Properties

Label 33.5.h.a.5.10
Level $33$
Weight $5$
Character 33.5
Analytic conductor $3.411$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [33,5,Mod(5,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 4]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.5");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 33.h (of order \(10\), 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: \(3.41120878177\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 5.10
Character \(\chi\) \(=\) 33.5
Dual form 33.5.h.a.20.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.36002 - 0.766817i) q^{2} +(-7.49818 - 4.97767i) q^{3} +(-7.96259 + 5.78516i) q^{4} +(-40.2655 - 13.0831i) q^{5} +(-21.5128 - 5.99767i) q^{6} +(50.3841 - 36.6062i) q^{7} +(-37.6929 + 51.8798i) q^{8} +(31.4455 + 74.6470i) q^{9} +O(q^{10})\) \(q+(2.36002 - 0.766817i) q^{2} +(-7.49818 - 4.97767i) q^{3} +(-7.96259 + 5.78516i) q^{4} +(-40.2655 - 13.0831i) q^{5} +(-21.5128 - 5.99767i) q^{6} +(50.3841 - 36.6062i) q^{7} +(-37.6929 + 51.8798i) q^{8} +(31.4455 + 74.6470i) q^{9} -105.060 q^{10} +(-31.4973 - 116.829i) q^{11} +(88.5016 - 3.74302i) q^{12} +(-16.7307 - 51.4918i) q^{13} +(90.8372 - 125.027i) q^{14} +(236.795 + 298.528i) q^{15} +(-0.510564 + 1.57135i) q^{16} +(-286.232 - 93.0025i) q^{17} +(131.453 + 152.055i) q^{18} +(26.2484 + 19.0705i) q^{19} +(396.306 - 128.767i) q^{20} +(-560.003 + 23.6843i) q^{21} +(-163.920 - 251.565i) q^{22} +422.615i q^{23} +(540.869 - 201.381i) q^{24} +(944.511 + 686.227i) q^{25} +(-78.9695 - 108.692i) q^{26} +(135.784 - 716.243i) q^{27} +(-189.415 + 582.960i) q^{28} +(-350.116 - 481.893i) q^{29} +(787.757 + 522.953i) q^{30} +(-281.574 - 866.597i) q^{31} -1021.93i q^{32} +(-345.362 + 1032.79i) q^{33} -746.830 q^{34} +(-2507.66 + 814.789i) q^{35} +(-682.233 - 412.466i) q^{36} +(-1047.11 + 760.770i) q^{37} +(76.5702 + 24.8792i) q^{38} +(-130.859 + 469.375i) q^{39} +(2196.47 - 1595.83i) q^{40} +(825.931 - 1136.80i) q^{41} +(-1303.46 + 485.315i) q^{42} -883.407 q^{43} +(926.672 + 748.041i) q^{44} +(-289.559 - 3417.11i) q^{45} +(324.068 + 997.380i) q^{46} +(-848.681 + 1168.11i) q^{47} +(11.6500 - 9.24087i) q^{48} +(456.594 - 1405.25i) q^{49} +(2755.27 + 895.243i) q^{50} +(1683.29 + 2122.12i) q^{51} +(431.108 + 313.218i) q^{52} +(3520.73 - 1143.96i) q^{53} +(-228.774 - 1794.47i) q^{54} +(-260.220 + 5116.25i) q^{55} +3993.71i q^{56} +(-101.888 - 273.650i) q^{57} +(-1195.80 - 868.802i) q^{58} +(948.882 + 1306.02i) q^{59} +(-3612.53 - 1007.16i) q^{60} +(2098.97 - 6459.97i) q^{61} +(-1329.04 - 1829.27i) q^{62} +(4316.90 + 2609.92i) q^{63} +(-791.803 - 2436.92i) q^{64} +2292.23i q^{65} +(-23.1035 + 2702.22i) q^{66} -1694.79 q^{67} +(2817.19 - 915.359i) q^{68} +(2103.64 - 3168.85i) q^{69} +(-5293.34 + 3845.84i) q^{70} +(3613.35 + 1174.05i) q^{71} +(-5057.94 - 1182.27i) q^{72} +(1040.84 - 756.211i) q^{73} +(-1887.83 + 2598.37i) q^{74} +(-3666.30 - 9846.93i) q^{75} -319.331 q^{76} +(-5863.61 - 4733.31i) q^{77} +(51.0936 + 1208.08i) q^{78} +(1496.64 + 4606.20i) q^{79} +(41.1162 - 56.5916i) q^{80} +(-4583.36 + 4694.63i) q^{81} +(1077.50 - 3316.20i) q^{82} +(-8647.58 - 2809.77i) q^{83} +(4322.06 - 3428.30i) q^{84} +(10308.5 + 7489.59i) q^{85} +(-2084.86 + 677.411i) q^{86} +(226.526 + 5356.08i) q^{87} +(7248.26 + 2769.53i) q^{88} -42.1422i q^{89} +(-3303.66 - 7842.40i) q^{90} +(-2727.88 - 1981.92i) q^{91} +(-2444.90 - 3365.11i) q^{92} +(-2202.34 + 7899.49i) q^{93} +(-1107.18 + 3407.54i) q^{94} +(-807.403 - 1111.29i) q^{95} +(-5086.84 + 7662.62i) q^{96} +(-3031.59 - 9330.26i) q^{97} -3666.55i q^{98} +(7730.46 - 6024.92i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 90 q^{4} - 83 q^{6} - 86 q^{7} + 232 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 90 q^{4} - 83 q^{6} - 86 q^{7} + 232 q^{9} + 136 q^{10} - 710 q^{12} + 94 q^{13} - 406 q^{15} + 334 q^{16} + 1149 q^{18} + 958 q^{19} - 728 q^{21} - 1300 q^{22} + 795 q^{24} - 1740 q^{25} - 1026 q^{27} - 4962 q^{28} - 744 q^{30} - 130 q^{31} - 2875 q^{33} + 4844 q^{34} + 11631 q^{36} + 2802 q^{37} + 8696 q^{39} - 626 q^{40} + 8804 q^{42} - 980 q^{43} - 17356 q^{45} + 8698 q^{46} - 17854 q^{48} + 7516 q^{49} + 1461 q^{51} + 11818 q^{52} - 9082 q^{54} - 4916 q^{55} - 2661 q^{57} - 38922 q^{58} - 28194 q^{60} - 15150 q^{61} - 488 q^{63} - 30690 q^{64} + 20100 q^{66} + 40544 q^{67} + 25662 q^{69} + 15720 q^{70} + 72430 q^{72} - 20554 q^{73} + 28841 q^{75} + 70996 q^{76} - 39716 q^{78} + 46458 q^{79} - 24284 q^{81} + 26200 q^{82} - 8346 q^{84} - 15494 q^{85} - 66228 q^{87} - 78050 q^{88} - 43484 q^{90} - 49854 q^{91} - 30184 q^{93} - 119550 q^{94} + 50098 q^{96} - 64476 q^{97} + 52640 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.36002 0.766817i 0.590005 0.191704i 0.00122714 0.999999i \(-0.499609\pi\)
0.588778 + 0.808295i \(0.299609\pi\)
\(3\) −7.49818 4.97767i −0.833132 0.553075i
\(4\) −7.96259 + 5.78516i −0.497662 + 0.361573i
\(5\) −40.2655 13.0831i −1.61062 0.523323i −0.640918 0.767609i \(-0.721446\pi\)
−0.969703 + 0.244287i \(0.921446\pi\)
\(6\) −21.5128 5.99767i −0.597578 0.166602i
\(7\) 50.3841 36.6062i 1.02825 0.747065i 0.0602898 0.998181i \(-0.480798\pi\)
0.967957 + 0.251116i \(0.0807975\pi\)
\(8\) −37.6929 + 51.8798i −0.588951 + 0.810621i
\(9\) 31.4455 + 74.6470i 0.388216 + 0.921568i
\(10\) −105.060 −1.05060
\(11\) −31.4973 116.829i −0.260308 0.965526i
\(12\) 88.5016 3.74302i 0.614595 0.0259932i
\(13\) −16.7307 51.4918i −0.0989982 0.304685i 0.889277 0.457369i \(-0.151208\pi\)
−0.988275 + 0.152684i \(0.951208\pi\)
\(14\) 90.8372 125.027i 0.463455 0.637891i
\(15\) 236.795 + 298.528i 1.05242 + 1.32679i
\(16\) −0.510564 + 1.57135i −0.00199439 + 0.00613810i
\(17\) −286.232 93.0025i −0.990423 0.321808i −0.231391 0.972861i \(-0.574328\pi\)
−0.759032 + 0.651053i \(0.774328\pi\)
\(18\) 131.453 + 152.055i 0.405718 + 0.469307i
\(19\) 26.2484 + 19.0705i 0.0727101 + 0.0528270i 0.623547 0.781786i \(-0.285691\pi\)
−0.550836 + 0.834613i \(0.685691\pi\)
\(20\) 396.306 128.767i 0.990764 0.321919i
\(21\) −560.003 + 23.6843i −1.26985 + 0.0537060i
\(22\) −163.920 251.565i −0.338678 0.519762i
\(23\) 422.615i 0.798894i 0.916756 + 0.399447i \(0.130798\pi\)
−0.916756 + 0.399447i \(0.869202\pi\)
\(24\) 540.869 201.381i 0.939008 0.349620i
\(25\) 944.511 + 686.227i 1.51122 + 1.09796i
\(26\) −78.9695 108.692i −0.116819 0.160787i
\(27\) 135.784 716.243i 0.186261 0.982500i
\(28\) −189.415 + 582.960i −0.241601 + 0.743572i
\(29\) −350.116 481.893i −0.416309 0.573000i 0.548434 0.836194i \(-0.315224\pi\)
−0.964743 + 0.263194i \(0.915224\pi\)
\(30\) 787.757 + 522.953i 0.875286 + 0.581059i
\(31\) −281.574 866.597i −0.293001 0.901766i −0.983885 0.178800i \(-0.942778\pi\)
0.690884 0.722966i \(-0.257222\pi\)
\(32\) 1021.93i 0.997979i
\(33\) −345.362 + 1032.79i −0.317137 + 0.948380i
\(34\) −746.830 −0.646046
\(35\) −2507.66 + 814.789i −2.04707 + 0.665134i
\(36\) −682.233 412.466i −0.526414 0.318261i
\(37\) −1047.11 + 760.770i −0.764872 + 0.555712i −0.900401 0.435061i \(-0.856727\pi\)
0.135529 + 0.990773i \(0.456727\pi\)
\(38\) 76.5702 + 24.8792i 0.0530265 + 0.0172293i
\(39\) −130.859 + 469.375i −0.0860351 + 0.308596i
\(40\) 2196.47 1595.83i 1.37279 0.997393i
\(41\) 825.931 1136.80i 0.491333 0.676262i −0.489300 0.872116i \(-0.662748\pi\)
0.980633 + 0.195853i \(0.0627477\pi\)
\(42\) −1303.46 + 485.315i −0.738921 + 0.275122i
\(43\) −883.407 −0.477776 −0.238888 0.971047i \(-0.576783\pi\)
−0.238888 + 0.971047i \(0.576783\pi\)
\(44\) 926.672 + 748.041i 0.478653 + 0.386385i
\(45\) −289.559 3417.11i −0.142992 1.68746i
\(46\) 324.068 + 997.380i 0.153151 + 0.471351i
\(47\) −848.681 + 1168.11i −0.384192 + 0.528795i −0.956689 0.291112i \(-0.905975\pi\)
0.572497 + 0.819907i \(0.305975\pi\)
\(48\) 11.6500 9.24087i 0.00505642 0.00401080i
\(49\) 456.594 1405.25i 0.190168 0.585278i
\(50\) 2755.27 + 895.243i 1.10211 + 0.358097i
\(51\) 1683.29 + 2122.12i 0.647169 + 0.815887i
\(52\) 431.108 + 313.218i 0.159433 + 0.115835i
\(53\) 3520.73 1143.96i 1.25338 0.407247i 0.394247 0.919005i \(-0.371006\pi\)
0.859130 + 0.511758i \(0.171006\pi\)
\(54\) −228.774 1794.47i −0.0784546 0.615387i
\(55\) −260.220 + 5116.25i −0.0860231 + 1.69132i
\(56\) 3993.71i 1.27350i
\(57\) −101.888 273.650i −0.0313598 0.0842260i
\(58\) −1195.80 868.802i −0.355471 0.258264i
\(59\) 948.882 + 1306.02i 0.272589 + 0.375186i 0.923262 0.384172i \(-0.125513\pi\)
−0.650673 + 0.759358i \(0.725513\pi\)
\(60\) −3612.53 1007.16i −1.00348 0.279766i
\(61\) 2098.97 6459.97i 0.564088 1.73608i −0.106559 0.994306i \(-0.533983\pi\)
0.670647 0.741777i \(-0.266017\pi\)
\(62\) −1329.04 1829.27i −0.345744 0.475876i
\(63\) 4316.90 + 2609.92i 1.08765 + 0.657577i
\(64\) −791.803 2436.92i −0.193311 0.594951i
\(65\) 2292.23i 0.542540i
\(66\) −23.1035 + 2702.22i −0.00530384 + 0.620345i
\(67\) −1694.79 −0.377542 −0.188771 0.982021i \(-0.560450\pi\)
−0.188771 + 0.982021i \(0.560450\pi\)
\(68\) 2817.19 915.359i 0.609253 0.197958i
\(69\) 2103.64 3168.85i 0.441848 0.665584i
\(70\) −5293.34 + 3845.84i −1.08027 + 0.784865i
\(71\) 3613.35 + 1174.05i 0.716793 + 0.232900i 0.644632 0.764493i \(-0.277010\pi\)
0.0721610 + 0.997393i \(0.477010\pi\)
\(72\) −5057.94 1182.27i −0.975683 0.228062i
\(73\) 1040.84 756.211i 0.195315 0.141905i −0.485830 0.874054i \(-0.661482\pi\)
0.681145 + 0.732149i \(0.261482\pi\)
\(74\) −1887.83 + 2598.37i −0.344746 + 0.474502i
\(75\) −3666.30 9846.93i −0.651787 1.75056i
\(76\) −319.331 −0.0552858
\(77\) −5863.61 4733.31i −0.988972 0.798331i
\(78\) 51.0936 + 1208.08i 0.00839802 + 0.198566i
\(79\) 1496.64 + 4606.20i 0.239808 + 0.738054i 0.996447 + 0.0842210i \(0.0268402\pi\)
−0.756639 + 0.653833i \(0.773160\pi\)
\(80\) 41.1162 56.5916i 0.00642441 0.00884244i
\(81\) −4583.36 + 4694.63i −0.698576 + 0.715536i
\(82\) 1077.50 3316.20i 0.160247 0.493188i
\(83\) −8647.58 2809.77i −1.25527 0.407863i −0.395466 0.918481i \(-0.629417\pi\)
−0.859808 + 0.510617i \(0.829417\pi\)
\(84\) 4322.06 3428.30i 0.612536 0.485870i
\(85\) 10308.5 + 7489.59i 1.42679 + 1.03662i
\(86\) −2084.86 + 677.411i −0.281890 + 0.0915916i
\(87\) 226.526 + 5356.08i 0.0299281 + 0.707634i
\(88\) 7248.26 + 2769.53i 0.935984 + 0.357636i
\(89\) 42.1422i 0.00532031i −0.999996 0.00266016i \(-0.999153\pi\)
0.999996 0.00266016i \(-0.000846755\pi\)
\(90\) −3303.66 7842.40i −0.407859 0.968197i
\(91\) −2727.88 1981.92i −0.329414 0.239333i
\(92\) −2444.90 3365.11i −0.288858 0.397579i
\(93\) −2202.34 + 7899.49i −0.254635 + 0.913341i
\(94\) −1107.18 + 3407.54i −0.125303 + 0.385643i
\(95\) −807.403 1111.29i −0.0894629 0.123135i
\(96\) −5086.84 + 7662.62i −0.551957 + 0.831448i
\(97\) −3031.59 9330.26i −0.322201 0.991631i −0.972688 0.232115i \(-0.925436\pi\)
0.650488 0.759517i \(-0.274564\pi\)
\(98\) 3666.55i 0.381773i
\(99\) 7730.46 6024.92i 0.788742 0.614725i
\(100\) −11490.7 −1.14907
\(101\) 9769.71 3174.37i 0.957720 0.311182i 0.211872 0.977298i \(-0.432044\pi\)
0.745849 + 0.666115i \(0.232044\pi\)
\(102\) 5599.87 + 3717.47i 0.538242 + 0.357312i
\(103\) −4920.14 + 3574.69i −0.463771 + 0.336949i −0.795009 0.606598i \(-0.792534\pi\)
0.331238 + 0.943547i \(0.392534\pi\)
\(104\) 3302.01 + 1072.89i 0.305289 + 0.0991945i
\(105\) 22858.7 + 6372.89i 2.07335 + 0.578040i
\(106\) 7431.79 5399.51i 0.661427 0.480555i
\(107\) 2945.41 4054.01i 0.257264 0.354093i −0.660775 0.750584i \(-0.729772\pi\)
0.918039 + 0.396491i \(0.129772\pi\)
\(108\) 3062.39 + 6488.68i 0.262550 + 0.556300i
\(109\) −8684.63 −0.730968 −0.365484 0.930818i \(-0.619096\pi\)
−0.365484 + 0.930818i \(0.619096\pi\)
\(110\) 3309.10 + 12274.0i 0.273479 + 1.01438i
\(111\) 11638.3 492.221i 0.944589 0.0399498i
\(112\) 31.7970 + 97.8610i 0.00253483 + 0.00780142i
\(113\) −61.0132 + 83.9774i −0.00477823 + 0.00657666i −0.811399 0.584492i \(-0.801294\pi\)
0.806621 + 0.591069i \(0.201294\pi\)
\(114\) −450.297 567.690i −0.0346489 0.0436819i
\(115\) 5529.10 17016.8i 0.418079 1.28672i
\(116\) 5575.66 + 1811.64i 0.414362 + 0.134634i
\(117\) 3317.60 2868.08i 0.242355 0.209517i
\(118\) 3240.86 + 2354.62i 0.232754 + 0.169105i
\(119\) −17826.0 + 5792.03i −1.25881 + 0.409013i
\(120\) −24413.0 + 1032.51i −1.69535 + 0.0717019i
\(121\) −12656.8 + 7359.57i −0.864479 + 0.502669i
\(122\) 16855.2i 1.13244i
\(123\) −11851.6 + 4412.69i −0.783369 + 0.291671i
\(124\) 7255.46 + 5271.40i 0.471869 + 0.342833i
\(125\) −13499.9 18581.0i −0.863991 1.18918i
\(126\) 12189.3 + 2849.20i 0.767781 + 0.179466i
\(127\) −746.647 + 2297.94i −0.0462922 + 0.142473i −0.971531 0.236913i \(-0.923865\pi\)
0.925239 + 0.379385i \(0.123865\pi\)
\(128\) 5873.48 + 8084.15i 0.358488 + 0.493417i
\(129\) 6623.95 + 4397.31i 0.398050 + 0.264246i
\(130\) 1757.72 + 5409.71i 0.104007 + 0.320101i
\(131\) 10439.5i 0.608327i 0.952620 + 0.304164i \(0.0983770\pi\)
−0.952620 + 0.304164i \(0.901623\pi\)
\(132\) −3224.85 10221.6i −0.185081 0.586640i
\(133\) 2020.60 0.114229
\(134\) −3999.73 + 1299.59i −0.222752 + 0.0723764i
\(135\) −14838.1 + 27063.4i −0.814160 + 1.48496i
\(136\) 15613.9 11344.1i 0.844175 0.613329i
\(137\) −7320.35 2378.53i −0.390023 0.126726i 0.107439 0.994212i \(-0.465735\pi\)
−0.497463 + 0.867485i \(0.665735\pi\)
\(138\) 2534.71 9091.64i 0.133097 0.477402i
\(139\) 1033.29 750.730i 0.0534802 0.0388556i −0.560724 0.828003i \(-0.689477\pi\)
0.614204 + 0.789147i \(0.289477\pi\)
\(140\) 15253.8 20995.1i 0.778256 1.07118i
\(141\) 12178.0 4534.24i 0.612546 0.228069i
\(142\) 9427.87 0.467559
\(143\) −5488.74 + 3576.48i −0.268411 + 0.174897i
\(144\) −133.352 + 11.3000i −0.00643093 + 0.000544945i
\(145\) 7792.96 + 23984.3i 0.370652 + 1.14075i
\(146\) 1876.52 2582.80i 0.0880332 0.121167i
\(147\) −10418.5 + 8264.06i −0.482138 + 0.382436i
\(148\) 3936.53 12115.4i 0.179717 0.553113i
\(149\) −25630.3 8327.78i −1.15447 0.375108i −0.331642 0.943405i \(-0.607602\pi\)
−0.822823 + 0.568297i \(0.807602\pi\)
\(150\) −16203.3 20427.6i −0.720148 0.907891i
\(151\) −28175.4 20470.6i −1.23571 0.897794i −0.238403 0.971166i \(-0.576624\pi\)
−0.997305 + 0.0733722i \(0.976624\pi\)
\(152\) −1978.75 + 642.935i −0.0856454 + 0.0278279i
\(153\) −2058.36 24290.9i −0.0879305 1.03767i
\(154\) −17467.8 6674.38i −0.736541 0.281429i
\(155\) 38577.8i 1.60574i
\(156\) −1673.43 4494.48i −0.0687635 0.184684i
\(157\) −10727.2 7793.75i −0.435197 0.316189i 0.348527 0.937299i \(-0.386682\pi\)
−0.783724 + 0.621110i \(0.786682\pi\)
\(158\) 7064.22 + 9723.06i 0.282976 + 0.389483i
\(159\) −32093.3 8947.47i −1.26947 0.353921i
\(160\) −13370.0 + 41148.6i −0.522265 + 1.60737i
\(161\) 15470.3 + 21293.1i 0.596826 + 0.821461i
\(162\) −7216.89 + 14594.0i −0.274992 + 0.556089i
\(163\) 2198.17 + 6765.27i 0.0827343 + 0.254630i 0.983864 0.178921i \(-0.0572605\pi\)
−0.901129 + 0.433551i \(0.857261\pi\)
\(164\) 13830.0i 0.514202i
\(165\) 27418.2 37067.3i 1.00710 1.36152i
\(166\) −22563.0 −0.818807
\(167\) 36019.7 11703.5i 1.29154 0.419646i 0.418908 0.908029i \(-0.362413\pi\)
0.872630 + 0.488382i \(0.162413\pi\)
\(168\) 19879.4 29945.5i 0.704343 1.06100i
\(169\) 20734.8 15064.7i 0.725985 0.527459i
\(170\) 30071.5 + 9770.82i 1.04054 + 0.338091i
\(171\) −598.166 + 2559.04i −0.0204564 + 0.0875156i
\(172\) 7034.21 5110.65i 0.237771 0.172751i
\(173\) −16959.3 + 23342.5i −0.566651 + 0.779928i −0.992153 0.125030i \(-0.960097\pi\)
0.425502 + 0.904957i \(0.360097\pi\)
\(174\) 4641.74 + 12466.8i 0.153314 + 0.411770i
\(175\) 72708.5 2.37416
\(176\) 199.660 + 10.1550i 0.00644565 + 0.000327835i
\(177\) −613.930 14516.0i −0.0195962 0.463342i
\(178\) −32.3153 99.4564i −0.00101993 0.00313901i
\(179\) 17155.7 23612.9i 0.535431 0.736958i −0.452515 0.891757i \(-0.649473\pi\)
0.987946 + 0.154799i \(0.0494731\pi\)
\(180\) 22074.1 + 25533.9i 0.681301 + 0.788082i
\(181\) −10840.4 + 33363.3i −0.330893 + 1.01838i 0.637817 + 0.770188i \(0.279838\pi\)
−0.968710 + 0.248195i \(0.920162\pi\)
\(182\) −7957.61 2585.58i −0.240237 0.0780577i
\(183\) −47894.1 + 37990.0i −1.43014 + 1.13440i
\(184\) −21925.2 15929.6i −0.647601 0.470510i
\(185\) 52115.6 16933.4i 1.52274 0.494767i
\(186\) 859.895 + 20331.7i 0.0248553 + 0.587690i
\(187\) −1849.80 + 36369.5i −0.0528984 + 1.04005i
\(188\) 14210.9i 0.402075i
\(189\) −19377.6 41057.8i −0.542469 1.14940i
\(190\) −2757.64 2003.55i −0.0763891 0.0554999i
\(191\) 38245.3 + 52640.1i 1.04836 + 1.44295i 0.890221 + 0.455529i \(0.150550\pi\)
0.158141 + 0.987417i \(0.449450\pi\)
\(192\) −6193.10 + 22213.8i −0.167999 + 0.602588i
\(193\) 18552.1 57097.4i 0.498056 1.53286i −0.314084 0.949395i \(-0.601697\pi\)
0.812140 0.583463i \(-0.198303\pi\)
\(194\) −14309.2 19694.9i −0.380200 0.523300i
\(195\) 11410.0 17187.6i 0.300065 0.452007i
\(196\) 4493.94 + 13830.9i 0.116981 + 0.360030i
\(197\) 41792.9i 1.07689i −0.842661 0.538444i \(-0.819012\pi\)
0.842661 0.538444i \(-0.180988\pi\)
\(198\) 13624.0 20146.8i 0.347516 0.513896i
\(199\) 9442.99 0.238453 0.119227 0.992867i \(-0.461958\pi\)
0.119227 + 0.992867i \(0.461958\pi\)
\(200\) −71202.6 + 23135.1i −1.78007 + 0.578378i
\(201\) 12707.8 + 8436.10i 0.314542 + 0.208809i
\(202\) 20622.5 14983.1i 0.505405 0.367198i
\(203\) −35280.5 11463.3i −0.856136 0.278176i
\(204\) −25680.1 7159.50i −0.617074 0.172037i
\(205\) −48129.3 + 34968.0i −1.14525 + 0.832076i
\(206\) −8870.50 + 12209.2i −0.209032 + 0.287708i
\(207\) −31547.0 + 13289.4i −0.736236 + 0.310144i
\(208\) 89.4538 0.00206763
\(209\) 1401.23 3667.23i 0.0320788 0.0839548i
\(210\) 58833.7 2488.27i 1.33410 0.0564234i
\(211\) 1547.67 + 4763.25i 0.0347628 + 0.106989i 0.966932 0.255033i \(-0.0820865\pi\)
−0.932169 + 0.362022i \(0.882086\pi\)
\(212\) −21416.2 + 29476.9i −0.476508 + 0.655858i
\(213\) −21249.6 26789.3i −0.468372 0.590477i
\(214\) 3842.54 11826.1i 0.0839057 0.258235i
\(215\) 35570.9 + 11557.7i 0.769516 + 0.250031i
\(216\) 32040.4 + 34041.7i 0.686737 + 0.729632i
\(217\) −45909.7 33355.3i −0.974956 0.708347i
\(218\) −20495.9 + 6659.52i −0.431274 + 0.140130i
\(219\) −11568.5 + 489.271i −0.241207 + 0.0102014i
\(220\) −27526.3 42244.0i −0.568725 0.872810i
\(221\) 16294.6i 0.333626i
\(222\) 27089.1 10086.1i 0.549654 0.204652i
\(223\) −72342.8 52560.1i −1.45474 1.05693i −0.984694 0.174290i \(-0.944237\pi\)
−0.470047 0.882642i \(-0.655763\pi\)
\(224\) −37409.0 51489.1i −0.745555 1.02617i
\(225\) −21524.2 + 92083.7i −0.425169 + 1.81894i
\(226\) −79.5970 + 244.974i −0.00155840 + 0.00479627i
\(227\) −48550.4 66823.9i −0.942195 1.29682i −0.954908 0.296901i \(-0.904047\pi\)
0.0127131 0.999919i \(-0.495953\pi\)
\(228\) 2394.40 + 1589.53i 0.0460604 + 0.0305772i
\(229\) 21492.8 + 66148.2i 0.409848 + 1.26138i 0.916779 + 0.399396i \(0.130780\pi\)
−0.506931 + 0.861987i \(0.669220\pi\)
\(230\) 44399.8i 0.839316i
\(231\) 20405.6 + 64678.4i 0.382407 + 1.21209i
\(232\) 38197.3 0.709671
\(233\) −16153.8 + 5248.67i −0.297551 + 0.0966803i −0.453988 0.891008i \(-0.649999\pi\)
0.156437 + 0.987688i \(0.449999\pi\)
\(234\) 5630.31 9312.72i 0.102825 0.170077i
\(235\) 49455.0 35931.2i 0.895519 0.650633i
\(236\) −15111.1 4909.90i −0.271314 0.0881553i
\(237\) 11706.0 41987.9i 0.208407 0.747528i
\(238\) −37628.3 + 27338.6i −0.664295 + 0.482639i
\(239\) 49253.2 67791.2i 0.862260 1.18680i −0.118766 0.992922i \(-0.537894\pi\)
0.981026 0.193877i \(-0.0621063\pi\)
\(240\) −589.992 + 219.671i −0.0102429 + 0.00381374i
\(241\) 99776.0 1.71788 0.858939 0.512079i \(-0.171124\pi\)
0.858939 + 0.512079i \(0.171124\pi\)
\(242\) −24226.9 + 27074.2i −0.413683 + 0.462301i
\(243\) 57735.2 12386.7i 0.977751 0.209771i
\(244\) 20658.7 + 63580.9i 0.346995 + 1.06794i
\(245\) −36770.0 + 50609.6i −0.612578 + 0.843142i
\(246\) −24586.2 + 19502.0i −0.406277 + 0.322262i
\(247\) 542.823 1670.64i 0.00889742 0.0273835i
\(248\) 55572.2 + 18056.5i 0.903554 + 0.293583i
\(249\) 50855.0 + 64113.0i 0.820229 + 1.03406i
\(250\) −46108.1 33499.5i −0.737730 0.535992i
\(251\) 37301.0 12119.8i 0.592070 0.192375i 0.00236919 0.999997i \(-0.499246\pi\)
0.589700 + 0.807622i \(0.299246\pi\)
\(252\) −49472.5 + 4192.20i −0.779045 + 0.0660148i
\(253\) 49373.5 13311.2i 0.771353 0.207959i
\(254\) 5995.73i 0.0929340i
\(255\) −40014.6 107471.i −0.615372 1.65276i
\(256\) 53228.0 + 38672.4i 0.812195 + 0.590094i
\(257\) −11240.3 15471.0i −0.170182 0.234235i 0.715404 0.698711i \(-0.246243\pi\)
−0.885586 + 0.464476i \(0.846243\pi\)
\(258\) 19004.6 + 5298.39i 0.285508 + 0.0795984i
\(259\) −24908.8 + 76661.4i −0.371324 + 1.14282i
\(260\) −13260.9 18252.1i −0.196168 0.270002i
\(261\) 24962.3 41288.5i 0.366441 0.606105i
\(262\) 8005.19 + 24637.4i 0.116619 + 0.358916i
\(263\) 113300.i 1.63802i 0.573779 + 0.819010i \(0.305477\pi\)
−0.573779 + 0.819010i \(0.694523\pi\)
\(264\) −40563.0 56845.9i −0.581999 0.815627i
\(265\) −156731. −2.23184
\(266\) 4768.65 1549.43i 0.0673957 0.0218982i
\(267\) −209.770 + 315.990i −0.00294253 + 0.00443252i
\(268\) 13494.9 9804.61i 0.187888 0.136509i
\(269\) 56479.3 + 18351.2i 0.780521 + 0.253607i 0.672063 0.740494i \(-0.265409\pi\)
0.108458 + 0.994101i \(0.465409\pi\)
\(270\) −14265.5 + 75248.3i −0.195685 + 1.03221i
\(271\) 15889.7 11544.5i 0.216360 0.157195i −0.474327 0.880349i \(-0.657308\pi\)
0.690687 + 0.723154i \(0.257308\pi\)
\(272\) 292.280 402.288i 0.00395058 0.00543751i
\(273\) 10588.8 + 28439.3i 0.142076 + 0.381587i
\(274\) −19100.1 −0.254410
\(275\) 50421.4 131960.i 0.666730 1.74493i
\(276\) 1581.86 + 37402.1i 0.0207658 + 0.490996i
\(277\) 14794.2 + 45532.0i 0.192812 + 0.593413i 0.999995 + 0.00311241i \(0.000990713\pi\)
−0.807184 + 0.590300i \(0.799009\pi\)
\(278\) 1862.91 2564.08i 0.0241048 0.0331774i
\(279\) 55834.6 48269.3i 0.717291 0.620101i
\(280\) 52249.9 160809.i 0.666453 2.05113i
\(281\) −17718.2 5757.00i −0.224392 0.0729094i 0.194663 0.980870i \(-0.437639\pi\)
−0.419055 + 0.907961i \(0.637639\pi\)
\(282\) 25263.5 20039.2i 0.317683 0.251989i
\(283\) 24583.0 + 17860.6i 0.306947 + 0.223010i 0.730585 0.682822i \(-0.239247\pi\)
−0.423639 + 0.905831i \(0.639247\pi\)
\(284\) −35563.7 + 11555.4i −0.440931 + 0.143267i
\(285\) 522.393 + 12351.7i 0.00643143 + 0.152067i
\(286\) −10211.0 + 12649.4i −0.124835 + 0.154646i
\(287\) 87510.7i 1.06242i
\(288\) 76284.1 32135.2i 0.919706 0.387432i
\(289\) 5709.60 + 4148.26i 0.0683612 + 0.0496673i
\(290\) 36783.1 + 50627.5i 0.437373 + 0.601992i
\(291\) −23711.6 + 85050.2i −0.280011 + 1.00436i
\(292\) −3912.94 + 12042.8i −0.0458921 + 0.141241i
\(293\) 52963.8 + 72898.4i 0.616941 + 0.849147i 0.997126 0.0757640i \(-0.0241395\pi\)
−0.380185 + 0.924911i \(0.624140\pi\)
\(294\) −18250.9 + 27492.4i −0.211149 + 0.318067i
\(295\) −21120.4 65002.0i −0.242694 0.746935i
\(296\) 82999.4i 0.947309i
\(297\) −87954.5 + 6696.24i −0.997114 + 0.0759134i
\(298\) −66873.8 −0.753050
\(299\) 21761.2 7070.64i 0.243411 0.0790891i
\(300\) 86159.3 + 57196.9i 0.957326 + 0.635521i
\(301\) −44509.7 + 32338.2i −0.491271 + 0.356930i
\(302\) −82191.6 26705.7i −0.901184 0.292812i
\(303\) −89056.0 24828.4i −0.970014 0.270435i
\(304\) −43.3680 + 31.5087i −0.000469269 + 0.000340944i
\(305\) −169032. + 232653.i −1.81706 + 2.50097i
\(306\) −23484.5 55748.6i −0.250806 0.595376i
\(307\) 21209.5 0.225037 0.112518 0.993650i \(-0.464108\pi\)
0.112518 + 0.993650i \(0.464108\pi\)
\(308\) 74072.5 + 3767.44i 0.780828 + 0.0397141i
\(309\) 54685.8 2312.84i 0.572740 0.0242230i
\(310\) 29582.1 + 91044.4i 0.307827 + 0.947393i
\(311\) 69175.3 95211.7i 0.715205 0.984395i −0.284465 0.958687i \(-0.591816\pi\)
0.999669 0.0257084i \(-0.00818415\pi\)
\(312\) −19418.6 24481.0i −0.199484 0.251490i
\(313\) 29878.3 91956.0i 0.304977 0.938623i −0.674709 0.738084i \(-0.735731\pi\)
0.979686 0.200539i \(-0.0642693\pi\)
\(314\) −31292.7 10167.6i −0.317383 0.103124i
\(315\) −139676. 161568.i −1.40767 1.62830i
\(316\) −38564.7 28018.9i −0.386204 0.280593i
\(317\) −119767. + 38914.8i −1.19184 + 0.387254i −0.836755 0.547578i \(-0.815550\pi\)
−0.355090 + 0.934832i \(0.615550\pi\)
\(318\) −82602.0 + 3493.51i −0.816838 + 0.0345468i
\(319\) −45271.2 + 56081.9i −0.444877 + 0.551113i
\(320\) 108483.i 1.05940i
\(321\) −42264.8 + 15736.4i −0.410175 + 0.152720i
\(322\) 52838.2 + 38389.2i 0.509608 + 0.370252i
\(323\) −5739.52 7899.77i −0.0550137 0.0757198i
\(324\) 9336.21 63896.9i 0.0889366 0.608681i
\(325\) 19532.7 60115.6i 0.184925 0.569142i
\(326\) 10375.4 + 14280.6i 0.0976273 + 0.134372i
\(327\) 65118.9 + 43229.2i 0.608992 + 0.404280i
\(328\) 27845.0 + 85698.2i 0.258821 + 0.796570i
\(329\) 89921.1i 0.830749i
\(330\) 36283.6 108504.i 0.333183 0.996365i
\(331\) 58328.1 0.532380 0.266190 0.963921i \(-0.414235\pi\)
0.266190 + 0.963921i \(0.414235\pi\)
\(332\) 85112.1 27654.6i 0.772174 0.250895i
\(333\) −89716.1 54240.8i −0.809062 0.489145i
\(334\) 76032.7 55241.0i 0.681566 0.495186i
\(335\) 68241.5 + 22173.0i 0.608078 + 0.197576i
\(336\) 248.701 892.054i 0.00220292 0.00790156i
\(337\) 134151. 97466.6i 1.18123 0.858215i 0.188922 0.981992i \(-0.439501\pi\)
0.992310 + 0.123777i \(0.0395008\pi\)
\(338\) 37382.7 51452.9i 0.327218 0.450377i
\(339\) 875.500 325.975i 0.00761828 0.00283651i
\(340\) −125411. −1.08487
\(341\) −92374.5 + 60191.4i −0.794407 + 0.517638i
\(342\) 550.635 + 6498.08i 0.00470773 + 0.0555562i
\(343\) 17771.4 + 54694.8i 0.151055 + 0.464898i
\(344\) 33298.1 45831.0i 0.281386 0.387295i
\(345\) −126162. + 100073.i −1.05997 + 0.840775i
\(346\) −22124.9 + 68093.3i −0.184811 + 0.568790i
\(347\) 25571.7 + 8308.75i 0.212374 + 0.0690044i 0.413272 0.910608i \(-0.364386\pi\)
−0.200898 + 0.979612i \(0.564386\pi\)
\(348\) −32789.5 41337.8i −0.270755 0.341341i
\(349\) −42027.2 30534.6i −0.345048 0.250692i 0.401740 0.915754i \(-0.368405\pi\)
−0.746789 + 0.665061i \(0.768405\pi\)
\(350\) 171593. 55754.1i 1.40076 0.455135i
\(351\) −39152.4 + 4991.47i −0.317793 + 0.0405148i
\(352\) −119391. + 32188.1i −0.963574 + 0.259782i
\(353\) 126542.i 1.01551i −0.861500 0.507757i \(-0.830475\pi\)
0.861500 0.507757i \(-0.169525\pi\)
\(354\) −12580.0 33787.3i −0.100386 0.269617i
\(355\) −130133. 94547.5i −1.03260 0.750228i
\(356\) 243.799 + 335.561i 0.00192368 + 0.00264772i
\(357\) 162494. + 45302.5i 1.27497 + 0.355456i
\(358\) 22381.2 68882.1i 0.174629 0.537453i
\(359\) 110663. + 152315.i 0.858647 + 1.18183i 0.981890 + 0.189450i \(0.0606704\pi\)
−0.123243 + 0.992376i \(0.539330\pi\)
\(360\) 188193. + 113778.i 1.45211 + 0.877919i
\(361\) −39946.1 122941.i −0.306521 0.943374i
\(362\) 87050.5i 0.664284i
\(363\) 131537. + 7818.18i 0.998238 + 0.0593324i
\(364\) 33186.7 0.250473
\(365\) −51803.3 + 16831.9i −0.388841 + 0.126342i
\(366\) −83899.5 + 126383.i −0.626322 + 0.943468i
\(367\) −203373. + 147759.i −1.50995 + 1.09704i −0.543745 + 0.839251i \(0.682994\pi\)
−0.966201 + 0.257789i \(0.917006\pi\)
\(368\) −664.078 215.772i −0.00490369 0.00159331i
\(369\) 110830. + 25906.1i 0.813965 + 0.190261i
\(370\) 110009. 79926.3i 0.803572 0.583830i
\(371\) 135513. 186518.i 0.984540 1.35510i
\(372\) −28163.5 75641.3i −0.203517 0.546604i
\(373\) 104933. 0.754216 0.377108 0.926169i \(-0.376919\pi\)
0.377108 + 0.926169i \(0.376919\pi\)
\(374\) 23523.1 + 87251.1i 0.168171 + 0.623774i
\(375\) 8734.46 + 206521.i 0.0621117 + 1.46860i
\(376\) −28612.0 88058.7i −0.202382 0.622869i
\(377\) −18955.8 + 26090.5i −0.133371 + 0.183569i
\(378\) −77215.2 82038.1i −0.540405 0.574159i
\(379\) −45491.5 + 140008.i −0.316703 + 0.974711i 0.658345 + 0.752716i \(0.271257\pi\)
−0.975048 + 0.221995i \(0.928743\pi\)
\(380\) 12858.0 + 4177.83i 0.0890446 + 0.0289323i
\(381\) 17036.9 13513.8i 0.117366 0.0930955i
\(382\) 130625. + 94904.5i 0.895157 + 0.650370i
\(383\) −214444. + 69677.1i −1.46190 + 0.474999i −0.928649 0.370960i \(-0.879029\pi\)
−0.533247 + 0.845959i \(0.679029\pi\)
\(384\) −3800.16 89852.7i −0.0257715 0.609352i
\(385\) 174175. + 267303.i 1.17507 + 1.80336i
\(386\) 148977.i 0.999873i
\(387\) −27779.2 65943.7i −0.185480 0.440303i
\(388\) 78116.3 + 56754.8i 0.518894 + 0.376998i
\(389\) −41285.2 56824.3i −0.272832 0.375521i 0.650511 0.759497i \(-0.274555\pi\)
−0.923343 + 0.383975i \(0.874555\pi\)
\(390\) 13748.1 49312.4i 0.0903883 0.324210i
\(391\) 39304.3 120966.i 0.257091 0.791244i
\(392\) 55693.8 + 76656.0i 0.362439 + 0.498854i
\(393\) 51964.5 78277.4i 0.336451 0.506817i
\(394\) −32047.5 98632.1i −0.206444 0.635369i
\(395\) 205052.i 1.31422i
\(396\) −26699.4 + 92695.9i −0.170259 + 0.591112i
\(397\) −170477. −1.08165 −0.540824 0.841136i \(-0.681887\pi\)
−0.540824 + 0.841136i \(0.681887\pi\)
\(398\) 22285.6 7241.04i 0.140689 0.0457125i
\(399\) −15150.8 10057.9i −0.0951679 0.0631773i
\(400\) −1560.54 + 1133.80i −0.00975336 + 0.00708623i
\(401\) −219706. 71386.8i −1.36632 0.443945i −0.468174 0.883637i \(-0.655088\pi\)
−0.898149 + 0.439691i \(0.855088\pi\)
\(402\) 36459.6 + 10164.8i 0.225611 + 0.0628993i
\(403\) −39911.7 + 28997.5i −0.245748 + 0.178546i
\(404\) −59427.9 + 81795.5i −0.364106 + 0.501149i
\(405\) 245971. 129067.i 1.49960 0.786877i
\(406\) −92053.0 −0.558452
\(407\) 121861. + 98370.1i 0.735657 + 0.593847i
\(408\) −173543. + 7339.70i −1.04253 + 0.0440918i
\(409\) −35411.7 108986.i −0.211690 0.651514i −0.999372 0.0354325i \(-0.988719\pi\)
0.787682 0.616082i \(-0.211281\pi\)
\(410\) −86772.1 + 119432.i −0.516193 + 0.710479i
\(411\) 43049.8 + 54272.9i 0.254852 + 0.321292i
\(412\) 18496.9 56927.6i 0.108969 0.335374i
\(413\) 95617.1 + 31067.9i 0.560577 + 0.182143i
\(414\) −64260.9 + 55553.9i −0.374927 + 0.324126i
\(415\) 311439. + 226274.i 1.80833 + 1.31383i
\(416\) −52621.0 + 17097.6i −0.304069 + 0.0987981i
\(417\) −11484.7 + 485.725i −0.0660461 + 0.00279331i
\(418\) 494.842 9729.22i 0.00283214 0.0556833i
\(419\) 101705.i 0.579313i −0.957131 0.289656i \(-0.906459\pi\)
0.957131 0.289656i \(-0.0935410\pi\)
\(420\) −218882. + 81496.4i −1.24083 + 0.461998i
\(421\) 64516.7 + 46874.1i 0.364006 + 0.264466i 0.754721 0.656046i \(-0.227772\pi\)
−0.390715 + 0.920512i \(0.627772\pi\)
\(422\) 7305.07 + 10054.6i 0.0410204 + 0.0564597i
\(423\) −113883. 26619.7i −0.636471 0.148772i
\(424\) −73358.4 + 225774.i −0.408054 + 1.25586i
\(425\) −206529. 284262.i −1.14341 1.57377i
\(426\) −70691.9 46928.8i −0.389538 0.258595i
\(427\) −130720. 402315.i −0.716946 2.20653i
\(428\) 49320.1i 0.269238i
\(429\) 58958.1 + 504.082i 0.320353 + 0.00273896i
\(430\) 92810.5 0.501950
\(431\) −83407.5 + 27100.7i −0.449004 + 0.145890i −0.524786 0.851234i \(-0.675855\pi\)
0.0757818 + 0.997124i \(0.475855\pi\)
\(432\) 1056.14 + 579.052i 0.00565921 + 0.00310278i
\(433\) −124523. + 90471.2i −0.664161 + 0.482541i −0.868066 0.496449i \(-0.834637\pi\)
0.203904 + 0.978991i \(0.434637\pi\)
\(434\) −133925. 43514.9i −0.711021 0.231025i
\(435\) 60952.8 218629.i 0.322118 1.15539i
\(436\) 69152.1 50242.0i 0.363775 0.264298i
\(437\) −8059.50 + 11093.0i −0.0422032 + 0.0580877i
\(438\) −26926.8 + 10025.6i −0.140358 + 0.0522594i
\(439\) 151417. 0.785678 0.392839 0.919607i \(-0.371493\pi\)
0.392839 + 0.919607i \(0.371493\pi\)
\(440\) −255621. 206346.i −1.32036 1.06584i
\(441\) 119256. 10105.5i 0.613200 0.0519614i
\(442\) 12495.0 + 38455.6i 0.0639574 + 0.196841i
\(443\) 17596.8 24220.0i 0.0896659 0.123415i −0.761827 0.647780i \(-0.775698\pi\)
0.851493 + 0.524366i \(0.175698\pi\)
\(444\) −89823.3 + 71248.7i −0.455641 + 0.361419i
\(445\) −551.349 + 1696.88i −0.00278424 + 0.00856901i
\(446\) −211034. 68569.2i −1.06092 0.344715i
\(447\) 150728. + 190022.i 0.754358 + 0.951020i
\(448\) −129101. 93797.0i −0.643238 0.467340i
\(449\) 91659.2 29781.9i 0.454657 0.147727i −0.0727312 0.997352i \(-0.523172\pi\)
0.527388 + 0.849625i \(0.323172\pi\)
\(450\) 19813.8 + 233824.i 0.0978461 + 1.15469i
\(451\) −158825. 60686.3i −0.780846 0.298358i
\(452\) 1021.65i 0.00500063i
\(453\) 109368. + 293740.i 0.532960 + 1.43142i
\(454\) −165821. 120476.i −0.804505 0.584507i
\(455\) 83909.9 + 115492.i 0.405313 + 0.557865i
\(456\) 18037.4 + 5028.73i 0.0867448 + 0.0241840i
\(457\) 33940.0 104457.i 0.162510 0.500153i −0.836334 0.548220i \(-0.815306\pi\)
0.998844 + 0.0480661i \(0.0153058\pi\)
\(458\) 101447. + 139630.i 0.483624 + 0.665652i
\(459\) −105478. + 192384.i −0.500654 + 0.913151i
\(460\) 54419.1 + 167485.i 0.257179 + 0.791516i
\(461\) 202036.i 0.950663i −0.879807 0.475331i \(-0.842328\pi\)
0.879807 0.475331i \(-0.157672\pi\)
\(462\) 97754.0 + 136995.i 0.457984 + 0.641830i
\(463\) 32028.7 0.149409 0.0747046 0.997206i \(-0.476199\pi\)
0.0747046 + 0.997206i \(0.476199\pi\)
\(464\) 935.980 304.118i 0.00434741 0.00141256i
\(465\) 192028. 289264.i 0.888093 1.33779i
\(466\) −34098.4 + 24773.9i −0.157023 + 0.114084i
\(467\) 249117. + 80942.9i 1.14227 + 0.371146i 0.818226 0.574896i \(-0.194958\pi\)
0.324044 + 0.946042i \(0.394958\pi\)
\(468\) −9824.39 + 42030.2i −0.0448553 + 0.191898i
\(469\) −85390.3 + 62039.7i −0.388207 + 0.282049i
\(470\) 89162.2 122721.i 0.403632 0.555551i
\(471\) 41639.6 + 111835.i 0.187700 + 0.504124i
\(472\) −103522. −0.464676
\(473\) 27825.0 + 103207.i 0.124369 + 0.461305i
\(474\) −4570.57 108069.i −0.0203430 0.480998i
\(475\) 11705.1 + 36024.7i 0.0518787 + 0.159666i
\(476\) 108434. 149246.i 0.478575 0.658702i
\(477\) 196104. + 226840.i 0.861887 + 0.996972i
\(478\) 64255.0 197757.i 0.281223 0.865516i
\(479\) −67738.2 22009.5i −0.295231 0.0959264i 0.157656 0.987494i \(-0.449606\pi\)
−0.452888 + 0.891568i \(0.649606\pi\)
\(480\) 305075. 241988.i 1.32411 1.05030i
\(481\) 56692.2 + 41189.3i 0.245038 + 0.178031i
\(482\) 235473. 76509.9i 1.01356 0.329324i
\(483\) −10009.4 236666.i −0.0429054 1.01447i
\(484\) 58204.9 131823.i 0.248467 0.562731i
\(485\) 415350.i 1.76576i
\(486\) 126758. 73505.3i 0.536664 0.311204i
\(487\) 77046.1 + 55977.3i 0.324857 + 0.236023i 0.738245 0.674532i \(-0.235655\pi\)
−0.413388 + 0.910555i \(0.635655\pi\)
\(488\) 256025. + 352389.i 1.07509 + 1.47973i
\(489\) 17193.0 61669.0i 0.0719009 0.257899i
\(490\) −47969.7 + 147635.i −0.199790 + 0.614891i
\(491\) −156518. 215429.i −0.649234 0.893595i 0.349831 0.936813i \(-0.386239\pi\)
−0.999066 + 0.0432182i \(0.986239\pi\)
\(492\) 68841.2 103700.i 0.284392 0.428398i
\(493\) 55397.2 + 170495.i 0.227926 + 0.701484i
\(494\) 4358.98i 0.0178620i
\(495\) −390095. + 141458.i −1.59206 + 0.577322i
\(496\) 1505.49 0.00611948
\(497\) 225033. 73117.7i 0.911032 0.296012i
\(498\) 169182. + 112311.i 0.682174 + 0.452861i
\(499\) 305576. 222014.i 1.22721 0.891619i 0.230530 0.973065i \(-0.425954\pi\)
0.996678 + 0.0814466i \(0.0259540\pi\)
\(500\) 214988. + 69853.8i 0.859951 + 0.279415i
\(501\) −328339. 91539.3i −1.30812 0.364697i
\(502\) 78737.3 57206.0i 0.312445 0.227004i
\(503\) −245604. + 338045.i −0.970731 + 1.33610i −0.0290545 + 0.999578i \(0.509250\pi\)
−0.941677 + 0.336519i \(0.890750\pi\)
\(504\) −298118. + 125584.i −1.17362 + 0.494395i
\(505\) −434913. −1.70537
\(506\) 106315. 69275.2i 0.415235 0.270568i
\(507\) −230461. + 9746.95i −0.896565 + 0.0379186i
\(508\) −7348.73 22617.1i −0.0284764 0.0876413i
\(509\) −71723.5 + 98718.9i −0.276838 + 0.381035i −0.924683 0.380737i \(-0.875670\pi\)
0.647845 + 0.761772i \(0.275670\pi\)
\(510\) −176846. 222950.i −0.679914 0.857168i
\(511\) 24759.5 76202.0i 0.0948202 0.291826i
\(512\) 3218.07 + 1045.61i 0.0122760 + 0.00398870i
\(513\) 17223.3 16210.7i 0.0654456 0.0615981i
\(514\) −38390.8 27892.6i −0.145312 0.105575i
\(515\) 244880. 79566.4i 0.923292 0.299996i
\(516\) −78183.0 + 3306.61i −0.293638 + 0.0124189i
\(517\) 163200. + 62357.9i 0.610574 + 0.233298i
\(518\) 200023.i 0.745453i
\(519\) 243355. 90608.2i 0.903453 0.336382i
\(520\) −118920. 86400.8i −0.439795 0.319530i
\(521\) −302718. 416656.i −1.11523 1.53498i −0.813483 0.581588i \(-0.802431\pi\)
−0.301743 0.953389i \(-0.597569\pi\)
\(522\) 27250.8 116583.i 0.100009 0.427853i
\(523\) −36028.9 + 110885.i −0.131719 + 0.405388i −0.995065 0.0992231i \(-0.968364\pi\)
0.863347 + 0.504611i \(0.168364\pi\)
\(524\) −60394.2 83125.5i −0.219955 0.302741i
\(525\) −545182. 361919.i −1.97798 1.31309i
\(526\) 86880.5 + 267391.i 0.314015 + 0.966440i
\(527\) 274235.i 0.987420i
\(528\) −1446.54 1069.99i −0.00518875 0.00383805i
\(529\) 101237. 0.361768
\(530\) −369887. + 120184.i −1.31679 + 0.427852i
\(531\) −67652.7 + 111900.i −0.239936 + 0.396863i
\(532\) −16089.2 + 11689.5i −0.0568475 + 0.0413021i
\(533\) −72354.1 23509.3i −0.254688 0.0827532i
\(534\) −252.755 + 906.597i −0.000886375 + 0.00317930i
\(535\) −171638. + 124702.i −0.599659 + 0.435678i
\(536\) 63881.4 87925.2i 0.222354 0.306044i
\(537\) −246174. + 91657.8i −0.853677 + 0.317849i
\(538\) 147364. 0.509129
\(539\) −178555. 9081.58i −0.614603 0.0312596i
\(540\) −38416.7 301336.i −0.131745 1.03339i
\(541\) −82687.6 254486.i −0.282518 0.869501i −0.987132 0.159910i \(-0.948880\pi\)
0.704614 0.709591i \(-0.251120\pi\)
\(542\) 28647.4 39429.8i 0.0975185 0.134223i
\(543\) 247355. 196204.i 0.838919 0.665439i
\(544\) −95042.2 + 292510.i −0.321158 + 0.988422i
\(545\) 349691. + 113622.i 1.17731 + 0.382532i
\(546\) 46797.4 + 58997.6i 0.156977 + 0.197901i
\(547\) 251502. + 182727.i 0.840557 + 0.610700i 0.922526 0.385934i \(-0.126121\pi\)
−0.0819692 + 0.996635i \(0.526121\pi\)
\(548\) 72049.1 23410.2i 0.239920 0.0779549i
\(549\) 548221. 46455.1i 1.81891 0.154131i
\(550\) 17806.2 350093.i 0.0588635 1.15733i
\(551\) 19325.8i 0.0636552i
\(552\) 85106.8 + 228579.i 0.279310 + 0.750168i
\(553\) 244022. + 177293.i 0.797957 + 0.579749i
\(554\) 69829.3 + 96111.8i 0.227519 + 0.313154i
\(555\) −475062. 132445.i −1.54228 0.429981i
\(556\) −3884.58 + 11955.5i −0.0125659 + 0.0386739i
\(557\) 145059. + 199657.i 0.467557 + 0.643538i 0.976054 0.217526i \(-0.0697987\pi\)
−0.508497 + 0.861064i \(0.669799\pi\)
\(558\) 94757.1 156731.i 0.304329 0.503370i
\(559\) 14780.0 + 45488.2i 0.0472989 + 0.145571i
\(560\) 4356.43i 0.0138917i
\(561\) 194905. 263497.i 0.619296 0.837240i
\(562\) −46229.9 −0.146369
\(563\) −247637. + 80462.2i −0.781266 + 0.253849i −0.672381 0.740205i \(-0.734728\pi\)
−0.108886 + 0.994054i \(0.534728\pi\)
\(564\) −70737.4 + 106556.i −0.222377 + 0.334981i
\(565\) 3555.41 2583.16i 0.0111376 0.00809196i
\(566\) 71712.3 + 23300.7i 0.223852 + 0.0727339i
\(567\) −59075.8 + 404314.i −0.183757 + 1.25763i
\(568\) −197107. + 143207.i −0.610950 + 0.443881i
\(569\) 333884. 459551.i 1.03127 1.41942i 0.127273 0.991868i \(-0.459378\pi\)
0.903993 0.427548i \(-0.140622\pi\)
\(570\) 10704.3 + 28749.6i 0.0329465 + 0.0884876i
\(571\) −317468. −0.973707 −0.486853 0.873484i \(-0.661855\pi\)
−0.486853 + 0.873484i \(0.661855\pi\)
\(572\) 23014.1 60231.2i 0.0703399 0.184090i
\(573\) −24744.8 585078.i −0.0753660 1.78199i
\(574\) −67104.6 206527.i −0.203671 0.626834i
\(575\) −290010. + 399165.i −0.877157 + 1.20730i
\(576\) 157010. 135736.i 0.473241 0.409119i
\(577\) 714.336 2198.50i 0.00214561 0.00660351i −0.949978 0.312317i \(-0.898895\pi\)
0.952124 + 0.305713i \(0.0988949\pi\)
\(578\) 16655.7 + 5411.77i 0.0498549 + 0.0161988i
\(579\) −423319. + 335781.i −1.26273 + 1.00161i
\(580\) −200805. 145893.i −0.596923 0.433690i
\(581\) −538555. + 174987.i −1.59543 + 0.518387i
\(582\) 9258.10 + 218903.i 0.0273323 + 0.646257i
\(583\) −244540. 375291.i −0.719471 1.10416i
\(584\) 82502.0i 0.241902i
\(585\) −171108. + 72080.4i −0.499988 + 0.210623i
\(586\) 180895. + 131428.i 0.526783 + 0.382730i
\(587\) −380539. 523767.i −1.10439 1.52006i −0.829433 0.558606i \(-0.811336\pi\)
−0.274958 0.961456i \(-0.588664\pi\)
\(588\) 35149.4 126076.i 0.101663 0.364652i
\(589\) 9135.61 28116.5i 0.0263334 0.0810459i
\(590\) −99689.3 137211.i −0.286381 0.394170i
\(591\) −208032. + 313371.i −0.595599 + 0.897189i
\(592\) −660.822 2033.80i −0.00188556 0.00580316i
\(593\) 163543.i 0.465074i 0.972587 + 0.232537i \(0.0747027\pi\)
−0.972587 + 0.232537i \(0.925297\pi\)
\(594\) −202439. + 83248.2i −0.573749 + 0.235940i
\(595\) 793552. 2.24151
\(596\) 252261. 81964.6i 0.710162 0.230746i
\(597\) −70805.2 47004.1i −0.198663 0.131882i
\(598\) 45935.0 33373.7i 0.128452 0.0933259i
\(599\) 441139. + 143335.i 1.22948 + 0.399482i 0.850526 0.525933i \(-0.176284\pi\)
0.378954 + 0.925415i \(0.376284\pi\)
\(600\) 649050. + 180952.i 1.80292 + 0.502644i
\(601\) −164405. + 119448.i −0.455163 + 0.330695i −0.791631 0.611000i \(-0.790768\pi\)
0.336468 + 0.941695i \(0.390768\pi\)
\(602\) −80246.2 + 110449.i −0.221428 + 0.304769i
\(603\) −53293.5 126511.i −0.146568 0.347931i
\(604\) 342775. 0.939582
\(605\) 605920. 130747.i 1.65541 0.357208i
\(606\) −229213. + 9694.15i −0.624157 + 0.0263976i
\(607\) 15539.4 + 47825.5i 0.0421753 + 0.129802i 0.969927 0.243396i \(-0.0782613\pi\)
−0.927752 + 0.373198i \(0.878261\pi\)
\(608\) 19488.8 26824.0i 0.0527202 0.0725632i
\(609\) 207479. + 261569.i 0.559422 + 0.705264i
\(610\) −220517. + 678682.i −0.592629 + 1.82392i
\(611\) 74347.0 + 24156.8i 0.199150 + 0.0647079i
\(612\) 156917. + 181511.i 0.418954 + 0.484618i
\(613\) −423338. 307573.i −1.12659 0.818517i −0.141397 0.989953i \(-0.545159\pi\)
−0.985195 + 0.171436i \(0.945159\pi\)
\(614\) 50054.8 16263.8i 0.132773 0.0431405i
\(615\) 534942. 22624.4i 1.41435 0.0598174i
\(616\) 466579. 125791.i 1.22960 0.331504i
\(617\) 245951.i 0.646067i 0.946388 + 0.323033i \(0.104703\pi\)
−0.946388 + 0.323033i \(0.895297\pi\)
\(618\) 127286. 47392.3i 0.333276 0.124088i
\(619\) −315525. 229242.i −0.823479 0.598293i 0.0942276 0.995551i \(-0.469962\pi\)
−0.917707 + 0.397258i \(0.869962\pi\)
\(620\) −223179. 307180.i −0.580591 0.799114i
\(621\) 302695. + 57384.5i 0.784914 + 0.148803i
\(622\) 90245.2 277746.i 0.233262 0.717905i
\(623\) −1542.67 2123.30i −0.00397462 0.00547059i
\(624\) −670.741 445.272i −0.00172261 0.00114355i
\(625\) 75001.3 + 230830.i 0.192003 + 0.590925i
\(626\) 239929.i 0.612258i
\(627\) −28761.0 + 20522.7i −0.0731591 + 0.0522034i
\(628\) 130504. 0.330906
\(629\) 370470. 120373.i 0.936380 0.304248i
\(630\) −453532. 274198.i −1.14269 0.690848i
\(631\) −235710. + 171253.i −0.591995 + 0.430110i −0.843029 0.537869i \(-0.819230\pi\)
0.251033 + 0.967978i \(0.419230\pi\)
\(632\) −295381. 95975.2i −0.739518 0.240284i
\(633\) 12105.2 43419.5i 0.0302108 0.108362i
\(634\) −252813. + 183679.i −0.628956 + 0.456963i
\(635\) 60128.3 82759.5i 0.149118 0.205244i
\(636\) 307309. 114420.i 0.759732 0.282871i
\(637\) −79998.1 −0.197152
\(638\) −63836.3 + 167069.i −0.156829 + 0.410444i
\(639\) 25984.5 + 306645.i 0.0636374 + 0.750990i
\(640\) −130733. 402355.i −0.319173 0.982313i
\(641\) 133364. 183559.i 0.324580 0.446746i −0.615279 0.788310i \(-0.710956\pi\)
0.939859 + 0.341564i \(0.110956\pi\)
\(642\) −87678.8 + 69547.6i −0.212728 + 0.168738i
\(643\) −187062. + 575718.i −0.452443 + 1.39248i 0.421668 + 0.906750i \(0.361445\pi\)
−0.874111 + 0.485727i \(0.838555\pi\)
\(644\) −246368. 80049.7i −0.594035 0.193014i
\(645\) −209187. 263722.i −0.502822 0.633908i
\(646\) −19603.0 14242.4i −0.0469741 0.0341287i
\(647\) 195188. 63420.3i 0.466277 0.151502i −0.0664502 0.997790i \(-0.521167\pi\)
0.532727 + 0.846287i \(0.321167\pi\)
\(648\) −70796.5 414738.i −0.168602 0.987696i
\(649\) 122694. 151993.i 0.291295 0.360856i
\(650\) 156852.i 0.371247i
\(651\) 178207. + 478628.i 0.420497 + 1.12937i
\(652\) −56641.3 41152.3i −0.133241 0.0968053i
\(653\) 235646. + 324339.i 0.552629 + 0.760629i 0.990366 0.138474i \(-0.0442198\pi\)
−0.437737 + 0.899103i \(0.644220\pi\)
\(654\) 186831. + 52087.5i 0.436810 + 0.121781i
\(655\) 136581. 420352.i 0.318352 0.979785i
\(656\) 1364.62 + 1878.24i 0.00317105 + 0.00436458i
\(657\) 89178.5 + 53915.8i 0.206600 + 0.124907i
\(658\) 68953.0 + 212215.i 0.159258 + 0.490146i
\(659\) 591347.i 1.36167i 0.732438 + 0.680834i \(0.238383\pi\)
−0.732438 + 0.680834i \(0.761617\pi\)
\(660\) −3879.66 + 453770.i −0.00890647 + 1.04171i
\(661\) 177064. 0.405255 0.202627 0.979256i \(-0.435052\pi\)
0.202627 + 0.979256i \(0.435052\pi\)
\(662\) 137655. 44726.9i 0.314107 0.102059i
\(663\) 81109.2 122180.i 0.184520 0.277954i
\(664\) 471722. 342726.i 1.06992 0.777340i
\(665\) −81360.5 26435.6i −0.183980 0.0597787i
\(666\) −253324. 59213.6i −0.571122 0.133497i
\(667\) 203655. 147964.i 0.457766 0.332587i
\(668\) −219103. + 301570.i −0.491017 + 0.675827i
\(669\) 280813. + 754205.i 0.627429 + 1.68514i
\(670\) 178054. 0.396645
\(671\) −820821. 41748.1i −1.82307 0.0927240i
\(672\) 24203.8 + 572284.i 0.0535975 + 1.26728i
\(673\) −134472. 413863.i −0.296895 0.913749i −0.982578 0.185849i \(-0.940497\pi\)
0.685683 0.727900i \(-0.259503\pi\)
\(674\) 241861. 332893.i 0.532409 0.732798i
\(675\) 619755. 583320.i 1.36023 1.28026i
\(676\) −77951.1 + 239909.i −0.170580 + 0.524992i
\(677\) −827565. 268892.i −1.80561 0.586679i −0.805630 0.592419i \(-0.798173\pi\)
−0.999984 + 0.00573954i \(0.998173\pi\)
\(678\) 1816.23 1440.65i 0.00395105 0.00313401i
\(679\) −494289. 359122.i −1.07211 0.778937i
\(680\) −777117. + 252501.i −1.68062 + 0.546065i
\(681\) 31412.3 + 742725.i 0.0677338 + 1.60153i
\(682\) −171850. + 212887.i −0.369471 + 0.457700i
\(683\) 518249.i 1.11096i −0.831531 0.555479i \(-0.812535\pi\)
0.831531 0.555479i \(-0.187465\pi\)
\(684\) −10041.5 23837.1i −0.0214629 0.0509497i
\(685\) 263639. + 191545.i 0.561861 + 0.408216i
\(686\) 83881.8 + 115453.i 0.178246 + 0.245334i
\(687\) 168107. 602975.i 0.356182 1.27757i
\(688\) 451.036 1388.14i 0.000952871 0.00293263i
\(689\) −117809. 162150.i −0.248164 0.341568i
\(690\) −221008. + 332918.i −0.464205 + 0.699261i
\(691\) −19772.5 60853.4i −0.0414099 0.127447i 0.928214 0.372046i \(-0.121344\pi\)
−0.969624 + 0.244599i \(0.921344\pi\)
\(692\) 283979.i 0.593026i
\(693\) 168943. 586543.i 0.351782 1.22133i
\(694\) 66721.0 0.138530
\(695\) −51427.9 + 16709.9i −0.106470 + 0.0345943i
\(696\) −286411. 190134.i −0.591250 0.392501i
\(697\) −342133. + 248574.i −0.704255 + 0.511671i
\(698\) −122600. 39835.0i −0.251639 0.0817625i
\(699\) 147250. + 41052.6i 0.301371 + 0.0840207i
\(700\) −578948. + 420630.i −1.18153 + 0.858429i
\(701\) 276626. 380744.i 0.562934 0.774812i −0.428762 0.903418i \(-0.641050\pi\)
0.991696 + 0.128605i \(0.0410500\pi\)
\(702\) −88572.8 + 41802.6i −0.179732 + 0.0848261i
\(703\) −41993.2 −0.0849705
\(704\) −259762. + 169262.i −0.524119 + 0.341517i
\(705\) −549677. + 23247.6i −1.10593 + 0.0467735i
\(706\) −97034.7 298642.i −0.194678 0.599159i
\(707\) 376036. 517569.i 0.752300 1.03545i
\(708\) 88866.1 + 112034.i 0.177284 + 0.223502i
\(709\) −135622. + 417402.i −0.269797 + 0.830351i 0.720752 + 0.693193i \(0.243797\pi\)
−0.990549 + 0.137158i \(0.956203\pi\)
\(710\) −379618. 123345.i −0.753061 0.244684i
\(711\) −296776. + 256564.i −0.587070 + 0.507524i
\(712\) 2186.33 + 1588.46i 0.00431276 + 0.00313340i
\(713\) 366237. 118998.i 0.720416 0.234077i
\(714\) 418227. 17688.2i 0.820381 0.0346966i
\(715\) 267798. 72199.2i 0.523836 0.141228i
\(716\) 287268.i 0.560353i
\(717\) −706752. + 263144.i −1.37477 + 0.511866i
\(718\) 377965. + 274608.i 0.733167 + 0.532677i
\(719\) 323463. + 445209.i 0.625701 + 0.861204i 0.997752 0.0670082i \(-0.0213454\pi\)
−0.372051 + 0.928212i \(0.621345\pi\)
\(720\) 5517.32 + 1289.65i 0.0106430 + 0.00248775i
\(721\) −117041. + 360215.i −0.225148 + 0.692934i
\(722\) −188547. 259513.i −0.361698 0.497834i
\(723\) −748139. 496652.i −1.43122 0.950115i
\(724\) −106694. 328371.i −0.203547 0.626452i
\(725\) 695412.i 1.32302i
\(726\) 316425. 82413.6i 0.600340 0.156360i
\(727\) −307836. −0.582440 −0.291220 0.956656i \(-0.594061\pi\)
−0.291220 + 0.956656i \(0.594061\pi\)
\(728\) 205643. 66817.5i 0.388017 0.126074i
\(729\) −494566. 194509.i −0.930614 0.366003i
\(730\) −109350. + 79447.3i −0.205198 + 0.149085i
\(731\) 252860. + 82159.1i 0.473200 + 0.153752i
\(732\) 161582. 579574.i 0.301559 1.08165i
\(733\) 798862. 580407.i 1.48684 1.08025i 0.511565 0.859244i \(-0.329066\pi\)
0.975272 0.221006i \(-0.0709342\pi\)
\(734\) −366660. + 504664.i −0.680568 + 0.936722i
\(735\) 527626. 196451.i 0.976679 0.363646i
\(736\) 431883. 0.797280
\(737\) 53381.2 + 198000.i 0.0982774 + 0.364527i
\(738\) 281427. 23847.6i 0.516717 0.0437856i
\(739\) 202258. + 622485.i 0.370353 + 1.13983i 0.946561 + 0.322526i \(0.104532\pi\)
−0.576207 + 0.817303i \(0.695468\pi\)
\(740\) −317013. + 436331.i −0.578913 + 0.796806i
\(741\) −12386.1 + 9824.75i −0.0225578 + 0.0178931i
\(742\) 176789. 544099.i 0.321104 0.988258i
\(743\) 470010. + 152716.i 0.851392 + 0.276634i 0.702029 0.712148i \(-0.252278\pi\)
0.149363 + 0.988782i \(0.452278\pi\)
\(744\) −326811. 412011.i −0.590406 0.744326i
\(745\) 923064. + 670645.i 1.66310 + 1.20832i
\(746\) 247645. 80464.6i 0.444991 0.144586i
\(747\) −62186.8 733871.i −0.111444 1.31516i
\(748\) −195674. 300296.i −0.349727 0.536719i
\(749\) 312078.i 0.556288i
\(750\) 178978. + 480697.i 0.318182 + 0.854572i
\(751\) 142450. + 103496.i 0.252571 + 0.183504i 0.706866 0.707348i \(-0.250109\pi\)
−0.454294 + 0.890852i \(0.650109\pi\)
\(752\) −1402.21 1929.97i −0.00247957 0.00341283i
\(753\) −340018. 94795.4i −0.599670 0.167185i
\(754\) −24729.5 + 76109.7i −0.0434984 + 0.133874i
\(755\) 866678. + 1.19288e6i 1.52042 + 2.09268i
\(756\) 391821. + 214824.i 0.685559 + 0.375871i
\(757\) −46810.8 144069.i −0.0816873 0.251408i 0.901869 0.432010i \(-0.142195\pi\)
−0.983556 + 0.180602i \(0.942195\pi\)
\(758\) 365306.i 0.635797i
\(759\) −436471. 145955.i −0.757655 0.253359i
\(760\) 88087.0 0.152505
\(761\) 436830. 141935.i 0.754298 0.245086i 0.0934685 0.995622i \(-0.470205\pi\)
0.660830 + 0.750536i \(0.270205\pi\)
\(762\) 29844.8 44957.1i 0.0513995 0.0774263i
\(763\) −437567. + 317911.i −0.751615 + 0.546080i
\(764\) −609063. 197897.i −1.04346 0.339040i
\(765\) −234918. + 1.00502e6i −0.401416 + 1.71732i
\(766\) −452663. + 328879.i −0.771466 + 0.560503i
\(767\) 51374.0 70710.3i 0.0873279 0.120197i
\(768\) −206615. 554925.i −0.350299 0.940831i
\(769\) −686932. −1.16161 −0.580806 0.814042i \(-0.697263\pi\)
−0.580806 + 0.814042i \(0.697263\pi\)
\(770\) 616030. + 497280.i 1.03901 + 0.838725i
\(771\) 7272.54 + 171955.i 0.0122343 + 0.289272i
\(772\) 182595. + 561970.i 0.306376 + 0.942929i
\(773\) −399325. + 549624.i −0.668294 + 0.919828i −0.999720 0.0236528i \(-0.992470\pi\)
0.331426 + 0.943481i \(0.392470\pi\)
\(774\) −116126. 134327.i −0.193842 0.224223i
\(775\) 328732. 1.01173e6i 0.547317 1.68447i
\(776\) 598321. + 194406.i 0.993598 + 0.322840i
\(777\) 568366. 450833.i 0.941426 0.746748i
\(778\) −141008. 102448.i −0.232961 0.169256i
\(779\) 43358.7 14088.1i 0.0714498 0.0232154i
\(780\) 8579.87 + 202866.i 0.0141024 + 0.333442i
\(781\) 23351.7 459123.i 0.0382838 0.752708i
\(782\) 315622.i 0.516123i
\(783\) −392692. + 185334.i −0.640515 + 0.302296i
\(784\) 1975.03 + 1434.94i 0.00321322 + 0.00233454i
\(785\) 329969. + 454164.i 0.535469 + 0.737009i
\(786\) 62612.7 224583.i 0.101349 0.363523i
\(787\) −217386. + 669047.i −0.350980 + 1.08021i 0.607323 + 0.794455i \(0.292243\pi\)
−0.958304 + 0.285752i \(0.907757\pi\)
\(788\) 241779. + 332780.i 0.389373 + 0.535926i
\(789\) 563972. 849546.i 0.905948 1.36469i
\(790\) −157237. 483926.i −0.251942 0.775398i
\(791\) 6464.59i 0.0103321i
\(792\) 21188.3 + 628151.i 0.0337789 + 1.00141i
\(793\) −367752. −0.584802
\(794\) −402330. + 130725.i −0.638177 + 0.207356i
\(795\) 1.17520e6 + 780154.i 1.85941 + 1.23437i
\(796\) −75190.6 + 54629.2i −0.118669 + 0.0862181i
\(797\) −224589. 72973.5i −0.353568 0.114881i 0.126848 0.991922i \(-0.459514\pi\)
−0.480415 + 0.877041i \(0.659514\pi\)
\(798\) −43468.8 12118.9i −0.0682609 0.0190308i
\(799\) 351557. 255421.i 0.550684 0.400095i
\(800\) 701277. 965225.i 1.09575 1.50816i
\(801\) 3145.79 1325.18i 0.00490303 0.00206543i
\(802\) −573251. −0.891243
\(803\) −121131. 97780.7i −0.187855 0.151643i
\(804\) −149991. + 6343.62i −0.232035 + 0.00981353i
\(805\) −344342. 1.05978e6i −0.531372 1.63539i
\(806\) −71956.5 + 99039.6i −0.110764 + 0.152454i
\(807\) −332146. 418736.i −0.510013 0.642974i
\(808\) −203563. + 626501.i −0.311799 + 0.959620i
\(809\) 544292. + 176851.i 0.831639 + 0.270216i 0.693735 0.720230i \(-0.255964\pi\)
0.137903 + 0.990446i \(0.455964\pi\)
\(810\) 481526. 493217.i 0.733922 0.751740i
\(811\) 725780. + 527310.i 1.10348 + 0.801723i 0.981624 0.190825i \(-0.0611163\pi\)
0.121853 + 0.992548i \(0.461116\pi\)
\(812\) 347242. 112826.i 0.526647 0.171118i
\(813\) −176609. + 7469.36i −0.267197 + 0.0113006i
\(814\) 363026. + 138711.i 0.547884 + 0.209344i
\(815\) 301166.i 0.453409i
\(816\) −4194.03 + 1561.56i −0.00629870 + 0.00234519i
\(817\) −23188.0 16847.1i −0.0347391 0.0252395i
\(818\) −167144. 230055.i −0.249796 0.343815i
\(819\) 62164.8 265950.i 0.0926781 0.396491i
\(820\) 180939. 556872.i 0.269094 0.828185i
\(821\) −32582.8 44846.4i −0.0483396 0.0665337i 0.784163 0.620555i \(-0.213093\pi\)
−0.832503 + 0.554021i \(0.813093\pi\)
\(822\) 143216. + 95073.8i 0.211957 + 0.140708i
\(823\) 116561. + 358738.i 0.172089 + 0.529636i 0.999489 0.0319778i \(-0.0101806\pi\)
−0.827399 + 0.561614i \(0.810181\pi\)
\(824\) 389996.i 0.574389i
\(825\) −1.03492e6 + 738481.i −1.52055 + 1.08500i
\(826\) 249482. 0.365661
\(827\) −643847. + 209199.i −0.941395 + 0.305878i −0.739214 0.673470i \(-0.764803\pi\)
−0.202181 + 0.979348i \(0.564803\pi\)
\(828\) 174314. 288322.i 0.254257 0.420549i
\(829\) 656852. 477231.i 0.955781 0.694416i 0.00361429 0.999993i \(-0.498850\pi\)
0.952167 + 0.305578i \(0.0988495\pi\)
\(830\) 908513. + 295194.i 1.31879 + 0.428500i
\(831\) 115713. 415048.i 0.167564 0.601030i
\(832\) −112234. + 81542.6i −0.162135 + 0.117798i
\(833\) −261384. + 359764.i −0.376694 + 0.518475i
\(834\) −26731.6 + 9952.98i −0.0384320 + 0.0143094i
\(835\) −1.60347e6 −2.29979
\(836\) 10058.1 + 37307.0i 0.0143914 + 0.0533799i
\(837\) −658927. + 84005.4i −0.940560 + 0.119910i
\(838\) −77988.8 240025.i −0.111057 0.341797i
\(839\) −240483. + 330997.i −0.341634 + 0.470218i −0.944918 0.327308i \(-0.893859\pi\)
0.603284 + 0.797526i \(0.293859\pi\)
\(840\) −1.19223e6 + 945690.i −1.68967 + 1.34026i
\(841\) 108922. 335228.i 0.154001 0.473967i
\(842\) 188205. + 61151.4i 0.265464 + 0.0862545i
\(843\) 104198. + 131363.i 0.146624 + 0.184849i
\(844\) −39879.6 28974.2i −0.0559843 0.0406750i
\(845\) −1.03199e6 + 335315.i −1.44532 + 0.469612i
\(846\) −289179. + 24504.4i −0.404041 + 0.0342377i
\(847\) −368297. + 834124.i −0.513372 + 1.16269i
\(848\) 6116.38i 0.00850555i
\(849\) −95423.8 256289.i −0.132386 0.355561i
\(850\) −705389. 512495.i −0.976317 0.709336i
\(851\) −321513. 442524.i −0.443955 0.611052i
\(852\) 324182. + 90380.5i 0.446591 + 0.124507i
\(853\) 61041.9 187868.i 0.0838938 0.258199i −0.900307 0.435256i \(-0.856658\pi\)
0.984201 + 0.177057i \(0.0566578\pi\)
\(854\) −617003. 849232.i −0.846003 1.16442i
\(855\) 57565.6 95215.5i 0.0787465 0.130249i
\(856\) 99300.2 + 305615.i 0.135520 + 0.417087i
\(857\) 298001.i 0.405747i 0.979205 + 0.202874i \(0.0650281\pi\)
−0.979205 + 0.202874i \(0.934972\pi\)
\(858\) 139529. 44020.4i 0.189535 0.0597970i
\(859\) 322700. 0.437333 0.218667 0.975800i \(-0.429829\pi\)
0.218667 + 0.975800i \(0.429829\pi\)
\(860\) −350099. + 113754.i −0.473363 + 0.153805i
\(861\) −435599. + 656171.i −0.587599 + 0.885137i
\(862\) −176062. + 127917.i −0.236947 + 0.172152i
\(863\) −610114. 198238.i −0.819200 0.266174i −0.130710 0.991421i \(-0.541726\pi\)
−0.688489 + 0.725247i \(0.741726\pi\)
\(864\) −731950. 138762.i −0.980515 0.185885i
\(865\) 988265. 718017.i 1.32081 0.959627i
\(866\) −224502. + 309000.i −0.299353 + 0.412024i
\(867\) −22162.9 59524.9i −0.0294841 0.0791883i
\(868\) 558526. 0.741317
\(869\) 490995. 319934.i 0.650186 0.423663i
\(870\) −23798.8 562709.i −0.0314424 0.743439i
\(871\) 28355.0 + 87267.6i 0.0373760 + 0.115031i
\(872\) 327348. 450556.i 0.430504 0.592538i
\(873\) 601146. 519694.i 0.788772 0.681897i
\(874\) −10514.3 + 32359.7i −0.0137644 + 0.0423625i
\(875\) −1.36036e6 442007.i −1.77679 0.577315i
\(876\) 89285.1 70821.8i 0.116351 0.0922908i
\(877\) 974345. + 707903.i 1.26682 + 0.920396i 0.999071 0.0430934i \(-0.0137213\pi\)
0.267746 + 0.963490i \(0.413721\pi\)
\(878\) 357346. 116109.i 0.463554 0.150618i
\(879\) −34267.8 810242.i −0.0443515 1.04867i
\(880\) −7906.57 3021.07i −0.0102099 0.00390117i
\(881\) 1.48732e6i 1.91625i 0.286353 + 0.958124i \(0.407557\pi\)
−0.286353 + 0.958124i \(0.592443\pi\)
\(882\) 273697. 115296.i 0.351830 0.148210i
\(883\) 404328. + 293762.i 0.518576 + 0.376768i 0.816067 0.577957i \(-0.196150\pi\)
−0.297491 + 0.954725i \(0.596150\pi\)
\(884\) −94266.9 129747.i −0.120630 0.166033i
\(885\) −165194. + 592528.i −0.210915 + 0.756523i
\(886\) 22956.6 70653.2i 0.0292442 0.0900045i
\(887\) −521536. 717832.i −0.662883 0.912380i 0.336690 0.941616i \(-0.390693\pi\)
−0.999573 + 0.0292356i \(0.990693\pi\)
\(888\) −413144. + 622345.i −0.523933 + 0.789233i
\(889\) 46499.8 + 143112.i 0.0588366 + 0.181080i
\(890\) 4427.45i 0.00558951i
\(891\) 692830. + 387599.i 0.872713 + 0.488233i
\(892\) 880105. 1.10613
\(893\) −44553.0 + 14476.1i −0.0558694 + 0.0181531i
\(894\) 501432. + 332876.i 0.627389 + 0.416493i
\(895\) −999714. + 726335.i −1.24804 + 0.906756i
\(896\) 591859. + 192307.i 0.737229 + 0.239540i
\(897\) −198365. 55303.2i −0.246536 0.0687330i
\(898\) 193480. 140572.i 0.239930 0.174319i
\(899\) −319023. + 439098.i −0.394733 + 0.543303i
\(900\) −361331. 857746.i −0.446087 1.05895i
\(901\) −1.11414e6 −1.37243
\(902\) −421365. 21431.3i −0.517900 0.0263411i
\(903\) 494711. 20922.9i 0.606702 0.0256594i
\(904\) −2056.97 6330.70i −0.00251704 0.00774666i
\(905\) 872987. 1.20156e6i 1.06589 1.46707i
\(906\) 483356. + 609367.i 0.588858 + 0.742374i
\(907\) 379037. 1.16656e6i 0.460751 1.41805i −0.403496 0.914981i \(-0.632205\pi\)
0.864248 0.503066i \(-0.167795\pi\)
\(908\) 773173. + 251219.i 0.937789 + 0.304706i
\(909\) 544171. + 629460.i 0.658578 + 0.761799i
\(910\) 286590. + 208220.i 0.346082 + 0.251443i
\(911\) 675515. 219488.i 0.813951 0.264469i 0.127681 0.991815i \(-0.459247\pi\)
0.686270 + 0.727347i \(0.259247\pi\)
\(912\) 482.021 20.3862i 0.000579531 2.45102e-5i
\(913\) −55885.8 + 1.09878e6i −0.0670440 + 1.31817i
\(914\) 272545.i 0.326247i
\(915\) 2.42551e6 903087.i 2.89708 1.07867i
\(916\) −553816. 402371.i −0.660047 0.479552i
\(917\) 382151. + 525985.i 0.454460 + 0.625511i
\(918\) −101408. + 534911.i −0.120333 + 0.634741i
\(919\) −35490.4 + 109228.i −0.0420223 + 0.129331i −0.969867 0.243636i \(-0.921660\pi\)
0.927844 + 0.372967i \(0.121660\pi\)
\(920\) 674421. + 928261.i 0.796811 + 1.09672i
\(921\) −159033. 105574.i −0.187485 0.124462i
\(922\) −154924. 476808.i −0.182246 0.560896i
\(923\) 205701.i 0.241453i
\(924\) −536656. 396958.i −0.628568 0.464943i
\(925\) −1.51107e6 −1.76604
\(926\) 75588.4 24560.2i 0.0881522 0.0286424i
\(927\) −421557. 254866.i −0.490565 0.296587i
\(928\) −492461. + 357794.i −0.571842 + 0.415468i
\(929\) −1.10210e6 358093.i −1.27699 0.414921i −0.409474 0.912322i \(-0.634288\pi\)
−0.867520 + 0.497401i \(0.834288\pi\)
\(930\) 231377. 829918.i 0.267519 0.959554i
\(931\) 38783.8 28178.1i 0.0447456 0.0325096i
\(932\) 98261.3 135245.i 0.113123 0.155700i
\(933\) −992622. + 369582.i −1.14030 + 0.424569i
\(934\) 649988. 0.745095
\(935\) 550307. 1.44023e6i 0.629480 1.64744i
\(936\) 23745.5 + 280223.i 0.0271038 + 0.319854i
\(937\) 221814. + 682673.i 0.252644 + 0.777559i 0.994285 + 0.106762i \(0.0340481\pi\)
−0.741640 + 0.670798i \(0.765952\pi\)
\(938\) −153950. + 211894.i −0.174974 + 0.240831i
\(939\) −681760. + 540778.i −0.773215 + 0.613321i
\(940\) −185923. + 572211.i −0.210415 + 0.647590i
\(941\) 338288. + 109916.i 0.382038 + 0.124132i 0.493739 0.869610i \(-0.335630\pi\)
−0.111701 + 0.993742i \(0.535630\pi\)
\(942\) 184027. + 232003.i 0.207387 + 0.261452i
\(943\) 480427. + 349051.i 0.540262 + 0.392523i
\(944\) −2536.69 + 824.220i −0.00284658 + 0.000924910i
\(945\) 243086. + 1.90673e6i 0.272205 + 2.13514i
\(946\) 144808. + 222234.i 0.161812 + 0.248330i
\(947\) 333162.i 0.371497i −0.982597 0.185748i \(-0.940529\pi\)
0.982597 0.185748i \(-0.0594709\pi\)
\(948\) 149696. + 402054.i 0.166569 + 0.447371i
\(949\) −56352.5 40942.5i −0.0625721 0.0454613i
\(950\) 55248.6 + 76043.2i 0.0612173 + 0.0842584i
\(951\) 1.09174e6 + 304373.i 1.20714 + 0.336546i
\(952\) 371425. 1.14313e6i 0.409824 1.26131i
\(953\) −827584. 1.13907e6i −0.911226 1.25419i −0.966746 0.255737i \(-0.917682\pi\)
0.0555203 0.998458i \(-0.482318\pi\)
\(954\) 636754. + 384971.i 0.699641 + 0.422991i
\(955\) −851273. 2.61995e6i −0.933387 2.87267i
\(956\) 824731.i 0.902394i
\(957\) 618609. 195167.i 0.675448 0.213099i
\(958\) −176741. −0.192577
\(959\) −455898. + 148130.i −0.495713 + 0.161067i
\(960\) 539993. 813425.i 0.585930 0.882623i
\(961\) 75438.1 54809.0i 0.0816853 0.0593479i
\(962\) 165379. + 53735.0i 0.178703 + 0.0580641i
\(963\) 395240. + 92385.7i 0.426195 + 0.0996213i
\(964\) −794476. + 577220.i −0.854922 + 0.621137i
\(965\) −1.49402e6 + 2.05634e6i −1.60436 + 2.20821i
\(966\) −205101. 550860.i −0.219793 0.590319i
\(967\) 1.49664e6 1.60053 0.800265 0.599646i \(-0.204692\pi\)
0.800265 + 0.599646i \(0.204692\pi\)
\(968\) 95259.4 934037.i 0.101662 0.996812i
\(969\) 3713.49 + 87803.4i 0.00395489 + 0.0935112i
\(970\) 318498. + 980235.i 0.338503 + 1.04181i
\(971\) −47056.7 + 64768.0i −0.0499095 + 0.0686945i −0.833242 0.552908i \(-0.813518\pi\)
0.783333 + 0.621603i \(0.213518\pi\)
\(972\) −388062. + 432638.i −0.410742 + 0.457923i
\(973\) 24580.1 75649.7i 0.0259632 0.0799064i
\(974\) 224755. + 73027.2i 0.236914 + 0.0769780i
\(975\) −445696. + 353530.i −0.468845 + 0.371892i
\(976\) 9079.23 + 6596.45i 0.00953124 + 0.00692485i
\(977\) 1.38860e6 451183.i 1.45475 0.472676i 0.528286 0.849067i \(-0.322835\pi\)
0.926461 + 0.376391i \(0.122835\pi\)
\(978\) −6712.95 158724.i −0.00701836 0.165945i
\(979\) −4923.41 + 1327.37i −0.00513690 + 0.00138492i
\(980\) 615704.i 0.641091i
\(981\) −273093. 648282.i −0.283774 0.673637i
\(982\) −534580. 388395.i −0.554357 0.402764i
\(983\) −262361. 361109.i −0.271514 0.373707i 0.651386 0.758746i \(-0.274188\pi\)
−0.922900 + 0.385040i \(0.874188\pi\)
\(984\) 217791. 781185.i 0.224931 0.806795i
\(985\) −546780. + 1.68281e6i −0.563560 + 1.73446i
\(986\) 261477. + 359892.i 0.268955 + 0.370185i
\(987\) 447598. 674245.i 0.459466 0.692123i
\(988\) 5342.63 + 16442.9i 0.00547320 + 0.0168448i
\(989\) 373341.i 0.381692i
\(990\) −812160. + 632976.i −0.828650 + 0.645828i
\(991\) 448310. 0.456490 0.228245 0.973604i \(-0.426701\pi\)
0.228245 + 0.973604i \(0.426701\pi\)
\(992\) −885602. + 287750.i −0.899944 + 0.292409i
\(993\) −437355. 290338.i −0.443543 0.294446i
\(994\) 475015. 345118.i 0.480766 0.349297i
\(995\) −380227. 123543.i −0.384058 0.124788i
\(996\) −775842. 216301.i −0.782086 0.218042i
\(997\) 649687. 472025.i 0.653602 0.474870i −0.210894 0.977509i \(-0.567637\pi\)
0.864496 + 0.502639i \(0.167637\pi\)
\(998\) 550921. 758278.i 0.553131 0.761320i
\(999\) 402715. + 853285.i 0.403521 + 0.854994i
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 33.5.h.a.5.10 yes 56
3.2 odd 2 inner 33.5.h.a.5.5 56
11.9 even 5 inner 33.5.h.a.20.5 yes 56
33.20 odd 10 inner 33.5.h.a.20.10 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.5.h.a.5.5 56 3.2 odd 2 inner
33.5.h.a.5.10 yes 56 1.1 even 1 trivial
33.5.h.a.20.5 yes 56 11.9 even 5 inner
33.5.h.a.20.10 yes 56 33.20 odd 10 inner