Properties

Label 115.4.e.a.22.7
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 22.7
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.7

$q$-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} +(-10.7567 - 109.778i) 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} +(681.220 - 66.7494i) 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 −0.348505 0.937307i \(-0.613310\pi\)
0.937307 + 0.348505i \(0.113310\pi\)
\(8\) −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 \(-0.916400\pi\)
0.965709 0.259628i \(-0.0836001\pi\)
\(12\) −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 −0.374899 0.927066i \(-0.622323\pi\)
0.927066 + 0.374899i \(0.122323\pi\)
\(18\) 45.3837 45.3837i 0.594281 0.594281i
\(19\) −123.640 −1.49290 −0.746448 0.665444i \(-0.768242\pi\)
−0.746448 + 0.665444i \(0.768242\pi\)
\(20\) −51.9447 45.9906i −0.580759 0.514190i
\(21\) 48.6969i 0.506026i
\(22\) −50.4874 + 50.4874i −0.489271 + 0.489271i
\(23\) −10.7567 109.778i −0.0975182 0.995234i
\(24\) 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 \(-0.349339\pi\)
0.890062 0.455839i \(-0.150661\pi\)
\(38\) 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 0.375646 0.926763i \(-0.377421\pi\)
−0.926763 + 0.375646i \(0.877421\pi\)
\(44\) 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 0.994196 0.107586i \(-0.0343121\pi\)
−0.107586 + 0.994196i \(0.534312\pi\)
\(54\) 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 \(-0.797838\pi\)
0.805006 0.593267i \(-0.202162\pi\)
\(62\) −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 −0.703403 0.710791i \(-0.748337\pi\)
0.710791 + 0.703403i \(0.248337\pi\)
\(68\) 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 \(-0.424847\pi\)
0.233914 + 0.972257i \(0.424847\pi\)
\(80\) −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 \(-0.976236\pi\)
−0.0745876 0.997214i \(-0.523764\pi\)
\(84\) −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 \(-0.536910\pi\)
−0.115696 + 0.993285i \(0.536910\pi\)
\(90\) 43.5461 + 716.257i 0.0510018 + 0.838891i
\(91\) 958.835i 1.10454i
\(92\) 681.220 66.7494i 0.771979 0.0756425i
\(93\) −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 \(0.539835\pi\)
−0.992179 + 0.124820i \(0.960165\pi\)
\(98\) 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 0.326129 0.945325i \(-0.394255\pi\)
−0.945325 + 0.326129i \(0.894255\pi\)
\(104\) 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 −0.0138547 0.999904i \(-0.504410\pi\)
0.999904 + 0.0138547i \(0.00441024\pi\)
\(108\) 610.048 610.048i 0.543536 0.543536i
\(109\) −26.4427 −0.0232362 −0.0116181 0.999933i \(-0.503698\pi\)
−0.0116181 + 0.999933i \(0.503698\pi\)
\(110\) −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 0.735931 0.677057i \(-0.236745\pi\)
−0.677057 + 0.735931i \(0.736745\pi\)
\(114\) −1471.49 −1.20892
\(115\) 998.663 + 723.566i 0.809790 + 0.586720i
\(116\) −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 −0.880509 0.474029i \(-0.842799\pi\)
0.474029 + 0.880509i \(0.342799\pi\)
\(138\) −128.019 1306.51i −0.0789688 0.805926i
\(139\) 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 \(-0.286489\pi\)
0.621584 + 0.783347i \(0.286489\pi\)
\(150\) −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 \(0.542489\pi\)
−0.991105 + 0.133086i \(0.957511\pi\)
\(158\) −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 \(-0.956258\pi\)
0.990573 0.136987i \(-0.0437417\pi\)
\(182\) −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 \(-0.935170\pi\)
0.979331 0.202263i \(-0.0648297\pi\)
\(192\) −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 \(-0.292510\pi\)
0.606657 + 0.794964i \(0.292510\pi\)
\(200\) 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
\(207\) 1869.41 183.175i 0.627697 0.0615050i
\(208\) 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 −0.425724 0.904853i \(-0.639981\pi\)
0.904853 + 0.425724i \(0.139981\pi\)
\(228\) 1713.11 + 1713.11i 0.497603 + 0.497603i
\(229\) 2319.00 0.669188 0.334594 0.942362i \(-0.391401\pi\)
0.334594 + 0.942362i \(0.391401\pi\)
\(230\) −733.160 4589.89i −0.210187 1.31586i
\(231\) 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 \(0.285588\pi\)
−0.623799 + 0.781585i \(0.714412\pi\)
\(242\) −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 \(0.314917\pi\)
−0.549241 + 0.835664i \(0.685083\pi\)
\(252\) −1152.33 + 1152.33i −0.288055 + 0.288055i
\(253\) −2079.64 + 203.774i −0.516782 + 0.0506370i
\(254\) 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 \(-0.971064\pi\)
−0.0907786 0.995871i \(-0.528936\pi\)
\(264\) −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 \(0.0993921\pi\)
−0.951645 + 0.307200i \(0.900608\pi\)
\(282\) 2787.50 + 2787.50i 0.588628 + 0.588628i
\(283\) −1464.96 1464.96i −0.307714 0.307714i 0.536308 0.844022i \(-0.319819\pi\)
−0.844022 + 0.536308i \(0.819819\pi\)
\(284\) 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 0.581409 0.813611i \(-0.302502\pi\)
−0.813611 + 0.581409i \(0.802502\pi\)
\(294\) 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 0.909041 0.416708i \(-0.136816\pi\)
−0.416708 + 0.909041i \(0.636816\pi\)
\(314\) 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
\(322\) 625.224 + 6380.80i 0.108206 + 1.10431i
\(323\) −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 −0.450567 0.892743i \(-0.648778\pi\)
0.892743 + 0.450567i \(0.148778\pi\)
\(338\) −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
\(345\) −3845.44 + 614.245i −0.600091 + 0.0958546i
\(346\) −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 \(-0.519369\pi\)
−0.0608108 + 0.998149i \(0.519369\pi\)
\(360\) 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 −0.708750 0.705459i \(-0.750741\pi\)
0.705459 + 0.708750i \(0.250741\pi\)
\(368\) −808.214 8248.33i −0.114487 1.16841i
\(369\) 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 0.169042 0.985609i \(-0.445933\pi\)
−0.985609 + 0.169042i \(0.945933\pi\)
\(374\) 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 \(-0.680202\pi\)
−0.536362 + 0.843988i \(0.680202\pi\)
\(380\) 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 0.966442 0.256886i \(-0.0826965\pi\)
−0.256886 + 0.966442i \(0.582696\pi\)
\(384\) 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 \(-0.444908\pi\)
0.172214 + 0.985060i \(0.444908\pi\)
\(390\) 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 \(-0.783837\pi\)
0.778141 0.628090i \(-0.216163\pi\)
\(402\) 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 \(-0.446584\pi\)
0.167025 + 0.985953i \(0.446584\pi\)
\(420\) 2239.60 2529.55i 0.260194 0.293879i
\(421\) 8714.92i 1.00888i 0.863446 + 0.504441i \(0.168301\pi\)
−0.863446 + 0.504441i \(0.831699\pi\)
\(422\) 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 \(-0.791060\pi\)
0.792192 0.610272i \(-0.208940\pi\)
\(432\) −7386.57 7386.57i −0.822654 0.822654i
\(433\) 4506.50 + 4506.50i 0.500158 + 0.500158i 0.911487 0.411329i \(-0.134935\pi\)
−0.411329 + 0.911487i \(0.634935\pi\)
\(434\) −19934.0 −2.20475
\(435\) 2079.25 126.411i 0.229178 0.0139333i
\(436\) 164.088i 0.0180238i
\(437\) 1329.96 + 13573.0i 0.145584 + 1.48578i
\(438\) 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 −0.831682 0.555253i \(-0.812622\pi\)
0.555253 + 0.831682i \(0.312622\pi\)
\(458\) −6180.35 6180.35i −0.630543 0.630543i
\(459\) −7609.69 −0.773834
\(460\) −4490.02 + 6197.11i −0.455105 + 0.628134i
\(461\) −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 −0.768051 0.640389i \(-0.778773\pi\)
0.640389 + 0.768051i \(0.278773\pi\)
\(468\) −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 \(-0.294043\pi\)
0.602822 + 0.797876i \(0.294043\pi\)
\(480\) −5361.08 + 6055.14i −0.509789 + 0.575788i
\(481\) 26634.4i 2.52479i
\(482\) 15586.3 15586.3i 1.47290 1.47290i
\(483\) 5345.87 523.816i 0.503614 0.0493467i
\(484\) 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 0.453308 0.891354i \(-0.350244\pi\)
−0.891354 + 0.453308i \(0.850244\pi\)
\(504\) −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 \(0.421463\pi\)
−0.244236 + 0.969716i \(0.578537\pi\)
\(522\) 2677.83 + 2677.83i 0.224531 + 0.224531i
\(523\) −4272.34 4272.34i −0.357202 0.357202i 0.505579 0.862781i \(-0.331279\pi\)
−0.862781 + 0.505579i \(0.831279\pi\)
\(524\) 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
\(552\) −2344.66 + 229.742i −0.180789 + 0.0177146i
\(553\) 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 −0.267239 0.963630i \(-0.586111\pi\)
0.963630 + 0.267239i \(0.0861114\pi\)
\(558\) 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 0.618858 0.785503i \(-0.287596\pi\)
−0.785503 + 0.618858i \(0.787596\pi\)
\(564\) 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 \(-0.590300\pi\)
−0.279897 + 0.960030i \(0.590300\pi\)
\(570\) 10905.7 12317.6i 0.801388 0.905139i
\(571\) 11583.9i 0.848988i 0.905431 + 0.424494i \(0.139548\pi\)
−0.905431 + 0.424494i \(0.860452\pi\)
\(572\) 5168.19 5168.19i 0.377785 0.377785i
\(573\) 2384.25 + 2384.25i 0.173828 + 0.173828i
\(574\) −8011.82 −0.582591
\(575\) −13458.3 + 2997.08i −0.976090 + 0.217368i
\(576\) −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
\(598\) 2520.67 + 25725.0i 0.172371 + 1.75916i
\(599\) 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 \(0.0110807\pi\)
0.0348041 + 0.999394i \(0.488919\pi\)
\(614\) 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 −0.408382 0.912811i \(-0.633907\pi\)
0.912811 + 0.408382i \(0.133907\pi\)
\(618\) −7703.37 7703.37i −0.501416 0.501416i
\(619\) 18911.8 1.22799 0.613997 0.789308i \(-0.289561\pi\)
0.613997 + 0.789308i \(0.289561\pi\)
\(620\) −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 \(-0.946687\pi\)
0.986007 0.166707i \(-0.0533133\pi\)
\(632\) −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 \(-0.844861\pi\)
0.883561 0.468316i \(-0.155139\pi\)
\(642\) 12988.9 12988.9i 0.798488 0.798488i
\(643\) 7121.12 + 7121.12i 0.436749 + 0.436749i 0.890916 0.454168i \(-0.150063\pi\)
−0.454168 + 0.890916i \(0.650063\pi\)
\(644\) 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 \(-0.514380\pi\)
−0.0451615 + 0.998980i \(0.514380\pi\)
\(660\) −251.852 4142.53i −0.0148535 0.244315i
\(661\) 29321.0i 1.72535i 0.505759 + 0.862675i \(0.331212\pi\)
−0.505759 + 0.862675i \(0.668788\pi\)
\(662\) 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
\(667\) 6477.38 634.688i 0.376020 0.0368444i
\(668\) 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 \(0.543758\pi\)
−0.990566 + 0.137038i \(0.956242\pi\)
\(678\) 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
\(690\) 11885.5 + 8611.42i 0.655756 + 0.475118i
\(691\) −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 \(-0.837984\pi\)
0.873237 0.487295i \(-0.162016\pi\)
\(702\) 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 \(-0.598062\pi\)
−0.303221 + 0.952920i \(0.598062\pi\)
\(710\) −23407.1 + 1423.07i −1.23726 + 0.0752211i
\(711\) 5593.90i 0.295060i
\(712\) 929.200 929.200i 0.0489091 0.0489091i
\(713\) −3689.03 37648.9i −0.193766 1.97751i
\(714\) 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 −0.836976 0.547240i \(-0.815679\pi\)
0.547240 + 0.836976i \(0.315679\pi\)
\(728\) 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 0.977629 0.210338i \(-0.0674564\pi\)
−0.210338 + 0.977629i \(0.567456\pi\)
\(734\) 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 0.975449 0.220226i \(-0.0706796\pi\)
−0.220226 + 0.975449i \(0.570680\pi\)
\(744\) 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 \(0.210503\pi\)
−0.789185 + 0.614155i \(0.789497\pi\)
\(752\) 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 −0.907030 0.421065i \(-0.861656\pi\)
0.421065 + 0.907030i \(0.361656\pi\)
\(758\) 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 \(-0.335637\pi\)
0.493720 + 0.869621i \(0.335637\pi\)
\(770\) −9217.24 8160.72i −0.431385 0.381937i
\(771\) −5867.50 −0.274076
\(772\) 2593.09 + 2593.09i 0.120890 + 0.120890i