Properties

Label 210.2.t.e.89.3
Level $210$
Weight $2$
Character 210.89
Analytic conductor $1.677$
Analytic rank $0$
Dimension $8$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,2,Mod(59,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.59");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.t (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.3317760000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.3
Root \(1.72286 + 0.178197i\) of defining polynomial
Character \(\chi\) \(=\) 210.89
Dual form 210.2.t.e.59.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.01575 - 1.40294i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.20711 - 0.358719i) q^{5} +(0.707107 + 1.58114i) q^{6} +(-1.41421 + 2.23607i) q^{7} +1.00000 q^{8} +(-0.936492 - 2.85008i) q^{9} +(-0.792893 + 2.09077i) q^{10} +(4.05781 - 2.34278i) q^{11} +(-1.72286 - 0.178197i) q^{12} -1.04456 q^{13} +(-1.22938 - 2.34278i) q^{14} +(1.73861 - 3.46081i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.73861 - 1.58114i) q^{17} +(2.93649 + 0.614017i) q^{18} +(-1.23861 - 0.715113i) q^{19} +(-1.41421 - 1.73205i) q^{20} +(1.70058 + 4.25535i) q^{21} +4.68556i q^{22} +(-2.23861 + 3.87739i) q^{23} +(1.01575 - 1.40294i) q^{24} +(4.74264 - 1.58346i) q^{25} +(0.522278 - 0.904612i) q^{26} +(-4.94975 - 1.58114i) q^{27} +(2.64360 + 0.106711i) q^{28} +6.92163i q^{29} +(2.12785 + 3.23609i) q^{30} +(-5.73861 + 3.31319i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.834952 - 8.07256i) q^{33} +3.16228i q^{34} +(-2.31920 + 5.44255i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(-2.30615 - 1.33146i) q^{37} +(1.23861 - 0.715113i) q^{38} +(-1.06101 + 1.46545i) q^{39} +(2.20711 - 0.358719i) q^{40} +1.04456 q^{41} +(-4.53553 - 0.654929i) q^{42} +6.92163i q^{43} +(-4.05781 - 2.34278i) q^{44} +(-3.08932 - 5.95450i) q^{45} +(-2.23861 - 3.87739i) q^{46} +(-9.71584 - 5.60944i) q^{47} +(0.707107 + 1.58114i) q^{48} +(-3.00000 - 6.32456i) q^{49} +(-1.00000 + 4.89898i) q^{50} +(0.563508 - 5.44816i) q^{51} +(0.522278 + 0.904612i) q^{52} +(-2.50000 - 4.33013i) q^{53} +(3.84418 - 3.49604i) q^{54} +(8.11562 - 6.62638i) q^{55} +(-1.41421 + 2.23607i) q^{56} +(-2.26139 + 1.01132i) q^{57} +(-5.99430 - 3.46081i) q^{58} +(5.28720 + 9.15769i) q^{59} +(-3.86646 + 0.224724i) q^{60} +(3.00000 + 1.73205i) q^{61} -6.62638i q^{62} +(7.69738 + 1.93657i) q^{63} +1.00000 q^{64} +(-2.30545 + 0.374703i) q^{65} +(6.57357 + 4.75937i) q^{66} +(-12.3583 + 7.13505i) q^{67} +(-2.73861 - 1.58114i) q^{68} +(3.16588 + 7.07912i) q^{69} +(-3.55378 - 4.72976i) q^{70} -6.92163i q^{71} +(-0.936492 - 2.85008i) q^{72} +(-1.75166 - 3.03397i) q^{73} +(2.30615 - 1.33146i) q^{74} +(2.59584 - 8.26206i) q^{75} +1.43023i q^{76} +(-0.500000 + 12.3867i) q^{77} +(-0.738613 - 1.65159i) q^{78} +(-5.73861 + 9.93957i) q^{79} +(-0.792893 + 2.09077i) q^{80} +(-7.24597 + 5.33816i) q^{81} +(-0.522278 + 0.904612i) q^{82} +4.06775i q^{83} +(2.83495 - 3.60042i) q^{84} +(5.47723 - 4.47214i) q^{85} +(-5.99430 - 3.46081i) q^{86} +(9.71064 + 7.03066i) q^{87} +(4.05781 - 2.34278i) q^{88} +(2.45877 - 4.25871i) q^{89} +(6.70141 + 0.301824i) q^{90} +(1.47723 - 2.33570i) q^{91} +4.47723 q^{92} +(-1.18080 + 11.4163i) q^{93} +(9.71584 - 5.60944i) q^{94} +(-2.99028 - 1.13402i) q^{95} +(-1.72286 - 0.178197i) q^{96} +11.9886 q^{97} +(6.97723 + 0.564201i) q^{98} +(-10.4772 - 9.37112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} + 12 q^{5} + 8 q^{8} + 8 q^{9} - 12 q^{10} - 8 q^{15} - 4 q^{16} + 8 q^{18} + 12 q^{19} + 4 q^{21} + 4 q^{23} + 4 q^{25} + 4 q^{30} - 24 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{35}+ \cdots - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 1.01575 1.40294i 0.586445 0.809989i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.20711 0.358719i 0.987048 0.160424i
\(6\) 0.707107 + 1.58114i 0.288675 + 0.645497i
\(7\) −1.41421 + 2.23607i −0.534522 + 0.845154i
\(8\) 1.00000 0.353553
\(9\) −0.936492 2.85008i −0.312164 0.950028i
\(10\) −0.792893 + 2.09077i −0.250735 + 0.661160i
\(11\) 4.05781 2.34278i 1.22348 0.706374i 0.257819 0.966193i \(-0.416996\pi\)
0.965657 + 0.259819i \(0.0836628\pi\)
\(12\) −1.72286 0.178197i −0.497347 0.0514410i
\(13\) −1.04456 −0.289708 −0.144854 0.989453i \(-0.546271\pi\)
−0.144854 + 0.989453i \(0.546271\pi\)
\(14\) −1.22938 2.34278i −0.328567 0.626134i
\(15\) 1.73861 3.46081i 0.448908 0.893578i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.73861 1.58114i 0.664211 0.383482i −0.129668 0.991557i \(-0.541391\pi\)
0.793880 + 0.608075i \(0.208058\pi\)
\(18\) 2.93649 + 0.614017i 0.692138 + 0.144725i
\(19\) −1.23861 0.715113i −0.284157 0.164058i 0.351147 0.936320i \(-0.385792\pi\)
−0.635304 + 0.772262i \(0.719125\pi\)
\(20\) −1.41421 1.73205i −0.316228 0.387298i
\(21\) 1.70058 + 4.25535i 0.371097 + 0.928594i
\(22\) 4.68556i 0.998964i
\(23\) −2.23861 + 3.87739i −0.466783 + 0.808492i −0.999280 0.0379400i \(-0.987920\pi\)
0.532497 + 0.846432i \(0.321254\pi\)
\(24\) 1.01575 1.40294i 0.207340 0.286374i
\(25\) 4.74264 1.58346i 0.948528 0.316693i
\(26\) 0.522278 0.904612i 0.102427 0.177409i
\(27\) −4.94975 1.58114i −0.952579 0.304290i
\(28\) 2.64360 + 0.106711i 0.499593 + 0.0201665i
\(29\) 6.92163i 1.28531i 0.766154 + 0.642657i \(0.222168\pi\)
−0.766154 + 0.642657i \(0.777832\pi\)
\(30\) 2.12785 + 3.23609i 0.388490 + 0.590826i
\(31\) −5.73861 + 3.31319i −1.03069 + 0.595066i −0.917181 0.398471i \(-0.869541\pi\)
−0.113504 + 0.993537i \(0.536208\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0.834952 8.07256i 0.145347 1.40525i
\(34\) 3.16228i 0.542326i
\(35\) −2.31920 + 5.44255i −0.392016 + 0.919958i
\(36\) −2.00000 + 2.23607i −0.333333 + 0.372678i
\(37\) −2.30615 1.33146i −0.379129 0.218890i 0.298310 0.954469i \(-0.403577\pi\)
−0.677439 + 0.735579i \(0.736910\pi\)
\(38\) 1.23861 0.715113i 0.200930 0.116007i
\(39\) −1.06101 + 1.46545i −0.169898 + 0.234660i
\(40\) 2.20711 0.358719i 0.348974 0.0567185i
\(41\) 1.04456 0.163132 0.0815661 0.996668i \(-0.474008\pi\)
0.0815661 + 0.996668i \(0.474008\pi\)
\(42\) −4.53553 0.654929i −0.699848 0.101058i
\(43\) 6.92163i 1.05554i 0.849388 + 0.527769i \(0.176971\pi\)
−0.849388 + 0.527769i \(0.823029\pi\)
\(44\) −4.05781 2.34278i −0.611738 0.353187i
\(45\) −3.08932 5.95450i −0.460528 0.887645i
\(46\) −2.23861 3.87739i −0.330065 0.571690i
\(47\) −9.71584 5.60944i −1.41720 0.818221i −0.421149 0.906992i \(-0.638373\pi\)
−0.996052 + 0.0887705i \(0.971706\pi\)
\(48\) 0.707107 + 1.58114i 0.102062 + 0.228218i
\(49\) −3.00000 6.32456i −0.428571 0.903508i
\(50\) −1.00000 + 4.89898i −0.141421 + 0.692820i
\(51\) 0.563508 5.44816i 0.0789069 0.762895i
\(52\) 0.522278 + 0.904612i 0.0724269 + 0.125447i
\(53\) −2.50000 4.33013i −0.343401 0.594789i 0.641661 0.766989i \(-0.278246\pi\)
−0.985062 + 0.172200i \(0.944912\pi\)
\(54\) 3.84418 3.49604i 0.523127 0.475750i
\(55\) 8.11562 6.62638i 1.09431 0.893501i
\(56\) −1.41421 + 2.23607i −0.188982 + 0.298807i
\(57\) −2.26139 + 1.01132i −0.299528 + 0.133953i
\(58\) −5.99430 3.46081i −0.787091 0.454427i
\(59\) 5.28720 + 9.15769i 0.688334 + 1.19223i 0.972376 + 0.233418i \(0.0749911\pi\)
−0.284042 + 0.958812i \(0.591676\pi\)
\(60\) −3.86646 + 0.224724i −0.499158 + 0.0290117i
\(61\) 3.00000 + 1.73205i 0.384111 + 0.221766i 0.679605 0.733578i \(-0.262151\pi\)
−0.295495 + 0.955344i \(0.595484\pi\)
\(62\) 6.62638i 0.841551i
\(63\) 7.69738 + 1.93657i 0.969779 + 0.243985i
\(64\) 1.00000 0.125000
\(65\) −2.30545 + 0.374703i −0.285956 + 0.0464761i
\(66\) 6.57357 + 4.75937i 0.809150 + 0.585838i
\(67\) −12.3583 + 7.13505i −1.50980 + 0.871685i −0.509868 + 0.860253i \(0.670306\pi\)
−0.999935 + 0.0114319i \(0.996361\pi\)
\(68\) −2.73861 1.58114i −0.332106 0.191741i
\(69\) 3.16588 + 7.07912i 0.381127 + 0.852225i
\(70\) −3.55378 4.72976i −0.424758 0.565314i
\(71\) 6.92163i 0.821446i −0.911760 0.410723i \(-0.865276\pi\)
0.911760 0.410723i \(-0.134724\pi\)
\(72\) −0.936492 2.85008i −0.110367 0.335886i
\(73\) −1.75166 3.03397i −0.205017 0.355099i 0.745121 0.666929i \(-0.232392\pi\)
−0.950138 + 0.311830i \(0.899058\pi\)
\(74\) 2.30615 1.33146i 0.268084 0.154779i
\(75\) 2.59584 8.26206i 0.299742 0.954020i
\(76\) 1.43023i 0.164058i
\(77\) −0.500000 + 12.3867i −0.0569803 + 1.41160i
\(78\) −0.738613 1.65159i −0.0836314 0.187006i
\(79\) −5.73861 + 9.93957i −0.645644 + 1.11829i 0.338508 + 0.940964i \(0.390078\pi\)
−0.984152 + 0.177325i \(0.943256\pi\)
\(80\) −0.792893 + 2.09077i −0.0886482 + 0.233755i
\(81\) −7.24597 + 5.33816i −0.805107 + 0.593129i
\(82\) −0.522278 + 0.904612i −0.0576760 + 0.0998977i
\(83\) 4.06775i 0.446494i 0.974762 + 0.223247i \(0.0716656\pi\)
−0.974762 + 0.223247i \(0.928334\pi\)
\(84\) 2.83495 3.60042i 0.309319 0.392838i
\(85\) 5.47723 4.47214i 0.594089 0.485071i
\(86\) −5.99430 3.46081i −0.646382 0.373189i
\(87\) 9.71064 + 7.03066i 1.04109 + 0.753766i
\(88\) 4.05781 2.34278i 0.432564 0.249741i
\(89\) 2.45877 4.25871i 0.260629 0.451423i −0.705780 0.708431i \(-0.749403\pi\)
0.966409 + 0.257008i \(0.0827367\pi\)
\(90\) 6.70141 + 0.301824i 0.706391 + 0.0318150i
\(91\) 1.47723 2.33570i 0.154855 0.244848i
\(92\) 4.47723 0.466783
\(93\) −1.18080 + 11.4163i −0.122443 + 1.18382i
\(94\) 9.71584 5.60944i 1.00211 0.578570i
\(95\) −2.99028 1.13402i −0.306796 0.116348i
\(96\) −1.72286 0.178197i −0.175839 0.0181872i
\(97\) 11.9886 1.21726 0.608629 0.793455i \(-0.291720\pi\)
0.608629 + 0.793455i \(0.291720\pi\)
\(98\) 6.97723 + 0.564201i 0.704806 + 0.0569930i
\(99\) −10.4772 9.37112i −1.05300 0.941833i
\(100\) −3.74264 3.31552i −0.374264 0.331552i
\(101\) −5.65685 9.79796i −0.562878 0.974933i −0.997244 0.0741967i \(-0.976361\pi\)
0.434366 0.900737i \(-0.356973\pi\)
\(102\) 4.43649 + 3.21209i 0.439278 + 0.318045i
\(103\) 2.45877 4.25871i 0.242270 0.419624i −0.719091 0.694916i \(-0.755441\pi\)
0.961360 + 0.275293i \(0.0887748\pi\)
\(104\) −1.04456 −0.102427
\(105\) 5.27984 + 8.78198i 0.515260 + 0.857034i
\(106\) 5.00000 0.485643
\(107\) 2.73861 4.74342i 0.264752 0.458563i −0.702747 0.711440i \(-0.748043\pi\)
0.967499 + 0.252877i \(0.0813767\pi\)
\(108\) 1.10557 + 5.07718i 0.106383 + 0.488552i
\(109\) 10.2158 + 17.6944i 0.978500 + 1.69481i 0.667866 + 0.744282i \(0.267208\pi\)
0.310634 + 0.950529i \(0.399459\pi\)
\(110\) 1.68080 + 10.3415i 0.160258 + 0.986026i
\(111\) −4.21043 + 1.88296i −0.399637 + 0.178723i
\(112\) −1.22938 2.34278i −0.116166 0.221372i
\(113\) 17.4772 1.64412 0.822060 0.569402i \(-0.192825\pi\)
0.822060 + 0.569402i \(0.192825\pi\)
\(114\) 0.254862 2.46408i 0.0238700 0.230782i
\(115\) −3.54996 + 9.36085i −0.331036 + 0.872904i
\(116\) 5.99430 3.46081i 0.556557 0.321328i
\(117\) 0.978218 + 2.97707i 0.0904363 + 0.275231i
\(118\) −10.5744 −0.973452
\(119\) −0.337449 + 8.35979i −0.0309339 + 0.766341i
\(120\) 1.73861 3.46081i 0.158713 0.315928i
\(121\) 5.47723 9.48683i 0.497930 0.862439i
\(122\) −3.00000 + 1.73205i −0.271607 + 0.156813i
\(123\) 1.06101 1.46545i 0.0956682 0.132135i
\(124\) 5.73861 + 3.31319i 0.515343 + 0.297533i
\(125\) 9.89949 5.19615i 0.885438 0.464758i
\(126\) −5.52581 + 5.69784i −0.492278 + 0.507604i
\(127\) 8.73085i 0.774738i −0.921925 0.387369i \(-0.873384\pi\)
0.921925 0.387369i \(-0.126616\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 9.71064 + 7.03066i 0.854974 + 0.619015i
\(130\) 0.828222 2.18393i 0.0726398 0.191543i
\(131\) 6.88624 11.9273i 0.601654 1.04209i −0.390917 0.920426i \(-0.627842\pi\)
0.992571 0.121669i \(-0.0388245\pi\)
\(132\) −7.40852 + 3.31319i −0.644829 + 0.288376i
\(133\) 3.35071 1.75830i 0.290543 0.152464i
\(134\) 14.2701i 1.23275i
\(135\) −11.4918 1.71417i −0.989057 0.147532i
\(136\) 2.73861 1.58114i 0.234834 0.135582i
\(137\) 1.73861 + 3.01137i 0.148540 + 0.257278i 0.930688 0.365814i \(-0.119209\pi\)
−0.782148 + 0.623092i \(0.785876\pi\)
\(138\) −7.71363 0.797828i −0.656628 0.0679156i
\(139\) 20.1810i 1.71173i −0.517202 0.855863i \(-0.673026\pi\)
0.517202 0.855863i \(-0.326974\pi\)
\(140\) 5.87298 0.712788i 0.496358 0.0602416i
\(141\) −17.7386 + 7.93295i −1.49386 + 0.668075i
\(142\) 5.99430 + 3.46081i 0.503031 + 0.290425i
\(143\) −4.23861 + 2.44716i −0.354451 + 0.204642i
\(144\) 2.93649 + 0.614017i 0.244708 + 0.0511681i
\(145\) 2.48292 + 15.2768i 0.206195 + 1.26867i
\(146\) 3.50333 0.289937
\(147\) −11.9202 2.21536i −0.983165 0.182720i
\(148\) 2.66291i 0.218890i
\(149\) 2.12132 + 1.22474i 0.173785 + 0.100335i 0.584370 0.811488i \(-0.301342\pi\)
−0.410584 + 0.911823i \(0.634675\pi\)
\(150\) 5.85723 + 6.37909i 0.478241 + 0.520851i
\(151\) 1.00000 + 1.73205i 0.0813788 + 0.140952i 0.903842 0.427865i \(-0.140734\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) −1.23861 0.715113i −0.100465 0.0580034i
\(153\) −7.07107 6.32456i −0.571662 0.511310i
\(154\) −10.4772 6.62638i −0.844279 0.533969i
\(155\) −11.4772 + 9.37112i −0.921873 + 0.752706i
\(156\) 1.79962 + 0.186137i 0.144085 + 0.0149029i
\(157\) −7.22369 12.5118i −0.576513 0.998550i −0.995875 0.0907311i \(-0.971080\pi\)
0.419362 0.907819i \(-0.362254\pi\)
\(158\) −5.73861 9.93957i −0.456540 0.790750i
\(159\) −8.61430 0.890985i −0.683158 0.0706597i
\(160\) −1.41421 1.73205i −0.111803 0.136931i
\(161\) −5.50423 10.4891i −0.433794 0.826661i
\(162\) −1.00000 8.94427i −0.0785674 0.702728i
\(163\) −12.7279 7.34847i −0.996928 0.575577i −0.0895899 0.995979i \(-0.528556\pi\)
−0.907338 + 0.420402i \(0.861889\pi\)
\(164\) −0.522278 0.904612i −0.0407831 0.0706383i
\(165\) −1.05296 18.1165i −0.0819725 1.41037i
\(166\) −3.52277 2.03387i −0.273420 0.157859i
\(167\) 4.29068i 0.332023i 0.986124 + 0.166011i \(0.0530889\pi\)
−0.986124 + 0.166011i \(0.946911\pi\)
\(168\) 1.70058 + 4.25535i 0.131203 + 0.328308i
\(169\) −11.9089 −0.916069
\(170\) 1.13437 + 6.97948i 0.0870023 + 0.535302i
\(171\) −0.878183 + 4.19985i −0.0671564 + 0.321170i
\(172\) 5.99430 3.46081i 0.457061 0.263885i
\(173\) 0.977226 + 0.564201i 0.0742971 + 0.0428954i 0.536688 0.843781i \(-0.319675\pi\)
−0.462391 + 0.886676i \(0.653008\pi\)
\(174\) −10.9441 + 4.89433i −0.829666 + 0.371038i
\(175\) −3.16637 + 12.8442i −0.239355 + 0.970932i
\(176\) 4.68556i 0.353187i
\(177\) 18.2182 + 1.88433i 1.36936 + 0.141635i
\(178\) 2.45877 + 4.25871i 0.184293 + 0.319204i
\(179\) −16.7857 + 9.69125i −1.25462 + 0.724358i −0.972024 0.234880i \(-0.924530\pi\)
−0.282600 + 0.959238i \(0.591197\pi\)
\(180\) −3.61209 + 5.65268i −0.269229 + 0.421326i
\(181\) 3.16228i 0.235050i −0.993070 0.117525i \(-0.962504\pi\)
0.993070 0.117525i \(-0.0374961\pi\)
\(182\) 1.28416 + 2.44716i 0.0951884 + 0.181396i
\(183\) 5.47723 2.44949i 0.404888 0.181071i
\(184\) −2.23861 + 3.87739i −0.165033 + 0.285845i
\(185\) −5.56754 2.11140i −0.409333 0.155234i
\(186\) −9.29642 6.73076i −0.681647 0.493524i
\(187\) 7.40852 12.8319i 0.541764 0.938364i
\(188\) 11.2189i 0.818221i
\(189\) 10.5355 8.83190i 0.766347 0.642426i
\(190\) 2.47723 2.02265i 0.179717 0.146738i
\(191\) 14.1099 + 8.14637i 1.02096 + 0.589451i 0.914381 0.404854i \(-0.132678\pi\)
0.106577 + 0.994304i \(0.466011\pi\)
\(192\) 1.01575 1.40294i 0.0733057 0.101249i
\(193\) −6.36396 + 3.67423i −0.458088 + 0.264477i −0.711240 0.702949i \(-0.751866\pi\)
0.253152 + 0.967427i \(0.418533\pi\)
\(194\) −5.99430 + 10.3824i −0.430366 + 0.745416i
\(195\) −1.81608 + 3.61501i −0.130052 + 0.258877i
\(196\) −3.97723 + 5.76035i −0.284088 + 0.411454i
\(197\) 9.00000 0.641223 0.320612 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(198\) 13.3542 4.38799i 0.949044 0.311841i
\(199\) 13.4317 7.75478i 0.952146 0.549722i 0.0583993 0.998293i \(-0.481400\pi\)
0.893747 + 0.448571i \(0.148067\pi\)
\(200\) 4.74264 1.58346i 0.335355 0.111968i
\(201\) −2.54289 + 24.5854i −0.179361 + 1.73412i
\(202\) 11.3137 0.796030
\(203\) −15.4772 9.78866i −1.08629 0.687029i
\(204\) −5.00000 + 2.23607i −0.350070 + 0.156556i
\(205\) 2.30545 0.374703i 0.161019 0.0261704i
\(206\) 2.45877 + 4.25871i 0.171311 + 0.296719i
\(207\) 13.1473 + 2.74909i 0.913803 + 0.191075i
\(208\) 0.522278 0.904612i 0.0362135 0.0627236i
\(209\) −6.70141 −0.463546
\(210\) −10.2453 + 0.181486i −0.706996 + 0.0125237i
\(211\) 24.4772 1.68508 0.842541 0.538632i \(-0.181059\pi\)
0.842541 + 0.538632i \(0.181059\pi\)
\(212\) −2.50000 + 4.33013i −0.171701 + 0.297394i
\(213\) −9.71064 7.03066i −0.665362 0.481733i
\(214\) 2.73861 + 4.74342i 0.187208 + 0.324253i
\(215\) 2.48292 + 15.2768i 0.169334 + 1.04187i
\(216\) −4.94975 1.58114i −0.336788 0.107583i
\(217\) 0.707107 17.5175i 0.0480015 1.18916i
\(218\) −20.4317 −1.38381
\(219\) −6.03574 0.624282i −0.407857 0.0421851i
\(220\) −9.79642 3.71515i −0.660475 0.250475i
\(221\) −2.86064 + 1.65159i −0.192427 + 0.111098i
\(222\) 0.474523 4.58782i 0.0318479 0.307915i
\(223\) 21.8881 1.46574 0.732868 0.680371i \(-0.238181\pi\)
0.732868 + 0.680371i \(0.238181\pi\)
\(224\) 2.64360 + 0.106711i 0.176633 + 0.00712992i
\(225\) −8.95445 12.0340i −0.596963 0.802268i
\(226\) −8.73861 + 15.1357i −0.581284 + 1.00681i
\(227\) 9.00000 5.19615i 0.597351 0.344881i −0.170648 0.985332i \(-0.554586\pi\)
0.767999 + 0.640451i \(0.221253\pi\)
\(228\) 2.00653 + 1.45276i 0.132885 + 0.0962112i
\(229\) −11.7386 6.77729i −0.775709 0.447856i 0.0591982 0.998246i \(-0.481146\pi\)
−0.834908 + 0.550390i \(0.814479\pi\)
\(230\) −6.33175 7.75478i −0.417503 0.511335i
\(231\) 16.8700 + 13.2833i 1.10996 + 0.873979i
\(232\) 6.92163i 0.454427i
\(233\) 2.00000 3.46410i 0.131024 0.226941i −0.793047 0.609160i \(-0.791507\pi\)
0.924072 + 0.382219i \(0.124840\pi\)
\(234\) −3.06733 0.641375i −0.200518 0.0419280i
\(235\) −23.4561 8.89538i −1.53011 0.580270i
\(236\) 5.28720 9.15769i 0.344167 0.596115i
\(237\) 8.11562 + 18.1471i 0.527166 + 1.17878i
\(238\) −7.07107 4.47214i −0.458349 0.289886i
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 2.12785 + 3.23609i 0.137352 + 0.208889i
\(241\) −18.4545 + 10.6547i −1.18876 + 0.686328i −0.958024 0.286689i \(-0.907445\pi\)
−0.230732 + 0.973017i \(0.574112\pi\)
\(242\) 5.47723 + 9.48683i 0.352089 + 0.609837i
\(243\) 0.129018 + 15.5879i 0.00827648 + 0.999966i
\(244\) 3.46410i 0.221766i
\(245\) −8.89006 12.8828i −0.567965 0.823053i
\(246\) 0.738613 + 1.65159i 0.0470922 + 0.105301i
\(247\) 1.29380 + 0.746976i 0.0823226 + 0.0475290i
\(248\) −5.73861 + 3.31319i −0.364402 + 0.210388i
\(249\) 5.70682 + 4.13183i 0.361655 + 0.261844i
\(250\) −0.449747 + 11.1713i −0.0284445 + 0.706534i
\(251\) 8.85494 0.558919 0.279459 0.960158i \(-0.409845\pi\)
0.279459 + 0.960158i \(0.409845\pi\)
\(252\) −2.17157 7.63441i −0.136796 0.480923i
\(253\) 20.9783i 1.31889i
\(254\) 7.56114 + 4.36543i 0.474428 + 0.273911i
\(255\) −0.710638 12.2268i −0.0445019 0.765673i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.52277 5.49798i −0.594014 0.342954i 0.172669 0.984980i \(-0.444761\pi\)
−0.766683 + 0.642026i \(0.778094\pi\)
\(258\) −10.9441 + 4.89433i −0.681347 + 0.304708i
\(259\) 6.23861 3.27374i 0.387649 0.203421i
\(260\) 1.47723 + 1.80922i 0.0916136 + 0.112203i
\(261\) 19.7272 6.48204i 1.22108 0.401229i
\(262\) 6.88624 + 11.9273i 0.425433 + 0.736872i
\(263\) 1.00000 + 1.73205i 0.0616626 + 0.106803i 0.895209 0.445647i \(-0.147026\pi\)
−0.833546 + 0.552450i \(0.813693\pi\)
\(264\) 0.834952 8.07256i 0.0513878 0.496832i
\(265\) −7.07107 8.66025i −0.434372 0.531995i
\(266\) −0.152621 + 3.78095i −0.00935778 + 0.231825i
\(267\) −3.47723 7.77531i −0.212803 0.475841i
\(268\) 12.3583 + 7.13505i 0.754901 + 0.435842i
\(269\) −8.79052 15.2256i −0.535968 0.928323i −0.999116 0.0420423i \(-0.986614\pi\)
0.463148 0.886281i \(-0.346720\pi\)
\(270\) 7.23042 9.09511i 0.440029 0.553511i
\(271\) −5.47723 3.16228i −0.332718 0.192095i 0.324329 0.945944i \(-0.394861\pi\)
−0.657047 + 0.753850i \(0.728195\pi\)
\(272\) 3.16228i 0.191741i
\(273\) −1.77635 4.44495i −0.107510 0.269021i
\(274\) −3.47723 −0.210067
\(275\) 15.5350 17.5364i 0.936798 1.05748i
\(276\) 4.54776 6.28129i 0.273743 0.378089i
\(277\) 8.48528 4.89898i 0.509831 0.294351i −0.222933 0.974834i \(-0.571563\pi\)
0.732764 + 0.680483i \(0.238230\pi\)
\(278\) 17.4772 + 10.0905i 1.04821 + 0.605187i
\(279\) 14.8170 + 13.2528i 0.887073 + 0.793422i
\(280\) −2.31920 + 5.44255i −0.138599 + 0.325254i
\(281\) 1.80922i 0.107929i −0.998543 0.0539646i \(-0.982814\pi\)
0.998543 0.0539646i \(-0.0171858\pi\)
\(282\) 1.99917 19.3286i 0.119049 1.15100i
\(283\) −4.61230 7.98873i −0.274173 0.474881i 0.695753 0.718281i \(-0.255071\pi\)
−0.969926 + 0.243400i \(0.921737\pi\)
\(284\) −5.99430 + 3.46081i −0.355696 + 0.205361i
\(285\) −4.62834 + 3.04330i −0.274159 + 0.180270i
\(286\) 4.89433i 0.289408i
\(287\) −1.47723 + 2.33570i −0.0871979 + 0.137872i
\(288\) −2.00000 + 2.23607i −0.117851 + 0.131762i
\(289\) −3.50000 + 6.06218i −0.205882 + 0.356599i
\(290\) −14.4715 5.48811i −0.849797 0.322273i
\(291\) 12.1775 16.8193i 0.713856 0.985966i
\(292\) −1.75166 + 3.03397i −0.102508 + 0.177550i
\(293\) 8.05661i 0.470672i −0.971914 0.235336i \(-0.924381\pi\)
0.971914 0.235336i \(-0.0756190\pi\)
\(294\) 7.87868 9.21555i 0.459494 0.537462i
\(295\) 14.9545 + 18.3154i 0.870682 + 1.06636i
\(296\) −2.30615 1.33146i −0.134042 0.0773893i
\(297\) −23.7894 + 5.18020i −1.38040 + 0.300586i
\(298\) −2.12132 + 1.22474i −0.122885 + 0.0709476i
\(299\) 2.33836 4.05015i 0.135231 0.234226i
\(300\) −8.45307 + 1.88296i −0.488038 + 0.108713i
\(301\) −15.4772 9.78866i −0.892092 0.564209i
\(302\) −2.00000 −0.115087
\(303\) −19.4919 2.01607i −1.11978 0.115820i
\(304\) 1.23861 0.715113i 0.0710393 0.0410146i
\(305\) 7.24264 + 2.74666i 0.414712 + 0.157273i
\(306\) 9.01276 2.96145i 0.515225 0.169295i
\(307\) −11.9886 −0.684226 −0.342113 0.939659i \(-0.611143\pi\)
−0.342113 + 0.939659i \(0.611143\pi\)
\(308\) 10.9772 5.76035i 0.625485 0.328227i
\(309\) −3.47723 7.77531i −0.197812 0.442322i
\(310\) −2.37701 14.6251i −0.135005 0.830651i
\(311\) −8.79052 15.2256i −0.498465 0.863366i 0.501534 0.865138i \(-0.332769\pi\)
−0.999998 + 0.00177176i \(0.999436\pi\)
\(312\) −1.06101 + 1.46545i −0.0600679 + 0.0829649i
\(313\) −11.6190 + 20.1246i −0.656742 + 1.13751i 0.324712 + 0.945813i \(0.394733\pi\)
−0.981454 + 0.191697i \(0.938601\pi\)
\(314\) 14.4474 0.815313
\(315\) 17.6836 + 1.51301i 0.996360 + 0.0852487i
\(316\) 11.4772 0.645644
\(317\) 4.95445 8.58136i 0.278270 0.481977i −0.692685 0.721240i \(-0.743572\pi\)
0.970955 + 0.239263i \(0.0769058\pi\)
\(318\) 5.07877 7.01471i 0.284803 0.393365i
\(319\) 16.2158 + 28.0867i 0.907913 + 1.57255i
\(320\) 2.20711 0.358719i 0.123381 0.0200530i
\(321\) −3.87298 8.66025i −0.216169 0.483368i
\(322\) 11.8360 + 0.477769i 0.659594 + 0.0266250i
\(323\) −4.52277 −0.251654
\(324\) 8.24597 + 3.60611i 0.458109 + 0.200339i
\(325\) −4.95395 + 1.65402i −0.274796 + 0.0917484i
\(326\) 12.7279 7.34847i 0.704934 0.406994i
\(327\) 35.2009 + 3.64086i 1.94662 + 0.201340i
\(328\) 1.04456 0.0576760
\(329\) 26.2834 13.7923i 1.44905 0.760396i
\(330\) 16.2158 + 8.14637i 0.892653 + 0.448443i
\(331\) −10.7158 + 18.5604i −0.588996 + 1.02017i 0.405369 + 0.914153i \(0.367143\pi\)
−0.994364 + 0.106017i \(0.966190\pi\)
\(332\) 3.52277 2.03387i 0.193337 0.111623i
\(333\) −1.63507 + 7.81962i −0.0896014 + 0.428512i
\(334\) −3.71584 2.14534i −0.203322 0.117388i
\(335\) −24.7165 + 20.1810i −1.35041 + 1.10260i
\(336\) −4.53553 0.654929i −0.247434 0.0357293i
\(337\) 17.1464i 0.934025i 0.884251 + 0.467013i \(0.154670\pi\)
−0.884251 + 0.467013i \(0.845330\pi\)
\(338\) 5.95445 10.3134i 0.323879 0.560976i
\(339\) 17.7525 24.5195i 0.964186 1.33172i
\(340\) −6.61160 2.50735i −0.358564 0.135980i
\(341\) −15.5241 + 26.8886i −0.840679 + 1.45610i
\(342\) −3.19808 2.86045i −0.172933 0.154676i
\(343\) 18.3848 + 2.23607i 0.992685 + 0.120736i
\(344\) 6.92163i 0.373189i
\(345\) 9.52684 + 14.4887i 0.512908 + 0.780045i
\(346\) −0.977226 + 0.564201i −0.0525360 + 0.0303317i
\(347\) 8.73861 + 15.1357i 0.469113 + 0.812528i 0.999377 0.0353049i \(-0.0112402\pi\)
−0.530263 + 0.847833i \(0.677907\pi\)
\(348\) 1.23341 11.9250i 0.0661179 0.639247i
\(349\) 11.7436i 0.628623i 0.949320 + 0.314311i \(0.101774\pi\)
−0.949320 + 0.314311i \(0.898226\pi\)
\(350\) −9.54024 9.16427i −0.509947 0.489851i
\(351\) 5.17029 + 1.65159i 0.275970 + 0.0881553i
\(352\) −4.05781 2.34278i −0.216282 0.124871i
\(353\) 0.522774 0.301824i 0.0278245 0.0160645i −0.486023 0.873946i \(-0.661553\pi\)
0.513848 + 0.857881i \(0.328220\pi\)
\(354\) −10.7410 + 14.8353i −0.570876 + 0.788485i
\(355\) −2.48292 15.2768i −0.131780 0.810807i
\(356\) −4.91754 −0.260629
\(357\) 11.3855 + 8.96491i 0.602587 + 0.474473i
\(358\) 19.3825i 1.02440i
\(359\) −9.86729 5.69688i −0.520775 0.300670i 0.216476 0.976288i \(-0.430544\pi\)
−0.737252 + 0.675618i \(0.763877\pi\)
\(360\) −3.08932 5.95450i −0.162821 0.313830i
\(361\) −8.47723 14.6830i −0.446170 0.772789i
\(362\) 2.73861 + 1.58114i 0.143938 + 0.0831028i
\(363\) −7.74597 17.3205i −0.406558 0.909091i
\(364\) −2.76139 0.111466i −0.144736 0.00584238i
\(365\) −4.95445 6.06794i −0.259328 0.317610i
\(366\) −0.617292 + 5.96816i −0.0322664 + 0.311961i
\(367\) −0.184829 0.320133i −0.00964798 0.0167108i 0.861161 0.508332i \(-0.169738\pi\)
−0.870809 + 0.491621i \(0.836404\pi\)
\(368\) −2.23861 3.87739i −0.116696 0.202123i
\(369\) −0.978218 2.97707i −0.0509240 0.154980i
\(370\) 4.61230 3.76593i 0.239782 0.195781i
\(371\) 13.2180 + 0.533554i 0.686244 + 0.0277008i
\(372\) 10.4772 4.68556i 0.543219 0.242935i
\(373\) 20.1042 + 11.6072i 1.04096 + 0.600997i 0.920104 0.391673i \(-0.128104\pi\)
0.120853 + 0.992670i \(0.461437\pi\)
\(374\) 7.40852 + 12.8319i 0.383085 + 0.663523i
\(375\) 2.76554 19.1664i 0.142812 0.989750i
\(376\) −9.71584 5.60944i −0.501056 0.289285i
\(377\) 7.23003i 0.372365i
\(378\) 2.38089 + 13.5400i 0.122460 + 0.696422i
\(379\) −20.4772 −1.05184 −0.525922 0.850533i \(-0.676280\pi\)
−0.525922 + 0.850533i \(0.676280\pi\)
\(380\) 0.513050 + 3.15666i 0.0263189 + 0.161933i
\(381\) −12.2489 8.86839i −0.627529 0.454341i
\(382\) −14.1099 + 8.14637i −0.721927 + 0.416805i
\(383\) 15.7158 + 9.07354i 0.803042 + 0.463636i 0.844534 0.535502i \(-0.179878\pi\)
−0.0414919 + 0.999139i \(0.513211\pi\)
\(384\) 0.707107 + 1.58114i 0.0360844 + 0.0806872i
\(385\) 3.33981 + 27.5182i 0.170212 + 1.40246i
\(386\) 7.34847i 0.374027i
\(387\) 19.7272 6.48204i 1.00279 0.329501i
\(388\) −5.99430 10.3824i −0.304315 0.527088i
\(389\) −6.36396 + 3.67423i −0.322666 + 0.186291i −0.652580 0.757720i \(-0.726313\pi\)
0.329914 + 0.944011i \(0.392980\pi\)
\(390\) −2.22265 3.38028i −0.112548 0.171167i
\(391\) 14.1582i 0.716012i
\(392\) −3.00000 6.32456i −0.151523 0.319438i
\(393\) −9.73861 21.7762i −0.491248 1.09846i
\(394\) −4.50000 + 7.79423i −0.226707 + 0.392668i
\(395\) −9.10021 + 23.9962i −0.457881 + 1.20738i
\(396\) −2.87701 + 13.7591i −0.144575 + 0.691421i
\(397\) −7.44073 + 12.8877i −0.373439 + 0.646816i −0.990092 0.140419i \(-0.955155\pi\)
0.616653 + 0.787235i \(0.288488\pi\)
\(398\) 15.5096i 0.777424i
\(399\) 0.936697 6.48684i 0.0468935 0.324748i
\(400\) −1.00000 + 4.89898i −0.0500000 + 0.244949i
\(401\) 0.827520 + 0.477769i 0.0413244 + 0.0238586i 0.520520 0.853850i \(-0.325738\pi\)
−0.479195 + 0.877708i \(0.659072\pi\)
\(402\) −20.0201 14.4949i −0.998513 0.722939i
\(403\) 5.99430 3.46081i 0.298598 0.172395i
\(404\) −5.65685 + 9.79796i −0.281439 + 0.487467i
\(405\) −14.0777 + 14.3812i −0.699528 + 0.714606i
\(406\) 16.2158 8.50934i 0.804779 0.422312i
\(407\) −12.4772 −0.618473
\(408\) 0.563508 5.44816i 0.0278978 0.269724i
\(409\) 13.4317 7.75478i 0.664154 0.383449i −0.129704 0.991553i \(-0.541403\pi\)
0.793858 + 0.608103i \(0.208069\pi\)
\(410\) −0.828222 + 2.18393i −0.0409029 + 0.107856i
\(411\) 5.99077 + 0.619631i 0.295503 + 0.0305641i
\(412\) −4.91754 −0.242270
\(413\) −27.9545 1.12840i −1.37555 0.0555251i
\(414\) −8.95445 + 10.0114i −0.440087 + 0.492033i
\(415\) 1.45918 + 8.97796i 0.0716284 + 0.440711i
\(416\) 0.522278 + 0.904612i 0.0256068 + 0.0443523i
\(417\) −28.3127 20.4989i −1.38648 1.00383i
\(418\) 3.35071 5.80359i 0.163888 0.283863i
\(419\) −8.85494 −0.432592 −0.216296 0.976328i \(-0.569398\pi\)
−0.216296 + 0.976328i \(0.569398\pi\)
\(420\) 4.96550 8.96347i 0.242292 0.437373i
\(421\) 18.9545 0.923783 0.461892 0.886936i \(-0.347171\pi\)
0.461892 + 0.886936i \(0.347171\pi\)
\(422\) −12.2386 + 21.1979i −0.595766 + 1.03190i
\(423\) −6.88858 + 32.9442i −0.334934 + 1.60180i
\(424\) −2.50000 4.33013i −0.121411 0.210290i
\(425\) 10.4846 11.8353i 0.508577 0.574095i
\(426\) 10.9441 4.89433i 0.530241 0.237131i
\(427\) −8.11562 + 4.25871i −0.392743 + 0.206094i
\(428\) −5.47723 −0.264752
\(429\) −0.872155 + 8.43224i −0.0421080 + 0.407112i
\(430\) −14.4715 5.48811i −0.697879 0.264660i
\(431\) −6.63699 + 3.83187i −0.319693 + 0.184575i −0.651256 0.758858i \(-0.725757\pi\)
0.331563 + 0.943433i \(0.392424\pi\)
\(432\) 3.84418 3.49604i 0.184953 0.168203i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 14.8170 + 9.37112i 0.711240 + 0.449828i
\(435\) 23.9545 + 12.0340i 1.14853 + 0.576987i
\(436\) 10.2158 17.6944i 0.489250 0.847406i
\(437\) 5.54555 3.20172i 0.265280 0.153159i
\(438\) 3.55851 4.91496i 0.170032 0.234846i
\(439\) −7.69306 4.44159i −0.367170 0.211986i 0.305051 0.952336i \(-0.401326\pi\)
−0.672221 + 0.740350i \(0.734660\pi\)
\(440\) 8.11562 6.62638i 0.386897 0.315900i
\(441\) −15.2160 + 14.4731i −0.724574 + 0.689198i
\(442\) 3.30318i 0.157116i
\(443\) 7.52277 13.0298i 0.357418 0.619066i −0.630111 0.776505i \(-0.716991\pi\)
0.987529 + 0.157439i \(0.0503239\pi\)
\(444\) 3.73591 + 2.70486i 0.177298 + 0.128367i
\(445\) 3.89908 10.2814i 0.184834 0.487387i
\(446\) −10.9441 + 18.9557i −0.518216 + 0.897576i
\(447\) 3.87298 1.73205i 0.183186 0.0819232i
\(448\) −1.41421 + 2.23607i −0.0668153 + 0.105644i
\(449\) 25.8773i 1.22122i −0.791930 0.610612i \(-0.790923\pi\)
0.791930 0.610612i \(-0.209077\pi\)
\(450\) 14.8990 1.73777i 0.702346 0.0819192i
\(451\) 4.23861 2.44716i 0.199588 0.115232i
\(452\) −8.73861 15.1357i −0.411030 0.711924i
\(453\) 3.44572 + 0.356394i 0.161894 + 0.0167448i
\(454\) 10.3923i 0.487735i
\(455\) 2.42253 5.68505i 0.113570 0.266519i
\(456\) −2.26139 + 1.01132i −0.105899 + 0.0473595i
\(457\) −9.59425 5.53924i −0.448800 0.259115i 0.258523 0.966005i \(-0.416764\pi\)
−0.707323 + 0.706890i \(0.750098\pi\)
\(458\) 11.7386 6.77729i 0.548509 0.316682i
\(459\) −16.0554 + 3.49611i −0.749404 + 0.163184i
\(460\) 9.88171 1.60607i 0.460737 0.0748833i
\(461\) −31.7876 −1.48050 −0.740248 0.672334i \(-0.765292\pi\)
−0.740248 + 0.672334i \(0.765292\pi\)
\(462\) −19.9387 + 7.96817i −0.927632 + 0.370713i
\(463\) 22.5741i 1.04911i −0.851377 0.524554i \(-0.824232\pi\)
0.851377 0.524554i \(-0.175768\pi\)
\(464\) −5.99430 3.46081i −0.278279 0.160664i
\(465\) 1.48910 + 25.6206i 0.0690555 + 1.18813i
\(466\) 2.00000 + 3.46410i 0.0926482 + 0.160471i
\(467\) −24.2614 14.0073i −1.12268 0.648181i −0.180599 0.983557i \(-0.557803\pi\)
−0.942085 + 0.335375i \(0.891137\pi\)
\(468\) 2.08911 2.33570i 0.0965693 0.107968i
\(469\) 1.52277 37.7244i 0.0703152 1.74195i
\(470\) 19.4317 15.8659i 0.896316 0.731839i
\(471\) −24.8908 2.57448i −1.14691 0.118626i
\(472\) 5.28720 + 9.15769i 0.243363 + 0.421517i
\(473\) 16.2158 + 28.0867i 0.745605 + 1.29143i
\(474\) −19.7737 2.04521i −0.908234 0.0939395i
\(475\) −7.00665 1.43023i −0.321487 0.0656233i
\(476\) 7.40852 3.88766i 0.339569 0.178190i
\(477\) −10.0000 + 11.1803i −0.457869 + 0.511913i
\(478\) 0 0
\(479\) 21.1810 + 36.6866i 0.967784 + 1.67625i 0.701940 + 0.712236i \(0.252317\pi\)
0.265844 + 0.964016i \(0.414349\pi\)
\(480\) −3.86646 + 0.224724i −0.176479 + 0.0102572i
\(481\) 2.40890 + 1.39078i 0.109836 + 0.0634141i
\(482\) 21.3094i 0.970615i
\(483\) −20.3066 2.93227i −0.923983 0.133423i
\(484\) −10.9545 −0.497930
\(485\) 26.4601 4.30055i 1.20149 0.195278i
\(486\) −13.5640 7.68223i −0.615278 0.348473i
\(487\) 14.7526 8.51743i 0.668505 0.385962i −0.127005 0.991902i \(-0.540536\pi\)
0.795510 + 0.605941i \(0.207203\pi\)
\(488\) 3.00000 + 1.73205i 0.135804 + 0.0784063i
\(489\) −23.2379 + 10.3923i −1.05085 + 0.469956i
\(490\) 15.6019 1.25761i 0.704821 0.0568132i
\(491\) 13.8433i 0.624737i 0.949961 + 0.312369i \(0.101122\pi\)
−0.949961 + 0.312369i \(0.898878\pi\)
\(492\) −1.79962 0.186137i −0.0811333 0.00839169i
\(493\) 10.9441 + 18.9557i 0.492895 + 0.853720i
\(494\) −1.29380 + 0.746976i −0.0582108 + 0.0336080i
\(495\) −26.4860 16.9247i −1.19046 0.760707i
\(496\) 6.62638i 0.297533i
\(497\) 15.4772 + 9.78866i 0.694248 + 0.439081i
\(498\) −6.43168 + 2.87633i −0.288210 + 0.128892i
\(499\) −0.954451 + 1.65316i −0.0427271 + 0.0740055i −0.886598 0.462541i \(-0.846938\pi\)
0.843871 + 0.536546i \(0.180271\pi\)
\(500\) −9.44975 5.97514i −0.422606 0.267216i
\(501\) 6.01958 + 4.35827i 0.268935 + 0.194713i
\(502\) −4.42747 + 7.66860i −0.197608 + 0.342266i
\(503\) 15.5096i 0.691537i −0.938320 0.345769i \(-0.887618\pi\)
0.938320 0.345769i \(-0.112382\pi\)
\(504\) 7.69738 + 1.93657i 0.342869 + 0.0862617i
\(505\) −16.0000 19.5959i −0.711991 0.872007i
\(506\) −18.1677 10.4891i −0.807655 0.466300i
\(507\) −12.0965 + 16.7075i −0.537225 + 0.742006i
\(508\) −7.56114 + 4.36543i −0.335471 + 0.193684i
\(509\) 12.3583 21.4051i 0.547770 0.948766i −0.450656 0.892697i \(-0.648810\pi\)
0.998427 0.0560688i \(-0.0178566\pi\)
\(510\) 10.9441 + 5.49798i 0.484611 + 0.243454i
\(511\) 9.26139 + 0.373843i 0.409700 + 0.0165378i
\(512\) 1.00000 0.0441942
\(513\) 5.00013 + 5.49805i 0.220761 + 0.242745i
\(514\) 9.52277 5.49798i 0.420032 0.242505i
\(515\) 3.89908 10.2814i 0.171814 0.453055i
\(516\) 1.23341 11.9250i 0.0542980 0.524968i
\(517\) −52.5667 −2.31188
\(518\) −0.284162 + 7.03967i −0.0124853 + 0.309305i
\(519\) 1.78416 0.797901i 0.0783160 0.0350240i
\(520\) −2.30545 + 0.374703i −0.101101 + 0.0164318i
\(521\) 17.7981 + 30.8272i 0.779748 + 1.35056i 0.932087 + 0.362235i \(0.117986\pi\)
−0.152339 + 0.988328i \(0.548680\pi\)
\(522\) −4.24999 + 20.3253i −0.186017 + 0.889614i
\(523\) 8.45307 14.6412i 0.369627 0.640213i −0.619880 0.784697i \(-0.712819\pi\)
0.989507 + 0.144484i \(0.0461521\pi\)
\(524\) −13.7725 −0.601654
\(525\) 14.8034 + 17.4888i 0.646075 + 0.763274i
\(526\) −2.00000 −0.0872041
\(527\) −10.4772 + 18.1471i −0.456395 + 0.790500i
\(528\) 6.57357 + 4.75937i 0.286078 + 0.207125i
\(529\) 1.47723 + 2.55863i 0.0642272 + 0.111245i
\(530\) 11.0355 1.79360i 0.479353 0.0779089i
\(531\) 21.1488 23.6451i 0.917779 1.02611i
\(532\) −3.19808 2.02265i −0.138655 0.0876928i
\(533\) −1.09110 −0.0472607
\(534\) 8.47223 + 0.876291i 0.366629 + 0.0379208i
\(535\) 4.34286 11.4516i 0.187758 0.495097i
\(536\) −12.3583 + 7.13505i −0.533796 + 0.308187i
\(537\) −3.45390 + 33.3933i −0.149047 + 1.44103i
\(538\) 17.5810 0.757973
\(539\) −26.9905 18.6355i −1.16256 0.802689i
\(540\) 4.26139 + 10.8093i 0.183381 + 0.465157i
\(541\) −4.26139 + 7.38094i −0.183211 + 0.317331i −0.942972 0.332871i \(-0.891983\pi\)
0.759761 + 0.650202i \(0.225316\pi\)
\(542\) 5.47723 3.16228i 0.235267 0.135831i
\(543\) −4.43649 3.21209i −0.190388 0.137844i
\(544\) −2.73861 1.58114i −0.117417 0.0677908i
\(545\) 28.8948 + 35.3887i 1.23772 + 1.51589i
\(546\) 4.73762 + 0.684110i 0.202751 + 0.0292772i
\(547\) 3.61845i 0.154714i 0.997003 + 0.0773569i \(0.0246481\pi\)
−0.997003 + 0.0773569i \(0.975352\pi\)
\(548\) 1.73861 3.01137i 0.0742699 0.128639i
\(549\) 2.12702 10.1723i 0.0907789 0.434143i
\(550\) 7.41941 + 22.2219i 0.316365 + 0.947546i
\(551\) 4.94975 8.57321i 0.210866 0.365231i
\(552\) 3.16588 + 7.07912i 0.134749 + 0.301307i
\(553\) −14.1099 26.8886i −0.600015 1.14342i
\(554\) 9.79796i 0.416275i
\(555\) −8.61742 + 5.66626i −0.365789 + 0.240520i
\(556\) −17.4772 + 10.0905i −0.741199 + 0.427932i
\(557\) −13.9317 24.1304i −0.590304 1.02244i −0.994191 0.107628i \(-0.965674\pi\)
0.403887 0.914809i \(-0.367659\pi\)
\(558\) −18.8857 + 6.20555i −0.799497 + 0.262702i
\(559\) 7.23003i 0.305798i
\(560\) −3.55378 4.72976i −0.150175 0.199869i
\(561\) −10.4772 23.4278i −0.442349 0.989122i
\(562\) 1.56683 + 0.904612i 0.0660929 + 0.0381588i
\(563\) 9.00000 5.19615i 0.379305 0.218992i −0.298211 0.954500i \(-0.596390\pi\)
0.677516 + 0.735508i \(0.263057\pi\)
\(564\) 15.7394 + 11.3956i 0.662750 + 0.479842i
\(565\) 38.5741 6.26942i 1.62282 0.263757i
\(566\) 9.22460 0.387739
\(567\) −1.68915 23.7518i −0.0709375 0.997481i
\(568\) 6.92163i 0.290425i
\(569\) 6.54879 + 3.78095i 0.274540 + 0.158505i 0.630949 0.775824i \(-0.282666\pi\)
−0.356409 + 0.934330i \(0.615999\pi\)
\(570\) −0.321406 5.52991i −0.0134622 0.231623i
\(571\) −7.47723 12.9509i −0.312912 0.541980i 0.666079 0.745881i \(-0.267971\pi\)
−0.978991 + 0.203901i \(0.934638\pi\)
\(572\) 4.23861 + 2.44716i 0.177225 + 0.102321i
\(573\) 25.7611 11.5207i 1.07618 0.481284i
\(574\) −1.28416 2.44716i −0.0535999 0.102143i
\(575\) −4.47723 + 21.9338i −0.186713 + 0.914704i
\(576\) −0.936492 2.85008i −0.0390205 0.118754i
\(577\) 0.337449 + 0.584480i 0.0140482 + 0.0243322i 0.872964 0.487785i \(-0.162195\pi\)
−0.858916 + 0.512117i \(0.828862\pi\)
\(578\) −3.50000 6.06218i −0.145581 0.252153i
\(579\) −1.30948 + 12.6604i −0.0544199 + 0.526148i
\(580\) 11.9886 9.78866i 0.497800 0.406452i
\(581\) −9.09576 5.75267i −0.377356 0.238661i
\(582\) 8.47723 + 18.9557i 0.351392 + 0.785737i
\(583\) −20.2891 11.7139i −0.840287 0.485140i
\(584\) −1.75166 3.03397i −0.0724843 0.125547i
\(585\) 3.22697 + 6.21981i 0.133419 + 0.257158i
\(586\) 6.97723 + 4.02830i 0.288227 + 0.166408i
\(587\) 21.0864i 0.870330i 0.900351 + 0.435165i \(0.143310\pi\)
−0.900351 + 0.435165i \(0.856690\pi\)
\(588\) 4.04156 + 11.4309i 0.166671 + 0.471403i
\(589\) 9.47723 0.390502
\(590\) −23.3388 + 3.79324i −0.960844 + 0.156165i
\(591\) 9.14178 12.6265i 0.376042 0.519384i
\(592\) 2.30615 1.33146i 0.0947821 0.0547225i
\(593\) −1.43168 0.826579i −0.0587919 0.0339435i 0.470316 0.882498i \(-0.344140\pi\)
−0.529108 + 0.848555i \(0.677473\pi\)
\(594\) 7.40852 23.1923i 0.303975 0.951593i
\(595\) 2.25403 + 18.5720i 0.0924064 + 0.761378i
\(596\) 2.44949i 0.100335i
\(597\) 2.76376 26.7208i 0.113113 1.09361i
\(598\) 2.33836 + 4.05015i 0.0956225 + 0.165623i
\(599\) 20.4739 11.8206i 0.836540 0.482977i −0.0195464 0.999809i \(-0.506222\pi\)
0.856087 + 0.516832i \(0.172889\pi\)
\(600\) 2.59584 8.26206i 0.105975 0.337297i
\(601\) 4.06775i 0.165927i 0.996553 + 0.0829635i \(0.0264385\pi\)
−0.996553 + 0.0829635i \(0.973562\pi\)
\(602\) 16.2158 8.50934i 0.660908 0.346815i
\(603\) 31.9089 + 28.5402i 1.29943 + 1.16225i
\(604\) 1.00000 1.73205i 0.0406894 0.0704761i
\(605\) 8.68571 22.9032i 0.353124 0.931149i
\(606\) 11.4919 15.8725i 0.466828 0.644775i
\(607\) −6.14692 + 10.6468i −0.249496 + 0.432140i −0.963386 0.268118i \(-0.913598\pi\)
0.713890 + 0.700258i \(0.246932\pi\)
\(608\) 1.43023i 0.0580034i
\(609\) −29.4540 + 11.7708i −1.19353 + 0.476976i
\(610\) −6.00000 + 4.89898i −0.242933 + 0.198354i
\(611\) 10.1487 + 5.85938i 0.410574 + 0.237045i
\(612\) −1.94169 + 9.28600i −0.0784882 + 0.375364i
\(613\) −5.07016 + 2.92726i −0.204782 + 0.118231i −0.598884 0.800836i \(-0.704389\pi\)
0.394102 + 0.919067i \(0.371056\pi\)
\(614\) 5.99430 10.3824i 0.241910 0.419001i
\(615\) 1.81608 3.61501i 0.0732314 0.145771i
\(616\) −0.500000 + 12.3867i −0.0201456 + 0.499076i
\(617\) 14.5228 0.584665 0.292332 0.956317i \(-0.405569\pi\)
0.292332 + 0.956317i \(0.405569\pi\)
\(618\) 8.47223 + 0.876291i 0.340803 + 0.0352496i
\(619\) 26.1475 15.0963i 1.05096 0.606771i 0.128040 0.991769i \(-0.459131\pi\)
0.922917 + 0.384998i \(0.125798\pi\)
\(620\) 13.8542 + 5.25401i 0.556400 + 0.211006i
\(621\) 17.2113 15.6525i 0.690664 0.628115i
\(622\) 17.5810 0.704936
\(623\) 6.04555 + 11.5207i 0.242210 + 0.461567i
\(624\) −0.738613 1.65159i −0.0295682 0.0661165i
\(625\) 19.9853 15.0196i 0.799411 0.600784i
\(626\) −11.6190 20.1246i −0.464387 0.804341i
\(627\) −6.80698 + 9.40169i −0.271845 + 0.375467i
\(628\) −7.22369 + 12.5118i −0.288257 + 0.499275i
\(629\) −8.42087 −0.335762
\(630\) −10.1521 + 14.5580i −0.404470 + 0.580003i
\(631\) 3.47723 0.138426 0.0692131 0.997602i \(-0.477951\pi\)
0.0692131 + 0.997602i \(0.477951\pi\)
\(632\) −5.73861 + 9.93957i −0.228270 + 0.395375i
\(633\) 24.8628 34.3401i 0.988208 1.36490i
\(634\) 4.95445 + 8.58136i 0.196766 + 0.340809i
\(635\) −3.13193 19.2699i −0.124287 0.764703i
\(636\) 3.53553 + 7.90569i 0.140193 + 0.313481i
\(637\) 3.13367 + 6.60635i 0.124160 + 0.261753i
\(638\) −32.4317 −1.28398
\(639\) −19.7272 + 6.48204i −0.780397 + 0.256426i
\(640\) −0.792893 + 2.09077i −0.0313419 + 0.0826450i
\(641\) −13.9251 + 8.03966i −0.550008 + 0.317547i −0.749125 0.662428i \(-0.769526\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(642\) 9.43649 + 0.976025i 0.372429 + 0.0385206i
\(643\) 26.0663 1.02796 0.513978 0.857803i \(-0.328171\pi\)
0.513978 + 0.857803i \(0.328171\pi\)
\(644\) −6.33175 + 10.0114i −0.249506 + 0.394504i
\(645\) 23.9545 + 12.0340i 0.943206 + 0.473839i
\(646\) 2.26139 3.91684i 0.0889731 0.154106i
\(647\) 17.6703 10.2019i 0.694691 0.401080i −0.110676 0.993857i \(-0.535302\pi\)
0.805367 + 0.592777i \(0.201968\pi\)
\(648\) −7.24597 + 5.33816i −0.284648 + 0.209703i
\(649\) 42.9089 + 24.7735i 1.68432 + 0.972444i
\(650\) 1.04456 5.11726i 0.0409709 0.200715i
\(651\) −23.8578 18.7855i −0.935060 0.736261i
\(652\) 14.6969i 0.575577i
\(653\) −19.9317 + 34.5227i −0.779987 + 1.35098i 0.151962 + 0.988386i \(0.451441\pi\)
−0.931949 + 0.362590i \(0.881892\pi\)
\(654\) −20.7535 + 28.6645i −0.811528 + 1.12087i
\(655\) 10.9201 28.7951i 0.426684 1.12512i
\(656\) −0.522278 + 0.904612i −0.0203915 + 0.0353192i
\(657\) −7.00665 + 7.83368i −0.273356 + 0.305621i
\(658\) −1.19718 + 29.6582i −0.0466708 + 1.15620i
\(659\) 34.2929i 1.33586i −0.744224 0.667930i \(-0.767181\pi\)
0.744224 0.667930i \(-0.232819\pi\)
\(660\) −15.1629 + 9.97014i −0.590214 + 0.388087i
\(661\) 0.522774 0.301824i 0.0203336 0.0117396i −0.489799 0.871836i \(-0.662930\pi\)
0.510132 + 0.860096i \(0.329596\pi\)
\(662\) −10.7158 18.5604i −0.416483 0.721370i
\(663\) −0.588616 + 5.69091i −0.0228600 + 0.221017i
\(664\) 4.06775i 0.157859i
\(665\) 6.76463 5.08272i 0.262321 0.197099i
\(666\) −5.95445 5.32582i −0.230730 0.206371i
\(667\) −26.8378 15.4948i −1.03917 0.599963i
\(668\) 3.71584 2.14534i 0.143770 0.0830057i
\(669\) 22.2329 30.7077i 0.859574 1.18723i
\(670\) −5.11896 31.4956i −0.197763 1.21678i
\(671\) 16.2312 0.626600
\(672\) 2.83495 3.60042i 0.109361 0.138889i
\(673\) 14.1585i 0.545771i −0.962047 0.272885i \(-0.912022\pi\)
0.962047 0.272885i \(-0.0879780\pi\)
\(674\) −14.8492 8.57321i −0.571971 0.330228i
\(675\) −25.9786 + 0.338975i −0.999915 + 0.0130472i
\(676\) 5.95445 + 10.3134i 0.229017 + 0.396670i
\(677\) −28.5000 16.4545i −1.09534 0.632397i −0.160350 0.987060i \(-0.551262\pi\)
−0.934994 + 0.354663i \(0.884596\pi\)
\(678\) 12.3583 + 27.6339i 0.474616 + 1.06127i
\(679\) −16.9545 + 26.8073i −0.650652 + 1.02877i
\(680\) 5.47723 4.47214i 0.210042 0.171499i
\(681\) 1.85188 17.9045i 0.0709641 0.686101i
\(682\) −15.5241 26.8886i −0.594450 1.02962i
\(683\) 9.47723 + 16.4150i 0.362636 + 0.628104i 0.988394 0.151913i \(-0.0485435\pi\)
−0.625758 + 0.780017i \(0.715210\pi\)
\(684\) 4.07627 1.33940i 0.155860 0.0512131i
\(685\) 4.91754 + 6.02273i 0.187890 + 0.230117i
\(686\) −11.1289 + 14.8036i −0.424903 + 0.565206i
\(687\) −21.4317 + 9.58454i −0.817669 + 0.365673i
\(688\) −5.99430 3.46081i −0.228531 0.131942i
\(689\) 2.61139 + 4.52306i 0.0994861 + 0.172315i
\(690\) −17.3110 + 1.00614i −0.659019 + 0.0383030i
\(691\) 3.00000 + 1.73205i 0.114125 + 0.0658903i 0.555976 0.831198i \(-0.312345\pi\)
−0.441851 + 0.897089i \(0.645678\pi\)
\(692\) 1.12840i 0.0428954i
\(693\) 35.7715 10.1750i 1.35885 0.386517i
\(694\) −17.4772 −0.663426
\(695\) −7.23930 44.5415i −0.274602 1.68956i
\(696\) 9.71064 + 7.03066i 0.368081 + 0.266497i
\(697\) 2.86064 1.65159i 0.108354 0.0625584i
\(698\) −10.1703 5.87182i −0.384951 0.222252i
\(699\) −2.82843 6.32456i −0.106981 0.239217i
\(700\) 12.7066 3.67995i 0.480265 0.139089i
\(701\) 51.7546i 1.95474i 0.211531 + 0.977371i \(0.432155\pi\)
−0.211531 + 0.977371i \(0.567845\pi\)
\(702\) −4.01546 + 3.65181i −0.151554 + 0.137829i
\(703\) 1.90428 + 3.29832i 0.0718214 + 0.124398i
\(704\) 4.05781 2.34278i 0.152935 0.0882968i
\(705\) −36.3053 + 23.8721i −1.36734 + 0.899073i
\(706\) 0.603648i 0.0227186i
\(707\) 29.9089 + 1.20730i 1.12484 + 0.0454050i
\(708\) −7.47723 16.7196i −0.281011 0.628360i
\(709\) 11.2158 19.4264i 0.421220 0.729574i −0.574839 0.818266i \(-0.694935\pi\)
0.996059 + 0.0886924i \(0.0282688\pi\)
\(710\) 14.4715 + 5.48811i 0.543107 + 0.205965i
\(711\) 33.7028 + 7.04721i 1.26395 + 0.264291i
\(712\) 2.45877 4.25871i 0.0921463 0.159602i
\(713\) 29.6678i 1.11107i
\(714\) −13.4566 + 5.37771i −0.503601 + 0.201256i
\(715\) −8.47723 + 6.92163i −0.317030 + 0.258854i
\(716\) 16.7857 + 9.69125i 0.627312 + 0.362179i
\(717\) 0 0
\(718\) 9.86729 5.69688i 0.368244 0.212606i
\(719\) −0.401865 + 0.696051i −0.0149870 + 0.0259583i −0.873422 0.486965i \(-0.838104\pi\)
0.858435 + 0.512923i \(0.171437\pi\)
\(720\) 6.70141 + 0.301824i 0.249747 + 0.0112483i
\(721\) 6.04555 + 11.5207i 0.225148 + 0.429054i
\(722\) 16.9545 0.630979
\(723\) −3.79726 + 36.7130i −0.141222 + 1.36537i
\(724\) −2.73861 + 1.58114i −0.101780 + 0.0587626i
\(725\) 10.9601 + 32.8268i 0.407050 + 1.21916i
\(726\) 18.8730 + 1.95205i 0.700442 + 0.0724474i
\(727\) 15.1223 0.560854 0.280427 0.959875i \(-0.409524\pi\)
0.280427 + 0.959875i \(0.409524\pi\)
\(728\) 1.47723 2.33570i 0.0547496 0.0865668i
\(729\) 22.0000 + 15.6525i 0.814815 + 0.579721i
\(730\) 7.73221 1.25671i 0.286182 0.0465130i
\(731\) 10.9441 + 18.9557i 0.404780 + 0.701100i
\(732\) −4.85993 3.51867i −0.179628 0.130054i
\(733\) −1.19718 + 2.07357i −0.0442187 + 0.0765891i −0.887288 0.461216i \(-0.847413\pi\)
0.843069 + 0.537805i \(0.180747\pi\)
\(734\) 0.369657 0.0136443
\(735\) −27.1039 0.613514i −0.999744 0.0226298i
\(736\) 4.47723 0.165033
\(737\) −33.4317 + 57.9054i −1.23147 + 2.13297i
\(738\) 3.06733 + 0.641375i 0.112910 + 0.0236093i
\(739\) −3.23861 5.60944i −0.119134 0.206347i 0.800291 0.599612i \(-0.204679\pi\)
−0.919425 + 0.393266i \(0.871345\pi\)
\(740\) 0.955238 + 5.87733i 0.0351153 + 0.216055i
\(741\) 2.36215 1.05638i 0.0867756 0.0388072i
\(742\) −7.07107 + 11.1803i −0.259587 + 0.410443i
\(743\) 13.4317 0.492760 0.246380 0.969173i \(-0.420759\pi\)
0.246380 + 0.969173i \(0.420759\pi\)
\(744\) −1.18080 + 11.4163i −0.0432903 + 0.418543i
\(745\) 5.12132 + 1.94218i 0.187631 + 0.0711561i
\(746\) −20.1042 + 11.6072i −0.736068 + 0.424969i
\(747\) 11.5934 3.80941i 0.424181 0.139379i
\(748\) −14.8170 −0.541764
\(749\) 6.73362 + 12.8319i 0.246041 + 0.468868i
\(750\) 15.2158 + 11.9782i 0.555604 + 0.437384i
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) 9.71584 5.60944i 0.354300 0.204555i
\(753\) 8.99443 12.4230i 0.327775 0.452718i
\(754\) 6.26139 + 3.61501i 0.228026 + 0.131651i
\(755\) 2.82843 + 3.46410i 0.102937 + 0.126072i
\(756\) −12.9164 4.70809i −0.469766 0.171232i
\(757\) 48.1361i 1.74954i −0.484541 0.874768i \(-0.661014\pi\)
0.484541 0.874768i \(-0.338986\pi\)
\(758\) 10.2386 17.7338i 0.371883 0.644121i
\(759\) 29.4313 + 21.3088i 1.06829 + 0.773459i
\(760\) −2.99028 1.13402i −0.108469 0.0411351i
\(761\) 0.891935 1.54488i 0.0323326 0.0560018i −0.849406 0.527739i \(-0.823040\pi\)
0.881739 + 0.471738i \(0.156373\pi\)
\(762\) 13.8047 6.17364i 0.500091 0.223648i
\(763\) −54.0131 2.18028i −1.95541 0.0789315i
\(764\) 16.2927i 0.589451i
\(765\) −17.8753 11.4224i −0.646284 0.412979i
\(766\) −15.7158 + 9.07354i −0.567836 + 0.327840i
\(767\) −5.52277 9.56573i −0.199416 0.345398i
\(768\) −1.72286 0.178197i −0.0621683 0.00643013i
\(769\) 16.1921i 0.583902i 0.956433 + 0.291951i \(0.0943045\pi\)
−0.956433 + 0.291951i \(0.905696\pi\)
\(770\) −25.5014 10.8667i −0.919005 0.391610i
\(771\) −17.3861 + 7.77531i −0.626146 + 0.280021i
\(772\) 6.36396 + 3.67423i 0.229044 + 0.132239i
\(773\) −14.0228 + 8.09605i −0.504364 + 0.291195i −0.730514 0.682898i \(-0.760719\pi\)
0.226150 + 0.974093i \(0.427386\pi\)
\(774\) −4.24999 + 20.3253i −0.152763 + 0.730578i
\(775\) −21.9699 + 24.8002i −0.789181 + 0.890848i
\(776\) 11.9886 0.430366
\(777\) 1.74402 12.0777i 0.0625663 0.433286i
\(778\) 7.34847i 0.263455i
\(779\) −1.29380 0.746976i −0.0463552 0.0267632i
\(780\) 4.03873 0.234736i 0.144610 0.00840491i
\(781\) −16.2158 28.0867i −0.580248 1.00502i
\(782\) −12.2614 7.07912i −0.438466 0.253149i
\(783\) 10.9441 34.2603i 0.391108 1.22436i
\(784\) 6.97723 + 0.564201i 0.249187 + 0.0201501i
\(785\) −20.4317 25.0236i −0.729238 0.893130i
\(786\) 23.7280 + 2.45421i 0.846351 + 0.0875389i
\(787\) 25.0862 + 43.4506i 0.894226 + 1.54884i 0.834760 + 0.550615i \(0.185607\pi\)
0.0594664 + 0.998230i \(0.481060\pi\)
\(788\) −4.50000 7.79423i −0.160306 0.277658i
\(789\) 3.44572 + 0.356394i 0.122671 + 0.0126880i
\(790\) −16.2312 19.8791i −0.577482 0.707268i
\(791\) −24.7165 + 39.0803i −0.878819 + 1.38953i
\(792\) −10.4772 9.37112i −0.372292 0.332988i
\(793\) −3.13367 1.80922i −0.111280 0.0642474i
\(794\) −7.44073 12.8877i −0.264061 0.457368i
\(795\) −19.3323 + 1.12362i −0.685646 + 0.0398506i
\(796\) −13.4317 7.75478i −0.476073 0.274861i
\(797\) 54.2183i 1.92051i −0.279121 0.960256i \(-0.590043\pi\)
0.279121 0.960256i \(-0.409957\pi\)
\(798\) 5.14942 + 4.05462i 0.182288 + 0.143532i
\(799\) −35.4772 −1.25509
\(800\) −3.74264 3.31552i −0.132322 0.117221i
\(801\) −14.4403 3.01945i −0.510223 0.106687i
\(802\) −0.827520 + 0.477769i −0.0292207 + 0.0168706i
\(803\) −14.2158 8.20752i −0.501666 0.289637i
\(804\) 22.5630 10.0905i 0.795736 0.355864i
\(805\) −15.9111 21.1762i −0.560792 0.746363i
\(806\) 6.92163i 0.243804i
\(807\) −30.2897 3.13289i −1.06625 0.110283i
\(808\) −5.65685 9.79796i −0.199007 0.344691i
\(809\) −7.65776 + 4.42121i −0.269233 + 0.155441i −0.628539 0.777778i \(-0.716347\pi\)
0.359306 + 0.933220i \(0.383013\pi\)
\(810\) −5.41559 19.3822i −0.190284 0.681023i
\(811\) 38.3280i 1.34588i 0.739697 + 0.672940i \(0.234969\pi\)
−0.739697 + 0.672940i \(0.765031\pi\)
\(812\) −0.738613 + 18.2980i −0.0259202 + 0.642134i
\(813\) −10.0000 + 4.47214i −0.350715 + 0.156845i
\(814\) 6.23861 10.8056i 0.218663 0.378736i
\(815\) −30.7279 11.6531i −1.07635 0.408190i
\(816\) 4.43649 + 3.21209i 0.155308 + 0.112446i
\(817\) 4.94975 8.57321i 0.173170 0.299939i
\(818\) 15.5096i 0.542279i
\(819\) −8.04035 2.02286i −0.280953 0.0706843i
\(820\) −1.47723 1.80922i −0.0515870 0.0631809i
\(821\) −10.1403 5.85452i −0.353900 0.204324i 0.312502 0.949917i \(-0.398833\pi\)
−0.666401 + 0.745593i \(0.732166\pi\)
\(822\) −3.53200 + 4.87835i −0.123193 + 0.170152i
\(823\) 2.76401 1.59580i 0.0963474 0.0556262i −0.451052 0.892498i \(-0.648951\pi\)
0.547400 + 0.836871i \(0.315618\pi\)
\(824\) 2.45877 4.25871i 0.0856553 0.148359i
\(825\) −8.82273 39.6074i −0.307168 1.37895i
\(826\) 14.9545 23.6451i 0.520332 0.822717i
\(827\) −3.90890 −0.135926 −0.0679629 0.997688i \(-0.521650\pi\)
−0.0679629 + 0.997688i \(0.521650\pi\)
\(828\) −4.19288 12.7605i −0.145713 0.443457i
\(829\) −43.6931 + 25.2262i −1.51752 + 0.876142i −0.517735 + 0.855541i \(0.673225\pi\)
−0.999788 + 0.0206012i \(0.993442\pi\)
\(830\) −8.50473 3.22529i −0.295203 0.111951i
\(831\) 1.74597 16.8805i 0.0605669 0.585578i
\(832\) −1.04456 −0.0362135
\(833\) −18.2158 12.5771i −0.631141 0.435770i
\(834\) 31.9089 14.2701i 1.10491 0.494133i
\(835\) 1.53915 + 9.46999i 0.0532645 + 0.327723i
\(836\) 3.35071 + 5.80359i 0.115887 + 0.200721i
\(837\) 33.6433 7.32591i 1.16288 0.253220i
\(838\) 4.42747 7.66860i 0.152944 0.264907i
\(839\) 40.1440 1.38593 0.692963 0.720973i \(-0.256305\pi\)
0.692963 + 0.720973i \(0.256305\pi\)
\(840\) 5.27984 + 8.78198i 0.182172 + 0.303007i
\(841\) −18.9089 −0.652031
\(842\) −9.47723 + 16.4150i −0.326607 + 0.565700i
\(843\) −2.53824 1.83773i −0.0874215 0.0632946i
\(844\) −12.2386 21.1979i −0.421270 0.729662i
\(845\) −26.2842 + 4.27196i −0.904205 + 0.146960i
\(846\) −25.0862 22.4378i −0.862481 0.771426i
\(847\) 13.4672 + 25.6639i 0.462740 + 0.881821i
\(848\) 5.00000 0.171701
\(849\) −15.8927 1.64380i −0.545436 0.0564149i
\(850\) 5.00735 + 14.9975i 0.171751 + 0.514412i
\(851\) 10.3251 5.96123i 0.353942 0.204348i
\(852\) −1.23341 + 11.9250i −0.0422560 + 0.408543i
\(853\) −31.2891 −1.07132 −0.535659 0.844434i \(-0.679937\pi\)
−0.535659 + 0.844434i \(0.679937\pi\)
\(854\) 0.369657 9.15769i 0.0126494 0.313370i
\(855\) −0.431677 + 9.58454i −0.0147630 + 0.327784i
\(856\) 2.73861 4.74342i 0.0936039 0.162127i
\(857\) 13.0455 7.53185i 0.445627 0.257283i −0.260354 0.965513i \(-0.583839\pi\)
0.705982 + 0.708230i \(0.250506\pi\)
\(858\) −6.86646 4.97143i −0.234417 0.169722i
\(859\) −26.4772 15.2866i −0.903391 0.521573i −0.0250924 0.999685i \(-0.507988\pi\)
−0.878299 + 0.478112i \(0.841321\pi\)
\(860\) 11.9886 9.78866i 0.408808 0.333790i
\(861\) 1.77635 + 4.44495i 0.0605380 + 0.151484i
\(862\) 7.66374i 0.261028i
\(863\) 13.2386 22.9299i 0.450648 0.780545i −0.547779 0.836623i \(-0.684526\pi\)
0.998426 + 0.0560787i \(0.0178598\pi\)
\(864\) 1.10557 + 5.07718i 0.0376122 + 0.172729i
\(865\) 2.35923 + 0.894703i 0.0802163 + 0.0304208i
\(866\) 0 0
\(867\) 4.94975 + 11.0680i 0.168102 + 0.375888i
\(868\) −15.5241 + 8.14637i −0.526924 + 0.276506i
\(869\) 53.7772i 1.82427i
\(870\) −22.3990 + 14.7281i −0.759397 + 0.499331i
\(871\) 12.9089 7.45296i 0.437401 0.252534i
\(872\) 10.2158 + 17.6944i 0.345952 + 0.599206i
\(873\) −11.2272 34.1685i −0.379984 1.15643i
\(874\) 6.40345i 0.216600i
\(875\) −2.38105 + 29.4844i −0.0804942 + 0.996755i
\(876\) 2.47723 + 5.53924i 0.0836977 + 0.187154i
\(877\) 48.2359 + 27.8490i 1.62881 + 0.940394i 0.984449 + 0.175673i \(0.0562101\pi\)
0.644361 + 0.764721i \(0.277123\pi\)
\(878\) 7.69306 4.44159i 0.259628 0.149896i
\(879\) −11.3029 8.18352i −0.381239 0.276023i
\(880\) 1.68080 + 10.3415i 0.0566598 + 0.348613i
\(881\) 18.7544 0.631853 0.315926 0.948784i \(-0.397685\pi\)
0.315926 + 0.948784i \(0.397685\pi\)
\(882\) −4.92609 20.4141i −0.165870 0.687377i
\(883\) 24.3833i 0.820564i 0.911959 + 0.410282i \(0.134570\pi\)
−0.911959 + 0.410282i \(0.865430\pi\)
\(884\) 2.86064 + 1.65159i 0.0962136 + 0.0555489i
\(885\) 40.8855 2.37632i 1.37435 0.0798790i
\(886\) 7.52277 + 13.0298i 0.252733 + 0.437746i
\(887\) 3.00000 + 1.73205i 0.100730 + 0.0581566i 0.549519 0.835481i \(-0.314811\pi\)
−0.448789 + 0.893638i \(0.648144\pi\)
\(888\) −4.21043 + 1.88296i −0.141293 + 0.0631881i
\(889\) 19.5228 + 12.3473i 0.654773 + 0.414115i
\(890\) 6.95445 + 8.51743i 0.233114 + 0.285505i
\(891\) −16.8966 + 38.6370i −0.566059 + 1.29439i
\(892\) −10.9441 18.9557i −0.366434 0.634682i
\(893\) 8.02277 + 13.8959i 0.268472 + 0.465007i
\(894\) −0.436492 + 4.22013i −0.0145985 + 0.141142i
\(895\) −33.5715 + 27.4110i −1.12217 + 0.916248i
\(896\) −1.22938 2.34278i −0.0410709 0.0782667i
\(897\) −3.30694 7.39453i −0.110415 0.246896i
\(898\) 22.4104 + 12.9386i 0.747844 + 0.431768i
\(899\) −22.9327 39.7205i −0.764847 1.32475i
\(900\) −5.94455 + 13.7718i −0.198152 + 0.459060i
\(901\) −13.6931 7.90569i −0.456182 0.263377i
\(902\) 4.89433i 0.162963i
\(903\) −29.4540 + 11.7708i −0.980166 + 0.391707i
\(904\) 17.4772 0.581284
\(905\) −1.13437 6.97948i −0.0377078 0.232006i
\(906\) −2.03151 + 2.80588i −0.0674923 + 0.0932192i
\(907\) 8.48528 4.89898i 0.281749 0.162668i −0.352466 0.935825i \(-0.614657\pi\)
0.634215 + 0.773157i \(0.281323\pi\)
\(908\) −9.00000 5.19615i −0.298675 0.172440i
\(909\) −22.6274 + 25.2982i −0.750504 + 0.839089i
\(910\) 3.71213 + 4.94050i 0.123056 + 0.163776i
\(911\) 24.0681i 0.797410i −0.917079 0.398705i \(-0.869460\pi\)
0.917079 0.398705i \(-0.130540\pi\)
\(912\) 0.254862 2.46408i 0.00843933 0.0815939i
\(913\) 9.52984 + 16.5062i 0.315392 + 0.546274i
\(914\) 9.59425 5.53924i 0.317350 0.183222i
\(915\) 11.2101 7.37107i 0.370596 0.243680i
\(916\) 13.5546i 0.447856i
\(917\) 16.9317 + 32.2659i 0.559133 + 1.06551i
\(918\) 5.00000 15.6525i 0.165025 0.516609i
\(919\) −0.215838 + 0.373843i −0.00711985 + 0.0123319i −0.869563 0.493821i \(-0.835600\pi\)
0.862444 + 0.506153i \(0.168933\pi\)
\(920\) −3.54996 + 9.36085i −0.117039 + 0.308618i
\(921\) −12.1775 + 16.8193i −0.401261 + 0.554215i
\(922\) 15.8938 27.5289i 0.523434 0.906615i
\(923\) 7.23003i 0.237979i
\(924\) 3.06871 21.2515i 0.100953 0.699123i
\(925\) −13.0455 2.66291i −0.428935 0.0875560i
\(926\) 19.5497 + 11.2871i 0.642444 + 0.370916i
\(927\) −14.4403 3.01945i −0.474282 0.0991718i
\(928\) 5.99430 3.46081i 0.196773 0.113607i
\(929\) −7.96300 + 13.7923i −0.261258 + 0.452512i −0.966576 0.256379i \(-0.917471\pi\)
0.705319 + 0.708890i \(0.250804\pi\)
\(930\) −22.9327 11.5207i −0.751991 0.377779i
\(931\) −0.806936 + 9.97902i −0.0264463 + 0.327049i
\(932\) −4.00000 −0.131024
\(933\) −30.2897 3.13289i −0.991640 0.102566i
\(934\) 24.2614 14.0073i 0.793857 0.458333i
\(935\) 11.7483 30.9790i 0.384211 1.01312i
\(936\) 0.978218 + 2.97707i 0.0319741 + 0.0973087i
\(937\) 53.6757 1.75351 0.876754 0.480938i \(-0.159704\pi\)
0.876754 + 0.480938i \(0.159704\pi\)
\(938\) 31.9089 + 20.1810i 1.04186 + 0.658932i
\(939\) 16.4317 + 36.7423i 0.536228 + 1.19904i
\(940\) 4.02443 + 24.7613i 0.131262 + 0.807624i
\(941\) 10.2369 + 17.7309i 0.333715 + 0.578011i 0.983237 0.182331i \(-0.0583644\pi\)
−0.649522 + 0.760343i \(0.725031\pi\)
\(942\) 14.6750 20.2688i 0.478136 0.660394i
\(943\) −2.33836 + 4.05015i −0.0761474 + 0.131891i
\(944\) −10.5744 −0.344167
\(945\) 20.0849 23.2723i 0.653361 0.757047i
\(946\) −32.4317 −1.05444
\(947\) −16.4317 + 28.4605i −0.533958 + 0.924842i 0.465255 + 0.885177i \(0.345963\pi\)
−0.999213 + 0.0396654i \(0.987371\pi\)
\(948\) 11.6580 16.1019i 0.378635 0.522965i
\(949\) 1.82971 + 3.16915i 0.0593949 + 0.102875i
\(950\) 4.74194 5.35283i 0.153849 0.173669i
\(951\) −7.00665 15.6674i −0.227206 0.508049i
\(952\) −0.337449 + 8.35979i −0.0109368 + 0.270942i
\(953\) 46.9545 1.52100 0.760502 0.649336i \(-0.224953\pi\)
0.760502 + 0.649336i \(0.224953\pi\)
\(954\) −4.68246 14.2504i −0.151600 0.461375i
\(955\) 34.0644 + 12.9184i 1.10230 + 0.418030i
\(956\) 0 0
\(957\) 55.8752 + 5.77923i 1.80619 + 0.186816i
\(958\) −42.3620 −1.36865
\(959\) −9.19239 0.371058i −0.296838 0.0119821i
\(960\) 1.73861 3.46081i 0.0561135 0.111697i
\(961\) 6.45445 11.1794i 0.208208 0.360627i
\(962\) −2.40890 + 1.39078i −0.0776661 + 0.0448406i
\(963\) −16.0838 3.36311i −0.518294 0.108375i
\(964\) 18.4545 + 10.6547i 0.594378 + 0.343164i
\(965\) −12.7279 + 10.3923i −0.409726 + 0.334540i
\(966\) 12.6927 16.1199i 0.408382 0.518649i
\(967\) 7.23690i 0.232723i 0.993207 + 0.116361i \(0.0371231\pi\)
−0.993207 + 0.116361i \(0.962877\pi\)
\(968\) 5.47723 9.48683i 0.176045 0.304918i
\(969\) −4.59402 + 6.34519i −0.147581 + 0.203837i
\(970\) −9.50569 + 25.0654i −0.305209 + 0.804802i
\(971\) 18.8748 32.6922i 0.605723 1.04914i −0.386214 0.922409i \(-0.626217\pi\)
0.991937 0.126733i \(-0.0404492\pi\)
\(972\) 13.4350 7.90569i 0.430929 0.253575i
\(973\) 45.1260 + 28.5402i 1.44667 + 0.914956i
\(974\) 17.0349i 0.545832i
\(975\) −2.71150 + 8.63018i −0.0868376 + 0.276387i
\(976\) −3.00000 + 1.73205i −0.0960277 + 0.0554416i
\(977\) −1.95445 3.38521i −0.0625284 0.108302i 0.833067 0.553173i \(-0.186583\pi\)
−0.895595 + 0.444870i \(0.853250\pi\)
\(978\) 2.61895 25.3208i 0.0837448 0.809669i
\(979\) 23.0414i 0.736407i
\(980\) −6.71181 + 14.1404i −0.214401 + 0.451699i
\(981\) 40.8634 45.6866i 1.30467 1.45866i
\(982\) −11.9886 6.92163i −0.382572 0.220878i
\(983\) −45.7158 + 26.3941i −1.45811 + 0.841840i −0.998918 0.0464984i \(-0.985194\pi\)
−0.459190 + 0.888338i \(0.651860\pi\)
\(984\) 1.06101 1.46545i 0.0338238 0.0467169i
\(985\) 19.8640 3.22848i 0.632918 0.102868i
\(986\) −21.8881 −0.697059
\(987\) 7.34757 50.8836i 0.233876 1.61964i
\(988\) 1.49395i 0.0475290i
\(989\) −26.8378 15.4948i −0.853394 0.492707i
\(990\) 27.9002 14.4752i 0.886726 0.460051i
\(991\) −5.26139 9.11299i −0.167133 0.289484i 0.770277 0.637709i \(-0.220118\pi\)
−0.937411 + 0.348225i \(0.886784\pi\)
\(992\) 5.73861 + 3.31319i 0.182201 + 0.105194i
\(993\) 15.1545 + 33.8865i 0.480913 + 1.07535i
\(994\) −16.2158 + 8.50934i −0.514335 + 0.269900i
\(995\) 26.8634 21.9338i 0.851626 0.695349i
\(996\) 0.724861 7.00816i 0.0229681 0.222062i
\(997\) −7.74597 13.4164i −0.245317 0.424902i 0.716904 0.697172i \(-0.245559\pi\)
−0.962221 + 0.272270i \(0.912225\pi\)
\(998\) −0.954451 1.65316i −0.0302126 0.0523298i
\(999\) 9.30964 + 10.2367i 0.294544 + 0.323875i
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 210.2.t.e.89.3 yes 8
3.2 odd 2 210.2.t.f.89.1 yes 8
5.2 odd 4 1050.2.s.i.551.1 16
5.3 odd 4 1050.2.s.i.551.8 16
5.4 even 2 210.2.t.f.89.2 yes 8
7.2 even 3 1470.2.d.f.1469.7 8
7.3 odd 6 inner 210.2.t.e.59.4 yes 8
7.5 odd 6 1470.2.d.f.1469.2 8
15.2 even 4 1050.2.s.i.551.7 16
15.8 even 4 1050.2.s.i.551.2 16
15.14 odd 2 inner 210.2.t.e.89.4 yes 8
21.2 odd 6 1470.2.d.e.1469.6 8
21.5 even 6 1470.2.d.e.1469.3 8
21.17 even 6 210.2.t.f.59.2 yes 8
35.3 even 12 1050.2.s.i.101.2 16
35.9 even 6 1470.2.d.e.1469.2 8
35.17 even 12 1050.2.s.i.101.7 16
35.19 odd 6 1470.2.d.e.1469.7 8
35.24 odd 6 210.2.t.f.59.1 yes 8
105.17 odd 12 1050.2.s.i.101.1 16
105.38 odd 12 1050.2.s.i.101.8 16
105.44 odd 6 1470.2.d.f.1469.3 8
105.59 even 6 inner 210.2.t.e.59.3 8
105.89 even 6 1470.2.d.f.1469.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.t.e.59.3 8 105.59 even 6 inner
210.2.t.e.59.4 yes 8 7.3 odd 6 inner
210.2.t.e.89.3 yes 8 1.1 even 1 trivial
210.2.t.e.89.4 yes 8 15.14 odd 2 inner
210.2.t.f.59.1 yes 8 35.24 odd 6
210.2.t.f.59.2 yes 8 21.17 even 6
210.2.t.f.89.1 yes 8 3.2 odd 2
210.2.t.f.89.2 yes 8 5.4 even 2
1050.2.s.i.101.1 16 105.17 odd 12
1050.2.s.i.101.2 16 35.3 even 12
1050.2.s.i.101.7 16 35.17 even 12
1050.2.s.i.101.8 16 105.38 odd 12
1050.2.s.i.551.1 16 5.2 odd 4
1050.2.s.i.551.2 16 15.8 even 4
1050.2.s.i.551.7 16 15.2 even 4
1050.2.s.i.551.8 16 5.3 odd 4
1470.2.d.e.1469.2 8 35.9 even 6
1470.2.d.e.1469.3 8 21.5 even 6
1470.2.d.e.1469.6 8 21.2 odd 6
1470.2.d.e.1469.7 8 35.19 odd 6
1470.2.d.f.1469.2 8 7.5 odd 6
1470.2.d.f.1469.3 8 105.44 odd 6
1470.2.d.f.1469.6 8 105.89 even 6
1470.2.d.f.1469.7 8 7.2 even 3