Properties

Label 115.4.e.a.22.6
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 22.6
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.78118 - 2.78118i) q^{2} +(1.69288 - 1.69288i) q^{3} +7.46996i q^{4} +(9.46680 + 5.94809i) q^{5} -9.41642 q^{6} +(-1.06728 + 1.06728i) q^{7} +(-1.47414 + 1.47414i) q^{8} +21.2683i q^{9} +O(q^{10})\) \(q+(-2.78118 - 2.78118i) q^{2} +(1.69288 - 1.69288i) q^{3} +7.46996i q^{4} +(9.46680 + 5.94809i) q^{5} -9.41642 q^{6} +(-1.06728 + 1.06728i) q^{7} +(-1.47414 + 1.47414i) q^{8} +21.2683i q^{9} +(-9.78619 - 42.8716i) q^{10} +55.8655i q^{11} +(12.6457 + 12.6457i) q^{12} +(-55.7428 + 55.7428i) q^{13} +5.93659 q^{14} +(26.0956 - 5.95676i) q^{15} +67.9594 q^{16} +(44.0172 - 44.0172i) q^{17} +(59.1511 - 59.1511i) q^{18} -15.1850 q^{19} +(-44.4320 + 70.7166i) q^{20} +3.61355i q^{21} +(155.372 - 155.372i) q^{22} +(-32.0899 - 105.533i) q^{23} +4.99109i q^{24} +(54.2406 + 112.619i) q^{25} +310.062 q^{26} +(81.7125 + 81.7125i) q^{27} +(-7.97253 - 7.97253i) q^{28} +43.6739i q^{29} +(-89.1434 - 56.0097i) q^{30} +31.1324 q^{31} +(-177.214 - 177.214i) q^{32} +(94.5737 + 94.5737i) q^{33} -244.840 q^{34} +(-16.4520 + 3.75545i) q^{35} -158.873 q^{36} +(203.098 - 203.098i) q^{37} +(42.2323 + 42.2323i) q^{38} +188.732i q^{39} +(-22.7237 + 5.18708i) q^{40} -419.020 q^{41} +(10.0499 - 10.0499i) q^{42} +(390.269 + 390.269i) q^{43} -417.313 q^{44} +(-126.506 + 201.343i) q^{45} +(-204.259 + 382.755i) q^{46} +(-329.500 - 329.500i) q^{47} +(115.047 - 115.047i) q^{48} +340.722i q^{49} +(162.360 - 464.066i) q^{50} -149.032i q^{51} +(-416.397 - 416.397i) q^{52} +(-144.476 - 144.476i) q^{53} -454.515i q^{54} +(-332.293 + 528.868i) q^{55} -3.14664i q^{56} +(-25.7064 + 25.7064i) q^{57} +(121.465 - 121.465i) q^{58} -274.910i q^{59} +(44.4968 + 194.933i) q^{60} +300.181i q^{61} +(-86.5849 - 86.5849i) q^{62} +(-22.6992 - 22.6992i) q^{63} +442.056i q^{64} +(-859.269 + 196.143i) q^{65} -526.053i q^{66} +(632.542 - 632.542i) q^{67} +(328.807 + 328.807i) q^{68} +(-232.979 - 124.331i) q^{69} +(56.2005 + 35.3114i) q^{70} +401.846 q^{71} +(-31.3525 - 31.3525i) q^{72} +(-308.059 + 308.059i) q^{73} -1129.70 q^{74} +(282.473 + 98.8272i) q^{75} -113.432i q^{76} +(-59.6241 - 59.6241i) q^{77} +(524.898 - 524.898i) q^{78} -8.07381 q^{79} +(643.358 + 404.228i) q^{80} -297.585 q^{81} +(1165.37 + 1165.37i) q^{82} +(806.388 + 806.388i) q^{83} -26.9931 q^{84} +(678.520 - 154.884i) q^{85} -2170.82i q^{86} +(73.9346 + 73.9346i) q^{87} +(-82.3537 - 82.3537i) q^{88} +1253.12 q^{89} +(911.807 - 208.136i) q^{90} -118.986i q^{91} +(788.328 - 239.710i) q^{92} +(52.7034 - 52.7034i) q^{93} +1832.80i q^{94} +(-143.754 - 90.3219i) q^{95} -600.006 q^{96} +(-461.250 + 461.250i) q^{97} +(947.610 - 947.610i) q^{98} -1188.17 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78118 2.78118i −0.983297 0.983297i 0.0165661 0.999863i \(-0.494727\pi\)
−0.999863 + 0.0165661i \(0.994727\pi\)
\(3\) 1.69288 1.69288i 0.325795 0.325795i −0.525190 0.850985i \(-0.676006\pi\)
0.850985 + 0.525190i \(0.176006\pi\)
\(4\) 7.46996i 0.933745i
\(5\) 9.46680 + 5.94809i 0.846736 + 0.532013i
\(6\) −9.41642 −0.640706
\(7\) −1.06728 + 1.06728i −0.0576276 + 0.0576276i −0.735333 0.677706i \(-0.762974\pi\)
0.677706 + 0.735333i \(0.262974\pi\)
\(8\) −1.47414 + 1.47414i −0.0651485 + 0.0651485i
\(9\) 21.2683i 0.787715i
\(10\) −9.78619 42.8716i −0.309466 1.35572i
\(11\) 55.8655i 1.53128i 0.643269 + 0.765641i \(0.277578\pi\)
−0.643269 + 0.765641i \(0.722422\pi\)
\(12\) 12.6457 + 12.6457i 0.304209 + 0.304209i
\(13\) −55.7428 + 55.7428i −1.18925 + 1.18925i −0.211978 + 0.977275i \(0.567990\pi\)
−0.977275 + 0.211978i \(0.932010\pi\)
\(14\) 5.93659 0.113330
\(15\) 26.0956 5.95676i 0.449190 0.102535i
\(16\) 67.9594 1.06187
\(17\) 44.0172 44.0172i 0.627985 0.627985i −0.319576 0.947561i \(-0.603540\pi\)
0.947561 + 0.319576i \(0.103540\pi\)
\(18\) 59.1511 59.1511i 0.774558 0.774558i
\(19\) −15.1850 −0.183352 −0.0916759 0.995789i \(-0.529222\pi\)
−0.0916759 + 0.995789i \(0.529222\pi\)
\(20\) −44.4320 + 70.7166i −0.496764 + 0.790636i
\(21\) 3.61355i 0.0375496i
\(22\) 155.372 155.372i 1.50570 1.50570i
\(23\) −32.0899 105.533i −0.290922 0.956747i
\(24\) 4.99109i 0.0424501i
\(25\) 54.2406 + 112.619i 0.433924 + 0.900949i
\(26\) 310.062 2.33878
\(27\) 81.7125 + 81.7125i 0.582429 + 0.582429i
\(28\) −7.97253 7.97253i −0.0538095 0.0538095i
\(29\) 43.6739i 0.279656i 0.990176 + 0.139828i \(0.0446550\pi\)
−0.990176 + 0.139828i \(0.955345\pi\)
\(30\) −89.1434 56.0097i −0.542509 0.340864i
\(31\) 31.1324 0.180372 0.0901862 0.995925i \(-0.471254\pi\)
0.0901862 + 0.995925i \(0.471254\pi\)
\(32\) −177.214 177.214i −0.978980 0.978980i
\(33\) 94.5737 + 94.5737i 0.498884 + 0.498884i
\(34\) −244.840 −1.23499
\(35\) −16.4520 + 3.75545i −0.0794540 + 0.0181368i
\(36\) −158.873 −0.735525
\(37\) 203.098 203.098i 0.902407 0.902407i −0.0932372 0.995644i \(-0.529721\pi\)
0.995644 + 0.0932372i \(0.0297215\pi\)
\(38\) 42.2323 + 42.2323i 0.180289 + 0.180289i
\(39\) 188.732i 0.774905i
\(40\) −22.7237 + 5.18708i −0.0898234 + 0.0205037i
\(41\) −419.020 −1.59610 −0.798048 0.602594i \(-0.794134\pi\)
−0.798048 + 0.602594i \(0.794134\pi\)
\(42\) 10.0499 10.0499i 0.0369224 0.0369224i
\(43\) 390.269 + 390.269i 1.38408 + 1.38408i 0.837229 + 0.546852i \(0.184174\pi\)
0.546852 + 0.837229i \(0.315826\pi\)
\(44\) −417.313 −1.42983
\(45\) −126.506 + 201.343i −0.419075 + 0.666987i
\(46\) −204.259 + 382.755i −0.654703 + 1.22683i
\(47\) −329.500 329.500i −1.02261 1.02261i −0.999738 0.0228692i \(-0.992720\pi\)
−0.0228692 0.999738i \(-0.507280\pi\)
\(48\) 115.047 115.047i 0.345950 0.345950i
\(49\) 340.722i 0.993358i
\(50\) 162.360 464.066i 0.459224 1.31258i
\(51\) 149.032i 0.409189i
\(52\) −416.397 416.397i −1.11046 1.11046i
\(53\) −144.476 144.476i −0.374440 0.374440i 0.494652 0.869091i \(-0.335296\pi\)
−0.869091 + 0.494652i \(0.835296\pi\)
\(54\) 454.515i 1.14540i
\(55\) −332.293 + 528.868i −0.814661 + 1.29659i
\(56\) 3.14664i 0.00750870i
\(57\) −25.7064 + 25.7064i −0.0597351 + 0.0597351i
\(58\) 121.465 121.465i 0.274985 0.274985i
\(59\) 274.910i 0.606614i −0.952893 0.303307i \(-0.901909\pi\)
0.952893 0.303307i \(-0.0980907\pi\)
\(60\) 44.4968 + 194.933i 0.0957418 + 0.419428i
\(61\) 300.181i 0.630069i 0.949080 + 0.315034i \(0.102016\pi\)
−0.949080 + 0.315034i \(0.897984\pi\)
\(62\) −86.5849 86.5849i −0.177360 0.177360i
\(63\) −22.6992 22.6992i −0.0453941 0.0453941i
\(64\) 442.056i 0.863391i
\(65\) −859.269 + 196.143i −1.63968 + 0.374285i
\(66\) 526.053i 0.981102i
\(67\) 632.542 632.542i 1.15339 1.15339i 0.167524 0.985868i \(-0.446423\pi\)
0.985868 0.167524i \(-0.0535771\pi\)
\(68\) 328.807 + 328.807i 0.586378 + 0.586378i
\(69\) −232.979 124.331i −0.406484 0.216922i
\(70\) 56.2005 + 35.3114i 0.0959607 + 0.0602931i
\(71\) 401.846 0.671695 0.335848 0.941916i \(-0.390977\pi\)
0.335848 + 0.941916i \(0.390977\pi\)
\(72\) −31.3525 31.3525i −0.0513185 0.0513185i
\(73\) −308.059 + 308.059i −0.493912 + 0.493912i −0.909536 0.415625i \(-0.863563\pi\)
0.415625 + 0.909536i \(0.363563\pi\)
\(74\) −1129.70 −1.77467
\(75\) 282.473 + 98.8272i 0.434895 + 0.152154i
\(76\) 113.432i 0.171204i
\(77\) −59.6241 59.6241i −0.0882441 0.0882441i
\(78\) 524.898 524.898i 0.761961 0.761961i
\(79\) −8.07381 −0.0114984 −0.00574921 0.999983i \(-0.501830\pi\)
−0.00574921 + 0.999983i \(0.501830\pi\)
\(80\) 643.358 + 404.228i 0.899120 + 0.564926i
\(81\) −297.585 −0.408210
\(82\) 1165.37 + 1165.37i 1.56944 + 1.56944i
\(83\) 806.388 + 806.388i 1.06642 + 1.06642i 0.997632 + 0.0687846i \(0.0219121\pi\)
0.0687846 + 0.997632i \(0.478088\pi\)
\(84\) −26.9931 −0.0350617
\(85\) 678.520 154.884i 0.865834 0.197641i
\(86\) 2170.82i 2.72193i
\(87\) 73.9346 + 73.9346i 0.0911106 + 0.0911106i
\(88\) −82.3537 82.3537i −0.0997607 0.0997607i
\(89\) 1253.12 1.49248 0.746238 0.665679i \(-0.231858\pi\)
0.746238 + 0.665679i \(0.231858\pi\)
\(90\) 911.807 208.136i 1.06792 0.243771i
\(91\) 118.986i 0.137068i
\(92\) 788.328 239.710i 0.893357 0.271647i
\(93\) 52.7034 52.7034i 0.0587644 0.0587644i
\(94\) 1832.80i 2.01105i
\(95\) −143.754 90.3219i −0.155251 0.0975455i
\(96\) −600.006 −0.637894
\(97\) −461.250 + 461.250i −0.482813 + 0.482813i −0.906029 0.423216i \(-0.860901\pi\)
0.423216 + 0.906029i \(0.360901\pi\)
\(98\) 947.610 947.610i 0.976766 0.976766i
\(99\) −1188.17 −1.20621
\(100\) −841.257 + 405.175i −0.841257 + 0.405175i
\(101\) 1174.66 1.15725 0.578627 0.815593i \(-0.303589\pi\)
0.578627 + 0.815593i \(0.303589\pi\)
\(102\) −414.485 + 414.485i −0.402354 + 0.402354i
\(103\) −43.2418 43.2418i −0.0413664 0.0413664i 0.686121 0.727487i \(-0.259312\pi\)
−0.727487 + 0.686121i \(0.759312\pi\)
\(104\) 164.346i 0.154956i
\(105\) −21.4937 + 34.2087i −0.0199769 + 0.0317946i
\(106\) 803.628i 0.736370i
\(107\) −583.833 + 583.833i −0.527489 + 0.527489i −0.919823 0.392334i \(-0.871668\pi\)
0.392334 + 0.919823i \(0.371668\pi\)
\(108\) −610.389 + 610.389i −0.543840 + 0.543840i
\(109\) 149.681 0.131531 0.0657653 0.997835i \(-0.479051\pi\)
0.0657653 + 0.997835i \(0.479051\pi\)
\(110\) 2395.05 546.710i 2.07599 0.473880i
\(111\) 687.640i 0.587999i
\(112\) −72.5316 + 72.5316i −0.0611928 + 0.0611928i
\(113\) −1391.83 1391.83i −1.15869 1.15869i −0.984757 0.173933i \(-0.944352\pi\)
−0.173933 0.984757i \(-0.555648\pi\)
\(114\) 142.989 0.117475
\(115\) 323.931 1189.93i 0.262667 0.964886i
\(116\) −326.242 −0.261128
\(117\) −1185.56 1185.56i −0.936792 0.936792i
\(118\) −764.574 + 764.574i −0.596481 + 0.596481i
\(119\) 93.9573i 0.0723785i
\(120\) −29.6874 + 47.2497i −0.0225840 + 0.0359440i
\(121\) −1789.96 −1.34482
\(122\) 834.858 834.858i 0.619545 0.619545i
\(123\) −709.351 + 709.351i −0.520000 + 0.520000i
\(124\) 232.558i 0.168422i
\(125\) −156.381 + 1388.77i −0.111897 + 0.993720i
\(126\) 126.261i 0.0892718i
\(127\) 586.535 + 586.535i 0.409816 + 0.409816i 0.881674 0.471859i \(-0.156417\pi\)
−0.471859 + 0.881674i \(0.656417\pi\)
\(128\) −188.276 + 188.276i −0.130011 + 0.130011i
\(129\) 1321.36 0.901854
\(130\) 2935.29 + 1844.28i 1.98033 + 1.24426i
\(131\) −461.539 −0.307823 −0.153912 0.988085i \(-0.549187\pi\)
−0.153912 + 0.988085i \(0.549187\pi\)
\(132\) −706.462 + 706.462i −0.465830 + 0.465830i
\(133\) 16.2067 16.2067i 0.0105661 0.0105661i
\(134\) −3518.43 −2.26825
\(135\) 287.523 + 1259.59i 0.183304 + 0.803023i
\(136\) 129.775i 0.0818245i
\(137\) 1134.30 1134.30i 0.707369 0.707369i −0.258612 0.965981i \(-0.583265\pi\)
0.965981 + 0.258612i \(0.0832651\pi\)
\(138\) 302.172 + 993.744i 0.186396 + 0.612994i
\(139\) 827.765i 0.505109i −0.967583 0.252554i \(-0.918729\pi\)
0.967583 0.252554i \(-0.0812707\pi\)
\(140\) −28.0530 122.896i −0.0169351 0.0741898i
\(141\) −1115.61 −0.666321
\(142\) −1117.61 1117.61i −0.660476 0.660476i
\(143\) −3114.10 3114.10i −1.82108 1.82108i
\(144\) 1445.38i 0.836448i
\(145\) −259.776 + 413.452i −0.148781 + 0.236795i
\(146\) 1713.54 0.971324
\(147\) 576.801 + 576.801i 0.323631 + 0.323631i
\(148\) 1517.13 + 1517.13i 0.842618 + 0.842618i
\(149\) 1269.84 0.698185 0.349092 0.937088i \(-0.386490\pi\)
0.349092 + 0.937088i \(0.386490\pi\)
\(150\) −510.752 1060.46i −0.278018 0.577244i
\(151\) 1708.16 0.920581 0.460291 0.887768i \(-0.347745\pi\)
0.460291 + 0.887768i \(0.347745\pi\)
\(152\) 22.3849 22.3849i 0.0119451 0.0119451i
\(153\) 936.172 + 936.172i 0.494673 + 0.494673i
\(154\) 331.651i 0.173540i
\(155\) 294.724 + 185.178i 0.152728 + 0.0959604i
\(156\) −1409.82 −0.723563
\(157\) −938.008 + 938.008i −0.476823 + 0.476823i −0.904114 0.427291i \(-0.859468\pi\)
0.427291 + 0.904114i \(0.359468\pi\)
\(158\) 22.4547 + 22.4547i 0.0113063 + 0.0113063i
\(159\) −489.161 −0.243981
\(160\) −623.566 2731.74i −0.308108 1.34977i
\(161\) 146.882 + 78.3843i 0.0719002 + 0.0383699i
\(162\) 827.640 + 827.640i 0.401392 + 0.401392i
\(163\) 1076.56 1076.56i 0.517315 0.517315i −0.399443 0.916758i \(-0.630796\pi\)
0.916758 + 0.399443i \(0.130796\pi\)
\(164\) 3130.06i 1.49035i
\(165\) 332.778 + 1457.84i 0.157010 + 0.687836i
\(166\) 4485.42i 2.09721i
\(167\) 173.874 + 173.874i 0.0805677 + 0.0805677i 0.746242 0.665675i \(-0.231856\pi\)
−0.665675 + 0.746242i \(0.731856\pi\)
\(168\) −5.32689 5.32689i −0.00244630 0.00244630i
\(169\) 4017.52i 1.82864i
\(170\) −2317.85 1456.33i −1.04571 0.657031i
\(171\) 322.960i 0.144429i
\(172\) −2915.30 + 2915.30i −1.29238 + 1.29238i
\(173\) 59.3069 59.3069i 0.0260637 0.0260637i −0.693955 0.720019i \(-0.744133\pi\)
0.720019 + 0.693955i \(0.244133\pi\)
\(174\) 411.251i 0.179178i
\(175\) −178.085 62.3057i −0.0769256 0.0269135i
\(176\) 3796.59i 1.62601i
\(177\) −465.389 465.389i −0.197632 0.197632i
\(178\) −3485.15 3485.15i −1.46755 1.46755i
\(179\) 2017.71i 0.842518i 0.906940 + 0.421259i \(0.138412\pi\)
−0.906940 + 0.421259i \(0.861588\pi\)
\(180\) −1504.02 944.993i −0.622796 0.391309i
\(181\) 964.154i 0.395939i 0.980208 + 0.197970i \(0.0634348\pi\)
−0.980208 + 0.197970i \(0.936565\pi\)
\(182\) −330.922 + 330.922i −0.134778 + 0.134778i
\(183\) 508.170 + 508.170i 0.205273 + 0.205273i
\(184\) 202.876 + 108.266i 0.0812837 + 0.0433775i
\(185\) 3130.73 714.642i 1.24419 0.284008i
\(186\) −293.156 −0.115566
\(187\) 2459.05 + 2459.05i 0.961622 + 0.961622i
\(188\) 2461.35 2461.35i 0.954855 0.954855i
\(189\) −174.420 −0.0671280
\(190\) 148.604 + 651.007i 0.0567412 + 0.248574i
\(191\) 284.307i 0.107705i −0.998549 0.0538527i \(-0.982850\pi\)
0.998549 0.0538527i \(-0.0171501\pi\)
\(192\) 748.348 + 748.348i 0.281288 + 0.281288i
\(193\) −1594.75 + 1594.75i −0.594782 + 0.594782i −0.938919 0.344138i \(-0.888171\pi\)
0.344138 + 0.938919i \(0.388171\pi\)
\(194\) 2565.64 0.949496
\(195\) −1122.59 + 1786.69i −0.412259 + 0.656140i
\(196\) −2545.18 −0.927543
\(197\) −2755.55 2755.55i −0.996572 0.996572i 0.00342214 0.999994i \(-0.498911\pi\)
−0.999994 + 0.00342214i \(0.998911\pi\)
\(198\) 3304.51 + 3304.51i 1.18607 + 1.18607i
\(199\) 4380.57 1.56046 0.780228 0.625495i \(-0.215103\pi\)
0.780228 + 0.625495i \(0.215103\pi\)
\(200\) −245.974 86.0576i −0.0869650 0.0304260i
\(201\) 2141.63i 0.751539i
\(202\) −3266.93 3266.93i −1.13792 1.13792i
\(203\) −46.6122 46.6122i −0.0161159 0.0161159i
\(204\) 1113.26 0.382078
\(205\) −3966.78 2492.37i −1.35147 0.849144i
\(206\) 240.527i 0.0813509i
\(207\) 2244.51 682.498i 0.753644 0.229164i
\(208\) −3788.25 + 3788.25i −1.26283 + 1.26283i
\(209\) 848.320i 0.280763i
\(210\) 154.919 35.3629i 0.0509067 0.0116203i
\(211\) 1826.57 0.595954 0.297977 0.954573i \(-0.403688\pi\)
0.297977 + 0.954573i \(0.403688\pi\)
\(212\) 1079.23 1079.23i 0.349631 0.349631i
\(213\) 680.278 680.278i 0.218835 0.218835i
\(214\) 3247.49 1.03736
\(215\) 1373.25 + 6015.96i 0.435603 + 1.90830i
\(216\) −240.912 −0.0758887
\(217\) −33.2269 + 33.2269i −0.0103944 + 0.0103944i
\(218\) −416.290 416.290i −0.129334 0.129334i
\(219\) 1043.01i 0.321828i
\(220\) −3950.62 2482.21i −1.21069 0.760686i
\(221\) 4907.29i 1.49366i
\(222\) −1912.45 + 1912.45i −0.578178 + 0.578178i
\(223\) 1398.92 1398.92i 0.420083 0.420083i −0.465149 0.885232i \(-0.653999\pi\)
0.885232 + 0.465149i \(0.153999\pi\)
\(224\) 378.274 0.112833
\(225\) −2395.21 + 1153.60i −0.709691 + 0.341809i
\(226\) 7741.85i 2.27867i
\(227\) 1385.38 1385.38i 0.405069 0.405069i −0.474946 0.880015i \(-0.657532\pi\)
0.880015 + 0.474946i \(0.157532\pi\)
\(228\) −192.026 192.026i −0.0557774 0.0557774i
\(229\) −3112.68 −0.898216 −0.449108 0.893477i \(-0.648258\pi\)
−0.449108 + 0.893477i \(0.648258\pi\)
\(230\) −4210.34 + 2408.51i −1.20705 + 0.690490i
\(231\) −201.873 −0.0574990
\(232\) −64.3815 64.3815i −0.0182192 0.0182192i
\(233\) 623.692 623.692i 0.175362 0.175362i −0.613968 0.789331i \(-0.710428\pi\)
0.789331 + 0.613968i \(0.210428\pi\)
\(234\) 6594.49i 1.84229i
\(235\) −1159.42 5079.21i −0.321838 1.40992i
\(236\) 2053.56 0.566422
\(237\) −13.6680 + 13.6680i −0.00374612 + 0.00374612i
\(238\) 261.312 261.312i 0.0711696 0.0711696i
\(239\) 2723.56i 0.737122i −0.929604 0.368561i \(-0.879851\pi\)
0.929604 0.368561i \(-0.120149\pi\)
\(240\) 1773.44 404.818i 0.476979 0.108879i
\(241\) 2073.21i 0.554139i −0.960850 0.277069i \(-0.910637\pi\)
0.960850 0.277069i \(-0.0893632\pi\)
\(242\) 4978.20 + 4978.20i 1.32236 + 1.32236i
\(243\) −2710.01 + 2710.01i −0.715422 + 0.715422i
\(244\) −2242.34 −0.588324
\(245\) −2026.64 + 3225.55i −0.528479 + 0.841112i
\(246\) 3945.67 1.02263
\(247\) 846.456 846.456i 0.218052 0.218052i
\(248\) −45.8936 + 45.8936i −0.0117510 + 0.0117510i
\(249\) 2730.24 0.694866
\(250\) 4297.34 3427.49i 1.08715 0.867093i
\(251\) 3142.79i 0.790324i −0.918612 0.395162i \(-0.870689\pi\)
0.918612 0.395162i \(-0.129311\pi\)
\(252\) 169.562 169.562i 0.0423866 0.0423866i
\(253\) 5895.66 1792.72i 1.46505 0.445484i
\(254\) 3262.52i 0.805941i
\(255\) 886.454 1410.85i 0.217694 0.346475i
\(256\) 4583.71 1.11907
\(257\) −448.441 448.441i −0.108844 0.108844i 0.650587 0.759432i \(-0.274523\pi\)
−0.759432 + 0.650587i \(0.774523\pi\)
\(258\) −3674.94 3674.94i −0.886790 0.886790i
\(259\) 433.523i 0.104007i
\(260\) −1465.18 6418.71i −0.349487 1.53104i
\(261\) −928.869 −0.220289
\(262\) 1283.63 + 1283.63i 0.302682 + 0.302682i
\(263\) 2924.69 + 2924.69i 0.685718 + 0.685718i 0.961283 0.275564i \(-0.0888647\pi\)
−0.275564 + 0.961283i \(0.588865\pi\)
\(264\) −278.830 −0.0650031
\(265\) −508.369 2227.08i −0.117845 0.516258i
\(266\) −90.1473 −0.0207793
\(267\) 2121.38 2121.38i 0.486241 0.486241i
\(268\) 4725.06 + 4725.06i 1.07697 + 1.07697i
\(269\) 3493.00i 0.791717i −0.918311 0.395859i \(-0.870447\pi\)
0.918311 0.395859i \(-0.129553\pi\)
\(270\) 2703.49 4302.80i 0.609368 0.969852i
\(271\) 5852.09 1.31177 0.655884 0.754862i \(-0.272296\pi\)
0.655884 + 0.754862i \(0.272296\pi\)
\(272\) 2991.38 2991.38i 0.666835 0.666835i
\(273\) −201.429 201.429i −0.0446559 0.0446559i
\(274\) −6309.38 −1.39111
\(275\) −6291.50 + 3030.18i −1.37961 + 0.664460i
\(276\) 928.744 1740.35i 0.202550 0.379553i
\(277\) 2313.86 + 2313.86i 0.501900 + 0.501900i 0.912028 0.410128i \(-0.134516\pi\)
−0.410128 + 0.912028i \(0.634516\pi\)
\(278\) −2302.17 + 2302.17i −0.496672 + 0.496672i
\(279\) 662.133i 0.142082i
\(280\) 18.7165 29.7886i 0.00399473 0.00635789i
\(281\) 4058.84i 0.861673i −0.902430 0.430836i \(-0.858219\pi\)
0.902430 0.430836i \(-0.141781\pi\)
\(282\) 3102.71 + 3102.71i 0.655191 + 0.655191i
\(283\) 1249.60 + 1249.60i 0.262477 + 0.262477i 0.826060 0.563583i \(-0.190577\pi\)
−0.563583 + 0.826060i \(0.690577\pi\)
\(284\) 3001.78i 0.627192i
\(285\) −396.262 + 90.4536i −0.0823597 + 0.0188000i
\(286\) 17321.8i 3.58132i
\(287\) 447.211 447.211i 0.0919792 0.0919792i
\(288\) 3769.05 3769.05i 0.771158 0.771158i
\(289\) 1037.97i 0.211270i
\(290\) 1872.37 427.400i 0.379135 0.0865442i
\(291\) 1561.68i 0.314596i
\(292\) −2301.19 2301.19i −0.461188 0.461188i
\(293\) −3999.83 3999.83i −0.797517 0.797517i 0.185187 0.982703i \(-0.440711\pi\)
−0.982703 + 0.185187i \(0.940711\pi\)
\(294\) 3208.38i 0.636451i
\(295\) 1635.19 2602.52i 0.322726 0.513642i
\(296\) 598.790i 0.117581i
\(297\) −4564.91 + 4564.91i −0.891862 + 0.891862i
\(298\) −3531.66 3531.66i −0.686523 0.686523i
\(299\) 7671.50 + 4093.93i 1.48379 + 0.791833i
\(300\) −738.235 + 2110.06i −0.142073 + 0.406081i
\(301\) −833.052 −0.159523
\(302\) −4750.69 4750.69i −0.905204 0.905204i
\(303\) 1988.55 1988.55i 0.377027 0.377027i
\(304\) −1031.97 −0.194695
\(305\) −1785.50 + 2841.75i −0.335205 + 0.533502i
\(306\) 5207.33i 0.972821i
\(307\) −3915.49 3915.49i −0.727911 0.727911i 0.242292 0.970203i \(-0.422101\pi\)
−0.970203 + 0.242292i \(0.922101\pi\)
\(308\) 445.389 445.389i 0.0823975 0.0823975i
\(309\) −146.406 −0.0269539
\(310\) −304.667 1334.70i −0.0558192 0.244534i
\(311\) −4574.55 −0.834080 −0.417040 0.908888i \(-0.636933\pi\)
−0.417040 + 0.908888i \(0.636933\pi\)
\(312\) −278.218 278.218i −0.0504839 0.0504839i
\(313\) −5080.39 5080.39i −0.917446 0.917446i 0.0793967 0.996843i \(-0.474701\pi\)
−0.996843 + 0.0793967i \(0.974701\pi\)
\(314\) 5217.55 0.937717
\(315\) −79.8720 349.906i −0.0142866 0.0625871i
\(316\) 60.3110i 0.0107366i
\(317\) −2685.75 2685.75i −0.475857 0.475857i 0.427947 0.903804i \(-0.359237\pi\)
−0.903804 + 0.427947i \(0.859237\pi\)
\(318\) 1360.45 + 1360.45i 0.239906 + 0.239906i
\(319\) −2439.86 −0.428232
\(320\) −2629.39 + 4184.86i −0.459335 + 0.731064i
\(321\) 1976.72i 0.343706i
\(322\) −190.505 626.507i −0.0329702 0.108428i
\(323\) −668.403 + 668.403i −0.115142 + 0.115142i
\(324\) 2222.95i 0.381164i
\(325\) −9301.20 3254.16i −1.58750 0.555410i
\(326\) −5988.20 −1.01735
\(327\) 253.392 253.392i 0.0428520 0.0428520i
\(328\) 617.695 617.695i 0.103983 0.103983i
\(329\) 703.337 0.117861
\(330\) 3129.01 4980.04i 0.521959 0.830734i
\(331\) 4017.20 0.667085 0.333543 0.942735i \(-0.391756\pi\)
0.333543 + 0.942735i \(0.391756\pi\)
\(332\) −6023.68 + 6023.68i −0.995761 + 0.995761i
\(333\) 4319.54 + 4319.54i 0.710839 + 0.710839i
\(334\) 967.153i 0.158444i
\(335\) 9750.56 2225.73i 1.59024 0.362999i
\(336\) 245.575i 0.0398726i
\(337\) −7559.60 + 7559.60i −1.22195 + 1.22195i −0.255015 + 0.966937i \(0.582080\pi\)
−0.966937 + 0.255015i \(0.917920\pi\)
\(338\) −11173.5 + 11173.5i −1.79810 + 1.79810i
\(339\) −4712.39 −0.754991
\(340\) 1156.98 + 5068.52i 0.184547 + 0.808468i
\(341\) 1739.23i 0.276201i
\(342\) −898.211 + 898.211i −0.142017 + 0.142017i
\(343\) −729.722 729.722i −0.114872 0.114872i
\(344\) −1150.62 −0.180342
\(345\) −1466.04 2562.79i −0.228779 0.399931i
\(346\) −329.887 −0.0512567
\(347\) 2105.15 + 2105.15i 0.325679 + 0.325679i 0.850941 0.525262i \(-0.176033\pi\)
−0.525262 + 0.850941i \(0.676033\pi\)
\(348\) −552.289 + 552.289i −0.0850741 + 0.0850741i
\(349\) 5497.97i 0.843265i −0.906767 0.421632i \(-0.861457\pi\)
0.906767 0.421632i \(-0.138543\pi\)
\(350\) 322.004 + 668.571i 0.0491767 + 0.102105i
\(351\) −9109.77 −1.38531
\(352\) 9900.18 9900.18i 1.49909 1.49909i
\(353\) −3337.40 + 3337.40i −0.503207 + 0.503207i −0.912433 0.409226i \(-0.865799\pi\)
0.409226 + 0.912433i \(0.365799\pi\)
\(354\) 2588.67i 0.388661i
\(355\) 3804.20 + 2390.22i 0.568749 + 0.357351i
\(356\) 9360.75i 1.39359i
\(357\) 159.058 + 159.058i 0.0235806 + 0.0235806i
\(358\) 5611.62 5611.62i 0.828445 0.828445i
\(359\) 4077.39 0.599433 0.299717 0.954028i \(-0.403108\pi\)
0.299717 + 0.954028i \(0.403108\pi\)
\(360\) −110.320 483.295i −0.0161511 0.0707553i
\(361\) −6628.41 −0.966382
\(362\) 2681.49 2681.49i 0.389326 0.389326i
\(363\) −3030.19 + 3030.19i −0.438136 + 0.438136i
\(364\) 888.822 0.127986
\(365\) −4748.69 + 1083.97i −0.680980 + 0.155446i
\(366\) 2826.63i 0.403689i
\(367\) −3299.02 + 3299.02i −0.469230 + 0.469230i −0.901665 0.432435i \(-0.857655\pi\)
0.432435 + 0.901665i \(0.357655\pi\)
\(368\) −2180.81 7171.97i −0.308920 1.01594i
\(369\) 8911.85i 1.25727i
\(370\) −10694.7 6719.57i −1.50267 0.944146i
\(371\) 308.392 0.0431561
\(372\) 393.692 + 393.692i 0.0548710 + 0.0548710i
\(373\) 2478.22 + 2478.22i 0.344014 + 0.344014i 0.857874 0.513860i \(-0.171785\pi\)
−0.513860 + 0.857874i \(0.671785\pi\)
\(374\) 13678.1i 1.89112i
\(375\) 2086.28 + 2615.75i 0.287293 + 0.360204i
\(376\) 971.461 0.133243
\(377\) −2434.50 2434.50i −0.332582 0.332582i
\(378\) 485.094 + 485.094i 0.0660067 + 0.0660067i
\(379\) 290.087 0.0393161 0.0196580 0.999807i \(-0.493742\pi\)
0.0196580 + 0.999807i \(0.493742\pi\)
\(380\) 674.701 1073.83i 0.0910826 0.144964i
\(381\) 1985.87 0.267032
\(382\) −790.709 + 790.709i −0.105906 + 0.105906i
\(383\) 5194.83 + 5194.83i 0.693064 + 0.693064i 0.962905 0.269841i \(-0.0869711\pi\)
−0.269841 + 0.962905i \(0.586971\pi\)
\(384\) 637.458i 0.0847139i
\(385\) −209.800 919.098i −0.0277725 0.121666i
\(386\) 8870.60 1.16969
\(387\) −8300.37 + 8300.37i −1.09026 + 1.09026i
\(388\) −3445.52 3445.52i −0.450824 0.450824i
\(389\) 9641.89 1.25672 0.628359 0.777924i \(-0.283727\pi\)
0.628359 + 0.777924i \(0.283727\pi\)
\(390\) 8091.24 1846.97i 1.05055 0.239807i
\(391\) −6057.78 3232.77i −0.783517 0.418128i
\(392\) −502.272 502.272i −0.0647158 0.0647158i
\(393\) −781.331 + 781.331i −0.100287 + 0.100287i
\(394\) 15327.4i 1.95985i
\(395\) −76.4331 48.0237i −0.00973612 0.00611730i
\(396\) 8875.55i 1.12630i
\(397\) 8236.95 + 8236.95i 1.04131 + 1.04131i 0.999109 + 0.0422024i \(0.0134374\pi\)
0.0422024 + 0.999109i \(0.486563\pi\)
\(398\) −12183.2 12183.2i −1.53439 1.53439i
\(399\) 54.8719i 0.00688478i
\(400\) 3686.15 + 7653.50i 0.460769 + 0.956687i
\(401\) 8063.16i 1.00413i −0.864831 0.502063i \(-0.832574\pi\)
0.864831 0.502063i \(-0.167426\pi\)
\(402\) −5956.28 + 5956.28i −0.738985 + 0.738985i
\(403\) −1735.41 + 1735.41i −0.214508 + 0.214508i
\(404\) 8774.63i 1.08058i
\(405\) −2817.18 1770.06i −0.345647 0.217173i
\(406\) 259.274i 0.0316935i
\(407\) 11346.2 + 11346.2i 1.38184 + 1.38184i
\(408\) 219.694 + 219.694i 0.0266580 + 0.0266580i
\(409\) 4934.18i 0.596527i −0.954484 0.298264i \(-0.903593\pi\)
0.954484 0.298264i \(-0.0964075\pi\)
\(410\) 4100.61 + 17964.1i 0.493938 + 2.16386i
\(411\) 3840.46i 0.460915i
\(412\) 323.014 323.014i 0.0386257 0.0386257i
\(413\) 293.405 + 293.405i 0.0349577 + 0.0349577i
\(414\) −8140.55 4344.24i −0.966392 0.515720i
\(415\) 2837.45 + 12430.4i 0.335626 + 1.47032i
\(416\) 19756.9 2.32851
\(417\) −1401.31 1401.31i −0.164562 0.164562i
\(418\) −2359.33 + 2359.33i −0.276074 + 0.276074i
\(419\) 9132.74 1.06483 0.532415 0.846483i \(-0.321285\pi\)
0.532415 + 0.846483i \(0.321285\pi\)
\(420\) −255.538 160.557i −0.0296880 0.0186533i
\(421\) 13814.9i 1.59928i −0.600478 0.799642i \(-0.705023\pi\)
0.600478 0.799642i \(-0.294977\pi\)
\(422\) −5080.03 5080.03i −0.586000 0.586000i
\(423\) 7007.91 7007.91i 0.805524 0.805524i
\(424\) 425.956 0.0487883
\(425\) 7344.68 + 2569.64i 0.838281 + 0.293285i
\(426\) −3783.95 −0.430360
\(427\) −320.376 320.376i −0.0363094 0.0363094i
\(428\) −4361.21 4361.21i −0.492540 0.492540i
\(429\) −10543.6 −1.18660
\(430\) 12912.2 20550.7i 1.44810 2.30475i
\(431\) 7808.71i 0.872697i −0.899778 0.436349i \(-0.856271\pi\)
0.899778 0.436349i \(-0.143729\pi\)
\(432\) 5553.13 + 5553.13i 0.618461 + 0.618461i
\(433\) 7463.44 + 7463.44i 0.828337 + 0.828337i 0.987287 0.158949i \(-0.0508107\pi\)
−0.158949 + 0.987287i \(0.550811\pi\)
\(434\) 184.820 0.0204416
\(435\) 260.155 + 1139.69i 0.0286746 + 0.125619i
\(436\) 1118.11i 0.122816i
\(437\) 487.286 + 1602.52i 0.0533411 + 0.175421i
\(438\) 2900.81 2900.81i 0.316452 0.316452i
\(439\) 14368.5i 1.56213i 0.624453 + 0.781063i \(0.285322\pi\)
−0.624453 + 0.781063i \(0.714678\pi\)
\(440\) −289.779 1269.47i −0.0313970 0.137545i
\(441\) −7246.58 −0.782483
\(442\) 13648.1 13648.1i 1.46872 1.46872i
\(443\) 3022.02 3022.02i 0.324109 0.324109i −0.526232 0.850341i \(-0.676396\pi\)
0.850341 + 0.526232i \(0.176396\pi\)
\(444\) 5136.64 0.549041
\(445\) 11863.0 + 7453.66i 1.26373 + 0.794016i
\(446\) −7781.29 −0.826132
\(447\) 2149.69 2149.69i 0.227465 0.227465i
\(448\) −471.797 471.797i −0.0497551 0.0497551i
\(449\) 6140.06i 0.645362i 0.946508 + 0.322681i \(0.104584\pi\)
−0.946508 + 0.322681i \(0.895416\pi\)
\(450\) 9869.90 + 3453.13i 1.03394 + 0.361738i
\(451\) 23408.8i 2.44407i
\(452\) 10396.9 10396.9i 1.08192 1.08192i
\(453\) 2891.70 2891.70i 0.299921 0.299921i
\(454\) −7705.97 −0.796606
\(455\) 707.740 1126.42i 0.0729217 0.116060i
\(456\) 75.7899i 0.00778330i
\(457\) −3490.79 + 3490.79i −0.357314 + 0.357314i −0.862822 0.505508i \(-0.831305\pi\)
0.505508 + 0.862822i \(0.331305\pi\)
\(458\) 8656.93 + 8656.93i 0.883213 + 0.883213i
\(459\) 7193.51 0.731513
\(460\) 8888.76 + 2419.75i 0.900958 + 0.245264i
\(461\) −1500.76 −0.151621 −0.0758103 0.997122i \(-0.524154\pi\)
−0.0758103 + 0.997122i \(0.524154\pi\)
\(462\) 561.445 + 561.445i 0.0565385 + 0.0565385i
\(463\) 7235.48 7235.48i 0.726266 0.726266i −0.243608 0.969874i \(-0.578331\pi\)
0.969874 + 0.243608i \(0.0783309\pi\)
\(464\) 2968.05i 0.296957i
\(465\) 812.417 185.448i 0.0810214 0.0184945i
\(466\) −3469.20 −0.344866
\(467\) −3378.86 + 3378.86i −0.334807 + 0.334807i −0.854409 0.519601i \(-0.826080\pi\)
0.519601 + 0.854409i \(0.326080\pi\)
\(468\) 8856.05 8856.05i 0.874725 0.874725i
\(469\) 1350.20i 0.132934i
\(470\) −10901.7 + 17350.8i −1.06991 + 1.70283i
\(471\) 3175.87i 0.310693i
\(472\) 405.256 + 405.256i 0.0395200 + 0.0395200i
\(473\) −21802.6 + 21802.6i −2.11942 + 2.11942i
\(474\) 76.0264 0.00736710
\(475\) −823.644 1710.12i −0.0795608 0.165191i
\(476\) −701.857 −0.0675831
\(477\) 3072.76 3072.76i 0.294952 0.294952i
\(478\) −7574.71 + 7574.71i −0.724810 + 0.724810i
\(479\) −3085.56 −0.294327 −0.147164 0.989112i \(-0.547014\pi\)
−0.147164 + 0.989112i \(0.547014\pi\)
\(480\) −5680.13 3568.88i −0.540128 0.339368i
\(481\) 22642.5i 2.14638i
\(482\) −5765.99 + 5765.99i −0.544883 + 0.544883i
\(483\) 381.349 115.958i 0.0359254 0.0109240i
\(484\) 13370.9i 1.25572i
\(485\) −7110.11 + 1623.01i −0.665678 + 0.151952i
\(486\) 15074.1 1.40694
\(487\) 3690.56 + 3690.56i 0.343399 + 0.343399i 0.857644 0.514245i \(-0.171928\pi\)
−0.514245 + 0.857644i \(0.671928\pi\)
\(488\) −442.509 442.509i −0.0410480 0.0410480i
\(489\) 3644.96i 0.337077i
\(490\) 14607.3 3334.37i 1.34671 0.307411i
\(491\) −19160.4 −1.76109 −0.880546 0.473961i \(-0.842824\pi\)
−0.880546 + 0.473961i \(0.842824\pi\)
\(492\) −5298.82 5298.82i −0.485547 0.485547i
\(493\) 1922.40 + 1922.40i 0.175620 + 0.175620i
\(494\) −4708.30 −0.428819
\(495\) −11248.1 7067.31i −1.02134 0.641721i
\(496\) 2115.74 0.191531
\(497\) −428.882 + 428.882i −0.0387082 + 0.0387082i
\(498\) −7593.29 7593.29i −0.683260 0.683260i
\(499\) 8432.30i 0.756476i 0.925708 + 0.378238i \(0.123470\pi\)
−0.925708 + 0.378238i \(0.876530\pi\)
\(500\) −10374.0 1168.16i −0.927881 0.104483i
\(501\) 588.697 0.0524971
\(502\) −8740.68 + 8740.68i −0.777123 + 0.777123i
\(503\) −1153.57 1153.57i −0.102256 0.102256i 0.654128 0.756384i \(-0.273036\pi\)
−0.756384 + 0.654128i \(0.773036\pi\)
\(504\) 66.9237 0.00591472
\(505\) 11120.2 + 6986.95i 0.979888 + 0.615674i
\(506\) −21382.8 11411.0i −1.87862 1.00253i
\(507\) −6801.19 6801.19i −0.595762 0.595762i
\(508\) −4381.39 + 4381.39i −0.382663 + 0.382663i
\(509\) 14551.4i 1.26715i 0.773682 + 0.633575i \(0.218413\pi\)
−0.773682 + 0.633575i \(0.781587\pi\)
\(510\) −6389.23 + 1458.45i −0.554745 + 0.126630i
\(511\) 657.569i 0.0569259i
\(512\) −11241.9 11241.9i −0.970366 0.970366i
\(513\) −1240.81 1240.81i −0.106789 0.106789i
\(514\) 2494.40i 0.214053i
\(515\) −152.155 666.567i −0.0130190 0.0570339i
\(516\) 9870.49i 0.842101i
\(517\) 18407.7 18407.7i 1.56590 1.56590i
\(518\) 1205.71 1205.71i 0.102270 0.102270i
\(519\) 200.799i 0.0169828i
\(520\) 977.542 1555.83i 0.0824386 0.131207i
\(521\) 16272.7i 1.36837i 0.729310 + 0.684184i \(0.239841\pi\)
−0.729310 + 0.684184i \(0.760159\pi\)
\(522\) 2583.35 + 2583.35i 0.216610 + 0.216610i
\(523\) 12124.5 + 12124.5i 1.01371 + 1.01371i 0.999905 + 0.0138021i \(0.00439349\pi\)
0.0138021 + 0.999905i \(0.495607\pi\)
\(524\) 3447.68i 0.287429i
\(525\) −406.953 + 196.001i −0.0338303 + 0.0162937i
\(526\) 16268.2i 1.34853i
\(527\) 1370.36 1370.36i 0.113271 0.113271i
\(528\) 6427.17 + 6427.17i 0.529747 + 0.529747i
\(529\) −10107.5 + 6773.10i −0.830729 + 0.556678i
\(530\) −4780.05 + 7607.78i −0.391759 + 0.623511i
\(531\) 5846.87 0.477839
\(532\) 121.063 + 121.063i 0.00986607 + 0.00986607i
\(533\) 23357.4 23357.4i 1.89816 1.89816i
\(534\) −11799.9 −0.956239
\(535\) −8999.72 + 2054.34i −0.727275 + 0.166013i
\(536\) 1864.91i 0.150283i
\(537\) 3415.74 + 3415.74i 0.274488 + 0.274488i
\(538\) −9714.67 + 9714.67i −0.778493 + 0.778493i
\(539\) −19034.6 −1.52111
\(540\) −9409.07 + 2147.78i −0.749819 + 0.171159i
\(541\) 10496.2 0.834137 0.417068 0.908875i \(-0.363058\pi\)
0.417068 + 0.908875i \(0.363058\pi\)
\(542\) −16275.7 16275.7i −1.28986 1.28986i
\(543\) 1632.20 + 1632.20i 0.128995 + 0.128995i
\(544\) −15601.0 −1.22957
\(545\) 1417.00 + 890.315i 0.111372 + 0.0699760i
\(546\) 1120.42i 0.0878200i
\(547\) −12797.8 12797.8i −1.00036 1.00036i −1.00000 0.000357937i \(-0.999886\pi\)
−0.000357937 1.00000i \(-0.500114\pi\)
\(548\) 8473.16 + 8473.16i 0.660502 + 0.660502i
\(549\) −6384.34 −0.496315
\(550\) 25925.3 + 9070.34i 2.00992 + 0.703201i
\(551\) 663.189i 0.0512755i
\(552\) 526.726 160.164i 0.0406140 0.0123497i
\(553\) 8.61700 8.61700i 0.000662626 0.000662626i
\(554\) 12870.5i 0.987033i
\(555\) 4090.14 6509.75i 0.312823 0.497880i
\(556\) 6183.37 0.471643
\(557\) −3834.37 + 3834.37i −0.291683 + 0.291683i −0.837745 0.546062i \(-0.816126\pi\)
0.546062 + 0.837745i \(0.316126\pi\)
\(558\) 1841.51 1841.51i 0.139709 0.139709i
\(559\) −43509.4 −3.29204
\(560\) −1118.07 + 255.218i −0.0843695 + 0.0192588i
\(561\) 8325.74 0.626583
\(562\) −11288.4 + 11288.4i −0.847280 + 0.847280i
\(563\) 2578.60 + 2578.60i 0.193029 + 0.193029i 0.797003 0.603975i \(-0.206417\pi\)
−0.603975 + 0.797003i \(0.706417\pi\)
\(564\) 8333.56i 0.622174i
\(565\) −4897.44 21454.8i −0.364667 1.59754i
\(566\) 6950.74i 0.516186i
\(567\) 317.606 317.606i 0.0235242 0.0235242i
\(568\) −592.378 + 592.378i −0.0437599 + 0.0437599i
\(569\) 27117.7 1.99795 0.998974 0.0452860i \(-0.0144199\pi\)
0.998974 + 0.0452860i \(0.0144199\pi\)
\(570\) 1353.64 + 850.509i 0.0994701 + 0.0624980i
\(571\) 8880.25i 0.650835i 0.945570 + 0.325417i \(0.105505\pi\)
−0.945570 + 0.325417i \(0.894495\pi\)
\(572\) 23262.2 23262.2i 1.70042 1.70042i
\(573\) −481.297 481.297i −0.0350899 0.0350899i
\(574\) −2487.55 −0.180886
\(575\) 10144.4 9338.10i 0.735742 0.677262i
\(576\) −9401.79 −0.680106
\(577\) 8211.41 + 8211.41i 0.592453 + 0.592453i 0.938293 0.345840i \(-0.112406\pi\)
−0.345840 + 0.938293i \(0.612406\pi\)
\(578\) 2886.78 2886.78i 0.207741 0.207741i
\(579\) 5399.45i 0.387554i
\(580\) −3088.47 1940.51i −0.221106 0.138923i
\(581\) −1721.28 −0.122910
\(582\) 4343.32 4343.32i 0.309341 0.309341i
\(583\) 8071.23 8071.23i 0.573372 0.573372i
\(584\) 908.245i 0.0643552i
\(585\) −4171.63 18275.2i −0.294830 1.29160i
\(586\) 22248.5i 1.56839i
\(587\) 9371.65 + 9371.65i 0.658960 + 0.658960i 0.955134 0.296174i \(-0.0957109\pi\)
−0.296174 + 0.955134i \(0.595711\pi\)
\(588\) −4308.68 + 4308.68i −0.302189 + 0.302189i
\(589\) −472.746 −0.0330716
\(590\) −11785.8 + 2690.32i −0.822398 + 0.187726i
\(591\) −9329.63 −0.649356
\(592\) 13802.4 13802.4i 0.958234 0.958234i
\(593\) −8845.92 + 8845.92i −0.612577 + 0.612577i −0.943617 0.331040i \(-0.892601\pi\)
0.331040 + 0.943617i \(0.392601\pi\)
\(594\) 25391.7 1.75393
\(595\) −558.866 + 889.474i −0.0385063 + 0.0612855i
\(596\) 9485.67i 0.651926i
\(597\) 7415.79 7415.79i 0.508389 0.508389i
\(598\) −9949.86 32721.8i −0.680402 2.23762i
\(599\) 19547.1i 1.33334i −0.745352 0.666671i \(-0.767719\pi\)
0.745352 0.666671i \(-0.232281\pi\)
\(600\) −562.090 + 270.720i −0.0382454 + 0.0184201i
\(601\) 6473.70 0.439381 0.219690 0.975570i \(-0.429495\pi\)
0.219690 + 0.975570i \(0.429495\pi\)
\(602\) 2316.87 + 2316.87i 0.156858 + 0.156858i
\(603\) 13453.1 + 13453.1i 0.908544 + 0.908544i
\(604\) 12759.9i 0.859588i
\(605\) −16945.2 10646.8i −1.13871 0.715463i
\(606\) −11061.1 −0.741460
\(607\) −15087.9 15087.9i −1.00889 1.00889i −0.999960 0.00893393i \(-0.997156\pi\)
−0.00893393 0.999960i \(-0.502844\pi\)
\(608\) 2691.01 + 2691.01i 0.179498 + 0.179498i
\(609\) −157.818 −0.0105010
\(610\) 12869.2 2937.62i 0.854197 0.194985i
\(611\) 36734.6 2.43228
\(612\) −6993.17 + 6993.17i −0.461899 + 0.461899i
\(613\) −7465.03 7465.03i −0.491859 0.491859i 0.417032 0.908892i \(-0.363070\pi\)
−0.908892 + 0.417032i \(0.863070\pi\)
\(614\) 21779.4i 1.43151i
\(615\) −10934.6 + 2496.00i −0.716950 + 0.163656i
\(616\) 175.789 0.0114979
\(617\) −5029.07 + 5029.07i −0.328140 + 0.328140i −0.851879 0.523739i \(-0.824537\pi\)
0.523739 + 0.851879i \(0.324537\pi\)
\(618\) 407.183 + 407.183i 0.0265037 + 0.0265037i
\(619\) 2258.07 0.146623 0.0733115 0.997309i \(-0.476643\pi\)
0.0733115 + 0.997309i \(0.476643\pi\)
\(620\) −1383.27 + 2201.58i −0.0896025 + 0.142609i
\(621\) 6001.23 11245.5i 0.387795 0.726678i
\(622\) 12722.7 + 12722.7i 0.820148 + 0.820148i
\(623\) −1337.43 + 1337.43i −0.0860078 + 0.0860078i
\(624\) 12826.1i 0.822845i
\(625\) −9740.92 + 12217.0i −0.623419 + 0.781888i
\(626\) 28259.0i 1.80424i
\(627\) −1436.10 1436.10i −0.0914713 0.0914713i
\(628\) −7006.88 7006.88i −0.445231 0.445231i
\(629\) 17879.6i 1.13340i
\(630\) −751.013 + 1195.29i −0.0474938 + 0.0755897i
\(631\) 7288.79i 0.459845i −0.973209 0.229922i \(-0.926153\pi\)
0.973209 0.229922i \(-0.0738472\pi\)
\(632\) 11.9019 11.9019i 0.000749104 0.000749104i
\(633\) 3092.17 3092.17i 0.194159 0.194159i
\(634\) 14939.1i 0.935818i
\(635\) 2063.85 + 9041.37i 0.128979 + 0.565033i
\(636\) 3654.01i 0.227816i
\(637\) −18992.8 18992.8i −1.18135 1.18135i
\(638\) 6785.71 + 6785.71i 0.421079 + 0.421079i
\(639\) 8546.59i 0.529105i
\(640\) −2902.25 + 662.489i −0.179253 + 0.0409175i
\(641\) 13007.3i 0.801493i −0.916189 0.400747i \(-0.868751\pi\)
0.916189 0.400747i \(-0.131249\pi\)
\(642\) 5497.62 5497.62i 0.337965 0.337965i
\(643\) 2348.81 + 2348.81i 0.144056 + 0.144056i 0.775457 0.631401i \(-0.217520\pi\)
−0.631401 + 0.775457i \(0.717520\pi\)
\(644\) −585.528 + 1097.20i −0.0358277 + 0.0671364i
\(645\) 12509.0 + 7859.55i 0.763632 + 0.479798i
\(646\) 3717.90 0.226438
\(647\) 1079.02 + 1079.02i 0.0655651 + 0.0655651i 0.739129 0.673564i \(-0.235237\pi\)
−0.673564 + 0.739129i \(0.735237\pi\)
\(648\) 438.683 438.683i 0.0265943 0.0265943i
\(649\) 15358.0 0.928896
\(650\) 16817.9 + 34918.8i 1.01485 + 2.10712i
\(651\) 112.498i 0.00677290i
\(652\) 8041.83 + 8041.83i 0.483040 + 0.483040i
\(653\) −10600.2 + 10600.2i −0.635249 + 0.635249i −0.949380 0.314131i \(-0.898287\pi\)
0.314131 + 0.949380i \(0.398287\pi\)
\(654\) −1409.46 −0.0842725
\(655\) −4369.30 2745.28i −0.260645 0.163766i
\(656\) −28476.3 −1.69484
\(657\) −6551.89 6551.89i −0.389062 0.389062i
\(658\) −1956.11 1956.11i −0.115892 0.115892i
\(659\) −28717.5 −1.69754 −0.848768 0.528765i \(-0.822655\pi\)
−0.848768 + 0.528765i \(0.822655\pi\)
\(660\) −10890.0 + 2485.84i −0.642263 + 0.146608i
\(661\) 20493.0i 1.20588i 0.797787 + 0.602940i \(0.206004\pi\)
−0.797787 + 0.602940i \(0.793996\pi\)
\(662\) −11172.6 11172.6i −0.655943 0.655943i
\(663\) 8307.45 + 8307.45i 0.486629 + 0.486629i
\(664\) −2377.46 −0.138951
\(665\) 249.824 57.0266i 0.0145680 0.00332541i
\(666\) 24026.9i 1.39793i
\(667\) 4609.04 1401.49i 0.267560 0.0813582i
\(668\) −1298.84 + 1298.84i −0.0752297 + 0.0752297i
\(669\) 4736.40i 0.273722i
\(670\) −33308.2 20927.9i −1.92061 1.20674i
\(671\) −16769.8 −0.964813
\(672\) 640.373 640.373i 0.0367603 0.0367603i
\(673\) 18282.5 18282.5i 1.04716 1.04716i 0.0483273 0.998832i \(-0.484611\pi\)
0.998832 0.0483273i \(-0.0153890\pi\)
\(674\) 42049.3 2.40308
\(675\) −4770.22 + 13634.5i −0.272009 + 0.777469i
\(676\) 30010.7 1.70748
\(677\) 4075.44 4075.44i 0.231362 0.231362i −0.581899 0.813261i \(-0.697690\pi\)
0.813261 + 0.581899i \(0.197690\pi\)
\(678\) 13106.0 + 13106.0i 0.742380 + 0.742380i
\(679\) 984.564i 0.0556467i
\(680\) −771.914 + 1228.56i −0.0435317 + 0.0692838i
\(681\) 4690.55i 0.263939i
\(682\) 4837.11 4837.11i 0.271587 0.271587i
\(683\) 11380.6 11380.6i 0.637578 0.637578i −0.312379 0.949957i \(-0.601126\pi\)
0.949957 + 0.312379i \(0.101126\pi\)
\(684\) 2412.50 0.134860
\(685\) 17485.1 3991.27i 0.975285 0.222626i
\(686\) 4058.98i 0.225907i
\(687\) −5269.39 + 5269.39i −0.292634 + 0.292634i
\(688\) 26522.5 + 26522.5i 1.46971 + 1.46971i
\(689\) 16107.0 0.890606
\(690\) −3050.27 + 11204.9i −0.168293 + 0.618209i
\(691\) −30731.6 −1.69187 −0.845936 0.533284i \(-0.820958\pi\)
−0.845936 + 0.533284i \(0.820958\pi\)
\(692\) 443.020 + 443.020i 0.0243368 + 0.0243368i
\(693\) 1268.10 1268.10i 0.0695112 0.0695112i
\(694\) 11709.6i 0.640478i
\(695\) 4923.62 7836.29i 0.268724 0.427694i
\(696\) −217.980 −0.0118714
\(697\) −18444.1 + 18444.1i −1.00232 + 1.00232i
\(698\) −15290.9 + 15290.9i −0.829180 + 0.829180i
\(699\) 2111.67i 0.114264i
\(700\) 465.421 1330.29i 0.0251304 0.0718289i
\(701\) 18984.7i 1.02289i −0.859317 0.511443i \(-0.829111\pi\)
0.859317 0.511443i \(-0.170889\pi\)
\(702\) 25335.9 + 25335.9i 1.36217 + 1.36217i
\(703\) −3084.04 + 3084.04i −0.165458 + 0.165458i
\(704\) −24695.7 −1.32209
\(705\) −10561.2 6635.74i −0.564198 0.354491i
\(706\) 18563.9 0.989604
\(707\) −1253.68 + 1253.68i −0.0666898 + 0.0666898i
\(708\) 3476.44 3476.44i 0.184538 0.184538i
\(709\) −11238.0 −0.595275 −0.297638 0.954679i \(-0.596199\pi\)
−0.297638 + 0.954679i \(0.596199\pi\)
\(710\) −3932.54 17227.8i −0.207867 0.910631i
\(711\) 171.716i 0.00905747i
\(712\) −1847.28 + 1847.28i −0.0972325 + 0.0972325i
\(713\) −999.036 3285.50i −0.0524743 0.172571i
\(714\) 884.741i 0.0463734i
\(715\) −10957.6 48003.5i −0.573136 2.51081i
\(716\) −15072.2 −0.786697
\(717\) −4610.66 4610.66i −0.240151 0.240151i
\(718\) −11340.0 11340.0i −0.589421 0.589421i
\(719\) 11223.6i 0.582158i −0.956699 0.291079i \(-0.905986\pi\)
0.956699 0.291079i \(-0.0940142\pi\)
\(720\) −8597.25 + 13683.1i −0.445001 + 0.708250i
\(721\) 92.3020 0.00476769
\(722\) 18434.8 + 18434.8i 0.950240 + 0.950240i
\(723\) −3509.70 3509.70i −0.180536 0.180536i
\(724\) −7202.19 −0.369706
\(725\) −4918.49 + 2368.89i −0.251956 + 0.121350i
\(726\) 16855.0 0.861636
\(727\) 21942.3 21942.3i 1.11939 1.11939i 0.127555 0.991832i \(-0.459287\pi\)
0.991832 0.127555i \(-0.0407128\pi\)
\(728\) 175.403 + 175.403i 0.00892974 + 0.00892974i
\(729\) 1140.65i 0.0579512i
\(730\) 16221.7 + 10192.3i 0.822455 + 0.516757i
\(731\) 34357.1 1.73836
\(732\) −3796.01 + 3796.01i −0.191673 + 0.191673i
\(733\) −8102.69 8102.69i −0.408294 0.408294i 0.472849 0.881143i \(-0.343226\pi\)
−0.881143 + 0.472849i \(0.843226\pi\)
\(734\) 18350.4 0.922785
\(735\) 2029.60 + 8891.33i 0.101854 + 0.446206i
\(736\) −13015.2 + 24388.8i −0.651829 + 1.22144i
\(737\) 35337.3 + 35337.3i 1.76617 + 1.76617i
\(738\) −24785.5 + 24785.5i −1.23627 + 1.23627i
\(739\) 7554.88i 0.376063i −0.982163 0.188032i \(-0.939789\pi\)
0.982163 0.188032i \(-0.0602107\pi\)
\(740\) 5338.35 + 23386.4i 0.265191 + 1.16176i
\(741\) 2865.90i 0.142080i
\(742\) −857.695 857.695i −0.0424353 0.0424353i
\(743\) −39.8165 39.8165i −0.00196598 0.00196598i 0.706123 0.708089i \(-0.250443\pi\)
−0.708089 + 0.706123i \(0.750443\pi\)
\(744\) 155.385i 0.00765682i
\(745\) 12021.3 + 7553.13i 0.591178 + 0.371443i
\(746\) 13784.8i 0.676536i
\(747\) −17150.5 + 17150.5i −0.840032 + 0.840032i
\(748\) −18369.0 + 18369.0i −0.897909 + 0.897909i
\(749\) 1246.23i 0.0607958i
\(750\) 1472.55 13077.2i 0.0716932 0.636683i
\(751\) 3501.49i 0.170135i −0.996375 0.0850673i \(-0.972889\pi\)
0.996375 0.0850673i \(-0.0271105\pi\)
\(752\) −22392.6 22392.6i −1.08587 1.08587i
\(753\) −5320.37 5320.37i −0.257483 0.257483i
\(754\) 13541.6i 0.654053i
\(755\) 16170.8 + 10160.3i 0.779489 + 0.489761i
\(756\) 1302.91i 0.0626804i
\(757\) −6113.41 + 6113.41i −0.293521 + 0.293521i −0.838470 0.544948i \(-0.816549\pi\)
0.544948 + 0.838470i \(0.316549\pi\)
\(758\) −806.786 806.786i −0.0386594 0.0386594i
\(759\) 6945.79 13015.5i 0.332169 0.622442i
\(760\) 345.061 78.7660i 0.0164693 0.00375940i
\(761\) −1162.97 −0.0553976 −0.0276988 0.999616i \(-0.508818\pi\)
−0.0276988 + 0.999616i \(0.508818\pi\)
\(762\) −5523.06 5523.06i −0.262572 0.262572i
\(763\) −159.751 + 159.751i −0.00757979 + 0.00757979i
\(764\) 2123.76 0.100569
\(765\) 3294.12 + 14431.0i 0.155685 + 0.682030i
\(766\) 28895.6i 1.36297i
\(767\) 15324.2 + 15324.2i 0.721417 + 0.721417i
\(768\) 7759.67 7759.67i 0.364587 0.364587i
\(769\) 38945.9 1.82630 0.913151 0.407621i \(-0.133642\pi\)
0.913151 + 0.407621i \(0.133642\pi\)
\(770\) −1972.69 + 3139.67i −0.0923257 + 0.146943i
\(771\) −1518.32 −0.0709219
\(772\) −11912.7