Properties

Label 32.3.h.a.19.1
Level $32$
Weight $3$
Character 32.19
Analytic conductor $0.872$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [32,3,Mod(3,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 32.h (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: \(0.871936845953\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 19.1
Character \(\chi\) \(=\) 32.19
Dual form 32.3.h.a.27.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.98676 - 0.229757i) q^{2} +(1.58190 + 0.655246i) q^{3} +(3.89442 + 0.912943i) q^{4} +(4.18866 - 1.73500i) q^{5} +(-2.99232 - 1.66527i) q^{6} +(3.93197 + 3.93197i) q^{7} +(-7.52753 - 2.70857i) q^{8} +(-4.29089 - 4.29089i) q^{9} +O(q^{10})\) \(q+(-1.98676 - 0.229757i) q^{2} +(1.58190 + 0.655246i) q^{3} +(3.89442 + 0.912943i) q^{4} +(4.18866 - 1.73500i) q^{5} +(-2.99232 - 1.66527i) q^{6} +(3.93197 + 3.93197i) q^{7} +(-7.52753 - 2.70857i) q^{8} +(-4.29089 - 4.29089i) q^{9} +(-8.72048 + 2.48465i) q^{10} +(-14.2355 + 5.89652i) q^{11} +(5.56240 + 3.99600i) q^{12} +(0.454935 + 0.188440i) q^{13} +(-6.90848 - 8.71527i) q^{14} +7.76291 q^{15} +(14.3331 + 7.11077i) q^{16} -26.5635i q^{17} +(7.53910 + 9.51082i) q^{18} +(-7.25040 + 17.5040i) q^{19} +(17.8964 - 2.93282i) q^{20} +(3.64359 + 8.79641i) q^{21} +(29.6372 - 8.44428i) q^{22} +(0.775848 - 0.775848i) q^{23} +(-10.1331 - 9.21708i) q^{24} +(-3.14303 + 3.14303i) q^{25} +(-0.860551 - 0.478910i) q^{26} +(-9.87340 - 23.8365i) q^{27} +(11.7231 + 18.9024i) q^{28} +(-17.9907 + 43.4334i) q^{29} +(-15.4230 - 1.78358i) q^{30} -39.6852i q^{31} +(-26.8426 - 17.4205i) q^{32} -26.3828 q^{33} +(-6.10315 + 52.7753i) q^{34} +(23.2916 + 9.64771i) q^{35} +(-12.7932 - 20.6279i) q^{36} +(36.4715 - 15.1070i) q^{37} +(18.4265 - 33.1104i) q^{38} +(0.596189 + 0.596189i) q^{39} +(-36.2296 + 1.71499i) q^{40} +(38.9661 + 38.9661i) q^{41} +(-5.21791 - 18.3135i) q^{42} +(-14.2899 + 5.91907i) q^{43} +(-60.8221 + 9.96739i) q^{44} +(-25.4177 - 10.5284i) q^{45} +(-1.71968 + 1.36317i) q^{46} +62.1759 q^{47} +(18.0142 + 20.6403i) q^{48} -18.0792i q^{49} +(6.96658 - 5.52232i) q^{50} +(17.4057 - 42.0210i) q^{51} +(1.59968 + 1.14920i) q^{52} +(11.4986 + 27.7600i) q^{53} +(14.1395 + 49.6259i) q^{54} +(-49.3970 + 49.3970i) q^{55} +(-18.9480 - 40.2480i) q^{56} +(-22.9389 + 22.9389i) q^{57} +(45.7223 - 82.1583i) q^{58} +(-5.30584 - 12.8094i) q^{59} +(30.2321 + 7.08709i) q^{60} +(14.1407 - 34.1386i) q^{61} +(-9.11794 + 78.8449i) q^{62} -33.7433i q^{63} +(49.3273 + 40.7776i) q^{64} +2.23251 q^{65} +(52.4163 + 6.06163i) q^{66} +(26.1257 + 10.8216i) q^{67} +(24.2510 - 103.450i) q^{68} +(1.73569 - 0.718946i) q^{69} +(-44.0583 - 24.5191i) q^{70} +(17.7859 + 17.7859i) q^{71} +(20.6776 + 43.9219i) q^{72} +(12.8313 + 12.8313i) q^{73} +(-75.9311 + 21.6344i) q^{74} +(-7.03144 + 2.91252i) q^{75} +(-44.2163 + 61.5488i) q^{76} +(-79.1584 - 32.7885i) q^{77} +(-1.04751 - 1.32146i) q^{78} -144.157 q^{79} +(72.3735 + 4.91674i) q^{80} +10.4375i q^{81} +(-68.4635 - 86.3689i) q^{82} +(-10.9897 + 26.5314i) q^{83} +(6.15907 + 37.5833i) q^{84} +(-46.0877 - 111.266i) q^{85} +(29.7506 - 8.47657i) q^{86} +(-56.9192 + 56.9192i) q^{87} +(123.129 - 5.82851i) q^{88} +(-5.92267 + 5.92267i) q^{89} +(48.0800 + 26.7572i) q^{90} +(1.04785 + 2.52973i) q^{91} +(3.72978 - 2.31318i) q^{92} +(26.0036 - 62.7782i) q^{93} +(-123.529 - 14.2853i) q^{94} +85.8978i q^{95} +(-31.0477 - 45.1461i) q^{96} +66.9192 q^{97} +(-4.15383 + 35.9191i) q^{98} +(86.3841 + 35.7815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.98676 0.229757i −0.993380 0.114878i
\(3\) 1.58190 + 0.655246i 0.527302 + 0.218415i 0.630421 0.776254i \(-0.282882\pi\)
−0.103119 + 0.994669i \(0.532882\pi\)
\(4\) 3.89442 + 0.912943i 0.973606 + 0.228236i
\(5\) 4.18866 1.73500i 0.837732 0.347000i 0.0777729 0.996971i \(-0.475219\pi\)
0.759959 + 0.649971i \(0.225219\pi\)
\(6\) −2.99232 1.66527i −0.498719 0.277545i
\(7\) 3.93197 + 3.93197i 0.561710 + 0.561710i 0.929793 0.368083i \(-0.119986\pi\)
−0.368083 + 0.929793i \(0.619986\pi\)
\(8\) −7.52753 2.70857i −0.940941 0.338571i
\(9\) −4.29089 4.29089i −0.476765 0.476765i
\(10\) −8.72048 + 2.48465i −0.872048 + 0.248465i
\(11\) −14.2355 + 5.89652i −1.29413 + 0.536048i −0.920215 0.391414i \(-0.871986\pi\)
−0.373919 + 0.927462i \(0.621986\pi\)
\(12\) 5.56240 + 3.99600i 0.463534 + 0.333000i
\(13\) 0.454935 + 0.188440i 0.0349950 + 0.0144954i 0.400112 0.916466i \(-0.368971\pi\)
−0.365117 + 0.930962i \(0.618971\pi\)
\(14\) −6.90848 8.71527i −0.493463 0.622520i
\(15\) 7.76291 0.517527
\(16\) 14.3331 + 7.11077i 0.895817 + 0.444423i
\(17\) 26.5635i 1.56256i −0.624181 0.781280i \(-0.714567\pi\)
0.624181 0.781280i \(-0.285433\pi\)
\(18\) 7.53910 + 9.51082i 0.418839 + 0.528379i
\(19\) −7.25040 + 17.5040i −0.381600 + 0.921264i 0.610057 + 0.792358i \(0.291147\pi\)
−0.991657 + 0.128906i \(0.958853\pi\)
\(20\) 17.8964 2.93282i 0.894818 0.146641i
\(21\) 3.64359 + 8.79641i 0.173504 + 0.418877i
\(22\) 29.6372 8.44428i 1.34715 0.383831i
\(23\) 0.775848 0.775848i 0.0337325 0.0337325i −0.690039 0.723772i \(-0.742407\pi\)
0.723772 + 0.690039i \(0.242407\pi\)
\(24\) −10.1331 9.21708i −0.422210 0.384045i
\(25\) −3.14303 + 3.14303i −0.125721 + 0.125721i
\(26\) −0.860551 0.478910i −0.0330981 0.0184196i
\(27\) −9.87340 23.8365i −0.365682 0.882833i
\(28\) 11.7231 + 18.9024i 0.418682 + 0.675086i
\(29\) −17.9907 + 43.4334i −0.620369 + 1.49770i 0.230901 + 0.972977i \(0.425833\pi\)
−0.851271 + 0.524727i \(0.824167\pi\)
\(30\) −15.4230 1.78358i −0.514101 0.0594527i
\(31\) 39.6852i 1.28017i −0.768306 0.640083i \(-0.778900\pi\)
0.768306 0.640083i \(-0.221100\pi\)
\(32\) −26.8426 17.4205i −0.838832 0.544391i
\(33\) −26.3828 −0.799480
\(34\) −6.10315 + 52.7753i −0.179504 + 1.55222i
\(35\) 23.2916 + 9.64771i 0.665475 + 0.275649i
\(36\) −12.7932 20.6279i −0.355366 0.572996i
\(37\) 36.4715 15.1070i 0.985717 0.408297i 0.169177 0.985586i \(-0.445889\pi\)
0.816540 + 0.577288i \(0.195889\pi\)
\(38\) 18.4265 33.1104i 0.484907 0.871327i
\(39\) 0.596189 + 0.596189i 0.0152869 + 0.0152869i
\(40\) −36.2296 + 1.71499i −0.905740 + 0.0428746i
\(41\) 38.9661 + 38.9661i 0.950392 + 0.950392i 0.998826 0.0484342i \(-0.0154231\pi\)
−0.0484342 + 0.998826i \(0.515423\pi\)
\(42\) −5.21791 18.3135i −0.124236 0.436035i
\(43\) −14.2899 + 5.91907i −0.332324 + 0.137653i −0.542605 0.839988i \(-0.682562\pi\)
0.210282 + 0.977641i \(0.432562\pi\)
\(44\) −60.8221 + 9.96739i −1.38232 + 0.226532i
\(45\) −25.4177 10.5284i −0.564839 0.233964i
\(46\) −1.71968 + 1.36317i −0.0373843 + 0.0296341i
\(47\) 62.1759 1.32289 0.661446 0.749993i \(-0.269943\pi\)
0.661446 + 0.749993i \(0.269943\pi\)
\(48\) 18.0142 + 20.6403i 0.375297 + 0.430005i
\(49\) 18.0792i 0.368964i
\(50\) 6.96658 5.52232i 0.139332 0.110446i
\(51\) 17.4057 42.0210i 0.341287 0.823940i
\(52\) 1.59968 + 1.14920i 0.0307630 + 0.0220999i
\(53\) 11.4986 + 27.7600i 0.216954 + 0.523773i 0.994462 0.105100i \(-0.0335163\pi\)
−0.777508 + 0.628874i \(0.783516\pi\)
\(54\) 14.1395 + 49.6259i 0.261842 + 0.918998i
\(55\) −49.3970 + 49.3970i −0.898128 + 0.898128i
\(56\) −18.9480 40.2480i −0.338357 0.718715i
\(57\) −22.9389 + 22.9389i −0.402437 + 0.402437i
\(58\) 45.7223 82.1583i 0.788316 1.41652i
\(59\) −5.30584 12.8094i −0.0899295 0.217109i 0.872515 0.488587i \(-0.162488\pi\)
−0.962445 + 0.271478i \(0.912488\pi\)
\(60\) 30.2321 + 7.08709i 0.503868 + 0.118118i
\(61\) 14.1407 34.1386i 0.231814 0.559650i −0.764576 0.644533i \(-0.777052\pi\)
0.996391 + 0.0848835i \(0.0270518\pi\)
\(62\) −9.11794 + 78.8449i −0.147064 + 1.27169i
\(63\) 33.7433i 0.535607i
\(64\) 49.3273 + 40.7776i 0.770739 + 0.637151i
\(65\) 2.23251 0.0343463
\(66\) 52.4163 + 6.06163i 0.794187 + 0.0918430i
\(67\) 26.1257 + 10.8216i 0.389937 + 0.161517i 0.569033 0.822314i \(-0.307318\pi\)
−0.179097 + 0.983831i \(0.557318\pi\)
\(68\) 24.2510 103.450i 0.356632 1.52132i
\(69\) 1.73569 0.718946i 0.0251549 0.0104195i
\(70\) −44.0583 24.5191i −0.629404 0.350273i
\(71\) 17.7859 + 17.7859i 0.250505 + 0.250505i 0.821178 0.570672i \(-0.193317\pi\)
−0.570672 + 0.821178i \(0.693317\pi\)
\(72\) 20.6776 + 43.9219i 0.287189 + 0.610027i
\(73\) 12.8313 + 12.8313i 0.175771 + 0.175771i 0.789510 0.613738i \(-0.210335\pi\)
−0.613738 + 0.789510i \(0.710335\pi\)
\(74\) −75.9311 + 21.6344i −1.02610 + 0.292357i
\(75\) −7.03144 + 2.91252i −0.0937525 + 0.0388336i
\(76\) −44.2163 + 61.5488i −0.581793 + 0.809853i
\(77\) −79.1584 32.7885i −1.02803 0.425824i
\(78\) −1.04751 1.32146i −0.0134296 0.0169418i
\(79\) −144.157 −1.82477 −0.912383 0.409337i \(-0.865760\pi\)
−0.912383 + 0.409337i \(0.865760\pi\)
\(80\) 72.3735 + 4.91674i 0.904669 + 0.0614592i
\(81\) 10.4375i 0.128858i
\(82\) −68.4635 86.3689i −0.834921 1.05328i
\(83\) −10.9897 + 26.5314i −0.132406 + 0.319655i −0.976153 0.217086i \(-0.930345\pi\)
0.843747 + 0.536741i \(0.180345\pi\)
\(84\) 6.15907 + 37.5833i 0.0733223 + 0.447421i
\(85\) −46.0877 111.266i −0.542208 1.30901i
\(86\) 29.7506 8.47657i 0.345937 0.0985648i
\(87\) −56.9192 + 56.9192i −0.654244 + 0.654244i
\(88\) 123.129 5.82851i 1.39919 0.0662330i
\(89\) −5.92267 + 5.92267i −0.0665469 + 0.0665469i −0.739597 0.673050i \(-0.764984\pi\)
0.673050 + 0.739597i \(0.264984\pi\)
\(90\) 48.0800 + 26.7572i 0.534222 + 0.297303i
\(91\) 1.04785 + 2.52973i 0.0115148 + 0.0277993i
\(92\) 3.72978 2.31318i 0.0405411 0.0251432i
\(93\) 26.0036 62.7782i 0.279608 0.675034i
\(94\) −123.529 14.2853i −1.31413 0.151972i
\(95\) 85.8978i 0.904187i
\(96\) −31.0477 45.1461i −0.323414 0.470272i
\(97\) 66.9192 0.689889 0.344944 0.938623i \(-0.387898\pi\)
0.344944 + 0.938623i \(0.387898\pi\)
\(98\) −4.15383 + 35.9191i −0.0423860 + 0.366521i
\(99\) 86.3841 + 35.7815i 0.872566 + 0.361429i
\(100\) −15.1097 + 9.37089i −0.151097 + 0.0937089i
\(101\) 23.3697 9.68007i 0.231384 0.0958422i −0.263979 0.964528i \(-0.585035\pi\)
0.495363 + 0.868686i \(0.335035\pi\)
\(102\) −44.2354 + 79.4865i −0.433681 + 0.779279i
\(103\) −15.5454 15.5454i −0.150927 0.150927i 0.627605 0.778532i \(-0.284035\pi\)
−0.778532 + 0.627605i \(0.784035\pi\)
\(104\) −2.91413 2.65071i −0.0280205 0.0254876i
\(105\) 30.5235 + 30.5235i 0.290700 + 0.290700i
\(106\) −16.4668 57.7943i −0.155347 0.545229i
\(107\) 107.060 44.3456i 1.00056 0.414444i 0.178556 0.983930i \(-0.442857\pi\)
0.822001 + 0.569485i \(0.192857\pi\)
\(108\) −16.6898 101.843i −0.154536 0.942994i
\(109\) 82.3132 + 34.0952i 0.755167 + 0.312800i 0.726848 0.686799i \(-0.240985\pi\)
0.0283190 + 0.999599i \(0.490985\pi\)
\(110\) 109.489 86.7907i 0.995358 0.789006i
\(111\) 67.5933 0.608949
\(112\) 28.3979 + 84.3165i 0.253552 + 0.752826i
\(113\) 9.91566i 0.0877492i 0.999037 + 0.0438746i \(0.0139702\pi\)
−0.999037 + 0.0438746i \(0.986030\pi\)
\(114\) 50.8444 40.3037i 0.446004 0.353541i
\(115\) 1.90367 4.59586i 0.0165536 0.0399640i
\(116\) −109.716 + 152.724i −0.945825 + 1.31658i
\(117\) −1.14350 2.76065i −0.00977350 0.0235953i
\(118\) 7.59837 + 26.6683i 0.0643930 + 0.226003i
\(119\) 104.447 104.447i 0.877705 0.877705i
\(120\) −58.4355 21.0264i −0.486963 0.175220i
\(121\) 82.3196 82.3196i 0.680327 0.680327i
\(122\) −35.9377 + 64.5763i −0.294571 + 0.529314i
\(123\) 36.1082 + 87.1730i 0.293563 + 0.708724i
\(124\) 36.2303 154.551i 0.292180 1.24638i
\(125\) −51.0869 + 123.335i −0.408695 + 0.986678i
\(126\) −7.75275 + 67.0397i −0.0615297 + 0.532061i
\(127\) 59.4093i 0.467790i 0.972262 + 0.233895i \(0.0751471\pi\)
−0.972262 + 0.233895i \(0.924853\pi\)
\(128\) −88.6326 92.3486i −0.692442 0.721474i
\(129\) −26.4837 −0.205300
\(130\) −4.43546 0.512935i −0.0341190 0.00394565i
\(131\) −176.426 73.0781i −1.34676 0.557848i −0.411375 0.911466i \(-0.634951\pi\)
−0.935390 + 0.353618i \(0.884951\pi\)
\(132\) −102.746 24.0860i −0.778378 0.182470i
\(133\) −97.3336 + 40.3169i −0.731832 + 0.303135i
\(134\) −49.4192 27.5026i −0.368800 0.205243i
\(135\) −82.7126 82.7126i −0.612686 0.612686i
\(136\) −71.9491 + 199.958i −0.529038 + 1.47028i
\(137\) −138.710 138.710i −1.01248 1.01248i −0.999921 0.0125608i \(-0.996002\pi\)
−0.0125608 0.999921i \(-0.503998\pi\)
\(138\) −3.61358 + 1.02959i −0.0261853 + 0.00746077i
\(139\) −63.7662 + 26.4128i −0.458750 + 0.190020i −0.600077 0.799943i \(-0.704863\pi\)
0.141327 + 0.989963i \(0.454863\pi\)
\(140\) 81.8997 + 58.8362i 0.584998 + 0.420259i
\(141\) 98.3563 + 40.7405i 0.697563 + 0.288940i
\(142\) −31.2498 39.4227i −0.220069 0.277624i
\(143\) −7.58736 −0.0530584
\(144\) −30.9901 92.0131i −0.215209 0.638980i
\(145\) 213.142i 1.46994i
\(146\) −22.5446 28.4408i −0.154415 0.194800i
\(147\) 11.8464 28.5996i 0.0805874 0.194555i
\(148\) 155.827 25.5366i 1.05289 0.172545i
\(149\) 41.3888 + 99.9214i 0.277777 + 0.670613i 0.999773 0.0212835i \(-0.00677526\pi\)
−0.721996 + 0.691897i \(0.756775\pi\)
\(150\) 14.6390 4.17095i 0.0975930 0.0278063i
\(151\) 159.036 159.036i 1.05322 1.05322i 0.0547164 0.998502i \(-0.482575\pi\)
0.998502 0.0547164i \(-0.0174255\pi\)
\(152\) 101.988 112.124i 0.670976 0.737656i
\(153\) −113.981 + 113.981i −0.744974 + 0.744974i
\(154\) 149.735 + 83.3300i 0.972307 + 0.541104i
\(155\) −68.8537 166.228i −0.444218 1.07244i
\(156\) 1.77753 + 2.86610i 0.0113944 + 0.0183724i
\(157\) 31.5775 76.2349i 0.201131 0.485573i −0.790843 0.612020i \(-0.790357\pi\)
0.991973 + 0.126447i \(0.0403573\pi\)
\(158\) 286.404 + 33.1210i 1.81269 + 0.209626i
\(159\) 51.4480i 0.323573i
\(160\) −142.659 26.3967i −0.891619 0.164979i
\(161\) 6.10122 0.0378958
\(162\) 2.39808 20.7367i 0.0148030 0.128005i
\(163\) −192.658 79.8016i −1.18195 0.489581i −0.296826 0.954932i \(-0.595928\pi\)
−0.885126 + 0.465351i \(0.845928\pi\)
\(164\) 116.177 + 187.324i 0.708394 + 1.14222i
\(165\) −110.509 + 45.7742i −0.669749 + 0.277419i
\(166\) 27.9296 50.1865i 0.168251 0.302329i
\(167\) 76.7432 + 76.7432i 0.459540 + 0.459540i 0.898504 0.438964i \(-0.144655\pi\)
−0.438964 + 0.898504i \(0.644655\pi\)
\(168\) −3.60156 76.0841i −0.0214379 0.452882i
\(169\) −119.330 119.330i −0.706092 0.706092i
\(170\) 66.0011 + 231.647i 0.388242 + 1.36263i
\(171\) 106.218 43.9971i 0.621160 0.257293i
\(172\) −61.0547 + 10.0055i −0.354969 + 0.0581716i
\(173\) 46.0052 + 19.0560i 0.265926 + 0.110150i 0.511663 0.859187i \(-0.329030\pi\)
−0.245737 + 0.969337i \(0.579030\pi\)
\(174\) 126.162 100.007i 0.725071 0.574754i
\(175\) −24.7166 −0.141238
\(176\) −245.967 16.7099i −1.39754 0.0949426i
\(177\) 23.7399i 0.134124i
\(178\) 13.1277 10.4062i 0.0737511 0.0584615i
\(179\) −29.4799 + 71.1707i −0.164692 + 0.397602i −0.984583 0.174918i \(-0.944034\pi\)
0.819891 + 0.572520i \(0.194034\pi\)
\(180\) −89.3756 64.2069i −0.496531 0.356705i
\(181\) 46.7381 + 112.836i 0.258222 + 0.623402i 0.998821 0.0485445i \(-0.0154583\pi\)
−0.740599 + 0.671947i \(0.765458\pi\)
\(182\) −1.50060 5.26672i −0.00824506 0.0289380i
\(183\) 44.7384 44.7384i 0.244472 0.244472i
\(184\) −7.94165 + 3.73878i −0.0431611 + 0.0203194i
\(185\) 126.556 126.556i 0.684087 0.684087i
\(186\) −66.0865 + 118.751i −0.355304 + 0.638444i
\(187\) 156.632 + 378.144i 0.837606 + 2.02216i
\(188\) 242.139 + 56.7630i 1.28797 + 0.301931i
\(189\) 54.9025 132.546i 0.290489 0.701303i
\(190\) 19.7356 170.658i 0.103872 0.898201i
\(191\) 227.376i 1.19045i −0.803559 0.595226i \(-0.797063\pi\)
0.803559 0.595226i \(-0.202937\pi\)
\(192\) 51.3117 + 96.8279i 0.267249 + 0.504312i
\(193\) −46.4565 −0.240707 −0.120354 0.992731i \(-0.538403\pi\)
−0.120354 + 0.992731i \(0.538403\pi\)
\(194\) −132.952 15.3751i −0.685321 0.0792533i
\(195\) 3.53162 + 1.46285i 0.0181109 + 0.00750177i
\(196\) 16.5053 70.4082i 0.0842107 0.359225i
\(197\) −186.490 + 77.2467i −0.946650 + 0.392115i −0.801971 0.597363i \(-0.796215\pi\)
−0.144680 + 0.989479i \(0.546215\pi\)
\(198\) −163.403 90.9365i −0.825269 0.459275i
\(199\) 54.5057 + 54.5057i 0.273898 + 0.273898i 0.830667 0.556769i \(-0.187959\pi\)
−0.556769 + 0.830667i \(0.687959\pi\)
\(200\) 32.1724 15.1461i 0.160862 0.0757307i
\(201\) 34.2376 + 34.2376i 0.170336 + 0.170336i
\(202\) −48.6541 + 13.8626i −0.240862 + 0.0686267i
\(203\) −241.518 + 100.040i −1.18974 + 0.492808i
\(204\) 106.148 147.757i 0.520332 0.724299i
\(205\) 230.822 + 95.6095i 1.12596 + 0.466388i
\(206\) 27.3134 + 34.4567i 0.132589 + 0.167266i
\(207\) −6.65815 −0.0321650
\(208\) 5.18066 + 5.93587i 0.0249070 + 0.0285378i
\(209\) 291.930i 1.39679i
\(210\) −53.6299 67.6559i −0.255381 0.322171i
\(211\) 35.0586 84.6390i 0.166155 0.401133i −0.818769 0.574123i \(-0.805343\pi\)
0.984923 + 0.172991i \(0.0553430\pi\)
\(212\) 19.4370 + 118.607i 0.0916839 + 0.559465i
\(213\) 16.4814 + 39.7897i 0.0773776 + 0.186806i
\(214\) −222.890 + 63.5062i −1.04154 + 0.296758i
\(215\) −49.5860 + 49.5860i −0.230632 + 0.230632i
\(216\) 9.75951 + 206.173i 0.0451829 + 0.954503i
\(217\) 156.041 156.041i 0.719082 0.719082i
\(218\) −155.703 86.6510i −0.714233 0.397482i
\(219\) 11.8902 + 28.7056i 0.0542933 + 0.131076i
\(220\) −237.470 + 147.276i −1.07941 + 0.669438i
\(221\) 5.00564 12.0847i 0.0226499 0.0546818i
\(222\) −134.292 15.5300i −0.604917 0.0699551i
\(223\) 428.136i 1.91989i 0.280181 + 0.959947i \(0.409606\pi\)
−0.280181 + 0.959947i \(0.590394\pi\)
\(224\) −37.0474 174.041i −0.165390 0.776970i
\(225\) 26.9728 0.119879
\(226\) 2.27819 19.7000i 0.0100805 0.0871683i
\(227\) −112.195 46.4728i −0.494252 0.204726i 0.121613 0.992578i \(-0.461193\pi\)
−0.615865 + 0.787852i \(0.711193\pi\)
\(228\) −110.276 + 68.3918i −0.483665 + 0.299964i
\(229\) 128.033 53.0331i 0.559097 0.231586i −0.0851960 0.996364i \(-0.527152\pi\)
0.644293 + 0.764779i \(0.277152\pi\)
\(230\) −4.83806 + 8.69348i −0.0210350 + 0.0377977i
\(231\) −103.736 103.736i −0.449076 0.449076i
\(232\) 253.068 278.217i 1.09081 1.19921i
\(233\) −90.6042 90.6042i −0.388859 0.388859i 0.485421 0.874280i \(-0.338666\pi\)
−0.874280 + 0.485421i \(0.838666\pi\)
\(234\) 1.63758 + 5.74748i 0.00699820 + 0.0245619i
\(235\) 260.434 107.875i 1.10823 0.459043i
\(236\) −8.96891 54.7293i −0.0380039 0.231904i
\(237\) −228.042 94.4581i −0.962202 0.398557i
\(238\) −231.508 + 183.514i −0.972724 + 0.771065i
\(239\) 283.775 1.18734 0.593672 0.804707i \(-0.297677\pi\)
0.593672 + 0.804707i \(0.297677\pi\)
\(240\) 111.266 + 55.2003i 0.463610 + 0.230001i
\(241\) 309.483i 1.28416i 0.766636 + 0.642082i \(0.221929\pi\)
−0.766636 + 0.642082i \(0.778071\pi\)
\(242\) −182.463 + 144.636i −0.753978 + 0.597668i
\(243\) −95.6997 + 231.040i −0.393826 + 0.950780i
\(244\) 86.2364 120.041i 0.353428 0.491970i
\(245\) −31.3674 75.7277i −0.128030 0.309093i
\(246\) −51.7098 181.488i −0.210202 0.737756i
\(247\) −6.59693 + 6.59693i −0.0267082 + 0.0267082i
\(248\) −107.490 + 298.731i −0.433427 + 1.20456i
\(249\) −34.7692 + 34.7692i −0.139635 + 0.139635i
\(250\) 129.834 233.299i 0.519337 0.933195i
\(251\) −33.9351 81.9265i −0.135199 0.326400i 0.841751 0.539866i \(-0.181525\pi\)
−0.976951 + 0.213465i \(0.931525\pi\)
\(252\) 30.8057 131.411i 0.122245 0.521471i
\(253\) −6.46975 + 15.6194i −0.0255721 + 0.0617366i
\(254\) 13.6497 118.032i 0.0537389 0.464693i
\(255\) 206.210i 0.808668i
\(256\) 154.874 + 203.838i 0.604976 + 0.796244i
\(257\) 193.069 0.751241 0.375621 0.926774i \(-0.377430\pi\)
0.375621 + 0.926774i \(0.377430\pi\)
\(258\) 52.6168 + 6.08482i 0.203941 + 0.0235846i
\(259\) 202.805 + 84.0047i 0.783032 + 0.324342i
\(260\) 8.69435 + 2.03816i 0.0334398 + 0.00783906i
\(261\) 263.564 109.172i 1.00982 0.418283i
\(262\) 333.726 + 185.724i 1.27376 + 0.708869i
\(263\) −14.4799 14.4799i −0.0550568 0.0550568i 0.679042 0.734099i \(-0.262395\pi\)
−0.734099 + 0.679042i \(0.762395\pi\)
\(264\) 198.597 + 71.4597i 0.752263 + 0.270681i
\(265\) 96.3271 + 96.3271i 0.363498 + 0.363498i
\(266\) 202.642 57.7369i 0.761810 0.217056i
\(267\) −13.2499 + 5.48830i −0.0496252 + 0.0205554i
\(268\) 91.8652 + 65.9954i 0.342781 + 0.246251i
\(269\) −125.951 52.1707i −0.468220 0.193943i 0.136083 0.990697i \(-0.456549\pi\)
−0.604303 + 0.796754i \(0.706549\pi\)
\(270\) 145.326 + 183.334i 0.538245 + 0.679014i
\(271\) −490.650 −1.81052 −0.905258 0.424863i \(-0.860322\pi\)
−0.905258 + 0.424863i \(0.860322\pi\)
\(272\) 188.887 380.737i 0.694438 1.39977i
\(273\) 4.68840i 0.0171736i
\(274\) 243.714 + 307.453i 0.889466 + 1.12209i
\(275\) 26.2096 63.2755i 0.0953076 0.230093i
\(276\) 7.41586 1.21529i 0.0268691 0.00440324i
\(277\) −183.667 443.412i −0.663059 1.60076i −0.792985 0.609241i \(-0.791474\pi\)
0.129926 0.991524i \(-0.458526\pi\)
\(278\) 132.757 37.8252i 0.477542 0.136062i
\(279\) −170.285 + 170.285i −0.610339 + 0.610339i
\(280\) −149.197 135.710i −0.532846 0.484680i
\(281\) −164.474 + 164.474i −0.585316 + 0.585316i −0.936359 0.351043i \(-0.885827\pi\)
0.351043 + 0.936359i \(0.385827\pi\)
\(282\) −186.050 103.540i −0.659752 0.367162i
\(283\) −98.6436 238.147i −0.348564 0.841508i −0.996790 0.0800601i \(-0.974489\pi\)
0.648226 0.761448i \(-0.275511\pi\)
\(284\) 53.0282 + 85.5032i 0.186719 + 0.301068i
\(285\) −56.2842 + 135.882i −0.197488 + 0.476779i
\(286\) 15.0743 + 1.74325i 0.0527072 + 0.00609527i
\(287\) 306.427i 1.06769i
\(288\) 40.4291 + 189.928i 0.140379 + 0.659472i
\(289\) −416.621 −1.44159
\(290\) 48.9707 423.461i 0.168865 1.46021i
\(291\) 105.860 + 43.8486i 0.363779 + 0.150682i
\(292\) 38.2563 + 61.6848i 0.131015 + 0.211249i
\(293\) −60.5536 + 25.0821i −0.206668 + 0.0856045i −0.483616 0.875280i \(-0.660677\pi\)
0.276948 + 0.960885i \(0.410677\pi\)
\(294\) −30.1068 + 54.0988i −0.102404 + 0.184009i
\(295\) −44.4487 44.4487i −0.150674 0.150674i
\(296\) −315.459 + 14.9327i −1.06574 + 0.0504484i
\(297\) 281.105 + 281.105i 0.946481 + 0.946481i
\(298\) −59.2719 208.029i −0.198899 0.698084i
\(299\) 0.499162 0.206759i 0.00166944 0.000691503i
\(300\) −30.0424 + 4.92328i −0.100141 + 0.0164109i
\(301\) −79.4611 32.9139i −0.263990 0.109348i
\(302\) −352.506 + 279.427i −1.16724 + 0.925254i
\(303\) 43.3115 0.142942
\(304\) −228.388 + 199.330i −0.751275 + 0.655692i
\(305\) 167.529i 0.549276i
\(306\) 252.641 200.265i 0.825623 0.654461i
\(307\) 166.166 401.160i 0.541257 1.30671i −0.382580 0.923923i \(-0.624964\pi\)
0.923836 0.382787i \(-0.125036\pi\)
\(308\) −278.342 199.959i −0.903708 0.649218i
\(309\) −14.4053 34.7775i −0.0466191 0.112548i
\(310\) 98.6038 + 346.074i 0.318077 + 1.11637i
\(311\) −261.640 + 261.640i −0.841288 + 0.841288i −0.989026 0.147739i \(-0.952801\pi\)
0.147739 + 0.989026i \(0.452801\pi\)
\(312\) −2.87301 6.10265i −0.00920837 0.0195598i
\(313\) −301.723 + 301.723i −0.963972 + 0.963972i −0.999373 0.0354015i \(-0.988729\pi\)
0.0354015 + 0.999373i \(0.488729\pi\)
\(314\) −80.2525 + 144.205i −0.255581 + 0.459252i
\(315\) −58.5445 141.339i −0.185856 0.448695i
\(316\) −561.407 131.607i −1.77660 0.416477i
\(317\) 11.4511 27.6454i 0.0361233 0.0872094i −0.904788 0.425862i \(-0.859971\pi\)
0.940912 + 0.338652i \(0.109971\pi\)
\(318\) 11.8205 102.215i 0.0371715 0.321430i
\(319\) 724.378i 2.27078i
\(320\) 277.364 + 85.2207i 0.866764 + 0.266315i
\(321\) 198.415 0.618117
\(322\) −12.1217 1.40180i −0.0376449 0.00435341i
\(323\) 464.968 + 192.596i 1.43953 + 0.596273i
\(324\) −9.52882 + 40.6479i −0.0294099 + 0.125457i
\(325\) −2.02215 + 0.837602i −0.00622200 + 0.00257724i
\(326\) 364.430 + 202.811i 1.11788 + 0.622120i
\(327\) 107.871 + 107.871i 0.329880 + 0.329880i
\(328\) −187.776 398.860i −0.572488 1.21604i
\(329\) 244.474 + 244.474i 0.743081 + 0.743081i
\(330\) 230.071 65.5522i 0.697185 0.198643i
\(331\) −117.333 + 48.6009i −0.354480 + 0.146830i −0.552815 0.833304i \(-0.686447\pi\)
0.198335 + 0.980134i \(0.436447\pi\)
\(332\) −67.0201 + 93.2916i −0.201868 + 0.280999i
\(333\) −221.318 91.6728i −0.664617 0.275294i
\(334\) −134.838 170.103i −0.403707 0.509289i
\(335\) 128.207 0.382709
\(336\) −10.3254 + 151.988i −0.0307304 + 0.452346i
\(337\) 148.325i 0.440134i 0.975485 + 0.220067i \(0.0706276\pi\)
−0.975485 + 0.220067i \(0.929372\pi\)
\(338\) 209.662 + 264.496i 0.620303 + 0.782532i
\(339\) −6.49720 + 15.6856i −0.0191658 + 0.0462703i
\(340\) −77.9059 475.390i −0.229135 1.39821i
\(341\) 234.004 + 564.937i 0.686230 + 1.65671i
\(342\) −221.139 + 63.0072i −0.646605 + 0.184232i
\(343\) 263.753 263.753i 0.768961 0.768961i
\(344\) 123.600 5.85080i 0.359302 0.0170081i
\(345\) 6.02284 6.02284i 0.0174575 0.0174575i
\(346\) −87.0230 48.4296i −0.251512 0.139970i
\(347\) −215.625 520.565i −0.621398 1.50019i −0.850062 0.526682i \(-0.823436\pi\)
0.228664 0.973505i \(-0.426564\pi\)
\(348\) −273.631 + 169.703i −0.786297 + 0.487654i
\(349\) −92.9006 + 224.282i −0.266191 + 0.642641i −0.999298 0.0374720i \(-0.988070\pi\)
0.733107 + 0.680113i \(0.238070\pi\)
\(350\) 49.1060 + 5.67881i 0.140303 + 0.0162252i
\(351\) 12.7046i 0.0361955i
\(352\) 484.838 + 89.7111i 1.37738 + 0.254861i
\(353\) 453.234 1.28395 0.641975 0.766726i \(-0.278115\pi\)
0.641975 + 0.766726i \(0.278115\pi\)
\(354\) −5.45441 + 47.1655i −0.0154079 + 0.133236i
\(355\) 105.357 + 43.6405i 0.296782 + 0.122931i
\(356\) −28.4725 + 17.6583i −0.0799788 + 0.0496021i
\(357\) 233.664 96.7866i 0.654520 0.271111i
\(358\) 74.9214 134.626i 0.209278 0.376050i
\(359\) 175.857 + 175.857i 0.489852 + 0.489852i 0.908259 0.418407i \(-0.137412\pi\)
−0.418407 + 0.908259i \(0.637412\pi\)
\(360\) 162.816 + 148.098i 0.452266 + 0.411384i
\(361\) 1.44333 + 1.44333i 0.00399816 + 0.00399816i
\(362\) −66.9326 234.916i −0.184897 0.648939i
\(363\) 184.161 76.2821i 0.507332 0.210144i
\(364\) 1.77127 + 10.8085i 0.00486612 + 0.0296936i
\(365\) 76.0082 + 31.4836i 0.208242 + 0.0862566i
\(366\) −99.1634 + 78.6055i −0.270938 + 0.214769i
\(367\) 115.194 0.313879 0.156939 0.987608i \(-0.449837\pi\)
0.156939 + 0.987608i \(0.449837\pi\)
\(368\) 16.6372 5.60340i 0.0452097 0.0152266i
\(369\) 334.398i 0.906228i
\(370\) −280.514 + 222.359i −0.758145 + 0.600971i
\(371\) −63.9394 + 154.363i −0.172343 + 0.416074i
\(372\) 158.582 220.745i 0.426295 0.593400i
\(373\) −95.1961 229.824i −0.255217 0.616149i 0.743393 0.668855i \(-0.233215\pi\)
−0.998610 + 0.0527059i \(0.983215\pi\)
\(374\) −224.310 787.269i −0.599758 2.10500i
\(375\) −161.629 + 161.629i −0.431011 + 0.431011i
\(376\) −468.031 168.408i −1.24476 0.447893i
\(377\) −16.3692 + 16.3692i −0.0434197 + 0.0434197i
\(378\) −139.531 + 250.723i −0.369131 + 0.663289i
\(379\) 264.738 + 639.134i 0.698517 + 1.68637i 0.726873 + 0.686772i \(0.240973\pi\)
−0.0283560 + 0.999598i \(0.509027\pi\)
\(380\) −78.4198 + 334.522i −0.206368 + 0.880322i
\(381\) −38.9277 + 93.9798i −0.102172 + 0.246666i
\(382\) −52.2412 + 451.742i −0.136757 + 1.18257i
\(383\) 217.725i 0.568473i −0.958754 0.284236i \(-0.908260\pi\)
0.958754 0.284236i \(-0.0917401\pi\)
\(384\) −79.6972 204.163i −0.207545 0.531674i
\(385\) −388.455 −1.00897
\(386\) 92.2979 + 10.6737i 0.239114 + 0.0276521i
\(387\) 86.7145 + 35.9183i 0.224068 + 0.0928122i
\(388\) 260.612 + 61.0934i 0.671680 + 0.157457i
\(389\) 452.405 187.392i 1.16299 0.481728i 0.284123 0.958788i \(-0.408297\pi\)
0.878871 + 0.477060i \(0.158297\pi\)
\(390\) −6.68038 3.71774i −0.0171292 0.00953266i
\(391\) −20.6092 20.6092i −0.0527091 0.0527091i
\(392\) −48.9688 + 136.092i −0.124920 + 0.347173i
\(393\) −231.205 231.205i −0.588308 0.588308i
\(394\) 388.259 110.623i 0.985429 0.280770i
\(395\) −603.823 + 250.112i −1.52866 + 0.633194i
\(396\) 303.750 + 218.212i 0.767045 + 0.551040i
\(397\) −281.846 116.745i −0.709940 0.294067i −0.00166042 0.999999i \(-0.500529\pi\)
−0.708280 + 0.705932i \(0.750529\pi\)
\(398\) −95.7667 120.813i −0.240620 0.303550i
\(399\) −180.390 −0.452105
\(400\) −67.3987 + 22.6999i −0.168497 + 0.0567498i
\(401\) 173.814i 0.433452i −0.976232 0.216726i \(-0.930462\pi\)
0.976232 0.216726i \(-0.0695378\pi\)
\(402\) −60.1555 75.8882i −0.149641 0.188777i
\(403\) 7.47829 18.0542i 0.0185565 0.0447995i
\(404\) 99.8490 16.3630i 0.247151 0.0405026i
\(405\) 18.1090 + 43.7190i 0.0447136 + 0.107948i
\(406\) 502.823 143.265i 1.23848 0.352869i
\(407\) −430.110 + 430.110i −1.05678 + 1.05678i
\(408\) −244.838 + 269.169i −0.600093 + 0.659729i
\(409\) 322.065 322.065i 0.787446 0.787446i −0.193629 0.981075i \(-0.562026\pi\)
0.981075 + 0.193629i \(0.0620258\pi\)
\(410\) −436.620 242.986i −1.06493 0.592648i
\(411\) −128.537 310.315i −0.312742 0.755025i
\(412\) −46.3484 74.7326i −0.112496 0.181390i
\(413\) 29.5039 71.2287i 0.0714380 0.172467i
\(414\) 13.2281 + 1.52976i 0.0319520 + 0.00369506i
\(415\) 130.198i 0.313730i
\(416\) −8.92892 12.9834i −0.0214638 0.0312102i
\(417\) −118.179 −0.283403
\(418\) −67.0729 + 579.994i −0.160461 + 1.38755i
\(419\) 13.9903 + 5.79496i 0.0333896 + 0.0138304i 0.399316 0.916813i \(-0.369248\pi\)
−0.365926 + 0.930644i \(0.619248\pi\)
\(420\) 91.0053 + 146.738i 0.216679 + 0.349376i
\(421\) −507.883 + 210.372i −1.20637 + 0.499696i −0.893053 0.449952i \(-0.851441\pi\)
−0.313320 + 0.949648i \(0.601441\pi\)
\(422\) −89.0994 + 160.102i −0.211136 + 0.379389i
\(423\) −266.790 266.790i −0.630708 0.630708i
\(424\) −11.3659 240.109i −0.0268064 0.566294i
\(425\) 83.4900 + 83.4900i 0.196447 + 0.196447i
\(426\) −23.6027 82.8393i −0.0554054 0.194458i
\(427\) 189.833 78.6313i 0.444573 0.184148i
\(428\) 457.421 74.9610i 1.06874 0.175143i
\(429\) −12.0025 4.97159i −0.0279778 0.0115888i
\(430\) 109.908 87.1227i 0.255600 0.202611i
\(431\) 654.734 1.51910 0.759552 0.650447i \(-0.225418\pi\)
0.759552 + 0.650447i \(0.225418\pi\)
\(432\) 27.9798 411.858i 0.0647680 0.953375i
\(433\) 366.488i 0.846392i −0.906038 0.423196i \(-0.860908\pi\)
0.906038 0.423196i \(-0.139092\pi\)
\(434\) −345.867 + 274.164i −0.796929 + 0.631715i
\(435\) −139.660 + 337.170i −0.321058 + 0.775103i
\(436\) 289.435 + 207.929i 0.663843 + 0.476900i
\(437\) 7.95524 + 19.2057i 0.0182042 + 0.0439489i
\(438\) −17.0277 59.7629i −0.0388761 0.136445i
\(439\) 124.489 124.489i 0.283573 0.283573i −0.550959 0.834532i \(-0.685738\pi\)
0.834532 + 0.550959i \(0.185738\pi\)
\(440\) 505.633 238.042i 1.14917 0.541005i
\(441\) −77.5759 + 77.5759i −0.175909 + 0.175909i
\(442\) −12.7215 + 22.8593i −0.0287818 + 0.0517178i
\(443\) 147.480 + 356.047i 0.332911 + 0.803718i 0.998359 + 0.0572735i \(0.0182407\pi\)
−0.665448 + 0.746445i \(0.731759\pi\)
\(444\) 263.237 + 61.7088i 0.592876 + 0.138984i
\(445\) −14.5322 + 35.0839i −0.0326567 + 0.0788402i
\(446\) 98.3673 850.604i 0.220554 1.90718i
\(447\) 185.186i 0.414286i
\(448\) 33.6171 + 354.290i 0.0750381 + 0.790826i
\(449\) −689.326 −1.53525 −0.767623 0.640901i \(-0.778561\pi\)
−0.767623 + 0.640901i \(0.778561\pi\)
\(450\) −53.5885 6.19718i −0.119085 0.0137715i
\(451\) −784.465 324.936i −1.73939 0.720479i
\(452\) −9.05244 + 38.6158i −0.0200275 + 0.0854332i
\(453\) 355.788 147.372i 0.785403 0.325325i
\(454\) 212.228 + 118.108i 0.467462 + 0.260150i
\(455\) 8.77817 + 8.77817i 0.0192927 + 0.0192927i
\(456\) 234.805 110.542i 0.514922 0.242416i
\(457\) 86.4503 + 86.4503i 0.189169 + 0.189169i 0.795337 0.606168i \(-0.207294\pi\)
−0.606168 + 0.795337i \(0.707294\pi\)
\(458\) −266.556 + 75.9475i −0.582000 + 0.165824i
\(459\) −633.181 + 262.272i −1.37948 + 0.571399i
\(460\) 11.6094 16.1603i 0.0252379 0.0351310i
\(461\) −3.31579 1.37344i −0.00719259 0.00297927i 0.379084 0.925362i \(-0.376239\pi\)
−0.386277 + 0.922383i \(0.626239\pi\)
\(462\) 182.265 + 229.934i 0.394513 + 0.497692i
\(463\) 113.007 0.244075 0.122038 0.992525i \(-0.461057\pi\)
0.122038 + 0.992525i \(0.461057\pi\)
\(464\) −566.707 + 494.606i −1.22135 + 1.06596i
\(465\) 308.072i 0.662521i
\(466\) 159.192 + 200.826i 0.341613 + 0.430956i
\(467\) −150.402 + 363.102i −0.322059 + 0.777520i 0.677075 + 0.735914i \(0.263247\pi\)
−0.999134 + 0.0416055i \(0.986753\pi\)
\(468\) −1.93295 11.7951i −0.00413024 0.0252032i
\(469\) 60.1753 + 145.276i 0.128306 + 0.309757i
\(470\) −542.204 + 154.485i −1.15363 + 0.328692i
\(471\) 99.9053 99.9053i 0.212113 0.212113i
\(472\) 5.24464 + 110.795i 0.0111115 + 0.234734i
\(473\) 168.522 168.522i 0.356282 0.356282i
\(474\) 431.362 + 240.060i 0.910047 + 0.506455i
\(475\) −32.2275 77.8040i −0.0678473 0.163798i
\(476\) 502.115 311.407i 1.05486 0.654215i
\(477\) 69.7759 168.454i 0.146281 0.353153i
\(478\) −563.793 65.1993i −1.17948 0.136400i
\(479\) 205.624i 0.429278i −0.976693 0.214639i \(-0.931142\pi\)
0.976693 0.214639i \(-0.0688575\pi\)
\(480\) −208.377 135.234i −0.434118 0.281737i
\(481\) 19.4390 0.0404136
\(482\) 71.1059 614.869i 0.147523 1.27566i
\(483\) 9.65155 + 3.99780i 0.0199825 + 0.00827702i
\(484\) 395.740 245.434i 0.817646 0.507096i
\(485\) 280.302 116.105i 0.577942 0.239391i
\(486\) 243.215 437.032i 0.500443 0.899244i
\(487\) 573.249 + 573.249i 1.17710 + 1.17710i 0.980479 + 0.196623i \(0.0629975\pi\)
0.196623 + 0.980479i \(0.437002\pi\)
\(488\) −198.911 + 218.678i −0.407605 + 0.448112i
\(489\) −252.477 252.477i −0.516313 0.516313i
\(490\) 44.9206 + 157.660i 0.0916747 + 0.321754i
\(491\) 421.115 174.432i 0.857669 0.355258i 0.0898735 0.995953i \(-0.471354\pi\)
0.767795 + 0.640695i \(0.221354\pi\)
\(492\) 61.0368 + 372.453i 0.124059 + 0.757019i
\(493\) 1153.74 + 477.897i 2.34025 + 0.969364i
\(494\) 14.6222 11.5908i 0.0295996 0.0234632i
\(495\) 423.914 0.856392
\(496\) 282.192 568.810i 0.568936 1.14679i
\(497\) 139.867i 0.281423i
\(498\) 77.0665 61.0896i 0.154752 0.122670i
\(499\) 115.301 278.361i 0.231064 0.557837i −0.765239 0.643746i \(-0.777379\pi\)
0.996303 + 0.0859086i \(0.0273793\pi\)
\(500\) −311.552 + 433.678i −0.623103 + 0.867356i
\(501\) 71.1147 + 171.686i 0.141946 + 0.342687i
\(502\) 48.5976 + 170.565i 0.0968080 + 0.339771i
\(503\) 526.474 526.474i 1.04667 1.04667i 0.0478110 0.998856i \(-0.484775\pi\)
0.998856 0.0478110i \(-0.0152245\pi\)
\(504\) −91.3959 + 254.003i −0.181341 + 0.503975i
\(505\) 81.0930 81.0930i 0.160580 0.160580i
\(506\) 16.4425 29.5454i 0.0324950 0.0583902i
\(507\) −110.578 266.958i −0.218102 0.526545i
\(508\) −54.2373 + 231.365i −0.106766 + 0.455443i
\(509\) −98.1719 + 237.008i −0.192872 + 0.465634i −0.990500 0.137516i \(-0.956088\pi\)
0.797628 + 0.603150i \(0.206088\pi\)
\(510\) −47.3782 + 409.690i −0.0928984 + 0.803314i
\(511\) 100.905i 0.197465i
\(512\) −260.864 440.561i −0.509499 0.860471i
\(513\) 488.821 0.952867
\(514\) −383.582 44.3589i −0.746268 0.0863014i
\(515\) −92.0858 38.1432i −0.178807 0.0740644i
\(516\) −103.139 24.1781i −0.199882 0.0468569i
\(517\) −885.103 + 366.622i −1.71200 + 0.709133i
\(518\) −383.624 213.493i −0.740588 0.412149i
\(519\) 60.2895 + 60.2895i 0.116165 + 0.116165i
\(520\) −16.8053 6.04691i −0.0323179 0.0116287i
\(521\) −42.3980 42.3980i −0.0813781 0.0813781i 0.665246 0.746624i \(-0.268327\pi\)
−0.746624 + 0.665246i \(0.768327\pi\)
\(522\) −548.721 + 156.342i −1.05119 + 0.299506i
\(523\) 160.929 66.6589i 0.307703 0.127455i −0.223488 0.974707i \(-0.571744\pi\)
0.531192 + 0.847252i \(0.321744\pi\)
\(524\) −620.362 445.664i −1.18390 0.850504i
\(525\) −39.0993 16.1955i −0.0744749 0.0308485i
\(526\) 25.4413 + 32.0950i 0.0483674 + 0.0610171i
\(527\) −1054.18 −2.00034
\(528\) −378.147 187.602i −0.716187 0.355307i
\(529\) 527.796i 0.997724i
\(530\) −169.247 213.511i −0.319334 0.402850i
\(531\) −32.1971 + 77.7306i −0.0606348 + 0.146385i
\(532\) −415.865 + 68.1511i −0.781702 + 0.128103i
\(533\) 10.3843 + 25.0698i 0.0194827 + 0.0470353i
\(534\) 27.5854 7.85966i 0.0516580 0.0147185i
\(535\) 371.497 371.497i 0.694386 0.694386i
\(536\) −167.351 152.224i −0.312222 0.283999i
\(537\) −93.2687 + 93.2687i −0.173685 + 0.173685i
\(538\) 238.248 + 132.589i 0.442841 + 0.246448i
\(539\) 106.605 + 257.366i 0.197782 + 0.477488i
\(540\) −246.606 397.630i −0.456678 0.736352i
\(541\) −29.6178 + 71.5038i −0.0547465 + 0.132170i −0.948886 0.315618i \(-0.897788\pi\)
0.894140 + 0.447788i \(0.147788\pi\)
\(542\) 974.803 + 112.730i 1.79853 + 0.207989i
\(543\) 209.121i 0.385121i
\(544\) −462.750 + 713.034i −0.850644 + 1.31072i
\(545\) 403.937 0.741169
\(546\) 1.07719 9.31472i 0.00197288 0.0170599i
\(547\) 157.659 + 65.3046i 0.288225 + 0.119387i 0.522112 0.852877i \(-0.325144\pi\)
−0.233886 + 0.972264i \(0.575144\pi\)
\(548\) −413.561 666.830i −0.754674 1.21684i
\(549\) −207.161 + 85.8089i −0.377342 + 0.156300i
\(550\) −66.6101 + 119.691i −0.121109 + 0.217621i
\(551\) −629.819 629.819i −1.14305 1.14305i
\(552\) −15.0128 + 0.710653i −0.0271970 + 0.00128741i
\(553\) −566.819 566.819i −1.02499 1.02499i
\(554\) 263.026 + 923.151i 0.474775 + 1.66634i
\(555\) 283.125 117.274i 0.510136 0.211305i
\(556\) −272.446 + 44.6479i −0.490011 + 0.0803019i
\(557\) −890.709 368.944i −1.59912 0.662376i −0.607827 0.794069i \(-0.707959\pi\)
−0.991291 + 0.131693i \(0.957959\pi\)
\(558\) 377.438 299.190i 0.676413 0.536183i
\(559\) −7.61638 −0.0136250
\(560\) 265.238 + 303.903i 0.473639 + 0.542684i
\(561\) 700.821i 1.24923i
\(562\) 364.559 288.981i 0.648681 0.514201i
\(563\) 106.191 256.369i 0.188617 0.455362i −0.801077 0.598562i \(-0.795739\pi\)
0.989694 + 0.143200i \(0.0457392\pi\)
\(564\) 345.847 + 248.455i 0.613205 + 0.440522i
\(565\) 17.2037 + 41.5333i 0.0304490 + 0.0735103i
\(566\) 141.265 + 495.804i 0.249585 + 0.875979i
\(567\) −41.0398 + 41.0398i −0.0723806 + 0.0723806i
\(568\) −85.7094 182.058i −0.150897 0.320525i
\(569\) −351.714 + 351.714i −0.618126 + 0.618126i −0.945050 0.326925i \(-0.893988\pi\)
0.326925 + 0.945050i \(0.393988\pi\)
\(570\) 143.043 257.033i 0.250953 0.450936i
\(571\) 179.708 + 433.854i 0.314725 + 0.759814i 0.999517 + 0.0310755i \(0.00989322\pi\)
−0.684792 + 0.728739i \(0.740107\pi\)
\(572\) −29.5484 6.92683i −0.0516580 0.0121098i
\(573\) 148.987 359.688i 0.260013 0.627727i
\(574\) 70.4037 608.796i 0.122654 1.06062i
\(575\) 4.87703i 0.00848179i
\(576\) −36.6857 386.630i −0.0636904 0.671233i
\(577\) 662.602 1.14836 0.574179 0.818730i \(-0.305321\pi\)
0.574179 + 0.818730i \(0.305321\pi\)
\(578\) 827.725 + 95.7214i 1.43205 + 0.165608i
\(579\) −73.4898 30.4405i −0.126925 0.0525742i
\(580\) −194.586 + 830.064i −0.335493 + 1.43114i
\(581\) −147.532 + 61.1096i −0.253927 + 0.105180i
\(582\) −200.243 111.439i −0.344061 0.191475i
\(583\) −327.375 327.375i −0.561535 0.561535i
\(584\) −61.8335 131.342i −0.105879 0.224901i
\(585\) −9.57946 9.57946i −0.0163751 0.0163751i
\(586\) 126.068 35.9195i 0.215133 0.0612961i
\(587\) 650.448 269.424i 1.10809 0.458985i 0.247809 0.968809i \(-0.420289\pi\)
0.860279 + 0.509824i \(0.170289\pi\)
\(588\) 72.2445 100.564i 0.122865 0.171027i
\(589\) 694.650 + 287.733i 1.17937 + 0.488512i
\(590\) 78.0965 + 98.5213i 0.132367 + 0.166985i
\(591\) −345.625 −0.584814
\(592\) 630.172 + 42.8111i 1.06448 + 0.0723160i
\(593\) 430.692i 0.726293i 0.931732 + 0.363147i \(0.118298\pi\)
−0.931732 + 0.363147i \(0.881702\pi\)
\(594\) −493.902 623.074i −0.831485 1.04895i
\(595\) 256.277 618.708i 0.430718 1.03985i
\(596\) 69.9630 + 426.922i 0.117388 + 0.716312i
\(597\) 50.5082 + 121.938i 0.0846033 + 0.204250i
\(598\) −1.03922 + 0.296095i −0.00173782 + 0.000495143i
\(599\) −16.0528 + 16.0528i −0.0267993 + 0.0267993i −0.720379 0.693580i \(-0.756032\pi\)
0.693580 + 0.720379i \(0.256032\pi\)
\(600\) 60.8181 2.87892i 0.101364 0.00479820i
\(601\) 201.233 201.233i 0.334831 0.334831i −0.519587 0.854418i \(-0.673914\pi\)
0.854418 + 0.519587i \(0.173914\pi\)
\(602\) 150.308 + 83.6487i 0.249681 + 0.138951i
\(603\) −65.6682 158.537i −0.108902 0.262914i
\(604\) 764.544 474.163i 1.26580 0.785038i
\(605\) 201.984 487.633i 0.333858 0.806005i
\(606\) −86.0496 9.95112i −0.141996 0.0164210i
\(607\) 713.329i 1.17517i 0.809162 + 0.587586i \(0.199921\pi\)
−0.809162 + 0.587586i \(0.800079\pi\)
\(608\) 499.549 343.548i 0.821626 0.565046i
\(609\) −447.609 −0.734990
\(610\) −38.4910 + 332.840i −0.0630999 + 0.545639i
\(611\) 28.2860 + 11.7164i 0.0462946 + 0.0191759i
\(612\) −547.949 + 339.832i −0.895341 + 0.555281i
\(613\) −349.658 + 144.833i −0.570404 + 0.236269i −0.649195 0.760622i \(-0.724894\pi\)
0.0787907 + 0.996891i \(0.474894\pi\)
\(614\) −422.301 + 758.830i −0.687786 + 1.23588i
\(615\) 302.490 + 302.490i 0.491854 + 0.491854i
\(616\) 507.057 + 461.222i 0.823144 + 0.748737i
\(617\) 185.331 + 185.331i 0.300374 + 0.300374i 0.841160 0.540786i \(-0.181873\pi\)
−0.540786 + 0.841160i \(0.681873\pi\)
\(618\) 20.6295 + 72.4042i 0.0333811 + 0.117159i
\(619\) −740.280 + 306.634i −1.19593 + 0.495370i −0.889681 0.456582i \(-0.849074\pi\)
−0.306248 + 0.951952i \(0.599074\pi\)
\(620\) −116.389 710.220i −0.187725 1.14552i
\(621\) −26.1538 10.8332i −0.0421156 0.0174448i
\(622\) 579.930 459.703i 0.932364 0.739072i
\(623\) −46.5755 −0.0747601
\(624\) 4.30586 + 12.7846i 0.00690041 + 0.0204881i
\(625\) 494.120i 0.790591i
\(626\) 668.774 530.128i 1.06833 0.846850i
\(627\) 191.286 461.805i 0.305081 0.736532i
\(628\) 192.574 268.063i 0.306647 0.426851i
\(629\) −401.295 968.812i −0.637989 1.54024i
\(630\) 83.8403 + 294.258i 0.133080 + 0.467076i
\(631\) 25.0415 25.0415i 0.0396854 0.0396854i −0.686986 0.726671i \(-0.741066\pi\)
0.726671 + 0.686986i \(0.241066\pi\)
\(632\) 1085.14 + 390.458i 1.71700 + 0.617813i
\(633\) 110.919 110.919i 0.175227 0.175227i
\(634\) −29.1023 + 52.2937i −0.0459026 + 0.0824822i
\(635\) 103.075 + 248.845i 0.162323 + 0.391882i
\(636\) −46.9691 + 200.360i −0.0738508 + 0.315032i
\(637\) 3.40686 8.22488i 0.00534828 0.0129119i
\(638\) −166.431 + 1439.16i −0.260863 + 2.25574i
\(639\) 152.634i 0.238864i
\(640\) −531.476 233.039i −0.830432 0.364124i
\(641\) −150.813 −0.235278 −0.117639 0.993056i \(-0.537533\pi\)
−0.117639 + 0.993056i \(0.537533\pi\)
\(642\) −394.204 45.5873i −0.614024 0.0710082i
\(643\) −635.355 263.173i −0.988110 0.409289i −0.170686 0.985325i \(-0.554598\pi\)
−0.817424 + 0.576037i \(0.804598\pi\)
\(644\) 23.7607 + 5.57007i 0.0368955 + 0.00864917i
\(645\) −110.931 + 45.9492i −0.171987 + 0.0712391i
\(646\) −879.530 489.472i −1.36150 0.757696i
\(647\) −460.454 460.454i −0.711675 0.711675i 0.255211 0.966885i \(-0.417855\pi\)
−0.966885 + 0.255211i \(0.917855\pi\)
\(648\) 28.2706 78.5683i 0.0436275 0.121247i
\(649\) 151.062 + 151.062i 0.232762 + 0.232762i
\(650\) 4.20997 1.19951i 0.00647688 0.00184540i
\(651\) 349.087 144.597i 0.536232 0.222115i
\(652\) −677.438 486.667i −1.03902 0.746422i
\(653\) 308.661 + 127.852i 0.472682 + 0.195791i 0.606291 0.795243i \(-0.292657\pi\)
−0.133609 + 0.991034i \(0.542657\pi\)
\(654\) −189.529 239.097i −0.289800 0.365592i
\(655\) −865.779 −1.32180
\(656\) 281.425 + 835.583i 0.429001 + 1.27375i
\(657\) 110.115i 0.167603i
\(658\) −429.541 541.880i −0.652798 0.823526i
\(659\) −187.311 + 452.209i −0.284235 + 0.686205i −0.999925 0.0122131i \(-0.996112\pi\)
0.715690 + 0.698418i \(0.246112\pi\)
\(660\) −472.157 + 77.3760i −0.715389 + 0.117236i
\(661\) −279.659 675.156i −0.423084 1.02142i −0.981432 0.191809i \(-0.938564\pi\)
0.558348 0.829607i \(-0.311436\pi\)
\(662\) 244.279 69.6002i 0.369001 0.105136i
\(663\) 15.8369 15.8369i 0.0238867 0.0238867i
\(664\) 154.587 169.950i 0.232812 0.255948i
\(665\) −337.747 + 337.747i −0.507891 + 0.507891i
\(666\) 418.642 + 232.981i 0.628592 + 0.349821i
\(667\) 19.7397 + 47.6558i 0.0295947 + 0.0714479i
\(668\) 228.808 + 368.933i 0.342527 + 0.552294i
\(669\) −280.535 + 677.271i −0.419335 + 1.01236i
\(670\) −254.717 29.4565i −0.380175 0.0439649i
\(671\) 569.360i 0.848525i
\(672\) 55.4345 299.592i 0.0824918 0.445821i
\(673\) 74.6107 0.110863 0.0554314 0.998462i \(-0.482347\pi\)
0.0554314 + 0.998462i \(0.482347\pi\)
\(674\) 34.0787 294.686i 0.0505619 0.437220i
\(675\) 105.951 + 43.8865i 0.156965 + 0.0650170i
\(676\) −355.779 573.661i −0.526300 0.848611i
\(677\) −250.770 + 103.872i −0.370413 + 0.153430i −0.560122 0.828410i \(-0.689246\pi\)
0.189709 + 0.981840i \(0.439246\pi\)
\(678\) 16.5123 29.6708i 0.0243544 0.0437622i
\(679\) 263.124 + 263.124i 0.387517 + 0.387517i
\(680\) 45.5560 + 962.386i 0.0669942 + 1.41527i
\(681\) −147.031 147.031i −0.215905 0.215905i
\(682\) −335.112 1176.16i −0.491367 1.72457i
\(683\) 1198.32 496.359i 1.75449 0.726734i 0.757200 0.653183i \(-0.226567\pi\)
0.997291 0.0735510i \(-0.0234332\pi\)
\(684\) 453.826 74.3720i 0.663489 0.108731i
\(685\) −821.671 340.347i −1.19952 0.496857i
\(686\) −584.614 + 463.415i −0.852207 + 0.675533i
\(687\) 237.286 0.345395
\(688\) −246.907 16.7738i −0.358877 0.0243805i
\(689\) 14.7958i 0.0214743i
\(690\) −13.3497 + 10.5821i −0.0193474 + 0.0153364i
\(691\) −337.819 + 815.567i −0.488884 + 1.18027i 0.466398 + 0.884575i \(0.345551\pi\)
−0.955282 + 0.295696i \(0.904449\pi\)
\(692\) 161.767 + 116.212i 0.233767 + 0.167937i
\(693\) 198.968 + 480.351i 0.287111 + 0.693147i
\(694\) 308.792 + 1083.78i 0.444945 + 1.56164i
\(695\) −221.269 + 221.269i −0.318372 + 0.318372i
\(696\) 582.630 274.291i 0.837112 0.394097i
\(697\) 1035.08 1035.08i 1.48504 1.48504i
\(698\) 236.101 424.250i 0.338254 0.607807i
\(699\) −83.9591 202.695i −0.120113 0.289979i
\(700\) −96.2570 22.5649i −0.137510 0.0322355i
\(701\) 487.432 1176.77i 0.695338 1.67870i −0.0383989 0.999262i \(-0.512226\pi\)
0.733737 0.679433i \(-0.237774\pi\)
\(702\) −2.91897 + 25.2410i −0.00415808 + 0.0359559i
\(703\) 747.930i 1.06391i
\(704\) −942.644 289.629i −1.33898 0.411405i
\(705\) 482.666 0.684632
\(706\) −900.467 104.134i −1.27545 0.147498i
\(707\) 129.951 + 53.8274i 0.183806 + 0.0761349i
\(708\) 21.6732 92.4534i 0.0306119 0.130584i
\(709\) 949.384 393.248i 1.33905 0.554651i 0.405824 0.913951i \(-0.366985\pi\)
0.933222 + 0.359300i \(0.116985\pi\)
\(710\) −199.293 110.910i −0.280695 0.156211i
\(711\) 618.559 + 618.559i 0.869985 + 0.869985i
\(712\) 60.6250 28.5411i 0.0851475 0.0400858i
\(713\) −30.7896 30.7896i −0.0431832 0.0431832i
\(714\) −486.471 + 138.606i −0.681332 + 0.194126i
\(715\) −31.7809 + 13.1641i −0.0444487 + 0.0184113i
\(716\) −179.782 + 250.255i −0.251092 + 0.349519i
\(717\) 448.906 + 185.943i 0.626089 + 0.259335i
\(718\) −308.981 389.790i −0.430336 0.542882i
\(719\) 349.072 0.485496 0.242748 0.970089i \(-0.421951\pi\)
0.242748 + 0.970089i \(0.421951\pi\)
\(720\) −289.449 331.644i −0.402013 0.460616i
\(721\) 122.248i 0.169554i
\(722\) −2.53594 3.19917i −0.00351239 0.00443099i
\(723\) −202.788 + 489.573i −0.280481 + 0.677141i
\(724\) 79.0054 + 482.100i 0.109123 + 0.665884i
\(725\) −79.9673 193.058i −0.110300 0.266287i
\(726\) −383.411 + 109.242i −0.528114 + 0.150471i
\(727\) −256.931 + 256.931i −0.353413 + 0.353413i −0.861378 0.507965i \(-0.830398\pi\)
0.507965 + 0.861378i \(0.330398\pi\)
\(728\) −1.03576 21.8808i −0.00142275 0.0300561i
\(729\) −236.352 + 236.352i −0.324214 + 0.324214i
\(730\) −143.776 80.0138i −0.196954 0.109608i
\(731\) 157.231 + 379.590i 0.215091 + 0.519275i
\(732\) 215.074 133.387i 0.293817 0.182222i
\(733\) 473.293 1142.63i 0.645694 1.55884i −0.173194 0.984888i \(-0.555409\pi\)
0.818887 0.573955i \(-0.194591\pi\)
\(734\) −228.862 26.4665i −0.311801 0.0360579i
\(735\) 140.347i 0.190949i
\(736\) −34.3414 + 7.31011i −0.0466596 + 0.00993222i
\(737\) −435.722 −0.591211
\(738\) −76.8302 + 664.368i −0.104106 + 0.900228i
\(739\) −137.009 56.7511i −0.185398 0.0767945i 0.288053 0.957614i \(-0.406992\pi\)
−0.473451 + 0.880820i \(0.656992\pi\)
\(740\) 608.402 377.325i 0.822165 0.509898i
\(741\) −14.7583 + 6.11310i −0.0199168 + 0.00824979i
\(742\) 162.498 291.992i 0.219000 0.393521i
\(743\) −644.593 644.593i −0.867555 0.867555i 0.124647 0.992201i \(-0.460220\pi\)
−0.992201 + 0.124647i \(0.960220\pi\)
\(744\) −365.781 + 402.132i −0.491642 + 0.540500i
\(745\) 346.727 + 346.727i 0.465405 + 0.465405i
\(746\) 136.328 + 478.476i 0.182746 + 0.641389i
\(747\) 160.999 66.6878i 0.215527 0.0892742i
\(748\) 264.769 + 1615.65i 0.353969 + 2.15996i
\(749\) 595.321 + 246.590i 0.794821 + 0.329225i
\(750\) 358.254 283.983i 0.477672 0.378644i
\(751\) −18.5402 −0.0246873 −0.0123437 0.999924i \(-0.503929\pi\)
−0.0123437 + 0.999924i \(0.503929\pi\)
\(752\) 891.171 + 442.119i 1.18507 + 0.587924i
\(753\) 151.836i 0.201641i
\(754\) 36.2826 28.7608i 0.0481202 0.0381442i
\(755\) 390.220 942.075i 0.516848 1.24778i
\(756\) 334.821 466.069i 0.442885 0.616493i
\(757\) 100.854 + 243.482i 0.133228 + 0.321641i 0.976389 0.216021i \(-0.0693079\pi\)
−0.843161 + 0.537661i \(0.819308\pi\)
\(758\) −379.125 1330.63i −0.500165 1.75545i
\(759\) −20.4691 + 20.4691i −0.0269685 + 0.0269685i
\(760\) 232.660 646.598i 0.306132 0.850787i
\(761\) −272.267 + 272.267i −0.357775 + 0.357775i −0.862992 0.505217i \(-0.831412\pi\)
0.505217 + 0.862992i \(0.331412\pi\)
\(762\) 98.9325 177.771i 0.129833 0.233296i
\(763\) 189.591 + 457.714i 0.248482 + 0.599888i
\(764\) 207.582 885.499i 0.271704 1.15903i
\(765\) −279.671 + 675.185i −0.365583 + 0.882594i
\(766\) −50.0238 + 432.567i −0.0653053 + 0.564709i
\(767\) 6.82730i 0.00890130i
\(768\) 111.431 + 423.933i 0.145093 + 0.551997i
\(769\) −341.927 −0.444638 −0.222319 0.974974i \(-0.571363\pi\)
−0.222319 + 0.974974i \(0.571363\pi\)
\(770\) 771.767 + 89.2503i 1.00229 + 0.115909i
\(771\) 305.417 + 126.508i 0.396131 + 0.164083i
\(772\) −180.921 42.4121i −0.234354 0.0549380i
\(773\) −366.728 + 151.904i −0.474421 + 0.196512i −0.607065 0.794652i \(-0.707653\pi\)
0.132644 + 0.991164i \(0.457653\pi\)
\(774\) −164.028 91.2843i −0.211923 0.117938i
\(775\) 124.732 + 124.732i 0.160944 + 0.160944i
\(776\) −503.736 181.255i −0.649144 0.233576i
\(777\) 265.775 + 265.775i 0.342053 + 0.342053i
\(778\) −941.874 + 268.360i −1.21063 + 0.344936i
\(779\) −964.582 + 399.543i −1.23823 + 0.512892i
\(780\) 12.4181 + 8.92111i 0.0159207 + 0.0114373i
\(781\) −358.065 148.315i −0.458470 0.189904i
\(782\) 36.2105 + 45.6807i 0.0463050 + 0.0584153i
\(783\) 1212.93 1.54908
\(784\) 128.557 259.131i 0.163976 0.330524i
\(785\) 374.109i 0.476572i
\(786\) 406.228 + 512.470i 0.516830 + 0.651997i
\(787\) 167.684 404.824i 0.213067 0.514389i −0.780825 0.624750i \(-0.785201\pi\)
0.993892 + 0.110361i \(0.0352008\pi\)
\(788\) −796.793 + 130.577i −1.01116 + 0.165706i
\(789\) −13.4179 32.3938i −0.0170063 0.0410568i
\(790\) 1257.11 358.179i 1.59128 0.453391i
\(791\) −38.9881 + 38.9881i −0.0492896 + 0.0492896i
\(792\) −553.342 503.323i −0.698664 0.635509i
\(793\) 12.8662 12.8662i 0.0162247 0.0162247i
\(794\) 533.138 + 296.699i 0.671458 + 0.373677i
\(795\) 89.2623 + 215.498i 0.112280 + 0.271067i
\(796\) 162.508 + 262.029i 0.204155 + 0.329182i
\(797\) −230.548 + 556.591i −0.289269 + 0.698358i −0.999987 0.00511971i \(-0.998370\pi\)
0.710718 + 0.703477i \(0.248370\pi\)
\(798\) 358.391 + 41.4458i 0.449112 + 0.0519371i
\(799\) 1651.61i 2.06710i
\(800\) 139.120 29.6140i 0.173901 0.0370175i
\(801\) 50.8270 0.0634545
\(802\) −39.9350 + 345.327i −0.0497943 + 0.430582i
\(803\) −258.320 106.999i −0.321693 0.133250i
\(804\) 102.079 + 164.593i 0.126964 + 0.204717i
\(805\) 25.5559 10.5856i 0.0317465 0.0131498i
\(806\) −19.0056 + 34.1511i −0.0235802 + 0.0423711i
\(807\) −165.058 165.058i −0.204533 0.204533i
\(808\) −202.136 + 9.56840i −0.250168 + 0.0118421i
\(809\) 195.031 + 195.031i 0.241077 + 0.241077i 0.817296 0.576219i \(-0.195472\pi\)
−0.576219 + 0.817296i \(0.695472\pi\)
\(810\) −25.9335 91.0198i −0.0320166 0.112370i
\(811\) −889.956 + 368.632i −1.09736 + 0.454540i −0.856566 0.516037i \(-0.827407\pi\)
−0.240791 + 0.970577i \(0.577407\pi\)
\(812\) −1031.90 + 169.106i −1.27082 + 0.208259i
\(813\) −776.161 321.496i −0.954688 0.395445i
\(814\) 953.347 755.705i 1.17119 0.928385i
\(815\) −945.435 −1.16004
\(816\) 548.278 478.522i 0.671909 0.586424i
\(817\) 293.046i 0.358686i
\(818\) −713.863 + 565.870i −0.872693 + 0.691772i
\(819\) 6.35859 15.3510i 0.00776385 0.0187436i
\(820\) 811.631 + 583.071i 0.989794 + 0.711062i
\(821\) 328.443 + 792.932i 0.400052 + 0.965812i 0.987653 + 0.156660i \(0.0500728\pi\)
−0.587600 + 0.809151i \(0.699927\pi\)
\(822\) 184.075 + 646.054i 0.223935 + 0.785954i
\(823\) −319.915 + 319.915i −0.388718 + 0.388718i −0.874230 0.485512i \(-0.838633\pi\)
0.485512 + 0.874230i \(0.338633\pi\)
\(824\) 74.9128 + 159.125i 0.0909136 + 0.193112i
\(825\) 82.9221 82.9221i 0.100512 0.100512i
\(826\) −74.9824 + 134.736i −0.0907777 + 0.163118i
\(827\) −352.335 850.612i −0.426040 1.02855i −0.980532 0.196362i \(-0.937087\pi\)
0.554492 0.832189i \(-0.312913\pi\)
\(828\) −25.9297 6.07851i −0.0313160 0.00734120i
\(829\) −459.660 + 1109.72i −0.554475 + 1.33862i 0.359611 + 0.933102i \(0.382909\pi\)
−0.914086 + 0.405519i \(0.867091\pi\)
\(830\) 29.9139 258.672i 0.0360408 0.311653i
\(831\) 821.783i 0.988908i
\(832\) 14.7566 + 27.8464i 0.0177363 + 0.0334693i
\(833\) −480.248 −0.576528
\(834\) 234.793 + 27.1524i 0.281527 + 0.0325569i
\(835\) 454.600 + 188.302i 0.544432 + 0.225511i
\(836\) 266.515 1136.90i 0.318798 1.35993i
\(837\) −945.956 + 391.828i −1.13017 + 0.468133i
\(838\) −26.4638 14.7275i −0.0315798 0.0175746i
\(839\) 439.790 + 439.790i 0.524184 + 0.524184i 0.918832 0.394648i \(-0.129134\pi\)
−0.394648 + 0.918832i \(0.629134\pi\)
\(840\) −147.092 312.442i −0.175109 0.371954i
\(841\) −968.120 968.120i −1.15115 1.15115i
\(842\) 1057.38 301.269i 1.25579 0.357801i
\(843\) −367.953 + 152.411i −0.436480 + 0.180796i
\(844\) 213.804 297.613i 0.253322 0.352623i
\(845\) −706.868 292.794i −0.836530 0.346502i
\(846\) 468.750 + 591.344i 0.554078 + 0.698988i
\(847\) 647.356 0.764293
\(848\) −32.5853 + 479.649i −0.0384260 + 0.565624i
\(849\) 441.361i 0.519860i
\(850\) −146.692 185.057i −0.172579 0.217714i
\(851\) 16.5756 40.0171i 0.0194778 0.0470236i
\(852\) 27.8600 + 170.005i 0.0326995 + 0.199536i
\(853\) 639.942 + 1544.96i 0.750225 + 1.81120i 0.557977 + 0.829857i \(0.311578\pi\)
0.192248 + 0.981346i \(0.438422\pi\)
\(854\) −395.218 + 112.606i −0.462785 + 0.131857i
\(855\) 368.578 368.578i 0.431085 0.431085i
\(856\) −926.007 + 43.8340i −1.08178 + 0.0512080i
\(857\) −628.373 + 628.373i −0.733224 + 0.733224i −0.971257 0.238033i \(-0.923497\pi\)
0.238033 + 0.971257i \(0.423497\pi\)
\(858\) 22.7038 + 12.6350i 0.0264613 + 0.0147261i
\(859\) −467.557 1128.78i −0.544304 1.31407i −0.921660 0.387998i \(-0.873167\pi\)
0.377357 0.926068i \(-0.376833\pi\)
\(860\) −238.378 + 147.840i −0.277184 + 0.171906i
\(861\) −200.785 + 484.738i −0.233200 + 0.562994i
\(862\) −1300.80 150.430i −1.50905 0.174512i
\(863\) 709.297i 0.821896i −0.911659 0.410948i \(-0.865198\pi\)
0.911659 0.410948i \(-0.134802\pi\)
\(864\) −150.216 + 811.834i −0.173861 + 0.939622i
\(865\) 225.762 0.260997
\(866\) −84.2030 + 728.123i −0.0972321 + 0.840788i
\(867\) −659.054 272.989i −0.760155 0.314866i
\(868\) 750.146 465.233i 0.864223 0.535982i
\(869\) 2052.14 850.023i 2.36149 0.978162i
\(870\) 354.938 637.787i 0.407975 0.733089i
\(871\) 9.84629 + 9.84629i 0.0113046 + 0.0113046i
\(872\) −527.265 479.604i −0.604662 0.550004i
\(873\) −287.143 287.143i −0.328915 0.328915i
\(874\) −11.3925 39.9848i −0.0130349 0.0457492i
\(875\) −685.820 + 284.076i −0.783795 + 0.324658i
\(876\) 20.0991 + 122.647i 0.0229441 + 0.140008i
\(877\) 927.972 + 384.378i 1.05812 + 0.438288i 0.842784 0.538252i \(-0.180915\pi\)
0.215337 + 0.976540i \(0.430915\pi\)
\(878\) −275.931 + 218.727i −0.314272 + 0.249119i
\(879\) −112.225 −0.127673
\(880\) −1059.26 + 356.760i −1.20371 + 0.405409i
\(881\) 660.780i 0.750034i −0.927018 0.375017i \(-0.877637\pi\)
0.927018 0.375017i \(-0.122363\pi\)
\(882\) 171.948 136.301i 0.194953 0.154536i
\(883\) −476.753 + 1150.98i −0.539924 + 1.30349i 0.384851 + 0.922979i \(0.374253\pi\)
−0.924775 + 0.380514i \(0.875747\pi\)
\(884\) 30.5267 42.4930i 0.0345325 0.0480690i
\(885\) −41.1888 99.4385i −0.0465410 0.112360i
\(886\) −211.202 741.264i −0.238377 0.836641i
\(887\) 248.725 248.725i 0.280411 0.280411i −0.552862 0.833273i \(-0.686464\pi\)
0.833273 + 0.552862i \(0.186464\pi\)
\(888\) −508.810 183.081i −0.572985 0.206172i
\(889\) −233.595 + 233.595i −0.262762 + 0.262762i
\(890\) 36.9328 66.3644i 0.0414975 0.0745667i
\(891\) −61.5448 148.582i −0.0690738 0.166759i
\(892\) −390.864 + 1667.34i −0.438189 + 1.86922i
\(893\) −450.800 + 1088.33i −0.504815 + 1.21873i
\(894\) 42.5477 367.920i 0.0475926 0.411544i
\(895\) 349.257i 0.390232i
\(896\) 14.6115 711.613i 0.0163075 0.794210i
\(897\) 0.925104 0.00103133
\(898\) 1369.52 + 158.377i 1.52508 + 0.176367i
\(899\) 1723.66 + 713.964i 1.91731 + 0.794176i
\(900\) 105.043 + 24.6246i 0.116715 + 0.0273607i
\(901\) 737.403 305.442i 0.818427 0.339004i
\(902\) 1483.89 + 825.806i 1.64511 + 0.915527i
\(903\) −104.133 104.133i −0.115319 0.115319i
\(904\) 26.8573 74.6404i 0.0297094 0.0825668i
\(905\) 391.540 + 391.540i 0.432641 + 0.432641i
\(906\) −740.724 + 211.048i −0.817576 + 0.232945i
\(907\) 301.032 124.692i 0.331899 0.137477i −0.210510 0.977592i \(-0.567512\pi\)
0.542409 + 0.840115i \(0.317512\pi\)
\(908\) −394.509 283.413i −0.434481 0.312129i
\(909\) −141.813 58.7409i −0.156010 0.0646214i
\(910\) −15.4233 19.4570i −0.0169486 0.0213813i
\(911\) 1283.61 1.40901 0.704507 0.709697i \(-0.251168\pi\)
0.704507 + 0.709697i \(0.251168\pi\)
\(912\) −491.898 + 165.671i −0.539362 + 0.181657i
\(913\) 442.488i 0.484652i
\(914\) −151.893 191.618i −0.166185 0.209648i
\(915\) 109.773 265.015i 0.119970 0.289634i
\(916\) 547.032 89.6463i 0.597196 0.0978672i
\(917\) −406.361 981.043i −0.443142 1.06984i
\(918\) 1318.24 375.594i 1.43599 0.409144i
\(919\) 299.609 299.609i 0.326017 0.326017i −0.525053 0.851070i \(-0.675954\pi\)
0.851070 + 0.525053i \(0.175954\pi\)
\(920\) −26.7781 + 29.4392i −0.0291066 + 0.0319992i
\(921\) 525.717 525.717i 0.570811 0.570811i
\(922\) 6.27211 + 3.49053i 0.00680272 + 0.00378582i
\(923\) 4.73985 + 11.4430i 0.00513526 + 0.0123976i
\(924\) −309.288 498.699i −0.334728 0.539718i
\(925\) −67.1494 + 162.113i −0.0725940 + 0.175257i
\(926\) −224.517 25.9641i −0.242459 0.0280390i
\(927\) 133.407i 0.143913i
\(928\) 1239.55 852.459i 1.33572 0.918598i
\(929\) 166.333 0.179045 0.0895225 0.995985i \(-0.471466\pi\)
0.0895225 + 0.995985i \(0.471466\pi\)
\(930\) −70.7817 + 612.066i −0.0761094 + 0.658135i
\(931\) 316.459 + 131.082i 0.339913 + 0.140797i
\(932\) −270.135 435.568i −0.289844 0.467347i
\(933\) −585.329 + 242.451i −0.627363 + 0.259862i
\(934\) 382.237 686.840i 0.409247 0.735374i
\(935\) 1312.16 + 1312.16i 1.40338 + 1.40338i
\(936\) 1.13031 + 23.8781i 0.00120759 + 0.0255108i
\(937\) 919.394 + 919.394i 0.981211 + 0.981211i 0.999827 0.0186162i \(-0.00592605\pi\)
−0.0186162 + 0.999827i \(0.505926\pi\)
\(938\) −86.1756 302.454i −0.0918717 0.322446i
\(939\) −675.000 + 279.594i −0.718850 + 0.297757i
\(940\) 1112.72 182.350i 1.18375 0.193990i
\(941\) 540.855 + 224.029i 0.574766 + 0.238076i 0.651082 0.759008i \(-0.274316\pi\)
−0.0763153 + 0.997084i \(0.524316\pi\)
\(942\) −221.442 + 175.534i −0.235076 + 0.186342i
\(943\) 60.4635 0.0641182
\(944\) 15.0360 221.327i 0.0159279 0.234457i
\(945\) 650.447i 0.688304i
\(946\) −373.531 + 296.093i −0.394853 + 0.312995i
\(947\) −149.824 + 361.708i −0.158209 + 0.381951i −0.983030 0.183443i \(-0.941276\pi\)
0.824821 + 0.565394i \(0.191276\pi\)
\(948\) −801.857 576.049i −0.845841 0.607647i
\(949\) 3.41948 + 8.25535i 0.00360324 + 0.00869900i
\(950\) 46.1522 + 161.982i 0.0485813 + 0.170508i
\(951\) 36.2291 36.2291i 0.0380958 0.0380958i
\(952\) −1069.13 + 503.326i −1.12303 + 0.528703i
\(953\) −400.363 + 400.363i −0.420108 + 0.420108i −0.885241 0.465133i \(-0.846006\pi\)
0.465133 + 0.885241i \(0.346006\pi\)
\(954\) −177.331 + 318.646i −0.185882 + 0.334010i
\(955\) −394.498 952.401i −0.413086 0.997279i
\(956\) 1105.14 + 259.071i 1.15601 + 0.270995i
\(957\) 474.646 1145.90i 0.495973 1.19738i
\(958\) −47.2436 + 408.526i −0.0493148 + 0.426436i
\(959\) 1090.81i 1.13744i
\(960\) 382.924 + 316.553i 0.398879 + 0.329743i
\(961\) −613.912 −0.638827
\(962\) −38.6205 4.46623i −0.0401461 0.00464265i
\(963\) −649.662 269.099i −0.674623 0.279438i
\(964\) −282.541 + 1205.26i −0.293092 + 1.25027i
\(965\) −194.590 + 80.6020i −0.201648 + 0.0835254i
\(966\) −18.2568 10.1602i −0.0188994 0.0105178i
\(967\) −450.402 450.402i −0.465772 0.465772i 0.434770 0.900542i \(-0.356830\pi\)
−0.900542 + 0.434770i \(0.856830\pi\)
\(968\) −842.631 + 396.695i −0.870487 + 0.409809i
\(969\) 609.338 + 609.338i 0.628831 + 0.628831i
\(970\) −583.568 + 166.271i −0.601616 + 0.171413i
\(971\) 1287.15 533.155i 1.32559 0.549079i 0.396198 0.918165i \(-0.370329\pi\)
0.929395 + 0.369086i \(0.120329\pi\)
\(972\) −583.621 + 812.398i −0.600433 + 0.835800i
\(973\) −354.581 146.872i −0.364421 0.150948i
\(974\) −1007.20 1270.62i −1.03409 1.30453i
\(975\) −3.74769 −0.00384378
\(976\) 445.431 388.760i 0.456385 0.398320i
\(977\) 1408.92i 1.44208i 0.692891 + 0.721042i \(0.256336\pi\)
−0.692891 + 0.721042i \(0.743664\pi\)
\(978\) 443.603 + 559.620i 0.453582 + 0.572208i
\(979\) 49.3888 119.235i 0.0504482 0.121793i
\(980\) −53.0230 323.553i −0.0541051 0.330156i
\(981\) −206.898 499.495i −0.210905 0.509169i
\(982\) −876.732 + 249.800i −0.892802 + 0.254378i
\(983\) −748.725 + 748.725i −0.761674 + 0.761674i −0.976625 0.214951i \(-0.931041\pi\)
0.214951 + 0.976625i \(0.431041\pi\)
\(984\) −35.6917 753.999i −0.0362721 0.766259i
\(985\) −647.120 + 647.120i −0.656975 + 0.656975i
\(986\) −2182.41 1214.55i −2.21340 1.23179i
\(987\) 226.544 + 546.925i 0.229527 + 0.554128i
\(988\) −31.7138 + 19.6686i −0.0320990 + 0.0199075i
\(989\) −6.49449 + 15.6791i −0.00656673 + 0.0158535i
\(990\) −842.215 97.3972i −0.850723 0.0983810i
\(991\) 1179.74i 1.19045i 0.803559 + 0.595225i \(0.202937\pi\)
−0.803559 + 0.595225i \(0.797063\pi\)
\(992\) −691.336 + 1065.25i −0.696911 + 1.07384i
\(993\) −217.455 −0.218988
\(994\) 32.1354 277.882i 0.0323294 0.279559i
\(995\) 322.873 + 133.738i 0.324496 + 0.134411i
\(996\) −167.148 + 103.664i −0.167820 + 0.104080i
\(997\) 1523.14 630.907i 1.52773 0.632805i 0.548606 0.836081i \(-0.315159\pi\)
0.979121 + 0.203276i \(0.0651588\pi\)
\(998\) −293.030 + 526.545i −0.293618 + 0.527600i
\(999\) −720.196 720.196i −0.720917 0.720917i
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 32.3.h.a.19.1 28
3.2 odd 2 288.3.u.a.19.7 28
4.3 odd 2 128.3.h.a.111.3 28
8.3 odd 2 256.3.h.a.223.5 28
8.5 even 2 256.3.h.b.223.3 28
32.5 even 8 128.3.h.a.15.3 28
32.11 odd 8 256.3.h.b.31.3 28
32.21 even 8 256.3.h.a.31.5 28
32.27 odd 8 inner 32.3.h.a.27.1 yes 28
96.59 even 8 288.3.u.a.91.7 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.3.h.a.19.1 28 1.1 even 1 trivial
32.3.h.a.27.1 yes 28 32.27 odd 8 inner
128.3.h.a.15.3 28 32.5 even 8
128.3.h.a.111.3 28 4.3 odd 2
256.3.h.a.31.5 28 32.21 even 8
256.3.h.a.223.5 28 8.3 odd 2
256.3.h.b.31.3 28 32.11 odd 8
256.3.h.b.223.3 28 8.5 even 2
288.3.u.a.19.7 28 3.2 odd 2
288.3.u.a.91.7 28 96.59 even 8