Properties

Label 115.4.e.a.22.8
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 22.8
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.66509 - 2.66509i) q^{2} +(-2.23283 + 2.23283i) q^{3} +6.20541i q^{4} +(7.41137 - 8.37088i) q^{5} +11.9014 q^{6} +(-10.9048 + 10.9048i) q^{7} +(-4.78275 + 4.78275i) q^{8} +17.0290i q^{9} +O(q^{10})\) \(q+(-2.66509 - 2.66509i) q^{2} +(-2.23283 + 2.23283i) q^{3} +6.20541i q^{4} +(7.41137 - 8.37088i) q^{5} +11.9014 q^{6} +(-10.9048 + 10.9048i) q^{7} +(-4.78275 + 4.78275i) q^{8} +17.0290i q^{9} +(-42.0611 + 2.55718i) q^{10} +18.9440i q^{11} +(-13.8556 - 13.8556i) q^{12} +(43.9640 - 43.9640i) q^{13} +58.1244 q^{14} +(2.14242 + 35.2390i) q^{15} +75.1362 q^{16} +(-38.7029 + 38.7029i) q^{17} +(45.3837 - 45.3837i) q^{18} +123.640 q^{19} +(51.9447 + 45.9906i) q^{20} -48.6969i q^{21} +(50.4874 - 50.4874i) q^{22} +(109.778 + 10.7567i) q^{23} -21.3581i q^{24} +(-15.1432 - 124.079i) q^{25} -234.336 q^{26} +(-98.3091 - 98.3091i) q^{27} +(-67.6686 - 67.6686i) q^{28} +59.0042i q^{29} +(88.2054 - 99.6249i) q^{30} +342.953 q^{31} +(-161.983 - 161.983i) q^{32} +(-42.2986 - 42.2986i) q^{33} +206.293 q^{34} +(10.4632 + 172.102i) q^{35} -105.672 q^{36} +(-302.912 + 302.912i) q^{37} +(-329.512 - 329.512i) q^{38} +196.328i q^{39} +(4.58909 + 75.4826i) q^{40} +137.839 q^{41} +(-129.782 + 129.782i) q^{42} +(155.399 + 155.399i) q^{43} -117.555 q^{44} +(142.547 + 126.208i) q^{45} +(-263.902 - 321.237i) q^{46} +(234.217 + 234.217i) q^{47} +(-167.766 + 167.766i) q^{48} +105.172i q^{49} +(-290.325 + 371.041i) q^{50} -172.834i q^{51} +(272.815 + 272.815i) q^{52} +(-342.095 - 342.095i) q^{53} +524.005i q^{54} +(158.578 + 140.401i) q^{55} -104.310i q^{56} +(-276.067 + 276.067i) q^{57} +(157.251 - 157.251i) q^{58} -87.0009i q^{59} +(-218.672 + 13.2946i) q^{60} +565.294i q^{61} +(-914.002 - 914.002i) q^{62} +(-185.697 - 185.697i) q^{63} +262.307i q^{64} +(-42.1838 - 693.851i) q^{65} +225.459i q^{66} +(-4.05177 + 4.05177i) q^{67} +(-240.167 - 240.167i) q^{68} +(-269.134 + 221.098i) q^{69} +(430.782 - 486.552i) q^{70} -556.502 q^{71} +(-81.4453 - 81.4453i) q^{72} +(305.536 - 305.536i) q^{73} +1614.57 q^{74} +(310.860 + 243.236i) q^{75} +767.238i q^{76} +(-206.580 - 206.580i) q^{77} +(523.232 - 523.232i) q^{78} -328.493 q^{79} +(556.862 - 628.956i) q^{80} -20.7681 q^{81} +(-367.354 - 367.354i) q^{82} +(810.460 + 810.460i) q^{83} +302.184 q^{84} +(37.1357 + 610.818i) q^{85} -828.302i q^{86} +(-131.746 - 131.746i) q^{87} +(-90.6043 - 90.6043i) q^{88} +194.282 q^{89} +(-43.5461 - 716.257i) q^{90} +958.835i q^{91} +(-66.7494 + 681.220i) q^{92} +(-765.755 + 765.755i) q^{93} -1248.42i q^{94} +(916.343 - 1034.98i) q^{95} +723.358 q^{96} +(1067.11 - 1067.11i) q^{97} +(280.292 - 280.292i) q^{98} -322.596 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66509 2.66509i −0.942252 0.942252i 0.0561697 0.998421i \(-0.482111\pi\)
−0.998421 + 0.0561697i \(0.982111\pi\)
\(3\) −2.23283 + 2.23283i −0.429708 + 0.429708i −0.888529 0.458821i \(-0.848272\pi\)
0.458821 + 0.888529i \(0.348272\pi\)
\(4\) 6.20541i 0.775676i
\(5\) 7.41137 8.37088i 0.662893 0.748714i
\(6\) 11.9014 0.809785
\(7\) −10.9048 + 10.9048i −0.588803 + 0.588803i −0.937307 0.348505i \(-0.886690\pi\)
0.348505 + 0.937307i \(0.386690\pi\)
\(8\) −4.78275 + 4.78275i −0.211370 + 0.211370i
\(9\) 17.0290i 0.630703i
\(10\) −42.0611 + 2.55718i −1.33009 + 0.0808650i
\(11\) 18.9440i 0.519257i 0.965709 + 0.259628i \(0.0836001\pi\)
−0.965709 + 0.259628i \(0.916400\pi\)
\(12\) −13.8556 13.8556i −0.333314 0.333314i
\(13\) 43.9640 43.9640i 0.937955 0.937955i −0.0602292 0.998185i \(-0.519183\pi\)
0.998185 + 0.0602292i \(0.0191832\pi\)
\(14\) 58.1244 1.10960
\(15\) 2.14242 + 35.2390i 0.0368780 + 0.606578i
\(16\) 75.1362 1.17400
\(17\) −38.7029 + 38.7029i −0.552166 + 0.552166i −0.927066 0.374899i \(-0.877677\pi\)
0.374899 + 0.927066i \(0.377677\pi\)
\(18\) 45.3837 45.3837i 0.594281 0.594281i
\(19\) 123.640 1.49290 0.746448 0.665444i \(-0.231758\pi\)
0.746448 + 0.665444i \(0.231758\pi\)
\(20\) 51.9447 + 45.9906i 0.580759 + 0.514190i
\(21\) 48.6969i 0.506026i
\(22\) 50.4874 50.4874i 0.489271 0.489271i
\(23\) 109.778 + 10.7567i 0.995234 + 0.0975182i
\(24\) 21.3581i 0.181654i
\(25\) −15.1432 124.079i −0.121146 0.992635i
\(26\) −234.336 −1.76758
\(27\) −98.3091 98.3091i −0.700725 0.700725i
\(28\) −67.6686 67.6686i −0.456720 0.456720i
\(29\) 59.0042i 0.377821i 0.981994 + 0.188910i \(0.0604955\pi\)
−0.981994 + 0.188910i \(0.939504\pi\)
\(30\) 88.2054 99.6249i 0.536801 0.606298i
\(31\) 342.953 1.98698 0.993488 0.113938i \(-0.0363464\pi\)
0.993488 + 0.113938i \(0.0363464\pi\)
\(32\) −161.983 161.983i −0.894836 0.894836i
\(33\) −42.2986 42.2986i −0.223129 0.223129i
\(34\) 206.293 1.04056
\(35\) 10.4632 + 172.102i 0.0505317 + 0.831158i
\(36\) −105.672 −0.489221
\(37\) −302.912 + 302.912i −1.34590 + 1.34590i −0.455839 + 0.890062i \(0.650661\pi\)
−0.890062 + 0.455839i \(0.849339\pi\)
\(38\) −329.512 329.512i −1.40668 1.40668i
\(39\) 196.328i 0.806093i
\(40\) 4.58909 + 75.4826i 0.0181400 + 0.298371i
\(41\) 137.839 0.525045 0.262523 0.964926i \(-0.415446\pi\)
0.262523 + 0.964926i \(0.415446\pi\)
\(42\) −129.782 + 129.782i −0.476804 + 0.476804i
\(43\) 155.399 + 155.399i 0.551118 + 0.551118i 0.926763 0.375646i \(-0.122579\pi\)
−0.375646 + 0.926763i \(0.622579\pi\)
\(44\) −117.555 −0.402775
\(45\) 142.547 + 126.208i 0.472216 + 0.418088i
\(46\) −263.902 321.237i −0.845874 1.02965i
\(47\) 234.217 + 234.217i 0.726894 + 0.726894i 0.970000 0.243106i \(-0.0781662\pi\)
−0.243106 + 0.970000i \(0.578166\pi\)
\(48\) −167.766 + 167.766i −0.504478 + 0.504478i
\(49\) 105.172i 0.306623i
\(50\) −290.325 + 371.041i −0.821162 + 1.04946i
\(51\) 172.834i 0.474540i
\(52\) 272.815 + 272.815i 0.727549 + 0.727549i
\(53\) −342.095 342.095i −0.886610 0.886610i 0.107586 0.994196i \(-0.465688\pi\)
−0.994196 + 0.107586i \(0.965688\pi\)
\(54\) 524.005i 1.32052i
\(55\) 158.578 + 140.401i 0.388775 + 0.344212i
\(56\) 104.310i 0.248910i
\(57\) −276.067 + 276.067i −0.641509 + 0.641509i
\(58\) 157.251 157.251i 0.356002 0.356002i
\(59\) 87.0009i 0.191975i −0.995383 0.0959877i \(-0.969399\pi\)
0.995383 0.0959877i \(-0.0306009\pi\)
\(60\) −218.672 + 13.2946i −0.470508 + 0.0286053i
\(61\) 565.294i 1.18653i 0.805006 + 0.593267i \(0.202162\pi\)
−0.805006 + 0.593267i \(0.797838\pi\)
\(62\) −914.002 914.002i −1.87223 1.87223i
\(63\) −185.697 185.697i −0.371359 0.371359i
\(64\) 262.307i 0.512319i
\(65\) −42.1838 693.851i −0.0804963 1.32402i
\(66\) 225.459i 0.420487i
\(67\) −4.05177 + 4.05177i −0.00738809 + 0.00738809i −0.710791 0.703403i \(-0.751663\pi\)
0.703403 + 0.710791i \(0.251663\pi\)
\(68\) −240.167 240.167i −0.428302 0.428302i
\(69\) −269.134 + 221.098i −0.469564 + 0.385755i
\(70\) 430.782 486.552i 0.735546 0.830773i
\(71\) −556.502 −0.930206 −0.465103 0.885257i \(-0.653983\pi\)
−0.465103 + 0.885257i \(0.653983\pi\)
\(72\) −81.4453 81.4453i −0.133311 0.133311i
\(73\) 305.536 305.536i 0.489866 0.489866i −0.418398 0.908264i \(-0.637408\pi\)
0.908264 + 0.418398i \(0.137408\pi\)
\(74\) 1614.57 2.53636
\(75\) 310.860 + 243.236i 0.478600 + 0.374486i
\(76\) 767.238i 1.15800i
\(77\) −206.580 206.580i −0.305740 0.305740i
\(78\) 523.232 523.232i 0.759543 0.759543i
\(79\) −328.493 −0.467828 −0.233914 0.972257i \(-0.575153\pi\)
−0.233914 + 0.972257i \(0.575153\pi\)
\(80\) 556.862 628.956i 0.778238 0.878992i
\(81\) −20.7681 −0.0284885
\(82\) −367.354 367.354i −0.494725 0.494725i
\(83\) 810.460 + 810.460i 1.07180 + 1.07180i 0.997214 + 0.0745876i \(0.0237641\pi\)
0.0745876 + 0.997214i \(0.476236\pi\)
\(84\) 302.184 0.392512
\(85\) 37.1357 + 610.818i 0.0473875 + 0.779442i
\(86\) 828.302i 1.03858i
\(87\) −131.746 131.746i −0.162352 0.162352i
\(88\) −90.6043 90.6043i −0.109755 0.109755i
\(89\) 194.282 0.231391 0.115696 0.993285i \(-0.463090\pi\)
0.115696 + 0.993285i \(0.463090\pi\)
\(90\) −43.5461 716.257i −0.0510018 0.838891i
\(91\) 958.835i 1.10454i
\(92\) −66.7494 + 681.220i −0.0756425 + 0.771979i
\(93\) −765.755 + 765.755i −0.853819 + 0.853819i
\(94\) 1248.42i 1.36983i
\(95\) 916.343 1034.98i 0.989630 1.11775i
\(96\) 723.358 0.769036
\(97\) 1067.11 1067.11i 1.11700 1.11700i 0.124820 0.992179i \(-0.460165\pi\)
0.992179 0.124820i \(-0.0398353\pi\)
\(98\) 280.292 280.292i 0.288916 0.288916i
\(99\) −322.596 −0.327497
\(100\) 769.963 93.9697i 0.769963 0.0939697i
\(101\) −1196.74 −1.17901 −0.589504 0.807766i \(-0.700677\pi\)
−0.589504 + 0.807766i \(0.700677\pi\)
\(102\) −460.617 + 460.617i −0.447136 + 0.447136i
\(103\) 647.268 + 647.268i 0.619196 + 0.619196i 0.945325 0.326129i \(-0.105745\pi\)
−0.326129 + 0.945325i \(0.605745\pi\)
\(104\) 420.538i 0.396511i
\(105\) −407.636 360.911i −0.378869 0.335441i
\(106\) 1823.43i 1.67082i
\(107\) −1091.38 + 1091.38i −0.986049 + 0.986049i −0.999904 0.0138547i \(-0.995590\pi\)
0.0138547 + 0.999904i \(0.495590\pi\)
\(108\) 610.048 610.048i 0.543536 0.543536i
\(109\) 26.4427 0.0232362 0.0116181 0.999933i \(-0.496302\pi\)
0.0116181 + 0.999933i \(0.496302\pi\)
\(110\) −48.4431 796.805i −0.0419897 0.690658i
\(111\) 1352.70i 1.15669i
\(112\) −819.343 + 819.343i −0.691256 + 0.691256i
\(113\) −70.7193 70.7193i −0.0588736 0.0588736i 0.677057 0.735931i \(-0.263255\pi\)
−0.735931 + 0.677057i \(0.763255\pi\)
\(114\) 1471.49 1.20892
\(115\) 903.651 839.220i 0.732747 0.680501i
\(116\) −366.145 −0.293066
\(117\) 748.662 + 748.662i 0.591571 + 0.591571i
\(118\) −231.865 + 231.865i −0.180889 + 0.180889i
\(119\) 844.093i 0.650234i
\(120\) −178.786 158.293i −0.136007 0.120417i
\(121\) 972.126 0.730372
\(122\) 1506.56 1506.56i 1.11801 1.11801i
\(123\) −307.771 + 307.771i −0.225616 + 0.225616i
\(124\) 2128.17i 1.54125i
\(125\) −1150.88 792.836i −0.823506 0.567307i
\(126\) 989.799i 0.699828i
\(127\) 556.054 + 556.054i 0.388518 + 0.388518i 0.874159 0.485640i \(-0.161414\pi\)
−0.485640 + 0.874159i \(0.661414\pi\)
\(128\) −596.789 + 596.789i −0.412103 + 0.412103i
\(129\) −693.956 −0.473639
\(130\) −1736.75 + 1961.60i −1.17172 + 1.32341i
\(131\) 423.960 0.282760 0.141380 0.989955i \(-0.454846\pi\)
0.141380 + 0.989955i \(0.454846\pi\)
\(132\) 262.480 262.480i 0.173075 0.173075i
\(133\) −1348.27 + 1348.27i −0.879021 + 0.879021i
\(134\) 21.5966 0.0139229
\(135\) −1551.54 + 94.3284i −0.989149 + 0.0601370i
\(136\) 370.212i 0.233422i
\(137\) 651.809 651.809i 0.406480 0.406480i −0.474029 0.880509i \(-0.657201\pi\)
0.880509 + 0.474029i \(0.157201\pi\)
\(138\) 1306.51 + 128.019i 0.805926 + 0.0789688i
\(139\) 959.361i 0.585409i −0.956203 0.292705i \(-0.905445\pi\)
0.956203 0.292705i \(-0.0945553\pi\)
\(140\) −1067.96 + 64.9286i −0.644709 + 0.0391962i
\(141\) −1045.93 −0.624704
\(142\) 1483.13 + 1483.13i 0.876488 + 0.876488i
\(143\) 832.853 + 832.853i 0.487040 + 0.487040i
\(144\) 1279.49i 0.740447i
\(145\) 493.917 + 437.302i 0.282880 + 0.250455i
\(146\) −1628.56 −0.923155
\(147\) −234.830 234.830i −0.131758 0.131758i
\(148\) −1879.69 1879.69i −1.04398 1.04398i
\(149\) −2261.05 −1.24317 −0.621584 0.783347i \(-0.713511\pi\)
−0.621584 + 0.783347i \(0.713511\pi\)
\(150\) −180.225 1476.71i −0.0981019 0.803821i
\(151\) 676.556 0.364618 0.182309 0.983241i \(-0.441643\pi\)
0.182309 + 0.983241i \(0.441643\pi\)
\(152\) −591.340 + 591.340i −0.315553 + 0.315553i
\(153\) −659.070 659.070i −0.348253 0.348253i
\(154\) 1101.11i 0.576167i
\(155\) 2541.75 2870.82i 1.31715 1.48768i
\(156\) −1218.29 −0.625267
\(157\) 2211.51 2211.51i 1.12419 1.12419i 0.133086 0.991105i \(-0.457511\pi\)
0.991105 0.133086i \(-0.0424886\pi\)
\(158\) 875.464 + 875.464i 0.440811 + 0.440811i
\(159\) 1527.68 0.761966
\(160\) −2556.45 + 155.424i −1.26316 + 0.0767958i
\(161\) −1314.41 + 1079.81i −0.643415 + 0.528577i
\(162\) 55.3490 + 55.3490i 0.0268434 + 0.0268434i
\(163\) −11.1549 + 11.1549i −0.00536025 + 0.00536025i −0.709782 0.704422i \(-0.751206\pi\)
0.704422 + 0.709782i \(0.251206\pi\)
\(164\) 855.348i 0.407265i
\(165\) −667.567 + 40.5859i −0.314970 + 0.0191491i
\(166\) 4319.90i 2.01981i
\(167\) −2023.17 2023.17i −0.937470 0.937470i 0.0606869 0.998157i \(-0.480671\pi\)
−0.998157 + 0.0606869i \(0.980671\pi\)
\(168\) 232.905 + 232.905i 0.106959 + 0.106959i
\(169\) 1668.67i 0.759521i
\(170\) 1528.92 1726.86i 0.689779 0.779081i
\(171\) 2105.47i 0.941573i
\(172\) −964.312 + 964.312i −0.427489 + 0.427489i
\(173\) 305.721 305.721i 0.134356 0.134356i −0.636731 0.771086i \(-0.719714\pi\)
0.771086 + 0.636731i \(0.219714\pi\)
\(174\) 702.230i 0.305954i
\(175\) 1518.19 + 1187.92i 0.655797 + 0.513135i
\(176\) 1423.38i 0.609609i
\(177\) 194.258 + 194.258i 0.0824933 + 0.0824933i
\(178\) −517.778 517.778i −0.218029 0.218029i
\(179\) 3865.17i 1.61395i −0.590587 0.806974i \(-0.701104\pi\)
0.590587 0.806974i \(-0.298896\pi\)
\(180\) −783.172 + 884.565i −0.324301 + 0.366287i
\(181\) 667.154i 0.273973i 0.990573 + 0.136987i \(0.0437417\pi\)
−0.990573 + 0.136987i \(0.956258\pi\)
\(182\) 2555.38 2555.38i 1.04076 1.04076i
\(183\) −1262.20 1262.20i −0.509863 0.509863i
\(184\) −576.489 + 473.596i −0.230975 + 0.189750i
\(185\) 290.646 + 4780.62i 0.115507 + 1.89988i
\(186\) 4081.61 1.60902
\(187\) −733.187 733.187i −0.286716 0.286716i
\(188\) −1453.41 + 1453.41i −0.563834 + 0.563834i
\(189\) 2144.08 0.825178
\(190\) −5200.45 + 316.170i −1.98568 + 0.120723i
\(191\) 1067.82i 0.404527i 0.979331 + 0.202263i \(0.0648297\pi\)
−0.979331 + 0.202263i \(0.935170\pi\)
\(192\) −585.686 585.686i −0.220147 0.220147i
\(193\) 417.876 417.876i 0.155852 0.155852i −0.624874 0.780726i \(-0.714850\pi\)
0.780726 + 0.624874i \(0.214850\pi\)
\(194\) −5687.91 −2.10499
\(195\) 1643.44 + 1455.06i 0.603533 + 0.534354i
\(196\) −652.633 −0.237840
\(197\) 572.015 + 572.015i 0.206875 + 0.206875i 0.802938 0.596063i \(-0.203269\pi\)
−0.596063 + 0.802938i \(0.703269\pi\)
\(198\) 859.749 + 859.749i 0.308584 + 0.308584i
\(199\) −3406.06 −1.21331 −0.606657 0.794964i \(-0.707490\pi\)
−0.606657 + 0.794964i \(0.707490\pi\)
\(200\) 665.867 + 521.014i 0.235419 + 0.184206i
\(201\) 18.0938i 0.00634944i
\(202\) 3189.41 + 3189.41i 1.11092 + 1.11092i
\(203\) −643.427 643.427i −0.222462 0.222462i
\(204\) 1072.50 0.368089
\(205\) 1021.58 1153.83i 0.348049 0.393109i
\(206\) 3450.05i 1.16688i
\(207\) −183.175 + 1869.41i −0.0615050 + 0.627697i
\(208\) 3303.29 3303.29i 1.10116 1.10116i
\(209\) 2342.24i 0.775196i
\(210\) 124.527 + 2048.25i 0.0409198 + 0.673060i
\(211\) −2577.48 −0.840954 −0.420477 0.907303i \(-0.638137\pi\)
−0.420477 + 0.907303i \(0.638137\pi\)
\(212\) 2122.84 2122.84i 0.687722 0.687722i
\(213\) 1242.57 1242.57i 0.399717 0.399717i
\(214\) 5817.23 1.85821
\(215\) 2452.54 149.106i 0.777962 0.0472975i
\(216\) 940.375 0.296224
\(217\) −3739.83 + 3739.83i −1.16994 + 1.16994i
\(218\) −70.4721 70.4721i −0.0218944 0.0218944i
\(219\) 1364.42i 0.420999i
\(220\) −871.244 + 984.039i −0.266997 + 0.301563i
\(221\) 3403.07i 1.03581i
\(222\) −3605.06 + 3605.06i −1.08989 + 1.08989i
\(223\) −1070.51 + 1070.51i −0.321465 + 0.321465i −0.849329 0.527864i \(-0.822993\pi\)
0.527864 + 0.849329i \(0.322993\pi\)
\(224\) 3532.77 1.05376
\(225\) 2112.94 257.873i 0.626057 0.0764069i
\(226\) 376.947i 0.110947i
\(227\) −1638.67 + 1638.67i −0.479129 + 0.479129i −0.904853 0.425724i \(-0.860019\pi\)
0.425724 + 0.904853i \(0.360019\pi\)
\(228\) −1713.11 1713.11i −0.497603 0.497603i
\(229\) −2319.00 −0.669188 −0.334594 0.942362i \(-0.608599\pi\)
−0.334594 + 0.942362i \(0.608599\pi\)
\(230\) −4644.91 171.714i −1.33164 0.0492283i
\(231\) 922.514 0.262757
\(232\) −282.202 282.202i −0.0798598 0.0798598i
\(233\) 597.533 597.533i 0.168007 0.168007i −0.618096 0.786103i \(-0.712096\pi\)
0.786103 + 0.618096i \(0.212096\pi\)
\(234\) 3990.50i 1.11482i
\(235\) 3696.47 224.733i 1.02609 0.0623828i
\(236\) 539.876 0.148911
\(237\) 733.468 733.468i 0.201029 0.201029i
\(238\) −2249.58 + 2249.58i −0.612684 + 0.612684i
\(239\) 226.067i 0.0611845i 0.999532 + 0.0305922i \(0.00973933\pi\)
−0.999532 + 0.0305922i \(0.990261\pi\)
\(240\) 160.973 + 2647.73i 0.0432948 + 0.712125i
\(241\) 5848.33i 1.56317i −0.623799 0.781585i \(-0.714412\pi\)
0.623799 0.781585i \(-0.285588\pi\)
\(242\) −2590.80 2590.80i −0.688195 0.688195i
\(243\) 2700.72 2700.72i 0.712967 0.712967i
\(244\) −3507.88 −0.920365
\(245\) 880.379 + 779.466i 0.229573 + 0.203258i
\(246\) 1640.47 0.425174
\(247\) 5435.72 5435.72i 1.40027 1.40027i
\(248\) −1640.26 + 1640.26i −0.419987 + 0.419987i
\(249\) −3619.23 −0.921123
\(250\) 954.232 + 5180.19i 0.241404 + 1.31050i
\(251\) 6646.18i 1.67133i −0.549241 0.835664i \(-0.685083\pi\)
0.549241 0.835664i \(-0.314917\pi\)
\(252\) 1152.33 1152.33i 0.288055 0.288055i
\(253\) −203.774 + 2079.64i −0.0506370 + 0.516782i
\(254\) 2963.87i 0.732164i
\(255\) −1446.77 1280.93i −0.355295 0.314569i
\(256\) 5279.45 1.28893
\(257\) 1313.92 + 1313.92i 0.318910 + 0.318910i 0.848348 0.529438i \(-0.177597\pi\)
−0.529438 + 0.848348i \(0.677597\pi\)
\(258\) 1849.46 + 1849.46i 0.446287 + 0.446287i
\(259\) 6606.37i 1.58494i
\(260\) 4305.63 261.768i 1.02701 0.0624390i
\(261\) −1004.78 −0.238292
\(262\) −1129.89 1129.89i −0.266431 0.266431i
\(263\) 4634.72 + 4634.72i 1.08665 + 1.08665i 0.995871 + 0.0907786i \(0.0289356\pi\)
0.0907786 + 0.995871i \(0.471064\pi\)
\(264\) 404.608 0.0943253
\(265\) −5399.02 + 328.243i −1.25154 + 0.0760898i
\(266\) 7186.52 1.65652
\(267\) −433.797 + 433.797i −0.0994305 + 0.0994305i
\(268\) −25.1429 25.1429i −0.00573076 0.00573076i
\(269\) 4119.24i 0.933661i −0.884347 0.466830i \(-0.845396\pi\)
0.884347 0.466830i \(-0.154604\pi\)
\(270\) 4386.38 + 3883.59i 0.988691 + 0.875363i
\(271\) 5232.41 1.17287 0.586433 0.809998i \(-0.300532\pi\)
0.586433 + 0.809998i \(0.300532\pi\)
\(272\) −2907.99 + 2907.99i −0.648245 + 0.648245i
\(273\) −2140.91 2140.91i −0.474630 0.474630i
\(274\) −3474.26 −0.766014
\(275\) 2350.56 286.872i 0.515432 0.0629057i
\(276\) −1372.01 1670.09i −0.299221 0.364229i
\(277\) −6408.30 6408.30i −1.39003 1.39003i −0.825229 0.564798i \(-0.808954\pi\)
−0.564798 0.825229i \(-0.691046\pi\)
\(278\) −2556.78 + 2556.78i −0.551603 + 0.551603i
\(279\) 5840.14i 1.25319i
\(280\) −873.163 773.077i −0.186362 0.165001i
\(281\) 2894.08i 0.614400i −0.951645 0.307200i \(-0.900608\pi\)
0.951645 0.307200i \(-0.0993921\pi\)
\(282\) 2787.50 + 2787.50i 0.588628 + 0.588628i
\(283\) 1464.96 + 1464.96i 0.307714 + 0.307714i 0.844022 0.536308i \(-0.180181\pi\)
−0.536308 + 0.844022i \(0.680181\pi\)
\(284\) 3453.32i 0.721538i
\(285\) 264.889 + 4356.96i 0.0550549 + 0.905558i
\(286\) 4439.26i 0.917828i
\(287\) −1503.11 + 1503.11i −0.309148 + 0.309148i
\(288\) 2758.40 2758.40i 0.564376 0.564376i
\(289\) 1917.17i 0.390225i
\(290\) −150.884 2481.78i −0.0305525 0.502535i
\(291\) 4765.36i 0.959966i
\(292\) 1895.97 + 1895.97i 0.379977 + 0.379977i
\(293\) 1164.58 + 1164.58i 0.232202 + 0.232202i 0.813611 0.581409i \(-0.197498\pi\)
−0.581409 + 0.813611i \(0.697498\pi\)
\(294\) 1251.69i 0.248299i
\(295\) −728.274 644.796i −0.143735 0.127259i
\(296\) 2897.50i 0.568966i
\(297\) 1862.36 1862.36i 0.363856 0.363856i
\(298\) 6025.89 + 6025.89i 1.17138 + 1.17138i
\(299\) 5299.20 4353.39i 1.02495 0.842017i
\(300\) −1509.38 + 1929.01i −0.290479 + 0.371238i
\(301\) −3389.17 −0.648999
\(302\) −1803.08 1803.08i −0.343562 0.343562i
\(303\) 2672.10 2672.10i 0.506628 0.506628i
\(304\) 9289.85 1.75266
\(305\) 4732.01 + 4189.61i 0.888374 + 0.786545i
\(306\) 3512.96i 0.656283i
\(307\) 1757.91 + 1757.91i 0.326806 + 0.326806i 0.851371 0.524565i \(-0.175772\pi\)
−0.524565 + 0.851371i \(0.675772\pi\)
\(308\) 1281.91 1281.91i 0.237155 0.237155i
\(309\) −2890.47 −0.532146
\(310\) −14425.0 + 876.992i −2.64285 + 0.160677i
\(311\) 2236.39 0.407762 0.203881 0.978996i \(-0.434644\pi\)
0.203881 + 0.978996i \(0.434644\pi\)
\(312\) −938.988 938.988i −0.170384 0.170384i
\(313\) −2726.31 2726.31i −0.492333 0.492333i 0.416708 0.909041i \(-0.363184\pi\)
−0.909041 + 0.416708i \(0.863184\pi\)
\(314\) −11787.8 −2.11854
\(315\) −2930.72 + 178.178i −0.524214 + 0.0318704i
\(316\) 2038.43i 0.362883i
\(317\) −2582.03 2582.03i −0.457480 0.457480i 0.440348 0.897827i \(-0.354855\pi\)
−0.897827 + 0.440348i \(0.854855\pi\)
\(318\) −4071.39 4071.39i −0.717964 0.717964i
\(319\) −1117.77 −0.196186
\(320\) 2195.74 + 1944.06i 0.383580 + 0.339613i
\(321\) 4873.71i 0.847426i
\(322\) 6380.80 + 625.224i 1.10431 + 0.108206i
\(323\) −4785.23 + 4785.23i −0.824327 + 0.824327i
\(324\) 128.875i 0.0220979i
\(325\) −6120.78 4789.27i −1.04468 0.817418i
\(326\) 59.4577 0.0101014
\(327\) −59.0419 + 59.0419i −0.00998478 + 0.00998478i
\(328\) −659.250 + 659.250i −0.110979 + 0.110979i
\(329\) −5108.16 −0.855994
\(330\) 1887.29 + 1670.96i 0.314824 + 0.278738i
\(331\) −6499.87 −1.07935 −0.539676 0.841873i \(-0.681453\pi\)
−0.539676 + 0.841873i \(0.681453\pi\)
\(332\) −5029.24 + 5029.24i −0.831371 + 0.831371i
\(333\) −5158.27 5158.27i −0.848864 0.848864i
\(334\) 10783.9i 1.76666i
\(335\) 3.88770 + 63.9460i 0.000634053 + 0.0104291i
\(336\) 3658.90i 0.594076i
\(337\) −2735.52 + 2735.52i −0.442176 + 0.442176i −0.892743 0.450567i \(-0.851222\pi\)
0.450567 + 0.892743i \(0.351222\pi\)
\(338\) −4447.15 + 4447.15i −0.715659 + 0.715659i
\(339\) 315.808 0.0505968
\(340\) −3790.38 + 230.442i −0.604594 + 0.0367573i
\(341\) 6496.90i 1.03175i
\(342\) 5611.26 5611.26i 0.887199 0.887199i
\(343\) −4887.21 4887.21i −0.769343 0.769343i
\(344\) −1486.47 −0.232979
\(345\) −143.863 + 3891.53i −0.0224502 + 0.607284i
\(346\) −1629.55 −0.253194
\(347\) 6733.74 + 6733.74i 1.04175 + 1.04175i 0.999090 + 0.0426573i \(0.0135824\pi\)
0.0426573 + 0.999090i \(0.486418\pi\)
\(348\) 817.538 817.538i 0.125933 0.125933i
\(349\) 6515.26i 0.999295i 0.866229 + 0.499648i \(0.166537\pi\)
−0.866229 + 0.499648i \(0.833463\pi\)
\(350\) −880.190 7212.04i −0.134423 1.10143i
\(351\) −8644.12 −1.31450
\(352\) 3068.60 3068.60i 0.464650 0.464650i
\(353\) −639.089 + 639.089i −0.0963605 + 0.0963605i −0.753644 0.657283i \(-0.771706\pi\)
0.657283 + 0.753644i \(0.271706\pi\)
\(354\) 1035.43i 0.155459i
\(355\) −4124.44 + 4658.41i −0.616627 + 0.696458i
\(356\) 1205.60i 0.179484i
\(357\) 1884.71 + 1884.71i 0.279410 + 0.279410i
\(358\) −10301.0 + 10301.0i −1.52075 + 1.52075i
\(359\) 827.280 0.121622 0.0608108 0.998149i \(-0.480631\pi\)
0.0608108 + 0.998149i \(0.480631\pi\)
\(360\) −1285.39 + 78.1475i −0.188183 + 0.0114409i
\(361\) 8427.91 1.22874
\(362\) 1778.02 1778.02i 0.258152 0.258152i
\(363\) −2170.59 + 2170.59i −0.313847 + 0.313847i
\(364\) −5949.96 −0.856766
\(365\) −293.164 4822.04i −0.0420408 0.691499i
\(366\) 6727.78i 0.960837i
\(367\) 23.1366 23.1366i 0.00329079 0.00329079i −0.705459 0.708750i \(-0.749259\pi\)
0.708750 + 0.705459i \(0.249259\pi\)
\(368\) 8248.33 + 808.214i 1.16841 + 0.114487i
\(369\) 2347.26i 0.331148i
\(370\) 11966.2 13515.4i 1.68133 1.89900i
\(371\) 7460.93 1.04408
\(372\) −4751.82 4751.82i −0.662287 0.662287i
\(373\) 5882.41 + 5882.41i 0.816567 + 0.816567i 0.985609 0.169042i \(-0.0540672\pi\)
−0.169042 + 0.985609i \(0.554067\pi\)
\(374\) 3908.02i 0.540317i
\(375\) 4339.99 799.461i 0.597643 0.110091i
\(376\) −2240.40 −0.307287
\(377\) 2594.06 + 2594.06i 0.354379 + 0.354379i
\(378\) −5714.16 5714.16i −0.777525 0.777525i
\(379\) 7914.92 1.07272 0.536362 0.843988i \(-0.319798\pi\)
0.536362 + 0.843988i \(0.319798\pi\)
\(380\) 6422.46 + 5686.28i 0.867013 + 0.767632i
\(381\) −2483.14 −0.333899
\(382\) 2845.83 2845.83i 0.381166 0.381166i
\(383\) −5318.45 5318.45i −0.709556 0.709556i 0.256886 0.966442i \(-0.417304\pi\)
−0.966442 + 0.256886i \(0.917304\pi\)
\(384\) 2665.05i 0.354168i
\(385\) −3260.29 + 198.215i −0.431584 + 0.0262389i
\(386\) −2227.35 −0.293703
\(387\) −2646.28 + 2646.28i −0.347591 + 0.347591i
\(388\) 6621.87 + 6621.87i 0.866429 + 0.866429i
\(389\) −2642.55 −0.344428 −0.172214 0.985060i \(-0.555092\pi\)
−0.172214 + 0.985060i \(0.555092\pi\)
\(390\) −502.045 8257.77i −0.0651847 1.07218i
\(391\) −4665.05 + 3832.43i −0.603381 + 0.495688i
\(392\) −503.010 503.010i −0.0648108 0.0648108i
\(393\) −946.630 + 946.630i −0.121504 + 0.121504i
\(394\) 3048.94i 0.389857i
\(395\) −2434.58 + 2749.78i −0.310120 + 0.350269i
\(396\) 2001.84i 0.254031i
\(397\) 7988.94 + 7988.94i 1.00996 + 1.00996i 0.999950 + 0.0100085i \(0.00318586\pi\)
0.0100085 + 0.999950i \(0.496814\pi\)
\(398\) 9077.46 + 9077.46i 1.14325 + 1.14325i
\(399\) 6020.90i 0.755444i
\(400\) −1137.80 9322.85i −0.142225 1.16536i
\(401\) 10087.1i 1.25618i 0.778141 + 0.628090i \(0.216163\pi\)
−0.778141 + 0.628090i \(0.783837\pi\)
\(402\) −48.2215 + 48.2215i −0.00598277 + 0.00598277i
\(403\) 15077.6 15077.6i 1.86369 1.86369i
\(404\) 7426.24i 0.914527i
\(405\) −153.920 + 173.848i −0.0188849 + 0.0213298i
\(406\) 3429.58i 0.419230i
\(407\) −5738.35 5738.35i −0.698868 0.698868i
\(408\) 826.620 + 826.620i 0.100303 + 0.100303i
\(409\) 378.591i 0.0457705i −0.999738 0.0228853i \(-0.992715\pi\)
0.999738 0.0228853i \(-0.00728524\pi\)
\(410\) −5797.67 + 352.479i −0.698357 + 0.0424578i
\(411\) 2910.75i 0.349335i
\(412\) −4016.56 + 4016.56i −0.480295 + 0.480295i
\(413\) 948.725 + 948.725i 0.113036 + 0.113036i
\(414\) 5470.33 4493.98i 0.649401 0.533495i
\(415\) 12790.9 777.643i 1.51296 0.0919832i
\(416\) −14242.8 −1.67863
\(417\) 2142.09 + 2142.09i 0.251555 + 0.251555i
\(418\) 6242.27 6242.27i 0.730430 0.730430i
\(419\) −2865.04 −0.334049 −0.167025 0.985953i \(-0.553416\pi\)
−0.167025 + 0.985953i \(0.553416\pi\)
\(420\) 2239.60 2529.55i 0.260194 0.293879i
\(421\) 8714.92i 1.00888i −0.863446 0.504441i \(-0.831699\pi\)
0.863446 0.504441i \(-0.168301\pi\)
\(422\) 6869.23 + 6869.23i 0.792390 + 0.792390i
\(423\) −3988.47 + 3988.47i −0.458454 + 0.458454i
\(424\) 3272.31 0.374805
\(425\) 5388.31 + 4216.14i 0.614992 + 0.481207i
\(426\) −6623.13 −0.753267
\(427\) −6164.41 6164.41i −0.698634 0.698634i
\(428\) −6772.43 6772.43i −0.764855 0.764855i
\(429\) −3719.23 −0.418569
\(430\) −6933.62 6138.86i −0.777602 0.688470i
\(431\) 10921.2i 1.22054i 0.792192 + 0.610272i \(0.208940\pi\)
−0.792192 + 0.610272i \(0.791060\pi\)
\(432\) −7386.57 7386.57i −0.822654 0.822654i
\(433\) −4506.50 4506.50i −0.500158 0.500158i 0.411329 0.911487i \(-0.365065\pi\)
−0.911487 + 0.411329i \(0.865065\pi\)
\(434\) 19934.0 2.20475
\(435\) −2079.25 + 126.411i −0.229178 + 0.0139333i
\(436\) 164.088i 0.0180238i
\(437\) 13573.0 + 1329.96i 1.48578 + 0.145584i
\(438\) 3636.29 3636.29i 0.396687 0.396687i
\(439\) 3381.56i 0.367638i 0.982960 + 0.183819i \(0.0588461\pi\)
−0.982960 + 0.183819i \(0.941154\pi\)
\(440\) −1429.94 + 86.9356i −0.154931 + 0.00941930i
\(441\) −1790.97 −0.193388
\(442\) 9069.48 9069.48i 0.975998 0.975998i
\(443\) 6813.81 6813.81i 0.730776 0.730776i −0.239997 0.970774i \(-0.577147\pi\)
0.970774 + 0.239997i \(0.0771466\pi\)
\(444\) 8394.04 0.897215
\(445\) 1439.89 1626.31i 0.153387 0.173246i
\(446\) 5706.01 0.605802
\(447\) 5048.52 5048.52i 0.534199 0.534199i
\(448\) −2860.40 2860.40i −0.301655 0.301655i
\(449\) 7966.78i 0.837363i −0.908133 0.418681i \(-0.862492\pi\)
0.908133 0.418681i \(-0.137508\pi\)
\(450\) −6318.44 4943.93i −0.661898 0.517909i
\(451\) 2611.22i 0.272633i
\(452\) 438.842 438.842i 0.0456668 0.0456668i
\(453\) −1510.63 + 1510.63i −0.156679 + 0.156679i
\(454\) 8734.39 0.902919
\(455\) 8026.29 + 7106.28i 0.826986 + 0.732193i
\(456\) 2640.72i 0.271191i
\(457\) 2700.58 2700.58i 0.276429 0.276429i −0.555253 0.831682i \(-0.687378\pi\)
0.831682 + 0.555253i \(0.187378\pi\)
\(458\) 6180.35 + 6180.35i 0.630543 + 0.630543i
\(459\) 7609.69 0.773834
\(460\) 5207.70 + 5607.52i 0.527849 + 0.568374i
\(461\) −5487.65 −0.554415 −0.277207 0.960810i \(-0.589409\pi\)
−0.277207 + 0.960810i \(0.589409\pi\)
\(462\) −2458.58 2458.58i −0.247584 0.247584i
\(463\) 3096.37 3096.37i 0.310801 0.310801i −0.534419 0.845220i \(-0.679470\pi\)
0.845220 + 0.534419i \(0.179470\pi\)
\(464\) 4433.35i 0.443562i
\(465\) 734.749 + 12085.3i 0.0732756 + 1.20526i
\(466\) −3184.96 −0.316610
\(467\) 1288.36 1288.36i 0.127662 0.127662i −0.640389 0.768051i \(-0.721227\pi\)
0.768051 + 0.640389i \(0.221227\pi\)
\(468\) −4645.75 + 4645.75i −0.458867 + 0.458867i
\(469\) 88.3672i 0.00870025i
\(470\) −10450.3 9252.48i −1.02561 0.908053i
\(471\) 9875.85i 0.966146i
\(472\) 416.103 + 416.103i 0.0405778 + 0.0405778i
\(473\) −2943.87 + 2943.87i −0.286172 + 0.286172i
\(474\) −3909.52 −0.378840
\(475\) −1872.31 15341.2i −0.180858 1.48190i
\(476\) 5237.94 0.504371
\(477\) 5825.52 5825.52i 0.559187 0.559187i
\(478\) 602.490 602.490i 0.0576511 0.0576511i
\(479\) −12639.3 −1.20564 −0.602822 0.797876i \(-0.705957\pi\)
−0.602822 + 0.797876i \(0.705957\pi\)
\(480\) 5361.08 6055.14i 0.509789 0.575788i
\(481\) 26634.4i 2.52479i
\(482\) −15586.3 + 15586.3i −1.47290 + 1.47290i
\(483\) 523.816 5345.87i 0.0493467 0.503614i
\(484\) 6032.44i 0.566532i
\(485\) −1023.90 16841.4i −0.0958620 1.57676i
\(486\) −14395.3 −1.34359
\(487\) 4365.88 + 4365.88i 0.406236 + 0.406236i 0.880424 0.474188i \(-0.157258\pi\)
−0.474188 + 0.880424i \(0.657258\pi\)
\(488\) −2703.66 2703.66i −0.250797 0.250797i
\(489\) 49.8140i 0.00460668i
\(490\) −268.943 4423.64i −0.0247951 0.407836i
\(491\) −3537.80 −0.325170 −0.162585 0.986695i \(-0.551983\pi\)
−0.162585 + 0.986695i \(0.551983\pi\)
\(492\) −1909.84 1909.84i −0.175005 0.175005i
\(493\) −2283.63 2283.63i −0.208620 0.208620i
\(494\) −28973.4 −2.63881
\(495\) −2390.88 + 2700.42i −0.217095 + 0.245201i
\(496\) 25768.2 2.33272
\(497\) 6068.53 6068.53i 0.547708 0.547708i
\(498\) 9645.58 + 9645.58i 0.867930 + 0.867930i
\(499\) 10053.3i 0.901902i 0.892549 + 0.450951i \(0.148915\pi\)
−0.892549 + 0.450951i \(0.851085\pi\)
\(500\) 4919.87 7141.71i 0.440047 0.638774i
\(501\) 9034.77 0.805676
\(502\) −17712.7 + 17712.7i −1.57481 + 1.57481i
\(503\) 4941.64 + 4941.64i 0.438046 + 0.438046i 0.891354 0.453308i \(-0.149756\pi\)
−0.453308 + 0.891354i \(0.649756\pi\)
\(504\) 1776.29 0.156988
\(505\) −8869.45 + 10017.7i −0.781556 + 0.882739i
\(506\) 6085.50 4999.35i 0.534651 0.439226i
\(507\) 3725.84 + 3725.84i 0.326372 + 0.326372i
\(508\) −3450.54 + 3450.54i −0.301364 + 0.301364i
\(509\) 15010.7i 1.30715i 0.756864 + 0.653573i \(0.226731\pi\)
−0.756864 + 0.653573i \(0.773269\pi\)
\(510\) 441.966 + 7269.57i 0.0383737 + 0.631181i
\(511\) 6663.60i 0.576869i
\(512\) −9295.90 9295.90i −0.802392 0.802392i
\(513\) −12155.0 12155.0i −1.04611 1.04611i
\(514\) 7003.41i 0.600987i
\(515\) 10215.3 621.059i 0.874061 0.0531400i
\(516\) 4306.28i 0.367390i
\(517\) −4437.00 + 4437.00i −0.377445 + 0.377445i
\(518\) −17606.6 + 17606.6i −1.49341 + 1.49341i
\(519\) 1365.25i 0.115467i
\(520\) 3520.27 + 3116.76i 0.296873 + 0.262844i
\(521\) 23063.8i 1.93943i −0.244236 0.969716i \(-0.578537\pi\)
0.244236 0.969716i \(-0.421463\pi\)
\(522\) 2677.83 + 2677.83i 0.224531 + 0.224531i
\(523\) 4272.34 + 4272.34i 0.357202 + 0.357202i 0.862781 0.505579i \(-0.168721\pi\)
−0.505579 + 0.862781i \(0.668721\pi\)
\(524\) 2630.85i 0.219330i
\(525\) −6042.29 + 737.428i −0.502299 + 0.0613028i
\(526\) 24703.9i 2.04779i
\(527\) −13273.3 + 13273.3i −1.09714 + 1.09714i
\(528\) −3178.16 3178.16i −0.261954 0.261954i
\(529\) 11935.6 + 2361.70i 0.980980 + 0.194107i
\(530\) 15263.7 + 13514.1i 1.25097 + 1.10757i
\(531\) 1481.54 0.121079
\(532\) −8366.56 8366.56i −0.681835 0.681835i
\(533\) 6059.96 6059.96i 0.492469 0.492469i
\(534\) 2312.22 0.187377
\(535\) 1047.18 + 17224.4i 0.0846238 + 1.39191i
\(536\) 38.7572i 0.00312324i
\(537\) 8630.26 + 8630.26i 0.693526 + 0.693526i
\(538\) −10978.2 + 10978.2i −0.879743 + 0.879743i
\(539\) −1992.37 −0.159216
\(540\) −585.346 9627.92i −0.0466468 0.767259i
\(541\) −19660.0 −1.56238 −0.781192 0.624290i \(-0.785388\pi\)
−0.781192 + 0.624290i \(0.785388\pi\)
\(542\) −13944.9 13944.9i −1.10513 1.10513i
\(543\) −1489.64 1489.64i −0.117728 0.117728i
\(544\) 12538.4 0.988197
\(545\) 195.976 221.348i 0.0154031 0.0173973i
\(546\) 11411.4i 0.894441i
\(547\) −9956.97 9956.97i −0.778299 0.778299i 0.201243 0.979541i \(-0.435502\pi\)
−0.979541 + 0.201243i \(0.935502\pi\)
\(548\) 4044.74 + 4044.74i 0.315297 + 0.315297i
\(549\) −9626.38 −0.748350
\(550\) −7028.99 5499.90i −0.544940 0.426394i
\(551\) 7295.29i 0.564047i
\(552\) 229.742 2344.66i 0.0177146 0.180789i
\(553\) 3582.15 3582.15i 0.275458 0.275458i
\(554\) 34157.4i 2.61951i
\(555\) −11323.3 10025.3i −0.866029 0.766761i
\(556\) 5953.22 0.454088
\(557\) −9154.53 + 9154.53i −0.696391 + 0.696391i −0.963630 0.267239i \(-0.913889\pi\)
0.267239 + 0.963630i \(0.413889\pi\)
\(558\) 15564.5 15564.5i 1.18082 1.18082i
\(559\) 13663.9 1.03385
\(560\) 786.167 + 12931.1i 0.0593243 + 0.975782i
\(561\) 3274.16 0.246408
\(562\) −7712.99 + 7712.99i −0.578919 + 0.578919i
\(563\) 2226.16 + 2226.16i 0.166645 + 0.166645i 0.785503 0.618858i \(-0.212404\pi\)
−0.618858 + 0.785503i \(0.712404\pi\)
\(564\) 6490.42i 0.484568i
\(565\) −1116.11 + 67.8558i −0.0831063 + 0.00505259i
\(566\) 7808.52i 0.579888i
\(567\) 226.472 226.472i 0.0167741 0.0167741i
\(568\) 2661.61 2661.61i 0.196617 0.196617i
\(569\) 7597.95 0.559794 0.279897 0.960030i \(-0.409700\pi\)
0.279897 + 0.960030i \(0.409700\pi\)
\(570\) 10905.7 12317.6i 0.801388 0.905139i
\(571\) 11583.9i 0.848988i −0.905431 0.424494i \(-0.860452\pi\)
0.905431 0.424494i \(-0.139548\pi\)
\(572\) −5168.19 + 5168.19i −0.377785 + 0.377785i
\(573\) −2384.25 2384.25i −0.173828 0.173828i
\(574\) 8011.82 0.582591
\(575\) −327.717 13784.1i −0.0237683 0.999717i
\(576\) −4466.82 −0.323121
\(577\) −17653.1 17653.1i −1.27367 1.27367i −0.944146 0.329527i \(-0.893111\pi\)
−0.329527 0.944146i \(-0.606889\pi\)
\(578\) 5109.44 5109.44i 0.367690 0.367690i
\(579\) 1866.09i 0.133941i
\(580\) −2713.63 + 3064.95i −0.194272 + 0.219423i
\(581\) −17675.8 −1.26216
\(582\) 12700.1 12700.1i 0.904530 0.904530i
\(583\) 6480.64 6480.64i 0.460378 0.460378i
\(584\) 2922.60i 0.207086i
\(585\) 11815.6 718.347i 0.835066 0.0507692i
\(586\) 6207.40i 0.437586i
\(587\) 316.403 + 316.403i 0.0222476 + 0.0222476i 0.718143 0.695895i \(-0.244992\pi\)
−0.695895 + 0.718143i \(0.744992\pi\)
\(588\) 1457.22 1457.22i 0.102202 0.102202i
\(589\) 42402.8 2.96635
\(590\) 222.477 + 3659.35i 0.0155241 + 0.255344i
\(591\) −2554.42 −0.177792
\(592\) −22759.6 + 22759.6i −1.58009 + 1.58009i
\(593\) −15783.6 + 15783.6i −1.09301 + 1.09301i −0.0978059 + 0.995206i \(0.531182\pi\)
−0.995206 + 0.0978059i \(0.968818\pi\)
\(594\) −9926.74 −0.685689
\(595\) −7065.80 6255.88i −0.486839 0.431036i
\(596\) 14030.7i 0.964296i
\(597\) 7605.14 7605.14i 0.521370 0.521370i
\(598\) −25725.0 2520.67i −1.75916 0.172371i
\(599\) 3848.82i 0.262535i −0.991347 0.131268i \(-0.958095\pi\)
0.991347 0.131268i \(-0.0419047\pi\)
\(600\) −2650.10 + 323.430i −0.180316 + 0.0220066i
\(601\) 11585.6 0.786335 0.393168 0.919467i \(-0.371379\pi\)
0.393168 + 0.919467i \(0.371379\pi\)
\(602\) 9032.45 + 9032.45i 0.611520 + 0.611520i
\(603\) −68.9974 68.9974i −0.00465969 0.00465969i
\(604\) 4198.30i 0.282825i
\(605\) 7204.78 8137.55i 0.484159 0.546840i
\(606\) −14242.8 −0.954743
\(607\) −3419.34 3419.34i −0.228644 0.228644i 0.583482 0.812126i \(-0.301690\pi\)
−0.812126 + 0.583482i \(0.801690\pi\)
\(608\) −20027.6 20027.6i −1.33590 1.33590i
\(609\) 2873.32 0.191187
\(610\) −1445.56 23776.9i −0.0959490 1.57820i
\(611\) 20594.2 1.36359
\(612\) 4089.80 4089.80i 0.270131 0.270131i
\(613\) −15696.2 15696.2i −1.03420 1.03420i −0.999394 0.0348041i \(-0.988919\pi\)
−0.0348041 0.999394i \(-0.511081\pi\)
\(614\) 9370.00i 0.615867i
\(615\) 295.309 + 4857.32i 0.0193626 + 0.318481i
\(616\) 1976.04 0.129248
\(617\) −7730.86 + 7730.86i −0.504429 + 0.504429i −0.912811 0.408382i \(-0.866093\pi\)
0.408382 + 0.912811i \(0.366093\pi\)
\(618\) 7703.37 + 7703.37i 0.501416 + 0.501416i
\(619\) −18911.8 −1.22799 −0.613997 0.789308i \(-0.710439\pi\)
−0.613997 + 0.789308i \(0.710439\pi\)
\(620\) 17814.6 + 15772.6i 1.15396 + 1.02168i
\(621\) −9734.73 11849.7i −0.629052 0.765719i
\(622\) −5960.18 5960.18i −0.384214 0.384214i
\(623\) −2118.60 + 2118.60i −0.136244 + 0.136244i
\(624\) 14751.3i 0.946356i
\(625\) −15166.4 + 3757.92i −0.970647 + 0.240507i
\(626\) 14531.7i 0.927803i
\(627\) −5229.81 5229.81i −0.333108 0.333108i
\(628\) 13723.3 + 13723.3i 0.872007 + 0.872007i
\(629\) 23447.1i 1.48632i
\(630\) 8285.49 + 7335.77i 0.523971 + 0.463911i
\(631\) 5284.78i 0.333414i 0.986007 + 0.166707i \(0.0533133\pi\)
−0.986007 + 0.166707i \(0.946687\pi\)
\(632\) 1571.10 1571.10i 0.0988846 0.0988846i
\(633\) 5755.08 5755.08i 0.361364 0.361364i
\(634\) 13762.7i 0.862122i
\(635\) 8775.78 533.539i 0.548435 0.0333430i
\(636\) 9479.85i 0.591039i
\(637\) 4623.77 + 4623.77i 0.287599 + 0.287599i
\(638\) 2978.97 + 2978.97i 0.184856 + 0.184856i
\(639\) 9476.66i 0.586683i
\(640\) 572.624 + 9418.67i 0.0353671 + 0.581728i
\(641\) 15200.5i 0.936633i 0.883561 + 0.468316i \(0.155139\pi\)
−0.883561 + 0.468316i \(0.844861\pi\)
\(642\) −12988.9 + 12988.9i −0.798488 + 0.798488i
\(643\) −7121.12 7121.12i −0.436749 0.436749i 0.454168 0.890916i \(-0.349937\pi\)
−0.890916 + 0.454168i \(0.849937\pi\)
\(644\) −6700.66 8156.44i −0.410005 0.499082i
\(645\) −5143.17 + 5809.02i −0.313972 + 0.354620i
\(646\) 25506.2 1.55345
\(647\) −8196.32 8196.32i −0.498038 0.498038i 0.412789 0.910827i \(-0.364555\pi\)
−0.910827 + 0.412789i \(0.864555\pi\)
\(648\) 99.3288 99.3288i 0.00602161 0.00602161i
\(649\) 1648.14 0.0996845
\(650\) 3548.60 + 29076.3i 0.214135 + 1.75456i
\(651\) 16700.8i 1.00546i
\(652\) −69.2208 69.2208i −0.00415782 0.00415782i
\(653\) 18159.3 18159.3i 1.08825 1.08825i 0.0925400 0.995709i \(-0.470501\pi\)
0.995709 0.0925400i \(-0.0294986\pi\)
\(654\) 314.704 0.0188164
\(655\) 3142.13 3548.92i 0.187440 0.211707i
\(656\) 10356.7 0.616405
\(657\) 5202.96 + 5202.96i 0.308960 + 0.308960i
\(658\) 13613.7 + 13613.7i 0.806562 + 0.806562i
\(659\) 1528.01 0.0903230 0.0451615 0.998980i \(-0.485620\pi\)
0.0451615 + 0.998980i \(0.485620\pi\)
\(660\) −251.852 4142.53i −0.0148535 0.244315i
\(661\) 29321.0i 1.72535i −0.505759 0.862675i \(-0.668788\pi\)
0.505759 0.862675i \(-0.331212\pi\)
\(662\) 17322.7 + 17322.7i 1.01702 + 1.01702i
\(663\) −7598.46 7598.46i −0.445098 0.445098i
\(664\) −7752.46 −0.453093
\(665\) 1293.68 + 21278.7i 0.0754385 + 1.24083i
\(666\) 27494.5i 1.59969i
\(667\) −634.688 + 6477.38i −0.0368444 + 0.376020i
\(668\) 12554.6 12554.6i 0.727173 0.727173i
\(669\) 4780.53i 0.276272i
\(670\) 160.061 180.783i 0.00922938 0.0104243i
\(671\) −10708.9 −0.616116
\(672\) −7888.06 + 7888.06i −0.452810 + 0.452810i
\(673\) 9123.62 9123.62i 0.522570 0.522570i −0.395777 0.918347i \(-0.629525\pi\)
0.918347 + 0.395777i \(0.129525\pi\)
\(674\) 14580.8 0.833282
\(675\) −10709.4 + 13686.8i −0.610675 + 0.780454i
\(676\) 10354.8 0.589142
\(677\) 19862.8 19862.8i 1.12760 1.12760i 0.137038 0.990566i \(-0.456242\pi\)
0.990566 0.137038i \(-0.0437581\pi\)
\(678\) −841.656 841.656i −0.0476749 0.0476749i
\(679\) 23273.3i 1.31538i
\(680\) −3099.00 2743.78i −0.174767 0.154734i
\(681\) 7317.72i 0.411771i
\(682\) 17314.8 17314.8i 0.972169 0.972169i
\(683\) −9499.06 + 9499.06i −0.532169 + 0.532169i −0.921217 0.389048i \(-0.872804\pi\)
0.389048 + 0.921217i \(0.372804\pi\)
\(684\) −13065.3 −0.730356
\(685\) −625.416 10287.0i −0.0348846 0.573791i
\(686\) 26049.7i 1.44983i
\(687\) 5177.93 5177.93i 0.287555 0.287555i
\(688\) 11676.1 + 11676.1i 0.647014 + 0.647014i
\(689\) −30079.7 −1.66320
\(690\) 10754.7 9987.86i 0.593368 0.551060i
\(691\) −13891.8 −0.764791 −0.382395 0.923999i \(-0.624901\pi\)
−0.382395 + 0.923999i \(0.624901\pi\)
\(692\) 1897.13 + 1897.13i 0.104217 + 0.104217i
\(693\) 3517.84 3517.84i 0.192831 0.192831i
\(694\) 35892.1i 1.96318i
\(695\) −8030.69 7110.18i −0.438304 0.388064i
\(696\) 1260.22 0.0686328
\(697\) −5334.77 + 5334.77i −0.289912 + 0.289912i
\(698\) 17363.8 17363.8i 0.941588 0.941588i
\(699\) 2668.38i 0.144388i
\(700\) −7371.55 + 9420.99i −0.398027 + 0.508686i
\(701\) 18088.4i 0.974591i 0.873237 + 0.487295i \(0.162016\pi\)
−0.873237 + 0.487295i \(0.837984\pi\)
\(702\) 23037.4 + 23037.4i 1.23859 + 1.23859i
\(703\) −37452.1 + 37452.1i −2.00929 + 2.00929i
\(704\) −4969.14 −0.266025
\(705\) −7751.78 + 8755.36i −0.414112 + 0.467725i
\(706\) 3406.46 0.181592
\(707\) 13050.1 13050.1i 0.694202 0.694202i
\(708\) −1205.45 + 1205.45i −0.0639881 + 0.0639881i
\(709\) 11448.7 0.606441 0.303221 0.952920i \(-0.401938\pi\)
0.303221 + 0.952920i \(0.401938\pi\)
\(710\) 23407.1 1423.07i 1.23726 0.0752211i
\(711\) 5593.90i 0.295060i
\(712\) −929.200 + 929.200i −0.0489091 + 0.0489091i
\(713\) 37648.9 + 3689.03i 1.97751 + 0.193766i
\(714\) 10045.9i 0.526550i
\(715\) 13144.3 799.130i 0.687509 0.0417983i
\(716\) 23985.0 1.25190
\(717\) −504.769 504.769i −0.0262914 0.0262914i
\(718\) −2204.78 2204.78i −0.114598 0.114598i
\(719\) 14259.4i 0.739619i −0.929108 0.369810i \(-0.879423\pi\)
0.929108 0.369810i \(-0.120577\pi\)
\(720\) 10710.5 + 9482.79i 0.554383 + 0.490837i
\(721\) −14116.6 −0.729168
\(722\) −22461.1 22461.1i −1.15778 1.15778i
\(723\) 13058.3 + 13058.3i 0.671706 + 0.671706i
\(724\) −4139.96 −0.212514
\(725\) 7321.20 893.512i 0.375038 0.0457713i
\(726\) 11569.6 0.591445
\(727\) 5679.43 5679.43i 0.289737 0.289737i −0.547240 0.836976i \(-0.684321\pi\)
0.836976 + 0.547240i \(0.184321\pi\)
\(728\) −4585.87 4585.87i −0.233467 0.233467i
\(729\) 11499.7i 0.584246i
\(730\) −12069.9 + 13632.5i −0.611953 + 0.691179i
\(731\) −12028.7 −0.608617
\(732\) 7832.49 7832.49i 0.395488 0.395488i
\(733\) −15227.1 15227.1i −0.767291 0.767291i 0.210338 0.977629i \(-0.432544\pi\)
−0.977629 + 0.210338i \(0.932544\pi\)
\(734\) −123.322 −0.00620150
\(735\) −3706.15 + 225.321i −0.185991 + 0.0113076i
\(736\) −16039.8 19524.6i −0.803308 0.977834i
\(737\) −76.7566 76.7566i −0.00383632 0.00383632i
\(738\) 6255.66 6255.66i 0.312024 0.312024i
\(739\) 35436.4i 1.76393i 0.471311 + 0.881967i \(0.343781\pi\)
−0.471311 + 0.881967i \(0.656219\pi\)
\(740\) −29665.7 + 1803.58i −1.47369 + 0.0895957i
\(741\) 24274.0i 1.20341i
\(742\) −19884.1 19884.1i −0.983783 0.983783i
\(743\) −15295.3 15295.3i −0.755222 0.755222i 0.220226 0.975449i \(-0.429320\pi\)
−0.975449 + 0.220226i \(0.929320\pi\)
\(744\) 7324.84i 0.360943i
\(745\) −16757.5 + 18926.9i −0.824088 + 0.930778i
\(746\) 31354.3i 1.53882i
\(747\) −13801.3 + 13801.3i −0.675988 + 0.675988i
\(748\) 4549.72 4549.72i 0.222399 0.222399i
\(749\) 23802.4i 1.16118i
\(750\) −13697.1 9435.83i −0.666863 0.459397i
\(751\) 25279.5i 1.22831i −0.789185 0.614155i \(-0.789497\pi\)
0.789185 0.614155i \(-0.210503\pi\)
\(752\) 17598.1 + 17598.1i 0.853376 + 0.853376i
\(753\) 14839.8 + 14839.8i 0.718183 + 0.718183i
\(754\) 13826.8i 0.667828i
\(755\) 5014.20 5663.36i 0.241703 0.272995i
\(756\) 13304.9i 0.640071i
\(757\) 10121.6 10121.6i 0.485965 0.485965i −0.421065 0.907030i \(-0.638344\pi\)
0.907030 + 0.421065i \(0.138344\pi\)
\(758\) −21094.0 21094.0i −1.01078 1.01078i
\(759\) −4188.48 5098.47i −0.200306 0.243824i
\(760\) 567.396 + 9332.68i 0.0270811 + 0.445437i
\(761\) 33559.8 1.59861 0.799305 0.600926i \(-0.205201\pi\)
0.799305 + 0.600926i \(0.205201\pi\)
\(762\) 6617.80 + 6617.80i 0.314616 + 0.314616i
\(763\) −288.351 + 288.351i −0.0136815 + 0.0136815i
\(764\) −6626.25 −0.313782
\(765\) −10401.6 + 632.383i −0.491596 + 0.0298874i
\(766\) 28348.3i 1.33716i
\(767\) −3824.91 3824.91i −0.180064 0.180064i
\(768\) −11788.1 + 11788.1i −0.553862 + 0.553862i
\(769\) −21057.2 −0.987440 −0.493720 0.869621i \(-0.664363\pi\)
−0.493720 + 0.869621i \(0.664363\pi\)
\(770\) 9217.24 + 8160.72i 0.431385 + 0.381937i
\(771\) −5867.50 −0.274076
\(772\) 2593.09 + 2593.09i 0.120890 +