Properties

Label 197.3.c.a.14.17
Level $197$
Weight $3$
Character 197.14
Analytic conductor $5.368$
Analytic rank $0$
Dimension $64$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [197,3,Mod(14,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.14");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 197.c (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: \(5.36786120790\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 14.17
Character \(\chi\) \(=\) 197.14
Dual form 197.3.c.a.183.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.00732944 + 0.00732944i) q^{2} +(0.226886 - 0.226886i) q^{3} +3.99989i q^{4} +(-2.04970 + 2.04970i) q^{5} +0.00332589i q^{6} -5.87781i q^{7} +(-0.0586348 - 0.0586348i) q^{8} +8.89705i q^{9} +O(q^{10})\) \(q+(-0.00732944 + 0.00732944i) q^{2} +(0.226886 - 0.226886i) q^{3} +3.99989i q^{4} +(-2.04970 + 2.04970i) q^{5} +0.00332589i q^{6} -5.87781i q^{7} +(-0.0586348 - 0.0586348i) q^{8} +8.89705i q^{9} -0.0300462i q^{10} +(-5.65729 + 5.65729i) q^{11} +(0.907518 + 0.907518i) q^{12} +(-5.84645 + 5.84645i) q^{13} +(0.0430811 + 0.0430811i) q^{14} +0.930093i q^{15} -15.9987 q^{16} +(-2.92822 - 2.92822i) q^{17} +(-0.0652104 - 0.0652104i) q^{18} +11.3486i q^{19} +(-8.19856 - 8.19856i) q^{20} +(-1.33359 - 1.33359i) q^{21} -0.0829295i q^{22} -21.0549 q^{23} -0.0266068 q^{24} +16.5975i q^{25} -0.0857025i q^{26} +(4.06058 + 4.06058i) q^{27} +23.5106 q^{28} +33.7493 q^{29} +(-0.00681706 - 0.00681706i) q^{30} +(-10.5120 + 10.5120i) q^{31} +(0.351801 - 0.351801i) q^{32} +2.56711i q^{33} +0.0429244 q^{34} +(12.0477 + 12.0477i) q^{35} -35.5872 q^{36} +56.8394 q^{37} +(-0.0831791 - 0.0831791i) q^{38} +2.65295i q^{39} +0.240367 q^{40} +38.9030i q^{41} +0.0195489 q^{42} -3.83137i q^{43} +(-22.6285 - 22.6285i) q^{44} +(-18.2362 - 18.2362i) q^{45} +(0.154320 - 0.154320i) q^{46} -81.9341i q^{47} +(-3.62988 + 3.62988i) q^{48} +14.4514 q^{49} +(-0.121650 - 0.121650i) q^{50} -1.32874 q^{51} +(-23.3852 - 23.3852i) q^{52} -6.52021 q^{53} -0.0595236 q^{54} -23.1914i q^{55} +(-0.344644 + 0.344644i) q^{56} +(2.57484 + 2.57484i) q^{57} +(-0.247364 + 0.247364i) q^{58} -99.4993 q^{59} -3.72027 q^{60} +93.2962 q^{61} -0.154094i q^{62} +52.2951 q^{63} -63.9897i q^{64} -23.9669i q^{65} +(-0.0188155 - 0.0188155i) q^{66} +(77.0195 - 77.0195i) q^{67} +(11.7126 - 11.7126i) q^{68} +(-4.77705 + 4.77705i) q^{69} -0.176606 q^{70} +(60.7264 + 60.7264i) q^{71} +(0.521676 - 0.521676i) q^{72} +(2.12145 - 2.12145i) q^{73} +(-0.416601 + 0.416601i) q^{74} +(3.76573 + 3.76573i) q^{75} -45.3933 q^{76} +(33.2524 + 33.2524i) q^{77} +(-0.0194447 - 0.0194447i) q^{78} +(61.5250 + 61.5250i) q^{79} +(32.7925 - 32.7925i) q^{80} -78.2308 q^{81} +(-0.285138 - 0.285138i) q^{82} -15.6373i q^{83} +(5.33422 - 5.33422i) q^{84} +12.0039 q^{85} +(0.0280818 + 0.0280818i) q^{86} +(7.65723 - 7.65723i) q^{87} +0.663427 q^{88} +(38.3862 + 38.3862i) q^{89} +0.267323 q^{90} +(34.3643 + 34.3643i) q^{91} -84.2172i q^{92} +4.77005i q^{93} +(0.600531 + 0.600531i) q^{94} +(-23.2612 - 23.2612i) q^{95} -0.159637i q^{96} +25.4365i q^{97} +(-0.105921 + 0.105921i) q^{98} +(-50.3331 - 50.3331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28} + 56 q^{29} - 70 q^{30} - 64 q^{31} - 156 q^{32} - 52 q^{34} - 92 q^{35} - 36 q^{36} - 160 q^{37} + 40 q^{38} + 52 q^{40} + 80 q^{42} + 140 q^{44} + 324 q^{45} + 214 q^{46} + 216 q^{48} - 836 q^{49} + 126 q^{50} + 124 q^{51} - 10 q^{52} - 16 q^{53} + 400 q^{54} - 40 q^{56} + 68 q^{57} - 266 q^{58} - 364 q^{59} - 68 q^{60} - 168 q^{61} - 12 q^{63} + 238 q^{66} - 112 q^{67} - 148 q^{68} - 48 q^{69} + 48 q^{70} + 150 q^{71} - 474 q^{72} + 18 q^{73} + 236 q^{74} + 64 q^{75} - 260 q^{76} - 388 q^{77} - 782 q^{78} + 202 q^{79} + 796 q^{80} - 516 q^{81} + 72 q^{82} - 294 q^{84} - 696 q^{85} + 618 q^{86} + 464 q^{87} - 244 q^{88} - 536 q^{89} + 1484 q^{90} + 212 q^{91} + 132 q^{94} + 370 q^{95} - 530 q^{98} - 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/197\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.00732944 + 0.00732944i −0.00366472 + 0.00366472i −0.708937 0.705272i \(-0.750825\pi\)
0.705272 + 0.708937i \(0.250825\pi\)
\(3\) 0.226886 0.226886i 0.0756285 0.0756285i −0.668281 0.743909i \(-0.732969\pi\)
0.743909 + 0.668281i \(0.232969\pi\)
\(4\) 3.99989i 0.999973i
\(5\) −2.04970 + 2.04970i −0.409939 + 0.409939i −0.881717 0.471778i \(-0.843612\pi\)
0.471778 + 0.881717i \(0.343612\pi\)
\(6\) 0.00332589i 0.000554315i
\(7\) 5.87781i 0.839687i −0.907597 0.419843i \(-0.862085\pi\)
0.907597 0.419843i \(-0.137915\pi\)
\(8\) −0.0586348 0.0586348i −0.00732935 0.00732935i
\(9\) 8.89705i 0.988561i
\(10\) 0.0300462i 0.00300462i
\(11\) −5.65729 + 5.65729i −0.514299 + 0.514299i −0.915841 0.401542i \(-0.868474\pi\)
0.401542 + 0.915841i \(0.368474\pi\)
\(12\) 0.907518 + 0.907518i 0.0756265 + 0.0756265i
\(13\) −5.84645 + 5.84645i −0.449727 + 0.449727i −0.895264 0.445537i \(-0.853013\pi\)
0.445537 + 0.895264i \(0.353013\pi\)
\(14\) 0.0430811 + 0.0430811i 0.00307722 + 0.00307722i
\(15\) 0.930093i 0.0620062i
\(16\) −15.9987 −0.999919
\(17\) −2.92822 2.92822i −0.172248 0.172248i 0.615718 0.787966i \(-0.288866\pi\)
−0.787966 + 0.615718i \(0.788866\pi\)
\(18\) −0.0652104 0.0652104i −0.00362280 0.00362280i
\(19\) 11.3486i 0.597296i 0.954363 + 0.298648i \(0.0965357\pi\)
−0.954363 + 0.298648i \(0.903464\pi\)
\(20\) −8.19856 8.19856i −0.409928 0.409928i
\(21\) −1.33359 1.33359i −0.0635043 0.0635043i
\(22\) 0.0829295i 0.00376952i
\(23\) −21.0549 −0.915429 −0.457714 0.889099i \(-0.651332\pi\)
−0.457714 + 0.889099i \(0.651332\pi\)
\(24\) −0.0266068 −0.00110862
\(25\) 16.5975i 0.663900i
\(26\) 0.0857025i 0.00329625i
\(27\) 4.06058 + 4.06058i 0.150392 + 0.150392i
\(28\) 23.5106 0.839664
\(29\) 33.7493 1.16377 0.581884 0.813271i \(-0.302316\pi\)
0.581884 + 0.813271i \(0.302316\pi\)
\(30\) −0.00681706 0.00681706i −0.000227235 0.000227235i
\(31\) −10.5120 + 10.5120i −0.339097 + 0.339097i −0.856028 0.516930i \(-0.827075\pi\)
0.516930 + 0.856028i \(0.327075\pi\)
\(32\) 0.351801 0.351801i 0.0109938 0.0109938i
\(33\) 2.56711i 0.0777913i
\(34\) 0.0429244 0.00126248
\(35\) 12.0477 + 12.0477i 0.344220 + 0.344220i
\(36\) −35.5872 −0.988534
\(37\) 56.8394 1.53620 0.768100 0.640330i \(-0.221203\pi\)
0.768100 + 0.640330i \(0.221203\pi\)
\(38\) −0.0831791 0.0831791i −0.00218892 0.00218892i
\(39\) 2.65295i 0.0680244i
\(40\) 0.240367 0.00600917
\(41\) 38.9030i 0.948854i 0.880295 + 0.474427i \(0.157345\pi\)
−0.880295 + 0.474427i \(0.842655\pi\)
\(42\) 0.0195489 0.000465451
\(43\) 3.83137i 0.0891017i −0.999007 0.0445509i \(-0.985814\pi\)
0.999007 0.0445509i \(-0.0141857\pi\)
\(44\) −22.6285 22.6285i −0.514285 0.514285i
\(45\) −18.2362 18.2362i −0.405250 0.405250i
\(46\) 0.154320 0.154320i 0.00335479 0.00335479i
\(47\) 81.9341i 1.74328i −0.490148 0.871639i \(-0.663057\pi\)
0.490148 0.871639i \(-0.336943\pi\)
\(48\) −3.62988 + 3.62988i −0.0756224 + 0.0756224i
\(49\) 14.4514 0.294926
\(50\) −0.121650 0.121650i −0.00243301 0.00243301i
\(51\) −1.32874 −0.0260538
\(52\) −23.3852 23.3852i −0.449715 0.449715i
\(53\) −6.52021 −0.123023 −0.0615114 0.998106i \(-0.519592\pi\)
−0.0615114 + 0.998106i \(0.519592\pi\)
\(54\) −0.0595236 −0.00110229
\(55\) 23.1914i 0.421662i
\(56\) −0.344644 + 0.344644i −0.00615435 + 0.00615435i
\(57\) 2.57484 + 2.57484i 0.0451726 + 0.0451726i
\(58\) −0.247364 + 0.247364i −0.00426489 + 0.00426489i
\(59\) −99.4993 −1.68643 −0.843215 0.537577i \(-0.819340\pi\)
−0.843215 + 0.537577i \(0.819340\pi\)
\(60\) −3.72027 −0.0620045
\(61\) 93.2962 1.52945 0.764723 0.644359i \(-0.222876\pi\)
0.764723 + 0.644359i \(0.222876\pi\)
\(62\) 0.154094i 0.00248539i
\(63\) 52.2951 0.830081
\(64\) 63.9897i 0.999839i
\(65\) 23.9669i 0.368721i
\(66\) −0.0188155 0.0188155i −0.000285084 0.000285084i
\(67\) 77.0195 77.0195i 1.14955 1.14955i 0.162903 0.986642i \(-0.447914\pi\)
0.986642 0.162903i \(-0.0520857\pi\)
\(68\) 11.7126 11.7126i 0.172244 0.172244i
\(69\) −4.77705 + 4.77705i −0.0692326 + 0.0692326i
\(70\) −0.176606 −0.00252294
\(71\) 60.7264 + 60.7264i 0.855301 + 0.855301i 0.990780 0.135479i \(-0.0432574\pi\)
−0.135479 + 0.990780i \(0.543257\pi\)
\(72\) 0.521676 0.521676i 0.00724550 0.00724550i
\(73\) 2.12145 2.12145i 0.0290609 0.0290609i −0.692427 0.721488i \(-0.743459\pi\)
0.721488 + 0.692427i \(0.243459\pi\)
\(74\) −0.416601 + 0.416601i −0.00562974 + 0.00562974i
\(75\) 3.76573 + 3.76573i 0.0502098 + 0.0502098i
\(76\) −45.3933 −0.597280
\(77\) 33.2524 + 33.2524i 0.431850 + 0.431850i
\(78\) −0.0194447 0.0194447i −0.000249291 0.000249291i
\(79\) 61.5250 + 61.5250i 0.778798 + 0.778798i 0.979626 0.200829i \(-0.0643635\pi\)
−0.200829 + 0.979626i \(0.564363\pi\)
\(80\) 32.7925 32.7925i 0.409906 0.409906i
\(81\) −78.2308 −0.965813
\(82\) −0.285138 0.285138i −0.00347729 0.00347729i
\(83\) 15.6373i 0.188401i −0.995553 0.0942004i \(-0.969971\pi\)
0.995553 0.0942004i \(-0.0300294\pi\)
\(84\) 5.33422 5.33422i 0.0635026 0.0635026i
\(85\) 12.0039 0.141223
\(86\) 0.0280818 + 0.0280818i 0.000326533 + 0.000326533i
\(87\) 7.65723 7.65723i 0.0880142 0.0880142i
\(88\) 0.663427 0.00753895
\(89\) 38.3862 + 38.3862i 0.431306 + 0.431306i 0.889072 0.457767i \(-0.151350\pi\)
−0.457767 + 0.889072i \(0.651350\pi\)
\(90\) 0.267323 0.00297025
\(91\) 34.3643 + 34.3643i 0.377630 + 0.377630i
\(92\) 84.2172i 0.915404i
\(93\) 4.77005i 0.0512909i
\(94\) 0.600531 + 0.600531i 0.00638863 + 0.00638863i
\(95\) −23.2612 23.2612i −0.244855 0.244855i
\(96\) 0.159637i 0.00166289i
\(97\) 25.4365i 0.262232i 0.991367 + 0.131116i \(0.0418560\pi\)
−0.991367 + 0.131116i \(0.958144\pi\)
\(98\) −0.105921 + 0.105921i −0.00108082 + 0.00108082i
\(99\) −50.3331 50.3331i −0.508416 0.508416i
\(100\) −66.3882 −0.663882
\(101\) −131.668 −1.30364 −0.651821 0.758372i \(-0.725995\pi\)
−0.651821 + 0.758372i \(0.725995\pi\)
\(102\) 0.00973894 0.00973894i 9.54798e−5 9.54798e-5i
\(103\) −16.5178 + 16.5178i −0.160367 + 0.160367i −0.782729 0.622362i \(-0.786173\pi\)
0.622362 + 0.782729i \(0.286173\pi\)
\(104\) 0.685611 0.00659241
\(105\) 5.46691 0.0520658
\(106\) 0.0477895 0.0477895i 0.000450844 0.000450844i
\(107\) 7.67967i 0.0717726i 0.999356 + 0.0358863i \(0.0114254\pi\)
−0.999356 + 0.0358863i \(0.988575\pi\)
\(108\) −16.2419 + 16.2419i −0.150388 + 0.150388i
\(109\) 37.2333i 0.341590i 0.985307 + 0.170795i \(0.0546336\pi\)
−0.985307 + 0.170795i \(0.945366\pi\)
\(110\) 0.169980 + 0.169980i 0.00154528 + 0.00154528i
\(111\) 12.8960 12.8960i 0.116180 0.116180i
\(112\) 94.0373i 0.839619i
\(113\) 31.6821 + 31.6821i 0.280373 + 0.280373i 0.833258 0.552885i \(-0.186473\pi\)
−0.552885 + 0.833258i \(0.686473\pi\)
\(114\) −0.0377443 −0.000331090
\(115\) 43.1561 43.1561i 0.375270 0.375270i
\(116\) 134.994i 1.16374i
\(117\) −52.0162 52.0162i −0.444583 0.444583i
\(118\) 0.729275 0.729275i 0.00618029 0.00618029i
\(119\) −17.2115 + 17.2115i −0.144635 + 0.144635i
\(120\) 0.0545358 0.0545358i 0.000454465 0.000454465i
\(121\) 56.9902i 0.470993i
\(122\) −0.683809 + 0.683809i −0.00560499 + 0.00560499i
\(123\) 8.82654 + 8.82654i 0.0717605 + 0.0717605i
\(124\) −42.0469 42.0469i −0.339088 0.339088i
\(125\) −85.2622 85.2622i −0.682098 0.682098i
\(126\) −0.383294 + 0.383294i −0.00304202 + 0.00304202i
\(127\) 180.700i 1.42284i 0.702769 + 0.711418i \(0.251947\pi\)
−0.702769 + 0.711418i \(0.748053\pi\)
\(128\) 1.87621 + 1.87621i 0.0146579 + 0.0146579i
\(129\) −0.869284 0.869284i −0.00673863 0.00673863i
\(130\) 0.175664 + 0.175664i 0.00135126 + 0.00135126i
\(131\) −14.9408 + 14.9408i −0.114052 + 0.114052i −0.761829 0.647778i \(-0.775699\pi\)
0.647778 + 0.761829i \(0.275699\pi\)
\(132\) −10.2682 −0.0777892
\(133\) 66.7050 0.501542
\(134\) 1.12902i 0.00842553i
\(135\) −16.6459 −0.123303
\(136\) 0.343391i 0.00252493i
\(137\) 15.3616i 0.112128i 0.998427 + 0.0560642i \(0.0178552\pi\)
−0.998427 + 0.0560642i \(0.982145\pi\)
\(138\) 0.0700262i 0.000507436i
\(139\) −20.1644 20.1644i −0.145067 0.145067i 0.630843 0.775910i \(-0.282709\pi\)
−0.775910 + 0.630843i \(0.782709\pi\)
\(140\) −48.1896 + 48.1896i −0.344211 + 0.344211i
\(141\) −18.5897 18.5897i −0.131842 0.131842i
\(142\) −0.890181 −0.00626888
\(143\) 66.1501i 0.462588i
\(144\) 142.341i 0.988481i
\(145\) −69.1758 + 69.1758i −0.477074 + 0.477074i
\(146\) 0.0310980i 0.000213000i
\(147\) 3.27881 3.27881i 0.0223048 0.0223048i
\(148\) 227.351i 1.53616i
\(149\) −191.036 191.036i −1.28212 1.28212i −0.939458 0.342665i \(-0.888671\pi\)
−0.342665 0.939458i \(-0.611329\pi\)
\(150\) −0.0552015 −0.000368010
\(151\) 161.939 + 161.939i 1.07245 + 1.07245i 0.997162 + 0.0752837i \(0.0239862\pi\)
0.0752837 + 0.997162i \(0.476014\pi\)
\(152\) 0.665424 0.665424i 0.00437779 0.00437779i
\(153\) 26.0525 26.0525i 0.170278 0.170278i
\(154\) −0.487444 −0.00316522
\(155\) 43.0929i 0.278018i
\(156\) −10.6115 −0.0680226
\(157\) 86.2449i 0.549330i 0.961540 + 0.274665i \(0.0885670\pi\)
−0.961540 + 0.274665i \(0.911433\pi\)
\(158\) −0.901888 −0.00570815
\(159\) −1.47934 + 1.47934i −0.00930404 + 0.00930404i
\(160\) 1.44217i 0.00901355i
\(161\) 123.756i 0.768674i
\(162\) 0.573389 0.573389i 0.00353944 0.00353944i
\(163\) 75.5332i 0.463394i 0.972788 + 0.231697i \(0.0744277\pi\)
−0.972788 + 0.231697i \(0.925572\pi\)
\(164\) −155.608 −0.948829
\(165\) −5.26180 5.26180i −0.0318897 0.0318897i
\(166\) 0.114612 + 0.114612i 0.000690436 + 0.000690436i
\(167\) 128.317 128.317i 0.768366 0.768366i −0.209453 0.977819i \(-0.567168\pi\)
0.977819 + 0.209453i \(0.0671683\pi\)
\(168\) 0.156389i 0.000930890i
\(169\) 100.638i 0.595491i
\(170\) −0.0879820 + 0.0879820i −0.000517541 + 0.000517541i
\(171\) −100.969 −0.590464
\(172\) 15.3251 0.0890993
\(173\) 172.986i 0.999921i 0.866048 + 0.499961i \(0.166652\pi\)
−0.866048 + 0.499961i \(0.833348\pi\)
\(174\) 0.112246i 0.000645095i
\(175\) 97.5569 0.557468
\(176\) 90.5093 90.5093i 0.514257 0.514257i
\(177\) −22.5750 + 22.5750i −0.127542 + 0.127542i
\(178\) −0.562699 −0.00316123
\(179\) 61.7576 61.7576i 0.345015 0.345015i −0.513234 0.858249i \(-0.671553\pi\)
0.858249 + 0.513234i \(0.171553\pi\)
\(180\) 72.9430 72.9430i 0.405239 0.405239i
\(181\) 97.4434i 0.538361i −0.963090 0.269181i \(-0.913247\pi\)
0.963090 0.269181i \(-0.0867529\pi\)
\(182\) −0.503743 −0.00276782
\(183\) 21.1676 21.1676i 0.115670 0.115670i
\(184\) 1.23455 + 1.23455i 0.00670950 + 0.00670950i
\(185\) −116.503 + 116.503i −0.629748 + 0.629748i
\(186\) −0.0349618 0.0349618i −0.000187967 0.000187967i
\(187\) 33.1316 0.177174
\(188\) 327.727 1.74323
\(189\) 23.8673 23.8673i 0.126282 0.126282i
\(190\) 0.340984 0.00179465
\(191\) 60.5718 0.317130 0.158565 0.987349i \(-0.449313\pi\)
0.158565 + 0.987349i \(0.449313\pi\)
\(192\) −14.5183 14.5183i −0.0756164 0.0756164i
\(193\) −221.023 −1.14520 −0.572600 0.819835i \(-0.694065\pi\)
−0.572600 + 0.819835i \(0.694065\pi\)
\(194\) −0.186435 0.186435i −0.000961006 0.000961006i
\(195\) −5.43774 5.43774i −0.0278859 0.0278859i
\(196\) 57.8040i 0.294918i
\(197\) −24.1709 + 195.512i −0.122695 + 0.992444i
\(198\) 0.737828 0.00372640
\(199\) 74.6513 74.6513i 0.375132 0.375132i −0.494210 0.869342i \(-0.664543\pi\)
0.869342 + 0.494210i \(0.164543\pi\)
\(200\) 0.973191 0.973191i 0.00486595 0.00486595i
\(201\) 34.9492i 0.173877i
\(202\) 0.965053 0.965053i 0.00477749 0.00477749i
\(203\) 198.372i 0.977201i
\(204\) 5.31482i 0.0260531i
\(205\) −79.7393 79.7393i −0.388972 0.388972i
\(206\) 0.242133i 0.00117540i
\(207\) 187.326i 0.904957i
\(208\) 93.5357 93.5357i 0.449691 0.449691i
\(209\) −64.2024 64.2024i −0.307189 0.307189i
\(210\) −0.0400694 + 0.0400694i −0.000190807 + 0.000190807i
\(211\) −142.085 142.085i −0.673388 0.673388i 0.285107 0.958496i \(-0.407971\pi\)
−0.958496 + 0.285107i \(0.907971\pi\)
\(212\) 26.0801i 0.123020i
\(213\) 27.5559 0.129370
\(214\) −0.0562877 0.0562877i −0.000263027 0.000263027i
\(215\) 7.85315 + 7.85315i 0.0365263 + 0.0365263i
\(216\) 0.476183i 0.00220455i
\(217\) 61.7876 + 61.7876i 0.284736 + 0.284736i
\(218\) −0.272899 0.272899i −0.00125183 0.00125183i
\(219\) 0.962651i 0.00439567i
\(220\) 92.7632 0.421651
\(221\) 34.2394 0.154929
\(222\) 0.189042i 0.000851538i
\(223\) 112.294i 0.503562i −0.967784 0.251781i \(-0.918984\pi\)
0.967784 0.251781i \(-0.0810162\pi\)
\(224\) −2.06782 2.06782i −0.00923132 0.00923132i
\(225\) −147.669 −0.656305
\(226\) −0.464425 −0.00205498
\(227\) −251.351 251.351i −1.10727 1.10727i −0.993508 0.113765i \(-0.963709\pi\)
−0.113765 0.993508i \(-0.536291\pi\)
\(228\) −10.2991 + 10.2991i −0.0451714 + 0.0451714i
\(229\) 227.368 227.368i 0.992872 0.992872i −0.00710277 0.999975i \(-0.502261\pi\)
0.999975 + 0.00710277i \(0.00226090\pi\)
\(230\) 0.632620i 0.00275052i
\(231\) 15.0890 0.0653204
\(232\) −1.97888 1.97888i −0.00852966 0.00852966i
\(233\) 106.854 0.458599 0.229299 0.973356i \(-0.426357\pi\)
0.229299 + 0.973356i \(0.426357\pi\)
\(234\) 0.762499 0.00325854
\(235\) 167.940 + 167.940i 0.714638 + 0.714638i
\(236\) 397.987i 1.68638i
\(237\) 27.9183 0.117799
\(238\) 0.252302i 0.00106009i
\(239\) −61.1321 −0.255783 −0.127891 0.991788i \(-0.540821\pi\)
−0.127891 + 0.991788i \(0.540821\pi\)
\(240\) 14.8803i 0.0620012i
\(241\) 40.4113 + 40.4113i 0.167682 + 0.167682i 0.785960 0.618278i \(-0.212169\pi\)
−0.618278 + 0.785960i \(0.712169\pi\)
\(242\) −0.417707 0.417707i −0.00172606 0.00172606i
\(243\) −54.2947 + 54.2947i −0.223435 + 0.223435i
\(244\) 373.175i 1.52940i
\(245\) −29.6209 + 29.6209i −0.120902 + 0.120902i
\(246\) −0.129387 −0.000525964
\(247\) −66.3492 66.3492i −0.268620 0.268620i
\(248\) 1.23274 0.00497072
\(249\) −3.54787 3.54787i −0.0142485 0.0142485i
\(250\) 1.24985 0.00499940
\(251\) 280.451 1.11733 0.558667 0.829392i \(-0.311313\pi\)
0.558667 + 0.829392i \(0.311313\pi\)
\(252\) 209.175i 0.830059i
\(253\) 119.113 119.113i 0.470804 0.470804i
\(254\) −1.32443 1.32443i −0.00521430 0.00521430i
\(255\) 2.72352 2.72352i 0.0106805 0.0106805i
\(256\) 255.931 0.999731
\(257\) −192.747 −0.749988 −0.374994 0.927027i \(-0.622355\pi\)
−0.374994 + 0.927027i \(0.622355\pi\)
\(258\) 0.0127427 4.93904e−5
\(259\) 334.091i 1.28993i
\(260\) 95.8650 0.368712
\(261\) 300.269i 1.15046i
\(262\) 0.219015i 0.000835935i
\(263\) −120.728 120.728i −0.459043 0.459043i 0.439298 0.898341i \(-0.355227\pi\)
−0.898341 + 0.439298i \(0.855227\pi\)
\(264\) 0.150522 0.150522i 0.000570160 0.000570160i
\(265\) 13.3644 13.3644i 0.0504319 0.0504319i
\(266\) −0.488911 + 0.488911i −0.00183801 + 0.00183801i
\(267\) 17.4186 0.0652381
\(268\) 308.070 + 308.070i 1.14951 + 1.14951i
\(269\) −68.8046 + 68.8046i −0.255779 + 0.255779i −0.823335 0.567556i \(-0.807889\pi\)
0.567556 + 0.823335i \(0.307889\pi\)
\(270\) 0.122005 0.122005i 0.000451871 0.000451871i
\(271\) 175.987 175.987i 0.649398 0.649398i −0.303450 0.952847i \(-0.598138\pi\)
0.952847 + 0.303450i \(0.0981384\pi\)
\(272\) 46.8477 + 46.8477i 0.172234 + 0.172234i
\(273\) 15.5935 0.0571192
\(274\) −0.112592 0.112592i −0.000410919 0.000410919i
\(275\) −93.8968 93.8968i −0.341443 0.341443i
\(276\) −19.1077 19.1077i −0.0692307 0.0692307i
\(277\) −278.555 + 278.555i −1.00561 + 1.00561i −0.00563058 + 0.999984i \(0.501792\pi\)
−0.999984 + 0.00563058i \(0.998208\pi\)
\(278\) 0.295587 0.00106326
\(279\) −93.5259 93.5259i −0.335218 0.335218i
\(280\) 1.41283i 0.00504582i
\(281\) 136.367 136.367i 0.485291 0.485291i −0.421526 0.906817i \(-0.638505\pi\)
0.906817 + 0.421526i \(0.138505\pi\)
\(282\) 0.272504 0.000966325
\(283\) −34.2361 34.2361i −0.120976 0.120976i 0.644027 0.765003i \(-0.277262\pi\)
−0.765003 + 0.644027i \(0.777262\pi\)
\(284\) −242.899 + 242.899i −0.855278 + 0.855278i
\(285\) −10.5553 −0.0370361
\(286\) 0.484844 + 0.484844i 0.00169526 + 0.00169526i
\(287\) 228.664 0.796740
\(288\) 3.12999 + 3.12999i 0.0108680 + 0.0108680i
\(289\) 271.851i 0.940661i
\(290\) 1.01404i 0.00349669i
\(291\) 5.77117 + 5.77117i 0.0198322 + 0.0198322i
\(292\) 8.48556 + 8.48556i 0.0290601 + 0.0290601i
\(293\) 85.5844i 0.292097i 0.989277 + 0.146048i \(0.0466555\pi\)
−0.989277 + 0.146048i \(0.953344\pi\)
\(294\) 0.0480637i 0.000163482i
\(295\) 203.943 203.943i 0.691333 0.691333i
\(296\) −3.33276 3.33276i −0.0112593 0.0112593i
\(297\) −45.9438 −0.154693
\(298\) 2.80038 0.00939724
\(299\) 123.096 123.096i 0.411693 0.411693i
\(300\) −15.0625 + 15.0625i −0.0502084 + 0.0502084i
\(301\) −22.5201 −0.0748175
\(302\) −2.37385 −0.00786043
\(303\) −29.8736 + 29.8736i −0.0985926 + 0.0985926i
\(304\) 181.563i 0.597248i
\(305\) −191.229 + 191.229i −0.626979 + 0.626979i
\(306\) 0.381901i 0.00124804i
\(307\) 252.391 + 252.391i 0.822121 + 0.822121i 0.986412 0.164291i \(-0.0525336\pi\)
−0.164291 + 0.986412i \(0.552534\pi\)
\(308\) −133.006 + 133.006i −0.431838 + 0.431838i
\(309\) 7.49531i 0.0242567i
\(310\) 0.315847 + 0.315847i 0.00101886 + 0.00101886i
\(311\) −335.754 −1.07960 −0.539798 0.841795i \(-0.681499\pi\)
−0.539798 + 0.841795i \(0.681499\pi\)
\(312\) 0.155555 0.155555i 0.000498575 0.000498575i
\(313\) 84.4574i 0.269832i −0.990857 0.134916i \(-0.956924\pi\)
0.990857 0.134916i \(-0.0430764\pi\)
\(314\) −0.632127 0.632127i −0.00201314 0.00201314i
\(315\) −107.189 + 107.189i −0.340283 + 0.340283i
\(316\) −246.093 + 246.093i −0.778777 + 0.778777i
\(317\) −142.081 + 142.081i −0.448204 + 0.448204i −0.894757 0.446553i \(-0.852651\pi\)
0.446553 + 0.894757i \(0.352651\pi\)
\(318\) 0.0216855i 6.81934e-5i
\(319\) −190.929 + 190.929i −0.598525 + 0.598525i
\(320\) 131.159 + 131.159i 0.409873 + 0.409873i
\(321\) 1.74241 + 1.74241i 0.00542806 + 0.00542806i
\(322\) −0.907066 0.907066i −0.00281697 0.00281697i
\(323\) 33.2313 33.2313i 0.102883 0.102883i
\(324\) 312.915i 0.965787i
\(325\) −97.0365 97.0365i −0.298574 0.298574i
\(326\) −0.553616 0.553616i −0.00169821 0.00169821i
\(327\) 8.44770 + 8.44770i 0.0258340 + 0.0258340i
\(328\) 2.28107 2.28107i 0.00695448 0.00695448i
\(329\) −481.593 −1.46381
\(330\) 0.0771322 0.000233734
\(331\) 212.794i 0.642883i −0.946929 0.321442i \(-0.895833\pi\)
0.946929 0.321442i \(-0.104167\pi\)
\(332\) 62.5474 0.188396
\(333\) 505.702i 1.51863i
\(334\) 1.88099i 0.00563169i
\(335\) 315.733i 0.942487i
\(336\) 21.3357 + 21.3357i 0.0634992 + 0.0634992i
\(337\) 341.860 341.860i 1.01442 1.01442i 0.0145276 0.999894i \(-0.495376\pi\)
0.999894 0.0145276i \(-0.00462445\pi\)
\(338\) −0.737620 0.737620i −0.00218231 0.00218231i
\(339\) 14.3764 0.0424084
\(340\) 48.0144i 0.141219i
\(341\) 118.939i 0.348795i
\(342\) 0.740049 0.740049i 0.00216388 0.00216388i
\(343\) 372.955i 1.08733i
\(344\) −0.224652 + 0.224652i −0.000653057 + 0.000653057i
\(345\) 19.5830i 0.0567623i
\(346\) −1.26789 1.26789i −0.00366443 0.00366443i
\(347\) 35.9197 0.103515 0.0517574 0.998660i \(-0.483518\pi\)
0.0517574 + 0.998660i \(0.483518\pi\)
\(348\) 30.6281 + 30.6281i 0.0880118 + 0.0880118i
\(349\) −153.115 + 153.115i −0.438724 + 0.438724i −0.891582 0.452858i \(-0.850404\pi\)
0.452858 + 0.891582i \(0.350404\pi\)
\(350\) −0.715038 + 0.715038i −0.00204297 + 0.00204297i
\(351\) −47.4800 −0.135271
\(352\) 3.98047i 0.0113082i
\(353\) 400.782 1.13536 0.567680 0.823249i \(-0.307841\pi\)
0.567680 + 0.823249i \(0.307841\pi\)
\(354\) 0.330924i 0.000934813i
\(355\) −248.941 −0.701242
\(356\) −153.541 + 153.541i −0.431294 + 0.431294i
\(357\) 7.81009i 0.0218770i
\(358\) 0.905298i 0.00252877i
\(359\) −54.3951 + 54.3951i −0.151519 + 0.151519i −0.778796 0.627277i \(-0.784169\pi\)
0.627277 + 0.778796i \(0.284169\pi\)
\(360\) 2.13855i 0.00594043i
\(361\) 232.209 0.643237
\(362\) 0.714206 + 0.714206i 0.00197295 + 0.00197295i
\(363\) 12.9303 + 12.9303i 0.0356205 + 0.0356205i
\(364\) −137.454 + 137.454i −0.377620 + 0.377620i
\(365\) 8.69664i 0.0238264i
\(366\) 0.310293i 0.000847795i
\(367\) −439.539 + 439.539i −1.19765 + 1.19765i −0.222787 + 0.974867i \(0.571515\pi\)
−0.974867 + 0.222787i \(0.928485\pi\)
\(368\) 336.851 0.915355
\(369\) −346.122 −0.938000
\(370\) 1.70781i 0.00461570i
\(371\) 38.3245i 0.103301i
\(372\) −19.0797 −0.0512895
\(373\) −372.613 + 372.613i −0.998962 + 0.998962i −0.999999 0.00103710i \(-0.999670\pi\)
0.00103710 + 0.999999i \(0.499670\pi\)
\(374\) −0.242836 + 0.242836i −0.000649294 + 0.000649294i
\(375\) −38.6895 −0.103172
\(376\) −4.80418 + 4.80418i −0.0127771 + 0.0127771i
\(377\) −197.314 + 197.314i −0.523379 + 0.523379i
\(378\) 0.349868i 0.000925578i
\(379\) −372.333 −0.982409 −0.491205 0.871044i \(-0.663443\pi\)
−0.491205 + 0.871044i \(0.663443\pi\)
\(380\) 93.0424 93.0424i 0.244848 0.244848i
\(381\) 40.9983 + 40.9983i 0.107607 + 0.107607i
\(382\) −0.443957 + 0.443957i −0.00116219 + 0.00116219i
\(383\) 445.610 + 445.610i 1.16347 + 1.16347i 0.983710 + 0.179761i \(0.0575325\pi\)
0.179761 + 0.983710i \(0.442468\pi\)
\(384\) 0.851371 0.00221711
\(385\) −136.315 −0.354064
\(386\) 1.61998 1.61998i 0.00419684 0.00419684i
\(387\) 34.0879 0.0880825
\(388\) −101.743 −0.262224
\(389\) −46.5326 46.5326i −0.119621 0.119621i 0.644762 0.764383i \(-0.276956\pi\)
−0.764383 + 0.644762i \(0.776956\pi\)
\(390\) 0.0797113 0.000204388
\(391\) 61.6533 + 61.6533i 0.157681 + 0.157681i
\(392\) −0.847354 0.847354i −0.00216162 0.00216162i
\(393\) 6.77969i 0.0172511i
\(394\) −1.25583 1.61015i −0.00318739 0.00408668i
\(395\) −252.215 −0.638519
\(396\) 201.327 201.327i 0.508402 0.508402i
\(397\) 526.089 526.089i 1.32516 1.32516i 0.415627 0.909535i \(-0.363562\pi\)
0.909535 0.415627i \(-0.136438\pi\)
\(398\) 1.09431i 0.00274951i
\(399\) 15.1344 15.1344i 0.0379309 0.0379309i
\(400\) 265.539i 0.663847i
\(401\) 290.623i 0.724746i 0.932033 + 0.362373i \(0.118033\pi\)
−0.932033 + 0.362373i \(0.881967\pi\)
\(402\) 0.256159 + 0.256159i 0.000637210 + 0.000637210i
\(403\) 122.916i 0.305003i
\(404\) 526.658i 1.30361i
\(405\) 160.349 160.349i 0.395924 0.395924i
\(406\) 1.45396 + 1.45396i 0.00358117 + 0.00358117i
\(407\) −321.557 + 321.557i −0.790065 + 0.790065i
\(408\) 0.0779105 + 0.0779105i 0.000190957 + 0.000190957i
\(409\) 671.240i 1.64117i 0.571523 + 0.820586i \(0.306353\pi\)
−0.571523 + 0.820586i \(0.693647\pi\)
\(410\) 1.16889 0.00285095
\(411\) 3.48532 + 3.48532i 0.00848011 + 0.00848011i
\(412\) −66.0695 66.0695i −0.160363 0.160363i
\(413\) 584.838i 1.41607i
\(414\) 1.37300 + 1.37300i 0.00331642 + 0.00331642i
\(415\) 32.0516 + 32.0516i 0.0772328 + 0.0772328i
\(416\) 4.11357i 0.00988840i
\(417\) −9.15001 −0.0219425
\(418\) 0.941136 0.00225152
\(419\) 231.411i 0.552294i −0.961115 0.276147i \(-0.910942\pi\)
0.961115 0.276147i \(-0.0890577\pi\)
\(420\) 21.8670i 0.0520644i
\(421\) 381.980 + 381.980i 0.907315 + 0.907315i 0.996055 0.0887396i \(-0.0282839\pi\)
−0.0887396 + 0.996055i \(0.528284\pi\)
\(422\) 2.08281 0.00493556
\(423\) 728.971 1.72334
\(424\) 0.382311 + 0.382311i 0.000901677 + 0.000901677i
\(425\) 48.6011 48.6011i 0.114356 0.114356i
\(426\) −0.201969 + 0.201969i −0.000474106 + 0.000474106i
\(427\) 548.377i 1.28426i
\(428\) −30.7179 −0.0717707
\(429\) −15.0085 15.0085i −0.0349849 0.0349849i
\(430\) −0.115118 −0.000267717
\(431\) 772.033 1.79126 0.895630 0.444801i \(-0.146725\pi\)
0.895630 + 0.444801i \(0.146725\pi\)
\(432\) −64.9641 64.9641i −0.150380 0.150380i
\(433\) 277.661i 0.641249i −0.947206 0.320624i \(-0.896107\pi\)
0.947206 0.320624i \(-0.103893\pi\)
\(434\) −0.905738 −0.00208695
\(435\) 31.3900i 0.0721609i
\(436\) −148.929 −0.341581
\(437\) 238.944i 0.546782i
\(438\) 0.00705570 + 0.00705570i 1.61089e−5 + 1.61089e-5i
\(439\) −243.712 243.712i −0.555152 0.555152i 0.372771 0.927923i \(-0.378408\pi\)
−0.927923 + 0.372771i \(0.878408\pi\)
\(440\) −1.35982 + 1.35982i −0.00309051 + 0.00309051i
\(441\) 128.575i 0.291552i
\(442\) −0.250956 + 0.250956i −0.000567773 + 0.000567773i
\(443\) 270.977 0.611686 0.305843 0.952082i \(-0.401062\pi\)
0.305843 + 0.952082i \(0.401062\pi\)
\(444\) 51.5828 + 51.5828i 0.116177 + 0.116177i
\(445\) −157.360 −0.353618
\(446\) 0.823054 + 0.823054i 0.00184541 + 0.00184541i
\(447\) −86.6868 −0.193930
\(448\) −376.119 −0.839551
\(449\) 320.320i 0.713408i −0.934217 0.356704i \(-0.883900\pi\)
0.934217 0.356704i \(-0.116100\pi\)
\(450\) 1.08233 1.08233i 0.00240518 0.00240518i
\(451\) −220.086 220.086i −0.487995 0.487995i
\(452\) −126.725 + 126.725i −0.280365 + 0.280365i
\(453\) 73.4834 0.162215
\(454\) 3.68453 0.00811570
\(455\) −140.873 −0.309611
\(456\) 0.301950i 0.000662172i
\(457\) −25.2138 −0.0551724 −0.0275862 0.999619i \(-0.508782\pi\)
−0.0275862 + 0.999619i \(0.508782\pi\)
\(458\) 3.33296i 0.00727720i
\(459\) 23.7806i 0.0518095i
\(460\) 172.620 + 172.620i 0.375260 + 0.375260i
\(461\) 222.666 222.666i 0.483007 0.483007i −0.423084 0.906091i \(-0.639052\pi\)
0.906091 + 0.423084i \(0.139052\pi\)
\(462\) −0.110594 + 0.110594i −0.000239381 + 0.000239381i
\(463\) 300.059 300.059i 0.648075 0.648075i −0.304453 0.952527i \(-0.598474\pi\)
0.952527 + 0.304453i \(0.0984735\pi\)
\(464\) −539.945 −1.16368
\(465\) −9.77715 9.77715i −0.0210261 0.0210261i
\(466\) −0.783177 + 0.783177i −0.00168064 + 0.00168064i
\(467\) 169.461 169.461i 0.362871 0.362871i −0.501998 0.864869i \(-0.667402\pi\)
0.864869 + 0.501998i \(0.167402\pi\)
\(468\) 208.059 208.059i 0.444571 0.444571i
\(469\) −452.706 452.706i −0.965258 0.965258i
\(470\) −2.46181 −0.00523790
\(471\) 19.5677 + 19.5677i 0.0415451 + 0.0415451i
\(472\) 5.83412 + 5.83412i 0.0123604 + 0.0123604i
\(473\) 21.6752 + 21.6752i 0.0458249 + 0.0458249i
\(474\) −0.204625 + 0.204625i −0.000431699 + 0.000431699i
\(475\) −188.359 −0.396545
\(476\) −68.8442 68.8442i −0.144631 0.144631i
\(477\) 58.0106i 0.121616i
\(478\) 0.448064 0.448064i 0.000937372 0.000937372i
\(479\) 755.524 1.57729 0.788647 0.614846i \(-0.210782\pi\)
0.788647 + 0.614846i \(0.210782\pi\)
\(480\) 0.327207 + 0.327207i 0.000681682 + 0.000681682i
\(481\) −332.309 + 332.309i −0.690871 + 0.690871i
\(482\) −0.592385 −0.00122901
\(483\) 28.0786 + 28.0786i 0.0581337 + 0.0581337i
\(484\) −227.955 −0.470981
\(485\) −52.1370 52.1370i −0.107499 0.107499i
\(486\) 0.795900i 0.00163765i
\(487\) 58.4693i 0.120060i 0.998197 + 0.0600301i \(0.0191197\pi\)
−0.998197 + 0.0600301i \(0.980880\pi\)
\(488\) −5.47040 5.47040i −0.0112098 0.0112098i
\(489\) 17.1374 + 17.1374i 0.0350458 + 0.0350458i
\(490\) 0.434210i 0.000886143i
\(491\) 1.83661i 0.00374054i −0.999998 0.00187027i \(-0.999405\pi\)
0.999998 0.00187027i \(-0.000595326\pi\)
\(492\) −35.3052 + 35.3052i −0.0717585 + 0.0717585i
\(493\) −98.8253 98.8253i −0.200457 0.200457i
\(494\) 0.972606 0.00196884
\(495\) 206.335 0.416839
\(496\) 168.179 168.179i 0.339070 0.339070i
\(497\) 356.938 356.938i 0.718185 0.718185i
\(498\) 0.0520078 0.000104433
\(499\) 5.28124 0.0105837 0.00529183 0.999986i \(-0.498316\pi\)
0.00529183 + 0.999986i \(0.498316\pi\)
\(500\) 341.040 341.040i 0.682079 0.682079i
\(501\) 58.2266i 0.116221i
\(502\) −2.05555 + 2.05555i −0.00409472 + 0.00409472i
\(503\) 638.934i 1.27025i 0.772411 + 0.635123i \(0.219051\pi\)
−0.772411 + 0.635123i \(0.780949\pi\)
\(504\) −3.06631 3.06631i −0.00608395 0.00608395i
\(505\) 269.879 269.879i 0.534414 0.534414i
\(506\) 1.74607i 0.00345073i
\(507\) 22.8333 + 22.8333i 0.0450361 + 0.0450361i
\(508\) −722.781 −1.42280
\(509\) 591.679 591.679i 1.16243 1.16243i 0.178492 0.983941i \(-0.442878\pi\)
0.983941 0.178492i \(-0.0571218\pi\)
\(510\) 0.0399237i 7.82818e-5i
\(511\) −12.4695 12.4695i −0.0244021 0.0244021i
\(512\) −9.38068 + 9.38068i −0.0183216 + 0.0183216i
\(513\) −46.0820 + 46.0820i −0.0898285 + 0.0898285i
\(514\) 1.41273 1.41273i 0.00274850 0.00274850i
\(515\) 67.7130i 0.131482i
\(516\) 3.47704 3.47704i 0.00673845 0.00673845i
\(517\) 463.524 + 463.524i 0.896566 + 0.896566i
\(518\) 2.44870 + 2.44870i 0.00472722 + 0.00472722i
\(519\) 39.2481 + 39.2481i 0.0756226 + 0.0756226i
\(520\) −1.40529 + 1.40529i −0.00270249 + 0.00270249i
\(521\) 102.268i 0.196292i −0.995172 0.0981462i \(-0.968709\pi\)
0.995172 0.0981462i \(-0.0312913\pi\)
\(522\) −2.20081 2.20081i −0.00421610 0.00421610i
\(523\) 118.578 + 118.578i 0.226726 + 0.226726i 0.811324 0.584597i \(-0.198747\pi\)
−0.584597 + 0.811324i \(0.698747\pi\)
\(524\) −59.7615 59.7615i −0.114049 0.114049i
\(525\) 22.1343 22.1343i 0.0421605 0.0421605i
\(526\) 1.76974 0.00336453
\(527\) 61.5630 0.116818
\(528\) 41.0705i 0.0777851i
\(529\) −85.6926 −0.161990
\(530\) 0.195908i 0.000369637i
\(531\) 885.250i 1.66714i
\(532\) 266.813i 0.501528i
\(533\) −227.445 227.445i −0.426726 0.426726i
\(534\) −0.127668 + 0.127668i −0.000239079 + 0.000239079i
\(535\) −15.7410 15.7410i −0.0294224 0.0294224i
\(536\) −9.03204 −0.0168508
\(537\) 28.0238i 0.0521859i
\(538\) 1.00860i 0.00187472i
\(539\) −81.7556 + 81.7556i −0.151680 + 0.151680i
\(540\) 66.5819i 0.123300i
\(541\) −351.869 + 351.869i −0.650405 + 0.650405i −0.953090 0.302686i \(-0.902117\pi\)
0.302686 + 0.953090i \(0.402117\pi\)
\(542\) 2.57977i 0.00475972i
\(543\) −22.1085 22.1085i −0.0407155 0.0407155i
\(544\) −2.06030 −0.00378731
\(545\) −76.3169 76.3169i −0.140031 0.140031i
\(546\) −0.114292 + 0.114292i −0.000209326 + 0.000209326i
\(547\) 557.805 557.805i 1.01975 1.01975i 0.0199526 0.999801i \(-0.493648\pi\)
0.999801 0.0199526i \(-0.00635154\pi\)
\(548\) −61.4447 −0.112125
\(549\) 830.060i 1.51195i
\(550\) 1.37642 0.00250259
\(551\) 383.008i 0.695115i
\(552\) 0.560202 0.00101486
\(553\) 361.632 361.632i 0.653946 0.653946i
\(554\) 4.08331i 0.00737060i
\(555\) 52.8659i 0.0952538i
\(556\) 80.6553 80.6553i 0.145063 0.145063i
\(557\) 175.481i 0.315046i 0.987515 + 0.157523i \(0.0503509\pi\)
−0.987515 + 0.157523i \(0.949649\pi\)
\(558\) 1.37099 0.00245696
\(559\) 22.4000 + 22.4000i 0.0400715 + 0.0400715i
\(560\) −192.748 192.748i −0.344193 0.344193i
\(561\) 7.51707 7.51707i 0.0133994 0.0133994i
\(562\) 1.99898i 0.00355691i
\(563\) 684.768i 1.21628i 0.793828 + 0.608142i \(0.208085\pi\)
−0.793828 + 0.608142i \(0.791915\pi\)
\(564\) 74.3566 74.3566i 0.131838 0.131838i
\(565\) −129.877 −0.229871
\(566\) 0.501863 0.000886684
\(567\) 459.826i 0.810980i
\(568\) 7.12135i 0.0125376i
\(569\) −406.858 −0.715040 −0.357520 0.933906i \(-0.616378\pi\)
−0.357520 + 0.933906i \(0.616378\pi\)
\(570\) 0.0773643 0.0773643i 0.000135727 0.000135727i
\(571\) −235.347 + 235.347i −0.412166 + 0.412166i −0.882492 0.470327i \(-0.844136\pi\)
0.470327 + 0.882492i \(0.344136\pi\)
\(572\) 264.593 0.462576
\(573\) 13.7429 13.7429i 0.0239841 0.0239841i
\(574\) −1.67598 + 1.67598i −0.00291983 + 0.00291983i
\(575\) 349.458i 0.607753i
\(576\) 569.319 0.988401
\(577\) 242.576 242.576i 0.420409 0.420409i −0.464936 0.885344i \(-0.653923\pi\)
0.885344 + 0.464936i \(0.153923\pi\)
\(578\) 1.99252 + 1.99252i 0.00344726 + 0.00344726i
\(579\) −50.1471 + 50.1471i −0.0866098 + 0.0866098i
\(580\) −276.696 276.696i −0.477061 0.477061i
\(581\) −91.9128 −0.158198
\(582\) −0.0845989 −0.000145359
\(583\) 36.8867 36.8867i 0.0632705 0.0632705i
\(584\) −0.248781 −0.000425995
\(585\) 213.235 0.364504
\(586\) −0.627286 0.627286i −0.00107045 0.00107045i
\(587\) 318.880 0.543237 0.271619 0.962405i \(-0.412441\pi\)
0.271619 + 0.962405i \(0.412441\pi\)
\(588\) 13.1149 + 13.1149i 0.0223042 + 0.0223042i
\(589\) −119.297 119.297i −0.202542 0.202542i
\(590\) 2.98958i 0.00506709i
\(591\) 38.8747 + 49.8428i 0.0657779 + 0.0843364i
\(592\) −909.357 −1.53608
\(593\) 32.5096 32.5096i 0.0548223 0.0548223i −0.679164 0.733986i \(-0.737658\pi\)
0.733986 + 0.679164i \(0.237658\pi\)
\(594\) 0.336742 0.336742i 0.000566906 0.000566906i
\(595\) 70.5567i 0.118583i
\(596\) 764.124 764.124i 1.28209 1.28209i
\(597\) 33.8746i 0.0567414i
\(598\) 1.80445i 0.00301748i
\(599\) −251.559 251.559i −0.419965 0.419965i 0.465227 0.885192i \(-0.345973\pi\)
−0.885192 + 0.465227i \(0.845973\pi\)
\(600\) 0.441606i 0.000736010i
\(601\) 114.185i 0.189992i −0.995478 0.0949961i \(-0.969716\pi\)
0.995478 0.0949961i \(-0.0302839\pi\)
\(602\) 0.165060 0.165060i 0.000274185 0.000274185i
\(603\) 685.246 + 685.246i 1.13639 + 1.13639i
\(604\) −647.740 + 647.740i −1.07242 + 1.07242i
\(605\) −116.813 116.813i −0.193079 0.193079i
\(606\) 0.437913i 0.000722629i
\(607\) 552.493 0.910203 0.455102 0.890439i \(-0.349603\pi\)
0.455102 + 0.890439i \(0.349603\pi\)
\(608\) 3.99246 + 3.99246i 0.00656654 + 0.00656654i
\(609\) −45.0077 45.0077i −0.0739043 0.0739043i
\(610\) 2.80320i 0.00459541i
\(611\) 479.024 + 479.024i 0.784000 + 0.784000i
\(612\) 104.207 + 104.207i 0.170273 + 0.170273i
\(613\) 799.816i 1.30476i 0.757893 + 0.652379i \(0.226229\pi\)
−0.757893 + 0.652379i \(0.773771\pi\)
\(614\) −3.69977 −0.00602569
\(615\) −36.1834 −0.0588348
\(616\) 3.89950i 0.00633035i
\(617\) 765.442i 1.24059i 0.784370 + 0.620293i \(0.212986\pi\)
−0.784370 + 0.620293i \(0.787014\pi\)
\(618\) −0.0549365 0.0549365i −8.88940e−5 8.88940e-5i
\(619\) −901.535 −1.45644 −0.728219 0.685345i \(-0.759652\pi\)
−0.728219 + 0.685345i \(0.759652\pi\)
\(620\) 172.367 0.278011
\(621\) −85.4950 85.4950i −0.137673 0.137673i
\(622\) 2.46089 2.46089i 0.00395642 0.00395642i
\(623\) 225.627 225.627i 0.362162 0.362162i
\(624\) 42.4438i 0.0680189i
\(625\) −65.4145 −0.104663
\(626\) 0.619026 + 0.619026i 0.000988859 + 0.000988859i
\(627\) −29.1332 −0.0464645
\(628\) −344.970 −0.549316
\(629\) −166.438 166.438i −0.264608 0.264608i
\(630\) 1.57127i 0.00249408i
\(631\) 416.921 0.660731 0.330366 0.943853i \(-0.392828\pi\)
0.330366 + 0.943853i \(0.392828\pi\)
\(632\) 7.21501i 0.0114162i
\(633\) −64.4740 −0.101855
\(634\) 2.08275i 0.00328509i
\(635\) −370.380 370.380i −0.583276 0.583276i
\(636\) −5.91721 5.91721i −0.00930379 0.00930379i
\(637\) −84.4894 + 84.4894i −0.132636 + 0.132636i
\(638\) 2.79881i 0.00438686i
\(639\) −540.285 + 540.285i −0.845517 + 0.845517i
\(640\) −7.69132 −0.0120177
\(641\) 341.347 + 341.347i 0.532523 + 0.532523i 0.921322 0.388799i \(-0.127110\pi\)
−0.388799 + 0.921322i \(0.627110\pi\)
\(642\) −0.0255417 −3.97847e−5
\(643\) −882.329 882.329i −1.37221 1.37221i −0.857165 0.515042i \(-0.827776\pi\)
−0.515042 0.857165i \(-0.672224\pi\)
\(644\) −495.012 −0.768653
\(645\) 3.56353 0.00552486
\(646\) 0.487133i 0.000754077i
\(647\) −775.713 + 775.713i −1.19894 + 1.19894i −0.224454 + 0.974485i \(0.572060\pi\)
−0.974485 + 0.224454i \(0.927940\pi\)
\(648\) 4.58705 + 4.58705i 0.00707878 + 0.00707878i
\(649\) 562.896 562.896i 0.867328 0.867328i
\(650\) 1.42245 0.00218838
\(651\) 28.0374 0.0430683
\(652\) −302.125 −0.463381
\(653\) 885.398i 1.35589i 0.735112 + 0.677946i \(0.237130\pi\)
−0.735112 + 0.677946i \(0.762870\pi\)
\(654\) −0.123834 −0.000189348
\(655\) 61.2480i 0.0935085i
\(656\) 622.398i 0.948778i
\(657\) 18.8746 + 18.8746i 0.0287285 + 0.0287285i
\(658\) 3.52981 3.52981i 0.00536445 0.00536445i
\(659\) 52.5487 52.5487i 0.0797400 0.0797400i −0.666112 0.745852i \(-0.732043\pi\)
0.745852 + 0.666112i \(0.232043\pi\)
\(660\) 21.0466 21.0466i 0.0318888 0.0318888i
\(661\) −931.681 −1.40950 −0.704751 0.709455i \(-0.748941\pi\)
−0.704751 + 0.709455i \(0.748941\pi\)
\(662\) 1.55966 + 1.55966i 0.00235599 + 0.00235599i
\(663\) 7.76843 7.76843i 0.0117171 0.0117171i
\(664\) −0.916887 + 0.916887i −0.00138085 + 0.00138085i
\(665\) −136.725 + 136.725i −0.205602 + 0.205602i
\(666\) −3.70652 3.70652i −0.00556534 0.00556534i
\(667\) −710.587 −1.06535
\(668\) 513.255 + 513.255i 0.768345 + 0.768345i
\(669\) −25.4779 25.4779i −0.0380836 0.0380836i
\(670\) −2.31415 2.31415i −0.00345395 0.00345395i
\(671\) −527.803 + 527.803i −0.786592 + 0.786592i
\(672\) −0.938316 −0.00139630
\(673\) 421.492 + 421.492i 0.626288 + 0.626288i 0.947132 0.320844i \(-0.103967\pi\)
−0.320844 + 0.947132i \(0.603967\pi\)
\(674\) 5.01129i 0.00743515i
\(675\) −67.3955 + 67.3955i −0.0998452 + 0.0998452i
\(676\) −402.541 −0.595475
\(677\) −654.188 654.188i −0.966304 0.966304i 0.0331466 0.999451i \(-0.489447\pi\)
−0.999451 + 0.0331466i \(0.989447\pi\)
\(678\) −0.105371 + 0.105371i −0.000155415 + 0.000155415i
\(679\) 149.511 0.220192
\(680\) −0.703847 0.703847i −0.00103507 0.00103507i
\(681\) −114.056 −0.167483
\(682\) 0.871757 + 0.871757i 0.00127824 + 0.00127824i
\(683\) 643.512i 0.942184i −0.882084 0.471092i \(-0.843860\pi\)
0.882084 0.471092i \(-0.156140\pi\)
\(684\) 403.866i 0.590448i
\(685\) −31.4866 31.4866i −0.0459658 0.0459658i
\(686\) 2.73355 + 2.73355i 0.00398477 + 0.00398477i
\(687\) 103.173i 0.150179i
\(688\) 61.2971i 0.0890946i
\(689\) 38.1201 38.1201i 0.0553267 0.0553267i
\(690\) 0.143532 + 0.143532i 0.000208018 + 0.000208018i
\(691\) 311.201 0.450363 0.225181 0.974317i \(-0.427703\pi\)
0.225181 + 0.974317i \(0.427703\pi\)
\(692\) −691.927 −0.999894
\(693\) −295.848 + 295.848i −0.426910 + 0.426910i
\(694\) −0.263271 + 0.263271i −0.000379353 + 0.000379353i
\(695\) 82.6616 0.118938
\(696\) −0.897960 −0.00129017
\(697\) 113.917 113.917i 0.163438 0.163438i
\(698\) 2.24449i 0.00321560i
\(699\) 24.2435 24.2435i 0.0346832 0.0346832i
\(700\) 390.217i 0.557453i
\(701\) 401.880 + 401.880i 0.573295 + 0.573295i 0.933048 0.359753i \(-0.117139\pi\)
−0.359753 + 0.933048i \(0.617139\pi\)
\(702\) 0.348002 0.348002i 0.000495729 0.000495729i
\(703\) 645.049i 0.917566i
\(704\) 362.008 + 362.008i 0.514216 + 0.514216i
\(705\) 76.2063 0.108094
\(706\) −2.93751 + 2.93751i −0.00416078 + 0.00416078i
\(707\) 773.919i 1.09465i
\(708\) −90.2974 90.2974i −0.127539 0.127539i
\(709\) 806.040 806.040i 1.13687 1.13687i 0.147860 0.989008i \(-0.452761\pi\)
0.989008 0.147860i \(-0.0472386\pi\)
\(710\) 1.82460 1.82460i 0.00256986 0.00256986i
\(711\) −547.391 + 547.391i −0.769889 + 0.769889i
\(712\) 4.50153i 0.00632238i
\(713\) 221.329 221.329i 0.310420 0.310420i
\(714\) −0.0572436 0.0572436i −8.01731e−5 8.01731e-5i
\(715\) 135.588 + 135.588i 0.189633 + 0.189633i
\(716\) 247.024 + 247.024i 0.345005 + 0.345005i
\(717\) −13.8700 + 13.8700i −0.0193445 + 0.0193445i
\(718\) 0.797372i 0.00111055i
\(719\) 211.161 + 211.161i 0.293688 + 0.293688i 0.838535 0.544848i \(-0.183412\pi\)
−0.544848 + 0.838535i \(0.683412\pi\)
\(720\) 291.756 + 291.756i 0.405217 + 0.405217i
\(721\) 97.0886 + 97.0886i 0.134658 + 0.134658i
\(722\) −1.70196 + 1.70196i −0.00235729 + 0.00235729i
\(723\) 18.3375 0.0253631
\(724\) 389.763 0.538347
\(725\) 560.154i 0.772626i
\(726\) −0.189543 −0.000261079
\(727\) 512.206i 0.704547i −0.935897 0.352274i \(-0.885409\pi\)
0.935897 0.352274i \(-0.114591\pi\)
\(728\) 4.02989i 0.00553556i
\(729\) 679.440i 0.932017i
\(730\) −0.0637415 0.0637415i −8.73171e−5 8.73171e-5i
\(731\) −11.2191 + 11.2191i −0.0153476 + 0.0153476i
\(732\) 84.6680 + 84.6680i 0.115667 + 0.115667i
\(733\) 1317.24 1.79706 0.898528 0.438917i \(-0.144638\pi\)
0.898528 + 0.438917i \(0.144638\pi\)
\(734\) 6.44315i 0.00877814i
\(735\) 13.4411i 0.0182872i
\(736\) −7.40712 + 7.40712i −0.0100640 + 0.0100640i
\(737\) 871.443i 1.18242i
\(738\) 2.53688 2.53688i 0.00343751 0.00343751i
\(739\) 857.242i 1.16000i 0.814616 + 0.580001i \(0.196948\pi\)
−0.814616 + 0.580001i \(0.803052\pi\)
\(740\) −466.001 466.001i −0.629731 0.629731i
\(741\) −30.1074 −0.0406307
\(742\) −0.280898 0.280898i −0.000378568 0.000378568i
\(743\) 142.304 142.304i 0.191526 0.191526i −0.604829 0.796355i \(-0.706759\pi\)
0.796355 + 0.604829i \(0.206759\pi\)
\(744\) 0.279691 0.279691i 0.000375929 0.000375929i
\(745\) 783.132 1.05118
\(746\) 5.46209i 0.00732184i
\(747\) 139.125 0.186246
\(748\) 132.523i 0.177169i
\(749\) 45.1396 0.0602665
\(750\) 0.283573 0.283573i 0.000378097 0.000378097i
\(751\) 954.184i 1.27055i −0.772285 0.635276i \(-0.780886\pi\)
0.772285 0.635276i \(-0.219114\pi\)
\(752\) 1310.84i 1.74314i
\(753\) 63.6303 63.6303i 0.0845024 0.0845024i
\(754\) 2.89240i 0.00383607i
\(755\) −663.852 −0.879275
\(756\) 95.4667 + 95.4667i 0.126279 + 0.126279i
\(757\) −458.813 458.813i −0.606093 0.606093i 0.335829 0.941923i \(-0.390983\pi\)
−0.941923 + 0.335829i \(0.890983\pi\)
\(758\) 2.72899 2.72899i 0.00360026 0.00360026i
\(759\) 54.0502i 0.0712124i
\(760\) 2.72783i 0.00358925i
\(761\) 273.306 273.306i 0.359141 0.359141i −0.504355 0.863496i \(-0.668270\pi\)
0.863496 + 0.504355i \(0.168270\pi\)
\(762\) −0.600989 −0.000788700
\(763\) 218.850 0.286829
\(764\) 242.281i 0.317121i
\(765\) 106.799i 0.139607i
\(766\) −6.53214 −0.00852760
\(767\) 581.718 581.718i 0.758433 0.758433i
\(768\) 58.0671 58.0671i 0.0756082 0.0756082i
\(769\) −51.2391 −0.0666309 −0.0333154 0.999445i \(-0.510607\pi\)
−0.0333154 + 0.999445i \(0.510607\pi\)
\(770\) 0.999111 0.999111i 0.00129755 0.00129755i
\(771\) −43.7315 + 43.7315i −0.0567205 + 0.0567205i
\(772\) 884.070i 1.14517i
\(773\) 1036.82 1.34130 0.670648 0.741776i \(-0.266016\pi\)
0.670648 + 0.741776i \(0.266016\pi\)
\(774\)