Properties

Label 216.3.x.a.101.25
Level $216$
Weight $3$
Character 216.101
Analytic conductor $5.886$
Analytic rank $0$
Dimension $420$
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] = [216,3,Mod(5,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 216.x (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.88557371018\)
Analytic rank: \(0\)
Dimension: \(420\)
Relative dimension: \(70\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 101.25
Character \(\chi\) \(=\) 216.101
Dual form 216.3.x.a.77.25

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.896883 + 1.78762i) q^{2} +(2.22122 + 2.01648i) q^{3} +(-2.39120 - 3.20658i) q^{4} +(-1.17275 - 6.65098i) q^{5} +(-5.59688 + 2.16217i) q^{6} +(-3.53673 - 2.96767i) q^{7} +(7.87679 - 1.39864i) q^{8} +(0.867653 + 8.95808i) q^{9} +O(q^{10})\) \(q+(-0.896883 + 1.78762i) q^{2} +(2.22122 + 2.01648i) q^{3} +(-2.39120 - 3.20658i) q^{4} +(-1.17275 - 6.65098i) q^{5} +(-5.59688 + 2.16217i) q^{6} +(-3.53673 - 2.96767i) q^{7} +(7.87679 - 1.39864i) q^{8} +(0.867653 + 8.95808i) q^{9} +(12.9413 + 3.86872i) q^{10} +(0.262671 - 1.48968i) q^{11} +(1.15460 - 11.9443i) q^{12} +(7.29340 - 20.0384i) q^{13} +(8.47712 - 3.66070i) q^{14} +(10.8066 - 17.1381i) q^{15} +(-4.56431 + 15.3352i) q^{16} +(24.0282 - 13.8727i) q^{17} +(-16.7919 - 6.48331i) q^{18} +(-7.52360 - 4.34375i) q^{19} +(-18.5226 + 19.6643i) q^{20} +(-1.87163 - 13.7236i) q^{21} +(2.42741 + 1.80563i) q^{22} +(0.193029 + 0.230043i) q^{23} +(20.3164 + 12.7767i) q^{24} +(-19.3678 + 7.04931i) q^{25} +(29.2799 + 31.0100i) q^{26} +(-16.1365 + 21.6475i) q^{27} +(-1.05903 + 18.4371i) q^{28} +(34.3747 - 12.5114i) q^{29} +(20.9442 + 34.6890i) q^{30} +(-15.7150 + 13.1865i) q^{31} +(-23.3199 - 21.9131i) q^{32} +(3.58736 - 2.77925i) q^{33} +(3.24867 + 55.3955i) q^{34} +(-15.5902 + 27.0030i) q^{35} +(26.6501 - 24.2028i) q^{36} +(-51.2331 + 29.5794i) q^{37} +(14.5128 - 9.55353i) q^{38} +(56.6073 - 29.8029i) q^{39} +(-18.5398 - 50.7481i) q^{40} +(9.84988 - 27.0623i) q^{41} +(26.2113 + 8.96268i) q^{42} +(-11.8578 - 2.09086i) q^{43} +(-5.40489 + 2.71986i) q^{44} +(58.5624 - 16.2763i) q^{45} +(-0.584355 + 0.138742i) q^{46} +(24.8603 - 29.6273i) q^{47} +(-41.0613 + 24.8590i) q^{48} +(-4.80736 - 27.2639i) q^{49} +(4.76915 - 40.9448i) q^{50} +(81.3458 + 17.6379i) q^{51} +(-81.6949 + 24.5291i) q^{52} +13.4919 q^{53} +(-24.2250 - 48.2613i) q^{54} -10.2159 q^{55} +(-32.0088 - 18.4291i) q^{56} +(-7.95251 - 24.8196i) q^{57} +(-8.46444 + 72.6702i) q^{58} +(16.1605 + 91.6506i) q^{59} +(-80.7955 + 6.32846i) q^{60} +(-48.6442 + 57.9719i) q^{61} +(-9.47793 - 39.9193i) q^{62} +(23.5160 - 34.2572i) q^{63} +(60.0876 - 22.0337i) q^{64} +(-141.829 - 25.0082i) q^{65} +(1.75081 + 8.90551i) q^{66} +(32.0270 - 87.9936i) q^{67} +(-101.940 - 43.8759i) q^{68} +(-0.0351159 + 0.900216i) q^{69} +(-34.2887 - 52.0880i) q^{70} +(-5.14249 + 2.96902i) q^{71} +(19.3635 + 69.3474i) q^{72} +(-13.7221 + 23.7675i) q^{73} +(-6.92684 - 118.115i) q^{74} +(-57.2350 - 23.3967i) q^{75} +(4.06186 + 34.5118i) q^{76} +(-5.34989 + 4.48909i) q^{77} +(2.50624 + 127.922i) q^{78} +(99.9884 - 36.3928i) q^{79} +(107.347 + 12.3728i) q^{80} +(-79.4944 + 15.5450i) q^{81} +(39.5431 + 41.8796i) q^{82} +(-80.7850 + 29.4033i) q^{83} +(-39.5303 + 38.8174i) q^{84} +(-120.446 - 143.542i) q^{85} +(14.3728 - 19.3221i) q^{86} +(101.583 + 41.5252i) q^{87} +(-0.0145308 - 12.1013i) q^{88} +(-15.4244 - 8.90528i) q^{89} +(-23.4277 + 119.286i) q^{90} +(-85.2623 + 49.2262i) q^{91} +(0.276080 - 1.16904i) q^{92} +(-61.4968 - 2.39889i) q^{93} +(30.6658 + 71.0131i) q^{94} +(-20.0669 + 55.1334i) q^{95} +(-7.61133 - 95.6978i) q^{96} +(-3.49905 + 19.8441i) q^{97} +(53.0492 + 15.8588i) q^{98} +(13.5726 + 1.06050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 420 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 420 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 51 q^{12} + 39 q^{14} - 12 q^{15} - 6 q^{16} - 18 q^{17} - 27 q^{18} + 57 q^{20} - 6 q^{22} - 12 q^{23} + 126 q^{24} - 12 q^{25} - 12 q^{28} + 87 q^{30} - 12 q^{31} + 84 q^{32} - 36 q^{33} - 18 q^{34} - 36 q^{36} - 108 q^{38} - 12 q^{39} + 69 q^{40} - 84 q^{41} + 114 q^{42} - 657 q^{44} - 3 q^{46} - 12 q^{47} - 453 q^{48} - 12 q^{49} + 153 q^{50} + 21 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 66 q^{57} + 129 q^{58} + 210 q^{60} - 900 q^{62} + 468 q^{63} - 3 q^{64} - 12 q^{65} - 855 q^{66} + 279 q^{68} + 153 q^{70} - 18 q^{71} - 156 q^{72} - 6 q^{73} + 423 q^{74} - 54 q^{76} + 642 q^{78} - 12 q^{79} - 12 q^{81} - 12 q^{82} + 192 q^{84} + 606 q^{86} - 588 q^{87} + 186 q^{88} - 18 q^{89} - 534 q^{90} - 735 q^{92} + 345 q^{94} - 162 q^{95} - 486 q^{96} - 12 q^{97} - 1548 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{7}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.896883 + 1.78762i −0.448441 + 0.893812i
\(3\) 2.22122 + 2.01648i 0.740407 + 0.672158i
\(4\) −2.39120 3.20658i −0.597801 0.801645i
\(5\) −1.17275 6.65098i −0.234549 1.33020i −0.843561 0.537034i \(-0.819545\pi\)
0.609012 0.793161i \(-0.291566\pi\)
\(6\) −5.59688 + 2.16217i −0.932813 + 0.360361i
\(7\) −3.53673 2.96767i −0.505247 0.423953i 0.354206 0.935168i \(-0.384751\pi\)
−0.859453 + 0.511215i \(0.829196\pi\)
\(8\) 7.87679 1.39864i 0.984599 0.174831i
\(9\) 0.867653 + 8.95808i 0.0964059 + 0.995342i
\(10\) 12.9413 + 3.86872i 1.29413 + 0.386872i
\(11\) 0.262671 1.48968i 0.0238792 0.135426i −0.970538 0.240950i \(-0.922541\pi\)
0.994417 + 0.105524i \(0.0336521\pi\)
\(12\) 1.15460 11.9443i 0.0962166 0.995360i
\(13\) 7.29340 20.0384i 0.561031 1.54142i −0.257099 0.966385i \(-0.582767\pi\)
0.818130 0.575034i \(-0.195011\pi\)
\(14\) 8.47712 3.66070i 0.605508 0.261478i
\(15\) 10.8066 17.1381i 0.720440 1.14254i
\(16\) −4.56431 + 15.3352i −0.285269 + 0.958447i
\(17\) 24.0282 13.8727i 1.41342 0.816040i 0.417713 0.908579i \(-0.362832\pi\)
0.995709 + 0.0925390i \(0.0294983\pi\)
\(18\) −16.7919 6.48331i −0.932881 0.360184i
\(19\) −7.52360 4.34375i −0.395979 0.228618i 0.288769 0.957399i \(-0.406754\pi\)
−0.684747 + 0.728780i \(0.740087\pi\)
\(20\) −18.5226 + 19.6643i −0.926130 + 0.983216i
\(21\) −1.87163 13.7236i −0.0891253 0.653504i
\(22\) 2.42741 + 1.80563i 0.110337 + 0.0820741i
\(23\) 0.193029 + 0.230043i 0.00839257 + 0.0100019i 0.770224 0.637773i \(-0.220144\pi\)
−0.761832 + 0.647775i \(0.775700\pi\)
\(24\) 20.3164 + 12.7767i 0.846518 + 0.532360i
\(25\) −19.3678 + 7.04931i −0.774713 + 0.281972i
\(26\) 29.2799 + 31.0100i 1.12615 + 1.19269i
\(27\) −16.1365 + 21.6475i −0.597648 + 0.801759i
\(28\) −1.05903 + 18.4371i −0.0378225 + 0.658468i
\(29\) 34.3747 12.5114i 1.18533 0.431426i 0.327250 0.944938i \(-0.393878\pi\)
0.858083 + 0.513512i \(0.171656\pi\)
\(30\) 20.9442 + 34.6890i 0.698141 + 1.15630i
\(31\) −15.7150 + 13.1865i −0.506937 + 0.425370i −0.860050 0.510210i \(-0.829568\pi\)
0.353113 + 0.935581i \(0.385123\pi\)
\(32\) −23.3199 21.9131i −0.728746 0.684785i
\(33\) 3.58736 2.77925i 0.108708 0.0842196i
\(34\) 3.24867 + 55.3955i 0.0955491 + 1.62928i
\(35\) −15.5902 + 27.0030i −0.445435 + 0.771515i
\(36\) 26.6501 24.2028i 0.740279 0.672299i
\(37\) −51.2331 + 29.5794i −1.38468 + 0.799444i −0.992709 0.120534i \(-0.961539\pi\)
−0.391969 + 0.919979i \(0.628206\pi\)
\(38\) 14.5128 9.55353i 0.381915 0.251409i
\(39\) 56.6073 29.8029i 1.45147 0.764176i
\(40\) −18.5398 50.7481i −0.463496 1.26870i
\(41\) 9.84988 27.0623i 0.240241 0.660057i −0.759711 0.650261i \(-0.774660\pi\)
0.999952 0.00979585i \(-0.00311816\pi\)
\(42\) 26.2113 + 8.96268i 0.624078 + 0.213397i
\(43\) −11.8578 2.09086i −0.275764 0.0486246i 0.0340560 0.999420i \(-0.489158\pi\)
−0.309820 + 0.950795i \(0.600269\pi\)
\(44\) −5.40489 + 2.71986i −0.122838 + 0.0618149i
\(45\) 58.5624 16.2763i 1.30139 0.361695i
\(46\) −0.584355 + 0.138742i −0.0127034 + 0.00301613i
\(47\) 24.8603 29.6273i 0.528942 0.630368i −0.433729 0.901043i \(-0.642802\pi\)
0.962671 + 0.270675i \(0.0872469\pi\)
\(48\) −41.0613 + 24.8590i −0.855444 + 0.517895i
\(49\) −4.80736 27.2639i −0.0981093 0.556405i
\(50\) 4.76915 40.9448i 0.0953830 0.818896i
\(51\) 81.3458 + 17.6379i 1.59502 + 0.345842i
\(52\) −81.6949 + 24.5291i −1.57105 + 0.471714i
\(53\) 13.4919 0.254564 0.127282 0.991867i \(-0.459375\pi\)
0.127282 + 0.991867i \(0.459375\pi\)
\(54\) −24.2250 48.2613i −0.448611 0.893727i
\(55\) −10.2159 −0.185744
\(56\) −32.0088 18.4291i −0.571586 0.329091i
\(57\) −7.95251 24.8196i −0.139518 0.435431i
\(58\) −8.46444 + 72.6702i −0.145939 + 1.25293i
\(59\) 16.1605 + 91.6506i 0.273906 + 1.55340i 0.742414 + 0.669941i \(0.233681\pi\)
−0.468508 + 0.883459i \(0.655208\pi\)
\(60\) −80.7955 + 6.32846i −1.34659 + 0.105474i
\(61\) −48.6442 + 57.9719i −0.797446 + 0.950359i −0.999579 0.0289990i \(-0.990768\pi\)
0.202134 + 0.979358i \(0.435212\pi\)
\(62\) −9.47793 39.9193i −0.152870 0.643860i
\(63\) 23.5160 34.2572i 0.373269 0.543766i
\(64\) 60.0876 22.0337i 0.938869 0.344276i
\(65\) −141.829 25.0082i −2.18198 0.384741i
\(66\) 1.75081 + 8.90551i 0.0265274 + 0.134932i
\(67\) 32.0270 87.9936i 0.478015 1.31334i −0.433160 0.901317i \(-0.642601\pi\)
0.911175 0.412019i \(-0.135176\pi\)
\(68\) −101.940 43.8759i −1.49912 0.645234i
\(69\) −0.0351159 + 0.900216i −0.000508926 + 0.0130466i
\(70\) −34.2887 52.0880i −0.489839 0.744114i
\(71\) −5.14249 + 2.96902i −0.0724294 + 0.0418171i −0.535777 0.844359i \(-0.679981\pi\)
0.463348 + 0.886176i \(0.346648\pi\)
\(72\) 19.3635 + 69.3474i 0.268937 + 0.963158i
\(73\) −13.7221 + 23.7675i −0.187975 + 0.325582i −0.944575 0.328296i \(-0.893526\pi\)
0.756600 + 0.653878i \(0.226859\pi\)
\(74\) −6.92684 118.115i −0.0936060 1.59615i
\(75\) −57.2350 23.3967i −0.763133 0.311955i
\(76\) 4.06186 + 34.5118i 0.0534455 + 0.454103i
\(77\) −5.34989 + 4.48909i −0.0694791 + 0.0582999i
\(78\) 2.50624 + 127.922i 0.0321313 + 1.64003i
\(79\) 99.9884 36.3928i 1.26568 0.460668i 0.380006 0.924984i \(-0.375922\pi\)
0.885670 + 0.464316i \(0.153700\pi\)
\(80\) 107.347 + 12.3728i 1.34183 + 0.154660i
\(81\) −79.4944 + 15.5450i −0.981412 + 0.191914i
\(82\) 39.5431 + 41.8796i 0.482233 + 0.510727i
\(83\) −80.7850 + 29.4033i −0.973313 + 0.354257i −0.779237 0.626729i \(-0.784393\pi\)
−0.194076 + 0.980986i \(0.562171\pi\)
\(84\) −39.5303 + 38.8174i −0.470599 + 0.462112i
\(85\) −120.446 143.542i −1.41701 1.68873i
\(86\) 14.3728 19.3221i 0.167125 0.224676i
\(87\) 101.583 + 41.5252i 1.16762 + 0.477301i
\(88\) −0.0145308 12.1013i −0.000165123 0.137515i
\(89\) −15.4244 8.90528i −0.173308 0.100059i 0.410837 0.911709i \(-0.365237\pi\)
−0.584145 + 0.811650i \(0.698570\pi\)
\(90\) −23.4277 + 119.286i −0.260308 + 1.32539i
\(91\) −85.2623 + 49.2262i −0.936948 + 0.540947i
\(92\) 0.276080 1.16904i 0.00300087 0.0127070i
\(93\) −61.4968 2.39889i −0.661256 0.0257945i
\(94\) 30.6658 + 71.0131i 0.326232 + 0.755458i
\(95\) −20.0669 + 55.1334i −0.211231 + 0.580351i
\(96\) −7.61133 95.6978i −0.0792847 0.996852i
\(97\) −3.49905 + 19.8441i −0.0360727 + 0.204579i −0.997517 0.0704197i \(-0.977566\pi\)
0.961445 + 0.274998i \(0.0886773\pi\)
\(98\) 53.0492 + 15.8588i 0.541318 + 0.161824i
\(99\) 13.5726 + 1.06050i 0.137097 + 0.0107121i
\(100\) 68.9165 + 45.2481i 0.689165 + 0.452481i
\(101\) −34.9272 29.3074i −0.345814 0.290172i 0.453293 0.891362i \(-0.350249\pi\)
−0.799107 + 0.601189i \(0.794694\pi\)
\(102\) −104.488 + 129.597i −1.02439 + 1.27056i
\(103\) 33.1318 + 187.900i 0.321668 + 1.82427i 0.532122 + 0.846668i \(0.321395\pi\)
−0.210454 + 0.977604i \(0.567494\pi\)
\(104\) 29.4219 168.039i 0.282903 1.61576i
\(105\) −89.0803 + 28.5425i −0.848384 + 0.271833i
\(106\) −12.1007 + 24.1185i −0.114157 + 0.227533i
\(107\) 185.803 1.73647 0.868237 0.496150i \(-0.165253\pi\)
0.868237 + 0.496150i \(0.165253\pi\)
\(108\) 108.000 0.0205447i 1.00000 0.000190229i
\(109\) 134.904i 1.23765i −0.785529 0.618825i \(-0.787609\pi\)
0.785529 0.618825i \(-0.212391\pi\)
\(110\) 9.16246 18.2622i 0.0832951 0.166020i
\(111\) −173.446 37.6078i −1.56258 0.338809i
\(112\) 61.6524 40.6910i 0.550468 0.363312i
\(113\) 97.6617 17.2204i 0.864262 0.152393i 0.276093 0.961131i \(-0.410960\pi\)
0.588169 + 0.808738i \(0.299849\pi\)
\(114\) 51.5006 + 8.04416i 0.451759 + 0.0705628i
\(115\) 1.30364 1.55361i 0.0113360 0.0135097i
\(116\) −122.315 80.3079i −1.05444 0.692310i
\(117\) 185.834 + 47.9484i 1.58833 + 0.409815i
\(118\) −178.331 53.3110i −1.51128 0.451788i
\(119\) −126.151 22.2438i −1.06009 0.186923i
\(120\) 61.1512 150.108i 0.509593 1.25090i
\(121\) 111.553 + 40.6018i 0.921923 + 0.335552i
\(122\) −60.0038 138.952i −0.491835 1.13895i
\(123\) 76.4493 40.2494i 0.621539 0.327231i
\(124\) 79.8613 + 18.8600i 0.644043 + 0.152097i
\(125\) −14.8214 25.6714i −0.118571 0.205371i
\(126\) 40.1480 + 72.7625i 0.318635 + 0.577480i
\(127\) 24.6917 42.7672i 0.194423 0.336750i −0.752288 0.658834i \(-0.771050\pi\)
0.946711 + 0.322084i \(0.104383\pi\)
\(128\) −14.5036 + 127.176i −0.113310 + 0.993560i
\(129\) −22.1227 28.5553i −0.171494 0.221359i
\(130\) 171.909 231.107i 1.32238 1.77774i
\(131\) −169.319 + 142.076i −1.29251 + 1.08455i −0.301127 + 0.953584i \(0.597363\pi\)
−0.991387 + 0.130964i \(0.958193\pi\)
\(132\) −17.4900 4.85742i −0.132500 0.0367986i
\(133\) 13.7181 + 37.6902i 0.103144 + 0.283385i
\(134\) 128.575 + 136.172i 0.959514 + 1.01621i
\(135\) 162.901 + 81.9364i 1.20667 + 0.606937i
\(136\) 169.862 142.879i 1.24898 1.05058i
\(137\) 73.0046 + 200.579i 0.532881 + 1.46408i 0.855627 + 0.517592i \(0.173172\pi\)
−0.322747 + 0.946485i \(0.604606\pi\)
\(138\) −1.57775 0.870162i −0.0114330 0.00630552i
\(139\) 38.1115 + 45.4195i 0.274183 + 0.326759i 0.885511 0.464619i \(-0.153809\pi\)
−0.611328 + 0.791378i \(0.709364\pi\)
\(140\) 123.867 14.5785i 0.884763 0.104132i
\(141\) 114.963 15.6787i 0.815340 0.111197i
\(142\) −0.695277 11.8557i −0.00489632 0.0834908i
\(143\) −27.9352 16.1284i −0.195351 0.112786i
\(144\) −141.334 27.5818i −0.981485 0.191540i
\(145\) −123.525 213.952i −0.851900 1.47553i
\(146\) −30.1801 45.8467i −0.206713 0.314018i
\(147\) 44.2987 70.2530i 0.301352 0.477912i
\(148\) 217.357 + 93.5526i 1.46863 + 0.632112i
\(149\) 92.2544 + 33.5779i 0.619157 + 0.225355i 0.632505 0.774556i \(-0.282027\pi\)
−0.0133481 + 0.999911i \(0.504249\pi\)
\(150\) 93.1575 81.3306i 0.621050 0.542204i
\(151\) −30.3340 + 172.033i −0.200888 + 1.13929i 0.702893 + 0.711295i \(0.251891\pi\)
−0.903781 + 0.427995i \(0.859220\pi\)
\(152\) −65.3371 23.6920i −0.429850 0.155868i
\(153\) 145.121 + 203.210i 0.948501 + 1.32817i
\(154\) −3.22658 13.5898i −0.0209518 0.0882453i
\(155\) 106.133 + 89.0559i 0.684727 + 0.574554i
\(156\) −230.925 110.251i −1.48029 0.706738i
\(157\) 19.9968 3.52597i 0.127368 0.0224584i −0.109601 0.993976i \(-0.534957\pi\)
0.236969 + 0.971517i \(0.423846\pi\)
\(158\) −24.6212 + 211.382i −0.155831 + 1.33786i
\(159\) 29.9685 + 27.2061i 0.188481 + 0.171108i
\(160\) −118.395 + 180.798i −0.739970 + 1.12999i
\(161\) 1.38645i 0.00861148i
\(162\) 43.5085 156.048i 0.268571 0.963260i
\(163\) 25.6271i 0.157221i 0.996905 + 0.0786106i \(0.0250484\pi\)
−0.996905 + 0.0786106i \(0.974952\pi\)
\(164\) −110.331 + 33.1271i −0.672747 + 0.201994i
\(165\) −22.6918 20.6001i −0.137526 0.124849i
\(166\) 19.8926 170.785i 0.119835 1.02882i
\(167\) 85.9494 15.1552i 0.514667 0.0907497i 0.0897186 0.995967i \(-0.471403\pi\)
0.424949 + 0.905217i \(0.360292\pi\)
\(168\) −33.9369 105.480i −0.202005 0.627857i
\(169\) −218.884 183.666i −1.29517 1.08678i
\(170\) 364.624 86.5717i 2.14485 0.509245i
\(171\) 32.3838 71.1658i 0.189379 0.416174i
\(172\) 21.6500 + 43.0228i 0.125872 + 0.250132i
\(173\) −29.4634 + 167.095i −0.170308 + 0.965867i 0.773112 + 0.634269i \(0.218699\pi\)
−0.943421 + 0.331598i \(0.892412\pi\)
\(174\) −165.339 + 144.348i −0.950225 + 0.829588i
\(175\) 89.4188 + 32.5458i 0.510965 + 0.185976i
\(176\) 21.6456 + 10.8275i 0.122986 + 0.0615198i
\(177\) −148.915 + 236.164i −0.841329 + 1.33426i
\(178\) 29.7532 19.5860i 0.167153 0.110034i
\(179\) 22.6142 + 39.1690i 0.126336 + 0.218821i 0.922255 0.386583i \(-0.126345\pi\)
−0.795918 + 0.605404i \(0.793011\pi\)
\(180\) −192.226 148.865i −1.06792 0.827029i
\(181\) 6.62060 + 3.82241i 0.0365779 + 0.0211183i 0.518177 0.855273i \(-0.326611\pi\)
−0.481600 + 0.876391i \(0.659944\pi\)
\(182\) −11.5277 196.567i −0.0633389 1.08004i
\(183\) −224.948 + 30.6786i −1.22923 + 0.167643i
\(184\) 1.84220 + 1.54202i 0.0100120 + 0.00838056i
\(185\) 256.815 + 306.061i 1.38819 + 1.65438i
\(186\) 59.4437 107.782i 0.319590 0.579471i
\(187\) −14.3544 39.4383i −0.0767614 0.210900i
\(188\) −154.448 8.87154i −0.821533 0.0471890i
\(189\) 121.313 28.6735i 0.641868 0.151712i
\(190\) −80.5601 85.3203i −0.424000 0.449054i
\(191\) −66.6588 183.144i −0.348999 0.958867i −0.982686 0.185278i \(-0.940682\pi\)
0.633687 0.773590i \(-0.281541\pi\)
\(192\) 177.898 + 72.2235i 0.926553 + 0.376164i
\(193\) −177.211 + 148.697i −0.918190 + 0.770453i −0.973659 0.228007i \(-0.926779\pi\)
0.0554691 + 0.998460i \(0.482335\pi\)
\(194\) −32.3356 24.0528i −0.166678 0.123984i
\(195\) −264.604 341.542i −1.35694 1.75150i
\(196\) −75.9284 + 80.6086i −0.387390 + 0.411268i
\(197\) −98.1177 + 169.945i −0.498059 + 0.862664i −0.999997 0.00223957i \(-0.999287\pi\)
0.501938 + 0.864903i \(0.332620\pi\)
\(198\) −14.0688 + 23.3116i −0.0710546 + 0.117735i
\(199\) −93.8065 162.478i −0.471389 0.816470i 0.528075 0.849198i \(-0.322914\pi\)
−0.999464 + 0.0327275i \(0.989581\pi\)
\(200\) −142.697 + 82.6146i −0.713484 + 0.413073i
\(201\) 248.576 130.871i 1.23670 0.651102i
\(202\) 83.7162 36.1514i 0.414437 0.178967i
\(203\) −158.704 57.7634i −0.781791 0.284549i
\(204\) −137.957 303.018i −0.676259 1.48538i
\(205\) −191.542 33.7741i −0.934352 0.164752i
\(206\) −365.610 109.297i −1.77481 0.530568i
\(207\) −1.89326 + 1.92877i −0.00914620 + 0.00931772i
\(208\) 274.003 + 203.307i 1.31732 + 0.977438i
\(209\) −8.44704 + 10.0668i −0.0404165 + 0.0481665i
\(210\) 28.8714 184.841i 0.137483 0.880197i
\(211\) 340.134 59.9747i 1.61201 0.284240i 0.706226 0.707986i \(-0.250396\pi\)
0.905781 + 0.423746i \(0.139285\pi\)
\(212\) −32.2619 43.2629i −0.152179 0.204070i
\(213\) −17.4095 3.77485i −0.0817350 0.0177223i
\(214\) −166.643 + 332.145i −0.778707 + 1.55208i
\(215\) 81.3182i 0.378224i
\(216\) −96.8266 + 193.082i −0.448271 + 0.893897i
\(217\) 94.7130 0.436466
\(218\) 241.157 + 120.993i 1.10623 + 0.555014i
\(219\) −78.4064 + 25.1224i −0.358020 + 0.114714i
\(220\) 24.4283 + 32.7581i 0.111038 + 0.148900i
\(221\) −102.740 582.666i −0.464886 2.63650i
\(222\) 222.790 276.327i 1.00356 1.24472i
\(223\) 60.5699 + 50.8242i 0.271614 + 0.227911i 0.768413 0.639955i \(-0.221047\pi\)
−0.496799 + 0.867866i \(0.665491\pi\)
\(224\) 17.4452 + 146.706i 0.0778804 + 0.654939i
\(225\) −79.9528 167.382i −0.355346 0.743920i
\(226\) −56.8075 + 190.027i −0.251361 + 0.840828i
\(227\) −55.5632 + 315.115i −0.244772 + 1.38817i 0.576250 + 0.817274i \(0.304516\pi\)
−0.821022 + 0.570897i \(0.806595\pi\)
\(228\) −60.5699 + 84.8490i −0.265657 + 0.372145i
\(229\) −144.032 + 395.724i −0.628959 + 1.72805i 0.0549550 + 0.998489i \(0.482498\pi\)
−0.683914 + 0.729562i \(0.739724\pi\)
\(230\) 1.60807 + 3.72382i 0.00699161 + 0.0161905i
\(231\) −20.9354 0.816655i −0.0906295 0.00353530i
\(232\) 253.263 146.627i 1.09165 0.632014i
\(233\) 309.337 178.596i 1.32763 0.766505i 0.342693 0.939447i \(-0.388661\pi\)
0.984932 + 0.172943i \(0.0553275\pi\)
\(234\) −252.385 + 289.197i −1.07857 + 1.23589i
\(235\) −226.205 130.600i −0.962576 0.555743i
\(236\) 255.242 270.975i 1.08153 1.14820i
\(237\) 295.482 + 120.788i 1.24676 + 0.509652i
\(238\) 152.906 205.560i 0.642462 0.863698i
\(239\) −42.6736 50.8564i −0.178551 0.212788i 0.669345 0.742952i \(-0.266575\pi\)
−0.847895 + 0.530164i \(0.822130\pi\)
\(240\) 213.491 + 243.944i 0.889546 + 1.01644i
\(241\) 211.125 76.8430i 0.876035 0.318851i 0.135427 0.990787i \(-0.456759\pi\)
0.740609 + 0.671937i \(0.234537\pi\)
\(242\) −172.631 + 162.999i −0.713349 + 0.673550i
\(243\) −207.921 125.769i −0.855641 0.517570i
\(244\) 302.210 + 17.3590i 1.23856 + 0.0711433i
\(245\) −175.693 + 63.9472i −0.717116 + 0.261009i
\(246\) 3.38472 + 172.762i 0.0137590 + 0.702283i
\(247\) −141.915 + 119.080i −0.574553 + 0.482107i
\(248\) −105.341 + 125.847i −0.424761 + 0.507447i
\(249\) −238.733 97.5897i −0.958765 0.391926i
\(250\) 59.1839 3.47084i 0.236735 0.0138833i
\(251\) 15.5259 26.8916i 0.0618560 0.107138i −0.833439 0.552611i \(-0.813631\pi\)
0.895295 + 0.445474i \(0.146965\pi\)
\(252\) −166.080 + 6.51014i −0.659048 + 0.0258339i
\(253\) 0.393395 0.227127i 0.00155492 0.000897734i
\(254\) 54.3062 + 82.4967i 0.213804 + 0.324790i
\(255\) 21.9115 561.714i 0.0859275 2.20280i
\(256\) −214.334 139.989i −0.837243 0.546831i
\(257\) 69.7447 191.622i 0.271380 0.745611i −0.726886 0.686758i \(-0.759033\pi\)
0.998267 0.0588532i \(-0.0187444\pi\)
\(258\) 70.8876 13.9364i 0.274758 0.0540169i
\(259\) 268.980 + 47.4284i 1.03853 + 0.183121i
\(260\) 258.950 + 514.584i 0.995961 + 1.97917i
\(261\) 141.903 + 297.075i 0.543690 + 1.13822i
\(262\) −102.119 430.105i −0.389765 1.64162i
\(263\) −71.1094 + 84.7449i −0.270378 + 0.322224i −0.884100 0.467299i \(-0.845227\pi\)
0.613722 + 0.789522i \(0.289672\pi\)
\(264\) 24.3697 26.9090i 0.0923095 0.101928i
\(265\) −15.8226 89.7344i −0.0597079 0.338620i
\(266\) −79.6795 9.28088i −0.299547 0.0348905i
\(267\) −16.3037 50.8835i −0.0610626 0.190575i
\(268\) −358.741 + 107.713i −1.33859 + 0.401915i
\(269\) 272.800 1.01413 0.507064 0.861909i \(-0.330731\pi\)
0.507064 + 0.861909i \(0.330731\pi\)
\(270\) −292.575 + 217.718i −1.08361 + 0.806364i
\(271\) −379.900 −1.40185 −0.700923 0.713237i \(-0.747228\pi\)
−0.700923 + 0.713237i \(0.747228\pi\)
\(272\) 103.068 + 431.795i 0.378926 + 1.58748i
\(273\) −288.650 62.5870i −1.05733 0.229256i
\(274\) −424.036 49.3906i −1.54758 0.180258i
\(275\) 5.41387 + 30.7036i 0.0196868 + 0.111649i
\(276\) 2.97058 2.04000i 0.0107630 0.00739129i
\(277\) 45.8845 54.6830i 0.165648 0.197412i −0.676835 0.736135i \(-0.736649\pi\)
0.842483 + 0.538723i \(0.181093\pi\)
\(278\) −115.374 + 27.3930i −0.415016 + 0.0985361i
\(279\) −131.761 129.335i −0.472261 0.463567i
\(280\) −85.0332 + 234.502i −0.303690 + 0.837509i
\(281\) −124.554 21.9623i −0.443254 0.0781577i −0.0524334 0.998624i \(-0.516698\pi\)
−0.390821 + 0.920467i \(0.627809\pi\)
\(282\) −75.0806 + 219.573i −0.266243 + 0.778626i
\(283\) 25.1636 69.1363i 0.0889172 0.244298i −0.887261 0.461267i \(-0.847395\pi\)
0.976178 + 0.216969i \(0.0696172\pi\)
\(284\) 21.8171 + 9.39027i 0.0768208 + 0.0330643i
\(285\) −155.748 + 81.9990i −0.546485 + 0.287716i
\(286\) 53.8861 35.4723i 0.188413 0.124029i
\(287\) −115.148 + 66.4810i −0.401214 + 0.231641i
\(288\) 176.066 227.914i 0.611340 0.791368i
\(289\) 240.402 416.389i 0.831842 1.44079i
\(290\) 493.254 28.9269i 1.70088 0.0997479i
\(291\) −47.7874 + 37.0224i −0.164218 + 0.127225i
\(292\) 109.025 12.8316i 0.373372 0.0439439i
\(293\) 96.2867 80.7942i 0.328624 0.275748i −0.463515 0.886089i \(-0.653412\pi\)
0.792139 + 0.610341i \(0.208968\pi\)
\(294\) 85.8552 + 142.198i 0.292025 + 0.483667i
\(295\) 590.614 214.966i 2.00208 0.728698i
\(296\) −362.181 + 304.648i −1.22358 + 1.02922i
\(297\) 28.0093 + 29.7244i 0.0943074 + 0.100082i
\(298\) −142.766 + 134.801i −0.479080 + 0.452352i
\(299\) 6.01755 2.19021i 0.0201256 0.00732511i
\(300\) 61.8372 + 239.475i 0.206124 + 0.798249i
\(301\) 35.7330 + 42.5850i 0.118714 + 0.141478i
\(302\) −280.324 208.519i −0.928225 0.690461i
\(303\) −18.4834 135.528i −0.0610013 0.447287i
\(304\) 100.952 95.5493i 0.332079 0.314307i
\(305\) 442.617 + 255.545i 1.45120 + 0.837852i
\(306\) −493.419 + 77.1660i −1.61248 + 0.252176i
\(307\) 363.521 209.879i 1.18411 0.683646i 0.227147 0.973860i \(-0.427060\pi\)
0.956962 + 0.290215i \(0.0937268\pi\)
\(308\) 27.1873 + 6.42052i 0.0882704 + 0.0208459i
\(309\) −305.302 + 484.177i −0.988034 + 1.56692i
\(310\) −254.387 + 109.853i −0.820604 + 0.354364i
\(311\) −137.760 + 378.491i −0.442957 + 1.21701i 0.494582 + 0.869131i \(0.335321\pi\)
−0.937538 + 0.347882i \(0.886901\pi\)
\(312\) 404.200 313.924i 1.29551 1.00617i
\(313\) 21.6919 123.021i 0.0693033 0.393038i −0.930349 0.366675i \(-0.880496\pi\)
0.999652 0.0263635i \(-0.00839274\pi\)
\(314\) −11.6316 + 38.9091i −0.0370435 + 0.123914i
\(315\) −255.422 116.229i −0.810864 0.368981i
\(316\) −355.789 233.598i −1.12591 0.739235i
\(317\) −4.40653 3.69751i −0.0139007 0.0116641i 0.635811 0.771845i \(-0.280666\pi\)
−0.649712 + 0.760181i \(0.725110\pi\)
\(318\) −75.5126 + 29.1718i −0.237461 + 0.0917352i
\(319\) −9.60871 54.4937i −0.0301214 0.170827i
\(320\) −217.013 373.801i −0.678165 1.16813i
\(321\) 412.709 + 374.667i 1.28570 + 1.16719i
\(322\) 2.47845 + 1.24348i 0.00769705 + 0.00386174i
\(323\) −241.038 −0.746247
\(324\) 239.933 + 217.734i 0.740535 + 0.672018i
\(325\) 439.514i 1.35235i
\(326\) −45.8115 22.9845i −0.140526 0.0705045i
\(327\) 272.030 299.651i 0.831897 0.916365i
\(328\) 39.7348 226.941i 0.121143 0.691892i
\(329\) −175.848 + 31.0068i −0.534493 + 0.0942456i
\(330\) 57.1771 22.0885i 0.173264 0.0669348i
\(331\) −34.1666 + 40.7182i −0.103222 + 0.123016i −0.815182 0.579204i \(-0.803363\pi\)
0.711960 + 0.702220i \(0.247808\pi\)
\(332\) 287.457 + 188.734i 0.865836 + 0.568477i
\(333\) −309.427 433.285i −0.929212 1.30116i
\(334\) −49.9948 + 167.238i −0.149685 + 0.500712i
\(335\) −622.803 109.817i −1.85911 0.327812i
\(336\) 218.996 + 33.9369i 0.651774 + 0.101003i
\(337\) 578.615 + 210.599i 1.71696 + 0.624922i 0.997569 0.0696839i \(-0.0221991\pi\)
0.719390 + 0.694606i \(0.244421\pi\)
\(338\) 524.639 226.556i 1.55218 0.670284i
\(339\) 251.653 + 158.682i 0.742338 + 0.468089i
\(340\) −172.268 + 729.456i −0.506670 + 2.14546i
\(341\) 15.5158 + 26.8741i 0.0455009 + 0.0788098i
\(342\) 98.1733 + 121.717i 0.287056 + 0.355899i
\(343\) −177.021 + 306.610i −0.516097 + 0.893906i
\(344\) −96.3260 + 0.115665i −0.280018 + 0.000336236i
\(345\) 6.02849 0.822170i 0.0174739 0.00238310i
\(346\) −272.278 202.534i −0.786931 0.585359i
\(347\) 469.614 394.053i 1.35336 1.13560i 0.375382 0.926870i \(-0.377512\pi\)
0.977973 0.208729i \(-0.0669328\pi\)
\(348\) −109.751 425.028i −0.315376 1.22134i
\(349\) −3.09870 8.51362i −0.00887880 0.0243943i 0.935174 0.354188i \(-0.115243\pi\)
−0.944053 + 0.329794i \(0.893021\pi\)
\(350\) −138.378 + 130.658i −0.395365 + 0.373307i
\(351\) 316.092 + 481.234i 0.900547 + 1.37104i
\(352\) −38.7690 + 28.9833i −0.110139 + 0.0823388i
\(353\) −48.5823 133.479i −0.137627 0.378127i 0.851663 0.524090i \(-0.175594\pi\)
−0.989290 + 0.145963i \(0.953372\pi\)
\(354\) −288.612 478.016i −0.815289 1.35033i
\(355\) 25.7777 + 30.7206i 0.0726132 + 0.0865370i
\(356\) 8.32736 + 70.7538i 0.0233915 + 0.198747i
\(357\) −235.355 303.788i −0.659257 0.850948i
\(358\) −90.3017 + 5.29575i −0.252240 + 0.0147926i
\(359\) −283.244 163.531i −0.788980 0.455518i 0.0506232 0.998718i \(-0.483879\pi\)
−0.839603 + 0.543200i \(0.817213\pi\)
\(360\) 438.519 210.113i 1.21811 0.583647i
\(361\) −142.764 247.274i −0.395467 0.684969i
\(362\) −12.7709 + 8.40690i −0.0352788 + 0.0232235i
\(363\) 165.911 + 315.129i 0.457054 + 0.868124i
\(364\) 361.727 + 155.691i 0.993756 + 0.427721i
\(365\) 174.169 + 63.3925i 0.477176 + 0.173678i
\(366\) 146.911 429.638i 0.401395 1.17388i
\(367\) 12.6456 71.7170i 0.0344568 0.195414i −0.962720 0.270499i \(-0.912811\pi\)
0.997177 + 0.0750843i \(0.0239226\pi\)
\(368\) −4.40879 + 1.91015i −0.0119804 + 0.00519061i
\(369\) 250.973 + 64.7553i 0.680143 + 0.175489i
\(370\) −777.455 + 184.589i −2.10123 + 0.498889i
\(371\) −47.7173 40.0396i −0.128618 0.107923i
\(372\) 139.359 + 202.931i 0.374621 + 0.545512i
\(373\) −223.960 + 39.4902i −0.600429 + 0.105872i −0.465597 0.884997i \(-0.654160\pi\)
−0.134832 + 0.990869i \(0.543049\pi\)
\(374\) 83.3751 + 9.71133i 0.222928 + 0.0259661i
\(375\) 18.8441 86.9088i 0.0502511 0.231757i
\(376\) 154.381 268.139i 0.410588 0.713135i
\(377\) 780.065i 2.06914i
\(378\) −57.5461 + 242.579i −0.152238 + 0.641743i
\(379\) 429.196i 1.13244i −0.824253 0.566222i \(-0.808405\pi\)
0.824253 0.566222i \(-0.191595\pi\)
\(380\) 224.774 67.4889i 0.591509 0.177602i
\(381\) 141.085 45.2054i 0.370301 0.118649i
\(382\) 387.177 + 45.0974i 1.01355 + 0.118056i
\(383\) 524.816 92.5392i 1.37028 0.241617i 0.560403 0.828220i \(-0.310646\pi\)
0.809874 + 0.586604i \(0.199535\pi\)
\(384\) −288.662 + 253.239i −0.751725 + 0.659477i
\(385\) 36.1309 + 30.3174i 0.0938464 + 0.0787465i
\(386\) −106.878 450.150i −0.276886 1.16619i
\(387\) 8.44157 108.038i 0.0218128 0.279167i
\(388\) 71.9987 36.2313i 0.185564 0.0933797i
\(389\) 70.0590 397.324i 0.180100 1.02140i −0.751991 0.659174i \(-0.770906\pi\)
0.932091 0.362225i \(-0.117983\pi\)
\(390\) 847.869 166.689i 2.17402 0.427408i
\(391\) 7.82946 + 2.84969i 0.0200242 + 0.00728821i
\(392\) −75.9990 208.028i −0.193875 0.530684i
\(393\) −662.588 25.8464i −1.68598 0.0657670i
\(394\) −215.797 327.818i −0.547709 0.832026i
\(395\) −359.309 622.341i −0.909642 1.57555i
\(396\) −29.0543 46.0575i −0.0733694 0.116307i
\(397\) 194.922 + 112.538i 0.490987 + 0.283472i 0.724984 0.688766i \(-0.241847\pi\)
−0.233997 + 0.972237i \(0.575180\pi\)
\(398\) 374.582 21.9674i 0.941162 0.0551944i
\(399\) −45.5304 + 111.381i −0.114111 + 0.279149i
\(400\) −19.7016 329.184i −0.0492541 0.822960i
\(401\) −85.0091 101.310i −0.211993 0.252643i 0.649561 0.760310i \(-0.274953\pi\)
−0.861554 + 0.507666i \(0.830508\pi\)
\(402\) 11.0055 + 561.737i 0.0273768 + 1.39736i
\(403\) 149.621 + 411.079i 0.371267 + 1.02005i
\(404\) −10.4585 + 182.077i −0.0258874 + 0.450685i
\(405\) 196.616 + 510.485i 0.485472 + 1.26046i
\(406\) 245.598 231.895i 0.604920 0.571171i
\(407\) 30.6065 + 84.0907i 0.0752003 + 0.206611i
\(408\) 665.413 + 25.1564i 1.63091 + 0.0616580i
\(409\) −240.749 + 202.012i −0.588628 + 0.493917i −0.887768 0.460292i \(-0.847745\pi\)
0.299140 + 0.954209i \(0.403300\pi\)
\(410\) 232.166 312.114i 0.566259 0.761254i
\(411\) −242.302 + 592.742i −0.589543 + 1.44219i
\(412\) 523.291 555.547i 1.27012 1.34841i
\(413\) 214.834 372.103i 0.520178 0.900975i
\(414\) −1.74988 5.11432i −0.00422676 0.0123534i
\(415\) 290.301 + 502.816i 0.699521 + 1.21161i
\(416\) −609.186 + 307.473i −1.46439 + 0.739117i
\(417\) −6.93324 + 177.738i −0.0166265 + 0.426229i
\(418\) −10.4196 24.1289i −0.0249274 0.0577246i
\(419\) −288.570 105.031i −0.688711 0.250670i −0.0261278 0.999659i \(-0.508318\pi\)
−0.662583 + 0.748988i \(0.730540\pi\)
\(420\) 304.533 + 217.392i 0.725078 + 0.517601i
\(421\) 229.897 + 40.5370i 0.546073 + 0.0962874i 0.439877 0.898058i \(-0.355022\pi\)
0.106196 + 0.994345i \(0.466133\pi\)
\(422\) −197.848 + 661.821i −0.468833 + 1.56830i
\(423\) 286.974 + 196.994i 0.678425 + 0.465707i
\(424\) 106.273 18.8704i 0.250644 0.0445056i
\(425\) −367.581 + 438.066i −0.864896 + 1.03074i
\(426\) 22.3623 27.7361i 0.0524938 0.0651083i
\(427\) 344.083 60.6711i 0.805815 0.142087i
\(428\) −444.292 595.791i −1.03806 1.39204i
\(429\) −29.5277 92.1553i −0.0688292 0.214814i
\(430\) −145.366 72.9329i −0.338061 0.169611i
\(431\) 829.976i 1.92570i −0.270038 0.962850i \(-0.587036\pi\)
0.270038 0.962850i \(-0.412964\pi\)
\(432\) −258.316 346.261i −0.597953 0.801531i
\(433\) −402.629 −0.929860 −0.464930 0.885348i \(-0.653920\pi\)
−0.464930 + 0.885348i \(0.653920\pi\)
\(434\) −84.9465 + 169.311i −0.195729 + 0.390118i
\(435\) 157.052 724.322i 0.361040 1.66511i
\(436\) −432.580 + 322.582i −0.992156 + 0.739868i
\(437\) −0.453023 2.56922i −0.00103667 0.00587923i
\(438\) 25.4119 162.693i 0.0580181 0.371445i
\(439\) −76.5436 64.2277i −0.174359 0.146305i 0.551432 0.834220i \(-0.314082\pi\)
−0.725791 + 0.687915i \(0.758526\pi\)
\(440\) −80.4684 + 14.2884i −0.182883 + 0.0324736i
\(441\) 240.061 66.7203i 0.544355 0.151293i
\(442\) 1133.73 + 338.923i 2.56501 + 0.766795i
\(443\) 59.7205 338.692i 0.134809 0.764542i −0.840183 0.542303i \(-0.817553\pi\)
0.974992 0.222239i \(-0.0713364\pi\)
\(444\) 294.153 + 646.097i 0.662506 + 1.45517i
\(445\) −41.1399 + 113.031i −0.0924491 + 0.254002i
\(446\) −145.179 + 62.6929i −0.325513 + 0.140567i
\(447\) 137.209 + 260.613i 0.306954 + 0.583026i
\(448\) −277.902 100.393i −0.620318 0.224092i
\(449\) 185.905 107.332i 0.414042 0.239048i −0.278483 0.960441i \(-0.589831\pi\)
0.692525 + 0.721394i \(0.256498\pi\)
\(450\) 370.925 + 7.19652i 0.824277 + 0.0159923i
\(451\) −37.7270 21.7817i −0.0836519 0.0482964i
\(452\) −288.747 271.982i −0.638821 0.601731i
\(453\) −414.279 + 320.955i −0.914523 + 0.708511i
\(454\) −513.473 381.947i −1.13100 0.841294i
\(455\) 427.393 + 509.348i 0.939326 + 1.11945i
\(456\) −97.3540 184.376i −0.213496 0.404333i
\(457\) −123.857 + 45.0802i −0.271022 + 0.0986438i −0.473956 0.880549i \(-0.657174\pi\)
0.202934 + 0.979192i \(0.434952\pi\)
\(458\) −578.226 612.392i −1.26250 1.33710i
\(459\) −87.4221 + 744.006i −0.190462 + 1.62093i
\(460\) −8.09905 0.465211i −0.0176066 0.00101133i
\(461\) −12.6968 + 4.62125i −0.0275418 + 0.0100244i −0.355754 0.934580i \(-0.615776\pi\)
0.328213 + 0.944604i \(0.393554\pi\)
\(462\) 20.2365 36.6922i 0.0438019 0.0794204i
\(463\) −393.676 + 330.333i −0.850271 + 0.713462i −0.959849 0.280516i \(-0.909494\pi\)
0.109578 + 0.993978i \(0.465050\pi\)
\(464\) 34.9671 + 584.246i 0.0753602 + 1.25915i
\(465\) 56.1652 + 411.827i 0.120785 + 0.885649i
\(466\) 41.8231 + 713.157i 0.0897491 + 1.53038i
\(467\) −194.018 + 336.049i −0.415456 + 0.719591i −0.995476 0.0950112i \(-0.969711\pi\)
0.580020 + 0.814602i \(0.303045\pi\)
\(468\) −290.617 710.546i −0.620975 1.51826i
\(469\) −374.407 + 216.164i −0.798309 + 0.460904i
\(470\) 436.343 287.238i 0.928389 0.611144i
\(471\) 51.5273 + 32.4910i 0.109400 + 0.0689831i
\(472\) 255.479 + 699.310i 0.541270 + 1.48159i
\(473\) −6.22943 + 17.1152i −0.0131700 + 0.0361844i
\(474\) −480.935 + 419.878i −1.01463 + 0.885818i
\(475\) 176.336 + 31.0928i 0.371234 + 0.0654585i
\(476\) 230.326 + 457.702i 0.483877 + 0.961559i
\(477\) 11.7063 + 120.862i 0.0245415 + 0.253379i
\(478\) 129.185 30.6721i 0.270262 0.0641676i
\(479\) 295.351 351.985i 0.616599 0.734834i −0.363883 0.931445i \(-0.618549\pi\)
0.980482 + 0.196611i \(0.0629935\pi\)
\(480\) −627.557 + 162.852i −1.30741 + 0.339275i
\(481\) 219.063 + 1242.37i 0.455432 + 2.58288i
\(482\) −51.9875 + 446.331i −0.107858 + 0.925997i
\(483\) 2.79574 3.07961i 0.00578828 0.00637600i
\(484\) −136.552 454.790i −0.282132 0.939648i
\(485\) 136.086 0.280590
\(486\) 411.309 258.884i 0.846315 0.532682i
\(487\) −426.550 −0.875874 −0.437937 0.899006i \(-0.644291\pi\)
−0.437937 + 0.899006i \(0.644291\pi\)
\(488\) −302.078 + 524.668i −0.619012 + 1.07514i
\(489\) −51.6763 + 56.9234i −0.105678 + 0.116408i
\(490\) 43.2629 371.427i 0.0882917 0.758015i
\(491\) 136.796 + 775.806i 0.278606 + 1.58005i 0.727269 + 0.686352i \(0.240789\pi\)
−0.448663 + 0.893701i \(0.648100\pi\)
\(492\) −311.869 148.896i −0.633879 0.302635i
\(493\) 652.395 777.494i 1.32332 1.57707i
\(494\) −85.5904 360.491i −0.173260 0.729739i
\(495\) −8.86385 91.5148i −0.0179068 0.184878i
\(496\) −130.489 301.180i −0.263082 0.607217i
\(497\) 26.9987 + 4.76059i 0.0543232 + 0.00957865i
\(498\) 388.569 339.238i 0.780259 0.681200i
\(499\) −133.879 + 367.831i −0.268295 + 0.737135i 0.730248 + 0.683182i \(0.239404\pi\)
−0.998543 + 0.0539534i \(0.982818\pi\)
\(500\) −46.8764 + 108.911i −0.0937529 + 0.217823i
\(501\) 221.473 + 139.652i 0.442062 + 0.278746i
\(502\) 34.1472 + 51.8730i 0.0680223 + 0.103333i
\(503\) −152.172 + 87.8566i −0.302529 + 0.174665i −0.643578 0.765380i \(-0.722551\pi\)
0.341049 + 0.940045i \(0.389218\pi\)
\(504\) 137.317 302.727i 0.272454 0.600650i
\(505\) −153.962 + 266.670i −0.304875 + 0.528060i
\(506\) 0.0531880 + 0.906948i 0.000105115 + 0.00179239i
\(507\) −115.833 849.336i −0.228468 1.67522i
\(508\) −196.179 + 23.0893i −0.386180 + 0.0454513i
\(509\) 129.577 108.728i 0.254572 0.213611i −0.506566 0.862201i \(-0.669085\pi\)
0.761138 + 0.648590i \(0.224641\pi\)
\(510\) 984.482 + 542.961i 1.93036 + 1.06463i
\(511\) 119.066 43.3363i 0.233005 0.0848069i
\(512\) 442.480 257.596i 0.864219 0.503116i
\(513\) 215.436 92.7740i 0.419953 0.180846i
\(514\) 279.995 + 296.540i 0.544738 + 0.576926i
\(515\) 1210.86 440.718i 2.35119 0.855763i
\(516\) −38.6649 + 139.220i −0.0749320 + 0.269806i
\(517\) −37.6052 44.8162i −0.0727374 0.0866851i
\(518\) −326.027 + 438.297i −0.629397 + 0.846133i
\(519\) −402.388 + 311.743i −0.775314 + 0.600661i
\(520\) −1152.13 + 1.38344i −2.21564 + 0.00266046i
\(521\) −210.954 121.794i −0.404901 0.233770i 0.283695 0.958914i \(-0.408440\pi\)
−0.688597 + 0.725145i \(0.741773\pi\)
\(522\) −658.330 12.7726i −1.26117 0.0244686i
\(523\) −328.518 + 189.670i −0.628142 + 0.362658i −0.780032 0.625740i \(-0.784797\pi\)
0.151890 + 0.988397i \(0.451464\pi\)
\(524\) 860.454 + 203.204i 1.64209 + 0.387794i
\(525\) 132.991 + 252.602i 0.253317 + 0.481147i
\(526\) −87.7152 203.123i −0.166759 0.386166i
\(527\) −194.672 + 534.857i −0.369397 + 1.01491i
\(528\) 26.2464 + 67.6981i 0.0497091 + 0.128216i
\(529\) 91.8442 520.874i 0.173619 0.984640i
\(530\) 174.602 + 52.1964i 0.329438 + 0.0984837i
\(531\) −806.992 + 224.288i −1.51976 + 0.422388i
\(532\) 88.0539 134.113i 0.165515 0.252093i
\(533\) −470.448 394.753i −0.882641 0.740624i
\(534\) 105.583 + 16.4916i 0.197721 + 0.0308832i
\(535\) −217.899 1235.77i −0.407289 2.30985i
\(536\) 129.198 737.901i 0.241042 1.37668i
\(537\) −28.7521 + 132.604i −0.0535421 + 0.246935i
\(538\) −244.670 + 487.664i −0.454777 + 0.906439i
\(539\) −41.8773 −0.0776944
\(540\) −126.793 718.281i −0.234802 1.33015i
\(541\) 78.5874i 0.145263i −0.997359 0.0726316i \(-0.976860\pi\)
0.997359 0.0726316i \(-0.0231397\pi\)
\(542\) 340.726 679.119i 0.628646 1.25299i
\(543\) 6.99804 + 21.8407i 0.0128877 + 0.0402223i
\(544\) −864.327 203.023i −1.58884 0.373205i
\(545\) −897.242 + 158.208i −1.64632 + 0.290290i
\(546\) 370.767 459.864i 0.679061 0.842243i
\(547\) −610.299 + 727.326i −1.11572 + 1.32966i −0.177303 + 0.984156i \(0.556737\pi\)
−0.938416 + 0.345506i \(0.887707\pi\)
\(548\) 468.602 713.719i 0.855114 1.30241i
\(549\) −561.523 385.459i −1.02281 0.702111i
\(550\) −59.7421 17.8595i −0.108622 0.0324719i
\(551\) −312.967 55.1846i −0.567999 0.100153i
\(552\) 0.982482 + 7.13992i 0.00177986 + 0.0129346i
\(553\) −461.634 168.021i −0.834781 0.303835i
\(554\) 56.5997 + 131.069i 0.102165 + 0.236586i
\(555\) −46.7199 + 1197.69i −0.0841800 + 2.15800i
\(556\) 54.5090 230.815i 0.0980377 0.415134i
\(557\) −282.367 489.074i −0.506943 0.878050i −0.999968 0.00803517i \(-0.997442\pi\)
0.493025 0.870015i \(-0.335891\pi\)
\(558\) 349.377 119.540i 0.626123 0.214230i
\(559\) −128.381 + 222.363i −0.229663 + 0.397787i
\(560\) −342.937 362.329i −0.612388 0.647015i
\(561\) 47.6422 116.547i 0.0849237 0.207748i
\(562\) 150.971 202.959i 0.268632 0.361137i
\(563\) −256.406 + 215.150i −0.455428 + 0.382149i −0.841445 0.540342i \(-0.818295\pi\)
0.386018 + 0.922491i \(0.373850\pi\)
\(564\) −325.175 331.147i −0.576551 0.587140i
\(565\) −229.065 629.350i −0.405424 1.11389i
\(566\) 101.021 + 106.990i 0.178482 + 0.189029i
\(567\) 327.283 + 180.935i 0.577218 + 0.319108i
\(568\) −36.3537 + 30.5788i −0.0640029 + 0.0538359i
\(569\) 199.326 + 547.645i 0.350310 + 0.962469i 0.982271 + 0.187468i \(0.0600282\pi\)
−0.631961 + 0.775000i \(0.717750\pi\)
\(570\) −6.89561 351.963i −0.0120976 0.617478i
\(571\) −359.610 428.567i −0.629790 0.750555i 0.352930 0.935650i \(-0.385185\pi\)
−0.982721 + 0.185095i \(0.940741\pi\)
\(572\) 15.0817 + 128.143i 0.0263666 + 0.224025i
\(573\) 221.241 541.219i 0.386109 0.944535i
\(574\) −15.5684 265.468i −0.0271226 0.462488i
\(575\) −5.36020 3.09471i −0.00932209 0.00538211i
\(576\) 249.514 + 519.152i 0.433185 + 0.901305i
\(577\) −378.530 655.633i −0.656031 1.13628i −0.981634 0.190773i \(-0.938901\pi\)
0.325603 0.945507i \(-0.394433\pi\)
\(578\) 528.735 + 803.201i 0.914766 + 1.38962i
\(579\) −693.469 27.0510i −1.19770 0.0467203i
\(580\) −390.681 + 907.697i −0.673588 + 1.56500i
\(581\) 372.974 + 135.752i 0.641952 + 0.233652i
\(582\) −23.3226 118.631i −0.0400731 0.203833i
\(583\) 3.54394 20.0987i 0.00607880 0.0344746i
\(584\) −74.8442 + 206.404i −0.128158 + 0.353431i
\(585\) 100.967 1292.21i 0.172594 2.20890i
\(586\) 58.0717 + 244.587i 0.0990984 + 0.417385i
\(587\) 474.276 + 397.965i 0.807967 + 0.677964i 0.950122 0.311880i \(-0.100959\pi\)
−0.142155 + 0.989844i \(0.545403\pi\)
\(588\) −331.199 + 25.9418i −0.563264 + 0.0441187i
\(589\) 175.512 30.9476i 0.297984 0.0525426i
\(590\) −145.433 + 1248.60i −0.246497 + 2.11626i
\(591\) −560.631 + 179.633i −0.948614 + 0.303948i
\(592\) −219.762 920.677i −0.371219 1.55520i
\(593\) 959.784i 1.61852i 0.587448 + 0.809262i \(0.300133\pi\)
−0.587448 + 0.809262i \(0.699867\pi\)
\(594\) −78.2572 + 23.4108i −0.131746 + 0.0394121i
\(595\) 865.112i 1.45397i
\(596\) −112.929 376.112i −0.189478 0.631061i
\(597\) 119.267 550.057i 0.199777 0.921369i
\(598\) −1.48177 + 12.7215i −0.00247787 + 0.0212734i
\(599\) 654.900 115.477i 1.09332 0.192782i 0.402223 0.915542i \(-0.368238\pi\)
0.691100 + 0.722760i \(0.257127\pi\)
\(600\) −483.551 104.239i −0.805919 0.173732i
\(601\) 636.219 + 533.851i 1.05860 + 0.888271i 0.993972 0.109638i \(-0.0349692\pi\)
0.0646290 + 0.997909i \(0.479414\pi\)
\(602\) −108.174 + 25.6835i −0.179691 + 0.0426636i
\(603\) 816.042 + 210.553i 1.35330 + 0.349175i
\(604\) 624.172 314.097i 1.03340 0.520028i
\(605\) 139.219 789.550i 0.230114 1.30504i
\(606\) 258.851 + 88.5114i 0.427147 + 0.146058i
\(607\) 643.962 + 234.383i 1.06089 + 0.386133i 0.812764 0.582594i \(-0.197962\pi\)
0.248129 + 0.968727i \(0.420184\pi\)
\(608\) 80.2641 + 266.161i 0.132013 + 0.437765i
\(609\) −236.037 448.327i −0.387582 0.736169i
\(610\) −853.794 + 562.039i −1.39966 + 0.921375i
\(611\) −412.370 714.245i −0.674909 1.16898i
\(612\) 304.595 951.256i 0.497705 1.55434i
\(613\) 798.026 + 460.740i 1.30184 + 0.751616i 0.980719 0.195423i \(-0.0626081\pi\)
0.321118 + 0.947039i \(0.395941\pi\)
\(614\) 49.1490 + 838.077i 0.0800472 + 1.36495i
\(615\) −357.353 461.260i −0.581062 0.750016i
\(616\) −35.8613 + 42.8422i −0.0582164 + 0.0695490i
\(617\) −35.9791 42.8782i −0.0583130 0.0694947i 0.736099 0.676873i \(-0.236666\pi\)
−0.794412 + 0.607379i \(0.792221\pi\)
\(618\) −591.706 980.016i −0.957453 1.58579i
\(619\) −34.2041 93.9751i −0.0552571 0.151818i 0.908993 0.416811i \(-0.136852\pi\)
−0.964250 + 0.264994i \(0.914630\pi\)
\(620\) 31.7801 553.274i 0.0512583 0.892377i
\(621\) −8.09467 + 0.466504i −0.0130349 + 0.000751215i
\(622\) −553.046 585.725i −0.889141 0.941679i
\(623\) 28.1240 + 77.2701i 0.0451429 + 0.124029i
\(624\) 198.659 + 1004.11i 0.318364 + 1.60915i
\(625\) −548.078 + 459.892i −0.876925 + 0.735827i
\(626\) 200.460 + 149.112i 0.320224 + 0.238199i
\(627\) −39.0622 + 5.32733i −0.0623002 + 0.00849654i
\(628\) −59.1226 55.6899i −0.0941443 0.0886782i
\(629\) −820.692 + 1421.48i −1.30476 + 2.25990i
\(630\) 436.858 352.355i 0.693425 0.559294i
\(631\) 4.39162 + 7.60651i 0.00695978 + 0.0120547i 0.869484 0.493961i \(-0.164451\pi\)
−0.862525 + 0.506015i \(0.831118\pi\)
\(632\) 736.687 426.507i 1.16564 0.674852i
\(633\) 876.450 + 552.654i 1.38460 + 0.873071i
\(634\) 10.5619 4.56097i 0.0166592 0.00719397i
\(635\) −313.401 114.069i −0.493545 0.179636i
\(636\) 15.5777 161.152i 0.0244933 0.253383i
\(637\) −581.387 102.514i −0.912696 0.160933i
\(638\) 106.032 + 31.6977i 0.166195 + 0.0496829i
\(639\) −31.0586 43.4907i −0.0486050 0.0680606i
\(640\) 862.851 52.6815i 1.34820 0.0823148i
\(641\) 101.090 120.475i 0.157707 0.187948i −0.681405 0.731907i \(-0.738631\pi\)
0.839112 + 0.543959i \(0.183075\pi\)
\(642\) −1039.91 + 401.737i −1.61980 + 0.625758i
\(643\) 560.102 98.7611i 0.871076 0.153594i 0.279795 0.960060i \(-0.409734\pi\)
0.591281 + 0.806466i \(0.298622\pi\)
\(644\) −4.44576 + 3.31528i −0.00690335 + 0.00514795i
\(645\) −163.976 + 180.626i −0.254227 + 0.280040i
\(646\) 216.183 430.885i 0.334648 0.667005i
\(647\) 155.463i 0.240283i 0.992757 + 0.120142i \(0.0383348\pi\)
−0.992757 + 0.120142i \(0.961665\pi\)
\(648\) −604.418 + 233.629i −0.932744 + 0.360539i
\(649\) 140.775 0.216911
\(650\) −785.687 394.193i −1.20875 0.606451i
\(651\) 210.379 + 190.986i 0.323162 + 0.293374i
\(652\) 82.1752 61.2795i 0.126036 0.0939869i
\(653\) 104.601 + 593.221i 0.160185 + 0.908455i 0.953891 + 0.300153i \(0.0970378\pi\)
−0.793706 + 0.608302i \(0.791851\pi\)
\(654\) 291.685 + 755.040i 0.446001 + 1.15450i
\(655\) 1143.51 + 959.520i 1.74582 + 1.46492i
\(656\) 370.047 + 274.570i 0.564096 + 0.418552i
\(657\) −224.817 102.302i −0.342187 0.155711i
\(658\) 102.287 342.160i 0.155451 0.520000i
\(659\) 6.80449 38.5902i 0.0103255 0.0585587i −0.979210 0.202851i \(-0.934979\pi\)
0.989535 + 0.144292i \(0.0460905\pi\)
\(660\) −11.7953 + 122.022i −0.0178716 + 0.184882i
\(661\) −15.9939 + 43.9429i −0.0241966 + 0.0664795i −0.951203 0.308566i \(-0.900151\pi\)
0.927006 + 0.375046i \(0.122373\pi\)
\(662\) −42.1454 97.5966i −0.0636637 0.147427i
\(663\) 946.725 1501.40i 1.42794 2.26456i
\(664\) −595.202 + 344.593i −0.896388 + 0.518966i
\(665\) 234.589 135.440i 0.352765 0.203669i
\(666\) 1052.07 164.534i 1.57969 0.247048i
\(667\) 9.51346 + 5.49260i 0.0142631 + 0.00823478i
\(668\) −254.119 239.365i −0.380417 0.358330i
\(669\) 32.0535 + 235.030i 0.0479125 + 0.351315i
\(670\) 754.892 1014.84i 1.12671 1.51469i
\(671\) 73.5823 + 87.6920i 0.109661 + 0.130689i
\(672\) −257.080 + 361.045i −0.382560 + 0.537270i
\(673\) −994.980 + 362.143i −1.47843 + 0.538103i −0.950374 0.311110i \(-0.899299\pi\)
−0.528051 + 0.849212i \(0.677077\pi\)
\(674\) −895.422 + 845.464i −1.32852 + 1.25440i
\(675\) 159.929 533.016i 0.236932 0.789653i
\(676\) −65.5422 + 1141.05i −0.0969559 + 1.68795i
\(677\) −527.675 + 192.058i −0.779432 + 0.283690i −0.700936 0.713224i \(-0.747234\pi\)
−0.0784962 + 0.996914i \(0.525012\pi\)
\(678\) −509.367 + 307.541i −0.751279 + 0.453601i
\(679\) 71.2660 59.7993i 0.104957 0.0880697i
\(680\) −1149.49 962.187i −1.69043 1.41498i
\(681\) −758.840 + 587.898i −1.11430 + 0.863286i
\(682\) −61.9567 + 3.63345i −0.0908456 + 0.00532764i
\(683\) 13.1552 22.7854i 0.0192608 0.0333608i −0.856234 0.516588i \(-0.827202\pi\)
0.875495 + 0.483227i \(0.160535\pi\)
\(684\) −305.635 + 66.3307i −0.446835 + 0.0969747i
\(685\) 1248.43 720.780i 1.82252 1.05223i
\(686\) −389.336 591.441i −0.567545 0.862159i
\(687\) −1117.89 + 588.554i −1.62721 + 0.856701i
\(688\) 86.1864 172.299i 0.125271 0.250434i
\(689\) 98.4019 270.357i 0.142818 0.392390i
\(690\) −3.93712 + 11.5141i −0.00570597 + 0.0166871i
\(691\) 136.748 + 24.1123i 0.197899 + 0.0348949i 0.271719 0.962377i \(-0.412408\pi\)
−0.0738201 + 0.997272i \(0.523519\pi\)
\(692\) 606.256 305.081i 0.876093 0.440869i
\(693\) −44.8555 44.0297i −0.0647265 0.0635350i
\(694\) 283.230 + 1192.91i 0.408112 + 1.71890i
\(695\) 257.389 306.744i 0.370344 0.441358i
\(696\) 858.223 + 185.007i 1.23308 + 0.265815i
\(697\) −138.752 786.903i −0.199071 1.12899i
\(698\) 17.9983 + 2.09640i 0.0257856 + 0.00300344i
\(699\) 1047.24 + 227.069i 1.49820 + 0.324849i
\(700\) −109.458 364.552i −0.156368 0.520789i
\(701\) 662.723 0.945397 0.472698 0.881224i \(-0.343280\pi\)
0.472698 + 0.881224i \(0.343280\pi\)
\(702\) −1143.76 + 133.443i −1.62929 + 0.190090i
\(703\) 513.943 0.731071
\(704\) −17.0399 95.2991i −0.0242044 0.135368i
\(705\) −239.101 746.229i −0.339151 1.05848i
\(706\) 282.183 + 32.8679i 0.399692 + 0.0465552i
\(707\) 36.5534 + 207.305i 0.0517022 + 0.293218i
\(708\) 1113.36 87.2063i 1.57255 0.123173i
\(709\) 83.5220 99.5377i 0.117803 0.140392i −0.703920 0.710279i \(-0.748569\pi\)
0.821723 + 0.569887i \(0.193013\pi\)
\(710\) −78.0365 + 18.5280i −0.109911 + 0.0260958i
\(711\) 412.765 + 864.127i 0.580541 + 1.21537i
\(712\) −133.950 48.5717i −0.188132 0.0682187i
\(713\) −6.06692 1.06976i −0.00850901 0.00150037i
\(714\) 754.145 148.263i 1.05623 0.207652i
\(715\) −74.5086 + 204.711i −0.104208 + 0.286309i
\(716\) 71.5233 166.175i 0.0998929 0.232088i
\(717\) 7.76318 199.014i 0.0108273 0.277564i
\(718\) 546.368 359.666i 0.760959 0.500927i
\(719\) 290.621 167.790i 0.404202 0.233366i −0.284093 0.958797i \(-0.591693\pi\)
0.688295 + 0.725430i \(0.258359\pi\)
\(720\) −17.6972 + 972.354i −0.0245795 + 1.35049i
\(721\) 440.447 762.876i 0.610883 1.05808i
\(722\) 570.075 33.4321i 0.789578 0.0463048i
\(723\) 623.907 + 255.042i 0.862941 + 0.352755i
\(724\) −3.57435 30.3696i −0.00493694 0.0419470i
\(725\) −577.566 + 484.635i −0.796642 + 0.668462i
\(726\) −712.134 + 13.9521i −0.980901 + 0.0192177i
\(727\) 531.818 193.566i 0.731524 0.266253i 0.0507142 0.998713i \(-0.483850\pi\)
0.680810 + 0.732460i \(0.261628\pi\)
\(728\) −602.743 + 506.996i −0.827944 + 0.696423i
\(729\) −208.227 698.629i −0.285634 0.958339i
\(730\) −269.531 + 254.494i −0.369221 + 0.348622i
\(731\) −313.928 + 114.260i −0.429450 + 0.156307i
\(732\) 636.271 + 647.956i 0.869222 + 0.885186i
\(733\) −184.057 219.351i −0.251101 0.299251i 0.625739 0.780032i \(-0.284797\pi\)
−0.876840 + 0.480782i \(0.840353\pi\)
\(734\) 116.861 + 86.9275i 0.159212 + 0.118430i
\(735\) −519.202 212.241i −0.706398 0.288763i
\(736\) 0.539549 9.59444i 0.000733082 0.0130359i
\(737\) −122.670 70.8235i −0.166445 0.0960971i
\(738\) −340.851 + 390.567i −0.461858 + 0.529224i
\(739\) 329.157 190.039i 0.445409 0.257157i −0.260480 0.965479i \(-0.583881\pi\)
0.705889 + 0.708322i \(0.250548\pi\)
\(740\) 367.311 1555.35i 0.496366 2.10183i
\(741\) −555.347 21.6631i −0.749456 0.0292350i
\(742\) 114.373 49.3898i 0.154141 0.0665631i
\(743\) −107.259 + 294.691i −0.144359 + 0.396624i −0.990708 0.136005i \(-0.956574\pi\)
0.846349 + 0.532629i \(0.178796\pi\)
\(744\) −487.753 + 67.1167i −0.655581 + 0.0902106i
\(745\) 115.134 652.960i 0.154543 0.876456i
\(746\) 130.272 435.774i 0.174628 0.584148i
\(747\) −333.491 698.167i −0.446440 0.934627i
\(748\) −92.1379 + 140.333i −0.123179 + 0.187612i
\(749\) −657.134 551.401i −0.877349 0.736183i
\(750\) 138.459 + 111.633i 0.184612 + 0.148844i
\(751\) −152.092 862.554i −0.202519 1.14854i −0.901297 0.433202i \(-0.857384\pi\)
0.698778 0.715338i \(-0.253727\pi\)
\(752\) 340.870 + 516.464i 0.453284 + 0.686788i
\(753\) 88.7126 28.4247i 0.117812 0.0377486i
\(754\) 1394.46 + 699.627i 1.84942 + 0.927887i
\(755\) 1179.76 1.56260
\(756\) −382.028 320.436i −0.505328 0.423857i
\(757\) 554.865i 0.732979i 0.930422 + 0.366489i \(0.119440\pi\)
−0.930422 + 0.366489i \(0.880560\pi\)
\(758\) 767.242 + 384.939i 1.01219 + 0.507835i
\(759\) 1.33181 + 0.288772i 0.00175469 + 0.000380464i
\(760\) −80.9508 + 462.340i −0.106514 + 0.608343i
\(761\) −842.183 + 148.500i −1.10668 + 0.195137i −0.696985 0.717086i \(-0.745476\pi\)
−0.409694 + 0.912223i \(0.634365\pi\)
\(762\) −45.7263 + 292.751i −0.0600083 + 0.384187i
\(763\) −400.350 + 477.119i −0.524705 + 0.625319i
\(764\) −427.870 + 651.680i −0.560039 + 0.852985i
\(765\) 1181.35 1203.51i 1.54425 1.57321i
\(766\) −305.273 + 1021.17i −0.398529 + 1.33312i
\(767\) 1954.40 + 344.614i 2.54811 + 0.449301i
\(768\) −193.800 743.146i −0.252344 0.967638i
\(769\) 434.350 + 158.091i 0.564825 + 0.205580i 0.608621 0.793461i \(-0.291723\pi\)
−0.0437961 + 0.999040i \(0.513945\pi\)
\(770\) −86.6013 + 37.3973i −0.112469 + 0.0485679i
\(771\) 541.320 284.996i 0.702101 0.369645i
\(772\) 900.557 + 212.675i 1.16652 + 0.275485i
\(773\) 299.847 + 519.350i 0.387900 + 0.671862i 0.992167 0.124920i \(-0.0398673\pi\)
−0.604267 + 0.796782i \(0.706534\pi\)
\(774\) 185.560 + 111.987i 0.239741 + 0.144687i
\(775\) 211.410 366.174i 0.272788 0.472482i
\(776\) 0.193566 + 161.202i 0.000249441 + 0.207734i
\(777\) 501.825 + 647.740i 0.645850 + 0.833642i
\(778\) 647.432 + 481.592i 0.832174 + 0.619013i
\(779\) −191.658 + 160.821i −0.246031 + 0.206445i
\(780\) −462.461 + 1665.17i −0.592899 + 2.13484i
\(781\) 3.07211 + 8.44055i 0.00393356 + 0.0108074i
\(782\) −12.1163 + 11.4403i −0.0154940 + 0.0146295i
\(783\) −283.847 + 946.014i −0.362512 + 1.20819i
\(784\) 440.038 + 50.7191i 0.561273 + 0.0646927i
\(785\) −46.9023 128.863i −0.0597481 0.164157i
\(786\) 640.468 1161.28i 0.814844 1.47745i
\(787\) −943.074 1123.91i −1.19831 1.42810i −0.876574 0.481268i \(-0.840176\pi\)
−0.321741 0.946828i \(-0.604268\pi\)
\(788\) 779.561 91.7502i 0.989290 0.116434i
\(789\) −328.836 + 44.8468i −0.416775 + 0.0568401i
\(790\) 1434.77 84.1420i 1.81616 0.106509i
\(791\) −396.508 228.924i −0.501274 0.289411i
\(792\) 108.392 10.6299i 0.136858 0.0134216i
\(793\) 806.885 + 1397.57i 1.01751 + 1.76238i
\(794\) −375.998 + 247.514i −0.473549 + 0.311730i
\(795\) 145.802 231.226i 0.183398 0.290850i
\(796\) −296.687 + 689.315i −0.372722 + 0.865973i
\(797\) 585.575 + 213.132i 0.734724 + 0.267418i 0.682163 0.731200i \(-0.261039\pi\)
0.0525610 + 0.998618i \(0.483262\pi\)
\(798\) −158.271 181.287i −0.198335 0.227176i
\(799\) 186.337 1056.77i 0.233213 1.32261i
\(800\) 606.127 + 260.020i 0.757659 + 0.325025i
\(801\) 66.3911 145.900i 0.0828853 0.182147i
\(802\) 257.347 61.1012i 0.320882 0.0761861i
\(803\) 31.8016 + 26.6847i 0.0396034 + 0.0332312i
\(804\) −1014.05 484.139i −1.26125 0.602162i
\(805\) −9.22123 + 1.62595i −0.0114549 + 0.00201982i
\(806\) −869.047 101.224i −1.07822 0.125589i
\(807\) 605.950 + 550.095i 0.750867 + 0.681654i
\(808\) −316.105 181.997i −0.391219 0.225244i
\(809\) 1369.65i 1.69301i −0.532381 0.846505i \(-0.678703\pi\)
0.532381 0.846505i \(-0.321297\pi\)
\(810\) −1088.90 106.369i −1.34432 0.131320i
\(811\) 320.745i 0.395494i −0.980253 0.197747i \(-0.936638\pi\)
0.980253 0.197747i \(-0.0633624\pi\)
\(812\) 194.269 + 647.019i 0.239248 + 0.796822i
\(813\) −843.843 766.060i −1.03794 0.942263i
\(814\) −177.773 20.7066i −0.218394 0.0254381i
\(815\) 170.445 30.0540i 0.209135 0.0368761i
\(816\) −641.768 + 1166.95i −0.786480 + 1.43008i
\(817\) 80.1314 + 67.2382i 0.0980801 + 0.0822989i
\(818\) −145.198 611.550i −0.177504 0.747616i
\(819\) −514.950 721.075i −0.628755 0.880434i
\(820\) 349.717 + 694.956i 0.426484 + 0.847507i
\(821\) −180.910 + 1025.99i −0.220353 + 1.24969i 0.651018 + 0.759062i \(0.274342\pi\)
−0.871371 + 0.490624i \(0.836769\pi\)
\(822\) −842.283 964.765i −1.02467 1.17368i
\(823\) −1071.75 390.085i −1.30225 0.473980i −0.404520 0.914529i \(-0.632561\pi\)
−0.897728 + 0.440550i \(0.854784\pi\)
\(824\) 523.778 + 1433.71i 0.635652 + 1.73994i
\(825\) −49.8876 + 79.1164i −0.0604698 + 0.0958986i
\(826\) 472.499 + 717.774i 0.572033 + 0.868976i
\(827\) −582.080 1008.19i −0.703845 1.21910i −0.967107 0.254371i \(-0.918132\pi\)
0.263262 0.964724i \(-0.415202\pi\)
\(828\) 10.7119 + 1.45882i 0.0129371 + 0.00176186i
\(829\) −122.099 70.4938i −0.147284 0.0850347i 0.424547 0.905406i \(-0.360433\pi\)
−0.571831 + 0.820371i \(0.693767\pi\)
\(830\) −1159.21 + 67.9820i −1.39664 + 0.0819061i
\(831\) 212.187 28.9381i 0.255339 0.0348233i
\(832\) −3.27753 1364.76i −0.00393934 1.64034i
\(833\) −493.735 588.410i −0.592719 0.706375i
\(834\) −311.510 171.804i −0.373513 0.206000i
\(835\) −201.594 553.874i −0.241430 0.663323i
\(836\) 52.4786 + 3.01438i 0.0627734 + 0.00360572i
\(837\) −31.8685 552.975i −0.0380747 0.660663i
\(838\) 446.569 421.654i 0.532899 0.503167i
\(839\) −168.542 463.064i −0.200884 0.551924i 0.797816 0.602901i \(-0.205989\pi\)
−0.998700 + 0.0509772i \(0.983766\pi\)
\(840\) −661.746 + 349.415i −0.787793 + 0.415970i
\(841\) 380.840 319.562i 0.452842 0.379979i
\(842\) −278.655 + 374.612i −0.330945 + 0.444907i
\(843\) −232.377 299.944i −0.275654 0.355806i
\(844\) −1005.64 947.254i −1.19152 1.12234i
\(845\) −964.860 + 1671.19i −1.14185 + 1.97773i
\(846\) −609.533 + 336.321i −0.720489 + 0.397543i
\(847\) −274.039 474.649i −0.323541 0.560389i
\(848\) −61.5812 + 206.901i −0.0726194 + 0.243987i
\(849\) 195.306 102.825i 0.230042 0.121114i
\(850\) −453.420 1049.99i −0.533435 1.23528i
\(851\) −16.6940 6.07613i −0.0196170 0.00713999i
\(852\) 29.5254 + 64.8515i 0.0346542 + 0.0761168i
\(853\) −1415.64 249.616i −1.65960 0.292633i −0.736286 0.676670i \(-0.763422\pi\)
−0.923318 + 0.384037i \(0.874533\pi\)
\(854\) −200.145 + 669.506i −0.234362 + 0.783965i
\(855\) −511.300 131.924i −0.598012 0.154297i
\(856\) 1463.53 259.872i 1.70973 0.303589i
\(857\) −360.304 + 429.394i −0.420425 + 0.501043i −0.934135 0.356921i \(-0.883827\pi\)
0.513709 + 0.857964i \(0.328271\pi\)
\(858\) 191.222 + 29.8680i 0.222869 + 0.0348112i
\(859\) −546.928 + 96.4382i −0.636703 + 0.112268i −0.482677 0.875799i \(-0.660335\pi\)
−0.154027 + 0.988067i \(0.549224\pi\)
\(860\) 260.753 194.448i 0.303202 0.226103i
\(861\) −389.828 84.5250i −0.452761 0.0981707i
\(862\) 1483.69 + 744.392i 1.72121 + 0.863563i
\(863\) 854.303i 0.989922i 0.868915 + 0.494961i \(0.164818\pi\)
−0.868915 + 0.494961i \(0.835182\pi\)
\(864\) 850.664 151.215i 0.984565 0.175018i
\(865\) 1145.90 1.32474
\(866\) 361.111 719.750i 0.416988 0.831120i
\(867\) 1373.63 440.127i 1.58434 0.507644i
\(868\) −226.478 303.705i −0.260919 0.349890i
\(869\) −27.9497 158.510i −0.0321630 0.182405i
\(870\) 1153.96 + 930.382i 1.32639 + 1.06940i
\(871\) −1529.67 1283.54i −1.75622 1.47364i
\(872\) −188.683 1062.61i −0.216379 1.21859i
\(873\) −180.801 14.1270i −0.207103 0.0161821i
\(874\) 4.99911 + 1.49446i 0.00571981 + 0.00170990i
\(875\) −23.7650 + 134.778i −0.0271600 + 0.154032i
\(876\) 268.043 + 191.344i 0.305985 + 0.218429i
\(877\) −181.532 + 498.754i −0.206992 + 0.568705i −0.999133 0.0416327i \(-0.986744\pi\)
0.792141 + 0.610338i \(0.208966\pi\)
\(878\) 183.466 79.2264i 0.208959 0.0902351i
\(879\) 376.794 + 14.6981i 0.428662 + 0.0167214i
\(880\) 46.6285 156.662i 0.0529869 0.178025i
\(881\) 377.339 217.857i 0.428307 0.247283i −0.270318 0.962771i \(-0.587129\pi\)
0.698625 + 0.715488i \(0.253795\pi\)
\(882\) −96.0356 + 488.979i −0.108884 + 0.554398i
\(883\) −918.967 530.566i −1.04073 0.600867i −0.120692 0.992690i \(-0.538511\pi\)
−0.920041 + 0.391823i \(0.871845\pi\)
\(884\) −1622.69 + 1722.72i −1.83563 + 1.94877i
\(885\) 1745.36 + 713.472i 1.97216 + 0.806183i
\(886\) 551.892 + 410.525i 0.622902 + 0.463346i
\(887\) 14.9599 + 17.8285i 0.0168657 + 0.0200998i 0.774411 0.632682i \(-0.218046\pi\)
−0.757546 + 0.652782i \(0.773602\pi\)
\(888\) −1418.80 53.6388i −1.59775 0.0604040i
\(889\) −214.247 + 77.9795i −0.240998 + 0.0877160i
\(890\) −165.159 174.918i −0.185572 0.196537i
\(891\) 2.27626 + 122.505i 0.00255472 + 0.137491i
\(892\) 18.1369 315.753i 0.0203329 0.353984i
\(893\) −315.732 + 114.917i −0.353564 + 0.128687i
\(894\) −588.937 + 11.5384i −0.658767 + 0.0129065i
\(895\) 233.991 196.342i 0.261443 0.219376i
\(896\) 428.711 406.744i 0.478472 0.453956i
\(897\) 17.7828 + 7.26930i 0.0198248 + 0.00810401i
\(898\) 25.1348 + 428.593i 0.0279898 + 0.477275i
\(899\) −375.218 + 649.897i −0.417373 + 0.722911i
\(900\) −345.541 + 656.620i −0.383934 + 0.729577i
\(901\) 324.186 187.169i 0.359807 0.207735i
\(902\) 72.7742 47.9061i 0.0806809 0.0531110i
\(903\) −6.50055 + 166.645i −0.00719884 + 0.184546i
\(904\) 745.175 272.235i 0.824309 0.301145i
\(905\) 17.6584 48.5162i 0.0195121 0.0536090i
\(906\) −202.188 1028.43i −0.223166 1.13514i
\(907\) −409.870 72.2712i −0.451897 0.0796816i −0.0569324 0.998378i \(-0.518132\pi\)
−0.394964 + 0.918696i \(0.629243\pi\)
\(908\) 1143.30 575.335i 1.25915 0.633629i
\(909\) 232.233 338.309i 0.255482 0.372177i
\(910\) −1293.84 + 307.194i −1.42181 + 0.337575i
\(911\) −367.170 + 437.577i −0.403041 + 0.480326i −0.928945 0.370219i \(-0.879283\pi\)
0.525904 + 0.850544i \(0.323727\pi\)
\(912\) 416.910 8.66886i 0.457138 0.00950533i
\(913\) 22.5818 + 128.067i 0.0247336 + 0.140271i
\(914\) 30.4986 261.841i 0.0333683 0.286478i
\(915\) 467.850 + 1460.15i 0.511312 + 1.59579i
\(916\) 1613.33 484.406i 1.76128 0.528828i
\(917\) 1020.47 1.11284
\(918\) −1251.60 823.564i −1.36339 0.897129i
\(919\) −1268.54 −1.38034 −0.690172 0.723645i \(-0.742465\pi\)
−0.690172 + 0.723645i \(0.742465\pi\)
\(920\) 8.09552 14.0608i 0.00879948 0.0152835i
\(921\) 1230.68 + 266.844i 1.33624 + 0.289733i
\(922\) 3.12646 26.8418i 0.00339096 0.0291125i
\(923\) 21.9883 + 124.702i 0.0238226 + 0.135105i
\(924\) 47.4422 + 69.0839i 0.0513443 + 0.0747661i
\(925\) 783.759 934.047i 0.847307 1.00978i
\(926\) −237.430 1000.01i −0.256404 1.07993i
\(927\) −1654.48 + 459.830i −1.78476 + 0.496041i
\(928\) −1075.77 461.493i −1.15924 0.497298i
\(929\) −704.463 124.216i −0.758303 0.133709i −0.218889 0.975750i \(-0.570243\pi\)
−0.539414 + 0.842041i \(0.681354\pi\)
\(930\) −786.566 268.958i −0.845770 0.289202i
\(931\) −82.2588 + 226.004i −0.0883553 + 0.242754i
\(932\) −1312.37 564.854i −1.40812 0.606067i
\(933\) −1069.21 + 562.924i −1.14599 + 0.603349i
\(934\) −426.718 648.228i −0.456871 0.694034i
\(935\) −245.469 + 141.722i −0.262534 + 0.151574i
\(936\) 1530.84 + 117.764i 1.63551 + 0.125816i
\(937\) −404.578 + 700.749i −0.431780 + 0.747865i −0.997027 0.0770572i \(-0.975448\pi\)
0.565247 + 0.824922i \(0.308781\pi\)
\(938\) −50.6208 863.173i −0.0539667 0.920227i
\(939\) 296.251 229.516i 0.315497 0.244426i
\(940\) 122.124 + 1037.64i 0.129919 + 1.10387i
\(941\) 1000.74 839.722i 1.06349 0.892372i 0.0690412 0.997614i \(-0.478006\pi\)
0.994447 + 0.105242i \(0.0335616\pi\)
\(942\) −104.296 + 62.9708i −0.110717 + 0.0668479i
\(943\) 8.12682 2.95792i 0.00861805 0.00313671i
\(944\) −1479.24 170.498i −1.56699 0.180612i
\(945\) −332.976 773.223i −0.352356 0.818226i
\(946\) −25.0085 26.4862i −0.0264361 0.0279981i
\(947\) −827.453 + 301.168i −0.873762 + 0.318023i −0.739690 0.672948i \(-0.765028\pi\)
−0.134072 + 0.990972i \(0.542805\pi\)
\(948\) −319.241 1236.31i −0.336752 1.30413i
\(949\) 376.182 + 448.316i 0.396398 + 0.472409i
\(950\) −213.735 + 287.336i −0.224984 + 0.302459i
\(951\) −2.33192 17.0986i −0.00245208 0.0179797i
\(952\) −1024.77 + 1.23052i −1.07644 + 0.00129256i
\(953\) 735.694 + 424.753i 0.771976 + 0.445701i 0.833579 0.552400i \(-0.186288\pi\)
−0.0616028 + 0.998101i \(0.519621\pi\)
\(954\) −226.554 87.4723i −0.237478 0.0916900i
\(955\) −1139.91 + 658.127i −1.19362 + 0.689139i
\(956\) −61.0339 + 258.444i −0.0638430 + 0.270339i
\(957\) 88.5422 140.418i 0.0925206 0.146728i
\(958\) 364.323 + 843.666i 0.380295 + 0.880654i
\(959\) 337.053 926.047i 0.351463 0.965638i
\(960\) 271.727 1267.90i 0.283049 1.32073i
\(961\) −93.7968 + 531.948i −0.0976033 + 0.553536i
\(962\) −2417.36 722.655i −2.51285 0.751201i
\(963\) 161.212 + 1664.44i 0.167406 + 1.72839i
\(964\) −751.245 493.240i −0.779300 0.511660i
\(965\) 1196.81 + 1004.24i 1.24021 + 1.04066i
\(966\) 2.99773 + 7.75978i 0.00310324 + 0.00803290i
\(967\) −62.4498 354.170i −0.0645810 0.366257i −0.999922 0.0125090i \(-0.996018\pi\)
0.935341 0.353748i \(-0.115093\pi\)
\(968\) 935.464 + 163.790i 0.966389 + 0.169204i
\(969\) −535.398 486.047i −0.552527 0.501596i
\(970\) −122.053 + 243.271i −0.125828 + 0.250795i
\(971\) 854.823 0.880354 0.440177 0.897911i \(-0.354916\pi\)
0.440177 + 0.897911i \(0.354916\pi\)
\(972\) 93.8906 + 967.455i 0.0965953 + 0.995324i
\(973\) 273.739i 0.281335i
\(974\) 382.566 762.512i 0.392778 0.782867i
\(975\) −886.270 + 976.259i −0.908995 + 1.00129i
\(976\) −666.981 1010.57i −0.683382 1.03542i
\(977\) 1622.79 286.141i 1.66099 0.292878i 0.737172 0.675706i \(-0.236161\pi\)
0.923820 + 0.382828i \(0.125050\pi\)
\(978\) −55.4100 143.431i −0.0566564 0.146658i
\(979\) −17.3176 + 20.6383i −0.0176891 + 0.0210810i
\(980\) 625.170 + 410.465i 0.637929 + 0.418841i
\(981\) 1208.48 117.050i 1.23189 0.119317i
\(982\) −1509.54 451.268i −1.53721 0.459540i
\(983\) 1408.61 + 248.376i 1.43297 + 0.252672i 0.835621 0.549307i \(-0.185108\pi\)
0.597353 + 0.801979i \(0.296219\pi\)
\(984\) 545.880 423.961i 0.554756 0.430855i
\(985\) 1245.37 + 453.276i 1.26433 + 0.460179i
\(986\) 804.745 + 1863.56i 0.816171 + 1.89002i
\(987\) −453.122 285.721i −0.459091 0.289484i
\(988\) 721.187 + 170.315i 0.729947 + 0.172384i
\(989\) −1.80792 3.13141i −0.00182803 0.00316624i
\(990\) 171.544 + 66.2328i 0.173277 + 0.0669018i
\(991\) −975.574 + 1689.74i −0.984434 + 1.70509i −0.340010 + 0.940422i \(0.610431\pi\)
−0.644424 + 0.764668i \(0.722903\pi\)
\(992\) 655.429 + 36.8584i 0.660715 + 0.0371557i
\(993\) −157.999 + 21.5480i −0.159113 + 0.0216999i
\(994\) −32.7248 + 43.9938i −0.0329223 + 0.0442593i
\(995\) −970.623 + 814.449i −0.975501 + 0.818542i
\(996\) 257.929 + 998.872i 0.258965 + 1.00288i
\(997\) 280.247 + 769.974i 0.281091 + 0.772290i 0.997233 + 0.0743363i \(0.0236838\pi\)
−0.716143 + 0.697954i \(0.754094\pi\)
\(998\) −537.469 569.227i −0.538546 0.570368i
\(999\) 186.402 1586.38i 0.186589 1.58796i
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 216.3.x.a.101.25 yes 420
8.5 even 2 inner 216.3.x.a.101.63 yes 420
27.23 odd 18 inner 216.3.x.a.77.63 yes 420
216.77 odd 18 inner 216.3.x.a.77.25 420
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.3.x.a.77.25 420 216.77 odd 18 inner
216.3.x.a.77.63 yes 420 27.23 odd 18 inner
216.3.x.a.101.25 yes 420 1.1 even 1 trivial
216.3.x.a.101.63 yes 420 8.5 even 2 inner