Properties

Label 429.2.p.b.230.18
Level $429$
Weight $2$
Character 429.230
Analytic conductor $3.426$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(230,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.230");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.p (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 230.18
Character \(\chi\) \(=\) 429.230
Dual form 429.2.p.b.263.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.570464 + 0.988072i) q^{2} +(1.47818 - 0.902759i) q^{3} +(0.349142 + 0.604732i) q^{4} -0.927976i q^{5} +(0.0487410 + 1.97554i) q^{6} +(1.26517 - 0.730447i) q^{7} -3.07855 q^{8} +(1.37005 - 2.66889i) q^{9} +O(q^{10})\) \(q+(-0.570464 + 0.988072i) q^{2} +(1.47818 - 0.902759i) q^{3} +(0.349142 + 0.604732i) q^{4} -0.927976i q^{5} +(0.0487410 + 1.97554i) q^{6} +(1.26517 - 0.730447i) q^{7} -3.07855 q^{8} +(1.37005 - 2.66889i) q^{9} +(0.916907 + 0.529376i) q^{10} +(1.11647 + 3.12306i) q^{11} +(1.06202 + 0.578714i) q^{12} +(3.28660 - 1.48265i) q^{13} +1.66677i q^{14} +(-0.837738 - 1.37172i) q^{15} +(1.05791 - 1.83236i) q^{16} +(1.09224 + 1.89182i) q^{17} +(1.85549 + 2.87621i) q^{18} +(0.853358 - 0.492686i) q^{19} +(0.561177 - 0.323996i) q^{20} +(1.21074 - 2.22188i) q^{21} +(-3.72271 - 0.678436i) q^{22} +(-0.289443 - 0.167110i) q^{23} +(-4.55066 + 2.77919i) q^{24} +4.13886 q^{25} +(-0.409919 + 4.09320i) q^{26} +(-0.384172 - 5.18193i) q^{27} +(0.883449 + 0.510060i) q^{28} +(0.566826 - 0.981772i) q^{29} +(1.83326 - 0.0452304i) q^{30} -6.43584 q^{31} +(-1.87154 - 3.24161i) q^{32} +(4.46972 + 3.60855i) q^{33} -2.49234 q^{34} +(-0.677837 - 1.17405i) q^{35} +(2.09231 - 0.103306i) q^{36} +(-3.87545 + 6.71248i) q^{37} +1.12424i q^{38} +(3.51972 - 5.15864i) q^{39} +2.85682i q^{40} +(1.63404 - 2.83023i) q^{41} +(1.50469 + 2.46380i) q^{42} +(3.51723 - 2.03067i) q^{43} +(-1.49881 + 1.76556i) q^{44} +(-2.47666 - 1.27138i) q^{45} +(0.330233 - 0.190660i) q^{46} +0.882849i q^{47} +(-0.0903892 - 3.66361i) q^{48} +(-2.43290 + 4.21390i) q^{49} +(-2.36107 + 4.08949i) q^{50} +(3.32240 + 1.81043i) q^{51} +(2.04410 + 1.46986i) q^{52} -4.09066i q^{53} +(5.33928 + 2.57651i) q^{54} +(2.89812 - 1.03606i) q^{55} +(-3.89489 + 2.24871i) q^{56} +(0.816642 - 1.49866i) q^{57} +(0.646708 + 1.12013i) q^{58} +(0.429046 - 0.247710i) q^{59} +(0.537032 - 0.985532i) q^{60} +(-10.3437 + 5.97196i) q^{61} +(3.67141 - 6.35907i) q^{62} +(-0.216129 - 4.37735i) q^{63} +8.50225 q^{64} +(-1.37587 - 3.04989i) q^{65} +(-6.11532 + 2.35786i) q^{66} +(-2.17232 + 3.76256i) q^{67} +(-0.762698 + 1.32103i) q^{68} +(-0.578709 + 0.0142780i) q^{69} +1.54673 q^{70} +(-9.85358 + 5.68897i) q^{71} +(-4.21777 + 8.21629i) q^{72} +4.71804i q^{73} +(-4.42161 - 7.65845i) q^{74} +(6.11800 - 3.73639i) q^{75} +(0.595887 + 0.344035i) q^{76} +(3.69376 + 3.13568i) q^{77} +(3.08924 + 6.42055i) q^{78} -5.61036i q^{79} +(-1.70039 - 0.981719i) q^{80} +(-5.24591 - 7.31303i) q^{81} +(1.86432 + 3.22909i) q^{82} -10.2994 q^{83} +(1.76636 - 0.0435800i) q^{84} +(1.75557 - 1.01358i) q^{85} +4.63370i q^{86} +(-0.0484302 - 1.96295i) q^{87} +(-3.43711 - 9.61448i) q^{88} +(-10.3876 - 5.99731i) q^{89} +(2.66906 - 1.72185i) q^{90} +(3.07511 - 4.27650i) q^{91} -0.233380i q^{92} +(-9.51335 + 5.81001i) q^{93} +(-0.872318 - 0.503633i) q^{94} +(-0.457201 - 0.791895i) q^{95} +(-5.69287 - 3.10214i) q^{96} +(-1.49898 - 2.59630i) q^{97} +(-2.77576 - 4.80775i) q^{98} +(9.86471 + 1.29901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 2 q^{3} - 60 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 2 q^{3} - 60 q^{4} - 2 q^{9} + 28 q^{12} - 8 q^{15} - 44 q^{16} + 16 q^{22} - 56 q^{25} + 44 q^{27} - 40 q^{31} - 16 q^{33} - 56 q^{34} + 40 q^{36} + 28 q^{37} - 22 q^{42} - 10 q^{45} + 24 q^{48} - 8 q^{49} - 12 q^{55} - 16 q^{58} - 76 q^{60} + 104 q^{64} + 68 q^{66} - 24 q^{67} + 30 q^{69} + 88 q^{70} - 66 q^{75} - 28 q^{78} - 66 q^{81} + 32 q^{82} - 8 q^{88} - 80 q^{91} + 30 q^{93} - 80 q^{97} - 68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.570464 + 0.988072i −0.403379 + 0.698672i −0.994131 0.108180i \(-0.965498\pi\)
0.590753 + 0.806853i \(0.298831\pi\)
\(3\) 1.47818 0.902759i 0.853430 0.521208i
\(4\) 0.349142 + 0.604732i 0.174571 + 0.302366i
\(5\) 0.927976i 0.415003i −0.978235 0.207502i \(-0.933467\pi\)
0.978235 0.207502i \(-0.0665332\pi\)
\(6\) 0.0487410 + 1.97554i 0.0198984 + 0.806512i
\(7\) 1.26517 0.730447i 0.478190 0.276083i −0.241472 0.970408i \(-0.577630\pi\)
0.719662 + 0.694325i \(0.244297\pi\)
\(8\) −3.07855 −1.08843
\(9\) 1.37005 2.66889i 0.456684 0.889629i
\(10\) 0.916907 + 0.529376i 0.289951 + 0.167404i
\(11\) 1.11647 + 3.12306i 0.336629 + 0.941637i
\(12\) 1.06202 + 0.578714i 0.306580 + 0.167060i
\(13\) 3.28660 1.48265i 0.911539 0.411214i
\(14\) 1.66677i 0.445464i
\(15\) −0.837738 1.37172i −0.216303 0.354176i
\(16\) 1.05791 1.83236i 0.264479 0.458090i
\(17\) 1.09224 + 1.89182i 0.264908 + 0.458834i 0.967540 0.252720i \(-0.0813250\pi\)
−0.702631 + 0.711554i \(0.747992\pi\)
\(18\) 1.85549 + 2.87621i 0.437343 + 0.677930i
\(19\) 0.853358 0.492686i 0.195774 0.113030i −0.398909 0.916991i \(-0.630611\pi\)
0.594683 + 0.803961i \(0.297278\pi\)
\(20\) 0.561177 0.323996i 0.125483 0.0724476i
\(21\) 1.21074 2.22188i 0.264205 0.484854i
\(22\) −3.72271 0.678436i −0.793685 0.144643i
\(23\) −0.289443 0.167110i −0.0603529 0.0348448i 0.469520 0.882922i \(-0.344427\pi\)
−0.529873 + 0.848077i \(0.677760\pi\)
\(24\) −4.55066 + 2.77919i −0.928899 + 0.567299i
\(25\) 4.13886 0.827772
\(26\) −0.409919 + 4.09320i −0.0803917 + 0.802742i
\(27\) −0.384172 5.18193i −0.0739340 0.997263i
\(28\) 0.883449 + 0.510060i 0.166956 + 0.0963922i
\(29\) 0.566826 0.981772i 0.105257 0.182310i −0.808586 0.588378i \(-0.799767\pi\)
0.913843 + 0.406067i \(0.133100\pi\)
\(30\) 1.83326 0.0452304i 0.334705 0.00825791i
\(31\) −6.43584 −1.15591 −0.577955 0.816069i \(-0.696149\pi\)
−0.577955 + 0.816069i \(0.696149\pi\)
\(32\) −1.87154 3.24161i −0.330845 0.573041i
\(33\) 4.46972 + 3.60855i 0.778078 + 0.628167i
\(34\) −2.49234 −0.427433
\(35\) −0.677837 1.17405i −0.114575 0.198450i
\(36\) 2.09231 0.103306i 0.348718 0.0172177i
\(37\) −3.87545 + 6.71248i −0.637121 + 1.10353i 0.348941 + 0.937145i \(0.386541\pi\)
−0.986062 + 0.166380i \(0.946792\pi\)
\(38\) 1.12424i 0.182376i
\(39\) 3.51972 5.15864i 0.563606 0.826043i
\(40\) 2.85682i 0.451702i
\(41\) 1.63404 2.83023i 0.255194 0.442008i −0.709754 0.704449i \(-0.751194\pi\)
0.964948 + 0.262441i \(0.0845275\pi\)
\(42\) 1.50469 + 2.46380i 0.232179 + 0.380172i
\(43\) 3.51723 2.03067i 0.536373 0.309675i −0.207235 0.978291i \(-0.566446\pi\)
0.743608 + 0.668616i \(0.233113\pi\)
\(44\) −1.49881 + 1.76556i −0.225953 + 0.266168i
\(45\) −2.47666 1.27138i −0.369199 0.189525i
\(46\) 0.330233 0.190660i 0.0486902 0.0281113i
\(47\) 0.882849i 0.128777i 0.997925 + 0.0643884i \(0.0205096\pi\)
−0.997925 + 0.0643884i \(0.979490\pi\)
\(48\) −0.0903892 3.66361i −0.0130466 0.528796i
\(49\) −2.43290 + 4.21390i −0.347556 + 0.601985i
\(50\) −2.36107 + 4.08949i −0.333906 + 0.578342i
\(51\) 3.32240 + 1.81043i 0.465229 + 0.253511i
\(52\) 2.04410 + 1.46986i 0.283466 + 0.203832i
\(53\) 4.09066i 0.561896i −0.959723 0.280948i \(-0.909351\pi\)
0.959723 0.280948i \(-0.0906489\pi\)
\(54\) 5.33928 + 2.57651i 0.726584 + 0.350619i
\(55\) 2.89812 1.03606i 0.390783 0.139702i
\(56\) −3.89489 + 2.24871i −0.520476 + 0.300497i
\(57\) 0.816642 1.49866i 0.108167 0.198502i
\(58\) 0.646708 + 1.12013i 0.0849169 + 0.147080i
\(59\) 0.429046 0.247710i 0.0558571 0.0322491i −0.471811 0.881699i \(-0.656400\pi\)
0.527668 + 0.849450i \(0.323066\pi\)
\(60\) 0.537032 0.985532i 0.0693306 0.127232i
\(61\) −10.3437 + 5.97196i −1.32438 + 0.764632i −0.984424 0.175810i \(-0.943746\pi\)
−0.339957 + 0.940441i \(0.610412\pi\)
\(62\) 3.67141 6.35907i 0.466270 0.807603i
\(63\) −0.216129 4.37735i −0.0272297 0.551494i
\(64\) 8.50225 1.06278
\(65\) −1.37587 3.04989i −0.170655 0.378292i
\(66\) −6.11532 + 2.35786i −0.752743 + 0.290233i
\(67\) −2.17232 + 3.76256i −0.265391 + 0.459670i −0.967666 0.252235i \(-0.918834\pi\)
0.702275 + 0.711906i \(0.252168\pi\)
\(68\) −0.762698 + 1.32103i −0.0924907 + 0.160199i
\(69\) −0.578709 + 0.0142780i −0.0696684 + 0.00171887i
\(70\) 1.54673 0.184869
\(71\) −9.85358 + 5.68897i −1.16941 + 0.675156i −0.953540 0.301267i \(-0.902591\pi\)
−0.215865 + 0.976423i \(0.569257\pi\)
\(72\) −4.21777 + 8.21629i −0.497069 + 0.968299i
\(73\) 4.71804i 0.552205i 0.961128 + 0.276103i \(0.0890430\pi\)
−0.961128 + 0.276103i \(0.910957\pi\)
\(74\) −4.42161 7.65845i −0.514002 0.890277i
\(75\) 6.11800 3.73639i 0.706445 0.431442i
\(76\) 0.595887 + 0.344035i 0.0683529 + 0.0394636i
\(77\) 3.69376 + 3.13568i 0.420943 + 0.357344i
\(78\) 3.08924 + 6.42055i 0.349787 + 0.726985i
\(79\) 5.61036i 0.631215i −0.948890 0.315607i \(-0.897792\pi\)
0.948890 0.315607i \(-0.102208\pi\)
\(80\) −1.70039 0.981719i −0.190109 0.109760i
\(81\) −5.24591 7.31303i −0.582879 0.812559i
\(82\) 1.86432 + 3.22909i 0.205879 + 0.356593i
\(83\) −10.2994 −1.13050 −0.565251 0.824919i \(-0.691221\pi\)
−0.565251 + 0.824919i \(0.691221\pi\)
\(84\) 1.76636 0.0435800i 0.192726 0.00475497i
\(85\) 1.75557 1.01358i 0.190418 0.109938i
\(86\) 4.63370i 0.499665i
\(87\) −0.0484302 1.96295i −0.00519226 0.210450i
\(88\) −3.43711 9.61448i −0.366397 1.02491i
\(89\) −10.3876 5.99731i −1.10109 0.635713i −0.164581 0.986363i \(-0.552627\pi\)
−0.936507 + 0.350650i \(0.885961\pi\)
\(90\) 2.66906 1.72185i 0.281343 0.181499i
\(91\) 3.07511 4.27650i 0.322359 0.448298i
\(92\) 0.233380i 0.0243316i
\(93\) −9.51335 + 5.81001i −0.986488 + 0.602470i
\(94\) −0.872318 0.503633i −0.0899728 0.0519458i
\(95\) −0.457201 0.791895i −0.0469078 0.0812467i
\(96\) −5.69287 3.10214i −0.581027 0.316611i
\(97\) −1.49898 2.59630i −0.152198 0.263615i 0.779837 0.625982i \(-0.215302\pi\)
−0.932035 + 0.362368i \(0.881968\pi\)
\(98\) −2.77576 4.80775i −0.280394 0.485656i
\(99\) 9.86471 + 1.29901i 0.991441 + 0.130556i
\(100\) 1.44505 + 2.50290i 0.144505 + 0.250290i
\(101\) 2.75019 4.76346i 0.273654 0.473982i −0.696141 0.717905i \(-0.745101\pi\)
0.969795 + 0.243923i \(0.0784344\pi\)
\(102\) −3.68414 + 2.24999i −0.364784 + 0.222782i
\(103\) −0.171113 −0.0168602 −0.00843012 0.999964i \(-0.502683\pi\)
−0.00843012 + 0.999964i \(0.502683\pi\)
\(104\) −10.1180 + 4.56441i −0.992147 + 0.447578i
\(105\) −2.06185 1.12353i −0.201216 0.109646i
\(106\) 4.04187 + 2.33358i 0.392581 + 0.226657i
\(107\) 5.08718 8.81125i 0.491796 0.851815i −0.508160 0.861263i \(-0.669674\pi\)
0.999955 + 0.00944760i \(0.00300731\pi\)
\(108\) 2.99955 2.04155i 0.288632 0.196449i
\(109\) 20.1337i 1.92846i −0.265076 0.964228i \(-0.585397\pi\)
0.265076 0.964228i \(-0.414603\pi\)
\(110\) −0.629572 + 3.45459i −0.0600273 + 0.329382i
\(111\) 0.331122 + 13.4209i 0.0314287 + 1.27385i
\(112\) 3.09100i 0.292072i
\(113\) 14.6725 8.47119i 1.38028 0.796902i 0.388084 0.921624i \(-0.373137\pi\)
0.992192 + 0.124722i \(0.0398039\pi\)
\(114\) 1.01492 + 1.66183i 0.0950556 + 0.155645i
\(115\) −0.155074 + 0.268596i −0.0144607 + 0.0250467i
\(116\) 0.791612 0.0734993
\(117\) 0.545784 10.8029i 0.0504578 0.998726i
\(118\) 0.565238i 0.0520344i
\(119\) 2.76375 + 1.59565i 0.253353 + 0.146273i
\(120\) 2.57902 + 4.22290i 0.235431 + 0.385496i
\(121\) −8.50698 + 6.97362i −0.773362 + 0.633965i
\(122\) 13.6272i 1.23374i
\(123\) −0.139614 5.65875i −0.0125885 0.510232i
\(124\) −2.24702 3.89196i −0.201789 0.349508i
\(125\) 8.48064i 0.758532i
\(126\) 4.44843 + 2.28357i 0.396298 + 0.203436i
\(127\) −1.98295 1.14486i −0.175959 0.101590i 0.409434 0.912340i \(-0.365726\pi\)
−0.585393 + 0.810750i \(0.699060\pi\)
\(128\) −1.10714 + 1.91762i −0.0978581 + 0.169495i
\(129\) 3.36590 6.17692i 0.296351 0.543848i
\(130\) 3.79839 + 0.380395i 0.333141 + 0.0333628i
\(131\) −14.3552 −1.25422 −0.627111 0.778930i \(-0.715763\pi\)
−0.627111 + 0.778930i \(0.715763\pi\)
\(132\) −0.621636 + 3.96288i −0.0541065 + 0.344924i
\(133\) 0.719762 1.24666i 0.0624113 0.108100i
\(134\) −2.47846 4.29281i −0.214106 0.370843i
\(135\) −4.80871 + 0.356503i −0.413868 + 0.0306829i
\(136\) −3.36253 5.82407i −0.288334 0.499410i
\(137\) −6.15737 + 3.55496i −0.526060 + 0.303721i −0.739410 0.673255i \(-0.764896\pi\)
0.213351 + 0.976976i \(0.431562\pi\)
\(138\) 0.316025 0.579951i 0.0269018 0.0493687i
\(139\) −17.4767 + 10.0902i −1.48235 + 0.855838i −0.999799 0.0200280i \(-0.993624\pi\)
−0.482555 + 0.875866i \(0.660291\pi\)
\(140\) 0.473323 0.819820i 0.0400031 0.0692874i
\(141\) 0.797000 + 1.30501i 0.0671195 + 0.109902i
\(142\) 12.9814i 1.08937i
\(143\) 8.29981 + 8.60890i 0.694065 + 0.719913i
\(144\) −3.44097 5.33389i −0.286747 0.444490i
\(145\) −0.911061 0.526001i −0.0756595 0.0436820i
\(146\) −4.66177 2.69147i −0.385811 0.222748i
\(147\) 0.207869 + 8.42523i 0.0171447 + 0.694901i
\(148\) −5.41234 −0.444891
\(149\) 5.00064 + 8.66136i 0.409668 + 0.709567i 0.994852 0.101334i \(-0.0323111\pi\)
−0.585184 + 0.810901i \(0.698978\pi\)
\(150\) 0.201732 + 8.17650i 0.0164714 + 0.667608i
\(151\) 10.4882i 0.853516i 0.904366 + 0.426758i \(0.140344\pi\)
−0.904366 + 0.426758i \(0.859656\pi\)
\(152\) −2.62710 + 1.51676i −0.213086 + 0.123025i
\(153\) 6.54549 0.323180i 0.529172 0.0261275i
\(154\) −5.20543 + 1.86091i −0.419465 + 0.149956i
\(155\) 5.97230i 0.479707i
\(156\) 4.34848 + 0.327389i 0.348157 + 0.0262121i
\(157\) −21.5349 −1.71867 −0.859335 0.511413i \(-0.829122\pi\)
−0.859335 + 0.511413i \(0.829122\pi\)
\(158\) 5.54344 + 3.20051i 0.441012 + 0.254619i
\(159\) −3.69288 6.04675i −0.292865 0.479539i
\(160\) −3.00813 + 1.73675i −0.237814 + 0.137302i
\(161\) −0.488259 −0.0384802
\(162\) 10.2184 1.01152i 0.802834 0.0794726i
\(163\) 0.112393 + 0.194671i 0.00880334 + 0.0152478i 0.870394 0.492357i \(-0.163864\pi\)
−0.861590 + 0.507605i \(0.830531\pi\)
\(164\) 2.28205 0.178198
\(165\) 3.34864 4.14779i 0.260692 0.322905i
\(166\) 5.87541 10.1765i 0.456020 0.789850i
\(167\) 0.169742 0.294001i 0.0131350 0.0227505i −0.859383 0.511332i \(-0.829152\pi\)
0.872518 + 0.488582i \(0.162486\pi\)
\(168\) −3.72731 + 6.84016i −0.287568 + 0.527730i
\(169\) 8.60348 9.74577i 0.661807 0.749675i
\(170\) 2.31283i 0.177386i
\(171\) −0.145779 2.95252i −0.0111480 0.225785i
\(172\) 2.45603 + 1.41799i 0.187270 + 0.108121i
\(173\) 12.4673 + 21.5940i 0.947872 + 1.64176i 0.749896 + 0.661555i \(0.230103\pi\)
0.197976 + 0.980207i \(0.436563\pi\)
\(174\) 1.96716 + 1.07194i 0.149130 + 0.0812633i
\(175\) 5.23637 3.02322i 0.395832 0.228534i
\(176\) 6.90370 + 1.25815i 0.520386 + 0.0948364i
\(177\) 0.410587 0.753486i 0.0308616 0.0566355i
\(178\) 11.8515 6.84249i 0.888311 0.512867i
\(179\) 6.83500 + 3.94619i 0.510872 + 0.294952i 0.733192 0.680022i \(-0.238030\pi\)
−0.222320 + 0.974974i \(0.571363\pi\)
\(180\) −0.0958658 1.94161i −0.00714541 0.144719i
\(181\) 2.98530 0.221896 0.110948 0.993826i \(-0.464611\pi\)
0.110948 + 0.993826i \(0.464611\pi\)
\(182\) 2.47125 + 5.47802i 0.183181 + 0.406058i
\(183\) −9.89871 + 18.1656i −0.731734 + 1.34284i
\(184\) 0.891063 + 0.514455i 0.0656900 + 0.0379261i
\(185\) 6.22902 + 3.59633i 0.457967 + 0.264407i
\(186\) −0.313689 12.7143i −0.0230008 0.932256i
\(187\) −4.68881 + 5.52331i −0.342880 + 0.403904i
\(188\) −0.533887 + 0.308240i −0.0389377 + 0.0224807i
\(189\) −4.27117 6.27541i −0.310682 0.456469i
\(190\) 1.04327 0.0756865
\(191\) 18.4730 10.6654i 1.33666 0.771719i 0.350346 0.936620i \(-0.386064\pi\)
0.986310 + 0.164901i \(0.0527306\pi\)
\(192\) 12.5679 7.67548i 0.907009 0.553930i
\(193\) 16.9112 + 9.76367i 1.21729 + 0.702804i 0.964338 0.264674i \(-0.0852643\pi\)
0.252955 + 0.967478i \(0.418598\pi\)
\(194\) 3.42045 0.245574
\(195\) −4.78709 3.26622i −0.342811 0.233899i
\(196\) −3.39771 −0.242693
\(197\) −1.01805 + 1.76331i −0.0725329 + 0.125631i −0.900011 0.435868i \(-0.856442\pi\)
0.827478 + 0.561498i \(0.189775\pi\)
\(198\) −6.91098 + 9.00601i −0.491142 + 0.640029i
\(199\) −0.495891 0.858908i −0.0351528 0.0608864i 0.847914 0.530134i \(-0.177858\pi\)
−0.883067 + 0.469248i \(0.844525\pi\)
\(200\) −12.7417 −0.900973
\(201\) 0.185605 + 7.52284i 0.0130916 + 0.530620i
\(202\) 3.13776 + 5.43476i 0.220772 + 0.382389i
\(203\) 1.65615i 0.116239i
\(204\) 0.0651656 + 2.64126i 0.00456250 + 0.184925i
\(205\) −2.62639 1.51635i −0.183435 0.105906i
\(206\) 0.0976137 0.169072i 0.00680107 0.0117798i
\(207\) −0.842548 + 0.543540i −0.0585612 + 0.0377787i
\(208\) 0.760187 7.59076i 0.0527095 0.526325i
\(209\) 2.49144 + 2.11501i 0.172336 + 0.146299i
\(210\) 2.28634 1.39632i 0.157773 0.0963552i
\(211\) 16.5731 + 9.56849i 1.14094 + 0.658722i 0.946663 0.322224i \(-0.104431\pi\)
0.194277 + 0.980947i \(0.437764\pi\)
\(212\) 2.47376 1.42822i 0.169898 0.0980909i
\(213\) −9.42964 + 17.3047i −0.646108 + 1.18570i
\(214\) 5.80410 + 10.0530i 0.396760 + 0.687208i
\(215\) −1.88442 3.26390i −0.128516 0.222596i
\(216\) 1.18269 + 15.9528i 0.0804720 + 1.08545i
\(217\) −8.14243 + 4.70104i −0.552744 + 0.319127i
\(218\) 19.8935 + 11.4855i 1.34736 + 0.777898i
\(219\) 4.25926 + 6.97413i 0.287814 + 0.471268i
\(220\) 1.63840 + 1.39086i 0.110461 + 0.0937715i
\(221\) 6.39469 + 4.59825i 0.430153 + 0.309312i
\(222\) −13.4497 7.32895i −0.902684 0.491887i
\(223\) 4.07415 7.05663i 0.272825 0.472547i −0.696759 0.717305i \(-0.745375\pi\)
0.969584 + 0.244758i \(0.0787087\pi\)
\(224\) −4.73564 2.73413i −0.316414 0.182681i
\(225\) 5.67046 11.0462i 0.378030 0.736410i
\(226\) 19.3300i 1.28581i
\(227\) 12.9851 + 22.4908i 0.861850 + 1.49277i 0.870141 + 0.492803i \(0.164028\pi\)
−0.00829052 + 0.999966i \(0.502639\pi\)
\(228\) 1.19141 0.0293947i 0.0789031 0.00194671i
\(229\) 0.699004 0.0461915 0.0230958 0.999733i \(-0.492648\pi\)
0.0230958 + 0.999733i \(0.492648\pi\)
\(230\) −0.176928 0.306448i −0.0116663 0.0202066i
\(231\) 8.29081 + 1.30054i 0.545495 + 0.0855690i
\(232\) −1.74500 + 3.02243i −0.114565 + 0.198432i
\(233\) 1.12199 0.0735038 0.0367519 0.999324i \(-0.488299\pi\)
0.0367519 + 0.999324i \(0.488299\pi\)
\(234\) 10.3627 + 6.70192i 0.677429 + 0.438118i
\(235\) 0.819262 0.0534428
\(236\) 0.299596 + 0.172972i 0.0195021 + 0.0112595i
\(237\) −5.06480 8.29314i −0.328994 0.538697i
\(238\) −3.15324 + 1.82052i −0.204394 + 0.118007i
\(239\) −19.9061 −1.28762 −0.643808 0.765187i \(-0.722647\pi\)
−0.643808 + 0.765187i \(0.722647\pi\)
\(240\) −3.39974 + 0.0838790i −0.219452 + 0.00541437i
\(241\) 10.4129 6.01186i 0.670751 0.387258i −0.125610 0.992080i \(-0.540089\pi\)
0.796361 + 0.604822i \(0.206756\pi\)
\(242\) −2.03751 12.3837i −0.130976 0.796055i
\(243\) −14.3563 6.07421i −0.920959 0.389660i
\(244\) −7.22288 4.17013i −0.462397 0.266965i
\(245\) 3.91040 + 2.25767i 0.249826 + 0.144237i
\(246\) 5.67089 + 3.09016i 0.361563 + 0.197021i
\(247\) 2.07416 2.88450i 0.131976 0.183536i
\(248\) 19.8130 1.25813
\(249\) −15.2243 + 9.29784i −0.964803 + 0.589226i
\(250\) 8.37949 + 4.83790i 0.529965 + 0.305976i
\(251\) −9.03861 + 5.21845i −0.570512 + 0.329385i −0.757354 0.653005i \(-0.773508\pi\)
0.186842 + 0.982390i \(0.440175\pi\)
\(252\) 2.57166 1.65902i 0.162000 0.104508i
\(253\) 0.198739 1.09052i 0.0124946 0.0685604i
\(254\) 2.26241 1.30620i 0.141956 0.0819583i
\(255\) 1.68003 3.08310i 0.105208 0.193071i
\(256\) 7.23908 + 12.5385i 0.452443 + 0.783654i
\(257\) −2.27187 1.31167i −0.141716 0.0818196i 0.427466 0.904032i \(-0.359406\pi\)
−0.569181 + 0.822212i \(0.692740\pi\)
\(258\) 4.18312 + 6.84946i 0.260430 + 0.426429i
\(259\) 11.3232i 0.703592i
\(260\) 1.36399 1.89687i 0.0845911 0.117639i
\(261\) −1.84366 2.85787i −0.114119 0.176898i
\(262\) 8.18913 14.1840i 0.505926 0.876290i
\(263\) −10.3913 + 17.9982i −0.640754 + 1.10982i 0.344511 + 0.938782i \(0.388045\pi\)
−0.985265 + 0.171036i \(0.945289\pi\)
\(264\) −13.7602 11.1091i −0.846884 0.683717i
\(265\) −3.79604 −0.233189
\(266\) 0.821196 + 1.42235i 0.0503508 + 0.0872101i
\(267\) −20.7690 + 0.512416i −1.27104 + 0.0313593i
\(268\) −3.03379 −0.185318
\(269\) 10.4288 6.02109i 0.635858 0.367113i −0.147159 0.989113i \(-0.547013\pi\)
0.783017 + 0.622000i \(0.213680\pi\)
\(270\) 2.39094 4.95472i 0.145508 0.301535i
\(271\) −21.9876 12.6945i −1.33565 0.771139i −0.349492 0.936939i \(-0.613646\pi\)
−0.986159 + 0.165801i \(0.946979\pi\)
\(272\) 4.62201 0.280250
\(273\) 0.684936 9.09753i 0.0414542 0.550608i
\(274\) 8.11191i 0.490058i
\(275\) 4.62092 + 12.9259i 0.278652 + 0.779461i
\(276\) −0.210686 0.344979i −0.0126818 0.0207653i
\(277\) 13.4320 7.75496i 0.807050 0.465950i −0.0388805 0.999244i \(-0.512379\pi\)
0.845930 + 0.533293i \(0.179046\pi\)
\(278\) 23.0243i 1.38091i
\(279\) −8.81743 + 17.1765i −0.527886 + 1.02833i
\(280\) 2.08675 + 3.61436i 0.124707 + 0.215999i
\(281\) 2.72537 0.162582 0.0812910 0.996690i \(-0.474096\pi\)
0.0812910 + 0.996690i \(0.474096\pi\)
\(282\) −1.74411 + 0.0430309i −0.103860 + 0.00256245i
\(283\) 11.2432 + 6.49127i 0.668339 + 0.385866i 0.795447 0.606023i \(-0.207236\pi\)
−0.127108 + 0.991889i \(0.540569\pi\)
\(284\) −6.88061 3.97252i −0.408289 0.235726i
\(285\) −1.39072 0.757824i −0.0823790 0.0448896i
\(286\) −13.2410 + 3.28974i −0.782954 + 0.194527i
\(287\) 4.77431i 0.281818i
\(288\) −11.2156 + 0.553764i −0.660885 + 0.0326308i
\(289\) 6.11400 10.5898i 0.359647 0.622927i
\(290\) 1.03945 0.600129i 0.0610388 0.0352408i
\(291\) −4.55960 2.48460i −0.267288 0.145650i
\(292\) −2.85315 + 1.64727i −0.166968 + 0.0963991i
\(293\) 15.1442 + 26.2305i 0.884734 + 1.53240i 0.846018 + 0.533154i \(0.178993\pi\)
0.0387155 + 0.999250i \(0.487673\pi\)
\(294\) −8.44332 4.60090i −0.492424 0.268330i
\(295\) −0.229869 0.398144i −0.0133835 0.0231809i
\(296\) 11.9308 20.6647i 0.693462 1.20111i
\(297\) 15.7546 6.98528i 0.914172 0.405327i
\(298\) −11.4107 −0.661006
\(299\) −1.19905 0.120080i −0.0693427 0.00694442i
\(300\) 4.39557 + 2.39522i 0.253778 + 0.138288i
\(301\) 2.96660 5.13830i 0.170992 0.296167i
\(302\) −10.3631 5.98312i −0.596328 0.344290i
\(303\) −0.234978 9.52403i −0.0134992 0.547141i
\(304\) 2.08488i 0.119576i
\(305\) 5.54184 + 9.59874i 0.317325 + 0.549622i
\(306\) −3.41464 + 6.65178i −0.195202 + 0.380257i
\(307\) 26.8409i 1.53189i −0.642904 0.765946i \(-0.722271\pi\)
0.642904 0.765946i \(-0.277729\pi\)
\(308\) −0.606599 + 3.32853i −0.0345642 + 0.189661i
\(309\) −0.252936 + 0.154474i −0.0143890 + 0.00878770i
\(310\) −5.90106 3.40698i −0.335158 0.193503i
\(311\) 0.0891930i 0.00505767i 0.999997 + 0.00252884i \(0.000804955\pi\)
−0.999997 + 0.00252884i \(0.999195\pi\)
\(312\) −10.8356 + 15.8811i −0.613446 + 0.899091i
\(313\) −4.46668 −0.252472 −0.126236 0.992000i \(-0.540290\pi\)
−0.126236 + 0.992000i \(0.540290\pi\)
\(314\) 12.2849 21.2780i 0.693275 1.20079i
\(315\) −4.06207 + 0.200562i −0.228872 + 0.0113004i
\(316\) 3.39276 1.95881i 0.190858 0.110192i
\(317\) 31.8200i 1.78719i −0.448876 0.893594i \(-0.648175\pi\)
0.448876 0.893594i \(-0.351825\pi\)
\(318\) 8.08128 0.199383i 0.453176 0.0111808i
\(319\) 3.69898 + 0.674110i 0.207103 + 0.0377429i
\(320\) 7.88988i 0.441058i
\(321\) −0.434653 17.6171i −0.0242600 0.983292i
\(322\) 0.278534 0.482435i 0.0155221 0.0268851i
\(323\) 1.86415 + 1.07627i 0.103724 + 0.0598851i
\(324\) 2.59086 5.72566i 0.143936 0.318092i
\(325\) 13.6028 6.13649i 0.754547 0.340391i
\(326\) −0.256466 −0.0142043
\(327\) −18.1758 29.7612i −1.00513 1.64580i
\(328\) −5.03046 + 8.71301i −0.277761 + 0.481095i
\(329\) 0.644874 + 1.11695i 0.0355531 + 0.0615797i
\(330\) 2.18804 + 5.67487i 0.120447 + 0.312391i
\(331\) 12.7427 + 22.0711i 0.700405 + 1.21314i 0.968324 + 0.249695i \(0.0803305\pi\)
−0.267920 + 0.963441i \(0.586336\pi\)
\(332\) −3.59594 6.22835i −0.197353 0.341825i
\(333\) 12.6053 + 19.5396i 0.690765 + 1.07076i
\(334\) 0.193663 + 0.335434i 0.0105968 + 0.0183541i
\(335\) 3.49157 + 2.01586i 0.190765 + 0.110138i
\(336\) −2.79043 4.56907i −0.152230 0.249263i
\(337\) 4.47706i 0.243881i 0.992537 + 0.121940i \(0.0389117\pi\)
−0.992537 + 0.121940i \(0.961088\pi\)
\(338\) 4.72155 + 14.0605i 0.256818 + 0.764789i
\(339\) 14.0412 25.7677i 0.762616 1.39951i
\(340\) 1.22588 + 0.707765i 0.0664829 + 0.0383839i
\(341\) −7.18543 20.0995i −0.389113 1.08845i
\(342\) 3.00047 + 1.54027i 0.162247 + 0.0832880i
\(343\) 17.3347i 0.935983i
\(344\) −10.8280 + 6.25153i −0.583804 + 0.337060i
\(345\) 0.0132497 + 0.537028i 0.000713337 + 0.0289126i
\(346\) −28.4486 −1.52941
\(347\) −7.41987 12.8516i −0.398319 0.689909i 0.595199 0.803578i \(-0.297073\pi\)
−0.993519 + 0.113669i \(0.963740\pi\)
\(348\) 1.17015 0.714635i 0.0627265 0.0383085i
\(349\) −9.50013 5.48490i −0.508530 0.293600i 0.223699 0.974658i \(-0.428187\pi\)
−0.732229 + 0.681058i \(0.761520\pi\)
\(350\) 6.89854i 0.368743i
\(351\) −8.94562 16.4613i −0.477482 0.878642i
\(352\) 8.03420 9.46410i 0.428224 0.504438i
\(353\) 29.8543 + 17.2364i 1.58898 + 0.917399i 0.993475 + 0.114049i \(0.0363820\pi\)
0.595507 + 0.803350i \(0.296951\pi\)
\(354\) 0.510274 + 0.835526i 0.0271207 + 0.0444077i
\(355\) 5.27922 + 9.14389i 0.280192 + 0.485307i
\(356\) 8.37566i 0.443909i
\(357\) 5.52582 0.136334i 0.292458 0.00721557i
\(358\) −7.79824 + 4.50231i −0.412150 + 0.237955i
\(359\) −18.6671 −0.985210 −0.492605 0.870253i \(-0.663955\pi\)
−0.492605 + 0.870253i \(0.663955\pi\)
\(360\) 7.62452 + 3.91399i 0.401848 + 0.206285i
\(361\) −9.01452 + 15.6136i −0.474448 + 0.821769i
\(362\) −1.70301 + 2.94969i −0.0895080 + 0.155032i
\(363\) −6.27938 + 17.9880i −0.329582 + 0.944127i
\(364\) 3.65979 + 0.366514i 0.191825 + 0.0192106i
\(365\) 4.37823 0.229167
\(366\) −12.3020 20.1434i −0.643038 1.05291i
\(367\) −11.9648 + 20.7237i −0.624559 + 1.08177i 0.364067 + 0.931373i \(0.381388\pi\)
−0.988626 + 0.150395i \(0.951946\pi\)
\(368\) −0.612411 + 0.353576i −0.0319241 + 0.0184314i
\(369\) −5.31486 8.23863i −0.276680 0.428886i
\(370\) −7.10686 + 4.10315i −0.369468 + 0.213312i
\(371\) −2.98801 5.17539i −0.155130 0.268693i
\(372\) −6.83501 3.72451i −0.354379 0.193107i
\(373\) 3.76666 2.17468i 0.195030 0.112601i −0.399305 0.916818i \(-0.630749\pi\)
0.594335 + 0.804217i \(0.297415\pi\)
\(374\) −2.78263 7.78373i −0.143887 0.402487i
\(375\) −7.65597 12.5359i −0.395353 0.647353i
\(376\) 2.71789i 0.140165i
\(377\) 0.407305 4.06710i 0.0209773 0.209466i
\(378\) 8.63711 0.640328i 0.444245 0.0329349i
\(379\) 15.0007 25.9820i 0.770535 1.33461i −0.166734 0.986002i \(-0.553322\pi\)
0.937270 0.348605i \(-0.113344\pi\)
\(380\) 0.319256 0.552968i 0.0163775 0.0283667i
\(381\) −3.96470 + 0.0978178i −0.203118 + 0.00501136i
\(382\) 24.3368i 1.24518i
\(383\) −18.1198 + 10.4615i −0.925877 + 0.534555i −0.885505 0.464629i \(-0.846188\pi\)
−0.0403719 + 0.999185i \(0.512854\pi\)
\(384\) 0.0945949 + 3.83407i 0.00482727 + 0.195657i
\(385\) 2.90983 3.42772i 0.148299 0.174693i
\(386\) −19.2944 + 11.1396i −0.982060 + 0.566993i
\(387\) −0.600848 12.1692i −0.0305428 0.618596i
\(388\) 1.04671 1.81296i 0.0531387 0.0920390i
\(389\) 26.4952i 1.34336i −0.740841 0.671681i \(-0.765573\pi\)
0.740841 0.671681i \(-0.234427\pi\)
\(390\) 5.95812 2.86674i 0.301701 0.145163i
\(391\) 0.730099i 0.0369227i
\(392\) 7.48978 12.9727i 0.378291 0.655219i
\(393\) −21.2196 + 12.9593i −1.07039 + 0.653710i
\(394\) −1.16152 2.01181i −0.0585165 0.101353i
\(395\) −5.20628 −0.261956
\(396\) 2.65863 + 6.41905i 0.133601 + 0.322569i
\(397\) −6.87478 11.9075i −0.345035 0.597618i 0.640325 0.768104i \(-0.278800\pi\)
−0.985360 + 0.170486i \(0.945466\pi\)
\(398\) 1.13155 0.0567195
\(399\) −0.0614972 2.49257i −0.00307871 0.124785i
\(400\) 4.37856 7.58389i 0.218928 0.379195i
\(401\) 20.7433 + 11.9761i 1.03587 + 0.598059i 0.918660 0.395048i \(-0.129272\pi\)
0.117209 + 0.993107i \(0.462605\pi\)
\(402\) −7.53899 4.10812i −0.376011 0.204894i
\(403\) −21.1520 + 9.54211i −1.05366 + 0.475326i
\(404\) 3.84083 0.191088
\(405\) −6.78631 + 4.86808i −0.337215 + 0.241897i
\(406\) 1.63639 + 0.944771i 0.0812127 + 0.0468882i
\(407\) −25.2903 4.60896i −1.25359 0.228458i
\(408\) −10.2282 5.57349i −0.506369 0.275929i
\(409\) 17.8360 10.2976i 0.881934 0.509185i 0.0106384 0.999943i \(-0.496614\pi\)
0.871296 + 0.490759i \(0.163280\pi\)
\(410\) 2.99652 1.73004i 0.147987 0.0854406i
\(411\) −5.89245 + 10.8135i −0.290653 + 0.533391i
\(412\) −0.0597427 0.103477i −0.00294331 0.00509797i
\(413\) 0.361878 0.626791i 0.0178068 0.0308424i
\(414\) −0.0564137 1.14257i −0.00277258 0.0561542i
\(415\) 9.55755i 0.469162i
\(416\) −10.9572 7.87902i −0.537221 0.386301i
\(417\) −16.7248 + 30.6924i −0.819016 + 1.50301i
\(418\) −3.51106 + 1.25518i −0.171732 + 0.0613929i
\(419\) 22.0337 + 12.7212i 1.07642 + 0.621469i 0.929927 0.367743i \(-0.119869\pi\)
0.146489 + 0.989212i \(0.453203\pi\)
\(420\) −0.0404412 1.63914i −0.00197333 0.0799819i
\(421\) 16.6923 0.813533 0.406766 0.913532i \(-0.366656\pi\)
0.406766 + 0.913532i \(0.366656\pi\)
\(422\) −18.9087 + 10.9170i −0.920462 + 0.531429i
\(423\) 2.35622 + 1.20955i 0.114564 + 0.0588103i
\(424\) 12.5933i 0.611585i
\(425\) 4.52065 + 7.82999i 0.219284 + 0.379810i
\(426\) −11.7191 19.1889i −0.567791 0.929705i
\(427\) −8.72440 + 15.1111i −0.422203 + 0.731278i
\(428\) 7.10459 0.343413
\(429\) 20.0404 + 5.23281i 0.967560 + 0.252642i
\(430\) 4.29996 0.207363
\(431\) 16.5858 28.7275i 0.798911 1.38375i −0.121415 0.992602i \(-0.538743\pi\)
0.920326 0.391153i \(-0.127924\pi\)
\(432\) −9.90159 4.77810i −0.476391 0.229886i
\(433\) −3.58780 6.21425i −0.172419 0.298638i 0.766846 0.641831i \(-0.221825\pi\)
−0.939265 + 0.343193i \(0.888491\pi\)
\(434\) 10.7271i 0.514916i
\(435\) −1.82157 + 0.0449420i −0.0873374 + 0.00215481i
\(436\) 12.1755 7.02951i 0.583100 0.336653i
\(437\) −0.329331 −0.0157540
\(438\) −9.32070 + 0.229962i −0.445360 + 0.0109880i
\(439\) −28.5542 16.4858i −1.36282 0.786824i −0.372821 0.927903i \(-0.621609\pi\)
−0.989998 + 0.141080i \(0.954943\pi\)
\(440\) −8.92200 + 3.18956i −0.425340 + 0.152056i
\(441\) 7.91322 + 12.2664i 0.376820 + 0.584113i
\(442\) −8.19134 + 3.69528i −0.389622 + 0.175766i
\(443\) 19.5140i 0.927138i 0.886061 + 0.463569i \(0.153431\pi\)
−0.886061 + 0.463569i \(0.846569\pi\)
\(444\) −8.00043 + 4.88604i −0.379684 + 0.231881i
\(445\) −5.56536 + 9.63948i −0.263823 + 0.456955i
\(446\) 4.64830 + 8.05110i 0.220104 + 0.381231i
\(447\) 15.2110 + 8.28871i 0.719455 + 0.392043i
\(448\) 10.7568 6.21044i 0.508211 0.293416i
\(449\) −17.5197 + 10.1150i −0.826807 + 0.477357i −0.852758 0.522306i \(-0.825072\pi\)
0.0259510 + 0.999663i \(0.491739\pi\)
\(450\) 7.67960 + 11.9042i 0.362020 + 0.561172i
\(451\) 10.6633 + 1.94331i 0.502117 + 0.0915069i
\(452\) 10.2456 + 5.91530i 0.481913 + 0.278232i
\(453\) 9.46830 + 15.5035i 0.444859 + 0.728416i
\(454\) −29.6301 −1.39061
\(455\) −3.96848 2.85363i −0.186045 0.133780i
\(456\) −2.51407 + 4.61369i −0.117732 + 0.216056i
\(457\) 25.3479 + 14.6346i 1.18573 + 0.684579i 0.957332 0.288990i \(-0.0933194\pi\)
0.228394 + 0.973569i \(0.426653\pi\)
\(458\) −0.398757 + 0.690667i −0.0186327 + 0.0322727i
\(459\) 9.38369 6.38672i 0.437993 0.298107i
\(460\) −0.216571 −0.0100977
\(461\) −4.44578 7.70032i −0.207061 0.358640i 0.743727 0.668484i \(-0.233056\pi\)
−0.950787 + 0.309844i \(0.899723\pi\)
\(462\) −6.01463 + 7.45001i −0.279826 + 0.346606i
\(463\) 14.9512 0.694841 0.347421 0.937709i \(-0.387058\pi\)
0.347421 + 0.937709i \(0.387058\pi\)
\(464\) −1.19931 2.07726i −0.0556765 0.0964344i
\(465\) 5.39155 + 8.82815i 0.250027 + 0.409396i
\(466\) −0.640053 + 1.10860i −0.0296499 + 0.0513551i
\(467\) 18.2674i 0.845315i 0.906289 + 0.422658i \(0.138903\pi\)
−0.906289 + 0.422658i \(0.861097\pi\)
\(468\) 6.72340 3.44169i 0.310789 0.159092i
\(469\) 6.34705i 0.293079i
\(470\) −0.467359 + 0.809490i −0.0215577 + 0.0373390i
\(471\) −31.8325 + 19.4408i −1.46676 + 0.895785i
\(472\) −1.32084 + 0.762587i −0.0607965 + 0.0351009i
\(473\) 10.2688 + 8.71732i 0.472160 + 0.400823i
\(474\) 11.0835 0.273454i 0.509082 0.0125602i
\(475\) 3.53193 2.03916i 0.162056 0.0935631i
\(476\) 2.22844i 0.102140i
\(477\) −10.9175 5.60443i −0.499879 0.256609i
\(478\) 11.3557 19.6686i 0.519397 0.899622i
\(479\) 0.382625 0.662726i 0.0174826 0.0302807i −0.857152 0.515064i \(-0.827768\pi\)
0.874634 + 0.484783i \(0.161101\pi\)
\(480\) −2.87871 + 5.28285i −0.131395 + 0.241128i
\(481\) −2.78479 + 27.8072i −0.126975 + 1.26790i
\(482\) 13.7182i 0.624847i
\(483\) −0.721736 + 0.440780i −0.0328401 + 0.0200562i
\(484\) −7.18732 2.70966i −0.326696 0.123166i
\(485\) −2.40931 + 1.39101i −0.109401 + 0.0631627i
\(486\) 14.1915 10.7200i 0.643740 0.486268i
\(487\) 15.8042 + 27.3737i 0.716157 + 1.24042i 0.962512 + 0.271240i \(0.0874338\pi\)
−0.246355 + 0.969180i \(0.579233\pi\)
\(488\) 31.8437 18.3850i 1.44150 0.832249i
\(489\) 0.341879 + 0.186296i 0.0154603 + 0.00842457i
\(490\) −4.46148 + 2.57583i −0.201549 + 0.116364i
\(491\) −18.2734 + 31.6505i −0.824669 + 1.42837i 0.0775032 + 0.996992i \(0.475305\pi\)
−0.902172 + 0.431376i \(0.858028\pi\)
\(492\) 3.37328 2.06014i 0.152079 0.0928781i
\(493\) 2.47645 0.111534
\(494\) 1.66685 + 3.69492i 0.0749953 + 0.166242i
\(495\) 1.20545 9.15421i 0.0541811 0.411451i
\(496\) −6.80856 + 11.7928i −0.305714 + 0.529511i
\(497\) −8.31098 + 14.3950i −0.372798 + 0.645706i
\(498\) −0.502001 20.3468i −0.0224952 0.911763i
\(499\) −5.55202 −0.248542 −0.124271 0.992248i \(-0.539659\pi\)
−0.124271 + 0.992248i \(0.539659\pi\)
\(500\) 5.12852 2.96095i 0.229354 0.132418i
\(501\) −0.0145029 0.587824i −0.000647941 0.0262620i
\(502\) 11.9077i 0.531468i
\(503\) −18.4675 31.9866i −0.823425 1.42621i −0.903117 0.429394i \(-0.858727\pi\)
0.0796920 0.996820i \(-0.474606\pi\)
\(504\) 0.665363 + 13.4759i 0.0296376 + 0.600263i
\(505\) −4.42038 2.55211i −0.196704 0.113567i
\(506\) 0.964138 + 0.818470i 0.0428612 + 0.0363854i
\(507\) 3.91945 22.1729i 0.174069 0.984734i
\(508\) 1.59888i 0.0709386i
\(509\) −14.2923 8.25165i −0.633494 0.365748i 0.148610 0.988896i \(-0.452520\pi\)
−0.782104 + 0.623148i \(0.785853\pi\)
\(510\) 2.08793 + 3.41879i 0.0924552 + 0.151387i
\(511\) 3.44628 + 5.96913i 0.152454 + 0.264059i
\(512\) −20.9471 −0.925739
\(513\) −2.88090 4.23276i −0.127195 0.186881i
\(514\) 2.59204 1.49652i 0.114330 0.0660085i
\(515\) 0.158789i 0.00699706i
\(516\) 4.91056 0.121154i 0.216175 0.00533352i
\(517\) −2.75719 + 0.985677i −0.121261 + 0.0433500i
\(518\) −11.1882 6.45950i −0.491581 0.283814i
\(519\) 37.9232 + 20.6649i 1.66464 + 0.907090i
\(520\) 4.23567 + 9.38922i 0.185746 + 0.411744i
\(521\) 33.1045i 1.45033i −0.688573 0.725167i \(-0.741762\pi\)
0.688573 0.725167i \(-0.258238\pi\)
\(522\) 3.87552 0.191352i 0.169627 0.00837524i
\(523\) 0.280617 + 0.162014i 0.0122705 + 0.00708438i 0.506123 0.862461i \(-0.331078\pi\)
−0.493852 + 0.869546i \(0.664412\pi\)
\(524\) −5.01201 8.68106i −0.218951 0.379234i
\(525\) 5.01107 9.19605i 0.218701 0.401348i
\(526\) −11.8557 20.5347i −0.516933 0.895354i
\(527\) −7.02951 12.1755i −0.306210 0.530371i
\(528\) 11.3407 4.37261i 0.493543 0.190293i
\(529\) −11.4441 19.8218i −0.497572 0.861819i
\(530\) 2.16550 3.75076i 0.0940634 0.162923i
\(531\) −0.0732939 1.48445i −0.00318069 0.0644197i
\(532\) 1.00520 0.0435808
\(533\) 1.17417 11.7246i 0.0508590 0.507847i
\(534\) 11.3416 20.8136i 0.490801 0.900690i
\(535\) −8.17662 4.72078i −0.353506 0.204097i
\(536\) 6.68758 11.5832i 0.288859 0.500319i
\(537\) 13.6658 0.337166i 0.589725 0.0145498i
\(538\) 13.7393i 0.592342i
\(539\) −15.8765 2.89337i −0.683850 0.124626i
\(540\) −1.89451 2.78351i −0.0815268 0.119783i
\(541\) 21.2252i 0.912544i −0.889840 0.456272i \(-0.849184\pi\)
0.889840 0.456272i \(-0.150816\pi\)
\(542\) 25.0863 14.4836i 1.07755 0.622122i
\(543\) 4.41282 2.69501i 0.189372 0.115654i
\(544\) 4.08837 7.08126i 0.175287 0.303606i
\(545\) −18.6836 −0.800315
\(546\) 8.59828 + 5.86658i 0.367973 + 0.251066i
\(547\) 7.35324i 0.314402i 0.987567 + 0.157201i \(0.0502470\pi\)
−0.987567 + 0.157201i \(0.949753\pi\)
\(548\) −4.29960 2.48237i −0.183670 0.106042i
\(549\) 1.76702 + 35.7882i 0.0754146 + 1.52740i
\(550\) −15.4078 2.80795i −0.656990 0.119731i
\(551\) 1.11707i 0.0475888i
\(552\) 1.78158 0.0439555i 0.0758292 0.00187087i
\(553\) −4.09807 7.09806i −0.174268 0.301840i
\(554\) 17.6957i 0.751818i
\(555\) 12.4542 0.307274i 0.528653 0.0130430i
\(556\) −12.2037 7.04582i −0.517553 0.298809i
\(557\) 17.0356 29.5065i 0.721820 1.25023i −0.238450 0.971155i \(-0.576639\pi\)
0.960270 0.279074i \(-0.0900274\pi\)
\(558\) −11.9416 18.5108i −0.505529 0.783626i
\(559\) 8.54895 11.8888i 0.361582 0.502845i
\(560\) −2.86837 −0.121211
\(561\) −1.94470 + 12.3973i −0.0821055 + 0.523416i
\(562\) −1.55472 + 2.69286i −0.0655821 + 0.113592i
\(563\) 16.0450 + 27.7907i 0.676215 + 1.17124i 0.976112 + 0.217267i \(0.0697142\pi\)
−0.299898 + 0.953971i \(0.596953\pi\)
\(564\) −0.510917 + 0.937607i −0.0215135 + 0.0394804i
\(565\) −7.86106 13.6157i −0.330717 0.572819i
\(566\) −12.8277 + 7.40607i −0.539188 + 0.311300i
\(567\) −11.9788 5.42037i −0.503060 0.227634i
\(568\) 30.3347 17.5138i 1.27282 0.734861i
\(569\) −15.4440 + 26.7497i −0.647445 + 1.12141i 0.336286 + 0.941760i \(0.390829\pi\)
−0.983731 + 0.179647i \(0.942504\pi\)
\(570\) 1.54214 0.941818i 0.0645931 0.0394484i
\(571\) 33.7922i 1.41416i −0.707134 0.707079i \(-0.750012\pi\)
0.707134 0.707079i \(-0.249988\pi\)
\(572\) −2.30827 + 8.02489i −0.0965135 + 0.335538i
\(573\) 17.6782 32.4420i 0.738516 1.35528i
\(574\) 4.71736 + 2.72357i 0.196899 + 0.113680i
\(575\) −1.19796 0.691644i −0.0499585 0.0288435i
\(576\) 11.6485 22.6915i 0.485355 0.945481i
\(577\) 32.5975 1.35705 0.678526 0.734576i \(-0.262619\pi\)
0.678526 + 0.734576i \(0.262619\pi\)
\(578\) 6.97563 + 12.0822i 0.290148 + 0.502551i
\(579\) 33.8120 0.834217i 1.40518 0.0346689i
\(580\) 0.734597i 0.0305025i
\(581\) −13.0304 + 7.52313i −0.540594 + 0.312112i
\(582\) 5.05605 3.08784i 0.209580 0.127995i
\(583\) 12.7754 4.56712i 0.529102 0.189151i
\(584\) 14.5247i 0.601037i
\(585\) −10.0248 0.506475i −0.414475 0.0209401i
\(586\) −34.5569 −1.42753
\(587\) 17.4298 + 10.0631i 0.719406 + 0.415349i 0.814534 0.580116i \(-0.196993\pi\)
−0.0951283 + 0.995465i \(0.530326\pi\)
\(588\) −5.02243 + 3.06731i −0.207122 + 0.126494i
\(589\) −5.49207 + 3.17085i −0.226297 + 0.130653i
\(590\) 0.524527 0.0215944
\(591\) 0.0869830 + 3.52555i 0.00357800 + 0.145022i
\(592\) 8.19980 + 14.2025i 0.337010 + 0.583718i
\(593\) 16.8279 0.691038 0.345519 0.938412i \(-0.387703\pi\)
0.345519 + 0.938412i \(0.387703\pi\)
\(594\) −2.08544 + 19.5515i −0.0855668 + 0.802207i
\(595\) 1.48073 2.56469i 0.0607039 0.105142i
\(596\) −3.49187 + 6.04810i −0.143033 + 0.247740i
\(597\) −1.50840 0.821954i −0.0617349 0.0336403i
\(598\) 0.802661 1.11624i 0.0328233 0.0456466i
\(599\) 28.3471i 1.15823i 0.815245 + 0.579116i \(0.196602\pi\)
−0.815245 + 0.579116i \(0.803398\pi\)
\(600\) −18.8345 + 11.5027i −0.768917 + 0.469594i
\(601\) −31.4831 18.1768i −1.28422 0.741447i −0.306607 0.951836i \(-0.599194\pi\)
−0.977618 + 0.210389i \(0.932527\pi\)
\(602\) 3.38467 + 5.86243i 0.137949 + 0.238935i
\(603\) 7.06567 + 10.9526i 0.287736 + 0.446024i
\(604\) −6.34254 + 3.66187i −0.258074 + 0.148999i
\(605\) 6.47135 + 7.89427i 0.263098 + 0.320948i
\(606\) 9.54447 + 5.20093i 0.387718 + 0.211274i
\(607\) −26.8179 + 15.4833i −1.08851 + 0.628449i −0.933178 0.359414i \(-0.882976\pi\)
−0.155327 + 0.987863i \(0.549643\pi\)
\(608\) −3.19419 1.84417i −0.129542 0.0747909i
\(609\) −1.49510 2.44809i −0.0605845 0.0992015i
\(610\) −12.6457 −0.512008
\(611\) 1.30896 + 2.90157i 0.0529548 + 0.117385i
\(612\) 2.48075 + 3.84544i 0.100278 + 0.155443i
\(613\) 0.00609717 + 0.00352020i 0.000246262 + 0.000142180i 0.500123 0.865954i \(-0.333288\pi\)
−0.499877 + 0.866096i \(0.666621\pi\)
\(614\) 26.5208 + 15.3118i 1.07029 + 0.617933i
\(615\) −5.25118 + 0.129558i −0.211748 + 0.00522428i
\(616\) −11.3714 9.65333i −0.458167 0.388944i
\(617\) 11.1686 6.44820i 0.449632 0.259595i −0.258043 0.966133i \(-0.583078\pi\)
0.707675 + 0.706539i \(0.249744\pi\)
\(618\) −0.00834020 0.338041i −0.000335492 0.0135980i
\(619\) −1.88578 −0.0757958 −0.0378979 0.999282i \(-0.512066\pi\)
−0.0378979 + 0.999282i \(0.512066\pi\)
\(620\) −3.61164 + 2.08518i −0.145047 + 0.0837429i
\(621\) −0.754755 + 1.56407i −0.0302873 + 0.0627640i
\(622\) −0.0881292 0.0508814i −0.00353366 0.00204016i
\(623\) −17.5229 −0.702039
\(624\) −5.72893 11.9068i −0.229341 0.476654i
\(625\) 12.8245 0.512979
\(626\) 2.54808 4.41340i 0.101842 0.176395i
\(627\) 5.59215 + 0.877211i 0.223329 + 0.0350324i
\(628\) −7.51874 13.0228i −0.300030 0.519668i
\(629\) −16.9318 −0.675114
\(630\) 2.11909 4.12803i 0.0844268 0.164465i
\(631\) 2.37182 + 4.10811i 0.0944205 + 0.163541i 0.909367 0.415996i \(-0.136567\pi\)
−0.814946 + 0.579537i \(0.803234\pi\)
\(632\) 17.2717i 0.687033i
\(633\) 33.1362 0.817541i 1.31704 0.0324943i
\(634\) 31.4404 + 18.1521i 1.24866 + 0.720914i
\(635\) −1.06240 + 1.84013i −0.0421601 + 0.0730235i
\(636\) 2.36732 4.34438i 0.0938705 0.172266i
\(637\) −1.74821 + 17.4565i −0.0692666 + 0.691653i
\(638\) −2.77620 + 3.27030i −0.109911 + 0.129472i
\(639\) 1.68329 + 34.0923i 0.0665898 + 1.34867i
\(640\) 1.77950 + 1.02740i 0.0703410 + 0.0406114i
\(641\) −17.9765 + 10.3787i −0.710030 + 0.409936i −0.811072 0.584946i \(-0.801116\pi\)
0.101042 + 0.994882i \(0.467782\pi\)
\(642\) 17.6550 + 9.62047i 0.696785 + 0.379689i
\(643\) −5.73014 9.92489i −0.225975 0.391400i 0.730637 0.682766i \(-0.239223\pi\)
−0.956611 + 0.291367i \(0.905890\pi\)
\(644\) −0.170472 0.295266i −0.00671753 0.0116351i
\(645\) −5.73203 3.12348i −0.225699 0.122987i
\(646\) −2.12686 + 1.22794i −0.0836802 + 0.0483128i
\(647\) −19.5067 11.2622i −0.766889 0.442763i 0.0648750 0.997893i \(-0.479335\pi\)
−0.831764 + 0.555130i \(0.812668\pi\)
\(648\) 16.1498 + 22.5135i 0.634424 + 0.884414i
\(649\) 1.25263 + 1.06337i 0.0491701 + 0.0417411i
\(650\) −1.69660 + 16.9412i −0.0665460 + 0.664488i
\(651\) −7.79211 + 14.2996i −0.305397 + 0.560447i
\(652\) −0.0784826 + 0.135936i −0.00307362 + 0.00532366i
\(653\) 31.2376 + 18.0350i 1.22242 + 0.705766i 0.965434 0.260648i \(-0.0839364\pi\)
0.256989 + 0.966414i \(0.417270\pi\)
\(654\) 39.7749 0.981334i 1.55532 0.0383732i
\(655\) 13.3213i 0.520506i
\(656\) −3.45734 5.98829i −0.134987 0.233803i
\(657\) 12.5919 + 6.46397i 0.491258 + 0.252183i
\(658\) −1.47151 −0.0573654
\(659\) 0.111070 + 0.192378i 0.00432666 + 0.00749400i 0.868181 0.496248i \(-0.165289\pi\)
−0.863854 + 0.503742i \(0.831956\pi\)
\(660\) 3.67746 + 0.576863i 0.143145 + 0.0224544i
\(661\) 19.1900 33.2380i 0.746403 1.29281i −0.203133 0.979151i \(-0.565112\pi\)
0.949536 0.313657i \(-0.101554\pi\)
\(662\) −29.0771 −1.13011
\(663\) 13.6036 + 1.02419i 0.528321 + 0.0397763i
\(664\) 31.7071 1.23047
\(665\) −1.15687 0.667922i −0.0448617 0.0259009i
\(666\) −26.4974 + 1.30829i −1.02675 + 0.0506953i
\(667\) −0.328127 + 0.189444i −0.0127051 + 0.00733532i
\(668\) 0.237056 0.00917198
\(669\) −0.348099 14.1090i −0.0134583 0.545484i
\(670\) −3.98363 + 2.29995i −0.153901 + 0.0888547i
\(671\) −30.1993 25.6366i −1.16583 0.989689i
\(672\) −9.46841 + 0.233606i −0.365252 + 0.00901156i
\(673\) −10.1639 5.86813i −0.391789 0.226200i 0.291146 0.956679i \(-0.405964\pi\)
−0.682935 + 0.730479i \(0.739297\pi\)
\(674\) −4.42365 2.55400i −0.170393 0.0983763i
\(675\) −1.59004 21.4473i −0.0612005 0.825507i
\(676\) 8.89742 + 1.80014i 0.342209 + 0.0692363i
\(677\) 14.4852 0.556713 0.278356 0.960478i \(-0.410210\pi\)
0.278356 + 0.960478i \(0.410210\pi\)
\(678\) 17.4503 + 28.5733i 0.670177 + 1.09735i
\(679\) −3.79292 2.18984i −0.145559 0.0840385i
\(680\) −5.40459 + 3.12034i −0.207257 + 0.119660i
\(681\) 39.4981 + 21.5232i 1.51357 + 0.824770i
\(682\) 23.9588 + 4.36630i 0.917429 + 0.167194i
\(683\) 10.7004 6.17790i 0.409441 0.236391i −0.281109 0.959676i \(-0.590702\pi\)
0.690550 + 0.723285i \(0.257369\pi\)
\(684\) 1.73459 1.11901i 0.0663236 0.0427863i
\(685\) 3.29892 + 5.71389i 0.126045 + 0.218317i
\(686\) −17.1279 9.88879i −0.653946 0.377556i
\(687\) 1.03326 0.631033i 0.0394212 0.0240754i
\(688\) 8.59312i 0.327610i
\(689\) −6.06503 13.4444i −0.231059 0.512190i
\(690\) −0.538181 0.293263i −0.0204882 0.0111643i
\(691\) 10.4899 18.1691i 0.399055 0.691183i −0.594555 0.804055i \(-0.702672\pi\)
0.993610 + 0.112872i \(0.0360049\pi\)
\(692\) −8.70573 + 15.0788i −0.330942 + 0.573209i
\(693\) 13.4294 5.56217i 0.510141 0.211289i
\(694\) 16.9311 0.642694
\(695\) 9.36344 + 16.2180i 0.355176 + 0.615182i
\(696\) 0.149095 + 6.04302i 0.00565141 + 0.229060i
\(697\) 7.13907 0.270412
\(698\) 10.8390 6.25788i 0.410261 0.236864i
\(699\) 1.65850 1.01288i 0.0627303 0.0383108i
\(700\) 3.65647 + 2.11107i 0.138202 + 0.0797908i
\(701\) 13.5912 0.513331 0.256666 0.966500i \(-0.417376\pi\)
0.256666 + 0.966500i \(0.417376\pi\)
\(702\) 21.3681 + 0.551678i 0.806489 + 0.0208217i
\(703\) 7.63753i 0.288055i
\(704\) 9.49253 + 26.5530i 0.357763 + 1.00075i
\(705\) 1.21102 0.739597i 0.0456097 0.0278548i
\(706\) −34.0615 + 19.6654i −1.28192 + 0.740119i
\(707\) 8.03546i 0.302204i
\(708\) 0.599010 0.0147789i 0.0225122 0.000555425i
\(709\) −18.3661 31.8110i −0.689753 1.19469i −0.971918 0.235321i \(-0.924386\pi\)
0.282164 0.959366i \(-0.408948\pi\)
\(710\) −12.0464 −0.452094
\(711\) −14.9734 7.68648i −0.561547 0.288266i
\(712\) 31.9788 + 18.4630i 1.19846 + 0.691930i
\(713\) 1.86280 + 1.07549i 0.0697626 + 0.0402774i
\(714\) −3.01757 + 5.53768i −0.112930 + 0.207243i
\(715\) 7.98885 7.70202i 0.298766 0.288039i
\(716\) 5.51113i 0.205960i
\(717\) −29.4248 + 17.9704i −1.09889 + 0.671116i
\(718\) 10.6489 18.4444i 0.397413 0.688339i
\(719\) −33.0241 + 19.0665i −1.23159 + 0.711059i −0.967361 0.253401i \(-0.918451\pi\)
−0.264229 + 0.964460i \(0.585118\pi\)
\(720\) −4.94972 + 3.19313i −0.184465 + 0.119001i
\(721\) −0.216487 + 0.124989i −0.00806240 + 0.00465483i
\(722\) −10.2849 17.8140i −0.382765 0.662968i
\(723\) 9.96484 18.2869i 0.370596 0.680098i
\(724\) 1.04229 + 1.80531i 0.0387366 + 0.0670937i
\(725\) 2.34602 4.06342i 0.0871288 0.150912i
\(726\) −14.1913 16.4660i −0.526689 0.611111i
\(727\) −1.65635 −0.0614305 −0.0307153 0.999528i \(-0.509779\pi\)
−0.0307153 + 0.999528i \(0.509779\pi\)
\(728\) −9.46688 + 13.1654i −0.350866 + 0.487942i
\(729\) −26.7048 + 3.98151i −0.989068 + 0.147463i
\(730\) −2.49762 + 4.32601i −0.0924411 + 0.160113i
\(731\) 7.68335 + 4.43599i 0.284179 + 0.164071i
\(732\) −14.4414 + 0.356300i −0.533768 + 0.0131692i
\(733\) 30.4682i 1.12537i −0.826672 0.562684i \(-0.809769\pi\)
0.826672 0.562684i \(-0.190231\pi\)
\(734\) −13.6510 23.6442i −0.503867 0.872724i
\(735\) 7.81841 0.192897i 0.288386 0.00711512i
\(736\) 1.25101i 0.0461129i
\(737\) −14.1760 2.58347i −0.522181 0.0951634i
\(738\) 11.1723 0.551625i 0.411258 0.0203056i
\(739\) 22.7806 + 13.1524i 0.837997 + 0.483818i 0.856583 0.516010i \(-0.172583\pi\)
−0.0185860 + 0.999827i \(0.505916\pi\)
\(740\) 5.02252i 0.184631i
\(741\) 0.461989 6.13628i 0.0169716 0.225422i
\(742\) 6.81821 0.250304
\(743\) −5.15860 + 8.93496i −0.189251 + 0.327792i −0.945001 0.327069i \(-0.893939\pi\)
0.755750 + 0.654860i \(0.227273\pi\)
\(744\) 29.2873 17.8864i 1.07372 0.655747i
\(745\) 8.03753 4.64047i 0.294472 0.170014i
\(746\) 4.96231i 0.181683i
\(747\) −14.1107 + 27.4878i −0.516282 + 1.00573i
\(748\) −4.97719 0.907054i −0.181984 0.0331652i
\(749\) 14.8636i 0.543106i
\(750\) 16.7539 0.413355i 0.611765 0.0150936i
\(751\) −1.29775 + 2.24777i −0.0473557 + 0.0820224i −0.888732 0.458428i \(-0.848413\pi\)
0.841376 + 0.540450i \(0.181746\pi\)
\(752\) 1.61770 + 0.933979i 0.0589914 + 0.0340587i
\(753\) −8.64973 + 15.8735i −0.315214 + 0.578463i
\(754\) 3.78623 + 2.72258i 0.137886 + 0.0991505i
\(755\) 9.73277 0.354212
\(756\) 2.30370 4.77393i 0.0837847 0.173626i
\(757\) −0.596083 + 1.03245i −0.0216650 + 0.0375249i −0.876655 0.481120i \(-0.840230\pi\)
0.854990 + 0.518645i \(0.173563\pi\)
\(758\) 17.1147 + 29.6436i 0.621635 + 1.07670i
\(759\) −0.690704 1.79140i −0.0250710 0.0650237i
\(760\) 1.40751 + 2.43789i 0.0510559 + 0.0884314i
\(761\) −16.4748 28.5353i −0.597213 1.03440i −0.993231 0.116160i \(-0.962941\pi\)
0.396018 0.918243i \(-0.370392\pi\)
\(762\) 2.16507 3.97321i 0.0784321 0.143934i
\(763\) −14.7066 25.4725i −0.532414 0.922167i
\(764\) 12.8994 + 7.44746i 0.466683 + 0.269440i
\(765\) −0.299903 6.07406i −0.0108430 0.219608i
\(766\) 23.8715i 0.862513i
\(767\) 1.04284 1.45025i 0.0376546 0.0523655i
\(768\) 22.0199 + 11.9990i 0.794575 + 0.432977i
\(769\) −0.297604 0.171822i −0.0107319 0.00619605i 0.494624 0.869107i \(-0.335306\pi\)
−0.505356 + 0.862911i \(0.668639\pi\)
\(770\) 1.72688 + 4.83051i 0.0622323 + 0.174080i
\(771\) −4.54237 + 0.112070i −0.163589 + 0.00403611i
\(772\) 13.6356i 0.490757i
\(773\) 23.1464 13.3636i 0.832518 0.480655i −0.0221959 0.999754i \(-0.507066\pi\)
0.854714 + 0.519099i \(0.173732\pi\)
\(774\) 12.3668 + 6.34842i 0.444517 + 0.228189i
\(775\) −26.6370 −0.956830
\(776\) 4.61467 + 7.99284i 0.165657 + 0.286926i
\(777\) 10.2222 + 16.7378i 0.366718 + 0.600467i
\(778\) 26.1792 + 15.1146i 0.938570 + 0.541884i
\(779\) 3.22027i 0.115378i
\(780\) 0.303809 4.03528i 0.0108781 0.144486i
\(781\) −28.7682 24.4217i −1.02941 0.873878i
\(782\) 0.721390 + 0.416495i 0.0257969 + 0.0148938i
\(783\) −5.30523 2.56009i −0.189594 0.0914900i
\(784\) 5.14759 + 8.91589i 0.183843 + 0.318425i
\(785\) 19.9838i 0.713254i
\(786\) −0.699687 28.3594i −0.0249570 1.01154i
\(787\) 23.0465 13.3059i 0.821519 0.474304i −0.0294211 0.999567i \(-0.509366\pi\)
0.850940 + 0.525263i \(0.176033\pi\)
\(788\) −1.42177 −0.0506486
\(789\) 0.887841 + 35.9855i 0.0316080 + 1.28112i
\(790\) 2.96999 5.14418i 0.105668 0.183022i
\(791\) 12.3755 21.4350i 0.440022 0.762141i
\(792\) −30.3690 3.99908i −1.07911 0.142101i
\(793\) −25.1414 + 34.9636i −0.892798 + 1.24160i
\(794\) 15.6872 0.556719
\(795\) −5.61124 + 3.42691i −0.199010 + 0.121540i
\(796\) 0.346273 0.599762i 0.0122733 0.0212580i
\(797\) −6.87213 + 3.96762i −0.243423 + 0.140540i −0.616749 0.787160i \(-0.711551\pi\)
0.373326 + 0.927700i \(0.378217\pi\)
\(798\) 2.49792 + 1.36116i 0.0884255 + 0.0481845i
\(799\) −1.67019 + 0.964287i −0.0590872 + 0.0341140i
\(800\) −7.74606 13.4166i −0.273864 0.474347i
\(801\) −30.2378 + 19.5068i −1.06840 + 0.689239i
\(802\) −23.6666 + 13.6639i −0.835695 + 0.482489i
\(803\) −14.7347 + 5.26757i −0.519977 + 0.185888i
\(804\) −4.48450 + 2.73878i −0.158156 + 0.0965894i
\(805\) 0.453093i 0.0159694i
\(806\) 2.63817 26.3431i 0.0929256 0.927898i
\(807\) 9.98014 18.3150i 0.351318 0.644719i
\(808\) −8.46658 + 14.6645i −0.297853 + 0.515897i
\(809\) 21.1995 36.7186i 0.745335 1.29096i −0.204702 0.978824i \(-0.565623\pi\)
0.950038 0.312135i \(-0.101044\pi\)
\(810\) −0.938667 9.48243i −0.0329814 0.333179i
\(811\) 2.68971i 0.0944484i 0.998884 + 0.0472242i \(0.0150375\pi\)
−0.998884 + 0.0472242i \(0.984962\pi\)
\(812\) 1.00152 0.578231i 0.0351466 0.0202919i
\(813\) −43.9618 + 1.08463i −1.54181 + 0.0380398i
\(814\) 18.9812 22.3594i 0.665290 0.783696i
\(815\) 0.180650 0.104298i 0.00632790 0.00365341i
\(816\) 6.83217 4.17256i 0.239174 0.146069i
\(817\) 2.00097 3.46578i 0.0700051 0.121252i
\(818\) 23.4977i 0.821577i
\(819\) −7.20041 14.0661i −0.251603 0.491511i
\(820\) 2.11768i 0.0739527i
\(821\) 8.84254 15.3157i 0.308607 0.534523i −0.669451 0.742856i \(-0.733471\pi\)
0.978058 + 0.208333i \(0.0668039\pi\)
\(822\) −7.32309 11.9909i −0.255422 0.418230i
\(823\) 2.04737 + 3.54615i 0.0713669 + 0.123611i 0.899501 0.436920i \(-0.143931\pi\)
−0.828134 + 0.560531i \(0.810597\pi\)
\(824\) 0.526779 0.0183512
\(825\) 18.4995 + 14.9353i 0.644072 + 0.519979i
\(826\) 0.412876 + 0.715123i 0.0143658 + 0.0248823i
\(827\) 18.0329 0.627066 0.313533 0.949577i \(-0.398487\pi\)
0.313533 + 0.949577i \(0.398487\pi\)
\(828\) −0.622866 0.319743i −0.0216461 0.0111118i
\(829\) −19.6934 + 34.1099i −0.683979 + 1.18469i 0.289778 + 0.957094i \(0.406419\pi\)
−0.973757 + 0.227592i \(0.926915\pi\)
\(830\) −9.44355 5.45224i −0.327790 0.189250i
\(831\) 12.8541 23.5891i 0.445903 0.818297i
\(832\) 27.9435 12.6059i 0.968766 0.437030i
\(833\) −10.6293 −0.368282
\(834\) −20.7854 34.0342i −0.719740 1.17851i
\(835\) −0.272826 0.157516i −0.00944153 0.00545107i
\(836\) −0.409151 + 2.24509i −0.0141508 + 0.0776482i
\(837\) 2.47247 + 33.3501i 0.0854611 + 1.15275i
\(838\) −25.1388 + 14.5139i −0.868407 + 0.501375i
\(839\) −47.9875 + 27.7056i −1.65671 + 0.956504i −0.682497 + 0.730888i \(0.739106\pi\)
−0.974216 + 0.225616i \(0.927561\pi\)
\(840\) 6.34750 + 3.45885i 0.219010 + 0.119342i
\(841\) 13.8574 + 24.0017i 0.477842 + 0.827646i
\(842\) −9.52235 + 16.4932i −0.328162 + 0.568393i
\(843\) 4.02860 2.46035i 0.138752 0.0847390i
\(844\) 13.3631i 0.459976i
\(845\) −9.04384 7.98382i −0.311118 0.274652i
\(846\) −2.53926 + 1.63812i −0.0873016 + 0.0563196i
\(847\) −5.66893 + 15.0367i −0.194787 + 0.516667i
\(848\) −7.49558 4.32757i −0.257399 0.148610i
\(849\) 22.4796 0.554620i 0.771497 0.0190345i
\(850\) −10.3155 −0.353817
\(851\) 2.24344 1.29525i 0.0769042 0.0444007i
\(852\) −13.7570 + 0.339416i −0.471308 + 0.0116282i
\(853\) 25.7157i 0.880488i 0.897878 + 0.440244i \(0.145108\pi\)
−0.897878 + 0.440244i \(0.854892\pi\)
\(854\) −9.95391 17.2407i −0.340616 0.589964i
\(855\) −2.73987 + 0.135279i −0.0937015 + 0.00462646i
\(856\) −15.6611 + 27.1258i −0.535286 + 0.927142i
\(857\) 53.1020 1.81393 0.906966 0.421205i \(-0.138393\pi\)
0.906966 + 0.421205i \(0.138393\pi\)
\(858\) −16.6027 + 16.8162i −0.566807 + 0.574097i
\(859\) −22.3863 −0.763812 −0.381906 0.924201i \(-0.624732\pi\)
−0.381906 + 0.924201i \(0.624732\pi\)
\(860\) 1.31586 2.27913i 0.0448704 0.0777179i
\(861\) −4.31005 7.05730i −0.146886 0.240512i
\(862\) 18.9232 + 32.7760i 0.644528 + 1.11635i
\(863\) 35.1190i 1.19547i −0.801695 0.597733i \(-0.796068\pi\)
0.801695 0.597733i \(-0.203932\pi\)
\(864\) −16.0788 + 10.9435i −0.547012 + 0.372307i
\(865\) 20.0387 11.5694i 0.681337 0.393370i
\(866\) 8.18683 0.278200
\(867\) −0.522386 21.1731i −0.0177412 0.719076i
\(868\) −5.68574 3.28266i −0.192986 0.111421i
\(869\) 17.5215 6.26381i 0.594375 0.212485i
\(870\) 0.994732 1.82548i 0.0337246 0.0618895i
\(871\) −1.56097 + 15.5868i −0.0528913 + 0.528140i
\(872\) 61.9824i 2.09899i
\(873\) −8.98291 + 0.443526i −0.304026 + 0.0150111i
\(874\) 0.187871 0.325402i 0.00635484 0.0110069i
\(875\) −6.19466 10.7295i −0.209418 0.362722i
\(876\) −2.73040 + 5.01067i −0.0922516 + 0.169295i
\(877\) −16.0175 + 9.24768i −0.540871 + 0.312272i −0.745432 0.666582i \(-0.767757\pi\)
0.204561 + 0.978854i \(0.434423\pi\)
\(878\) 32.5783 18.8091i 1.09946 0.634776i
\(879\) 46.0658 + 25.1020i 1.55376 + 0.846668i
\(880\) 1.16753 6.40647i 0.0393574 0.215962i
\(881\) −43.3756 25.0429i −1.46136 0.843718i −0.462288 0.886730i \(-0.652971\pi\)
−0.999075 + 0.0430115i \(0.986305\pi\)
\(882\) −16.6343 + 0.821308i −0.560105 + 0.0276549i
\(883\) 8.28310 0.278749 0.139374 0.990240i \(-0.455491\pi\)
0.139374 + 0.990240i \(0.455491\pi\)
\(884\) −0.548053 + 5.47252i −0.0184330 + 0.184061i
\(885\) −0.699217 0.381014i −0.0235039 0.0128077i
\(886\) −19.2812 11.1320i −0.647766 0.373988i
\(887\) 21.5798 37.3774i 0.724580 1.25501i −0.234566 0.972100i \(-0.575367\pi\)
0.959146 0.282910i \(-0.0912997\pi\)
\(888\) −1.01938 41.3168i −0.0342080 1.38650i
\(889\) −3.34503 −0.112189
\(890\) −6.34967 10.9979i −0.212841 0.368652i
\(891\) 16.9821 24.5481i 0.568922 0.822392i
\(892\) 5.68983 0.190510
\(893\) 0.434968 + 0.753386i 0.0145556 + 0.0252111i
\(894\) −16.8672 + 10.3011i −0.564122 + 0.344522i
\(895\) 3.66197 6.34271i 0.122406 0.212014i
\(896\) 3.23482i 0.108068i
\(897\) −1.88082 + 0.904950i −0.0627986 + 0.0302154i
\(898\) 23.0810i 0.770223i
\(899\) −3.64800 + 6.31852i −0.121668 + 0.210735i
\(900\) 8.65976 0.427571i 0.288659 0.0142524i
\(901\) 7.73881 4.46801i 0.257817 0.148851i
\(902\) −8.00318 + 9.42756i −0.266477 + 0.313903i
\(903\) −0.253469 10.2735i −0.00843492 0.341880i
\(904\) −45.1701 + 26.0789i −1.50233 + 0.867373i
\(905\) 2.77029i 0.0920874i
\(906\) −20.7198 + 0.511204i −0.688371 + 0.0169836i
\(907\) −19.0463 + 32.9892i −0.632422 + 1.09539i 0.354633 + 0.935005i \(0.384606\pi\)
−0.987055 + 0.160381i \(0.948728\pi\)
\(908\) −9.06729 + 15.7050i −0.300908 + 0.521189i
\(909\) −8.94524 13.8661i −0.296695 0.459910i
\(910\) 5.08347 2.29326i 0.168515 0.0760207i
\(911\) 15.8601i 0.525467i −0.964868 0.262734i \(-0.915376\pi\)
0.964868 0.262734i \(-0.0846240\pi\)
\(912\) −1.88214 3.08183i −0.0623240 0.102050i
\(913\) −11.4990 32.1655i −0.380560 1.06452i
\(914\) −28.9201 + 16.6970i −0.956593 + 0.552289i
\(915\) 16.8572 + 9.18576i 0.557282 + 0.303672i
\(916\) 0.244052 + 0.422711i 0.00806371 + 0.0139667i
\(917\) −18.1618 + 10.4857i −0.599756 + 0.346269i
\(918\) 0.957489 + 12.9152i 0.0316019 + 0.426264i
\(919\) 15.7894 9.11604i 0.520846 0.300710i −0.216435 0.976297i \(-0.569443\pi\)
0.737281 + 0.675587i \(0.236110\pi\)
\(920\) 0.477402 0.826884i 0.0157395 0.0272616i
\(921\) −24.2309 39.6758i −0.798435 1.30736i
\(922\) 10.1446 0.334095
\(923\) −23.9500 + 33.3068i −0.788325 + 1.09631i
\(924\) 2.10820 + 5.46779i 0.0693546 + 0.179877i
\(925\) −16.0400 + 27.7820i −0.527391 + 0.913467i
\(926\) −8.52912 + 14.7729i −0.280284 + 0.485466i
\(927\) −0.234434 + 0.456681i −0.00769981 + 0.0149994i
\(928\) −4.24336 −0.139295
\(929\) 10.5977 6.11859i 0.347700 0.200744i −0.315972 0.948769i \(-0.602331\pi\)
0.663672 + 0.748024i \(0.268997\pi\)
\(930\) −11.7985 + 0.291096i −0.386889 + 0.00954540i
\(931\) 4.79462i 0.157137i
\(932\) 0.391733 + 0.678502i 0.0128316 + 0.0222251i
\(933\) 0.0805198 + 0.131844i 0.00263610 + 0.00431637i
\(934\) −18.0495 10.4209i −0.590598 0.340982i
\(935\) 5.12550 + 4.35110i 0.167622 + 0.142296i
\(936\) −1.68022 + 33.2572i −0.0549198 + 1.08704i
\(937\) 9.67073i 0.315929i 0.987445 + 0.157964i \(0.0504931\pi\)
−0.987445 + 0.157964i \(0.949507\pi\)
\(938\) −6.27134 3.62076i −0.204767 0.118222i
\(939\) −6.60258 + 4.03234i −0.215467 + 0.131590i
\(940\) 0.286039 + 0.495434i 0.00932957 + 0.0161593i
\(941\) 33.9337 1.10621 0.553103 0.833113i \(-0.313444\pi\)
0.553103 + 0.833113i \(0.313444\pi\)
\(942\) −1.04963 42.5431i −0.0341988 1.38613i
\(943\) −0.945919 + 0.546127i −0.0308034 + 0.0177843i
\(944\) 1.04822i 0.0341168i
\(945\) −5.82343 + 3.96354i −0.189436 + 0.128934i
\(946\) −14.4713 + 5.17340i −0.470503 + 0.168202i
\(947\) −2.44723 1.41291i −0.0795244 0.0459134i 0.459711 0.888069i \(-0.347953\pi\)
−0.539235 + 0.842155i \(0.681286\pi\)
\(948\) 3.24679 5.95833i 0.105451 0.193518i
\(949\) 6.99522 + 15.5063i 0.227074 + 0.503357i
\(950\) 4.65307i 0.150965i
\(951\) −28.7258 47.0358i −0.931497 1.52524i
\(952\) −8.50834 4.91229i −0.275757 0.159208i
\(953\) −24.6226 42.6477i −0.797605 1.38149i −0.921172 0.389157i \(-0.872766\pi\)
0.123566 0.992336i \(-0.460567\pi\)
\(954\) 11.7656 7.59018i 0.380926 0.245741i
\(955\) −9.89720 17.1425i −0.320266 0.554717i
\(956\) −6.95005 12.0378i −0.224781 0.389332i
\(957\) 6.07632 2.34283i 0.196420 0.0757328i
\(958\) 0.436548 + 0.756123i 0.0141042 + 0.0244292i
\(959\) −5.19342 + 8.99527i −0.167704 + 0.290472i
\(960\) −7.12266 11.6627i −0.229883 0.376412i
\(961\) 10.4200 0.336128
\(962\) −25.8869 18.6146i −0.834627 0.600158i
\(963\) −16.5465 25.6490i −0.533204 0.826526i
\(964\) 7.27113 + 4.19799i 0.234187 + 0.135208i
\(965\) 9.06045 15.6932i 0.291666 0.505181i
\(966\) −0.0237982 0.964577i −0.000765695 0.0310347i
\(967\) 23.3248i 0.750077i −0.927009 0.375038i \(-0.877630\pi\)
0.927009 0.375038i \(-0.122370\pi\)
\(968\) 26.1891 21.4686i 0.841751 0.690027i
\(969\) 3.72717 0.0919573i 0.119734 0.00295410i
\(970\) 3.17409i 0.101914i
\(971\) 36.8305 21.2641i 1.18195 0.682398i 0.225484 0.974247i \(-0.427604\pi\)
0.956464 + 0.291849i \(0.0942704\pi\)
\(972\) −1.33913 10.8025i −0.0429527 0.346490i
\(973\) −14.7407 + 25.5316i −0.472564 + 0.818505i
\(974\) −36.0629 −1.15553
\(975\) 14.5676 21.3509i 0.466538 0.683776i
\(976\) 25.2713i 0.808915i
\(977\) −17.8953 10.3318i −0.572521 0.330545i 0.185635 0.982619i \(-0.440566\pi\)
−0.758156 + 0.652074i \(0.773899\pi\)
\(978\) −0.379103 + 0.231527i −0.0121224 + 0.00740340i
\(979\) 7.13242 39.1370i 0.227953 1.25083i
\(980\) 3.15299i 0.100719i
\(981\) −53.7345 27.5842i −1.71561 0.880695i
\(982\) −20.8487 36.1110i −0.665308 1.15235i
\(983\) 16.8674i 0.537987i −0.963142 0.268994i \(-0.913309\pi\)
0.963142 0.268994i \(-0.0866910\pi\)
\(984\) 0.429807 + 17.4207i 0.0137017 + 0.555352i
\(985\) 1.63631 + 0.944724i 0.0521371 + 0.0301014i
\(986\) −1.41273 + 2.44691i −0.0449904 + 0.0779256i
\(987\) 1.96158 + 1.06890i 0.0624379 + 0.0340234i
\(988\) 2.46853 + 0.247214i 0.0785343 + 0.00786492i
\(989\) −1.35738 −0.0431622
\(990\) 8.35736 + 6.41322i 0.265614 + 0.203826i
\(991\) 10.9943 19.0427i 0.349246 0.604912i −0.636870 0.770972i \(-0.719771\pi\)
0.986116 + 0.166059i \(0.0531044\pi\)
\(992\) 12.0449 + 20.8625i 0.382427 + 0.662384i
\(993\) 38.7610 + 21.1215i 1.23004 + 0.670270i
\(994\) −9.48222 16.4237i −0.300758 0.520928i
\(995\) −0.797046 + 0.460174i −0.0252680 + 0.0145885i
\(996\) −10.9382 5.96038i −0.346589 0.188862i
\(997\) 10.3297 5.96384i 0.327144 0.188877i −0.327428 0.944876i \(-0.606182\pi\)
0.654572 + 0.755999i \(0.272849\pi\)
\(998\) 3.16723 5.48579i 0.100257 0.173650i
\(999\) 36.2725 + 17.5036i 1.14761 + 0.553789i
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 429.2.p.b.230.18 yes 96
3.2 odd 2 inner 429.2.p.b.230.31 yes 96
11.10 odd 2 inner 429.2.p.b.230.32 yes 96
13.3 even 3 inner 429.2.p.b.263.17 yes 96
33.32 even 2 inner 429.2.p.b.230.17 96
39.29 odd 6 inner 429.2.p.b.263.32 yes 96
143.120 odd 6 inner 429.2.p.b.263.31 yes 96
429.263 even 6 inner 429.2.p.b.263.18 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.p.b.230.17 96 33.32 even 2 inner
429.2.p.b.230.18 yes 96 1.1 even 1 trivial
429.2.p.b.230.31 yes 96 3.2 odd 2 inner
429.2.p.b.230.32 yes 96 11.10 odd 2 inner
429.2.p.b.263.17 yes 96 13.3 even 3 inner
429.2.p.b.263.18 yes 96 429.263 even 6 inner
429.2.p.b.263.31 yes 96 143.120 odd 6 inner
429.2.p.b.263.32 yes 96 39.29 odd 6 inner