Properties

Label 115.4.e.a.22.18
Level $115$
Weight $4$
Character 115.22
Analytic conductor $6.785$
Analytic rank $0$
Dimension $68$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [115,4,Mod(22,115)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(115, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([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("115.22");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 115.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: \(6.78521965066\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.18
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.152517 - 0.152517i) q^{2} +(-2.82764 + 2.82764i) q^{3} -7.95348i q^{4} +(5.56672 - 9.69596i) q^{5} +0.862527 q^{6} +(-20.1728 + 20.1728i) q^{7} +(-2.43318 + 2.43318i) q^{8} +11.0089i q^{9} +O(q^{10})\) \(q+(-0.152517 - 0.152517i) q^{2} +(-2.82764 + 2.82764i) q^{3} -7.95348i q^{4} +(5.56672 - 9.69596i) q^{5} +0.862527 q^{6} +(-20.1728 + 20.1728i) q^{7} +(-2.43318 + 2.43318i) q^{8} +11.0089i q^{9} +(-2.32782 + 0.629778i) q^{10} -48.5783i q^{11} +(22.4896 + 22.4896i) q^{12} +(-61.6739 + 61.6739i) q^{13} +6.15339 q^{14} +(11.6760 + 43.1574i) q^{15} -62.8856 q^{16} +(24.1697 - 24.1697i) q^{17} +(1.67904 - 1.67904i) q^{18} -87.2590 q^{19} +(-77.1166 - 44.2748i) q^{20} -114.083i q^{21} +(-7.40901 + 7.40901i) q^{22} +(-108.677 - 18.8738i) q^{23} -13.7603i q^{24} +(-63.0232 - 107.949i) q^{25} +18.8126 q^{26} +(-107.476 - 107.476i) q^{27} +(160.444 + 160.444i) q^{28} +183.651i q^{29} +(4.80145 - 8.36303i) q^{30} +164.628 q^{31} +(29.0565 + 29.0565i) q^{32} +(137.362 + 137.362i) q^{33} -7.37259 q^{34} +(83.2983 + 307.891i) q^{35} +87.5587 q^{36} +(34.0164 - 34.0164i) q^{37} +(13.3085 + 13.3085i) q^{38} -348.784i q^{39} +(10.0472 + 37.1368i) q^{40} +182.638 q^{41} +(-17.3996 + 17.3996i) q^{42} +(-7.70151 - 7.70151i) q^{43} -386.366 q^{44} +(106.741 + 61.2833i) q^{45} +(13.6966 + 19.4537i) q^{46} +(-177.458 - 177.458i) q^{47} +(177.818 - 177.818i) q^{48} -470.886i q^{49} +(-6.85201 + 26.0762i) q^{50} +136.687i q^{51} +(490.522 + 490.522i) q^{52} +(177.851 + 177.851i) q^{53} +32.7837i q^{54} +(-471.013 - 270.422i) q^{55} -98.1680i q^{56} +(246.737 - 246.737i) q^{57} +(28.0098 - 28.0098i) q^{58} -485.174i q^{59} +(343.252 - 92.8649i) q^{60} +10.0230i q^{61} +(-25.1086 - 25.1086i) q^{62} +(-222.080 - 222.080i) q^{63} +494.222i q^{64} +(254.666 + 941.309i) q^{65} -41.9001i q^{66} +(576.830 - 576.830i) q^{67} +(-192.234 - 192.234i) q^{68} +(360.669 - 253.933i) q^{69} +(34.2542 - 59.6631i) q^{70} -694.183 q^{71} +(-26.7865 - 26.7865i) q^{72} +(66.3843 - 66.3843i) q^{73} -10.3762 q^{74} +(483.450 + 127.035i) q^{75} +694.013i q^{76} +(979.961 + 979.961i) q^{77} +(-53.1954 + 53.1954i) q^{78} -1348.05 q^{79} +(-350.067 + 609.736i) q^{80} +310.566 q^{81} +(-27.8554 - 27.8554i) q^{82} +(-102.112 - 102.112i) q^{83} -907.358 q^{84} +(-99.8026 - 368.895i) q^{85} +2.34922i q^{86} +(-519.299 - 519.299i) q^{87} +(118.199 + 118.199i) q^{88} +420.903 q^{89} +(-6.93314 - 25.6266i) q^{90} -2488.27i q^{91} +(-150.112 + 864.363i) q^{92} +(-465.510 + 465.510i) q^{93} +54.1308i q^{94} +(-485.747 + 846.060i) q^{95} -164.323 q^{96} +(128.060 - 128.060i) q^{97} +(-71.8181 + 71.8181i) q^{98} +534.791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 68 q - 4 q^{2} + 4 q^{3} + 32 q^{6} + 28 q^{8} + 200 q^{12} - 100 q^{13} - 832 q^{16} - 112 q^{18} - 46 q^{23} - 372 q^{25} - 312 q^{26} - 704 q^{27} - 1056 q^{31} + 560 q^{32} - 348 q^{35} + 2424 q^{36} + 2248 q^{41} - 96 q^{46} - 1412 q^{47} + 1532 q^{48} - 620 q^{50} + 112 q^{52} + 2688 q^{55} + 2044 q^{58} + 3948 q^{62} - 1836 q^{70} - 2272 q^{71} + 1128 q^{72} + 1100 q^{73} + 2828 q^{75} + 4216 q^{77} - 9180 q^{78} - 3580 q^{81} - 6516 q^{82} - 2684 q^{85} - 6304 q^{87} - 688 q^{92} - 1608 q^{93} - 8616 q^{95} - 544 q^{96} - 3612 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.152517 0.152517i −0.0539229 0.0539229i 0.679631 0.733554i \(-0.262140\pi\)
−0.733554 + 0.679631i \(0.762140\pi\)
\(3\) −2.82764 + 2.82764i −0.544180 + 0.544180i −0.924752 0.380571i \(-0.875727\pi\)
0.380571 + 0.924752i \(0.375727\pi\)
\(4\) 7.95348i 0.994185i
\(5\) 5.56672 9.69596i 0.497903 0.867233i
\(6\) 0.862527 0.0586875
\(7\) −20.1728 + 20.1728i −1.08923 + 1.08923i −0.0936225 + 0.995608i \(0.529845\pi\)
−0.995608 + 0.0936225i \(0.970155\pi\)
\(8\) −2.43318 + 2.43318i −0.107532 + 0.107532i
\(9\) 11.0089i 0.407736i
\(10\) −2.32782 + 0.629778i −0.0736120 + 0.0199153i
\(11\) 48.5783i 1.33154i −0.746159 0.665768i \(-0.768104\pi\)
0.746159 0.665768i \(-0.231896\pi\)
\(12\) 22.4896 + 22.4896i 0.541016 + 0.541016i
\(13\) −61.6739 + 61.6739i −1.31579 + 1.31579i −0.398713 + 0.917076i \(0.630543\pi\)
−0.917076 + 0.398713i \(0.869457\pi\)
\(14\) 6.15339 0.117469
\(15\) 11.6760 + 43.1574i 0.200982 + 0.742880i
\(16\) −62.8856 −0.982588
\(17\) 24.1697 24.1697i 0.344825 0.344825i −0.513353 0.858178i \(-0.671597\pi\)
0.858178 + 0.513353i \(0.171597\pi\)
\(18\) 1.67904 1.67904i 0.0219863 0.0219863i
\(19\) −87.2590 −1.05361 −0.526805 0.849986i \(-0.676610\pi\)
−0.526805 + 0.849986i \(0.676610\pi\)
\(20\) −77.1166 44.2748i −0.862190 0.495007i
\(21\) 114.083i 1.18548i
\(22\) −7.40901 + 7.40901i −0.0718002 + 0.0718002i
\(23\) −108.677 18.8738i −0.985252 0.171107i
\(24\) 13.7603i 0.117034i
\(25\) −63.0232 107.949i −0.504186 0.863595i
\(26\) 18.8126 0.141902
\(27\) −107.476 107.476i −0.766062 0.766062i
\(28\) 160.444 + 160.444i 1.08290 + 1.08290i
\(29\) 183.651i 1.17597i 0.808872 + 0.587984i \(0.200078\pi\)
−0.808872 + 0.587984i \(0.799922\pi\)
\(30\) 4.80145 8.36303i 0.0292207 0.0508958i
\(31\) 164.628 0.953810 0.476905 0.878955i \(-0.341759\pi\)
0.476905 + 0.878955i \(0.341759\pi\)
\(32\) 29.0565 + 29.0565i 0.160516 + 0.160516i
\(33\) 137.362 + 137.362i 0.724596 + 0.724596i
\(34\) −7.37259 −0.0371879
\(35\) 83.2983 + 307.891i 0.402285 + 1.48695i
\(36\) 87.5587 0.405364
\(37\) 34.0164 34.0164i 0.151142 0.151142i −0.627486 0.778628i \(-0.715916\pi\)
0.778628 + 0.627486i \(0.215916\pi\)
\(38\) 13.3085 + 13.3085i 0.0568137 + 0.0568137i
\(39\) 348.784i 1.43205i
\(40\) 10.0472 + 37.1368i 0.0397149 + 0.146796i
\(41\) 182.638 0.695689 0.347844 0.937552i \(-0.386914\pi\)
0.347844 + 0.937552i \(0.386914\pi\)
\(42\) −17.3996 + 17.3996i −0.0639242 + 0.0639242i
\(43\) −7.70151 7.70151i −0.0273133 0.0273133i 0.693318 0.720632i \(-0.256148\pi\)
−0.720632 + 0.693318i \(0.756148\pi\)
\(44\) −386.366 −1.32379
\(45\) 106.741 + 61.2833i 0.353602 + 0.203013i
\(46\) 13.6966 + 19.4537i 0.0439011 + 0.0623542i
\(47\) −177.458 177.458i −0.550743 0.550743i 0.375912 0.926655i \(-0.377330\pi\)
−0.926655 + 0.375912i \(0.877330\pi\)
\(48\) 177.818 177.818i 0.534705 0.534705i
\(49\) 470.886i 1.37285i
\(50\) −6.85201 + 26.0762i −0.0193804 + 0.0737547i
\(51\) 136.687i 0.375294i
\(52\) 490.522 + 490.522i 1.30814 + 1.30814i
\(53\) 177.851 + 177.851i 0.460937 + 0.460937i 0.898963 0.438025i \(-0.144322\pi\)
−0.438025 + 0.898963i \(0.644322\pi\)
\(54\) 32.7837i 0.0826165i
\(55\) −471.013 270.422i −1.15475 0.662975i
\(56\) 98.1680i 0.234255i
\(57\) 246.737 246.737i 0.573354 0.573354i
\(58\) 28.0098 28.0098i 0.0634116 0.0634116i
\(59\) 485.174i 1.07058i −0.844668 0.535291i \(-0.820202\pi\)
0.844668 0.535291i \(-0.179798\pi\)
\(60\) 343.252 92.8649i 0.738560 0.199813i
\(61\) 10.0230i 0.0210380i 0.999945 + 0.0105190i \(0.00334836\pi\)
−0.999945 + 0.0105190i \(0.996652\pi\)
\(62\) −25.1086 25.1086i −0.0514322 0.0514322i
\(63\) −222.080 222.080i −0.444118 0.444118i
\(64\) 494.222i 0.965277i
\(65\) 254.666 + 941.309i 0.485960 + 1.79623i
\(66\) 41.9001i 0.0781446i
\(67\) 576.830 576.830i 1.05181 1.05181i 0.0532231 0.998583i \(-0.483051\pi\)
0.998583 0.0532231i \(-0.0169494\pi\)
\(68\) −192.234 192.234i −0.342820 0.342820i
\(69\) 360.669 253.933i 0.629268 0.443042i
\(70\) 34.2542 59.6631i 0.0584881 0.101873i
\(71\) −694.183 −1.16034 −0.580172 0.814494i \(-0.697015\pi\)
−0.580172 + 0.814494i \(0.697015\pi\)
\(72\) −26.7865 26.7865i −0.0438447 0.0438447i
\(73\) 66.3843 66.3843i 0.106434 0.106434i −0.651884 0.758318i \(-0.726021\pi\)
0.758318 + 0.651884i \(0.226021\pi\)
\(74\) −10.3762 −0.0163001
\(75\) 483.450 + 127.035i 0.744319 + 0.195584i
\(76\) 694.013i 1.04748i
\(77\) 979.961 + 979.961i 1.45035 + 1.45035i
\(78\) −53.1954 + 53.1954i −0.0772204 + 0.0772204i
\(79\) −1348.05 −1.91984 −0.959922 0.280266i \(-0.909577\pi\)
−0.959922 + 0.280266i \(0.909577\pi\)
\(80\) −350.067 + 609.736i −0.489233 + 0.852132i
\(81\) 310.566 0.426016
\(82\) −27.8554 27.8554i −0.0375135 0.0375135i
\(83\) −102.112 102.112i −0.135039 0.135039i 0.636356 0.771395i \(-0.280441\pi\)
−0.771395 + 0.636356i \(0.780441\pi\)
\(84\) −907.358 −1.17858
\(85\) −99.8026 368.895i −0.127354 0.470733i
\(86\) 2.34922i 0.00294562i
\(87\) −519.299 519.299i −0.639939 0.639939i
\(88\) 118.199 + 118.199i 0.143183 + 0.143183i
\(89\) 420.903 0.501299 0.250650 0.968078i \(-0.419356\pi\)
0.250650 + 0.968078i \(0.419356\pi\)
\(90\) −6.93314 25.6266i −0.00812019 0.0300142i
\(91\) 2488.27i 2.86639i
\(92\) −150.112 + 864.363i −0.170112 + 0.979523i
\(93\) −465.510 + 465.510i −0.519044 + 0.519044i
\(94\) 54.1308i 0.0593953i
\(95\) −485.747 + 846.060i −0.524595 + 0.913725i
\(96\) −164.323 −0.174699
\(97\) 128.060 128.060i 0.134047 0.134047i −0.636900 0.770947i \(-0.719783\pi\)
0.770947 + 0.636900i \(0.219783\pi\)
\(98\) −71.8181 + 71.8181i −0.0740278 + 0.0740278i
\(99\) 534.791 0.542914
\(100\) −858.573 + 501.254i −0.858573 + 0.501254i
\(101\) 459.222 0.452419 0.226209 0.974079i \(-0.427367\pi\)
0.226209 + 0.974079i \(0.427367\pi\)
\(102\) 20.8471 20.8471i 0.0202369 0.0202369i
\(103\) 646.462 + 646.462i 0.618425 + 0.618425i 0.945127 0.326702i \(-0.105937\pi\)
−0.326702 + 0.945127i \(0.605937\pi\)
\(104\) 300.127i 0.282979i
\(105\) −1106.15 635.069i −1.02808 0.590252i
\(106\) 54.2505i 0.0497101i
\(107\) 208.922 208.922i 0.188759 0.188759i −0.606400 0.795159i \(-0.707387\pi\)
0.795159 + 0.606400i \(0.207387\pi\)
\(108\) −854.804 + 854.804i −0.761607 + 0.761607i
\(109\) −640.595 −0.562916 −0.281458 0.959573i \(-0.590818\pi\)
−0.281458 + 0.959573i \(0.590818\pi\)
\(110\) 30.5935 + 113.081i 0.0265180 + 0.0980171i
\(111\) 192.373i 0.164497i
\(112\) 1268.58 1268.58i 1.07026 1.07026i
\(113\) −1134.27 1134.27i −0.944276 0.944276i 0.0542509 0.998527i \(-0.482723\pi\)
−0.998527 + 0.0542509i \(0.982723\pi\)
\(114\) −75.2633 −0.0618338
\(115\) −787.976 + 948.667i −0.638949 + 0.769249i
\(116\) 1460.66 1.16913
\(117\) −678.959 678.959i −0.536494 0.536494i
\(118\) −73.9973 + 73.9973i −0.0577288 + 0.0577288i
\(119\) 975.144i 0.751188i
\(120\) −133.419 76.5998i −0.101496 0.0582714i
\(121\) −1028.85 −0.772988
\(122\) 1.52868 1.52868i 0.00113443 0.00113443i
\(123\) −516.435 + 516.435i −0.378580 + 0.378580i
\(124\) 1309.37i 0.948263i
\(125\) −1397.51 + 10.1457i −0.999974 + 0.00725971i
\(126\) 67.7419i 0.0478962i
\(127\) −353.968 353.968i −0.247320 0.247320i 0.572550 0.819870i \(-0.305954\pi\)
−0.819870 + 0.572550i \(0.805954\pi\)
\(128\) 307.829 307.829i 0.212567 0.212567i
\(129\) 43.5543 0.0297267
\(130\) 104.725 182.406i 0.0706535 0.123062i
\(131\) 749.649 0.499978 0.249989 0.968249i \(-0.419573\pi\)
0.249989 + 0.968249i \(0.419573\pi\)
\(132\) 1092.51 1092.51i 0.720382 0.720382i
\(133\) 1760.26 1760.26i 1.14762 1.14762i
\(134\) −175.953 −0.113433
\(135\) −1640.36 + 443.792i −1.04578 + 0.282930i
\(136\) 117.618i 0.0741596i
\(137\) −1354.35 + 1354.35i −0.844596 + 0.844596i −0.989453 0.144856i \(-0.953728\pi\)
0.144856 + 0.989453i \(0.453728\pi\)
\(138\) −93.7372 16.2791i −0.0578220 0.0100418i
\(139\) 2511.60i 1.53260i 0.642482 + 0.766300i \(0.277905\pi\)
−0.642482 + 0.766300i \(0.722095\pi\)
\(140\) 2448.81 662.511i 1.47830 0.399946i
\(141\) 1003.58 0.599408
\(142\) 105.875 + 105.875i 0.0625690 + 0.0625690i
\(143\) 2996.01 + 2996.01i 1.75202 + 1.75202i
\(144\) 692.299i 0.400636i
\(145\) 1780.67 + 1022.33i 1.01984 + 0.585518i
\(146\) −20.2495 −0.0114785
\(147\) 1331.50 + 1331.50i 0.747075 + 0.747075i
\(148\) −270.549 270.549i −0.150263 0.150263i
\(149\) 255.150 0.140287 0.0701433 0.997537i \(-0.477654\pi\)
0.0701433 + 0.997537i \(0.477654\pi\)
\(150\) −54.3592 93.1093i −0.0295894 0.0506823i
\(151\) 419.421 0.226040 0.113020 0.993593i \(-0.463948\pi\)
0.113020 + 0.993593i \(0.463948\pi\)
\(152\) 212.316 212.316i 0.113297 0.113297i
\(153\) 266.081 + 266.081i 0.140597 + 0.140597i
\(154\) 298.921i 0.156414i
\(155\) 916.440 1596.23i 0.474905 0.827175i
\(156\) −2774.04 −1.42372
\(157\) −2275.84 + 2275.84i −1.15689 + 1.15689i −0.171747 + 0.985141i \(0.554941\pi\)
−0.985141 + 0.171747i \(0.945059\pi\)
\(158\) 205.601 + 205.601i 0.103524 + 0.103524i
\(159\) −1005.80 −0.501666
\(160\) 443.480 119.981i 0.219126 0.0592834i
\(161\) 2573.07 1811.59i 1.25954 0.886792i
\(162\) −47.3665 47.3665i −0.0229720 0.0229720i
\(163\) −843.225 + 843.225i −0.405193 + 0.405193i −0.880059 0.474865i \(-0.842497\pi\)
0.474865 + 0.880059i \(0.342497\pi\)
\(164\) 1452.61i 0.691643i
\(165\) 2096.51 567.200i 0.989171 0.267615i
\(166\) 31.1476i 0.0145634i
\(167\) −1622.65 1622.65i −0.751883 0.751883i 0.222948 0.974830i \(-0.428432\pi\)
−0.974830 + 0.222948i \(0.928432\pi\)
\(168\) 277.584 + 277.584i 0.127477 + 0.127477i
\(169\) 5410.33i 2.46260i
\(170\) −41.0412 + 71.4843i −0.0185160 + 0.0322506i
\(171\) 960.622i 0.429594i
\(172\) −61.2538 + 61.2538i −0.0271544 + 0.0271544i
\(173\) 430.076 430.076i 0.189006 0.189006i −0.606260 0.795266i \(-0.707331\pi\)
0.795266 + 0.606260i \(0.207331\pi\)
\(174\) 158.404i 0.0690147i
\(175\) 3449.00 + 906.289i 1.48983 + 0.391480i
\(176\) 3054.87i 1.30835i
\(177\) 1371.90 + 1371.90i 0.582589 + 0.582589i
\(178\) −64.1948 64.1948i −0.0270315 0.0270315i
\(179\) 2121.70i 0.885942i 0.896536 + 0.442971i \(0.146076\pi\)
−0.896536 + 0.442971i \(0.853924\pi\)
\(180\) 487.415 848.966i 0.201832 0.351545i
\(181\) 2432.37i 0.998876i −0.866350 0.499438i \(-0.833540\pi\)
0.866350 0.499438i \(-0.166460\pi\)
\(182\) −379.504 + 379.504i −0.154564 + 0.154564i
\(183\) −28.3415 28.3415i −0.0114484 0.0114484i
\(184\) 310.354 218.508i 0.124346 0.0875469i
\(185\) −140.462 519.182i −0.0558214 0.206330i
\(186\) 141.996 0.0559767
\(187\) −1174.12 1174.12i −0.459147 0.459147i
\(188\) −1411.41 + 1411.41i −0.547541 + 0.547541i
\(189\) 4336.17 1.66884
\(190\) 203.123 54.9538i 0.0775584 0.0209830i
\(191\) 1592.49i 0.603292i 0.953420 + 0.301646i \(0.0975361\pi\)
−0.953420 + 0.301646i \(0.902464\pi\)
\(192\) −1397.48 1397.48i −0.525285 0.525285i
\(193\) −1429.27 + 1429.27i −0.533063 + 0.533063i −0.921483 0.388419i \(-0.873021\pi\)
0.388419 + 0.921483i \(0.373021\pi\)
\(194\) −39.0628 −0.0144564
\(195\) −3381.79 1941.58i −1.24192 0.713023i
\(196\) −3745.18 −1.36486
\(197\) 2448.81 + 2448.81i 0.885637 + 0.885637i 0.994100 0.108463i \(-0.0345929\pi\)
−0.108463 + 0.994100i \(0.534593\pi\)
\(198\) −81.5647 81.5647i −0.0292755 0.0292755i
\(199\) −3207.30 −1.14251 −0.571255 0.820773i \(-0.693543\pi\)
−0.571255 + 0.820773i \(0.693543\pi\)
\(200\) 416.006 + 109.313i 0.147080 + 0.0386481i
\(201\) 3262.14i 1.14474i
\(202\) −70.0391 70.0391i −0.0243957 0.0243957i
\(203\) −3704.75 3704.75i −1.28090 1.28090i
\(204\) 1087.14 0.373112
\(205\) 1016.69 1770.85i 0.346385 0.603324i
\(206\) 197.193i 0.0666945i
\(207\) 207.779 1196.41i 0.0697663 0.401722i
\(208\) 3878.40 3878.40i 1.29288 1.29288i
\(209\) 4238.89i 1.40292i
\(210\) 71.8471 + 265.565i 0.0236091 + 0.0872653i
\(211\) 2538.48 0.828228 0.414114 0.910225i \(-0.364091\pi\)
0.414114 + 0.910225i \(0.364091\pi\)
\(212\) 1414.53 1414.53i 0.458257 0.458257i
\(213\) 1962.90 1962.90i 0.631436 0.631436i
\(214\) −63.7282 −0.0203569
\(215\) −117.546 + 31.8014i −0.0372863 + 0.0100876i
\(216\) 523.014 0.164753
\(217\) −3321.02 + 3321.02i −1.03892 + 1.03892i
\(218\) 97.7016 + 97.7016i 0.0303541 + 0.0303541i
\(219\) 375.423i 0.115839i
\(220\) −2150.79 + 3746.19i −0.659120 + 1.14804i
\(221\) 2981.28i 0.907434i
\(222\) 29.3401 29.3401i 0.00887017 0.00887017i
\(223\) 419.102 419.102i 0.125853 0.125853i −0.641375 0.767228i \(-0.721636\pi\)
0.767228 + 0.641375i \(0.221636\pi\)
\(224\) −1172.30 −0.349678
\(225\) 1188.40 693.813i 0.352118 0.205574i
\(226\) 345.991i 0.101836i
\(227\) −2814.03 + 2814.03i −0.822792 + 0.822792i −0.986508 0.163716i \(-0.947652\pi\)
0.163716 + 0.986508i \(0.447652\pi\)
\(228\) −1962.42 1962.42i −0.570020 0.570020i
\(229\) 4220.31 1.21784 0.608921 0.793231i \(-0.291603\pi\)
0.608921 + 0.793231i \(0.291603\pi\)
\(230\) 264.867 24.5080i 0.0759341 0.00702612i
\(231\) −5541.96 −1.57850
\(232\) −446.854 446.854i −0.126454 0.126454i
\(233\) −2305.47 + 2305.47i −0.648223 + 0.648223i −0.952563 0.304340i \(-0.901564\pi\)
0.304340 + 0.952563i \(0.401564\pi\)
\(234\) 207.105i 0.0578586i
\(235\) −2708.49 + 732.767i −0.751839 + 0.203406i
\(236\) −3858.82 −1.06436
\(237\) 3811.81 3811.81i 1.04474 1.04474i
\(238\) 148.726 148.726i 0.0405062 0.0405062i
\(239\) 5560.29i 1.50488i 0.658663 + 0.752438i \(0.271122\pi\)
−0.658663 + 0.752438i \(0.728878\pi\)
\(240\) −734.253 2713.98i −0.197483 0.729945i
\(241\) 1209.88i 0.323384i 0.986841 + 0.161692i \(0.0516951\pi\)
−0.986841 + 0.161692i \(0.948305\pi\)
\(242\) 156.917 + 156.917i 0.0416817 + 0.0416817i
\(243\) 2023.67 2023.67i 0.534232 0.534232i
\(244\) 79.7178 0.0209156
\(245\) −4565.69 2621.29i −1.19058 0.683544i
\(246\) 157.530 0.0408283
\(247\) 5381.60 5381.60i 1.38633 1.38633i
\(248\) −400.569 + 400.569i −0.102565 + 0.102565i
\(249\) 577.473 0.146971
\(250\) 214.691 + 211.596i 0.0543129 + 0.0535300i
\(251\) 3522.53i 0.885817i 0.896567 + 0.442908i \(0.146053\pi\)
−0.896567 + 0.442908i \(0.853947\pi\)
\(252\) −1766.31 + 1766.31i −0.441535 + 0.441535i
\(253\) −916.855 + 5279.36i −0.227835 + 1.31190i
\(254\) 107.972i 0.0266724i
\(255\) 1325.31 + 760.898i 0.325467 + 0.186860i
\(256\) 3859.88 0.942352
\(257\) −4757.06 4757.06i −1.15462 1.15462i −0.985615 0.169005i \(-0.945945\pi\)
−0.169005 0.985615i \(-0.554055\pi\)
\(258\) −6.64276 6.64276i −0.00160295 0.00160295i
\(259\) 1372.41i 0.329258i
\(260\) 7486.68 2025.48i 1.78578 0.483134i
\(261\) −2021.78 −0.479484
\(262\) −114.334 114.334i −0.0269603 0.0269603i
\(263\) −5045.14 5045.14i −1.18288 1.18288i −0.978996 0.203881i \(-0.934644\pi\)
−0.203881 0.978996i \(-0.565356\pi\)
\(264\) −668.452 −0.155835
\(265\) 2714.48 734.388i 0.629242 0.170238i
\(266\) −536.939 −0.123766
\(267\) −1190.16 + 1190.16i −0.272797 + 0.272797i
\(268\) −4587.80 4587.80i −1.04569 1.04569i
\(269\) 623.748i 0.141378i −0.997498 0.0706888i \(-0.977480\pi\)
0.997498 0.0706888i \(-0.0225197\pi\)
\(270\) 317.869 + 182.498i 0.0716478 + 0.0411350i
\(271\) 358.574 0.0803758 0.0401879 0.999192i \(-0.487204\pi\)
0.0401879 + 0.999192i \(0.487204\pi\)
\(272\) −1519.93 + 1519.93i −0.338821 + 0.338821i
\(273\) 7035.95 + 7035.95i 1.55984 + 1.55984i
\(274\) 413.122 0.0910861
\(275\) −5243.99 + 3061.56i −1.14991 + 0.671341i
\(276\) −2019.65 2868.58i −0.440466 0.625609i
\(277\) −1737.97 1737.97i −0.376983 0.376983i 0.493030 0.870012i \(-0.335889\pi\)
−0.870012 + 0.493030i \(0.835889\pi\)
\(278\) 383.062 383.062i 0.0826422 0.0826422i
\(279\) 1812.37i 0.388902i
\(280\) −951.833 546.474i −0.203153 0.116636i
\(281\) 7366.47i 1.56387i −0.623362 0.781933i \(-0.714234\pi\)
0.623362 0.781933i \(-0.285766\pi\)
\(282\) −153.063 153.063i −0.0323218 0.0323218i
\(283\) −2739.17 2739.17i −0.575360 0.575360i 0.358261 0.933621i \(-0.383370\pi\)
−0.933621 + 0.358261i \(0.883370\pi\)
\(284\) 5521.17i 1.15360i
\(285\) −1018.84 3765.88i −0.211757 0.782706i
\(286\) 913.884i 0.188948i
\(287\) −3684.32 + 3684.32i −0.757765 + 0.757765i
\(288\) −319.879 + 319.879i −0.0654481 + 0.0654481i
\(289\) 3744.65i 0.762191i
\(290\) −115.659 427.505i −0.0234198 0.0865654i
\(291\) 724.218i 0.145892i
\(292\) −527.986 527.986i −0.105815 0.105815i
\(293\) 2678.26 + 2678.26i 0.534013 + 0.534013i 0.921764 0.387751i \(-0.126748\pi\)
−0.387751 + 0.921764i \(0.626748\pi\)
\(294\) 406.152i 0.0805689i
\(295\) −4704.23 2700.83i −0.928443 0.533046i
\(296\) 165.536i 0.0325053i
\(297\) −5220.97 + 5220.97i −1.02004 + 1.02004i
\(298\) −38.9147 38.9147i −0.00756465 0.00756465i
\(299\) 7866.58 5538.54i 1.52152 1.07124i
\(300\) 1010.37 3845.11i 0.194446 0.739991i
\(301\) 310.723 0.0595008
\(302\) −63.9688 63.9688i −0.0121887 0.0121887i
\(303\) −1298.52 + 1298.52i −0.246197 + 0.246197i
\(304\) 5487.34 1.03526
\(305\) 97.1827 + 55.7953i 0.0182448 + 0.0104749i
\(306\) 81.1638i 0.0151628i
\(307\) 4062.20 + 4062.20i 0.755185 + 0.755185i 0.975442 0.220257i \(-0.0706895\pi\)
−0.220257 + 0.975442i \(0.570690\pi\)
\(308\) 7794.10 7794.10i 1.44191 1.44191i
\(309\) −3655.93 −0.673070
\(310\) −383.224 + 103.679i −0.0702119 + 0.0189954i
\(311\) 5901.80 1.07608 0.538039 0.842920i \(-0.319165\pi\)
0.538039 + 0.842920i \(0.319165\pi\)
\(312\) 848.651 + 848.651i 0.153992 + 0.153992i
\(313\) −3378.24 3378.24i −0.610061 0.610061i 0.332901 0.942962i \(-0.391973\pi\)
−0.942962 + 0.332901i \(0.891973\pi\)
\(314\) 694.207 0.124765
\(315\) −3389.53 + 917.020i −0.606281 + 0.164026i
\(316\) 10721.7i 1.90868i
\(317\) 4748.42 + 4748.42i 0.841318 + 0.841318i 0.989030 0.147712i \(-0.0471910\pi\)
−0.147712 + 0.989030i \(0.547191\pi\)
\(318\) 153.401 + 153.401i 0.0270513 + 0.0270513i
\(319\) 8921.43 1.56584
\(320\) 4791.95 + 2751.20i 0.837120 + 0.480614i
\(321\) 1181.51i 0.205438i
\(322\) −668.735 116.138i −0.115736 0.0200997i
\(323\) −2109.03 + 2109.03i −0.363311 + 0.363311i
\(324\) 2470.08i 0.423539i
\(325\) 10544.5 + 2770.77i 1.79971 + 0.472907i
\(326\) 257.212 0.0436984
\(327\) 1811.38 1811.38i 0.306328 0.306328i
\(328\) −444.390 + 444.390i −0.0748089 + 0.0748089i
\(329\) 7159.67 1.19977
\(330\) −406.261 233.246i −0.0677695 0.0389084i
\(331\) −7123.86 −1.18297 −0.591485 0.806316i \(-0.701458\pi\)
−0.591485 + 0.806316i \(0.701458\pi\)
\(332\) −812.146 + 812.146i −0.134254 + 0.134254i
\(333\) 374.482 + 374.482i 0.0616261 + 0.0616261i
\(334\) 494.963i 0.0810873i
\(335\) −2381.87 8803.97i −0.388463 1.43586i
\(336\) 7174.19i 1.16483i
\(337\) −26.7824 + 26.7824i −0.00432916 + 0.00432916i −0.709268 0.704939i \(-0.750974\pi\)
0.704939 + 0.709268i \(0.250974\pi\)
\(338\) −825.167 + 825.167i −0.132790 + 0.132790i
\(339\) 6414.63 1.02771
\(340\) −2934.00 + 793.777i −0.467995 + 0.126614i
\(341\) 7997.35i 1.27003i
\(342\) −146.511 + 146.511i −0.0231650 + 0.0231650i
\(343\) 2579.82 + 2579.82i 0.406114 + 0.406114i
\(344\) 37.4783 0.00587411
\(345\) −454.374 4910.61i −0.0709064 0.766314i
\(346\) −131.188 −0.0203835
\(347\) −404.268 404.268i −0.0625426 0.0625426i 0.675144 0.737686i \(-0.264082\pi\)
−0.737686 + 0.675144i \(0.764082\pi\)
\(348\) −4130.23 + 4130.23i −0.636217 + 0.636217i
\(349\) 10153.4i 1.55731i −0.627451 0.778656i \(-0.715902\pi\)
0.627451 0.778656i \(-0.284098\pi\)
\(350\) −387.807 664.255i −0.0592261 0.101446i
\(351\) 13256.9 2.01595
\(352\) 1411.52 1411.52i 0.213733 0.213733i
\(353\) 5380.07 5380.07i 0.811196 0.811196i −0.173617 0.984813i \(-0.555546\pi\)
0.984813 + 0.173617i \(0.0555456\pi\)
\(354\) 418.476i 0.0628298i
\(355\) −3864.32 + 6730.77i −0.577738 + 1.00629i
\(356\) 3347.64i 0.498384i
\(357\) −2757.36 2757.36i −0.408782 0.408782i
\(358\) 323.596 323.596i 0.0477725 0.0477725i
\(359\) −1005.40 −0.147807 −0.0739036 0.997265i \(-0.523546\pi\)
−0.0739036 + 0.997265i \(0.523546\pi\)
\(360\) −408.833 + 110.608i −0.0598539 + 0.0161932i
\(361\) 755.138 0.110094
\(362\) −370.977 + 370.977i −0.0538623 + 0.0538623i
\(363\) 2909.21 2909.21i 0.420645 0.420645i
\(364\) −19790.4 −2.84972
\(365\) −274.117 1013.20i −0.0393094 0.145297i
\(366\) 8.64512i 0.00123467i
\(367\) 1949.12 1949.12i 0.277229 0.277229i −0.554773 0.832002i \(-0.687195\pi\)
0.832002 + 0.554773i \(0.187195\pi\)
\(368\) 6834.25 + 1186.89i 0.968097 + 0.168127i
\(369\) 2010.63i 0.283657i
\(370\) −57.7612 + 100.607i −0.00811584 + 0.0141359i
\(371\) −7175.51 −1.00413
\(372\) 3702.42 + 3702.42i 0.516026 + 0.516026i
\(373\) 4285.50 + 4285.50i 0.594892 + 0.594892i 0.938949 0.344057i \(-0.111801\pi\)
−0.344057 + 0.938949i \(0.611801\pi\)
\(374\) 358.148i 0.0495170i
\(375\) 3922.96 3980.34i 0.540215 0.548117i
\(376\) 863.574 0.118445
\(377\) −11326.5 11326.5i −1.54733 1.54733i
\(378\) −661.339 661.339i −0.0899884 0.0899884i
\(379\) −12954.9 −1.75580 −0.877901 0.478843i \(-0.841056\pi\)
−0.877901 + 0.478843i \(0.841056\pi\)
\(380\) 6729.12 + 3863.38i 0.908412 + 0.521545i
\(381\) 2001.79 0.269173
\(382\) 242.882 242.882i 0.0325313 0.0325313i
\(383\) −1598.62 1598.62i −0.213279 0.213279i 0.592380 0.805659i \(-0.298189\pi\)
−0.805659 + 0.592380i \(0.798189\pi\)
\(384\) 1740.86i 0.231349i
\(385\) 14956.8 4046.49i 1.97992 0.535657i
\(386\) 435.976 0.0574886
\(387\) 84.7849 84.7849i 0.0111366 0.0111366i
\(388\) −1018.53 1018.53i −0.133268 0.133268i
\(389\) −8449.24 −1.10127 −0.550635 0.834746i \(-0.685614\pi\)
−0.550635 + 0.834746i \(0.685614\pi\)
\(390\) 219.656 + 811.904i 0.0285198 + 0.105416i
\(391\) −3082.88 + 2170.53i −0.398742 + 0.280738i
\(392\) 1145.75 + 1145.75i 0.147625 + 0.147625i
\(393\) −2119.74 + 2119.74i −0.272078 + 0.272078i
\(394\) 746.970i 0.0955122i
\(395\) −7504.23 + 13070.7i −0.955896 + 1.66495i
\(396\) 4253.45i 0.539757i
\(397\) 1669.22 + 1669.22i 0.211022 + 0.211022i 0.804702 0.593679i \(-0.202325\pi\)
−0.593679 + 0.804702i \(0.702325\pi\)
\(398\) 489.167 + 489.167i 0.0616074 + 0.0616074i
\(399\) 9954.78i 1.24903i
\(400\) 3963.25 + 6788.47i 0.495407 + 0.848558i
\(401\) 1774.08i 0.220931i 0.993880 + 0.110465i \(0.0352341\pi\)
−0.993880 + 0.110465i \(0.964766\pi\)
\(402\) 497.531 497.531i 0.0617279 0.0617279i
\(403\) −10153.3 + 10153.3i −1.25501 + 1.25501i
\(404\) 3652.41i 0.449788i
\(405\) 1728.83 3011.23i 0.212115 0.369455i
\(406\) 1130.08i 0.138140i
\(407\) −1652.46 1652.46i −0.201251 0.201251i
\(408\) −332.583 332.583i −0.0403562 0.0403562i
\(409\) 154.883i 0.0187248i 0.999956 + 0.00936242i \(0.00298019\pi\)
−0.999956 + 0.00936242i \(0.997020\pi\)
\(410\) −425.147 + 115.021i −0.0512111 + 0.0138549i
\(411\) 7659.22i 0.919225i
\(412\) 5141.62 5141.62i 0.614829 0.614829i
\(413\) 9787.34 + 9787.34i 1.16611 + 1.16611i
\(414\) −214.163 + 150.784i −0.0254240 + 0.0179000i
\(415\) −1558.50 + 421.645i −0.184347 + 0.0498741i
\(416\) −3584.06 −0.422411
\(417\) −7101.92 7101.92i −0.834011 0.834011i
\(418\) 646.503 646.503i 0.0756495 0.0756495i
\(419\) 12895.1 1.50350 0.751750 0.659448i \(-0.229210\pi\)
0.751750 + 0.659448i \(0.229210\pi\)
\(420\) −5051.01 + 8797.70i −0.586819 + 1.02210i
\(421\) 10599.6i 1.22706i 0.789671 + 0.613530i \(0.210251\pi\)
−0.789671 + 0.613530i \(0.789749\pi\)
\(422\) −387.161 387.161i −0.0446604 0.0446604i
\(423\) 1953.61 1953.61i 0.224558 0.224558i
\(424\) −865.484 −0.0991312
\(425\) −4132.37 1085.86i −0.471645 0.123933i
\(426\) −598.752 −0.0680977
\(427\) −202.193 202.193i −0.0229152 0.0229152i
\(428\) −1661.65 1661.65i −0.187661 0.187661i
\(429\) −16943.3 −1.90683
\(430\) 22.7780 + 13.0775i 0.00255454 + 0.00146663i
\(431\) 7566.71i 0.845651i −0.906211 0.422826i \(-0.861038\pi\)
0.906211 0.422826i \(-0.138962\pi\)
\(432\) 6758.66 + 6758.66i 0.752723 + 0.752723i
\(433\) −9598.56 9598.56i −1.06531 1.06531i −0.997713 0.0675932i \(-0.978468\pi\)
−0.0675932 0.997713i \(-0.521532\pi\)
\(434\) 1013.02 0.112043
\(435\) −7925.89 + 2144.31i −0.873603 + 0.236349i
\(436\) 5094.96i 0.559643i
\(437\) 9483.09 + 1646.91i 1.03807 + 0.180280i
\(438\) 57.2583 57.2583i 0.00624636 0.00624636i
\(439\) 12702.1i 1.38095i −0.723355 0.690476i \(-0.757401\pi\)
0.723355 0.690476i \(-0.242599\pi\)
\(440\) 1804.04 488.073i 0.195464 0.0528818i
\(441\) 5183.92 0.559758
\(442\) 454.696 454.696i 0.0489314 0.0489314i
\(443\) −5143.81 + 5143.81i −0.551670 + 0.551670i −0.926923 0.375253i \(-0.877556\pi\)
0.375253 + 0.926923i \(0.377556\pi\)
\(444\) 1530.03 0.163541
\(445\) 2343.05 4081.06i 0.249598 0.434743i
\(446\) −127.840 −0.0135727
\(447\) −721.473 + 721.473i −0.0763412 + 0.0763412i
\(448\) −9969.85 9969.85i −1.05141 1.05141i
\(449\) 8132.95i 0.854827i −0.904056 0.427414i \(-0.859425\pi\)
0.904056 0.427414i \(-0.140575\pi\)
\(450\) −287.069 75.4328i −0.0300724 0.00790208i
\(451\) 8872.23i 0.926335i
\(452\) −9021.40 + 9021.40i −0.938785 + 0.938785i
\(453\) −1185.97 + 1185.97i −0.123006 + 0.123006i
\(454\) 858.375 0.0887346
\(455\) −24126.2 13851.5i −2.48583 1.42719i
\(456\) 1200.71i 0.123308i
\(457\) −2945.88 + 2945.88i −0.301538 + 0.301538i −0.841615 0.540078i \(-0.818395\pi\)
0.540078 + 0.841615i \(0.318395\pi\)
\(458\) −643.668 643.668i −0.0656695 0.0656695i
\(459\) −5195.31 −0.528315
\(460\) 7545.20 + 6267.15i 0.764775 + 0.635234i
\(461\) −5248.51 −0.530255 −0.265127 0.964213i \(-0.585414\pi\)
−0.265127 + 0.964213i \(0.585414\pi\)
\(462\) 845.243 + 845.243i 0.0851174 + 0.0851174i
\(463\) 6738.21 6738.21i 0.676353 0.676353i −0.282820 0.959173i \(-0.591270\pi\)
0.959173 + 0.282820i \(0.0912700\pi\)
\(464\) 11549.0i 1.15549i
\(465\) 1922.20 + 7104.93i 0.191699 + 0.708566i
\(466\) 703.245 0.0699081
\(467\) 9075.02 9075.02i 0.899233 0.899233i −0.0961355 0.995368i \(-0.530648\pi\)
0.995368 + 0.0961355i \(0.0306482\pi\)
\(468\) −5400.08 + 5400.08i −0.533374 + 0.533374i
\(469\) 23272.6i 2.29132i
\(470\) 524.850 + 301.331i 0.0515096 + 0.0295731i
\(471\) 12870.5i 1.25911i
\(472\) 1180.51 + 1180.51i 0.115122 + 0.115122i
\(473\) −374.126 + 374.126i −0.0363686 + 0.0363686i
\(474\) −1162.73 −0.112671
\(475\) 5499.34 + 9419.56i 0.531215 + 0.909893i
\(476\) 7755.79 0.746819
\(477\) −1957.93 + 1957.93i −0.187941 + 0.187941i
\(478\) 848.039 848.039i 0.0811473 0.0811473i
\(479\) −7363.67 −0.702410 −0.351205 0.936299i \(-0.614228\pi\)
−0.351205 + 0.936299i \(0.614228\pi\)
\(480\) −914.741 + 1593.27i −0.0869833 + 0.151505i
\(481\) 4195.85i 0.397743i
\(482\) 184.528 184.528i 0.0174378 0.0174378i
\(483\) −2153.18 + 12398.3i −0.202843 + 1.16799i
\(484\) 8182.91i 0.768493i
\(485\) −528.791 1954.54i −0.0495076 0.182992i
\(486\) −617.288 −0.0576147
\(487\) 9037.28 + 9037.28i 0.840900 + 0.840900i 0.988976 0.148076i \(-0.0473081\pi\)
−0.148076 + 0.988976i \(0.547308\pi\)
\(488\) −24.3878 24.3878i −0.00226226 0.00226226i
\(489\) 4768.68i 0.440996i
\(490\) 296.554 + 1096.14i 0.0273407 + 0.101058i
\(491\) −3626.58 −0.333330 −0.166665 0.986014i \(-0.553300\pi\)
−0.166665 + 0.986014i \(0.553300\pi\)
\(492\) 4107.45 + 4107.45i 0.376379 + 0.376379i
\(493\) 4438.79 + 4438.79i 0.405503 + 0.405503i
\(494\) −1641.57 −0.149510
\(495\) 2977.03 5185.31i 0.270319 0.470833i
\(496\) −10352.7 −0.937202
\(497\) 14003.6 14003.6i 1.26388 1.26388i
\(498\) −88.0744 88.0744i −0.00792512 0.00792512i
\(499\) 20124.4i 1.80539i −0.430280 0.902696i \(-0.641585\pi\)
0.430280 0.902696i \(-0.358415\pi\)
\(500\) 80.6940 + 11115.0i 0.00721749 + 0.994158i
\(501\) 9176.55 0.818319
\(502\) 537.245 537.245i 0.0477658 0.0477658i
\(503\) 1542.29 + 1542.29i 0.136714 + 0.136714i 0.772152 0.635438i \(-0.219180\pi\)
−0.635438 + 0.772152i \(0.719180\pi\)
\(504\) 1080.72 0.0955139
\(505\) 2556.36 4452.60i 0.225261 0.392352i
\(506\) 945.028 665.356i 0.0830269 0.0584559i
\(507\) 15298.5 + 15298.5i 1.34010 + 1.34010i
\(508\) −2815.28 + 2815.28i −0.245881 + 0.245881i
\(509\) 3694.28i 0.321701i −0.986979 0.160851i \(-0.948576\pi\)
0.986979 0.160851i \(-0.0514238\pi\)
\(510\) −86.0824 318.182i −0.00747411 0.0276262i
\(511\) 2678.32i 0.231863i
\(512\) −3051.33 3051.33i −0.263381 0.263381i
\(513\) 9378.21 + 9378.21i 0.807131 + 0.807131i
\(514\) 1451.06i 0.124521i
\(515\) 9866.74 2669.39i 0.844234 0.228403i
\(516\) 346.408i 0.0295538i
\(517\) −8620.61 + 8620.61i −0.733335 + 0.733335i
\(518\) 209.316 209.316i 0.0177545 0.0177545i
\(519\) 2432.20i 0.205707i
\(520\) −2910.02 1670.72i −0.245409 0.140896i
\(521\) 21028.9i 1.76832i −0.467185 0.884159i \(-0.654732\pi\)
0.467185 0.884159i \(-0.345268\pi\)
\(522\) 308.356 + 308.356i 0.0258552 + 0.0258552i
\(523\) 1509.77 + 1509.77i 0.126229 + 0.126229i 0.767399 0.641170i \(-0.221551\pi\)
−0.641170 + 0.767399i \(0.721551\pi\)
\(524\) 5962.32i 0.497071i
\(525\) −12315.2 + 7189.88i −1.02377 + 0.597700i
\(526\) 1538.94i 0.127568i
\(527\) 3979.02 3979.02i 0.328897 0.328897i
\(528\) −8638.10 8638.10i −0.711979 0.711979i
\(529\) 11454.6 + 4102.31i 0.941445 + 0.337167i
\(530\) −526.011 301.998i −0.0431103 0.0247508i
\(531\) 5341.22 0.436514
\(532\) −14000.2 14000.2i −1.14095 1.14095i
\(533\) −11264.0 + 11264.0i −0.915379 + 0.915379i
\(534\) 363.040 0.0294200
\(535\) −862.687 3188.71i −0.0697144 0.257682i
\(536\) 2807.06i 0.226206i
\(537\) −5999.42 5999.42i −0.482112 0.482112i
\(538\) −95.1321 + 95.1321i −0.00762349 + 0.00762349i
\(539\) −22874.8 −1.82799
\(540\) 3529.69 + 13046.6i 0.281284 + 1.03970i
\(541\) −3725.12 −0.296036 −0.148018 0.988985i \(-0.547289\pi\)
−0.148018 + 0.988985i \(0.547289\pi\)
\(542\) −54.6887 54.6887i −0.00433409 0.00433409i
\(543\) 6877.87 + 6877.87i 0.543569 + 0.543569i
\(544\) 1404.58 0.110700
\(545\) −3566.02 + 6211.18i −0.280278 + 0.488180i
\(546\) 2146.20i 0.168222i
\(547\) 2088.71 + 2088.71i 0.163267 + 0.163267i 0.784012 0.620745i \(-0.213170\pi\)
−0.620745 + 0.784012i \(0.713170\pi\)
\(548\) 10771.8 + 10771.8i 0.839685 + 0.839685i
\(549\) −110.342 −0.00857792
\(550\) 1266.74 + 332.859i 0.0982070 + 0.0258057i
\(551\) 16025.2i 1.23901i
\(552\) −259.709 + 1495.43i −0.0200253 + 0.115308i
\(553\) 27194.0 27194.0i 2.09115 2.09115i
\(554\) 530.138i 0.0406560i
\(555\) 1865.24 + 1070.89i 0.142657 + 0.0819037i
\(556\) 19976.0 1.52369
\(557\) −3109.09 + 3109.09i −0.236511 + 0.236511i −0.815404 0.578893i \(-0.803485\pi\)
0.578893 + 0.815404i \(0.303485\pi\)
\(558\) 276.417 276.417i 0.0209707 0.0209707i
\(559\) 949.964 0.0718769
\(560\) −5238.27 19361.9i −0.395281 1.46106i
\(561\) 6640.01 0.499717
\(562\) −1123.51 + 1123.51i −0.0843282 + 0.0843282i
\(563\) −2839.63 2839.63i −0.212569 0.212569i 0.592789 0.805358i \(-0.298027\pi\)
−0.805358 + 0.592789i \(0.798027\pi\)
\(564\) 7981.93i 0.595922i
\(565\) −17312.0 + 4683.67i −1.28907 + 0.348750i
\(566\) 835.540i 0.0620501i
\(567\) −6264.99 + 6264.99i −0.464030 + 0.464030i
\(568\) 1689.07 1689.07i 0.124774 0.124774i
\(569\) 21412.4 1.57760 0.788801 0.614648i \(-0.210702\pi\)
0.788801 + 0.614648i \(0.210702\pi\)
\(570\) −418.970 + 729.750i −0.0307872 + 0.0536243i
\(571\) 23655.9i 1.73375i 0.498529 + 0.866873i \(0.333874\pi\)
−0.498529 + 0.866873i \(0.666126\pi\)
\(572\) 23828.7 23828.7i 1.74183 1.74183i
\(573\) −4503.01 4503.01i −0.328300 0.328300i
\(574\) 1123.84 0.0817218
\(575\) 4811.78 + 12921.1i 0.348983 + 0.937129i
\(576\) −5440.82 −0.393578
\(577\) 2241.32 + 2241.32i 0.161711 + 0.161711i 0.783324 0.621613i \(-0.213522\pi\)
−0.621613 + 0.783324i \(0.713522\pi\)
\(578\) 571.122 571.122i 0.0410996 0.0410996i
\(579\) 8082.94i 0.580165i
\(580\) 8131.10 14162.5i 0.582113 1.01391i
\(581\) 4119.78 0.294178
\(582\) 110.456 110.456i 0.00786689 0.00786689i
\(583\) 8639.68 8639.68i 0.613755 0.613755i
\(584\) 323.049i 0.0228902i
\(585\) −10362.7 + 2803.58i −0.732387 + 0.198143i
\(586\) 816.961i 0.0575910i
\(587\) −309.864 309.864i −0.0217878 0.0217878i 0.696129 0.717917i \(-0.254904\pi\)
−0.717917 + 0.696129i \(0.754904\pi\)
\(588\) 10590.0 10590.0i 0.742731 0.742731i
\(589\) −14365.3 −1.00494
\(590\) 305.552 + 1129.40i 0.0213210 + 0.0788077i
\(591\) −13848.7 −0.963893
\(592\) −2139.14 + 2139.14i −0.148511 + 0.148511i
\(593\) −6326.79 + 6326.79i −0.438129 + 0.438129i −0.891382 0.453253i \(-0.850263\pi\)
0.453253 + 0.891382i \(0.350263\pi\)
\(594\) 1592.57 0.110007
\(595\) 9454.96 + 5428.36i 0.651455 + 0.374018i
\(596\) 2029.33i 0.139471i
\(597\) 9069.10 9069.10i 0.621731 0.621731i
\(598\) −2044.51 355.065i −0.139810 0.0242804i
\(599\) 20846.0i 1.42195i 0.703219 + 0.710973i \(0.251745\pi\)
−0.703219 + 0.710973i \(0.748255\pi\)
\(600\) −1485.42 + 867.218i −0.101070 + 0.0590067i
\(601\) 12657.4 0.859076 0.429538 0.903049i \(-0.358676\pi\)
0.429538 + 0.903049i \(0.358676\pi\)
\(602\) −47.3905 47.3905i −0.00320846 0.00320846i
\(603\) 6350.24 + 6350.24i 0.428859 + 0.428859i
\(604\) 3335.86i 0.224725i
\(605\) −5727.31 + 9975.66i −0.384873 + 0.670361i
\(606\) 396.091 0.0265513
\(607\) −2602.74 2602.74i −0.174040 0.174040i 0.614712 0.788752i \(-0.289272\pi\)
−0.788752 + 0.614712i \(0.789272\pi\)
\(608\) −2535.44 2535.44i −0.169121 0.169121i
\(609\) 20951.5 1.39408
\(610\) −6.31228 23.3317i −0.000418978 0.00154865i
\(611\) 21889.1 1.44932
\(612\) 2116.27 2116.27i 0.139780 0.139780i
\(613\) −13533.1 13533.1i −0.891677 0.891677i 0.103004 0.994681i \(-0.467154\pi\)
−0.994681 + 0.103004i \(0.967154\pi\)
\(614\) 1239.11i 0.0814435i
\(615\) 2132.48 + 7882.18i 0.139821 + 0.516813i
\(616\) −4768.83 −0.311918
\(617\) −10432.9 + 10432.9i −0.680735 + 0.680735i −0.960166 0.279431i \(-0.909854\pi\)
0.279431 + 0.960166i \(0.409854\pi\)
\(618\) 557.591 + 557.591i 0.0362938 + 0.0362938i
\(619\) −1265.25 −0.0821560 −0.0410780 0.999156i \(-0.513079\pi\)
−0.0410780 + 0.999156i \(0.513079\pi\)
\(620\) −12695.6 7288.88i −0.822365 0.472143i
\(621\) 9651.69 + 13708.6i 0.623686 + 0.885843i
\(622\) −900.124 900.124i −0.0580252 0.0580252i
\(623\) −8490.80 + 8490.80i −0.546030 + 0.546030i
\(624\) 21933.5i 1.40712i
\(625\) −7681.15 + 13606.6i −0.491594 + 0.870825i
\(626\) 1030.48i 0.0657925i
\(627\) −11986.1 11986.1i −0.763441 0.763441i
\(628\) 18100.8 + 18100.8i 1.15016 + 1.15016i
\(629\) 1644.34i 0.104235i
\(630\) 656.822 + 377.100i 0.0415372 + 0.0238477i
\(631\) 7345.29i 0.463409i 0.972786 + 0.231705i \(0.0744303\pi\)
−0.972786 + 0.231705i \(0.925570\pi\)
\(632\) 3280.05 3280.05i 0.206445 0.206445i
\(633\) −7177.91 + 7177.91i −0.450705 + 0.450705i
\(634\) 1448.43i 0.0907326i
\(635\) −5402.50 + 1461.62i −0.337625 + 0.0913425i
\(636\) 7999.59i 0.498749i
\(637\) 29041.4 + 29041.4i 1.80637 + 1.80637i
\(638\) −1360.67 1360.67i −0.0844348 0.0844348i
\(639\) 7642.16i 0.473113i
\(640\) −1271.10 4698.30i −0.0785072 0.290182i
\(641\) 18144.7i 1.11805i 0.829150 + 0.559026i \(0.188825\pi\)
−0.829150 + 0.559026i \(0.811175\pi\)
\(642\) 180.201 180.201i 0.0110778 0.0110778i
\(643\) −1948.11 1948.11i −0.119481 0.119481i 0.644838 0.764319i \(-0.276925\pi\)
−0.764319 + 0.644838i \(0.776925\pi\)
\(644\) −14408.5 20464.8i −0.881635 1.25222i
\(645\) 242.455 422.300i 0.0148010 0.0257799i
\(646\) 643.325 0.0391816
\(647\) −5349.46 5349.46i −0.325052 0.325052i 0.525649 0.850702i \(-0.323823\pi\)
−0.850702 + 0.525649i \(0.823823\pi\)
\(648\) −755.661 + 755.661i −0.0458104 + 0.0458104i
\(649\) −23568.9 −1.42552
\(650\) −1185.63 2030.81i −0.0715451 0.122546i
\(651\) 18781.3i 1.13072i
\(652\) 6706.57 + 6706.57i 0.402837 + 0.402837i
\(653\) 12033.8 12033.8i 0.721162 0.721162i −0.247680 0.968842i \(-0.579668\pi\)
0.968842 + 0.247680i \(0.0796681\pi\)
\(654\) −552.531 −0.0330362
\(655\) 4173.09 7268.56i 0.248941 0.433597i
\(656\) −11485.3 −0.683575
\(657\) 730.816 + 730.816i 0.0433970 + 0.0433970i
\(658\) −1091.97 1091.97i −0.0646952 0.0646952i
\(659\) 12528.0 0.740548 0.370274 0.928923i \(-0.379264\pi\)
0.370274 + 0.928923i \(0.379264\pi\)
\(660\) −4511.21 16674.6i −0.266059 0.983419i
\(661\) 25302.7i 1.48890i −0.667681 0.744448i \(-0.732713\pi\)
0.667681 0.744448i \(-0.267287\pi\)
\(662\) 1086.51 + 1086.51i 0.0637891 + 0.0637891i
\(663\) −8430.01 8430.01i −0.493808 0.493808i
\(664\) 496.913 0.0290421
\(665\) −7268.53 26866.3i −0.423852 1.56666i
\(666\) 114.230i 0.00664611i
\(667\) 3466.18 19958.7i 0.201216 1.15863i
\(668\) −12905.7 + 12905.7i −0.747510 + 0.747510i
\(669\) 2370.14i 0.136973i
\(670\) −979.479 + 1706.03i −0.0564785 + 0.0983726i
\(671\) 486.901 0.0280128
\(672\) 3314.86 3314.86i 0.190288 0.190288i
\(673\) −686.837 + 686.837i −0.0393397 + 0.0393397i −0.726503 0.687163i \(-0.758856\pi\)
0.687163 + 0.726503i \(0.258856\pi\)
\(674\) 8.16953 0.000466882
\(675\) −4828.47 + 18375.4i −0.275330 + 1.04780i
\(676\) −43031.0 −2.44828
\(677\) −12180.4 + 12180.4i −0.691480 + 0.691480i −0.962558 0.271077i \(-0.912620\pi\)
0.271077 + 0.962558i \(0.412620\pi\)
\(678\) −978.339 978.339i −0.0554173 0.0554173i
\(679\) 5166.68i 0.292016i
\(680\) 1140.42 + 654.749i 0.0643136 + 0.0369243i
\(681\) 15914.2i 0.895495i
\(682\) −1219.73 + 1219.73i −0.0684838 + 0.0684838i
\(683\) −10593.3 + 10593.3i −0.593472 + 0.593472i −0.938567 0.345096i \(-0.887846\pi\)
0.345096 + 0.938567i \(0.387846\pi\)
\(684\) −7640.29 −0.427096
\(685\) 5592.42 + 20671.0i 0.311935 + 1.15299i
\(686\) 786.932i 0.0437977i
\(687\) −11933.5 + 11933.5i −0.662726 + 0.662726i
\(688\) 484.314 + 484.314i 0.0268377 + 0.0268377i
\(689\) −21937.5 −1.21299
\(690\) −679.651 + 818.251i −0.0374984 + 0.0451453i
\(691\) −24172.7 −1.33079 −0.665393 0.746493i \(-0.731736\pi\)
−0.665393 + 0.746493i \(0.731736\pi\)
\(692\) −3420.60 3420.60i −0.187907 0.187907i
\(693\) −10788.2 + 10788.2i −0.591359 + 0.591359i
\(694\) 123.316i 0.00674495i
\(695\) 24352.4 + 13981.4i 1.32912 + 0.763086i
\(696\) 2527.09 0.137628
\(697\) 4414.31 4414.31i 0.239891 0.239891i
\(698\) −1548.57 + 1548.57i −0.0839747 + 0.0839747i
\(699\) 13038.1i 0.705501i
\(700\) 7208.15 27431.6i 0.389203 1.48116i
\(701\) 25716.3i 1.38558i 0.721140 + 0.692789i \(0.243618\pi\)
−0.721140 + 0.692789i \(0.756382\pi\)
\(702\) −2021.90 2021.90i −0.108706 0.108706i
\(703\) −2968.24 + 2968.24i −0.159245 + 0.159245i
\(704\) 24008.4 1.28530
\(705\) 5586.64 9730.64i 0.298447 0.519826i
\(706\) −1641.10 −0.0874840
\(707\) −9263.80 + 9263.80i −0.492788 + 0.492788i
\(708\) 10911.4 10911.4i 0.579201 0.579201i
\(709\) 19177.0 1.01581 0.507904 0.861414i \(-0.330420\pi\)
0.507904 + 0.861414i \(0.330420\pi\)
\(710\) 1615.93 437.181i 0.0854152 0.0231086i
\(711\) 14840.5i 0.782789i
\(712\) −1024.13 + 1024.13i −0.0539058 + 0.0539058i
\(713\) −17891.4 3107.16i −0.939743 0.163203i
\(714\) 841.088i 0.0440854i
\(715\) 45727.1 12371.2i 2.39175 0.647074i
\(716\) 16874.9 0.880790
\(717\) −15722.5 15722.5i −0.818924 0.818924i
\(718\) 153.340 + 153.340i 0.00797019 + 0.00797019i
\(719\) 14794.9i 0.767395i 0.923459 + 0.383698i \(0.125349\pi\)
−0.923459 + 0.383698i \(0.874651\pi\)
\(720\) −6712.50 3853.84i −0.347445 0.199478i
\(721\) −26081.9 −1.34721
\(722\) −115.171 115.171i −0.00593661 0.00593661i
\(723\) −3421.12 3421.12i −0.175979 0.175979i
\(724\) −19345.8 −0.993067
\(725\) 19825.0 11574.3i 1.01556 0.592906i
\(726\) −887.408 −0.0453648
\(727\) −15023.5 + 15023.5i −0.766425 + 0.766425i −0.977475 0.211050i \(-0.932312\pi\)
0.211050 + 0.977475i \(0.432312\pi\)
\(728\) 6054.40 + 6054.40i 0.308230 + 0.308230i
\(729\) 19829.7i 1.00745i
\(730\) −112.723 + 196.338i −0.00571517 + 0.00995451i
\(731\) −372.287 −0.0188366
\(732\) −225.414 + 225.414i −0.0113819 + 0.0113819i
\(733\) −17508.2 17508.2i −0.882236 0.882236i 0.111526 0.993762i \(-0.464426\pi\)
−0.993762 + 0.111526i \(0.964426\pi\)
\(734\) −594.546 −0.0298980
\(735\) 20322.2 5498.07i 1.01986 0.275917i
\(736\) −2609.38 3706.19i −0.130684 0.185614i
\(737\) −28021.4 28021.4i −1.40052 1.40052i
\(738\) 306.656 306.656i 0.0152956 0.0152956i
\(739\) 7862.85i 0.391393i 0.980664 + 0.195697i \(0.0626968\pi\)
−0.980664 + 0.195697i \(0.937303\pi\)
\(740\) −4129.30 + 1117.16i −0.205130 + 0.0554968i
\(741\) 30434.5i 1.50883i
\(742\) 1094.39 + 1094.39i 0.0541458 + 0.0541458i
\(743\) −2166.34 2166.34i −0.106965 0.106965i 0.651599 0.758564i \(-0.274099\pi\)
−0.758564 + 0.651599i \(0.774099\pi\)
\(744\) 2265.33i 0.111628i
\(745\) 1420.35 2473.92i 0.0698491 0.121661i
\(746\) 1307.22i 0.0641565i
\(747\) 1124.14 1124.14i 0.0550603 0.0550603i
\(748\) −9338.37 + 9338.37i −0.456477 + 0.456477i
\(749\) 8429.09i 0.411204i
\(750\) −1205.39 + 8.75098i −0.0586860 + 0.000426054i
\(751\) 8223.92i 0.399594i 0.979837 + 0.199797i \(0.0640282\pi\)
−0.979837 + 0.199797i \(0.935972\pi\)
\(752\) 11159.6 + 11159.6i 0.541154 + 0.541154i
\(753\) −9960.45 9960.45i −0.482044 0.482044i
\(754\) 3454.95i 0.166873i
\(755\) 2334.80 4066.69i 0.112546 0.196029i
\(756\) 34487.6i 1.65913i
\(757\) −10751.2 + 10751.2i −0.516194 + 0.516194i −0.916418 0.400223i \(-0.868933\pi\)
0.400223 + 0.916418i \(0.368933\pi\)
\(758\) 1975.84 + 1975.84i 0.0946778 + 0.0946778i
\(759\) −12335.6 17520.7i −0.589927 0.837893i
\(760\) −876.705 3240.52i −0.0418440 0.154666i
\(761\) −37399.6 −1.78152 −0.890759 0.454476i \(-0.849827\pi\)
−0.890759 + 0.454476i \(0.849827\pi\)
\(762\) −305.307 305.307i −0.0145146 0.0145146i
\(763\) 12922.6 12922.6i 0.613146 0.613146i
\(764\) 12665.9 0.599784
\(765\) 4061.11 1098.71i 0.191935 0.0519268i
\(766\) 487.634i 0.0230012i
\(767\) 29922.6 + 29922.6i 1.40866 + 1.40866i
\(768\) −10914.4 + 10914.4i −0.512810 + 0.512810i
\(769\) 16567.4 0.776902 0.388451 0.921469i \(-0.373010\pi\)
0.388451 + 0.921469i \(0.373010\pi\)
\(770\) −2898.33 1664.01i −0.135647 0.0778790i
\(771\) 26902.6 1.25664
\(772\) 11367.7 </