Properties

Label 29.6.d.a.25.1
Level $29$
Weight $6$
Character 29.25
Analytic conductor $4.651$
Analytic rank $0$
Dimension $66$
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] = [29,6,Mod(7,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([6]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.7");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 29.d (of order \(7\), 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: \(4.65113077458\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 25.1
Character \(\chi\) \(=\) 29.25
Dual form 29.6.d.a.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.41509 + 10.5812i) q^{2} +(0.690047 - 0.332309i) q^{3} +(-77.2985 - 37.2250i) q^{4} +(19.1233 - 83.7844i) q^{5} +(1.84971 + 8.10409i) q^{6} +(-158.450 + 76.3053i) q^{7} +(364.027 - 456.475i) q^{8} +(-151.142 + 189.526i) q^{9} +O(q^{10})\) \(q+(-2.41509 + 10.5812i) q^{2} +(0.690047 - 0.332309i) q^{3} +(-77.2985 - 37.2250i) q^{4} +(19.1233 - 83.7844i) q^{5} +(1.84971 + 8.10409i) q^{6} +(-158.450 + 76.3053i) q^{7} +(364.027 - 456.475i) q^{8} +(-151.142 + 189.526i) q^{9} +(840.357 + 404.695i) q^{10} +(16.8666 + 21.1500i) q^{11} -65.7098 q^{12} +(-511.423 - 641.304i) q^{13} +(-424.732 - 1860.87i) q^{14} +(-14.6464 - 64.1700i) q^{15} +(2239.15 + 2807.81i) q^{16} -554.010 q^{17} +(-1640.40 - 2056.99i) q^{18} +(10.6979 + 5.15182i) q^{19} +(-4597.07 + 5764.55i) q^{20} +(-83.9807 + 105.308i) q^{21} +(-264.528 + 127.390i) q^{22} +(370.089 + 1621.47i) q^{23} +(99.5047 - 435.959i) q^{24} +(-3838.61 - 1848.58i) q^{25} +(8020.91 - 3862.67i) q^{26} +(-82.7278 + 362.454i) q^{27} +15088.4 q^{28} +(-4508.40 + 430.668i) q^{29} +714.369 q^{30} +(1029.85 - 4512.08i) q^{31} +(-18284.7 + 8805.46i) q^{32} +(18.6671 + 8.98960i) q^{33} +(1337.99 - 5862.10i) q^{34} +(3363.13 + 14734.8i) q^{35} +(18738.2 - 9023.84i) q^{36} +(-584.821 + 733.342i) q^{37} +(-80.3490 + 100.754i) q^{38} +(-566.017 - 272.579i) q^{39} +(-31284.1 - 39229.1i) q^{40} -2228.94 q^{41} +(-911.471 - 1142.95i) q^{42} +(2404.61 + 10535.3i) q^{43} +(-516.452 - 2262.73i) q^{44} +(12989.0 + 16287.7i) q^{45} -18050.9 q^{46} +(-1498.10 - 1878.56i) q^{47} +(2478.18 + 1193.43i) q^{48} +(8804.78 - 11040.8i) q^{49} +(28830.8 - 36152.7i) q^{50} +(-382.293 + 184.103i) q^{51} +(15659.7 + 68609.6i) q^{52} +(-651.964 + 2856.44i) q^{53} +(-3635.41 - 1750.72i) q^{54} +(2094.59 - 1008.70i) q^{55} +(-22848.4 + 100105. i) q^{56} +9.09403 q^{57} +(6331.22 - 48744.5i) q^{58} -19070.4 q^{59} +(-1256.59 + 5505.46i) q^{60} +(27375.2 - 13183.2i) q^{61} +(45256.1 + 21794.2i) q^{62} +(9486.56 - 41563.3i) q^{63} +(-23440.5 - 102700. i) q^{64} +(-63511.4 + 30585.5i) q^{65} +(-140.204 + 175.810i) q^{66} +(-3024.86 + 3793.06i) q^{67} +(42824.1 + 20623.0i) q^{68} +(794.207 + 995.904i) q^{69} -164035. q^{70} +(-46785.9 - 58667.6i) q^{71} +(31494.3 + 137985. i) q^{72} +(13666.4 + 59876.4i) q^{73} +(-6347.26 - 7959.21i) q^{74} -3263.12 q^{75} +(-635.153 - 796.457i) q^{76} +(-4286.37 - 2064.21i) q^{77} +(4251.21 - 5330.84i) q^{78} +(57406.3 - 71985.3i) q^{79} +(278071. - 133912. i) q^{80} +(-13044.6 - 57151.9i) q^{81} +(5383.10 - 23584.9i) q^{82} +(25116.4 + 12095.4i) q^{83} +(10411.7 - 5014.01i) q^{84} +(-10594.5 + 46417.4i) q^{85} -117284. q^{86} +(-2967.89 + 1795.36i) q^{87} +15794.4 q^{88} +(15242.4 - 66781.3i) q^{89} +(-203714. + 98103.4i) q^{90} +(129970. + 62590.1i) q^{91} +(31751.8 - 139114. i) q^{92} +(-788.759 - 3455.78i) q^{93} +(23495.6 - 11314.9i) q^{94} +(636.221 - 797.796i) q^{95} +(-9691.19 + 12152.4i) q^{96} +(-141126. - 67962.8i) q^{97} +(95561.2 + 119830. i) q^{98} -6557.75 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 11 q^{2} - 5 q^{3} - 171 q^{4} + 29 q^{5} + 445 q^{6} + 17 q^{7} + 1046 q^{8} - 732 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 11 q^{2} - 5 q^{3} - 171 q^{4} + 29 q^{5} + 445 q^{6} + 17 q^{7} + 1046 q^{8} - 732 q^{9} - 141 q^{10} + 1125 q^{11} - 248 q^{12} - 1789 q^{13} + 1233 q^{14} + 1061 q^{15} + 2629 q^{16} + 676 q^{17} - 10896 q^{18} - 1903 q^{19} + 4081 q^{20} - 439 q^{21} - 2980 q^{22} + 9945 q^{23} + 10741 q^{24} - 22114 q^{25} - 1641 q^{26} - 4427 q^{27} + 7508 q^{28} - 13100 q^{29} - 40018 q^{30} + 8541 q^{31} + 18996 q^{32} + 20725 q^{33} - 8839 q^{34} + 14127 q^{35} + 70172 q^{36} + 3791 q^{37} + 36322 q^{38} + 25843 q^{39} - 72621 q^{40} - 18720 q^{41} - 72614 q^{42} - 10419 q^{43} + 35796 q^{44} + 23163 q^{45} + 15848 q^{46} - 40549 q^{47} - 4194 q^{48} + 19808 q^{49} + 201932 q^{50} + 51998 q^{51} + 8330 q^{52} - 72275 q^{53} - 197108 q^{54} + 42183 q^{55} + 31599 q^{56} - 40162 q^{57} - 258031 q^{58} - 333512 q^{59} + 26920 q^{60} - 175281 q^{61} + 213745 q^{62} + 354423 q^{63} - 19790 q^{64} - 79593 q^{65} + 103783 q^{66} + 135179 q^{67} + 334644 q^{68} + 73673 q^{69} - 511678 q^{70} - 187563 q^{71} - 17551 q^{72} - 56675 q^{73} + 159980 q^{74} + 538208 q^{75} - 215041 q^{76} + 106099 q^{77} + 37481 q^{78} + 273775 q^{79} + 571652 q^{80} - 61356 q^{81} - 37092 q^{82} - 237831 q^{83} + 127523 q^{84} - 148844 q^{85} - 348400 q^{86} - 110493 q^{87} - 985638 q^{88} + 74239 q^{89} - 630714 q^{90} + 100309 q^{91} + 132694 q^{92} - 307921 q^{93} + 206074 q^{94} + 37965 q^{95} + 687094 q^{96} + 136055 q^{97} - 115704 q^{98} + 438608 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{7}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41509 + 10.5812i −0.426932 + 1.87051i 0.0618152 + 0.998088i \(0.480311\pi\)
−0.488748 + 0.872425i \(0.662546\pi\)
\(3\) 0.690047 0.332309i 0.0442665 0.0213176i −0.411620 0.911356i \(-0.635037\pi\)
0.455886 + 0.890038i \(0.349322\pi\)
\(4\) −77.2985 37.2250i −2.41558 1.16328i
\(5\) 19.1233 83.7844i 0.342087 1.49878i −0.452573 0.891727i \(-0.649494\pi\)
0.794660 0.607054i \(-0.207649\pi\)
\(6\) 1.84971 + 8.10409i 0.0209761 + 0.0919023i
\(7\) −158.450 + 76.3053i −1.22221 + 0.588586i −0.929926 0.367746i \(-0.880130\pi\)
−0.292284 + 0.956331i \(0.594415\pi\)
\(8\) 364.027 456.475i 2.01098 2.52169i
\(9\) −151.142 + 189.526i −0.621985 + 0.779944i
\(10\) 840.357 + 404.695i 2.65744 + 1.27976i
\(11\) 16.8666 + 21.1500i 0.0420287 + 0.0527023i 0.802402 0.596784i \(-0.203555\pi\)
−0.760373 + 0.649487i \(0.774984\pi\)
\(12\) −65.7098 −0.131728
\(13\) −511.423 641.304i −0.839309 1.05246i −0.997878 0.0651123i \(-0.979259\pi\)
0.158569 0.987348i \(-0.449312\pi\)
\(14\) −424.732 1860.87i −0.579156 2.53745i
\(15\) −14.6464 64.1700i −0.0168075 0.0736384i
\(16\) 2239.15 + 2807.81i 2.18667 + 2.74200i
\(17\) −554.010 −0.464938 −0.232469 0.972604i \(-0.574680\pi\)
−0.232469 + 0.972604i \(0.574680\pi\)
\(18\) −1640.40 2056.99i −1.19335 1.49641i
\(19\) 10.6979 + 5.15182i 0.00679851 + 0.00327399i 0.437280 0.899325i \(-0.355942\pi\)
−0.430481 + 0.902599i \(0.641656\pi\)
\(20\) −4597.07 + 5764.55i −2.56984 + 3.22248i
\(21\) −83.9807 + 105.308i −0.0415558 + 0.0521093i
\(22\) −264.528 + 127.390i −0.116524 + 0.0561149i
\(23\) 370.089 + 1621.47i 0.145877 + 0.639129i 0.994005 + 0.109337i \(0.0348728\pi\)
−0.848128 + 0.529792i \(0.822270\pi\)
\(24\) 99.5047 435.959i 0.0352627 0.154496i
\(25\) −3838.61 1848.58i −1.22835 0.591544i
\(26\) 8020.91 3862.67i 2.32697 1.12061i
\(27\) −82.7278 + 362.454i −0.0218395 + 0.0956850i
\(28\) 15088.4 3.63704
\(29\) −4508.40 + 430.668i −0.995468 + 0.0950927i
\(30\) 714.369 0.144917
\(31\) 1029.85 4512.08i 0.192474 0.843282i −0.782799 0.622275i \(-0.786209\pi\)
0.975272 0.221007i \(-0.0709343\pi\)
\(32\) −18284.7 + 8805.46i −3.15656 + 1.52012i
\(33\) 18.6671 + 8.98960i 0.00298395 + 0.00143700i
\(34\) 1337.99 5862.10i 0.198497 0.869673i
\(35\) 3363.13 + 14734.8i 0.464059 + 2.03317i
\(36\) 18738.2 9023.84i 2.40975 1.16047i
\(37\) −584.821 + 733.342i −0.0702293 + 0.0880648i −0.815705 0.578468i \(-0.803651\pi\)
0.745476 + 0.666533i \(0.232222\pi\)
\(38\) −80.3490 + 100.754i −0.00902654 + 0.0113189i
\(39\) −566.017 272.579i −0.0595893 0.0286967i
\(40\) −31284.1 39229.1i −3.09154 3.87666i
\(41\) −2228.94 −0.207080 −0.103540 0.994625i \(-0.533017\pi\)
−0.103540 + 0.994625i \(0.533017\pi\)
\(42\) −911.471 1142.95i −0.0797296 0.0999777i
\(43\) 2404.61 + 10535.3i 0.198323 + 0.868911i 0.971935 + 0.235251i \(0.0755912\pi\)
−0.773611 + 0.633660i \(0.781552\pi\)
\(44\) −516.452 2262.73i −0.0402160 0.176198i
\(45\) 12989.0 + 16287.7i 0.956193 + 1.19903i
\(46\) −18050.9 −1.25778
\(47\) −1498.10 1878.56i −0.0989230 0.124046i 0.729906 0.683548i \(-0.239564\pi\)
−0.828829 + 0.559502i \(0.810992\pi\)
\(48\) 2478.18 + 1193.43i 0.155249 + 0.0747642i
\(49\) 8804.78 11040.8i 0.523876 0.656920i
\(50\) 28830.8 36152.7i 1.63092 2.04510i
\(51\) −382.293 + 184.103i −0.0205812 + 0.00991138i
\(52\) 15659.7 + 68609.6i 0.803109 + 3.51865i
\(53\) −651.964 + 2856.44i −0.0318811 + 0.139680i −0.988364 0.152109i \(-0.951393\pi\)
0.956483 + 0.291789i \(0.0942506\pi\)
\(54\) −3635.41 1750.72i −0.169656 0.0817020i
\(55\) 2094.59 1008.70i 0.0933667 0.0449630i
\(56\) −22848.4 + 100105.i −0.973613 + 4.26568i
\(57\) 9.09403 0.000370740
\(58\) 6331.22 48744.5i 0.247125 1.90263i
\(59\) −19070.4 −0.713229 −0.356614 0.934252i \(-0.616069\pi\)
−0.356614 + 0.934252i \(0.616069\pi\)
\(60\) −1256.59 + 5505.46i −0.0450623 + 0.197431i
\(61\) 27375.2 13183.2i 0.941962 0.453625i 0.101101 0.994876i \(-0.467763\pi\)
0.840861 + 0.541251i \(0.182049\pi\)
\(62\) 45256.1 + 21794.2i 1.49520 + 0.720049i
\(63\) 9486.56 41563.3i 0.301132 1.31935i
\(64\) −23440.5 102700.i −0.715349 3.13415i
\(65\) −63511.4 + 30585.5i −1.86452 + 0.897908i
\(66\) −140.204 + 175.810i −0.00396186 + 0.00496802i
\(67\) −3024.86 + 3793.06i −0.0823225 + 0.103229i −0.821287 0.570515i \(-0.806744\pi\)
0.738965 + 0.673744i \(0.235315\pi\)
\(68\) 42824.1 + 20623.0i 1.12309 + 0.540854i
\(69\) 794.207 + 995.904i 0.0200822 + 0.0251823i
\(70\) −164035. −4.00120
\(71\) −46785.9 58667.6i −1.10146 1.38119i −0.917255 0.398300i \(-0.869600\pi\)
−0.184205 0.982888i \(-0.558971\pi\)
\(72\) 31494.3 + 137985.i 0.715979 + 3.13691i
\(73\) 13666.4 + 59876.4i 0.300156 + 1.31507i 0.869892 + 0.493242i \(0.164188\pi\)
−0.569736 + 0.821828i \(0.692955\pi\)
\(74\) −6347.26 7959.21i −0.134743 0.168963i
\(75\) −3263.12 −0.0669853
\(76\) −635.153 796.457i −0.0126138 0.0158171i
\(77\) −4286.37 2064.21i −0.0823877 0.0396758i
\(78\) 4251.21 5330.84i 0.0791181 0.0992109i
\(79\) 57406.3 71985.3i 1.03489 1.29770i 0.0812648 0.996693i \(-0.474104\pi\)
0.953620 0.301012i \(-0.0973245\pi\)
\(80\) 278071. 133912.i 4.85770 2.33934i
\(81\) −13044.6 57151.9i −0.220911 0.967873i
\(82\) 5383.10 23584.9i 0.0884093 0.387347i
\(83\) 25116.4 + 12095.4i 0.400186 + 0.192720i 0.623142 0.782109i \(-0.285856\pi\)
−0.222955 + 0.974829i \(0.571570\pi\)
\(84\) 10411.7 5014.01i 0.160999 0.0775330i
\(85\) −10594.5 + 46417.4i −0.159049 + 0.696841i
\(86\) −117284. −1.70998
\(87\) −2967.89 + 1795.36i −0.0420388 + 0.0254305i
\(88\) 15794.4 0.217418
\(89\) 15242.4 66781.3i 0.203976 0.893675i −0.764511 0.644610i \(-0.777020\pi\)
0.968487 0.249065i \(-0.0801233\pi\)
\(90\) −203714. + 98103.4i −2.65103 + 1.27667i
\(91\) 129970. + 62590.1i 1.64528 + 0.792323i
\(92\) 31751.8 139114.i 0.391109 1.71356i
\(93\) −788.759 3455.78i −0.00945664 0.0414322i
\(94\) 23495.6 11314.9i 0.274262 0.132078i
\(95\) 636.221 797.796i 0.00723268 0.00906949i
\(96\) −9691.19 + 12152.4i −0.107325 + 0.134581i
\(97\) −141126. 67962.8i −1.52292 0.733401i −0.529544 0.848282i \(-0.677637\pi\)
−0.993379 + 0.114881i \(0.963351\pi\)
\(98\) 95561.2 + 119830.i 1.00512 + 1.26038i
\(99\) −6557.75 −0.0672460
\(100\) 227905. + 285784.i 2.27905 + 2.85784i
\(101\) −245.589 1076.00i −0.00239556 0.0104956i 0.973716 0.227766i \(-0.0731420\pi\)
−0.976112 + 0.217270i \(0.930285\pi\)
\(102\) −1024.76 4489.75i −0.00975259 0.0427289i
\(103\) 78794.5 + 98805.2i 0.731818 + 0.917671i 0.998942 0.0459916i \(-0.0146448\pi\)
−0.267124 + 0.963662i \(0.586073\pi\)
\(104\) −478911. −4.34182
\(105\) 7217.23 + 9050.12i 0.0638847 + 0.0801089i
\(106\) −28650.1 13797.1i −0.247663 0.119268i
\(107\) 60540.4 75915.2i 0.511194 0.641017i −0.457519 0.889200i \(-0.651262\pi\)
0.968713 + 0.248183i \(0.0798334\pi\)
\(108\) 19887.1 24937.6i 0.164063 0.205729i
\(109\) −147706. + 71131.6i −1.19078 + 0.573451i −0.921035 0.389480i \(-0.872655\pi\)
−0.269748 + 0.962931i \(0.586941\pi\)
\(110\) 5614.66 + 24599.4i 0.0442427 + 0.193840i
\(111\) −159.858 + 700.382i −0.00123148 + 0.00539545i
\(112\) −569044. 274037.i −4.28648 2.06426i
\(113\) −32842.1 + 15815.9i −0.241955 + 0.116519i −0.550932 0.834550i \(-0.685728\pi\)
0.308977 + 0.951070i \(0.400013\pi\)
\(114\) −21.9629 + 96.2260i −0.000158281 + 0.000693474i
\(115\) 142931. 1.00782
\(116\) 364524. + 134535.i 2.51525 + 0.928306i
\(117\) 198842. 1.34290
\(118\) 46056.7 201788.i 0.304500 1.33410i
\(119\) 87782.7 42273.9i 0.568252 0.273656i
\(120\) −34623.7 16673.9i −0.219493 0.105702i
\(121\) 35674.4 156300.i 0.221510 0.970498i
\(122\) 73380.8 + 321502.i 0.446357 + 1.95562i
\(123\) −1538.07 + 740.698i −0.00916673 + 0.00441447i
\(124\) −247568. + 310441.i −1.44591 + 1.81311i
\(125\) −60844.3 + 76296.3i −0.348293 + 0.436746i
\(126\) 416880. + 200759.i 2.33929 + 1.12654i
\(127\) −100927. 126559.i −0.555263 0.696277i 0.422411 0.906404i \(-0.361184\pi\)
−0.977674 + 0.210127i \(0.932612\pi\)
\(128\) 493875. 2.66435
\(129\) 5160.27 + 6470.77i 0.0273022 + 0.0342359i
\(130\) −170246. 745895.i −0.883522 3.87096i
\(131\) 82930.6 + 363343.i 0.422218 + 1.84986i 0.519317 + 0.854582i \(0.326186\pi\)
−0.0970991 + 0.995275i \(0.530956\pi\)
\(132\) −1108.30 1389.77i −0.00553634 0.00694235i
\(133\) −2088.19 −0.0102362
\(134\) −32829.9 41167.3i −0.157945 0.198057i
\(135\) 28786.0 + 13862.6i 0.135940 + 0.0654652i
\(136\) −201674. + 252892.i −0.934983 + 1.17243i
\(137\) −204586. + 256543.i −0.931270 + 1.16778i 0.0543033 + 0.998524i \(0.482706\pi\)
−0.985573 + 0.169251i \(0.945865\pi\)
\(138\) −12456.0 + 5998.48i −0.0556775 + 0.0268129i
\(139\) 13934.2 + 61049.7i 0.0611709 + 0.268007i 0.996260 0.0864054i \(-0.0275380\pi\)
−0.935089 + 0.354412i \(0.884681\pi\)
\(140\) 288539. 1.26417e6i 1.24418 5.45112i
\(141\) −1658.03 798.463i −0.00702334 0.00338226i
\(142\) 733767. 353364.i 3.05378 1.47062i
\(143\) 4937.65 21633.2i 0.0201920 0.0884670i
\(144\) −870585. −3.49869
\(145\) −50132.0 + 385970.i −0.198014 + 1.52452i
\(146\) −666571. −2.58800
\(147\) 2406.74 10544.6i 0.00918619 0.0402473i
\(148\) 72504.4 34916.3i 0.272089 0.131031i
\(149\) −322180. 155154.i −1.18886 0.572527i −0.268383 0.963312i \(-0.586489\pi\)
−0.920482 + 0.390785i \(0.872203\pi\)
\(150\) 7880.74 34527.8i 0.0285982 0.125297i
\(151\) −38935.1 170586.i −0.138963 0.608836i −0.995664 0.0930228i \(-0.970347\pi\)
0.856701 0.515813i \(-0.172510\pi\)
\(152\) 6245.99 3007.91i 0.0219277 0.0105598i
\(153\) 83734.3 105000.i 0.289184 0.362626i
\(154\) 32193.8 40369.7i 0.109388 0.137168i
\(155\) −358348. 172571.i −1.19805 0.576952i
\(156\) 33605.5 + 42140.0i 0.110560 + 0.138638i
\(157\) −20207.3 −0.0654274 −0.0327137 0.999465i \(-0.510415\pi\)
−0.0327137 + 0.999465i \(0.510415\pi\)
\(158\) 623050. + 781280.i 1.98555 + 2.48980i
\(159\) 499.335 + 2187.73i 0.00156639 + 0.00686279i
\(160\) 388097. + 1.70037e6i 1.19851 + 5.25100i
\(161\) −182367. 228681.i −0.554475 0.695289i
\(162\) 636241. 1.90473
\(163\) −286909. 359773.i −0.845815 1.06062i −0.997392 0.0721727i \(-0.977007\pi\)
0.151577 0.988445i \(-0.451565\pi\)
\(164\) 172294. + 82972.4i 0.500219 + 0.240893i
\(165\) 1110.16 1392.10i 0.00317451 0.00398072i
\(166\) −188643. + 236551.i −0.531337 + 0.666276i
\(167\) 303292. 146058.i 0.841530 0.405260i 0.0371035 0.999311i \(-0.488187\pi\)
0.804427 + 0.594052i \(0.202473\pi\)
\(168\) 17499.5 + 76670.2i 0.0478357 + 0.209582i
\(169\) −67097.1 + 293971.i −0.180712 + 0.791751i
\(170\) −465566. 224205.i −1.23555 0.595008i
\(171\) −2593.31 + 1248.87i −0.00678209 + 0.00326608i
\(172\) 206303. 903874.i 0.531723 2.32963i
\(173\) −642789. −1.63288 −0.816438 0.577433i \(-0.804055\pi\)
−0.816438 + 0.577433i \(0.804055\pi\)
\(174\) −11829.4 35739.9i −0.0296203 0.0894912i
\(175\) 749282. 1.84948
\(176\) −21618.4 + 94716.4i −0.0526068 + 0.230485i
\(177\) −13159.4 + 6337.25i −0.0315722 + 0.0152043i
\(178\) 669816. + 322566.i 1.58455 + 0.763078i
\(179\) −97542.8 + 427363.i −0.227542 + 0.996929i 0.724094 + 0.689702i \(0.242258\pi\)
−0.951636 + 0.307227i \(0.900599\pi\)
\(180\) −397722. 1.74253e6i −0.914952 4.00867i
\(181\) −18462.4 + 8891.01i −0.0418881 + 0.0201723i −0.454711 0.890639i \(-0.650257\pi\)
0.412822 + 0.910812i \(0.364543\pi\)
\(182\) −976169. + 1.22408e6i −2.18447 + 2.73924i
\(183\) 14509.3 18194.1i 0.0320272 0.0401608i
\(184\) 874882. + 421321.i 1.90504 + 0.917421i
\(185\) 50259.0 + 63022.8i 0.107965 + 0.135384i
\(186\) 38471.3 0.0815369
\(187\) −9344.26 11717.3i −0.0195407 0.0245033i
\(188\) 45871.7 + 200977.i 0.0946565 + 0.414717i
\(189\) −14549.0 63743.3i −0.0296264 0.129802i
\(190\) 6905.12 + 8658.75i 0.0138767 + 0.0174009i
\(191\) −219622. −0.435605 −0.217802 0.975993i \(-0.569889\pi\)
−0.217802 + 0.975993i \(0.569889\pi\)
\(192\) −50303.1 63078.1i −0.0984786 0.123488i
\(193\) 114335. + 55060.8i 0.220946 + 0.106402i 0.541083 0.840969i \(-0.318015\pi\)
−0.320137 + 0.947371i \(0.603729\pi\)
\(194\) 1.05996e6 1.32915e6i 2.02202 2.53554i
\(195\) −33662.0 + 42210.8i −0.0633948 + 0.0794945i
\(196\) −1.09159e6 + 525683.i −2.02965 + 0.977426i
\(197\) 38283.9 + 167733.i 0.0702831 + 0.307930i 0.997835 0.0657635i \(-0.0209483\pi\)
−0.927552 + 0.373694i \(0.878091\pi\)
\(198\) 15837.6 69389.0i 0.0287095 0.125785i
\(199\) 204573. + 98517.0i 0.366197 + 0.176351i 0.607928 0.793992i \(-0.292001\pi\)
−0.241731 + 0.970343i \(0.577715\pi\)
\(200\) −2.24119e6 + 1.07930e6i −3.96189 + 1.90795i
\(201\) −826.830 + 3622.58i −0.00144353 + 0.00632452i
\(202\) 11978.5 0.0206549
\(203\) 681492. 412254.i 1.16070 0.702142i
\(204\) 36403.9 0.0612452
\(205\) −42624.6 + 186751.i −0.0708396 + 0.310368i
\(206\) −1.23578e6 + 595118.i −2.02895 + 0.977091i
\(207\) −363247. 174931.i −0.589218 0.283753i
\(208\) 655506. 2.87196e6i 1.05055 4.60277i
\(209\) 71.4754 + 313.154i 0.000113186 + 0.000495898i
\(210\) −113192. + 54510.2i −0.177119 + 0.0852961i
\(211\) 488453. 612501.i 0.755295 0.947110i −0.244451 0.969662i \(-0.578608\pi\)
0.999746 + 0.0225517i \(0.00717904\pi\)
\(212\) 156727. 196529.i 0.239499 0.300322i
\(213\) −51780.2 24936.0i −0.0782015 0.0376598i
\(214\) 657065. + 823933.i 0.980785 + 1.22987i
\(215\) 928678. 1.37015
\(216\) 135336. + 169706.i 0.197369 + 0.247493i
\(217\) 181116. + 793521.i 0.261100 + 1.14396i
\(218\) −395934. 1.73470e6i −0.564264 2.47220i
\(219\) 29327.9 + 36776.1i 0.0413210 + 0.0518150i
\(220\) −199457. −0.277839
\(221\) 283333. + 355289.i 0.390227 + 0.489329i
\(222\) −7024.82 3382.98i −0.00956650 0.00460698i
\(223\) −300241. + 376490.i −0.404303 + 0.506980i −0.941748 0.336319i \(-0.890818\pi\)
0.537445 + 0.843299i \(0.319390\pi\)
\(224\) 2.22530e6 2.79044e6i 2.96326 3.71581i
\(225\) 930530. 448120.i 1.22539 0.590116i
\(226\) −88035.0 385706.i −0.114653 0.502326i
\(227\) −103191. + 452109.i −0.132916 + 0.582343i 0.863974 + 0.503537i \(0.167968\pi\)
−0.996890 + 0.0788065i \(0.974889\pi\)
\(228\) −702.955 338.525i −0.000895551 0.000431275i
\(229\) 138509. 66702.5i 0.174538 0.0840530i −0.344575 0.938759i \(-0.611977\pi\)
0.519113 + 0.854706i \(0.326263\pi\)
\(230\) −345192. + 1.51238e6i −0.430270 + 1.88514i
\(231\) −3643.75 −0.00449281
\(232\) −1.44459e6 + 2.21475e6i −1.76208 + 2.70150i
\(233\) −62645.9 −0.0755967 −0.0377983 0.999285i \(-0.512034\pi\)
−0.0377983 + 0.999285i \(0.512034\pi\)
\(234\) −480222. + 2.10399e6i −0.573326 + 2.51191i
\(235\) −186043. + 89593.6i −0.219758 + 0.105830i
\(236\) 1.47411e6 + 709894.i 1.72286 + 0.829685i
\(237\) 15691.7 68749.9i 0.0181468 0.0795062i
\(238\) 235306. + 1.03094e6i 0.269272 + 1.17976i
\(239\) 345520. 166394.i 0.391272 0.188427i −0.227896 0.973686i \(-0.573184\pi\)
0.619168 + 0.785259i \(0.287470\pi\)
\(240\) 147382. 184811.i 0.165164 0.207109i
\(241\) 704854. 883859.i 0.781730 0.980258i −0.218261 0.975891i \(-0.570038\pi\)
0.999990 0.00436765i \(-0.00139027\pi\)
\(242\) 1.56768e6 + 754957.i 1.72076 + 0.828674i
\(243\) −84320.4 105734.i −0.0916045 0.114868i
\(244\) −2.60681e6 −2.80308
\(245\) −756675. 948841.i −0.805368 1.00990i
\(246\) −4122.89 18063.6i −0.00434374 0.0190312i
\(247\) −2167.25 9495.35i −0.00226031 0.00990304i
\(248\) −1.68476e6 2.11262e6i −1.73944 2.18119i
\(249\) 21350.9 0.0218232
\(250\) −660363. 828069.i −0.668241 0.837947i
\(251\) −1.56470e6 753520.i −1.56764 0.754937i −0.569876 0.821731i \(-0.693009\pi\)
−0.997767 + 0.0667939i \(0.978723\pi\)
\(252\) −2.28049e6 + 2.85965e6i −2.26218 + 2.83668i
\(253\) −28052.0 + 35176.0i −0.0275525 + 0.0345498i
\(254\) 1.58289e6 762281.i 1.53946 0.741363i
\(255\) 8114.25 + 35550.8i 0.00781444 + 0.0342373i
\(256\) −442657. + 1.93941e6i −0.422151 + 1.84956i
\(257\) −902312. 434530.i −0.852165 0.410381i −0.0437843 0.999041i \(-0.513941\pi\)
−0.808381 + 0.588660i \(0.799656\pi\)
\(258\) −80931.2 + 38974.4i −0.0756949 + 0.0364527i
\(259\) 36706.7 160823.i 0.0340014 0.148970i
\(260\) 6.04788e6 5.54843
\(261\) 599787. 919553.i 0.544999 0.835556i
\(262\) −4.04489e6 −3.64044
\(263\) −362876. + 1.58986e6i −0.323496 + 1.41733i 0.507788 + 0.861482i \(0.330463\pi\)
−0.831284 + 0.555847i \(0.812394\pi\)
\(264\) 10898.9 5248.61i 0.00962434 0.00463484i
\(265\) 226857. + 109249.i 0.198444 + 0.0955657i
\(266\) 5043.16 22095.5i 0.00437018 0.0191470i
\(267\) −11674.1 51147.4i −0.0100218 0.0439082i
\(268\) 375014. 180597.i 0.318941 0.153594i
\(269\) 663073. 831467.i 0.558703 0.700591i −0.419615 0.907702i \(-0.637835\pi\)
0.978317 + 0.207111i \(0.0664062\pi\)
\(270\) −216204. + 271111.i −0.180491 + 0.226328i
\(271\) −781409. 376307.i −0.646332 0.311257i 0.0818464 0.996645i \(-0.473918\pi\)
−0.728178 + 0.685388i \(0.759633\pi\)
\(272\) −1.24051e6 1.55555e6i −1.01667 1.27486i
\(273\) 110484. 0.0897211
\(274\) −2.22045e6 2.78435e6i −1.78675 2.24051i
\(275\) −25646.8 112366.i −0.0204504 0.0895989i
\(276\) −24318.5 106546.i −0.0192160 0.0841910i
\(277\) 781007. + 979352.i 0.611583 + 0.766901i 0.987133 0.159901i \(-0.0511175\pi\)
−0.375550 + 0.926802i \(0.622546\pi\)
\(278\) −679632. −0.527426
\(279\) 699505. + 877151.i 0.537997 + 0.674627i
\(280\) 7.95035e6 + 3.82869e6i 6.06026 + 2.91847i
\(281\) −500936. + 628154.i −0.378457 + 0.474570i −0.934182 0.356796i \(-0.883869\pi\)
0.555725 + 0.831366i \(0.312441\pi\)
\(282\) 12453.0 15615.6i 0.00932505 0.0116932i
\(283\) −1.08034e6 + 520265.i −0.801853 + 0.386152i −0.789484 0.613771i \(-0.789652\pi\)
−0.0123693 + 0.999923i \(0.503937\pi\)
\(284\) 1.43258e6 + 6.27652e6i 1.05395 + 4.61767i
\(285\) 173.907 761.939i 0.000126825 0.000555658i
\(286\) 216981. + 104493.i 0.156858 + 0.0755389i
\(287\) 353175. 170080.i 0.253096 0.121885i
\(288\) 1.09473e6 4.79632e6i 0.777723 3.40743i
\(289\) −1.11293e6 −0.783832
\(290\) −3.96296e6 1.46261e6i −2.76710 1.02125i
\(291\) −119968. −0.0830489
\(292\) 1.17251e6 5.13709e6i 0.804745 3.52582i
\(293\) −463510. + 223215.i −0.315421 + 0.151899i −0.584895 0.811109i \(-0.698864\pi\)
0.269474 + 0.963008i \(0.413150\pi\)
\(294\) 105762. + 50932.5i 0.0713613 + 0.0343658i
\(295\) −364687. + 1.59780e6i −0.243986 + 1.06897i
\(296\) 121862. + 533913.i 0.0808424 + 0.354194i
\(297\) −9061.26 + 4363.67i −0.00596070 + 0.00287052i
\(298\) 2.41981e6 3.03434e6i 1.57848 1.97936i
\(299\) 850581. 1.06660e6i 0.550222 0.689956i
\(300\) 252234. + 121470.i 0.161808 + 0.0779227i
\(301\) −1.18491e6 1.48583e6i −0.753821 0.945262i
\(302\) 1.89904e6 1.19816
\(303\) −527.032 660.877i −0.000329785 0.000413537i
\(304\) 9488.84 + 41573.3i 0.00588883 + 0.0258007i
\(305\) −581045. 2.54573e6i −0.357652 1.56697i
\(306\) 908797. + 1.13960e6i 0.554834 + 0.695740i
\(307\) 2.39552e6 1.45062 0.725309 0.688423i \(-0.241697\pi\)
0.725309 + 0.688423i \(0.241697\pi\)
\(308\) 254490. + 319120.i 0.152860 + 0.191680i
\(309\) 87205.8 + 41996.1i 0.0519576 + 0.0250215i
\(310\) 2.69146e6 3.37498e6i 1.59068 1.99465i
\(311\) −559787. + 701951.i −0.328187 + 0.411534i −0.918362 0.395742i \(-0.870488\pi\)
0.590174 + 0.807276i \(0.299059\pi\)
\(312\) −330471. + 159147.i −0.192197 + 0.0925573i
\(313\) 460650. + 2.01824e6i 0.265772 + 1.16442i 0.914879 + 0.403728i \(0.132286\pi\)
−0.649107 + 0.760697i \(0.724857\pi\)
\(314\) 48802.6 213818.i 0.0279331 0.122383i
\(315\) −3.30095e6 1.58965e6i −1.87440 0.902663i
\(316\) −7.11708e6 + 3.42740e6i −4.00944 + 1.93085i
\(317\) −295086. + 1.29286e6i −0.164931 + 0.722608i 0.823042 + 0.567980i \(0.192275\pi\)
−0.987973 + 0.154628i \(0.950582\pi\)
\(318\) −24354.8 −0.0135057
\(319\) −85150.0 88089.0i −0.0468498 0.0484669i
\(320\) −9.05290e6 −4.94211
\(321\) 16548.4 72503.2i 0.00896381 0.0392730i
\(322\) 2.86016e6 1.37738e6i 1.53727 0.740310i
\(323\) −5926.73 2854.16i −0.00316089 0.00152220i
\(324\) −1.11916e6 + 4.90334e6i −0.592282 + 2.59496i
\(325\) 777653. + 3.40712e6i 0.408392 + 1.78928i
\(326\) 4.49974e6 2.16696e6i 2.34501 1.12930i
\(327\) −78286.6 + 98168.3i −0.0404872 + 0.0507694i
\(328\) −811395. + 1.01746e6i −0.416435 + 0.522193i
\(329\) 380718. + 183344.i 0.193916 + 0.0933851i
\(330\) 12049.0 + 15108.9i 0.00609068 + 0.00763747i
\(331\) −2.03266e6 −1.01975 −0.509876 0.860248i \(-0.670309\pi\)
−0.509876 + 0.860248i \(0.670309\pi\)
\(332\) −1.49121e6 1.86992e6i −0.742494 0.931059i
\(333\) −50596.6 221678.i −0.0250041 0.109550i
\(334\) 812990. + 3.56194e6i 0.398767 + 1.74711i
\(335\) 259954. + 325972.i 0.126557 + 0.158697i
\(336\) −483732. −0.233753
\(337\) 1.23047e6 + 1.54296e6i 0.590197 + 0.740084i 0.983814 0.179191i \(-0.0573479\pi\)
−0.393617 + 0.919274i \(0.628776\pi\)
\(338\) −2.94853e6 1.41994e6i −1.40383 0.676048i
\(339\) −17406.8 + 21827.5i −0.00822659 + 0.0103158i
\(340\) 2.54683e6 3.19362e6i 1.19482 1.49825i
\(341\) 112801. 54322.0i 0.0525323 0.0252982i
\(342\) −6951.50 30456.5i −0.00321376 0.0140804i
\(343\) 105083. 460399.i 0.0482278 0.211300i
\(344\) 5.68444e6 + 2.73748e6i 2.58995 + 1.24726i
\(345\) 98629.1 47497.3i 0.0446126 0.0214843i
\(346\) 1.55240e6 6.80149e6i 0.697128 3.05432i
\(347\) 2.70370e6 1.20541 0.602705 0.797964i \(-0.294090\pi\)
0.602705 + 0.797964i \(0.294090\pi\)
\(348\) 296246. 28299.1i 0.131131 0.0125263i
\(349\) 3.38561e6 1.48790 0.743948 0.668237i \(-0.232951\pi\)
0.743948 + 0.668237i \(0.232951\pi\)
\(350\) −1.80959e6 + 7.92832e6i −0.789604 + 3.45948i
\(351\) 274752. 132314.i 0.119035 0.0573241i
\(352\) −494637. 238205.i −0.212780 0.102469i
\(353\) 576948. 2.52777e6i 0.246434 1.07970i −0.688601 0.725140i \(-0.741775\pi\)
0.935035 0.354556i \(-0.115368\pi\)
\(354\) −35274.6 154548.i −0.0149608 0.0655473i
\(355\) −5.81013e6 + 2.79801e6i −2.44689 + 1.17836i
\(356\) −3.66415e6 + 4.59470e6i −1.53231 + 1.92146i
\(357\) 46526.1 58341.9i 0.0193209 0.0242276i
\(358\) −4.28644e6 2.06424e6i −1.76762 0.851242i
\(359\) 1.66524e6 + 2.08815e6i 0.681932 + 0.855115i 0.995531 0.0944402i \(-0.0301061\pi\)
−0.313599 + 0.949556i \(0.601535\pi\)
\(360\) 1.21633e7 4.94647
\(361\) −1.54373e6 1.93578e6i −0.623454 0.781787i
\(362\) −49489.4 216827.i −0.0198491 0.0869645i
\(363\) −27322.8 119709.i −0.0108833 0.0476826i
\(364\) −7.71655e6 9.67624e6i −3.05260 3.82784i
\(365\) 5.27806e6 2.07368
\(366\) 157474. + 197466.i 0.0614479 + 0.0770532i
\(367\) −193952. 93402.2i −0.0751672 0.0361986i 0.395922 0.918284i \(-0.370425\pi\)
−0.471090 + 0.882085i \(0.656139\pi\)
\(368\) −3.72408e6 + 4.66985e6i −1.43351 + 1.79756i
\(369\) 336887. 422443.i 0.128801 0.161511i
\(370\) −788238. + 379595.i −0.299332 + 0.144151i
\(371\) −114658. 502350.i −0.0432484 0.189484i
\(372\) −67671.5 + 296488.i −0.0253541 + 0.111084i
\(373\) 3.68520e6 + 1.77470e6i 1.37148 + 0.660469i 0.967164 0.254151i \(-0.0817962\pi\)
0.404314 + 0.914620i \(0.367510\pi\)
\(374\) 146551. 70575.2i 0.0541763 0.0260900i
\(375\) −16631.4 + 72867.1i −0.00610734 + 0.0267580i
\(376\) −1.40287e6 −0.511737
\(377\) 2.58189e6 + 2.67100e6i 0.935587 + 0.967879i
\(378\) 709619. 0.255444
\(379\) −309497. + 1.35599e6i −0.110677 + 0.484909i 0.888960 + 0.457984i \(0.151428\pi\)
−0.999637 + 0.0269243i \(0.991429\pi\)
\(380\) −78876.9 + 37985.1i −0.0280215 + 0.0134944i
\(381\) −111701. 53792.4i −0.0394225 0.0189849i
\(382\) 530408. 2.32387e6i 0.185974 0.814805i
\(383\) −197489. 865254.i −0.0687931 0.301402i 0.928813 0.370548i \(-0.120830\pi\)
−0.997607 + 0.0691452i \(0.977973\pi\)
\(384\) 340797. 164119.i 0.117942 0.0567977i
\(385\) −254918. + 319656.i −0.0876492 + 0.109909i
\(386\) −858739. + 1.07683e6i −0.293355 + 0.367855i
\(387\) −2.36015e6 1.13659e6i −0.801056 0.385768i
\(388\) 8.37892e6 + 1.05068e7i 2.82559 + 3.54318i
\(389\) −3.95319e6 −1.32457 −0.662284 0.749253i \(-0.730413\pi\)
−0.662284 + 0.749253i \(0.730413\pi\)
\(390\) −365345. 458128.i −0.121630 0.152520i
\(391\) −205033. 898309.i −0.0678238 0.297155i
\(392\) −1.83470e6 8.03833e6i −0.603044 2.64211i
\(393\) 177968. + 223165.i 0.0581247 + 0.0728860i
\(394\) −1.86728e6 −0.605994
\(395\) −4.93345e6 6.18635e6i −1.59096 1.99499i
\(396\) 506904. + 244112.i 0.162438 + 0.0782261i
\(397\) 1.42114e6 1.78205e6i 0.452542 0.567470i −0.502258 0.864718i \(-0.667497\pi\)
0.954800 + 0.297248i \(0.0960687\pi\)
\(398\) −1.53649e6 + 1.92670e6i −0.486209 + 0.609687i
\(399\) −1440.95 + 693.923i −0.000453122 + 0.000218212i
\(400\) −3.40478e6 1.49173e7i −1.06399 4.66166i
\(401\) 554519. 2.42951e6i 0.172209 0.754496i −0.812877 0.582435i \(-0.802100\pi\)
0.985086 0.172061i \(-0.0550427\pi\)
\(402\) −36334.4 17497.7i −0.0112138 0.00540028i
\(403\) −3.42031e6 + 1.64713e6i −1.04907 + 0.505203i
\(404\) −21070.3 + 92315.1i −0.00642270 + 0.0281397i
\(405\) −5.03790e6 −1.52620
\(406\) 2.71628e6 + 8.20665e6i 0.817824 + 2.47087i
\(407\) −25374.2 −0.00759286
\(408\) −55126.6 + 241525.i −0.0163950 + 0.0718311i
\(409\) −1.96789e6 + 947684.i −0.581690 + 0.280127i −0.701500 0.712670i \(-0.747486\pi\)
0.119809 + 0.992797i \(0.461772\pi\)
\(410\) −1.87311e6 902041.i −0.550304 0.265013i
\(411\) −55922.6 + 245013.i −0.0163299 + 0.0715458i
\(412\) −2.41268e6 1.05706e7i −0.700254 3.06802i
\(413\) 3.02169e6 1.45517e6i 0.871716 0.419796i
\(414\) 2.72825e6 3.42112e6i 0.782319 0.980997i
\(415\) 1.49372e6 1.87306e6i 0.425743 0.533865i
\(416\) 1.49982e7 + 7.22276e6i 4.24919 + 2.04630i
\(417\) 29902.6 + 37496.7i 0.00842110 + 0.0105597i
\(418\) −3486.17 −0.000975907
\(419\) 2.59080e6 + 3.24877e6i 0.720941 + 0.904031i 0.998391 0.0567092i \(-0.0180608\pi\)
−0.277450 + 0.960740i \(0.589489\pi\)
\(420\) −220990. 968222.i −0.0611294 0.267825i
\(421\) −667064. 2.92260e6i −0.183427 0.803645i −0.979983 0.199081i \(-0.936204\pi\)
0.796556 0.604564i \(-0.206653\pi\)
\(422\) 5.30134e6 + 6.64767e6i 1.44912 + 1.81714i
\(423\) 582464. 0.158277
\(424\) 1.06656e6 + 1.33743e6i 0.288119 + 0.361289i
\(425\) 2.12663e6 + 1.02413e6i 0.571109 + 0.275032i
\(426\) 388908. 487675.i 0.103830 0.130199i
\(427\) −3.33165e6 + 4.17775e6i −0.884279 + 1.10885i
\(428\) −7.50562e6 + 3.61452e6i −1.98051 + 0.953764i
\(429\) −3781.71 16568.8i −0.000992077 0.00434657i
\(430\) −2.24284e6 + 9.82654e6i −0.584962 + 2.56289i
\(431\) −1.51437e6 729280.i −0.392679 0.189104i 0.227116 0.973868i \(-0.427070\pi\)
−0.619796 + 0.784763i \(0.712784\pi\)
\(432\) −1.20294e6 + 579307.i −0.310124 + 0.149348i
\(433\) 1.29982e6 5.69486e6i 0.333167 1.45970i −0.479793 0.877381i \(-0.659288\pi\)
0.812961 0.582319i \(-0.197854\pi\)
\(434\) −8.83383e6 −2.25126
\(435\) 93667.7 + 282996.i 0.0237338 + 0.0717064i
\(436\) 1.40654e7 3.54352
\(437\) −4394.35 + 19252.9i −0.00110075 + 0.00482272i
\(438\) −459965. + 221508.i −0.114562 + 0.0551701i
\(439\) 6.34241e6 + 3.05434e6i 1.57070 + 0.756408i 0.997991 0.0633519i \(-0.0201791\pi\)
0.572707 + 0.819760i \(0.305893\pi\)
\(440\) 302040. 1.32332e6i 0.0743759 0.325862i
\(441\) 761758. + 3.33748e6i 0.186518 + 0.817188i
\(442\) −4.44367e6 + 2.13996e6i −1.08190 + 0.521014i
\(443\) 1.36584e6 1.71272e6i 0.330668 0.414644i −0.588508 0.808491i \(-0.700285\pi\)
0.919176 + 0.393847i \(0.128856\pi\)
\(444\) 38428.5 48187.8i 0.00925115 0.0116006i
\(445\) −5.30375e6 2.55415e6i −1.26965 0.611430i
\(446\) −3.25861e6 4.08617e6i −0.775703 0.972701i
\(447\) −273878. −0.0648318
\(448\) 1.15507e7 + 1.44841e7i 2.71902 + 3.40954i
\(449\) −1.52425e6 6.67819e6i −0.356813 1.56330i −0.761079 0.648659i \(-0.775330\pi\)
0.404266 0.914642i \(-0.367527\pi\)
\(450\) 2.49433e6 + 1.09284e7i 0.580662 + 2.54405i
\(451\) −37594.7 47142.2i −0.00870332 0.0109136i
\(452\) 3.12739e6 0.720006
\(453\) −83554.2 104774.i −0.0191303 0.0239887i
\(454\) −4.53465e6 2.18377e6i −1.03253 0.497242i
\(455\) 7.72952e6 9.69251e6i 1.75035 2.19487i
\(456\) 3310.47 4151.20i 0.000745552 0.000934892i
\(457\) −5.64998e6 + 2.72089e6i −1.26548 + 0.609424i −0.941619 0.336680i \(-0.890696\pi\)
−0.323863 + 0.946104i \(0.604982\pi\)
\(458\) 371281. + 1.62669e6i 0.0827064 + 0.362360i
\(459\) 45832.0 200803.i 0.0101540 0.0444876i
\(460\) −1.10484e7 5.32061e6i −2.43446 1.17238i
\(461\) 5.98889e6 2.88410e6i 1.31248 0.632059i 0.358953 0.933355i \(-0.383134\pi\)
0.953531 + 0.301296i \(0.0974194\pi\)
\(462\) 8799.99 38555.3i 0.00191813 0.00840386i
\(463\) 8.73922e6 1.89461 0.947306 0.320331i \(-0.103794\pi\)
0.947306 + 0.320331i \(0.103794\pi\)
\(464\) −1.13042e7 1.16944e7i −2.43751 2.52164i
\(465\) −304624. −0.0653329
\(466\) 151296. 662870.i 0.0322747 0.141405i
\(467\) −5.99474e6 + 2.88692e6i −1.27197 + 0.612550i −0.943315 0.331898i \(-0.892311\pi\)
−0.328659 + 0.944449i \(0.606597\pi\)
\(468\) −1.53702e7 7.40188e6i −3.24387 1.56217i
\(469\) 189858. 831822.i 0.0398563 0.174622i
\(470\) −498698. 2.18494e6i −0.104134 0.456241i
\(471\) −13944.0 + 6715.08i −0.00289624 + 0.00139476i
\(472\) −6.94212e6 + 8.70514e6i −1.43429 + 1.79854i
\(473\) −182264. + 228552.i −0.0374584 + 0.0469713i
\(474\) 689560. + 332075.i 0.140970 + 0.0678875i
\(475\) −31541.4 39551.7i −0.00641427 0.00804323i
\(476\) −8.35911e6 −1.69100
\(477\) −442831. 555293.i −0.0891133 0.111745i
\(478\) 926185. + 4.05788e6i 0.185408 + 0.812325i
\(479\) 1.37769e6 + 6.03607e6i 0.274356 + 1.20203i 0.904814 + 0.425807i \(0.140010\pi\)
−0.630458 + 0.776223i \(0.717133\pi\)
\(480\) 832852. + 1.04436e6i 0.164993 + 0.206894i
\(481\) 769386. 0.151629
\(482\) 7.65002e6 + 9.59282e6i 1.49984 + 1.88074i
\(483\) −201835. 97198.4i −0.0393666 0.0189579i
\(484\) −8.57583e6 + 1.07538e7i −1.66404 + 2.08664i
\(485\) −8.39301e6 + 1.05245e7i −1.62018 + 2.03164i
\(486\) 1.32244e6 636854.i 0.253972 0.122306i
\(487\) 953778. + 4.17877e6i 0.182232 + 0.798411i 0.980565 + 0.196195i \(0.0628584\pi\)
−0.798333 + 0.602216i \(0.794284\pi\)
\(488\) 3.94751e6 1.72952e7i 0.750367 3.28757i
\(489\) −317536. 152917.i −0.0600512 0.0289191i
\(490\) 1.18673e7 5.71501e6i 2.23287 1.07529i
\(491\) −849530. + 3.72203e6i −0.159028 + 0.696749i 0.831046 + 0.556204i \(0.187743\pi\)
−0.990074 + 0.140545i \(0.955114\pi\)
\(492\) 146463. 0.0272782
\(493\) 2.49770e6 238594.i 0.462831 0.0442123i
\(494\) 105707. 0.0194888
\(495\) −125405. + 549437.i −0.0230040 + 0.100787i
\(496\) 1.49751e7 7.21161e6i 2.73316 1.31622i
\(497\) 1.18899e7 + 5.72585e6i 2.15916 + 1.03980i
\(498\) −51564.5 + 225919.i −0.00931702 + 0.0408206i
\(499\) 1.52662e6 + 6.68857e6i 0.274461 + 1.20249i 0.904686 + 0.426079i \(0.140105\pi\)
−0.630225 + 0.776412i \(0.717037\pi\)
\(500\) 7.54330e6 3.63266e6i 1.34939 0.649831i
\(501\) 160749. 201573.i 0.0286124 0.0358789i
\(502\) 1.17521e7 1.47366e7i 2.08140 2.60999i
\(503\) −1.83224e6 882359.i −0.322895 0.155498i 0.265413 0.964135i \(-0.414492\pi\)
−0.588309 + 0.808637i \(0.700206\pi\)
\(504\) −1.55193e7 1.94606e7i −2.72142 3.41255i
\(505\) −94848.3 −0.0165501
\(506\) −304457. 381777.i −0.0528628 0.0662878i
\(507\) 51389.3 + 225151.i 0.00887876 + 0.0389004i
\(508\) 3.09037e6 + 1.35398e7i 0.531314 + 2.32784i
\(509\) −4.83147e6 6.05847e6i −0.826579 1.03650i −0.998677 0.0514176i \(-0.983626\pi\)
0.172098 0.985080i \(-0.444945\pi\)
\(510\) −395768. −0.0673775
\(511\) −6.73433e6 8.44458e6i −1.14089 1.43062i
\(512\) −5.21332e6 2.51060e6i −0.878900 0.423256i
\(513\) −2752.31 + 3451.29i −0.000461747 + 0.000579013i
\(514\) 6.77703e6 8.49812e6i 1.13144 1.41878i
\(515\) 9.78515e6 4.71228e6i 1.62573 0.782912i
\(516\) −158007. 692272.i −0.0261247 0.114460i
\(517\) 14463.8 63370.0i 0.00237988 0.0104269i
\(518\) 1.61305e6 + 776804.i 0.264133 + 0.127200i
\(519\) −443555. + 213605.i −0.0722818 + 0.0348091i
\(520\) −9.15834e6 + 4.01253e7i −1.48528 + 6.50744i
\(521\) −5.82860e6 −0.940741 −0.470370 0.882469i \(-0.655880\pi\)
−0.470370 + 0.882469i \(0.655880\pi\)
\(522\) 8.28145e6 + 8.56729e6i 1.33024 + 1.37615i
\(523\) −1.49622e6 −0.239189 −0.119595 0.992823i \(-0.538159\pi\)
−0.119595 + 0.992823i \(0.538159\pi\)
\(524\) 7.11502e6 3.11729e7i 1.13200 4.95963i
\(525\) 517040. 248993.i 0.0818701 0.0394266i
\(526\) −1.59463e7 7.67935e6i −2.51302 1.21021i
\(527\) −570549. + 2.49974e6i −0.0894883 + 0.392074i
\(528\) 16557.4 + 72542.7i 0.00258468 + 0.0113242i
\(529\) 3.30676e6 1.59245e6i 0.513763 0.247415i
\(530\) −1.70387e6 + 2.13658e6i −0.263479 + 0.330392i
\(531\) 2.88234e6 3.61434e6i 0.443617 0.556279i
\(532\) 161414. + 77732.7i 0.0247264 + 0.0119076i
\(533\) 1.13993e6 + 1.42943e6i 0.173804 + 0.217944i
\(534\) 569396. 0.0864094
\(535\) −5.20279e6 6.52409e6i −0.785871 0.985452i
\(536\) 630306. + 2.76155e6i 0.0947631 + 0.415184i
\(537\) 74707.4 + 327315.i 0.0111796 + 0.0489812i
\(538\) 7.19655e6 + 9.02419e6i 1.07194 + 1.34417i
\(539\) 382021. 0.0566390
\(540\) −1.70908e6 2.14312e6i −0.252219 0.316273i
\(541\) −2.66584e6 1.28380e6i −0.391598 0.188584i 0.227715 0.973728i \(-0.426875\pi\)
−0.619313 + 0.785144i \(0.712589\pi\)
\(542\) 5.86896e6 7.35945e6i 0.858150 1.07609i
\(543\) −9785.34 + 12270.4i −0.00142422 + 0.00178591i
\(544\) 1.01299e7 4.87831e6i 1.46760 0.706761i
\(545\) 3.13510e6 + 1.37358e7i 0.452126 + 1.98089i
\(546\) −266830. + 1.16906e6i −0.0383048 + 0.167824i
\(547\) −4.82167e6 2.32199e6i −0.689016 0.331813i 0.0564038 0.998408i \(-0.482037\pi\)
−0.745420 + 0.666595i \(0.767751\pi\)
\(548\) 2.53641e7 1.22147e7i 3.60801 1.73752i
\(549\) −1.63899e6 + 7.18087e6i −0.232084 + 1.01683i
\(550\) 1.25091e6 0.176327
\(551\) −50449.0 18619.3i −0.00707903 0.00261266i
\(552\) 743718. 0.103887
\(553\) −3.60315e6 + 1.57864e7i −0.501037 + 2.19519i
\(554\) −1.22489e7 + 5.89878e6i −1.69560 + 0.816559i
\(555\) 55624.1 + 26787.2i 0.00766533 + 0.00369143i
\(556\) 1.19548e6 5.23775e6i 0.164005 0.718551i
\(557\) 49914.4 + 218689.i 0.00681692 + 0.0298669i 0.978222 0.207561i \(-0.0665527\pi\)
−0.971405 + 0.237428i \(0.923696\pi\)
\(558\) −1.09707e7 + 5.28321e6i −1.49159 + 0.718311i
\(559\) 5.52655e6 6.93008e6i 0.748040 0.938012i
\(560\) −3.38420e7 + 4.24365e7i −4.56022 + 5.71834i
\(561\) −10341.8 4980.33i −0.00138735 0.000668114i
\(562\) −5.43683e6 6.81757e6i −0.726114 0.910518i
\(563\) −6.48001e6 −0.861598 −0.430799 0.902448i \(-0.641768\pi\)
−0.430799 + 0.902448i \(0.641768\pi\)
\(564\) 98440.1 + 123440.i 0.0130309 + 0.0163402i
\(565\) 697081. + 3.05411e6i 0.0918675 + 0.402498i
\(566\) −2.89591e6 1.26878e7i −0.379965 1.66474i
\(567\) 6.42790e6 + 8.06033e6i 0.839676 + 1.05292i
\(568\) −4.38116e7 −5.69795
\(569\) −3.57251e6 4.47979e6i −0.462586 0.580065i 0.494752 0.869034i \(-0.335259\pi\)
−0.957338 + 0.288969i \(0.906687\pi\)
\(570\) 7642.24 + 3680.31i 0.000985220 + 0.000474457i
\(571\) −1.20979e6 + 1.51703e6i −0.155281 + 0.194716i −0.853387 0.521279i \(-0.825455\pi\)
0.698105 + 0.715995i \(0.254027\pi\)
\(572\) −1.18697e6 + 1.48841e6i −0.151687 + 0.190210i
\(573\) −151550. + 72982.4i −0.0192827 + 0.00928607i
\(574\) 946704. + 4.14778e6i 0.119932 + 0.525456i
\(575\) 1.57678e6 6.90831e6i 0.198884 0.871369i
\(576\) 2.30072e7 + 1.10797e7i 2.88940 + 1.39146i
\(577\) −5.31930e6 + 2.56164e6i −0.665143 + 0.320316i −0.735814 0.677184i \(-0.763200\pi\)
0.0706712 + 0.997500i \(0.477486\pi\)
\(578\) 2.68783e6 1.17762e7i 0.334643 1.46617i
\(579\) 97193.6 0.0120487
\(580\) 1.82428e7 2.79687e7i 2.25176 3.45225i
\(581\) −4.90263e6 −0.602544
\(582\) 289735. 1.26941e6i 0.0354563 0.155344i
\(583\) −71410.2 + 34389.3i −0.00870140 + 0.00419037i
\(584\) 3.23070e7 + 1.55583e7i 3.91981 + 1.88768i
\(585\) 3.80250e6 1.66598e7i 0.459388 2.01271i
\(586\) −1.24246e6 5.44359e6i −0.149465 0.654849i
\(587\) −3.62179e6 + 1.74416e6i −0.433838 + 0.208925i −0.638040 0.770003i \(-0.720254\pi\)
0.204202 + 0.978929i \(0.434540\pi\)
\(588\) −578560. + 725492.i −0.0690089 + 0.0865345i
\(589\) 34262.7 42964.1i 0.00406943 0.00510290i
\(590\) −1.60259e7 7.71767e6i −1.89536 0.912759i
\(591\) 82156.8 + 103021.i 0.00967553 + 0.0121327i
\(592\) −3.36859e6 −0.395043
\(593\) 205778. + 258037.i 0.0240304 + 0.0301332i 0.793702 0.608307i \(-0.208151\pi\)
−0.769671 + 0.638441i \(0.779580\pi\)
\(594\) −24289.2 106418.i −0.00282453 0.0123751i
\(595\) −1.86321e6 8.16324e6i −0.215759 0.945301i
\(596\) 1.91284e7 + 2.39863e7i 2.20579 + 2.76597i
\(597\) 173903. 0.0199697
\(598\) 9.23164e6 + 1.15761e7i 1.05566 + 1.32376i
\(599\) −8.77325e6 4.22498e6i −0.999065 0.481124i −0.138444 0.990370i \(-0.544210\pi\)
−0.860621 + 0.509246i \(0.829924\pi\)
\(600\) −1.18786e6 + 1.48953e6i −0.134706 + 0.168916i
\(601\) 563288. 706340.i 0.0636127 0.0797679i −0.749007 0.662562i \(-0.769469\pi\)
0.812620 + 0.582794i \(0.198041\pi\)
\(602\) 1.85835e7 8.94936e6i 2.08996 1.00647i
\(603\) −261700. 1.14658e6i −0.0293096 0.128414i
\(604\) −3.34043e6 + 1.46354e7i −0.372572 + 1.63234i
\(605\) −1.24133e7 5.97792e6i −1.37879 0.663990i
\(606\) 8265.72 3980.56i 0.000914322 0.000440314i
\(607\) 110527. 484252.i 0.0121758 0.0533458i −0.968475 0.249111i \(-0.919862\pi\)
0.980651 + 0.195765i \(0.0627189\pi\)
\(608\) −240972. −0.0264367
\(609\) 333266. 510941.i 0.0364122 0.0558248i
\(610\) 2.83402e7 3.08374
\(611\) −438566. + 1.92148e6i −0.0475260 + 0.208225i
\(612\) −1.03811e7 + 4.99930e6i −1.12038 + 0.539548i
\(613\) 3.78284e6 + 1.82172e6i 0.406600 + 0.195808i 0.625993 0.779828i \(-0.284694\pi\)
−0.219394 + 0.975636i \(0.570408\pi\)
\(614\) −5.78540e6 + 2.53475e7i −0.619316 + 2.71340i
\(615\) 32646.0 + 143031.i 0.00348050 + 0.0152491i
\(616\) −2.50261e6 + 1.20519e6i −0.265731 + 0.127969i
\(617\) −1.61132e6 + 2.02054e6i −0.170400 + 0.213675i −0.859697 0.510804i \(-0.829348\pi\)
0.689297 + 0.724479i \(0.257919\pi\)
\(618\) −654980. + 821319.i −0.0689853 + 0.0865049i
\(619\) 4.22546e6 + 2.03487e6i 0.443249 + 0.213457i 0.642176 0.766557i \(-0.278032\pi\)
−0.198928 + 0.980014i \(0.563746\pi\)
\(620\) 2.12758e7 + 2.66790e7i 2.22283 + 2.78734i
\(621\) −618324. −0.0643409
\(622\) −6.07556e6 7.61851e6i −0.629666 0.789576i
\(623\) 2.68062e6 + 1.17445e7i 0.276703 + 1.21232i
\(624\) −502048. 2.19962e6i −0.0516159 0.226144i
\(625\) −3.07234e6 3.85259e6i −0.314608 0.394506i
\(626\) −2.24679e7 −2.29154
\(627\) 153.385 + 192.339i 1.55817e−5 + 1.95388e-5i
\(628\) 1.56200e6 + 752218.i 0.158045 + 0.0761105i
\(629\) 323997. 406279.i 0.0326523 0.0409447i
\(630\) 2.47926e7 3.10889e7i 2.48869 3.12071i
\(631\) 1.31058e7 6.31141e6i 1.31036 0.631034i 0.357345 0.933972i \(-0.383682\pi\)
0.953010 + 0.302938i \(0.0979676\pi\)
\(632\) −1.19620e7 5.24091e7i −1.19128 5.21933i
\(633\) 133516. 584972.i 0.0132441 0.0580264i
\(634\) −1.29674e7 6.24475e6i −1.28123 0.617009i
\(635\) −1.25337e7 + 6.03591e6i −1.23352 + 0.594030i
\(636\) 42840.4 187696.i 0.00419963 0.0183998i
\(637\) −1.15835e7 −1.13108
\(638\) 1.13773e6 688248.i 0.110660 0.0669411i
\(639\) 1.81904e7 1.76234
\(640\) 9.44450e6 4.13790e7i 0.911442 3.99329i
\(641\) −3.69402e6 + 1.77895e6i −0.355103 + 0.171008i −0.602927 0.797797i \(-0.705999\pi\)
0.247824 + 0.968805i \(0.420285\pi\)
\(642\) 727206. + 350204.i 0.0696338 + 0.0335339i
\(643\) −409982. + 1.79625e6i −0.0391055 + 0.171332i −0.990710 0.135994i \(-0.956577\pi\)
0.951604 + 0.307326i \(0.0994343\pi\)
\(644\) 5.58405e6 + 2.44653e7i 0.530560 + 2.32454i
\(645\) 640831. 308608.i 0.0606519 0.0292084i
\(646\) 44514.1 55818.9i 0.00419678 0.00526260i
\(647\) −2.72443e6 + 3.41632e6i −0.255867 + 0.320847i −0.893129 0.449800i \(-0.851495\pi\)
0.637262 + 0.770647i \(0.280067\pi\)
\(648\) −3.08370e7 1.48503e7i −2.88493 1.38931i
\(649\) −321652. 403339.i −0.0299761 0.0375888i
\(650\) −3.79296e7 −3.52123
\(651\) 388673. + 487380.i 0.0359444 + 0.0450729i
\(652\) 8.78511e6 + 3.84901e7i 0.809335 + 3.54593i
\(653\) −3.38562e6 1.48334e7i −0.310710 1.36131i −0.853348 0.521342i \(-0.825432\pi\)
0.542638 0.839967i \(-0.317426\pi\)
\(654\) −849671. 1.06545e6i −0.0776795 0.0974070i
\(655\) 3.20284e7 2.91697
\(656\) −4.99094e6 6.25845e6i −0.452817 0.567815i
\(657\) −1.34137e7 6.45972e6i −1.21237 0.583848i
\(658\) −2.85948e6 + 3.58567e6i −0.257467 + 0.322854i
\(659\) −6.85498e6 + 8.59587e6i −0.614883 + 0.771039i −0.987614 0.156900i \(-0.949850\pi\)
0.372732 + 0.927939i \(0.378421\pi\)
\(660\) −137635. + 66281.5i −0.0122990 + 0.00592288i
\(661\) 2.21927e6 + 9.72326e6i 0.197563 + 0.865582i 0.972381 + 0.233397i \(0.0749843\pi\)
−0.774818 + 0.632184i \(0.782159\pi\)
\(662\) 4.90907e6 2.15080e7i 0.435366 1.90746i
\(663\) 313579. + 151012.i 0.0277053 + 0.0133422i
\(664\) 1.46643e7 7.06196e6i 1.29075 0.621591i
\(665\) −39932.9 + 174957.i −0.00350168 + 0.0153419i
\(666\) 2.46782e6 0.215590
\(667\) −2.36682e6 7.15084e6i −0.205992 0.622361i
\(668\) −2.88810e7 −2.50421
\(669\) −82069.1 + 359568.i −0.00708948 + 0.0310610i
\(670\) −4.07700e6 + 1.96338e6i −0.350876 + 0.168973i
\(671\) 740553. + 356632.i 0.0634965 + 0.0305783i
\(672\) 608275. 2.66503e6i 0.0519609 0.227656i
\(673\) −587891. 2.57572e6i −0.0500333 0.219210i 0.943731 0.330715i \(-0.107290\pi\)
−0.993764 + 0.111505i \(0.964433\pi\)
\(674\) −1.92981e7 + 9.29349e6i −1.63631 + 0.788006i
\(675\) 987583. 1.23839e6i 0.0834285 0.104616i
\(676\) 1.61296e7 2.02259e7i 1.35755 1.70232i
\(677\) 2.11781e6 + 1.01988e6i 0.177589 + 0.0855222i 0.520566 0.853822i \(-0.325721\pi\)
−0.342977 + 0.939344i \(0.611435\pi\)
\(678\) −188922. 236901.i −0.0157837 0.0197921i
\(679\) 2.75473e7 2.29300
\(680\) 1.73317e7 + 2.17333e7i 1.43737 + 1.80241i
\(681\) 79033.4 + 346268.i 0.00653045 + 0.0286118i
\(682\) 302369. + 1.32476e6i 0.0248929 + 0.109063i
\(683\) 571111. + 716150.i 0.0468456 + 0.0587425i 0.804702 0.593678i \(-0.202325\pi\)
−0.757857 + 0.652421i \(0.773753\pi\)
\(684\) 246948. 0.0201821
\(685\) 1.75820e7 + 2.20471e7i 1.43166 + 1.79525i
\(686\) 4.61780e6 + 2.22382e6i 0.374649 + 0.180422i
\(687\) 73411.9 92055.7i 0.00593437 0.00744147i
\(688\) −2.41968e7 + 3.03418e7i −1.94889 + 2.44383i
\(689\) 2.16528e6 1.04274e6i 0.173766 0.0836813i
\(690\) 264380. + 1.15833e6i 0.0211401 + 0.0926207i
\(691\) 4.77125e6 2.09042e7i 0.380135 1.66548i −0.316913 0.948454i \(-0.602646\pi\)
0.697048 0.717024i \(-0.254496\pi\)
\(692\) 4.96866e7 + 2.39278e7i 3.94434 + 1.89949i
\(693\) 1.03907e6 500391.i 0.0821888 0.0395801i
\(694\) −6.52969e6 + 2.86084e7i −0.514629 + 2.25473i
\(695\) 5.38148e6 0.422610
\(696\) −260854. + 2.00833e6i −0.0204115 + 0.157149i
\(697\) 1.23486e6 0.0962796
\(698\) −8.17655e6 + 3.58238e7i −0.635231 + 2.78313i
\(699\) −43228.6 + 20817.8i −0.00334640 + 0.00161154i
\(700\) −5.79184e7 2.78920e7i −4.46757 2.15147i
\(701\) 1.10286e6 4.83193e6i 0.0847664 0.371386i −0.914697 0.404140i \(-0.867571\pi\)
0.999463 + 0.0327544i \(0.0104279\pi\)
\(702\) 736488. + 3.22676e6i 0.0564057 + 0.247129i
\(703\) −10034.4 + 4832.31i −0.000765778 + 0.000368779i
\(704\) 1.77674e6 2.22796e6i 0.135112 0.169425i
\(705\) −98605.7 + 123648.i −0.00747187 + 0.00936942i
\(706\) 2.53536e7 + 1.22096e7i 1.91438 + 0.921915i
\(707\) 121018. + 151752.i 0.00910544 + 0.0114179i
\(708\) 1.25311e6 0.0939519
\(709\) −1.01156e7 1.26845e7i −0.755746 0.947675i 0.244010 0.969773i \(-0.421537\pi\)
−0.999756 + 0.0220976i \(0.992966\pi\)
\(710\) −1.55744e7 6.82357e7i −1.15948 5.08003i
\(711\) 4.96659e6 + 2.17600e7i 0.368455 + 1.61431i
\(712\) −2.49354e7 3.12680e7i −1.84338 2.31153i
\(713\) 7.69733e6 0.567043
\(714\) 504964. + 633205.i 0.0370693 + 0.0464835i
\(715\) −1.71811e6 827396.i −0.125685 0.0605269i
\(716\) 2.34485e7 2.94035e7i 1.70936 2.14346i
\(717\) 183131. 229639.i 0.0133034 0.0166820i
\(718\) −2.61168e7 + 1.25772e7i −1.89064 + 0.910486i
\(719\) 3.79562e6 + 1.66297e7i 0.273817 + 1.19967i 0.905467 + 0.424417i \(0.139521\pi\)
−0.631649 + 0.775254i \(0.717622\pi\)
\(720\) −1.66484e7 + 7.29415e7i −1.19686 + 5.24377i
\(721\) −2.00243e7 9.64321e6i −1.43456 0.690849i
\(722\) 2.42112e7 1.16595e7i 1.72852 0.832409i
\(723\) 192668. 844134.i 0.0137077 0.0600573i
\(724\) 1.75808e6 0.124650
\(725\) 1.81021e7 + 6.68096e6i 1.27904 + 0.472056i
\(726\) 1.33265e6 0.0938374
\(727\) 1.73251e6 7.59063e6i 0.121574 0.532650i −0.877059 0.480382i \(-0.840498\pi\)
0.998633 0.0522676i \(-0.0166449\pi\)
\(728\) 7.58833e7 3.65435e7i 5.30662 2.55553i
\(729\) 1.27410e7 + 6.13577e6i 0.887946 + 0.427612i
\(730\) −1.27470e7 + 5.58483e7i −0.885322 + 3.87885i
\(731\) −1.33218e6 5.83666e6i −0.0922081 0.403990i
\(732\) −1.79882e6 + 866267.i −0.124082 + 0.0597550i
\(733\) 6.98773e6 8.76233e6i 0.480370 0.602365i −0.481306 0.876553i \(-0.659837\pi\)
0.961676 + 0.274187i \(0.0884089\pi\)
\(734\) 1.45672e6 1.82667e6i 0.0998013 0.125147i
\(735\) −837450. 403295.i −0.0571795 0.0275362i
\(736\) −2.10447e7 2.63893e7i −1.43202 1.79570i
\(737\) −131242. −0.00890032
\(738\) 3.65635e6 + 4.58492e6i 0.247120 + 0.309878i
\(739\) −4.31454e6 1.89032e7i −0.290619 1.27328i −0.883667 0.468117i \(-0.844933\pi\)
0.593048 0.805167i \(-0.297924\pi\)
\(740\) −1.53892e6 6.74246e6i −0.103309 0.452625i
\(741\) −4650.90 5832.04i −0.000311165 0.000390189i
\(742\) 5.59238e6 0.372896
\(743\) −1.56192e7 1.95858e7i −1.03797 1.30158i −0.952271 0.305255i \(-0.901258\pi\)
−0.0857017 0.996321i \(-0.527313\pi\)
\(744\) −1.86461e6 897947.i −0.123497 0.0594728i
\(745\) −1.91606e7 + 2.40266e7i −1.26479 + 1.58599i
\(746\) −2.76786e7 + 3.47078e7i −1.82094 + 2.28339i
\(747\) −6.08855e6 + 2.93209e6i −0.399220 + 0.192254i
\(748\) 286120. + 1.25357e6i 0.0186979 + 0.0819211i
\(749\) −3.79986e6 + 1.66483e7i −0.247493 + 1.08434i
\(750\) −730857. 351962.i −0.0474438 0.0228477i
\(751\) −2.53971e7 + 1.22306e7i −1.64318 + 0.791311i −0.643510 + 0.765438i \(0.722522\pi\)
−0.999665 + 0.0258736i \(0.991763\pi\)
\(752\) 1.92016e6 8.41279e6i 0.123821 0.542494i
\(753\) −1.33012e6 −0.0854876
\(754\) −3.44980e7 + 2.08688e7i −2.20986 + 1.33681i
\(755\) −1.50370e7 −0.960049
\(756\) −1.24823e6 + 5.46885e6i −0.0794309 + 0.348010i
\(757\) 2.03226e7 9.78684e6i 1.28896 0.620730i 0.341282 0.939961i \(-0.389139\pi\)
0.947677 + 0.319231i \(0.103424\pi\)
\(758\) −1.36006e7 6.54971e6i −0.859776 0.414046i
\(759\) −7667.85 + 33595.0i −0.000483135 + 0.00211675i
\(760\) −132573. 580838.i −0.00832568 0.0364772i
\(761\) 1.25618e7 6.04944e6i 0.786303 0.378664i 0.00275618 0.999996i \(-0.499123\pi\)
0.783547 + 0.621333i \(0.213408\pi\)
\(762\) 838957. 1.05202e6i 0.0523423 0.0656351i
\(763\) 1.79763e7 2.25415e7i 1.11786 1.40176i
\(764\) 1.69765e7 + 8.17544e6i 1.05224 + 0.506731i
\(765\) −7.19605e6 9.02357e6i −0.444571 0.557474i
\(766\) 9.63240e6 0.593147
\(767\) 9.75302e6 + 1.22299e7i 0.598619 + 0.750645i
\(768\) 339028. + 1.48538e6i 0.0207412 + 0.0908730i
\(769\) −4.07674e6 1.78614e7i −0.248598 1.08918i −0.932944 0.360021i \(-0.882769\pi\)
0.684346 0.729157i \(-0.260088\pi\)
\(770\) −2.76671e6 3.46934e6i −0.168165 0.210872i
\(771\) −767036. −0.0464707
\(772\) −6.78828e6 8.51223e6i −0.409936 0.514044i
\(773\) 1.31220e6 + 631921.i 0.0789861 + 0.0380377i 0.472960 0.881084i \(-0.343186\pi\)
−0.393974 + 0.919122i \(0.628900\pi\)
\(774\) 1.77265e7 2.22283e7i 1.06358 1.33369i
\(775\) −1.22941e7 + 1.54164e7i −0.735264 + 0.921992i
\(776\) −8.23970e7 + 3.96803e7i −4.91199 + 2.36549i
\(777\) −28113.5 123173.i −0.00167056 0.00731920i
\(778\) 9.54734e6 4.18296e7i 0.565501 2.47762i
\(779\) −23844.9 11483.1i −0.00140784 0.000677979i
\(780\) 4.17332e6 2.00977e6i 0.245610 0.118279i
\(781\) 451704. 1.97905e6i 0.0264988 0.116099i
\(782\) 1.00004e7 0.584789
\(783\) 216873. 1.66972e6i 0.0126416 0.0973281i
\(784\) 5.07159e7 2.94682
\(785\) −386430. + 1.69306e6i −0.0223819 + 0.0980614i
\(786\) −2.79117e6 + 1.34415e6i −0.161150 + 0.0776056i
\(787\) −1.94615e7 9.37215e6i −1.12005 0.539389i −0.220145 0.975467i \(-0.570653\pi\)
−0.899909 + 0.436078i \(0.856367\pi\)
\(788\) 3.28456e6 1.43906e7i 0.188435 0.825588i
\(789\) 277925. + 1.21767e6i 0.0158941 + 0.0696364i
\(790\) 7.73739e7 3.72613e7i 4.41089 2.12417i
\(791\) 3.99698e6 5.01205e6i 0.227138 0.284823i
\(792\) −2.38720e6 + 2.99345e6i −0.135231 + 0.169574i
\(793\) −2.24548e7 1.08137e7i −1.26802 0.610646i
\(794\) 1.54241e7 + 1.93412e7i 0.868255 + 1.08876i
\(795\) 192847. 0.0108217
\(796\) −1.21459e7 1.52304e7i −0.679432 0.851981i
\(797\) 2.43888e6 + 1.06854e7i 0.136002 + 0.595863i 0.996290 + 0.0860556i \(0.0274263\pi\)
−0.860288 + 0.509808i \(0.829717\pi\)
\(798\) −3862.53 16922.9i −0.000214716 0.000940733i
\(799\) 829965. + 1.04074e6i 0.0459931 + 0.0576735i
\(800\) 8.64655e7 4.77659
\(801\) 1.03531e7 + 1.29823e7i 0.570147 + 0.714942i
\(802\) 2.43679e7 + 1.17350e7i 1.33777 + 0.644238i
\(803\) −1.03588e6 + 1.29896e6i −0.0566920 + 0.0710896i
\(804\) 198763. 249241.i 0.0108442 0.0135981i
\(805\) −2.26474e7 + 1.09064e7i −1.23177 + 0.593187i
\(806\) −9.16832e6 4.01690e7i −0.497109 2.17798i
\(807\) 181247. 794097.i 0.00979688 0.0429229i
\(808\) −580567. 279587.i −0.0312841 0.0150657i
\(809\) 2.29912e7 1.10720e7i 1.23507 0.594778i 0.301599 0.953435i \(-0.402480\pi\)
0.933469 + 0.358657i \(0.116765\pi\)
\(810\) 1.21670e7 5.33071e7i 0.651585 2.85478i
\(811\) −6.48288e6 −0.346111 −0.173056 0.984912i \(-0.555364\pi\)
−0.173056 + 0.984912i \(0.555364\pi\)
\(812\) −6.80245e7 + 6.49808e6i −3.62055 + 0.345856i
\(813\) −664259. −0.0352461
\(814\) 61281.0 268490.i 0.00324164 0.0142026i
\(815\) −3.56300e7 + 1.71585e7i −1.87898 + 0.904868i
\(816\) −1.37294e6 661172.i −0.0721814 0.0347607i
\(817\) −28551.7 + 125093.i −0.00149650 + 0.00655661i
\(818\) −5.27502e6 2.31114e7i −0.275639 1.20765i
\(819\) −3.15064e7 + 1.51727e7i −1.64130 + 0.790410i
\(820\) 1.02466e7 1.28488e7i 0.532164 0.667313i
\(821\) −6.01621e6 + 7.54409e6i −0.311505 + 0.390615i −0.912796 0.408415i \(-0.866082\pi\)
0.601291 + 0.799030i \(0.294653\pi\)
\(822\) −2.45748e6 1.18346e6i −0.126856 0.0610905i
\(823\) 2.39932e6 + 3.00865e6i 0.123478 + 0.154836i 0.839728 0.543008i \(-0.182715\pi\)
−0.716250 + 0.697843i \(0.754143\pi\)
\(824\) 7.37855e7 3.78576
\(825\) −55037.7 69015.1i −0.00281530 0.00353028i
\(826\) 8.09980e6 + 3.54875e7i 0.413070 + 1.80978i
\(827\) 4.97239e6 + 2.17855e7i 0.252814 + 1.10765i 0.928755 + 0.370695i \(0.120881\pi\)
−0.675940 + 0.736956i \(0.736262\pi\)
\(828\) 2.15667e7 + 2.70437e7i 1.09322 + 1.37085i
\(829\) 1.84970e7 0.934794 0.467397 0.884048i \(-0.345192\pi\)
0.467397 + 0.884048i \(0.345192\pi\)
\(830\) 1.62118e7 + 2.03290e7i 0.816838 + 1.02428i
\(831\) 864379. + 416263.i 0.0434212 + 0.0209105i
\(832\) −5.38737e7 + 6.75555e7i −2.69817 + 3.38339i
\(833\) −4.87794e6 + 6.11674e6i −0.243570 + 0.305427i
\(834\) −468978. + 225848.i −0.0233473 + 0.0112435i
\(835\) −6.43744e6 2.82043e7i −0.319519 1.39990i
\(836\) 6132.22 26867.0i 0.000303461 0.00132955i
\(837\) 1.55023e6 + 746549.i 0.0764859 + 0.0368337i
\(838\) −4.06329e7 + 1.95678e7i −1.99879 + 0.962569i
\(839\) 5.14042e6 2.25216e7i 0.252112 1.10458i −0.677351 0.735660i \(-0.736872\pi\)
0.929463 0.368915i \(-0.120271\pi\)
\(840\) 6.75842e6 0.330481
\(841\) 2.01402e7 3.88325e6i 0.981915 0.189324i
\(842\) 3.25357e7 1.58154
\(843\) −136928. + 599922.i −0.00663627 + 0.0290754i
\(844\) −6.05570e7 + 2.91627e7i −2.92623 + 1.40920i
\(845\) 2.33471e7 + 1.12434e7i 1.12484 + 0.541695i
\(846\) −1.40671e6 + 6.16318e6i −0.0675737 + 0.296060i
\(847\) 6.27390e6 + 2.74878e7i 0.300489 + 1.31653i
\(848\) −9.48018e6 + 4.56542e6i −0.452717 + 0.218017i
\(849\) −572597. + 718014.i −0.0272634 + 0.0341872i
\(850\) −1.59725e7 + 2.00289e7i −0.758275 + 0.950847i
\(851\) −1.40553e6 676866.i −0.0665296 0.0320390i
\(852\) 3.07429e6 + 3.85504e6i 0.145093 + 0.181941i
\(853\) −3.05880e6 −0.143939 −0.0719694 0.997407i \(-0.522928\pi\)
−0.0719694 + 0.997407i \(0.522928\pi\)
\(854\) −3.61595e7 4.53425e7i −1.69659 2.12746i
\(855\) 55043.5 + 241161.i 0.00257508 + 0.0112822i
\(856\) −1.26151e7 5.52704e7i −0.588445 2.57815i
\(857\) −2.04857e7 2.56883e7i −0.952795 1.19477i −0.980772 0.195159i \(-0.937478\pi\)
0.0279765 0.999609i \(-0.491094\pi\)
\(858\) 184451. 0.00855387
\(859\) −1.25716e7 1.57643e7i −0.581311 0.728941i 0.401025 0.916067i \(-0.368654\pi\)
−0.982336 + 0.187127i \(0.940083\pi\)
\(860\) −7.17854e7 3.45700e7i −3.30971 1.59387i
\(861\) 187188. 234726.i 0.00860539 0.0107908i
\(862\) 1.13740e7 1.42626e7i 0.521369 0.653777i
\(863\) 1.57795e7 7.59899e6i 0.721216 0.347319i −0.0370066 0.999315i \(-0.511782\pi\)
0.758223 + 0.651996i \(0.226068\pi\)
\(864\) −1.67892e6 7.35583e6i −0.0765149 0.335234i
\(865\) −1.22922e7 + 5.38557e7i −0.558586 + 2.44733i
\(866\) 5.71194e7 + 2.75073e7i 2.58815 + 1.24639i
\(867\) −767974. + 369837.i −0.0346975 + 0.0167095i
\(868\) 1.55388e7 6.80800e7i 0.700033 3.06705i
\(869\) 2.49074e6 0.111887
\(870\) −3.22066e6 + 307656.i −0.144260 + 0.0137806i
\(871\) 3.97949e6 0.177739
\(872\) −2.12992e7 + 9.33181e7i −0.948578 + 4.15599i
\(873\) 3.42109e7 1.64751e7i 1.51925 0.731631i
\(874\) −193106. 92995.1i −0.00855102 0.00411795i
\(875\) 3.81894e6 1.67319e7i 0.168625 0.738795i
\(876\) −898017. 3.93447e6i −0.0395389 0.173231i
\(877\) −7.85138e6 + 3.78102e6i −0.344704 + 0.166001i −0.598223 0.801330i \(-0.704126\pi\)
0.253519 + 0.967330i \(0.418412\pi\)
\(878\) −4.76362e7 + 5.97339e7i −2.08545 + 2.61508i
\(879\) −245668. + 308057.i −0.0107245 + 0.0134481i
\(880\) 7.52235e6 + 3.62257e6i 0.327451 + 0.157692i
\(881\) −1.65510e7 2.07543e7i −0.718429 0.900882i 0.279819 0.960053i \(-0.409726\pi\)
−0.998248 + 0.0591710i \(0.981154\pi\)
\(882\) −3.71543e7 −1.60819
\(883\) 5.13892e6 + 6.44401e6i 0.221805 + 0.278134i 0.880266 0.474480i \(-0.157364\pi\)
−0.658462 + 0.752614i \(0.728793\pi\)
\(884\) −8.67562e6 3.80104e7i −0.373396 1.63596i
\(885\) 279312. + 1.22375e6i 0.0119876 + 0.0525210i
\(886\) 1.48240e7 + 1.85887e7i 0.634425 + 0.795544i
\(887\) −1.94108e7 −0.828388 −0.414194 0.910189i \(-0.635936\pi\)
−0.414194 + 0.910189i \(0.635936\pi\)
\(888\) 261514. + 327929.i 0.0111292 + 0.0139556i
\(889\) 2.56490e7 + 1.23519e7i 1.08847 + 0.524178i
\(890\) 3.98351e7 4.99516e7i 1.68574 2.11385i
\(891\) 988749. 1.23985e6i 0.0417246 0.0523209i
\(892\) 3.72230e7 1.79256e7i 1.56639 0.754332i
\(893\) −6348.50 27814.6i −0.000266405 0.00116720i
\(894\) 661441. 2.89796e6i 0.0276788 0.121269i
\(895\) 3.39410e7 + 1.63451e7i 1.41634 + 0.682073i
\(896\) −7.82543e7 + 3.76853e7i −3.25640 + 1.56820i
\(897\) 232502. 1.01866e6i 0.00964817 0.0422714i
\(898\) 7.43446e7 3.07651
\(899\) −2.69978e6 + 2.07858e7i −0.111411 + 0.857763i
\(900\) −8.86098e7 −3.64649
\(901\) 361194. 1.58250e6i 0.0148228 0.0649427i
\(902\) 589617. 283944.i 0.0241298 0.0116203i
\(903\) −1.31140e6 631535.i −0.0535198 0.0257738i
\(904\) −4.73583e6 + 2.07490e7i −0.192741 + 0.844455i
\(905\) 391868. + 1.71688e6i 0.0159044 + 0.0696819i
\(906\) 1.31042e6 631067.i 0.0530385 0.0255420i
\(907\) 9.49910e6 1.19115e7i 0.383411 0.480782i −0.552252 0.833677i \(-0.686231\pi\)
0.935663 + 0.352895i \(0.114803\pi\)
\(908\) 2.48063e7 3.11061e7i 0.998498 1.25208i
\(909\) 241049. + 116083.i 0.00967599 + 0.00465971i
\(910\) 8.38911e7 + 1.05196e8i 3.35824 + 4.21110i
\(911\) 8.62539e6 0.344336 0.172168 0.985068i \(-0.444923\pi\)
0.172168 + 0.985068i \(0.444923\pi\)
\(912\) 20362.9 + 25534.3i 0.000810687 + 0.00101657i
\(913\) 167810. + 735222.i 0.00666254 + 0.0291905i
\(914\) −1.51451e7 6.63548e7i −0.599660 2.62728i
\(915\) −1.24692e6 1.56358e6i −0.0492362 0.0617402i
\(916\) −1.31895e7 −0.519387
\(917\) −4.08653e7 5.12434e7i −1.60484 2.01240i
\(918\) 2.01405e6 + 969917.i 0.0788795 + 0.0379864i
\(919\) −9.57485e6 + 1.20065e7i −0.373976 + 0.468951i −0.932831 0.360315i \(-0.882669\pi\)
0.558855 + 0.829265i \(0.311241\pi\)
\(920\) 5.20307e7 6.52445e7i 2.02670 2.54141i
\(921\) 1.65302e6 796052.i 0.0642139 0.0309238i
\(922\) 1.60535e7 + 7.03351e7i 0.621933 + 2.72486i
\(923\) −1.36964e7 + 6.00079e7i −0.529179 + 2.31849i
\(924\) 281656. + 135638.i 0.0108527 + 0.00522640i
\(925\) 3.60054e6 1.73393e6i 0.138361 0.0666310i
\(926\) −2.11060e7 + 9.24716e7i −0.808871 + 3.54390i
\(927\) −3.06354e7 −1.17091
\(928\) 7.86427e7 4.75732e7i 2.99770 1.81339i
\(929\) 9.71862e6 0.369458 0.184729 0.982789i \(-0.440859\pi\)
0.184729 + 0.982789i \(0.440859\pi\)
\(930\) 735696. 3.22329e6i 0.0278927 0.122206i
\(931\) 151073. 72752.9i 0.00571232 0.00275091i
\(932\) 4.84243e6 + 2.33199e6i 0.182610 + 0.0879402i
\(933\) −153015. + 670401.i −0.00575478 + 0.0252134i
\(934\) −1.60692e7 7.04038e7i −0.602737 2.64076i
\(935\) −1.16042e6 + 558830.i −0.0434098 + 0.0209050i
\(936\) 7.23837e7 9.07663e7i 2.70054 3.38638i
\(937\) −1.27740e7 + 1.60181e7i −0.475311 + 0.596021i −0.960463 0.278409i \(-0.910193\pi\)
0.485152 + 0.874430i \(0.338764\pi\)
\(938\) 8.34316e6 + 4.01786e6i 0.309616 + 0.149103i
\(939\) 988548. + 1.23960e6i 0.0365876 + 0.0458794i
\(940\) 1.77160e7 0.653951
\(941\) 2.45220e7 + 3.07497e7i 0.902781 + 1.13205i 0.990719 + 0.135925i \(0.0434008\pi\)
−0.0879382 + 0.996126i \(0.528028\pi\)
\(942\) −37377.6 163762.i −0.00137241 0.00601293i
\(943\) −824907. 3.61416e6i −0.0302083 0.132351i
\(944\) −4.27015e7 5.35459e7i −1.55960 1.95567i
\(945\) −5.61892e6 −0.204679
\(946\) −1.97818e6 2.48055e6i −0.0718682 0.0901199i
\(947\) 3.28105e7 + 1.58007e7i 1.18888 + 0.572535i 0.920487 0.390774i \(-0.127793\pi\)
0.268395 + 0.963309i \(0.413507\pi\)
\(948\) −3.77216e6 + 4.73014e6i −0.136323 + 0.170944i
\(949\) 3.14097e7 3.93865e7i 1.13213 1.41965i
\(950\) 494680. 238225.i 0.0177834 0.00856405i
\(951\) 226005. + 990193.i 0.00810339 + 0.0355033i
\(952\) 1.26583e7 5.54594e7i 0.452670 1.98328i
\(953\) 2.80955e7 + 1.35301e7i 1.00209 + 0.482579i 0.861646 0.507510i \(-0.169434\pi\)
0.140440 + 0.990089i \(0.455148\pi\)
\(954\) 6.94516e6 3.34461e6i 0.247065 0.118980i
\(955\) −4.19989e6 + 1.84009e7i −0.149015 + 0.652877i
\(956\) −3.29022e7 −1.16434
\(957\) −88030.3 32489.4i −0.00310708 0.00114673i
\(958\) −6.71962e7 −2.36554
\(959\) 1.28410e7 5.62602e7i 0.450872 1.97540i
\(960\) −6.24693e6 + 3.00836e6i −0.218770 + 0.105354i
\(961\) 6.49568e6 + 3.12815e6i 0.226890 + 0.109265i
\(962\) −1.85814e6 + 8.14104e6i −0.0647353 + 0.283624i
\(963\) 5.23773e6 + 2.29480e7i 0.182003 + 0.797405i
\(964\) −8.73858e7 + 4.20828e7i −3.02865 + 1.45852i
\(965\) 6.79969e6 8.52654e6i 0.235056 0.294751i
\(966\) 1.51593e6 1.90091e6i 0.0522679 0.0655419i
\(967\) −1.27310e7 6.13094e6i −0.437822 0.210844i 0.201971 0.979392i \(-0.435265\pi\)
−0.639793 + 0.768548i \(0.720980\pi\)
\(968\) −5.83605e7 7.31817e7i −2.00185 2.51023i
\(969\) −5038.18 −0.000172371
\(970\) −9.10922e7 1.14226e8i −3.10851 3.89794i
\(971\) 8.09435e6 + 3.54637e7i 0.275508 + 1.20708i 0.903407 + 0.428784i \(0.141058\pi\)
−0.627900 + 0.778294i \(0.716085\pi\)
\(972\) 2.58188e6 + 1.13119e7i 0.0876536 + 0.384036i
\(973\) −6.86628e6 8.61004e6i −0.232509 0.291557i
\(974\) −4.65200e7 −1.57124
\(975\) 1.66883e6 + 2.09265e6i 0.0562214 + 0.0704994i
\(976\) 9.83134e7 + 4.73452e7i 3.30360 + 1.59093i
\(977\) 1.77879e7 2.23053e7i 0.596195 0.747605i −0.388584 0.921413i \(-0.627036\pi\)
0.984780 + 0.173808i \(0.0556071\pi\)
\(978\) 2.38493e6 2.99061e6i 0.0797313 0.0999799i
\(979\) 1.66951e6 803996.i 0.0556716 0.0268100i
\(980\) 2.31693e7 + 1.01511e8i 0.770632 + 3.37636i
\(981\) 8.84335e6 3.87452e7i 0.293389 1.28542i
\(982\) −3.73320e7 1.79781e7i −1.23538 0.594930i
\(983\) −2.95123e7 + 1.42124e7i −0.974135 + 0.469119i −0.852084 0.523405i \(-0.824661\pi\)
−0.122051 + 0.992524i \(0.538947\pi\)
\(984\) −221790. + 971727.i −0.00730222 + 0.0319931i
\(985\) 1.47855e7 0.485563
\(986\) −3.50756e6 + 2.70049e7i −0.114898 + 0.884608i
\(987\) 323641. 0.0105747
\(988\) −185939. + 814653.i −0.00606008 + 0.0265510i
\(989\) −1.61927e7 + 7.79800e6i −0.526416 + 0.253508i
\(990\) −5.51085e6 2.65389e6i −0.178703 0.0860586i
\(991\) 5.17674e6 2.26808e7i 0.167445 0.733625i −0.819568 0.572982i \(-0.805786\pi\)
0.987013 0.160642i \(-0.0513565\pi\)
\(992\) 2.09004e7 + 9.15706e7i 0.674334 + 2.95445i
\(993\) −1.40263e6 + 675472.i −0.0451409 + 0.0217387i
\(994\) −8.93016e7 + 1.11981e8i −2.86677 + 3.59482i
\(995\) 1.21663e7 1.52560e7i 0.389583 0.488522i
\(996\) −1.65039e6 794788.i −0.0527156 0.0253865i
\(997\) −2.51312e7 3.15136e7i −0.800712 1.00406i −0.999710 0.0240609i \(-0.992340\pi\)
0.198999 0.980000i \(-0.436231\pi\)
\(998\) −7.44602e7 −2.36645
\(999\) −217422. 272639.i −0.00689271 0.00864318i
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 29.6.d.a.25.1 yes 66
29.6 even 14 841.6.a.h.1.1 33
29.7 even 7 inner 29.6.d.a.7.1 66
29.23 even 7 841.6.a.i.1.33 33
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.6.d.a.7.1 66 29.7 even 7 inner
29.6.d.a.25.1 yes 66 1.1 even 1 trivial
841.6.a.h.1.1 33 29.6 even 14
841.6.a.i.1.33 33 29.23 even 7