Properties

Label 804.2.bd.a.23.3
Level $804$
Weight $2$
Character 804.23
Analytic conductor $6.420$
Analytic rank $0$
Dimension $2640$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [804,2,Mod(23,804)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(804, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([33, 33, 28]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("804.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 804.bd (of order \(66\), degree \(20\), 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: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(2640\)
Relative dimension: \(132\) over \(\Q(\zeta_{66})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 23.3
Character \(\chi\) \(=\) 804.23
Dual form 804.2.bd.a.35.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41021 + 0.106353i) q^{2} +(0.881313 + 1.49107i) q^{3} +(1.97738 - 0.299961i) q^{4} +(-1.21127 + 0.553168i) q^{5} +(-1.40142 - 2.00899i) q^{6} +(-1.08361 - 1.13646i) q^{7} +(-2.75661 + 0.633309i) q^{8} +(-1.44658 + 2.62820i) q^{9} +O(q^{10})\) \(q+(-1.41021 + 0.106353i) q^{2} +(0.881313 + 1.49107i) q^{3} +(1.97738 - 0.299961i) q^{4} +(-1.21127 + 0.553168i) q^{5} +(-1.40142 - 2.00899i) q^{6} +(-1.08361 - 1.13646i) q^{7} +(-2.75661 + 0.633309i) q^{8} +(-1.44658 + 2.62820i) q^{9} +(1.64931 - 0.908906i) q^{10} +(1.25029 + 0.119389i) q^{11} +(2.18995 + 2.68405i) q^{12} +(-0.394523 - 0.0760380i) q^{13} +(1.64899 + 1.48740i) q^{14} +(-1.89232 - 1.31857i) q^{15} +(3.82005 - 1.18627i) q^{16} +(0.992017 - 1.92424i) q^{17} +(1.76046 - 3.86015i) q^{18} +(-5.54672 + 5.81724i) q^{19} +(-2.22921 + 1.45716i) q^{20} +(0.739539 - 2.61732i) q^{21} +(-1.77587 - 0.0353898i) q^{22} +(-1.10694 + 0.443150i) q^{23} +(-3.37375 - 3.55216i) q^{24} +(-2.11312 + 2.43868i) q^{25} +(0.564446 + 0.0652707i) q^{26} +(-5.19371 + 0.159317i) q^{27} +(-2.48360 - 1.92217i) q^{28} +(-6.34401 - 3.66271i) q^{29} +(2.80880 + 1.65821i) q^{30} +(-0.0714776 - 0.370861i) q^{31} +(-5.26090 + 2.07917i) q^{32} +(0.923883 + 1.96949i) q^{33} +(-1.19430 + 2.81909i) q^{34} +(1.94120 + 0.777139i) q^{35} +(-2.07207 + 5.63085i) q^{36} +(-0.164311 - 0.284595i) q^{37} +(7.20336 - 8.79343i) q^{38} +(-0.234320 - 0.655274i) q^{39} +(2.98868 - 2.29198i) q^{40} +(-10.5865 + 0.504295i) q^{41} +(-0.764544 + 3.76962i) q^{42} +(4.52097 + 7.03477i) q^{43} +(2.50812 - 0.138963i) q^{44} +(0.298359 - 3.98366i) q^{45} +(1.51388 - 0.742661i) q^{46} +(-0.246085 - 0.193523i) q^{47} +(5.13547 + 4.65048i) q^{48} +(0.215748 - 4.52911i) q^{49} +(2.72059 - 3.66378i) q^{50} +(3.74346 - 0.216695i) q^{51} +(-0.802929 - 0.0320145i) q^{52} +(3.76196 - 5.85372i) q^{53} +(7.30727 - 0.777038i) q^{54} +(-1.58049 + 0.547011i) q^{55} +(3.70683 + 2.44652i) q^{56} +(-13.5623 - 3.14375i) q^{57} +(9.33591 + 4.49048i) q^{58} +(2.90403 + 3.35143i) q^{59} +(-4.13735 - 2.03970i) q^{60} +(-7.52455 + 0.718507i) q^{61} +(0.140241 + 0.515389i) q^{62} +(4.55437 - 1.20397i) q^{63} +(7.19784 - 3.49157i) q^{64} +(0.519935 - 0.126135i) q^{65} +(-1.51233 - 2.67914i) q^{66} +(2.25814 - 7.86770i) q^{67} +(1.38439 - 4.10252i) q^{68} +(-1.63632 - 1.25996i) q^{69} +(-2.82015 - 0.889475i) q^{70} +(1.69621 - 0.874459i) q^{71} +(2.32319 - 8.16105i) q^{72} +(-0.924416 + 0.0882711i) q^{73} +(0.261981 + 0.383864i) q^{74} +(-5.49856 - 1.00158i) q^{75} +(-9.22302 + 13.1667i) q^{76} +(-1.21915 - 1.55028i) q^{77} +(0.400131 + 0.899153i) q^{78} +(-0.351000 + 0.121482i) q^{79} +(-3.97090 + 3.55002i) q^{80} +(-4.81483 - 7.60377i) q^{81} +(14.8755 - 1.83707i) q^{82} +(-4.69899 + 6.59880i) q^{83} +(0.677256 - 5.39726i) q^{84} +(-0.137169 + 2.87953i) q^{85} +(-7.12368 - 9.43967i) q^{86} +(-0.129692 - 12.6873i) q^{87} +(-3.52219 + 0.462714i) q^{88} +(-3.01184 + 0.433038i) q^{89} +(0.00292670 + 5.64952i) q^{90} +(0.341096 + 0.530755i) q^{91} +(-2.05590 + 1.20831i) q^{92} +(0.489985 - 0.433422i) q^{93} +(0.367613 + 0.246736i) q^{94} +(3.50067 - 10.1145i) q^{95} +(-7.73668 - 6.01197i) q^{96} +(-4.97724 - 8.62084i) q^{97} +(0.177436 + 6.40993i) q^{98} +(-2.12242 + 3.11331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{14}{33}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41021 + 0.106353i −0.997168 + 0.0752032i
\(3\) 0.881313 + 1.49107i 0.508826 + 0.860869i
\(4\) 1.97738 0.299961i 0.988689 0.149981i
\(5\) −1.21127 + 0.553168i −0.541696 + 0.247384i −0.667421 0.744681i \(-0.732602\pi\)
0.125725 + 0.992065i \(0.459874\pi\)
\(6\) −1.40142 2.00899i −0.572125 0.820166i
\(7\) −1.08361 1.13646i −0.409567 0.429541i 0.486349 0.873764i \(-0.338328\pi\)
−0.895916 + 0.444223i \(0.853480\pi\)
\(8\) −2.75661 + 0.633309i −0.974610 + 0.223908i
\(9\) −1.44658 + 2.62820i −0.482192 + 0.876065i
\(10\) 1.64931 0.908906i 0.521558 0.287421i
\(11\) 1.25029 + 0.119389i 0.376978 + 0.0359970i 0.281825 0.959466i \(-0.409060\pi\)
0.0951524 + 0.995463i \(0.469666\pi\)
\(12\) 2.18995 + 2.68405i 0.632184 + 0.774818i
\(13\) −0.394523 0.0760380i −0.109421 0.0210892i 0.134247 0.990948i \(-0.457139\pi\)
−0.243668 + 0.969859i \(0.578351\pi\)
\(14\) 1.64899 + 1.48740i 0.440710 + 0.397524i
\(15\) −1.89232 1.31857i −0.488595 0.340454i
\(16\) 3.82005 1.18627i 0.955012 0.296568i
\(17\) 0.992017 1.92424i 0.240599 0.466698i −0.737358 0.675502i \(-0.763927\pi\)
0.977957 + 0.208804i \(0.0669572\pi\)
\(18\) 1.76046 3.86015i 0.414944 0.909847i
\(19\) −5.54672 + 5.81724i −1.27251 + 1.33457i −0.356030 + 0.934474i \(0.615870\pi\)
−0.916475 + 0.400091i \(0.868978\pi\)
\(20\) −2.22921 + 1.45716i −0.498466 + 0.325830i
\(21\) 0.739539 2.61732i 0.161381 0.571145i
\(22\) −1.77587 0.0353898i −0.378617 0.00754514i
\(23\) −1.10694 + 0.443150i −0.230812 + 0.0924032i −0.484186 0.874965i \(-0.660884\pi\)
0.253374 + 0.967369i \(0.418460\pi\)
\(24\) −3.37375 3.55216i −0.688663 0.725082i
\(25\) −2.11312 + 2.43868i −0.422625 + 0.487735i
\(26\) 0.564446 + 0.0652707i 0.110697 + 0.0128006i
\(27\) −5.19371 + 0.159317i −0.999530 + 0.0306605i
\(28\) −2.48360 1.92217i −0.469357 0.363256i
\(29\) −6.34401 3.66271i −1.17805 0.680149i −0.222489 0.974935i \(-0.571418\pi\)
−0.955563 + 0.294786i \(0.904751\pi\)
\(30\) 2.80880 + 1.65821i 0.512814 + 0.302746i
\(31\) −0.0714776 0.370861i −0.0128378 0.0666086i 0.974945 0.222447i \(-0.0714043\pi\)
−0.987783 + 0.155838i \(0.950192\pi\)
\(32\) −5.26090 + 2.07917i −0.930004 + 0.367548i
\(33\) 0.923883 + 1.96949i 0.160827 + 0.342845i
\(34\) −1.19430 + 2.81909i −0.204821 + 0.483470i
\(35\) 1.94120 + 0.777139i 0.328123 + 0.131360i
\(36\) −2.07207 + 5.63085i −0.345345 + 0.938476i
\(37\) −0.164311 0.284595i −0.0270126 0.0467872i 0.852203 0.523211i \(-0.175266\pi\)
−0.879216 + 0.476424i \(0.841933\pi\)
\(38\) 7.20336 8.79343i 1.16854 1.42648i
\(39\) −0.234320 0.655274i −0.0375212 0.104928i
\(40\) 2.98868 2.29198i 0.472551 0.362394i
\(41\) −10.5865 + 0.504295i −1.65333 + 0.0787576i −0.853371 0.521303i \(-0.825446\pi\)
−0.799954 + 0.600061i \(0.795143\pi\)
\(42\) −0.764544 + 3.76962i −0.117972 + 0.581664i
\(43\) 4.52097 + 7.03477i 0.689441 + 1.07279i 0.992785 + 0.119910i \(0.0382607\pi\)
−0.303343 + 0.952881i \(0.598103\pi\)
\(44\) 2.50812 0.138963i 0.378113 0.0209495i
\(45\) 0.298359 3.98366i 0.0444767 0.593848i
\(46\) 1.51388 0.742661i 0.223209 0.109499i
\(47\) −0.246085 0.193523i −0.0358952 0.0282283i 0.600050 0.799962i \(-0.295147\pi\)
−0.635945 + 0.771734i \(0.719390\pi\)
\(48\) 5.13547 + 4.65048i 0.741241 + 0.671239i
\(49\) 0.215748 4.52911i 0.0308211 0.647016i
\(50\) 2.72059 3.66378i 0.384749 0.518137i
\(51\) 3.74346 0.216695i 0.524189 0.0303433i
\(52\) −0.802929 0.0320145i −0.111346 0.00443961i
\(53\) 3.76196 5.85372i 0.516745 0.804070i −0.480597 0.876942i \(-0.659580\pi\)
0.997341 + 0.0728713i \(0.0232162\pi\)
\(54\) 7.30727 0.777038i 0.994394 0.105742i
\(55\) −1.58049 + 0.547011i −0.213113 + 0.0737590i
\(56\) 3.70683 + 2.44652i 0.495346 + 0.326930i
\(57\) −13.5623 3.14375i −1.79637 0.416399i
\(58\) 9.33591 + 4.49048i 1.22587 + 0.589629i
\(59\) 2.90403 + 3.35143i 0.378073 + 0.436320i 0.912614 0.408823i \(-0.134061\pi\)
−0.534540 + 0.845143i \(0.679515\pi\)
\(60\) −4.13735 2.03970i −0.534130 0.263324i
\(61\) −7.52455 + 0.718507i −0.963419 + 0.0919954i −0.564895 0.825163i \(-0.691083\pi\)
−0.398524 + 0.917158i \(0.630477\pi\)
\(62\) 0.140241 + 0.515389i 0.0178106 + 0.0654545i
\(63\) 4.55437 1.20397i 0.573796 0.151686i
\(64\) 7.19784 3.49157i 0.899730 0.436447i
\(65\) 0.519935 0.126135i 0.0644900 0.0156451i
\(66\) −1.51233 2.67914i −0.186155 0.329779i
\(67\) 2.25814 7.86770i 0.275876 0.961193i
\(68\) 1.38439 4.10252i 0.167882 0.497504i
\(69\) −1.63632 1.25996i −0.196990 0.151682i
\(70\) −2.82015 0.889475i −0.337072 0.106313i
\(71\) 1.69621 0.874459i 0.201303 0.103779i −0.354627 0.935008i \(-0.615392\pi\)
0.555931 + 0.831229i \(0.312362\pi\)
\(72\) 2.32319 8.16105i 0.273791 0.961789i
\(73\) −0.924416 + 0.0882711i −0.108195 + 0.0103313i −0.149013 0.988835i \(-0.547610\pi\)
0.0408182 + 0.999167i \(0.487004\pi\)
\(74\) 0.261981 + 0.383864i 0.0304547 + 0.0446233i
\(75\) −5.49856 1.00158i −0.634919 0.115652i
\(76\) −9.22302 + 13.1667i −1.05795 + 1.51032i
\(77\) −1.21915 1.55028i −0.138935 0.176671i
\(78\) 0.400131 + 0.899153i 0.0453059 + 0.101809i
\(79\) −0.351000 + 0.121482i −0.0394906 + 0.0136678i −0.346742 0.937961i \(-0.612712\pi\)
0.307251 + 0.951628i \(0.400591\pi\)
\(80\) −3.97090 + 3.55002i −0.443960 + 0.396905i
\(81\) −4.81483 7.60377i −0.534982 0.844864i
\(82\) 14.8755 1.83707i 1.64272 0.202870i
\(83\) −4.69899 + 6.59880i −0.515781 + 0.724313i −0.987532 0.157419i \(-0.949683\pi\)
0.471751 + 0.881732i \(0.343622\pi\)
\(84\) 0.677256 5.39726i 0.0738947 0.588889i
\(85\) −0.137169 + 2.87953i −0.0148781 + 0.312329i
\(86\) −7.12368 9.43967i −0.768166 1.01791i
\(87\) −0.129692 12.6873i −0.0139044 1.36023i
\(88\) −3.52219 + 0.462714i −0.375466 + 0.0493254i
\(89\) −3.01184 + 0.433038i −0.319255 + 0.0459019i −0.300079 0.953914i \(-0.597013\pi\)
−0.0191754 + 0.999816i \(0.506104\pi\)
\(90\) 0.00292670 + 5.64952i 0.000308502 + 0.595511i
\(91\) 0.341096 + 0.530755i 0.0357565 + 0.0556382i
\(92\) −2.05590 + 1.20831i −0.214343 + 0.125975i
\(93\) 0.489985 0.433422i 0.0508091 0.0449438i
\(94\) 0.367613 + 0.246736i 0.0379164 + 0.0254489i
\(95\) 3.50067 10.1145i 0.359161 1.03773i
\(96\) −7.73668 6.01197i −0.789622 0.613594i
\(97\) −4.97724 8.62084i −0.505362 0.875313i −0.999981 0.00620311i \(-0.998025\pi\)
0.494618 0.869110i \(-0.335308\pi\)
\(98\) 0.177436 + 6.40993i 0.0179238 + 0.647501i
\(99\) −2.12242 + 3.11331i −0.213311 + 0.312900i
\(100\) −3.44694 + 5.45604i −0.344694 + 0.545604i
\(101\) 3.10299 + 0.752777i 0.308759 + 0.0749041i 0.387145 0.922019i \(-0.373461\pi\)
−0.0783858 + 0.996923i \(0.524977\pi\)
\(102\) −5.25601 + 0.703714i −0.520423 + 0.0696781i
\(103\) 1.67198 + 8.67503i 0.164745 + 0.854776i 0.966410 + 0.257004i \(0.0827353\pi\)
−0.801666 + 0.597772i \(0.796053\pi\)
\(104\) 1.13570 0.0402472i 0.111365 0.00394656i
\(105\) 0.552035 + 3.57937i 0.0538731 + 0.349310i
\(106\) −4.68258 + 8.65507i −0.454813 + 0.840654i
\(107\) −6.32274 + 13.8449i −0.611242 + 1.33843i 0.310479 + 0.950580i \(0.399511\pi\)
−0.921721 + 0.387854i \(0.873217\pi\)
\(108\) −10.2221 + 1.87294i −0.983626 + 0.180224i
\(109\) −9.63599 + 11.1205i −0.922961 + 1.06515i 0.0747280 + 0.997204i \(0.476191\pi\)
−0.997689 + 0.0679496i \(0.978354\pi\)
\(110\) 2.17064 0.939490i 0.206962 0.0895769i
\(111\) 0.279542 0.495817i 0.0265330 0.0470609i
\(112\) −5.48760 3.05587i −0.518529 0.288753i
\(113\) 2.12920 1.51620i 0.200298 0.142632i −0.475507 0.879712i \(-0.657735\pi\)
0.675805 + 0.737080i \(0.263796\pi\)
\(114\) 19.4600 + 2.99094i 1.82260 + 0.280127i
\(115\) 1.09566 1.14910i 0.102171 0.107154i
\(116\) −13.6432 5.33961i −1.26674 0.495771i
\(117\) 0.770550 0.926889i 0.0712374 0.0856909i
\(118\) −4.45173 4.41737i −0.409815 0.406652i
\(119\) −3.26179 + 0.957747i −0.299008 + 0.0877965i
\(120\) 6.05146 + 2.43637i 0.552420 + 0.222410i
\(121\) −9.25223 1.78322i −0.841112 0.162111i
\(122\) 10.5348 1.81351i 0.953773 0.164187i
\(123\) −10.0819 15.3407i −0.909055 1.38322i
\(124\) −0.252582 0.711892i −0.0226825 0.0639298i
\(125\) 3.08635 10.5111i 0.276051 0.940144i
\(126\) −6.29456 + 2.18222i −0.560764 + 0.194408i
\(127\) 9.12403 + 9.56901i 0.809627 + 0.849112i 0.990939 0.134314i \(-0.0428829\pi\)
−0.181312 + 0.983426i \(0.558034\pi\)
\(128\) −9.77912 + 5.68936i −0.864360 + 0.502873i
\(129\) −6.50494 + 12.9409i −0.572728 + 1.13938i
\(130\) −0.719803 + 0.233174i −0.0631309 + 0.0204507i
\(131\) −1.13221 + 7.87466i −0.0989213 + 0.688012i 0.878659 + 0.477450i \(0.158439\pi\)
−0.977580 + 0.210563i \(0.932470\pi\)
\(132\) 2.41764 + 3.61730i 0.210428 + 0.314846i
\(133\) 12.6216 1.09443
\(134\) −2.34770 + 11.3353i −0.202810 + 0.979218i
\(135\) 6.20285 3.06597i 0.533857 0.263877i
\(136\) −1.51597 + 5.93265i −0.129993 + 0.508721i
\(137\) 14.4822 + 2.08222i 1.23729 + 0.177896i 0.729741 0.683724i \(-0.239641\pi\)
0.507554 + 0.861620i \(0.330550\pi\)
\(138\) 2.44156 + 1.60278i 0.207839 + 0.136438i
\(139\) −2.03419 + 0.928982i −0.172538 + 0.0787952i −0.499811 0.866134i \(-0.666597\pi\)
0.327274 + 0.944930i \(0.393870\pi\)
\(140\) 4.07160 + 0.954414i 0.344113 + 0.0806627i
\(141\) 0.0716789 0.537484i 0.00603646 0.0452643i
\(142\) −2.29901 + 1.41357i −0.192929 + 0.118624i
\(143\) −0.484191 0.142171i −0.0404901 0.0118890i
\(144\) −2.40823 + 11.7559i −0.200686 + 0.979656i
\(145\) 9.71040 + 0.927231i 0.806405 + 0.0770023i
\(146\) 1.29423 0.222795i 0.107111 0.0184387i
\(147\) 6.94336 3.66987i 0.572678 0.302685i
\(148\) −0.410273 0.513466i −0.0337242 0.0422066i
\(149\) −3.68264 12.5419i −0.301694 1.02748i −0.961218 0.275791i \(-0.911060\pi\)
0.659524 0.751684i \(-0.270758\pi\)
\(150\) 7.86064 + 0.827647i 0.641818 + 0.0675771i
\(151\) 4.48884 8.70713i 0.365296 0.708576i −0.632526 0.774539i \(-0.717982\pi\)
0.997822 + 0.0659632i \(0.0210120\pi\)
\(152\) 11.6061 19.5487i 0.941377 1.58561i
\(153\) 3.62226 + 5.39078i 0.292843 + 0.435819i
\(154\) 1.88414 + 2.05656i 0.151828 + 0.165722i
\(155\) 0.291727 + 0.409673i 0.0234321 + 0.0329058i
\(156\) −0.659896 1.22544i −0.0528339 0.0981136i
\(157\) −8.75452 + 3.50478i −0.698687 + 0.279712i −0.693688 0.720275i \(-0.744015\pi\)
−0.00499875 + 0.999988i \(0.501591\pi\)
\(158\) 0.482063 0.208645i 0.0383509 0.0165989i
\(159\) 12.0438 + 0.450383i 0.955133 + 0.0357177i
\(160\) 5.22224 5.42860i 0.412854 0.429168i
\(161\) 1.70311 + 0.777785i 0.134224 + 0.0612980i
\(162\) 7.59861 + 10.2108i 0.597003 + 0.802239i
\(163\) 6.81989 + 3.93747i 0.534175 + 0.308406i 0.742715 0.669608i \(-0.233538\pi\)
−0.208540 + 0.978014i \(0.566871\pi\)
\(164\) −20.7821 + 4.17270i −1.62281 + 0.325833i
\(165\) −2.20853 1.87453i −0.171934 0.145932i
\(166\) 5.92475 9.80544i 0.459849 0.761050i
\(167\) 1.72287 7.10176i 0.133320 0.549551i −0.865497 0.500914i \(-0.832997\pi\)
0.998817 0.0486365i \(-0.0154876\pi\)
\(168\) −0.381055 + 7.68329i −0.0293990 + 0.592779i
\(169\) −11.9189 4.77161i −0.916840 0.367047i
\(170\) −0.112811 4.07533i −0.00865221 0.312563i
\(171\) −7.26508 22.9930i −0.555575 1.75832i
\(172\) 11.0498 + 12.5543i 0.842541 + 0.957255i
\(173\) 22.6596 + 7.84256i 1.72278 + 0.596259i 0.995896 0.0905042i \(-0.0288478\pi\)
0.726881 + 0.686763i \(0.240969\pi\)
\(174\) 1.53223 + 17.8780i 0.116158 + 1.35533i
\(175\) 5.06126 0.241098i 0.382596 0.0182253i
\(176\) 4.91781 1.02712i 0.370694 0.0774220i
\(177\) −2.43786 + 7.28378i −0.183241 + 0.547482i
\(178\) 4.20127 0.930993i 0.314899 0.0697809i
\(179\) 2.10379 + 14.6322i 0.157245 + 1.09366i 0.903682 + 0.428205i \(0.140854\pi\)
−0.746437 + 0.665456i \(0.768237\pi\)
\(180\) −0.604973 7.96669i −0.0450920 0.593802i
\(181\) 15.6206 + 12.2842i 1.16107 + 0.913074i 0.997301 0.0734251i \(-0.0233930\pi\)
0.163767 + 0.986499i \(0.447635\pi\)
\(182\) −0.537463 0.712199i −0.0398394 0.0527917i
\(183\) −7.70282 10.5864i −0.569409 0.782568i
\(184\) 2.77074 1.92263i 0.204262 0.141738i
\(185\) 0.356454 + 0.253830i 0.0262071 + 0.0186620i
\(186\) −0.644886 + 0.663328i −0.0472853 + 0.0486375i
\(187\) 1.47005 2.28744i 0.107500 0.167274i
\(188\) −0.544652 0.308853i −0.0397228 0.0225254i
\(189\) 5.80902 + 5.72980i 0.422544 + 0.416782i
\(190\) −3.86096 + 14.6359i −0.280103 + 1.06180i
\(191\) 14.7266 11.5811i 1.06558 0.837981i 0.0782927 0.996930i \(-0.475053\pi\)
0.987287 + 0.158949i \(0.0508107\pi\)
\(192\) 11.5497 + 7.65531i 0.833530 + 0.552475i
\(193\) 10.8629 + 12.5364i 0.781927 + 0.902392i 0.997247 0.0741516i \(-0.0236249\pi\)
−0.215320 + 0.976544i \(0.569079\pi\)
\(194\) 7.93581 + 11.6278i 0.569758 + 0.834830i
\(195\) 0.646302 + 0.664095i 0.0462826 + 0.0475569i
\(196\) −0.931941 9.02048i −0.0665672 0.644320i
\(197\) 8.31078 + 16.1207i 0.592118 + 1.14855i 0.974467 + 0.224531i \(0.0720851\pi\)
−0.382348 + 0.924018i \(0.624885\pi\)
\(198\) 2.66195 4.61615i 0.189176 0.328055i
\(199\) −18.6679 + 4.52879i −1.32333 + 0.321037i −0.834340 0.551250i \(-0.814151\pi\)
−0.488993 + 0.872288i \(0.662636\pi\)
\(200\) 4.28063 8.06075i 0.302687 0.569981i
\(201\) 13.7214 3.56686i 0.967835 0.251587i
\(202\) −4.45592 0.731559i −0.313517 0.0514723i
\(203\) 2.71191 + 11.1787i 0.190339 + 0.784588i
\(204\) 7.33723 1.55138i 0.513709 0.108618i
\(205\) 12.5441 6.46693i 0.876117 0.451670i
\(206\) −3.28045 12.0558i −0.228560 0.839966i
\(207\) 0.436581 3.55030i 0.0303445 0.246763i
\(208\) −1.59730 + 0.177543i −0.110753 + 0.0123104i
\(209\) −7.62955 + 6.61104i −0.527747 + 0.457295i
\(210\) −1.15916 4.98894i −0.0799898 0.344270i
\(211\) 6.09443 + 7.74970i 0.419558 + 0.533511i 0.949185 0.314719i \(-0.101910\pi\)
−0.529627 + 0.848231i \(0.677668\pi\)
\(212\) 5.68292 12.7035i 0.390305 0.872477i
\(213\) 2.79877 + 1.75850i 0.191769 + 0.120490i
\(214\) 7.44393 20.1966i 0.508857 1.38061i
\(215\) −9.36752 6.02014i −0.638860 0.410570i
\(216\) 14.2162 3.72840i 0.967287 0.253685i
\(217\) −0.344014 + 0.483101i −0.0233532 + 0.0327950i
\(218\) 12.4061 16.7071i 0.840244 1.13155i
\(219\) −0.946318 1.30057i −0.0639463 0.0878847i
\(220\) −2.96113 + 1.55573i −0.199640 + 0.104887i
\(221\) −0.537689 + 0.683727i −0.0361689 + 0.0459925i
\(222\) −0.341481 + 0.728936i −0.0229187 + 0.0489230i
\(223\) −10.8903 + 1.56580i −0.729271 + 0.104853i −0.496942 0.867784i \(-0.665544\pi\)
−0.232329 + 0.972637i \(0.574635\pi\)
\(224\) 8.06366 + 3.72579i 0.538776 + 0.248940i
\(225\) −3.35252 9.08144i −0.223502 0.605429i
\(226\) −2.84137 + 2.36460i −0.189005 + 0.157291i
\(227\) 0.0803747 + 1.68727i 0.00533466 + 0.111988i 0.999964 + 0.00848702i \(0.00270154\pi\)
−0.994629 + 0.103501i \(0.966995\pi\)
\(228\) −27.7608 2.14821i −1.83850 0.142269i
\(229\) 4.88369 14.1105i 0.322723 0.932447i −0.660625 0.750716i \(-0.729709\pi\)
0.983348 0.181731i \(-0.0581701\pi\)
\(230\) −1.42290 + 1.73699i −0.0938233 + 0.114534i
\(231\) 1.23712 3.18412i 0.0813965 0.209500i
\(232\) 19.8076 + 6.07897i 1.30043 + 0.399104i
\(233\) −0.501584 + 1.25290i −0.0328599 + 0.0820800i −0.943890 0.330259i \(-0.892864\pi\)
0.911030 + 0.412339i \(0.135288\pi\)
\(234\) −0.988059 + 1.38906i −0.0645914 + 0.0908055i
\(235\) 0.405126 + 0.0982825i 0.0264275 + 0.00641124i
\(236\) 6.74767 + 5.75596i 0.439236 + 0.374681i
\(237\) −0.490479 0.416301i −0.0318600 0.0270417i
\(238\) 4.49794 1.69753i 0.291558 0.110034i
\(239\) −8.76847 + 15.1874i −0.567185 + 0.982394i 0.429657 + 0.902992i \(0.358634\pi\)
−0.996843 + 0.0794018i \(0.974699\pi\)
\(240\) −8.79294 2.79220i −0.567582 0.180236i
\(241\) −3.94821 + 8.64537i −0.254326 + 0.556897i −0.993129 0.117025i \(-0.962664\pi\)
0.738803 + 0.673922i \(0.235392\pi\)
\(242\) 13.2372 + 1.53071i 0.850922 + 0.0983977i
\(243\) 7.09438 13.8806i 0.455105 0.890438i
\(244\) −14.6633 + 3.67783i −0.938724 + 0.235449i
\(245\) 2.24403 + 5.60532i 0.143366 + 0.358111i
\(246\) 15.8491 + 20.5613i 1.01050 + 1.31094i
\(247\) 2.63064 1.87327i 0.167384 0.119193i
\(248\) 0.431905 + 0.977053i 0.0274260 + 0.0620429i
\(249\) −13.9805 1.19091i −0.885981 0.0754707i
\(250\) −3.23450 + 15.1511i −0.204568 + 0.958242i
\(251\) 3.35589 + 1.73008i 0.211822 + 0.109202i 0.560873 0.827902i \(-0.310466\pi\)
−0.349051 + 0.937104i \(0.613496\pi\)
\(252\) 8.64456 3.74684i 0.544556 0.236028i
\(253\) −1.43690 + 0.421913i −0.0903373 + 0.0265254i
\(254\) −13.8845 12.5239i −0.871190 0.785821i
\(255\) −4.41447 + 2.33324i −0.276445 + 0.146113i
\(256\) 13.1855 9.06323i 0.824095 0.566452i
\(257\) −1.43549 + 15.0331i −0.0895431 + 0.937738i 0.833366 + 0.552721i \(0.186410\pi\)
−0.922909 + 0.385017i \(0.874196\pi\)
\(258\) 7.79701 18.9412i 0.485421 1.17923i
\(259\) −0.145382 + 0.495124i −0.00903357 + 0.0307655i
\(260\) 0.990273 0.405377i 0.0614141 0.0251404i
\(261\) 18.8034 11.3749i 1.16390 0.704088i
\(262\) 0.759149 11.2253i 0.0469004 0.693503i
\(263\) 8.81204 + 19.2957i 0.543374 + 1.18982i 0.959808 + 0.280657i \(0.0905522\pi\)
−0.416435 + 0.909166i \(0.636721\pi\)
\(264\) −3.79409 4.84403i −0.233510 0.298130i
\(265\) −1.31865 + 9.17143i −0.0810042 + 0.563397i
\(266\) −17.7990 + 1.34234i −1.09133 + 0.0823044i
\(267\) −3.30006 4.10923i −0.201961 0.251481i
\(268\) 2.10520 16.2348i 0.128596 0.991697i
\(269\) 4.39856i 0.268185i −0.990969 0.134092i \(-0.957188\pi\)
0.990969 0.134092i \(-0.0428119\pi\)
\(270\) −8.42124 + 4.98335i −0.512501 + 0.303277i
\(271\) −21.4555 3.08484i −1.30333 0.187391i −0.544546 0.838731i \(-0.683298\pi\)
−0.758786 + 0.651340i \(0.774207\pi\)
\(272\) 1.50687 8.52750i 0.0913676 0.517056i
\(273\) −0.490781 + 0.976358i −0.0297034 + 0.0590919i
\(274\) −20.6443 1.39614i −1.24717 0.0843438i
\(275\) −2.93318 + 2.79678i −0.176877 + 0.168652i
\(276\) −3.61357 2.00059i −0.217511 0.120422i
\(277\) 26.0949 + 7.66217i 1.56789 + 0.460375i 0.946387 0.323034i \(-0.104703\pi\)
0.621506 + 0.783409i \(0.286521\pi\)
\(278\) 2.76983 1.52640i 0.166123 0.0915475i
\(279\) 1.07809 + 0.348621i 0.0645437 + 0.0208714i
\(280\) −5.84331 0.912894i −0.349204 0.0545559i
\(281\) −1.89960 + 9.85607i −0.113321 + 0.587964i 0.880227 + 0.474552i \(0.157390\pi\)
−0.993548 + 0.113411i \(0.963822\pi\)
\(282\) −0.0439190 + 0.765588i −0.00261534 + 0.0455901i
\(283\) 2.94129 + 10.0171i 0.174841 + 0.595455i 0.999553 + 0.0299012i \(0.00951928\pi\)
−0.824712 + 0.565554i \(0.808663\pi\)
\(284\) 3.09175 2.23793i 0.183462 0.132797i
\(285\) 18.1666 3.69431i 1.07610 0.218832i
\(286\) 0.697931 + 0.148996i 0.0412696 + 0.00881032i
\(287\) 12.0447 + 11.4846i 0.710977 + 0.677915i
\(288\) 2.14583 16.8344i 0.126444 0.991974i
\(289\) 7.14235 + 10.0300i 0.420138 + 0.590002i
\(290\) −13.7923 0.274855i −0.809912 0.0161400i
\(291\) 8.46776 15.0191i 0.496389 0.880433i
\(292\) −1.80144 + 0.451834i −0.105421 + 0.0264416i
\(293\) 4.72490 + 4.09415i 0.276032 + 0.239183i 0.781864 0.623449i \(-0.214269\pi\)
−0.505832 + 0.862632i \(0.668815\pi\)
\(294\) −9.40128 + 5.91373i −0.548294 + 0.344896i
\(295\) −5.37148 2.45307i −0.312739 0.142823i
\(296\) 0.633180 + 0.680460i 0.0368028 + 0.0395509i
\(297\) −6.51268 0.420877i −0.377904 0.0244218i
\(298\) 6.52717 + 17.2951i 0.378109 + 1.00188i
\(299\) 0.470408 0.0906637i 0.0272044 0.00524322i
\(300\) −11.1732 0.331149i −0.645083 0.0191189i
\(301\) 3.09575 12.7609i 0.178436 0.735523i
\(302\) −5.40417 + 12.7563i −0.310975 + 0.734041i
\(303\) 1.61226 + 5.29020i 0.0926219 + 0.303914i
\(304\) −14.2879 + 28.8020i −0.819468 + 1.65191i
\(305\) 8.71680 5.03265i 0.499122 0.288168i
\(306\) −5.68148 7.21689i −0.324788 0.412562i
\(307\) 2.74094 + 0.948648i 0.156434 + 0.0541422i 0.404163 0.914687i \(-0.367563\pi\)
−0.247729 + 0.968829i \(0.579684\pi\)
\(308\) −2.87575 2.69979i −0.163861 0.153835i
\(309\) −11.4615 + 10.1384i −0.652024 + 0.576756i
\(310\) −0.454966 0.546699i −0.0258403 0.0310504i
\(311\) 20.0123 12.8611i 1.13479 0.729288i 0.168239 0.985746i \(-0.446192\pi\)
0.966555 + 0.256459i \(0.0825557\pi\)
\(312\) 1.06092 + 1.65794i 0.0600628 + 0.0938624i
\(313\) −2.19338 15.2553i −0.123977 0.862281i −0.952979 0.303035i \(-0.902000\pi\)
0.829002 0.559246i \(-0.188909\pi\)
\(314\) 11.9730 5.87355i 0.675673 0.331463i
\(315\) −4.85057 + 3.97766i −0.273299 + 0.224116i
\(316\) −0.657619 + 0.345503i −0.0369940 + 0.0194360i
\(317\) −16.9683 0.808302i −0.953037 0.0453988i −0.434700 0.900575i \(-0.643146\pi\)
−0.518337 + 0.855176i \(0.673449\pi\)
\(318\) −17.0321 + 0.645761i −0.955114 + 0.0362125i
\(319\) −7.49459 5.33687i −0.419616 0.298807i
\(320\) −6.78710 + 8.21086i −0.379410 + 0.459001i
\(321\) −26.2160 + 2.77401i −1.46323 + 0.154830i
\(322\) −2.48446 0.915708i −0.138454 0.0510304i
\(323\) 5.69134 + 16.4440i 0.316675 + 0.914971i
\(324\) −11.8016 13.5913i −0.655643 0.755071i
\(325\) 1.01911 0.801435i 0.0565299 0.0444556i
\(326\) −10.0362 4.82733i −0.555856 0.267361i
\(327\) −25.0738 4.56727i −1.38658 0.252571i
\(328\) 28.8634 8.09464i 1.59371 0.446951i
\(329\) 0.0467291 + 0.489369i 0.00257626 + 0.0269798i
\(330\) 3.31386 + 2.40859i 0.182422 + 0.132588i
\(331\) −7.83977 15.2070i −0.430913 0.835854i −0.999909 0.0135137i \(-0.995698\pi\)
0.568996 0.822340i \(-0.307332\pi\)
\(332\) −7.31229 + 14.4578i −0.401314 + 0.793477i
\(333\) 0.985662 0.0201532i 0.0540139 0.00110439i
\(334\) −1.67431 + 10.1982i −0.0916140 + 0.558020i
\(335\) 1.61694 + 10.7790i 0.0883430 + 0.588922i
\(336\) −0.279776 10.8756i −0.0152631 0.593311i
\(337\) −1.09976 4.53329i −0.0599080 0.246944i 0.933982 0.357320i \(-0.116310\pi\)
−0.993890 + 0.110376i \(0.964794\pi\)
\(338\) 17.3156 + 5.46136i 0.941847 + 0.297059i
\(339\) 4.13725 + 1.83854i 0.224704 + 0.0998560i
\(340\) 0.592512 + 5.73507i 0.0321335 + 0.311028i
\(341\) −0.0450914 0.472219i −0.00244184 0.0255721i
\(342\) 12.6907 + 31.6522i 0.686232 + 1.71156i
\(343\) −13.6881 + 11.8608i −0.739086 + 0.640422i
\(344\) −16.9177 16.5290i −0.912144 0.891182i
\(345\) 2.67900 + 0.620994i 0.144233 + 0.0334332i
\(346\) −32.7888 8.64973i −1.76274 0.465012i
\(347\) −1.24180 3.58794i −0.0666632 0.192611i 0.906749 0.421670i \(-0.138556\pi\)
−0.973412 + 0.229060i \(0.926435\pi\)
\(348\) −4.06216 25.0488i −0.217755 1.34276i
\(349\) −12.4839 8.02294i −0.668250 0.429458i 0.162044 0.986783i \(-0.448191\pi\)
−0.830294 + 0.557325i \(0.811828\pi\)
\(350\) −7.11180 + 0.878281i −0.380142 + 0.0469461i
\(351\) 2.06115 + 0.332065i 0.110016 + 0.0177243i
\(352\) −6.82590 + 1.97148i −0.363822 + 0.105080i
\(353\) −12.2977 0.585813i −0.654542 0.0311797i −0.282316 0.959322i \(-0.591103\pi\)
−0.372227 + 0.928142i \(0.621406\pi\)
\(354\) 2.66324 10.5309i 0.141549 0.559712i
\(355\) −1.57085 + 1.99750i −0.0833720 + 0.106016i
\(356\) −5.82566 + 1.75971i −0.308759 + 0.0932647i
\(357\) −4.30272 4.01948i −0.227724 0.212733i
\(358\) −4.52297 20.4107i −0.239046 1.07874i
\(359\) −23.8177 + 15.3067i −1.25705 + 0.807856i −0.987877 0.155237i \(-0.950386\pi\)
−0.269170 + 0.963093i \(0.586749\pi\)
\(360\) 1.70042 + 11.1704i 0.0896201 + 0.588729i
\(361\) −2.17004 45.5547i −0.114213 2.39762i
\(362\) −23.3347 15.6619i −1.22645 0.823172i
\(363\) −5.49520 15.3673i −0.288423 0.806574i
\(364\) 0.833681 + 0.947188i 0.0436967 + 0.0496461i
\(365\) 1.07089 0.618278i 0.0560529 0.0323621i
\(366\) 11.9885 + 14.1098i 0.626648 + 0.737531i
\(367\) 12.7677 31.8921i 0.666466 1.66475i −0.0778831 0.996962i \(-0.524816\pi\)
0.744350 0.667790i \(-0.232760\pi\)
\(368\) −3.70285 + 3.00598i −0.193024 + 0.156698i
\(369\) 13.9887 28.5528i 0.728224 1.48640i
\(370\) −0.529671 0.320043i −0.0275363 0.0166383i
\(371\) −10.7290 + 2.06785i −0.557023 + 0.107357i
\(372\) 0.838876 1.00402i 0.0434937 0.0520558i
\(373\) 7.82556 13.5543i 0.405192 0.701814i −0.589152 0.808023i \(-0.700538\pi\)
0.994344 + 0.106209i \(0.0338712\pi\)
\(374\) −1.82979 + 3.38211i −0.0946164 + 0.174885i
\(375\) 18.3929 4.66163i 0.949803 0.240726i
\(376\) 0.800921 + 0.377621i 0.0413043 + 0.0194743i
\(377\) 2.22435 + 1.92741i 0.114560 + 0.0992666i
\(378\) −8.80132 7.46241i −0.452691 0.383825i
\(379\) 12.4791 + 31.1712i 0.641007 + 1.60116i 0.790546 + 0.612403i \(0.209797\pi\)
−0.149539 + 0.988756i \(0.547779\pi\)
\(380\) 3.88818 21.0503i 0.199460 1.07986i
\(381\) −6.22693 + 22.0378i −0.319015 + 1.12903i
\(382\) −19.5359 + 17.8980i −0.999543 + 0.915743i
\(383\) −21.4499 20.4524i −1.09604 1.04507i −0.998759 0.0498129i \(-0.984138\pi\)
−0.0972793 0.995257i \(-0.531014\pi\)
\(384\) −17.1017 9.56724i −0.872717 0.488226i
\(385\) 2.33429 + 1.20341i 0.118966 + 0.0613314i
\(386\) −16.6522 16.5237i −0.847576 0.841033i
\(387\) −25.0287 + 1.70567i −1.27228 + 0.0867041i
\(388\) −12.4278 15.5537i −0.630926 0.789618i
\(389\) 6.44550 33.4424i 0.326800 1.69560i −0.332000 0.943279i \(-0.607723\pi\)
0.658800 0.752318i \(-0.271064\pi\)
\(390\) −0.982049 0.867777i −0.0497280 0.0439416i
\(391\) −0.245370 + 2.56963i −0.0124089 + 0.129952i
\(392\) 2.27359 + 12.6216i 0.114834 + 0.637489i
\(393\) −12.7395 + 5.25184i −0.642623 + 0.264920i
\(394\) −13.4344 21.8496i −0.676816 1.10077i
\(395\) 0.357955 0.341310i 0.0180107 0.0171732i
\(396\) −3.26296 + 6.79284i −0.163970 + 0.341353i
\(397\) 12.4869 + 27.3425i 0.626699 + 1.37228i 0.910545 + 0.413410i \(0.135662\pi\)
−0.283846 + 0.958870i \(0.591610\pi\)
\(398\) 25.8440 8.37193i 1.29544 0.419647i
\(399\) 11.1235 + 18.8196i 0.556873 + 0.942159i
\(400\) −5.17930 + 11.8226i −0.258965 + 0.591130i
\(401\) 3.24464i 0.162030i −0.996713 0.0810148i \(-0.974184\pi\)
0.996713 0.0810148i \(-0.0258161\pi\)
\(402\) −18.9707 + 6.48933i −0.946174 + 0.323658i
\(403\) 0.151748i 0.00755911i
\(404\) 6.36158 + 0.557748i 0.316501 + 0.0277490i
\(405\) 10.0382 + 6.54681i 0.498804 + 0.325313i
\(406\) −5.01326 15.4758i −0.248804 0.768053i
\(407\) −0.171460 0.375445i −0.00849895 0.0186101i
\(408\) −10.1820 + 2.96811i −0.504086 + 0.146943i
\(409\) −2.97971 + 2.84115i −0.147337 + 0.140486i −0.760163 0.649732i \(-0.774881\pi\)
0.612826 + 0.790218i \(0.290033\pi\)
\(410\) −17.0020 + 10.4538i −0.839669 + 0.516278i
\(411\) 9.65858 + 23.4290i 0.476423 + 1.15567i
\(412\) 5.90830 + 16.6523i 0.291081 + 0.820399i
\(413\) 0.661923 6.93197i 0.0325711 0.341100i
\(414\) −0.238085 + 5.05309i −0.0117012 + 0.248346i
\(415\) 2.04149 10.5923i 0.100213 0.519954i
\(416\) 2.23364 0.420250i 0.109513 0.0206045i
\(417\) −3.17793 2.21439i −0.155624 0.108439i
\(418\) 10.0561 10.1344i 0.491862 0.495688i
\(419\) 8.75938 + 4.51578i 0.427924 + 0.220610i 0.658714 0.752393i \(-0.271101\pi\)
−0.230790 + 0.973004i \(0.574131\pi\)
\(420\) 2.16525 + 6.91217i 0.105654 + 0.337279i
\(421\) 1.05138 + 1.00249i 0.0512410 + 0.0488582i 0.715267 0.698851i \(-0.246305\pi\)
−0.664026 + 0.747709i \(0.731154\pi\)
\(422\) −9.41863 10.2805i −0.458492 0.500448i
\(423\) 0.864597 0.366813i 0.0420382 0.0178351i
\(424\) −6.66305 + 18.5189i −0.323587 + 0.899359i
\(425\) 2.59635 + 6.48537i 0.125942 + 0.314587i
\(426\) −4.13388 2.18219i −0.200287 0.105728i
\(427\) 8.97024 + 7.77276i 0.434100 + 0.376150i
\(428\) −8.34952 + 29.2731i −0.403590 + 1.41497i
\(429\) −0.214737 0.847261i −0.0103676 0.0409061i
\(430\) 13.8504 + 7.49339i 0.667927 + 0.361363i
\(431\) −14.1428 + 24.4960i −0.681235 + 1.17993i 0.293370 + 0.955999i \(0.405223\pi\)
−0.974604 + 0.223934i \(0.928110\pi\)
\(432\) −19.6512 + 6.76975i −0.945470 + 0.325710i
\(433\) 7.16645 1.38122i 0.344397 0.0663772i −0.0141197 0.999900i \(-0.504495\pi\)
0.358517 + 0.933523i \(0.383282\pi\)
\(434\) 0.433753 0.717860i 0.0208208 0.0344584i
\(435\) 7.17533 + 15.2961i 0.344031 + 0.733390i
\(436\) −15.7183 + 24.8799i −0.752769 + 1.19153i
\(437\) 3.56196 8.89734i 0.170392 0.425618i
\(438\) 1.47283 + 1.73344i 0.0703744 + 0.0828269i
\(439\) 21.2896 12.2916i 1.01610 0.586644i 0.103127 0.994668i \(-0.467115\pi\)
0.912971 + 0.408024i \(0.133782\pi\)
\(440\) 4.01036 2.50883i 0.191186 0.119604i
\(441\) 11.5913 + 7.11873i 0.551966 + 0.338987i
\(442\) 0.685537 1.02138i 0.0326077 0.0485822i
\(443\) −1.27611 26.7888i −0.0606297 1.27277i −0.800216 0.599712i \(-0.795282\pi\)
0.739586 0.673062i \(-0.235021\pi\)
\(444\) 0.404034 1.06427i 0.0191746 0.0505080i
\(445\) 3.40861 2.19058i 0.161584 0.103844i
\(446\) 15.1911 3.36632i 0.719321 0.159400i
\(447\) 15.4553 16.5444i 0.731012 0.782525i
\(448\) −11.7677 4.39654i −0.555972 0.207717i
\(449\) −22.9121 + 29.1352i −1.08129 + 1.37497i −0.159539 + 0.987192i \(0.551001\pi\)
−0.921751 + 0.387781i \(0.873242\pi\)
\(450\) 5.69360 + 12.4502i 0.268399 + 0.586907i
\(451\) −13.2964 0.633385i −0.626102 0.0298249i
\(452\) 3.75544 3.63677i 0.176641 0.171059i
\(453\) 16.9390 0.980534i 0.795864 0.0460695i
\(454\) −0.292792 2.37086i −0.0137414 0.111270i
\(455\) −0.706755 0.454204i −0.0331332 0.0212934i
\(456\) 39.3770 + 0.0769756i 1.84400 + 0.00360471i
\(457\) −3.40645 9.84229i −0.159347 0.460403i 0.836860 0.547417i \(-0.184389\pi\)
−0.996207 + 0.0870140i \(0.972268\pi\)
\(458\) −5.38632 + 20.4181i −0.251686 + 0.954076i
\(459\) −4.84568 + 10.1520i −0.226177 + 0.473855i
\(460\) 1.82185 2.60085i 0.0849443 0.121265i
\(461\) −15.9427 + 13.8144i −0.742525 + 0.643401i −0.941658 0.336571i \(-0.890733\pi\)
0.199133 + 0.979972i \(0.436187\pi\)
\(462\) −1.40595 + 4.62185i −0.0654109 + 0.215028i
\(463\) −1.43328 15.0099i −0.0666099 0.697571i −0.965675 0.259755i \(-0.916358\pi\)
0.899065 0.437816i \(-0.144248\pi\)
\(464\) −28.5794 6.46602i −1.32676 0.300177i
\(465\) −0.353749 + 0.796036i −0.0164047 + 0.0369153i
\(466\) 0.574089 1.82019i 0.0265942 0.0843188i
\(467\) 9.70176 + 39.9912i 0.448944 + 1.85057i 0.521565 + 0.853212i \(0.325348\pi\)
−0.0726213 + 0.997360i \(0.523136\pi\)
\(468\) 1.24564 2.06394i 0.0575797 0.0954059i
\(469\) −11.3883 + 5.95925i −0.525862 + 0.275173i
\(470\) −0.581765 0.0955123i −0.0268348 0.00440565i
\(471\) −12.9413 9.96479i −0.596306 0.459153i
\(472\) −10.1278 7.39946i −0.466169 0.340588i
\(473\) 4.81267 + 9.33528i 0.221287 + 0.429236i
\(474\) 0.735953 + 0.534908i 0.0338034 + 0.0245691i
\(475\) −2.46544 25.8192i −0.113122 1.18467i
\(476\) −6.16250 + 2.87224i −0.282458 + 0.131649i
\(477\) 9.94277 + 18.3550i 0.455248 + 0.840419i
\(478\) 10.7501 22.3500i 0.491700 1.02227i
\(479\) 1.78606 1.40458i 0.0816073 0.0641767i −0.576522 0.817082i \(-0.695590\pi\)
0.658129 + 0.752905i \(0.271348\pi\)
\(480\) 12.6968 + 3.00243i 0.579529 + 0.137042i
\(481\) 0.0431845 + 0.124773i 0.00196904 + 0.00568917i
\(482\) 4.64833 12.6117i 0.211726 0.574446i
\(483\) 0.341242 + 3.22493i 0.0155271 + 0.146739i
\(484\) −18.8301 0.750794i −0.855912 0.0341270i
\(485\) 10.7976 + 7.68891i 0.490292 + 0.349135i
\(486\) −8.52832 + 20.3290i −0.386852 + 0.922142i
\(487\) −2.91964 0.139080i −0.132302 0.00630231i −0.0186734 0.999826i \(-0.505944\pi\)
−0.113628 + 0.993523i \(0.536247\pi\)
\(488\) 20.2872 6.74600i 0.918360 0.305377i
\(489\) 0.139420 + 13.6391i 0.00630480 + 0.616780i
\(490\) −3.76070 7.66601i −0.169891 0.346315i
\(491\) −3.92759 27.3170i −0.177250 1.23280i −0.863091 0.505049i \(-0.831475\pi\)
0.685841 0.727751i \(-0.259435\pi\)
\(492\) −24.5374 27.3102i −1.10623 1.23124i
\(493\) −13.3413 + 8.57394i −0.600863 + 0.386151i
\(494\) −3.51052 + 2.92148i −0.157946 + 0.131444i
\(495\) 0.848640 4.94512i 0.0381435 0.222267i
\(496\) −0.712990 1.33191i −0.0320142 0.0598047i
\(497\) −2.83182 0.980104i −0.127025 0.0439637i
\(498\) 19.8421 + 0.192549i 0.889148 + 0.00862832i
\(499\) 9.94167 5.73983i 0.445050 0.256950i −0.260687 0.965423i \(-0.583949\pi\)
0.705738 + 0.708473i \(0.250616\pi\)
\(500\) 2.94994 21.7103i 0.131926 0.970912i
\(501\) 12.1076 3.68995i 0.540928 0.164855i
\(502\) −4.91651 2.08287i −0.219435 0.0929630i
\(503\) 1.15909 4.77785i 0.0516814 0.213034i −0.940116 0.340855i \(-0.889283\pi\)
0.991797 + 0.127822i \(0.0407985\pi\)
\(504\) −11.7921 + 6.20320i −0.525264 + 0.276312i
\(505\) −4.17497 + 0.804659i −0.185784 + 0.0358068i
\(506\) 1.98146 0.747804i 0.0880867 0.0332440i
\(507\) −3.38948 21.9772i −0.150532 0.976042i
\(508\) 20.9120 + 16.1847i 0.927819 + 0.718079i
\(509\) −7.74189 3.53560i −0.343153 0.156713i 0.236382 0.971660i \(-0.424038\pi\)
−0.579535 + 0.814948i \(0.696766\pi\)
\(510\) 5.97718 3.75985i 0.264674 0.166489i
\(511\) 1.10203 + 0.954910i 0.0487507 + 0.0422427i
\(512\) −17.6304 + 14.1834i −0.779162 + 0.626823i
\(513\) 27.8813 31.0967i 1.23099 1.37295i
\(514\) 0.425515 21.3525i 0.0187686 0.941817i
\(515\) −6.82397 9.58292i −0.300700 0.422274i
\(516\) −8.98095 + 27.5403i −0.395364 + 1.21239i
\(517\) −0.284574 0.271341i −0.0125155 0.0119335i
\(518\) 0.152360 0.713690i 0.00669433 0.0313578i
\(519\) 8.27638 + 40.6988i 0.363293 + 1.78648i
\(520\) −1.35338 + 0.676985i −0.0593496 + 0.0296878i
\(521\) 11.6776 + 39.7704i 0.511607 + 1.74237i 0.657874 + 0.753128i \(0.271456\pi\)
−0.146267 + 0.989245i \(0.546726\pi\)
\(522\) −25.3070 + 18.0408i −1.10766 + 0.789624i
\(523\) 0.500274 2.59567i 0.0218755 0.113501i −0.969350 0.245685i \(-0.920987\pi\)
0.991225 + 0.132185i \(0.0421992\pi\)
\(524\) 0.123294 + 15.9108i 0.00538610 + 0.695067i
\(525\) 4.82005 + 7.33421i 0.210364 + 0.320091i
\(526\) −14.4790 26.2737i −0.631313 1.14559i
\(527\) −0.784534 0.230360i −0.0341748 0.0100346i
\(528\) 5.86563 + 6.42758i 0.255269 + 0.279725i
\(529\) −15.6170 + 14.8907i −0.678998 + 0.647423i
\(530\) 0.884163 13.0739i 0.0384056 0.567893i
\(531\) −13.0091 + 2.78427i −0.564548 + 0.120827i
\(532\) 24.9576 3.78597i 1.08205 0.164143i
\(533\) 4.21494 + 0.606017i 0.182569 + 0.0262495i
\(534\) 5.09081 + 5.44389i 0.220301 + 0.235580i
\(535\) 20.2674i 0.876237i
\(536\) −1.24215 + 23.1183i −0.0536527 + 0.998560i
\(537\) −19.9635 + 16.0324i −0.861489 + 0.691851i
\(538\) 0.467801 + 6.20288i 0.0201683 + 0.267425i
\(539\) 0.810472 5.63696i 0.0349095 0.242801i
\(540\) 11.3457 7.92320i 0.488242 0.340960i
\(541\) −10.6960 23.4209i −0.459856 1.00694i −0.987520 0.157491i \(-0.949659\pi\)
0.527665 0.849453i \(-0.323068\pi\)
\(542\) 30.5849 + 2.06840i 1.31373 + 0.0888454i
\(543\) −4.54992 + 34.1175i −0.195256 + 1.46412i
\(544\) −1.21808 + 12.1858i −0.0522246 + 0.522463i
\(545\) 5.52026 18.8003i 0.236462 0.805316i
\(546\) 0.588264 1.42907i 0.0251754 0.0611583i
\(547\) 2.96983 31.1015i 0.126981 1.32980i −0.677367 0.735646i \(-0.736879\pi\)
0.804348 0.594159i \(-0.202515\pi\)
\(548\) 29.2613 0.226747i 1.24998 0.00968616i
\(549\) 8.99645 20.8154i 0.383959 0.888378i
\(550\) 3.83895 4.25600i 0.163693 0.181476i
\(551\) 56.4953 16.5885i 2.40678 0.706695i
\(552\) 5.30866 + 2.43694i 0.225952 + 0.103723i
\(553\) 0.518407 + 0.267258i 0.0220449 + 0.0113649i
\(554\) −37.6142 8.02997i −1.59808 0.341161i
\(555\) −0.0643305 + 0.755202i −0.00273068 + 0.0320565i
\(556\) −3.74370 + 2.44713i −0.158768 + 0.103781i
\(557\) −6.69693 + 4.76886i −0.283758 + 0.202063i −0.713069 0.701093i \(-0.752696\pi\)
0.429312 + 0.903156i \(0.358756\pi\)
\(558\) −1.55741 0.376970i −0.0659306 0.0159584i
\(559\) −1.24872 3.11914i −0.0528150 0.131926i
\(560\) 8.33737 + 0.665916i 0.352318 + 0.0281401i
\(561\) 4.70629 + 0.175994i 0.198700 + 0.00743049i
\(562\) 1.63061 14.1011i 0.0687830 0.594821i
\(563\) 14.8135 32.4370i 0.624313 1.36706i −0.288027 0.957622i \(-0.592999\pi\)
0.912340 0.409433i \(-0.134274\pi\)
\(564\) −0.0194879 1.08431i −0.000820587 0.0456577i
\(565\) −1.74032 + 3.01433i −0.0732160 + 0.126814i
\(566\) −5.21318 13.8134i −0.219126 0.580620i
\(567\) −3.42397 + 13.7114i −0.143793 + 0.575825i
\(568\) −4.12200 + 3.48477i −0.172955 + 0.146218i
\(569\) −21.6522 5.25277i −0.907708 0.220208i −0.245385 0.969426i \(-0.578914\pi\)
−0.662323 + 0.749218i \(0.730429\pi\)
\(570\) −25.2258 + 7.14183i −1.05659 + 0.299138i
\(571\) 9.02301 22.5384i 0.377601 0.943202i −0.610861 0.791738i \(-0.709177\pi\)
0.988463 0.151465i \(-0.0483990\pi\)
\(572\) −1.00008 0.135888i −0.0418152 0.00568177i
\(573\) 30.2470 + 11.7518i 1.26359 + 0.490938i
\(574\) −18.2070 14.9147i −0.759945 0.622528i
\(575\) 1.25839 3.63589i 0.0524786 0.151627i
\(576\) −1.23568 + 23.9682i −0.0514868 + 0.998674i
\(577\) −0.154498 3.24331i −0.00643183 0.135021i −0.999799 0.0200372i \(-0.993622\pi\)
0.993367 0.114983i \(-0.0366815\pi\)
\(578\) −11.1389 13.3848i −0.463318 0.556735i
\(579\) −9.11910 + 27.2458i −0.378977 + 1.13230i
\(580\) 19.4793 1.07926i 0.808832 0.0448136i
\(581\) 12.5911 1.81033i 0.522369 0.0751053i
\(582\) −10.3440 + 22.0806i −0.428772 + 0.915270i
\(583\) 5.40242 6.86974i 0.223745 0.284515i
\(584\) 2.49236 0.828770i 0.103134 0.0342948i
\(585\) −0.420619 + 1.54896i −0.0173904 + 0.0640415i
\(586\) −7.09853 5.27110i −0.293237 0.217747i
\(587\) −2.96514 + 4.16396i −0.122385 + 0.171865i −0.871223 0.490888i \(-0.836673\pi\)
0.748838 + 0.662753i \(0.230612\pi\)
\(588\) 12.6288 9.33945i 0.520804 0.385152i
\(589\) 2.55385 + 1.64126i 0.105230 + 0.0676270i
\(590\) 7.83580 + 2.88807i 0.322595 + 0.118900i
\(591\) −16.7126 + 26.5993i −0.687466 + 1.09415i
\(592\) −0.965285 0.892250i −0.0396730 0.0366713i
\(593\) −12.0063 15.2673i −0.493040 0.626951i 0.474322 0.880352i \(-0.342693\pi\)
−0.967361 + 0.253401i \(0.918451\pi\)
\(594\) 9.22901 0.0991217i 0.378671 0.00406701i
\(595\) 3.42111 2.96441i 0.140252 0.121529i
\(596\) −11.0441 23.6955i −0.452383 0.970605i
\(597\) −23.2050 23.8439i −0.949717 0.975865i
\(598\) −0.653731 + 0.177884i −0.0267330 + 0.00727422i
\(599\) 15.4293 7.95438i 0.630426 0.325007i −0.113231 0.993569i \(-0.536120\pi\)
0.743657 + 0.668561i \(0.233090\pi\)
\(600\) 15.7917 0.721315i 0.644694 0.0294475i
\(601\) −5.24221 21.6087i −0.213834 0.881437i −0.973049 0.230597i \(-0.925932\pi\)
0.759215 0.650840i \(-0.225583\pi\)
\(602\) −3.00849 + 18.3247i −0.122617 + 0.746860i
\(603\) 17.4113 + 17.3161i 0.709043 + 0.705165i
\(604\) 6.26433 18.5638i 0.254892 0.755349i
\(605\) 12.1934 2.95808i 0.495731 0.120263i
\(606\) −2.83625 7.28882i −0.115215 0.296088i
\(607\) −2.70028 5.23782i −0.109601 0.212596i 0.827656 0.561236i \(-0.189674\pi\)
−0.937257 + 0.348640i \(0.886644\pi\)
\(608\) 17.0858 42.1365i 0.692919 1.70886i
\(609\) −14.2781 + 13.8956i −0.578579 + 0.563076i
\(610\) −11.7573 + 8.02414i −0.476038 + 0.324888i
\(611\) 0.0823709 + 0.0950611i 0.00333237 + 0.00384576i
\(612\) 8.77961 + 9.57307i 0.354895 + 0.386969i
\(613\) 28.0984 22.0969i 1.13489 0.892484i 0.139671 0.990198i \(-0.455395\pi\)
0.995215 + 0.0977140i \(0.0311530\pi\)
\(614\) −3.96619 1.04628i −0.160062 0.0422246i
\(615\) 20.6979 + 13.0047i 0.834620 + 0.524401i
\(616\) 4.34254 + 3.50142i 0.174966 + 0.141076i
\(617\) −5.66757 + 8.81892i −0.228168 + 0.355036i −0.936395 0.350949i \(-0.885859\pi\)
0.708227 + 0.705985i \(0.249495\pi\)
\(618\) 15.0849 15.5163i 0.606804 0.624157i
\(619\) 27.4318 + 19.5341i 1.10258 + 0.785140i 0.978318 0.207110i \(-0.0664056\pi\)
0.124258 + 0.992250i \(0.460345\pi\)
\(620\) 0.699741 + 0.722572i 0.0281023 + 0.0290192i
\(621\) 5.67850 2.47795i 0.227870 0.0994366i
\(622\) −26.8537 + 20.2653i −1.07674 + 0.812563i
\(623\) 3.75580 + 2.95359i 0.150473 + 0.118333i
\(624\) −1.67245 2.22521i −0.0669515 0.0890797i
\(625\) −0.220102 1.53085i −0.00880410 0.0612338i
\(626\) 4.71558 + 21.2799i 0.188473 + 0.850516i
\(627\) −16.5815 5.54979i −0.662203 0.221637i
\(628\) −16.2597 + 9.55629i −0.648833 + 0.381338i
\(629\) −0.710631 + 0.0338515i −0.0283347 + 0.00134975i
\(630\) 6.41728 6.12521i 0.255670 0.244034i
\(631\) 14.9631 + 5.17877i 0.595670 + 0.206163i 0.608234 0.793758i \(-0.291878\pi\)
−0.0125641 + 0.999921i \(0.503999\pi\)
\(632\) 0.890635 0.557171i 0.0354276 0.0221631i
\(633\) −6.18424 + 15.9171i −0.245802 + 0.632649i
\(634\) 24.0149 0.664767i 0.953753 0.0264013i
\(635\) −16.3449 6.54352i −0.648629 0.259672i
\(636\) 23.9502 2.72208i 0.949686 0.107938i
\(637\) −0.429502 + 1.77043i −0.0170175 + 0.0701471i
\(638\) 11.1365 + 6.72903i 0.440899 + 0.266405i
\(639\) −0.155453 + 5.72295i −0.00614961 + 0.226396i
\(640\) 8.69797 12.3009i 0.343818 0.486234i
\(641\) −3.03653 1.75314i −0.119936 0.0692449i 0.438832 0.898569i \(-0.355392\pi\)
−0.558768 + 0.829324i \(0.688726\pi\)
\(642\) 36.6750 6.70009i 1.44745 0.264432i
\(643\) −13.1414 6.00147i −0.518246 0.236675i 0.139081 0.990281i \(-0.455585\pi\)
−0.657326 + 0.753606i \(0.728313\pi\)
\(644\) 3.60100 + 1.02711i 0.141899 + 0.0404737i
\(645\) 0.720734 19.2733i 0.0283789 0.758884i
\(646\) −9.77486 22.5842i −0.384587 0.888565i
\(647\) −18.8067 + 7.52906i −0.739367 + 0.295998i −0.710608 0.703589i \(-0.751580\pi\)
−0.0287592 + 0.999586i \(0.509156\pi\)
\(648\) 18.0882 + 17.9114i 0.710571 + 0.703626i
\(649\) 3.23077 + 4.53699i 0.126819 + 0.178092i
\(650\) −1.35192 + 1.23858i −0.0530267 + 0.0485810i
\(651\) −1.02352 0.0871867i −0.0401149 0.00341712i
\(652\) 14.6666 + 5.74016i 0.574388 + 0.224802i
\(653\) 9.67162 18.7603i 0.378480 0.734148i −0.620257 0.784399i \(-0.712972\pi\)
0.998737 + 0.0502505i \(0.0160020\pi\)
\(654\) 35.8450 + 3.77413i 1.40165 + 0.147580i
\(655\) −2.98461 10.1646i −0.116618 0.397165i
\(656\) −39.8425 + 14.4848i −1.55559 + 0.565538i
\(657\) 1.10525 2.55724i 0.0431197 0.0997674i
\(658\) −0.117944 0.685143i −0.00459793 0.0267097i
\(659\) 4.75584 + 0.454128i 0.185261 + 0.0176903i 0.187274 0.982308i \(-0.440035\pi\)
−0.00201302 + 0.999998i \(0.500641\pi\)
\(660\) −4.92939 3.04417i −0.191876 0.118494i
\(661\) −3.15566 0.926587i −0.122741 0.0360400i 0.219785 0.975548i \(-0.429464\pi\)
−0.342526 + 0.939508i \(0.611283\pi\)
\(662\) 12.6730 + 20.6113i 0.492551 + 0.801081i
\(663\) −1.49336 0.199154i −0.0579972 0.00773451i
\(664\) 8.77421 21.1663i 0.340505 0.821410i
\(665\) −15.2881 + 6.98184i −0.592847 + 0.270744i
\(666\) −1.38785 + 0.133249i −0.0537779 + 0.00516328i
\(667\) 8.64554 + 1.24304i 0.334757 + 0.0481307i
\(668\) 1.27651 14.5597i 0.0493897 0.563330i
\(669\) −11.9325 14.8583i −0.461337 0.574455i
\(670\) −3.42662 15.0287i −0.132382 0.580611i
\(671\) −9.49367 −0.366499
\(672\) 1.55120 + 15.3071i 0.0598387 + 0.590483i
\(673\) −3.68981 + 25.6632i −0.142232 + 0.989242i 0.786262 + 0.617894i \(0.212014\pi\)
−0.928493 + 0.371349i \(0.878895\pi\)
\(674\) 2.03303 + 6.27592i 0.0783093 + 0.241739i
\(675\) 10.5864 13.0024i 0.407472 0.500464i
\(676\) −24.9995 5.86007i −0.961519 0.225387i
\(677\) −18.8629 19.7828i −0.724959 0.760315i 0.253371 0.967369i \(-0.418461\pi\)
−0.978329 + 0.207055i \(0.933612\pi\)
\(678\) −6.02992 2.15272i −0.231578 0.0826747i
\(679\) −4.40383 + 14.9981i −0.169004 + 0.575573i
\(680\) −1.44551 8.02462i −0.0554328 0.307730i
\(681\) −2.44501 + 1.60686i −0.0936928 + 0.0615750i
\(682\) 0.113810 + 0.661131i 0.00435802 + 0.0253160i
\(683\) −33.7153 6.49810i −1.29008 0.248643i −0.502352 0.864663i \(-0.667532\pi\)
−0.787730 + 0.616021i \(0.788744\pi\)
\(684\) −21.2628 43.2865i −0.813004 1.65510i
\(685\) −18.6936 + 5.48894i −0.714247 + 0.209722i
\(686\) 18.0416 18.1819i 0.688831 0.694190i
\(687\) 25.3438 5.15383i 0.966925 0.196631i
\(688\) 25.6155 + 21.5100i 0.976580 + 0.820062i
\(689\) −1.92928 + 2.02337i −0.0734999 + 0.0770844i
\(690\) −3.84400 0.590810i −0.146339 0.0224918i
\(691\) −3.27757 + 2.33395i −0.124685 + 0.0887877i −0.640698 0.767793i \(-0.721355\pi\)
0.516013 + 0.856581i \(0.327416\pi\)
\(692\) 47.1591 + 8.71071i 1.79272 + 0.331132i
\(693\) 5.83804 0.961577i 0.221769 0.0365273i
\(694\) 2.13278 + 4.92767i 0.0809593 + 0.187052i
\(695\) 1.95007 2.25050i 0.0739702 0.0853662i
\(696\) 8.39252 + 34.8920i 0.318117 + 1.32258i
\(697\) −9.53155 + 20.8712i −0.361033 + 0.790552i
\(698\) 18.4582 + 9.98631i 0.698654 + 0.377988i
\(699\) −2.31021 + 0.356297i −0.0873802 + 0.0134764i
\(700\) 9.93571 1.99492i 0.375535 0.0754010i
\(701\) 1.94582 + 10.0959i 0.0734928 + 0.381317i 0.999987 + 0.00500886i \(0.00159438\pi\)
−0.926495 + 0.376308i \(0.877194\pi\)
\(702\) −2.94197 0.249071i −0.111037 0.00940059i
\(703\) 2.56695 + 0.622735i 0.0968143 + 0.0234869i
\(704\) 9.41627 3.50615i 0.354889 0.132143i
\(705\) 0.210497 + 0.690688i 0.00792776 + 0.0260128i
\(706\) 17.4047 0.481787i 0.655033 0.0181323i
\(707\) −2.50693 4.34214i −0.0942830 0.163303i
\(708\) −2.63572 + 15.1340i −0.0990564 + 0.568772i
\(709\) −14.2973 + 41.3093i −0.536946 + 1.55140i 0.271261 + 0.962506i \(0.412559\pi\)
−0.808207 + 0.588898i \(0.799562\pi\)
\(710\) 2.00278 2.98395i 0.0751631 0.111986i
\(711\) 0.188469 1.09823i 0.00706814 0.0411868i
\(712\) 8.02824 3.10114i 0.300871 0.116220i
\(713\) 0.243468 + 0.378844i 0.00911796 + 0.0141878i
\(714\) 6.49522 + 5.21069i 0.243078 + 0.195005i
\(715\) 0.665131 0.0956314i 0.0248745 0.00357641i
\(716\) 8.54908 + 28.3023i 0.319494 + 1.05771i
\(717\) −30.3733 + 0.310480i −1.13431 + 0.0115951i
\(718\) 31.9599 24.1187i 1.19273 0.900102i
\(719\) 0.423487 8.89009i 0.0157934 0.331544i −0.977119 0.212694i \(-0.931776\pi\)
0.992912 0.118850i \(-0.0379208\pi\)
\(720\) −3.58596 15.5717i −0.133641 0.580322i
\(721\) 8.04705 11.3005i 0.299688 0.420853i
\(722\) 7.90511 + 64.0109i 0.294198 + 2.38224i
\(723\) −16.3705 + 1.73222i −0.608824 + 0.0644220i
\(724\) 34.5725 + 19.6049i 1.28488 + 0.728609i
\(725\) 22.3378 7.73120i 0.829607 0.287130i
\(726\) 9.38375 + 21.0867i 0.348264 + 0.782600i
\(727\) −18.0993 23.0151i −0.671266 0.853584i 0.324464 0.945898i \(-0.394816\pi\)
−0.995730 + 0.0923141i \(0.970574\pi\)
\(728\) −1.27640 1.24707i −0.0473065 0.0462194i
\(729\) 26.9492 1.65489i 0.998120 0.0612922i
\(730\) −1.44442 + 0.985794i −0.0534604 + 0.0364859i
\(731\) 18.0215 1.72084i 0.666549 0.0636477i
\(732\) −18.4069 18.6227i −0.680338 0.688317i
\(733\) −15.9478 + 8.22164i −0.589044 + 0.303673i −0.726861 0.686784i \(-0.759022\pi\)
0.137817 + 0.990458i \(0.455991\pi\)
\(734\) −14.6132 + 46.3324i −0.539384 + 1.71016i
\(735\) −6.38023 + 8.28604i −0.235338 + 0.305635i
\(736\) 4.90210 4.63287i 0.180694 0.170770i
\(737\) 3.76266 9.56735i 0.138599 0.352418i
\(738\) −16.6903 + 41.7531i −0.614380 + 1.53695i
\(739\) 1.78939 0.434102i 0.0658238 0.0159687i −0.202712 0.979238i \(-0.564975\pi\)
0.268536 + 0.963270i \(0.413460\pi\)
\(740\) 0.780984 + 0.394996i 0.0287096 + 0.0145203i
\(741\) 5.11159 + 2.27153i 0.187779 + 0.0834468i
\(742\) 14.9102 4.05717i 0.547372 0.148943i
\(743\) −31.9976 + 3.05540i −1.17388 + 0.112092i −0.663715 0.747985i \(-0.731021\pi\)
−0.510164 + 0.860077i \(0.670415\pi\)
\(744\) −1.07621 + 1.50509i −0.0394558 + 0.0551793i
\(745\) 11.3985 + 13.1545i 0.417608 + 0.481945i
\(746\) −9.59414 + 19.9466i −0.351266 + 0.730298i
\(747\) −10.5455 21.8955i −0.385840 0.801115i
\(748\) 2.22069 4.96408i 0.0811966 0.181505i
\(749\) 22.5855 7.81693i 0.825257 0.285624i
\(750\) −25.4420 + 8.53002i −0.929010 + 0.311472i
\(751\) −26.4194 + 41.1093i −0.964056 + 1.50010i −0.101067 + 0.994880i \(0.532225\pi\)
−0.862990 + 0.505221i \(0.831411\pi\)
\(752\) −1.16963 0.447344i −0.0426519 0.0163130i
\(753\) 0.377917 + 6.52862i 0.0137721 + 0.237916i
\(754\) −3.34178 2.48148i −0.121701 0.0903703i
\(755\) −0.620684 + 13.0298i −0.0225890 + 0.474202i
\(756\) 13.2054 + 9.58751i 0.480274 + 0.348694i
\(757\) 8.90886 + 7.00600i 0.323798 + 0.254638i 0.766804 0.641881i \(-0.221846\pi\)
−0.443006 + 0.896518i \(0.646088\pi\)
\(758\) −20.9133 42.6307i −0.759604 1.54842i
\(759\) −1.89546 1.77068i −0.0688009 0.0642718i
\(760\) −3.24438 + 30.0988i −0.117686 + 1.09180i
\(761\) 5.60040 + 8.71440i 0.203014 + 0.315897i 0.927800 0.373078i \(-0.121698\pi\)
−0.724786 + 0.688974i \(0.758061\pi\)
\(762\) 6.43747 31.7402i 0.233205 1.14983i
\(763\) 23.0797 1.09942i 0.835542 0.0398018i
\(764\) 25.6462 27.3177i 0.927846 0.988319i
\(765\) −7.36955 4.52597i −0.266447 0.163637i
\(766\) 32.4240 + 26.5609i 1.17153 + 0.959685i
\(767\) −0.890871 1.54303i −0.0321675 0.0557157i
\(768\) 25.1345 + 11.6730i 0.906962 + 0.421212i
\(769\) 18.7902 + 7.52247i 0.677593 + 0.271267i 0.684826 0.728706i \(-0.259878\pi\)
−0.00723306 + 0.999974i \(0.502302\pi\)
\(770\) −3.41982 1.44880i −0.123242 0.0522111i
\(771\) −23.6805 + 11.1084i −0.852832 + 0.400061i
\(772\) 25.2405 + 21.5308i 0.908424 + 0.774911i
\(773\) −4.65094 24.1314i −0.167283 0.867945i −0.964466 0.264208i \(-0.914890\pi\)
0.797183 0.603738i \(-0.206323\pi\)
\(774\) 35.1143 5.06724i 1.26216 0.182138i
\(775\) 1.05545 + 0.609365i 0.0379129 + 0.0218890i
\(776\) 19.1800 + 20.6122i 0.688521 + 0.739934i
\(777\) −0.866391 + 0.219585i −0.0310816 + 0.00787757i
\(778\) −5.53278 + 47.8463i −0.198360 + 1.71537i
\(779\) 55.7865 64.3811i 1.99876 2.30669i
\(780\) 1.47719 + 1.11930i 0.0528917 + 0.0400775i
\(781\) 2.22517 0.890822i 0.0796227 0.0318761i
\(782\) 0.0727339 3.64981i 0.00260096 0.130517i
\(783\) 33.5325 + 18.0124i 1.19835 + 0.643709i
\(784\) −4.54859 17.5573i −0.162450 0.627048i
\(785\) 8.66535 9.08796i 0.309280 0.324363i
\(786\) 17.4068 8.76108i 0.620880 0.312497i
\(787\) −23.4750 + 45.5351i −0.836792 + 1.62315i −0.0559407 + 0.998434i \(0.517816\pi\)
−0.780852 + 0.624717i \(0.785215\pi\)
\(788\) 21.2691 + 29.3837i 0.757681 + 1.04675i
\(789\) −21.0050 + 30.1449i −0.747799 + 1.07319i
\(790\) −0.468492 + 0.519388i −0.0166682 + 0.0184790i
\(791\) −4.03033 0.776781i −0.143302 0.0276192i
\(792\) 3.87901 9.92635i 0.137835 0.352718i
\(793\) 3.02324 + 0.288684i 0.107358 + 0.0102515i
\(794\) −20.5171 37.2306i −0.728124 1.32126i
\(795\) −14.8374 + 6.11669i −0.526228 + 0.216937i
\(796\) −35.5551 + 14.5548i −1.26022 + 0.515880i
\(797\) −20.7456 21.7574i −0.734847 0.770686i 0.245195 0.969474i \(-0.421148\pi\)
−0.980043 + 0.198788i \(0.936299\pi\)
\(798\) −17.6880 25.3566i −0.626149 0.897612i
\(799\) −0.616506 + 0.281549i −0.0218104 + 0.00996048i
\(800\) 6.04652 17.2232i 0.213777 0.608931i
\(801\) 3.21875 8.54214i 0.113729 0.301822i
\(802\) 0.345078 + 4.57562i 0.0121851 + 0.161571i
\(803\) −1.16633 −0.0411589
\(804\) 26.0625 11.1689i 0.919154 0.393897i
\(805\) −2.49317 −0.0878728
\(806\) −0.0161389 0.213996i −0.000568469 0.00753770i
\(807\) 6.55855 3.87650i 0.230872 0.136459i
\(808\) −9.03048 0.109966i −0.317691 0.00386859i
\(809\) 33.0928 15.1130i 1.16348 0.531344i 0.262384 0.964963i \(-0.415491\pi\)
0.901096 + 0.433620i \(0.142764\pi\)
\(810\) −14.8523 8.16477i −0.521856 0.286881i
\(811\) −21.7316 22.7915i −0.763101 0.800317i 0.221495 0.975161i \(-0.428906\pi\)
−0.984596 + 0.174844i \(0.944058\pi\)
\(812\) 8.71564 + 21.2910i 0.305859 + 0.747167i
\(813\) −14.3093 34.7104i −0.501850 1.21735i
\(814\) 0.281724 + 0.511220i 0.00987443 + 0.0179183i
\(815\) −10.4388 0.996785i −0.365656 0.0349159i
\(816\) 14.0431 5.26855i 0.491608 0.184436i
\(817\) −65.9995 12.7204i −2.30903 0.445029i
\(818\) 3.89984 4.32351i 0.136355 0.151168i
\(819\) −1.88835 + 0.128688i −0.0659843 + 0.00449674i
\(820\) 22.8646 16.5503i 0.798466 0.577961i
\(821\) 17.8897 34.7012i 0.624355 1.21108i −0.338476 0.940975i \(-0.609911\pi\)
0.962831 0.270105i \(-0.0870584\pi\)
\(822\) −16.1124 32.0126i −0.561983 1.11657i
\(823\) −24.1071 + 25.2828i −0.840321 + 0.881303i −0.994283 0.106774i \(-0.965948\pi\)
0.153963 + 0.988077i \(0.450796\pi\)
\(824\) −10.1030 22.8548i −0.351953 0.796186i
\(825\) −6.75524 1.90873i −0.235187 0.0664536i
\(826\) −0.196211 + 9.84593i −0.00682705 + 0.342584i
\(827\) 6.86677 2.74904i 0.238781 0.0955935i −0.249186 0.968456i \(-0.580163\pi\)
0.487967 + 0.872862i \(0.337739\pi\)
\(828\) −0.201664 7.15123i −0.00700831 0.248523i
\(829\) −30.2719 + 34.9356i −1.05139 + 1.21336i −0.0750329 + 0.997181i \(0.523906\pi\)
−0.976353 + 0.216183i \(0.930639\pi\)
\(830\) −1.75241 + 15.1544i −0.0608269 + 0.526017i
\(831\) 11.5730 + 45.6621i 0.401462 + 1.58400i
\(832\) −3.10520 + 0.830196i −0.107654 + 0.0287819i
\(833\) −8.50109 4.90810i −0.294545 0.170056i
\(834\) 4.71706 + 2.78477i 0.163338 + 0.0964287i
\(835\) 1.84161 + 9.55518i 0.0637315 + 0.330671i
\(836\) −13.1034 + 15.3611i −0.453192 + 0.531274i
\(837\) 0.430318 + 1.91476i 0.0148740 + 0.0661836i
\(838\) −12.8328 5.43660i −0.443303 0.187804i
\(839\) −43.6784 17.4862i −1.50795 0.603691i −0.537127 0.843501i \(-0.680490\pi\)
−0.970820 + 0.239811i \(0.922915\pi\)
\(840\) −3.78859 9.51732i −0.130719 0.328379i
\(841\) 12.3309 + 21.3578i 0.425205 + 0.736476i
\(842\) −1.58928 1.30190i −0.0547702 0.0448663i
\(843\) −16.3702 + 5.85384i −0.563820 + 0.201617i
\(844\) 14.3756 + 13.4960i 0.494829 + 0.464551i
\(845\) 17.0765 0.813455i 0.587450 0.0279837i
\(846\) −1.18025 + 0.609236i −0.0405779 + 0.0209460i
\(847\) 7.99927 + 12.4471i 0.274858 + 0.427688i
\(848\) 7.42675 26.8242i 0.255036 0.921147i
\(849\) −12.3440 + 13.2139i −0.423645 + 0.453498i
\(850\) −4.35114 8.86960i −0.149243 0.304225i
\(851\) 0.308001 + 0.242214i 0.0105581 + 0.00830300i
\(852\) 6.06171 + 2.63770i 0.207671 + 0.0903660i
\(853\) −0.836479 + 17.5599i −0.0286405 + 0.601238i 0.938236 + 0.345995i \(0.112459\pi\)
−0.966877 + 0.255243i \(0.917845\pi\)
\(854\) −13.4766 10.0072i −0.461159 0.342439i
\(855\) 21.5189 + 23.8319i 0.735932 + 0.815032i
\(856\) 8.66128 42.1692i 0.296036 1.44131i
\(857\) −27.4453 + 42.7058i −0.937515 + 1.45880i −0.0496139 + 0.998768i \(0.515799\pi\)
−0.887901 + 0.460034i \(0.847837\pi\)
\(858\) 0.392932 + 1.17198i 0.0134145 + 0.0400106i
\(859\) −35.1564 + 12.1678i −1.19952 + 0.415158i −0.852514 0.522704i \(-0.824923\pi\)
−0.347007 + 0.937863i \(0.612802\pi\)
\(860\) −20.3289 9.09420i −0.693211 0.310110i
\(861\) −6.50920 + 28.0810i −0.221833 + 0.956999i
\(862\) 17.3391 36.0487i 0.590571 1.22782i
\(863\) −18.4755 21.3219i −0.628915 0.725807i 0.348459 0.937324i \(-0.386705\pi\)
−0.977374 + 0.211517i \(0.932160\pi\)
\(864\) 26.9923 11.6367i 0.918298 0.395890i
\(865\) −31.7851 + 3.03511i −1.08073 + 0.103197i
\(866\) −9.95929 + 2.70998i −0.338430 + 0.0920890i
\(867\) −8.66082 + 19.4893i −0.294137 + 0.661892i
\(868\) −0.535335 + 1.05846i −0.0181705 + 0.0359266i
\(869\) −0.453357 + 0.109983i −0.0153791 + 0.00373092i
\(870\) −11.7455 20.8075i −0.398210 0.705441i
\(871\) −1.48913 + 2.93228i −0.0504574 + 0.0993567i
\(872\) 19.5200 36.7576i 0.661030 1.24477i
\(873\) 29.8572 0.610472i 1.01051 0.0206614i
\(874\) −4.07684 + 12.9259i −0.137901 + 0.437226i
\(875\) −15.2899 + 7.88248i −0.516892 + 0.266476i
\(876\) −2.26135 2.28787i −0.0764039 0.0772999i
\(877\) 36.4443 3.48001i 1.23064 0.117512i 0.540596 0.841282i \(-0.318199\pi\)
0.690041 + 0.723771i \(0.257593\pi\)
\(878\) −28.7155 + 19.5979i −0.969103 + 0.661397i
\(879\) −1.94055 + 10.6534i −0.0654531 + 0.359330i
\(880\) −5.38862 + 3.96449i −0.181650 + 0.133643i
\(881\) 27.6077 + 35.1060i 0.930127 + 1.18275i 0.982899 + 0.184146i \(0.0589518\pi\)
−0.0527723 + 0.998607i \(0.516806\pi\)
\(882\) −17.1032 8.80612i −0.575896 0.296518i
\(883\) 30.9077 10.6973i 1.04013 0.359992i 0.246980 0.969021i \(-0.420562\pi\)
0.793148 + 0.609029i \(0.208441\pi\)
\(884\) −0.858123 + 1.51327i −0.0288618 + 0.0508969i
\(885\) −1.07625 10.1712i −0.0361778 0.341900i
\(886\) 4.64866 + 37.6421i 0.156175 + 1.26461i
\(887\) 23.1530 32.5138i 0.777400 1.09171i −0.215931 0.976409i \(-0.569279\pi\)
0.993331 0.115297i \(-0.0367820\pi\)
\(888\) −0.456584 + 1.54381i −0.0153220 + 0.0518070i
\(889\) 0.987881 20.7382i 0.0331325 0.695536i
\(890\) −4.57388 + 3.45170i −0.153317 + 0.115701i
\(891\) −5.11215 10.0818i −0.171264 0.337753i
\(892\) −21.0646 + 6.36285i −0.705297 + 0.213044i
\(893\) 2.49073 0.358114i 0.0833492 0.0119838i
\(894\) −20.0357 + 24.9748i −0.670094 + 0.835284i
\(895\) −10.6423 16.5598i −0.355734 0.553532i
\(896\) 17.0625 + 4.94851i 0.570018 + 0.165318i
\(897\) 0.549762 + 0.621508i 0.0183560 + 0.0207515i
\(898\) 29.2123 43.5234i 0.974826 1.45240i
\(899\) −0.904903 + 2.61455i −0.0301802 + 0.0872000i
\(900\) −9.35328 16.9518i −0.311776 0.565060i
\(901\) −7.53206 13.0459i −0.250929 0.434622i
\(902\) 18.8180 0.520911i 0.626572 0.0173444i
\(903\) 21.7556 6.63032i 0.723983 0.220643i
\(904\) −4.90917 + 5.52801i −0.163276 + 0.183859i
\(905\) −25.7159 6.23862i −0.854826 0.207379i
\(906\) −23.7833 + 3.18428i −0.790146 + 0.105791i
\(907\) 5.55063 + 28.7994i 0.184305 + 0.956268i 0.949808 + 0.312834i \(0.101278\pi\)
−0.765502 + 0.643433i \(0.777509\pi\)
\(908\) 0.665047 + 3.31227i 0.0220704 + 0.109921i
\(909\) −6.46715 + 7.06631i −0.214502 + 0.234375i
\(910\) 1.04498 + 0.565357i 0.0346407 + 0.0187414i
\(911\) −18.7747 + 41.1108i −0.622032 + 1.36206i 0.292000 + 0.956418i \(0.405679\pi\)
−0.914032 + 0.405642i \(0.867048\pi\)
\(912\) −55.5380 + 4.07933i −1.83905 + 0.135080i
\(913\) −6.66293 + 7.68944i −0.220511 + 0.254483i
\(914\) 5.85056 + 13.5174i 0.193519 + 0.447116i
\(915\) 15.1862 + 8.56202i 0.502042 + 0.283052i
\(916\) 5.42430 29.3667i 0.179224 0.970302i
\(917\) 10.1761 7.24637i 0.336045 0.239296i
\(918\) 5.75372 14.8318i 0.189901 0.489523i
\(919\) −28.9336 + 30.3447i −0.954431 + 1.00098i 0.0455673 + 0.998961i \(0.485490\pi\)
−0.999998 + 0.00201684i \(0.999358\pi\)
\(920\) −2.29258 + 3.86151i −0.0755842 + 0.127310i
\(921\) 1.00112 + 4.92298i 0.0329881 + 0.162218i
\(922\) 21.0133 21.1768i 0.692036 0.697420i
\(923\) −0.735687 + 0.216017i −0.0242154 + 0.00711029i
\(924\) 1.49114 6.66730i 0.0490549 0.219338i
\(925\) 1.04125 + 0.200684i 0.0342360 + 0.00659844i
\(926\) 3.61758 + 21.0147i 0.118881 + 0.690586i
\(927\) −25.2183 8.15482i −0.828278 0.267839i
\(928\) 40.9906 + 6.07892i 1.34558 + 0.199550i
\(929\) 4.76592 16.2312i 0.156365 0.532529i −0.843626 0.536932i \(-0.819583\pi\)
0.999990 + 0.00440250i \(0.00140137\pi\)
\(930\) 0.414198 1.16020i 0.0135821 0.0380444i
\(931\) 25.1502 + 26.3768i 0.824265 + 0.864464i
\(932\) −0.616002 + 2.62791i −0.0201778 + 0.0860800i
\(933\) 36.8139 + 18.5051i 1.20523 + 0.605829i
\(934\) −17.9347 55.3641i −0.586841 1.81157i
\(935\) −0.515285 + 3.58388i −0.0168516 + 0.117206i
\(936\) −1.53710 + 3.04307i −0.0502418 + 0.0994659i
\(937\) −52.7537 −1.72339 −0.861695 0.507427i \(-0.830597\pi\)
−0.861695 + 0.507427i \(0.830597\pi\)
\(938\) 15.4261 9.61497i 0.503679 0.313940i
\(939\) 20.8137 16.7152i 0.679229 0.545479i
\(940\) 0.830568 + 0.0728196i 0.0270901 + 0.00237511i
\(941\) −25.5815 3.67807i −0.833933 0.119902i −0.287895 0.957662i \(-0.592956\pi\)
−0.546038 + 0.837760i \(0.683865\pi\)
\(942\) 19.3098 + 12.6761i 0.629147 + 0.413009i
\(943\) 11.4950 5.24961i 0.374330 0.170951i
\(944\) 15.0693 + 9.35766i 0.490463 + 0.304566i
\(945\) −10.2058 3.72697i −0.331996 0.121238i
\(946\) −7.77971 12.6528i −0.252940 0.411380i
\(947\) 29.9349 + 8.78969i 0.972754 + 0.285626i 0.729230 0.684268i \(-0.239878\pi\)
0.243524 + 0.969895i \(0.421697\pi\)
\(948\) −1.09474 0.676061i −0.0355554 0.0219574i
\(949\) 0.371415 + 0.0354659i 0.0120567 + 0.00115127i
\(950\) 6.22274 + 36.1483i 0.201892 + 1.17280i
\(951\) −13.7492 26.0134i −0.445848 0.843541i
\(952\) 8.38494 4.70586i 0.271757 0.152518i
\(953\) −6.26379 21.3325i −0.202904 0.691027i −0.996576 0.0826815i \(-0.973652\pi\)
0.793672 0.608346i \(-0.208167\pi\)
\(954\) −15.9735 24.8270i −0.517161 0.803803i
\(955\) −11.4316 + 22.1742i −0.369917 + 0.717539i
\(956\) −12.7829 + 32.6615i −0.413430 + 1.05635i
\(957\) 1.35257 15.8784i 0.0437224 0.513276i
\(958\) −2.36934 + 2.17070i −0.0765499 + 0.0701321i
\(959\) −13.3267 18.7147i −0.430341 0.604330i
\(960\) −18.2245 2.88370i −0.588194 0.0930712i
\(961\) 28.6470 11.4685i 0.924096 0.369952i
\(962\) −0.0741692 0.171364i −0.00239131 0.00552498i
\(963\) −27.2407 36.6451i −0.877820 1.18087i
\(964\) −5.21383 + 18.2795i −0.167926 + 0.588742i
\(965\) −20.0926 9.17600i −0.646805 0.295386i
\(966\) −0.824205 4.51153i −0.0265184 0.145156i
\(967\) 30.4292 + 17.5683i 0.978538 + 0.564959i 0.901828 0.432094i \(-0.142225\pi\)
0.0767096 + 0.997053i \(0.475559\pi\)
\(968\) 26.6342 0.943864i 0.856055 0.0303370i
\(969\) −19.5034 + 22.9785i −0.626538 + 0.738177i
\(970\) −16.0446 9.69461i −0.515160 0.311275i
\(971\) 2.44886 10.0943i 0.0785875 0.323942i −0.918925 0.394432i \(-0.870941\pi\)
0.997512 + 0.0704902i \(0.0224564\pi\)
\(972\) 9.86465 29.5751i 0.316409 0.948623i
\(973\) 3.26002 + 1.30512i 0.104511 + 0.0418401i
\(974\) 4.13210 0.114383i 0.132401 0.00366505i
\(975\) 2.09315 + 0.813246i 0.0670344 + 0.0260447i
\(976\) −27.8918 + 11.6709i −0.892794 + 0.373576i
\(977\) −24.8445 8.59876i −0.794845 0.275099i −0.100684 0.994918i \(-0.532103\pi\)
−0.694161 + 0.719820i \(0.744224\pi\)
\(978\) −1.64717 19.2191i −0.0526708 0.614559i
\(979\) −3.81739 + 0.181845i −0.122004 + 0.00581178i
\(980\) 6.11867 + 10.4107i 0.195454 + 0.332558i
\(981\) −15.2877 41.4120i −0.488100 1.32218i
\(982\) 8.44399 + 38.1050i 0.269458 + 1.21598i
\(983\) −2.67790 18.6252i −0.0854118 0.594052i −0.986910 0.161270i \(-0.948441\pi\)
0.901499 0.432782i \(-0.142468\pi\)
\(984\) 37.5073 + 35.9034i 1.19569 + 1.14456i
\(985\) −18.9840 14.9292i −0.604882 0.475684i
\(986\) 17.9022 13.5099i 0.570121 0.430244i
\(987\) −0.688501 + 0.500964i −0.0219152 + 0.0159459i
\(988\) 4.63986 4.49325i 0.147614 0.142949i
\(989\) −8.12188 5.78357i −0.258261 0.183907i
\(990\) −0.670829 + 7.06391i −0.0213203 + 0.224506i
\(991\) 0.740302 1.15193i 0.0235165 0.0365924i −0.829296 0.558809i \(-0.811258\pi\)
0.852813 + 0.522217i \(0.174895\pi\)
\(992\) 1.14712 + 1.80245i 0.0364210 + 0.0572278i
\(993\) 15.7655 25.0918i 0.500301 0.796264i
\(994\) 4.09770 + 1.08098i 0.129971 + 0.0342865i
\(995\) 20.1067 15.8121i 0.637425 0.501277i
\(996\) −28.0021 + 1.83875i −0.887279 + 0.0582629i
\(997\) 14.6521 + 16.9095i 0.464038 + 0.535529i 0.938744 0.344616i \(-0.111991\pi\)
−0.474706 + 0.880145i \(0.657445\pi\)
\(998\) −13.4094 + 9.15168i −0.424467 + 0.289692i
\(999\) 0.898726 + 1.45193i 0.0284344 + 0.0459370i
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 804.2.bd.a.23.3 2640
3.2 odd 2 inner 804.2.bd.a.23.130 yes 2640
4.3 odd 2 inner 804.2.bd.a.23.17 yes 2640
12.11 even 2 inner 804.2.bd.a.23.116 yes 2640
67.35 even 33 inner 804.2.bd.a.35.116 yes 2640
201.35 odd 66 inner 804.2.bd.a.35.17 yes 2640
268.35 odd 66 inner 804.2.bd.a.35.130 yes 2640
804.35 even 66 inner 804.2.bd.a.35.3 yes 2640
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
804.2.bd.a.23.3 2640 1.1 even 1 trivial
804.2.bd.a.23.17 yes 2640 4.3 odd 2 inner
804.2.bd.a.23.116 yes 2640 12.11 even 2 inner
804.2.bd.a.23.130 yes 2640 3.2 odd 2 inner
804.2.bd.a.35.3 yes 2640 804.35 even 66 inner
804.2.bd.a.35.17 yes 2640 201.35 odd 66 inner
804.2.bd.a.35.116 yes 2640 67.35 even 33 inner
804.2.bd.a.35.130 yes 2640 268.35 odd 66 inner