Properties

Label 17.4.d.a.15.2
Level $17$
Weight $4$
Character 17.15
Analytic conductor $1.003$
Analytic rank $0$
Dimension $12$
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] = [17,4,Mod(2,17)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(17, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([7]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("17.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 17.d (of order \(8\), 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: \(1.00303247010\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 15.2
Root \(1.22788i\) of defining polynomial
Character \(\chi\) \(=\) 17.15
Dual form 17.4.d.a.8.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.161134 - 0.161134i) q^{2} +(3.15299 + 7.61199i) q^{3} -7.94807i q^{4} +(2.54200 - 1.05293i) q^{5} +(0.718496 - 1.73460i) q^{6} +(-19.8837 - 8.23610i) q^{7} +(-2.56978 + 2.56978i) q^{8} +(-28.9092 + 28.9092i) q^{9} +O(q^{10})\) \(q+(-0.161134 - 0.161134i) q^{2} +(3.15299 + 7.61199i) q^{3} -7.94807i q^{4} +(2.54200 - 1.05293i) q^{5} +(0.718496 - 1.73460i) q^{6} +(-19.8837 - 8.23610i) q^{7} +(-2.56978 + 2.56978i) q^{8} +(-28.9092 + 28.9092i) q^{9} +(-0.579266 - 0.239940i) q^{10} +(20.8709 - 50.3869i) q^{11} +(60.5007 - 25.0602i) q^{12} +52.4827i q^{13} +(1.87682 + 4.53105i) q^{14} +(16.0298 + 16.0298i) q^{15} -62.7564 q^{16} +(33.5380 + 61.5484i) q^{17} +9.31650 q^{18} +(13.8808 + 13.8808i) q^{19} +(-8.36878 - 20.2040i) q^{20} -177.323i q^{21} +(-11.4821 + 4.75602i) q^{22} +(-5.33276 + 12.8744i) q^{23} +(-27.6636 - 11.4586i) q^{24} +(-83.0352 + 83.0352i) q^{25} +(8.45675 - 8.45675i) q^{26} +(-105.683 - 43.7754i) q^{27} +(-65.4611 + 158.037i) q^{28} +(64.6920 - 26.7963i) q^{29} -5.16589i q^{30} +(-63.9131 - 154.300i) q^{31} +(30.6704 + 30.6704i) q^{32} +449.350 q^{33} +(4.51343 - 15.3216i) q^{34} -59.2165 q^{35} +(229.772 + 229.772i) q^{36} +(-76.0152 - 183.517i) q^{37} -4.47334i q^{38} +(-399.498 + 165.477i) q^{39} +(-3.82658 + 9.23817i) q^{40} +(401.250 + 166.203i) q^{41} +(-28.5727 + 28.5727i) q^{42} +(89.9025 - 89.9025i) q^{43} +(-400.479 - 165.884i) q^{44} +(-43.0478 + 103.927i) q^{45} +(2.93379 - 1.21522i) q^{46} -207.303i q^{47} +(-197.870 - 477.701i) q^{48} +(84.9906 + 84.9906i) q^{49} +26.7596 q^{50} +(-362.761 + 449.352i) q^{51} +417.136 q^{52} +(-220.673 - 220.673i) q^{53} +(9.97543 + 24.0828i) q^{54} -150.059i q^{55} +(72.2616 - 29.9317i) q^{56} +(-61.8946 + 149.427i) q^{57} +(-14.7419 - 6.10628i) q^{58} +(-407.819 + 407.819i) q^{59} +(127.406 - 127.406i) q^{60} +(72.4205 + 29.9976i) q^{61} +(-14.5644 + 35.1615i) q^{62} +(812.920 - 336.723i) q^{63} +492.167i q^{64} +(55.2607 + 133.411i) q^{65} +(-72.4056 - 72.4056i) q^{66} +359.997 q^{67} +(489.191 - 266.562i) q^{68} -114.814 q^{69} +(9.54178 + 9.54178i) q^{70} +(81.5842 + 196.962i) q^{71} -148.580i q^{72} +(26.8357 - 11.1157i) q^{73} +(-17.3222 + 41.8194i) q^{74} +(-893.873 - 370.254i) q^{75} +(110.326 - 110.326i) q^{76} +(-829.983 + 829.983i) q^{77} +(91.0367 + 37.7086i) q^{78} +(327.389 - 790.386i) q^{79} +(-159.527 + 66.0782i) q^{80} +161.379i q^{81} +(-37.8740 - 91.4360i) q^{82} +(9.67821 + 9.67821i) q^{83} -1409.38 q^{84} +(150.060 + 121.143i) q^{85} -28.9727 q^{86} +(407.946 + 407.946i) q^{87} +(75.8494 + 183.117i) q^{88} -651.126i q^{89} +(23.6826 - 9.80964i) q^{90} +(432.253 - 1043.55i) q^{91} +(102.327 + 42.3851i) q^{92} +(973.012 - 973.012i) q^{93} +(-33.4035 + 33.4035i) q^{94} +(49.9006 + 20.6695i) q^{95} +(-136.759 + 330.166i) q^{96} +(-1107.41 + 458.705i) q^{97} -27.3897i q^{98} +(853.282 + 2060.01i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 4 q^{2} - 4 q^{3} - 20 q^{5} + 20 q^{6} - 4 q^{7} + 28 q^{8} - 64 q^{9} - 116 q^{10} + 40 q^{11} + 56 q^{12} - 132 q^{14} + 244 q^{15} + 184 q^{16} + 52 q^{17} - 12 q^{19} + 572 q^{20} - 620 q^{22} - 276 q^{23} - 184 q^{24} - 464 q^{25} - 708 q^{26} - 664 q^{27} + 452 q^{28} + 632 q^{29} + 188 q^{31} + 700 q^{32} + 1400 q^{33} + 764 q^{34} - 632 q^{35} + 524 q^{36} + 940 q^{37} - 1112 q^{39} - 1864 q^{40} + 176 q^{41} + 48 q^{42} - 1360 q^{43} - 1364 q^{44} - 32 q^{45} + 452 q^{46} - 540 q^{48} + 1044 q^{49} + 2856 q^{50} + 340 q^{51} + 792 q^{52} - 360 q^{53} - 244 q^{54} - 1788 q^{56} - 148 q^{57} - 360 q^{58} - 584 q^{59} - 1792 q^{60} - 1052 q^{61} - 380 q^{62} + 1752 q^{63} + 404 q^{65} + 1372 q^{66} + 1080 q^{67} + 2532 q^{68} - 344 q^{69} + 2072 q^{70} + 28 q^{71} + 824 q^{73} - 2292 q^{74} + 400 q^{75} + 1328 q^{76} - 1252 q^{77} + 1128 q^{78} - 196 q^{79} - 904 q^{80} - 1528 q^{82} - 1008 q^{83} - 4768 q^{84} - 2824 q^{85} - 1200 q^{86} - 2516 q^{87} - 56 q^{88} - 860 q^{90} + 2456 q^{91} + 396 q^{92} - 836 q^{93} + 6360 q^{94} + 2172 q^{95} + 1668 q^{96} - 904 q^{97} + 3280 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.161134 0.161134i −0.0569694 0.0569694i 0.678048 0.735018i \(-0.262826\pi\)
−0.735018 + 0.678048i \(0.762826\pi\)
\(3\) 3.15299 + 7.61199i 0.606793 + 1.46493i 0.866468 + 0.499232i \(0.166385\pi\)
−0.259675 + 0.965696i \(0.583615\pi\)
\(4\) 7.94807i 0.993509i
\(5\) 2.54200 1.05293i 0.227364 0.0941771i −0.266094 0.963947i \(-0.585733\pi\)
0.493457 + 0.869770i \(0.335733\pi\)
\(6\) 0.718496 1.73460i 0.0488875 0.118025i
\(7\) −19.8837 8.23610i −1.07362 0.444707i −0.225352 0.974277i \(-0.572353\pi\)
−0.848266 + 0.529570i \(0.822353\pi\)
\(8\) −2.56978 + 2.56978i −0.113569 + 0.113569i
\(9\) −28.9092 + 28.9092i −1.07071 + 1.07071i
\(10\) −0.579266 0.239940i −0.0183180 0.00758756i
\(11\) 20.8709 50.3869i 0.572075 1.38111i −0.327711 0.944778i \(-0.606277\pi\)
0.899785 0.436333i \(-0.143723\pi\)
\(12\) 60.5007 25.0602i 1.45542 0.602855i
\(13\) 52.4827i 1.11970i 0.828594 + 0.559850i \(0.189141\pi\)
−0.828594 + 0.559850i \(0.810859\pi\)
\(14\) 1.87682 + 4.53105i 0.0358287 + 0.0864982i
\(15\) 16.0298 + 16.0298i 0.275925 + 0.275925i
\(16\) −62.7564 −0.980569
\(17\) 33.5380 + 61.5484i 0.478479 + 0.878099i
\(18\) 9.31650 0.121996
\(19\) 13.8808 + 13.8808i 0.167604 + 0.167604i 0.785925 0.618321i \(-0.212187\pi\)
−0.618321 + 0.785925i \(0.712187\pi\)
\(20\) −8.36878 20.2040i −0.0935658 0.225888i
\(21\) 177.323i 1.84262i
\(22\) −11.4821 + 4.75602i −0.111272 + 0.0460903i
\(23\) −5.33276 + 12.8744i −0.0483460 + 0.116717i −0.946207 0.323560i \(-0.895120\pi\)
0.897862 + 0.440278i \(0.145120\pi\)
\(24\) −27.6636 11.4586i −0.235284 0.0974576i
\(25\) −83.0352 + 83.0352i −0.664282 + 0.664282i
\(26\) 8.45675 8.45675i 0.0637886 0.0637886i
\(27\) −105.683 43.7754i −0.753286 0.312021i
\(28\) −65.4611 + 158.037i −0.441821 + 1.06665i
\(29\) 64.6920 26.7963i 0.414241 0.171584i −0.165822 0.986156i \(-0.553028\pi\)
0.580063 + 0.814571i \(0.303028\pi\)
\(30\) 5.16589i 0.0314386i
\(31\) −63.9131 154.300i −0.370295 0.893971i −0.993700 0.112072i \(-0.964251\pi\)
0.623405 0.781899i \(-0.285749\pi\)
\(32\) 30.6704 + 30.6704i 0.169432 + 0.169432i
\(33\) 449.350 2.37036
\(34\) 4.51343 15.3216i 0.0227661 0.0772835i
\(35\) −59.2165 −0.285983
\(36\) 229.772 + 229.772i 1.06376 + 1.06376i
\(37\) −76.0152 183.517i −0.337752 0.815405i −0.997931 0.0642968i \(-0.979520\pi\)
0.660179 0.751108i \(-0.270480\pi\)
\(38\) 4.47334i 0.0190966i
\(39\) −399.498 + 165.477i −1.64028 + 0.679426i
\(40\) −3.82658 + 9.23817i −0.0151259 + 0.0365171i
\(41\) 401.250 + 166.203i 1.52841 + 0.633087i 0.979254 0.202634i \(-0.0649503\pi\)
0.549153 + 0.835722i \(0.314950\pi\)
\(42\) −28.5727 + 28.5727i −0.104973 + 0.104973i
\(43\) 89.9025 89.9025i 0.318837 0.318837i −0.529483 0.848320i \(-0.677614\pi\)
0.848320 + 0.529483i \(0.177614\pi\)
\(44\) −400.479 165.884i −1.37215 0.568361i
\(45\) −43.0478 + 103.927i −0.142604 + 0.344277i
\(46\) 2.93379 1.21522i 0.00940357 0.00389509i
\(47\) 207.303i 0.643366i −0.946847 0.321683i \(-0.895751\pi\)
0.946847 0.321683i \(-0.104249\pi\)
\(48\) −197.870 477.701i −0.595003 1.43646i
\(49\) 84.9906 + 84.9906i 0.247786 + 0.247786i
\(50\) 26.7596 0.0756875
\(51\) −362.761 + 449.352i −0.996014 + 1.23376i
\(52\) 417.136 1.11243
\(53\) −220.673 220.673i −0.571920 0.571920i 0.360745 0.932665i \(-0.382523\pi\)
−0.932665 + 0.360745i \(0.882523\pi\)
\(54\) 9.97543 + 24.0828i 0.0251386 + 0.0606900i
\(55\) 150.059i 0.367891i
\(56\) 72.2616 29.9317i 0.172435 0.0714249i
\(57\) −61.8946 + 149.427i −0.143827 + 0.347229i
\(58\) −14.7419 6.10628i −0.0333742 0.0138240i
\(59\) −407.819 + 407.819i −0.899890 + 0.899890i −0.995426 0.0955362i \(-0.969543\pi\)
0.0955362 + 0.995426i \(0.469543\pi\)
\(60\) 127.406 127.406i 0.274134 0.274134i
\(61\) 72.4205 + 29.9976i 0.152008 + 0.0629639i 0.457390 0.889266i \(-0.348784\pi\)
−0.305382 + 0.952230i \(0.598784\pi\)
\(62\) −14.5644 + 35.1615i −0.0298335 + 0.0720245i
\(63\) 812.920 336.723i 1.62569 0.673382i
\(64\) 492.167i 0.961264i
\(65\) 55.2607 + 133.411i 0.105450 + 0.254579i
\(66\) −72.4056 72.4056i −0.135038 0.135038i
\(67\) 359.997 0.656428 0.328214 0.944603i \(-0.393553\pi\)
0.328214 + 0.944603i \(0.393553\pi\)
\(68\) 489.191 266.562i 0.872399 0.475373i
\(69\) −114.814 −0.200319
\(70\) 9.54178 + 9.54178i 0.0162923 + 0.0162923i
\(71\) 81.5842 + 196.962i 0.136370 + 0.329226i 0.977281 0.211947i \(-0.0679804\pi\)
−0.840911 + 0.541173i \(0.817980\pi\)
\(72\) 148.580i 0.243199i
\(73\) 26.8357 11.1157i 0.0430258 0.0178219i −0.361067 0.932540i \(-0.617587\pi\)
0.404093 + 0.914718i \(0.367587\pi\)
\(74\) −17.3222 + 41.8194i −0.0272116 + 0.0656947i
\(75\) −893.873 370.254i −1.37621 0.570044i
\(76\) 110.326 110.326i 0.166516 0.166516i
\(77\) −829.983 + 829.983i −1.22838 + 1.22838i
\(78\) 91.0367 + 37.7086i 0.132152 + 0.0547393i
\(79\) 327.389 790.386i 0.466254 1.12564i −0.499531 0.866296i \(-0.666494\pi\)
0.965786 0.259342i \(-0.0835056\pi\)
\(80\) −159.527 + 66.0782i −0.222946 + 0.0923471i
\(81\) 161.379i 0.221371i
\(82\) −37.8740 91.4360i −0.0510059 0.123139i
\(83\) 9.67821 + 9.67821i 0.0127991 + 0.0127991i 0.713477 0.700678i \(-0.247119\pi\)
−0.700678 + 0.713477i \(0.747119\pi\)
\(84\) −1409.38 −1.83066
\(85\) 150.060 + 121.143i 0.191486 + 0.154586i
\(86\) −28.9727 −0.0363280
\(87\) 407.946 + 407.946i 0.502718 + 0.502718i
\(88\) 75.8494 + 183.117i 0.0918815 + 0.221822i
\(89\) 651.126i 0.775497i −0.921765 0.387748i \(-0.873253\pi\)
0.921765 0.387748i \(-0.126747\pi\)
\(90\) 23.6826 9.80964i 0.0277374 0.0114892i
\(91\) 432.253 1043.55i 0.497939 1.20213i
\(92\) 102.327 + 42.3851i 0.115960 + 0.0480321i
\(93\) 973.012 973.012i 1.08491 1.08491i
\(94\) −33.4035 + 33.4035i −0.0366522 + 0.0366522i
\(95\) 49.9006 + 20.6695i 0.0538915 + 0.0223226i
\(96\) −136.759 + 330.166i −0.145395 + 0.351015i
\(97\) −1107.41 + 458.705i −1.15918 + 0.480149i −0.877602 0.479389i \(-0.840858\pi\)
−0.281579 + 0.959538i \(0.590858\pi\)
\(98\) 27.3897i 0.0282325i
\(99\) 853.282 + 2060.01i 0.866243 + 2.09130i
\(100\) 659.970 + 659.970i 0.659970 + 0.659970i
\(101\) 89.2435 0.0879214 0.0439607 0.999033i \(-0.486002\pi\)
0.0439607 + 0.999033i \(0.486002\pi\)
\(102\) 130.859 13.9527i 0.127029 0.0135444i
\(103\) −1242.17 −1.18830 −0.594150 0.804354i \(-0.702511\pi\)
−0.594150 + 0.804354i \(0.702511\pi\)
\(104\) −134.869 134.869i −0.127163 0.127163i
\(105\) −186.709 450.755i −0.173533 0.418945i
\(106\) 71.1158i 0.0651639i
\(107\) 1420.54 588.407i 1.28345 0.531621i 0.366420 0.930449i \(-0.380583\pi\)
0.917025 + 0.398829i \(0.130583\pi\)
\(108\) −347.930 + 839.977i −0.309996 + 0.748396i
\(109\) 95.9730 + 39.7533i 0.0843353 + 0.0349328i 0.424452 0.905450i \(-0.360467\pi\)
−0.340117 + 0.940383i \(0.610467\pi\)
\(110\) −24.1796 + 24.1796i −0.0209585 + 0.0209585i
\(111\) 1157.25 1157.25i 0.989565 0.989565i
\(112\) 1247.83 + 516.868i 1.05276 + 0.436066i
\(113\) −140.908 + 340.183i −0.117306 + 0.283201i −0.971617 0.236562i \(-0.923980\pi\)
0.854311 + 0.519762i \(0.173980\pi\)
\(114\) 34.0510 14.1044i 0.0279752 0.0115877i
\(115\) 38.3418i 0.0310904i
\(116\) −212.979 514.176i −0.170471 0.411552i
\(117\) −1517.23 1517.23i −1.19887 1.19887i
\(118\) 131.427 0.102532
\(119\) −159.940 1500.03i −0.123207 1.15553i
\(120\) −82.3860 −0.0626732
\(121\) −1162.08 1162.08i −0.873091 0.873091i
\(122\) −6.83578 16.5030i −0.00507281 0.0122468i
\(123\) 3578.35i 2.62316i
\(124\) −1226.39 + 507.986i −0.888168 + 0.367891i
\(125\) −255.262 + 616.256i −0.182650 + 0.440957i
\(126\) −185.247 76.7316i −0.130977 0.0542524i
\(127\) −886.309 + 886.309i −0.619269 + 0.619269i −0.945344 0.326075i \(-0.894274\pi\)
0.326075 + 0.945344i \(0.394274\pi\)
\(128\) 324.668 324.668i 0.224194 0.224194i
\(129\) 967.799 + 400.875i 0.660542 + 0.273605i
\(130\) 12.5927 30.4014i 0.00849578 0.0205106i
\(131\) −1806.01 + 748.072i −1.20452 + 0.498927i −0.892455 0.451136i \(-0.851019\pi\)
−0.312060 + 0.950062i \(0.601019\pi\)
\(132\) 3571.47i 2.35497i
\(133\) −161.678 390.326i −0.105408 0.254478i
\(134\) −58.0078 58.0078i −0.0373963 0.0373963i
\(135\) −314.739 −0.200655
\(136\) −244.351 71.9806i −0.154065 0.0453844i
\(137\) 1749.91 1.09127 0.545637 0.838022i \(-0.316288\pi\)
0.545637 + 0.838022i \(0.316288\pi\)
\(138\) 18.5004 + 18.5004i 0.0114120 + 0.0114120i
\(139\) 78.9509 + 190.604i 0.0481765 + 0.116308i 0.946136 0.323770i \(-0.104951\pi\)
−0.897959 + 0.440079i \(0.854951\pi\)
\(140\) 470.657i 0.284127i
\(141\) 1577.99 653.624i 0.942486 0.390390i
\(142\) 18.5912 44.8832i 0.0109869 0.0265248i
\(143\) 2644.44 + 1095.36i 1.54643 + 0.640552i
\(144\) 1814.24 1814.24i 1.04991 1.04991i
\(145\) 136.232 136.232i 0.0780241 0.0780241i
\(146\) −6.11526 2.53303i −0.00346646 0.00143585i
\(147\) −378.973 + 914.922i −0.212634 + 0.513343i
\(148\) −1458.61 + 604.174i −0.810112 + 0.335559i
\(149\) 2013.39i 1.10700i 0.832849 + 0.553501i \(0.186708\pi\)
−0.832849 + 0.553501i \(0.813292\pi\)
\(150\) 84.3727 + 203.694i 0.0459267 + 0.110877i
\(151\) 53.4946 + 53.4946i 0.0288300 + 0.0288300i 0.721375 0.692545i \(-0.243511\pi\)
−0.692545 + 0.721375i \(0.743511\pi\)
\(152\) −71.3412 −0.0380693
\(153\) −2748.87 809.759i −1.45250 0.427877i
\(154\) 267.477 0.139960
\(155\) −324.935 324.935i −0.168383 0.168383i
\(156\) 1315.23 + 3175.24i 0.675016 + 1.62963i
\(157\) 2301.81i 1.17009i 0.811000 + 0.585046i \(0.198924\pi\)
−0.811000 + 0.585046i \(0.801076\pi\)
\(158\) −180.111 + 74.6046i −0.0906892 + 0.0375647i
\(159\) 983.980 2375.54i 0.490784 1.18486i
\(160\) 110.258 + 45.6704i 0.0544791 + 0.0225660i
\(161\) 212.070 212.070i 0.103810 0.103810i
\(162\) 26.0037 26.0037i 0.0126114 0.0126114i
\(163\) −1748.91 724.420i −0.840398 0.348104i −0.0793874 0.996844i \(-0.525296\pi\)
−0.761010 + 0.648740i \(0.775296\pi\)
\(164\) 1320.99 3189.16i 0.628978 1.51849i
\(165\) 1142.25 473.135i 0.538933 0.223234i
\(166\) 3.11898i 0.00145831i
\(167\) 41.5126 + 100.220i 0.0192356 + 0.0464388i 0.933205 0.359343i \(-0.116999\pi\)
−0.913970 + 0.405782i \(0.866999\pi\)
\(168\) 455.680 + 455.680i 0.209265 + 0.209265i
\(169\) −557.436 −0.253726
\(170\) −4.65948 43.7000i −0.00210215 0.0197155i
\(171\) −802.566 −0.358911
\(172\) −714.551 714.551i −0.316768 0.316768i
\(173\) −1054.59 2546.01i −0.463463 1.11890i −0.966966 0.254905i \(-0.917956\pi\)
0.503504 0.863993i \(-0.332044\pi\)
\(174\) 131.468i 0.0572791i
\(175\) 2334.93 967.161i 1.00860 0.417774i
\(176\) −1309.78 + 3162.10i −0.560959 + 1.35427i
\(177\) −4390.16 1818.47i −1.86432 0.772227i
\(178\) −104.918 + 104.918i −0.0441796 + 0.0441796i
\(179\) −1418.56 + 1418.56i −0.592337 + 0.592337i −0.938262 0.345925i \(-0.887565\pi\)
0.345925 + 0.938262i \(0.387565\pi\)
\(180\) 826.016 + 342.147i 0.342042 + 0.141679i
\(181\) −927.705 + 2239.68i −0.380971 + 0.919745i 0.610808 + 0.791779i \(0.290845\pi\)
−0.991779 + 0.127966i \(0.959155\pi\)
\(182\) −237.802 + 98.5008i −0.0968520 + 0.0401174i
\(183\) 645.847i 0.260887i
\(184\) −19.3804 46.7883i −0.00776489 0.0187461i
\(185\) −386.461 386.461i −0.153585 0.153585i
\(186\) −313.571 −0.123614
\(187\) 3801.20 405.300i 1.48648 0.158495i
\(188\) −1647.66 −0.639190
\(189\) 1740.83 + 1740.83i 0.669984 + 0.669984i
\(190\) −4.71012 11.3712i −0.00179846 0.00434188i
\(191\) 4153.64i 1.57354i −0.617243 0.786772i \(-0.711751\pi\)
0.617243 0.786772i \(-0.288249\pi\)
\(192\) −3746.37 + 1551.80i −1.40818 + 0.583289i
\(193\) 794.611 1918.36i 0.296360 0.715475i −0.703628 0.710568i \(-0.748438\pi\)
0.999988 0.00490706i \(-0.00156197\pi\)
\(194\) 252.355 + 104.529i 0.0933917 + 0.0386841i
\(195\) −841.288 + 841.288i −0.308953 + 0.308953i
\(196\) 675.511 675.511i 0.246178 0.246178i
\(197\) 3513.98 + 1455.54i 1.27087 + 0.526410i 0.913227 0.407450i \(-0.133582\pi\)
0.357638 + 0.933860i \(0.383582\pi\)
\(198\) 194.444 469.430i 0.0697906 0.168489i
\(199\) 3346.19 1386.04i 1.19199 0.493736i 0.303584 0.952805i \(-0.401817\pi\)
0.888401 + 0.459068i \(0.151817\pi\)
\(200\) 426.764i 0.150884i
\(201\) 1135.07 + 2740.30i 0.398316 + 0.961620i
\(202\) −14.3802 14.3802i −0.00500883 0.00500883i
\(203\) −1507.01 −0.521042
\(204\) 3571.48 + 2883.25i 1.22575 + 0.989549i
\(205\) 1194.98 0.407127
\(206\) 200.156 + 200.156i 0.0676968 + 0.0676968i
\(207\) −218.023 526.355i −0.0732061 0.176735i
\(208\) 3293.63i 1.09794i
\(209\) 989.117 409.706i 0.327362 0.135598i
\(210\) −42.5468 + 102.717i −0.0139810 + 0.0337531i
\(211\) −584.358 242.049i −0.190658 0.0789732i 0.285312 0.958435i \(-0.407903\pi\)
−0.475970 + 0.879462i \(0.657903\pi\)
\(212\) −1753.92 + 1753.92i −0.568207 + 0.568207i
\(213\) −1242.04 + 1242.04i −0.399545 + 0.399545i
\(214\) −323.709 134.085i −0.103403 0.0428311i
\(215\) 133.871 323.193i 0.0424648 0.102519i
\(216\) 384.075 159.089i 0.120986 0.0501140i
\(217\) 3594.45i 1.12446i
\(218\) −9.05890 21.8701i −0.00281443 0.00679464i
\(219\) 169.226 + 169.226i 0.0522155 + 0.0522155i
\(220\) −1192.68 −0.365503
\(221\) −3230.23 + 1760.16i −0.983206 + 0.535753i
\(222\) −372.946 −0.112750
\(223\) 377.462 + 377.462i 0.113348 + 0.113348i 0.761506 0.648158i \(-0.224460\pi\)
−0.648158 + 0.761506i \(0.724460\pi\)
\(224\) −357.237 862.445i −0.106557 0.257252i
\(225\) 4800.96i 1.42251i
\(226\) 77.5201 32.1099i 0.0228166 0.00945096i
\(227\) 225.340 544.019i 0.0658870 0.159065i −0.887506 0.460795i \(-0.847564\pi\)
0.953393 + 0.301730i \(0.0975642\pi\)
\(228\) 1187.65 + 491.943i 0.344975 + 0.142893i
\(229\) 1867.57 1867.57i 0.538920 0.538920i −0.384292 0.923212i \(-0.625554\pi\)
0.923212 + 0.384292i \(0.125554\pi\)
\(230\) 6.17817 6.17817i 0.00177120 0.00177120i
\(231\) −8934.75 3700.89i −2.54486 1.05412i
\(232\) −97.3834 + 235.104i −0.0275583 + 0.0665317i
\(233\) 354.195 146.712i 0.0995882 0.0412508i −0.332333 0.943162i \(-0.607836\pi\)
0.431921 + 0.901911i \(0.357836\pi\)
\(234\) 488.955i 0.136598i
\(235\) −218.276 526.964i −0.0605904 0.146278i
\(236\) 3241.37 + 3241.37i 0.894049 + 0.894049i
\(237\) 7048.67 1.93190
\(238\) −215.934 + 267.478i −0.0588107 + 0.0728488i
\(239\) −4344.62 −1.17586 −0.587929 0.808913i \(-0.700056\pi\)
−0.587929 + 0.808913i \(0.700056\pi\)
\(240\) −1005.97 1005.97i −0.270564 0.270564i
\(241\) −785.906 1897.34i −0.210061 0.507131i 0.783371 0.621554i \(-0.213498\pi\)
−0.993432 + 0.114422i \(0.963498\pi\)
\(242\) 374.502i 0.0994790i
\(243\) −4081.86 + 1690.76i −1.07758 + 0.446348i
\(244\) 238.423 575.604i 0.0625552 0.151022i
\(245\) 305.535 + 126.557i 0.0796732 + 0.0330017i
\(246\) 576.593 576.593i 0.149440 0.149440i
\(247\) −728.503 + 728.503i −0.187666 + 0.187666i
\(248\) 560.759 + 232.274i 0.143581 + 0.0594734i
\(249\) −43.1552 + 104.186i −0.0109833 + 0.0265161i
\(250\) 140.431 58.1685i 0.0355266 0.0147156i
\(251\) 907.953i 0.228325i −0.993462 0.114162i \(-0.963582\pi\)
0.993462 0.114162i \(-0.0364184\pi\)
\(252\) −2676.30 6461.15i −0.669011 1.61514i
\(253\) 537.402 + 537.402i 0.133542 + 0.133542i
\(254\) 285.629 0.0705589
\(255\) −449.002 + 1524.22i −0.110265 + 0.374314i
\(256\) 3832.71 0.935720
\(257\) 5296.81 + 5296.81i 1.28563 + 1.28563i 0.937417 + 0.348209i \(0.113210\pi\)
0.348209 + 0.937417i \(0.386790\pi\)
\(258\) −91.3506 220.540i −0.0220436 0.0532179i
\(259\) 4275.06i 1.02564i
\(260\) 1060.36 439.216i 0.252926 0.104765i
\(261\) −1095.53 + 2644.85i −0.259815 + 0.627250i
\(262\) 411.549 + 170.469i 0.0970441 + 0.0401970i
\(263\) −5558.34 + 5558.34i −1.30320 + 1.30320i −0.376982 + 0.926221i \(0.623038\pi\)
−0.926221 + 0.376982i \(0.876962\pi\)
\(264\) −1154.73 + 1154.73i −0.269200 + 0.269200i
\(265\) −793.304 328.597i −0.183895 0.0761720i
\(266\) −36.8429 + 88.9466i −0.00849241 + 0.0205025i
\(267\) 4956.36 2052.99i 1.13605 0.470566i
\(268\) 2861.29i 0.652167i
\(269\) −2890.74 6978.86i −0.655210 1.58182i −0.805117 0.593116i \(-0.797898\pi\)
0.149908 0.988700i \(-0.452102\pi\)
\(270\) 50.7151 + 50.7151i 0.0114312 + 0.0114312i
\(271\) 6394.46 1.43334 0.716672 0.697411i \(-0.245665\pi\)
0.716672 + 0.697411i \(0.245665\pi\)
\(272\) −2104.72 3862.56i −0.469182 0.861037i
\(273\) 9306.39 2.06318
\(274\) −281.969 281.969i −0.0621693 0.0621693i
\(275\) 2450.86 + 5916.91i 0.537428 + 1.29747i
\(276\) 912.551i 0.199018i
\(277\) −6247.84 + 2587.94i −1.35522 + 0.561351i −0.937741 0.347335i \(-0.887087\pi\)
−0.417480 + 0.908686i \(0.637087\pi\)
\(278\) 17.9912 43.4345i 0.00388143 0.00937061i
\(279\) 6308.36 + 2613.01i 1.35366 + 0.560705i
\(280\) 152.173 152.173i 0.0324788 0.0324788i
\(281\) 4453.39 4453.39i 0.945433 0.945433i −0.0531529 0.998586i \(-0.516927\pi\)
0.998586 + 0.0531529i \(0.0169271\pi\)
\(282\) −359.588 148.946i −0.0759332 0.0314526i
\(283\) −1022.77 + 2469.18i −0.214831 + 0.518648i −0.994154 0.107975i \(-0.965563\pi\)
0.779323 + 0.626623i \(0.215563\pi\)
\(284\) 1565.47 648.437i 0.327089 0.135485i
\(285\) 445.014i 0.0924924i
\(286\) −249.609 602.609i −0.0516073 0.124591i
\(287\) −6609.47 6609.47i −1.35939 1.35939i
\(288\) −1773.31 −0.362824
\(289\) −2663.41 + 4128.41i −0.542115 + 0.840304i
\(290\) −43.9033 −0.00888998
\(291\) −6983.32 6983.32i −1.40677 1.40677i
\(292\) −88.3485 213.292i −0.0177062 0.0427465i
\(293\) 2183.30i 0.435323i −0.976024 0.217661i \(-0.930157\pi\)
0.976024 0.217661i \(-0.0698428\pi\)
\(294\) 208.490 86.3595i 0.0413585 0.0171313i
\(295\) −607.271 + 1466.08i −0.119853 + 0.289351i
\(296\) 666.939 + 276.255i 0.130963 + 0.0542467i
\(297\) −4411.41 + 4411.41i −0.861872 + 0.861872i
\(298\) 324.425 324.425i 0.0630653 0.0630653i
\(299\) −675.684 279.878i −0.130688 0.0541329i
\(300\) −2942.81 + 7104.57i −0.566344 + 1.36727i
\(301\) −2528.04 + 1047.15i −0.484099 + 0.200520i
\(302\) 17.2396i 0.00328485i
\(303\) 281.384 + 679.321i 0.0533501 + 0.128799i
\(304\) −871.110 871.110i −0.164347 0.164347i
\(305\) 215.679 0.0404909
\(306\) 312.456 + 573.416i 0.0583724 + 0.107124i
\(307\) −3905.30 −0.726018 −0.363009 0.931786i \(-0.618250\pi\)
−0.363009 + 0.931786i \(0.618250\pi\)
\(308\) 6596.76 + 6596.76i 1.22041 + 1.22041i
\(309\) −3916.56 9455.40i −0.721052 1.74077i
\(310\) 104.716i 0.0191854i
\(311\) 6806.60 2819.39i 1.24105 0.514060i 0.337008 0.941502i \(-0.390585\pi\)
0.904043 + 0.427441i \(0.140585\pi\)
\(312\) 601.380 1451.86i 0.109123 0.263447i
\(313\) −2149.71 890.438i −0.388207 0.160800i 0.180039 0.983659i \(-0.442378\pi\)
−0.568246 + 0.822859i \(0.692378\pi\)
\(314\) 370.900 370.900i 0.0666595 0.0666595i
\(315\) 1711.90 1711.90i 0.306205 0.306205i
\(316\) −6282.05 2602.11i −1.11833 0.463228i
\(317\) 2858.75 6901.62i 0.506508 1.22282i −0.439372 0.898305i \(-0.644799\pi\)
0.945881 0.324514i \(-0.105201\pi\)
\(318\) −541.333 + 224.227i −0.0954604 + 0.0395410i
\(319\) 3818.89i 0.670272i
\(320\) 518.218 + 1251.09i 0.0905290 + 0.218556i
\(321\) 8957.89 + 8957.89i 1.55757 + 1.55757i
\(322\) −68.3433 −0.0118280
\(323\) −388.808 + 1319.88i −0.0669779 + 0.227368i
\(324\) 1282.66 0.219934
\(325\) −4357.92 4357.92i −0.743796 0.743796i
\(326\) 165.079 + 398.537i 0.0280457 + 0.0677083i
\(327\) 855.888i 0.144742i
\(328\) −1458.23 + 604.017i −0.245479 + 0.101681i
\(329\) −1707.37 + 4121.95i −0.286110 + 0.690730i
\(330\) −260.293 107.817i −0.0434202 0.0179852i
\(331\) 6613.70 6613.70i 1.09825 1.09825i 0.103637 0.994615i \(-0.466952\pi\)
0.994615 0.103637i \(-0.0330482\pi\)
\(332\) 76.9231 76.9231i 0.0127160 0.0127160i
\(333\) 7502.86 + 3107.79i 1.23470 + 0.511428i
\(334\) 9.45981 22.8380i 0.00154975 0.00374143i
\(335\) 915.114 379.053i 0.149248 0.0618205i
\(336\) 11128.1i 1.80682i
\(337\) 2657.39 + 6415.50i 0.429546 + 1.03702i 0.979432 + 0.201776i \(0.0646714\pi\)
−0.549885 + 0.835240i \(0.685329\pi\)
\(338\) 89.8218 + 89.8218i 0.0144546 + 0.0144546i
\(339\) −3033.75 −0.486049
\(340\) 962.853 1192.69i 0.153582 0.190243i
\(341\) −9108.62 −1.44651
\(342\) 129.321 + 129.321i 0.0204470 + 0.0204470i
\(343\) 1835.05 + 4430.19i 0.288872 + 0.697399i
\(344\) 462.058i 0.0724201i
\(345\) −291.858 + 120.891i −0.0455452 + 0.0188654i
\(346\) −240.318 + 580.178i −0.0373398 + 0.0901462i
\(347\) 2226.53 + 922.261i 0.344457 + 0.142679i 0.548204 0.836345i \(-0.315312\pi\)
−0.203747 + 0.979024i \(0.565312\pi\)
\(348\) 3242.39 3242.39i 0.499454 0.499454i
\(349\) −7781.94 + 7781.94i −1.19357 + 1.19357i −0.217518 + 0.976056i \(0.569796\pi\)
−0.976056 + 0.217518i \(0.930204\pi\)
\(350\) −532.080 220.395i −0.0812596 0.0336588i
\(351\) 2297.45 5546.54i 0.349370 0.843454i
\(352\) 2185.51 905.266i 0.330931 0.137076i
\(353\) 7713.23i 1.16299i −0.813552 0.581493i \(-0.802469\pi\)
0.813552 0.581493i \(-0.197531\pi\)
\(354\) 414.388 + 1000.42i 0.0622160 + 0.150203i
\(355\) 414.775 + 414.775i 0.0620111 + 0.0620111i
\(356\) −5175.20 −0.770463
\(357\) 10913.9 5947.05i 1.61800 0.881656i
\(358\) 457.157 0.0674902
\(359\) 7226.67 + 7226.67i 1.06242 + 1.06242i 0.997917 + 0.0645037i \(0.0205464\pi\)
0.0645037 + 0.997917i \(0.479454\pi\)
\(360\) −156.445 377.691i −0.0229038 0.0552947i
\(361\) 6473.65i 0.943818i
\(362\) 510.373 211.403i 0.0741011 0.0306937i
\(363\) 5181.73 12509.8i 0.749230 1.80880i
\(364\) −8294.22 3435.58i −1.19433 0.494706i
\(365\) 56.5124 56.5124i 0.00810409 0.00810409i
\(366\) 104.068 104.068i 0.0148626 0.0148626i
\(367\) 9536.68 + 3950.22i 1.35643 + 0.561853i 0.938076 0.346430i \(-0.112606\pi\)
0.418356 + 0.908283i \(0.362606\pi\)
\(368\) 334.665 807.952i 0.0474065 0.114450i
\(369\) −16404.6 + 6795.01i −2.31434 + 0.958629i
\(370\) 124.544i 0.0174993i
\(371\) 2570.31 + 6205.27i 0.359687 + 0.868361i
\(372\) −7733.57 7733.57i −1.07787 1.07787i
\(373\) −2744.09 −0.380921 −0.190461 0.981695i \(-0.560998\pi\)
−0.190461 + 0.981695i \(0.560998\pi\)
\(374\) −677.810 547.195i −0.0937132 0.0756545i
\(375\) −5495.78 −0.756802
\(376\) 532.722 + 532.722i 0.0730666 + 0.0730666i
\(377\) 1406.34 + 3395.21i 0.192123 + 0.463826i
\(378\) 561.014i 0.0763372i
\(379\) −5917.45 + 2451.09i −0.802003 + 0.332200i −0.745758 0.666217i \(-0.767913\pi\)
−0.0562446 + 0.998417i \(0.517913\pi\)
\(380\) 164.283 396.614i 0.0221777 0.0535417i
\(381\) −9541.10 3952.05i −1.28295 0.531417i
\(382\) −669.293 + 669.293i −0.0896440 + 0.0896440i
\(383\) −2611.23 + 2611.23i −0.348375 + 0.348375i −0.859504 0.511129i \(-0.829227\pi\)
0.511129 + 0.859504i \(0.329227\pi\)
\(384\) 3495.04 + 1447.69i 0.464468 + 0.192389i
\(385\) −1235.90 + 2983.73i −0.163604 + 0.394974i
\(386\) −437.152 + 181.074i −0.0576437 + 0.0238768i
\(387\) 5198.01i 0.682765i
\(388\) 3645.82 + 8801.79i 0.477032 + 1.15166i
\(389\) −1508.22 1508.22i −0.196581 0.196581i 0.601952 0.798532i \(-0.294390\pi\)
−0.798532 + 0.601952i \(0.794390\pi\)
\(390\) 271.120 0.0352018
\(391\) −971.250 + 103.559i −0.125622 + 0.0133944i
\(392\) −436.813 −0.0562816
\(393\) −11388.6 11388.6i −1.46178 1.46178i
\(394\) −331.685 800.758i −0.0424112 0.102390i
\(395\) 2353.88i 0.299840i
\(396\) 16373.1 6781.95i 2.07772 0.860621i
\(397\) −904.995 + 2184.85i −0.114409 + 0.276208i −0.970704 0.240280i \(-0.922761\pi\)
0.856295 + 0.516488i \(0.172761\pi\)
\(398\) −762.522 315.847i −0.0960346 0.0397788i
\(399\) 2461.39 2461.39i 0.308831 0.308831i
\(400\) 5210.99 5210.99i 0.651374 0.651374i
\(401\) 1906.65 + 789.759i 0.237440 + 0.0983509i 0.498231 0.867044i \(-0.333983\pi\)
−0.260791 + 0.965395i \(0.583983\pi\)
\(402\) 258.657 624.453i 0.0320911 0.0774748i
\(403\) 8098.08 3354.33i 1.00098 0.414619i
\(404\) 709.314i 0.0873507i
\(405\) 169.922 + 410.227i 0.0208481 + 0.0503317i
\(406\) 242.831 + 242.831i 0.0296835 + 0.0296835i
\(407\) −10833.4 −1.31938
\(408\) −222.519 2086.95i −0.0270009 0.253234i
\(409\) 9245.03 1.11769 0.558847 0.829271i \(-0.311244\pi\)
0.558847 + 0.829271i \(0.311244\pi\)
\(410\) −192.552 192.552i −0.0231938 0.0231938i
\(411\) 5517.43 + 13320.3i 0.662178 + 1.59864i
\(412\) 9872.87i 1.18059i
\(413\) 11467.8 4750.11i 1.36633 0.565951i
\(414\) −49.6826 + 119.945i −0.00589799 + 0.0142390i
\(415\) 34.7925 + 14.4115i 0.00411542 + 0.00170466i
\(416\) −1609.67 + 1609.67i −0.189712 + 0.189712i
\(417\) −1201.95 + 1201.95i −0.141150 + 0.141150i
\(418\) −225.398 93.3628i −0.0263746 0.0109247i
\(419\) 1590.19 3839.06i 0.185408 0.447614i −0.803657 0.595092i \(-0.797116\pi\)
0.989065 + 0.147478i \(0.0471155\pi\)
\(420\) −3582.63 + 1483.98i −0.416225 + 0.172406i
\(421\) 4609.26i 0.533591i −0.963753 0.266795i \(-0.914035\pi\)
0.963753 0.266795i \(-0.0859648\pi\)
\(422\) 55.1576 + 133.162i 0.00636263 + 0.0153608i
\(423\) 5992.96 + 5992.96i 0.688859 + 0.688859i
\(424\) 1134.16 0.129905
\(425\) −7895.52 2325.85i −0.901150 0.265460i
\(426\) 400.269 0.0455237
\(427\) −1192.93 1192.93i −0.135198 0.135198i
\(428\) −4676.70 11290.5i −0.528170 1.27511i
\(429\) 23583.1i 2.65409i
\(430\) −73.6486 + 30.5063i −0.00825965 + 0.00342126i
\(431\) −6632.04 + 16011.2i −0.741193 + 1.78940i −0.140235 + 0.990118i \(0.544786\pi\)
−0.600958 + 0.799281i \(0.705214\pi\)
\(432\) 6632.29 + 2747.19i 0.738649 + 0.305958i
\(433\) 8028.41 8028.41i 0.891041 0.891041i −0.103580 0.994621i \(-0.533030\pi\)
0.994621 + 0.103580i \(0.0330297\pi\)
\(434\) 579.188 579.188i 0.0640597 0.0640597i
\(435\) 1466.54 + 607.461i 0.161644 + 0.0669552i
\(436\) 315.962 762.801i 0.0347061 0.0837879i
\(437\) −252.730 + 104.684i −0.0276653 + 0.0114593i
\(438\) 54.5359i 0.00594938i
\(439\) −1962.43 4737.72i −0.213352 0.515078i 0.780582 0.625053i \(-0.214923\pi\)
−0.993934 + 0.109975i \(0.964923\pi\)
\(440\) 385.619 + 385.619i 0.0417810 + 0.0417810i
\(441\) −4914.02 −0.530614
\(442\) 804.121 + 236.877i 0.0865343 + 0.0254912i
\(443\) −3133.00 −0.336012 −0.168006 0.985786i \(-0.553733\pi\)
−0.168006 + 0.985786i \(0.553733\pi\)
\(444\) −9197.94 9197.94i −0.983141 0.983141i
\(445\) −685.591 1655.16i −0.0730340 0.176320i
\(446\) 121.644i 0.0129148i
\(447\) −15325.9 + 6348.19i −1.62168 + 0.671721i
\(448\) 4053.54 9786.11i 0.427481 1.03203i
\(449\) 10855.2 + 4496.37i 1.14095 + 0.472599i 0.871491 0.490411i \(-0.163154\pi\)
0.269464 + 0.963010i \(0.413154\pi\)
\(450\) −773.598 + 773.598i −0.0810395 + 0.0810395i
\(451\) 16748.9 16748.9i 1.74873 1.74873i
\(452\) 2703.80 + 1119.95i 0.281363 + 0.116544i
\(453\) −238.532 + 575.868i −0.0247400 + 0.0597277i
\(454\) −123.970 + 51.3500i −0.0128154 + 0.00530831i
\(455\) 3107.84i 0.320215i
\(456\) −224.938 543.048i −0.0231002 0.0557688i
\(457\) −8774.30 8774.30i −0.898128 0.898128i 0.0971425 0.995270i \(-0.469030\pi\)
−0.995270 + 0.0971425i \(0.969030\pi\)
\(458\) −601.859 −0.0614039
\(459\) −850.090 7972.76i −0.0864462 0.810755i
\(460\) 304.744 0.0308886
\(461\) 5211.73 + 5211.73i 0.526539 + 0.526539i 0.919539 0.393000i \(-0.128563\pi\)
−0.393000 + 0.919539i \(0.628563\pi\)
\(462\) 843.352 + 2036.03i 0.0849270 + 0.205032i
\(463\) 11446.9i 1.14899i 0.818508 + 0.574495i \(0.194802\pi\)
−0.818508 + 0.574495i \(0.805198\pi\)
\(464\) −4059.84 + 1681.64i −0.406192 + 0.168250i
\(465\) 1448.88 3497.91i 0.144495 0.348843i
\(466\) −80.7131 33.4325i −0.00802352 0.00332345i
\(467\) 3124.20 3124.20i 0.309573 0.309573i −0.535171 0.844744i \(-0.679753\pi\)
0.844744 + 0.535171i \(0.179753\pi\)
\(468\) −12059.1 + 12059.1i −1.19109 + 1.19109i
\(469\) −7158.08 2964.97i −0.704754 0.291919i
\(470\) −49.7402 + 120.083i −0.00488158 + 0.0117852i
\(471\) −17521.4 + 7257.59i −1.71410 + 0.710004i
\(472\) 2096.01i 0.204399i
\(473\) −2653.56 6406.25i −0.257951 0.622748i
\(474\) −1135.78 1135.78i −0.110059 0.110059i
\(475\) −2305.19 −0.222673
\(476\) −11922.4 + 1271.21i −1.14803 + 0.122407i
\(477\) 12758.9 1.22472
\(478\) 700.065 + 700.065i 0.0669879 + 0.0669879i
\(479\) −108.152 261.102i −0.0103165 0.0249062i 0.918637 0.395102i \(-0.129291\pi\)
−0.928954 + 0.370196i \(0.879291\pi\)
\(480\) 983.281i 0.0935009i
\(481\) 9631.46 3989.48i 0.913008 0.378180i
\(482\) −179.090 + 432.363i −0.0169240 + 0.0408580i
\(483\) 2282.93 + 945.620i 0.215066 + 0.0890832i
\(484\) −9236.32 + 9236.32i −0.867423 + 0.867423i
\(485\) −2332.06 + 2332.06i −0.218337 + 0.218337i
\(486\) 930.166 + 385.287i 0.0868172 + 0.0359609i
\(487\) −2909.21 + 7023.45i −0.270696 + 0.653518i −0.999513 0.0311903i \(-0.990070\pi\)
0.728818 + 0.684708i \(0.240070\pi\)
\(488\) −263.192 + 109.018i −0.0244142 + 0.0101127i
\(489\) 15596.7i 1.44235i
\(490\) −28.8395 69.6247i −0.00265885 0.00641903i
\(491\) −9075.67 9075.67i −0.834174 0.834174i 0.153911 0.988085i \(-0.450813\pi\)
−0.988085 + 0.153911i \(0.950813\pi\)
\(492\) 28441.0 2.60613
\(493\) 3818.91 + 3082.99i 0.348874 + 0.281645i
\(494\) 234.773 0.0213825
\(495\) 4338.09 + 4338.09i 0.393904 + 0.393904i
\(496\) 4010.96 + 9683.31i 0.363100 + 0.876600i
\(497\) 4588.27i 0.414108i
\(498\) 23.7416 9.83410i 0.00213632 0.000884893i
\(499\) 1039.84 2510.39i 0.0932855 0.225211i −0.870349 0.492436i \(-0.836107\pi\)
0.963634 + 0.267225i \(0.0861066\pi\)
\(500\) 4898.05 + 2028.84i 0.438095 + 0.181465i
\(501\) −631.988 + 631.988i −0.0563575 + 0.0563575i
\(502\) −146.302 + 146.302i −0.0130075 + 0.0130075i
\(503\) 7589.15 + 3143.53i 0.672731 + 0.278654i 0.692784 0.721145i \(-0.256384\pi\)
−0.0200537 + 0.999799i \(0.506384\pi\)
\(504\) −1223.72 + 2954.32i −0.108153 + 0.261103i
\(505\) 226.857 93.9673i 0.0199901 0.00828018i
\(506\) 173.187i 0.0152157i
\(507\) −1757.59 4243.20i −0.153959 0.371690i
\(508\) 7044.45 + 7044.45i 0.615250 + 0.615250i
\(509\) 8243.18 0.717824 0.358912 0.933371i \(-0.383148\pi\)
0.358912 + 0.933371i \(0.383148\pi\)
\(510\) 317.953 173.253i 0.0276062 0.0150427i
\(511\) −625.144 −0.0541188
\(512\) −3214.92 3214.92i −0.277502 0.277502i
\(513\) −859.330 2074.61i −0.0739578 0.178550i
\(514\) 1706.99i 0.146483i
\(515\) −3157.60 + 1307.92i −0.270176 + 0.111911i
\(516\) 3186.19 7692.13i 0.271829 0.656254i
\(517\) −10445.3 4326.60i −0.888560 0.368054i
\(518\) 688.858 688.858i 0.0584299 0.0584299i
\(519\) 16055.1 16055.1i 1.35788 1.35788i
\(520\) −484.844 200.829i −0.0408881 0.0169364i
\(521\) −3426.22 + 8271.63i −0.288110 + 0.695559i −0.999977 0.00675482i \(-0.997850\pi\)
0.711867 + 0.702314i \(0.247850\pi\)
\(522\) 602.703 249.648i 0.0505356 0.0209325i
\(523\) 15665.1i 1.30973i 0.755747 + 0.654864i \(0.227274\pi\)
−0.755747 + 0.654864i \(0.772726\pi\)
\(524\) 5945.73 + 14354.3i 0.495688 + 1.19670i
\(525\) 14724.0 + 14724.0i 1.22402 + 1.22402i
\(526\) 1791.28 0.148485
\(527\) 7353.40 9108.65i 0.607816 0.752902i
\(528\) −28199.6 −2.32430
\(529\) 8466.06 + 8466.06i 0.695821 + 0.695821i
\(530\) 74.8800 + 180.776i 0.00613694 + 0.0148159i
\(531\) 23579.4i 1.92704i
\(532\) −3102.34 + 1285.03i −0.252826 + 0.104724i
\(533\) −8722.79 + 21058.7i −0.708867 + 1.71136i
\(534\) −1129.45 467.832i −0.0915279 0.0379121i
\(535\) 2991.46 2991.46i 0.241742 0.241742i
\(536\) −925.113 + 925.113i −0.0745500 + 0.0745500i
\(537\) −15270.8 6325.37i −1.22716 0.508305i
\(538\) −658.735 + 1590.33i −0.0527882 + 0.127442i
\(539\) 6056.24 2508.58i 0.483972 0.200468i
\(540\) 2501.57i 0.199353i
\(541\) −3547.46 8564.31i −0.281917 0.680607i 0.717963 0.696081i \(-0.245074\pi\)
−0.999880 + 0.0154734i \(0.995074\pi\)
\(542\) −1030.37 1030.37i −0.0816568 0.0816568i
\(543\) −19973.4 −1.57853
\(544\) −859.092 + 2916.34i −0.0677082 + 0.229847i
\(545\) 285.821 0.0224647
\(546\) −1499.57 1499.57i −0.117538 0.117538i
\(547\) −6005.27 14498.0i −0.469409 1.13325i −0.964422 0.264368i \(-0.914837\pi\)
0.495013 0.868886i \(-0.335163\pi\)
\(548\) 13908.4i 1.08419i
\(549\) −2960.82 + 1226.41i −0.230173 + 0.0953407i
\(550\) 558.498 1348.33i 0.0432989 0.104533i
\(551\) 1269.93 + 526.023i 0.0981868 + 0.0406703i
\(552\) 295.046 295.046i 0.0227500 0.0227500i
\(553\) −13019.4 + 13019.4i −1.00116 + 1.00116i
\(554\) 1423.74 + 589.734i 0.109186 + 0.0452263i
\(555\) 1723.23 4160.25i 0.131797 0.318185i
\(556\) 1514.94 627.508i 0.115553 0.0478638i
\(557\) 3540.22i 0.269307i −0.990893 0.134654i \(-0.957008\pi\)
0.990893 0.134654i \(-0.0429922\pi\)
\(558\) −595.447 1437.54i −0.0451743 0.109060i
\(559\) 4718.33 + 4718.33i 0.357002 + 0.357002i
\(560\) 3716.21 0.280426
\(561\) 15070.3 + 27656.8i 1.13417 + 2.08141i
\(562\) −1435.18 −0.107722
\(563\) −222.747 222.747i −0.0166744 0.0166744i 0.698720 0.715395i \(-0.253753\pi\)
−0.715395 + 0.698720i \(0.753753\pi\)
\(564\) −5195.05 12542.0i −0.387856 0.936368i
\(565\) 1013.11i 0.0754371i
\(566\) 562.671 233.066i 0.0417859 0.0173083i
\(567\) 1329.14 3208.82i 0.0984453 0.237668i
\(568\) −715.801 296.494i −0.0528773 0.0219025i
\(569\) −6032.76 + 6032.76i −0.444475 + 0.444475i −0.893513 0.449038i \(-0.851767\pi\)
0.449038 + 0.893513i \(0.351767\pi\)
\(570\) 71.7068 71.7068i 0.00526924 0.00526924i
\(571\) −8156.50 3378.53i −0.597791 0.247613i 0.0632073 0.998000i \(-0.479867\pi\)
−0.660999 + 0.750387i \(0.729867\pi\)
\(572\) 8706.03 21018.2i 0.636394 1.53639i
\(573\) 31617.5 13096.4i 2.30513 0.954816i
\(574\) 2130.02i 0.154887i
\(575\) −626.223 1511.84i −0.0454180 0.109649i
\(576\) −14228.2 14228.2i −1.02924 1.02924i
\(577\) −21726.1 −1.56754 −0.783769 0.621052i \(-0.786705\pi\)
−0.783769 + 0.621052i \(0.786705\pi\)
\(578\) 1094.39 236.062i 0.0787557 0.0169877i
\(579\) 17108.0 1.22795
\(580\) −1082.79 1082.79i −0.0775176 0.0775176i
\(581\) −112.728 272.149i −0.00804947 0.0194331i
\(582\) 2250.50i 0.160286i
\(583\) −15724.7 + 6513.37i −1.11707 + 0.462704i
\(584\) −40.3969 + 97.5267i −0.00286239 + 0.00691042i
\(585\) −5454.35 2259.27i −0.385487 0.159674i
\(586\) −351.803 + 351.803i −0.0248001 + 0.0248001i
\(587\) −17447.6 + 17447.6i −1.22682 + 1.22682i −0.261653 + 0.965162i \(0.584268\pi\)
−0.965162 + 0.261653i \(0.915732\pi\)
\(588\) 7271.87 + 3012.11i 0.510011 + 0.211254i
\(589\) 1254.64 3028.98i 0.0877702 0.211896i
\(590\) 334.087 138.384i 0.0233121 0.00965621i
\(591\) 31337.7i 2.18115i
\(592\) 4770.44 + 11516.9i 0.331189 + 0.799561i
\(593\) 6673.49 + 6673.49i 0.462137 + 0.462137i 0.899356 0.437218i \(-0.144036\pi\)
−0.437218 + 0.899356i \(0.644036\pi\)
\(594\) 1421.66 0.0982007
\(595\) −1986.00 3644.68i −0.136837 0.251121i
\(596\) 16002.6 1.09982
\(597\) 21101.0 + 21101.0i 1.44658 + 1.44658i
\(598\) 63.7779 + 153.973i 0.00436132 + 0.0105292i
\(599\) 28257.9i 1.92753i −0.266759 0.963763i \(-0.585953\pi\)
0.266759 0.963763i \(-0.414047\pi\)
\(600\) 3248.52 1345.58i 0.221034 0.0915553i
\(601\) 6674.25 16113.1i 0.452993 1.09362i −0.518186 0.855268i \(-0.673393\pi\)
0.971179 0.238353i \(-0.0766075\pi\)
\(602\) 576.084 + 238.622i 0.0390024 + 0.0161553i
\(603\) −10407.2 + 10407.2i −0.702845 + 0.702845i
\(604\) 425.179 425.179i 0.0286428 0.0286428i
\(605\) −4177.61 1730.42i −0.280734 0.116284i
\(606\) 64.1211 154.802i 0.00429826 0.0103769i
\(607\) 418.146 173.202i 0.0279605 0.0115816i −0.368659 0.929565i \(-0.620183\pi\)
0.396620 + 0.917983i \(0.370183\pi\)
\(608\) 851.460i 0.0567948i
\(609\) −4751.60 11471.4i −0.316165 0.763289i
\(610\) −34.7531 34.7531i −0.00230674 0.00230674i
\(611\) 10879.8 0.720377
\(612\) −6436.03 + 21848.2i −0.425100 + 1.44307i
\(613\) −10731.9 −0.707106 −0.353553 0.935415i \(-0.615027\pi\)
−0.353553 + 0.935415i \(0.615027\pi\)
\(614\) 629.277 + 629.277i 0.0413608 + 0.0413608i
\(615\) 3767.76 + 9096.17i 0.247042 + 0.596411i
\(616\) 4265.74i 0.279012i
\(617\) 18626.4 7715.29i 1.21535 0.503413i 0.319420 0.947613i \(-0.396512\pi\)
0.895928 + 0.444200i \(0.146512\pi\)
\(618\) −892.496 + 2154.68i −0.0580930 + 0.140249i
\(619\) 2395.44 + 992.223i 0.155543 + 0.0644278i 0.459096 0.888386i \(-0.348173\pi\)
−0.303554 + 0.952814i \(0.598173\pi\)
\(620\) −2582.60 + 2582.60i −0.167290 + 0.167290i
\(621\) 1127.16 1127.16i 0.0728367 0.0728367i
\(622\) −1551.07 642.476i −0.0999877 0.0414163i
\(623\) −5362.74 + 12946.8i −0.344869 + 0.832588i
\(624\) 25071.1 10384.8i 1.60841 0.666224i
\(625\) 12843.4i 0.821977i
\(626\) 202.911 + 489.871i 0.0129552 + 0.0312766i
\(627\) 6237.35 + 6237.35i 0.397282 + 0.397282i
\(628\) 18295.0 1.16250
\(629\) 8745.78 10833.4i 0.554399 0.686734i
\(630\) −551.690 −0.0348887
\(631\) −14799.4 14799.4i −0.933685 0.933685i 0.0642487 0.997934i \(-0.479535\pi\)
−0.997934 + 0.0642487i \(0.979535\pi\)
\(632\) 1189.80 + 2872.43i 0.0748856 + 0.180790i
\(633\) 5211.31i 0.327221i
\(634\) −1572.73 + 651.445i −0.0985188 + 0.0408078i
\(635\) −1319.78 + 3186.22i −0.0824783 + 0.199120i
\(636\) −18881.0 7820.75i −1.17717 0.487599i
\(637\) −4460.54 + 4460.54i −0.277446 + 0.277446i
\(638\) −615.353 + 615.353i −0.0381850 + 0.0381850i
\(639\) −8052.54 3335.47i −0.498519 0.206493i
\(640\) 483.453 1167.16i 0.0298596 0.0720876i
\(641\) −8975.50 + 3717.77i −0.553059 + 0.229085i −0.641669 0.766982i \(-0.721758\pi\)
0.0886097 + 0.996066i \(0.471758\pi\)
\(642\) 2886.84i 0.177468i
\(643\) −9268.20 22375.4i −0.568433 1.37232i −0.902876 0.429902i \(-0.858548\pi\)
0.334443 0.942416i \(-0.391452\pi\)
\(644\) −1685.55 1685.55i −0.103136 0.103136i
\(645\) 2882.24 0.175951
\(646\) 275.327 150.027i 0.0167687 0.00913734i
\(647\) 5143.07 0.312511 0.156256 0.987717i \(-0.450058\pi\)
0.156256 + 0.987717i \(0.450058\pi\)
\(648\) −414.709 414.709i −0.0251409 0.0251409i
\(649\) 12037.2 + 29060.3i 0.728043 + 1.75765i
\(650\) 1404.42i 0.0847473i
\(651\) −27360.9 + 11333.3i −1.64725 + 0.682313i
\(652\) −5757.74 + 13900.4i −0.345845 + 0.834943i
\(653\) −2700.35 1118.52i −0.161827 0.0670308i 0.300300 0.953845i \(-0.402913\pi\)
−0.462126 + 0.886814i \(0.652913\pi\)
\(654\) 137.913 137.913i 0.00824588 0.00824588i
\(655\) −3803.20 + 3803.20i −0.226875 + 0.226875i
\(656\) −25181.0 10430.3i −1.49871 0.620786i
\(657\) −454.452 + 1097.15i −0.0269861 + 0.0651502i
\(658\) 939.300 389.071i 0.0556500 0.0230510i
\(659\) 17368.4i 1.02667i 0.858188 + 0.513336i \(0.171591\pi\)
−0.858188 + 0.513336i \(0.828409\pi\)
\(660\) −3760.51 9078.68i −0.221785 0.535435i
\(661\) 5685.94 + 5685.94i 0.334580 + 0.334580i 0.854323 0.519743i \(-0.173972\pi\)
−0.519743 + 0.854323i \(0.673972\pi\)
\(662\) −2131.38 −0.125134
\(663\) −23583.2 19038.7i −1.38144 1.11524i
\(664\) −49.7417 −0.00290715
\(665\) −821.973 821.973i −0.0479319 0.0479319i
\(666\) −708.196 1709.74i −0.0412042 0.0994758i
\(667\) 975.769i 0.0566446i
\(668\) 796.558 329.945i 0.0461374 0.0191107i
\(669\) −1683.10 + 4063.37i −0.0972683 + 0.234826i
\(670\) −208.534 86.3777i −0.0120244 0.00498069i
\(671\) 3022.97 3022.97i 0.173920 0.173920i
\(672\) 5438.56 5438.56i 0.312198 0.312198i
\(673\) 8385.45 + 3473.37i 0.480290 + 0.198943i 0.609675 0.792652i \(-0.291300\pi\)
−0.129384 + 0.991595i \(0.541300\pi\)
\(674\) 605.559 1461.95i 0.0346072 0.0835493i
\(675\) 12410.3 5140.52i 0.707664 0.293124i
\(676\) 4430.54i 0.252079i
\(677\) −9550.85 23057.8i −0.542199 1.30899i −0.923168 0.384397i \(-0.874409\pi\)
0.380969 0.924588i \(-0.375591\pi\)
\(678\) 488.840 + 488.840i 0.0276900 + 0.0276900i
\(679\) 25797.4 1.45805
\(680\) −696.930 + 74.3097i −0.0393030 + 0.00419066i
\(681\) 4851.56 0.272999
\(682\) 1467.71 + 1467.71i 0.0824068 + 0.0824068i
\(683\) −2322.36 5606.67i −0.130106 0.314105i 0.845380 0.534166i \(-0.179374\pi\)
−0.975486 + 0.220061i \(0.929374\pi\)
\(684\) 6378.85i 0.356581i
\(685\) 4448.26 1842.53i 0.248116 0.102773i
\(686\) 418.166 1009.54i 0.0232735 0.0561873i
\(687\) 20104.4 + 8327.51i 1.11649 + 0.462466i
\(688\) −5641.96 + 5641.96i −0.312642 + 0.312642i
\(689\) 11581.5 11581.5i 0.640378 0.640378i
\(690\) 66.5079 + 27.5485i 0.00366944 + 0.00151993i
\(691\) 6641.71 16034.5i 0.365648 0.882752i −0.628804 0.777564i \(-0.716455\pi\)
0.994452 0.105189i \(-0.0335446\pi\)
\(692\) −20235.8 + 8381.96i −1.11163 + 0.460454i
\(693\) 47988.2i 2.63048i
\(694\) −210.163 507.378i −0.0114952 0.0277519i
\(695\) 401.387 + 401.387i 0.0219072 + 0.0219072i
\(696\) −2096.66 −0.114186
\(697\) 3227.56 + 30270.4i 0.175398 + 1.64501i
\(698\) 2507.87 0.135995
\(699\) 2233.54 + 2233.54i 0.120859 + 0.120859i
\(700\) −7687.07 18558.2i −0.415063 1.00205i
\(701\) 34827.5i 1.87649i 0.345976 + 0.938243i \(0.387548\pi\)
−0.345976 + 0.938243i \(0.612452\pi\)
\(702\) −1263.93 + 523.538i −0.0679545 + 0.0281477i
\(703\) 1492.21 3602.52i 0.0800566 0.193274i
\(704\) 24798.8 + 10272.0i 1.32761 + 0.549915i
\(705\) 3323.03 3323.03i 0.177521 0.177521i
\(706\) −1242.86 + 1242.86i −0.0662546 + 0.0662546i
\(707\) −1774.49 735.018i −0.0943941 0.0390993i
\(708\) −14453.3 + 34893.3i −0.767215 + 1.85222i
\(709\) −23731.7 + 9830.00i −1.25707 + 0.520696i −0.909009 0.416775i \(-0.863160\pi\)
−0.348062 + 0.937472i \(0.613160\pi\)
\(710\) 133.669i 0.00706548i
\(711\) 13384.9 + 32314.0i 0.706009 + 1.70446i
\(712\) 1673.25 + 1673.25i 0.0880725 + 0.0880725i
\(713\) 2327.35 0.122244
\(714\) −2716.88 800.335i −0.142404 0.0419493i
\(715\) 7875.52 0.411927
\(716\) 11274.8 + 11274.8i 0.588492 + 0.588492i
\(717\) −13698.5 33071.2i −0.713502 1.72255i
\(718\) 2328.92i 0.121051i
\(719\) −16792.7 + 6955.77i −0.871018 + 0.360788i −0.773007 0.634398i \(-0.781248\pi\)
−0.0980115 + 0.995185i \(0.531248\pi\)
\(720\) 2701.53 6522.06i 0.139833 0.337587i
\(721\) 24699.0 + 10230.7i 1.27578 + 0.528446i
\(722\) −1043.12 + 1043.12i −0.0537688 + 0.0537688i
\(723\) 11964.6 11964.6i 0.615448 0.615448i
\(724\) 17801.1 + 7373.46i 0.913775 + 0.378498i
\(725\) −3146.68 + 7596.75i −0.161193 + 0.389153i
\(726\) −2850.71 + 1180.80i −0.145730 + 0.0603632i
\(727\) 8657.73i 0.441674i 0.975311 + 0.220837i \(0.0708789\pi\)
−0.975311 + 0.220837i \(0.929121\pi\)
\(728\) 1570.90 + 3792.48i 0.0799744 + 0.193075i
\(729\) −22659.1 22659.1i −1.15120 1.15120i
\(730\) −18.2121 −0.000923371
\(731\) 8548.50 + 2518.21i 0.432528 + 0.127414i
\(732\) 5133.24 0.259194
\(733\) −7989.74 7989.74i −0.402603 0.402603i 0.476546 0.879149i \(-0.341888\pi\)
−0.879149 + 0.476546i \(0.841888\pi\)
\(734\) −900.168 2173.20i −0.0452668 0.109284i
\(735\) 2724.77i 0.136741i
\(736\) −558.421 + 231.306i −0.0279670 + 0.0115843i
\(737\) 7513.48 18139.1i 0.375526 0.906600i
\(738\) 3738.25 + 1548.43i 0.186459 + 0.0772338i
\(739\) 8885.48 8885.48i 0.442297 0.442297i −0.450486 0.892783i \(-0.648749\pi\)
0.892783 + 0.450486i \(0.148749\pi\)
\(740\) −3071.62 + 3071.62i −0.152588 + 0.152588i
\(741\) −7842.32 3248.40i −0.388792 0.161043i
\(742\) 585.716 1414.04i 0.0289789 0.0699612i
\(743\) 12980.0 5376.49i 0.640902 0.265470i −0.0384753 0.999260i \(-0.512250\pi\)
0.679377 + 0.733789i \(0.262250\pi\)
\(744\) 5000.85i 0.246425i
\(745\) 2119.96 + 5118.04i 0.104254 + 0.251692i
\(746\) 442.166 + 442.166i 0.0217009 + 0.0217009i
\(747\) −559.578 −0.0274082
\(748\) −3221.36 30212.2i −0.157466 1.47683i
\(749\) −33091.7 −1.61435
\(750\) 885.556 + 885.556i 0.0431146 + 0.0431146i
\(751\) −3111.79 7512.52i −0.151199 0.365027i 0.830073 0.557655i \(-0.188299\pi\)
−0.981272 + 0.192628i \(0.938299\pi\)
\(752\) 13009.6i 0.630865i
\(753\) 6911.33 2862.77i 0.334479 0.138546i
\(754\) 320.474 773.693i 0.0154788 0.0373690i
\(755\) 192.309 + 79.6572i 0.00927001 + 0.00383976i
\(756\) 13836.3 13836.3i 0.665635 0.665635i
\(757\) 16245.0 16245.0i 0.779964 0.779964i −0.199860 0.979824i \(-0.564049\pi\)
0.979824 + 0.199860i \(0.0640488\pi\)
\(758\) 1348.46 + 558.549i 0.0646149 + 0.0267644i
\(759\) −2396.28 + 5785.12i −0.114597 + 0.276662i
\(760\) −181.349 + 75.1174i −0.00865557 + 0.00358525i
\(761\) 15071.9i 0.717946i −0.933348 0.358973i \(-0.883127\pi\)
0.933348 0.358973i \(-0.116873\pi\)
\(762\) 900.585 + 2174.20i 0.0428146 + 0.103364i
\(763\) −1580.89 1580.89i −0.0750091 0.0750091i
\(764\) −33013.4 −1.56333
\(765\) −7840.25 + 835.961i −0.370542 + 0.0395088i
\(766\) 841.515 0.0396934
\(767\) −21403.4 21403.4i −1.00761 1.00761i
\(768\) 12084.5 + 29174.5i 0.567788 + 1.37076i
\(769\) 10392.1i 0.487321i −0.969861 0.243660i \(-0.921652\pi\)
0.969861 0.243660i \(-0.0783482\pi\)
\(770\) 679.926 281.635i 0.0318219 0.0131811i
\(771\) −23618.5 + 57020.0i −1.10324 + 2.66346i
\(772\) −15247.3 6315.63i −0.710831 0.294436i
\(773\) −24316.4 + 24316.4i −1.13144 + 1.13144i −0.141499 + 0.989938i \(0.545192\pi\)
−0.989938 + 0.141499i \(0.954808\pi\)
\(774\) 837.577 837.577i 0.0388967 0.0388967i
\(775\) 18119.4 + 7505.29i 0.839829 + 0.347868i
\(776\) 1667.03 4024.57i 0.0771172 0.186177i
\(777\) −32541.7 + 13479.2i −1.50248 + 0.622348i
\(778\) 486.052i 0.0223982i
\(779\) 3262.64 + 7876.71i 0.150059 + 0.362275i
\(780\) 6686.62 + 6686.62i 0.306948 + 0.306948i
\(781\) 11627.0 0.532712
\(782\) 173.188 + 139.814i 0.00791968 + 0.00639355i
\(783\) −8009.87 −0.365580
\(784\) −5333.70 5333.70i −0.242971 0.242971i
\(785\) 2423.65 + 5851.21i 0.110196 + 0.266036i
\(786\) 3670.19i 0.166554i
\(787\) 23671.4 9805.02i 1.07217 0.444106i 0.224411 0.974494i \(-0.427954\pi\)
0.847754 + 0.530389i \(0.177954\pi\)
\(788\) 11568.7 27929.3i 0.522993 1.26262i
\(789\) −59835.5 24784.7i −2.69987 1.11832i
\(790\) −379.290 + 379.290i −0.0170817 + 0.0170817i
\(791\) 5603.56 5603.56i 0.251883 0.251883i
\(792\) −7486.50 3101.01i −0.335885 0.139128i
\(793\) −1574.35 + 3800.83i −0.0705006 + 0.170203i
\(794\) 497.879 206.228i 0.0222532 0.00921759i
\(795\) 7074.69i 0.315614i
\(796\) −11016.3 26595.7i −0.490532 1.18425i
\(797\) 20108.4 + 20108.4i 0.893698 + 0.893698i 0.994869 0.101171i \(-0.0322589\pi\)
−0.101171 + 0.994869i \(0.532259\pi\)
\(798\) −793.226 −0.0351878
\(799\) 12759.2 6952.51i 0.564939 0.307838i
\(800\) −5093.45 −0.225101
\(801\) 18823.5 + 18823.5i 0.830333 + 0.830333i
\(802\) −179.969 434.483i −0.00792383 0.0191298i
\(803\) 1584.16i 0.0696188i
\(804\) 21780.1 9021.60i 0.955378 0.395731i
\(805\) 315.787 762.377i 0.0138261 0.0333792i
\(806\) −1845.37 764.378i −0.0806458 0.0334046i
\(807\) 44008.5 44008.5i 1.91967 1.91967i
\(808\) −229.336 + 229.336i −0.00998515 + 0.00998515i
\(809\) 20652.5 + 8554.55i 0.897532 + 0.371770i 0.783271 0.621681i \(-0.213550\pi\)
0.114261 + 0.993451i \(0.463550\pi\)
\(810\) 38.7213 93.4816i 0.00167967 0.00405507i
\(811\) −5572.70 + 2308.29i −0.241287 + 0.0999444i −0.500050 0.865996i \(-0.666685\pi\)
0.258763 + 0.965941i \(0.416685\pi\)
\(812\) 11977.8i 0.517660i
\(813\) 20161.7 + 48674.6i 0.869743 + 2.09975i
\(814\) 1745.62 + 1745.62i 0.0751646 + 0.0751646i
\(815\) −5208.49 −0.223859
\(816\) 22765.6 28199.7i 0.976660 1.20979i
\(817\) 2495.84 0.106877
\(818\) −1489.69 1489.69i −0.0636744 0.0636744i
\(819\) 17672.1 + 42664.3i 0.753985 + 1.82028i
\(820\) 9497.78i 0.404484i
\(821\) 11698.6 4845.73i 0.497302 0.205989i −0.119912 0.992785i \(-0.538261\pi\)
0.617214 + 0.786795i \(0.288261\pi\)
\(822\) 1257.30 3035.39i 0.0533496 0.128797i
\(823\) 10190.3 + 4220.95i 0.431605 + 0.178777i 0.587900 0.808934i \(-0.299955\pi\)
−0.156295 + 0.987710i \(0.549955\pi\)
\(824\) 3192.10 3192.10i 0.134954 0.134954i
\(825\) −37311.9 + 37311.9i −1.57459 + 1.57459i
\(826\) −2613.25 1082.44i −0.110081 0.0455969i
\(827\) 10962.5 26465.9i 0.460948 1.11283i −0.507060 0.861911i \(-0.669268\pi\)
0.968009 0.250917i \(-0.0807322\pi\)
\(828\) −4183.50 + 1732.86i −0.175588 + 0.0727309i
\(829\) 15663.7i 0.656239i 0.944636 + 0.328120i \(0.106415\pi\)
−0.944636 + 0.328120i \(0.893585\pi\)
\(830\) −3.28407 7.92844i −0.000137339 0.000331567i
\(831\) −39398.8 39398.8i −1.64468 1.64468i
\(832\) −25830.3 −1.07633
\(833\) −2380.62 + 8081.44i −0.0990201 + 0.336141i
\(834\) 387.349 0.0160825
\(835\) 211.050 + 211.050i 0.00874694 + 0.00874694i
\(836\) −3256.37 7861.57i −0.134718 0.325237i
\(837\) 19104.7i 0.788955i
\(838\) −874.837 + 362.369i −0.0360629 + 0.0149378i
\(839\) 8669.06 20929.0i 0.356721 0.861201i −0.639036 0.769177i \(-0.720666\pi\)
0.995757 0.0920240i \(-0.0293337\pi\)
\(840\) 1638.14 + 678.540i 0.0672871 + 0.0278712i
\(841\) −13778.6 + 13778.6i −0.564952 + 0.564952i
\(842\) −742.709 + 742.709i −0.0303984 + 0.0303984i
\(843\) 47940.6 + 19857.7i 1.95868 + 0.811310i
\(844\) −1923.82 + 4644.52i −0.0784606 + 0.189421i
\(845\) −1417.00 + 586.942i −0.0576880 + 0.0238952i
\(846\) 1931.34i 0.0784879i
\(847\) 13535.5 + 32677.6i 0.549097 + 1.32564i
\(848\) 13848.6 + 13848.6i 0.560807 + 0.560807i
\(849\) −22020.1 −0.890141
\(850\) 897.462 + 1647.01i 0.0362149 + 0.0664611i
\(851\) 2768.04 0.111501
\(852\) 9871.80 + 9871.80i 0.396951 + 0.396951i
\(853\) −1702.92 4111.21i −0.0683551 0.165024i 0.886010 0.463666i \(-0.153466\pi\)
−0.954365 + 0.298642i \(0.903466\pi\)
\(854\) 384.442i 0.0154044i
\(855\) −2040.12 + 845.047i −0.0816033 + 0.0338012i
\(856\) −2138.39 + 5162.54i −0.0853841 + 0.206135i
\(857\) −20994.3 8696.11i −0.836815 0.346620i −0.0772178 0.997014i \(-0.524604\pi\)
−0.759597 + 0.650394i \(0.774604\pi\)
\(858\) 3800.04 3800.04i 0.151202 0.151202i
\(859\) −29733.4 + 29733.4i −1.18102 + 1.18102i −0.201533 + 0.979482i \(0.564592\pi\)
−0.979482 + 0.201533i \(0.935408\pi\)
\(860\) −2568.76 1064.02i −0.101854 0.0421892i
\(861\) 29471.6 71150.8i 1.16654 2.81628i
\(862\) 3648.59 1511.30i 0.144166 0.0597157i
\(863\) 7875.51i 0.310644i 0.987864 + 0.155322i \(0.0496414\pi\)
−0.987864 + 0.155322i \(0.950359\pi\)
\(864\) −1898.73 4583.95i −0.0747642 0.180497i
\(865\) −5361.54 5361.54i −0.210749 0.210749i
\(866\) −2587.30 −0.101524
\(867\) −39823.2 7257.02i −1.55994 0.284269i
\(868\) 28568.9 1.11716
\(869\) −32992.2 32992.2i −1.28790 1.28790i
\(870\) −138.427 334.192i −0.00539438 0.0130232i
\(871\) 18893.6i 0.735002i
\(872\) −348.786 + 144.472i −0.0135452 + 0.00561060i
\(873\) 18753.6 45275.2i 0.727048 1.75525i
\(874\) 57.5917 + 23.8552i 0.00222891 + 0.000923244i
\(875\) 10151.1 10151.1i 0.392194 0.392194i
\(876\) 1345.02 1345.02i 0.0518766 0.0518766i
\(877\) −24138.0 9998.27i −0.929397 0.384969i −0.133947 0.990988i \(-0.542765\pi\)
−0.795450 + 0.606020i \(0.792765\pi\)
\(878\) −447.194 + 1079.62i −0.0171891 + 0.0414983i
\(879\) 16619.2 6883.91i 0.637716 0.264151i
\(880\) 9417.18i 0.360742i
\(881\) 2449.18 + 5912.84i 0.0936604 + 0.226116i 0.963766 0.266749i \(-0.0859495\pi\)
−0.870106 + 0.492865i \(0.835949\pi\)
\(882\) 791.815 + 791.815i 0.0302288 + 0.0302288i
\(883\) −43393.3 −1.65379 −0.826897 0.562354i \(-0.809896\pi\)
−0.826897 + 0.562354i \(0.809896\pi\)
\(884\) 13989.9 + 25674.1i 0.532275 + 0.976824i
\(885\) −13074.5 −0.496605
\(886\) 504.832 + 504.832i 0.0191424 + 0.0191424i
\(887\) 7831.78 + 18907.6i 0.296466 + 0.715733i 0.999987 + 0.00505836i \(0.00161013\pi\)
−0.703521 + 0.710675i \(0.748390\pi\)
\(888\) 5947.77i 0.224768i
\(889\) 24922.8 10323.4i 0.940253 0.389466i
\(890\) −156.231 + 377.175i −0.00588413 + 0.0142055i
\(891\) 8131.41 + 3368.14i 0.305738 + 0.126641i
\(892\) 3000.09 3000.09i 0.112613 0.112613i
\(893\) 2877.53 2877.53i 0.107831 0.107831i
\(894\) 3492.43 + 1446.61i 0.130654 + 0.0541185i
\(895\) −2112.34 + 5099.64i −0.0788913 + 0.190460i
\(896\) −9129.60 + 3781.60i −0.340400 + 0.140998i
\(897\) 6025.76i 0.224297i
\(898\) −1024.62 2473.66i −0.0380759 0.0919233i
\(899\) −8269.33 8269.33i −0.306783 0.306783i
\(900\) −38158.4 −1.41327
\(901\) 6181.15 20983.0i 0.228550 0.775854i
\(902\) −5397.64 −0.199248
\(903\) −15941.8 15941.8i −0.587496 0.587496i
\(904\) −512.091 1236.30i −0.0188406 0.0454852i
\(905\) 6670.07i 0.244995i
\(906\) 131.228 54.3562i 0.00481208 0.00199323i
\(907\) −11555.0 + 27896.3i −0.423019 + 1.02126i 0.558433 + 0.829550i \(0.311403\pi\)
−0.981452 + 0.191709i \(0.938597\pi\)
\(908\) −4323.90 1791.02i −0.158033 0.0654593i
\(909\) −2579.96 + 2579.96i −0.0941384 + 0.0941384i
\(910\) −500.779 + 500.779i −0.0182425 + 0.0182425i
\(911\) 21246.6 + 8800.64i 0.772703 + 0.320064i 0.733967 0.679185i \(-0.237667\pi\)
0.0387363 + 0.999249i \(0.487667\pi\)
\(912\) 3884.28 9377.49i 0.141032 0.340482i
\(913\) 689.648 285.662i 0.0249989 0.0103549i
\(914\) 2827.68i 0.102332i
\(915\) 680.032 + 1641.74i 0.0245696 + 0.0593162i
\(916\) −14843.6 14843.6i −0.535422 0.535422i
\(917\) 42071.3 1.51507
\(918\) −1147.70 + 1421.66i −0.0412635 + 0.0511131i
\(919\) −40432.8 −1.45131 −0.725656 0.688057i \(-0.758464\pi\)
−0.725656 + 0.688057i \(0.758464\pi\)
\(920\) −98.5299 98.5299i −0.00353091 0.00353091i
\(921\) −12313.4 29727.1i −0.440543 1.06356i
\(922\) 1679.57i 0.0599932i
\(923\) −10337.1 + 4281.76i −0.368634 + 0.152693i
\(924\) −29415.0 + 71014.0i −1.04727 + 2.52834i
\(925\) 21550.3 + 8926.43i 0.766021 + 0.317296i
\(926\) 1844.48 1844.48i 0.0654574 0.0654574i
\(927\) 35910.2 35910.2i 1.27232 1.27232i
\(928\) 2805.98 + 1162.28i 0.0992574 + 0.0411137i
\(929\) −13044.2 + 31491.4i −0.460673 + 1.11216i 0.507448 + 0.861682i \(0.330589\pi\)
−0.968121 + 0.250482i \(0.919411\pi\)
\(930\) −797.097 + 330.168i −0.0281052 + 0.0116416i
\(931\) 2359.48i 0.0830599i
\(932\) −1166.08 2815.16i −0.0409830 0.0989418i
\(933\) 42922.3 + 42922.3i 1.50612 + 1.50612i
\(934\) −1006.83 −0.0352724
\(935\) 9235.91 5032.68i 0.323044 0.176028i
\(936\) 7797.89 0.272310
\(937\) −539.977 539.977i −0.0188263 0.0188263i 0.697631 0.716457i \(-0.254238\pi\)
−0.716457 + 0.697631i \(0.754238\pi\)
\(938\) 675.652 + 1631.17i 0.0235190 + 0.0567799i
\(939\) 19171.1i 0.666268i
\(940\) −4188.35 + 1734.87i −0.145329 + 0.0601971i
\(941\) −170.281 + 411.094i −0.00589904 + 0.0142415i −0.926802 0.375551i \(-0.877453\pi\)
0.920903 + 0.389793i \(0.127453\pi\)
\(942\) 3992.73 + 1653.84i 0.138100 + 0.0572029i
\(943\) −4279.54 + 4279.54i −0.147785 + 0.147785i
\(944\) 25593.3 25593.3i 0.882404 0.882404i
\(945\) 6258.18 + 2592.22i 0.215427 + 0.0892328i
\(946\) −604.687 + 1459.84i −0.0207823 + 0.0501729i
\(947\) −10304.9 + 4268.42i −0.353604 + 0.146468i −0.552413 0.833571i \(-0.686293\pi\)
0.198808 + 0.980038i \(0.436293\pi\)
\(948\) 56023.3i 1.91936i
\(949\) 583.383 + 1408.41i 0.0199551 + 0.0481759i
\(950\) 371.445 + 371.445i 0.0126855 + 0.0126855i
\(951\) 61548.7 2.09869
\(952\) 4265.75 + 3443.74i 0.145225 + 0.117240i
\(953\) 48344.2 1.64325 0.821627 0.570026i \(-0.193067\pi\)
0.821627 + 0.570026i \(0.193067\pi\)
\(954\) −2055.90 2055.90i −0.0697717 0.0697717i
\(955\) −4373.50 10558.6i −0.148192 0.357767i
\(956\) 34531.3i 1.16822i
\(957\) 29069.4 12040.9i 0.981901 0.406717i
\(958\) −24.6455 + 59.4994i −0.000831168 + 0.00200662i
\(959\) −34794.6 14412.4i −1.17161 0.485298i
\(960\) −7889.35 + 7889.35i −0.265237 + 0.265237i
\(961\) 1341.84 1341.84i 0.0450417 0.0450417i
\(962\) −2194.80 909.115i −0.0735583 0.0304688i
\(963\) −24056.3 + 58077.0i −0.804987 + 1.94341i
\(964\) −15080.2 + 6246.43i −0.503840 + 0.208697i
\(965\) 5713.15i 0.190583i
\(966\) −215.486 520.229i −0.00717717 0.0173272i
\(967\) −618.214 618.214i −0.0205589 0.0205589i 0.696753 0.717311i \(-0.254628\pi\)
−0.717311 + 0.696753i \(0.754628\pi\)
\(968\) 5972.59 0.198312
\(969\) −11272.8 + 1201.95i −0.373720 + 0.0398476i
\(970\) 751.547 0.0248770
\(971\) 20420.3 + 20420.3i 0.674892 + 0.674892i 0.958840 0.283948i \(-0.0916443\pi\)
−0.283948 + 0.958840i \(0.591644\pi\)
\(972\) 13438.3 + 32442.9i 0.443450 + 1.07058i
\(973\) 4440.17i 0.146295i
\(974\) 1600.49 662.944i 0.0526519 0.0218091i
\(975\) 19432.0 46912.9i 0.638277 1.54094i
\(976\) −4544.85 1882.54i −0.149055 0.0617404i
\(977\) −3143.83 + 3143.83i −0.102948 + 0.102948i −0.756705 0.653757i \(-0.773192\pi\)
0.653757 + 0.756705i \(0.273192\pi\)
\(978\) −2513.16 + 2513.16i −0.0821699 + 0.0821699i
\(979\) −32808.2 13589.6i −1.07105 0.443642i
\(980\) 1005.88 2428.42i 0.0327875 0.0791561i
\(981\) −3923.74 + 1625.27i −0.127702 + 0.0528958i
\(982\) 2924.80i 0.0950448i
\(983\) −15780.7 38098.1i −0.512032 1.23615i −0.942699 0.333644i \(-0.891722\pi\)
0.430667 0.902511i \(-0.358278\pi\)
\(984\) −9195.55 9195.55i −0.297910 0.297910i
\(985\) 10465.1 0.338524
\(986\) −118.580 1112.13i −0.00382998 0.0359203i
\(987\) −36759.5 −1.18548
\(988\) 5790.19 + 5790.19i 0.186448 + 0.186448i
\(989\) 678.014 + 1636.87i 0.0217994 + 0.0526284i
\(990\) 1398.03i 0.0448810i
\(991\) −30566.7 + 12661.1i −0.979801 + 0.405847i −0.814352 0.580372i \(-0.802907\pi\)
−0.165449 + 0.986218i \(0.552907\pi\)
\(992\) 2772.20 6692.68i 0.0887272 0.214206i
\(993\) 71196.3 + 29490.5i 2.27527 + 0.942449i
\(994\) −739.325 + 739.325i −0.0235915 + 0.0235915i
\(995\) 7046.62 7046.62i 0.224515 0.224515i
\(996\) 828.076 + 343.000i 0.0263440 + 0.0109120i
\(997\) −4318.18 + 10425.0i −0.137170 + 0.331157i −0.977506 0.210909i \(-0.932358\pi\)
0.840336 + 0.542066i \(0.182358\pi\)
\(998\) −572.061 + 236.956i −0.0181446 + 0.00751573i
\(999\) 22722.2i 0.719619i
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 17.4.d.a.15.2 yes 12
3.2 odd 2 153.4.l.a.100.2 12
17.3 odd 16 289.4.b.e.288.6 12
17.5 odd 16 289.4.a.g.1.7 12
17.8 even 8 inner 17.4.d.a.8.2 12
17.12 odd 16 289.4.a.g.1.8 12
17.14 odd 16 289.4.b.e.288.5 12
51.8 odd 8 153.4.l.a.127.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.d.a.8.2 12 17.8 even 8 inner
17.4.d.a.15.2 yes 12 1.1 even 1 trivial
153.4.l.a.100.2 12 3.2 odd 2
153.4.l.a.127.2 12 51.8 odd 8
289.4.a.g.1.7 12 17.5 odd 16
289.4.a.g.1.8 12 17.12 odd 16
289.4.b.e.288.5 12 17.14 odd 16
289.4.b.e.288.6 12 17.3 odd 16