Properties

Label 144.4.k.a.109.2
Level $144$
Weight $4$
Character 144.109
Analytic conductor $8.496$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [144,4,Mod(37,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 144.k (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: \(8.49627504083\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 109.2
Root \(0.932438 - 1.76934i\) of defining polynomial
Character \(\chi\) \(=\) 144.109
Dual form 144.4.k.a.37.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.836901 + 2.70178i) q^{2} +(-6.59919 - 4.52224i) q^{4} +(0.596848 - 0.596848i) q^{5} +29.0828i q^{7} +(17.7410 - 14.0449i) q^{8} +O(q^{10})\) \(q+(-0.836901 + 2.70178i) q^{2} +(-6.59919 - 4.52224i) q^{4} +(0.596848 - 0.596848i) q^{5} +29.0828i q^{7} +(17.7410 - 14.0449i) q^{8} +(1.11305 + 2.11205i) q^{10} +(-12.1291 + 12.1291i) q^{11} +(-48.5658 - 48.5658i) q^{13} +(-78.5754 - 24.3395i) q^{14} +(23.0987 + 59.6863i) q^{16} -86.7193 q^{17} +(-54.8442 - 54.8442i) q^{19} +(-6.63780 + 1.23963i) q^{20} +(-22.6193 - 42.9211i) q^{22} -70.2145i q^{23} +124.288i q^{25} +(171.859 - 90.5692i) q^{26} +(131.520 - 191.923i) q^{28} +(-63.4021 - 63.4021i) q^{29} -8.86868 q^{31} +(-180.590 + 12.4560i) q^{32} +(72.5755 - 234.296i) q^{34} +(17.3580 + 17.3580i) q^{35} +(-21.7145 + 21.7145i) q^{37} +(194.076 - 102.278i) q^{38} +(2.20599 - 18.9713i) q^{40} +153.274i q^{41} +(-120.951 + 120.951i) q^{43} +(134.893 - 25.1917i) q^{44} +(189.704 + 58.7626i) q^{46} +99.9792 q^{47} -502.812 q^{49} +(-335.797 - 104.016i) q^{50} +(100.869 + 540.122i) q^{52} +(-389.132 + 389.132i) q^{53} +14.4785i q^{55} +(408.465 + 515.957i) q^{56} +(224.359 - 118.237i) q^{58} +(324.819 - 324.819i) q^{59} +(-0.339194 - 0.339194i) q^{61} +(7.42220 - 23.9612i) q^{62} +(117.483 - 498.339i) q^{64} -57.9728 q^{65} +(565.288 + 565.288i) q^{67} +(572.278 + 392.166i) q^{68} +(-61.4245 + 32.3706i) q^{70} +419.500i q^{71} +374.833i q^{73} +(-40.4947 - 76.8404i) q^{74} +(113.909 + 609.946i) q^{76} +(-352.750 - 352.750i) q^{77} -705.750 q^{79} +(49.4100 + 21.8372i) q^{80} +(-414.113 - 128.275i) q^{82} +(947.092 + 947.092i) q^{83} +(-51.7582 + 51.7582i) q^{85} +(-225.558 - 428.005i) q^{86} +(-44.8302 + 385.535i) q^{88} +4.72918i q^{89} +(1412.43 - 1412.43i) q^{91} +(-317.527 + 463.359i) q^{92} +(-83.6727 + 270.121i) q^{94} -65.4673 q^{95} +379.542 q^{97} +(420.804 - 1358.49i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8} - 68 q^{10} - 18 q^{11} - 2 q^{13} - 188 q^{14} + 280 q^{16} + 4 q^{17} - 26 q^{19} + 196 q^{20} - 588 q^{22} + 264 q^{26} + 280 q^{28} + 202 q^{29} + 368 q^{31} - 968 q^{32} + 436 q^{34} - 476 q^{35} - 10 q^{37} + 1232 q^{38} - 1336 q^{40} - 838 q^{43} - 868 q^{44} + 1132 q^{46} + 944 q^{47} + 94 q^{49} - 726 q^{50} - 236 q^{52} + 378 q^{53} + 488 q^{56} + 8 q^{58} - 1706 q^{59} + 910 q^{61} + 80 q^{62} + 512 q^{64} + 492 q^{65} + 1942 q^{67} + 880 q^{68} + 160 q^{70} + 452 q^{74} - 1228 q^{76} + 268 q^{77} - 4416 q^{79} + 2648 q^{80} - 704 q^{82} + 2562 q^{83} - 12 q^{85} - 3764 q^{86} + 1528 q^{88} + 3332 q^{91} - 632 q^{92} - 3248 q^{94} - 6900 q^{95} - 4 q^{97} - 314 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.836901 + 2.70178i −0.295889 + 0.955222i
\(3\) 0 0
\(4\) −6.59919 4.52224i −0.824899 0.565280i
\(5\) 0.596848 0.596848i 0.0533837 0.0533837i −0.679911 0.733295i \(-0.737982\pi\)
0.733295 + 0.679911i \(0.237982\pi\)
\(6\) 0 0
\(7\) 29.0828i 1.57033i 0.619289 + 0.785163i \(0.287421\pi\)
−0.619289 + 0.785163i \(0.712579\pi\)
\(8\) 17.7410 14.0449i 0.784047 0.620702i
\(9\) 0 0
\(10\) 1.11305 + 2.11205i 0.0351976 + 0.0667890i
\(11\) −12.1291 + 12.1291i −0.332461 + 0.332461i −0.853520 0.521059i \(-0.825537\pi\)
0.521059 + 0.853520i \(0.325537\pi\)
\(12\) 0 0
\(13\) −48.5658 48.5658i −1.03613 1.03613i −0.999322 0.0368113i \(-0.988280\pi\)
−0.0368113 0.999322i \(-0.511720\pi\)
\(14\) −78.5754 24.3395i −1.50001 0.464643i
\(15\) 0 0
\(16\) 23.0987 + 59.6863i 0.360917 + 0.932598i
\(17\) −86.7193 −1.23721 −0.618604 0.785703i \(-0.712301\pi\)
−0.618604 + 0.785703i \(0.712301\pi\)
\(18\) 0 0
\(19\) −54.8442 54.8442i −0.662217 0.662217i 0.293685 0.955902i \(-0.405118\pi\)
−0.955902 + 0.293685i \(0.905118\pi\)
\(20\) −6.63780 + 1.23963i −0.0742129 + 0.0138594i
\(21\) 0 0
\(22\) −22.6193 42.9211i −0.219203 0.415946i
\(23\) 70.2145i 0.636554i −0.947998 0.318277i \(-0.896896\pi\)
0.947998 0.318277i \(-0.103104\pi\)
\(24\) 0 0
\(25\) 124.288i 0.994300i
\(26\) 171.859 90.5692i 1.29632 0.683157i
\(27\) 0 0
\(28\) 131.520 191.923i 0.887674 1.29536i
\(29\) −63.4021 63.4021i −0.405982 0.405982i 0.474353 0.880335i \(-0.342682\pi\)
−0.880335 + 0.474353i \(0.842682\pi\)
\(30\) 0 0
\(31\) −8.86868 −0.0513826 −0.0256913 0.999670i \(-0.508179\pi\)
−0.0256913 + 0.999670i \(0.508179\pi\)
\(32\) −180.590 + 12.4560i −0.997630 + 0.0688106i
\(33\) 0 0
\(34\) 72.5755 234.296i 0.366076 1.18181i
\(35\) 17.3580 + 17.3580i 0.0838298 + 0.0838298i
\(36\) 0 0
\(37\) −21.7145 + 21.7145i −0.0964820 + 0.0964820i −0.753700 0.657218i \(-0.771733\pi\)
0.657218 + 0.753700i \(0.271733\pi\)
\(38\) 194.076 102.278i 0.828508 0.436622i
\(39\) 0 0
\(40\) 2.20599 18.9713i 0.00871995 0.0749907i
\(41\) 153.274i 0.583840i 0.956443 + 0.291920i \(0.0942941\pi\)
−0.956443 + 0.291920i \(0.905706\pi\)
\(42\) 0 0
\(43\) −120.951 + 120.951i −0.428949 + 0.428949i −0.888270 0.459322i \(-0.848093\pi\)
0.459322 + 0.888270i \(0.348093\pi\)
\(44\) 134.893 25.1917i 0.462181 0.0863133i
\(45\) 0 0
\(46\) 189.704 + 58.7626i 0.608051 + 0.188349i
\(47\) 99.9792 0.310286 0.155143 0.987892i \(-0.450416\pi\)
0.155143 + 0.987892i \(0.450416\pi\)
\(48\) 0 0
\(49\) −502.812 −1.46592
\(50\) −335.797 104.016i −0.949778 0.294203i
\(51\) 0 0
\(52\) 100.869 + 540.122i 0.269000 + 1.44041i
\(53\) −389.132 + 389.132i −1.00852 + 1.00852i −0.00855213 + 0.999963i \(0.502722\pi\)
−0.999963 + 0.00855213i \(0.997278\pi\)
\(54\) 0 0
\(55\) 14.4785i 0.0354960i
\(56\) 408.465 + 515.957i 0.974704 + 1.23121i
\(57\) 0 0
\(58\) 224.359 118.237i 0.507928 0.267677i
\(59\) 324.819 324.819i 0.716744 0.716744i −0.251193 0.967937i \(-0.580823\pi\)
0.967937 + 0.251193i \(0.0808229\pi\)
\(60\) 0 0
\(61\) −0.339194 0.339194i −0.000711957 0.000711957i 0.706751 0.707463i \(-0.250160\pi\)
−0.707463 + 0.706751i \(0.750160\pi\)
\(62\) 7.42220 23.9612i 0.0152036 0.0490818i
\(63\) 0 0
\(64\) 117.483 498.339i 0.229458 0.973318i
\(65\) −57.9728 −0.110625
\(66\) 0 0
\(67\) 565.288 + 565.288i 1.03076 + 1.03076i 0.999512 + 0.0312478i \(0.00994810\pi\)
0.0312478 + 0.999512i \(0.490052\pi\)
\(68\) 572.278 + 392.166i 1.02057 + 0.699368i
\(69\) 0 0
\(70\) −61.4245 + 32.3706i −0.104880 + 0.0552718i
\(71\) 419.500i 0.701205i 0.936524 + 0.350602i \(0.114023\pi\)
−0.936524 + 0.350602i \(0.885977\pi\)
\(72\) 0 0
\(73\) 374.833i 0.600971i 0.953786 + 0.300485i \(0.0971487\pi\)
−0.953786 + 0.300485i \(0.902851\pi\)
\(74\) −40.4947 76.8404i −0.0636138 0.120710i
\(75\) 0 0
\(76\) 113.909 + 609.946i 0.171924 + 0.920600i
\(77\) −352.750 352.750i −0.522072 0.522072i
\(78\) 0 0
\(79\) −705.750 −1.00510 −0.502551 0.864547i \(-0.667605\pi\)
−0.502551 + 0.864547i \(0.667605\pi\)
\(80\) 49.4100 + 21.8372i 0.0690526 + 0.0305184i
\(81\) 0 0
\(82\) −414.113 128.275i −0.557697 0.172752i
\(83\) 947.092 + 947.092i 1.25249 + 1.25249i 0.954599 + 0.297893i \(0.0962839\pi\)
0.297893 + 0.954599i \(0.403716\pi\)
\(84\) 0 0
\(85\) −51.7582 + 51.7582i −0.0660467 + 0.0660467i
\(86\) −225.558 428.005i −0.282820 0.536662i
\(87\) 0 0
\(88\) −44.8302 + 385.535i −0.0543058 + 0.467024i
\(89\) 4.72918i 0.00563249i 0.999996 + 0.00281625i \(0.000896440\pi\)
−0.999996 + 0.00281625i \(0.999104\pi\)
\(90\) 0 0
\(91\) 1412.43 1412.43i 1.62707 1.62707i
\(92\) −317.527 + 463.359i −0.359831 + 0.525093i
\(93\) 0 0
\(94\) −83.6727 + 270.121i −0.0918104 + 0.296392i
\(95\) −65.4673 −0.0707032
\(96\) 0 0
\(97\) 379.542 0.397285 0.198643 0.980072i \(-0.436347\pi\)
0.198643 + 0.980072i \(0.436347\pi\)
\(98\) 420.804 1358.49i 0.433751 1.40028i
\(99\) 0 0
\(100\) 562.058 820.198i 0.562058 0.820198i
\(101\) 391.005 391.005i 0.385212 0.385212i −0.487764 0.872976i \(-0.662187\pi\)
0.872976 + 0.487764i \(0.162187\pi\)
\(102\) 0 0
\(103\) 307.935i 0.294580i −0.989093 0.147290i \(-0.952945\pi\)
0.989093 0.147290i \(-0.0470551\pi\)
\(104\) −1543.71 179.503i −1.45551 0.169247i
\(105\) 0 0
\(106\) −725.682 1377.01i −0.664948 1.26177i
\(107\) 601.607 601.607i 0.543548 0.543548i −0.381019 0.924567i \(-0.624427\pi\)
0.924567 + 0.381019i \(0.124427\pi\)
\(108\) 0 0
\(109\) −948.890 948.890i −0.833827 0.833827i 0.154211 0.988038i \(-0.450717\pi\)
−0.988038 + 0.154211i \(0.950717\pi\)
\(110\) −39.1177 12.1171i −0.0339066 0.0105029i
\(111\) 0 0
\(112\) −1735.85 + 671.776i −1.46448 + 0.566758i
\(113\) −1824.02 −1.51849 −0.759244 0.650807i \(-0.774431\pi\)
−0.759244 + 0.650807i \(0.774431\pi\)
\(114\) 0 0
\(115\) −41.9074 41.9074i −0.0339816 0.0339816i
\(116\) 131.683 + 705.122i 0.105401 + 0.564387i
\(117\) 0 0
\(118\) 605.748 + 1149.43i 0.472573 + 0.896727i
\(119\) 2522.04i 1.94282i
\(120\) 0 0
\(121\) 1036.77i 0.778939i
\(122\) 1.20030 0.632555i 0.000890738 0.000469417i
\(123\) 0 0
\(124\) 58.5261 + 40.1063i 0.0423855 + 0.0290456i
\(125\) 148.787 + 148.787i 0.106463 + 0.106463i
\(126\) 0 0
\(127\) 988.748 0.690844 0.345422 0.938447i \(-0.387736\pi\)
0.345422 + 0.938447i \(0.387736\pi\)
\(128\) 1248.08 + 734.473i 0.861841 + 0.507178i
\(129\) 0 0
\(130\) 48.5175 156.630i 0.0327328 0.105672i
\(131\) −793.572 793.572i −0.529273 0.529273i 0.391083 0.920356i \(-0.372101\pi\)
−0.920356 + 0.391083i \(0.872101\pi\)
\(132\) 0 0
\(133\) 1595.03 1595.03i 1.03990 1.03990i
\(134\) −2000.37 + 1054.19i −1.28959 + 0.679614i
\(135\) 0 0
\(136\) −1538.48 + 1217.96i −0.970028 + 0.767937i
\(137\) 1595.30i 0.994856i 0.867505 + 0.497428i \(0.165722\pi\)
−0.867505 + 0.497428i \(0.834278\pi\)
\(138\) 0 0
\(139\) −277.696 + 277.696i −0.169452 + 0.169452i −0.786738 0.617286i \(-0.788232\pi\)
0.617286 + 0.786738i \(0.288232\pi\)
\(140\) −36.0518 193.046i −0.0217638 0.116538i
\(141\) 0 0
\(142\) −1133.40 351.080i −0.669806 0.207479i
\(143\) 1178.12 0.688948
\(144\) 0 0
\(145\) −75.6828 −0.0433456
\(146\) −1012.71 313.698i −0.574061 0.177821i
\(147\) 0 0
\(148\) 241.496 45.0999i 0.134127 0.0250486i
\(149\) 593.272 593.272i 0.326193 0.326193i −0.524944 0.851137i \(-0.675914\pi\)
0.851137 + 0.524944i \(0.175914\pi\)
\(150\) 0 0
\(151\) 160.655i 0.0865821i −0.999063 0.0432911i \(-0.986216\pi\)
0.999063 0.0432911i \(-0.0137843\pi\)
\(152\) −1743.27 202.708i −0.930249 0.108170i
\(153\) 0 0
\(154\) 1248.27 657.835i 0.653171 0.344220i
\(155\) −5.29325 + 5.29325i −0.00274299 + 0.00274299i
\(156\) 0 0
\(157\) −705.762 705.762i −0.358764 0.358764i 0.504593 0.863357i \(-0.331642\pi\)
−0.863357 + 0.504593i \(0.831642\pi\)
\(158\) 590.643 1906.78i 0.297399 0.960096i
\(159\) 0 0
\(160\) −100.351 + 115.219i −0.0495838 + 0.0569305i
\(161\) 2042.04 0.999598
\(162\) 0 0
\(163\) 1872.64 + 1872.64i 0.899855 + 0.899855i 0.995423 0.0955676i \(-0.0304666\pi\)
−0.0955676 + 0.995423i \(0.530467\pi\)
\(164\) 693.143 1011.49i 0.330033 0.481609i
\(165\) 0 0
\(166\) −3351.45 + 1766.21i −1.56701 + 0.825810i
\(167\) 3852.19i 1.78498i 0.451066 + 0.892490i \(0.351044\pi\)
−0.451066 + 0.892490i \(0.648956\pi\)
\(168\) 0 0
\(169\) 2520.28i 1.14715i
\(170\) −96.5227 183.156i −0.0435468 0.0826318i
\(171\) 0 0
\(172\) 1345.14 251.209i 0.596315 0.111363i
\(173\) −2625.61 2625.61i −1.15388 1.15388i −0.985768 0.168112i \(-0.946233\pi\)
−0.168112 0.985768i \(-0.553767\pi\)
\(174\) 0 0
\(175\) −3614.64 −1.56138
\(176\) −1004.11 443.776i −0.430044 0.190062i
\(177\) 0 0
\(178\) −12.7772 3.95785i −0.00538028 0.00166659i
\(179\) 1236.73 + 1236.73i 0.516413 + 0.516413i 0.916484 0.400071i \(-0.131015\pi\)
−0.400071 + 0.916484i \(0.631015\pi\)
\(180\) 0 0
\(181\) 1574.90 1574.90i 0.646748 0.646748i −0.305458 0.952206i \(-0.598809\pi\)
0.952206 + 0.305458i \(0.0988094\pi\)
\(182\) 2634.01 + 4998.14i 1.07278 + 2.03564i
\(183\) 0 0
\(184\) −986.155 1245.67i −0.395110 0.499088i
\(185\) 25.9204i 0.0103011i
\(186\) 0 0
\(187\) 1051.83 1051.83i 0.411323 0.411323i
\(188\) −659.782 452.130i −0.255955 0.175399i
\(189\) 0 0
\(190\) 54.7897 176.878i 0.0209203 0.0675373i
\(191\) −3585.92 −1.35847 −0.679236 0.733920i \(-0.737689\pi\)
−0.679236 + 0.733920i \(0.737689\pi\)
\(192\) 0 0
\(193\) 523.601 0.195283 0.0976415 0.995222i \(-0.468870\pi\)
0.0976415 + 0.995222i \(0.468870\pi\)
\(194\) −317.639 + 1025.44i −0.117552 + 0.379496i
\(195\) 0 0
\(196\) 3318.15 + 2273.84i 1.20924 + 0.828658i
\(197\) 1125.64 1125.64i 0.407098 0.407098i −0.473627 0.880725i \(-0.657056\pi\)
0.880725 + 0.473627i \(0.157056\pi\)
\(198\) 0 0
\(199\) 2312.48i 0.823757i −0.911239 0.411878i \(-0.864873\pi\)
0.911239 0.411878i \(-0.135127\pi\)
\(200\) 1745.60 + 2204.98i 0.617164 + 0.779578i
\(201\) 0 0
\(202\) 729.175 + 1383.64i 0.253983 + 0.481943i
\(203\) 1843.91 1843.91i 0.637524 0.637524i
\(204\) 0 0
\(205\) 91.4815 + 91.4815i 0.0311675 + 0.0311675i
\(206\) 831.973 + 257.711i 0.281390 + 0.0871631i
\(207\) 0 0
\(208\) 1776.90 4020.52i 0.592337 1.34025i
\(209\) 1330.43 0.440323
\(210\) 0 0
\(211\) 1418.59 + 1418.59i 0.462842 + 0.462842i 0.899586 0.436744i \(-0.143868\pi\)
−0.436744 + 0.899586i \(0.643868\pi\)
\(212\) 4327.70 808.208i 1.40202 0.261830i
\(213\) 0 0
\(214\) 1121.92 + 2128.89i 0.358379 + 0.680039i
\(215\) 144.378i 0.0457977i
\(216\) 0 0
\(217\) 257.926i 0.0806875i
\(218\) 3357.82 1769.56i 1.04321 0.549770i
\(219\) 0 0
\(220\) 65.4752 95.5464i 0.0200652 0.0292806i
\(221\) 4211.60 + 4211.60i 1.28191 + 1.28191i
\(222\) 0 0
\(223\) −4315.08 −1.29578 −0.647890 0.761734i \(-0.724349\pi\)
−0.647890 + 0.761734i \(0.724349\pi\)
\(224\) −362.257 5252.08i −0.108055 1.56660i
\(225\) 0 0
\(226\) 1526.52 4928.09i 0.449304 1.45049i
\(227\) −701.203 701.203i −0.205024 0.205024i 0.597124 0.802149i \(-0.296310\pi\)
−0.802149 + 0.597124i \(0.796310\pi\)
\(228\) 0 0
\(229\) −663.351 + 663.351i −0.191421 + 0.191421i −0.796310 0.604889i \(-0.793218\pi\)
0.604889 + 0.796310i \(0.293218\pi\)
\(230\) 148.297 78.1521i 0.0425148 0.0224052i
\(231\) 0 0
\(232\) −2015.29 234.339i −0.570302 0.0663150i
\(233\) 3490.15i 0.981318i 0.871352 + 0.490659i \(0.163244\pi\)
−0.871352 + 0.490659i \(0.836756\pi\)
\(234\) 0 0
\(235\) 59.6724 59.6724i 0.0165642 0.0165642i
\(236\) −3612.46 + 674.635i −0.996402 + 0.186081i
\(237\) 0 0
\(238\) 6814.00 + 2110.70i 1.85582 + 0.574859i
\(239\) −2950.43 −0.798525 −0.399263 0.916837i \(-0.630734\pi\)
−0.399263 + 0.916837i \(0.630734\pi\)
\(240\) 0 0
\(241\) −1128.96 −0.301755 −0.150877 0.988552i \(-0.548210\pi\)
−0.150877 + 0.988552i \(0.548210\pi\)
\(242\) −2801.12 867.672i −0.744060 0.230480i
\(243\) 0 0
\(244\) 0.704491 + 3.77233i 0.000184838 + 0.000989748i
\(245\) −300.102 + 300.102i −0.0782565 + 0.0782565i
\(246\) 0 0
\(247\) 5327.11i 1.37229i
\(248\) −157.339 + 124.559i −0.0402864 + 0.0318933i
\(249\) 0 0
\(250\) −526.508 + 277.469i −0.133197 + 0.0701947i
\(251\) −4621.86 + 4621.86i −1.16227 + 1.16227i −0.178291 + 0.983978i \(0.557057\pi\)
−0.983978 + 0.178291i \(0.942943\pi\)
\(252\) 0 0
\(253\) 851.642 + 851.642i 0.211630 + 0.211630i
\(254\) −827.485 + 2671.38i −0.204413 + 0.659910i
\(255\) 0 0
\(256\) −3028.90 + 2757.35i −0.739477 + 0.673181i
\(257\) −610.977 −0.148295 −0.0741473 0.997247i \(-0.523623\pi\)
−0.0741473 + 0.997247i \(0.523623\pi\)
\(258\) 0 0
\(259\) −631.518 631.518i −0.151508 0.151508i
\(260\) 382.574 + 262.167i 0.0912547 + 0.0625342i
\(261\) 0 0
\(262\) 2808.20 1479.91i 0.662179 0.348967i
\(263\) 4973.57i 1.16610i −0.812438 0.583048i \(-0.801860\pi\)
0.812438 0.583048i \(-0.198140\pi\)
\(264\) 0 0
\(265\) 464.505i 0.107677i
\(266\) 2974.53 + 5644.28i 0.685638 + 1.30103i
\(267\) 0 0
\(268\) −1174.08 6286.81i −0.267605 1.43294i
\(269\) 938.415 + 938.415i 0.212700 + 0.212700i 0.805413 0.592714i \(-0.201943\pi\)
−0.592714 + 0.805413i \(0.701943\pi\)
\(270\) 0 0
\(271\) −4010.64 −0.898999 −0.449500 0.893280i \(-0.648398\pi\)
−0.449500 + 0.893280i \(0.648398\pi\)
\(272\) −2003.10 5175.95i −0.446530 1.15382i
\(273\) 0 0
\(274\) −4310.13 1335.10i −0.950309 0.294367i
\(275\) −1507.50 1507.50i −0.330566 0.330566i
\(276\) 0 0
\(277\) −3534.99 + 3534.99i −0.766776 + 0.766776i −0.977538 0.210762i \(-0.932406\pi\)
0.210762 + 0.977538i \(0.432406\pi\)
\(278\) −517.868 982.675i −0.111725 0.212003i
\(279\) 0 0
\(280\) 551.740 + 64.1566i 0.117760 + 0.0136932i
\(281\) 7468.35i 1.58550i −0.609550 0.792748i \(-0.708650\pi\)
0.609550 0.792748i \(-0.291350\pi\)
\(282\) 0 0
\(283\) −2249.22 + 2249.22i −0.472447 + 0.472447i −0.902705 0.430259i \(-0.858422\pi\)
0.430259 + 0.902705i \(0.358422\pi\)
\(284\) 1897.08 2768.36i 0.396377 0.578423i
\(285\) 0 0
\(286\) −985.973 + 3183.03i −0.203852 + 0.658099i
\(287\) −4457.66 −0.916819
\(288\) 0 0
\(289\) 2607.24 0.530682
\(290\) 63.3390 204.478i 0.0128255 0.0414047i
\(291\) 0 0
\(292\) 1695.08 2473.60i 0.339717 0.495740i
\(293\) 3952.79 3952.79i 0.788139 0.788139i −0.193050 0.981189i \(-0.561838\pi\)
0.981189 + 0.193050i \(0.0618381\pi\)
\(294\) 0 0
\(295\) 387.736i 0.0765249i
\(296\) −80.2582 + 690.212i −0.0157598 + 0.135533i
\(297\) 0 0
\(298\) 1106.38 + 2099.40i 0.215070 + 0.408104i
\(299\) −3410.03 + 3410.03i −0.659555 + 0.659555i
\(300\) 0 0
\(301\) −3517.59 3517.59i −0.673589 0.673589i
\(302\) 434.053 + 134.452i 0.0827052 + 0.0256187i
\(303\) 0 0
\(304\) 2006.62 4540.28i 0.378577 0.856588i
\(305\) −0.404895 −7.60138e−5
\(306\) 0 0
\(307\) −3855.24 3855.24i −0.716711 0.716711i 0.251219 0.967930i \(-0.419168\pi\)
−0.967930 + 0.251219i \(0.919168\pi\)
\(308\) 732.645 + 3923.08i 0.135540 + 0.725774i
\(309\) 0 0
\(310\) −9.87125 18.7311i −0.00180855 0.00343179i
\(311\) 5194.39i 0.947096i 0.880768 + 0.473548i \(0.157027\pi\)
−0.880768 + 0.473548i \(0.842973\pi\)
\(312\) 0 0
\(313\) 4710.01i 0.850561i 0.905062 + 0.425281i \(0.139825\pi\)
−0.905062 + 0.425281i \(0.860175\pi\)
\(314\) 2497.46 1316.16i 0.448854 0.236545i
\(315\) 0 0
\(316\) 4657.38 + 3191.57i 0.829108 + 0.568164i
\(317\) −5680.21 5680.21i −1.00641 1.00641i −0.999979 0.00643263i \(-0.997952\pi\)
−0.00643263 0.999979i \(-0.502048\pi\)
\(318\) 0 0
\(319\) 1538.03 0.269946
\(320\) −227.313 367.552i −0.0397100 0.0642087i
\(321\) 0 0
\(322\) −1708.98 + 5517.13i −0.295770 + 0.954838i
\(323\) 4756.05 + 4756.05i 0.819300 + 0.819300i
\(324\) 0 0
\(325\) 6036.13 6036.13i 1.03023 1.03023i
\(326\) −6626.67 + 3492.24i −1.12582 + 0.593304i
\(327\) 0 0
\(328\) 2152.72 + 2719.23i 0.362390 + 0.457758i
\(329\) 2907.68i 0.487251i
\(330\) 0 0
\(331\) 1815.80 1815.80i 0.301526 0.301526i −0.540084 0.841611i \(-0.681608\pi\)
0.841611 + 0.540084i \(0.181608\pi\)
\(332\) −1967.07 10533.0i −0.325171 1.74119i
\(333\) 0 0
\(334\) −10407.8 3223.91i −1.70505 0.528157i
\(335\) 674.782 0.110052
\(336\) 0 0
\(337\) −2683.29 −0.433733 −0.216867 0.976201i \(-0.569584\pi\)
−0.216867 + 0.976201i \(0.569584\pi\)
\(338\) −6809.23 2109.22i −1.09578 0.339428i
\(339\) 0 0
\(340\) 575.626 107.500i 0.0918167 0.0171470i
\(341\) 107.569 107.569i 0.0170827 0.0170827i
\(342\) 0 0
\(343\) 4647.79i 0.731653i
\(344\) −447.042 + 3844.51i −0.0700665 + 0.602565i
\(345\) 0 0
\(346\) 9291.18 4896.43i 1.44363 0.760791i
\(347\) 5291.81 5291.81i 0.818671 0.818671i −0.167244 0.985916i \(-0.553487\pi\)
0.985916 + 0.167244i \(0.0534868\pi\)
\(348\) 0 0
\(349\) 73.7084 + 73.7084i 0.0113052 + 0.0113052i 0.712737 0.701432i \(-0.247455\pi\)
−0.701432 + 0.712737i \(0.747455\pi\)
\(350\) 3025.09 9765.94i 0.461994 1.49146i
\(351\) 0 0
\(352\) 2039.32 2341.49i 0.308796 0.354550i
\(353\) 5067.25 0.764030 0.382015 0.924156i \(-0.375230\pi\)
0.382015 + 0.924156i \(0.375230\pi\)
\(354\) 0 0
\(355\) 250.378 + 250.378i 0.0374329 + 0.0374329i
\(356\) 21.3865 31.2088i 0.00318393 0.00464624i
\(357\) 0 0
\(358\) −4376.41 + 2306.36i −0.646090 + 0.340488i
\(359\) 970.230i 0.142637i −0.997454 0.0713186i \(-0.977279\pi\)
0.997454 0.0713186i \(-0.0227207\pi\)
\(360\) 0 0
\(361\) 843.224i 0.122937i
\(362\) 2936.99 + 5573.06i 0.426422 + 0.809154i
\(363\) 0 0
\(364\) −15708.3 + 2933.56i −2.26192 + 0.422418i
\(365\) 223.718 + 223.718i 0.0320821 + 0.0320821i
\(366\) 0 0
\(367\) 13451.4 1.91323 0.956617 0.291347i \(-0.0941035\pi\)
0.956617 + 0.291347i \(0.0941035\pi\)
\(368\) 4190.84 1621.86i 0.593649 0.229743i
\(369\) 0 0
\(370\) −70.0313 21.6928i −0.00983987 0.00304799i
\(371\) −11317.1 11317.1i −1.58370 1.58370i
\(372\) 0 0
\(373\) 5898.22 5898.22i 0.818762 0.818762i −0.167167 0.985929i \(-0.553462\pi\)
0.985929 + 0.167167i \(0.0534619\pi\)
\(374\) 1961.53 + 3722.09i 0.271199 + 0.514611i
\(375\) 0 0
\(376\) 1773.73 1404.20i 0.243279 0.192595i
\(377\) 6158.35i 0.841302i
\(378\) 0 0
\(379\) −4446.72 + 4446.72i −0.602673 + 0.602673i −0.941021 0.338348i \(-0.890132\pi\)
0.338348 + 0.941021i \(0.390132\pi\)
\(380\) 432.031 + 296.059i 0.0583230 + 0.0399671i
\(381\) 0 0
\(382\) 3001.06 9688.35i 0.401957 1.29764i
\(383\) 6417.68 0.856209 0.428105 0.903729i \(-0.359181\pi\)
0.428105 + 0.903729i \(0.359181\pi\)
\(384\) 0 0
\(385\) −421.076 −0.0557403
\(386\) −438.202 + 1414.65i −0.0577821 + 0.186539i
\(387\) 0 0
\(388\) −2504.67 1716.38i −0.327720 0.224577i
\(389\) −6555.61 + 6555.61i −0.854455 + 0.854455i −0.990678 0.136223i \(-0.956503\pi\)
0.136223 + 0.990678i \(0.456503\pi\)
\(390\) 0 0
\(391\) 6088.96i 0.787549i
\(392\) −8920.36 + 7061.93i −1.14935 + 0.909902i
\(393\) 0 0
\(394\) 2099.17 + 3983.27i 0.268413 + 0.509325i
\(395\) −421.226 + 421.226i −0.0536561 + 0.0536561i
\(396\) 0 0
\(397\) 8902.51 + 8902.51i 1.12545 + 1.12545i 0.990908 + 0.134543i \(0.0429566\pi\)
0.134543 + 0.990908i \(0.457043\pi\)
\(398\) 6247.81 + 1935.32i 0.786871 + 0.243741i
\(399\) 0 0
\(400\) −7418.26 + 2870.88i −0.927282 + 0.358860i
\(401\) 6425.77 0.800218 0.400109 0.916468i \(-0.368972\pi\)
0.400109 + 0.916468i \(0.368972\pi\)
\(402\) 0 0
\(403\) 430.715 + 430.715i 0.0532393 + 0.0532393i
\(404\) −4348.53 + 812.098i −0.535514 + 0.100008i
\(405\) 0 0
\(406\) 3438.67 + 6525.01i 0.420340 + 0.797613i
\(407\) 526.755i 0.0641530i
\(408\) 0 0
\(409\) 12796.0i 1.54699i −0.633801 0.773496i \(-0.718506\pi\)
0.633801 0.773496i \(-0.281494\pi\)
\(410\) −323.723 + 170.602i −0.0389941 + 0.0205498i
\(411\) 0 0
\(412\) −1392.56 + 2032.13i −0.166520 + 0.242999i
\(413\) 9446.67 + 9446.67i 1.12552 + 1.12552i
\(414\) 0 0
\(415\) 1130.54 0.133725
\(416\) 9375.45 + 8165.58i 1.10497 + 0.962381i
\(417\) 0 0
\(418\) −1113.44 + 3594.51i −0.130287 + 0.420606i
\(419\) 6545.21 + 6545.21i 0.763137 + 0.763137i 0.976888 0.213751i \(-0.0685681\pi\)
−0.213751 + 0.976888i \(0.568568\pi\)
\(420\) 0 0
\(421\) −6390.00 + 6390.00i −0.739738 + 0.739738i −0.972527 0.232789i \(-0.925215\pi\)
0.232789 + 0.972527i \(0.425215\pi\)
\(422\) −5019.93 + 2645.49i −0.579067 + 0.305167i
\(423\) 0 0
\(424\) −1438.26 + 12368.9i −0.164736 + 1.41671i
\(425\) 10778.1i 1.23016i
\(426\) 0 0
\(427\) 9.86474 9.86474i 0.00111801 0.00111801i
\(428\) −6690.74 + 1249.51i −0.755628 + 0.141115i
\(429\) 0 0
\(430\) −390.078 120.830i −0.0437470 0.0135510i
\(431\) 10639.3 1.18904 0.594519 0.804081i \(-0.297342\pi\)
0.594519 + 0.804081i \(0.297342\pi\)
\(432\) 0 0
\(433\) 3806.14 0.422428 0.211214 0.977440i \(-0.432258\pi\)
0.211214 + 0.977440i \(0.432258\pi\)
\(434\) 696.859 + 215.859i 0.0770745 + 0.0238746i
\(435\) 0 0
\(436\) 1970.80 + 10553.0i 0.216478 + 1.15917i
\(437\) −3850.86 + 3850.86i −0.421537 + 0.421537i
\(438\) 0 0
\(439\) 14102.8i 1.53323i −0.642106 0.766616i \(-0.721939\pi\)
0.642106 0.766616i \(-0.278061\pi\)
\(440\) 203.349 + 256.862i 0.0220324 + 0.0278305i
\(441\) 0 0
\(442\) −14903.5 + 7854.10i −1.60381 + 0.845207i
\(443\) 7662.45 7662.45i 0.821792 0.821792i −0.164573 0.986365i \(-0.552625\pi\)
0.986365 + 0.164573i \(0.0526246\pi\)
\(444\) 0 0
\(445\) 2.82260 + 2.82260i 0.000300683 + 0.000300683i
\(446\) 3611.29 11658.4i 0.383408 1.23776i
\(447\) 0 0
\(448\) 14493.1 + 3416.73i 1.52843 + 0.360325i
\(449\) −13679.4 −1.43779 −0.718897 0.695117i \(-0.755353\pi\)
−0.718897 + 0.695117i \(0.755353\pi\)
\(450\) 0 0
\(451\) −1859.09 1859.09i −0.194104 0.194104i
\(452\) 12037.0 + 8248.64i 1.25260 + 0.858370i
\(453\) 0 0
\(454\) 2481.33 1307.66i 0.256508 0.135179i
\(455\) 1686.01i 0.173718i
\(456\) 0 0
\(457\) 7913.48i 0.810016i −0.914313 0.405008i \(-0.867269\pi\)
0.914313 0.405008i \(-0.132731\pi\)
\(458\) −1237.07 2347.39i −0.126210 0.239489i
\(459\) 0 0
\(460\) 87.0397 + 466.070i 0.00882228 + 0.0472405i
\(461\) 580.215 + 580.215i 0.0586189 + 0.0586189i 0.735809 0.677190i \(-0.236802\pi\)
−0.677190 + 0.735809i \(0.736802\pi\)
\(462\) 0 0
\(463\) 14236.5 1.42899 0.714497 0.699638i \(-0.246656\pi\)
0.714497 + 0.699638i \(0.246656\pi\)
\(464\) 2319.73 5248.74i 0.232092 0.525143i
\(465\) 0 0
\(466\) −9429.60 2920.91i −0.937377 0.290361i
\(467\) 8344.57 + 8344.57i 0.826853 + 0.826853i 0.987080 0.160227i \(-0.0512225\pi\)
−0.160227 + 0.987080i \(0.551223\pi\)
\(468\) 0 0
\(469\) −16440.2 + 16440.2i −1.61863 + 1.61863i
\(470\) 111.282 + 211.161i 0.0109213 + 0.0207237i
\(471\) 0 0
\(472\) 1200.56 10324.7i 0.117076 1.00684i
\(473\) 2934.05i 0.285217i
\(474\) 0 0
\(475\) 6816.45 6816.45i 0.658443 0.658443i
\(476\) −11405.3 + 16643.5i −1.09824 + 1.60263i
\(477\) 0 0
\(478\) 2469.22 7971.41i 0.236275 0.762769i
\(479\) 5563.77 0.530720 0.265360 0.964149i \(-0.414509\pi\)
0.265360 + 0.964149i \(0.414509\pi\)
\(480\) 0 0
\(481\) 2109.16 0.199936
\(482\) 944.830 3050.20i 0.0892859 0.288243i
\(483\) 0 0
\(484\) 4688.51 6841.83i 0.440319 0.642546i
\(485\) 226.529 226.529i 0.0212085 0.0212085i
\(486\) 0 0
\(487\) 18150.5i 1.68886i 0.535662 + 0.844432i \(0.320062\pi\)
−0.535662 + 0.844432i \(0.679938\pi\)
\(488\) −10.7816 1.25369i −0.00100012 0.000116295i
\(489\) 0 0
\(490\) −559.653 1061.97i −0.0515971 0.0979076i
\(491\) −11593.0 + 11593.0i −1.06555 + 1.06555i −0.0678570 + 0.997695i \(0.521616\pi\)
−0.997695 + 0.0678570i \(0.978384\pi\)
\(492\) 0 0
\(493\) 5498.18 + 5498.18i 0.502284 + 0.502284i
\(494\) −14392.7 4458.26i −1.31084 0.406046i
\(495\) 0 0
\(496\) −204.855 529.338i −0.0185449 0.0479193i
\(497\) −12200.3 −1.10112
\(498\) 0 0
\(499\) 3109.58 + 3109.58i 0.278966 + 0.278966i 0.832696 0.553730i \(-0.186796\pi\)
−0.553730 + 0.832696i \(0.686796\pi\)
\(500\) −309.023 1654.72i −0.0276399 0.148003i
\(501\) 0 0
\(502\) −8619.20 16355.3i −0.766322 1.45413i
\(503\) 6221.21i 0.551471i −0.961233 0.275736i \(-0.911079\pi\)
0.961233 0.275736i \(-0.0889215\pi\)
\(504\) 0 0
\(505\) 466.740i 0.0411281i
\(506\) −3013.69 + 1588.21i −0.264772 + 0.139534i
\(507\) 0 0
\(508\) −6524.94 4471.36i −0.569877 0.390520i
\(509\) −13800.4 13800.4i −1.20176 1.20176i −0.973632 0.228124i \(-0.926741\pi\)
−0.228124 0.973632i \(-0.573259\pi\)
\(510\) 0 0
\(511\) −10901.2 −0.943720
\(512\) −4914.86 10491.0i −0.424234 0.905552i
\(513\) 0 0
\(514\) 511.327 1650.72i 0.0438787 0.141654i
\(515\) −183.791 183.791i −0.0157258 0.0157258i
\(516\) 0 0
\(517\) −1212.66 + 1212.66i −0.103158 + 0.103158i
\(518\) 2234.74 1177.70i 0.189554 0.0998944i
\(519\) 0 0
\(520\) −1028.49 + 814.221i −0.0867354 + 0.0686653i
\(521\) 6874.63i 0.578086i −0.957316 0.289043i \(-0.906663\pi\)
0.957316 0.289043i \(-0.0933371\pi\)
\(522\) 0 0
\(523\) 2306.52 2306.52i 0.192843 0.192843i −0.604080 0.796924i \(-0.706459\pi\)
0.796924 + 0.604080i \(0.206459\pi\)
\(524\) 1648.21 + 8825.66i 0.137409 + 0.735784i
\(525\) 0 0
\(526\) 13437.5 + 4162.38i 1.11388 + 0.345035i
\(527\) 769.086 0.0635710
\(528\) 0 0
\(529\) 7236.92 0.594799
\(530\) −1254.99 388.744i −0.102855 0.0318603i
\(531\) 0 0
\(532\) −17739.0 + 3312.80i −1.44564 + 0.269977i
\(533\) 7443.90 7443.90i 0.604936 0.604936i
\(534\) 0 0
\(535\) 718.136i 0.0580332i
\(536\) 17968.1 + 2089.34i 1.44796 + 0.168369i
\(537\) 0 0
\(538\) −3320.75 + 1750.03i −0.266111 + 0.140240i
\(539\) 6098.68 6098.68i 0.487363 0.487363i
\(540\) 0 0
\(541\) −13240.0 13240.0i −1.05218 1.05218i −0.998561 0.0536210i \(-0.982924\pi\)
−0.0536210 0.998561i \(-0.517076\pi\)
\(542\) 3356.51 10835.8i 0.266004 0.858744i
\(543\) 0 0
\(544\) 15660.7 1080.18i 1.23427 0.0851330i
\(545\) −1132.69 −0.0890256
\(546\) 0 0
\(547\) −13271.3 13271.3i −1.03737 1.03737i −0.999274 0.0380940i \(-0.987871\pi\)
−0.0380940 0.999274i \(-0.512129\pi\)
\(548\) 7214.31 10527.7i 0.562372 0.820656i
\(549\) 0 0
\(550\) 5334.56 2811.30i 0.413575 0.217953i
\(551\) 6954.47i 0.537696i
\(552\) 0 0
\(553\) 20525.2i 1.57834i
\(554\) −6592.32 12509.2i −0.505561 0.959322i
\(555\) 0 0
\(556\) 3088.37 576.761i 0.235569 0.0439930i
\(557\) 8500.61 + 8500.61i 0.646647 + 0.646647i 0.952181 0.305534i \(-0.0988349\pi\)
−0.305534 + 0.952181i \(0.598835\pi\)
\(558\) 0 0
\(559\) 11748.1 0.888896
\(560\) −635.088 + 1436.98i −0.0479239 + 0.108435i
\(561\) 0 0
\(562\) 20177.8 + 6250.27i 1.51450 + 0.469131i
\(563\) −17327.2 17327.2i −1.29708 1.29708i −0.930314 0.366763i \(-0.880466\pi\)
−0.366763 0.930314i \(-0.619534\pi\)
\(564\) 0 0
\(565\) −1088.66 + 1088.66i −0.0810625 + 0.0810625i
\(566\) −4194.52 7959.27i −0.311500 0.591083i
\(567\) 0 0
\(568\) 5891.83 + 7442.33i 0.435239 + 0.549777i
\(569\) 8998.54i 0.662985i 0.943458 + 0.331492i \(0.107552\pi\)
−0.943458 + 0.331492i \(0.892448\pi\)
\(570\) 0 0
\(571\) −9849.25 + 9849.25i −0.721853 + 0.721853i −0.968983 0.247129i \(-0.920513\pi\)
0.247129 + 0.968983i \(0.420513\pi\)
\(572\) −7774.66 5327.75i −0.568313 0.389449i
\(573\) 0 0
\(574\) 3730.62 12043.6i 0.271277 0.875766i
\(575\) 8726.79 0.632926
\(576\) 0 0
\(577\) −20584.4 −1.48516 −0.742580 0.669757i \(-0.766398\pi\)
−0.742580 + 0.669757i \(0.766398\pi\)
\(578\) −2182.00 + 7044.18i −0.157023 + 0.506919i
\(579\) 0 0
\(580\) 499.445 + 342.256i 0.0357558 + 0.0245024i
\(581\) −27544.1 + 27544.1i −1.96682 + 1.96682i
\(582\) 0 0
\(583\) 9439.66i 0.670585i
\(584\) 5264.48 + 6649.89i 0.373024 + 0.471189i
\(585\) 0 0
\(586\) 7371.47 + 13987.7i 0.519646 + 0.986049i
\(587\) 2586.77 2586.77i 0.181887 0.181887i −0.610291 0.792177i \(-0.708947\pi\)
0.792177 + 0.610291i \(0.208947\pi\)
\(588\) 0 0
\(589\) 486.396 + 486.396i 0.0340265 + 0.0340265i
\(590\) 1047.57 + 324.496i 0.0730983 + 0.0226429i
\(591\) 0 0
\(592\) −1797.63 794.479i −0.124801 0.0551569i
\(593\) 6035.89 0.417984 0.208992 0.977917i \(-0.432982\pi\)
0.208992 + 0.977917i \(0.432982\pi\)
\(594\) 0 0
\(595\) −1505.28 1505.28i −0.103715 0.103715i
\(596\) −6598.04 + 1232.20i −0.453467 + 0.0846860i
\(597\) 0 0
\(598\) −6359.28 12067.0i −0.434866 0.825177i
\(599\) 5427.20i 0.370199i −0.982720 0.185100i \(-0.940739\pi\)
0.982720 0.185100i \(-0.0592608\pi\)
\(600\) 0 0
\(601\) 17725.7i 1.20307i 0.798847 + 0.601535i \(0.205444\pi\)
−0.798847 + 0.601535i \(0.794556\pi\)
\(602\) 12447.6 6559.86i 0.842735 0.444120i
\(603\) 0 0
\(604\) −726.520 + 1060.19i −0.0489431 + 0.0714215i
\(605\) 618.793 + 618.793i 0.0415827 + 0.0415827i
\(606\) 0 0
\(607\) 13487.6 0.901884 0.450942 0.892553i \(-0.351088\pi\)
0.450942 + 0.892553i \(0.351088\pi\)
\(608\) 10587.5 + 9221.19i 0.706215 + 0.615080i
\(609\) 0 0
\(610\) 0.338857 1.09394i 2.24917e−5 7.26101e-5i
\(611\) −4855.57 4855.57i −0.321498 0.321498i
\(612\) 0 0
\(613\) −16850.4 + 16850.4i −1.11025 + 1.11025i −0.117129 + 0.993117i \(0.537369\pi\)
−0.993117 + 0.117129i \(0.962631\pi\)
\(614\) 13642.5 7189.54i 0.896685 0.472551i
\(615\) 0 0
\(616\) −11212.4 1303.79i −0.733381 0.0852779i
\(617\) 535.243i 0.0349239i 0.999848 + 0.0174620i \(0.00555860\pi\)
−0.999848 + 0.0174620i \(0.994441\pi\)
\(618\) 0 0
\(619\) −19691.0 + 19691.0i −1.27859 + 1.27859i −0.337130 + 0.941458i \(0.609456\pi\)
−0.941458 + 0.337130i \(0.890544\pi\)
\(620\) 58.8685 10.9938i 0.00381325 0.000712134i
\(621\) 0 0
\(622\) −14034.1 4347.19i −0.904688 0.280236i
\(623\) −137.538 −0.00884485
\(624\) 0 0
\(625\) −15358.3 −0.982934
\(626\) −12725.4 3941.81i −0.812475 0.251672i
\(627\) 0 0
\(628\) 1465.84 + 7849.09i 0.0931420 + 0.498746i
\(629\) 1883.06 1883.06i 0.119368 0.119368i
\(630\) 0 0
\(631\) 11880.2i 0.749511i −0.927124 0.374755i \(-0.877727\pi\)
0.927124 0.374755i \(-0.122273\pi\)
\(632\) −12520.7 + 9912.18i −0.788047 + 0.623869i
\(633\) 0 0
\(634\) 20100.4 10592.9i 1.25913 0.663561i
\(635\) 590.132 590.132i 0.0368798 0.0368798i
\(636\) 0 0
\(637\) 24419.5 + 24419.5i 1.51889 + 1.51889i
\(638\) −1287.17 + 4155.40i −0.0798742 + 0.257859i
\(639\) 0 0
\(640\) 1183.28 306.545i 0.0730833 0.0189332i
\(641\) −18341.0 −1.13015 −0.565074 0.825040i \(-0.691152\pi\)
−0.565074 + 0.825040i \(0.691152\pi\)
\(642\) 0 0
\(643\) 7026.21 + 7026.21i 0.430928 + 0.430928i 0.888944 0.458016i \(-0.151440\pi\)
−0.458016 + 0.888944i \(0.651440\pi\)
\(644\) −13475.8 9234.59i −0.824567 0.565052i
\(645\) 0 0
\(646\) −16830.1 + 8869.45i −1.02504 + 0.540192i
\(647\) 21429.7i 1.30215i 0.759015 + 0.651073i \(0.225681\pi\)
−0.759015 + 0.651073i \(0.774319\pi\)
\(648\) 0 0
\(649\) 7879.56i 0.476579i
\(650\) 11256.6 + 21359.9i 0.679263 + 1.28893i
\(651\) 0 0
\(652\) −3889.39 20826.4i −0.233620 1.25096i
\(653\) −8681.22 8681.22i −0.520248 0.520248i 0.397398 0.917646i \(-0.369913\pi\)
−0.917646 + 0.397398i \(0.869913\pi\)
\(654\) 0 0
\(655\) −947.284 −0.0565091
\(656\) −9148.37 + 3540.44i −0.544488 + 0.210718i
\(657\) 0 0
\(658\) −7855.90 2433.44i −0.465433 0.144172i
\(659\) 4151.60 + 4151.60i 0.245407 + 0.245407i 0.819083 0.573675i \(-0.194483\pi\)
−0.573675 + 0.819083i \(0.694483\pi\)
\(660\) 0 0
\(661\) 12239.0 12239.0i 0.720182 0.720182i −0.248460 0.968642i \(-0.579924\pi\)
0.968642 + 0.248460i \(0.0799244\pi\)
\(662\) 3386.23 + 6425.52i 0.198806 + 0.377243i
\(663\) 0 0
\(664\) 30104.1 + 3500.52i 1.75944 + 0.204588i
\(665\) 1903.98i 0.111027i
\(666\) 0 0
\(667\) −4451.75 + 4451.75i −0.258429 + 0.258429i
\(668\) 17420.5 25421.4i 1.00901 1.47243i
\(669\) 0 0
\(670\) −564.725 + 1823.11i −0.0325631 + 0.105124i
\(671\) 8.22827 0.000473396
\(672\) 0 0
\(673\) 6528.62 0.373937 0.186969 0.982366i \(-0.440134\pi\)
0.186969 + 0.982366i \(0.440134\pi\)
\(674\) 2245.65 7249.65i 0.128337 0.414312i
\(675\) 0 0
\(676\) 11397.3 16631.8i 0.648458 0.946279i
\(677\) 14220.6 14220.6i 0.807299 0.807299i −0.176925 0.984224i \(-0.556615\pi\)
0.984224 + 0.176925i \(0.0566151\pi\)
\(678\) 0 0
\(679\) 11038.2i 0.623867i
\(680\) −191.302 + 1645.18i −0.0107884 + 0.0927790i
\(681\) 0 0
\(682\) 200.604 + 380.653i 0.0112632 + 0.0213724i
\(683\) −21419.5 + 21419.5i −1.19999 + 1.19999i −0.225827 + 0.974167i \(0.572508\pi\)
−0.974167 + 0.225827i \(0.927492\pi\)
\(684\) 0 0
\(685\) 952.149 + 952.149i 0.0531091 + 0.0531091i
\(686\) 12557.3 + 3889.74i 0.698891 + 0.216488i
\(687\) 0 0
\(688\) −10012.9 4425.28i −0.554851 0.245222i
\(689\) 37797.0 2.08991
\(690\) 0 0
\(691\) −16537.1 16537.1i −0.910423 0.910423i 0.0858818 0.996305i \(-0.472629\pi\)
−0.996305 + 0.0858818i \(0.972629\pi\)
\(692\) 5453.27 + 29200.5i 0.299570 + 1.60410i
\(693\) 0 0
\(694\) 9868.56 + 18726.0i 0.539777 + 1.02425i
\(695\) 331.484i 0.0180920i
\(696\) 0 0
\(697\) 13291.8i 0.722331i
\(698\) −260.830 + 137.457i −0.0141441 + 0.00745390i
\(699\) 0 0
\(700\) 23853.7 + 16346.2i 1.28798 + 0.882614i
\(701\) 3026.52 + 3026.52i 0.163067 + 0.163067i 0.783924 0.620857i \(-0.213215\pi\)
−0.620857 + 0.783924i \(0.713215\pi\)
\(702\) 0 0
\(703\) 2381.82 0.127784
\(704\) 4619.46 + 7469.39i 0.247305 + 0.399877i
\(705\) 0 0
\(706\) −4240.79 + 13690.6i −0.226068 + 0.729819i
\(707\) 11371.5 + 11371.5i 0.604908 + 0.604908i
\(708\) 0 0
\(709\) 3981.14 3981.14i 0.210881 0.210881i −0.593761 0.804642i \(-0.702357\pi\)
0.804642 + 0.593761i \(0.202357\pi\)
\(710\) −886.007 + 466.924i −0.0468327 + 0.0246807i
\(711\) 0 0
\(712\) 66.4207 + 83.9001i 0.00349610 + 0.00441614i
\(713\) 622.710i 0.0327078i
\(714\) 0 0
\(715\) 703.160 703.160i 0.0367786 0.0367786i
\(716\) −2568.64 13754.3i −0.134071 0.717906i
\(717\) 0 0
\(718\) 2621.34 + 811.986i 0.136250 + 0.0422048i
\(719\) 5682.25 0.294732 0.147366 0.989082i \(-0.452921\pi\)
0.147366 + 0.989082i \(0.452921\pi\)
\(720\) 0 0
\(721\) 8955.64 0.462587
\(722\) 2278.20 + 705.695i 0.117432 + 0.0363757i
\(723\) 0 0
\(724\) −17515.1 + 3271.00i −0.899096 + 0.167908i
\(725\) 7880.09 7880.09i 0.403668 0.403668i
\(726\) 0 0
\(727\) 18883.0i 0.963317i 0.876359 + 0.481658i \(0.159965\pi\)
−0.876359 + 0.481658i \(0.840035\pi\)
\(728\) 5220.45 44895.3i 0.265773 2.28562i
\(729\) 0 0
\(730\) −791.667 + 417.207i −0.0401382 + 0.0211528i
\(731\) 10488.8 10488.8i 0.530698 0.530698i
\(732\) 0 0
\(733\) −24962.5 24962.5i −1.25786 1.25786i −0.952113 0.305748i \(-0.901094\pi\)
−0.305748 0.952113i \(-0.598906\pi\)
\(734\) −11257.5 + 36342.7i −0.566105 + 1.82756i
\(735\) 0 0
\(736\) 874.596 + 12680.1i 0.0438017 + 0.635045i
\(737\) −13712.9 −0.685375
\(738\) 0 0
\(739\) 6202.38 + 6202.38i 0.308739 + 0.308739i 0.844420 0.535681i \(-0.179945\pi\)
−0.535681 + 0.844420i \(0.679945\pi\)
\(740\) 117.218 171.054i 0.00582302 0.00849739i
\(741\) 0 0
\(742\) 40047.4 21104.9i 1.98138 1.04418i
\(743\) 30.9140i 0.00152641i 1.00000 0.000763205i \(0.000242936\pi\)
−1.00000 0.000763205i \(0.999757\pi\)
\(744\) 0 0
\(745\) 708.187i 0.0348268i
\(746\) 10999.4 + 20871.9i 0.539837 + 1.02436i
\(747\) 0 0
\(748\) −11697.9 + 2184.60i −0.571813 + 0.106787i
\(749\) 17496.5 + 17496.5i 0.853547 + 0.853547i
\(750\) 0 0
\(751\) −16318.5 −0.792905 −0.396453 0.918055i \(-0.629759\pi\)
−0.396453 + 0.918055i \(0.629759\pi\)
\(752\) 2309.39 + 5967.38i 0.111988 + 0.289372i
\(753\) 0 0
\(754\) −16638.5 5153.93i −0.803631 0.248932i
\(755\) −95.8865 95.8865i −0.00462208 0.00462208i
\(756\) 0 0
\(757\) 9854.59 9854.59i 0.473146 0.473146i −0.429786 0.902931i \(-0.641411\pi\)
0.902931 + 0.429786i \(0.141411\pi\)
\(758\) −8292.59 15735.5i −0.397362 0.754011i
\(759\) 0 0
\(760\) −1161.45 + 919.480i −0.0554346 + 0.0438856i
\(761\) 3823.42i 0.182127i −0.995845 0.0910637i \(-0.970973\pi\)
0.995845 0.0910637i \(-0.0290267\pi\)
\(762\) 0 0
\(763\) 27596.4 27596.4i 1.30938 1.30938i
\(764\) 23664.2 + 16216.4i 1.12060 + 0.767917i
\(765\) 0 0
\(766\) −5370.96 + 17339.1i −0.253343 + 0.817870i
\(767\) −31550.2 −1.48528
\(768\) 0 0
\(769\) 31689.1 1.48601 0.743003 0.669288i \(-0.233401\pi\)
0.743003 + 0.669288i \(0.233401\pi\)
\(770\) 352.399 1137.65i 0.0164930 0.0532444i
\(771\) 0 0
\(772\) −3455.34 2367.85i −0.161089 0.110390i
\(773\) 1305.84 1305.84i 0.0607604 0.0607604i −0.676074 0.736834i \(-0.736320\pi\)
0.736834 + 0.676074i \(0.236320\pi\)
\(774\) 0 0
\(775\) 1102.27i 0.0510898i
\(776\) 6733.44 5330.62i 0.311490 0.246596i
\(777\) 0 0
\(778\) −12225.4 23198.2i −0.563370 1.06902i
\(779\) 8406.21 8406.21i 0.386629 0.386629i
\(780\) 0 0
\(781\) −5088.18 5088.18i −0.233123 0.233123i
\(782\) −16451.0 5095.85i −0.752285 0.233027i
\(783\) 0 0
\(784\) −11614.3 30011.0i −0.529077 1.36712i
\(785\) −842.465 −0.0383043
\(786\) 0 0
\(787\) 14399.5 + 14399.5i 0.652209 + 0.652209i 0.953524 0.301316i \(-0.0974258\pi\)
−0.301316 + 0.953524i \(0.597426\pi\)
\(788\) −12518.7 + 2337.90i −0.565939 + 0.105691i
\(789\) 0 0
\(790\) −785.533 1490.58i −0.0353772 0.0671297i
\(791\) 53047.6i 2.38452i
\(792\) 0 0
\(793\) 32.9465i 0.00147537i
\(794\) −31503.1 + 16602.1i −1.40806 + 0.742047i
\(795\) 0 0
\(796\) −10457.6 + 15260.5i −0.465653 + 0.679516i
\(797\) 5572.19 + 5572.19i 0.247650 + 0.247650i 0.820006 0.572356i \(-0.193970\pi\)
−0.572356 + 0.820006i \(0.693970\pi\)
\(798\) 0 0
\(799\) −8670.13 −0.383889
\(800\) −1548.13 22445.1i −0.0684184 0.991944i
\(801\) 0 0
\(802\) −5377.73 + 17361.0i −0.236776 + 0.764386i
\(803\) −4546.40 4546.40i −0.199800 0.199800i
\(804\) 0 0
\(805\) 1218.79 1218.79i 0.0533622 0.0533622i
\(806\) −1524.16 + 803.229i −0.0666082 + 0.0351024i
\(807\) 0 0
\(808\) 1445.18 12428.4i 0.0629224 0.541126i
\(809\) 5081.28i 0.220826i −0.993886 0.110413i \(-0.964783\pi\)
0.993886 0.110413i \(-0.0352174\pi\)
\(810\) 0 0
\(811\) 4493.19 4493.19i 0.194546 0.194546i −0.603111 0.797657i \(-0.706072\pi\)
0.797657 + 0.603111i \(0.206072\pi\)
\(812\) −20507.0 + 3829.72i −0.886272 + 0.165513i
\(813\) 0 0
\(814\) 1423.17 + 440.842i 0.0612804 + 0.0189822i
\(815\) 2235.36 0.0960752
\(816\) 0 0
\(817\) 13266.9 0.568114
\(818\) 34571.8 + 10709.0i 1.47772 + 0.457738i
\(819\) 0 0
\(820\) −190.003 1017.41i −0.00809169 0.0433284i
\(821\) −2115.54 + 2115.54i −0.0899304 + 0.0899304i −0.750641 0.660710i \(-0.770255\pi\)
0.660710 + 0.750641i \(0.270255\pi\)
\(822\) 0 0
\(823\) 24432.6i 1.03483i 0.855734 + 0.517416i \(0.173106\pi\)
−0.855734 + 0.517416i \(0.826894\pi\)
\(824\) −4324.92 5463.07i −0.182847 0.230965i
\(825\) 0 0
\(826\) −33428.7 + 17616.9i −1.40815 + 0.742094i
\(827\) −21051.4 + 21051.4i −0.885162 + 0.885162i −0.994054 0.108892i \(-0.965270\pi\)
0.108892 + 0.994054i \(0.465270\pi\)
\(828\) 0 0
\(829\) 25442.0 + 25442.0i 1.06591 + 1.06591i 0.997669 + 0.0682392i \(0.0217381\pi\)
0.0682392 + 0.997669i \(0.478262\pi\)
\(830\) −946.150 + 3054.47i −0.0395679 + 0.127737i
\(831\) 0 0
\(832\) −29907.9 + 18496.6i −1.24624 + 0.770738i
\(833\) 43603.5 1.81365
\(834\) 0 0
\(835\) 2299.17 + 2299.17i 0.0952889 + 0.0952889i
\(836\) −8779.74 6016.51i −0.363222 0.248906i
\(837\) 0 0
\(838\) −23161.4 + 12206.0i −0.954770 + 0.503162i
\(839\) 18757.2i 0.771837i 0.922533 + 0.385919i \(0.126115\pi\)
−0.922533 + 0.385919i \(0.873885\pi\)
\(840\) 0 0
\(841\) 16349.4i 0.670358i
\(842\) −11916.6 22612.2i −0.487734 0.925495i
\(843\) 0 0
\(844\) −2946.35 15776.8i −0.120163 0.643434i
\(845\) 1504.22 + 1504.22i 0.0612389 + 0.0612389i
\(846\) 0 0
\(847\) −30152.2 −1.22319
\(848\) −32214.2 14237.4i −1.30453 0.576549i
\(849\) 0 0
\(850\) 29120.1 + 9020.23i 1.17507 + 0.363990i
\(851\) 1524.67 + 1524.67i 0.0614160 + 0.0614160i
\(852\) 0 0
\(853\) −6100.17 + 6100.17i −0.244860 + 0.244860i −0.818857 0.573997i \(-0.805392\pi\)
0.573997 + 0.818857i \(0.305392\pi\)
\(854\) 18.3965 + 34.9081i 0.000737138 + 0.00139875i
\(855\) 0 0
\(856\) 2223.58 19122.6i 0.0887857 0.763548i
\(857\) 2079.04i 0.0828687i −0.999141 0.0414344i \(-0.986807\pi\)
0.999141 0.0414344i \(-0.0131927\pi\)
\(858\) 0 0
\(859\) 8301.95 8301.95i 0.329754 0.329754i −0.522739 0.852493i \(-0.675090\pi\)
0.852493 + 0.522739i \(0.175090\pi\)
\(860\) 652.913 952.779i 0.0258885 0.0377785i
\(861\) 0 0
\(862\) −8904.02 + 28744.9i −0.351824 + 1.13580i
\(863\) −43830.8 −1.72887 −0.864436 0.502743i \(-0.832324\pi\)
−0.864436 + 0.502743i \(0.832324\pi\)
\(864\) 0 0
\(865\) −3134.18 −0.123197
\(866\) −3185.36 + 10283.3i −0.124992 + 0.403512i
\(867\) 0 0
\(868\) −1166.40 + 1702.11i −0.0456110 + 0.0665590i
\(869\) 8560.14 8560.14i 0.334158 0.334158i
\(870\) 0 0
\(871\) 54907.3i 2.13601i
\(872\) −30161.3 3507.17i −1.17132 0.136201i
\(873\) 0 0
\(874\) −7181.38 13627.0i −0.277933 0.527390i
\(875\) −4327.14 + 4327.14i −0.167182 + 0.167182i
\(876\) 0 0
\(877\) −2565.89 2565.89i −0.0987958 0.0987958i 0.655981 0.754777i \(-0.272255\pi\)
−0.754777 + 0.655981i \(0.772255\pi\)
\(878\) 38102.6 + 11802.6i 1.46458 + 0.453667i
\(879\) 0 0
\(880\) −864.168 + 334.435i −0.0331035 + 0.0128111i
\(881\) −26429.8 −1.01072 −0.505360 0.862909i \(-0.668640\pi\)
−0.505360 + 0.862909i \(0.668640\pi\)
\(882\) 0 0
\(883\) −20708.4 20708.4i −0.789232 0.789232i 0.192136 0.981368i \(-0.438458\pi\)
−0.981368 + 0.192136i \(0.938458\pi\)
\(884\) −8747.29 46839.0i −0.332809 1.78209i
\(885\) 0 0
\(886\) 14289.5 + 27114.9i 0.541835 + 1.02815i
\(887\) 22350.0i 0.846042i 0.906120 + 0.423021i \(0.139030\pi\)
−0.906120 + 0.423021i \(0.860970\pi\)
\(888\) 0 0
\(889\) 28755.6i 1.08485i
\(890\) −9.98827 + 5.26380i −0.000376188 + 0.000198250i
\(891\) 0 0
\(892\) 28476.0 + 19513.8i 1.06889 + 0.732479i
\(893\) −5483.28 5483.28i −0.205477 0.205477i
\(894\) 0 0
\(895\) 1476.28 0.0551360
\(896\) −21360.6 + 36297.7i −0.796435 + 1.35337i
\(897\) 0 0
\(898\) 11448.3 36958.6i 0.425428 1.37341i
\(899\) 562.292 + 562.292i 0.0208604 + 0.0208604i
\(900\) 0 0
\(901\) 33745.2 33745.2i 1.24774 1.24774i
\(902\) 6578.71 3466.96i 0.242846 0.127979i
\(903\) 0 0
\(904\) −32359.8 + 25618.1i −1.19056 + 0.942528i
\(905\) 1879.95i 0.0690516i
\(906\) 0 0
\(907\) −4086.93 + 4086.93i −0.149619 + 0.149619i −0.777948 0.628329i \(-0.783739\pi\)
0.628329 + 0.777948i \(0.283739\pi\)
\(908\) 1456.37 + 7798.38i 0.0532282 + 0.285020i
\(909\) 0 0
\(910\) 4555.23 + 1411.03i 0.165939 + 0.0514012i
\(911\) 20024.6 0.728259 0.364130 0.931348i \(-0.381367\pi\)
0.364130 + 0.931348i \(0.381367\pi\)
\(912\) 0 0
\(913\) −22974.8 −0.832810
\(914\) 21380.5 + 6622.80i 0.773745 + 0.239675i
\(915\) 0 0
\(916\) 7377.42 1377.75i 0.266110 0.0496967i
\(917\) 23079.3 23079.3i 0.831131 0.831131i
\(918\) 0 0
\(919\) 26977.7i 0.968349i −0.874971 0.484175i \(-0.839120\pi\)
0.874971 0.484175i \(-0.160880\pi\)
\(920\) −1332.06 154.893i −0.0477356 0.00555072i
\(921\) 0 0
\(922\) −2053.19 + 1082.03i −0.0733388 + 0.0386494i
\(923\) 20373.4 20373.4i 0.726542 0.726542i
\(924\) 0 0
\(925\) −2698.84 2698.84i −0.0959321 0.0959321i
\(926\) −11914.5 + 38463.7i −0.422824 + 1.36501i
\(927\) 0 0
\(928\) 12239.5 + 10660.1i 0.432955 + 0.377084i
\(929\) 34371.4 1.21387 0.606937 0.794750i \(-0.292398\pi\)
0.606937 + 0.794750i \(0.292398\pi\)
\(930\) 0 0
\(931\) 27576.3 + 27576.3i 0.970760 + 0.970760i
\(932\) 15783.3 23032.2i 0.554719 0.809489i
\(933\) 0 0
\(934\) −29528.7 + 15561.6i −1.03449 + 0.545172i
\(935\) 1255.57i 0.0439159i
\(936\) 0 0
\(937\) 32901.8i 1.14712i 0.819163 + 0.573561i \(0.194439\pi\)
−0.819163 + 0.573561i \(0.805561\pi\)
\(938\) −30658.9 58176.5i −1.06722 2.02508i
\(939\) 0 0
\(940\) −663.642 + 123.937i −0.0230273 + 0.00430039i
\(941\) −33381.6 33381.6i −1.15644 1.15644i −0.985236 0.171204i \(-0.945234\pi\)
−0.171204 0.985236i \(-0.554766\pi\)
\(942\) 0 0
\(943\) 10762.1 0.371646
\(944\) 26890.2 + 11884.3i 0.927119 + 0.409749i
\(945\) 0 0
\(946\) 7927.15 + 2455.51i 0.272446 + 0.0843928i
\(947\) −13611.9 13611.9i −0.467084 0.467084i 0.433884 0.900969i \(-0.357143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(948\) 0 0
\(949\) 18204.1 18204.1i 0.622686 0.622686i
\(950\) 12711.8 + 24121.2i 0.434133 + 0.823785i
\(951\) 0 0
\(952\) −35421.8 44743.5i −1.20591 1.52326i
\(953\) 4572.49i 0.155422i −0.996976 0.0777112i \(-0.975239\pi\)
0.996976 0.0777112i \(-0.0247612\pi\)
\(954\) 0 0
\(955\) −2140.25 + 2140.25i −0.0725202 + 0.0725202i
\(956\) 19470.5 + 13342.6i 0.658703 + 0.451390i
\(957\) 0 0
\(958\) −4656.32 + 15032.1i −0.157034 + 0.506956i
\(959\) −46395.7 −1.56225
\(960\) 0 0
\(961\) −29712.3 −0.997360
\(962\) −1765.16 + 5698.48i −0.0591590 + 0.190984i
\(963\) 0 0
\(964\) 7450.24 + 5105.44i 0.248917 + 0.170576i
\(965\) 312.510 312.510i 0.0104249 0.0104249i
\(966\) 0 0
\(967\) 33060.9i 1.09945i 0.835346 + 0.549725i \(0.185268\pi\)
−0.835346 + 0.549725i \(0.814732\pi\)
\(968\) 14561.3 + 18393.3i 0.483489 + 0.610725i
\(969\) 0 0
\(970\) 422.448 + 801.613i 0.0139835 + 0.0265343i
\(971\) 15553.4 15553.4i 0.514041 0.514041i −0.401721 0.915762i \(-0.631588\pi\)
0.915762 + 0.401721i \(0.131588\pi\)
\(972\) 0 0
\(973\) −8076.18 8076.18i −0.266095 0.266095i
\(974\) −49038.6 15190.2i −1.61324 0.499717i
\(975\) 0 0
\(976\) 12.4103 28.0802i 0.000407012 0.000920928i
\(977\) −1241.54 −0.0406555 −0.0203277 0.999793i \(-0.506471\pi\)
−0.0203277 + 0.999793i \(0.506471\pi\)
\(978\) 0 0
\(979\) −57.3608 57.3608i −0.00187258 0.00187258i
\(980\) 3337.57 623.299i 0.108790 0.0203169i
\(981\) 0 0
\(982\) −21619.6 41024.0i −0.702554 1.33312i
\(983\) 10797.7i 0.350349i 0.984537 + 0.175175i \(0.0560490\pi\)
−0.984537 + 0.175175i \(0.943951\pi\)
\(984\) 0 0
\(985\) 1343.67i 0.0434648i
\(986\) −19456.3 + 10253.4i −0.628413 + 0.331172i
\(987\) 0 0
\(988\) 24090.5 35154.6i 0.775728 1.13200i
\(989\) 8492.49 + 8492.49i 0.273049 + 0.273049i
\(990\) 0 0
\(991\) −10204.8 −0.327112 −0.163556 0.986534i \(-0.552296\pi\)
−0.163556 + 0.986534i \(0.552296\pi\)
\(992\) 1601.60 110.469i 0.0512608 0.00353567i
\(993\) 0 0
\(994\) 10210.4 32962.4i 0.325809 1.05181i
\(995\) −1380.20 1380.20i −0.0439752 0.0439752i
\(996\) 0 0
\(997\) 15046.7 15046.7i 0.477967 0.477967i −0.426514 0.904481i \(-0.640259\pi\)
0.904481 + 0.426514i \(0.140259\pi\)
\(998\) −11003.8 + 5798.98i −0.349017 + 0.183931i
\(999\) 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 144.4.k.a.109.2 10
3.2 odd 2 16.4.e.a.13.4 yes 10
4.3 odd 2 576.4.k.a.145.3 10
12.11 even 2 64.4.e.a.17.2 10
16.5 even 4 inner 144.4.k.a.37.2 10
16.11 odd 4 576.4.k.a.433.3 10
24.5 odd 2 128.4.e.b.33.2 10
24.11 even 2 128.4.e.a.33.4 10
48.5 odd 4 16.4.e.a.5.4 10
48.11 even 4 64.4.e.a.49.2 10
48.29 odd 4 128.4.e.b.97.2 10
48.35 even 4 128.4.e.a.97.4 10
96.5 odd 8 1024.4.a.n.1.4 10
96.11 even 8 1024.4.a.m.1.4 10
96.29 odd 8 1024.4.b.j.513.7 10
96.35 even 8 1024.4.b.k.513.4 10
96.53 odd 8 1024.4.a.n.1.7 10
96.59 even 8 1024.4.a.m.1.7 10
96.77 odd 8 1024.4.b.j.513.4 10
96.83 even 8 1024.4.b.k.513.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.4.e.a.5.4 10 48.5 odd 4
16.4.e.a.13.4 yes 10 3.2 odd 2
64.4.e.a.17.2 10 12.11 even 2
64.4.e.a.49.2 10 48.11 even 4
128.4.e.a.33.4 10 24.11 even 2
128.4.e.a.97.4 10 48.35 even 4
128.4.e.b.33.2 10 24.5 odd 2
128.4.e.b.97.2 10 48.29 odd 4
144.4.k.a.37.2 10 16.5 even 4 inner
144.4.k.a.109.2 10 1.1 even 1 trivial
576.4.k.a.145.3 10 4.3 odd 2
576.4.k.a.433.3 10 16.11 odd 4
1024.4.a.m.1.4 10 96.11 even 8
1024.4.a.m.1.7 10 96.59 even 8
1024.4.a.n.1.4 10 96.5 odd 8
1024.4.a.n.1.7 10 96.53 odd 8
1024.4.b.j.513.4 10 96.77 odd 8
1024.4.b.j.513.7 10 96.29 odd 8
1024.4.b.k.513.4 10 96.35 even 8
1024.4.b.k.513.7 10 96.83 even 8