Properties

Label 115.4.e.a.22.20
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 22.20
Character \(\chi\) \(=\) 115.22
Dual form 115.4.e.a.68.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.304528 + 0.304528i) q^{2} +(5.13977 - 5.13977i) q^{3} -7.81453i q^{4} +(11.1201 - 1.15901i) q^{5} +3.13040 q^{6} +(-2.31330 + 2.31330i) q^{7} +(4.81596 - 4.81596i) q^{8} -25.8345i q^{9} +O(q^{10})\) \(q+(0.304528 + 0.304528i) q^{2} +(5.13977 - 5.13977i) q^{3} -7.81453i q^{4} +(11.1201 - 1.15901i) q^{5} +3.13040 q^{6} +(-2.31330 + 2.31330i) q^{7} +(4.81596 - 4.81596i) q^{8} -25.8345i q^{9} +(3.73933 + 3.03343i) q^{10} +24.7697i q^{11} +(-40.1649 - 40.1649i) q^{12} +(-14.5454 + 14.5454i) q^{13} -1.40893 q^{14} +(51.1977 - 63.1118i) q^{15} -59.5830 q^{16} +(4.31972 - 4.31972i) q^{17} +(7.86731 - 7.86731i) q^{18} -65.9718 q^{19} +(-9.05711 - 86.8983i) q^{20} +23.7797i q^{21} +(-7.54305 + 7.54305i) q^{22} +(100.668 + 45.0889i) q^{23} -49.5059i q^{24} +(122.313 - 25.7766i) q^{25} -8.85894 q^{26} +(5.99056 + 5.99056i) q^{27} +(18.0774 + 18.0774i) q^{28} -98.5450i q^{29} +(34.8104 - 3.62817i) q^{30} +202.871 q^{31} +(-56.6724 - 56.6724i) q^{32} +(127.310 + 127.310i) q^{33} +2.63095 q^{34} +(-23.0430 + 28.4053i) q^{35} -201.884 q^{36} +(-213.017 + 213.017i) q^{37} +(-20.0902 - 20.0902i) q^{38} +149.520i q^{39} +(47.9722 - 59.1357i) q^{40} +22.2460 q^{41} +(-7.24157 + 7.24157i) q^{42} +(-290.702 - 290.702i) q^{43} +193.563 q^{44} +(-29.9424 - 287.282i) q^{45} +(16.9253 + 44.3869i) q^{46} +(78.9374 + 78.9374i) q^{47} +(-306.243 + 306.243i) q^{48} +332.297i q^{49} +(45.0975 + 29.3981i) q^{50} -44.4047i q^{51} +(113.665 + 113.665i) q^{52} +(35.7564 + 35.7564i) q^{53} +3.64858i q^{54} +(28.7083 + 275.441i) q^{55} +22.2815i q^{56} +(-339.080 + 339.080i) q^{57} +(30.0097 - 30.0097i) q^{58} +286.127i q^{59} +(-493.189 - 400.086i) q^{60} +317.718i q^{61} +(61.7798 + 61.7798i) q^{62} +(59.7629 + 59.7629i) q^{63} +442.148i q^{64} +(-144.888 + 178.604i) q^{65} +77.5391i q^{66} +(109.385 - 109.385i) q^{67} +(-33.7566 - 33.7566i) q^{68} +(749.156 - 285.662i) q^{69} +(-15.6674 + 1.63296i) q^{70} -587.707 q^{71} +(-124.418 - 124.418i) q^{72} +(373.870 - 373.870i) q^{73} -129.739 q^{74} +(496.177 - 761.149i) q^{75} +515.538i q^{76} +(-57.2997 - 57.2997i) q^{77} +(-45.5329 + 45.5329i) q^{78} +1070.48 q^{79} +(-662.569 + 69.0573i) q^{80} +759.111 q^{81} +(6.77452 + 6.77452i) q^{82} +(-793.800 - 793.800i) q^{83} +185.827 q^{84} +(43.0291 - 53.0423i) q^{85} -177.054i q^{86} +(-506.499 - 506.499i) q^{87} +(119.290 + 119.290i) q^{88} +741.611 q^{89} +(78.3670 - 96.6036i) q^{90} -67.2957i q^{91} +(352.349 - 786.670i) q^{92} +(1042.71 - 1042.71i) q^{93} +48.0772i q^{94} +(-733.613 + 76.4619i) q^{95} -582.566 q^{96} +(-663.583 + 663.583i) q^{97} +(-101.194 + 101.194i) q^{98} +639.911 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.304528 + 0.304528i 0.107667 + 0.107667i 0.758888 0.651221i \(-0.225743\pi\)
−0.651221 + 0.758888i \(0.725743\pi\)
\(3\) 5.13977 5.13977i 0.989149 0.989149i −0.0107926 0.999942i \(-0.503435\pi\)
0.999942 + 0.0107926i \(0.00343545\pi\)
\(4\) 7.81453i 0.976816i
\(5\) 11.1201 1.15901i 0.994612 0.103665i
\(6\) 3.13040 0.212997
\(7\) −2.31330 + 2.31330i −0.124907 + 0.124907i −0.766797 0.641890i \(-0.778151\pi\)
0.641890 + 0.766797i \(0.278151\pi\)
\(8\) 4.81596 4.81596i 0.212837 0.212837i
\(9\) 25.8345i 0.956832i
\(10\) 3.73933 + 3.03343i 0.118248 + 0.0959254i
\(11\) 24.7697i 0.678940i 0.940617 + 0.339470i \(0.110248\pi\)
−0.940617 + 0.339470i \(0.889752\pi\)
\(12\) −40.1649 40.1649i −0.966216 0.966216i
\(13\) −14.5454 + 14.5454i −0.310320 + 0.310320i −0.845034 0.534713i \(-0.820420\pi\)
0.534713 + 0.845034i \(0.320420\pi\)
\(14\) −1.40893 −0.0268966
\(15\) 51.1977 63.1118i 0.881280 1.08636i
\(16\) −59.5830 −0.930985
\(17\) 4.31972 4.31972i 0.0616286 0.0616286i −0.675621 0.737249i \(-0.736124\pi\)
0.737249 + 0.675621i \(0.236124\pi\)
\(18\) 7.86731 7.86731i 0.103019 0.103019i
\(19\) −65.9718 −0.796577 −0.398288 0.917260i \(-0.630396\pi\)
−0.398288 + 0.917260i \(0.630396\pi\)
\(20\) −9.05711 86.8983i −0.101262 0.971553i
\(21\) 23.7797i 0.247102i
\(22\) −7.54305 + 7.54305i −0.0730993 + 0.0730993i
\(23\) 100.668 + 45.0889i 0.912638 + 0.408769i
\(24\) 49.5059i 0.421056i
\(25\) 122.313 25.7766i 0.978507 0.206213i
\(26\) −8.85894 −0.0668224
\(27\) 5.99056 + 5.99056i 0.0426994 + 0.0426994i
\(28\) 18.0774 + 18.0774i 0.122011 + 0.122011i
\(29\) 98.5450i 0.631012i −0.948924 0.315506i \(-0.897826\pi\)
0.948924 0.315506i \(-0.102174\pi\)
\(30\) 34.8104 3.62817i 0.211849 0.0220803i
\(31\) 202.871 1.17538 0.587689 0.809087i \(-0.300038\pi\)
0.587689 + 0.809087i \(0.300038\pi\)
\(32\) −56.6724 56.6724i −0.313074 0.313074i
\(33\) 127.310 + 127.310i 0.671573 + 0.671573i
\(34\) 2.63095 0.0132707
\(35\) −23.0430 + 28.4053i −0.111285 + 0.137182i
\(36\) −201.884 −0.934649
\(37\) −213.017 + 213.017i −0.946480 + 0.946480i −0.998639 0.0521590i \(-0.983390\pi\)
0.0521590 + 0.998639i \(0.483390\pi\)
\(38\) −20.0902 20.0902i −0.0857649 0.0857649i
\(39\) 149.520i 0.613906i
\(40\) 47.9722 59.1357i 0.189627 0.233754i
\(41\) 22.2460 0.0847375 0.0423688 0.999102i \(-0.486510\pi\)
0.0423688 + 0.999102i \(0.486510\pi\)
\(42\) −7.24157 + 7.24157i −0.0266047 + 0.0266047i
\(43\) −290.702 290.702i −1.03097 1.03097i −0.999505 0.0314652i \(-0.989983\pi\)
−0.0314652 0.999505i \(-0.510017\pi\)
\(44\) 193.563 0.663199
\(45\) −29.9424 287.282i −0.0991900 0.951677i
\(46\) 16.9253 + 44.3869i 0.0542499 + 0.142272i
\(47\) 78.9374 + 78.9374i 0.244983 + 0.244983i 0.818908 0.573925i \(-0.194580\pi\)
−0.573925 + 0.818908i \(0.694580\pi\)
\(48\) −306.243 + 306.243i −0.920883 + 0.920883i
\(49\) 332.297i 0.968797i
\(50\) 45.0975 + 29.3981i 0.127555 + 0.0831505i
\(51\) 44.4047i 0.121920i
\(52\) 113.665 + 113.665i 0.303126 + 0.303126i
\(53\) 35.7564 + 35.7564i 0.0926702 + 0.0926702i 0.751922 0.659252i \(-0.229127\pi\)
−0.659252 + 0.751922i \(0.729127\pi\)
\(54\) 3.64858i 0.00919462i
\(55\) 28.7083 + 275.441i 0.0703823 + 0.675282i
\(56\) 22.2815i 0.0531696i
\(57\) −339.080 + 339.080i −0.787933 + 0.787933i
\(58\) 30.0097 30.0097i 0.0679391 0.0679391i
\(59\) 286.127i 0.631367i 0.948865 + 0.315683i \(0.102234\pi\)
−0.948865 + 0.315683i \(0.897766\pi\)
\(60\) −493.189 400.086i −1.06117 0.860848i
\(61\) 317.718i 0.666880i 0.942771 + 0.333440i \(0.108209\pi\)
−0.942771 + 0.333440i \(0.891791\pi\)
\(62\) 61.7798 + 61.7798i 0.126549 + 0.126549i
\(63\) 59.7629 + 59.7629i 0.119515 + 0.119515i
\(64\) 442.148i 0.863569i
\(65\) −144.888 + 178.604i −0.276479 + 0.340818i
\(66\) 77.5391i 0.144612i
\(67\) 109.385 109.385i 0.199455 0.199455i −0.600311 0.799766i \(-0.704957\pi\)
0.799766 + 0.600311i \(0.204957\pi\)
\(68\) −33.7566 33.7566i −0.0601998 0.0601998i
\(69\) 749.156 285.662i 1.30707 0.498401i
\(70\) −15.6674 + 1.63296i −0.0267517 + 0.00278823i
\(71\) −587.707 −0.982366 −0.491183 0.871056i \(-0.663435\pi\)
−0.491183 + 0.871056i \(0.663435\pi\)
\(72\) −124.418 124.418i −0.203650 0.203650i
\(73\) 373.870 373.870i 0.599426 0.599426i −0.340734 0.940160i \(-0.610675\pi\)
0.940160 + 0.340734i \(0.110675\pi\)
\(74\) −129.739 −0.203809
\(75\) 496.177 761.149i 0.763914 1.17186i
\(76\) 515.538i 0.778109i
\(77\) −57.2997 57.2997i −0.0848040 0.0848040i
\(78\) −45.5329 + 45.5329i −0.0660973 + 0.0660973i
\(79\) 1070.48 1.52453 0.762267 0.647263i \(-0.224086\pi\)
0.762267 + 0.647263i \(0.224086\pi\)
\(80\) −662.569 + 69.0573i −0.925969 + 0.0965105i
\(81\) 759.111 1.04130
\(82\) 6.77452 + 6.77452i 0.00912342 + 0.00912342i
\(83\) −793.800 793.800i −1.04977 1.04977i −0.998695 0.0510752i \(-0.983735\pi\)
−0.0510752 0.998695i \(-0.516265\pi\)
\(84\) 185.827 0.241374
\(85\) 43.0291 53.0423i 0.0549078 0.0676853i
\(86\) 177.054i 0.222002i
\(87\) −506.499 506.499i −0.624165 0.624165i
\(88\) 119.290 + 119.290i 0.144504 + 0.144504i
\(89\) 741.611 0.883265 0.441632 0.897196i \(-0.354400\pi\)
0.441632 + 0.897196i \(0.354400\pi\)
\(90\) 78.3670 96.6036i 0.0917846 0.113143i
\(91\) 67.2957i 0.0775221i
\(92\) 352.349 786.670i 0.399292 0.891479i
\(93\) 1042.71 1042.71i 1.16262 1.16262i
\(94\) 48.0772i 0.0527531i
\(95\) −733.613 + 76.4619i −0.792285 + 0.0825771i
\(96\) −582.566 −0.619353
\(97\) −663.583 + 663.583i −0.694605 + 0.694605i −0.963242 0.268637i \(-0.913427\pi\)
0.268637 + 0.963242i \(0.413427\pi\)
\(98\) −101.194 + 101.194i −0.104307 + 0.104307i
\(99\) 639.911 0.649631
\(100\) −201.432 955.821i −0.201432 0.955821i
\(101\) −298.855 −0.294427 −0.147214 0.989105i \(-0.547030\pi\)
−0.147214 + 0.989105i \(0.547030\pi\)
\(102\) 13.5225 13.5225i 0.0131267 0.0131267i
\(103\) −1146.23 1146.23i −1.09652 1.09652i −0.994814 0.101707i \(-0.967570\pi\)
−0.101707 0.994814i \(-0.532430\pi\)
\(104\) 140.100i 0.132096i
\(105\) 27.5609 + 264.433i 0.0256159 + 0.245771i
\(106\) 21.7776i 0.0199550i
\(107\) −902.367 + 902.367i −0.815282 + 0.815282i −0.985420 0.170138i \(-0.945578\pi\)
0.170138 + 0.985420i \(0.445578\pi\)
\(108\) 46.8134 46.8134i 0.0417094 0.0417094i
\(109\) 2121.09 1.86389 0.931944 0.362603i \(-0.118112\pi\)
0.931944 + 0.362603i \(0.118112\pi\)
\(110\) −75.1370 + 92.6220i −0.0651276 + 0.0802833i
\(111\) 2189.72i 1.87242i
\(112\) 137.834 137.834i 0.116286 0.116286i
\(113\) −307.526 307.526i −0.256015 0.256015i 0.567416 0.823431i \(-0.307943\pi\)
−0.823431 + 0.567416i \(0.807943\pi\)
\(114\) −206.518 −0.169669
\(115\) 1171.69 + 384.719i 0.950096 + 0.311958i
\(116\) −770.083 −0.616383
\(117\) 375.772 + 375.772i 0.296924 + 0.296924i
\(118\) −87.1337 + 87.1337i −0.0679772 + 0.0679772i
\(119\) 19.9856i 0.0153956i
\(120\) −57.3778 550.510i −0.0436487 0.418787i
\(121\) 717.463 0.539041
\(122\) −96.7540 + 96.7540i −0.0718008 + 0.0718008i
\(123\) 114.339 114.339i 0.0838180 0.0838180i
\(124\) 1585.34i 1.14813i
\(125\) 1330.26 428.401i 0.951858 0.306539i
\(126\) 36.3989i 0.0257355i
\(127\) −868.410 868.410i −0.606763 0.606763i 0.335335 0.942099i \(-0.391150\pi\)
−0.942099 + 0.335335i \(0.891150\pi\)
\(128\) −588.025 + 588.025i −0.406051 + 0.406051i
\(129\) −2988.29 −2.03957
\(130\) −98.5124 + 10.2676i −0.0664623 + 0.00692714i
\(131\) −1840.71 −1.22766 −0.613830 0.789438i \(-0.710372\pi\)
−0.613830 + 0.789438i \(0.710372\pi\)
\(132\) 994.871 994.871i 0.656003 0.656003i
\(133\) 152.613 152.613i 0.0994977 0.0994977i
\(134\) 66.6215 0.0429494
\(135\) 73.5588 + 59.6725i 0.0468958 + 0.0380429i
\(136\) 41.6072i 0.0262337i
\(137\) 609.378 609.378i 0.380020 0.380020i −0.491090 0.871109i \(-0.663401\pi\)
0.871109 + 0.491090i \(0.163401\pi\)
\(138\) 315.131 + 141.147i 0.194389 + 0.0870667i
\(139\) 47.1483i 0.0287703i 0.999897 + 0.0143851i \(0.00457909\pi\)
−0.999897 + 0.0143851i \(0.995421\pi\)
\(140\) 221.974 + 180.070i 0.134002 + 0.108705i
\(141\) 811.440 0.484650
\(142\) −178.973 178.973i −0.105768 0.105768i
\(143\) −360.284 360.284i −0.210689 0.210689i
\(144\) 1539.30i 0.890796i
\(145\) −114.215 1095.83i −0.0654139 0.627612i
\(146\) 227.707 0.129077
\(147\) 1707.93 + 1707.93i 0.958284 + 0.958284i
\(148\) 1664.63 + 1664.63i 0.924536 + 0.924536i
\(149\) −2441.05 −1.34214 −0.671069 0.741395i \(-0.734165\pi\)
−0.671069 + 0.741395i \(0.734165\pi\)
\(150\) 382.890 80.6912i 0.208419 0.0439227i
\(151\) 616.144 0.332060 0.166030 0.986121i \(-0.446905\pi\)
0.166030 + 0.986121i \(0.446905\pi\)
\(152\) −317.717 + 317.717i −0.169541 + 0.169541i
\(153\) −111.598 111.598i −0.0589682 0.0589682i
\(154\) 34.8987i 0.0182612i
\(155\) 2255.95 235.129i 1.16904 0.121845i
\(156\) 1168.43 0.599673
\(157\) −1802.35 + 1802.35i −0.916198 + 0.916198i −0.996750 0.0805521i \(-0.974332\pi\)
0.0805521 + 0.996750i \(0.474332\pi\)
\(158\) 325.990 + 325.990i 0.164142 + 0.164142i
\(159\) 367.559 0.183329
\(160\) −695.886 564.519i −0.343842 0.278932i
\(161\) −337.179 + 128.570i −0.165052 + 0.0629365i
\(162\) 231.170 + 231.170i 0.112114 + 0.112114i
\(163\) 531.615 531.615i 0.255456 0.255456i −0.567747 0.823203i \(-0.692185\pi\)
0.823203 + 0.567747i \(0.192185\pi\)
\(164\) 173.842i 0.0827729i
\(165\) 1563.26 + 1268.15i 0.737573 + 0.598336i
\(166\) 483.468i 0.226051i
\(167\) −1846.93 1846.93i −0.855807 0.855807i 0.135034 0.990841i \(-0.456886\pi\)
−0.990841 + 0.135034i \(0.956886\pi\)
\(168\) 114.522 + 114.522i 0.0525927 + 0.0525927i
\(169\) 1773.86i 0.807403i
\(170\) 29.2564 3.04929i 0.0131992 0.00137571i
\(171\) 1704.35i 0.762190i
\(172\) −2271.70 + 2271.70i −1.00707 + 1.00707i
\(173\) −2998.10 + 2998.10i −1.31758 + 1.31758i −0.401894 + 0.915686i \(0.631648\pi\)
−0.915686 + 0.401894i \(0.868352\pi\)
\(174\) 308.486i 0.134404i
\(175\) −223.319 + 342.577i −0.0964646 + 0.147979i
\(176\) 1475.85i 0.632083i
\(177\) 1470.63 + 1470.63i 0.624516 + 0.624516i
\(178\) 225.841 + 225.841i 0.0950983 + 0.0950983i
\(179\) 1619.24i 0.676134i 0.941122 + 0.338067i \(0.109773\pi\)
−0.941122 + 0.338067i \(0.890227\pi\)
\(180\) −2244.97 + 233.986i −0.929613 + 0.0968903i
\(181\) 3192.22i 1.31092i −0.755231 0.655458i \(-0.772475\pi\)
0.755231 0.655458i \(-0.227525\pi\)
\(182\) 20.4934 20.4934i 0.00834655 0.00834655i
\(183\) 1633.00 + 1633.00i 0.659644 + 0.659644i
\(184\) 701.958 267.665i 0.281245 0.107242i
\(185\) −2121.88 + 2615.66i −0.843264 + 1.03950i
\(186\) 635.068 0.250352
\(187\) 106.998 + 106.998i 0.0418421 + 0.0418421i
\(188\) 616.858 616.858i 0.239303 0.239303i
\(189\) −27.7160 −0.0106669
\(190\) −246.690 200.121i −0.0941936 0.0764120i
\(191\) 3592.18i 1.36084i −0.732821 0.680421i \(-0.761797\pi\)
0.732821 0.680421i \(-0.238203\pi\)
\(192\) 2272.54 + 2272.54i 0.854199 + 0.854199i
\(193\) −1667.87 + 1667.87i −0.622051 + 0.622051i −0.946056 0.324005i \(-0.894971\pi\)
0.324005 + 0.946056i \(0.394971\pi\)
\(194\) −404.159 −0.149572
\(195\) 173.295 + 1662.68i 0.0636405 + 0.610598i
\(196\) 2596.75 0.946336
\(197\) −2169.51 2169.51i −0.784627 0.784627i 0.195981 0.980608i \(-0.437211\pi\)
−0.980608 + 0.195981i \(0.937211\pi\)
\(198\) 194.871 + 194.871i 0.0699437 + 0.0699437i
\(199\) −2457.79 −0.875519 −0.437759 0.899092i \(-0.644228\pi\)
−0.437759 + 0.899092i \(0.644228\pi\)
\(200\) 464.917 713.196i 0.164373 0.252153i
\(201\) 1124.43i 0.394582i
\(202\) −91.0095 91.0095i −0.0317000 0.0317000i
\(203\) 227.964 + 227.964i 0.0788176 + 0.0788176i
\(204\) −347.002 −0.119093
\(205\) 247.378 25.7833i 0.0842810 0.00878431i
\(206\) 698.120i 0.236118i
\(207\) 1164.85 2600.70i 0.391124 0.873241i
\(208\) 866.658 866.658i 0.288903 0.288903i
\(209\) 1634.10i 0.540828i
\(210\) −72.1340 + 88.9201i −0.0237034 + 0.0292194i
\(211\) −2528.40 −0.824939 −0.412470 0.910971i \(-0.635334\pi\)
−0.412470 + 0.910971i \(0.635334\pi\)
\(212\) 279.419 279.419i 0.0905217 0.0905217i
\(213\) −3020.68 + 3020.68i −0.971707 + 0.971707i
\(214\) −549.592 −0.175558
\(215\) −3569.57 2895.71i −1.13229 0.918540i
\(216\) 57.7006 0.0181761
\(217\) −469.302 + 469.302i −0.146812 + 0.146812i
\(218\) 645.931 + 645.931i 0.200679 + 0.200679i
\(219\) 3843.21i 1.18584i
\(220\) 2152.44 224.342i 0.659626 0.0687505i
\(221\) 125.664i 0.0382492i
\(222\) −666.829 + 666.829i −0.201597 + 0.201597i
\(223\) 3482.60 3482.60i 1.04579 1.04579i 0.0468945 0.998900i \(-0.485068\pi\)
0.998900 0.0468945i \(-0.0149324\pi\)
\(224\) 262.201 0.0782099
\(225\) −665.925 3159.90i −0.197311 0.936267i
\(226\) 187.301i 0.0551285i
\(227\) 1838.75 1838.75i 0.537630 0.537630i −0.385202 0.922832i \(-0.625868\pi\)
0.922832 + 0.385202i \(0.125868\pi\)
\(228\) 2649.75 + 2649.75i 0.769666 + 0.769666i
\(229\) 1512.72 0.436521 0.218261 0.975891i \(-0.429962\pi\)
0.218261 + 0.975891i \(0.429962\pi\)
\(230\) 239.656 + 473.971i 0.0687062 + 0.135881i
\(231\) −589.015 −0.167768
\(232\) −474.589 474.589i −0.134303 0.134303i
\(233\) 822.614 822.614i 0.231293 0.231293i −0.581939 0.813232i \(-0.697706\pi\)
0.813232 + 0.581939i \(0.197706\pi\)
\(234\) 228.866i 0.0639378i
\(235\) 969.281 + 786.303i 0.269059 + 0.218267i
\(236\) 2235.95 0.616729
\(237\) 5502.01 5502.01i 1.50799 1.50799i
\(238\) −6.08618 + 6.08618i −0.00165760 + 0.00165760i
\(239\) 5813.88i 1.57351i −0.617266 0.786754i \(-0.711760\pi\)
0.617266 0.786754i \(-0.288240\pi\)
\(240\) −3050.52 + 3760.39i −0.820458 + 1.01138i
\(241\) 2941.31i 0.786168i 0.919503 + 0.393084i \(0.128592\pi\)
−0.919503 + 0.393084i \(0.871408\pi\)
\(242\) 218.487 + 218.487i 0.0580368 + 0.0580368i
\(243\) 3739.91 3739.91i 0.987306 0.987306i
\(244\) 2482.82 0.651419
\(245\) 385.136 + 3695.18i 0.100430 + 0.963577i
\(246\) 69.6389 0.0180488
\(247\) 959.584 959.584i 0.247194 0.247194i
\(248\) 977.019 977.019i 0.250164 0.250164i
\(249\) −8159.90 −2.07676
\(250\) 535.562 + 274.642i 0.135488 + 0.0694795i
\(251\) 3965.30i 0.997161i 0.866844 + 0.498580i \(0.166145\pi\)
−0.866844 + 0.498580i \(0.833855\pi\)
\(252\) 467.019 467.019i 0.116744 0.116744i
\(253\) −1116.84 + 2493.51i −0.277530 + 0.619626i
\(254\) 528.910i 0.130657i
\(255\) −51.4655 493.785i −0.0126388 0.121263i
\(256\) 3179.04 0.776133
\(257\) −242.191 242.191i −0.0587839 0.0587839i 0.677104 0.735888i \(-0.263235\pi\)
−0.735888 + 0.677104i \(0.763235\pi\)
\(258\) −910.016 910.016i −0.219594 0.219594i
\(259\) 985.545i 0.236443i
\(260\) 1395.71 + 1132.23i 0.332916 + 0.270069i
\(261\) −2545.86 −0.603773
\(262\) −560.547 560.547i −0.132178 0.132178i
\(263\) −3573.39 3573.39i −0.837812 0.837812i 0.150759 0.988571i \(-0.451828\pi\)
−0.988571 + 0.150759i \(0.951828\pi\)
\(264\) 1226.24 0.285872
\(265\) 439.057 + 356.173i 0.101778 + 0.0825643i
\(266\) 92.9496 0.0214252
\(267\) 3811.71 3811.71i 0.873681 0.873681i
\(268\) −854.791 854.791i −0.194831 0.194831i
\(269\) 3039.10i 0.688836i 0.938816 + 0.344418i \(0.111924\pi\)
−0.938816 + 0.344418i \(0.888076\pi\)
\(270\) 4.22874 + 40.5726i 0.000953159 + 0.00914508i
\(271\) −3967.09 −0.889238 −0.444619 0.895720i \(-0.646661\pi\)
−0.444619 + 0.895720i \(0.646661\pi\)
\(272\) −257.382 + 257.382i −0.0573753 + 0.0573753i
\(273\) −345.885 345.885i −0.0766809 0.0766809i
\(274\) 371.145 0.0818310
\(275\) 638.478 + 3029.66i 0.140006 + 0.664347i
\(276\) −2232.31 5854.30i −0.486846 1.27677i
\(277\) 5303.66 + 5303.66i 1.15042 + 1.15042i 0.986469 + 0.163950i \(0.0524235\pi\)
0.163950 + 0.986469i \(0.447577\pi\)
\(278\) −14.3580 + 14.3580i −0.00309760 + 0.00309760i
\(279\) 5241.06i 1.12464i
\(280\) 25.8245 + 247.773i 0.00551182 + 0.0528831i
\(281\) 6554.71i 1.39154i −0.718267 0.695768i \(-0.755064\pi\)
0.718267 0.695768i \(-0.244936\pi\)
\(282\) 247.106 + 247.106i 0.0521807 + 0.0521807i
\(283\) −2157.97 2157.97i −0.453279 0.453279i 0.443162 0.896441i \(-0.353857\pi\)
−0.896441 + 0.443162i \(0.853857\pi\)
\(284\) 4592.65i 0.959591i
\(285\) −3377.60 + 4163.60i −0.702007 + 0.865369i
\(286\) 219.433i 0.0453684i
\(287\) −51.4617 + 51.4617i −0.0105843 + 0.0105843i
\(288\) −1464.10 + 1464.10i −0.299559 + 0.299559i
\(289\) 4875.68i 0.992404i
\(290\) 298.929 368.492i 0.0605301 0.0746159i
\(291\) 6821.33i 1.37414i
\(292\) −2921.61 2921.61i −0.585529 0.585529i
\(293\) −1783.11 1783.11i −0.355531 0.355531i 0.506632 0.862163i \(-0.330890\pi\)
−0.862163 + 0.506632i \(0.830890\pi\)
\(294\) 1040.22i 0.206351i
\(295\) 331.624 + 3181.77i 0.0654506 + 0.627965i
\(296\) 2051.76i 0.402893i
\(297\) −148.384 + 148.384i −0.0289903 + 0.0289903i
\(298\) −743.368 743.368i −0.144504 0.144504i
\(299\) −2120.09 + 808.414i −0.410059 + 0.156361i
\(300\) −5948.01 3877.39i −1.14470 0.746203i
\(301\) 1344.97 0.257550
\(302\) 187.633 + 187.633i 0.0357519 + 0.0357519i
\(303\) −1536.04 + 1536.04i −0.291232 + 0.291232i
\(304\) 3930.80 0.741601
\(305\) 368.239 + 3533.06i 0.0691321 + 0.663287i
\(306\) 67.9692i 0.0126978i
\(307\) −838.712 838.712i −0.155921 0.155921i 0.624835 0.780757i \(-0.285166\pi\)
−0.780757 + 0.624835i \(0.785166\pi\)
\(308\) −447.770 + 447.770i −0.0828379 + 0.0828379i
\(309\) −11782.8 −2.16925
\(310\) 758.601 + 615.395i 0.138986 + 0.112749i
\(311\) 1829.59 0.333589 0.166795 0.985992i \(-0.446658\pi\)
0.166795 + 0.985992i \(0.446658\pi\)
\(312\) 720.082 + 720.082i 0.130662 + 0.130662i
\(313\) 1833.46 + 1833.46i 0.331098 + 0.331098i 0.853003 0.521906i \(-0.174779\pi\)
−0.521906 + 0.853003i \(0.674779\pi\)
\(314\) −1097.73 −0.197288
\(315\) 733.836 + 595.304i 0.131260 + 0.106481i
\(316\) 8365.28i 1.48919i
\(317\) 4633.41 + 4633.41i 0.820940 + 0.820940i 0.986243 0.165303i \(-0.0528601\pi\)
−0.165303 + 0.986243i \(0.552860\pi\)
\(318\) 111.932 + 111.932i 0.0197385 + 0.0197385i
\(319\) 2440.93 0.428419
\(320\) 512.453 + 4916.73i 0.0895219 + 0.858917i
\(321\) 9275.92i 1.61287i
\(322\) −141.834 63.5271i −0.0245468 0.0109945i
\(323\) −284.980 + 284.980i −0.0490919 + 0.0490919i
\(324\) 5932.09i 1.01716i
\(325\) −1404.16 + 2154.03i −0.239659 + 0.367643i
\(326\) 323.783 0.0550083
\(327\) 10901.9 10901.9i 1.84366 1.84366i
\(328\) 107.136 107.136i 0.0180353 0.0180353i
\(329\) −365.212 −0.0612000
\(330\) 89.8685 + 862.243i 0.0149912 + 0.143833i
\(331\) 9248.11 1.53572 0.767858 0.640620i \(-0.221323\pi\)
0.767858 + 0.640620i \(0.221323\pi\)
\(332\) −6203.17 + 6203.17i −1.02543 + 1.02543i
\(333\) 5503.18 + 5503.18i 0.905622 + 0.905622i
\(334\) 1124.88i 0.184284i
\(335\) 1089.59 1343.15i 0.177704 0.219057i
\(336\) 1416.87i 0.230049i
\(337\) −4331.81 + 4331.81i −0.700204 + 0.700204i −0.964454 0.264250i \(-0.914876\pi\)
0.264250 + 0.964454i \(0.414876\pi\)
\(338\) −540.191 + 540.191i −0.0869305 + 0.0869305i
\(339\) −3161.23 −0.506473
\(340\) −414.501 336.252i −0.0661160 0.0536348i
\(341\) 5025.05i 0.798010i
\(342\) −519.020 + 519.020i −0.0820626 + 0.0820626i
\(343\) −1562.17 1562.17i −0.245916 0.245916i
\(344\) −2800.02 −0.438858
\(345\) 7999.60 4044.87i 1.24836 0.631213i
\(346\) −1826.01 −0.283719
\(347\) 6187.40 + 6187.40i 0.957225 + 0.957225i 0.999122 0.0418965i \(-0.0133400\pi\)
−0.0418965 + 0.999122i \(0.513340\pi\)
\(348\) −3958.05 + 3958.05i −0.609694 + 0.609694i
\(349\) 5497.75i 0.843232i 0.906775 + 0.421616i \(0.138537\pi\)
−0.906775 + 0.421616i \(0.861463\pi\)
\(350\) −172.331 + 36.3174i −0.0263185 + 0.00554642i
\(351\) −174.270 −0.0265010
\(352\) 1403.76 1403.76i 0.212558 0.212558i
\(353\) 5378.94 5378.94i 0.811025 0.811025i −0.173762 0.984788i \(-0.555592\pi\)
0.984788 + 0.173762i \(0.0555924\pi\)
\(354\) 895.695i 0.134479i
\(355\) −6535.36 + 681.158i −0.977074 + 0.101837i
\(356\) 5795.34i 0.862787i
\(357\) 102.722 + 102.722i 0.0152286 + 0.0152286i
\(358\) −493.104 + 493.104i −0.0727972 + 0.0727972i
\(359\) 10265.3 1.50915 0.754573 0.656217i \(-0.227844\pi\)
0.754573 + 0.656217i \(0.227844\pi\)
\(360\) −1527.74 1239.34i −0.223664 0.181441i
\(361\) −2506.73 −0.365465
\(362\) 972.120 972.120i 0.141142 0.141142i
\(363\) 3687.60 3687.60i 0.533192 0.533192i
\(364\) −525.884 −0.0757248
\(365\) 3724.15 4590.79i 0.534057 0.658336i
\(366\) 994.587i 0.142043i
\(367\) −2084.89 + 2084.89i −0.296541 + 0.296541i −0.839657 0.543116i \(-0.817244\pi\)
0.543116 + 0.839657i \(0.317244\pi\)
\(368\) −5998.09 2686.54i −0.849652 0.380558i
\(369\) 574.713i 0.0810796i
\(370\) −1442.71 + 150.369i −0.202711 + 0.0211278i
\(371\) −165.431 −0.0231502
\(372\) −8148.28 8148.28i −1.13567 1.13567i
\(373\) 1979.61 + 1979.61i 0.274800 + 0.274800i 0.831029 0.556229i \(-0.187752\pi\)
−0.556229 + 0.831029i \(0.687752\pi\)
\(374\) 65.1677i 0.00901001i
\(375\) 4635.36 9039.12i 0.638317 1.24474i
\(376\) 760.319 0.104283
\(377\) 1433.38 + 1433.38i 0.195816 + 0.195816i
\(378\) −8.44027 8.44027i −0.00114847 0.00114847i
\(379\) 922.821 0.125072 0.0625358 0.998043i \(-0.480081\pi\)
0.0625358 + 0.998043i \(0.480081\pi\)
\(380\) 597.514 + 5732.84i 0.0806626 + 0.773917i
\(381\) −8926.86 −1.20036
\(382\) 1093.92 1093.92i 0.146518 0.146518i
\(383\) 1069.80 + 1069.80i 0.142726 + 0.142726i 0.774860 0.632133i \(-0.217820\pi\)
−0.632133 + 0.774860i \(0.717820\pi\)
\(384\) 6044.63i 0.803291i
\(385\) −703.590 570.768i −0.0931383 0.0755559i
\(386\) −1015.82 −0.133948
\(387\) −7510.14 + 7510.14i −0.986465 + 0.986465i
\(388\) 5185.59 + 5185.59i 0.678501 + 0.678501i
\(389\) −13533.7 −1.76398 −0.881990 0.471268i \(-0.843796\pi\)
−0.881990 + 0.471268i \(0.843796\pi\)
\(390\) −453.558 + 559.104i −0.0588892 + 0.0725931i
\(391\) 629.628 240.085i 0.0814364 0.0310527i
\(392\) 1600.33 + 1600.33i 0.206196 + 0.206196i
\(393\) −9460.82 + 9460.82i −1.21434 + 1.21434i
\(394\) 1321.35i 0.168956i
\(395\) 11903.8 1240.69i 1.51632 0.158041i
\(396\) 5000.60i 0.634570i
\(397\) −4049.00 4049.00i −0.511872 0.511872i 0.403227 0.915100i \(-0.367888\pi\)
−0.915100 + 0.403227i \(0.867888\pi\)
\(398\) −748.465 748.465i −0.0942643 0.0942643i
\(399\) 1568.79i 0.196836i
\(400\) −7287.80 + 1535.85i −0.910975 + 0.191981i
\(401\) 7115.73i 0.886141i 0.896487 + 0.443071i \(0.146111\pi\)
−0.896487 + 0.443071i \(0.853889\pi\)
\(402\) 342.419 342.419i 0.0424834 0.0424834i
\(403\) −2950.84 + 2950.84i −0.364743 + 0.364743i
\(404\) 2335.41i 0.287601i
\(405\) 8441.39 879.817i 1.03569 0.107947i
\(406\) 138.843i 0.0169721i
\(407\) −5276.36 5276.36i −0.642603 0.642603i
\(408\) −213.851 213.851i −0.0259491 0.0259491i
\(409\) 642.014i 0.0776174i 0.999247 + 0.0388087i \(0.0123563\pi\)
−0.999247 + 0.0388087i \(0.987644\pi\)
\(410\) 83.1851 + 67.4816i 0.0100200 + 0.00812848i
\(411\) 6264.12i 0.751792i
\(412\) −8957.27 + 8957.27i −1.07110 + 1.07110i
\(413\) −661.899 661.899i −0.0788618 0.0788618i
\(414\) 1146.71 437.255i 0.136130 0.0519080i
\(415\) −9747.16 7907.12i −1.15294 0.935290i
\(416\) 1648.64 0.194306
\(417\) 242.331 + 242.331i 0.0284581 + 0.0284581i
\(418\) 497.628 497.628i 0.0582292 0.0582292i
\(419\) 14103.4 1.64438 0.822190 0.569213i \(-0.192752\pi\)
0.822190 + 0.569213i \(0.192752\pi\)
\(420\) 2066.41 215.375i 0.240073 0.0250220i
\(421\) 11302.9i 1.30848i −0.756286 0.654241i \(-0.772988\pi\)
0.756286 0.654241i \(-0.227012\pi\)
\(422\) −769.968 769.968i −0.0888186 0.0888186i
\(423\) 2039.31 2039.31i 0.234408 0.234408i
\(424\) 344.403 0.0394474
\(425\) 417.012 639.707i 0.0475954 0.0730126i
\(426\) −1839.76 −0.209241
\(427\) −734.979 734.979i −0.0832977 0.0832977i
\(428\) 7051.57 + 7051.57i 0.796380 + 0.796380i
\(429\) −3703.56 −0.416805
\(430\) −205.207 1968.86i −0.0230139 0.220806i
\(431\) 9957.81i 1.11288i 0.830888 + 0.556439i \(0.187833\pi\)
−0.830888 + 0.556439i \(0.812167\pi\)
\(432\) −356.936 356.936i −0.0397525 0.0397525i
\(433\) 4561.99 + 4561.99i 0.506317 + 0.506317i 0.913394 0.407077i \(-0.133452\pi\)
−0.407077 + 0.913394i \(0.633452\pi\)
\(434\) −285.831 −0.0316136
\(435\) −6219.36 5045.28i −0.685506 0.556098i
\(436\) 16575.3i 1.82067i
\(437\) −6641.23 2974.60i −0.726986 0.325616i
\(438\) 1170.36 1170.36i 0.127676 0.127676i
\(439\) 12098.0i 1.31527i −0.753335 0.657637i \(-0.771556\pi\)
0.753335 0.657637i \(-0.228444\pi\)
\(440\) 1464.77 + 1188.26i 0.158705 + 0.128745i
\(441\) 8584.72 0.926976
\(442\) −38.2681 + 38.2681i −0.00411817 + 0.00411817i
\(443\) 10142.1 10142.1i 1.08773 1.08773i 0.0919679 0.995762i \(-0.470684\pi\)
0.995762 0.0919679i \(-0.0293157\pi\)
\(444\) 17111.6 1.82901
\(445\) 8246.79 859.534i 0.878506 0.0915636i
\(446\) 2121.10 0.225195
\(447\) −12546.4 + 12546.4i −1.32758 + 1.32758i
\(448\) −1022.82 1022.82i −0.107866 0.107866i
\(449\) 14130.9i 1.48525i −0.669709 0.742624i \(-0.733581\pi\)
0.669709 0.742624i \(-0.266419\pi\)
\(450\) 759.485 1165.07i 0.0795610 0.122049i
\(451\) 551.026i 0.0575317i
\(452\) −2403.17 + 2403.17i −0.250079 + 0.250079i
\(453\) 3166.84 3166.84i 0.328457 0.328457i
\(454\) 1119.90 0.115770
\(455\) −77.9964 748.335i −0.00803632 0.0771044i
\(456\) 3265.99i 0.335403i
\(457\) 4456.26 4456.26i 0.456138 0.456138i −0.441248 0.897385i \(-0.645464\pi\)
0.897385 + 0.441248i \(0.145464\pi\)
\(458\) 460.665 + 460.665i 0.0469988 + 0.0469988i
\(459\) 51.7551 0.00526301
\(460\) 3006.40 9156.23i 0.304726 0.928068i
\(461\) 18006.9 1.81923 0.909614 0.415454i \(-0.136377\pi\)
0.909614 + 0.415454i \(0.136377\pi\)
\(462\) −179.371 179.371i −0.0180630 0.0180630i
\(463\) −7678.61 + 7678.61i −0.770746 + 0.770746i −0.978237 0.207491i \(-0.933470\pi\)
0.207491 + 0.978237i \(0.433470\pi\)
\(464\) 5871.61i 0.587463i
\(465\) 10386.5 12803.6i 1.03584 1.27688i
\(466\) 501.018 0.0498051
\(467\) 7093.03 7093.03i 0.702840 0.702840i −0.262179 0.965019i \(-0.584441\pi\)
0.965019 + 0.262179i \(0.0844412\pi\)
\(468\) 2936.48 2936.48i 0.290040 0.290040i
\(469\) 506.081i 0.0498265i
\(470\) 55.7220 + 534.624i 0.00546865 + 0.0524689i
\(471\) 18527.3i 1.81251i
\(472\) 1377.98 + 1377.98i 0.134378 + 0.134378i
\(473\) 7200.61 7200.61i 0.699967 0.699967i
\(474\) 3351.03 0.324721
\(475\) −8069.23 + 1700.53i −0.779456 + 0.164264i
\(476\) 156.178 0.0150387
\(477\) 923.748 923.748i 0.0886698 0.0886698i
\(478\) 1770.49 1770.49i 0.169415 0.169415i
\(479\) 11004.1 1.04966 0.524831 0.851206i \(-0.324128\pi\)
0.524831 + 0.851206i \(0.324128\pi\)
\(480\) −6478.19 + 675.199i −0.616016 + 0.0642052i
\(481\) 6196.82i 0.587424i
\(482\) −895.710 + 895.710i −0.0846441 + 0.0846441i
\(483\) −1072.20 + 2393.85i −0.101008 + 0.225515i
\(484\) 5606.64i 0.526544i
\(485\) −6610.01 + 8148.21i −0.618856 + 0.762869i
\(486\) 2277.81 0.212600
\(487\) −11809.0 11809.0i −1.09881 1.09881i −0.994550 0.104257i \(-0.966754\pi\)
−0.104257 0.994550i \(-0.533246\pi\)
\(488\) 1530.12 + 1530.12i 0.141937 + 0.141937i
\(489\) 5464.76i 0.505368i
\(490\) −1008.00 + 1242.57i −0.0929323 + 0.114558i
\(491\) −16493.9 −1.51601 −0.758003 0.652251i \(-0.773825\pi\)
−0.758003 + 0.652251i \(0.773825\pi\)
\(492\) −893.507 893.507i −0.0818748 0.0818748i
\(493\) −425.687 425.687i −0.0388884 0.0388884i
\(494\) 584.440 0.0532292
\(495\) 7115.88 741.663i 0.646131 0.0673440i
\(496\) −12087.7 −1.09426
\(497\) 1359.54 1359.54i 0.122704 0.122704i
\(498\) −2484.92 2484.92i −0.223598 0.223598i
\(499\) 17340.0i 1.55560i 0.628512 + 0.777800i \(0.283664\pi\)
−0.628512 + 0.777800i \(0.716336\pi\)
\(500\) −3347.75 10395.4i −0.299432 0.929790i
\(501\) −18985.6 −1.69304
\(502\) −1207.54 + 1207.54i −0.107361 + 0.107361i
\(503\) −9582.46 9582.46i −0.849425 0.849425i 0.140636 0.990061i \(-0.455085\pi\)
−0.990061 + 0.140636i \(0.955085\pi\)
\(504\) 575.632 0.0508744
\(505\) −3323.29 + 346.375i −0.292841 + 0.0305218i
\(506\) −1099.45 + 419.233i −0.0965939 + 0.0368324i
\(507\) 9117.25 + 9117.25i 0.798642 + 0.798642i
\(508\) −6786.21 + 6786.21i −0.592696 + 0.592696i
\(509\) 12955.1i 1.12815i −0.825725 0.564073i \(-0.809234\pi\)
0.825725 0.564073i \(-0.190766\pi\)
\(510\) 134.699 166.044i 0.0116952 0.0144168i
\(511\) 1729.75i 0.149745i
\(512\) 5672.31 + 5672.31i 0.489615 + 0.489615i
\(513\) −395.208 395.208i −0.0340134 0.0340134i
\(514\) 147.508i 0.0126581i
\(515\) −14074.7 11417.7i −1.20428 0.976943i
\(516\) 23352.1i 1.99228i
\(517\) −1955.25 + 1955.25i −0.166329 + 0.166329i
\(518\) 300.126 300.126i 0.0254571 0.0254571i
\(519\) 30819.1i 2.60657i
\(520\) 162.377 + 1557.93i 0.0136937 + 0.131384i
\(521\) 14860.4i 1.24961i 0.780781 + 0.624805i \(0.214821\pi\)
−0.780781 + 0.624805i \(0.785179\pi\)
\(522\) −775.284 775.284i −0.0650063 0.0650063i
\(523\) −4919.23 4919.23i −0.411286 0.411286i 0.470900 0.882187i \(-0.343929\pi\)
−0.882187 + 0.470900i \(0.843929\pi\)
\(524\) 14384.3i 1.19920i
\(525\) 612.960 + 2908.57i 0.0509557 + 0.241792i
\(526\) 2176.39i 0.180409i
\(527\) 876.346 876.346i 0.0724368 0.0724368i
\(528\) −7585.54 7585.54i −0.625224 0.625224i
\(529\) 8100.97 + 9078.00i 0.665815 + 0.746117i
\(530\) 25.2405 + 242.170i 0.00206863 + 0.0198475i
\(531\) 7391.95 0.604112
\(532\) −1192.60 1192.60i −0.0971909 0.0971909i
\(533\) −323.576 + 323.576i −0.0262958 + 0.0262958i
\(534\) 2321.54 0.188133
\(535\) −8988.57 + 11080.3i −0.726373 + 0.895405i
\(536\) 1053.59i 0.0849030i
\(537\) 8322.54 + 8322.54i 0.668797 + 0.668797i
\(538\) −925.489 + 925.489i −0.0741648 + 0.0741648i
\(539\) −8230.89 −0.657755
\(540\) 466.313 574.827i 0.0371609 0.0458085i
\(541\) −4292.94 −0.341161 −0.170580 0.985344i \(-0.554564\pi\)
−0.170580 + 0.985344i \(0.554564\pi\)
\(542\) −1208.09 1208.09i −0.0957414 0.0957414i
\(543\) −16407.3 16407.3i −1.29669 1.29669i
\(544\) −489.617 −0.0385886
\(545\) 23586.8 2458.37i 1.85385 0.193220i
\(546\) 210.663i 0.0165120i
\(547\) −923.661 923.661i −0.0721990 0.0721990i 0.670085 0.742284i \(-0.266258\pi\)
−0.742284 + 0.670085i \(0.766258\pi\)
\(548\) −4762.00 4762.00i −0.371209 0.371209i
\(549\) 8208.08 0.638092
\(550\) −728.182 + 1117.05i −0.0564541 + 0.0866022i
\(551\) 6501.19i 0.502650i
\(552\) 2232.17 4983.64i 0.172115 0.384272i
\(553\) −2476.34 + 2476.34i −0.190424 + 0.190424i
\(554\) 3230.22i 0.247724i
\(555\) 2537.90 + 24349.9i 0.194104 + 1.86233i
\(556\) 368.442 0.0281032
\(557\) 5210.56 5210.56i 0.396371 0.396371i −0.480580 0.876951i \(-0.659574\pi\)
0.876951 + 0.480580i \(0.159574\pi\)
\(558\) 1596.05 1596.05i 0.121086 0.121086i
\(559\) 8456.76 0.639862
\(560\) 1372.97 1692.47i 0.103605 0.127714i
\(561\) 1099.89 0.0827761
\(562\) 1996.09 1996.09i 0.149822 0.149822i
\(563\) −3376.16 3376.16i −0.252732 0.252732i 0.569358 0.822090i \(-0.307192\pi\)
−0.822090 + 0.569358i \(0.807192\pi\)
\(564\) 6341.02i 0.473413i
\(565\) −3776.15 3063.30i −0.281175 0.228095i
\(566\) 1314.32i 0.0976062i
\(567\) −1756.05 + 1756.05i −0.130066 + 0.130066i
\(568\) −2830.38 + 2830.38i −0.209084 + 0.209084i
\(569\) 2722.51 0.200586 0.100293 0.994958i \(-0.468022\pi\)
0.100293 + 0.994958i \(0.468022\pi\)
\(570\) −2296.51 + 239.357i −0.168754 + 0.0175887i
\(571\) 12138.6i 0.889639i 0.895620 + 0.444819i \(0.146732\pi\)
−0.895620 + 0.444819i \(0.853268\pi\)
\(572\) −2815.45 + 2815.45i −0.205804 + 0.205804i
\(573\) −18463.0 18463.0i −1.34608 1.34608i
\(574\) −31.3430 −0.00227915
\(575\) 13475.2 + 2920.11i 0.977316 + 0.211786i
\(576\) 11422.6 0.826291
\(577\) 706.491 + 706.491i 0.0509734 + 0.0509734i 0.732134 0.681161i \(-0.238524\pi\)
−0.681161 + 0.732134i \(0.738524\pi\)
\(578\) −1484.78 + 1484.78i −0.106849 + 0.106849i
\(579\) 17144.9i 1.23060i
\(580\) −8563.40 + 892.533i −0.613062 + 0.0638973i
\(581\) 3672.60 0.262246
\(582\) −2077.28 + 2077.28i −0.147949 + 0.147949i
\(583\) −885.675 + 885.675i −0.0629175 + 0.0629175i
\(584\) 3601.08i 0.255161i
\(585\) 4614.15 + 3743.10i 0.326105 + 0.264544i
\(586\) 1086.01i 0.0765577i
\(587\) 8053.21 + 8053.21i 0.566255 + 0.566255i 0.931077 0.364822i \(-0.118870\pi\)
−0.364822 + 0.931077i \(0.618870\pi\)
\(588\) 13346.7 13346.7i 0.936067 0.936067i
\(589\) −13383.8 −0.936279
\(590\) −867.947 + 1069.93i −0.0605641 + 0.0746578i
\(591\) −22301.6 −1.55223
\(592\) 12692.2 12692.2i 0.881158 0.881158i
\(593\) 15840.6 15840.6i 1.09696 1.09696i 0.102192 0.994765i \(-0.467415\pi\)
0.994765 0.102192i \(-0.0325855\pi\)
\(594\) −90.3742 −0.00624259
\(595\) 23.1635 + 222.242i 0.00159599 + 0.0153127i
\(596\) 19075.7i 1.31102i
\(597\) −12632.5 + 12632.5i −0.866018 + 0.866018i
\(598\) −891.809 399.440i −0.0609846 0.0273149i
\(599\) 14283.6i 0.974309i −0.873316 0.487155i \(-0.838035\pi\)
0.873316 0.487155i \(-0.161965\pi\)
\(600\) −1276.09 6055.23i −0.0868271 0.412006i
\(601\) 13120.6 0.890515 0.445258 0.895402i \(-0.353112\pi\)
0.445258 + 0.895402i \(0.353112\pi\)
\(602\) 409.579 + 409.579i 0.0277296 + 0.0277296i
\(603\) −2825.90 2825.90i −0.190845 0.190845i
\(604\) 4814.87i 0.324362i
\(605\) 7978.27 831.547i 0.536137 0.0558796i
\(606\) −935.536 −0.0627121
\(607\) 19416.6 + 19416.6i 1.29835 + 1.29835i 0.929485 + 0.368860i \(0.120252\pi\)
0.368860 + 0.929485i \(0.379748\pi\)
\(608\) 3738.78 + 3738.78i 0.249387 + 0.249387i
\(609\) 2343.37 0.155925
\(610\) −963.776 + 1188.05i −0.0639707 + 0.0788572i
\(611\) −2296.35 −0.152046
\(612\) −872.083 + 872.083i −0.0576011 + 0.0576011i
\(613\) 18475.3 + 18475.3i 1.21731 + 1.21731i 0.968571 + 0.248737i \(0.0800155\pi\)
0.248737 + 0.968571i \(0.419985\pi\)
\(614\) 510.822i 0.0335751i
\(615\) 1138.94 1403.98i 0.0746775 0.0920555i
\(616\) −551.907 −0.0360989
\(617\) −12645.9 + 12645.9i −0.825130 + 0.825130i −0.986839 0.161708i \(-0.948300\pi\)
0.161708 + 0.986839i \(0.448300\pi\)
\(618\) −3588.17 3588.17i −0.233556 0.233556i
\(619\) 21109.8 1.37072 0.685358 0.728206i \(-0.259646\pi\)
0.685358 + 0.728206i \(0.259646\pi\)
\(620\) −1837.42 17629.1i −0.119021 1.14194i
\(621\) 332.948 + 873.164i 0.0215149 + 0.0564233i
\(622\) 557.159 + 557.159i 0.0359165 + 0.0359165i
\(623\) −1715.57 + 1715.57i −0.110326 + 0.110326i
\(624\) 8908.84i 0.571537i
\(625\) 14296.1 6305.65i 0.914953 0.403562i
\(626\) 1116.68i 0.0712964i
\(627\) −8398.89 8398.89i −0.534959 0.534959i
\(628\) 14084.5 + 14084.5i 0.894957 + 0.894957i
\(629\) 1840.35i 0.116660i
\(630\) 42.1867 + 404.760i 0.00266787 + 0.0255969i
\(631\) 24590.2i 1.55138i −0.631114 0.775690i \(-0.717402\pi\)
0.631114 0.775690i \(-0.282598\pi\)
\(632\) 5155.38 5155.38i 0.324478 0.324478i
\(633\) −12995.4 + 12995.4i −0.815988 + 0.815988i
\(634\) 2822.00i 0.176776i
\(635\) −10663.3 8650.32i −0.666394 0.540594i
\(636\) 2872.30i 0.179079i
\(637\) −4833.39 4833.39i −0.300637 0.300637i
\(638\) 743.330 + 743.330i 0.0461265 + 0.0461265i
\(639\) 15183.1i 0.939960i
\(640\) −5857.37 + 7220.43i −0.361770 + 0.445957i
\(641\) 7415.93i 0.456960i 0.973549 + 0.228480i \(0.0733756\pi\)
−0.973549 + 0.228480i \(0.926624\pi\)
\(642\) −2824.77 + 2824.77i −0.173653 + 0.173653i
\(643\) 3798.58 + 3798.58i 0.232973 + 0.232973i 0.813932 0.580960i \(-0.197323\pi\)
−0.580960 + 0.813932i \(0.697323\pi\)
\(644\) 1004.72 + 2634.90i 0.0614773 + 0.161226i
\(645\) −33230.1 + 3463.45i −2.02858 + 0.211432i
\(646\) −173.568 −0.0105711
\(647\) −16792.3 16792.3i −1.02036 1.02036i −0.999788 0.0205700i \(-0.993452\pi\)
−0.0205700 0.999788i \(-0.506548\pi\)
\(648\) 3655.85 3655.85i 0.221629 0.221629i
\(649\) −7087.28 −0.428660
\(650\) −1083.57 + 228.353i −0.0653862 + 0.0137796i
\(651\) 4824.21i 0.290439i
\(652\) −4154.32 4154.32i −0.249533 0.249533i
\(653\) −5572.37 + 5572.37i −0.333942 + 0.333942i −0.854081 0.520140i \(-0.825880\pi\)
0.520140 + 0.854081i \(0.325880\pi\)
\(654\) 6639.88 0.397003
\(655\) −20468.9 + 2133.40i −1.22105 + 0.127265i
\(656\) −1325.48 −0.0788893
\(657\) −9658.72 9658.72i −0.573550 0.573550i
\(658\) −111.217 111.217i −0.00658921 0.00658921i
\(659\) −5055.49 −0.298838 −0.149419 0.988774i \(-0.547740\pi\)
−0.149419 + 0.988774i \(0.547740\pi\)
\(660\) 9910.00 12216.1i 0.584464 0.720473i
\(661\) 22670.3i 1.33400i −0.745060 0.666998i \(-0.767579\pi\)
0.745060 0.666998i \(-0.232421\pi\)
\(662\) 2816.30 + 2816.30i 0.165346 + 0.165346i
\(663\) 645.884 + 645.884i 0.0378342 + 0.0378342i
\(664\) −7645.82 −0.446861
\(665\) 1520.19 1873.95i 0.0886472 0.109276i
\(666\) 3351.74i 0.195011i
\(667\) 4443.29 9920.30i 0.257938 0.575886i
\(668\) −14432.9 + 14432.9i −0.835965 + 0.835965i
\(669\) 35799.5i 2.06889i
\(670\) 740.838 77.2149i 0.0427180 0.00445235i
\(671\) −7869.78 −0.452771
\(672\) 1347.65 1347.65i 0.0773613 0.0773613i
\(673\) −4450.84 + 4450.84i −0.254929 + 0.254929i −0.822988 0.568059i \(-0.807695\pi\)
0.568059 + 0.822988i \(0.307695\pi\)
\(674\) −2638.31 −0.150777
\(675\) 887.142 + 578.309i 0.0505868 + 0.0329765i
\(676\) 13861.9 0.788684
\(677\) 6334.06 6334.06i 0.359583 0.359583i −0.504076 0.863659i \(-0.668167\pi\)
0.863659 + 0.504076i \(0.168167\pi\)
\(678\) −962.682 962.682i −0.0545303 0.0545303i
\(679\) 3070.14i 0.173521i
\(680\) −48.2231 462.676i −0.00271952 0.0260924i
\(681\) 18901.5i 1.06359i
\(682\) −1530.27 + 1530.27i −0.0859192 + 0.0859192i
\(683\) −8429.80 + 8429.80i −0.472266 + 0.472266i −0.902647 0.430381i \(-0.858379\pi\)
0.430381 + 0.902647i \(0.358379\pi\)
\(684\) 13318.7 0.744520
\(685\) 6070.07 7482.62i 0.338577 0.417367i
\(686\) 951.446i 0.0529539i
\(687\) 7775.03 7775.03i 0.431784 0.431784i
\(688\) 17320.9 + 17320.9i 0.959817 + 0.959817i
\(689\) −1040.18 −0.0575149
\(690\) 3667.88 + 1204.33i 0.202368 + 0.0664462i
\(691\) 1898.29 0.104507 0.0522534 0.998634i \(-0.483360\pi\)
0.0522534 + 0.998634i \(0.483360\pi\)
\(692\) 23428.7 + 23428.7i 1.28703 + 1.28703i
\(693\) −1480.31 + 1480.31i −0.0811432 + 0.0811432i
\(694\) 3768.47i 0.206123i
\(695\) 54.6453 + 524.294i 0.00298247 + 0.0286153i
\(696\) −4878.56 −0.265691
\(697\) 96.0964 96.0964i 0.00522225 0.00522225i
\(698\) −1674.22 + 1674.22i −0.0907881 + 0.0907881i
\(699\) 8456.09i 0.457566i
\(700\) 2677.08 + 1745.13i 0.144549 + 0.0942282i
\(701\) 5394.79i 0.290668i −0.989383 0.145334i \(-0.953574\pi\)
0.989383 0.145334i \(-0.0464257\pi\)
\(702\) −53.0700 53.0700i −0.00285328 0.00285328i
\(703\) 14053.1 14053.1i 0.753944 0.753944i
\(704\) −10951.9 −0.586312
\(705\) 9023.30 940.467i 0.482038 0.0502412i
\(706\) 3276.07 0.174641
\(707\) 691.341 691.341i 0.0367759 0.0367759i
\(708\) 11492.3 11492.3i 0.610037 0.610037i
\(709\) −21018.7 −1.11336 −0.556682 0.830726i \(-0.687926\pi\)
−0.556682 + 0.830726i \(0.687926\pi\)
\(710\) −2197.63 1782.77i −0.116163 0.0942339i
\(711\) 27655.2i 1.45872i
\(712\) 3571.57 3571.57i 0.187992 0.187992i
\(713\) 20422.6 + 9147.24i 1.07269 + 0.480458i
\(714\) 62.5631i 0.00327922i
\(715\) −4423.97 3588.83i −0.231395 0.187713i
\(716\) 12653.6 0.660458
\(717\) −29882.0 29882.0i −1.55643 1.55643i
\(718\) 3126.08 + 3126.08i 0.162485 + 0.162485i
\(719\) 18369.4i 0.952798i 0.879229 + 0.476399i \(0.158058\pi\)
−0.879229 + 0.476399i \(0.841942\pi\)
\(720\) 1784.06 + 17117.1i 0.0923443 + 0.885997i
\(721\) 5303.17 0.273926
\(722\) −763.367 763.367i −0.0393485 0.0393485i
\(723\) 15117.7 + 15117.7i 0.777637 + 0.777637i
\(724\) −24945.7 −1.28052
\(725\) −2540.16 12053.4i −0.130123 0.617450i
\(726\) 2245.95 0.114814
\(727\) −21955.4 + 21955.4i −1.12006 + 1.12006i −0.128324 + 0.991732i \(0.540960\pi\)
−0.991732 + 0.128324i \(0.959040\pi\)
\(728\) −324.094 324.094i −0.0164996 0.0164996i
\(729\) 17948.6i 0.911881i
\(730\) 2532.13 263.915i 0.128381 0.0133807i
\(731\) −2511.51 −0.127074
\(732\) 12761.1 12761.1i 0.644350 0.644350i
\(733\) 7769.78 + 7769.78i 0.391519 + 0.391519i 0.875229 0.483710i \(-0.160711\pi\)
−0.483710 + 0.875229i \(0.660711\pi\)
\(734\) −1269.82 −0.0638552
\(735\) 20971.9 + 17012.9i 1.05246 + 0.853781i
\(736\) −3149.78 8260.37i −0.157748 0.413698i
\(737\) 2709.43 + 2709.43i 0.135418 + 0.135418i
\(738\) 175.016 175.016i 0.00872958 0.00872958i
\(739\) 24124.6i 1.20086i −0.799676 0.600432i \(-0.794995\pi\)
0.799676 0.600432i \(-0.205005\pi\)
\(740\) 20440.1 + 16581.5i 1.01540 + 0.823713i
\(741\) 9864.09i 0.489023i
\(742\) −50.3782 50.3782i −0.00249251 0.00249251i
\(743\) −17115.2 17115.2i −0.845082 0.845082i 0.144432 0.989515i \(-0.453864\pi\)
−0.989515 + 0.144432i \(0.953864\pi\)
\(744\) 10043.3i 0.494900i
\(745\) −27144.7 + 2829.20i −1.33491 + 0.139133i
\(746\) 1205.69i 0.0591737i
\(747\) −20507.4 + 20507.4i −1.00445 + 1.00445i
\(748\) 836.139 836.139i 0.0408720 0.0408720i
\(749\) 4174.90i 0.203668i
\(750\) 4164.26 1341.07i 0.202743 0.0652918i
\(751\) 993.038i 0.0482509i −0.999709 0.0241255i \(-0.992320\pi\)
0.999709 0.0241255i \(-0.00768012\pi\)
\(752\) −4703.33 4703.33i −0.228075 0.228075i
\(753\) 20380.7 + 20380.7i 0.986341 + 0.986341i
\(754\) 873.005i 0.0421657i
\(755\) 6851.59 714.117i 0.330271 0.0344230i
\(756\) 216.587i 0.0104196i
\(757\) 18301.2 18301.2i 0.878689 0.878689i −0.114710 0.993399i \(-0.536594\pi\)
0.993399 + 0.114710i \(0.0365940\pi\)
\(758\) 281.025 + 281.025i 0.0134661 + 0.0134661i
\(759\) 7075.76 + 18556.3i 0.338384 + 0.887421i
\(760\) −3164.81 + 3901.29i −0.151052 + 0.186203i
\(761\) 11272.9 0.536979 0.268489 0.963283i \(-0.413476\pi\)
0.268489 + 0.963283i \(0.413476\pi\)
\(762\) −2718.48 2718.48i −0.129239 0.129239i
\(763\) −4906.73 + 4906.73i −0.232812 + 0.232812i
\(764\) −28071.2 −1.32929
\(765\) −1370.32 1111.63i −0.0647634 0.0525376i
\(766\) 651.567i 0.0307338i
\(767\) −4161.83 4161.83i −0.195926 0.195926i
\(768\) 16339.5 16339.5i 0.767711 0.767711i
\(769\) 27473.6 1.28833 0.644164 0.764888i \(-0.277206\pi\)
0.644164 + 0.764888i \(0.277206\pi\)
\(770\) −40.4479 388.077i −0.00189304 0.0181628i
\(771\) −2489.61 −0.116292
\(772\) 13033.6 + 13033.6i 0.607629