Properties

Label 100.4.e.f.7.5
Level $100$
Weight $4$
Character 100.7
Analytic conductor $5.900$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [100,4,Mod(7,100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(100, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("100.7");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 100.e (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: \(5.90019100057\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.5
Character \(\chi\) \(=\) 100.7
Dual form 100.4.e.f.43.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.52596 + 2.38148i) q^{2} +(-0.243692 - 0.243692i) q^{3} +(-3.34287 - 7.26809i) q^{4} +(0.952213 - 0.208482i) q^{6} +(-9.53656 + 9.53656i) q^{7} +(22.4099 + 3.12986i) q^{8} -26.8812i q^{9} +O(q^{10})\) \(q+(-1.52596 + 2.38148i) q^{2} +(-0.243692 - 0.243692i) q^{3} +(-3.34287 - 7.26809i) q^{4} +(0.952213 - 0.208482i) q^{6} +(-9.53656 + 9.53656i) q^{7} +(22.4099 + 3.12986i) q^{8} -26.8812i q^{9} -42.2652i q^{11} +(-0.956545 + 2.58581i) q^{12} +(41.7119 - 41.7119i) q^{13} +(-8.15866 - 37.2635i) q^{14} +(-41.6504 + 48.5926i) q^{16} +(34.1474 + 34.1474i) q^{17} +(64.0170 + 41.0198i) q^{18} +130.653 q^{19} +4.64797 q^{21} +(100.654 + 64.4951i) q^{22} +(-107.427 - 107.427i) q^{23} +(-4.69839 - 6.22384i) q^{24} +(35.6852 + 162.987i) q^{26} +(-13.1304 + 13.1304i) q^{27} +(101.192 + 37.4331i) q^{28} +80.4104i q^{29} -273.244i q^{31} +(-52.1653 - 173.340i) q^{32} +(-10.2997 + 10.2997i) q^{33} +(-133.429 + 29.2136i) q^{34} +(-195.375 + 89.8605i) q^{36} +(-134.502 - 134.502i) q^{37} +(-199.371 + 311.147i) q^{38} -20.3297 q^{39} +155.583 q^{41} +(-7.09263 + 11.0690i) q^{42} +(-223.543 - 223.543i) q^{43} +(-307.187 + 141.287i) q^{44} +(419.765 - 91.9055i) q^{46} +(-72.1171 + 72.1171i) q^{47} +(21.9915 - 1.69177i) q^{48} +161.108i q^{49} -16.6429i q^{51} +(-442.604 - 163.728i) q^{52} +(-305.746 + 305.746i) q^{53} +(-11.2333 - 51.3064i) q^{54} +(-243.561 + 183.865i) q^{56} +(-31.8391 - 31.8391i) q^{57} +(-191.496 - 122.703i) q^{58} -177.142 q^{59} -41.4688 q^{61} +(650.725 + 416.960i) q^{62} +(256.354 + 256.354i) q^{63} +(492.408 + 140.280i) q^{64} +(-8.81153 - 40.2454i) q^{66} +(261.744 - 261.744i) q^{67} +(134.036 - 362.337i) q^{68} +52.3583i q^{69} +741.456i q^{71} +(84.1346 - 602.406i) q^{72} +(516.828 - 516.828i) q^{73} +(525.557 - 115.068i) q^{74} +(-436.756 - 949.597i) q^{76} +(403.064 + 403.064i) q^{77} +(31.0224 - 48.4148i) q^{78} +222.727 q^{79} -719.394 q^{81} +(-237.414 + 370.518i) q^{82} +(824.724 + 824.724i) q^{83} +(-15.5376 - 33.7819i) q^{84} +(873.480 - 191.244i) q^{86} +(19.5954 - 19.5954i) q^{87} +(132.284 - 947.158i) q^{88} -1447.03i q^{89} +795.576i q^{91} +(-421.675 + 1139.91i) q^{92} +(-66.5874 + 66.5874i) q^{93} +(-61.6973 - 281.793i) q^{94} +(-29.5293 + 54.9539i) q^{96} +(196.252 + 196.252i) q^{97} +(-383.676 - 245.845i) q^{98} -1136.14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 36 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 36 q^{6} - 676 q^{16} + 512 q^{21} + 2072 q^{26} - 4600 q^{36} - 392 q^{41} + 5016 q^{46} - 8224 q^{56} + 1088 q^{61} + 11140 q^{66} - 6700 q^{76} - 2424 q^{81} + 5216 q^{86} + 796 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(77\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.52596 + 2.38148i −0.539509 + 0.841980i
\(3\) −0.243692 0.243692i −0.0468986 0.0468986i 0.683269 0.730167i \(-0.260558\pi\)
−0.730167 + 0.683269i \(0.760558\pi\)
\(4\) −3.34287 7.26809i −0.417859 0.908512i
\(5\) 0 0
\(6\) 0.952213 0.208482i 0.0647899 0.0141854i
\(7\) −9.53656 + 9.53656i −0.514926 + 0.514926i −0.916032 0.401106i \(-0.868626\pi\)
0.401106 + 0.916032i \(0.368626\pi\)
\(8\) 22.4099 + 3.12986i 0.990387 + 0.138322i
\(9\) 26.8812i 0.995601i
\(10\) 0 0
\(11\) 42.2652i 1.15849i −0.815152 0.579247i \(-0.803347\pi\)
0.815152 0.579247i \(-0.196653\pi\)
\(12\) −0.956545 + 2.58581i −0.0230109 + 0.0622049i
\(13\) 41.7119 41.7119i 0.889908 0.889908i −0.104606 0.994514i \(-0.533358\pi\)
0.994514 + 0.104606i \(0.0333582\pi\)
\(14\) −8.15866 37.2635i −0.155750 0.711364i
\(15\) 0 0
\(16\) −41.6504 + 48.5926i −0.650787 + 0.759260i
\(17\) 34.1474 + 34.1474i 0.487174 + 0.487174i 0.907413 0.420239i \(-0.138054\pi\)
−0.420239 + 0.907413i \(0.638054\pi\)
\(18\) 64.0170 + 41.0198i 0.838276 + 0.537136i
\(19\) 130.653 1.57757 0.788784 0.614670i \(-0.210711\pi\)
0.788784 + 0.614670i \(0.210711\pi\)
\(20\) 0 0
\(21\) 4.64797 0.0482986
\(22\) 100.654 + 64.4951i 0.975428 + 0.625018i
\(23\) −107.427 107.427i −0.973918 0.973918i 0.0257506 0.999668i \(-0.491802\pi\)
−0.999668 + 0.0257506i \(0.991802\pi\)
\(24\) −4.69839 6.22384i −0.0399607 0.0529348i
\(25\) 0 0
\(26\) 35.6852 + 162.987i 0.269171 + 1.22940i
\(27\) −13.1304 + 13.1304i −0.0935908 + 0.0935908i
\(28\) 101.192 + 37.4331i 0.682982 + 0.252650i
\(29\) 80.4104i 0.514891i 0.966293 + 0.257446i \(0.0828808\pi\)
−0.966293 + 0.257446i \(0.917119\pi\)
\(30\) 0 0
\(31\) 273.244i 1.58310i −0.611105 0.791550i \(-0.709275\pi\)
0.611105 0.791550i \(-0.290725\pi\)
\(32\) −52.1653 173.340i −0.288175 0.957578i
\(33\) −10.2997 + 10.2997i −0.0543317 + 0.0543317i
\(34\) −133.429 + 29.2136i −0.673026 + 0.147356i
\(35\) 0 0
\(36\) −195.375 + 89.8605i −0.904515 + 0.416021i
\(37\) −134.502 134.502i −0.597620 0.597620i 0.342059 0.939679i \(-0.388876\pi\)
−0.939679 + 0.342059i \(0.888876\pi\)
\(38\) −199.371 + 311.147i −0.851113 + 1.32828i
\(39\) −20.3297 −0.0834708
\(40\) 0 0
\(41\) 155.583 0.592635 0.296317 0.955090i \(-0.404241\pi\)
0.296317 + 0.955090i \(0.404241\pi\)
\(42\) −7.09263 + 11.0690i −0.0260575 + 0.0406664i
\(43\) −223.543 223.543i −0.792789 0.792789i 0.189157 0.981947i \(-0.439424\pi\)
−0.981947 + 0.189157i \(0.939424\pi\)
\(44\) −307.187 + 141.287i −1.05250 + 0.484087i
\(45\) 0 0
\(46\) 419.765 91.9055i 1.34546 0.294581i
\(47\) −72.1171 + 72.1171i −0.223816 + 0.223816i −0.810103 0.586287i \(-0.800589\pi\)
0.586287 + 0.810103i \(0.300589\pi\)
\(48\) 21.9915 1.69177i 0.0661292 0.00508721i
\(49\) 161.108i 0.469703i
\(50\) 0 0
\(51\) 16.6429i 0.0456955i
\(52\) −442.604 163.728i −1.18035 0.436636i
\(53\) −305.746 + 305.746i −0.792403 + 0.792403i −0.981884 0.189481i \(-0.939319\pi\)
0.189481 + 0.981884i \(0.439319\pi\)
\(54\) −11.2333 51.3064i −0.0283084 0.129295i
\(55\) 0 0
\(56\) −243.561 + 183.865i −0.581201 + 0.438750i
\(57\) −31.8391 31.8391i −0.0739857 0.0739857i
\(58\) −191.496 122.703i −0.433528 0.277789i
\(59\) −177.142 −0.390880 −0.195440 0.980716i \(-0.562613\pi\)
−0.195440 + 0.980716i \(0.562613\pi\)
\(60\) 0 0
\(61\) −41.4688 −0.0870416 −0.0435208 0.999053i \(-0.513857\pi\)
−0.0435208 + 0.999053i \(0.513857\pi\)
\(62\) 650.725 + 416.960i 1.33294 + 0.854097i
\(63\) 256.354 + 256.354i 0.512660 + 0.512660i
\(64\) 492.408 + 140.280i 0.961734 + 0.273984i
\(65\) 0 0
\(66\) −8.81153 40.2454i −0.0164337 0.0750586i
\(67\) 261.744 261.744i 0.477271 0.477271i −0.426987 0.904258i \(-0.640425\pi\)
0.904258 + 0.426987i \(0.140425\pi\)
\(68\) 134.036 362.337i 0.239033 0.646174i
\(69\) 52.3583i 0.0913507i
\(70\) 0 0
\(71\) 741.456i 1.23936i 0.784854 + 0.619680i \(0.212738\pi\)
−0.784854 + 0.619680i \(0.787262\pi\)
\(72\) 84.1346 602.406i 0.137713 0.986031i
\(73\) 516.828 516.828i 0.828631 0.828631i −0.158696 0.987327i \(-0.550729\pi\)
0.987327 + 0.158696i \(0.0507290\pi\)
\(74\) 525.557 115.068i 0.825605 0.180762i
\(75\) 0 0
\(76\) −436.756 949.597i −0.659202 1.43324i
\(77\) 403.064 + 403.064i 0.596538 + 0.596538i
\(78\) 31.0224 48.4148i 0.0450333 0.0702807i
\(79\) 222.727 0.317200 0.158600 0.987343i \(-0.449302\pi\)
0.158600 + 0.987343i \(0.449302\pi\)
\(80\) 0 0
\(81\) −719.394 −0.986822
\(82\) −237.414 + 370.518i −0.319732 + 0.498986i
\(83\) 824.724 + 824.724i 1.09066 + 1.09066i 0.995457 + 0.0952072i \(0.0303514\pi\)
0.0952072 + 0.995457i \(0.469649\pi\)
\(84\) −15.5376 33.7819i −0.0201820 0.0438798i
\(85\) 0 0
\(86\) 873.480 191.244i 1.09523 0.239795i
\(87\) 19.5954 19.5954i 0.0241477 0.0241477i
\(88\) 132.284 947.158i 0.160245 1.14736i
\(89\) 1447.03i 1.72342i −0.507400 0.861711i \(-0.669393\pi\)
0.507400 0.861711i \(-0.330607\pi\)
\(90\) 0 0
\(91\) 795.576i 0.916473i
\(92\) −421.675 + 1139.91i −0.477855 + 1.29178i
\(93\) −66.5874 + 66.5874i −0.0742451 + 0.0742451i
\(94\) −61.6973 281.793i −0.0676977 0.309200i
\(95\) 0 0
\(96\) −29.5293 + 54.9539i −0.0313940 + 0.0584240i
\(97\) 196.252 + 196.252i 0.205426 + 0.205426i 0.802320 0.596894i \(-0.203599\pi\)
−0.596894 + 0.802320i \(0.703599\pi\)
\(98\) −383.676 245.845i −0.395481 0.253409i
\(99\) −1136.14 −1.15340
\(100\) 0 0
\(101\) 594.739 0.585928 0.292964 0.956123i \(-0.405358\pi\)
0.292964 + 0.956123i \(0.405358\pi\)
\(102\) 39.6347 + 25.3965i 0.0384747 + 0.0246532i
\(103\) 499.830 + 499.830i 0.478153 + 0.478153i 0.904540 0.426388i \(-0.140214\pi\)
−0.426388 + 0.904540i \(0.640214\pi\)
\(104\) 1065.31 804.207i 1.00445 0.758260i
\(105\) 0 0
\(106\) −261.570 1194.68i −0.239678 1.09470i
\(107\) −716.517 + 716.517i −0.647367 + 0.647367i −0.952356 0.304989i \(-0.901347\pi\)
0.304989 + 0.952356i \(0.401347\pi\)
\(108\) 139.327 + 51.5398i 0.124136 + 0.0459206i
\(109\) 680.181i 0.597702i 0.954300 + 0.298851i \(0.0966034\pi\)
−0.954300 + 0.298851i \(0.903397\pi\)
\(110\) 0 0
\(111\) 65.5540i 0.0560550i
\(112\) −66.2051 860.608i −0.0558553 0.726070i
\(113\) 30.3535 30.3535i 0.0252692 0.0252692i −0.694359 0.719629i \(-0.744312\pi\)
0.719629 + 0.694359i \(0.244312\pi\)
\(114\) 124.409 27.2388i 0.102210 0.0223785i
\(115\) 0 0
\(116\) 584.431 268.802i 0.467785 0.215152i
\(117\) −1121.27 1121.27i −0.885993 0.885993i
\(118\) 270.312 421.859i 0.210883 0.329113i
\(119\) −651.297 −0.501717
\(120\) 0 0
\(121\) −455.344 −0.342107
\(122\) 63.2799 98.7571i 0.0469598 0.0732872i
\(123\) −37.9144 37.9144i −0.0277937 0.0277937i
\(124\) −1985.96 + 913.420i −1.43826 + 0.661513i
\(125\) 0 0
\(126\) −1001.69 + 219.315i −0.708235 + 0.155064i
\(127\) 1252.53 1252.53i 0.875147 0.875147i −0.117880 0.993028i \(-0.537610\pi\)
0.993028 + 0.117880i \(0.0376100\pi\)
\(128\) −1085.47 + 958.596i −0.749554 + 0.661943i
\(129\) 108.951i 0.0743614i
\(130\) 0 0
\(131\) 262.746i 0.175238i −0.996154 0.0876192i \(-0.972074\pi\)
0.996154 0.0876192i \(-0.0279259\pi\)
\(132\) 109.290 + 40.4285i 0.0720640 + 0.0266580i
\(133\) −1245.98 + 1245.98i −0.812331 + 0.812331i
\(134\) 223.926 + 1022.75i 0.144360 + 0.659345i
\(135\) 0 0
\(136\) 658.363 + 872.117i 0.415104 + 0.549878i
\(137\) 1252.60 + 1252.60i 0.781146 + 0.781146i 0.980024 0.198878i \(-0.0637298\pi\)
−0.198878 + 0.980024i \(0.563730\pi\)
\(138\) −124.690 79.8968i −0.0769154 0.0492846i
\(139\) 2028.30 1.23768 0.618842 0.785516i \(-0.287602\pi\)
0.618842 + 0.785516i \(0.287602\pi\)
\(140\) 0 0
\(141\) 35.1487 0.0209933
\(142\) −1765.76 1131.43i −1.04352 0.668647i
\(143\) −1762.96 1762.96i −1.03095 1.03095i
\(144\) 1306.23 + 1119.61i 0.755920 + 0.647925i
\(145\) 0 0
\(146\) 442.154 + 2019.47i 0.250636 + 1.14475i
\(147\) 39.2608 39.2608i 0.0220284 0.0220284i
\(148\) −527.948 + 1427.19i −0.293224 + 0.792665i
\(149\) 2992.83i 1.64552i 0.568392 + 0.822758i \(0.307566\pi\)
−0.568392 + 0.822758i \(0.692434\pi\)
\(150\) 0 0
\(151\) 184.103i 0.0992192i −0.998769 0.0496096i \(-0.984202\pi\)
0.998769 0.0496096i \(-0.0157977\pi\)
\(152\) 2927.92 + 408.926i 1.56240 + 0.218212i
\(153\) 917.924 917.924i 0.485031 0.485031i
\(154\) −1574.95 + 344.827i −0.824110 + 0.180435i
\(155\) 0 0
\(156\) 67.9597 + 147.758i 0.0348790 + 0.0758342i
\(157\) −1301.36 1301.36i −0.661530 0.661530i 0.294211 0.955741i \(-0.404943\pi\)
−0.955741 + 0.294211i \(0.904943\pi\)
\(158\) −339.874 + 530.420i −0.171132 + 0.267076i
\(159\) 149.016 0.0743252
\(160\) 0 0
\(161\) 2048.97 1.00299
\(162\) 1097.77 1713.22i 0.532400 0.830884i
\(163\) −1460.57 1460.57i −0.701843 0.701843i 0.262963 0.964806i \(-0.415300\pi\)
−0.964806 + 0.262963i \(0.915300\pi\)
\(164\) −520.095 1130.79i −0.247638 0.538416i
\(165\) 0 0
\(166\) −3222.56 + 705.563i −1.50674 + 0.329894i
\(167\) −1656.63 + 1656.63i −0.767626 + 0.767626i −0.977688 0.210062i \(-0.932633\pi\)
0.210062 + 0.977688i \(0.432633\pi\)
\(168\) 104.161 + 14.5475i 0.0478343 + 0.00668074i
\(169\) 1282.77i 0.583872i
\(170\) 0 0
\(171\) 3512.11i 1.57063i
\(172\) −877.455 + 2372.00i −0.388984 + 1.05153i
\(173\) −1601.81 + 1601.81i −0.703952 + 0.703952i −0.965256 0.261304i \(-0.915847\pi\)
0.261304 + 0.965256i \(0.415847\pi\)
\(174\) 16.7641 + 76.5678i 0.00730395 + 0.0333597i
\(175\) 0 0
\(176\) 2053.78 + 1760.36i 0.879598 + 0.753933i
\(177\) 43.1681 + 43.1681i 0.0183317 + 0.0183317i
\(178\) 3446.06 + 2208.11i 1.45109 + 0.929802i
\(179\) 37.6748 0.0157316 0.00786578 0.999969i \(-0.497496\pi\)
0.00786578 + 0.999969i \(0.497496\pi\)
\(180\) 0 0
\(181\) −1360.64 −0.558762 −0.279381 0.960180i \(-0.590129\pi\)
−0.279381 + 0.960180i \(0.590129\pi\)
\(182\) −1894.65 1214.02i −0.771651 0.494446i
\(183\) 10.1056 + 10.1056i 0.00408213 + 0.00408213i
\(184\) −2071.20 2743.66i −0.829842 1.09927i
\(185\) 0 0
\(186\) −56.9665 260.186i −0.0224569 0.102569i
\(187\) 1443.24 1443.24i 0.564388 0.564388i
\(188\) 765.232 + 283.076i 0.296863 + 0.109816i
\(189\) 250.438i 0.0963846i
\(190\) 0 0
\(191\) 3587.14i 1.35893i −0.733706 0.679467i \(-0.762211\pi\)
0.733706 0.679467i \(-0.237789\pi\)
\(192\) −85.8108 154.181i −0.0322545 0.0579534i
\(193\) 3631.68 3631.68i 1.35448 1.35448i 0.473894 0.880582i \(-0.342848\pi\)
0.880582 0.473894i \(-0.157152\pi\)
\(194\) −766.843 + 167.896i −0.283794 + 0.0621354i
\(195\) 0 0
\(196\) 1170.95 538.564i 0.426731 0.196270i
\(197\) −235.786 235.786i −0.0852746 0.0852746i 0.663183 0.748457i \(-0.269205\pi\)
−0.748457 + 0.663183i \(0.769205\pi\)
\(198\) 1733.71 2705.69i 0.622269 0.971137i
\(199\) 2893.75 1.03081 0.515407 0.856945i \(-0.327641\pi\)
0.515407 + 0.856945i \(0.327641\pi\)
\(200\) 0 0
\(201\) −127.570 −0.0447667
\(202\) −907.550 + 1416.36i −0.316114 + 0.493340i
\(203\) −766.838 766.838i −0.265131 0.265131i
\(204\) −120.962 + 55.6351i −0.0415149 + 0.0190943i
\(205\) 0 0
\(206\) −1953.06 + 427.612i −0.660563 + 0.144627i
\(207\) −2887.77 + 2887.77i −0.969634 + 0.969634i
\(208\) 289.574 + 3764.21i 0.0965306 + 1.25481i
\(209\) 5522.06i 1.82760i
\(210\) 0 0
\(211\) 2956.45i 0.964599i 0.876006 + 0.482300i \(0.160198\pi\)
−0.876006 + 0.482300i \(0.839802\pi\)
\(212\) 3244.26 + 1200.12i 1.05102 + 0.388795i
\(213\) 180.687 180.687i 0.0581242 0.0581242i
\(214\) −612.991 2799.75i −0.195809 0.894331i
\(215\) 0 0
\(216\) −335.348 + 253.155i −0.105637 + 0.0797455i
\(217\) 2605.81 + 2605.81i 0.815178 + 0.815178i
\(218\) −1619.84 1037.93i −0.503253 0.322466i
\(219\) −251.894 −0.0777233
\(220\) 0 0
\(221\) 2848.71 0.867080
\(222\) −156.115 100.033i −0.0471972 0.0302422i
\(223\) 1581.62 + 1581.62i 0.474946 + 0.474946i 0.903511 0.428565i \(-0.140981\pi\)
−0.428565 + 0.903511i \(0.640981\pi\)
\(224\) 2150.54 + 1155.59i 0.641470 + 0.344692i
\(225\) 0 0
\(226\) 25.9679 + 118.605i 0.00764318 + 0.0349091i
\(227\) −668.464 + 668.464i −0.195452 + 0.195452i −0.798047 0.602595i \(-0.794133\pi\)
0.602595 + 0.798047i \(0.294133\pi\)
\(228\) −124.975 + 337.843i −0.0363013 + 0.0981325i
\(229\) 3515.88i 1.01457i 0.861779 + 0.507284i \(0.169350\pi\)
−0.861779 + 0.507284i \(0.830650\pi\)
\(230\) 0 0
\(231\) 196.447i 0.0559535i
\(232\) −251.674 + 1801.99i −0.0712206 + 0.509942i
\(233\) 1658.86 1658.86i 0.466420 0.466420i −0.434333 0.900752i \(-0.643016\pi\)
0.900752 + 0.434333i \(0.143016\pi\)
\(234\) 4381.29 959.261i 1.22399 0.267986i
\(235\) 0 0
\(236\) 592.163 + 1287.48i 0.163333 + 0.355119i
\(237\) −54.2769 54.2769i −0.0148762 0.0148762i
\(238\) 993.855 1551.05i 0.270681 0.422435i
\(239\) −1712.05 −0.463360 −0.231680 0.972792i \(-0.574422\pi\)
−0.231680 + 0.972792i \(0.574422\pi\)
\(240\) 0 0
\(241\) −5796.70 −1.54937 −0.774685 0.632348i \(-0.782091\pi\)
−0.774685 + 0.632348i \(0.782091\pi\)
\(242\) 694.838 1084.39i 0.184570 0.288047i
\(243\) 529.832 + 529.832i 0.139871 + 0.139871i
\(244\) 138.625 + 301.399i 0.0363711 + 0.0790783i
\(245\) 0 0
\(246\) 148.148 32.4364i 0.0383967 0.00840677i
\(247\) 5449.78 5449.78i 1.40389 1.40389i
\(248\) 855.217 6123.37i 0.218977 1.56788i
\(249\) 401.957i 0.102301i
\(250\) 0 0
\(251\) 2040.48i 0.513123i 0.966528 + 0.256562i \(0.0825897\pi\)
−0.966528 + 0.256562i \(0.917410\pi\)
\(252\) 1006.25 2720.17i 0.251538 0.679978i
\(253\) −4540.43 + 4540.43i −1.12828 + 1.12828i
\(254\) 1071.55 + 4894.17i 0.264706 + 1.20901i
\(255\) 0 0
\(256\) −626.489 4047.81i −0.152952 0.988234i
\(257\) −757.135 757.135i −0.183770 0.183770i 0.609227 0.792996i \(-0.291480\pi\)
−0.792996 + 0.609227i \(0.791480\pi\)
\(258\) −259.465 166.256i −0.0626108 0.0401187i
\(259\) 2565.36 0.615459
\(260\) 0 0
\(261\) 2161.53 0.512626
\(262\) 625.724 + 400.941i 0.147547 + 0.0945428i
\(263\) 1842.73 + 1842.73i 0.432045 + 0.432045i 0.889323 0.457279i \(-0.151176\pi\)
−0.457279 + 0.889323i \(0.651176\pi\)
\(264\) −263.052 + 198.578i −0.0613247 + 0.0462942i
\(265\) 0 0
\(266\) −1065.95 4868.58i −0.245706 1.12223i
\(267\) −352.629 + 352.629i −0.0808260 + 0.0808260i
\(268\) −2777.36 1027.40i −0.633039 0.234174i
\(269\) 4651.65i 1.05433i 0.849762 + 0.527167i \(0.176746\pi\)
−0.849762 + 0.527167i \(0.823254\pi\)
\(270\) 0 0
\(271\) 8533.48i 1.91281i 0.292040 + 0.956406i \(0.405666\pi\)
−0.292040 + 0.956406i \(0.594334\pi\)
\(272\) −3081.56 + 237.060i −0.686939 + 0.0528450i
\(273\) 193.876 193.876i 0.0429813 0.0429813i
\(274\) −4894.47 + 1071.62i −1.07914 + 0.236273i
\(275\) 0 0
\(276\) 380.545 175.027i 0.0829932 0.0381717i
\(277\) −1883.72 1883.72i −0.408598 0.408598i 0.472652 0.881249i \(-0.343297\pi\)
−0.881249 + 0.472652i \(0.843297\pi\)
\(278\) −3095.11 + 4830.35i −0.667742 + 1.04210i
\(279\) −7345.13 −1.57614
\(280\) 0 0
\(281\) −1365.56 −0.289902 −0.144951 0.989439i \(-0.546303\pi\)
−0.144951 + 0.989439i \(0.546303\pi\)
\(282\) −53.6357 + 83.7060i −0.0113261 + 0.0176759i
\(283\) 2275.91 + 2275.91i 0.478052 + 0.478052i 0.904508 0.426456i \(-0.140238\pi\)
−0.426456 + 0.904508i \(0.640238\pi\)
\(284\) 5388.97 2478.59i 1.12597 0.517878i
\(285\) 0 0
\(286\) 6888.66 1508.24i 1.42425 0.311832i
\(287\) −1483.73 + 1483.73i −0.305163 + 0.305163i
\(288\) −4659.59 + 1402.27i −0.953365 + 0.286908i
\(289\) 2580.91i 0.525323i
\(290\) 0 0
\(291\) 95.6501i 0.0192684i
\(292\) −5484.04 2028.66i −1.09907 0.406570i
\(293\) −2859.58 + 2859.58i −0.570165 + 0.570165i −0.932175 0.362009i \(-0.882091\pi\)
0.362009 + 0.932175i \(0.382091\pi\)
\(294\) 33.5882 + 153.409i 0.00666294 + 0.0304320i
\(295\) 0 0
\(296\) −2593.20 3435.14i −0.509211 0.674539i
\(297\) 554.960 + 554.960i 0.108424 + 0.108424i
\(298\) −7127.35 4566.94i −1.38549 0.887771i
\(299\) −8961.98 −1.73339
\(300\) 0 0
\(301\) 4263.66 0.816455
\(302\) 438.437 + 280.935i 0.0835405 + 0.0535297i
\(303\) −144.933 144.933i −0.0274792 0.0274792i
\(304\) −5441.74 + 6348.76i −1.02666 + 1.19778i
\(305\) 0 0
\(306\) 785.297 + 3586.73i 0.146707 + 0.670065i
\(307\) −528.300 + 528.300i −0.0982139 + 0.0982139i −0.754507 0.656293i \(-0.772124\pi\)
0.656293 + 0.754507i \(0.272124\pi\)
\(308\) 1582.12 4276.90i 0.292693 0.791230i
\(309\) 243.609i 0.0448494i
\(310\) 0 0
\(311\) 395.402i 0.0720938i 0.999350 + 0.0360469i \(0.0114766\pi\)
−0.999350 + 0.0360469i \(0.988523\pi\)
\(312\) −455.587 63.6293i −0.0826684 0.0115458i
\(313\) −804.658 + 804.658i −0.145310 + 0.145310i −0.776019 0.630709i \(-0.782764\pi\)
0.630709 + 0.776019i \(0.282764\pi\)
\(314\) 5085.00 1113.34i 0.913896 0.200093i
\(315\) 0 0
\(316\) −744.549 1618.80i −0.132545 0.288180i
\(317\) −3696.00 3696.00i −0.654852 0.654852i 0.299305 0.954157i \(-0.403245\pi\)
−0.954157 + 0.299305i \(0.903245\pi\)
\(318\) −227.392 + 354.877i −0.0400991 + 0.0625803i
\(319\) 3398.56 0.596498
\(320\) 0 0
\(321\) 349.219 0.0607212
\(322\) −3126.65 + 4879.58i −0.541123 + 0.844497i
\(323\) 4461.45 + 4461.45i 0.768551 + 0.768551i
\(324\) 2404.84 + 5228.62i 0.412353 + 0.896540i
\(325\) 0 0
\(326\) 5707.08 1249.54i 0.969588 0.212287i
\(327\) 165.755 165.755i 0.0280314 0.0280314i
\(328\) 3486.61 + 486.955i 0.586938 + 0.0819743i
\(329\) 1375.50i 0.230497i
\(330\) 0 0
\(331\) 1388.78i 0.230617i 0.993330 + 0.115308i \(0.0367856\pi\)
−0.993330 + 0.115308i \(0.963214\pi\)
\(332\) 3237.22 8751.11i 0.535137 1.44663i
\(333\) −3615.57 + 3615.57i −0.594991 + 0.594991i
\(334\) −1417.27 6473.17i −0.232184 1.06047i
\(335\) 0 0
\(336\) −193.590 + 225.857i −0.0314321 + 0.0366712i
\(337\) 2766.70 + 2766.70i 0.447216 + 0.447216i 0.894428 0.447212i \(-0.147583\pi\)
−0.447212 + 0.894428i \(0.647583\pi\)
\(338\) 3054.88 + 1957.45i 0.491608 + 0.315004i
\(339\) −14.7938 −0.00237018
\(340\) 0 0
\(341\) −11548.7 −1.83401
\(342\) 8364.01 + 5359.35i 1.32244 + 0.847369i
\(343\) −4807.46 4807.46i −0.756788 0.756788i
\(344\) −4309.91 5709.23i −0.675509 0.894829i
\(345\) 0 0
\(346\) −1370.38 6259.00i −0.212925 0.972502i
\(347\) 2069.91 2069.91i 0.320227 0.320227i −0.528627 0.848854i \(-0.677293\pi\)
0.848854 + 0.528627i \(0.177293\pi\)
\(348\) −207.926 76.9162i −0.0320288 0.0118481i
\(349\) 5774.64i 0.885700i 0.896596 + 0.442850i \(0.146033\pi\)
−0.896596 + 0.442850i \(0.853967\pi\)
\(350\) 0 0
\(351\) 1095.39i 0.166574i
\(352\) −7326.25 + 2204.78i −1.10935 + 0.333849i
\(353\) 7965.11 7965.11i 1.20096 1.20096i 0.227089 0.973874i \(-0.427079\pi\)
0.973874 0.227089i \(-0.0729208\pi\)
\(354\) −168.677 + 36.9309i −0.0253250 + 0.00554479i
\(355\) 0 0
\(356\) −10517.1 + 4837.23i −1.56575 + 0.720148i
\(357\) 158.716 + 158.716i 0.0235298 + 0.0235298i
\(358\) −57.4904 + 89.7218i −0.00848733 + 0.0132457i
\(359\) 6227.61 0.915545 0.457773 0.889069i \(-0.348647\pi\)
0.457773 + 0.889069i \(0.348647\pi\)
\(360\) 0 0
\(361\) 10211.2 1.48872
\(362\) 2076.29 3240.35i 0.301457 0.470466i
\(363\) 110.964 + 110.964i 0.0160443 + 0.0160443i
\(364\) 5782.32 2659.51i 0.832626 0.382956i
\(365\) 0 0
\(366\) −39.4871 + 8.64551i −0.00563941 + 0.00123472i
\(367\) 3426.52 3426.52i 0.487365 0.487365i −0.420109 0.907474i \(-0.638008\pi\)
0.907474 + 0.420109i \(0.138008\pi\)
\(368\) 9694.55 745.786i 1.37327 0.105643i
\(369\) 4182.27i 0.590028i
\(370\) 0 0
\(371\) 5831.52i 0.816058i
\(372\) 706.557 + 261.370i 0.0984765 + 0.0364285i
\(373\) 4631.53 4631.53i 0.642926 0.642926i −0.308347 0.951274i \(-0.599776\pi\)
0.951274 + 0.308347i \(0.0997759\pi\)
\(374\) 1234.72 + 5639.39i 0.170710 + 0.779696i
\(375\) 0 0
\(376\) −1841.85 + 1390.42i −0.252623 + 0.190706i
\(377\) 3354.07 + 3354.07i 0.458206 + 0.458206i
\(378\) 596.413 + 382.159i 0.0811539 + 0.0520004i
\(379\) 10644.7 1.44269 0.721347 0.692574i \(-0.243523\pi\)
0.721347 + 0.692574i \(0.243523\pi\)
\(380\) 0 0
\(381\) −610.461 −0.0820863
\(382\) 8542.70 + 5473.85i 1.14419 + 0.733158i
\(383\) 2301.02 + 2301.02i 0.306988 + 0.306988i 0.843740 0.536752i \(-0.180349\pi\)
−0.536752 + 0.843740i \(0.680349\pi\)
\(384\) 498.123 + 30.9180i 0.0661972 + 0.00410880i
\(385\) 0 0
\(386\) 3106.95 + 14190.6i 0.409688 + 1.87119i
\(387\) −6009.10 + 6009.10i −0.789302 + 0.789302i
\(388\) 770.332 2082.42i 0.100793 0.272472i
\(389\) 5636.87i 0.734706i −0.930082 0.367353i \(-0.880264\pi\)
0.930082 0.367353i \(-0.119736\pi\)
\(390\) 0 0
\(391\) 7336.71i 0.948935i
\(392\) −504.247 + 3610.42i −0.0649702 + 0.465188i
\(393\) −64.0291 + 64.0291i −0.00821843 + 0.00821843i
\(394\) 921.322 201.719i 0.117806 0.0257930i
\(395\) 0 0
\(396\) 3797.97 + 8257.57i 0.481958 + 1.04787i
\(397\) 6539.04 + 6539.04i 0.826663 + 0.826663i 0.987054 0.160391i \(-0.0512754\pi\)
−0.160391 + 0.987054i \(0.551275\pi\)
\(398\) −4415.75 + 6891.39i −0.556134 + 0.867925i
\(399\) 607.270 0.0761943
\(400\) 0 0
\(401\) −5980.28 −0.744740 −0.372370 0.928084i \(-0.621455\pi\)
−0.372370 + 0.928084i \(0.621455\pi\)
\(402\) 194.667 303.805i 0.0241521 0.0376926i
\(403\) −11397.5 11397.5i −1.40881 1.40881i
\(404\) −1988.14 4322.62i −0.244835 0.532323i
\(405\) 0 0
\(406\) 2996.38 656.042i 0.366275 0.0801941i
\(407\) −5684.73 + 5684.73i −0.692338 + 0.692338i
\(408\) 52.0900 372.966i 0.00632069 0.0452563i
\(409\) 5150.66i 0.622698i −0.950296 0.311349i \(-0.899219\pi\)
0.950296 0.311349i \(-0.100781\pi\)
\(410\) 0 0
\(411\) 610.499i 0.0732693i
\(412\) 1961.94 5303.68i 0.234607 0.634208i
\(413\) 1689.32 1689.32i 0.201274 0.201274i
\(414\) −2470.53 11283.8i −0.293285 1.33954i
\(415\) 0 0
\(416\) −9406.26 5054.43i −1.10861 0.595706i
\(417\) −494.280 494.280i −0.0580456 0.0580456i
\(418\) 13150.7 + 8426.46i 1.53880 + 0.986009i
\(419\) −3080.65 −0.359188 −0.179594 0.983741i \(-0.557478\pi\)
−0.179594 + 0.983741i \(0.557478\pi\)
\(420\) 0 0
\(421\) 5636.62 0.652523 0.326261 0.945280i \(-0.394211\pi\)
0.326261 + 0.945280i \(0.394211\pi\)
\(422\) −7040.72 4511.43i −0.812173 0.520410i
\(423\) 1938.60 + 1938.60i 0.222832 + 0.222832i
\(424\) −7808.67 + 5894.79i −0.894393 + 0.675180i
\(425\) 0 0
\(426\) 154.580 + 706.023i 0.0175808 + 0.0802980i
\(427\) 395.470 395.470i 0.0448199 0.0448199i
\(428\) 7602.94 + 2812.49i 0.858649 + 0.317632i
\(429\) 859.239i 0.0967004i
\(430\) 0 0
\(431\) 12970.7i 1.44959i −0.688963 0.724797i \(-0.741934\pi\)
0.688963 0.724797i \(-0.258066\pi\)
\(432\) −91.1547 1184.93i −0.0101520 0.131968i
\(433\) −181.752 + 181.752i −0.0201719 + 0.0201719i −0.717121 0.696949i \(-0.754540\pi\)
0.696949 + 0.717121i \(0.254540\pi\)
\(434\) −10182.0 + 2229.31i −1.12616 + 0.246567i
\(435\) 0 0
\(436\) 4943.62 2273.76i 0.543020 0.249755i
\(437\) −14035.7 14035.7i −1.53642 1.53642i
\(438\) 384.380 599.879i 0.0419324 0.0654414i
\(439\) 5465.06 0.594153 0.297076 0.954854i \(-0.403988\pi\)
0.297076 + 0.954854i \(0.403988\pi\)
\(440\) 0 0
\(441\) 4330.79 0.467637
\(442\) −4347.02 + 6784.13i −0.467798 + 0.730064i
\(443\) −4982.88 4982.88i −0.534410 0.534410i 0.387472 0.921882i \(-0.373349\pi\)
−0.921882 + 0.387472i \(0.873349\pi\)
\(444\) 476.452 219.139i 0.0509266 0.0234231i
\(445\) 0 0
\(446\) −6180.07 + 1353.10i −0.656132 + 0.143657i
\(447\) 729.328 729.328i 0.0771724 0.0771724i
\(448\) −6033.66 + 3358.09i −0.636303 + 0.354140i
\(449\) 11884.7i 1.24916i 0.780960 + 0.624581i \(0.214730\pi\)
−0.780960 + 0.624581i \(0.785270\pi\)
\(450\) 0 0
\(451\) 6575.75i 0.686563i
\(452\) −322.080 119.144i −0.0335164 0.0123984i
\(453\) −44.8645 + 44.8645i −0.00465324 + 0.00465324i
\(454\) −571.881 2611.98i −0.0591183 0.270014i
\(455\) 0 0
\(456\) −613.858 813.162i −0.0630407 0.0835084i
\(457\) −1360.58 1360.58i −0.139267 0.139267i 0.634036 0.773303i \(-0.281397\pi\)
−0.773303 + 0.634036i \(0.781397\pi\)
\(458\) −8372.99 5365.10i −0.854245 0.547369i
\(459\) −896.740 −0.0911901
\(460\) 0 0
\(461\) 8133.56 0.821730 0.410865 0.911696i \(-0.365227\pi\)
0.410865 + 0.911696i \(0.365227\pi\)
\(462\) 467.834 + 299.771i 0.0471117 + 0.0301875i
\(463\) −1938.32 1938.32i −0.194560 0.194560i 0.603103 0.797663i \(-0.293931\pi\)
−0.797663 + 0.603103i \(0.793931\pi\)
\(464\) −3907.35 3349.13i −0.390936 0.335085i
\(465\) 0 0
\(466\) 1419.18 + 6481.91i 0.141078 + 0.644354i
\(467\) 8462.63 8462.63i 0.838552 0.838552i −0.150116 0.988668i \(-0.547965\pi\)
0.988668 + 0.150116i \(0.0479648\pi\)
\(468\) −4401.22 + 11897.7i −0.434715 + 1.17516i
\(469\) 4992.28i 0.491518i
\(470\) 0 0
\(471\) 634.264i 0.0620496i
\(472\) −3969.73 554.430i −0.387122 0.0540671i
\(473\) −9448.07 + 9448.07i −0.918441 + 0.918441i
\(474\) 212.084 46.4347i 0.0205513 0.00449961i
\(475\) 0 0
\(476\) 2177.20 + 4733.69i 0.209647 + 0.455816i
\(477\) 8218.81 + 8218.81i 0.788918 + 0.788918i
\(478\) 2612.52 4077.20i 0.249987 0.390140i
\(479\) −7570.70 −0.722158 −0.361079 0.932535i \(-0.617592\pi\)
−0.361079 + 0.932535i \(0.617592\pi\)
\(480\) 0 0
\(481\) −11220.6 −1.06365
\(482\) 8845.55 13804.7i 0.835899 1.30454i
\(483\) −499.318 499.318i −0.0470388 0.0470388i
\(484\) 1522.16 + 3309.48i 0.142952 + 0.310808i
\(485\) 0 0
\(486\) −2070.29 + 453.279i −0.193231 + 0.0423069i
\(487\) −9502.42 + 9502.42i −0.884181 + 0.884181i −0.993956 0.109776i \(-0.964987\pi\)
0.109776 + 0.993956i \(0.464987\pi\)
\(488\) −929.312 129.792i −0.0862049 0.0120397i
\(489\) 711.857i 0.0658309i
\(490\) 0 0
\(491\) 8188.17i 0.752601i 0.926498 + 0.376300i \(0.122804\pi\)
−0.926498 + 0.376300i \(0.877196\pi\)
\(492\) −148.823 + 402.309i −0.0136371 + 0.0368648i
\(493\) −2745.81 + 2745.81i −0.250842 + 0.250842i
\(494\) 4662.36 + 21294.7i 0.424635 + 1.93946i
\(495\) 0 0
\(496\) 13277.6 + 11380.7i 1.20198 + 1.03026i
\(497\) −7070.93 7070.93i −0.638178 0.638178i
\(498\) 957.252 + 613.372i 0.0861355 + 0.0551925i
\(499\) 429.740 0.0385527 0.0192764 0.999814i \(-0.493864\pi\)
0.0192764 + 0.999814i \(0.493864\pi\)
\(500\) 0 0
\(501\) 807.414 0.0720012
\(502\) −4859.36 3113.70i −0.432039 0.276835i
\(503\) −8511.42 8511.42i −0.754484 0.754484i 0.220829 0.975313i \(-0.429124\pi\)
−0.975313 + 0.220829i \(0.929124\pi\)
\(504\) 4942.52 + 6547.23i 0.436820 + 0.578645i
\(505\) 0 0
\(506\) −3884.40 17741.4i −0.341270 1.55870i
\(507\) −312.600 + 312.600i −0.0273827 + 0.0273827i
\(508\) −13290.5 4916.44i −1.16077 0.429393i
\(509\) 3762.37i 0.327631i −0.986491 0.163816i \(-0.947620\pi\)
0.986491 0.163816i \(-0.0523802\pi\)
\(510\) 0 0
\(511\) 9857.51i 0.853367i
\(512\) 10595.8 + 4684.83i 0.914591 + 0.404379i
\(513\) −1715.53 + 1715.53i −0.147646 + 0.147646i
\(514\) 2958.46 647.740i 0.253876 0.0555848i
\(515\) 0 0
\(516\) 791.868 364.210i 0.0675582 0.0310726i
\(517\) 3048.04 + 3048.04i 0.259290 + 0.259290i
\(518\) −3914.65 + 6109.36i −0.332046 + 0.518204i
\(519\) 780.699 0.0660287
\(520\) 0 0
\(521\) 818.504 0.0688279 0.0344139 0.999408i \(-0.489044\pi\)
0.0344139 + 0.999408i \(0.489044\pi\)
\(522\) −3298.42 + 5147.64i −0.276567 + 0.431621i
\(523\) 14975.1 + 14975.1i 1.25203 + 1.25203i 0.954807 + 0.297227i \(0.0960618\pi\)
0.297227 + 0.954807i \(0.403938\pi\)
\(524\) −1909.66 + 878.327i −0.159206 + 0.0732250i
\(525\) 0 0
\(526\) −7200.37 + 1576.48i −0.596865 + 0.130681i
\(527\) 9330.57 9330.57i 0.771245 0.771245i
\(528\) −71.5030 929.475i −0.00589350 0.0766102i
\(529\) 10914.2i 0.897032i
\(530\) 0 0
\(531\) 4761.79i 0.389160i
\(532\) 13221.0 + 4890.74i 1.07745 + 0.398572i
\(533\) 6489.68 6489.68i 0.527390 0.527390i
\(534\) −301.679 1377.88i −0.0244475 0.111660i
\(535\) 0 0
\(536\) 6684.89 5046.45i 0.538701 0.406666i
\(537\) −9.18106 9.18106i −0.000737788 0.000737788i
\(538\) −11077.8 7098.24i −0.887728 0.568823i
\(539\) 6809.26 0.544148
\(540\) 0 0
\(541\) −1894.75 −0.150576 −0.0752879 0.997162i \(-0.523988\pi\)
−0.0752879 + 0.997162i \(0.523988\pi\)
\(542\) −20322.3 13021.8i −1.61055 1.03198i
\(543\) 331.578 + 331.578i 0.0262051 + 0.0262051i
\(544\) 4137.80 7700.42i 0.326115 0.606899i
\(545\) 0 0
\(546\) 165.863 + 757.557i 0.0130005 + 0.0593781i
\(547\) 8079.10 8079.10i 0.631513 0.631513i −0.316935 0.948447i \(-0.602654\pi\)
0.948447 + 0.316935i \(0.102654\pi\)
\(548\) 4916.74 13291.3i 0.383271 1.03609i
\(549\) 1114.73i 0.0866587i
\(550\) 0 0
\(551\) 10505.8i 0.812276i
\(552\) −163.874 + 1173.34i −0.0126358 + 0.0904726i
\(553\) −2124.05 + 2124.05i −0.163334 + 0.163334i
\(554\) 7360.51 1611.55i 0.564473 0.123589i
\(555\) 0 0
\(556\) −6780.34 14741.9i −0.517177 1.12445i
\(557\) 11900.0 + 11900.0i 0.905243 + 0.905243i 0.995884 0.0906404i \(-0.0288914\pi\)
−0.0906404 + 0.995884i \(0.528891\pi\)
\(558\) 11208.4 17492.3i 0.850340 1.32707i
\(559\) −18648.8 −1.41102
\(560\) 0 0
\(561\) −703.415 −0.0529380
\(562\) 2083.80 3252.06i 0.156405 0.244092i
\(563\) 11749.3 + 11749.3i 0.879526 + 0.879526i 0.993485 0.113959i \(-0.0363533\pi\)
−0.113959 + 0.993485i \(0.536353\pi\)
\(564\) −117.498 255.464i −0.00877225 0.0190727i
\(565\) 0 0
\(566\) −8892.97 + 1947.07i −0.660423 + 0.144596i
\(567\) 6860.54 6860.54i 0.508140 0.508140i
\(568\) −2320.66 + 16616.0i −0.171431 + 1.22745i
\(569\) 2172.30i 0.160049i −0.996793 0.0800243i \(-0.974500\pi\)
0.996793 0.0800243i \(-0.0254998\pi\)
\(570\) 0 0
\(571\) 5608.37i 0.411039i 0.978653 + 0.205519i \(0.0658884\pi\)
−0.978653 + 0.205519i \(0.934112\pi\)
\(572\) −6920.01 + 18706.7i −0.505839 + 1.36742i
\(573\) −874.158 + 874.158i −0.0637321 + 0.0637321i
\(574\) −1269.35 5797.58i −0.0923027 0.421579i
\(575\) 0 0
\(576\) 3770.90 13236.5i 0.272779 0.957504i
\(577\) −16686.9 16686.9i −1.20396 1.20396i −0.972951 0.231010i \(-0.925797\pi\)
−0.231010 0.972951i \(-0.574203\pi\)
\(578\) 6146.38 + 3938.38i 0.442311 + 0.283417i
\(579\) −1770.02 −0.127046
\(580\) 0 0
\(581\) −15730.0 −1.12322
\(582\) 227.789 + 145.959i 0.0162236 + 0.0103955i
\(583\) 12922.4 + 12922.4i 0.917994 + 0.917994i
\(584\) 13199.7 9964.46i 0.935284 0.706048i
\(585\) 0 0
\(586\) −2446.41 11173.6i −0.172458 0.787677i
\(587\) −19717.2 + 19717.2i −1.38640 + 1.38640i −0.553650 + 0.832749i \(0.686766\pi\)
−0.832749 + 0.553650i \(0.813234\pi\)
\(588\) −416.595 154.107i −0.0292178 0.0108083i
\(589\) 35700.1i 2.49745i
\(590\) 0 0
\(591\) 114.919i 0.00799851i
\(592\) 12137.8 933.743i 0.842672 0.0648254i
\(593\) −168.200 + 168.200i −0.0116478 + 0.0116478i −0.712907 0.701259i \(-0.752622\pi\)
0.701259 + 0.712907i \(0.252622\pi\)
\(594\) −2168.47 + 474.776i −0.149787 + 0.0327951i
\(595\) 0 0
\(596\) 21752.1 10004.6i 1.49497 0.687594i
\(597\) −705.183 705.183i −0.0483438 0.0483438i
\(598\) 13675.7 21342.8i 0.935182 1.45948i
\(599\) −3488.67 −0.237969 −0.118984 0.992896i \(-0.537964\pi\)
−0.118984 + 0.992896i \(0.537964\pi\)
\(600\) 0 0
\(601\) 10909.5 0.740443 0.370222 0.928943i \(-0.379282\pi\)
0.370222 + 0.928943i \(0.379282\pi\)
\(602\) −6506.18 + 10153.8i −0.440485 + 0.687439i
\(603\) −7036.01 7036.01i −0.475172 0.475172i
\(604\) −1338.08 + 615.433i −0.0901418 + 0.0414596i
\(605\) 0 0
\(606\) 566.318 123.993i 0.0379622 0.00831164i
\(607\) −12048.9 + 12048.9i −0.805683 + 0.805683i −0.983977 0.178294i \(-0.942942\pi\)
0.178294 + 0.983977i \(0.442942\pi\)
\(608\) −6815.55 22647.4i −0.454617 1.51064i
\(609\) 373.745i 0.0248685i
\(610\) 0 0
\(611\) 6016.28i 0.398352i
\(612\) −9740.06 3603.05i −0.643331 0.237982i
\(613\) 7796.28 7796.28i 0.513685 0.513685i −0.401969 0.915653i \(-0.631674\pi\)
0.915653 + 0.401969i \(0.131674\pi\)
\(614\) −451.969 2064.30i −0.0297068 0.135681i
\(615\) 0 0
\(616\) 7771.09 + 10294.2i 0.508289 + 0.673318i
\(617\) 20235.1 + 20235.1i 1.32031 + 1.32031i 0.913521 + 0.406791i \(0.133352\pi\)
0.406791 + 0.913521i \(0.366648\pi\)
\(618\) 580.150 + 371.739i 0.0377622 + 0.0241967i
\(619\) −22702.2 −1.47411 −0.737057 0.675830i \(-0.763785\pi\)
−0.737057 + 0.675830i \(0.763785\pi\)
\(620\) 0 0
\(621\) 2821.13 0.182300
\(622\) −941.641 603.369i −0.0607015 0.0388953i
\(623\) 13799.7 + 13799.7i 0.887434 + 0.887434i
\(624\) 846.741 987.875i 0.0543218 0.0633760i
\(625\) 0 0
\(626\) −688.397 3144.15i −0.0439519 0.200744i
\(627\) −1345.68 + 1345.68i −0.0857120 + 0.0857120i
\(628\) −5108.14 + 13808.7i −0.324581 + 0.877434i
\(629\) 9185.76i 0.582289i
\(630\) 0 0
\(631\) 5787.42i 0.365125i 0.983194 + 0.182562i \(0.0584391\pi\)
−0.983194 + 0.182562i \(0.941561\pi\)
\(632\) 4991.30 + 697.106i 0.314151 + 0.0438756i
\(633\) 720.464 720.464i 0.0452383 0.0452383i
\(634\) 14441.9 3161.98i 0.904671 0.198073i
\(635\) 0 0
\(636\) −498.140 1083.06i −0.0310575 0.0675253i
\(637\) 6720.13 + 6720.13i 0.417993 + 0.417993i
\(638\) −5186.08 + 8093.59i −0.321816 + 0.502239i
\(639\) 19931.2 1.23391
\(640\) 0 0
\(641\) 8721.43 0.537404 0.268702 0.963223i \(-0.413405\pi\)
0.268702 + 0.963223i \(0.413405\pi\)
\(642\) −532.895 + 831.658i −0.0327597 + 0.0511260i
\(643\) 2937.61 + 2937.61i 0.180168 + 0.180168i 0.791429 0.611261i \(-0.209337\pi\)
−0.611261 + 0.791429i \(0.709337\pi\)
\(644\) −6849.45 14892.1i −0.419109 0.911229i
\(645\) 0 0
\(646\) −17432.9 + 3816.84i −1.06174 + 0.232464i
\(647\) 18130.5 18130.5i 1.10167 1.10167i 0.107465 0.994209i \(-0.465727\pi\)
0.994209 0.107465i \(-0.0342733\pi\)
\(648\) −16121.5 2251.60i −0.977337 0.136499i
\(649\) 7486.92i 0.452831i
\(650\) 0 0
\(651\) 1270.03i 0.0764614i
\(652\) −5733.05 + 15498.0i −0.344361 + 0.930904i
\(653\) 14359.8 14359.8i 0.860555 0.860555i −0.130847 0.991403i \(-0.541770\pi\)
0.991403 + 0.130847i \(0.0417698\pi\)
\(654\) 141.806 + 647.677i 0.00847866 + 0.0387251i
\(655\) 0 0
\(656\) −6480.11 + 7560.20i −0.385679 + 0.449964i
\(657\) −13893.0 13893.0i −0.824986 0.824986i
\(658\) 3275.72 + 2098.96i 0.194074 + 0.124356i
\(659\) 14608.8 0.863550 0.431775 0.901981i \(-0.357887\pi\)
0.431775 + 0.901981i \(0.357887\pi\)
\(660\) 0 0
\(661\) −26434.7 −1.55551 −0.777755 0.628567i \(-0.783642\pi\)
−0.777755 + 0.628567i \(0.783642\pi\)
\(662\) −3307.34 2119.22i −0.194175 0.124420i
\(663\) −694.207 694.207i −0.0406648 0.0406648i
\(664\) 15900.7 + 21063.3i 0.929318 + 1.23104i
\(665\) 0 0
\(666\) −3093.17 14127.6i −0.179967 0.821973i
\(667\) 8638.26 8638.26i 0.501462 0.501462i
\(668\) 17578.4 + 6502.62i 1.01816 + 0.376638i
\(669\) 770.855i 0.0445485i
\(670\) 0 0
\(671\) 1752.69i 0.100837i
\(672\) −242.463 805.679i −0.0139185 0.0462496i
\(673\) −16012.9 + 16012.9i −0.917167 + 0.917167i −0.996822 0.0796554i \(-0.974618\pi\)
0.0796554 + 0.996822i \(0.474618\pi\)
\(674\) −10810.7 + 2366.95i −0.617824 + 0.135269i
\(675\) 0 0
\(676\) −9323.26 + 4288.12i −0.530454 + 0.243976i
\(677\) −5496.28 5496.28i −0.312023 0.312023i 0.533670 0.845693i \(-0.320812\pi\)
−0.845693 + 0.533670i \(0.820812\pi\)
\(678\) 22.5749 35.2312i 0.00127873 0.00199564i
\(679\) −3743.14 −0.211559
\(680\) 0 0
\(681\) 325.799 0.0183328
\(682\) 17622.9 27503.0i 0.989465 1.54420i
\(683\) −12875.9 12875.9i −0.721351 0.721351i 0.247530 0.968880i \(-0.420381\pi\)
−0.968880 + 0.247530i \(0.920381\pi\)
\(684\) −25526.3 + 11740.5i −1.42694 + 0.656302i
\(685\) 0 0
\(686\) 18784.9 4112.85i 1.04549 0.228906i
\(687\) 856.792 856.792i 0.0475818 0.0475818i
\(688\) 20173.2 1551.89i 1.11787 0.0859959i
\(689\) 25506.5i 1.41033i
\(690\) 0 0
\(691\) 9091.60i 0.500522i −0.968178 0.250261i \(-0.919484\pi\)
0.968178 0.250261i \(-0.0805164\pi\)
\(692\) 16996.8 + 6287.48i 0.933702 + 0.345396i
\(693\) 10834.9 10834.9i 0.593914 0.593914i
\(694\) 1770.84 + 8088.07i 0.0968592 + 0.442390i
\(695\) 0 0
\(696\) 500.462 377.800i 0.0272557 0.0205754i
\(697\) 5312.76 + 5312.76i 0.288716 + 0.288716i
\(698\) −13752.2 8811.88i −0.745741 0.477843i
\(699\) −808.504 −0.0437488
\(700\) 0 0
\(701\) 19437.4 1.04728 0.523639 0.851941i \(-0.324574\pi\)
0.523639 + 0.851941i \(0.324574\pi\)
\(702\) −2608.65 1671.53i −0.140252 0.0898685i
\(703\) −17573.0 17573.0i −0.942786 0.942786i
\(704\) 5928.95 20811.7i 0.317409 1.11416i
\(705\) 0 0
\(706\) 6814.27 + 31123.2i 0.363255 + 1.65912i
\(707\) −5671.76 + 5671.76i −0.301709 + 0.301709i
\(708\) 169.444 458.055i 0.00899449 0.0243146i
\(709\) 10638.6i 0.563525i 0.959484 + 0.281763i \(0.0909190\pi\)
−0.959484 + 0.281763i \(0.909081\pi\)
\(710\) 0 0
\(711\) 5987.18i 0.315804i
\(712\) 4529.00 32427.7i 0.238387 1.70685i
\(713\) −29353.8 + 29353.8i −1.54181 + 1.54181i
\(714\) −620.173 + 135.784i −0.0325062 + 0.00711706i
\(715\) 0 0
\(716\) −125.942 273.824i −0.00657358 0.0142923i
\(717\) 417.213 + 417.213i 0.0217309 + 0.0217309i
\(718\) −9503.10 + 14830.9i −0.493945 + 0.770870i
\(719\) 26377.6 1.36818 0.684089 0.729399i \(-0.260200\pi\)
0.684089 + 0.729399i \(0.260200\pi\)
\(720\) 0 0
\(721\) −9533.32 −0.492426
\(722\) −15581.8 + 24317.6i −0.803180 + 1.25347i
\(723\) 1412.61 + 1412.61i 0.0726632 + 0.0726632i
\(724\) 4548.46 + 9889.29i 0.233484 + 0.507642i
\(725\) 0 0
\(726\) −433.584 + 94.9311i −0.0221650 + 0.00485292i
\(727\) −15452.7 + 15452.7i −0.788321 + 0.788321i −0.981219 0.192898i \(-0.938211\pi\)
0.192898 + 0.981219i \(0.438211\pi\)
\(728\) −2490.04 + 17828.8i −0.126768 + 0.907663i
\(729\) 19165.4i 0.973703i
\(730\) 0 0
\(731\) 15266.8i 0.772453i
\(732\) 39.6668 107.230i 0.00200291 0.00541441i
\(733\) 628.566 628.566i 0.0316734 0.0316734i −0.691093 0.722766i \(-0.742870\pi\)
0.722766 + 0.691093i \(0.242870\pi\)
\(734\) 2931.44 + 13388.9i 0.147413 + 0.673290i
\(735\) 0 0
\(736\) −13017.5 + 24225.4i −0.651943 + 1.21326i
\(737\) −11062.7 11062.7i −0.552916 0.552916i
\(738\) 9959.98 + 6381.99i 0.496791 + 0.318326i
\(739\) −27295.7 −1.35871 −0.679356 0.733809i \(-0.737741\pi\)
−0.679356 + 0.733809i \(0.737741\pi\)
\(740\) 0 0
\(741\) −2656.14 −0.131681
\(742\) 13887.6 + 8898.68i 0.687104 + 0.440271i
\(743\) −19570.2 19570.2i −0.966300 0.966300i 0.0331505 0.999450i \(-0.489446\pi\)
−0.999450 + 0.0331505i \(0.989446\pi\)
\(744\) −1700.63 + 1283.81i −0.0838011 + 0.0632617i
\(745\) 0 0
\(746\) 3962.34 + 18097.4i 0.194466 + 0.888196i
\(747\) 22169.6 22169.6i 1.08587 1.08587i
\(748\) −15314.2 5665.06i −0.748588 0.276918i
\(749\) 13666.2i 0.666692i
\(750\) 0 0
\(751\) 23982.8i 1.16530i −0.812722 0.582652i \(-0.802015\pi\)
0.812722 0.582652i \(-0.197985\pi\)
\(752\) −500.655 6508.07i −0.0242779 0.315591i
\(753\) 497.249 497.249i 0.0240648 0.0240648i
\(754\) −13105.8 + 2869.46i −0.633006 + 0.138594i
\(755\) 0 0
\(756\) −1820.21 + 837.183i −0.0875666 + 0.0402752i
\(757\) −8554.31 8554.31i −0.410716 0.410716i 0.471272 0.881988i \(-0.343795\pi\)
−0.881988 + 0.471272i \(0.843795\pi\)
\(758\) −16243.4 + 25350.1i −0.778347 + 1.21472i
\(759\) 2212.93 0.105829
\(760\) 0 0
\(761\) 32552.3 1.55062 0.775308 0.631583i \(-0.217594\pi\)
0.775308 + 0.631583i \(0.217594\pi\)
\(762\) 931.542 1453.80i 0.0442863 0.0691150i
\(763\) −6486.59 6486.59i −0.307772 0.307772i
\(764\) −26071.7 + 11991.4i −1.23461 + 0.567843i
\(765\) 0 0
\(766\) −8991.08 + 1968.55i −0.424100 + 0.0928547i
\(767\) −7388.92 + 7388.92i −0.347847 + 0.347847i
\(768\) −833.748 + 1139.09i −0.0391735 + 0.0535200i
\(769\) 1314.72i 0.0616516i 0.999525 + 0.0308258i \(0.00981371\pi\)
−0.999525 + 0.0308258i \(0.990186\pi\)
\(770\) 0 0
\(771\) 369.016i 0.0172371i
\(772\) −38535.6 14255.1i −1.79654 0.664577i
\(773\) 12385.8 12385.8i 0.576307 0.576307i −0.357576 0.933884i \(-0.616397\pi\)
0.933884 + 0.357576i \(0.116397\pi\)
\(774\) −5140.88 23480.2i −0.238740 1.09041i
\(775\) 0 0
\(776\) 3783.75 + 5012.23i 0.175037 + 0.231867i
\(777\) −625.159 625.159i −0.0288642 0.0288642i
\(778\) 13424.1 + 8601.65i 0.618607 + 0.396381i
\(779\) 20327.4 0.934922
\(780\) 0 0
\(781\) 31337.7 1.43579
\(782\) 17472.2 + 11195.6i 0.798984 + 0.511959i
\(783\) −1055.82 1055.82i −0.0481891 0.0481891i
\(784\) −7828.67 6710.22i −0.356627 0.305677i
\(785\) 0 0
\(786\) −54.7779 250.190i −0.00248583 0.0113537i
\(787\) −25390.5 + 25390.5i −1.15003 + 1.15003i −0.163485 + 0.986546i \(0.552273\pi\)
−0.986546 + 0.163485i \(0.947727\pi\)
\(788\) −925.514 + 2501.92i −0.0418402 + 0.113106i
\(789\) 898.119i 0.0405245i
\(790\) 0 0
\(791\) 578.937i 0.0260235i
\(792\) −25460.8 3555.96i −1.14231 0.159540i
\(793\) −1729.74 + 1729.74i −0.0774590 + 0.0774590i
\(794\) −25550.9 + 5594.25i −1.14203 + 0.250041i
\(795\) 0 0
\(796\) −9673.43 21032.0i −0.430736 0.936508i
\(797\) 22408.5 + 22408.5i 0.995921 + 0.995921i 0.999992 0.00407064i \(-0.00129573\pi\)
−0.00407064 + 0.999992i \(0.501296\pi\)
\(798\) −926.671 + 1446.20i −0.0411075 + 0.0641540i
\(799\) −4925.22 −0.218075
\(800\) 0 0
\(801\) −38897.9 −1.71584
\(802\) 9125.68 14241.9i 0.401794 0.627056i
\(803\) −21843.8 21843.8i −0.959964 0.959964i
\(804\) 426.451 + 927.192i 0.0187062 + 0.0406711i
\(805\) 0 0
\(806\) 44535.2 9750.75i 1.94626 0.426124i
\(807\) 1133.57 1133.57i 0.0494468 0.0494468i
\(808\) 13328.0 + 1861.45i 0.580296 + 0.0810466i
\(809\) 1556.16i 0.0676286i −0.999428 0.0338143i \(-0.989235\pi\)
0.999428 0.0338143i \(-0.0107655\pi\)
\(810\) 0 0
\(811\) 42796.7i 1.85302i −0.376274 0.926508i \(-0.622795\pi\)
0.376274 0.926508i \(-0.377205\pi\)
\(812\) −3010.01 + 8136.90i −0.130087 + 0.351662i
\(813\) 2079.54 2079.54i 0.0897082 0.0897082i
\(814\) −4863.37 22212.8i −0.209412 0.956458i
\(815\) 0 0
\(816\) 808.723 + 693.183i 0.0346948 + 0.0297381i
\(817\) −29206.5 29206.5i −1.25068 1.25068i
\(818\) 12266.2 + 7859.71i 0.524299 + 0.335952i
\(819\) 21386.1 0.912441
\(820\) 0 0
\(821\) −23614.4 −1.00384 −0.501918 0.864915i \(-0.667372\pi\)
−0.501918 + 0.864915i \(0.667372\pi\)
\(822\) 1453.89 + 931.598i 0.0616912 + 0.0395295i
\(823\) 23159.2 + 23159.2i 0.980897 + 0.980897i 0.999821 0.0189236i \(-0.00602393\pi\)
−0.0189236 + 0.999821i \(0.506024\pi\)
\(824\) 9636.75 + 12765.5i 0.407417 + 0.539695i
\(825\) 0 0
\(826\) 1445.24 + 6600.93i 0.0608793 + 0.278058i
\(827\) 10727.9 10727.9i 0.451083 0.451083i −0.444631 0.895714i \(-0.646665\pi\)
0.895714 + 0.444631i \(0.146665\pi\)
\(828\) 30642.1 + 11335.1i 1.28609 + 0.475753i
\(829\) 19535.2i 0.818437i −0.912436 0.409219i \(-0.865801\pi\)
0.912436 0.409219i \(-0.134199\pi\)
\(830\) 0 0
\(831\) 918.094i 0.0383253i
\(832\) 26390.6 14687.9i 1.09968 0.612034i
\(833\) −5501.43 + 5501.43i −0.228827 + 0.228827i
\(834\) 1931.37 422.864i 0.0801893 0.0175571i
\(835\) 0 0
\(836\) −40134.9 + 18459.6i −1.66040 + 0.763681i
\(837\) 3587.81 + 3587.81i 0.148164 + 0.148164i
\(838\) 4700.96 7336.50i 0.193785 0.302429i
\(839\) −25953.9 −1.06797 −0.533986 0.845493i \(-0.679307\pi\)
−0.533986 + 0.845493i \(0.679307\pi\)
\(840\) 0 0
\(841\) 17923.2 0.734887
\(842\) −8601.27 + 13423.5i −0.352042 + 0.549411i
\(843\) 332.777 + 332.777i 0.0135960 + 0.0135960i
\(844\) 21487.8 9883.04i 0.876350 0.403067i
\(845\) 0 0
\(846\) −7574.95 + 1658.50i −0.307839 + 0.0673999i
\(847\) 4342.41 4342.41i 0.176159 0.176159i
\(848\) −2122.56 27591.4i −0.0859541 1.11733i
\(849\) 1109.24i 0.0448399i
\(850\) 0 0
\(851\) 28898.2i 1.16406i
\(852\) −1917.26 709.236i −0.0770943 0.0285188i
\(853\) 18421.1 18421.1i 0.739421 0.739421i −0.233045 0.972466i \(-0.574869\pi\)
0.972466 + 0.233045i \(0.0748689\pi\)
\(854\) 338.330 + 1545.27i 0.0135567 + 0.0619183i
\(855\) 0 0
\(856\) −18299.7 + 13814.5i −0.730689 + 0.551599i
\(857\) 10613.8 + 10613.8i 0.423060 + 0.423060i 0.886256 0.463196i \(-0.153297\pi\)
−0.463196 + 0.886256i \(0.653297\pi\)
\(858\) −2046.26 1311.17i −0.0814197 0.0521708i
\(859\) 16534.0 0.656732 0.328366 0.944551i \(-0.393502\pi\)
0.328366 + 0.944551i \(0.393502\pi\)
\(860\) 0 0
\(861\) 723.146 0.0286234
\(862\) 30889.3 + 19792.7i 1.22053 + 0.782069i
\(863\) −3057.61 3057.61i −0.120605 0.120605i 0.644228 0.764833i \(-0.277179\pi\)
−0.764833 + 0.644228i \(0.777179\pi\)
\(864\) 2960.98 + 1591.08i 0.116591 + 0.0626499i
\(865\) 0 0
\(866\) −155.491 710.184i −0.00610140 0.0278673i
\(867\) −628.948 + 628.948i −0.0246369 + 0.0246369i
\(868\) 10228.4 27650.1i 0.399969 1.08123i
\(869\) 9413.60i 0.367474i
\(870\) 0 0
\(871\) 21835.7i 0.849455i
\(872\) −2128.88 + 15242.8i −0.0826753 + 0.591957i
\(873\) 5275.49 5275.49i 0.204523 0.204523i
\(874\) 54843.5 12007.7i 2.12255 0.464722i
\(875\) 0 0
\(876\) 842.049 + 1830.79i 0.0324774 + 0.0706125i
\(877\) 27748.3 + 27748.3i 1.06841 + 1.06841i 0.997482 + 0.0709256i \(0.0225953\pi\)
0.0709256 + 0.997482i \(0.477405\pi\)
\(878\) −8339.48 + 13014.9i −0.320551 + 0.500264i
\(879\) 1393.71 0.0534799
\(880\) 0 0
\(881\) 11660.4 0.445911 0.222955 0.974829i \(-0.428430\pi\)
0.222955 + 0.974829i \(0.428430\pi\)
\(882\) −6608.62 + 10313.7i −0.252295 + 0.393741i
\(883\) 15502.9 + 15502.9i 0.590844 + 0.590844i 0.937859 0.347016i \(-0.112805\pi\)
−0.347016 + 0.937859i \(0.612805\pi\)
\(884\) −9522.86 20704.7i −0.362317 0.787752i
\(885\) 0 0
\(886\) 19470.3 4262.93i 0.738282 0.161643i
\(887\) 4784.23 4784.23i 0.181103 0.181103i −0.610733 0.791836i \(-0.709125\pi\)
0.791836 + 0.610733i \(0.209125\pi\)
\(888\) −205.175 + 1469.06i −0.00775363 + 0.0555162i
\(889\) 23889.6i 0.901272i
\(890\) 0 0
\(891\) 30405.3i 1.14323i
\(892\) 6208.19 16782.5i 0.233033 0.629954i
\(893\) −9422.30 + 9422.30i −0.353085 + 0.353085i
\(894\) 623.951 + 2849.81i 0.0233423 + 0.106613i
\(895\) 0 0
\(896\) 1209.93 19493.4i 0.0451128 0.726816i
\(897\) 2183.96 + 2183.96i 0.0812937 + 0.0812937i
\(898\) −28303.1 18135.6i −1.05177 0.673934i
\(899\) 21971.7 0.815124
\(900\) 0 0
\(901\) −20880.8 −0.772077
\(902\) 15660.0 + 10034.4i 0.578072 + 0.370407i
\(903\) −1039.02 1039.02i −0.0382906 0.0382906i
\(904\) 775.223 585.218i 0.0285216 0.0215310i
\(905\) 0 0
\(906\) −38.3822 175.305i −0.00140747 0.00642840i
\(907\) −27277.3 + 27277.3i −0.998598 + 0.998598i −0.999999 0.00140132i \(-0.999554\pi\)
0.00140132 + 0.999999i \(0.499554\pi\)
\(908\) 7093.05 + 2623.87i 0.259241 + 0.0958989i
\(909\) 15987.3i 0.583351i
\(910\) 0 0
\(911\) 37452.0i 1.36206i 0.732254 + 0.681032i \(0.238469\pi\)
−0.732254 + 0.681032i \(0.761531\pi\)
\(912\) 2873.25 221.035i 0.104323 0.00802542i
\(913\) 34857.1 34857.1i 1.26353 1.26353i
\(914\) 5316.37 1163.99i 0.192396 0.0421242i
\(915\) 0 0
\(916\) 25553.7 11753.1i 0.921746 0.423946i
\(917\) 2505.69 + 2505.69i 0.0902347 + 0.0902347i
\(918\) 1368.39 2135.57i 0.0491979 0.0767802i
\(919\) −7803.81 −0.280113 −0.140057 0.990144i \(-0.544728\pi\)
−0.140057 + 0.990144i \(0.544728\pi\)
\(920\) 0 0
\(921\) 257.485 0.00921219
\(922\) −12411.5 + 19369.9i −0.443331 + 0.691880i
\(923\) 30927.5 + 30927.5i 1.10292 + 1.10292i
\(924\) −1427.80 + 656.698i −0.0508345 + 0.0233807i
\(925\) 0 0
\(926\) 7573.88 1658.26i 0.268783 0.0588487i
\(927\) 13436.0 13436.0i 0.476049 0.476049i
\(928\) 13938.3 4194.64i 0.493048 0.148379i
\(929\) 6045.30i 0.213498i −0.994286 0.106749i \(-0.965956\pi\)
0.994286 0.106749i \(-0.0340442\pi\)
\(930\) 0 0
\(931\) 21049.2i 0.740989i
\(932\) −17602.1 6511.41i −0.618645 0.228850i
\(933\) 96.3563 96.3563i 0.00338110 0.00338110i
\(934\) 7239.91 + 33067.2i 0.253637 + 1.15845i
\(935\) 0 0
\(936\) −21618.1 28636.9i −0.754924 1.00003i
\(937\) −6094.14 6094.14i −0.212473 0.212473i 0.592844 0.805317i \(-0.298005\pi\)
−0.805317 + 0.592844i \(0.798005\pi\)
\(938\) −11889.0 7618.04i −0.413849 0.265179i
\(939\) 392.178 0.0136296
\(940\) 0 0
\(941\) −11090.5 −0.384207 −0.192103 0.981375i \(-0.561531\pi\)
−0.192103 + 0.981375i \(0.561531\pi\)
\(942\) −1510.49 967.864i −0.0522445 0.0334763i
\(943\) −16713.9 16713.9i −0.577178 0.577178i
\(944\) 7378.02 8607.79i 0.254379 0.296779i
\(945\) 0 0
\(946\) −8082.96 36917.8i −0.277801 1.26882i
\(947\) 35216.3 35216.3i 1.20842 1.20842i 0.236886 0.971537i \(-0.423873\pi\)
0.971537 0.236886i \(-0.0761268\pi\)
\(948\) −213.049 + 575.930i −0.00729905 + 0.0197314i
\(949\) 43115.7i 1.47481i
\(950\) 0 0
\(951\) 1801.37i 0.0614233i
\(952\) −14595.5 2038.47i −0.496894 0.0693984i
\(953\) −28821.7 + 28821.7i −0.979670 + 0.979670i −0.999797 0.0201277i \(-0.993593\pi\)
0.0201277 + 0.999797i \(0.493593\pi\)
\(954\) −32114.5 + 7031.32i −1.08988 + 0.238624i
\(955\) 0 0
\(956\) 5723.16 + 12443.3i 0.193619 + 0.420968i
\(957\) −828.202 828.202i −0.0279749 0.0279749i
\(958\) 11552.6 18029.4i 0.389611 0.608043i
\(959\) −23891.0 −0.804464
\(960\) 0 0
\(961\) −44871.3 −1.50620
\(962\) 17122.3 26721.7i 0.573851 0.895574i
\(963\) 19260.9 + 19260.9i 0.644520 + 0.644520i
\(964\) 19377.6 + 42130.9i 0.647418 + 1.40762i
\(965\) 0 0
\(966\) 1951.06 427.174i 0.0649836 0.0142278i
\(967\) −224.697 + 224.697i −0.00747237 + 0.00747237i −0.710833 0.703361i \(-0.751682\pi\)
0.703361 + 0.710833i \(0.251682\pi\)
\(968\) −10204.2 1425.16i −0.338818 0.0473208i
\(969\) 2174.44i 0.0720878i
\(970\) 0 0
\(971\) 1315.64i 0.0434818i −0.999764 0.0217409i \(-0.993079\pi\)
0.999764 0.0217409i \(-0.00692089\pi\)
\(972\) 2079.71 5622.03i 0.0686283 0.185521i
\(973\) −19343.0 + 19343.0i −0.637315 + 0.637315i
\(974\) −8129.46 37130.2i −0.267438 1.22149i
\(975\) 0 0
\(976\) 1727.19 2015.08i 0.0566456 0.0660872i
\(977\) 2608.70 + 2608.70i 0.0854246 + 0.0854246i 0.748528 0.663103i \(-0.230761\pi\)
−0.663103 + 0.748528i \(0.730761\pi\)
\(978\) −1695.27 1086.27i −0.0554283 0.0355164i
\(979\) −61158.8 −1.99657
\(980\) 0 0
\(981\) 18284.1 0.595073
\(982\) −19500.0 12494.8i −0.633675 0.406035i
\(983\) 38327.7 + 38327.7i 1.24360 + 1.24360i 0.958495 + 0.285109i \(0.0920297\pi\)
0.285109 + 0.958495i \(0.407970\pi\)
\(984\) −730.992 968.326i −0.0236821 0.0313710i
\(985\) 0 0
\(986\) −2349.08 10729.1i −0.0758721 0.346535i
\(987\) −335.198 + 335.198i −0.0108100 + 0.0108100i
\(988\) −57827.4 21391.6i −1.86208 0.688823i
\(989\) 48029.1i 1.54422i
\(990\) 0 0
\(991\) 3912.43i 0.125411i −0.998032 0.0627055i \(-0.980027\pi\)
0.998032 0.0627055i \(-0.0199729\pi\)
\(992\) −47364.1 + 14253.9i −1.51594 + 0.456210i
\(993\) 338.434 338.434i 0.0108156 0.0108156i
\(994\) 27629.2 6049.29i 0.881636 0.193030i
\(995\) 0 0
\(996\) −2921.46 + 1343.69i −0.0929419 + 0.0427475i
\(997\) −41715.2 41715.2i −1.32511 1.32511i −0.909579 0.415531i \(-0.863596\pi\)
−0.415531 0.909579i \(-0.636404\pi\)
\(998\) −655.767 + 1023.42i −0.0207995 + 0.0324606i
\(999\) 3532.13 0.111863
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 100.4.e.f.7.5 yes 24
4.3 odd 2 inner 100.4.e.f.7.11 yes 24
5.2 odd 4 inner 100.4.e.f.43.2 yes 24
5.3 odd 4 inner 100.4.e.f.43.11 yes 24
5.4 even 2 inner 100.4.e.f.7.8 yes 24
20.3 even 4 inner 100.4.e.f.43.5 yes 24
20.7 even 4 inner 100.4.e.f.43.8 yes 24
20.19 odd 2 inner 100.4.e.f.7.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
100.4.e.f.7.2 24 20.19 odd 2 inner
100.4.e.f.7.5 yes 24 1.1 even 1 trivial
100.4.e.f.7.8 yes 24 5.4 even 2 inner
100.4.e.f.7.11 yes 24 4.3 odd 2 inner
100.4.e.f.43.2 yes 24 5.2 odd 4 inner
100.4.e.f.43.5 yes 24 20.3 even 4 inner
100.4.e.f.43.8 yes 24 20.7 even 4 inner
100.4.e.f.43.11 yes 24 5.3 odd 4 inner