Properties

Label 76.5.l.a.23.11
Level $76$
Weight $5$
Character 76.23
Analytic conductor $7.856$
Analytic rank $0$
Dimension $228$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,5,Mod(23,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.23");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.l (of order \(18\), degree \(6\), 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: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(228\)
Relative dimension: \(38\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 23.11
Character \(\chi\) \(=\) 76.23
Dual form 76.5.l.a.43.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.96694 + 2.68277i) q^{2} +(-1.05794 + 0.186543i) q^{3} +(1.60551 - 15.9192i) q^{4} +(1.47493 - 1.23761i) q^{5} +(2.63839 - 3.39166i) q^{6} +(26.6122 + 15.3646i) q^{7} +(37.9442 + 51.5387i) q^{8} +(-75.0307 + 27.3089i) q^{9} +O(q^{10})\) \(q+(-2.96694 + 2.68277i) q^{2} +(-1.05794 + 0.186543i) q^{3} +(1.60551 - 15.9192i) q^{4} +(1.47493 - 1.23761i) q^{5} +(2.63839 - 3.39166i) q^{6} +(26.6122 + 15.3646i) q^{7} +(37.9442 + 51.5387i) q^{8} +(-75.0307 + 27.3089i) q^{9} +(-1.05580 + 7.62880i) q^{10} +(29.9069 - 17.2667i) q^{11} +(1.27109 + 17.1410i) q^{12} +(-42.0617 + 238.544i) q^{13} +(-120.176 + 25.8086i) q^{14} +(-1.32951 + 1.58445i) q^{15} +(-250.845 - 51.1171i) q^{16} +(-280.382 - 102.051i) q^{17} +(149.348 - 282.314i) q^{18} +(-242.275 - 267.627i) q^{19} +(-17.3338 - 25.4667i) q^{20} +(-31.0201 - 11.2904i) q^{21} +(-42.4094 + 131.463i) q^{22} +(-421.407 + 502.214i) q^{23} +(-49.7567 - 47.4465i) q^{24} +(-107.886 + 611.854i) q^{25} +(-515.163 - 820.588i) q^{26} +(149.640 - 86.3949i) q^{27} +(287.318 - 398.978i) q^{28} +(-1218.39 + 443.456i) q^{29} +(-0.306126 - 8.26774i) q^{30} +(961.830 + 555.313i) q^{31} +(881.377 - 521.297i) q^{32} +(-28.4186 + 23.8460i) q^{33} +(1105.66 - 449.422i) q^{34} +(58.2664 - 10.2739i) q^{35} +(314.275 + 1238.28i) q^{36} +198.579 q^{37} +(1436.80 + 144.067i) q^{38} -260.210i q^{39} +(119.750 + 29.0557i) q^{40} +(-143.868 - 815.918i) q^{41} +(122.325 - 49.7218i) q^{42} +(2296.43 + 2736.77i) q^{43} +(-226.858 - 503.817i) q^{44} +(-76.8669 + 133.137i) q^{45} +(-97.0309 - 2620.58i) q^{46} +(-173.023 - 475.377i) q^{47} +(274.913 + 7.28537i) q^{48} +(-728.361 - 1261.56i) q^{49} +(-1321.37 - 2104.77i) q^{50} +(315.663 + 55.6600i) q^{51} +(3729.91 + 1052.58i) q^{52} +(1203.51 + 1009.87i) q^{53} +(-212.197 + 657.779i) q^{54} +(22.7409 - 62.4802i) q^{55} +(217.908 + 1954.55i) q^{56} +(306.235 + 237.937i) q^{57} +(2425.19 - 4584.35i) q^{58} +(-438.959 + 1206.03i) q^{59} +(23.0887 + 23.7086i) q^{60} +(-674.737 - 566.171i) q^{61} +(-4343.47 + 932.785i) q^{62} +(-2416.32 - 426.063i) q^{63} +(-1216.48 + 3911.19i) q^{64} +(233.186 + 403.890i) q^{65} +(20.3430 - 146.990i) q^{66} +(-1261.58 - 3466.17i) q^{67} +(-2074.73 + 4299.63i) q^{68} +(352.138 - 609.921i) q^{69} +(-145.310 + 186.797i) q^{70} +(-2360.72 - 2813.40i) q^{71} +(-4254.44 - 2830.77i) q^{72} +(313.651 + 1778.80i) q^{73} +(-589.173 + 532.741i) q^{74} -667.428i q^{75} +(-4649.39 + 3427.15i) q^{76} +1061.18 q^{77} +(698.084 + 772.030i) q^{78} +(4380.83 - 772.458i) q^{79} +(-433.240 + 235.054i) q^{80} +(4812.22 - 4037.93i) q^{81} +(2615.77 + 2034.82i) q^{82} +(-6444.01 - 3720.45i) q^{83} +(-229.538 + 475.690i) q^{84} +(-539.842 + 196.487i) q^{85} +(-14155.5 - 1959.08i) q^{86} +(1206.25 - 696.429i) q^{87} +(2024.70 + 886.190i) q^{88} +(-61.4577 + 348.544i) q^{89} +(-129.117 - 601.227i) q^{90} +(-4784.47 + 5701.92i) q^{91} +(7318.29 + 7514.80i) q^{92} +(-1121.14 - 408.063i) q^{93} +(1788.68 + 946.237i) q^{94} +(-688.554 - 94.8883i) q^{95} +(-835.197 + 715.913i) q^{96} +(1927.50 + 701.553i) q^{97} +(5545.47 + 1788.95i) q^{98} +(-1772.40 + 2112.26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 228 q - 6 q^{2} - 48 q^{4} - 12 q^{5} - 60 q^{6} - 3 q^{8} - 180 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 228 q - 6 q^{2} - 48 q^{4} - 12 q^{5} - 60 q^{6} - 3 q^{8} - 180 q^{9} - 453 q^{10} - 3 q^{12} + 516 q^{13} + 81 q^{14} - 720 q^{16} - 12 q^{17} - 12 q^{18} - 1182 q^{20} - 930 q^{21} - 54 q^{22} - 2664 q^{24} - 12 q^{25} - 3099 q^{26} - 4824 q^{28} - 12 q^{29} + 5814 q^{30} + 7419 q^{32} + 1542 q^{33} + 6912 q^{34} + 8547 q^{36} - 24 q^{37} - 1536 q^{38} - 6942 q^{40} + 6396 q^{41} - 18855 q^{42} - 1143 q^{44} - 6 q^{45} - 1488 q^{46} + 6093 q^{48} + 26748 q^{49} + 8070 q^{50} - 12591 q^{52} + 2436 q^{53} - 7365 q^{54} - 14418 q^{56} - 12 q^{57} + 8268 q^{58} + 34632 q^{60} - 31068 q^{61} + 27396 q^{62} + 4575 q^{64} + 3594 q^{65} - 29556 q^{66} - 22782 q^{68} + 29370 q^{69} - 71541 q^{70} - 30174 q^{72} - 6348 q^{73} - 417 q^{74} + 43194 q^{76} - 50436 q^{77} + 45537 q^{78} + 30081 q^{80} - 41994 q^{81} + 72219 q^{82} + 13779 q^{84} - 59244 q^{85} + 19200 q^{86} - 22395 q^{88} + 1860 q^{89} + 45594 q^{90} - 64140 q^{92} + 59118 q^{93} - 55590 q^{94} - 98646 q^{96} - 5556 q^{97} - 52215 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.96694 + 2.68277i −0.741736 + 0.670692i
\(3\) −1.05794 + 0.186543i −0.117548 + 0.0207270i −0.232113 0.972689i \(-0.574564\pi\)
0.114564 + 0.993416i \(0.463453\pi\)
\(4\) 1.60551 15.9192i 0.100345 0.994953i
\(5\) 1.47493 1.23761i 0.0589970 0.0495044i −0.612812 0.790228i \(-0.709962\pi\)
0.671809 + 0.740724i \(0.265517\pi\)
\(6\) 2.63839 3.39166i 0.0732885 0.0942127i
\(7\) 26.6122 + 15.3646i 0.543106 + 0.313562i 0.746337 0.665568i \(-0.231811\pi\)
−0.203231 + 0.979131i \(0.565144\pi\)
\(8\) 37.9442 + 51.5387i 0.592878 + 0.805293i
\(9\) −75.0307 + 27.3089i −0.926305 + 0.337147i
\(10\) −1.05580 + 7.62880i −0.0105580 + 0.0762880i
\(11\) 29.9069 17.2667i 0.247164 0.142700i −0.371301 0.928513i \(-0.621088\pi\)
0.618465 + 0.785812i \(0.287755\pi\)
\(12\) 1.27109 + 17.1410i 0.00882701 + 0.119035i
\(13\) −42.0617 + 238.544i −0.248886 + 1.41150i 0.562406 + 0.826861i \(0.309876\pi\)
−0.811292 + 0.584641i \(0.801235\pi\)
\(14\) −120.176 + 25.8086i −0.613145 + 0.131676i
\(15\) −1.32951 + 1.58445i −0.00590893 + 0.00704199i
\(16\) −250.845 51.1171i −0.979862 0.199676i
\(17\) −280.382 102.051i −0.970181 0.353117i −0.192166 0.981362i \(-0.561551\pi\)
−0.778015 + 0.628245i \(0.783773\pi\)
\(18\) 149.348 282.314i 0.460951 0.871339i
\(19\) −242.275 267.627i −0.671121 0.741348i
\(20\) −17.3338 25.4667i −0.0433345 0.0636668i
\(21\) −31.0201 11.2904i −0.0703405 0.0256018i
\(22\) −42.4094 + 131.463i −0.0876227 + 0.271617i
\(23\) −421.407 + 502.214i −0.796611 + 0.949365i −0.999555 0.0298259i \(-0.990505\pi\)
0.202944 + 0.979190i \(0.434949\pi\)
\(24\) −49.7567 47.4465i −0.0863831 0.0823723i
\(25\) −107.886 + 611.854i −0.172618 + 0.978967i
\(26\) −515.163 820.588i −0.762075 1.21389i
\(27\) 149.640 86.3949i 0.205268 0.118512i
\(28\) 287.318 398.978i 0.366478 0.508901i
\(29\) −1218.39 + 443.456i −1.44873 + 0.527296i −0.942237 0.334946i \(-0.891282\pi\)
−0.506497 + 0.862242i \(0.669060\pi\)
\(30\) −0.306126 8.26774i −0.000340140 0.00918637i
\(31\) 961.830 + 555.313i 1.00086 + 0.577849i 0.908504 0.417877i \(-0.137226\pi\)
0.0923598 + 0.995726i \(0.470559\pi\)
\(32\) 881.377 521.297i 0.860720 0.509079i
\(33\) −28.4186 + 23.8460i −0.0260960 + 0.0218972i
\(34\) 1105.66 449.422i 0.956451 0.388773i
\(35\) 58.2664 10.2739i 0.0475644 0.00838688i
\(36\) 314.275 + 1238.28i 0.242496 + 0.955460i
\(37\) 198.579 0.145054 0.0725270 0.997366i \(-0.476894\pi\)
0.0725270 + 0.997366i \(0.476894\pi\)
\(38\) 1436.80 + 144.067i 0.995011 + 0.0997695i
\(39\) 260.210i 0.171078i
\(40\) 119.750 + 29.0557i 0.0748435 + 0.0181598i
\(41\) −143.868 815.918i −0.0855850 0.485377i −0.997229 0.0743955i \(-0.976297\pi\)
0.911644 0.410981i \(-0.134814\pi\)
\(42\) 122.325 49.7218i 0.0693450 0.0281870i
\(43\) 2296.43 + 2736.77i 1.24198 + 1.48014i 0.818786 + 0.574099i \(0.194648\pi\)
0.423197 + 0.906038i \(0.360908\pi\)
\(44\) −226.858 503.817i −0.117179 0.260236i
\(45\) −76.8669 + 133.137i −0.0379590 + 0.0657468i
\(46\) −97.0309 2620.58i −0.0458558 1.23846i
\(47\) −173.023 475.377i −0.0783265 0.215200i 0.894349 0.447371i \(-0.147640\pi\)
−0.972675 + 0.232170i \(0.925417\pi\)
\(48\) 274.913 + 7.28537i 0.119320 + 0.00316205i
\(49\) −728.361 1261.56i −0.303357 0.525430i
\(50\) −1321.37 2104.77i −0.528548 0.841908i
\(51\) 315.663 + 55.6600i 0.121362 + 0.0213995i
\(52\) 3729.91 + 1052.58i 1.37940 + 0.389266i
\(53\) 1203.51 + 1009.87i 0.428449 + 0.359511i 0.831366 0.555725i \(-0.187559\pi\)
−0.402917 + 0.915236i \(0.632004\pi\)
\(54\) −212.197 + 657.779i −0.0727699 + 0.225576i
\(55\) 22.7409 62.4802i 0.00751767 0.0206546i
\(56\) 217.908 + 1954.55i 0.0694860 + 0.623263i
\(57\) 306.235 + 237.937i 0.0942551 + 0.0732340i
\(58\) 2425.19 4584.35i 0.720925 1.36277i
\(59\) −438.959 + 1206.03i −0.126101 + 0.346461i −0.986638 0.162928i \(-0.947906\pi\)
0.860537 + 0.509389i \(0.170128\pi\)
\(60\) 23.0887 + 23.7086i 0.00641352 + 0.00658574i
\(61\) −674.737 566.171i −0.181332 0.152156i 0.547604 0.836738i \(-0.315540\pi\)
−0.728936 + 0.684582i \(0.759985\pi\)
\(62\) −4343.47 + 932.785i −1.12994 + 0.242660i
\(63\) −2416.32 426.063i −0.608798 0.107348i
\(64\) −1216.48 + 3911.19i −0.296992 + 0.954880i
\(65\) 233.186 + 403.890i 0.0551920 + 0.0955954i
\(66\) 20.3430 146.990i 0.00467011 0.0337443i
\(67\) −1261.58 3466.17i −0.281039 0.772148i −0.997239 0.0742537i \(-0.976343\pi\)
0.716200 0.697895i \(-0.245880\pi\)
\(68\) −2074.73 + 4299.63i −0.448687 + 0.929851i
\(69\) 352.138 609.921i 0.0739630 0.128108i
\(70\) −145.310 + 186.797i −0.0296552 + 0.0381219i
\(71\) −2360.72 2813.40i −0.468304 0.558103i 0.479258 0.877674i \(-0.340906\pi\)
−0.947562 + 0.319571i \(0.896461\pi\)
\(72\) −4254.44 2830.77i −0.820688 0.546059i
\(73\) 313.651 + 1778.80i 0.0588573 + 0.333796i 0.999991 0.00423816i \(-0.00134905\pi\)
−0.941134 + 0.338035i \(0.890238\pi\)
\(74\) −589.173 + 532.741i −0.107592 + 0.0972866i
\(75\) 667.428i 0.118654i
\(76\) −4649.39 + 3427.15i −0.804950 + 0.593343i
\(77\) 1061.18 0.178982
\(78\) 698.084 + 772.030i 0.114741 + 0.126895i
\(79\) 4380.83 772.458i 0.701943 0.123772i 0.188725 0.982030i \(-0.439564\pi\)
0.513218 + 0.858258i \(0.328453\pi\)
\(80\) −433.240 + 235.054i −0.0676938 + 0.0367272i
\(81\) 4812.22 4037.93i 0.733458 0.615444i
\(82\) 2615.77 + 2034.82i 0.389020 + 0.302620i
\(83\) −6444.01 3720.45i −0.935405 0.540057i −0.0468884 0.998900i \(-0.514931\pi\)
−0.888517 + 0.458844i \(0.848264\pi\)
\(84\) −229.538 + 475.690i −0.0325309 + 0.0674164i
\(85\) −539.842 + 196.487i −0.0747187 + 0.0271954i
\(86\) −14155.5 1959.08i −1.91394 0.264883i
\(87\) 1206.25 696.429i 0.159367 0.0920107i
\(88\) 2024.70 + 886.190i 0.261454 + 0.114436i
\(89\) −61.4577 + 348.544i −0.00775884 + 0.0440025i −0.988441 0.151604i \(-0.951556\pi\)
0.980683 + 0.195606i \(0.0626674\pi\)
\(90\) −129.117 601.227i −0.0159404 0.0742256i
\(91\) −4784.47 + 5701.92i −0.577765 + 0.688554i
\(92\) 7318.29 + 7514.80i 0.864637 + 0.887854i
\(93\) −1121.14 408.063i −0.129627 0.0471804i
\(94\) 1788.68 + 946.237i 0.202431 + 0.107089i
\(95\) −688.554 94.8883i −0.0762941 0.0105139i
\(96\) −835.197 + 715.913i −0.0906246 + 0.0776815i
\(97\) 1927.50 + 701.553i 0.204857 + 0.0745619i 0.442411 0.896813i \(-0.354123\pi\)
−0.237554 + 0.971374i \(0.576346\pi\)
\(98\) 5545.47 + 1788.95i 0.577413 + 0.186271i
\(99\) −1772.40 + 2112.26i −0.180838 + 0.215515i
\(100\) 9567.04 + 2699.81i 0.956704 + 0.269981i
\(101\) −1583.91 + 8982.83i −0.155271 + 0.880583i 0.803268 + 0.595618i \(0.203093\pi\)
−0.958538 + 0.284965i \(0.908018\pi\)
\(102\) −1085.88 + 681.712i −0.104371 + 0.0655240i
\(103\) 15678.8 9052.18i 1.47788 0.853255i 0.478194 0.878254i \(-0.341292\pi\)
0.999687 + 0.0249993i \(0.00795836\pi\)
\(104\) −13890.2 + 6883.54i −1.28423 + 0.636422i
\(105\) −59.7255 + 21.7383i −0.00541728 + 0.00197173i
\(106\) −6279.99 + 232.526i −0.558917 + 0.0206948i
\(107\) −3008.15 1736.76i −0.262744 0.151695i 0.362842 0.931851i \(-0.381807\pi\)
−0.625585 + 0.780156i \(0.715140\pi\)
\(108\) −1135.09 2520.87i −0.0973159 0.216124i
\(109\) 15491.5 12998.9i 1.30389 1.09409i 0.314427 0.949282i \(-0.398188\pi\)
0.989460 0.144809i \(-0.0462567\pi\)
\(110\) 100.149 + 246.384i 0.00827676 + 0.0203623i
\(111\) −210.084 + 37.0434i −0.0170509 + 0.00300653i
\(112\) −5890.14 5214.46i −0.469558 0.415693i
\(113\) 12687.8 0.993640 0.496820 0.867854i \(-0.334501\pi\)
0.496820 + 0.867854i \(0.334501\pi\)
\(114\) −1546.91 + 115.610i −0.119030 + 0.00889580i
\(115\) 1262.27i 0.0954455i
\(116\) 5103.35 + 20107.8i 0.379262 + 1.49433i
\(117\) −3358.46 19046.8i −0.245340 1.39139i
\(118\) −1933.13 4755.85i −0.138834 0.341558i
\(119\) −5893.63 7023.75i −0.416187 0.495992i
\(120\) −132.108 8.40066i −0.00917414 0.000583379i
\(121\) −6724.22 + 11646.7i −0.459273 + 0.795485i
\(122\) 3520.81 130.363i 0.236550 0.00875863i
\(123\) 304.407 + 836.352i 0.0201208 + 0.0552814i
\(124\) 10384.4 14420.0i 0.675363 0.937828i
\(125\) 1199.79 + 2078.10i 0.0767868 + 0.132999i
\(126\) 8312.12 5218.32i 0.523565 0.328693i
\(127\) −6827.43 1203.86i −0.423301 0.0746395i −0.0420603 0.999115i \(-0.513392\pi\)
−0.381241 + 0.924476i \(0.624503\pi\)
\(128\) −6883.58 14867.8i −0.420141 0.907459i
\(129\) −2940.00 2466.95i −0.176672 0.148245i
\(130\) −1775.39 572.736i −0.105053 0.0338897i
\(131\) −6537.46 + 17961.5i −0.380949 + 1.04665i 0.590009 + 0.807397i \(0.299124\pi\)
−0.970958 + 0.239251i \(0.923098\pi\)
\(132\) 333.984 + 490.687i 0.0191681 + 0.0281616i
\(133\) −2335.49 10844.6i −0.132031 0.613069i
\(134\) 13042.0 + 6899.41i 0.726330 + 0.384240i
\(135\) 113.785 312.622i 0.00624336 0.0171535i
\(136\) −5379.31 18322.8i −0.290836 0.990635i
\(137\) −15911.1 13351.0i −0.847731 0.711330i 0.111558 0.993758i \(-0.464416\pi\)
−0.959289 + 0.282427i \(0.908860\pi\)
\(138\) 591.502 + 2754.30i 0.0310598 + 0.144628i
\(139\) 24163.0 + 4260.60i 1.25061 + 0.220516i 0.759457 0.650557i \(-0.225465\pi\)
0.491153 + 0.871073i \(0.336576\pi\)
\(140\) −70.0059 944.051i −0.00357173 0.0481659i
\(141\) 271.726 + 470.643i 0.0136676 + 0.0236730i
\(142\) 14551.8 + 2013.93i 0.721673 + 0.0998774i
\(143\) 2860.94 + 7860.37i 0.139906 + 0.384389i
\(144\) 20217.0 3014.95i 0.974971 0.145397i
\(145\) −1248.20 + 2161.95i −0.0593676 + 0.102828i
\(146\) −5702.69 4436.15i −0.267531 0.208114i
\(147\) 1005.89 + 1198.78i 0.0465497 + 0.0554758i
\(148\) 318.821 3161.23i 0.0145554 0.144322i
\(149\) 6773.45 + 38414.2i 0.305097 + 1.73029i 0.623049 + 0.782183i \(0.285894\pi\)
−0.317952 + 0.948107i \(0.602995\pi\)
\(150\) 1790.55 + 1980.22i 0.0795802 + 0.0880098i
\(151\) 12457.9i 0.546376i 0.961961 + 0.273188i \(0.0880781\pi\)
−0.961961 + 0.273188i \(0.911922\pi\)
\(152\) 4600.23 22641.4i 0.199110 0.979977i
\(153\) 23824.2 1.01774
\(154\) −3148.47 + 2846.91i −0.132757 + 0.120042i
\(155\) 2105.89 371.325i 0.0876540 0.0154558i
\(156\) −4142.35 417.771i −0.170215 0.0171668i
\(157\) −23219.9 + 19483.8i −0.942022 + 0.790450i −0.977936 0.208904i \(-0.933010\pi\)
0.0359139 + 0.999355i \(0.488566\pi\)
\(158\) −10925.3 + 14044.6i −0.437644 + 0.562594i
\(159\) −1461.62 843.868i −0.0578151 0.0333795i
\(160\) 654.805 1859.67i 0.0255783 0.0726436i
\(161\) −18930.9 + 6890.27i −0.730330 + 0.265818i
\(162\) −3444.75 + 24890.4i −0.131259 + 0.948421i
\(163\) 804.336 464.383i 0.0302735 0.0174784i −0.484787 0.874632i \(-0.661103\pi\)
0.515060 + 0.857154i \(0.327770\pi\)
\(164\) −13219.8 + 980.310i −0.491515 + 0.0364482i
\(165\) −12.4032 + 70.3422i −0.000455582 + 0.00258374i
\(166\) 29100.1 6249.41i 1.05604 0.226790i
\(167\) 26942.4 32108.7i 0.966057 1.15130i −0.0223920 0.999749i \(-0.507128\pi\)
0.988449 0.151553i \(-0.0484274\pi\)
\(168\) −595.141 2027.14i −0.0210863 0.0718234i
\(169\) −28295.4 10298.7i −0.990700 0.360585i
\(170\) 1074.55 2031.24i 0.0371818 0.0702850i
\(171\) 25486.6 + 13464.0i 0.871606 + 0.460448i
\(172\) 47254.3 32163.4i 1.59729 1.08719i
\(173\) −8168.58 2973.12i −0.272932 0.0993391i 0.201928 0.979400i \(-0.435279\pi\)
−0.474860 + 0.880061i \(0.657501\pi\)
\(174\) −1710.52 + 5302.36i −0.0564975 + 0.175134i
\(175\) −12272.0 + 14625.2i −0.400717 + 0.477556i
\(176\) −8384.61 + 2802.52i −0.270681 + 0.0904739i
\(177\) 239.414 1357.79i 0.00764194 0.0433396i
\(178\) −752.722 1198.99i −0.0237571 0.0378421i
\(179\) −43479.5 + 25102.9i −1.35699 + 0.783461i −0.989218 0.146453i \(-0.953214\pi\)
−0.367777 + 0.929914i \(0.619881\pi\)
\(180\) 1996.04 + 1437.42i 0.0616060 + 0.0443647i
\(181\) −43830.8 + 15953.1i −1.33789 + 0.486954i −0.909149 0.416471i \(-0.863267\pi\)
−0.428746 + 0.903425i \(0.641044\pi\)
\(182\) −1101.65 29752.9i −0.0332583 0.898228i
\(183\) 819.443 + 473.106i 0.0244690 + 0.0141272i
\(184\) −41873.4 2662.71i −1.23681 0.0786481i
\(185\) 292.889 245.763i 0.00855776 0.00718081i
\(186\) 4421.11 1797.07i 0.127792 0.0519444i
\(187\) −10147.4 + 1789.27i −0.290184 + 0.0511673i
\(188\) −7845.44 + 1991.18i −0.221974 + 0.0563370i
\(189\) 5309.68 0.148643
\(190\) 2297.47 1565.70i 0.0636417 0.0433713i
\(191\) 42743.4i 1.17166i −0.810433 0.585831i \(-0.800768\pi\)
0.810433 0.585831i \(-0.199232\pi\)
\(192\) 557.354 4364.71i 0.0151192 0.118400i
\(193\) 6491.41 + 36814.6i 0.174271 + 0.988339i 0.938982 + 0.343966i \(0.111770\pi\)
−0.764711 + 0.644373i \(0.777118\pi\)
\(194\) −7600.89 + 3089.57i −0.201958 + 0.0820908i
\(195\) −322.039 383.791i −0.00846914 0.0100931i
\(196\) −21252.4 + 9569.50i −0.553218 + 0.249102i
\(197\) −5405.57 + 9362.72i −0.139286 + 0.241251i −0.927227 0.374500i \(-0.877814\pi\)
0.787940 + 0.615752i \(0.211148\pi\)
\(198\) −408.102 11021.9i −0.0104097 0.281142i
\(199\) 6245.16 + 17158.4i 0.157702 + 0.433283i 0.993230 0.116165i \(-0.0370602\pi\)
−0.835528 + 0.549448i \(0.814838\pi\)
\(200\) −35627.8 + 17656.0i −0.890696 + 0.441399i
\(201\) 1981.26 + 3431.65i 0.0490400 + 0.0849398i
\(202\) −19399.5 30900.8i −0.475430 0.757299i
\(203\) −39237.4 6918.62i −0.952157 0.167891i
\(204\) 1392.87 4935.76i 0.0334695 0.118602i
\(205\) −1221.98 1025.37i −0.0290775 0.0243990i
\(206\) −22233.3 + 68920.0i −0.523926 + 1.62409i
\(207\) 17903.6 49189.6i 0.417829 1.14798i
\(208\) 22744.6 57687.4i 0.525717 1.33338i
\(209\) −11866.7 3820.59i −0.271668 0.0874657i
\(210\) 118.883 224.726i 0.00269577 0.00509583i
\(211\) −17736.2 + 48729.8i −0.398378 + 1.09453i 0.564697 + 0.825299i \(0.308993\pi\)
−0.963074 + 0.269236i \(0.913229\pi\)
\(212\) 18008.6 17537.7i 0.400689 0.390211i
\(213\) 3022.31 + 2536.02i 0.0666162 + 0.0558976i
\(214\) 13584.3 2917.31i 0.296627 0.0637023i
\(215\) 6774.12 + 1194.46i 0.146547 + 0.0258401i
\(216\) 10130.7 + 4434.09i 0.217135 + 0.0950379i
\(217\) 17064.3 + 29556.2i 0.362383 + 0.627666i
\(218\) −11089.3 + 80127.0i −0.233342 + 1.68603i
\(219\) −663.644 1823.35i −0.0138372 0.0380173i
\(220\) −958.127 462.331i −0.0197960 0.00955230i
\(221\) 36137.0 62591.0i 0.739890 1.28153i
\(222\) 523.928 673.512i 0.0106308 0.0136659i
\(223\) −12729.6 15170.6i −0.255980 0.305066i 0.622715 0.782449i \(-0.286030\pi\)
−0.878695 + 0.477383i \(0.841585\pi\)
\(224\) 31464.9 330.872i 0.627090 0.00659423i
\(225\) −8614.29 48854.1i −0.170159 0.965019i
\(226\) −37644.0 + 34038.4i −0.737018 + 0.666426i
\(227\) 4175.20i 0.0810263i 0.999179 + 0.0405131i \(0.0128993\pi\)
−0.999179 + 0.0405131i \(0.987101\pi\)
\(228\) 4279.45 4493.01i 0.0823224 0.0864307i
\(229\) 63595.1 1.21270 0.606349 0.795199i \(-0.292633\pi\)
0.606349 + 0.795199i \(0.292633\pi\)
\(230\) −3386.37 3745.07i −0.0640145 0.0707953i
\(231\) −1122.66 + 197.956i −0.0210390 + 0.00370975i
\(232\) −69085.8 45967.5i −1.28355 0.854033i
\(233\) 6618.26 5553.38i 0.121908 0.102293i −0.579796 0.814762i \(-0.696868\pi\)
0.701703 + 0.712469i \(0.252423\pi\)
\(234\) 61062.4 + 47500.7i 1.11517 + 0.867498i
\(235\) −843.528 487.011i −0.0152744 0.00881867i
\(236\) 18494.3 + 8924.19i 0.332058 + 0.160230i
\(237\) −4490.54 + 1634.42i −0.0799469 + 0.0290983i
\(238\) 36329.1 + 5027.84i 0.641359 + 0.0887621i
\(239\) 62748.1 36227.6i 1.09851 0.634226i 0.162682 0.986679i \(-0.447985\pi\)
0.935830 + 0.352452i \(0.114652\pi\)
\(240\) 414.493 329.490i 0.00719606 0.00572031i
\(241\) 8433.63 47829.5i 0.145205 0.823496i −0.821998 0.569490i \(-0.807141\pi\)
0.967203 0.254006i \(-0.0817483\pi\)
\(242\) −11295.0 52594.6i −0.192866 0.898070i
\(243\) −13334.2 + 15891.1i −0.225816 + 0.269117i
\(244\) −10096.3 + 9832.30i −0.169583 + 0.165149i
\(245\) −2635.59 959.278i −0.0439083 0.0159813i
\(246\) −3146.90 1664.76i −0.0520011 0.0275093i
\(247\) 74031.2 46536.2i 1.21345 0.762777i
\(248\) 7875.73 + 70642.4i 0.128052 + 1.14858i
\(249\) 7511.37 + 2733.92i 0.121149 + 0.0440947i
\(250\) −9134.79 2946.85i −0.146157 0.0471496i
\(251\) −59628.7 + 71062.7i −0.946472 + 1.12796i 0.0451750 + 0.998979i \(0.485615\pi\)
−0.991647 + 0.128982i \(0.958829\pi\)
\(252\) −10662.0 + 37782.0i −0.167895 + 0.594954i
\(253\) −3931.38 + 22296.0i −0.0614192 + 0.348326i
\(254\) 23486.3 14744.6i 0.364038 0.228542i
\(255\) 534.465 308.574i 0.00821938 0.00474546i
\(256\) 60310.1 + 25644.9i 0.920259 + 0.391310i
\(257\) 61612.7 22425.2i 0.932833 0.339524i 0.169501 0.985530i \(-0.445784\pi\)
0.763332 + 0.646006i \(0.223562\pi\)
\(258\) 15341.1 568.026i 0.230471 0.00853353i
\(259\) 5284.62 + 3051.08i 0.0787797 + 0.0454835i
\(260\) 6804.01 3063.70i 0.100651 0.0453210i
\(261\) 79306.0 66545.6i 1.16419 0.976874i
\(262\) −28790.3 70829.3i −0.419415 1.03184i
\(263\) 82922.0 14621.4i 1.19883 0.211387i 0.461639 0.887068i \(-0.347262\pi\)
0.737194 + 0.675681i \(0.236151\pi\)
\(264\) −2307.31 559.840i −0.0331054 0.00803260i
\(265\) 3024.91 0.0430746
\(266\) 36022.8 + 25909.7i 0.509112 + 0.366183i
\(267\) 380.202i 0.00533325i
\(268\) −57204.4 + 14518.5i −0.796452 + 0.202140i
\(269\) −2374.72 13467.7i −0.0328176 0.186118i 0.963992 0.265930i \(-0.0856791\pi\)
−0.996810 + 0.0798121i \(0.974568\pi\)
\(270\) 501.099 + 1232.79i 0.00687379 + 0.0169107i
\(271\) −29631.4 35313.3i −0.403472 0.480839i 0.525604 0.850730i \(-0.323840\pi\)
−0.929075 + 0.369891i \(0.879395\pi\)
\(272\) 65115.9 + 39931.2i 0.880135 + 0.539728i
\(273\) 3998.02 6924.77i 0.0536438 0.0929138i
\(274\) 83024.7 3074.12i 1.10588 0.0409468i
\(275\) 7338.18 + 20161.5i 0.0970338 + 0.266598i
\(276\) −9144.11 6585.00i −0.120039 0.0864446i
\(277\) −24346.2 42168.8i −0.317301 0.549581i 0.662623 0.748953i \(-0.269443\pi\)
−0.979924 + 0.199372i \(0.936110\pi\)
\(278\) −83120.6 + 52182.9i −1.07552 + 0.675209i
\(279\) −87331.7 15398.9i −1.12192 0.197826i
\(280\) 2740.37 + 2613.14i 0.0349537 + 0.0333308i
\(281\) 48409.6 + 40620.5i 0.613083 + 0.514438i 0.895621 0.444819i \(-0.146732\pi\)
−0.282538 + 0.959256i \(0.591176\pi\)
\(282\) −2068.82 667.394i −0.0260150 0.00839235i
\(283\) −29724.1 + 81666.3i −0.371138 + 1.01969i 0.603784 + 0.797148i \(0.293659\pi\)
−0.974922 + 0.222546i \(0.928563\pi\)
\(284\) −48577.3 + 33064.0i −0.602278 + 0.409938i
\(285\) 746.147 28.0591i 0.00918618 0.000345449i
\(286\) −29575.8 15646.0i −0.361580 0.191281i
\(287\) 8707.57 23923.9i 0.105714 0.290447i
\(288\) −51894.3 + 63182.7i −0.625654 + 0.761751i
\(289\) 4219.10 + 3540.25i 0.0505155 + 0.0423875i
\(290\) −2096.66 9763.02i −0.0249306 0.116088i
\(291\) −2170.04 382.637i −0.0256261 0.00451857i
\(292\) 28820.7 2137.19i 0.338018 0.0250656i
\(293\) 7867.42 + 13626.8i 0.0916425 + 0.158730i 0.908202 0.418531i \(-0.137455\pi\)
−0.816560 + 0.577261i \(0.804122\pi\)
\(294\) −6200.47 858.126i −0.0717348 0.00992787i
\(295\) 845.162 + 2322.06i 0.00971172 + 0.0266827i
\(296\) 7534.91 + 10234.5i 0.0859993 + 0.116811i
\(297\) 2983.52 5167.60i 0.0338233 0.0585836i
\(298\) −123153. 95801.0i −1.38679 1.07879i
\(299\) −102075. 121648.i −1.14176 1.36070i
\(300\) −10624.9 1071.56i −0.118055 0.0119063i
\(301\) 19063.6 + 108115.i 0.210413 + 1.19331i
\(302\) −33421.7 36961.9i −0.366450 0.405267i
\(303\) 9798.72i 0.106729i
\(304\) 47093.0 + 79517.1i 0.509576 + 0.860426i
\(305\) −1695.89 −0.0182304
\(306\) −70685.0 + 63914.7i −0.754891 + 0.682587i
\(307\) 106858. 18841.9i 1.13378 0.199916i 0.424898 0.905241i \(-0.360310\pi\)
0.708884 + 0.705325i \(0.249199\pi\)
\(308\) 1703.74 16893.2i 0.0179599 0.178079i
\(309\) −14898.6 + 12501.4i −0.156037 + 0.130931i
\(310\) −5251.87 + 6751.31i −0.0546501 + 0.0702530i
\(311\) −110041. 63532.2i −1.13772 0.656861i −0.191852 0.981424i \(-0.561449\pi\)
−0.945864 + 0.324563i \(0.894783\pi\)
\(312\) 13410.9 9873.47i 0.137768 0.101429i
\(313\) −124322. + 45249.6i −1.26900 + 0.461877i −0.886778 0.462195i \(-0.847062\pi\)
−0.382218 + 0.924072i \(0.624840\pi\)
\(314\) 16621.6 120101.i 0.168583 1.21811i
\(315\) −4091.19 + 2362.05i −0.0412315 + 0.0238050i
\(316\) −5263.48 70979.7i −0.0527107 0.710820i
\(317\) 16052.8 91039.7i 0.159746 0.905967i −0.794571 0.607171i \(-0.792304\pi\)
0.954317 0.298795i \(-0.0965848\pi\)
\(318\) 6600.45 1417.48i 0.0652709 0.0140173i
\(319\) −28781.1 + 34299.9i −0.282830 + 0.337064i
\(320\) 3046.31 + 7274.24i 0.0297491 + 0.0710375i
\(321\) 3506.41 + 1276.23i 0.0340293 + 0.0123856i
\(322\) 37681.8 71230.2i 0.363430 0.686993i
\(323\) 40618.0 + 99762.1i 0.389326 + 0.956226i
\(324\) −56554.7 83089.8i −0.538739 0.791512i
\(325\) −141416. 51471.3i −1.33885 0.487302i
\(326\) −1140.59 + 3535.65i −0.0107323 + 0.0332685i
\(327\) −13964.1 + 16641.8i −0.130593 + 0.155634i
\(328\) 36592.4 38374.1i 0.340129 0.356690i
\(329\) 2699.44 15309.3i 0.0249391 0.141437i
\(330\) −151.912 241.976i −0.00139497 0.00222201i
\(331\) 41940.2 24214.2i 0.382802 0.221011i −0.296234 0.955115i \(-0.595731\pi\)
0.679037 + 0.734104i \(0.262398\pi\)
\(332\) −69572.7 + 96610.5i −0.631194 + 0.876493i
\(333\) −14899.5 + 5422.98i −0.134364 + 0.0489046i
\(334\) 6203.60 + 167545.i 0.0556097 + 1.50189i
\(335\) −6150.51 3551.00i −0.0548052 0.0316418i
\(336\) 7204.11 + 4417.80i 0.0638119 + 0.0391316i
\(337\) −116649. + 97880.4i −1.02712 + 0.861859i −0.990506 0.137471i \(-0.956103\pi\)
−0.0366172 + 0.999329i \(0.511658\pi\)
\(338\) 111580. 45354.4i 0.976680 0.396996i
\(339\) −13422.9 + 2366.81i −0.116801 + 0.0205951i
\(340\) 2261.19 + 8909.34i 0.0195605 + 0.0770704i
\(341\) 38353.8 0.329837
\(342\) −111738. + 28427.9i −0.955320 + 0.243048i
\(343\) 118544.i 1.00761i
\(344\) −53913.8 + 222199.i −0.455600 + 1.87770i
\(345\) −235.466 1335.40i −0.00197829 0.0112195i
\(346\) 32211.9 13093.3i 0.269069 0.109370i
\(347\) 60588.5 + 72206.5i 0.503189 + 0.599677i 0.956521 0.291665i \(-0.0942092\pi\)
−0.453332 + 0.891342i \(0.649765\pi\)
\(348\) −9149.97 20320.7i −0.0755547 0.167796i
\(349\) −68961.6 + 119445.i −0.566183 + 0.980657i 0.430756 + 0.902468i \(0.358247\pi\)
−0.996939 + 0.0781887i \(0.975086\pi\)
\(350\) −2825.67 76314.8i −0.0230667 0.622978i
\(351\) 14314.8 + 39329.7i 0.116191 + 0.319232i
\(352\) 17358.2 30808.9i 0.140094 0.248651i
\(353\) 55756.5 + 96573.0i 0.447451 + 0.775008i 0.998219 0.0596499i \(-0.0189984\pi\)
−0.550768 + 0.834658i \(0.685665\pi\)
\(354\) 2932.30 + 4670.77i 0.0233992 + 0.0372719i
\(355\) −6963.78 1227.90i −0.0552571 0.00974332i
\(356\) 5449.89 + 1537.95i 0.0430019 + 0.0121351i
\(357\) 7545.31 + 6331.26i 0.0592026 + 0.0496768i
\(358\) 61655.9 191124.i 0.481071 1.49125i
\(359\) −25263.6 + 69411.2i −0.196023 + 0.538568i −0.998294 0.0583920i \(-0.981403\pi\)
0.802271 + 0.596960i \(0.203625\pi\)
\(360\) −9778.38 + 1090.17i −0.0754505 + 0.00841177i
\(361\) −12927.1 + 129678.i −0.0991944 + 0.995068i
\(362\) 87245.0 164920.i 0.665769 1.25851i
\(363\) 4941.19 13575.8i 0.0374989 0.103027i
\(364\) 83088.6 + 85319.7i 0.627103 + 0.643942i
\(365\) 2664.07 + 2235.42i 0.0199968 + 0.0167793i
\(366\) −3700.48 + 794.698i −0.0276246 + 0.00593253i
\(367\) 211573. + 37306.0i 1.57082 + 0.276979i 0.890171 0.455627i \(-0.150585\pi\)
0.680653 + 0.732606i \(0.261696\pi\)
\(368\) 131380. 104437.i 0.970135 0.771182i
\(369\) 33076.4 + 57290.0i 0.242921 + 0.420752i
\(370\) −209.660 + 1514.92i −0.00153148 + 0.0110659i
\(371\) 16512.0 + 45366.2i 0.119964 + 0.329598i
\(372\) −8296.06 + 17192.6i −0.0599496 + 0.124238i
\(373\) −43607.7 + 75530.7i −0.313433 + 0.542883i −0.979103 0.203364i \(-0.934813\pi\)
0.665670 + 0.746246i \(0.268146\pi\)
\(374\) 25306.7 32531.9i 0.180923 0.232577i
\(375\) −1656.96 1974.69i −0.0117828 0.0140422i
\(376\) 17935.1 26955.2i 0.126861 0.190663i
\(377\) −54536.3 309291.i −0.383710 2.17613i
\(378\) −15753.5 + 14244.6i −0.110254 + 0.0996937i
\(379\) 281714.i 1.96124i 0.195926 + 0.980619i \(0.437229\pi\)
−0.195926 + 0.980619i \(0.562771\pi\)
\(380\) −2616.03 + 10808.9i −0.0181166 + 0.0748540i
\(381\) 7447.55 0.0513055
\(382\) 114671. + 126817.i 0.785825 + 0.869065i
\(383\) 134510. 23717.8i 0.916977 0.161688i 0.304807 0.952414i \(-0.401408\pi\)
0.612170 + 0.790726i \(0.290297\pi\)
\(384\) 10055.9 + 14445.1i 0.0681957 + 0.0979621i
\(385\) 1565.17 1313.33i 0.0105594 0.00886039i
\(386\) −118025. 91812.0i −0.792134 0.616205i
\(387\) −247041. 142629.i −1.64948 0.952327i
\(388\) 14262.8 29558.0i 0.0947418 0.196341i
\(389\) −15617.5 + 5684.29i −0.103208 + 0.0375645i −0.393108 0.919492i \(-0.628600\pi\)
0.289900 + 0.957057i \(0.406378\pi\)
\(390\) 1985.09 + 274.731i 0.0130512 + 0.00180625i
\(391\) 169407. 97806.9i 1.10809 0.639759i
\(392\) 37382.0 85407.5i 0.243271 0.555807i
\(393\) 3565.62 20221.7i 0.0230861 0.130928i
\(394\) −9079.99 42280.6i −0.0584915 0.272363i
\(395\) 5505.40 6561.08i 0.0352853 0.0420514i
\(396\) 30780.0 + 31606.5i 0.196281 + 0.201551i
\(397\) −72026.8 26215.6i −0.456996 0.166333i 0.103256 0.994655i \(-0.467074\pi\)
−0.560253 + 0.828322i \(0.689296\pi\)
\(398\) −64561.1 34153.8i −0.407573 0.215612i
\(399\) 4493.78 + 11037.2i 0.0282271 + 0.0693287i
\(400\) 58338.9 147965.i 0.364618 0.924784i
\(401\) −253861. 92397.8i −1.57873 0.574610i −0.603801 0.797135i \(-0.706348\pi\)
−0.974927 + 0.222525i \(0.928570\pi\)
\(402\) −15084.6 4866.24i −0.0933431 0.0301121i
\(403\) −172923. + 206081.i −1.06474 + 1.26890i
\(404\) 140457. + 39636.8i 0.860558 + 0.242849i
\(405\) 2100.28 11911.3i 0.0128046 0.0726188i
\(406\) 134976. 84737.8i 0.818852 0.514073i
\(407\) 5938.88 3428.81i 0.0358522 0.0206993i
\(408\) 9108.94 + 18380.9i 0.0547202 + 0.110419i
\(409\) 165272. 60154.0i 0.987989 0.359598i 0.203047 0.979169i \(-0.434915\pi\)
0.784941 + 0.619570i \(0.212693\pi\)
\(410\) 6376.38 236.095i 0.0379320 0.00140449i
\(411\) 19323.4 + 11156.4i 0.114393 + 0.0660449i
\(412\) −118931. 264129.i −0.700651 1.55604i
\(413\) −30211.8 + 25350.7i −0.177123 + 0.148624i
\(414\) 78845.5 + 193974.i 0.460019 + 1.13173i
\(415\) −14108.9 + 2487.78i −0.0819213 + 0.0144449i
\(416\) 87279.8 + 232174.i 0.504344 + 1.34161i
\(417\) −26357.7 −0.151578
\(418\) 45457.6 20500.2i 0.260168 0.117329i
\(419\) 89944.2i 0.512324i −0.966634 0.256162i \(-0.917542\pi\)
0.966634 0.256162i \(-0.0824581\pi\)
\(420\) 250.168 + 985.687i 0.00141818 + 0.00558779i
\(421\) 14276.4 + 80965.4i 0.0805478 + 0.456810i 0.998229 + 0.0594915i \(0.0189479\pi\)
−0.917681 + 0.397318i \(0.869941\pi\)
\(422\) −78108.4 192161.i −0.438604 1.07904i
\(423\) 25964.1 + 30942.8i 0.145108 + 0.172933i
\(424\) −6380.96 + 100346.i −0.0354940 + 0.558173i
\(425\) 92689.7 160543.i 0.513161 0.888820i
\(426\) −15770.6 + 583.930i −0.0869017 + 0.00321767i
\(427\) −9257.25 25434.1i −0.0507722 0.139496i
\(428\) −32477.5 + 45099.1i −0.177294 + 0.246196i
\(429\) −4492.99 7782.08i −0.0244130 0.0422845i
\(430\) −23302.9 + 14629.5i −0.126030 + 0.0791211i
\(431\) −44948.7 7925.68i −0.241971 0.0426660i 0.0513474 0.998681i \(-0.483648\pi\)
−0.293318 + 0.956015i \(0.594760\pi\)
\(432\) −41952.7 + 14022.5i −0.224798 + 0.0751378i
\(433\) 233398. + 195844.i 1.24486 + 1.04456i 0.997128 + 0.0757357i \(0.0241305\pi\)
0.247735 + 0.968828i \(0.420314\pi\)
\(434\) −129921. 41912.1i −0.689764 0.222515i
\(435\) 917.223 2520.05i 0.00484726 0.0133177i
\(436\) −182061. 267482.i −0.957731 1.40709i
\(437\) 236502. 8893.72i 1.23843 0.0465716i
\(438\) 6860.62 + 3629.37i 0.0357614 + 0.0189183i
\(439\) 39489.9 108498.i 0.204907 0.562977i −0.794088 0.607803i \(-0.792051\pi\)
0.998995 + 0.0448257i \(0.0142733\pi\)
\(440\) 4083.04 1198.72i 0.0210901 0.00619174i
\(441\) 89101.2 + 74764.8i 0.458148 + 0.384432i
\(442\) 60700.9 + 282651.i 0.310707 + 1.44679i
\(443\) 101076. + 17822.4i 0.515039 + 0.0908152i 0.425126 0.905134i \(-0.360230\pi\)
0.0899132 + 0.995950i \(0.471341\pi\)
\(444\) 252.412 + 3403.85i 0.00128039 + 0.0172665i
\(445\) 340.716 + 590.138i 0.00172057 + 0.00298012i
\(446\) 78467.4 + 10859.6i 0.394475 + 0.0545941i
\(447\) −14331.8 39376.2i −0.0717273 0.197069i
\(448\) −92466.9 + 85394.6i −0.460713 + 0.425476i
\(449\) 107849. 186800.i 0.534962 0.926582i −0.464203 0.885729i \(-0.653659\pi\)
0.999165 0.0408532i \(-0.0130076\pi\)
\(450\) 156622. + 121837.i 0.773443 + 0.601665i
\(451\) −18390.9 21917.4i −0.0904170 0.107755i
\(452\) 20370.4 201980.i 0.0997063 0.988625i
\(453\) −2323.93 13179.7i −0.0113247 0.0642256i
\(454\) −11201.1 12387.6i −0.0543437 0.0601001i
\(455\) 14331.2i 0.0692246i
\(456\) −643.166 + 24811.3i −0.00309309 + 0.119322i
\(457\) −389470. −1.86484 −0.932421 0.361375i \(-0.882307\pi\)
−0.932421 + 0.361375i \(0.882307\pi\)
\(458\) −188683. + 170611.i −0.899502 + 0.813347i
\(459\) −50773.2 + 8952.68i −0.240996 + 0.0424940i
\(460\) 20094.3 + 2026.58i 0.0949637 + 0.00957743i
\(461\) −54286.0 + 45551.4i −0.255438 + 0.214338i −0.761510 0.648153i \(-0.775542\pi\)
0.506072 + 0.862492i \(0.331097\pi\)
\(462\) 2799.81 3599.17i 0.0131173 0.0168624i
\(463\) −144753. 83573.3i −0.675253 0.389857i 0.122811 0.992430i \(-0.460809\pi\)
−0.798064 + 0.602573i \(0.794142\pi\)
\(464\) 328294. 48958.3i 1.52485 0.227400i
\(465\) −2158.63 + 785.676i −0.00998324 + 0.00363360i
\(466\) −4737.58 + 34231.8i −0.0218165 + 0.157637i
\(467\) −85114.8 + 49141.1i −0.390276 + 0.225326i −0.682280 0.731091i \(-0.739011\pi\)
0.292004 + 0.956417i \(0.405678\pi\)
\(468\) −308602. + 22884.3i −1.40899 + 0.104483i
\(469\) 19682.7 111626.i 0.0894827 0.507482i
\(470\) 3809.24 818.056i 0.0172442 0.00370328i
\(471\) 20930.6 24944.1i 0.0943496 0.112441i
\(472\) −78813.2 + 23138.4i −0.353765 + 0.103860i
\(473\) 115934. + 42196.6i 0.518190 + 0.188606i
\(474\) 8938.40 16896.3i 0.0397835 0.0752030i
\(475\) 189887. 119363.i 0.841603 0.529034i
\(476\) −121275. + 82545.3i −0.535251 + 0.364316i
\(477\) −117879. 42904.4i −0.518082 0.188567i
\(478\) −88979.8 + 275824.i −0.389435 + 1.20719i
\(479\) −255987. + 305073.i −1.11570 + 1.32964i −0.177269 + 0.984163i \(0.556726\pi\)
−0.938429 + 0.345473i \(0.887718\pi\)
\(480\) −345.833 + 2089.57i −0.00150101 + 0.00906930i
\(481\) −8352.57 + 47369.8i −0.0361019 + 0.204744i
\(482\) 103293. + 164533.i 0.444609 + 0.708204i
\(483\) 18742.3 10820.9i 0.0803395 0.0463840i
\(484\) 174611. + 125743.i 0.745384 + 0.536778i
\(485\) 3711.17 1350.75i 0.0157771 0.00574239i
\(486\) −3070.26 82920.6i −0.0129988 0.351067i
\(487\) 151988. + 87750.4i 0.640843 + 0.369991i 0.784939 0.619573i \(-0.212694\pi\)
−0.144096 + 0.989564i \(0.546027\pi\)
\(488\) 3577.42 56258.0i 0.0150221 0.236235i
\(489\) −764.308 + 641.331i −0.00319632 + 0.00268203i
\(490\) 10393.2 4224.56i 0.0432869 0.0175950i
\(491\) 288778. 50919.4i 1.19785 0.211213i 0.461080 0.887359i \(-0.347462\pi\)
0.736768 + 0.676146i \(0.236351\pi\)
\(492\) 13802.8 3503.16i 0.0570214 0.0144720i
\(493\) 386869. 1.59173
\(494\) −94800.4 + 336679.i −0.388469 + 1.37963i
\(495\) 5308.96i 0.0216670i
\(496\) −212884. 188463.i −0.865325 0.766061i
\(497\) −19597.4 111142.i −0.0793387 0.449952i
\(498\) −29620.3 + 12039.9i −0.119435 + 0.0485472i
\(499\) −172306. 205346.i −0.691987 0.824678i 0.299607 0.954063i \(-0.403144\pi\)
−0.991595 + 0.129384i \(0.958700\pi\)
\(500\) 35008.1 15763.4i 0.140032 0.0630535i
\(501\) −22513.7 + 38994.8i −0.0896955 + 0.155357i
\(502\) −13729.8 370809.i −0.0544823 1.47144i
\(503\) −136035. 373752.i −0.537668 1.47723i −0.849756 0.527177i \(-0.823251\pi\)
0.312088 0.950053i \(-0.398972\pi\)
\(504\) −69726.6 140701.i −0.274497 0.553905i
\(505\) 8781.08 + 15209.3i 0.0344322 + 0.0596384i
\(506\) −48150.8 76697.9i −0.188062 0.299559i
\(507\) 31855.9 + 5617.05i 0.123929 + 0.0218520i
\(508\) −30126.1 + 106755.i −0.116739 + 0.413675i
\(509\) −105103. 88191.7i −0.405676 0.340402i 0.417007 0.908903i \(-0.363079\pi\)
−0.822682 + 0.568501i \(0.807524\pi\)
\(510\) −757.897 + 2349.37i −0.00291387 + 0.00903256i
\(511\) −18983.6 + 52156.9i −0.0727002 + 0.199742i
\(512\) −247736. + 85711.0i −0.945038 + 0.326962i
\(513\) −59375.6 19116.5i −0.225618 0.0726395i
\(514\) −122640. + 231827.i −0.464200 + 0.877481i
\(515\) 11922.1 32755.6i 0.0449507 0.123501i
\(516\) −43992.2 + 42841.8i −0.165225 + 0.160905i
\(517\) −13382.8 11229.5i −0.0500687 0.0420126i
\(518\) −23864.5 + 5125.04i −0.0889392 + 0.0191002i
\(519\) 9196.44 + 1621.58i 0.0341417 + 0.00602010i
\(520\) −11967.9 + 27343.4i −0.0442601 + 0.101122i
\(521\) 206253. + 357241.i 0.759845 + 1.31609i 0.942929 + 0.332993i \(0.108059\pi\)
−0.183084 + 0.983097i \(0.558608\pi\)
\(522\) −56769.9 + 410197.i −0.208342 + 1.50540i
\(523\) −66765.9 183438.i −0.244091 0.670634i −0.999875 0.0158131i \(-0.994966\pi\)
0.755784 0.654821i \(-0.227256\pi\)
\(524\) 275438. + 132909.i 1.00314 + 0.484051i
\(525\) 10254.7 17761.7i 0.0372054 0.0644416i
\(526\) −206799. + 265841.i −0.747442 + 0.960840i
\(527\) −213010. 253855.i −0.766971 0.914040i
\(528\) 8347.59 4528.97i 0.0299429 0.0162455i
\(529\) −26040.6 147684.i −0.0930551 0.527742i
\(530\) −8974.75 + 8115.14i −0.0319500 + 0.0288898i
\(531\) 102477.i 0.363443i
\(532\) −176387. + 19768.1i −0.623223 + 0.0698462i
\(533\) 200684. 0.706411
\(534\) 1019.99 + 1128.04i 0.00357697 + 0.00395586i
\(535\) −6586.23 + 1161.33i −0.0230107 + 0.00405740i
\(536\) 130772. 196542.i 0.455184 0.684108i
\(537\) 41315.7 34668.0i 0.143274 0.120221i
\(538\) 43176.4 + 33587.1i 0.149170 + 0.116040i
\(539\) −43566.0 25152.8i −0.149958 0.0865784i
\(540\) −4794.03 2313.29i −0.0164404 0.00793311i
\(541\) −154367. + 56184.8i −0.527423 + 0.191966i −0.591987 0.805947i \(-0.701656\pi\)
0.0645645 + 0.997914i \(0.479434\pi\)
\(542\) 182652. + 25278.5i 0.621764 + 0.0860502i
\(543\) 43394.2 25053.7i 0.147174 0.0849712i
\(544\) −300321. + 56217.1i −1.01482 + 0.189964i
\(545\) 6761.22 38344.8i 0.0227631 0.129096i
\(546\) 6715.66 + 31271.2i 0.0225270 + 0.104896i
\(547\) −264723. + 315484.i −0.884741 + 1.05439i 0.113406 + 0.993549i \(0.463824\pi\)
−0.998147 + 0.0608450i \(0.980620\pi\)
\(548\) −238083. + 231857.i −0.792805 + 0.772074i
\(549\) 66087.5 + 24053.9i 0.219268 + 0.0798069i
\(550\) −75860.6 40131.4i −0.250779 0.132666i
\(551\) 413864. + 218634.i 1.36319 + 0.720137i
\(552\) 44796.1 4994.20i 0.147015 0.0163903i
\(553\) 128452. + 46752.7i 0.420040 + 0.152882i
\(554\) 185363. + 59797.4i 0.603953 + 0.194833i
\(555\) −264.013 + 314.638i −0.000857115 + 0.00102147i
\(556\) 106620. 377817.i 0.344895 1.22217i
\(557\) 4951.95 28083.9i 0.0159612 0.0905205i −0.975787 0.218725i \(-0.929810\pi\)
0.991748 + 0.128204i \(0.0409214\pi\)
\(558\) 300420. 188603.i 0.964852 0.605732i
\(559\) −749432. + 432685.i −2.39833 + 1.38468i
\(560\) −15141.0 401.245i −0.0482812 0.00127948i
\(561\) 10401.6 3785.86i 0.0330501 0.0120293i
\(562\) −252604. + 9353.05i −0.799775 + 0.0296129i
\(563\) 261239. + 150827.i 0.824180 + 0.475840i 0.851856 0.523777i \(-0.175477\pi\)
−0.0276761 + 0.999617i \(0.508811\pi\)
\(564\) 7928.53 3570.04i 0.0249250 0.0112232i
\(565\) 18713.5 15702.5i 0.0586218 0.0491895i
\(566\) −130902. 322042.i −0.408614 1.00526i
\(567\) 190105. 33520.6i 0.591326 0.104267i
\(568\) 55423.3 228421.i 0.171789 0.708009i
\(569\) −262214. −0.809901 −0.404950 0.914339i \(-0.632711\pi\)
−0.404950 + 0.914339i \(0.632711\pi\)
\(570\) −2138.50 + 2084.99i −0.00658203 + 0.00641733i
\(571\) 275355.i 0.844541i −0.906470 0.422270i \(-0.861233\pi\)
0.906470 0.422270i \(-0.138767\pi\)
\(572\) 129724. 32924.1i 0.396488 0.100629i
\(573\) 7973.47 + 45219.8i 0.0242850 + 0.137727i
\(574\) 38347.3 + 94341.1i 0.116389 + 0.286337i
\(575\) −261817. 312022.i −0.791886 0.943734i
\(576\) −15537.1 326680.i −0.0468301 0.984640i
\(577\) −8506.76 + 14734.1i −0.0255513 + 0.0442561i −0.878518 0.477709i \(-0.841467\pi\)
0.852967 + 0.521965i \(0.174801\pi\)
\(578\) −22015.5 + 815.158i −0.0658981 + 0.00243998i
\(579\) −13735.0 37736.6i −0.0409705 0.112566i
\(580\) 32412.6 + 23341.5i 0.0963514 + 0.0693861i
\(581\) −114326. 198019.i −0.338683 0.586616i
\(582\) 7464.92 4686.45i 0.0220383 0.0138356i
\(583\) 53430.4 + 9421.23i 0.157200 + 0.0277185i
\(584\) −79775.9 + 83660.3i −0.233909 + 0.245298i
\(585\) −28525.9 23936.1i −0.0833543 0.0699426i
\(586\) −59899.7 19323.4i −0.174433 0.0562715i
\(587\) 140107. 384941.i 0.406615 1.11717i −0.552342 0.833617i \(-0.686266\pi\)
0.958958 0.283549i \(-0.0915119\pi\)
\(588\) 20698.6 14088.4i 0.0598668 0.0407481i
\(589\) −84410.3 391949.i −0.243313 1.12979i
\(590\) −8737.11 4622.06i −0.0250994 0.0132780i
\(591\) 3972.20 10913.5i 0.0113725 0.0312457i
\(592\) −49812.5 10150.8i −0.142133 0.0289638i
\(593\) 422035. + 354130.i 1.20016 + 1.00705i 0.999625 + 0.0273681i \(0.00871261\pi\)
0.200535 + 0.979686i \(0.435732\pi\)
\(594\) 5011.55 + 23336.1i 0.0142036 + 0.0661386i
\(595\) −17385.3 3065.50i −0.0491076 0.00865900i
\(596\) 622399. 46153.8i 1.75217 0.129932i
\(597\) −9807.76 16987.5i −0.0275183 0.0476630i
\(598\) 629204. + 87079.9i 1.75950 + 0.243509i
\(599\) 196915. + 541020.i 0.548814 + 1.50785i 0.835313 + 0.549774i \(0.185286\pi\)
−0.286499 + 0.958080i \(0.592492\pi\)
\(600\) 34398.4 25325.0i 0.0955510 0.0703472i
\(601\) 203661. 352750.i 0.563843 0.976604i −0.433314 0.901243i \(-0.642656\pi\)
0.997156 0.0753610i \(-0.0240109\pi\)
\(602\) −346608. 269628.i −0.956415 0.743999i
\(603\) 189315. + 225617.i 0.520655 + 0.620493i
\(604\) 198321. + 20001.3i 0.543618 + 0.0548258i
\(605\) 4496.33 + 25500.0i 0.0122842 + 0.0696673i
\(606\) 26287.7 + 29072.3i 0.0715826 + 0.0791651i
\(607\) 495565.i 1.34500i 0.740096 + 0.672501i \(0.234780\pi\)
−0.740096 + 0.672501i \(0.765220\pi\)
\(608\) −353048. 109583.i −0.955051 0.296440i
\(609\) 42801.3 0.115404
\(610\) 5031.60 4549.67i 0.0135222 0.0122270i
\(611\) 120676. 21278.4i 0.323250 0.0569977i
\(612\) 38250.0 379263.i 0.102124 1.01260i
\(613\) −198660. + 166695.i −0.528676 + 0.443612i −0.867644 0.497186i \(-0.834367\pi\)
0.338968 + 0.940798i \(0.389922\pi\)
\(614\) −266493. + 342578.i −0.706885 + 0.908704i
\(615\) 1484.06 + 856.820i 0.00392374 + 0.00226537i
\(616\) 40265.7 + 54692.1i 0.106114 + 0.144133i
\(617\) −280206. + 101987.i −0.736049 + 0.267900i −0.682723 0.730677i \(-0.739204\pi\)
−0.0533259 + 0.998577i \(0.516982\pi\)
\(618\) 10664.9 77060.4i 0.0279242 0.201769i
\(619\) 353496. 204091.i 0.922578 0.532651i 0.0381215 0.999273i \(-0.487863\pi\)
0.884457 + 0.466622i \(0.154529\pi\)
\(620\) −2530.18 34120.3i −0.00658216 0.0887625i
\(621\) −19670.8 + 111559.i −0.0510082 + 0.289282i
\(622\) 496928. 106718.i 1.28444 0.275840i
\(623\) −6990.75 + 8331.26i −0.0180114 + 0.0214652i
\(624\) −13301.2 + 65272.4i −0.0341603 + 0.167633i
\(625\) −360549. 131229.i −0.923005 0.335946i
\(626\) 247463. 467781.i 0.631483 1.19370i
\(627\) 13266.9 + 1828.29i 0.0337470 + 0.00465061i
\(628\) 272888. + 400925.i 0.691934 + 1.01658i
\(629\) −55678.0 20265.1i −0.140729 0.0512211i
\(630\) 5801.50 17983.8i 0.0146170 0.0453107i
\(631\) 25799.0 30746.0i 0.0647953 0.0772201i −0.732673 0.680581i \(-0.761728\pi\)
0.797468 + 0.603361i \(0.206172\pi\)
\(632\) 206038. + 196472.i 0.515839 + 0.491888i
\(633\) 9673.57 54861.5i 0.0241423 0.136918i
\(634\) 196611. + 313176.i 0.489135 + 0.779129i
\(635\) −11559.9 + 6674.09i −0.0286685 + 0.0165518i
\(636\) −15780.4 + 21913.1i −0.0390125 + 0.0541738i
\(637\) 331573. 120683.i 0.817147 0.297417i
\(638\) −6626.97 178979.i −0.0162807 0.439704i
\(639\) 253957. + 146622.i 0.621955 + 0.359086i
\(640\) −28553.3 13409.7i −0.0697103 0.0327386i
\(641\) −208497. + 174950.i −0.507440 + 0.425793i −0.860227 0.509911i \(-0.829678\pi\)
0.352787 + 0.935704i \(0.385234\pi\)
\(642\) −13827.1 + 5620.39i −0.0335477 + 0.0136363i
\(643\) 271066. 47796.3i 0.655622 0.115604i 0.164066 0.986449i \(-0.447539\pi\)
0.491557 + 0.870846i \(0.336428\pi\)
\(644\) 79294.2 + 312428.i 0.191192 + 0.753317i
\(645\) −7389.40 −0.0177619
\(646\) −388150. 187020.i −0.930110 0.448150i
\(647\) 589628.i 1.40854i 0.709931 + 0.704271i \(0.248726\pi\)
−0.709931 + 0.704271i \(0.751274\pi\)
\(648\) 390705. + 94799.6i 0.930463 + 0.225765i
\(649\) 7696.32 + 43648.0i 0.0182723 + 0.103627i
\(650\) 557659. 226674.i 1.31990 0.536507i
\(651\) −23566.4 28085.3i −0.0556072 0.0662701i
\(652\) −6101.26 13550.0i −0.0143524 0.0318745i
\(653\) −330617. + 572646.i −0.775353 + 1.34295i 0.159244 + 0.987239i \(0.449094\pi\)
−0.934596 + 0.355711i \(0.884239\pi\)
\(654\) −3215.31 86837.9i −0.00751738 0.203027i
\(655\) 12587.1 + 34582.7i 0.0293388 + 0.0806078i
\(656\) −5618.74 + 212023.i −0.0130566 + 0.492692i
\(657\) −72110.6 124899.i −0.167058 0.289354i
\(658\) 33062.1 + 52663.7i 0.0763623 + 0.121635i
\(659\) 8296.81 + 1462.95i 0.0191047 + 0.00336867i 0.183192 0.983077i \(-0.441357\pi\)
−0.164088 + 0.986446i \(0.552468\pi\)
\(660\) 1099.88 + 310.385i 0.00252498 + 0.000712547i
\(661\) 32728.3 + 27462.3i 0.0749066 + 0.0628541i 0.679472 0.733701i \(-0.262209\pi\)
−0.604566 + 0.796555i \(0.706653\pi\)
\(662\) −59473.2 + 184358.i −0.135708 + 0.420674i
\(663\) −26554.7 + 72958.4i −0.0604107 + 0.165977i
\(664\) −52765.3 473285.i −0.119678 1.07346i
\(665\) −16866.0 13104.5i −0.0381390 0.0296332i
\(666\) 29657.4 56061.6i 0.0668629 0.126391i
\(667\) 290727. 798766.i 0.653482 1.79543i
\(668\) −467889. 480453.i −1.04855 1.07671i
\(669\) 16297.1 + 13674.9i 0.0364132 + 0.0305543i
\(670\) 27774.7 5964.78i 0.0618729 0.0132876i
\(671\) −29955.2 5281.91i −0.0665315 0.0117313i
\(672\) −33226.1 + 6219.58i −0.0735768 + 0.0137728i
\(673\) −80756.2 139874.i −0.178298 0.308821i 0.763000 0.646399i \(-0.223726\pi\)
−0.941298 + 0.337578i \(0.890392\pi\)
\(674\) 83501.6 603349.i 0.183812 1.32815i
\(675\) 36716.9 + 100879.i 0.0805858 + 0.221408i
\(676\) −209376. + 433907.i −0.458177 + 0.949517i
\(677\) −308124. + 533687.i −0.672277 + 1.16442i 0.304980 + 0.952359i \(0.401350\pi\)
−0.977257 + 0.212059i \(0.931983\pi\)
\(678\) 33475.3 43032.6i 0.0728224 0.0936135i
\(679\) 40516.0 + 48285.0i 0.0878793 + 0.104730i
\(680\) −30610.5 20367.3i −0.0661993 0.0440469i
\(681\) −778.854 4417.10i −0.00167943 0.00952451i
\(682\) −113794. + 102894.i −0.244652 + 0.221219i
\(683\) 718732.i 1.54073i 0.637605 + 0.770363i \(0.279925\pi\)
−0.637605 + 0.770363i \(0.720075\pi\)
\(684\) 255255. 384111.i 0.545585 0.821003i
\(685\) −39990.9 −0.0852276
\(686\) 318027. + 351715.i 0.675796 + 0.747381i
\(687\) −67279.6 + 11863.2i −0.142551 + 0.0251356i
\(688\) −436150. 803892.i −0.921423 1.69832i
\(689\) −291519. + 244614.i −0.614086 + 0.515279i
\(690\) 4281.18 + 3330.35i 0.00899218 + 0.00699505i
\(691\) −760038. 438808.i −1.59177 0.919007i −0.993004 0.118079i \(-0.962326\pi\)
−0.598762 0.800927i \(-0.704340\pi\)
\(692\) −60444.5 + 125264.i −0.126225 + 0.261586i
\(693\) −79621.3 + 28979.8i −0.165792 + 0.0603433i
\(694\) −373476. 51687.9i −0.775432 0.107317i
\(695\) 40911.7 23620.4i 0.0846988 0.0489009i
\(696\) 81663.2 + 35743.2i 0.168581 + 0.0737861i
\(697\) −42927.0 + 243451.i −0.0883619 + 0.501125i
\(698\) −115838. 539395.i −0.237761 1.10712i
\(699\) −5965.75 + 7109.71i −0.0122099 + 0.0145511i
\(700\) 213119. + 218841.i 0.434936 + 0.446615i
\(701\) 225769. + 82173.4i 0.459440 + 0.167223i 0.561363 0.827570i \(-0.310277\pi\)
−0.101923 + 0.994792i \(0.532499\pi\)
\(702\) −147984. 78285.6i −0.300289 0.158857i
\(703\) −48110.6 53145.0i −0.0973487 0.107536i
\(704\) 31152.4 + 137976.i 0.0628559 + 0.278393i
\(705\) 983.247 + 357.873i 0.00197827 + 0.000720030i
\(706\) −424509. 136945.i −0.851683 0.274750i
\(707\) −180169. + 214717.i −0.360446 + 0.429563i
\(708\) −21230.6 5991.24i −0.0423540 0.0119523i
\(709\) 112137. 635962.i 0.223079 1.26514i −0.643246 0.765660i \(-0.722413\pi\)
0.866324 0.499482i \(-0.166476\pi\)
\(710\) 23955.3 15039.1i 0.0475210 0.0298335i
\(711\) −307602. + 177594.i −0.608484 + 0.351309i
\(712\) −20295.5 + 10057.8i −0.0400350 + 0.0198400i
\(713\) −684208. + 249031.i −1.34589 + 0.489863i
\(714\) −39371.8 + 1457.80i −0.0772305 + 0.00285958i
\(715\) 13947.7 + 8052.74i 0.0272830 + 0.0157518i
\(716\) 329812. + 732463.i 0.643340 + 1.42876i
\(717\) −59625.5 + 50031.7i −0.115983 + 0.0973211i
\(718\) −111258. 273715.i −0.215816 0.530946i
\(719\) −801864. + 141390.i −1.55111 + 0.273503i −0.882573 0.470176i \(-0.844190\pi\)
−0.668538 + 0.743678i \(0.733079\pi\)
\(720\) 26087.2 29467.6i 0.0503226 0.0568433i
\(721\) 556331. 1.07020
\(722\) −309543. 419429.i −0.593808 0.804607i
\(723\) 52173.8i 0.0998104i
\(724\) 183590. + 723366.i 0.350246 + 1.38001i
\(725\) −139883. 793317.i −0.266127 1.50928i
\(726\) 21760.5 + 53534.7i 0.0412853 + 0.101569i
\(727\) −4522.84 5390.11i −0.00855740 0.0101983i 0.761749 0.647873i \(-0.224341\pi\)
−0.770306 + 0.637674i \(0.779897\pi\)
\(728\) −475412. 30231.3i −0.897032 0.0570418i
\(729\) −243275. + 421364.i −0.457764 + 0.792871i
\(730\) −13901.3 + 514.716i −0.0260861 + 0.000965877i
\(731\) −364587. 1.00170e6i −0.682286 1.87457i
\(732\) 8847.11 12285.3i 0.0165112 0.0229279i
\(733\) 76340.1 + 132225.i 0.142084 + 0.246097i 0.928281 0.371879i \(-0.121286\pi\)
−0.786197 + 0.617976i \(0.787953\pi\)
\(734\) −727808. + 456916.i −1.35090 + 0.848094i
\(735\) 2967.24 + 523.204i 0.00549259 + 0.000968492i
\(736\) −109617. + 662318.i −0.202358 + 1.22267i
\(737\) −97579.6 81879.0i −0.179649 0.150743i
\(738\) −251832. 81239.9i −0.462378 0.149162i
\(739\) 70886.3 194758.i 0.129800 0.356621i −0.857720 0.514117i \(-0.828120\pi\)
0.987520 + 0.157495i \(0.0503420\pi\)
\(740\) −3442.13 5057.15i −0.00628584 0.00923512i
\(741\) −69639.2 + 63042.3i −0.126829 + 0.114814i
\(742\) −170697. 90301.3i −0.310040 0.164016i
\(743\) 363477. 998646.i 0.658415 1.80898i 0.0744150 0.997227i \(-0.476291\pi\)
0.584000 0.811754i \(-0.301487\pi\)
\(744\) −21509.8 73265.9i −0.0388590 0.132360i
\(745\) 57532.1 + 48275.1i 0.103657 + 0.0869783i
\(746\) −73249.8 341085.i −0.131622 0.612893i
\(747\) 585100. + 103169.i 1.04855 + 0.184887i
\(748\) 12192.0 + 164412.i 0.0217907 + 0.293854i
\(749\) −53369.0 92437.8i −0.0951318 0.164773i
\(750\) 10213.7 + 1413.55i 0.0181577 + 0.00251298i
\(751\) 83957.5 + 230671.i 0.148861 + 0.408991i 0.991602 0.129328i \(-0.0412819\pi\)
−0.842741 + 0.538319i \(0.819060\pi\)
\(752\) 19102.1 + 128090.i 0.0337788 + 0.226507i
\(753\) 49827.1 86303.1i 0.0878771 0.152208i
\(754\) 991562. + 771340.i 1.74412 + 1.35676i
\(755\) 15418.0 + 18374.5i 0.0270480 + 0.0322346i
\(756\) 8524.75 84526.1i 0.0149155 0.147893i
\(757\) 99403.1 + 563743.i 0.173464 + 0.983761i 0.939902 + 0.341443i \(0.110916\pi\)
−0.766439 + 0.642317i \(0.777973\pi\)
\(758\) −755774. 835830.i −1.31539 1.45472i
\(759\) 24321.1i 0.0422182i
\(760\) −21236.2 39087.7i −0.0367663 0.0676726i
\(761\) 574516. 0.992048 0.496024 0.868309i \(-0.334793\pi\)
0.496024 + 0.868309i \(0.334793\pi\)
\(762\) −22096.5 + 19980.1i −0.0380551 + 0.0344102i
\(763\) 611984. 107909.i 1.05121 0.185357i
\(764\) −680443. 68625.1i −1.16575 0.117570i
\(765\) 35138.9 29485.0i 0.0600434 0.0503824i
\(766\) −335456. + 431230.i −0.571712 + 0.734939i
\(767\) −269228. 155439.i −0.457645 0.264221i
\(768\) −68588.1 15880.2i −0.116286 0.0269237i
\(769\) 576342. 209771.i 0.974603 0.354726i 0.194863 0.980830i \(-0.437574\pi\)
0.779740 + 0.626104i \(0.215351\pi\)
\(770\) −1120.40 + 8095.56i −0.00188970 + 0.0136542i
\(771\) −60999.1 + 35217.8i −0.102616 + 0.0592453i
\(772\) 596483. 44232.1i 1.00084 0.0742169i
\(773\) −93399.9 + 529697.i −0.156310 + 0.886479i 0.801268 + 0.598306i \(0.204159\pi\)
−0.957578 + 0.288174i \(0.906952\pi\)
\(774\) 1.11560e6 239581.i 1.86220 0.399917i
\(775\) −443539. + 528589.i −0.738462 + 0.880065i
\(776\) 36980.3 + 125961.i 0.0614111 + 0.209176i
\(777\) −6159.95 2242.04i −0.0102032 0.00371365i
\(778\) 31086.5 58763.0i 0.0513586 0.0970834i
\(779\) −183506. + 236179.i −0.302395 + 0.389195i
\(780\) −6626.70 + 4510.43i −0.0108920 + 0.00741360i
\(781\) −119180. 43378.0i −0.195390 0.0711160i
\(782\) −240226. + 744666.i −0.392832 + 1.21772i
\(783\) −144007. + 171621.i −0.234888 + 0.279929i
\(784\) 118218. + 353687.i 0.192332 + 0.575422i
\(785\) −10134.3 + 57474.4i −0.0164457 + 0.0932685i
\(786\) 43671.0 + 69562.3i 0.0706884 + 0.112597i
\(787\) −117193. + 67661.5i −0.189214 + 0.109243i −0.591614 0.806221i \(-0.701509\pi\)
0.402401 + 0.915464i \(0.368176\pi\)
\(788\) 140369. + 101085.i 0.226057 + 0.162792i
\(789\) −84998.7 + 30937.0i −0.136539 + 0.0496963i
\(790\) 1267.64 + 34236.0i 0.00203115 + 0.0548567i
\(791\) 337650. + 194942.i 0.539652 + 0.311568i
\(792\) −176115. 11199.1i −0.280768 0.0178539i
\(793\) 163437. 137140.i 0.259899 0.218081i
\(794\) 284030. 115451.i 0.450529 0.183129i
\(795\) −3200.16 + 564.275i −0.00506335 + 0.000892805i
\(796\) 283176. 71870.1i 0.446920 0.113429i
\(797\) 709113. 1.11635 0.558173 0.829725i \(-0.311503\pi\)
0.558173 + 0.829725i \(0.311503\pi\)
\(798\) −42943.0 20691.0i −0.0674352 0.0324919i
\(799\) 150945.i 0.236442i
\(800\) 223869. + 595515.i 0.349795 + 0.930492i
\(801\) −4907.15 27829.9i −0.00764829 0.0433756i
\(802\) 1.00107e6 406911.i 1.55639 0.632631i
\(803\) 40094.4 + 47782.7i 0.0621803 + 0.0741036i
\(804\) 57810.2 26030.7i 0.0894319 0.0402692i
\(805\) −19394.2 + 33591.7i −0.0299281 + 0.0518370i
\(806\) −39816.2 1.07534e6i −0.0612900 1.65530i
\(807\) 5024.60 + 13805.0i 0.00771533 + 0.0211977i
\(808\) −523064. + 259213.i −0.801183 + 0.397040i
\(809\) −558745. 967775.i −0.853723 1.47869i −0.877825 0.478981i \(-0.841006\pi\)
0.0241025 0.999709i \(-0.492327\pi\)
\(810\) 25723.8 + 40974.7i 0.0392072 + 0.0624519i
\(811\) 1.13514e6 + 200156.i 1.72587 + 0.304318i 0.946610 0.322380i \(-0.104483\pi\)
0.779262 + 0.626698i \(0.215594\pi\)
\(812\) −173135. + 613522.i −0.262587 + 0.930504i
\(813\) 37935.5 + 31831.7i 0.0573938 + 0.0481591i
\(814\) −8421.61 + 26105.7i −0.0127100 + 0.0393992i
\(815\) 611.610 1680.39i 0.000920788 0.00252984i
\(816\) −76337.3 30097.8i −0.114645 0.0452017i
\(817\) 176068. 1.27764e6i 0.263777 1.91409i
\(818\) −328973. + 621859.i −0.491647 + 0.929363i
\(819\) 203269. 558477.i 0.303043 0.832603i
\(820\) −18285.0 + 17806.8i −0.0271936 + 0.0264825i
\(821\) 190250. + 159639.i 0.282253 + 0.236838i 0.772912 0.634513i \(-0.218799\pi\)
−0.490659 + 0.871352i \(0.663244\pi\)
\(822\) −87261.4 + 18739.9i −0.129145 + 0.0277347i
\(823\) −528598. 93206.0i −0.780415 0.137608i −0.230772 0.973008i \(-0.574125\pi\)
−0.549643 + 0.835400i \(0.685236\pi\)
\(824\) 1.06146e6 + 464590.i 1.56332 + 0.684251i
\(825\) −11524.3 19960.7i −0.0169319 0.0293270i
\(826\) 21626.6 156265.i 0.0316978 0.229035i
\(827\) −193265. 530991.i −0.282580 0.776383i −0.997053 0.0767193i \(-0.975555\pi\)
0.714473 0.699664i \(-0.246667\pi\)
\(828\) −754317. 363986.i −1.10026 0.530913i
\(829\) 665506. 1.15269e6i 0.968373 1.67727i 0.268107 0.963389i \(-0.413602\pi\)
0.700266 0.713882i \(-0.253065\pi\)
\(830\) 35186.2 45232.0i 0.0510759 0.0656583i
\(831\) 33623.0 + 40070.3i 0.0486894 + 0.0580257i
\(832\) −881822. 454695.i −1.27390 0.656861i
\(833\) 75476.5 + 428048.i 0.108773 + 0.616883i
\(834\) 78201.9 70711.7i 0.112431 0.101662i
\(835\) 80702.0i 0.115747i
\(836\) −79873.0 + 182775.i −0.114285 + 0.261520i
\(837\) 191905. 0.273927
\(838\) 241299. + 266859.i 0.343612 + 0.380009i
\(839\) 128677. 22689.1i 0.182800 0.0322325i −0.0814988 0.996673i \(-0.525971\pi\)
0.264299 + 0.964441i \(0.414860\pi\)
\(840\) −3386.60 2253.34i −0.00479961 0.00319350i
\(841\) 746001. 625969.i 1.05475 0.885036i
\(842\) −259569. 201920.i −0.366124 0.284809i
\(843\) −58791.8 33943.4i −0.0827297 0.0477640i
\(844\) 747265. + 360583.i 1.04903 + 0.506198i
\(845\) −54479.4 + 19828.9i −0.0762989 + 0.0277705i
\(846\) −160046. 22149.9i −0.223617 0.0309479i
\(847\) −357892. + 206629.i −0.498868 + 0.288022i
\(848\) −250273. 314840.i −0.348035 0.437822i
\(849\) 16211.9 91942.5i 0.0224916 0.127556i
\(850\) 155695. + 724988.i 0.215495 + 1.00344i
\(851\) −83682.7 + 99729.1i −0.115552 + 0.137709i
\(852\) 45223.9 44041.3i 0.0623001 0.0606710i
\(853\) 375817. + 136786.i 0.516510 + 0.187994i 0.587105 0.809511i \(-0.300268\pi\)
−0.0705952 + 0.997505i \(0.522490\pi\)
\(854\) 95699.5 + 50626.5i 0.131218 + 0.0694164i
\(855\) 54254.0 11684.2i 0.0742163 0.0159832i
\(856\) −24631.6 220936.i −0.0336159 0.301522i
\(857\) 1.20095e6 + 437111.i 1.63518 + 0.595156i 0.986186 0.165641i \(-0.0529692\pi\)
0.648991 + 0.760796i \(0.275191\pi\)
\(858\) 34208.0 + 11035.4i 0.0464678 + 0.0149904i
\(859\) −28522.7 + 33992.1i −0.0386549 + 0.0460672i −0.785026 0.619463i \(-0.787350\pi\)
0.746371 + 0.665531i \(0.231795\pi\)
\(860\) 29890.8 105921.i 0.0404148 0.143214i
\(861\) −4749.23 + 26934.2i −0.00640645 + 0.0363328i
\(862\) 154623. 97072.0i 0.208094 0.130641i
\(863\) −243979. + 140861.i −0.327590 + 0.189134i −0.654771 0.755828i \(-0.727235\pi\)
0.327181 + 0.944962i \(0.393901\pi\)
\(864\) 86852.3 154154.i 0.116347 0.206503i
\(865\) −15727.6 + 5724.38i −0.0210199 + 0.00765061i
\(866\) −1.21788e6 + 45094.0i −1.62394 + 0.0601289i
\(867\) −5123.95 2958.31i −0.00681658 0.00393555i
\(868\) 497909. 224197.i 0.660862 0.297571i
\(869\) 117679. 98744.5i 0.155833 0.130760i
\(870\) 4039.36 + 9937.54i 0.00533671 + 0.0131293i
\(871\) 879899. 155150.i 1.15984 0.204510i
\(872\) 1.25776e6 + 305179.i 1.65411 + 0.401348i
\(873\) −163780. −0.214898
\(874\) −677829. + 660868.i −0.887354 + 0.865150i
\(875\) 73737.2i 0.0963098i
\(876\) −30091.8 + 7637.31i −0.0392139 + 0.00995250i
\(877\) −77887.4 441722.i −0.101267 0.574314i −0.992646 0.121055i \(-0.961372\pi\)
0.891379 0.453259i \(-0.149739\pi\)
\(878\) 173909. + 427848.i 0.225597 + 0.555010i
\(879\) −10865.2 12948.6i −0.0140624 0.0167589i
\(880\) −8898.25 + 14510.4i −0.0114905 + 0.0187376i
\(881\) −605822. + 1.04931e6i −0.780536 + 1.35193i 0.151093 + 0.988519i \(0.451721\pi\)
−0.931630 + 0.363409i \(0.881613\pi\)
\(882\) −464935. + 17214.9i −0.597661 + 0.0221293i
\(883\) −346321. 951509.i −0.444178 1.22037i −0.936719 0.350081i \(-0.886154\pi\)
0.492541 0.870289i \(-0.336068\pi\)
\(884\) −938384. 675764.i −1.20081 0.864749i
\(885\) −1327.29 2298.94i −0.00169465 0.00293522i
\(886\) −347700. + 218285.i −0.442932 + 0.278071i
\(887\) 684116. + 120628.i 0.869526 + 0.153321i 0.590573 0.806984i \(-0.298902\pi\)
0.278953 + 0.960305i \(0.410013\pi\)
\(888\) −9880.63 9421.87i −0.0125302 0.0119484i
\(889\) −163196. 136938.i −0.206493 0.173269i
\(890\) −2594.09 836.843i −0.00327495 0.00105649i
\(891\) 74196.5 203853.i 0.0934605 0.256781i
\(892\) −261942. + 178290.i −0.329212 + 0.224077i
\(893\) −85304.6 + 161477.i −0.106972 + 0.202493i
\(894\) 148159. + 78378.1i 0.185375 + 0.0980663i
\(895\) −33061.4 + 90835.5i −0.0412739 + 0.113399i
\(896\) 45250.0 501428.i 0.0563641 0.624587i
\(897\) 130681. + 109655.i 0.162416 + 0.136283i
\(898\) 181159. + 843559.i 0.224650 + 1.04607i
\(899\) −1.41814e6 250056.i −1.75468 0.309398i
\(900\) −791550. + 58697.2i −0.977223 + 0.0724657i
\(901\) −234386. 405968.i −0.288723 0.500084i
\(902\) 113364. + 15689.3i 0.139336 + 0.0192836i
\(903\) −40336.2 110823.i −0.0494674 0.135911i
\(904\) 481428. + 653912.i 0.589107 + 0.800171i
\(905\) −44903.4 + 77775.0i −0.0548255 + 0.0949605i
\(906\) 42253.0 + 32868.8i 0.0514756 + 0.0400431i
\(907\) −197748. 235667.i −0.240380 0.286474i 0.632344 0.774688i \(-0.282093\pi\)
−0.872724 + 0.488214i \(0.837649\pi\)
\(908\) 66466.1 + 6703.34i 0.0806173 + 0.00813054i
\(909\) −126469. 717243.i −0.153058 0.868037i
\(910\) −38447.3 42519.9i −0.0464284 0.0513463i
\(911\) 1.20690e6i 1.45424i 0.686510 + 0.727120i \(0.259142\pi\)
−0.686510 + 0.727120i \(0.740858\pi\)
\(912\) −64654.7 75339.1i −0.0777339 0.0905797i
\(913\) −256960. −0.308265
\(914\) 1.15554e6 1.04486e6i 1.38322 1.25073i
\(915\) 1794.14 316.355i 0.00214296 0.000377861i
\(916\) 102103. 1.01239e6i 0.121688 1.20658i
\(917\) −449947. + 377550.i −0.535085 + 0.448990i
\(918\) 126623. 162775.i 0.150255 0.193153i
\(919\) −603764. 348583.i −0.714885 0.412739i 0.0979823 0.995188i \(-0.468761\pi\)
−0.812867 + 0.582449i \(0.802094\pi\)
\(920\) −65055.6 + 47895.6i −0.0768615 + 0.0565875i
\(921\) −109534. + 39867.1i −0.129131 + 0.0469997i
\(922\) 38859.8 280785.i 0.0457129 0.330303i
\(923\) 770415. 444799.i 0.904318 0.522108i
\(924\) 1348.86 + 18189.8i 0.00157987 + 0.0213051i
\(925\) −21424.0 + 121501.i −0.0250390 + 0.142003i
\(926\) 653683. 140382.i 0.762334 0.163715i
\(927\) −929189. + 1.10736e6i −1.08130 + 1.28864i
\(928\) −842685. + 1.02599e6i −0.978519 + 1.19137i
\(929\) −568742. 207005.i −0.658998 0.239856i −0.00919416 0.999958i \(-0.502927\pi\)
−0.649804 + 0.760102i \(0.725149\pi\)
\(930\) 4296.74 8122.15i 0.00496790 0.00939086i
\(931\) −161163. + 500572.i −0.185937 + 0.577520i
\(932\) −77779.9 114274.i −0.0895438 0.131557i
\(933\) 128268. + 46685.7i 0.147351 + 0.0536315i
\(934\) 120697. 374142.i 0.138357 0.428887i
\(935\) −12752.3 + 15197.6i −0.0145870 + 0.0173841i
\(936\) 854212. 895804.i 0.975021 1.02250i
\(937\) −193611. + 1.09802e6i −0.220521 + 1.25064i 0.650543 + 0.759469i \(0.274541\pi\)
−0.871064 + 0.491169i \(0.836570\pi\)
\(938\) 241070. + 383993.i 0.273991 + 0.436433i
\(939\) 123084. 71062.6i 0.139595 0.0805953i
\(940\) −9107.15 + 12646.4i −0.0103069 + 0.0143124i
\(941\) 111679. 40648.0i 0.126123 0.0459050i −0.278188 0.960527i \(-0.589734\pi\)
0.404311 + 0.914622i \(0.367511\pi\)
\(942\) 4819.37 + 130160.i 0.00543110 + 0.146681i
\(943\) 470393. + 271581.i 0.528978 + 0.305405i
\(944\) 171759. 280088.i 0.192742 0.314304i
\(945\) 7831.38 6571.31i 0.00876950 0.00735848i
\(946\) −457174. + 185829.i −0.510856 + 0.207650i
\(947\) 703354. 124020.i 0.784285 0.138291i 0.232855 0.972512i \(-0.425193\pi\)
0.551430 + 0.834221i \(0.314082\pi\)
\(948\) 18809.2 + 74110.1i 0.0209292 + 0.0824633i
\(949\) −437515. −0.485803
\(950\) −243159. + 863566.i −0.269428 + 0.956860i
\(951\) 99308.7i 0.109806i
\(952\) 138366. 570260.i 0.152671 0.629215i
\(953\) 19007.8 + 107798.i 0.0209288 + 0.118693i 0.993482 0.113986i \(-0.0363619\pi\)
−0.972554 + 0.232679i \(0.925251\pi\)
\(954\) 464842. 188947.i 0.510750 0.207607i
\(955\) −52899.7 63043.4i −0.0580025 0.0691246i
\(956\) −475974. 1.05707e6i −0.520795 1.15661i
\(957\) 24050.1 41656.0i 0.0262599 0.0454835i
\(958\) −58942.1 1.59189e6i −0.0642236 1.73453i
\(959\) −218297. 599765.i −0.237361 0.652144i
\(960\) −4579.75 7127.41i −0.00496935 0.00773374i
\(961\) 154984. + 268440.i 0.167819 + 0.290670i
\(962\) −102301. 162951.i −0.110542 0.176079i
\(963\) 273133. + 48160.6i 0.294524 + 0.0519326i
\(964\) −747869. 211048.i −0.804769 0.227105i
\(965\) 55136.5 + 46265.0i 0.0592086 + 0.0496819i
\(966\) −26577.5 + 82386.3i −0.0284813 + 0.0882878i
\(967\) 350816. 963859.i 0.375168 1.03077i −0.598165 0.801373i \(-0.704103\pi\)
0.973334 0.229394i \(-0.0736744\pi\)
\(968\) −855400. + 95366.3i −0.912891 + 0.101776i
\(969\) −61581.1 97965.0i −0.0655843 0.104333i
\(970\) −7387.07 + 13963.8i −0.00785106 + 0.0148409i
\(971\) −190713. + 523978.i −0.202274 + 0.555744i −0.998806 0.0488527i \(-0.984444\pi\)
0.796532 + 0.604597i \(0.206666\pi\)
\(972\) 231566. + 237784.i 0.245099 + 0.251681i
\(973\) 577569. + 484638.i 0.610068 + 0.511908i
\(974\) −686354. + 147398.i −0.723487 + 0.155373i
\(975\) 159211. + 28073.2i 0.167480 + 0.0295313i
\(976\) 140313. + 176512.i 0.147299 + 0.185299i
\(977\) 317969. + 550739.i 0.333116 + 0.576974i 0.983121 0.182956i \(-0.0585665\pi\)
−0.650005 + 0.759930i \(0.725233\pi\)
\(978\) 547.118 3953.25i 0.000572010 0.00413311i
\(979\) 4180.21 + 11485.0i 0.00436147 + 0.0119830i
\(980\) −19502.5 + 40416.5i −0.0203066 + 0.0420830i
\(981\) −807350. + 1.39837e6i −0.838926 + 1.45306i
\(982\) −720184. + 925800.i −0.746828 + 0.960051i
\(983\) 689336. + 821518.i 0.713384 + 0.850178i 0.993970 0.109651i \(-0.0349732\pi\)
−0.280586 + 0.959829i \(0.590529\pi\)
\(984\) −31554.0 + 47423.4i −0.0325885 + 0.0489782i
\(985\) 3614.58 + 20499.3i 0.00372551 + 0.0211284i
\(986\) −1.14782e6 + 1.03788e6i −1.18064 + 1.06756i
\(987\) 16699.8i 0.0171426i
\(988\) −621964. 1.25323e6i −0.637164 1.28386i
\(989\) −2.34218e6 −2.39457
\(990\) −14242.7 15751.4i −0.0145319 0.0160712i
\(991\) −1.05166e6 + 185436.i −1.07085 + 0.188819i −0.681165 0.732130i \(-0.738526\pi\)
−0.389682 + 0.920949i \(0.627415\pi\)
\(992\) 1.13722e6 11958.5i 1.15563 0.0121522i
\(993\) −39853.1 + 33440.7i −0.0404169 + 0.0339138i
\(994\) 356313. + 277177.i 0.360627 + 0.280534i
\(995\) 30446.6 + 17578.3i 0.0307534 + 0.0177555i
\(996\) 55581.5 115186.i 0.0560288 0.116113i
\(997\) 347211. 126374.i 0.349303 0.127136i −0.161409 0.986888i \(-0.551604\pi\)
0.510712 + 0.859752i \(0.329382\pi\)
\(998\) 1.06212e6 + 146994.i 1.06638 + 0.147583i
\(999\) 29715.4 17156.2i 0.0297749 0.0171906i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 76.5.l.a.23.11 228
4.3 odd 2 inner 76.5.l.a.23.19 yes 228
19.5 even 9 inner 76.5.l.a.43.19 yes 228
76.43 odd 18 inner 76.5.l.a.43.11 yes 228
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.5.l.a.23.11 228 1.1 even 1 trivial
76.5.l.a.23.19 yes 228 4.3 odd 2 inner
76.5.l.a.43.11 yes 228 76.43 odd 18 inner
76.5.l.a.43.19 yes 228 19.5 even 9 inner