Properties

Label 115.4.e.a.22.3
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 22.3
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.67169 - 3.67169i) q^{2} +(-4.81114 + 4.81114i) q^{3} +18.9626i q^{4} +(-0.398194 - 11.1732i) q^{5} +35.3300 q^{6} +(20.1910 - 20.1910i) q^{7} +(40.2512 - 40.2512i) q^{8} -19.2941i q^{9} +O(q^{10})\) \(q+(-3.67169 - 3.67169i) q^{2} +(-4.81114 + 4.81114i) q^{3} +18.9626i q^{4} +(-0.398194 - 11.1732i) q^{5} +35.3300 q^{6} +(20.1910 - 20.1910i) q^{7} +(40.2512 - 40.2512i) q^{8} -19.2941i q^{9} +(-39.5626 + 42.4867i) q^{10} +18.3142i q^{11} +(-91.2316 - 91.2316i) q^{12} +(-26.6019 + 26.6019i) q^{13} -148.270 q^{14} +(55.6718 + 51.8403i) q^{15} -143.879 q^{16} +(41.2449 - 41.2449i) q^{17} +(-70.8419 + 70.8419i) q^{18} -76.5780 q^{19} +(211.874 - 7.55078i) q^{20} +194.283i q^{21} +(67.2439 - 67.2439i) q^{22} +(-31.1185 - 105.824i) q^{23} +387.308i q^{24} +(-124.683 + 8.89824i) q^{25} +195.348 q^{26} +(-37.0742 - 37.0742i) q^{27} +(382.874 + 382.874i) q^{28} +90.1157i q^{29} +(-14.0682 - 394.751i) q^{30} -271.752 q^{31} +(206.268 + 206.268i) q^{32} +(-88.1120 - 88.1120i) q^{33} -302.877 q^{34} +(-233.639 - 217.559i) q^{35} +365.866 q^{36} +(-275.386 + 275.386i) q^{37} +(281.171 + 281.171i) q^{38} -255.971i q^{39} +(-465.764 - 433.708i) q^{40} +371.644 q^{41} +(713.348 - 713.348i) q^{42} +(141.411 + 141.411i) q^{43} -347.284 q^{44} +(-215.578 + 7.68279i) q^{45} +(-274.294 + 502.809i) q^{46} +(-262.585 - 262.585i) q^{47} +(692.220 - 692.220i) q^{48} -472.354i q^{49} +(490.468 + 425.125i) q^{50} +396.870i q^{51} +(-504.441 - 504.441i) q^{52} +(-377.393 - 377.393i) q^{53} +272.249i q^{54} +(204.629 - 7.29259i) q^{55} -1625.42i q^{56} +(368.428 - 368.428i) q^{57} +(330.877 - 330.877i) q^{58} +193.149i q^{59} +(-983.025 + 1055.68i) q^{60} -295.893i q^{61} +(997.790 + 997.790i) q^{62} +(-389.567 - 389.567i) q^{63} -363.677i q^{64} +(307.823 + 286.637i) q^{65} +647.040i q^{66} +(-240.325 + 240.325i) q^{67} +(782.109 + 782.109i) q^{68} +(658.847 + 359.417i) q^{69} +(59.0403 + 1656.66i) q^{70} -730.125 q^{71} +(-776.610 - 776.610i) q^{72} +(-266.909 + 266.909i) q^{73} +2022.27 q^{74} +(557.056 - 642.677i) q^{75} -1452.12i q^{76} +(369.782 + 369.782i) q^{77} +(-939.846 + 939.846i) q^{78} -16.0835 q^{79} +(57.2916 + 1607.59i) q^{80} +877.678 q^{81} +(-1364.56 - 1364.56i) q^{82} +(-241.530 - 241.530i) q^{83} -3684.12 q^{84} +(-477.263 - 444.416i) q^{85} -1038.43i q^{86} +(-433.559 - 433.559i) q^{87} +(737.167 + 737.167i) q^{88} -967.565 q^{89} +(819.743 + 763.325i) q^{90} +1074.24i q^{91} +(2006.69 - 590.087i) q^{92} +(1307.44 - 1307.44i) q^{93} +1928.26i q^{94} +(30.4929 + 855.625i) q^{95} -1984.77 q^{96} +(434.431 - 434.431i) q^{97} +(-1734.34 + 1734.34i) q^{98} +353.356 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.67169 3.67169i −1.29814 1.29814i −0.929621 0.368516i \(-0.879866\pi\)
−0.368516 0.929621i \(-0.620134\pi\)
\(3\) −4.81114 + 4.81114i −0.925904 + 0.925904i −0.997438 0.0715342i \(-0.977210\pi\)
0.0715342 + 0.997438i \(0.477210\pi\)
\(4\) 18.9626i 2.37032i
\(5\) −0.398194 11.1732i −0.0356155 0.999366i
\(6\) 35.3300 2.40390
\(7\) 20.1910 20.1910i 1.09021 1.09021i 0.0947070 0.995505i \(-0.469809\pi\)
0.995505 0.0947070i \(-0.0301914\pi\)
\(8\) 40.2512 40.2512i 1.77887 1.77887i
\(9\) 19.2941i 0.714596i
\(10\) −39.5626 + 42.4867i −1.25108 + 1.34355i
\(11\) 18.3142i 0.501994i 0.967988 + 0.250997i \(0.0807584\pi\)
−0.967988 + 0.250997i \(0.919242\pi\)
\(12\) −91.2316 91.2316i −2.19469 2.19469i
\(13\) −26.6019 + 26.6019i −0.567542 + 0.567542i −0.931439 0.363897i \(-0.881446\pi\)
0.363897 + 0.931439i \(0.381446\pi\)
\(14\) −148.270 −2.83049
\(15\) 55.6718 + 51.8403i 0.958293 + 0.892340i
\(16\) −143.879 −2.24811
\(17\) 41.2449 41.2449i 0.588433 0.588433i −0.348774 0.937207i \(-0.613402\pi\)
0.937207 + 0.348774i \(0.113402\pi\)
\(18\) −70.8419 + 70.8419i −0.927644 + 0.927644i
\(19\) −76.5780 −0.924642 −0.462321 0.886713i \(-0.652983\pi\)
−0.462321 + 0.886713i \(0.652983\pi\)
\(20\) 211.874 7.55078i 2.36882 0.0844203i
\(21\) 194.283i 2.01886i
\(22\) 67.2439 67.2439i 0.651657 0.651657i
\(23\) −31.1185 105.824i −0.282115 0.959381i
\(24\) 387.308i 3.29412i
\(25\) −124.683 + 8.89824i −0.997463 + 0.0711859i
\(26\) 195.348 1.47350
\(27\) −37.0742 37.0742i −0.264256 0.264256i
\(28\) 382.874 + 382.874i 2.58415 + 2.58415i
\(29\) 90.1157i 0.577037i 0.957474 + 0.288518i \(0.0931626\pi\)
−0.957474 + 0.288518i \(0.906837\pi\)
\(30\) −14.0682 394.751i −0.0856163 2.40238i
\(31\) −271.752 −1.57446 −0.787229 0.616661i \(-0.788485\pi\)
−0.787229 + 0.616661i \(0.788485\pi\)
\(32\) 206.268 + 206.268i 1.13948 + 1.13948i
\(33\) −88.1120 88.1120i −0.464798 0.464798i
\(34\) −302.877 −1.52773
\(35\) −233.639 217.559i −1.12835 1.05069i
\(36\) 365.866 1.69382
\(37\) −275.386 + 275.386i −1.22360 + 1.22360i −0.257259 + 0.966343i \(0.582819\pi\)
−0.966343 + 0.257259i \(0.917181\pi\)
\(38\) 281.171 + 281.171i 1.20031 + 1.20031i
\(39\) 255.971i 1.05098i
\(40\) −465.764 433.708i −1.84109 1.71438i
\(41\) 371.644 1.41564 0.707818 0.706395i \(-0.249680\pi\)
0.707818 + 0.706395i \(0.249680\pi\)
\(42\) 713.348 713.348i 2.62076 2.62076i
\(43\) 141.411 + 141.411i 0.501511 + 0.501511i 0.911907 0.410397i \(-0.134610\pi\)
−0.410397 + 0.911907i \(0.634610\pi\)
\(44\) −347.284 −1.18989
\(45\) −215.578 + 7.68279i −0.714143 + 0.0254507i
\(46\) −274.294 + 502.809i −0.879183 + 1.61163i
\(47\) −262.585 262.585i −0.814937 0.814937i 0.170433 0.985369i \(-0.445483\pi\)
−0.985369 + 0.170433i \(0.945483\pi\)
\(48\) 692.220 692.220i 2.08153 2.08153i
\(49\) 472.354i 1.37713i
\(50\) 490.468 + 425.125i 1.38725 + 1.20244i
\(51\) 396.870i 1.08966i
\(52\) −504.441 504.441i −1.34526 1.34526i
\(53\) −377.393 377.393i −0.978093 0.978093i 0.0216720 0.999765i \(-0.493101\pi\)
−0.999765 + 0.0216720i \(0.993101\pi\)
\(54\) 272.249i 0.686083i
\(55\) 204.629 7.29259i 0.501675 0.0178788i
\(56\) 1625.42i 3.87868i
\(57\) 368.428 368.428i 0.856130 0.856130i
\(58\) 330.877 330.877i 0.749073 0.749073i
\(59\) 193.149i 0.426201i 0.977030 + 0.213100i \(0.0683562\pi\)
−0.977030 + 0.213100i \(0.931644\pi\)
\(60\) −983.025 + 1055.68i −2.11513 + 2.27146i
\(61\) 295.893i 0.621068i −0.950562 0.310534i \(-0.899492\pi\)
0.950562 0.310534i \(-0.100508\pi\)
\(62\) 997.790 + 997.790i 2.04386 + 2.04386i
\(63\) −389.567 389.567i −0.779061 0.779061i
\(64\) 363.677i 0.710306i
\(65\) 307.823 + 286.637i 0.587396 + 0.546969i
\(66\) 647.040i 1.20674i
\(67\) −240.325 + 240.325i −0.438214 + 0.438214i −0.891411 0.453197i \(-0.850284\pi\)
0.453197 + 0.891411i \(0.350284\pi\)
\(68\) 782.109 + 782.109i 1.39477 + 1.39477i
\(69\) 658.847 + 359.417i 1.14951 + 0.627083i
\(70\) 59.0403 + 1656.66i 0.100809 + 2.82870i
\(71\) −730.125 −1.22042 −0.610211 0.792239i \(-0.708915\pi\)
−0.610211 + 0.792239i \(0.708915\pi\)
\(72\) −776.610 776.610i −1.27117 1.27117i
\(73\) −266.909 + 266.909i −0.427936 + 0.427936i −0.887925 0.459989i \(-0.847853\pi\)
0.459989 + 0.887925i \(0.347853\pi\)
\(74\) 2022.27 3.17681
\(75\) 557.056 642.677i 0.857644 0.989466i
\(76\) 1452.12i 2.19170i
\(77\) 369.782 + 369.782i 0.547280 + 0.547280i
\(78\) −939.846 + 939.846i −1.36432 + 1.36432i
\(79\) −16.0835 −0.0229055 −0.0114528 0.999934i \(-0.503646\pi\)
−0.0114528 + 0.999934i \(0.503646\pi\)
\(80\) 57.2916 + 1607.59i 0.0800675 + 2.24668i
\(81\) 877.678 1.20395
\(82\) −1364.56 1364.56i −1.83769 1.83769i
\(83\) −241.530 241.530i −0.319414 0.319414i 0.529128 0.848542i \(-0.322519\pi\)
−0.848542 + 0.529128i \(0.822519\pi\)
\(84\) −3684.12 −4.78536
\(85\) −477.263 444.416i −0.609017 0.567102i
\(86\) 1038.43i 1.30206i
\(87\) −433.559 433.559i −0.534280 0.534280i
\(88\) 737.167 + 737.167i 0.892980 + 0.892980i
\(89\) −967.565 −1.15238 −0.576189 0.817316i \(-0.695461\pi\)
−0.576189 + 0.817316i \(0.695461\pi\)
\(90\) 819.743 + 763.325i 0.960094 + 0.894017i
\(91\) 1074.24i 1.23748i
\(92\) 2006.69 590.087i 2.27404 0.668704i
\(93\) 1307.44 1307.44i 1.45780 1.45780i
\(94\) 1928.26i 2.11580i
\(95\) 30.4929 + 855.625i 0.0329316 + 0.924056i
\(96\) −1984.77 −2.11010
\(97\) 434.431 434.431i 0.454740 0.454740i −0.442184 0.896924i \(-0.645796\pi\)
0.896924 + 0.442184i \(0.145796\pi\)
\(98\) −1734.34 + 1734.34i −1.78770 + 1.78770i
\(99\) 353.356 0.358723
\(100\) −168.734 2364.31i −0.168734 2.36431i
\(101\) −377.853 −0.372255 −0.186128 0.982526i \(-0.559594\pi\)
−0.186128 + 0.982526i \(0.559594\pi\)
\(102\) 1457.18 1457.18i 1.41453 1.41453i
\(103\) 230.760 + 230.760i 0.220752 + 0.220752i 0.808815 0.588063i \(-0.200109\pi\)
−0.588063 + 0.808815i \(0.700109\pi\)
\(104\) 2141.52i 2.01916i
\(105\) 2170.78 77.3625i 2.01758 0.0719029i
\(106\) 2771.34i 2.53940i
\(107\) −584.277 + 584.277i −0.527890 + 0.527890i −0.919943 0.392053i \(-0.871765\pi\)
0.392053 + 0.919943i \(0.371765\pi\)
\(108\) 703.022 703.022i 0.626373 0.626373i
\(109\) 1836.70 1.61398 0.806991 0.590564i \(-0.201095\pi\)
0.806991 + 0.590564i \(0.201095\pi\)
\(110\) −778.109 724.557i −0.674453 0.628034i
\(111\) 2649.84i 2.26587i
\(112\) −2905.06 + 2905.06i −2.45091 + 2.45091i
\(113\) −883.649 883.649i −0.735635 0.735635i 0.236095 0.971730i \(-0.424132\pi\)
−0.971730 + 0.236095i \(0.924132\pi\)
\(114\) −2705.50 −2.22275
\(115\) −1170.00 + 389.833i −0.948724 + 0.316105i
\(116\) −1708.83 −1.36776
\(117\) 513.260 + 513.260i 0.405564 + 0.405564i
\(118\) 709.183 709.183i 0.553267 0.553267i
\(119\) 1665.55i 1.28303i
\(120\) 4327.49 154.224i 3.29203 0.117322i
\(121\) 995.591 0.748002
\(122\) −1086.42 + 1086.42i −0.806232 + 0.806232i
\(123\) −1788.03 + 1788.03i −1.31074 + 1.31074i
\(124\) 5153.13i 3.73197i
\(125\) 149.070 + 1389.57i 0.106666 + 0.994295i
\(126\) 2860.74i 2.02266i
\(127\) −399.009 399.009i −0.278790 0.278790i 0.553836 0.832626i \(-0.313164\pi\)
−0.832626 + 0.553836i \(0.813164\pi\)
\(128\) 314.840 314.840i 0.217408 0.217408i
\(129\) −1360.69 −0.928701
\(130\) −77.7864 2182.67i −0.0524794 1.47256i
\(131\) −988.878 −0.659532 −0.329766 0.944063i \(-0.606970\pi\)
−0.329766 + 0.944063i \(0.606970\pi\)
\(132\) 1670.83 1670.83i 1.10172 1.10172i
\(133\) −1546.19 + 1546.19i −1.00806 + 1.00806i
\(134\) 1764.79 1.13772
\(135\) −399.476 + 429.001i −0.254677 + 0.273500i
\(136\) 3320.31i 2.09349i
\(137\) −1205.08 + 1205.08i −0.751511 + 0.751511i −0.974761 0.223250i \(-0.928333\pi\)
0.223250 + 0.974761i \(0.428333\pi\)
\(138\) −1099.42 3738.75i −0.678177 2.30626i
\(139\) 837.217i 0.510877i −0.966825 0.255438i \(-0.917780\pi\)
0.966825 0.255438i \(-0.0822198\pi\)
\(140\) 4125.48 4430.40i 2.49048 2.67455i
\(141\) 2526.67 1.50911
\(142\) 2680.79 + 2680.79i 1.58427 + 1.58427i
\(143\) −487.193 487.193i −0.284903 0.284903i
\(144\) 2776.01i 1.60649i
\(145\) 1006.88 35.8835i 0.576670 0.0205515i
\(146\) 1960.01 1.11104
\(147\) 2272.56 + 2272.56i 1.27509 + 1.27509i
\(148\) −5222.04 5222.04i −2.90033 2.90033i
\(149\) 3160.69 1.73781 0.868904 0.494980i \(-0.164825\pi\)
0.868904 + 0.494980i \(0.164825\pi\)
\(150\) −4405.05 + 314.375i −2.39780 + 0.171124i
\(151\) −908.090 −0.489400 −0.244700 0.969599i \(-0.578689\pi\)
−0.244700 + 0.969599i \(0.578689\pi\)
\(152\) −3082.35 + 3082.35i −1.64482 + 1.64482i
\(153\) −795.783 795.783i −0.420492 0.420492i
\(154\) 2715.45i 1.42089i
\(155\) 108.210 + 3036.36i 0.0560752 + 1.57346i
\(156\) 4853.87 2.49116
\(157\) 1430.81 1430.81i 0.727333 0.727333i −0.242755 0.970088i \(-0.578051\pi\)
0.970088 + 0.242755i \(0.0780510\pi\)
\(158\) 59.0536 + 59.0536i 0.0297345 + 0.0297345i
\(159\) 3631.38 1.81124
\(160\) 2222.55 2386.82i 1.09818 1.17934i
\(161\) −2765.00 1508.37i −1.35349 0.738363i
\(162\) −3222.56 3222.56i −1.56289 1.56289i
\(163\) −1328.21 + 1328.21i −0.638244 + 0.638244i −0.950122 0.311878i \(-0.899042\pi\)
0.311878 + 0.950122i \(0.399042\pi\)
\(164\) 7047.33i 3.35551i
\(165\) −949.412 + 1019.58i −0.447949 + 0.481057i
\(166\) 1773.65i 0.829288i
\(167\) 294.654 + 294.654i 0.136533 + 0.136533i 0.772070 0.635537i \(-0.219221\pi\)
−0.635537 + 0.772070i \(0.719221\pi\)
\(168\) 7820.14 + 7820.14i 3.59129 + 3.59129i
\(169\) 781.673i 0.355791i
\(170\) 120.604 + 3384.12i 0.0544110 + 1.52676i
\(171\) 1477.50i 0.660746i
\(172\) −2681.51 + 2681.51i −1.18874 + 1.18874i
\(173\) −614.961 + 614.961i −0.270258 + 0.270258i −0.829204 0.558946i \(-0.811206\pi\)
0.558946 + 0.829204i \(0.311206\pi\)
\(174\) 3183.79i 1.38714i
\(175\) −2337.81 + 2697.14i −1.00984 + 1.16505i
\(176\) 2635.02i 1.12853i
\(177\) −929.266 929.266i −0.394621 0.394621i
\(178\) 3552.60 + 3552.60i 1.49595 + 1.49595i
\(179\) 1930.02i 0.805900i −0.915222 0.402950i \(-0.867985\pi\)
0.915222 0.402950i \(-0.132015\pi\)
\(180\) −145.686 4087.91i −0.0603264 1.69275i
\(181\) 3583.35i 1.47154i −0.677234 0.735768i \(-0.736821\pi\)
0.677234 0.735768i \(-0.263179\pi\)
\(182\) 3944.27 3944.27i 1.60642 1.60642i
\(183\) 1423.58 + 1423.58i 0.575049 + 0.575049i
\(184\) −5512.08 3006.97i −2.20846 1.20476i
\(185\) 3186.62 + 2967.30i 1.26640 + 1.17925i
\(186\) −9601.01 −3.78484
\(187\) 755.366 + 755.366i 0.295390 + 0.295390i
\(188\) 4979.30 4979.30i 1.93166 1.93166i
\(189\) −1497.13 −0.576191
\(190\) 3029.63 3253.55i 1.15680 1.24230i
\(191\) 80.7412i 0.0305876i −0.999883 0.0152938i \(-0.995132\pi\)
0.999883 0.0152938i \(-0.00486835\pi\)
\(192\) 1749.70 + 1749.70i 0.657675 + 0.657675i
\(193\) 254.892 254.892i 0.0950648 0.0950648i −0.657975 0.753040i \(-0.728587\pi\)
0.753040 + 0.657975i \(0.228587\pi\)
\(194\) −3190.19 −1.18063
\(195\) −2860.03 + 101.926i −1.05031 + 0.0374312i
\(196\) 8957.05 3.26423
\(197\) −3020.45 3020.45i −1.09238 1.09238i −0.995274 0.0971034i \(-0.969042\pi\)
−0.0971034 0.995274i \(-0.530958\pi\)
\(198\) −1297.41 1297.41i −0.465672 0.465672i
\(199\) 1507.84 0.537127 0.268563 0.963262i \(-0.413451\pi\)
0.268563 + 0.963262i \(0.413451\pi\)
\(200\) −4660.47 + 5376.79i −1.64772 + 1.90098i
\(201\) 2312.47i 0.811488i
\(202\) 1387.36 + 1387.36i 0.483238 + 0.483238i
\(203\) 1819.53 + 1819.53i 0.629092 + 0.629092i
\(204\) −7525.67 −2.58286
\(205\) −147.987 4152.47i −0.0504187 1.41474i
\(206\) 1694.56i 0.573134i
\(207\) −2041.77 + 600.403i −0.685570 + 0.201599i
\(208\) 3827.45 3827.45i 1.27590 1.27590i
\(209\) 1402.46i 0.464165i
\(210\) −8254.47 7686.37i −2.71244 2.52576i
\(211\) −2713.28 −0.885261 −0.442630 0.896704i \(-0.645955\pi\)
−0.442630 + 0.896704i \(0.645955\pi\)
\(212\) 7156.35 7156.35i 2.31840 2.31840i
\(213\) 3512.73 3512.73i 1.12999 1.12999i
\(214\) 4290.57 1.37055
\(215\) 1523.71 1636.33i 0.483331 0.519054i
\(216\) −2984.56 −0.940154
\(217\) −5486.96 + 5486.96i −1.71649 + 1.71649i
\(218\) −6743.79 6743.79i −2.09517 2.09517i
\(219\) 2568.27i 0.792455i
\(220\) 138.286 + 3880.29i 0.0423785 + 1.18913i
\(221\) 2194.39i 0.667921i
\(222\) −9729.40 + 9729.40i −2.94142 + 2.94142i
\(223\) −977.212 + 977.212i −0.293448 + 0.293448i −0.838441 0.544993i \(-0.816532\pi\)
0.544993 + 0.838441i \(0.316532\pi\)
\(224\) 8329.54 2.48456
\(225\) 171.683 + 2405.64i 0.0508692 + 0.712783i
\(226\) 6488.97i 1.90991i
\(227\) 3341.08 3341.08i 0.976895 0.976895i −0.0228436 0.999739i \(-0.507272\pi\)
0.999739 + 0.0228436i \(0.00727196\pi\)
\(228\) 6986.34 + 6986.34i 2.02930 + 2.02930i
\(229\) 2356.44 0.679990 0.339995 0.940427i \(-0.389575\pi\)
0.339995 + 0.940427i \(0.389575\pi\)
\(230\) 5727.23 + 2864.54i 1.64192 + 0.821226i
\(231\) −3558.14 −1.01346
\(232\) 3627.26 + 3627.26i 1.02647 + 1.02647i
\(233\) 3740.03 3740.03i 1.05158 1.05158i 0.0529823 0.998595i \(-0.483127\pi\)
0.998595 0.0529823i \(-0.0168727\pi\)
\(234\) 3769.06i 1.05295i
\(235\) −2829.37 + 3038.49i −0.785395 + 0.843444i
\(236\) −3662.60 −1.01023
\(237\) 77.3800 77.3800i 0.0212083 0.0212083i
\(238\) −6115.39 + 6115.39i −1.66555 + 1.66555i
\(239\) 6284.37i 1.70085i −0.526099 0.850423i \(-0.676346\pi\)
0.526099 0.850423i \(-0.323654\pi\)
\(240\) −8009.99 7458.71i −2.15434 2.00607i
\(241\) 732.131i 0.195688i −0.995202 0.0978438i \(-0.968805\pi\)
0.995202 0.0978438i \(-0.0311945\pi\)
\(242\) −3655.50 3655.50i −0.971010 0.971010i
\(243\) −3221.63 + 3221.63i −0.850484 + 0.850484i
\(244\) 5610.88 1.47213
\(245\) −5277.73 + 188.088i −1.37625 + 0.0490471i
\(246\) 13130.2 3.40305
\(247\) 2037.12 2037.12i 0.524774 0.524774i
\(248\) −10938.4 + 10938.4i −2.80075 + 2.80075i
\(249\) 2324.07 0.591494
\(250\) 4554.73 5649.40i 1.15226 1.42920i
\(251\) 1879.74i 0.472701i 0.971668 + 0.236350i \(0.0759513\pi\)
−0.971668 + 0.236350i \(0.924049\pi\)
\(252\) 7387.20 7387.20i 1.84663 1.84663i
\(253\) 1938.07 569.909i 0.481603 0.141620i
\(254\) 2930.07i 0.723816i
\(255\) 4434.32 158.031i 1.08897 0.0388090i
\(256\) −5221.40 −1.27476
\(257\) 1137.79 + 1137.79i 0.276161 + 0.276161i 0.831574 0.555414i \(-0.187440\pi\)
−0.555414 + 0.831574i \(0.687440\pi\)
\(258\) 4996.05 + 4996.05i 1.20558 + 1.20558i
\(259\) 11120.7i 2.66797i
\(260\) −5435.38 + 5837.11i −1.29649 + 1.39232i
\(261\) 1738.70 0.412348
\(262\) 3630.85 + 3630.85i 0.856163 + 0.856163i
\(263\) −847.390 847.390i −0.198678 0.198678i 0.600755 0.799433i \(-0.294867\pi\)
−0.799433 + 0.600755i \(0.794867\pi\)
\(264\) −7093.22 −1.65363
\(265\) −4066.43 + 4366.98i −0.942637 + 1.01231i
\(266\) 11354.2 2.61719
\(267\) 4655.09 4655.09i 1.06699 1.06699i
\(268\) −4557.18 4557.18i −1.03871 1.03871i
\(269\) 2791.78i 0.632781i 0.948629 + 0.316391i \(0.102471\pi\)
−0.948629 + 0.316391i \(0.897529\pi\)
\(270\) 3041.91 108.408i 0.685647 0.0244352i
\(271\) 838.427 0.187937 0.0939683 0.995575i \(-0.470045\pi\)
0.0939683 + 0.995575i \(0.470045\pi\)
\(272\) −5934.26 + 5934.26i −1.32286 + 1.32286i
\(273\) −5168.32 5168.32i −1.14579 1.14579i
\(274\) 8849.37 1.95113
\(275\) −162.964 2283.46i −0.0357349 0.500720i
\(276\) −6815.47 + 12493.4i −1.48639 + 2.72470i
\(277\) −1818.99 1818.99i −0.394557 0.394557i 0.481751 0.876308i \(-0.340001\pi\)
−0.876308 + 0.481751i \(0.840001\pi\)
\(278\) −3074.00 + 3074.00i −0.663188 + 0.663188i
\(279\) 5243.22i 1.12510i
\(280\) −18161.3 + 647.234i −3.87622 + 0.138141i
\(281\) 6108.34i 1.29677i 0.761312 + 0.648386i \(0.224556\pi\)
−0.761312 + 0.648386i \(0.775444\pi\)
\(282\) −9277.14 9277.14i −1.95903 1.95903i
\(283\) −914.034 914.034i −0.191992 0.191992i 0.604564 0.796556i \(-0.293347\pi\)
−0.796556 + 0.604564i \(0.793347\pi\)
\(284\) 13845.1i 2.89279i
\(285\) −4263.24 3969.83i −0.886078 0.825095i
\(286\) 3577.64i 0.739686i
\(287\) 7503.87 7503.87i 1.54334 1.54334i
\(288\) 3979.76 3979.76i 0.814270 0.814270i
\(289\) 1510.72i 0.307494i
\(290\) −3828.72 3565.21i −0.775276 0.721919i
\(291\) 4180.22i 0.842092i
\(292\) −5061.28 5061.28i −1.01435 1.01435i
\(293\) −232.977 232.977i −0.0464529 0.0464529i 0.683499 0.729952i \(-0.260457\pi\)
−0.729952 + 0.683499i \(0.760457\pi\)
\(294\) 16688.3i 3.31047i
\(295\) 2158.10 76.9107i 0.425931 0.0151794i
\(296\) 22169.2i 4.35325i
\(297\) 678.983 678.983i 0.132655 0.132655i
\(298\) −11605.1 11605.1i −2.25591 2.25591i
\(299\) 3642.93 + 1987.30i 0.704602 + 0.384377i
\(300\) 12186.8 + 10563.2i 2.34535 + 2.03289i
\(301\) 5710.46 1.09351
\(302\) 3334.22 + 3334.22i 0.635308 + 0.635308i
\(303\) 1817.90 1817.90i 0.344672 0.344672i
\(304\) 11018.0 2.07869
\(305\) −3306.08 + 117.823i −0.620674 + 0.0221197i
\(306\) 5843.73i 1.09171i
\(307\) 2586.28 + 2586.28i 0.480803 + 0.480803i 0.905388 0.424585i \(-0.139580\pi\)
−0.424585 + 0.905388i \(0.639580\pi\)
\(308\) −7012.02 + 7012.02i −1.29723 + 1.29723i
\(309\) −2220.44 −0.408791
\(310\) 10751.2 11545.9i 1.96977 2.11536i
\(311\) 3111.56 0.567332 0.283666 0.958923i \(-0.408449\pi\)
0.283666 + 0.958923i \(0.408449\pi\)
\(312\) −10303.1 10303.1i −1.86955 1.86955i
\(313\) 7226.99 + 7226.99i 1.30509 + 1.30509i 0.924913 + 0.380180i \(0.124138\pi\)
0.380180 + 0.924913i \(0.375862\pi\)
\(314\) −10507.0 −1.88836
\(315\) −4197.61 + 4507.86i −0.750821 + 0.806314i
\(316\) 304.985i 0.0542935i
\(317\) 3991.64 + 3991.64i 0.707232 + 0.707232i 0.965952 0.258720i \(-0.0833007\pi\)
−0.258720 + 0.965952i \(0.583301\pi\)
\(318\) −13333.3 13333.3i −2.35124 2.35124i
\(319\) −1650.39 −0.289669
\(320\) −4063.45 + 144.814i −0.709856 + 0.0252979i
\(321\) 5622.08i 0.977550i
\(322\) 4613.94 + 15690.5i 0.798525 + 2.71552i
\(323\) −3158.45 + 3158.45i −0.544090 + 0.544090i
\(324\) 16643.0i 2.85375i
\(325\) 3080.10 3553.52i 0.525702 0.606504i
\(326\) 9753.58 1.65706
\(327\) −8836.62 + 8836.62i −1.49439 + 1.49439i
\(328\) 14959.1 14959.1i 2.51823 2.51823i
\(329\) −10603.7 −1.77691
\(330\) 7229.53 257.647i 1.20598 0.0429788i
\(331\) 7322.09 1.21589 0.607943 0.793981i \(-0.291995\pi\)
0.607943 + 0.793981i \(0.291995\pi\)
\(332\) 4580.04 4580.04i 0.757115 0.757115i
\(333\) 5313.33 + 5313.33i 0.874381 + 0.874381i
\(334\) 2163.75i 0.354477i
\(335\) 2780.90 + 2589.51i 0.453543 + 0.422329i
\(336\) 27953.3i 4.53862i
\(337\) 3410.34 3410.34i 0.551255 0.551255i −0.375548 0.926803i \(-0.622545\pi\)
0.926803 + 0.375548i \(0.122545\pi\)
\(338\) 2870.06 2870.06i 0.461866 0.461866i
\(339\) 8502.72 1.36225
\(340\) 8427.27 9050.13i 1.34421 1.44357i
\(341\) 4976.92i 0.790368i
\(342\) 5424.93 5424.93i 0.857739 0.857739i
\(343\) −2611.79 2611.79i −0.411147 0.411147i
\(344\) 11383.9 1.78424
\(345\) 3753.50 7504.58i 0.585744 1.17111i
\(346\) 4515.89 0.701664
\(347\) −6101.85 6101.85i −0.943989 0.943989i 0.0545233 0.998512i \(-0.482636\pi\)
−0.998512 + 0.0545233i \(0.982636\pi\)
\(348\) 8221.39 8221.39i 1.26642 1.26642i
\(349\) 180.625i 0.0277038i 0.999904 + 0.0138519i \(0.00440934\pi\)
−0.999904 + 0.0138519i \(0.995591\pi\)
\(350\) 18486.8 1319.34i 2.82331 0.201491i
\(351\) 1972.49 0.299954
\(352\) −3777.64 + 3777.64i −0.572013 + 0.572013i
\(353\) 4463.50 4463.50i 0.672997 0.672997i −0.285409 0.958406i \(-0.592129\pi\)
0.958406 + 0.285409i \(0.0921294\pi\)
\(354\) 6823.95i 1.02454i
\(355\) 290.731 + 8157.87i 0.0434660 + 1.21965i
\(356\) 18347.5i 2.73151i
\(357\) 8013.20 + 8013.20i 1.18797 + 1.18797i
\(358\) −7086.42 + 7086.42i −1.04617 + 1.04617i
\(359\) −7203.43 −1.05900 −0.529502 0.848308i \(-0.677621\pi\)
−0.529502 + 0.848308i \(0.677621\pi\)
\(360\) −8368.01 + 8986.49i −1.22509 + 1.31564i
\(361\) −994.804 −0.145036
\(362\) −13156.9 + 13156.9i −1.91026 + 1.91026i
\(363\) −4789.93 + 4789.93i −0.692578 + 0.692578i
\(364\) −20370.4 −2.93323
\(365\) 3088.52 + 2875.96i 0.442905 + 0.412423i
\(366\) 10453.9i 1.49299i
\(367\) −710.775 + 710.775i −0.101096 + 0.101096i −0.755846 0.654750i \(-0.772774\pi\)
0.654750 + 0.755846i \(0.272774\pi\)
\(368\) 4477.29 + 15225.8i 0.634225 + 2.15679i
\(369\) 7170.54i 1.01161i
\(370\) −805.254 22595.3i −0.113144 3.17479i
\(371\) −15239.9 −2.13266
\(372\) 24792.4 + 24792.4i 3.45545 + 3.45545i
\(373\) 2220.82 + 2220.82i 0.308283 + 0.308283i 0.844243 0.535960i \(-0.180050\pi\)
−0.535960 + 0.844243i \(0.680050\pi\)
\(374\) 5546.94i 0.766913i
\(375\) −7402.61 5968.21i −1.01938 0.821859i
\(376\) −21138.7 −2.89933
\(377\) −2397.25 2397.25i −0.327493 0.327493i
\(378\) 5496.99 + 5496.99i 0.747976 + 0.747976i
\(379\) −5382.66 −0.729521 −0.364760 0.931101i \(-0.618849\pi\)
−0.364760 + 0.931101i \(0.618849\pi\)
\(380\) −16224.9 + 578.224i −2.19031 + 0.0780586i
\(381\) 3839.38 0.516266
\(382\) −296.456 + 296.456i −0.0397069 + 0.0397069i
\(383\) −4841.63 4841.63i −0.645942 0.645942i 0.306068 0.952010i \(-0.400987\pi\)
−0.952010 + 0.306068i \(0.900987\pi\)
\(384\) 3029.48i 0.402598i
\(385\) 3984.42 4278.91i 0.527441 0.566424i
\(386\) −1871.76 −0.246814
\(387\) 2728.40 2728.40i 0.358378 0.358378i
\(388\) 8237.94 + 8237.94i 1.07788 + 1.07788i
\(389\) −4378.54 −0.570696 −0.285348 0.958424i \(-0.592109\pi\)
−0.285348 + 0.958424i \(0.592109\pi\)
\(390\) 10875.4 + 10126.9i 1.41204 + 1.31486i
\(391\) −5648.16 3081.21i −0.730537 0.398525i
\(392\) −19012.8 19012.8i −2.44972 2.44972i
\(393\) 4757.63 4757.63i 0.610663 0.610663i
\(394\) 22180.3i 2.83611i
\(395\) 6.40436 + 179.705i 0.000815793 + 0.0228910i
\(396\) 6700.53i 0.850289i
\(397\) −2915.35 2915.35i −0.368557 0.368557i 0.498394 0.866951i \(-0.333923\pi\)
−0.866951 + 0.498394i \(0.833923\pi\)
\(398\) −5536.33 5536.33i −0.697264 0.697264i
\(399\) 14877.8i 1.86673i
\(400\) 17939.2 1280.27i 2.24240 0.160033i
\(401\) 4777.39i 0.594941i 0.954731 + 0.297470i \(0.0961430\pi\)
−0.954731 + 0.297470i \(0.903857\pi\)
\(402\) −8490.67 + 8490.67i −1.05342 + 1.05342i
\(403\) 7229.14 7229.14i 0.893571 0.893571i
\(404\) 7165.06i 0.882365i
\(405\) −349.486 9806.52i −0.0428793 1.20318i
\(406\) 13361.5i 1.63330i
\(407\) −5043.48 5043.48i −0.614240 0.614240i
\(408\) 15974.5 + 15974.5i 1.93837 + 1.93837i
\(409\) 15620.1i 1.88843i −0.329334 0.944214i \(-0.606824\pi\)
0.329334 0.944214i \(-0.393176\pi\)
\(410\) −14703.2 + 15789.9i −1.77107 + 1.90198i
\(411\) 11595.6i 1.39165i
\(412\) −4375.81 + 4375.81i −0.523254 + 0.523254i
\(413\) 3899.87 + 3899.87i 0.464649 + 0.464649i
\(414\) 9701.24 + 5292.25i 1.15167 + 0.628261i
\(415\) −2602.50 + 2794.85i −0.307836 + 0.330588i
\(416\) −10974.3 −1.29341
\(417\) 4027.97 + 4027.97i 0.473023 + 0.473023i
\(418\) −5149.41 + 5149.41i −0.602550 + 0.602550i
\(419\) 6392.96 0.745386 0.372693 0.927955i \(-0.378434\pi\)
0.372693 + 0.927955i \(0.378434\pi\)
\(420\) 1466.99 + 41163.5i 0.170433 + 4.78232i
\(421\) 4253.43i 0.492398i −0.969219 0.246199i \(-0.920818\pi\)
0.969219 0.246199i \(-0.0791817\pi\)
\(422\) 9962.32 + 9962.32i 1.14919 + 1.14919i
\(423\) −5066.35 + 5066.35i −0.582351 + 0.582351i
\(424\) −30381.0 −3.47979
\(425\) −4775.52 + 5509.54i −0.545052 + 0.628828i
\(426\) −25795.3 −2.93377
\(427\) −5974.37 5974.37i −0.677096 0.677096i
\(428\) −11079.4 11079.4i −1.25127 1.25127i
\(429\) 4687.90 0.527585
\(430\) −11602.7 + 413.498i −1.30123 + 0.0463736i
\(431\) 4130.06i 0.461573i −0.973004 0.230786i \(-0.925870\pi\)
0.973004 0.230786i \(-0.0741299\pi\)
\(432\) 5334.18 + 5334.18i 0.594076 + 0.594076i
\(433\) 7004.73 + 7004.73i 0.777427 + 0.777427i 0.979393 0.201966i \(-0.0647329\pi\)
−0.201966 + 0.979393i \(0.564733\pi\)
\(434\) 40292.8 4.45649
\(435\) −4671.62 + 5016.90i −0.514913 + 0.552970i
\(436\) 34828.6i 3.82566i
\(437\) 2382.99 + 8103.77i 0.260856 + 0.887084i
\(438\) −9429.88 + 9429.88i −1.02872 + 1.02872i
\(439\) 6315.50i 0.686612i 0.939224 + 0.343306i \(0.111547\pi\)
−0.939224 + 0.343306i \(0.888453\pi\)
\(440\) 7943.01 8530.08i 0.860610 0.924218i
\(441\) −9113.64 −0.984088
\(442\) 8057.11 8057.11i 0.867053 0.867053i
\(443\) −2468.06 + 2468.06i −0.264697 + 0.264697i −0.826959 0.562262i \(-0.809931\pi\)
0.562262 + 0.826959i \(0.309931\pi\)
\(444\) 50247.9 5.37085
\(445\) 385.278 + 10810.8i 0.0410426 + 1.15165i
\(446\) 7176.04 0.761872
\(447\) −15206.5 + 15206.5i −1.60904 + 1.60904i
\(448\) −7343.00 7343.00i −0.774384 0.774384i
\(449\) 11622.4i 1.22160i 0.791787 + 0.610798i \(0.209151\pi\)
−0.791787 + 0.610798i \(0.790849\pi\)
\(450\) 8202.40 9463.14i 0.859256 0.991326i
\(451\) 6806.36i 0.710641i
\(452\) 16756.3 16756.3i 1.74369 1.74369i
\(453\) 4368.95 4368.95i 0.453137 0.453137i
\(454\) −24534.8 −2.53629
\(455\) 12002.8 427.756i 1.23670 0.0440736i
\(456\) 29659.3i 3.04588i
\(457\) −3074.23 + 3074.23i −0.314675 + 0.314675i −0.846718 0.532043i \(-0.821425\pi\)
0.532043 + 0.846718i \(0.321425\pi\)
\(458\) −8652.10 8652.10i −0.882720 0.882720i
\(459\) −3058.24 −0.310994
\(460\) −7392.23 22186.3i −0.749271 2.24878i
\(461\) 8203.72 0.828818 0.414409 0.910091i \(-0.363988\pi\)
0.414409 + 0.910091i \(0.363988\pi\)
\(462\) 13064.4 + 13064.4i 1.31561 + 1.31561i
\(463\) 5229.70 5229.70i 0.524935 0.524935i −0.394123 0.919058i \(-0.628952\pi\)
0.919058 + 0.394123i \(0.128952\pi\)
\(464\) 12965.7i 1.29724i
\(465\) −15128.9 14087.7i −1.50879 1.40495i
\(466\) −27464.5 −2.73019
\(467\) 4944.29 4944.29i 0.489924 0.489924i −0.418358 0.908282i \(-0.637394\pi\)
0.908282 + 0.418358i \(0.137394\pi\)
\(468\) −9732.74 + 9732.74i −0.961317 + 0.961317i
\(469\) 9704.80i 0.955492i
\(470\) 21545.0 767.823i 2.11446 0.0753554i
\(471\) 13767.7i 1.34688i
\(472\) 7774.47 + 7774.47i 0.758155 + 0.758155i
\(473\) −2589.82 + 2589.82i −0.251755 + 0.251755i
\(474\) −568.230 −0.0550626
\(475\) 9547.97 681.410i 0.922297 0.0658215i
\(476\) 31583.2 3.04120
\(477\) −7281.46 + 7281.46i −0.698942 + 0.698942i
\(478\) −23074.3 + 23074.3i −2.20793 + 2.20793i
\(479\) −2742.21 −0.261576 −0.130788 0.991410i \(-0.541751\pi\)
−0.130788 + 0.991410i \(0.541751\pi\)
\(480\) 790.324 + 22176.3i 0.0751525 + 2.10876i
\(481\) 14651.6i 1.38889i
\(482\) −2688.16 + 2688.16i −0.254029 + 0.254029i
\(483\) 20559.8 6045.81i 1.93686 0.569552i
\(484\) 18879.0i 1.77301i
\(485\) −5027.00 4681.02i −0.470648 0.438256i
\(486\) 23657.6 2.20809
\(487\) −12344.9 12344.9i −1.14866 1.14866i −0.986816 0.161848i \(-0.948255\pi\)
−0.161848 0.986816i \(-0.551745\pi\)
\(488\) −11910.0 11910.0i −1.10480 1.10480i
\(489\) 12780.4i 1.18191i
\(490\) 20068.8 + 18687.6i 1.85023 + 1.72289i
\(491\) −16225.7 −1.49135 −0.745677 0.666308i \(-0.767874\pi\)
−0.745677 + 0.666308i \(0.767874\pi\)
\(492\) −33905.7 33905.7i −3.10688 3.10688i
\(493\) 3716.81 + 3716.81i 0.339547 + 0.339547i
\(494\) −14959.4 −1.36246
\(495\) −140.704 3948.13i −0.0127761 0.358495i
\(496\) 39099.4 3.53955
\(497\) −14742.0 + 14742.0i −1.33052 + 1.33052i
\(498\) −8533.26 8533.26i −0.767841 0.767841i
\(499\) 5959.63i 0.534649i 0.963607 + 0.267324i \(0.0861395\pi\)
−0.963607 + 0.267324i \(0.913860\pi\)
\(500\) −26349.8 + 2826.75i −2.35680 + 0.252833i
\(501\) −2835.24 −0.252833
\(502\) 6901.80 6901.80i 0.613630 0.613630i
\(503\) −5153.36 5153.36i −0.456813 0.456813i 0.440795 0.897608i \(-0.354697\pi\)
−0.897608 + 0.440795i \(0.854697\pi\)
\(504\) −31361.1 −2.77169
\(505\) 150.459 + 4221.84i 0.0132581 + 0.372019i
\(506\) −9208.53 5023.47i −0.809029 0.441345i
\(507\) −3760.74 3760.74i −0.329428 0.329428i
\(508\) 7566.24 7566.24i 0.660823 0.660823i
\(509\) 4818.93i 0.419638i −0.977740 0.209819i \(-0.932713\pi\)
0.977740 0.209819i \(-0.0672874\pi\)
\(510\) −16861.7 15701.2i −1.46402 1.36326i
\(511\) 10778.3i 0.933082i
\(512\) 16652.6 + 16652.6i 1.43740 + 1.43740i
\(513\) 2839.07 + 2839.07i 0.244343 + 0.244343i
\(514\) 8355.21i 0.716989i
\(515\) 2486.45 2670.23i 0.212750 0.228474i
\(516\) 25802.3i 2.20132i
\(517\) 4809.04 4809.04i 0.409093 0.409093i
\(518\) 40831.6 40831.6i 3.46339 3.46339i
\(519\) 5917.33i 0.500466i
\(520\) 23927.7 852.739i 2.01788 0.0719137i
\(521\) 23119.8i 1.94414i −0.234688 0.972071i \(-0.575407\pi\)
0.234688 0.972071i \(-0.424593\pi\)
\(522\) −6383.96 6383.96i −0.535285 0.535285i
\(523\) −2126.53 2126.53i −0.177795 0.177795i 0.612599 0.790394i \(-0.290124\pi\)
−0.790394 + 0.612599i \(0.790124\pi\)
\(524\) 18751.7i 1.56330i
\(525\) −1728.78 24223.8i −0.143715 2.01374i
\(526\) 6222.70i 0.515823i
\(527\) −11208.4 + 11208.4i −0.926462 + 0.926462i
\(528\) 12677.4 + 12677.4i 1.04491 + 1.04491i
\(529\) −10230.3 + 6586.14i −0.840822 + 0.541312i
\(530\) 30964.9 1103.53i 2.53779 0.0904421i
\(531\) 3726.64 0.304562
\(532\) −29319.7 29319.7i −2.38942 2.38942i
\(533\) −9886.46 + 9886.46i −0.803434 + 0.803434i
\(534\) −34184.1 −2.77020
\(535\) 6760.93 + 6295.62i 0.546356 + 0.508754i
\(536\) 19346.7i 1.55905i
\(537\) 9285.57 + 9285.57i 0.746186 + 0.746186i
\(538\) 10250.6 10250.6i 0.821437 0.821437i
\(539\) 8650.77 0.691308
\(540\) −8134.97 7575.10i −0.648284 0.603667i
\(541\) −10945.4 −0.869835 −0.434918 0.900470i \(-0.643223\pi\)
−0.434918 + 0.900470i \(0.643223\pi\)
\(542\) −3078.44 3078.44i −0.243967 0.243967i
\(543\) 17240.0 + 17240.0i 1.36250 + 1.36250i
\(544\) 17015.0 1.34102
\(545\) −731.363 20521.9i −0.0574828 1.61296i
\(546\) 37952.9i 2.97479i
\(547\) 1481.90 + 1481.90i 0.115834 + 0.115834i 0.762648 0.646814i \(-0.223899\pi\)
−0.646814 + 0.762648i \(0.723899\pi\)
\(548\) −22851.5 22851.5i −1.78132 1.78132i
\(549\) −5708.98 −0.443813
\(550\) −7785.82 + 8982.52i −0.603615 + 0.696393i
\(551\) 6900.88i 0.533552i
\(552\) 40986.3 12052.4i 3.16031 0.929322i
\(553\) −324.742 + 324.742i −0.0249719 + 0.0249719i
\(554\) 13357.5i 1.02438i
\(555\) −29607.4 + 1055.15i −2.26444 + 0.0807004i
\(556\) 15875.8 1.21094
\(557\) 6652.66 6652.66i 0.506072 0.506072i −0.407246 0.913318i \(-0.633511\pi\)
0.913318 + 0.407246i \(0.133511\pi\)
\(558\) 19251.5 19251.5i 1.46054 1.46054i
\(559\) −7523.61 −0.569257
\(560\) 33615.7 + 31302.1i 2.53665 + 2.36207i
\(561\) −7268.34 −0.547005
\(562\) 22427.9 22427.9i 1.68339 1.68339i
\(563\) 11329.6 + 11329.6i 0.848113 + 0.848113i 0.989898 0.141784i \(-0.0452839\pi\)
−0.141784 + 0.989898i \(0.545284\pi\)
\(564\) 47912.2i 3.57707i
\(565\) −9521.37 + 10225.1i −0.708968 + 0.761368i
\(566\) 6712.10i 0.498464i
\(567\) 17721.2 17721.2i 1.31256 1.31256i
\(568\) −29388.4 + 29388.4i −2.17097 + 2.17097i
\(569\) 21524.2 1.58584 0.792918 0.609328i \(-0.208561\pi\)
0.792918 + 0.609328i \(0.208561\pi\)
\(570\) 1077.31 + 30229.2i 0.0791644 + 2.22134i
\(571\) 7519.61i 0.551114i 0.961285 + 0.275557i \(0.0888623\pi\)
−0.961285 + 0.275557i \(0.911138\pi\)
\(572\) 9238.43 9238.43i 0.675311 0.675311i
\(573\) 388.457 + 388.457i 0.0283211 + 0.0283211i
\(574\) −55103.8 −4.00695
\(575\) 4821.59 + 12917.5i 0.349694 + 0.936864i
\(576\) −7016.82 −0.507582
\(577\) 6511.92 + 6511.92i 0.469835 + 0.469835i 0.901861 0.432026i \(-0.142201\pi\)
−0.432026 + 0.901861i \(0.642201\pi\)
\(578\) 5546.89 5546.89i 0.399170 0.399170i
\(579\) 2452.64i 0.176042i
\(580\) 680.444 + 19093.1i 0.0487136 + 1.36689i
\(581\) −9753.48 −0.696459
\(582\) 15348.5 15348.5i 1.09315 1.09315i
\(583\) 6911.65 6911.65i 0.490997 0.490997i
\(584\) 21486.8i 1.52248i
\(585\) 5530.41 5939.16i 0.390862 0.419751i
\(586\) 1710.84i 0.120604i
\(587\) 2743.83 + 2743.83i 0.192930 + 0.192930i 0.796961 0.604031i \(-0.206440\pi\)
−0.604031 + 0.796961i \(0.706440\pi\)
\(588\) −43093.6 + 43093.6i −3.02236 + 3.02236i
\(589\) 20810.3 1.45581
\(590\) −8206.27 7641.48i −0.572621 0.533211i
\(591\) 29063.6 2.02287
\(592\) 39622.2 39622.2i 2.75078 2.75078i
\(593\) −1092.92 + 1092.92i −0.0756846 + 0.0756846i −0.743936 0.668251i \(-0.767043\pi\)
0.668251 + 0.743936i \(0.267043\pi\)
\(594\) −4986.02 −0.344409
\(595\) −18609.6 + 663.213i −1.28222 + 0.0456959i
\(596\) 59934.8i 4.11917i
\(597\) −7254.45 + 7254.45i −0.497328 + 0.497328i
\(598\) −6078.93 20672.4i −0.415696 1.41364i
\(599\) 6383.64i 0.435440i −0.976011 0.217720i \(-0.930138\pi\)
0.976011 0.217720i \(-0.0698619\pi\)
\(600\) −3446.36 48290.6i −0.234495 3.28576i
\(601\) −6670.80 −0.452758 −0.226379 0.974039i \(-0.572689\pi\)
−0.226379 + 0.974039i \(0.572689\pi\)
\(602\) −20967.0 20967.0i −1.41952 1.41952i
\(603\) 4636.85 + 4636.85i 0.313146 + 0.313146i
\(604\) 17219.7i 1.16003i
\(605\) −396.438 11124.0i −0.0266405 0.747528i
\(606\) −13349.5 −0.894865
\(607\) −2243.00 2243.00i −0.149985 0.149985i 0.628126 0.778111i \(-0.283822\pi\)
−0.778111 + 0.628126i \(0.783822\pi\)
\(608\) −15795.6 15795.6i −1.05361 1.05361i
\(609\) −17508.0 −1.16496
\(610\) 12571.5 + 11706.3i 0.834435 + 0.777006i
\(611\) 13970.6 0.925022
\(612\) 15090.1 15090.1i 0.996701 0.996701i
\(613\) 8564.97 + 8564.97i 0.564333 + 0.564333i 0.930535 0.366202i \(-0.119342\pi\)
−0.366202 + 0.930535i \(0.619342\pi\)
\(614\) 18992.0i 1.24830i
\(615\) 20690.1 + 19266.1i 1.35659 + 1.26323i
\(616\) 29768.3 1.94708
\(617\) −7116.71 + 7116.71i −0.464357 + 0.464357i −0.900080 0.435724i \(-0.856492\pi\)
0.435724 + 0.900080i \(0.356492\pi\)
\(618\) 8152.76 + 8152.76i 0.530667 + 0.530667i
\(619\) −15344.2 −0.996341 −0.498171 0.867079i \(-0.665995\pi\)
−0.498171 + 0.867079i \(0.665995\pi\)
\(620\) −57577.2 + 2051.94i −3.72960 + 0.132916i
\(621\) −2769.63 + 5077.01i −0.178972 + 0.328073i
\(622\) −11424.7 11424.7i −0.736476 0.736476i
\(623\) −19536.1 + 19536.1i −1.25634 + 1.25634i
\(624\) 36828.8i 2.36271i
\(625\) 15466.6 2218.92i 0.989865 0.142011i
\(626\) 53070.5i 3.38838i
\(627\) 6747.45 + 6747.45i 0.429772 + 0.429772i
\(628\) 27131.9 + 27131.9i 1.72401 + 1.72401i
\(629\) 22716.6i 1.44001i
\(630\) 31963.7 1139.13i 2.02137 0.0720381i
\(631\) 22474.0i 1.41787i −0.705275 0.708934i \(-0.749176\pi\)
0.705275 0.708934i \(-0.250824\pi\)
\(632\) −647.380 + 647.380i −0.0407459 + 0.0407459i
\(633\) 13054.0 13054.0i 0.819666 0.819666i
\(634\) 29312.1i 1.83617i
\(635\) −4299.35 + 4617.11i −0.268684 + 0.288543i
\(636\) 68860.3i 4.29322i
\(637\) 12565.5 + 12565.5i 0.781577 + 0.781577i
\(638\) 6059.73 + 6059.73i 0.376030 + 0.376030i
\(639\) 14087.1i 0.872108i
\(640\) −3643.15 3392.42i −0.225013 0.209527i
\(641\) 3183.83i 0.196183i −0.995177 0.0980917i \(-0.968726\pi\)
0.995177 0.0980917i \(-0.0312739\pi\)
\(642\) −20642.5 + 20642.5i −1.26899 + 1.26899i
\(643\) −22311.5 22311.5i −1.36840 1.36840i −0.862730 0.505666i \(-0.831247\pi\)
−0.505666 0.862730i \(-0.668753\pi\)
\(644\) 28602.6 52431.5i 1.75016 3.20822i
\(645\) 541.820 + 15203.4i 0.0330762 + 0.928112i
\(646\) 23193.7 1.41261
\(647\) 20243.5 + 20243.5i 1.23007 + 1.23007i 0.963937 + 0.266130i \(0.0857452\pi\)
0.266130 + 0.963937i \(0.414255\pi\)
\(648\) 35327.6 35327.6i 2.14166 2.14166i
\(649\) −3537.36 −0.213950
\(650\) −24356.6 + 1738.25i −1.46976 + 0.104892i
\(651\) 52797.0i 3.17862i
\(652\) −25186.4 25186.4i −1.51284 1.51284i
\(653\) −4223.67 + 4223.67i −0.253116 + 0.253116i −0.822247 0.569131i \(-0.807280\pi\)
0.569131 + 0.822247i \(0.307280\pi\)
\(654\) 64890.6 3.87985
\(655\) 393.765 + 11049.0i 0.0234896 + 0.659113i
\(656\) −53471.7 −3.18250
\(657\) 5149.76 + 5149.76i 0.305801 + 0.305801i
\(658\) 38933.6 + 38933.6i 2.30667 + 2.30667i
\(659\) 17496.4 1.03424 0.517118 0.855914i \(-0.327005\pi\)
0.517118 + 0.855914i \(0.327005\pi\)
\(660\) −19333.9 18003.3i −1.14026 1.06178i
\(661\) 7380.69i 0.434305i −0.976138 0.217152i \(-0.930323\pi\)
0.976138 0.217152i \(-0.0696769\pi\)
\(662\) −26884.4 26884.4i −1.57839 1.57839i
\(663\) −10557.5 10557.5i −0.618431 0.618431i
\(664\) −19443.8 −1.13639
\(665\) 17891.6 + 16660.3i 1.04332 + 0.971514i
\(666\) 39017.8i 2.27013i
\(667\) 9536.37 2804.26i 0.553598 0.162791i
\(668\) −5587.40 + 5587.40i −0.323627 + 0.323627i
\(669\) 9403.01i 0.543410i
\(670\) −702.730 19718.5i −0.0405207 1.13700i
\(671\) 5419.03 0.311772
\(672\) −40074.6 + 40074.6i −2.30046 + 2.30046i
\(673\) −10467.7 + 10467.7i −0.599554 + 0.599554i −0.940194 0.340640i \(-0.889356\pi\)
0.340640 + 0.940194i \(0.389356\pi\)
\(674\) −25043.4 −1.43121
\(675\) 4952.41 + 4292.62i 0.282397 + 0.244775i
\(676\) −14822.5 −0.843340
\(677\) −6843.41 + 6843.41i −0.388498 + 0.388498i −0.874152 0.485653i \(-0.838582\pi\)
0.485653 + 0.874152i \(0.338582\pi\)
\(678\) −31219.3 31219.3i −1.76839 1.76839i
\(679\) 17543.2i 0.991527i
\(680\) −37098.6 + 1322.13i −2.09216 + 0.0745607i
\(681\) 32148.8i 1.80902i
\(682\) −18273.7 + 18273.7i −1.02601 + 1.02601i
\(683\) −5285.58 + 5285.58i −0.296116 + 0.296116i −0.839490 0.543375i \(-0.817146\pi\)
0.543375 + 0.839490i \(0.317146\pi\)
\(684\) −28017.3 −1.56618
\(685\) 13944.5 + 12984.8i 0.777800 + 0.724269i
\(686\) 19179.3i 1.06745i
\(687\) −11337.1 + 11337.1i −0.629605 + 0.629605i
\(688\) −20346.0 20346.0i −1.12745 1.12745i
\(689\) 20078.8 1.11022
\(690\) −41336.2 + 13772.8i −2.28064 + 0.759886i
\(691\) −11849.4 −0.652347 −0.326174 0.945310i \(-0.605759\pi\)
−0.326174 + 0.945310i \(0.605759\pi\)
\(692\) −11661.3 11661.3i −0.640599 0.640599i
\(693\) 7134.61 7134.61i 0.391084 0.391084i
\(694\) 44808.1i 2.45086i
\(695\) −9354.43 + 333.375i −0.510552 + 0.0181951i
\(696\) −34902.5 −1.90083
\(697\) 15328.4 15328.4i 0.833007 0.833007i
\(698\) 663.199 663.199i 0.0359634 0.0359634i
\(699\) 35987.6i 1.94732i
\(700\) −51144.7 44330.9i −2.76155 2.39364i
\(701\) 22547.4i 1.21484i 0.794380 + 0.607421i \(0.207796\pi\)
−0.794380 + 0.607421i \(0.792204\pi\)
\(702\) −7242.36 7242.36i −0.389381 0.389381i
\(703\) 21088.6 21088.6i 1.13139 1.13139i
\(704\) 6660.44 0.356569
\(705\) −1006.10 28231.1i −0.0537476 1.50815i
\(706\) −32777.1 −1.74729
\(707\) −7629.23 + 7629.23i −0.405837 + 0.405837i
\(708\) 17621.3 17621.3i 0.935379 0.935379i
\(709\) 3412.31 0.180750 0.0903752 0.995908i \(-0.471193\pi\)
0.0903752 + 0.995908i \(0.471193\pi\)
\(710\) 28885.7 31020.6i 1.52684 1.63969i
\(711\) 310.317i 0.0163682i
\(712\) −38945.6 + 38945.6i −2.04993 + 2.04993i
\(713\) 8456.52 + 28757.8i 0.444179 + 1.51050i
\(714\) 58843.9i 3.08428i
\(715\) −5249.53 + 5637.52i −0.274575 + 0.294869i
\(716\) 36598.1 1.91024
\(717\) 30235.0 + 30235.0i 1.57482 + 1.57482i
\(718\) 26448.8 + 26448.8i 1.37473 + 1.37473i
\(719\) 35687.9i 1.85109i −0.378636 0.925546i \(-0.623607\pi\)
0.378636 0.925546i \(-0.376393\pi\)
\(720\) 31017.0 1105.39i 1.60547 0.0572159i
\(721\) 9318.57 0.481334
\(722\) 3652.61 + 3652.61i 0.188277 + 0.188277i
\(723\) 3522.38 + 3522.38i 0.181188 + 0.181188i
\(724\) 67949.5 3.48801
\(725\) −801.871 11235.9i −0.0410769 0.575573i
\(726\) 35174.2 1.79812
\(727\) 23811.5 23811.5i 1.21475 1.21475i 0.245300 0.969447i \(-0.421113\pi\)
0.969447 0.245300i \(-0.0788865\pi\)
\(728\) 43239.4 + 43239.4i 2.20132 + 2.20132i
\(729\) 7302.09i 0.370985i
\(730\) −780.465 21899.7i −0.0395703 1.11033i
\(731\) 11665.0 0.590210
\(732\) −26994.7 + 26994.7i −1.36305 + 1.36305i
\(733\) −9594.16 9594.16i −0.483449 0.483449i 0.422782 0.906231i \(-0.361054\pi\)
−0.906231 + 0.422782i \(0.861054\pi\)
\(734\) 5219.49 0.262472
\(735\) 24487.0 26296.8i 1.22886 1.31969i
\(736\) 15409.3 28246.8i 0.771732 1.41466i
\(737\) −4401.35 4401.35i −0.219981 0.219981i
\(738\) −26328.0 + 26328.0i −1.31321 + 1.31321i
\(739\) 34108.4i 1.69783i 0.528526 + 0.848917i \(0.322745\pi\)
−0.528526 + 0.848917i \(0.677255\pi\)
\(740\) −56267.7 + 60426.5i −2.79519 + 3.00179i
\(741\) 19601.8i 0.971780i
\(742\) 55956.2 + 55956.2i 2.76848 + 2.76848i
\(743\) −9077.44 9077.44i −0.448209 0.448209i 0.446550 0.894759i \(-0.352653\pi\)
−0.894759 + 0.446550i \(0.852653\pi\)
\(744\) 105252.i 5.18645i
\(745\) −1258.57 35315.1i −0.0618930 1.73671i
\(746\) 16308.3i 0.800388i
\(747\) −4660.11 + 4660.11i −0.228252 + 0.228252i
\(748\) −14323.7 + 14323.7i −0.700168 + 0.700168i
\(749\) 23594.3i 1.15102i
\(750\) 5266.65 + 49093.5i 0.256414 + 2.39019i
\(751\) 14588.8i 0.708860i −0.935082 0.354430i \(-0.884675\pi\)
0.935082 0.354430i \(-0.115325\pi\)
\(752\) 37780.5 + 37780.5i 1.83206 + 1.83206i
\(753\) −9043.67 9043.67i −0.437675 0.437675i
\(754\) 17603.9i 0.850261i
\(755\) 361.596 + 10146.3i 0.0174302 + 0.489089i
\(756\) 28389.4i 1.36576i
\(757\) −18303.0 + 18303.0i −0.878774 + 0.878774i −0.993408 0.114634i \(-0.963431\pi\)
0.114634 + 0.993408i \(0.463431\pi\)
\(758\) 19763.4 + 19763.4i 0.947019 + 0.947019i
\(759\) −6582.42 + 12066.2i −0.314792 + 0.577045i
\(760\) 35667.3 + 33212.5i 1.70235 + 1.58519i
\(761\) −1763.55 −0.0840061 −0.0420031 0.999117i \(-0.513374\pi\)
−0.0420031 + 0.999117i \(0.513374\pi\)
\(762\) −14097.0 14097.0i −0.670184 0.670184i
\(763\) 37084.8 37084.8i 1.75958 1.75958i
\(764\) 1531.06 0.0725024
\(765\) −8574.60 + 9208.35i −0.405249 + 0.435201i
\(766\) 35553.9i 1.67704i
\(767\) −5138.14 5138.14i −0.241887 0.241887i
\(768\) 25120.9 25120.9i 1.18030 1.18030i
\(769\) −3221.87 −0.151084 −0.0755420 0.997143i \(-0.524069\pi\)
−0.0755420 + 0.997143i \(0.524069\pi\)
\(770\) −30340.4 + 1081.27i −1.41999 + 0.0506057i
\(771\) −10948.1 −0.511396
\(772\) 4833.40 + 4833.40i 0.225334 + 0.225334i