Properties

Label 19.4.e.a.9.1
Level $19$
Weight $4$
Character 19.9
Analytic conductor $1.121$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [19,4,Mod(4,19)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(19, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("19.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 19.e (of order \(9\), 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: \(1.12103629011\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 9.1
Character \(\chi\) \(=\) 19.9
Dual form 19.4.e.a.17.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.851642 - 4.82990i) q^{2} +(0.458552 - 0.384771i) q^{3} +(-15.0851 + 5.49052i) q^{4} +(6.94640 + 2.52828i) q^{5} +(-2.24893 - 1.88707i) q^{6} +(14.5751 - 25.2448i) q^{7} +(19.7481 + 34.2048i) q^{8} +(-4.62628 + 26.2369i) q^{9} +O(q^{10})\) \(q+(-0.851642 - 4.82990i) q^{2} +(0.458552 - 0.384771i) q^{3} +(-15.0851 + 5.49052i) q^{4} +(6.94640 + 2.52828i) q^{5} +(-2.24893 - 1.88707i) q^{6} +(14.5751 - 25.2448i) q^{7} +(19.7481 + 34.2048i) q^{8} +(-4.62628 + 26.2369i) q^{9} +(6.29551 - 35.7036i) q^{10} +(26.3895 + 45.7080i) q^{11} +(-4.80470 + 8.32199i) q^{12} +(-30.9868 - 26.0010i) q^{13} +(-134.343 - 48.8967i) q^{14} +(4.15809 - 1.51342i) q^{15} +(50.0074 - 41.9612i) q^{16} +(-0.0277382 - 0.157311i) q^{17} +130.662 q^{18} +(-13.4549 + 81.7188i) q^{19} -118.669 q^{20} +(-3.03002 - 17.1841i) q^{21} +(198.291 - 166.386i) q^{22} +(-39.4491 + 14.3583i) q^{23} +(22.2165 + 8.08616i) q^{24} +(-53.8953 - 45.2235i) q^{25} +(-99.1927 + 171.807i) q^{26} +(16.0549 + 27.8079i) q^{27} +(-81.2594 + 460.845i) q^{28} +(11.8095 - 66.9751i) q^{29} +(-10.8509 - 18.7943i) q^{30} +(108.113 - 187.257i) q^{31} +(-3.20963 - 2.69320i) q^{32} +(29.6881 + 10.8056i) q^{33} +(-0.736175 + 0.267946i) q^{34} +(165.071 - 138.511i) q^{35} +(-74.2667 - 421.187i) q^{36} -288.898 q^{37} +(406.152 - 4.60942i) q^{38} -24.2135 q^{39} +(50.6991 + 287.529i) q^{40} +(-24.4278 + 20.4974i) q^{41} +(-80.4171 + 29.2694i) q^{42} +(128.653 + 46.8260i) q^{43} +(-649.050 - 544.617i) q^{44} +(-98.4704 + 170.556i) q^{45} +(102.946 + 178.307i) q^{46} +(-32.7846 + 185.931i) q^{47} +(6.78555 - 38.4828i) q^{48} +(-253.367 - 438.844i) q^{49} +(-172.526 + 298.823i) q^{50} +(-0.0732482 - 0.0614625i) q^{51} +(610.199 + 222.094i) q^{52} +(-31.5953 + 11.4998i) q^{53} +(120.636 - 101.226i) q^{54} +(67.7495 + 384.227i) q^{55} +1151.32 q^{56} +(25.2732 + 42.6494i) q^{57} -333.540 q^{58} +(50.5342 + 286.594i) q^{59} +(-54.4157 + 45.6602i) q^{60} +(-10.9927 + 4.00101i) q^{61} +(-996.508 - 362.699i) q^{62} +(594.918 + 499.195i) q^{63} +(250.846 - 434.478i) q^{64} +(-149.509 - 258.957i) q^{65} +(26.9063 - 152.593i) q^{66} +(61.8269 - 350.638i) q^{67} +(1.28216 + 2.22076i) q^{68} +(-12.5648 + 21.7629i) q^{69} +(-809.573 - 679.313i) q^{70} +(-237.468 - 86.4315i) q^{71} +(-988.789 + 359.890i) q^{72} +(-619.706 + 519.995i) q^{73} +(246.037 + 1395.35i) q^{74} -42.1145 q^{75} +(-245.711 - 1306.61i) q^{76} +1538.52 q^{77} +(20.6212 + 116.949i) q^{78} +(540.834 - 453.814i) q^{79} +(453.461 - 165.046i) q^{80} +(-657.883 - 239.450i) q^{81} +(119.804 + 100.528i) q^{82} +(608.912 - 1054.67i) q^{83} +(140.058 + 242.588i) q^{84} +(0.205047 - 1.16288i) q^{85} +(116.598 - 661.261i) q^{86} +(-20.3548 - 35.2555i) q^{87} +(-1042.29 + 1805.30i) q^{88} +(895.877 + 751.730i) q^{89} +(907.628 + 330.350i) q^{90} +(-1108.03 + 403.289i) q^{91} +(516.259 - 433.193i) q^{92} +(-22.4757 - 127.466i) q^{93} +925.947 q^{94} +(-300.071 + 533.634i) q^{95} -2.50805 q^{96} +(-69.0328 - 391.505i) q^{97} +(-1903.80 + 1597.48i) q^{98} +(-1321.32 + 480.923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{2} - 3 q^{3} - 24 q^{4} - 6 q^{5} + 42 q^{6} + 3 q^{7} - 75 q^{8} - 51 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{2} - 3 q^{3} - 24 q^{4} - 6 q^{5} + 42 q^{6} + 3 q^{7} - 75 q^{8} - 51 q^{9} + 75 q^{10} + 39 q^{11} - 219 q^{12} - 156 q^{13} + 93 q^{14} - 192 q^{15} + 504 q^{16} + 12 q^{17} + 264 q^{18} + 546 q^{19} - 198 q^{20} + 453 q^{21} - 6 q^{22} + 6 q^{23} + 192 q^{24} - 498 q^{25} - 639 q^{26} - 870 q^{27} - 1368 q^{28} - 630 q^{29} - 522 q^{30} - 591 q^{31} + 147 q^{32} + 1506 q^{33} - 408 q^{34} + 2001 q^{35} + 1059 q^{36} - 72 q^{37} + 2934 q^{38} + 336 q^{39} + 2886 q^{40} - 477 q^{41} + 237 q^{42} + 588 q^{43} - 3423 q^{44} - 1569 q^{45} - 1728 q^{46} - 1242 q^{47} - 4599 q^{48} - 639 q^{49} - 1788 q^{50} + 9 q^{51} + 2733 q^{52} - 300 q^{53} + 3777 q^{54} + 315 q^{55} + 4638 q^{56} + 3342 q^{57} - 2820 q^{58} + 2097 q^{59} + 1116 q^{60} - 2316 q^{61} - 1320 q^{62} - 2979 q^{63} - 1785 q^{64} - 2433 q^{65} - 1590 q^{66} + 57 q^{67} - 438 q^{68} - 1767 q^{69} - 213 q^{70} - 792 q^{71} - 1686 q^{72} + 4068 q^{73} + 4287 q^{74} + 1332 q^{75} + 5538 q^{76} + 3786 q^{77} + 2121 q^{78} + 1824 q^{79} - 2739 q^{80} + 1536 q^{81} + 2205 q^{82} + 1071 q^{83} - 1437 q^{84} - 2394 q^{85} - 5256 q^{86} + 759 q^{87} + 1101 q^{88} - 3006 q^{89} - 3822 q^{90} - 3285 q^{91} - 1452 q^{92} - 135 q^{93} - 1086 q^{94} - 3078 q^{95} - 1590 q^{96} - 2535 q^{97} - 2403 q^{98} + 492 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.851642 4.82990i −0.301101 1.70763i −0.641314 0.767279i \(-0.721610\pi\)
0.340213 0.940348i \(-0.389501\pi\)
\(3\) 0.458552 0.384771i 0.0882483 0.0740492i −0.597596 0.801797i \(-0.703877\pi\)
0.685845 + 0.727748i \(0.259433\pi\)
\(4\) −15.0851 + 5.49052i −1.88564 + 0.686315i
\(5\) 6.94640 + 2.52828i 0.621305 + 0.226137i 0.633442 0.773790i \(-0.281641\pi\)
−0.0121374 + 0.999926i \(0.503864\pi\)
\(6\) −2.24893 1.88707i −0.153020 0.128399i
\(7\) 14.5751 25.2448i 0.786981 1.36309i −0.140827 0.990034i \(-0.544976\pi\)
0.927808 0.373057i \(-0.121691\pi\)
\(8\) 19.7481 + 34.2048i 0.872752 + 1.51165i
\(9\) −4.62628 + 26.2369i −0.171344 + 0.971738i
\(10\) 6.29551 35.7036i 0.199081 1.12905i
\(11\) 26.3895 + 45.7080i 0.723341 + 1.25286i 0.959653 + 0.281186i \(0.0907277\pi\)
−0.236313 + 0.971677i \(0.575939\pi\)
\(12\) −4.80470 + 8.32199i −0.115583 + 0.200196i
\(13\) −30.9868 26.0010i −0.661092 0.554722i 0.249322 0.968421i \(-0.419792\pi\)
−0.910414 + 0.413698i \(0.864237\pi\)
\(14\) −134.343 48.8967i −2.56461 0.933443i
\(15\) 4.15809 1.51342i 0.0715744 0.0260509i
\(16\) 50.0074 41.9612i 0.781366 0.655644i
\(17\) −0.0277382 0.157311i −0.000395736 0.00224433i 0.984609 0.174770i \(-0.0559183\pi\)
−0.985005 + 0.172526i \(0.944807\pi\)
\(18\) 130.662 1.71096
\(19\) −13.4549 + 81.7188i −0.162461 + 0.986715i
\(20\) −118.669 −1.32676
\(21\) −3.03002 17.1841i −0.0314860 0.178566i
\(22\) 198.291 166.386i 1.92162 1.61243i
\(23\) −39.4491 + 14.3583i −0.357640 + 0.130170i −0.514590 0.857436i \(-0.672056\pi\)
0.156950 + 0.987606i \(0.449834\pi\)
\(24\) 22.2165 + 8.08616i 0.188955 + 0.0687742i
\(25\) −53.8953 45.2235i −0.431162 0.361788i
\(26\) −99.1927 + 171.807i −0.748204 + 1.29593i
\(27\) 16.0549 + 27.8079i 0.114436 + 0.198208i
\(28\) −81.2594 + 460.845i −0.548450 + 3.11041i
\(29\) 11.8095 66.9751i 0.0756197 0.428861i −0.923370 0.383912i \(-0.874577\pi\)
0.998989 0.0449484i \(-0.0143123\pi\)
\(30\) −10.8509 18.7943i −0.0660364 0.114378i
\(31\) 108.113 187.257i 0.626377 1.08492i −0.361896 0.932219i \(-0.617870\pi\)
0.988273 0.152698i \(-0.0487963\pi\)
\(32\) −3.20963 2.69320i −0.0177309 0.0148780i
\(33\) 29.6881 + 10.8056i 0.156607 + 0.0570003i
\(34\) −0.736175 + 0.267946i −0.00371332 + 0.00135154i
\(35\) 165.071 138.511i 0.797200 0.668930i
\(36\) −74.2667 421.187i −0.343827 1.94994i
\(37\) −288.898 −1.28363 −0.641817 0.766858i \(-0.721819\pi\)
−0.641817 + 0.766858i \(0.721819\pi\)
\(38\) 406.152 4.60942i 1.73386 0.0196775i
\(39\) −24.2135 −0.0994170
\(40\) 50.6991 + 287.529i 0.200406 + 1.13656i
\(41\) −24.4278 + 20.4974i −0.0930485 + 0.0780769i −0.688125 0.725592i \(-0.741566\pi\)
0.595077 + 0.803669i \(0.297122\pi\)
\(42\) −80.4171 + 29.2694i −0.295444 + 0.107533i
\(43\) 128.653 + 46.8260i 0.456266 + 0.166067i 0.559921 0.828546i \(-0.310831\pi\)
−0.103655 + 0.994613i \(0.533054\pi\)
\(44\) −649.050 544.617i −2.22382 1.86600i
\(45\) −98.4704 + 170.556i −0.326202 + 0.564999i
\(46\) 102.946 + 178.307i 0.329968 + 0.571521i
\(47\) −32.7846 + 185.931i −0.101747 + 0.577038i 0.890722 + 0.454548i \(0.150199\pi\)
−0.992470 + 0.122490i \(0.960912\pi\)
\(48\) 6.78555 38.4828i 0.0204044 0.115719i
\(49\) −253.367 438.844i −0.738679 1.27943i
\(50\) −172.526 + 298.823i −0.487976 + 0.845199i
\(51\) −0.0732482 0.0614625i −0.000201114 0.000168754i
\(52\) 610.199 + 222.094i 1.62729 + 0.592287i
\(53\) −31.5953 + 11.4998i −0.0818859 + 0.0298040i −0.382638 0.923898i \(-0.624984\pi\)
0.300752 + 0.953702i \(0.402762\pi\)
\(54\) 120.636 101.226i 0.304009 0.255094i
\(55\) 67.7495 + 384.227i 0.166097 + 0.941984i
\(56\) 1151.32 2.74736
\(57\) 25.2732 + 42.6494i 0.0587285 + 0.0991061i
\(58\) −333.540 −0.755103
\(59\) 50.5342 + 286.594i 0.111508 + 0.632395i 0.988420 + 0.151743i \(0.0484888\pi\)
−0.876912 + 0.480652i \(0.840400\pi\)
\(60\) −54.4157 + 45.6602i −0.117084 + 0.0982452i
\(61\) −10.9927 + 4.00101i −0.0230732 + 0.00839798i −0.353531 0.935423i \(-0.615019\pi\)
0.330458 + 0.943821i \(0.392797\pi\)
\(62\) −996.508 362.699i −2.04124 0.742949i
\(63\) 594.918 + 499.195i 1.18972 + 0.998297i
\(64\) 250.846 434.478i 0.489933 0.848589i
\(65\) −149.509 258.957i −0.285297 0.494149i
\(66\) 26.9063 152.593i 0.0501808 0.284589i
\(67\) 61.8269 350.638i 0.112737 0.639362i −0.875109 0.483926i \(-0.839211\pi\)
0.987846 0.155436i \(-0.0496784\pi\)
\(68\) 1.28216 + 2.22076i 0.00228653 + 0.00396039i
\(69\) −12.5648 + 21.7629i −0.0219221 + 0.0379702i
\(70\) −809.573 679.313i −1.38232 1.15991i
\(71\) −237.468 86.4315i −0.396934 0.144472i 0.135838 0.990731i \(-0.456627\pi\)
−0.532772 + 0.846259i \(0.678850\pi\)
\(72\) −988.789 + 359.890i −1.61847 + 0.589075i
\(73\) −619.706 + 519.995i −0.993577 + 0.833710i −0.986082 0.166262i \(-0.946830\pi\)
−0.00749546 + 0.999972i \(0.502386\pi\)
\(74\) 246.037 + 1395.35i 0.386503 + 2.19197i
\(75\) −42.1145 −0.0648395
\(76\) −245.711 1306.61i −0.370855 1.97209i
\(77\) 1538.52 2.27702
\(78\) 20.6212 + 116.949i 0.0299345 + 0.169767i
\(79\) 540.834 453.814i 0.770235 0.646304i −0.170534 0.985352i \(-0.554549\pi\)
0.940769 + 0.339048i \(0.110105\pi\)
\(80\) 453.461 165.046i 0.633732 0.230659i
\(81\) −657.883 239.450i −0.902446 0.328463i
\(82\) 119.804 + 100.528i 0.161343 + 0.135383i
\(83\) 608.912 1054.67i 0.805263 1.39476i −0.110851 0.993837i \(-0.535358\pi\)
0.916113 0.400919i \(-0.131309\pi\)
\(84\) 140.058 + 242.588i 0.181924 + 0.315101i
\(85\) 0.205047 1.16288i 0.000261652 0.00148390i
\(86\) 116.598 661.261i 0.146199 0.829136i
\(87\) −20.3548 35.2555i −0.0250834 0.0434458i
\(88\) −1042.29 + 1805.30i −1.26259 + 2.18688i
\(89\) 895.877 + 751.730i 1.06700 + 0.895318i 0.994777 0.102071i \(-0.0325469\pi\)
0.0722208 + 0.997389i \(0.476991\pi\)
\(90\) 907.628 + 330.350i 1.06303 + 0.386910i
\(91\) −1108.03 + 403.289i −1.27640 + 0.464573i
\(92\) 516.259 433.193i 0.585041 0.490907i
\(93\) −22.4757 127.466i −0.0250604 0.142125i
\(94\) 925.947 1.01600
\(95\) −300.071 + 533.634i −0.324070 + 0.576313i
\(96\) −2.50805 −0.00266642
\(97\) −69.0328 391.505i −0.0722600 0.409807i −0.999385 0.0350556i \(-0.988839\pi\)
0.927125 0.374751i \(-0.122272\pi\)
\(98\) −1903.80 + 1597.48i −1.96237 + 1.64663i
\(99\) −1321.32 + 480.923i −1.34139 + 0.488228i
\(100\) 1061.32 + 386.287i 1.06132 + 0.386287i
\(101\) −264.263 221.743i −0.260348 0.218458i 0.503265 0.864132i \(-0.332132\pi\)
−0.763613 + 0.645674i \(0.776576\pi\)
\(102\) −0.234477 + 0.406126i −0.000227614 + 0.000394239i
\(103\) −412.120 713.813i −0.394247 0.682855i 0.598758 0.800930i \(-0.295661\pi\)
−0.993005 + 0.118075i \(0.962328\pi\)
\(104\) 277.427 1573.37i 0.261577 1.48348i
\(105\) 22.3986 127.029i 0.0208179 0.118064i
\(106\) 82.4506 + 142.809i 0.0755501 + 0.130857i
\(107\) 166.554 288.479i 0.150480 0.260639i −0.780924 0.624626i \(-0.785251\pi\)
0.931404 + 0.363987i \(0.118585\pi\)
\(108\) −394.869 331.334i −0.351817 0.295210i
\(109\) 1381.61 + 502.866i 1.21408 + 0.441889i 0.868117 0.496360i \(-0.165330\pi\)
0.345962 + 0.938248i \(0.387553\pi\)
\(110\) 1798.08 654.447i 1.55855 0.567264i
\(111\) −132.475 + 111.159i −0.113279 + 0.0950521i
\(112\) −330.440 1874.02i −0.278782 1.58105i
\(113\) −2149.63 −1.78956 −0.894778 0.446511i \(-0.852666\pi\)
−0.894778 + 0.446511i \(0.852666\pi\)
\(114\) 184.468 158.389i 0.151553 0.130127i
\(115\) −310.331 −0.251640
\(116\) 189.581 + 1075.17i 0.151742 + 0.860574i
\(117\) 825.541 692.711i 0.652319 0.547361i
\(118\) 1341.18 488.150i 1.04632 0.380829i
\(119\) −4.37558 1.59258i −0.00337066 0.00122682i
\(120\) 133.881 + 112.339i 0.101847 + 0.0854595i
\(121\) −727.316 + 1259.75i −0.546444 + 0.946468i
\(122\) 28.6863 + 49.6861i 0.0212880 + 0.0368719i
\(123\) −3.31464 + 18.7982i −0.00242984 + 0.0137803i
\(124\) −602.755 + 3418.39i −0.436524 + 2.47565i
\(125\) −722.053 1250.63i −0.516659 0.894880i
\(126\) 1904.41 3298.53i 1.34649 2.33219i
\(127\) −581.035 487.547i −0.405973 0.340652i 0.416824 0.908987i \(-0.363143\pi\)
−0.822797 + 0.568336i \(0.807588\pi\)
\(128\) −2343.61 853.005i −1.61834 0.589029i
\(129\) 77.0115 28.0299i 0.0525619 0.0191310i
\(130\) −1123.41 + 942.652i −0.757919 + 0.635970i
\(131\) 0.740327 + 4.19860i 0.000493761 + 0.00280026i 0.985054 0.172248i \(-0.0551030\pi\)
−0.984560 + 0.175048i \(0.943992\pi\)
\(132\) −507.176 −0.334424
\(133\) 1866.87 + 1530.73i 1.21713 + 0.997976i
\(134\) −1746.20 −1.12574
\(135\) 41.2175 + 233.756i 0.0262773 + 0.149026i
\(136\) 4.83302 4.05538i 0.00304726 0.00255696i
\(137\) 826.086 300.671i 0.515163 0.187504i −0.0713386 0.997452i \(-0.522727\pi\)
0.586501 + 0.809948i \(0.300505\pi\)
\(138\) 115.813 + 42.1526i 0.0714397 + 0.0260019i
\(139\) 1508.17 + 1265.50i 0.920295 + 0.772219i 0.974049 0.226335i \(-0.0726745\pi\)
−0.0537547 + 0.998554i \(0.517119\pi\)
\(140\) −1729.61 + 2995.77i −1.04413 + 1.80849i
\(141\) 56.5072 + 97.8734i 0.0337501 + 0.0584569i
\(142\) −215.217 + 1220.56i −0.127188 + 0.721316i
\(143\) 370.728 2102.50i 0.216796 1.22951i
\(144\) 869.585 + 1506.17i 0.503232 + 0.871624i
\(145\) 251.365 435.378i 0.143964 0.249353i
\(146\) 3039.29 + 2550.27i 1.72283 + 1.44563i
\(147\) −285.036 103.745i −0.159928 0.0582090i
\(148\) 4358.05 1586.20i 2.42047 0.880978i
\(149\) 1153.19 967.640i 0.634046 0.532028i −0.268137 0.963381i \(-0.586408\pi\)
0.902183 + 0.431353i \(0.141964\pi\)
\(150\) 35.8664 + 203.409i 0.0195232 + 0.110722i
\(151\) −2394.72 −1.29059 −0.645296 0.763933i \(-0.723266\pi\)
−0.645296 + 0.763933i \(0.723266\pi\)
\(152\) −3060.88 + 1153.57i −1.63336 + 0.615573i
\(153\) 4.25569 0.00224871
\(154\) −1310.27 7430.90i −0.685613 3.88831i
\(155\) 1224.44 1027.42i 0.634511 0.532418i
\(156\) 365.263 132.945i 0.187464 0.0682314i
\(157\) 2541.54 + 925.045i 1.29196 + 0.470233i 0.894368 0.447331i \(-0.147625\pi\)
0.397587 + 0.917564i \(0.369848\pi\)
\(158\) −2652.47 2225.69i −1.33556 1.12067i
\(159\) −10.0633 + 17.4302i −0.00501933 + 0.00869374i
\(160\) −15.4862 26.8229i −0.00765183 0.0132534i
\(161\) −212.502 + 1205.16i −0.104022 + 0.589937i
\(162\) −596.238 + 3381.43i −0.289166 + 1.63994i
\(163\) 927.459 + 1606.41i 0.445670 + 0.771923i 0.998099 0.0616373i \(-0.0196322\pi\)
−0.552429 + 0.833560i \(0.686299\pi\)
\(164\) 255.955 443.327i 0.121870 0.211085i
\(165\) 178.906 + 150.120i 0.0844109 + 0.0708292i
\(166\) −5612.51 2042.79i −2.62419 0.955127i
\(167\) −835.550 + 304.115i −0.387166 + 0.140917i −0.528267 0.849078i \(-0.677158\pi\)
0.141101 + 0.989995i \(0.454936\pi\)
\(168\) 527.942 442.996i 0.242450 0.203440i
\(169\) −97.3753 552.243i −0.0443219 0.251362i
\(170\) −5.79121 −0.00261274
\(171\) −2081.81 731.069i −0.930992 0.326937i
\(172\) −2197.85 −0.974327
\(173\) 604.938 + 3430.77i 0.265853 + 1.50773i 0.766595 + 0.642130i \(0.221949\pi\)
−0.500743 + 0.865596i \(0.666940\pi\)
\(174\) −152.945 + 128.336i −0.0666366 + 0.0559147i
\(175\) −1927.19 + 701.439i −0.832467 + 0.302993i
\(176\) 3237.64 + 1178.40i 1.38663 + 0.504690i
\(177\) 133.445 + 111.974i 0.0566688 + 0.0475507i
\(178\) 2867.82 4967.20i 1.20759 2.09162i
\(179\) 52.0088 + 90.0818i 0.0217169 + 0.0376147i 0.876680 0.481075i \(-0.159753\pi\)
−0.854963 + 0.518689i \(0.826420\pi\)
\(180\) 548.994 3113.50i 0.227331 1.28926i
\(181\) 191.556 1086.37i 0.0786642 0.446127i −0.919881 0.392199i \(-0.871715\pi\)
0.998545 0.0539284i \(-0.0171743\pi\)
\(182\) 2891.49 + 5008.20i 1.17764 + 2.03974i
\(183\) −3.50124 + 6.06433i −0.00141431 + 0.00244966i
\(184\) −1270.17 1065.80i −0.508903 0.427020i
\(185\) −2006.80 730.415i −0.797529 0.290277i
\(186\) −596.507 + 217.111i −0.235150 + 0.0855878i
\(187\) 6.45839 5.41924i 0.00252559 0.00211922i
\(188\) −526.298 2984.79i −0.204172 1.15791i
\(189\) 936.005 0.360235
\(190\) 2832.95 + 994.849i 1.08170 + 0.379863i
\(191\) 2275.97 0.862216 0.431108 0.902300i \(-0.358123\pi\)
0.431108 + 0.902300i \(0.358123\pi\)
\(192\) −52.1485 295.749i −0.0196015 0.111166i
\(193\) −444.200 + 372.728i −0.165669 + 0.139013i −0.721853 0.692046i \(-0.756709\pi\)
0.556184 + 0.831059i \(0.312265\pi\)
\(194\) −1832.14 + 666.843i −0.678040 + 0.246786i
\(195\) −168.197 61.2186i −0.0617683 0.0224818i
\(196\) 6231.55 + 5228.89i 2.27097 + 1.90557i
\(197\) 300.114 519.812i 0.108539 0.187995i −0.806639 0.591044i \(-0.798716\pi\)
0.915179 + 0.403048i \(0.132049\pi\)
\(198\) 3448.10 + 5972.29i 1.23761 + 2.14360i
\(199\) −193.396 + 1096.81i −0.0688920 + 0.390706i 0.930792 + 0.365550i \(0.119119\pi\)
−0.999684 + 0.0251556i \(0.991992\pi\)
\(200\) 482.529 2736.56i 0.170600 0.967518i
\(201\) −106.564 184.575i −0.0373954 0.0647707i
\(202\) −845.940 + 1465.21i −0.294654 + 0.510356i
\(203\) −1518.65 1274.30i −0.525065 0.440582i
\(204\) 1.44242 + 0.524997i 0.000495046 + 0.000180182i
\(205\) −221.509 + 80.6226i −0.0754675 + 0.0274679i
\(206\) −3096.67 + 2598.41i −1.04735 + 0.878834i
\(207\) −194.215 1101.45i −0.0652121 0.369836i
\(208\) −2640.61 −0.880255
\(209\) −4090.28 + 1541.53i −1.35373 + 0.510190i
\(210\) −632.611 −0.207878
\(211\) −151.430 858.804i −0.0494071 0.280201i 0.950088 0.311983i \(-0.100993\pi\)
−0.999495 + 0.0317813i \(0.989882\pi\)
\(212\) 413.479 346.950i 0.133952 0.112399i
\(213\) −142.148 + 51.7376i −0.0457268 + 0.0166432i
\(214\) −1535.17 558.756i −0.490384 0.178485i
\(215\) 775.288 + 650.544i 0.245927 + 0.206357i
\(216\) −634.107 + 1098.31i −0.199748 + 0.345974i
\(217\) −3151.52 5458.59i −0.985894 1.70762i
\(218\) 1252.15 7101.32i 0.389021 2.20625i
\(219\) −84.0885 + 476.890i −0.0259460 + 0.147147i
\(220\) −3131.61 5424.11i −0.959697 1.66224i
\(221\) −3.23074 + 5.59580i −0.000983362 + 0.00170323i
\(222\) 649.709 + 545.171i 0.196422 + 0.164817i
\(223\) 4308.68 + 1568.23i 1.29386 + 0.470926i 0.894992 0.446082i \(-0.147181\pi\)
0.398867 + 0.917009i \(0.369403\pi\)
\(224\) −114.770 + 41.7729i −0.0342339 + 0.0124601i
\(225\) 1435.86 1204.83i 0.425440 0.356987i
\(226\) 1830.71 + 10382.5i 0.538837 + 3.05589i
\(227\) 2444.50 0.714744 0.357372 0.933962i \(-0.383673\pi\)
0.357372 + 0.933962i \(0.383673\pi\)
\(228\) −615.417 504.606i −0.178759 0.146572i
\(229\) 225.313 0.0650178 0.0325089 0.999471i \(-0.489650\pi\)
0.0325089 + 0.999471i \(0.489650\pi\)
\(230\) 264.291 + 1498.87i 0.0757689 + 0.429707i
\(231\) 705.492 591.978i 0.200943 0.168612i
\(232\) 2524.08 918.691i 0.714285 0.259978i
\(233\) 1158.16 + 421.534i 0.325636 + 0.118522i 0.499665 0.866219i \(-0.333456\pi\)
−0.174029 + 0.984741i \(0.555679\pi\)
\(234\) −4048.79 3397.34i −1.13110 0.949107i
\(235\) −697.820 + 1208.66i −0.193705 + 0.335508i
\(236\) −2335.86 4045.83i −0.644287 1.11594i
\(237\) 73.3862 416.194i 0.0201137 0.114071i
\(238\) −3.96558 + 22.4899i −0.00108004 + 0.00612523i
\(239\) −1193.70 2067.54i −0.323070 0.559574i 0.658050 0.752975i \(-0.271382\pi\)
−0.981120 + 0.193400i \(0.938048\pi\)
\(240\) 144.431 250.161i 0.0388456 0.0672826i
\(241\) −1170.63 982.276i −0.312892 0.262548i 0.472794 0.881173i \(-0.343245\pi\)
−0.785686 + 0.618625i \(0.787690\pi\)
\(242\) 6703.87 + 2440.01i 1.78075 + 0.648140i
\(243\) −1208.49 + 439.853i −0.319030 + 0.116118i
\(244\) 143.858 120.711i 0.0377441 0.0316711i
\(245\) −650.466 3688.97i −0.169619 0.961959i
\(246\) 93.6164 0.0242633
\(247\) 2541.70 2182.37i 0.654755 0.562189i
\(248\) 8540.13 2.18669
\(249\) −126.587 717.911i −0.0322174 0.182714i
\(250\) −5425.50 + 4552.54i −1.37256 + 1.15171i
\(251\) 5132.44 1868.06i 1.29067 0.469764i 0.396720 0.917940i \(-0.370148\pi\)
0.893945 + 0.448176i \(0.147926\pi\)
\(252\) −11715.2 4264.00i −2.92853 1.06590i
\(253\) −1697.33 1424.23i −0.421781 0.353916i
\(254\) −1859.97 + 3221.56i −0.459467 + 0.795821i
\(255\) −0.353417 0.612136i −8.67914e−5 0.000150327i
\(256\) −1427.07 + 8093.30i −0.348405 + 1.97590i
\(257\) −893.499 + 5067.29i −0.216867 + 1.22992i 0.660769 + 0.750589i \(0.270230\pi\)
−0.877636 + 0.479327i \(0.840881\pi\)
\(258\) −200.968 348.086i −0.0484950 0.0839957i
\(259\) −4210.71 + 7293.17i −1.01020 + 1.74971i
\(260\) 3677.17 + 3085.51i 0.877108 + 0.735981i
\(261\) 1702.59 + 619.691i 0.403783 + 0.146965i
\(262\) 19.6483 7.15141i 0.00463312 0.00168632i
\(263\) −2709.39 + 2273.45i −0.635241 + 0.533030i −0.902553 0.430580i \(-0.858309\pi\)
0.267312 + 0.963610i \(0.413865\pi\)
\(264\) 216.682 + 1228.86i 0.0505146 + 0.286482i
\(265\) −248.548 −0.0576159
\(266\) 5803.35 10320.4i 1.33769 2.37889i
\(267\) 700.050 0.160458
\(268\) 992.521 + 5628.87i 0.226223 + 1.28298i
\(269\) −3470.12 + 2911.78i −0.786532 + 0.659979i −0.944884 0.327404i \(-0.893826\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(270\) 1093.91 398.152i 0.246569 0.0897436i
\(271\) 2619.55 + 953.438i 0.587182 + 0.213717i 0.618490 0.785793i \(-0.287745\pi\)
−0.0313075 + 0.999510i \(0.509967\pi\)
\(272\) −7.98809 6.70280i −0.00178070 0.00149418i
\(273\) −352.914 + 611.265i −0.0782394 + 0.135515i
\(274\) −2155.74 3733.85i −0.475303 0.823248i
\(275\) 644.806 3656.88i 0.141394 0.801883i
\(276\) 70.0517 397.283i 0.0152776 0.0866435i
\(277\) −715.482 1239.25i −0.155196 0.268807i 0.777935 0.628345i \(-0.216267\pi\)
−0.933130 + 0.359539i \(0.882934\pi\)
\(278\) 4827.83 8362.04i 1.04156 1.80404i
\(279\) 4412.90 + 3702.86i 0.946930 + 0.794568i
\(280\) 7997.56 + 2910.87i 1.70695 + 0.621278i
\(281\) −7973.14 + 2901.99i −1.69266 + 0.616078i −0.994956 0.100308i \(-0.968017\pi\)
−0.697704 + 0.716386i \(0.745795\pi\)
\(282\) 424.595 356.277i 0.0896605 0.0752341i
\(283\) −1171.22 6642.33i −0.246014 1.39521i −0.818126 0.575039i \(-0.804987\pi\)
0.572112 0.820176i \(-0.306124\pi\)
\(284\) 4056.79 0.847627
\(285\) 67.7284 + 360.158i 0.0140768 + 0.0748558i
\(286\) −10470.6 −2.16482
\(287\) 161.415 + 915.428i 0.0331986 + 0.188279i
\(288\) 85.5099 71.7514i 0.0174956 0.0146805i
\(289\) 4616.69 1680.34i 0.939688 0.342018i
\(290\) −2316.90 843.284i −0.469149 0.170756i
\(291\) −182.295 152.963i −0.0367227 0.0308140i
\(292\) 6493.28 11246.7i 1.30134 2.25398i
\(293\) 3990.52 + 6911.78i 0.795660 + 1.37812i 0.922419 + 0.386190i \(0.126209\pi\)
−0.126759 + 0.991934i \(0.540458\pi\)
\(294\) −258.328 + 1465.05i −0.0512449 + 0.290624i
\(295\) −373.559 + 2118.56i −0.0737270 + 0.418126i
\(296\) −5705.19 9881.68i −1.12030 1.94041i
\(297\) −847.362 + 1467.67i −0.165552 + 0.286744i
\(298\) −5655.71 4745.70i −1.09942 0.922521i
\(299\) 1595.73 + 580.800i 0.308641 + 0.112336i
\(300\) 635.300 231.230i 0.122264 0.0445003i
\(301\) 3057.25 2565.34i 0.585438 0.491241i
\(302\) 2039.44 + 11566.2i 0.388598 + 2.20385i
\(303\) −206.499 −0.0391520
\(304\) 2756.18 + 4651.13i 0.519992 + 0.877502i
\(305\) −86.4752 −0.0162346
\(306\) −3.62432 20.5546i −0.000677088 0.00383995i
\(307\) 3138.81 2633.77i 0.583522 0.489633i −0.302580 0.953124i \(-0.597848\pi\)
0.886102 + 0.463491i \(0.153403\pi\)
\(308\) −23208.7 + 8447.29i −4.29364 + 1.56276i
\(309\) −463.633 168.749i −0.0853565 0.0310672i
\(310\) −6005.14 5038.91i −1.10022 0.923196i
\(311\) −4343.64 + 7523.40i −0.791978 + 1.37175i 0.132763 + 0.991148i \(0.457615\pi\)
−0.924741 + 0.380598i \(0.875718\pi\)
\(312\) −478.172 828.217i −0.0867665 0.150284i
\(313\) 1160.01 6578.73i 0.209481 1.18803i −0.680750 0.732516i \(-0.738346\pi\)
0.890231 0.455510i \(-0.150543\pi\)
\(314\) 2303.39 13063.2i 0.413974 2.34777i
\(315\) 2870.43 + 4971.73i 0.513430 + 0.889287i
\(316\) −5666.85 + 9815.28i −1.00881 + 1.74732i
\(317\) −7872.02 6605.41i −1.39475 1.17034i −0.963373 0.268166i \(-0.913583\pi\)
−0.431380 0.902170i \(-0.641973\pi\)
\(318\) 92.7564 + 33.7606i 0.0163570 + 0.00595346i
\(319\) 3372.95 1227.65i 0.592002 0.215471i
\(320\) 2840.96 2383.85i 0.496295 0.416441i
\(321\) −34.6249 196.368i −0.00602048 0.0341439i
\(322\) 6001.78 1.03871
\(323\) 13.2285 0.150130i 0.00227881 2.58621e-5i
\(324\) 11238.9 1.92711
\(325\) 494.186 + 2802.67i 0.0843461 + 0.478351i
\(326\) 6968.92 5847.61i 1.18396 0.993464i
\(327\) 827.030 301.014i 0.139862 0.0509056i
\(328\) −1183.51 430.763i −0.199233 0.0725150i
\(329\) 4215.95 + 3537.60i 0.706482 + 0.592809i
\(330\) 572.700 991.945i 0.0955336 0.165469i
\(331\) 867.289 + 1502.19i 0.144020 + 0.249449i 0.929007 0.370063i \(-0.120664\pi\)
−0.784987 + 0.619512i \(0.787330\pi\)
\(332\) −3394.82 + 19253.0i −0.561190 + 3.18267i
\(333\) 1336.52 7579.79i 0.219943 1.24736i
\(334\) 2180.43 + 3776.62i 0.357210 + 0.618705i
\(335\) 1315.99 2279.36i 0.214627 0.371745i
\(336\) −872.590 732.190i −0.141678 0.118882i
\(337\) −7972.22 2901.65i −1.28865 0.469029i −0.395365 0.918524i \(-0.629382\pi\)
−0.893283 + 0.449495i \(0.851604\pi\)
\(338\) −2584.35 + 940.626i −0.415888 + 0.151371i
\(339\) −985.715 + 827.113i −0.157925 + 0.132515i
\(340\) 3.29166 + 18.6679i 0.000525045 + 0.00297768i
\(341\) 11412.2 1.81234
\(342\) −1758.04 + 10677.5i −0.277964 + 1.68823i
\(343\) −4772.88 −0.751344
\(344\) 938.991 + 5325.28i 0.147171 + 0.834651i
\(345\) −142.303 + 119.406i −0.0222068 + 0.0186337i
\(346\) 16055.1 5843.57i 2.49459 0.907955i
\(347\) 1475.13 + 536.902i 0.228210 + 0.0830618i 0.453594 0.891208i \(-0.350141\pi\)
−0.225384 + 0.974270i \(0.572364\pi\)
\(348\) 500.625 + 420.074i 0.0771158 + 0.0647078i
\(349\) 3113.45 5392.65i 0.477533 0.827112i −0.522135 0.852863i \(-0.674864\pi\)
0.999668 + 0.0257507i \(0.00819762\pi\)
\(350\) 5029.15 + 8710.75i 0.768056 + 1.33031i
\(351\) 225.544 1279.12i 0.0342981 0.194514i
\(352\) 38.4002 217.778i 0.00581459 0.0329762i
\(353\) 3022.18 + 5234.56i 0.455678 + 0.789257i 0.998727 0.0504440i \(-0.0160636\pi\)
−0.543049 + 0.839701i \(0.682730\pi\)
\(354\) 427.175 739.889i 0.0641359 0.111087i
\(355\) −1431.03 1200.78i −0.213947 0.179523i
\(356\) −17641.8 6421.08i −2.62644 0.955946i
\(357\) −2.61921 + 0.953315i −0.000388301 + 0.000141330i
\(358\) 390.793 327.914i 0.0576929 0.0484101i
\(359\) −1718.83 9747.95i −0.252691 1.43308i −0.801930 0.597418i \(-0.796193\pi\)
0.549239 0.835665i \(-0.314918\pi\)
\(360\) −7778.43 −1.13878
\(361\) −6496.93 2199.03i −0.947213 0.320606i
\(362\) −5410.18 −0.785505
\(363\) 151.202 + 857.510i 0.0218624 + 0.123988i
\(364\) 14500.4 12167.3i 2.08799 1.75203i
\(365\) −5619.42 + 2045.30i −0.805847 + 0.293304i
\(366\) 32.2719 + 11.7460i 0.00460896 + 0.00167752i
\(367\) −6820.82 5723.35i −0.970147 0.814050i 0.0124266 0.999923i \(-0.496044\pi\)
−0.982574 + 0.185873i \(0.940489\pi\)
\(368\) −1370.26 + 2373.36i −0.194102 + 0.336195i
\(369\) −424.779 735.738i −0.0599271 0.103797i
\(370\) −1818.76 + 10314.7i −0.255548 + 1.44928i
\(371\) −170.196 + 965.228i −0.0238170 + 0.135073i
\(372\) 1038.90 + 1799.43i 0.144797 + 0.250796i
\(373\) −3961.67 + 6861.81i −0.549939 + 0.952523i 0.448339 + 0.893864i \(0.352016\pi\)
−0.998278 + 0.0586591i \(0.981318\pi\)
\(374\) −31.6746 26.5781i −0.00437929 0.00367466i
\(375\) −812.306 295.655i −0.111859 0.0407135i
\(376\) −7007.15 + 2550.39i −0.961080 + 0.349805i
\(377\) −2107.36 + 1768.29i −0.287890 + 0.241569i
\(378\) −797.141 4520.81i −0.108467 0.615147i
\(379\) 566.318 0.0767541 0.0383771 0.999263i \(-0.487781\pi\)
0.0383771 + 0.999263i \(0.487781\pi\)
\(380\) 1596.67 9697.47i 0.215546 1.30913i
\(381\) −454.028 −0.0610514
\(382\) −1938.31 10992.7i −0.259614 1.47234i
\(383\) −1836.22 + 1540.78i −0.244978 + 0.205561i −0.757006 0.653408i \(-0.773339\pi\)
0.512028 + 0.858969i \(0.328894\pi\)
\(384\) −1402.88 + 510.606i −0.186433 + 0.0678561i
\(385\) 10687.2 + 3889.82i 1.41473 + 0.514918i
\(386\) 2178.54 + 1828.01i 0.287266 + 0.241045i
\(387\) −1823.76 + 3158.84i −0.239552 + 0.414917i
\(388\) 3190.93 + 5526.86i 0.417513 + 0.723154i
\(389\) −1961.56 + 11124.5i −0.255668 + 1.44997i 0.538684 + 0.842508i \(0.318922\pi\)
−0.794352 + 0.607458i \(0.792189\pi\)
\(390\) −152.436 + 864.510i −0.0197921 + 0.112247i
\(391\) 3.35297 + 5.80752i 0.000433676 + 0.000751148i
\(392\) 10007.0 17332.7i 1.28937 2.23325i
\(393\) 1.95498 + 1.64042i 0.000250930 + 0.000210556i
\(394\) −2766.23 1006.83i −0.353707 0.128739i
\(395\) 4904.22 1784.99i 0.624704 0.227374i
\(396\) 17291.8 14509.5i 2.19430 1.84124i
\(397\) 297.045 + 1684.63i 0.0375523 + 0.212970i 0.997810 0.0661451i \(-0.0210700\pi\)
−0.960258 + 0.279115i \(0.909959\pi\)
\(398\) 5462.16 0.687924
\(399\) 1445.04 16.3997i 0.181309 0.00205767i
\(400\) −4592.80 −0.574100
\(401\) −1599.12 9069.07i −0.199143 1.12940i −0.906394 0.422434i \(-0.861176\pi\)
0.707251 0.706963i \(-0.249935\pi\)
\(402\) −800.723 + 671.887i −0.0993444 + 0.0833599i
\(403\) −8218.97 + 2991.46i −1.01592 + 0.369765i
\(404\) 5203.92 + 1894.07i 0.640854 + 0.233252i
\(405\) −3964.52 3326.63i −0.486417 0.408152i
\(406\) −4861.38 + 8420.16i −0.594252 + 1.02927i
\(407\) −7623.88 13204.9i −0.928505 1.60822i
\(408\) 0.655797 3.71921i 7.95754e−5 0.000451295i
\(409\) −1876.27 + 10640.9i −0.226835 + 1.28645i 0.632310 + 0.774715i \(0.282107\pi\)
−0.859146 + 0.511731i \(0.829004\pi\)
\(410\) 578.045 + 1001.20i 0.0696283 + 0.120600i
\(411\) 263.114 455.727i 0.0315778 0.0546943i
\(412\) 10136.1 + 8505.18i 1.21206 + 1.01704i
\(413\) 7971.54 + 2901.40i 0.949768 + 0.345687i
\(414\) −5154.49 + 1876.08i −0.611907 + 0.222716i
\(415\) 6896.25 5786.64i 0.815719 0.684470i
\(416\) 29.4303 + 166.907i 0.00346860 + 0.0196714i
\(417\) 1178.50 0.138397
\(418\) 10928.9 + 18442.8i 1.27882 + 2.15805i
\(419\) −15330.6 −1.78747 −0.893735 0.448596i \(-0.851924\pi\)
−0.893735 + 0.448596i \(0.851924\pi\)
\(420\) 359.569 + 2039.22i 0.0417742 + 0.236913i
\(421\) −126.027 + 105.750i −0.0145896 + 0.0122421i −0.650053 0.759889i \(-0.725253\pi\)
0.635464 + 0.772131i \(0.280809\pi\)
\(422\) −4018.97 + 1462.79i −0.463603 + 0.168738i
\(423\) −4726.58 1720.33i −0.543296 0.197744i
\(424\) −1017.30 853.612i −0.116519 0.0977714i
\(425\) −5.61921 + 9.73276i −0.000641345 + 0.00111084i
\(426\) 370.946 + 642.498i 0.0421888 + 0.0730731i
\(427\) −59.2147 + 335.823i −0.00671101 + 0.0380600i
\(428\) −928.574 + 5266.20i −0.104870 + 0.594747i
\(429\) −638.984 1106.75i −0.0719124 0.124556i
\(430\) 2481.79 4298.59i 0.278332 0.482085i
\(431\) 9869.95 + 8281.87i 1.10306 + 0.925577i 0.997627 0.0688493i \(-0.0219328\pi\)
0.105433 + 0.994426i \(0.466377\pi\)
\(432\) 1969.71 + 716.917i 0.219370 + 0.0798442i
\(433\) 9951.14 3621.92i 1.10444 0.401982i 0.275487 0.961305i \(-0.411161\pi\)
0.828950 + 0.559323i \(0.188939\pi\)
\(434\) −23680.5 + 19870.3i −2.61912 + 2.19771i
\(435\) −52.2565 296.361i −0.00575979 0.0326654i
\(436\) −23602.8 −2.59259
\(437\) −642.561 3416.93i −0.0703383 0.374036i
\(438\) 2374.94 0.259085
\(439\) 2617.95 + 14847.1i 0.284619 + 1.61415i 0.706643 + 0.707570i \(0.250209\pi\)
−0.422024 + 0.906584i \(0.638680\pi\)
\(440\) −11804.5 + 9905.11i −1.27899 + 1.07320i
\(441\) 12686.1 4617.36i 1.36984 0.498581i
\(442\) 29.7786 + 10.8385i 0.00320458 + 0.00116637i
\(443\) −277.823 233.122i −0.0297964 0.0250021i 0.627768 0.778401i \(-0.283969\pi\)
−0.657564 + 0.753398i \(0.728413\pi\)
\(444\) 1388.07 2404.20i 0.148367 0.256979i
\(445\) 4322.54 + 7486.85i 0.460467 + 0.797552i
\(446\) 3904.95 22146.1i 0.414584 2.35123i
\(447\) 156.477 887.426i 0.0165573 0.0939012i
\(448\) −7312.20 12665.1i −0.771136 1.33565i
\(449\) 6292.87 10899.6i 0.661423 1.14562i −0.318819 0.947816i \(-0.603286\pi\)
0.980242 0.197802i \(-0.0633805\pi\)
\(450\) −7042.05 5908.98i −0.737701 0.619004i
\(451\) −1581.53 575.632i −0.165125 0.0601007i
\(452\) 32427.3 11802.6i 3.37445 1.22820i
\(453\) −1098.10 + 921.417i −0.113893 + 0.0955672i
\(454\) −2081.83 11806.7i −0.215210 1.22052i
\(455\) −8716.43 −0.898094
\(456\) −959.712 + 1706.71i −0.0985584 + 0.175272i
\(457\) 19220.1 1.96735 0.983673 0.179965i \(-0.0575984\pi\)
0.983673 + 0.179965i \(0.0575984\pi\)
\(458\) −191.886 1088.24i −0.0195769 0.111026i
\(459\) 3.92916 3.29695i 0.000399559 0.000335269i
\(460\) 4681.38 1703.88i 0.474501 0.172704i
\(461\) −5961.69 2169.88i −0.602307 0.219222i 0.0228268 0.999739i \(-0.492733\pi\)
−0.625134 + 0.780518i \(0.714956\pi\)
\(462\) −3460.02 2903.30i −0.348430 0.292367i
\(463\) −2665.67 + 4617.07i −0.267568 + 0.463442i −0.968233 0.250049i \(-0.919553\pi\)
0.700665 + 0.713490i \(0.252887\pi\)
\(464\) −2219.79 3844.79i −0.222093 0.384677i
\(465\) 166.145 942.255i 0.0165694 0.0939699i
\(466\) 1049.63 5952.77i 0.104342 0.591752i
\(467\) 2903.91 + 5029.71i 0.287745 + 0.498388i 0.973271 0.229659i \(-0.0737612\pi\)
−0.685526 + 0.728048i \(0.740428\pi\)
\(468\) −8650.02 + 14982.3i −0.854374 + 1.47982i
\(469\) −7950.66 6671.39i −0.782787 0.656836i
\(470\) 6432.00 + 2341.06i 0.631247 + 0.229755i
\(471\) 1521.36 553.729i 0.148833 0.0541709i
\(472\) −8804.91 + 7388.20i −0.858642 + 0.720486i
\(473\) 1254.78 + 7116.21i 0.121976 + 0.691762i
\(474\) −2072.67 −0.200846
\(475\) 4420.77 3795.78i 0.427029 0.366658i
\(476\) 74.7502 0.00719783
\(477\) −155.550 882.166i −0.0149311 0.0846784i
\(478\) −8969.42 + 7526.24i −0.858268 + 0.720172i
\(479\) 7365.10 2680.68i 0.702547 0.255706i 0.0340492 0.999420i \(-0.489160\pi\)
0.668498 + 0.743714i \(0.266937\pi\)
\(480\) −17.4219 6.34105i −0.00165666 0.000602975i
\(481\) 8952.02 + 7511.64i 0.848601 + 0.712061i
\(482\) −3747.34 + 6490.58i −0.354121 + 0.613356i
\(483\) 366.267 + 634.393i 0.0345046 + 0.0597637i
\(484\) 4054.95 22996.8i 0.380818 2.15973i
\(485\) 510.305 2894.08i 0.0477768 0.270956i
\(486\) 3153.64 + 5462.27i 0.294346 + 0.509822i
\(487\) 453.583 785.629i 0.0422049 0.0731011i −0.844151 0.536105i \(-0.819895\pi\)
0.886356 + 0.463004i \(0.153228\pi\)
\(488\) −353.938 296.990i −0.0328320 0.0275494i
\(489\) 1043.39 + 379.761i 0.0964899 + 0.0351194i
\(490\) −17263.4 + 6283.37i −1.59159 + 0.579293i
\(491\) 9362.55 7856.11i 0.860542 0.722080i −0.101543 0.994831i \(-0.532378\pi\)
0.962085 + 0.272751i \(0.0879334\pi\)
\(492\) −53.2106 301.772i −0.00487585 0.0276523i
\(493\) −10.8635 −0.000992430
\(494\) −12705.2 10417.6i −1.15716 0.948801i
\(495\) −10394.4 −0.943821
\(496\) −2451.09 13900.8i −0.221889 1.25840i
\(497\) −5643.07 + 4735.10i −0.509309 + 0.427361i
\(498\) −3359.63 + 1222.81i −0.302307 + 0.110031i
\(499\) −16468.4 5994.00i −1.47741 0.537732i −0.527307 0.849675i \(-0.676798\pi\)
−0.950101 + 0.311943i \(0.899020\pi\)
\(500\) 17758.9 + 14901.5i 1.58840 + 1.33283i
\(501\) −266.128 + 460.948i −0.0237320 + 0.0411050i
\(502\) −13393.5 23198.3i −1.19080 2.06253i
\(503\) 1352.90 7672.65i 0.119926 0.680133i −0.864267 0.503033i \(-0.832217\pi\)
0.984193 0.177100i \(-0.0566715\pi\)
\(504\) −5326.35 + 30207.2i −0.470743 + 2.66971i
\(505\) −1275.05 2208.45i −0.112354 0.194603i
\(506\) −5433.38 + 9410.89i −0.477358 + 0.826809i
\(507\) −257.138 215.765i −0.0225245 0.0189003i
\(508\) 11441.9 + 4164.49i 0.999311 + 0.363720i
\(509\) −17576.7 + 6397.40i −1.53060 + 0.557092i −0.963768 0.266743i \(-0.914053\pi\)
−0.566830 + 0.823835i \(0.691830\pi\)
\(510\) −2.65557 + 2.22829i −0.000230570 + 0.000193471i
\(511\) 4094.90 + 23223.3i 0.354497 + 2.01045i
\(512\) 20353.0 1.75681
\(513\) −2488.44 + 937.834i −0.214166 + 0.0807142i
\(514\) 25235.4 2.16554
\(515\) −1058.03 6000.39i −0.0905289 0.513415i
\(516\) −1007.83 + 845.667i −0.0859827 + 0.0721481i
\(517\) −9363.70 + 3408.11i −0.796547 + 0.289920i
\(518\) 38811.3 + 14126.2i 3.29203 + 1.19820i
\(519\) 1597.46 + 1340.42i 0.135107 + 0.113368i
\(520\) 5905.05 10227.8i 0.497987 0.862539i
\(521\) 7347.85 + 12726.8i 0.617879 + 1.07020i 0.989872 + 0.141963i \(0.0453413\pi\)
−0.371993 + 0.928236i \(0.621325\pi\)
\(522\) 1543.05 8751.07i 0.129382 0.733763i
\(523\) 580.974 3294.87i 0.0485741 0.275477i −0.950841 0.309680i \(-0.899778\pi\)
0.999415 + 0.0342028i \(0.0108892\pi\)
\(524\) −34.2204 59.2715i −0.00285291 0.00494139i
\(525\) −613.822 + 1063.17i −0.0510274 + 0.0883821i
\(526\) 13288.0 + 11149.9i 1.10149 + 0.924259i
\(527\) −32.4566 11.8132i −0.00268279 0.000976456i
\(528\) 1938.04 705.389i 0.159739 0.0581404i
\(529\) −7970.39 + 6687.95i −0.655083 + 0.549680i
\(530\) 211.674 + 1200.46i 0.0173482 + 0.0983865i
\(531\) −7753.12 −0.633629
\(532\) −36566.4 12841.0i −2.97999 1.04648i
\(533\) 1289.89 0.104825
\(534\) −596.192 3381.17i −0.0483141 0.274003i
\(535\) 1886.31 1582.80i 0.152434 0.127907i
\(536\) 13214.5 4809.67i 1.06488 0.387586i
\(537\) 58.5096 + 21.2957i 0.00470181 + 0.00171132i
\(538\) 17018.9 + 14280.5i 1.36382 + 1.14438i
\(539\) 13372.5 23161.8i 1.06863 1.85093i
\(540\) −1905.21 3299.92i −0.151828 0.262974i
\(541\) 276.383 1567.44i 0.0219642 0.124565i −0.971854 0.235583i \(-0.924300\pi\)
0.993818 + 0.111018i \(0.0354111\pi\)
\(542\) 2374.09 13464.2i 0.188148 1.06704i
\(543\) −330.164 571.860i −0.0260933 0.0451950i
\(544\) −0.334641 + 0.579616i −2.63743e−5 + 4.56817e-5i
\(545\) 8325.86 + 6986.22i 0.654386 + 0.549095i
\(546\) 3252.91 + 1183.96i 0.254966 + 0.0928001i
\(547\) −3803.34 + 1384.30i −0.297293 + 0.108206i −0.486360 0.873758i \(-0.661676\pi\)
0.189068 + 0.981964i \(0.439453\pi\)
\(548\) −10810.7 + 9071.29i −0.842723 + 0.707128i
\(549\) −54.1190 306.924i −0.00420718 0.0238601i
\(550\) −18211.5 −1.41189
\(551\) 5314.23 + 1866.20i 0.410878 + 0.144288i
\(552\) −992.527 −0.0765303
\(553\) −3573.73 20267.6i −0.274811 1.55853i
\(554\) −5376.13 + 4511.11i −0.412292 + 0.345954i
\(555\) −1201.26 + 437.224i −0.0918753 + 0.0334399i
\(556\) −29699.1 10809.6i −2.26533 0.824512i
\(557\) −6337.57 5317.86i −0.482103 0.404533i 0.369083 0.929397i \(-0.379672\pi\)
−0.851186 + 0.524864i \(0.824116\pi\)
\(558\) 14126.2 24467.4i 1.07171 1.85625i
\(559\) −2769.03 4796.11i −0.209513 0.362887i
\(560\) 2442.68 13853.1i 0.184325 1.04536i
\(561\) 0.876345 4.97000i 6.59525e−5 0.000374035i
\(562\) 20806.6 + 36038.0i 1.56169 + 2.70493i
\(563\) −6349.65 + 10997.9i −0.475321 + 0.823281i −0.999600 0.0282659i \(-0.991002\pi\)
0.524279 + 0.851546i \(0.324335\pi\)
\(564\) −1389.79 1166.17i −0.103760 0.0870653i
\(565\) −14932.2 5434.86i −1.11186 0.404684i
\(566\) −31084.3 + 11313.8i −2.30843 + 0.840200i
\(567\) −15633.6 + 13118.1i −1.15793 + 0.971622i
\(568\) −1733.19 9829.41i −0.128034 0.726114i
\(569\) 2775.56 0.204495 0.102247 0.994759i \(-0.467397\pi\)
0.102247 + 0.994759i \(0.467397\pi\)
\(570\) 1681.84 633.847i 0.123587 0.0465770i
\(571\) 12723.9 0.932537 0.466269 0.884643i \(-0.345598\pi\)
0.466269 + 0.884643i \(0.345598\pi\)
\(572\) 5951.38 + 33751.9i 0.435034 + 2.46720i
\(573\) 1043.65 875.725i 0.0760891 0.0638463i
\(574\) 4283.96 1559.23i 0.311514 0.113382i
\(575\) 2775.46 + 1010.18i 0.201295 + 0.0732653i
\(576\) 10238.9 + 8591.44i 0.740660 + 0.621487i
\(577\) 2815.52 4876.63i 0.203140 0.351849i −0.746399 0.665499i \(-0.768219\pi\)
0.949538 + 0.313651i \(0.101552\pi\)
\(578\) −12047.6 20867.1i −0.866981 1.50165i
\(579\) −60.2738 + 341.830i −0.00432624 + 0.0245353i
\(580\) −1401.42 + 7947.84i −0.100329 + 0.568993i
\(581\) −17749.9 30743.8i −1.26745 2.19529i
\(582\) −583.548 + 1010.73i −0.0415616 + 0.0719868i
\(583\) −1359.42 1140.69i −0.0965718 0.0810333i
\(584\) −30024.4 10928.0i −2.12743 0.774320i
\(585\) 7485.91 2724.65i 0.529067 0.192565i
\(586\) 29984.7 25160.1i 2.11375 1.77364i
\(587\) 3296.82 + 18697.2i 0.231813 + 1.31468i 0.849222 + 0.528036i \(0.177071\pi\)
−0.617409 + 0.786642i \(0.711818\pi\)
\(588\) 4869.41 0.341516
\(589\) 13847.8 + 11354.4i 0.968742 + 0.794313i
\(590\) 10550.6 0.736203
\(591\) −62.3908 353.836i −0.00434250 0.0246275i
\(592\) −14447.0 + 12122.5i −1.00299 + 0.841607i
\(593\) −2738.32 + 996.668i −0.189628 + 0.0690190i −0.435089 0.900388i \(-0.643283\pi\)
0.245461 + 0.969407i \(0.421061\pi\)
\(594\) 7810.36 + 2842.74i 0.539500 + 0.196362i
\(595\) −26.3681 22.1254i −0.00181678 0.00152446i
\(596\) −12083.1 + 20928.5i −0.830442 + 1.43837i
\(597\) 333.336 + 577.356i 0.0228518 + 0.0395806i
\(598\) 1446.21 8201.87i 0.0988963 0.560869i
\(599\) 3247.07 18415.0i 0.221488 1.25612i −0.647797 0.761813i \(-0.724310\pi\)
0.869286 0.494310i \(-0.164579\pi\)
\(600\) −831.682 1440.52i −0.0565888 0.0980147i
\(601\) 12297.4 21299.7i 0.834645 1.44565i −0.0596744 0.998218i \(-0.519006\pi\)
0.894319 0.447429i \(-0.147660\pi\)
\(602\) −14994.0 12581.5i −1.01513 0.851797i
\(603\) 8913.64 + 3244.30i 0.601976 + 0.219101i
\(604\) 36124.5 13148.3i 2.43359 0.885753i
\(605\) −8237.23 + 6911.86i −0.553539 + 0.464475i
\(606\) 175.863 + 997.368i 0.0117887 + 0.0668570i
\(607\) 8927.76 0.596980 0.298490 0.954413i \(-0.403517\pi\)
0.298490 + 0.954413i \(0.403517\pi\)
\(608\) 263.270 226.051i 0.0175609 0.0150782i
\(609\) −1186.69 −0.0789608
\(610\) 73.6459 + 417.667i 0.00488825 + 0.0277227i
\(611\) 5850.28 4908.97i 0.387360 0.325034i
\(612\) −64.1975 + 23.3660i −0.00424025 + 0.00154332i
\(613\) −6800.54 2475.19i −0.448077 0.163087i 0.108119 0.994138i \(-0.465517\pi\)
−0.556196 + 0.831051i \(0.687740\pi\)
\(614\) −15394.0 12917.1i −1.01181 0.849009i
\(615\) −70.5520 + 122.200i −0.00462591 + 0.00801231i
\(616\) 30382.9 + 52624.8i 1.98728 + 3.44206i
\(617\) −1209.90 + 6861.70i −0.0789447 + 0.447718i 0.919555 + 0.392961i \(0.128549\pi\)
−0.998500 + 0.0547564i \(0.982562\pi\)
\(618\) −420.189 + 2383.01i −0.0273503 + 0.155111i
\(619\) 10772.8 + 18659.0i 0.699508 + 1.21158i 0.968637 + 0.248479i \(0.0799307\pi\)
−0.269130 + 0.963104i \(0.586736\pi\)
\(620\) −12829.6 + 22221.6i −0.831050 + 1.43942i
\(621\) −1032.62 866.475i −0.0667275 0.0559911i
\(622\) 40036.5 + 14572.1i 2.58090 + 0.939369i
\(623\) 32034.8 11659.7i 2.06011 0.749818i
\(624\) −1210.86 + 1016.03i −0.0776811 + 0.0651822i
\(625\) −326.584 1852.15i −0.0209014 0.118537i
\(626\) −32762.5 −2.09178
\(627\) −1282.47 + 2280.69i −0.0816856 + 0.145266i
\(628\) −43418.3 −2.75889
\(629\) 8.01351 + 45.4469i 0.000507980 + 0.00288090i
\(630\) 21568.4 18098.0i 1.36398 1.14451i
\(631\) −24103.4 + 8772.92i −1.52067 + 0.553478i −0.961315 0.275451i \(-0.911173\pi\)
−0.559353 + 0.828929i \(0.688950\pi\)
\(632\) 26203.0 + 9537.13i 1.64921 + 0.600264i
\(633\) −399.881 335.540i −0.0251088 0.0210688i
\(634\) −25199.3 + 43646.5i −1.57854 + 2.73411i
\(635\) −2803.45 4855.72i −0.175199 0.303454i
\(636\) 56.1053 318.189i 0.00349799 0.0198381i
\(637\) −3559.37 + 20186.2i −0.221393 + 1.25558i
\(638\) −8801.98 15245.5i −0.546197 0.946041i
\(639\) 3366.29 5830.59i 0.208401 0.360962i
\(640\) −14123.0 11850.6i −0.872284 0.731933i
\(641\) −3534.42 1286.42i −0.217786 0.0792678i 0.230823 0.972996i \(-0.425858\pi\)
−0.448609 + 0.893728i \(0.648080\pi\)
\(642\) −918.948 + 334.470i −0.0564922 + 0.0205615i
\(643\) −4012.59 + 3366.96i −0.246098 + 0.206501i −0.757490 0.652847i \(-0.773574\pi\)
0.511392 + 0.859348i \(0.329130\pi\)
\(644\) −3411.34 19346.7i −0.208736 1.18380i
\(645\) 605.820 0.0369832
\(646\) −11.9911 63.7645i −0.000730313 0.00388356i
\(647\) 1791.60 0.108864 0.0544320 0.998517i \(-0.482665\pi\)
0.0544320 + 0.998517i \(0.482665\pi\)
\(648\) −4801.64 27231.4i −0.291090 1.65085i
\(649\) −11766.1 + 9872.90i −0.711646 + 0.597142i
\(650\) 13115.7 4773.73i 0.791448 0.288064i
\(651\) −3545.44 1290.43i −0.213451 0.0776899i
\(652\) −22810.8 19140.5i −1.37015 1.14970i
\(653\) −3041.86 + 5268.66i −0.182293 + 0.315741i −0.942661 0.333752i \(-0.891685\pi\)
0.760368 + 0.649492i \(0.225019\pi\)
\(654\) −2158.20 3738.11i −0.129040 0.223504i
\(655\) −5.47265 + 31.0369i −0.000326464 + 0.00185147i
\(656\) −361.478 + 2050.04i −0.0215142 + 0.122013i
\(657\) −10776.1 18664.8i −0.639905 1.10835i
\(658\) 13495.8 23375.4i 0.799574 1.38490i
\(659\) 23608.8 + 19810.1i 1.39555 + 1.17101i 0.963034 + 0.269379i \(0.0868184\pi\)
0.432515 + 0.901627i \(0.357626\pi\)
\(660\) −3523.05 1282.28i −0.207779 0.0756255i
\(661\) −7588.81 + 2762.10i −0.446551 + 0.162531i −0.555501 0.831516i \(-0.687474\pi\)
0.108950 + 0.994047i \(0.465251\pi\)
\(662\) 6516.80 5468.24i 0.382602 0.321041i
\(663\) 0.671640 + 3.80906i 3.93429e−5 + 0.000223125i
\(664\) 48099.5 2.81118
\(665\) 9097.92 + 15353.0i 0.530530 + 0.895285i
\(666\) −37747.9 −2.19625
\(667\) 495.774 + 2811.67i 0.0287803 + 0.163221i
\(668\) 10934.6 9175.21i 0.633341 0.531436i
\(669\) 2579.16 938.739i 0.149053 0.0542507i
\(670\) −12129.8 4414.89i −0.699426 0.254570i
\(671\) −472.970 396.869i −0.0272113 0.0228330i
\(672\) −36.5550 + 63.3152i −0.00209842 + 0.00363458i
\(673\) 4863.53 + 8423.89i 0.278567 + 0.482492i 0.971029 0.238963i \(-0.0768073\pi\)
−0.692462 + 0.721454i \(0.743474\pi\)
\(674\) −7225.20 + 40976.2i −0.412915 + 2.34175i
\(675\) 392.287 2224.77i 0.0223691 0.126861i
\(676\) 4501.02 + 7795.99i 0.256089 + 0.443559i
\(677\) 13853.0 23994.0i 0.786429 1.36214i −0.141712 0.989908i \(-0.545261\pi\)
0.928142 0.372227i \(-0.121406\pi\)
\(678\) 4834.35 + 4056.50i 0.273838 + 0.229777i
\(679\) −10889.6 3963.50i −0.615472 0.224013i
\(680\) 43.8253 15.9511i 0.00247150 0.000899553i
\(681\) 1120.93 940.570i 0.0630750 0.0529262i
\(682\) −9719.13 55119.9i −0.545696 3.09479i
\(683\) −18109.8 −1.01457 −0.507285 0.861778i \(-0.669351\pi\)
−0.507285 + 0.861778i \(0.669351\pi\)
\(684\) 35418.2 401.961i 1.97989 0.0224698i
\(685\) 6498.51 0.362475
\(686\) 4064.78 + 23052.5i 0.226230 + 1.28302i
\(687\) 103.318 86.6937i 0.00573771 0.00481451i
\(688\) 8398.49 3056.80i 0.465392 0.169389i
\(689\) 1278.04 + 465.170i 0.0706671 + 0.0257207i
\(690\) 697.912 + 585.618i 0.0385059 + 0.0323103i
\(691\) −1319.21 + 2284.94i −0.0726267 + 0.125793i −0.900052 0.435783i \(-0.856471\pi\)
0.827425 + 0.561576i \(0.189805\pi\)
\(692\) −27962.3 48432.1i −1.53608 2.66057i
\(693\) −7117.63 + 40366.1i −0.390153 + 2.21267i
\(694\) 1336.90 7581.96i 0.0731242 0.414708i
\(695\) 7276.78 + 12603.8i 0.397157 + 0.687896i
\(696\) 803.937 1392.46i 0.0437833 0.0758349i
\(697\) 3.90206 + 3.27421i 0.000212053 + 0.000177934i
\(698\) −28697.5 10445.0i −1.55618 0.566405i
\(699\) 693.268 252.329i 0.0375133 0.0136537i
\(700\) 25220.5 21162.5i 1.36178 1.14267i
\(701\) 1096.82 + 6220.39i 0.0590962 + 0.335151i 0.999994 0.00354027i \(-0.00112690\pi\)
−0.940898 + 0.338691i \(0.890016\pi\)
\(702\) −6370.11 −0.342485
\(703\) 3887.08 23608.4i 0.208541 1.26658i
\(704\) 26478.8 1.41755
\(705\) 145.070 + 822.734i 0.00774988 + 0.0439517i
\(706\) 22708.6 19054.8i 1.21055 1.01577i
\(707\) −9449.53 + 3439.35i −0.502668 + 0.182956i
\(708\) −2627.83 956.452i −0.139491 0.0507707i
\(709\) −16129.5 13534.3i −0.854382 0.716911i 0.106368 0.994327i \(-0.466078\pi\)
−0.960750 + 0.277416i \(0.910522\pi\)
\(710\) −4580.90 + 7934.35i −0.242138 + 0.419396i
\(711\) 9404.63 + 16289.3i 0.496063 + 0.859207i
\(712\) −8020.86 + 45488.5i −0.422183 + 2.39432i
\(713\) −1576.27 + 8939.47i −0.0827935 + 0.469545i
\(714\) 6.83504 + 11.8386i 0.000358256 + 0.000620518i
\(715\) 7890.95 13667.5i 0.412734 0.714876i
\(716\) −1279.15 1073.34i −0.0667656 0.0560230i
\(717\) −1342.90 488.776i −0.0699464 0.0254584i
\(718\) −45617.8 + 16603.5i −2.37109 + 0.863005i
\(719\) 10752.4 9022.34i 0.557715 0.467978i −0.319829 0.947475i \(-0.603625\pi\)
0.877543 + 0.479497i \(0.159181\pi\)
\(720\) 2232.47 + 12661.0i 0.115555 + 0.655343i
\(721\) −24026.8 −1.24106
\(722\) −5088.06 + 33252.3i −0.262268 + 1.71402i
\(723\) −914.746 −0.0470536
\(724\) 3075.09 + 17439.7i 0.157852 + 0.895222i
\(725\) −3665.32 + 3075.57i −0.187761 + 0.157550i
\(726\) 4012.92 1460.58i 0.205142 0.0746657i
\(727\) −3622.30 1318.41i −0.184792 0.0672587i 0.247967 0.968769i \(-0.420238\pi\)
−0.432759 + 0.901510i \(0.642460\pi\)
\(728\) −35675.9 29935.6i −1.81626 1.52402i
\(729\) 9066.50 15703.6i 0.460626 0.797828i
\(730\) 14664.3 + 25399.4i 0.743495 + 1.28777i
\(731\) 3.79764 21.5375i 0.000192149 0.00108973i
\(732\) 19.5202 110.705i 0.000985639 0.00558984i
\(733\) −6023.55 10433.1i −0.303526 0.525723i 0.673406 0.739273i \(-0.264831\pi\)
−0.976932 + 0.213550i \(0.931497\pi\)
\(734\) −21834.3 + 37818.1i −1.09798 + 1.90176i
\(735\) −1717.68 1441.31i −0.0862008 0.0723311i
\(736\) 165.287 + 60.1595i 0.00827793 + 0.00301292i
\(737\) 17658.6 6427.19i 0.882580 0.321233i
\(738\) −3191.78 + 2678.22i −0.159202 + 0.133586i
\(739\) 4354.89 + 24697.8i 0.216776 + 1.22940i 0.877798 + 0.479030i \(0.159012\pi\)
−0.661023 + 0.750366i \(0.729877\pi\)
\(740\) 34283.1 1.70307
\(741\) 325.790 1978.70i 0.0161514 0.0980963i
\(742\) 4806.90 0.237826
\(743\) −34.8023 197.374i −0.00171840 0.00974554i 0.983936 0.178519i \(-0.0571305\pi\)
−0.985655 + 0.168773i \(0.946019\pi\)
\(744\) 3916.09 3285.99i 0.192972 0.161922i
\(745\) 10457.0 3806.03i 0.514247 0.187171i
\(746\) 36515.8 + 13290.7i 1.79214 + 0.652286i
\(747\) 24854.2 + 20855.2i 1.21736 + 1.02149i
\(748\) −67.6710 + 117.210i −0.00330788 + 0.00572942i
\(749\) −4855.07 8409.23i −0.236850 0.410236i
\(750\) −736.191 + 4175.15i −0.0358425 + 0.203273i
\(751\) 3146.09 17842.4i 0.152866 0.866947i −0.807845 0.589396i \(-0.799366\pi\)
0.960711 0.277552i \(-0.0895229\pi\)
\(752\) 6162.40 + 10673.6i 0.298829 + 0.517588i
\(753\) 1634.72 2831.42i 0.0791135 0.137029i
\(754\) 10335.4 + 8672.39i 0.499193 + 0.418873i
\(755\) −16634.7 6054.52i −0.801851 0.291850i
\(756\) −14119.7 + 5139.16i −0.679272 + 0.247235i
\(757\) 15248.9 12795.4i 0.732143 0.614341i −0.198572 0.980086i \(-0.563630\pi\)
0.930715 + 0.365745i \(0.119186\pi\)
\(758\) −482.300 2735.26i −0.0231107 0.131067i
\(759\) −1326.32 −0.0634286
\(760\) −24178.7 + 274.404i −1.15402 + 0.0130969i
\(761\) −34118.1 −1.62520 −0.812602 0.582819i \(-0.801950\pi\)
−0.812602 + 0.582819i \(0.801950\pi\)
\(762\) 386.669 + 2192.91i 0.0183826 + 0.104253i
\(763\) 32831.9 27549.3i 1.55779 1.30714i
\(764\) −34333.2 + 12496.2i −1.62582 + 0.591752i
\(765\) 29.5617 + 10.7596i 0.00139713 + 0.000508515i
\(766\) 9005.60 + 7556.59i 0.424785 + 0.356437i
\(767\) 5885.84 10194.6i 0.277086 0.479928i
\(768\) 2459.68 + 4260.29i 0.115568 + 0.200169i
\(769\) 4352.49 24684.2i 0.204103 1.15752i −0.694743 0.719258i \(-0.744482\pi\)
0.898846 0.438265i \(-0.144407\pi\)
\(770\) 9685.77 54930.7i 0.453313 2.57087i
\(771\) 1540.03 + 2667.41i 0.0719361 + 0.124597i
\(772\) 4654.32 8061.52i 0.216985 0.375830i
\(773\) −5471.15 4590.84i −0.254571 0.213611i 0.506566 0.862201i \(-0.330915\pi\)
−0.761138 + 0.648590i \(0.775359\pi\)
\(774\) 16810.1 + 6118.36i 0.780652 + 0.284134i
\(775\) −14295.2 + 5203.04i −0.662580 + 0.241159i
\(776\) 12028.1 10092.7i 0.556420 0.466892i
\(777\) 875.367 + 4964.45i 0.0404165 + 0.229213i
\(778\) 55401.0 2.55298
\(779\) −1346.35 2272.00i −0.0619229 0.104497i
\(780\) 2873.39 0.131902
\(781\) −2316.07 13135.1i −0.106115 0.601807i
\(782\) 25.1942 21.1405i 0.00115210 0.000966728i
\(783\) 2052.03 746.879i 0.0936573 0.0340885i
\(784\) −31084.7 11313.9i −1.41603 0.515392i
\(785\) 15315.8 + 12851.5i 0.696361 + 0.584317i
\(786\) 6.25813 10.8394i 0.000283995 0.000491894i
\(787\) 2634.37 + 4562.86i 0.119320 + 0.206669i 0.919499 0.393093i \(-0.128595\pi\)
−0.800178 + 0.599762i \(0.795262\pi\)
\(788\) −1673.20 + 9489.20i −0.0756413 + 0.428983i
\(789\) −367.640 + 2084.99i −0.0165885 + 0.0940781i
\(790\) −12798.0 22166.7i −0.576368 0.998299i
\(791\) −31331.0 + 54266.9i −1.40835 + 2.43933i
\(792\) −42543.5 35698.3i −1.90874 1.60162i
\(793\) 444.659 + 161.843i 0.0199121 + 0.00724741i
\(794\) 7883.61 2869.40i 0.352366 0.128251i
\(795\) −113.972 + 95.6342i −0.00508451 + 0.00426641i
\(796\) −3104.63 17607.3i −0.138242 0.784011i
\(797\) 25762.7 1.14500 0.572498 0.819906i \(-0.305974\pi\)
0.572498 + 0.819906i \(0.305974\pi\)
\(798\) −1309.86 6965.41i −0.0581060 0.308988i
\(799\) 30.1584 0.00133533
\(800\) 51.1880 + 290.302i 0.00226221 + 0.0128296i
\(801\) −23867.7 + 20027.4i −1.05284 + 0.883436i
\(802\) −42440.8 + 15447.2i −1.86863 + 0.680124i
\(803\) −40121.7 14603.1i −1.76322 0.641759i
\(804\) 2620.95 + 2199.23i 0.114967 + 0.0964689i
\(805\) −4523.11 + 7834.26i −0.198036 + 0.343008i
\(806\) 21448.1 + 37149.1i 0.937315 + 1.62348i
\(807\) −470.864 + 2670.40i −0.0205393 + 0.116484i
\(808\) 2365.97 13418.1i 0.103013 0.584216i
\(809\) −740.433 1282.47i −0.0321783 0.0557344i 0.849488 0.527608i \(-0.176911\pi\)
−0.881666 + 0.471874i \(0.843578\pi\)
\(810\) −12690.9 + 21981.3i −0.550511 + 0.953513i
\(811\) −27059.9 22705.9i −1.17164 0.983124i −0.171644 0.985159i \(-0.554908\pi\)
−0.999998 + 0.00203518i \(0.999352\pi\)
\(812\) 29905.5 + 10884.7i 1.29246 + 0.470417i
\(813\) 1568.05 570.725i 0.0676434 0.0246202i
\(814\) −57285.7 + 48068.4i −2.46666 + 2.06978i
\(815\) 2381.05 + 13503.6i 0.102337 + 0.580382i
\(816\) −6.24200 −0.000267786
\(817\) −5557.58 + 9883.36i −0.237987 + 0.423225i
\(818\) 52992.2 2.26507
\(819\) −5455.02 30937.0i −0.232740 1.31993i
\(820\) 2898.82 2432.40i 0.123453 0.103589i
\(821\) 25174.3 9162.69i 1.07014 0.389501i 0.253913 0.967227i \(-0.418282\pi\)
0.816230 + 0.577726i \(0.196060\pi\)
\(822\) −2425.19 882.698i −0.102906 0.0374545i
\(823\) −18047.9 15144.0i −0.764413 0.641418i 0.174859 0.984594i \(-0.444053\pi\)
−0.939271 + 0.343175i \(0.888498\pi\)
\(824\) 16277.2 28192.9i 0.688159 1.19193i
\(825\) −1111.38 1924.97i −0.0469010 0.0812349i
\(826\) 7224.59 40972.7i 0.304329 1.72594i
\(827\) 2209.39 12530.1i 0.0928997 0.526860i −0.902471 0.430750i \(-0.858249\pi\)
0.995371 0.0961097i \(-0.0306400\pi\)
\(828\) 8977.29 + 15549.1i 0.376790 + 0.652620i
\(829\) 11425.4 19789.4i 0.478675 0.829089i −0.521026 0.853541i \(-0.674451\pi\)
0.999701 + 0.0244514i \(0.00778390\pi\)
\(830\) −33822.0 28380.0i −1.41443 1.18685i
\(831\) −804.914 292.965i −0.0336007 0.0122296i
\(832\) −19069.8 + 6940.83i −0.794622 + 0.289219i
\(833\) −62.0073 + 52.0303i −0.00257914 + 0.00216416i
\(834\) −1003.66 5692.04i −0.0416713 0.236330i
\(835\) −6572.95 −0.272415
\(836\) 53238.4 45711.8i 2.20250 1.89112i
\(837\) 6942.97 0.286719
\(838\) 13056.2 + 74045.3i 0.538208 + 3.05233i
\(839\) 5552.00 4658.68i 0.228458 0.191699i −0.521372 0.853329i \(-0.674580\pi\)
0.749830 + 0.661630i \(0.230135\pi\)
\(840\) 4787.31 1742.44i 0.196640 0.0715713i
\(841\) 18572.0 + 6759.64i 0.761490 + 0.277160i
\(842\) 618.090 + 518.639i 0.0252979 + 0.0212274i
\(843\) −2539.50 + 4398.54i −0.103754 + 0.179708i
\(844\) 6999.62 + 12123.7i 0.285470 + 0.494449i
\(845\) 719.818 4082.29i 0.0293047 0.166195i
\(846\) −4283.69 + 24294.0i −0.174085 + 0.987288i
\(847\) 21201.4 + 36721.9i 0.860082 + 1.48971i
\(848\) −1097.46 + 1900.85i −0.0444420 + 0.0769758i
\(849\) −3092.84 2595.20i −0.125025 0.104908i
\(850\) 51.7938 + 18.8514i 0.00209001 + 0.000760703i
\(851\) 11396.8 4148.08i 0.459079 0.167091i
\(852\) 1860.25 1560.93i 0.0748017 0.0627661i
\(853\) 6179.49 + 35045.6i 0.248044 + 1.40673i 0.813315 + 0.581823i \(0.197660\pi\)
−0.565271 + 0.824905i \(0.691229\pi\)
\(854\) 1672.42 0.0670130
\(855\) −12612.7 10341.7i −0.504498 0.413659i
\(856\) 13156.5 0.525327
\(857\) 6165.17 + 34964.4i 0.245739 + 1.39365i 0.818771 + 0.574121i \(0.194656\pi\)
−0.573032 + 0.819533i \(0.694233\pi\)
\(858\) −4801.32 + 4028.78i −0.191042 + 0.160303i
\(859\) −25869.5 + 9415.74i −1.02754 + 0.373994i −0.800144 0.599808i \(-0.795244\pi\)
−0.227397 + 0.973802i \(0.573021\pi\)
\(860\) −15267.1 5556.78i −0.605354 0.220331i
\(861\) 426.247 + 357.663i 0.0168716 + 0.0141570i
\(862\) 31594.9 54724.0i 1.24841 2.16231i
\(863\) −13821.9 23940.2i −0.545195 0.944305i −0.998595 0.0529979i \(-0.983122\pi\)
0.453400 0.891307i \(-0.350211\pi\)
\(864\) 23.3619 132.492i 0.000919893 0.00521697i
\(865\) −4471.82 + 25361.0i −0.175776 + 0.996877i
\(866\) −25968.3 44978.4i −1.01898 1.76493i
\(867\) 1470.45 2546.89i 0.0575997 0.0997656i
\(868\) 77511.5 + 65039.8i 3.03100 + 2.54331i
\(869\) 35015.3 + 12744.5i 1.36687 + 0.497501i
\(870\) −1386.89 + 504.787i −0.0540460 + 0.0196711i
\(871\) −11032.8 + 9257.60i −0.429198 + 0.360140i
\(872\) 10083.9 + 57188.5i 0.391609 + 2.22092i
\(873\) 10591.2 0.410607
\(874\) −15956.2 + 6013.50i −0.617535 + 0.232734i
\(875\) −42096.0 −1.62640
\(876\) −1349.89 7655.61i −0.0520646 0.295273i
\(877\) −23394.5 + 19630.3i −0.900770 + 0.755836i −0.970341 0.241741i \(-0.922282\pi\)
0.0695706 + 0.997577i \(0.477837\pi\)
\(878\) 69480.5 25288.8i 2.67067 0.972046i
\(879\) 4489.31 + 1633.97i 0.172265 + 0.0626992i
\(880\) 19510.6 + 16371.3i 0.747388 + 0.627133i
\(881\) 4483.15 7765.04i 0.171443 0.296948i −0.767482 0.641071i \(-0.778490\pi\)
0.938925 + 0.344123i \(0.111824\pi\)
\(882\) −33105.4 57340.2i −1.26385 2.18905i
\(883\) 2935.50 16648.0i 0.111877 0.634486i −0.876372 0.481635i \(-0.840043\pi\)
0.988249 0.152851i \(-0.0488456\pi\)
\(884\) 18.0121 102.152i 0.000685308 0.00388657i
\(885\) 643.863 + 1115.20i 0.0244556 + 0.0423584i
\(886\) −889.348 + 1540.40i −0.0337226 + 0.0584093i
\(887\) 25811.5 + 21658.4i 0.977075 + 0.819863i 0.983645 0.180115i \(-0.0576471\pi\)
−0.00657087 + 0.999978i \(0.502092\pi\)
\(888\) −6418.31 2336.07i −0.242550 0.0882809i
\(889\) −20776.7 + 7562.09i −0.783832 + 0.285292i
\(890\) 32479.5 27253.5i 1.22328 1.02645i
\(891\) −6416.45 36389.5i −0.241256 1.36823i
\(892\) −73607.2 −2.76295
\(893\) −14752.9 5180.79i −0.552842 0.194142i
\(894\) −4419.44 −0.165334
\(895\) 133.521 + 757.237i 0.00498673 + 0.0282812i
\(896\) −55692.3 + 46731.4i −2.07651 + 1.74240i
\(897\) 955.202 347.665i 0.0355555 0.0129411i
\(898\) −58003.1 21111.4i −2.15544 0.784517i
\(899\) −11264.8 9452.30i −0.417912 0.350669i
\(900\) −15044.9 + 26058.6i −0.557220 + 0.965133i
\(901\) 2.68544 + 4.65132i 9.92953e−5 + 0.000171984i
\(902\) −1433.34 + 8128.89i −0.0529103 + 0.300069i
\(903\) 414.841 2352.68i 0.0152880 0.0867024i
\(904\) −42451.1 73527.5i −1.56184 2.70518i
\(905\) 4077.27 7062.03i 0.149760 0.259392i
\(906\) 5385.54 + 4519.01i 0.197486 + 0.165711i
\(907\) 40322.1 + 14676.1i 1.47616 + 0.537277i 0.949765 0.312965i \(-0.101322\pi\)
0.526392 + 0.850242i \(0.323544\pi\)
\(908\) −36875.4 + 13421.6i −1.34775 + 0.490540i
\(909\) 7040.42 5907.61i 0.256893 0.215559i
\(910\) 7423.28 + 42099.5i 0.270417 + 1.53361i
\(911\) 11606.2 0.422097 0.211048 0.977476i \(-0.432312\pi\)
0.211048 + 0.977476i \(0.432312\pi\)
\(912\) 3053.47 + 1072.29i 0.110867 + 0.0389331i
\(913\) 64275.7 2.32992
\(914\) −16368.6 92831.0i −0.592369 3.35949i
\(915\) −39.6534 + 33.2731i −0.00143268 + 0.00120216i
\(916\) −3398.86 + 1237.08i −0.122600 + 0.0446227i
\(917\) 116.783 + 42.5056i 0.00420559 + 0.00153071i
\(918\) −19.2702 16.1696i −0.000692822 0.000581347i
\(919\) −11281.4 + 19539.9i −0.404938 + 0.701373i −0.994314 0.106485i \(-0.966040\pi\)
0.589376 + 0.807859i \(0.299374\pi\)
\(920\) −6128.46 10614.8i −0.219619 0.380391i
\(921\) 425.908 2415.44i 0.0152379 0.0864186i
\(922\) −5403.07 + 30642.3i −0.192994 + 1.09452i
\(923\) 5111.09 + 8852.66i 0.182268 + 0.315698i
\(924\) −7392.14 + 12803.6i −0.263186 + 0.455851i
\(925\) 15570.2 + 13065.0i 0.553455 + 0.464404i
\(926\) 24570.2 + 8942.81i 0.871951 + 0.317364i
\(927\) 20634.8 7510.47i 0.731108 0.266102i
\(928\) −218.281 + 183.160i −0.00772138 + 0.00647900i
\(929\) −7163.93 40628.7i −0.253004 1.43486i −0.801144 0.598472i \(-0.795775\pi\)
0.548139 0.836387i \(-0.315336\pi\)
\(930\) −4692.49 −0.165455
\(931\) 39270.9 14800.3i 1.38244 0.521008i
\(932\) −19785.3 −0.695375
\(933\) 903.001 + 5121.17i 0.0316859 + 0.179700i
\(934\) 21819.9 18309.1i 0.764421 0.641426i
\(935\) 58.5640 21.3155i 0.00204839 0.000745554i
\(936\) 39996.9 + 14557.7i 1.39673 + 0.508369i
\(937\) −37364.5 31352.5i −1.30271 1.09311i −0.989669 0.143369i \(-0.954206\pi\)
−0.313045 0.949738i \(-0.601349\pi\)
\(938\) −25451.0 + 44082.5i −0.885934 + 1.53448i
\(939\) −1999.38 3463.03i −0.0694859 0.120353i
\(940\) 3890.51 22064.2i 0.134994 0.765589i
\(941\) 592.705 3361.39i 0.0205331 0.116449i −0.972819 0.231569i \(-0.925614\pi\)
0.993352 + 0.115120i \(0.0367253\pi\)
\(942\) −3970.11 6876.43i −0.137318 0.237841i
\(943\) 669.349 1159.35i 0.0231145 0.0400355i
\(944\) 14552.9 + 12211.3i 0.501755 + 0.421022i
\(945\) 6501.87 + 2366.49i 0.223816 + 0.0814622i
\(946\) 33301.9 12120.9i 1.14454 0.416580i
\(947\) −36827.9 + 30902.3i −1.26372 + 1.06039i −0.268449 + 0.963294i \(0.586511\pi\)
−0.995275 + 0.0970969i \(0.969044\pi\)
\(948\) 1178.09 + 6681.25i 0.0403612 + 0.228900i
\(949\) 32723.2 1.11932
\(950\) −22098.2 18119.2i −0.754693 0.618805i
\(951\) −6151.29 −0.209747
\(952\) −31.9357 181.116i −0.00108723 0.00616598i
\(953\) −16480.5 + 13828.8i −0.560184 + 0.470050i −0.878372 0.477978i \(-0.841370\pi\)
0.318188 + 0.948028i \(0.396926\pi\)
\(954\) −4128.30 + 1502.58i −0.140103 + 0.0509935i
\(955\) 15809.8 + 5754.29i 0.535699 + 0.194978i
\(956\) 29358.9 + 24635.1i 0.993238 + 0.833425i
\(957\) 1074.31 1860.75i 0.0362878 0.0628522i
\(958\) −19219.8 33289.7i −0.648189 1.12270i
\(959\) 4449.91 25236.7i 0.149838 0.849776i
\(960\) 385.492 2186.23i 0.0129601 0.0735004i
\(961\) −8481.40 14690.2i −0.284697 0.493109i
\(962\) 28656.5 49634.6i 0.960420 1.66350i
\(963\) 6798.29 + 5704.44i 0.227489 + 0.190886i
\(964\) 23052.3 + 8390.35i 0.770191 + 0.280327i
\(965\) −4027.95 + 1466.05i −0.134367 + 0.0489056i
\(966\) 2752.13 2309.31i 0.0916648 0.0769159i
\(967\) −7269.67 41228.4i −0.241755 1.37106i −0.827910 0.560861i \(-0.810470\pi\)
0.586155 0.810199i \(-0.300641\pi\)
\(968\) −57452.6 −1.90764
\(969\) 6.00819 5.15879i 0.000199186 0.000171026i
\(970\) −14412.7 −0.477077
\(971\) 6597.37 + 37415.5i 0.218043 + 1.23658i 0.875548 + 0.483132i \(0.160501\pi\)
−0.657505 + 0.753450i \(0.728388\pi\)
\(972\) 15815.1 13270.4i 0.521882 0.437911i
\(973\) 53929.0 19628.6i 1.77686 0.646724i
\(974\) −4180.80 1521.69i −0.137537 0.0500595i
\(975\) 1304.99 + 1095.02i 0.0428649 + 0.0359679i
\(976\) −381.828 + 661.346i −0.0125226 + 0.0216897i
\(977\) 17478.5 + 30273.6i 0.572350 + 0.991339i 0.996324 + 0.0856649i \(0.0273015\pi\)
−0.423974 + 0.905674i \(0.639365\pi\)
\(978\) 945.618 5362.87i 0.0309177 0.175343i
\(979\) −10718.3 + 60786.6i −0.349907 + 1.98442i
\(980\) 30066.7 + 52077.1i 0.980047 + 1.69749i
\(981\) −19585.4 + 33922.9i −0.637425 + 1.10405i
\(982\) −45917.8 38529.6i −1.49215 1.25207i
\(983\) −43607.8 15871.9i −1.41493 0.514991i −0.482354 0.875976i \(-0.660218\pi\)
−0.932571 + 0.360986i \(0.882440\pi\)
\(984\) −708.447 + 257.854i −0.0229517 + 0.00835373i
\(985\) 3398.94 2852.05i 0.109949 0.0922578i
\(986\) 9.25182 + 52.4697i 0.000298821 + 0.00169470i
\(987\) 3294.39 0.106243
\(988\) −26359.4 + 46876.5i −0.848790 + 1.50945i
\(989\) −5747.60 −0.184796
\(990\) 8852.27 + 50203.7i 0.284185 + 1.61170i
\(991\) 8935.82 7498.04i 0.286434 0.240346i −0.488237 0.872711i \(-0.662360\pi\)
0.774671 + 0.632365i \(0.217916\pi\)
\(992\) −851.325 + 309.857i −0.0272476 + 0.00991730i
\(993\) 975.695 + 355.124i 0.0311810 + 0.0113490i
\(994\) 27675.9 + 23222.9i 0.883126 + 0.741031i
\(995\) −4116.44 + 7129.89i −0.131156 + 0.227169i
\(996\) 5851.29 + 10134.7i 0.186150 + 0.322421i
\(997\) −877.467 + 4976.36i −0.0278733 + 0.158077i −0.995568 0.0940494i \(-0.970019\pi\)
0.967694 + 0.252127i \(0.0811299\pi\)
\(998\) −14925.3 + 84645.4i −0.473398 + 2.68477i
\(999\) −4638.22 8033.63i −0.146894 0.254427i
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 19.4.e.a.9.1 24
3.2 odd 2 171.4.u.b.28.4 24
19.6 even 9 361.4.a.n.1.1 12
19.13 odd 18 361.4.a.m.1.12 12
19.17 even 9 inner 19.4.e.a.17.1 yes 24
57.17 odd 18 171.4.u.b.55.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.4.e.a.9.1 24 1.1 even 1 trivial
19.4.e.a.17.1 yes 24 19.17 even 9 inner
171.4.u.b.28.4 24 3.2 odd 2
171.4.u.b.55.4 24 57.17 odd 18
361.4.a.m.1.12 12 19.13 odd 18
361.4.a.n.1.1 12 19.6 even 9