Properties

Label 225.2.u.a.34.25
Level $225$
Weight $2$
Character 225.34
Analytic conductor $1.797$
Analytic rank $0$
Dimension $224$
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] = [225,2,Mod(4,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.u (of order \(30\), 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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 34.25
Character \(\chi\) \(=\) 225.34
Dual form 225.2.u.a.139.25

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965505 + 2.16856i) q^{2} +(-0.975360 - 1.43132i) q^{3} +(-2.43219 + 2.70122i) q^{4} +(2.21576 + 0.300654i) q^{5} +(2.16218 - 3.49707i) q^{6} +(2.25809 + 1.30371i) q^{7} +(-3.69084 - 1.19923i) q^{8} +(-1.09735 + 2.79210i) q^{9} +O(q^{10})\) \(q+(0.965505 + 2.16856i) q^{2} +(-0.975360 - 1.43132i) q^{3} +(-2.43219 + 2.70122i) q^{4} +(2.21576 + 0.300654i) q^{5} +(2.16218 - 3.49707i) q^{6} +(2.25809 + 1.30371i) q^{7} +(-3.69084 - 1.19923i) q^{8} +(-1.09735 + 2.79210i) q^{9} +(1.48734 + 5.09530i) q^{10} +(-0.754795 + 0.336057i) q^{11} +(6.23857 + 0.846576i) q^{12} +(-0.594762 + 1.33586i) q^{13} +(-0.646974 + 6.15555i) q^{14} +(-1.73083 - 3.46471i) q^{15} +(-0.203039 - 1.93179i) q^{16} +(-5.67281 - 1.84321i) q^{17} +(-7.11433 + 0.316127i) q^{18} +(1.76500 - 5.43210i) q^{19} +(-6.20129 + 5.25401i) q^{20} +(-0.336428 - 4.50364i) q^{21} +(-1.45752 - 1.31235i) q^{22} +(2.85090 + 0.299642i) q^{23} +(1.88342 + 6.45245i) q^{24} +(4.81921 + 1.33236i) q^{25} -3.47113 q^{26} +(5.06669 - 1.15265i) q^{27} +(-9.01371 + 2.92873i) q^{28} +(0.136804 + 0.0290786i) q^{29} +(5.84230 - 7.09861i) q^{30} +(7.92771 - 1.68509i) q^{31} +(-2.72854 + 1.57532i) q^{32} +(1.21720 + 0.752577i) q^{33} +(-1.48002 - 14.0815i) q^{34} +(4.61143 + 3.56762i) q^{35} +(-4.87313 - 9.75509i) q^{36} +(-5.44323 - 7.49197i) q^{37} +(13.4839 - 1.41722i) q^{38} +(2.49215 - 0.451648i) q^{39} +(-7.81748 - 3.76687i) q^{40} +(-1.96953 - 0.876890i) q^{41} +(9.44158 - 5.07785i) q^{42} +(-8.27980 - 4.78035i) q^{43} +(0.928042 - 2.85622i) q^{44} +(-3.27092 + 5.85671i) q^{45} +(2.10277 + 6.47165i) q^{46} +(0.999222 - 4.70097i) q^{47} +(-2.56697 + 2.17481i) q^{48} +(-0.100680 - 0.174382i) q^{49} +(1.76368 + 11.7371i) q^{50} +(2.89482 + 9.91740i) q^{51} +(-2.16187 - 4.85564i) q^{52} +(-10.4505 + 3.39558i) q^{53} +(7.39151 + 9.87454i) q^{54} +(-1.77348 + 0.517689i) q^{55} +(-6.77081 - 7.51975i) q^{56} +(-9.49657 + 2.77198i) q^{57} +(0.0690262 + 0.324743i) q^{58} +(-4.37069 - 1.94596i) q^{59} +(13.5687 + 3.75147i) q^{60} +(13.2410 - 5.89526i) q^{61} +(11.3085 + 15.5647i) q^{62} +(-6.11800 + 4.87420i) q^{63} +(-9.19352 - 6.67948i) q^{64} +(-1.71948 + 2.78113i) q^{65} +(-0.456794 + 3.36619i) q^{66} +(1.13167 + 5.32410i) q^{67} +(18.7763 - 10.8405i) q^{68} +(-2.35177 - 4.37280i) q^{69} +(-3.28423 + 13.4447i) q^{70} +(-0.103022 - 0.317070i) q^{71} +(7.39849 - 8.98923i) q^{72} +(-4.10585 + 5.65122i) q^{73} +(10.9913 - 19.0375i) q^{74} +(-2.79344 - 8.19736i) q^{75} +(10.3805 + 17.9795i) q^{76} +(-2.14252 - 0.225188i) q^{77} +(3.38560 + 4.96830i) q^{78} +(12.9249 + 2.74727i) q^{79} +(0.130914 - 4.34144i) q^{80} +(-6.59166 - 6.12780i) q^{81} -5.11768i q^{82} +(0.522544 - 0.470501i) q^{83} +(12.9836 + 10.0449i) q^{84} +(-12.0154 - 5.78967i) q^{85} +(2.37228 - 22.5707i) q^{86} +(-0.0918123 - 0.224172i) q^{87} +(3.18884 - 0.335160i) q^{88} +(3.90464 + 2.83689i) q^{89} +(-15.8587 - 1.43849i) q^{90} +(-3.08460 + 2.24109i) q^{91} +(-7.74332 + 6.97212i) q^{92} +(-10.1443 - 9.70351i) q^{93} +(11.1591 - 2.37194i) q^{94} +(5.54400 - 11.5056i) q^{95} +(4.91610 + 2.36890i) q^{96} +(-3.20980 + 15.1009i) q^{97} +(0.280951 - 0.386697i) q^{98} +(-0.110032 - 2.47624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9} - 12 q^{10} + 5 q^{11} - 30 q^{12} - 5 q^{13} - 23 q^{14} + 18 q^{15} + 15 q^{16} - 20 q^{17} - 12 q^{19} - 17 q^{20} - 27 q^{21} - 5 q^{22} - 5 q^{23} - 46 q^{24} - 16 q^{25} + 72 q^{26} - 25 q^{27} - 60 q^{28} - 15 q^{29} + 2 q^{30} - 9 q^{31} - 35 q^{33} - 7 q^{34} - 46 q^{35} - 66 q^{36} - 20 q^{37} - 75 q^{38} + 32 q^{39} - q^{40} + 13 q^{41} - 140 q^{42} + 20 q^{44} + 90 q^{45} - 4 q^{46} + 20 q^{47} + 165 q^{48} + 56 q^{49} - 29 q^{50} - 6 q^{51} - 15 q^{52} - 20 q^{53} + 61 q^{54} - 44 q^{55} + 22 q^{56} - 5 q^{58} - 30 q^{59} - 149 q^{60} - 3 q^{61} + 40 q^{62} - 12 q^{64} + 45 q^{65} + 98 q^{66} + 10 q^{67} - 14 q^{69} - 12 q^{70} - 106 q^{71} + 40 q^{72} - 20 q^{73} + 82 q^{74} + 43 q^{75} + 8 q^{76} - 115 q^{77} + 110 q^{78} - 15 q^{79} - 22 q^{80} + 72 q^{81} + 65 q^{83} + 57 q^{84} - 21 q^{85} - 15 q^{86} + 115 q^{87} - 5 q^{88} + 26 q^{89} - 29 q^{90} - 54 q^{91} + 95 q^{92} + 41 q^{94} - 17 q^{95} - 47 q^{96} - 5 q^{97} - 70 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965505 + 2.16856i 0.682715 + 1.53340i 0.838081 + 0.545546i \(0.183678\pi\)
−0.155366 + 0.987857i \(0.549656\pi\)
\(3\) −0.975360 1.43132i −0.563124 0.826372i
\(4\) −2.43219 + 2.70122i −1.21609 + 1.35061i
\(5\) 2.21576 + 0.300654i 0.990919 + 0.134457i
\(6\) 2.16218 3.49707i 0.882708 1.42767i
\(7\) 2.25809 + 1.30371i 0.853479 + 0.492756i 0.861823 0.507209i \(-0.169323\pi\)
−0.00834440 + 0.999965i \(0.502656\pi\)
\(8\) −3.69084 1.19923i −1.30491 0.423991i
\(9\) −1.09735 + 2.79210i −0.365782 + 0.930701i
\(10\) 1.48734 + 5.09530i 0.470339 + 1.61127i
\(11\) −0.754795 + 0.336057i −0.227579 + 0.101325i −0.517359 0.855769i \(-0.673085\pi\)
0.289779 + 0.957093i \(0.406418\pi\)
\(12\) 6.23857 + 0.846576i 1.80092 + 0.244386i
\(13\) −0.594762 + 1.33586i −0.164957 + 0.370500i −0.977044 0.213036i \(-0.931665\pi\)
0.812087 + 0.583536i \(0.198331\pi\)
\(14\) −0.646974 + 6.15555i −0.172911 + 1.64514i
\(15\) −1.73083 3.46471i −0.446899 0.894584i
\(16\) −0.203039 1.93179i −0.0507598 0.482948i
\(17\) −5.67281 1.84321i −1.37586 0.447044i −0.474553 0.880227i \(-0.657390\pi\)
−0.901306 + 0.433183i \(0.857390\pi\)
\(18\) −7.11433 + 0.316127i −1.67686 + 0.0745119i
\(19\) 1.76500 5.43210i 0.404918 1.24621i −0.516046 0.856561i \(-0.672597\pi\)
0.920964 0.389648i \(-0.127403\pi\)
\(20\) −6.20129 + 5.25401i −1.38665 + 1.17483i
\(21\) −0.336428 4.50364i −0.0734146 0.982774i
\(22\) −1.45752 1.31235i −0.310744 0.279795i
\(23\) 2.85090 + 0.299642i 0.594454 + 0.0624796i 0.396978 0.917828i \(-0.370059\pi\)
0.197476 + 0.980308i \(0.436726\pi\)
\(24\) 1.88342 + 6.45245i 0.384452 + 1.31710i
\(25\) 4.81921 + 1.33236i 0.963843 + 0.266472i
\(26\) −3.47113 −0.680745
\(27\) 5.06669 1.15265i 0.975086 0.221828i
\(28\) −9.01371 + 2.92873i −1.70343 + 0.553479i
\(29\) 0.136804 + 0.0290786i 0.0254038 + 0.00539975i 0.220596 0.975365i \(-0.429200\pi\)
−0.195192 + 0.980765i \(0.562533\pi\)
\(30\) 5.84230 7.09861i 1.06665 1.29602i
\(31\) 7.92771 1.68509i 1.42386 0.302650i 0.569353 0.822093i \(-0.307194\pi\)
0.854505 + 0.519443i \(0.173860\pi\)
\(32\) −2.72854 + 1.57532i −0.482342 + 0.278480i
\(33\) 1.21720 + 0.752577i 0.211888 + 0.131007i
\(34\) −1.48002 14.0815i −0.253822 2.41495i
\(35\) 4.61143 + 3.56762i 0.779474 + 0.603038i
\(36\) −4.87313 9.75509i −0.812188 1.62585i
\(37\) −5.44323 7.49197i −0.894862 1.23167i −0.972078 0.234657i \(-0.924603\pi\)
0.0772163 0.997014i \(-0.475397\pi\)
\(38\) 13.4839 1.41722i 2.18738 0.229903i
\(39\) 2.49215 0.451648i 0.399063 0.0723215i
\(40\) −7.81748 3.76687i −1.23605 0.595594i
\(41\) −1.96953 0.876890i −0.307589 0.136947i 0.247137 0.968980i \(-0.420510\pi\)
−0.554726 + 0.832033i \(0.687177\pi\)
\(42\) 9.44158 5.07785i 1.45687 0.783529i
\(43\) −8.27980 4.78035i −1.26266 0.728996i −0.289070 0.957308i \(-0.593346\pi\)
−0.973588 + 0.228312i \(0.926679\pi\)
\(44\) 0.928042 2.85622i 0.139908 0.430592i
\(45\) −3.27092 + 5.85671i −0.487600 + 0.873067i
\(46\) 2.10277 + 6.47165i 0.310036 + 0.954193i
\(47\) 0.999222 4.70097i 0.145751 0.685707i −0.843216 0.537575i \(-0.819341\pi\)
0.988968 0.148132i \(-0.0473261\pi\)
\(48\) −2.56697 + 2.17481i −0.370510 + 0.313906i
\(49\) −0.100680 0.174382i −0.0143828 0.0249117i
\(50\) 1.76368 + 11.7371i 0.249422 + 1.65988i
\(51\) 2.89482 + 9.91740i 0.405355 + 1.38871i
\(52\) −2.16187 4.85564i −0.299798 0.673356i
\(53\) −10.4505 + 3.39558i −1.43549 + 0.466418i −0.920488 0.390772i \(-0.872208\pi\)
−0.515000 + 0.857190i \(0.672208\pi\)
\(54\) 7.39151 + 9.87454i 1.00586 + 1.34375i
\(55\) −1.77348 + 0.517689i −0.239137 + 0.0698052i
\(56\) −6.77081 7.51975i −0.904788 1.00487i
\(57\) −9.49657 + 2.77198i −1.25785 + 0.367158i
\(58\) 0.0690262 + 0.324743i 0.00906359 + 0.0426408i
\(59\) −4.37069 1.94596i −0.569016 0.253342i 0.102001 0.994784i \(-0.467475\pi\)
−0.671017 + 0.741442i \(0.734142\pi\)
\(60\) 13.5687 + 3.75147i 1.75171 + 0.484312i
\(61\) 13.2410 5.89526i 1.69533 0.754810i 0.696008 0.718034i \(-0.254958\pi\)
0.999324 0.0367765i \(-0.0117090\pi\)
\(62\) 11.3085 + 15.5647i 1.43617 + 1.97672i
\(63\) −6.11800 + 4.87420i −0.770796 + 0.614092i
\(64\) −9.19352 6.67948i −1.14919 0.834935i
\(65\) −1.71948 + 2.78113i −0.213276 + 0.344956i
\(66\) −0.456794 + 3.36619i −0.0562274 + 0.414349i
\(67\) 1.13167 + 5.32410i 0.138256 + 0.650443i 0.991627 + 0.129138i \(0.0412211\pi\)
−0.853371 + 0.521305i \(0.825446\pi\)
\(68\) 18.7763 10.8405i 2.27696 1.31460i
\(69\) −2.35177 4.37280i −0.283120 0.526424i
\(70\) −3.28423 + 13.4447i −0.392541 + 1.60695i
\(71\) −0.103022 0.317070i −0.0122265 0.0376293i 0.944757 0.327771i \(-0.106298\pi\)
−0.956984 + 0.290142i \(0.906298\pi\)
\(72\) 7.39849 8.98923i 0.871921 1.05939i
\(73\) −4.10585 + 5.65122i −0.480554 + 0.661425i −0.978611 0.205719i \(-0.934047\pi\)
0.498057 + 0.867144i \(0.334047\pi\)
\(74\) 10.9913 19.0375i 1.27771 2.21306i
\(75\) −2.79344 8.19736i −0.322559 0.946550i
\(76\) 10.3805 + 17.9795i 1.19072 + 2.06239i
\(77\) −2.14252 0.225188i −0.244163 0.0256625i
\(78\) 3.38560 + 4.96830i 0.383344 + 0.562549i
\(79\) 12.9249 + 2.74727i 1.45416 + 0.309092i 0.866160 0.499767i \(-0.166581\pi\)
0.588003 + 0.808859i \(0.299914\pi\)
\(80\) 0.130914 4.34144i 0.0146367 0.485387i
\(81\) −6.59166 6.12780i −0.732407 0.680867i
\(82\) 5.11768i 0.565153i
\(83\) 0.522544 0.470501i 0.0573567 0.0516442i −0.639954 0.768413i \(-0.721047\pi\)
0.697311 + 0.716769i \(0.254380\pi\)
\(84\) 12.9836 + 10.0449i 1.41662 + 1.09599i
\(85\) −12.0154 5.78967i −1.30326 0.627978i
\(86\) 2.37228 22.5707i 0.255809 2.43386i
\(87\) −0.0918123 0.224172i −0.00984332 0.0240338i
\(88\) 3.18884 0.335160i 0.339931 0.0357282i
\(89\) 3.90464 + 2.83689i 0.413891 + 0.300709i 0.775175 0.631746i \(-0.217662\pi\)
−0.361284 + 0.932456i \(0.617662\pi\)
\(90\) −15.8587 1.43849i −1.67166 0.151630i
\(91\) −3.08460 + 2.24109i −0.323354 + 0.234930i
\(92\) −7.74332 + 6.97212i −0.807297 + 0.726894i
\(93\) −10.1443 9.70351i −1.05191 1.00621i
\(94\) 11.1591 2.37194i 1.15097 0.244647i
\(95\) 5.54400 11.5056i 0.568802 1.18045i
\(96\) 4.91610 + 2.36890i 0.501747 + 0.241775i
\(97\) −3.20980 + 15.1009i −0.325906 + 1.53327i 0.444538 + 0.895760i \(0.353368\pi\)
−0.770444 + 0.637507i \(0.779966\pi\)
\(98\) 0.280951 0.386697i 0.0283804 0.0390623i
\(99\) −0.110032 2.47624i −0.0110586 0.248871i
\(100\) −15.3202 + 9.77721i −1.53202 + 0.977721i
\(101\) −8.77250 + 15.1944i −0.872897 + 1.51190i −0.0139103 + 0.999903i \(0.504428\pi\)
−0.858986 + 0.511998i \(0.828905\pi\)
\(102\) −18.7115 + 15.8529i −1.85272 + 1.56967i
\(103\) −1.54606 1.39208i −0.152338 0.137166i 0.589438 0.807814i \(-0.299349\pi\)
−0.741776 + 0.670648i \(0.766016\pi\)
\(104\) 3.79717 4.21718i 0.372343 0.413529i
\(105\) 0.608594 10.0801i 0.0593927 0.983721i
\(106\) −17.4535 19.3841i −1.69524 1.88275i
\(107\) 4.06188i 0.392677i 0.980536 + 0.196338i \(0.0629051\pi\)
−0.980536 + 0.196338i \(0.937095\pi\)
\(108\) −9.20959 + 16.4897i −0.886194 + 1.58672i
\(109\) 5.87401 4.26772i 0.562628 0.408773i −0.269792 0.962919i \(-0.586955\pi\)
0.832420 + 0.554146i \(0.186955\pi\)
\(110\) −2.83495 3.34608i −0.270302 0.319036i
\(111\) −5.41428 + 15.0984i −0.513901 + 1.43307i
\(112\) 2.06001 4.62687i 0.194653 0.437198i
\(113\) 0.844305 1.89634i 0.0794255 0.178393i −0.869468 0.493990i \(-0.835538\pi\)
0.948893 + 0.315597i \(0.102205\pi\)
\(114\) −15.1802 17.9175i −1.42176 1.67813i
\(115\) 6.22683 + 1.52107i 0.580655 + 0.141841i
\(116\) −0.411281 + 0.298813i −0.0381864 + 0.0277441i
\(117\) −3.07719 3.12654i −0.284486 0.289048i
\(118\) 11.3569i 1.04549i
\(119\) −10.4067 11.5578i −0.953983 1.05951i
\(120\) 2.23326 + 14.8634i 0.203868 + 1.35683i
\(121\) −6.90365 + 7.66729i −0.627605 + 0.697026i
\(122\) 25.5684 + 23.0219i 2.31486 + 2.08431i
\(123\) 0.665889 + 3.67431i 0.0600412 + 0.331301i
\(124\) −14.7299 + 25.5129i −1.32278 + 2.29113i
\(125\) 10.2777 + 4.40111i 0.919262 + 0.393647i
\(126\) −16.4770 8.56118i −1.46788 0.762691i
\(127\) 8.29185 11.4128i 0.735783 1.01272i −0.263067 0.964777i \(-0.584734\pi\)
0.998850 0.0479408i \(-0.0152659\pi\)
\(128\) 4.29836 20.2222i 0.379925 1.78740i
\(129\) 1.23359 + 16.5136i 0.108611 + 1.45394i
\(130\) −7.69121 1.04361i −0.674564 0.0915308i
\(131\) −9.86335 + 2.09652i −0.861765 + 0.183174i −0.617535 0.786543i \(-0.711869\pi\)
−0.244230 + 0.969717i \(0.578535\pi\)
\(132\) −4.99334 + 1.45752i −0.434614 + 0.126861i
\(133\) 11.0674 9.96514i 0.959666 0.864087i
\(134\) −10.4530 + 7.59455i −0.903002 + 0.656069i
\(135\) 11.5731 1.03068i 0.996058 0.0887067i
\(136\) 18.7270 + 13.6060i 1.60583 + 1.16670i
\(137\) −10.4999 + 1.10359i −0.897068 + 0.0942857i −0.541828 0.840489i \(-0.682268\pi\)
−0.355240 + 0.934775i \(0.615601\pi\)
\(138\) 7.21204 9.32192i 0.613929 0.793534i
\(139\) 0.291441 2.77287i 0.0247197 0.235192i −0.975185 0.221391i \(-0.928940\pi\)
0.999905 0.0138009i \(-0.00439311\pi\)
\(140\) −20.8528 + 3.77937i −1.76238 + 0.319415i
\(141\) −7.70319 + 3.15493i −0.648725 + 0.265693i
\(142\) 0.588117 0.529543i 0.0493537 0.0444383i
\(143\) 1.20817i 0.101033i
\(144\) 5.61656 + 1.55294i 0.468047 + 0.129411i
\(145\) 0.294382 + 0.105562i 0.0244471 + 0.00876644i
\(146\) −16.2192 3.44750i −1.34231 0.285317i
\(147\) −0.151398 + 0.314190i −0.0124871 + 0.0259140i
\(148\) 33.4764 + 3.51851i 2.75174 + 0.289220i
\(149\) −0.847420 1.46777i −0.0694233 0.120245i 0.829224 0.558916i \(-0.188783\pi\)
−0.898648 + 0.438671i \(0.855449\pi\)
\(150\) 15.0794 13.9723i 1.23123 1.14084i
\(151\) −1.69179 + 2.93027i −0.137676 + 0.238462i −0.926616 0.376008i \(-0.877297\pi\)
0.788941 + 0.614469i \(0.210630\pi\)
\(152\) −13.0286 + 17.9324i −1.05676 + 1.45451i
\(153\) 11.3715 13.8164i 0.919329 1.11699i
\(154\) −1.58028 4.86360i −0.127342 0.391920i
\(155\) 18.0726 1.35025i 1.45162 0.108455i
\(156\) −4.84137 + 7.83033i −0.387620 + 0.626928i
\(157\) 14.2000 8.19840i 1.13329 0.654303i 0.188527 0.982068i \(-0.439629\pi\)
0.944759 + 0.327765i \(0.106295\pi\)
\(158\) 6.52142 + 30.6809i 0.518816 + 2.44084i
\(159\) 15.0532 + 11.6461i 1.19379 + 0.923596i
\(160\) −6.51942 + 2.67019i −0.515406 + 0.211097i
\(161\) 6.04695 + 4.39336i 0.476566 + 0.346246i
\(162\) 6.92423 20.2108i 0.544019 1.58791i
\(163\) 6.73381 + 9.26829i 0.527433 + 0.725949i 0.986736 0.162331i \(-0.0519011\pi\)
−0.459304 + 0.888279i \(0.651901\pi\)
\(164\) 7.15894 3.18736i 0.559019 0.248891i
\(165\) 2.47076 + 2.03349i 0.192349 + 0.158307i
\(166\) 1.52483 + 0.678897i 0.118350 + 0.0526926i
\(167\) 1.85138 + 8.71007i 0.143264 + 0.674006i 0.989892 + 0.141821i \(0.0452956\pi\)
−0.846628 + 0.532185i \(0.821371\pi\)
\(168\) −4.15918 + 17.0257i −0.320888 + 1.31356i
\(169\) 7.26792 + 8.07185i 0.559071 + 0.620911i
\(170\) 0.954277 31.6462i 0.0731897 2.42715i
\(171\) 13.2302 + 10.8889i 1.01174 + 0.832698i
\(172\) 33.0508 10.7389i 2.52010 0.818830i
\(173\) −0.0874639 0.196447i −0.00664975 0.0149356i 0.910190 0.414191i \(-0.135935\pi\)
−0.916840 + 0.399255i \(0.869269\pi\)
\(174\) 0.397485 0.415540i 0.0301333 0.0315020i
\(175\) 9.14522 + 9.29145i 0.691314 + 0.702367i
\(176\) 0.802444 + 1.38987i 0.0604865 + 0.104766i
\(177\) 1.47771 + 8.15386i 0.111072 + 0.612882i
\(178\) −2.38201 + 11.2065i −0.178539 + 0.839960i
\(179\) −6.20421 19.0946i −0.463724 1.42720i −0.860580 0.509315i \(-0.829899\pi\)
0.396856 0.917881i \(-0.370101\pi\)
\(180\) −7.86478 23.0801i −0.586206 1.72029i
\(181\) −1.43938 + 4.42997i −0.106989 + 0.329277i −0.990192 0.139713i \(-0.955382\pi\)
0.883203 + 0.468990i \(0.155382\pi\)
\(182\) −7.83814 4.52535i −0.581002 0.335441i
\(183\) −21.3527 13.2020i −1.57844 0.975923i
\(184\) −10.1629 4.52480i −0.749217 0.333573i
\(185\) −9.80842 18.2370i −0.721129 1.34081i
\(186\) 11.2483 31.3672i 0.824766 2.29996i
\(187\) 4.90124 0.515141i 0.358414 0.0376708i
\(188\) 10.2681 + 14.1328i 0.748875 + 1.03074i
\(189\) 12.9438 + 4.00271i 0.941522 + 0.291154i
\(190\) 30.3033 + 0.913784i 2.19843 + 0.0662929i
\(191\) 1.51767 + 14.4397i 0.109815 + 1.04482i 0.901171 + 0.433463i \(0.142709\pi\)
−0.791356 + 0.611355i \(0.790625\pi\)
\(192\) −0.593478 + 19.6738i −0.0428306 + 1.41983i
\(193\) −20.4023 + 11.7793i −1.46859 + 0.847892i −0.999381 0.0351930i \(-0.988795\pi\)
−0.469212 + 0.883085i \(0.655462\pi\)
\(194\) −35.8463 + 7.61937i −2.57362 + 0.547039i
\(195\) 5.65779 0.251470i 0.405163 0.0180082i
\(196\) 0.715916 + 0.152173i 0.0511369 + 0.0108695i
\(197\) 3.67126 1.19286i 0.261566 0.0849881i −0.175298 0.984515i \(-0.556089\pi\)
0.436864 + 0.899527i \(0.356089\pi\)
\(198\) 5.26363 2.62943i 0.374070 0.186865i
\(199\) −11.7357 −0.831919 −0.415960 0.909383i \(-0.636554\pi\)
−0.415960 + 0.909383i \(0.636554\pi\)
\(200\) −16.1891 10.6969i −1.14475 0.756382i
\(201\) 6.51670 6.81270i 0.459653 0.480531i
\(202\) −41.4199 4.35341i −2.91429 0.306305i
\(203\) 0.271006 + 0.244015i 0.0190209 + 0.0171265i
\(204\) −33.8298 16.3015i −2.36856 1.14133i
\(205\) −4.10037 2.53513i −0.286382 0.177061i
\(206\) 1.52608 4.69678i 0.106327 0.327240i
\(207\) −3.96505 + 7.63119i −0.275590 + 0.530404i
\(208\) 2.70136 + 0.877724i 0.187305 + 0.0608592i
\(209\) 0.493282 + 4.69326i 0.0341210 + 0.324640i
\(210\) 22.4470 8.41265i 1.54899 0.580528i
\(211\) 0.298466 2.83971i 0.0205472 0.195494i −0.979433 0.201769i \(-0.935331\pi\)
0.999980 + 0.00627545i \(0.00199755\pi\)
\(212\) 16.2454 36.4878i 1.11574 2.50599i
\(213\) −0.353345 + 0.456715i −0.0242108 + 0.0312936i
\(214\) −8.80843 + 3.92176i −0.602132 + 0.268086i
\(215\) −16.9088 13.0815i −1.15317 0.892149i
\(216\) −20.0827 1.82186i −1.36645 0.123962i
\(217\) 20.0984 + 6.53035i 1.36437 + 0.443309i
\(218\) 14.9262 + 8.61763i 1.01093 + 0.583660i
\(219\) 12.0934 + 0.364809i 0.817195 + 0.0246515i
\(220\) 2.91506 6.04969i 0.196533 0.407870i
\(221\) 5.83624 6.48180i 0.392588 0.436013i
\(222\) −37.9692 + 2.83635i −2.54833 + 0.190364i
\(223\) 2.67143 + 6.00012i 0.178892 + 0.401798i 0.980628 0.195881i \(-0.0627565\pi\)
−0.801736 + 0.597679i \(0.796090\pi\)
\(224\) −8.21506 −0.548892
\(225\) −9.00843 + 11.9937i −0.600562 + 0.799578i
\(226\) 4.92751 0.327773
\(227\) −0.536959 1.20603i −0.0356393 0.0800471i 0.894849 0.446370i \(-0.147283\pi\)
−0.930488 + 0.366323i \(0.880617\pi\)
\(228\) 15.6097 32.3943i 1.03378 2.14537i
\(229\) −2.53269 + 2.81284i −0.167365 + 0.185878i −0.820993 0.570938i \(-0.806580\pi\)
0.653628 + 0.756816i \(0.273246\pi\)
\(230\) 2.71350 + 14.9718i 0.178923 + 0.987214i
\(231\) 1.76741 + 3.28626i 0.116287 + 0.216220i
\(232\) −0.470050 0.271383i −0.0308603 0.0178172i
\(233\) 0.806245 + 0.261965i 0.0528188 + 0.0171619i 0.335307 0.942109i \(-0.391160\pi\)
−0.282488 + 0.959271i \(0.591160\pi\)
\(234\) 3.80903 9.69176i 0.249004 0.633570i
\(235\) 3.62741 10.1158i 0.236626 0.659883i
\(236\) 15.8868 7.07326i 1.03414 0.460430i
\(237\) −8.67419 21.1792i −0.563449 1.37574i
\(238\) 15.0161 33.7268i 0.973351 2.18618i
\(239\) −1.53837 + 14.6366i −0.0995086 + 0.946762i 0.824880 + 0.565309i \(0.191243\pi\)
−0.924388 + 0.381453i \(0.875424\pi\)
\(240\) −6.34167 + 4.04708i −0.409353 + 0.261238i
\(241\) −0.428846 4.08020i −0.0276244 0.262829i −0.999613 0.0278025i \(-0.991149\pi\)
0.971989 0.235026i \(-0.0755176\pi\)
\(242\) −23.2925 7.56818i −1.49730 0.486501i
\(243\) −2.34160 + 15.4116i −0.150214 + 0.988654i
\(244\) −16.2801 + 50.1051i −1.04223 + 3.20765i
\(245\) −0.170653 0.416659i −0.0109026 0.0266194i
\(246\) −7.32503 + 4.99158i −0.467027 + 0.318252i
\(247\) 6.20676 + 5.58859i 0.394927 + 0.355594i
\(248\) −31.2807 3.28773i −1.98633 0.208771i
\(249\) −1.18311 0.289020i −0.0749762 0.0183159i
\(250\) 0.379063 + 26.5370i 0.0239741 + 1.67835i
\(251\) 14.7545 0.931295 0.465648 0.884970i \(-0.345821\pi\)
0.465648 + 0.884970i \(0.345821\pi\)
\(252\) 1.71384 28.3810i 0.107962 1.78784i
\(253\) −2.25254 + 0.731895i −0.141616 + 0.0460139i
\(254\) 32.7551 + 6.96230i 2.05524 + 0.436854i
\(255\) 3.43252 + 22.8449i 0.214953 + 1.43061i
\(256\) 25.7721 5.47803i 1.61076 0.342377i
\(257\) 21.1572 12.2151i 1.31975 0.761958i 0.336062 0.941840i \(-0.390905\pi\)
0.983688 + 0.179882i \(0.0575717\pi\)
\(258\) −34.6197 + 18.6191i −2.15533 + 1.15917i
\(259\) −2.52397 24.0139i −0.156832 1.49215i
\(260\) −3.33032 11.4089i −0.206538 0.707552i
\(261\) −0.231312 + 0.350061i −0.0143178 + 0.0216682i
\(262\) −14.0695 19.3651i −0.869219 1.19638i
\(263\) −14.1515 + 1.48738i −0.872618 + 0.0917158i −0.530241 0.847847i \(-0.677899\pi\)
−0.342377 + 0.939563i \(0.611232\pi\)
\(264\) −3.58998 4.23734i −0.220948 0.260790i
\(265\) −24.1767 + 4.38180i −1.48517 + 0.269172i
\(266\) 32.2956 + 14.3789i 1.98017 + 0.881630i
\(267\) 0.252060 8.35576i 0.0154258 0.511364i
\(268\) −17.1340 9.89233i −1.04663 0.604270i
\(269\) 6.23881 19.2011i 0.380387 1.17071i −0.559385 0.828908i \(-0.688963\pi\)
0.939772 0.341802i \(-0.111037\pi\)
\(270\) 13.4090 + 24.1019i 0.816047 + 1.46680i
\(271\) −4.49635 13.8383i −0.273134 0.840620i −0.989707 0.143108i \(-0.954290\pi\)
0.716573 0.697512i \(-0.245710\pi\)
\(272\) −2.40889 + 11.3329i −0.146060 + 0.687160i
\(273\) 6.21631 + 2.22917i 0.376228 + 0.134916i
\(274\) −12.5309 21.7042i −0.757020 1.31120i
\(275\) −4.08527 + 0.613871i −0.246351 + 0.0370178i
\(276\) 17.5319 + 4.28284i 1.05529 + 0.257797i
\(277\) −0.00321910 0.00723021i −0.000193417 0.000434421i 0.913449 0.406954i \(-0.133409\pi\)
−0.913642 + 0.406519i \(0.866742\pi\)
\(278\) 6.29453 2.04522i 0.377521 0.122664i
\(279\) −3.99451 + 23.9841i −0.239145 + 1.43589i
\(280\) −12.7417 18.6977i −0.761461 1.11740i
\(281\) 7.23254 + 8.03255i 0.431457 + 0.479182i 0.919192 0.393810i \(-0.128843\pi\)
−0.487735 + 0.872992i \(0.662177\pi\)
\(282\) −14.2791 13.6587i −0.850309 0.813365i
\(283\) −1.22785 5.77658i −0.0729881 0.343382i 0.926467 0.376375i \(-0.122830\pi\)
−0.999456 + 0.0329927i \(0.989496\pi\)
\(284\) 1.10705 + 0.492889i 0.0656911 + 0.0292476i
\(285\) −21.8756 + 3.28687i −1.29580 + 0.194697i
\(286\) 2.62000 1.16650i 0.154924 0.0689764i
\(287\) −3.30416 4.54779i −0.195039 0.268448i
\(288\) −1.40431 9.34703i −0.0827497 0.550779i
\(289\) 15.0301 + 10.9200i 0.884124 + 0.642354i
\(290\) 0.0553104 + 0.740306i 0.00324794 + 0.0434723i
\(291\) 24.7450 10.1346i 1.45057 0.594100i
\(292\) −5.27898 24.8357i −0.308929 1.45340i
\(293\) 10.7763 6.22170i 0.629558 0.363476i −0.151023 0.988530i \(-0.548257\pi\)
0.780581 + 0.625055i \(0.214923\pi\)
\(294\) −0.827515 0.0249628i −0.0482616 0.00145586i
\(295\) −9.09936 5.62585i −0.529785 0.327550i
\(296\) 11.1055 + 34.1793i 0.645496 + 1.98663i
\(297\) −3.43696 + 2.57271i −0.199433 + 0.149284i
\(298\) 2.36477 3.25482i 0.136987 0.188547i
\(299\) −2.09589 + 3.63018i −0.121208 + 0.209939i
\(300\) 28.9370 + 12.3918i 1.67068 + 0.715443i
\(301\) −12.4644 21.5889i −0.718434 1.24436i
\(302\) −7.98789 0.839561i −0.459651 0.0483113i
\(303\) 30.3044 2.26378i 1.74094 0.130051i
\(304\) −10.8520 2.30667i −0.622407 0.132297i
\(305\) 31.1113 9.08154i 1.78143 0.520007i
\(306\) 40.9410 + 11.3199i 2.34044 + 0.647114i
\(307\) 13.8244i 0.789000i 0.918896 + 0.394500i \(0.129082\pi\)
−0.918896 + 0.394500i \(0.870918\pi\)
\(308\) 5.81929 5.23971i 0.331585 0.298560i
\(309\) −0.484544 + 3.57068i −0.0275647 + 0.203129i
\(310\) 20.3772 + 37.8877i 1.15735 + 2.15188i
\(311\) −1.33955 + 12.7450i −0.0759588 + 0.722700i 0.888573 + 0.458735i \(0.151697\pi\)
−0.964532 + 0.263965i \(0.914970\pi\)
\(312\) −9.73974 1.32169i −0.551404 0.0748258i
\(313\) −22.5486 + 2.36995i −1.27452 + 0.133957i −0.717510 0.696548i \(-0.754718\pi\)
−0.557010 + 0.830506i \(0.688052\pi\)
\(314\) 31.4889 + 22.8780i 1.77702 + 1.29108i
\(315\) −15.0215 + 8.96067i −0.846365 + 0.504877i
\(316\) −38.8567 + 28.2311i −2.18586 + 1.58812i
\(317\) 22.2718 20.0536i 1.25091 1.12632i 0.264089 0.964498i \(-0.414929\pi\)
0.986819 0.161825i \(-0.0517381\pi\)
\(318\) −10.7214 + 43.8880i −0.601224 + 2.46112i
\(319\) −0.113031 + 0.0240255i −0.00632852 + 0.00134517i
\(320\) −18.3624 17.5642i −1.02649 0.981870i
\(321\) 5.81384 3.96179i 0.324497 0.221126i
\(322\) −3.68891 + 17.3550i −0.205575 + 0.967155i
\(323\) −20.0250 + 27.5620i −1.11422 + 1.53359i
\(324\) 32.5847 2.90155i 1.81026 0.161197i
\(325\) −4.64613 + 5.64535i −0.257721 + 0.313148i
\(326\) −13.5973 + 23.5512i −0.753086 + 1.30438i
\(327\) −11.8377 4.24502i −0.654628 0.234750i
\(328\) 6.21762 + 5.59837i 0.343311 + 0.309118i
\(329\) 8.38504 9.31253i 0.462282 0.513416i
\(330\) −2.02421 + 7.32134i −0.111429 + 0.403027i
\(331\) −1.51584 1.68351i −0.0833183 0.0925344i 0.700044 0.714100i \(-0.253164\pi\)
−0.783362 + 0.621565i \(0.786497\pi\)
\(332\) 2.55585i 0.140271i
\(333\) 26.8914 6.97678i 1.47364 0.382325i
\(334\) −17.1008 + 12.4245i −0.935714 + 0.679836i
\(335\) 0.906805 + 12.1372i 0.0495440 + 0.663126i
\(336\) −8.63177 + 1.56432i −0.470902 + 0.0853409i
\(337\) −2.62962 + 5.90623i −0.143245 + 0.321733i −0.970893 0.239515i \(-0.923012\pi\)
0.827648 + 0.561247i \(0.189678\pi\)
\(338\) −10.4871 + 23.5543i −0.570421 + 1.28119i
\(339\) −3.53777 + 0.641144i −0.192145 + 0.0348222i
\(340\) 44.8630 18.3748i 2.43304 0.996512i
\(341\) −5.41751 + 3.93605i −0.293375 + 0.213149i
\(342\) −10.8395 + 39.2037i −0.586135 + 2.11989i
\(343\) 18.7770i 1.01386i
\(344\) 24.8267 + 27.5729i 1.33857 + 1.48663i
\(345\) −3.89626 10.3962i −0.209768 0.559711i
\(346\) 0.341560 0.379341i 0.0183624 0.0203935i
\(347\) −21.6526 19.4961i −1.16237 1.04661i −0.998188 0.0601765i \(-0.980834\pi\)
−0.164186 0.986429i \(-0.552500\pi\)
\(348\) 0.828843 + 0.297223i 0.0444306 + 0.0159329i
\(349\) −17.3116 + 29.9846i −0.926670 + 1.60504i −0.137817 + 0.990458i \(0.544009\pi\)
−0.788853 + 0.614582i \(0.789325\pi\)
\(350\) −11.3193 + 28.8029i −0.605042 + 1.53958i
\(351\) −1.47370 + 7.45394i −0.0786603 + 0.397862i
\(352\) 1.53009 2.10599i 0.0815541 0.112250i
\(353\) 2.35198 11.0652i 0.125183 0.588940i −0.870179 0.492737i \(-0.835997\pi\)
0.995362 0.0962037i \(-0.0306700\pi\)
\(354\) −16.2554 + 11.0771i −0.863965 + 0.588741i
\(355\) −0.132945 0.733527i −0.00705597 0.0389315i
\(356\) −17.1599 + 3.64744i −0.909471 + 0.193314i
\(357\) −6.39265 + 26.1684i −0.338335 + 1.38498i
\(358\) 35.4175 31.8901i 1.87188 1.68544i
\(359\) 11.2407 8.16685i 0.593262 0.431030i −0.250219 0.968189i \(-0.580503\pi\)
0.843481 + 0.537159i \(0.180503\pi\)
\(360\) 19.0960 17.6936i 1.00645 0.932536i
\(361\) −11.0212 8.00735i −0.580062 0.421440i
\(362\) −10.9964 + 1.15577i −0.577957 + 0.0607458i
\(363\) 17.7079 + 2.40297i 0.929422 + 0.126123i
\(364\) 1.44865 13.7829i 0.0759297 0.722422i
\(365\) −10.7967 + 11.2873i −0.565123 + 0.590806i
\(366\) 8.01328 59.0512i 0.418861 3.08666i
\(367\) −1.62571 + 1.46380i −0.0848614 + 0.0764095i −0.710470 0.703728i \(-0.751517\pi\)
0.625608 + 0.780137i \(0.284851\pi\)
\(368\) 5.56818i 0.290261i
\(369\) 4.60962 4.53687i 0.239967 0.236180i
\(370\) 30.0778 38.8780i 1.56367 2.02117i
\(371\) −28.0251 5.95691i −1.45499 0.309267i
\(372\) 50.8841 3.80111i 2.63822 0.197078i
\(373\) −16.7268 1.75806i −0.866083 0.0910290i −0.338943 0.940807i \(-0.610069\pi\)
−0.527141 + 0.849778i \(0.676736\pi\)
\(374\) 5.84928 + 10.1313i 0.302459 + 0.523875i
\(375\) −3.72503 19.0033i −0.192360 0.981325i
\(376\) −9.32550 + 16.1522i −0.480926 + 0.832988i
\(377\) −0.120211 + 0.165456i −0.00619116 + 0.00852140i
\(378\) 3.81718 + 31.9340i 0.196335 + 1.64251i
\(379\) −4.64771 14.3042i −0.238737 0.734757i −0.996604 0.0823473i \(-0.973758\pi\)
0.757867 0.652409i \(-0.226242\pi\)
\(380\) 17.5951 + 42.9593i 0.902609 + 2.20377i
\(381\) −24.4228 0.736739i −1.25122 0.0377443i
\(382\) −29.8480 + 17.2327i −1.52716 + 0.881704i
\(383\) −0.189475 0.891409i −0.00968171 0.0455489i 0.973042 0.230630i \(-0.0740786\pi\)
−0.982723 + 0.185081i \(0.940745\pi\)
\(384\) −33.1368 + 13.5716i −1.69101 + 0.692572i
\(385\) −4.67961 1.14312i −0.238495 0.0582588i
\(386\) −45.2427 32.8707i −2.30279 1.67308i
\(387\) 22.4330 17.8724i 1.14033 0.908503i
\(388\) −32.9841 45.3987i −1.67451 2.30477i
\(389\) −15.5454 + 6.92124i −0.788182 + 0.350921i −0.761035 0.648710i \(-0.775309\pi\)
−0.0271462 + 0.999631i \(0.508642\pi\)
\(390\) 6.00796 + 12.0265i 0.304225 + 0.608984i
\(391\) −15.6203 6.95461i −0.789953 0.351710i
\(392\) 0.162469 + 0.764354i 0.00820590 + 0.0386057i
\(393\) 12.6211 + 12.0727i 0.636651 + 0.608989i
\(394\) 6.13141 + 6.80963i 0.308896 + 0.343064i
\(395\) 27.8125 + 9.97322i 1.39940 + 0.501807i
\(396\) 6.95648 + 5.72545i 0.349576 + 0.287715i
\(397\) −29.8578 + 9.70138i −1.49852 + 0.486898i −0.939586 0.342314i \(-0.888789\pi\)
−0.558934 + 0.829212i \(0.688789\pi\)
\(398\) −11.3308 25.4495i −0.567964 1.27567i
\(399\) −25.0580 6.12139i −1.25447 0.306453i
\(400\) 1.59535 9.58023i 0.0797673 0.479012i
\(401\) 6.70082 + 11.6062i 0.334623 + 0.579584i 0.983412 0.181384i \(-0.0580576\pi\)
−0.648789 + 0.760968i \(0.724724\pi\)
\(402\) 21.0657 + 7.55416i 1.05066 + 0.376767i
\(403\) −2.46407 + 11.5925i −0.122744 + 0.577464i
\(404\) −19.7071 60.6522i −0.980464 3.01756i
\(405\) −12.7632 15.5596i −0.634209 0.773162i
\(406\) −0.267503 + 0.823290i −0.0132760 + 0.0408592i
\(407\) 6.62625 + 3.82567i 0.328451 + 0.189631i
\(408\) 1.20890 40.0751i 0.0598497 1.98401i
\(409\) −3.21388 1.43091i −0.158916 0.0707540i 0.325737 0.945460i \(-0.394388\pi\)
−0.484653 + 0.874706i \(0.661054\pi\)
\(410\) 1.53865 11.3396i 0.0759887 0.560021i
\(411\) 11.8208 + 13.9523i 0.583076 + 0.688218i
\(412\) 7.52062 0.790450i 0.370515 0.0389427i
\(413\) −7.33246 10.0923i −0.360807 0.496608i
\(414\) −20.3770 1.23050i −1.00147 0.0604759i
\(415\) 1.29929 0.885413i 0.0637797 0.0434632i
\(416\) −0.481575 4.58188i −0.0236112 0.224645i
\(417\) −4.25313 + 2.28741i −0.208277 + 0.112015i
\(418\) −9.70135 + 5.60108i −0.474509 + 0.273958i
\(419\) 29.1390 6.19368i 1.42353 0.302581i 0.569153 0.822231i \(-0.307271\pi\)
0.854379 + 0.519650i \(0.173938\pi\)
\(420\) 25.7485 + 26.1608i 1.25640 + 1.27651i
\(421\) 24.7915 + 5.26960i 1.20827 + 0.256825i 0.767649 0.640871i \(-0.221427\pi\)
0.440617 + 0.897695i \(0.354760\pi\)
\(422\) 6.44625 2.09451i 0.313799 0.101959i
\(423\) 12.0291 + 7.94852i 0.584874 + 0.386470i
\(424\) 42.6432 2.07094
\(425\) −24.8827 16.4410i −1.20699 0.797508i
\(426\) −1.33157 0.325288i −0.0645148 0.0157602i
\(427\) 37.5850 + 3.95035i 1.81887 + 0.191171i
\(428\) −10.9720 9.87926i −0.530353 0.477532i
\(429\) −1.72928 + 1.17840i −0.0834905 + 0.0568939i
\(430\) 12.0424 49.2981i 0.580735 2.37736i
\(431\) 2.54269 7.82560i 0.122477 0.376946i −0.870956 0.491361i \(-0.836499\pi\)
0.993433 + 0.114415i \(0.0364995\pi\)
\(432\) −3.25542 9.55376i −0.156626 0.459656i
\(433\) 0.225475 + 0.0732614i 0.0108357 + 0.00352072i 0.314430 0.949281i \(-0.398187\pi\)
−0.303594 + 0.952801i \(0.598187\pi\)
\(434\) 5.24361 + 49.8896i 0.251701 + 2.39478i
\(435\) −0.136036 0.524316i −0.00652243 0.0251390i
\(436\) −2.75866 + 26.2469i −0.132116 + 1.25700i
\(437\) 6.65951 14.9575i 0.318568 0.715514i
\(438\) 10.8851 + 26.5774i 0.520111 + 1.26992i
\(439\) −4.97554 + 2.21525i −0.237469 + 0.105728i −0.522021 0.852932i \(-0.674822\pi\)
0.284552 + 0.958661i \(0.408155\pi\)
\(440\) 7.16648 + 0.216102i 0.341648 + 0.0103023i
\(441\) 0.597373 0.0897500i 0.0284463 0.00427381i
\(442\) 19.6911 + 6.39802i 0.936610 + 0.304323i
\(443\) 26.6686 + 15.3971i 1.26706 + 0.731538i 0.974431 0.224687i \(-0.0721360\pi\)
0.292631 + 0.956226i \(0.405469\pi\)
\(444\) −27.6154 51.3472i −1.31057 2.43683i
\(445\) 7.79883 + 7.45981i 0.369700 + 0.353629i
\(446\) −10.4323 + 11.5863i −0.493986 + 0.548627i
\(447\) −1.27431 + 2.64454i −0.0602730 + 0.125082i
\(448\) −12.0517 27.0686i −0.569390 1.27887i
\(449\) −16.9775 −0.801219 −0.400609 0.916249i \(-0.631202\pi\)
−0.400609 + 0.916249i \(0.631202\pi\)
\(450\) −34.7067 7.95535i −1.63609 0.375019i
\(451\) 1.78128 0.0838770
\(452\) 3.06892 + 6.89291i 0.144350 + 0.324215i
\(453\) 5.84425 0.436573i 0.274587 0.0205120i
\(454\) 2.09691 2.32886i 0.0984130 0.109299i
\(455\) −7.50854 + 4.03833i −0.352006 + 0.189320i
\(456\) 38.3746 + 1.15761i 1.79705 + 0.0542099i
\(457\) −8.43924 4.87240i −0.394771 0.227921i 0.289454 0.957192i \(-0.406526\pi\)
−0.684225 + 0.729271i \(0.739860\pi\)
\(458\) −8.54514 2.77648i −0.399288 0.129737i
\(459\) −30.8670 2.80020i −1.44075 0.130702i
\(460\) −19.2536 + 13.1205i −0.897702 + 0.611747i
\(461\) −4.79972 + 2.13697i −0.223545 + 0.0995288i −0.515453 0.856918i \(-0.672377\pi\)
0.291908 + 0.956446i \(0.405710\pi\)
\(462\) −5.42002 + 7.00564i −0.252162 + 0.325932i
\(463\) −12.6438 + 28.3985i −0.587609 + 1.31979i 0.337942 + 0.941167i \(0.390269\pi\)
−0.925551 + 0.378624i \(0.876398\pi\)
\(464\) 0.0283971 0.270181i 0.00131830 0.0125428i
\(465\) −19.5599 24.5506i −0.907068 1.13851i
\(466\) 0.210347 + 2.00132i 0.00974413 + 0.0927092i
\(467\) 10.4415 + 3.39266i 0.483176 + 0.156993i 0.540469 0.841364i \(-0.318247\pi\)
−0.0572929 + 0.998357i \(0.518247\pi\)
\(468\) 15.9298 0.707843i 0.736354 0.0327201i
\(469\) −4.38567 + 13.4977i −0.202511 + 0.623266i
\(470\) 25.4390 1.90062i 1.17341 0.0876692i
\(471\) −25.5847 12.3284i −1.17888 0.568062i
\(472\) 13.7979 + 12.4237i 0.635099 + 0.571846i
\(473\) 7.85602 + 0.825701i 0.361220 + 0.0379658i
\(474\) 37.5534 39.2591i 1.72488 1.80323i
\(475\) 15.7434 23.8268i 0.722357 1.09325i
\(476\) 56.5314 2.59111
\(477\) 1.98703 32.9050i 0.0909800 1.50662i
\(478\) −33.2256 + 10.7956i −1.51970 + 0.493781i
\(479\) −20.2685 4.30821i −0.926093 0.196847i −0.279907 0.960027i \(-0.590304\pi\)
−0.646186 + 0.763180i \(0.723637\pi\)
\(480\) 10.1807 + 6.72697i 0.464683 + 0.307043i
\(481\) 13.2456 2.81545i 0.603949 0.128373i
\(482\) 8.43410 4.86943i 0.384163 0.221796i
\(483\) 0.390355 12.9402i 0.0177618 0.588800i
\(484\) −3.92003 37.2966i −0.178183 1.69530i
\(485\) −11.6523 + 32.4950i −0.529105 + 1.47552i
\(486\) −35.6818 + 9.80207i −1.61856 + 0.444631i
\(487\) 16.9736 + 23.3621i 0.769145 + 1.05864i 0.996398 + 0.0848015i \(0.0270256\pi\)
−0.227253 + 0.973836i \(0.572974\pi\)
\(488\) −55.9400 + 5.87953i −2.53229 + 0.266154i
\(489\) 6.69799 18.6781i 0.302894 0.844655i
\(490\) 0.738784 0.772359i 0.0333749 0.0348916i
\(491\) −34.6472 15.4259i −1.56361 0.696163i −0.571389 0.820679i \(-0.693595\pi\)
−0.992218 + 0.124516i \(0.960262\pi\)
\(492\) −11.5447 7.13789i −0.520474 0.321801i
\(493\) −0.722465 0.417115i −0.0325382 0.0187859i
\(494\) −6.12654 + 18.8555i −0.275646 + 0.848351i
\(495\) 0.500686 5.51983i 0.0225042 0.248098i
\(496\) −4.86487 14.9725i −0.218439 0.672287i
\(497\) 0.180734 0.850285i 0.00810701 0.0381405i
\(498\) −0.515538 2.84468i −0.0231018 0.127473i
\(499\) −0.527872 0.914302i −0.0236308 0.0409298i 0.853968 0.520325i \(-0.174189\pi\)
−0.877599 + 0.479395i \(0.840856\pi\)
\(500\) −36.8856 + 17.0579i −1.64957 + 0.762852i
\(501\) 10.6611 11.1454i 0.476304 0.497939i
\(502\) 14.2455 + 31.9960i 0.635809 + 1.42805i
\(503\) −10.4983 + 3.41110i −0.468096 + 0.152094i −0.533562 0.845761i \(-0.679147\pi\)
0.0654656 + 0.997855i \(0.479147\pi\)
\(504\) 28.4258 10.6530i 1.26619 0.474524i
\(505\) −24.0061 + 31.0298i −1.06826 + 1.38081i
\(506\) −3.76200 4.17812i −0.167241 0.185740i
\(507\) 4.46454 18.2757i 0.198277 0.811651i
\(508\) 10.6610 + 50.1561i 0.473006 + 2.22532i
\(509\) 33.1550 + 14.7616i 1.46957 + 0.654295i 0.976465 0.215674i \(-0.0691948\pi\)
0.493106 + 0.869969i \(0.335861\pi\)
\(510\) −46.2265 + 29.5005i −2.04694 + 1.30631i
\(511\) −16.6390 + 7.40814i −0.736064 + 0.327717i
\(512\) 12.4588 + 17.1481i 0.550607 + 0.757846i
\(513\) 2.68138 29.5572i 0.118386 1.30498i
\(514\) 46.9166 + 34.0869i 2.06940 + 1.50351i
\(515\) −3.00717 3.54935i −0.132512 0.156403i
\(516\) −47.6072 36.8320i −2.09579 1.62144i
\(517\) 0.825584 + 3.88407i 0.0363091 + 0.170821i
\(518\) 49.6388 28.6590i 2.18100 1.25920i
\(519\) −0.195870 + 0.316795i −0.00859772 + 0.0139058i
\(520\) 9.68154 8.20264i 0.424564 0.359710i
\(521\) 7.44646 + 22.9178i 0.326235 + 1.00405i 0.970880 + 0.239567i \(0.0770053\pi\)
−0.644645 + 0.764482i \(0.722995\pi\)
\(522\) −0.982461 0.163627i −0.0430011 0.00716176i
\(523\) 9.29398 12.7921i 0.406397 0.559358i −0.555938 0.831224i \(-0.687641\pi\)
0.962335 + 0.271866i \(0.0876407\pi\)
\(524\) 18.3264 31.7422i 0.800591 1.38666i
\(525\) 4.37914 22.1522i 0.191121 0.966802i
\(526\) −16.8888 29.2523i −0.736387 1.27546i
\(527\) −48.0784 5.05324i −2.09433 0.220123i
\(528\) 1.20668 2.50418i 0.0525140 0.108980i
\(529\) −14.4596 3.07347i −0.628676 0.133629i
\(530\) −32.8450 48.1981i −1.42669 2.09359i
\(531\) 10.2295 10.0680i 0.443921 0.436915i
\(532\) 54.1326i 2.34695i
\(533\) 2.34280 2.10947i 0.101478 0.0913712i
\(534\) 18.3633 7.52092i 0.794659 0.325462i
\(535\) −1.22122 + 9.00016i −0.0527980 + 0.389111i
\(536\) 2.20798 21.0076i 0.0953703 0.907388i
\(537\) −21.2791 + 27.5043i −0.918261 + 1.18690i
\(538\) 47.6623 5.00951i 2.05487 0.215975i
\(539\) 0.134595 + 0.0977888i 0.00579741 + 0.00421206i
\(540\) −25.3640 + 33.7684i −1.09149 + 1.45316i
\(541\) −5.30115 + 3.85151i −0.227914 + 0.165589i −0.695882 0.718156i \(-0.744986\pi\)
0.467968 + 0.883746i \(0.344986\pi\)
\(542\) 25.6680 23.1116i 1.10254 0.992728i
\(543\) 7.74462 2.26060i 0.332353 0.0970115i
\(544\) 18.3821 3.90725i 0.788128 0.167522i
\(545\) 14.2985 7.69020i 0.612481 0.329412i
\(546\) 1.16779 + 15.6327i 0.0499766 + 0.669019i
\(547\) 4.62526 21.7601i 0.197762 0.930397i −0.761563 0.648091i \(-0.775568\pi\)
0.959325 0.282305i \(-0.0910991\pi\)
\(548\) 22.5567 31.0467i 0.963576 1.32625i
\(549\) 1.93023 + 43.4393i 0.0823804 + 1.85394i
\(550\) −5.27556 8.26645i −0.224951 0.352483i
\(551\) 0.399416 0.691809i 0.0170157 0.0294720i
\(552\) 3.43602 + 18.9596i 0.146247 + 0.806975i
\(553\) 25.6039 + 23.0539i 1.08879 + 0.980351i
\(554\) 0.0125711 0.0139616i 0.000534095 0.000593172i
\(555\) −16.5362 + 31.8266i −0.701921 + 1.35096i
\(556\) 6.78130 + 7.53140i 0.287591 + 0.319403i
\(557\) 11.6691i 0.494436i 0.968960 + 0.247218i \(0.0795163\pi\)
−0.968960 + 0.247218i \(0.920484\pi\)
\(558\) −55.8676 + 14.4944i −2.36507 + 0.613598i
\(559\) 11.3104 8.21747i 0.478378 0.347562i
\(560\) 5.95559 9.63269i 0.251670 0.407055i
\(561\) −5.51780 6.51278i −0.232962 0.274970i
\(562\) −10.4360 + 23.4397i −0.440216 + 0.988742i
\(563\) −12.2391 + 27.4895i −0.515817 + 1.15854i 0.448498 + 0.893784i \(0.351959\pi\)
−0.964315 + 0.264759i \(0.914707\pi\)
\(564\) 10.2134 28.4814i 0.430063 1.19928i
\(565\) 2.44092 3.94800i 0.102690 0.166093i
\(566\) 11.3414 8.23998i 0.476713 0.346352i
\(567\) −6.89570 22.4308i −0.289592 0.942004i
\(568\) 1.29380i 0.0542867i
\(569\) 0.655613 + 0.728132i 0.0274847 + 0.0305249i 0.756730 0.653727i \(-0.226796\pi\)
−0.729246 + 0.684252i \(0.760129\pi\)
\(570\) −28.2487 44.2650i −1.18321 1.85406i
\(571\) 8.04211 8.93167i 0.336552 0.373779i −0.550985 0.834515i \(-0.685748\pi\)
0.887537 + 0.460736i \(0.152415\pi\)
\(572\) 3.26354 + 2.93851i 0.136455 + 0.122865i
\(573\) 19.1875 16.2562i 0.801570 0.679111i
\(574\) 6.67197 11.5562i 0.278483 0.482346i
\(575\) 13.3399 + 5.24246i 0.556311 + 0.218625i
\(576\) 28.7383 18.3395i 1.19743 0.764147i
\(577\) 18.0991 24.9113i 0.753477 1.03707i −0.244252 0.969712i \(-0.578542\pi\)
0.997729 0.0673602i \(-0.0214577\pi\)
\(578\) −9.16906 + 43.1370i −0.381382 + 1.79426i
\(579\) 36.7596 + 17.7132i 1.52767 + 0.736135i
\(580\) −1.00114 + 0.538445i −0.0415701 + 0.0223577i
\(581\) 1.79335 0.381188i 0.0744007 0.0158144i
\(582\) 45.8688 + 43.8759i 1.90132 + 1.81871i
\(583\) 6.74689 6.07493i 0.279428 0.251598i
\(584\) 21.9311 15.9339i 0.907517 0.659350i
\(585\) −5.87832 7.85283i −0.243039 0.324675i
\(586\) 23.8967 + 17.3620i 0.987164 + 0.717216i
\(587\) −10.7940 + 1.13450i −0.445518 + 0.0468258i −0.324631 0.945841i \(-0.605240\pi\)
−0.120886 + 0.992666i \(0.538574\pi\)
\(588\) −0.480468 1.17313i −0.0198142 0.0483790i
\(589\) 4.83882 46.0383i 0.199380 1.89697i
\(590\) 3.41451 25.1643i 0.140573 1.03600i
\(591\) −5.28817 4.09127i −0.217526 0.168292i
\(592\) −13.3677 + 12.0363i −0.549410 + 0.494691i
\(593\) 13.8202i 0.567526i −0.958894 0.283763i \(-0.908417\pi\)
0.958894 0.283763i \(-0.0915829\pi\)
\(594\) −8.89748 4.96929i −0.365068 0.203892i
\(595\) −19.5839 28.7383i −0.802863 1.17815i
\(596\) 6.02587 + 1.28084i 0.246829 + 0.0524651i
\(597\) 11.4465 + 16.7975i 0.468474 + 0.687475i
\(598\) −9.89585 1.04010i −0.404671 0.0425327i
\(599\) −6.17025 10.6872i −0.252110 0.436667i 0.711997 0.702183i \(-0.247791\pi\)
−0.964106 + 0.265516i \(0.914458\pi\)
\(600\) 0.479644 + 33.6051i 0.0195814 + 1.37192i
\(601\) 6.51951 11.2921i 0.265936 0.460616i −0.701872 0.712303i \(-0.747652\pi\)
0.967809 + 0.251688i \(0.0809855\pi\)
\(602\) 34.7825 47.8739i 1.41763 1.95120i
\(603\) −16.1073 2.68264i −0.655939 0.109246i
\(604\) −3.80054 11.6969i −0.154642 0.475938i
\(605\) −17.6021 + 14.9133i −0.715626 + 0.606311i
\(606\) 34.1682 + 63.5312i 1.38799 + 2.58078i
\(607\) 23.2519 13.4245i 0.943765 0.544883i 0.0526263 0.998614i \(-0.483241\pi\)
0.891139 + 0.453731i \(0.149907\pi\)
\(608\) 3.74145 + 17.6021i 0.151736 + 0.713861i
\(609\) 0.0849346 0.625898i 0.00344173 0.0253627i
\(610\) 49.7319 + 58.6984i 2.01359 + 2.37663i
\(611\) 5.68553 + 4.13078i 0.230012 + 0.167113i
\(612\) 9.66366 + 64.3210i 0.390630 + 2.60002i
\(613\) −5.48183 7.54509i −0.221409 0.304743i 0.683834 0.729638i \(-0.260311\pi\)
−0.905243 + 0.424894i \(0.860311\pi\)
\(614\) −29.9790 + 13.3475i −1.20985 + 0.538662i
\(615\) 0.370756 + 8.34159i 0.0149503 + 0.336366i
\(616\) 7.63764 + 3.40050i 0.307729 + 0.137010i
\(617\) 7.01950 + 33.0241i 0.282594 + 1.32950i 0.858848 + 0.512231i \(0.171181\pi\)
−0.576254 + 0.817271i \(0.695486\pi\)
\(618\) −8.21107 + 2.39675i −0.330298 + 0.0964115i
\(619\) −23.8569 26.4958i −0.958890 1.06496i −0.997839 0.0657138i \(-0.979068\pi\)
0.0389487 0.999241i \(-0.487599\pi\)
\(620\) −40.3085 + 52.1020i −1.61883 + 2.09247i
\(621\) 14.7900 1.76790i 0.593503 0.0709434i
\(622\) −28.9315 + 9.40042i −1.16005 + 0.376923i
\(623\) 5.11856 + 11.4965i 0.205071 + 0.460596i
\(624\) −1.37849 4.72260i −0.0551839 0.189055i
\(625\) 21.4496 + 12.8418i 0.857986 + 0.513674i
\(626\) −26.9101 46.6097i −1.07554 1.86290i
\(627\) 6.23643 5.28366i 0.249059 0.211009i
\(628\) −12.3915 + 58.2975i −0.494475 + 2.32632i
\(629\) 17.0692 + 52.5335i 0.680593 + 2.09465i
\(630\) −33.9351 23.9234i −1.35201 0.953132i
\(631\) 8.45439 26.0199i 0.336564 1.03584i −0.629382 0.777096i \(-0.716692\pi\)
0.965946 0.258742i \(-0.0833080\pi\)
\(632\) −44.4091 25.6396i −1.76650 1.01989i
\(633\) −4.35564 + 2.34254i −0.173121 + 0.0931077i
\(634\) 64.9910 + 28.9359i 2.58112 + 1.14919i
\(635\) 21.8041 22.7950i 0.865268 0.904591i
\(636\) −68.0708 + 12.3364i −2.69918 + 0.489169i
\(637\) 0.292830 0.0307777i 0.0116024 0.00121946i
\(638\) −0.161233 0.221918i −0.00638326 0.00878581i
\(639\) 0.998343 + 0.0602869i 0.0394939 + 0.00238491i
\(640\) 15.6040 43.5152i 0.616803 1.72009i
\(641\) −1.47552 14.0386i −0.0582794 0.554491i −0.984236 0.176861i \(-0.943406\pi\)
0.925956 0.377630i \(-0.123261\pi\)
\(642\) 14.2047 + 8.78253i 0.560614 + 0.346619i
\(643\) 16.0668 9.27616i 0.633612 0.365816i −0.148538 0.988907i \(-0.547457\pi\)
0.782149 + 0.623091i \(0.214123\pi\)
\(644\) −26.5748 + 5.64864i −1.04719 + 0.222588i
\(645\) −2.23155 + 36.9611i −0.0878670 + 1.45534i
\(646\) −79.1041 16.8141i −3.11231 0.661542i
\(647\) −6.00549 + 1.95130i −0.236100 + 0.0767136i −0.424677 0.905345i \(-0.639612\pi\)
0.188577 + 0.982058i \(0.439612\pi\)
\(648\) 16.9801 + 30.5216i 0.667043 + 1.19900i
\(649\) 3.95293 0.155166
\(650\) −16.7281 4.62479i −0.656131 0.181399i
\(651\) −10.2561 35.1366i −0.401969 1.37711i
\(652\) −41.4136 4.35274i −1.62188 0.170467i
\(653\) −4.27745 3.85144i −0.167390 0.150718i 0.581179 0.813776i \(-0.302592\pi\)
−0.748568 + 0.663058i \(0.769258\pi\)
\(654\) −2.22382 29.7694i −0.0869581 1.16408i
\(655\) −22.4852 + 1.67993i −0.878569 + 0.0656404i
\(656\) −1.29408 + 3.98276i −0.0505252 + 0.155501i
\(657\) −11.2732 17.6653i −0.439811 0.689189i
\(658\) 28.2906 + 9.19216i 1.10288 + 0.358348i
\(659\) −5.34970 50.8990i −0.208395 1.98274i −0.183286 0.983060i \(-0.558673\pi\)
−0.0251089 0.999685i \(-0.507993\pi\)
\(660\) −11.5023 + 1.72825i −0.447725 + 0.0672719i
\(661\) 1.25398 11.9309i 0.0487743 0.464057i −0.942689 0.333672i \(-0.891712\pi\)
0.991464 0.130385i \(-0.0416212\pi\)
\(662\) 2.18725 4.91264i 0.0850098 0.190935i
\(663\) −14.9700 2.03143i −0.581385 0.0788942i
\(664\) −2.49286 + 1.10989i −0.0967419 + 0.0430723i
\(665\) 27.5188 18.7529i 1.06713 0.727207i
\(666\) 41.0934 + 51.5796i 1.59234 + 1.99867i
\(667\) 0.381301 + 0.123892i 0.0147640 + 0.00479712i
\(668\) −28.0307 16.1836i −1.08454 0.626160i
\(669\) 5.98249 9.67594i 0.231296 0.374094i
\(670\) −25.4447 + 13.6850i −0.983015 + 0.528697i
\(671\) −8.01308 + 8.89943i −0.309341 + 0.343559i
\(672\) 8.01264 + 11.7584i 0.309094 + 0.453589i
\(673\) 12.9808 + 29.1554i 0.500375 + 1.12386i 0.970465 + 0.241242i \(0.0775546\pi\)
−0.470091 + 0.882618i \(0.655779\pi\)
\(674\) −15.3469 −0.591141
\(675\) 25.9532 + 1.19578i 0.998940 + 0.0460255i
\(676\) −39.4808 −1.51849
\(677\) 16.8097 + 37.7551i 0.646048 + 1.45105i 0.878164 + 0.478359i \(0.158768\pi\)
−0.232116 + 0.972688i \(0.574565\pi\)
\(678\) −4.80609 7.05283i −0.184577 0.270862i
\(679\) −26.9353 + 29.9146i −1.03368 + 1.14802i
\(680\) 37.4040 + 35.7780i 1.43438 + 1.37202i
\(681\) −1.20249 + 1.94487i −0.0460793 + 0.0745277i
\(682\) −13.7662 7.94792i −0.527135 0.304342i
\(683\) −16.8583 5.47760i −0.645065 0.209594i −0.0318282 0.999493i \(-0.510133\pi\)
−0.613237 + 0.789899i \(0.710133\pi\)
\(684\) −61.5917 + 9.25361i −2.35502 + 0.353820i
\(685\) −23.5971 0.711562i −0.901600 0.0271874i
\(686\) 40.7190 18.1293i 1.55466 0.692178i
\(687\) 6.49636 + 0.881559i 0.247852 + 0.0336336i
\(688\) −7.55350 + 16.9654i −0.287975 + 0.646802i
\(689\) 1.67956 15.9800i 0.0639862 0.608788i
\(690\) 18.7828 18.4868i 0.715051 0.703781i
\(691\) 0.855877 + 8.14313i 0.0325591 + 0.309779i 0.998666 + 0.0516367i \(0.0164438\pi\)
−0.966107 + 0.258143i \(0.916890\pi\)
\(692\) 0.743375 + 0.241537i 0.0282589 + 0.00918187i
\(693\) 2.97983 5.73502i 0.113194 0.217855i
\(694\) 21.3728 65.7786i 0.811299 2.49692i
\(695\) 1.47944 6.05641i 0.0561184 0.229733i
\(696\) 0.0700316 + 0.937487i 0.00265454 + 0.0355354i
\(697\) 9.55647 + 8.60469i 0.361977 + 0.325926i
\(698\) −81.7379 8.59100i −3.09382 0.325174i
\(699\) −0.411424 1.40950i −0.0155615 0.0533123i
\(700\) −47.3411 + 2.10470i −1.78933 + 0.0795500i
\(701\) 13.3120 0.502788 0.251394 0.967885i \(-0.419111\pi\)
0.251394 + 0.967885i \(0.419111\pi\)
\(702\) −17.5872 + 4.00101i −0.663785 + 0.151008i
\(703\) −50.3044 + 16.3449i −1.89727 + 0.616459i
\(704\) 9.18391 + 1.95210i 0.346132 + 0.0735725i
\(705\) −18.0170 + 4.67459i −0.678559 + 0.176055i
\(706\) 26.2664 5.58309i 0.988547 0.210122i
\(707\) −39.6182 + 22.8736i −1.49000 + 0.860250i
\(708\) −25.6194 15.8401i −0.962838 0.595308i
\(709\) 4.70841 + 44.7975i 0.176828 + 1.68241i 0.618933 + 0.785444i \(0.287565\pi\)
−0.442105 + 0.896963i \(0.645768\pi\)
\(710\) 1.46234 0.996522i 0.0548805 0.0373988i
\(711\) −21.8537 + 33.0729i −0.819578 + 1.24033i
\(712\) −11.0093 15.1530i −0.412592 0.567884i
\(713\) 23.1060 2.42854i 0.865327 0.0909495i
\(714\) −62.9199 + 11.4029i −2.35472 + 0.426742i
\(715\) 0.363243 2.67703i 0.0135845 0.100115i
\(716\) 66.6685 + 29.6827i 2.49152 + 1.10929i
\(717\) 22.4501 12.0740i 0.838413 0.450913i
\(718\) 28.5633 + 16.4910i 1.06597 + 0.615439i
\(719\) −10.7325 + 33.0313i −0.400256 + 1.23186i 0.524536 + 0.851388i \(0.324239\pi\)
−0.924792 + 0.380473i \(0.875761\pi\)
\(720\) 11.9781 + 5.12958i 0.446396 + 0.191168i
\(721\) −1.67628 5.15906i −0.0624279 0.192133i
\(722\) 6.72342 31.6312i 0.250220 1.17719i
\(723\) −5.42179 + 4.59348i −0.201638 + 0.170833i
\(724\) −8.46547 14.6626i −0.314617 0.544932i
\(725\) 0.620544 + 0.322408i 0.0230464 + 0.0119739i
\(726\) 11.8861 + 40.7207i 0.441133 + 1.51129i
\(727\) 5.58256 + 12.5386i 0.207046 + 0.465032i 0.986983 0.160826i \(-0.0514157\pi\)
−0.779937 + 0.625858i \(0.784749\pi\)
\(728\) 14.0723 4.57238i 0.521556 0.169464i
\(729\) 24.3428 11.6803i 0.901585 0.432603i
\(730\) −34.9015 12.5152i −1.29176 0.463210i
\(731\) 38.1586 + 42.3794i 1.41135 + 1.56746i
\(732\) 87.5954 25.5685i 3.23762 0.945037i
\(733\) 0.734008 + 3.45324i 0.0271112 + 0.127548i 0.989622 0.143695i \(-0.0458985\pi\)
−0.962511 + 0.271243i \(0.912565\pi\)
\(734\) −4.74396 2.11215i −0.175103 0.0779608i
\(735\) −0.429924 + 0.650652i −0.0158580 + 0.0239997i
\(736\) −8.25082 + 3.67350i −0.304129 + 0.135407i
\(737\) −2.64338 3.63830i −0.0973702 0.134019i
\(738\) 14.2891 + 5.61587i 0.525988 + 0.206723i
\(739\) 10.9424 + 7.95013i 0.402523 + 0.292450i 0.770568 0.637358i \(-0.219973\pi\)
−0.368045 + 0.929808i \(0.619973\pi\)
\(740\) 73.1180 + 17.8610i 2.68787 + 0.656584i
\(741\) 1.94523 14.3347i 0.0714599 0.526600i
\(742\) −14.1404 66.5254i −0.519111 2.44223i
\(743\) 9.55547 5.51685i 0.350556 0.202394i −0.314374 0.949299i \(-0.601795\pi\)
0.664930 + 0.746905i \(0.268461\pi\)
\(744\) 25.8041 + 47.9794i 0.946026 + 1.75901i
\(745\) −1.43639 3.50702i −0.0526252 0.128487i
\(746\) −12.3374 37.9706i −0.451704 1.39020i
\(747\) 0.740274 + 1.97530i 0.0270852 + 0.0722724i
\(748\) −10.5292 + 14.4922i −0.384987 + 0.529889i
\(749\) −5.29551 + 9.17210i −0.193494 + 0.335141i
\(750\) 37.6132 26.4257i 1.37344 0.964930i
\(751\) 7.42785 + 12.8654i 0.271046 + 0.469466i 0.969130 0.246550i \(-0.0792971\pi\)
−0.698084 + 0.716016i \(0.745964\pi\)
\(752\) −9.28417 0.975806i −0.338559 0.0355840i
\(753\) −14.3909 21.1184i −0.524435 0.769597i
\(754\) −0.474865 0.100936i −0.0172935 0.00367586i
\(755\) −4.62960 + 5.98413i −0.168489 + 0.217785i
\(756\) −42.2939 + 25.2287i −1.53822 + 0.917558i
\(757\) 14.4671i 0.525817i −0.964821 0.262909i \(-0.915318\pi\)
0.964821 0.262909i \(-0.0846818\pi\)
\(758\) 26.5321 23.8896i 0.963689 0.867709i
\(759\) 3.24461 + 2.51024i 0.117772 + 0.0911161i
\(760\) −34.2598 + 35.8168i −1.24273 + 1.29921i
\(761\) 2.26937 21.5916i 0.0822645 0.782695i −0.873155 0.487443i \(-0.837930\pi\)
0.955419 0.295252i \(-0.0954036\pi\)
\(762\) −21.9827 53.6737i −0.796349 1.94439i
\(763\) 18.8279 1.97889i 0.681616 0.0716408i
\(764\) −42.6960 31.0205i −1.54469 1.12228i
\(765\) 29.3505 27.1951i 1.06117 0.983240i
\(766\) 1.75013 1.27155i 0.0632349 0.0459429i
\(767\) 5.19905 4.68124i 0.187727 0.169030i
\(768\) −32.9779 31.5450i −1.18999 1.13828i
\(769\) 19.1956 4.08016i 0.692212 0.147134i 0.151645 0.988435i \(-0.451543\pi\)
0.540567 + 0.841301i \(0.318210\pi\)
\(770\) −2.03926 11.2517i −0.0734899 0.405483i
\(771\) −38.1196 18.3686i −1.37284 0.661528i
\(772\) 17.8039 83.7607i 0.640776 3.01461i
\(773\) 6.19465 8.52620i 0.222806 0.306666i −0.682951 0.730465i \(-0.739304\pi\)
0.905756 + 0.423799i \(0.139304\pi\)
\(774\) 60.4165 + 31.3915i 2.17162 + 1.12834i
\(775\) 40.4505 + 2.44175i 1.45302 + 0.0877104i
\(776\) 29.9563 51.8858i 1.07537 1.86259i
\(777\) −31.9098 + 27.0348i −1.14476 + 0.969870i
\(778\) −30.0183 27.0286i −1.07621 0.969021i
\(779\) −8.23957 + 9.15096i −0.295213 + 0.327867i
\(780\) −13.0816 + 15.8946i −0.468395 + 0.569117i
\(781\) 0.184314 + 0.204702i 0.00659528 + 0.00732480i
\(782\) 40.5883i 1.45143i
\(783\) 0.726661 0.0103550i 0.0259687 0.000370059i
\(784\) −0.316428 + 0.229898i −0.0113010 + 0.00821066i
\(785\) 33.9288 13.8964i 1.21097 0.495984i
\(786\) −13.9947 + 39.0259i −0.499175 + 1.39201i
\(787\) 12.8885 28.9480i 0.459425 1.03189i −0.524190 0.851602i \(-0.675632\pi\)
0.983615 0.180284i \(-0.0577017\pi\)
\(788\) −5.70701 + 12.8181i −0.203304 + 0.456628i
\(789\) 15.9317 + 18.8046i 0.567184 + 0.669460i
\(790\) 5.22558 + 69.9422i 0.185918 + 2.48843i
\(791\) 4.37880 3.18138i 0.155692 0.113117i
\(792\) −2.56346 + 9.27134i −0.0910885 + 0.329443i
\(793\) 21.1943i 0.752633i
\(794\) −49.8659 55.3817i −1.76967 1.96542i
\(795\) 29.8528 + 30.3308i 1.05877 + 1.07572i
\(796\) 28.5434 31.7006i 1.01169 1.12360i
\(797\) 13.4647 + 12.1236i 0.476943 + 0.429441i 0.872215 0.489123i \(-0.162683\pi\)
−0.395272 + 0.918564i \(0.629350\pi\)
\(798\) −10.9190 60.2500i −0.386529 2.13283i
\(799\) −14.3333 + 24.8260i −0.507075 + 0.878279i
\(800\) −15.2483 + 3.95643i −0.539109 + 0.139881i
\(801\) −12.2056 + 7.78910i −0.431264 + 0.275214i
\(802\) −18.6990 + 25.7369i −0.660284 + 0.908803i
\(803\) 1.19995 5.64531i 0.0423453 0.199219i
\(804\) 2.55276 + 34.1728i 0.0900288 + 1.20518i
\(805\) 12.0777 + 11.5527i 0.425684 + 0.407179i
\(806\) −27.5181 + 5.84916i −0.969285 + 0.206028i
\(807\) −33.5679 + 9.79824i −1.18165 + 0.344914i
\(808\) 50.5995 45.5600i 1.78008 1.60279i
\(809\) 1.25928 0.914920i 0.0442739 0.0321669i −0.565428 0.824798i \(-0.691289\pi\)
0.609702 + 0.792631i \(0.291289\pi\)
\(810\) 21.4189 42.7006i 0.752584 1.50035i
\(811\) −12.8701 9.35065i −0.451929 0.328346i 0.338428 0.940992i \(-0.390105\pi\)
−0.790357 + 0.612647i \(0.790105\pi\)
\(812\) −1.31827 + 0.138556i −0.0462624 + 0.00486237i
\(813\) −15.4215 + 19.9331i −0.540856 + 0.699084i
\(814\) −1.89851 + 18.0631i −0.0665427 + 0.633112i
\(815\) 12.1340 + 22.5609i 0.425035 + 0.790274i
\(816\) 18.5706 7.60580i 0.650100 0.266256i
\(817\) −40.5811 + 36.5394i −1.41975 + 1.27835i
\(818\) 8.35104i 0.291987i
\(819\) −2.87249 11.0718i −0.100373 0.386879i
\(820\) 16.8208 4.91008i 0.587408 0.171467i
\(821\) 10.1889 + 2.16572i 0.355595 + 0.0755840i 0.382245 0.924061i \(-0.375151\pi\)
−0.0266508 + 0.999645i \(0.508484\pi\)
\(822\) −18.8434 + 39.1051i −0.657240 + 1.36395i
\(823\) −3.24942 0.341527i −0.113267 0.0119049i 0.0477251 0.998861i \(-0.484803\pi\)
−0.160993 + 0.986956i \(0.551470\pi\)
\(824\) 4.03684 + 6.99202i 0.140630 + 0.243579i
\(825\) 4.86325 + 5.24858i 0.169317 + 0.182732i
\(826\) 14.8062 25.6450i 0.515172 0.892304i
\(827\) 29.1131 40.0708i 1.01236 1.39340i 0.0949395 0.995483i \(-0.469734\pi\)
0.917423 0.397914i \(-0.130266\pi\)
\(828\) −10.9698 29.2710i −0.381225 1.01724i
\(829\) 6.83019 + 21.0212i 0.237222 + 0.730095i 0.996819 + 0.0797008i \(0.0253965\pi\)
−0.759596 + 0.650395i \(0.774604\pi\)
\(830\) 3.17454 + 1.96272i 0.110190 + 0.0681271i
\(831\) −0.00720896 + 0.0116596i −0.000250076 + 0.000404468i
\(832\) 14.3908 8.30853i 0.498911 0.288046i
\(833\) 0.249714 + 1.17481i 0.00865207 + 0.0407048i
\(834\) −9.06679 7.01466i −0.313957 0.242898i
\(835\) 1.48350 + 19.8561i 0.0513388 + 0.687148i
\(836\) −13.8773 10.0824i −0.479956 0.348708i
\(837\) 38.2250 17.6757i 1.32125 0.610962i
\(838\) 41.5652 + 57.2096i 1.43585 + 1.97627i
\(839\) −6.32977 + 2.81820i −0.218528 + 0.0972949i −0.513081 0.858340i \(-0.671496\pi\)
0.294553 + 0.955635i \(0.404829\pi\)
\(840\) −14.3346 + 36.4743i −0.494591 + 1.25848i
\(841\) −26.4749 11.7874i −0.912929 0.406462i
\(842\) 12.5089 + 58.8497i 0.431085 + 2.02810i
\(843\) 4.44281 18.1867i 0.153018 0.626383i
\(844\) 6.94476 + 7.71294i 0.239049 + 0.265490i
\(845\) 13.6772 + 20.0704i 0.470509 + 0.690444i
\(846\) −5.62269 + 33.7601i −0.193312 + 1.16070i
\(847\) −25.5850 + 8.31307i −0.879111 + 0.285641i
\(848\) 8.68141 + 19.4988i 0.298121 + 0.669590i
\(849\) −7.07053 + 7.39169i −0.242660 + 0.253682i
\(850\) 11.6290 69.8335i 0.398872 2.39527i
\(851\) −13.2732 22.9899i −0.454999 0.788082i
\(852\) −0.374288 2.06528i −0.0128229 0.0707553i
\(853\) 9.30379 43.7709i 0.318556 1.49869i −0.469418 0.882976i \(-0.655536\pi\)
0.787973 0.615710i \(-0.211131\pi\)
\(854\) 27.7220 + 85.3194i 0.948626 + 2.91957i
\(855\) 26.0411 + 28.1050i 0.890587 + 0.961172i
\(856\) 4.87111 14.9917i 0.166491 0.512407i
\(857\) 43.4944 + 25.1115i 1.48574 + 0.857793i 0.999868 0.0162366i \(-0.00516849\pi\)
0.485873 + 0.874030i \(0.338502\pi\)
\(858\) −4.22507 2.61229i −0.144241 0.0891822i
\(859\) −14.6584 6.52633i −0.500137 0.222675i 0.141133 0.989991i \(-0.454926\pi\)
−0.641270 + 0.767315i \(0.721592\pi\)
\(860\) 76.4615 13.8579i 2.60731 0.472550i
\(861\) −3.28659 + 9.16505i −0.112007 + 0.312344i
\(862\) 19.4253 2.04168i 0.661627 0.0695398i
\(863\) −3.06032 4.21217i −0.104174 0.143384i 0.753747 0.657165i \(-0.228244\pi\)
−0.857921 + 0.513781i \(0.828244\pi\)
\(864\) −12.0089 + 11.1267i −0.408550 + 0.378539i
\(865\) −0.134737 0.461577i −0.00458118 0.0156941i
\(866\) 0.0588259 + 0.559691i 0.00199898 + 0.0190191i
\(867\) 0.970254 32.1638i 0.0329516 1.09234i
\(868\) −66.5229 + 38.4070i −2.25794 + 1.30362i
\(869\) −10.6789 + 2.26987i −0.362256 + 0.0769999i
\(870\) 1.00567 0.801232i 0.0340953 0.0271643i
\(871\) −7.78532 1.65482i −0.263796 0.0560715i
\(872\) −26.7980 + 8.70719i −0.907494 + 0.294863i
\(873\) −38.6411 25.5330i −1.30780 0.864162i
\(874\) 38.8660 1.31466
\(875\) 17.4701 + 23.3372i 0.590598 + 0.788941i
\(876\) −30.3988 + 31.7796i −1.02708 + 1.07373i
\(877\) −32.4195 3.40742i −1.09473 0.115061i −0.460092 0.887871i \(-0.652183\pi\)
−0.634636 + 0.772811i \(0.718850\pi\)
\(878\) −9.60781 8.65091i −0.324248 0.291954i
\(879\) −19.4160 9.35593i −0.654886 0.315568i
\(880\) 1.36015 + 3.32089i 0.0458508 + 0.111947i
\(881\) 4.65942 14.3402i 0.156980 0.483135i −0.841376 0.540450i \(-0.818254\pi\)
0.998356 + 0.0573153i \(0.0182540\pi\)
\(882\) 0.771395 + 1.20879i 0.0259742 + 0.0407019i
\(883\) 53.7463 + 17.4632i 1.80871 + 0.587684i 1.00000 0.000529301i \(-0.000168482\pi\)
0.808706 + 0.588213i \(0.200168\pi\)
\(884\) 3.31393 + 31.5299i 0.111460 + 1.06047i
\(885\) 0.822766 + 18.5113i 0.0276570 + 0.622251i
\(886\) −7.64090 + 72.6983i −0.256701 + 2.44235i
\(887\) −11.4838 + 25.7930i −0.385588 + 0.866045i 0.611604 + 0.791164i \(0.290524\pi\)
−0.997192 + 0.0748814i \(0.976142\pi\)
\(888\) 38.0896 49.2327i 1.27820 1.65214i
\(889\) 33.6027 14.9609i 1.12700 0.501772i
\(890\) −8.64724 + 24.1147i −0.289856 + 0.808327i
\(891\) 7.03464 + 2.41007i 0.235669 + 0.0807403i
\(892\) −22.7051 7.37732i −0.760222 0.247011i
\(893\) −23.7725 13.7251i −0.795517 0.459292i
\(894\) −6.96519 0.210112i −0.232951 0.00702719i
\(895\) −8.00618 44.1744i −0.267617 1.47659i
\(896\) 36.0699 40.0597i 1.20501 1.33830i
\(897\) 7.24019 0.540852i 0.241743 0.0180585i
\(898\) −16.3919 36.8168i −0.547004 1.22859i
\(899\) 1.13354 0.0378057
\(900\) −10.4874 53.5046i −0.349579 1.78349i
\(901\) 65.5425 2.18354
\(902\) 1.71983 + 3.86280i 0.0572641 + 0.128617i
\(903\) −18.7434 + 38.8975i −0.623741 + 1.29443i
\(904\) −5.39034 + 5.98657i −0.179280 + 0.199110i
\(905\) −4.52123 + 9.38301i −0.150291 + 0.311902i
\(906\) 6.58939 + 12.2521i 0.218918 + 0.407048i
\(907\) −27.2608 15.7390i −0.905180 0.522606i −0.0263030 0.999654i \(-0.508373\pi\)
−0.878877 + 0.477048i \(0.841707\pi\)
\(908\) 4.56374 + 1.48285i 0.151453 + 0.0492101i
\(909\) −32.7979 41.1673i −1.08784 1.36543i
\(910\) −16.0069 12.3837i −0.530623 0.410515i
\(911\) 33.3178 14.8341i 1.10387 0.491474i 0.227824 0.973702i \(-0.426839\pi\)
0.876046 + 0.482228i \(0.160172\pi\)
\(912\) 7.28306 + 17.7826i 0.241166 + 0.588840i
\(913\) −0.236299 + 0.530736i −0.00782036 + 0.0175648i
\(914\) 2.41796 23.0053i 0.0799789 0.760948i
\(915\) −43.3433 35.6724i −1.43288 1.17929i
\(916\) −1.43811 13.6827i −0.0475165 0.452090i
\(917\) −25.0056 8.12482i −0.825758 0.268305i
\(918\) −23.7298 69.6405i −0.783201 2.29848i
\(919\) −4.69139 + 14.4386i −0.154755 + 0.476286i −0.998136 0.0610294i \(-0.980562\pi\)
0.843381 + 0.537316i \(0.180562\pi\)
\(920\) −21.1581 13.0814i −0.697563 0.431281i
\(921\) 19.7871 13.4838i 0.652008 0.444305i
\(922\) −9.26831 8.34522i −0.305236 0.274835i
\(923\) 0.484835 + 0.0509582i 0.0159585 + 0.00167731i
\(924\) −13.1756 3.21865i −0.433445 0.105886i
\(925\) −16.2501 43.3577i −0.534301 1.42559i
\(926\) −73.7915 −2.42494
\(927\) 5.58339 2.78917i 0.183383 0.0916082i
\(928\) −0.419083 + 0.136168i −0.0137571 + 0.00446994i
\(929\) −28.6602 6.09191i −0.940311 0.199869i −0.287836 0.957680i \(-0.592936\pi\)
−0.652475 + 0.757810i \(0.726269\pi\)
\(930\) 34.3543 66.1205i 1.12652 2.16818i
\(931\) −1.12496 + 0.239118i −0.0368691 + 0.00783677i
\(932\) −2.66856 + 1.54070i −0.0874117 + 0.0504672i
\(933\) 19.5486 10.5136i 0.639993 0.344200i
\(934\) 2.72416 + 25.9187i 0.0891373 + 0.848085i
\(935\) 11.0149 + 0.332149i 0.360224 + 0.0108624i
\(936\) 7.60800 + 15.2298i 0.248675 + 0.497801i
\(937\) −0.860125 1.18386i −0.0280991 0.0386750i 0.794736 0.606955i \(-0.207609\pi\)
−0.822835 + 0.568280i \(0.807609\pi\)
\(938\) −33.5049 + 3.52151i −1.09397 + 0.114981i
\(939\) 25.3851 + 29.9626i 0.828412 + 0.977793i
\(940\) 18.5025 + 34.4020i 0.603485 + 1.12207i
\(941\) 49.8887 + 22.2119i 1.62633 + 0.724087i 0.998525 0.0542873i \(-0.0172887\pi\)
0.627801 + 0.778374i \(0.283955\pi\)
\(942\) 2.03274 67.3850i 0.0662301 2.19552i
\(943\) −5.35217 3.09008i −0.174291 0.100627i
\(944\) −2.87176 + 8.83837i −0.0934678 + 0.287664i
\(945\) 27.4769 + 12.7607i 0.893825 + 0.415104i
\(946\) 5.79445 + 17.8335i 0.188394 + 0.579816i
\(947\) 5.21980 24.5572i 0.169621 0.798003i −0.808258 0.588829i \(-0.799589\pi\)
0.977878 0.209174i \(-0.0670774\pi\)
\(948\) 78.3069 + 28.0809i 2.54329 + 0.912025i
\(949\) −5.10722 8.84597i −0.165787 0.287152i
\(950\) 66.8703 + 11.1356i 2.16956 + 0.361285i
\(951\) −50.4261 12.3185i −1.63518 0.399456i
\(952\) 24.5491 + 55.1382i 0.795641 + 1.78704i
\(953\) −21.6721 + 7.04171i −0.702030 + 0.228103i −0.638215 0.769859i \(-0.720327\pi\)
−0.0638150 + 0.997962i \(0.520327\pi\)
\(954\) 73.2749 27.4609i 2.37236 0.889081i
\(955\) −0.978553 + 32.4512i −0.0316652 + 1.05010i
\(956\) −35.7950 39.7544i −1.15769 1.28575i
\(957\) 0.144634 + 0.138350i 0.00467535 + 0.00447222i
\(958\) −10.2268 48.1131i −0.330412 1.55447i
\(959\) −25.1485 11.1968i −0.812088 0.361565i
\(960\) −7.23001 + 43.4140i −0.233348 + 1.40118i
\(961\) 31.6891 14.1089i 1.02223 0.455126i
\(962\) 18.8942 + 26.0056i 0.609173 + 0.838455i
\(963\) −11.3412 4.45729i −0.365464 0.143634i
\(964\) 12.0645 + 8.76541i 0.388573 + 0.282315i
\(965\) −48.7483 + 19.9661i −1.56926 + 0.642731i
\(966\) 28.4385 11.6473i 0.914995 0.374747i
\(967\) 4.86324 + 22.8797i 0.156391 + 0.735763i 0.984527 + 0.175235i \(0.0560685\pi\)
−0.828135 + 0.560528i \(0.810598\pi\)
\(968\) 34.6751 20.0197i 1.11450 0.643457i
\(969\) 58.9816 + 1.77924i 1.89476 + 0.0571574i
\(970\) −81.7178 + 6.10537i −2.62380 + 0.196032i
\(971\) 0.573657 + 1.76553i 0.0184095 + 0.0566587i 0.959839 0.280551i \(-0.0905170\pi\)
−0.941430 + 0.337209i \(0.890517\pi\)
\(972\) −35.9349 43.8091i −1.15261 1.40518i
\(973\) 4.27313 5.88145i 0.136990 0.188551i
\(974\) −34.2740 + 59.3644i −1.09821 + 1.90216i
\(975\) 12.6119 + 1.14384i 0.403905 + 0.0366323i
\(976\) −14.0768 24.3818i −0.450589 0.780443i
\(977\) 7.11819 + 0.748152i 0.227731 + 0.0239355i 0.217707 0.976014i \(-0.430142\pi\)
0.0100245 + 0.999950i \(0.496809\pi\)
\(978\) 46.9716 3.50884i 1.50199 0.112200i
\(979\) −3.90056 0.829089i −0.124662 0.0264978i
\(980\) 1.54055 + 0.552422i 0.0492111 + 0.0176465i
\(981\) 5.47008 + 21.0840i 0.174646 + 0.673160i
\(982\) 90.0284i 2.87292i
\(983\) −10.8669 + 9.78464i −0.346602 + 0.312081i −0.823983 0.566615i \(-0.808253\pi\)
0.477381 + 0.878696i \(0.341586\pi\)
\(984\) 1.94864 14.3598i 0.0621202 0.457775i
\(985\) 8.49328 1.53932i 0.270618 0.0490470i
\(986\) 0.206996 1.96944i 0.00659210 0.0627196i
\(987\) −21.5076 2.91859i −0.684595 0.0928999i
\(988\) −30.1920 + 3.17331i −0.960536 + 0.100956i
\(989\) −22.1725 16.1093i −0.705044 0.512245i
\(990\) 12.4535 4.24366i 0.395798 0.134872i
\(991\) −5.71565 + 4.15266i −0.181564 + 0.131914i −0.674855 0.737951i \(-0.735794\pi\)
0.493291 + 0.869864i \(0.335794\pi\)
\(992\) −18.9765 + 17.0865i −0.602505 + 0.542498i
\(993\) −0.931153 + 3.81169i −0.0295493 + 0.120960i
\(994\) 2.01839 0.429023i 0.0640195 0.0136078i
\(995\) −26.0035 3.52838i −0.824365 0.111857i
\(996\) 3.65824 2.49288i 0.115916 0.0789898i
\(997\) −1.43222 + 6.73805i −0.0453588 + 0.213396i −0.994990 0.0999729i \(-0.968124\pi\)
0.949631 + 0.313369i \(0.101458\pi\)
\(998\) 1.47305 2.02749i 0.0466287 0.0641789i
\(999\) −36.2148 31.6854i −1.14579 1.00248i
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 225.2.u.a.34.25 224
3.2 odd 2 675.2.y.a.559.4 224
9.4 even 3 inner 225.2.u.a.184.4 yes 224
9.5 odd 6 675.2.y.a.334.25 224
25.14 even 10 inner 225.2.u.a.214.4 yes 224
75.14 odd 10 675.2.y.a.289.25 224
225.14 odd 30 675.2.y.a.64.4 224
225.139 even 30 inner 225.2.u.a.139.25 yes 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.u.a.34.25 224 1.1 even 1 trivial
225.2.u.a.139.25 yes 224 225.139 even 30 inner
225.2.u.a.184.4 yes 224 9.4 even 3 inner
225.2.u.a.214.4 yes 224 25.14 even 10 inner
675.2.y.a.64.4 224 225.14 odd 30
675.2.y.a.289.25 224 75.14 odd 10
675.2.y.a.334.25 224 9.5 odd 6
675.2.y.a.559.4 224 3.2 odd 2