Properties

Label 216.3.p.b.19.10
Level $216$
Weight $3$
Character 216.19
Analytic conductor $5.886$
Analytic rank $0$
Dimension $40$
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] = [216,3,Mod(19,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 216.p (of order \(6\), degree \(2\), not 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: \(5.88557371018\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.10
Character \(\chi\) \(=\) 216.19
Dual form 216.3.p.b.91.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.263796 - 1.98253i) q^{2} +(-3.86082 - 1.04596i) q^{4} +(-4.40783 + 2.54486i) q^{5} +(10.9609 + 6.32830i) q^{7} +(-3.09212 + 7.37826i) q^{8} +O(q^{10})\) \(q+(0.263796 - 1.98253i) q^{2} +(-3.86082 - 1.04596i) q^{4} +(-4.40783 + 2.54486i) q^{5} +(10.9609 + 6.32830i) q^{7} +(-3.09212 + 7.37826i) q^{8} +(3.88249 + 9.40996i) q^{10} +(-4.51244 + 7.81578i) q^{11} +(-9.68283 + 5.59038i) q^{13} +(15.4375 - 20.0610i) q^{14} +(13.8119 + 8.07657i) q^{16} +19.2305 q^{17} +14.2413 q^{19} +(19.6797 - 5.21483i) q^{20} +(14.3046 + 11.0078i) q^{22} +(4.28195 - 2.47218i) q^{23} +(0.452634 - 0.783986i) q^{25} +(8.52879 + 20.6712i) q^{26} +(-35.6990 - 35.8972i) q^{28} +(7.55576 + 4.36232i) q^{29} +(-33.9931 + 19.6259i) q^{31} +(19.6555 - 25.2519i) q^{32} +(5.07292 - 38.1249i) q^{34} -64.4185 q^{35} +19.9238i q^{37} +(3.75679 - 28.2337i) q^{38} +(-5.14712 - 40.3911i) q^{40} +(17.3873 + 30.1157i) q^{41} +(-3.02841 + 5.24536i) q^{43} +(25.5968 - 25.4555i) q^{44} +(-3.77161 - 9.14123i) q^{46} +(-52.8256 - 30.4989i) q^{47} +(55.5947 + 96.2928i) q^{49} +(-1.43487 - 1.10417i) q^{50} +(43.2310 - 11.4556i) q^{52} -6.53131i q^{53} -45.9341i q^{55} +(-80.5844 + 61.3048i) q^{56} +(10.6416 - 13.8287i) q^{58} +(25.0669 + 43.4171i) q^{59} +(-0.149359 - 0.0862322i) q^{61} +(29.9417 + 72.5695i) q^{62} +(-44.8776 - 45.6290i) q^{64} +(28.4535 - 49.2829i) q^{65} +(-40.4370 - 70.0389i) q^{67} +(-74.2455 - 20.1144i) q^{68} +(-16.9933 + 127.711i) q^{70} -50.4875i q^{71} +24.0274 q^{73} +(39.4995 + 5.25583i) q^{74} +(-54.9831 - 14.8959i) q^{76} +(-98.9211 + 57.1121i) q^{77} +(-2.84873 - 1.64471i) q^{79} +(-81.4343 - 0.450718i) q^{80} +(64.2919 - 26.5264i) q^{82} +(-18.4770 + 32.0032i) q^{83} +(-84.7646 + 48.9389i) q^{85} +(9.60018 + 7.38761i) q^{86} +(-43.7139 - 57.4613i) q^{88} -13.0096 q^{89} -141.510 q^{91} +(-19.1177 + 5.06590i) q^{92} +(-74.4000 + 96.6826i) q^{94} +(-62.7731 + 36.2421i) q^{95} +(44.7519 - 77.5126i) q^{97} +(205.569 - 84.8163i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.263796 1.98253i 0.131898 0.991263i
\(3\) 0 0
\(4\) −3.86082 1.04596i −0.965206 0.261491i
\(5\) −4.40783 + 2.54486i −0.881566 + 0.508972i −0.871174 0.490974i \(-0.836641\pi\)
−0.0103914 + 0.999946i \(0.503308\pi\)
\(6\) 0 0
\(7\) 10.9609 + 6.32830i 1.56585 + 0.904042i 0.996645 + 0.0818449i \(0.0260812\pi\)
0.569202 + 0.822198i \(0.307252\pi\)
\(8\) −3.09212 + 7.37826i −0.386515 + 0.922283i
\(9\) 0 0
\(10\) 3.88249 + 9.40996i 0.388249 + 0.940996i
\(11\) −4.51244 + 7.81578i −0.410222 + 0.710525i −0.994914 0.100730i \(-0.967882\pi\)
0.584692 + 0.811255i \(0.301215\pi\)
\(12\) 0 0
\(13\) −9.68283 + 5.59038i −0.744833 + 0.430029i −0.823824 0.566846i \(-0.808164\pi\)
0.0789910 + 0.996875i \(0.474830\pi\)
\(14\) 15.4375 20.0610i 1.10268 1.43293i
\(15\) 0 0
\(16\) 13.8119 + 8.07657i 0.863245 + 0.504785i
\(17\) 19.2305 1.13120 0.565602 0.824678i \(-0.308644\pi\)
0.565602 + 0.824678i \(0.308644\pi\)
\(18\) 0 0
\(19\) 14.2413 0.749541 0.374770 0.927118i \(-0.377722\pi\)
0.374770 + 0.927118i \(0.377722\pi\)
\(20\) 19.6797 5.21483i 0.983984 0.260741i
\(21\) 0 0
\(22\) 14.3046 + 11.0078i 0.650210 + 0.500355i
\(23\) 4.28195 2.47218i 0.186172 0.107486i −0.404017 0.914751i \(-0.632386\pi\)
0.590189 + 0.807265i \(0.299053\pi\)
\(24\) 0 0
\(25\) 0.452634 0.783986i 0.0181054 0.0313594i
\(26\) 8.52879 + 20.6712i 0.328031 + 0.795046i
\(27\) 0 0
\(28\) −35.6990 35.8972i −1.27497 1.28204i
\(29\) 7.55576 + 4.36232i 0.260543 + 0.150425i 0.624582 0.780959i \(-0.285269\pi\)
−0.364039 + 0.931384i \(0.618603\pi\)
\(30\) 0 0
\(31\) −33.9931 + 19.6259i −1.09655 + 0.633095i −0.935313 0.353820i \(-0.884882\pi\)
−0.161239 + 0.986915i \(0.551549\pi\)
\(32\) 19.6555 25.2519i 0.614236 0.789123i
\(33\) 0 0
\(34\) 5.07292 38.1249i 0.149203 1.12132i
\(35\) −64.4185 −1.84053
\(36\) 0 0
\(37\) 19.9238i 0.538482i 0.963073 + 0.269241i \(0.0867728\pi\)
−0.963073 + 0.269241i \(0.913227\pi\)
\(38\) 3.75679 28.2337i 0.0988629 0.742992i
\(39\) 0 0
\(40\) −5.14712 40.3911i −0.128678 1.00978i
\(41\) 17.3873 + 30.1157i 0.424081 + 0.734529i 0.996334 0.0855475i \(-0.0272639\pi\)
−0.572253 + 0.820077i \(0.693931\pi\)
\(42\) 0 0
\(43\) −3.02841 + 5.24536i −0.0704281 + 0.121985i −0.899089 0.437766i \(-0.855770\pi\)
0.828661 + 0.559751i \(0.189103\pi\)
\(44\) 25.5968 25.4555i 0.581745 0.578534i
\(45\) 0 0
\(46\) −3.77161 9.14123i −0.0819916 0.198722i
\(47\) −52.8256 30.4989i −1.12395 0.648912i −0.181542 0.983383i \(-0.558109\pi\)
−0.942406 + 0.334471i \(0.891442\pi\)
\(48\) 0 0
\(49\) 55.5947 + 96.2928i 1.13459 + 1.96516i
\(50\) −1.43487 1.10417i −0.0286974 0.0220834i
\(51\) 0 0
\(52\) 43.2310 11.4556i 0.831366 0.220300i
\(53\) 6.53131i 0.123232i −0.998100 0.0616161i \(-0.980375\pi\)
0.998100 0.0616161i \(-0.0196254\pi\)
\(54\) 0 0
\(55\) 45.9341i 0.835166i
\(56\) −80.5844 + 61.3048i −1.43901 + 1.09473i
\(57\) 0 0
\(58\) 10.6416 13.8287i 0.183476 0.238426i
\(59\) 25.0669 + 43.4171i 0.424862 + 0.735882i 0.996408 0.0846879i \(-0.0269893\pi\)
−0.571546 + 0.820570i \(0.693656\pi\)
\(60\) 0 0
\(61\) −0.149359 0.0862322i −0.00244850 0.00141364i 0.498775 0.866731i \(-0.333783\pi\)
−0.501224 + 0.865318i \(0.667117\pi\)
\(62\) 29.9417 + 72.5695i 0.482931 + 1.17048i
\(63\) 0 0
\(64\) −44.8776 45.6290i −0.701212 0.712953i
\(65\) 28.4535 49.2829i 0.437746 0.758198i
\(66\) 0 0
\(67\) −40.4370 70.0389i −0.603537 1.04536i −0.992281 0.124011i \(-0.960424\pi\)
0.388744 0.921346i \(-0.372909\pi\)
\(68\) −74.2455 20.1144i −1.09185 0.295800i
\(69\) 0 0
\(70\) −16.9933 + 127.711i −0.242762 + 1.82445i
\(71\) 50.4875i 0.711092i −0.934659 0.355546i \(-0.884295\pi\)
0.934659 0.355546i \(-0.115705\pi\)
\(72\) 0 0
\(73\) 24.0274 0.329142 0.164571 0.986365i \(-0.447376\pi\)
0.164571 + 0.986365i \(0.447376\pi\)
\(74\) 39.4995 + 5.25583i 0.533778 + 0.0710247i
\(75\) 0 0
\(76\) −54.9831 14.8959i −0.723461 0.195998i
\(77\) −98.9211 + 57.1121i −1.28469 + 0.741716i
\(78\) 0 0
\(79\) −2.84873 1.64471i −0.0360599 0.0208192i 0.481862 0.876247i \(-0.339961\pi\)
−0.517922 + 0.855428i \(0.673294\pi\)
\(80\) −81.4343 0.450718i −1.01793 0.00563397i
\(81\) 0 0
\(82\) 64.2919 26.5264i 0.784047 0.323493i
\(83\) −18.4770 + 32.0032i −0.222615 + 0.385580i −0.955601 0.294663i \(-0.904793\pi\)
0.732986 + 0.680243i \(0.238126\pi\)
\(84\) 0 0
\(85\) −84.7646 + 48.9389i −0.997231 + 0.575752i
\(86\) 9.60018 + 7.38761i 0.111630 + 0.0859024i
\(87\) 0 0
\(88\) −43.7139 57.4613i −0.496748 0.652969i
\(89\) −13.0096 −0.146175 −0.0730876 0.997326i \(-0.523285\pi\)
−0.0730876 + 0.997326i \(0.523285\pi\)
\(90\) 0 0
\(91\) −141.510 −1.55506
\(92\) −19.1177 + 5.06590i −0.207801 + 0.0550642i
\(93\) 0 0
\(94\) −74.4000 + 96.6826i −0.791489 + 1.02854i
\(95\) −62.7731 + 36.2421i −0.660770 + 0.381496i
\(96\) 0 0
\(97\) 44.7519 77.5126i 0.461360 0.799099i −0.537669 0.843156i \(-0.680695\pi\)
0.999029 + 0.0440568i \(0.0140283\pi\)
\(98\) 205.569 84.8163i 2.09764 0.865472i
\(99\) 0 0
\(100\) −2.56756 + 2.55339i −0.0256756 + 0.0255339i
\(101\) 98.5033 + 56.8709i 0.975280 + 0.563078i 0.900842 0.434147i \(-0.142950\pi\)
0.0744384 + 0.997226i \(0.476284\pi\)
\(102\) 0 0
\(103\) 169.831 98.0520i 1.64885 0.951961i 0.671313 0.741174i \(-0.265731\pi\)
0.977532 0.210787i \(-0.0676027\pi\)
\(104\) −11.3068 88.7286i −0.108720 0.853160i
\(105\) 0 0
\(106\) −12.9485 1.72293i −0.122156 0.0162541i
\(107\) −31.7982 −0.297179 −0.148590 0.988899i \(-0.547473\pi\)
−0.148590 + 0.988899i \(0.547473\pi\)
\(108\) 0 0
\(109\) 114.940i 1.05449i −0.849712 0.527247i \(-0.823224\pi\)
0.849712 0.527247i \(-0.176776\pi\)
\(110\) −91.0657 12.1172i −0.827870 0.110157i
\(111\) 0 0
\(112\) 100.281 + 175.933i 0.895362 + 1.57083i
\(113\) 16.4795 + 28.5433i 0.145836 + 0.252596i 0.929685 0.368357i \(-0.120079\pi\)
−0.783848 + 0.620952i \(0.786746\pi\)
\(114\) 0 0
\(115\) −12.5827 + 21.7939i −0.109415 + 0.189512i
\(116\) −24.6086 24.7452i −0.212143 0.213321i
\(117\) 0 0
\(118\) 92.6880 38.2425i 0.785492 0.324089i
\(119\) 210.784 + 121.696i 1.77129 + 1.02266i
\(120\) 0 0
\(121\) 19.7758 + 34.2526i 0.163436 + 0.283079i
\(122\) −0.210358 + 0.273360i −0.00172424 + 0.00224065i
\(123\) 0 0
\(124\) 151.770 40.2167i 1.22395 0.324328i
\(125\) 122.635i 0.981084i
\(126\) 0 0
\(127\) 74.7526i 0.588603i 0.955713 + 0.294302i \(0.0950870\pi\)
−0.955713 + 0.294302i \(0.904913\pi\)
\(128\) −102.299 + 76.9342i −0.799212 + 0.601049i
\(129\) 0 0
\(130\) −90.1988 69.4104i −0.693837 0.533926i
\(131\) −41.0887 71.1677i −0.313654 0.543265i 0.665497 0.746401i \(-0.268220\pi\)
−0.979150 + 0.203136i \(0.934887\pi\)
\(132\) 0 0
\(133\) 156.098 + 90.1230i 1.17367 + 0.677617i
\(134\) −149.521 + 61.6914i −1.11583 + 0.460384i
\(135\) 0 0
\(136\) −59.4630 + 141.888i −0.437228 + 1.04329i
\(137\) 91.7121 158.850i 0.669432 1.15949i −0.308632 0.951182i \(-0.599871\pi\)
0.978063 0.208308i \(-0.0667956\pi\)
\(138\) 0 0
\(139\) −103.570 179.388i −0.745105 1.29056i −0.950146 0.311807i \(-0.899066\pi\)
0.205040 0.978754i \(-0.434267\pi\)
\(140\) 248.709 + 67.3795i 1.77649 + 0.481282i
\(141\) 0 0
\(142\) −100.093 13.3184i −0.704879 0.0937915i
\(143\) 100.905i 0.705630i
\(144\) 0 0
\(145\) −44.4060 −0.306248
\(146\) 6.33832 47.6349i 0.0434132 0.326267i
\(147\) 0 0
\(148\) 20.8396 76.9224i 0.140808 0.519746i
\(149\) 195.664 112.967i 1.31318 0.758167i 0.330561 0.943785i \(-0.392762\pi\)
0.982622 + 0.185618i \(0.0594287\pi\)
\(150\) 0 0
\(151\) −123.589 71.3540i −0.818469 0.472543i 0.0314192 0.999506i \(-0.489997\pi\)
−0.849888 + 0.526963i \(0.823331\pi\)
\(152\) −44.0358 + 105.076i −0.289709 + 0.691289i
\(153\) 0 0
\(154\) 87.1313 + 211.180i 0.565788 + 1.37130i
\(155\) 99.8906 173.016i 0.644455 1.11623i
\(156\) 0 0
\(157\) 8.21204 4.74122i 0.0523060 0.0301989i −0.473619 0.880730i \(-0.657053\pi\)
0.525925 + 0.850531i \(0.323719\pi\)
\(158\) −4.01217 + 5.21381i −0.0253935 + 0.0329988i
\(159\) 0 0
\(160\) −22.3756 + 161.327i −0.139847 + 1.00829i
\(161\) 62.5789 0.388689
\(162\) 0 0
\(163\) 305.669 1.87527 0.937635 0.347622i \(-0.113011\pi\)
0.937635 + 0.347622i \(0.113011\pi\)
\(164\) −35.6294 134.458i −0.217252 0.819865i
\(165\) 0 0
\(166\) 58.5730 + 45.0735i 0.352849 + 0.271527i
\(167\) −13.4105 + 7.74257i −0.0803026 + 0.0463627i −0.539614 0.841913i \(-0.681430\pi\)
0.459311 + 0.888275i \(0.348096\pi\)
\(168\) 0 0
\(169\) −21.9952 + 38.0969i −0.130149 + 0.225425i
\(170\) 74.6621 + 180.958i 0.439189 + 1.06446i
\(171\) 0 0
\(172\) 17.1786 17.0838i 0.0998757 0.0993244i
\(173\) 79.3643 + 45.8210i 0.458753 + 0.264861i 0.711520 0.702666i \(-0.248007\pi\)
−0.252767 + 0.967527i \(0.581341\pi\)
\(174\) 0 0
\(175\) 9.92259 5.72881i 0.0567005 0.0327361i
\(176\) −125.450 + 71.5058i −0.712785 + 0.406283i
\(177\) 0 0
\(178\) −3.43187 + 25.7918i −0.0192802 + 0.144898i
\(179\) −125.988 −0.703846 −0.351923 0.936029i \(-0.614472\pi\)
−0.351923 + 0.936029i \(0.614472\pi\)
\(180\) 0 0
\(181\) 23.0017i 0.127081i 0.997979 + 0.0635405i \(0.0202392\pi\)
−0.997979 + 0.0635405i \(0.979761\pi\)
\(182\) −37.3299 + 280.548i −0.205109 + 1.54147i
\(183\) 0 0
\(184\) 5.00012 + 39.2376i 0.0271746 + 0.213248i
\(185\) −50.7034 87.8209i −0.274072 0.474707i
\(186\) 0 0
\(187\) −86.7764 + 150.301i −0.464045 + 0.803749i
\(188\) 172.050 + 173.004i 0.915157 + 0.920236i
\(189\) 0 0
\(190\) 55.2916 + 134.010i 0.291008 + 0.705315i
\(191\) 20.4240 + 11.7918i 0.106932 + 0.0617371i 0.552512 0.833505i \(-0.313669\pi\)
−0.445580 + 0.895242i \(0.647003\pi\)
\(192\) 0 0
\(193\) −31.0142 53.7183i −0.160696 0.278333i 0.774423 0.632668i \(-0.218040\pi\)
−0.935118 + 0.354336i \(0.884707\pi\)
\(194\) −141.865 109.169i −0.731265 0.562729i
\(195\) 0 0
\(196\) −113.922 429.920i −0.581237 2.19347i
\(197\) 385.821i 1.95848i 0.202698 + 0.979241i \(0.435029\pi\)
−0.202698 + 0.979241i \(0.564971\pi\)
\(198\) 0 0
\(199\) 214.957i 1.08018i 0.841606 + 0.540092i \(0.181611\pi\)
−0.841606 + 0.540092i \(0.818389\pi\)
\(200\) 4.38485 + 5.76384i 0.0219243 + 0.0288192i
\(201\) 0 0
\(202\) 138.733 180.283i 0.686796 0.892491i
\(203\) 55.2121 + 95.6302i 0.271981 + 0.471085i
\(204\) 0 0
\(205\) −153.281 88.4966i −0.747710 0.431691i
\(206\) −149.590 362.560i −0.726165 1.76000i
\(207\) 0 0
\(208\) −178.890 0.990107i −0.860046 0.00476013i
\(209\) −64.2629 + 111.307i −0.307478 + 0.532568i
\(210\) 0 0
\(211\) 50.4896 + 87.4505i 0.239287 + 0.414457i 0.960510 0.278246i \(-0.0897530\pi\)
−0.721223 + 0.692703i \(0.756420\pi\)
\(212\) −6.83151 + 25.2162i −0.0322241 + 0.118944i
\(213\) 0 0
\(214\) −8.38823 + 63.0408i −0.0391973 + 0.294583i
\(215\) 30.8275i 0.143384i
\(216\) 0 0
\(217\) −496.795 −2.28938
\(218\) −227.871 30.3206i −1.04528 0.139085i
\(219\) 0 0
\(220\) −48.0455 + 177.344i −0.218389 + 0.806107i
\(221\) −186.205 + 107.506i −0.842558 + 0.486451i
\(222\) 0 0
\(223\) 66.2290 + 38.2373i 0.296991 + 0.171468i 0.641090 0.767465i \(-0.278482\pi\)
−0.344099 + 0.938933i \(0.611816\pi\)
\(224\) 375.245 152.399i 1.67520 0.680351i
\(225\) 0 0
\(226\) 60.9351 25.1414i 0.269624 0.111245i
\(227\) −37.4197 + 64.8128i −0.164844 + 0.285519i −0.936600 0.350400i \(-0.886046\pi\)
0.771756 + 0.635919i \(0.219379\pi\)
\(228\) 0 0
\(229\) 255.666 147.609i 1.11645 0.644581i 0.175956 0.984398i \(-0.443698\pi\)
0.940492 + 0.339817i \(0.110365\pi\)
\(230\) 39.8878 + 30.6947i 0.173425 + 0.133455i
\(231\) 0 0
\(232\) −55.5497 + 42.2596i −0.239438 + 0.182153i
\(233\) −354.235 −1.52032 −0.760162 0.649734i \(-0.774880\pi\)
−0.760162 + 0.649734i \(0.774880\pi\)
\(234\) 0 0
\(235\) 310.461 1.32111
\(236\) −51.3660 193.845i −0.217652 0.821376i
\(237\) 0 0
\(238\) 296.870 385.782i 1.24735 1.62093i
\(239\) 107.843 62.2632i 0.451226 0.260516i −0.257122 0.966379i \(-0.582774\pi\)
0.708348 + 0.705863i \(0.249441\pi\)
\(240\) 0 0
\(241\) 189.676 328.528i 0.787036 1.36319i −0.140740 0.990047i \(-0.544948\pi\)
0.927775 0.373139i \(-0.121719\pi\)
\(242\) 73.1235 30.1703i 0.302163 0.124671i
\(243\) 0 0
\(244\) 0.486451 + 0.489151i 0.00199365 + 0.00200472i
\(245\) −490.104 282.961i −2.00042 1.15494i
\(246\) 0 0
\(247\) −137.896 + 79.6142i −0.558283 + 0.322325i
\(248\) −39.6945 311.496i −0.160059 1.25603i
\(249\) 0 0
\(250\) −243.128 32.3507i −0.972512 0.129403i
\(251\) 385.891 1.53741 0.768707 0.639601i \(-0.220901\pi\)
0.768707 + 0.639601i \(0.220901\pi\)
\(252\) 0 0
\(253\) 44.6223i 0.176373i
\(254\) 148.199 + 19.7194i 0.583461 + 0.0776355i
\(255\) 0 0
\(256\) 125.538 + 223.106i 0.490383 + 0.871507i
\(257\) 228.629 + 395.997i 0.889607 + 1.54084i 0.840341 + 0.542058i \(0.182355\pi\)
0.0492659 + 0.998786i \(0.484312\pi\)
\(258\) 0 0
\(259\) −126.084 + 218.384i −0.486811 + 0.843181i
\(260\) −161.402 + 160.511i −0.620777 + 0.617351i
\(261\) 0 0
\(262\) −151.931 + 62.6856i −0.579889 + 0.239258i
\(263\) −404.801 233.712i −1.53917 0.888638i −0.998888 0.0471517i \(-0.984986\pi\)
−0.540278 0.841486i \(-0.681681\pi\)
\(264\) 0 0
\(265\) 16.6213 + 28.7889i 0.0627218 + 0.108637i
\(266\) 219.849 285.694i 0.826501 1.07404i
\(267\) 0 0
\(268\) 82.8619 + 312.704i 0.309186 + 1.16680i
\(269\) 463.103i 1.72157i −0.508966 0.860787i \(-0.669972\pi\)
0.508966 0.860787i \(-0.330028\pi\)
\(270\) 0 0
\(271\) 324.633i 1.19791i −0.800784 0.598954i \(-0.795583\pi\)
0.800784 0.598954i \(-0.204417\pi\)
\(272\) 265.610 + 155.316i 0.976506 + 0.571016i
\(273\) 0 0
\(274\) −290.731 223.726i −1.06106 0.816517i
\(275\) 4.08497 + 7.07538i 0.0148544 + 0.0257287i
\(276\) 0 0
\(277\) −249.678 144.151i −0.901363 0.520402i −0.0237212 0.999719i \(-0.507551\pi\)
−0.877642 + 0.479316i \(0.840885\pi\)
\(278\) −382.962 + 158.008i −1.37756 + 0.568373i
\(279\) 0 0
\(280\) 199.190 475.297i 0.711393 1.69749i
\(281\) −172.969 + 299.590i −0.615546 + 1.06616i 0.374742 + 0.927129i \(0.377731\pi\)
−0.990288 + 0.139028i \(0.955602\pi\)
\(282\) 0 0
\(283\) −7.83064 13.5631i −0.0276701 0.0479260i 0.851859 0.523772i \(-0.175475\pi\)
−0.879529 + 0.475846i \(0.842142\pi\)
\(284\) −52.8082 + 194.923i −0.185944 + 0.686350i
\(285\) 0 0
\(286\) −200.047 26.6183i −0.699465 0.0930711i
\(287\) 440.128i 1.53355i
\(288\) 0 0
\(289\) 80.8112 0.279623
\(290\) −11.7141 + 88.0361i −0.0403935 + 0.303573i
\(291\) 0 0
\(292\) −92.7655 25.1318i −0.317690 0.0860678i
\(293\) 91.8784 53.0460i 0.313578 0.181045i −0.334948 0.942237i \(-0.608719\pi\)
0.648527 + 0.761192i \(0.275386\pi\)
\(294\) 0 0
\(295\) −220.981 127.583i −0.749087 0.432486i
\(296\) −147.003 61.6069i −0.496633 0.208132i
\(297\) 0 0
\(298\) −172.344 417.710i −0.578337 1.40171i
\(299\) −27.6409 + 47.8755i −0.0924445 + 0.160119i
\(300\) 0 0
\(301\) −66.3884 + 38.3294i −0.220559 + 0.127340i
\(302\) −174.064 + 226.195i −0.576369 + 0.748991i
\(303\) 0 0
\(304\) 196.699 + 115.021i 0.647037 + 0.378357i
\(305\) 0.877796 0.00287802
\(306\) 0 0
\(307\) 329.540 1.07342 0.536710 0.843767i \(-0.319667\pi\)
0.536710 + 0.843767i \(0.319667\pi\)
\(308\) 441.654 117.032i 1.43394 0.379974i
\(309\) 0 0
\(310\) −316.657 243.677i −1.02148 0.786053i
\(311\) −342.791 + 197.911i −1.10222 + 0.636369i −0.936804 0.349855i \(-0.886231\pi\)
−0.165419 + 0.986223i \(0.552898\pi\)
\(312\) 0 0
\(313\) −51.1983 + 88.6781i −0.163573 + 0.283317i −0.936148 0.351607i \(-0.885635\pi\)
0.772575 + 0.634924i \(0.218969\pi\)
\(314\) −7.23330 17.5313i −0.0230360 0.0558322i
\(315\) 0 0
\(316\) 9.27813 + 9.32962i 0.0293612 + 0.0295241i
\(317\) 237.016 + 136.841i 0.747685 + 0.431676i 0.824857 0.565341i \(-0.191256\pi\)
−0.0771716 + 0.997018i \(0.524589\pi\)
\(318\) 0 0
\(319\) −68.1898 + 39.3694i −0.213761 + 0.123415i
\(320\) 313.932 + 86.9175i 0.981038 + 0.271617i
\(321\) 0 0
\(322\) 16.5080 124.064i 0.0512672 0.385293i
\(323\) 273.867 0.847884
\(324\) 0 0
\(325\) 10.1216i 0.0311434i
\(326\) 80.6342 605.997i 0.247344 1.85889i
\(327\) 0 0
\(328\) −275.965 + 35.1668i −0.841358 + 0.107216i
\(329\) −386.012 668.592i −1.17329 2.03219i
\(330\) 0 0
\(331\) −145.019 + 251.179i −0.438122 + 0.758850i −0.997545 0.0700325i \(-0.977690\pi\)
0.559422 + 0.828883i \(0.311023\pi\)
\(332\) 104.811 104.232i 0.315695 0.313953i
\(333\) 0 0
\(334\) 11.8122 + 28.6292i 0.0353659 + 0.0857161i
\(335\) 356.479 + 205.813i 1.06412 + 0.614367i
\(336\) 0 0
\(337\) 190.788 + 330.455i 0.566137 + 0.980578i 0.996943 + 0.0781332i \(0.0248960\pi\)
−0.430806 + 0.902445i \(0.641771\pi\)
\(338\) 69.7258 + 53.6559i 0.206289 + 0.158745i
\(339\) 0 0
\(340\) 378.450 100.284i 1.11309 0.294952i
\(341\) 354.244i 1.03884i
\(342\) 0 0
\(343\) 787.105i 2.29477i
\(344\) −29.3374 38.5637i −0.0852833 0.112104i
\(345\) 0 0
\(346\) 111.777 145.254i 0.323056 0.419810i
\(347\) 71.1923 + 123.309i 0.205165 + 0.355356i 0.950185 0.311686i \(-0.100894\pi\)
−0.745020 + 0.667042i \(0.767560\pi\)
\(348\) 0 0
\(349\) 533.855 + 308.222i 1.52967 + 0.883156i 0.999375 + 0.0353439i \(0.0112527\pi\)
0.530296 + 0.847812i \(0.322081\pi\)
\(350\) −8.73998 21.1830i −0.0249714 0.0605230i
\(351\) 0 0
\(352\) 108.669 + 267.571i 0.308719 + 0.760145i
\(353\) −205.510 + 355.953i −0.582181 + 1.00837i 0.413040 + 0.910713i \(0.364467\pi\)
−0.995220 + 0.0976536i \(0.968866\pi\)
\(354\) 0 0
\(355\) 128.484 + 222.540i 0.361926 + 0.626874i
\(356\) 50.2277 + 13.6076i 0.141089 + 0.0382235i
\(357\) 0 0
\(358\) −33.2352 + 249.775i −0.0928358 + 0.697697i
\(359\) 131.102i 0.365186i 0.983189 + 0.182593i \(0.0584491\pi\)
−0.983189 + 0.182593i \(0.941551\pi\)
\(360\) 0 0
\(361\) −158.186 −0.438188
\(362\) 45.6014 + 6.06774i 0.125971 + 0.0167617i
\(363\) 0 0
\(364\) 546.347 + 148.015i 1.50095 + 0.406634i
\(365\) −105.909 + 61.1463i −0.290160 + 0.167524i
\(366\) 0 0
\(367\) 93.3059 + 53.8702i 0.254239 + 0.146785i 0.621704 0.783252i \(-0.286441\pi\)
−0.367465 + 0.930038i \(0.619774\pi\)
\(368\) 79.1087 + 0.437846i 0.214969 + 0.00118980i
\(369\) 0 0
\(370\) −187.483 + 77.3541i −0.506710 + 0.209065i
\(371\) 41.3320 71.5892i 0.111407 0.192963i
\(372\) 0 0
\(373\) −560.553 + 323.636i −1.50282 + 0.867656i −0.502829 + 0.864386i \(0.667707\pi\)
−0.999995 + 0.00326975i \(0.998959\pi\)
\(374\) 275.085 + 211.685i 0.735521 + 0.566003i
\(375\) 0 0
\(376\) 388.372 295.455i 1.03290 0.785784i
\(377\) −97.5482 −0.258748
\(378\) 0 0
\(379\) −225.686 −0.595477 −0.297739 0.954647i \(-0.596232\pi\)
−0.297739 + 0.954647i \(0.596232\pi\)
\(380\) 280.264 74.2658i 0.737536 0.195436i
\(381\) 0 0
\(382\) 28.7653 37.3804i 0.0753018 0.0978546i
\(383\) 413.047 238.473i 1.07845 0.622644i 0.147973 0.988991i \(-0.452725\pi\)
0.930478 + 0.366348i \(0.119392\pi\)
\(384\) 0 0
\(385\) 290.685 503.481i 0.755026 1.30774i
\(386\) −114.679 + 47.3159i −0.297097 + 0.122580i
\(387\) 0 0
\(388\) −253.855 + 252.454i −0.654265 + 0.650654i
\(389\) −10.3892 5.99823i −0.0267076 0.0154196i 0.486587 0.873632i \(-0.338242\pi\)
−0.513294 + 0.858213i \(0.671575\pi\)
\(390\) 0 0
\(391\) 82.3439 47.5413i 0.210598 0.121589i
\(392\) −882.379 + 112.443i −2.25097 + 0.286845i
\(393\) 0 0
\(394\) 764.901 + 101.778i 1.94137 + 0.258320i
\(395\) 16.7423 0.0423855
\(396\) 0 0
\(397\) 3.42581i 0.00862924i 0.999991 + 0.00431462i \(0.00137339\pi\)
−0.999991 + 0.00431462i \(0.998627\pi\)
\(398\) 426.157 + 56.7047i 1.07075 + 0.142474i
\(399\) 0 0
\(400\) 12.5837 7.17261i 0.0314592 0.0179315i
\(401\) −23.8998 41.3956i −0.0596004 0.103231i 0.834686 0.550727i \(-0.185649\pi\)
−0.894286 + 0.447496i \(0.852316\pi\)
\(402\) 0 0
\(403\) 219.433 380.069i 0.544499 0.943100i
\(404\) −320.819 322.600i −0.794106 0.798514i
\(405\) 0 0
\(406\) 204.154 84.2326i 0.502843 0.207470i
\(407\) −155.720 89.9052i −0.382605 0.220897i
\(408\) 0 0
\(409\) −113.468 196.532i −0.277428 0.480519i 0.693317 0.720633i \(-0.256149\pi\)
−0.970745 + 0.240114i \(0.922815\pi\)
\(410\) −215.882 + 280.538i −0.526540 + 0.684238i
\(411\) 0 0
\(412\) −758.247 + 200.924i −1.84040 + 0.487680i
\(413\) 634.522i 1.53637i
\(414\) 0 0
\(415\) 188.086i 0.453219i
\(416\) −49.1532 + 354.392i −0.118157 + 0.851904i
\(417\) 0 0
\(418\) 203.716 + 156.765i 0.487359 + 0.375036i
\(419\) −174.977 303.068i −0.417605 0.723314i 0.578093 0.815971i \(-0.303797\pi\)
−0.995698 + 0.0926575i \(0.970464\pi\)
\(420\) 0 0
\(421\) 173.344 + 100.080i 0.411743 + 0.237720i 0.691538 0.722340i \(-0.256933\pi\)
−0.279796 + 0.960060i \(0.590267\pi\)
\(422\) 186.692 77.0278i 0.442398 0.182530i
\(423\) 0 0
\(424\) 48.1897 + 20.1956i 0.113655 + 0.0476311i
\(425\) 8.70438 15.0764i 0.0204809 0.0354739i
\(426\) 0 0
\(427\) −1.09141 1.89037i −0.00255599 0.00442710i
\(428\) 122.767 + 33.2598i 0.286839 + 0.0777098i
\(429\) 0 0
\(430\) −61.1164 8.13217i −0.142131 0.0189120i
\(431\) 332.817i 0.772198i −0.922457 0.386099i \(-0.873822\pi\)
0.922457 0.386099i \(-0.126178\pi\)
\(432\) 0 0
\(433\) 276.314 0.638139 0.319069 0.947731i \(-0.396630\pi\)
0.319069 + 0.947731i \(0.396630\pi\)
\(434\) −131.052 + 984.910i −0.301964 + 2.26938i
\(435\) 0 0
\(436\) −120.223 + 443.762i −0.275741 + 1.01780i
\(437\) 60.9804 35.2071i 0.139543 0.0805654i
\(438\) 0 0
\(439\) −41.6495 24.0464i −0.0948736 0.0547753i 0.451813 0.892113i \(-0.350778\pi\)
−0.546686 + 0.837338i \(0.684111\pi\)
\(440\) 338.914 + 142.034i 0.770260 + 0.322804i
\(441\) 0 0
\(442\) 164.013 + 397.517i 0.371070 + 0.899359i
\(443\) 190.236 329.498i 0.429426 0.743787i −0.567397 0.823445i \(-0.692049\pi\)
0.996822 + 0.0796575i \(0.0253827\pi\)
\(444\) 0 0
\(445\) 57.3440 33.1076i 0.128863 0.0743991i
\(446\) 93.2775 121.214i 0.209142 0.271780i
\(447\) 0 0
\(448\) −203.146 784.135i −0.453452 1.75030i
\(449\) 638.660 1.42240 0.711202 0.702987i \(-0.248151\pi\)
0.711202 + 0.702987i \(0.248151\pi\)
\(450\) 0 0
\(451\) −313.837 −0.695869
\(452\) −33.7691 127.438i −0.0747104 0.281942i
\(453\) 0 0
\(454\) 118.622 + 91.2829i 0.261282 + 0.201064i
\(455\) 623.754 360.124i 1.37089 0.791482i
\(456\) 0 0
\(457\) −278.126 + 481.729i −0.608591 + 1.05411i 0.382882 + 0.923797i \(0.374932\pi\)
−0.991473 + 0.130313i \(0.958402\pi\)
\(458\) −225.195 545.804i −0.491693 1.19171i
\(459\) 0 0
\(460\) 71.3754 70.9814i 0.155164 0.154307i
\(461\) 181.920 + 105.032i 0.394620 + 0.227834i 0.684160 0.729332i \(-0.260169\pi\)
−0.289540 + 0.957166i \(0.593502\pi\)
\(462\) 0 0
\(463\) 156.561 90.3903i 0.338144 0.195227i −0.321307 0.946975i \(-0.604122\pi\)
0.659451 + 0.751748i \(0.270789\pi\)
\(464\) 69.1270 + 121.277i 0.148981 + 0.261372i
\(465\) 0 0
\(466\) −93.4458 + 702.281i −0.200527 + 1.50704i
\(467\) −10.4709 −0.0224215 −0.0112108 0.999937i \(-0.503569\pi\)
−0.0112108 + 0.999937i \(0.503569\pi\)
\(468\) 0 0
\(469\) 1023.59i 2.18249i
\(470\) 81.8984 615.498i 0.174252 1.30957i
\(471\) 0 0
\(472\) −397.852 + 50.6990i −0.842907 + 0.107413i
\(473\) −27.3310 47.3388i −0.0577823 0.100082i
\(474\) 0 0
\(475\) 6.44609 11.1650i 0.0135707 0.0235052i
\(476\) −686.510 690.320i −1.44225 1.45025i
\(477\) 0 0
\(478\) −94.9900 230.227i −0.198724 0.481645i
\(479\) −364.147 210.240i −0.760223 0.438915i 0.0691526 0.997606i \(-0.477970\pi\)
−0.829376 + 0.558691i \(0.811304\pi\)
\(480\) 0 0
\(481\) −111.382 192.919i −0.231563 0.401079i
\(482\) −601.279 462.701i −1.24747 0.959961i
\(483\) 0 0
\(484\) −40.5237 152.928i −0.0837266 0.315967i
\(485\) 455.550i 0.939278i
\(486\) 0 0
\(487\) 865.055i 1.77629i −0.459560 0.888147i \(-0.651993\pi\)
0.459560 0.888147i \(-0.348007\pi\)
\(488\) 1.09808 0.835367i 0.00225016 0.00171182i
\(489\) 0 0
\(490\) −690.266 + 896.999i −1.40871 + 1.83061i
\(491\) 31.8734 + 55.2063i 0.0649152 + 0.112436i 0.896656 0.442727i \(-0.145989\pi\)
−0.831741 + 0.555164i \(0.812656\pi\)
\(492\) 0 0
\(493\) 145.301 + 83.8895i 0.294728 + 0.170161i
\(494\) 121.461 + 294.384i 0.245872 + 0.595919i
\(495\) 0 0
\(496\) −628.021 3.47593i −1.26617 0.00700792i
\(497\) 319.500 553.390i 0.642857 1.11346i
\(498\) 0 0
\(499\) −363.674 629.902i −0.728806 1.26233i −0.957388 0.288805i \(-0.906742\pi\)
0.228582 0.973525i \(-0.426591\pi\)
\(500\) −128.272 + 473.474i −0.256545 + 0.946948i
\(501\) 0 0
\(502\) 101.796 765.039i 0.202782 1.52398i
\(503\) 348.449i 0.692742i 0.938098 + 0.346371i \(0.112586\pi\)
−0.938098 + 0.346371i \(0.887414\pi\)
\(504\) 0 0
\(505\) −578.914 −1.14636
\(506\) 88.4650 + 11.7712i 0.174832 + 0.0232632i
\(507\) 0 0
\(508\) 78.1886 288.607i 0.153915 0.568123i
\(509\) 706.201 407.725i 1.38743 0.801032i 0.394403 0.918938i \(-0.370952\pi\)
0.993025 + 0.117906i \(0.0376182\pi\)
\(510\) 0 0
\(511\) 263.362 + 152.052i 0.515386 + 0.297559i
\(512\) 475.430 190.028i 0.928573 0.371149i
\(513\) 0 0
\(514\) 845.386 348.801i 1.64472 0.678600i
\(515\) −499.057 + 864.393i −0.969043 + 1.67843i
\(516\) 0 0
\(517\) 476.745 275.249i 0.922136 0.532396i
\(518\) 399.691 + 307.574i 0.771605 + 0.593771i
\(519\) 0 0
\(520\) 275.641 + 362.326i 0.530078 + 0.696781i
\(521\) 335.561 0.644072 0.322036 0.946727i \(-0.395633\pi\)
0.322036 + 0.946727i \(0.395633\pi\)
\(522\) 0 0
\(523\) 215.728 0.412481 0.206241 0.978501i \(-0.433877\pi\)
0.206241 + 0.978501i \(0.433877\pi\)
\(524\) 84.1973 + 317.743i 0.160682 + 0.606380i
\(525\) 0 0
\(526\) −570.125 + 740.876i −1.08389 + 1.40851i
\(527\) −653.704 + 377.416i −1.24043 + 0.716160i
\(528\) 0 0
\(529\) −252.277 + 436.956i −0.476893 + 0.826004i
\(530\) 61.4593 25.3577i 0.115961 0.0478448i
\(531\) 0 0
\(532\) −508.400 511.222i −0.955639 0.960943i
\(533\) −336.717 194.403i −0.631739 0.364734i
\(534\) 0 0
\(535\) 140.161 80.9220i 0.261983 0.151256i
\(536\) 641.802 81.7860i 1.19739 0.152586i
\(537\) 0 0
\(538\) −918.115 122.165i −1.70653 0.227072i
\(539\) −1003.47 −1.86173
\(540\) 0 0
\(541\) 130.450i 0.241128i 0.992706 + 0.120564i \(0.0384703\pi\)
−0.992706 + 0.120564i \(0.961530\pi\)
\(542\) −643.593 85.6368i −1.18744 0.158001i
\(543\) 0 0
\(544\) 377.985 485.607i 0.694826 0.892659i
\(545\) 292.506 + 506.635i 0.536708 + 0.929605i
\(546\) 0 0
\(547\) 130.466 225.973i 0.238511 0.413114i −0.721776 0.692127i \(-0.756674\pi\)
0.960287 + 0.279013i \(0.0900072\pi\)
\(548\) −520.236 + 517.365i −0.949336 + 0.944096i
\(549\) 0 0
\(550\) 15.1047 6.23211i 0.0274631 0.0113311i
\(551\) 107.604 + 62.1250i 0.195288 + 0.112750i
\(552\) 0 0
\(553\) −20.8165 36.0552i −0.0376428 0.0651993i
\(554\) −351.648 + 456.966i −0.634744 + 0.824849i
\(555\) 0 0
\(556\) 212.231 + 800.915i 0.381710 + 1.44049i
\(557\) 133.587i 0.239833i −0.992784 0.119917i \(-0.961737\pi\)
0.992784 0.119917i \(-0.0382627\pi\)
\(558\) 0 0
\(559\) 67.7199i 0.121145i
\(560\) −889.744 520.281i −1.58883 0.929073i
\(561\) 0 0
\(562\) 548.317 + 421.945i 0.975654 + 0.750792i
\(563\) −438.575 759.634i −0.778997 1.34926i −0.932521 0.361117i \(-0.882396\pi\)
0.153524 0.988145i \(-0.450938\pi\)
\(564\) 0 0
\(565\) −145.277 83.8760i −0.257128 0.148453i
\(566\) −28.9548 + 11.9466i −0.0511569 + 0.0211070i
\(567\) 0 0
\(568\) 372.510 + 156.114i 0.655828 + 0.274848i
\(569\) 346.763 600.612i 0.609426 1.05556i −0.381909 0.924200i \(-0.624733\pi\)
0.991335 0.131357i \(-0.0419335\pi\)
\(570\) 0 0
\(571\) −159.760 276.712i −0.279789 0.484609i 0.691543 0.722335i \(-0.256931\pi\)
−0.971332 + 0.237726i \(0.923598\pi\)
\(572\) −105.543 + 389.577i −0.184516 + 0.681078i
\(573\) 0 0
\(574\) 872.566 + 116.104i 1.52015 + 0.202272i
\(575\) 4.47598i 0.00778432i
\(576\) 0 0
\(577\) 878.170 1.52196 0.760979 0.648776i \(-0.224719\pi\)
0.760979 + 0.648776i \(0.224719\pi\)
\(578\) 21.3177 160.210i 0.0368818 0.277180i
\(579\) 0 0
\(580\) 171.444 + 46.4471i 0.295593 + 0.0800812i
\(581\) −405.051 + 233.856i −0.697162 + 0.402507i
\(582\) 0 0
\(583\) 51.0472 + 29.4721i 0.0875596 + 0.0505525i
\(584\) −74.2956 + 177.280i −0.127218 + 0.303562i
\(585\) 0 0
\(586\) −80.9280 196.145i −0.138102 0.334718i
\(587\) −277.395 + 480.462i −0.472564 + 0.818505i −0.999507 0.0313957i \(-0.990005\pi\)
0.526943 + 0.849901i \(0.323338\pi\)
\(588\) 0 0
\(589\) −484.106 + 279.499i −0.821911 + 0.474531i
\(590\) −311.231 + 404.444i −0.527510 + 0.685499i
\(591\) 0 0
\(592\) −160.916 + 275.186i −0.271818 + 0.464842i
\(593\) 673.984 1.13657 0.568283 0.822833i \(-0.307608\pi\)
0.568283 + 0.822833i \(0.307608\pi\)
\(594\) 0 0
\(595\) −1238.80 −2.08202
\(596\) −873.584 + 231.487i −1.46575 + 0.388401i
\(597\) 0 0
\(598\) 87.6228 + 67.4282i 0.146526 + 0.112756i
\(599\) 222.534 128.480i 0.371509 0.214491i −0.302608 0.953115i \(-0.597857\pi\)
0.674118 + 0.738624i \(0.264524\pi\)
\(600\) 0 0
\(601\) 196.757 340.793i 0.327383 0.567044i −0.654609 0.755968i \(-0.727167\pi\)
0.981992 + 0.188924i \(0.0605000\pi\)
\(602\) 58.4760 + 141.728i 0.0971362 + 0.235428i
\(603\) 0 0
\(604\) 402.521 + 404.755i 0.666425 + 0.670124i
\(605\) −174.336 100.653i −0.288159 0.166369i
\(606\) 0 0
\(607\) −501.576 + 289.585i −0.826319 + 0.477076i −0.852591 0.522579i \(-0.824970\pi\)
0.0262715 + 0.999655i \(0.491637\pi\)
\(608\) 279.920 359.620i 0.460395 0.591480i
\(609\) 0 0
\(610\) 0.231559 1.74025i 0.000379605 0.00285288i
\(611\) 682.001 1.11621
\(612\) 0 0
\(613\) 825.194i 1.34616i 0.739571 + 0.673079i \(0.235028\pi\)
−0.739571 + 0.673079i \(0.764972\pi\)
\(614\) 86.9312 653.321i 0.141582 1.06404i
\(615\) 0 0
\(616\) −115.512 906.464i −0.187520 1.47153i
\(617\) −146.033 252.936i −0.236682 0.409945i 0.723078 0.690766i \(-0.242727\pi\)
−0.959760 + 0.280821i \(0.909393\pi\)
\(618\) 0 0
\(619\) 230.497 399.233i 0.372370 0.644964i −0.617559 0.786524i \(-0.711878\pi\)
0.989930 + 0.141560i \(0.0452118\pi\)
\(620\) −566.628 + 563.501i −0.913916 + 0.908872i
\(621\) 0 0
\(622\) 301.936 + 731.801i 0.485428 + 1.17653i
\(623\) −142.597 82.3285i −0.228888 0.132148i
\(624\) 0 0
\(625\) 323.406 + 560.156i 0.517450 + 0.896249i
\(626\) 162.301 + 124.895i 0.259266 + 0.199513i
\(627\) 0 0
\(628\) −36.6644 + 9.71553i −0.0583828 + 0.0154706i
\(629\) 383.145i 0.609133i
\(630\) 0 0
\(631\) 110.500i 0.175119i −0.996159 0.0875597i \(-0.972093\pi\)
0.996159 0.0875597i \(-0.0279069\pi\)
\(632\) 20.9438 15.9330i 0.0331388 0.0252105i
\(633\) 0 0
\(634\) 333.816 433.793i 0.526523 0.684216i
\(635\) −190.235 329.497i −0.299583 0.518892i
\(636\) 0 0
\(637\) −1076.63 621.591i −1.69015 0.975810i
\(638\) 60.0627 + 145.574i 0.0941422 + 0.228172i
\(639\) 0 0
\(640\) 255.130 599.450i 0.398641 0.936641i
\(641\) −134.761 + 233.413i −0.210236 + 0.364139i −0.951788 0.306756i \(-0.900756\pi\)
0.741553 + 0.670895i \(0.234090\pi\)
\(642\) 0 0
\(643\) 284.721 + 493.151i 0.442800 + 0.766953i 0.997896 0.0648336i \(-0.0206517\pi\)
−0.555096 + 0.831787i \(0.687318\pi\)
\(644\) −241.606 65.4553i −0.375165 0.101639i
\(645\) 0 0
\(646\) 72.2448 542.948i 0.111834 0.840476i
\(647\) 420.048i 0.649223i −0.945847 0.324612i \(-0.894766\pi\)
0.945847 0.324612i \(-0.105234\pi\)
\(648\) 0 0
\(649\) −452.451 −0.697151
\(650\) 20.0663 + 2.67004i 0.0308713 + 0.00410775i
\(651\) 0 0
\(652\) −1180.13 319.719i −1.81002 0.490366i
\(653\) 211.083 121.869i 0.323251 0.186629i −0.329590 0.944124i \(-0.606910\pi\)
0.652841 + 0.757495i \(0.273577\pi\)
\(654\) 0 0
\(655\) 362.224 + 209.130i 0.553013 + 0.319282i
\(656\) −3.07945 + 556.385i −0.00469428 + 0.848149i
\(657\) 0 0
\(658\) −1427.33 + 588.907i −2.16919 + 0.894995i
\(659\) 268.514 465.080i 0.407457 0.705736i −0.587147 0.809480i \(-0.699749\pi\)
0.994604 + 0.103744i \(0.0330823\pi\)
\(660\) 0 0
\(661\) 190.176 109.798i 0.287710 0.166109i −0.349199 0.937049i \(-0.613546\pi\)
0.636909 + 0.770939i \(0.280213\pi\)
\(662\) 459.715 + 353.763i 0.694433 + 0.534385i
\(663\) 0 0
\(664\) −178.995 235.286i −0.269570 0.354347i
\(665\) −917.402 −1.37955
\(666\) 0 0
\(667\) 43.1378 0.0646744
\(668\) 59.8741 15.8658i 0.0896319 0.0237512i
\(669\) 0 0
\(670\) 502.067 652.436i 0.749354 0.973785i
\(671\) 1.34794 0.778236i 0.00200886 0.00115981i
\(672\) 0 0
\(673\) 52.2858 90.5617i 0.0776907 0.134564i −0.824563 0.565771i \(-0.808579\pi\)
0.902253 + 0.431207i \(0.141912\pi\)
\(674\) 705.464 291.070i 1.04668 0.431855i
\(675\) 0 0
\(676\) 124.768 124.079i 0.184568 0.183549i
\(677\) 460.805 + 266.046i 0.680657 + 0.392977i 0.800102 0.599863i \(-0.204778\pi\)
−0.119446 + 0.992841i \(0.538112\pi\)
\(678\) 0 0
\(679\) 981.046 566.407i 1.44484 0.834178i
\(680\) −98.9815 776.741i −0.145561 1.14227i
\(681\) 0 0
\(682\) −702.297 93.4480i −1.02976 0.137021i
\(683\) −782.844 −1.14618 −0.573092 0.819491i \(-0.694256\pi\)
−0.573092 + 0.819491i \(0.694256\pi\)
\(684\) 0 0
\(685\) 933.579i 1.36289i
\(686\) 1560.46 + 207.635i 2.27472 + 0.302675i
\(687\) 0 0
\(688\) −84.1927 + 47.9893i −0.122373 + 0.0697519i
\(689\) 36.5125 + 63.2415i 0.0529935 + 0.0917874i
\(690\) 0 0
\(691\) −445.414 + 771.480i −0.644593 + 1.11647i 0.339802 + 0.940497i \(0.389640\pi\)
−0.984395 + 0.175971i \(0.943693\pi\)
\(692\) −258.484 259.919i −0.373532 0.375605i
\(693\) 0 0
\(694\) 263.243 108.612i 0.379312 0.156502i
\(695\) 913.034 + 527.141i 1.31372 + 0.758476i
\(696\) 0 0
\(697\) 334.366 + 579.139i 0.479722 + 0.830903i
\(698\) 751.886 977.075i 1.07720 1.39982i
\(699\) 0 0
\(700\) −44.3015 + 11.7392i −0.0632879 + 0.0167704i
\(701\) 292.848i 0.417757i 0.977942 + 0.208878i \(0.0669813\pi\)
−0.977942 + 0.208878i \(0.933019\pi\)
\(702\) 0 0
\(703\) 283.741i 0.403614i
\(704\) 559.133 144.855i 0.794223 0.205760i
\(705\) 0 0
\(706\) 651.474 + 501.328i 0.922768 + 0.710096i
\(707\) 719.792 + 1246.72i 1.01809 + 1.76339i
\(708\) 0 0
\(709\) −251.105 144.976i −0.354168 0.204479i 0.312351 0.949967i \(-0.398883\pi\)
−0.666520 + 0.745487i \(0.732217\pi\)
\(710\) 475.086 196.017i 0.669135 0.276081i
\(711\) 0 0
\(712\) 40.2272 95.9882i 0.0564989 0.134815i
\(713\) −97.0379 + 168.075i −0.136098 + 0.235729i
\(714\) 0 0
\(715\) 256.789 + 444.772i 0.359146 + 0.622059i
\(716\) 486.419 + 131.779i 0.679356 + 0.184049i
\(717\) 0 0
\(718\) 259.913 + 34.5841i 0.361996 + 0.0481673i
\(719\) 1132.71i 1.57540i −0.616058 0.787701i \(-0.711271\pi\)
0.616058 0.787701i \(-0.288729\pi\)
\(720\) 0 0
\(721\) 2482.01 3.44245
\(722\) −41.7288 + 313.608i −0.0577961 + 0.434360i
\(723\) 0 0
\(724\) 24.0589 88.8053i 0.0332305 0.122659i
\(725\) 6.83999 3.94907i 0.00943447 0.00544700i
\(726\) 0 0
\(727\) −42.5708 24.5783i −0.0585569 0.0338078i 0.470436 0.882434i \(-0.344097\pi\)
−0.528993 + 0.848626i \(0.677430\pi\)
\(728\) 437.567 1044.10i 0.601054 1.43421i
\(729\) 0 0
\(730\) 93.2860 + 226.097i 0.127789 + 0.309722i
\(731\) −58.2378 + 100.871i −0.0796686 + 0.137990i
\(732\) 0 0
\(733\) 827.604 477.817i 1.12906 0.651865i 0.185364 0.982670i \(-0.440653\pi\)
0.943699 + 0.330805i \(0.107320\pi\)
\(734\) 131.413 170.771i 0.179036 0.232658i
\(735\) 0 0
\(736\) 21.7366 156.720i 0.0295334 0.212934i
\(737\) 729.878 0.990337
\(738\) 0 0
\(739\) −279.034 −0.377583 −0.188791 0.982017i \(-0.560457\pi\)
−0.188791 + 0.982017i \(0.560457\pi\)
\(740\) 103.899 + 392.095i 0.140405 + 0.529858i
\(741\) 0 0
\(742\) −131.024 100.827i −0.176583 0.135885i
\(743\) −19.7539 + 11.4049i −0.0265866 + 0.0153498i −0.513234 0.858248i \(-0.671553\pi\)
0.486648 + 0.873598i \(0.338220\pi\)
\(744\) 0 0
\(745\) −574.970 + 995.877i −0.771771 + 1.33675i
\(746\) 493.745 + 1196.69i 0.661856 + 1.60414i
\(747\) 0 0
\(748\) 492.238 489.521i 0.658072 0.654440i
\(749\) −348.538 201.228i −0.465338 0.268663i
\(750\) 0 0
\(751\) −983.960 + 568.090i −1.31020 + 0.756444i −0.982129 0.188209i \(-0.939732\pi\)
−0.328071 + 0.944653i \(0.606398\pi\)
\(752\) −483.296 847.897i −0.642681 1.12752i
\(753\) 0 0
\(754\) −25.7328 + 193.392i −0.0341284 + 0.256488i
\(755\) 726.344 0.962046
\(756\) 0 0
\(757\) 1067.71i 1.41045i 0.708984 + 0.705224i \(0.249154\pi\)
−0.708984 + 0.705224i \(0.750846\pi\)
\(758\) −59.5350 + 447.428i −0.0785422 + 0.590275i
\(759\) 0 0
\(760\) −73.3015 575.222i −0.0964494 0.756870i
\(761\) −291.003 504.031i −0.382395 0.662327i 0.609009 0.793163i \(-0.291567\pi\)
−0.991404 + 0.130836i \(0.958234\pi\)
\(762\) 0 0
\(763\) 727.373 1259.85i 0.953307 1.65118i
\(764\) −66.5196 66.8888i −0.0870675 0.0875507i
\(765\) 0 0
\(766\) −363.818 881.784i −0.474959 1.15115i
\(767\) −485.436 280.267i −0.632902 0.365406i
\(768\) 0 0
\(769\) −517.987 897.181i −0.673586 1.16668i −0.976880 0.213788i \(-0.931420\pi\)
0.303294 0.952897i \(-0.401913\pi\)
\(770\) −921.483 709.107i −1.19673 0.920918i
\(771\) 0 0
\(772\) 63.5532 + 239.836i 0.0823227 + 0.310669i
\(773\) 1067.29i 1.38071i −0.723471 0.690355i \(-0.757454\pi\)
0.723471 0.690355i \(-0.242546\pi\)
\(774\) 0 0
\(775\) 35.5335i 0.0458497i
\(776\) 433.530 + 569.870i 0.558673 + 0.734369i
\(777\) 0 0
\(778\) −14.6323 + 19.0146i −0.0188076 + 0.0244404i
\(779\) 247.618 + 428.886i 0.317866 + 0.550560i
\(780\) 0 0
\(781\) 394.599 + 227.822i 0.505249 + 0.291705i
\(782\) −72.5299 175.790i −0.0927492 0.224796i
\(783\) 0 0
\(784\) −9.84631 + 1779.00i −0.0125591 + 2.26914i
\(785\) −24.1315 + 41.7970i −0.0307408 + 0.0532446i
\(786\) 0 0
\(787\) −549.400 951.588i −0.698094 1.20913i −0.969127 0.246564i \(-0.920699\pi\)
0.271033 0.962570i \(-0.412635\pi\)
\(788\) 403.555 1489.59i 0.512126 1.89034i
\(789\) 0 0
\(790\) 4.41654 33.1920i 0.00559056 0.0420152i
\(791\) 417.148i 0.527368i
\(792\) 0 0
\(793\) 1.92828 0.00243163
\(794\) 6.79176 + 0.903714i 0.00855385 + 0.00113818i
\(795\) 0 0
\(796\) 224.837 829.910i 0.282459 1.04260i
\(797\) −973.877 + 562.268i −1.22193 + 0.705481i −0.965329 0.261037i \(-0.915936\pi\)
−0.256600 + 0.966518i \(0.582602\pi\)
\(798\) 0 0
\(799\) −1015.86 586.508i −1.27142 0.734052i
\(800\) −10.9004 26.8396i −0.0136255 0.0335494i
\(801\) 0 0
\(802\) −88.3725 + 36.4619i −0.110190 + 0.0454637i
\(803\) −108.422 + 187.793i −0.135021 + 0.233864i
\(804\) 0 0
\(805\) −275.837 + 159.255i −0.342655 + 0.197832i
\(806\) −695.612 535.293i −0.863042 0.664135i
\(807\) 0 0
\(808\) −724.193 + 550.932i −0.896278 + 0.681846i
\(809\) −1468.01 −1.81460 −0.907300 0.420484i \(-0.861860\pi\)
−0.907300 + 0.420484i \(0.861860\pi\)
\(810\) 0 0
\(811\) −90.2707 −0.111308 −0.0556540 0.998450i \(-0.517724\pi\)
−0.0556540 + 0.998450i \(0.517724\pi\)
\(812\) −113.138 426.961i −0.139333 0.525814i
\(813\) 0 0
\(814\) −219.318 + 285.003i −0.269432 + 0.350127i
\(815\) −1347.34 + 777.885i −1.65317 + 0.954460i
\(816\) 0 0
\(817\) −43.1284 + 74.7006i −0.0527888 + 0.0914328i
\(818\) −419.562 + 173.109i −0.512913 + 0.211624i
\(819\) 0 0
\(820\) 499.225 + 501.996i 0.608811 + 0.612190i
\(821\) 1001.79 + 578.386i 1.22021 + 0.704489i 0.964963 0.262386i \(-0.0845094\pi\)
0.255248 + 0.966875i \(0.417843\pi\)
\(822\) 0 0
\(823\) −516.742 + 298.341i −0.627876 + 0.362504i −0.779929 0.625868i \(-0.784745\pi\)
0.152053 + 0.988372i \(0.451412\pi\)
\(824\) 198.315 + 1556.25i 0.240674 + 1.88865i
\(825\) 0 0
\(826\) 1257.96 + 167.384i 1.52295 + 0.202644i
\(827\) −601.527 −0.727360 −0.363680 0.931524i \(-0.618480\pi\)
−0.363680 + 0.931524i \(0.618480\pi\)
\(828\) 0 0
\(829\) 375.459i 0.452906i −0.974022 0.226453i \(-0.927287\pi\)
0.974022 0.226453i \(-0.0727130\pi\)
\(830\) −372.885 49.6163i −0.449259 0.0597787i
\(831\) 0 0
\(832\) 689.625 + 190.935i 0.828877 + 0.229489i
\(833\) 1069.11 + 1851.76i 1.28345 + 2.22300i
\(834\) 0 0
\(835\) 39.4075 68.2559i 0.0471947 0.0817435i
\(836\) 364.531 362.519i 0.436041 0.433635i
\(837\) 0 0
\(838\) −646.999 + 266.948i −0.772076 + 0.318553i
\(839\) −856.558 494.534i −1.02093 0.589433i −0.106555 0.994307i \(-0.533982\pi\)
−0.914372 + 0.404874i \(0.867315\pi\)
\(840\) 0 0
\(841\) −382.440 662.406i −0.454745 0.787641i
\(842\) 244.139 317.258i 0.289951 0.376791i
\(843\) 0 0
\(844\) −103.461 390.441i −0.122584 0.462608i
\(845\) 223.899i 0.264969i
\(846\) 0 0
\(847\) 500.587i 0.591012i
\(848\) 52.7505 90.2099i 0.0622058 0.106380i
\(849\) 0 0
\(850\) −27.5932 21.2338i −0.0324626 0.0249809i
\(851\) 49.2554 + 85.3129i 0.0578795 + 0.100250i
\(852\) 0 0
\(853\) 329.989 + 190.519i 0.386857 + 0.223352i 0.680798 0.732472i \(-0.261633\pi\)
−0.293940 + 0.955824i \(0.594967\pi\)
\(854\) −4.03562 + 1.66507i −0.00472555 + 0.00194973i
\(855\) 0 0
\(856\) 98.3239 234.616i 0.114864 0.274084i
\(857\) 82.2028 142.379i 0.0959193 0.166137i −0.814073 0.580763i \(-0.802754\pi\)
0.909992 + 0.414626i \(0.136088\pi\)
\(858\) 0 0
\(859\) 813.298 + 1408.67i 0.946796 + 1.63990i 0.752114 + 0.659033i \(0.229034\pi\)
0.194682 + 0.980866i \(0.437632\pi\)
\(860\) −32.2445 + 119.020i −0.0374936 + 0.138395i
\(861\) 0 0
\(862\) −659.819 87.7958i −0.765451 0.101851i
\(863\) 1256.44i 1.45590i 0.685628 + 0.727952i \(0.259527\pi\)
−0.685628 + 0.727952i \(0.740473\pi\)
\(864\) 0 0
\(865\) −466.432 −0.539228
\(866\) 72.8905 547.800i 0.0841692 0.632564i
\(867\) 0 0
\(868\) 1918.04 + 519.630i 2.20972 + 0.598652i
\(869\) 25.7094 14.8434i 0.0295851 0.0170810i
\(870\) 0 0
\(871\) 783.089 + 452.117i 0.899069 + 0.519077i
\(872\) 848.056 + 355.408i 0.972542 + 0.407578i
\(873\) 0 0
\(874\) −53.7126 130.183i −0.0614560 0.148951i
\(875\) 776.074 1344.20i 0.886941 1.53623i
\(876\) 0 0
\(877\) 6.97163 4.02507i 0.00794940 0.00458959i −0.496020 0.868311i \(-0.665206\pi\)
0.503969 + 0.863721i \(0.331872\pi\)
\(878\) −58.6595 + 76.2280i −0.0668104 + 0.0868200i
\(879\) 0 0
\(880\) 370.990 634.439i 0.421580 0.720953i
\(881\) −842.573 −0.956382 −0.478191 0.878256i \(-0.658707\pi\)
−0.478191 + 0.878256i \(0.658707\pi\)
\(882\) 0 0
\(883\) 621.919 0.704325 0.352163 0.935939i \(-0.385446\pi\)
0.352163 + 0.935939i \(0.385446\pi\)
\(884\) 831.353 220.296i 0.940445 0.249204i
\(885\) 0 0
\(886\) −603.055 464.067i −0.680649 0.523778i
\(887\) −413.440 + 238.700i −0.466110 + 0.269109i −0.714610 0.699523i \(-0.753396\pi\)
0.248500 + 0.968632i \(0.420063\pi\)
\(888\) 0 0
\(889\) −473.057 + 819.358i −0.532122 + 0.921663i
\(890\) −50.5096 122.420i −0.0567523 0.137550i
\(891\) 0 0
\(892\) −215.704 216.901i −0.241820 0.243162i
\(893\) −752.304 434.343i −0.842445 0.486386i
\(894\) 0 0
\(895\) 555.335 320.623i 0.620486 0.358238i
\(896\) −1608.16 + 195.891i −1.79482 + 0.218629i
\(897\) 0 0
\(898\) 168.476 1266.16i 0.187612 1.40998i
\(899\) −342.459 −0.380933
\(900\) 0 0
\(901\) 125.600i 0.139401i
\(902\) −82.7888 + 622.190i −0.0917836 + 0.689789i
\(903\) 0 0
\(904\) −261.557 + 33.3306i −0.289332 + 0.0368702i
\(905\) −58.5360 101.387i −0.0646807 0.112030i
\(906\) 0 0
\(907\) −310.221 + 537.319i −0.342030 + 0.592414i −0.984810 0.173638i \(-0.944448\pi\)
0.642779 + 0.766051i \(0.277781\pi\)
\(908\) 212.263 211.091i 0.233770 0.232479i
\(909\) 0 0
\(910\) −549.412 1331.61i −0.603750 1.46330i
\(911\) 1065.40 + 615.107i 1.16948 + 0.675200i 0.953558 0.301210i \(-0.0973907\pi\)
0.215923 + 0.976410i \(0.430724\pi\)
\(912\) 0 0
\(913\) −166.753 288.825i −0.182643 0.316347i
\(914\) 881.671 + 678.470i 0.964629 + 0.742309i
\(915\) 0 0
\(916\) −1141.48 + 302.475i −1.24615 + 0.330213i
\(917\) 1040.09i 1.13423i
\(918\) 0 0
\(919\) 211.088i 0.229693i −0.993383 0.114847i \(-0.963362\pi\)
0.993383 0.114847i \(-0.0366377\pi\)
\(920\) −121.894 160.228i −0.132494 0.174161i
\(921\) 0 0
\(922\) 256.218 332.954i 0.277893 0.361122i
\(923\) 282.245 + 488.862i 0.305790 + 0.529645i
\(924\) 0 0
\(925\) 15.6200 + 9.01822i 0.0168865 + 0.00974942i
\(926\) −137.901 334.230i −0.148921 0.360940i
\(927\) 0 0
\(928\) 258.670 105.054i 0.278739 0.113204i
\(929\) −524.859 + 909.082i −0.564972 + 0.978560i 0.432081 + 0.901835i \(0.357780\pi\)
−0.997052 + 0.0767247i \(0.975554\pi\)
\(930\) 0 0
\(931\) 791.739 + 1371.33i 0.850418 + 1.47297i
\(932\) 1367.64 + 370.518i 1.46742 + 0.397551i
\(933\) 0 0
\(934\) −2.76217 + 20.7588i −0.00295735 + 0.0222256i
\(935\) 883.335i 0.944744i
\(936\) 0 0
\(937\) −14.8972 −0.0158988 −0.00794939 0.999968i \(-0.502530\pi\)
−0.00794939 + 0.999968i \(0.502530\pi\)
\(938\) −2029.29 270.018i −2.16342 0.287866i
\(939\) 0 0
\(940\) −1198.64 324.732i −1.27515 0.345459i
\(941\) −494.297 + 285.383i −0.525289 + 0.303276i −0.739096 0.673600i \(-0.764747\pi\)
0.213807 + 0.976876i \(0.431414\pi\)
\(942\) 0 0
\(943\) 148.903 + 85.9693i 0.157904 + 0.0911657i
\(944\) −4.43956 + 802.127i −0.00470293 + 0.849711i
\(945\) 0 0
\(946\) −101.060 + 41.6968i −0.106829 + 0.0440769i
\(947\) 15.4417 26.7459i 0.0163059 0.0282427i −0.857757 0.514055i \(-0.828143\pi\)
0.874063 + 0.485812i \(0.161476\pi\)
\(948\) 0 0
\(949\) −232.653 + 134.322i −0.245156 + 0.141541i
\(950\) −20.4344 15.7248i −0.0215099 0.0165524i
\(951\) 0 0
\(952\) −1549.68 + 1178.92i −1.62781 + 1.23836i
\(953\) 1048.23 1.09993 0.549965 0.835188i \(-0.314641\pi\)
0.549965 + 0.835188i \(0.314641\pi\)
\(954\) 0 0
\(955\) −120.034 −0.125690
\(956\) −481.488 + 127.587i −0.503649 + 0.133460i
\(957\) 0 0
\(958\) −512.867 + 666.470i −0.535352 + 0.695689i
\(959\) 2010.50 1160.76i 2.09646 1.21039i
\(960\) 0 0
\(961\) 289.855 502.044i 0.301618 0.522418i
\(962\) −411.849 + 169.926i −0.428118 + 0.176639i
\(963\) 0 0
\(964\) −1075.93 + 1069.99i −1.11611 + 1.10995i
\(965\) 273.411 + 157.854i 0.283327 + 0.163579i
\(966\) 0 0
\(967\) −833.473 + 481.206i −0.861916 + 0.497628i −0.864654 0.502369i \(-0.832462\pi\)
0.00273711 + 0.999996i \(0.499129\pi\)
\(968\) −313.874 + 39.9975i −0.324250 + 0.0413197i
\(969\) 0 0
\(970\) 903.140 + 120.172i 0.931072 + 0.123889i
\(971\) −848.612 −0.873957 −0.436978 0.899472i \(-0.643951\pi\)
−0.436978 + 0.899472i \(0.643951\pi\)
\(972\) 0 0
\(973\) 2621.68i 2.69443i
\(974\) −1714.99 228.198i −1.76077 0.234289i
\(975\) 0 0
\(976\) −1.36647 2.39734i −0.00140007 0.00245629i
\(977\) −559.484 969.055i −0.572655 0.991868i −0.996292 0.0860361i \(-0.972580\pi\)
0.423637 0.905832i \(-0.360753\pi\)
\(978\) 0 0
\(979\) 58.7050 101.680i 0.0599642 0.103861i
\(980\) 1596.24 + 1605.10i 1.62881 + 1.63785i
\(981\) 0 0
\(982\) 117.856 48.6266i 0.120016 0.0495180i
\(983\) 598.966 + 345.813i 0.609324 + 0.351793i 0.772701 0.634770i \(-0.218905\pi\)
−0.163377 + 0.986564i \(0.552239\pi\)
\(984\) 0 0
\(985\) −981.861 1700.63i −0.996813 1.72653i
\(986\) 204.643 265.933i 0.207549 0.269709i
\(987\) 0 0
\(988\) 615.665 163.142i 0.623143 0.165124i
\(989\) 29.9472i 0.0302802i
\(990\) 0 0
\(991\) 361.650i 0.364935i −0.983212 0.182467i \(-0.941592\pi\)
0.983212 0.182467i \(-0.0584084\pi\)
\(992\) −172.560 + 1244.15i −0.173952 + 1.25418i
\(993\) 0 0
\(994\) −1012.83 779.399i −1.01894 0.784104i
\(995\) −547.035 947.492i −0.549784 0.952254i
\(996\) 0 0
\(997\) −1162.72 671.298i −1.16622 0.673318i −0.213434 0.976958i \(-0.568465\pi\)
−0.952787 + 0.303640i \(0.901798\pi\)
\(998\) −1344.73 + 554.828i −1.34743 + 0.555940i
\(999\) 0 0
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 216.3.p.b.19.10 40
3.2 odd 2 72.3.p.b.43.11 yes 40
4.3 odd 2 864.3.t.b.559.6 40
8.3 odd 2 inner 216.3.p.b.19.16 40
8.5 even 2 864.3.t.b.559.15 40
9.2 odd 6 648.3.b.f.163.17 20
9.4 even 3 inner 216.3.p.b.91.16 40
9.5 odd 6 72.3.p.b.67.5 yes 40
9.7 even 3 648.3.b.e.163.4 20
12.11 even 2 288.3.t.b.79.10 40
24.5 odd 2 288.3.t.b.79.9 40
24.11 even 2 72.3.p.b.43.5 40
36.7 odd 6 2592.3.b.f.1135.6 20
36.11 even 6 2592.3.b.e.1135.15 20
36.23 even 6 288.3.t.b.175.9 40
36.31 odd 6 864.3.t.b.847.15 40
72.5 odd 6 288.3.t.b.175.10 40
72.11 even 6 648.3.b.f.163.18 20
72.13 even 6 864.3.t.b.847.6 40
72.29 odd 6 2592.3.b.e.1135.6 20
72.43 odd 6 648.3.b.e.163.3 20
72.59 even 6 72.3.p.b.67.11 yes 40
72.61 even 6 2592.3.b.f.1135.15 20
72.67 odd 6 inner 216.3.p.b.91.10 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.3.p.b.43.5 40 24.11 even 2
72.3.p.b.43.11 yes 40 3.2 odd 2
72.3.p.b.67.5 yes 40 9.5 odd 6
72.3.p.b.67.11 yes 40 72.59 even 6
216.3.p.b.19.10 40 1.1 even 1 trivial
216.3.p.b.19.16 40 8.3 odd 2 inner
216.3.p.b.91.10 40 72.67 odd 6 inner
216.3.p.b.91.16 40 9.4 even 3 inner
288.3.t.b.79.9 40 24.5 odd 2
288.3.t.b.79.10 40 12.11 even 2
288.3.t.b.175.9 40 36.23 even 6
288.3.t.b.175.10 40 72.5 odd 6
648.3.b.e.163.3 20 72.43 odd 6
648.3.b.e.163.4 20 9.7 even 3
648.3.b.f.163.17 20 9.2 odd 6
648.3.b.f.163.18 20 72.11 even 6
864.3.t.b.559.6 40 4.3 odd 2
864.3.t.b.559.15 40 8.5 even 2
864.3.t.b.847.6 40 72.13 even 6
864.3.t.b.847.15 40 36.31 odd 6
2592.3.b.e.1135.6 20 72.29 odd 6
2592.3.b.e.1135.15 20 36.11 even 6
2592.3.b.f.1135.6 20 36.7 odd 6
2592.3.b.f.1135.15 20 72.61 even 6