Properties

Label 17.4.d.a.8.2
Level $17$
Weight $4$
Character 17.8
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 8.2
Root \(-1.22788i\) of defining polynomial
Character \(\chi\) \(=\) 17.8
Dual form 17.4.d.a.15.2

$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\)

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 −0.735018 0.678048i \(-0.762826\pi\)
0.678048 + 0.735018i \(0.262826\pi\)
\(3\) 3.15299 7.61199i 0.606793 1.46493i −0.259675 0.965696i \(-0.583615\pi\)
0.866468 0.499232i \(-0.166385\pi\)
\(4\) 7.94807i 0.993509i
\(5\) 2.54200 + 1.05293i 0.227364 + 0.0941771i 0.493457 0.869770i \(-0.335733\pi\)
−0.266094 + 0.963947i \(0.585733\pi\)
\(6\) 0.718496 + 1.73460i 0.0488875 + 0.118025i
\(7\) −19.8837 + 8.23610i −1.07362 + 0.444707i −0.848266 0.529570i \(-0.822353\pi\)
−0.225352 + 0.974277i \(0.572353\pi\)
\(8\) −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 0.899785 + 0.436333i \(0.143723\pi\)
−0.327711 + 0.944778i \(0.606277\pi\)
\(12\) 60.5007 + 25.0602i 1.45542 + 0.602855i
\(13\) 52.4827i 1.11970i −0.828594 0.559850i \(-0.810859\pi\)
0.828594 0.559850i \(-0.189141\pi\)
\(14\) 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 −0.618321 0.785925i \(-0.712187\pi\)
0.785925 + 0.618321i \(0.212187\pi\)
\(20\) −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 0.897862 0.440278i \(-0.145120\pi\)
−0.946207 + 0.323560i \(0.895120\pi\)
\(24\) −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 0.580063 0.814571i \(-0.303028\pi\)
−0.165822 + 0.986156i \(0.553028\pi\)
\(30\) 5.16589i 0.0314386i
\(31\) −63.9131 + 154.300i −0.370295 + 0.893971i 0.623405 + 0.781899i \(0.285749\pi\)
−0.993700 + 0.112072i \(0.964251\pi\)
\(32\) 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 0.660179 + 0.751108i \(0.270480\pi\)
−0.997931 + 0.0642968i \(0.979520\pi\)
\(38\) 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 0.549153 0.835722i \(-0.314950\pi\)
0.979254 + 0.202634i \(0.0649503\pi\)
\(42\) −28.5727 28.5727i −0.104973 0.104973i
\(43\) 89.9025 + 89.9025i 0.318837 + 0.318837i 0.848320 0.529483i \(-0.177614\pi\)
−0.529483 + 0.848320i \(0.677614\pi\)
\(44\) −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 \(0.104249\pi\)
−0.946847 + 0.321683i \(0.895751\pi\)
\(48\) −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 −0.932665 0.360745i \(-0.882523\pi\)
0.360745 + 0.932665i \(0.382523\pi\)
\(54\) 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 0.0955362 0.995426i \(-0.469543\pi\)
−0.995426 + 0.0955362i \(0.969543\pi\)
\(60\) 127.406 + 127.406i 0.274134 + 0.274134i
\(61\) 72.4205 29.9976i 0.152008 0.0629639i −0.305382 0.952230i \(-0.598784\pi\)
0.457390 + 0.889266i \(0.348784\pi\)
\(62\) −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 −0.840911 0.541173i \(-0.817980\pi\)
0.977281 + 0.211947i \(0.0679804\pi\)
\(72\) 148.580i 0.243199i
\(73\) 26.8357 + 11.1157i 0.0430258 + 0.0178219i 0.404093 0.914718i \(-0.367587\pi\)
−0.361067 + 0.932540i \(0.617587\pi\)
\(74\) −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 0.965786 + 0.259342i \(0.0835056\pi\)
−0.499531 + 0.866296i \(0.666494\pi\)
\(80\) −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 −0.700678 0.713477i \(-0.747119\pi\)
0.713477 + 0.700678i \(0.247119\pi\)
\(84\) −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 \(0.126747\pi\)
−0.921765 + 0.387748i \(0.873253\pi\)
\(90\) 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 −0.281579 0.959538i \(-0.590858\pi\)
−0.877602 + 0.479389i \(0.840858\pi\)
\(98\) 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 0.917025 0.398829i \(-0.130583\pi\)
0.366420 + 0.930449i \(0.380583\pi\)
\(108\) −347.930 839.977i −0.309996 0.748396i
\(109\) 95.9730 39.7533i 0.0843353 0.0349328i −0.340117 0.940383i \(-0.610467\pi\)
0.424452 + 0.905450i \(0.360467\pi\)
\(110\) −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 0.854311 0.519762i \(-0.173980\pi\)
−0.971617 + 0.236562i \(0.923980\pi\)
\(114\) 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 0.326075 0.945344i \(-0.394274\pi\)
−0.945344 + 0.326075i \(0.894274\pi\)
\(128\) 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 −0.312060 0.950062i \(-0.601019\pi\)
−0.892455 + 0.451136i \(0.851019\pi\)
\(132\) 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 −0.897959 0.440079i \(-0.854951\pi\)
0.946136 + 0.323770i \(0.104951\pi\)
\(140\) 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 \(-0.813292\pi\)
0.832849 0.553501i \(-0.186708\pi\)
\(150\) 84.3727 203.694i 0.0459267 0.110877i
\(151\) 53.4946 53.4946i 0.0288300 0.0288300i −0.692545 0.721375i \(-0.743511\pi\)
0.721375 + 0.692545i \(0.243511\pi\)
\(152\) −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 \(-0.801076\pi\)
0.811000 0.585046i \(-0.198924\pi\)
\(158\) −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 −0.761010 0.648740i \(-0.775296\pi\)
−0.0793874 + 0.996844i \(0.525296\pi\)
\(164\) 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 −0.913970 0.405782i \(-0.866999\pi\)
0.933205 + 0.359343i \(0.116999\pi\)
\(168\) 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 0.503504 + 0.863993i \(0.332044\pi\)
−0.966966 + 0.254905i \(0.917956\pi\)
\(174\) 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 0.345925 0.938262i \(-0.387565\pi\)
−0.938262 + 0.345925i \(0.887565\pi\)
\(180\) 826.016 342.147i 0.342042 0.141679i
\(181\) −927.705 2239.68i −0.380971 0.919745i −0.991779 0.127966i \(-0.959155\pi\)
0.610808 0.791779i \(-0.290845\pi\)
\(182\) −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 \(0.288249\pi\)
−0.617243 + 0.786772i \(0.711751\pi\)
\(192\) −3746.37 1551.80i −1.40818 0.583289i
\(193\) 794.611 + 1918.36i 0.296360 + 0.715475i 0.999988 + 0.00490706i \(0.00156197\pi\)
−0.703628 + 0.710568i \(0.748438\pi\)
\(194\) 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 0.357638 0.933860i \(-0.383582\pi\)
0.913227 + 0.407450i \(0.133582\pi\)
\(198\) 194.444 + 469.430i 0.0697906 + 0.168489i
\(199\) 3346.19 + 1386.04i 1.19199 + 0.493736i 0.888401 0.459068i \(-0.151817\pi\)
0.303584 + 0.952805i \(0.401817\pi\)
\(200\) 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 −0.475970 0.879462i \(-0.657903\pi\)
0.285312 + 0.958435i \(0.407903\pi\)
\(212\) −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 −0.648158 0.761506i \(-0.724460\pi\)
0.761506 + 0.648158i \(0.224460\pi\)
\(224\) −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 0.953393 0.301730i \(-0.0975642\pi\)
−0.887506 + 0.460795i \(0.847564\pi\)
\(228\) 1187.65 491.943i 0.344975 0.142893i
\(229\) 1867.57 + 1867.57i 0.538920 + 0.538920i 0.923212 0.384292i \(-0.125554\pi\)
−0.384292 + 0.923212i \(0.625554\pi\)
\(230\) 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 0.431921 0.901911i \(-0.357836\pi\)
−0.332333 + 0.943162i \(0.607836\pi\)
\(234\) 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 −0.993432 0.114422i \(-0.963498\pi\)
0.783371 + 0.621554i \(0.213498\pi\)
\(242\) 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 \(0.0364184\pi\)
−0.993462 + 0.114162i \(0.963582\pi\)
\(252\) −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 0.348209 0.937417i \(-0.386790\pi\)
0.937417 0.348209i \(-0.113210\pi\)
\(258\) −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 −0.926221 0.376982i \(-0.876962\pi\)
−0.376982 0.926221i \(-0.623038\pi\)
\(264\) −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 0.149908 + 0.988700i \(0.452102\pi\)
−0.805117 + 0.593116i \(0.797898\pi\)
\(270\) 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 −0.417480 0.908686i \(-0.637087\pi\)
−0.937741 + 0.347335i \(0.887087\pi\)
\(278\) 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 0.998586 0.0531529i \(-0.0169271\pi\)
−0.0531529 + 0.998586i \(0.516927\pi\)
\(282\) −359.588 + 148.946i −0.0759332 + 0.0314526i
\(283\) −1022.77 2469.18i −0.214831 0.518648i 0.779323 0.626623i \(-0.215563\pi\)
−0.994154 + 0.107975i \(0.965563\pi\)
\(284\) 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 \(0.0698428\pi\)
−0.976024 + 0.217661i \(0.930157\pi\)
\(294\) 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 0.904043 0.427441i \(-0.140585\pi\)
0.337008 + 0.941502i \(0.390585\pi\)
\(312\) 601.380 + 1451.86i 0.109123 + 0.263447i
\(313\) −2149.71 + 890.438i −0.388207 + 0.160800i −0.568246 0.822859i \(-0.692378\pi\)
0.180039 + 0.983659i \(0.442378\pi\)
\(314\) 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 0.945881 + 0.324514i \(0.105201\pi\)
−0.439372 + 0.898305i \(0.644799\pi\)
\(318\) −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 0.994615 + 0.103637i \(0.0330482\pi\)
0.103637 + 0.994615i \(0.466952\pi\)
\(332\) 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 −0.549885 0.835240i \(-0.685329\pi\)
0.979432 0.201776i \(-0.0646714\pi\)
\(338\) 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 −0.203747 0.979024i \(-0.565312\pi\)
0.548204 + 0.836345i \(0.315312\pi\)
\(348\) 3242.39 + 3242.39i 0.499454 + 0.499454i
\(349\) −7781.94 7781.94i −1.19357 1.19357i −0.976056 0.217518i \(-0.930204\pi\)
−0.217518 0.976056i \(-0.569796\pi\)
\(350\) −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 \(0.197531\pi\)
−0.813552 + 0.581493i \(0.802469\pi\)
\(354\) 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 0.0645037 0.997917i \(-0.479454\pi\)
0.997917 0.0645037i \(-0.0205464\pi\)
\(360\) −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 0.418356 0.908283i \(-0.362606\pi\)
0.938076 + 0.346430i \(0.112606\pi\)
\(368\) 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 −0.0562446 0.998417i \(-0.517913\pi\)
−0.745758 + 0.666217i \(0.767913\pi\)
\(380\) 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 0.511129 0.859504i \(-0.329227\pi\)
−0.859504 + 0.511129i \(0.829227\pi\)
\(384\) 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 −0.798532 0.601952i \(-0.794390\pi\)
0.601952 + 0.798532i \(0.294390\pi\)
\(390\) 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 0.856295 0.516488i \(-0.172761\pi\)
−0.970704 + 0.240280i \(0.922761\pi\)
\(398\) −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 −0.260791 0.965395i \(-0.583983\pi\)
0.498231 + 0.867044i \(0.333983\pi\)
\(402\) 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 0.989065 0.147478i \(-0.0471155\pi\)
−0.803657 + 0.595092i \(0.797116\pi\)
\(420\) −3582.63 1483.98i −0.416225 0.172406i
\(421\) 4609.26i 0.533591i 0.963753 + 0.266795i \(0.0859648\pi\)
−0.963753 + 0.266795i \(0.914035\pi\)
\(422\) 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 −0.600958 0.799281i \(-0.705214\pi\)
−0.140235 0.990118i \(-0.544786\pi\)
\(432\) 6632.29 2747.19i 0.738649 0.305958i
\(433\) 8028.41 + 8028.41i 0.891041 + 0.891041i 0.994621 0.103580i \(-0.0330297\pi\)
−0.103580 + 0.994621i \(0.533030\pi\)
\(434\) 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 −0.993934 0.109975i \(-0.964923\pi\)
0.780582 + 0.625053i \(0.214923\pi\)
\(440\) 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 0.269464 0.963010i \(-0.413154\pi\)
0.871491 + 0.490411i \(0.163154\pi\)
\(450\) −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 −0.995270 0.0971425i \(-0.969030\pi\)
0.0971425 + 0.995270i \(0.469030\pi\)
\(458\) −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 −0.393000 0.919539i \(-0.628563\pi\)
0.919539 + 0.393000i \(0.128563\pi\)
\(462\) 843.352 2036.03i 0.0849270 0.205032i
\(463\) 11446.9i 1.14899i −0.818508 0.574495i \(-0.805198\pi\)
0.818508 0.574495i \(-0.194802\pi\)
\(464\) −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 0.844744 0.535171i \(-0.179753\pi\)
−0.535171 + 0.844744i \(0.679753\pi\)
\(468\) −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 −0.928954 0.370196i \(-0.879291\pi\)
0.918637 + 0.395102i \(0.129291\pi\)
\(480\) 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 0.728818 0.684708i \(-0.240070\pi\)
−0.999513 + 0.0311903i \(0.990070\pi\)
\(488\) −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 −0.988085 0.153911i \(-0.950813\pi\)
0.153911 + 0.988085i \(0.450813\pi\)
\(492\) 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 0.963634 0.267225i \(-0.0861066\pi\)
−0.870349 + 0.492436i \(0.836107\pi\)
\(500\) 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 −0.0200537 0.999799i \(-0.506384\pi\)
0.692784 + 0.721145i \(0.256384\pi\)
\(504\) −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 0.711867 0.702314i \(-0.247850\pi\)
−0.999977 + 0.00675482i \(0.997850\pi\)
\(522\) 602.703 + 249.648i 0.0505356 + 0.0209325i
\(523\) 15665.1i 1.30973i −0.755747 0.654864i \(-0.772726\pi\)
0.755747 0.654864i \(-0.227274\pi\)
\(524\) 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 −0.999880 0.0154734i \(-0.995074\pi\)
0.717963 + 0.696081i \(0.245074\pi\)
\(542\) −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 0.495013 + 0.868886i \(0.335163\pi\)
−0.964422 + 0.264368i \(0.914837\pi\)
\(548\) 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 \(0.0429922\pi\)
−0.990893 + 0.134654i \(0.957008\pi\)
\(558\) −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 −0.715395 0.698720i \(-0.753753\pi\)
0.698720 + 0.715395i \(0.253753\pi\)
\(564\) −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 0.449038 0.893513i \(-0.351767\pi\)
−0.893513 + 0.449038i \(0.851767\pi\)
\(570\) 71.7068 + 71.7068i 0.00526924 + 0.00526924i
\(571\) −8156.50 + 3378.53i −0.597791 + 0.247613i −0.660999 0.750387i \(-0.729867\pi\)
0.0632073 + 0.998000i \(0.479867\pi\)
\(572\) 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 −0.965162 0.261653i \(-0.915732\pi\)
−0.261653 0.965162i \(-0.584268\pi\)
\(588\) 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 −0.437218 0.899356i \(-0.644036\pi\)
0.899356 + 0.437218i \(0.144036\pi\)
\(594\) 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 \(0.414047\pi\)
−0.266759 + 0.963763i \(0.585953\pi\)
\(600\) 3248.52 + 1345.58i 0.221034 + 0.0915553i
\(601\) 6674.25 + 16113.1i 0.452993 + 1.09362i 0.971179 + 0.238353i \(0.0766075\pi\)
−0.518186 + 0.855268i \(0.673393\pi\)
\(602\) 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 0.396620 0.917983i \(-0.370183\pi\)
−0.368659 + 0.929565i \(0.620183\pi\)
\(608\) 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 0.895928 0.444200i \(-0.146512\pi\)
0.319420 + 0.947613i \(0.396512\pi\)
\(618\) −892.496 2154.68i −0.0580930 0.140249i
\(619\) 2395.44 992.223i 0.155543 0.0644278i −0.303554 0.952814i \(-0.598173\pi\)
0.459096 + 0.888386i \(0.348173\pi\)
\(620\) −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 −0.997934 0.0642487i \(-0.979535\pi\)
0.0642487 + 0.997934i \(0.479535\pi\)
\(632\) 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 0.0886097 0.996066i \(-0.471758\pi\)
−0.641669 + 0.766982i \(0.721758\pi\)
\(642\) 2886.84i 0.177468i
\(643\) −9268.20 + 22375.4i −0.568433 + 1.37232i 0.334443 + 0.942416i \(0.391452\pi\)
−0.902876 + 0.429902i \(0.858548\pi\)
\(644\) −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 −0.462126 0.886814i \(-0.652913\pi\)
0.300300 + 0.953845i \(0.402913\pi\)
\(654\) 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 \(-0.828409\pi\)
0.858188 0.513336i \(-0.171591\pi\)
\(660\) −3760.51 + 9078.68i −0.221785 + 0.535435i
\(661\) 5685.94 5685.94i 0.334580 0.334580i −0.519743 0.854323i \(-0.673972\pi\)
0.854323 + 0.519743i \(0.173972\pi\)
\(662\) −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 −0.129384 0.991595i \(-0.541300\pi\)
0.609675 + 0.792652i \(0.291300\pi\)
\(674\) 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 0.380969 + 0.924588i \(0.375591\pi\)
−0.923168 + 0.384397i \(0.874409\pi\)
\(678\) 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 −0.975486 0.220061i \(-0.929374\pi\)
0.845380 + 0.534166i \(0.179374\pi\)
\(684\) 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 0.994452 + 0.105189i \(0.0335446\pi\)
−0.628804 + 0.777564i \(0.716455\pi\)
\(692\) −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 \(-0.612452\pi\)
0.345976 0.938243i \(-0.387548\pi\)
\(702\) −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 −0.348062 0.937472i \(-0.613160\pi\)
−0.909009 + 0.416775i \(0.863160\pi\)
\(710\) 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 −0.0980115 0.995185i \(-0.531248\pi\)
−0.773007 + 0.634398i \(0.781248\pi\)
\(720\) 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 \(-0.929121\pi\)
0.975311 0.220837i \(-0.0708789\pi\)
\(728\) 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 −0.879149 0.476546i \(-0.841888\pi\)
0.476546 + 0.879149i \(0.341888\pi\)
\(734\) −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 0.892783 0.450486i \(-0.148749\pi\)
−0.450486 + 0.892783i \(0.648749\pi\)
\(740\) −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 0.679377 0.733789i \(-0.262250\pi\)
−0.0384753 + 0.999260i \(0.512250\pi\)
\(744\) 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 −0.981272 0.192628i \(-0.938299\pi\)
0.830073 + 0.557655i \(0.188299\pi\)
\(752\) 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 0.979824 0.199860i \(-0.0640488\pi\)
−0.199860 + 0.979824i \(0.564049\pi\)
\(758\) 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 \(0.116873\pi\)
−0.933348 + 0.358973i \(0.883127\pi\)
\(762\) 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 \(0.0783482\pi\)
−0.969861 + 0.243660i \(0.921652\pi\)
\(770\) 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 −0.989938 0.141499i \(-0.954808\pi\)
−0.141499 0.989938i \(-0.545192\pi\)
\(774\) 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 0.847754 0.530389i \(-0.177954\pi\)
0.224411 + 0.974494i \(0.427954\pi\)
\(788\) 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 −0.101171 0.994869i \(-0.532259\pi\)
0.994869 + 0.101171i \(0.0322589\pi\)
\(798\) −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 0.114261 0.993451i \(-0.463550\pi\)
0.783271 + 0.621681i \(0.213550\pi\)
\(810\) 38.7213 + 93.4816i 0.00167967 + 0.00405507i
\(811\) −5572.70 2308.29i −0.241287 0.0999444i 0.258763 0.965941i \(-0.416685\pi\)
−0.500050 + 0.865996i \(0.666685\pi\)
\(812\) 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 0.617214 0.786795i \(-0.288261\pi\)
−0.119912 + 0.992785i \(0.538261\pi\)
\(822\) 1257.30 + 3035.39i 0.0533496 + 0.128797i
\(823\) 10190.3 4220.95i 0.431605 0.178777i −0.156295 0.987710i \(-0.549955\pi\)
0.587900 + 0.808934i \(0.299955\pi\)
\(824\) 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 0.968009 + 0.250917i \(0.0807322\pi\)
−0.507060 + 0.861911i \(0.669268\pi\)
\(828\) −4183.50 1732.86i −0.175588 0.0727309i
\(829\) 15663.7i 0.656239i −0.944636 0.328120i \(-0.893585\pi\)
0.944636 0.328120i \(-0.106415\pi\)
\(830\) −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 0.995757 + 0.0920240i \(0.0293337\pi\)
−0.639036 + 0.769177i \(0.720666\pi\)
\(840\) 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 −0.954365 0.298642i \(-0.903466\pi\)
0.886010 + 0.463666i \(0.153466\pi\)
\(854\) 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 −0.759597 0.650394i \(-0.774604\pi\)
−0.0772178 + 0.997014i \(0.524604\pi\)
\(858\) 3800.04 + 3800.04i 0.151202 + 0.151202i
\(859\) −29733.4 29733.4i −1.18102 1.18102i −0.979482 0.201533i \(-0.935408\pi\)
−0.201533 0.979482i \(-0.564592\pi\)
\(860\) −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 \(-0.950359\pi\)
0.987864 0.155322i \(-0.0496414\pi\)
\(864\) −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 −0.795450 0.606020i \(-0.792765\pi\)
−0.133947 + 0.990988i \(0.542765\pi\)
\(878\) −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 −0.870106 0.492865i \(-0.835949\pi\)
0.963766 + 0.266749i \(0.0859495\pi\)
\(882\) 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 −0.703521 0.710675i \(-0.748390\pi\)
0.999987 0.00505836i \(-0.00161013\pi\)
\(888\) 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 −0.981452 0.191709i \(-0.938597\pi\)
0.558433 0.829550i \(-0.311403\pi\)
\(908\) −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 0.0387363 0.999249i \(-0.487667\pi\)
0.733967 + 0.679185i \(0.237667\pi\)
\(912\) 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 −0.968121 0.250482i \(-0.919411\pi\)
0.507448 0.861682i \(-0.330589\pi\)
\(930\) −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 −0.716457 0.697631i \(-0.754238\pi\)
0.697631 + 0.716457i \(0.254238\pi\)
\(938\) 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 0.920903 0.389793i \(-0.127453\pi\)
−0.926802 + 0.375551i \(0.877453\pi\)
\(942\) 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 0.198808 0.980038i \(-0.436293\pi\)
−0.552413 + 0.833571i \(0.686293\pi\)
\(948\) 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 −0.717311 0.696753i \(-0.754628\pi\)
0.696753 + 0.717311i \(0.254628\pi\)
\(968\) 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 −0.283948 0.958840i \(-0.591644\pi\)
0.958840 + 0.283948i \(0.0916443\pi\)
\(972\) 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 0.653757 0.756705i \(-0.273192\pi\)
−0.756705 + 0.653757i \(0.773192\pi\)
\(978\) −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 0.430667 + 0.902511i \(0.358278\pi\)
−0.942699 + 0.333644i \(0.891722\pi\)
\(984\) −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 −0.165449 0.986218i \(-0.552907\pi\)
−0.814352 + 0.580372i \(0.802907\pi\)
\(992\) 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 0.840336 0.542066i \(-0.182358\pi\)
−0.977506 + 0.210909i \(0.932358\pi\)
\(998\) −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.8.2 12
3.2 odd 2 153.4.l.a.127.2 12
17.6 odd 16 289.4.b.e.288.5 12
17.7 odd 16 289.4.a.g.1.7 12
17.10 odd 16 289.4.a.g.1.8 12
17.11 odd 16 289.4.b.e.288.6 12
17.15 even 8 inner 17.4.d.a.15.2 yes 12
51.32 odd 8 153.4.l.a.100.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.d.a.8.2 12 1.1 even 1 trivial
17.4.d.a.15.2 yes 12 17.15 even 8 inner
153.4.l.a.100.2 12 51.32 odd 8
153.4.l.a.127.2 12 3.2 odd 2
289.4.a.g.1.7 12 17.7 odd 16
289.4.a.g.1.8 12 17.10 odd 16
289.4.b.e.288.5 12 17.6 odd 16
289.4.b.e.288.6 12 17.11 odd 16