Properties

Label 115.4.e.a.22.4
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 22.4
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.4

$q$-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} +(105.824 + 31.1185i) 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} +(-590.087 + 2006.69i) 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 \(0.530191\pi\)
−0.995505 + 0.0947070i \(0.969809\pi\)
\(8\) 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 \(-0.919242\pi\)
0.967988 0.250997i \(-0.0807584\pi\)
\(12\) −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 −0.937207 0.348774i \(-0.886598\pi\)
0.348774 + 0.937207i \(0.386598\pi\)
\(18\) −70.8419 + 70.8419i −0.927644 + 0.927644i
\(19\) 76.5780 0.924642 0.462321 0.886713i \(-0.347017\pi\)
0.462321 + 0.886713i \(0.347017\pi\)
\(20\) −211.874 + 7.55078i −2.36882 + 0.0844203i
\(21\) 194.283i 2.01886i
\(22\) −67.2439 + 67.2439i −0.651657 + 0.651657i
\(23\) 105.824 + 31.1185i 0.959381 + 0.282115i
\(24\) 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 \(-0.417181\pi\)
0.966343 0.257259i \(-0.0828192\pi\)
\(38\) −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 0.410397 0.911907i \(-0.365390\pi\)
−0.911907 + 0.410397i \(0.865390\pi\)
\(44\) 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 0.999765 0.0216720i \(-0.00689894\pi\)
−0.0216720 + 0.999765i \(0.506899\pi\)
\(54\) 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 \(0.100508\pi\)
−0.950562 + 0.310534i \(0.899492\pi\)
\(62\) 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 −0.453197 0.891411i \(-0.649716\pi\)
0.891411 + 0.453197i \(0.149716\pi\)
\(68\) −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 \(-0.496354\pi\)
0.0114528 + 0.999934i \(0.496354\pi\)
\(80\) −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 0.848542 0.529128i \(-0.177481\pi\)
−0.529128 + 0.848542i \(0.677481\pi\)
\(84\) 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 \(-0.304539\pi\)
0.576189 + 0.817316i \(0.304539\pi\)
\(90\) −819.743 763.325i −0.960094 0.894017i
\(91\) 1074.24i 1.23748i
\(92\) −590.087 + 2006.69i −0.668704 + 2.27404i
\(93\) 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 −0.896924 0.442184i \(-0.854204\pi\)
0.442184 + 0.896924i \(0.354204\pi\)
\(98\) −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 0.588063 0.808815i \(-0.299891\pi\)
−0.808815 + 0.588063i \(0.799891\pi\)
\(104\) 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 −0.392053 0.919943i \(-0.628235\pi\)
0.919943 + 0.392053i \(0.128235\pi\)
\(108\) 703.022 703.022i 0.626373 0.626373i
\(109\) −1836.70 −1.61398 −0.806991 0.590564i \(-0.798905\pi\)
−0.806991 + 0.590564i \(0.798905\pi\)
\(110\) −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 0.971730 0.236095i \(-0.0758677\pi\)
−0.236095 + 0.971730i \(0.575868\pi\)
\(114\) 2705.50 2.22275
\(115\) −305.556 + 1194.78i −0.247767 + 0.968820i
\(116\) −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 −0.223250 0.974761i \(-0.571667\pi\)
0.974761 + 0.223250i \(0.0716666\pi\)
\(138\) 3738.75 + 1099.42i 2.30626 + 0.678177i
\(139\) 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 \(-0.835175\pi\)
−0.868904 + 0.494980i \(0.835175\pi\)
\(150\) −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 −0.970088 0.242755i \(-0.921949\pi\)
0.242755 + 0.970088i \(0.421949\pi\)
\(158\) −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 \(0.263179\pi\)
−0.677234 + 0.735768i \(0.736821\pi\)
\(182\) −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 \(0.00486835\pi\)
−0.999883 + 0.0152938i \(0.995132\pi\)
\(192\) 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 \(-0.586549\pi\)
−0.268563 + 0.963262i \(0.586549\pi\)
\(200\) −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
\(207\) 600.403 2041.77i 0.201599 0.685570i
\(208\) 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 −0.999739 0.0228436i \(-0.992728\pi\)
0.0228436 + 0.999739i \(0.492728\pi\)
\(228\) −6986.34 6986.34i −2.02930 2.02930i
\(229\) −2356.44 −0.679990 −0.339995 0.940427i \(-0.610425\pi\)
−0.339995 + 0.940427i \(0.610425\pi\)
\(230\) 5508.78 3264.97i 1.57930 0.936025i
\(231\) −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 \(0.0311945\pi\)
−0.995202 + 0.0978438i \(0.968805\pi\)
\(242\) −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 \(-0.924049\pi\)
0.971668 0.236350i \(-0.0759513\pi\)
\(252\) −7387.20 + 7387.20i −1.84663 + 1.84663i
\(253\) 569.909 1938.07i 0.141620 0.481603i
\(254\) 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 0.799433 0.600755i \(-0.205133\pi\)
−0.600755 + 0.799433i \(0.705133\pi\)
\(264\) 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 \(-0.775444\pi\)
0.761312 0.648386i \(-0.224556\pi\)
\(282\) −9277.14 9277.14i −1.95903 1.95903i
\(283\) 914.034 + 914.034i 0.191992 + 0.191992i 0.796556 0.604564i \(-0.206653\pi\)
−0.604564 + 0.796556i \(0.706653\pi\)
\(284\) 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 0.729952 0.683499i \(-0.239543\pi\)
−0.683499 + 0.729952i \(0.739543\pi\)
\(294\) 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 \(-0.875862\pi\)
−0.380180 0.924913i \(-0.624138\pi\)
\(314\) 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
\(322\) 15690.5 + 4613.94i 2.71552 + 0.798525i
\(323\) −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 −0.926803 0.375548i \(-0.877455\pi\)
0.375548 + 0.926803i \(0.377455\pi\)
\(338\) 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
\(345\) −4278.20 7218.35i −0.667625 1.12644i
\(346\) 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 \(-0.322379\pi\)
0.529502 + 0.848308i \(0.322379\pi\)
\(360\) 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 −0.654750 0.755846i \(-0.727226\pi\)
0.755846 + 0.654750i \(0.227226\pi\)
\(368\) −15225.8 4477.29i −2.15679 0.634225i
\(369\) 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 0.535960 0.844243i \(-0.319950\pi\)
−0.844243 + 0.535960i \(0.819950\pi\)
\(374\) 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 \(-0.381151\pi\)
0.364760 + 0.931101i \(0.381151\pi\)
\(380\) −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 0.952010 0.306068i \(-0.0990134\pi\)
−0.306068 + 0.952010i \(0.599013\pi\)
\(384\) 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 \(-0.407891\pi\)
0.285348 + 0.958424i \(0.407891\pi\)
\(390\) −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 \(-0.903857\pi\)
0.954731 0.297470i \(-0.0961430\pi\)
\(402\) 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 \(-0.621566\pi\)
−0.372693 + 0.927955i \(0.621566\pi\)
\(420\) 1466.99 + 41163.5i 0.170433 + 4.78232i
\(421\) 4253.43i 0.492398i 0.969219 + 0.246199i \(0.0791817\pi\)
−0.969219 + 0.246199i \(0.920818\pi\)
\(422\) 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 \(0.0741299\pi\)
−0.973004 + 0.230786i \(0.925870\pi\)
\(432\) 5334.18 + 5334.18i 0.594076 + 0.594076i
\(433\) −7004.73 7004.73i −0.777427 0.777427i 0.201966 0.979393i \(-0.435267\pi\)
−0.979393 + 0.201966i \(0.935267\pi\)
\(434\) −40292.8 −4.45649
\(435\) 4671.62 5016.90i 0.514913 0.552970i
\(436\) 34828.6i 3.82566i
\(437\) 8103.77 + 2382.99i 0.887084 + 0.260856i
\(438\) −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 −0.532043 0.846718i \(-0.678575\pi\)
0.846718 + 0.532043i \(0.178575\pi\)
\(458\) 8652.10 + 8652.10i 0.882720 + 0.882720i
\(459\) 3058.24 0.310994
\(460\) −22656.2 5794.13i −2.29641 0.587289i
\(461\) 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 −0.908282 0.418358i \(-0.862606\pi\)
0.418358 + 0.908282i \(0.362606\pi\)
\(468\) −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 \(-0.458249\pi\)
0.130788 + 0.991410i \(0.458249\pi\)
\(480\) −790.324 22176.3i −0.0751525 2.10876i
\(481\) 14651.6i 1.38889i
\(482\) 2688.16 2688.16i 0.254029 0.254029i
\(483\) 6045.81 20559.8i 0.569552 1.93686i
\(484\) 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 0.897608 0.440795i \(-0.145303\pi\)
−0.440795 + 0.897608i \(0.645303\pi\)
\(504\) 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 \(0.424593\pi\)
−0.234688 + 0.972071i \(0.575407\pi\)
\(522\) −6383.96 6383.96i −0.535285 0.535285i
\(523\) 2126.53 + 2126.53i 0.177795 + 0.177795i 0.790394 0.612599i \(-0.209876\pi\)
−0.612599 + 0.790394i \(0.709876\pi\)
\(524\) 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
\(552\) −12052.4 + 40986.3i −0.929322 + 3.16031i
\(553\) −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 −0.913318 0.407246i \(-0.866489\pi\)
0.407246 + 0.913318i \(0.366489\pi\)
\(558\) 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 0.141784 0.989898i \(-0.454716\pi\)
−0.989898 + 0.141784i \(0.954716\pi\)
\(564\) 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 \(-0.791439\pi\)
−0.792918 + 0.609328i \(0.791439\pi\)
\(570\) 1077.31 + 30229.2i 0.0791644 + 2.22134i
\(571\) 7519.61i 0.551114i −0.961285 0.275557i \(-0.911138\pi\)
0.961285 0.275557i \(-0.0888623\pi\)
\(572\) −9238.43 + 9238.43i −0.675311 + 0.675311i
\(573\) −388.457 388.457i −0.0283211 0.0283211i
\(574\) 55103.8 4.00695
\(575\) −13471.3 2938.30i −0.977029 0.213105i
\(576\) −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
\(598\) 20672.4 + 6078.93i 1.41364 + 0.415696i
\(599\) 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 0.366202 0.930535i \(-0.380658\pi\)
−0.930535 + 0.366202i \(0.880658\pi\)
\(614\) 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 −0.435724 0.900080i \(-0.643508\pi\)
0.900080 + 0.435724i \(0.143508\pi\)
\(618\) −8152.76 8152.76i −0.530667 0.530667i
\(619\) 15344.2 0.996341 0.498171 0.867079i \(-0.334005\pi\)
0.498171 + 0.867079i \(0.334005\pi\)
\(620\) 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 \(0.250824\pi\)
−0.705275 + 0.708934i \(0.749176\pi\)
\(632\) 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 \(0.0312739\pi\)
−0.995177 + 0.0980917i \(0.968726\pi\)
\(642\) 20642.5 20642.5i 1.26899 1.26899i
\(643\) 22311.5 + 22311.5i 1.36840 + 1.36840i 0.862730 + 0.505666i \(0.168753\pi\)
0.505666 + 0.862730i \(0.331247\pi\)
\(644\) −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 \(-0.672995\pi\)
−0.517118 + 0.855914i \(0.672995\pi\)
\(660\) −19333.9 18003.3i −1.14026 1.06178i
\(661\) 7380.69i 0.434305i 0.976138 + 0.217152i \(0.0696769\pi\)
−0.976138 + 0.217152i \(0.930323\pi\)
\(662\) −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
\(667\) −2804.26 + 9536.37i −0.162791 + 0.553598i
\(668\) −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 −0.485653 0.874152i \(-0.661418\pi\)
0.874152 + 0.485653i \(0.161418\pi\)
\(678\) 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
\(690\) −10795.3 + 42211.7i −0.595609 + 2.32895i
\(691\) −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 \(-0.792204\pi\)
0.794380 0.607421i \(-0.207796\pi\)
\(702\) −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 \(-0.528807\pi\)
−0.0903752 + 0.995908i \(0.528807\pi\)
\(710\) −28885.7 + 31020.6i −1.52684 + 1.63969i
\(711\) 310.317i 0.0163682i
\(712\) 38945.6 38945.6i 2.04993 2.04993i
\(713\) −28757.8 8456.52i −1.51050 0.444179i
\(714\) 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 \(0.578887\pi\)
−0.969447 + 0.245300i \(0.921113\pi\)
\(728\) −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 0.906231 0.422782i \(-0.138946\pi\)
−0.422782 + 0.906231i \(0.638946\pi\)
\(734\) −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 0.894759 0.446550i \(-0.147347\pi\)
−0.446550 + 0.894759i \(0.647347\pi\)
\(744\) 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 \(0.115325\pi\)
−0.935082 + 0.354430i \(0.884675\pi\)
\(752\) 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 −0.114634 0.993408i \(-0.536569\pi\)
0.993408 + 0.114634i \(0.0365694\pi\)
\(758\) −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 \(-0.475931\pi\)
0.0755420 + 0.997143i \(0.475931\pi\)
\(770\) 30340.4 1081.27i 1.41999 0.0506057i
\(771\) −10948.1 −0.511396
\(772\) 4833.40 + 4833.40i 0.225334 + 0.225334i