Properties

Label 45.4.j.a.34.1
Level $45$
Weight $4$
Character 45.34
Analytic conductor $2.655$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,4,Mod(4,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.j (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.65508595026\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 34.1
Character \(\chi\) \(=\) 45.34
Dual form 45.4.j.a.4.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.37720 - 2.52718i) q^{2} +(5.16592 - 0.559681i) q^{3} +(8.77324 + 15.1957i) q^{4} +(-3.07459 + 10.7493i) q^{5} +(-24.0267 - 10.6054i) q^{6} +(18.1967 + 10.5059i) q^{7} -48.2513i q^{8} +(26.3735 - 5.78253i) q^{9} +O(q^{10})\) \(q+(-4.37720 - 2.52718i) q^{2} +(5.16592 - 0.559681i) q^{3} +(8.77324 + 15.1957i) q^{4} +(-3.07459 + 10.7493i) q^{5} +(-24.0267 - 10.6054i) q^{6} +(18.1967 + 10.5059i) q^{7} -48.2513i q^{8} +(26.3735 - 5.78253i) q^{9} +(40.6234 - 39.2817i) q^{10} +(14.2815 - 24.7362i) q^{11} +(53.8266 + 73.5896i) q^{12} +(-8.72122 + 5.03520i) q^{13} +(-53.1003 - 91.9724i) q^{14} +(-9.86691 + 57.2507i) q^{15} +(-51.7535 + 89.6398i) q^{16} +82.7541i q^{17} +(-130.056 - 41.3392i) q^{18} -1.91981 q^{19} +(-190.317 + 47.5855i) q^{20} +(99.8826 + 44.0881i) q^{21} +(-125.026 + 72.1836i) q^{22} +(147.712 - 85.2818i) q^{23} +(-27.0053 - 249.262i) q^{24} +(-106.094 - 66.0991i) q^{25} +50.8993 q^{26} +(133.007 - 44.6329i) q^{27} +368.682i q^{28} +(-128.214 + 222.074i) q^{29} +(187.872 - 225.662i) q^{30} +(-24.0262 - 41.6147i) q^{31} +(118.776 - 68.5756i) q^{32} +(59.9326 - 135.779i) q^{33} +(209.134 - 362.231i) q^{34} +(-168.878 + 163.300i) q^{35} +(319.251 + 350.032i) q^{36} -161.834i q^{37} +(8.40337 + 4.85169i) q^{38} +(-42.2350 + 30.8925i) q^{39} +(518.666 + 148.353i) q^{40} +(-139.674 - 241.922i) q^{41} +(-325.787 - 445.403i) q^{42} +(-233.024 - 134.536i) q^{43} +501.179 q^{44} +(-18.9296 + 301.275i) q^{45} -862.088 q^{46} +(-8.30380 - 4.79420i) q^{47} +(-217.185 + 492.038i) q^{48} +(49.2462 + 85.2969i) q^{49} +(297.349 + 557.447i) q^{50} +(46.3158 + 427.501i) q^{51} +(-153.027 - 88.3500i) q^{52} +35.7716i q^{53} +(-694.994 - 140.766i) q^{54} +(221.987 + 229.569i) q^{55} +(506.921 - 878.013i) q^{56} +(-9.91757 + 1.07448i) q^{57} +(1122.44 - 648.040i) q^{58} +(-281.385 - 487.374i) q^{59} +(-956.529 + 352.340i) q^{60} +(39.6621 - 68.6968i) q^{61} +242.874i q^{62} +(540.661 + 171.854i) q^{63} +134.846 q^{64} +(-27.3106 - 109.228i) q^{65} +(-605.473 + 442.869i) q^{66} +(-404.219 + 233.376i) q^{67} +(-1257.51 + 726.021i) q^{68} +(715.340 - 523.231i) q^{69} +(1151.90 - 288.013i) q^{70} +316.854 q^{71} +(-279.015 - 1272.56i) q^{72} -633.515i q^{73} +(-408.984 + 708.381i) q^{74} +(-585.067 - 282.084i) q^{75} +(-16.8429 - 29.1728i) q^{76} +(519.751 - 300.078i) q^{77} +(262.942 - 28.4874i) q^{78} +(-395.658 + 685.299i) q^{79} +(-804.442 - 831.918i) q^{80} +(662.125 - 305.011i) q^{81} +1411.92i q^{82} +(-197.521 - 114.039i) q^{83} +(206.344 + 1904.58i) q^{84} +(-889.546 - 254.435i) q^{85} +(679.994 + 1177.78i) q^{86} +(-538.054 + 1218.97i) q^{87} +(-1193.55 - 689.099i) q^{88} -53.9091 q^{89} +(844.234 - 1270.90i) q^{90} -211.596 q^{91} +(2591.83 + 1496.39i) q^{92} +(-147.409 - 201.531i) q^{93} +(24.2316 + 41.9704i) q^{94} +(5.90261 - 20.6365i) q^{95} +(575.209 - 420.733i) q^{96} +(-83.7394 - 48.3470i) q^{97} -497.815i q^{98} +(233.614 - 734.964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 54 q^{4} + 3 q^{5} - 12 q^{6} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 54 q^{4} + 3 q^{5} - 12 q^{6} - 18 q^{9} - 20 q^{10} + 90 q^{11} - 102 q^{14} - 87 q^{15} - 146 q^{16} - 8 q^{19} - 6 q^{20} + 30 q^{21} + 462 q^{24} + 71 q^{25} - 936 q^{26} - 516 q^{29} - 66 q^{30} - 38 q^{31} + 212 q^{34} - 534 q^{35} + 864 q^{36} + 330 q^{39} + 44 q^{40} + 576 q^{41} + 3288 q^{44} + 1053 q^{45} - 580 q^{46} - 4 q^{49} + 558 q^{50} + 1260 q^{51} - 3726 q^{54} + 30 q^{55} + 2430 q^{56} - 2202 q^{59} - 5052 q^{60} - 20 q^{61} + 644 q^{64} + 339 q^{65} - 5052 q^{66} + 1452 q^{69} + 636 q^{70} - 5904 q^{71} - 4080 q^{74} + 2283 q^{75} + 396 q^{76} - 218 q^{79} + 2532 q^{80} + 198 q^{81} + 4662 q^{84} - 704 q^{85} + 6108 q^{86} + 8148 q^{89} + 6408 q^{90} - 1884 q^{91} - 1078 q^{94} - 1692 q^{95} + 11874 q^{96} - 1602 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.37720 2.52718i −1.54757 0.893492i −0.998326 0.0578315i \(-0.981581\pi\)
−0.549247 0.835660i \(-0.685085\pi\)
\(3\) 5.16592 0.559681i 0.994182 0.107711i
\(4\) 8.77324 + 15.1957i 1.09665 + 1.89946i
\(5\) −3.07459 + 10.7493i −0.274999 + 0.961444i
\(6\) −24.0267 10.6054i −1.63481 0.721604i
\(7\) 18.1967 + 10.5059i 0.982529 + 0.567263i 0.903033 0.429572i \(-0.141336\pi\)
0.0794959 + 0.996835i \(0.474669\pi\)
\(8\) 48.2513i 2.13243i
\(9\) 26.3735 5.78253i 0.976797 0.214168i
\(10\) 40.6234 39.2817i 1.28462 1.24220i
\(11\) 14.2815 24.7362i 0.391457 0.678023i −0.601185 0.799110i \(-0.705305\pi\)
0.992642 + 0.121087i \(0.0386379\pi\)
\(12\) 53.8266 + 73.5896i 1.29487 + 1.77029i
\(13\) −8.72122 + 5.03520i −0.186064 + 0.107424i −0.590139 0.807302i \(-0.700927\pi\)
0.404075 + 0.914726i \(0.367594\pi\)
\(14\) −53.1003 91.9724i −1.01369 1.75576i
\(15\) −9.86691 + 57.2507i −0.169842 + 0.985471i
\(16\) −51.7535 + 89.6398i −0.808649 + 1.40062i
\(17\) 82.7541i 1.18064i 0.807171 + 0.590318i \(0.200998\pi\)
−0.807171 + 0.590318i \(0.799002\pi\)
\(18\) −130.056 41.3392i −1.70302 0.541319i
\(19\) −1.91981 −0.0231807 −0.0115904 0.999933i \(-0.503689\pi\)
−0.0115904 + 0.999933i \(0.503689\pi\)
\(20\) −190.317 + 47.5855i −2.12781 + 0.532022i
\(21\) 99.8826 + 44.0881i 1.03791 + 0.458134i
\(22\) −125.026 + 72.1836i −1.21162 + 0.699527i
\(23\) 147.712 85.2818i 1.33914 0.773151i 0.352458 0.935828i \(-0.385346\pi\)
0.986679 + 0.162677i \(0.0520127\pi\)
\(24\) −27.0053 249.262i −0.229685 2.12002i
\(25\) −106.094 66.0991i −0.848751 0.528793i
\(26\) 50.8993 0.383930
\(27\) 133.007 44.6329i 0.948046 0.318133i
\(28\) 368.682i 2.48837i
\(29\) −128.214 + 222.074i −0.820993 + 1.42200i 0.0839514 + 0.996470i \(0.473246\pi\)
−0.904944 + 0.425531i \(0.860087\pi\)
\(30\) 187.872 225.662i 1.14335 1.37334i
\(31\) −24.0262 41.6147i −0.139201 0.241104i 0.787993 0.615684i \(-0.211120\pi\)
−0.927195 + 0.374580i \(0.877787\pi\)
\(32\) 118.776 68.5756i 0.656153 0.378830i
\(33\) 59.9326 135.779i 0.316149 0.716243i
\(34\) 209.134 362.231i 1.05489 1.82712i
\(35\) −168.878 + 163.300i −0.815587 + 0.788650i
\(36\) 319.251 + 350.032i 1.47801 + 1.62052i
\(37\) 161.834i 0.719065i −0.933132 0.359533i \(-0.882936\pi\)
0.933132 0.359533i \(-0.117064\pi\)
\(38\) 8.40337 + 4.85169i 0.0358739 + 0.0207118i
\(39\) −42.2350 + 30.8925i −0.173411 + 0.126840i
\(40\) 518.666 + 148.353i 2.05021 + 0.586416i
\(41\) −139.674 241.922i −0.532034 0.921510i −0.999301 0.0373937i \(-0.988094\pi\)
0.467266 0.884117i \(-0.345239\pi\)
\(42\) −325.787 445.403i −1.19691 1.63636i
\(43\) −233.024 134.536i −0.826414 0.477130i 0.0262093 0.999656i \(-0.491656\pi\)
−0.852623 + 0.522526i \(0.824990\pi\)
\(44\) 501.179 1.71717
\(45\) −18.9296 + 301.275i −0.0627080 + 0.998032i
\(46\) −862.088 −2.76322
\(47\) −8.30380 4.79420i −0.0257709 0.0148789i 0.487059 0.873369i \(-0.338070\pi\)
−0.512830 + 0.858490i \(0.671403\pi\)
\(48\) −217.185 + 492.038i −0.653083 + 1.47957i
\(49\) 49.2462 + 85.2969i 0.143575 + 0.248679i
\(50\) 297.349 + 557.447i 0.841031 + 1.57670i
\(51\) 46.3158 + 427.501i 0.127167 + 1.17377i
\(52\) −153.027 88.3500i −0.408096 0.235614i
\(53\) 35.7716i 0.0927095i 0.998925 + 0.0463547i \(0.0147605\pi\)
−0.998925 + 0.0463547i \(0.985240\pi\)
\(54\) −694.994 140.766i −1.75142 0.354737i
\(55\) 221.987 + 229.569i 0.544231 + 0.562820i
\(56\) 506.921 878.013i 1.20965 2.09517i
\(57\) −9.91757 + 1.07448i −0.0230459 + 0.00249681i
\(58\) 1122.44 648.040i 2.54109 1.46710i
\(59\) −281.385 487.374i −0.620903 1.07544i −0.989318 0.145774i \(-0.953433\pi\)
0.368415 0.929661i \(-0.379900\pi\)
\(60\) −956.529 + 352.340i −2.05812 + 0.758114i
\(61\) 39.6621 68.6968i 0.0832494 0.144192i −0.821395 0.570360i \(-0.806804\pi\)
0.904644 + 0.426168i \(0.140137\pi\)
\(62\) 242.874i 0.497501i
\(63\) 540.661 + 171.854i 1.08122 + 0.343675i
\(64\) 134.846 0.263372
\(65\) −27.3106 109.228i −0.0521148 0.208432i
\(66\) −605.473 + 442.869i −1.12922 + 0.825961i
\(67\) −404.219 + 233.376i −0.737063 + 0.425544i −0.821001 0.570927i \(-0.806584\pi\)
0.0839374 + 0.996471i \(0.473250\pi\)
\(68\) −1257.51 + 726.021i −2.24257 + 1.29475i
\(69\) 715.340 523.231i 1.24807 0.912892i
\(70\) 1151.90 288.013i 1.96683 0.491773i
\(71\) 316.854 0.529628 0.264814 0.964299i \(-0.414689\pi\)
0.264814 + 0.964299i \(0.414689\pi\)
\(72\) −279.015 1272.56i −0.456697 2.08295i
\(73\) 633.515i 1.01572i −0.861440 0.507859i \(-0.830437\pi\)
0.861440 0.507859i \(-0.169563\pi\)
\(74\) −408.984 + 708.381i −0.642479 + 1.11281i
\(75\) −585.067 282.084i −0.900770 0.434297i
\(76\) −16.8429 29.1728i −0.0254213 0.0440309i
\(77\) 519.751 300.078i 0.769235 0.444118i
\(78\) 262.942 28.4874i 0.381696 0.0413533i
\(79\) −395.658 + 685.299i −0.563481 + 0.975977i 0.433709 + 0.901053i \(0.357205\pi\)
−0.997189 + 0.0749238i \(0.976129\pi\)
\(80\) −804.442 831.918i −1.12424 1.16264i
\(81\) 662.125 305.011i 0.908264 0.418397i
\(82\) 1411.92i 1.90147i
\(83\) −197.521 114.039i −0.261214 0.150812i 0.363674 0.931526i \(-0.381522\pi\)
−0.624888 + 0.780714i \(0.714855\pi\)
\(84\) 206.344 + 1904.58i 0.268024 + 2.47389i
\(85\) −889.546 254.435i −1.13512 0.324674i
\(86\) 679.994 + 1177.78i 0.852624 + 1.47679i
\(87\) −538.054 + 1218.97i −0.663052 + 1.50216i
\(88\) −1193.55 689.099i −1.44583 0.834752i
\(89\) −53.9091 −0.0642062 −0.0321031 0.999485i \(-0.510220\pi\)
−0.0321031 + 0.999485i \(0.510220\pi\)
\(90\) 844.234 1270.90i 0.988778 1.48850i
\(91\) −211.596 −0.243751
\(92\) 2591.83 + 1496.39i 2.93714 + 1.69576i
\(93\) −147.409 201.531i −0.164361 0.224708i
\(94\) 24.2316 + 41.9704i 0.0265883 + 0.0460522i
\(95\) 5.90261 20.6365i 0.00637469 0.0222870i
\(96\) 575.209 420.733i 0.611532 0.447301i
\(97\) −83.7394 48.3470i −0.0876541 0.0506071i 0.455532 0.890219i \(-0.349449\pi\)
−0.543186 + 0.839612i \(0.682782\pi\)
\(98\) 497.815i 0.513132i
\(99\) 233.614 734.964i 0.237163 0.746128i
\(100\) 73.6360 2192.07i 0.0736360 2.19207i
\(101\) 541.711 938.271i 0.533686 0.924371i −0.465540 0.885027i \(-0.654140\pi\)
0.999226 0.0393438i \(-0.0125267\pi\)
\(102\) 877.637 1988.31i 0.851951 1.93011i
\(103\) 372.670 215.161i 0.356507 0.205830i −0.311040 0.950397i \(-0.600677\pi\)
0.667548 + 0.744567i \(0.267344\pi\)
\(104\) 242.955 + 420.810i 0.229074 + 0.396767i
\(105\) −781.013 + 938.113i −0.725896 + 0.871909i
\(106\) 90.4010 156.579i 0.0828351 0.143475i
\(107\) 12.9348i 0.0116865i −0.999983 0.00584323i \(-0.998140\pi\)
0.999983 0.00584323i \(-0.00185997\pi\)
\(108\) 1845.13 + 1629.56i 1.64396 + 1.45189i
\(109\) 20.1087 0.0176703 0.00883517 0.999961i \(-0.497188\pi\)
0.00883517 + 0.999961i \(0.497188\pi\)
\(110\) −391.519 1565.87i −0.339363 1.35727i
\(111\) −90.5756 836.024i −0.0774510 0.714882i
\(112\) −1883.49 + 1087.43i −1.58904 + 0.917434i
\(113\) 979.163 565.320i 0.815150 0.470627i −0.0335912 0.999436i \(-0.510694\pi\)
0.848741 + 0.528809i \(0.177361\pi\)
\(114\) 46.1266 + 20.3602i 0.0378960 + 0.0167273i
\(115\) 462.563 + 1850.01i 0.375080 + 1.50012i
\(116\) −4499.42 −3.60138
\(117\) −200.893 + 183.227i −0.158740 + 0.144780i
\(118\) 2844.44i 2.21909i
\(119\) −869.403 + 1505.85i −0.669731 + 1.16001i
\(120\) 2762.42 + 476.091i 2.10144 + 0.362175i
\(121\) 257.579 + 446.140i 0.193523 + 0.335192i
\(122\) −347.218 + 200.466i −0.257669 + 0.148765i
\(123\) −856.944 1171.58i −0.628195 0.858843i
\(124\) 421.576 730.191i 0.305312 0.528815i
\(125\) 1036.71 937.204i 0.741811 0.670609i
\(126\) −1932.28 2118.58i −1.36620 1.49792i
\(127\) 277.149i 0.193646i 0.995302 + 0.0968228i \(0.0308680\pi\)
−0.995302 + 0.0968228i \(0.969132\pi\)
\(128\) −1540.46 889.385i −1.06374 0.614151i
\(129\) −1279.08 564.586i −0.872998 0.385341i
\(130\) −156.494 + 547.131i −0.105581 + 0.369127i
\(131\) 251.299 + 435.263i 0.167604 + 0.290299i 0.937577 0.347778i \(-0.113064\pi\)
−0.769973 + 0.638077i \(0.779730\pi\)
\(132\) 2589.05 280.500i 1.70718 0.184958i
\(133\) −34.9341 20.1692i −0.0227757 0.0131496i
\(134\) 2359.13 1.52088
\(135\) 70.8290 + 1566.96i 0.0451555 + 0.998980i
\(136\) 3992.99 2.51762
\(137\) −1923.55 1110.56i −1.19956 0.692566i −0.239103 0.970994i \(-0.576853\pi\)
−0.960457 + 0.278428i \(0.910187\pi\)
\(138\) −4453.48 + 482.494i −2.74714 + 0.297628i
\(139\) 1316.39 + 2280.06i 0.803273 + 1.39131i 0.917451 + 0.397850i \(0.130244\pi\)
−0.114177 + 0.993460i \(0.536423\pi\)
\(140\) −3963.06 1133.54i −2.39243 0.684299i
\(141\) −45.5800 20.1190i −0.0272236 0.0120165i
\(142\) −1386.93 800.745i −0.819638 0.473218i
\(143\) 287.640i 0.168208i
\(144\) −846.578 + 2663.38i −0.489918 + 1.54131i
\(145\) −1992.92 2060.99i −1.14140 1.18039i
\(146\) −1601.00 + 2773.02i −0.907535 + 1.57190i
\(147\) 302.141 + 413.075i 0.169525 + 0.231768i
\(148\) 2459.19 1419.81i 1.36584 0.788567i
\(149\) −1282.86 2221.97i −0.705340 1.22169i −0.966569 0.256408i \(-0.917461\pi\)
0.261228 0.965277i \(-0.415872\pi\)
\(150\) 1848.08 + 2713.31i 1.00597 + 1.47694i
\(151\) 752.244 1302.93i 0.405409 0.702189i −0.588960 0.808162i \(-0.700462\pi\)
0.994369 + 0.105973i \(0.0337957\pi\)
\(152\) 92.6331i 0.0494312i
\(153\) 478.528 + 2182.52i 0.252854 + 1.15324i
\(154\) −3033.40 −1.58726
\(155\) 521.198 130.317i 0.270088 0.0675309i
\(156\) −839.972 370.763i −0.431100 0.190287i
\(157\) 1037.66 599.094i 0.527481 0.304541i −0.212509 0.977159i \(-0.568164\pi\)
0.739990 + 0.672618i \(0.234830\pi\)
\(158\) 3463.74 1999.79i 1.74405 1.00693i
\(159\) 20.0206 + 184.793i 0.00998579 + 0.0921701i
\(160\) 371.950 + 1487.60i 0.183782 + 0.735033i
\(161\) 3583.83 1.75432
\(162\) −3669.07 338.210i −1.77944 0.164026i
\(163\) 2204.91i 1.05952i 0.848148 + 0.529760i \(0.177718\pi\)
−0.848148 + 0.529760i \(0.822282\pi\)
\(164\) 2450.79 4244.88i 1.16692 2.02116i
\(165\) 1275.25 + 1061.69i 0.601687 + 0.500926i
\(166\) 576.392 + 998.341i 0.269498 + 0.466785i
\(167\) 980.439 566.057i 0.454303 0.262292i −0.255343 0.966851i \(-0.582188\pi\)
0.709646 + 0.704558i \(0.248855\pi\)
\(168\) 2127.31 4819.46i 0.976937 2.21327i
\(169\) −1047.79 + 1814.83i −0.476920 + 0.826050i
\(170\) 3250.72 + 3361.75i 1.46658 + 1.51667i
\(171\) −50.6320 + 11.1013i −0.0226429 + 0.00496457i
\(172\) 4721.28i 2.09299i
\(173\) 1605.61 + 926.998i 0.705619 + 0.407389i 0.809437 0.587207i \(-0.199773\pi\)
−0.103818 + 0.994596i \(0.533106\pi\)
\(174\) 5435.73 3975.93i 2.36829 1.73227i
\(175\) −1236.13 2317.39i −0.533957 1.00102i
\(176\) 1478.23 + 2560.38i 0.633102 + 1.09657i
\(177\) −1726.39 2360.25i −0.733126 1.00230i
\(178\) 235.971 + 136.238i 0.0993638 + 0.0573677i
\(179\) −3205.81 −1.33862 −0.669312 0.742981i \(-0.733411\pi\)
−0.669312 + 0.742981i \(0.733411\pi\)
\(180\) −4744.16 + 2355.51i −1.96449 + 0.975385i
\(181\) 2278.79 0.935806 0.467903 0.883780i \(-0.345010\pi\)
0.467903 + 0.883780i \(0.345010\pi\)
\(182\) 926.199 + 534.741i 0.377222 + 0.217789i
\(183\) 166.443 377.080i 0.0672341 0.152320i
\(184\) −4114.95 7127.31i −1.64869 2.85561i
\(185\) 1739.60 + 497.574i 0.691341 + 0.197743i
\(186\) 135.932 + 1254.67i 0.0535861 + 0.494607i
\(187\) 2047.02 + 1181.85i 0.800498 + 0.462168i
\(188\) 168.243i 0.0652679i
\(189\) 2889.20 + 585.185i 1.11195 + 0.225216i
\(190\) −77.9890 + 75.4132i −0.0297785 + 0.0287950i
\(191\) −1694.33 + 2934.66i −0.641870 + 1.11175i 0.343145 + 0.939282i \(0.388508\pi\)
−0.985015 + 0.172469i \(0.944826\pi\)
\(192\) 696.606 75.4709i 0.261840 0.0283679i
\(193\) −2406.01 + 1389.11i −0.897349 + 0.518085i −0.876339 0.481695i \(-0.840021\pi\)
−0.0210098 + 0.999779i \(0.506688\pi\)
\(194\) 244.363 + 423.249i 0.0904341 + 0.156636i
\(195\) −202.217 548.978i −0.0742619 0.201606i
\(196\) −864.097 + 1496.66i −0.314904 + 0.545430i
\(197\) 2941.71i 1.06390i 0.846776 + 0.531950i \(0.178541\pi\)
−0.846776 + 0.531950i \(0.821459\pi\)
\(198\) −2879.96 + 2626.70i −1.03369 + 0.942785i
\(199\) 4929.28 1.75592 0.877959 0.478737i \(-0.158905\pi\)
0.877959 + 0.478737i \(0.158905\pi\)
\(200\) −3189.37 + 5119.16i −1.12761 + 1.80990i
\(201\) −1957.55 + 1431.84i −0.686940 + 0.502457i
\(202\) −4742.35 + 2738.00i −1.65183 + 0.953687i
\(203\) −4666.15 + 2694.00i −1.61330 + 0.931438i
\(204\) −6089.84 + 4454.37i −2.09007 + 1.52877i
\(205\) 3029.93 757.582i 1.03229 0.258107i
\(206\) −2175.00 −0.735628
\(207\) 3402.55 3103.33i 1.14248 1.04201i
\(208\) 1042.36i 0.347474i
\(209\) −27.4177 + 47.4888i −0.00907425 + 0.0157171i
\(210\) 5789.42 2132.55i 1.90242 0.700761i
\(211\) −2709.25 4692.57i −0.883947 1.53104i −0.846916 0.531727i \(-0.821543\pi\)
−0.0370311 0.999314i \(-0.511790\pi\)
\(212\) −543.574 + 313.832i −0.176098 + 0.101670i
\(213\) 1636.84 177.337i 0.526547 0.0570466i
\(214\) −32.6884 + 56.6180i −0.0104417 + 0.0180856i
\(215\) 2162.62 2091.19i 0.685998 0.663341i
\(216\) −2153.59 6417.76i −0.678395 2.02164i
\(217\) 1009.67i 0.315855i
\(218\) −88.0199 50.8183i −0.0273461 0.0157883i
\(219\) −354.566 3272.69i −0.109403 1.00981i
\(220\) −1540.92 + 5387.31i −0.472221 + 1.65097i
\(221\) −416.683 721.716i −0.126829 0.219674i
\(222\) −1716.31 + 3888.34i −0.518880 + 1.17553i
\(223\) −3537.15 2042.18i −1.06218 0.613248i −0.136143 0.990689i \(-0.543471\pi\)
−0.926033 + 0.377442i \(0.876804\pi\)
\(224\) 2881.78 0.859586
\(225\) −3180.29 1129.78i −0.942308 0.334748i
\(226\) −5714.65 −1.68201
\(227\) −192.110 110.915i −0.0561708 0.0324302i 0.471652 0.881785i \(-0.343658\pi\)
−0.527822 + 0.849355i \(0.676991\pi\)
\(228\) −103.337 141.278i −0.0300160 0.0410366i
\(229\) −799.037 1383.97i −0.230576 0.399369i 0.727402 0.686212i \(-0.240728\pi\)
−0.957978 + 0.286843i \(0.907394\pi\)
\(230\) 2650.56 9266.82i 0.759883 2.65668i
\(231\) 2517.04 1841.08i 0.716924 0.524389i
\(232\) 10715.3 + 6186.50i 3.03231 + 1.75071i
\(233\) 6620.40i 1.86144i 0.365727 + 0.930722i \(0.380820\pi\)
−0.365727 + 0.930722i \(0.619180\pi\)
\(234\) 1342.39 294.327i 0.375022 0.0822255i
\(235\) 77.0650 74.5197i 0.0213922 0.0206857i
\(236\) 4937.32 8551.69i 1.36183 2.35876i
\(237\) −1660.39 + 3761.64i −0.455079 + 1.03099i
\(238\) 7611.09 4394.27i 2.07292 1.19680i
\(239\) 1778.60 + 3080.62i 0.481372 + 0.833761i 0.999771 0.0213776i \(-0.00680523\pi\)
−0.518399 + 0.855139i \(0.673472\pi\)
\(240\) −4621.29 3847.40i −1.24293 1.03478i
\(241\) −1483.67 + 2569.79i −0.396563 + 0.686867i −0.993299 0.115570i \(-0.963131\pi\)
0.596736 + 0.802437i \(0.296464\pi\)
\(242\) 2603.79i 0.691645i
\(243\) 3249.78 1946.24i 0.857914 0.513793i
\(244\) 1391.86 0.365183
\(245\) −1068.29 + 267.108i −0.278574 + 0.0696527i
\(246\) 790.226 + 7293.88i 0.204809 + 1.89041i
\(247\) 16.7431 9.66661i 0.00431310 0.00249017i
\(248\) −2007.96 + 1159.30i −0.514136 + 0.296836i
\(249\) −1084.20 478.567i −0.275938 0.121799i
\(250\) −6906.38 + 1482.37i −1.74719 + 0.375014i
\(251\) −903.562 −0.227220 −0.113610 0.993525i \(-0.536241\pi\)
−0.113610 + 0.993525i \(0.536241\pi\)
\(252\) 2131.91 + 9723.43i 0.532928 + 2.43063i
\(253\) 4871.79i 1.21062i
\(254\) 700.404 1213.14i 0.173021 0.299681i
\(255\) −4737.73 816.527i −1.16348 0.200521i
\(256\) 3955.88 + 6851.79i 0.965791 + 1.67280i
\(257\) 1285.61 742.247i 0.312039 0.180156i −0.335799 0.941934i \(-0.609006\pi\)
0.647839 + 0.761778i \(0.275673\pi\)
\(258\) 4171.98 + 5703.76i 1.00673 + 1.37636i
\(259\) 1700.21 2944.85i 0.407899 0.706502i
\(260\) 1420.19 1373.29i 0.338756 0.327568i
\(261\) −2097.31 + 6598.26i −0.497396 + 1.56484i
\(262\) 2540.31i 0.599011i
\(263\) −2352.69 1358.33i −0.551609 0.318472i 0.198162 0.980169i \(-0.436503\pi\)
−0.749771 + 0.661698i \(0.769836\pi\)
\(264\) −6551.49 2891.82i −1.52733 0.674164i
\(265\) −384.518 109.983i −0.0891350 0.0254950i
\(266\) 101.942 + 176.569i 0.0234981 + 0.0406998i
\(267\) −278.490 + 30.1719i −0.0638327 + 0.00691569i
\(268\) −7092.62 4094.93i −1.61661 0.933349i
\(269\) −7492.51 −1.69824 −0.849120 0.528201i \(-0.822867\pi\)
−0.849120 + 0.528201i \(0.822867\pi\)
\(270\) 3649.95 7037.88i 0.822699 1.58634i
\(271\) 2013.02 0.451226 0.225613 0.974217i \(-0.427561\pi\)
0.225613 + 0.974217i \(0.427561\pi\)
\(272\) −7418.06 4282.82i −1.65362 0.954720i
\(273\) −1093.09 + 118.426i −0.242333 + 0.0262545i
\(274\) 5613.16 + 9722.28i 1.23760 + 2.14359i
\(275\) −3150.22 + 1680.37i −0.690783 + 0.368473i
\(276\) 14226.7 + 6279.66i 3.10271 + 1.36953i
\(277\) −3092.55 1785.48i −0.670806 0.387290i 0.125576 0.992084i \(-0.459922\pi\)
−0.796382 + 0.604794i \(0.793255\pi\)
\(278\) 13307.0i 2.87087i
\(279\) −874.295 958.593i −0.187608 0.205697i
\(280\) 7879.43 + 8148.56i 1.68174 + 1.73918i
\(281\) 3380.70 5855.54i 0.717707 1.24310i −0.244200 0.969725i \(-0.578525\pi\)
0.961906 0.273379i \(-0.0881415\pi\)
\(282\) 148.669 + 203.254i 0.0313939 + 0.0429205i
\(283\) −3474.74 + 2006.14i −0.729866 + 0.421388i −0.818373 0.574687i \(-0.805124\pi\)
0.0885075 + 0.996076i \(0.471790\pi\)
\(284\) 2779.83 + 4814.81i 0.580819 + 1.00601i
\(285\) 18.9426 109.910i 0.00393706 0.0228439i
\(286\) 726.917 1259.06i 0.150292 0.260313i
\(287\) 5869.58i 1.20721i
\(288\) 2736.01 2495.41i 0.559795 0.510567i
\(289\) −1935.23 −0.393901
\(290\) 3514.93 + 14057.8i 0.711737 + 2.84657i
\(291\) −459.650 202.889i −0.0925951 0.0408714i
\(292\) 9626.71 5557.98i 1.92932 1.11389i
\(293\) −2118.34 + 1223.02i −0.422371 + 0.243856i −0.696091 0.717953i \(-0.745079\pi\)
0.273720 + 0.961809i \(0.411746\pi\)
\(294\) −278.617 2571.67i −0.0552697 0.510147i
\(295\) 6104.06 1526.22i 1.20472 0.301219i
\(296\) −7808.72 −1.53335
\(297\) 795.489 3927.52i 0.155417 0.767332i
\(298\) 12968.0i 2.52086i
\(299\) −858.821 + 1487.52i −0.166110 + 0.287711i
\(300\) −846.463 11365.3i −0.162902 2.18725i
\(301\) −2826.84 4896.23i −0.541317 0.937588i
\(302\) −6585.45 + 3802.11i −1.25480 + 0.724459i
\(303\) 2273.30 5150.22i 0.431016 0.976476i
\(304\) 99.3568 172.091i 0.0187451 0.0324674i
\(305\) 616.496 + 637.553i 0.115739 + 0.119692i
\(306\) 3420.99 10762.6i 0.639101 2.01065i
\(307\) 5539.06i 1.02974i 0.857268 + 0.514871i \(0.172160\pi\)
−0.857268 + 0.514871i \(0.827840\pi\)
\(308\) 9119.79 + 5265.32i 1.68717 + 0.974088i
\(309\) 1804.76 1320.08i 0.332263 0.243032i
\(310\) −2610.72 746.738i −0.478319 0.136812i
\(311\) 1762.60 + 3052.92i 0.321376 + 0.556640i 0.980772 0.195156i \(-0.0625213\pi\)
−0.659396 + 0.751796i \(0.729188\pi\)
\(312\) 1490.60 + 2037.89i 0.270477 + 0.369785i
\(313\) 5984.75 + 3455.30i 1.08076 + 0.623977i 0.931101 0.364761i \(-0.118849\pi\)
0.149659 + 0.988738i \(0.452183\pi\)
\(314\) −6056.07 −1.08842
\(315\) −3509.61 + 5283.34i −0.627759 + 0.945023i
\(316\) −13884.8 −2.47177
\(317\) 3645.67 + 2104.83i 0.645934 + 0.372930i 0.786897 0.617085i \(-0.211686\pi\)
−0.140963 + 0.990015i \(0.545020\pi\)
\(318\) 379.370 859.472i 0.0668995 0.151562i
\(319\) 3662.17 + 6343.07i 0.642766 + 1.11330i
\(320\) −414.597 + 1449.50i −0.0724271 + 0.253217i
\(321\) −7.23933 66.8200i −0.00125875 0.0116185i
\(322\) −15687.1 9056.98i −2.71494 1.56747i
\(323\) 158.872i 0.0273680i
\(324\) 10443.8 + 7385.51i 1.79078 + 1.26638i
\(325\) 1258.09 + 42.2617i 0.214727 + 0.00721310i
\(326\) 5572.19 9651.32i 0.946672 1.63968i
\(327\) 103.880 11.2545i 0.0175675 0.00190328i
\(328\) −11673.1 + 6739.44i −1.96505 + 1.13452i
\(329\) −100.734 174.477i −0.0168805 0.0292378i
\(330\) −2898.94 7870.03i −0.483581 1.31282i
\(331\) 848.119 1468.99i 0.140836 0.243936i −0.786975 0.616984i \(-0.788354\pi\)
0.927812 + 0.373049i \(0.121688\pi\)
\(332\) 4001.96i 0.661554i
\(333\) −935.813 4268.14i −0.154001 0.702381i
\(334\) −5722.10 −0.937423
\(335\) −1265.82 5062.60i −0.206445 0.825669i
\(336\) −9121.33 + 6671.74i −1.48098 + 1.08325i
\(337\) 6239.90 3602.61i 1.00863 0.582334i 0.0978413 0.995202i \(-0.468806\pi\)
0.910791 + 0.412868i \(0.135473\pi\)
\(338\) 9172.80 5295.92i 1.47614 0.852248i
\(339\) 4741.88 3468.42i 0.759716 0.555689i
\(340\) −3937.89 15749.5i −0.628124 2.51216i
\(341\) −1372.52 −0.217965
\(342\) 249.682 + 79.3633i 0.0394773 + 0.0125482i
\(343\) 5137.53i 0.808747i
\(344\) −6491.55 + 11243.7i −1.01744 + 1.76227i
\(345\) 3424.98 + 9298.10i 0.534477 + 1.45099i
\(346\) −4685.37 8115.30i −0.727998 1.26093i
\(347\) −5626.26 + 3248.32i −0.870413 + 0.502533i −0.867485 0.497463i \(-0.834265\pi\)
−0.00292757 + 0.999996i \(0.500932\pi\)
\(348\) −23243.6 + 2518.24i −3.58043 + 0.387907i
\(349\) −3232.25 + 5598.43i −0.495755 + 0.858673i −0.999988 0.00489459i \(-0.998442\pi\)
0.504233 + 0.863568i \(0.331775\pi\)
\(350\) −445.684 + 13267.6i −0.0680652 + 2.02624i
\(351\) −935.249 + 1058.97i −0.142222 + 0.161036i
\(352\) 3917.44i 0.593183i
\(353\) 10261.5 + 5924.50i 1.54721 + 0.893284i 0.998353 + 0.0573694i \(0.0182713\pi\)
0.548860 + 0.835914i \(0.315062\pi\)
\(354\) 1591.98 + 14694.2i 0.239019 + 2.20618i
\(355\) −974.194 + 3405.95i −0.145647 + 0.509208i
\(356\) −472.957 819.186i −0.0704121 0.121957i
\(357\) −3648.47 + 8265.69i −0.540890 + 1.22540i
\(358\) 14032.5 + 8101.66i 2.07162 + 1.19605i
\(359\) 11702.9 1.72048 0.860242 0.509886i \(-0.170312\pi\)
0.860242 + 0.509886i \(0.170312\pi\)
\(360\) 14536.9 + 913.377i 2.12823 + 0.133720i
\(361\) −6855.31 −0.999463
\(362\) −9974.70 5758.90i −1.44823 0.836135i
\(363\) 1580.33 + 2160.57i 0.228501 + 0.312397i
\(364\) −1856.39 3215.35i −0.267311 0.462995i
\(365\) 6809.83 + 1947.80i 0.976556 + 0.279322i
\(366\) −1681.50 + 1229.92i −0.240146 + 0.175654i
\(367\) 2234.79 + 1290.26i 0.317861 + 0.183517i 0.650439 0.759559i \(-0.274585\pi\)
−0.332578 + 0.943076i \(0.607918\pi\)
\(368\) 17654.5i 2.50083i
\(369\) −5082.62 5572.67i −0.717047 0.786184i
\(370\) −6357.13 6574.26i −0.893220 0.923729i
\(371\) −375.811 + 650.924i −0.0525907 + 0.0910897i
\(372\) 1769.16 4008.06i 0.246576 0.558624i
\(373\) −3896.74 + 2249.78i −0.540926 + 0.312304i −0.745454 0.666557i \(-0.767767\pi\)
0.204528 + 0.978861i \(0.434434\pi\)
\(374\) −5973.48 10346.4i −0.825886 1.43048i
\(375\) 4831.04 5421.75i 0.665264 0.746608i
\(376\) −231.326 + 400.669i −0.0317281 + 0.0549546i
\(377\) 2582.34i 0.352777i
\(378\) −11167.7 9862.98i −1.51959 1.34205i
\(379\) 5888.24 0.798044 0.399022 0.916941i \(-0.369350\pi\)
0.399022 + 0.916941i \(0.369350\pi\)
\(380\) 365.371 91.3549i 0.0493241 0.0123327i
\(381\) 155.115 + 1431.73i 0.0208577 + 0.192519i
\(382\) 14832.8 8563.72i 1.98668 1.14701i
\(383\) 6945.66 4010.08i 0.926650 0.535001i 0.0408993 0.999163i \(-0.486978\pi\)
0.885750 + 0.464162i \(0.153644\pi\)
\(384\) −8455.67 3732.33i −1.12370 0.496002i
\(385\) 1627.60 + 6509.56i 0.215456 + 0.861709i
\(386\) 14042.1 1.85162
\(387\) −6923.62 2200.73i −0.909425 0.289068i
\(388\) 1696.64i 0.221994i
\(389\) −83.6900 + 144.955i −0.0109081 + 0.0188934i −0.871428 0.490524i \(-0.836806\pi\)
0.860520 + 0.509417i \(0.170139\pi\)
\(390\) −502.219 + 2914.02i −0.0652074 + 0.378352i
\(391\) 7057.41 + 12223.8i 0.912810 + 1.58103i
\(392\) 4115.68 2376.19i 0.530289 0.306163i
\(393\) 1541.80 + 2107.89i 0.197897 + 0.270557i
\(394\) 7434.22 12876.5i 0.950586 1.64646i
\(395\) −6149.99 6360.04i −0.783391 0.810148i
\(396\) 13217.9 2898.08i 1.67733 0.367763i
\(397\) 5893.09i 0.745002i 0.928032 + 0.372501i \(0.121500\pi\)
−0.928032 + 0.372501i \(0.878500\pi\)
\(398\) −21576.4 12457.2i −2.71741 1.56890i
\(399\) −191.755 84.6407i −0.0240596 0.0106199i
\(400\) 11415.8 6089.36i 1.42698 0.761170i
\(401\) 1316.43 + 2280.12i 0.163938 + 0.283950i 0.936278 0.351260i \(-0.114247\pi\)
−0.772339 + 0.635210i \(0.780913\pi\)
\(402\) 12187.1 1320.36i 1.51203 0.163815i
\(403\) 419.076 + 241.954i 0.0518007 + 0.0299071i
\(404\) 19010.2 2.34108
\(405\) 1242.89 + 8055.14i 0.152493 + 0.988304i
\(406\) 27232.9 3.32893
\(407\) −4003.17 2311.23i −0.487543 0.281483i
\(408\) 20627.5 2234.80i 2.50297 0.271174i
\(409\) −6845.15 11856.2i −0.827558 1.43337i −0.899949 0.435996i \(-0.856396\pi\)
0.0723910 0.997376i \(-0.476937\pi\)
\(410\) −15177.1 4341.08i −1.82816 0.522904i
\(411\) −10558.5 4660.50i −1.26718 0.559332i
\(412\) 6539.04 + 3775.32i 0.781931 + 0.451448i
\(413\) 11824.8i 1.40886i
\(414\) −22736.3 + 4985.05i −2.69910 + 0.591792i
\(415\) 1833.13 1772.59i 0.216831 0.209669i
\(416\) −690.584 + 1196.13i −0.0813910 + 0.140973i
\(417\) 8076.49 + 11041.9i 0.948459 + 1.29670i
\(418\) 240.025 138.578i 0.0280861 0.0162155i
\(419\) 129.486 + 224.277i 0.0150974 + 0.0261495i 0.873475 0.486868i \(-0.161861\pi\)
−0.858378 + 0.513018i \(0.828527\pi\)
\(420\) −21107.3 3637.75i −2.45221 0.422629i
\(421\) −6821.55 + 11815.3i −0.789696 + 1.36779i 0.136457 + 0.990646i \(0.456428\pi\)
−0.926153 + 0.377147i \(0.876905\pi\)
\(422\) 27387.1i 3.15920i
\(423\) −246.723 78.4230i −0.0283596 0.00901432i
\(424\) 1726.02 0.197696
\(425\) 5469.97 8779.70i 0.624312 1.00207i
\(426\) −7612.94 3360.35i −0.865840 0.382182i
\(427\) 1443.44 833.369i 0.163590 0.0944486i
\(428\) 196.553 113.480i 0.0221980 0.0128160i
\(429\) 160.987 + 1485.93i 0.0181177 + 0.167229i
\(430\) −14751.0 + 3688.24i −1.65432 + 0.413635i
\(431\) −13258.5 −1.48176 −0.740881 0.671636i \(-0.765592\pi\)
−0.740881 + 0.671636i \(0.765592\pi\)
\(432\) −2882.71 + 14232.6i −0.321052 + 1.58511i
\(433\) 14980.2i 1.66259i −0.555832 0.831295i \(-0.687600\pi\)
0.555832 0.831295i \(-0.312400\pi\)
\(434\) −2551.60 + 4419.50i −0.282214 + 0.488809i
\(435\) −11448.8 9531.54i −1.26190 1.05058i
\(436\) 176.419 + 305.566i 0.0193783 + 0.0335641i
\(437\) −283.579 + 163.724i −0.0310422 + 0.0179222i
\(438\) −6718.66 + 15221.3i −0.732945 + 1.66050i
\(439\) −3681.30 + 6376.19i −0.400225 + 0.693210i −0.993753 0.111604i \(-0.964401\pi\)
0.593528 + 0.804813i \(0.297735\pi\)
\(440\) 11077.0 10711.2i 1.20017 1.16053i
\(441\) 1792.03 + 1964.81i 0.193503 + 0.212160i
\(442\) 4212.13i 0.453282i
\(443\) −1375.08 793.903i −0.147476 0.0851456i 0.424446 0.905453i \(-0.360469\pi\)
−0.571922 + 0.820308i \(0.693802\pi\)
\(444\) 11909.3 8711.00i 1.27295 0.931094i
\(445\) 165.748 579.484i 0.0176567 0.0617307i
\(446\) 10321.9 + 17878.0i 1.09586 + 1.89809i
\(447\) −7870.73 10760.6i −0.832825 1.13861i
\(448\) 2453.76 + 1416.68i 0.258770 + 0.149401i
\(449\) 7331.63 0.770604 0.385302 0.922791i \(-0.374097\pi\)
0.385302 + 0.922791i \(0.374097\pi\)
\(450\) 11065.6 + 12982.4i 1.15919 + 1.35999i
\(451\) −7978.99 −0.833074
\(452\) 17180.9 + 9919.38i 1.78788 + 1.03223i
\(453\) 3156.81 7151.83i 0.327417 0.741771i
\(454\) 560.601 + 970.990i 0.0579523 + 0.100376i
\(455\) 650.571 2274.51i 0.0670313 0.234353i
\(456\) 51.8450 + 478.535i 0.00532426 + 0.0491436i
\(457\) −5453.21 3148.41i −0.558185 0.322268i 0.194232 0.980956i \(-0.437779\pi\)
−0.752417 + 0.658687i \(0.771112\pi\)
\(458\) 8077.23i 0.824070i
\(459\) 3693.55 + 11006.9i 0.375600 + 1.11930i
\(460\) −24054.0 + 23259.5i −2.43809 + 2.35757i
\(461\) −3167.73 + 5486.67i −0.320034 + 0.554316i −0.980495 0.196545i \(-0.937028\pi\)
0.660461 + 0.750861i \(0.270361\pi\)
\(462\) −15670.3 + 1697.74i −1.57803 + 0.170965i
\(463\) 1988.15 1147.86i 0.199562 0.115217i −0.396889 0.917867i \(-0.629910\pi\)
0.596451 + 0.802649i \(0.296577\pi\)
\(464\) −13271.1 22986.2i −1.32779 2.29980i
\(465\) 2619.53 964.911i 0.261243 0.0962294i
\(466\) 16730.9 28978.8i 1.66319 2.88072i
\(467\) 6182.82i 0.612648i −0.951927 0.306324i \(-0.900901\pi\)
0.951927 0.306324i \(-0.0990991\pi\)
\(468\) −4546.74 1445.22i −0.449088 0.142746i
\(469\) −9807.26 −0.965581
\(470\) −525.653 + 131.431i −0.0515884 + 0.0128988i
\(471\) 5025.18 3675.63i 0.491609 0.359585i
\(472\) −23516.4 + 13577.2i −2.29328 + 1.32403i
\(473\) −6655.84 + 3842.75i −0.647011 + 0.373552i
\(474\) 16774.2 12269.4i 1.62545 1.18893i
\(475\) 203.680 + 126.898i 0.0196747 + 0.0122578i
\(476\) −30509.9 −2.93786
\(477\) 206.850 + 943.422i 0.0198554 + 0.0905583i
\(478\) 17979.3i 1.72041i
\(479\) 1949.18 3376.08i 0.185930 0.322040i −0.757960 0.652302i \(-0.773804\pi\)
0.943889 + 0.330262i \(0.107137\pi\)
\(480\) 2754.04 + 7476.66i 0.261884 + 0.710961i
\(481\) 814.869 + 1411.39i 0.0772449 + 0.133792i
\(482\) 12988.6 7499.00i 1.22742 0.708652i
\(483\) 18513.8 2005.80i 1.74411 0.188959i
\(484\) −4519.61 + 7828.19i −0.424456 + 0.735180i
\(485\) 777.159 751.491i 0.0727608 0.0703576i
\(486\) −19143.4 + 306.339i −1.78675 + 0.0285923i
\(487\) 14776.3i 1.37490i 0.726232 + 0.687450i \(0.241270\pi\)
−0.726232 + 0.687450i \(0.758730\pi\)
\(488\) −3314.71 1913.75i −0.307479 0.177523i
\(489\) 1234.04 + 11390.4i 0.114121 + 1.05336i
\(490\) 5351.15 + 1530.58i 0.493348 + 0.141111i
\(491\) −1818.62 3149.94i −0.167155 0.289521i 0.770263 0.637726i \(-0.220125\pi\)
−0.937418 + 0.348205i \(0.886791\pi\)
\(492\) 10284.8 23300.4i 0.942427 2.13509i
\(493\) −18377.5 10610.2i −1.67886 0.969293i
\(494\) −97.7169 −0.00889978
\(495\) 7182.07 + 4770.90i 0.652141 + 0.433204i
\(496\) 4973.77 0.450260
\(497\) 5765.68 + 3328.82i 0.520375 + 0.300439i
\(498\) 3536.35 + 4834.76i 0.318208 + 0.435041i
\(499\) −1628.87 2821.29i −0.146129 0.253103i 0.783665 0.621184i \(-0.213348\pi\)
−0.929794 + 0.368081i \(0.880015\pi\)
\(500\) 23336.8 + 7531.25i 2.08731 + 0.673616i
\(501\) 4748.06 3472.94i 0.423409 0.309699i
\(502\) 3955.07 + 2283.46i 0.351640 + 0.203019i
\(503\) 20857.4i 1.84888i 0.381327 + 0.924440i \(0.375467\pi\)
−0.381327 + 0.924440i \(0.624533\pi\)
\(504\) 8292.15 26087.6i 0.732861 2.30562i
\(505\) 8420.19 + 8707.79i 0.741968 + 0.767310i
\(506\) −12311.9 + 21324.8i −1.08168 + 1.87352i
\(507\) −4397.09 + 9961.71i −0.385171 + 0.872614i
\(508\) −4211.47 + 2431.49i −0.367822 + 0.212362i
\(509\) −9953.74 17240.4i −0.866781 1.50131i −0.865267 0.501311i \(-0.832851\pi\)
−0.00151390 0.999999i \(-0.500482\pi\)
\(510\) 18674.5 + 15547.2i 1.62141 + 1.34988i
\(511\) 6655.62 11527.9i 0.576179 0.997971i
\(512\) 25758.7i 2.22340i
\(513\) −255.348 + 85.6865i −0.0219764 + 0.00737456i
\(514\) −7503.15 −0.643871
\(515\) 1167.02 + 4667.46i 0.0998544 + 0.399365i
\(516\) −2642.41 24389.8i −0.225437 2.08081i
\(517\) −237.181 + 136.937i −0.0201764 + 0.0116489i
\(518\) −14884.3 + 8593.46i −1.26251 + 0.728909i
\(519\) 8813.26 + 3890.17i 0.745394 + 0.329016i
\(520\) −5270.39 + 1317.77i −0.444465 + 0.111131i
\(521\) −4264.69 −0.358617 −0.179308 0.983793i \(-0.557386\pi\)
−0.179308 + 0.983793i \(0.557386\pi\)
\(522\) 25855.3 23581.6i 2.16792 1.97728i
\(523\) 3687.86i 0.308334i 0.988045 + 0.154167i \(0.0492694\pi\)
−0.988045 + 0.154167i \(0.950731\pi\)
\(524\) −4409.42 + 7637.34i −0.367607 + 0.636715i
\(525\) −7682.74 11279.6i −0.638671 0.937683i
\(526\) 6865.46 + 11891.3i 0.569103 + 0.985716i
\(527\) 3443.78 1988.27i 0.284656 0.164346i
\(528\) 9069.43 + 12399.4i 0.747531 + 1.02199i
\(529\) 8462.46 14657.4i 0.695525 1.20469i
\(530\) 1405.17 + 1453.16i 0.115163 + 0.119097i
\(531\) −10239.4 11226.6i −0.836819 0.917504i
\(532\) 707.798i 0.0576822i
\(533\) 2436.25 + 1406.57i 0.197985 + 0.114307i
\(534\) 1295.26 + 571.726i 0.104965 + 0.0463314i
\(535\) 139.039 + 39.7690i 0.0112359 + 0.00321377i
\(536\) 11260.7 + 19504.1i 0.907440 + 1.57173i
\(537\) −16561.0 + 1794.23i −1.33084 + 0.144184i
\(538\) 32796.2 + 18934.9i 2.62815 + 1.51736i
\(539\) 2813.23 0.224813
\(540\) −23189.6 + 14823.6i −1.84800 + 1.18131i
\(541\) 21551.0 1.71266 0.856331 0.516428i \(-0.172739\pi\)
0.856331 + 0.516428i \(0.172739\pi\)
\(542\) −8811.39 5087.26i −0.698305 0.403167i
\(543\) 11772.0 1275.39i 0.930362 0.100796i
\(544\) 5674.91 + 9829.23i 0.447261 + 0.774678i
\(545\) −61.8260 + 216.154i −0.00485933 + 0.0169891i
\(546\) 5083.96 + 2244.06i 0.398486 + 0.175891i
\(547\) −17240.0 9953.52i −1.34759 0.778029i −0.359678 0.933076i \(-0.617114\pi\)
−0.987907 + 0.155048i \(0.950447\pi\)
\(548\) 38972.8i 3.03802i
\(549\) 648.788 2041.12i 0.0504364 0.158676i
\(550\) 18035.7 + 605.855i 1.39826 + 0.0469704i
\(551\) 246.146 426.338i 0.0190312 0.0329630i
\(552\) −25246.5 34516.1i −1.94667 2.66142i
\(553\) −14399.3 + 8313.45i −1.10727 + 0.639283i
\(554\) 9024.46 + 15630.8i 0.692081 + 1.19872i
\(555\) 9265.14 + 1596.81i 0.708618 + 0.122127i
\(556\) −23098.1 + 40007.0i −1.76183 + 3.05157i
\(557\) 1747.00i 0.132896i −0.997790 0.0664479i \(-0.978833\pi\)
0.997790 0.0664479i \(-0.0211666\pi\)
\(558\) 1404.43 + 6405.45i 0.106549 + 0.485957i
\(559\) 2709.67 0.205021
\(560\) −5898.16 23589.5i −0.445076 1.78007i
\(561\) 11236.2 + 4959.66i 0.845622 + 0.373257i
\(562\) −29596.0 + 17087.2i −2.22141 + 1.28253i
\(563\) −1837.74 + 1061.02i −0.137569 + 0.0794257i −0.567205 0.823577i \(-0.691975\pi\)
0.429636 + 0.903002i \(0.358642\pi\)
\(564\) −94.1622 869.129i −0.00703004 0.0648882i
\(565\) 3066.26 + 12263.4i 0.228316 + 0.913143i
\(566\) 20279.5 1.50603
\(567\) 15252.9 + 1405.99i 1.12974 + 0.104138i
\(568\) 15288.6i 1.12939i
\(569\) 5376.54 9312.43i 0.396127 0.686112i −0.597118 0.802154i \(-0.703687\pi\)
0.993244 + 0.116042i \(0.0370207\pi\)
\(570\) −360.678 + 433.228i −0.0265038 + 0.0318349i
\(571\) −362.873 628.514i −0.0265950 0.0460639i 0.852422 0.522855i \(-0.175133\pi\)
−0.879017 + 0.476791i \(0.841800\pi\)
\(572\) −4370.89 + 2523.54i −0.319504 + 0.184466i
\(573\) −7110.29 + 16108.5i −0.518388 + 1.17442i
\(574\) −14833.5 + 25692.3i −1.07864 + 1.86825i
\(575\) −21308.4 715.791i −1.54543 0.0519140i
\(576\) 3556.37 779.753i 0.257261 0.0564058i
\(577\) 23839.3i 1.72001i −0.510290 0.860003i \(-0.670462\pi\)
0.510290 0.860003i \(-0.329538\pi\)
\(578\) 8470.91 + 4890.68i 0.609590 + 0.351947i
\(579\) −11651.8 + 8522.63i −0.836325 + 0.611725i
\(580\) 13833.8 48365.5i 0.990378 3.46253i
\(581\) −2396.15 4150.26i −0.171100 0.296354i
\(582\) 1499.24 + 2049.70i 0.106779 + 0.145985i
\(583\) 884.853 + 510.870i 0.0628592 + 0.0362917i
\(584\) −30567.9 −2.16594
\(585\) −1351.89 2722.80i −0.0955450 0.192434i
\(586\) 12363.2 0.871534
\(587\) 6735.67 + 3888.84i 0.473613 + 0.273440i 0.717751 0.696300i \(-0.245172\pi\)
−0.244138 + 0.969740i \(0.578505\pi\)
\(588\) −3626.21 + 8215.25i −0.254324 + 0.576175i
\(589\) 46.1257 + 79.8921i 0.00322679 + 0.00558896i
\(590\) −30575.7 8745.48i −2.13353 0.610247i
\(591\) 1646.42 + 15196.7i 0.114593 + 1.05771i
\(592\) 14506.8 + 8375.51i 1.00714 + 0.581472i
\(593\) 6677.79i 0.462435i 0.972902 + 0.231217i \(0.0742709\pi\)
−0.972902 + 0.231217i \(0.925729\pi\)
\(594\) −13407.5 + 15181.2i −0.926125 + 1.04864i
\(595\) −13513.7 13975.3i −0.931108 0.962911i
\(596\) 22509.6 38987.8i 1.54703 2.67953i
\(597\) 25464.3 2758.82i 1.74570 0.189131i
\(598\) 7518.46 4340.79i 0.514135 0.296836i
\(599\) 6473.45 + 11212.3i 0.441566 + 0.764815i 0.997806 0.0662068i \(-0.0210897\pi\)
−0.556240 + 0.831022i \(0.687756\pi\)
\(600\) −13610.9 + 28230.2i −0.926107 + 1.92082i
\(601\) 2183.05 3781.15i 0.148167 0.256633i −0.782383 0.622797i \(-0.785996\pi\)
0.930550 + 0.366165i \(0.119329\pi\)
\(602\) 28575.7i 1.93465i
\(603\) −9311.17 + 8492.36i −0.628823 + 0.573525i
\(604\) 26398.5 1.77838
\(605\) −5587.64 + 1397.09i −0.375487 + 0.0938842i
\(606\) −22966.2 + 16798.5i −1.53950 + 1.12606i
\(607\) 20938.3 12088.7i 1.40010 0.808347i 0.405697 0.914008i \(-0.367029\pi\)
0.994402 + 0.105660i \(0.0336956\pi\)
\(608\) −228.028 + 131.652i −0.0152101 + 0.00878156i
\(609\) −22597.2 + 16528.6i −1.50359 + 1.09979i
\(610\) −1087.32 4348.69i −0.0721707 0.288645i
\(611\) 96.5591 0.00639339
\(612\) −28966.6 + 26419.3i −1.91324 + 1.74499i
\(613\) 7772.63i 0.512127i 0.966660 + 0.256063i \(0.0824256\pi\)
−0.966660 + 0.256063i \(0.917574\pi\)
\(614\) 13998.2 24245.5i 0.920066 1.59360i
\(615\) 15228.4 5609.40i 0.998484 0.367794i
\(616\) −14479.2 25078.6i −0.947048 1.64034i
\(617\) −542.357 + 313.130i −0.0353881 + 0.0204313i −0.517590 0.855629i \(-0.673171\pi\)
0.482202 + 0.876060i \(0.339837\pi\)
\(618\) −11235.9 + 1217.30i −0.731348 + 0.0792349i
\(619\) 11417.5 19775.8i 0.741373 1.28410i −0.210497 0.977594i \(-0.567508\pi\)
0.951870 0.306501i \(-0.0991583\pi\)
\(620\) 6552.85 + 6776.67i 0.424466 + 0.438964i
\(621\) 15840.4 17935.9i 1.02360 1.15901i
\(622\) 17817.6i 1.14859i
\(623\) −980.967 566.361i −0.0630844 0.0364218i
\(624\) −583.387 5384.74i −0.0374266 0.345452i
\(625\) 6886.80 + 14025.4i 0.440756 + 0.897627i
\(626\) −17464.3 30249.0i −1.11504 1.93130i
\(627\) −115.059 + 260.668i −0.00732857 + 0.0166030i
\(628\) 18207.3 + 10512.0i 1.15693 + 0.667953i
\(629\) 13392.5 0.848954
\(630\) 28714.2 14256.8i 1.81587 0.901594i
\(631\) −26862.1 −1.69471 −0.847355 0.531027i \(-0.821806\pi\)
−0.847355 + 0.531027i \(0.821806\pi\)
\(632\) 33066.6 + 19091.0i 2.08120 + 1.20158i
\(633\) −16622.1 22725.1i −1.04371 1.42692i
\(634\) −10638.5 18426.5i −0.666420 1.15427i
\(635\) −2979.15 852.118i −0.186179 0.0532524i
\(636\) −2632.41 + 1925.46i −0.164123 + 0.120046i
\(637\) −858.973 495.929i −0.0534282 0.0308468i
\(638\) 37019.8i 2.29723i
\(639\) 8356.54 1832.22i 0.517339 0.113429i
\(640\) 14296.5 13824.3i 0.883000 0.853836i
\(641\) −4304.99 + 7456.46i −0.265268 + 0.459458i −0.967634 0.252358i \(-0.918794\pi\)
0.702366 + 0.711816i \(0.252127\pi\)
\(642\) −137.178 + 310.779i −0.00843299 + 0.0191051i
\(643\) −14872.6 + 8586.71i −0.912160 + 0.526636i −0.881125 0.472882i \(-0.843214\pi\)
−0.0310345 + 0.999518i \(0.509880\pi\)
\(644\) 31441.8 + 54458.8i 1.92388 + 3.33227i
\(645\) 10001.5 12013.3i 0.610558 0.733371i
\(646\) −401.497 + 695.413i −0.0244531 + 0.0423540i
\(647\) 1258.94i 0.0764978i −0.999268 0.0382489i \(-0.987822\pi\)
0.999268 0.0382489i \(-0.0121780\pi\)
\(648\) −14717.2 31948.4i −0.892200 1.93681i
\(649\) −16074.4 −0.972226
\(650\) −5400.11 3364.40i −0.325861 0.203020i
\(651\) −565.090 5215.85i −0.0340209 0.314017i
\(652\) −33505.1 + 19344.2i −2.01252 + 1.16193i
\(653\) −2200.06 + 1270.21i −0.131845 + 0.0761209i −0.564472 0.825452i \(-0.690920\pi\)
0.432627 + 0.901573i \(0.357587\pi\)
\(654\) −483.146 213.260i −0.0288876 0.0127510i
\(655\) −5451.40 + 1363.03i −0.325197 + 0.0813100i
\(656\) 28914.5 1.72092
\(657\) −3663.32 16708.0i −0.217534 0.992149i
\(658\) 1018.29i 0.0603302i
\(659\) −13099.9 + 22689.7i −0.774356 + 1.34122i 0.160800 + 0.986987i \(0.448593\pi\)
−0.935156 + 0.354237i \(0.884741\pi\)
\(660\) −4945.09 + 28692.9i −0.291648 + 1.69222i
\(661\) 2721.89 + 4714.44i 0.160165 + 0.277414i 0.934928 0.354838i \(-0.115464\pi\)
−0.774763 + 0.632252i \(0.782131\pi\)
\(662\) −7424.77 + 4286.69i −0.435909 + 0.251672i
\(663\) −2556.48 3495.12i −0.149752 0.204735i
\(664\) −5502.52 + 9530.64i −0.321595 + 0.557019i
\(665\) 324.212 313.504i 0.0189059 0.0182815i
\(666\) −6690.11 + 21047.5i −0.389244 + 1.22458i
\(667\) 43737.3i 2.53901i
\(668\) 17203.3 + 9932.30i 0.996428 + 0.575288i
\(669\) −19415.6 8570.05i −1.12205 0.495272i
\(670\) −7253.35 + 25358.9i −0.418241 + 1.46224i
\(671\) −1132.87 1962.18i −0.0651771 0.112890i
\(672\) 14887.1 1612.88i 0.854585 0.0925865i
\(673\) 14567.3 + 8410.41i 0.834364 + 0.481720i 0.855344 0.518060i \(-0.173346\pi\)
−0.0209808 + 0.999780i \(0.506679\pi\)
\(674\) −36417.7 −2.08124
\(675\) −17061.4 4056.39i −0.972881 0.231304i
\(676\) −36770.2 −2.09207
\(677\) −20091.4 11599.7i −1.14058 0.658515i −0.194007 0.981000i \(-0.562148\pi\)
−0.946574 + 0.322485i \(0.895482\pi\)
\(678\) −29521.5 + 3198.38i −1.67222 + 0.181170i
\(679\) −1015.85 1759.51i −0.0574151 0.0994459i
\(680\) −12276.8 + 42921.7i −0.692343 + 2.42055i
\(681\) −1054.50 465.456i −0.0593371 0.0261914i
\(682\) 6007.79 + 3468.60i 0.337317 + 0.194750i
\(683\) 24902.4i 1.39512i 0.716528 + 0.697558i \(0.245730\pi\)
−0.716528 + 0.697558i \(0.754270\pi\)
\(684\) −612.900 671.994i −0.0342614 0.0375648i
\(685\) 17851.8 17262.2i 0.995742 0.962855i
\(686\) −12983.4 + 22488.0i −0.722609 + 1.25160i
\(687\) −4902.35 6702.29i −0.272251 0.372210i
\(688\) 24119.6 13925.5i 1.33656 0.771662i
\(689\) −180.117 311.972i −0.00995923 0.0172499i
\(690\) 8506.15 49355.2i 0.469310 2.72307i
\(691\) −4233.73 + 7333.03i −0.233080 + 0.403707i −0.958713 0.284375i \(-0.908214\pi\)
0.725633 + 0.688082i \(0.241547\pi\)
\(692\) 32531.1i 1.78706i
\(693\) 11972.4 10919.6i 0.656270 0.598558i
\(694\) 32836.3 1.79604
\(695\) −28556.4 + 7140.03i −1.55857 + 0.389693i
\(696\) 58817.0 + 25961.8i 3.20324 + 1.41391i
\(697\) 20020.1 11558.6i 1.08797 0.628139i
\(698\) 28296.4 16336.9i 1.53443 0.885906i
\(699\) 3705.31 + 34200.5i 0.200497 + 1.85062i
\(700\) 24369.5 39114.9i 1.31583 2.11200i
\(701\) 5972.30 0.321784 0.160892 0.986972i \(-0.448563\pi\)
0.160892 + 0.986972i \(0.448563\pi\)
\(702\) 6769.98 2271.78i 0.363983 0.122141i
\(703\) 310.691i 0.0166685i
\(704\) 1925.80 3335.59i 0.103099 0.178572i
\(705\) 356.404 428.095i 0.0190397 0.0228695i
\(706\) −29944.5 51865.4i −1.59628 2.76484i
\(707\) 19714.7 11382.3i 1.04872 0.605480i
\(708\) 20719.6 46940.7i 1.09985 2.49172i
\(709\) −3774.89 + 6538.30i −0.199956 + 0.346334i −0.948514 0.316735i \(-0.897413\pi\)
0.748558 + 0.663070i \(0.230747\pi\)
\(710\) 12871.7 12446.5i 0.680373 0.657902i
\(711\) −6472.12 + 20361.7i −0.341383 + 1.07401i
\(712\) 2601.18i 0.136915i
\(713\) −7097.94 4098.00i −0.372819 0.215247i
\(714\) 36858.9 26960.2i 1.93195 1.41311i
\(715\) −3091.92 884.374i −0.161722 0.0462570i
\(716\) −28125.4 48714.6i −1.46801 2.54267i
\(717\) 10912.3 + 14918.8i 0.568377 + 0.777062i
\(718\) −51225.8 29575.2i −2.66257 1.53724i
\(719\) 31449.7 1.63126 0.815631 0.578573i \(-0.196390\pi\)
0.815631 + 0.578573i \(0.196390\pi\)
\(720\) −26026.6 17288.9i −1.34716 0.894888i
\(721\) 9041.81 0.467038
\(722\) 30007.1 + 17324.6i 1.54674 + 0.893012i
\(723\) −6226.27 + 14105.7i −0.320273 + 0.725585i
\(724\) 19992.3 + 34627.8i 1.02626 + 1.77753i
\(725\) 28281.6 15085.8i 1.44876 0.772789i
\(726\) −1457.29 13451.0i −0.0744975 0.687622i
\(727\) −6895.32 3981.01i −0.351765 0.203092i 0.313697 0.949523i \(-0.398432\pi\)
−0.665462 + 0.746431i \(0.731766\pi\)
\(728\) 10209.8i 0.519780i
\(729\) 15698.8 11873.0i 0.797582 0.603210i
\(730\) −24885.5 25735.5i −1.26172 1.30481i
\(731\) 11133.4 19283.7i 0.563317 0.975694i
\(732\) 7190.25 778.998i 0.363059 0.0393341i
\(733\) 9529.06 5501.61i 0.480169 0.277226i −0.240318 0.970694i \(-0.577252\pi\)
0.720487 + 0.693469i \(0.243918\pi\)
\(734\) −6521.41 11295.4i −0.327942 0.568012i
\(735\) −5369.21 + 1977.76i −0.269451 + 0.0992528i
\(736\) 11696.5 20258.9i 0.585786 1.01461i
\(737\) 13331.8i 0.666328i
\(738\) 8164.49 + 37237.4i 0.407234 + 1.85735i
\(739\) −24719.1 −1.23046 −0.615228 0.788349i \(-0.710936\pi\)
−0.615228 + 0.788349i \(0.710936\pi\)
\(740\) 7700.97 + 30799.8i 0.382559 + 1.53003i
\(741\) 81.0831 59.3077i 0.00401979 0.00294025i
\(742\) 3290.00 1899.48i 0.162776 0.0939786i
\(743\) 11541.3 6663.39i 0.569866 0.329012i −0.187230 0.982316i \(-0.559951\pi\)
0.757096 + 0.653304i \(0.226618\pi\)
\(744\) −9724.13 + 7112.65i −0.479172 + 0.350487i
\(745\) 27828.9 6958.13i 1.36855 0.342183i
\(746\) 22742.4 1.11616
\(747\) −5868.76 1865.43i −0.287452 0.0913689i
\(748\) 41474.6i 2.02735i
\(749\) 135.891 235.370i 0.00662929 0.0114823i
\(750\) −34848.2 + 11523.2i −1.69663 + 0.561023i
\(751\) 11900.5 + 20612.2i 0.578234 + 1.00153i 0.995682 + 0.0928298i \(0.0295913\pi\)
−0.417448 + 0.908701i \(0.637075\pi\)
\(752\) 859.503 496.234i 0.0416793 0.0240636i
\(753\) −4667.73 + 505.706i −0.225898 + 0.0244740i
\(754\) −6526.02 + 11303.4i −0.315204 + 0.545949i
\(755\) 11692.7 + 12092.0i 0.563629 + 0.582880i
\(756\) 16455.3 + 49037.3i 0.791633 + 2.35909i
\(757\) 20867.5i 1.00191i 0.865474 + 0.500953i \(0.167017\pi\)
−0.865474 + 0.500953i \(0.832983\pi\)
\(758\) −25774.0 14880.6i −1.23503 0.713046i
\(759\) −2726.65 25167.3i −0.130397 1.20358i
\(760\) −995.739 284.808i −0.0475253 0.0135935i
\(761\) 7743.76 + 13412.6i 0.368871 + 0.638904i 0.989389 0.145288i \(-0.0464110\pi\)
−0.620518 + 0.784192i \(0.713078\pi\)
\(762\) 2939.27 6658.97i 0.139735 0.316573i
\(763\) 365.912 + 211.260i 0.0173616 + 0.0100237i
\(764\) −59458.9 −2.81564
\(765\) −24931.7 1566.50i −1.17831 0.0740353i
\(766\) −40536.7 −1.91208
\(767\) 4908.05 + 2833.66i 0.231055 + 0.133400i
\(768\) 24270.6 + 33181.8i 1.14035 + 1.55904i
\(769\) −9233.99 15993.7i −0.433012 0.749999i 0.564119 0.825693i \(-0.309216\pi\)
−0.997131 + 0.0756946i \(0.975883\pi\)
\(770\) 9326.46 32606.9i 0.436496 1.52607i
\(771\) 6225.94 4553.92i 0.290819 0.212718i
\(772\) −42217.0 24374.0i −1.96816 1.13632i
\(773\) 15379.9i 0.715621i −0.933794 0.357810i \(-0.883523\pi\)
0.933794 0.357810i \(-0.116477\pi\)
\(774\) 24744.4 + 27130.2i 1.14912 + 1.25992i
\(775\) −201.658 + 6003.17i −0.00934681 + 0.278246i
\(776\) −2332.80 + 4040.53i −0.107916 + 0.186916i
\(777\) 7134.98 16164.4i 0.329428 0.746327i
\(778\) 732.655 422.999i 0.0337622 0.0194926i
\(779\) 268.147 + 464.444i 0.0123329 + 0.0213613i
\(780\) 6568.00 7889.15i 0.301503 0.362150i
\(781\) 4525.13 7837.76i 0.207327 0.359100i
\(782\) 71341.3i 3.26235i
\(783\) −7141.63 + 35259.9i −0.325953 + 1.60931i
\(784\) −10194.7 −0.464407
\(785\) 3249.45 + 12996.1i 0.147742 + 0.590892i
\(786\) −1421.76 13123.0i −0.0645198 0.595526i
\(787\) 33127.1 19125.9i 1.50045 0.866284i 0.500448 0.865767i \(-0.333169\pi\)
1.00000 0.000517066i \(-0.000164587\pi\)
\(788\) −44701.4 + 25808.3i −2.02084 + 1.16673i
\(789\) −12914.0 5700.26i −0.582703 0.257205i
\(790\) 10846.7 + 43381.3i 0.488494 + 1.95372i
\(791\) 23756.7 1.06788
\(792\) −35463.0 11272.2i −1.59106 0.505732i
\(793\) 798.826i 0.0357720i
\(794\) 14892.9 25795.2i 0.665653 1.15295i
\(795\) −2047.95 352.955i −0.0913625 0.0157459i
\(796\) 43245.8 + 74903.9i 1.92564 + 3.33530i
\(797\) −33759.1 + 19490.8i −1.50039 + 0.866249i −0.500388 + 0.865801i \(0.666809\pi\)
−1.00000 0.000448165i \(0.999857\pi\)
\(798\) 625.449 + 855.088i 0.0277452 + 0.0379321i
\(799\) 396.740 687.174i 0.0175665 0.0304261i
\(800\) −17134.2 575.572i −0.757233 0.0254369i
\(801\) −1421.77 + 311.731i −0.0627164 + 0.0137509i
\(802\) 13307.4i 0.585911i
\(803\) −15670.8 9047.53i −0.688680 0.397609i
\(804\) −38931.8 17184.5i −1.70773 0.753793i
\(805\) −11018.8 + 38523.6i −0.482437 + 1.68668i
\(806\) −1222.92 2118.16i −0.0534436 0.0925670i
\(807\) −38705.7 + 4193.41i −1.68836 + 0.182918i
\(808\) −45272.8 26138.2i −1.97115 1.13804i
\(809\) 4490.50 0.195152 0.0975758 0.995228i \(-0.468891\pi\)
0.0975758 + 0.995228i \(0.468891\pi\)
\(810\) 14916.4 38400.0i 0.647047 1.66573i
\(811\) 33791.9 1.46312 0.731562 0.681775i \(-0.238792\pi\)
0.731562 + 0.681775i \(0.238792\pi\)
\(812\) −81874.5 47270.2i −3.53846 2.04293i
\(813\) 10399.1 1126.65i 0.448601 0.0486018i
\(814\) 11681.8 + 20233.5i 0.503006 + 0.871231i
\(815\) −23701.2 6779.18i −1.01867 0.291367i
\(816\) −40718.1 17973.0i −1.74684 0.771053i
\(817\) 447.361 + 258.284i 0.0191569 + 0.0110602i
\(818\) 69195.7i 2.95766i
\(819\) −5580.54 + 1223.56i −0.238095 + 0.0522036i
\(820\) 38094.3 + 39395.4i 1.62233 + 1.67774i
\(821\) −3382.78 + 5859.15i −0.143800 + 0.249069i −0.928925 0.370269i \(-0.879266\pi\)
0.785125 + 0.619338i \(0.212599\pi\)
\(822\) 34438.5 + 47083.0i 1.46129 + 1.99782i
\(823\) 34076.3 19674.0i 1.44329 0.833282i 0.445219 0.895422i \(-0.353126\pi\)
0.998067 + 0.0621398i \(0.0197925\pi\)
\(824\) −10381.8 17981.8i −0.438916 0.760225i
\(825\) −15333.3 + 10443.8i −0.647076 + 0.440734i
\(826\) −29883.3 + 51759.4i −1.25881 + 2.18031i
\(827\) 632.071i 0.0265771i −0.999912 0.0132885i \(-0.995770\pi\)
0.999912 0.0132885i \(-0.00423000\pi\)
\(828\) 77008.7 + 24477.8i 3.23217 + 1.02737i
\(829\) 19585.8 0.820560 0.410280 0.911959i \(-0.365431\pi\)
0.410280 + 0.911959i \(0.365431\pi\)
\(830\) −12503.6 + 3126.31i −0.522899 + 0.130742i
\(831\) −16975.2 7492.83i −0.708618 0.312784i
\(832\) −1176.02 + 678.978i −0.0490040 + 0.0282925i
\(833\) −7058.66 + 4075.32i −0.293599 + 0.169510i
\(834\) −7447.69 68743.1i −0.309223 2.85417i
\(835\) 3070.26 + 12279.4i 0.127246 + 0.508918i
\(836\) −962.167 −0.0398053
\(837\) −5053.04 4462.69i −0.208672 0.184293i
\(838\) 1308.94i 0.0539577i
\(839\) 5836.32 10108.8i 0.240157 0.415965i −0.720602 0.693349i \(-0.756134\pi\)
0.960759 + 0.277385i \(0.0894676\pi\)
\(840\) 45265.1 + 37684.9i 1.85928 + 1.54792i
\(841\) −20683.3 35824.5i −0.848057 1.46888i
\(842\) 59718.5 34478.5i 2.44422 1.41117i
\(843\) 14187.2 32141.4i 0.579636 1.31318i
\(844\) 47537.9 82338.0i 1.93877 3.35805i
\(845\) −16286.6 16842.9i −0.663048 0.685695i
\(846\) 881.767 + 966.786i 0.0358343 + 0.0392893i
\(847\) 10824.4i 0.439114i
\(848\) −3206.55 1851.31i −0.129851 0.0749694i
\(849\) −16827.4 + 12308.3i −0.680231 + 0.497551i
\(850\) −46131.0 + 24606.9i −1.86151 + 0.992952i
\(851\) −13801.5 23904.9i −0.555946 0.962927i
\(852\) 17055.2 + 23317.1i 0.685798 + 0.937596i
\(853\) 19140.0 + 11050.5i 0.768276 + 0.443565i 0.832259 0.554386i \(-0.187047\pi\)
−0.0639830 + 0.997951i \(0.520380\pi\)
\(854\) −8424.28 −0.337556
\(855\) 36.3412 578.390i 0.00145362 0.0231351i
\(856\) −624.118 −0.0249205
\(857\) −25892.3 14948.9i −1.03205 0.595853i −0.114477 0.993426i \(-0.536519\pi\)
−0.917571 + 0.397573i \(0.869853\pi\)
\(858\) 3050.53 6911.04i 0.121379 0.274987i
\(859\) 7041.73 + 12196.6i 0.279698 + 0.484452i 0.971310 0.237818i \(-0.0764322\pi\)
−0.691611 + 0.722270i \(0.743099\pi\)
\(860\) 50750.3 + 14516.0i 2.01229 + 0.575571i
\(861\) −3285.09 30321.8i −0.130030 1.20019i
\(862\) 58035.1 + 33506.6i 2.29313 + 1.32394i
\(863\) 11367.8i 0.448396i −0.974544 0.224198i \(-0.928024\pi\)
0.974544 0.224198i \(-0.0719762\pi\)
\(864\) 12737.4 14422.4i 0.501545 0.567893i
\(865\) −14901.1 + 14409.0i −0.585727 + 0.566381i
\(866\) −37857.5 + 65571.2i −1.48551 + 2.57298i
\(867\) −9997.27 + 1083.11i −0.391609 + 0.0424273i
\(868\) 15342.6 8858.04i 0.599955 0.346384i
\(869\) 11301.1 + 19574.2i 0.441157 + 0.764106i
\(870\) 26025.7 + 70654.5i 1.01420 + 2.75335i
\(871\) 2350.19 4070.65i 0.0914272 0.158357i
\(872\) 970.272i 0.0376807i
\(873\) −2488.07 790.854i −0.0964587 0.0306602i
\(874\) 1655.04 0.0640534
\(875\) 28710.9 6162.45i 1.10926 0.238090i
\(876\) 46620.1 34100.0i 1.79811 1.31522i
\(877\) −38815.9 + 22410.4i −1.49455 + 0.862879i −0.999980 0.00625950i \(-0.998008\pi\)
−0.494569 + 0.869138i \(0.664674\pi\)
\(878\) 32227.5 18606.6i 1.23875 0.715195i
\(879\) −10258.7 + 7503.64i −0.393648 + 0.287931i
\(880\) −32067.1 + 8017.84i −1.22839 + 0.307138i
\(881\) 11986.7 0.458391 0.229196 0.973380i \(-0.426390\pi\)
0.229196 + 0.973380i \(0.426390\pi\)
\(882\) −2878.63 13129.1i −0.109896 0.501226i
\(883\) 14223.4i 0.542078i −0.962568 0.271039i \(-0.912633\pi\)
0.962568 0.271039i \(-0.0873672\pi\)
\(884\) 7311.32 12663.6i 0.278175 0.481813i
\(885\) 30678.9 11300.6i 1.16527 0.429228i
\(886\) 4012.67 + 6950.14i 0.152154 + 0.263538i
\(887\) 20039.8 11570.0i 0.758592 0.437973i −0.0701980 0.997533i \(-0.522363\pi\)
0.828790 + 0.559560i \(0.189030\pi\)
\(888\) −40339.2 + 4370.39i −1.52443 + 0.165158i
\(889\) −2911.69 + 5043.19i −0.109848 + 0.190262i
\(890\) −2189.97 + 2117.64i −0.0824809 + 0.0797567i
\(891\) 1911.28 20734.5i 0.0718633 0.779608i
\(892\) 71666.0i 2.69008i
\(893\) 15.9417 + 9.20394i 0.000597389 + 0.000344903i
\(894\) 7257.95 + 66991.8i 0.271524 + 2.50620i
\(895\) 9856.55 34460.2i 0.368121 1.28701i
\(896\) −18687.5 32367.7i −0.696770 1.20684i
\(897\) −3604.07 + 8165.09i −0.134154 + 0.303929i
\(898\) −32092.0 18528.3i −1.19257 0.688528i
\(899\) 12322.0 0.457133
\(900\) −10733.7 58238.5i −0.397544 2.15698i
\(901\) −2960.24 −0.109456
\(902\) 34925.6 + 20164.3i 1.28924 + 0.744344i
\(903\) −17343.6 23711.4i −0.639156 0.873828i
\(904\) −27277.4 47245.9i −1.00358 1.73825i
\(905\) −7006.33 + 24495.3i −0.257346 + 0.899726i
\(906\) −31891.9 + 23327.1i −1.16947 + 0.855400i
\(907\) −21240.0 12262.9i −0.777576 0.448934i 0.0579945 0.998317i \(-0.481529\pi\)
−0.835571 + 0.549383i \(0.814863\pi\)
\(908\) 3892.32i 0.142259i
\(909\) 8861.24 27878.0i 0.323332 1.01722i
\(910\) −8595.76 + 8311.86i −0.313128 + 0.302786i
\(911\) 4226.93 7321.26i 0.153726 0.266261i −0.778868 0.627187i \(-0.784206\pi\)
0.932594 + 0.360926i \(0.117539\pi\)
\(912\) 416.954 944.617i 0.0151389 0.0342976i
\(913\) −5641.78 + 3257.28i −0.204508 + 0.118073i
\(914\) 15913.2 + 27562.5i 0.575888 + 0.997467i
\(915\) 3541.60 + 2948.51i 0.127958 + 0.106530i
\(916\) 14020.3 24283.8i 0.505724 0.875940i
\(917\) 10560.5i 0.380302i
\(918\) 11648.9 57513.6i 0.418815 2.06779i
\(919\) −29199.7 −1.04811 −0.524053 0.851686i \(-0.675581\pi\)
−0.524053 + 0.851686i \(0.675581\pi\)
\(920\) 89265.2 22319.2i 3.19890 0.799830i
\(921\) 3100.10 + 28614.3i 0.110914 + 1.02375i
\(922\) 27731.5 16010.8i 0.990553 0.571896i
\(923\) −2763.35 + 1595.42i −0.0985447 + 0.0568948i
\(924\) 50059.0 + 22096.0i 1.78227 + 0.786695i
\(925\) −10697.1 + 17169.6i −0.380237 + 0.610307i
\(926\) −11603.4 −0.411783
\(927\) 8584.44 7829.53i 0.304153 0.277406i
\(928\) 35169.5i 1.24407i
\(929\) −25303.4 + 43826.7i −0.893624 + 1.54780i −0.0581262 + 0.998309i \(0.518513\pi\)
−0.835498 + 0.549493i \(0.814821\pi\)
\(930\) −13904.7 2396.42i −0.490273 0.0844964i
\(931\) −94.5431 163.754i −0.00332817 0.00576456i
\(932\) −100602. + 58082.3i −3.53574 + 2.04136i
\(933\) 10814.1 + 14784.6i 0.379462 + 0.518786i
\(934\) −15625.1 + 27063.4i −0.547396 + 0.948118i
\(935\) −18997.8 + 18370.3i −0.664485 + 0.642539i
\(936\) 8840.92 + 9693.34i 0.308733 + 0.338501i
\(937\) 30351.9i 1.05822i −0.848553 0.529110i \(-0.822526\pi\)
0.848553 0.529110i \(-0.177474\pi\)
\(938\) 42928.3 + 24784.7i 1.49431 + 0.862738i
\(939\) 32850.6 + 14500.2i 1.14168 + 0.503938i
\(940\) 1808.49 + 517.277i 0.0627515 + 0.0179486i
\(941\) 11250.3 + 19486.0i 0.389743 + 0.675054i 0.992415 0.122935i \(-0.0392306\pi\)
−0.602672 + 0.797989i \(0.705897\pi\)
\(942\) −31285.2 + 3389.46i −1.08209 + 0.117234i
\(943\) −41263.1 23823.3i −1.42493 0.822686i
\(944\) 58250.8 2.00837
\(945\) −15173.4 + 29257.6i −0.522318 + 1.00714i
\(946\) 38845.3 1.33506
\(947\) 31722.1 + 18314.7i 1.08852 + 0.628457i 0.933182 0.359404i \(-0.117020\pi\)
0.155338 + 0.987861i \(0.450353\pi\)
\(948\) −71727.8 + 7771.05i −2.45739 + 0.266236i
\(949\) 3189.88 + 5525.03i 0.109112 + 0.188988i
\(950\) −570.853 1070.19i −0.0194957 0.0365490i
\(951\) 20011.3 + 8832.97i 0.682345 + 0.301187i
\(952\) 72659.1 + 41949.8i 2.47363 + 1.42815i
\(953\) 29632.2i 1.00722i −0.863931 0.503611i \(-0.832005\pi\)
0.863931 0.503611i \(-0.167995\pi\)
\(954\) 1478.77 4652.29i 0.0501854 0.157886i
\(955\) −26336.1 27235.6i −0.892373 0.922853i
\(956\) −31208.1 + 54054.1i −1.05580 + 1.82870i
\(957\) 22468.6 + 30718.2i 0.758941 + 1.03759i
\(958\) −17063.9 + 9851.85i −0.575480 + 0.332254i
\(959\) −23334.8 40417.0i −0.785734 1.36093i
\(960\) −1330.52 + 7720.05i −0.0447315 + 0.259545i
\(961\) 13741.0 23800.1i 0.461246 0.798901i
\(962\) 8237.27i 0.276071i
\(963\) −74.7957 341.135i −0.00250286 0.0114153i
\(964\) −52066.4 −1.73957
\(965\) −7534.44 30133.8i −0.251339 1.00522i
\(966\) −86107.6 38007.9i −2.86798 1.26592i
\(967\) −43054.3 + 24857.4i −1.43178 + 0.826639i −0.997257 0.0740216i \(-0.976417\pi\)
−0.434524 + 0.900660i \(0.643083\pi\)
\(968\) 21526.8 12428.5i 0.714772 0.412674i
\(969\) −88.9175 820.719i −0.00294782 0.0272088i
\(970\) −5300.93 + 1325.41i −0.175467 + 0.0438724i
\(971\) −22201.1 −0.733745 −0.366872 0.930271i \(-0.619571\pi\)
−0.366872 + 0.930271i \(0.619571\pi\)
\(972\) 58085.6 + 32307.7i 1.91677 + 1.06612i
\(973\) 55319.4i 1.82267i
\(974\) 37342.2 64678.6i 1.22846 2.12776i
\(975\) 6522.85 485.808i 0.214255 0.0159572i
\(976\) 4105.31 + 7110.61i 0.134639 + 0.233202i
\(977\) −6847.97 + 3953.68i −0.224244 + 0.129467i −0.607914 0.794003i \(-0.707993\pi\)
0.383670 + 0.923470i \(0.374660\pi\)
\(978\) 23383.9 52976.6i 0.764553 1.73211i
\(979\) −769.901 + 1333.51i −0.0251340 + 0.0435333i
\(980\) −13431.3 13890.0i −0.437802 0.452756i
\(981\) 530.338 116.279i 0.0172603 0.00378442i
\(982\) 18383.9i 0.597406i
\(983\) 7088.28 + 4092.42i 0.229991 + 0.132785i 0.610568 0.791964i \(-0.290941\pi\)
−0.380577 + 0.924749i \(0.624275\pi\)
\(984\) −56530.2 + 41348.6i −1.83142 + 1.33958i
\(985\) −31621.3 9044.55i −1.02288 0.292572i
\(986\) 53627.9 + 92886.3i 1.73211 + 3.00010i
\(987\) −618.038 844.957i −0.0199315 0.0272495i
\(988\) 293.782 + 169.615i 0.00945996 + 0.00546171i
\(989\) −45894.0 −1.47558
\(990\) −19380.4 39033.5i −0.622172 1.25310i
\(991\) −4964.85 −0.159146 −0.0795729 0.996829i \(-0.525356\pi\)
−0.0795729 + 0.996829i \(0.525356\pi\)
\(992\) −5707.50 3295.23i −0.182675 0.105467i
\(993\) 3559.16 8063.34i 0.113743 0.257686i
\(994\) −16825.0 29141.8i −0.536879 0.929901i
\(995\) −15155.5 + 52986.2i −0.482876 + 1.68822i
\(996\) −2239.82 20673.8i −0.0712564 0.657706i
\(997\) 6147.30 + 3549.14i 0.195273 + 0.112741i 0.594449 0.804134i \(-0.297370\pi\)
−0.399176 + 0.916874i \(0.630704\pi\)
\(998\) 16465.8i 0.522261i
\(999\) −7223.14 21525.1i −0.228759 0.681707i
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 45.4.j.a.34.1 yes 32
3.2 odd 2 135.4.j.a.19.16 32
5.2 odd 4 225.4.e.g.151.16 32
5.3 odd 4 225.4.e.g.151.1 32
5.4 even 2 inner 45.4.j.a.34.16 yes 32
9.2 odd 6 405.4.b.f.244.1 16
9.4 even 3 inner 45.4.j.a.4.16 yes 32
9.5 odd 6 135.4.j.a.64.1 32
9.7 even 3 405.4.b.e.244.16 16
15.14 odd 2 135.4.j.a.19.1 32
45.2 even 12 2025.4.a.bl.1.16 16
45.4 even 6 inner 45.4.j.a.4.1 32
45.7 odd 12 2025.4.a.bk.1.1 16
45.13 odd 12 225.4.e.g.76.1 32
45.14 odd 6 135.4.j.a.64.16 32
45.22 odd 12 225.4.e.g.76.16 32
45.29 odd 6 405.4.b.f.244.16 16
45.34 even 6 405.4.b.e.244.1 16
45.38 even 12 2025.4.a.bl.1.1 16
45.43 odd 12 2025.4.a.bk.1.16 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.j.a.4.1 32 45.4 even 6 inner
45.4.j.a.4.16 yes 32 9.4 even 3 inner
45.4.j.a.34.1 yes 32 1.1 even 1 trivial
45.4.j.a.34.16 yes 32 5.4 even 2 inner
135.4.j.a.19.1 32 15.14 odd 2
135.4.j.a.19.16 32 3.2 odd 2
135.4.j.a.64.1 32 9.5 odd 6
135.4.j.a.64.16 32 45.14 odd 6
225.4.e.g.76.1 32 45.13 odd 12
225.4.e.g.76.16 32 45.22 odd 12
225.4.e.g.151.1 32 5.3 odd 4
225.4.e.g.151.16 32 5.2 odd 4
405.4.b.e.244.1 16 45.34 even 6
405.4.b.e.244.16 16 9.7 even 3
405.4.b.f.244.1 16 9.2 odd 6
405.4.b.f.244.16 16 45.29 odd 6
2025.4.a.bk.1.1 16 45.7 odd 12
2025.4.a.bk.1.16 16 45.43 odd 12
2025.4.a.bl.1.1 16 45.38 even 12
2025.4.a.bl.1.16 16 45.2 even 12