Properties

Label 48.4.k.a.11.5
Level $48$
Weight $4$
Character 48.11
Analytic conductor $2.832$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [48,4,Mod(11,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.11");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 48.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: \(2.83209168028\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 11.5
Character \(\chi\) \(=\) 48.11
Dual form 48.4.k.a.35.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.44754 + 1.41758i) q^{2} +(0.563550 - 5.16550i) q^{3} +(3.98092 - 6.93918i) q^{4} +(-13.1633 + 13.1633i) q^{5} +(5.94321 + 13.4417i) q^{6} -13.2717 q^{7} +(0.0933841 + 22.6272i) q^{8} +(-26.3648 - 5.82204i) q^{9} +O(q^{10})\) \(q+(-2.44754 + 1.41758i) q^{2} +(0.563550 - 5.16550i) q^{3} +(3.98092 - 6.93918i) q^{4} +(-13.1633 + 13.1633i) q^{5} +(5.94321 + 13.4417i) q^{6} -13.2717 q^{7} +(0.0933841 + 22.6272i) q^{8} +(-26.3648 - 5.82204i) q^{9} +(13.5576 - 50.8776i) q^{10} +(-24.0957 - 24.0957i) q^{11} +(-33.6009 - 24.4740i) q^{12} +(-30.7791 + 30.7791i) q^{13} +(32.4831 - 18.8138i) q^{14} +(60.5767 + 75.4130i) q^{15} +(-32.3045 - 55.2487i) q^{16} -56.8818i q^{17} +(72.7822 - 23.1246i) q^{18} +(74.2316 + 74.2316i) q^{19} +(38.9403 + 143.744i) q^{20} +(-7.47929 + 68.5552i) q^{21} +(93.1328 + 24.8176i) q^{22} +21.7929i q^{23} +(116.934 + 12.2692i) q^{24} -221.543i q^{25} +(31.7013 - 118.965i) q^{26} +(-44.9316 + 132.907i) q^{27} +(-52.8338 + 92.0950i) q^{28} +(-102.661 - 102.661i) q^{29} +(-255.168 - 98.7041i) q^{30} -219.823i q^{31} +(157.386 + 89.4292i) q^{32} +(-138.045 + 110.887i) q^{33} +(80.6347 + 139.221i) q^{34} +(174.699 - 174.699i) q^{35} +(-145.357 + 159.773i) q^{36} +(83.3409 + 83.3409i) q^{37} +(-286.914 - 76.4556i) q^{38} +(141.644 + 176.335i) q^{39} +(-299.077 - 296.619i) q^{40} +7.92823 q^{41} +(-78.8767 - 178.394i) q^{42} +(-153.514 + 153.514i) q^{43} +(-263.127 + 71.2813i) q^{44} +(423.684 - 270.410i) q^{45} +(-30.8932 - 53.3391i) q^{46} +208.337 q^{47} +(-303.592 + 135.734i) q^{48} -166.861 q^{49} +(314.055 + 542.236i) q^{50} +(-293.823 - 32.0558i) q^{51} +(91.0527 + 336.111i) q^{52} +(-390.157 + 390.157i) q^{53} +(-78.4338 - 388.989i) q^{54} +634.355 q^{55} +(-1.23937 - 300.303i) q^{56} +(425.277 - 341.610i) q^{57} +(396.798 + 105.737i) q^{58} +(-221.945 - 221.945i) q^{59} +(764.456 - 120.139i) q^{60} +(-416.398 + 416.398i) q^{61} +(311.617 + 538.025i) q^{62} +(349.907 + 77.2685i) q^{63} +(-511.983 + 4.22604i) q^{64} -810.308i q^{65} +(180.680 - 467.092i) q^{66} +(-284.375 - 284.375i) q^{67} +(-394.713 - 226.442i) q^{68} +(112.571 + 12.2814i) q^{69} +(-179.933 + 675.234i) q^{70} -26.9657i q^{71} +(129.274 - 597.106i) q^{72} +839.440i q^{73} +(-322.123 - 85.8378i) q^{74} +(-1144.38 - 124.850i) q^{75} +(810.617 - 219.596i) q^{76} +(319.791 + 319.791i) q^{77} +(-596.650 - 230.796i) q^{78} -557.000i q^{79} +(1152.49 + 302.020i) q^{80} +(661.208 + 306.994i) q^{81} +(-19.4047 + 11.2389i) q^{82} +(-400.085 + 400.085i) q^{83} +(445.942 + 324.813i) q^{84} +(748.750 + 748.750i) q^{85} +(158.114 - 593.352i) q^{86} +(-588.151 + 472.441i) q^{87} +(542.968 - 547.468i) q^{88} +974.352 q^{89} +(-653.656 + 1262.45i) q^{90} +(408.492 - 408.492i) q^{91} +(151.225 + 86.7559i) q^{92} +(-1135.49 - 123.881i) q^{93} +(-509.913 + 295.334i) q^{94} -1954.26 q^{95} +(550.642 - 762.581i) q^{96} -1555.38 q^{97} +(408.399 - 236.539i) q^{98} +(494.992 + 775.564i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33} + 520 q^{34} - 604 q^{36} - 4 q^{37} + 596 q^{39} + 632 q^{40} + 696 q^{42} - 436 q^{43} - 252 q^{45} + 664 q^{46} + 1200 q^{48} + 972 q^{49} - 648 q^{51} + 320 q^{52} + 1592 q^{54} + 280 q^{55} - 424 q^{58} + 800 q^{60} - 916 q^{61} - 2056 q^{64} - 668 q^{66} - 1636 q^{67} + 52 q^{69} - 5192 q^{70} - 3704 q^{72} + 1454 q^{75} - 568 q^{76} - 4932 q^{78} - 4 q^{81} + 768 q^{82} - 2096 q^{84} + 736 q^{85} + 1284 q^{87} + 8864 q^{88} + 2672 q^{90} + 424 q^{91} - 2084 q^{93} + 5616 q^{94} + 8008 q^{96} - 8 q^{97} + 1196 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44754 + 1.41758i −0.865337 + 0.501191i
\(3\) 0.563550 5.16550i 0.108455 0.994101i
\(4\) 3.98092 6.93918i 0.497615 0.867398i
\(5\) −13.1633 + 13.1633i −1.17736 + 1.17736i −0.196943 + 0.980415i \(0.563101\pi\)
−0.980415 + 0.196943i \(0.936899\pi\)
\(6\) 5.94321 + 13.4417i 0.404384 + 0.914589i
\(7\) −13.2717 −0.716606 −0.358303 0.933605i \(-0.616645\pi\)
−0.358303 + 0.933605i \(0.616645\pi\)
\(8\) 0.0933841 + 22.6272i 0.00412703 + 0.999991i
\(9\) −26.3648 5.82204i −0.976475 0.215631i
\(10\) 13.5576 50.8776i 0.428730 1.60889i
\(11\) −24.0957 24.0957i −0.660465 0.660465i 0.295024 0.955490i \(-0.404672\pi\)
−0.955490 + 0.295024i \(0.904672\pi\)
\(12\) −33.6009 24.4740i −0.808312 0.588754i
\(13\) −30.7791 + 30.7791i −0.656661 + 0.656661i −0.954589 0.297927i \(-0.903705\pi\)
0.297927 + 0.954589i \(0.403705\pi\)
\(14\) 32.4831 18.8138i 0.620106 0.359157i
\(15\) 60.5767 + 75.4130i 1.04272 + 1.29810i
\(16\) −32.3045 55.2487i −0.504758 0.863261i
\(17\) 56.8818i 0.811522i −0.913979 0.405761i \(-0.867007\pi\)
0.913979 0.405761i \(-0.132993\pi\)
\(18\) 72.7822 23.1246i 0.953052 0.302807i
\(19\) 74.2316 + 74.2316i 0.896311 + 0.896311i 0.995108 0.0987969i \(-0.0314994\pi\)
−0.0987969 + 0.995108i \(0.531499\pi\)
\(20\) 38.9403 + 143.744i 0.435366 + 1.60711i
\(21\) −7.47929 + 68.5552i −0.0777197 + 0.712379i
\(22\) 93.1328 + 24.8176i 0.902544 + 0.240506i
\(23\) 21.7929i 0.197571i 0.995109 + 0.0987856i \(0.0314958\pi\)
−0.995109 + 0.0987856i \(0.968504\pi\)
\(24\) 116.934 + 12.2692i 0.994540 + 0.104352i
\(25\) 221.543i 1.77234i
\(26\) 31.7013 118.965i 0.239120 0.897346i
\(27\) −44.9316 + 132.907i −0.320263 + 0.947329i
\(28\) −52.8338 + 92.0950i −0.356594 + 0.621583i
\(29\) −102.661 102.661i −0.657369 0.657369i 0.297388 0.954757i \(-0.403884\pi\)
−0.954757 + 0.297388i \(0.903884\pi\)
\(30\) −255.168 98.7041i −1.55290 0.600694i
\(31\) 219.823i 1.27359i −0.771033 0.636795i \(-0.780260\pi\)
0.771033 0.636795i \(-0.219740\pi\)
\(32\) 157.386 + 89.4292i 0.869444 + 0.494031i
\(33\) −138.045 + 110.887i −0.728201 + 0.584939i
\(34\) 80.6347 + 139.221i 0.406727 + 0.702240i
\(35\) 174.699 174.699i 0.843702 0.843702i
\(36\) −145.357 + 159.773i −0.672947 + 0.739691i
\(37\) 83.3409 + 83.3409i 0.370302 + 0.370302i 0.867587 0.497285i \(-0.165670\pi\)
−0.497285 + 0.867587i \(0.665670\pi\)
\(38\) −286.914 76.4556i −1.22483 0.326388i
\(39\) 141.644 + 176.335i 0.581569 + 0.724006i
\(40\) −299.077 296.619i −1.18221 1.17249i
\(41\) 7.92823 0.0301995 0.0150998 0.999886i \(-0.495193\pi\)
0.0150998 + 0.999886i \(0.495193\pi\)
\(42\) −78.8767 178.394i −0.289784 0.655400i
\(43\) −153.514 + 153.514i −0.544435 + 0.544435i −0.924826 0.380391i \(-0.875790\pi\)
0.380391 + 0.924826i \(0.375790\pi\)
\(44\) −263.127 + 71.2813i −0.901544 + 0.244229i
\(45\) 423.684 270.410i 1.40354 0.895786i
\(46\) −30.8932 53.3391i −0.0990209 0.170966i
\(47\) 208.337 0.646575 0.323287 0.946301i \(-0.395212\pi\)
0.323287 + 0.946301i \(0.395212\pi\)
\(48\) −303.592 + 135.734i −0.912912 + 0.408155i
\(49\) −166.861 −0.486475
\(50\) 314.055 + 542.236i 0.888282 + 1.53367i
\(51\) −293.823 32.0558i −0.806735 0.0880138i
\(52\) 91.0527 + 336.111i 0.242822 + 0.896351i
\(53\) −390.157 + 390.157i −1.01117 + 1.01117i −0.0112374 + 0.999937i \(0.503577\pi\)
−0.999937 + 0.0112374i \(0.996423\pi\)
\(54\) −78.4338 388.989i −0.197657 0.980271i
\(55\) 634.355 1.55521
\(56\) −1.23937 300.303i −0.00295746 0.716600i
\(57\) 425.277 341.610i 0.988233 0.793814i
\(58\) 396.798 + 105.737i 0.898312 + 0.239378i
\(59\) −221.945 221.945i −0.489741 0.489741i 0.418483 0.908225i \(-0.362562\pi\)
−0.908225 + 0.418483i \(0.862562\pi\)
\(60\) 764.456 120.139i 1.64485 0.258499i
\(61\) −416.398 + 416.398i −0.874005 + 0.874005i −0.992906 0.118901i \(-0.962063\pi\)
0.118901 + 0.992906i \(0.462063\pi\)
\(62\) 311.617 + 538.025i 0.638312 + 1.10208i
\(63\) 349.907 + 77.2685i 0.699748 + 0.154523i
\(64\) −511.983 + 4.22604i −0.999966 + 0.00825399i
\(65\) 810.308i 1.54625i
\(66\) 180.680 467.092i 0.336973 0.871136i
\(67\) −284.375 284.375i −0.518537 0.518537i 0.398592 0.917129i \(-0.369499\pi\)
−0.917129 + 0.398592i \(0.869499\pi\)
\(68\) −394.713 226.442i −0.703912 0.403826i
\(69\) 112.571 + 12.2814i 0.196406 + 0.0214276i
\(70\) −179.933 + 675.234i −0.307231 + 1.15294i
\(71\) 26.9657i 0.0450738i −0.999746 0.0225369i \(-0.992826\pi\)
0.999746 0.0225369i \(-0.00717433\pi\)
\(72\) 129.274 597.106i 0.211599 0.977357i
\(73\) 839.440i 1.34588i 0.739698 + 0.672939i \(0.234968\pi\)
−0.739698 + 0.672939i \(0.765032\pi\)
\(74\) −322.123 85.8378i −0.506027 0.134844i
\(75\) −1144.38 124.850i −1.76189 0.192220i
\(76\) 810.617 219.596i 1.22348 0.331440i
\(77\) 319.791 + 319.791i 0.473294 + 0.473294i
\(78\) −596.650 230.796i −0.866119 0.335032i
\(79\) 557.000i 0.793258i −0.917979 0.396629i \(-0.870180\pi\)
0.917979 0.396629i \(-0.129820\pi\)
\(80\) 1152.49 + 302.020i 1.61065 + 0.422086i
\(81\) 661.208 + 306.994i 0.907007 + 0.421117i
\(82\) −19.4047 + 11.2389i −0.0261328 + 0.0151357i
\(83\) −400.085 + 400.085i −0.529097 + 0.529097i −0.920303 0.391206i \(-0.872058\pi\)
0.391206 + 0.920303i \(0.372058\pi\)
\(84\) 445.942 + 324.813i 0.579242 + 0.421905i
\(85\) 748.750 + 748.750i 0.955452 + 0.955452i
\(86\) 158.114 593.352i 0.198254 0.743986i
\(87\) −588.151 + 472.441i −0.724786 + 0.582196i
\(88\) 542.968 547.468i 0.657734 0.663186i
\(89\) 974.352 1.16046 0.580231 0.814452i \(-0.302962\pi\)
0.580231 + 0.814452i \(0.302962\pi\)
\(90\) −653.656 + 1262.45i −0.765571 + 1.47860i
\(91\) 408.492 408.492i 0.470568 0.470568i
\(92\) 151.225 + 86.7559i 0.171373 + 0.0983145i
\(93\) −1135.49 123.881i −1.26608 0.138128i
\(94\) −509.913 + 295.334i −0.559505 + 0.324058i
\(95\) −1954.26 −2.11056
\(96\) 550.642 762.581i 0.585413 0.810735i
\(97\) −1555.38 −1.62809 −0.814046 0.580800i \(-0.802740\pi\)
−0.814046 + 0.580800i \(0.802740\pi\)
\(98\) 408.399 236.539i 0.420965 0.243817i
\(99\) 494.992 + 775.564i 0.502511 + 0.787345i
\(100\) −1537.33 881.945i −1.53733 0.881945i
\(101\) 387.041 387.041i 0.381307 0.381307i −0.490266 0.871573i \(-0.663100\pi\)
0.871573 + 0.490266i \(0.163100\pi\)
\(102\) 764.586 338.061i 0.742209 0.328167i
\(103\) 109.160 0.104426 0.0522130 0.998636i \(-0.483373\pi\)
0.0522130 + 0.998636i \(0.483373\pi\)
\(104\) −699.321 693.572i −0.659366 0.653946i
\(105\) −803.958 1000.86i −0.747221 0.930229i
\(106\) 401.846 1508.01i 0.368215 1.38180i
\(107\) 542.909 + 542.909i 0.490514 + 0.490514i 0.908468 0.417954i \(-0.137253\pi\)
−0.417954 + 0.908468i \(0.637253\pi\)
\(108\) 743.393 + 840.880i 0.662343 + 0.749201i
\(109\) 233.764 233.764i 0.205417 0.205417i −0.596899 0.802316i \(-0.703601\pi\)
0.802316 + 0.596899i \(0.203601\pi\)
\(110\) −1552.61 + 899.251i −1.34578 + 0.779456i
\(111\) 477.464 383.531i 0.408278 0.327956i
\(112\) 428.737 + 733.246i 0.361713 + 0.618618i
\(113\) 158.058i 0.131583i 0.997833 + 0.0657914i \(0.0209572\pi\)
−0.997833 + 0.0657914i \(0.979043\pi\)
\(114\) −556.622 + 1438.97i −0.457302 + 1.18221i
\(115\) −286.866 286.866i −0.232612 0.232612i
\(116\) −1121.07 + 303.698i −0.897317 + 0.243083i
\(117\) 990.684 632.289i 0.782810 0.499617i
\(118\) 857.844 + 228.594i 0.669245 + 0.178337i
\(119\) 754.921i 0.581542i
\(120\) −1700.73 + 1377.72i −1.29379 + 1.04807i
\(121\) 169.797i 0.127571i
\(122\) 428.874 1609.43i 0.318265 1.19435i
\(123\) 4.46795 40.9533i 0.00327530 0.0300214i
\(124\) −1525.39 875.097i −1.10471 0.633758i
\(125\) 1270.82 + 1270.82i 0.909324 + 0.909324i
\(126\) −965.946 + 306.904i −0.682963 + 0.216993i
\(127\) 6.82092i 0.00476582i −0.999997 0.00238291i \(-0.999241\pi\)
0.999997 0.00238291i \(-0.000758504\pi\)
\(128\) 1247.11 736.121i 0.861170 0.508316i
\(129\) 706.466 + 879.492i 0.482177 + 0.600271i
\(130\) 1148.68 + 1983.26i 0.774967 + 1.33803i
\(131\) 1494.05 1494.05i 0.996454 0.996454i −0.00353941 0.999994i \(-0.501127\pi\)
0.999994 + 0.00353941i \(0.00112663\pi\)
\(132\) 219.918 + 1399.36i 0.145011 + 0.922714i
\(133\) −985.182 985.182i −0.642302 0.642302i
\(134\) 1099.15 + 292.895i 0.708595 + 0.188823i
\(135\) −1158.04 2340.93i −0.738281 1.49241i
\(136\) 1287.08 5.31186i 0.811515 0.00334918i
\(137\) −966.981 −0.603027 −0.301514 0.953462i \(-0.597492\pi\)
−0.301514 + 0.953462i \(0.597492\pi\)
\(138\) −292.933 + 129.520i −0.180696 + 0.0798947i
\(139\) 1555.13 1555.13i 0.948955 0.948955i −0.0498036 0.998759i \(-0.515860\pi\)
0.998759 + 0.0498036i \(0.0158595\pi\)
\(140\) −516.806 1907.73i −0.311986 1.15166i
\(141\) 117.408 1076.16i 0.0701244 0.642761i
\(142\) 38.2261 + 65.9997i 0.0225906 + 0.0390040i
\(143\) 1483.29 0.867404
\(144\) 530.043 + 1644.70i 0.306738 + 0.951794i
\(145\) 2702.71 1.54792
\(146\) −1189.98 2054.57i −0.674542 1.16464i
\(147\) −94.0345 + 861.921i −0.0527608 + 0.483606i
\(148\) 910.091 246.544i 0.505466 0.136931i
\(149\) −2186.31 + 2186.31i −1.20207 + 1.20207i −0.228540 + 0.973534i \(0.573395\pi\)
−0.973534 + 0.228540i \(0.926605\pi\)
\(150\) 2977.90 1316.68i 1.62097 0.716708i
\(151\) −530.420 −0.285861 −0.142930 0.989733i \(-0.545653\pi\)
−0.142930 + 0.989733i \(0.545653\pi\)
\(152\) −1672.72 + 1686.59i −0.892604 + 0.900002i
\(153\) −331.168 + 1499.68i −0.174989 + 0.792431i
\(154\) −1236.03 329.372i −0.646769 0.172348i
\(155\) 2893.58 + 2893.58i 1.49947 + 1.49947i
\(156\) 1787.50 280.917i 0.917399 0.144175i
\(157\) 131.535 131.535i 0.0668637 0.0668637i −0.672884 0.739748i \(-0.734945\pi\)
0.739748 + 0.672884i \(0.234945\pi\)
\(158\) 789.593 + 1363.28i 0.397574 + 0.686435i
\(159\) 1795.49 + 2235.23i 0.895543 + 1.11488i
\(160\) −3248.90 + 894.535i −1.60530 + 0.441995i
\(161\) 289.230i 0.141581i
\(162\) −2053.52 + 185.936i −0.995926 + 0.0901758i
\(163\) 215.002 + 215.002i 0.103314 + 0.103314i 0.756875 0.653560i \(-0.226725\pi\)
−0.653560 + 0.756875i \(0.726725\pi\)
\(164\) 31.5617 55.0154i 0.0150278 0.0261950i
\(165\) 357.491 3276.76i 0.168670 1.54603i
\(166\) 412.072 1546.38i 0.192669 0.723026i
\(167\) 1360.80i 0.630548i −0.949001 0.315274i \(-0.897903\pi\)
0.949001 0.315274i \(-0.102097\pi\)
\(168\) −1551.91 162.834i −0.712694 0.0747790i
\(169\) 302.290i 0.137592i
\(170\) −2894.01 771.183i −1.30565 0.347924i
\(171\) −1524.92 2389.28i −0.681953 1.06850i
\(172\) 454.135 + 1676.39i 0.201323 + 0.743161i
\(173\) −1069.50 1069.50i −0.470014 0.470014i 0.431905 0.901919i \(-0.357842\pi\)
−0.901919 + 0.431905i \(0.857842\pi\)
\(174\) 769.799 1990.07i 0.335393 0.867052i
\(175\) 2940.26i 1.27007i
\(176\) −552.856 + 2109.65i −0.236779 + 0.903529i
\(177\) −1271.53 + 1021.38i −0.539968 + 0.433738i
\(178\) −2384.77 + 1381.22i −1.00419 + 0.581613i
\(179\) −315.583 + 315.583i −0.131775 + 0.131775i −0.769918 0.638143i \(-0.779703\pi\)
0.638143 + 0.769918i \(0.279703\pi\)
\(180\) −189.771 4016.50i −0.0785817 1.66318i
\(181\) −3368.56 3368.56i −1.38333 1.38333i −0.838629 0.544703i \(-0.816642\pi\)
−0.544703 0.838629i \(-0.683358\pi\)
\(182\) −420.731 + 1578.87i −0.171355 + 0.643044i
\(183\) 1916.24 + 2385.57i 0.774060 + 0.963640i
\(184\) −493.113 + 2.03511i −0.197570 + 0.000815383i
\(185\) −2194.08 −0.871955
\(186\) 2954.78 1306.45i 1.16481 0.515020i
\(187\) −1370.61 + 1370.61i −0.535982 + 0.535982i
\(188\) 829.372 1445.69i 0.321746 0.560838i
\(189\) 596.321 1763.90i 0.229502 0.678862i
\(190\) 4783.13 2770.32i 1.82634 1.05779i
\(191\) −4403.49 −1.66820 −0.834098 0.551616i \(-0.814011\pi\)
−0.834098 + 0.551616i \(0.814011\pi\)
\(192\) −266.698 + 2647.03i −0.100246 + 0.994963i
\(193\) 17.1480 0.00639554 0.00319777 0.999995i \(-0.498982\pi\)
0.00319777 + 0.999995i \(0.498982\pi\)
\(194\) 3806.86 2204.88i 1.40885 0.815985i
\(195\) −4185.65 456.649i −1.53713 0.167699i
\(196\) −664.261 + 1157.88i −0.242078 + 0.421968i
\(197\) 630.686 630.686i 0.228094 0.228094i −0.583802 0.811896i \(-0.698436\pi\)
0.811896 + 0.583802i \(0.198436\pi\)
\(198\) −2310.94 1196.53i −0.829451 0.429464i
\(199\) −2149.16 −0.765579 −0.382789 0.923836i \(-0.625036\pi\)
−0.382789 + 0.923836i \(0.625036\pi\)
\(200\) 5012.90 20.6886i 1.77233 0.00731452i
\(201\) −1629.20 + 1308.68i −0.571716 + 0.459240i
\(202\) −398.637 + 1495.96i −0.138851 + 0.521067i
\(203\) 1362.49 + 1362.49i 0.471074 + 0.471074i
\(204\) −1392.13 + 1911.28i −0.477787 + 0.655963i
\(205\) −104.361 + 104.361i −0.0355557 + 0.0355557i
\(206\) −267.174 + 154.744i −0.0903636 + 0.0523373i
\(207\) 126.879 574.566i 0.0426025 0.192923i
\(208\) 2694.81 + 706.202i 0.898325 + 0.235415i
\(209\) 3577.32i 1.18396i
\(210\) 3386.52 + 1309.97i 1.11282 + 0.430461i
\(211\) 3221.52 + 3221.52i 1.05108 + 1.05108i 0.998623 + 0.0524606i \(0.0167064\pi\)
0.0524606 + 0.998623i \(0.483294\pi\)
\(212\) 1154.19 + 4260.56i 0.373914 + 1.38027i
\(213\) −139.291 15.1965i −0.0448079 0.00488849i
\(214\) −2098.41 559.174i −0.670301 0.178619i
\(215\) 4041.50i 1.28199i
\(216\) −3011.50 1004.27i −0.948642 0.316350i
\(217\) 2917.43i 0.912663i
\(218\) −240.767 + 903.526i −0.0748019 + 0.280709i
\(219\) 4336.13 + 473.067i 1.33794 + 0.145967i
\(220\) 2525.32 4401.91i 0.773896 1.34898i
\(221\) 1750.77 + 1750.77i 0.532895 + 0.532895i
\(222\) −624.928 + 1615.55i −0.188930 + 0.488418i
\(223\) 131.078i 0.0393615i 0.999806 + 0.0196807i \(0.00626498\pi\)
−0.999806 + 0.0196807i \(0.993735\pi\)
\(224\) −2088.79 1186.88i −0.623049 0.354026i
\(225\) −1289.83 + 5840.94i −0.382172 + 1.73065i
\(226\) −224.060 386.854i −0.0659481 0.113863i
\(227\) 2803.34 2803.34i 0.819666 0.819666i −0.166394 0.986059i \(-0.553212\pi\)
0.986059 + 0.166394i \(0.0532122\pi\)
\(228\) −677.502 4311.00i −0.196793 1.25221i
\(229\) 4610.81 + 4610.81i 1.33053 + 1.33053i 0.904897 + 0.425630i \(0.139947\pi\)
0.425630 + 0.904897i \(0.360053\pi\)
\(230\) 1108.77 + 295.460i 0.317871 + 0.0847047i
\(231\) 1832.10 1471.66i 0.521833 0.419171i
\(232\) 2313.35 2332.52i 0.654650 0.660076i
\(233\) 555.570 0.156209 0.0781043 0.996945i \(-0.475113\pi\)
0.0781043 + 0.996945i \(0.475113\pi\)
\(234\) −1528.42 + 2951.93i −0.426991 + 0.824674i
\(235\) −2742.39 + 2742.39i −0.761250 + 0.761250i
\(236\) −2423.66 + 656.570i −0.668504 + 0.181098i
\(237\) −2877.18 313.897i −0.788579 0.0860330i
\(238\) −1070.16 1847.70i −0.291463 0.503229i
\(239\) −3068.21 −0.830401 −0.415201 0.909730i \(-0.636289\pi\)
−0.415201 + 0.909730i \(0.636289\pi\)
\(240\) 2209.57 5782.96i 0.594280 1.55537i
\(241\) 2482.51 0.663538 0.331769 0.943361i \(-0.392355\pi\)
0.331769 + 0.943361i \(0.392355\pi\)
\(242\) 240.701 + 415.585i 0.0639373 + 0.110392i
\(243\) 1958.40 3242.46i 0.517002 0.855984i
\(244\) 1231.81 + 4547.11i 0.323192 + 1.19303i
\(245\) 2196.44 2196.44i 0.572756 0.572756i
\(246\) 47.1191 + 106.569i 0.0122122 + 0.0276202i
\(247\) −4569.57 −1.17714
\(248\) 4973.97 20.5279i 1.27358 0.00525615i
\(249\) 1841.17 + 2292.11i 0.468593 + 0.583360i
\(250\) −4911.87 1308.89i −1.24262 0.331127i
\(251\) −3369.93 3369.93i −0.847443 0.847443i 0.142370 0.989813i \(-0.454528\pi\)
−0.989813 + 0.142370i \(0.954528\pi\)
\(252\) 1929.13 2120.47i 0.482238 0.530067i
\(253\) 525.115 525.115i 0.130489 0.130489i
\(254\) 9.66921 + 16.6945i 0.00238858 + 0.00412404i
\(255\) 4289.63 3445.71i 1.05344 0.846192i
\(256\) −2008.84 + 3569.56i −0.490439 + 0.871476i
\(257\) 1660.41i 0.403010i 0.979487 + 0.201505i \(0.0645832\pi\)
−0.979487 + 0.201505i \(0.935417\pi\)
\(258\) −2975.86 1151.12i −0.718096 0.277774i
\(259\) −1106.08 1106.08i −0.265360 0.265360i
\(260\) −5622.87 3225.77i −1.34121 0.769438i
\(261\) 2108.95 + 3304.34i 0.500155 + 0.783653i
\(262\) −1538.81 + 5774.68i −0.362855 + 1.36168i
\(263\) 3786.64i 0.887811i 0.896074 + 0.443906i \(0.146407\pi\)
−0.896074 + 0.443906i \(0.853593\pi\)
\(264\) −2521.96 3113.23i −0.587939 0.725780i
\(265\) 10271.5i 2.38103i
\(266\) 3807.85 + 1014.70i 0.877723 + 0.233892i
\(267\) 549.096 5033.02i 0.125858 1.15362i
\(268\) −3105.41 + 841.256i −0.707810 + 0.191746i
\(269\) 150.137 + 150.137i 0.0340298 + 0.0340298i 0.723917 0.689887i \(-0.242340\pi\)
−0.689887 + 0.723917i \(0.742340\pi\)
\(270\) 6152.80 + 4087.91i 1.38684 + 0.921417i
\(271\) 4680.39i 1.04913i −0.851371 0.524564i \(-0.824228\pi\)
0.851371 0.524564i \(-0.175772\pi\)
\(272\) −3142.65 + 1837.54i −0.700555 + 0.409622i
\(273\) −1879.86 2340.27i −0.416756 0.518827i
\(274\) 2366.73 1370.77i 0.521822 0.302232i
\(275\) −5338.23 + 5338.23i −1.17057 + 1.17057i
\(276\) 533.361 732.262i 0.116321 0.159699i
\(277\) −3252.08 3252.08i −0.705411 0.705411i 0.260156 0.965567i \(-0.416226\pi\)
−0.965567 + 0.260156i \(0.916226\pi\)
\(278\) −1601.73 + 6010.79i −0.345558 + 1.29677i
\(279\) −1279.82 + 5795.58i −0.274626 + 1.24363i
\(280\) 3969.27 + 3936.65i 0.847177 + 0.840213i
\(281\) 5915.11 1.25575 0.627875 0.778314i \(-0.283925\pi\)
0.627875 + 0.778314i \(0.283925\pi\)
\(282\) 1238.19 + 2800.39i 0.261465 + 0.591351i
\(283\) 4831.85 4831.85i 1.01493 1.01493i 0.0150381 0.999887i \(-0.495213\pi\)
0.999887 0.0150381i \(-0.00478696\pi\)
\(284\) −187.120 107.348i −0.0390969 0.0224294i
\(285\) −1101.32 + 10094.7i −0.228901 + 2.09811i
\(286\) −3630.41 + 2102.68i −0.750597 + 0.434735i
\(287\) −105.221 −0.0216412
\(288\) −3628.80 3274.09i −0.742462 0.669888i
\(289\) 1677.46 0.341432
\(290\) −6615.00 + 3831.31i −1.33947 + 0.775801i
\(291\) −876.535 + 8034.32i −0.176575 + 1.61849i
\(292\) 5825.03 + 3341.75i 1.16741 + 0.669729i
\(293\) −2284.81 + 2284.81i −0.455563 + 0.455563i −0.897196 0.441633i \(-0.854399\pi\)
0.441633 + 0.897196i \(0.354399\pi\)
\(294\) −991.690 2242.89i −0.196723 0.444925i
\(295\) 5843.03 1.15320
\(296\) −1877.99 + 1893.56i −0.368770 + 0.371827i
\(297\) 4285.13 2119.81i 0.837200 0.414155i
\(298\) 2251.81 8450.34i 0.437731 1.64267i
\(299\) −670.767 670.767i −0.129737 0.129737i
\(300\) −5422.05 + 7444.04i −1.04347 + 1.43261i
\(301\) 2037.40 2037.40i 0.390146 0.390146i
\(302\) 1298.23 751.915i 0.247366 0.143271i
\(303\) −1781.15 2217.38i −0.337703 0.420413i
\(304\) 1703.18 6499.22i 0.321330 1.22617i
\(305\) 10962.3i 2.05803i
\(306\) −1315.37 4139.99i −0.245734 0.773422i
\(307\) −6603.53 6603.53i −1.22763 1.22763i −0.964857 0.262777i \(-0.915362\pi\)
−0.262777 0.964857i \(-0.584638\pi\)
\(308\) 3492.16 946.026i 0.646052 0.175016i
\(309\) 61.5172 563.867i 0.0113255 0.103810i
\(310\) −11184.1 2980.27i −2.04907 0.546026i
\(311\) 173.626i 0.0316574i −0.999875 0.0158287i \(-0.994961\pi\)
0.999875 0.0158287i \(-0.00503864\pi\)
\(312\) −3976.75 + 3221.48i −0.721600 + 0.584552i
\(313\) 1738.22i 0.313898i 0.987607 + 0.156949i \(0.0501658\pi\)
−0.987607 + 0.156949i \(0.949834\pi\)
\(314\) −135.475 + 508.397i −0.0243481 + 0.0913711i
\(315\) −5623.02 + 3588.81i −1.00578 + 0.641926i
\(316\) −3865.12 2217.37i −0.688070 0.394737i
\(317\) 2486.10 + 2486.10i 0.440484 + 0.440484i 0.892175 0.451691i \(-0.149179\pi\)
−0.451691 + 0.892175i \(0.649179\pi\)
\(318\) −7563.15 2925.58i −1.33371 0.515906i
\(319\) 4947.38i 0.868338i
\(320\) 6683.73 6794.99i 1.16760 1.18704i
\(321\) 3110.35 2498.44i 0.540819 0.434422i
\(322\) 410.007 + 707.902i 0.0709590 + 0.122515i
\(323\) 4222.43 4222.43i 0.727376 0.727376i
\(324\) 4762.50 3366.12i 0.816616 0.577181i
\(325\) 6818.90 + 6818.90i 1.16383 + 1.16383i
\(326\) −831.008 221.443i −0.141182 0.0376215i
\(327\) −1075.77 1339.24i −0.181927 0.226484i
\(328\) 0.740370 + 179.394i 0.000124634 + 0.0301993i
\(329\) −2764.99 −0.463340
\(330\) 3770.11 + 8526.79i 0.628902 + 1.42238i
\(331\) −6593.02 + 6593.02i −1.09482 + 1.09482i −0.0998138 + 0.995006i \(0.531825\pi\)
−0.995006 + 0.0998138i \(0.968175\pi\)
\(332\) 1183.56 + 4368.97i 0.195651 + 0.722225i
\(333\) −1712.05 2682.48i −0.281742 0.441439i
\(334\) 1929.04 + 3330.61i 0.316025 + 0.545637i
\(335\) 7486.61 1.22101
\(336\) 4029.20 1801.42i 0.654199 0.292487i
\(337\) −9437.22 −1.52545 −0.762727 0.646721i \(-0.776140\pi\)
−0.762727 + 0.646721i \(0.776140\pi\)
\(338\) −428.521 739.868i −0.0689600 0.119064i
\(339\) 816.449 + 89.0736i 0.130807 + 0.0142708i
\(340\) 8176.43 2215.00i 1.30420 0.353309i
\(341\) −5296.77 + 5296.77i −0.841162 + 0.841162i
\(342\) 7119.32 + 3686.16i 1.12564 + 0.582822i
\(343\) 6766.74 1.06522
\(344\) −3487.94 3459.27i −0.546678 0.542184i
\(345\) −1643.47 + 1320.14i −0.256468 + 0.206012i
\(346\) 4133.74 + 1101.54i 0.642287 + 0.171154i
\(347\) −4032.00 4032.00i −0.623772 0.623772i 0.322722 0.946494i \(-0.395402\pi\)
−0.946494 + 0.322722i \(0.895402\pi\)
\(348\) 936.975 + 5962.04i 0.144331 + 0.918387i
\(349\) 2360.04 2360.04i 0.361978 0.361978i −0.502563 0.864541i \(-0.667609\pi\)
0.864541 + 0.502563i \(0.167609\pi\)
\(350\) −4168.06 7196.41i −0.636549 1.09904i
\(351\) −2707.79 5473.70i −0.411770 0.832378i
\(352\) −1637.47 5947.18i −0.247947 0.900528i
\(353\) 10824.1i 1.63203i 0.578028 + 0.816017i \(0.303822\pi\)
−0.578028 + 0.816017i \(0.696178\pi\)
\(354\) 1664.24 4302.37i 0.249869 0.645956i
\(355\) 354.957 + 354.957i 0.0530680 + 0.0530680i
\(356\) 3878.82 6761.21i 0.577464 1.00658i
\(357\) 3899.54 + 425.435i 0.578111 + 0.0630712i
\(358\) 325.038 1219.77i 0.0479854 0.180074i
\(359\) 6848.83i 1.00687i 0.864032 + 0.503437i \(0.167931\pi\)
−0.864032 + 0.503437i \(0.832069\pi\)
\(360\) 6158.19 + 9561.54i 0.901570 + 1.39983i
\(361\) 4161.67i 0.606746i
\(362\) 13019.9 + 3469.48i 1.89036 + 0.503735i
\(363\) −877.085 95.6889i −0.126818 0.0138357i
\(364\) −1208.43 4460.78i −0.174008 0.642331i
\(365\) −11049.8 11049.8i −1.58458 1.58458i
\(366\) −8071.83 3122.34i −1.15279 0.445922i
\(367\) 3892.20i 0.553600i 0.960928 + 0.276800i \(0.0892739\pi\)
−0.960928 + 0.276800i \(0.910726\pi\)
\(368\) 1204.03 704.009i 0.170556 0.0997256i
\(369\) −209.026 46.1584i −0.0294891 0.00651196i
\(370\) 5370.09 3110.28i 0.754535 0.437016i
\(371\) 5178.07 5178.07i 0.724614 0.724614i
\(372\) −5379.95 + 7386.24i −0.749831 + 1.02946i
\(373\) 726.671 + 726.671i 0.100873 + 0.100873i 0.755742 0.654869i \(-0.227276\pi\)
−0.654869 + 0.755742i \(0.727276\pi\)
\(374\) 1411.67 5297.56i 0.195176 0.732434i
\(375\) 7280.59 5848.25i 1.00258 0.805339i
\(376\) 19.4553 + 4714.08i 0.00266844 + 0.646569i
\(377\) 6319.64 0.863337
\(378\) 1040.95 + 5162.55i 0.141642 + 0.702469i
\(379\) −9599.40 + 9599.40i −1.30102 + 1.30102i −0.373323 + 0.927701i \(0.621782\pi\)
−0.927701 + 0.373323i \(0.878218\pi\)
\(380\) −7779.76 + 13561.0i −1.05025 + 1.83069i
\(381\) −35.2335 3.84393i −0.00473770 0.000516878i
\(382\) 10777.7 6242.31i 1.44355 0.836085i
\(383\) 1980.73 0.264257 0.132129 0.991233i \(-0.457819\pi\)
0.132129 + 0.991233i \(0.457819\pi\)
\(384\) −3099.63 6856.78i −0.411919 0.911220i
\(385\) −8419.00 −1.11447
\(386\) −41.9704 + 24.3087i −0.00553429 + 0.00320538i
\(387\) 4941.15 3153.61i 0.649025 0.414230i
\(388\) −6191.85 + 10793.1i −0.810164 + 1.41220i
\(389\) 1173.36 1173.36i 0.152935 0.152935i −0.626493 0.779427i \(-0.715510\pi\)
0.779427 + 0.626493i \(0.215510\pi\)
\(390\) 10891.9 4815.83i 1.41418 0.625279i
\(391\) 1239.62 0.160333
\(392\) −15.5822 3775.60i −0.00200770 0.486471i
\(393\) −6875.53 8559.47i −0.882506 1.09865i
\(394\) −649.581 + 2437.68i −0.0830595 + 0.311697i
\(395\) 7331.93 + 7331.93i 0.933948 + 0.933948i
\(396\) 7352.31 347.381i 0.932998 0.0440822i
\(397\) 4110.76 4110.76i 0.519681 0.519681i −0.397794 0.917475i \(-0.630224\pi\)
0.917475 + 0.397794i \(0.130224\pi\)
\(398\) 5260.17 3046.61i 0.662483 0.383701i
\(399\) −5644.16 + 4533.76i −0.708174 + 0.568852i
\(400\) −12240.0 + 7156.83i −1.52999 + 0.894604i
\(401\) 4583.73i 0.570824i 0.958405 + 0.285412i \(0.0921305\pi\)
−0.958405 + 0.285412i \(0.907870\pi\)
\(402\) 2132.37 5512.58i 0.264560 0.683937i
\(403\) 6765.95 + 6765.95i 0.836317 + 0.836317i
\(404\) −1144.97 4226.53i −0.141001 0.520489i
\(405\) −12744.7 + 4662.61i −1.56368 + 0.572066i
\(406\) −5266.20 1403.31i −0.643736 0.171540i
\(407\) 4016.31i 0.489143i
\(408\) 697.894 6651.40i 0.0846836 0.807091i
\(409\) 1993.36i 0.240991i −0.992714 0.120495i \(-0.961552\pi\)
0.992714 0.120495i \(-0.0384483\pi\)
\(410\) 107.488 403.369i 0.0129474 0.0485878i
\(411\) −544.942 + 4994.94i −0.0654015 + 0.599470i
\(412\) 434.558 757.483i 0.0519640 0.0905789i
\(413\) 2945.59 + 2945.59i 0.350952 + 0.350952i
\(414\) 503.953 + 1586.14i 0.0598259 + 0.188296i
\(415\) 10532.9i 1.24587i
\(416\) −7596.76 + 2091.66i −0.895341 + 0.246519i
\(417\) −7156.66 8909.45i −0.840439 1.04628i
\(418\) 5071.15 + 8755.65i 0.593392 + 1.02453i
\(419\) −11865.9 + 11865.9i −1.38350 + 1.38350i −0.545172 + 0.838324i \(0.683536\pi\)
−0.838324 + 0.545172i \(0.816464\pi\)
\(420\) −10145.7 + 1594.46i −1.17871 + 0.185242i
\(421\) −6803.31 6803.31i −0.787584 0.787584i 0.193513 0.981098i \(-0.438012\pi\)
−0.981098 + 0.193513i \(0.938012\pi\)
\(422\) −12451.6 3318.04i −1.43633 0.382748i
\(423\) −5492.76 1212.94i −0.631364 0.139422i
\(424\) −8864.61 8791.74i −1.01534 1.00699i
\(425\) −12601.8 −1.43830
\(426\) 362.464 160.263i 0.0412240 0.0182271i
\(427\) 5526.33 5526.33i 0.626318 0.626318i
\(428\) 5928.62 1606.07i 0.669558 0.181383i
\(429\) 835.907 7661.93i 0.0940745 0.862288i
\(430\) 5729.16 + 9891.74i 0.642522 + 1.10935i
\(431\) 9052.23 1.01167 0.505836 0.862630i \(-0.331184\pi\)
0.505836 + 0.862630i \(0.331184\pi\)
\(432\) 8794.41 1811.07i 0.979447 0.201701i
\(433\) 16081.2 1.78479 0.892395 0.451255i \(-0.149023\pi\)
0.892395 + 0.451255i \(0.149023\pi\)
\(434\) −4135.69 7140.52i −0.457418 0.789761i
\(435\) 1523.11 13960.9i 0.167880 1.53879i
\(436\) −691.534 2552.72i −0.0759598 0.280398i
\(437\) −1617.72 + 1617.72i −0.177085 + 0.177085i
\(438\) −11283.5 + 4988.97i −1.23093 + 0.544252i
\(439\) −2902.39 −0.315543 −0.157771 0.987476i \(-0.550431\pi\)
−0.157771 + 0.987476i \(0.550431\pi\)
\(440\) 59.2387 + 14353.7i 0.00641840 + 1.55520i
\(441\) 4399.26 + 971.471i 0.475031 + 0.104899i
\(442\) −6766.96 1803.23i −0.728216 0.194051i
\(443\) −9852.62 9852.62i −1.05669 1.05669i −0.998294 0.0583928i \(-0.981402\pi\)
−0.0583928 0.998294i \(-0.518598\pi\)
\(444\) −760.641 4840.02i −0.0813028 0.517336i
\(445\) −12825.6 + 12825.6i −1.36628 + 1.36628i
\(446\) −185.813 320.818i −0.0197276 0.0340609i
\(447\) 10061.3 + 12525.5i 1.06461 + 1.32536i
\(448\) 6794.90 56.0869i 0.716582 0.00591486i
\(449\) 8127.08i 0.854210i 0.904202 + 0.427105i \(0.140467\pi\)
−0.904202 + 0.427105i \(0.859533\pi\)
\(450\) −5123.09 16124.4i −0.536678 1.68914i
\(451\) −191.036 191.036i −0.0199458 0.0199458i
\(452\) 1096.79 + 629.217i 0.114135 + 0.0654776i
\(453\) −298.918 + 2739.89i −0.0310031 + 0.284175i
\(454\) −2887.33 + 10835.3i −0.298478 + 1.12010i
\(455\) 10754.2i 1.10805i
\(456\) 7769.41 + 9590.93i 0.797886 + 0.984949i
\(457\) 6183.95i 0.632982i −0.948596 0.316491i \(-0.897495\pi\)
0.948596 0.316491i \(-0.102505\pi\)
\(458\) −17821.3 4748.95i −1.81820 0.484506i
\(459\) 7559.97 + 2555.79i 0.768778 + 0.259900i
\(460\) −3132.61 + 848.624i −0.317518 + 0.0860158i
\(461\) 11493.6 + 11493.6i 1.16119 + 1.16119i 0.984215 + 0.176979i \(0.0566326\pi\)
0.176979 + 0.984215i \(0.443367\pi\)
\(462\) −2397.94 + 6199.12i −0.241477 + 0.624262i
\(463\) 6524.21i 0.654872i 0.944873 + 0.327436i \(0.106185\pi\)
−0.944873 + 0.327436i \(0.893815\pi\)
\(464\) −2355.48 + 8988.31i −0.235669 + 0.899293i
\(465\) 16577.5 13316.1i 1.65325 1.32800i
\(466\) −1359.78 + 787.566i −0.135173 + 0.0782904i
\(467\) −1512.73 + 1512.73i −0.149895 + 0.149895i −0.778071 0.628176i \(-0.783802\pi\)
0.628176 + 0.778071i \(0.283802\pi\)
\(468\) −443.735 9391.63i −0.0438283 0.927624i
\(469\) 3774.15 + 3774.15i 0.371587 + 0.371587i
\(470\) 2824.55 10599.7i 0.277206 1.04027i
\(471\) −605.316 753.568i −0.0592176 0.0737210i
\(472\) 5001.27 5042.72i 0.487716 0.491758i
\(473\) 7398.07 0.719162
\(474\) 7487.00 3310.37i 0.725505 0.320781i
\(475\) 16445.5 16445.5i 1.58857 1.58857i
\(476\) 5238.53 + 3005.28i 0.504428 + 0.289384i
\(477\) 12557.9 8014.92i 1.20543 0.769346i
\(478\) 7509.57 4349.44i 0.718577 0.416190i
\(479\) 7262.60 0.692769 0.346385 0.938093i \(-0.387409\pi\)
0.346385 + 0.938093i \(0.387409\pi\)
\(480\) 2789.81 + 17286.3i 0.265285 + 1.64377i
\(481\) −5130.32 −0.486325
\(482\) −6076.05 + 3519.16i −0.574183 + 0.332559i
\(483\) −1494.02 162.995i −0.140746 0.0153552i
\(484\) −1178.25 675.948i −0.110655 0.0634812i
\(485\) 20473.9 20473.9i 1.91685 1.91685i
\(486\) −196.812 + 10712.3i −0.0183695 + 0.999831i
\(487\) −5716.55 −0.531913 −0.265957 0.963985i \(-0.585688\pi\)
−0.265957 + 0.963985i \(0.585688\pi\)
\(488\) −9460.82 9383.05i −0.877605 0.870391i
\(489\) 1231.76 989.427i 0.113910 0.0914999i
\(490\) −2262.24 + 8489.50i −0.208567 + 0.782686i
\(491\) 3886.38 + 3886.38i 0.357209 + 0.357209i 0.862783 0.505574i \(-0.168719\pi\)
−0.505574 + 0.862783i \(0.668719\pi\)
\(492\) −266.396 194.036i −0.0244107 0.0177801i
\(493\) −5839.55 + 5839.55i −0.533469 + 0.533469i
\(494\) 11184.2 6477.74i 1.01863 0.589974i
\(495\) −16724.7 3693.24i −1.51862 0.335351i
\(496\) −12144.9 + 7101.26i −1.09944 + 0.642855i
\(497\) 357.882i 0.0323002i
\(498\) −7755.60 3000.02i −0.697865 0.269948i
\(499\) 2623.92 + 2623.92i 0.235396 + 0.235396i 0.814941 0.579544i \(-0.196769\pi\)
−0.579544 + 0.814941i \(0.696769\pi\)
\(500\) 13877.5 3759.41i 1.24124 0.336252i
\(501\) −7029.20 766.877i −0.626829 0.0683863i
\(502\) 13025.2 + 3470.89i 1.15805 + 0.308593i
\(503\) 8844.21i 0.783983i −0.919969 0.391992i \(-0.871786\pi\)
0.919969 0.391992i \(-0.128214\pi\)
\(504\) −1715.70 + 7924.64i −0.151633 + 0.700380i
\(505\) 10189.4i 0.897870i
\(506\) −540.848 + 2029.64i −0.0475170 + 0.178317i
\(507\) 1561.48 + 170.356i 0.136781 + 0.0149226i
\(508\) −47.3316 27.1536i −0.00413386 0.00237154i
\(509\) −6445.60 6445.60i −0.561289 0.561289i 0.368385 0.929673i \(-0.379911\pi\)
−0.929673 + 0.368385i \(0.879911\pi\)
\(510\) −5614.47 + 14514.4i −0.487476 + 1.26022i
\(511\) 11140.8i 0.964464i
\(512\) −143.435 11584.3i −0.0123808 0.999923i
\(513\) −13201.2 + 6530.52i −1.13616 + 0.562046i
\(514\) −2353.77 4063.92i −0.201985 0.348739i
\(515\) −1436.90 + 1436.90i −0.122947 + 0.122947i
\(516\) 8915.34 1401.11i 0.760612 0.119535i
\(517\) −5020.01 5020.01i −0.427040 0.427040i
\(518\) 4275.13 + 1139.22i 0.362622 + 0.0966299i
\(519\) −6127.21 + 4921.78i −0.518217 + 0.416266i
\(520\) 18335.0 75.6698i 1.54624 0.00638143i
\(521\) −3935.63 −0.330946 −0.165473 0.986214i \(-0.552915\pi\)
−0.165473 + 0.986214i \(0.552915\pi\)
\(522\) −9845.90 5097.90i −0.825562 0.427451i
\(523\) 7725.31 7725.31i 0.645897 0.645897i −0.306102 0.951999i \(-0.599025\pi\)
0.951999 + 0.306102i \(0.0990248\pi\)
\(524\) −4419.78 16315.2i −0.368471 1.36017i
\(525\) 15187.9 + 1656.98i 1.26258 + 0.137746i
\(526\) −5367.88 9267.97i −0.444963 0.768256i
\(527\) −12503.9 −1.03355
\(528\) 10585.9 + 4044.67i 0.872520 + 0.333375i
\(529\) 11692.1 0.960966
\(530\) 14560.7 + 25139.9i 1.19335 + 2.06039i
\(531\) 4559.36 + 7143.70i 0.372617 + 0.583824i
\(532\) −10758.3 + 2914.43i −0.876751 + 0.237512i
\(533\) −244.024 + 244.024i −0.0198309 + 0.0198309i
\(534\) 5790.78 + 13096.9i 0.469272 + 1.06135i
\(535\) −14292.9 −1.15502
\(536\) 6408.07 6461.18i 0.516393 0.520673i
\(537\) 1452.30 + 1807.99i 0.116706 + 0.145290i
\(538\) −580.298 154.635i −0.0465027 0.0123918i
\(539\) 4020.63 + 4020.63i 0.321300 + 0.321300i
\(540\) −20854.2 1283.24i −1.66189 0.102262i
\(541\) −11787.8 + 11787.8i −0.936779 + 0.936779i −0.998117 0.0613379i \(-0.980463\pi\)
0.0613379 + 0.998117i \(0.480463\pi\)
\(542\) 6634.84 + 11455.5i 0.525813 + 0.907848i
\(543\) −19298.7 + 15502.0i −1.52520 + 1.22514i
\(544\) 5086.90 8952.42i 0.400917 0.705573i
\(545\) 6154.19i 0.483700i
\(546\) 7918.57 + 3063.06i 0.620666 + 0.240086i
\(547\) 2125.15 + 2125.15i 0.166115 + 0.166115i 0.785269 0.619154i \(-0.212524\pi\)
−0.619154 + 0.785269i \(0.712524\pi\)
\(548\) −3849.48 + 6710.05i −0.300076 + 0.523064i
\(549\) 13402.6 8553.98i 1.04191 0.664982i
\(550\) 5498.16 20632.9i 0.426259 1.59962i
\(551\) 15241.4i 1.17841i
\(552\) −267.382 + 2548.32i −0.0206169 + 0.196493i
\(553\) 7392.35i 0.568454i
\(554\) 12569.7 + 3349.52i 0.963964 + 0.256872i
\(555\) −1236.47 + 11333.5i −0.0945681 + 0.866811i
\(556\) −4600.49 16982.2i −0.350907 1.29534i
\(557\) −16766.5 16766.5i −1.27544 1.27544i −0.943194 0.332244i \(-0.892194\pi\)
−0.332244 0.943194i \(-0.607806\pi\)
\(558\) −5083.31 15999.2i −0.385652 1.21380i
\(559\) 9450.08i 0.715019i
\(560\) −15295.5 4008.33i −1.15420 0.302470i
\(561\) 6307.46 + 7852.27i 0.474690 + 0.590951i
\(562\) −14477.5 + 8385.15i −1.08665 + 0.629371i
\(563\) 146.888 146.888i 0.0109957 0.0109957i −0.701588 0.712583i \(-0.747525\pi\)
0.712583 + 0.701588i \(0.247525\pi\)
\(564\) −7000.30 5098.84i −0.522635 0.380674i
\(565\) −2080.56 2080.56i −0.154920 0.154920i
\(566\) −4976.61 + 18675.7i −0.369581 + 1.38692i
\(567\) −8775.37 4074.34i −0.649967 0.301775i
\(568\) 610.159 2.51817i 0.0450734 0.000186021i
\(569\) −8315.12 −0.612632 −0.306316 0.951930i \(-0.599096\pi\)
−0.306316 + 0.951930i \(0.599096\pi\)
\(570\) −11614.6 26268.5i −0.853476 1.93029i
\(571\) −923.361 + 923.361i −0.0676733 + 0.0676733i −0.740133 0.672460i \(-0.765238\pi\)
0.672460 + 0.740133i \(0.265238\pi\)
\(572\) 5904.86 10292.8i 0.431634 0.752384i
\(573\) −2481.59 + 22746.2i −0.180925 + 1.65836i
\(574\) 257.534 149.160i 0.0187269 0.0108464i
\(575\) 4828.07 0.350164
\(576\) 13522.9 + 2869.36i 0.978221 + 0.207564i
\(577\) −6240.12 −0.450225 −0.225112 0.974333i \(-0.572275\pi\)
−0.225112 + 0.974333i \(0.572275\pi\)
\(578\) −4105.65 + 2377.93i −0.295454 + 0.171123i
\(579\) 9.66374 88.5779i 0.000693629 0.00635781i
\(580\) 10759.3 18754.6i 0.770267 1.34266i
\(581\) 5309.83 5309.83i 0.379154 0.379154i
\(582\) −9243.95 20906.9i −0.658375 1.48904i
\(583\) 18802.2 1.33569
\(584\) −18994.2 + 78.3904i −1.34587 + 0.00555448i
\(585\) −4717.64 + 21363.6i −0.333420 + 1.50987i
\(586\) 2353.26 8831.07i 0.165891 0.622540i
\(587\) −13765.9 13765.9i −0.967940 0.967940i 0.0315623 0.999502i \(-0.489952\pi\)
−0.999502 + 0.0315623i \(0.989952\pi\)
\(588\) 5606.68 + 4083.76i 0.393224 + 0.286414i
\(589\) 16317.8 16317.8i 1.14153 1.14153i
\(590\) −14301.1 + 8282.98i −0.997908 + 0.577974i
\(591\) −2902.39 3613.23i −0.202011 0.251486i
\(592\) 1912.19 7296.76i 0.132754 0.506579i
\(593\) 19423.3i 1.34506i 0.740070 + 0.672529i \(0.234792\pi\)
−0.740070 + 0.672529i \(0.765208\pi\)
\(594\) −7483.03 + 11262.9i −0.516889 + 0.777981i
\(595\) −9937.22 9937.22i −0.684683 0.684683i
\(596\) 6467.66 + 23874.7i 0.444506 + 1.64085i
\(597\) −1211.16 + 11101.5i −0.0830310 + 0.761063i
\(598\) 2592.60 + 690.863i 0.177290 + 0.0472433i
\(599\) 3592.25i 0.245034i −0.992466 0.122517i \(-0.960903\pi\)
0.992466 0.122517i \(-0.0390966\pi\)
\(600\) 2718.15 25905.8i 0.184947 1.76267i
\(601\) 18367.9i 1.24666i 0.781959 + 0.623330i \(0.214221\pi\)
−0.781959 + 0.623330i \(0.785779\pi\)
\(602\) −2098.44 + 7874.81i −0.142070 + 0.533145i
\(603\) 5841.86 + 9153.15i 0.394526 + 0.618151i
\(604\) −2111.56 + 3680.68i −0.142249 + 0.247955i
\(605\) 2235.08 + 2235.08i 0.150196 + 0.150196i
\(606\) 7502.74 + 2902.21i 0.502934 + 0.194545i
\(607\) 3812.82i 0.254955i −0.991841 0.127477i \(-0.959312\pi\)
0.991841 0.127477i \(-0.0406880\pi\)
\(608\) 5044.56 + 18321.5i 0.336486 + 1.22210i
\(609\) 7805.78 6270.12i 0.519386 0.417205i
\(610\) 15540.0 + 26830.7i 1.03147 + 1.78089i
\(611\) −6412.42 + 6412.42i −0.424581 + 0.424581i
\(612\) 9088.19 + 8268.14i 0.600275 + 0.546111i
\(613\) 2161.57 + 2161.57i 0.142422 + 0.142422i 0.774723 0.632301i \(-0.217889\pi\)
−0.632301 + 0.774723i \(0.717889\pi\)
\(614\) 25523.5 + 6801.37i 1.67759 + 0.447038i
\(615\) 480.266 + 597.891i 0.0314897 + 0.0392021i
\(616\) −7206.13 + 7265.86i −0.471336 + 0.475243i
\(617\) −14720.8 −0.960514 −0.480257 0.877128i \(-0.659457\pi\)
−0.480257 + 0.877128i \(0.659457\pi\)
\(618\) 648.762 + 1467.29i 0.0422282 + 0.0955069i
\(619\) 717.009 717.009i 0.0465574 0.0465574i −0.683445 0.730002i \(-0.739519\pi\)
0.730002 + 0.683445i \(0.239519\pi\)
\(620\) 31598.2 8559.97i 2.04680 0.554478i
\(621\) −2896.42 979.192i −0.187165 0.0632747i
\(622\) 246.130 + 424.958i 0.0158664 + 0.0273943i
\(623\) −12931.3 −0.831594
\(624\) 5166.55 13522.1i 0.331454 0.867494i
\(625\) −5763.39 −0.368857
\(626\) −2464.07 4254.36i −0.157323 0.271627i
\(627\) −18478.7 2016.00i −1.17698 0.128407i
\(628\) −389.113 1436.37i −0.0247250 0.0912698i
\(629\) 4740.58 4740.58i 0.300508 0.300508i
\(630\) 8675.15 16754.9i 0.548613 1.05957i
\(631\) −12334.5 −0.778177 −0.389089 0.921200i \(-0.627210\pi\)
−0.389089 + 0.921200i \(0.627210\pi\)
\(632\) 12603.4 52.0149i 0.793251 0.00327380i
\(633\) 18456.3 14825.3i 1.15888 0.930888i
\(634\) −9609.09 2560.59i −0.601933 0.160400i
\(635\) 89.7855 + 89.7855i 0.00561107 + 0.00561107i
\(636\) 22658.4 3560.92i 1.41268 0.222012i
\(637\) 5135.84 5135.84i 0.319450 0.319450i
\(638\) −7013.31 12108.9i −0.435203 0.751405i
\(639\) −156.995 + 710.946i −0.00971931 + 0.0440134i
\(640\) −6726.26 + 26105.8i −0.415436 + 1.61238i
\(641\) 8618.93i 0.531088i −0.964099 0.265544i \(-0.914448\pi\)
0.964099 0.265544i \(-0.0855515\pi\)
\(642\) −4070.97 + 10524.2i −0.250263 + 0.646975i
\(643\) −13452.6 13452.6i −0.825069 0.825069i 0.161761 0.986830i \(-0.448283\pi\)
−0.986830 + 0.161761i \(0.948283\pi\)
\(644\) −2007.02 1151.40i −0.122807 0.0704528i
\(645\) −20876.4 2277.59i −1.27443 0.139039i
\(646\) −4348.94 + 16320.2i −0.264871 + 0.993979i
\(647\) 1049.63i 0.0637792i −0.999491 0.0318896i \(-0.989848\pi\)
0.999491 0.0318896i \(-0.0101525\pi\)
\(648\) −6884.67 + 14990.0i −0.417370 + 0.908737i
\(649\) 10695.8i 0.646915i
\(650\) −26355.9 7023.19i −1.59040 0.423803i
\(651\) 15070.0 + 1644.12i 0.907279 + 0.0989831i
\(652\) 2347.84 636.031i 0.141025 0.0382038i
\(653\) −1524.78 1524.78i −0.0913773 0.0913773i 0.659941 0.751318i \(-0.270581\pi\)
−0.751318 + 0.659941i \(0.770581\pi\)
\(654\) 4531.48 + 1752.87i 0.270940 + 0.104805i
\(655\) 39333.1i 2.34637i
\(656\) −256.117 438.024i −0.0152435 0.0260701i
\(657\) 4887.25 22131.7i 0.290213 1.31422i
\(658\) 6767.43 3919.60i 0.400945 0.232222i
\(659\) 4377.44 4377.44i 0.258757 0.258757i −0.565791 0.824548i \(-0.691429\pi\)
0.824548 + 0.565791i \(0.191429\pi\)
\(660\) −21314.9 15525.2i −1.25709 0.915635i
\(661\) −15078.1 15078.1i −0.887249 0.887249i 0.107009 0.994258i \(-0.465873\pi\)
−0.994258 + 0.107009i \(0.965873\pi\)
\(662\) 6790.55 25482.9i 0.398674 1.49610i
\(663\) 10030.3 8056.98i 0.587547 0.471956i
\(664\) −9090.18 9015.46i −0.531276 0.526909i
\(665\) 25936.4 1.51244
\(666\) 7992.96 + 4138.51i 0.465046 + 0.240787i
\(667\) 2237.29 2237.29i 0.129877 0.129877i
\(668\) −9442.82 5417.23i −0.546936 0.313771i
\(669\) 677.082 + 73.8688i 0.0391293 + 0.00426896i
\(670\) −18323.8 + 10612.9i −1.05658 + 0.611958i
\(671\) 20066.8 1.15450
\(672\) −7307.97 + 10120.8i −0.419511 + 0.580978i
\(673\) −7399.64 −0.423826 −0.211913 0.977288i \(-0.567969\pi\)
−0.211913 + 0.977288i \(0.567969\pi\)
\(674\) 23098.0 13378.0i 1.32003 0.764544i
\(675\) 29444.5 + 9954.28i 1.67899 + 0.567616i
\(676\) 2097.65 + 1203.39i 0.119347 + 0.0684680i
\(677\) 9744.54 9744.54i 0.553195 0.553195i −0.374166 0.927362i \(-0.622071\pi\)
0.927362 + 0.374166i \(0.122071\pi\)
\(678\) −2124.56 + 939.372i −0.120344 + 0.0532100i
\(679\) 20642.6 1.16670
\(680\) −16872.2 + 17012.1i −0.951500 + 0.959387i
\(681\) −12900.8 16060.5i −0.725934 0.903728i
\(682\) 5455.46 20472.7i 0.306306 1.14947i
\(683\) −10398.5 10398.5i −0.582560 0.582560i 0.353046 0.935606i \(-0.385146\pi\)
−0.935606 + 0.353046i \(0.885146\pi\)
\(684\) −22650.3 + 1070.18i −1.26616 + 0.0598235i
\(685\) 12728.6 12728.6i 0.709979 0.709979i
\(686\) −16561.9 + 9592.41i −0.921772 + 0.533877i
\(687\) 26415.6 21218.7i 1.46698 1.17838i
\(688\) 13440.7 + 3522.26i 0.744798 + 0.195182i
\(689\) 24017.4i 1.32800i
\(690\) 2151.05 5560.86i 0.118680 0.306809i
\(691\) 20999.5 + 20999.5i 1.15609 + 1.15609i 0.985309 + 0.170779i \(0.0546285\pi\)
0.170779 + 0.985309i \(0.445371\pi\)
\(692\) −11679.0 + 3163.85i −0.641575 + 0.173803i
\(693\) −6569.41 10293.1i −0.360103 0.564216i
\(694\) 15584.2 + 4152.79i 0.852402 + 0.227144i
\(695\) 40941.3i 2.23452i
\(696\) −10745.0 13264.1i −0.585182 0.722377i
\(697\) 450.972i 0.0245076i
\(698\) −2430.75 + 9121.86i −0.131813 + 0.494653i
\(699\) 313.092 2869.80i 0.0169416 0.155287i
\(700\) 20403.0 + 11704.9i 1.10166 + 0.632007i
\(701\) 5471.04 + 5471.04i 0.294777 + 0.294777i 0.838964 0.544187i \(-0.183162\pi\)
−0.544187 + 0.838964i \(0.683162\pi\)
\(702\) 14386.9 + 9558.61i 0.773500 + 0.513912i
\(703\) 12373.1i 0.663810i
\(704\) 12438.4 + 12234.7i 0.665894 + 0.654991i
\(705\) 12620.3 + 15711.3i 0.674198 + 0.839321i
\(706\) −15344.0 26492.4i −0.817960 1.41226i
\(707\) −5136.71 + 5136.71i −0.273247 + 0.273247i
\(708\) 2025.66 + 12889.4i 0.107527 + 0.684201i
\(709\) 12117.6 + 12117.6i 0.641872 + 0.641872i 0.951015 0.309144i \(-0.100042\pi\)
−0.309144 + 0.951015i \(0.600042\pi\)
\(710\) −1371.95 365.591i −0.0725189 0.0193245i
\(711\) −3242.87 + 14685.2i −0.171051 + 0.774596i
\(712\) 90.9890 + 22046.9i 0.00478926 + 1.16045i
\(713\) 4790.58 0.251625
\(714\) −10147.4 + 4486.65i −0.531872 + 0.235166i
\(715\) −19524.9 + 19524.9i −1.02124 + 1.02124i
\(716\) 933.575 + 3446.20i 0.0487281 + 0.179875i
\(717\) −1729.09 + 15848.8i −0.0900614 + 0.825503i
\(718\) −9708.78 16762.8i −0.504636 0.871285i
\(719\) 9829.79 0.509860 0.254930 0.966960i \(-0.417948\pi\)
0.254930 + 0.966960i \(0.417948\pi\)
\(720\) −28626.7 14672.5i −1.48174 0.759462i
\(721\) −1448.75 −0.0748323
\(722\) −5899.51 10185.9i −0.304095 0.525039i
\(723\) 1399.02 12823.4i 0.0719641 0.659624i
\(724\) −36785.0 + 9965.08i −1.88827 + 0.511532i
\(725\) −22743.8 + 22743.8i −1.16508 + 1.16508i
\(726\) 2282.35 1009.14i 0.116675 0.0515876i
\(727\) 16104.0 0.821544 0.410772 0.911738i \(-0.365259\pi\)
0.410772 + 0.911738i \(0.365259\pi\)
\(728\) 9281.20 + 9204.90i 0.472506 + 0.468621i
\(729\) −15645.3 11943.4i −0.794863 0.606788i
\(730\) 42708.7 + 11380.8i 2.16537 + 0.577018i
\(731\) 8732.18 + 8732.18i 0.441821 + 0.441821i
\(732\) 24182.3 3800.41i 1.22104 0.191895i
\(733\) −7100.49 + 7100.49i −0.357794 + 0.357794i −0.862999 0.505205i \(-0.831417\pi\)
0.505205 + 0.862999i \(0.331417\pi\)
\(734\) −5517.51 9526.32i −0.277459 0.479050i
\(735\) −10107.9 12583.5i −0.507259 0.631495i
\(736\) −1948.92 + 3429.90i −0.0976064 + 0.171777i
\(737\) 13704.4i 0.684952i
\(738\) 577.034 183.337i 0.0287817 0.00914463i
\(739\) −22439.6 22439.6i −1.11699 1.11699i −0.992181 0.124809i \(-0.960168\pi\)
−0.124809 0.992181i \(-0.539832\pi\)
\(740\) −8734.45 + 15225.1i −0.433898 + 0.756332i
\(741\) −2575.18 + 23604.1i −0.127668 + 1.17020i
\(742\) −5333.20 + 20013.9i −0.263865 + 0.990205i
\(743\) 35681.0i 1.76179i −0.473315 0.880893i \(-0.656943\pi\)
0.473315 0.880893i \(-0.343057\pi\)
\(744\) 2697.05 25704.6i 0.132901 1.26664i
\(745\) 57557.8i 2.83054i
\(746\) −2808.67 748.442i −0.137846 0.0367324i
\(747\) 12877.5 8218.87i 0.630740 0.402560i
\(748\) 4054.61 + 14967.2i 0.198197 + 0.731623i
\(749\) −7205.34 7205.34i −0.351505 0.351505i
\(750\) −9529.18 + 24634.7i −0.463942 + 1.19937i
\(751\) 18143.3i 0.881570i −0.897613 0.440785i \(-0.854700\pi\)
0.897613 0.440785i \(-0.145300\pi\)
\(752\) −6730.21 11510.3i −0.326364 0.558163i
\(753\) −19306.5 + 15508.3i −0.934354 + 0.750535i
\(754\) −15467.6 + 8958.61i −0.747077 + 0.432697i
\(755\) 6982.06 6982.06i 0.336561 0.336561i
\(756\) −9866.12 11159.9i −0.474639 0.536882i
\(757\) 15294.6 + 15294.6i 0.734333 + 0.734333i 0.971475 0.237142i \(-0.0762107\pi\)
−0.237142 + 0.971475i \(0.576211\pi\)
\(758\) 9887.00 37102.9i 0.473763 1.77789i
\(759\) −2416.55 3008.41i −0.115567 0.143871i
\(760\) −182.497 44219.5i −0.00871034 2.11054i
\(761\) −8250.67 −0.393018 −0.196509 0.980502i \(-0.562960\pi\)
−0.196509 + 0.980502i \(0.562960\pi\)
\(762\) 91.6845 40.5382i 0.00435876 0.00192722i
\(763\) −3102.45 + 3102.45i −0.147203 + 0.147203i
\(764\) −17530.0 + 30556.6i −0.830120 + 1.44699i
\(765\) −15381.4 24099.9i −0.726950 1.13900i
\(766\) −4847.91 + 2807.84i −0.228671 + 0.132443i
\(767\) 13662.5 0.643188
\(768\) 17306.5 + 12388.3i 0.813144 + 0.582062i
\(769\) 13914.2 0.652480 0.326240 0.945287i \(-0.394218\pi\)
0.326240 + 0.945287i \(0.394218\pi\)
\(770\) 20605.8 11934.6i 0.964394 0.558563i
\(771\) 8576.85 + 935.724i 0.400633 + 0.0437085i
\(772\) 68.2648 118.993i 0.00318252 0.00554747i
\(773\) −22064.4 + 22064.4i −1.02665 + 1.02665i −0.0270161 + 0.999635i \(0.508601\pi\)
−0.999635 + 0.0270161i \(0.991399\pi\)
\(774\) −7623.16 + 14723.1i −0.354016 + 0.683734i
\(775\) −48700.1 −2.25724
\(776\) −145.248 35193.9i −0.00671919 1.62808i
\(777\) −6336.78 + 5090.12i −0.292575 + 0.235015i
\(778\) −1208.51 + 4535.17i −0.0556905 + 0.208990i
\(779\) 588.525 + 588.525i 0.0270682 + 0.0270682i
\(780\) −19831.5 + 27227.1i −0.910361 + 1.24985i
\(781\) −649.757 + 649.757i −0.0297697 + 0.0297697i
\(782\) −3034.02 + 1757.26i −0.138742 + 0.0803576i
\(783\) 18257.1 9031.60i 0.833275 0.412213i
\(784\) 5390.36 + 9218.86i 0.245552 + 0.419955i
\(785\) 3462.85i 0.157445i
\(786\) 28961.9 + 11203.0i 1.31430 + 0.508396i
\(787\) 23376.5 + 23376.5i 1.05881 + 1.05881i 0.998159 + 0.0606482i \(0.0193168\pi\)
0.0606482 + 0.998159i \(0.480683\pi\)
\(788\) −1865.73 6887.16i −0.0843451 0.311351i
\(789\) 19559.9 + 2133.96i 0.882574 + 0.0962878i
\(790\) −28338.8 7551.60i −1.27627 0.340093i
\(791\) 2097.70i 0.0942930i
\(792\) −17502.6 + 11272.7i −0.785264 + 0.505756i
\(793\) 25632.8i 1.14785i
\(794\) −4233.92 + 15888.6i −0.189240 + 0.710158i
\(795\) −53057.4 5788.50i −2.36698 0.258235i
\(796\) −8555.65 + 14913.4i −0.380964 + 0.664061i
\(797\) 12076.4 + 12076.4i 0.536722 + 0.536722i 0.922565 0.385843i \(-0.126089\pi\)
−0.385843 + 0.922565i \(0.626089\pi\)
\(798\) 7387.34 19097.6i 0.327706 0.847179i
\(799\) 11850.6i 0.524710i
\(800\) 19812.4 34867.8i 0.875593 1.54095i
\(801\) −25688.6 5672.71i −1.13316 0.250232i
\(802\) −6497.81 11218.9i −0.286092 0.493955i
\(803\) 20226.9 20226.9i 0.888906 0.888906i
\(804\) 2595.46 + 16515.1i 0.113849 + 0.724431i
\(805\) 3807.21 + 3807.21i 0.166691 + 0.166691i
\(806\) −26151.2 6968.66i −1.14285 0.304541i
\(807\) 860.143 690.924i 0.0375198 0.0301384i
\(808\) 8793.81 + 8721.52i 0.382878 + 0.379730i
\(809\) −6997.79 −0.304115 −0.152058 0.988372i \(-0.548590\pi\)
−0.152058 + 0.988372i \(0.548590\pi\)
\(810\) 24583.5 29478.6i 1.06639 1.27873i
\(811\) −16186.9 + 16186.9i −0.700860 + 0.700860i −0.964595 0.263735i \(-0.915046\pi\)
0.263735 + 0.964595i \(0.415046\pi\)
\(812\) 14878.5 4030.60i 0.643023 0.174195i
\(813\) −24176.6 2637.63i −1.04294 0.113783i
\(814\) 5693.45 + 9830.09i 0.245154 + 0.423273i
\(815\) −5660.25 −0.243276
\(816\) 7720.78 + 17268.9i 0.331227 + 0.740848i
\(817\) −22791.2 −0.975967
\(818\) 2825.75 + 4878.82i 0.120782 + 0.208538i
\(819\) −13148.1 + 8391.57i −0.560966 + 0.358028i
\(820\) 308.728 + 1139.64i 0.0131479 + 0.0485339i
\(821\) 11255.6 11255.6i 0.478467 0.478467i −0.426174 0.904641i \(-0.640139\pi\)
0.904641 + 0.426174i \(0.140139\pi\)
\(822\) −5746.97 12997.8i −0.243855 0.551522i
\(823\) 22030.1 0.933073 0.466537 0.884502i \(-0.345502\pi\)
0.466537 + 0.884502i \(0.345502\pi\)
\(824\) 10.1938 + 2469.99i 0.000430969 + 0.104425i
\(825\) 24566.3 + 30583.0i 1.03671 + 1.29062i
\(826\) −11385.1 3033.84i −0.479585 0.127798i
\(827\) 25411.8 + 25411.8i 1.06851 + 1.06851i 0.997474 + 0.0710322i \(0.0226293\pi\)
0.0710322 + 0.997474i \(0.477371\pi\)
\(828\) −3481.93 3167.74i −0.146142 0.132955i
\(829\) 5834.97 5834.97i 0.244459 0.244459i −0.574233 0.818692i \(-0.694700\pi\)
0.818692 + 0.574233i \(0.194700\pi\)
\(830\) 14931.2 + 25779.6i 0.624420 + 1.07810i
\(831\) −18631.4 + 14965.9i −0.777756 + 0.624744i
\(832\) 15628.3 15888.5i 0.651219 0.662059i
\(833\) 9491.36i 0.394785i
\(834\) 30146.1 + 11661.1i 1.25165 + 0.484162i
\(835\) 17912.5 + 17912.5i 0.742381 + 0.742381i
\(836\) −24823.7 14241.0i −1.02697 0.589159i
\(837\) 29215.9 + 9876.99i 1.20651 + 0.407884i
\(838\) 12221.4 45863.0i 0.503794 1.89059i
\(839\) 45330.1i 1.86528i 0.360809 + 0.932640i \(0.382501\pi\)
−0.360809 + 0.932640i \(0.617499\pi\)
\(840\) 22571.6 18284.8i 0.927138 0.751054i
\(841\) 3310.39i 0.135733i
\(842\) 26295.6 + 7007.14i 1.07626 + 0.286796i
\(843\) 3333.46 30554.5i 0.136193 1.24834i
\(844\) 35179.3 9530.09i 1.43474 0.388672i
\(845\) −3979.12 3979.12i −0.161995 0.161995i
\(846\) 15163.2 4817.71i 0.616220 0.195787i
\(847\) 2253.50i 0.0914180i
\(848\) 34159.5 + 8951.85i 1.38331 + 0.362509i
\(849\) −22236.0 27681.9i −0.898864 1.11901i
\(850\) 30843.4 17864.0i 1.24461 0.720860i
\(851\) −1816.24 + 1816.24i −0.0731609 + 0.0731609i
\(852\) −659.960 + 906.072i −0.0265374 + 0.0364337i
\(853\) −6205.70 6205.70i −0.249096 0.249096i 0.571503 0.820600i \(-0.306360\pi\)
−0.820600 + 0.571503i \(0.806360\pi\)
\(854\) −5691.90 + 21359.9i −0.228071 + 0.855881i
\(855\) 51523.7 + 11377.8i 2.06091 + 0.455101i
\(856\) −12233.8 + 12335.2i −0.488485 + 0.492534i
\(857\) −29172.6 −1.16280 −0.581398 0.813619i \(-0.697494\pi\)
−0.581398 + 0.813619i \(0.697494\pi\)
\(858\) 8815.49 + 19937.9i 0.350765 + 0.793318i
\(859\) −20666.9 + 20666.9i −0.820891 + 0.820891i −0.986236 0.165344i \(-0.947126\pi\)
0.165344 + 0.986236i \(0.447126\pi\)
\(860\) −28044.7 16088.9i −1.11200 0.637938i
\(861\) −59.2975 + 543.521i −0.00234710 + 0.0215135i
\(862\) −22155.7 + 12832.3i −0.875437 + 0.507041i
\(863\) −43877.1 −1.73070 −0.865351 0.501167i \(-0.832904\pi\)
−0.865351 + 0.501167i \(0.832904\pi\)
\(864\) −18957.3 + 16899.5i −0.746461 + 0.665429i
\(865\) 28156.2 1.10675
\(866\) −39359.5 + 22796.4i −1.54444 + 0.894521i
\(867\) 945.331 8664.91i 0.0370301 0.339418i
\(868\) 20244.6 + 11614.1i 0.791642 + 0.454155i
\(869\) −13421.3 + 13421.3i −0.523919 + 0.523919i
\(870\) 16062.8 + 36328.9i 0.625953 + 1.41571i
\(871\) 17505.7 0.681006
\(872\) 5311.25 + 5267.59i 0.206263 + 0.204568i
\(873\) 41007.3 + 9055.48i 1.58979 + 0.351067i
\(874\) 1666.19 6252.70i 0.0644848 0.241992i
\(875\) −16866.0 16866.0i −0.651628 0.651628i
\(876\) 20544.5 28206.0i 0.792391 1.08789i
\(877\) −14728.7 + 14728.7i −0.567105 + 0.567105i −0.931316 0.364211i \(-0.881339\pi\)
0.364211 + 0.931316i \(0.381339\pi\)
\(878\) 7103.71 4114.37i 0.273051 0.158147i
\(879\) 10514.6 + 13089.8i 0.403468 + 0.502284i
\(880\) −20492.5 35047.3i −0.785004 1.34255i
\(881\) 40741.9i 1.55804i −0.627002 0.779018i \(-0.715718\pi\)
0.627002 0.779018i \(-0.284282\pi\)
\(882\) −12144.5 + 3858.60i −0.463636 + 0.147308i
\(883\) −10680.5 10680.5i −0.407054 0.407054i 0.473656 0.880710i \(-0.342934\pi\)
−0.880710 + 0.473656i \(0.842934\pi\)
\(884\) 19118.6 5179.24i 0.727409 0.197055i
\(885\) 3292.84 30182.2i 0.125071 1.14640i
\(886\) 38081.6 + 10147.8i 1.44399 + 0.384788i
\(887\) 7595.40i 0.287518i 0.989613 + 0.143759i \(0.0459191\pi\)
−0.989613 + 0.143759i \(0.954081\pi\)
\(888\) 8722.82 + 10767.9i 0.329638 + 0.406921i
\(889\) 90.5254i 0.00341521i
\(890\) 13209.9 49572.7i 0.497525 1.86706i
\(891\) −8535.02 23329.5i −0.320914 0.877179i
\(892\) 909.572 + 521.810i 0.0341421 + 0.0195869i
\(893\) 15465.2 + 15465.2i 0.579532 + 0.579532i
\(894\) −42381.3 16393.9i −1.58550 0.613305i
\(895\) 8308.19i 0.310293i
\(896\) −16551.3 + 9769.60i −0.617120 + 0.364263i
\(897\) −3842.86 + 3086.84i −0.143043 + 0.114901i
\(898\) −11520.8 19891.4i −0.428123 0.739180i
\(899\) −22567.2 + 22567.2i −0.837218 + 0.837218i
\(900\) 35396.6 + 32202.7i 1.31099 + 1.19269i
\(901\) 22192.9 + 22192.9i 0.820590 + 0.820590i
\(902\) 738.378 + 196.759i 0.0272564 + 0.00726316i
\(903\) −9376.03 11672.4i −0.345531 0.430158i
\(904\) −3576.41 + 14.7601i −0.131582 + 0.000543046i
\(905\) 88682.5 3.25735
\(906\) −3152.40 7129.73i −0.115598 0.261445i
\(907\) −17601.6 + 17601.6i −0.644379 + 0.644379i −0.951629 0.307250i \(-0.900591\pi\)
0.307250 + 0.951629i \(0.400591\pi\)
\(908\) −8293.00 30612.8i −0.303098 1.11885i
\(909\) −12457.6 + 7950.90i −0.454559 + 0.290115i
\(910\) −15244.9 26321.3i −0.555346 0.958839i
\(911\) 19080.4 0.693922 0.346961 0.937880i \(-0.387214\pi\)
0.346961 + 0.937880i \(0.387214\pi\)
\(912\) −32611.9 12460.4i −1.18409 0.452419i
\(913\) 19280.7 0.698901
\(914\) 8766.25 + 15135.5i 0.317245 + 0.547743i
\(915\) −56625.9 6177.81i −2.04589 0.223205i
\(916\) 50350.5 13640.0i 1.81619 0.492006i
\(917\) −19828.6 + 19828.6i −0.714065 + 0.714065i
\(918\) −22126.4 + 4461.46i −0.795511 + 0.160403i
\(919\) −51887.0 −1.86245 −0.931226 0.364441i \(-0.881260\pi\)
−0.931226 + 0.364441i \(0.881260\pi\)
\(920\) 6464.19 6517.77i 0.231650 0.233570i
\(921\) −37832.0 + 30389.1i −1.35354 + 1.08725i
\(922\) −44424.2 11837.9i −1.58680 0.422844i
\(923\) 829.981 + 829.981i 0.0295982 + 0.0295982i
\(924\) −2918.70 18571.9i −0.103916 0.661223i
\(925\) 18463.6 18463.6i 0.656301 0.656301i
\(926\) −9248.60 15968.3i −0.328216 0.566685i
\(927\) −2877.99 635.535i −0.101969 0.0225175i
\(928\) −6976.54 25338.3i −0.246785 0.896306i
\(929\) 40398.2i 1.42672i −0.700799 0.713359i \(-0.747173\pi\)
0.700799 0.713359i \(-0.252827\pi\)
\(930\) −21697.4 + 56091.7i −0.765038 + 1.97776i
\(931\) −12386.4 12386.4i −0.436033 0.436033i
\(932\) 2211.68 3855.20i 0.0777318 0.135495i
\(933\) −896.867 97.8471i −0.0314706 0.00343341i
\(934\) 1558.05 5846.89i 0.0545835 0.204835i
\(935\) 36083.3i 1.26209i
\(936\) 14399.5 + 22357.4i 0.502843 + 0.780741i
\(937\) 19890.2i 0.693472i 0.937963 + 0.346736i \(0.112710\pi\)
−0.937963 + 0.346736i \(0.887290\pi\)
\(938\) −14587.6 3887.23i −0.507784 0.135312i
\(939\) 8978.78 + 979.573i 0.312046 + 0.0340438i
\(940\) 8112.70 + 29947.2i 0.281497 + 1.03912i
\(941\) 17075.6 + 17075.6i 0.591550 + 0.591550i 0.938050 0.346500i \(-0.112630\pi\)
−0.346500 + 0.938050i \(0.612630\pi\)
\(942\) 2549.78 + 986.305i 0.0881914 + 0.0341142i
\(943\) 172.779i 0.00596656i
\(944\) −5092.34 + 19432.0i −0.175574 + 0.669976i
\(945\) 15369.2 + 31068.2i 0.529057 + 1.06947i
\(946\) −18107.1 + 10487.4i −0.622317 + 0.360437i
\(947\) −13508.1 + 13508.1i −0.463522 + 0.463522i −0.899808 0.436286i \(-0.856294\pi\)
0.436286 + 0.899808i \(0.356294\pi\)
\(948\) −13632.0 + 18715.7i −0.467034 + 0.641200i
\(949\) −25837.2 25837.2i −0.883786 0.883786i
\(950\) −16938.2 + 63563.9i −0.578471 + 2.17082i
\(951\) 14243.0 11440.9i 0.485658 0.390113i
\(952\) −17081.8 + 70.4976i −0.581537 + 0.00240004i
\(953\) −8590.20 −0.291987 −0.145994 0.989286i \(-0.546638\pi\)
−0.145994 + 0.989286i \(0.546638\pi\)
\(954\) −19374.3 + 37418.8i −0.657511 + 1.26989i
\(955\) 57964.3 57964.3i 1.96406 1.96406i
\(956\) −12214.3 + 21290.9i −0.413220 + 0.720288i
\(957\) 25555.7 + 2788.09i 0.863216 + 0.0941759i
\(958\) −17775.5 + 10295.3i −0.599479 + 0.347210i
\(959\) 12833.5 0.432133
\(960\) −31332.9 38354.1i −1.05340 1.28945i
\(961\) −18531.0 −0.622032
\(962\) 12556.7 7272.65i 0.420835 0.243742i
\(963\) −11152.9 17474.5i −0.373204 0.584744i
\(964\) 9882.68 17226.6i 0.330186 0.575551i
\(965\) −225.723 + 225.723i −0.00752983 + 0.00752983i
\(966\) 3887.73 1718.95i 0.129488 0.0572530i
\(967\) 46277.4 1.53897 0.769483 0.638667i \(-0.220514\pi\)
0.769483 + 0.638667i \(0.220514\pi\)
\(968\) 3842.03 15.8563i 0.127570 0.000526489i
\(969\) −19431.4 24190.5i −0.644197 0.801973i
\(970\) −21087.3 + 79134.1i −0.698012 + 2.61943i
\(971\) −17326.3 17326.3i −0.572634 0.572634i 0.360230 0.932864i \(-0.382698\pi\)
−0.932864 + 0.360230i \(0.882698\pi\)
\(972\) −14703.8 26497.7i −0.485211 0.874397i
\(973\) −20639.3 + 20639.3i −0.680027 + 0.680027i
\(974\) 13991.5 8103.68i 0.460284 0.266590i
\(975\) 39065.8 31380.2i 1.28319 1.03074i
\(976\) 36457.0 + 9553.92i 1.19566 + 0.313334i
\(977\) 30452.9i 0.997212i 0.866829 + 0.498606i \(0.166154\pi\)
−0.866829 + 0.498606i \(0.833846\pi\)
\(978\) −1612.18 + 4167.78i −0.0527115 + 0.136269i
\(979\) −23477.7 23477.7i −0.766445 0.766445i
\(980\) −6497.63 23985.3i −0.211795 0.781819i
\(981\) −7524.12 + 4802.16i −0.244879 + 0.156291i
\(982\) −15021.3 4002.81i −0.488136 0.130076i
\(983\) 45808.8i 1.48634i 0.669102 + 0.743170i \(0.266679\pi\)
−0.669102 + 0.743170i \(0.733321\pi\)
\(984\) 927.076 + 97.2730i 0.0300347 + 0.00315137i
\(985\) 16603.8i 0.537096i
\(986\) 6014.50 22570.6i 0.194261 0.729000i
\(987\) −1558.21 + 14282.6i −0.0502516 + 0.460607i
\(988\) −18191.1 + 31709.1i −0.585765 + 1.02105i
\(989\) −3345.53 3345.53i −0.107565 0.107565i
\(990\) 46169.8 14669.2i 1.48219 0.470928i
\(991\) 40677.8i 1.30391i −0.758258 0.651954i \(-0.773949\pi\)
0.758258 0.651954i \(-0.226051\pi\)
\(992\) 19658.6 34597.0i 0.629194 1.10732i
\(993\) 30340.8 + 37771.8i 0.969623 + 1.20710i
\(994\) −507.326 875.930i −0.0161886 0.0279505i
\(995\) 28290.0 28290.0i 0.901360 0.901360i
\(996\) 23234.9 3651.53i 0.739184 0.116168i
\(997\) −24051.1 24051.1i −0.763998 0.763998i 0.213045 0.977042i \(-0.431662\pi\)
−0.977042 + 0.213045i \(0.931662\pi\)
\(998\) −10141.8 2702.53i −0.321676 0.0857186i
\(999\) −14821.2 + 7331.91i −0.469391 + 0.232203i
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 48.4.k.a.11.5 44
3.2 odd 2 inner 48.4.k.a.11.18 yes 44
4.3 odd 2 192.4.k.a.143.10 44
8.3 odd 2 384.4.k.a.287.13 44
8.5 even 2 384.4.k.b.287.10 44
12.11 even 2 192.4.k.a.143.21 44
16.3 odd 4 inner 48.4.k.a.35.18 yes 44
16.5 even 4 384.4.k.a.95.2 44
16.11 odd 4 384.4.k.b.95.21 44
16.13 even 4 192.4.k.a.47.21 44
24.5 odd 2 384.4.k.b.287.21 44
24.11 even 2 384.4.k.a.287.2 44
48.5 odd 4 384.4.k.a.95.13 44
48.11 even 4 384.4.k.b.95.10 44
48.29 odd 4 192.4.k.a.47.10 44
48.35 even 4 inner 48.4.k.a.35.5 yes 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.4.k.a.11.5 44 1.1 even 1 trivial
48.4.k.a.11.18 yes 44 3.2 odd 2 inner
48.4.k.a.35.5 yes 44 48.35 even 4 inner
48.4.k.a.35.18 yes 44 16.3 odd 4 inner
192.4.k.a.47.10 44 48.29 odd 4
192.4.k.a.47.21 44 16.13 even 4
192.4.k.a.143.10 44 4.3 odd 2
192.4.k.a.143.21 44 12.11 even 2
384.4.k.a.95.2 44 16.5 even 4
384.4.k.a.95.13 44 48.5 odd 4
384.4.k.a.287.2 44 24.11 even 2
384.4.k.a.287.13 44 8.3 odd 2
384.4.k.b.95.10 44 48.11 even 4
384.4.k.b.95.21 44 16.11 odd 4
384.4.k.b.287.10 44 8.5 even 2
384.4.k.b.287.21 44 24.5 odd 2