\pi\)
\(578\) 6.28966e7 + 3.00742e7i 0.325719 + 0.155744i
\(579\) 8.27572e7 8.27572e7i 0.426354 0.426354i
\(580\) 1.07483e7 + 1.33252e7i 0.0550878 + 0.0682951i
\(581\) −1.01756e7 + 1.01756e7i −0.0518839 + 0.0518839i
\(582\) −1.63634e8 + 5.77693e7i −0.830050 + 0.293041i
\(583\) 1.38411e8 0.698498
\(584\) 1.19101e8 2.82315e7i 0.597965 0.141741i
\(585\) 467402.i 0.00233466i
\(586\) 2.49210e8 8.79810e7i 1.23843 0.437216i
\(587\) 1.31381e8 + 1.31381e8i 0.649558 + 0.649558i 0.952886 0.303328i \(-0.0980979\pi\)
−0.303328 + 0.952886i \(0.598098\pi\)
\(588\) −1.10126e8 1.17883e7i −0.541701 0.0579855i
\(589\) 1.53260e7 + 1.53260e7i 0.0750037 + 0.0750037i
\(590\) −2.54020e7 1.21460e7i −0.123683 0.0591396i
\(591\) 2.16706e8i 1.04981i
\(592\) −9.13806e6 1.41902e7i −0.0440442 0.0683950i
\(593\) 3.40528e7 0.163301 0.0816504 0.996661i \(-0.473981\pi\)
0.0816504 + 0.996661i \(0.473981\pi\)
\(594\) 1.43333e7 2.99764e7i 0.0683892 0.143028i
\(595\) −8.58381e6 + 8.58381e6i −0.0407501 + 0.0407501i
\(596\) −2.80868e8 3.00651e7i −1.32667 0.142011i
\(597\) 1.19242e8 1.19242e8i 0.560412 0.560412i
\(598\) −1.64951e6 4.67230e6i −0.00771349 0.0218488i
\(599\) 3.20600e8 1.49170 0.745852 0.666112i \(-0.232043\pi\)
0.745852 + 0.666112i \(0.232043\pi\)
\(600\) 5.94306e7 9.63587e7i 0.275142 0.446105i
\(601\) 1.29953e8i 0.598635i 0.954154 + 0.299318i \(0.0967590\pi\)
−0.954154 + 0.299318i \(0.903241\pi\)
\(602\) −2.99187e6 8.47460e6i −0.0137137 0.0388445i
\(603\) −3.79452e7 3.79452e7i −0.173063 0.173063i
\(604\) 3.22591e7 + 3.99932e7i 0.146400 + 0.181500i
\(605\) 1.52788e7 + 1.52788e7i 0.0689958 + 0.0689958i
\(606\) 2.83960e7 5.93868e7i 0.127597 0.266853i
\(607\) 2.92063e8i 1.30590i −0.757401 0.652950i \(-0.773531\pi\)
0.757401 0.652950i \(-0.226469\pi\)
\(608\) 4.67645e7 + 3.68868e8i 0.208068 + 1.64120i
\(609\) 8.94903e6 0.0396209
\(610\) 1.81316e7 + 8.66966e6i 0.0798814 + 0.0381955i
\(611\) −6.84481e6 + 6.84481e6i −0.0300081 + 0.0300081i
\(612\) −4.75385e7 + 3.83452e7i −0.207392 + 0.167285i
\(613\) −1.14280e8 + 1.14280e8i −0.496123 + 0.496123i −0.910229 0.414106i \(-0.864094\pi\)
0.414106 + 0.910229i \(0.364094\pi\)
\(614\) −4.37954e7 + 1.54615e7i −0.189201 + 0.0667955i
\(615\) −2.79944e6 −0.0120350
\(616\) 2.40028e7 3.89173e7i 0.102688 0.166495i
\(617\) 9.88451e6i 0.0420823i −0.999779 0.0210412i \(-0.993302\pi\)
0.999779 0.0210412i \(-0.00669811\pi\)
\(618\) −2.12741e8 + 7.51061e7i −0.901335 + 0.318207i
\(619\) 7.00948e7 + 7.00948e7i 0.295539 + 0.295539i 0.839263 0.543725i \(-0.182987\pi\)
−0.543725 + 0.839263i \(0.682987\pi\)
\(620\) −493803. + 4.61311e6i −0.00207195 + 0.0193561i
\(621\) 3.27329e7 + 3.27329e7i 0.136682 + 0.136682i
\(622\) 3.47164e8 + 1.65997e8i 1.44266 + 0.689811i
\(623\) 7.50298e7i 0.310291i
\(624\) 684954. 3.16276e6i 0.00281908 0.0130171i
\(625\) −1.78701e8 −0.731958
\(626\) −5.51833e7 + 1.15409e8i −0.224949 + 0.470455i
\(627\) 1.37140e8 1.37140e8i 0.556366 0.556366i
\(628\) 4.82914e7 4.51138e8i 0.194980 1.82151i
\(629\) 1.14427e7 1.14427e7i 0.0459809 0.0459809i
\(630\) 2.00044e6 + 5.66632e6i 0.00800025 + 0.0226610i
\(631\) 3.77054e8 1.50078 0.750388 0.660998i \(-0.229867\pi\)
0.750388 + 0.660998i \(0.229867\pi\)
\(632\) −4.21327e8 + 9.98708e7i −1.66905 + 0.395628i
\(633\) 2.12342e8i 0.837192i
\(634\) −1.12440e8 3.18490e8i −0.441217 1.24977i
\(635\) 3.44854e7 + 3.44854e7i 0.134684 + 0.134684i
\(636\) −9.80253e7 + 7.90686e7i −0.381037 + 0.307349i
\(637\) 3.97854e6 + 3.97854e6i 0.0153924 + 0.0153924i
\(638\) 2.66703e7 5.57777e7i 0.102699 0.214782i
\(639\) 6.32235e7i 0.242313i
\(640\) −5.51723e7 + 5.73635e7i −0.210466 + 0.218824i
\(641\) 9.95731e7 0.378066 0.189033 0.981971i \(-0.439465\pi\)
0.189033 + 0.981971i \(0.439465\pi\)
\(642\) 1.10101e8 + 5.26450e7i 0.416088 + 0.198954i
\(643\) −1.77761e8 + 1.77761e8i −0.668659 + 0.668659i −0.957406 0.288747i \(-0.906761\pi\)
0.288747 + 0.957406i \(0.406761\pi\)
\(644\) 3.99940e7 + 4.95826e7i 0.149740 + 0.185640i
\(645\) 5.76990e6 5.76990e6i 0.0215025 0.0215025i
\(646\) −3.36164e8 + 1.18679e8i −1.24696 + 0.440228i
\(647\) 3.33059e7 0.122973 0.0614864 0.998108i \(-0.480416\pi\)
0.0614864 + 0.998108i \(0.480416\pi\)
\(648\) 6.97319e6 + 2.94179e7i 0.0256275 + 0.108115i
\(649\) 1.01684e8i 0.371978i
\(650\) −5.42326e6 + 1.91463e6i −0.0197479 + 0.00697178i
\(651\) 1.71487e6 + 1.71487e6i 0.00621567 + 0.00621567i
\(652\) −4.54847e8 4.86884e7i −1.64105 0.175664i
\(653\) 6.98414e7 + 6.98414e7i 0.250826 + 0.250826i 0.821309 0.570483i \(-0.193244\pi\)
−0.570483 + 0.821309i \(0.693244\pi\)
\(654\) 1.30872e8 + 6.25768e7i 0.467857 + 0.223707i
\(655\) 1.43709e8i 0.511400i
\(656\) −1.89429e7 4.10244e6i −0.0671021 0.0145322i
\(657\) 5.80926e7 0.204845
\(658\) 5.36846e7 1.12275e8i 0.188439 0.394099i
\(659\) −1.42365e7 + 1.42365e7i −0.0497448 + 0.0497448i −0.731542 0.681797i \(-0.761199\pi\)
0.681797 + 0.731542i \(0.261199\pi\)
\(660\) 4.12789e7 + 4.41864e6i 0.143581 + 0.0153694i
\(661\) 3.36860e7 3.36860e7i 0.116639 0.116639i −0.646378 0.763017i \(-0.723717\pi\)
0.763017 + 0.646378i \(0.223717\pi\)
\(662\) 5.75240e7 + 1.62939e8i 0.198278 + 0.561631i
\(663\) 3.10273e6 0.0106464
\(664\) −7.69947e7 4.74876e7i −0.263000 0.162209i
\(665\) 3.50748e7i 0.119270i
\(666\) −2.66670e6 7.55354e6i −0.00902718 0.0255698i
\(667\) 6.09067e7 + 6.09067e7i 0.205252 + 0.205252i
\(668\) −1.27365e8 1.57901e8i −0.427289 0.529731i
\(669\) 1.39982e8 + 1.39982e8i 0.467512 + 0.467512i
\(670\) 2.89228e7 6.04885e7i 0.0961646 0.201117i
\(671\) 7.25803e7i 0.240243i
\(672\) 5.23262e6 + 4.12737e7i 0.0172429 + 0.136008i
\(673\) 1.32491e8 0.434651 0.217325 0.976099i \(-0.430267\pi\)
0.217325 + 0.976099i \(0.430267\pi\)
\(674\) 2.31189e8 + 1.10544e8i 0.755071 + 0.361040i
\(675\) 3.79939e7 3.79939e7i 0.123539 0.123539i
\(676\) 2.40317e8 1.93843e8i 0.777937 0.627495i
\(677\) 1.24130e8 1.24130e8i 0.400048 0.400048i −0.478202 0.878250i \(-0.658711\pi\)
0.878250 + 0.478202i \(0.158711\pi\)
\(678\) −1.77771e8 + 6.27602e7i −0.570390 + 0.201370i
\(679\) −1.13336e8 −0.362043
\(680\) −6.49501e7 4.00589e7i −0.206563 0.127401i
\(681\) 2.13054e8i 0.674604i
\(682\) 1.57992e7 5.57774e6i 0.0498060 0.0175835i
\(683\) −2.13536e8 2.13536e8i −0.670207 0.670207i 0.287557 0.957764i \(-0.407157\pi\)
−0.957764 + 0.287557i \(0.907157\pi\)
\(684\) −1.87826e7 + 1.75467e8i −0.0586932 + 0.548312i
\(685\) −1.17955e8 1.17955e8i −0.366983 0.366983i
\(686\) −1.34419e8 6.42728e7i −0.416378 0.199093i
\(687\) 1.64576e8i 0.507570i
\(688\) 4.74986e7 3.05876e7i 0.145853 0.0939248i
\(689\) 6.39788e6 0.0195604
\(690\) −2.49498e7 + 5.21796e7i −0.0759487 + 0.158838i
\(691\) −2.45627e8 + 2.45627e8i −0.744460 + 0.744460i −0.973433 0.228973i \(-0.926463\pi\)
0.228973 + 0.973433i \(0.426463\pi\)
\(692\) 1.26511e6 1.18187e7i 0.00381778 0.0356657i
\(693\) 1.53450e7 1.53450e7i 0.0461069 0.0461069i
\(694\) −1.70503e7 4.82956e7i −0.0510097 0.144487i
\(695\) 1.59797e7 0.0476009
\(696\) 1.29751e7 + 5.47384e7i 0.0384843 + 0.162355i
\(697\) 1.85834e7i 0.0548815i
\(698\) −1.29171e8 3.65882e8i −0.379838 1.07591i
\(699\) 1.73479e8 + 1.73479e8i 0.507942 + 0.507942i
\(700\) 5.75518e7 4.64220e7i 0.167789 0.135341i
\(701\) −1.47613e8 1.47613e8i −0.428519 0.428519i 0.459605 0.888124i \(-0.347991\pi\)
−0.888124 + 0.459605i \(0.847991\pi\)
\(702\) 662540. 1.38562e6i 0.00191514 0.00400529i
\(703\) 4.67567e7i 0.134579i
\(704\) 2.72846e8 + 9.03917e7i 0.781987 + 0.259066i
\(705\) 1.12993e8 0.322466
\(706\) 1.16301e7 + 5.56095e6i 0.0330497 + 0.0158028i
\(707\) 3.04001e7 3.04001e7i 0.0860236 0.0860236i
\(708\) −5.80878e7 7.20143e7i −0.163676 0.202917i
\(709\) −3.51942e8 + 3.51942e8i −0.987490 + 0.987490i −0.999923 0.0124323i \(-0.996043\pi\)
0.0124323 + 0.999923i \(0.496043\pi\)
\(710\) 7.44876e7 2.62971e7i 0.208118 0.0734739i
\(711\) −2.05507e8 −0.571765
\(712\) 4.58934e8 1.08785e8i 1.27148 0.301390i
\(713\) 2.33426e7i 0.0643994i
\(714\) −3.76144e7 + 1.32794e7i −0.103338 + 0.0364824i
\(715\) −1.49129e6 1.49129e6i −0.00407983 0.00407983i
\(716\) −3.13639e8 3.35730e7i −0.854459 0.0914642i
\(717\) −1.97954e8 1.97954e8i −0.537039 0.537039i
\(718\) 2.02315e8 + 9.67375e7i 0.546581 + 0.261349i
\(719\) 1.45173e8i 0.390571i 0.980746 + 0.195286i \(0.0625634\pi\)
−0.980746 + 0.195286i \(0.937437\pi\)
\(720\) −3.17587e7 + 2.04516e7i −0.0850874 + 0.0547936i
\(721\) −1.47349e8 −0.393135
\(722\) −2.81982e8 + 5.89732e8i −0.749221 + 1.56691i
\(723\) −1.95058e8 + 1.95058e8i −0.516118 + 0.516118i
\(724\) 2.96767e8 + 3.17670e7i 0.781989 + 0.0837067i
\(725\) 7.06960e7 7.06960e7i 0.185516 0.185516i
\(726\) 2.36367e7 + 6.69518e7i 0.0617698 + 0.174966i
\(727\) −6.00279e8 −1.56225 −0.781124 0.624375i \(-0.785354\pi\)
−0.781124 + 0.624375i \(0.785354\pi\)
\(728\) 1.10950e6 1.79890e6i 0.00287563 0.00466244i
\(729\) 1.43489e7i 0.0370370i
\(730\) 2.41630e7 + 6.84426e7i 0.0621129 + 0.175937i
\(731\) 3.83020e7 + 3.83020e7i 0.0980549 + 0.0980549i
\(732\) 4.14622e7 + 5.14028e7i 0.105711 + 0.131055i
\(733\) 2.06518e8 + 2.06518e8i 0.524381 + 0.524381i 0.918891 0.394511i \(-0.129086\pi\)
−0.394511 + 0.918891i \(0.629086\pi\)
\(734\) 4.47457e7 9.35804e7i 0.113152 0.236645i
\(735\) 6.56770e7i 0.165406i
\(736\) −2.45294e8 + 3.16520e8i −0.615253 + 0.793904i
\(737\) −2.42135e8 −0.604859
\(738\) −8.29901e6 3.96819e6i −0.0206470 0.00987243i
\(739\) −2.55773e8 + 2.55773e8i −0.633755 + 0.633755i −0.949008 0.315252i \(-0.897911\pi\)
0.315252 + 0.949008i \(0.397911\pi\)
\(740\) 7.79012e6 6.28362e6i 0.0192242 0.0155065i
\(741\) 6.33911e6 6.33911e6i 0.0155802 0.0155802i
\(742\) −7.75615e7 + 2.73823e7i −0.189860 + 0.0670283i
\(743\) −3.84449e8 −0.937285 −0.468643 0.883388i \(-0.655257\pi\)
−0.468643 + 0.883388i \(0.655257\pi\)
\(744\) −8.00295e6 + 1.29757e7i −0.0194326 + 0.0315073i
\(745\) 1.67504e8i 0.405094i
\(746\) 1.29202e8 4.56136e7i 0.311211 0.109870i
\(747\) −3.03588e7 3.03588e7i −0.0728320 0.0728320i
\(748\) −2.93320e7 + 2.74019e8i −0.0700868 + 0.654751i
\(749\) 5.63606e7 + 5.63606e7i 0.134131 + 0.134131i
\(750\) 1.27282e8 + 6.08604e7i 0.301706 + 0.144262i
\(751\) 5.91852e8i 1.39731i 0.715458 + 0.698656i \(0.246218\pi\)
−0.715458 + 0.698656i \(0.753782\pi\)
\(752\) 7.64587e8 + 1.65585e8i 1.79793 + 0.389375i
\(753\) −3.75415e8 −0.879278
\(754\) 1.23280e6 2.57825e6i 0.00287593 0.00601467i
\(755\) −2.15449e7 + 2.15449e7i −0.0500614 + 0.0500614i
\(756\) −2.10164e6 + 1.96335e7i −0.00486399 + 0.0454395i
\(757\) 2.68713e8 2.68713e8i 0.619442 0.619442i −0.325946 0.945388i \(-0.605683\pi\)
0.945388 + 0.325946i \(0.105683\pi\)
\(758\) −2.83265e7 8.02359e7i −0.0650407 0.184230i
\(759\) 2.08874e8 0.477705
\(760\) −2.14541e8 + 5.08546e7i −0.488731 + 0.115848i
\(761\) 4.52025e8i 1.02567i −0.858487 0.512836i \(-0.828595\pi\)
0.858487 0.512836i \(-0.171405\pi\)
\(762\) 5.33499e7 + 1.51116e8i 0.120578 + 0.341543i
\(763\) 6.69934e7 + 6.69934e7i 0.150820 + 0.150820i
\(764\) 5.01266e8 4.04328e8i 1.12406 0.906679i
\(765\) −2.56096e7 2.56096e7i −0.0572030 0.0572030i
\(766\) 2.21140e8 4.62489e8i 0.492019 1.02900i
\(767\) 4.70020e6i 0.0104167i
\(768\) −2.44872e8 + 9.18488e7i −0.540574 + 0.202763i
\(769\) −3.89939e8 −0.857466 −0.428733 0.903431i \(-0.641040\pi\)
−0.428733 + 0.903431i \(0.641040\pi\)
\(770\) 2.44614e7 + 1.16963e7i 0.0535809 + 0.0256198i
\(771\) −3.66823e7 + 3.66823e7i −0.0800376 + 0.0800376i
\(772\) 3.01675e8 + 3.74001e8i 0.655673 + 0.812870i
\(773\) 1.43202e8 1.43202e8i 0.310035 0.310035i −0.534888 0.844923i \(-0.679646\pi\)
0.844923 + 0.534888i \(0.179646\pi\)
\(774\) 2.52838e7 8.92619e6i 0.0545280 0.0192506i
\(775\) 2.70944e7 0.0582069
\(776\) −1.64325e8 6.93243e8i −0.351657 1.48354i
\(777\) 5.23175e6i 0.0111528i
\(778\) −3.02729e8 + 1.06875e8i −0.642858 + 0.226954i
\(779\) −3.79672e7 3.79672e7i −0.0803150 0.0803150i
\(780\) 1.90807e6 + 204246.i 0.00402077 + 0.000430397i
\(781\) −2.01720e8 2.01720e8i −0.423444 0.423444i
\(782\) −3.46381e8 1.65623e8i −0.724325 0.346338i
\(783\) 2.66993e7i 0.0556178i
\(784\) 9.62463e7 4.44415e8i 0.199727 0.922234i
\(785\) 2.69049e8 0.556189
\(786\) 2.03707e8 4.26029e8i 0.419506 0.877347i
\(787\) 6.07213e8 6.07213e8i 1.24571 1.24571i 0.288114 0.957596i \(-0.406972\pi\)
0.957596 0.288114i \(-0.0930281\pi\)
\(788\) 8.84656e8 + 9.46966e7i 1.80799 + 0.193533i
\(789\) −5.82459e6 + 5.82459e6i −0.0118586 + 0.0118586i
\(790\) −8.54782e7 2.42121e8i −0.173370 0.491078i
\(791\) −1.23128e8 −0.248787
\(792\) 1.16109e8 + 7.16118e7i 0.233717 + 0.144148i
\(793\) 3.35494e6i 0.00672767i
\(794\) −3.25898e8 9.23119e8i −0.651058 1.84415i
\(795\) −5.28075e7 5.28075e7i −0.105098 0.105098i
\(796\) 4.34674e8 + 5.38887e8i 0.861836 + 1.06846i
\(797\) 5.04366e7 + 5.04366e7i 0.0996255 + 0.0996255i 0.755163 0.655537i \(-0.227558\pi\)
−0.655537 + 0.755163i \(0.727558\pi\)
\(798\) −4.97183e7 + 1.03980e8i −0.0978380 + 0.204616i
\(799\) 7.50074e8i 1.47049i
\(800\) 3.67393e8 + 2.84719e8i 0.717564 + 0.556092i
\(801\) 2.23850e8 0.435571
\(802\) 4.26250e8 + 2.03812e8i 0.826306 + 0.395101i
\(803\) 1.85349e8 1.85349e8i 0.357968 0.357968i
\(804\) 1.71484e8 1.38322e8i 0.329956 0.266147i
\(805\) −2.67108e7 + 2.67108e7i −0.0512034 + 0.0512034i
\(806\) 730298. 257824.i 0.00139474 0.000492401i
\(807\) 1.58205e8 0.301023
\(808\) 2.30025e8 + 1.41871e8i 0.436055 + 0.268943i
\(809\) 4.00282e8i 0.755997i −0.925806 0.377999i \(-0.876612\pi\)
0.925806 0.377999i \(-0.123388\pi\)
\(810\) −1.69054e7 + 5.96827e6i −0.0318104 + 0.0112303i
\(811\) 8.86243e7 + 8.86243e7i 0.166146 + 0.166146i 0.785283 0.619137i \(-0.212517\pi\)
−0.619137 + 0.785283i \(0.712517\pi\)
\(812\) −3.91056e6 + 3.65325e7i −0.00730417 + 0.0682356i
\(813\) 4.86483e7 + 4.86483e7i 0.0905308 + 0.0905308i
\(814\) −3.26085e7 1.55919e7i −0.0604586 0.0289085i
\(815\) 2.71261e8i 0.501089i
\(816\) −1.35763e8 2.10822e8i −0.249867 0.388012i
\(817\) 1.56508e8 0.286992
\(818\) −2.50732e8 + 5.24376e8i −0.458089 + 0.958039i
\(819\) 709301. 709301.i 0.00129116 0.00129116i
\(820\) 1.22330e6 1.14281e7i 0.00221867 0.0207268i
\(821\) −2.23870e8 + 2.23870e8i −0.404545 + 0.404545i −0.879831 0.475286i \(-0.842344\pi\)
0.475286 + 0.879831i \(0.342344\pi\)
\(822\) −1.82480e8 5.16882e8i −0.328549 0.930628i
\(823\) 1.27752e8 0.229175 0.114587 0.993413i \(-0.463445\pi\)
0.114587 + 0.993413i \(0.463445\pi\)
\(824\) −2.13640e8 9.01289e8i −0.381858 1.61095i
\(825\) 2.42446e8i 0.431770i
\(826\) −2.01164e7 5.69806e7i −0.0356953 0.101108i
\(827\) −4.55767e8 4.55767e8i −0.805798 0.805798i 0.178197 0.983995i \(-0.442974\pi\)
−0.983995 + 0.178197i \(0.942974\pi\)
\(828\) −1.47929e8 + 1.19321e8i −0.260592 + 0.210197i
\(829\) 3.03952e8 + 3.03952e8i 0.533509 + 0.533509i 0.921615 0.388106i \(-0.126870\pi\)
−0.388106 + 0.921615i \(0.626870\pi\)
\(830\) 2.31402e7 4.83950e7i 0.0404700 0.0846381i
\(831\) 5.62944e8i 0.980984i
\(832\) 1.26120e7 + 4.17824e6i 0.0218984 + 0.00725477i
\(833\) 4.35980e8 0.754277
\(834\) 4.73722e7 + 2.26512e7i 0.0816631 + 0.0390475i
\(835\) 8.50633e7 8.50633e7i 0.146111 0.146111i
\(836\) 4.99915e8 + 6.19770e8i 0.855613 + 1.06075i
\(837\) −5.11628e6 + 5.11628e6i −0.00872525 + 0.00872525i
\(838\) −2.08842e8 + 7.37297e7i −0.354884 + 0.125288i
\(839\) 2.05872e8 0.348588 0.174294 0.984694i \(-0.444236\pi\)
0.174294 + 0.984694i \(0.444236\pi\)
\(840\) −2.40057e7 + 5.69027e6i −0.0405019 + 0.00960053i
\(841\) 5.45144e8i 0.916480i
\(842\) −4.11023e8 + 1.45108e8i −0.688542 + 0.243083i
\(843\) 1.36131e8 + 1.36131e8i 0.227235 + 0.227235i
\(844\) −8.66840e8 9.27895e7i −1.44182 0.154338i
\(845\) 1.29462e8 + 1.29462e8i 0.214571 + 0.214571i
\(846\) 3.34970e8 + 1.60167e8i 0.553216 + 0.264522i
\(847\) 4.63723e7i 0.0763147i
\(848\) −2.79945e8 4.34718e8i −0.459076 0.712886i
\(849\) −4.13672e8 −0.675979
\(850\) −1.92243e8 + 4.02053e8i −0.313035 + 0.654676i
\(851\) 3.56071e7 3.56071e7i 0.0577760 0.0577760i
\(852\) 2.58096e8 + 2.76275e7i 0.417314 + 0.0446707i
\(853\) 8.70314e8 8.70314e8i 1.40226 1.40226i 0.609391 0.792870i \(-0.291414\pi\)
0.792870 0.609391i \(-0.208586\pi\)
\(854\) 1.43588e7 + 4.06719e7i 0.0230539 + 0.0653012i
\(855\) −1.04645e8 −0.167425
\(856\) −2.63023e8 + 4.26457e8i −0.419347 + 0.679914i
\(857\) 3.02830e8i 0.481124i 0.970634 + 0.240562i \(0.0773318\pi\)
−0.970634 + 0.240562i \(0.922668\pi\)
\(858\) −2.30706e6 6.53483e6i −0.00365255 0.0103460i
\(859\) 4.31496e8 + 4.31496e8i 0.680765 + 0.680765i 0.960173 0.279408i \(-0.0901381\pi\)
−0.279408 + 0.960173i \(0.590138\pi\)
\(860\) 2.10330e7 + 2.60757e7i 0.0330679 + 0.0409959i
\(861\) −4.24827e6 4.24827e6i −0.00665583 0.00665583i
\(862\) −2.65349e7 + 5.54946e7i −0.0414282 + 0.0866422i
\(863\) 3.92538e8i 0.610729i 0.952235 + 0.305365i \(0.0987784\pi\)
−0.952235 + 0.305365i \(0.901222\pi\)
\(864\) −1.23139e8 + 1.56114e7i −0.190922 + 0.0242048i
\(865\) 7.04841e6 0.0108904
\(866\) −4.41558e8 2.11132e8i −0.679883 0.325088i
\(867\) −9.60585e7 + 9.60585e7i −0.147394 + 0.147394i
\(868\) −7.74994e6 + 6.25121e6i −0.0118506 + 0.00955884i
\(869\) −6.55686e8 + 6.55686e8i −0.999164 + 0.999164i
\(870\) −3.14561e7 + 1.11053e7i −0.0477691 + 0.0168644i
\(871\) −1.11924e7 −0.0169382
\(872\) −3.12645e8 + 5.06911e8i −0.471521 + 0.764508i
\(873\) 3.38137e8i 0.508218i
\(874\) −1.04606e9 + 3.69302e8i −1.56684 + 0.553156i
\(875\) 6.51559e7 + 6.51559e7i 0.0972589 + 0.0972589i
\(876\) −2.53854e7 + 2.37150e8i −0.0377634 + 0.352786i
\(877\) −7.63567e8 7.63567e8i −1.13201 1.13201i −0.989843 0.142162i \(-0.954595\pi\)
−0.142162 0.989843i \(-0.545405\pi\)
\(878\) −1.77906e8 8.50661e7i −0.262849 0.125682i
\(879\) 5.14973e8i 0.758260i
\(880\) −3.60762e7 + 1.66581e8i −0.0529387 + 0.244443i
\(881\) −8.54724e8 −1.24997 −0.624983 0.780638i \(-0.714894\pi\)
−0.624983 + 0.780638i \(0.714894\pi\)
\(882\) 9.30968e7 1.94701e8i 0.135684 0.283767i
\(883\) 4.53290e8 4.53290e8i 0.658406 0.658406i −0.296596 0.955003i \(-0.595852\pi\)
0.955003 + 0.296596i \(0.0958516\pi\)
\(884\) −1.35583e6 + 1.26662e7i −0.00196268 + 0.0183354i
\(885\) 3.87950e7 3.87950e7i 0.0559689 0.0559689i
\(886\) −1.64265e8 4.65287e8i −0.236180 0.668991i
\(887\) −9.71858e8 −1.39262 −0.696309 0.717742i \(-0.745176\pi\)
−0.696309 + 0.717742i \(0.745176\pi\)
\(888\) 3.20010e7 7.58547e6i 0.0457009 0.0108329i
\(889\) 1.04666e8i 0.148971i
\(890\) 9.31078e7 + 2.63732e8i 0.132074 + 0.374104i
\(891\) 4.57814e7 + 4.57814e7i 0.0647226 + 0.0647226i
\(892\) −6.32613e8 + 5.10275e8i −0.891341 + 0.718968i
\(893\) 1.53246e9 + 1.53246e9i 2.15196 + 2.15196i
\(894\) 2.37435e8 4.96568e8i 0.332302 0.694970i
\(895\) 1.87048e8i 0.260906i
\(896\) −1.70778e8 + 3.32518e6i −0.237414 + 0.00462265i
\(897\) 9.65495e6 0.0133774
\(898\) −1.22603e7 5.86228e6i −0.0169305 0.00809538i
\(899\) −9.51995e6 + 9.51995e6i −0.0131025 + 0.0131025i
\(900\) 1.38499e8 + 1.71705e8i 0.189985 + 0.235534i
\(901\) 3.50549e8 3.50549e8i 0.479263 0.479263i
\(902\) −3.91395e7 + 1.38178e7i −0.0533330 + 0.0188287i
\(903\) 1.75121e7 0.0237835
\(904\) −1.78522e8 7.53136e8i −0.241650 1.01945i
\(905\) 1.76986e8i 0.238777i
\(906\) −9.44099e7 + 3.33305e7i −0.126950 + 0.0448184i
\(907\) −1.75732e8 1.75732e8i −0.235521 0.235521i 0.579472 0.814992i \(-0.303259\pi\)
−0.814992 + 0.579472i \(0.803259\pi\)
\(908\) 8.69747e8 + 9.31007e7i 1.16181 + 0.124364i
\(909\) 9.06982e7 + 9.06982e7i 0.120756 + 0.120756i
\(910\) 1.13070e6 + 540647.i 0.00150045 + 0.000717447i
\(911\) 6.20037e8i 0.820091i 0.912065 + 0.410046i \(0.134487\pi\)
−0.912065 + 0.410046i \(0.865513\pi\)
\(912\) −7.08099e8 1.53352e8i −0.933489 0.202164i
\(913\) −1.93724e8 −0.254549
\(914\) −4.37845e8 + 9.15701e8i −0.573432 + 1.19926i
\(915\) −2.76913e7 + 2.76913e7i −0.0361477 + 0.0361477i
\(916\) −6.71845e8 7.19166e7i −0.874144 0.0935713i
\(917\) 2.18084e8 2.18084e8i 0.282824 0.282824i
\(918\) −3.96188e7 1.12222e8i −0.0512121 0.145060i
\(919\) −6.45209e8 −0.831292 −0.415646 0.909526i \(-0.636445\pi\)
−0.415646 + 0.909526i \(0.636445\pi\)
\(920\) −2.02109e8 1.24654e8i −0.259551 0.160082i
\(921\) 9.04999e7i 0.115843i
\(922\) 3.73186e8 + 1.05706e9i 0.476137 + 1.34868i
\(923\) −9.32425e6 9.32425e6i −0.0118579 0.0118579i
\(924\) 5.59370e7 + 6.93479e7i 0.0709060 + 0.0879057i
\(925\) −4.13300e7 4.13300e7i −0.0522204 0.0522204i
\(926\) −2.69939e8 + 5.64545e8i −0.339964 + 0.710994i
\(927\) 4.39613e8i 0.551864i
\(928\) −2.29128e8 + 2.90484e7i −0.286704 + 0.0363479i
\(929\) 8.35063e8 1.04153 0.520765 0.853700i \(-0.325647\pi\)
0.520765 + 0.853700i \(0.325647\pi\)
\(930\) −8.15587e6 3.89975e6i −0.0101396 0.00484829i
\(931\) 8.90740e8 8.90740e8i 1.10383 1.10383i
\(932\) −7.83995e8 + 6.32381e8i −0.968424 + 0.781144i
\(933\) −5.30204e8 + 5.30204e8i −0.652827 + 0.652827i
\(934\) 4.43218e8 1.56473e8i 0.543972 0.192044i
\(935\) −1.63419e8 −0.199926
\(936\) 5.36699e6 + 3.31017e6i 0.00654490 + 0.00403666i
\(937\) 9.19162e8i 1.11731i −0.829401 0.558654i \(-0.811318\pi\)
0.829401 0.558654i \(-0.188682\pi\)
\(938\) 1.35685e8 4.79023e7i 0.164408 0.0580427i
\(939\) −1.76258e8 1.76258e8i −0.212889 0.212889i
\(940\) −4.93758e7 + 4.61269e8i −0.0594471 + 0.555355i
\(941\) 4.64558e8 + 4.64558e8i 0.557534 + 0.557534i 0.928605 0.371071i \(-0.121009\pi\)
−0.371071 + 0.928605i \(0.621009\pi\)
\(942\) 7.97602e8 + 3.81376e8i 0.954187 + 0.456247i
\(943\) 5.78270e7i 0.0689598i
\(944\) 3.19366e8 2.05662e8i 0.379641 0.244477i
\(945\) −1.17090e7 −0.0138747
\(946\) 5.21903e7 1.09150e8i 0.0616477 0.128929i
\(947\) 2.95450e8 2.95450e8i 0.347884 0.347884i −0.511437 0.859321i \(-0.670887\pi\)
0.859321 + 0.511437i \(0.170887\pi\)
\(948\) 8.98026e7 8.38936e8i 0.105406 0.984700i
\(949\) 8.56754e6 8.56754e6i 0.0100244 0.0100244i
\(950\) 4.28658e8 + 1.21419e9i 0.499966 + 1.41617i
\(951\) 6.58136e8 0.765199
\(952\) −3.77734e7 1.59355e8i −0.0437799 0.184695i
\(953\) 9.92140e8i 1.14629i 0.819454 + 0.573145i \(0.194277\pi\)
−0.819454 + 0.573145i \(0.805723\pi\)
\(954\) −8.16946e7 2.31403e8i −0.0940910 0.266517i
\(955\) 2.70038e8 + 2.70038e8i 0.310038 + 0.310038i
\(956\) 8.94604e8 7.21600e8i 1.02390 0.825891i
\(957\) 8.51862e7 + 8.51862e7i 0.0971927 + 0.0971927i
\(958\) 5.10622e8 1.06790e9i 0.580768 1.21461i
\(959\) 3.58004e8i 0.405912i
\(960\) −6.96112e7 1.38585e8i −0.0786802 0.156640i
\(961\) 8.83855e8 0.995889
\(962\) −1.50729e6 720715.i −0.00169306 0.000809540i
\(963\) −1.68151e8 + 1.68151e8i −0.188287 + 0.188287i
\(964\) −7.11045e8 8.81518e8i −0.793718 0.984012i
\(965\) −2.01479e8 + 2.01479e8i −0.224207 + 0.224207i
\(966\) −1.17047e8 + 4.13223e7i −0.129846 + 0.0458409i
\(967\) −4.13366e8 −0.457147 −0.228573 0.973527i \(-0.573406\pi\)
−0.228573 + 0.973527i \(0.573406\pi\)
\(968\) −2.83645e8 + 6.72348e7i −0.312715 + 0.0741256i
\(969\) 6.94657e8i 0.763483i
\(970\) 3.98380e8 1.40644e8i 0.436499 0.154101i
\(971\) −8.79406e8 8.79406e8i −0.960576 0.960576i 0.0386761 0.999252i \(-0.487686\pi\)
−0.999252 + 0.0386761i \(0.987686\pi\)
\(972\) −5.85763e7 6.27020e6i −0.0637856 0.00682783i
\(973\) 2.42499e7 + 2.42499e7i 0.0263252 + 0.0263252i
\(974\) −1.05859e9 5.06167e8i −1.14565 0.547794i
\(975\) 1.12067e7i 0.0120911i
\(976\) −2.27959e8 + 1.46798e8i −0.245192 + 0.157896i
\(977\) −1.52615e9 −1.63649 −0.818243 0.574873i \(-0.805052\pi\)
−0.818243 + 0.574873i \(0.805052\pi\)
\(978\) 3.84511e8 8.04159e8i 0.411048 0.859658i
\(979\) 7.14211e8 7.14211e8i 0.761165 0.761165i
\(980\) 2.68112e8 + 2.86996e7i 0.284864 + 0.0304928i
\(981\) −1.99873e8 + 1.99873e8i −0.211713 + 0.211713i
\(982\) −1.92052e8 5.43995e8i −0.202808 0.574461i
\(983\) 1.39922e9 1.47308 0.736538 0.676396i \(-0.236459\pi\)
0.736538 + 0.676396i \(0.236459\pi\)
\(984\) 1.98258e7 3.21448e7i 0.0208087 0.0337385i
\(985\) 5.27590e8i 0.552062i
\(986\) −7.37193e7 2.08813e8i −0.0769043 0.217835i
\(987\) 1.71471e8 + 1.71471e8i 0.178336 + 0.178336i
\(988\) 2.31079e7 + 2.86481e7i 0.0239602 + 0.0297047i
\(989\) 1.19187e8 + 1.19187e8i 0.123208 + 0.123208i
\(990\) −3.48957e7 + 7.29802e7i −0.0359639 + 0.0752141i
\(991\) 5.93840e8i 0.610167i −0.952326 0.305083i \(-0.901316\pi\)
0.952326 0.305083i \(-0.0986843\pi\)
\(992\) −4.94733e7 3.83404e7i −0.0506799 0.0392755i
\(993\) −3.36701e8 −0.343872
\(994\) 1.52945e8 + 7.31310e7i 0.155731 + 0.0744634i
\(995\) −2.90306e8 + 2.90306e8i −0.294704 + 0.294704i
\(996\) 1.37199e8 1.10667e8i 0.138859 0.112006i
\(997\) 3.37349e8 3.37349e8i 0.340403 0.340403i −0.516116 0.856519i \(-0.672623\pi\)
0.856519 + 0.516116i \(0.172623\pi\)
\(998\) 1.59910e9 5.64544e8i 1.60873 0.567945i
\(999\) 1.56088e7 0.0156557
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 48.7.l.a.19.5 48
4.3 odd 2 192.7.l.a.175.4 48
8.3 odd 2 384.7.l.a.223.21 48
8.5 even 2 384.7.l.b.223.4 48
16.3 odd 4 384.7.l.b.31.4 48
16.5 even 4 192.7.l.a.79.4 48
16.11 odd 4 inner 48.7.l.a.43.5 yes 48
16.13 even 4 384.7.l.a.31.21 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.7.l.a.19.5 48 1.1 even 1 trivial
48.7.l.a.43.5 yes 48 16.11 odd 4 inner
192.7.l.a.79.4 48 16.5 even 4
192.7.l.a.175.4 48 4.3 odd 2
384.7.l.a.31.21 48 16.13 even 4
384.7.l.a.223.21 48 8.3 odd 2
384.7.l.b.31.4 48 16.3 odd 4
384.7.l.b.223.4 48 8.5 even 2