Properties

Label 60.4.j.b.7.14
Level $60$
Weight $4$
Character 60.7
Analytic conductor $3.540$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [60,4,Mod(7,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.7");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 60.j (of order \(4\), 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: \(3.54011460034\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.14
Character \(\chi\) \(=\) 60.7
Dual form 60.4.j.b.43.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.79539 - 0.431034i) q^{2} +(2.12132 + 2.12132i) q^{3} +(7.62842 - 2.40982i) q^{4} +(2.54602 - 10.8866i) q^{5} +(6.84428 + 5.01556i) q^{6} +(-9.77420 + 9.77420i) q^{7} +(20.2857 - 10.0245i) q^{8} +9.00000i q^{9} +O(q^{10})\) \(q+(2.79539 - 0.431034i) q^{2} +(2.12132 + 2.12132i) q^{3} +(7.62842 - 2.40982i) q^{4} +(2.54602 - 10.8866i) q^{5} +(6.84428 + 5.01556i) q^{6} +(-9.77420 + 9.77420i) q^{7} +(20.2857 - 10.0245i) q^{8} +9.00000i q^{9} +(2.42464 - 31.5297i) q^{10} +32.5528i q^{11} +(21.2943 + 11.0703i) q^{12} +(-5.95358 + 5.95358i) q^{13} +(-23.1097 + 31.5357i) q^{14} +(28.4949 - 17.6930i) q^{15} +(52.3856 - 36.7662i) q^{16} +(-71.0654 - 71.0654i) q^{17} +(3.87930 + 25.1585i) q^{18} -104.985 q^{19} +(-6.81253 - 89.1829i) q^{20} -41.4684 q^{21} +(14.0314 + 90.9978i) q^{22} +(83.3400 + 83.3400i) q^{23} +(64.2976 + 21.7673i) q^{24} +(-112.036 - 55.4350i) q^{25} +(-14.0764 + 19.2088i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(-51.0077 + 98.1157i) q^{28} +171.025i q^{29} +(72.0280 - 61.7411i) q^{30} -123.188i q^{31} +(130.591 - 125.356i) q^{32} +(-69.0549 + 69.0549i) q^{33} +(-229.287 - 168.024i) q^{34} +(81.5224 + 131.293i) q^{35} +(21.6883 + 68.6558i) q^{36} +(-52.1044 - 52.1044i) q^{37} +(-293.474 + 45.2521i) q^{38} -25.2589 q^{39} +(-57.4845 - 246.365i) q^{40} +471.285 q^{41} +(-115.920 + 17.8743i) q^{42} +(-258.032 - 258.032i) q^{43} +(78.4463 + 248.326i) q^{44} +(97.9793 + 22.9142i) q^{45} +(268.890 + 197.045i) q^{46} +(-54.3382 + 54.3382i) q^{47} +(189.119 + 33.1338i) q^{48} +151.930i q^{49} +(-337.077 - 106.671i) q^{50} -301.505i q^{51} +(-31.0694 + 59.7635i) q^{52} +(331.639 - 331.639i) q^{53} +(-45.1400 + 61.5985i) q^{54} +(354.389 + 82.8802i) q^{55} +(-100.295 + 296.258i) q^{56} +(-222.707 - 222.707i) q^{57} +(73.7175 + 478.081i) q^{58} +567.547 q^{59} +(174.734 - 203.637i) q^{60} +832.043 q^{61} +(-53.0982 - 344.358i) q^{62} +(-87.9678 - 87.9678i) q^{63} +(311.019 - 406.707i) q^{64} +(49.6562 + 79.9722i) q^{65} +(-163.271 + 222.801i) q^{66} +(38.6168 - 38.6168i) q^{67} +(-713.371 - 370.862i) q^{68} +353.581i q^{69} +(284.479 + 331.877i) q^{70} +534.459i q^{71} +(90.2203 + 182.571i) q^{72} +(-418.286 + 418.286i) q^{73} +(-168.111 - 123.193i) q^{74} +(-120.068 - 355.259i) q^{75} +(-800.870 + 252.995i) q^{76} +(-318.178 - 318.178i) q^{77} +(-70.6085 + 10.8874i) q^{78} +76.6095 q^{79} +(-266.883 - 663.908i) q^{80} -81.0000 q^{81} +(1317.43 - 203.140i) q^{82} +(-908.404 - 908.404i) q^{83} +(-316.339 + 99.9313i) q^{84} +(-954.594 + 592.726i) q^{85} +(-832.522 - 610.081i) q^{86} +(-362.799 + 362.799i) q^{87} +(326.325 + 660.357i) q^{88} -12.1097i q^{89} +(283.767 + 21.8218i) q^{90} -116.383i q^{91} +(836.586 + 434.918i) q^{92} +(261.321 - 261.321i) q^{93} +(-128.475 + 175.318i) q^{94} +(-267.294 + 1142.93i) q^{95} +(542.944 + 11.1050i) q^{96} +(-613.459 - 613.459i) q^{97} +(65.4869 + 424.704i) q^{98} -292.975 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 24 q^{5} - 36 q^{6} + 84 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 24 q^{5} - 36 q^{6} + 84 q^{8} + 128 q^{10} + 24 q^{12} - 412 q^{13} - 180 q^{16} + 20 q^{17} + 52 q^{20} + 144 q^{21} - 436 q^{22} + 132 q^{25} + 704 q^{26} + 508 q^{28} + 480 q^{30} + 340 q^{32} - 96 q^{33} + 324 q^{36} + 508 q^{37} - 1792 q^{38} - 2696 q^{40} - 1696 q^{41} - 1500 q^{42} + 612 q^{45} + 2584 q^{46} + 528 q^{48} + 832 q^{50} + 504 q^{52} + 1772 q^{53} - 512 q^{56} + 720 q^{57} - 1060 q^{58} - 84 q^{60} + 2096 q^{61} - 472 q^{62} + 28 q^{65} - 648 q^{66} + 5872 q^{68} + 2956 q^{70} + 756 q^{72} - 3348 q^{73} - 3480 q^{76} - 384 q^{77} - 1032 q^{78} - 4828 q^{80} - 2268 q^{81} - 928 q^{82} - 476 q^{85} - 3616 q^{86} + 380 q^{88} - 1116 q^{90} + 472 q^{92} - 2688 q^{93} + 396 q^{96} + 8300 q^{97} + 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.79539 0.431034i 0.988320 0.152393i
\(3\) 2.12132 + 2.12132i 0.408248 + 0.408248i
\(4\) 7.62842 2.40982i 0.953552 0.301227i
\(5\) 2.54602 10.8866i 0.227723 0.973726i
\(6\) 6.84428 + 5.01556i 0.465694 + 0.341266i
\(7\) −9.77420 + 9.77420i −0.527757 + 0.527757i −0.919903 0.392146i \(-0.871733\pi\)
0.392146 + 0.919903i \(0.371733\pi\)
\(8\) 20.2857 10.0245i 0.896510 0.443024i
\(9\) 9.00000i 0.333333i
\(10\) 2.42464 31.5297i 0.0766740 0.997056i
\(11\) 32.5528i 0.892276i 0.894964 + 0.446138i \(0.147201\pi\)
−0.894964 + 0.446138i \(0.852799\pi\)
\(12\) 21.2943 + 11.0703i 0.512262 + 0.266311i
\(13\) −5.95358 + 5.95358i −0.127017 + 0.127017i −0.767758 0.640740i \(-0.778628\pi\)
0.640740 + 0.767758i \(0.278628\pi\)
\(14\) −23.1097 + 31.5357i −0.441166 + 0.602020i
\(15\) 28.4949 17.6930i 0.490490 0.304554i
\(16\) 52.3856 36.7662i 0.818525 0.574471i
\(17\) −71.0654 71.0654i −1.01388 1.01388i −0.999902 0.0139739i \(-0.995552\pi\)
−0.0139739 0.999902i \(-0.504448\pi\)
\(18\) 3.87930 + 25.1585i 0.0507978 + 0.329440i
\(19\) −104.985 −1.26764 −0.633822 0.773479i \(-0.718515\pi\)
−0.633822 + 0.773479i \(0.718515\pi\)
\(20\) −6.81253 89.1829i −0.0761664 0.997095i
\(21\) −41.4684 −0.430912
\(22\) 14.0314 + 90.9978i 0.135977 + 0.881855i
\(23\) 83.3400 + 83.3400i 0.755547 + 0.755547i 0.975509 0.219962i \(-0.0705932\pi\)
−0.219962 + 0.975509i \(0.570593\pi\)
\(24\) 64.2976 + 21.7673i 0.546862 + 0.185135i
\(25\) −112.036 55.4350i −0.896284 0.443480i
\(26\) −14.0764 + 19.2088i −0.106177 + 0.144891i
\(27\) −19.0919 + 19.0919i −0.136083 + 0.136083i
\(28\) −51.0077 + 98.1157i −0.344270 + 0.662219i
\(29\) 171.025i 1.09512i 0.836766 + 0.547561i \(0.184443\pi\)
−0.836766 + 0.547561i \(0.815557\pi\)
\(30\) 72.0280 61.7411i 0.438349 0.375744i
\(31\) 123.188i 0.713716i −0.934159 0.356858i \(-0.883848\pi\)
0.934159 0.356858i \(-0.116152\pi\)
\(32\) 130.591 125.356i 0.721419 0.692499i
\(33\) −69.0549 + 69.0549i −0.364270 + 0.364270i
\(34\) −229.287 168.024i −1.15654 0.847526i
\(35\) 81.5224 + 131.293i 0.393708 + 0.634074i
\(36\) 21.6883 + 68.6558i 0.100409 + 0.317851i
\(37\) −52.1044 52.1044i −0.231511 0.231511i 0.581812 0.813323i \(-0.302344\pi\)
−0.813323 + 0.581812i \(0.802344\pi\)
\(38\) −293.474 + 45.2521i −1.25284 + 0.193181i
\(39\) −25.2589 −0.103709
\(40\) −57.4845 246.365i −0.227228 0.973842i
\(41\) 471.285 1.79518 0.897590 0.440831i \(-0.145316\pi\)
0.897590 + 0.440831i \(0.145316\pi\)
\(42\) −115.920 + 17.8743i −0.425879 + 0.0656682i
\(43\) −258.032 258.032i −0.915106 0.915106i 0.0815622 0.996668i \(-0.474009\pi\)
−0.996668 + 0.0815622i \(0.974009\pi\)
\(44\) 78.4463 + 248.326i 0.268778 + 0.850832i
\(45\) 97.9793 + 22.9142i 0.324575 + 0.0759078i
\(46\) 268.890 + 197.045i 0.861863 + 0.631582i
\(47\) −54.3382 + 54.3382i −0.168639 + 0.168639i −0.786381 0.617742i \(-0.788048\pi\)
0.617742 + 0.786381i \(0.288048\pi\)
\(48\) 189.119 + 33.1338i 0.568688 + 0.0996343i
\(49\) 151.930i 0.442944i
\(50\) −337.077 106.671i −0.953399 0.301712i
\(51\) 301.505i 0.827827i
\(52\) −31.0694 + 59.7635i −0.0828567 + 0.159379i
\(53\) 331.639 331.639i 0.859511 0.859511i −0.131770 0.991280i \(-0.542066\pi\)
0.991280 + 0.131770i \(0.0420660\pi\)
\(54\) −45.1400 + 61.5985i −0.113755 + 0.155231i
\(55\) 354.389 + 82.8802i 0.868833 + 0.203192i
\(56\) −100.295 + 296.258i −0.239331 + 0.706949i
\(57\) −222.707 222.707i −0.517513 0.517513i
\(58\) 73.7175 + 478.081i 0.166889 + 1.08233i
\(59\) 567.547 1.25234 0.626172 0.779685i \(-0.284621\pi\)
0.626172 + 0.779685i \(0.284621\pi\)
\(60\) 174.734 203.637i 0.375968 0.438157i
\(61\) 832.043 1.74643 0.873215 0.487336i \(-0.162031\pi\)
0.873215 + 0.487336i \(0.162031\pi\)
\(62\) −53.0982 344.358i −0.108766 0.705380i
\(63\) −87.9678 87.9678i −0.175919 0.175919i
\(64\) 311.019 406.707i 0.607460 0.794350i
\(65\) 49.6562 + 79.9722i 0.0947554 + 0.152605i
\(66\) −163.271 + 222.801i −0.304503 + 0.415528i
\(67\) 38.6168 38.6168i 0.0704148 0.0704148i −0.671022 0.741437i \(-0.734145\pi\)
0.741437 + 0.671022i \(0.234145\pi\)
\(68\) −713.371 370.862i −1.27219 0.661377i
\(69\) 353.581i 0.616902i
\(70\) 284.479 + 331.877i 0.485738 + 0.566669i
\(71\) 534.459i 0.893361i 0.894694 + 0.446680i \(0.147394\pi\)
−0.894694 + 0.446680i \(0.852606\pi\)
\(72\) 90.2203 + 182.571i 0.147675 + 0.298837i
\(73\) −418.286 + 418.286i −0.670640 + 0.670640i −0.957864 0.287224i \(-0.907268\pi\)
0.287224 + 0.957864i \(0.407268\pi\)
\(74\) −168.111 123.193i −0.264088 0.193526i
\(75\) −120.068 355.259i −0.184857 0.546956i
\(76\) −800.870 + 252.995i −1.20876 + 0.381848i
\(77\) −318.178 318.178i −0.470905 0.470905i
\(78\) −70.6085 + 10.8874i −0.102498 + 0.0158046i
\(79\) 76.6095 0.109104 0.0545522 0.998511i \(-0.482627\pi\)
0.0545522 + 0.998511i \(0.482627\pi\)
\(80\) −266.883 663.908i −0.372981 0.927839i
\(81\) −81.0000 −0.111111
\(82\) 1317.43 203.140i 1.77421 0.273574i
\(83\) −908.404 908.404i −1.20133 1.20133i −0.973763 0.227565i \(-0.926923\pi\)
−0.227565 0.973763i \(-0.573077\pi\)
\(84\) −316.339 + 99.9313i −0.410897 + 0.129802i
\(85\) −954.594 + 592.726i −1.21812 + 0.756354i
\(86\) −832.522 610.081i −1.04387 0.764961i
\(87\) −362.799 + 362.799i −0.447081 + 0.447081i
\(88\) 326.325 + 660.357i 0.395300 + 0.799935i
\(89\) 12.1097i 0.0144227i −0.999974 0.00721136i \(-0.997705\pi\)
0.999974 0.00721136i \(-0.00229547\pi\)
\(90\) 283.767 + 21.8218i 0.332352 + 0.0255580i
\(91\) 116.383i 0.134069i
\(92\) 836.586 + 434.918i 0.948045 + 0.492863i
\(93\) 261.321 261.321i 0.291374 0.291374i
\(94\) −128.475 + 175.318i −0.140970 + 0.192369i
\(95\) −267.294 + 1142.93i −0.288672 + 1.23434i
\(96\) 542.944 + 11.1050i 0.577230 + 0.0118062i
\(97\) −613.459 613.459i −0.642138 0.642138i 0.308943 0.951081i \(-0.400025\pi\)
−0.951081 + 0.308943i \(0.900025\pi\)
\(98\) 65.4869 + 424.704i 0.0675018 + 0.437771i
\(99\) −292.975 −0.297425
\(100\) −988.242 152.897i −0.988242 0.152897i
\(101\) −941.741 −0.927789 −0.463895 0.885890i \(-0.653548\pi\)
−0.463895 + 0.885890i \(0.653548\pi\)
\(102\) −129.959 842.824i −0.126155 0.818157i
\(103\) 779.115 + 779.115i 0.745325 + 0.745325i 0.973597 0.228272i \(-0.0733076\pi\)
−0.228272 + 0.973597i \(0.573308\pi\)
\(104\) −61.0910 + 180.454i −0.0576007 + 0.170144i
\(105\) −105.580 + 451.450i −0.0981287 + 0.419590i
\(106\) 784.112 1070.01i 0.718488 0.980455i
\(107\) −541.238 + 541.238i −0.489004 + 0.489004i −0.907992 0.418988i \(-0.862385\pi\)
0.418988 + 0.907992i \(0.362385\pi\)
\(108\) −99.6330 + 191.649i −0.0887703 + 0.170754i
\(109\) 697.524i 0.612942i −0.951880 0.306471i \(-0.900852\pi\)
0.951880 0.306471i \(-0.0991482\pi\)
\(110\) 1026.38 + 78.9290i 0.889650 + 0.0684144i
\(111\) 221.060i 0.189028i
\(112\) −152.667 + 871.387i −0.128801 + 0.735164i
\(113\) 715.431 715.431i 0.595593 0.595593i −0.343543 0.939137i \(-0.611627\pi\)
0.939137 + 0.343543i \(0.111627\pi\)
\(114\) −718.547 526.559i −0.590334 0.432603i
\(115\) 1119.47 695.102i 0.907751 0.563640i
\(116\) 412.138 + 1304.65i 0.329880 + 1.04426i
\(117\) −53.5823 53.5823i −0.0423392 0.0423392i
\(118\) 1586.51 244.632i 1.23772 0.190849i
\(119\) 1389.22 1.07016
\(120\) 400.675 644.561i 0.304804 0.490334i
\(121\) 271.315 0.203843
\(122\) 2325.89 358.639i 1.72603 0.266144i
\(123\) 999.747 + 999.747i 0.732879 + 0.732879i
\(124\) −296.860 939.729i −0.214991 0.680566i
\(125\) −888.743 + 1078.55i −0.635933 + 0.771744i
\(126\) −283.822 207.987i −0.200673 0.147055i
\(127\) −1377.02 + 1377.02i −0.962130 + 0.962130i −0.999309 0.0371786i \(-0.988163\pi\)
0.0371786 + 0.999309i \(0.488163\pi\)
\(128\) 694.116 1270.97i 0.479311 0.877645i
\(129\) 1094.74i 0.747181i
\(130\) 173.279 + 202.150i 0.116905 + 0.136382i
\(131\) 2511.90i 1.67531i −0.546198 0.837656i \(-0.683925\pi\)
0.546198 0.837656i \(-0.316075\pi\)
\(132\) −360.370 + 693.190i −0.237623 + 0.457079i
\(133\) 1026.15 1026.15i 0.669008 0.669008i
\(134\) 91.3038 124.594i 0.0588616 0.0803231i
\(135\) 159.237 + 256.454i 0.101518 + 0.163497i
\(136\) −2154.01 729.218i −1.35812 0.459779i
\(137\) 681.328 + 681.328i 0.424889 + 0.424889i 0.886883 0.461994i \(-0.152866\pi\)
−0.461994 + 0.886883i \(0.652866\pi\)
\(138\) 152.406 + 988.398i 0.0940118 + 0.609696i
\(139\) −2059.15 −1.25651 −0.628254 0.778009i \(-0.716230\pi\)
−0.628254 + 0.778009i \(0.716230\pi\)
\(140\) 938.279 + 805.105i 0.566422 + 0.486027i
\(141\) −230.537 −0.137693
\(142\) 230.370 + 1494.02i 0.136142 + 0.882926i
\(143\) −193.806 193.806i −0.113335 0.113335i
\(144\) 330.896 + 471.470i 0.191490 + 0.272842i
\(145\) 1861.88 + 435.433i 1.06635 + 0.249385i
\(146\) −988.978 + 1349.57i −0.560606 + 0.765008i
\(147\) −322.292 + 322.292i −0.180831 + 0.180831i
\(148\) −523.036 271.912i −0.290495 0.151021i
\(149\) 1201.46i 0.660586i 0.943878 + 0.330293i \(0.107148\pi\)
−0.943878 + 0.330293i \(0.892852\pi\)
\(150\) −488.765 941.333i −0.266050 0.512397i
\(151\) 1112.39i 0.599505i 0.954017 + 0.299752i \(0.0969041\pi\)
−0.954017 + 0.299752i \(0.903096\pi\)
\(152\) −2129.70 + 1052.42i −1.13645 + 0.561596i
\(153\) 639.589 639.589i 0.337959 0.337959i
\(154\) −1026.58 752.286i −0.537168 0.393642i
\(155\) −1341.10 313.639i −0.694964 0.162530i
\(156\) −192.686 + 60.8693i −0.0988923 + 0.0312400i
\(157\) −614.705 614.705i −0.312476 0.312476i 0.533392 0.845868i \(-0.320917\pi\)
−0.845868 + 0.533392i \(0.820917\pi\)
\(158\) 214.153 33.0213i 0.107830 0.0166268i
\(159\) 1407.02 0.701787
\(160\) −1032.21 1740.85i −0.510021 0.860162i
\(161\) −1629.16 −0.797491
\(162\) −226.427 + 34.9137i −0.109813 + 0.0169326i
\(163\) −1714.95 1714.95i −0.824081 0.824081i 0.162609 0.986691i \(-0.448009\pi\)
−0.986691 + 0.162609i \(0.948009\pi\)
\(164\) 3595.16 1135.71i 1.71180 0.540757i
\(165\) 575.957 + 927.588i 0.271747 + 0.437652i
\(166\) −2930.90 2147.79i −1.37037 1.00422i
\(167\) 1908.98 1908.98i 0.884559 0.884559i −0.109435 0.993994i \(-0.534904\pi\)
0.993994 + 0.109435i \(0.0349042\pi\)
\(168\) −841.216 + 415.700i −0.386317 + 0.190904i
\(169\) 2126.11i 0.967733i
\(170\) −2412.98 + 2068.36i −1.08863 + 0.933154i
\(171\) 944.866i 0.422548i
\(172\) −2590.19 1346.57i −1.14826 0.596947i
\(173\) −55.3986 + 55.3986i −0.0243461 + 0.0243461i −0.719175 0.694829i \(-0.755480\pi\)
0.694829 + 0.719175i \(0.255480\pi\)
\(174\) −857.785 + 1170.54i −0.373727 + 0.509992i
\(175\) 1636.89 553.225i 0.707070 0.238971i
\(176\) 1196.84 + 1705.30i 0.512587 + 0.730350i
\(177\) 1203.95 + 1203.95i 0.511267 + 0.511267i
\(178\) −5.21967 33.8512i −0.00219793 0.0142543i
\(179\) −75.7074 −0.0316125 −0.0158062 0.999875i \(-0.505031\pi\)
−0.0158062 + 0.999875i \(0.505031\pi\)
\(180\) 802.646 61.3128i 0.332365 0.0253888i
\(181\) 1328.71 0.545649 0.272824 0.962064i \(-0.412042\pi\)
0.272824 + 0.962064i \(0.412042\pi\)
\(182\) −50.1650 325.336i −0.0204312 0.132503i
\(183\) 1765.03 + 1765.03i 0.712977 + 0.712977i
\(184\) 2526.05 + 855.170i 1.01208 + 0.342630i
\(185\) −699.898 + 434.580i −0.278149 + 0.172708i
\(186\) 617.856 843.133i 0.243567 0.332374i
\(187\) 2313.38 2313.38i 0.904658 0.904658i
\(188\) −283.570 + 545.460i −0.110008 + 0.211605i
\(189\) 373.216i 0.143637i
\(190\) −254.551 + 3310.15i −0.0971953 + 1.26391i
\(191\) 527.413i 0.199803i −0.994997 0.0999013i \(-0.968147\pi\)
0.994997 0.0999013i \(-0.0318527\pi\)
\(192\) 1522.53 202.985i 0.572287 0.0762977i
\(193\) −1186.43 + 1186.43i −0.442491 + 0.442491i −0.892848 0.450357i \(-0.851297\pi\)
0.450357 + 0.892848i \(0.351297\pi\)
\(194\) −1979.28 1450.44i −0.732495 0.536780i
\(195\) −64.3098 + 274.983i −0.0236170 + 0.100984i
\(196\) 366.123 + 1158.99i 0.133427 + 0.422371i
\(197\) −34.2184 34.2184i −0.0123754 0.0123754i 0.700892 0.713267i \(-0.252785\pi\)
−0.713267 + 0.700892i \(0.752785\pi\)
\(198\) −818.980 + 126.282i −0.293952 + 0.0453257i
\(199\) −549.266 −0.195660 −0.0978302 0.995203i \(-0.531190\pi\)
−0.0978302 + 0.995203i \(0.531190\pi\)
\(200\) −2828.43 1.43981i −1.00000 0.000509049i
\(201\) 163.837 0.0574934
\(202\) −2632.53 + 405.922i −0.916953 + 0.141389i
\(203\) −1671.63 1671.63i −0.577958 0.577958i
\(204\) −726.572 2300.01i −0.249364 0.789376i
\(205\) 1199.90 5130.69i 0.408804 1.74801i
\(206\) 2513.76 + 1842.11i 0.850202 + 0.623037i
\(207\) −750.060 + 750.060i −0.251849 + 0.251849i
\(208\) −92.9915 + 530.772i −0.0309990 + 0.176935i
\(209\) 3417.56i 1.13109i
\(210\) −100.546 + 1307.49i −0.0330397 + 0.429644i
\(211\) 3610.84i 1.17811i 0.808094 + 0.589054i \(0.200499\pi\)
−0.808094 + 0.589054i \(0.799501\pi\)
\(212\) 1730.69 3329.07i 0.560681 1.07850i
\(213\) −1133.76 + 1133.76i −0.364713 + 0.364713i
\(214\) −1279.68 + 1746.26i −0.408772 + 0.557814i
\(215\) −3466.05 + 2152.13i −1.09945 + 0.682672i
\(216\) −195.906 + 578.679i −0.0617116 + 0.182287i
\(217\) 1204.06 + 1204.06i 0.376669 + 0.376669i
\(218\) −300.656 1949.85i −0.0934083 0.605783i
\(219\) −1774.64 −0.547575
\(220\) 2903.15 221.767i 0.889684 0.0679615i
\(221\) 846.188 0.257560
\(222\) −95.2844 617.950i −0.0288066 0.186820i
\(223\) 1003.49 + 1003.49i 0.301339 + 0.301339i 0.841538 0.540199i \(-0.181651\pi\)
−0.540199 + 0.841538i \(0.681651\pi\)
\(224\) −51.1673 + 2501.67i −0.0152623 + 0.746206i
\(225\) 498.915 1008.32i 0.147827 0.298761i
\(226\) 1691.53 2308.28i 0.497872 0.679401i
\(227\) 1594.19 1594.19i 0.466123 0.466123i −0.434533 0.900656i \(-0.643087\pi\)
0.900656 + 0.434533i \(0.143087\pi\)
\(228\) −2235.58 1162.22i −0.649365 0.337587i
\(229\) 1802.27i 0.520074i 0.965599 + 0.260037i \(0.0837348\pi\)
−0.965599 + 0.260037i \(0.916265\pi\)
\(230\) 2829.75 2425.61i 0.811254 0.695392i
\(231\) 1349.91i 0.384493i
\(232\) 1714.44 + 3469.36i 0.485165 + 0.981787i
\(233\) −1616.15 + 1616.15i −0.454410 + 0.454410i −0.896815 0.442406i \(-0.854125\pi\)
0.442406 + 0.896815i \(0.354125\pi\)
\(234\) −172.879 126.688i −0.0482968 0.0353924i
\(235\) 453.211 + 729.904i 0.125805 + 0.202611i
\(236\) 4329.48 1367.68i 1.19418 0.377240i
\(237\) 162.513 + 162.513i 0.0445417 + 0.0445417i
\(238\) 3883.40 598.799i 1.05766 0.163086i
\(239\) −321.450 −0.0869995 −0.0434998 0.999053i \(-0.513851\pi\)
−0.0434998 + 0.999053i \(0.513851\pi\)
\(240\) 842.216 1974.51i 0.226520 0.531057i
\(241\) −1712.86 −0.457822 −0.228911 0.973447i \(-0.573517\pi\)
−0.228911 + 0.973447i \(0.573517\pi\)
\(242\) 758.431 116.946i 0.201462 0.0310643i
\(243\) −171.827 171.827i −0.0453609 0.0453609i
\(244\) 6347.17 2005.07i 1.66531 0.526072i
\(245\) 1654.00 + 386.817i 0.431306 + 0.100869i
\(246\) 3225.61 + 2363.76i 0.836005 + 0.612633i
\(247\) 625.037 625.037i 0.161013 0.161013i
\(248\) −1234.90 2498.95i −0.316193 0.639854i
\(249\) 3854.03i 0.980880i
\(250\) −2019.49 + 3398.03i −0.510896 + 0.859642i
\(251\) 5379.04i 1.35268i 0.736591 + 0.676339i \(0.236434\pi\)
−0.736591 + 0.676339i \(0.763566\pi\)
\(252\) −883.042 459.069i −0.220740 0.114757i
\(253\) −2712.95 + 2712.95i −0.674157 + 0.674157i
\(254\) −3255.76 + 4442.84i −0.804270 + 1.09751i
\(255\) −3282.36 767.639i −0.806076 0.188515i
\(256\) 1392.50 3852.03i 0.339965 0.940438i
\(257\) 1432.19 + 1432.19i 0.347617 + 0.347617i 0.859221 0.511604i \(-0.170949\pi\)
−0.511604 + 0.859221i \(0.670949\pi\)
\(258\) −471.869 3060.22i −0.113865 0.738454i
\(259\) 1018.56 0.244363
\(260\) 571.517 + 490.399i 0.136323 + 0.116974i
\(261\) −1539.22 −0.365040
\(262\) −1082.71 7021.75i −0.255307 1.65574i
\(263\) 3876.88 + 3876.88i 0.908969 + 0.908969i 0.996189 0.0872200i \(-0.0277983\pi\)
−0.0872200 + 0.996189i \(0.527798\pi\)
\(264\) −708.588 + 2093.07i −0.165192 + 0.487952i
\(265\) −2766.05 4454.77i −0.641197 1.03266i
\(266\) 2426.17 3310.78i 0.559242 0.763147i
\(267\) 25.6885 25.6885i 0.00588805 0.00588805i
\(268\) 201.526 387.644i 0.0459333 0.0883550i
\(269\) 970.808i 0.220042i −0.993929 0.110021i \(-0.964908\pi\)
0.993929 0.110021i \(-0.0350918\pi\)
\(270\) 555.670 + 648.252i 0.125248 + 0.146116i
\(271\) 6724.75i 1.50738i 0.657231 + 0.753689i \(0.271727\pi\)
−0.657231 + 0.753689i \(0.728273\pi\)
\(272\) −6335.61 1110.00i −1.41233 0.247440i
\(273\) 246.886 246.886i 0.0547334 0.0547334i
\(274\) 2198.25 + 1610.90i 0.484677 + 0.355176i
\(275\) 1804.57 3647.07i 0.395707 0.799733i
\(276\) 852.066 + 2697.27i 0.185827 + 0.588248i
\(277\) −3393.42 3393.42i −0.736067 0.736067i 0.235747 0.971814i \(-0.424246\pi\)
−0.971814 + 0.235747i \(0.924246\pi\)
\(278\) −5756.12 + 887.562i −1.24183 + 0.191483i
\(279\) 1108.69 0.237905
\(280\) 2969.88 + 1846.15i 0.633873 + 0.394031i
\(281\) −3173.60 −0.673740 −0.336870 0.941551i \(-0.609368\pi\)
−0.336870 + 0.941551i \(0.609368\pi\)
\(282\) −644.442 + 99.3694i −0.136085 + 0.0209836i
\(283\) −2902.60 2902.60i −0.609687 0.609687i 0.333177 0.942864i \(-0.391879\pi\)
−0.942864 + 0.333177i \(0.891879\pi\)
\(284\) 1287.95 + 4077.08i 0.269104 + 0.851866i
\(285\) −2991.54 + 1857.50i −0.621766 + 0.386066i
\(286\) −625.300 458.226i −0.129282 0.0947395i
\(287\) −4606.44 + 4606.44i −0.947420 + 0.947420i
\(288\) 1128.20 + 1175.32i 0.230833 + 0.240473i
\(289\) 5187.59i 1.05589i
\(290\) 5392.36 + 414.674i 1.09190 + 0.0839673i
\(291\) 2602.69i 0.524303i
\(292\) −2182.87 + 4198.86i −0.437476 + 0.841505i
\(293\) −664.490 + 664.490i −0.132491 + 0.132491i −0.770242 0.637751i \(-0.779865\pi\)
0.637751 + 0.770242i \(0.279865\pi\)
\(294\) −762.013 + 1039.85i −0.151162 + 0.206277i
\(295\) 1444.99 6178.65i 0.285188 1.21944i
\(296\) −1579.29 534.655i −0.310117 0.104987i
\(297\) −621.494 621.494i −0.121423 0.121423i
\(298\) 517.869 + 3358.54i 0.100669 + 0.652870i
\(299\) −992.343 −0.191935
\(300\) −1772.04 2420.72i −0.341028 0.465868i
\(301\) 5044.12 0.965908
\(302\) 479.479 + 3109.57i 0.0913606 + 0.592503i
\(303\) −1997.73 1997.73i −0.378768 0.378768i
\(304\) −5499.70 + 3859.90i −1.03760 + 0.728225i
\(305\) 2118.40 9058.11i 0.397703 1.70054i
\(306\) 1512.22 2063.59i 0.282509 0.385514i
\(307\) 3273.06 3273.06i 0.608480 0.608480i −0.334069 0.942549i \(-0.608422\pi\)
0.942549 + 0.334069i \(0.108422\pi\)
\(308\) −3193.94 1660.44i −0.590882 0.307184i
\(309\) 3305.51i 0.608556i
\(310\) −3884.08 298.687i −0.711615 0.0547235i
\(311\) 7895.36i 1.43957i −0.694199 0.719783i \(-0.744241\pi\)
0.694199 0.719783i \(-0.255759\pi\)
\(312\) −512.395 + 253.208i −0.0929764 + 0.0459457i
\(313\) −6267.74 + 6267.74i −1.13187 + 1.13187i −0.141999 + 0.989867i \(0.545353\pi\)
−0.989867 + 0.141999i \(0.954647\pi\)
\(314\) −1983.30 1453.38i −0.356446 0.261207i
\(315\) −1181.64 + 733.701i −0.211358 + 0.131236i
\(316\) 584.409 184.615i 0.104037 0.0328652i
\(317\) 5075.26 + 5075.26i 0.899227 + 0.899227i 0.995368 0.0961407i \(-0.0306499\pi\)
−0.0961407 + 0.995368i \(0.530650\pi\)
\(318\) 3933.18 606.475i 0.693590 0.106948i
\(319\) −5567.34 −0.977151
\(320\) −3635.79 4421.43i −0.635147 0.772391i
\(321\) −2296.28 −0.399270
\(322\) −4554.15 + 702.224i −0.788176 + 0.121532i
\(323\) 7460.81 + 7460.81i 1.28523 + 1.28523i
\(324\) −617.902 + 195.195i −0.105950 + 0.0334697i
\(325\) 997.050 336.976i 0.170173 0.0575140i
\(326\) −5533.16 4054.75i −0.940040 0.688871i
\(327\) 1479.67 1479.67i 0.250232 0.250232i
\(328\) 9560.35 4724.39i 1.60940 0.795307i
\(329\) 1062.23i 0.178001i
\(330\) 2009.85 + 2344.71i 0.335268 + 0.391128i
\(331\) 3395.92i 0.563918i 0.959426 + 0.281959i \(0.0909842\pi\)
−0.959426 + 0.281959i \(0.909016\pi\)
\(332\) −9118.77 4740.60i −1.50740 0.783657i
\(333\) 468.940 468.940i 0.0771704 0.0771704i
\(334\) 4513.51 6159.18i 0.739426 1.00903i
\(335\) −322.086 518.724i −0.0525296 0.0845998i
\(336\) −2172.35 + 1524.64i −0.352712 + 0.247547i
\(337\) 6558.61 + 6558.61i 1.06015 + 1.06015i 0.998071 + 0.0620770i \(0.0197724\pi\)
0.0620770 + 0.998071i \(0.480228\pi\)
\(338\) 916.425 + 5943.31i 0.147476 + 0.956430i
\(339\) 3035.32 0.486300
\(340\) −5853.68 + 6821.96i −0.933708 + 1.08815i
\(341\) 4010.11 0.636832
\(342\) −407.269 2641.27i −0.0643935 0.417612i
\(343\) −4837.55 4837.55i −0.761524 0.761524i
\(344\) −7821.01 2647.73i −1.22582 0.414988i
\(345\) 3849.30 + 900.227i 0.600693 + 0.140483i
\(346\) −130.982 + 178.739i −0.0203516 + 0.0277719i
\(347\) −2120.84 + 2120.84i −0.328106 + 0.328106i −0.851866 0.523760i \(-0.824529\pi\)
0.523760 + 0.851866i \(0.324529\pi\)
\(348\) −1893.30 + 3641.86i −0.291643 + 0.560989i
\(349\) 9509.41i 1.45853i −0.684231 0.729265i \(-0.739862\pi\)
0.684231 0.729265i \(-0.260138\pi\)
\(350\) 4337.29 2252.04i 0.662394 0.343932i
\(351\) 227.330i 0.0345698i
\(352\) 4080.68 + 4251.09i 0.617901 + 0.643705i
\(353\) 5502.52 5502.52i 0.829659 0.829659i −0.157811 0.987469i \(-0.550444\pi\)
0.987469 + 0.157811i \(0.0504436\pi\)
\(354\) 3884.45 + 2846.56i 0.583209 + 0.427382i
\(355\) 5818.43 + 1360.75i 0.869889 + 0.203439i
\(356\) −29.1820 92.3776i −0.00434451 0.0137528i
\(357\) 2946.97 + 2946.97i 0.436892 + 0.436892i
\(358\) −211.632 + 32.6324i −0.0312433 + 0.00481754i
\(359\) 3705.16 0.544709 0.272355 0.962197i \(-0.412198\pi\)
0.272355 + 0.962197i \(0.412198\pi\)
\(360\) 2217.28 517.361i 0.324614 0.0757425i
\(361\) 4162.86 0.606920
\(362\) 3714.27 572.720i 0.539275 0.0831533i
\(363\) 575.546 + 575.546i 0.0832185 + 0.0832185i
\(364\) −280.462 887.819i −0.0403851 0.127842i
\(365\) 3488.74 + 5618.68i 0.500299 + 0.805740i
\(366\) 5694.74 + 4173.16i 0.813302 + 0.595996i
\(367\) 6714.02 6714.02i 0.954956 0.954956i −0.0440720 0.999028i \(-0.514033\pi\)
0.999028 + 0.0440720i \(0.0140331\pi\)
\(368\) 7429.90 + 1301.72i 1.05247 + 0.184394i
\(369\) 4241.57i 0.598393i
\(370\) −1769.17 + 1516.50i −0.248580 + 0.213079i
\(371\) 6483.00i 0.907226i
\(372\) 1363.73 2623.20i 0.190070 0.365610i
\(373\) 6819.34 6819.34i 0.946627 0.946627i −0.0520187 0.998646i \(-0.516566\pi\)
0.998646 + 0.0520187i \(0.0165655\pi\)
\(374\) 5469.65 7463.94i 0.756227 1.03196i
\(375\) −4173.25 + 402.632i −0.574682 + 0.0554449i
\(376\) −557.576 + 1647.00i −0.0764755 + 0.225898i
\(377\) −1018.21 1018.21i −0.139100 0.139100i
\(378\) −160.869 1043.28i −0.0218894 0.141960i
\(379\) −12484.6 −1.69206 −0.846030 0.533136i \(-0.821014\pi\)
−0.846030 + 0.533136i \(0.821014\pi\)
\(380\) 715.214 + 9362.87i 0.0965519 + 1.26396i
\(381\) −5842.19 −0.785576
\(382\) −227.333 1474.33i −0.0304486 0.197469i
\(383\) 3159.41 + 3159.41i 0.421510 + 0.421510i 0.885723 0.464213i \(-0.153663\pi\)
−0.464213 + 0.885723i \(0.653663\pi\)
\(384\) 4168.57 1223.68i 0.553975 0.162619i
\(385\) −4273.96 + 2653.78i −0.565769 + 0.351297i
\(386\) −2805.14 + 3827.91i −0.369890 + 0.504756i
\(387\) 2322.29 2322.29i 0.305035 0.305035i
\(388\) −6158.05 3201.40i −0.805741 0.418883i
\(389\) 2757.53i 0.359414i −0.983720 0.179707i \(-0.942485\pi\)
0.983720 0.179707i \(-0.0575150\pi\)
\(390\) −61.2439 + 796.406i −0.00795181 + 0.103404i
\(391\) 11845.2i 1.53206i
\(392\) 1523.02 + 3082.01i 0.196235 + 0.397104i
\(393\) 5328.55 5328.55i 0.683943 0.683943i
\(394\) −110.403 80.9045i −0.0141168 0.0103449i
\(395\) 195.050 834.016i 0.0248456 0.106238i
\(396\) −2234.94 + 706.016i −0.283611 + 0.0895926i
\(397\) −1824.49 1824.49i −0.230651 0.230651i 0.582314 0.812964i \(-0.302148\pi\)
−0.812964 + 0.582314i \(0.802148\pi\)
\(398\) −1535.41 + 236.752i −0.193375 + 0.0298174i
\(399\) 4353.57 0.546243
\(400\) −7907.18 + 1215.12i −0.988397 + 0.151890i
\(401\) −2771.47 −0.345139 −0.172569 0.984997i \(-0.555207\pi\)
−0.172569 + 0.984997i \(0.555207\pi\)
\(402\) 457.989 70.6193i 0.0568219 0.00876162i
\(403\) 733.410 + 733.410i 0.0906545 + 0.0906545i
\(404\) −7184.00 + 2269.42i −0.884696 + 0.279475i
\(405\) −206.228 + 881.814i −0.0253026 + 0.108192i
\(406\) −5393.39 3952.33i −0.659285 0.483131i
\(407\) 1696.14 1696.14i 0.206572 0.206572i
\(408\) −3022.43 6116.24i −0.366747 0.742155i
\(409\) 6.56085i 0.000793186i 1.00000 0.000396593i \(0.000126239\pi\)
−1.00000 0.000396593i \(0.999874\pi\)
\(410\) 1142.70 14859.5i 0.137644 1.78990i
\(411\) 2890.63i 0.346920i
\(412\) 7820.94 + 4065.89i 0.935219 + 0.486195i
\(413\) −5547.32 + 5547.32i −0.660934 + 0.660934i
\(414\) −1773.41 + 2420.01i −0.210527 + 0.287288i
\(415\) −12202.2 + 7576.60i −1.44333 + 0.896194i
\(416\) −31.1666 + 1523.80i −0.00367324 + 0.179592i
\(417\) −4368.11 4368.11i −0.512967 0.512967i
\(418\) −1473.08 9553.41i −0.172370 1.11788i
\(419\) 1900.10 0.221542 0.110771 0.993846i \(-0.464668\pi\)
0.110771 + 0.993846i \(0.464668\pi\)
\(420\) 282.505 + 3698.27i 0.0328210 + 0.429660i
\(421\) −6030.55 −0.698125 −0.349063 0.937099i \(-0.613500\pi\)
−0.349063 + 0.937099i \(0.613500\pi\)
\(422\) 1556.39 + 10093.7i 0.179536 + 1.16435i
\(423\) −489.044 489.044i −0.0562131 0.0562131i
\(424\) 3403.02 10052.0i 0.389776 1.15134i
\(425\) 4022.34 + 11901.4i 0.459087 + 1.35836i
\(426\) −2680.61 + 3657.99i −0.304873 + 0.416033i
\(427\) −8132.56 + 8132.56i −0.921691 + 0.921691i
\(428\) −2824.51 + 5433.08i −0.318990 + 0.613593i
\(429\) 822.249i 0.0925374i
\(430\) −8761.31 + 7510.04i −0.982577 + 0.842247i
\(431\) 14432.2i 1.61294i −0.591278 0.806468i \(-0.701376\pi\)
0.591278 0.806468i \(-0.298624\pi\)
\(432\) −298.204 + 1702.07i −0.0332114 + 0.189563i
\(433\) −6260.77 + 6260.77i −0.694858 + 0.694858i −0.963297 0.268439i \(-0.913492\pi\)
0.268439 + 0.963297i \(0.413492\pi\)
\(434\) 3884.82 + 2846.84i 0.429671 + 0.314868i
\(435\) 3025.94 + 4873.33i 0.333524 + 0.537146i
\(436\) −1680.90 5321.00i −0.184635 0.584472i
\(437\) −8749.45 8749.45i −0.957764 0.957764i
\(438\) −4960.81 + 764.929i −0.541179 + 0.0834469i
\(439\) 15053.8 1.63663 0.818315 0.574770i \(-0.194909\pi\)
0.818315 + 0.574770i \(0.194909\pi\)
\(440\) 8019.86 1871.28i 0.868936 0.202750i
\(441\) −1367.37 −0.147648
\(442\) 2365.43 364.736i 0.254552 0.0392505i
\(443\) −2684.03 2684.03i −0.287860 0.287860i 0.548374 0.836233i \(-0.315247\pi\)
−0.836233 + 0.548374i \(0.815247\pi\)
\(444\) −532.714 1686.34i −0.0569403 0.180248i
\(445\) −131.833 30.8315i −0.0140438 0.00328439i
\(446\) 3237.68 + 2372.61i 0.343741 + 0.251897i
\(447\) −2548.68 + 2548.68i −0.269683 + 0.269683i
\(448\) 935.273 + 7015.21i 0.0986328 + 0.739816i
\(449\) 3435.64i 0.361108i 0.983565 + 0.180554i \(0.0577891\pi\)
−0.983565 + 0.180554i \(0.942211\pi\)
\(450\) 960.043 3033.70i 0.100571 0.317800i
\(451\) 15341.7i 1.60180i
\(452\) 3733.55 7181.66i 0.388521 0.747338i
\(453\) −2359.74 + 2359.74i −0.244747 + 0.244747i
\(454\) 3769.22 5143.52i 0.389644 0.531712i
\(455\) −1267.01 296.314i −0.130546 0.0305306i
\(456\) −6750.29 2285.25i −0.693226 0.234685i
\(457\) −3751.73 3751.73i −0.384023 0.384023i 0.488526 0.872549i \(-0.337535\pi\)
−0.872549 + 0.488526i \(0.837535\pi\)
\(458\) 776.837 + 5038.04i 0.0792559 + 0.514000i
\(459\) 2713.55 0.275942
\(460\) 6864.74 8000.25i 0.695805 0.810900i
\(461\) −18065.6 −1.82516 −0.912579 0.408900i \(-0.865913\pi\)
−0.912579 + 0.408900i \(0.865913\pi\)
\(462\) −581.858 3773.54i −0.0585942 0.380002i
\(463\) −3971.95 3971.95i −0.398687 0.398687i 0.479083 0.877770i \(-0.340969\pi\)
−0.877770 + 0.479083i \(0.840969\pi\)
\(464\) 6287.93 + 8959.24i 0.629116 + 0.896384i
\(465\) −2179.57 3510.22i −0.217365 0.350070i
\(466\) −3821.15 + 5214.38i −0.379853 + 0.518351i
\(467\) −2742.42 + 2742.42i −0.271743 + 0.271743i −0.829802 0.558058i \(-0.811547\pi\)
0.558058 + 0.829802i \(0.311547\pi\)
\(468\) −537.871 279.625i −0.0531263 0.0276189i
\(469\) 754.896i 0.0743238i
\(470\) 1581.52 + 1845.02i 0.155213 + 0.181073i
\(471\) 2607.97i 0.255136i
\(472\) 11513.1 5689.36i 1.12274 0.554818i
\(473\) 8399.68 8399.68i 0.816528 0.816528i
\(474\) 524.337 + 384.239i 0.0508093 + 0.0372335i
\(475\) 11762.1 + 5819.85i 1.13617 + 0.562175i
\(476\) 10597.5 3347.75i 1.02045 0.322361i
\(477\) 2984.75 + 2984.75i 0.286504 + 0.286504i
\(478\) −898.579 + 138.556i −0.0859833 + 0.0132582i
\(479\) −16289.2 −1.55380 −0.776901 0.629623i \(-0.783209\pi\)
−0.776901 + 0.629623i \(0.783209\pi\)
\(480\) 1503.24 5882.54i 0.142945 0.559375i
\(481\) 620.416 0.0588119
\(482\) −4788.12 + 738.302i −0.452475 + 0.0697691i
\(483\) −3455.98 3455.98i −0.325574 0.325574i
\(484\) 2069.70 653.819i 0.194375 0.0614029i
\(485\) −8240.36 + 5116.60i −0.771496 + 0.479036i
\(486\) −554.387 406.260i −0.0517438 0.0379184i
\(487\) −5831.62 + 5831.62i −0.542620 + 0.542620i −0.924296 0.381676i \(-0.875347\pi\)
0.381676 + 0.924296i \(0.375347\pi\)
\(488\) 16878.6 8340.80i 1.56569 0.773710i
\(489\) 7275.92i 0.672860i
\(490\) 4790.30 + 368.376i 0.441640 + 0.0339623i
\(491\) 2534.03i 0.232911i 0.993196 + 0.116455i \(0.0371532\pi\)
−0.993196 + 0.116455i \(0.962847\pi\)
\(492\) 10035.7 + 5217.28i 0.919602 + 0.478076i
\(493\) 12154.0 12154.0i 1.11032 1.11032i
\(494\) 1477.81 2016.64i 0.134595 0.183670i
\(495\) −745.922 + 3189.50i −0.0677307 + 0.289611i
\(496\) −4529.15 6453.27i −0.410010 0.584195i
\(497\) −5223.91 5223.91i −0.471478 0.471478i
\(498\) −1661.22 10773.5i −0.149480 0.969424i
\(499\) 12553.8 1.12623 0.563113 0.826380i \(-0.309603\pi\)
0.563113 + 0.826380i \(0.309603\pi\)
\(500\) −4180.61 + 10369.3i −0.373925 + 0.927459i
\(501\) 8099.12 0.722239
\(502\) 2318.55 + 15036.5i 0.206139 + 1.33688i
\(503\) −2754.13 2754.13i −0.244137 0.244137i 0.574422 0.818559i \(-0.305227\pi\)
−0.818559 + 0.574422i \(0.805227\pi\)
\(504\) −2666.32 902.657i −0.235650 0.0797769i
\(505\) −2397.69 + 10252.3i −0.211279 + 0.903413i
\(506\) −6414.38 + 8753.13i −0.563546 + 0.769020i
\(507\) −4510.16 + 4510.16i −0.395075 + 0.395075i
\(508\) −7186.11 + 13822.8i −0.627622 + 1.20726i
\(509\) 6936.37i 0.604026i 0.953304 + 0.302013i \(0.0976586\pi\)
−0.953304 + 0.302013i \(0.902341\pi\)
\(510\) −9506.36 731.042i −0.825390 0.0634728i
\(511\) 8176.83i 0.707870i
\(512\) 2232.22 11368.2i 0.192678 0.981262i
\(513\) 2004.36 2004.36i 0.172504 0.172504i
\(514\) 4620.85 + 3386.21i 0.396531 + 0.290582i
\(515\) 10465.6 6498.26i 0.895470 0.556015i
\(516\) −2638.12 8351.12i −0.225071 0.712476i
\(517\) −1768.86 1768.86i −0.150473 0.150473i
\(518\) 2847.27 439.033i 0.241509 0.0372394i
\(519\) −235.036 −0.0198785
\(520\) 1808.99 + 1124.51i 0.152557 + 0.0948330i
\(521\) 16877.0 1.41918 0.709591 0.704613i \(-0.248880\pi\)
0.709591 + 0.704613i \(0.248880\pi\)
\(522\) −4302.73 + 663.457i −0.360777 + 0.0556298i
\(523\) 1435.21 + 1435.21i 0.119995 + 0.119995i 0.764554 0.644560i \(-0.222959\pi\)
−0.644560 + 0.764554i \(0.722959\pi\)
\(524\) −6053.22 19161.8i −0.504649 1.59750i
\(525\) 4645.94 + 2298.80i 0.386220 + 0.191101i
\(526\) 12508.5 + 9166.34i 1.03687 + 0.759831i
\(527\) −8754.40 + 8754.40i −0.723620 + 0.723620i
\(528\) −1078.60 + 6156.37i −0.0889013 + 0.507427i
\(529\) 1724.10i 0.141703i
\(530\) −9652.35 11260.6i −0.791078 0.922882i
\(531\) 5107.92i 0.417448i
\(532\) 5355.05 10300.7i 0.436411 0.839458i
\(533\) −2805.84 + 2805.84i −0.228019 + 0.228019i
\(534\) 60.7367 82.8819i 0.00492197 0.00671657i
\(535\) 4514.23 + 7270.24i 0.364799 + 0.587514i
\(536\) 396.255 1170.48i 0.0319321 0.0943229i
\(537\) −160.600 160.600i −0.0129057 0.0129057i
\(538\) −418.451 2713.79i −0.0335329 0.217472i
\(539\) −4945.75 −0.395229
\(540\) 1832.73 + 1572.61i 0.146052 + 0.125323i
\(541\) 16524.6 1.31321 0.656606 0.754234i \(-0.271992\pi\)
0.656606 + 0.754234i \(0.271992\pi\)
\(542\) 2898.59 + 18798.3i 0.229714 + 1.48977i
\(543\) 2818.62 + 2818.62i 0.222760 + 0.222760i
\(544\) −18188.9 372.023i −1.43354 0.0293205i
\(545\) −7593.65 1775.91i −0.596837 0.139581i
\(546\) 583.726 796.558i 0.0457531 0.0624351i
\(547\) 15728.1 15728.1i 1.22940 1.22940i 0.265215 0.964189i \(-0.414557\pi\)
0.964189 0.265215i \(-0.0854428\pi\)
\(548\) 6839.33 + 3555.58i 0.533142 + 0.277166i
\(549\) 7488.39i 0.582143i
\(550\) 3472.45 10972.8i 0.269211 0.850695i
\(551\) 17955.1i 1.38822i
\(552\) 3544.47 + 7172.65i 0.273302 + 0.553058i
\(553\) −748.797 + 748.797i −0.0575806 + 0.0575806i
\(554\) −10948.6 8023.25i −0.839642 0.615298i
\(555\) −2406.59 562.825i −0.184061 0.0430461i
\(556\) −15708.0 + 4962.16i −1.19815 + 0.378494i
\(557\) −3378.87 3378.87i −0.257033 0.257033i 0.566813 0.823846i \(-0.308176\pi\)
−0.823846 + 0.566813i \(0.808176\pi\)
\(558\) 3099.23 477.884i 0.235127 0.0362552i
\(559\) 3072.43 0.232469
\(560\) 9097.74 + 3880.60i 0.686517 + 0.292831i
\(561\) 9814.84 0.738650
\(562\) −8871.45 + 1367.93i −0.665871 + 0.102674i
\(563\) −6575.77 6575.77i −0.492248 0.492248i 0.416766 0.909014i \(-0.363163\pi\)
−0.909014 + 0.416766i \(0.863163\pi\)
\(564\) −1758.64 + 555.553i −0.131298 + 0.0414769i
\(565\) −5967.09 9610.10i −0.444314 0.715575i
\(566\) −9365.01 6862.77i −0.695478 0.509653i
\(567\) 791.710 791.710i 0.0586397 0.0586397i
\(568\) 5357.68 + 10841.9i 0.395780 + 0.800907i
\(569\) 5653.99i 0.416569i −0.978068 0.208284i \(-0.933212\pi\)
0.978068 0.208284i \(-0.0667879\pi\)
\(570\) −7561.87 + 6481.90i −0.555670 + 0.476310i
\(571\) 4182.86i 0.306562i 0.988183 + 0.153281i \(0.0489840\pi\)
−0.988183 + 0.153281i \(0.951016\pi\)
\(572\) −1945.47 1011.40i −0.142210 0.0739311i
\(573\) 1118.81 1118.81i 0.0815691 0.0815691i
\(574\) −10891.3 + 14862.3i −0.791973 + 1.08073i
\(575\) −4717.09 13957.0i −0.342115 1.01225i
\(576\) 3660.37 + 2799.18i 0.264783 + 0.202487i
\(577\) 4154.43 + 4154.43i 0.299742 + 0.299742i 0.840913 0.541171i \(-0.182019\pi\)
−0.541171 + 0.840913i \(0.682019\pi\)
\(578\) 2236.03 + 14501.3i 0.160911 + 1.04356i
\(579\) −5033.58 −0.361293
\(580\) 15252.5 1165.11i 1.09194 0.0834115i
\(581\) 17757.8 1.26802
\(582\) −1121.85 7275.53i −0.0799004 0.518179i
\(583\) 10795.8 + 10795.8i 0.766921 + 0.766921i
\(584\) −4292.13 + 12678.3i −0.304126 + 0.898345i
\(585\) −719.750 + 446.906i −0.0508683 + 0.0315851i
\(586\) −1571.09 + 2143.93i −0.110753 + 0.151135i
\(587\) 867.446 867.446i 0.0609938 0.0609938i −0.675952 0.736946i \(-0.736267\pi\)
0.736946 + 0.675952i \(0.236267\pi\)
\(588\) −1681.91 + 3235.24i −0.117961 + 0.226903i
\(589\) 12932.9i 0.904738i
\(590\) 1376.10 17894.6i 0.0960222 1.24866i
\(591\) 145.176i 0.0101045i
\(592\) −4645.20 813.840i −0.322494 0.0565010i
\(593\) −6391.46 + 6391.46i −0.442607 + 0.442607i −0.892887 0.450280i \(-0.851324\pi\)
0.450280 + 0.892887i \(0.351324\pi\)
\(594\) −2005.20 1469.43i −0.138509 0.101501i
\(595\) 3536.98 15123.8i 0.243701 1.04204i
\(596\) 2895.29 + 9165.23i 0.198986 + 0.629903i
\(597\) −1165.17 1165.17i −0.0798780 0.0798780i
\(598\) −2773.99 + 427.733i −0.189694 + 0.0292497i
\(599\) 9411.66 0.641986 0.320993 0.947081i \(-0.395983\pi\)
0.320993 + 0.947081i \(0.395983\pi\)
\(600\) −5996.94 6003.05i −0.408040 0.408456i
\(601\) −3491.06 −0.236944 −0.118472 0.992957i \(-0.537800\pi\)
−0.118472 + 0.992957i \(0.537800\pi\)
\(602\) 14100.3 2174.19i 0.954626 0.147198i
\(603\) 347.551 + 347.551i 0.0234716 + 0.0234716i
\(604\) 2680.66 + 8485.80i 0.180587 + 0.571659i
\(605\) 690.774 2953.69i 0.0464197 0.198487i
\(606\) −6445.54 4723.36i −0.432066 0.316623i
\(607\) −19182.5 + 19182.5i −1.28269 + 1.28269i −0.343559 + 0.939131i \(0.611633\pi\)
−0.939131 + 0.343559i \(0.888367\pi\)
\(608\) −13710.1 + 13160.5i −0.914501 + 0.877842i
\(609\) 7092.13i 0.471901i
\(610\) 2017.41 26234.1i 0.133906 1.74129i
\(611\) 647.014i 0.0428402i
\(612\) 3337.76 6420.34i 0.220459 0.424064i
\(613\) 8775.20 8775.20i 0.578184 0.578184i −0.356219 0.934403i \(-0.615934\pi\)
0.934403 + 0.356219i \(0.115934\pi\)
\(614\) 7738.68 10560.3i 0.508645 0.694101i
\(615\) 13429.2 8338.45i 0.880517 0.546730i
\(616\) −9644.03 3264.89i −0.630794 0.213549i
\(617\) 1130.84 + 1130.84i 0.0737861 + 0.0737861i 0.743037 0.669251i \(-0.233385\pi\)
−0.669251 + 0.743037i \(0.733385\pi\)
\(618\) 1424.78 + 9240.18i 0.0927399 + 0.601448i
\(619\) −8002.68 −0.519636 −0.259818 0.965658i \(-0.583663\pi\)
−0.259818 + 0.965658i \(0.583663\pi\)
\(620\) −10986.3 + 839.222i −0.711643 + 0.0543612i
\(621\) −3182.23 −0.205634
\(622\) −3403.17 22070.6i −0.219380 1.42275i
\(623\) 118.362 + 118.362i 0.00761169 + 0.00761169i
\(624\) −1323.20 + 928.674i −0.0848886 + 0.0595780i
\(625\) 9478.92 + 12421.4i 0.606651 + 0.794968i
\(626\) −14819.2 + 20222.4i −0.946156 + 1.29113i
\(627\) 7249.74 7249.74i 0.461765 0.461765i
\(628\) −6170.55 3207.90i −0.392089 0.203836i
\(629\) 7405.64i 0.469447i
\(630\) −2986.89 + 2560.31i −0.188890 + 0.161913i
\(631\) 15919.5i 1.00435i −0.864766 0.502175i \(-0.832533\pi\)
0.864766 0.502175i \(-0.167467\pi\)
\(632\) 1554.08 767.971i 0.0978131 0.0483358i
\(633\) −7659.75 + 7659.75i −0.480960 + 0.480960i
\(634\) 16374.9 + 11999.7i 1.02576 + 0.751688i
\(635\) 11485.1 + 18496.9i 0.717752 + 1.15595i
\(636\) 10733.4 3390.67i 0.669191 0.211397i
\(637\) −904.528 904.528i −0.0562617 0.0562617i
\(638\) −15562.9 + 2399.71i −0.965738 + 0.148911i
\(639\) −4810.13 −0.297787
\(640\) −12069.2 10792.5i −0.745436 0.666578i
\(641\) 2408.32 0.148398 0.0741989 0.997243i \(-0.476360\pi\)
0.0741989 + 0.997243i \(0.476360\pi\)
\(642\) −6419.00 + 989.774i −0.394607 + 0.0608462i
\(643\) −9551.66 9551.66i −0.585818 0.585818i 0.350678 0.936496i \(-0.385951\pi\)
−0.936496 + 0.350678i \(0.885951\pi\)
\(644\) −12427.9 + 3925.98i −0.760449 + 0.240226i
\(645\) −11918.0 2787.23i −0.727549 0.170150i
\(646\) 24071.7 + 17640.0i 1.46608 + 1.07436i
\(647\) 8983.66 8983.66i 0.545880 0.545880i −0.379367 0.925246i \(-0.623858\pi\)
0.925246 + 0.379367i \(0.123858\pi\)
\(648\) −1643.14 + 811.983i −0.0996122 + 0.0492249i
\(649\) 18475.2i 1.11744i
\(650\) 2641.90 1371.74i 0.159421 0.0827756i
\(651\) 5108.41i 0.307549i
\(652\) −17215.1 8949.64i −1.03404 0.537569i
\(653\) −14719.0 + 14719.0i −0.882084 + 0.882084i −0.993746 0.111662i \(-0.964382\pi\)
0.111662 + 0.993746i \(0.464382\pi\)
\(654\) 3498.47 4774.05i 0.209176 0.285443i
\(655\) −27346.0 6395.36i −1.63129 0.381508i
\(656\) 24688.6 17327.4i 1.46940 1.03128i
\(657\) −3764.58 3764.58i −0.223547 0.223547i
\(658\) −457.855 2969.33i −0.0271262 0.175922i
\(659\) 6602.59 0.390289 0.195145 0.980774i \(-0.437482\pi\)
0.195145 + 0.980774i \(0.437482\pi\)
\(660\) 6628.96 + 5688.08i 0.390957 + 0.335467i
\(661\) −13404.0 −0.788735 −0.394367 0.918953i \(-0.629036\pi\)
−0.394367 + 0.918953i \(0.629036\pi\)
\(662\) 1463.76 + 9492.93i 0.0859374 + 0.557331i
\(663\) 1795.04 + 1795.04i 0.105148 + 0.105148i
\(664\) −27533.9 9321.33i −1.60922 0.544786i
\(665\) −8558.63 13783.8i −0.499082 0.803779i
\(666\) 1108.74 1513.00i 0.0645088 0.0880293i
\(667\) −14253.2 + 14253.2i −0.827416 + 0.827416i
\(668\) 9962.21 19162.8i 0.577020 1.10993i
\(669\) 4257.44i 0.246042i
\(670\) −1123.94 1311.21i −0.0648085 0.0756065i
\(671\) 27085.3i 1.55830i
\(672\) −5415.39 + 5198.31i −0.310868 + 0.298406i
\(673\) 5480.21 5480.21i 0.313888 0.313888i −0.532526 0.846414i \(-0.678757\pi\)
0.846414 + 0.532526i \(0.178757\pi\)
\(674\) 21160.8 + 15506.9i 1.20933 + 0.886206i
\(675\) 3197.33 1080.61i 0.182319 0.0616188i
\(676\) 5123.53 + 16218.9i 0.291507 + 0.922784i
\(677\) 13646.9 + 13646.9i 0.774733 + 0.774733i 0.978930 0.204197i \(-0.0654583\pi\)
−0.204197 + 0.978930i \(0.565458\pi\)
\(678\) 8484.89 1308.32i 0.480620 0.0741089i
\(679\) 11992.2 0.677786
\(680\) −13422.8 + 21593.2i −0.756974 + 1.21774i
\(681\) 6763.56 0.380588
\(682\) 11209.8 1728.49i 0.629394 0.0970491i
\(683\) −19003.1 19003.1i −1.06462 1.06462i −0.997763 0.0668566i \(-0.978703\pi\)
−0.0668566 0.997763i \(-0.521297\pi\)
\(684\) −2276.95 7207.83i −0.127283 0.402922i
\(685\) 9152.01 5682.66i 0.510482 0.316968i
\(686\) −15608.0 11437.7i −0.868681 0.636578i
\(687\) −3823.18 + 3823.18i −0.212319 + 0.212319i
\(688\) −23004.0 4030.31i −1.27474 0.223335i
\(689\) 3948.88i 0.218346i
\(690\) 11148.3 + 857.309i 0.615086 + 0.0473003i
\(691\) 6492.09i 0.357411i −0.983903 0.178705i \(-0.942809\pi\)
0.983903 0.178705i \(-0.0571909\pi\)
\(692\) −289.104 + 556.104i −0.0158816 + 0.0305490i
\(693\) 2863.60 2863.60i 0.156968 0.156968i
\(694\) −5014.43 + 6842.74i −0.274273 + 0.374275i
\(695\) −5242.64 + 22417.1i −0.286136 + 1.22349i
\(696\) −3722.76 + 10996.5i −0.202745 + 0.598881i
\(697\) −33492.1 33492.1i −1.82009 1.82009i
\(698\) −4098.88 26582.5i −0.222271 1.44149i
\(699\) −6856.74 −0.371024
\(700\) 11153.7 8164.84i 0.602244 0.440860i
\(701\) 15538.8 0.837220 0.418610 0.908166i \(-0.362517\pi\)
0.418610 + 0.908166i \(0.362517\pi\)
\(702\) −97.9870 635.477i −0.00526821 0.0341660i
\(703\) 5470.18 + 5470.18i 0.293474 + 0.293474i
\(704\) 13239.5 + 10124.6i 0.708780 + 0.542022i
\(705\) −586.954 + 2509.77i −0.0313560 + 0.134076i
\(706\) 13009.9 17753.5i 0.693534 0.946403i
\(707\) 9204.77 9204.77i 0.489648 0.489648i
\(708\) 12085.5 + 6282.93i 0.641528 + 0.333513i
\(709\) 34906.4i 1.84899i −0.381189 0.924497i \(-0.624485\pi\)
0.381189 0.924497i \(-0.375515\pi\)
\(710\) 16851.3 + 1295.87i 0.890731 + 0.0684975i
\(711\) 689.485i 0.0363681i
\(712\) −121.393 245.653i −0.00638960 0.0129301i
\(713\) 10266.5 10266.5i 0.539246 0.539246i
\(714\) 9508.18 + 6967.69i 0.498368 + 0.365209i
\(715\) −2603.32 + 1616.45i −0.136166 + 0.0845480i
\(716\) −577.528 + 182.441i −0.0301442 + 0.00952253i
\(717\) −681.899 681.899i −0.0355174 0.0355174i
\(718\) 10357.4 1597.05i 0.538347 0.0830102i
\(719\) 31209.2 1.61879 0.809394 0.587266i \(-0.199796\pi\)
0.809394 + 0.587266i \(0.199796\pi\)
\(720\) 5975.17 2401.95i 0.309280 0.124327i
\(721\) −15230.5 −0.786702
\(722\) 11636.8 1794.33i 0.599831 0.0924906i
\(723\) −3633.53 3633.53i −0.186905 0.186905i
\(724\) 10136.0 3201.95i 0.520304 0.164364i
\(725\) 9480.77 19160.9i 0.485665 0.981540i
\(726\) 1856.95 + 1360.80i 0.0949284 + 0.0695645i
\(727\) 12172.2 12172.2i 0.620965 0.620965i −0.324813 0.945778i \(-0.605301\pi\)
0.945778 + 0.324813i \(0.105301\pi\)
\(728\) −1166.68 2360.91i −0.0593957 0.120194i
\(729\) 729.000i 0.0370370i
\(730\) 12174.2 + 14202.6i 0.617245 + 0.720086i
\(731\) 36674.4i 1.85561i
\(732\) 17717.8 + 9210.99i 0.894629 + 0.465093i
\(733\) −17574.9 + 17574.9i −0.885598 + 0.885598i −0.994097 0.108499i \(-0.965396\pi\)
0.108499 + 0.994097i \(0.465396\pi\)
\(734\) 15874.3 21662.3i 0.798273 1.08933i
\(735\) 2688.10 + 4329.22i 0.134901 + 0.217260i
\(736\) 21330.6 + 436.279i 1.06828 + 0.0218498i
\(737\) 1257.08 + 1257.08i 0.0628294 + 0.0628294i
\(738\) 1828.26 + 11856.8i 0.0911912 + 0.591404i
\(739\) −22421.6 −1.11609 −0.558046 0.829810i \(-0.688449\pi\)
−0.558046 + 0.829810i \(0.688449\pi\)
\(740\) −4291.86 + 5001.78i −0.213205 + 0.248472i
\(741\) 2651.81 0.131466
\(742\) 2794.39 + 18122.5i 0.138255 + 0.896630i
\(743\) 21443.3 + 21443.3i 1.05879 + 1.05879i 0.998161 + 0.0606244i \(0.0193092\pi\)
0.0606244 + 0.998161i \(0.480691\pi\)
\(744\) 2681.47 7920.69i 0.132134 0.390305i
\(745\) 13079.8 + 3058.94i 0.643229 + 0.150431i
\(746\) 16123.4 22002.1i 0.791311 1.07983i
\(747\) 8175.63 8175.63i 0.400443 0.400443i
\(748\) 12072.6 23222.2i 0.590131 1.13515i
\(749\) 10580.3i 0.516151i
\(750\) −11492.3 + 2924.33i −0.559520 + 0.142375i
\(751\) 17054.5i 0.828663i −0.910126 0.414332i \(-0.864015\pi\)
0.910126 0.414332i \(-0.135985\pi\)
\(752\) −848.730 + 4844.35i −0.0411569 + 0.234914i
\(753\) −11410.7 + 11410.7i −0.552228 + 0.552228i
\(754\) −3285.18 2407.41i −0.158673 0.116277i
\(755\) 12110.2 + 2832.18i 0.583754 + 0.136521i
\(756\) −899.381 2847.05i −0.0432674 0.136966i
\(757\) 17641.7 + 17641.7i 0.847025 + 0.847025i 0.989761 0.142735i \(-0.0455898\pi\)
−0.142735 + 0.989761i \(0.545590\pi\)
\(758\) −34899.3 + 5381.28i −1.67230 + 0.257859i
\(759\) −11510.1 −0.550447
\(760\) 6035.02 + 25864.6i 0.288044 + 1.23448i
\(761\) −20703.5 −0.986206 −0.493103 0.869971i \(-0.664137\pi\)
−0.493103 + 0.869971i \(0.664137\pi\)
\(762\) −16331.2 + 2518.18i −0.776400 + 0.119717i
\(763\) 6817.74 + 6817.74i 0.323484 + 0.323484i
\(764\) −1270.97 4023.33i −0.0601859 0.190522i
\(765\) −5334.53 8591.35i −0.252118 0.406040i
\(766\) 10193.6 + 7469.98i 0.480822 + 0.352352i
\(767\) −3378.94 + 3378.94i −0.159070 + 0.159070i
\(768\) 11125.3 5217.47i 0.522722 0.245142i
\(769\) 476.229i 0.0223319i 0.999938 + 0.0111660i \(0.00355431\pi\)
−0.999938 + 0.0111660i \(0.996446\pi\)
\(770\) −10803.5 + 9260.58i −0.505625 + 0.433413i
\(771\) 6076.26i 0.283828i
\(772\) −6191.49 + 11909.6i −0.288648 + 0.555229i
\(773\) 12209.8 12209.8i 0.568118 0.568118i −0.363483 0.931601i \(-0.618413\pi\)
0.931601 + 0.363483i \(0.118413\pi\)
\(774\) 5490.72 7492.70i 0.254987 0.347958i
\(775\) −6828.93 + 13801.4i −0.316519 + 0.639693i
\(776\) −18594.1 6294.84i −0.860165 0.291201i
\(777\) 2160.69 + 2160.69i 0.0997609 + 0.0997609i
\(778\) −1188.59 7708.36i −0.0547723 0.355216i
\(779\) −49477.9 −2.27565
\(780\) 172.077 + 2252.66i 0.00789917 + 0.103408i
\(781\) −17398.1 −0.797125
\(782\) −5105.67 33111.9i −0.233476 1.51417i
\(783\) −3265.19 3265.19i −0.149027 0.149027i
\(784\) 5585.88 + 7958.94i 0.254459 + 0.362561i
\(785\) −8257.09 + 5126.98i −0.375424 + 0.233108i
\(786\) 12598.6 17192.2i 0.571726 0.780183i
\(787\) 623.561 623.561i 0.0282434 0.0282434i −0.692844 0.721087i \(-0.743643\pi\)
0.721087 + 0.692844i \(0.243643\pi\)
\(788\) −343.492 178.572i −0.0155284 0.00807280i
\(789\) 16448.2i 0.742170i
\(790\) 185.751 2415.47i 0.00836546 0.108783i
\(791\) 13985.5i 0.628658i
\(792\) −5943.21 + 2936.93i −0.266645 + 0.131767i
\(793\) −4953.64 + 4953.64i −0.221827 + 0.221827i
\(794\) −5886.57 4313.74i −0.263106 0.192807i
\(795\) 3582.31 15317.7i 0.159813 0.683349i
\(796\) −4190.03 + 1323.63i −0.186572 + 0.0589382i
\(797\) −8360.92 8360.92i −0.371592 0.371592i 0.496465 0.868057i \(-0.334631\pi\)
−0.868057 + 0.496465i \(0.834631\pi\)
\(798\) 12169.9 1876.53i 0.539863 0.0832438i
\(799\) 7723.13 0.341959
\(800\) −21579.9 + 6805.00i −0.953706 + 0.300742i
\(801\) 108.987 0.00480757
\(802\) −7747.34 + 1194.60i −0.341107 + 0.0525969i
\(803\) −13616.4 13616.4i −0.598396 0.598396i
\(804\) 1249.82 394.817i 0.0548230 0.0173186i
\(805\) −4147.89 + 17736.0i −0.181607 + 0.776538i
\(806\) 2366.29 + 1734.04i 0.103411 + 0.0757805i
\(807\) 2059.40 2059.40i 0.0898317 0.0898317i
\(808\) −19103.9 + 9440.47i −0.831772 + 0.411033i
\(809\) 954.713i 0.0414906i 0.999785 + 0.0207453i \(0.00660391\pi\)
−0.999785 + 0.0207453i \(0.993396\pi\)
\(810\) −196.396 + 2553.90i −0.00851933 + 0.110784i
\(811\) 22684.6i 0.982200i −0.871103 0.491100i \(-0.836595\pi\)
0.871103 0.491100i \(-0.163405\pi\)
\(812\) −16780.2 8723.58i −0.725210 0.377017i
\(813\) −14265.3 + 14265.3i −0.615384 + 0.615384i
\(814\) 4010.29 5472.48i 0.172679 0.235639i
\(815\) −23036.3 + 14303.6i −0.990092 + 0.614767i
\(816\) −11085.2 15794.5i −0.475563 0.677596i
\(817\) 27089.5 + 27089.5i 1.16003 + 1.16003i
\(818\) 2.82795 + 18.3401i 0.000120876 + 0.000783921i
\(819\) 1047.45 0.0446896
\(820\) −3210.65 42030.6i −0.136732 1.78997i
\(821\) −19186.8 −0.815621 −0.407810 0.913067i \(-0.633708\pi\)
−0.407810 + 0.913067i \(0.633708\pi\)
\(822\) 1245.96 + 8080.44i 0.0528684 + 0.342868i
\(823\) 21296.2 + 21296.2i 0.901990 + 0.901990i 0.995608 0.0936185i \(-0.0298434\pi\)
−0.0936185 + 0.995608i \(0.529843\pi\)
\(824\) 23615.1 + 7994.67i 0.998388 + 0.337995i
\(825\) 11564.7 3908.55i 0.488036 0.164943i
\(826\) −13115.8 + 17898.0i −0.552492 + 0.753936i
\(827\) 24547.4 24547.4i 1.03216 1.03216i 0.0326970 0.999465i \(-0.489590\pi\)
0.999465 0.0326970i \(-0.0104096\pi\)
\(828\) −3914.26 + 7529.27i −0.164288 + 0.316015i
\(829\) 16962.8i 0.710667i −0.934740 0.355333i \(-0.884367\pi\)
0.934740 0.355333i \(-0.115633\pi\)
\(830\) −30844.2 + 26439.1i −1.28990 + 1.10568i
\(831\) 14397.0i 0.600996i
\(832\) 569.686 + 4273.05i 0.0237383 + 0.178054i
\(833\) 10797.0 10797.0i 0.449091 0.449091i
\(834\) −14093.4 10327.8i −0.585148 0.428803i
\(835\) −15922.0 25642.6i −0.659883 1.06275i
\(836\) −8235.69 26070.6i −0.340714 1.07855i
\(837\) 2351.89 + 2351.89i 0.0971245 + 0.0971245i
\(838\) 5311.52 819.007i 0.218954 0.0337615i
\(839\) 18232.5 0.750244 0.375122 0.926975i \(-0.377601\pi\)
0.375122 + 0.926975i \(0.377601\pi\)
\(840\) 2383.79 + 10216.4i 0.0979151 + 0.419640i
\(841\) −4860.51 −0.199291
\(842\) −16857.7 + 2599.37i −0.689971 + 0.106390i
\(843\) −6732.22 6732.22i −0.275053 0.275053i
\(844\) 8701.46 + 27545.0i 0.354878 + 1.12339i
\(845\) 23146.1 + 5413.12i 0.942307 + 0.220375i
\(846\) −1577.86 1156.27i −0.0641230 0.0469900i
\(847\) −2651.89 + 2651.89i −0.107580 + 0.107580i
\(848\) 5180.00 29566.2i 0.209766 1.19729i
\(849\) 12314.7i 0.497807i
\(850\) 16373.9 + 31535.2i 0.660730 + 1.27253i
\(851\) 8684.76i 0.349835i
\(852\) −5916.64 + 11380.9i −0.237912 + 0.457634i
\(853\) −8029.34 + 8029.34i −0.322297 + 0.322297i −0.849648 0.527351i \(-0.823185\pi\)
0.527351 + 0.849648i \(0.323185\pi\)
\(854\) −19228.3 + 26239.1i −0.770466 + 1.05139i
\(855\) −10286.4 2405.65i −0.411446 0.0962240i
\(856\) −5553.77 + 16405.0i −0.221757 + 0.655038i
\(857\) 10547.5 + 10547.5i 0.420414 + 0.420414i 0.885346 0.464932i \(-0.153921\pi\)
−0.464932 + 0.885346i \(0.653921\pi\)
\(858\) −354.417 2298.51i −0.0141021 0.0914565i
\(859\) 6249.45 0.248229 0.124114 0.992268i \(-0.460391\pi\)
0.124114 + 0.992268i \(0.460391\pi\)
\(860\) −21254.2 + 24769.9i −0.842747 + 0.982148i
\(861\) −19543.5 −0.773565
\(862\) −6220.77 40343.7i −0.245801 1.59410i
\(863\) −5052.25 5052.25i −0.199282 0.199282i 0.600410 0.799692i \(-0.295004\pi\)
−0.799692 + 0.600410i \(0.795004\pi\)
\(864\) −99.9447 + 4886.50i −0.00393540 + 0.192410i
\(865\) 462.056 + 744.148i 0.0181623 + 0.0292506i
\(866\) −14802.7 + 20199.9i −0.580850 + 0.792634i
\(867\) −11004.5 + 11004.5i −0.431065 + 0.431065i
\(868\) 12086.7 + 6283.53i 0.472637 + 0.245711i
\(869\) 2493.85i 0.0973512i
\(870\) 10559.3 + 12318.6i 0.411486 + 0.480045i
\(871\) 459.816i 0.0178878i
\(872\) −6992.31 14149.8i −0.271548 0.549508i
\(873\) 5521.13 5521.13i 0.214046 0.214046i
\(874\) −28229.4 20686.8i −1.09253 0.800620i
\(875\) −1855.17 19228.7i −0.0716756 0.742912i
\(876\) −13537.7 + 4276.55i −0.522142 + 0.164944i
\(877\) 29012.5 + 29012.5i 1.11709 + 1.11709i 0.992167 + 0.124919i \(0.0398669\pi\)
0.124919 + 0.992167i \(0.460133\pi\)
\(878\) 42081.4 6488.71i 1.61751 0.249412i
\(879\) −2819.19 −0.108179
\(880\) 21612.1 8687.80i 0.827889 0.332802i
\(881\) 8105.88 0.309982 0.154991 0.987916i \(-0.450465\pi\)
0.154991 + 0.987916i \(0.450465\pi\)
\(882\) −3822.33 + 589.382i −0.145924 + 0.0225006i
\(883\) 19045.9 + 19045.9i 0.725873 + 0.725873i 0.969795 0.243922i \(-0.0784341\pi\)
−0.243922 + 0.969795i \(0.578434\pi\)
\(884\) 6455.08 2039.16i 0.245597 0.0775840i
\(885\) 16172.2 10041.6i 0.614262 0.381407i
\(886\) −8659.81 6346.00i −0.328366 0.240630i
\(887\) 8078.84 8078.84i 0.305818 0.305818i −0.537467 0.843285i \(-0.680619\pi\)
0.843285 + 0.537467i \(0.180619\pi\)
\(888\) −2216.01 4484.36i −0.0837439 0.169465i
\(889\) 26918.5i 1.01554i
\(890\) −381.814 29.3616i −0.0143803 0.00110585i
\(891\) 2636.78i 0.0991418i
\(892\) 10073.3 + 5236.81i 0.378114 + 0.196571i
\(893\) 5704.70 5704.70i 0.213774 0.213774i
\(894\) −6025.98 + 8223.12i −0.225435 + 0.307631i
\(895\) −192.753 + 824.195i −0.00719890 + 0.0307819i
\(896\) 5638.24 + 19207.1i 0.210224 + 0.716144i
\(897\) −2105.08 2105.08i −0.0783573 0.0783573i
\(898\) 1480.88 + 9603.95i 0.0550306 + 0.356891i
\(899\) 21068.2 0.781606
\(900\) 1376.07 8894.18i 0.0509655 0.329414i
\(901\) −47136.1 −1.74287
\(902\) 6612.77 + 42885.9i 0.244103 + 1.58309i
\(903\) 10700.2 + 10700.2i 0.394330 + 0.394330i
\(904\) 7341.19 21684.8i 0.270093 0.797817i
\(905\) 3382.93 14465.1i 0.124257 0.531312i
\(906\) −5579.27 + 7613.53i −0.204590 + 0.279186i
\(907\) 11565.2 11565.2i 0.423393 0.423393i −0.462978 0.886370i \(-0.653219\pi\)
0.886370 + 0.462978i \(0.153219\pi\)
\(908\) 8319.43 16002.8i 0.304064 0.584881i
\(909\) 8475.67i 0.309263i
\(910\) −3669.52 282.188i −0.133674 0.0102796i
\(911\) 14979.7i 0.544787i 0.962186 + 0.272394i \(0.0878153\pi\)
−0.962186 + 0.272394i \(0.912185\pi\)
\(912\) −19854.7 3478.55i −0.720894 0.126301i
\(913\) 29571.1 29571.1i 1.07192 1.07192i
\(914\) −12104.7 8870.43i −0.438060 0.321015i
\(915\) 23709.0 14721.3i 0.856605 0.531883i
\(916\) 4343.13 + 13748.4i 0.156660 + 0.495918i
\(917\) 24551.8 + 24551.8i 0.884158 + 0.884158i
\(918\) 7585.42 1169.63i 0.272719 0.0420518i
\(919\) 14228.6 0.510727 0.255364 0.966845i \(-0.417805\pi\)
0.255364 + 0.966845i \(0.417805\pi\)
\(920\) 15741.3 25322.8i 0.564102 0.907464i
\(921\) 13886.4 0.496822
\(922\) −50500.4 + 7786.88i −1.80384 + 0.278142i
\(923\) −3181.95 3181.95i −0.113472 0.113472i
\(924\) −3253.04 10297.7i −0.115820 0.366634i
\(925\) 2949.14 + 8725.95i 0.104829 + 0.310170i
\(926\) −12815.2 9391.11i −0.454788 0.333273i
\(927\) −7012.04 + 7012.04i −0.248442 + 0.248442i
\(928\) 21439.0 + 22334.3i 0.758371 + 0.790041i
\(929\) 21373.3i 0.754830i 0.926044 + 0.377415i \(0.123187\pi\)
−0.926044 + 0.377415i \(0.876813\pi\)
\(930\) −7605.76 8872.98i −0.268175 0.312857i
\(931\) 15950.4i 0.561496i
\(932\) −8434.04 + 16223.3i −0.296423 + 0.570184i
\(933\) 16748.6 16748.6i 0.587700 0.587700i
\(934\) −6484.06 + 8848.21i −0.227157 + 0.309981i
\(935\) −19294.9 31074.7i −0.674877 1.08690i
\(936\) −1624.09 549.819i −0.0567147 0.0192002i
\(937\) 18353.3 + 18353.3i 0.639888 + 0.639888i 0.950528 0.310639i \(-0.100543\pi\)
−0.310639 + 0.950528i \(0.600543\pi\)
\(938\) 325.386 + 2110.23i 0.0113265 + 0.0734557i
\(939\) −26591.8 −0.924164
\(940\) 5216.22 + 4475.86i 0.180994 + 0.155305i
\(941\) −3056.37 −0.105882 −0.0529409 0.998598i \(-0.516859\pi\)
−0.0529409 + 0.998598i \(0.516859\pi\)
\(942\) −1124.12 7290.30i −0.0388810 0.252156i
\(943\) 39276.9 + 39276.9i 1.35634 + 1.35634i
\(944\) 29731.3 20866.5i 1.02507 0.719436i
\(945\) −4063.05 950.216i −0.139863 0.0327096i
\(946\) 19859.8 27100.9i 0.682557 0.931424i
\(947\) 10860.0 10860.0i 0.372652 0.372652i −0.495791 0.868442i \(-0.665122\pi\)
0.868442 + 0.495791i \(0.165122\pi\)
\(948\) 1631.35 + 848.092i 0.0558900 + 0.0290557i
\(949\) 4980.61i 0.170366i
\(950\) 35388.1 + 11198.9i 1.20857 + 0.382464i
\(951\) 21532.5i 0.734216i
\(952\) 28181.2 13926.2i 0.959410 0.474107i
\(953\) −19966.0 + 19966.0i −0.678659 + 0.678659i −0.959697 0.281037i \(-0.909322\pi\)
0.281037 + 0.959697i \(0.409322\pi\)
\(954\) 9630.06 + 7057.01i 0.326818 + 0.239496i
\(955\) −5741.73 1342.81i −0.194553 0.0454997i
\(956\) −2452.16 + 774.636i −0.0829586 + 0.0262066i
\(957\) −11810.1 11810.1i −0.398920 0.398920i
\(958\) −45534.6 + 7021.18i −1.53565 + 0.236789i
\(959\) −13318.9 −0.448477
\(960\) 1666.58 17091.9i 0.0560299 0.574625i
\(961\) 14615.7 0.490609
\(962\) 1734.30 267.420i 0.0581250 0.00896255i
\(963\) −4871.14 4871.14i −0.163001 0.163001i
\(964\) −13066.4 + 4127.68i −0.436558 + 0.137908i
\(965\) 9895.46 + 15936.8i 0.330100 + 0.531631i
\(966\) −11150.4 8171.16i −0.371387 0.272156i
\(967\) −17217.7 + 17217.7i −0.572580 + 0.572580i −0.932849 0.360269i \(-0.882685\pi\)
0.360269 + 0.932849i \(0.382685\pi\)
\(968\) 5503.81 2719.79i 0.182747 0.0903072i
\(969\) 31653.5i 1.04939i
\(970\) −20829.6 + 17854.8i −0.689483 + 0.591012i
\(971\) 10164.9i 0.335950i 0.985791 + 0.167975i \(0.0537228\pi\)
−0.985791 + 0.167975i \(0.946277\pi\)
\(972\) −1724.84 896.697i −0.0569180 0.0295901i
\(973\) 20126.5 20126.5i 0.663131 0.663131i
\(974\) −13788.0 + 18815.3i −0.453590 + 0.618974i
\(975\) 2829.90 + 1400.23i 0.0929530 + 0.0459930i
\(976\) 43587.1 30591.0i 1.42950 1.00327i
\(977\) 9513.40 + 9513.40i 0.311526 + 0.311526i 0.845500 0.533975i \(-0.179302\pi\)
−0.533975 + 0.845500i \(0.679302\pi\)
\(978\) −3136.17 20339.0i −0.102539 0.665000i
\(979\) 394.203 0.0128690
\(980\) 13549.6 1035.03i 0.441658 0.0337375i
\(981\) 6277.71 0.204314
\(982\) 1092.25 + 7083.61i 0.0354941 + 0.230191i
\(983\) −6749.01 6749.01i −0.218983 0.218983i 0.589087 0.808070i \(-0.299488\pi\)
−0.808070 + 0.589087i \(0.799488\pi\)
\(984\) 30302.5 + 10258.6i 0.981716 + 0.332351i
\(985\) −459.642 + 285.401i −0.0148684 + 0.00923210i
\(986\) 28736.3 39213.8i 0.928144 1.26655i
\(987\) 2253.32 2253.32i 0.0726687 0.0726687i
\(988\) 3261.82 6274.27i 0.105033 0.202036i
\(989\) 43008.8i 1.38281i
\(990\) −710.361 + 9237.42i −0.0228048 + 0.296550i
\(991\) 7199.32i 0.230771i −0.993321 0.115385i \(-0.963190\pi\)
0.993321 0.115385i \(-0.0368103\pi\)
\(992\) −15442.3 16087.2i −0.494248 0.514888i
\(993\) −7203.84 + 7203.84i −0.230218 + 0.230218i
\(994\) −16854.6 12351.2i −0.537821 0.394121i
\(995\) −1398.44 + 5979.63i −0.0445564 + 0.190520i
\(996\) −9287.50 29400.2i −0.295468 0.935321i
\(997\) −15867.5 15867.5i −0.504041 0.504041i 0.408650 0.912691i \(-0.366000\pi\)
−0.912691 + 0.408650i \(0.866000\pi\)
\(998\) 35092.9 5411.13i 1.11307 0.171630i
\(999\) 1989.54 0.0630093
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 60.4.j.b.7.14 yes 28
3.2 odd 2 180.4.k.f.127.1 28
4.3 odd 2 inner 60.4.j.b.7.7 28
5.3 odd 4 inner 60.4.j.b.43.7 yes 28
12.11 even 2 180.4.k.f.127.8 28
15.8 even 4 180.4.k.f.163.8 28
20.3 even 4 inner 60.4.j.b.43.14 yes 28
60.23 odd 4 180.4.k.f.163.1 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.4.j.b.7.7 28 4.3 odd 2 inner
60.4.j.b.7.14 yes 28 1.1 even 1 trivial
60.4.j.b.43.7 yes 28 5.3 odd 4 inner
60.4.j.b.43.14 yes 28 20.3 even 4 inner
180.4.k.f.127.1 28 3.2 odd 2
180.4.k.f.127.8 28 12.11 even 2
180.4.k.f.163.1 28 60.23 odd 4
180.4.k.f.163.8 28 15.8 even 4