Properties

Label 126.3.r.a.11.7
Level $126$
Weight $3$
Character 126.11
Analytic conductor $3.433$
Analytic rank $0$
Dimension $32$
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] = [126,3,Mod(11,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.r (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: \(3.43325133094\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.7
Character \(\chi\) \(=\) 126.11
Dual form 126.3.r.a.23.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421i q^{2} +(2.36405 + 1.84696i) q^{3} -2.00000 q^{4} +(1.22482 + 0.707152i) q^{5} +(2.61199 - 3.34328i) q^{6} +(3.10205 - 6.27513i) q^{7} +2.82843i q^{8} +(2.17750 + 8.73261i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(2.36405 + 1.84696i) q^{3} -2.00000 q^{4} +(1.22482 + 0.707152i) q^{5} +(2.61199 - 3.34328i) q^{6} +(3.10205 - 6.27513i) q^{7} +2.82843i q^{8} +(2.17750 + 8.73261i) q^{9} +(1.00006 - 1.73216i) q^{10} +(15.1176 - 8.72813i) q^{11} +(-4.72811 - 3.69391i) q^{12} +(8.59030 + 14.8788i) q^{13} +(-8.87438 - 4.38696i) q^{14} +(1.58947 + 3.93394i) q^{15} +4.00000 q^{16} +(-20.8700 - 12.0493i) q^{17} +(12.3498 - 3.07945i) q^{18} +(11.7810 + 20.4053i) q^{19} +(-2.44965 - 1.41430i) q^{20} +(18.9233 - 9.10540i) q^{21} +(-12.3434 - 21.3795i) q^{22} +(-27.1025 - 15.6476i) q^{23} +(-5.22398 + 6.68655i) q^{24} +(-11.4999 - 19.9184i) q^{25} +(21.0419 - 12.1485i) q^{26} +(-10.9810 + 24.6661i) q^{27} +(-6.20409 + 12.5503i) q^{28} +(-13.7563 - 7.94218i) q^{29} +(5.56344 - 2.24785i) q^{30} -32.1938 q^{31} -5.65685i q^{32} +(51.8592 + 7.28773i) q^{33} +(-17.0403 + 29.5146i) q^{34} +(8.23694 - 5.49231i) q^{35} +(-4.35500 - 17.4652i) q^{36} +(15.7030 + 27.1985i) q^{37} +(28.8574 - 16.6608i) q^{38} +(-7.17265 + 51.0403i) q^{39} +(-2.00013 + 3.46433i) q^{40} +(8.67466 - 5.00832i) q^{41} +(-12.8770 - 26.7616i) q^{42} +(-31.6891 + 54.8871i) q^{43} +(-30.2351 + 17.4563i) q^{44} +(-3.50824 + 12.2357i) q^{45} +(-22.1291 + 38.3287i) q^{46} +4.27193i q^{47} +(9.45621 + 7.38783i) q^{48} +(-29.7546 - 38.9315i) q^{49} +(-28.1688 + 16.2633i) q^{50} +(-27.0832 - 67.0311i) q^{51} +(-17.1806 - 29.7577i) q^{52} +(-45.3154 - 26.1629i) q^{53} +(34.8831 + 15.5295i) q^{54} +24.6885 q^{55} +(17.7488 + 8.77391i) q^{56} +(-9.83677 + 69.9981i) q^{57} +(-11.2319 + 19.4543i) q^{58} +42.1881i q^{59} +(-3.17894 - 7.86789i) q^{60} -12.4785 q^{61} +45.5289i q^{62} +(61.5530 + 13.4249i) q^{63} -8.00000 q^{64} +24.2986i q^{65} +(10.3064 - 73.3400i) q^{66} +96.1382 q^{67} +(41.7399 + 24.0986i) q^{68} +(-35.1712 - 87.0489i) q^{69} +(-7.76730 - 11.6488i) q^{70} -20.8017i q^{71} +(-24.6996 + 6.15889i) q^{72} +(41.6824 - 72.1961i) q^{73} +(38.4644 - 22.2075i) q^{74} +(9.60205 - 68.3278i) q^{75} +(-23.5620 - 40.8105i) q^{76} +(-7.87478 - 121.940i) q^{77} +(72.1819 + 10.1437i) q^{78} -45.1639 q^{79} +(4.89930 + 2.82861i) q^{80} +(-71.5170 + 38.0305i) q^{81} +(-7.08283 - 12.2678i) q^{82} +(3.73381 + 2.15572i) q^{83} +(-37.8466 + 18.2108i) q^{84} +(-17.0414 - 29.5165i) q^{85} +(77.6221 + 44.8151i) q^{86} +(-17.8517 - 44.1830i) q^{87} +(24.6869 + 42.7589i) q^{88} +(123.803 - 71.4779i) q^{89} +(17.3039 + 4.96139i) q^{90} +(120.014 - 7.75043i) q^{91} +(54.2049 + 31.2952i) q^{92} +(-76.1079 - 59.4606i) q^{93} +6.04143 q^{94} +33.3238i q^{95} +(10.4480 - 13.3731i) q^{96} +(-17.5457 + 30.3901i) q^{97} +(-55.0575 + 42.0794i) q^{98} +(109.138 + 113.010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27} - 4 q^{28} + 36 q^{29} + 76 q^{30} + 16 q^{31} - 40 q^{33} - 90 q^{35} + 40 q^{36} + 22 q^{37} + 46 q^{39} + 72 q^{41} + 120 q^{42} + 16 q^{43} + 72 q^{44} + 464 q^{45} - 12 q^{46} + 2 q^{49} - 288 q^{50} - 286 q^{51} - 20 q^{52} - 72 q^{53} - 160 q^{54} - 24 q^{55} - 72 q^{56} - 282 q^{57} - 24 q^{58} - 20 q^{60} + 124 q^{61} + 66 q^{63} - 256 q^{64} - 16 q^{66} - 140 q^{67} + 108 q^{68} + 218 q^{69} + 72 q^{70} + 196 q^{73} + 216 q^{74} + 658 q^{75} - 56 q^{76} + 486 q^{77} + 32 q^{78} + 76 q^{79} - 380 q^{81} - 56 q^{84} + 60 q^{85} - 144 q^{86} - 740 q^{87} - 486 q^{89} + 296 q^{90} - 122 q^{91} + 252 q^{92} + 238 q^{93} - 336 q^{94} + 32 q^{96} - 38 q^{97} + 288 q^{98} + 394 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 2.36405 + 1.84696i 0.788018 + 0.615652i
\(4\) −2.00000 −0.500000
\(5\) 1.22482 + 0.707152i 0.244965 + 0.141430i 0.617456 0.786605i \(-0.288163\pi\)
−0.372492 + 0.928036i \(0.621496\pi\)
\(6\) 2.61199 3.34328i 0.435332 0.557213i
\(7\) 3.10205 6.27513i 0.443150 0.896448i
\(8\) 2.82843i 0.353553i
\(9\) 2.17750 + 8.73261i 0.241944 + 0.970290i
\(10\) 1.00006 1.73216i 0.100006 0.173216i
\(11\) 15.1176 8.72813i 1.37432 0.793466i 0.382855 0.923809i \(-0.374941\pi\)
0.991469 + 0.130343i \(0.0416077\pi\)
\(12\) −4.72811 3.69391i −0.394009 0.307826i
\(13\) 8.59030 + 14.8788i 0.660793 + 1.14453i 0.980408 + 0.196979i \(0.0631130\pi\)
−0.319615 + 0.947547i \(0.603554\pi\)
\(14\) −8.87438 4.38696i −0.633884 0.313354i
\(15\) 1.58947 + 3.93394i 0.105965 + 0.262263i
\(16\) 4.00000 0.250000
\(17\) −20.8700 12.0493i −1.22765 0.708781i −0.261109 0.965309i \(-0.584088\pi\)
−0.966537 + 0.256528i \(0.917421\pi\)
\(18\) 12.3498 3.07945i 0.686099 0.171080i
\(19\) 11.7810 + 20.4053i 0.620051 + 1.07396i 0.989476 + 0.144700i \(0.0462216\pi\)
−0.369424 + 0.929261i \(0.620445\pi\)
\(20\) −2.44965 1.41430i −0.122482 0.0707152i
\(21\) 18.9233 9.10540i 0.901110 0.433591i
\(22\) −12.3434 21.3795i −0.561065 0.971794i
\(23\) −27.1025 15.6476i −1.17837 0.680331i −0.222731 0.974880i \(-0.571497\pi\)
−0.955636 + 0.294549i \(0.904831\pi\)
\(24\) −5.22398 + 6.68655i −0.217666 + 0.278606i
\(25\) −11.4999 19.9184i −0.459995 0.796734i
\(26\) 21.0419 12.1485i 0.809302 0.467251i
\(27\) −10.9810 + 24.6661i −0.406705 + 0.913560i
\(28\) −6.20409 + 12.5503i −0.221575 + 0.448224i
\(29\) −13.7563 7.94218i −0.474354 0.273868i 0.243707 0.969849i \(-0.421637\pi\)
−0.718061 + 0.695981i \(0.754970\pi\)
\(30\) 5.56344 2.24785i 0.185448 0.0749283i
\(31\) −32.1938 −1.03851 −0.519255 0.854619i \(-0.673791\pi\)
−0.519255 + 0.854619i \(0.673791\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 51.8592 + 7.28773i 1.57149 + 0.220840i
\(34\) −17.0403 + 29.5146i −0.501184 + 0.868076i
\(35\) 8.23694 5.49231i 0.235341 0.156923i
\(36\) −4.35500 17.4652i −0.120972 0.485145i
\(37\) 15.7030 + 27.1985i 0.424407 + 0.735094i 0.996365 0.0851890i \(-0.0271494\pi\)
−0.571958 + 0.820283i \(0.693816\pi\)
\(38\) 28.8574 16.6608i 0.759405 0.438443i
\(39\) −7.17265 + 51.0403i −0.183914 + 1.30873i
\(40\) −2.00013 + 3.46433i −0.0500032 + 0.0866081i
\(41\) 8.67466 5.00832i 0.211577 0.122154i −0.390467 0.920617i \(-0.627686\pi\)
0.602044 + 0.798463i \(0.294353\pi\)
\(42\) −12.8770 26.7616i −0.306595 0.637181i
\(43\) −31.6891 + 54.8871i −0.736956 + 1.27644i 0.216904 + 0.976193i \(0.430404\pi\)
−0.953860 + 0.300252i \(0.902929\pi\)
\(44\) −30.2351 + 17.4563i −0.687162 + 0.396733i
\(45\) −3.50824 + 12.2357i −0.0779608 + 0.271905i
\(46\) −22.1291 + 38.3287i −0.481067 + 0.833232i
\(47\) 4.27193i 0.0908922i 0.998967 + 0.0454461i \(0.0144709\pi\)
−0.998967 + 0.0454461i \(0.985529\pi\)
\(48\) 9.45621 + 7.38783i 0.197004 + 0.153913i
\(49\) −29.7546 38.9315i −0.607237 0.794521i
\(50\) −28.1688 + 16.2633i −0.563376 + 0.325265i
\(51\) −27.0832 67.0311i −0.531044 1.31434i
\(52\) −17.1806 29.7577i −0.330396 0.572263i
\(53\) −45.3154 26.1629i −0.855008 0.493639i 0.00732944 0.999973i \(-0.497667\pi\)
−0.862337 + 0.506334i \(0.831000\pi\)
\(54\) 34.8831 + 15.5295i 0.645984 + 0.287584i
\(55\) 24.6885 0.448881
\(56\) 17.7488 + 8.77391i 0.316942 + 0.156677i
\(57\) −9.83677 + 69.9981i −0.172575 + 1.22804i
\(58\) −11.2319 + 19.4543i −0.193654 + 0.335419i
\(59\) 42.1881i 0.715053i 0.933903 + 0.357527i \(0.116380\pi\)
−0.933903 + 0.357527i \(0.883620\pi\)
\(60\) −3.17894 7.86789i −0.0529823 0.131131i
\(61\) −12.4785 −0.204565 −0.102282 0.994755i \(-0.532615\pi\)
−0.102282 + 0.994755i \(0.532615\pi\)
\(62\) 45.5289i 0.734338i
\(63\) 61.5530 + 13.4249i 0.977032 + 0.213093i
\(64\) −8.00000 −0.125000
\(65\) 24.2986i 0.373825i
\(66\) 10.3064 73.3400i 0.156158 1.11121i
\(67\) 96.1382 1.43490 0.717449 0.696611i \(-0.245310\pi\)
0.717449 + 0.696611i \(0.245310\pi\)
\(68\) 41.7399 + 24.0986i 0.613823 + 0.354391i
\(69\) −35.1712 87.0489i −0.509727 1.26158i
\(70\) −7.76730 11.6488i −0.110961 0.166411i
\(71\) 20.8017i 0.292982i −0.989212 0.146491i \(-0.953202\pi\)
0.989212 0.146491i \(-0.0467980\pi\)
\(72\) −24.6996 + 6.15889i −0.343049 + 0.0855402i
\(73\) 41.6824 72.1961i 0.570992 0.988987i −0.425472 0.904971i \(-0.639892\pi\)
0.996464 0.0840158i \(-0.0267746\pi\)
\(74\) 38.4644 22.2075i 0.519790 0.300101i
\(75\) 9.60205 68.3278i 0.128027 0.911038i
\(76\) −23.5620 40.8105i −0.310026 0.536980i
\(77\) −7.87478 121.940i −0.102270 1.58363i
\(78\) 72.1819 + 10.1437i 0.925409 + 0.130047i
\(79\) −45.1639 −0.571695 −0.285848 0.958275i \(-0.592275\pi\)
−0.285848 + 0.958275i \(0.592275\pi\)
\(80\) 4.89930 + 2.82861i 0.0612412 + 0.0353576i
\(81\) −71.5170 + 38.0305i −0.882926 + 0.469512i
\(82\) −7.08283 12.2678i −0.0863760 0.149608i
\(83\) 3.73381 + 2.15572i 0.0449856 + 0.0259725i 0.522324 0.852747i \(-0.325065\pi\)
−0.477339 + 0.878719i \(0.658398\pi\)
\(84\) −37.8466 + 18.2108i −0.450555 + 0.216795i
\(85\) −17.0414 29.5165i −0.200487 0.347253i
\(86\) 77.6221 + 44.8151i 0.902583 + 0.521106i
\(87\) −17.8517 44.1830i −0.205192 0.507850i
\(88\) 24.6869 + 42.7589i 0.280533 + 0.485897i
\(89\) 123.803 71.4779i 1.39105 0.803122i 0.397617 0.917552i \(-0.369837\pi\)
0.993431 + 0.114430i \(0.0365041\pi\)
\(90\) 17.3039 + 4.96139i 0.192266 + 0.0551266i
\(91\) 120.014 7.75043i 1.31884 0.0851696i
\(92\) 54.2049 + 31.2952i 0.589184 + 0.340165i
\(93\) −76.1079 59.4606i −0.818365 0.639361i
\(94\) 6.04143 0.0642705
\(95\) 33.3238i 0.350777i
\(96\) 10.4480 13.3731i 0.108833 0.139303i
\(97\) −17.5457 + 30.3901i −0.180884 + 0.313300i −0.942182 0.335102i \(-0.891229\pi\)
0.761298 + 0.648402i \(0.224562\pi\)
\(98\) −55.0575 + 42.0794i −0.561811 + 0.429381i
\(99\) 109.138 + 113.010i 1.10240 + 1.14152i
\(100\) 22.9997 + 39.8367i 0.229997 + 0.398367i
\(101\) −35.9483 + 20.7548i −0.355924 + 0.205493i −0.667291 0.744797i \(-0.732546\pi\)
0.311367 + 0.950290i \(0.399213\pi\)
\(102\) −94.7963 + 38.3015i −0.929375 + 0.375504i
\(103\) 16.9344 29.3312i 0.164412 0.284769i −0.772035 0.635580i \(-0.780761\pi\)
0.936446 + 0.350811i \(0.114094\pi\)
\(104\) −42.0837 + 24.2970i −0.404651 + 0.233625i
\(105\) 29.6166 + 2.22915i 0.282063 + 0.0212300i
\(106\) −36.9999 + 64.0857i −0.349056 + 0.604582i
\(107\) −39.7440 + 22.9462i −0.371439 + 0.214450i −0.674087 0.738652i \(-0.735463\pi\)
0.302648 + 0.953102i \(0.402129\pi\)
\(108\) 21.9621 49.3322i 0.203353 0.456780i
\(109\) 21.6535 37.5049i 0.198656 0.344082i −0.749437 0.662075i \(-0.769676\pi\)
0.948093 + 0.317994i \(0.103009\pi\)
\(110\) 34.9148i 0.317407i
\(111\) −13.1116 + 93.3015i −0.118122 + 0.840554i
\(112\) 12.4082 25.1005i 0.110787 0.224112i
\(113\) −78.3902 + 45.2586i −0.693719 + 0.400519i −0.805004 0.593270i \(-0.797837\pi\)
0.111285 + 0.993789i \(0.464503\pi\)
\(114\) 98.9922 + 13.9113i 0.868353 + 0.122029i
\(115\) −22.1305 38.3311i −0.192439 0.333314i
\(116\) 27.5125 + 15.8844i 0.237177 + 0.136934i
\(117\) −111.226 + 107.414i −0.950648 + 0.918072i
\(118\) 59.6630 0.505619
\(119\) −140.351 + 93.5844i −1.17942 + 0.786424i
\(120\) −11.1269 + 4.49570i −0.0927239 + 0.0374641i
\(121\) 91.8604 159.107i 0.759177 1.31493i
\(122\) 17.6472i 0.144649i
\(123\) 29.7575 + 4.18180i 0.241931 + 0.0339983i
\(124\) 64.3877 0.519255
\(125\) 67.8863i 0.543090i
\(126\) 18.9856 87.0491i 0.150680 0.690866i
\(127\) −135.543 −1.06727 −0.533635 0.845715i \(-0.679174\pi\)
−0.533635 + 0.845715i \(0.679174\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −176.289 + 71.2277i −1.36658 + 0.552153i
\(130\) 34.3634 0.264334
\(131\) 192.988 + 111.422i 1.47319 + 0.850546i 0.999545 0.0301696i \(-0.00960475\pi\)
0.473645 + 0.880716i \(0.342938\pi\)
\(132\) −103.718 14.5755i −0.785745 0.110420i
\(133\) 164.591 10.6292i 1.23753 0.0799185i
\(134\) 135.960i 1.01463i
\(135\) −30.8925 + 22.4464i −0.228834 + 0.166269i
\(136\) 34.0805 59.0292i 0.250592 0.434038i
\(137\) −74.8448 + 43.2117i −0.546313 + 0.315414i −0.747633 0.664112i \(-0.768810\pi\)
0.201321 + 0.979525i \(0.435477\pi\)
\(138\) −123.106 + 49.7396i −0.892070 + 0.360432i
\(139\) 1.61343 + 2.79455i 0.0116074 + 0.0201047i 0.871771 0.489914i \(-0.162972\pi\)
−0.860163 + 0.510019i \(0.829638\pi\)
\(140\) −16.4739 + 10.9846i −0.117671 + 0.0784616i
\(141\) −7.89008 + 10.0991i −0.0559580 + 0.0716247i
\(142\) −29.4181 −0.207170
\(143\) 259.729 + 149.955i 1.81629 + 1.04863i
\(144\) 8.70999 + 34.9304i 0.0604861 + 0.242573i
\(145\) −11.2327 19.4555i −0.0774667 0.134176i
\(146\) −102.101 58.9478i −0.699320 0.403752i
\(147\) 1.56337 146.992i 0.0106352 0.999943i
\(148\) −31.4061 54.3969i −0.212203 0.367547i
\(149\) −169.581 97.9078i −1.13813 0.657100i −0.192163 0.981363i \(-0.561550\pi\)
−0.945967 + 0.324264i \(0.894884\pi\)
\(150\) −96.6302 13.5793i −0.644201 0.0905290i
\(151\) 15.7499 + 27.2796i 0.104304 + 0.180659i 0.913454 0.406943i \(-0.133405\pi\)
−0.809150 + 0.587602i \(0.800072\pi\)
\(152\) −57.7148 + 33.3216i −0.379702 + 0.219221i
\(153\) 59.7774 208.487i 0.390702 1.36266i
\(154\) −172.449 + 11.1366i −1.11980 + 0.0723157i
\(155\) −39.4318 22.7659i −0.254399 0.146877i
\(156\) 14.3453 102.081i 0.0919570 0.654363i
\(157\) 89.3761 0.569274 0.284637 0.958635i \(-0.408127\pi\)
0.284637 + 0.958635i \(0.408127\pi\)
\(158\) 63.8714i 0.404249i
\(159\) −58.8064 145.546i −0.369851 0.915384i
\(160\) 4.00026 6.92865i 0.0250016 0.0433041i
\(161\) −182.264 + 121.532i −1.13207 + 0.754857i
\(162\) 53.7832 + 101.140i 0.331995 + 0.624323i
\(163\) 105.258 + 182.312i 0.645755 + 1.11848i 0.984127 + 0.177467i \(0.0567904\pi\)
−0.338372 + 0.941012i \(0.609876\pi\)
\(164\) −17.3493 + 10.0166i −0.105789 + 0.0610770i
\(165\) 58.3649 + 45.5985i 0.353726 + 0.276355i
\(166\) 3.04864 5.28040i 0.0183653 0.0318097i
\(167\) 97.8810 56.5116i 0.586114 0.338393i −0.177446 0.984131i \(-0.556783\pi\)
0.763559 + 0.645738i \(0.223450\pi\)
\(168\) 25.7540 + 53.5232i 0.153297 + 0.318590i
\(169\) −63.0866 + 109.269i −0.373294 + 0.646564i
\(170\) −41.7426 + 24.1001i −0.245545 + 0.141765i
\(171\) −152.538 + 147.311i −0.892036 + 0.861468i
\(172\) 63.3782 109.774i 0.368478 0.638222i
\(173\) 51.8246i 0.299564i 0.988719 + 0.149782i \(0.0478572\pi\)
−0.988719 + 0.149782i \(0.952143\pi\)
\(174\) −62.4842 + 25.2461i −0.359104 + 0.145092i
\(175\) −160.664 + 10.3755i −0.918077 + 0.0592888i
\(176\) 60.4702 34.9125i 0.343581 0.198367i
\(177\) −77.9197 + 99.7350i −0.440224 + 0.563475i
\(178\) −101.085 175.084i −0.567893 0.983620i
\(179\) 167.471 + 96.6894i 0.935592 + 0.540164i 0.888576 0.458730i \(-0.151695\pi\)
0.0470161 + 0.998894i \(0.485029\pi\)
\(180\) 7.01647 24.4715i 0.0389804 0.135953i
\(181\) 175.825 0.971411 0.485705 0.874123i \(-0.338563\pi\)
0.485705 + 0.874123i \(0.338563\pi\)
\(182\) −10.9608 169.726i −0.0602240 0.932559i
\(183\) −29.4997 23.0472i −0.161201 0.125941i
\(184\) 44.2581 76.6573i 0.240533 0.416616i
\(185\) 44.4178i 0.240096i
\(186\) −84.0900 + 107.633i −0.452097 + 0.578671i
\(187\) −420.671 −2.24958
\(188\) 8.54387i 0.0454461i
\(189\) 120.719 + 145.423i 0.638727 + 0.769433i
\(190\) 47.1270 0.248037
\(191\) 23.2901i 0.121938i −0.998140 0.0609690i \(-0.980581\pi\)
0.998140 0.0609690i \(-0.0194191\pi\)
\(192\) −18.9124 14.7757i −0.0985022 0.0769566i
\(193\) 84.8341 0.439555 0.219777 0.975550i \(-0.429467\pi\)
0.219777 + 0.975550i \(0.429467\pi\)
\(194\) 42.9780 + 24.8134i 0.221536 + 0.127904i
\(195\) −44.8785 + 57.4432i −0.230146 + 0.294581i
\(196\) 59.5092 + 77.8630i 0.303618 + 0.397260i
\(197\) 153.183i 0.777579i −0.921327 0.388789i \(-0.872893\pi\)
0.921327 0.388789i \(-0.127107\pi\)
\(198\) 159.821 154.344i 0.807175 0.779516i
\(199\) 0.561812 0.973087i 0.00282317 0.00488988i −0.864610 0.502443i \(-0.832435\pi\)
0.867434 + 0.497553i \(0.165768\pi\)
\(200\) 56.3376 32.5265i 0.281688 0.162633i
\(201\) 227.276 + 177.563i 1.13073 + 0.883399i
\(202\) 29.3517 + 50.8386i 0.145305 + 0.251676i
\(203\) −92.5108 + 61.6854i −0.455718 + 0.303869i
\(204\) 54.1664 + 134.062i 0.265522 + 0.657168i
\(205\) 14.1666 0.0691053
\(206\) −41.4806 23.9488i −0.201362 0.116257i
\(207\) 77.6290 270.748i 0.375019 1.30796i
\(208\) 34.3612 + 59.5154i 0.165198 + 0.286132i
\(209\) 356.199 + 205.652i 1.70430 + 0.983980i
\(210\) 3.15249 41.8842i 0.0150119 0.199449i
\(211\) −78.9195 136.693i −0.374026 0.647832i 0.616155 0.787625i \(-0.288690\pi\)
−0.990181 + 0.139793i \(0.955356\pi\)
\(212\) 90.6308 + 52.3257i 0.427504 + 0.246820i
\(213\) 38.4199 49.1764i 0.180375 0.230875i
\(214\) 32.4508 + 56.2064i 0.151639 + 0.262647i
\(215\) −77.6271 + 44.8180i −0.361056 + 0.208456i
\(216\) −69.7663 31.0591i −0.322992 0.143792i
\(217\) −99.8668 + 202.021i −0.460215 + 0.930970i
\(218\) −53.0399 30.6226i −0.243302 0.140471i
\(219\) 231.883 93.6897i 1.05882 0.427807i
\(220\) −49.3769 −0.224441
\(221\) 414.028i 1.87343i
\(222\) 131.948 + 18.5426i 0.594361 + 0.0835251i
\(223\) 52.8284 91.5014i 0.236899 0.410320i −0.722924 0.690927i \(-0.757202\pi\)
0.959823 + 0.280607i \(0.0905358\pi\)
\(224\) −35.4975 17.5478i −0.158471 0.0783385i
\(225\) 148.898 143.796i 0.661770 0.639094i
\(226\) 64.0053 + 110.860i 0.283209 + 0.490533i
\(227\) 52.0479 30.0498i 0.229286 0.132378i −0.380957 0.924593i \(-0.624405\pi\)
0.610243 + 0.792215i \(0.291072\pi\)
\(228\) 19.6735 139.996i 0.0862874 0.614018i
\(229\) −25.5005 + 44.1681i −0.111356 + 0.192874i −0.916317 0.400453i \(-0.868853\pi\)
0.804961 + 0.593327i \(0.202186\pi\)
\(230\) −54.2084 + 31.2972i −0.235689 + 0.136075i
\(231\) 206.601 302.817i 0.894377 1.31089i
\(232\) 22.4639 38.9086i 0.0968271 0.167709i
\(233\) 19.7391 11.3964i 0.0847171 0.0489114i −0.457043 0.889445i \(-0.651091\pi\)
0.541760 + 0.840533i \(0.317758\pi\)
\(234\) 151.907 + 157.297i 0.649175 + 0.672209i
\(235\) −3.02091 + 5.23237i −0.0128549 + 0.0222654i
\(236\) 84.3763i 0.357527i
\(237\) −106.770 83.4158i −0.450506 0.351965i
\(238\) 132.348 + 198.486i 0.556086 + 0.833973i
\(239\) 350.226 202.203i 1.46538 0.846039i 0.466131 0.884716i \(-0.345648\pi\)
0.999252 + 0.0386769i \(0.0123143\pi\)
\(240\) 6.35788 + 15.7358i 0.0264912 + 0.0655657i
\(241\) 151.820 + 262.961i 0.629961 + 1.09112i 0.987559 + 0.157248i \(0.0502623\pi\)
−0.357599 + 0.933875i \(0.616404\pi\)
\(242\) −225.011 129.910i −0.929798 0.536819i
\(243\) −239.311 42.1827i −0.984818 0.173591i
\(244\) 24.9569 0.102282
\(245\) −8.91364 68.7253i −0.0363822 0.280511i
\(246\) 5.91395 42.0835i 0.0240405 0.171071i
\(247\) −202.404 + 350.575i −0.819451 + 1.41933i
\(248\) 91.0579i 0.367169i
\(249\) 4.84541 + 11.9924i 0.0194595 + 0.0481623i
\(250\) −96.0057 −0.384023
\(251\) 233.378i 0.929793i 0.885365 + 0.464897i \(0.153908\pi\)
−0.885365 + 0.464897i \(0.846092\pi\)
\(252\) −123.106 26.8498i −0.488516 0.106547i
\(253\) −546.297 −2.15928
\(254\) 191.687i 0.754674i
\(255\) 14.2290 101.253i 0.0558001 0.397072i
\(256\) 16.0000 0.0625000
\(257\) −163.518 94.4073i −0.636258 0.367344i 0.146914 0.989149i \(-0.453066\pi\)
−0.783172 + 0.621806i \(0.786399\pi\)
\(258\) 100.731 + 249.310i 0.390431 + 0.966318i
\(259\) 219.386 14.1678i 0.847049 0.0547018i
\(260\) 48.5972i 0.186912i
\(261\) 39.4018 137.422i 0.150965 0.526522i
\(262\) 157.574 272.926i 0.601427 1.04170i
\(263\) −154.166 + 89.0076i −0.586181 + 0.338432i −0.763586 0.645706i \(-0.776563\pi\)
0.177405 + 0.984138i \(0.443230\pi\)
\(264\) −20.6128 + 146.680i −0.0780788 + 0.555606i
\(265\) −37.0023 64.0898i −0.139631 0.241848i
\(266\) −15.0319 232.767i −0.0565109 0.875062i
\(267\) 424.694 + 59.6819i 1.59061 + 0.223528i
\(268\) −192.276 −0.717449
\(269\) 446.874 + 258.003i 1.66124 + 0.959119i 0.972123 + 0.234472i \(0.0753362\pi\)
0.689120 + 0.724647i \(0.257997\pi\)
\(270\) 31.7440 + 43.6886i 0.117570 + 0.161810i
\(271\) −117.718 203.894i −0.434385 0.752377i 0.562860 0.826552i \(-0.309701\pi\)
−0.997245 + 0.0741751i \(0.976368\pi\)
\(272\) −83.4799 48.1971i −0.306911 0.177195i
\(273\) 298.035 + 203.339i 1.09170 + 0.744831i
\(274\) 61.1106 + 105.847i 0.223031 + 0.386301i
\(275\) −347.700 200.745i −1.26436 0.729981i
\(276\) 70.3424 + 174.098i 0.254864 + 0.630789i
\(277\) −254.239 440.354i −0.917830 1.58973i −0.802705 0.596376i \(-0.796607\pi\)
−0.115125 0.993351i \(-0.536727\pi\)
\(278\) 3.95209 2.28174i 0.0142161 0.00820769i
\(279\) −70.1020 281.136i −0.251262 1.00766i
\(280\) 15.5346 + 23.2976i 0.0554807 + 0.0832056i
\(281\) −13.5306 7.81192i −0.0481517 0.0278004i 0.475731 0.879591i \(-0.342184\pi\)
−0.523883 + 0.851790i \(0.675517\pi\)
\(282\) 14.2823 + 11.1583i 0.0506463 + 0.0395683i
\(283\) −509.979 −1.80205 −0.901023 0.433772i \(-0.857182\pi\)
−0.901023 + 0.433772i \(0.857182\pi\)
\(284\) 41.6035i 0.146491i
\(285\) −61.5476 + 78.7792i −0.215957 + 0.276418i
\(286\) 212.068 367.312i 0.741496 1.28431i
\(287\) −4.51866 69.9707i −0.0157444 0.243800i
\(288\) 49.3991 12.3178i 0.171525 0.0427701i
\(289\) 145.870 + 252.655i 0.504742 + 0.874239i
\(290\) −27.5143 + 15.8854i −0.0948769 + 0.0547772i
\(291\) −97.6081 + 39.4375i −0.335423 + 0.135524i
\(292\) −83.3648 + 144.392i −0.285496 + 0.494494i
\(293\) −378.046 + 218.265i −1.29026 + 0.744932i −0.978700 0.205294i \(-0.934185\pi\)
−0.311560 + 0.950226i \(0.600852\pi\)
\(294\) −207.878 2.21094i −0.707067 0.00752020i
\(295\) −29.8334 + 51.6730i −0.101130 + 0.175163i
\(296\) −76.9289 + 44.4149i −0.259895 + 0.150050i
\(297\) 49.2824 + 468.735i 0.165934 + 1.57823i
\(298\) −138.463 + 239.824i −0.464640 + 0.804779i
\(299\) 537.671i 1.79823i
\(300\) −19.2041 + 136.656i −0.0640137 + 0.455519i
\(301\) 246.123 + 369.116i 0.817684 + 1.22630i
\(302\) 38.5791 22.2737i 0.127745 0.0737539i
\(303\) −123.317 17.3296i −0.406986 0.0571934i
\(304\) 47.1239 + 81.6210i 0.155013 + 0.268490i
\(305\) −15.2839 8.82417i −0.0501112 0.0289317i
\(306\) −294.845 84.5380i −0.963545 0.276268i
\(307\) −402.350 −1.31059 −0.655294 0.755374i \(-0.727455\pi\)
−0.655294 + 0.755374i \(0.727455\pi\)
\(308\) 15.7496 + 243.880i 0.0511349 + 0.791817i
\(309\) 94.2073 38.0635i 0.304878 0.123183i
\(310\) −32.1959 + 55.7649i −0.103858 + 0.179887i
\(311\) 93.9460i 0.302077i 0.988528 + 0.151039i \(0.0482618\pi\)
−0.988528 + 0.151039i \(0.951738\pi\)
\(312\) −144.364 20.2873i −0.462704 0.0650234i
\(313\) 404.222 1.29144 0.645722 0.763572i \(-0.276556\pi\)
0.645722 + 0.763572i \(0.276556\pi\)
\(314\) 126.397i 0.402538i
\(315\) 65.8982 + 59.9705i 0.209201 + 0.190382i
\(316\) 90.3278 0.285848
\(317\) 116.706i 0.368157i −0.982912 0.184078i \(-0.941070\pi\)
0.982912 0.184078i \(-0.0589300\pi\)
\(318\) −205.833 + 83.1648i −0.647274 + 0.261524i
\(319\) −277.281 −0.869221
\(320\) −9.79859 5.65722i −0.0306206 0.0176788i
\(321\) −136.337 19.1594i −0.424727 0.0596865i
\(322\) 171.872 + 257.760i 0.533764 + 0.800497i
\(323\) 567.809i 1.75792i
\(324\) 143.034 76.0610i 0.441463 0.234756i
\(325\) 197.575 342.210i 0.607922 1.05295i
\(326\) 257.828 148.857i 0.790885 0.456617i
\(327\) 120.460 48.6706i 0.368379 0.148840i
\(328\) 14.1657 + 24.5356i 0.0431880 + 0.0748038i
\(329\) 26.8070 + 13.2517i 0.0814801 + 0.0402788i
\(330\) 64.4861 82.5404i 0.195412 0.250122i
\(331\) 611.339 1.84695 0.923474 0.383662i \(-0.125337\pi\)
0.923474 + 0.383662i \(0.125337\pi\)
\(332\) −7.46762 4.31143i −0.0224928 0.0129862i
\(333\) −203.320 + 196.353i −0.610571 + 0.589649i
\(334\) −79.9195 138.425i −0.239280 0.414445i
\(335\) 117.752 + 67.9844i 0.351500 + 0.202938i
\(336\) 75.6932 36.4216i 0.225277 0.108398i
\(337\) 3.59903 + 6.23370i 0.0106796 + 0.0184976i 0.871316 0.490723i \(-0.163267\pi\)
−0.860636 + 0.509220i \(0.829934\pi\)
\(338\) 154.530 + 89.2180i 0.457190 + 0.263959i
\(339\) −268.909 37.7896i −0.793243 0.111474i
\(340\) 34.0827 + 59.0330i 0.100243 + 0.173626i
\(341\) −486.692 + 280.992i −1.42725 + 0.824023i
\(342\) 208.329 + 215.721i 0.609150 + 0.630764i
\(343\) −336.601 + 65.9467i −0.981343 + 0.192265i
\(344\) −155.244 89.6303i −0.451291 0.260553i
\(345\) 18.4783 131.491i 0.0535603 0.381133i
\(346\) 73.2911 0.211824
\(347\) 546.466i 1.57483i 0.616422 + 0.787416i \(0.288581\pi\)
−0.616422 + 0.787416i \(0.711419\pi\)
\(348\) 35.7033 + 88.3659i 0.102596 + 0.253925i
\(349\) −65.1506 + 112.844i −0.186678 + 0.323336i −0.944141 0.329543i \(-0.893105\pi\)
0.757463 + 0.652878i \(0.226439\pi\)
\(350\) 14.6732 + 227.213i 0.0419235 + 0.649179i
\(351\) −461.334 + 48.5042i −1.31434 + 0.138189i
\(352\) −49.3737 85.5178i −0.140266 0.242948i
\(353\) 19.1736 11.0699i 0.0543162 0.0313595i −0.472596 0.881279i \(-0.656683\pi\)
0.526912 + 0.849920i \(0.323350\pi\)
\(354\) 141.047 + 110.195i 0.398437 + 0.311285i
\(355\) 14.7100 25.4785i 0.0414366 0.0717703i
\(356\) −247.607 + 142.956i −0.695524 + 0.401561i
\(357\) −504.643 37.9828i −1.41356 0.106394i
\(358\) 136.739 236.840i 0.381954 0.661563i
\(359\) 52.1828 30.1278i 0.145356 0.0839214i −0.425558 0.904931i \(-0.639922\pi\)
0.570914 + 0.821010i \(0.306589\pi\)
\(360\) −34.6079 9.92279i −0.0961330 0.0275633i
\(361\) −97.0829 + 168.152i −0.268928 + 0.465796i
\(362\) 248.655i 0.686891i
\(363\) 511.027 206.475i 1.40779 0.568802i
\(364\) −240.029 + 15.5009i −0.659419 + 0.0425848i
\(365\) 102.107 58.9516i 0.279746 0.161511i
\(366\) −32.5936 + 41.7189i −0.0890536 + 0.113986i
\(367\) 3.71386 + 6.43260i 0.0101195 + 0.0175275i 0.871041 0.491211i \(-0.163445\pi\)
−0.860921 + 0.508738i \(0.830112\pi\)
\(368\) −108.410 62.5904i −0.294592 0.170083i
\(369\) 62.6248 + 64.8468i 0.169715 + 0.175737i
\(370\) 62.8162 0.169774
\(371\) −304.746 + 203.202i −0.821418 + 0.547714i
\(372\) 152.216 + 118.921i 0.409182 + 0.319681i
\(373\) 297.356 515.036i 0.797201 1.38079i −0.124230 0.992253i \(-0.539646\pi\)
0.921432 0.388540i \(-0.127020\pi\)
\(374\) 594.918i 1.59069i
\(375\) 125.383 160.487i 0.334355 0.427965i
\(376\) −12.0829 −0.0321352
\(377\) 272.903i 0.723881i
\(378\) 205.659 170.723i 0.544072 0.451648i
\(379\) 651.058 1.71783 0.858915 0.512118i \(-0.171139\pi\)
0.858915 + 0.512118i \(0.171139\pi\)
\(380\) 66.6476i 0.175388i
\(381\) −320.432 250.343i −0.841028 0.657068i
\(382\) −32.9372 −0.0862231
\(383\) 287.209 + 165.820i 0.749893 + 0.432951i 0.825655 0.564175i \(-0.190806\pi\)
−0.0757623 + 0.997126i \(0.524139\pi\)
\(384\) −20.8959 + 26.7462i −0.0544165 + 0.0696516i
\(385\) 76.5848 154.923i 0.198922 0.402398i
\(386\) 119.973i 0.310812i
\(387\) −548.311 157.212i −1.41682 0.406232i
\(388\) 35.0914 60.7801i 0.0904418 0.156650i
\(389\) 18.0923 10.4456i 0.0465098 0.0268524i −0.476565 0.879139i \(-0.658118\pi\)
0.523075 + 0.852287i \(0.324785\pi\)
\(390\) 81.2370 + 63.4678i 0.208300 + 0.162738i
\(391\) 377.085 + 653.130i 0.964412 + 1.67041i
\(392\) 110.115 84.1587i 0.280906 0.214691i
\(393\) 250.443 + 619.847i 0.637259 + 1.57722i
\(394\) −216.633 −0.549831
\(395\) −55.3178 31.9378i −0.140045 0.0808551i
\(396\) −218.276 226.021i −0.551201 0.570759i
\(397\) −309.823 536.629i −0.780410 1.35171i −0.931703 0.363222i \(-0.881677\pi\)
0.151292 0.988489i \(-0.451657\pi\)
\(398\) −1.37615 0.794522i −0.00345767 0.00199629i
\(399\) 408.733 + 278.864i 1.02439 + 0.698908i
\(400\) −45.9995 79.6734i −0.114999 0.199184i
\(401\) −248.826 143.660i −0.620513 0.358253i 0.156556 0.987669i \(-0.449961\pi\)
−0.777069 + 0.629416i \(0.783294\pi\)
\(402\) 251.112 321.417i 0.624657 0.799544i
\(403\) −276.555 479.007i −0.686240 1.18860i
\(404\) 71.8966 41.5095i 0.177962 0.102746i
\(405\) −114.489 3.99277i −0.282689 0.00985869i
\(406\) 87.2363 + 130.830i 0.214868 + 0.322242i
\(407\) 474.783 + 274.116i 1.16654 + 0.673504i
\(408\) 189.593 76.6029i 0.464688 0.187752i
\(409\) 441.994 1.08067 0.540335 0.841450i \(-0.318297\pi\)
0.540335 + 0.841450i \(0.318297\pi\)
\(410\) 20.0346i 0.0488648i
\(411\) −256.747 36.0805i −0.624689 0.0877870i
\(412\) −33.8688 + 58.6624i −0.0822058 + 0.142385i
\(413\) 264.736 + 130.870i 0.641008 + 0.316875i
\(414\) −382.895 109.784i −0.924868 0.265179i
\(415\) 3.04884 + 5.28074i 0.00734660 + 0.0127247i
\(416\) 84.1674 48.5941i 0.202326 0.116813i
\(417\) −1.34717 + 9.58640i −0.00323062 + 0.0229890i
\(418\) 290.835 503.742i 0.695779 1.20512i
\(419\) 281.777 162.684i 0.672500 0.388268i −0.124523 0.992217i \(-0.539740\pi\)
0.797023 + 0.603949i \(0.206407\pi\)
\(420\) −59.2333 4.45830i −0.141032 0.0106150i
\(421\) −201.041 + 348.214i −0.477533 + 0.827111i −0.999668 0.0257517i \(-0.991802\pi\)
0.522136 + 0.852862i \(0.325135\pi\)
\(422\) −193.312 + 111.609i −0.458086 + 0.264476i
\(423\) −37.3051 + 9.30213i −0.0881918 + 0.0219908i
\(424\) 73.9998 128.171i 0.174528 0.302291i
\(425\) 554.261i 1.30414i
\(426\) −69.5459 54.3340i −0.163253 0.127545i
\(427\) −38.7087 + 78.3039i −0.0906528 + 0.183382i
\(428\) 79.4879 45.8924i 0.185719 0.107225i
\(429\) 337.053 + 834.209i 0.785672 + 1.94454i
\(430\) 63.3823 + 109.781i 0.147401 + 0.255305i
\(431\) 148.166 + 85.5439i 0.343774 + 0.198478i 0.661939 0.749557i \(-0.269734\pi\)
−0.318166 + 0.948035i \(0.603067\pi\)
\(432\) −43.9242 + 98.6644i −0.101676 + 0.228390i
\(433\) −225.192 −0.520075 −0.260038 0.965599i \(-0.583735\pi\)
−0.260038 + 0.965599i \(0.583735\pi\)
\(434\) 285.700 + 141.233i 0.658295 + 0.325422i
\(435\) 9.37894 66.7402i 0.0215608 0.153426i
\(436\) −43.3069 + 75.0098i −0.0993278 + 0.172041i
\(437\) 737.377i 1.68736i
\(438\) −132.497 327.931i −0.302505 0.748702i
\(439\) −59.3313 −0.135151 −0.0675755 0.997714i \(-0.521526\pi\)
−0.0675755 + 0.997714i \(0.521526\pi\)
\(440\) 69.8295i 0.158703i
\(441\) 275.183 344.609i 0.623998 0.781426i
\(442\) −585.524 −1.32472
\(443\) 306.058i 0.690875i 0.938442 + 0.345438i \(0.112270\pi\)
−0.938442 + 0.345438i \(0.887730\pi\)
\(444\) 26.2231 186.603i 0.0590611 0.420277i
\(445\) 202.183 0.454344
\(446\) −129.403 74.7106i −0.290140 0.167513i
\(447\) −220.068 544.669i −0.492322 1.21850i
\(448\) −24.8164 + 50.2011i −0.0553937 + 0.112056i
\(449\) 446.116i 0.993578i −0.867871 0.496789i \(-0.834512\pi\)
0.867871 0.496789i \(-0.165488\pi\)
\(450\) −203.358 210.574i −0.451908 0.467942i
\(451\) 87.4265 151.427i 0.193850 0.335759i
\(452\) 156.780 90.5172i 0.346859 0.200259i
\(453\) −13.1507 + 93.5797i −0.0290302 + 0.206578i
\(454\) −42.4969 73.6068i −0.0936055 0.162129i
\(455\) 152.477 + 75.3755i 0.335114 + 0.165660i
\(456\) −197.984 27.8226i −0.434176 0.0610144i
\(457\) 317.688 0.695160 0.347580 0.937650i \(-0.387004\pi\)
0.347580 + 0.937650i \(0.387004\pi\)
\(458\) 62.4632 + 36.0631i 0.136382 + 0.0787404i
\(459\) 526.383 382.467i 1.14680 0.833262i
\(460\) 44.2610 + 76.6623i 0.0962195 + 0.166657i
\(461\) −66.3830 38.3263i −0.143998 0.0831372i 0.426270 0.904596i \(-0.359827\pi\)
−0.570268 + 0.821459i \(0.693161\pi\)
\(462\) −428.247 292.178i −0.926942 0.632420i
\(463\) 155.730 + 269.733i 0.336350 + 0.582576i 0.983743 0.179580i \(-0.0574740\pi\)
−0.647393 + 0.762156i \(0.724141\pi\)
\(464\) −55.0250 31.7687i −0.118588 0.0684671i
\(465\) −51.1711 126.649i −0.110045 0.272363i
\(466\) −16.1169 27.9153i −0.0345856 0.0599040i
\(467\) 265.027 153.013i 0.567510 0.327652i −0.188644 0.982045i \(-0.560409\pi\)
0.756154 + 0.654394i \(0.227076\pi\)
\(468\) 222.452 214.829i 0.475324 0.459036i
\(469\) 298.225 603.280i 0.635875 1.28631i
\(470\) 7.39968 + 4.27221i 0.0157440 + 0.00908981i
\(471\) 211.290 + 165.074i 0.448598 + 0.350475i
\(472\) −119.326 −0.252809
\(473\) 1106.35i 2.33900i
\(474\) −117.968 + 150.995i −0.248877 + 0.318556i
\(475\) 270.959 469.316i 0.570441 0.988033i
\(476\) 280.701 187.169i 0.589708 0.393212i
\(477\) 129.796 452.692i 0.272109 0.949039i
\(478\) −285.959 495.295i −0.598240 1.03618i
\(479\) −408.566 + 235.886i −0.852956 + 0.492454i −0.861647 0.507508i \(-0.830567\pi\)
0.00869133 + 0.999962i \(0.497233\pi\)
\(480\) 22.2537 8.99139i 0.0463620 0.0187321i
\(481\) −269.788 + 467.286i −0.560889 + 0.971489i
\(482\) 371.883 214.707i 0.771541 0.445449i
\(483\) −655.346 49.3258i −1.35682 0.102124i
\(484\) −183.721 + 318.214i −0.379588 + 0.657466i
\(485\) −42.9808 + 24.8150i −0.0886202 + 0.0511649i
\(486\) −59.6554 + 338.436i −0.122748 + 0.696371i
\(487\) 195.229 338.146i 0.400880 0.694345i −0.592952 0.805238i \(-0.702038\pi\)
0.993832 + 0.110893i \(0.0353710\pi\)
\(488\) 35.2944i 0.0723246i
\(489\) −87.8873 + 625.403i −0.179729 + 1.27894i
\(490\) −97.1923 + 12.6058i −0.198352 + 0.0257261i
\(491\) −498.578 + 287.854i −1.01543 + 0.586261i −0.912778 0.408456i \(-0.866067\pi\)
−0.102656 + 0.994717i \(0.532734\pi\)
\(492\) −59.5150 8.36359i −0.120965 0.0169992i
\(493\) 191.395 + 331.506i 0.388226 + 0.672426i
\(494\) 495.787 + 286.243i 1.00362 + 0.579439i
\(495\) 53.7591 + 215.595i 0.108604 + 0.435545i
\(496\) −128.775 −0.259628
\(497\) −130.534 64.5280i −0.262643 0.129835i
\(498\) 16.9598 6.85244i 0.0340559 0.0137599i
\(499\) 359.065 621.919i 0.719569 1.24633i −0.241602 0.970375i \(-0.577673\pi\)
0.961171 0.275954i \(-0.0889939\pi\)
\(500\) 135.773i 0.271545i
\(501\) 335.770 + 47.1855i 0.670200 + 0.0941826i
\(502\) 330.046 0.657463
\(503\) 475.997i 0.946316i 0.880978 + 0.473158i \(0.156886\pi\)
−0.880978 + 0.473158i \(0.843114\pi\)
\(504\) −37.9713 + 174.098i −0.0753399 + 0.345433i
\(505\) −58.7071 −0.116252
\(506\) 772.581i 1.52684i
\(507\) −350.956 + 141.800i −0.692221 + 0.279685i
\(508\) 271.087 0.533635
\(509\) 439.257 + 253.605i 0.862981 + 0.498242i 0.865009 0.501756i \(-0.167312\pi\)
−0.00202828 + 0.999998i \(0.500646\pi\)
\(510\) −143.194 20.1229i −0.280772 0.0394566i
\(511\) −323.739 485.518i −0.633540 0.950134i
\(512\) 22.6274i 0.0441942i
\(513\) −632.685 + 66.5200i −1.23331 + 0.129669i
\(514\) −133.512 + 231.250i −0.259751 + 0.449902i
\(515\) 41.4833 23.9504i 0.0805501 0.0465056i
\(516\) 352.578 142.455i 0.683290 0.276076i
\(517\) 37.2860 + 64.5812i 0.0721199 + 0.124915i
\(518\) −20.0362 310.258i −0.0386800 0.598954i
\(519\) −95.7178 + 122.516i −0.184427 + 0.236062i
\(520\) −68.7269 −0.132167
\(521\) −332.558 192.003i −0.638308 0.368527i 0.145655 0.989336i \(-0.453471\pi\)
−0.783962 + 0.620808i \(0.786805\pi\)
\(522\) −194.344 55.7225i −0.372307 0.106748i
\(523\) 182.193 + 315.567i 0.348361 + 0.603379i 0.985959 0.166990i \(-0.0534049\pi\)
−0.637597 + 0.770370i \(0.720072\pi\)
\(524\) −385.976 222.843i −0.736595 0.425273i
\(525\) −398.980 272.210i −0.759963 0.518496i
\(526\) 125.876 + 218.023i 0.239308 + 0.414493i
\(527\) 671.884 + 387.913i 1.27492 + 0.736077i
\(528\) 207.437 + 29.1509i 0.392873 + 0.0552100i
\(529\) 225.195 + 390.050i 0.425700 + 0.737335i
\(530\) −90.6367 + 52.3291i −0.171013 + 0.0987342i
\(531\) −368.413 + 91.8646i −0.693809 + 0.173003i
\(532\) −329.182 + 21.2583i −0.618763 + 0.0399592i
\(533\) 149.036 + 86.0459i 0.279617 + 0.161437i
\(534\) 84.4029 600.608i 0.158058 1.12473i
\(535\) −64.9058 −0.121319
\(536\) 271.920i 0.507313i
\(537\) 217.329 + 537.891i 0.404710 + 1.00166i
\(538\) 364.871 631.976i 0.678200 1.17468i
\(539\) −789.616 328.848i −1.46497 0.610107i
\(540\) 61.7851 44.8927i 0.114417 0.0831347i
\(541\) 473.259 + 819.709i 0.874786 + 1.51517i 0.856990 + 0.515333i \(0.172332\pi\)
0.0177960 + 0.999842i \(0.494335\pi\)
\(542\) −288.350 + 166.479i −0.532011 + 0.307157i
\(543\) 415.661 + 324.742i 0.765489 + 0.598051i
\(544\) −68.1610 + 118.058i −0.125296 + 0.217019i
\(545\) 53.0434 30.6246i 0.0973273 0.0561919i
\(546\) 287.564 421.485i 0.526675 0.771950i
\(547\) −294.515 + 510.116i −0.538419 + 0.932570i 0.460570 + 0.887623i \(0.347645\pi\)
−0.998989 + 0.0449464i \(0.985688\pi\)
\(548\) 149.690 86.4234i 0.273156 0.157707i
\(549\) −27.1718 108.969i −0.0494933 0.198487i
\(550\) −283.896 + 491.722i −0.516174 + 0.894040i
\(551\) 374.267i 0.679250i
\(552\) 246.211 99.4792i 0.446035 0.180216i
\(553\) −140.101 + 283.410i −0.253346 + 0.512495i
\(554\) −622.755 + 359.548i −1.12411 + 0.649003i
\(555\) −82.0377 + 105.006i −0.147816 + 0.189200i
\(556\) −3.22687 5.58910i −0.00580372 0.0100523i
\(557\) −531.266 306.727i −0.953799 0.550676i −0.0595401 0.998226i \(-0.518963\pi\)
−0.894259 + 0.447550i \(0.852297\pi\)
\(558\) −397.587 + 99.1392i −0.712521 + 0.177669i
\(559\) −1088.88 −1.94790
\(560\) 32.9478 21.9693i 0.0588353 0.0392308i
\(561\) −994.488 776.961i −1.77271 1.38496i
\(562\) −11.0477 + 19.1352i −0.0196579 + 0.0340484i
\(563\) 208.343i 0.370059i −0.982733 0.185030i \(-0.940762\pi\)
0.982733 0.185030i \(-0.0592381\pi\)
\(564\) 15.7802 20.1982i 0.0279790 0.0358123i
\(565\) −128.019 −0.226582
\(566\) 721.219i 1.27424i
\(567\) 16.7973 + 566.751i 0.0296249 + 0.999561i
\(568\) 58.8362 0.103585
\(569\) 944.539i 1.66000i −0.557765 0.829999i \(-0.688341\pi\)
0.557765 0.829999i \(-0.311659\pi\)
\(570\) 111.411 + 87.0415i 0.195457 + 0.152704i
\(571\) −114.520 −0.200561 −0.100280 0.994959i \(-0.531974\pi\)
−0.100280 + 0.994959i \(0.531974\pi\)
\(572\) −519.458 299.909i −0.908143 0.524317i
\(573\) 43.0159 55.0592i 0.0750714 0.0960893i
\(574\) −98.9535 + 6.39035i −0.172393 + 0.0111330i
\(575\) 719.782i 1.25179i
\(576\) −17.4200 69.8609i −0.0302430 0.121286i
\(577\) 493.595 854.932i 0.855451 1.48168i −0.0207756 0.999784i \(-0.506614\pi\)
0.876226 0.481900i \(-0.160053\pi\)
\(578\) 357.308 206.292i 0.618180 0.356907i
\(579\) 200.552 + 156.685i 0.346377 + 0.270613i
\(580\) 22.4653 + 38.9111i 0.0387333 + 0.0670881i
\(581\) 25.1099 16.7430i 0.0432183 0.0288176i
\(582\) 55.7731 + 138.039i 0.0958301 + 0.237180i
\(583\) −913.411 −1.56674
\(584\) 204.201 + 117.896i 0.349660 + 0.201876i
\(585\) −212.190 + 52.9102i −0.362719 + 0.0904448i
\(586\) 308.674 + 534.638i 0.526747 + 0.912352i
\(587\) −439.957 254.009i −0.749501 0.432725i 0.0760123 0.997107i \(-0.475781\pi\)
−0.825514 + 0.564382i \(0.809115\pi\)
\(588\) −3.12674 + 293.983i −0.00531759 + 0.499972i
\(589\) −379.275 656.923i −0.643930 1.11532i
\(590\) 73.0767 + 42.1909i 0.123859 + 0.0715099i
\(591\) 282.922 362.133i 0.478718 0.612746i
\(592\) 62.8122 + 108.794i 0.106102 + 0.183773i
\(593\) 105.925 61.1560i 0.178626 0.103130i −0.408021 0.912973i \(-0.633781\pi\)
0.586647 + 0.809843i \(0.300448\pi\)
\(594\) 662.892 69.6959i 1.11598 0.117333i
\(595\) −238.083 + 15.3752i −0.400140 + 0.0258407i
\(596\) 339.163 + 195.816i 0.569065 + 0.328550i
\(597\) 3.12540 1.26279i 0.00523518 0.00211522i
\(598\) −760.382 −1.27154
\(599\) 934.348i 1.55985i −0.625875 0.779923i \(-0.715258\pi\)
0.625875 0.779923i \(-0.284742\pi\)
\(600\) 193.260 + 27.1587i 0.322101 + 0.0452645i
\(601\) 109.192 189.127i 0.181685 0.314687i −0.760770 0.649022i \(-0.775178\pi\)
0.942454 + 0.334335i \(0.108512\pi\)
\(602\) 522.009 348.070i 0.867124 0.578190i
\(603\) 209.341 + 839.538i 0.347165 + 1.39227i
\(604\) −31.4997 54.5591i −0.0521519 0.0903297i
\(605\) 225.026 129.919i 0.371943 0.214742i
\(606\) −24.5078 + 174.396i −0.0404419 + 0.287783i
\(607\) 532.851 922.924i 0.877843 1.52047i 0.0241397 0.999709i \(-0.492315\pi\)
0.853703 0.520760i \(-0.174351\pi\)
\(608\) 115.430 66.6433i 0.189851 0.109611i
\(609\) −332.631 25.0360i −0.546192 0.0411101i
\(610\) −12.4793 + 21.6147i −0.0204578 + 0.0354339i
\(611\) −63.5614 + 36.6972i −0.104029 + 0.0600609i
\(612\) −119.555 + 416.973i −0.195351 + 0.681329i
\(613\) −146.885 + 254.412i −0.239616 + 0.415027i −0.960604 0.277920i \(-0.910355\pi\)
0.720988 + 0.692947i \(0.243688\pi\)
\(614\) 569.009i 0.926725i
\(615\) 33.4905 + 26.1651i 0.0544562 + 0.0425448i
\(616\) 344.898 22.2732i 0.559899 0.0361579i
\(617\) −103.145 + 59.5509i −0.167172 + 0.0965168i −0.581252 0.813724i \(-0.697437\pi\)
0.414080 + 0.910241i \(0.364103\pi\)
\(618\) −53.8299 133.229i −0.0871034 0.215581i
\(619\) 211.746 + 366.755i 0.342077 + 0.592495i 0.984818 0.173588i \(-0.0555362\pi\)
−0.642741 + 0.766084i \(0.722203\pi\)
\(620\) 78.8635 + 45.5319i 0.127199 + 0.0734385i
\(621\) 683.579 496.685i 1.10077 0.799815i
\(622\) 132.860 0.213601
\(623\) −64.4895 998.610i −0.103514 1.60290i
\(624\) −28.6906 + 204.161i −0.0459785 + 0.327181i
\(625\) −239.491 + 414.810i −0.383185 + 0.663696i
\(626\) 571.657i 0.913189i
\(627\) 462.244 + 1144.06i 0.737231 + 1.82465i
\(628\) −178.752 −0.284637
\(629\) 756.842i 1.20325i
\(630\) 84.8111 93.1941i 0.134621 0.147927i
\(631\) 1159.89 1.83818 0.919091 0.394046i \(-0.128925\pi\)
0.919091 + 0.394046i \(0.128925\pi\)
\(632\) 127.743i 0.202125i
\(633\) 65.8954 468.909i 0.104100 0.740773i
\(634\) −165.047 −0.260326
\(635\) −166.017 95.8498i −0.261444 0.150945i
\(636\) 117.613 + 291.092i 0.184926 + 0.457692i
\(637\) 323.655 777.148i 0.508092 1.22001i
\(638\) 392.135i 0.614632i
\(639\) 181.653 45.2957i 0.284278 0.0708853i
\(640\) −8.00052 + 13.8573i −0.0125008 + 0.0216520i
\(641\) −320.420 + 184.994i −0.499875 + 0.288603i −0.728662 0.684874i \(-0.759857\pi\)
0.228787 + 0.973476i \(0.426524\pi\)
\(642\) −27.0955 + 192.810i −0.0422048 + 0.300328i
\(643\) 223.115 + 386.446i 0.346990 + 0.601005i 0.985713 0.168432i \(-0.0538704\pi\)
−0.638723 + 0.769437i \(0.720537\pi\)
\(644\) 364.528 243.064i 0.566037 0.377428i
\(645\) −266.292 37.4217i −0.412855 0.0580182i
\(646\) −803.004 −1.24304
\(647\) −287.119 165.768i −0.443770 0.256210i 0.261426 0.965224i \(-0.415807\pi\)
−0.705195 + 0.709013i \(0.749141\pi\)
\(648\) −107.566 202.281i −0.165998 0.312161i
\(649\) 368.223 + 637.782i 0.567370 + 0.982714i
\(650\) −483.957 279.413i −0.744550 0.429866i
\(651\) −609.214 + 293.138i −0.935812 + 0.450288i
\(652\) −210.516 364.624i −0.322877 0.559240i
\(653\) −689.144 397.877i −1.05535 0.609307i −0.131208 0.991355i \(-0.541886\pi\)
−0.924143 + 0.382048i \(0.875219\pi\)
\(654\) −68.8306 170.356i −0.105246 0.260483i
\(655\) 157.584 + 272.944i 0.240586 + 0.416708i
\(656\) 34.6986 20.0333i 0.0528943 0.0305385i
\(657\) 721.224 + 206.790i 1.09775 + 0.314748i
\(658\) 18.7408 37.9108i 0.0284814 0.0576151i
\(659\) −647.026 373.560i −0.981830 0.566860i −0.0790076 0.996874i \(-0.525175\pi\)
−0.902822 + 0.430014i \(0.858508\pi\)
\(660\) −116.730 91.1971i −0.176863 0.138177i
\(661\) −1126.89 −1.70482 −0.852411 0.522872i \(-0.824861\pi\)
−0.852411 + 0.522872i \(0.824861\pi\)
\(662\) 864.565i 1.30599i
\(663\) 764.692 978.784i 1.15338 1.47630i
\(664\) −6.09728 + 10.5608i −0.00918266 + 0.0159048i
\(665\) 209.111 + 103.372i 0.314453 + 0.155447i
\(666\) 277.685 + 287.538i 0.416945 + 0.431739i
\(667\) 248.552 + 430.505i 0.372642 + 0.645435i
\(668\) −195.762 + 113.023i −0.293057 + 0.169196i
\(669\) 293.888 118.743i 0.439295 0.177493i
\(670\) 96.1444 166.527i 0.143499 0.248548i
\(671\) −188.644 + 108.913i −0.281138 + 0.162315i
\(672\) −51.5079 107.046i −0.0766487 0.159295i
\(673\) 264.569 458.246i 0.393118 0.680901i −0.599741 0.800194i \(-0.704730\pi\)
0.992859 + 0.119294i \(0.0380630\pi\)
\(674\) 8.81578 5.08979i 0.0130798 0.00755162i
\(675\) 617.589 64.9328i 0.914947 0.0961967i
\(676\) 126.173 218.539i 0.186647 0.323282i
\(677\) 188.228i 0.278032i 0.990290 + 0.139016i \(0.0443940\pi\)
−0.990290 + 0.139016i \(0.955606\pi\)
\(678\) −53.4425 + 380.295i −0.0788238 + 0.560907i
\(679\) 136.274 + 204.373i 0.200698 + 0.300991i
\(680\) 83.4853 48.2002i 0.122772 0.0708827i
\(681\) 178.545 + 25.0907i 0.262180 + 0.0368439i
\(682\) 397.382 + 688.287i 0.582672 + 1.00922i
\(683\) 300.248 + 173.348i 0.439601 + 0.253804i 0.703429 0.710766i \(-0.251652\pi\)
−0.263827 + 0.964570i \(0.584985\pi\)
\(684\) 305.076 294.622i 0.446018 0.430734i
\(685\) −122.229 −0.178436
\(686\) 93.2628 + 476.025i 0.135952 + 0.693914i
\(687\) −141.861 + 57.3175i −0.206494 + 0.0834316i
\(688\) −126.756 + 219.548i −0.184239 + 0.319111i
\(689\) 898.988i 1.30477i
\(690\) −185.956 26.1323i −0.269502 0.0378728i
\(691\) 795.908 1.15182 0.575910 0.817513i \(-0.304648\pi\)
0.575910 + 0.817513i \(0.304648\pi\)
\(692\) 103.649i 0.149782i
\(693\) 1047.71 334.291i 1.51184 0.482382i
\(694\) 772.820 1.11357
\(695\) 4.56377i 0.00656658i
\(696\) 124.968 50.4921i 0.179552 0.0725462i
\(697\) −241.387 −0.346322
\(698\) 159.586 + 92.1368i 0.228633 + 0.132001i
\(699\) 67.7128 + 9.51562i 0.0968710 + 0.0136132i
\(700\) 321.327 20.7511i 0.459039 0.0296444i
\(701\) 1048.99i 1.49643i 0.663459 + 0.748213i \(0.269088\pi\)
−0.663459 + 0.748213i \(0.730912\pi\)
\(702\) 68.5953 + 652.424i 0.0977141 + 0.929379i
\(703\) −369.994 + 640.849i −0.526308 + 0.911592i
\(704\) −120.940 + 69.8250i −0.171790 + 0.0991833i
\(705\) −16.8055 + 6.79011i −0.0238377 + 0.00963136i
\(706\) −15.6552 27.1156i −0.0221745 0.0384074i
\(707\) 18.7256 + 289.963i 0.0264860 + 0.410131i
\(708\) 155.839 199.470i 0.220112 0.281737i
\(709\) −1020.18 −1.43890 −0.719448 0.694547i \(-0.755605\pi\)
−0.719448 + 0.694547i \(0.755605\pi\)
\(710\) −36.0320 20.8031i −0.0507493 0.0293001i
\(711\) −98.3443 394.399i −0.138318 0.554710i
\(712\) 202.170 + 350.169i 0.283946 + 0.491810i
\(713\) 872.532 + 503.756i 1.22375 + 0.706531i
\(714\) −53.7158 + 713.672i −0.0752322 + 0.999541i
\(715\) 212.081 + 367.336i 0.296617 + 0.513756i
\(716\) −334.942 193.379i −0.467796 0.270082i
\(717\) 1201.41 + 168.834i 1.67561 + 0.235472i
\(718\) −42.6071 73.7977i −0.0593414 0.102782i
\(719\) −836.024 + 482.679i −1.16276 + 0.671320i −0.951964 0.306210i \(-0.900939\pi\)
−0.210796 + 0.977530i \(0.567606\pi\)
\(720\) −14.0329 + 48.9429i −0.0194902 + 0.0679763i
\(721\) −131.526 197.252i −0.182422 0.273582i
\(722\) 237.803 + 137.296i 0.329368 + 0.190161i
\(723\) −126.766 + 902.059i −0.175333 + 1.24766i
\(724\) −351.651 −0.485705
\(725\) 365.336i 0.503912i
\(726\) −292.000 722.701i −0.402203 0.995455i
\(727\) −679.328 + 1176.63i −0.934426 + 1.61847i −0.158773 + 0.987315i \(0.550754\pi\)
−0.775654 + 0.631159i \(0.782580\pi\)
\(728\) 21.9215 + 339.452i 0.0301120 + 0.466280i
\(729\) −487.834 541.719i −0.669182 0.743099i
\(730\) −83.3702 144.401i −0.114206 0.197810i
\(731\) 1322.70 763.662i 1.80944 1.04468i
\(732\) 58.9994 + 46.0943i 0.0806003 + 0.0629704i
\(733\) 106.923 185.196i 0.145871 0.252655i −0.783827 0.620980i \(-0.786735\pi\)
0.929697 + 0.368324i \(0.120068\pi\)
\(734\) 9.09707 5.25220i 0.0123938 0.00715558i
\(735\) 105.860 178.933i 0.144028 0.243447i
\(736\) −88.5163 + 153.315i −0.120267 + 0.208308i
\(737\) 1453.38 839.106i 1.97201 1.13854i
\(738\) 91.7073 88.5648i 0.124265 0.120006i
\(739\) −23.9766 + 41.5286i −0.0324446 + 0.0561957i −0.881792 0.471639i \(-0.843663\pi\)
0.849347 + 0.527835i \(0.176996\pi\)
\(740\) 88.8356i 0.120048i
\(741\) −1125.99 + 454.945i −1.51956 + 0.613961i
\(742\) 287.371 + 430.976i 0.387292 + 0.580830i
\(743\) 646.371 373.182i 0.869947 0.502264i 0.00261651 0.999997i \(-0.499167\pi\)
0.867331 + 0.497732i \(0.165834\pi\)
\(744\) 168.180 215.266i 0.226048 0.289336i
\(745\) −138.472 239.840i −0.185868 0.321932i
\(746\) −728.371 420.525i −0.976368 0.563707i
\(747\) −10.6947 + 37.3000i −0.0143168 + 0.0499330i
\(748\) 841.341 1.12479
\(749\) 20.7027 + 320.579i 0.0276405 + 0.428009i
\(750\) −226.963 177.318i −0.302617 0.236425i
\(751\) 538.756 933.153i 0.717385 1.24255i −0.244647 0.969612i \(-0.578672\pi\)
0.962032 0.272935i \(-0.0879945\pi\)
\(752\) 17.0877i 0.0227230i
\(753\) −431.039 + 551.718i −0.572429 + 0.732694i
\(754\) −385.943 −0.511861
\(755\) 44.5502i 0.0590069i
\(756\) −241.439 290.846i −0.319364 0.384717i
\(757\) 50.0542 0.0661217 0.0330609 0.999453i \(-0.489474\pi\)
0.0330609 + 0.999453i \(0.489474\pi\)
\(758\) 920.734i 1.21469i
\(759\) −1291.48 1008.99i −1.70155 1.32936i
\(760\) −94.2539 −0.124018
\(761\) 13.0930 + 7.55923i 0.0172050 + 0.00993329i 0.508578 0.861016i \(-0.330171\pi\)
−0.491373 + 0.870949i \(0.663505\pi\)
\(762\) −354.038 + 453.159i −0.464617 + 0.594697i
\(763\) −168.178 252.220i −0.220417 0.330564i
\(764\) 46.5803i 0.0609690i
\(765\) 220.649 213.088i 0.288430 0.278546i
\(766\) 234.505 406.175i 0.306142 0.530254i
\(767\) −627.711 + 362.409i −0.818397 + 0.472502i
\(768\) 37.8249 + 29.5513i 0.0492511 + 0.0384783i
\(769\) −268.317 464.739i −0.348917 0.604342i 0.637140 0.770748i \(-0.280117\pi\)
−0.986057 + 0.166406i \(0.946784\pi\)
\(770\) −219.095 108.307i −0.284539 0.140659i
\(771\) −212.200 525.195i −0.275227 0.681187i
\(772\) −169.668 −0.219777
\(773\) −965.601 557.490i −1.24916 0.721203i −0.278219 0.960518i \(-0.589744\pi\)
−0.970942 + 0.239315i \(0.923077\pi\)
\(774\) −222.331 + 775.429i −0.287250 + 1.00185i
\(775\) 370.225 + 641.248i 0.477709 + 0.827417i
\(776\) −85.9561 49.6267i −0.110768 0.0639520i
\(777\) 544.807 + 371.702i 0.701167 + 0.478382i
\(778\) −14.7723 25.5864i −0.0189875 0.0328874i
\(779\) 204.392 + 118.006i 0.262377 + 0.151484i
\(780\) 89.7570 114.886i 0.115073 0.147290i
\(781\) −181.560 314.471i −0.232471 0.402652i
\(782\) 923.666 533.279i 1.18116 0.681942i
\(783\) 346.961 252.100i 0.443117 0.321967i
\(784\) −119.018 155.726i −0.151809 0.198630i
\(785\) 109.470 + 63.2025i 0.139452 + 0.0805127i
\(786\) 876.596 354.179i 1.11526 0.450610i
\(787\) −512.099 −0.650698 −0.325349 0.945594i \(-0.605482\pi\)
−0.325349 + 0.945594i \(0.605482\pi\)
\(788\) 306.366i 0.388789i
\(789\) −528.849 74.3187i −0.670278 0.0941935i
\(790\) −45.1668 + 78.2312i −0.0571732 + 0.0990269i
\(791\) 40.8337 + 632.303i 0.0516229 + 0.799372i
\(792\) −319.641 + 308.688i −0.403588 + 0.389758i
\(793\) −107.194 185.665i −0.135175 0.234130i
\(794\) −758.908 + 438.156i −0.955804 + 0.551834i
\(795\) 30.8958 219.853i 0.0388626 0.276545i
\(796\) −1.12362 + 1.94617i −0.00141159 + 0.00244494i
\(797\) −205.675 + 118.747i −0.258061 + 0.148992i −0.623450 0.781863i \(-0.714269\pi\)
0.365388 + 0.930855i \(0.380936\pi\)
\(798\) 394.374 578.036i 0.494203 0.724356i
\(799\) 51.4737 89.1551i 0.0644227 0.111583i
\(800\) −112.675 + 65.0531i −0.140844 + 0.0813164i
\(801\) 893.770 + 925.483i 1.11582 + 1.15541i
\(802\) −203.165 + 351.892i −0.253323 + 0.438769i
\(803\) 1455.24i 1.81225i
\(804\) −454.552 355.126i −0.565363 0.441699i
\(805\) −309.183 + 19.9668i −0.384078 + 0.0248035i
\(806\) −677.418 + 391.107i −0.840469 + 0.485245i
\(807\) 579.914 + 1435.29i 0.718605 + 1.77855i
\(808\) −58.7033 101.677i −0.0726526 0.125838i
\(809\) 227.210 + 131.180i 0.280853 + 0.162150i 0.633809 0.773489i \(-0.281490\pi\)
−0.352957 + 0.935640i \(0.614824\pi\)
\(810\) −5.64663 + 161.912i −0.00697115 + 0.199891i
\(811\) 241.274 0.297502 0.148751 0.988875i \(-0.452475\pi\)
0.148751 + 0.988875i \(0.452475\pi\)
\(812\) 185.022 123.371i 0.227859 0.151934i
\(813\) 98.2913 699.438i 0.120900 0.860317i
\(814\) 387.659 671.445i 0.476240 0.824871i
\(815\) 297.734i 0.365317i
\(816\) −108.333 268.124i −0.132761 0.328584i
\(817\) −1493.31 −1.82780
\(818\) 625.074i 0.764150i
\(819\) 329.012 + 1031.16i 0.401724 + 1.25905i
\(820\) −28.3332 −0.0345526
\(821\) 928.640i 1.13111i 0.824711 + 0.565554i \(0.191338\pi\)
−0.824711 + 0.565554i \(0.808662\pi\)
\(822\) −51.0255 + 363.096i −0.0620748 + 0.441722i
\(823\) −133.546 −0.162268 −0.0811339 0.996703i \(-0.525854\pi\)
−0.0811339 + 0.996703i \(0.525854\pi\)
\(824\) 82.9612 + 47.8977i 0.100681 + 0.0581283i
\(825\) −451.215 1116.76i −0.546927 1.35365i
\(826\) 185.078 374.394i 0.224065 0.453261i
\(827\) 880.144i 1.06426i 0.846662 + 0.532130i \(0.178608\pi\)
−0.846662 + 0.532130i \(0.821392\pi\)
\(828\) −155.258 + 541.496i −0.187510 + 0.653980i
\(829\) −268.250 + 464.622i −0.323582 + 0.560461i −0.981224 0.192870i \(-0.938221\pi\)
0.657642 + 0.753330i \(0.271554\pi\)
\(830\) 7.46810 4.31171i 0.00899771 0.00519483i
\(831\) 212.282 1510.59i 0.255453 1.81780i
\(832\) −68.7224 119.031i −0.0825991 0.143066i
\(833\) 151.881 + 1171.02i 0.182330 + 1.40579i
\(834\) 13.5572 + 1.90518i 0.0162557 + 0.00228439i
\(835\) 159.849 0.191436
\(836\) −712.399 411.303i −0.852151 0.491990i
\(837\) 353.522 794.096i 0.422368 0.948741i
\(838\) −230.070 398.493i −0.274547 0.475529i
\(839\) 1336.23 + 771.471i 1.59264 + 0.919513i 0.992852 + 0.119356i \(0.0380830\pi\)
0.599791 + 0.800157i \(0.295250\pi\)
\(840\) −6.30498 + 83.7685i −0.00750593 + 0.0997244i
\(841\) −294.344 509.818i −0.349992 0.606204i
\(842\) 492.448 + 284.315i 0.584856 + 0.337666i
\(843\) −17.5589 43.4583i −0.0208290 0.0515520i
\(844\) 157.839 + 273.385i 0.187013 + 0.323916i
\(845\) −154.540 + 89.2237i −0.182888 + 0.105590i
\(846\) 13.1552 + 52.7574i 0.0155499 + 0.0623610i
\(847\) −713.462 1069.99i −0.842340 1.26327i
\(848\) −181.262 104.651i −0.213752 0.123410i
\(849\) −1205.62 941.909i −1.42004 1.10943i
\(850\) 783.843 0.922168
\(851\) 982.860i 1.15495i
\(852\) −76.8398 + 98.3528i −0.0901876 + 0.115438i
\(853\) −470.293 + 814.571i −0.551340 + 0.954948i 0.446839 + 0.894615i \(0.352550\pi\)
−0.998178 + 0.0603337i \(0.980784\pi\)
\(854\) 110.739 + 54.7424i 0.129670 + 0.0641012i
\(855\) −291.004 + 72.5625i −0.340355 + 0.0848684i
\(856\) −64.9016 112.413i −0.0758196 0.131323i
\(857\) −553.341 + 319.471i −0.645672 + 0.372779i −0.786796 0.617213i \(-0.788262\pi\)
0.141124 + 0.989992i \(0.454928\pi\)
\(858\) 1179.75 476.665i 1.37500 0.555554i
\(859\) −149.147 + 258.330i −0.173628 + 0.300733i −0.939686 0.342039i \(-0.888882\pi\)
0.766057 + 0.642772i \(0.222216\pi\)
\(860\) 155.254 89.6361i 0.180528 0.104228i
\(861\) 118.551 173.760i 0.137689 0.201812i
\(862\) 120.977 209.539i 0.140345 0.243085i
\(863\) −949.481 + 548.183i −1.10021 + 0.635207i −0.936276 0.351265i \(-0.885752\pi\)
−0.163934 + 0.986471i \(0.552418\pi\)
\(864\) 139.533 + 62.1181i 0.161496 + 0.0718960i
\(865\) −36.6479 + 63.4760i −0.0423675 + 0.0733827i
\(866\) 318.470i 0.367749i
\(867\) −121.798 + 866.707i −0.140482 + 0.999662i
\(868\) 199.734 404.041i 0.230108 0.465485i
\(869\) −682.768 + 394.196i −0.785694 + 0.453621i
\(870\) −94.3849 13.2638i −0.108488 0.0152458i
\(871\) 825.856 + 1430.43i 0.948170 + 1.64228i
\(872\) 106.080 + 61.2452i 0.121651 + 0.0702354i
\(873\) −303.590 87.0455i −0.347755 0.0997085i
\(874\) −1042.81 −1.19314
\(875\) −425.995 210.586i −0.486852 0.240670i
\(876\) −463.765 + 187.379i −0.529412 + 0.213903i
\(877\) −91.0649 + 157.729i −0.103837 + 0.179851i −0.913262 0.407372i \(-0.866445\pi\)
0.809426 + 0.587223i \(0.199779\pi\)
\(878\) 83.9072i 0.0955662i
\(879\) −1296.85 182.245i −1.47537 0.207332i
\(880\) 98.7539 0.112220
\(881\) 447.835i 0.508325i −0.967161 0.254163i \(-0.918200\pi\)
0.967161 0.254163i \(-0.0817999\pi\)
\(882\) −487.350 389.168i −0.552551 0.441233i
\(883\) 576.635 0.653040 0.326520 0.945190i \(-0.394124\pi\)
0.326520 + 0.945190i \(0.394124\pi\)
\(884\) 828.056i 0.936715i
\(885\) −165.966 + 67.0567i −0.187532 + 0.0757703i
\(886\) 432.831 0.488523
\(887\) 1412.61 + 815.571i 1.59257 + 0.919471i 0.992864 + 0.119252i \(0.0380495\pi\)
0.599707 + 0.800220i \(0.295284\pi\)
\(888\) −263.896 37.0851i −0.297181 0.0417625i
\(889\) −420.462 + 850.553i −0.472961 + 0.956752i
\(890\) 285.930i 0.321270i
\(891\) −749.228 + 1199.14i −0.840884 + 1.34583i
\(892\) −105.657 + 183.003i −0.118449 + 0.205160i
\(893\) −87.1699 + 50.3275i −0.0976146 + 0.0563578i
\(894\) −770.278 + 311.223i −0.861609 + 0.348124i
\(895\) 136.748 + 236.855i 0.152791 + 0.264642i
\(896\) 70.9950 + 35.0957i 0.0792355 + 0.0391693i
\(897\) 993.055 1271.08i 1.10708 1.41704i
\(898\) −630.904 −0.702566
\(899\) 442.867 + 255.689i 0.492621 + 0.284415i
\(900\) −297.797 + 287.592i −0.330885 + 0.319547i
\(901\) 630.488 + 1092.04i 0.699764 + 1.21203i
\(902\) −214.150 123.640i −0.237417 0.137073i
\(903\) −99.8931 + 1327.19i −0.110624 + 1.46975i
\(904\) −128.011 221.721i −0.141605 0.245267i
\(905\) 215.355 + 124.335i 0.237961 + 0.137387i
\(906\) 132.342 + 18.5979i 0.146072 + 0.0205274i
\(907\) 477.583 + 827.199i 0.526553 + 0.912016i 0.999521 + 0.0309368i \(0.00984906\pi\)
−0.472969 + 0.881079i \(0.656818\pi\)
\(908\) −104.096 + 60.0997i −0.114643 + 0.0661891i
\(909\) −259.521 268.729i −0.285501 0.295632i
\(910\) 106.597 215.635i 0.117140 0.236962i
\(911\) 198.257 + 114.464i 0.217625 + 0.125646i 0.604850 0.796339i \(-0.293233\pi\)
−0.387225 + 0.921985i \(0.626566\pi\)
\(912\) −39.3471 + 279.992i −0.0431437 + 0.307009i
\(913\) 75.2614 0.0824331
\(914\) 449.279i 0.491552i
\(915\) −19.8341 49.0895i −0.0216766 0.0536497i
\(916\) 51.0009 88.3362i 0.0556779 0.0964369i
\(917\) 1297.84 865.389i 1.41531 0.943718i
\(918\) −540.890 744.418i −0.589205 0.810913i
\(919\) −431.028 746.563i −0.469019 0.812364i 0.530354 0.847776i \(-0.322059\pi\)
−0.999373 + 0.0354120i \(0.988726\pi\)
\(920\) 108.417 62.5945i 0.117844 0.0680375i
\(921\) −951.178 743.124i −1.03277 0.806866i
\(922\) −54.2015 + 93.8798i −0.0587869 + 0.101822i
\(923\) 309.506 178.693i 0.335326 0.193600i
\(924\) −413.202 + 605.633i −0.447189 + 0.655447i
\(925\) 361.166 625.558i 0.390450 0.676279i
\(926\) 381.460 220.236i 0.411943 0.237836i
\(927\) 293.013 + 84.0128i 0.316087 + 0.0906287i
\(928\) −44.9278 + 77.8172i −0.0484135 + 0.0838547i
\(929\) 1396.41i 1.50313i 0.659658 + 0.751566i \(0.270701\pi\)
−0.659658 + 0.751566i \(0.729299\pi\)
\(930\) −179.108 + 72.3668i −0.192590 + 0.0778138i
\(931\) 443.869 1065.80i 0.476766 1.14479i
\(932\) −39.4781 + 22.7927i −0.0423585 + 0.0244557i
\(933\) −173.514 + 222.093i −0.185975 + 0.238042i
\(934\) −216.394 374.805i −0.231685 0.401290i
\(935\) −515.248 297.478i −0.551067 0.318159i
\(936\) −303.814 314.594i −0.324588 0.336105i
\(937\) −744.918 −0.795003 −0.397501 0.917602i \(-0.630123\pi\)
−0.397501 + 0.917602i \(0.630123\pi\)
\(938\) −853.167 421.754i −0.909560 0.449631i
\(939\) 955.603 + 746.581i 1.01768 + 0.795081i
\(940\) 6.04182 10.4647i 0.00642746 0.0111327i
\(941\) 1615.42i 1.71671i 0.513056 + 0.858355i \(0.328513\pi\)
−0.513056 + 0.858355i \(0.671487\pi\)
\(942\) 233.450 298.809i 0.247823 0.317207i
\(943\) −313.473 −0.332421
\(944\) 168.753i 0.178763i
\(945\) 45.0239 + 263.484i 0.0476443 + 0.278820i
\(946\) 1564.61 1.65392
\(947\) 685.435i 0.723796i −0.932218 0.361898i \(-0.882129\pi\)
0.932218 0.361898i \(-0.117871\pi\)
\(948\) 213.540 + 166.832i 0.225253 + 0.175983i
\(949\) 1432.26 1.50923
\(950\) −663.712 383.195i −0.698645 0.403363i
\(951\) 215.550 275.898i 0.226657 0.290114i
\(952\) −264.697 396.971i −0.278043 0.416987i
\(953\) 988.352i 1.03710i 0.855049 + 0.518548i \(0.173527\pi\)
−0.855049 + 0.518548i \(0.826473\pi\)
\(954\) −640.203 183.559i −0.671072 0.192410i
\(955\) 16.4697 28.5263i 0.0172457 0.0298705i
\(956\) −700.453 + 404.407i −0.732691 + 0.423019i
\(957\) −655.508 512.127i −0.684962 0.535138i
\(958\) 333.593 + 577.799i 0.348218 + 0.603131i
\(959\) 38.9869 + 603.706i 0.0406537 + 0.629516i
\(960\) −12.7158 31.4715i −0.0132456 0.0327829i
\(961\) 75.4424 0.0785040
\(962\) 660.842 + 381.538i 0.686946 + 0.396609i
\(963\) −286.923 297.103i −0.297947 0.308518i
\(964\) −303.641 525.922i −0.314980 0.545562i
\(965\) 103.907 + 59.9906i 0.107675 + 0.0621664i
\(966\) −69.7572 + 926.799i −0.0722124 + 0.959419i
\(967\) −252.350 437.083i −0.260962 0.451999i 0.705536 0.708674i \(-0.250706\pi\)
−0.966498 + 0.256675i \(0.917373\pi\)
\(968\) 450.022 + 259.820i 0.464899 + 0.268410i
\(969\) 1048.72 1342.33i 1.08227 1.38528i
\(970\) 35.0937 + 60.7840i 0.0361790 + 0.0626640i
\(971\) −1011.31 + 583.878i −1.04151 + 0.601316i −0.920261 0.391306i \(-0.872024\pi\)
−0.121250 + 0.992622i \(0.538690\pi\)
\(972\) 478.621 + 84.3655i 0.492409 + 0.0867957i
\(973\) 22.5411 1.45569i 0.0231666 0.00149608i
\(974\) −478.211 276.095i −0.490976 0.283465i
\(975\) 1099.12 444.090i 1.12731 0.455476i
\(976\) −49.9138 −0.0511412
\(977\) 294.617i 0.301552i −0.988568 0.150776i \(-0.951823\pi\)
0.988568 0.150776i \(-0.0481773\pi\)
\(978\) 884.453 + 124.291i 0.904349 + 0.127087i
\(979\) 1247.74 2161.14i 1.27450 2.20750i
\(980\) 17.8273 + 137.451i 0.0181911 + 0.140256i
\(981\) 374.666 + 107.424i 0.381923 + 0.109505i
\(982\) 407.087 + 705.096i 0.414549 + 0.718020i
\(983\) −539.646 + 311.565i −0.548978 + 0.316953i −0.748710 0.662898i \(-0.769326\pi\)
0.199731 + 0.979851i \(0.435993\pi\)
\(984\) −11.8279 + 84.1670i −0.0120202 + 0.0855355i
\(985\) 108.324 187.622i 0.109973 0.190479i
\(986\) 468.821 270.674i 0.475477 0.274517i
\(987\) 38.8977 + 80.8391i 0.0394100 + 0.0819039i
\(988\) 404.809 701.149i 0.409725 0.709665i
\(989\) 1717.70 991.717i 1.73681 1.00275i
\(990\) 304.897 76.0268i 0.307977 0.0767948i
\(991\) 272.200 471.464i 0.274672 0.475746i −0.695380 0.718642i \(-0.744764\pi\)
0.970052 + 0.242896i \(0.0780974\pi\)
\(992\) 182.116i 0.183584i
\(993\) 1445.24 + 1129.12i 1.45543 + 1.13708i
\(994\) −91.2563 + 184.602i −0.0918072 + 0.185717i
\(995\) 1.37624 0.794573i 0.00138316 0.000798566i
\(996\) −9.69082 23.9848i −0.00972974 0.0240811i
\(997\) 523.979 + 907.559i 0.525556 + 0.910290i 0.999557 + 0.0297653i \(0.00947600\pi\)
−0.474001 + 0.880524i \(0.657191\pi\)
\(998\) −879.526 507.794i −0.881288 0.508812i
\(999\) −843.316 + 88.6655i −0.844160 + 0.0887543i
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 126.3.r.a.11.7 yes 32
3.2 odd 2 378.3.r.a.305.12 32
7.2 even 3 126.3.i.a.65.1 32
9.4 even 3 378.3.i.a.179.12 32
9.5 odd 6 126.3.i.a.95.1 yes 32
21.2 odd 6 378.3.i.a.359.13 32
63.23 odd 6 inner 126.3.r.a.23.15 yes 32
63.58 even 3 378.3.r.a.233.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.3.i.a.65.1 32 7.2 even 3
126.3.i.a.95.1 yes 32 9.5 odd 6
126.3.r.a.11.7 yes 32 1.1 even 1 trivial
126.3.r.a.23.15 yes 32 63.23 odd 6 inner
378.3.i.a.179.12 32 9.4 even 3
378.3.i.a.359.13 32 21.2 odd 6
378.3.r.a.233.4 32 63.58 even 3
378.3.r.a.305.12 32 3.2 odd 2