Properties

Label 38.4.e.b.23.3
Level $38$
Weight $4$
Character 38.23
Analytic conductor $2.242$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [38,4,Mod(5,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 38.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: \(2.24207258022\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} + 165 x^{16} - 56 x^{15} + 18435 x^{14} - 11748 x^{13} + 1092662 x^{12} - 1833567 x^{11} + 46842546 x^{10} - 93643115 x^{9} + 1273086000 x^{8} + \cdots + 3892796082289 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 23.3
Root \(2.15332 + 3.72966i\) of defining polynomial
Character \(\chi\) \(=\) 38.23
Dual form 38.4.e.b.5.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.87939 + 0.684040i) q^{2} +(0.900544 + 5.10724i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-10.9611 + 9.19749i) q^{5} +(-1.80109 + 10.2145i) q^{6} +(16.0725 - 27.8383i) q^{7} +(4.00000 + 6.92820i) q^{8} +(0.0987659 - 0.0359478i) q^{9} +O(q^{10})\) \(q+(1.87939 + 0.684040i) q^{2} +(0.900544 + 5.10724i) q^{3} +(3.06418 + 2.57115i) q^{4} +(-10.9611 + 9.19749i) q^{5} +(-1.80109 + 10.2145i) q^{6} +(16.0725 - 27.8383i) q^{7} +(4.00000 + 6.92820i) q^{8} +(0.0987659 - 0.0359478i) q^{9} +(-26.8917 + 9.78776i) q^{10} +(16.0815 + 27.8541i) q^{11} +(-10.3721 + 17.9649i) q^{12} +(10.2414 - 58.0818i) q^{13} +(49.2489 - 41.3247i) q^{14} +(-56.8448 - 47.6984i) q^{15} +(2.77837 + 15.7569i) q^{16} +(0.248658 + 0.0905043i) q^{17} +0.210209 q^{18} +(-82.8189 + 0.155735i) q^{19} -57.2350 q^{20} +(156.651 + 57.0163i) q^{21} +(11.1701 + 63.3489i) q^{22} +(-125.908 - 105.649i) q^{23} +(-31.7818 + 26.6681i) q^{24} +(13.8468 - 78.5289i) q^{25} +(58.9778 - 102.153i) q^{26} +(70.2839 + 121.735i) q^{27} +(120.825 - 43.9768i) q^{28} +(69.8012 - 25.4055i) q^{29} +(-74.2056 - 128.528i) q^{30} +(-113.990 + 197.437i) q^{31} +(-5.55674 + 31.5138i) q^{32} +(-127.775 + 107.216i) q^{33} +(0.405416 + 0.340185i) q^{34} +(79.8701 + 452.966i) q^{35} +(0.395063 + 0.143791i) q^{36} +112.024 q^{37} +(-155.755 - 56.3588i) q^{38} +305.861 q^{39} +(-107.567 - 39.1510i) q^{40} +(-33.2568 - 188.609i) q^{41} +(255.406 + 214.311i) q^{42} +(44.7716 - 37.5679i) q^{43} +(-22.3403 + 126.698i) q^{44} +(-0.751957 + 1.30243i) q^{45} +(-164.361 - 284.682i) q^{46} +(-84.3281 + 30.6929i) q^{47} +(-77.9724 + 28.3796i) q^{48} +(-345.148 - 597.814i) q^{49} +(79.7403 - 138.114i) q^{50} +(-0.238299 + 1.35146i) q^{51} +(180.719 - 151.641i) q^{52} +(297.397 + 249.546i) q^{53} +(48.8187 + 276.865i) q^{54} +(-432.459 - 157.402i) q^{55} +257.159 q^{56} +(-75.3775 - 422.836i) q^{57} +148.562 q^{58} +(-350.865 - 127.704i) q^{59} +(-51.5427 - 292.313i) q^{60} +(-398.991 - 334.793i) q^{61} +(-349.286 + 293.086i) q^{62} +(0.586683 - 3.32725i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(421.949 + 730.838i) q^{65} +(-313.479 + 114.097i) q^{66} +(-61.8342 + 22.5058i) q^{67} +(0.529233 + 0.916659i) q^{68} +(426.191 - 738.185i) q^{69} +(-159.740 + 905.932i) q^{70} +(405.586 - 340.327i) q^{71} +(0.644117 + 0.540479i) q^{72} +(66.8256 + 378.987i) q^{73} +(210.536 + 76.6289i) q^{74} +413.536 q^{75} +(-254.172 - 212.463i) q^{76} +1033.88 q^{77} +(574.830 + 209.221i) q^{78} +(88.6111 + 502.539i) q^{79} +(-175.378 - 147.160i) q^{80} +(-556.264 + 466.761i) q^{81} +(66.5136 - 377.218i) q^{82} +(-679.754 + 1177.37i) q^{83} +(333.409 + 577.481i) q^{84} +(-3.55799 + 1.29500i) q^{85} +(109.841 - 39.9789i) q^{86} +(192.611 + 333.613i) q^{87} +(-128.652 + 222.832i) q^{88} +(51.9243 - 294.477i) q^{89} +(-2.30413 + 1.93339i) q^{90} +(-1452.30 - 1218.62i) q^{91} +(-114.164 - 647.457i) q^{92} +(-1111.01 - 404.375i) q^{93} -179.480 q^{94} +(906.357 - 763.433i) q^{95} -165.953 q^{96} +(1581.49 + 575.614i) q^{97} +(-239.737 - 1359.62i) q^{98} +(2.58960 + 2.17293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 6 q^{3} - 12 q^{6} - 33 q^{7} + 72 q^{8} + 42 q^{9} - 75 q^{11} + 36 q^{12} + 99 q^{13} + 162 q^{14} - 183 q^{15} - 111 q^{17} - 408 q^{18} - 372 q^{19} + 24 q^{20} - 207 q^{21} - 180 q^{22} + 198 q^{23} - 48 q^{24} + 534 q^{25} + 180 q^{26} + 678 q^{27} + 216 q^{28} + 669 q^{29} - 42 q^{31} + 315 q^{33} - 48 q^{34} - 1995 q^{35} + 168 q^{36} - 1056 q^{37} - 180 q^{38} + 1812 q^{39} - 210 q^{41} - 342 q^{42} - 399 q^{43} + 360 q^{44} + 1494 q^{45} + 672 q^{46} + 1149 q^{47} - 192 q^{48} - 858 q^{49} + 1068 q^{50} + 2646 q^{51} - 468 q^{52} - 633 q^{53} - 2898 q^{54} - 3483 q^{55} - 528 q^{56} - 2814 q^{57} + 636 q^{58} + 51 q^{59} - 84 q^{60} - 4104 q^{61} - 1326 q^{62} + 1215 q^{63} - 576 q^{64} + 1755 q^{65} + 2340 q^{66} - 675 q^{67} - 948 q^{68} + 3693 q^{69} + 3990 q^{70} + 2964 q^{71} + 672 q^{72} - 2004 q^{73} - 486 q^{74} - 4446 q^{75} - 408 q^{76} + 5820 q^{77} + 4992 q^{78} + 543 q^{79} + 1722 q^{81} + 420 q^{82} + 381 q^{83} + 1092 q^{84} + 1266 q^{85} - 3396 q^{86} - 4506 q^{87} + 600 q^{88} + 4386 q^{89} - 2148 q^{90} - 1356 q^{91} - 2628 q^{92} - 8604 q^{93} - 3264 q^{94} + 921 q^{95} + 576 q^{96} + 7599 q^{97} - 954 q^{98} - 5055 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.87939 + 0.684040i 0.664463 + 0.241845i
\(3\) 0.900544 + 5.10724i 0.173310 + 0.982889i 0.940077 + 0.340963i \(0.110753\pi\)
−0.766767 + 0.641926i \(0.778136\pi\)
\(4\) 3.06418 + 2.57115i 0.383022 + 0.321394i
\(5\) −10.9611 + 9.19749i −0.980394 + 0.822648i −0.984149 0.177345i \(-0.943249\pi\)
0.00375477 + 0.999993i \(0.498805\pi\)
\(6\) −1.80109 + 10.2145i −0.122549 + 0.695008i
\(7\) 16.0725 27.8383i 0.867831 1.50313i 0.00362339 0.999993i \(-0.498847\pi\)
0.864208 0.503135i \(-0.167820\pi\)
\(8\) 4.00000 + 6.92820i 0.176777 + 0.306186i
\(9\) 0.0987659 0.0359478i 0.00365799 0.00133140i
\(10\) −26.8917 + 9.78776i −0.850389 + 0.309516i
\(11\) 16.0815 + 27.8541i 0.440797 + 0.763483i 0.997749 0.0670618i \(-0.0213625\pi\)
−0.556952 + 0.830545i \(0.688029\pi\)
\(12\) −10.3721 + 17.9649i −0.249513 + 0.432169i
\(13\) 10.2414 58.0818i 0.218496 1.23915i −0.656239 0.754553i \(-0.727854\pi\)
0.874735 0.484601i \(-0.161035\pi\)
\(14\) 49.2489 41.3247i 0.940166 0.788893i
\(15\) −56.8448 47.6984i −0.978484 0.821046i
\(16\) 2.77837 + 15.7569i 0.0434120 + 0.246202i
\(17\) 0.248658 + 0.0905043i 0.00354756 + 0.00129121i 0.343793 0.939045i \(-0.388288\pi\)
−0.340246 + 0.940337i \(0.610510\pi\)
\(18\) 0.210209 0.00275259
\(19\) −82.8189 + 0.155735i −0.999998 + 0.00188042i
\(20\) −57.2350 −0.639907
\(21\) 156.651 + 57.0163i 1.62781 + 0.592475i
\(22\) 11.1701 + 63.3489i 0.108249 + 0.613911i
\(23\) −125.908 105.649i −1.14146 0.957801i −0.141977 0.989870i \(-0.545346\pi\)
−0.999486 + 0.0320694i \(0.989790\pi\)
\(24\) −31.7818 + 26.6681i −0.270310 + 0.226817i
\(25\) 13.8468 78.5289i 0.110774 0.628231i
\(26\) 58.9778 102.153i 0.444865 0.770530i
\(27\) 70.2839 + 121.735i 0.500968 + 0.867703i
\(28\) 120.825 43.9768i 0.815495 0.296816i
\(29\) 69.8012 25.4055i 0.446957 0.162679i −0.108729 0.994071i \(-0.534678\pi\)
0.555686 + 0.831392i \(0.312456\pi\)
\(30\) −74.2056 128.528i −0.451601 0.782196i
\(31\) −113.990 + 197.437i −0.660427 + 1.14389i 0.320076 + 0.947392i \(0.396291\pi\)
−0.980503 + 0.196502i \(0.937042\pi\)
\(32\) −5.55674 + 31.5138i −0.0306970 + 0.174091i
\(33\) −127.775 + 107.216i −0.674025 + 0.565574i
\(34\) 0.405416 + 0.340185i 0.00204495 + 0.00171592i
\(35\) 79.8701 + 452.966i 0.385729 + 2.18758i
\(36\) 0.395063 + 0.143791i 0.00182900 + 0.000665701i
\(37\) 112.024 0.497746 0.248873 0.968536i \(-0.419940\pi\)
0.248873 + 0.968536i \(0.419940\pi\)
\(38\) −155.755 56.3588i −0.664917 0.240595i
\(39\) 305.861 1.25582
\(40\) −107.567 39.1510i −0.425194 0.154758i
\(41\) −33.2568 188.609i −0.126679 0.718433i −0.980296 0.197532i \(-0.936707\pi\)
0.853617 0.520901i \(-0.174404\pi\)
\(42\) 255.406 + 214.311i 0.938334 + 0.787356i
\(43\) 44.7716 37.5679i 0.158782 0.133234i −0.559935 0.828536i \(-0.689174\pi\)
0.718717 + 0.695303i \(0.244730\pi\)
\(44\) −22.3403 + 126.698i −0.0765436 + 0.434100i
\(45\) −0.751957 + 1.30243i −0.00249100 + 0.00431454i
\(46\) −164.361 284.682i −0.526820 0.912480i
\(47\) −84.3281 + 30.6929i −0.261713 + 0.0952558i −0.469544 0.882909i \(-0.655582\pi\)
0.207831 + 0.978165i \(0.433360\pi\)
\(48\) −77.9724 + 28.3796i −0.234465 + 0.0853384i
\(49\) −345.148 597.814i −1.00626 1.74290i
\(50\) 79.7403 138.114i 0.225540 0.390646i
\(51\) −0.238299 + 1.35146i −0.000654285 + 0.00371064i
\(52\) 180.719 151.641i 0.481945 0.404400i
\(53\) 297.397 + 249.546i 0.770766 + 0.646749i 0.940905 0.338671i \(-0.109977\pi\)
−0.170139 + 0.985420i \(0.554422\pi\)
\(54\) 48.8187 + 276.865i 0.123026 + 0.697713i
\(55\) −432.459 157.402i −1.06023 0.385893i
\(56\) 257.159 0.613649
\(57\) −75.3775 422.836i −0.175158 0.982561i
\(58\) 148.562 0.336329
\(59\) −350.865 127.704i −0.774216 0.281791i −0.0754571 0.997149i \(-0.524042\pi\)
−0.698759 + 0.715358i \(0.746264\pi\)
\(60\) −51.5427 292.313i −0.110902 0.628957i
\(61\) −398.991 334.793i −0.837469 0.702720i 0.119524 0.992831i \(-0.461863\pi\)
−0.956993 + 0.290112i \(0.906308\pi\)
\(62\) −349.286 + 293.086i −0.715474 + 0.600354i
\(63\) 0.586683 3.32725i 0.00117326 0.00665387i
\(64\) −32.0000 + 55.4256i −0.0625000 + 0.108253i
\(65\) 421.949 + 730.838i 0.805175 + 1.39460i
\(66\) −313.479 + 114.097i −0.584646 + 0.212794i
\(67\) −61.8342 + 22.5058i −0.112750 + 0.0410376i −0.397779 0.917481i \(-0.630219\pi\)
0.285029 + 0.958519i \(0.407997\pi\)
\(68\) 0.529233 + 0.916659i 0.000943809 + 0.00163472i
\(69\) 426.191 738.185i 0.743585 1.28793i
\(70\) −159.740 + 905.932i −0.272752 + 1.54685i
\(71\) 405.586 340.327i 0.677947 0.568865i −0.237459 0.971398i \(-0.576314\pi\)
0.915406 + 0.402532i \(0.131870\pi\)
\(72\) 0.644117 + 0.540479i 0.00105430 + 0.000884667i
\(73\) 66.8256 + 378.987i 0.107142 + 0.607630i 0.990343 + 0.138637i \(0.0442721\pi\)
−0.883202 + 0.468993i \(0.844617\pi\)
\(74\) 210.536 + 76.6289i 0.330734 + 0.120377i
\(75\) 413.536 0.636680
\(76\) −254.172 212.463i −0.383626 0.320673i
\(77\) 1033.88 1.53015
\(78\) 574.830 + 209.221i 0.834445 + 0.303713i
\(79\) 88.6111 + 502.539i 0.126197 + 0.715697i 0.980590 + 0.196070i \(0.0628179\pi\)
−0.854393 + 0.519627i \(0.826071\pi\)
\(80\) −175.378 147.160i −0.245099 0.205662i
\(81\) −556.264 + 466.761i −0.763051 + 0.640276i
\(82\) 66.5136 377.218i 0.0895756 0.508009i
\(83\) −679.754 + 1177.37i −0.898948 + 1.55702i −0.0701069 + 0.997539i \(0.522334\pi\)
−0.828841 + 0.559484i \(0.810999\pi\)
\(84\) 333.409 + 577.481i 0.433070 + 0.750100i
\(85\) −3.55799 + 1.29500i −0.00454021 + 0.00165250i
\(86\) 109.841 39.9789i 0.137726 0.0501283i
\(87\) 192.611 + 333.613i 0.237358 + 0.411115i
\(88\) −128.652 + 222.832i −0.155845 + 0.269932i
\(89\) 51.9243 294.477i 0.0618423 0.350725i −0.938148 0.346236i \(-0.887460\pi\)
0.999990 0.00448961i \(-0.00142909\pi\)
\(90\) −2.30413 + 1.93339i −0.00269863 + 0.00226442i
\(91\) −1452.30 1218.62i −1.67299 1.40380i
\(92\) −114.164 647.457i −0.129374 0.733718i
\(93\) −1111.01 404.375i −1.23878 0.450879i
\(94\) −179.480 −0.196936
\(95\) 906.357 763.433i 0.978845 0.824490i
\(96\) −165.953 −0.176432
\(97\) 1581.49 + 575.614i 1.65542 + 0.602523i 0.989633 0.143619i \(-0.0458739\pi\)
0.665787 + 0.746142i \(0.268096\pi\)
\(98\) −239.737 1359.62i −0.247114 1.40145i
\(99\) 2.58960 + 2.17293i 0.00262894 + 0.00220594i
\(100\) 244.339 205.024i 0.244339 0.205024i
\(101\) −318.759 + 1807.77i −0.314036 + 1.78099i 0.263536 + 0.964649i \(0.415111\pi\)
−0.577573 + 0.816339i \(0.696000\pi\)
\(102\) −1.37231 + 2.37691i −0.00133215 + 0.00230735i
\(103\) −699.131 1210.93i −0.668810 1.15841i −0.978237 0.207490i \(-0.933471\pi\)
0.309427 0.950923i \(-0.399863\pi\)
\(104\) 443.368 161.373i 0.418037 0.152153i
\(105\) −2241.48 + 815.832i −2.08330 + 0.758258i
\(106\) 388.224 + 672.424i 0.355732 + 0.616147i
\(107\) 71.3226 123.534i 0.0644394 0.111612i −0.832006 0.554767i \(-0.812807\pi\)
0.896445 + 0.443155i \(0.146141\pi\)
\(108\) −97.6374 + 553.729i −0.0869923 + 0.493358i
\(109\) 1417.84 1189.71i 1.24591 1.04544i 0.248873 0.968536i \(-0.419940\pi\)
0.997038 0.0769073i \(-0.0245046\pi\)
\(110\) −705.088 591.639i −0.611159 0.512824i
\(111\) 100.883 + 572.133i 0.0862644 + 0.489230i
\(112\) 483.302 + 175.907i 0.407747 + 0.148408i
\(113\) −530.132 −0.441333 −0.220666 0.975349i \(-0.570823\pi\)
−0.220666 + 0.975349i \(0.570823\pi\)
\(114\) 147.574 846.233i 0.121241 0.695237i
\(115\) 2351.80 1.90702
\(116\) 279.205 + 101.622i 0.223478 + 0.0813395i
\(117\) −1.07642 6.10466i −0.000850553 0.00482372i
\(118\) −572.055 480.011i −0.446288 0.374480i
\(119\) 6.51604 5.46761i 0.00501953 0.00421189i
\(120\) 103.085 584.626i 0.0784197 0.444740i
\(121\) 148.268 256.807i 0.111396 0.192943i
\(122\) −520.846 902.132i −0.386518 0.669469i
\(123\) 933.321 339.701i 0.684185 0.249023i
\(124\) −856.926 + 311.896i −0.620599 + 0.225879i
\(125\) −323.805 560.846i −0.231696 0.401309i
\(126\) 3.37857 5.85186i 0.00238879 0.00413750i
\(127\) −137.262 + 778.451i −0.0959057 + 0.543908i 0.898560 + 0.438850i \(0.144614\pi\)
−0.994466 + 0.105058i \(0.966497\pi\)
\(128\) −98.0537 + 82.2768i −0.0677094 + 0.0568149i
\(129\) 232.187 + 194.828i 0.158472 + 0.132974i
\(130\) 293.083 + 1662.16i 0.197731 + 1.12139i
\(131\) −324.270 118.025i −0.216272 0.0787165i 0.231612 0.972808i \(-0.425600\pi\)
−0.447884 + 0.894092i \(0.647822\pi\)
\(132\) −667.195 −0.439938
\(133\) −1326.77 + 2308.04i −0.865003 + 1.50476i
\(134\) −131.605 −0.0848429
\(135\) −1890.05 687.922i −1.20496 0.438570i
\(136\) 0.367602 + 2.08477i 0.000231776 + 0.00131447i
\(137\) −633.977 531.970i −0.395360 0.331747i 0.423337 0.905972i \(-0.360859\pi\)
−0.818697 + 0.574226i \(0.805303\pi\)
\(138\) 1305.93 1095.80i 0.805563 0.675948i
\(139\) −366.513 + 2078.60i −0.223649 + 1.26838i 0.641601 + 0.767038i \(0.278270\pi\)
−0.865251 + 0.501340i \(0.832841\pi\)
\(140\) −919.907 + 1593.33i −0.555331 + 0.961862i
\(141\) −232.697 403.044i −0.138983 0.240726i
\(142\) 995.051 362.169i 0.588048 0.214032i
\(143\) 1782.51 648.781i 1.04239 0.379397i
\(144\) 0.840835 + 1.45637i 0.000486595 + 0.000842807i
\(145\) −531.433 + 920.469i −0.304366 + 0.527178i
\(146\) −133.651 + 757.973i −0.0757606 + 0.429660i
\(147\) 2742.36 2301.11i 1.53868 1.29111i
\(148\) 343.261 + 288.030i 0.190648 + 0.159973i
\(149\) 245.803 + 1394.02i 0.135147 + 0.766458i 0.974757 + 0.223268i \(0.0716725\pi\)
−0.839610 + 0.543190i \(0.817216\pi\)
\(150\) 777.193 + 282.875i 0.423050 + 0.153978i
\(151\) 777.767 0.419164 0.209582 0.977791i \(-0.432790\pi\)
0.209582 + 0.977791i \(0.432790\pi\)
\(152\) −332.355 573.163i −0.177352 0.305853i
\(153\) 0.0278124 1.46961e−5
\(154\) 1943.06 + 707.216i 1.01673 + 0.370059i
\(155\) −566.460 3212.56i −0.293543 1.66477i
\(156\) 937.211 + 786.414i 0.481006 + 0.403612i
\(157\) 2762.25 2317.80i 1.40415 1.17822i 0.444930 0.895565i \(-0.353228\pi\)
0.959221 0.282658i \(-0.0912160\pi\)
\(158\) −177.222 + 1005.08i −0.0892345 + 0.506074i
\(159\) −1006.67 + 1743.60i −0.502102 + 0.869665i
\(160\) −228.940 396.536i −0.113121 0.195931i
\(161\) −4964.75 + 1807.02i −2.43029 + 0.884555i
\(162\) −1364.72 + 496.717i −0.661866 + 0.240900i
\(163\) 1212.12 + 2099.45i 0.582456 + 1.00884i 0.995187 + 0.0979903i \(0.0312414\pi\)
−0.412732 + 0.910853i \(0.635425\pi\)
\(164\) 383.037 663.439i 0.182379 0.315890i
\(165\) 414.443 2350.42i 0.195541 1.10897i
\(166\) −2082.89 + 1747.75i −0.973876 + 0.817179i
\(167\) 1738.00 + 1458.36i 0.805335 + 0.675756i 0.949489 0.313799i \(-0.101602\pi\)
−0.144155 + 0.989555i \(0.546046\pi\)
\(168\) 231.583 + 1313.38i 0.106352 + 0.603149i
\(169\) −1204.11 438.259i −0.548068 0.199481i
\(170\) −7.57267 −0.00341645
\(171\) −8.17408 + 2.99254i −0.00365548 + 0.00133828i
\(172\) 233.781 0.103637
\(173\) 1541.66 + 561.120i 0.677518 + 0.246596i 0.657781 0.753209i \(-0.271495\pi\)
0.0197365 + 0.999805i \(0.493717\pi\)
\(174\) 133.786 + 758.741i 0.0582892 + 0.330575i
\(175\) −1963.56 1647.62i −0.848179 0.711706i
\(176\) −394.214 + 330.785i −0.168835 + 0.141669i
\(177\) 336.248 1906.96i 0.142791 0.809805i
\(178\) 299.020 517.918i 0.125913 0.218088i
\(179\) −1148.00 1988.40i −0.479361 0.830278i 0.520359 0.853948i \(-0.325798\pi\)
−0.999720 + 0.0236700i \(0.992465\pi\)
\(180\) −5.65286 + 2.05747i −0.00234078 + 0.000851973i
\(181\) −1513.95 + 551.032i −0.621717 + 0.226287i −0.633622 0.773643i \(-0.718433\pi\)
0.0119049 + 0.999929i \(0.496210\pi\)
\(182\) −1895.84 3283.69i −0.772136 1.33738i
\(183\) 1350.56 2339.24i 0.545554 0.944927i
\(184\) 228.328 1294.91i 0.0914814 0.518817i
\(185\) −1227.91 + 1030.34i −0.487988 + 0.409470i
\(186\) −1811.41 1519.95i −0.714080 0.599184i
\(187\) 1.47790 + 8.38159i 0.000577940 + 0.00327766i
\(188\) −337.313 122.772i −0.130857 0.0476279i
\(189\) 4518.54 1.73902
\(190\) 2225.61 814.800i 0.849805 0.311115i
\(191\) −1080.21 −0.409221 −0.204610 0.978844i \(-0.565593\pi\)
−0.204610 + 0.978844i \(0.565593\pi\)
\(192\) −311.889 113.518i −0.117233 0.0426692i
\(193\) −100.901 572.237i −0.0376322 0.213423i 0.960193 0.279337i \(-0.0901147\pi\)
−0.997825 + 0.0659145i \(0.979004\pi\)
\(194\) 2578.48 + 2163.60i 0.954248 + 0.800709i
\(195\) −3352.58 + 2813.15i −1.23120 + 1.03310i
\(196\) 479.475 2719.24i 0.174736 0.990975i
\(197\) 742.256 1285.62i 0.268444 0.464959i −0.700016 0.714127i \(-0.746824\pi\)
0.968460 + 0.249168i \(0.0801571\pi\)
\(198\) 3.38048 + 5.85517i 0.00121334 + 0.00210156i
\(199\) −868.594 + 316.142i −0.309412 + 0.112617i −0.492059 0.870562i \(-0.663756\pi\)
0.182647 + 0.983179i \(0.441533\pi\)
\(200\) 599.451 218.182i 0.211938 0.0771391i
\(201\) −170.627 295.534i −0.0598761 0.103708i
\(202\) −1835.66 + 3179.45i −0.639388 + 1.10745i
\(203\) 414.629 2351.48i 0.143356 0.813012i
\(204\) −4.20500 + 3.52842i −0.00144318 + 0.00121097i
\(205\) 2099.26 + 1761.49i 0.715213 + 0.600135i
\(206\) −485.611 2754.04i −0.164243 0.931471i
\(207\) −16.2333 5.90843i −0.00545068 0.00198389i
\(208\) 943.645 0.314567
\(209\) −1336.19 2304.34i −0.442232 0.762653i
\(210\) −4770.67 −1.56765
\(211\) −880.714 320.554i −0.287350 0.104587i 0.194324 0.980937i \(-0.437749\pi\)
−0.481674 + 0.876351i \(0.659971\pi\)
\(212\) 269.658 + 1529.30i 0.0873592 + 0.495439i
\(213\) 2103.38 + 1764.95i 0.676626 + 0.567757i
\(214\) 218.545 183.381i 0.0698104 0.0585779i
\(215\) −145.218 + 823.573i −0.0460642 + 0.261243i
\(216\) −562.271 + 973.883i −0.177119 + 0.306779i
\(217\) 3664.21 + 6346.59i 1.14628 + 1.98541i
\(218\) 3478.47 1266.06i 1.08070 0.393341i
\(219\) −1875.40 + 682.588i −0.578665 + 0.210617i
\(220\) −920.427 1594.23i −0.282069 0.488558i
\(221\) 7.80326 13.5156i 0.00237513 0.00411385i
\(222\) −201.765 + 1144.27i −0.0609981 + 0.345938i
\(223\) −304.007 + 255.092i −0.0912907 + 0.0766020i −0.687291 0.726382i \(-0.741200\pi\)
0.596000 + 0.802984i \(0.296756\pi\)
\(224\) 787.982 + 661.196i 0.235041 + 0.197223i
\(225\) −1.45536 8.25373i −0.000431217 0.00244555i
\(226\) −996.321 362.631i −0.293249 0.106734i
\(227\) 655.356 0.191619 0.0958095 0.995400i \(-0.469456\pi\)
0.0958095 + 0.995400i \(0.469456\pi\)
\(228\) 856.205 1489.45i 0.248700 0.432637i
\(229\) −1958.69 −0.565213 −0.282606 0.959236i \(-0.591199\pi\)
−0.282606 + 0.959236i \(0.591199\pi\)
\(230\) 4419.95 + 1608.73i 1.26714 + 0.461202i
\(231\) 931.055 + 5280.28i 0.265190 + 1.50397i
\(232\) 455.220 + 381.975i 0.128822 + 0.108094i
\(233\) −3228.93 + 2709.39i −0.907872 + 0.761795i −0.971713 0.236165i \(-0.924109\pi\)
0.0638407 + 0.997960i \(0.479665\pi\)
\(234\) 2.15283 12.2093i 0.000601431 0.00341089i
\(235\) 642.035 1112.04i 0.178220 0.308686i
\(236\) −746.765 1293.44i −0.205976 0.356760i
\(237\) −2486.79 + 905.117i −0.681579 + 0.248075i
\(238\) 15.9862 5.81850i 0.00435392 0.00158470i
\(239\) 2719.45 + 4710.23i 0.736012 + 1.27481i 0.954278 + 0.298920i \(0.0966264\pi\)
−0.218267 + 0.975889i \(0.570040\pi\)
\(240\) 593.645 1028.22i 0.159665 0.276548i
\(241\) 586.162 3324.29i 0.156672 0.888533i −0.800569 0.599241i \(-0.795469\pi\)
0.957241 0.289292i \(-0.0934198\pi\)
\(242\) 454.319 381.218i 0.120681 0.101263i
\(243\) 22.5917 + 18.9567i 0.00596402 + 0.00500440i
\(244\) −361.776 2051.73i −0.0949194 0.538315i
\(245\) 9281.60 + 3378.23i 2.42033 + 0.880927i
\(246\) 1986.44 0.514840
\(247\) −839.136 + 4811.87i −0.216166 + 1.23956i
\(248\) −1823.84 −0.466993
\(249\) −6625.25 2411.39i −1.68618 0.613719i
\(250\) −224.912 1275.54i −0.0568988 0.322689i
\(251\) −1761.60 1478.16i −0.442992 0.371715i 0.393835 0.919181i \(-0.371148\pi\)
−0.836828 + 0.547466i \(0.815592\pi\)
\(252\) 10.3526 8.68682i 0.00258789 0.00217150i
\(253\) 917.968 5206.05i 0.228111 1.29368i
\(254\) −790.460 + 1369.12i −0.195267 + 0.338213i
\(255\) −9.81802 17.0053i −0.00241109 0.00417613i
\(256\) −240.561 + 87.5572i −0.0587308 + 0.0213763i
\(257\) 2359.67 858.848i 0.572731 0.208457i −0.0393861 0.999224i \(-0.512540\pi\)
0.612117 + 0.790767i \(0.290318\pi\)
\(258\) 303.099 + 524.982i 0.0731399 + 0.126682i
\(259\) 1800.50 3118.56i 0.431960 0.748177i
\(260\) −586.166 + 3324.31i −0.139817 + 0.792943i
\(261\) 5.98070 5.01840i 0.00141838 0.00119016i
\(262\) −528.695 443.627i −0.124667 0.104608i
\(263\) −485.151 2751.43i −0.113748 0.645096i −0.987363 0.158478i \(-0.949341\pi\)
0.873615 0.486618i \(-0.161770\pi\)
\(264\) −1253.92 456.388i −0.292323 0.106397i
\(265\) −5555.00 −1.28770
\(266\) −4072.30 + 3430.14i −0.938680 + 0.790659i
\(267\) 1550.73 0.355442
\(268\) −247.337 90.0232i −0.0563750 0.0205188i
\(269\) −498.369 2826.39i −0.112960 0.640625i −0.987740 0.156106i \(-0.950106\pi\)
0.874781 0.484519i \(-0.161005\pi\)
\(270\) −3081.57 2585.74i −0.694586 0.582827i
\(271\) 1372.02 1151.26i 0.307544 0.258060i −0.475932 0.879482i \(-0.657889\pi\)
0.783476 + 0.621422i \(0.213445\pi\)
\(272\) −0.735203 + 4.16955i −0.000163891 + 0.000929470i
\(273\) 4915.93 8514.65i 1.08984 1.88766i
\(274\) −827.599 1433.44i −0.182471 0.316049i
\(275\) 2410.03 877.178i 0.528473 0.192348i
\(276\) 3203.91 1166.13i 0.698741 0.254321i
\(277\) −2974.62 5152.19i −0.645225 1.11756i −0.984249 0.176785i \(-0.943430\pi\)
0.339024 0.940778i \(-0.389903\pi\)
\(278\) −2110.67 + 3655.78i −0.455357 + 0.788702i
\(279\) −4.16091 + 23.5977i −0.000892858 + 0.00506365i
\(280\) −2818.76 + 2365.22i −0.601618 + 0.504818i
\(281\) −264.606 222.031i −0.0561747 0.0471361i 0.614268 0.789097i \(-0.289451\pi\)
−0.670443 + 0.741961i \(0.733896\pi\)
\(282\) −161.630 916.649i −0.0341309 0.193566i
\(283\) −4237.39 1542.28i −0.890058 0.323955i −0.143797 0.989607i \(-0.545931\pi\)
−0.746262 + 0.665652i \(0.768153\pi\)
\(284\) 2117.82 0.442499
\(285\) 4715.25 + 3941.48i 0.980026 + 0.819204i
\(286\) 3793.82 0.784382
\(287\) −5785.07 2105.59i −1.18983 0.433064i
\(288\) 0.584038 + 3.31225i 0.000119496 + 0.000677694i
\(289\) −3763.52 3157.97i −0.766034 0.642778i
\(290\) −1628.41 + 1366.39i −0.329735 + 0.276681i
\(291\) −1515.60 + 8595.40i −0.305313 + 1.73152i
\(292\) −769.666 + 1333.10i −0.154251 + 0.267171i
\(293\) −439.298 760.887i −0.0875907 0.151712i 0.818902 0.573934i \(-0.194583\pi\)
−0.906492 + 0.422222i \(0.861250\pi\)
\(294\) 6728.00 2448.79i 1.33464 0.485770i
\(295\) 5020.44 1827.29i 0.990852 0.360640i
\(296\) 448.096 + 776.125i 0.0879900 + 0.152403i
\(297\) −2260.55 + 3915.39i −0.441651 + 0.764962i
\(298\) −491.605 + 2788.03i −0.0955635 + 0.541968i
\(299\) −7425.78 + 6230.97i −1.43627 + 1.20517i
\(300\) 1267.15 + 1063.26i 0.243863 + 0.204625i
\(301\) −326.236 1850.18i −0.0624715 0.354293i
\(302\) 1461.72 + 532.024i 0.278519 + 0.101373i
\(303\) −9519.78 −1.80494
\(304\) −232.556 1304.54i −0.0438749 0.246120i
\(305\) 7452.66 1.39914
\(306\) 0.0522702 + 0.0190248i 9.76499e−6 + 3.55417e-6i
\(307\) 727.986 + 4128.61i 0.135337 + 0.767532i 0.974625 + 0.223845i \(0.0718611\pi\)
−0.839288 + 0.543687i \(0.817028\pi\)
\(308\) 3167.99 + 2658.26i 0.586082 + 0.491781i
\(309\) 5554.91 4661.13i 1.02268 0.858130i
\(310\) 1132.92 6425.11i 0.207566 1.17717i
\(311\) 4805.18 8322.82i 0.876131 1.51750i 0.0205789 0.999788i \(-0.493449\pi\)
0.855553 0.517716i \(-0.173218\pi\)
\(312\) 1223.44 + 2119.06i 0.221999 + 0.384514i
\(313\) 2612.86 951.005i 0.471846 0.171738i −0.0951423 0.995464i \(-0.530331\pi\)
0.566988 + 0.823726i \(0.308108\pi\)
\(314\) 6776.81 2466.56i 1.21795 0.443299i
\(315\) 24.1716 + 41.8664i 0.00432354 + 0.00748859i
\(316\) −1020.58 + 1767.70i −0.181684 + 0.314686i
\(317\) 86.1475 488.567i 0.0152635 0.0865635i −0.976224 0.216762i \(-0.930450\pi\)
0.991488 + 0.130199i \(0.0415615\pi\)
\(318\) −3084.62 + 2588.30i −0.543952 + 0.456430i
\(319\) 1830.16 + 1535.69i 0.321220 + 0.269536i
\(320\) −159.020 901.848i −0.0277797 0.157546i
\(321\) 695.149 + 253.013i 0.120870 + 0.0439932i
\(322\) −10566.8 −1.82877
\(323\) −20.6077 7.45674i −0.00354998 0.00128453i
\(324\) −2904.60 −0.498046
\(325\) −4419.29 1608.49i −0.754271 0.274532i
\(326\) 841.927 + 4774.81i 0.143037 + 0.811203i
\(327\) 7352.95 + 6169.86i 1.24348 + 1.04341i
\(328\) 1173.69 984.845i 0.197580 0.165790i
\(329\) −500.921 + 2840.86i −0.0839413 + 0.476055i
\(330\) 2386.68 4133.85i 0.398129 0.689579i
\(331\) 1854.52 + 3212.13i 0.307957 + 0.533398i 0.977915 0.209001i \(-0.0670213\pi\)
−0.669958 + 0.742399i \(0.733688\pi\)
\(332\) −5110.08 + 1859.92i −0.844735 + 0.307458i
\(333\) 11.0641 4.02702i 0.00182075 0.000662700i
\(334\) 2268.80 + 3929.68i 0.371687 + 0.643781i
\(335\) 470.776 815.408i 0.0767798 0.132987i
\(336\) −463.167 + 2626.75i −0.0752019 + 0.426491i
\(337\) 4763.15 3996.76i 0.769927 0.646045i −0.170763 0.985312i \(-0.554623\pi\)
0.940690 + 0.339267i \(0.110179\pi\)
\(338\) −1963.19 1647.31i −0.315928 0.265095i
\(339\) −477.407 2707.51i −0.0764873 0.433781i
\(340\) −14.2320 5.18001i −0.00227011 0.000826252i
\(341\) −7332.55 −1.16446
\(342\) −17.4093 + 0.0327368i −0.00275259 + 5.17603e-6i
\(343\) −11163.8 −1.75740
\(344\) 439.364 + 159.916i 0.0688632 + 0.0250641i
\(345\) 2117.90 + 12011.2i 0.330505 + 1.87439i
\(346\) 2513.55 + 2109.12i 0.390548 + 0.327708i
\(347\) 2170.03 1820.87i 0.335715 0.281698i −0.459309 0.888277i \(-0.651903\pi\)
0.795024 + 0.606578i \(0.207458\pi\)
\(348\) −267.573 + 1517.48i −0.0412167 + 0.233752i
\(349\) −5409.94 + 9370.29i −0.829763 + 1.43719i 0.0684604 + 0.997654i \(0.478191\pi\)
−0.898224 + 0.439538i \(0.855142\pi\)
\(350\) −2563.25 4439.67i −0.391461 0.678030i
\(351\) 7790.41 2835.48i 1.18468 0.431187i
\(352\) −967.150 + 352.014i −0.146447 + 0.0533022i
\(353\) 3635.71 + 6297.24i 0.548185 + 0.949485i 0.998399 + 0.0565638i \(0.0180144\pi\)
−0.450214 + 0.892921i \(0.648652\pi\)
\(354\) 1936.37 3353.90i 0.290726 0.503553i
\(355\) −1315.53 + 7460.75i −0.196679 + 1.11542i
\(356\) 916.251 768.826i 0.136408 0.114460i
\(357\) 33.7924 + 28.3552i 0.00500975 + 0.00420368i
\(358\) −797.393 4522.24i −0.117719 0.667620i
\(359\) −9893.45 3600.92i −1.45447 0.529385i −0.510637 0.859796i \(-0.670590\pi\)
−0.943837 + 0.330411i \(0.892813\pi\)
\(360\) −12.0313 −0.00176140
\(361\) 6858.95 25.7956i 0.999993 0.00376083i
\(362\) −3222.22 −0.467834
\(363\) 1445.10 + 525.973i 0.208948 + 0.0760507i
\(364\) −1316.83 7468.14i −0.189618 1.07538i
\(365\) −4218.21 3539.50i −0.604907 0.507577i
\(366\) 4138.36 3472.50i 0.591026 0.495930i
\(367\) 1133.06 6425.91i 0.161159 0.913977i −0.791778 0.610809i \(-0.790844\pi\)
0.952937 0.303168i \(-0.0980445\pi\)
\(368\) 1314.89 2277.46i 0.186259 0.322610i
\(369\) −10.0647 17.4326i −0.00141991 0.00245936i
\(370\) −3012.51 + 1096.46i −0.423278 + 0.154061i
\(371\) 11726.8 4268.22i 1.64104 0.597290i
\(372\) −2364.63 4095.65i −0.329570 0.570832i
\(373\) −1204.11 + 2085.58i −0.167149 + 0.289510i −0.937416 0.348211i \(-0.886789\pi\)
0.770268 + 0.637721i \(0.220123\pi\)
\(374\) −2.95580 + 16.7632i −0.000408665 + 0.00231766i
\(375\) 2572.78 2158.82i 0.354287 0.297282i
\(376\) −549.959 461.471i −0.0754308 0.0632940i
\(377\) −760.739 4314.37i −0.103926 0.589393i
\(378\) 8492.08 + 3090.87i 1.15552 + 0.420574i
\(379\) 11466.3 1.55405 0.777023 0.629473i \(-0.216729\pi\)
0.777023 + 0.629473i \(0.216729\pi\)
\(380\) 4740.14 8.91347i 0.639906 0.00120329i
\(381\) −4099.35 −0.551223
\(382\) −2030.13 738.906i −0.271912 0.0989678i
\(383\) 773.276 + 4385.46i 0.103166 + 0.585083i 0.991937 + 0.126732i \(0.0404487\pi\)
−0.888771 + 0.458351i \(0.848440\pi\)
\(384\) −508.509 426.690i −0.0675775 0.0567042i
\(385\) −11332.5 + 9509.10i −1.50015 + 1.25878i
\(386\) 201.802 1144.47i 0.0266100 0.150913i
\(387\) 3.07143 5.31987i 0.000403435 0.000698770i
\(388\) 3365.97 + 5830.03i 0.440415 + 0.762822i
\(389\) −7722.34 + 2810.70i −1.00652 + 0.366345i −0.792097 0.610395i \(-0.791011\pi\)
−0.214427 + 0.976740i \(0.568789\pi\)
\(390\) −8225.10 + 2993.69i −1.06793 + 0.388696i
\(391\) −21.7464 37.6658i −0.00281269 0.00487172i
\(392\) 2761.18 4782.51i 0.355768 0.616208i
\(393\) 310.761 1762.41i 0.0398875 0.226213i
\(394\) 2274.40 1908.45i 0.290819 0.244026i
\(395\) −5593.37 4693.40i −0.712489 0.597849i
\(396\) 2.34806 + 13.3165i 0.000297966 + 0.00168985i
\(397\) 3223.91 + 1173.41i 0.407566 + 0.148342i 0.537664 0.843159i \(-0.319307\pi\)
−0.130098 + 0.991501i \(0.541529\pi\)
\(398\) −1848.68 −0.232829
\(399\) −12982.5 4697.63i −1.62892 0.589413i
\(400\) 1275.85 0.159481
\(401\) −1439.78 524.035i −0.179299 0.0652595i 0.250811 0.968036i \(-0.419303\pi\)
−0.430110 + 0.902777i \(0.641525\pi\)
\(402\) −118.516 672.139i −0.0147041 0.0833911i
\(403\) 10300.1 + 8642.78i 1.27316 + 1.06831i
\(404\) −5624.78 + 4719.75i −0.692682 + 0.581229i
\(405\) 1804.26 10232.5i 0.221369 1.25544i
\(406\) 2387.75 4135.71i 0.291877 0.505546i
\(407\) 1801.52 + 3120.32i 0.219405 + 0.380021i
\(408\) −10.3164 + 3.75486i −0.00125181 + 0.000455621i
\(409\) 14114.3 5137.18i 1.70637 0.621068i 0.709846 0.704357i \(-0.248765\pi\)
0.996525 + 0.0832886i \(0.0265423\pi\)
\(410\) 2740.39 + 4746.49i 0.330093 + 0.571738i
\(411\) 2145.98 3716.94i 0.257550 0.446090i
\(412\) 971.222 5508.08i 0.116138 0.658649i
\(413\) −9194.34 + 7714.97i −1.09546 + 0.919198i
\(414\) −26.4670 22.2084i −0.00314198 0.00263644i
\(415\) −3377.95 19157.3i −0.399560 2.26601i
\(416\) 1773.47 + 645.491i 0.209018 + 0.0760765i
\(417\) −10946.0 −1.28544
\(418\) −934.964 5244.75i −0.109403 0.613706i
\(419\) −1478.31 −0.172363 −0.0861816 0.996279i \(-0.527467\pi\)
−0.0861816 + 0.996279i \(0.527467\pi\)
\(420\) −8965.92 3263.33i −1.04165 0.379129i
\(421\) −1158.17 6568.32i −0.134076 0.760381i −0.975499 0.220004i \(-0.929393\pi\)
0.841423 0.540377i \(-0.181718\pi\)
\(422\) −1435.93 1204.89i −0.165640 0.138988i
\(423\) −7.22540 + 6.06283i −0.000830522 + 0.000696891i
\(424\) −539.315 + 3058.61i −0.0617723 + 0.350328i
\(425\) 10.5503 18.2737i 0.00120415 0.00208566i
\(426\) 2745.77 + 4755.82i 0.312284 + 0.540892i
\(427\) −15732.9 + 5726.29i −1.78306 + 0.648981i
\(428\) 536.170 195.150i 0.0605532 0.0220396i
\(429\) 4918.71 + 8519.46i 0.553561 + 0.958796i
\(430\) −836.278 + 1448.48i −0.0937882 + 0.162446i
\(431\) 2598.26 14735.4i 0.290380 1.64682i −0.395031 0.918668i \(-0.629266\pi\)
0.685410 0.728157i \(-0.259623\pi\)
\(432\) −1722.90 + 1445.68i −0.191882 + 0.161008i
\(433\) 1412.71 + 1185.40i 0.156791 + 0.131563i 0.717808 0.696241i \(-0.245145\pi\)
−0.561017 + 0.827804i \(0.689590\pi\)
\(434\) 2545.13 + 14434.2i 0.281498 + 1.59646i
\(435\) −5179.64 1885.23i −0.570907 0.207793i
\(436\) 7403.43 0.813211
\(437\) 10444.0 + 8730.16i 1.14326 + 0.955652i
\(438\) −3991.51 −0.435438
\(439\) 6583.90 + 2396.34i 0.715791 + 0.260527i 0.674138 0.738606i \(-0.264515\pi\)
0.0416531 + 0.999132i \(0.486738\pi\)
\(440\) −639.322 3625.78i −0.0692693 0.392846i
\(441\) −55.5790 46.6363i −0.00600140 0.00503577i
\(442\) 23.9106 20.0634i 0.00257310 0.00215909i
\(443\) −616.463 + 3496.14i −0.0661152 + 0.374958i 0.933740 + 0.357952i \(0.116525\pi\)
−0.999855 + 0.0170065i \(0.994586\pi\)
\(444\) −1161.92 + 2012.50i −0.124194 + 0.215111i
\(445\) 2139.30 + 3705.38i 0.227894 + 0.394723i
\(446\) −745.840 + 271.464i −0.0791851 + 0.0288210i
\(447\) −6898.22 + 2510.75i −0.729921 + 0.265669i
\(448\) 1028.64 + 1781.65i 0.108479 + 0.187891i
\(449\) −4090.78 + 7085.43i −0.429968 + 0.744727i −0.996870 0.0790586i \(-0.974809\pi\)
0.566902 + 0.823785i \(0.308142\pi\)
\(450\) 2.91071 16.5075i 0.000304916 0.00172927i
\(451\) 4718.70 3959.46i 0.492671 0.413400i
\(452\) −1624.42 1363.05i −0.169040 0.141842i
\(453\) 700.413 + 3972.24i 0.0726452 + 0.411992i
\(454\) 1231.67 + 448.290i 0.127324 + 0.0463421i
\(455\) 27127.1 2.79503
\(456\) 2627.98 2213.57i 0.269883 0.227325i
\(457\) 7016.94 0.718247 0.359123 0.933290i \(-0.383076\pi\)
0.359123 + 0.933290i \(0.383076\pi\)
\(458\) −3681.13 1339.82i −0.375563 0.136694i
\(459\) 6.45912 + 36.6315i 0.000656832 + 0.00372508i
\(460\) 7206.34 + 6046.84i 0.730429 + 0.612903i
\(461\) 6345.80 5324.75i 0.641113 0.537958i −0.263247 0.964729i \(-0.584793\pi\)
0.904360 + 0.426771i \(0.140349\pi\)
\(462\) −1862.11 + 10560.6i −0.187518 + 1.06347i
\(463\) −7920.19 + 13718.2i −0.794994 + 1.37697i 0.127848 + 0.991794i \(0.459193\pi\)
−0.922843 + 0.385177i \(0.874140\pi\)
\(464\) 594.247 + 1029.27i 0.0594552 + 0.102979i
\(465\) 15897.2 5786.10i 1.58541 0.577041i
\(466\) −7921.74 + 2883.28i −0.787484 + 0.286621i
\(467\) −6952.32 12041.8i −0.688897 1.19320i −0.972195 0.234172i \(-0.924762\pi\)
0.283298 0.959032i \(-0.408571\pi\)
\(468\) 12.3977 21.4734i 0.00122453 0.00212096i
\(469\) −367.304 + 2083.08i −0.0361631 + 0.205091i
\(470\) 1967.31 1650.77i 0.193075 0.162009i
\(471\) 14325.1 + 12020.2i 1.40142 + 1.17593i
\(472\) −518.698 2941.68i −0.0505826 0.286868i
\(473\) 1766.41 + 642.922i 0.171712 + 0.0624981i
\(474\) −5292.77 −0.512880
\(475\) −1134.54 + 6505.84i −0.109593 + 0.628438i
\(476\) 34.0243 0.00327627
\(477\) 38.3433 + 13.9558i 0.00368054 + 0.00133961i
\(478\) 1888.91 + 10712.6i 0.180746 + 1.02506i
\(479\) −6966.95 5845.97i −0.664568 0.557639i 0.246884 0.969045i \(-0.420593\pi\)
−0.911452 + 0.411406i \(0.865038\pi\)
\(480\) 1819.03 1526.35i 0.172973 0.145142i
\(481\) 1147.28 6506.55i 0.108756 0.616784i
\(482\) 3375.57 5846.66i 0.318990 0.552507i
\(483\) −13699.9 23728.9i −1.29061 2.23541i
\(484\) 1114.61 405.684i 0.104678 0.0380996i
\(485\) −22629.1 + 8236.32i −2.11863 + 0.771118i
\(486\) 29.4913 + 51.0805i 0.00275258 + 0.00476761i
\(487\) −6539.74 + 11327.2i −0.608509 + 1.05397i 0.382978 + 0.923758i \(0.374899\pi\)
−0.991486 + 0.130210i \(0.958435\pi\)
\(488\) 723.552 4103.47i 0.0671181 0.380646i
\(489\) −9630.82 + 8081.22i −0.890635 + 0.747332i
\(490\) 15132.9 + 12698.0i 1.39517 + 1.17069i
\(491\) 1598.66 + 9066.44i 0.146938 + 0.833326i 0.965791 + 0.259322i \(0.0834992\pi\)
−0.818853 + 0.574003i \(0.805390\pi\)
\(492\) 3733.28 + 1358.80i 0.342092 + 0.124511i
\(493\) 19.6560 0.00179566
\(494\) −4868.57 + 8469.35i −0.443416 + 0.771365i
\(495\) −48.3705 −0.00439211
\(496\) −3427.70 1247.58i −0.310299 0.112940i
\(497\) −2955.37 16760.7i −0.266733 1.51272i
\(498\) −10801.9 9063.88i −0.971978 0.815587i
\(499\) 2832.41 2376.67i 0.254100 0.213215i −0.506835 0.862043i \(-0.669185\pi\)
0.760935 + 0.648828i \(0.224740\pi\)
\(500\) 449.825 2551.08i 0.0402335 0.228176i
\(501\) −5883.04 + 10189.7i −0.524621 + 0.908670i
\(502\) −2299.60 3983.03i −0.204455 0.354126i
\(503\) 14969.5 5448.45i 1.32695 0.482971i 0.421272 0.906934i \(-0.361584\pi\)
0.905679 + 0.423963i \(0.139361\pi\)
\(504\) 25.3986 9.24432i 0.00224473 0.000817014i
\(505\) −13133.0 22747.0i −1.15725 2.00441i
\(506\) 5286.37 9156.25i 0.464442 0.804437i
\(507\) 1153.94 6544.33i 0.101082 0.573262i
\(508\) −2422.11 + 2032.39i −0.211543 + 0.177505i
\(509\) −12873.5 10802.2i −1.12104 0.940662i −0.122381 0.992483i \(-0.539053\pi\)
−0.998656 + 0.0518208i \(0.983498\pi\)
\(510\) −6.81953 38.6754i −0.000592105 0.00335800i
\(511\) 11624.4 + 4230.94i 1.00633 + 0.366273i
\(512\) −512.000 −0.0441942
\(513\) −5839.80 10071.0i −0.502599 0.866759i
\(514\) 5022.21 0.430973
\(515\) 18800.8 + 6842.93i 1.60866 + 0.585506i
\(516\) 210.530 + 1193.98i 0.0179614 + 0.101864i
\(517\) −2211.05 1855.29i −0.188089 0.157825i
\(518\) 5517.05 4629.36i 0.467964 0.392668i
\(519\) −1477.44 + 8378.97i −0.124956 + 0.708662i
\(520\) −3375.60 + 5846.70i −0.284672 + 0.493067i
\(521\) 1774.76 + 3073.97i 0.149239 + 0.258489i 0.930946 0.365156i \(-0.118984\pi\)
−0.781707 + 0.623645i \(0.785651\pi\)
\(522\) 14.6728 5.34047i 0.00123029 0.000447789i
\(523\) −4118.94 + 1499.17i −0.344376 + 0.125343i −0.508417 0.861111i \(-0.669769\pi\)
0.164041 + 0.986453i \(0.447547\pi\)
\(524\) −690.162 1195.40i −0.0575379 0.0996586i
\(525\) 6646.54 11512.1i 0.552531 0.957011i
\(526\) 970.301 5502.85i 0.0804318 0.456152i
\(527\) −46.2135 + 38.7777i −0.00381991 + 0.00320528i
\(528\) −2044.40 1715.46i −0.168506 0.141393i
\(529\) 2578.26 + 14622.0i 0.211906 + 1.20178i
\(530\) −10440.0 3799.84i −0.855630 0.311424i
\(531\) −39.2442 −0.00320725
\(532\) −9999.78 + 3660.93i −0.814935 + 0.298349i
\(533\) −11295.3 −0.917927
\(534\) 2914.41 + 1060.76i 0.236178 + 0.0859617i
\(535\) 354.429 + 2010.06i 0.0286417 + 0.162435i
\(536\) −403.261 338.376i −0.0324967 0.0272680i
\(537\) 9121.39 7653.76i 0.732993 0.615054i
\(538\) 996.739 5652.79i 0.0798745 0.452991i
\(539\) 11101.0 19227.6i 0.887116 1.53653i
\(540\) −4022.70 6967.52i −0.320573 0.555249i
\(541\) −10725.9 + 3903.90i −0.852387 + 0.310244i −0.731013 0.682363i \(-0.760952\pi\)
−0.121374 + 0.992607i \(0.538730\pi\)
\(542\) 3366.07 1225.15i 0.266762 0.0970935i
\(543\) −4177.63 7235.87i −0.330164 0.571862i
\(544\) −4.23387 + 7.33327i −0.000333687 + 0.000577962i
\(545\) −4598.80 + 26081.1i −0.361451 + 2.04989i
\(546\) 15063.3 12639.6i 1.18068 0.990706i
\(547\) 1213.07 + 1017.89i 0.0948213 + 0.0795645i 0.688966 0.724794i \(-0.258065\pi\)
−0.594145 + 0.804358i \(0.702509\pi\)
\(548\) −574.844 3260.10i −0.0448104 0.254133i
\(549\) −51.4418 18.7233i −0.00399906 0.00145554i
\(550\) 5129.39 0.397669
\(551\) −5776.90 + 2114.93i −0.446650 + 0.163519i
\(552\) 6819.06 0.525794
\(553\) 15414.0 + 5610.25i 1.18530 + 0.431414i
\(554\) −2066.15 11717.7i −0.158452 0.898623i
\(555\) −6367.98 5343.37i −0.487037 0.408673i
\(556\) −6467.46 + 5426.84i −0.493312 + 0.413938i
\(557\) −1548.91 + 8784.28i −0.117826 + 0.668226i 0.867486 + 0.497462i \(0.165735\pi\)
−0.985312 + 0.170764i \(0.945376\pi\)
\(558\) −23.9617 + 41.5030i −0.00181789 + 0.00314867i
\(559\) −1723.49 2985.16i −0.130404 0.225866i
\(560\) −6915.44 + 2517.01i −0.521841 + 0.189934i
\(561\) −41.4759 + 15.0960i −0.00312142 + 0.00113610i
\(562\) −345.419 598.283i −0.0259264 0.0449058i
\(563\) −3682.64 + 6378.53i −0.275675 + 0.477483i −0.970305 0.241884i \(-0.922235\pi\)
0.694630 + 0.719367i \(0.255568\pi\)
\(564\) 323.260 1833.30i 0.0241342 0.136872i
\(565\) 5810.85 4875.88i 0.432680 0.363061i
\(566\) −6908.70 5797.09i −0.513064 0.430512i
\(567\) 4053.31 + 22987.5i 0.300217 + 1.70261i
\(568\) 3980.20 + 1448.68i 0.294024 + 0.107016i
\(569\) 4526.52 0.333500 0.166750 0.985999i \(-0.446673\pi\)
0.166750 + 0.985999i \(0.446673\pi\)
\(570\) 6165.64 + 10633.0i 0.453071 + 0.781345i
\(571\) −7339.30 −0.537899 −0.268949 0.963154i \(-0.586676\pi\)
−0.268949 + 0.963154i \(0.586676\pi\)
\(572\) 7130.05 + 2595.12i 0.521193 + 0.189699i
\(573\) −972.775 5516.88i −0.0709220 0.402218i
\(574\) −9432.06 7914.44i −0.685865 0.575509i
\(575\) −10039.9 + 8424.51i −0.728165 + 0.611003i
\(576\) −1.16808 + 6.62449i −8.44963e−5 + 0.000479202i
\(577\) 3730.22 6460.93i 0.269135 0.466156i −0.699504 0.714629i \(-0.746595\pi\)
0.968639 + 0.248473i \(0.0799288\pi\)
\(578\) −4912.93 8509.44i −0.353548 0.612364i
\(579\) 2831.69 1030.65i 0.203249 0.0739765i
\(580\) −3995.07 + 1454.09i −0.286011 + 0.104099i
\(581\) 21850.6 + 37846.4i 1.56027 + 2.70247i
\(582\) −8728.00 + 15117.3i −0.621628 + 1.07669i
\(583\) −2168.26 + 12296.8i −0.154031 + 0.873552i
\(584\) −2358.39 + 1978.93i −0.167108 + 0.140220i
\(585\) 67.9462 + 57.0137i 0.00480210 + 0.00402944i
\(586\) −305.133 1730.50i −0.0215101 0.121990i
\(587\) −4868.90 1772.14i −0.342353 0.124606i 0.165121 0.986273i \(-0.447198\pi\)
−0.507474 + 0.861667i \(0.669421\pi\)
\(588\) 14319.6 1.00430
\(589\) 9409.80 16369.3i 0.658275 1.14513i
\(590\) 10685.3 0.745603
\(591\) 7234.43 + 2633.12i 0.503527 + 0.183269i
\(592\) 311.244 + 1765.15i 0.0216082 + 0.122546i
\(593\) 8428.67 + 7072.49i 0.583683 + 0.489768i 0.886154 0.463390i \(-0.153367\pi\)
−0.302471 + 0.953158i \(0.597812\pi\)
\(594\) −6926.72 + 5812.21i −0.478463 + 0.401478i
\(595\) −21.1350 + 119.862i −0.00145622 + 0.00825862i
\(596\) −2831.04 + 4903.51i −0.194570 + 0.337006i
\(597\) −2396.82 4151.42i −0.164314 0.284600i
\(598\) −18218.1 + 6630.86i −1.24581 + 0.453438i
\(599\) −17456.9 + 6353.79i −1.19077 + 0.433403i −0.859992 0.510307i \(-0.829532\pi\)
−0.330774 + 0.943710i \(0.607310\pi\)
\(600\) 1654.14 + 2865.06i 0.112550 + 0.194943i
\(601\) 5556.85 9624.75i 0.377153 0.653247i −0.613494 0.789699i \(-0.710237\pi\)
0.990647 + 0.136452i \(0.0435699\pi\)
\(602\) 652.472 3700.35i 0.0441740 0.250523i
\(603\) −5.29807 + 4.44561i −0.000357801 + 0.000300231i
\(604\) 2383.22 + 1999.75i 0.160549 + 0.134717i
\(605\) 736.798 + 4178.59i 0.0495126 + 0.280800i
\(606\) −17891.3 6511.91i −1.19932 0.436515i
\(607\) −16028.2 −1.07177 −0.535884 0.844292i \(-0.680022\pi\)
−0.535884 + 0.844292i \(0.680022\pi\)
\(608\) 455.296 2610.81i 0.0303695 0.174148i
\(609\) 12383.0 0.823945
\(610\) 14006.4 + 5097.92i 0.929677 + 0.338375i
\(611\) 919.064 + 5212.27i 0.0608533 + 0.345116i
\(612\) 0.0852221 + 0.0715098i 5.62892e−6 + 4.72323e-6i
\(613\) 16755.5 14059.5i 1.10399 0.926358i 0.106304 0.994334i \(-0.466098\pi\)
0.997687 + 0.0679752i \(0.0216539\pi\)
\(614\) −1455.97 + 8257.23i −0.0956975 + 0.542727i
\(615\) −7105.87 + 12307.7i −0.465912 + 0.806984i
\(616\) 4135.52 + 7162.93i 0.270495 + 0.468511i
\(617\) 1309.45 476.600i 0.0854398 0.0310975i −0.298947 0.954270i \(-0.596635\pi\)
0.384386 + 0.923172i \(0.374413\pi\)
\(618\) 13628.2 4960.27i 0.887067 0.322866i
\(619\) −2933.23 5080.51i −0.190463 0.329892i 0.754941 0.655793i \(-0.227666\pi\)
−0.945404 + 0.325901i \(0.894332\pi\)
\(620\) 6524.23 11300.3i 0.422612 0.731985i
\(621\) 4011.95 22752.9i 0.259250 1.47028i
\(622\) 14723.9 12354.8i 0.949157 0.796438i
\(623\) −7363.20 6178.46i −0.473516 0.397327i
\(624\) 849.794 + 4819.42i 0.0545176 + 0.309185i
\(625\) 18074.1 + 6578.42i 1.15674 + 0.421019i
\(626\) 5561.11 0.355058
\(627\) 10565.5 8899.43i 0.672960 0.566840i
\(628\) 14423.5 0.916495
\(629\) 27.8557 + 10.1386i 0.00176579 + 0.000642693i
\(630\) 16.7894 + 95.2175i 0.00106176 + 0.00602152i
\(631\) −7998.15 6711.24i −0.504598 0.423408i 0.354626 0.935008i \(-0.384608\pi\)
−0.859223 + 0.511601i \(0.829053\pi\)
\(632\) −3127.25 + 2624.07i −0.196828 + 0.165158i
\(633\) 844.023 4786.69i 0.0529967 0.300559i
\(634\) 496.103 859.276i 0.0310769 0.0538269i
\(635\) −5655.25 9795.17i −0.353420 0.612141i
\(636\) −7567.69 + 2754.41i −0.471821 + 0.171729i
\(637\) −38256.9 + 13924.4i −2.37958 + 0.866097i
\(638\) 2389.10 + 4138.05i 0.148253 + 0.256782i
\(639\) 27.8241 48.1927i 0.00172254 0.00298353i
\(640\) 318.040 1803.70i 0.0196432 0.111402i
\(641\) 3482.55 2922.21i 0.214590 0.180063i −0.529156 0.848524i \(-0.677491\pi\)
0.743747 + 0.668462i \(0.233047\pi\)
\(642\) 1133.38 + 951.019i 0.0696744 + 0.0584638i
\(643\) −23.9538 135.849i −0.00146912 0.00833181i 0.984064 0.177813i \(-0.0569021\pi\)
−0.985534 + 0.169481i \(0.945791\pi\)
\(644\) −19859.0 7228.09i −1.21515 0.442277i
\(645\) −4336.96 −0.264756
\(646\) −33.6291 28.1106i −0.00204817 0.00171207i
\(647\) −339.837 −0.0206497 −0.0103249 0.999947i \(-0.503287\pi\)
−0.0103249 + 0.999947i \(0.503287\pi\)
\(648\) −5458.87 1986.87i −0.330933 0.120450i
\(649\) −2085.37 11826.7i −0.126129 0.715313i
\(650\) −7205.28 6045.95i −0.434791 0.364833i
\(651\) −29113.8 + 24429.4i −1.75278 + 1.47076i
\(652\) −1683.85 + 9549.61i −0.101142 + 0.573607i
\(653\) −8732.11 + 15124.5i −0.523299 + 0.906380i 0.476334 + 0.879265i \(0.341965\pi\)
−0.999632 + 0.0271153i \(0.991368\pi\)
\(654\) 9598.60 + 16625.3i 0.573906 + 0.994035i
\(655\) 4639.90 1688.78i 0.276787 0.100742i
\(656\) 2879.49 1048.05i 0.171380 0.0623773i
\(657\) 20.2238 + 35.0287i 0.00120092 + 0.00208006i
\(658\) −2884.69 + 4996.43i −0.170907 + 0.296020i
\(659\) −4005.07 + 22713.9i −0.236746 + 1.34265i 0.602160 + 0.798376i \(0.294307\pi\)
−0.838906 + 0.544277i \(0.816804\pi\)
\(660\) 7313.22 6136.52i 0.431313 0.361915i
\(661\) −12878.1 10806.0i −0.757792 0.635863i 0.179759 0.983711i \(-0.442468\pi\)
−0.937551 + 0.347848i \(0.886913\pi\)
\(662\) 1288.14 + 7305.40i 0.0756268 + 0.428901i
\(663\) 76.0548 + 27.6817i 0.00445509 + 0.00162152i
\(664\) −10876.1 −0.635652
\(665\) −6685.30 37501.7i −0.389842 2.18685i
\(666\) 23.5484 0.00137009
\(667\) −11472.6 4175.69i −0.665999 0.242404i
\(668\) 1575.89 + 8937.34i 0.0912773 + 0.517659i
\(669\) −1576.59 1322.92i −0.0911128 0.0764528i
\(670\) 1442.54 1210.44i 0.0831795 0.0697958i
\(671\) 2908.96 16497.5i 0.167361 0.949150i
\(672\) −2667.27 + 4619.85i −0.153113 + 0.265200i
\(673\) 16099.8 + 27885.6i 0.922140 + 1.59719i 0.796097 + 0.605169i \(0.206894\pi\)
0.126043 + 0.992025i \(0.459772\pi\)
\(674\) 11685.7 4253.26i 0.667831 0.243070i
\(675\) 10532.9 3833.68i 0.600612 0.218605i
\(676\) −2562.77 4438.84i −0.145811 0.252551i
\(677\) 14531.3 25169.0i 0.824940 1.42884i −0.0770258 0.997029i \(-0.524542\pi\)
0.901965 0.431808i \(-0.142124\pi\)
\(678\) 954.814 5415.02i 0.0540847 0.306729i
\(679\) 41442.5 34774.4i 2.34230 1.96542i
\(680\) −23.2040 19.4705i −0.00130858 0.00109803i
\(681\) 590.177 + 3347.06i 0.0332095 + 0.188340i
\(682\) −13780.7 5015.76i −0.773739 0.281618i
\(683\) 19892.9 1.11447 0.557233 0.830356i \(-0.311863\pi\)
0.557233 + 0.830356i \(0.311863\pi\)
\(684\) −32.7411 11.8471i −0.00183025 0.000662260i
\(685\) 11841.9 0.660520
\(686\) −20981.1 7636.50i −1.16773 0.425019i
\(687\) −1763.88 10003.5i −0.0979569 0.555541i
\(688\) 716.346 + 601.086i 0.0396954 + 0.0333084i
\(689\) 17539.8 14717.7i 0.969831 0.813785i
\(690\) −4235.81 + 24022.5i −0.233702 + 1.32539i
\(691\) −5145.10 + 8911.58i −0.283255 + 0.490611i −0.972184 0.234217i \(-0.924747\pi\)
0.688930 + 0.724828i \(0.258081\pi\)
\(692\) 3281.21 + 5683.22i 0.180250 + 0.312202i
\(693\) 102.112 37.1658i 0.00559728 0.00203724i
\(694\) 5323.86 1937.73i 0.291197 0.105987i
\(695\) −15100.5 26154.8i −0.824165 1.42750i
\(696\) −1540.89 + 2668.90i −0.0839185 + 0.145351i
\(697\) 8.80031 49.9090i 0.000478243 0.00271225i
\(698\) −16577.0 + 13909.8i −0.898925 + 0.754287i
\(699\) −16745.3 14051.0i −0.906104 0.760311i
\(700\) −1780.41 10097.2i −0.0961332 0.545199i
\(701\) −22607.0 8228.29i −1.21805 0.443336i −0.348564 0.937285i \(-0.613331\pi\)
−0.869491 + 0.493949i \(0.835553\pi\)
\(702\) 16580.8 0.891454
\(703\) −9277.70 + 17.4460i −0.497746 + 0.000935972i
\(704\) −2058.44 −0.110199
\(705\) 6257.62 + 2277.59i 0.334292 + 0.121672i
\(706\) 2525.34 + 14321.9i 0.134621 + 0.763473i
\(707\) 45202.1 + 37929.0i 2.40452 + 2.01763i
\(708\) 5933.39 4978.71i 0.314958 0.264281i
\(709\) −232.287 + 1317.36i −0.0123042 + 0.0697808i −0.990342 0.138649i \(-0.955724\pi\)
0.978037 + 0.208430i \(0.0668352\pi\)
\(710\) −7575.85 + 13121.7i −0.400446 + 0.693592i
\(711\) 26.8169 + 46.4483i 0.00141451 + 0.00245000i
\(712\) 2247.90 818.167i 0.118319 0.0430648i
\(713\) 35211.3 12815.9i 1.84947 0.673154i
\(714\) 44.1128 + 76.4056i 0.00231216 + 0.00400477i
\(715\) −13571.2 + 23506.0i −0.709838 + 1.22948i
\(716\) 1594.79 9044.48i 0.0832402 0.472078i
\(717\) −21607.3 + 18130.7i −1.12544 + 0.944355i
\(718\) −16130.4 13535.0i −0.838415 0.703514i
\(719\) −8.72801 49.4990i −0.000452712 0.00256746i 0.984581 0.174932i \(-0.0559705\pi\)
−0.985033 + 0.172364i \(0.944859\pi\)
\(720\) −22.6115 8.22990i −0.00117039 0.000425986i
\(721\) −44947.0 −2.32166
\(722\) 12908.3 + 4643.32i 0.665368 + 0.239344i
\(723\) 17505.8 0.900482
\(724\) −6055.79 2204.13i −0.310859 0.113143i
\(725\) −1028.55 5833.19i −0.0526888 0.298813i
\(726\) 2356.11 + 1977.01i 0.120445 + 0.101066i
\(727\) −1984.72 + 1665.38i −0.101251 + 0.0849593i −0.692008 0.721890i \(-0.743274\pi\)
0.590757 + 0.806849i \(0.298829\pi\)
\(728\) 2633.67 14936.3i 0.134080 0.760406i
\(729\) −9879.51 + 17111.8i −0.501931 + 0.869370i
\(730\) −5506.48 9537.50i −0.279183 0.483560i
\(731\) 14.5329 5.28954i 0.000735319 0.000267634i
\(732\) 10152.9 3695.35i 0.512653 0.186590i
\(733\) −2097.59 3633.14i −0.105698 0.183074i 0.808325 0.588736i \(-0.200374\pi\)
−0.914023 + 0.405662i \(0.867041\pi\)
\(734\) 6525.04 11301.7i 0.328125 0.568329i
\(735\) −8894.93 + 50445.6i −0.446387 + 2.53159i
\(736\) 4029.06 3380.78i 0.201784 0.169317i
\(737\) −1621.27 1360.40i −0.0810314 0.0679934i
\(738\) −6.99088 39.6472i −0.000348696 0.00197755i
\(739\) 13937.9 + 5073.00i 0.693797 + 0.252521i 0.664760 0.747057i \(-0.268534\pi\)
0.0290366 + 0.999578i \(0.490756\pi\)
\(740\) −6411.69 −0.318511
\(741\) −25331.1 + 47.6331i −1.25582 + 0.00236147i
\(742\) 24958.9 1.23486
\(743\) −5466.42 1989.61i −0.269910 0.0982393i 0.203519 0.979071i \(-0.434762\pi\)
−0.473430 + 0.880832i \(0.656984\pi\)
\(744\) −1642.45 9314.81i −0.0809344 0.459002i
\(745\) −15515.7 13019.2i −0.763023 0.640252i
\(746\) −3689.61 + 3095.95i −0.181081 + 0.151945i
\(747\) −24.8126 + 140.719i −0.00121532 + 0.00689244i
\(748\) −17.0218 + 29.4826i −0.000832056 + 0.00144116i
\(749\) −2292.66 3971.00i −0.111845 0.193721i
\(750\) 6311.95 2297.36i 0.307307 0.111850i
\(751\) −3926.00 + 1428.95i −0.190762 + 0.0694315i −0.435635 0.900124i \(-0.643476\pi\)
0.244873 + 0.969555i \(0.421254\pi\)
\(752\) −717.921 1243.48i −0.0348137 0.0602991i
\(753\) 5962.90 10328.1i 0.288579 0.499834i
\(754\) 1521.48 8628.73i 0.0734867 0.416764i
\(755\) −8525.21 + 7153.50i −0.410946 + 0.344824i
\(756\) 13845.6 + 11617.9i 0.666085 + 0.558912i
\(757\) 1780.93 + 10100.2i 0.0855074 + 0.484937i 0.997246 + 0.0741656i \(0.0236294\pi\)
−0.911739 + 0.410771i \(0.865260\pi\)
\(758\) 21549.6 + 7843.40i 1.03261 + 0.375838i
\(759\) 27415.2 1.31108
\(760\) 8914.65 + 3225.70i 0.425485 + 0.153958i
\(761\) 18417.3 0.877300 0.438650 0.898658i \(-0.355457\pi\)
0.438650 + 0.898658i \(0.355457\pi\)
\(762\) −7704.25 2804.12i −0.366267 0.133310i
\(763\) −10331.3 58591.8i −0.490195 2.78003i
\(764\) −3309.95 2777.38i −0.156741 0.131521i
\(765\) −0.304855 + 0.255804i −1.44079e−5 + 1.20897e-5i
\(766\) −1546.55 + 8770.93i −0.0729493 + 0.413716i
\(767\) −11010.6 + 19071.0i −0.518346 + 0.897802i
\(768\) −663.812 1149.76i −0.0311891 0.0540211i
\(769\) −1076.95 + 391.977i −0.0505016 + 0.0183811i −0.367147 0.930163i \(-0.619666\pi\)
0.316646 + 0.948544i \(0.397443\pi\)
\(770\) −27802.8 + 10119.4i −1.30122 + 0.473606i
\(771\) 6511.33 + 11278.0i 0.304150 + 0.526804i
\(772\) 1162.13 2012.87i 0.0541787 0.0938403i
\(773\) −6506.16 + 36898.3i −0.302730 + 1.71687i 0.331271 + 0.943536i \(0.392522\pi\)
−0.634001 + 0.773332i \(0.718589\pi\)
\(774\) 9.41139 7.89710i 0.000437061 0.000366738i
\(775\) 13926.1 + 11685.4i 0.645471 + 0.541615i
\(776\) 2337.98 + 13259.3i 0.108155 + 0.613379i
\(777\) 17548.7 + 6387.19i 0.810238 + 0.294902i
\(778\) −16435.9 −0.757397
\(779\) 2783.67 + 15615.2i 0.128030 + 0.718193i
\(780\) −17505.9 −0.803606
\(781\) 16002.0 + 5824.24i 0.733156 + 0.266847i
\(782\) −15.1049 85.6640i −0.000690728 0.00391731i
\(783\) 7998.65 + 6711.67i 0.365068 + 0.306329i
\(784\) 8460.76 7099.42i 0.385421 0.323407i
\(785\) −8959.45 + 50811.6i −0.407359 + 2.31025i
\(786\) 1789.60 3099.68i 0.0812123 0.140664i
\(787\) −1398.80 2422.79i −0.0633567 0.109737i 0.832607 0.553864i \(-0.186847\pi\)
−0.895964 + 0.444127i \(0.853514\pi\)
\(788\) 5579.94 2030.93i 0.252255 0.0918134i
\(789\) 13615.3 4955.56i 0.614344 0.223603i
\(790\) −7301.63 12646.8i −0.328836 0.569560i
\(791\) −8520.52 + 14758.0i −0.383002 + 0.663379i
\(792\) −4.69612 + 26.6330i −0.000210694 + 0.00119490i
\(793\) −23531.6 + 19745.4i −1.05376 + 0.884211i
\(794\) 5256.32 + 4410.57i 0.234937 + 0.197135i
\(795\) −5002.52 28370.7i −0.223171 1.26567i
\(796\) −3474.37 1264.57i −0.154706 0.0563084i
\(797\) 30493.0 1.35523 0.677615 0.735416i \(-0.263013\pi\)
0.677615 + 0.735416i \(0.263013\pi\)
\(798\) −21185.8 17709.2i −0.939813 0.785590i
\(799\) −23.7467 −0.00105144
\(800\) 2397.80 + 872.730i 0.105969 + 0.0385696i
\(801\) −5.45747 30.9509i −0.000240737 0.00136529i
\(802\) −2347.43 1969.73i −0.103355 0.0867251i
\(803\) −9481.65 + 7956.05i −0.416688 + 0.349643i
\(804\) 237.032 1344.28i 0.0103974 0.0589664i
\(805\) 37799.3 65470.3i 1.65497 2.86649i
\(806\) 13445.8 + 23288.8i 0.587602 + 1.01776i
\(807\) 13986.3 5090.59i 0.610087 0.222053i
\(808\) −13799.6 + 5022.66i −0.600829 + 0.218684i
\(809\) 347.652 + 602.151i 0.0151085 + 0.0261687i 0.873481 0.486859i \(-0.161857\pi\)
−0.858372 + 0.513027i \(0.828524\pi\)
\(810\) 10390.3 17996.6i 0.450714 0.780660i
\(811\) −1015.71 + 5760.36i −0.0439782 + 0.249413i −0.998869 0.0475439i \(-0.984861\pi\)
0.954891 + 0.296957i \(0.0959717\pi\)
\(812\) 7316.50 6139.27i 0.316205 0.265328i
\(813\) 7115.35 + 5970.49i 0.306945 + 0.257557i
\(814\) 1251.32 + 7096.60i 0.0538806 + 0.305572i
\(815\) −32595.8 11863.9i −1.40096 0.509907i
\(816\) −21.9570 −0.000941970
\(817\) −3702.09 + 3118.30i −0.158531 + 0.133532i
\(818\) 30040.2 1.28402
\(819\) −187.244 68.1513i −0.00798881 0.00290769i
\(820\) 1903.45 + 10795.0i 0.0810628 + 0.459730i
\(821\) −18602.1 15609.0i −0.790765 0.663530i 0.155170 0.987888i \(-0.450408\pi\)
−0.945935 + 0.324357i \(0.894852\pi\)
\(822\) 6575.65 5517.63i 0.279017 0.234123i
\(823\) 6942.78 39374.5i 0.294058 1.66769i −0.376946 0.926235i \(-0.623026\pi\)
0.671005 0.741453i \(-0.265863\pi\)
\(824\) 5593.05 9687.44i 0.236460 0.409561i
\(825\) 6650.29 + 11518.6i 0.280647 + 0.486094i
\(826\) −22557.1 + 8210.10i −0.950194 + 0.345842i
\(827\) 25365.6 9232.34i 1.06657 0.388198i 0.251674 0.967812i \(-0.419019\pi\)
0.814891 + 0.579614i \(0.196797\pi\)
\(828\) −34.5502 59.8427i −0.00145012 0.00251169i
\(829\) −19711.8 + 34141.9i −0.825839 + 1.43040i 0.0754371 + 0.997151i \(0.475965\pi\)
−0.901276 + 0.433245i \(0.857369\pi\)
\(830\) 6755.91 38314.6i 0.282531 1.60231i
\(831\) 23634.7 19831.9i 0.986616 0.827869i
\(832\) 2891.50 + 2426.25i 0.120486 + 0.101100i
\(833\) −31.7193 179.889i −0.00131934 0.00748233i
\(834\) −20571.7 7487.49i −0.854124 0.310876i
\(835\) −32463.8 −1.34545
\(836\) 1830.46 10496.5i 0.0757272 0.434244i
\(837\) −32046.7 −1.32341
\(838\) −2778.32 1011.22i −0.114529 0.0416852i
\(839\) 7433.41 + 42157.0i 0.305876 + 1.73471i 0.619354 + 0.785112i \(0.287395\pi\)
−0.313478 + 0.949596i \(0.601494\pi\)
\(840\) −14618.2 12266.1i −0.600446 0.503834i
\(841\) −14456.3 + 12130.3i −0.592738 + 0.497367i
\(842\) 2316.34 13136.6i 0.0948058 0.537670i
\(843\) 895.676 1551.36i 0.0365940 0.0633826i
\(844\) −1874.47 3246.68i −0.0764479 0.132412i
\(845\) 17229.3 6270.94i 0.701425 0.255298i
\(846\) −17.7265 + 6.45193i −0.000720391 + 0.000262201i
\(847\) −4766.05 8255.05i −0.193345 0.334884i
\(848\) −3105.79 + 5379.39i −0.125770 + 0.217841i
\(849\) 4060.86 23030.3i 0.164156 0.930973i
\(850\) 32.3280 27.1264i 0.00130452 0.00109462i
\(851\) −14104.7 11835.3i −0.568159 0.476742i
\(852\) 1907.19 + 10816.2i 0.0766894 + 0.434927i
\(853\) 4955.96 + 1803.82i 0.198932 + 0.0724052i 0.439565 0.898211i \(-0.355133\pi\)
−0.240633 + 0.970616i \(0.577355\pi\)
\(854\) −33485.1 −1.34173
\(855\) 62.0734 107.983i 0.00248288 0.00431922i
\(856\) 1141.16 0.0455655
\(857\) −20721.2 7541.92i −0.825933 0.300615i −0.105744 0.994393i \(-0.533722\pi\)
−0.720189 + 0.693778i \(0.755945\pi\)
\(858\) 3416.50 + 19375.9i 0.135941 + 0.770960i
\(859\) 3790.33 + 3180.46i 0.150552 + 0.126328i 0.714953 0.699173i \(-0.246448\pi\)
−0.564401 + 0.825501i \(0.690893\pi\)
\(860\) −2562.50 + 2150.20i −0.101605 + 0.0852571i
\(861\) 5544.06 31441.9i 0.219444 1.24453i
\(862\) 14962.8 25916.3i 0.591223 1.02403i
\(863\) −21066.6 36488.5i −0.830958 1.43926i −0.897279 0.441463i \(-0.854460\pi\)
0.0663214 0.997798i \(-0.478874\pi\)
\(864\) −4226.90 + 1538.47i −0.166438 + 0.0605783i
\(865\) −22059.3 + 8028.93i −0.867097 + 0.315597i
\(866\) 1844.16 + 3194.18i 0.0723638 + 0.125338i
\(867\) 12739.3 22065.1i 0.499019 0.864326i
\(868\) −5090.26 + 28868.3i −0.199049 + 1.12886i
\(869\) −12572.7 + 10549.8i −0.490795 + 0.411826i
\(870\) −8444.96 7086.16i −0.329093 0.276142i
\(871\) 673.909 + 3821.93i 0.0262165 + 0.148681i
\(872\) 13913.9 + 5064.24i 0.540348 + 0.196671i
\(873\) 176.889 0.00685772
\(874\) 13656.6 + 23551.5i 0.528535 + 0.911488i
\(875\) −20817.4 −0.804291
\(876\) −7501.59 2730.35i −0.289332 0.105308i
\(877\) 7270.07 + 41230.6i 0.279923 + 1.58752i 0.722875 + 0.690979i \(0.242820\pi\)
−0.442951 + 0.896546i \(0.646069\pi\)
\(878\) 10734.5 + 9007.30i 0.412610 + 0.346221i
\(879\) 3490.43 2928.82i 0.133935 0.112385i
\(880\) 1278.64 7251.55i 0.0489808 0.277784i
\(881\) 6256.58 10836.7i 0.239262 0.414414i −0.721241 0.692684i \(-0.756428\pi\)
0.960503 + 0.278271i \(0.0897612\pi\)
\(882\) −72.5532 125.666i −0.00276983 0.00479749i
\(883\) 7240.80 2635.44i 0.275960 0.100441i −0.200333 0.979728i \(-0.564202\pi\)
0.476293 + 0.879287i \(0.341980\pi\)
\(884\) 58.6613 21.3510i 0.00223189 0.000812343i
\(885\) 13853.5 + 23995.0i 0.526194 + 0.911395i
\(886\) −3550.07 + 6148.90i −0.134613 + 0.233156i
\(887\) 8776.45 49773.7i 0.332226 1.88415i −0.120844 0.992672i \(-0.538560\pi\)
0.453070 0.891475i \(-0.350329\pi\)
\(888\) −3560.33 + 2987.47i −0.134546 + 0.112897i
\(889\) 19464.6 + 16332.8i 0.734334 + 0.616179i
\(890\) 1485.94 + 8427.21i 0.0559651 + 0.317394i
\(891\) −21946.8 7987.97i −0.825190 0.300345i
\(892\) −1587.41 −0.0595858
\(893\) 6979.19 2555.09i 0.261534 0.0957478i
\(894\) −14681.9 −0.549256
\(895\) 30871.6 + 11236.4i 1.15299 + 0.419654i
\(896\) 714.484 + 4052.04i 0.0266398 + 0.151082i
\(897\) −38510.3 32314.0i −1.43347 1.20282i
\(898\) −12534.9 + 10518.0i −0.465806 + 0.390858i
\(899\) −2940.66 + 16677.3i −0.109095 + 0.618709i
\(900\) 16.7621 29.0329i 0.000620819 0.00107529i
\(901\) 51.3653 + 88.9673i 0.00189925 + 0.00328960i
\(902\) 11576.7 4213.57i 0.427341 0.155539i
\(903\) 9155.50 3332.33i 0.337404 0.122805i
\(904\) −2120.53 3672.86i −0.0780173 0.135130i
\(905\) 11526.5 19964.5i 0.423374 0.733305i
\(906\) −1400.83 + 7944.48i −0.0513679 + 0.291322i
\(907\) 30184.7 25328.0i 1.10503 0.927234i 0.107281 0.994229i \(-0.465786\pi\)
0.997753 + 0.0669950i \(0.0213412\pi\)
\(908\) 2008.13 + 1685.02i 0.0733943 + 0.0615852i
\(909\) 33.5029 + 190.005i 0.00122247 + 0.00693296i
\(910\) 50982.2 + 18556.0i 1.85719 + 0.675962i
\(911\) 17570.3 0.639001 0.319500 0.947586i \(-0.396485\pi\)
0.319500 + 0.947586i \(0.396485\pi\)
\(912\) 6453.17 2362.51i 0.234305 0.0857792i
\(913\) −43726.0 −1.58501
\(914\) 13187.5 + 4799.87i 0.477248 + 0.173704i
\(915\) 6711.45 + 38062.5i 0.242485 + 1.37520i
\(916\) −6001.77 5036.08i −0.216489 0.181656i
\(917\) −8497.42 + 7130.19i −0.306008 + 0.256772i
\(918\) −12.9182 + 73.2630i −0.000464451 + 0.00263403i
\(919\) 10307.7 17853.5i 0.369990 0.640842i −0.619573 0.784939i \(-0.712694\pi\)
0.989564 + 0.144097i \(0.0460277\pi\)
\(920\) 9407.21 + 16293.8i 0.337116 + 0.583902i
\(921\) −20430.2 + 7436.00i −0.730944 + 0.266042i
\(922\) 15568.5 5666.49i 0.556098 0.202403i
\(923\) −15613.1 27042.6i −0.556782 0.964376i
\(924\) −10723.5 + 18573.6i −0.381792 + 0.661284i
\(925\) 1551.17 8797.11i 0.0551374 0.312700i
\(926\) −24268.9 + 20364.0i −0.861258 + 0.722681i
\(927\) −112.581 94.4663i −0.00398882 0.00334701i
\(928\) 412.760 + 2340.88i 0.0146007 + 0.0828050i
\(929\) 39850.0 + 14504.2i 1.40736 + 0.512236i 0.930353 0.366664i \(-0.119500\pi\)
0.477005 + 0.878901i \(0.341722\pi\)
\(930\) 33834.8 1.19300
\(931\) 28677.9 + 49456.6i 1.00954 + 1.74100i
\(932\) −16860.3 −0.592572
\(933\) 46833.9 + 17046.2i 1.64338 + 0.598142i
\(934\) −4829.03 27386.8i −0.169176 0.959446i
\(935\) −93.2891 78.2788i −0.00326297 0.00273796i
\(936\) 37.9886 31.8762i 0.00132660 0.00111315i
\(937\) −196.515 + 1114.49i −0.00685152 + 0.0388569i −0.988042 0.154186i \(-0.950725\pi\)
0.981190 + 0.193043i \(0.0618356\pi\)
\(938\) −2115.22 + 3663.66i −0.0736293 + 0.127530i
\(939\) 7210.01 + 12488.1i 0.250575 + 0.434009i
\(940\) 4826.52 1756.71i 0.167472 0.0609549i
\(941\) −13074.0 + 4758.55i −0.452923 + 0.164850i −0.558401 0.829571i \(-0.688585\pi\)
0.105478 + 0.994422i \(0.466363\pi\)
\(942\) 18700.1 + 32389.6i 0.646797 + 1.12029i
\(943\) −15739.1 + 27260.9i −0.543516 + 0.941397i
\(944\) 1037.40 5883.36i 0.0357673 0.202847i
\(945\) −49528.4 + 41559.2i −1.70493 + 1.43061i
\(946\) 2879.99 + 2416.60i 0.0989815 + 0.0830553i
\(947\) −5658.41 32090.4i −0.194164 1.10116i −0.913604 0.406605i \(-0.866712\pi\)
0.719440 0.694555i \(-0.244399\pi\)
\(948\) −9947.15 3620.47i −0.340790 0.124037i
\(949\) 22696.6 0.776357
\(950\) −6582.50 + 11450.9i −0.224805 + 0.391070i
\(951\) 2572.81 0.0877276
\(952\) 63.9448 + 23.2740i 0.00217696 + 0.000792348i
\(953\) 3139.13 + 17802.9i 0.106701 + 0.605133i 0.990527 + 0.137317i \(0.0438479\pi\)
−0.883826 + 0.467816i \(0.845041\pi\)
\(954\) 62.5154 + 52.4567i 0.00212161 + 0.00178024i
\(955\) 11840.3 9935.20i 0.401197 0.336645i
\(956\) −3777.82 + 21425.1i −0.127807 + 0.724830i
\(957\) −6194.98 + 10730.0i −0.209253 + 0.362437i
\(958\) −9094.71 15752.5i −0.306719 0.531253i
\(959\) −24998.7 + 9098.80i −0.841764 + 0.306377i
\(960\) 4462.75 1624.31i 0.150036 0.0546086i
\(961\) −11092.0 19212.0i −0.372328 0.644891i
\(962\) 6606.93 11443.5i 0.221430 0.383528i
\(963\) 2.60344 14.7649i 8.71182e−5 0.000494072i
\(964\) 10343.4 8679.11i 0.345578 0.289974i
\(965\) 6369.14 + 5344.34i 0.212466 + 0.178280i
\(966\) −9515.84 53967.0i −0.316943 1.79747i
\(967\) −17380.3 6325.92i −0.577987 0.210370i 0.0364508 0.999335i \(-0.488395\pi\)
−0.614437 + 0.788966i \(0.710617\pi\)
\(968\) 2372.28 0.0787687
\(969\) 19.5252 111.964i 0.000647307 0.00371186i
\(970\) −48162.8 −1.59424
\(971\) −29529.0 10747.7i −0.975932 0.355210i −0.195675 0.980669i \(-0.562690\pi\)
−0.780257 + 0.625459i \(0.784912\pi\)
\(972\) 20.4845 + 116.173i 0.000675966 + 0.00383360i
\(973\) 51974.0 + 43611.3i 1.71244 + 1.43691i
\(974\) −20038.9 + 16814.6i −0.659228 + 0.553158i
\(975\) 4235.18 24018.9i 0.139112 0.788944i
\(976\) 4166.77 7217.06i 0.136655 0.236693i
\(977\) −17958.7 31105.3i −0.588074 1.01857i −0.994485 0.104883i \(-0.966553\pi\)
0.406411 0.913691i \(-0.366780\pi\)
\(978\) −23627.9 + 8599.85i −0.772533 + 0.281179i
\(979\) 9037.41 3289.35i 0.295033 0.107383i
\(980\) 19754.6 + 34215.9i 0.643914 + 1.11529i
\(981\) 97.2666 168.471i 0.00316563 0.00548303i
\(982\) −3197.32 + 18132.9i −0.103901 + 0.589250i
\(983\) 11539.0 9682.36i 0.374401 0.314160i −0.436098 0.899899i \(-0.643640\pi\)
0.810500 + 0.585739i \(0.199196\pi\)
\(984\) 6086.80 + 5107.43i 0.197195 + 0.165467i
\(985\) 3688.55 + 20918.8i 0.119317 + 0.676679i
\(986\) 36.9411 + 13.4455i 0.00119315 + 0.000434271i
\(987\) −14960.1 −0.482457
\(988\) −14943.3 + 12586.9i −0.481184 + 0.405306i
\(989\) −9606.13 −0.308854
\(990\) −90.9068 33.0874i −0.00291839 0.00106221i
\(991\) 382.946 + 2171.79i 0.0122752 + 0.0696159i 0.990330 0.138732i \(-0.0443026\pi\)
−0.978055 + 0.208348i \(0.933191\pi\)
\(992\) −5588.58 4689.37i −0.178869 0.150089i
\(993\) −14735.0 + 12364.2i −0.470899 + 0.395131i
\(994\) 5910.74 33521.5i 0.188609 1.06965i
\(995\) 6613.06 11454.2i 0.210702 0.364946i
\(996\) −14100.9 24423.5i −0.448598 0.776995i
\(997\) 36116.0 13145.2i 1.14725 0.417564i 0.302722 0.953079i \(-0.402105\pi\)
0.844526 + 0.535515i \(0.179882\pi\)
\(998\) 6948.92 2529.20i 0.220405 0.0802209i
\(999\) 7873.48 + 13637.3i 0.249355 + 0.431896i
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 38.4.e.b.23.3 yes 18
19.5 even 9 inner 38.4.e.b.5.3 18
19.9 even 9 722.4.a.t.1.8 9
19.10 odd 18 722.4.a.u.1.2 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.4.e.b.5.3 18 19.5 even 9 inner
38.4.e.b.23.3 yes 18 1.1 even 1 trivial
722.4.a.t.1.8 9 19.9 even 9
722.4.a.u.1.2 9 19.10 odd 18