Properties

Label 75.3.k.a.37.5
Level $75$
Weight $3$
Character 75.37
Analytic conductor $2.044$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,3,Mod(13,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.13");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.k (of order \(20\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.04360198270\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 37.5
Character \(\chi\) \(=\) 75.37
Dual form 75.3.k.a.73.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0337531 + 0.213109i) q^{2} +(1.54327 + 0.786335i) q^{3} +(3.75995 - 1.22168i) q^{4} +(-2.09142 - 4.54158i) q^{5} +(-0.115485 + 0.355426i) q^{6} +(2.53517 + 2.53517i) q^{7} +(0.779083 + 1.52904i) q^{8} +(1.76336 + 2.42705i) q^{9} +O(q^{10})\) \(q+(0.0337531 + 0.213109i) q^{2} +(1.54327 + 0.786335i) q^{3} +(3.75995 - 1.22168i) q^{4} +(-2.09142 - 4.54158i) q^{5} +(-0.115485 + 0.355426i) q^{6} +(2.53517 + 2.53517i) q^{7} +(0.779083 + 1.52904i) q^{8} +(1.76336 + 2.42705i) q^{9} +(0.897260 - 0.598992i) q^{10} +(-2.33076 - 1.69340i) q^{11} +(6.76326 + 1.07120i) q^{12} +(-2.20044 + 13.8930i) q^{13} +(-0.454698 + 0.625838i) q^{14} +(0.343588 - 8.65344i) q^{15} +(12.4941 - 9.07747i) q^{16} +(1.71203 - 0.872322i) q^{17} +(-0.457707 + 0.457707i) q^{18} +(-19.5166 - 6.34131i) q^{19} +(-13.4120 - 14.5211i) q^{20} +(1.91896 + 5.90595i) q^{21} +(0.282208 - 0.553864i) q^{22} +(-25.3336 + 4.01245i) q^{23} +2.97233i q^{24} +(-16.2520 + 18.9967i) q^{25} -3.03499 q^{26} +(0.812857 + 5.13218i) q^{27} +(12.6293 + 6.43495i) q^{28} +(-44.5241 + 14.4668i) q^{29} +(1.85572 - 0.218859i) q^{30} +(10.3207 - 31.7640i) q^{31} +(7.21000 + 7.21000i) q^{32} +(-2.26541 - 4.44613i) q^{33} +(0.243686 + 0.335405i) q^{34} +(6.21160 - 16.8158i) q^{35} +(9.59521 + 6.97133i) q^{36} +(43.7173 + 6.92413i) q^{37} +(0.692645 - 4.37319i) q^{38} +(-14.3204 + 19.7104i) q^{39} +(5.31486 - 6.73612i) q^{40} +(39.3860 - 28.6156i) q^{41} +(-1.19384 + 0.608292i) q^{42} +(-28.7978 + 28.7978i) q^{43} +(-10.8323 - 3.51964i) q^{44} +(7.33474 - 13.0844i) q^{45} +(-1.71018 - 5.26339i) q^{46} +(2.73434 - 5.36644i) q^{47} +(26.4196 - 4.18446i) q^{48} -36.1458i q^{49} +(-4.59692 - 2.82224i) q^{50} +3.32806 q^{51} +(8.69930 + 54.9252i) q^{52} +(74.3421 + 37.8792i) q^{53} +(-1.06628 + 0.346454i) q^{54} +(-2.81611 + 14.1269i) q^{55} +(-1.90126 + 5.85149i) q^{56} +(-25.1329 - 25.1329i) q^{57} +(-4.58582 - 9.00019i) q^{58} +(36.4952 + 50.2313i) q^{59} +(-9.27987 - 32.9562i) q^{60} +(-38.7829 - 28.1774i) q^{61} +(7.11755 + 1.12731i) q^{62} +(-1.68258 + 10.6234i) q^{63} +(35.0167 - 48.1964i) q^{64} +(67.6982 - 19.0626i) q^{65} +(0.871044 - 0.632851i) q^{66} +(21.6869 - 11.0500i) q^{67} +(5.37144 - 5.37144i) q^{68} +(-42.2517 - 13.7284i) q^{69} +(3.79326 + 0.756161i) q^{70} +(23.2547 + 71.5705i) q^{71} +(-2.33725 + 4.58711i) q^{72} +(-76.2776 + 12.0812i) q^{73} +9.55025i q^{74} +(-40.0189 + 16.5375i) q^{75} -81.1283 q^{76} +(-1.61583 - 10.2019i) q^{77} +(-4.68381 - 2.38652i) q^{78} +(16.4271 - 5.33748i) q^{79} +(-67.3564 - 37.7581i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(7.42765 + 7.42765i) q^{82} +(1.17541 + 2.30687i) q^{83} +(14.4304 + 19.8617i) q^{84} +(-7.54228 - 5.95093i) q^{85} +(-7.10909 - 5.16506i) q^{86} +(-80.0884 - 12.6848i) q^{87} +(0.773410 - 4.88312i) q^{88} +(36.0968 - 49.6829i) q^{89} +(3.03597 + 1.12146i) q^{90} +(-40.7997 + 29.6427i) q^{91} +(-90.3512 + 46.0362i) q^{92} +(40.9048 - 40.9048i) q^{93} +(1.23593 + 0.401578i) q^{94} +(12.0176 + 101.898i) q^{95} +(5.45750 + 16.7965i) q^{96} +(62.8839 - 123.417i) q^{97} +(7.70299 - 1.22003i) q^{98} -8.64294i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{9}{20}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0337531 + 0.213109i 0.0168766 + 0.106554i 0.994689 0.102929i \(-0.0328216\pi\)
−0.977812 + 0.209484i \(0.932822\pi\)
\(3\) 1.54327 + 0.786335i 0.514423 + 0.262112i
\(4\) 3.75995 1.22168i 0.939987 0.305420i
\(5\) −2.09142 4.54158i −0.418283 0.908317i
\(6\) −0.115485 + 0.355426i −0.0192475 + 0.0592376i
\(7\) 2.53517 + 2.53517i 0.362168 + 0.362168i 0.864610 0.502443i \(-0.167565\pi\)
−0.502443 + 0.864610i \(0.667565\pi\)
\(8\) 0.779083 + 1.52904i 0.0973854 + 0.191130i
\(9\) 1.76336 + 2.42705i 0.195928 + 0.269672i
\(10\) 0.897260 0.598992i 0.0897260 0.0598992i
\(11\) −2.33076 1.69340i −0.211887 0.153945i 0.476780 0.879023i \(-0.341804\pi\)
−0.688667 + 0.725078i \(0.741804\pi\)
\(12\) 6.76326 + 1.07120i 0.563605 + 0.0892663i
\(13\) −2.20044 + 13.8930i −0.169264 + 1.06869i 0.746032 + 0.665910i \(0.231957\pi\)
−0.915296 + 0.402782i \(0.868043\pi\)
\(14\) −0.454698 + 0.625838i −0.0324784 + 0.0447027i
\(15\) 0.343588 8.65344i 0.0229058 0.576896i
\(16\) 12.4941 9.07747i 0.780879 0.567342i
\(17\) 1.71203 0.872322i 0.100708 0.0513130i −0.402911 0.915239i \(-0.632002\pi\)
0.503619 + 0.863926i \(0.332002\pi\)
\(18\) −0.457707 + 0.457707i −0.0254282 + 0.0254282i
\(19\) −19.5166 6.34131i −1.02719 0.333753i −0.253509 0.967333i \(-0.581585\pi\)
−0.773677 + 0.633580i \(0.781585\pi\)
\(20\) −13.4120 14.5211i −0.670599 0.726054i
\(21\) 1.91896 + 5.90595i 0.0913790 + 0.281236i
\(22\) 0.282208 0.553864i 0.0128276 0.0251756i
\(23\) −25.3336 + 4.01245i −1.10146 + 0.174454i −0.680589 0.732665i \(-0.738276\pi\)
−0.420872 + 0.907120i \(0.638276\pi\)
\(24\) 2.97233i 0.123847i
\(25\) −16.2520 + 18.9967i −0.650078 + 0.759867i
\(26\) −3.03499 −0.116731
\(27\) 0.812857 + 5.13218i 0.0301058 + 0.190081i
\(28\) 12.6293 + 6.43495i 0.451047 + 0.229820i
\(29\) −44.5241 + 14.4668i −1.53531 + 0.498854i −0.950079 0.312010i \(-0.898998\pi\)
−0.585235 + 0.810864i \(0.698998\pi\)
\(30\) 1.85572 0.218859i 0.0618574 0.00729530i
\(31\) 10.3207 31.7640i 0.332927 1.02464i −0.634807 0.772671i \(-0.718920\pi\)
0.967734 0.251974i \(-0.0810797\pi\)
\(32\) 7.21000 + 7.21000i 0.225313 + 0.225313i
\(33\) −2.26541 4.44613i −0.0686489 0.134731i
\(34\) 0.243686 + 0.335405i 0.00716723 + 0.00986485i
\(35\) 6.21160 16.8158i 0.177474 0.480452i
\(36\) 9.59521 + 6.97133i 0.266534 + 0.193648i
\(37\) 43.7173 + 6.92413i 1.18155 + 0.187139i 0.716139 0.697957i \(-0.245908\pi\)
0.465408 + 0.885096i \(0.345908\pi\)
\(38\) 0.692645 4.37319i 0.0182275 0.115084i
\(39\) −14.3204 + 19.7104i −0.367190 + 0.505394i
\(40\) 5.31486 6.73612i 0.132872 0.168403i
\(41\) 39.3860 28.6156i 0.960635 0.697942i 0.00733688 0.999973i \(-0.497665\pi\)
0.953298 + 0.302031i \(0.0976646\pi\)
\(42\) −1.19384 + 0.608292i −0.0284248 + 0.0144831i
\(43\) −28.7978 + 28.7978i −0.669717 + 0.669717i −0.957650 0.287934i \(-0.907032\pi\)
0.287934 + 0.957650i \(0.407032\pi\)
\(44\) −10.8323 3.51964i −0.246190 0.0799918i
\(45\) 7.33474 13.0844i 0.162994 0.290764i
\(46\) −1.71018 5.26339i −0.0371778 0.114421i
\(47\) 2.73434 5.36644i 0.0581774 0.114180i −0.860087 0.510147i \(-0.829591\pi\)
0.918264 + 0.395968i \(0.129591\pi\)
\(48\) 26.4196 4.18446i 0.550409 0.0871762i
\(49\) 36.1458i 0.737669i
\(50\) −4.59692 2.82224i −0.0919383 0.0564448i
\(51\) 3.32806 0.0652560
\(52\) 8.69930 + 54.9252i 0.167294 + 1.05625i
\(53\) 74.3421 + 37.8792i 1.40268 + 0.714702i 0.981354 0.192207i \(-0.0615647\pi\)
0.421326 + 0.906909i \(0.361565\pi\)
\(54\) −1.06628 + 0.346454i −0.0197459 + 0.00641582i
\(55\) −2.81611 + 14.1269i −0.0512021 + 0.256854i
\(56\) −1.90126 + 5.85149i −0.0339511 + 0.104491i
\(57\) −25.1329 25.1329i −0.440928 0.440928i
\(58\) −4.58582 9.00019i −0.0790659 0.155176i
\(59\) 36.4952 + 50.2313i 0.618563 + 0.851378i 0.997247 0.0741474i \(-0.0236235\pi\)
−0.378685 + 0.925526i \(0.623624\pi\)
\(60\) −9.27987 32.9562i −0.154665 0.549271i
\(61\) −38.7829 28.1774i −0.635785 0.461925i 0.222614 0.974907i \(-0.428541\pi\)
−0.858400 + 0.512981i \(0.828541\pi\)
\(62\) 7.11755 + 1.12731i 0.114799 + 0.0181824i
\(63\) −1.68258 + 10.6234i −0.0267077 + 0.168626i
\(64\) 35.0167 48.1964i 0.547136 0.753068i
\(65\) 67.6982 19.0626i 1.04151 0.293271i
\(66\) 0.871044 0.632851i 0.0131976 0.00958865i
\(67\) 21.6869 11.0500i 0.323685 0.164926i −0.284596 0.958648i \(-0.591859\pi\)
0.608281 + 0.793722i \(0.291859\pi\)
\(68\) 5.37144 5.37144i 0.0789917 0.0789917i
\(69\) −42.2517 13.7284i −0.612343 0.198962i
\(70\) 3.79326 + 0.756161i 0.0541894 + 0.0108023i
\(71\) 23.2547 + 71.5705i 0.327530 + 1.00803i 0.970285 + 0.241963i \(0.0777912\pi\)
−0.642755 + 0.766072i \(0.722209\pi\)
\(72\) −2.33725 + 4.58711i −0.0324618 + 0.0637099i
\(73\) −76.2776 + 12.0812i −1.04490 + 0.165496i −0.655207 0.755449i \(-0.727419\pi\)
−0.389692 + 0.920945i \(0.627419\pi\)
\(74\) 9.55025i 0.129057i
\(75\) −40.0189 + 16.5375i −0.533585 + 0.220500i
\(76\) −81.1283 −1.06748
\(77\) −1.61583 10.2019i −0.0209848 0.132493i
\(78\) −4.68381 2.38652i −0.0600489 0.0305964i
\(79\) 16.4271 5.33748i 0.207937 0.0675630i −0.203196 0.979138i \(-0.565133\pi\)
0.411134 + 0.911575i \(0.365133\pi\)
\(80\) −67.3564 37.7581i −0.841955 0.471976i
\(81\) −2.78115 + 8.55951i −0.0343352 + 0.105673i
\(82\) 7.42765 + 7.42765i 0.0905811 + 0.0905811i
\(83\) 1.17541 + 2.30687i 0.0141616 + 0.0277937i 0.897979 0.440038i \(-0.145035\pi\)
−0.883817 + 0.467832i \(0.845035\pi\)
\(84\) 14.4304 + 19.8617i 0.171790 + 0.236449i
\(85\) −7.54228 5.95093i −0.0887327 0.0700109i
\(86\) −7.10909 5.16506i −0.0826638 0.0600588i
\(87\) −80.0884 12.6848i −0.920556 0.145802i
\(88\) 0.773410 4.88312i 0.00878875 0.0554900i
\(89\) 36.0968 49.6829i 0.405582 0.558235i −0.556552 0.830813i \(-0.687876\pi\)
0.962134 + 0.272577i \(0.0878761\pi\)
\(90\) 3.03597 + 1.12146i 0.0337330 + 0.0124607i
\(91\) −40.7997 + 29.6427i −0.448348 + 0.325744i
\(92\) −90.3512 + 46.0362i −0.982078 + 0.500394i
\(93\) 40.9048 40.9048i 0.439837 0.439837i
\(94\) 1.23593 + 0.401578i 0.0131482 + 0.00427210i
\(95\) 12.0176 + 101.898i 0.126501 + 1.07261i
\(96\) 5.45750 + 16.7965i 0.0568489 + 0.174963i
\(97\) 62.8839 123.417i 0.648287 1.27234i −0.299702 0.954033i \(-0.596887\pi\)
0.947989 0.318303i \(-0.103113\pi\)
\(98\) 7.70299 1.22003i 0.0786019 0.0124493i
\(99\) 8.64294i 0.0873024i
\(100\) −37.8987 + 91.2813i −0.378987 + 0.912813i
\(101\) 117.114 1.15955 0.579774 0.814777i \(-0.303141\pi\)
0.579774 + 0.814777i \(0.303141\pi\)
\(102\) 0.112332 + 0.709238i 0.00110130 + 0.00695332i
\(103\) −157.167 80.0806i −1.52589 0.777481i −0.528451 0.848964i \(-0.677227\pi\)
−0.997442 + 0.0714822i \(0.977227\pi\)
\(104\) −22.9572 + 7.45926i −0.220743 + 0.0717236i
\(105\) 22.8090 21.0669i 0.217229 0.200637i
\(106\) −5.56311 + 17.1215i −0.0524822 + 0.161524i
\(107\) −120.454 120.454i −1.12574 1.12574i −0.990863 0.134875i \(-0.956937\pi\)
−0.134875 0.990863i \(-0.543063\pi\)
\(108\) 9.32619 + 18.3037i 0.0863536 + 0.169479i
\(109\) 121.973 + 167.882i 1.11902 + 1.54020i 0.807411 + 0.589990i \(0.200868\pi\)
0.311610 + 0.950210i \(0.399132\pi\)
\(110\) −3.10563 0.123310i −0.0282330 0.00112100i
\(111\) 62.0228 + 45.0622i 0.558764 + 0.405966i
\(112\) 54.6876 + 8.66166i 0.488282 + 0.0773363i
\(113\) 28.0172 176.894i 0.247940 1.56543i −0.478430 0.878126i \(-0.658794\pi\)
0.726370 0.687304i \(-0.241206\pi\)
\(114\) 4.50773 6.20436i 0.0395415 0.0544242i
\(115\) 71.2060 + 106.663i 0.619183 + 0.927504i
\(116\) −149.735 + 108.789i −1.29082 + 0.937833i
\(117\) −37.5992 + 19.1577i −0.321360 + 0.163741i
\(118\) −9.47292 + 9.47292i −0.0802790 + 0.0802790i
\(119\) 6.55178 + 2.12880i 0.0550569 + 0.0178891i
\(120\) 13.4991 6.21639i 0.112493 0.0518032i
\(121\) −34.8262 107.184i −0.287820 0.885818i
\(122\) 4.69582 9.21606i 0.0384903 0.0755415i
\(123\) 83.2847 13.1910i 0.677111 0.107244i
\(124\) 132.040i 1.06484i
\(125\) 120.265 + 34.0797i 0.962117 + 0.272637i
\(126\) −2.32074 −0.0184185
\(127\) 17.1715 + 108.416i 0.135208 + 0.853673i 0.958300 + 0.285764i \(0.0922474\pi\)
−0.823092 + 0.567909i \(0.807753\pi\)
\(128\) 47.7935 + 24.3520i 0.373387 + 0.190250i
\(129\) −67.0875 + 21.7981i −0.520058 + 0.168977i
\(130\) 6.34744 + 13.7837i 0.0488264 + 0.106028i
\(131\) −5.96636 + 18.3626i −0.0455448 + 0.140172i −0.971243 0.238091i \(-0.923478\pi\)
0.925698 + 0.378263i \(0.123478\pi\)
\(132\) −13.9496 13.9496i −0.105679 0.105679i
\(133\) −33.4015 65.5542i −0.251139 0.492889i
\(134\) 3.08686 + 4.24870i 0.0230363 + 0.0317067i
\(135\) 21.6082 14.4252i 0.160061 0.106853i
\(136\) 2.66762 + 1.93814i 0.0196149 + 0.0142510i
\(137\) 71.9737 + 11.3995i 0.525355 + 0.0832081i 0.413478 0.910514i \(-0.364314\pi\)
0.111877 + 0.993722i \(0.464314\pi\)
\(138\) 1.49952 9.46759i 0.0108661 0.0686057i
\(139\) 134.161 184.657i 0.965187 1.32847i 0.0207459 0.999785i \(-0.493396\pi\)
0.944441 0.328681i \(-0.106604\pi\)
\(140\) 2.81174 70.8152i 0.0200839 0.505823i
\(141\) 8.43964 6.13176i 0.0598556 0.0434876i
\(142\) −14.4674 + 7.37150i −0.101883 + 0.0519120i
\(143\) 28.6551 28.6551i 0.200385 0.200385i
\(144\) 44.0630 + 14.3169i 0.305993 + 0.0994231i
\(145\) 158.820 + 171.954i 1.09531 + 1.18589i
\(146\) −5.14922 15.8477i −0.0352686 0.108546i
\(147\) 28.4227 55.7827i 0.193352 0.379474i
\(148\) 172.834 27.3742i 1.16780 0.184961i
\(149\) 104.646i 0.702319i 0.936316 + 0.351159i \(0.114212\pi\)
−0.936316 + 0.351159i \(0.885788\pi\)
\(150\) −4.87505 7.97019i −0.0325003 0.0531346i
\(151\) −1.36040 −0.00900927 −0.00450463 0.999990i \(-0.501434\pi\)
−0.00450463 + 0.999990i \(0.501434\pi\)
\(152\) −5.50892 34.7819i −0.0362429 0.228828i
\(153\) 5.13608 + 2.61697i 0.0335692 + 0.0171043i
\(154\) 2.11959 0.688695i 0.0137635 0.00447205i
\(155\) −165.844 + 19.5592i −1.06996 + 0.126188i
\(156\) −29.7642 + 91.6049i −0.190796 + 0.587211i
\(157\) −68.3515 68.3515i −0.435360 0.435360i 0.455087 0.890447i \(-0.349608\pi\)
−0.890447 + 0.455087i \(0.849608\pi\)
\(158\) 1.69193 + 3.32060i 0.0107084 + 0.0210164i
\(159\) 84.9441 + 116.916i 0.534240 + 0.735318i
\(160\) 17.6657 47.8240i 0.110411 0.298900i
\(161\) −74.3974 54.0529i −0.462095 0.335732i
\(162\) −1.91798 0.303778i −0.0118394 0.00187517i
\(163\) −17.7253 + 111.913i −0.108744 + 0.686585i 0.871737 + 0.489974i \(0.162994\pi\)
−0.980482 + 0.196611i \(0.937006\pi\)
\(164\) 113.130 155.711i 0.689819 0.949455i
\(165\) −15.4545 + 19.5873i −0.0936638 + 0.118711i
\(166\) −0.451942 + 0.328355i −0.00272254 + 0.00197804i
\(167\) −248.652 + 126.694i −1.48893 + 0.758648i −0.993906 0.110230i \(-0.964841\pi\)
−0.495025 + 0.868879i \(0.664841\pi\)
\(168\) −7.53538 + 7.53538i −0.0448535 + 0.0448535i
\(169\) −27.4450 8.91742i −0.162396 0.0527658i
\(170\) 1.01362 1.80819i 0.00596247 0.0106364i
\(171\) −19.0239 58.5497i −0.111251 0.342396i
\(172\) −73.0966 + 143.460i −0.424980 + 0.834071i
\(173\) −77.8868 + 12.3361i −0.450213 + 0.0713067i −0.377424 0.926041i \(-0.623190\pi\)
−0.0727890 + 0.997347i \(0.523190\pi\)
\(174\) 17.4957i 0.100550i
\(175\) −89.3614 + 6.95835i −0.510637 + 0.0397620i
\(176\) −44.4924 −0.252798
\(177\) 16.8233 + 106.218i 0.0950466 + 0.600101i
\(178\) 11.8063 + 6.01559i 0.0663273 + 0.0337954i
\(179\) −270.618 + 87.9292i −1.51183 + 0.491225i −0.943443 0.331534i \(-0.892434\pi\)
−0.568391 + 0.822759i \(0.692434\pi\)
\(180\) 11.5933 58.1574i 0.0644072 0.323097i
\(181\) −18.8719 + 58.0816i −0.104264 + 0.320893i −0.989557 0.144141i \(-0.953958\pi\)
0.885293 + 0.465034i \(0.153958\pi\)
\(182\) −7.69424 7.69424i −0.0422760 0.0422760i
\(183\) −37.6956 73.9817i −0.205987 0.404272i
\(184\) −25.8722 35.6100i −0.140610 0.193533i
\(185\) −59.9844 213.027i −0.324240 1.15150i
\(186\) 10.0978 + 7.33651i 0.0542895 + 0.0394436i
\(187\) −5.46752 0.865969i −0.0292381 0.00463085i
\(188\) 3.72489 23.5180i 0.0198133 0.125096i
\(189\) −10.9502 + 15.0717i −0.0579377 + 0.0797445i
\(190\) −21.3098 + 6.00045i −0.112157 + 0.0315813i
\(191\) −12.2266 + 8.88315i −0.0640136 + 0.0465086i −0.619332 0.785129i \(-0.712596\pi\)
0.555318 + 0.831638i \(0.312596\pi\)
\(192\) 91.9387 46.8451i 0.478847 0.243985i
\(193\) −32.8943 + 32.8943i −0.170437 + 0.170437i −0.787171 0.616734i \(-0.788455\pi\)
0.616734 + 0.787171i \(0.288455\pi\)
\(194\) 28.4237 + 9.23542i 0.146514 + 0.0476052i
\(195\) 119.466 + 23.8148i 0.612647 + 0.122127i
\(196\) −44.1586 135.906i −0.225299 0.693400i
\(197\) 58.7884 115.379i 0.298419 0.585679i −0.692300 0.721610i \(-0.743402\pi\)
0.990718 + 0.135931i \(0.0434024\pi\)
\(198\) 1.84189 0.291726i 0.00930246 0.00147337i
\(199\) 29.2447i 0.146958i 0.997297 + 0.0734791i \(0.0234102\pi\)
−0.997297 + 0.0734791i \(0.976590\pi\)
\(200\) −41.7082 10.0498i −0.208541 0.0502492i
\(201\) 42.1578 0.209740
\(202\) 3.95298 + 24.9581i 0.0195692 + 0.123555i
\(203\) −149.552 76.2006i −0.736710 0.375372i
\(204\) 12.5133 4.06582i 0.0613398 0.0199305i
\(205\) −212.333 119.028i −1.03577 0.580623i
\(206\) 11.7610 36.1967i 0.0570923 0.175712i
\(207\) −54.4106 54.4106i −0.262853 0.262853i
\(208\) 98.6209 + 193.554i 0.474139 + 0.930550i
\(209\) 34.7501 + 47.8294i 0.166268 + 0.228849i
\(210\) 5.25942 + 4.14973i 0.0250449 + 0.0197606i
\(211\) 95.9540 + 69.7146i 0.454758 + 0.330401i 0.791471 0.611206i \(-0.209315\pi\)
−0.336713 + 0.941607i \(0.609315\pi\)
\(212\) 325.799 + 51.6015i 1.53679 + 0.243403i
\(213\) −20.3902 + 128.738i −0.0957284 + 0.604405i
\(214\) 21.6041 29.7355i 0.100954 0.138951i
\(215\) 191.016 + 70.5595i 0.888446 + 0.328184i
\(216\) −7.21401 + 5.24128i −0.0333982 + 0.0242652i
\(217\) 106.692 54.3624i 0.491669 0.250518i
\(218\) −31.6601 + 31.6601i −0.145230 + 0.145230i
\(219\) −127.217 41.3352i −0.580898 0.188745i
\(220\) 6.67019 + 56.5570i 0.0303190 + 0.257077i
\(221\) 8.35196 + 25.7047i 0.0377917 + 0.116311i
\(222\) −7.50969 + 14.7386i −0.0338274 + 0.0663901i
\(223\) −73.2435 + 11.6006i −0.328446 + 0.0520208i −0.318480 0.947930i \(-0.603172\pi\)
−0.00996615 + 0.999950i \(0.503172\pi\)
\(224\) 36.5572i 0.163202i
\(225\) −74.7639 5.94643i −0.332284 0.0264286i
\(226\) 38.6433 0.170988
\(227\) −17.6629 111.519i −0.0778100 0.491273i −0.995561 0.0941170i \(-0.969997\pi\)
0.917751 0.397156i \(-0.130003\pi\)
\(228\) −125.203 63.7940i −0.549135 0.279798i
\(229\) −271.915 + 88.3506i −1.18740 + 0.385810i −0.835112 0.550080i \(-0.814597\pi\)
−0.352291 + 0.935891i \(0.614597\pi\)
\(230\) −20.3274 + 18.7748i −0.0883801 + 0.0816298i
\(231\) 5.52848 17.0149i 0.0239328 0.0736577i
\(232\) −56.8082 56.8082i −0.244863 0.244863i
\(233\) 109.169 + 214.256i 0.468536 + 0.919554i 0.997483 + 0.0708996i \(0.0225870\pi\)
−0.528947 + 0.848655i \(0.677413\pi\)
\(234\) −5.35177 7.36609i −0.0228708 0.0314790i
\(235\) −30.0908 1.19476i −0.128046 0.00508411i
\(236\) 198.587 + 144.282i 0.841469 + 0.611363i
\(237\) 29.5484 + 4.68001i 0.124677 + 0.0197469i
\(238\) −0.232523 + 1.46810i −0.000976989 + 0.00616847i
\(239\) 56.3018 77.4928i 0.235572 0.324238i −0.674821 0.737982i \(-0.735779\pi\)
0.910393 + 0.413744i \(0.135779\pi\)
\(240\) −74.2585 111.235i −0.309410 0.463481i
\(241\) 230.619 167.554i 0.956923 0.695246i 0.00448928 0.999990i \(-0.498571\pi\)
0.952434 + 0.304744i \(0.0985710\pi\)
\(242\) 21.6664 11.0396i 0.0895305 0.0456181i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) −180.246 58.5654i −0.738712 0.240022i
\(245\) −164.159 + 75.5959i −0.670037 + 0.308555i
\(246\) 5.62224 + 17.3035i 0.0228546 + 0.0703393i
\(247\) 131.045 257.190i 0.530546 1.04125i
\(248\) 56.6090 8.96599i 0.228262 0.0361532i
\(249\) 4.48439i 0.0180096i
\(250\) −3.20337 + 26.7798i −0.0128135 + 0.107119i
\(251\) 202.225 0.805679 0.402839 0.915271i \(-0.368023\pi\)
0.402839 + 0.915271i \(0.368023\pi\)
\(252\) 6.65200 + 41.9991i 0.0263968 + 0.166663i
\(253\) 65.8413 + 33.5478i 0.260242 + 0.132600i
\(254\) −22.5249 + 7.31879i −0.0886808 + 0.0288141i
\(255\) −6.96035 15.1146i −0.0272955 0.0592731i
\(256\) 70.0611 215.626i 0.273676 0.842288i
\(257\) 332.082 + 332.082i 1.29215 + 1.29215i 0.933456 + 0.358692i \(0.116777\pi\)
0.358692 + 0.933456i \(0.383223\pi\)
\(258\) −6.90977 13.5612i −0.0267821 0.0525628i
\(259\) 93.2770 + 128.385i 0.360143 + 0.495694i
\(260\) 231.254 154.380i 0.889437 0.593770i
\(261\) −113.623 82.5522i −0.435339 0.316292i
\(262\) −4.11461 0.651691i −0.0157046 0.00248737i
\(263\) −46.8408 + 295.741i −0.178102 + 1.12449i 0.722989 + 0.690860i \(0.242768\pi\)
−0.901091 + 0.433631i \(0.857232\pi\)
\(264\) 5.03334 6.92780i 0.0190657 0.0262417i
\(265\) 16.5512 416.852i 0.0624575 1.57303i
\(266\) 12.8428 9.33082i 0.0482811 0.0350783i
\(267\) 94.7744 48.2900i 0.354960 0.180861i
\(268\) 68.0421 68.0421i 0.253889 0.253889i
\(269\) −158.418 51.4731i −0.588914 0.191350i −0.000623854 1.00000i \(-0.500199\pi\)
−0.588290 + 0.808650i \(0.700199\pi\)
\(270\) 3.80348 + 4.11800i 0.0140870 + 0.0152519i
\(271\) 115.087 + 354.200i 0.424674 + 1.30701i 0.903306 + 0.428997i \(0.141133\pi\)
−0.478632 + 0.878016i \(0.658867\pi\)
\(272\) 13.4717 26.4397i 0.0495283 0.0972048i
\(273\) −86.2739 + 13.6644i −0.316022 + 0.0500529i
\(274\) 15.7230i 0.0573832i
\(275\) 70.0484 16.7557i 0.254721 0.0609298i
\(276\) −175.636 −0.636362
\(277\) 47.7149 + 301.260i 0.172256 + 1.08758i 0.910640 + 0.413201i \(0.135589\pi\)
−0.738384 + 0.674381i \(0.764411\pi\)
\(278\) 43.8804 + 22.3582i 0.157843 + 0.0804250i
\(279\) 95.2920 30.9622i 0.341548 0.110976i
\(280\) 30.5513 3.60315i 0.109112 0.0128684i
\(281\) 125.676 386.790i 0.447245 1.37648i −0.432758 0.901510i \(-0.642460\pi\)
0.880003 0.474968i \(-0.157540\pi\)
\(282\) 1.59160 + 1.59160i 0.00564396 + 0.00564396i
\(283\) −70.9340 139.216i −0.250650 0.491929i 0.731059 0.682314i \(-0.239026\pi\)
−0.981709 + 0.190385i \(0.939026\pi\)
\(284\) 174.873 + 240.692i 0.615749 + 0.847505i
\(285\) −61.5798 + 166.706i −0.216069 + 0.584935i
\(286\) 7.07385 + 5.13945i 0.0247337 + 0.0179701i
\(287\) 172.396 + 27.3049i 0.600683 + 0.0951389i
\(288\) −4.78525 + 30.2129i −0.0166154 + 0.104906i
\(289\) −167.700 + 230.819i −0.580276 + 0.798682i
\(290\) −31.2842 + 39.6500i −0.107877 + 0.136724i
\(291\) 194.093 141.017i 0.666988 0.484595i
\(292\) −272.041 + 138.612i −0.931646 + 0.474698i
\(293\) 24.2992 24.2992i 0.0829323 0.0829323i −0.664424 0.747356i \(-0.731323\pi\)
0.747356 + 0.664424i \(0.231323\pi\)
\(294\) 12.8471 + 4.17429i 0.0436977 + 0.0141983i
\(295\) 151.803 270.801i 0.514587 0.917968i
\(296\) 23.4721 + 72.2398i 0.0792977 + 0.244053i
\(297\) 6.79624 13.3384i 0.0228830 0.0449104i
\(298\) −22.3009 + 3.53211i −0.0748352 + 0.0118527i
\(299\) 360.789i 1.20665i
\(300\) −130.265 + 111.071i −0.434218 + 0.370235i
\(301\) −146.015 −0.485100
\(302\) −0.0459177 0.289913i −0.000152045 0.000959977i
\(303\) 180.739 + 92.0911i 0.596498 + 0.303931i
\(304\) −301.404 + 97.9321i −0.991461 + 0.322145i
\(305\) −46.8590 + 235.067i −0.153636 + 0.770710i
\(306\) −0.384340 + 1.18288i −0.00125601 + 0.00386561i
\(307\) −122.601 122.601i −0.399353 0.399353i 0.478652 0.878005i \(-0.341126\pi\)
−0.878005 + 0.478652i \(0.841126\pi\)
\(308\) −18.5390 36.3848i −0.0601914 0.118132i
\(309\) −179.581 247.172i −0.581167 0.799908i
\(310\) −9.76599 34.6826i −0.0315032 0.111879i
\(311\) −480.225 348.904i −1.54413 1.12188i −0.947677 0.319231i \(-0.896576\pi\)
−0.596455 0.802647i \(-0.703424\pi\)
\(312\) −41.2946 6.54043i −0.132355 0.0209629i
\(313\) −16.9010 + 106.708i −0.0539967 + 0.340922i 0.945869 + 0.324548i \(0.105212\pi\)
−0.999866 + 0.0163737i \(0.994788\pi\)
\(314\) 12.2592 16.8734i 0.0390422 0.0537369i
\(315\) 51.7661 14.5764i 0.164337 0.0462742i
\(316\) 55.2442 40.1373i 0.174824 0.127017i
\(317\) −238.066 + 121.300i −0.750995 + 0.382651i −0.787204 0.616693i \(-0.788472\pi\)
0.0362084 + 0.999344i \(0.488472\pi\)
\(318\) −22.0486 + 22.0486i −0.0693352 + 0.0693352i
\(319\) 128.273 + 41.6784i 0.402110 + 0.130653i
\(320\) −292.122 58.2327i −0.912882 0.181977i
\(321\) −91.1757 280.610i −0.284036 0.874174i
\(322\) 9.00800 17.6792i 0.0279752 0.0549043i
\(323\) −38.9445 + 6.16821i −0.120571 + 0.0190966i
\(324\) 35.5810i 0.109818i
\(325\) −228.160 267.589i −0.702029 0.823352i
\(326\) −24.4480 −0.0749939
\(327\) 56.2262 + 354.998i 0.171946 + 1.08562i
\(328\) 74.4393 + 37.9287i 0.226949 + 0.115636i
\(329\) 20.5369 6.67284i 0.0624222 0.0202822i
\(330\) −4.69586 2.63237i −0.0142299 0.00797687i
\(331\) −178.323 + 548.821i −0.538739 + 1.65807i 0.196689 + 0.980466i \(0.436981\pi\)
−0.735428 + 0.677602i \(0.763019\pi\)
\(332\) 7.23776 + 7.23776i 0.0218005 + 0.0218005i
\(333\) 60.2839 + 118.314i 0.181033 + 0.355296i
\(334\) −35.3925 48.7135i −0.105965 0.145849i
\(335\) −95.5411 75.3827i −0.285197 0.225023i
\(336\) 77.5867 + 56.3700i 0.230913 + 0.167768i
\(337\) −149.729 23.7148i −0.444301 0.0703704i −0.0697244 0.997566i \(-0.522212\pi\)
−0.374577 + 0.927196i \(0.622212\pi\)
\(338\) 0.974027 6.14977i 0.00288174 0.0181946i
\(339\) 182.336 250.963i 0.537863 0.740305i
\(340\) −35.6288 13.1609i −0.104790 0.0387086i
\(341\) −77.8443 + 56.5572i −0.228282 + 0.165857i
\(342\) 11.8353 6.03040i 0.0346062 0.0176328i
\(343\) 215.859 215.859i 0.629328 0.629328i
\(344\) −66.4688 21.5970i −0.193223 0.0627821i
\(345\) 26.0172 + 220.601i 0.0754121 + 0.639424i
\(346\) −5.25785 16.1820i −0.0151961 0.0467688i
\(347\) −160.349 + 314.703i −0.462102 + 0.906926i 0.535933 + 0.844261i \(0.319960\pi\)
−0.998035 + 0.0626654i \(0.980040\pi\)
\(348\) −316.625 + 50.1485i −0.909842 + 0.144105i
\(349\) 385.320i 1.10407i 0.833822 + 0.552034i \(0.186148\pi\)
−0.833822 + 0.552034i \(0.813852\pi\)
\(350\) −4.49911 18.8089i −0.0128546 0.0537396i
\(351\) −73.0900 −0.208234
\(352\) −4.59540 29.0142i −0.0130551 0.0824267i
\(353\) 190.641 + 97.1364i 0.540059 + 0.275174i 0.702669 0.711516i \(-0.251991\pi\)
−0.162610 + 0.986690i \(0.551991\pi\)
\(354\) −22.0681 + 7.17037i −0.0623394 + 0.0202553i
\(355\) 276.408 255.297i 0.778614 0.719145i
\(356\) 75.0253 230.904i 0.210745 0.648607i
\(357\) 8.43720 + 8.43720i 0.0236336 + 0.0236336i
\(358\) −27.8727 54.7033i −0.0778567 0.152802i
\(359\) −121.501 167.232i −0.338443 0.465827i 0.605543 0.795813i \(-0.292956\pi\)
−0.943986 + 0.329986i \(0.892956\pi\)
\(360\) 25.7209 + 1.02126i 0.0714470 + 0.00283683i
\(361\) 48.6284 + 35.3306i 0.134705 + 0.0978687i
\(362\) −13.0147 2.06132i −0.0359522 0.00569427i
\(363\) 30.5363 192.799i 0.0841221 0.531126i
\(364\) −117.191 + 161.299i −0.321953 + 0.443130i
\(365\) 214.396 + 321.154i 0.587386 + 0.879875i
\(366\) 14.4938 10.5304i 0.0396006 0.0287715i
\(367\) 322.659 164.403i 0.879181 0.447965i 0.0446990 0.999000i \(-0.485767\pi\)
0.834482 + 0.551035i \(0.185767\pi\)
\(368\) −280.097 + 280.097i −0.761133 + 0.761133i
\(369\) 138.903 + 45.1324i 0.376431 + 0.122310i
\(370\) 43.3733 19.9735i 0.117225 0.0539826i
\(371\) 92.4398 + 284.500i 0.249164 + 0.766848i
\(372\) 103.827 203.773i 0.279106 0.547776i
\(373\) 126.747 20.0747i 0.339803 0.0538196i 0.0157991 0.999875i \(-0.494971\pi\)
0.324004 + 0.946056i \(0.394971\pi\)
\(374\) 1.19441i 0.00319360i
\(375\) 158.803 + 147.162i 0.423474 + 0.392433i
\(376\) 10.3358 0.0274887
\(377\) −103.014 650.407i −0.273247 1.72522i
\(378\) −3.58152 1.82488i −0.00947492 0.00482771i
\(379\) 427.164 138.794i 1.12708 0.366211i 0.314616 0.949219i \(-0.398124\pi\)
0.812467 + 0.583008i \(0.198124\pi\)
\(380\) 169.673 + 368.451i 0.446508 + 0.969608i
\(381\) −58.7514 + 180.818i −0.154203 + 0.474588i
\(382\) −2.30576 2.30576i −0.00603603 0.00603603i
\(383\) −321.195 630.381i −0.838630 1.64590i −0.760846 0.648933i \(-0.775216\pi\)
−0.0777841 0.996970i \(-0.524784\pi\)
\(384\) 54.6094 + 75.1634i 0.142212 + 0.195738i
\(385\) −42.9536 + 28.6749i −0.111568 + 0.0744803i
\(386\) −8.12036 5.89979i −0.0210372 0.0152844i
\(387\) −120.675 19.1130i −0.311821 0.0493875i
\(388\) 85.6645 540.864i 0.220785 1.39398i
\(389\) −16.8577 + 23.2027i −0.0433361 + 0.0596470i −0.830135 0.557562i \(-0.811737\pi\)
0.786799 + 0.617209i \(0.211737\pi\)
\(390\) −1.04279 + 26.2631i −0.00267381 + 0.0673413i
\(391\) −39.8717 + 28.9685i −0.101974 + 0.0740882i
\(392\) 55.2682 28.1606i 0.140990 0.0718382i
\(393\) −23.6468 + 23.6468i −0.0601700 + 0.0601700i
\(394\) 26.5726 + 8.63395i 0.0674430 + 0.0219136i
\(395\) −58.5964 63.4420i −0.148345 0.160613i
\(396\) −10.5589 32.4970i −0.0266639 0.0820632i
\(397\) −33.0237 + 64.8126i −0.0831831 + 0.163256i −0.928851 0.370453i \(-0.879202\pi\)
0.845668 + 0.533709i \(0.179202\pi\)
\(398\) −6.23230 + 0.987099i −0.0156590 + 0.00248015i
\(399\) 127.432i 0.319380i
\(400\) −30.6112 + 384.872i −0.0765281 + 0.962181i
\(401\) −18.5608 −0.0462864 −0.0231432 0.999732i \(-0.507367\pi\)
−0.0231432 + 0.999732i \(0.507367\pi\)
\(402\) 1.42296 + 8.98420i 0.00353970 + 0.0223488i
\(403\) 418.587 + 213.281i 1.03868 + 0.529233i
\(404\) 440.344 143.076i 1.08996 0.354150i
\(405\) 44.6903 5.27066i 0.110346 0.0130140i
\(406\) 11.1912 34.4429i 0.0275645 0.0848347i
\(407\) −90.1692 90.1692i −0.221546 0.221546i
\(408\) 2.59283 + 5.08872i 0.00635498 + 0.0124723i
\(409\) 71.5061 + 98.4197i 0.174831 + 0.240635i 0.887436 0.460931i \(-0.152485\pi\)
−0.712604 + 0.701566i \(0.752485\pi\)
\(410\) 18.1990 49.2676i 0.0443878 0.120165i
\(411\) 102.111 + 74.1879i 0.248445 + 0.180506i
\(412\) −688.773 109.091i −1.67178 0.264784i
\(413\) −34.8235 + 219.867i −0.0843184 + 0.532365i
\(414\) 9.75885 13.4319i 0.0235721 0.0324442i
\(415\) 8.01859 10.1629i 0.0193219 0.0244888i
\(416\) −116.034 + 84.3035i −0.278927 + 0.202653i
\(417\) 352.248 179.480i 0.844720 0.430407i
\(418\) −9.01994 + 9.01994i −0.0215788 + 0.0215788i
\(419\) 152.900 + 49.6803i 0.364917 + 0.118569i 0.485735 0.874106i \(-0.338552\pi\)
−0.120818 + 0.992675i \(0.538552\pi\)
\(420\) 60.0237 107.076i 0.142914 0.254943i
\(421\) 110.319 + 339.528i 0.262041 + 0.806480i 0.992360 + 0.123374i \(0.0393714\pi\)
−0.730319 + 0.683106i \(0.760629\pi\)
\(422\) −11.6181 + 22.8017i −0.0275310 + 0.0540325i
\(423\) 17.8462 2.82657i 0.0421897 0.00668219i
\(424\) 143.183i 0.337695i
\(425\) −11.2526 + 46.6998i −0.0264767 + 0.109882i
\(426\) −28.1235 −0.0660177
\(427\) −26.8867 169.756i −0.0629666 0.397555i
\(428\) −600.057 305.744i −1.40200 0.714356i
\(429\) 66.7549 21.6900i 0.155606 0.0505594i
\(430\) −8.58947 + 43.0888i −0.0199755 + 0.100207i
\(431\) −44.0907 + 135.697i −0.102299 + 0.314843i −0.989087 0.147333i \(-0.952931\pi\)
0.886788 + 0.462176i \(0.152931\pi\)
\(432\) 56.7431 + 56.7431i 0.131350 + 0.131350i
\(433\) 23.3553 + 45.8375i 0.0539384 + 0.105860i 0.916402 0.400259i \(-0.131080\pi\)
−0.862464 + 0.506119i \(0.831080\pi\)
\(434\) 15.1863 + 20.9021i 0.0349915 + 0.0481616i
\(435\) 109.889 + 390.257i 0.252619 + 0.897143i
\(436\) 663.711 + 482.215i 1.52227 + 1.10600i
\(437\) 519.869 + 82.3391i 1.18963 + 0.188419i
\(438\) 4.51494 28.5062i 0.0103081 0.0650827i
\(439\) 74.2230 102.159i 0.169073 0.232709i −0.716070 0.698029i \(-0.754061\pi\)
0.885143 + 0.465320i \(0.154061\pi\)
\(440\) −23.7946 + 6.70012i −0.0540787 + 0.0152276i
\(441\) 87.7277 63.7379i 0.198929 0.144530i
\(442\) −5.19599 + 2.64749i −0.0117556 + 0.00598980i
\(443\) 272.201 272.201i 0.614449 0.614449i −0.329653 0.944102i \(-0.606932\pi\)
0.944102 + 0.329653i \(0.106932\pi\)
\(444\) 288.254 + 93.6595i 0.649221 + 0.210945i
\(445\) −301.132 60.0288i −0.676702 0.134896i
\(446\) −4.94440 15.2173i −0.0110861 0.0341195i
\(447\) −82.2864 + 161.496i −0.184086 + 0.361289i
\(448\) 210.960 33.4127i 0.470892 0.0745820i
\(449\) 335.363i 0.746910i −0.927648 0.373455i \(-0.878173\pi\)
0.927648 0.373455i \(-0.121827\pi\)
\(450\) −1.25628 16.1336i −0.00279173 0.0358524i
\(451\) −140.257 −0.310991
\(452\) −110.764 699.339i −0.245054 1.54721i
\(453\) −2.09946 1.06973i −0.00463457 0.00236143i
\(454\) 23.1695 7.52823i 0.0510342 0.0165820i
\(455\) 219.954 + 123.300i 0.483415 + 0.270989i
\(456\) 18.8485 58.0097i 0.0413344 0.127214i
\(457\) −137.686 137.686i −0.301282 0.301282i 0.540233 0.841515i \(-0.318336\pi\)
−0.841515 + 0.540233i \(0.818336\pi\)
\(458\) −28.0063 54.9654i −0.0611491 0.120012i
\(459\) 5.86855 + 8.07736i 0.0127855 + 0.0175977i
\(460\) 398.039 + 314.057i 0.865303 + 0.682732i
\(461\) −466.859 339.193i −1.01271 0.735777i −0.0479339 0.998851i \(-0.515264\pi\)
−0.964776 + 0.263074i \(0.915264\pi\)
\(462\) 3.81264 + 0.603862i 0.00825246 + 0.00130706i
\(463\) 71.2905 450.111i 0.153975 0.972161i −0.782811 0.622259i \(-0.786215\pi\)
0.936786 0.349902i \(-0.113785\pi\)
\(464\) −424.965 + 584.915i −0.915874 + 1.26059i
\(465\) −271.322 100.224i −0.583487 0.215535i
\(466\) −41.9751 + 30.4967i −0.0900753 + 0.0654436i
\(467\) −701.497 + 357.430i −1.50213 + 0.765375i −0.995316 0.0966775i \(-0.969178\pi\)
−0.506818 + 0.862053i \(0.669178\pi\)
\(468\) −117.966 + 117.966i −0.252065 + 0.252065i
\(469\) 82.9939 + 26.9664i 0.176959 + 0.0574976i
\(470\) −0.761043 6.45294i −0.00161924 0.0137297i
\(471\) −51.7376 159.232i −0.109846 0.338072i
\(472\) −48.3727 + 94.9369i −0.102485 + 0.201137i
\(473\) 115.887 18.3547i 0.245004 0.0388049i
\(474\) 6.45500i 0.0136181i
\(475\) 437.646 267.691i 0.921360 0.563560i
\(476\) 27.2351 0.0572165
\(477\) 39.1568 + 247.226i 0.0820898 + 0.518295i
\(478\) 18.4148 + 9.38279i 0.0385246 + 0.0196293i
\(479\) 823.815 267.674i 1.71987 0.558818i 0.727940 0.685641i \(-0.240478\pi\)
0.991925 + 0.126823i \(0.0404780\pi\)
\(480\) 64.8686 59.9140i 0.135143 0.124821i
\(481\) −192.394 + 592.128i −0.399987 + 1.23103i
\(482\) 43.4914 + 43.4914i 0.0902311 + 0.0902311i
\(483\) −72.3115 141.919i −0.149713 0.293829i
\(484\) −261.890 360.460i −0.541094 0.744752i
\(485\) −692.023 27.4770i −1.42685 0.0566536i
\(486\) −2.72109 1.97699i −0.00559895 0.00406787i
\(487\) −624.237 98.8694i −1.28180 0.203017i −0.521872 0.853024i \(-0.674766\pi\)
−0.759929 + 0.650006i \(0.774766\pi\)
\(488\) 12.8692 81.2531i 0.0263714 0.166502i
\(489\) −115.356 + 158.774i −0.235903 + 0.324692i
\(490\) −21.6510 32.4322i −0.0441858 0.0661881i
\(491\) −676.866 + 491.772i −1.37854 + 1.00157i −0.381531 + 0.924356i \(0.624603\pi\)
−0.997014 + 0.0772153i \(0.975397\pi\)
\(492\) 297.031 151.345i 0.603722 0.307612i
\(493\) −63.6068 + 63.6068i −0.129020 + 0.129020i
\(494\) 59.2326 + 19.2458i 0.119904 + 0.0389592i
\(495\) −39.2526 + 18.0760i −0.0792982 + 0.0365171i
\(496\) −159.389 490.548i −0.321348 0.989007i
\(497\) −122.489 + 240.398i −0.246457 + 0.483698i
\(498\) −0.955664 + 0.151362i −0.00191900 + 0.000303941i
\(499\) 184.320i 0.369378i −0.982797 0.184689i \(-0.940872\pi\)
0.982797 0.184689i \(-0.0591278\pi\)
\(500\) 493.823 18.7873i 0.987647 0.0375745i
\(501\) −483.360 −0.964791
\(502\) 6.82574 + 43.0960i 0.0135971 + 0.0858487i
\(503\) −45.2561 23.0591i −0.0899724 0.0458432i 0.408425 0.912792i \(-0.366078\pi\)
−0.498398 + 0.866949i \(0.666078\pi\)
\(504\) −17.5545 + 5.70379i −0.0348303 + 0.0113170i
\(505\) −244.935 531.885i −0.485019 1.05324i
\(506\) −4.92699 + 15.1637i −0.00973713 + 0.0299678i
\(507\) −35.3429 35.3429i −0.0697099 0.0697099i
\(508\) 197.014 + 386.662i 0.387823 + 0.761146i
\(509\) −130.328 179.381i −0.256047 0.352418i 0.661571 0.749883i \(-0.269890\pi\)
−0.917617 + 0.397465i \(0.869890\pi\)
\(510\) 2.98613 1.99348i 0.00585516 0.00390878i
\(511\) −224.005 162.749i −0.438366 0.318492i
\(512\) 260.235 + 41.2171i 0.508271 + 0.0805022i
\(513\) 16.6806 105.317i 0.0325157 0.205296i
\(514\) −59.5608 + 81.9785i −0.115877 + 0.159491i
\(515\) −34.9911 + 881.269i −0.0679438 + 1.71120i
\(516\) −225.615 + 163.919i −0.437239 + 0.317673i
\(517\) −15.4606 + 7.87757i −0.0299045 + 0.0152371i
\(518\) −24.2115 + 24.2115i −0.0467404 + 0.0467404i
\(519\) −129.901 42.2072i −0.250290 0.0813241i
\(520\) 81.8899 + 88.6618i 0.157481 + 0.170503i
\(521\) −14.5481 44.7746i −0.0279235 0.0859397i 0.936124 0.351671i \(-0.114387\pi\)
−0.964047 + 0.265732i \(0.914387\pi\)
\(522\) 13.7575 27.0006i 0.0263553 0.0517252i
\(523\) −204.537 + 32.3954i −0.391083 + 0.0619415i −0.348880 0.937168i \(-0.613438\pi\)
−0.0422036 + 0.999109i \(0.513438\pi\)
\(524\) 76.3314i 0.145671i
\(525\) −143.380 59.5294i −0.273105 0.113389i
\(526\) −64.6061 −0.122825
\(527\) −10.0390 63.3838i −0.0190494 0.120273i
\(528\) −68.6638 34.9859i −0.130045 0.0662613i
\(529\) 122.583 39.8297i 0.231726 0.0752925i
\(530\) 89.3935 10.5428i 0.168667 0.0198922i
\(531\) −57.5600 + 177.151i −0.108399 + 0.333618i
\(532\) −205.674 205.674i −0.386606 0.386606i
\(533\) 310.891 + 610.157i 0.583284 + 1.14476i
\(534\) 13.4900 + 18.5673i 0.0252621 + 0.0347703i
\(535\) −295.132 + 798.971i −0.551649 + 1.49340i
\(536\) 33.7918 + 24.5512i 0.0630445 + 0.0458045i
\(537\) −486.778 77.0981i −0.906478 0.143572i
\(538\) 5.62227 35.4976i 0.0104503 0.0659807i
\(539\) −61.2092 + 84.2472i −0.113561 + 0.156303i
\(540\) 63.6228 80.6363i 0.117820 0.149326i
\(541\) 92.2535 67.0261i 0.170524 0.123893i −0.499250 0.866458i \(-0.666391\pi\)
0.669774 + 0.742565i \(0.266391\pi\)
\(542\) −71.5987 + 36.4814i −0.132101 + 0.0673088i
\(543\) −74.7959 + 74.7959i −0.137746 + 0.137746i
\(544\) 18.6332 + 6.05428i 0.0342522 + 0.0111292i
\(545\) 507.352 905.062i 0.930922 1.66066i
\(546\) −5.82403 17.9245i −0.0106667 0.0328288i
\(547\) −216.121 + 424.162i −0.395103 + 0.775434i −0.999779 0.0210383i \(-0.993303\pi\)
0.604676 + 0.796472i \(0.293303\pi\)
\(548\) 284.544 45.0673i 0.519241 0.0822397i
\(549\) 143.815i 0.261958i
\(550\) 5.93514 + 14.3624i 0.0107912 + 0.0261134i
\(551\) 960.695 1.74355
\(552\) −11.9263 75.3000i −0.0216057 0.136413i
\(553\) 55.1769 + 28.1140i 0.0997774 + 0.0508391i
\(554\) −62.5907 + 20.3369i −0.112980 + 0.0367093i
\(555\) 74.9383 375.925i 0.135024 0.677343i
\(556\) 278.847 858.202i 0.501523 1.54353i
\(557\) 750.511 + 750.511i 1.34742 + 1.34742i 0.888457 + 0.458959i \(0.151778\pi\)
0.458959 + 0.888457i \(0.348222\pi\)
\(558\) 9.81473 + 19.2625i 0.0175891 + 0.0345206i
\(559\) −336.720 463.456i −0.602362 0.829080i
\(560\) −75.0368 266.483i −0.133994 0.475863i
\(561\) −7.75690 5.63572i −0.0138269 0.0100458i
\(562\) 86.6704 + 13.7272i 0.154218 + 0.0244257i
\(563\) −14.1060 + 89.0616i −0.0250550 + 0.158191i −0.997044 0.0768365i \(-0.975518\pi\)
0.971989 + 0.235028i \(0.0755181\pi\)
\(564\) 24.2416 33.3656i 0.0429815 0.0591589i
\(565\) −861.973 + 242.716i −1.52562 + 0.429585i
\(566\) 27.2739 19.8156i 0.0481871 0.0350100i
\(567\) −28.7506 + 14.6491i −0.0507064 + 0.0258362i
\(568\) −91.3165 + 91.3165i −0.160769 + 0.160769i
\(569\) 130.069 + 42.2620i 0.228592 + 0.0742742i 0.421074 0.907026i \(-0.361653\pi\)
−0.192481 + 0.981301i \(0.561653\pi\)
\(570\) −37.6051 7.49634i −0.0659739 0.0131515i
\(571\) −168.661 519.087i −0.295379 0.909083i −0.983094 0.183102i \(-0.941386\pi\)
0.687715 0.725981i \(-0.258614\pi\)
\(572\) 72.7342 142.749i 0.127158 0.249561i
\(573\) −25.8541 + 4.09488i −0.0451205 + 0.00714639i
\(574\) 37.6608i 0.0656111i
\(575\) 335.498 546.465i 0.583474 0.950373i
\(576\) 178.722 0.310281
\(577\) −16.8214 106.206i −0.0291532 0.184066i 0.968815 0.247787i \(-0.0797033\pi\)
−0.997968 + 0.0637208i \(0.979703\pi\)
\(578\) −54.8500 27.9475i −0.0948962 0.0483520i
\(579\) −76.6307 + 24.8988i −0.132350 + 0.0430032i
\(580\) 807.230 + 452.510i 1.39178 + 0.780190i
\(581\) −2.86846 + 8.82820i −0.00493710 + 0.0151948i
\(582\) 36.6033 + 36.6033i 0.0628922 + 0.0628922i
\(583\) −109.129 214.178i −0.187186 0.367372i
\(584\) −77.8992 107.219i −0.133389 0.183594i
\(585\) 165.642 + 130.693i 0.283149 + 0.223407i
\(586\) 5.99854 + 4.35820i 0.0102364 + 0.00743719i
\(587\) −188.391 29.8383i −0.320939 0.0508318i −0.00611368 0.999981i \(-0.501946\pi\)
−0.314826 + 0.949150i \(0.601946\pi\)
\(588\) 38.7192 244.463i 0.0658490 0.415754i
\(589\) −402.851 + 554.477i −0.683957 + 0.941386i
\(590\) 62.8338 + 23.2102i 0.106498 + 0.0393394i
\(591\) 181.453 131.833i 0.307027 0.223068i
\(592\) 609.060 310.331i 1.02882 0.524209i
\(593\) 324.975 324.975i 0.548019 0.548019i −0.377848 0.925867i \(-0.623336\pi\)
0.925867 + 0.377848i \(0.123336\pi\)
\(594\) 3.07192 + 0.998128i 0.00517159 + 0.00168035i
\(595\) −4.03436 34.2076i −0.00678044 0.0574918i
\(596\) 127.844 + 393.462i 0.214503 + 0.660171i
\(597\) −22.9961 + 45.1324i −0.0385194 + 0.0755986i
\(598\) 76.8874 12.1778i 0.128574 0.0203642i
\(599\) 916.574i 1.53017i 0.643927 + 0.765087i \(0.277304\pi\)
−0.643927 + 0.765087i \(0.722696\pi\)
\(600\) −56.4645 48.3063i −0.0941075 0.0805104i
\(601\) 351.969 0.585638 0.292819 0.956168i \(-0.405407\pi\)
0.292819 + 0.956168i \(0.405407\pi\)
\(602\) −4.92846 31.1171i −0.00818682 0.0516895i
\(603\) 65.0608 + 33.1501i 0.107895 + 0.0549753i
\(604\) −5.11503 + 1.66197i −0.00846860 + 0.00275161i
\(605\) −413.949 + 382.332i −0.684213 + 0.631955i
\(606\) −13.5249 + 41.6254i −0.0223184 + 0.0686888i
\(607\) 535.928 + 535.928i 0.882913 + 0.882913i 0.993830 0.110916i \(-0.0353786\pi\)
−0.110916 + 0.993830i \(0.535379\pi\)
\(608\) −94.9935 186.435i −0.156239 0.306637i
\(609\) −170.880 235.196i −0.280591 0.386200i
\(610\) −51.6764 2.05183i −0.0847154 0.00336366i
\(611\) 68.5392 + 49.7967i 0.112176 + 0.0815003i
\(612\) 22.5085 + 3.56500i 0.0367786 + 0.00582516i
\(613\) −45.2566 + 285.739i −0.0738281 + 0.466132i 0.922882 + 0.385083i \(0.125827\pi\)
−0.996710 + 0.0810495i \(0.974173\pi\)
\(614\) 21.9892 30.2656i 0.0358131 0.0492925i
\(615\) −234.091 350.657i −0.380636 0.570173i
\(616\) 14.3403 10.4188i 0.0232797 0.0169137i
\(617\) 617.881 314.826i 1.00143 0.510253i 0.125191 0.992133i \(-0.460046\pi\)
0.876238 + 0.481879i \(0.160046\pi\)
\(618\) 46.6131 46.6131i 0.0754257 0.0754257i
\(619\) 277.577 + 90.1904i 0.448429 + 0.145703i 0.524521 0.851397i \(-0.324244\pi\)
−0.0760924 + 0.997101i \(0.524244\pi\)
\(620\) −599.669 + 276.150i −0.967209 + 0.445403i
\(621\) −41.1852 126.755i −0.0663208 0.204114i
\(622\) 58.1454 114.117i 0.0934814 0.183468i
\(623\) 217.466 34.4433i 0.349063 0.0552862i
\(624\) 376.255i 0.602973i
\(625\) −96.7477 617.467i −0.154796 0.987946i
\(626\) −23.3110 −0.0372380
\(627\) 16.0188 + 101.139i 0.0255483 + 0.161306i
\(628\) −340.502 173.494i −0.542201 0.276265i
\(629\) 80.8852 26.2812i 0.128593 0.0417825i
\(630\) 4.85362 + 10.5398i 0.00770417 + 0.0167299i
\(631\) −82.7142 + 254.568i −0.131084 + 0.403436i −0.994960 0.100268i \(-0.968030\pi\)
0.863876 + 0.503704i \(0.168030\pi\)
\(632\) 20.9592 + 20.9592i 0.0331634 + 0.0331634i
\(633\) 93.2637 + 183.040i 0.147336 + 0.289163i
\(634\) −33.8857 46.6396i −0.0534474 0.0735641i
\(635\) 456.470 304.730i 0.718850 0.479889i
\(636\) 462.219 + 335.822i 0.726760 + 0.528022i
\(637\) 502.173 + 79.5365i 0.788341 + 0.124861i
\(638\) −4.55243 + 28.7429i −0.00713547 + 0.0450516i
\(639\) −132.699 + 182.644i −0.207667 + 0.285828i
\(640\) 10.6406 267.989i 0.0166259 0.418732i
\(641\) 749.586 544.606i 1.16940 0.849619i 0.178463 0.983947i \(-0.442887\pi\)
0.990937 + 0.134327i \(0.0428874\pi\)
\(642\) 56.7230 28.9018i 0.0883536 0.0450184i
\(643\) −546.871 + 546.871i −0.850499 + 0.850499i −0.990194 0.139696i \(-0.955388\pi\)
0.139696 + 0.990194i \(0.455388\pi\)
\(644\) −345.766 112.346i −0.536903 0.174450i
\(645\) 239.306 + 259.095i 0.371016 + 0.401697i
\(646\) −2.62900 8.09123i −0.00406966 0.0125251i
\(647\) −239.617 + 470.275i −0.370351 + 0.726855i −0.998695 0.0510810i \(-0.983733\pi\)
0.628343 + 0.777936i \(0.283733\pi\)
\(648\) −15.2546 + 2.41608i −0.0235410 + 0.00372852i
\(649\) 178.878i 0.275621i
\(650\) 49.3246 57.6548i 0.0758840 0.0886997i
\(651\) 207.402 0.318589
\(652\) 70.0762 + 442.443i 0.107479 + 0.678594i
\(653\) 479.923 + 244.533i 0.734951 + 0.374476i 0.781057 0.624460i \(-0.214681\pi\)
−0.0461053 + 0.998937i \(0.514681\pi\)
\(654\) −73.7555 + 23.9646i −0.112776 + 0.0366432i
\(655\) 95.8733 11.3071i 0.146371 0.0172627i
\(656\) 232.334 715.051i 0.354168 1.09002i
\(657\) −163.826 163.826i −0.249355 0.249355i
\(658\) 2.11523 + 4.15136i 0.00321463 + 0.00630907i
\(659\) −708.681 975.415i −1.07539 1.48014i −0.864499 0.502634i \(-0.832364\pi\)
−0.210889 0.977510i \(-0.567636\pi\)
\(660\) −34.1788 + 92.5277i −0.0517861 + 0.140193i
\(661\) 46.1717 + 33.5457i 0.0698513 + 0.0507500i 0.622163 0.782888i \(-0.286254\pi\)
−0.552312 + 0.833638i \(0.686254\pi\)
\(662\) −122.978 19.4777i −0.185767 0.0294225i
\(663\) −7.32317 + 46.2367i −0.0110455 + 0.0697386i
\(664\) −2.61155 + 3.59449i −0.00393306 + 0.00541340i
\(665\) −227.863 + 288.797i −0.342652 + 0.434281i
\(666\) −23.1789 + 16.8405i −0.0348032 + 0.0252860i
\(667\) 1069.91 545.146i 1.60406 0.817310i
\(668\) −780.137 + 780.137i −1.16787 + 1.16787i
\(669\) −122.156 39.6910i −0.182595 0.0593289i
\(670\) 12.8399 22.9051i 0.0191641 0.0341867i
\(671\) 42.6781 + 131.350i 0.0636038 + 0.195752i
\(672\) −28.7462 + 56.4176i −0.0427771 + 0.0839548i
\(673\) −512.305 + 81.1411i −0.761225 + 0.120566i −0.524965 0.851124i \(-0.675922\pi\)
−0.236260 + 0.971690i \(0.575922\pi\)
\(674\) 32.7091i 0.0485299i
\(675\) −110.705 67.9664i −0.164007 0.100691i
\(676\) −114.086 −0.168766
\(677\) −160.974 1016.35i −0.237775 1.50125i −0.760829 0.648953i \(-0.775207\pi\)
0.523054 0.852300i \(-0.324793\pi\)
\(678\) 59.6369 + 30.3865i 0.0879601 + 0.0448179i
\(679\) 472.304 153.461i 0.695588 0.226010i
\(680\) 3.22312 16.1687i 0.00473989 0.0237775i
\(681\) 60.4327 185.993i 0.0887411 0.273117i
\(682\) −14.6803 14.6803i −0.0215254 0.0215254i
\(683\) 10.9833 + 21.5559i 0.0160809 + 0.0315606i 0.898907 0.438139i \(-0.144362\pi\)
−0.882826 + 0.469700i \(0.844362\pi\)
\(684\) −143.058 196.903i −0.209149 0.287869i
\(685\) −98.7551 350.716i −0.144168 0.511994i
\(686\) 53.2875 + 38.7156i 0.0776786 + 0.0564368i
\(687\) −489.111 77.4676i −0.711952 0.112762i
\(688\) −98.3905 + 621.213i −0.143009 + 0.902926i
\(689\) −689.840 + 949.484i −1.00122 + 1.37806i
\(690\) −46.1340 + 12.9905i −0.0668608 + 0.0188268i
\(691\) −126.449 + 91.8707i −0.182994 + 0.132953i −0.675511 0.737350i \(-0.736077\pi\)
0.492517 + 0.870303i \(0.336077\pi\)
\(692\) −277.780 + 141.536i −0.401416 + 0.204532i
\(693\) 21.9114 21.9114i 0.0316181 0.0316181i
\(694\) −72.4784 23.5497i −0.104436 0.0339332i
\(695\) −1119.22 223.109i −1.61039 0.321020i
\(696\) −43.0000 132.341i −0.0617817 0.190144i
\(697\) 42.4679 83.3480i 0.0609296 0.119581i
\(698\) −82.1151 + 13.0058i −0.117643 + 0.0186329i
\(699\) 416.498i 0.595849i
\(700\) −327.494 + 135.334i −0.467848 + 0.193335i
\(701\) 440.747 0.628741 0.314370 0.949300i \(-0.398207\pi\)
0.314370 + 0.949300i \(0.398207\pi\)
\(702\) −2.46702 15.5761i −0.00351427 0.0221882i
\(703\) −809.302 412.360i −1.15121 0.586572i
\(704\) −163.231 + 53.0370i −0.231863 + 0.0753367i
\(705\) −45.4987 25.5053i −0.0645371 0.0361777i
\(706\) −14.2659 + 43.9059i −0.0202067 + 0.0621897i
\(707\) 296.905 + 296.905i 0.419951 + 0.419951i
\(708\) 193.019 + 378.821i 0.272626 + 0.535058i
\(709\) −224.658 309.215i −0.316866 0.436129i 0.620641 0.784095i \(-0.286872\pi\)
−0.937507 + 0.347966i \(0.886872\pi\)
\(710\) 63.7356 + 50.2880i 0.0897685 + 0.0708281i
\(711\) 41.9211 + 30.4574i 0.0589607 + 0.0428375i
\(712\) 104.089 + 16.4861i 0.146193 + 0.0231547i
\(713\) −134.010 + 846.108i −0.187953 + 1.18669i
\(714\) −1.51326 + 2.08282i −0.00211941 + 0.00291712i
\(715\) −190.069 70.2097i −0.265831 0.0981954i
\(716\) −910.090 + 661.219i −1.27107 + 0.923490i
\(717\) 147.824 75.3201i 0.206170 0.105049i
\(718\) 31.5376 31.5376i 0.0439242 0.0439242i
\(719\) 341.861 + 111.078i 0.475468 + 0.154489i 0.536941 0.843620i \(-0.319580\pi\)
−0.0614729 + 0.998109i \(0.519580\pi\)
\(720\) −27.1325 230.058i −0.0376840 0.319525i
\(721\) −195.427 601.464i −0.271051 0.834208i
\(722\) −5.88790 + 11.5557i −0.00815499 + 0.0160051i
\(723\) 487.660 77.2378i 0.674495 0.106830i
\(724\) 241.439i 0.333480i
\(725\) 448.784 1080.92i 0.619012 1.49093i
\(726\) 42.1178 0.0580136
\(727\) 129.530 + 817.821i 0.178171 + 1.12493i 0.900975 + 0.433872i \(0.142853\pi\)
−0.722804 + 0.691053i \(0.757147\pi\)
\(728\) −77.1111 39.2901i −0.105922 0.0539699i
\(729\) −25.6785 + 8.34346i −0.0352243 + 0.0114451i
\(730\) −61.2043 + 56.5297i −0.0838416 + 0.0774379i
\(731\) −24.1817 + 74.4236i −0.0330803 + 0.101811i
\(732\) −232.115 232.115i −0.317098 0.317098i
\(733\) 52.6684 + 103.368i 0.0718532 + 0.141020i 0.924139 0.382057i \(-0.124784\pi\)
−0.852286 + 0.523077i \(0.824784\pi\)
\(734\) 45.9265 + 63.2125i 0.0625702 + 0.0861205i
\(735\) −312.785 12.4192i −0.425558 0.0168969i
\(736\) −211.585 153.726i −0.287480 0.208866i
\(737\) −69.2592 10.9696i −0.0939744 0.0148841i
\(738\) −4.92969 + 31.1249i −0.00667980 + 0.0421746i
\(739\) 266.096 366.249i 0.360075 0.495601i −0.590094 0.807334i \(-0.700909\pi\)
0.950170 + 0.311733i \(0.100909\pi\)
\(740\) −485.789 727.688i −0.656472 0.983363i
\(741\) 404.474 293.868i 0.545850 0.396583i
\(742\) −57.5094 + 29.3025i −0.0775060 + 0.0394913i
\(743\) 853.549 853.549i 1.14879 1.14879i 0.161995 0.986792i \(-0.448207\pi\)
0.986792 0.161995i \(-0.0517930\pi\)
\(744\) 94.4132 + 30.6767i 0.126899 + 0.0412321i
\(745\) 475.256 218.857i 0.637928 0.293768i
\(746\) 8.55619 + 26.3333i 0.0114694 + 0.0352993i
\(747\) −3.52623 + 6.92062i −0.00472053 + 0.00926456i
\(748\) −21.6155 + 3.42356i −0.0288978 + 0.00457696i
\(749\) 610.744i 0.815412i
\(750\) −26.0015 + 38.8094i −0.0346687 + 0.0517459i
\(751\) −919.063 −1.22379 −0.611893 0.790941i \(-0.709592\pi\)
−0.611893 + 0.790941i \(0.709592\pi\)
\(752\) −14.5507 91.8695i −0.0193493 0.122167i
\(753\) 312.088 + 159.017i 0.414459 + 0.211178i
\(754\) 135.130 43.9065i 0.179218 0.0582315i
\(755\) 2.84516 + 6.17837i 0.00376842 + 0.00818327i
\(756\) −22.7595 + 70.0465i −0.0301052 + 0.0926542i
\(757\) 595.883 + 595.883i 0.787163 + 0.787163i 0.981028 0.193865i \(-0.0621024\pi\)
−0.193865 + 0.981028i \(0.562102\pi\)
\(758\) 43.9964 + 86.3478i 0.0580427 + 0.113915i
\(759\) 75.2310 + 103.547i 0.0991186 + 0.136425i
\(760\) −146.444 + 97.7627i −0.192689 + 0.128635i
\(761\) −587.568 426.893i −0.772099 0.560963i 0.130498 0.991449i \(-0.458342\pi\)
−0.902597 + 0.430486i \(0.858342\pi\)
\(762\) −40.5170 6.41727i −0.0531719 0.00842161i
\(763\) −116.386 + 734.833i −0.152537 + 0.963084i
\(764\) −35.1190 + 48.3372i −0.0459673 + 0.0632686i
\(765\) 1.14348 28.7991i 0.00149474 0.0376459i
\(766\) 123.498 89.7269i 0.161225 0.117137i
\(767\) −778.169 + 396.497i −1.01456 + 0.516945i
\(768\) 277.677 277.677i 0.361559 0.361559i
\(769\) 646.102 + 209.931i 0.840184 + 0.272992i 0.697329 0.716751i \(-0.254372\pi\)
0.142855 + 0.989744i \(0.454372\pi\)
\(770\) −7.56070 8.18593i −0.00981909 0.0106311i
\(771\) 251.364 + 773.619i 0.326024 + 1.00340i
\(772\) −83.4946 + 163.867i −0.108154 + 0.212264i
\(773\) −625.102 + 99.0065i −0.808670 + 0.128081i −0.547061 0.837093i \(-0.684253\pi\)
−0.261610 + 0.965174i \(0.584253\pi\)
\(774\) 26.3620i 0.0340594i
\(775\) 435.678 + 712.287i 0.562165 + 0.919080i
\(776\) 237.700 0.306315
\(777\) 42.9981 + 271.479i 0.0553386 + 0.349394i
\(778\) −5.51370 2.80937i −0.00708702 0.00361102i
\(779\) −950.140 + 308.719i −1.21969 + 0.396302i
\(780\) 478.281 56.4072i 0.613181 0.0723169i
\(781\) 66.9962 206.193i 0.0857826 0.264012i
\(782\) −7.51924 7.51924i −0.00961539 0.00961539i
\(783\) −110.438 216.746i −0.141044 0.276815i
\(784\) −328.112 451.608i −0.418510 0.576030i
\(785\) −167.473 + 453.376i −0.213341 + 0.577549i
\(786\) −5.83750 4.24120i −0.00742685 0.00539592i
\(787\) 164.241 + 26.0132i 0.208693 + 0.0330537i 0.259905 0.965634i \(-0.416309\pi\)
−0.0512127 + 0.998688i \(0.516309\pi\)
\(788\) 80.0854 505.639i 0.101631 0.641674i
\(789\) −304.839 + 419.575i −0.386361 + 0.531781i
\(790\) 11.5422 14.6288i 0.0146104 0.0185174i
\(791\) 519.484 377.428i 0.656744 0.477152i
\(792\) 13.2154 6.73357i 0.0166861 0.00850198i
\(793\) 476.808 476.808i 0.601272 0.601272i
\(794\) −14.9268 4.85001i −0.0187995 0.00610833i
\(795\) 353.328 630.300i 0.444438 0.792830i
\(796\) 35.7277 + 109.958i 0.0448840 + 0.138139i
\(797\) −216.996 + 425.878i −0.272266 + 0.534352i −0.986139 0.165924i \(-0.946939\pi\)
0.713873 + 0.700275i \(0.246939\pi\)
\(798\) 27.1570 4.30125i 0.0340313 0.00539003i
\(799\) 11.5727i 0.0144840i
\(800\) −254.143 + 19.7895i −0.317679 + 0.0247368i
\(801\) 184.234 0.230006
\(802\) −0.626486 3.95548i −0.000781155 0.00493202i
\(803\) 198.243 + 101.010i 0.246878 + 0.125791i
\(804\) 158.511 51.5034i 0.197153 0.0640589i
\(805\) −89.8897 + 450.929i −0.111664 + 0.560160i
\(806\) −31.3234 + 96.4035i −0.0388628 + 0.119607i
\(807\) −204.006 204.006i −0.252796 0.252796i
\(808\) 91.2418 + 179.072i 0.112923 + 0.221624i
\(809\) 221.907 + 305.428i 0.274297 + 0.377538i 0.923835 0.382792i \(-0.125037\pi\)
−0.649537 + 0.760330i \(0.725037\pi\)
\(810\) 2.63166 + 9.34599i 0.00324896 + 0.0115383i
\(811\) −750.736 545.442i −0.925692 0.672555i 0.0192421 0.999815i \(-0.493875\pi\)
−0.944934 + 0.327260i \(0.893875\pi\)
\(812\) −655.401 103.805i −0.807145 0.127839i
\(813\) −100.910 + 637.123i −0.124121 + 0.783669i
\(814\) 16.1724 22.2594i 0.0198678 0.0273456i
\(815\) 545.335 153.556i 0.669123 0.188413i
\(816\) 41.5809 30.2103i 0.0509570 0.0370224i
\(817\) 744.650 379.418i 0.911445 0.464404i
\(818\) −18.5606 + 18.5606i −0.0226902 + 0.0226902i
\(819\) −143.889 46.7522i −0.175688 0.0570846i
\(820\) −943.775 188.135i −1.15095 0.229433i
\(821\) 293.820 + 904.285i 0.357881 + 1.10144i 0.954320 + 0.298785i \(0.0965814\pi\)
−0.596440 + 0.802658i \(0.703419\pi\)
\(822\) −12.3635 + 24.2648i −0.0150408 + 0.0295192i
\(823\) −834.683 + 132.201i −1.01420 + 0.160633i −0.641340 0.767257i \(-0.721621\pi\)
−0.372855 + 0.927889i \(0.621621\pi\)
\(824\) 302.704i 0.367359i
\(825\) 121.279 + 29.2229i 0.147005 + 0.0354217i
\(826\) −48.0310 −0.0581489
\(827\) −125.235 790.702i −0.151433 0.956109i −0.940004 0.341165i \(-0.889179\pi\)
0.788571 0.614944i \(-0.210821\pi\)
\(828\) −271.054 138.109i −0.327359 0.166798i
\(829\) 817.552 265.639i 0.986190 0.320433i 0.228856 0.973460i \(-0.426501\pi\)
0.757334 + 0.653028i \(0.226501\pi\)
\(830\) 2.43645 + 1.36580i 0.00293548 + 0.00164555i
\(831\) −163.254 + 502.445i −0.196455 + 0.604627i
\(832\) 592.540 + 592.540i 0.712188 + 0.712188i
\(833\) −31.5308 61.8826i −0.0378520 0.0742888i
\(834\) 50.1382 + 69.0093i 0.0601177 + 0.0827449i
\(835\) 1095.43 + 864.301i 1.31189 + 1.03509i
\(836\) 189.091 + 137.382i 0.226185 + 0.164333i
\(837\) 171.408 + 27.1483i 0.204788 + 0.0324353i
\(838\) −5.42645 + 34.2613i −0.00647548 + 0.0408846i
\(839\) 510.533 702.688i 0.608501 0.837530i −0.387952 0.921680i \(-0.626817\pi\)
0.996453 + 0.0841493i \(0.0268173\pi\)
\(840\) 49.9822 + 18.4630i 0.0595026 + 0.0219797i
\(841\) 1092.73 793.912i 1.29932 0.944009i
\(842\) −68.6328 + 34.9702i −0.0815117 + 0.0415323i
\(843\) 498.098 498.098i 0.590864 0.590864i
\(844\) 445.951 + 144.898i 0.528378 + 0.171680i
\(845\) 16.8997 + 143.294i 0.0199996 + 0.169578i
\(846\) 1.20473 + 3.70779i 0.00142403 + 0.00438273i
\(847\) 183.440 360.021i 0.216576 0.425054i
\(848\) 1272.68 201.573i 1.50080 0.237704i
\(849\) 270.625i 0.318758i
\(850\) −10.3319 0.821763i −0.0121552 0.000966780i
\(851\) −1135.30 −1.33408
\(852\) 80.6114 + 508.960i 0.0946143 + 0.597371i
\(853\) 522.550 + 266.253i 0.612603 + 0.312137i 0.732623 0.680635i \(-0.238296\pi\)
−0.120020 + 0.992771i \(0.538296\pi\)
\(854\) 35.2690 11.4596i 0.0412986 0.0134187i
\(855\) −226.121 + 208.850i −0.264469 + 0.244270i
\(856\) 90.3349 278.022i 0.105531 0.324792i
\(857\) −800.024 800.024i −0.933517 0.933517i 0.0644063 0.997924i \(-0.479485\pi\)
−0.997924 + 0.0644063i \(0.979485\pi\)
\(858\) 6.87552 + 13.4940i 0.00801343 + 0.0157272i
\(859\) −111.410 153.343i −0.129698 0.178514i 0.739229 0.673454i \(-0.235190\pi\)
−0.868927 + 0.494940i \(0.835190\pi\)
\(860\) 804.412 + 31.9394i 0.935362 + 0.0371389i
\(861\) 244.583 + 177.700i 0.284068 + 0.206388i
\(862\) −30.4065 4.81591i −0.0352743 0.00558690i
\(863\) 169.246 1068.58i 0.196113 1.23821i −0.671513 0.740993i \(-0.734355\pi\)
0.867626 0.497217i \(-0.165645\pi\)
\(864\) −31.1423 + 42.8637i −0.0360444 + 0.0496108i
\(865\) 218.919 + 327.930i 0.253085 + 0.379109i
\(866\) −8.98005 + 6.52439i −0.0103696 + 0.00753394i
\(867\) −440.307 + 224.348i −0.507851 + 0.258763i
\(868\) 334.744 334.744i 0.385649 0.385649i
\(869\) −47.3260 15.3772i −0.0544603 0.0176952i
\(870\) −79.4582 + 36.5908i −0.0913312 + 0.0420584i
\(871\) 105.798 + 325.611i 0.121467 + 0.373836i
\(872\) −161.670 + 317.295i −0.185401 + 0.363871i
\(873\) 410.425 65.0049i 0.470132 0.0744615i
\(874\) 113.568i 0.129940i
\(875\) 218.494 + 391.290i 0.249707 + 0.447188i
\(876\) −528.827 −0.603684
\(877\) −143.299 904.757i −0.163397 1.03165i −0.923989 0.382419i \(-0.875091\pi\)
0.760592 0.649231i \(-0.224909\pi\)
\(878\) 24.2763 + 12.3694i 0.0276495 + 0.0140881i
\(879\) 56.6074 18.3929i 0.0643998 0.0209248i
\(880\) 93.0522 + 202.066i 0.105741 + 0.229621i
\(881\) 79.6614 245.173i 0.0904215 0.278289i −0.895612 0.444836i \(-0.853262\pi\)
0.986033 + 0.166547i \(0.0532619\pi\)
\(882\) 16.5442 + 16.5442i 0.0187576 + 0.0187576i
\(883\) −571.257 1121.16i −0.646951 1.26971i −0.948656 0.316311i \(-0.897556\pi\)
0.301705 0.953401i \(-0.402444\pi\)
\(884\) 62.8059 + 86.4449i 0.0710474 + 0.0977884i
\(885\) 447.213 298.550i 0.505325 0.337345i
\(886\) 67.1961 + 48.8208i 0.0758421 + 0.0551025i
\(887\) 1239.37 + 196.298i 1.39727 + 0.221305i 0.809212 0.587517i \(-0.199894\pi\)
0.588053 + 0.808822i \(0.299894\pi\)
\(888\) −20.5808 + 129.942i −0.0231766 + 0.146331i
\(889\) −231.322 + 318.387i −0.260205 + 0.358141i
\(890\) 2.62850 66.2002i 0.00295337 0.0743822i
\(891\) 20.9769 15.2406i 0.0235430 0.0171050i
\(892\) −261.220 + 133.098i −0.292847 + 0.149213i
\(893\) −87.3951 + 87.3951i −0.0978669 + 0.0978669i
\(894\) −37.1937 12.0850i −0.0416037 0.0135179i
\(895\) 965.313 + 1045.14i 1.07856 + 1.16775i
\(896\) 59.4283 + 182.902i 0.0663263 + 0.204131i
\(897\) 283.701 556.794i 0.316277 0.620730i
\(898\) 71.4688 11.3195i 0.0795866 0.0126053i
\(899\) 1563.57i 1.73923i
\(900\) −288.373 + 68.9794i −0.320415 + 0.0766438i
\(901\) 160.319 0.177934
\(902\) −4.73412 29.8900i −0.00524847 0.0331375i
\(903\) −225.340 114.817i −0.249546 0.127150i
\(904\) 292.305 94.9755i 0.323346 0.105061i
\(905\) 303.251 35.7647i 0.335084 0.0395190i
\(906\) 0.157105 0.483521i 0.000173405 0.000533687i
\(907\) −997.333 997.333i −1.09959 1.09959i −0.994458 0.105137i \(-0.966472\pi\)
−0.105137 0.994458i \(-0.533528\pi\)
\(908\) −202.652 397.727i −0.223185 0.438026i
\(909\) 206.514 + 284.243i 0.227188 + 0.312698i
\(910\) −18.8522 + 51.0359i −0.0207167 + 0.0560834i
\(911\) 645.932 + 469.297i 0.709036 + 0.515145i 0.882863 0.469631i \(-0.155613\pi\)
−0.173827 + 0.984776i \(0.555613\pi\)
\(912\) −542.155 85.8689i −0.594468 0.0941545i
\(913\) 1.16685 7.36721i 0.00127804 0.00806924i
\(914\) 24.6947 33.9894i 0.0270183 0.0371875i
\(915\) −257.157 + 325.924i −0.281046 + 0.356201i
\(916\) −914.451 + 664.388i −0.998309 + 0.725314i
\(917\) −61.6781 + 31.4266i −0.0672607 + 0.0342711i
\(918\) −1.52328 + 1.52328i −0.00165934 + 0.00165934i
\(919\) −1054.35 342.578i −1.14728 0.372773i −0.327160 0.944969i \(-0.606092\pi\)
−0.820117 + 0.572196i \(0.806092\pi\)
\(920\) −107.616 + 191.976i −0.116974 + 0.208669i
\(921\) −92.8011 285.612i −0.100761 0.310111i
\(922\) 56.5271 110.941i 0.0613092 0.120326i
\(923\) −1045.50 + 165.591i −1.13272 + 0.179405i
\(924\) 70.7293i 0.0765469i
\(925\) −842.027 + 717.952i −0.910299 + 0.776164i
\(926\) 98.3288 0.106187
\(927\) −82.7817 522.663i −0.0893006 0.563822i
\(928\) −425.324 216.714i −0.458324 0.233528i
\(929\) −194.991 + 63.3563i −0.209893 + 0.0681984i −0.412076 0.911149i \(-0.635196\pi\)
0.202183 + 0.979348i \(0.435196\pi\)
\(930\) 12.2006 61.2039i 0.0131189 0.0658107i
\(931\) −229.212 + 705.441i −0.246199 + 0.757724i
\(932\) 672.223 + 672.223i 0.721269 + 0.721269i
\(933\) −466.761 916.070i −0.500280 0.981854i
\(934\) −99.8493 137.431i −0.106905 0.147142i
\(935\) 7.50198 + 26.6423i 0.00802351 + 0.0284944i
\(936\) −58.5858 42.5650i −0.0625916 0.0454755i
\(937\) −1164.19 184.389i −1.24246 0.196787i −0.499615 0.866248i \(-0.666525\pi\)
−0.742847 + 0.669461i \(0.766525\pi\)
\(938\) −2.94547 + 18.5969i −0.00314016 + 0.0198262i
\(939\) −109.991 + 151.390i −0.117137 + 0.161225i
\(940\) −114.599 + 32.2691i −0.121914 + 0.0343288i
\(941\) −910.135 + 661.252i −0.967200 + 0.702712i −0.954812 0.297211i \(-0.903943\pi\)
−0.0123882 + 0.999923i \(0.503943\pi\)
\(942\) 32.1874 16.4003i 0.0341693 0.0174101i
\(943\) −882.972 + 882.972i −0.936343 + 0.936343i
\(944\) 911.946 + 296.309i 0.966045 + 0.313887i
\(945\) 91.3509 + 18.2102i 0.0966676 + 0.0192700i
\(946\) 7.82310 + 24.0770i 0.00826966 + 0.0254514i
\(947\) 197.207 387.040i 0.208244 0.408702i −0.763134 0.646240i \(-0.776341\pi\)
0.971378 + 0.237538i \(0.0763405\pi\)
\(948\) 116.818 18.5022i 0.123226 0.0195170i
\(949\) 1086.31i 1.14469i
\(950\) 71.8193 + 84.2309i 0.0755992 + 0.0886641i
\(951\) −462.782 −0.486626
\(952\) 1.84936 + 11.6764i 0.00194261 + 0.0122651i
\(953\) −256.133 130.506i −0.268765 0.136942i 0.314415 0.949286i \(-0.398192\pi\)
−0.583180 + 0.812343i \(0.698192\pi\)
\(954\) −51.3645 + 16.6893i −0.0538412 + 0.0174941i
\(955\) 65.9145 + 36.9498i 0.0690204 + 0.0386909i
\(956\) 117.020 360.152i 0.122406 0.376728i
\(957\) 165.187 + 165.187i 0.172609 + 0.172609i
\(958\) 84.8500 + 166.528i 0.0885700 + 0.173828i
\(959\) 153.566 + 211.366i 0.160131 + 0.220402i
\(960\) −405.033 319.575i −0.421909 0.332890i
\(961\) −124.968 90.7947i −0.130040 0.0944794i
\(962\) −132.682 21.0147i −0.137923 0.0218448i
\(963\) 79.9447 504.751i 0.0830163 0.524144i
\(964\) 662.416 911.738i 0.687154 0.945786i
\(965\) 218.188 + 80.5966i 0.226102 + 0.0835198i
\(966\) 27.8035 20.2004i 0.0287821 0.0209114i
\(967\) −1528.59 + 778.855i −1.58075 + 0.805435i −0.999963 0.00861751i \(-0.997257\pi\)
−0.580792 + 0.814052i \(0.697257\pi\)
\(968\) 136.756 136.756i 0.141277 0.141277i
\(969\) −64.9522 21.1042i −0.0670301 0.0217794i
\(970\) −17.5023 148.404i −0.0180437 0.152993i
\(971\) 131.434 + 404.512i 0.135359 + 0.416594i 0.995646 0.0932176i \(-0.0297152\pi\)
−0.860286 + 0.509811i \(0.829715\pi\)
\(972\) −27.9786 + 54.9111i −0.0287845 + 0.0564929i
\(973\) 808.258 128.016i 0.830687 0.131568i
\(974\) 136.368i 0.140008i
\(975\) −141.697 592.372i −0.145330 0.607561i
\(976\) −740.336 −0.758541
\(977\) −18.9491 119.640i −0.0193952 0.122457i 0.976091 0.217362i \(-0.0697452\pi\)
−0.995486 + 0.0949053i \(0.969745\pi\)
\(978\) −37.7299 19.2243i −0.0385786 0.0196568i
\(979\) −168.266 + 54.6729i −0.171875 + 0.0558457i
\(980\) −524.876 + 484.787i −0.535588 + 0.494680i
\(981\) −192.375 + 592.071i −0.196101 + 0.603538i
\(982\) −127.647 127.647i −0.129987 0.129987i
\(983\) 476.265 + 934.723i 0.484502 + 0.950888i 0.995806 + 0.0914884i \(0.0291624\pi\)
−0.511304 + 0.859400i \(0.670838\pi\)
\(984\) 85.0552 + 117.068i 0.0864382 + 0.118972i
\(985\) −646.954 25.6875i −0.656806 0.0260787i
\(986\) −15.7021 11.4083i −0.0159251 0.0115702i
\(987\) 36.9410 + 5.85088i 0.0374276 + 0.00592795i
\(988\) 178.518 1127.12i 0.180686 1.14081i
\(989\) 614.003 845.103i 0.620832 0.854502i
\(990\) −5.17705 7.75496i −0.00522935 0.00783330i
\(991\) 243.062 176.595i 0.245269 0.178199i −0.458358 0.888768i \(-0.651562\pi\)
0.703628 + 0.710569i \(0.251562\pi\)
\(992\) 303.431 154.606i 0.305878 0.155853i
\(993\) −706.756 + 706.756i −0.711739 + 0.711739i
\(994\) −55.3654 17.9893i −0.0556996 0.0180979i
\(995\) 132.817 61.1628i 0.133485 0.0614701i
\(996\) 5.47850 + 16.8611i 0.00550050 + 0.0169288i
\(997\) −316.377 + 620.925i −0.317329 + 0.622793i −0.993485 0.113965i \(-0.963645\pi\)
0.676156 + 0.736759i \(0.263645\pi\)
\(998\) 39.2802 6.22137i 0.0393589 0.00623384i
\(999\) 229.993i 0.230223i
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 75.3.k.a.37.5 80
3.2 odd 2 225.3.r.b.37.6 80
5.2 odd 4 375.3.k.b.43.6 80
5.3 odd 4 375.3.k.c.43.5 80
5.4 even 2 375.3.k.a.82.6 80
25.2 odd 20 375.3.k.a.343.6 80
25.11 even 5 375.3.k.c.157.5 80
25.14 even 10 375.3.k.b.157.6 80
25.23 odd 20 inner 75.3.k.a.73.5 yes 80
75.23 even 20 225.3.r.b.73.6 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.3.k.a.37.5 80 1.1 even 1 trivial
75.3.k.a.73.5 yes 80 25.23 odd 20 inner
225.3.r.b.37.6 80 3.2 odd 2
225.3.r.b.73.6 80 75.23 even 20
375.3.k.a.82.6 80 5.4 even 2
375.3.k.a.343.6 80 25.2 odd 20
375.3.k.b.43.6 80 5.2 odd 4
375.3.k.b.157.6 80 25.14 even 10
375.3.k.c.43.5 80 5.3 odd 4
375.3.k.c.157.5 80 25.11 even 5