Properties

Label 50.6.d.b.21.3
Level $50$
Weight $6$
Character 50.21
Analytic conductor $8.019$
Analytic rank $0$
Dimension $28$
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] = [50,6,Mod(11,50)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(50, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("50.11");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 50.d (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.01919099065\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 21.3
Character \(\chi\) \(=\) 50.21
Dual form 50.6.d.b.31.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23607 + 3.80423i) q^{2} +(-7.20148 - 5.23218i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-5.94028 + 55.5852i) q^{5} +(28.8059 - 20.9287i) q^{6} -16.8909 q^{7} +(51.7771 - 37.6183i) q^{8} +(-50.6055 - 155.748i) q^{9} +O(q^{10})\) \(q+(-1.23607 + 3.80423i) q^{2} +(-7.20148 - 5.23218i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-5.94028 + 55.5852i) q^{5} +(28.8059 - 20.9287i) q^{6} -16.8909 q^{7} +(51.7771 - 37.6183i) q^{8} +(-50.6055 - 155.748i) q^{9} +(-204.116 - 91.3052i) q^{10} +(158.710 - 488.460i) q^{11} +(44.0116 + 135.454i) q^{12} +(-161.333 - 496.533i) q^{13} +(20.8783 - 64.2569i) q^{14} +(333.611 - 369.215i) q^{15} +(79.1084 + 243.470i) q^{16} +(479.260 - 348.203i) q^{17} +655.052 q^{18} +(498.551 - 362.218i) q^{19} +(599.647 - 663.644i) q^{20} +(121.640 + 88.3764i) q^{21} +(1662.04 + 1207.54i) q^{22} +(442.325 - 1361.34i) q^{23} -569.697 q^{24} +(-3054.43 - 660.383i) q^{25} +2088.34 q^{26} +(-1118.89 + 3443.59i) q^{27} +(218.641 + 158.852i) q^{28} +(-6398.09 - 4648.49i) q^{29} +(992.212 + 1725.51i) q^{30} +(-460.025 + 334.228i) q^{31} -1024.00 q^{32} +(-3698.66 + 2687.23i) q^{33} +(732.245 + 2253.62i) q^{34} +(100.337 - 938.885i) q^{35} +(-809.688 + 2491.96i) q^{36} +(2908.55 + 8951.60i) q^{37} +(761.718 + 2344.33i) q^{38} +(-1436.11 + 4419.90i) q^{39} +(1783.45 + 3101.50i) q^{40} +(-2948.88 - 9075.73i) q^{41} +(-486.559 + 353.506i) q^{42} -1668.25 q^{43} +(-6648.14 + 4830.16i) q^{44} +(8957.88 - 1887.73i) q^{45} +(4632.09 + 3365.41i) q^{46} +(7201.89 + 5232.48i) q^{47} +(704.185 - 2167.26i) q^{48} -16521.7 q^{49} +(6287.72 - 10803.4i) q^{50} -5273.25 q^{51} +(-2581.33 + 7944.52i) q^{52} +(8259.40 + 6000.81i) q^{53} +(-11717.2 - 8513.03i) q^{54} +(26208.4 + 11723.5i) q^{55} +(-874.563 + 635.407i) q^{56} -5485.50 q^{57} +(25592.4 - 18593.9i) q^{58} +(-2401.25 - 7390.29i) q^{59} +(-7790.66 + 1641.76i) q^{60} +(16982.0 - 52265.2i) q^{61} +(-702.856 - 2163.17i) q^{62} +(854.774 + 2630.72i) q^{63} +(1265.73 - 3895.53i) q^{64} +(28558.2 - 6018.20i) q^{65} +(-5651.05 - 17392.1i) q^{66} +(-36904.6 + 26812.7i) q^{67} -9478.37 q^{68} +(-10308.2 + 7489.32i) q^{69} +(3447.71 + 1542.23i) q^{70} +(-46500.9 - 33784.9i) q^{71} +(-8479.17 - 6160.47i) q^{72} +(17212.3 - 52974.0i) q^{73} -37649.1 q^{74} +(18541.2 + 20737.1i) q^{75} -9859.88 q^{76} +(-2680.76 + 8250.54i) q^{77} +(-15039.2 - 10926.6i) q^{78} +(69422.4 + 50438.4i) q^{79} +(-14003.3 + 2950.97i) q^{80} +(-6119.13 + 4445.81i) q^{81} +38171.2 q^{82} +(38076.0 - 27663.8i) q^{83} +(-743.396 - 2287.94i) q^{84} +(16508.0 + 28708.2i) q^{85} +(2062.08 - 6346.41i) q^{86} +(21754.0 + 66952.0i) q^{87} +(-10157.5 - 31261.4i) q^{88} +(-9809.24 + 30189.7i) q^{89} +(-3891.19 + 36411.2i) q^{90} +(2725.07 + 8386.90i) q^{91} +(-18528.4 + 13461.6i) q^{92} +5061.61 q^{93} +(-28807.6 + 20929.9i) q^{94} +(17172.4 + 29863.7i) q^{95} +(7374.32 + 5357.76i) q^{96} +(17366.2 + 12617.3i) q^{97} +(20421.9 - 62852.3i) q^{98} -84108.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9} - 220 q^{10} - 389 q^{11} + 192 q^{12} + 1047 q^{13} + 164 q^{14} - 640 q^{15} - 1792 q^{16} + 909 q^{17} - 11576 q^{18} + 260 q^{19} - 1040 q^{20} - 1849 q^{21} + 556 q^{22} + 817 q^{23} + 2432 q^{24} + 16055 q^{25} - 4528 q^{26} + 1675 q^{27} + 2544 q^{28} - 2445 q^{29} - 5440 q^{30} + 16731 q^{31} - 28672 q^{32} + 29629 q^{33} - 7576 q^{34} - 825 q^{35} - 7136 q^{36} + 39819 q^{37} + 3100 q^{38} + 26008 q^{39} + 10231 q^{41} + 7396 q^{42} - 86148 q^{43} - 2224 q^{44} - 7870 q^{45} - 11708 q^{46} + 10019 q^{47} + 3072 q^{48} + 147076 q^{49} + 16520 q^{50} - 108074 q^{51} + 16752 q^{52} + 74512 q^{53} + 4260 q^{54} + 2735 q^{55} - 10176 q^{56} - 176840 q^{57} + 9780 q^{58} - 13430 q^{59} + 5760 q^{60} - 29774 q^{61} + 63956 q^{62} - 206818 q^{63} - 28672 q^{64} + 51235 q^{65} + 23264 q^{66} - 85061 q^{67} - 89696 q^{68} - 185227 q^{69} - 25260 q^{70} + 148501 q^{71} + 64064 q^{72} + 189082 q^{73} + 305304 q^{74} + 93630 q^{75} + 16480 q^{76} + 127243 q^{77} + 32028 q^{78} + 46930 q^{79} + 39680 q^{80} - 179812 q^{81} - 338864 q^{82} + 66807 q^{83} - 34464 q^{84} - 877380 q^{85} + 121332 q^{86} - 226000 q^{87} + 24896 q^{88} - 347190 q^{89} + 628660 q^{90} + 197001 q^{91} + 46832 q^{92} - 64906 q^{93} - 40076 q^{94} + 85970 q^{95} - 7168 q^{96} + 502364 q^{97} + 185056 q^{98} + 1151018 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).

\(n\) \(27\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23607 + 3.80423i −0.218508 + 0.672499i
\(3\) −7.20148 5.23218i −0.461975 0.335645i 0.332330 0.943163i \(-0.392165\pi\)
−0.794306 + 0.607518i \(0.792165\pi\)
\(4\) −12.9443 9.40456i −0.404508 0.293893i
\(5\) −5.94028 + 55.5852i −0.106263 + 0.994338i
\(6\) 28.8059 20.9287i 0.326666 0.237337i
\(7\) −16.8909 −0.130289 −0.0651446 0.997876i \(-0.520751\pi\)
−0.0651446 + 0.997876i \(0.520751\pi\)
\(8\) 51.7771 37.6183i 0.286031 0.207813i
\(9\) −50.6055 155.748i −0.208253 0.640937i
\(10\) −204.116 91.3052i −0.645472 0.288732i
\(11\) 158.710 488.460i 0.395479 1.21716i −0.533109 0.846046i \(-0.678976\pi\)
0.928588 0.371112i \(-0.121024\pi\)
\(12\) 44.0116 + 135.454i 0.0882294 + 0.271542i
\(13\) −161.333 496.533i −0.264768 0.814872i −0.991747 0.128212i \(-0.959076\pi\)
0.726979 0.686660i \(-0.240924\pi\)
\(14\) 20.8783 64.2569i 0.0284692 0.0876193i
\(15\) 333.611 369.215i 0.382835 0.423693i
\(16\) 79.1084 + 243.470i 0.0772542 + 0.237764i
\(17\) 479.260 348.203i 0.402207 0.292220i −0.368233 0.929734i \(-0.620037\pi\)
0.770439 + 0.637514i \(0.220037\pi\)
\(18\) 655.052 0.476534
\(19\) 498.551 362.218i 0.316829 0.230190i −0.417992 0.908451i \(-0.637266\pi\)
0.734821 + 0.678261i \(0.237266\pi\)
\(20\) 599.647 663.644i 0.335213 0.370988i
\(21\) 121.640 + 88.3764i 0.0601904 + 0.0437309i
\(22\) 1662.04 + 1207.54i 0.732122 + 0.531918i
\(23\) 442.325 1361.34i 0.174350 0.536594i −0.825253 0.564763i \(-0.808968\pi\)
0.999603 + 0.0281688i \(0.00896760\pi\)
\(24\) −569.697 −0.201891
\(25\) −3054.43 660.383i −0.977416 0.211323i
\(26\) 2088.34 0.605854
\(27\) −1118.89 + 3443.59i −0.295378 + 0.909081i
\(28\) 218.641 + 158.852i 0.0527031 + 0.0382910i
\(29\) −6398.09 4648.49i −1.41272 1.02640i −0.992920 0.118782i \(-0.962101\pi\)
−0.419797 0.907618i \(-0.637899\pi\)
\(30\) 992.212 + 1725.51i 0.201280 + 0.350036i
\(31\) −460.025 + 334.228i −0.0859761 + 0.0624653i −0.629943 0.776641i \(-0.716922\pi\)
0.543967 + 0.839107i \(0.316922\pi\)
\(32\) −1024.00 −0.176777
\(33\) −3698.66 + 2687.23i −0.591234 + 0.429557i
\(34\) 732.245 + 2253.62i 0.108632 + 0.334336i
\(35\) 100.337 938.885i 0.0138449 0.129552i
\(36\) −809.688 + 2491.96i −0.104127 + 0.320469i
\(37\) 2908.55 + 8951.60i 0.349279 + 1.07497i 0.959253 + 0.282549i \(0.0911798\pi\)
−0.609974 + 0.792421i \(0.708820\pi\)
\(38\) 761.718 + 2344.33i 0.0855727 + 0.263366i
\(39\) −1436.11 + 4419.90i −0.151191 + 0.465319i
\(40\) 1783.45 + 3101.50i 0.176242 + 0.306494i
\(41\) −2948.88 9075.73i −0.273967 0.843183i −0.989491 0.144595i \(-0.953812\pi\)
0.715524 0.698588i \(-0.246188\pi\)
\(42\) −486.559 + 353.506i −0.0425610 + 0.0309224i
\(43\) −1668.25 −0.137591 −0.0687957 0.997631i \(-0.521916\pi\)
−0.0687957 + 0.997631i \(0.521916\pi\)
\(44\) −6648.14 + 4830.16i −0.517689 + 0.376123i
\(45\) 8957.88 1887.73i 0.659438 0.138966i
\(46\) 4632.09 + 3365.41i 0.322762 + 0.234500i
\(47\) 7201.89 + 5232.48i 0.475556 + 0.345512i 0.799603 0.600529i \(-0.205043\pi\)
−0.324047 + 0.946041i \(0.605043\pi\)
\(48\) 704.185 2167.26i 0.0441147 0.135771i
\(49\) −16521.7 −0.983025
\(50\) 6287.72 10803.4i 0.355687 0.611135i
\(51\) −5273.25 −0.283892
\(52\) −2581.33 + 7944.52i −0.132384 + 0.407436i
\(53\) 8259.40 + 6000.81i 0.403886 + 0.293440i 0.771122 0.636687i \(-0.219696\pi\)
−0.367236 + 0.930128i \(0.619696\pi\)
\(54\) −11717.2 8513.03i −0.546813 0.397283i
\(55\) 26208.4 + 11723.5i 1.16824 + 0.522579i
\(56\) −874.563 + 635.407i −0.0372667 + 0.0270758i
\(57\) −5485.50 −0.223629
\(58\) 25592.4 18593.9i 0.998942 0.725774i
\(59\) −2401.25 7390.29i −0.0898064 0.276396i 0.896059 0.443935i \(-0.146418\pi\)
−0.985865 + 0.167539i \(0.946418\pi\)
\(60\) −7790.66 + 1641.76i −0.279380 + 0.0588750i
\(61\) 16982.0 52265.2i 0.584338 1.79841i −0.0175745 0.999846i \(-0.505594\pi\)
0.601913 0.798562i \(-0.294406\pi\)
\(62\) −702.856 2163.17i −0.0232213 0.0714680i
\(63\) 854.774 + 2630.72i 0.0271331 + 0.0835072i
\(64\) 1265.73 3895.53i 0.0386271 0.118882i
\(65\) 28558.2 6018.20i 0.838393 0.176678i
\(66\) −5651.05 17392.1i −0.159687 0.491466i
\(67\) −36904.6 + 26812.7i −1.00437 + 0.729716i −0.963020 0.269429i \(-0.913165\pi\)
−0.0413478 + 0.999145i \(0.513165\pi\)
\(68\) −9478.37 −0.248577
\(69\) −10308.2 + 7489.32i −0.260650 + 0.189374i
\(70\) 3447.71 + 1542.23i 0.0840980 + 0.0376187i
\(71\) −46500.9 33784.9i −1.09475 0.795384i −0.114556 0.993417i \(-0.536545\pi\)
−0.980195 + 0.198033i \(0.936545\pi\)
\(72\) −8479.17 6160.47i −0.192762 0.140050i
\(73\) 17212.3 52974.0i 0.378035 1.16347i −0.563373 0.826202i \(-0.690497\pi\)
0.941408 0.337269i \(-0.109503\pi\)
\(74\) −37649.1 −0.799236
\(75\) 18541.2 + 20737.1i 0.380613 + 0.425691i
\(76\) −9859.88 −0.195811
\(77\) −2680.76 + 8250.54i −0.0515266 + 0.158583i
\(78\) −15039.2 10926.6i −0.279890 0.203352i
\(79\) 69422.4 + 50438.4i 1.25150 + 0.909271i 0.998308 0.0581445i \(-0.0185184\pi\)
0.253196 + 0.967415i \(0.418518\pi\)
\(80\) −14003.3 + 2950.97i −0.244627 + 0.0515513i
\(81\) −6119.13 + 4445.81i −0.103628 + 0.0752902i
\(82\) 38171.2 0.626903
\(83\) 38076.0 27663.8i 0.606674 0.440775i −0.241567 0.970384i \(-0.577661\pi\)
0.848242 + 0.529609i \(0.177661\pi\)
\(84\) −743.396 2287.94i −0.0114953 0.0353790i
\(85\) 16508.0 + 28708.2i 0.247826 + 0.430982i
\(86\) 2062.08 6346.41i 0.0300648 0.0925300i
\(87\) 21754.0 + 66952.0i 0.308135 + 0.948343i
\(88\) −10157.5 31261.4i −0.139823 0.430331i
\(89\) −9809.24 + 30189.7i −0.131268 + 0.404003i −0.994991 0.0999650i \(-0.968127\pi\)
0.863723 + 0.503968i \(0.168127\pi\)
\(90\) −3891.19 + 36411.2i −0.0506379 + 0.473836i
\(91\) 2725.07 + 8386.90i 0.0344964 + 0.106169i
\(92\) −18528.4 + 13461.6i −0.228227 + 0.165817i
\(93\) 5061.61 0.0606850
\(94\) −28807.6 + 20929.9i −0.336269 + 0.244314i
\(95\) 17172.4 + 29863.7i 0.195219 + 0.339496i
\(96\) 7374.32 + 5357.76i 0.0816665 + 0.0593342i
\(97\) 17366.2 + 12617.3i 0.187403 + 0.136156i 0.677531 0.735494i \(-0.263050\pi\)
−0.490128 + 0.871650i \(0.663050\pi\)
\(98\) 20421.9 62852.3i 0.214799 0.661083i
\(99\) −84108.2 −0.862482
\(100\) 33326.7 + 37273.7i 0.333267 + 0.372737i
\(101\) −125521. −1.22437 −0.612184 0.790716i \(-0.709709\pi\)
−0.612184 + 0.790716i \(0.709709\pi\)
\(102\) 6518.09 20060.6i 0.0620326 0.190917i
\(103\) 147304. + 107023.i 1.36811 + 0.993992i 0.997882 + 0.0650528i \(0.0207216\pi\)
0.370231 + 0.928940i \(0.379278\pi\)
\(104\) −27032.1 19639.9i −0.245073 0.178056i
\(105\) −5634.99 + 6236.39i −0.0498793 + 0.0552026i
\(106\) −33037.6 + 24003.2i −0.285591 + 0.207494i
\(107\) −153788. −1.29856 −0.649280 0.760550i \(-0.724930\pi\)
−0.649280 + 0.760550i \(0.724930\pi\)
\(108\) 46868.7 34052.1i 0.386655 0.280921i
\(109\) −8833.67 27187.3i −0.0712156 0.219179i 0.909114 0.416548i \(-0.136760\pi\)
−0.980329 + 0.197369i \(0.936760\pi\)
\(110\) −76994.3 + 85211.4i −0.606704 + 0.671454i
\(111\) 25890.5 79682.9i 0.199450 0.613843i
\(112\) −1336.21 4112.44i −0.0100654 0.0309781i
\(113\) −31449.7 96792.1i −0.231697 0.713089i −0.997542 0.0700649i \(-0.977679\pi\)
0.765846 0.643024i \(-0.222321\pi\)
\(114\) 6780.45 20868.1i 0.0488648 0.150390i
\(115\) 73042.6 + 32673.4i 0.515029 + 0.230383i
\(116\) 39101.7 + 120343.i 0.269805 + 0.830375i
\(117\) −69169.5 + 50254.6i −0.467143 + 0.339399i
\(118\) 31082.4 0.205499
\(119\) −8095.15 + 5881.47i −0.0524032 + 0.0380731i
\(120\) 3384.16 31666.7i 0.0214535 0.200748i
\(121\) −83111.2 60383.8i −0.516055 0.374936i
\(122\) 177838. + 129207.i 1.08174 + 0.785933i
\(123\) −26249.6 + 80787.8i −0.156444 + 0.481485i
\(124\) 9097.96 0.0531361
\(125\) 54851.7 165858.i 0.313989 0.949427i
\(126\) −11064.4 −0.0620873
\(127\) 19292.3 59375.5i 0.106139 0.326662i −0.883857 0.467757i \(-0.845062\pi\)
0.989996 + 0.141095i \(0.0450623\pi\)
\(128\) 13254.9 + 9630.27i 0.0715077 + 0.0519534i
\(129\) 12013.9 + 8728.61i 0.0635638 + 0.0461818i
\(130\) −12405.3 + 116081.i −0.0643798 + 0.602424i
\(131\) −24021.6 + 17452.7i −0.122299 + 0.0888557i −0.647254 0.762275i \(-0.724082\pi\)
0.524954 + 0.851131i \(0.324082\pi\)
\(132\) 73148.8 0.365403
\(133\) −8420.99 + 6118.20i −0.0412794 + 0.0299913i
\(134\) −56385.1 173536.i −0.271271 0.834885i
\(135\) −184766. 82649.7i −0.872546 0.390308i
\(136\) 11715.9 36057.9i 0.0543161 0.167168i
\(137\) −93020.5 286288.i −0.423426 1.30317i −0.904494 0.426487i \(-0.859751\pi\)
0.481068 0.876683i \(-0.340249\pi\)
\(138\) −15749.5 48471.9i −0.0703993 0.216667i
\(139\) −20199.9 + 62168.9i −0.0886772 + 0.272921i −0.985554 0.169359i \(-0.945830\pi\)
0.896877 + 0.442280i \(0.145830\pi\)
\(140\) −10128.6 + 11209.6i −0.0436746 + 0.0483358i
\(141\) −24487.0 75363.2i −0.103726 0.319236i
\(142\) 186004. 135140.i 0.774106 0.562421i
\(143\) −268142. −1.09654
\(144\) 33916.7 24641.9i 0.136303 0.0990303i
\(145\) 296393. 328026.i 1.17071 1.29565i
\(146\) 180250. + 130959.i 0.699829 + 0.508456i
\(147\) 118981. + 86444.6i 0.454133 + 0.329947i
\(148\) 46536.8 143226.i 0.174639 0.537485i
\(149\) 361011. 1.33215 0.666077 0.745883i \(-0.267972\pi\)
0.666077 + 0.745883i \(0.267972\pi\)
\(150\) −101807. + 44902.3i −0.369443 + 0.162945i
\(151\) 403121. 1.43878 0.719388 0.694609i \(-0.244423\pi\)
0.719388 + 0.694609i \(0.244423\pi\)
\(152\) 12187.5 37509.2i 0.0427863 0.131683i
\(153\) −78485.1 57022.7i −0.271056 0.196933i
\(154\) −28073.3 20396.5i −0.0953876 0.0693032i
\(155\) −15845.5 27556.0i −0.0529755 0.0921270i
\(156\) 60156.6 43706.3i 0.197912 0.143791i
\(157\) −286202. −0.926667 −0.463334 0.886184i \(-0.653347\pi\)
−0.463334 + 0.886184i \(0.653347\pi\)
\(158\) −277690. + 201753.i −0.884947 + 0.642951i
\(159\) −28082.6 86429.4i −0.0880937 0.271125i
\(160\) 6082.85 56919.2i 0.0187848 0.175776i
\(161\) −7471.28 + 22994.2i −0.0227159 + 0.0699124i
\(162\) −9349.20 28773.9i −0.0279890 0.0861412i
\(163\) 194402. + 598308.i 0.573102 + 1.76383i 0.642552 + 0.766242i \(0.277876\pi\)
−0.0694500 + 0.997585i \(0.522124\pi\)
\(164\) −47182.1 + 145212.i −0.136983 + 0.421592i
\(165\) −127399. 221554.i −0.364299 0.633533i
\(166\) 58174.9 + 179044.i 0.163857 + 0.504300i
\(167\) −62082.2 + 45105.4i −0.172257 + 0.125152i −0.670573 0.741843i \(-0.733952\pi\)
0.498316 + 0.866995i \(0.333952\pi\)
\(168\) 9622.72 0.0263042
\(169\) 79866.1 58026.1i 0.215103 0.156281i
\(170\) −129617. + 27314.8i −0.343986 + 0.0724897i
\(171\) −81644.1 59317.9i −0.213518 0.155130i
\(172\) 21594.3 + 15689.2i 0.0556569 + 0.0404371i
\(173\) −132775. + 408641.i −0.337289 + 1.03807i 0.628294 + 0.777976i \(0.283754\pi\)
−0.965583 + 0.260094i \(0.916246\pi\)
\(174\) −281590. −0.705089
\(175\) 51592.1 + 11154.5i 0.127347 + 0.0275330i
\(176\) 131481. 0.319949
\(177\) −21374.8 + 65784.8i −0.0512824 + 0.157831i
\(178\) −102724. 74633.1i −0.243008 0.176556i
\(179\) 528551. + 384015.i 1.23298 + 0.895809i 0.997110 0.0759766i \(-0.0242074\pi\)
0.235866 + 0.971786i \(0.424207\pi\)
\(180\) −133707. 59809.6i −0.307589 0.137591i
\(181\) −89305.6 + 64884.3i −0.202620 + 0.147212i −0.684468 0.729043i \(-0.739966\pi\)
0.481848 + 0.876255i \(0.339966\pi\)
\(182\) −35274.0 −0.0789363
\(183\) −395757. + 287534.i −0.873576 + 0.634690i
\(184\) −28308.8 87125.5i −0.0616420 0.189715i
\(185\) −514854. + 108497.i −1.10600 + 0.233072i
\(186\) −6256.49 + 19255.5i −0.0132602 + 0.0408106i
\(187\) −94019.7 289363.i −0.196614 0.605116i
\(188\) −44014.0 135461.i −0.0908231 0.279525i
\(189\) 18899.1 58165.5i 0.0384846 0.118443i
\(190\) −134835. + 28414.3i −0.270968 + 0.0571022i
\(191\) 113065. + 347979.i 0.224257 + 0.690192i 0.998366 + 0.0571397i \(0.0181980\pi\)
−0.774109 + 0.633052i \(0.781802\pi\)
\(192\) −29497.3 + 21431.0i −0.0577469 + 0.0419556i
\(193\) −619378. −1.19691 −0.598457 0.801155i \(-0.704219\pi\)
−0.598457 + 0.801155i \(0.704219\pi\)
\(194\) −69465.0 + 50469.3i −0.132514 + 0.0962770i
\(195\) −237150. 106082.i −0.446618 0.199781i
\(196\) 213861. + 155379.i 0.397642 + 0.288904i
\(197\) 503197. + 365594.i 0.923788 + 0.671171i 0.944464 0.328615i \(-0.106582\pi\)
−0.0206758 + 0.999786i \(0.506582\pi\)
\(198\) 103963. 319966.i 0.188459 0.580018i
\(199\) 612135. 1.09576 0.547879 0.836558i \(-0.315435\pi\)
0.547879 + 0.836558i \(0.315435\pi\)
\(200\) −182992. + 80709.5i −0.323487 + 0.142676i
\(201\) 406057. 0.708919
\(202\) 155152. 477509.i 0.267534 0.823385i
\(203\) 108070. + 78517.2i 0.184062 + 0.133729i
\(204\) 68258.4 + 49592.6i 0.114837 + 0.0834337i
\(205\) 521993. 110002.i 0.867522 0.182817i
\(206\) −589217. + 428091.i −0.967402 + 0.702859i
\(207\) −234409. −0.380232
\(208\) 108128. 78559.8i 0.173293 0.125905i
\(209\) −97804.0 301010.i −0.154878 0.476667i
\(210\) −16759.4 29145.4i −0.0262247 0.0456060i
\(211\) −16676.0 + 51323.4i −0.0257861 + 0.0793614i −0.963121 0.269067i \(-0.913285\pi\)
0.937335 + 0.348429i \(0.113285\pi\)
\(212\) −50477.0 155352.i −0.0771354 0.237398i
\(213\) 158107. + 486603.i 0.238782 + 0.734895i
\(214\) 190092. 585043.i 0.283746 0.873279i
\(215\) 9909.89 92730.2i 0.0146209 0.136812i
\(216\) 71609.1 + 220390.i 0.104432 + 0.321409i
\(217\) 7770.26 5645.42i 0.0112018 0.00813855i
\(218\) 114345. 0.162959
\(219\) −401124. + 291434.i −0.565156 + 0.410610i
\(220\) −228993. 398231.i −0.318982 0.554725i
\(221\) −250215. 181792.i −0.344614 0.250376i
\(222\) 271129. + 196987.i 0.369227 + 0.268259i
\(223\) 30995.9 95395.6i 0.0417390 0.128459i −0.928016 0.372541i \(-0.878487\pi\)
0.969755 + 0.244082i \(0.0784865\pi\)
\(224\) 17296.3 0.0230321
\(225\) 51717.6 + 509139.i 0.0681055 + 0.670471i
\(226\) 407093. 0.530179
\(227\) 335115. 1.03138e6i 0.431647 1.32847i −0.464837 0.885396i \(-0.653887\pi\)
0.896484 0.443076i \(-0.146113\pi\)
\(228\) 71005.8 + 51588.7i 0.0904600 + 0.0657230i
\(229\) 942748. + 684947.i 1.18797 + 0.863114i 0.993049 0.117704i \(-0.0375534\pi\)
0.194926 + 0.980818i \(0.437553\pi\)
\(230\) −214583. + 237484.i −0.267470 + 0.296016i
\(231\) 62473.8 45389.9i 0.0770315 0.0559666i
\(232\) −506142. −0.617380
\(233\) 382634. 278000.i 0.461736 0.335471i −0.332476 0.943112i \(-0.607884\pi\)
0.794212 + 0.607641i \(0.207884\pi\)
\(234\) −105682. 325254.i −0.126171 0.388315i
\(235\) −333630. + 369236.i −0.394089 + 0.436148i
\(236\) −38420.0 + 118245.i −0.0449032 + 0.138198i
\(237\) −236042. 726462.i −0.272972 0.840121i
\(238\) −12368.3 38065.7i −0.0141536 0.0435603i
\(239\) 494526. 1.52199e6i 0.560008 1.72353i −0.122328 0.992490i \(-0.539036\pi\)
0.682337 0.731038i \(-0.260964\pi\)
\(240\) 116284. + 52016.4i 0.130315 + 0.0582924i
\(241\) 36524.9 + 112412.i 0.0405085 + 0.124672i 0.969266 0.246016i \(-0.0791217\pi\)
−0.928757 + 0.370689i \(0.879122\pi\)
\(242\) 332445. 241535.i 0.364906 0.265120i
\(243\) 947185. 1.02901
\(244\) −711351. + 516827.i −0.764908 + 0.555739i
\(245\) 98143.5 918362.i 0.104459 0.977459i
\(246\) −274889. 199719.i −0.289614 0.210417i
\(247\) −260286. 189109.i −0.271462 0.197228i
\(248\) −11245.7 + 34610.7i −0.0116107 + 0.0357340i
\(249\) −418946. −0.428212
\(250\) 563161. + 413680.i 0.569879 + 0.418615i
\(251\) −489205. −0.490125 −0.245062 0.969507i \(-0.578808\pi\)
−0.245062 + 0.969507i \(0.578808\pi\)
\(252\) 13676.4 42091.6i 0.0135666 0.0417536i
\(253\) −594757. 432116.i −0.584169 0.424423i
\(254\) 202031. + 146784.i 0.196487 + 0.142756i
\(255\) 31324.6 293114.i 0.0301672 0.282284i
\(256\) −53019.7 + 38521.1i −0.0505636 + 0.0367366i
\(257\) 225164. 0.212651 0.106325 0.994331i \(-0.466091\pi\)
0.106325 + 0.994331i \(0.466091\pi\)
\(258\) −48055.6 + 34914.4i −0.0449464 + 0.0326555i
\(259\) −49128.1 151201.i −0.0455073 0.140057i
\(260\) −426264. 190676.i −0.391062 0.174930i
\(261\) −400212. + 1.23173e6i −0.363655 + 1.11921i
\(262\) −36701.8 112957.i −0.0330319 0.101662i
\(263\) −412733. 1.27026e6i −0.367943 1.13241i −0.948118 0.317919i \(-0.897016\pi\)
0.580175 0.814492i \(-0.302984\pi\)
\(264\) −90416.8 + 278274.i −0.0798435 + 0.245733i
\(265\) −382619. + 423454.i −0.334697 + 0.370417i
\(266\) −12866.1 39597.8i −0.0111492 0.0343137i
\(267\) 228599. 166087.i 0.196244 0.142580i
\(268\) 729865. 0.620734
\(269\) −491227. + 356898.i −0.413906 + 0.300720i −0.775181 0.631739i \(-0.782342\pi\)
0.361275 + 0.932459i \(0.382342\pi\)
\(270\) 542802. 600732.i 0.453140 0.501501i
\(271\) −1.53712e6 1.11679e6i −1.27141 0.923734i −0.272152 0.962254i \(-0.587735\pi\)
−0.999258 + 0.0385206i \(0.987735\pi\)
\(272\) 122691. + 89140.0i 0.100552 + 0.0730550i
\(273\) 24257.3 74656.2i 0.0196986 0.0606260i
\(274\) 1.20408e6 0.968902
\(275\) −807339. + 1.38716e6i −0.643761 + 1.10610i
\(276\) 203865. 0.161091
\(277\) −660581. + 2.03306e6i −0.517281 + 1.59203i 0.261813 + 0.965119i \(0.415680\pi\)
−0.779093 + 0.626908i \(0.784320\pi\)
\(278\) −211536. 153690.i −0.164162 0.119271i
\(279\) 75335.1 + 54734.2i 0.0579411 + 0.0420967i
\(280\) −30124.1 52387.2i −0.0229625 0.0399329i
\(281\) 345196. 250800.i 0.260796 0.189479i −0.449702 0.893179i \(-0.648470\pi\)
0.710498 + 0.703700i \(0.248470\pi\)
\(282\) 316966. 0.237351
\(283\) 144371. 104892.i 0.107155 0.0778529i −0.532917 0.846167i \(-0.678904\pi\)
0.640073 + 0.768314i \(0.278904\pi\)
\(284\) 284188. + 874642.i 0.209079 + 0.643479i
\(285\) 32585.4 304912.i 0.0237635 0.222363i
\(286\) 331441. 1.02007e6i 0.239603 0.737421i
\(287\) 49809.4 + 153298.i 0.0356949 + 0.109858i
\(288\) 51820.0 + 159486.i 0.0368143 + 0.113303i
\(289\) −330315. + 1.01660e6i −0.232639 + 0.715991i
\(290\) 881522. + 1.53301e6i 0.615514 + 1.07041i
\(291\) −59046.6 181727.i −0.0408754 0.125802i
\(292\) −720998. + 523836.i −0.494854 + 0.359533i
\(293\) 165122. 0.112366 0.0561831 0.998420i \(-0.482107\pi\)
0.0561831 + 0.998420i \(0.482107\pi\)
\(294\) −475923. + 345778.i −0.321121 + 0.233308i
\(295\) 425055. 89573.6i 0.284374 0.0599273i
\(296\) 487340. + 354073.i 0.323298 + 0.234890i
\(297\) 1.50448e6 + 1.09307e6i 0.989680 + 0.719045i
\(298\) −446234. + 1.37337e6i −0.291087 + 0.895872i
\(299\) −747310. −0.483418
\(300\) −44978.8 442798.i −0.0288539 0.284055i
\(301\) 28178.4 0.0179267
\(302\) −498285. + 1.53356e6i −0.314384 + 0.967574i
\(303\) 903935. + 656747.i 0.565627 + 0.410952i
\(304\) 127629. + 92727.9i 0.0792073 + 0.0575475i
\(305\) 2.80429e6 + 1.25442e6i 1.72613 + 0.772134i
\(306\) 313940. 228091.i 0.191665 0.139253i
\(307\) −3.07543e6 −1.86234 −0.931171 0.364583i \(-0.881211\pi\)
−0.931171 + 0.364583i \(0.881211\pi\)
\(308\) 112293. 81585.8i 0.0674492 0.0490047i
\(309\) −500846. 1.54145e6i −0.298406 0.918400i
\(310\) 124415. 26218.6i 0.0735309 0.0154955i
\(311\) 849084. 2.61321e6i 0.497794 1.53205i −0.314763 0.949170i \(-0.601925\pi\)
0.812557 0.582882i \(-0.198075\pi\)
\(312\) 91911.1 + 282873.i 0.0534542 + 0.164515i
\(313\) −400062. 1.23126e6i −0.230816 0.710380i −0.997649 0.0685325i \(-0.978168\pi\)
0.766833 0.641847i \(-0.221832\pi\)
\(314\) 353765. 1.08878e6i 0.202484 0.623182i
\(315\) −151307. + 31885.5i −0.0859176 + 0.0181058i
\(316\) −424272. 1.30578e6i −0.239016 0.735615i
\(317\) 89655.4 65138.4i 0.0501104 0.0364074i −0.562448 0.826833i \(-0.690140\pi\)
0.612559 + 0.790425i \(0.290140\pi\)
\(318\) 363509. 0.201580
\(319\) −3.28604e6 + 2.38745e6i −1.80799 + 1.31358i
\(320\) 209015. + 93496.6i 0.114104 + 0.0510412i
\(321\) 1.10750e6 + 804645.i 0.599903 + 0.435855i
\(322\) −78240.3 56844.9i −0.0420524 0.0305528i
\(323\) 112810. 347194.i 0.0601647 0.185168i
\(324\) 121019. 0.0640457
\(325\) 164879. + 1.62316e6i 0.0865877 + 0.852421i
\(326\) −2.51639e6 −1.31140
\(327\) −78633.2 + 242008.i −0.0406665 + 0.125158i
\(328\) −494098. 358983.i −0.253588 0.184242i
\(329\) −121647. 88381.4i −0.0619598 0.0450164i
\(330\) 1.00031e6 210801.i 0.505652 0.106558i
\(331\) 364874. 265097.i 0.183051 0.132995i −0.492486 0.870320i \(-0.663912\pi\)
0.675537 + 0.737326i \(0.263912\pi\)
\(332\) −753032. −0.374945
\(333\) 1.24700e6 906001.i 0.616250 0.447732i
\(334\) −94853.2 291928.i −0.0465249 0.143189i
\(335\) −1.27117e6 2.21062e6i −0.618857 1.07622i
\(336\) −11894.3 + 36607.0i −0.00574767 + 0.0176895i
\(337\) −123025. 378632.i −0.0590090 0.181611i 0.917207 0.398411i \(-0.130438\pi\)
−0.976216 + 0.216800i \(0.930438\pi\)
\(338\) 122025. + 375553.i 0.0580972 + 0.178805i
\(339\) −279950. + 861597.i −0.132306 + 0.407198i
\(340\) 56304.2 526857.i 0.0264146 0.247170i
\(341\) 90246.3 + 277749.i 0.0420284 + 0.129350i
\(342\) 326576. 237272.i 0.150980 0.109693i
\(343\) 562953. 0.258367
\(344\) −86377.3 + 62756.8i −0.0393553 + 0.0285933i
\(345\) −355062. 617470.i −0.160604 0.279298i
\(346\) −1.39044e6 1.01022e6i −0.624400 0.453653i
\(347\) 3.46313e6 + 2.51611e6i 1.54399 + 1.12178i 0.947769 + 0.318959i \(0.103333\pi\)
0.596224 + 0.802818i \(0.296667\pi\)
\(348\) 348064. 1.07123e6i 0.154068 0.474171i
\(349\) −2.26805e6 −0.996755 −0.498378 0.866960i \(-0.666071\pi\)
−0.498378 + 0.866960i \(0.666071\pi\)
\(350\) −106205. + 182480.i −0.0463422 + 0.0796243i
\(351\) 1.89037e6 0.818991
\(352\) −162519. + 500183.i −0.0699114 + 0.215165i
\(353\) −1.37199e6 996812.i −0.586024 0.425771i 0.254867 0.966976i \(-0.417968\pi\)
−0.840891 + 0.541205i \(0.817968\pi\)
\(354\) −223840. 162629.i −0.0949356 0.0689747i
\(355\) 2.15417e6 2.38407e6i 0.907212 1.00403i
\(356\) 410895. 298533.i 0.171833 0.124844i
\(357\) 89070.0 0.0369880
\(358\) −2.11420e6 + 1.53606e6i −0.871845 + 0.633433i
\(359\) −1.25482e6 3.86194e6i −0.513861 1.58150i −0.785345 0.619058i \(-0.787514\pi\)
0.271484 0.962443i \(-0.412486\pi\)
\(360\) 392800. 434721.i 0.159740 0.176789i
\(361\) −647806. + 1.99374e6i −0.261624 + 0.805195i
\(362\) −136447. 419940.i −0.0547258 0.168429i
\(363\) 282585. + 869706.i 0.112559 + 0.346422i
\(364\) 43601.1 134190.i 0.0172482 0.0530845i
\(365\) 2.84233e6 + 1.27143e6i 1.11671 + 0.499528i
\(366\) −604663. 1.86096e6i −0.235945 0.726163i
\(367\) 3.67128e6 2.66734e6i 1.42283 1.03375i 0.431533 0.902097i \(-0.357973\pi\)
0.991296 0.131649i \(-0.0420272\pi\)
\(368\) 366437. 0.141052
\(369\) −1.26430e6 + 918564.i −0.483373 + 0.351191i
\(370\) 223646. 2.09273e6i 0.0849292 0.794711i
\(371\) −139509. 101359.i −0.0526220 0.0382321i
\(372\) −65518.8 47602.2i −0.0245476 0.0178349i
\(373\) 22176.0 68250.8i 0.00825300 0.0254001i −0.946845 0.321689i \(-0.895749\pi\)
0.955098 + 0.296289i \(0.0957493\pi\)
\(374\) 1.21702e6 0.449902
\(375\) −1.26281e6 + 907430.i −0.463725 + 0.333223i
\(376\) 569730. 0.207826
\(377\) −1.27590e6 + 3.92682e6i −0.462342 + 1.42294i
\(378\) 197914. + 143793.i 0.0712438 + 0.0517617i
\(379\) 1.96297e6 + 1.42618e6i 0.701964 + 0.510007i 0.880571 0.473913i \(-0.157159\pi\)
−0.178607 + 0.983921i \(0.557159\pi\)
\(380\) 58570.5 548063.i 0.0208075 0.194703i
\(381\) −449597. + 326651.i −0.158676 + 0.115285i
\(382\) −1.46355e6 −0.513155
\(383\) 3.97141e6 2.88540e6i 1.38340 1.00510i 0.386845 0.922145i \(-0.373565\pi\)
0.996553 0.0829534i \(-0.0264353\pi\)
\(384\) −45067.8 138705.i −0.0155969 0.0480024i
\(385\) −442683. 198021.i −0.152209 0.0680863i
\(386\) 765594. 2.35626e6i 0.261535 0.804922i
\(387\) 84422.8 + 259827.i 0.0286538 + 0.0881874i
\(388\) −106133. 326644.i −0.0357908 0.110153i
\(389\) 1.34644e6 4.14390e6i 0.451140 1.38847i −0.424467 0.905443i \(-0.639539\pi\)
0.875608 0.483023i \(-0.160461\pi\)
\(390\) 696693. 771047.i 0.231942 0.256696i
\(391\) −262033. 806454.i −0.0866789 0.266770i
\(392\) −855445. + 621517.i −0.281175 + 0.204286i
\(393\) 264307. 0.0863233
\(394\) −2.01279e6 + 1.46238e6i −0.653217 + 0.474590i
\(395\) −3.21601e6 + 3.55924e6i −1.03711 + 1.14780i
\(396\) 1.08872e6 + 791001.i 0.348881 + 0.253477i
\(397\) −1.79497e6 1.30412e6i −0.571584 0.415280i 0.264096 0.964496i \(-0.414926\pi\)
−0.835680 + 0.549216i \(0.814926\pi\)
\(398\) −756641. + 2.32870e6i −0.239432 + 0.736896i
\(399\) 92655.2 0.0291365
\(400\) −80846.9 795904.i −0.0252646 0.248720i
\(401\) −415051. −0.128896 −0.0644481 0.997921i \(-0.520529\pi\)
−0.0644481 + 0.997921i \(0.520529\pi\)
\(402\) −501914. + 1.54473e6i −0.154904 + 0.476747i
\(403\) 240173. + 174496.i 0.0736649 + 0.0535207i
\(404\) 1.62477e6 + 1.18047e6i 0.495267 + 0.359832i
\(405\) −210772. 366543.i −0.0638521 0.111042i
\(406\) −432279. + 314069.i −0.130151 + 0.0945605i
\(407\) 4.83411e6 1.44654
\(408\) −273033. + 198370.i −0.0812017 + 0.0589965i
\(409\) −1.14046e6 3.50996e6i −0.337109 1.03751i −0.965674 0.259757i \(-0.916357\pi\)
0.628565 0.777757i \(-0.283643\pi\)
\(410\) −226747. + 2.12175e6i −0.0666166 + 0.623354i
\(411\) −828024. + 2.54840e6i −0.241790 + 0.744153i
\(412\) −900243. 2.77066e6i −0.261286 0.804157i
\(413\) 40559.4 + 124829.i 0.0117008 + 0.0360114i
\(414\) 289746. 891746.i 0.0830838 0.255706i
\(415\) 1.31152e6 + 2.28079e6i 0.373812 + 0.650077i
\(416\) 165205. + 508449.i 0.0468048 + 0.144050i
\(417\) 470748. 342019.i 0.132571 0.0963185i
\(418\) 1.26600e6 0.354400
\(419\) −4.52052e6 + 3.28435e6i −1.25792 + 0.913932i −0.998654 0.0518739i \(-0.983481\pi\)
−0.259266 + 0.965806i \(0.583481\pi\)
\(420\) 131591. 27730.8i 0.0364002 0.00767078i
\(421\) 3.35679e6 + 2.43885e6i 0.923037 + 0.670625i 0.944278 0.329149i \(-0.106762\pi\)
−0.0212413 + 0.999774i \(0.506762\pi\)
\(422\) −174633. 126879.i −0.0477360 0.0346822i
\(423\) 450492. 1.38647e6i 0.122415 0.376756i
\(424\) 653388. 0.176505
\(425\) −1.69381e6 + 747065.i −0.454876 + 0.200625i
\(426\) −2.04658e6 −0.546392
\(427\) −286842. + 882808.i −0.0761329 + 0.234313i
\(428\) 1.99067e6 + 1.44631e6i 0.525278 + 0.381637i
\(429\) 1.93102e6 + 1.40297e6i 0.506574 + 0.368048i
\(430\) 340517. + 152320.i 0.0888113 + 0.0397271i
\(431\) −1.26566e6 + 919558.i −0.328190 + 0.238444i −0.739662 0.672978i \(-0.765015\pi\)
0.411472 + 0.911422i \(0.365015\pi\)
\(432\) −926927. −0.238966
\(433\) −263625. + 191535.i −0.0675721 + 0.0490940i −0.621059 0.783764i \(-0.713297\pi\)
0.553486 + 0.832858i \(0.313297\pi\)
\(434\) 11871.9 + 36537.9i 0.00302549 + 0.00931150i
\(435\) −3.85076e6 + 811488.i −0.975717 + 0.205617i
\(436\) −141339. + 434996.i −0.0356078 + 0.109590i
\(437\) −272580. 838914.i −0.0682794 0.210142i
\(438\) −612863. 1.88620e6i −0.152643 0.469788i
\(439\) −359917. + 1.10771e6i −0.0891335 + 0.274325i −0.985680 0.168624i \(-0.946068\pi\)
0.896547 + 0.442949i \(0.146068\pi\)
\(440\) 1.79801e6 378902.i 0.442752 0.0933030i
\(441\) 836089. + 2.57322e6i 0.204718 + 0.630057i
\(442\) 1.00086e6 727167.i 0.243679 0.177043i
\(443\) −6.07467e6 −1.47066 −0.735332 0.677707i \(-0.762974\pi\)
−0.735332 + 0.677707i \(0.762974\pi\)
\(444\) −1.08452e6 + 787948.i −0.261083 + 0.189688i
\(445\) −1.61983e6 724584.i −0.387766 0.173456i
\(446\) 324593. + 235831.i 0.0772685 + 0.0561388i
\(447\) −2.59981e6 1.88888e6i −0.615423 0.447131i
\(448\) −21379.4 + 65799.1i −0.00503270 + 0.0154890i
\(449\) 5.21186e6 1.22005 0.610024 0.792383i \(-0.291160\pi\)
0.610024 + 0.792383i \(0.291160\pi\)
\(450\) −2.00081e6 432585.i −0.465772 0.100702i
\(451\) −4.90115e6 −1.13464
\(452\) −503195. + 1.54867e6i −0.115848 + 0.356545i
\(453\) −2.90307e6 2.10920e6i −0.664679 0.482917i
\(454\) 3.50937e6 + 2.54970e6i 0.799078 + 0.580564i
\(455\) −482375. + 101653.i −0.109234 + 0.0230193i
\(456\) −284023. + 206355.i −0.0639649 + 0.0464732i
\(457\) −5.36086e6 −1.20073 −0.600363 0.799727i \(-0.704977\pi\)
−0.600363 + 0.799727i \(0.704977\pi\)
\(458\) −3.77099e6 + 2.73979e6i −0.840025 + 0.610314i
\(459\) 662830. + 2.03998e6i 0.146849 + 0.451954i
\(460\) −638204. 1.10987e6i −0.140626 0.244555i
\(461\) 353023. 1.08649e6i 0.0773662 0.238109i −0.904892 0.425641i \(-0.860049\pi\)
0.982258 + 0.187532i \(0.0600488\pi\)
\(462\) 95451.5 + 293770.i 0.0208055 + 0.0640327i
\(463\) 1.07672e6 + 3.31379e6i 0.233426 + 0.718411i 0.997326 + 0.0730770i \(0.0232819\pi\)
−0.763900 + 0.645334i \(0.776718\pi\)
\(464\) 625626. 1.92548e6i 0.134903 0.415187i
\(465\) −30067.4 + 281350.i −0.00644856 + 0.0603414i
\(466\) 584612. + 1.79925e6i 0.124711 + 0.383820i
\(467\) 6.00353e6 4.36182e6i 1.27384 0.925498i 0.274490 0.961590i \(-0.411491\pi\)
0.999348 + 0.0360922i \(0.0114910\pi\)
\(468\) 1.36797e6 0.288710
\(469\) 623352. 452892.i 0.130858 0.0950741i
\(470\) −992268. 1.72560e6i −0.207197 0.360326i
\(471\) 2.06108e6 + 1.49746e6i 0.428097 + 0.311031i
\(472\) −402340. 292317.i −0.0831262 0.0603947i
\(473\) −264769. + 814875.i −0.0544145 + 0.167470i
\(474\) 3.05539e6 0.624627
\(475\) −1.76199e6 + 777135.i −0.358319 + 0.158038i
\(476\) 160099. 0.0323869
\(477\) 516641. 1.59006e6i 0.103966 0.319976i
\(478\) 5.17874e6 + 3.76258e6i 1.03670 + 0.753209i
\(479\) 6.61576e6 + 4.80663e6i 1.31747 + 0.957198i 0.999960 + 0.00894376i \(0.00284693\pi\)
0.317511 + 0.948255i \(0.397153\pi\)
\(480\) −341617. + 378076.i −0.0676763 + 0.0748991i
\(481\) 3.97552e6 2.88838e6i 0.783485 0.569235i
\(482\) −472788. −0.0926934
\(483\) 174114. 126501.i 0.0339599 0.0246733i
\(484\) 507930. + 1.56325e6i 0.0985577 + 0.303330i
\(485\) −804496. + 890355.i −0.155299 + 0.171874i
\(486\) −1.17078e6 + 3.60331e6i −0.224847 + 0.692007i
\(487\) −2.30500e6 7.09405e6i −0.440400 1.35541i −0.887450 0.460904i \(-0.847525\pi\)
0.447050 0.894509i \(-0.352475\pi\)
\(488\) −1.08685e6 3.34497e6i −0.206595 0.635833i
\(489\) 1.73048e6 5.32586e6i 0.327260 1.00720i
\(490\) 3.37234e6 + 1.50852e6i 0.634515 + 0.283831i
\(491\) −1.17515e6 3.61675e6i −0.219984 0.677041i −0.998762 0.0497414i \(-0.984160\pi\)
0.778778 0.627299i \(-0.215840\pi\)
\(492\) 1.09956e6 798874.i 0.204788 0.148787i
\(493\) −4.68497e6 −0.868139
\(494\) 1.04114e6 756436.i 0.191952 0.139462i
\(495\) 499626. 4.67517e6i 0.0916499 0.857599i
\(496\) −117767. 85562.4i −0.0214940 0.0156163i
\(497\) 785444. + 570658.i 0.142634 + 0.103630i
\(498\) 517845. 1.59376e6i 0.0935678 0.287972i
\(499\) 3.80253e6 0.683630 0.341815 0.939767i \(-0.388958\pi\)
0.341815 + 0.939767i \(0.388958\pi\)
\(500\) −2.26984e6 + 1.63106e6i −0.406041 + 0.291772i
\(501\) 683084. 0.121585
\(502\) 604691. 1.86105e6i 0.107096 0.329608i
\(503\) 621806. + 451769.i 0.109581 + 0.0796152i 0.641226 0.767352i \(-0.278426\pi\)
−0.531645 + 0.846967i \(0.678426\pi\)
\(504\) 143221. + 104056.i 0.0251148 + 0.0182470i
\(505\) 745628. 6.97709e6i 0.130105 1.21743i
\(506\) 2.37903e6 1.72846e6i 0.413070 0.300113i
\(507\) −878758. −0.151827
\(508\) −808125. + 587137.i −0.138938 + 0.100944i
\(509\) −3.29945e6 1.01547e7i −0.564479 1.73729i −0.669496 0.742816i \(-0.733490\pi\)
0.105017 0.994470i \(-0.466510\pi\)
\(510\) 1.07635e6 + 481475.i 0.183244 + 0.0819688i
\(511\) −290732. + 894780.i −0.0492539 + 0.151588i
\(512\) −81007.0 249314.i −0.0136568 0.0420312i
\(513\) 689509. + 2.12209e6i 0.115677 + 0.356017i
\(514\) −278319. + 856576.i −0.0464659 + 0.143007i
\(515\) −6.82391e6 + 7.55219e6i −1.13374 + 1.25474i
\(516\) −73422.4 225971.i −0.0121396 0.0373619i
\(517\) 3.69887e6 2.68739e6i 0.608615 0.442185i
\(518\) 635928. 0.104132
\(519\) 3.09427e6 2.24812e6i 0.504242 0.366353i
\(520\) 1.25227e6 1.38592e6i 0.203090 0.224765i
\(521\) −1.03133e6 749308.i −0.166458 0.120939i 0.501437 0.865194i \(-0.332805\pi\)
−0.667896 + 0.744255i \(0.732805\pi\)
\(522\) −4.19108e6 3.04500e6i −0.673209 0.489115i
\(523\) −281561. + 866556.i −0.0450110 + 0.138529i −0.971036 0.238932i \(-0.923203\pi\)
0.926025 + 0.377461i \(0.123203\pi\)
\(524\) 475078. 0.0755852
\(525\) −313177. 350268.i −0.0495898 0.0554629i
\(526\) 5.34253e6 0.841943
\(527\) −104093. + 320365.i −0.0163265 + 0.0502479i
\(528\) −946857. 687932.i −0.147809 0.107389i
\(529\) 3.54953e6 + 2.57888e6i 0.551482 + 0.400675i
\(530\) −1.13797e6 1.97899e6i −0.175971 0.306023i
\(531\) −1.02950e6 + 747979.i −0.158450 + 0.115121i
\(532\) 166543. 0.0255121
\(533\) −4.03064e6 + 2.92843e6i −0.614549 + 0.446496i
\(534\) 349269. + 1.07494e6i 0.0530037 + 0.163129i
\(535\) 913541. 8.54831e6i 0.137989 1.29121i
\(536\) −902162. + 2.77657e6i −0.135635 + 0.417442i
\(537\) −1.79712e6 5.53095e6i −0.268931 0.827683i
\(538\) −750529. 2.30989e6i −0.111792 0.344061i
\(539\) −2.62216e6 + 8.07019e6i −0.388766 + 1.19650i
\(540\) 1.61438e6 + 2.80749e6i 0.238244 + 0.414318i
\(541\) 2.46082e6 + 7.57364e6i 0.361483 + 1.11253i 0.952154 + 0.305617i \(0.0988628\pi\)
−0.590672 + 0.806912i \(0.701137\pi\)
\(542\) 6.14850e6 4.46714e6i 0.899023 0.653178i
\(543\) 982620. 0.143016
\(544\) −490763. + 356560.i −0.0711008 + 0.0516577i
\(545\) 1.56368e6 329522.i 0.225506 0.0475218i
\(546\) 254025. + 184560.i 0.0364666 + 0.0264945i
\(547\) 188546. + 136986.i 0.0269431 + 0.0195753i 0.601175 0.799117i \(-0.294699\pi\)
−0.574232 + 0.818692i \(0.694699\pi\)
\(548\) −1.48833e6 + 4.58060e6i −0.211713 + 0.651585i
\(549\) −8.99957e6 −1.27436
\(550\) −4.27913e6 4.78592e6i −0.603182 0.674619i
\(551\) −4.87354e6 −0.683857
\(552\) −251991. + 775550.i −0.0351996 + 0.108333i
\(553\) −1.17261e6 851951.i −0.163057 0.118468i
\(554\) −6.91769e6 5.02600e6i −0.957606 0.695741i
\(555\) 4.27539e6 + 1.91247e6i 0.589174 + 0.263549i
\(556\) 846144. 614760.i 0.116080 0.0843371i
\(557\) −1.89788e6 −0.259197 −0.129599 0.991567i \(-0.541369\pi\)
−0.129599 + 0.991567i \(0.541369\pi\)
\(558\) −301340. + 218937.i −0.0409706 + 0.0297669i
\(559\) 269145. + 828343.i 0.0364298 + 0.112119i
\(560\) 236528. 49844.6i 0.0318723 0.00671658i
\(561\) −836918. + 2.57577e6i −0.112273 + 0.345541i
\(562\) 527413. + 1.62321e6i 0.0704385 + 0.216787i
\(563\) 4.06727e6 + 1.25178e7i 0.540794 + 1.66439i 0.730786 + 0.682606i \(0.239154\pi\)
−0.189992 + 0.981786i \(0.560846\pi\)
\(564\) −391792. + 1.20581e6i −0.0518630 + 0.159618i
\(565\) 5.56703e6 1.17316e6i 0.733673 0.154610i
\(566\) 220579. + 678873.i 0.0289417 + 0.0890733i
\(567\) 103358. 75093.9i 0.0135016 0.00980950i
\(568\) −3.67861e6 −0.478424
\(569\) 7.58893e6 5.51368e6i 0.982652 0.713938i 0.0243521 0.999703i \(-0.492248\pi\)
0.958300 + 0.285765i \(0.0922477\pi\)
\(570\) 1.11968e6 + 500855.i 0.144346 + 0.0645691i
\(571\) 5.49114e6 + 3.98954e6i 0.704810 + 0.512074i 0.881495 0.472193i \(-0.156537\pi\)
−0.176685 + 0.984267i \(0.556537\pi\)
\(572\) 3.47090e6 + 2.52175e6i 0.443559 + 0.322265i
\(573\) 1.00645e6 3.09754e6i 0.128058 0.394122i
\(574\) −644746. −0.0816787
\(575\) −2.25005e6 + 3.86600e6i −0.283807 + 0.487632i
\(576\) −670773. −0.0842402
\(577\) −4.16497e6 + 1.28185e7i −0.520802 + 1.60286i 0.251669 + 0.967813i \(0.419021\pi\)
−0.772471 + 0.635050i \(0.780979\pi\)
\(578\) −3.45910e6 2.51318e6i −0.430669 0.312899i
\(579\) 4.46044e6 + 3.24070e6i 0.552945 + 0.401738i
\(580\) −6.92154e6 + 1.45860e6i −0.854343 + 0.180039i
\(581\) −643138. + 467267.i −0.0790431 + 0.0574282i
\(582\) 764315. 0.0935330
\(583\) 4.24201e6 3.08200e6i 0.516892 0.375544i
\(584\) −1.10159e6 3.39034e6i −0.133656 0.411349i
\(585\) −2.38252e6 4.14333e6i −0.287838 0.500564i
\(586\) −204102. + 628161.i −0.0245529 + 0.0755660i
\(587\) 2.14573e6 + 6.60389e6i 0.257028 + 0.791051i 0.993423 + 0.114499i \(0.0365264\pi\)
−0.736395 + 0.676552i \(0.763474\pi\)
\(588\) −727145. 2.23792e6i −0.0867317 0.266933i
\(589\) −108283. + 333259.i −0.0128609 + 0.0395817i
\(590\) −184638. + 1.72772e6i −0.0218369 + 0.204336i
\(591\) −1.71091e6 5.26564e6i −0.201492 0.620129i
\(592\) −1.94936e6 + 1.41629e6i −0.228606 + 0.166092i
\(593\) −1.09158e7 −1.27474 −0.637369 0.770559i \(-0.719977\pi\)
−0.637369 + 0.770559i \(0.719977\pi\)
\(594\) −6.01791e6 + 4.37227e6i −0.699809 + 0.508441i
\(595\) −278835. 484908.i −0.0322891 0.0561522i
\(596\) −4.67302e6 3.39515e6i −0.538868 0.391510i
\(597\) −4.40828e6 3.20280e6i −0.506213 0.367786i
\(598\) 923726. 2.84294e6i 0.105631 0.325098i
\(599\) −5.98857e6 −0.681955 −0.340978 0.940071i \(-0.610758\pi\)
−0.340978 + 0.940071i \(0.610758\pi\)
\(600\) 1.74010e6 + 376219.i 0.197331 + 0.0426640i
\(601\) 6.79095e6 0.766910 0.383455 0.923560i \(-0.374734\pi\)
0.383455 + 0.923560i \(0.374734\pi\)
\(602\) −34830.4 + 107197.i −0.00391712 + 0.0120557i
\(603\) 6.04360e6 + 4.39093e6i 0.676865 + 0.491771i
\(604\) −5.21811e6 3.79118e6i −0.581997 0.422845i
\(605\) 3.85015e6 4.26105e6i 0.427651 0.473291i
\(606\) −3.61574e6 + 2.62699e6i −0.399959 + 0.290587i
\(607\) 8.98882e6 0.990219 0.495109 0.868831i \(-0.335128\pi\)
0.495109 + 0.868831i \(0.335128\pi\)
\(608\) −510516. + 370912.i −0.0560080 + 0.0406922i
\(609\) −367446. 1.13088e6i −0.0401467 0.123559i
\(610\) −8.23839e6 + 9.11762e6i −0.896432 + 0.992104i
\(611\) 1.43619e6 4.42015e6i 0.155636 0.478998i
\(612\) 479658. + 1.47624e6i 0.0517670 + 0.159322i
\(613\) 2.19871e6 + 6.76693e6i 0.236329 + 0.727345i 0.996942 + 0.0781402i \(0.0248982\pi\)
−0.760614 + 0.649205i \(0.775102\pi\)
\(614\) 3.80144e6 1.16996e7i 0.406937 1.25242i
\(615\) −4.33468e6 1.93899e6i −0.462135 0.206722i
\(616\) 171569. + 528035.i 0.0182174 + 0.0560674i
\(617\) −6.89367e6 + 5.00854e6i −0.729016 + 0.529661i −0.889252 0.457417i \(-0.848775\pi\)
0.160236 + 0.987079i \(0.448775\pi\)
\(618\) 6.48309e6 0.682827
\(619\) −4.80501e6 + 3.49104e6i −0.504043 + 0.366209i −0.810559 0.585657i \(-0.800837\pi\)
0.306516 + 0.951865i \(0.400837\pi\)
\(620\) −54044.4 + 505712.i −0.00564640 + 0.0528353i
\(621\) 4.19298e6 + 3.04638e6i 0.436308 + 0.316997i
\(622\) 8.89172e6 + 6.46021e6i 0.921531 + 0.669531i
\(623\) 165687. 509933.i 0.0171029 0.0526372i
\(624\) −1.18972e6 −0.122316
\(625\) 8.89341e6 + 4.03418e6i 0.910686 + 0.413100i
\(626\) 5.17851e6 0.528165
\(627\) −870605. + 2.67945e6i −0.0884407 + 0.272193i
\(628\) 3.70468e6 + 2.69161e6i 0.374845 + 0.272341i
\(629\) 4.51093e6 + 3.27738e6i 0.454610 + 0.330294i
\(630\) 65725.8 615018.i 0.00659758 0.0617357i
\(631\) 5.30615e6 3.85514e6i 0.530525 0.385449i −0.290029 0.957018i \(-0.593665\pi\)
0.820554 + 0.571569i \(0.193665\pi\)
\(632\) 5.49189e6 0.546927
\(633\) 388626. 282353.i 0.0385498 0.0280081i
\(634\) 136981. + 421585.i 0.0135344 + 0.0416545i
\(635\) 3.18580e6 + 1.42507e6i 0.313534 + 0.140250i
\(636\) −449322. + 1.38287e6i −0.0440468 + 0.135562i
\(637\) 2.66550e6 + 8.20356e6i 0.260273 + 0.801039i
\(638\) −5.02062e6 1.54519e7i −0.488322 1.50290i
\(639\) −2.90872e6 + 8.95211e6i −0.281806 + 0.867308i
\(640\) −614039. + 679572.i −0.0592578 + 0.0655821i
\(641\) −3.35196e6 1.03163e7i −0.322221 0.991694i −0.972679 0.232152i \(-0.925423\pi\)
0.650459 0.759542i \(-0.274577\pi\)
\(642\) −4.43000e6 + 3.21858e6i −0.424195 + 0.308196i
\(643\) 1.31460e7 1.25391 0.626957 0.779054i \(-0.284300\pi\)
0.626957 + 0.779054i \(0.284300\pi\)
\(644\) 312961. 227380.i 0.0297355 0.0216041i
\(645\) −556547. + 615945.i −0.0526748 + 0.0582965i
\(646\) 1.18136e6 + 858310.i 0.111379 + 0.0809213i
\(647\) 4.96469e6 + 3.60706e6i 0.466263 + 0.338760i 0.795983 0.605319i \(-0.206954\pi\)
−0.329720 + 0.944079i \(0.606954\pi\)
\(648\) −149587. + 460382.i −0.0139945 + 0.0430706i
\(649\) −3.99096e6 −0.371934
\(650\) −6.37868e6 1.37911e6i −0.592172 0.128031i
\(651\) −85495.3 −0.00790660
\(652\) 3.11043e6 9.57293e6i 0.286551 0.881914i
\(653\) −1.08472e7 7.88093e6i −0.995482 0.723260i −0.0343675 0.999409i \(-0.510942\pi\)
−0.961115 + 0.276149i \(0.910942\pi\)
\(654\) −823457. 598277.i −0.0752829 0.0546963i
\(655\) −827419. 1.43892e6i −0.0753567 0.131049i
\(656\) 1.97639e6 1.43593e6i 0.179314 0.130279i
\(657\) −9.12162e6 −0.824439
\(658\) 486586. 353526.i 0.0438122 0.0318314i
\(659\) 257156. + 791446.i 0.0230666 + 0.0709917i 0.961927 0.273306i \(-0.0881171\pi\)
−0.938861 + 0.344298i \(0.888117\pi\)
\(660\) −434524. + 4.06599e6i −0.0388288 + 0.363334i
\(661\) −715387. + 2.20173e6i −0.0636850 + 0.196002i −0.977836 0.209371i \(-0.932858\pi\)
0.914151 + 0.405373i \(0.132858\pi\)
\(662\) 557478. + 1.71574e6i 0.0494405 + 0.152162i
\(663\) 850750. + 2.61834e6i 0.0751654 + 0.231335i
\(664\) 930798. 2.86470e6i 0.0819286 0.252150i
\(665\) −290059. 504426.i −0.0254350 0.0442327i
\(666\) 1.90525e6 + 5.86376e6i 0.166443 + 0.512260i
\(667\) −9.15819e6 + 6.65381e6i −0.797067 + 0.579103i
\(668\) 1.22781e6 0.106461
\(669\) −722343. + 524813.i −0.0623991 + 0.0453356i
\(670\) 9.98095e6 2.10333e6i 0.858984 0.181017i
\(671\) −2.28342e7 1.65901e7i −1.95785 1.42246i
\(672\) −124559. 90497.5i −0.0106403 0.00773060i
\(673\) 5.44341e6 1.67531e7i 0.463270 1.42580i −0.397876 0.917439i \(-0.630253\pi\)
0.861146 0.508358i \(-0.169747\pi\)
\(674\) 1.59247e6 0.135027
\(675\) 5.69166e6 9.77931e6i 0.480817 0.826131i
\(676\) −1.57952e6 −0.132941
\(677\) 2.04533e6 6.29487e6i 0.171511 0.527855i −0.827946 0.560807i \(-0.810491\pi\)
0.999457 + 0.0329520i \(0.0104908\pi\)
\(678\) −2.93167e6 2.12999e6i −0.244930 0.177952i
\(679\) −293332. 213118.i −0.0244166 0.0177397i
\(680\) 1.93469e6 + 865425.i 0.160450 + 0.0717724i
\(681\) −7.80967e6 + 5.67406e6i −0.645305 + 0.468842i
\(682\) −1.16817e6 −0.0961714
\(683\) −9.43175e6 + 6.85257e6i −0.773643 + 0.562085i −0.903064 0.429505i \(-0.858688\pi\)
0.129421 + 0.991590i \(0.458688\pi\)
\(684\) 498964. + 1.53565e6i 0.0407783 + 0.125503i
\(685\) 1.64659e7 3.46993e6i 1.34079 0.282550i
\(686\) −695848. + 2.14160e6i −0.0564552 + 0.173751i
\(687\) −3.20542e6 9.86527e6i −0.259115 0.797475i
\(688\) −131973. 406171.i −0.0106295 0.0327143i
\(689\) 1.64708e6 5.06919e6i 0.132180 0.406809i
\(690\) 2.78787e6 587501.i 0.222921 0.0469770i
\(691\) −5.05220e6 1.55491e7i −0.402518 1.23882i −0.922950 0.384920i \(-0.874229\pi\)
0.520432 0.853903i \(-0.325771\pi\)
\(692\) 5.56177e6 4.04086e6i 0.441518 0.320781i
\(693\) 1.42066e6 0.112372
\(694\) −1.38525e7 + 1.00644e7i −1.09177 + 0.793216i
\(695\) −3.33568e6 1.49212e6i −0.261952 0.117176i
\(696\) 3.64498e6 + 2.64823e6i 0.285214 + 0.207220i
\(697\) −4.57348e6 3.32283e6i −0.356586 0.259075i
\(698\) 2.80346e6 8.62817e6i 0.217799 0.670317i
\(699\) −4.21008e6 −0.325910
\(700\) −562919. 629588.i −0.0434211 0.0485636i
\(701\) 3.15730e6 0.242672 0.121336 0.992611i \(-0.461282\pi\)
0.121336 + 0.992611i \(0.461282\pi\)
\(702\) −2.33663e6 + 7.19140e6i −0.178956 + 0.550770i
\(703\) 4.69249e6 + 3.40930e6i 0.358109 + 0.260182i
\(704\) −1.70192e6 1.23652e6i −0.129422 0.0940307i
\(705\) 4.33454e6 913436.i 0.328451 0.0692158i
\(706\) 5.48797e6 3.98725e6i 0.414381 0.301066i
\(707\) 2.12016e6 0.159522
\(708\) 895359. 650516.i 0.0671296 0.0487725i
\(709\) −1.38088e6 4.24992e6i −0.103167 0.317516i 0.886129 0.463439i \(-0.153385\pi\)
−0.989296 + 0.145923i \(0.953385\pi\)
\(710\) 6.40684e6 + 1.11418e7i 0.476978 + 0.829488i
\(711\) 4.34250e6 1.33648e7i 0.322156 0.991494i
\(712\) 627791. + 1.93214e6i 0.0464104 + 0.142837i
\(713\) 251516. + 774087.i 0.0185286 + 0.0570251i
\(714\) −110097. + 338843.i −0.00808218 + 0.0248744i
\(715\) 1.59284e6 1.49047e7i 0.116521 1.09033i
\(716\) −3.23022e6 9.94159e6i −0.235477 0.724725i
\(717\) −1.15247e7 + 8.37317e6i −0.837203 + 0.608264i
\(718\) 1.62427e7 1.17584
\(719\) 6.14151e6 4.46207e6i 0.443050 0.321895i −0.343796 0.939045i \(-0.611713\pi\)
0.786846 + 0.617150i \(0.211713\pi\)
\(720\) 1.16825e6 + 2.03164e6i 0.0839855 + 0.146055i
\(721\) −2.48810e6 1.80771e6i −0.178250 0.129506i
\(722\) −6.78391e6 4.92880e6i −0.484325 0.351883i
\(723\) 325127. 1.00064e6i 0.0231317 0.0711921i
\(724\) 1.76620e6 0.125226
\(725\) 1.64727e7 + 1.84236e7i 1.16391 + 1.30176i
\(726\) −3.65785e6 −0.257564
\(727\) 4.40017e6 1.35423e7i 0.308769 0.950292i −0.669476 0.742834i \(-0.733481\pi\)
0.978244 0.207458i \(-0.0665189\pi\)
\(728\) 456597. + 331737.i 0.0319304 + 0.0231988i
\(729\) −5.33419e6 3.87551e6i −0.371749 0.270091i
\(730\) −8.35011e6 + 9.24127e6i −0.579943 + 0.641837i
\(731\) −799528. + 580891.i −0.0553401 + 0.0402070i
\(732\) 7.82692e6 0.539900
\(733\) 2.16307e7 1.57156e7i 1.48700 1.08037i 0.511778 0.859118i \(-0.328987\pi\)
0.975218 0.221248i \(-0.0710129\pi\)
\(734\) 5.60922e6 + 1.72634e7i 0.384293 + 1.18273i
\(735\) −5.51182e6 + 6.10006e6i −0.376336 + 0.416501i
\(736\) −452941. + 1.39401e6i −0.0308210 + 0.0948573i
\(737\) 7.23981e6 + 2.22819e7i 0.490974 + 1.51106i
\(738\) −1.93167e6 5.94507e6i −0.130555 0.401806i
\(739\) −5.45632e6 + 1.67928e7i −0.367527 + 1.13113i 0.580857 + 0.814005i \(0.302717\pi\)
−0.948384 + 0.317125i \(0.897283\pi\)
\(740\) 7.68478e6 + 3.43756e6i 0.515884 + 0.230765i
\(741\) 884993. + 2.72373e6i 0.0592099 + 0.182229i
\(742\) 558036. 405437.i 0.0372094 0.0270342i
\(743\) 1.47880e6 0.0982737 0.0491368 0.998792i \(-0.484353\pi\)
0.0491368 + 0.998792i \(0.484353\pi\)
\(744\) 262075. 190409.i 0.0173578 0.0126112i
\(745\) −2.14451e6 + 2.00669e7i −0.141559 + 1.32461i
\(746\) 232230. + 168725.i 0.0152782 + 0.0111003i
\(747\) −6.23543e6 4.53030e6i −0.408851 0.297047i
\(748\) −1.50432e6 + 4.62981e6i −0.0983071 + 0.302558i
\(749\) 2.59762e6 0.169188
\(750\) −1.89115e6 5.92567e6i −0.122764 0.384666i
\(751\) −1.60998e7 −1.04165 −0.520824 0.853664i \(-0.674375\pi\)
−0.520824 + 0.853664i \(0.674375\pi\)
\(752\) −704224. + 2.16738e6i −0.0454116 + 0.139762i
\(753\) 3.52300e6 + 2.55961e6i 0.226426 + 0.164508i
\(754\) −1.33614e7 9.70762e6i −0.855901 0.621848i
\(755\) −2.39465e6 + 2.24076e7i −0.152888 + 1.43063i
\(756\) −791656. + 575172.i −0.0503770 + 0.0366010i
\(757\) −2.65168e7 −1.68183 −0.840914 0.541168i \(-0.817982\pi\)
−0.840914 + 0.541168i \(0.817982\pi\)
\(758\) −7.85187e6 + 5.70472e6i −0.496364 + 0.360629i
\(759\) 2.02222e6 + 6.22375e6i 0.127416 + 0.392146i
\(760\) 2.01256e6 + 900259.i 0.126391 + 0.0565371i
\(761\) 4.98907e6 1.53548e7i 0.312290 0.961130i −0.664566 0.747230i \(-0.731383\pi\)
0.976856 0.213900i \(-0.0686166\pi\)
\(762\) −686923. 2.11413e6i −0.0428569 0.131900i
\(763\) 149209. + 459218.i 0.00927862 + 0.0285567i
\(764\) 1.80904e6 5.56766e6i 0.112128 0.345096i
\(765\) 3.63584e6 4.02388e6i 0.224622 0.248594i
\(766\) 6.06777e6 + 1.86747e7i 0.373643 + 1.14996i
\(767\) −3.28212e6 + 2.38460e6i −0.201449 + 0.146362i
\(768\) 583370. 0.0356896
\(769\) 1.30116e7 9.45346e6i 0.793440 0.576468i −0.115542 0.993303i \(-0.536861\pi\)
0.908982 + 0.416835i \(0.136861\pi\)
\(770\) 1.30050e6 1.43930e6i 0.0790469 0.0874832i
\(771\) −1.62152e6 1.17810e6i −0.0982394 0.0713751i
\(772\) 8.01740e6 + 5.82498e6i 0.484162 + 0.351764i
\(773\) −8.17027e6 + 2.51455e7i −0.491799 + 1.51360i 0.330087 + 0.943951i \(0.392922\pi\)
−0.821886 + 0.569652i \(0.807078\pi\)
\(774\) −1.09279e6 −0.0655670
\(775\) 1.62583e6 717082.i 0.0972348 0.0428859i
\(776\) 1.37381e6 0.0818981
\(777\) −437315. + 1.34592e6i −0.0259861 + 0.0799771i
\(778\) 1.41001e7 + 1.02443e7i 0.835164 + 0.606782i
\(779\) −4.75757e6 3.45657e6i −0.280893 0.204081i
\(780\) 2.07208e6 + 3.60344e6i 0.121947 + 0.212071i
\(781\) −2.38827e7 + 1.73518e7i −1.40106 + 1.01793i
\(782\) 3.39182e6 0.198343
\(783\) 2.31663e7 1.68313e7i 1.35037 0.981099i
\(784\) −1.30700e6 4.02255e6i −0.0759428 0.233728i
\(785\) 1.70012e6 1.59086e7i 0.0984704 0.921421i
\(786\) −326702. + 1.00548e6i −0.0188623 + 0.0580523i
\(787\) −3.15846e6 9.72074e6i −0.181777 0.559451i 0.818101 0.575074i \(-0.195027\pi\)
−0.999878 + 0.0156229i \(0.995027\pi\)
\(788\) −3.07527e6 9.46470e6i −0.176428 0.542989i
\(789\) −3.67395e6 + 1.13073e7i −0.210107 + 0.646644i
\(790\) −9.56495e6 1.66339e7i −0.545274 0.948258i
\(791\) 531214. + 1.63491e6i 0.0301876 + 0.0929078i
\(792\) −4.35488e6 + 3.16400e6i −0.246696 + 0.179235i
\(793\) −2.86911e7 −1.62019
\(794\) 7.17986e6 5.21648e6i 0.404171 0.293647i
\(795\) 4.97101e6 1.04756e6i 0.278951 0.0587844i
\(796\) −7.92365e6 5.75687e6i −0.443244 0.322035i
\(797\) 2.29781e7 + 1.66946e7i 1.28135 + 0.930958i 0.999593 0.0285266i \(-0.00908154\pi\)
0.281761 + 0.959485i \(0.409082\pi\)
\(798\) −114528. + 352481.i −0.00636656 + 0.0195943i
\(799\) 5.27354e6 0.292237
\(800\) 3.12773e6 + 676232.i 0.172784 + 0.0373569i
\(801\) 5.19839e6 0.286277
\(802\) 513031. 1.57895e6i 0.0281649 0.0866826i
\(803\) −2.31439e7 1.68150e7i −1.26662 0.920257i
\(804\) −5.25611e6 3.81879e6i −0.286764 0.208346i
\(805\) −1.23376e6 551885.i −0.0671027 0.0300164i
\(806\) −960690. + 697982.i −0.0520890 + 0.0378449i
\(807\) 5.40492e6 0.292150
\(808\) −6.49909e6 + 4.72187e6i −0.350207 + 0.254440i
\(809\) 1.07447e7 + 3.30688e7i 0.577196 + 1.77643i 0.628578 + 0.777747i \(0.283637\pi\)
−0.0513817 + 0.998679i \(0.516363\pi\)
\(810\) 1.65494e6 348752.i 0.0886277 0.0186769i
\(811\) −931001. + 2.86533e6i −0.0497048 + 0.152976i −0.972828 0.231528i \(-0.925627\pi\)
0.923123 + 0.384504i \(0.125627\pi\)
\(812\) −660463. 2.03270e6i −0.0351527 0.108189i
\(813\) 5.22634e6 + 1.60850e7i 0.277314 + 0.853484i
\(814\) −5.97529e6 + 1.83901e7i −0.316081 + 0.972797i
\(815\) −3.44119e7 + 7.25176e6i −1.81474 + 0.382428i
\(816\) −417158. 1.28388e6i −0.0219318 0.0674993i
\(817\) −831709. + 604272.i −0.0435930 + 0.0316721i
\(818\) 1.47624e7 0.771388
\(819\) 1.16834e6 848846.i 0.0608637 0.0442201i
\(820\) −7.79134e6 3.48523e6i −0.404648 0.181007i
\(821\) −5.50752e6 4.00145e6i −0.285166 0.207185i 0.436001 0.899946i \(-0.356394\pi\)
−0.721168 + 0.692761i \(0.756394\pi\)
\(822\) −8.67118e6 6.29998e6i −0.447609 0.325207i
\(823\) 414188. 1.27474e6i 0.0213156 0.0656028i −0.939833 0.341635i \(-0.889019\pi\)
0.961149 + 0.276032i \(0.0890195\pi\)
\(824\) 1.16530e7 0.597887
\(825\) 1.30719e7 5.76543e6i 0.668657 0.294915i
\(826\) −525011. −0.0267743
\(827\) 7.10278e6 2.18601e7i 0.361131 1.11145i −0.591238 0.806497i \(-0.701361\pi\)
0.952369 0.304949i \(-0.0986394\pi\)
\(828\) 3.03426e6 + 2.20452e6i 0.153807 + 0.111747i
\(829\) −2.22988e7 1.62010e7i −1.12693 0.818760i −0.141681 0.989912i \(-0.545251\pi\)
−0.985245 + 0.171153i \(0.945251\pi\)
\(830\) −1.02978e7 + 2.17009e6i −0.518857 + 0.109341i
\(831\) 1.53945e7 1.11848e7i 0.773326 0.561855i
\(832\) −2.13846e6 −0.107101
\(833\) −7.91819e6 + 5.75290e6i −0.395379 + 0.287260i
\(834\) 719239. + 2.21359e6i 0.0358062 + 0.110200i
\(835\) −2.13841e6 3.71879e6i −0.106139 0.184580i
\(836\) −1.56486e6 + 4.81616e6i −0.0774392 + 0.238333i
\(837\) −636227. 1.95811e6i −0.0313905 0.0966101i
\(838\) −6.90673e6 2.12567e7i −0.339752 1.04565i
\(839\) 2.36854e6 7.28961e6i 0.116165 0.357519i −0.876023 0.482269i \(-0.839813\pi\)
0.992188 + 0.124750i \(0.0398128\pi\)
\(840\) −57161.6 + 534881.i −0.00279516 + 0.0261552i
\(841\) 1.29889e7 + 3.99756e7i 0.633258 + 1.94897i
\(842\) −1.34272e7 + 9.75540e6i −0.652686 + 0.474204i
\(843\) −3.79816e6 −0.184079
\(844\) 698533. 507514.i 0.0337544 0.0245240i
\(845\) 2.75097e6 + 4.78406e6i 0.132539 + 0.230492i
\(846\) 4.71761e6 + 3.42754e6i 0.226619 + 0.164648i
\(847\) 1.40382e6 + 1.01994e6i 0.0672364 + 0.0488501i
\(848\) −807632. + 2.48563e6i −0.0385677 + 0.118699i
\(849\) −1.58850e6 −0.0756341
\(850\) −748337. 7.36707e6i −0.0355263 0.349742i
\(851\) 1.34727e7 0.637719
\(852\) 2.52971e6 7.78564e6i 0.119391 0.367448i
\(853\) −5.64819e6 4.10365e6i −0.265789 0.193107i 0.446906 0.894581i \(-0.352526\pi\)
−0.712695 + 0.701474i \(0.752526\pi\)
\(854\) −3.00384e6 2.18242e6i −0.140940 0.102399i
\(855\) 3.78219e6 4.18584e6i 0.176941 0.195825i
\(856\) −7.96267e6 + 5.78522e6i −0.371428 + 0.269858i
\(857\) 2.99029e7 1.39079 0.695394 0.718629i \(-0.255230\pi\)
0.695394 + 0.718629i \(0.255230\pi\)
\(858\) −7.72407e6 + 5.61186e6i −0.358202 + 0.260249i
\(859\) −9.23253e6 2.84148e7i −0.426912 1.31390i −0.901152 0.433503i \(-0.857277\pi\)
0.474240 0.880395i \(-0.342723\pi\)
\(860\) −1.00036e6 + 1.10713e6i −0.0461224 + 0.0510448i
\(861\) 443379. 1.36458e6i 0.0203830 0.0627324i
\(862\) −1.93376e6 5.95151e6i −0.0886410 0.272809i
\(863\) 6.97915e6 + 2.14796e7i 0.318989 + 0.981746i 0.974081 + 0.226198i \(0.0726295\pi\)
−0.655093 + 0.755548i \(0.727370\pi\)
\(864\) 1.14574e6 3.52624e6i 0.0522160 0.160704i
\(865\) −2.19257e7 9.80779e6i −0.996351 0.445688i
\(866\) −402784. 1.23964e6i −0.0182506 0.0561696i
\(867\) 7.69782e6 5.59279e6i 0.347792 0.252686i
\(868\) −153673. −0.00692307
\(869\) 3.56552e7 2.59050e7i 1.60167 1.16368i
\(870\) 1.67272e6 1.56522e7i 0.0749248 0.701097i
\(871\) 1.92673e7 + 1.39985e7i 0.860550 + 0.625226i
\(872\) −1.48012e6 1.07537e6i −0.0659182 0.0478924i
\(873\) 1.08629e6 3.34326e6i 0.0482403 0.148469i
\(874\) 3.52834e6 0.156240
\(875\) −926495. + 2.80150e6i −0.0409094 + 0.123700i
\(876\) 7.93306e6 0.349286
\(877\) −200629. + 617472.i −0.00880835 + 0.0271093i −0.955364 0.295431i \(-0.904537\pi\)
0.946556 + 0.322540i \(0.104537\pi\)
\(878\) −3.76910e6 2.73841e6i −0.165007 0.119884i
\(879\) −1.18912e6 863948.i −0.0519104 0.0377151i
\(880\) −781033. + 7.30839e6i −0.0339987 + 0.318138i
\(881\) 1.35066e7 9.81310e6i 0.586281 0.425958i −0.254702 0.967020i \(-0.581977\pi\)
0.840983 + 0.541062i \(0.181977\pi\)
\(882\) −1.08226e7 −0.468445
\(883\) 2.29791e7 1.66953e7i 0.991818 0.720598i 0.0314998 0.999504i \(-0.489972\pi\)
0.960319 + 0.278906i \(0.0899716\pi\)
\(884\) 1.52918e6 + 4.70632e6i 0.0658153 + 0.202559i
\(885\) −3.52969e6 1.57890e6i −0.151488 0.0677637i
\(886\) 7.50871e6 2.31094e7i 0.321352 0.989019i
\(887\) 6.79384e6 + 2.09093e7i 0.289939 + 0.892339i 0.984875 + 0.173268i \(0.0554326\pi\)
−0.694936 + 0.719071i \(0.744567\pi\)
\(888\) −1.65699e6 5.09970e6i −0.0705161 0.217026i
\(889\) −325864. + 1.00291e6i −0.0138287 + 0.0425605i
\(890\) 4.75870e6 5.26657e6i 0.201379 0.222871i
\(891\) 1.20043e6 + 3.69455e6i 0.0506574 + 0.155907i
\(892\) −1.29837e6 + 943323.i −0.0546371 + 0.0396961i
\(893\) 5.48581e6 0.230203
\(894\) 1.03993e7 7.55550e6i 0.435170 0.316169i
\(895\) −2.44853e7 + 2.70985e7i −1.02176 + 1.13080i
\(896\) −223888. 162664.i −0.00931668 0.00676896i
\(897\) 5.38174e6 + 3.91006e6i 0.223327 + 0.162257i
\(898\) −6.44221e6 + 1.98271e7i −0.266590 + 0.820480i
\(899\) 4.49694e6 0.185574
\(900\) 4.11878e6 7.07682e6i 0.169497 0.291227i
\(901\) 6.04790e6 0.248195
\(902\) 6.05815e6 1.86451e7i 0.247927 0.763041i
\(903\) −202926. 147434.i −0.00828168 0.00601699i
\(904\) −5.26952e6 3.82853e6i −0.214462 0.155816i
\(905\) −3.07611e6 5.34950e6i −0.124848 0.217116i
\(906\) 1.16123e7 8.43681e6i 0.469999 0.341474i
\(907\) 1.03369e7 0.417227 0.208613 0.977998i \(-0.433105\pi\)
0.208613 + 0.977998i \(0.433105\pi\)
\(908\) −1.40375e7 + 1.01988e7i −0.565033 + 0.410521i
\(909\) 6.35204e6 + 1.95496e7i 0.254978 + 0.784743i
\(910\) 209538. 1.96071e6i 0.00838800 0.0784893i
\(911\) 770915. 2.37263e6i 0.0307759 0.0947185i −0.934489 0.355993i \(-0.884143\pi\)
0.965265 + 0.261274i \(0.0841427\pi\)
\(912\) −433949. 1.33556e6i −0.0172763 0.0531711i
\(913\) −7.46962e6 2.29891e7i −0.296566 0.912736i
\(914\) 6.62639e6 2.03939e7i 0.262368 0.807487i
\(915\) −1.36317e7 2.37062e7i −0.538268 0.936074i
\(916\) −5.76157e6 1.77323e7i −0.226883 0.698274i
\(917\) 405748. 294793.i 0.0159343 0.0115769i
\(918\) −8.57985e6 −0.336026
\(919\) 2.06836e7 1.50275e7i 0.807861 0.586946i −0.105349 0.994435i \(-0.533596\pi\)
0.913210 + 0.407490i \(0.133596\pi\)
\(920\) 5.01105e6 1.05600e6i 0.195191 0.0411334i
\(921\) 2.21476e7 + 1.60912e7i 0.860356 + 0.625085i
\(922\) 3.69691e6 + 2.68596e6i 0.143223 + 0.104057i
\(923\) −9.27316e6 + 2.85398e7i −0.358281 + 1.10267i
\(924\) −1.23555e6 −0.0476081
\(925\) −2.97247e6 2.92628e7i −0.114226 1.12450i
\(926\) −1.39373e7 −0.534136
\(927\) 9.21415e6 2.83582e7i 0.352173 1.08388i
\(928\) 6.55165e6 + 4.76005e6i 0.249736 + 0.181444i
\(929\) −1.90227e7 1.38208e7i −0.723158 0.525405i 0.164234 0.986421i \(-0.447485\pi\)
−0.887391 + 0.461017i \(0.847485\pi\)
\(930\) −1.03316e6 462151.i −0.0391704 0.0175217i
\(931\) −8.23691e6 + 5.98446e6i −0.311451 + 0.226282i
\(932\) −7.56738e6 −0.285368
\(933\) −1.97875e7 + 1.43764e7i −0.744194 + 0.540688i
\(934\) 9.17257e6 + 2.82303e7i 0.344052 + 1.05888i
\(935\) 1.66428e7 3.50721e6i 0.622583 0.131200i
\(936\) −1.69091e6 + 5.20407e6i −0.0630855 + 0.194157i
\(937\) −312690. 962361.i −0.0116350 0.0358088i 0.945070 0.326867i \(-0.105993\pi\)
−0.956705 + 0.291058i \(0.905993\pi\)
\(938\) 952397. + 2.93118e6i 0.0353436 + 0.108776i
\(939\) −3.56116e6 + 1.09601e7i −0.131804 + 0.405650i
\(940\) 7.79109e6 1.64185e6i 0.287593 0.0606058i
\(941\) 5.56408e6 + 1.71245e7i 0.204842 + 0.630439i 0.999720 + 0.0236693i \(0.00753488\pi\)
−0.794878 + 0.606769i \(0.792465\pi\)
\(942\) −8.24432e6 + 5.98985e6i −0.302711 + 0.219932i
\(943\) −1.36595e7 −0.500213
\(944\) 1.60936e6 1.16927e6i 0.0587791 0.0427055i
\(945\) 3.12087e6 + 1.39603e6i 0.113683 + 0.0508528i
\(946\) −2.77270e6 2.01448e6i −0.100734 0.0731873i
\(947\) −3.05159e7 2.21711e7i −1.10574 0.803365i −0.123750 0.992313i \(-0.539492\pi\)
−0.981987 + 0.188949i \(0.939492\pi\)
\(948\) −3.77667e6 + 1.16234e7i −0.136486 + 0.420061i
\(949\) −2.90802e7 −1.04817
\(950\) −778458. 7.66360e6i −0.0279850 0.275501i
\(951\) −986468. −0.0353697
\(952\) −197893. + 609051.i −0.00707681 + 0.0217802i
\(953\) −7.15157e6 5.19592e6i −0.255076 0.185323i 0.452898 0.891563i \(-0.350390\pi\)
−0.707973 + 0.706239i \(0.750390\pi\)
\(954\) 5.41033e6 + 3.93084e6i 0.192466 + 0.139834i
\(955\) −2.00141e7 + 4.21766e6i −0.710114 + 0.149645i
\(956\) −2.07150e7 + 1.50503e7i −0.733060 + 0.532599i
\(957\) 3.61559e7 1.27614
\(958\) −2.64630e7 + 1.92265e7i −0.931592 + 0.676842i
\(959\) 1.57120e6 + 4.83566e6i 0.0551678 + 0.169789i
\(960\) −1.01603e6 1.76692e6i −0.0355817 0.0618783i
\(961\) −8.74698e6 + 2.69204e7i −0.305527 + 0.940315i
\(962\) 6.07405e6 + 1.86940e7i 0.211612 + 0.651275i
\(963\) 7.78250e6 + 2.39521e7i 0.270429 + 0.832295i
\(964\) 584398. 1.79859e6i 0.0202543 0.0623362i
\(965\) 3.67928e6 3.44283e7i 0.127188 1.19014i
\(966\) 266023. + 818735.i 0.00917226 + 0.0282293i
\(967\) −2.97462e7 + 2.16119e7i −1.02297 + 0.743235i −0.966891 0.255191i \(-0.917862\pi\)
−0.0560841 + 0.998426i \(0.517862\pi\)
\(968\) −6.57479e6 −0.225524
\(969\) −2.62898e6 + 1.91007e6i −0.0899452 + 0.0653490i
\(970\) −2.39270e6 4.16102e6i −0.0816506 0.141994i
\(971\) 652637. + 474168.i 0.0222138 + 0.0161393i 0.598837 0.800871i \(-0.295630\pi\)
−0.576623 + 0.817010i \(0.695630\pi\)
\(972\) −1.22606e7 8.90786e6i −0.416243 0.302418i
\(973\) 341195. 1.05009e6i 0.0115537 0.0355586i
\(974\) 2.98365e7 1.00774
\(975\) 7.30532e6 1.25519e7i 0.246109 0.422860i
\(976\) 1.40685e7 0.472739
\(977\) 1.07937e7 3.32196e7i 0.361771 1.11342i −0.590208 0.807251i \(-0.700954\pi\)
0.951979 0.306165i \(-0.0990458\pi\)
\(978\) 1.81218e7 + 1.31662e7i 0.605834 + 0.440164i
\(979\) 1.31896e7 + 9.58284e6i 0.439822 + 0.319549i
\(980\) −9.90719e6 + 1.09645e7i −0.329523 + 0.364691i
\(981\) −3.78732e6 + 2.75165e6i −0.125649 + 0.0912895i
\(982\) 1.52115e7 0.503377
\(983\) −5.38823e6 + 3.91478e6i −0.177853 + 0.129218i −0.673150 0.739506i \(-0.735059\pi\)
0.495297 + 0.868724i \(0.335059\pi\)
\(984\) 1.67997e6 + 5.17042e6i 0.0553113 + 0.170231i
\(985\) −2.33107e7 + 2.57986e7i −0.765536 + 0.847237i
\(986\) 5.79094e6 1.78227e7i 0.189695 0.583822i
\(987\) 413608. + 1.27295e6i 0.0135144 + 0.0415930i
\(988\) 1.59073e6 + 4.89575e6i 0.0518446 + 0.159561i
\(989\) −737910. + 2.27105e6i −0.0239890 + 0.0738307i
\(990\) 1.71678e7 + 7.67951e6i 0.556708 + 0.249027i
\(991\) 1.37702e7 + 4.23803e7i 0.445405 + 1.37082i 0.882038 + 0.471177i \(0.156171\pi\)
−0.436633 + 0.899640i \(0.643829\pi\)
\(992\) 471066. 342250.i 0.0151986 0.0110424i
\(993\) −4.01467e6 −0.129204
\(994\) −3.14177e6 + 2.28263e6i −0.100858 + 0.0732774i
\(995\) −3.63625e6 + 3.40257e7i −0.116438 + 1.08955i
\(996\) 5.42294e6 + 3.94000e6i 0.173216 + 0.125848i
\(997\) −3.41613e7 2.48197e7i −1.08842 0.790784i −0.109289 0.994010i \(-0.534857\pi\)
−0.979132 + 0.203226i \(0.934857\pi\)
\(998\) −4.70018e6 + 1.44657e7i −0.149379 + 0.459740i
\(999\) −3.40800e7 −1.08040
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 50.6.d.b.21.3 28
25.6 even 5 inner 50.6.d.b.31.3 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
50.6.d.b.21.3 28 1.1 even 1 trivial
50.6.d.b.31.3 yes 28 25.6 even 5 inner