Properties

Label 38.7.f.a.3.5
Level $38$
Weight $7$
Character 38.3
Analytic conductor $8.742$
Analytic rank $0$
Dimension $60$
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] = [38,7,Mod(3,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([13]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.3");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 38.f (of order \(18\), degree \(6\), 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: \(8.74205517755\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(10\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 3.5
Character \(\chi\) \(=\) 38.3
Dual form 38.7.f.a.13.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.63616 + 4.33340i) q^{2} +(12.5750 + 34.5495i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(-24.6848 + 139.995i) q^{5} +(-195.442 - 71.1350i) q^{6} +(136.699 + 236.770i) q^{7} +(156.767 + 90.5097i) q^{8} +(-477.093 + 400.329i) q^{9} +O(q^{10})\) \(q+(-3.63616 + 4.33340i) q^{2} +(12.5750 + 34.5495i) q^{3} +(-5.55674 - 31.5138i) q^{4} +(-24.6848 + 139.995i) q^{5} +(-195.442 - 71.1350i) q^{6} +(136.699 + 236.770i) q^{7} +(156.767 + 90.5097i) q^{8} +(-477.093 + 400.329i) q^{9} +(-516.895 - 616.012i) q^{10} +(154.353 - 267.347i) q^{11} +(1018.91 - 588.270i) q^{12} +(192.920 - 530.044i) q^{13} +(-1523.08 - 268.560i) q^{14} +(-5147.16 + 907.583i) q^{15} +(-962.245 + 350.229i) q^{16} +(-7404.65 - 6213.24i) q^{17} -3523.10i q^{18} +(571.576 + 6835.14i) q^{19} +4548.94 q^{20} +(-6461.31 + 7700.29i) q^{21} +(597.272 + 1640.99i) q^{22} +(-790.114 - 4480.96i) q^{23} +(-1155.72 + 6554.40i) q^{24} +(-4306.46 - 1567.42i) q^{25} +(1595.41 + 2763.32i) q^{26} +(3381.48 + 1952.30i) q^{27} +(6701.94 - 5623.60i) q^{28} +(7702.41 + 9179.37i) q^{29} +(14783.0 - 25604.8i) q^{30} +(34857.0 - 20124.7i) q^{31} +(1981.19 - 5443.28i) q^{32} +(11177.7 + 1970.93i) q^{33} +(53848.9 - 9495.02i) q^{34} +(-36521.0 + 13292.6i) q^{35} +(15267.0 + 12810.5i) q^{36} +83779.7i q^{37} +(-31697.8 - 22376.8i) q^{38} +20738.8 q^{39} +(-16540.6 + 19712.4i) q^{40} +(10334.6 + 28394.2i) q^{41} +(-9874.12 - 55998.9i) q^{42} +(-17549.1 + 99525.8i) q^{43} +(-9282.84 - 3378.68i) q^{44} +(-44266.9 - 76672.6i) q^{45} +(22290.8 + 12869.6i) q^{46} +(17452.2 - 14644.2i) q^{47} +(-24200.5 - 28841.0i) q^{48} +(21451.0 - 37154.3i) q^{49} +(22451.2 - 12962.2i) q^{50} +(121551. - 333959. i) q^{51} +(-17775.7 - 3134.34i) q^{52} +(-136542. + 24076.1i) q^{53} +(-20755.7 + 7554.45i) q^{54} +(33617.0 + 28208.0i) q^{55} +49490.5i q^{56} +(-228963. + 105700. i) q^{57} -67785.0 q^{58} +(-28663.2 + 34159.5i) q^{59} +(57202.9 + 157164. i) q^{60} +(36239.2 + 205523. i) q^{61} +(-39537.1 + 224226. i) q^{62} +(-160004. - 58236.8i) q^{63} +(16384.0 + 28377.9i) q^{64} +(69441.1 + 40091.9i) q^{65} +(-49184.8 + 41270.9i) q^{66} +(-269824. - 321564. i) q^{67} +(-154657. + 267874. i) q^{68} +(144879. - 83646.2i) q^{69} +(75194.0 - 206594. i) q^{70} +(128224. + 22609.3i) q^{71} +(-111026. + 19576.9i) q^{72} +(498363. - 181389. i) q^{73} +(-363051. - 304636. i) q^{74} -168497. i q^{75} +(212226. - 55993.7i) q^{76} +84399.9 q^{77} +(-75409.4 + 89869.4i) q^{78} +(-57206.4 - 157173. i) q^{79} +(-25277.3 - 143355. i) q^{80} +(-103769. + 588503. i) q^{81} +(-160622. - 58461.5i) q^{82} +(315134. + 545828. i) q^{83} +(278570. + 160832. i) q^{84} +(1.05260e6 - 883239. i) q^{85} +(-367474. - 437939. i) q^{86} +(-220285. + 381545. i) q^{87} +(48395.0 - 27940.9i) q^{88} +(259935. - 714166. i) q^{89} +(493214. + 86967.0i) q^{90} +(151871. - 26778.9i) q^{91} +(-136822. + 49799.1i) q^{92} +(1.13363e6 + 951225. i) q^{93} +128876. i q^{94} +(-970993. - 88706.8i) q^{95} +212976. q^{96} +(-253212. + 301767. i) q^{97} +(83005.1 + 228055. i) q^{98} +(33386.0 + 189342. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9} - 3360 q^{11} + 9660 q^{13} + 2496 q^{14} - 37464 q^{15} + 7704 q^{17} + 46704 q^{19} + 21504 q^{20} + 78732 q^{21} - 20304 q^{22} - 54120 q^{23} + 7680 q^{24} - 41328 q^{25} - 25536 q^{26} - 124830 q^{27} + 65280 q^{28} - 21840 q^{29} + 30780 q^{31} - 54582 q^{33} - 70560 q^{34} - 56796 q^{35} - 22080 q^{36} + 52080 q^{38} + 496344 q^{39} + 83394 q^{41} + 38880 q^{42} - 294384 q^{43} - 8448 q^{44} - 391824 q^{45} + 738720 q^{46} + 639264 q^{47} + 61440 q^{48} - 85530 q^{49} - 689472 q^{50} - 215478 q^{51} - 456960 q^{52} - 1189428 q^{53} - 907200 q^{54} - 316512 q^{55} + 517776 q^{57} + 440640 q^{58} + 957390 q^{59} + 586752 q^{60} + 1390404 q^{61} + 978384 q^{62} + 2002152 q^{63} + 983040 q^{64} - 878940 q^{65} - 976992 q^{66} - 2920854 q^{67} - 78144 q^{68} - 2667600 q^{69} - 643392 q^{70} + 1585980 q^{71} + 706560 q^{72} + 1734648 q^{73} - 1167552 q^{74} - 411264 q^{76} - 1481400 q^{77} - 2170608 q^{78} + 4991952 q^{79} + 40002 q^{81} + 2299392 q^{82} - 30672 q^{83} + 1313280 q^{84} + 815976 q^{85} - 1424976 q^{86} - 125892 q^{87} - 6804636 q^{89} - 2283456 q^{90} - 3838704 q^{91} - 244992 q^{92} - 3271128 q^{93} - 4631640 q^{95} + 2112390 q^{97} + 7177728 q^{98} + 21467982 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.63616 + 4.33340i −0.454519 + 0.541675i
\(3\) 12.5750 + 34.5495i 0.465741 + 1.27961i 0.921107 + 0.389308i \(0.127286\pi\)
−0.455367 + 0.890304i \(0.650492\pi\)
\(4\) −5.55674 31.5138i −0.0868241 0.492404i
\(5\) −24.6848 + 139.995i −0.197479 + 1.11996i 0.711366 + 0.702822i \(0.248077\pi\)
−0.908844 + 0.417135i \(0.863034\pi\)
\(6\) −195.442 71.1350i −0.904823 0.329329i
\(7\) 136.699 + 236.770i 0.398541 + 0.690293i 0.993546 0.113429i \(-0.0361834\pi\)
−0.595005 + 0.803722i \(0.702850\pi\)
\(8\) 156.767 + 90.5097i 0.306186 + 0.176777i
\(9\) −477.093 + 400.329i −0.654449 + 0.549148i
\(10\) −516.895 616.012i −0.516895 0.616012i
\(11\) 154.353 267.347i 0.115968 0.200862i −0.802198 0.597057i \(-0.796336\pi\)
0.918166 + 0.396195i \(0.129670\pi\)
\(12\) 1018.91 588.270i 0.589649 0.340434i
\(13\) 192.920 530.044i 0.0878108 0.241258i −0.888012 0.459819i \(-0.847914\pi\)
0.975823 + 0.218561i \(0.0701363\pi\)
\(14\) −1523.08 268.560i −0.555059 0.0978719i
\(15\) −5147.16 + 907.583i −1.52508 + 0.268914i
\(16\) −962.245 + 350.229i −0.234923 + 0.0855050i
\(17\) −7404.65 6213.24i −1.50715 1.26465i −0.869072 0.494685i \(-0.835283\pi\)
−0.638083 0.769968i \(-0.720272\pi\)
\(18\) 3523.10i 0.604097i
\(19\) 571.576 + 6835.14i 0.0833322 + 0.996522i
\(20\) 4548.94 0.568617
\(21\) −6461.31 + 7700.29i −0.697690 + 0.831475i
\(22\) 597.272 + 1640.99i 0.0560924 + 0.154113i
\(23\) −790.114 4480.96i −0.0649391 0.368288i −0.999908 0.0135585i \(-0.995684\pi\)
0.934969 0.354730i \(-0.115427\pi\)
\(24\) −1155.72 + 6554.40i −0.0836022 + 0.474132i
\(25\) −4306.46 1567.42i −0.275613 0.100315i
\(26\) 1595.41 + 2763.32i 0.0907719 + 0.157221i
\(27\) 3381.48 + 1952.30i 0.171797 + 0.0991871i
\(28\) 6701.94 5623.60i 0.305300 0.256177i
\(29\) 7702.41 + 9179.37i 0.315815 + 0.376373i 0.900477 0.434903i \(-0.143217\pi\)
−0.584662 + 0.811277i \(0.698773\pi\)
\(30\) 14783.0 25604.8i 0.547517 0.948327i
\(31\) 34857.0 20124.7i 1.17005 0.675529i 0.216359 0.976314i \(-0.430582\pi\)
0.953692 + 0.300785i \(0.0972485\pi\)
\(32\) 1981.19 5443.28i 0.0604612 0.166116i
\(33\) 11177.7 + 1970.93i 0.311036 + 0.0548441i
\(34\) 53848.9 9495.02i 1.37006 0.241579i
\(35\) −36521.0 + 13292.6i −0.851801 + 0.310030i
\(36\) 15267.0 + 12810.5i 0.327225 + 0.274574i
\(37\) 83779.7i 1.65399i 0.562208 + 0.826996i \(0.309952\pi\)
−0.562208 + 0.826996i \(0.690048\pi\)
\(38\) −31697.8 22376.8i −0.577667 0.407800i
\(39\) 20738.8 0.349614
\(40\) −16540.6 + 19712.4i −0.258448 + 0.308006i
\(41\) 10334.6 + 28394.2i 0.149949 + 0.411982i 0.991811 0.127711i \(-0.0407629\pi\)
−0.841862 + 0.539692i \(0.818541\pi\)
\(42\) −9874.12 55998.9i −0.133276 0.755843i
\(43\) −17549.1 + 99525.8i −0.220724 + 1.25179i 0.649970 + 0.759960i \(0.274782\pi\)
−0.870693 + 0.491826i \(0.836329\pi\)
\(44\) −9282.84 3378.68i −0.108974 0.0396633i
\(45\) −44266.9 76672.6i −0.485782 0.841400i
\(46\) 22290.8 + 12869.6i 0.229009 + 0.132218i
\(47\) 17452.2 14644.2i 0.168096 0.141049i −0.554859 0.831944i \(-0.687228\pi\)
0.722955 + 0.690895i \(0.242783\pi\)
\(48\) −24200.5 28841.0i −0.218827 0.260787i
\(49\) 21451.0 37154.3i 0.182331 0.315806i
\(50\) 22451.2 12962.2i 0.179610 0.103698i
\(51\) 121551. 333959.i 0.916322 2.51757i
\(52\) −17775.7 3134.34i −0.126421 0.0222914i
\(53\) −136542. + 24076.1i −0.917149 + 0.161718i −0.612248 0.790666i \(-0.709735\pi\)
−0.304901 + 0.952384i \(0.598623\pi\)
\(54\) −20755.7 + 7554.45i −0.131812 + 0.0479758i
\(55\) 33617.0 + 28208.0i 0.202056 + 0.169545i
\(56\) 49490.5i 0.281811i
\(57\) −228963. + 105700.i −1.23635 + 0.570754i
\(58\) −67785.0 −0.347416
\(59\) −28663.2 + 34159.5i −0.139562 + 0.166324i −0.831298 0.555827i \(-0.812402\pi\)
0.691736 + 0.722151i \(0.256846\pi\)
\(60\) 57202.9 + 157164.i 0.264828 + 0.727610i
\(61\) 36239.2 + 205523.i 0.159658 + 0.905463i 0.954403 + 0.298520i \(0.0964931\pi\)
−0.794746 + 0.606943i \(0.792396\pi\)
\(62\) −39537.1 + 224226.i −0.165894 + 0.940829i
\(63\) −160004. 58236.8i −0.639897 0.232904i
\(64\) 16384.0 + 28377.9i 0.0625000 + 0.108253i
\(65\) 69441.1 + 40091.9i 0.252858 + 0.145988i
\(66\) −49184.8 + 41270.9i −0.171080 + 0.143553i
\(67\) −269824. 321564.i −0.897132 1.06916i −0.997245 0.0741837i \(-0.976365\pi\)
0.100113 0.994976i \(-0.468080\pi\)
\(68\) −154657. + 267874.i −0.491863 + 0.851931i
\(69\) 144879. 83646.2i 0.441021 0.254624i
\(70\) 75194.0 206594.i 0.219225 0.602315i
\(71\) 128224. + 22609.3i 0.358256 + 0.0631703i 0.349880 0.936795i \(-0.386222\pi\)
0.00837668 + 0.999965i \(0.497334\pi\)
\(72\) −111026. + 19576.9i −0.297460 + 0.0524502i
\(73\) 498363. 181389.i 1.28108 0.466276i 0.390293 0.920691i \(-0.372374\pi\)
0.890790 + 0.454415i \(0.150152\pi\)
\(74\) −363051. 304636.i −0.895927 0.751772i
\(75\) 168497.i 0.399399i
\(76\) 212226. 55993.7i 0.483456 0.127555i
\(77\) 84399.9 0.184871
\(78\) −75409.4 + 89869.4i −0.158906 + 0.189377i
\(79\) −57206.4 157173.i −0.116028 0.318785i 0.868062 0.496456i \(-0.165366\pi\)
−0.984090 + 0.177672i \(0.943144\pi\)
\(80\) −25277.3 143355.i −0.0493697 0.279989i
\(81\) −103769. + 588503.i −0.195260 + 1.10737i
\(82\) −160622. 58461.5i −0.291315 0.106030i
\(83\) 315134. + 545828.i 0.551139 + 0.954601i 0.998193 + 0.0600935i \(0.0191399\pi\)
−0.447054 + 0.894507i \(0.647527\pi\)
\(84\) 278570. + 160832.i 0.469998 + 0.271353i
\(85\) 1.05260e6 883239.i 1.71399 1.43821i
\(86\) −367474. 437939.i −0.577739 0.688522i
\(87\) −220285. + 381545.i −0.334524 + 0.579413i
\(88\) 48395.0 27940.9i 0.0710154 0.0410008i
\(89\) 259935. 714166.i 0.368719 1.01305i −0.607131 0.794602i \(-0.707680\pi\)
0.975849 0.218444i \(-0.0700981\pi\)
\(90\) 493214. + 86967.0i 0.676563 + 0.119296i
\(91\) 151871. 26778.9i 0.201535 0.0355360i
\(92\) −136822. + 49799.1i −0.175708 + 0.0639526i
\(93\) 1.13363e6 + 951225.i 1.40936 + 1.18259i
\(94\) 128876.i 0.155163i
\(95\) −970993. 88706.8i −1.13252 0.103463i
\(96\) 212976. 0.240723
\(97\) −253212. + 301767.i −0.277440 + 0.330641i −0.886713 0.462320i \(-0.847017\pi\)
0.609273 + 0.792961i \(0.291462\pi\)
\(98\) 83005.1 + 228055.i 0.0881914 + 0.242304i
\(99\) 33386.0 + 189342.i 0.0344080 + 0.195137i
\(100\) −25465.6 + 144423.i −0.0254656 + 0.144423i
\(101\) −13897.0 5058.10i −0.0134883 0.00490934i 0.335267 0.942123i \(-0.391173\pi\)
−0.348755 + 0.937214i \(0.613396\pi\)
\(102\) 1.00520e6 + 1.74106e6i 0.947222 + 1.64064i
\(103\) −723035. 417445.i −0.661680 0.382021i 0.131237 0.991351i \(-0.458105\pi\)
−0.792917 + 0.609330i \(0.791438\pi\)
\(104\) 78217.7 65632.5i 0.0695353 0.0583470i
\(105\) −918503. 1.09463e6i −0.793437 0.945582i
\(106\) 392158. 679238.i 0.329263 0.570301i
\(107\) −1.80257e6 + 1.04072e6i −1.47144 + 0.849535i −0.999485 0.0320892i \(-0.989784\pi\)
−0.471952 + 0.881624i \(0.656451\pi\)
\(108\) 42734.4 117412.i 0.0339240 0.0932054i
\(109\) 2.23666e6 + 394383.i 1.72711 + 0.304536i 0.947031 0.321143i \(-0.104067\pi\)
0.780080 + 0.625680i \(0.215178\pi\)
\(110\) −244473. + 43107.3i −0.183676 + 0.0323871i
\(111\) −2.89455e6 + 1.05353e6i −2.11647 + 0.770332i
\(112\) −214462. 179955.i −0.152650 0.128088i
\(113\) 960838.i 0.665909i −0.942943 0.332954i \(-0.891954\pi\)
0.942943 0.332954i \(-0.108046\pi\)
\(114\) 374508. 1.37653e6i 0.252782 0.929119i
\(115\) 646814. 0.425291
\(116\) 246477. 293740.i 0.157907 0.188187i
\(117\) 120151. + 330112.i 0.0750187 + 0.206112i
\(118\) −43802.9 248418.i −0.0266598 0.151195i
\(119\) 458900. 2.60255e6i 0.272318 1.54439i
\(120\) −889052. 323588.i −0.514498 0.187262i
\(121\) 838131. + 1.45169e6i 0.473103 + 0.819438i
\(122\) −1.02238e6 590274.i −0.563034 0.325068i
\(123\) −851048. + 714114.i −0.457339 + 0.383753i
\(124\) −827898. 986650.i −0.434222 0.517485i
\(125\) −784845. + 1.35939e6i −0.401841 + 0.696009i
\(126\) 834165. 481605.i 0.417004 0.240757i
\(127\) 834691. 2.29329e6i 0.407488 1.11956i −0.551019 0.834493i \(-0.685761\pi\)
0.958507 0.285071i \(-0.0920171\pi\)
\(128\) −182548. 32188.1i −0.0870455 0.0153485i
\(129\) −3.65925e6 + 645224.i −1.70460 + 0.300567i
\(130\) −426233. + 155136.i −0.194007 + 0.0706127i
\(131\) −2.24878e6 1.88695e6i −1.00031 0.839357i −0.0132799 0.999912i \(-0.504227\pi\)
−0.987027 + 0.160555i \(0.948672\pi\)
\(132\) 363205.i 0.157917i
\(133\) −1.54023e6 + 1.06969e6i −0.654680 + 0.454678i
\(134\) 2.37459e6 0.986901
\(135\) −356783. + 425197.i −0.145012 + 0.172818i
\(136\) −598449. 1.64423e6i −0.237909 0.653649i
\(137\) 763859. + 4.33206e6i 0.297065 + 1.68474i 0.658689 + 0.752415i \(0.271111\pi\)
−0.361624 + 0.932324i \(0.617778\pi\)
\(138\) −164332. + 931971.i −0.0625294 + 0.354622i
\(139\) 4.35019e6 + 1.58334e6i 1.61981 + 0.589562i 0.983346 0.181745i \(-0.0581745\pi\)
0.636463 + 0.771307i \(0.280397\pi\)
\(140\) 621837. + 1.07705e6i 0.226617 + 0.392512i
\(141\) 725410. + 418816.i 0.258777 + 0.149405i
\(142\) −564217. + 473435.i −0.197052 + 0.165346i
\(143\) −111928. 133391.i −0.0382764 0.0456160i
\(144\) 318874. 552306.i 0.106790 0.184966i
\(145\) −1.47520e6 + 851704.i −0.483889 + 0.279373i
\(146\) −1.02609e6 + 2.81917e6i −0.329707 + 0.905862i
\(147\) 1.55341e6 + 273908.i 0.489028 + 0.0862289i
\(148\) 2.64022e6 465542.i 0.814432 0.143606i
\(149\) 1.64029e6 597017.i 0.495864 0.180480i −0.0819690 0.996635i \(-0.526121\pi\)
0.577833 + 0.816155i \(0.303899\pi\)
\(150\) 730163. + 612680.i 0.216345 + 0.181535i
\(151\) 6.64385e6i 1.92970i −0.262806 0.964849i \(-0.584648\pi\)
0.262806 0.964849i \(-0.415352\pi\)
\(152\) −529042. + 1.12326e6i −0.150647 + 0.319852i
\(153\) 6.02005e6 1.68084
\(154\) −306891. + 365739.i −0.0840277 + 0.100140i
\(155\) 1.95691e6 + 5.37657e6i 0.525504 + 1.44381i
\(156\) −115240. 653558.i −0.0303549 0.172151i
\(157\) −73480.1 + 416726.i −0.0189876 + 0.107684i −0.992829 0.119546i \(-0.961856\pi\)
0.973841 + 0.227231i \(0.0729671\pi\)
\(158\) 889107. + 323608.i 0.225415 + 0.0820443i
\(159\) −2.54884e6 4.41472e6i −0.634090 1.09828i
\(160\) 713125. + 411723.i 0.174103 + 0.100518i
\(161\) 952951. 799621.i 0.228346 0.191605i
\(162\) −2.17290e6 2.58956e6i −0.511087 0.609090i
\(163\) 3.06903e6 5.31572e6i 0.708661 1.22744i −0.256693 0.966493i \(-0.582633\pi\)
0.965354 0.260944i \(-0.0840339\pi\)
\(164\) 837383. 483463.i 0.189842 0.109605i
\(165\) −551840. + 1.51617e6i −0.122846 + 0.337517i
\(166\) −3.51117e6 619114.i −0.767587 0.135346i
\(167\) 98994.6 17455.4i 0.0212550 0.00374784i −0.163011 0.986624i \(-0.552120\pi\)
0.184266 + 0.982876i \(0.441009\pi\)
\(168\) −1.70987e6 + 622343.i −0.360609 + 0.131251i
\(169\) 3.45382e6 + 2.89810e6i 0.715550 + 0.600417i
\(170\) 7.77294e6i 1.58212i
\(171\) −3.00900e6 3.03218e6i −0.601775 0.606411i
\(172\) 3.23396e6 0.635549
\(173\) 5.86281e6 6.98703e6i 1.13232 1.34944i 0.203424 0.979091i \(-0.434793\pi\)
0.928892 0.370351i \(-0.120762\pi\)
\(174\) −852397. 2.34194e6i −0.161806 0.444558i
\(175\) −217571. 1.23391e6i −0.0405964 0.230234i
\(176\) −54892.8 + 311313.i −0.0100688 + 0.0571030i
\(177\) −1.54063e6 560745.i −0.277830 0.101122i
\(178\) 2.14960e6 + 3.72322e6i 0.381152 + 0.660175i
\(179\) 7.88861e6 + 4.55449e6i 1.37544 + 0.794110i 0.991606 0.129293i \(-0.0412707\pi\)
0.383832 + 0.923403i \(0.374604\pi\)
\(180\) −2.17027e6 + 1.82107e6i −0.372131 + 0.312255i
\(181\) −3.12824e6 3.72809e6i −0.527551 0.628710i 0.434798 0.900528i \(-0.356820\pi\)
−0.962349 + 0.271817i \(0.912375\pi\)
\(182\) −436182. + 755490.i −0.0723526 + 0.125318i
\(183\) −6.64501e6 + 3.83650e6i −1.08428 + 0.626011i
\(184\) 281706. 773981.i 0.0452213 0.124244i
\(185\) −1.17287e7 2.06809e6i −1.85240 0.326628i
\(186\) −8.24408e6 + 1.45365e6i −1.28116 + 0.225903i
\(187\) −2.80402e6 + 1.02058e6i −0.428802 + 0.156071i
\(188\) −558471. 468613.i −0.0840480 0.0705246i
\(189\) 1.06751e6i 0.158120i
\(190\) 3.91508e6 3.88515e6i 0.570795 0.566431i
\(191\) −666840. −0.0957021 −0.0478510 0.998854i \(-0.515237\pi\)
−0.0478510 + 0.998854i \(0.515237\pi\)
\(192\) −774415. + 922912.i −0.109413 + 0.130394i
\(193\) 3.57029e6 + 9.80928e6i 0.496628 + 1.36447i 0.894514 + 0.447040i \(0.147522\pi\)
−0.397886 + 0.917435i \(0.630256\pi\)
\(194\) −386957. 2.19454e6i −0.0529978 0.300565i
\(195\) −511933. + 2.90331e6i −0.0690413 + 0.391553i
\(196\) −1.29007e6 469548.i −0.171335 0.0623608i
\(197\) −2.83200e6 4.90516e6i −0.370420 0.641585i 0.619211 0.785225i \(-0.287453\pi\)
−0.989630 + 0.143640i \(0.954119\pi\)
\(198\) −941890. 543800.i −0.121340 0.0700558i
\(199\) −3.17961e6 + 2.66801e6i −0.403473 + 0.338554i −0.821834 0.569727i \(-0.807049\pi\)
0.418361 + 0.908281i \(0.362605\pi\)
\(200\) −533245. 635497.i −0.0666557 0.0794371i
\(201\) 7.71684e6 1.33660e7i 0.950279 1.64593i
\(202\) 72450.4 41829.3i 0.00878996 0.00507489i
\(203\) −1.12049e6 + 3.07852e6i −0.133943 + 0.368005i
\(204\) −1.11998e7 1.97482e6i −1.31922 0.232614i
\(205\) −4.23014e6 + 745888.i −0.491013 + 0.0865789i
\(206\) 4.43802e6 1.61531e6i 0.507678 0.184780i
\(207\) 2.17082e6 + 1.82153e6i 0.244744 + 0.205365i
\(208\) 577599.i 0.0641854i
\(209\) 1.91558e6 + 902216.i 0.209827 + 0.0988261i
\(210\) 8.08329e6 0.872831
\(211\) 3.05991e6 3.64666e6i 0.325733 0.388193i −0.578181 0.815909i \(-0.696237\pi\)
0.903913 + 0.427716i \(0.140682\pi\)
\(212\) 1.51746e6 + 4.16919e6i 0.159261 + 0.437567i
\(213\) 831274. + 4.71439e6i 0.0860212 + 0.487850i
\(214\) 2.04460e6 1.15955e7i 0.208625 1.18317i
\(215\) −1.34999e7 4.91356e6i −1.35836 0.494402i
\(216\) 353404. + 612114.i 0.0350679 + 0.0607394i
\(217\) 9.52986e6 + 5.50207e6i 0.932626 + 0.538452i
\(218\) −9.84186e6 + 8.25830e6i −0.949965 + 0.797115i
\(219\) 1.25338e7 + 1.49372e7i 1.19331 + 1.42213i
\(220\) 702142. 1.21615e6i 0.0659412 0.114214i
\(221\) −4.72180e6 + 2.72613e6i −0.437452 + 0.252563i
\(222\) 5.95966e6 1.63740e7i 0.544707 1.49657i
\(223\) −1.15758e7 2.04113e6i −1.04385 0.184059i −0.374669 0.927158i \(-0.622244\pi\)
−0.669181 + 0.743099i \(0.733355\pi\)
\(224\) 1.55964e6 275006.i 0.138765 0.0244680i
\(225\) 2.68207e6 976193.i 0.235463 0.0857014i
\(226\) 4.16370e6 + 3.49376e6i 0.360706 + 0.302669i
\(227\) 3.04583e6i 0.260392i −0.991488 0.130196i \(-0.958439\pi\)
0.991488 0.130196i \(-0.0415607\pi\)
\(228\) 4.60329e6 + 6.62817e6i 0.388386 + 0.559229i
\(229\) −1.40837e7 −1.17276 −0.586380 0.810036i \(-0.699448\pi\)
−0.586380 + 0.810036i \(0.699448\pi\)
\(230\) −2.35192e6 + 2.80291e6i −0.193303 + 0.230370i
\(231\) 1.06133e6 + 2.91598e6i 0.0861022 + 0.236564i
\(232\) 376664. + 2.13617e6i 0.0301641 + 0.171069i
\(233\) 2.13831e6 1.21270e7i 0.169045 0.958703i −0.775750 0.631041i \(-0.782628\pi\)
0.944795 0.327663i \(-0.106261\pi\)
\(234\) −1.86740e6 679677.i −0.145743 0.0530463i
\(235\) 1.61930e6 + 2.80471e6i 0.124774 + 0.216114i
\(236\) 1.23577e6 + 713472.i 0.0940160 + 0.0542802i
\(237\) 4.71090e6 3.95291e6i 0.353882 0.296942i
\(238\) 9.60926e6 + 1.14519e7i 0.712786 + 0.849465i
\(239\) 7.85992e6 1.36138e7i 0.575737 0.997206i −0.420224 0.907421i \(-0.638048\pi\)
0.995961 0.0897859i \(-0.0286183\pi\)
\(240\) 4.63497e6 2.67600e6i 0.335284 0.193576i
\(241\) 47024.5 129199.i 0.00335949 0.00923013i −0.938002 0.346631i \(-0.887326\pi\)
0.941361 + 0.337401i \(0.109548\pi\)
\(242\) −9.33831e6 1.64660e6i −0.658904 0.116183i
\(243\) −1.88342e7 + 3.32098e6i −1.31259 + 0.231445i
\(244\) 6.27545e6 2.28408e6i 0.431991 0.157232i
\(245\) 4.67188e6 + 3.92017e6i 0.317683 + 0.266567i
\(246\) 6.28456e6i 0.422153i
\(247\) 3.73320e6 + 1.01568e6i 0.247737 + 0.0674008i
\(248\) 7.28592e6 0.477671
\(249\) −1.48953e7 + 1.77515e7i −0.964831 + 1.14984i
\(250\) −3.03697e6 8.34401e6i −0.194366 0.534017i
\(251\) −1.62888e6 9.23786e6i −0.103008 0.584185i −0.991997 0.126258i \(-0.959703\pi\)
0.888990 0.457927i \(-0.151408\pi\)
\(252\) −946164. + 5.36596e6i −0.0591241 + 0.335310i
\(253\) −1.31993e6 480415.i −0.0815059 0.0296657i
\(254\) 6.90270e6 + 1.19558e7i 0.421229 + 0.729590i
\(255\) 4.37520e7 + 2.52602e7i 2.63862 + 1.52341i
\(256\) 803256. 674012.i 0.0478778 0.0401742i
\(257\) −1.76339e6 2.10153e6i −0.103884 0.123804i 0.711597 0.702588i \(-0.247972\pi\)
−0.815481 + 0.578783i \(0.803528\pi\)
\(258\) 1.05096e7 1.82031e7i 0.611965 1.05995i
\(259\) −1.98365e7 + 1.14526e7i −1.14174 + 0.659183i
\(260\) 877582. 2.41114e6i 0.0499307 0.137184i
\(261\) −7.34953e6 1.29592e6i −0.413369 0.0728882i
\(262\) 1.63538e7 2.88362e6i 0.909318 0.160337i
\(263\) 1.32577e7 4.82541e6i 0.728787 0.265257i 0.0491359 0.998792i \(-0.484353\pi\)
0.679651 + 0.733535i \(0.262131\pi\)
\(264\) 1.57391e6 + 1.32067e6i 0.0855399 + 0.0717765i
\(265\) 1.97095e7i 1.05910i
\(266\) 965092. 1.05640e7i 0.0512771 0.561284i
\(267\) 2.79428e7 1.46803
\(268\) −8.63437e6 + 1.02900e7i −0.448566 + 0.534580i
\(269\) −6.50270e6 1.78660e7i −0.334070 0.917849i −0.987041 0.160466i \(-0.948700\pi\)
0.652972 0.757382i \(-0.273522\pi\)
\(270\) −545232. 3.09217e6i −0.0277007 0.157098i
\(271\) 99609.5 564914.i 0.00500487 0.0283840i −0.982203 0.187822i \(-0.939857\pi\)
0.987208 + 0.159438i \(0.0509682\pi\)
\(272\) 9.30115e6 + 3.38534e6i 0.462200 + 0.168227i
\(273\) 2.83498e6 + 4.91032e6i 0.139335 + 0.241336i
\(274\) −2.15501e7 1.24419e7i −1.04760 0.604834i
\(275\) −1.08376e6 + 909384.i −0.0521117 + 0.0437269i
\(276\) −3.44107e6 4.10091e6i −0.163669 0.195053i
\(277\) 7.73716e6 1.34011e7i 0.364034 0.630526i −0.624587 0.780956i \(-0.714732\pi\)
0.988621 + 0.150430i \(0.0480658\pi\)
\(278\) −2.26792e7 + 1.30938e7i −1.05559 + 0.609443i
\(279\) −8.57354e6 + 2.35556e7i −0.394773 + 1.08463i
\(280\) −6.92840e6 1.22166e6i −0.315616 0.0556516i
\(281\) −1.92810e7 + 3.39977e6i −0.868984 + 0.153225i −0.590326 0.807165i \(-0.701001\pi\)
−0.278658 + 0.960390i \(0.589890\pi\)
\(282\) −4.45260e6 + 1.62061e6i −0.198548 + 0.0722657i
\(283\) 8.68005e6 + 7.28343e6i 0.382969 + 0.321349i 0.813867 0.581052i \(-0.197359\pi\)
−0.430898 + 0.902401i \(0.641803\pi\)
\(284\) 4.16646e6i 0.181892i
\(285\) −9.14546e6 3.46628e7i −0.395067 1.49737i
\(286\) 985023. 0.0421064
\(287\) −5.31016e6 + 6.32841e6i −0.224627 + 0.267700i
\(288\) 1.23389e6 + 3.39008e6i 0.0516534 + 0.141916i
\(289\) 1.20331e7 + 6.82429e7i 0.498520 + 2.82725i
\(290\) 1.67326e6 9.48954e6i 0.0686073 0.389091i
\(291\) −1.36100e7 4.95365e6i −0.552307 0.201023i
\(292\) −8.48555e6 1.46974e7i −0.340825 0.590326i
\(293\) 2.15577e7 + 1.24463e7i 0.857035 + 0.494809i 0.863018 0.505173i \(-0.168571\pi\)
−0.00598315 + 0.999982i \(0.501905\pi\)
\(294\) −6.83539e6 + 5.73557e6i −0.268981 + 0.225702i
\(295\) −4.07460e6 4.85591e6i −0.158715 0.189149i
\(296\) −7.58287e6 + 1.31339e7i −0.292387 + 0.506430i
\(297\) 1.04388e6 602687.i 0.0398458 0.0230050i
\(298\) −3.37724e6 + 9.27889e6i −0.127618 + 0.350629i
\(299\) −2.52754e6 445673.i −0.0945549 0.0166726i
\(300\) −5.30997e6 + 936292.i −0.196666 + 0.0346775i
\(301\) −2.59637e7 + 9.45002e6i −0.952067 + 0.346524i
\(302\) 2.87905e7 + 2.41581e7i 1.04527 + 0.877085i
\(303\) 543741.i 0.0195463i
\(304\) −2.94386e6 6.37690e6i −0.104784 0.226981i
\(305\) −2.96667e7 −1.04561
\(306\) −2.18898e7 + 2.60873e7i −0.763973 + 0.910468i
\(307\) −3.97741e6 1.09279e7i −0.137463 0.377676i 0.851791 0.523881i \(-0.175516\pi\)
−0.989254 + 0.146205i \(0.953294\pi\)
\(308\) −468988. 2.65977e6i −0.0160513 0.0910314i
\(309\) 5.33035e6 3.02299e7i 0.180668 1.02462i
\(310\) −3.04145e7 1.10700e7i −1.02093 0.371587i
\(311\) −1.48886e7 2.57878e7i −0.494962 0.857299i 0.505021 0.863107i \(-0.331485\pi\)
−0.999983 + 0.00580778i \(0.998151\pi\)
\(312\) 3.25116e6 + 1.87706e6i 0.107047 + 0.0618036i
\(313\) −1.17692e7 + 9.87553e6i −0.383808 + 0.322053i −0.814195 0.580591i \(-0.802821\pi\)
0.430387 + 0.902644i \(0.358377\pi\)
\(314\) −1.53866e6 1.83370e6i −0.0496996 0.0592297i
\(315\) 1.21025e7 2.09622e7i 0.387208 0.670664i
\(316\) −4.63526e6 + 2.67617e6i −0.146897 + 0.0848110i
\(317\) 1.69378e7 4.65363e7i 0.531716 1.46088i −0.325311 0.945607i \(-0.605469\pi\)
0.857027 0.515271i \(-0.172309\pi\)
\(318\) 2.83987e7 + 5.00746e6i 0.883116 + 0.155717i
\(319\) 3.64297e6 642354.i 0.112223 0.0197880i
\(320\) −4.37719e6 + 1.59317e6i −0.133581 + 0.0486196i
\(321\) −5.86237e7 4.91911e7i −1.77238 1.48721i
\(322\) 7.03706e6i 0.210777i
\(323\) 3.82361e7 5.41632e7i 1.13466 1.60730i
\(324\) 1.91226e7 0.562228
\(325\) −1.66161e6 + 1.98023e6i −0.0484037 + 0.0576852i
\(326\) 1.18757e7 + 3.26281e7i 0.342772 + 0.941759i
\(327\) 1.45002e7 + 8.22349e7i 0.414698 + 2.35187i
\(328\) −949814. + 5.38667e6i −0.0269164 + 0.152651i
\(329\) 5.85301e6 + 2.13032e6i 0.164358 + 0.0598215i
\(330\) −4.56359e6 7.90437e6i −0.126989 0.219951i
\(331\) −8.30764e6 4.79642e6i −0.229083 0.132261i 0.381066 0.924548i \(-0.375557\pi\)
−0.610149 + 0.792287i \(0.708890\pi\)
\(332\) 1.54500e7 1.29641e7i 0.422197 0.354265i
\(333\) −3.35394e7 3.99707e7i −0.908286 1.08245i
\(334\) −284318. + 492454.i −0.00763072 + 0.0132168i
\(335\) 5.16778e7 2.98362e7i 1.37458 0.793613i
\(336\) 3.52050e6 9.67250e6i 0.0928083 0.254989i
\(337\) 6.94179e6 + 1.22402e6i 0.181377 + 0.0319816i 0.263599 0.964632i \(-0.415091\pi\)
−0.0822220 + 0.996614i \(0.526202\pi\)
\(338\) −2.51173e7 + 4.42885e6i −0.650463 + 0.114694i
\(339\) 3.31965e7 1.20825e7i 0.852105 0.310141i
\(340\) −3.36833e7 2.82636e7i −0.856994 0.719103i
\(341\) 1.24252e7i 0.313358i
\(342\) 2.40809e7 2.01372e6i 0.601996 0.0503408i
\(343\) 4.38945e7 1.08775
\(344\) −1.17592e7 + 1.40140e7i −0.288869 + 0.344261i
\(345\) 8.13369e6 + 2.23471e7i 0.198075 + 0.544208i
\(346\) 8.95950e6 + 5.08118e7i 0.216299 + 1.22669i
\(347\) −5.54360e6 + 3.14393e7i −0.132679 + 0.752463i 0.843768 + 0.536708i \(0.180332\pi\)
−0.976448 + 0.215755i \(0.930779\pi\)
\(348\) 1.32480e7 + 4.82189e6i 0.314350 + 0.114414i
\(349\) 3.80754e7 + 6.59486e7i 0.895712 + 1.55142i 0.832921 + 0.553392i \(0.186667\pi\)
0.0627914 + 0.998027i \(0.480000\pi\)
\(350\) 6.13814e6 + 3.54386e6i 0.143164 + 0.0826556i
\(351\) 1.68716e6 1.41570e6i 0.0390153 0.0327378i
\(352\) −1.14944e6 1.36985e6i −0.0263548 0.0314084i
\(353\) −2.27307e7 + 3.93707e7i −0.516759 + 0.895053i 0.483051 + 0.875592i \(0.339528\pi\)
−0.999811 + 0.0194613i \(0.993805\pi\)
\(354\) 8.03192e6 4.63723e6i 0.181055 0.104532i
\(355\) −6.33037e6 + 1.73925e7i −0.141496 + 0.388757i
\(356\) −2.39505e7 4.22312e6i −0.530841 0.0936017i
\(357\) 9.56875e7 1.68723e7i 2.10306 0.370825i
\(358\) −4.84206e7 + 1.76237e7i −1.05531 + 0.384103i
\(359\) 5.66548e7 + 4.75390e7i 1.22448 + 1.02746i 0.998578 + 0.0533158i \(0.0169790\pi\)
0.225907 + 0.974149i \(0.427465\pi\)
\(360\) 1.60263e7i 0.343500i
\(361\) −4.63925e7 + 7.81361e6i −0.986111 + 0.166085i
\(362\) 2.75301e7 0.580339
\(363\) −3.96155e7 + 4.72120e7i −0.828220 + 0.987034i
\(364\) −1.68781e6 4.63723e6i −0.0349962 0.0961512i
\(365\) 1.30915e7 + 7.42457e7i 0.269223 + 1.52684i
\(366\) 7.53721e6 4.27456e7i 0.153733 0.871863i
\(367\) 8.18123e6 + 2.97772e6i 0.165509 + 0.0602402i 0.423446 0.905922i \(-0.360820\pi\)
−0.257937 + 0.966162i \(0.583043\pi\)
\(368\) 2.32964e6 + 4.03506e6i 0.0467462 + 0.0809668i
\(369\) −1.62976e7 9.40942e6i −0.324373 0.187277i
\(370\) 5.16092e7 4.33053e7i 1.01888 0.854940i
\(371\) −2.43658e7 2.90380e7i −0.477154 0.568650i
\(372\) 2.36775e7 4.10106e7i 0.459946 0.796650i
\(373\) −4.24170e7 + 2.44894e7i −0.817359 + 0.471903i −0.849505 0.527581i \(-0.823099\pi\)
0.0321456 + 0.999483i \(0.489766\pi\)
\(374\) 5.77328e6 1.58620e7i 0.110359 0.303209i
\(375\) −5.68358e7 1.00217e7i −1.07777 0.190041i
\(376\) 4.06138e6 716130.i 0.0764029 0.0134719i
\(377\) 6.35142e6 2.31173e6i 0.118535 0.0431432i
\(378\) −4.62596e6 3.88164e6i −0.0856499 0.0718688i
\(379\) 2.34953e7i 0.431582i −0.976440 0.215791i \(-0.930767\pi\)
0.976440 0.215791i \(-0.0692329\pi\)
\(380\) 2.60006e6 + 3.10926e7i 0.0473841 + 0.566639i
\(381\) 8.97285e7 1.62239
\(382\) 2.42473e6 2.88968e6i 0.0434985 0.0518395i
\(383\) −1.13887e7 3.12903e7i −0.202712 0.556947i 0.796126 0.605130i \(-0.206879\pi\)
−0.998839 + 0.0481835i \(0.984657\pi\)
\(384\) −1.18345e6 6.71170e6i −0.0209006 0.118533i
\(385\) −2.08340e6 + 1.18155e7i −0.0365082 + 0.207048i
\(386\) −5.54897e7 2.01966e7i −0.964829 0.351169i
\(387\) −3.14705e7 5.45085e7i −0.542964 0.940441i
\(388\) 1.09169e7 + 6.30286e6i 0.186897 + 0.107905i
\(389\) 3.90526e7 3.27691e7i 0.663440 0.556692i −0.247676 0.968843i \(-0.579667\pi\)
0.911116 + 0.412151i \(0.135222\pi\)
\(390\) −1.07198e7 1.27753e7i −0.180714 0.215366i
\(391\) −2.19908e7 + 3.80891e7i −0.367883 + 0.637193i
\(392\) 6.72564e6 3.88305e6i 0.111654 0.0644636i
\(393\) 3.69149e7 1.01423e8i 0.608168 1.67093i
\(394\) 3.15536e7 + 5.56375e6i 0.515894 + 0.0909660i
\(395\) 2.34156e7 4.12880e6i 0.379938 0.0669934i
\(396\) 5.78137e6 2.10424e6i 0.0930990 0.0338853i
\(397\) −4.32889e7 3.63237e7i −0.691839 0.580522i 0.227600 0.973755i \(-0.426912\pi\)
−0.919439 + 0.393233i \(0.871357\pi\)
\(398\) 2.34798e7i 0.372431i
\(399\) −5.63257e7 3.97627e7i −0.886723 0.625975i
\(400\) 4.69283e6 0.0733254
\(401\) −2.93471e7 + 3.49745e7i −0.455126 + 0.542398i −0.943995 0.329959i \(-0.892965\pi\)
0.488869 + 0.872357i \(0.337409\pi\)
\(402\) 2.98604e7 + 8.20409e7i 0.459640 + 1.26285i
\(403\) −3.94236e6 2.23582e7i −0.0602339 0.341603i
\(404\) −82178.0 + 466055.i −0.00124627 + 0.00706794i
\(405\) −7.98258e7 2.90542e7i −1.20165 0.437365i
\(406\) −9.26618e6 1.60495e7i −0.138459 0.239819i
\(407\) 2.23983e7 + 1.29316e7i 0.332224 + 0.191810i
\(408\) 4.92817e7 4.13523e7i 0.725614 0.608862i
\(409\) −2.44302e6 2.91148e6i −0.0357073 0.0425543i 0.747895 0.663817i \(-0.231065\pi\)
−0.783603 + 0.621262i \(0.786620\pi\)
\(410\) 1.21492e7 2.10431e7i 0.176278 0.305322i
\(411\) −1.40065e8 + 8.08666e7i −2.01746 + 1.16478i
\(412\) −9.13757e6 + 2.51053e7i −0.130659 + 0.358982i
\(413\) −1.20062e7 2.11702e6i −0.170434 0.0300520i
\(414\) −1.57869e7 + 2.78365e6i −0.222482 + 0.0392295i
\(415\) −8.41920e7 + 3.06434e7i −1.17795 + 0.428739i
\(416\) −2.50297e6 2.10024e6i −0.0347676 0.0291735i
\(417\) 1.70208e8i 2.34731i
\(418\) −1.08750e7 + 5.02039e6i −0.148902 + 0.0687398i
\(419\) 2.58588e7 0.351533 0.175767 0.984432i \(-0.443760\pi\)
0.175767 + 0.984432i \(0.443760\pi\)
\(420\) −2.93921e7 + 3.50281e7i −0.396719 + 0.472791i
\(421\) −2.42195e7 6.65424e7i −0.324577 0.891768i −0.989458 0.144819i \(-0.953740\pi\)
0.664881 0.746949i \(-0.268482\pi\)
\(422\) 4.67613e6 + 2.65196e7i 0.0622227 + 0.352883i
\(423\) −2.46386e6 + 1.39733e7i −0.0325533 + 0.184619i
\(424\) −2.35845e7 8.58406e6i −0.309406 0.112615i
\(425\) 2.21491e7 + 3.83633e7i 0.288528 + 0.499746i
\(426\) −2.34520e7 1.35400e7i −0.303355 0.175142i
\(427\) −4.37079e7 + 3.66752e7i −0.561404 + 0.471074i
\(428\) 4.28134e7 + 5.10231e7i 0.546070 + 0.650781i
\(429\) 3.20109e6 5.54445e6i 0.0405440 0.0702242i
\(430\) 7.03801e7 4.06340e7i 0.885206 0.511074i
\(431\) 1.28022e7 3.51736e7i 0.159901 0.439324i −0.833707 0.552207i \(-0.813786\pi\)
0.993608 + 0.112882i \(0.0360082\pi\)
\(432\) −3.93757e6 694299.i −0.0488401 0.00861183i
\(433\) −1.31143e7 + 2.31241e6i −0.161541 + 0.0284840i −0.253833 0.967248i \(-0.581692\pi\)
0.0922929 + 0.995732i \(0.470580\pi\)
\(434\) −5.84947e7 + 2.12903e7i −0.715563 + 0.260444i
\(435\) −4.79766e7 4.02571e7i −0.582856 0.489074i
\(436\) 7.26772e7i 0.876877i
\(437\) 3.01764e7 7.96175e6i 0.361596 0.0954035i
\(438\) −1.10304e8 −1.31271
\(439\) 4.83498e7 5.76211e7i 0.571481 0.681064i −0.400454 0.916317i \(-0.631147\pi\)
0.971934 + 0.235253i \(0.0755919\pi\)
\(440\) 2.71695e6 + 7.46476e6i 0.0318951 + 0.0876310i
\(441\) 4.63978e6 + 2.63135e7i 0.0540981 + 0.306805i
\(442\) 5.35577e6 3.03741e7i 0.0620234 0.351752i
\(443\) −8.19699e7 2.98346e7i −0.942852 0.343170i −0.175560 0.984469i \(-0.556174\pi\)
−0.767291 + 0.641299i \(0.778396\pi\)
\(444\) 4.92850e7 + 8.53642e7i 0.563075 + 0.975274i
\(445\) 9.35629e7 + 5.40186e7i 1.06175 + 0.613004i
\(446\) 5.09366e7 4.27409e7i 0.574151 0.481769i
\(447\) 4.12533e7 + 4.91638e7i 0.461888 + 0.550457i
\(448\) −4.47937e6 + 7.75849e6i −0.0498176 + 0.0862866i
\(449\) 4.11482e7 2.37569e7i 0.454581 0.262453i −0.255182 0.966893i \(-0.582135\pi\)
0.709763 + 0.704440i \(0.248802\pi\)
\(450\) −5.52218e6 + 1.51721e7i −0.0606001 + 0.166497i
\(451\) 9.18629e6 + 1.61979e6i 0.100141 + 0.0176575i
\(452\) −3.02797e7 + 5.33913e6i −0.327896 + 0.0578169i
\(453\) 2.29542e8 8.35465e7i 2.46926 0.898739i
\(454\) 1.31988e7 + 1.10751e7i 0.141048 + 0.118353i
\(455\) 2.19221e7i 0.232728i
\(456\) −4.54608e7 4.15316e6i −0.479449 0.0438010i
\(457\) 5.19218e7 0.544003 0.272002 0.962297i \(-0.412314\pi\)
0.272002 + 0.962297i \(0.412314\pi\)
\(458\) 5.12104e7 6.10302e7i 0.533042 0.635255i
\(459\) −1.29086e7 3.54661e7i −0.133488 0.366754i
\(460\) −3.59418e6 2.03836e7i −0.0369255 0.209415i
\(461\) −9.68053e6 + 5.49010e7i −0.0988090 + 0.560374i 0.894704 + 0.446659i \(0.147386\pi\)
−0.993513 + 0.113715i \(0.963725\pi\)
\(462\) −1.64953e7 6.00378e6i −0.167276 0.0608834i
\(463\) 2.00833e6 + 3.47853e6i 0.0202345 + 0.0350471i 0.875965 0.482374i \(-0.160225\pi\)
−0.855731 + 0.517421i \(0.826892\pi\)
\(464\) −1.06265e7 6.13520e6i −0.106374 0.0614151i
\(465\) −1.61150e8 + 1.35221e8i −1.60277 + 1.34488i
\(466\) 4.47758e7 + 5.33617e7i 0.442472 + 0.527317i
\(467\) −2.86733e7 + 4.96635e7i −0.281531 + 0.487626i −0.971762 0.235963i \(-0.924176\pi\)
0.690231 + 0.723589i \(0.257509\pi\)
\(468\) 9.73546e6 5.62077e6i 0.0949771 0.0548350i
\(469\) 3.92520e7 1.07844e8i 0.380490 1.04539i
\(470\) −1.80419e7 3.18128e6i −0.173776 0.0306414i
\(471\) −1.53217e7 + 2.70163e6i −0.146637 + 0.0258561i
\(472\) −7.58522e6 + 2.76079e6i −0.0721343 + 0.0262547i
\(473\) 2.38992e7 + 2.00538e7i 0.225840 + 0.189502i
\(474\) 3.47876e7i 0.326655i
\(475\) 8.25209e6 3.03312e7i 0.0769987 0.283014i
\(476\) −8.45663e7 −0.784109
\(477\) 5.55051e7 6.61484e7i 0.511420 0.609487i
\(478\) 3.04141e7 + 8.35620e7i 0.278478 + 0.765112i
\(479\) −2.51051e7 1.42378e8i −0.228431 1.29550i −0.856016 0.516949i \(-0.827068\pi\)
0.627585 0.778548i \(-0.284043\pi\)
\(480\) −5.25728e6 + 2.98155e7i −0.0475377 + 0.269599i
\(481\) 4.44069e7 + 1.61628e7i 0.399039 + 0.145238i
\(482\) 388882. + 673564.i 0.00347278 + 0.00601503i
\(483\) 3.96099e7 + 2.28688e7i 0.351530 + 0.202956i
\(484\) 4.10909e7 3.44794e7i 0.362418 0.304105i
\(485\) −3.59952e7 4.28974e7i −0.315515 0.376016i
\(486\) 5.40930e7 9.36917e7i 0.471229 0.816192i
\(487\) 1.79201e6 1.03462e6i 0.0155151 0.00895763i −0.492222 0.870469i \(-0.663815\pi\)
0.507737 + 0.861512i \(0.330482\pi\)
\(488\) −1.29207e7 + 3.54993e7i −0.111180 + 0.305464i
\(489\) 2.22249e8 + 3.91885e7i 1.90070 + 0.335144i
\(490\) −3.39754e7 + 5.99078e6i −0.288786 + 0.0509208i
\(491\) 2.06873e8 7.52955e7i 1.74767 0.636099i 0.748046 0.663647i \(-0.230992\pi\)
0.999620 + 0.0275480i \(0.00876992\pi\)
\(492\) 2.72335e7 + 2.28516e7i 0.228670 + 0.191877i
\(493\) 1.15827e8i 0.966649i
\(494\) −1.79758e7 + 1.24843e7i −0.149110 + 0.103558i
\(495\) −2.73309e7 −0.225340
\(496\) −2.64927e7 + 3.15728e7i −0.217111 + 0.258743i
\(497\) 1.21749e7 + 3.34503e7i 0.0991738 + 0.272478i
\(498\) −2.27629e7 1.29095e8i −0.184306 1.04525i
\(499\) 1.91640e7 1.08684e8i 0.154235 0.874713i −0.805246 0.592941i \(-0.797967\pi\)
0.959481 0.281772i \(-0.0909221\pi\)
\(500\) 4.72009e7 + 1.71797e7i 0.377607 + 0.137438i
\(501\) 1.84793e6 + 3.20072e6i 0.0146951 + 0.0254527i
\(502\) 4.59542e7 + 2.65317e7i 0.363257 + 0.209727i
\(503\) −1.09452e8 + 9.18414e7i −0.860045 + 0.721663i −0.961978 0.273128i \(-0.911942\pi\)
0.101933 + 0.994791i \(0.467497\pi\)
\(504\) −1.98125e7 2.36116e7i −0.154756 0.184431i
\(505\) 1.05115e6 1.82065e6i 0.00816190 0.0141368i
\(506\) 6.88130e6 3.97292e6i 0.0531152 0.0306661i
\(507\) −5.66962e7 + 1.55772e8i −0.435041 + 1.19527i
\(508\) −7.69087e7 1.35611e7i −0.586657 0.103443i
\(509\) −2.28896e8 + 4.03605e7i −1.73574 + 0.306058i −0.949942 0.312425i \(-0.898859\pi\)
−0.785798 + 0.618483i \(0.787747\pi\)
\(510\) −2.68552e8 + 9.77448e7i −2.02450 + 0.736857i
\(511\) 1.11074e8 + 9.32018e7i 0.832431 + 0.698492i
\(512\) 5.93164e6i 0.0441942i
\(513\) −1.14115e7 + 2.42288e7i −0.0845259 + 0.179465i
\(514\) 1.55187e7 0.114279
\(515\) 7.62880e7 9.09165e7i 0.558515 0.665612i
\(516\) 4.06670e7 + 1.11732e8i 0.296001 + 0.813256i
\(517\) −1.22127e6 6.92617e6i −0.00883773 0.0501212i
\(518\) 2.24999e7 1.27603e8i 0.161879 0.918063i
\(519\) 3.15123e8 + 1.14696e8i 2.25413 + 0.820435i
\(520\) 7.25740e6 + 1.25702e7i 0.0516144 + 0.0893988i
\(521\) −1.48742e8 8.58762e7i −1.05177 0.607239i −0.128625 0.991693i \(-0.541056\pi\)
−0.923144 + 0.384455i \(0.874390\pi\)
\(522\) 3.23398e7 2.71363e7i 0.227366 0.190783i
\(523\) 1.13339e7 + 1.35073e7i 0.0792275 + 0.0944197i 0.804202 0.594356i \(-0.202593\pi\)
−0.724975 + 0.688776i \(0.758149\pi\)
\(524\) −4.69692e7 + 8.13530e7i −0.326452 + 0.565431i
\(525\) 3.98950e7 2.30334e7i 0.275702 0.159177i
\(526\) −2.72966e7 + 7.49969e7i −0.187565 + 0.515331i
\(527\) −3.83143e8 6.75585e7i −2.61776 0.461581i
\(528\) −1.14460e7 + 2.01824e6i −0.0777591 + 0.0137110i
\(529\) 1.19654e8 4.35503e7i 0.808274 0.294188i
\(530\) 8.54093e7 + 7.16669e7i 0.573690 + 0.481383i
\(531\) 2.77720e7i 0.185491i
\(532\) 4.22688e7 + 4.25944e7i 0.280727 + 0.282890i
\(533\) 1.70439e7 0.112561
\(534\) −1.01604e8 + 1.21087e8i −0.667250 + 0.795197i
\(535\) −1.01199e8 2.78041e8i −0.660865 1.81571i
\(536\) −1.31950e7 7.48324e7i −0.0856868 0.485954i
\(537\) −5.81563e7 + 3.29820e8i −0.375555 + 2.12988i
\(538\) 1.01065e8 + 3.67848e7i 0.649017 + 0.236223i
\(539\) −6.62206e6 1.14697e7i −0.0422890 0.0732466i
\(540\) 1.53821e7 + 8.88089e6i 0.0976867 + 0.0563995i
\(541\) 2.44570e7 2.05218e7i 0.154458 0.129606i −0.562284 0.826944i \(-0.690077\pi\)
0.716742 + 0.697339i \(0.245633\pi\)
\(542\) 2.08580e6 + 2.48576e6i 0.0131001 + 0.0156121i
\(543\) 8.94662e7 1.54960e8i 0.558804 0.967877i
\(544\) −4.84905e7 + 2.79960e7i −0.301203 + 0.173900i
\(545\) −1.10423e8 + 3.03385e8i −0.682135 + 1.87415i
\(546\) −3.15868e7 5.56961e6i −0.194056 0.0342174i
\(547\) 1.78000e8 3.13863e7i 1.08757 0.191769i 0.399012 0.916946i \(-0.369353\pi\)
0.688563 + 0.725177i \(0.258242\pi\)
\(548\) 1.32275e8 4.81443e7i 0.803780 0.292552i
\(549\) −9.95662e7 8.35460e7i −0.601721 0.504904i
\(550\) 8.00304e6i 0.0481024i
\(551\) −5.83398e7 + 5.78938e7i −0.348747 + 0.346080i
\(552\) 3.02832e7 0.180046
\(553\) 2.93939e7 3.50303e7i 0.173813 0.207142i
\(554\) 2.99391e7 + 8.22569e7i 0.176080 + 0.483774i
\(555\) −7.60370e7 4.31227e8i −0.444781 2.52248i
\(556\) 2.57242e7 1.45889e8i 0.149664 0.848788i
\(557\) −3.88624e7 1.41447e7i −0.224887 0.0818520i 0.227119 0.973867i \(-0.427069\pi\)
−0.452006 + 0.892015i \(0.649291\pi\)
\(558\) −7.09012e7 1.22805e8i −0.408085 0.706825i
\(559\) 4.93675e7 + 2.85023e7i 0.282622 + 0.163172i
\(560\) 3.04867e7 2.55814e7i 0.173599 0.145667i
\(561\) −7.05212e7 8.40439e7i −0.399421 0.476012i
\(562\) 5.53763e7 9.59146e7i 0.311972 0.540351i
\(563\) −9.35105e7 + 5.39883e7i −0.524005 + 0.302534i −0.738572 0.674175i \(-0.764499\pi\)
0.214567 + 0.976709i \(0.431166\pi\)
\(564\) 9.16758e6 2.51877e7i 0.0510996 0.140395i
\(565\) 1.34512e8 + 2.37181e7i 0.745789 + 0.131503i
\(566\) −6.31241e7 + 1.11305e7i −0.348133 + 0.0613853i
\(567\) −1.53525e8 + 5.58786e7i −0.842230 + 0.306547i
\(568\) 1.80550e7 + 1.51499e7i 0.0985261 + 0.0826732i
\(569\) 6.59347e7i 0.357913i 0.983857 + 0.178956i \(0.0572721\pi\)
−0.983857 + 0.178956i \(0.942728\pi\)
\(570\) 1.83462e8 + 8.64085e7i 0.990655 + 0.466586i
\(571\) −3.18970e8 −1.71333 −0.856667 0.515870i \(-0.827469\pi\)
−0.856667 + 0.515870i \(0.827469\pi\)
\(572\) −3.58170e6 + 4.26850e6i −0.0191382 + 0.0228080i
\(573\) −8.38551e6 2.30390e7i −0.0445724 0.122462i
\(574\) −8.11494e6 4.60221e7i −0.0429091 0.243350i
\(575\) −3.62097e6 + 2.05355e7i −0.0190468 + 0.108020i
\(576\) −1.91772e7 6.97993e6i −0.100350 0.0365244i
\(577\) −8.83027e7 1.52945e8i −0.459671 0.796173i 0.539273 0.842131i \(-0.318699\pi\)
−0.998943 + 0.0459583i \(0.985366\pi\)
\(578\) −3.39478e8 1.95998e8i −1.75804 1.01500i
\(579\) −2.94010e8 + 2.46704e8i −1.51470 + 1.27098i
\(580\) 3.50378e7 + 4.17564e7i 0.179578 + 0.214012i
\(581\) −8.61573e7 + 1.49229e8i −0.439303 + 0.760894i
\(582\) 7.09544e7 4.09656e7i 0.359924 0.207802i
\(583\) −1.46391e7 + 4.02205e7i −0.0738767 + 0.202975i
\(584\) 9.45445e7 + 1.66708e7i 0.474677 + 0.0836983i
\(585\) −4.91798e7 + 8.67173e6i −0.245652 + 0.0433150i
\(586\) −1.32322e8 + 4.81612e7i −0.657565 + 0.239334i
\(587\) 2.11776e8 + 1.77701e8i 1.04704 + 0.878570i 0.992779 0.119957i \(-0.0382756\pi\)
0.0542600 + 0.998527i \(0.482720\pi\)
\(588\) 5.04759e7i 0.248286i
\(589\) 1.57479e8 + 2.26750e8i 0.770683 + 1.10969i
\(590\) 3.58585e7 0.174597
\(591\) 1.33859e8 1.59527e8i 0.648461 0.772806i
\(592\) −2.93420e7 8.06166e7i −0.141425 0.388561i
\(593\) 4.70703e7 + 2.66949e8i 0.225726 + 1.28016i 0.861292 + 0.508111i \(0.169656\pi\)
−0.635565 + 0.772047i \(0.719233\pi\)
\(594\) −1.18404e6 + 6.71503e6i −0.00564947 + 0.0320397i
\(595\) 3.53015e8 + 1.28487e8i 1.67588 + 0.609970i
\(596\) −2.79290e7 4.83744e7i −0.131922 0.228495i
\(597\) −1.32162e8 7.63038e7i −0.621132 0.358611i
\(598\) 1.11218e7 9.33230e6i 0.0520082 0.0436400i
\(599\) −2.18949e7 2.60934e7i −0.101874 0.121409i 0.712698 0.701471i \(-0.247473\pi\)
−0.814572 + 0.580062i \(0.803028\pi\)
\(600\) 1.52506e7 2.64148e7i 0.0706045 0.122291i
\(601\) 6.10673e7 3.52572e7i 0.281310 0.162415i −0.352706 0.935734i \(-0.614738\pi\)
0.634016 + 0.773320i \(0.281405\pi\)
\(602\) 5.34574e7 1.46873e8i 0.245029 0.673213i
\(603\) 2.57462e8 + 4.53976e7i 1.17425 + 0.207053i
\(604\) −2.09373e8 + 3.69182e7i −0.950190 + 0.167544i
\(605\) −2.23917e8 + 8.14992e7i −1.01116 + 0.368033i
\(606\) 2.35625e6 + 1.97713e6i 0.0105877 + 0.00888416i
\(607\) 2.84658e8i 1.27279i 0.771362 + 0.636396i \(0.219576\pi\)
−0.771362 + 0.636396i \(0.780424\pi\)
\(608\) 3.83380e7 + 1.04305e7i 0.170576 + 0.0464081i
\(609\) −1.20451e8 −0.533286
\(610\) 1.07873e8 1.28558e8i 0.475250 0.566380i
\(611\) −4.39516e6 1.20756e7i −0.0192686 0.0529402i
\(612\) −3.34519e7 1.89715e8i −0.145937 0.827651i
\(613\) 2.16030e7 1.22517e8i 0.0937851 0.531881i −0.901328 0.433138i \(-0.857406\pi\)
0.995113 0.0987439i \(-0.0314825\pi\)
\(614\) 6.18173e7 + 2.24996e7i 0.267057 + 0.0972010i
\(615\) −7.89641e7 1.36770e8i −0.339472 0.587984i
\(616\) 1.32311e7 + 7.63901e6i 0.0566051 + 0.0326810i
\(617\) −7.60819e7 + 6.38403e7i −0.323911 + 0.271794i −0.790213 0.612832i \(-0.790030\pi\)
0.466302 + 0.884625i \(0.345586\pi\)
\(618\) 1.11616e8 + 1.33019e8i 0.472892 + 0.563571i
\(619\) 2.74391e7 4.75259e7i 0.115690 0.200382i −0.802365 0.596834i \(-0.796425\pi\)
0.918056 + 0.396452i \(0.129759\pi\)
\(620\) 1.58562e8 9.15460e7i 0.665311 0.384118i
\(621\) 6.07642e6 1.66948e7i 0.0253731 0.0697119i
\(622\) 1.65886e8 + 2.92502e7i 0.689348 + 0.121551i
\(623\) 2.04626e8 3.60811e7i 0.846248 0.149216i
\(624\) −1.99558e7 + 7.26331e6i −0.0821324 + 0.0298938i
\(625\) −2.25788e8 1.89458e8i −0.924827 0.776022i
\(626\) 8.69096e7i 0.354279i
\(627\) −7.08270e6 + 7.75278e7i −0.0287340 + 0.314525i
\(628\) 1.35410e7 0.0546727
\(629\) 5.20543e8 6.20359e8i 2.09173 2.49282i
\(630\) 4.68309e7 + 1.28667e8i 0.187288 + 0.514571i
\(631\) 1.03193e7 + 5.85234e7i 0.0410734 + 0.232939i 0.998433 0.0559601i \(-0.0178220\pi\)
−0.957360 + 0.288899i \(0.906711\pi\)
\(632\) 5.25761e6 2.98174e7i 0.0208275 0.118119i
\(633\) 1.64469e8 + 5.98617e7i 0.648444 + 0.236014i
\(634\) 1.40072e8 + 2.42612e8i 0.549646 + 0.952015i
\(635\) 3.00445e8 + 1.73462e8i 1.17339 + 0.677459i
\(636\) −1.24962e8 + 1.04855e8i −0.485741 + 0.407585i
\(637\) −1.55551e7 1.85378e7i −0.0601802 0.0717200i
\(638\) −1.04628e7 + 1.81222e7i −0.0402891 + 0.0697827i
\(639\) −7.02259e7 + 4.05450e7i −0.269150 + 0.155394i
\(640\) 9.01232e6 2.47611e7i 0.0343793 0.0944563i
\(641\) 7.62023e7 + 1.34365e7i 0.289330 + 0.0510168i 0.316430 0.948616i \(-0.397516\pi\)
−0.0270992 + 0.999633i \(0.508627\pi\)
\(642\) 4.26329e8 7.51734e7i 1.61117 0.284092i
\(643\) −2.18370e8 + 7.94802e7i −0.821410 + 0.298969i −0.718329 0.695704i \(-0.755093\pi\)
−0.103082 + 0.994673i \(0.532870\pi\)
\(644\) −3.04944e7 2.55879e7i −0.114173 0.0958024i
\(645\) 5.28203e8i 1.96844i
\(646\) 9.56786e7 + 3.62638e8i 0.354909 + 1.34517i
\(647\) −1.10057e8 −0.406355 −0.203177 0.979142i \(-0.565127\pi\)
−0.203177 + 0.979142i \(0.565127\pi\)
\(648\) −6.95328e7 + 8.28660e7i −0.255543 + 0.304545i
\(649\) 4.70819e6 + 1.29356e7i 0.0172234 + 0.0473210i
\(650\) −2.53925e6 1.44008e7i −0.00924626 0.0524381i
\(651\) −7.02559e7 + 3.98441e8i −0.254648 + 1.44418i
\(652\) −1.84573e8 6.71789e7i −0.665924 0.242376i
\(653\) 1.34217e8 + 2.32471e8i 0.482024 + 0.834890i 0.999787 0.0206339i \(-0.00656846\pi\)
−0.517763 + 0.855524i \(0.673235\pi\)
\(654\) −4.09082e8 2.36184e8i −1.46244 0.844338i
\(655\) 3.19674e8 2.68238e8i 1.13758 0.954546i
\(656\) −1.98889e7 2.37027e7i −0.0704530 0.0839626i
\(657\) −1.65150e8 + 2.86049e8i −0.582349 + 1.00866i
\(658\) −3.05140e7 + 1.76173e7i −0.107108 + 0.0618388i
\(659\) −9.33979e7 + 2.56609e8i −0.326348 + 0.896634i 0.662680 + 0.748903i \(0.269419\pi\)
−0.989028 + 0.147731i \(0.952803\pi\)
\(660\) 5.08467e7 + 8.96565e6i 0.176861 + 0.0311853i
\(661\) −3.91731e7 + 6.90728e6i −0.135639 + 0.0239168i −0.241055 0.970511i \(-0.577494\pi\)
0.105417 + 0.994428i \(0.466382\pi\)
\(662\) 5.09927e7 1.85598e7i 0.175766 0.0639734i
\(663\) −1.53563e8 1.28855e8i −0.526923 0.442141i
\(664\) 1.14091e8i 0.389714i
\(665\) −1.11731e8 2.42028e8i −0.379935 0.823003i
\(666\) 2.95164e8 0.999172
\(667\) 3.50466e7 4.17669e7i 0.118105 0.140752i
\(668\) −1.10017e6 3.02271e6i −0.00369090 0.0101407i
\(669\) −7.50461e7 4.25607e8i −0.250640 1.42145i
\(670\) −5.86163e7 + 3.32429e8i −0.194892 + 1.10529i
\(671\) 6.05396e7 + 2.20346e7i 0.200388 + 0.0729354i
\(672\) 2.91137e7 + 5.04265e7i 0.0959379 + 0.166169i
\(673\) 3.36382e8 + 1.94210e8i 1.10354 + 0.637128i 0.937148 0.348933i \(-0.113456\pi\)
0.166389 + 0.986060i \(0.446789\pi\)
\(674\) −3.05456e7 + 2.56308e7i −0.0997629 + 0.0837110i
\(675\) −1.15021e7 1.37077e7i −0.0373996 0.0445711i
\(676\) 7.21383e7 1.24947e8i 0.233521 0.404470i
\(677\) 2.95868e8 1.70820e8i 0.953526 0.550519i 0.0593517 0.998237i \(-0.481097\pi\)
0.894175 + 0.447718i \(0.147763\pi\)
\(678\) −6.83492e7 + 1.87788e8i −0.219303 + 0.602529i
\(679\) −1.06063e8 1.87018e7i −0.338810 0.0597414i
\(680\) 2.44955e8 4.31922e7i 0.779041 0.137366i
\(681\) 1.05232e8 3.83013e7i 0.333201 0.121275i
\(682\) 5.38435e7 + 4.51801e7i 0.169738 + 0.142428i
\(683\) 6.12319e8i 1.92183i 0.276838 + 0.960917i \(0.410713\pi\)
−0.276838 + 0.960917i \(0.589287\pi\)
\(684\) −7.88355e7 + 1.11674e8i −0.246351 + 0.348967i
\(685\) −6.25321e8 −1.94550
\(686\) −1.59607e8 + 1.90212e8i −0.494402 + 0.589205i
\(687\) −1.77102e8 4.86584e8i −0.546202 1.50068i
\(688\) −1.79703e7 1.01914e8i −0.0551809 0.312947i
\(689\) −1.35804e7 + 7.70183e7i −0.0415198 + 0.235470i
\(690\) −1.26414e8 4.60111e7i −0.384813 0.140060i
\(691\) −1.01508e8 1.75816e8i −0.307655 0.532875i 0.670194 0.742186i \(-0.266211\pi\)
−0.977849 + 0.209312i \(0.932878\pi\)
\(692\) −2.52766e8 1.45935e8i −0.762782 0.440393i
\(693\) −4.02666e7 + 3.37877e7i −0.120989 + 0.101522i
\(694\) −1.16082e8 1.38341e8i −0.347285 0.413878i
\(695\) −3.29043e8 + 5.69919e8i −0.980162 + 1.69769i
\(696\) −6.90670e7 + 3.98759e7i −0.204853 + 0.118272i
\(697\) 9.98955e7 2.74461e8i 0.295017 0.810554i
\(698\) −4.24230e8 7.48032e7i −1.24748 0.219965i
\(699\) 4.45870e8 7.86189e7i 1.30550 0.230195i
\(700\) −3.76762e7 + 1.37130e7i −0.109843 + 0.0399796i
\(701\) −1.51401e8 1.27041e8i −0.439516 0.368798i 0.396012 0.918245i \(-0.370394\pi\)
−0.835528 + 0.549447i \(0.814838\pi\)
\(702\) 1.24588e7i 0.0360136i
\(703\) −5.72646e8 + 4.78864e7i −1.64824 + 0.137831i
\(704\) 1.01157e7 0.0289919
\(705\) −7.65386e7 + 9.12152e7i −0.218430 + 0.260315i
\(706\) −8.79567e7 2.41659e8i −0.249951 0.686735i
\(707\) −702106. 3.98184e6i −0.00198675 0.0112674i
\(708\) −9.11032e6 + 5.16672e7i −0.0256705 + 0.145585i
\(709\) −1.61477e8 5.87727e7i −0.453076 0.164906i 0.105395 0.994430i \(-0.466389\pi\)
−0.558471 + 0.829524i \(0.688612\pi\)
\(710\) −5.23507e7 9.06740e7i −0.146267 0.253342i
\(711\) 9.02138e7 + 5.20850e7i 0.250995 + 0.144912i
\(712\) 1.05388e8 8.84313e7i 0.291979 0.245000i
\(713\) −1.17719e8 1.40292e8i −0.324772 0.387048i
\(714\) −2.74820e8 + 4.76003e8i −0.755013 + 1.30772i
\(715\) 2.14369e7 1.23766e7i 0.0586468 0.0338597i
\(716\) 9.96946e7 2.73909e8i 0.271602 0.746219i
\(717\) 5.69188e8 + 1.00363e8i 1.54418 + 0.272281i
\(718\) −4.12011e8 + 7.26487e7i −1.11310 + 0.196270i
\(719\) 3.15778e8 1.14934e8i 0.849561 0.309215i 0.119700 0.992810i \(-0.461807\pi\)
0.729861 + 0.683595i \(0.239585\pi\)
\(720\) 6.94486e7 + 5.82743e7i 0.186065 + 0.156127i
\(721\) 2.28258e8i 0.609004i
\(722\) 1.34831e8 2.29449e8i 0.358243 0.609641i
\(723\) 5.05510e6 0.0133756
\(724\) −1.00104e8 + 1.19299e8i −0.263775 + 0.314355i
\(725\) −1.87821e7 5.16035e7i −0.0492869 0.135415i
\(726\) −6.05401e7 3.43340e8i −0.158210 0.897253i
\(727\) 5.32699e7 3.02108e8i 0.138637 0.786248i −0.833621 0.552337i \(-0.813736\pi\)
0.972258 0.233911i \(-0.0751526\pi\)
\(728\) 2.62321e7 + 9.54772e6i 0.0679892 + 0.0247460i
\(729\) −1.33760e8 2.31679e8i −0.345257 0.598003i
\(730\) −3.69339e8 2.13238e8i −0.949417 0.548146i
\(731\) 7.48323e8 6.27917e8i 1.91574 1.60750i
\(732\) 1.57827e8 + 1.88091e8i 0.402392 + 0.479552i
\(733\) −3.39782e8 + 5.88520e8i −0.862757 + 1.49434i 0.00650012 + 0.999979i \(0.497931\pi\)
−0.869257 + 0.494360i \(0.835402\pi\)
\(734\) −4.26519e7 + 2.46251e7i −0.107857 + 0.0622715i
\(735\) −7.66913e7 + 2.10708e8i −0.193145 + 0.530662i
\(736\) −2.59565e7 4.57683e6i −0.0651048 0.0114797i
\(737\) −1.27617e8 + 2.25024e7i −0.318792 + 0.0562116i
\(738\) 1.00035e8 3.64099e7i 0.248877 0.0905838i
\(739\) −3.11526e7 2.61401e7i −0.0771899 0.0647700i 0.603376 0.797457i \(-0.293822\pi\)
−0.680566 + 0.732687i \(0.738266\pi\)
\(740\) 3.81108e8i 0.940488i
\(741\) 1.18538e7 + 1.41752e8i 0.0291341 + 0.348398i
\(742\) 2.14431e8 0.524899
\(743\) 1.01196e8 1.20600e8i 0.246715 0.294023i −0.628448 0.777852i \(-0.716310\pi\)
0.875163 + 0.483828i \(0.160754\pi\)
\(744\) 9.16204e7 + 2.51725e8i 0.222471 + 0.611234i
\(745\) 4.30889e7 + 2.44369e8i 0.104207 + 0.590987i
\(746\) 4.81121e7 2.72857e8i 0.115888 0.657232i
\(747\) −3.68859e8 1.34254e8i −0.884909 0.322081i
\(748\) 4.77437e7 + 8.26945e7i 0.114080 + 0.197593i
\(749\) −4.92822e8 2.84531e8i −1.17286 0.677148i
\(750\) 2.50092e8 2.09852e8i 0.592810 0.497427i
\(751\) 2.72704e8 + 3.24996e8i 0.643830 + 0.767287i 0.984970 0.172726i \(-0.0552574\pi\)
−0.341140 + 0.940013i \(0.610813\pi\)
\(752\) −1.16645e7 + 2.02035e7i −0.0274292 + 0.0475088i
\(753\) 2.98681e8 1.72443e8i 0.699555 0.403888i
\(754\) −1.30771e7 + 3.59291e7i −0.0305069 + 0.0838170i
\(755\) 9.30104e8 + 1.64002e8i 2.16118 + 0.381074i
\(756\) 3.36414e7 5.93189e6i 0.0778591 0.0137287i
\(757\) 4.75933e8 1.73226e8i 1.09713 0.399323i 0.270873 0.962615i \(-0.412688\pi\)
0.826258 + 0.563292i \(0.190465\pi\)
\(758\) 1.01814e8 + 8.54325e7i 0.233777 + 0.196162i
\(759\) 5.16442e7i 0.118113i
\(760\) −1.44191e8 1.01791e8i −0.328472 0.231882i
\(761\) −4.85628e8 −1.10192 −0.550960 0.834532i \(-0.685738\pi\)
−0.550960 + 0.834532i \(0.685738\pi\)
\(762\) −3.26267e8 + 3.88830e8i −0.737408 + 0.878809i
\(763\) 2.12372e8 + 5.83486e8i 0.478105 + 1.31358i
\(764\) 3.70546e6 + 2.10147e7i 0.00830925 + 0.0471241i
\(765\) −1.48604e8 + 8.42775e8i −0.331930 + 1.88247i
\(766\) 1.77005e8 + 6.44245e7i 0.393821 + 0.143339i
\(767\) 1.25763e7 + 2.17828e7i 0.0278720 + 0.0482756i
\(768\) 3.33877e7 + 1.92764e7i 0.0737061 + 0.0425542i
\(769\) −3.50744e8 + 2.94309e8i −0.771277 + 0.647179i −0.941036 0.338307i \(-0.890146\pi\)
0.169758 + 0.985486i \(0.445701\pi\)
\(770\) −4.36259e7 5.19913e7i −0.0955591 0.113883i
\(771\) 5.04322e7 8.73511e7i 0.110038 0.190592i
\(772\) 2.89289e8 1.67021e8i 0.628753 0.363011i
\(773\) 1.68370e8 4.62594e8i 0.364525 1.00152i −0.612885 0.790172i \(-0.709991\pi\)
0.977410 0.211352i \(-0.0677865\pi\)
\(774\) 3.50639e8 + 6.18271e7i 0.756201 + 0.133339i
\(775\) −1.81654e8 + 3.20305e7i −0.390248 + 0.0688112i
\(776\) −6.70082e7 + 2.43890e7i −0.143398 + 0.0521926i
\(777\) −6.45128e8 5.41326e8i −1.37525 1.15397i
\(778\) 2.88384e8i 0.612396i
\(779\) −1.88171e8 + 8.68682e7i −0.398053 + 0.183759i
\(780\) 9.43393e7 0.198797
\(781\) 2.58363e7 3.07905e7i 0.0542347 0.0646344i
\(782\) −8.50936e7 2.33793e8i −0.177941 0.488890i
\(783\) 8.12467e6 + 4.60773e7i 0.0169247 + 0.0959846i
\(784\) −7.62866e6 + 4.32643e7i −0.0158307 + 0.0897803i
\(785\) −5.65256e7 2.05736e7i −0.116852 0.0425307i
\(786\) 3.05277e8 + 5.28756e8i 0.628676 + 1.08890i
\(787\) −6.39495e8 3.69212e8i −1.31194 0.757447i −0.329519 0.944149i \(-0.606887\pi\)
−0.982417 + 0.186702i \(0.940220\pi\)
\(788\) −1.38844e8 + 1.16504e8i −0.283758 + 0.238101i
\(789\) 3.33431e8 + 3.97368e8i 0.678852 + 0.809024i
\(790\) −6.72509e7 + 1.16482e8i −0.136401 + 0.236253i
\(791\) 2.27498e8 1.31346e8i 0.459672 0.265392i
\(792\) −1.19034e7 + 3.27043e7i −0.0239605 + 0.0658309i
\(793\) 1.15928e8 + 2.04412e7i 0.232470 + 0.0409907i
\(794\) 3.14810e8 5.55096e7i 0.628909 0.110894i
\(795\) 6.80955e8 2.47847e8i 1.35524 0.493268i
\(796\) 1.01748e8 + 8.53763e7i 0.201737 + 0.169277i
\(797\) 1.94384e8i 0.383960i 0.981399 + 0.191980i \(0.0614908\pi\)
−0.981399 + 0.191980i \(0.938509\pi\)
\(798\) 3.77117e8 9.94986e7i 0.742108 0.195798i
\(799\) −2.20215e8 −0.431725
\(800\) −1.70638e7 + 2.03359e7i −0.0333278 + 0.0397186i
\(801\) 1.61888e8 + 4.44783e8i 0.315005 + 0.865468i
\(802\) −4.48479e7 2.54345e8i −0.0869399 0.493061i
\(803\) 2.84299e7 1.61234e8i 0.0549071 0.311394i
\(804\) −4.64093e8 1.68916e8i −0.892970 0.325015i
\(805\) 8.84192e7 + 1.53146e8i 0.169496 + 0.293575i
\(806\) 1.11222e8 + 6.42141e7i 0.212415 + 0.122638i
\(807\) 5.35491e8 4.49331e8i 1.01890 0.854959i
\(808\) −1.72079e6 2.05076e6i −0.00326207 0.00388759i
\(809\) 2.29037e8 3.96704e8i 0.432574 0.749239i −0.564521 0.825419i \(-0.690939\pi\)
0.997094 + 0.0761797i \(0.0242723\pi\)
\(810\) 4.16162e8 2.40272e8i 0.783083 0.452113i
\(811\) −4.77496e7 + 1.31191e8i −0.0895173 + 0.245947i −0.976370 0.216105i \(-0.930665\pi\)
0.886853 + 0.462052i \(0.152887\pi\)
\(812\) 1.03242e8 + 1.82044e7i 0.192836 + 0.0340023i
\(813\) 2.07701e7 3.66233e6i 0.0386515 0.00681531i
\(814\) −1.37482e8 + 5.00392e7i −0.254901 + 0.0927764i
\(815\) 6.68414e8 + 5.60866e8i 1.23473 + 1.03606i
\(816\) 3.63921e8i 0.669787i
\(817\) −6.90304e8 6.30640e7i −1.26583 0.115642i
\(818\) 2.14998e7 0.0392803
\(819\) −6.17362e7 + 7.35743e7i −0.112380 + 0.133929i
\(820\) 4.70116e7 + 1.29163e8i 0.0852636 + 0.234260i
\(821\) 1.21058e8 + 6.86554e8i 0.218758 + 1.24064i 0.874265 + 0.485449i \(0.161344\pi\)
−0.655507 + 0.755189i \(0.727545\pi\)
\(822\) 1.58871e8 9.01002e8i 0.286041 1.62222i
\(823\) 4.74375e6 + 1.72658e6i 0.00850986 + 0.00309733i 0.346272 0.938134i \(-0.387448\pi\)
−0.337762 + 0.941232i \(0.609670\pi\)
\(824\) −7.55655e7 1.30883e8i −0.135065 0.233939i
\(825\) −4.50471e7 2.60080e7i −0.0802241 0.0463174i
\(826\) 5.28303e7 4.43299e7i 0.0937438 0.0786604i
\(827\) −6.28587e8 7.49121e8i −1.11135 1.32445i −0.940747 0.339109i \(-0.889874\pi\)
−0.170598 0.985341i \(-0.554570\pi\)
\(828\) 4.53408e7 7.85326e7i 0.0798726 0.138343i
\(829\) 4.13903e8 2.38967e8i 0.726500 0.419445i −0.0906406 0.995884i \(-0.528891\pi\)
0.817140 + 0.576439i \(0.195558\pi\)
\(830\) 1.73345e8 4.76262e8i 0.303164 0.832936i
\(831\) 5.60298e8 + 9.87957e7i 0.976374 + 0.172161i
\(832\) 1.82024e7 3.20957e6i 0.0316051 0.00557284i
\(833\) −3.89686e8 + 1.41834e8i −0.674186 + 0.245383i
\(834\) −7.37578e8 6.18901e8i −1.27148 1.06690i
\(835\) 1.42896e7i 0.0245449i
\(836\) 1.77879e7 6.53807e7i 0.0304443 0.111900i
\(837\) 1.57158e8 0.268015
\(838\) −9.40267e7 + 1.12057e8i −0.159779 + 0.190417i
\(839\) −1.81053e8 4.97438e8i −0.306562 0.842273i −0.993321 0.115387i \(-0.963189\pi\)
0.686758 0.726886i \(-0.259033\pi\)
\(840\) −4.49167e7 2.54736e8i −0.0757828 0.429785i
\(841\) 7.83562e7 4.44380e8i 0.131730 0.747079i
\(842\) 3.76421e8 + 1.37006e8i 0.630576 + 0.229511i
\(843\) −3.59920e8 6.23399e8i −0.600790 1.04060i
\(844\) −1.31923e8 7.61660e7i −0.219429 0.126688i
\(845\) −4.90976e8 + 4.11977e8i −0.813748 + 0.682815i
\(846\) −5.15927e7 6.14858e7i −0.0852074 0.101546i
\(847\) −2.29144e8 + 3.96889e8i −0.377102 + 0.653159i
\(848\) 1.22955e8 7.09882e7i 0.201632 0.116412i
\(849\) −1.42487e8 + 3.91481e8i −0.232838 + 0.639717i
\(850\) −2.46781e8 4.35141e7i −0.401842 0.0708555i
\(851\) 3.75413e8 6.61955e7i 0.609146 0.107409i
\(852\) 1.43949e8 5.23933e7i 0.232751 0.0847143i
\(853\) −4.96225e8 4.16382e8i −0.799524 0.670881i 0.148559 0.988904i \(-0.452537\pi\)
−0.948083 + 0.318023i \(0.896981\pi\)
\(854\) 3.22761e8i 0.518211i
\(855\) 4.98766e8 3.46395e8i 0.797992 0.554208i
\(856\) −3.76780e8 −0.600712
\(857\) −5.10140e8 + 6.07962e8i −0.810489 + 0.965903i −0.999872 0.0159999i \(-0.994907\pi\)
0.189383 + 0.981903i \(0.439351\pi\)
\(858\) 1.23867e7 + 3.40321e7i 0.0196107 + 0.0538799i
\(859\) 1.83245e7 + 1.03923e8i 0.0289103 + 0.163958i 0.995845 0.0910663i \(-0.0290275\pi\)
−0.966935 + 0.255025i \(0.917916\pi\)
\(860\) −7.98297e7 + 4.52737e8i −0.125507 + 0.711787i
\(861\) −2.85419e8 1.03884e8i −0.447170 0.162757i
\(862\) 1.05871e8 + 1.83374e8i 0.165293 + 0.286296i
\(863\) 4.45885e8 + 2.57432e8i 0.693730 + 0.400525i 0.805008 0.593264i \(-0.202161\pi\)
−0.111278 + 0.993789i \(0.535494\pi\)
\(864\) 1.73263e7 1.45385e7i 0.0268636 0.0225412i
\(865\) 8.33424e8 + 9.93236e8i 1.28771 + 1.53463i
\(866\) 3.76651e7 6.52378e7i 0.0579943 0.100449i
\(867\) −2.20644e9 + 1.27389e9i −3.38560 + 1.95468i
\(868\) 1.20436e8 3.30896e8i 0.184161 0.505979i
\(869\) −5.08499e7 8.96620e6i −0.0774873 0.0136631i
\(870\) 3.48901e8 6.15206e7i 0.529839 0.0934249i
\(871\) −2.22498e8 + 8.09825e7i −0.336721 + 0.122557i
\(872\) 3.14940e8 + 2.64266e8i 0.474983 + 0.398558i
\(873\) 2.45339e8i 0.368743i
\(874\) −7.52246e7 + 1.59717e8i −0.112675 + 0.239230i
\(875\) −4.29152e8 −0.640600
\(876\) 4.01083e8 4.77992e8i 0.596653 0.711063i
\(877\) −1.33426e8 3.66584e8i −0.197806 0.543469i 0.800643 0.599142i \(-0.204492\pi\)
−0.998449 + 0.0556735i \(0.982269\pi\)
\(878\) 7.38878e7 + 4.19039e8i 0.109166 + 0.619114i
\(879\) −1.58927e8 + 9.01319e8i −0.234008 + 1.32713i
\(880\) −4.22271e7 1.53694e7i −0.0619645 0.0225532i
\(881\) −1.64461e8 2.84854e8i −0.240511 0.416577i 0.720349 0.693612i \(-0.243982\pi\)
−0.960860 + 0.277035i \(0.910648\pi\)
\(882\) −1.30898e8 7.55740e7i −0.190778 0.110145i
\(883\) 2.28387e8 1.91640e8i 0.331734 0.278358i −0.461672 0.887051i \(-0.652750\pi\)
0.793406 + 0.608693i \(0.208306\pi\)
\(884\) 1.12149e8 + 1.33654e8i 0.162345 + 0.193475i
\(885\) 1.16532e8 2.01839e8i 0.168118 0.291189i
\(886\) 4.27341e8 2.46725e8i 0.614431 0.354742i
\(887\) −2.49617e8 + 6.85818e8i −0.357688 + 0.982738i 0.622142 + 0.782904i \(0.286263\pi\)
−0.979830 + 0.199834i \(0.935960\pi\)
\(888\) −5.49125e8 9.68256e7i −0.784210 0.138277i
\(889\) 6.57086e8 1.15862e8i 0.935227 0.164906i
\(890\) −5.74294e8 + 2.09026e8i −0.814637 + 0.296504i
\(891\) 1.41318e8 + 1.18580e8i 0.199785 + 0.167640i
\(892\) 3.76142e8i 0.529977i
\(893\) 1.10070e8 + 1.10918e8i 0.154566 + 0.155757i
\(894\) −3.63050e8 −0.508106
\(895\) −8.32333e8 + 9.91936e8i −1.16099 + 1.38361i
\(896\) −1.73330e7 4.76220e7i −0.0240962 0.0662039i
\(897\) −1.63860e7 9.29296e7i −0.0227036 0.128759i
\(898\) −4.66729e7 + 2.64695e8i −0.0644520 + 0.365525i
\(899\) 4.53215e8 + 1.64957e8i 0.623771 + 0.227034i
\(900\) −4.56671e7 7.90978e7i −0.0626436 0.108502i
\(901\) 1.16064e9 + 6.70096e8i 1.58680 + 0.916141i
\(902\) −4.04220e7 + 3.39181e7i −0.0550805 + 0.0462181i
\(903\) −6.52988e8 7.78200e8i −0.886833 1.05689i
\(904\) 8.69651e7 1.50628e8i 0.117717 0.203892i
\(905\) 5.99133e8 3.45909e8i 0.808309 0.466677i
\(906\) −4.72610e8 + 1.29849e9i −0.635504 + 1.74603i
\(907\) −1.36774e9 2.41169e8i −1.83308 0.323221i −0.853012 0.521890i \(-0.825227\pi\)
−0.980067 + 0.198669i \(0.936338\pi\)
\(908\) −9.59857e7 + 1.69249e7i −0.128218 + 0.0226083i
\(909\) 8.65507e6 3.15019e6i 0.0115234 0.00419416i
\(910\) −9.49975e7 7.97123e7i −0.126063 0.105779i
\(911\) 1.53396e8i 0.202889i −0.994841 0.101444i \(-0.967654\pi\)
0.994841 0.101444i \(-0.0323464\pi\)
\(912\) 1.83300e8 1.81899e8i 0.241645 0.239797i
\(913\) 1.94568e8 0.255657
\(914\) −1.88796e8 + 2.24998e8i −0.247260 + 0.294673i
\(915\) −3.73058e8 1.02497e9i −0.486983 1.33797i
\(916\) 7.82593e7 + 4.43830e8i 0.101824 + 0.577472i
\(917\) 1.39367e8 7.90390e8i 0.180739 1.02502i
\(918\) 2.00626e8 + 7.30220e7i 0.259334 + 0.0943899i
\(919\) −4.84684e8 8.39498e8i −0.624471 1.08162i −0.988643 0.150284i \(-0.951981\pi\)
0.364171 0.931332i \(-0.381352\pi\)
\(920\) 1.01399e8 + 5.85430e7i 0.130218 + 0.0751815i
\(921\) 3.27536e8 2.74836e8i 0.419257 0.351799i
\(922\) −2.02708e8 2.41578e8i −0.258630 0.308223i
\(923\) 3.67209e7 6.36025e7i 0.0466991 0.0808852i
\(924\) 8.59961e7 4.96499e7i 0.109009 0.0629365i
\(925\) 1.31318e8 3.60794e8i 0.165920 0.455862i
\(926\) −2.23765e7 3.94557e6i −0.0281811 0.00496909i
\(927\) 5.12070e8 9.02918e7i 0.642822 0.113347i
\(928\) 6.52258e7 2.37403e7i 0.0816161 0.0297058i
\(929\) −1.73480e8 1.45567e8i −0.216373 0.181559i 0.528159 0.849146i \(-0.322883\pi\)
−0.744532 + 0.667587i \(0.767327\pi\)
\(930\) 1.19001e9i 1.47946i
\(931\) 2.66216e8 + 1.25384e8i 0.329902 + 0.155380i
\(932\) −3.94049e8 −0.486747
\(933\) 7.03731e8 8.38674e8i 0.866487 1.03264i
\(934\) −1.10952e8 3.04837e8i −0.136174 0.374134i
\(935\) −7.36590e7 4.17741e8i −0.0901138 0.511061i
\(936\) −1.10426e7 + 6.26256e7i −0.0134661 + 0.0763703i
\(937\) 8.14968e8 + 2.96624e8i 0.990653 + 0.360568i 0.785973 0.618261i \(-0.212162\pi\)
0.204680 + 0.978829i \(0.434385\pi\)
\(938\) 3.24605e8 + 5.62232e8i 0.393320 + 0.681251i
\(939\) −4.89193e8 2.82435e8i −0.590858 0.341132i
\(940\) 7.93890e7 6.66153e7i 0.0955822 0.0802030i
\(941\) 3.88433e8 + 4.62916e8i 0.466173 + 0.555563i 0.946992 0.321257i \(-0.104105\pi\)
−0.480819 + 0.876820i \(0.659661\pi\)
\(942\) 4.40049e7 7.62187e7i 0.0526439 0.0911819i
\(943\) 1.19068e8 6.87438e7i 0.141990 0.0819782i
\(944\) 1.56174e7 4.29085e7i 0.0185649 0.0510067i
\(945\) −1.49446e8 2.63514e7i −0.177088 0.0312254i
\(946\) −1.73802e8 + 3.06461e7i −0.205297 + 0.0361994i
\(947\) −9.79248e8 + 3.56417e8i −1.15304 + 0.419671i −0.846605 0.532222i \(-0.821357\pi\)
−0.306431 + 0.951893i \(0.599135\pi\)
\(948\) −1.50749e8 1.26493e8i −0.176941 0.148471i
\(949\) 2.99148e8i 0.350016i
\(950\) 1.01431e8 + 1.46048e8i 0.118304 + 0.170344i
\(951\) 1.82080e9 2.11700
\(952\) 3.07496e8 3.66460e8i 0.356393 0.424733i
\(953\) −3.12186e8 8.57724e8i −0.360691 0.990989i −0.978786 0.204886i \(-0.934318\pi\)
0.618095 0.786103i \(-0.287905\pi\)
\(954\) 8.48224e7 + 4.81052e8i 0.0976935 + 0.554047i
\(955\) 1.64608e7 9.33540e7i 0.0188991 0.107182i
\(956\) −4.72698e8 1.72048e8i −0.541016 0.196914i
\(957\) 6.80034e7 + 1.17785e8i 0.0775880 + 0.134386i
\(958\) 7.08267e8 + 4.08918e8i 0.805565 + 0.465093i
\(959\) −9.21284e8 + 7.73049e8i −1.04457 + 0.876499i
\(960\) −1.10086e8 1.31196e8i −0.124429 0.148288i
\(961\) 3.66255e8 6.34372e8i 0.412680 0.714782i
\(962\) −2.31510e8 + 1.33663e8i −0.260043 + 0.150136i
\(963\) 4.43367e8 1.21814e9i 0.496461 1.36401i
\(964\) −4.33286e6 764000.i −0.00483663 0.000852829i
\(965\) −1.46138e9 + 2.57681e8i −1.62623 + 0.286748i
\(966\) −2.43127e8 + 8.84911e7i −0.269713 + 0.0981676i
\(967\) 5.19251e8 + 4.35703e8i 0.574245 + 0.481849i 0.883052 0.469276i \(-0.155485\pi\)
−0.308806 + 0.951125i \(0.599929\pi\)
\(968\) 3.03436e8i 0.334534i
\(969\) 2.35213e9 + 6.39936e8i 2.58518 + 0.703340i
\(970\) 3.16776e8 0.347086
\(971\) 6.21367e8 7.40516e8i 0.678719 0.808866i −0.311223 0.950337i \(-0.600739\pi\)
0.989942 + 0.141471i \(0.0451831\pi\)
\(972\) 2.09314e8 + 5.75084e8i 0.227928 + 0.626228i
\(973\) 2.19781e8 + 1.24644e9i 0.238589 + 1.35311i
\(974\) −2.03261e6 + 1.15275e7i −0.00219977 + 0.0124755i
\(975\) −8.93106e7 3.25064e7i −0.0963583 0.0350716i
\(976\) −1.06851e8 1.85071e8i −0.114929 0.199063i
\(977\) 6.68630e7 + 3.86034e7i 0.0716972 + 0.0413944i 0.535420 0.844586i \(-0.320153\pi\)
−0.463723 + 0.885980i \(0.653487\pi\)
\(978\) −9.77951e8 + 8.20598e8i −1.04544 + 0.877231i
\(979\) −1.50809e8 1.79727e8i −0.160723 0.191542i
\(980\) 9.75793e7 1.69012e8i 0.103676 0.179573i
\(981\) −1.22498e9 + 7.07241e8i −1.29754 + 0.749136i
\(982\) −4.25936e8 + 1.17025e9i −0.449790 + 1.23579i
\(983\) −1.04399e8 1.84084e7i −0.109910 0.0193801i 0.118423 0.992963i \(-0.462216\pi\)
−0.228333 + 0.973583i \(0.573327\pi\)
\(984\) −1.98051e8 + 3.49217e7i −0.207870 + 0.0366530i
\(985\) 7.56603e8 2.75381e8i 0.791698 0.288155i
\(986\) 5.01925e8 + 4.21165e8i 0.523610 + 0.439361i
\(987\) 2.29008e8i 0.238176i
\(988\) 1.12635e7 1.23291e8i 0.0116789 0.127838i
\(989\) 4.59837e8 0.475352
\(990\) 9.93795e7 1.18436e8i 0.102422 0.122061i
\(991\) 5.00484e8 + 1.37507e9i 0.514244 + 1.41287i 0.876774 + 0.480903i \(0.159691\pi\)
−0.362530 + 0.931972i \(0.618087\pi\)
\(992\) −4.04860e7 2.29607e8i −0.0414734 0.235207i
\(993\) 6.12454e7 3.47340e8i 0.0625498 0.354738i
\(994\) −1.89223e8 6.88717e7i −0.192671 0.0701264i
\(995\) −2.95019e8 5.10988e8i −0.299489 0.518730i
\(996\) 6.42188e8 + 3.70768e8i 0.649957 + 0.375253i
\(997\) −1.23269e9 + 1.03435e9i −1.24385 + 1.04371i −0.246635 + 0.969109i \(0.579325\pi\)
−0.997213 + 0.0746037i \(0.976231\pi\)
\(998\) 4.01290e8 + 4.78239e8i 0.403707 + 0.481119i
\(999\) −1.63563e8 + 2.83299e8i −0.164055 + 0.284151i
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 38.7.f.a.3.5 60
19.13 odd 18 inner 38.7.f.a.13.5 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.7.f.a.3.5 60 1.1 even 1 trivial
38.7.f.a.13.5 yes 60 19.13 odd 18 inner