Properties

Label 69.6.g.a.5.19
Level $69$
Weight $6$
Character 69.5
Analytic conductor $11.066$
Analytic rank $0$
Dimension $380$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,6,Mod(5,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.5");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 69.g (of order \(22\), degree \(10\), 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: \(11.0664835671\)
Analytic rank: \(0\)
Dimension: \(380\)
Relative dimension: \(38\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.19
Character \(\chi\) \(=\) 69.5
Dual form 69.6.g.a.14.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.190214 + 0.647810i) q^{2} +(-15.2666 + 3.15135i) q^{3} +(26.5366 + 17.0541i) q^{4} +(-6.91235 + 48.0764i) q^{5} +(0.862446 - 10.4893i) q^{6} +(156.619 - 71.5256i) q^{7} +(-32.4235 + 28.0951i) q^{8} +(223.138 - 96.2208i) q^{9} +O(q^{10})\) \(q+(-0.190214 + 0.647810i) q^{2} +(-15.2666 + 3.15135i) q^{3} +(26.5366 + 17.0541i) q^{4} +(-6.91235 + 48.0764i) q^{5} +(0.862446 - 10.4893i) q^{6} +(156.619 - 71.5256i) q^{7} +(-32.4235 + 28.0951i) q^{8} +(223.138 - 96.2208i) q^{9} +(-29.8296 - 13.6227i) q^{10} +(-600.835 + 176.421i) q^{11} +(-458.867 - 176.731i) q^{12} +(-230.379 + 504.461i) q^{13} +(16.5438 + 115.065i) q^{14} +(-45.9777 - 755.747i) q^{15} +(407.293 + 891.846i) q^{16} +(259.023 - 166.464i) q^{17} +(19.8888 + 162.854i) q^{18} +(-828.997 + 1289.94i) q^{19} +(-1003.33 + 1157.90i) q^{20} +(-2165.64 + 1585.51i) q^{21} -422.785i q^{22} +(-2044.96 + 1501.50i) q^{23} +(406.458 - 531.094i) q^{24} +(734.854 + 215.773i) q^{25} +(-282.973 - 245.198i) q^{26} +(-3103.33 + 2172.15i) q^{27} +(5375.95 + 772.945i) q^{28} +(-2625.45 - 4085.28i) q^{29} +(498.326 + 113.969i) q^{30} +(-4374.58 - 5048.53i) q^{31} +(-2014.12 + 289.587i) q^{32} +(8616.75 - 4586.79i) q^{33} +(58.5672 + 199.461i) q^{34} +(2356.09 + 8024.10i) q^{35} +(7562.29 + 1252.03i) q^{36} +(-10053.0 + 1445.40i) q^{37} +(-677.952 - 782.398i) q^{38} +(1927.38 - 8427.40i) q^{39} +(-1126.59 - 1753.01i) q^{40} +(12174.1 + 1750.37i) q^{41} +(-615.176 - 1704.51i) q^{42} +(13024.2 + 11285.5i) q^{43} +(-18952.8 - 5565.06i) q^{44} +(3083.55 + 11392.8i) q^{45} +(-583.704 - 1610.35i) q^{46} -2734.58i q^{47} +(-9028.49 - 12331.9i) q^{48} +(8407.41 - 9702.67i) q^{49} +(-279.559 + 435.003i) q^{50} +(-3429.81 + 3357.61i) q^{51} +(-14716.6 + 9457.78i) q^{52} +(10138.0 + 22199.0i) q^{53} +(-816.843 - 2423.54i) q^{54} +(-4328.52 - 30105.5i) q^{55} +(-3068.62 + 6719.34i) q^{56} +(8590.89 - 22305.5i) q^{57} +(3145.88 - 923.714i) q^{58} +(33513.7 + 15305.2i) q^{59} +(11668.5 - 20839.1i) q^{60} +(34828.1 - 30178.8i) q^{61} +(4102.59 - 1873.59i) q^{62} +(28065.4 - 31030.1i) q^{63} +(-4269.51 + 29695.1i) q^{64} +(-22660.2 - 14562.8i) q^{65} +(1332.34 + 6454.49i) q^{66} +(-1671.88 + 5693.91i) q^{67} +9712.48 q^{68} +(26487.8 - 29367.1i) q^{69} -5646.25 q^{70} +(-15435.2 + 52567.3i) q^{71} +(-4531.57 + 9388.89i) q^{72} +(-17961.2 - 11543.0i) q^{73} +(975.876 - 6787.37i) q^{74} +(-11898.7 - 978.330i) q^{75} +(-43997.6 + 20093.0i) q^{76} +(-81483.7 + 70606.0i) q^{77} +(5092.74 + 2851.59i) q^{78} +(10415.3 + 4756.52i) q^{79} +(-45692.1 + 13416.4i) q^{80} +(40532.1 - 42941.0i) q^{81} +(-3449.59 + 7553.54i) q^{82} +(-4134.05 - 28752.9i) q^{83} +(-84508.2 + 5141.27i) q^{84} +(6212.53 + 13603.6i) q^{85} +(-9788.27 + 6290.54i) q^{86} +(52955.8 + 54094.6i) q^{87} +(14524.6 - 22600.7i) q^{88} +(-9058.24 + 10453.8i) q^{89} +(-7966.89 - 169.518i) q^{90} +95486.2i q^{91} +(-79872.9 + 4969.84i) q^{92} +(82694.6 + 63288.0i) q^{93} +(1771.49 + 520.155i) q^{94} +(-56285.6 - 48771.7i) q^{95} +(29836.2 - 10768.2i) q^{96} +(-32913.9 - 4732.31i) q^{97} +(4686.28 + 7291.99i) q^{98} +(-117094. + 97179.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 380 q - 11 q^{3} + 578 q^{4} + 64 q^{6} - 22 q^{7} + 433 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 380 q - 11 q^{3} + 578 q^{4} + 64 q^{6} - 22 q^{7} + 433 q^{9} - 22 q^{10} + 148 q^{12} - 542 q^{13} + 4620 q^{15} - 11102 q^{16} - 11526 q^{18} - 22 q^{19} + 12496 q^{21} + 15878 q^{24} - 17304 q^{25} - 21014 q^{27} - 22 q^{28} - 33627 q^{30} - 6566 q^{31} + 41250 q^{33} + 75988 q^{34} + 12154 q^{36} - 72138 q^{37} + 45205 q^{39} - 119372 q^{40} - 11 q^{42} + 59334 q^{43} + 119802 q^{46} + 5138 q^{48} + 147060 q^{49} - 11 q^{51} - 246042 q^{52} - 172143 q^{54} - 95048 q^{55} + 92422 q^{57} + 277528 q^{58} + 420629 q^{60} + 125158 q^{61} + 7194 q^{63} - 100196 q^{64} - 312378 q^{66} - 94380 q^{67} - 136956 q^{69} - 395908 q^{70} - 507803 q^{72} + 83336 q^{73} + 577756 q^{75} + 415338 q^{76} - 361512 q^{78} + 342958 q^{79} - 420607 q^{81} + 247868 q^{82} - 978505 q^{84} - 634728 q^{85} + 354721 q^{87} + 22506 q^{88} + 1636316 q^{90} + 1162112 q^{93} + 40940 q^{94} - 102479 q^{96} + 582824 q^{97} - 674663 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{1}{22}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.190214 + 0.647810i −0.0336254 + 0.114518i −0.974596 0.223972i \(-0.928098\pi\)
0.940970 + 0.338489i \(0.109916\pi\)
\(3\) −15.2666 + 3.15135i −0.979353 + 0.202159i
\(4\) 26.5366 + 17.0541i 0.829270 + 0.532939i
\(5\) −6.91235 + 48.0764i −0.123652 + 0.860017i 0.829712 + 0.558192i \(0.188505\pi\)
−0.953363 + 0.301825i \(0.902404\pi\)
\(6\) 0.862446 10.4893i 0.00978034 0.118951i
\(7\) 156.619 71.5256i 1.20809 0.551717i 0.293447 0.955975i \(-0.405198\pi\)
0.914645 + 0.404259i \(0.132470\pi\)
\(8\) −32.4235 + 28.0951i −0.179116 + 0.155205i
\(9\) 223.138 96.2208i 0.918263 0.395970i
\(10\) −29.8296 13.6227i −0.0943293 0.0430788i
\(11\) −600.835 + 176.421i −1.49718 + 0.439611i −0.924824 0.380394i \(-0.875788\pi\)
−0.572355 + 0.820006i \(0.693970\pi\)
\(12\) −458.867 176.731i −0.919886 0.354291i
\(13\) −230.379 + 504.461i −0.378081 + 0.827883i 0.620949 + 0.783851i \(0.286748\pi\)
−0.999030 + 0.0440316i \(0.985980\pi\)
\(14\) 16.5438 + 115.065i 0.0225588 + 0.156900i
\(15\) −45.9777 755.747i −0.0527617 0.867257i
\(16\) 407.293 + 891.846i 0.397747 + 0.870944i
\(17\) 259.023 166.464i 0.217378 0.139700i −0.427420 0.904053i \(-0.640578\pi\)
0.644799 + 0.764352i \(0.276941\pi\)
\(18\) 19.8888 + 162.854i 0.0144686 + 0.118472i
\(19\) −828.997 + 1289.94i −0.526828 + 0.819761i −0.998061 0.0622485i \(-0.980173\pi\)
0.471233 + 0.882009i \(0.343809\pi\)
\(20\) −1003.33 + 1157.90i −0.560878 + 0.647287i
\(21\) −2165.64 + 1585.51i −1.07161 + 0.784552i
\(22\) 422.785i 0.186236i
\(23\) −2044.96 + 1501.50i −0.806055 + 0.591841i
\(24\) 406.458 531.094i 0.144042 0.188210i
\(25\) 734.854 + 215.773i 0.235153 + 0.0690472i
\(26\) −282.973 245.198i −0.0820941 0.0711349i
\(27\) −3103.33 + 2172.15i −0.819254 + 0.573430i
\(28\) 5375.95 + 772.945i 1.29587 + 0.186317i
\(29\) −2625.45 4085.28i −0.579707 0.902041i 0.420279 0.907395i \(-0.361932\pi\)
−0.999986 + 0.00535364i \(0.998296\pi\)
\(30\) 498.326 + 113.969i 0.101090 + 0.0231197i
\(31\) −4374.58 5048.53i −0.817583 0.943541i 0.181624 0.983368i \(-0.441865\pi\)
−0.999207 + 0.0398272i \(0.987319\pi\)
\(32\) −2014.12 + 289.587i −0.347705 + 0.0499924i
\(33\) 8616.75 4586.79i 1.37739 0.733203i
\(34\) 58.5672 + 199.461i 0.00868874 + 0.0295911i
\(35\) 2356.09 + 8024.10i 0.325103 + 1.10720i
\(36\) 7562.29 + 1252.03i 0.972516 + 0.161012i
\(37\) −10053.0 + 1445.40i −1.20723 + 0.173574i −0.716406 0.697683i \(-0.754214\pi\)
−0.490827 + 0.871257i \(0.663305\pi\)
\(38\) −677.952 782.398i −0.0761623 0.0878959i
\(39\) 1927.38 8427.40i 0.202911 0.887222i
\(40\) −1126.59 1753.01i −0.111331 0.173234i
\(41\) 12174.1 + 1750.37i 1.13104 + 0.162618i 0.682318 0.731055i \(-0.260972\pi\)
0.448717 + 0.893674i \(0.351881\pi\)
\(42\) −615.176 1704.51i −0.0538117 0.149100i
\(43\) 13024.2 + 11285.5i 1.07419 + 0.930789i 0.997800 0.0662895i \(-0.0211161\pi\)
0.0763870 + 0.997078i \(0.475662\pi\)
\(44\) −18952.8 5565.06i −1.47585 0.433349i
\(45\) 3083.55 + 11392.8i 0.226996 + 0.838685i
\(46\) −583.704 1610.35i −0.0406723 0.112208i
\(47\) 2734.58i 0.180570i −0.995916 0.0902850i \(-0.971222\pi\)
0.995916 0.0902850i \(-0.0287778\pi\)
\(48\) −9028.49 12331.9i −0.565603 0.772553i
\(49\) 8407.41 9702.67i 0.500233 0.577299i
\(50\) −279.559 + 435.003i −0.0158143 + 0.0246075i
\(51\) −3429.81 + 3357.61i −0.184648 + 0.180761i
\(52\) −14716.6 + 9457.78i −0.754743 + 0.485044i
\(53\) 10138.0 + 22199.0i 0.495748 + 1.08554i 0.977828 + 0.209410i \(0.0671542\pi\)
−0.482080 + 0.876127i \(0.660119\pi\)
\(54\) −816.843 2423.54i −0.0381201 0.113101i
\(55\) −4328.52 30105.5i −0.192945 1.34196i
\(56\) −3068.62 + 6719.34i −0.130759 + 0.286323i
\(57\) 8590.89 22305.5i 0.350228 0.909338i
\(58\) 3145.88 923.714i 0.122793 0.0360552i
\(59\) 33513.7 + 15305.2i 1.25341 + 0.572412i 0.927795 0.373091i \(-0.121702\pi\)
0.325613 + 0.945503i \(0.394429\pi\)
\(60\) 11668.5 20839.1i 0.418442 0.747309i
\(61\) 34828.1 30178.8i 1.19841 1.03843i 0.200133 0.979769i \(-0.435863\pi\)
0.998278 0.0586598i \(-0.0186827\pi\)
\(62\) 4102.59 1873.59i 0.135544 0.0619007i
\(63\) 28065.4 31030.1i 0.890882 0.984990i
\(64\) −4269.51 + 29695.1i −0.130295 + 0.906223i
\(65\) −22660.2 14562.8i −0.665243 0.427526i
\(66\) 1332.34 + 6454.49i 0.0376493 + 0.182390i
\(67\) −1671.88 + 5693.91i −0.0455008 + 0.154961i −0.979110 0.203332i \(-0.934823\pi\)
0.933609 + 0.358293i \(0.116641\pi\)
\(68\) 9712.48 0.254717
\(69\) 26487.8 29367.1i 0.669766 0.742572i
\(70\) −5646.25 −0.137726
\(71\) −15435.2 + 52567.3i −0.363384 + 1.23757i 0.551610 + 0.834102i \(0.314014\pi\)
−0.914994 + 0.403468i \(0.867805\pi\)
\(72\) −4531.57 + 9388.89i −0.103019 + 0.213444i
\(73\) −17961.2 11543.0i −0.394484 0.253519i 0.328329 0.944564i \(-0.393515\pi\)
−0.722813 + 0.691044i \(0.757151\pi\)
\(74\) 975.876 6787.37i 0.0207164 0.144086i
\(75\) −11898.7 978.330i −0.244256 0.0200832i
\(76\) −43997.6 + 20093.0i −0.873765 + 0.399035i
\(77\) −81483.7 + 70606.0i −1.56619 + 1.35711i
\(78\) 5092.74 + 2851.59i 0.0947796 + 0.0530701i
\(79\) 10415.3 + 4756.52i 0.187761 + 0.0857475i 0.507077 0.861901i \(-0.330726\pi\)
−0.319316 + 0.947648i \(0.603453\pi\)
\(80\) −45692.1 + 13416.4i −0.798208 + 0.234375i
\(81\) 40532.1 42941.0i 0.686415 0.727210i
\(82\) −3449.59 + 7553.54i −0.0566542 + 0.124055i
\(83\) −4134.05 28752.9i −0.0658688 0.458128i −0.995886 0.0906124i \(-0.971118\pi\)
0.930017 0.367516i \(-0.119792\pi\)
\(84\) −84508.2 + 5141.27i −1.30678 + 0.0795009i
\(85\) 6212.53 + 13603.6i 0.0932656 + 0.204223i
\(86\) −9788.27 + 6290.54i −0.142712 + 0.0917153i
\(87\) 52955.8 + 54094.6i 0.750093 + 0.766223i
\(88\) 14524.6 22600.7i 0.199939 0.311111i
\(89\) −9058.24 + 10453.8i −0.121218 + 0.139894i −0.813115 0.582103i \(-0.802230\pi\)
0.691896 + 0.721997i \(0.256775\pi\)
\(90\) −7966.89 169.518i −0.103677 0.00220602i
\(91\) 95486.2i 1.20875i
\(92\) −79872.9 + 4969.84i −0.983852 + 0.0612171i
\(93\) 82694.6 + 63288.0i 0.991447 + 0.758777i
\(94\) 1771.49 + 520.155i 0.0206785 + 0.00607175i
\(95\) −56285.6 48771.7i −0.639865 0.554446i
\(96\) 29836.2 10768.2i 0.330419 0.119252i
\(97\) −32913.9 4732.31i −0.355182 0.0510674i −0.0375854 0.999293i \(-0.511967\pi\)
−0.317596 + 0.948226i \(0.602876\pi\)
\(98\) 4686.28 + 7291.99i 0.0492905 + 0.0766974i
\(99\) −117094. + 97179.1i −1.20073 + 0.996518i
\(100\) 15820.8 + 18258.1i 0.158208 + 0.182581i
\(101\) 135506. 19482.8i 1.32176 0.190041i 0.554936 0.831893i \(-0.312743\pi\)
0.766828 + 0.641852i \(0.221834\pi\)
\(102\) −1522.69 2860.53i −0.0144915 0.0272236i
\(103\) −21055.2 71707.4i −0.195554 0.665995i −0.997632 0.0687763i \(-0.978091\pi\)
0.802078 0.597219i \(-0.203728\pi\)
\(104\) −6703.17 22828.9i −0.0607710 0.206967i
\(105\) −61256.2 115076.i −0.542222 1.01862i
\(106\) −16309.1 + 2344.90i −0.140983 + 0.0202703i
\(107\) −70906.7 81830.7i −0.598726 0.690966i 0.372797 0.927913i \(-0.378399\pi\)
−0.971523 + 0.236947i \(0.923853\pi\)
\(108\) −119396. + 4717.16i −0.984987 + 0.0389154i
\(109\) 43086.5 + 67043.8i 0.347356 + 0.540496i 0.970342 0.241737i \(-0.0777170\pi\)
−0.622986 + 0.782233i \(0.714081\pi\)
\(110\) 20326.0 + 2922.44i 0.160166 + 0.0230284i
\(111\) 148920. 53746.9i 1.14722 0.414044i
\(112\) 127580. + 110548.i 0.961029 + 0.832736i
\(113\) 246775. + 72459.8i 1.81805 + 0.533827i 0.999193 0.0401717i \(-0.0127905\pi\)
0.818856 + 0.573999i \(0.194609\pi\)
\(114\) 12815.6 + 9808.09i 0.0923587 + 0.0706842i
\(115\) −58051.1 108693.i −0.409323 0.766403i
\(116\) 153184.i 1.05698i
\(117\) −2866.79 + 134732.i −0.0193611 + 0.909923i
\(118\) −16289.6 + 18799.2i −0.107698 + 0.124290i
\(119\) 28661.5 44598.2i 0.185538 0.288702i
\(120\) 22723.5 + 23212.2i 0.144053 + 0.147151i
\(121\) 194394. 124929.i 1.20703 0.775714i
\(122\) 12925.3 + 28302.4i 0.0786214 + 0.172157i
\(123\) −191373. + 11642.6i −1.14056 + 0.0693886i
\(124\) −29988.6 208575.i −0.175147 1.21817i
\(125\) −78506.4 + 171905.i −0.449397 + 0.984042i
\(126\) 14763.2 + 24083.4i 0.0828425 + 0.135142i
\(127\) −146723. + 43081.8i −0.807216 + 0.237020i −0.659203 0.751965i \(-0.729106\pi\)
−0.148013 + 0.988985i \(0.547288\pi\)
\(128\) −77655.1 35463.9i −0.418933 0.191320i
\(129\) −234400. 131248.i −1.24018 0.694413i
\(130\) 13744.2 11909.4i 0.0713283 0.0618064i
\(131\) 78116.4 35674.5i 0.397707 0.181627i −0.206513 0.978444i \(-0.566212\pi\)
0.604221 + 0.796817i \(0.293484\pi\)
\(132\) 306883. + 25232.4i 1.53299 + 0.126045i
\(133\) −37572.8 + 261325.i −0.184181 + 1.28101i
\(134\) −3370.56 2166.12i −0.0162158 0.0104213i
\(135\) −82977.9 164212.i −0.391857 0.775479i
\(136\) −3721.60 + 12674.6i −0.0172537 + 0.0587607i
\(137\) 134827. 0.613728 0.306864 0.951753i \(-0.400720\pi\)
0.306864 + 0.951753i \(0.400720\pi\)
\(138\) 13986.0 + 22745.1i 0.0625165 + 0.101669i
\(139\) −33800.0 −0.148382 −0.0741908 0.997244i \(-0.523637\pi\)
−0.0741908 + 0.997244i \(0.523637\pi\)
\(140\) −74320.8 + 253113.i −0.320472 + 1.09143i
\(141\) 8617.62 + 41747.7i 0.0365039 + 0.176842i
\(142\) −31117.6 19998.1i −0.129505 0.0832277i
\(143\) 49422.6 343742.i 0.202109 1.40570i
\(144\) 176697. + 159815.i 0.710104 + 0.642260i
\(145\) 214553. 97983.3i 0.847453 0.387019i
\(146\) 10894.1 9439.83i 0.0422971 0.0366507i
\(147\) −97776.1 + 174621.i −0.373198 + 0.666506i
\(148\) −291423. 133088.i −1.09363 0.499443i
\(149\) 473477. 139025.i 1.74716 0.513013i 0.757057 0.653349i \(-0.226637\pi\)
0.990104 + 0.140337i \(0.0448185\pi\)
\(150\) 2897.07 7522.00i 0.0105131 0.0272964i
\(151\) 112782. 246957.i 0.402528 0.881413i −0.594480 0.804111i \(-0.702642\pi\)
0.997008 0.0773028i \(-0.0246308\pi\)
\(152\) −9362.15 65115.2i −0.0328675 0.228598i
\(153\) 41780.6 62067.8i 0.144293 0.214357i
\(154\) −30239.9 66216.2i −0.102749 0.224990i
\(155\) 272954. 175417.i 0.912557 0.586465i
\(156\) 194868. 190765.i 0.641103 0.627607i
\(157\) −62372.2 + 97053.0i −0.201949 + 0.314239i −0.927425 0.374008i \(-0.877983\pi\)
0.725476 + 0.688247i \(0.241619\pi\)
\(158\) −5062.46 + 5842.39i −0.0161332 + 0.0186186i
\(159\) −224729. 306956.i −0.704963 0.962903i
\(160\) 98833.5i 0.305214i
\(161\) −212884. + 381430.i −0.647260 + 1.15971i
\(162\) 20107.8 + 34425.1i 0.0601974 + 0.103059i
\(163\) −242422. 71181.6i −0.714666 0.209845i −0.0958672 0.995394i \(-0.530562\pi\)
−0.618799 + 0.785549i \(0.712381\pi\)
\(164\) 293208. + 254066.i 0.851268 + 0.737628i
\(165\) 160955. + 445968.i 0.460250 + 1.27525i
\(166\) 19412.8 + 2791.14i 0.0546786 + 0.00786160i
\(167\) −332876. 517965.i −0.923615 1.43717i −0.899233 0.437470i \(-0.855875\pi\)
−0.0243816 0.999703i \(-0.507762\pi\)
\(168\) 25672.4 112252.i 0.0701767 0.306845i
\(169\) 41739.4 + 48169.8i 0.112416 + 0.129735i
\(170\) −9994.23 + 1436.95i −0.0265233 + 0.00381347i
\(171\) −60861.2 + 367602.i −0.159166 + 0.961364i
\(172\) 153154. + 521596.i 0.394737 + 1.34435i
\(173\) 46329.5 + 157784.i 0.117691 + 0.400818i 0.997175 0.0751094i \(-0.0239306\pi\)
−0.879484 + 0.475928i \(0.842112\pi\)
\(174\) −45115.9 + 24015.7i −0.112968 + 0.0601344i
\(175\) 130525. 18766.7i 0.322181 0.0463227i
\(176\) −402056. 463998.i −0.978375 1.12910i
\(177\) −559872. 128045.i −1.34325 0.307205i
\(178\) −5049.05 7856.47i −0.0119443 0.0185856i
\(179\) 252086. + 36244.5i 0.588053 + 0.0845492i 0.429917 0.902868i \(-0.358543\pi\)
0.158135 + 0.987417i \(0.449452\pi\)
\(180\) −112466. + 354913.i −0.258727 + 0.816471i
\(181\) 185867. + 161055.i 0.421703 + 0.365407i 0.839709 0.543037i \(-0.182726\pi\)
−0.418006 + 0.908444i \(0.637271\pi\)
\(182\) −61856.9 18162.8i −0.138423 0.0406448i
\(183\) −436603. + 570482.i −0.963739 + 1.25926i
\(184\) 24119.9 106137.i 0.0525208 0.231112i
\(185\) 493303.i 1.05970i
\(186\) −56728.3 + 41532.1i −0.120231 + 0.0880241i
\(187\) −126262. + 145715.i −0.264040 + 0.304719i
\(188\) 46635.7 72566.5i 0.0962329 0.149741i
\(189\) −330677. + 562168.i −0.673363 + 1.14475i
\(190\) 42301.1 27185.3i 0.0850096 0.0546324i
\(191\) 231368. + 506624.i 0.458901 + 1.00485i 0.987737 + 0.156129i \(0.0499015\pi\)
−0.528836 + 0.848724i \(0.677371\pi\)
\(192\) −28398.8 466798.i −0.0555964 0.913852i
\(193\) 73262.5 + 509552.i 0.141576 + 0.984679i 0.929478 + 0.368879i \(0.120258\pi\)
−0.787902 + 0.615801i \(0.788833\pi\)
\(194\) 9326.34 20421.8i 0.0177913 0.0389574i
\(195\) 391837. + 150915.i 0.737936 + 0.284213i
\(196\) 388574. 114096.i 0.722494 0.212143i
\(197\) −363769. 166128.i −0.667821 0.304984i 0.0525035 0.998621i \(-0.483280\pi\)
−0.720325 + 0.693637i \(0.756007\pi\)
\(198\) −40680.7 94339.4i −0.0737438 0.171013i
\(199\) 178259. 154462.i 0.319093 0.276496i −0.480555 0.876965i \(-0.659565\pi\)
0.799648 + 0.600469i \(0.205019\pi\)
\(200\) −29888.7 + 13649.7i −0.0528362 + 0.0241295i
\(201\) 7580.45 92195.3i 0.0132344 0.160960i
\(202\) −13154.0 + 91487.8i −0.0226818 + 0.157756i
\(203\) −703397. 452046.i −1.19801 0.769914i
\(204\) −148277. + 30607.5i −0.249458 + 0.0514934i
\(205\) −168303. + 573187.i −0.279709 + 0.952602i
\(206\) 50457.8 0.0828438
\(207\) −311832. + 531808.i −0.505819 + 0.862639i
\(208\) −543733. −0.871420
\(209\) 270517. 921297.i 0.428380 1.45893i
\(210\) 86199.0 17793.3i 0.134882 0.0278425i
\(211\) −291426. 187288.i −0.450632 0.289604i 0.295573 0.955320i \(-0.404490\pi\)
−0.746205 + 0.665717i \(0.768126\pi\)
\(212\) −109556. + 761981.i −0.167416 + 1.16441i
\(213\) 69984.3 851166.i 0.105694 1.28548i
\(214\) 66498.2 30368.7i 0.0992602 0.0453306i
\(215\) −632596. + 548148.i −0.933319 + 0.808726i
\(216\) 39594.0 157617.i 0.0577424 0.229863i
\(217\) −1.04624e6 477803.i −1.50828 0.688809i
\(218\) −51627.3 + 15159.1i −0.0735764 + 0.0216040i
\(219\) 310583. + 119620.i 0.437590 + 0.168536i
\(220\) 398557. 872718.i 0.555180 1.21567i
\(221\) 24300.9 + 169017.i 0.0334690 + 0.232782i
\(222\) 6491.07 + 106695.i 0.00883963 + 0.145299i
\(223\) 554759. + 1.21475e6i 0.747036 + 1.63578i 0.771620 + 0.636084i \(0.219447\pi\)
−0.0245834 + 0.999698i \(0.507826\pi\)
\(224\) −294737. + 189416.i −0.392478 + 0.252230i
\(225\) 184736. 22561.2i 0.243273 0.0297102i
\(226\) −93880.3 + 146081.i −0.122265 + 0.190249i
\(227\) −137627. + 158830.i −0.177272 + 0.204582i −0.837431 0.546543i \(-0.815943\pi\)
0.660159 + 0.751126i \(0.270489\pi\)
\(228\) 608373. 445404.i 0.775056 0.567436i
\(229\) 124225.i 0.156538i −0.996932 0.0782691i \(-0.975061\pi\)
0.996932 0.0782691i \(-0.0249393\pi\)
\(230\) 81454.6 16931.1i 0.101530 0.0211041i
\(231\) 1.02147e6 1.33470e6i 1.25950 1.64571i
\(232\) 199902. + 58696.6i 0.243836 + 0.0715967i
\(233\) 314027. + 272106.i 0.378946 + 0.328359i 0.823419 0.567433i \(-0.192064\pi\)
−0.444473 + 0.895792i \(0.646609\pi\)
\(234\) −86735.2 27485.0i −0.103551 0.0328138i
\(235\) 131469. + 18902.4i 0.155293 + 0.0223278i
\(236\) 628325. + 977693.i 0.734352 + 1.14267i
\(237\) −173996. 39793.5i −0.201219 0.0460195i
\(238\) 23439.3 + 27050.4i 0.0268227 + 0.0309551i
\(239\) 276531. 39759.2i 0.313148 0.0450239i 0.0160510 0.999871i \(-0.494891\pi\)
0.297097 + 0.954847i \(0.403981\pi\)
\(240\) 655283. 348815.i 0.734346 0.390901i
\(241\) −292153. 994982.i −0.324017 1.10350i −0.946991 0.321259i \(-0.895894\pi\)
0.622974 0.782242i \(-0.285924\pi\)
\(242\) 43954.0 + 149694.i 0.0482459 + 0.164310i
\(243\) −483465. + 783294.i −0.525230 + 0.850960i
\(244\) 1.43889e6 206881.i 1.54723 0.222457i
\(245\) 408355. + 471267.i 0.434633 + 0.501593i
\(246\) 28859.6 126188.i 0.0304055 0.132947i
\(247\) −459742. 715373.i −0.479482 0.746088i
\(248\) 283678. + 40786.7i 0.292884 + 0.0421104i
\(249\) 153723. + 425931.i 0.157124 + 0.435353i
\(250\) −96428.7 83556.0i −0.0975790 0.0845527i
\(251\) 206579. + 60657.0i 0.206967 + 0.0607710i 0.383573 0.923511i \(-0.374694\pi\)
−0.176606 + 0.984282i \(0.556512\pi\)
\(252\) 1.27395e6 344805.i 1.26372 0.342036i
\(253\) 963787. 1.26293e6i 0.946629 1.24044i
\(254\) 103244.i 0.100410i
\(255\) −137714. 188102.i −0.132626 0.181152i
\(256\) −590931. + 681971.i −0.563556 + 0.650378i
\(257\) −136861. + 212960.i −0.129255 + 0.201125i −0.899849 0.436202i \(-0.856323\pi\)
0.770594 + 0.637326i \(0.219960\pi\)
\(258\) 129610. 126881.i 0.121224 0.118672i
\(259\) −1.47111e6 + 945424.i −1.36268 + 0.875744i
\(260\) −352970. 772897.i −0.323821 0.709068i
\(261\) −978926. 658958.i −0.889505 0.598765i
\(262\) 8251.49 + 57390.3i 0.00742641 + 0.0516518i
\(263\) −39174.4 + 85779.9i −0.0349231 + 0.0764709i −0.926290 0.376812i \(-0.877020\pi\)
0.891366 + 0.453283i \(0.149747\pi\)
\(264\) −150518. + 390808.i −0.132917 + 0.345107i
\(265\) −1.13733e6 + 333949.i −0.994880 + 0.292123i
\(266\) −162142. 74047.6i −0.140505 0.0641663i
\(267\) 105345. 188139.i 0.0904349 0.161511i
\(268\) −141470. + 122585.i −0.120318 + 0.104256i
\(269\) 665156. 303766.i 0.560457 0.255952i −0.114982 0.993368i \(-0.536681\pi\)
0.675440 + 0.737415i \(0.263954\pi\)
\(270\) 122162. 22518.5i 0.101982 0.0187988i
\(271\) 249232. 1.73345e6i 0.206149 1.43380i −0.579423 0.815027i \(-0.696722\pi\)
0.785572 0.618770i \(-0.212369\pi\)
\(272\) 253958. + 163209.i 0.208133 + 0.133759i
\(273\) −300911. 1.45775e6i −0.244360 1.18379i
\(274\) −25646.0 + 87342.3i −0.0206369 + 0.0702827i
\(275\) −479593. −0.382421
\(276\) 1.20373e6 327580.i 0.951163 0.258848i
\(277\) 1.94623e6 1.52403 0.762017 0.647557i \(-0.224209\pi\)
0.762017 + 0.647557i \(0.224209\pi\)
\(278\) 6429.24 21896.0i 0.00498939 0.0169923i
\(279\) −1.46191e6 705593.i −1.12437 0.542680i
\(280\) −301830. 193975.i −0.230074 0.147860i
\(281\) −154343. + 1.07348e6i −0.116606 + 0.811015i 0.844642 + 0.535332i \(0.179813\pi\)
−0.961248 + 0.275684i \(0.911096\pi\)
\(282\) −28683.8 2358.43i −0.0214790 0.00176604i
\(283\) 80136.1 36596.9i 0.0594788 0.0271631i −0.385454 0.922727i \(-0.625955\pi\)
0.444932 + 0.895564i \(0.353228\pi\)
\(284\) −1.30608e6 + 1.13173e6i −0.960893 + 0.832619i
\(285\) 1.01299e6 + 567203.i 0.738740 + 0.413644i
\(286\) 213278. + 97400.9i 0.154181 + 0.0704122i
\(287\) 2.03189e6 596617.i 1.45611 0.427554i
\(288\) −421563. + 258418.i −0.299489 + 0.183587i
\(289\) −550447. + 1.20531e6i −0.387678 + 0.848896i
\(290\) 22663.4 + 157628.i 0.0158245 + 0.110062i
\(291\) 517397. 31477.1i 0.358172 0.0217903i
\(292\) −279776. 612624.i −0.192023 0.420472i
\(293\) −1.62526e6 + 1.04449e6i −1.10600 + 0.710782i −0.960417 0.278565i \(-0.910141\pi\)
−0.145580 + 0.989346i \(0.546505\pi\)
\(294\) −94523.1 96555.8i −0.0637778 0.0651493i
\(295\) −967477. + 1.50542e6i −0.647270 + 1.00717i
\(296\) 285344. 329305.i 0.189295 0.218458i
\(297\) 1.48138e6 1.85260e6i 0.974484 1.21868i
\(298\) 333167.i 0.217331i
\(299\) −286330. 1.37751e6i −0.185220 0.891083i
\(300\) −299067. 228883.i −0.191851 0.146828i
\(301\) 2.84704e6 + 835968.i 1.81125 + 0.531831i
\(302\) 138529. + 120036.i 0.0874022 + 0.0757345i
\(303\) −2.00731e6 + 724461.i −1.25605 + 0.453324i
\(304\) −1.48808e6 213953.i −0.923509 0.132781i
\(305\) 1.21014e6 + 1.88302e6i 0.744881 + 1.15906i
\(306\) 32260.9 + 38872.0i 0.0196958 + 0.0237320i
\(307\) −842939. 972804.i −0.510447 0.589087i 0.440766 0.897622i \(-0.354707\pi\)
−0.951213 + 0.308535i \(0.900161\pi\)
\(308\) −3.36642e6 + 484019.i −2.02205 + 0.290727i
\(309\) 547417. + 1.02838e6i 0.326153 + 0.612711i
\(310\) 61717.0 + 210189.i 0.0364755 + 0.124224i
\(311\) −423893. 1.44365e6i −0.248516 0.846369i −0.985386 0.170335i \(-0.945515\pi\)
0.736870 0.676035i \(-0.236303\pi\)
\(312\) 174276. + 327395.i 0.101357 + 0.190408i
\(313\) 1.51640e6 218026.i 0.874891 0.125790i 0.309783 0.950807i \(-0.399744\pi\)
0.565108 + 0.825017i \(0.308834\pi\)
\(314\) −51007.8 58866.1i −0.0291953 0.0336931i
\(315\) 1.29782e6 + 1.56378e6i 0.736949 + 0.887970i
\(316\) 195270. + 303846.i 0.110006 + 0.171173i
\(317\) −2.53339e6 364246.i −1.41597 0.203585i −0.608526 0.793534i \(-0.708239\pi\)
−0.807441 + 0.589948i \(0.799148\pi\)
\(318\) 241595. 87194.5i 0.133974 0.0483528i
\(319\) 2.29819e6 + 1.99139e6i 1.26447 + 1.09567i
\(320\) −1.39812e6 410526.i −0.763256 0.224112i
\(321\) 1.34038e6 + 1.02582e6i 0.726049 + 0.555662i
\(322\) −206600. 210462.i −0.111043 0.113118i
\(323\) 472123.i 0.251796i
\(324\) 1.80790e6 448274.i 0.956782 0.237236i
\(325\) −278144. + 320995.i −0.146070 + 0.168574i
\(326\) 92224.3 143504.i 0.0480619 0.0747858i
\(327\) −869062. 887751.i −0.449450 0.459115i
\(328\) −443902. + 285279.i −0.227826 + 0.146415i
\(329\) −195592. 428287.i −0.0996236 0.218145i
\(330\) −319518. + 19438.7i −0.161514 + 0.00982611i
\(331\) −261331. 1.81760e6i −0.131105 0.911859i −0.944117 0.329611i \(-0.893082\pi\)
0.813011 0.582248i \(-0.197827\pi\)
\(332\) 380650. 833508.i 0.189531 0.415016i
\(333\) −2.10413e6 + 1.28983e6i −1.03983 + 0.637415i
\(334\) 398860. 117116.i 0.195639 0.0574447i
\(335\) −262186. 119736.i −0.127643 0.0582927i
\(336\) −2.29608e6 1.28565e6i −1.10953 0.621261i
\(337\) 205433. 178008.i 0.0985360 0.0853819i −0.604200 0.796833i \(-0.706507\pi\)
0.702736 + 0.711451i \(0.251962\pi\)
\(338\) −39144.3 + 17876.6i −0.0186370 + 0.00851125i
\(339\) −3.99576e6 328538.i −1.88843 0.155270i
\(340\) −67136.1 + 466941.i −0.0314962 + 0.219061i
\(341\) 3.51907e6 + 2.26157e6i 1.63886 + 1.05323i
\(342\) −226560. 109350.i −0.104741 0.0505536i
\(343\) −192507. + 655617.i −0.0883507 + 0.300895i
\(344\) −739358. −0.336867
\(345\) 1.22877e6 + 1.47643e6i 0.555807 + 0.667831i
\(346\) −111027. −0.0498582
\(347\) 644112. 2.19364e6i 0.287169 0.978007i −0.681947 0.731402i \(-0.738867\pi\)
0.969116 0.246606i \(-0.0793153\pi\)
\(348\) 482737. + 2.33860e6i 0.213679 + 1.03516i
\(349\) −2.46440e6 1.58377e6i −1.08305 0.696033i −0.127788 0.991801i \(-0.540788\pi\)
−0.955260 + 0.295769i \(0.904424\pi\)
\(350\) −12670.5 + 88125.4i −0.00552872 + 0.0384531i
\(351\) −380821. 2.06593e6i −0.164988 0.895050i
\(352\) 1.15907e6 529328.i 0.498599 0.227703i
\(353\) 1.92414e6 1.66728e6i 0.821863 0.712149i −0.138662 0.990340i \(-0.544280\pi\)
0.960526 + 0.278191i \(0.0897349\pi\)
\(354\) 189444. 338335.i 0.0803477 0.143496i
\(355\) −2.42056e6 1.10543e6i −1.01940 0.465544i
\(356\) −418654. + 122928.i −0.175078 + 0.0514074i
\(357\) −297019. + 771186.i −0.123343 + 0.320249i
\(358\) −71429.9 + 156410.i −0.0294559 + 0.0644994i
\(359\) 335640. + 2.33443e6i 0.137448 + 0.955969i 0.935486 + 0.353363i \(0.114962\pi\)
−0.798039 + 0.602606i \(0.794129\pi\)
\(360\) −420061. 282761.i −0.170827 0.114991i
\(361\) 51888.0 + 113619.i 0.0209556 + 0.0458863i
\(362\) −139687. + 89771.7i −0.0560255 + 0.0360054i
\(363\) −2.57404e6 + 2.51985e6i −1.02529 + 1.00371i
\(364\) −1.62843e6 + 2.53388e6i −0.644192 + 1.00238i
\(365\) 679100. 783723.i 0.266810 0.307915i
\(366\) −286516. 391350.i −0.111801 0.152708i
\(367\) 3.32446e6i 1.28841i 0.764851 + 0.644207i \(0.222813\pi\)
−0.764851 + 0.644207i \(0.777187\pi\)
\(368\) −2.17200e6 1.21224e6i −0.836065 0.466626i
\(369\) 2.88492e6 780826.i 1.10298 0.298530i
\(370\) 319567. + 93833.2i 0.121355 + 0.0356330i
\(371\) 3.17560e6 + 2.75167e6i 1.19782 + 1.03792i
\(372\) 1.11512e6 + 3.08973e6i 0.417795 + 1.15761i
\(373\) 1.16142e6 + 166987.i 0.432232 + 0.0621456i 0.354997 0.934867i \(-0.384482\pi\)
0.0772349 + 0.997013i \(0.475391\pi\)
\(374\) −70378.4 109511.i −0.0260172 0.0404836i
\(375\) 656792. 2.87181e6i 0.241185 1.05457i
\(376\) 76828.2 + 88664.5i 0.0280254 + 0.0323430i
\(377\) 2.66571e6 383271.i 0.965961 0.138884i
\(378\) −301279. 321148.i −0.108452 0.115605i
\(379\) 602475. + 2.05184e6i 0.215447 + 0.733746i 0.994308 + 0.106548i \(0.0339799\pi\)
−0.778860 + 0.627197i \(0.784202\pi\)
\(380\) −661874. 2.25414e6i −0.235135 0.800795i
\(381\) 2.10420e6 1.12009e6i 0.742633 0.395312i
\(382\) −372206. + 53515.1i −0.130504 + 0.0187637i
\(383\) −1.38523e6 1.59863e6i −0.482529 0.556868i 0.461325 0.887231i \(-0.347374\pi\)
−0.943854 + 0.330363i \(0.892829\pi\)
\(384\) 1.29729e6 + 296694.i 0.448961 + 0.102679i
\(385\) −2.83124e6 4.40550e6i −0.973476 1.51476i
\(386\) −344028. 49463.8i −0.117524 0.0168974i
\(387\) 3.99210e6 + 1.26503e6i 1.35495 + 0.429363i
\(388\) −792720. 686896.i −0.267326 0.231639i
\(389\) −4.31260e6 1.26629e6i −1.44499 0.424288i −0.537109 0.843513i \(-0.680484\pi\)
−0.907882 + 0.419225i \(0.862302\pi\)
\(390\) −172297. + 225130.i −0.0573609 + 0.0749499i
\(391\) −279746. + 729334.i −0.0925384 + 0.241260i
\(392\) 550801.i 0.181042i
\(393\) −1.08015e6 + 790801.i −0.352778 + 0.258277i
\(394\) 176813. 204053.i 0.0573818 0.0662221i
\(395\) −300671. + 467853.i −0.0969613 + 0.150875i
\(396\) −4.76457e6 + 581883.i −1.52681 + 0.186465i
\(397\) 2.34943e6 1.50989e6i 0.748145 0.480804i −0.110179 0.993912i \(-0.535142\pi\)
0.858324 + 0.513108i \(0.171506\pi\)
\(398\) 66154.6 + 144858.i 0.0209340 + 0.0458391i
\(399\) −249917. 4.10794e6i −0.0785892 1.29179i
\(400\) 106865. + 743259.i 0.0333952 + 0.232269i
\(401\) −1.85304e6 + 4.05758e6i −0.575470 + 1.26010i 0.368363 + 0.929682i \(0.379918\pi\)
−0.943833 + 0.330422i \(0.892809\pi\)
\(402\) 58283.1 + 22447.5i 0.0179878 + 0.00692793i
\(403\) 3.55460e6 1.04372e6i 1.09025 0.320128i
\(404\) 3.92812e6 + 1.79391e6i 1.19738 + 0.546825i
\(405\) 1.78428e6 + 2.24546e6i 0.540537 + 0.680249i
\(406\) 426636. 369682.i 0.128452 0.111305i
\(407\) 5.78520e6 2.64201e6i 1.73114 0.790585i
\(408\) 16874.0 205226.i 0.00501844 0.0610355i
\(409\) 940945. 6.54441e6i 0.278135 1.93447i −0.0711722 0.997464i \(-0.522674\pi\)
0.349307 0.937008i \(-0.386417\pi\)
\(410\) −339302. 218056.i −0.0996844 0.0640633i
\(411\) −2.05835e6 + 424888.i −0.601056 + 0.124071i
\(412\) 664169. 2.26195e6i 0.192768 0.656508i
\(413\) 6.34360e6 1.83004
\(414\) −285196. 303166.i −0.0817791 0.0869319i
\(415\) 1.41091e6 0.402143
\(416\) 317927. 1.08276e6i 0.0900729 0.306760i
\(417\) 516011. 106516.i 0.145318 0.0299967i
\(418\) 545369. + 350487.i 0.152669 + 0.0981142i
\(419\) 136872. 951965.i 0.0380872 0.264902i −0.961876 0.273486i \(-0.911823\pi\)
0.999963 + 0.00858374i \(0.00273232\pi\)
\(420\) 336977. 4.09839e6i 0.0932130 1.13368i
\(421\) −2.65857e6 + 1.21413e6i −0.731043 + 0.333856i −0.745922 0.666033i \(-0.767991\pi\)
0.0148793 + 0.999889i \(0.495264\pi\)
\(422\) 176760. 153164.i 0.0483174 0.0418673i
\(423\) −263123. 610188.i −0.0715004 0.165811i
\(424\) −952392. 434943.i −0.257277 0.117494i
\(425\) 226262. 66436.6i 0.0607631 0.0178417i
\(426\) 538082. + 207240.i 0.143656 + 0.0553287i
\(427\) 3.29620e6 7.21767e6i 0.874871 1.91570i
\(428\) −486080. 3.38076e6i −0.128262 0.892082i
\(429\) 328736. + 5.40351e6i 0.0862390 + 1.41753i
\(430\) −234767. 514067.i −0.0612302 0.134075i
\(431\) 2.84523e6 1.82852e6i 0.737775 0.474139i −0.117004 0.993131i \(-0.537329\pi\)
0.854779 + 0.518992i \(0.173693\pi\)
\(432\) −3.20119e6 1.88299e6i −0.825281 0.485444i
\(433\) −3.27115e6 + 5.09001e6i −0.838456 + 1.30466i 0.111969 + 0.993712i \(0.464284\pi\)
−0.950426 + 0.310952i \(0.899352\pi\)
\(434\) 508535. 586881.i 0.129597 0.149563i
\(435\) −2.96672e6 + 2.17200e6i −0.751716 + 0.550348i
\(436\) 2.51392e6i 0.633337i
\(437\) −241584. 3.88262e6i −0.0605151 0.972570i
\(438\) −136568. + 178445.i −0.0340145 + 0.0444447i
\(439\) 1.51302e6 + 444262.i 0.374699 + 0.110021i 0.463659 0.886014i \(-0.346536\pi\)
−0.0889604 + 0.996035i \(0.528354\pi\)
\(440\) 986162. + 854514.i 0.242838 + 0.210420i
\(441\) 942414. 2.97400e6i 0.230752 0.728190i
\(442\) −114113. 16407.0i −0.0277830 0.00399460i
\(443\) −3.27103e6 5.08983e6i −0.791910 1.23224i −0.968760 0.247998i \(-0.920227\pi\)
0.176850 0.984238i \(-0.443409\pi\)
\(444\) 4.86844e6 + 1.11343e6i 1.17201 + 0.268044i
\(445\) −439966. 507748.i −0.105322 0.121548i
\(446\) −892451. + 128315.i −0.212445 + 0.0305450i
\(447\) −6.79026e6 + 3.61453e6i −1.60738 + 0.855625i
\(448\) 1.45527e6 + 4.95620e6i 0.342570 + 1.16669i
\(449\) 781379. + 2.66113e6i 0.182914 + 0.622947i 0.998987 + 0.0449984i \(0.0143283\pi\)
−0.816073 + 0.577948i \(0.803854\pi\)
\(450\) −20524.0 + 123965.i −0.00477782 + 0.0288581i
\(451\) −7.62342e6 + 1.09608e6i −1.76485 + 0.253747i
\(452\) 5.31285e6 + 6.13136e6i 1.22316 + 1.41160i
\(453\) −943543. + 4.12561e6i −0.216031 + 0.944589i
\(454\) −76713.1 119368.i −0.0174675 0.0271799i
\(455\) −4.59064e6 660034.i −1.03955 0.149464i
\(456\) 348129. + 964584.i 0.0784022 + 0.217234i
\(457\) 6.11006e6 + 5.29440e6i 1.36853 + 1.18584i 0.962274 + 0.272081i \(0.0877119\pi\)
0.406258 + 0.913759i \(0.366834\pi\)
\(458\) 80474.2 + 23629.4i 0.0179264 + 0.00526367i
\(459\) −442249. + 1.07923e6i −0.0979796 + 0.239101i
\(460\) 313177. 3.87436e6i 0.0690073 0.853699i
\(461\) 1.55690e6i 0.341200i −0.985340 0.170600i \(-0.945429\pi\)
0.985340 0.170600i \(-0.0545706\pi\)
\(462\) 670331. + 915600.i 0.146112 + 0.199573i
\(463\) −5.52402e6 + 6.37505e6i −1.19757 + 1.38207i −0.292805 + 0.956172i \(0.594589\pi\)
−0.904769 + 0.425902i \(0.859957\pi\)
\(464\) 2.57411e6 4.00540e6i 0.555051 0.863676i
\(465\) −3.61428e6 + 3.53819e6i −0.775156 + 0.758838i
\(466\) −236006. + 151672.i −0.0503451 + 0.0323548i
\(467\) −1.58185e6 3.46376e6i −0.335639 0.734946i 0.664283 0.747481i \(-0.268737\pi\)
−0.999921 + 0.0125351i \(0.996010\pi\)
\(468\) −2.37380e6 + 3.52643e6i −0.500990 + 0.744254i
\(469\) 145411. + 1.01136e6i 0.0305257 + 0.212311i
\(470\) −37252.3 + 81571.3i −0.00777873 + 0.0170331i
\(471\) 646363. 1.67823e6i 0.134253 0.348576i
\(472\) −1.51663e6 + 445323.i −0.313346 + 0.0920068i
\(473\) −9.81641e6 4.48300e6i −2.01744 0.921332i
\(474\) 58875.2 105147.i 0.0120361 0.0214957i
\(475\) −887526. + 769046.i −0.180488 + 0.156393i
\(476\) 1.52116e6 694691.i 0.307722 0.140532i
\(477\) 4.39817e6 + 3.97797e6i 0.885068 + 0.800507i
\(478\) −26843.8 + 186703.i −0.00537370 + 0.0373749i
\(479\) 3.78699e6 + 2.43375e6i 0.754145 + 0.484660i 0.860362 0.509683i \(-0.170237\pi\)
−0.106217 + 0.994343i \(0.533874\pi\)
\(480\) 311459. + 1.50885e6i 0.0617018 + 0.298912i
\(481\) 1.58685e6 5.40433e6i 0.312734 1.06507i
\(482\) 700131. 0.137266
\(483\) 2.04800e6 6.49401e6i 0.399449 1.26662i
\(484\) 7.28912e6 1.41437
\(485\) 455025. 1.54967e6i 0.0878377 0.299148i
\(486\) −415464. 462187.i −0.0797889 0.0887620i
\(487\) −505036. 324567.i −0.0964939 0.0620129i 0.491504 0.870875i \(-0.336447\pi\)
−0.587998 + 0.808862i \(0.700084\pi\)
\(488\) −281374. + 1.95700e6i −0.0534853 + 0.371998i
\(489\) 3.92528e6 + 322743.i 0.742333 + 0.0610358i
\(490\) −382966. + 174895.i −0.0720560 + 0.0329069i
\(491\) −3.90792e6 + 3.38623e6i −0.731547 + 0.633889i −0.938825 0.344393i \(-0.888085\pi\)
0.207279 + 0.978282i \(0.433539\pi\)
\(492\) −5.27694e6 2.95473e6i −0.982810 0.550306i
\(493\) −1.36010e6 621138.i −0.252031 0.115099i
\(494\) 550875. 161752.i 0.101563 0.0298216i
\(495\) −3.86263e6 6.30119e6i −0.708550 1.15587i
\(496\) 2.72078e6 5.95768e6i 0.496580 1.08736i
\(497\) 1.34247e6 + 9.33706e6i 0.243788 + 1.69558i
\(498\) −305163. + 18565.3i −0.0551389 + 0.00335451i
\(499\) −551611. 1.20786e6i −0.0991703 0.217153i 0.853544 0.521021i \(-0.174449\pi\)
−0.952714 + 0.303869i \(0.901722\pi\)
\(500\) −5.01497e6 + 3.22293e6i −0.897106 + 0.576535i
\(501\) 6.71417e6 + 6.85855e6i 1.19508 + 1.22078i
\(502\) −78588.4 + 122286.i −0.0139187 + 0.0216579i
\(503\) −5.62791e6 + 6.49495e6i −0.991806 + 1.14461i −0.00231741 + 0.999997i \(0.500738\pi\)
−0.989489 + 0.144608i \(0.953808\pi\)
\(504\) −38185.2 + 1.79460e6i −0.00669604 + 0.314697i
\(505\) 6.64930e6i 1.16024i
\(506\) 634810. + 864577.i 0.110222 + 0.150116i
\(507\) −789018. 603854.i −0.136322 0.104331i
\(508\) −4.62826e6 1.35898e6i −0.795717 0.233644i
\(509\) −2.11630e6 1.83378e6i −0.362062 0.313728i 0.454765 0.890612i \(-0.349723\pi\)
−0.816827 + 0.576883i \(0.804269\pi\)
\(510\) 148049. 53432.7i 0.0252047 0.00909665i
\(511\) −3.63869e6 523165.i −0.616444 0.0886312i
\(512\) −1.80632e6 2.81069e6i −0.304523 0.473848i
\(513\) −229301. 5.80383e6i −0.0384691 0.973692i
\(514\) −111925. 129168.i −0.0186861 0.0215649i
\(515\) 3.59298e6 516592.i 0.596948 0.0858282i
\(516\) −3.98188e6 7.48035e6i −0.658360 1.23679i
\(517\) 482438. + 1.64303e6i 0.0793807 + 0.270346i
\(518\) −332629. 1.13283e6i −0.0544673 0.185499i
\(519\) −1.20453e6 2.26282e6i −0.196290 0.368750i
\(520\) 1.14387e6 164463.i 0.185510 0.0266723i
\(521\) −4.03644e6 4.65830e6i −0.651484 0.751853i 0.329877 0.944024i \(-0.392993\pi\)
−0.981361 + 0.192171i \(0.938447\pi\)
\(522\) 613085. 508815.i 0.0984791 0.0817303i
\(523\) 3.75020e6 + 5.83543e6i 0.599515 + 0.932864i 0.999864 + 0.0165011i \(0.00525271\pi\)
−0.400348 + 0.916363i \(0.631111\pi\)
\(524\) 2.68134e6 + 385519.i 0.426603 + 0.0613362i
\(525\) −1.93354e6 + 697836.i −0.306164 + 0.110498i
\(526\) −48117.6 41694.1i −0.00758297 0.00657068i
\(527\) −1.97351e6 579476.i −0.309538 0.0908885i
\(528\) 7.60025e6 + 5.81665e6i 1.18643 + 0.908004i
\(529\) 1.92736e6 6.14099e6i 0.299449 0.954112i
\(530\) 800294.i 0.123754i
\(531\) 8.95086e6 + 190454.i 1.37762 + 0.0293126i
\(532\) −5.45370e6 + 6.29391e6i −0.835434 + 0.964142i
\(533\) −3.68765e6 + 5.73809e6i −0.562253 + 0.874882i
\(534\) 101840. + 104030.i 0.0154549 + 0.0157873i
\(535\) 4.42426e6 2.84330e6i 0.668276 0.429475i
\(536\) −105763. 231588.i −0.0159009 0.0348180i
\(537\) −3.96272e6 + 241082.i −0.593003 + 0.0360768i
\(538\) 70260.9 + 488675.i 0.0104654 + 0.0727888i
\(539\) −3.33971e6 + 7.31295e6i −0.495151 + 1.08423i
\(540\) 598522. 5.77274e6i 0.0883275 0.851917i
\(541\) 9.56226e6 2.80773e6i 1.40465 0.412442i 0.510370 0.859955i \(-0.329508\pi\)
0.894277 + 0.447513i \(0.147690\pi\)
\(542\) 1.07554e6 + 491182.i 0.157263 + 0.0718197i
\(543\) −3.34510e6 1.87303e6i −0.486866 0.272612i
\(544\) −473498. + 410288.i −0.0685995 + 0.0594418i
\(545\) −3.52106e6 + 1.60801e6i −0.507787 + 0.231899i
\(546\) 1.00158e6 + 82351.7i 0.143782 + 0.0118220i
\(547\) 581117. 4.04176e6i 0.0830415 0.577567i −0.905237 0.424907i \(-0.860307\pi\)
0.988279 0.152660i \(-0.0487840\pi\)
\(548\) 3.57786e6 + 2.29935e6i 0.508946 + 0.327080i
\(549\) 4.86766e6 1.00852e7i 0.689269 1.42809i
\(550\) 91225.4 310685.i 0.0128591 0.0437939i
\(551\) 7.44627e6 1.04486
\(552\) −33754.2 + 1.69636e6i −0.00471498 + 0.236958i
\(553\) 1.97145e6 0.274141
\(554\) −370201. + 1.26079e6i −0.0512463 + 0.174529i
\(555\) 1.55457e6 + 7.53106e6i 0.214229 + 1.03782i
\(556\) −896939. 576427.i −0.123048 0.0790784i
\(557\) −372575. + 2.59131e6i −0.0508833 + 0.353901i 0.948435 + 0.316973i \(0.102666\pi\)
−0.999318 + 0.0369283i \(0.988243\pi\)
\(558\) 735166. 812824.i 0.0999539 0.110512i
\(559\) −8.69362e6 + 3.97024e6i −1.17671 + 0.537387i
\(560\) −6.19664e6 + 5.36942e6i −0.835000 + 0.723532i
\(561\) 1.46840e6 2.62246e6i 0.196987 0.351805i
\(562\) −666054. 304177.i −0.0889547 0.0406242i
\(563\) −2.68139e6 + 787328.i −0.356525 + 0.104685i −0.455090 0.890446i \(-0.650393\pi\)
0.0985653 + 0.995131i \(0.468575\pi\)
\(564\) −483285. + 1.25481e6i −0.0639744 + 0.166104i
\(565\) −5.18940e6 + 1.13632e7i −0.683906 + 1.49754i
\(566\) 8464.84 + 58874.2i 0.00111065 + 0.00772474i
\(567\) 3.27672e6 9.62447e6i 0.428038 1.25724i
\(568\) −976422. 2.13807e6i −0.126989 0.278068i
\(569\) −5.12255e6 + 3.29206e6i −0.663293 + 0.426273i −0.828502 0.559986i \(-0.810807\pi\)
0.165209 + 0.986259i \(0.447170\pi\)
\(570\) −560124. + 548333.i −0.0722099 + 0.0706898i
\(571\) −5.90795e6 + 9.19295e6i −0.758309 + 1.17995i 0.220542 + 0.975378i \(0.429217\pi\)
−0.978851 + 0.204575i \(0.934419\pi\)
\(572\) 7.17370e6 8.27889e6i 0.916755 1.05799i
\(573\) −5.12875e6 7.00531e6i −0.652566 0.891334i
\(574\) 1.42976e6i 0.181127i
\(575\) −1.82673e6 + 662135.i −0.230411 + 0.0835174i
\(576\) 1.90460e6 + 7.03692e6i 0.239192 + 0.883744i
\(577\) 275852. + 80997.5i 0.0344935 + 0.0101282i 0.298934 0.954274i \(-0.403369\pi\)
−0.264440 + 0.964402i \(0.585187\pi\)
\(578\) −676110. 585852.i −0.0841778 0.0729405i
\(579\) −2.72424e6 7.54824e6i −0.337714 0.935728i
\(580\) 7.36454e6 + 1.05886e6i 0.909025 + 0.130698i
\(581\) −2.70404e6 4.20757e6i −0.332332 0.517119i
\(582\) −78025.1 + 341162.i −0.00954831 + 0.0417497i
\(583\) −1.00076e7 1.15494e7i −1.21944 1.40731i
\(584\) 906667. 130359.i 0.110006 0.0158164i
\(585\) −6.45760e6 1.06914e6i −0.780156 0.129165i
\(586\) −367485. 1.25154e6i −0.0442074 0.150557i
\(587\) −90424.2 307956.i −0.0108315 0.0368888i 0.953900 0.300125i \(-0.0970284\pi\)
−0.964731 + 0.263236i \(0.915210\pi\)
\(588\) −5.57265e6 + 2.96639e6i −0.664689 + 0.353822i
\(589\) 1.01388e7 1.45774e6i 1.20420 0.173138i
\(590\) −791201. 913094.i −0.0935743 0.107990i
\(591\) 6.07704e6 + 1.38984e6i 0.715688 + 0.163680i
\(592\) −5.38359e6 8.37702e6i −0.631346 0.982394i
\(593\) 6.78679e6 + 975793.i 0.792552 + 0.113952i 0.526688 0.850059i \(-0.323434\pi\)
0.265864 + 0.964010i \(0.414343\pi\)
\(594\) 918352. + 1.31204e6i 0.106793 + 0.152574i
\(595\) 1.94600e6 + 1.68622e6i 0.225347 + 0.195264i
\(596\) 1.49354e7 + 4.38543e6i 1.72227 + 0.505705i
\(597\) −2.23464e6 + 2.91986e6i −0.256609 + 0.335295i
\(598\) 946831. + 76535.5i 0.108273 + 0.00875205i
\(599\) 1.44231e7i 1.64244i −0.570609 0.821222i \(-0.693293\pi\)
0.570609 0.821222i \(-0.306707\pi\)
\(600\) 413283. 302574.i 0.0468672 0.0343126i
\(601\) 7.07789e6 8.16832e6i 0.799314 0.922458i −0.199029 0.979994i \(-0.563779\pi\)
0.998343 + 0.0575360i \(0.0183244\pi\)
\(602\) −1.08310e6 + 1.68533e6i −0.121808 + 0.189537i
\(603\) 174812. + 1.43140e6i 0.0195785 + 0.160312i
\(604\) 7.20447e6 4.63003e6i 0.803544 0.516407i
\(605\) 4.66244e6 + 1.02093e7i 0.517875 + 1.13399i
\(606\) −87494.0 1.43816e6i −0.00967824 0.159084i
\(607\) 213832. + 1.48724e6i 0.0235560 + 0.163836i 0.998204 0.0599088i \(-0.0190810\pi\)
−0.974648 + 0.223744i \(0.928172\pi\)
\(608\) 1.29615e6 2.83817e6i 0.142199 0.311372i
\(609\) 1.21630e7 + 4.68455e6i 1.32892 + 0.511829i
\(610\) −1.45002e6 + 425765.i −0.157779 + 0.0463282i
\(611\) 1.37949e6 + 629991.i 0.149491 + 0.0682702i
\(612\) 2.16722e6 934543.i 0.233897 0.100860i
\(613\) 793166. 687282.i 0.0852536 0.0738727i −0.611191 0.791483i \(-0.709309\pi\)
0.696445 + 0.717610i \(0.254764\pi\)
\(614\) 790531. 361023.i 0.0846248 0.0386469i
\(615\) 763098. 9.28099e6i 0.0813566 0.989479i
\(616\) 658301. 4.57858e6i 0.0698993 0.486160i
\(617\) −1.96649e6 1.26379e6i −0.207960 0.133648i 0.432515 0.901627i \(-0.357626\pi\)
−0.640475 + 0.767979i \(0.721263\pi\)
\(618\) −770319. + 159010.i −0.0811333 + 0.0167476i
\(619\) 2.86850e6 9.76922e6i 0.300905 1.02479i −0.660769 0.750589i \(-0.729770\pi\)
0.961673 0.274197i \(-0.0884121\pi\)
\(620\) 1.02348e7 1.06931
\(621\) 3.08471e6 9.10160e6i 0.320985 0.947084i
\(622\) 1.01584e6 0.105281
\(623\) −670982. + 2.28516e6i −0.0692614 + 0.235883i
\(624\) 8.30095e6 1.71349e6i 0.853427 0.176166i
\(625\) −5.70849e6 3.66862e6i −0.584549 0.375667i
\(626\) −147202. + 1.02381e6i −0.0150134 + 0.104420i
\(627\) −1.22655e6 + 1.49176e7i −0.124599 + 1.51541i
\(628\) −3.31029e6 + 1.51176e6i −0.334940 + 0.152962i
\(629\) −2.36335e6 + 2.04785e6i −0.238178 + 0.206382i
\(630\) −1.25989e6 + 543287.i −0.126468 + 0.0545353i
\(631\) 1.37641e6 + 628585.i 0.137618 + 0.0628479i 0.483034 0.875602i \(-0.339535\pi\)
−0.345416 + 0.938450i \(0.612262\pi\)
\(632\) −471336. + 138397.i −0.0469394 + 0.0137827i
\(633\) 5.03929e6 + 1.94087e6i 0.499874 + 0.192525i
\(634\) 717848. 1.57187e6i 0.0709266 0.155308i
\(635\) −1.05702e6 7.35173e6i −0.104028 0.723528i
\(636\) −728718. 1.19781e7i −0.0714359 1.17421i
\(637\) 2.95772e6 + 6.47650e6i 0.288808 + 0.632400i
\(638\) −1.72719e6 + 1.11000e6i −0.167992 + 0.107962i
\(639\) 1.61390e6 + 1.32149e7i 0.156360 + 1.28030i
\(640\) 2.24175e6 3.48824e6i 0.216341 0.336633i
\(641\) 8.55955e6 9.87824e6i 0.822822 0.949587i −0.176576 0.984287i \(-0.556502\pi\)
0.999398 + 0.0347002i \(0.0110476\pi\)
\(642\) −919499. + 673186.i −0.0880468 + 0.0644611i
\(643\) 1.34556e7i 1.28344i 0.766937 + 0.641722i \(0.221780\pi\)
−0.766937 + 0.641722i \(0.778220\pi\)
\(644\) −1.21542e7 + 6.49133e6i −1.15481 + 0.616764i
\(645\) 7.93018e6 1.03619e7i 0.750557 0.980707i
\(646\) −305846. 89804.5i −0.0288351 0.00846675i
\(647\) 1.90826e6 + 1.65352e6i 0.179216 + 0.155292i 0.739849 0.672773i \(-0.234897\pi\)
−0.560633 + 0.828064i \(0.689442\pi\)
\(648\) −107759. + 2.53105e6i −0.0100813 + 0.236790i
\(649\) −2.28364e7 3.28338e6i −2.12821 0.305991i
\(650\) −155037. 241242.i −0.0143930 0.0223960i
\(651\) 1.74783e7 + 3.99734e6i 1.61639 + 0.369674i
\(652\) −5.21914e6 6.02320e6i −0.480817 0.554892i
\(653\) −1.38395e7 + 1.98982e6i −1.27010 + 0.182612i −0.744212 0.667943i \(-0.767175\pi\)
−0.525885 + 0.850556i \(0.676266\pi\)
\(654\) 740402. 394124.i 0.0676898 0.0360320i
\(655\) 1.17514e6 + 4.00215e6i 0.107025 + 0.364494i
\(656\) 3.39735e6 + 1.15703e7i 0.308234 + 1.04975i
\(657\) −5.11851e6 847434.i −0.462626 0.0765936i
\(658\) 314653. 45240.3i 0.0283314 0.00407344i
\(659\) −129070. 148955.i −0.0115774 0.0133611i 0.749931 0.661516i \(-0.230087\pi\)
−0.761509 + 0.648155i \(0.775541\pi\)
\(660\) −3.33437e6 + 1.45794e7i −0.297957 + 1.30281i
\(661\) −319339. 496901.i −0.0284281 0.0442350i 0.826749 0.562571i \(-0.190188\pi\)
−0.855177 + 0.518336i \(0.826552\pi\)
\(662\) 1.22717e6 + 176440.i 0.108832 + 0.0156477i
\(663\) −903624. 2.50373e6i −0.0798369 0.221209i
\(664\) 941856. + 816123.i 0.0829018 + 0.0718349i
\(665\) −1.23038e7 3.61273e6i −1.07891 0.316797i
\(666\) −435331. 1.60842e6i −0.0380307 0.140512i
\(667\) 1.15030e7 + 4.41212e6i 1.00114 + 0.384001i
\(668\) 1.94219e7i 1.68403i
\(669\) −1.22974e7 1.67969e7i −1.06230 1.45099i
\(670\) 127438. 147071.i 0.0109676 0.0126573i
\(671\) −1.56018e7 + 2.42769e7i −1.33773 + 2.08155i
\(672\) 3.90272e6 3.82056e6i 0.333383 0.326365i
\(673\) −6.54670e6 + 4.20731e6i −0.557166 + 0.358069i −0.788720 0.614753i \(-0.789256\pi\)
0.231553 + 0.972822i \(0.425619\pi\)
\(674\) 76239.4 + 166941.i 0.00646442 + 0.0141551i
\(675\) −2.74919e6 + 926599.i −0.232244 + 0.0782767i
\(676\) 286132. + 1.99009e6i 0.0240824 + 0.167497i
\(677\) −1.17483e6 + 2.57252e6i −0.0985152 + 0.215718i −0.952472 0.304625i \(-0.901469\pi\)
0.853957 + 0.520343i \(0.174196\pi\)
\(678\) 972881. 2.52600e6i 0.0812804 0.211038i
\(679\) −5.49344e6 + 1.61302e6i −0.457267 + 0.134266i
\(680\) −583625. 266533.i −0.0484018 0.0221044i
\(681\) 1.60057e6 2.85851e6i 0.132253 0.236195i
\(682\) −2.13444e6 + 1.84950e6i −0.175721 + 0.152263i
\(683\) −5.96805e6 + 2.72551e6i −0.489531 + 0.223561i −0.644859 0.764302i \(-0.723084\pi\)
0.155328 + 0.987863i \(0.450357\pi\)
\(684\) −7.88416e6 + 8.71700e6i −0.644340 + 0.712405i
\(685\) −931972. + 6.48201e6i −0.0758886 + 0.527816i
\(686\) −388098. 249415.i −0.0314870 0.0202354i
\(687\) 391477. + 1.89649e6i 0.0316457 + 0.153306i
\(688\) −4.76030e6 + 1.62121e7i −0.383410 + 1.30577i
\(689\) −1.35341e7 −1.08613
\(690\) −1.19018e6 + 515173.i −0.0951677 + 0.0411936i
\(691\) 2.65609e6 0.211615 0.105808 0.994387i \(-0.466257\pi\)
0.105808 + 0.994387i \(0.466257\pi\)
\(692\) −1.46143e6 + 4.97716e6i −0.116014 + 0.395109i
\(693\) −1.13883e7 + 2.35953e7i −0.900798 + 1.86635i
\(694\) 1.29854e6 + 834524.i 0.102343 + 0.0657718i
\(695\) 233637. 1.62498e6i 0.0183476 0.127611i
\(696\) −3.23680e6 266135.i −0.253275 0.0208247i
\(697\) 3.44474e6 1.57316e6i 0.268580 0.122657i
\(698\) 1.49475e6 1.29521e6i 0.116126 0.100624i
\(699\) −5.65163e6 3.16453e6i −0.437503 0.244972i
\(700\) 3.78376e6 + 1.72798e6i 0.291862 + 0.133289i
\(701\) 697780. 204887.i 0.0536319 0.0157478i −0.254807 0.966992i \(-0.582012\pi\)
0.308438 + 0.951244i \(0.400194\pi\)
\(702\) 1.41077e6 + 146269.i 0.108047 + 0.0112024i
\(703\) 6.46941e6 1.41660e7i 0.493715 1.08109i
\(704\) −2.67357e6 1.85951e7i −0.203311 1.41406i
\(705\) −2.06665e6 + 125730.i −0.156601 + 0.00952719i
\(706\) 714079. + 1.56362e6i 0.0539181 + 0.118064i
\(707\) 1.98293e7 1.27435e7i 1.49196 0.958826i
\(708\) −1.26734e7 1.29460e7i −0.950192 0.970625i
\(709\) −4.53587e6 + 7.05796e6i −0.338880 + 0.527307i −0.968310 0.249749i \(-0.919652\pi\)
0.629431 + 0.777057i \(0.283288\pi\)
\(710\) 1.17653e6 1.35779e6i 0.0875907 0.101085i
\(711\) 2.78173e6 + 59189.0i 0.206367 + 0.00439104i
\(712\) 593439.i 0.0438709i
\(713\) 1.65262e7 + 3.75562e6i 1.21744 + 0.276667i
\(714\) −443084. 339102.i −0.0325268 0.0248935i
\(715\) 1.61842e7 + 4.75212e6i 1.18393 + 0.347634i
\(716\) 6.07140e6 + 5.26090e6i 0.442595 + 0.383511i
\(717\) −4.09640e6 + 1.47844e6i −0.297580 + 0.107400i
\(718\) −1.57611e6 226610.i −0.114097 0.0164047i
\(719\) 8.77176e6 + 1.36491e7i 0.632797 + 0.984651i 0.998544 + 0.0539371i \(0.0171771\pi\)
−0.365747 + 0.930714i \(0.619187\pi\)
\(720\) −8.90471e6 + 7.39024e6i −0.640160 + 0.531285i
\(721\) −8.42656e6 9.72477e6i −0.603688 0.696693i
\(722\) −83473.3 + 12001.7i −0.00595943 + 0.000856837i
\(723\) 7.59572e6 + 1.42693e7i 0.540410 + 1.01521i
\(724\) 2.18565e6 + 7.44364e6i 0.154965 + 0.527763i
\(725\) −1.04783e6 3.56858e6i −0.0740365 0.252145i
\(726\) −1.14277e6 2.14680e6i −0.0804666 0.151164i
\(727\) 1.38842e6 199624.i 0.0974281 0.0140080i −0.0934284 0.995626i \(-0.529783\pi\)
0.190856 + 0.981618i \(0.438874\pi\)
\(728\) −2.68269e6 3.09599e6i −0.187604 0.216507i
\(729\) 4.91243e6 1.34818e7i 0.342356 0.939570i
\(730\) 378529. + 589003.i 0.0262901 + 0.0409082i
\(731\) 5.25220e6 + 755153.i 0.363537 + 0.0522687i
\(732\) −2.13150e7 + 7.69283e6i −1.47031 + 0.530650i
\(733\) −649374. 562686.i −0.0446411 0.0386817i 0.632255 0.774761i \(-0.282130\pi\)
−0.676896 + 0.736079i \(0.736675\pi\)
\(734\) −2.15362e6 632359.i −0.147546 0.0433235i
\(735\) −7.71931e6 5.90777e6i −0.527060 0.403371i
\(736\) 3.68398e6 3.61639e6i 0.250682 0.246083i
\(737\) 3.71606e6i 0.252008i
\(738\) −42925.8 + 2.01740e6i −0.00290120 + 0.136349i
\(739\) 1.16709e7 1.34690e7i 0.786129 0.907242i −0.211407 0.977398i \(-0.567804\pi\)
0.997536 + 0.0701565i \(0.0223499\pi\)
\(740\) 8.41282e6 1.30906e7i 0.564758 0.878781i
\(741\) 9.27309e6 + 9.47250e6i 0.620410 + 0.633752i
\(742\) −2.38660e6 + 1.53378e6i −0.159137 + 0.102271i
\(743\) −1.67574e6 3.66937e6i −0.111362 0.243848i 0.845743 0.533591i \(-0.179158\pi\)
−0.957105 + 0.289742i \(0.906430\pi\)
\(744\) −4.45933e6 + 271294.i −0.295350 + 0.0179683i
\(745\) 3.41100e6 + 2.37240e7i 0.225160 + 1.56602i
\(746\) −329094. + 720616.i −0.0216508 + 0.0474086i
\(747\) −3.68909e6 6.01809e6i −0.241890 0.394600i
\(748\) −5.83560e6 + 1.71349e6i −0.381357 + 0.111977i
\(749\) −1.69583e7 7.74461e6i −1.10453 0.504423i
\(750\) 1.73545e6 + 971735.i 0.112657 + 0.0630804i
\(751\) 4.80358e6 4.16232e6i 0.310788 0.269300i −0.485474 0.874251i \(-0.661353\pi\)
0.796262 + 0.604951i \(0.206807\pi\)
\(752\) 2.43882e6 1.11377e6i 0.157266 0.0718211i
\(753\) −3.34491e6 275024.i −0.214979 0.0176759i
\(754\) −258769. + 1.79978e6i −0.0165761 + 0.115290i
\(755\) 1.10932e7 + 7.12919e6i 0.708257 + 0.455169i
\(756\) −1.83623e7 + 9.27866e6i −1.16848 + 0.590447i
\(757\) 3.79101e6 1.29110e7i 0.240445 0.818880i −0.747525 0.664234i \(-0.768758\pi\)
0.987970 0.154646i \(-0.0494238\pi\)
\(758\) −1.44380e6 −0.0912714
\(759\) −1.07338e7 + 2.23178e7i −0.676317 + 1.40620i
\(760\) 3.19522e6 0.200663
\(761\) 5.71116e6 1.94504e7i 0.357489 1.21750i −0.562911 0.826518i \(-0.690319\pi\)
0.920400 0.390978i \(-0.127863\pi\)
\(762\) 325357. + 1.57618e6i 0.0202989 + 0.0983372i
\(763\) 1.15435e7 + 7.41857e6i 0.717838 + 0.461327i
\(764\) −2.50028e6 + 1.73899e7i −0.154973 + 1.07786i
\(765\) 2.69520e6 + 2.43769e6i 0.166509 + 0.150600i
\(766\) 1.29910e6 593279.i 0.0799965 0.0365332i
\(767\) −1.54417e7 + 1.33803e7i −0.947780 + 0.821256i
\(768\) 6.87238e6 1.22736e7i 0.420440 0.750878i
\(769\) −1.30210e7 5.94648e6i −0.794014 0.362614i −0.0232456 0.999730i \(-0.507400\pi\)
−0.770768 + 0.637116i \(0.780127\pi\)
\(770\) 3.39247e6 996118.i 0.206200 0.0605458i
\(771\) 1.41829e6 3.68247e6i 0.0859269 0.223102i
\(772\) −6.74578e6 + 1.47712e7i −0.407370 + 0.892016i
\(773\) −2.86930e6 1.99564e7i −0.172714 1.20125i −0.873119 0.487507i \(-0.837906\pi\)
0.700405 0.713746i \(-0.253003\pi\)
\(774\) −1.57885e6 + 2.34549e6i −0.0947304 + 0.140728i
\(775\) −2.12534e6 4.65385e6i −0.127108 0.278329i
\(776\) 1.20014e6 771282.i 0.0715446 0.0459789i
\(777\) 1.94795e7 1.90694e7i 1.15751 1.13314i
\(778\) 1.64064e6 2.55288e6i 0.0971769 0.151210i
\(779\) −1.23501e7 + 1.42528e7i −0.729169 + 0.841506i
\(780\) 7.82432e6 + 1.06872e7i 0.460479 + 0.628965i
\(781\) 3.43074e7i 2.01261i
\(782\) −419258. 319952.i −0.0245168 0.0187097i
\(783\) 1.70215e7 + 6.97510e6i 0.992185 + 0.406580i
\(784\) 1.20776e7 + 3.54629e6i 0.701761 + 0.206056i
\(785\) −4.23482e6 3.66949e6i −0.245279 0.212536i
\(786\) −306829. 850152.i −0.0177150 0.0490840i
\(787\) −1.57513e7 2.26469e6i −0.906523 0.130338i −0.326745 0.945113i \(-0.605952\pi\)
−0.579778 + 0.814774i \(0.696861\pi\)
\(788\) −6.82005e6 1.06122e7i −0.391266 0.608822i
\(789\) 327737. 1.43302e6i 0.0187427 0.0819520i
\(790\) −245888. 283770.i −0.0140175 0.0161770i
\(791\) 4.38325e7 6.30216e6i 2.49089 0.358136i
\(792\) 1.06633e6 6.44064e6i 0.0604058 0.364852i
\(793\) 7.20030e6 + 2.45220e7i 0.406600 + 1.38475i
\(794\) 531224. + 1.80918e6i 0.0299038 + 0.101843i
\(795\) 1.63107e7 8.68239e6i 0.915283 0.487216i
\(796\) 7.36458e6 1.05887e6i 0.411970 0.0592323i
\(797\) 8.20621e6 + 9.47047e6i 0.457611 + 0.528112i 0.936924 0.349532i \(-0.113660\pi\)
−0.479313 + 0.877644i \(0.659114\pi\)
\(798\) 2.70870e6 + 619490.i 0.150575 + 0.0344371i
\(799\) −455209. 708319.i −0.0252257 0.0392520i
\(800\) −1.54257e6 221788.i −0.0852158 0.0122522i
\(801\) −1.01537e6 + 3.20422e6i −0.0559168 + 0.176458i
\(802\) −2.27607e6 1.97222e6i −0.124954 0.108273i
\(803\) 1.28282e7 + 3.76669e6i 0.702063 + 0.206144i
\(804\) 1.77346e6 2.31728e6i 0.0967570 0.126426i
\(805\) −1.68663e7 1.28713e7i −0.917337 0.700055i
\(806\) 2.50123e6i 0.135618i
\(807\) −9.19739e6 + 6.73362e6i −0.497142 + 0.363969i
\(808\) −3.84619e6 + 4.43874e6i −0.207254 + 0.239184i
\(809\) 1.38376e7 2.15317e7i 0.743344 1.15667i −0.239260 0.970955i \(-0.576905\pi\)
0.982604 0.185711i \(-0.0594587\pi\)
\(810\) −1.79403e6 + 728755.i −0.0960764 + 0.0390274i
\(811\) 3.31087e6 2.12777e6i 0.176763 0.113598i −0.449268 0.893397i \(-0.648315\pi\)
0.626030 + 0.779799i \(0.284679\pi\)
\(812\) −1.09566e7 2.39916e7i −0.583156 1.27693i
\(813\) 1.65778e6 + 2.72493e7i 0.0879629 + 1.44587i
\(814\) 611094. + 4.25025e6i 0.0323257 + 0.224830i
\(815\) 5.09786e6 1.11628e7i 0.268840 0.588678i
\(816\) −4.39141e6 1.69134e6i −0.230876 0.0889210i
\(817\) −2.53547e7 + 7.44482e6i −1.32894 + 0.390211i
\(818\) 4.06055e6 + 1.85439e6i 0.212179 + 0.0968988i
\(819\) 9.18776e6 + 2.13066e7i 0.478630 + 1.10995i
\(820\) −1.42414e7 + 1.23402e7i −0.739634 + 0.640896i
\(821\) −1.91179e7 + 8.73083e6i −0.989877 + 0.452062i −0.843478 0.537164i \(-0.819496\pi\)
−0.146399 + 0.989226i \(0.546768\pi\)
\(822\) 116281. 1.41424e6i 0.00600247 0.0730035i
\(823\) 2.31063e6 1.60708e7i 0.118913 0.827061i −0.839842 0.542830i \(-0.817353\pi\)
0.958756 0.284231i \(-0.0917382\pi\)
\(824\) 2.69731e6 + 1.73346e6i 0.138393 + 0.0889395i
\(825\) 7.32175e6 1.51137e6i 0.374525 0.0773099i
\(826\) −1.20664e6 + 4.10945e6i −0.0615359 + 0.209572i
\(827\) 7.70085e6 0.391539 0.195769 0.980650i \(-0.437280\pi\)
0.195769 + 0.980650i \(0.437280\pi\)
\(828\) −1.73445e7 + 8.79440e6i −0.879195 + 0.445790i
\(829\) −2.88541e7 −1.45822 −0.729108 0.684399i \(-0.760065\pi\)
−0.729108 + 0.684399i \(0.760065\pi\)
\(830\) −268376. + 914004.i −0.0135222 + 0.0460524i
\(831\) −2.97123e7 + 6.13326e6i −1.49257 + 0.308098i
\(832\) −1.39964e7 8.99495e6i −0.700984 0.450495i
\(833\) 562568. 3.91275e6i 0.0280907 0.195375i
\(834\) −29150.7 + 354538.i −0.00145122 + 0.0176501i
\(835\) 2.72028e7 1.24231e7i 1.35020 0.616615i
\(836\) 2.28905e7 1.98347e7i 1.13276 0.981545i
\(837\) 2.45419e7 + 6.16503e6i 1.21086 + 0.304173i
\(838\) 590657. + 269744.i 0.0290553 + 0.0132691i
\(839\) 3.20873e7 9.42169e6i 1.57373 0.462087i 0.625642 0.780110i \(-0.284837\pi\)
0.948083 + 0.318023i \(0.103019\pi\)
\(840\) 5.21920e6 + 2.01016e6i 0.255215 + 0.0982951i
\(841\) −1.27587e6 + 2.79376e6i −0.0622036 + 0.136207i
\(842\) −280827. 1.95319e6i −0.0136508 0.0949434i
\(843\) −1.02662e6 1.68748e7i −0.0497555 0.817843i
\(844\) −4.53944e6 9.93999e6i −0.219354 0.480319i
\(845\) −2.60435e6 + 1.67371e6i −0.125475 + 0.0806379i
\(846\) 445336. 54387.5i 0.0213925 0.00261260i
\(847\) 2.15102e7 3.34705e7i 1.03023 1.60307i
\(848\) −1.56690e7 + 1.80830e7i −0.748259 + 0.863537i
\(849\) −1.10808e6 + 811248.i −0.0527595 + 0.0386264i
\(850\) 159212.i 0.00755838i
\(851\) 1.83877e7 1.80503e7i 0.870368 0.854400i
\(852\) 1.63730e7 2.13936e7i 0.772732 1.00968i
\(853\) 2.69757e7 + 7.92077e6i 1.26940 + 0.372731i 0.845987 0.533204i \(-0.179012\pi\)
0.423417 + 0.905935i \(0.360830\pi\)
\(854\) 4.04870e6 + 3.50821e6i 0.189964 + 0.164604i
\(855\) −1.72523e7 5.46698e6i −0.807109 0.255760i
\(856\) 4.59808e6 + 661104.i 0.214483 + 0.0308379i
\(857\) 4.40448e6 + 6.85350e6i 0.204853 + 0.318758i 0.928445 0.371471i \(-0.121146\pi\)
−0.723592 + 0.690228i \(0.757510\pi\)
\(858\) −3.56298e6 814866.i −0.165232 0.0377892i
\(859\) 2.20385e7 + 2.54338e7i 1.01906 + 1.17605i 0.984272 + 0.176660i \(0.0565293\pi\)
0.0347852 + 0.999395i \(0.488925\pi\)
\(860\) −2.61351e7 + 3.75766e6i −1.20498 + 0.173249i
\(861\) −2.91399e7 + 1.55115e7i −1.33962 + 0.713093i
\(862\) 643329. + 2.19098e6i 0.0294893 + 0.100431i
\(863\) 3.07224e6 + 1.04631e7i 0.140420 + 0.478225i 0.999431 0.0337314i \(-0.0107391\pi\)
−0.859011 + 0.511956i \(0.828921\pi\)
\(864\) 5.62146e6 5.27366e6i 0.256192 0.240341i
\(865\) −7.90593e6 + 1.13670e6i −0.359263 + 0.0516543i
\(866\) −2.67514e6 3.08727e6i −0.121214 0.139888i
\(867\) 4.60510e6 2.01357e7i 0.208061 0.909742i
\(868\) −1.96153e7 3.05219e7i −0.883679 1.37503i
\(869\) −7.09705e6 1.02040e6i −0.318807 0.0458376i
\(870\) −842734. 2.33502e6i −0.0377478 0.104590i
\(871\) −2.48719e6 2.15516e6i −0.111087 0.0962574i
\(872\) −3.28061e6 963275.i −0.146105 0.0429002i
\(873\) −7.79970e6 + 2.11105e6i −0.346372 + 0.0937481i
\(874\) 2.56115e6 + 582028.i 0.113411 + 0.0257730i
\(875\) 3.25388e7i 1.43675i
\(876\) 6.20182e6 + 8.47101e6i 0.273061 + 0.372971i
\(877\) 9.08441e6 1.04840e7i 0.398839 0.460285i −0.520436 0.853901i \(-0.674231\pi\)
0.919275 + 0.393616i \(0.128776\pi\)
\(878\) −575594. + 895642.i −0.0251988 + 0.0392101i
\(879\) 2.15207e7 2.10676e7i 0.939471 0.919694i
\(880\) 2.50865e7 1.61221e7i 1.09203 0.701803i
\(881\) −5.44451e6 1.19218e7i −0.236330 0.517490i 0.753891 0.657000i \(-0.228175\pi\)
−0.990221 + 0.139509i \(0.955447\pi\)
\(882\) 1.74733e6 + 1.17620e6i 0.0756315 + 0.0509109i
\(883\) −4.54757e6 3.16291e7i −0.196281 1.36516i −0.814959 0.579519i \(-0.803240\pi\)
0.618678 0.785645i \(-0.287669\pi\)
\(884\) −2.23756e6 + 4.89957e6i −0.0963038 + 0.210876i
\(885\) 1.00260e7 2.60316e7i 0.430297 1.11723i
\(886\) 3.91944e6 1.15085e6i 0.167741 0.0492532i
\(887\) 1.21374e7 + 5.54295e6i 0.517983 + 0.236555i 0.657212 0.753705i \(-0.271735\pi\)
−0.139230 + 0.990260i \(0.544463\pi\)
\(888\) −3.31848e6 + 5.92658e6i −0.141223 + 0.252216i
\(889\) −1.98982e7 + 1.72419e7i −0.844423 + 0.731697i
\(890\) 412612. 188434.i 0.0174609 0.00797413i
\(891\) −1.67774e7 + 3.29512e7i −0.707996 + 1.39052i
\(892\) −5.99502e6 + 4.16963e7i −0.252278 + 1.75463i
\(893\) 3.52745e6 + 2.26696e6i 0.148024 + 0.0951294i
\(894\) −1.04993e6 5.08633e6i −0.0439355 0.212844i
\(895\) −3.48501e6 + 1.18689e7i −0.145428 + 0.495281i
\(896\) −1.46988e7 −0.611664
\(897\) 8.71231e6 + 2.01276e7i 0.361537 + 0.835241i
\(898\) −1.87254e6 −0.0774890
\(899\) −9.13942e6 + 3.11260e7i −0.377155 + 1.28447i
\(900\) 5.28702e6 + 2.55179e6i 0.217573 + 0.105012i
\(901\) 6.32131e6 + 4.06246e6i 0.259415 + 0.166716i
\(902\) 740029. 5.14701e6i 0.0302853 0.210639i
\(903\) −4.60991e7 3.79035e6i −1.88137 0.154689i
\(904\) −1.00371e7 + 4.58378e6i −0.408494 + 0.186553i
\(905\) −9.02772e6 + 7.82256e6i −0.366401 + 0.317488i
\(906\) −2.49314e6 1.39599e6i −0.100908 0.0565016i
\(907\) 5.63962e6 + 2.57553e6i 0.227631 + 0.103956i 0.525966 0.850506i \(-0.323704\pi\)
−0.298335 + 0.954461i \(0.596431\pi\)
\(908\) −6.36086e6 + 1.86772e6i −0.256036 + 0.0751790i
\(909\) 2.83618e7 1.73858e7i 1.13848 0.697887i
\(910\) 1.30078e6 2.84831e6i 0.0520715 0.114021i
\(911\) 1.37671e6 + 9.57521e6i 0.0549599 + 0.382254i 0.998673 + 0.0514906i \(0.0163972\pi\)
−0.943714 + 0.330764i \(0.892694\pi\)
\(912\) 2.33921e7 1.42312e6i 0.931284 0.0566569i
\(913\) 7.55651e6 + 1.65464e7i 0.300016 + 0.656943i
\(914\) −4.59198e6 + 2.95109e6i −0.181817 + 0.116847i
\(915\) −2.44088e7 2.49337e7i −0.963815 0.984541i
\(916\) 2.11854e6 3.29652e6i 0.0834254 0.129812i
\(917\) 9.68288e6 1.11746e7i 0.380260 0.438844i
\(918\) −615014. 491778.i −0.0240867 0.0192603i
\(919\) 2.46932e7i 0.964470i 0.876042 + 0.482235i \(0.160175\pi\)
−0.876042 + 0.482235i \(0.839825\pi\)
\(920\) 4.93596e6 + 1.89325e6i 0.192266 + 0.0737462i
\(921\) 1.59345e7 + 1.21950e7i 0.618997 + 0.473732i
\(922\) 1.00858e6 + 296145.i 0.0390735 + 0.0114730i
\(923\) −2.29622e7 1.98969e7i −0.887175 0.768741i
\(924\) 4.98685e7 1.79981e7i 1.92153 0.693500i
\(925\) −7.69936e6 1.10700e6i −0.295870 0.0425396i
\(926\) −3.07908e6 4.79114e6i −0.118003 0.183616i
\(927\) −1.15980e7 1.39747e7i −0.443284 0.534125i
\(928\) 6.47101e6 + 7.46795e6i 0.246662 + 0.284663i
\(929\) −2.74730e7 + 3.95002e6i −1.04440 + 0.150162i −0.643097 0.765784i \(-0.722351\pi\)
−0.401301 + 0.915946i \(0.631442\pi\)
\(930\) −1.60459e6 3.01438e6i −0.0608354 0.114285i
\(931\) 5.54619e6 + 1.88886e7i 0.209711 + 0.714209i
\(932\) 3.69271e6 + 1.25762e7i 0.139253 + 0.474254i
\(933\) 1.10208e7 + 2.07037e7i 0.414487 + 0.778654i
\(934\) 2.54475e6 365879.i 0.0954503 0.0137237i
\(935\) −6.13267e6 7.07747e6i −0.229414 0.264758i
\(936\) −3.69234e6 4.44901e6i −0.137757 0.165987i
\(937\) 1.25748e7 + 1.95667e7i 0.467898 + 0.728064i 0.992361 0.123370i \(-0.0393701\pi\)
−0.524463 + 0.851433i \(0.675734\pi\)
\(938\) −682827. 98175.7i −0.0253398 0.00364332i
\(939\) −2.24632e7 + 8.10724e6i −0.831397 + 0.300060i
\(940\) 3.16638e6 + 2.74368e6i 0.116881 + 0.101278i
\(941\) −2.66414e7 7.82261e6i −0.980805 0.287990i −0.248248 0.968696i \(-0.579855\pi\)
−0.732556 + 0.680706i \(0.761673\pi\)
\(942\) 964223. + 737942.i 0.0354038 + 0.0270954i
\(943\) −2.75236e7 + 1.46999e7i −1.00792 + 0.538313i
\(944\) 3.61228e7i 1.31932i
\(945\) −2.47413e7 1.97837e7i −0.901244 0.720655i
\(946\) 4.77135e6 5.50644e6i 0.173346 0.200052i
\(947\) −2.50275e7 + 3.89435e7i −0.906864 + 1.41111i 0.00471797 + 0.999989i \(0.498498\pi\)
−0.911582 + 0.411119i \(0.865138\pi\)
\(948\) −3.93863e6 4.02333e6i −0.142339 0.145400i
\(949\) 9.96088e6 6.40147e6i 0.359031 0.230735i
\(950\) −329375. 721232.i −0.0118408 0.0259278i
\(951\) 3.98240e7 2.42279e6i 1.42789 0.0868690i
\(952\) 323685. + 2.25128e6i 0.0115752 + 0.0805075i
\(953\) 1.09846e7 2.40530e7i 0.391790 0.857900i −0.606247 0.795276i \(-0.707326\pi\)
0.998037 0.0626241i \(-0.0199469\pi\)
\(954\) −3.41356e6 + 2.09252e6i −0.121433 + 0.0744385i
\(955\) −2.59560e7 + 7.62136e6i −0.920935 + 0.270411i
\(956\) 8.01627e6 + 3.66091e6i 0.283679 + 0.129552i
\(957\) −4.13611e7 2.31594e7i −1.45986 0.817424i
\(958\) −2.29694e6 + 1.99031e6i −0.0808605 + 0.0700660i
\(959\) 2.11165e7 9.64359e6i 0.741439 0.338604i
\(960\) 2.26383e7 + 1.86136e6i 0.792803 + 0.0651856i
\(961\) −2.27639e6 + 1.58326e7i −0.0795129 + 0.553024i
\(962\) 3.19914e6 + 2.05596e6i 0.111454 + 0.0716271i
\(963\) −2.36958e7 1.14368e7i −0.823390 0.397411i
\(964\) 9.21573e6 3.13859e7i 0.319401 1.08778i
\(965\) −2.50038e7 −0.864347
\(966\) 3.81733e6 + 2.56196e6i 0.131618 + 0.0883345i
\(967\) −4.65449e7 −1.60069 −0.800343 0.599543i \(-0.795349\pi\)
−0.800343 + 0.599543i \(0.795349\pi\)
\(968\) −2.79302e6 + 9.51216e6i −0.0958045 + 0.326280i
\(969\) −1.48783e6 7.20772e6i −0.0509029 0.246597i
\(970\) 917341. + 589540.i 0.0313041 + 0.0201179i
\(971\) −2.56425e6 + 1.78348e7i −0.0872796 + 0.607043i 0.898497 + 0.438980i \(0.144660\pi\)
−0.985776 + 0.168063i \(0.946249\pi\)
\(972\) −2.61879e7 + 1.25410e7i −0.889068 + 0.425760i
\(973\) −5.29373e6 + 2.41757e6i −0.179258 + 0.0818646i
\(974\) 306323. 265430.i 0.0103462 0.00896505i
\(975\) 3.23474e6 5.77704e6i 0.108975 0.194623i
\(976\) 4.11000e7 + 1.87698e7i 1.38108 + 0.630716i
\(977\) −5.26551e7 + 1.54609e7i −1.76484 + 0.518203i −0.993051 0.117682i \(-0.962454\pi\)
−0.771785 + 0.635884i \(0.780636\pi\)
\(978\) −955720. + 2.48145e6i −0.0319509 + 0.0829579i
\(979\) 3.59825e6 7.87906e6i 0.119987 0.262735i
\(980\) 2.79935e6 + 1.94699e7i 0.0931092 + 0.647589i
\(981\) 1.60652e7 + 1.08142e7i 0.532985 + 0.358775i
\(982\) −1.45029e6 3.17570e6i −0.0479929 0.105090i
\(983\) 3.01505e7 1.93766e7i 0.995202 0.639578i 0.0616797 0.998096i \(-0.480354\pi\)
0.933523 + 0.358518i \(0.116718\pi\)
\(984\) 5.87786e6 5.75413e6i 0.193523 0.189449i
\(985\) 1.05013e7 1.63404e7i 0.344869 0.536626i
\(986\) 661090. 762939.i 0.0216555 0.0249918i
\(987\) 4.33571e6 + 5.92211e6i 0.141667 + 0.193501i
\(988\) 2.68241e7i 0.874243i
\(989\) −4.35791e7 3.52265e6i −1.41673 0.114519i
\(990\) 4.81670e6 1.30368e6i 0.156193 0.0422748i
\(991\) −2.74800e7 8.06886e6i −0.888859 0.260993i −0.194742 0.980855i \(-0.562387\pi\)
−0.694117 + 0.719862i \(0.744205\pi\)
\(992\) 1.02729e7 + 8.90153e6i 0.331447 + 0.287201i
\(993\) 9.71752e6 + 2.69250e7i 0.312739 + 0.866527i
\(994\) −6.30400e6 906378.i −0.202372 0.0290967i
\(995\) 6.19379e6 + 9.63772e6i 0.198335 + 0.308615i
\(996\) −3.18456e6 + 1.39244e7i −0.101719 + 0.444762i
\(997\) −1.36649e7 1.57702e7i −0.435381 0.502457i 0.495080 0.868848i \(-0.335139\pi\)
−0.930461 + 0.366391i \(0.880593\pi\)
\(998\) 887387. 127587.i 0.0282025 0.00405490i
\(999\) 2.80582e7 2.63222e7i 0.889499 0.834465i
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 69.6.g.a.5.19 380
3.2 odd 2 inner 69.6.g.a.5.20 yes 380
23.14 odd 22 inner 69.6.g.a.14.20 yes 380
69.14 even 22 inner 69.6.g.a.14.19 yes 380
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.6.g.a.5.19 380 1.1 even 1 trivial
69.6.g.a.5.20 yes 380 3.2 odd 2 inner
69.6.g.a.14.19 yes 380 69.14 even 22 inner
69.6.g.a.14.20 yes 380 23.14 odd 22 inner