Properties

Label 154.2.i.a.87.4
Level $154$
Weight $2$
Character 154.87
Analytic conductor $1.230$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [154,2,Mod(87,154)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(154, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("154.87");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.i (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: \(1.22969619113\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} - 102 x^{7} + 144 x^{6} - 432 x^{5} + 502 x^{4} + 288 x^{3} + 72 x^{2} + 12 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 87.4
Root \(2.24352 - 0.601150i\) of defining polynomial
Character \(\chi\) \(=\) 154.87
Dual form 154.2.i.a.131.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(2.24749 + 1.29759i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.06486 + 1.76950i) q^{5} -2.59518 q^{6} +(-0.649221 + 2.56486i) q^{7} +1.00000i q^{8} +(1.86747 + 3.23456i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(2.24749 + 1.29759i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.06486 + 1.76950i) q^{5} -2.59518 q^{6} +(-0.649221 + 2.56486i) q^{7} +1.00000i q^{8} +(1.86747 + 3.23456i) q^{9} +(1.76950 - 3.06486i) q^{10} +(-0.926651 - 3.18454i) q^{11} +(2.24749 - 1.29759i) q^{12} +5.01680 q^{13} +(-0.720188 - 2.54585i) q^{14} -9.18432 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.94681 - 3.37197i) q^{17} +(-3.23456 - 1.86747i) q^{18} +(2.32819 + 4.03254i) q^{19} +3.53900i q^{20} +(-4.78725 + 4.92208i) q^{21} +(2.39477 + 2.29457i) q^{22} +(0.779812 + 1.35067i) q^{23} +(-1.29759 + 2.24749i) q^{24} +(3.76225 - 6.51641i) q^{25} +(-4.34467 + 2.50840i) q^{26} +1.90732i q^{27} +(1.89662 + 1.84467i) q^{28} -0.100205i q^{29} +(7.95386 - 4.59216i) q^{30} +(-0.242252 - 0.139864i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.04959 - 8.35964i) q^{33} +3.89362i q^{34} +(-2.54874 - 9.00974i) q^{35} +3.73495 q^{36} +(-0.352715 - 0.610920i) q^{37} +(-4.03254 - 2.32819i) q^{38} +(11.2752 + 6.50974i) q^{39} +(-1.76950 - 3.06486i) q^{40} -2.94809 q^{41} +(1.68484 - 6.65627i) q^{42} -9.03556i q^{43} +(-3.22122 - 0.789769i) q^{44} +(-11.4471 - 6.60898i) q^{45} +(-1.35067 - 0.779812i) q^{46} +(5.68935 - 3.28475i) q^{47} -2.59518i q^{48} +(-6.15702 - 3.33032i) q^{49} +7.52450i q^{50} +(8.75087 - 5.05232i) q^{51} +(2.50840 - 4.34467i) q^{52} +(-2.77029 + 4.79828i) q^{53} +(-0.953659 - 1.65179i) q^{54} +(8.47510 + 8.12048i) q^{55} +(-2.56486 - 0.649221i) q^{56} +12.0841i q^{57} +(0.0501023 + 0.0867797i) q^{58} +(12.5871 + 7.26719i) q^{59} +(-4.59216 + 7.95386i) q^{60} +(-5.56360 - 9.63644i) q^{61} +0.279729 q^{62} +(-9.50860 + 2.68987i) q^{63} -1.00000 q^{64} +(-15.3758 + 8.87721i) q^{65} +(2.40482 + 8.26446i) q^{66} +(-1.99196 + 3.45017i) q^{67} +(-1.94681 - 3.37197i) q^{68} +4.04750i q^{69} +(6.71215 + 6.52829i) q^{70} -8.45381 q^{71} +(-3.23456 + 1.86747i) q^{72} +(-1.94885 + 3.37552i) q^{73} +(0.610920 + 0.352715i) q^{74} +(16.9112 - 9.76370i) q^{75} +4.65637 q^{76} +(8.76951 - 0.309257i) q^{77} -13.0195 q^{78} +(-6.66824 + 3.84991i) q^{79} +(3.06486 + 1.76950i) q^{80} +(3.12751 - 5.41700i) q^{81} +(2.55312 - 1.47405i) q^{82} -2.87320 q^{83} +(1.86902 + 6.60692i) q^{84} +13.7795i q^{85} +(4.51778 + 7.82503i) q^{86} +(0.130024 - 0.225209i) q^{87} +(3.18454 - 0.926651i) q^{88} +(-5.15200 + 2.97451i) q^{89} +13.2180 q^{90} +(-3.25701 + 12.8674i) q^{91} +1.55962 q^{92} +(-0.362973 - 0.628687i) q^{93} +(-3.28475 + 5.68935i) q^{94} +(-14.2711 - 8.23945i) q^{95} +(1.29759 + 2.24749i) q^{96} -16.7587i q^{97} +(6.99730 - 0.194366i) q^{98} +(8.57010 - 8.94436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} - 36 q^{26} - 12 q^{31} - 24 q^{33} + 32 q^{36} - 16 q^{37} + 12 q^{38} + 12 q^{42} - 8 q^{44} - 108 q^{45} + 24 q^{47} + 8 q^{49} - 28 q^{53} - 4 q^{56} - 12 q^{58} + 60 q^{59} - 4 q^{60} - 16 q^{64} + 48 q^{66} + 12 q^{67} + 60 q^{70} + 8 q^{71} + 60 q^{75} + 44 q^{77} - 16 q^{78} + 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} + 96 q^{89} - 36 q^{91} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 2.24749 + 1.29759i 1.29759 + 0.749163i 0.979987 0.199061i \(-0.0637892\pi\)
0.317602 + 0.948224i \(0.397123\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −3.06486 + 1.76950i −1.37065 + 0.791344i −0.991010 0.133791i \(-0.957285\pi\)
−0.379638 + 0.925135i \(0.623951\pi\)
\(6\) −2.59518 −1.05948
\(7\) −0.649221 + 2.56486i −0.245383 + 0.969426i
\(8\) 1.00000i 0.353553i
\(9\) 1.86747 + 3.23456i 0.622491 + 1.07819i
\(10\) 1.76950 3.06486i 0.559564 0.969194i
\(11\) −0.926651 3.18454i −0.279396 0.960176i
\(12\) 2.24749 1.29759i 0.648794 0.374582i
\(13\) 5.01680 1.39141 0.695704 0.718328i \(-0.255092\pi\)
0.695704 + 0.718328i \(0.255092\pi\)
\(14\) −0.720188 2.54585i −0.192478 0.680406i
\(15\) −9.18432 −2.37138
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.94681 3.37197i 0.472171 0.817824i −0.527322 0.849665i \(-0.676804\pi\)
0.999493 + 0.0318416i \(0.0101372\pi\)
\(18\) −3.23456 1.86747i −0.762393 0.440168i
\(19\) 2.32819 + 4.03254i 0.534123 + 0.925128i 0.999205 + 0.0398605i \(0.0126914\pi\)
−0.465082 + 0.885267i \(0.653975\pi\)
\(20\) 3.53900i 0.791344i
\(21\) −4.78725 + 4.92208i −1.04466 + 1.07409i
\(22\) 2.39477 + 2.29457i 0.510568 + 0.489204i
\(23\) 0.779812 + 1.35067i 0.162602 + 0.281635i 0.935801 0.352528i \(-0.114678\pi\)
−0.773199 + 0.634163i \(0.781345\pi\)
\(24\) −1.29759 + 2.24749i −0.264869 + 0.458767i
\(25\) 3.76225 6.51641i 0.752450 1.30328i
\(26\) −4.34467 + 2.50840i −0.852060 + 0.491937i
\(27\) 1.90732i 0.367064i
\(28\) 1.89662 + 1.84467i 0.358428 + 0.348610i
\(29\) 0.100205i 0.0186075i −0.999957 0.00930376i \(-0.997038\pi\)
0.999957 0.00930376i \(-0.00296152\pi\)
\(30\) 7.95386 4.59216i 1.45217 0.838410i
\(31\) −0.242252 0.139864i −0.0435098 0.0251204i 0.478087 0.878312i \(-0.341330\pi\)
−0.521597 + 0.853192i \(0.674664\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 2.04959 8.35964i 0.356788 1.45523i
\(34\) 3.89362i 0.667750i
\(35\) −2.54874 9.00974i −0.430816 1.52292i
\(36\) 3.73495 0.622491
\(37\) −0.352715 0.610920i −0.0579860 0.100435i 0.835575 0.549376i \(-0.185135\pi\)
−0.893561 + 0.448941i \(0.851801\pi\)
\(38\) −4.03254 2.32819i −0.654164 0.377682i
\(39\) 11.2752 + 6.50974i 1.80548 + 1.04239i
\(40\) −1.76950 3.06486i −0.279782 0.484597i
\(41\) −2.94809 −0.460415 −0.230207 0.973142i \(-0.573940\pi\)
−0.230207 + 0.973142i \(0.573940\pi\)
\(42\) 1.68484 6.65627i 0.259977 1.02708i
\(43\) 9.03556i 1.37791i −0.724804 0.688955i \(-0.758070\pi\)
0.724804 0.688955i \(-0.241930\pi\)
\(44\) −3.22122 0.789769i −0.485617 0.119062i
\(45\) −11.4471 6.60898i −1.70643 0.985209i
\(46\) −1.35067 0.779812i −0.199146 0.114977i
\(47\) 5.68935 3.28475i 0.829876 0.479129i −0.0239340 0.999714i \(-0.507619\pi\)
0.853810 + 0.520584i \(0.174286\pi\)
\(48\) 2.59518i 0.374582i
\(49\) −6.15702 3.33032i −0.879575 0.475761i
\(50\) 7.52450i 1.06412i
\(51\) 8.75087 5.05232i 1.22537 0.707466i
\(52\) 2.50840 4.34467i 0.347852 0.602498i
\(53\) −2.77029 + 4.79828i −0.380529 + 0.659095i −0.991138 0.132837i \(-0.957591\pi\)
0.610609 + 0.791932i \(0.290925\pi\)
\(54\) −0.953659 1.65179i −0.129777 0.224780i
\(55\) 8.47510 + 8.12048i 1.14278 + 1.09496i
\(56\) −2.56486 0.649221i −0.342744 0.0867558i
\(57\) 12.0841i 1.60058i
\(58\) 0.0501023 + 0.0867797i 0.00657875 + 0.0113947i
\(59\) 12.5871 + 7.26719i 1.63871 + 0.946108i 0.981279 + 0.192589i \(0.0616884\pi\)
0.657427 + 0.753518i \(0.271645\pi\)
\(60\) −4.59216 + 7.95386i −0.592846 + 1.02684i
\(61\) −5.56360 9.63644i −0.712346 1.23382i −0.963974 0.265996i \(-0.914299\pi\)
0.251628 0.967824i \(-0.419034\pi\)
\(62\) 0.279729 0.0355256
\(63\) −9.50860 + 2.68987i −1.19797 + 0.338891i
\(64\) −1.00000 −0.125000
\(65\) −15.3758 + 8.87721i −1.90713 + 1.10108i
\(66\) 2.40482 + 8.26446i 0.296013 + 1.01728i
\(67\) −1.99196 + 3.45017i −0.243356 + 0.421506i −0.961668 0.274216i \(-0.911582\pi\)
0.718312 + 0.695721i \(0.244915\pi\)
\(68\) −1.94681 3.37197i −0.236085 0.408912i
\(69\) 4.04750i 0.487262i
\(70\) 6.71215 + 6.52829i 0.802255 + 0.780280i
\(71\) −8.45381 −1.00328 −0.501641 0.865076i \(-0.667270\pi\)
−0.501641 + 0.865076i \(0.667270\pi\)
\(72\) −3.23456 + 1.86747i −0.381196 + 0.220084i
\(73\) −1.94885 + 3.37552i −0.228096 + 0.395074i −0.957244 0.289282i \(-0.906583\pi\)
0.729148 + 0.684356i \(0.239917\pi\)
\(74\) 0.610920 + 0.352715i 0.0710180 + 0.0410023i
\(75\) 16.9112 9.76370i 1.95274 1.12742i
\(76\) 4.65637 0.534123
\(77\) 8.76951 0.309257i 0.999379 0.0352431i
\(78\) −13.0195 −1.47417
\(79\) −6.66824 + 3.84991i −0.750236 + 0.433149i −0.825779 0.563994i \(-0.809264\pi\)
0.0755434 + 0.997143i \(0.475931\pi\)
\(80\) 3.06486 + 1.76950i 0.342662 + 0.197836i
\(81\) 3.12751 5.41700i 0.347501 0.601889i
\(82\) 2.55312 1.47405i 0.281945 0.162781i
\(83\) −2.87320 −0.315375 −0.157687 0.987489i \(-0.550404\pi\)
−0.157687 + 0.987489i \(0.550404\pi\)
\(84\) 1.86902 + 6.60692i 0.203926 + 0.720874i
\(85\) 13.7795i 1.49460i
\(86\) 4.51778 + 7.82503i 0.487165 + 0.843794i
\(87\) 0.130024 0.225209i 0.0139401 0.0241449i
\(88\) 3.18454 0.926651i 0.339473 0.0987813i
\(89\) −5.15200 + 2.97451i −0.546111 + 0.315297i −0.747552 0.664203i \(-0.768771\pi\)
0.201441 + 0.979501i \(0.435438\pi\)
\(90\) 13.2180 1.39330
\(91\) −3.25701 + 12.8674i −0.341428 + 1.34887i
\(92\) 1.55962 0.162602
\(93\) −0.362973 0.628687i −0.0376385 0.0651919i
\(94\) −3.28475 + 5.68935i −0.338796 + 0.586811i
\(95\) −14.2711 8.23945i −1.46419 0.845349i
\(96\) 1.29759 + 2.24749i 0.132435 + 0.229383i
\(97\) 16.7587i 1.70159i −0.525502 0.850793i \(-0.676122\pi\)
0.525502 0.850793i \(-0.323878\pi\)
\(98\) 6.99730 0.194366i 0.706834 0.0196339i
\(99\) 8.57010 8.94436i 0.861327 0.898942i
\(100\) −3.76225 6.51641i −0.376225 0.651641i
\(101\) −0.701452 + 1.21495i −0.0697971 + 0.120892i −0.898812 0.438335i \(-0.855569\pi\)
0.829015 + 0.559227i \(0.188902\pi\)
\(102\) −5.05232 + 8.75087i −0.500254 + 0.866465i
\(103\) 1.78653 1.03145i 0.176032 0.101632i −0.409395 0.912357i \(-0.634260\pi\)
0.585427 + 0.810725i \(0.300927\pi\)
\(104\) 5.01680i 0.491937i
\(105\) 5.96266 23.5565i 0.581896 2.29888i
\(106\) 5.54058i 0.538149i
\(107\) 10.6222 6.13274i 1.02689 0.592875i 0.110797 0.993843i \(-0.464660\pi\)
0.916092 + 0.400968i \(0.131326\pi\)
\(108\) 1.65179 + 0.953659i 0.158943 + 0.0917659i
\(109\) −5.82394 3.36245i −0.557832 0.322065i 0.194443 0.980914i \(-0.437710\pi\)
−0.752275 + 0.658849i \(0.771043\pi\)
\(110\) −11.3999 2.79499i −1.08694 0.266492i
\(111\) 1.83072i 0.173764i
\(112\) 2.54585 0.720188i 0.240560 0.0680514i
\(113\) −11.9900 −1.12792 −0.563960 0.825802i \(-0.690723\pi\)
−0.563960 + 0.825802i \(0.690723\pi\)
\(114\) −6.04206 10.4652i −0.565891 0.980152i
\(115\) −4.78003 2.75975i −0.445740 0.257348i
\(116\) −0.0867797 0.0501023i −0.00805729 0.00465188i
\(117\) 9.36873 + 16.2271i 0.866140 + 1.50020i
\(118\) −14.5344 −1.33800
\(119\) 7.38473 + 7.18245i 0.676957 + 0.658415i
\(120\) 9.18432i 0.838410i
\(121\) −9.28264 + 5.90192i −0.843876 + 0.536538i
\(122\) 9.63644 + 5.56360i 0.872442 + 0.503705i
\(123\) −6.62581 3.82541i −0.597429 0.344926i
\(124\) −0.242252 + 0.139864i −0.0217549 + 0.0125602i
\(125\) 8.93419i 0.799098i
\(126\) 6.88975 7.08379i 0.613788 0.631074i
\(127\) 13.2199i 1.17308i 0.809922 + 0.586538i \(0.199509\pi\)
−0.809922 + 0.586538i \(0.800491\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 11.7244 20.3073i 1.03228 1.78796i
\(130\) 8.87721 15.3758i 0.778583 1.34855i
\(131\) 8.24931 + 14.2882i 0.720746 + 1.24837i 0.960701 + 0.277584i \(0.0895337\pi\)
−0.239956 + 0.970784i \(0.577133\pi\)
\(132\) −6.21487 5.95482i −0.540935 0.518300i
\(133\) −11.8544 + 3.35347i −1.02791 + 0.290782i
\(134\) 3.98392i 0.344158i
\(135\) −3.37500 5.84566i −0.290473 0.503115i
\(136\) 3.37197 + 1.94681i 0.289144 + 0.166938i
\(137\) −3.32187 + 5.75365i −0.283807 + 0.491568i −0.972319 0.233657i \(-0.924931\pi\)
0.688512 + 0.725225i \(0.258264\pi\)
\(138\) −2.02375 3.50524i −0.172273 0.298386i
\(139\) 14.3533 1.21743 0.608716 0.793388i \(-0.291685\pi\)
0.608716 + 0.793388i \(0.291685\pi\)
\(140\) −9.07703 2.29759i −0.767149 0.194182i
\(141\) 17.0490 1.43578
\(142\) 7.32121 4.22690i 0.614383 0.354714i
\(143\) −4.64882 15.9762i −0.388754 1.33600i
\(144\) 1.86747 3.23456i 0.155623 0.269547i
\(145\) 0.177312 + 0.307113i 0.0147249 + 0.0255044i
\(146\) 3.89771i 0.322577i
\(147\) −9.51645 15.4742i −0.784904 1.27629i
\(148\) −0.705430 −0.0579860
\(149\) 2.30871 1.33294i 0.189137 0.109198i −0.402441 0.915446i \(-0.631838\pi\)
0.591579 + 0.806247i \(0.298505\pi\)
\(150\) −9.76370 + 16.9112i −0.797203 + 1.38080i
\(151\) 8.99830 + 5.19517i 0.732271 + 0.422777i 0.819253 0.573433i \(-0.194389\pi\)
−0.0869812 + 0.996210i \(0.527722\pi\)
\(152\) −4.03254 + 2.32819i −0.327082 + 0.188841i
\(153\) 14.5425 1.17569
\(154\) −7.43999 + 4.65258i −0.599532 + 0.374916i
\(155\) 0.989959 0.0795154
\(156\) 11.2752 6.50974i 0.902738 0.521196i
\(157\) 7.25273 + 4.18736i 0.578831 + 0.334188i 0.760669 0.649140i \(-0.224871\pi\)
−0.181838 + 0.983329i \(0.558205\pi\)
\(158\) 3.84991 6.66824i 0.306282 0.530497i
\(159\) −12.4524 + 7.18940i −0.987540 + 0.570156i
\(160\) −3.53900 −0.279782
\(161\) −3.97056 + 1.12322i −0.312924 + 0.0885223i
\(162\) 6.25501i 0.491440i
\(163\) −1.53254 2.65444i −0.120038 0.207911i 0.799745 0.600340i \(-0.204968\pi\)
−0.919782 + 0.392429i \(0.871635\pi\)
\(164\) −1.47405 + 2.55312i −0.115104 + 0.199365i
\(165\) 8.51066 + 29.2479i 0.662554 + 2.27694i
\(166\) 2.48826 1.43660i 0.193127 0.111502i
\(167\) −10.0731 −0.779482 −0.389741 0.920925i \(-0.627435\pi\)
−0.389741 + 0.920925i \(0.627435\pi\)
\(168\) −4.92208 4.78725i −0.379746 0.369345i
\(169\) 12.1682 0.936018
\(170\) −6.88975 11.9334i −0.528420 0.915250i
\(171\) −8.69566 + 15.0613i −0.664973 + 1.15177i
\(172\) −7.82503 4.51778i −0.596653 0.344478i
\(173\) 0.0383013 + 0.0663398i 0.00291200 + 0.00504372i 0.867478 0.497476i \(-0.165740\pi\)
−0.864566 + 0.502520i \(0.832406\pi\)
\(174\) 0.260049i 0.0197142i
\(175\) 14.2711 + 13.8802i 1.07880 + 1.04925i
\(176\) −2.29457 + 2.39477i −0.172960 + 0.180513i
\(177\) 18.8596 + 32.6659i 1.41758 + 2.45532i
\(178\) 2.97451 5.15200i 0.222949 0.386159i
\(179\) 4.48746 7.77250i 0.335408 0.580944i −0.648155 0.761509i \(-0.724459\pi\)
0.983563 + 0.180564i \(0.0577924\pi\)
\(180\) −11.4471 + 6.60898i −0.853216 + 0.492604i
\(181\) 15.1450i 1.12572i −0.826554 0.562858i \(-0.809702\pi\)
0.826554 0.562858i \(-0.190298\pi\)
\(182\) −3.61304 12.7720i −0.267816 0.946723i
\(183\) 28.8771i 2.13465i
\(184\) −1.35067 + 0.779812i −0.0995730 + 0.0574885i
\(185\) 2.16204 + 1.24826i 0.158957 + 0.0917736i
\(186\) 0.628687 + 0.362973i 0.0460976 + 0.0266145i
\(187\) −12.5422 3.07506i −0.917177 0.224871i
\(188\) 6.56949i 0.479129i
\(189\) −4.89201 1.23827i −0.355841 0.0900710i
\(190\) 16.4789 1.19550
\(191\) −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i \(-0.236317\pi\)
−0.953912 + 0.300088i \(0.902984\pi\)
\(192\) −2.24749 1.29759i −0.162199 0.0936454i
\(193\) −12.8415 7.41403i −0.924350 0.533674i −0.0393299 0.999226i \(-0.512522\pi\)
−0.885020 + 0.465552i \(0.845856\pi\)
\(194\) 8.37933 + 14.5134i 0.601601 + 1.04200i
\(195\) −46.0759 −3.29956
\(196\) −5.96266 + 3.66698i −0.425904 + 0.261927i
\(197\) 14.4745i 1.03126i −0.856811 0.515631i \(-0.827557\pi\)
0.856811 0.515631i \(-0.172443\pi\)
\(198\) −2.94974 + 12.0311i −0.209629 + 0.855012i
\(199\) −9.72188 5.61293i −0.689166 0.397890i 0.114133 0.993465i \(-0.463591\pi\)
−0.803300 + 0.595575i \(0.796924\pi\)
\(200\) 6.51641 + 3.76225i 0.460779 + 0.266031i
\(201\) −8.95381 + 5.16948i −0.631553 + 0.364627i
\(202\) 1.40290i 0.0987080i
\(203\) 0.257011 + 0.0650550i 0.0180386 + 0.00456596i
\(204\) 10.1046i 0.707466i
\(205\) 9.03550 5.21665i 0.631066 0.364346i
\(206\) −1.03145 + 1.78653i −0.0718647 + 0.124473i
\(207\) −2.91256 + 5.04469i −0.202437 + 0.350630i
\(208\) −2.50840 4.34467i −0.173926 0.301249i
\(209\) 10.6844 11.1510i 0.739054 0.771329i
\(210\) 6.61444 + 23.3819i 0.456440 + 1.61350i
\(211\) 6.44038i 0.443374i 0.975118 + 0.221687i \(0.0711563\pi\)
−0.975118 + 0.221687i \(0.928844\pi\)
\(212\) 2.77029 + 4.79828i 0.190264 + 0.329548i
\(213\) −18.9999 10.9696i −1.30185 0.751622i
\(214\) −6.13274 + 10.6222i −0.419226 + 0.726120i
\(215\) 15.9884 + 27.6927i 1.09040 + 1.88863i
\(216\) −1.90732 −0.129777
\(217\) 0.516008 0.530540i 0.0350289 0.0360154i
\(218\) 6.72491 0.455468
\(219\) −8.76006 + 5.05762i −0.591950 + 0.341763i
\(220\) 11.2701 3.27941i 0.759829 0.221098i
\(221\) 9.76675 16.9165i 0.656983 1.13793i
\(222\) 0.915358 + 1.58545i 0.0614348 + 0.106408i
\(223\) 4.01793i 0.269061i −0.990909 0.134530i \(-0.957047\pi\)
0.990909 0.134530i \(-0.0429526\pi\)
\(224\) −1.84467 + 1.89662i −0.123252 + 0.126724i
\(225\) 28.1036 1.87357
\(226\) 10.3836 5.99498i 0.690707 0.398780i
\(227\) 6.36466 11.0239i 0.422437 0.731682i −0.573740 0.819037i \(-0.694508\pi\)
0.996177 + 0.0873549i \(0.0278414\pi\)
\(228\) 10.4652 + 6.04206i 0.693072 + 0.400145i
\(229\) −5.20780 + 3.00672i −0.344141 + 0.198690i −0.662102 0.749414i \(-0.730335\pi\)
0.317961 + 0.948104i \(0.397002\pi\)
\(230\) 5.51950 0.363945
\(231\) 20.1107 + 10.6842i 1.32319 + 0.702967i
\(232\) 0.100205 0.00657875
\(233\) 5.60053 3.23347i 0.366903 0.211832i −0.305202 0.952288i \(-0.598724\pi\)
0.672105 + 0.740456i \(0.265391\pi\)
\(234\) −16.2271 9.36873i −1.06080 0.612453i
\(235\) −11.6247 + 20.1346i −0.758312 + 1.31343i
\(236\) 12.5871 7.26719i 0.819353 0.473054i
\(237\) −19.9824 −1.29800
\(238\) −9.98659 2.52782i −0.647335 0.163854i
\(239\) 15.5775i 1.00762i −0.863813 0.503812i \(-0.831930\pi\)
0.863813 0.503812i \(-0.168070\pi\)
\(240\) 4.59216 + 7.95386i 0.296423 + 0.513419i
\(241\) −11.7381 + 20.3310i −0.756119 + 1.30964i 0.188697 + 0.982035i \(0.439573\pi\)
−0.944816 + 0.327601i \(0.893760\pi\)
\(242\) 5.08804 9.75253i 0.327072 0.626916i
\(243\) 19.0134 10.9774i 1.21971 0.704201i
\(244\) −11.1272 −0.712346
\(245\) 24.7634 0.687860i 1.58208 0.0439457i
\(246\) 7.65083 0.487799
\(247\) 11.6800 + 20.2304i 0.743183 + 1.28723i
\(248\) 0.139864 0.242252i 0.00888140 0.0153830i
\(249\) −6.45748 3.72823i −0.409226 0.236267i
\(250\) −4.46709 7.73723i −0.282524 0.489345i
\(251\) 18.2818i 1.15394i 0.816766 + 0.576968i \(0.195764\pi\)
−0.816766 + 0.576968i \(0.804236\pi\)
\(252\) −2.42481 + 9.57962i −0.152748 + 0.603459i
\(253\) 3.57867 3.73495i 0.224989 0.234814i
\(254\) −6.60994 11.4488i −0.414745 0.718359i
\(255\) −17.8801 + 30.9693i −1.11970 + 1.93937i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −8.33087 + 4.80983i −0.519666 + 0.300029i −0.736798 0.676113i \(-0.763663\pi\)
0.217132 + 0.976142i \(0.430330\pi\)
\(258\) 23.4489i 1.45986i
\(259\) 1.79591 0.508042i 0.111593 0.0315682i
\(260\) 17.7544i 1.10108i
\(261\) 0.324118 0.187129i 0.0200624 0.0115830i
\(262\) −14.2882 8.24931i −0.882729 0.509644i
\(263\) 0.501139 + 0.289333i 0.0309016 + 0.0178410i 0.515371 0.856967i \(-0.327654\pi\)
−0.484470 + 0.874808i \(0.660987\pi\)
\(264\) 8.35964 + 2.04959i 0.514500 + 0.126144i
\(265\) 19.6081i 1.20452i
\(266\) 8.58949 8.83139i 0.526655 0.541487i
\(267\) −15.4388 −0.944837
\(268\) 1.99196 + 3.45017i 0.121678 + 0.210753i
\(269\) 19.1302 + 11.0448i 1.16639 + 0.673413i 0.952826 0.303517i \(-0.0981608\pi\)
0.213560 + 0.976930i \(0.431494\pi\)
\(270\) 5.84566 + 3.37500i 0.355756 + 0.205396i
\(271\) 2.13111 + 3.69119i 0.129456 + 0.224224i 0.923466 0.383681i \(-0.125344\pi\)
−0.794010 + 0.607905i \(0.792010\pi\)
\(272\) −3.89362 −0.236085
\(273\) −24.0167 + 24.6931i −1.45356 + 1.49449i
\(274\) 6.64374i 0.401363i
\(275\) −24.2381 5.94261i −1.46161 0.358353i
\(276\) 3.50524 + 2.02375i 0.210991 + 0.121815i
\(277\) −15.9048 9.18263i −0.955626 0.551731i −0.0608016 0.998150i \(-0.519366\pi\)
−0.894824 + 0.446419i \(0.852699\pi\)
\(278\) −12.4303 + 7.17666i −0.745522 + 0.430427i
\(279\) 1.04477i 0.0625489i
\(280\) 9.00974 2.54874i 0.538435 0.152317i
\(281\) 3.72890i 0.222448i −0.993795 0.111224i \(-0.964523\pi\)
0.993795 0.111224i \(-0.0354771\pi\)
\(282\) −14.7649 + 8.52450i −0.879235 + 0.507626i
\(283\) 6.36576 11.0258i 0.378405 0.655417i −0.612425 0.790529i \(-0.709806\pi\)
0.990830 + 0.135111i \(0.0431392\pi\)
\(284\) −4.22690 + 7.32121i −0.250821 + 0.434434i
\(285\) −21.3828 37.0361i −1.26661 2.19383i
\(286\) 12.0141 + 11.5114i 0.710408 + 0.680683i
\(287\) 1.91397 7.56145i 0.112978 0.446338i
\(288\) 3.73495i 0.220084i
\(289\) 0.919861 + 1.59325i 0.0541094 + 0.0937203i
\(290\) −0.307113 0.177312i −0.0180343 0.0104121i
\(291\) 21.7459 37.6649i 1.27476 2.20796i
\(292\) 1.94885 + 3.37552i 0.114048 + 0.197537i
\(293\) 26.2251 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(294\) 15.9786 + 8.64278i 0.931889 + 0.504057i
\(295\) −51.4371 −2.99478
\(296\) 0.610920 0.352715i 0.0355090 0.0205011i
\(297\) 6.07394 1.76742i 0.352446 0.102556i
\(298\) −1.33294 + 2.30871i −0.0772149 + 0.133740i
\(299\) 3.91216 + 6.77605i 0.226246 + 0.391869i
\(300\) 19.5274i 1.12742i
\(301\) 23.1750 + 5.86608i 1.33578 + 0.338115i
\(302\) −10.3903 −0.597897
\(303\) −3.15301 + 1.82039i −0.181136 + 0.104579i
\(304\) 2.32819 4.03254i 0.133531 0.231282i
\(305\) 34.1033 + 19.6896i 1.95275 + 1.12742i
\(306\) −12.5941 + 7.27123i −0.719959 + 0.415669i
\(307\) −25.5942 −1.46074 −0.730369 0.683053i \(-0.760652\pi\)
−0.730369 + 0.683053i \(0.760652\pi\)
\(308\) 4.11693 7.74925i 0.234584 0.441554i
\(309\) 5.35360 0.304556
\(310\) −0.857330 + 0.494980i −0.0486931 + 0.0281129i
\(311\) −1.65385 0.954850i −0.0937811 0.0541446i 0.452376 0.891827i \(-0.350577\pi\)
−0.546157 + 0.837683i \(0.683910\pi\)
\(312\) −6.50974 + 11.2752i −0.368541 + 0.638332i
\(313\) −26.3707 + 15.2251i −1.49056 + 0.860576i −0.999942 0.0107985i \(-0.996563\pi\)
−0.490619 + 0.871374i \(0.663229\pi\)
\(314\) −8.37473 −0.472613
\(315\) 24.3828 25.0695i 1.37382 1.41251i
\(316\) 7.69982i 0.433149i
\(317\) −17.1971 29.7862i −0.965885 1.67296i −0.707220 0.706994i \(-0.750051\pi\)
−0.258665 0.965967i \(-0.583283\pi\)
\(318\) 7.18940 12.4524i 0.403161 0.698296i
\(319\) −0.319106 + 0.0928547i −0.0178665 + 0.00519886i
\(320\) 3.06486 1.76950i 0.171331 0.0989180i
\(321\) 31.8311 1.77664
\(322\) 2.87699 2.95802i 0.160329 0.164844i
\(323\) 18.1302 1.00879
\(324\) −3.12751 5.41700i −0.173750 0.300944i
\(325\) 18.8744 32.6915i 1.04697 1.81340i
\(326\) 2.65444 + 1.53254i 0.147016 + 0.0848795i
\(327\) −8.72616 15.1142i −0.482558 0.835815i
\(328\) 2.94809i 0.162781i
\(329\) 4.73127 + 16.7249i 0.260843 + 0.922074i
\(330\) −21.9944 21.0741i −1.21075 1.16009i
\(331\) −7.75642 13.4345i −0.426332 0.738428i 0.570212 0.821497i \(-0.306861\pi\)
−0.996544 + 0.0830696i \(0.973528\pi\)
\(332\) −1.43660 + 2.48826i −0.0788436 + 0.136561i
\(333\) 1.31737 2.28175i 0.0721915 0.125039i
\(334\) 8.72358 5.03656i 0.477333 0.275588i
\(335\) 14.0991i 0.770314i
\(336\) 6.65627 + 1.68484i 0.363129 + 0.0919158i
\(337\) 7.70882i 0.419926i 0.977709 + 0.209963i \(0.0673344\pi\)
−0.977709 + 0.209963i \(0.932666\pi\)
\(338\) −10.5380 + 6.08412i −0.573192 + 0.330933i
\(339\) −26.9473 15.5580i −1.46358 0.844997i
\(340\) 11.9334 + 6.88975i 0.647180 + 0.373649i
\(341\) −0.220921 + 0.901068i −0.0119635 + 0.0487956i
\(342\) 17.3913i 0.940415i
\(343\) 12.5391 13.6298i 0.677047 0.735940i
\(344\) 9.03556 0.487165
\(345\) −7.16204 12.4050i −0.385591 0.667864i
\(346\) −0.0663398 0.0383013i −0.00356645 0.00205909i
\(347\) 18.8285 + 10.8706i 1.01077 + 0.583567i 0.911416 0.411485i \(-0.134990\pi\)
0.0993513 + 0.995052i \(0.468323\pi\)
\(348\) −0.130024 0.225209i −0.00697004 0.0120725i
\(349\) −13.4565 −0.720307 −0.360154 0.932893i \(-0.617276\pi\)
−0.360154 + 0.932893i \(0.617276\pi\)
\(350\) −19.2993 4.88506i −1.03159 0.261118i
\(351\) 9.56862i 0.510735i
\(352\) 0.789769 3.22122i 0.0420948 0.171692i
\(353\) 5.80903 + 3.35384i 0.309183 + 0.178507i 0.646561 0.762862i \(-0.276207\pi\)
−0.337378 + 0.941369i \(0.609540\pi\)
\(354\) −32.6659 18.8596i −1.73617 1.00238i
\(355\) 25.9098 14.9590i 1.37515 0.793941i
\(356\) 5.94902i 0.315297i
\(357\) 7.27724 + 25.7248i 0.385152 + 1.36150i
\(358\) 8.97491i 0.474339i
\(359\) −26.8869 + 15.5232i −1.41904 + 0.819282i −0.996214 0.0869306i \(-0.972294\pi\)
−0.422823 + 0.906212i \(0.638961\pi\)
\(360\) 6.60898 11.4471i 0.348324 0.603315i
\(361\) −1.34091 + 2.32253i −0.0705744 + 0.122238i
\(362\) 7.57248 + 13.1159i 0.398001 + 0.689358i
\(363\) −28.5209 + 1.21946i −1.49696 + 0.0640050i
\(364\) 9.51498 + 9.25435i 0.498720 + 0.485060i
\(365\) 13.7940i 0.722010i
\(366\) 14.4385 + 25.0083i 0.754714 + 1.30720i
\(367\) 25.6770 + 14.8246i 1.34033 + 0.773838i 0.986855 0.161608i \(-0.0516679\pi\)
0.353471 + 0.935445i \(0.385001\pi\)
\(368\) 0.779812 1.35067i 0.0406505 0.0704087i
\(369\) −5.50549 9.53578i −0.286604 0.496413i
\(370\) −2.49651 −0.129788
\(371\) −10.5084 10.2206i −0.545569 0.530625i
\(372\) −0.725946 −0.0376385
\(373\) 7.60418 4.39027i 0.393729 0.227320i −0.290045 0.957013i \(-0.593670\pi\)
0.683775 + 0.729693i \(0.260337\pi\)
\(374\) 12.3994 3.60803i 0.641158 0.186567i
\(375\) −11.5929 + 20.0795i −0.598655 + 1.03690i
\(376\) 3.28475 + 5.68935i 0.169398 + 0.293406i
\(377\) 0.502706i 0.0258907i
\(378\) 4.85574 1.37363i 0.249752 0.0706518i
\(379\) 30.8135 1.58278 0.791391 0.611311i \(-0.209358\pi\)
0.791391 + 0.611311i \(0.209358\pi\)
\(380\) −14.2711 + 8.23945i −0.732094 + 0.422675i
\(381\) −17.1540 + 29.7116i −0.878825 + 1.52217i
\(382\) 5.19615 + 3.00000i 0.265858 + 0.153493i
\(383\) 4.58545 2.64741i 0.234305 0.135276i −0.378251 0.925703i \(-0.623474\pi\)
0.612557 + 0.790427i \(0.290141\pi\)
\(384\) 2.59518 0.132435
\(385\) −26.3301 + 16.4655i −1.34191 + 0.839158i
\(386\) 14.8281 0.754729
\(387\) 29.2261 16.8737i 1.48564 0.857737i
\(388\) −14.5134 8.37933i −0.736808 0.425396i
\(389\) −0.430119 + 0.744987i −0.0218079 + 0.0377724i −0.876723 0.480995i \(-0.840276\pi\)
0.854916 + 0.518767i \(0.173609\pi\)
\(390\) 39.9029 23.0379i 2.02056 1.16657i
\(391\) 6.07258 0.307104
\(392\) 3.33032 6.15702i 0.168207 0.310977i
\(393\) 42.8168i 2.15982i
\(394\) 7.23723 + 12.5353i 0.364606 + 0.631517i
\(395\) 13.6248 23.5989i 0.685539 1.18739i
\(396\) −3.46099 11.8941i −0.173921 0.597701i
\(397\) 10.6931 6.17367i 0.536672 0.309847i −0.207057 0.978329i \(-0.566389\pi\)
0.743729 + 0.668481i \(0.233055\pi\)
\(398\) 11.2259 0.562702
\(399\) −30.9941 7.84527i −1.55165 0.392755i
\(400\) −7.52450 −0.376225
\(401\) −16.8626 29.2069i −0.842078 1.45852i −0.888134 0.459584i \(-0.847999\pi\)
0.0460561 0.998939i \(-0.485335\pi\)
\(402\) 5.16948 8.95381i 0.257830 0.446575i
\(403\) −1.21533 0.701671i −0.0605399 0.0349527i
\(404\) 0.701452 + 1.21495i 0.0348985 + 0.0604461i
\(405\) 22.1365i 1.09997i
\(406\) −0.255105 + 0.0721662i −0.0126607 + 0.00358155i
\(407\) −1.61866 + 1.68935i −0.0802339 + 0.0837377i
\(408\) 5.05232 + 8.75087i 0.250127 + 0.433233i
\(409\) −19.1846 + 33.2287i −0.948616 + 1.64305i −0.200273 + 0.979740i \(0.564183\pi\)
−0.748343 + 0.663312i \(0.769150\pi\)
\(410\) −5.21665 + 9.03550i −0.257632 + 0.446231i
\(411\) −14.9317 + 8.62085i −0.736529 + 0.425235i
\(412\) 2.06291i 0.101632i
\(413\) −26.8112 + 27.5663i −1.31929 + 1.35645i
\(414\) 5.82511i 0.286289i
\(415\) 8.80595 5.08412i 0.432267 0.249570i
\(416\) 4.34467 + 2.50840i 0.213015 + 0.122984i
\(417\) 32.2589 + 18.6247i 1.57973 + 0.912056i
\(418\) −3.67746 + 14.9992i −0.179870 + 0.733636i
\(419\) 33.5023i 1.63670i 0.574723 + 0.818348i \(0.305110\pi\)
−0.574723 + 0.818348i \(0.694890\pi\)
\(420\) −17.4192 16.9421i −0.849970 0.826688i
\(421\) −23.0155 −1.12171 −0.560853 0.827915i \(-0.689527\pi\)
−0.560853 + 0.827915i \(0.689527\pi\)
\(422\) −3.22019 5.57753i −0.156756 0.271510i
\(423\) 21.2494 + 12.2683i 1.03318 + 0.596508i
\(424\) −4.79828 2.77029i −0.233025 0.134537i
\(425\) −14.6488 25.3724i −0.710570 1.23074i
\(426\) 21.9391 1.06295
\(427\) 28.3281 8.01368i 1.37089 0.387809i
\(428\) 12.2655i 0.592875i
\(429\) 10.2824 41.9386i 0.496438 2.02482i
\(430\) −27.6927 15.9884i −1.33546 0.771030i
\(431\) −23.2425 13.4191i −1.11955 0.646373i −0.178265 0.983983i \(-0.557048\pi\)
−0.941286 + 0.337609i \(0.890382\pi\)
\(432\) 1.65179 0.953659i 0.0794716 0.0458829i
\(433\) 30.6912i 1.47493i 0.675387 + 0.737463i \(0.263976\pi\)
−0.675387 + 0.737463i \(0.736024\pi\)
\(434\) −0.181606 + 0.717465i −0.00871736 + 0.0344394i
\(435\) 0.920312i 0.0441256i
\(436\) −5.82394 + 3.36245i −0.278916 + 0.161032i
\(437\) −3.63110 + 6.28924i −0.173699 + 0.300855i
\(438\) 5.05762 8.76006i 0.241663 0.418572i
\(439\) −8.42258 14.5883i −0.401988 0.696263i 0.591978 0.805954i \(-0.298347\pi\)
−0.993966 + 0.109691i \(0.965014\pi\)
\(440\) −8.12048 + 8.47510i −0.387129 + 0.404035i
\(441\) −0.725946 26.1345i −0.0345688 1.24450i
\(442\) 19.5335i 0.929114i
\(443\) 0.395295 + 0.684671i 0.0187810 + 0.0325297i 0.875263 0.483647i \(-0.160688\pi\)
−0.856482 + 0.516177i \(0.827355\pi\)
\(444\) −1.58545 0.915358i −0.0752419 0.0434410i
\(445\) 10.5268 18.2329i 0.499017 0.864323i
\(446\) 2.00897 + 3.47963i 0.0951273 + 0.164765i
\(447\) 6.91841 0.327230
\(448\) 0.649221 2.56486i 0.0306728 0.121178i
\(449\) 15.9734 0.753833 0.376917 0.926247i \(-0.376984\pi\)
0.376917 + 0.926247i \(0.376984\pi\)
\(450\) −24.3384 + 14.0518i −1.14732 + 0.662408i
\(451\) 2.73185 + 9.38833i 0.128638 + 0.442079i
\(452\) −5.99498 + 10.3836i −0.281980 + 0.488404i
\(453\) 13.4824 + 23.3522i 0.633458 + 1.09718i
\(454\) 12.7293i 0.597416i
\(455\) −12.7865 45.2000i −0.599442 2.11901i
\(456\) −12.0841 −0.565891
\(457\) 30.2530 17.4666i 1.41517 0.817052i 0.419305 0.907845i \(-0.362274\pi\)
0.995870 + 0.0907937i \(0.0289404\pi\)
\(458\) 3.00672 5.20780i 0.140495 0.243344i
\(459\) 6.43143 + 3.71319i 0.300193 + 0.173317i
\(460\) −4.78003 + 2.75975i −0.222870 + 0.128674i
\(461\) −20.8346 −0.970364 −0.485182 0.874413i \(-0.661247\pi\)
−0.485182 + 0.874413i \(0.661247\pi\)
\(462\) −22.7584 + 0.802576i −1.05882 + 0.0373392i
\(463\) 13.1724 0.612172 0.306086 0.952004i \(-0.400981\pi\)
0.306086 + 0.952004i \(0.400981\pi\)
\(464\) −0.0867797 + 0.0501023i −0.00402865 + 0.00232594i
\(465\) 2.22492 + 1.28456i 0.103178 + 0.0595700i
\(466\) −3.23347 + 5.60053i −0.149788 + 0.259440i
\(467\) −14.5651 + 8.40919i −0.673995 + 0.389131i −0.797589 0.603202i \(-0.793891\pi\)
0.123594 + 0.992333i \(0.460558\pi\)
\(468\) 18.7375 0.866140
\(469\) −7.55599 7.34902i −0.348903 0.339346i
\(470\) 23.2494i 1.07241i
\(471\) 10.8670 + 18.8221i 0.500723 + 0.867277i
\(472\) −7.26719 + 12.5871i −0.334500 + 0.579370i
\(473\) −28.7741 + 8.37281i −1.32304 + 0.384982i
\(474\) 17.3053 9.99120i 0.794857 0.458911i
\(475\) 35.0369 1.60760
\(476\) 9.91256 2.80414i 0.454341 0.128528i
\(477\) −20.6938 −0.947503
\(478\) 7.78874 + 13.4905i 0.356249 + 0.617041i
\(479\) −11.4291 + 19.7957i −0.522208 + 0.904491i 0.477458 + 0.878654i \(0.341558\pi\)
−0.999666 + 0.0258361i \(0.991775\pi\)
\(480\) −7.95386 4.59216i −0.363042 0.209603i
\(481\) −1.76950 3.06486i −0.0806822 0.139746i
\(482\) 23.4762i 1.06931i
\(483\) −10.3813 2.62772i −0.472364 0.119566i
\(484\) 0.469894 + 10.9900i 0.0213588 + 0.499544i
\(485\) 29.6544 + 51.3630i 1.34654 + 2.33227i
\(486\) −10.9774 + 19.0134i −0.497945 + 0.862467i
\(487\) −15.6314 + 27.0744i −0.708327 + 1.22686i 0.257150 + 0.966371i \(0.417217\pi\)
−0.965477 + 0.260487i \(0.916117\pi\)
\(488\) 9.63644 5.56360i 0.436221 0.251852i
\(489\) 7.95442i 0.359711i
\(490\) −21.1018 + 12.9774i −0.953283 + 0.586260i
\(491\) 22.4979i 1.01532i 0.861558 + 0.507659i \(0.169489\pi\)
−0.861558 + 0.507659i \(0.830511\pi\)
\(492\) −6.62581 + 3.82541i −0.298715 + 0.172463i
\(493\) −0.337887 0.195079i −0.0152177 0.00878593i
\(494\) −20.2304 11.6800i −0.910210 0.525510i
\(495\) −10.4391 + 42.5780i −0.469204 + 1.91374i
\(496\) 0.279729i 0.0125602i
\(497\) 5.48839 21.6828i 0.246188 0.972609i
\(498\) 7.45646 0.334132
\(499\) 15.9548 + 27.6346i 0.714236 + 1.23709i 0.963253 + 0.268595i \(0.0865592\pi\)
−0.249017 + 0.968499i \(0.580107\pi\)
\(500\) 7.73723 + 4.46709i 0.346020 + 0.199774i
\(501\) −22.6392 13.0708i −1.01145 0.583959i
\(502\) −9.14090 15.8325i −0.407978 0.706639i
\(503\) 30.2687 1.34962 0.674808 0.737994i \(-0.264227\pi\)
0.674808 + 0.737994i \(0.264227\pi\)
\(504\) −2.68987 9.50860i −0.119816 0.423547i
\(505\) 4.96487i 0.220934i
\(506\) −1.23174 + 5.02389i −0.0547576 + 0.223339i
\(507\) 27.3480 + 15.7894i 1.21457 + 0.701231i
\(508\) 11.4488 + 6.60994i 0.507956 + 0.293269i
\(509\) −19.9655 + 11.5271i −0.884957 + 0.510930i −0.872290 0.488989i \(-0.837366\pi\)
−0.0126676 + 0.999920i \(0.504032\pi\)
\(510\) 35.7603i 1.58349i
\(511\) −7.39249 7.19000i −0.327025 0.318067i
\(512\) 1.00000i 0.0441942i
\(513\) −7.69133 + 4.44059i −0.339581 + 0.196057i
\(514\) 4.80983 8.33087i 0.212153 0.367459i
\(515\) −3.65031 + 6.32252i −0.160852 + 0.278603i
\(516\) −11.7244 20.3073i −0.516140 0.893980i
\(517\) −15.7325 15.0742i −0.691912 0.662961i
\(518\) −1.30129 + 1.33793i −0.0571753 + 0.0587855i
\(519\) 0.198797i 0.00872624i
\(520\) −8.87721 15.3758i −0.389291 0.674273i
\(521\) −6.91351 3.99152i −0.302886 0.174872i 0.340852 0.940117i \(-0.389284\pi\)
−0.643739 + 0.765245i \(0.722618\pi\)
\(522\) −0.187129 + 0.324118i −0.00819043 + 0.0141862i
\(523\) 2.79140 + 4.83485i 0.122059 + 0.211413i 0.920580 0.390555i \(-0.127717\pi\)
−0.798520 + 0.601968i \(0.794383\pi\)
\(524\) 16.4986 0.720746
\(525\) 14.0634 + 49.7138i 0.613778 + 2.16969i
\(526\) −0.578666 −0.0252310
\(527\) −0.943238 + 0.544579i −0.0410881 + 0.0237222i
\(528\) −8.26446 + 2.40482i −0.359664 + 0.104657i
\(529\) 10.2838 17.8120i 0.447121 0.774437i
\(530\) 9.80405 + 16.9811i 0.425861 + 0.737612i
\(531\) 54.2851i 2.35577i
\(532\) −3.02302 + 11.9430i −0.131064 + 0.517793i
\(533\) −14.7900 −0.640625
\(534\) 13.3704 7.71938i 0.578592 0.334050i
\(535\) −21.7038 + 37.5920i −0.938335 + 1.62524i
\(536\) −3.45017 1.99196i −0.149025 0.0860395i
\(537\) 20.1710 11.6457i 0.870444 0.502551i
\(538\) −22.0896 −0.952350
\(539\) −4.90015 + 22.6934i −0.211065 + 0.977472i
\(540\) −6.74999 −0.290473
\(541\) 11.6066 6.70108i 0.499007 0.288102i −0.229296 0.973357i \(-0.573642\pi\)
0.728304 + 0.685255i \(0.240309\pi\)
\(542\) −3.69119 2.13111i −0.158550 0.0915390i
\(543\) 19.6519 34.0381i 0.843345 1.46072i
\(544\) 3.37197 1.94681i 0.144572 0.0834688i
\(545\) 23.7994 1.01946
\(546\) 8.45252 33.3931i 0.361735 1.42909i
\(547\) 24.5161i 1.04823i −0.851647 0.524116i \(-0.824396\pi\)
0.851647 0.524116i \(-0.175604\pi\)
\(548\) 3.32187 + 5.75365i 0.141903 + 0.245784i
\(549\) 20.7798 35.9916i 0.886858 1.53608i
\(550\) 23.9621 6.97258i 1.02175 0.297312i
\(551\) 0.404079 0.233295i 0.0172143 0.00993870i
\(552\) −4.04750 −0.172273
\(553\) −5.54532 19.6026i −0.235811 0.833585i
\(554\) 18.3653 0.780265
\(555\) 3.23945 + 5.61089i 0.137507 + 0.238169i
\(556\) 7.17666 12.4303i 0.304358 0.527164i
\(557\) 3.12772 + 1.80579i 0.132526 + 0.0765137i 0.564797 0.825230i \(-0.308954\pi\)
−0.432271 + 0.901744i \(0.642288\pi\)
\(558\) 0.522386 + 0.904799i 0.0221144 + 0.0383032i
\(559\) 45.3296i 1.91724i
\(560\) −6.52829 + 6.71215i −0.275871 + 0.283640i
\(561\) −24.1983 23.1858i −1.02165 0.978905i
\(562\) 1.86445 + 3.22933i 0.0786472 + 0.136221i
\(563\) 2.92902 5.07320i 0.123443 0.213810i −0.797680 0.603081i \(-0.793940\pi\)
0.921123 + 0.389271i \(0.127273\pi\)
\(564\) 8.52450 14.7649i 0.358946 0.621713i
\(565\) 36.7476 21.2162i 1.54598 0.892573i
\(566\) 12.7315i 0.535146i
\(567\) 11.8634 + 11.5384i 0.498216 + 0.484569i
\(568\) 8.45381i 0.354714i
\(569\) −29.9772 + 17.3073i −1.25671 + 0.725561i −0.972433 0.233182i \(-0.925086\pi\)
−0.284275 + 0.958743i \(0.591753\pi\)
\(570\) 37.0361 + 21.3828i 1.55127 + 0.895628i
\(571\) −6.89907 3.98318i −0.288717 0.166691i 0.348646 0.937254i \(-0.386642\pi\)
−0.637363 + 0.770564i \(0.719975\pi\)
\(572\) −16.1602 3.96211i −0.675692 0.165664i
\(573\) 15.5711i 0.650491i
\(574\) 2.12318 + 7.50539i 0.0886199 + 0.313269i
\(575\) 11.7354 0.489399
\(576\) −1.86747 3.23456i −0.0778114 0.134773i
\(577\) 15.9144 + 9.18819i 0.662525 + 0.382509i 0.793239 0.608911i \(-0.208393\pi\)
−0.130713 + 0.991420i \(0.541727\pi\)
\(578\) −1.59325 0.919861i −0.0662703 0.0382612i
\(579\) −19.2407 33.3259i −0.799618 1.38498i
\(580\) 0.354624 0.0147249
\(581\) 1.86534 7.36936i 0.0773874 0.305732i
\(582\) 43.4917i 1.80279i
\(583\) 17.8474 + 4.37578i 0.739165 + 0.181226i
\(584\) −3.37552 1.94885i −0.139680 0.0806442i
\(585\) −57.4277 33.1559i −2.37434 1.37083i
\(586\) −22.7116 + 13.1126i −0.938209 + 0.541675i
\(587\) 17.2267i 0.711021i −0.934672 0.355511i \(-0.884307\pi\)
0.934672 0.355511i \(-0.115693\pi\)
\(588\) −18.1592 + 0.504414i −0.748874 + 0.0208017i
\(589\) 1.30252i 0.0536695i
\(590\) 44.5459 25.7186i 1.83392 1.05882i
\(591\) 18.7819 32.5312i 0.772584 1.33816i
\(592\) −0.352715 + 0.610920i −0.0144965 + 0.0251087i
\(593\) 20.6214 + 35.7172i 0.846817 + 1.46673i 0.884033 + 0.467424i \(0.154818\pi\)
−0.0372161 + 0.999307i \(0.511849\pi\)
\(594\) −4.37648 + 4.56760i −0.179569 + 0.187411i
\(595\) −35.3425 8.94595i −1.44890 0.366748i
\(596\) 2.66587i 0.109198i
\(597\) −14.5666 25.2300i −0.596169 1.03260i
\(598\) −6.77605 3.91216i −0.277093 0.159980i
\(599\) −4.97720 + 8.62076i −0.203363 + 0.352235i −0.949610 0.313434i \(-0.898520\pi\)
0.746247 + 0.665669i \(0.231854\pi\)
\(600\) 9.76370 + 16.9112i 0.398602 + 0.690398i
\(601\) 4.76767 0.194477 0.0972386 0.995261i \(-0.468999\pi\)
0.0972386 + 0.995261i \(0.468999\pi\)
\(602\) −23.0031 + 6.50731i −0.937538 + 0.265218i
\(603\) −14.8797 −0.605949
\(604\) 8.99830 5.19517i 0.366136 0.211389i
\(605\) 18.0066 34.5142i 0.732071 1.40320i
\(606\) 1.82039 3.15301i 0.0739484 0.128082i
\(607\) −2.27672 3.94340i −0.0924094 0.160058i 0.816115 0.577889i \(-0.196124\pi\)
−0.908524 + 0.417832i \(0.862790\pi\)
\(608\) 4.65637i 0.188841i
\(609\) 0.493215 + 0.479705i 0.0199861 + 0.0194386i
\(610\) −39.3791 −1.59441
\(611\) 28.5423 16.4789i 1.15470 0.666665i
\(612\) 7.27123 12.5941i 0.293922 0.509088i
\(613\) 1.25482 + 0.724472i 0.0506818 + 0.0292611i 0.525127 0.851024i \(-0.324018\pi\)
−0.474445 + 0.880285i \(0.657351\pi\)
\(614\) 22.1652 12.7971i 0.894515 0.516449i
\(615\) 27.0762 1.09182
\(616\) 0.309257 + 8.76951i 0.0124603 + 0.353334i
\(617\) −2.96752 −0.119468 −0.0597340 0.998214i \(-0.519025\pi\)
−0.0597340 + 0.998214i \(0.519025\pi\)
\(618\) −4.63636 + 2.67680i −0.186502 + 0.107677i
\(619\) −10.0004 5.77375i −0.401951 0.232067i 0.285374 0.958416i \(-0.407882\pi\)
−0.687326 + 0.726349i \(0.741215\pi\)
\(620\) 0.494980 0.857330i 0.0198789 0.0344312i
\(621\) −2.57616 + 1.48735i −0.103378 + 0.0596853i
\(622\) 1.90970 0.0765720
\(623\) −4.28442 15.1453i −0.171651 0.606783i
\(624\) 13.0195i 0.521196i
\(625\) 3.00222 + 5.19999i 0.120089 + 0.208000i
\(626\) 15.2251 26.3707i 0.608519 1.05399i
\(627\) 38.4824 11.1978i 1.53684 0.447195i
\(628\) 7.25273 4.18736i 0.289415 0.167094i
\(629\) −2.74668 −0.109517
\(630\) −8.58138 + 33.9022i −0.341891 + 1.35070i
\(631\) −27.5215 −1.09562 −0.547808 0.836604i \(-0.684537\pi\)
−0.547808 + 0.836604i \(0.684537\pi\)
\(632\) −3.84991 6.66824i −0.153141 0.265248i
\(633\) −8.35696 + 14.4747i −0.332159 + 0.575317i
\(634\) 29.7862 + 17.1971i 1.18296 + 0.682983i
\(635\) −23.3926 40.5171i −0.928306 1.60787i
\(636\) 14.3788i 0.570156i
\(637\) −30.8885 16.7076i −1.22385 0.661978i
\(638\) 0.229926 0.239967i 0.00910288 0.00950040i
\(639\) −15.7873 27.3443i −0.624535 1.08173i
\(640\) −1.76950 + 3.06486i −0.0699456 + 0.121149i
\(641\) −16.8273 + 29.1458i −0.664639 + 1.15119i 0.314744 + 0.949177i \(0.398081\pi\)
−0.979383 + 0.202013i \(0.935252\pi\)
\(642\) −27.5666 + 15.9156i −1.08797 + 0.628137i
\(643\) 5.95261i 0.234748i 0.993088 + 0.117374i \(0.0374476\pi\)
−0.993088 + 0.117374i \(0.962552\pi\)
\(644\) −1.01254 + 4.00022i −0.0398997 + 0.157631i
\(645\) 82.9855i 3.26755i
\(646\) −15.7012 + 9.06508i −0.617754 + 0.356661i
\(647\) 10.1963 + 5.88686i 0.400860 + 0.231437i 0.686855 0.726795i \(-0.258991\pi\)
−0.285995 + 0.958231i \(0.592324\pi\)
\(648\) 5.41700 + 3.12751i 0.212800 + 0.122860i
\(649\) 11.4788 46.8184i 0.450582 1.83778i
\(650\) 37.7489i 1.48063i
\(651\) 1.84815 0.522818i 0.0724345 0.0204908i
\(652\) −3.06508 −0.120038
\(653\) −14.4335 24.9996i −0.564827 0.978309i −0.997066 0.0765498i \(-0.975610\pi\)
0.432239 0.901759i \(-0.357724\pi\)
\(654\) 15.1142 + 8.72616i 0.591010 + 0.341220i
\(655\) −50.5660 29.1943i −1.97578 1.14071i
\(656\) 1.47405 + 2.55312i 0.0575519 + 0.0996827i
\(657\) −14.5577 −0.567952
\(658\) −12.4599 12.1186i −0.485736 0.472431i
\(659\) 44.6812i 1.74053i 0.492581 + 0.870266i \(0.336053\pi\)
−0.492581 + 0.870266i \(0.663947\pi\)
\(660\) 29.5847 + 7.25349i 1.15158 + 0.282342i
\(661\) −34.3242 19.8171i −1.33505 0.770794i −0.348985 0.937128i \(-0.613474\pi\)
−0.986069 + 0.166334i \(0.946807\pi\)
\(662\) 13.4345 + 7.75642i 0.522147 + 0.301462i
\(663\) 43.9013 25.3464i 1.70499 0.984374i
\(664\) 2.87320i 0.111502i
\(665\) 30.3982 31.2543i 1.17879 1.21199i
\(666\) 2.63474i 0.102094i
\(667\) 0.135344 0.0781407i 0.00524053 0.00302562i
\(668\) −5.03656 + 8.72358i −0.194870 + 0.337525i
\(669\) 5.21362 9.03026i 0.201570 0.349130i
\(670\) 7.04953 + 12.2101i 0.272347 + 0.471719i
\(671\) −25.5321 + 26.6471i −0.985657 + 1.02870i
\(672\) −6.60692 + 1.86902i −0.254868 + 0.0720989i
\(673\) 2.71886i 0.104804i −0.998626 0.0524022i \(-0.983312\pi\)
0.998626 0.0524022i \(-0.0166878\pi\)
\(674\) −3.85441 6.67604i −0.148466 0.257151i
\(675\) 12.4289 + 7.17580i 0.478387 + 0.276197i
\(676\) 6.08412 10.5380i 0.234005 0.405308i
\(677\) −3.02973 5.24764i −0.116442 0.201683i 0.801913 0.597440i \(-0.203816\pi\)
−0.918355 + 0.395757i \(0.870482\pi\)
\(678\) 31.1161 1.19501
\(679\) 42.9837 + 10.8801i 1.64956 + 0.417539i
\(680\) −13.7795 −0.528420
\(681\) 28.6090 16.5174i 1.09630 0.632949i
\(682\) −0.259211 0.890808i −0.00992570 0.0341108i
\(683\) 3.01704 5.22567i 0.115444 0.199955i −0.802513 0.596634i \(-0.796504\pi\)
0.917957 + 0.396680i \(0.129838\pi\)
\(684\) 8.69566 + 15.0613i 0.332487 + 0.575884i
\(685\) 23.5122i 0.898354i
\(686\) −4.04428 + 18.0733i −0.154411 + 0.690041i
\(687\) −15.6060 −0.595405
\(688\) −7.82503 + 4.51778i −0.298326 + 0.172239i
\(689\) −13.8980 + 24.0720i −0.529471 + 0.917071i
\(690\) 12.4050 + 7.16204i 0.472251 + 0.272654i
\(691\) −17.1519 + 9.90263i −0.652487 + 0.376714i −0.789409 0.613868i \(-0.789613\pi\)
0.136921 + 0.990582i \(0.456279\pi\)
\(692\) 0.0766026 0.00291200
\(693\) 17.3771 + 27.7880i 0.660103 + 1.05558i
\(694\) −21.7413 −0.825288
\(695\) −43.9909 + 25.3982i −1.66867 + 0.963407i
\(696\) 0.225209 + 0.130024i 0.00853652 + 0.00492856i
\(697\) −5.73938 + 9.94090i −0.217394 + 0.376538i
\(698\) 11.6536 6.72823i 0.441096 0.254667i
\(699\) 16.7828 0.634786
\(700\) 19.1562 5.41905i 0.724037 0.204821i
\(701\) 26.0155i 0.982591i −0.870993 0.491296i \(-0.836524\pi\)
0.870993 0.491296i \(-0.163476\pi\)
\(702\) −4.78431 8.28667i −0.180572 0.312760i
\(703\) 1.64237 2.84467i 0.0619433 0.107289i
\(704\) 0.926651 + 3.18454i 0.0349245 + 0.120022i
\(705\) −52.2528 + 30.1682i −1.96795 + 1.13620i
\(706\) −6.70769 −0.252447
\(707\) −2.66078 2.58790i −0.100069 0.0973280i
\(708\) 37.7193 1.41758
\(709\) 12.4458 + 21.5568i 0.467413 + 0.809583i 0.999307 0.0372278i \(-0.0118527\pi\)
−0.531894 + 0.846811i \(0.678519\pi\)
\(710\) −14.9590 + 25.9098i −0.561401 + 0.972376i
\(711\) −24.9055 14.3792i −0.934030 0.539263i
\(712\) −2.97451 5.15200i −0.111474 0.193079i
\(713\) 0.436271i 0.0163385i
\(714\) −19.1647 18.6397i −0.717221 0.697575i
\(715\) 42.5178 + 40.7388i 1.59008 + 1.52354i
\(716\) −4.48746 7.77250i −0.167704 0.290472i
\(717\) 20.2132 35.0102i 0.754875 1.30748i
\(718\) 15.5232 26.8869i 0.579320 1.00341i
\(719\) −11.5156 + 6.64851i −0.429458 + 0.247948i −0.699116 0.715009i \(-0.746423\pi\)
0.269658 + 0.962956i \(0.413089\pi\)
\(720\) 13.2180i 0.492604i
\(721\) 1.48568 + 5.25184i 0.0553296 + 0.195589i
\(722\) 2.68183i 0.0998073i
\(723\) −52.7626 + 30.4625i −1.96226 + 1.13291i
\(724\) −13.1159 7.57248i −0.487449 0.281429i
\(725\) −0.652974 0.376995i −0.0242508 0.0140012i
\(726\) 24.0901 15.3165i 0.894067 0.568450i
\(727\) 5.67083i 0.210319i 0.994455 + 0.105160i \(0.0335354\pi\)
−0.994455 + 0.105160i \(0.966465\pi\)
\(728\) −12.8674 3.25701i −0.476897 0.120713i
\(729\) 38.2116 1.41525
\(730\) 6.89699 + 11.9459i 0.255269 + 0.442139i
\(731\) −30.4677 17.5905i −1.12689 0.650609i
\(732\) −25.0083 14.4385i −0.924332 0.533663i
\(733\) 20.6879 + 35.8326i 0.764127 + 1.32351i 0.940707 + 0.339220i \(0.110163\pi\)
−0.176580 + 0.984286i \(0.556504\pi\)
\(734\) −29.6492 −1.09437
\(735\) 56.5481 + 30.5868i 2.08581 + 1.12821i
\(736\) 1.55962i 0.0574885i
\(737\) 12.8331 + 3.14637i 0.472712 + 0.115898i
\(738\) 9.53578 + 5.50549i 0.351017 + 0.202660i
\(739\) 35.9749 + 20.7701i 1.32336 + 0.764042i 0.984263 0.176710i \(-0.0565453\pi\)
0.339097 + 0.940752i \(0.389879\pi\)
\(740\) 2.16204 1.24826i 0.0794783 0.0458868i
\(741\) 60.6236i 2.22706i
\(742\) 14.2108 + 3.59706i 0.521696 + 0.132052i
\(743\) 39.7404i 1.45793i −0.684549 0.728967i \(-0.740001\pi\)
0.684549 0.728967i \(-0.259999\pi\)
\(744\) 0.628687 0.362973i 0.0230488 0.0133072i
\(745\) −4.71725 + 8.17053i −0.172827 + 0.299345i
\(746\) −4.39027 + 7.60418i −0.160739 + 0.278409i
\(747\) −5.36562 9.29353i −0.196318 0.340033i
\(748\) −8.93419 + 9.32434i −0.326666 + 0.340932i
\(749\) 8.83346 + 31.2260i 0.322768 + 1.14097i
\(750\) 23.1858i 0.846626i
\(751\) −2.68263 4.64645i −0.0978905 0.169551i 0.812921 0.582374i \(-0.197876\pi\)
−0.910811 + 0.412823i \(0.864543\pi\)
\(752\) −5.68935 3.28475i −0.207469 0.119782i
\(753\) −23.7223 + 41.0882i −0.864487 + 1.49734i
\(754\) 0.251353 + 0.435356i 0.00915374 + 0.0158547i
\(755\) −36.7714 −1.33825
\(756\) −3.51838 + 3.61747i −0.127962 + 0.131566i
\(757\) 25.8962 0.941215 0.470607 0.882343i \(-0.344035\pi\)
0.470607 + 0.882343i \(0.344035\pi\)
\(758\) −26.6852 + 15.4067i −0.969251 + 0.559598i
\(759\) 12.8894 3.75062i 0.467857 0.136139i
\(760\) 8.23945 14.2711i 0.298876 0.517669i
\(761\) −7.61030 13.1814i −0.275873 0.477827i 0.694482 0.719510i \(-0.255634\pi\)
−0.970355 + 0.241684i \(0.922300\pi\)
\(762\) 34.3080i 1.24285i
\(763\) 12.4053 12.7546i 0.449100 0.461748i
\(764\) −6.00000 −0.217072
\(765\) −44.5706 + 25.7329i −1.61145 + 0.930374i
\(766\) −2.64741 + 4.58545i −0.0956548 + 0.165679i
\(767\) 63.1471 + 36.4580i 2.28011 + 1.31642i
\(768\) −2.24749 + 1.29759i −0.0810993 + 0.0468227i
\(769\) 22.5146 0.811898 0.405949 0.913896i \(-0.366941\pi\)
0.405949 + 0.913896i \(0.366941\pi\)
\(770\) 14.5698 27.4246i 0.525059 0.988313i
\(771\) −24.9647 −0.899083
\(772\) −12.8415 + 7.41403i −0.462175 + 0.266837i
\(773\) 24.2776 + 14.0167i 0.873204 + 0.504144i 0.868412 0.495844i \(-0.165141\pi\)
0.00479213 + 0.999989i \(0.498475\pi\)
\(774\) −16.8737 + 29.2261i −0.606512 + 1.05051i
\(775\) −1.82283 + 1.05241i −0.0654778 + 0.0378036i
\(776\) 16.7587 0.601601
\(777\) 4.69553 + 1.18854i 0.168451 + 0.0426386i
\(778\) 0.860237i 0.0308410i
\(779\) −6.86371 11.8883i −0.245918 0.425943i
\(780\) −23.0379 + 39.9029i −0.824891 + 1.42875i
\(781\) 7.83373 + 26.9215i 0.280313 + 0.963328i
\(782\) −5.25901 + 3.03629i −0.188062 + 0.108578i
\(783\) 0.191122 0.00683014
\(784\) 0.194366 + 6.99730i 0.00694163 + 0.249904i
\(785\) −29.6381 −1.05783
\(786\) −21.4084 37.0805i −0.763613 1.32262i
\(787\) −6.37160 + 11.0359i −0.227123 + 0.393388i −0.956954 0.290239i \(-0.906265\pi\)
0.729831 + 0.683627i \(0.239599\pi\)
\(788\) −12.5353 7.23723i −0.446550 0.257816i
\(789\) 0.750870 + 1.30054i 0.0267317 + 0.0463006i
\(790\) 27.2496i 0.969499i
\(791\) 7.78414 30.7526i 0.276772 1.09344i
\(792\) 8.94436 + 8.57010i 0.317824 + 0.304525i
\(793\) −27.9114 48.3440i −0.991165 1.71675i
\(794\) −6.17367 + 10.6931i −0.219095 + 0.379484i
\(795\) 25.4432 44.0690i 0.902379 1.56297i
\(796\) −9.72188 + 5.61293i −0.344583 + 0.198945i
\(797\) 5.63488i 0.199598i 0.995008 + 0.0997989i \(0.0318199\pi\)
−0.995008 + 0.0997989i \(0.968180\pi\)
\(798\) 30.7643 8.70284i 1.08904 0.308077i
\(799\) 25.5791i 0.904923i
\(800\) 6.51641 3.76225i 0.230390 0.133016i
\(801\) −19.2425 11.1096i −0.679899 0.392540i
\(802\) 29.2069 + 16.8626i 1.03133 + 0.595439i
\(803\) 12.5554 + 3.07829i 0.443070 + 0.108630i
\(804\) 10.3390i 0.364627i
\(805\) 10.1817 10.4684i 0.358857 0.368963i
\(806\) 1.40334 0.0494306
\(807\) 28.6632 + 49.6462i 1.00899 + 1.74763i
\(808\) −1.21495 0.701452i −0.0427418 0.0246770i
\(809\) −14.7572 8.52007i −0.518835 0.299550i 0.217623 0.976033i \(-0.430170\pi\)
−0.736458 + 0.676483i \(0.763503\pi\)
\(810\) −11.0682 19.1707i −0.388898 0.673591i
\(811\) 0.332109 0.0116619 0.00583097 0.999983i \(-0.498144\pi\)
0.00583097 + 0.999983i \(0.498144\pi\)
\(812\) 0.184845 0.190050i 0.00648678 0.00666946i
\(813\) 11.0612i 0.387934i
\(814\) 0.557126 2.27234i 0.0195273 0.0796456i
\(815\) 9.39404 + 5.42365i 0.329059 + 0.189982i
\(816\) −8.75087 5.05232i −0.306342 0.176867i
\(817\) 36.4363 21.0365i 1.27474 0.735973i
\(818\) 38.3692i 1.34155i
\(819\) −47.7027 + 13.4945i −1.66687 + 0.471536i
\(820\) 10.4333i 0.364346i
\(821\) −1.97706 + 1.14146i −0.0690000 + 0.0398372i −0.534103 0.845419i \(-0.679351\pi\)
0.465103 + 0.885257i \(0.346017\pi\)
\(822\) 8.62085 14.9317i 0.300687 0.520804i
\(823\) −5.04228 + 8.73348i −0.175763 + 0.304430i −0.940425 0.340001i \(-0.889572\pi\)
0.764662 + 0.644431i \(0.222906\pi\)
\(824\) 1.03145 + 1.78653i 0.0359324 + 0.0622367i
\(825\) −46.7637 44.8070i −1.62810 1.55998i
\(826\) 9.43603 37.2787i 0.328321 1.29709i
\(827\) 10.9337i 0.380204i −0.981764 0.190102i \(-0.939118\pi\)
0.981764 0.190102i \(-0.0608818\pi\)
\(828\) 2.91256 + 5.04469i 0.101218 + 0.175315i
\(829\) −10.0682 5.81287i −0.349683 0.201889i 0.314863 0.949137i \(-0.398041\pi\)
−0.664545 + 0.747248i \(0.731375\pi\)
\(830\) −5.08412 + 8.80595i −0.176472 + 0.305659i
\(831\) −23.8306 41.2757i −0.826673 1.43184i
\(832\) −5.01680 −0.173926
\(833\) −23.2163 + 14.2778i −0.804398 + 0.494697i
\(834\) −37.2494 −1.28984
\(835\) 30.8727 17.8244i 1.06839 0.616838i
\(836\) −4.31483 14.8284i −0.149232 0.512852i
\(837\) 0.266766 0.462052i 0.00922078 0.0159709i
\(838\) −16.7512 29.0139i −0.578659 1.00227i
\(839\) 23.4571i 0.809828i 0.914355 + 0.404914i \(0.132699\pi\)
−0.914355 + 0.404914i \(0.867301\pi\)
\(840\) 23.5565 + 5.96266i 0.812777 + 0.205731i
\(841\) 28.9900 0.999654
\(842\) 19.9320 11.5077i 0.686902 0.396583i
\(843\) 4.83858 8.38067i 0.166650 0.288646i
\(844\) 5.57753 + 3.22019i 0.191986 + 0.110843i
\(845\) −37.2940 + 21.5317i −1.28295 + 0.740712i
\(846\) −24.5367 −0.843589
\(847\) −9.11112 27.6403i −0.313062 0.949733i
\(848\) 5.54058 0.190264
\(849\) 28.6140 16.5203i 0.982029 0.566975i
\(850\) 25.3724 + 14.6488i 0.870266 + 0.502449i
\(851\) 0.550102 0.952805i 0.0188573 0.0326617i
\(852\) −18.9999 + 10.9696i −0.650924 + 0.375811i
\(853\) 38.5870 1.32119 0.660597 0.750741i \(-0.270303\pi\)
0.660597 + 0.750741i \(0.270303\pi\)
\(854\) −20.5260 + 21.1041i −0.702387 + 0.722168i
\(855\) 61.5478i 2.10489i
\(856\) 6.13274 + 10.6222i 0.209613 + 0.363060i
\(857\) 21.3007 36.8938i 0.727617 1.26027i −0.230271 0.973126i \(-0.573961\pi\)
0.957888 0.287142i \(-0.0927053\pi\)
\(858\) 12.0645 + 41.4611i 0.411875 + 1.41546i
\(859\) 10.7344 6.19752i 0.366254 0.211457i −0.305567 0.952171i \(-0.598846\pi\)
0.671821 + 0.740714i \(0.265513\pi\)
\(860\) 31.9768 1.09040
\(861\) 14.1133 14.5107i 0.480979 0.494525i
\(862\) 26.8381 0.914110
\(863\) 19.6374 + 34.0130i 0.668465 + 1.15781i 0.978333 + 0.207036i \(0.0663816\pi\)
−0.309869 + 0.950779i \(0.600285\pi\)
\(864\) −0.953659 + 1.65179i −0.0324441 + 0.0561949i
\(865\) −0.234776 0.135548i −0.00798264 0.00460878i
\(866\) −15.3456 26.5794i −0.521465 0.903204i
\(867\) 4.77440i 0.162147i
\(868\) −0.201457 0.712146i −0.00683791 0.0241718i
\(869\) 18.4393 + 17.6678i 0.625512 + 0.599338i
\(870\) −0.460156 0.797013i −0.0156007 0.0270213i
\(871\) −9.99325 + 17.3088i −0.338608 + 0.586487i
\(872\) 3.36245 5.82394i 0.113867 0.197223i
\(873\) 54.2069 31.2964i 1.83463 1.05922i
\(874\) 7.26219i 0.245647i
\(875\) −22.9149 5.80026i −0.774666 0.196085i
\(876\) 10.1152i 0.341763i
\(877\) −39.9403 + 23.0595i −1.34869 + 0.778665i −0.988064 0.154046i \(-0.950770\pi\)
−0.360624 + 0.932711i \(0.617436\pi\)
\(878\) 14.5883 + 8.42258i 0.492332 + 0.284248i
\(879\) 58.9407 + 34.0294i 1.98802 + 1.14778i
\(880\) 2.79499 11.3999i 0.0942191 0.384290i
\(881\) 14.9583i 0.503957i −0.967733 0.251978i \(-0.918919\pi\)
0.967733 0.251978i \(-0.0810812\pi\)
\(882\) 13.6960 + 22.2702i 0.461167 + 0.749877i
\(883\) −8.42386 −0.283485 −0.141743 0.989904i \(-0.545271\pi\)
−0.141743 + 0.989904i \(0.545271\pi\)
\(884\) −9.76675 16.9165i −0.328491 0.568964i
\(885\) −115.604 66.7442i −3.88600 2.24358i
\(886\) −0.684671 0.395295i −0.0230020 0.0132802i
\(887\) 5.66022 + 9.80379i 0.190052 + 0.329179i 0.945267 0.326298i \(-0.105801\pi\)
−0.755216 + 0.655477i \(0.772468\pi\)
\(888\) 1.83072 0.0614348
\(889\) −33.9072 8.58263i −1.13721 0.287852i
\(890\) 21.0536i 0.705717i
\(891\) −20.1488 4.94001i −0.675009 0.165497i
\(892\) −3.47963 2.00897i −0.116507 0.0672652i
\(893\) 26.4917 + 15.2950i 0.886512 + 0.511828i
\(894\) −5.99152 + 3.45920i −0.200386 + 0.115693i
\(895\) 31.7622i 1.06169i
\(896\) 0.720188 + 2.54585i 0.0240598 + 0.0850507i
\(897\) 20.3055i 0.677980i
\(898\) −13.8334 + 7.98672i −0.461627 + 0.266520i
\(899\) −0.0140151 + 0.0242748i −0.000467428 + 0.000809609i
\(900\) 14.0518 24.3384i 0.468393 0.811281i
\(901\) 10.7865 + 18.6827i 0.359349 + 0.622411i
\(902\) −7.06002 6.76461i −0.235073 0.225237i
\(903\) 44.4737 + 43.2555i 1.47999 + 1.43945i
\(904\) 11.9900i 0.398780i
\(905\) 26.7990 + 46.4172i 0.890828 + 1.54296i
\(906\) −23.3522 13.4824i −0.775825 0.447923i
\(907\) −27.4033 + 47.4638i −0.909910 + 1.57601i −0.0957232 + 0.995408i \(0.530516\pi\)
−0.814187 + 0.580603i \(0.802817\pi\)
\(908\) −6.36466 11.0239i −0.211219 0.365841i
\(909\) −5.23977 −0.173792
\(910\) 33.6735 + 32.7511i 1.11626 + 1.08569i
\(911\) 46.5914 1.54364 0.771820 0.635841i \(-0.219347\pi\)
0.771820 + 0.635841i \(0.219347\pi\)
\(912\) 10.4652 6.04206i 0.346536 0.200073i
\(913\) 2.66245 + 9.14983i 0.0881143 + 0.302815i
\(914\) −17.4666 + 30.2530i −0.577743 + 1.00068i
\(915\) 51.0979 + 88.5042i 1.68924 + 2.92586i
\(916\) 6.01345i 0.198690i
\(917\) −42.0029 + 11.8821i −1.38706 + 0.392382i
\(918\) −7.42637 −0.245107
\(919\) −47.0315 + 27.1536i −1.55142 + 0.895716i −0.553399 + 0.832916i \(0.686669\pi\)
−0.998026 + 0.0627991i \(0.979997\pi\)
\(920\) 2.75975 4.78003i 0.0909863 0.157593i
\(921\) −57.5227 33.2107i −1.89544 1.09433i
\(922\) 18.0433 10.4173i 0.594224 0.343076i
\(923\) −42.4110 −1.39598
\(924\) 19.3081 12.0743i 0.635190 0.397214i
\(925\) −5.30800 −0.174526
\(926\) −11.4076 + 6.58618i −0.374877 + 0.216435i
\(927\) 6.67259 + 3.85242i 0.219157 + 0.126530i
\(928\) 0.0501023 0.0867797i 0.00164469 0.00284868i
\(929\) −18.6550 + 10.7704i −0.612049 + 0.353367i −0.773767 0.633470i \(-0.781630\pi\)
0.161718 + 0.986837i \(0.448297\pi\)
\(930\) −2.56912 −0.0842447
\(931\) −0.905040 32.5821i −0.0296615 1.06783i
\(932\) 6.46694i 0.211832i
\(933\) −2.47801 4.29203i −0.0811262 0.140515i
\(934\) 8.40919 14.5651i 0.275157 0.476586i
\(935\) 43.8814 12.7688i 1.43508 0.417584i
\(936\) −16.2271 + 9.36873i −0.530400 + 0.306227i
\(937\) −15.2663 −0.498729 −0.249364 0.968410i \(-0.580222\pi\)
−0.249364 + 0.968410i \(0.580222\pi\)
\(938\) 10.2182 + 2.58644i 0.333636 + 0.0844504i
\(939\) −79.0239 −2.57885
\(940\) 11.6247 + 20.1346i 0.379156 + 0.656717i
\(941\) −18.0945 + 31.3405i −0.589863 + 1.02167i 0.404387 + 0.914588i \(0.367485\pi\)
−0.994250 + 0.107085i \(0.965848\pi\)
\(942\) −18.8221 10.8670i −0.613258 0.354064i
\(943\) −2.29896 3.98191i −0.0748644 0.129669i
\(944\) 14.5344i 0.473054i
\(945\) 17.1844 4.86127i 0.559010 0.158137i
\(946\) 20.7327 21.6381i 0.674079 0.703516i
\(947\) −19.9609 34.5733i −0.648641 1.12348i −0.983448 0.181193i \(-0.942004\pi\)
0.334806 0.942287i \(-0.391329\pi\)
\(948\) −9.99120 + 17.3053i −0.324499 + 0.562049i
\(949\) −9.77701 + 16.9343i −0.317375 + 0.549710i
\(950\) −30.3428 + 17.5184i −0.984451 + 0.568373i
\(951\) 89.2590i 2.89442i
\(952\) −7.18245 + 7.38473i −0.232785 + 0.239341i
\(953\) 8.97831i 0.290836i −0.989370 0.145418i \(-0.953547\pi\)
0.989370 0.145418i \(-0.0464527\pi\)
\(954\) 17.9213 10.3469i 0.580225 0.334993i
\(955\) 18.3892 + 10.6170i 0.595059 + 0.343558i
\(956\) −13.4905 7.78874i −0.436314 0.251906i
\(957\) −0.837674 0.205378i −0.0270782 0.00663894i
\(958\) 22.8582i 0.738513i
\(959\) −12.6007 12.2555i −0.406897 0.395752i
\(960\) 9.18432 0.296423
\(961\) −15.4609 26.7790i −0.498738 0.863839i
\(962\) 3.06486 + 1.76950i 0.0988151 + 0.0570509i
\(963\) 39.6734 + 22.9055i 1.27846 + 0.738119i
\(964\) 11.7381 + 20.3310i 0.378059 + 0.654818i
\(965\) 52.4765 1.68928
\(966\) 10.3043 2.91496i 0.331536 0.0937874i
\(967\) 51.5738i 1.65850i −0.558877 0.829251i \(-0.688768\pi\)
0.558877 0.829251i \(-0.311232\pi\)
\(968\) −5.90192 9.28264i −0.189695 0.298355i
\(969\) 40.7473 + 23.5255i 1.30899 + 0.755748i
\(970\) −51.3630 29.6544i −1.64917 0.952147i
\(971\) −29.0721 + 16.7848i −0.932967 + 0.538649i −0.887749 0.460328i \(-0.847732\pi\)
−0.0452186 + 0.998977i \(0.514398\pi\)
\(972\) 21.9548i 0.704201i
\(973\) −9.31848 + 36.8143i −0.298737 + 1.18021i
\(974\) 31.2628i 1.00173i
\(975\) 84.8402 48.9825i 2.71706 1.56870i
\(976\) −5.56360 + 9.63644i −0.178087 + 0.308455i
\(977\) 0.576295 0.998172i 0.0184373 0.0319344i −0.856660 0.515882i \(-0.827464\pi\)
0.875097 + 0.483948i \(0.160798\pi\)
\(978\) 3.97721 + 6.88873i 0.127177 + 0.220277i
\(979\) 14.2466 + 13.6504i 0.455322 + 0.436270i
\(980\) 11.7860 21.7897i 0.376490 0.696046i
\(981\) 25.1172i 0.801929i
\(982\) −11.2490 19.4838i −0.358969 0.621753i
\(983\) −14.3846 8.30496i −0.458798 0.264887i 0.252741 0.967534i \(-0.418668\pi\)
−0.711539 + 0.702647i \(0.752001\pi\)
\(984\) 3.82541 6.62581i 0.121950 0.211223i
\(985\) 25.6125 + 44.3622i 0.816083 + 1.41350i
\(986\) 0.390159 0.0124252
\(987\) −11.0686 + 43.7283i −0.352316 + 1.39189i
\(988\) 23.3601 0.743183
\(989\) 12.2041 7.04604i 0.388068 0.224051i
\(990\) −12.2484 42.0932i −0.389281 1.33781i
\(991\) 9.24571 16.0140i 0.293700 0.508703i −0.680982 0.732300i \(-0.738447\pi\)
0.974682 + 0.223598i \(0.0717801\pi\)
\(992\) −0.139864 0.242252i −0.00444070 0.00769151i
\(993\) 40.2586i 1.27757i
\(994\) 6.08833 + 21.5221i 0.193110 + 0.682639i
\(995\) 39.7283 1.25947
\(996\) −6.45748 + 3.72823i −0.204613 + 0.118134i
\(997\) 10.5865 18.3363i 0.335277 0.580717i −0.648261 0.761418i \(-0.724503\pi\)
0.983538 + 0.180701i \(0.0578367\pi\)
\(998\) −27.6346 15.9548i −0.874757 0.505041i
\(999\) 1.16522 0.672739i 0.0368659 0.0212845i
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 154.2.i.a.87.4 16
3.2 odd 2 1386.2.bk.c.703.8 16
4.3 odd 2 1232.2.bn.b.241.2 16
7.2 even 3 1078.2.i.c.901.5 16
7.3 odd 6 1078.2.c.b.1077.7 16
7.4 even 3 1078.2.c.b.1077.2 16
7.5 odd 6 inner 154.2.i.a.131.8 yes 16
7.6 odd 2 1078.2.i.c.1011.1 16
11.10 odd 2 inner 154.2.i.a.87.8 yes 16
21.5 even 6 1386.2.bk.c.901.4 16
28.19 even 6 1232.2.bn.b.593.1 16
33.32 even 2 1386.2.bk.c.703.4 16
44.43 even 2 1232.2.bn.b.241.1 16
77.10 even 6 1078.2.c.b.1077.15 16
77.32 odd 6 1078.2.c.b.1077.10 16
77.54 even 6 inner 154.2.i.a.131.4 yes 16
77.65 odd 6 1078.2.i.c.901.1 16
77.76 even 2 1078.2.i.c.1011.5 16
231.131 odd 6 1386.2.bk.c.901.8 16
308.131 odd 6 1232.2.bn.b.593.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.2.i.a.87.4 16 1.1 even 1 trivial
154.2.i.a.87.8 yes 16 11.10 odd 2 inner
154.2.i.a.131.4 yes 16 77.54 even 6 inner
154.2.i.a.131.8 yes 16 7.5 odd 6 inner
1078.2.c.b.1077.2 16 7.4 even 3
1078.2.c.b.1077.7 16 7.3 odd 6
1078.2.c.b.1077.10 16 77.32 odd 6
1078.2.c.b.1077.15 16 77.10 even 6
1078.2.i.c.901.1 16 77.65 odd 6
1078.2.i.c.901.5 16 7.2 even 3
1078.2.i.c.1011.1 16 7.6 odd 2
1078.2.i.c.1011.5 16 77.76 even 2
1232.2.bn.b.241.1 16 44.43 even 2
1232.2.bn.b.241.2 16 4.3 odd 2
1232.2.bn.b.593.1 16 28.19 even 6
1232.2.bn.b.593.2 16 308.131 odd 6
1386.2.bk.c.703.4 16 33.32 even 2
1386.2.bk.c.703.8 16 3.2 odd 2
1386.2.bk.c.901.4 16 21.5 even 6
1386.2.bk.c.901.8 16 231.131 odd 6